dcaabbcddacaddaadaccbcdabccbcdadaccbdacabcccadabbcabcacccdcbbddcabdcdcccbddddbadcddacddccdbccbcacccbaadcdbdbbbddadbbdbcadabbdbaacbababbdabdbbbacaacaadbadcaadbaadabcdbdbaddcbabcdccbadaccbbbbbcaacdbddaabcdbaabacbacccabdaccdbdcbbabccacadbdadcbcdcddbabadccdcacabcdbbcbadbbbcaaccabbbbccddaccbdbbdabccdbacacabaabcadbdaddccaaaccbaabbdcbdcdccbadcbbaababbcdbbcbcaabaadacdabdccbcddbcacbcdbabdcbdcdabbacbbcbcccdbcccdcaacbcccbdabdbdbddadaadbaadbbaccdcbacdcbddbcdadaddccacabcddddcbadabdbbcadaaabbbadcabdbbbcbbdddcbbbaadddcdcadbadddabaddcabbdbdaccabdbabddddcbbdabccdacbaacbdcbbabdbdccabadbdadbabccdaddcccdadadacddadcbcabdcdcbbbbcdbcacbcadacabdbcbcccccacbdbaccabadddddaabcbaddabacdbadaabaadbcacaccadbcdbcaacbdddbdababacbdaaddddabccabcbcdabbccaadcdababbdcddcddaacbcdddcdcbbacabccbdadcbbdcdbbbbdadaabccadddadaccdabaaddddcddcdbdabcababaadbdacddbbcaddadbcdacdbdabbcccddabcababdbabaaaaacabdcaaabaddbddcbcadcdddccbdddcabaaaaccaddbdbadaacdbbbdaccdbcadcdcdbddaabbabadabdaccdaddcddabbccdbadccacaabbcbcdcddbdbcdabbadaacddbbccadbbaabdaadbcddcdcacbdccdaacddddbbbaabddabbbbaaabdadbbdaccadddcbbcbbcccccdaaddabcaccabdcaabddacaccdabdabdddbaaabdcccccddcbabdbcaaaadbcabbbabaccaabcbbcdcabacdcabdccdccdcabbacacbcccdccbccdccddcdbcccaabdcdcccbbacccbadcddaaadcabbbdcddcabcaaabaccccabbcbadbbdcaadaccacdacadcdbcbdaccdccddaddadadaddbcacaddcadbddbacaacbcccaadacbdadbacdbcaadcbcabdaabdcaacdadbdabddabadaddbaabdccaaabadbabcdaaaccbadabcabcbdbbcdddbaabbbccbabdbbcdddcadacdaabcaabcaccbdadccccbdacdaccccabbccddadcdaddcdbaabbabdadbadddcabdcbaadbabdaabcaccccabacccbddccdccdaccddbbddbbcbaadcbaaaccabbacbbaadbdabdaadcdccdbdbdadbccaadbbaccacddcdcaacacdadaabbbdbdabddcdcbaadaabbdcbcdacadaadabcabbbcacdbbadacaddabdcbabbacbcbaddadabccbddadbdacbbbcaadabaabbcbbbccbbdbbbadbabaacbbbbdccacbbabdbbababdbdacaacaddacadbacdcdbddccdcbcbacdbddaadddbddddbdccbbdbcdaaaddaababbcacdaadddbdadbababbcddabadaccbdbcbddadadaabbdcccbbdcbdbbabcacdaddcdabcabdcbdcccbbddcddcadacccbdddcdacddbbbacacdcbbdadcdddbabbddddcccdcccddbcabddbadccddcdddaaaccbdcdadcaddbadbbdcbbbbdabadaabbdaaaddbddaccdcacbbcccbddabdbcadccdbadcbcaadcdabcddccacdcccdaddbdacccacccdcddbcdacdbcdcbdccccdbdacaadddcccdbcbadddabaabdbcbdbcbdddbaabbbacacdbccdbcbcdbaccdabbacbbbabbdadacbdaddbdbadcabdabbbcdaadbddadbaacbccdabbadaccaccaaacbadacaaacbababcadccdcccbdadbdbacacdabcabaccbaaccccddcbcacbcabddaddcddbdddabbcddcbacaacbdbddbbdcccadaccdaaabdaaabaacabaaaadbccbdbadcdccdccbcbddbcacbbdbaddcbbdbaadddddddabcdcaaccabcbdbbcbabddbabbbaaaddbdcbdcaddbbabccdadbcbccccdbbacdacddabaaaadabaccabadbbabcbdcaadadcdbcccbdabddabccdbcbbaadaababbdddcdbcbbbacccdcccbccbddcddbabccbdcaaadcccdabcdcbdcabcdbacdcbbadbdaaddbcabbddabbcbbcdddbdadbcabcdbabcdbcccadaaddacabdacbbabcddcbaddcacbbdbaccaabcdbdacdcbdcccaddcccaabbdcacacabbbdbcdddbcdcdacbcdabababdcddcabbadbbdabadabccabbcacacbbcbbabdcbcbadbabccbddbbbddbcabbcaabdadbacdaacdaacdcadcbbddddaaabdabbbdbacddbddddadacaaaadacdccddcddacacacacababcdddccbadcdbdaadaaabcacdadcbddaccccadbadbadcdbbbaadabdcadbdacadcdbcabdbcacabdabcbbbcbbaaadcbacacbdcbcdbbacbdcccaabcbcddccddaaacadbcbaccccbabccccdadbdabcadacbabadbdaadbcabbddacaddbabdccacddbbdabacacbacbcacdccaccdabaacdaccaaaccbcabadccccddcbabaacaaabdbabcbaacadcbccbcdcdddbdcaadbdbcdcdbccddacccadabdabbdaabccadaddcbdcbddbcabcbddbdcdaaaadaadbabbbabbaddaabaccaacbdadacbcadbabaddbdaaccbaddaaddbcdbbbbccdadaabadaccddabdbcbbaddacabcacbabcabbbabbbbcbbccbdcccdaabbcbcdabcdbcabacbcaccdabcdbddabddbdcbcbcdaadaaacddbdcbcaccbbddcdbbadbbbdccbabadbcdaabdcccbcadbbccaabccccdbbdcbadbbdadcddcddabadddbababccbcdaddcbdccbbacadcbdddaabdddabbcdadddbdbcbbdbbbdbaadaadbbbcacbcadbddaddcababbabccdbdaccbcbdaacdbbccbbbbcbbdabddcbbbcccdbcccdbddacbddaaddbcbabcabbaabbbccabbdddaaacaadabbbbdaabdcbbdbbaabbbadcaaddadcdcdbdbcacaabdddbbbcdbbbccddbcbcccacbcaabacbcbcbbdcbdddcccdadbdcdcabaddaccbddcdaaaaadbddbacbcbdcdbdadcbbccbadbabbdadcacdccadacdbadddbadcdddaddacdcccbbcdbbccccdccaccdaaadbdccbbacccacabcddacaaddcabdcbcdcbcdbcdcadddcdcbbaadaddccabcdbbcdaaaaaaaabcaaacbdbcadacacdcccbdcaaababddccadddcbcddcbcaaaddacdabddbbaacbaccaccdaaaaaaccbbcadddcbddcdbdbababadbacaccaddbcddabbbcacacddbbdbcdbababbaddcaaacbabcbbbdddbaaccccdbcadcbddbadadaaccbbcaddadddccccacabbcbabbdacbcaacabdcbadaaccbbbbddacbdcdbcdcccbbabadacdaccdbcdadcdbcdadcddaababbbaabaddcbaddacddcbdadbadbabcdccdcaadaacaaaadbbbddbdbdbcbdbccacaccacacccadbccaddadbbccbbcbcbbbbcbcdaddbdaacdabcbcaacddcbbbdcccbbbbbacccadaaaabdddabdadacddadbbabcabdbcbcbbcdaacbddcdddcacaabbcaddadbbdabdaddbaccdacadbbcabdbabaddcddbacaaabcacdacbcdbbaccdabcabcaadcdccbabcdacadabbbdcaacabccbbbacadabcbacaaadaddbababcbdcddbdcacadaaaddcdbdadcddddbdbccbbbccdcaddcccbbdadabccacbacbaaabacaadbadcdcdbaddddcacbcdaddbcbabacdacdbaacbcbcacbcaacbabdbbbbdcbbbaacdcddadcacaddacdacdacbbdbaaaabdcabbdcaadadbdadddbabcddcddbbbaadaacbaabacabababbbdacabaabadcdabcbadbcdddbbacacbacadddaccdababcbaccacbbcbdadabcdcdcaadcbdcaacdcbcbbaddaaaababccbbccdadabacdcadabbbddbbdadabdcbcaccbccdaabcdabacdbbbabaadcbbdbbacddbacaccdcdadbdbbbcdbadddbbbaccddaabccdccdacbcddbdadbcdbbbcdccbbabdabacaddddbcdcbbaddabcadbddbcdaadabaaabbdbbbbaacadcacbcccacddcabccaabcbbcaacddbaabccbabbddcaadcdbbcddccbcdcbcdddbdbbcdaadcaddcabcdddddccccaacddcacbcccdcadcbcdbaadcdcbadccdbdcdaacbabbddbdbbcccacaacabcabbacbbaabadbbaacdcdabcaabbabcdcacdaddcbccbdabdccbdcbdbdcabdaabbdbbababcadabaabdcddbadbcbacaddccccccbcdddbdacbddccbbbdcbabddcacbbaababdbbdddbaaadbdbdddaaaddbaaddbacaccdbdbaadadbcdabacddbbdbaaadbbbdbaddcbdcbdcdcaccbdddabcbabccabacddcbbdbacbdbbbadbbdbbbcbdaabbaaccabadbcdddbbdadbbcaacdcdccdbacacbcdbbcacabbdbddddccacdcaaabbcdaacadabcbcdccccadbdbbdcbbcccdbdbddbaacdabcaabcdadabacaaabddcccddddbbcccbbccdcbdbaddbdbbacdcabcdaadbadddccdbaabdbabaccbbcaadbbcdacacccbaadaaadaacabdbaacccbdddababddcbddbbbdaacdacacdddacabcbcabbcbdabddcaccacacbbccacbbadaacaadaaacbaaccaadbbbacdcbcdcdabcbddcdbbadcaccdcadcbbcadddaddacbdccbabbddcdcddbbbacddbcacbbacacababbdcbccccdbdbadbbcbcacdbbddccddbdcaabaaacccbabdcbaddabadbdbccadbdbaabcccbcdabbcbacccbdcaaaddcbabaacbcabdccabddbddadbbbacbcbdadacaccdaaacdbddddcdacadabbabdbacdcccddbccdadcbcbccbcabbbbddcbbddabcbddbdbacaaddbdbaacdccacdbdcacabacdadccccdcbddbdccccabccbcacccbadbccbcbddcccadadaddabdabaadbddbbbcadacbdacadcabacacdcdbdaaaacddadbacdabbdbccbdadcbcddaacdabdcabbaabdbdaabbddcaaabdbcbdbcdbddadcdaaadcaaddcbbadbdacbccddddccbabdccdacbbdbdcacddccabdcabcdcadbbbbcabbdbdccbcdddcccbdaaaddbcbdcdacbcdabddccddccbbddcbdbccacdbcddbccabbacabbcabaaabbbacabcdcacaaddabbaabcacbdbaadacddccacabaacbbccccdcababbabadaaacbaacdaddcacdaabaadabcadbbccbddcadcaadbdbdcdccdbcbdadcbdaacaaaacbaaaddcacabadddbdbabaabbabbbaacabdbcdbbabaadacbddcbbdacbcabdddbadcdccbddaacdabcdcbccdaaabcaccbadbbcabbcabddccbcbabbccccdacdbadcabbcddbcdddbababddabdbbbbbcdbdbbcabbcabbddcaabbcbbdcabbcbdcadabbcadcdadaccbbbabccdbdcbccdddbbaadbaabacdaddbbdbbabbaddcaacdadcdaaadadbccbacbcbbbcaabcaaacaaabaccddbacbadbdbacbcddababddbcdccbbbbdacdaddadaddccdddaabaadddbbccadbbddbcabdcdccbbdaabbbdaabdcbaccdcdaccdcbbacddaabccccbacbcdabccdcdabbbcadbcdbdbbddcabbdccadcacaabdaaacbaabadcbddababbbddacbbcaccabddcddabbaddaacbcacbcaccccacbcaaabcacdcadabbadabcbacdabadccaabbabacdddccdadcdbcabdcdddccbacbbcadbddcaccaddabbcaaddcdccccddcacdccdbacadcbdabdbdbabaddccdadcacdcbbddcbabddcacbbdbdcbddccbacdcdbdabdccacadcabcbbbcbababddaddcdcbddbdbccdcdbbaccbdaddaccabaddddccddbbdaaabbabdbadababadcababdcdbdbddadaaaadadddcbdabbdccacccbbcbaadcdcdbdcbccbcdcbbbabddcacdbcabdbbaabbcbbbbbbddcbddaccacdddaadaaaacaaccddacaddaaabcacacacdcbabbdcaccdccdddababcdabcbdcaacaccbaabddddbddcbacbdcdccdbdcacbbcaacccddcaddbadbbbaabbaaaaadacccbbacbcdbbaaaabcabaadabaddaadbaaabadbbdcaadcbbaaaaabaacccacdcdaaacaabcccdbabcddddaadaccaddaabdbbadadadabadaabbddccbcdddacdbabacbabcddabacdaadccbbdcbabddcdbabaabbbabdacacadddbcbdddacaaddacbcbdbcbbdcaadadddddcdabaddbdbcdbcbdcccabbcbacabadaabbbbdbabccbcccbacbbaadadcddcbcddcaddbbdcaaaabddaccdbbcccdcccccadaaacaadcacccdddcddaadbcddccbdcacbdbbcdaccdacbdaacacaddacddabbbabcbbcbcadacbbdddcbddaccdbcddaacabcddbacbcddabdbdabdbadcbccaaabbaabadcddabbacdaddddccbddbbadaadbabcababdbbccadcdbdaabdcdaaddacccbddbcabdccbbbaaacabdbacbabacadababaddccdbdcdcaadbbadaaabbadbbbdbbcbbaaaddaabababdcadadadccbddacaacacaddddccabcdacbaccdcbbadacdbcdbdbbdcbdcbdabbaabdcdacacbabddadbdddaacdbbbadbaaabccaabaddacdbcddabdddbaadbbbcbcddcbdbdccdbddbbaccadbcadbcccdabdacababcbcdcadbccbadddbaabbdbaabacbcdcacdaacccacbbcdcdbaccbdcbbbbaabddbddbbbbababccbabdccbcacdaacdbabddcbdcacdccdbdacbdbcdbadbdcadaaccacadbdcabbadddbbbccdcbcaaccddacdbdbccadbdbdacdbdbabbcbabcbbaaaddbcabbccddcbadadadbccbcbbadaaadabcbacddcdbbccaaabdccbdcdbbbadadbcdacaadcdbcccdcdbbaadbdcdccdcacdccdadcaddbdccddaccbcadbabcaabaabbadddbaaabadcabbbcccbadcbaddbbbbbcccbadcabbbaabddaccbcbbbcdabaadbcbcabbccaabcccdcbcadcababdddacaacdcbaaadcaccadccbddbccbaccaaacbddbbbdcabcdccddbaddccbcdabacbdccababcccdccdcdbcbcadbcadadddcabbcdcdaccacaabddcaaadbcbbbcdbbbaaabbaabadaccadbbdbddbaabbaabcbcaadadaadddcbdccbaccbacccdaabcadadcccdbcbddbcacadabaadccbbdabaaabbacabbbdaaacaaccdcaabbcadbbcaadbdcdbaabaddbaccdcbbdbccbbdabbacbbaccaddcccadcdacaccacbcbdacacbdbcabaabaddccbbdbacaacddacaccdcccbbaccbadcdcbdadcaccbbbdcdaddbaddbcacbcbbbbcabccabbabcdaaabadcddbbcddabddcaabcddbcacdccdcddaadacadbdacaabcdcbcabbcbbcabaaabbaaabbbdabbcdcdcabdabcaadcbcccaadbbcdaacbddccbdcacbbababccdbccdacddaddbdcdaadadcdcdabccbcdbbdddacadababdccacdddbadbbbcdcbccdcbcaacccabaaaabbddcbdbdaabdbddbccabdcbabbbdcdbacaacdbdbbbdabddcdacdaabadccbbcdddbdacbccadacbcaddcdadccbbcbdadcbccdabacbbbdaabcaccbdaacdadcbbaadcddbdddabdcdbcbdcbcabbbabbadaccdbabccbddbccacbbdbbbcbbbcdcccbdcbbcaccdcbbbdadbdbaabdcdddaccaacbbcdcbcddbdcdbbabbcccddcabcaaabcdabaddbaadaddbdaaabadaacdadbdbadbadcababaccaabacddabacbaacadbbbcbcaabdccbadbddbabbacccabcbddabcdaddaacdbdccbdabadcdbadcabdadbbbdcdbcadbcbbaaacaccddbdbbcddaaddaabddabdcbbbdaccdbbdbabacabdbbdddacaabdadddbcbcdbabcdaabbcbdabbbdbaabbccdcabacbaadadbccbcadaccadbdaacdbaadcbdbacccdbaccacdddaccdbabdcabddadbacabcbcddbbdbaaaaaaccabdabababadcbdbbabdcaaddbacccabcbbababdcdacbccbdcdbcbbddddabdbdddcaccdacbdbbcddcdacdacaaddcccabadbbadcbaabdddabbabdbbabaaccbcdacdabcadbbacdbcdbaaabdcbabdcbccbbbdddacdccaacbcbbdcdbadbadcaababdcdcadcaacbbcabcabbabcdcdbddabbccabacbaaddbcbdbdadcdbbbadadbabcaddabdaccbccbdbcdddcacacbcaaadbcabacdbbdbcdcbbcbaaaacbacadbbcbdbdbdacccbbacacddabcccbabcabdbbddabcbadbaabacbdbbcdbaadbdbaaadaccdbddbaccbbccaadbddbbacdddcddbcdddbbbbdbcbcddcdbacabccbaddadadcdcccdaddaddabcdabadcdbddaadaaadbbabbbcccbacaaadaccaabccddcadcbaaababddcbbcabcbaadaadbccbcccbaaaaadacdbddbacadcddbabcdadcabcdcdbbabbbcbdaccddaacacdacbbcbaddcaadcdddcddabbabcbcbdaddcdccaaddaddbadcdbcadcbcbbddcdabbadbaabcacdccbdcbcbccdcdabaacadcacdcddadcabbcccdcbdabdacccdacbbdbbcbababadcacddbcacadaaddaccdcbcacabadbadccdaacbdaddacadaabdaccaccacaadaababcaaacddcdccaddabdaaabbcdbbbdbcbcdcbabcadbcddbbddbddacadabdabdbbdbdbddbbaadcdbcccbdaaabbccbcaccdddacadadcaddbadccbcdbacdbbbaadabcdabaccaabcbdaddccddbadadcdaddcddbadaabbbdacbcadcddbacdbbabddcdbabdbcdccaaaacdbcaaacdbcacadddccdccadcbcccdbaddbaccdbbaadbdcdacbdbcddbcbcadacdbaabaabbdcbddddbcccabddabdccadcdadaccaddadabbdbccbaabbadbbddccbaaccbbdcacadabcabdcbccbbbbadabcbcadbccdadddaabaabcddbabbbbacdcbdaaaccdbaaacaaccdacddbbcaadadaaaabadbdabcbbcaabdadcbacbcddaaacdccabcadabdcbcacbdccdadaddcabdbcdcbbcdadddcccddcbccbbccbbdabcbbcbcbddacbbdddbadddacdcabaaccdbdabbbccdadbabcddcdbbdcadcbbabbbcbcbcbadbbaabbcbacdbbdbbaaccaaadbbdaabcbddddacaaabbababbabdccbcddabbabdabbdcddcdccdcbcccbcacdbabddddbbaacccdcdabbbdbddbadbdbabbddddacadcacadcbbcbcdcacabcccdacbabdcdcbbbabacbdccbaacdadbbcacaacbcabcdabbaadccacaacdaddcbddbababaabccadbadabccddadaaacdcccdbabcacdaacacbcacdbcacbbbdbbdcdbdbabbcdcbcaccddcaadbddcbcbccccabbbacdccdbcdcbbdbdbacddacdcdccdbcdcaacadaadddbacccbcdcdbdaabbbbadbccbdcbcdbaccadbacbadbdbaaacbaaacddadcaacdcaccddabdcdaddbddabbccdddcbdbbbdacabccadcdacbdabadcbcdbbabcbacdbbdcadcdbaccdaaabacccccbcaacadcbbccbadaadbccbcbacaabdcaddcccacbacdcbcdaccabacabadbaaadbcdcdabbbadcbbabbbbdadadcaabdaaadddabaddcdbddcadbcccdddbdccbaadaccddcdcacaadbccabddddacaccacacdbbadbdccdbdabacaacdcdccdacbadcbbcaadabdacadbcabbcdcacdcadcbaacccdbbbbcccbdbcdbdcbbdacaccdbadcbdcadbbbcbabddcddddbbccdacdacbbbddaccdbdcbdaacacdcbccdbadbdadabbdbccbacbdabcababccddaccaaccccbdbbbbcadaaaacdabdaacdadbbadbaaddacacdabcbdcaabcdacbdddbdbacadbcdddbccdcdbdcddadccbccdcdaddbdcdcdbaccbdcdbcacacbabbcaadcacbdcdbabdcccbccdacccdcabcbbcbbbccddbdadbcaabcaabaaaabaaabadabaaabbdbbcbbaadbaababbadcbcaadabddabadacadabbcadccbcabbdccacccdadaadcdaccbcdbbcdaaaddccdccaabaadcdcdcacaddcabbacdaaaddddbaaaaccaaaaabbcbddaacdabcddcdbcbccaccadccbcaccbcaaaaddbdadccdadbcacacbaddcaaccacaacdbacdbddbbcabbdcbbabbddcababbccccdadaadcabababacbdadbbbcdacbdccbccbddaddbacdadddddacadacaccdcbcddabdbdaaacbcccadcbadaaabdcbdaaddbaabdddcabaddccadccdccddbdacabacddcbcddbacadacdaccabdcdacaabcaaccaabccccbacbdaddcbcbdddabacdbabdcdcbbbdbccddadaabacbabbcdabcbccabbabadcbbacbddadbbddbbdbbbabdddadaddabdaddcdcbbbbadadcbdbdccacbdddcaabbccbacabbdacccadbcdbddbdbbaadbcabcaccddcdacbadabdbabdbcbcbaacbddcddddbbbddbaacccbbacdbbdcaabbbddabaaaaccbcbcdccdbcaaadbbcbdacbcddadcbadacccabdaccdadcaaacbcbcadabbddbaaadbcadcbcbdccdadcaabbbdabbcbcccaabbdbcccccbbcccdabbcddbadcbdcdddbaabbaaacddbdbadcddccbcddbdcbbddcdaaaccacacbdbdabaaacbbdcddbbdcaacbdbddcbdcaabacaaddcdddccadadabadbdddcccbdcabccbbbdbabddddcbdcdaddbdcdccbbccddcbacacbadbbbdaccdabbddbabcaccbccdbcddcbabdacacdcbcbacbaabdccbcdcccabacbbaccddddcbbacdbadcbcdacddadcbdaababdccaccbbdbbbddbaccacdbdbdbadbcabbdcdbcaadddcdcacaaacbcabbddcbdbbdddcaabbddadcccdcbcaabbcbcaaadababcdcccdbaabaaacbaadaabbbdbdcacccacaaadacdddacaaaddcbdaaddccdbcdbcbaaaadaabaacddcbadccbdbdaaabddaaadbacadccccddbcdcdabdddccbcadcdbbcaddabbbccddcdbcbacbcdcdcaccdcbbdadddbdcacacdadaaabddcaddbbabcccdcacbddbdabbdaababbabcacaaaddadaadcbcaaaccccbbdbbccaadaacbabaabdcdaddbcaadabbbbbbddadcccaaadbadcaababcbdcbcbcbbabccbcaaccacdabdccbcbdaacbacdaabcbbdababdbaccbbacabbbbbbcbbdcabbcbdadcdaabbdbcaddbdccdadabbddcbbcadaaccadccdccbabdddaacdacdccadddddadcddacdccbdabbcddacdcccdbdbbcddccabaabababddcdbcdbcddaadbabdcacdbbddbbdccccddccbdcdbbcbbacbbccbabbdbdbacdbabbddaacbcaccbdaabadbcdcaaadcbadcccababddcccadbadaaaddcbcbcdcdabccdcacbadadcdcbabdadbcddaacbbcdbbacccdcababccdcadbaaccbaaabbbacdbbcdbdcbbabacddadcbbacdccdbbbbdccdbababbcdcabacddaccacadbbcccacbbdadcacaccdddbbbabcaadabddcdaadddbacdbccacbcbcdbabcbdbadaabcddaadaaabacddcdbdbabcddabadbdcacabacbabbcabbacbdcbbcbdbccaccaccacababbbbcaaaadbdbcdbdaabbcacbaadbbcdaaabcdcdaadcbaccaacbdcaaabbdadbcadadaddcbdcddcaddcdbaccccaddacddaddaacccbbdbccbbabbbcdcddddbdaccaddbbcccbcaaacdabcddbccacdcaaaadcbaabbacccdacdcbccdcbccddacbdbdbbddaacaaaaccacdabcdbccabbabdcccaabacddcdadacbaccbcacbbddccbcdacdcabbcabdaddcdbbabbaadababcadcbabcbabbbcbadbaaddabadacdcdcdbdbcadbdadbcabcadccdbdccacbaabccddbbdbdaacbdcadcaababaacbdbcdaaabbcbbacacdacacadbddabdbdddccadbaadcdbdaddccbddcacdbcdbbabadaaddddadcdadbadbddbbdbdbadbdaabdbdbbaddddbcccdbadcbcdbcdaaccdadacdccbcbbcdbbaabbbabbdbdabccacadabbcaccddacdadbdbbadabbbbaaddcbbacaadbabaadadcaabddbacaaabbdababadbbdcabbddbabdacccacbbddbcadcacbdccdccbcaccbadbcccdcdacccbcaadbccccabcddcadbccbbaddbbadabaacacbccdaddcbbaccbaabadcdaddcbdababbccbaacdababaaacaccccabcabbdbadabbddaacccbbdbabccacdcadabdddbccbdabbdbacbabadccbbccadaacbcbaccacbbdcbddcdaccbacbdaccddcaadbdbdccdbbbcdcbcabbadbdadbaddcddaaacbabccdacadaddddabbbaddbbdabbbdabdacacabcbadcdadccbaacdcbbbcbdaccabbbacbdcacbdccbbdddcbabbaabbaabbbdaddaccbabdbcdddcbbadcbdbdacababcadaacbbbabcdbcdbbccbcdccdababddcaacaacbaaabdccabbcdcdabdcdadaccaddcabcdcbaaddabccdadabadabdbdadaaaadcdabdaacdccddacdcacbddbccabdabcbcdbcabaaaacbbbabccadbbddaddcdcbccdacbbcbabcbddddcdbadbcbdbccdaabdabdabaddaadbabdaaabadcccaddabaddaadcbbbcadacbcbcdcaadaadcbdacdccabbbbdbdadddcccdabbdadbcbbacdadcccbdbbcdcddacaddddddddabadddbddbdacbaaadacccabaccbdcaaddbcaaaddbadbdbcaaddcdccdcdccddabdcacaabbdcbdddacddcdaadcbabddcbcbcdaabdacbdbcdddbaacddddbcadbccbbadbdbdaacbdbacdcbbbbadcbbcdabdadddbcacdbbddacbaadccaddcbcdcdbdcbbdaccddacdbdcacaadacccccdabaacdddbacbbcbbdccdbdadadcbcdddaaaacdcdbbcddddddbbdcccdcccaadacadaaaddbdbbddbcbabbccdacbddcdbdadcaaaacadccdbaaddbdcaabccdbacacddacbbcbaaadccdcdcabdddacdcdabcdcccadbccdcccdaaadcacddddddbbcbaacbadabddcdbadcacbacaabdabbbcdcdccbadbacabcacccdbabbadabbaccdcbaccabcdcadbdaaaadcaacabcbccbbabcaddadacddbdbabdcddddadcacabddaddcdcbaaccbaaadbaababaaaddaabbdacbcaaacbbddcdacdbbadabdcacccbcdbaabdcbacdbbadaadcadcbadaaccadbdcaacbbdaabbddbadcaddabbbcdbcaabadcbcbabcaabddabbbbcdbcacaabaaccbadbcbdcabbadcbcacbcabcbacbdcccdbbddcabbcbababbdcdacdccaadcdadbdcbbdcdcacaadbbdcbdddacdcaccdaababadadbdbbabcacabbddccdbbbbdbdddcbcdacccbbcdbdbcccbcddbcaddbdcbbdaddbcdddcabdcbbdbcdbcbcccccadcbaaacbbddadacadbbbbddccacbcddbcabbbccdabbcddadcacacbbabddcdddadcaccdcdddcadaaadaaaacccddcababcbcddcabdadabcadbcacdbaaccacbbcbbcbbbdccccbbadadcdcbbadbccdabaaaadacaddcadbacabcabdaaaaacbaabdcdcbcbcaabbcdbcbddaacbbdacbdabdcaaccdbcbcdadbaadddbdccdbddacdcdbbcbbdcaaadbdacbbbcadaccabccddcddadabddcdbdbacdaabdccbaaabbabdabbccccadbdbacadabdbbdddacbcbcaabacbdcbbbcaccadcacdbbadcbadbadabcbcdabccabbcdcbdbacbcbddbadbacbdcbaababddbdabcdaacbdbbabcaadddaddccabcaacddbbabcddcbcdacbacabccddadccdbbddbaddadacadbddcbcdabaccdaabcbbccdcaccbbddbccbddababcccadcbbababdbbbddaadcdccbabdabacaabcbcbbadcaabbabaacababaacbcabaddddacbdcacabccdbdababcacdcdadcbaabbdbaddccbbbabdbdadbcadaabbcaaddcbdcccbbaaaabccbddaccdaccbcbbaabbaacbbddbbcabacdcbdabdabcbbdcbbddcbabdadddbdbcbddababbcbacacbaabaccdccababbdcdcddbbbccbddcdaddbcdcbcdccdbcdadbdbaacabaaaadadbcccdbbcdbccccaaabdadccaaddbcdbaacdbaaadaddccdcacadabbddbdccadaabbbbcbaabdabadabbadbdbdcabdbcbbbbbcadabccabadacdcdabadbdbcabababaadabdcbbcbccadcabdcbacabaabdcaadbabccbdbbcbbacbabcadacbabbbdacdadabacbbdaccbbbabbdaccdaaddabdcdadbcbbddbcabbddaaaddccbddabcdcdccbcbbbbcdbaddaaacbacabbcadbdddcccdddbdbbbdacdddbaacaabacbcbaacbbcdcccdadbccbadccbbccacacdadadcdbddacdcdaadbcbadabcdbdabdacdbdccadacacbacabdadcbdaaadadacdbdabccaccdaabcdbbcdbcdacbaabcbabbacbccbbbcdaaddbbbdcbbaacaddcaaadbbbbccdacbadaacbbdccdcddbabdddbbcdccaadacadcaaadbababacabbadadbbbbacbddacdcdadacaadbddacbbddbbcddaccbabbaacdcabaadcdaccbaadcadbcabdbadabacdbadcdacbaaccaabaaaacbdcacabbbabdcdbaabadcaabddbbaaddaadccbddacbcbbcadccaaaddabcabbccdbbacadcabcdddddcaababcabacbadacdabdacbcdcaabaacacdbabacccadaacaadbcbbdabcacbbaddaaadadabacbcbdccdabddbdccacbabccdbcdbbbbbdabdcccabdcaabcdbccddcccbdcbaacacacabcdcdacbadbddadddbcdcaadbddbdbabdaabccacabbcadcdcadbbdcbdbbddcdabbcccacaddcabdbcbdabbcbdabaadbdcbcabadbbbbbddacbabaaddcdbdbbbdcbdbddcbcdddccddacaccabacaddbccadacbdbadcbadbbacadcdcbbdbdbacbcddcbbbcddccaabbabbbddddbacdaccbcabcbbbccdcbdbdbabacadcbadccddcadabbddadccbccddccccaccdcbcbdbaacbbbdbbdabacdacaaaaddbbcadcdbbccbccadadccaadaabdcbccbdacabadbcabcacccaacbbaaabbbcadbaacbdccddcdcdcdadcbaabbcabcabdaddcbabaddbbacbdaaabddcbbcadabcdabccddbacbbbccdbcacbdbdcddcdaadbdadcadbcabdbcadddbbbddcabcdcdcdbcbabcccaaaaacababddcbbdbcddcadbcaabaacddabbdcddaabdaabcbcaddbbdcbdcccacabdcdbacadbabdcccdabdcdcdccbcacbcccbcdbbcaabdbdbbabddbddaaddcbdbabbaccbdcbcbcdddadacabbbcbdddbdabcdacaadadbcbddbcaccdadabbdbaacabccbcbcbbccaabaddcadcbbacaccacdcadbabdbcbdcaabcadddbddbcaacaaadcdbbcadaaadddabdaaddcccaccdbdabdbadacbcbdddbbcccaddababcbbcbdcdadabccbdacbcaadababbacaaadcdcaabacdbbcdddbcdbdbbcccabbbbcdaabbdcbcaaddcbcbacccaadccaccadcddacdbcddbdbdaaadbaacababddbaadccadcdbbadbcdaababbaaaaccababdaccddabbadcabbbddababccdcddcccdbcbabadbcabbadcccccadddabaaaccabbaacdababdadcbdaaaabadcddabcdaaaacadbdddadbbbdbacdcbccdddaccbbcadcdccacbbaabddcaddcbddbbabcbdcbdbdbdbaabdcabddcccdadcacadcbddddabbccdbdacbacdccddcdbbbcaccaabbcacaaaababcdcbdccccacbcabadcdcaabacaadabaadadaabaddcaaccacdbccbbbbabddcbccdcacbdcbcaadccaadaddaccbcdcdaaabbadadddababdcadacbcaadbacbcbcaddccdbacbcdbdcbacababcccddbdccbacabbacdaccbdaadddaaacdbcabaadaababdcbccbddbdcdbabaaadbbcdacaaaabaacdaababccaddcabdaadcaadbdccabbcbcddbbbbbcadaddbdcddcdbdcababcbbabdddccbccaadcdbbdbdbdcaadccbdadccccbadbdaaacbdbbdadcacbadbdddccdbdbbaddabbcacbdbdbacbadcacdadbabbcccabbccbdbddcbbbacaaacababcbaaccdbcdbaadabddcddaddddacacabbbabcddccaabdccdadabadccbdccdcbcdacbbdcbbcbaabddadbbbcdabbcacdddacbdbdcbdaccccdbabaccdbdbbcbbbacbdcabbcbbddabbbcadaabbabdbbbaaacbcbbadacbcdcdcbaabdbcdbadbddcaccbbdbdbccdadacacbbaabdddaacaababbaadbdcdccaadcacaaabcbaadaccbddcabcdcaadcdbbddcbdbdbcadbddacaaabbabcdbdaaaabaabdcabadbbbdacbcadacaaddbcdbacbdbcbdddaddaddabccbccaadbbabbcbdcaddabdccacaaccabbcdbaacbbabbdcdaacacdcdbdddccddabddacdccbacbbbbdcdcdcdbcdbcadcbacabbdadaacdbbbcdccacdaadbcadadccdacbaccabdcbbdaaddacaabcaacbadbbabbddacaccbbadbdbbcaaabcbbcacbaabcbccccccbbacddcbbadadabcbbdbbcabbdbbccacaccdcdcaaaddddbbdcdcadabdbdaabddabacddcacddbaacdbdabbbcbcddabbbacdabdabdabadccbbdbdddbacbaabaacbdcdaadbdcbacacdbbdbbbdcdacbdabdcdccdaaadcbddbbadbddadacabdcacdbbcdcbcdcddadbbcbbaccacbdddaaacbcacaacaccbbcdbaacbcbaaaabbddbccdccaacdaadcbbccdadddaccaaadcbccabbbbcaccbccabcacbccdaaccbbdaabacbdbaddccdcbbcaddcabdabccaddaabdbcbccdddaddaadbbbdacccdbacbcadacccbccbdaddbcbdcbdbadbbcccddcccddaddabbaabdaccbcbaaacddacbaddaddacdbcaddbcadbaddcaccdcadbabdddabdbdacdcdcdadacaabaacbcabaacacdaacacbaadcadccdcdcbbdadacaabaaddadbadcbdbacbbcbabdacccaccddabddbabadbcdbacdcbcbdbdcadbaabcbaccdbdbdcbddaadaccbacddcdaddbcddcbddbcbbadddccbabdcddaadbdaabbbbdbdbdaadaabbbcdacabcddbdcbbcbcacbbacaabadbcdcdccbdacddddabaabaadaadcbadcbadcbddadcbaccbcdddaadbcacabcadddacdaabddcacbdaddbcaddbcabbcddbbdcadcdcbddbacbbbdbacdacdddabdccacaccdbdbadddcdbddbcccbaabccdddabbbaddcdadaadcaaccabcadcccbdbbaabdbdccccdacbbaccdaddddbddaaddcacdaddbaccbabdbaabaabdddbbdcbbadbcbcbccbdccacccbbacaccdacdbbadccdcdddbbddaaccdbabacccbccbbacbadaabaacabadbadbdacabdbaacaadccddcdabddbbdadaabccadbcdccababcbcdacccbcdbcbccdddaaadccadbcdbababbadbabcdaadaaccbcabcbbddabbbdbccacccabcbdccbdbbbbcaccabcababaadabdacbbccdbabbcdabdaddddbabaddcccbbddcccbbadddabbccdbcabddbaababacaaaaddbcbacabdccabcdbddaabccbccadbccbbdbbdacabcbdadbccdbbcdabcbcbadcabbdbdbadcdcaaabaaccdcbbbddddaaabdccbdccaaacaadbcddbabdaabccaaababccbcccaaaaddbbdbdcdcacdabdbbbaabdcddbadbbacacddbcaadbcddaabadbcacbbdcdcabaddabaaaacdabdabcbbaacbaccbdcaaacaadbbdbadaabbbcbabdcbcccacbaabdbbcacbbbcadccbcbdcbacddddadbcdbacccdcabbcdcacbbcabbcaaaaccddcdbccdcdcbbbdbcddddbbbcabacadaacacaccdddddccdddbbdbdbcdbbacbdcdbcbcdcaaacbbdadacddbaaddbacbcbddcbbdccabcbdbdaaccaccdcdccdccdddddddbbcacbcbababcbdcaaccaddddbbcccdcbadaccabbbbadcddcbdbdcdcdddaabadacaadcadaabaddaddaaacccdadaccccbdabdddccbccdcdcbccbccdcdaccdbbadabdbcadbcbdcdcbcbcadcccabdacdcbbcbbcdbddcaabccadbdbdcaddaccadacbabbcbcdbcacaaaabddddbcdbdbbddbbabbdbdccbcacbdddbbaaabcdcbbdbdabadcabcccbdbdaddabcbdcabbcdbcaabbdaddabcbdbadbccddbcccacabcbdabbaabbdacbdbdaadcbaccdacdaacccbabdbcbcbcdddddddbddadcbaadbadbabbbcacbabcabcccdbdabacbcdbcdbaddaaacddadabaabacacaccacbbddcaabbaccddbabbcbcccdcddbbdbbabcbccbdcabadddcbdcbcaaacadcbcacbbbbcbcdcbacaddadcccabbbcccdbbaacdabcbcbcdadadababcddcabbbddbdcbddbabdcdbcddbdbabbdaaacdacbcdbdacddbddbdabcabbcabaddabdabdadbcabdcdaddcdddbbaddcabbccadcadadcbbbaabdadcdccbddddadccbcadccbcddabdacbacbabdabadbcbbaabbcdbacdcdbacdbacdadcbbaaaaacaacccbbaaccbbacbaadbaaabddccadbcdcadbacbdaacdaccaaadadddbdccbcbbcdcdbbbdcdccdbacadaccdbccadddcbbbddacdacdacdcdaddbcbacbbbdadbbccbdcbacdcadaabaccbddbdacbacdacbcaaaaaaabddbbdcddbcccccddcccdcacdcacaadccdbdacbabcddddbdddddaabddcdacccdcddaabdbdbdcbccccbbdaabddcaaadbdaadbdbdbcadbbdaaccadacaaccdcccabdbdcdcdcdbdbcbabbbbdaaadacacadadbcdbdbdccbdbdcabaaddddcbdadccabdbcbdbabadbccbadadcbaaaadaccadcddaddbddaaaabddccabbbbacaddadcbabcdbccbdccdcdccadcacbdabcbadabbcdbcbdcdbaabdaadabbcccadbcacdbaddbccdcdbcaacbbacaccadcdaaddadaaabdabcacdbddddaddbbbccdabcbbdabcbcbdbadbdabdcdbcdbaaabdaccabadadcacbcbdccadacbcdcabbccaadcabbbbbadbdddcccabdadbcbabbaabddbbbddcacbaccabdadabdbadbbbabbaabcabdaaddccdddbabcbbbbaababcdaacaacaaacdccaaaabbcbbbcccbddcaacacaabadacbbbbcdcddabcccbbabbaddcacddcabcbcbcdacadcdcbddccbcaadbacadcddbbcbbdaababdbcadcdbbabdaccbbddcadbadddcddbcddbabccbaacbcaddbdbaccdadddbbdadcbdcccaaaccbccdabbbdadaccdacdcaccadcabcdbddbbacabbdadccdcddacdbccbbcaabaddaccbdbaaadadaabddddbddadaccaadbbdcddbbaaaddabcdabdbcaaccbdbbacaddccbbaacbbdccdaacadadcbaddbdcaaaddcbabdaadaaaaddcbbbabcadbdcddddbbdabbbdcabdcddbbbbcacbcadccbdcabadaaababbddddabaadbdcdacacdcbddbdbbcadbdbbdbcdbcbabadbcdbcbbcdbddddbacdbddbdbcdbbbdcbabacadddcdccadbaadcdddcadbddadbcbacaacdbddbaaccbddddbddaadaccbacdcbdbadccacddbcabdacadddbcadcbbcdcdaccddddbabdccbddaadccbdaaddaaabbcbaddccbaabaacdcdaaddcbdbcbdbadcbbdbccabcbbdbddcaacddcdcaabcbaacccaacacaaddacdcbbdcbaabdcddbbadbcaddcdaadccabcadbacccddabbddccacadcdacdacdaddcbcbcabcbbbacbdbdabcbaaaabaaabddcaccdacabddbdcdccaacdbdbcadbbdcaadcdababcbbcdacbcaddaadbbcccbacdaccaaaddbabcddadbaaadadcccbcabbacbaaacabccbddbcacadbbdbccdcddacacdbaabccdcaababcabadccbcdbccdaabdbcabccbaccdcbaacdacdbdcbaadacaabcdaabcacbbacbcccccddcaadcdbdaccabdaddbcdbccbbcddbaababbbccadabaccbabacdddcdcbdccdddbacbcdcacacacbddcabaacbbcdaadaacaaabbcacdaabccdbbdbbabdadddabcdacddccbbbbcbcbadcababbaaaaaddbaaaadcaccdbabcbcabdddccddcdadcdbaaddacbbdcabadaadcdcbddbaddcbcdcbcdacacaadabbcdccccacbcaabbdbbcddbddaadadbaabdbdbdbdabddbbbbbccbbacdcbdadbaddddaaddbccdcbacdcbccddbacddacbcacccdadccaacaaddbcabbdcdccdcdbbbdadccbdcddaaadadbbdcdabdbdcdcddaabacaaabcddbdcbbccbdabcacdaabcccbcbadbcccbcadbbacdcbabdadbcdaadbadddaddbdaaabdddcbdccbbccaabbacbadabbcdccbcaabcdabadbdcbbbdddcdcacdbaccdaddadcdadabbacaaacddcddadaadbaaddadcababcbdbdbbccbddbdacacdcadabbaddbccacaaadcaadabacdcbaabadabbadbbbdcdaaaaddcccdacbaaccbdddbbcbabbdddbaccdccbdaaccaababacbccadaadcabbcbbdcbadcdabbaaddcbccbddddbbccabbddcbcadcacddbccddacbddbacbbbdabbaabacaabaaacabdbdaaaabbdbdabbbcdbdabdcbbdacbddbbbaddbccabbdcdbcbddbbddaaadbcaadddacbdbddcabaadcbadacbbbdbbbdaaadcacddbccdbdccccddbbccbbbcaaadadbbcbbbdbbcdccbcaabbacdcbabcbbcadbccdbdcdddcdaababbaccaabbbbcbcbdacadbcbbbbdcbbbabbdabaabbdbabddaababaacabdaacacbcddacbdcdbdacddabdadbdcdcdacbdacbadbcbabdabbbdcbbadcddccccccbcadccdbcdbccbabdcdabdabccdacdddbcacabbbdcdbbcbdcdbaccbdcccbcdcbcddacacdaccbdbadbcaddcdabccdbaddcbacdbbddcbcaadabcddccdbcbcacbcbdbadabbbdccabaacadccababbbdbacbaabdabbbbbaaccabcdccbddbbbbddabcdbcacaadbdcddadddadcbacdcdabbccbacddaacbbcdbadbdccbdddcbcdbcbbabcadbbcdcadccdccbaddabdbbbaadddcabadcccbcccacbbdabddcbdbbbabbcdbcccbbacabdcaacaacabcaaababbabdbccadaddacacbdabbbacbcacddbccaacaabddaaddcaaacdadaaabdcabbcdbccacdcddbddcccacdbadcdbcbdbcdbccbdacabdcdbcdacacacaccdaacccadccbaccbabcdbacaaaddcacabddcdcccbaddbacabbdbaacadadcccddaadabcbadcadcdbbccdbbabababcbbbdcdbccbbbccaabdbdccacabdbbdcadbcbcdabdcccbaacddbaccbdacdacabaddaababccbccadcbbcbbcbacabdabacbccddaaccabacdcadbbddbdacbdbadabccaddadbdbddcbcbdccacddddbddddaaadcddcccababcacbdbdacadcaabcacaccbcabcababdbaadcbbcbcadddabaccbcbcbdbbbadbdbcaccbbcdaaabcbcbdcbdbabdbcccadddcbcdbbbcbcbbaccaddabbcdcbbcadccababacddcadddcdabcabccbdccddabdcbcdbacdababdcbaccdbaabcadddaccdcadbbccdadcacbaccacdcadbadabadbcabacddaaaadbcdcadadbccbbbdbadacacabddaadcbbdddcdbbdabcdccbcbdbabbcbcbbcabccadadbbbcdaccbaadccbdcdddbabcdbaaadbbdccccbbaccddcddbcadadcbccadcbcaabcacdcdcdcdcacdcccddcbcdbdbbcabbaaddcddddbddabdaacbbcbdcbbdbadaaacababdacbbabaabdbbadaaaabddbdaddcbbaaddacaddabdabbaacccaacacadddacdaccaddddadcccdcbbcbaabdcbcddcdbaadadcbbdadbcdcacbbabbbbbdbadabcbadddddbaadacdbdddcabcbcaaaacbccdddbbdadbcabcaacacdcdbbabdcbbdccacddbccaaabadddbcccabaccaaacdadbacbbabcdadbacbdccabbbadaddccadacdbabccaddcbcdabaacacaabcbbcddbbacbcbcdbcccdacbabacdcdaababaaaacdccdcbabbdabbabaddcccabccaabbdcdacaddcbcccdcacdcaccdabddbdcaaddbdcddaddadaabcdcbdbaadcadcbdadccacacdcdbcdcdadbbcbabbaacdcddadacdabddccabaabadabddcbadcdbabbbaccabacaddcbbabacdcbccdbddabaddcccacdcadddbdcdbaadddbbbdcbaabcaabcdcbacaacddbdbaacbcdbacaabbcbccaacdaabdccbdcadcaddbcbaababbdcbccaabbcabacdbcbbcabdcaadcadabcdbacabdbacacacbddabcaacddcdcddbccbddaaacdbbdcdbaabcccbdcbdbbdadcccbbcbdbcacbcacbacacdabbbaacdbcaaaaccccbbbabccdcdaaacdadcdaacccbdbacbabdcdacdddcdbdacaacabadbdacdcbcabdadccbbadcccbdabbaddcddcacbccbabbdcacbcaadcccbdbabaaacbacddddaaaabdaddbdbaccdaaaaadcaaadddcbbcdcbcaacdbcccbbcdaddbccbccdcddbbdddbdddadacadaddbcacbadaccdbbbacadacdacdacccccbdadbcdacbdbddaccbdababdbacdcdbcabcbbbadbdaccabacdbbdcadbcabcbcabddcacdccbbdcccbaaaacbcdaacdcbaaaabdbdcaadcbbcdabaddccbbaccaccacaacabaabcbccaacabdbbadbbccacdbbccbabddddbabcdcccccdadbddddcaccabbabbbcbadcdabbbaadbbbbabccbdbbadaccbbacdcadaccbadbccdbbcddbbabcbdabaaaccbadbbaccdbabcdccbadaaaaabdbdcdacccbbdacdcdacaabadaadbdabdadcdababcabdadabbdcbccadbcdacbcbabbcdbbbcbcaabcbccaccccdbbacbdaddcbcdcdbbabdadabdbdbcbbbacbdccdbcbbcbbaaabdccdcbdabdbacbccdadadabdcdadccadbbdbbbaacccbdadddcabddbcddabaabdbdccbbbcbdbcabcaabdbcadccdabdcacaccaaccdcadacdcbdababacdbbabdcbccbdcdacdbabdaabbccacaacddccbcddbbaabddacbbdbdaccdacbcbbdbabbabbcaacbcdacbbacabdabdcdaaadccdddcbdbdcbdbbddacacbbcbbbcddabcccddbcdabdddaaabbdabcbdbbabbcbbacbcccabbbcccacdbaccccdadddaabbbbbaccbacbcdaabcdbbccbdcddcdcbcccbacacbcbbaccdadbbccadaddbbabddbbaabbcddbbdccabcdbdbdacbbacaddacadccccbdcdddddaddadaaccbbbbcbaaacddaababcbddcbacdbbdbacacacccccadcccbcaaacdbadaddbbbcccbaabcdabcdacdddcbdbbbabcdacbcdadabbdbbacadadcdbdcddddbdddbbabbcbcccacdadddacbccbdadbcbdbdcdbcaabadbbacbadcdddabdadacabcbbbadaaddcdacbbcbabcacddacdcabababcccdbbacddcaadcbccdcbdbccabdbbddaacdbacaccdcbdccddbbaaababaadbccccabcccdcaccbbbdcccbcdbbcbadaaddbcbddbcabaccacdbdcadbdcccbdddacbacdaadbbaddaaaacdccaddddbdadcacadadcddcdcccabdabdbbdccbccdbdaddbaccccdcaaabbcddbcbddcbadbbcbcaddbbadadabdabdadbcabcbbbaaaaaacdbaadacadbbdbaadccbccddabaadabcbdbcdaabcdcbaadacbabdbccaaacabbcdbbccbdcdcadadabaadcabcbabcbbddccdccdaabcdcaaaddcbacdbbddaaadaccbbdddbbdddbdcccbddcdcdcadcbcbcacaaddddadccacdadabcaacccbdabbabcabbcbbcddbcdacdadbcbdaaccacbddcaddacbdbdbcdadaaaddccdbbabbabbcadcbbabaadacacbcbbbdcccababaccaacaabadaddccccacacbbbaddababdabadaaacadbbbbabbddbadabdbcdddacabcadcabdaaabdddbadddaaacbcdddbcccbcabaabdbcacbcdbadcdbabadcacbddacdbdcdaabaccbaadcdadbbadbbbcccadcadddcbcbacccbabdcdcbbbddadaadbdabcdccaddaddacacdccdabbdbaaaabdccbcbbbbdcbdacdcdcadcdadbcabadacadcadbcacccaabcdcdbbcadcbacbbcbddccbdadddacdacddaaacbadacabcabdacdbdadaabdcbadcbdbbbacdcbbdbcbdadccbabbbbddbdbbbdddaaaddadcbdcbabcdacbddabdccadbbdcbcaabdbdaaaccddabcaddbdadaacaadbabaadacabcdcbbaaadcdbadbccbdcbbccdabcccbcdadbdaacdbccbdadbcaaaaccbbbbbcbcaadcaacdcadbbddaddacdacbabdcbbdabcbabdacaaccddccbccbadaacbccddacddabadadaabcbdbabdcabdbbbcacdcaaadcdbaaabdcdcdbcddddbbabdccbaabdabcaacabacacdadbacbabcacdbadabbbcbcaccdadadaccddbadaabccbbacbddaddcdacbacadcaddbddddaabadcdcdbdbadabccbabcacdddcbaccacdccbccacabccccbbbdcdcbccbacbdbacdabacabdadacdacbbdbcdadaaabdbdcccddccdadcbdabadbaabdbccdccdddbdcabbdcddbcbabcacabacabccddabadbbcbcddbaaaacbcdbccadddbbcdddadbbbddcdddbddbdababcaacbcbadbbcccaaacaabbbbcccaccacaaaaabacadbadaadcdddcaabdcbcdadcacdcabbdbdbccbdccbcdabbdacdcbdacbdddbccbcccaabbccbbbaabdbdadabcbbabbbacaccccbcabbbabdccbdddaddbcdcdbabdbbaacbcbbdcaccdbbcaccbcbbcddaddadddbbabcbbaaabccbbcabcadccacaacdccbbcbadbabbddabdcbcadaaabaddabbabaacdcdbcadccccbdaacdbbacccacdcacdcdcbbbadbccbddcbdacadcbbbcdcccbcbbccaacadaaaadcbaaadacadaabadcbabbaacaabaddbbddbadbccdbbbdbbabcdcddadbcadcdadacadabbbdbbccbbcbcddabddaddadadcdabcaccbbdbbaadcdbaabbbbddccbadcabdadbaddcdacadcdddbddaaacbacadcaddccdbabaddcbcccacddcbadcbbdbcaabcdaccbcccdbccbadbccdccdbaadbcdadaddacccbbcbbcbcbaabcaaabdcadcdbcccadacbcaaddbddacaabddaddbcdabddbcddccdcbcaccabbacadbcdacdadadaadbbbdaaabacdaacaccdcccdbdabbbbccaacacbdaccadadbccbbbcabcdccbdcdcbbdbadaabbaacddccbbbcbdccbbbdbbdbcabaabbbbddccbcdcbbadadbddcabbdbbccabaabaabaaddcbdbcbdbabbbbacccabcbbbdccddddacadbdccbdabdadaaddababdacbcbcbdddccbabcdcadbbbbbdbbadbdbdcaddadbbdacacabbdddbdacccbbaadddcaacaabcccbcacdbdbdadbbbccadaccacccaabddbbdcdccaacbadbacddddcadcbbbabadccdbaabbadbaacdadbcbcadccabaccbbacadcbddbbcdadccdbdadabbbbdaaadcbbbdaaabbabbacabcaacdadcccadcbbdbdacabadaccacacaddbbcdbbaacabcdcbbcdbaaaaaabbbbbbcbabbaacbcbcbbbdacccaaaccbacbdbbdbbacbbaadcdacbccaadacacbcccbdaaccadcbdbdadacabdcaddddccdbabdadacaddaadaaaddbababdccccdcdbcbdbbbcacacaddccbadaddacddabbcdadddddaaaddadcdbcacdbaabbbcacbbbdcdcdddadbbbacdbdbcbcabbabcabaccbcbdcccdcdcbacdaccdbcaacadbaadacdcdcabddbabbddbcadadaadbcddbabdcccdddadccabdbbdcdbcabacddbacaaaaccdabdcccdcbcdaaabbbccaddbbdbbbbdcbdaaaacacbddacdaddcbcbddddcbacaaddbdabddddccbcccadbacabdabccaaadcdbdcbcddabcddaaccabbcacbabbdaabbbbdbabdbcbadadacabddaddcabdbbbcacaccbbbbbdcacaaaabcadddacbdcadcbadbabbdccdabaddddacdbabcadcadbcbcdaccabcbbabcdcaacabadcbdcbbbaadbcbbddadcbaacbcabddbcbcadbbbbadacbdacaabadaddddaadbaddcdcaccccaacaddbdcadbacbcdcadcbdbcbbacaaddabcaaadbababdcbcabddcdcbacacdbbcbdcdcaaccaaaacdbddcadbcabcadbdcddaddaaabacbdcbdbbaabbdcaabaddccabdbdbdabbbabccbbcadadccadabdbaadadcaccacbdcaccaddbddaccddccbddccddadddcdbdcbdccdccdddadbcddcabbdacccbaddbcaaccddcccbdbdbcbcaaabcbcdcdbcbddcbabbadabdadadbdcdbbdbaaaaaabbdbbbcacdadcacbabbbcbabcccbddbddbbbacdddabcddadbabbaadbdcabccaccbaadcdcbdbdcddadaabccacbadaabdcddbdbdbabbacbadacbcaababddcbadaacbcbdbdccdcbabacdbdbdcbccdaaccbccdbbadaadbdcadbccacbbddcbcdcabbcddbcbbddcddbbbddabbcbaadabbdcbbddbacccccbdcdabcabdddaabbadacabadadbccdcdddabccacdbcaaacdddbbdadccdcbabcccdbdadddbccbbbcadcccbaacdaadaaaabdbabbaccabbaccbdbddcddadbaacbbcbcddbdbbcabdbcadbbccababdacbccaddbaadabcbbddcacdbbadcdddcaacaaabcbbcbdabdacddabdaabbcbdcacdcdbcdaaccccaabcbdbcaccdabaccbbacdbcbadcddbbaddbcaadcddddacdbcacacacbcddbaaaabacdbddcacdaaaabdacdddadbcdacbabcacabcbadbbccddbcccbbbabdddcdbdddccabccbdbccbcccbcbaabdbdcbadbdbddaacbccbdccdcdbaabbbbbbaadcaccdabbdacbcacbcccbdadccdbadabbcacbbadcbabbcddbacbbbaadcdcaaccdadbcdacabcaaccbbcbbdacaaccabadccbabbddbbcdbaadadbaadcdadcabbaabdabadddaddcbcdcbbdbbcaddbcdacdddacdccbcbdbdaccadbdbcdcadaaababbbccdbdcacbccdbbcbcabbbbddbddcabccdacdabbdbdcacbdcccadabbcbabccacdabaacdbddcbbddbbcbbbdccdcbbdddadaddbcccadccacbaadaccabaadadbcccbadcaacbdccddcbbbbcaacdcacdddbaccccaabcccbadcbbaacabcddccdcccddddbaabdcbadcdaaaddaccccbdbaccdcdcbabbabcdbddbdbcababccadbdbddacdbacdaddcabbcbcbdadbaccccadccbadadcabaacbddbcbbddbcaacacacdadcddccbcaabdccdbababcadccbacbccccaaadbaaaadacabcbccabbccdbabbbbdcdbdddddadcdbbadbaddcbbdbbbaccdbbccbabaacbdbbcbdbccbdcbdbddddccdababdbddccdcacdadabdbaacbcdbaaaacbdcccdcaaabccaabdcbdabadaddaddcdbcabcdacbabddcbacbccbaadddaaabadacbdddcaacbcccadbbaccbdabddddbbdadadbcadddcabcbcabdcdbddadcccacabdaccacdaacbdcbcddaaddabddcbdccbbbabbdccddcdcbaccaccbdadccbddbccdbacdadcdacbddadcadabcddbadbacbabdadddadbdaddabacdaddcbbbbacdabcadbcdbaddacbacccabadcbbdabaacabadcdabbbcbdbadcddddcbdbaddbcbaacbcbadaddccabddaabaabbaaccbccdacadbbbaddbbbbadcbcbccbbccbdbaccaddbcdaaaadbbaaabcddaddaccaddcccdcbadbbcaacaacbbbdaabcbbadadabbaacdaacadbdcdadabababbaccddbddddcccbadbbdbaccababaadcdacccccdababbbabdbcdacdbabadaaadcbdbccddcbdabcdbcbcdcaacabbdbcbcddabdccaaadbbacbbcaabbdddbbccdcbcccddbabbcccccaabcdbcdababdbdcdaddaccbcbadcacddccddabcabdabcbaabdbcddabbdddbadbaadbddbdcbabdbdccdacabadddbdadccdccbadacadadadacccbdbdcbbbacbbcbcbaddabcaacbadadaadadacabdacbdbbaddcadbdccdbaddcbcbdbdcadcadccccabcbddbbdcdbbcbbddcbaadabcbdadbdbbbccdcdddaacadcdbbdcccbcaccadbccbcdbbccacbadbbacbccccbcabdabbabdbaddabaacaadaccaabdcbaaacbccacbdcbcaabacbcdbcccddabbdcbbbacbdcbaacbcdbaabddcabbcdabacadcccdaccacdaacbcbbcccabddccdadaabdbaacbbbacccacbdddbddbdaabcdaabbacbbacbcbdaabdbacbbbcdcbdbaaccbcacdddabaccadcabdacadcbcccaabccbcadddbbcadbdabbbbaaaaadabccaaacbccbdadcddbccbacabadaacdadbaaaddcbabacdddddbdbcdabbcbbabcbbccabbcbbbcdbdbaacbabbddcbdcaccbcadbdbcbaaaacabcbbbdcccddbdcbadabbdbcdabacdaabbdcbaddbcadaabbdaacbaacbabbcdbacbadddcacabcdabbbdbdadbdcbdcbccccdbcdadaabadbabbbabdddcdadcbadbaaccbaabbaabdabaddccacbbcbcdcddacdddcaaabadaacadababcddbdadcbdcabbabbadcaabcbcdcdddbbaaabdcddccaaacdabbadbcaabdbaccbcccabcdccdadbadabaadcbcdbcdadbcdacddacdbcbadadacacabaabcbacbbdddbdbccbbddcbbaccddccaddabacdcddddddbbdbbabbdbcbbbbccdddaaccbdbbdacbdcddabaddbdbabcdbbcacbbacdaabbddcbbdacababcdddcbbbdcaccdddbdaddbbcbcccabddabacaaaccbbaaacadddbddacbddbcbbccbcaaaaabbcdadbcbaacaaabcbdddbbcaddaabdddcbcdbbdbbabcbcdaaabbcbcaabbdadabacddcdacbdbbccacacadcbbddcabadddacdaabcbdabbacdccbbbcbdddcabaacdabbaccbcbdbaabcbacddbcdadcbabcbabdabddbcaadcbbacddadaddbbbdbdaabbdcaadcbcbbabaddccbddcaacbccaddcaabdaadbdbbcabccdddcbcbcbabccccdadbdbbabbcdcabddadaabdcbddacaadabbaddadaddcdacbcddccbcabddcbaccdcdaacdaadbccddaabbcddcbabdcabcadabdddadccdbccaaaccbbcbcdaabbcddcbacddabcccadbdccdcdabbabcdddaacdbcdbbcbbcccdddacabbbddbbacbbbdabddccbabcbddbccbdcacccdcbdadddcabbaadcdcbcaccccbcaccabbbbbcbcdcbbabbbdcaabacbbdbbbbcacddcacbbdacbcdacaaadaddaabbccacbaddabaacdbadbcacbbacacaadababdbaccbbdcbaccaccbddaacddcaaaccaadaacadbaddccccdaddccacdacdcadbcadbdbaabcdcaaadbcbabbcacaaacddaaccdaadadddbccabdddbbacdbdcbbbaacdcbdadacbddabbabacabbcdacdaabccbaadddabbbcdaaddbbdbbdcaddaabcbabbabcabdcdaacdbbaabddbcbbdaaaacbcccddabaaddaadabdaccaddbacabaadccddbdabdbbdbccbdbaaaabacbbccaaaaccdbddadcdcbbccacbddcddabaccacdadbbdbdbacdbcbccbbcdcacdbabddbaadabaaaaaaddcaddcbabcbbcbaaaacbbddacdcbabaaaaaaaaaacadcadaaacccdbdcdbcbcddbcaacbcbbadbdacdcbdbbadcbdbcaccbdabacbabbddaccbddbbdabacaabdcbaacacdbccbaacabddbbacbaacadacadccbaccccbaddcaccdbaacbdcdadbababaaaabdadcbdcbddbdadbccacddbddbacbbbaaaccdaacdabdcbcdbadbbcadacdbaccdbbbcacabdbdbcdcdadcdbadcaccbbadcacdadaaaddadbcabcbadacddcadadccbcaadddacacdccbabcdcdccabbbbcacdcdbacadbcbcddcaacaabadcccddbbaadaaabbcdcbccabaacdbdacdbdcaabcdbccccbbdbdcabbcabbbbcdcddddcadcbcddbcabcadaccbccbdcadcaaabdcbbcbbadcbbccdbabaadddcabaadcbabadcdddbddbddbdcabbddcdbcabcdbacbddadcdcbbacbbdddbadcdbbbcaddddbacdcabacccdbdacaabdcadacbbcadaabcabbccaababaadcaabdabcabcadacdbbcbadadccdddcaadccbaccbbbdccdccbaabcbddbcbdcacabdbcdadbaccbdaaabdabccdccdadcacaabcacadcdbdbdbcdddcaaaadaadcdbbbbcacddaaaaabddcabcddddccacdadcbbddabdaccdcdbbadaababbadbcccaddcdccdbddcddbbddababdcbaaccbacdabacacbcbdbbabacbcadbaadadabbbcabcdbacccddadddadcbbacccdcabcdadaccccbbbccbbbabbbcbadbbbbbbbcdbabbbbbacacdbcdddbaabbcaabcabbccadadbbdccadabccacbadbcacaccaddacdbcabbccaadbdadbdabcdcabbcbacccdcddcaabcacacbbddaadbdcdddcadbbddcadcabbdadbbabcdbdcdabaadccaccdccdadadddbacbadbacabaacaaaadacbbabbdbcaaddbbcbbbcdddccbdcdabbcadabacbddcbaabcdbbbbbdbacbacdcdacabbdadabaddccdcbbdcdacbbddcbbbddabdccaabbaabbddbbcddddbdccbcbaddbcdaadccbccccaddcdaaacaadcdacddbdabcaaabaccccdacdaabbccbaaababbbaacabaadadcddbdaccbabcbbbddaccadbaadbccbbcabcbaccbdcbddbddbddcacbbbdaacdbabadbbddabdcbaadacbabdccdadcddabadccadbbbbaabccccadcdbcaadbadadbdbcdddbabcdbdcddbbbacbcccacdcbacccdadadccdbbdbbbbbcbbbdadbddbccabbacddcaddadbbadcaadaddddbdbddddaccbdcdcdabccdaaaacbccaadbbaccacadadcaaabcdcabdddadccadbdbcddbbdccdcdaacbdadadcbdbbccdaddbddabbddbdcbbbaaacadaacadbbdccabccbbabddcdaacaaabcccabcacbbddacbcbcadcbcdddbcbbababaaabcccdcddbbcdcbbadaabcdaccaadbbccacbccdadacbcbcdacadcdbdbdccbaadcdcadbabbbbcddacbbcddbdaacbddaacaaccbdbaacaadbabaaacbabbadabdaaddccbcddbacbbabbdccbdbdabaaccbdcdcbbabbdadddcadabcbcbdabcaabdacbacdcdbddabcaccbbdabcbabdcddbdaabaadcbccdbdaabdacadabcaadbcbdadddbdabdaacddadddacbcabbaababccccdbddabaaaaccdbabbdbacadddabdabdabccbbbbbacbadbaaadcaaadcbdcbadbbcdbbbbcddcacadbcbdabbcdabddcbbcbaaadccbbdacbadadbccdbbcaabbbddacbccdabddddaabdcddcbdadddbcbacdbaadcdbaddbbbccccccbdacbbbdcdababdacaabcdcbddbcdcccbbdadcabcbaabaccbbcccbdcabdbabdccacddcbbacabcbabacccabbddcdcbdcccbcdabaabdabbbacadcbdbbbaaddbacabbdbcbbdbbddbabbbcdbacabdccaabbbdccaaddbcddcaaacabcbacdaadcdaadddabdacadacacbdccbdababdbcadcacccccbadbdcabbbabccdcdababdadbcbcdddabacbcdcdaccdacbcccaabcacacdbacdabcabbbbbbabadddbababbcdddddabbcadcaacabdbbadcadbdbbccbcddddbbccaddaaddacddbdbdbddcadcdcddcbaddcbdcdcacbccaaadccbacdddcbabadbcdabaaacacbcbaacadaabdaddcdaababbaccdbbbdddcdcbabaacdcabbdcddcabbcacdaadadcadaacbcbdddadcdaabadcaadbddbbaccaacbbadcbadbaccadddddadaccabbbddccbadbabbdccbbbbaddabddcaccdccacbbdabaadbaacbacdaddddaaddaccaccbbdcbbdcbdbbdccdabbdacbbbacbbdcdbabccdcdcccdaadcbcdacbccddcaadaabddacbaccdcaadbdabccaabbcccabcbccbbdccdabdcdbccbcaccdabbbdcabadcaacddbbabdbaddbabaacbadaccbcbbbacdaaabcadccdabbdccdbbabacdcbacacbbddbdcbdcdcdcbcdcdabdbabdabccbbbadadacdbbbccbdcbaacadbdabccdddbddcdbcdccbacdccdcbabcbbababdbcddcbcdccaacbddbcbbbacdabadddbbdabababbabbcbccdadddaabbcbbbaadcaadabccdcacbabcabdcadabbdabccccaddddadddcddbccdcddbabacccdbabacbcadbdbbcadacccdbbdacabcbadcaccadbddcdacbbbdbdbbddaddcaddcaacbdcbbaaabadcbdddadbcacdabcdcaccaccbdaacdadddacabcddbcbadaccddcadcbdacdbacacbbcbdbadaaccbbabccdabcbaabcaaaadbbbdaacacdccddccabaaaddbaccbabdbbaabaccacdddcabbcbabadbadbcdbbcaaabdbbbcacbcaacabcaababddcbbbbaabacdcdaabbaddbcbacbadaaddabbbdbcabdadadcccccacddadbaccbddbacdcaacadbddabbcbcdbacdcaadcddcabccccbdbadccbccbadcbcdbadaabdbdbbaabcddbaccbdddcbcddbdddabccabbbdccaabdbcbddbbcabcdacbcbdcbaacbdbbdbcabcbcbabacbccddbacdabdddaacccabadcaccccddaabcdbcbbacdccccaabdbacbdadacbddbaabdababcbaacccbbabdcbdcdbcbcadbdbccbbaaaddbbdcbcbadacccbadcccaacdbabdadadaacaccbcabdaabdabbbbcbdbddbcbdcbbdddaccccabbcbddcddaacdcddbabdbcdcacdccbabddcaccbdcbccbcdadccbdaddabcacdbbcbaabacdbdddbcdbdabbbcabdddaadabaccdaddbaaccbbbcbbaabcdcbddcbcddadbaacdcaabcbbbdbdaccccdadcdcadadadcaadaabbcadbacbadacccdbbabacacaabccdcccabdaccdddccdcbdcddcbabbbbaadaadabcdaddcccccacadcbbcdddccabaacacdaaabbcadabacaacbabdbbcbbaacaacccdbadbbadacbddaacbbdbadacbccbbddbadcccbbaacadbdabaabacbdbdcaaacdbbaacdbcabbaccaabcbaaabccbbbabccdabbacbccdbccddcbacacbccccacddbccdccbdaaacccabdcbdabbbddcccddadacdbdcdaadabdbaacacbacabaabddcbcabbcaaccdbaccdbbdcbcbcdbcadacdbdbdaacaabaabcdddbaaadcdbbbaaddccbbccdcddbcbbaadaadbdcbabbdabddbccbbaabdbccbdcabdddbcbcaccddbdcccbabbcabbcaabcabcdcabbadbabddccbcbcaacdaaacbadbbcdacdcacacbbcbaadadbcbdcddbcccabaccdbaabbcadbaacdacccccbcaabadbbccccaacbdcadcdadaadaddabdddbaadcbdbaddadbacadccbcbadacccdbcddabcacaabcdcacbbcaacdcadcaccacacdcbddcaacdabbadabacbdbdbccccccbcacacdbcbbddcaacbdcbacaaddadddbaccbaccacddabddcabbddcbcddddadccdbdbbdcdadbaccbbadabadadccdcbabaddcdacddbcacadababbaccdbdbbcababbcbbabddcbddcadddcccbaadcaacacddcccadddddcbabcbbddddabaadbbbbdcdbdadcdbcacdadabcbddbabcaabdbbbaccbcabbbcbbbdccbcdddadbabbaccbdcadcabcddaaacbddbacabadaaabacbcccaabadddcdbcdddbccdbadaadcdaaddbbaacdabdaabddacbbddcaccadbbddbaacbdbaccbbacdddaabaaabbdabcdbbdcdbbcbbbdccdbbdddaaabdaaadcaadabacddbcacbcdcadbbabdcacadbdaacbadbddcbdcbbabbdcddbbdcaabbccbdacabbbadddcdabbdcbbdddccabcbdacbadacacaddacadcbcbcacbacbcaddbbaccabbcbcaaddaddcdbbcabddacadddbbdbabcdcdccabcabaacddacadcadabbcacbdbdabdaadabccddaaadcaadcccbbbccbbaabbbdbddcccbdccbddcaadadbcdbabcbcbcadaddabbabbabcabbdcbbacbcdddcaadccccbacacbdadabcadadcabcbbcaccbbaadbdcddababbacadcaaabcbbbcbbdbaccbdbaaaccaacbabaddcccadbccccbadadaadcdccbdababcdcaacaabbbcdcccbddcbcddacabdbdabbbcbbdbddbaadaddabbadaddbabdbbadbdcbddcdabcccdcdacdaacdabbbacbbbbcaacbbbccbacadabbbcdbdbcabdcddbcadbbcccddbccbcddabadcdcdbbcdccdaacabccddaaccbcccaaabbdbabaadcdbcadabcccaddcdccbdabcacbdbbbcdccdbaddbaaaaadbccbabadcdbdcbdbcaadbbaabbcaabdcacadbbbaabdbcbacacbccbbbadcdadbadaabbbbcaccccabcdadadbcbacbabbbdcbacaaddaadcdbdaadadbaaddacdabaadaccaabbbaaccdcaadadbaaabbddcbacccdcbdadbaaaccddcdbccadadaaacdaabadaddbdcabccaaccdcccacadbbbbbadabccababbccaddbcabcabbcbcbaacbacdbabaabadadddcdccbacbaddabcdadcbcacacbbdbaddbbbccdcdacddabadadbcaabcadcbdcaadcaaddacabbbccabdabaababcbbdcaabbacccacbcbacdbbccdcdaccaacbbabacbddabbccddadbdbbdbaaabadbcddbdaaadddabcdacbadbbdddcdbcabdbbbcacaaccacbaabdacbccbaacbaaaadbbddccbbbbcaabcabddcddbdaaccdbadcdddabbadbacddaabccbbbdadadcaccdcbbdacbcadaadcadcdaccdcdcddabbbcddcadadabccdbdcbcacaccbcccaaabbbbcdcadbaaacbacdcbccdcccbbaacbdbcadbdcbbdddabaabbddcbbdddddcabaacbadddcacacdbbbaaabbbddbaaccdbadaddbdadbcabacbaaaccaaabbbabbbbddaddbbdbcddcacabcbbcabcdaacdcccbabdabccaadabbabdcadbdabbdabcbcdddaabdbabaadacbbacdbdabbddaadaadbdcbcbaccabdcdbdcbacacdaabbdacbaadbacbdbcdacbdabdaacdbcdbbbaaacbdcdcbacaaaaaaaadcadbdaaaddaaadabcdcbabaabddabcdcacdbadccdbddaadbbbbdccbbcbabacccabbaddbabccaadddbcbbbdbcadcdabddbbbadcdbbbcabdbccaadcdbadbacbbcdbccbcabacddcdccbaccaadccdcbcdbaddddbcdcbddabacdcbbdbdaadacadaccbbbbbaadcacbcccacdadbabdacbabbcbdabdcdbdbcbbaccadaaaabcddddccbcddbbccddddaacccbcddbadcdcbddcaaabbacbdbddbbabdbcabdccaacacaaacbdacbcadabdbbcbbbdddccccacabaddaacaaadcbadadcdcdaadddcbacdaccdadacbadcdaddccdddcbdbdccdbbdcdbabccdcccacdadaaddcadcbacbaabadabdbbdcabcbdbdcccddcdacdcadadcbadddbcbacddcdcdaacaadacdbccbbabbbabbdbdddbacabdccabaccccdbacddadbdcdcdbdacbbbdddcdbcdabbdccabbccaacbccbbabcddaabccaaadbacbddbdcbcabbacccddacbcaaddadbcbcadabdaaabcacddcdcacdaaadcaddbcaacddabcadbcadcdbcacddcaaddbbdbbcaadddbbababbdbaacddbcdaabddcaaacadabcdaaacdccccbbaadacbadbaabcacccdcdacbdbadcdbdadcadbccacddaccaadacacaadbdccbdbdaadabaddacbaacbaddaaccbabbacacadbadbcdaddbbcbddaddcbdbdbabbcbddbbccbbbcabdabdddbadcacdaddcbbaaacbddabcbdbdcbbccbcdddcdaadbcdddaabdddcacbdabaccabdddabbdbbbdbbccbaccbdadcbabbdcdbbaccacdbbcdddbabbbddbaacbcbadbcadbcbdbbacdcaaddcacabbbbabcbadccabdadaadddcaddccbbbdbadadcbdacadaccbcbbbbdaacbdccbacbbccbdbacbabdacbcaccbcaaacaccacadadccaadccddbbcacbcacacaddcbadbcccccddbacaddaabdccadcbaddacaadbdcadddbaaaacaaadccbaadcaacbdcaaaaadadaaabcddddddcbdbdadaccccdbcddabacbaaaccbbbbdddbccdddbdcacbbbdbccccaacdbbbbcccaaddadccbbadadbbbdbdccbcacadacaddcddadaacbdcbbcabcddcbbdaacbbacbcdaddddcdabbdcadccaddbbdacbaccaddcbcadaadbbcbcbaddddcabcbdddcccaccdcaaddaacaacbddcaadcbbcdcbbbaabaadcacacbabbdddacbbbadabbbabdcccdabacddbacaacadcdbdbabcaadaaadcadadcbababcdbbaadacccddcddcbccacdcbbcadcdaddacdddbacdaadcccddbacdcacccbaacaaaabcdbbbcabbabaccdddddabcccbaabcbdbcbdbdbbbdadadcaddbcbbaddddabcbcbaccaadbcdccdaacbbadcbcbcbdaabddcbcdddadbbabaddcacbcbcbbacabaaaadadbbdaadbadcaccdcccdddcacbbdaabadbdcbababcbbddbbaccabbdaabdabdbacbbbaccacddaccbbdbbcaaaacbddcbdabcabadbdcadabcdcbdabbdbacbdadcbdccdadabcacbdbcdbbcbabadaaccdadddaddddbcccaaababcbaaaabbbbdacabaaacadbadbbcacbcbbcaabdcadbdcdcdbddacabccdcbddcdcabbcbcaccdccbdddccabadcdccadaccddabcaacdabdaabaacdbadcbbadcdcabbaddddcbcdaabddabdbadcdcaadacddcadabbadcbddadadccaaddddbdcaccccdbcbaccdcdccdbcbbbaadcbaaacbdccadbbbdccbbaccccadabcdbaaaabddccabdbddadaadacbbacbadbdbcdcbaaaadcbbdabcbdabcadddbbbcccbaaabbccacaabaabaddbdacddcdccadaabbcacdacbbcdbadbcdadbcbbbbabdacbaacabdabadabbaadaabdbbdacaabacabcacbdcbcccabdaadccdaccaddcbdbbacacbddcdbcdbdcccdbbdbdbabdbacddbdccabddcaadbdccacdbcaabdbacddacabcacabaaadadcaacadcdacdcbacdbaacbdbaadaadacbdcbdaabacbaccadabdabcbcbcdaabacbdbbdbbdbddbbaddcddbdcbcbbccaadacccacbcbccbbdbaddbddccaadabadbdccccbaabdcbdbbcddbddbcddcbadaddcbdcddbcdbdabdcacddaaadbddccdcbaaadaadcbcbadccbdbcdbcbbcabcddadacacbddaddddcdbbddccdaaccbabcbacbcacbdbdaddbdcddcbcdcddbdabddcbdcbacadbddbcdcaddbbbabaacbdddbbbbbbccbbdbbddbabdcddbdabcdadaababaabdbbcdabddbccbbdacdcaccbbdbcbcdcdccdbcbdabdddaaaabbdbccbddcbbbcccbcbabcdacddddbadabddcccacdadcacadaddcbdbdbbcddcccacaaabaaadaaacabaadacccdbccccbdcdbbbddbaccdadabbbbccbbbbabcabbdbbadddcbdcdcadccbcbcdbaadbcbadbadbcbddbccdddbbdcabdaabadddaccacdbcccbcdadddcccdcbacbadcaacbcdaccaababdbcaccaabadcbddabcbcacbdcdaaaacdcbcdcbbbbacabccdcaaccbddbacccaaabccacbdcadaadbdbbcadadbddcbdabbccaaacbadcccacdbaabdacaaaccaacddcdbacbaabcdbdbabcbdbcaaadbbcadccaaababccccacacccaddbcbacbcaacabdacabdbdabcaacacbccaabdbbbcacbcdcaaaddddcccdcddadbbdcdaadcabbddaadbcdbaadcbbcdcbddcadadbbaddaaaabcabacbbcbadacdabcbbcbaddabbddbbbadbdddadbcccabaadcddcccacbabbcaabbbdcccdbabbbdbcddbadbbaddcbccbaabbbdddccabdabaaadbabcdbdccaabbcdcbcacbddbbadcddccdcaadabddaaaaddddcaacdbddcacdadccddcadaacdabaadaadacbaadabcdccbcccaacbccaadbacaacbbbaacdaacdcaacdadaaaabbbccdbdcadadbbdcbddaadbcaabaaabcddaabbbdbbdbcbbbbbbdabcadddccacccccbabbabbccccbbdbadbcdccbabcdcbaddcaddddacabdacbdadbcaccaabbcdadabbbdddbdbcdabccabdbcadabccdbaaacbcdcabacaccabcbbaaddcdaacccbaacaddcacaaaccddddbbcbbcadbaaabaacbcbcabddbcadbaddbccabdddddbdabacbbaacbabbcacabcdaccdaaabccddcacdcbbadabacadbcbbbcacababcadccbacacdcddabcdddcabdcdadcccbdccadbdbadadcadaadbadccaddcabdcddcabadcbdcbdccaacdcbcabbbaacccbcddbbdbcbcaadaabbdcabdbdddcdbbcddbacdbddaabcbaddadcdacccdccdbadbbccdddbdbddccacacababbdaddcadccbacaaccacbbaccdbddcdbadccbdadcaabaaadbdabcaadcddbbbdaabcbdbdbdbdcaacdadadbcadccccabccadddbcbadaddbacdadbaddcaccbaacdbcbdacabaddcadcdbdbaddaccbcbcaccacabbdbdccddbdaadbcdbdbbcbbcbdaadddabdcadabcacbccbbcabbaccddbcddbcacdabcbccbbdcdbcccbcbcdbabcaaaaaaaccdadccbbbccbadabddcdaadcdcdadbabbdbbabacaadaadaaadadbdcacabbccacdcacbbcbbaaacddbadabbccdddcccadacccdaadbbbaabaaacaddcaddbdabcdaabbabbdddbaacaadbdbabaccadabbabcabbadaabbdbbcbbdbcdaadcaabccdaccccacbcbcabacccdcbaacdacddbbcaddbdbcbbbcdccaacbdcdadacbcadcbdbdaacaababccaccbbccbcabddbdaabdcdcabccaaccadcabadbbacccccacdacaacddcbabbcdbcdabcbcadabdbabbdbcdadccbabadbcbddacacdbbdaacaddcdddaacbcbbdddadcddcddcadcdadbdacddacdaddbddaabbadcadbdcaacbcbbabcbacbbcacddaaaacaabbacdbaabcabbaddcaaabbbdbdaccadacdbdbacabbdacacbcadcccbcdddbacddaacddcdaddddaacaabddcddddbbaaaacabccacccddbbaccdaaabaddabcabadbabcadaabcccaacbddacdacaabacdbddabcbbcbdcbcacdbdabcacacdccdaacdaadddadcaadccaaccbcccdcbdbcaaccccaaaddcbcdcadabbbdacdcbcbdbaadbddbadcadcddaccdbbaaddbdabbdcccaccdbaaaabdbbcddbdcdabadbbdadcaccadbcadabcadcaccbbaadbacbcccdcccddcbddddbddbddadadcddcdababdaccddabdacbacccbcbcdaddccbacdbccbbbadccdcaadbdadcdaacdaaacbbbbddcccccddcdbcdcdcddadcbbbdabadaddcbdaabcdbbadaccaddbcdbcadadbdccccdcccacadccdaddbbbbcadccccddaaaaabcbbdbdaabccaddbdacbadadbaabbbacbadcbabccdcaabacbbdcbadbcdbbcbcadcdcdccabbaccdbadbbbdaaabcdcadddbdaadccbdbcaacaadcabdadadcabcacadbbaaddbdcccaacabcbbcabbadabaaabacacaacacdcdcbadaabdcddacabddbcbdcbdabaaadcaaddcbcbbbdbcbdcdcdcddacbdadcbcdbbcbaadccadbbccadbbcccbdacdbacbadbdcacbccaaccacccbbbbaabdaacacddcbcadaadaadaabbdabaaccbbbdccdccddcadcdcbbdcadbbdbccdbdcaabddcdcadbadbdcccbcbdadddcdadcdbccdbbadabbbaadaaaaadcababbcabccddbcbdcaaacdcbdcacddcddbbccdbddbdbbaacccadbbacdcdbccbccddcccdbabccdccdbbbcbaadbbcbbadcbaadbdacaadcaaddbabbbbcbdbabcabcbdadacbccccbcdccdddcbacabcaacababccbbbaabbccbccccadddacdacacabdabbcbccbabadcccacbdccadaddccdabdacacaddabadbdbacaabcbcaacbbaabbdabdddcdcbacbddcbdcbbaadcaadbbabbaccaddcccbcabaacaaddcdcbdbcbddadccaadbbbddbccdccdcbcabdccacbbaddacdbcbbcaacdbbbabbacabbcdbbbbaadcdcdddbddddbcbccdcbcdacdacabbddcacdcdbcabcdacccbbccbcbdaddbbdcadcdadaadcbdbaacadccbbccabcccaabaaabacdaaadadbaaccacdbdcdadbbcadaaaaccbabdcbcdbccacaccdaccaacaaadabdbdbbdbbdbddacddbcbcdcadbdbcdadcdbcbacccdabdcbccccaacabbddccaaacddabbcaddcaabdcabbbbbdcbbbccdbabbcdbcdbabdaddbbcdacddadadbadddabacbdcabbbacaabcaacacbcbaacbbcccbddbbdcaaacdacbbddccbdbacaabaaababcdaccdcbdccddadcdccacbdaadcbbcabbcdbcdacbcdadcadbcdcabcbbbbaadbbdcbdbadcbcdcbaaaacbbbbaccadbdccddbbdccddcacadbbadacbbcaddabdcdaacddaccdddaaaaccbcdccadbdbbadaabbccddaacdabddabaacababdbbbccdddbccbcdcbdaabacadaacbbbacbbabadaddbabbbbbaccaccbddbadbcaacddccddbacbaaddbaccdbdddccaabbcacaaccbdacabaadcdbdbbdcacabbbdabccabacabddabaaacbbccdbdacdaaaddbbbcbacdabbdddaaaabbdbdcadcdcdaccdcdcabcbabbdbbbcacabcdbbcbbbddacbdbbadddddabdaddbabcbcddddbdccbcdadadaadcdbcbdbcaaabaabcdbcdcacccdadbcacbaabaaaddbbacddaccacadddcdabbacddbaaaadaaadabaabbaaaccadbaacaadbcbddddccdddababdaacbbbcbcdcdddcdcaccddcdcdcbcbadaadaaacbabcadacacadcbcbdbbcdbdbbbbacbbadcccbaddcacdcdaccbddadbdbdacdddbacdccddbadcaabbaacacbcdccccaabacbabcdcacbcbccbadbabaadcddadacdccaabbbabdcdcccbcdbabdacddbccddbabadaadccbcaabbabcccdaacbaadabdcdadabbbbacbdbdccdaadcacdccdcbabcbdbddbbbbaabacdaaabbcddcdbdbccddacbbadcacbccdbaddcdccbcbdaddbccdcaabbdcdbabbbadaaabaacdcaccadacacdaabaabdaabddccbcdbcbdaaacaaaadacbbdaaacdaabbbbdcacbdbbcddbcdbdabcabdccdddcbdacdbcbbbdcdbaddcaaccacababaaacdbaaadbbdacbddbdbcacbcbccdaadababaabbdccddbadcdabdbaaacbdcacdcaacbcbcdbddbcddcbdacbcdcabaddccabbdcaabcdcdababadccdcbdddabccdbdaabbbbbbdcdbccbbacbdacdccaacdaabdbdbdaacbacdcabadaabdccbcacbdbccabdddbbaccbccccaccaaadacbdddddabdcdbbaddadadcbcbdcbbbcbcaaabbcdacddabcbcadbaababdcaadbacbcadddcadbaccdcbdcabddbbadbabacdcdcaccbdaccdbcacdadadcabdbccccbddcdccdbaaaddcaadbcdddcbabadccdbbdacacaacccbdadbdaaaadcabbbdacbcbabbdcddcdacbacbbcabababbbcccdcadcdbbdacdcacabadbccbbabacdaacbcbcacadbbbbadacdadadccadaabacbadcdbacacbccccaaadcddbcbaaaddbaabdabdbdcadaddcaacdcbdbcccccacbdbaabadadcbbbbcbdcacccbddcabccadabbddbcdacaddadacdccacabbdcacdbcacbdcdbaacdaccbdcacdccadcbbcaaacdaaacaaddcdbcbdcdcacbddddcabbbdaccbbbbcccbcbbddbcccbdbbbcacccdddbcdcaddbacbdaacbbbdaabbbabbcbaaabcbacabddbddbabacddabbdccadbbbbbdcbcbdabcbbdcbabacaabaaaddadbabadabccbccccaadbbacbdddcabdcbbbabbbdcdcababadbcbbcdbaaaccccaaccabccbbdaabcbbbccbcbdaddacbcdabacbcdddaadddbdddcbcdbddcccacacdddbcbbbdbcabbacacadbabababbdcabbadbdccacbccdbaddabddbbabdacaacbdcbdaccaacbababddddaccddbacddbabadddbccadaaccbaabdcbacccbbdbadbaacacbbabcabaacaadaaccabddaccbaadcdadbdcbcabbbaccdaabdbcbdcbacbacbdccacbaadaabdcbdbbbadabdabcbbbdadaabadadaccdbdddcbdbaaabdbdcdabdddabcabbacbbacbaaccccbcaaabbddcaadaacbcdaddddcbbdccacdbacbddcdddbadbaccdadbdbccaacacdccccdcadaddbbcadcdaadbcaaaddccbacbbcddacbaadabdbddcdccbbdddbdcbadcbcdbabddbaddcbcbdadaaabdcccaacdccdaccabcbccdaaacdabcbdcaddcbcdcacaacadacdbdbddcbabdcabbbabadddcdabaddbbddcacdcabbaccaabbdaacbbcdbcbbccaabbaaadbcbddddcbadcdcadcaddbcbaccacdabdcaccacbbdbdbbaccbdbadcdbdbdaacdcbddaccaadbcbcbdaadaaddabbaadadcccdbddbacbddddbabdcbcaaabcddacddbcdbacdacacdddccbbdccbdcdacdccbdbccabdbcbbdbdabaaacdaaacaaccadccdcddbaacdcabccdbaaacdcaccddacacaabbcdcccdbcbbbcaaadbcddcbdaaaddcaddbddbbcbcbadbdadcdcacbcbbdbbabbccddacacadcddbdcbcdadbcbbccdbbabbdabbaddcaaddcdbaddacccadabcabcbdababdaccbdcdabbaaddcbaadaabbbcdaddbbaabbdaaacdbdabadcabddaccaadbdccadaabcabbbbdaabaccabbbdbdabaabdadddbdccccbcabcabccbcaaacbcccdbbcddcddaaddcaabadbbcaddbdaacaadabaabdcbabdbcacdabcdbacccdddaabcdccddbccbdacdabcdcbabbaddacdbbcaadabdcdccbcaadcadabbbccccdddaaadcccdbdcdabbdacbdadadddbcbbdccabbddaaddbdaacdadbaabcdcddcdabcbdbdbadbbdbcacdddcdbacbdccddcdcabacdabbbcaadaacbcbccccddabdadbccbbbccaaababaaddccbbccccbbcbddadbdddddabdcbbcddabadaccccadcaadddccbcbbaddcbcabbdbbcccaaddbcdabccdcadcccdbabacadacaaabcadabcadbdaacbdacddcddadddcabbabacbdcccbdcdbccdbccccbbdcbcbabacabccbccabbcbcccbbbdbdcaacbcaccababbadcbdaddaadaaaadacbbabbbbbabdcabaaddbacbdcddaacdacdbddbbddddcaadcbabbcdcdadcdabdbadbddbcbcdcbdbcdacbbabdddaaabbaabcbcabddcbcbdbbcbdbaddbcbbaaaaccabbbcdcbaabdccbdbcabccdbccbcbaadbcdadbadcccccdcbbdcaddadddacddbcdaaadbbcbaccbbacbababbabbadddaccaaaccbbbcabaacdacdccbdacbcbbbbdcdddcaabdbbdbacaacbdabdadadaacadcbdacabdbbadcadaadacdabbbbadbaadcdcaaabbdabaadaaaccbddaadacbcccddbdbadbbaacabccccddbcaaabdacddabdcdcbacaaabbcababdcdcbcccbdcbdaddbdbabdbaddabdddbbddbabacbaaaccdcddacdbacadcdbbacaabaacabbadabcccdabdcccbbaaabaaabcbbddabccdcbbbadbdabdcdaaaadbdccdddcbbbbacaddbabadddababbaabcacdbccdccacadccccbacaabacccccabbadaddacdbddccaabababdcdaccacbddcacbaacbbbaacbacadcaddcdcccdcabcbcddaddabcdcbdccaaabdcbbcabddccdcbdbbacccbdbbccbaaddbccdcbcdddabbdbdbdabddcdbcbcacbdbcbadbccdccccccadcccbbaccaddbbdabbccccdccdcadccbbbddaadaadccbbbbdcaadddbcabdccaaaddbcbbdbbbcdcadccaccdcdacaddbbcaabcddbabcdbabcdbdcdadbcdacbbadbaddacccccdacbcbcacdccaacdadacadaadddddbacdadccabbbbdabccbcbdbbbbbcaccccdcddbabacddacaccaaaaabaddbbdccbcadcadcacbcdccbaddcbabcbcaaaaccddacabbabccdddddaabbbcbcbadcddbccdbcdadcdbccabbdbaacaddadbcbccaaddbccadbcdbdcdacaaababdbbccabadbddabbddcbbbcaaaaadbaddccabcdaabdccddcdcabadacabcabaddadaabaacabbcaadcbdabccacdcbdbdcccabcbbcdaacdbcadadcbacbdcbbbdddbbdcaaacaadabcaaacbcbcadacdbcdddacbcbcabbbddbcaadcabdabcbbacabdcacaccdbbcbdccbacabcdbcdbbacbbddcbaabdbaccabccbcaaacaddbbbcbcdccacadaaacdddabdddadbbadccbddabcdddccbaacdaacdbdadddbabaccabbabaadadacdddcacababcdddaaadacdcccdbacaabcacdcbcaaccacbbbccbcbadbcdbdbabbaabcdbcbbaaccdcbccabcbdadccdbccddcadabbbdcdbcabdbdbddcaadbbdcbadacabddddbdcacabdabacdccdddadcdcbdbcabccadcdbddbacdddcbaabbbdddcdaccdbbbddadcbdbdaacdacdacacbbdabbcbddcaababacaaaaddcabcabbbccabbccababdcaaacaacdcbbadacbbdbbcdaadaaddcbbddbaaadcbbaacdcdbabdbabcacdabbaaddbccdacbccbdacadcdaaaddbbbdcbbcdcdbdddccdaddaabbbbcdccccdbbddcbbdcdadadadacadcbdbbcdddbdcddadadcbddbaababadbabdcdacdadbcdcadbdbaacbadcbbabdcdddddcdadddddbdaacaccdbdbdbbdbbdbdcdbcaccbddabadcadaaabdabbdaaadabcdccddcbbbabbbccbdaabbcdadbbbbacacdbcdaadcacacccbddababbcacbbdbabdbbbadcdbccccbdccdcadaddcbabcaabdaaaabacddacbcbadcacdcbadcddbcdbdaddaadaadccabdbdbdacbddadddddbcbadcdbacaddbbbaabacabdcabbdbdddbdbabbdaabbcbbbaaabcdaaaddbbdccabbdddabdddcddbbaaaaabcdcdbddacaddbcaaaccaacadcdcaaadcbdbbdaaacbdbdcdcaadadddbddbdbcbccdbadcdbaaabdddcabdabcacdbcbdcaacdbacddcddcdbaabadadbaabacbdddcbabdadbddaccddaabcadbbbccccbacbbbbcaadbaddaadcdcbbcacdabbcbbacddabdcdbbccadcbccbbacddaacbdbbdbcdcacdadcddbabdbbdacbcadcdccbdcbcabaacbcdaacabccbcbccbccaaaccabbbccabadcbbabcdcacccbbddaadcadbaacbacaaadddadbdcabbccacbdbcccccccbdccbabdddddcbcdaddccbaacbbbdcccccadbddaddabbdaadcbcbacaaccabcdbbbabbabbaaccddcacadcaadadcbdcdababadaacdaabcddcaacdddbbccbcddbacbdadacdacbdbbcbbadbcccccaddbdabdcddcccaccdddbdcbbdcaacbaacdabddacdabbcdbdccbabcdadbbcbddaaaaacdddcacbaabbbadabbdaadcddcaddbcadbabcadbaaaacabbacdcadcccabddccbcbddaddaccabcdcdabcbacdcbbabadbbcdabaabdacddbaaabbbddcbabcbddabbaadcbbaabababdadcdcdacdacdadcbccbcdcdabcdbadaacabbdcddbbaabbdacdbaccabadccabdcbaccdbacdbaacdcbcbaaacaccddbdbbcadcacbbcddcddbcdcccbaabbbabcddabbdbaabdcaabacdbddcdbbadaaddbaadadcdbabbaabaccdbabacbcdbbccdbbdbddbdaadacdacbcbbbbbabaabbcbbbbacdddbdadbbbdddaabaaaccbacbbdccddcbcbcbcabdaabadcabcbdbdcddbcbbdadcdbddcccaaaadccdcaabaaccdcbddabcdbbbdcaadacabcbdcaaadbbbaabcccbababbdcdabcbabaccaaccdabbaadcadbbbadcdddaaccbcdcaabbccddcadaabdcccccdccadcbdaaacbababbcbbccdccaabcddaadbcdbaacdcaccdaddacdcccabccbbabbcccdaddccbdddbbbbdbbabccdccbbdabdbbbdadcdbadbdbcbbbcabdacdcaaaddbcccaaddbbacddbbabcacaabdbbbdacabcdcbcaccbccbcaddbcbadbbbbcbbabbcaccbcbbaadbdcccabdaadbbccbcabbddcdaabcaddcacdbabdacdaccdbcddacacaabbcbdcccaacbbabdadababcdaddddbcaaaaadcdaababbdacccaddaaabadbabddabdabcdcbacadcdbbbabadcddbabadcbbdccaacddcbbdbbccbacbdbccacddacdabcabcaadcddcbdbccaccdcabccbbcddaadbbabdbcadbbcbbabaacabacbcacdbddcdcabdddabdababbddaaccacdcdccabcbacdbbaacabdacadaddcccdcacccccabcddccbabbbddaacaaadbbbadaadababacadccabcddddddbcadcaccbddbdbdccbabddcdbaddaabcbbbadbbbdddcccbbbdbabdacadddbdbbbdcbaccacbacacdccaacbbddaccbaabdcdbaaabdddccbdaccaddabcbabacdcccdbbcdccaadddccbcabddadccdcbacbccdaddabddaaadcaadcdcdadaddbbbbbdcccaabbaadbcbadcbccccdcdcbcdbdaaabccdccccbadbacdbdcdccdaaadabdbbababacbccabdadbbdaccddddcbbadcdbdaadbdcbabddbcbcaadcdaabbacdbdbbaaaadcbbcbcbcaddabcdcdadbddabddbaddabbddcacadcacaacbabdcdadcdbcddcdbaabdbcdabcbdacdbbddbcbdbcadddabbdabacabbadcdbbbabdbccaabbcdbdddbdbcdabbacaaaccabdccbcdbbcacdcbcddbcccdbcaaddbddabcdccdacccbbbccdadacdaadaddbdbbbbcdcbdabdcadaaaaacdabddacbcbcaddaadccaabdabdddaaabcaadcbbacaabadbcbadcbbaaddccdddacbddcccddbdbadacacbdbaaacbcdaadacbdbbdbddcbcbdcbbaaacdabcbcacdbbcbabccbadcbcadadbabcacacddcdbbbadabccbdadbbddccbccdcbdabaadbdbdabdadccbacddbbdcdabccbbcacccccdbacadbaadcabdccddddbaacacbcddbbdbcabcaabdabcbabadddacdbbddabcddaaccbcbdbbcdcbbddadacaaadacbbbddabdbadcdaddcbcdddddbdaccdbdbcdcdddbbdacbabbbcacacabaccccbabdcdcbccadabbadaaacabcdaccabccadcdcdbdddbdaacccbbcacdcbccacdbbcbbdaaccbdbaddcacaaabcddcbaddabadabbdaddabbbddcaabcbdbbacdccbdcadaddcbcdadbabababbbbaaadbbbbcdcadaccaccccabbcacdabbbdbcabbaacaddcbcbdbdccccadbbbcbcacdbbdcbaccbbbddaddccbbcdcaddcdcdcdbabacdcddbcdaabbcccbcbcbaacbbcadabbcabdacbacbbdcaccadcdccddbaacbcaccdbaccdabcaabbdbadadcaabdaaaabacdbdaacacdaacaccbcaabaccccdcababcacabbdbbcbbdccbaabcacaacacbbccacbddadabaaababcdaadcbcababadcabcadbdcaaddcdbdcabaabadddccbdacbaaaacacbdcacdbcccddadcbccddaaaaabddbbccdbddcadadacbdcbddccaaabacbaacdadacabbdaadbbbbacacbacccacdcbdacbdbbaadbacddaaacbadbcabdccacaabdbcbaadaaabbdddcbdbbbccdadddbacddbcbbacdccbdbabbbdabcbccbadbadcdcccbdddcddcabaddadcacddcbcccbadcbdaaaabddcacacbcaacadcdddcbdbcaacdccbcbbadadbccadacacabbdddcbbcababaccabcbccdbabbbadbbccdddbbcadddbcbbdcbdabcdddcccccaaadbdcaaadcbdcadabbdabcccdcaaccdabcabcabbcbdacdccddbbdcabbdddcadcbcdabdaacddddabbdbdadbcbadcdcacdadbbccdadcbabadabcdcdaaddadddacaaccdccccacaabdaabccddddccdbaabdccccbbdcbaabbbcbdddbbccdbcdbabadbcbbababdadcaabbdcadccdaaadcbcdddccabcbdabcacdbbbdadccadaccddbbbddbbbadccabddcccbbbacdaabbdadbcdcccccbcccdcbddadaaabcaddcbbddbbabbcabccacaccbabacbbacddaaacaaaadadbbdbcadacababcbdbacaaaabbcaabbbccdcccbddabbccccddaaadcdcdaddaadcbcbbbbacbdcbadacadccddbbaacabbdadcacacabadcaacacdccaacbccadbcdbababadcadbdbdccbbbdaddadbcabbccaaaabacbadbcbcdbbabaabacdbcdcccbaccbcbcbadaacdddcbdccdcdcdbdcbadbbcaabddbccbddccdacccdcbaccaaaadbddaabcbddccbababdaccacbccaccabcddbddaabdaddabbcadbccbadcaadcdaacbbbccbbabddcbbbcbdbddddacbcddcbbcdcdadcaaaddddbaadcadadddcbcbbbdbabadbcdacddddddabdacbaaddccadacdbbadadccadcbcccabdddcdbcccbccbdcaaaadbdacddcbbbbcbccdccccddcacbacccaddcabbdaadbdbabaddbbbadbbcbadcbaaaadcccbcaacaadbdbbadddbaccbdaaddbbcbdddabdbbcbccbabbbdbdacbdbabdbcabcbabdaabacadadaadaaddcdaacddbbbcbdcbbdbadaccdabdcbbbdbdcbddadcbacaddcdcdddcadaadbdcdcacabaaaaddbdabcbdddbdaacbaddbadabaccaacacaaacacddacbbcbdbcaccdccbabdbcaddcbcaddacaaaccccbadbadccddadbabcccaadbccdcbbdccdabbcacbbcddcbcdccadddcaddababcbccacdacaccabccdaccbccbdddbadbdcaadaddddcacccbbbcaacbccbadccbbbbbccdbadcccbbdabdddcaadaacadbbcbaaadbabbdbaddaccacdbcdcbcdcddadcadcdddcddccabaabcacbbcbcdcbcdcdbdacaaccdabaaccdbbbcdacaaadaccabdcaddcbaadababdabccdaddcadbcaddbddbaabacbabbdcaddcddbdcbaddabdaddcbdbabaabcbbacaddcdabdadcddbcccaabadadcdcbacccbbbabddbbdadcdcbacbcccbcdccdcddbcccbbcbbbdbacbdabcabdccdcdbdcdcbadacdbaccaaabaadbcdadcdcbdadbacdcaabcbdccdcacdbcbacadcabdddcabaaabdaaacccbdcaccdccbbccdcdcddabadaaddadbccddadcacdbdaabcdcdcddaccadabddacbbcbbbaaadabaadbbcbbbabcaadddcaacccbdbbbccdaacbadbcdbbdaccbadcddcacbdcdbcbaddadadddabcbccccdcabaddbdbcbbccdbdadacdddddabddadcbbbdaadbabdbabdcdadaaddcaaaadadbaddbcabaddaddcdccbbbababdbbccccbbacbcaddabaccaabdccddabbabaccbdddbadcbabdbccdcddbddcbbbbadcbabbbbddcaabbbcdaacccacdccacadadbdccdbdbcddcdddbabbbbddbcddaabdaaadbcadbacaadbaacbbdbdbadadcacaabacddacbdaaacacdccaabccbaaadcacdacccccbcaddbcdadabbaadcacbdcccbdcccaabbabaadabbcdbadcadaaccabcdbddccdcdbacacbbddcbcdddddadadbccabacbcbadaababdbacbcabcdabdadddbdabacaadcdcacbdbdddbdadcccaaddaabcdcbaaaadbcbbcdaabadccbbbbcccabadcbdabbcccadccdaabdabddcdbddabdbccddadcdcbdbbbadaadccdbbbcdddccdabacccbdccbbcacdccaccccbbabbdcddcdcbbccaabbbadbbddcabadbddabcbacabcacdccaaddccadbacaacbbabbadbcbacdcadaddcacbadcdbdbbcbaaabbabbdcbbbbbbcccdadcbddbdcccddccabdadbbddbbaaabadcaacdcdcccddacddbdadbdddaacadaacbadadcdaabadadbcdacadddddbcdcaaaabbadddddcadccbdbbdcccaaaadadccaacddabbabbddddacacdcbadadddaddbbdccabadadadbbadbaadbacdddbacbcdcbaabcdcadcccdccccbbcddcccadabdcabcccddbcabcbbdaadbcacbbaccaacacabacacddadbdcdbbdcaabbdacdcaddccdacaabaaabacababcabcdabbdcabdabbdbbccbcbddbaacbbccbaacdbaaddbddadccbdccdabccdccbcccbbadbadcaadaacbbacbbabccdcbdccbddccdbbadcdcdbaddcabbccbcadbbcbbacaadbaabdbcdbcbdccddcdabacdaaabcaadbdcadbdbbabacbaadcccbdbababaddacddcdcdaddccbcbbddbcdbdabadbdccdcaddcbabcbbacbbaaddccccbcacbdaddadcbcacacacdcacaccbadabdcdbbdbcabddabadcccddcdccccdabbdbcabcacbacccbcdccbdacabddbcdcaddcacaddccbdbccaacaabdbdadbbaddacadaaacacccdabadabbaaccbcadcddadadddabccddaddcdaaadccccdaaacaaacabadbbbadcdbcbbabccaccbcacadbdacdbbbccdabdcbdddaacaaddbacbddaadabcacaabcbadddabbbbdbdbaccbaddabbccaddcabbcbdbdbacdbbdabdbacbccbdcbcdadbcacbcdbabcdabbbabaddadadacacacbabcccbdabbbacdacccbcdbbcadaccdbacbccbccabbcadaacccbcaacdbbaadcdbcddbcabbaacaddbdbcccaaddbcabdbcdddcbadcadbabddadaaabbcbbcabbdbcccdbcdadaacdbdddabaacddabddbcbcbcdbcdccdadabddadbadaddaddcbadcbccbbccdddabdddcbcabcccabccbbabacddacaaccddcbccabbdbcadbccdbdcddadadddbbbddccccdbddbcdbcacdddacdabbdcabdbdbaacddabbdcccaacaabababdcbaaccbdadbccacdbdcddbaddadbcbdacabdcdababcaabaddbdbaccabdaabcabdcacddabbcdabbbcabcdcdbdbbbcdabadcddabbddcacbcadcadaaaccbcacdadabccdabdaddbdcdddccaabbcddbcbbacdadcbabbabbacdaabdadbadccaddcbdcbdbbbdbacbbacdaaacbcbadcadcddadbdbaacadcaddbbbdacacbdcbcdcdddadacadbbccacddaabbcaadcdccdcbdbcbcdddddbbdcdbaaabdaddadcbcacccdabcdcbaacdbdcacabaddbbadcaaacdabdcbabacdcaccaadcadcabcaadbcbdcbababcadcbddadadadcddbbccabdbccbbcbdbbcdbcccbadddbcabaddadbccaadddacbddbdaabacbcbabaabccbbacbadaaaccbabddccaacaccdadbcccdbabaadcaadcdcdacbcacacbadaaaaaccabdbbdbdcdaacbbbaaaabaabbabdcabbccdaccdaaaadbadbdbadabbdacddadadccbdcacdaabdddbbcccaacbadbdccbcadabcabbdbdadddbbcccddcaacaccabcacddddcadccacdcdabcdccbbaddabdaacbbccbcdaacdaabdacdadbbcdcccabbcccdbcbcbabcbcaacbbcaddbbdccacdcbdcdbddbbdcdcabddcdaaadcddddaddcaccdbccdcacdbaacaacdcdaacabcbdcccacdbcaddabccaadddcdadcacbbdcdbcadbabdabdacdaccadbadbccaddddaaccdabbcdacdcbcaaccdaaccbdaaaacddaacaaddaddbaadadbdbcbadccadbdddabacdcacabddacdaadabcddcccbabbacdccdbabccbcccbbbabbdbcadacdcdaaaacaabcddaaabcaaaabdccbbbdbbcbccadaaccaaaccabbbaaddadcadabbbdacdbddcdbddbabbdadbcaccdbaabccccabadbcddcaccbbacaccbcdccdaabcacbabdcaccacaddaaadbacabcacaaabcabacbddccdabbdadcdcbaacbcabdacbbcbbbdbcaacbdddcabbcadcdaccacacadacdcacbbddbbdccabbdaddcdcbaccaccacacbdadcabccdcaaabcaadcadcbbdddbbbcdbcabbccadabbdbbabaadabdcaddadcbbbadbcbbadcabbadbabcbabdaadcbcaaccbbbbdbdbbaaacdaddbbddbdbbcbbbcabdaaababdccbbdddcaaaacdacabbbaddaadacdbbaaaddccaccadccbcabdbbcbdbcacdcbdaabcaadbdabddddabbdbaddbdacbbcbabacabcbaaadddabbcaddababcbdcdacdacacbddacaadbabcaaccdbbbbdbbdaaabadaacccdcaddacabcbcaaccccbacdbbdbccbbabbbbaddbbadccadabaacdccbcccbcbddbdadaaadbaccaadacbdcadabbaaadcdbcdcddbcdcdcbaaddbacccdcabdbbcdaadacaaabdccccabdcccdcbdcdcbcdbbbccdbbaabdaaababdbbbbccababaadbdcaaabbbdadbcadddddbdbdbbcbaacadbadcbbddddacdddbaabadcdbdcddddaacaaacbbdbdadbccacbcacccadabbbadbbbddcadbdccdcdcdccdcdcaabbbacbaabacdcacdccdcdaaddcaadabadcadcddacdbaaaacdcccdcdbccbacbddbababbcadbbddccdbbdcaaddaabddbcdcbaadbddccdacadbadcabbbaaaadaacbdaacabababdabbbdcdacbacabdacccccbdbcbdcddddaabccdbdbddddaadbcdccdbbadabacabbdccbddacbcdcabadcccccbbddcdaacbaccddccdbbbcabcccaccaacdddcdccbbbbabddbdadcddddccddbccabbdabdcbcadaaaabdaddddaaabdabbadbbbcbbaddcdbddababcaadbbaacbbbacdabdacbcababddbcacddbbbcbbddbcabccddcaabdcaaacbccdbdbbddbabcbccdbaacccacacdcdadbcbaabbdcdabbcddcddbdababbddcddddbabadbacbbaccdbddbdcadbdbbdbccacbacccccdbbcccadaddaacbddabbcadcabddaccabbcacddacbdbcddbcbddbddcbcdccaccbbbdacdcdcddbdcdcbaaacdcbbaccbddcccbdbddadcacbbacddaabaccabacccdcdabacddbbadbccccbbbadddadbacddabddbbddccdaccccabccdcddbaddbdbadaacdcbacacbaadddbccccdbabbbacddbcdccdbcdddcdbdbddcdaabcacaacadadcadabbaaadccacababbadcbbbababbdddcdcbaacdaaccccccbaccdaadccbbdcccbcdaadcddcaaabaacaababaadcddbccbccbcdaacaabaccacdcacacbdcaadaddadbbbdadbcbacaaaadcabccaadadabdccaaacbdaacdcddaccdabdbcabddcaddccbacbcddbcbcaacbbccccadcbdbccabbbcbdaacabbdcacabdbabaabcdababbbcbbdcddcdcabacaccacdbbdadaadbacddaddaddbcbdaaadbbdbdcddbdbbcbcdbaaccacbbcbdaadaadbadabaccbbcdccaaaadbbdbcdacbdaadabbcdbaabccdcaadacddcbbcbcadbcdaacacccccaccbcbadbbbbcdcaacbcdabbbcabaddacbdbdcbbbabbadcadbadcacbdccbddbccccdacaabbdbdbbccdbdacbadbbcacbaaacbcdcdcbaadcddbbcbdcacdacddbbabccabadbddcaccacbadcdbcbadbabcdcadbdcdbbcaccdbcacaacdbcbbdcccbbabccaabdcbbadacdcabdbacbbacacabdcbaacbccddadbadddddadbacbdaabcbbdddccbccaaaacbaabcacbabbbbbbbbbddaadadadcabbdadbdbbdaacadbcadaddccbcddbcdaccbccdcbddadcdbcbbbddadbdcbcdbddaaccadabadaabbdbaaabdbdaaccdbbdbadcccbdddabdacbdbdbcabddadaddaabcbaaaadaadcaddcbacaddadcbbdbabcadcbadbdddcaadcbbccdbdbacccdcdabcdbbcbadbbdcdabdbddbcdbcaabccbccbabdbabcadabaabcddbaadabbbccabccccccbadabdbbdbbbabdadcccaabdcdcbcdaaabccbcbababbdccbaddbcbddbbacaacaadccdcbbdcabbccdcaaabbdcccaaccaaccddaaacdbcbcbcabdbdcadcddcadbadcddcdccccdbbcdbabddcbbdddcacdadcbcadcddcacadcadddddcdbcbbcaccabbdaacbcadbddcaaabddcadbcbbcdadbcbbddcbddcaadabddadbcabcdaabbbacbcdabbbabaacbdbdcbbdacabbaaadacaddcacaaadbbddbacbcbcdbdbdadacacadbaaabdcbcdcbcdbdccdccbabacbcbbbbcdbdcaacbdddbadbadacccbddabdacaaabcbcbbbcacaaacbdcdcbddcdcdabccaddbbacacaadcdbdaacccbacdadabababbcddabdddabbbdacdbcadcbaddbdcaccadbdcddbbcacdbcddbdcccdbaabadcbadddacbcdbddcbbbabcddbdacdabcbdddbabadbccbcbbacacdcbdbdacccacbbadcbcbcbbcacbcdcdadccaacbbdbabdbccaabdcabddcdbacadbddccbbbdbacbdacccdccdcbaaadadbdadccadbbccababdaddddcaaaabdbbacaabdcdddddaaadcddaddaadbaadcbdaccbadbdabbdddabbbcacabdbdadcdbdaabbdddcbaccdaadbdccdcaaddbadbadddcdbcddcccdbaadbdcbbccabbcacdaddaacbadbcbcccbdbcabdcabdbbcccaaabcbadacdddacbaccdbcaaaabbabdbdabdcadcbbdcbcdaddcbbdbbcdcaadcdcaaaabdabcbbcbbddbdadccdcdcdbdbbcaadadadacaaaadbadccbdcbddacbcbaadcbcbddbdbaabdabdbdcbbcbdbaadddbbabdcdaaddaccdcbaddddbdbcdcaabcaabbdccbbbdcaabcbaabcaccacaadcbdaaacaaacbbbcaabdcbbbbbcabacdabadcacddcabaaddcbbcdacbcdacbbbcdbadcbbabbaacddaabbdbcccbdbcdbcdcdbcbdabbdddadabddbaddadbcaacabcacaccbbadddadbddbbdcadcdcddacccbacabcbdacbdbbbadabdadaaabadaccbcaadbddccadcacddcbaaabbdcbadacabaddcdcacdbcaadddbcadbbdadcbbabcacaabdcbadaccbadcbaaaacacddbdcbabaaccacacaaaddbdbbdbabcdadcacbcadbcbdbdbcdabbbbabbacaadabccdaadaacbabbcbbaddcddcaccdcbbbbddcdbddccdabbdbbbacbdbdcbcbdcdadbaadadccbdddbddacaadcdbaacbdaaabcdbcdaabcbbbbbadbbbabccbbddcaacbddacdabccabcdbbbcdddaacaccddbcabcdccccccbdbdbbbdbcdadabaccbcccbdcdacabacccdcbccbabdddcdddcbcccdcbbcbaabbbbadabdbbbddaadaaddccbadddddccbadccacdbaaddcabacaabbacccbddaacddcbbddbadbbdcdcccddbccbdabaaadbcddccbaabdddacbaccccbacbbadabbaccabaccadcaaadcbdacacadacdccacabbcbcbcccdcabccddaddacbcbbcbbdbdcabaadbdacabaccbabadddabdadbacadbcbcdaddbdcbdaacadcdadddcbbadbcddcababadbcacaabacddcbbbcdcdaddbbbcddacdccbcbdabbdcdabcbacacccdccbdddcabdddbddcaaaddaadcdbdabacdcaddadbaaabaaddacabcbbaccbaccaccdbdcbccbbdcdbabadababaabdbaccaadccddcbbbdbaacaaaaaccccdaacabaacddadbdcbddcacbdadcacacbbcbccbcccdbcadadabdcacdaaacbccdcdaadacbcacddadcbbcbcdaacbbbabadadaadcdcdbdacddaacbbcccbbbbabacabaabddadddacbcddacdcdbdcbabdaadaaababbbdbaccdcbbdbbbccadbdbbcbababcadabddbcaabcbcdbccabacbbacddcbcbdadabdacdcbcabcdbdcabcdababdcacbacbadaccdbaadabbdccacbcbbdcdcbcbdaadbadddacbbaadbaddccddcdcdccbabacccbbdaabdaabcacccdaccadddbcababbbacaaacbdccdbaccddcccbadbbaabdaaadccadbaccdaaadaabcabbbcbdcadaacdbdabccbaacabbbdbcccabdbbbcabaadcdcdbbbdbbcbbddbbbbbdddabdddcbbcbcdaabacddabbbadcbacaacaddbabbadbacddcdcbabdddaaccbbacccdcaaaaddbdbdcdacbbccbaabadccbadbccdbaaccabdcbadadcabadaadcbddabccbaaccbdbbaddcccadcccddcdaaaccbaaddadbcdadbcbcdaabcaabcbbaacddbcdbbacddbcddacdbbadddacbccbdadccbcdcbcbddabcbcabbbaacccbadccdcbbcababbccbaccacddaccbbacaddaacdbbbabcbcaaabccccacabdbadbabacdbddadaccdcddaabdbabcdbcdbbacddaccdbcbcacaacacbadbcbccdcdbdccbadcccdbabbcabbadcdcccbadabcaabbbaaabbbadbbddbadbcccabcbcabccacadadcccccaaaadaaddaddabaacccabbbddadabdcddaacbaaddcddcdcddcdcbadbbcbcdacacdcccdccdbbbabbccbccabbaddbccabccbadabcaccdcbbaacacbadddaaabccbdcacbdddaadabcdccddcbbabaacdddadcabccbababcbbbcabadddbdbcdabcdabdccabbdddbabccdaddccabbbdbccbdadbdadadaccddddbbddcdbbacaabaccdddddadbddbdccddcaadccddbbadbcaddcadabbdbdbabbcdccabccbcbdabcaccbaddcbdaccdaddbbaacbbadcdccccabadaccabcbdaacdaaaabdcccccdababaadadcbcbadbacdbabdcddbcddacbdadbdccdbadaabacdabbbbbdcdbcaacbcdccddbdcbcacdaaaabdcdcbcadbadabbbbbaaadadaaabbaabaacbccccadbcacbcbabadabadcdbbcbadacdcbbababccdbcdacdddbaacdbacdbacbcbbacadcbcabdbccbcbbddacbaabdbbdbcaccacdbcdbadbbcabacccadadaabbccacbbbdaadcbbdbdccccdcbbddbbabbdcddcaccdbaadabcdccaaccacadbabddacdcbdcbbaabcbbbdabdaabacddacadabbcccbbabacdcbbdbcdcdccddcadbddddddcbdbbabdabcbdbbdbccddcdbdcbaaabddbabcbbcabaadcddcdbdbcdbdbbacdcbbcbbdabdabacadbcaaaacbbdbcbcbbaddacdacddbdabadcdacdaabacdbbccbdabbbbbbadbcdbbbcbbddcbbcccbacdccccacbbacbcdbcddbddcbddccacdcacdadababcaabbacbadcabbdabbcdbdbdabaddabccccbbcadbdcdbdccadcddbdcacacaaaadbabcbadbcaaddabbddcbcbabcacdadcbdcdccadddbadaacbcbdbabdaadaacdbdaaddaccaddcbdcdcbccbdbdbcababcbdacaadbacacaabcbcaacdcbcbacccddbdcdbdddddbacbabcdadbbbddbcadbadacbadbdbdccabaaababdaacbdddaadcabadaaaccbdcaadcbcadbbaaabcabcbbcdacabbdacbacddcbcabcadbbdbabaccddddbbbabbbcdddbcccdbbacadaccbbcdacadaacbccbbcccbaaccabbdbcbacbacdcabcbcccbbddccdccaabaaacddcacbbaccadcaacacadddacaaaadadcdbacdcdcdcbbcdaabbcccdbbbcdddaaaaabcdaaacdbcabbabbbacabbbbdbabadddcdacbcdaaacbbbddbdabcadcccccccbddccadabcbbcabaccccaccbdbabbaadddcdcaddcabdacaaccbdacccadaacccacdcccadbdabacccadcbbddcbacbdaaadbcdcadabcabbaddcacdbaaaacdccccbbbacdbbadacbbdbaaadcaaccbcdcaabaacccdbcbdabbcccdaaadcdabadbacbdbdacaabdacbabcbddabacbacaddbcbbbcbcbcbbacbaadadadccdbcdbdabbcbaccabbadadabcbacadcdcabdcddcbcbabdbaadbacdcbbdabccbccadcccdcdbaabbdddddadbcbccaaaabbcadadbbbbcdadaddbadbdbbaaaaadbbbdbabddabdbcadcaddcddcbbacdbabdacdacacccdaadbdbbaacdccadbaddcddbbcaacdcabcacaaddccdccabbdadbcdbadadacdcaabaabadccbdadcaccddcbdcaccdadbbbcadaadaccdaaaacbbdcbdacccacdccccbdaaddbdccaaaaaccdbcdbdadacdadbcdbabcaacaccbbbcadbbcadaacbbcdbabacbaacadddbbbbccbdddabdaabcbcaadcbcbabccccbdadbddcaaccaddcddbcccdacccbbdcbacdbaccabbdcabcacaadddacbdabdadcbddacbcdbcbcaabaadbabccdbadcdacbdbbacbddbbcdbbbabaccbdabdddbcdcbcdcacbccaadacbbadbaddaacddcddbacadddbdccbdcaacbcccadbbacbccabbdbdcacaaccbbcdacdbcdbdcddcbcbbbacabdbcdddddbdcdbbcbacabbcabdacacccccbaaacbcdbaacdbdabcbbdbcaddddaddbbddadbcdcaddabbabbddcdccdcbdcdbbacbbaccabbdcccaddbcbdabadbbdccdcacabccbcaaaacdccbdabcdbacbacbbcdaacdddbabbaadbbaccdaaccbdabdcadddbbcbdbcccbadaacaaadcbdacdcdabcbbabacbcbcaddacdadccbaabdcdbacaacaccddcacaddbcdcdaababddbbbcacdcbdddbdbddbdccbbbddaacdaabcccbdbcbadabaacdadbbbddcaadcbbcdaccdaddbbbbdbbdaadadaacbccdaaacdadbdacbddcacadbcdcddccabacdbbbaaacbdbcbabccaddcdabcdabbabcbdabadcacbbaccacabdccdbbbacabaaddbccacaadabcbbdccbadbdbdbcdbcbaabbaaabbbccdadbccccdcbdcabbddccbbcacacabcdbdaacdadaccdcabadbbdabdcacdcccdacaacddccdadddcdadbaacabbbccbdabcccaaaaacabbbabadaddcbcbcdcddaccbbacdadcddbdcdbbadbbdaaabbcabbbcacbadbaabddcbcbbdadbdcacadbbbcadbaacdbdacbbcccbdaabdaddcdcaabccbdddccbaabadbbbdacbcabbcdcadaadcbbcaddbacbabdcbaddadccbdadbcaacbaacccccacbbcaabcabbcbcaddabdbcadbbbbabaaadbccaddcdcabcabddcaddadbaddaacacdadbabdbaacaaabdacbcdacddbcddbbbaaacabbbabddacddbddbadadbdbbcdcadadaccdbbdbddadcacabbadccccbaadadabccbcbbbdddcbccccabdcbccbabbdbbcbcdabddbddcaadbbabbaaacddaadacbabadbbdcaabdbbadbbacbdacabcbbddbcbaadacccaccdcabbbcaaaccaddbdacdadbacbacaacbdacdbcdddabcbacbaddbaddbcccaadabaccbcabdbaacbbabdbdaaabdcdadbcbdadbcabbadcadadcccabbdbbdbdcdbcbdaadababbccbbadbcaccdbccbdacccbadadcbdbaddcdaadbaccbdabdabdbdaddacddccdbbddacbdccdabcbabddbbccbbdcdcbabdbcaaabcccccbaaabdbccacdacababbacddcdcbcdcacbaacccbbbcccdbdabaaddbbcccddbddcddbbbdacbacabacdabbcaaddccbcbcbadccbcaadcbcabcdbcbadacadccacdcddabacbaabdaabdcaabbbbabadcdaadacdccacdaabcdccbacdabadadbbdacccddbdaacbcbbdccccabcddaabadddcbacdaddabddaaadbbcbadabddcdabacacddabbbacbbcbcbacdadbacacbadccabcddabbadaddacabbccbaccbabbbacddacaabadcdbcaacdabaaccaacddcdbcbbcdbccadcabcaaabddbcababaccbcbadcdcacbddbcbdbdabacbbcdacadccbccbcadbcbadabdadcdacccaddadacbcdbcbaacabcdcdadbdaadbcdbadcbddcabaadccdbbcacabacacbcdadaddbadabcbcdaaabacbbbbadaccadcbcbacabddcaaccddcabdabbbccbcacacbcbaccddaaddadbabdaacdaaaddbbabdacbbcbaccdadabdaddcaddabdbdadcaadaabbcbcbaabaccabdcabaadbdadccaacddabadbaabdccdababcaddadcaadcdbaccabdadddcaabbbabcadbabcabbdcadccabccbbcdbcbccdbadcaabccccbcdabcbcacbbabdacdbcbdabcbcccdbddbaadbacdbbbbccabcdccbcdbdadbdbaaaacadbcddddbaacaccdbcbadcdbdbaacbcacdbdabdddaccbbcabdabbabcbacbcbbaaadddcdcbddabdbdaacadaabbddbccbdbbbbadcddccabbbbbbcaabbbcbbababdabccdbacbaccdbbabbcabcddbbbacadaccdbbdaaddddaabcdddbadabddcdccaaddcacdddbdacbaacaccbdabbadbadabcbcdbcbccacddbcacbdcdcdabbdacbddcabcaacccccabdacabaaaccaadcaddbbaacbbcdbabdbababddabbcacddccbbbcdcadacacdcdcbcdabaddabadcacacdbaadadcbcabaccbcbccabdcacdbbacdcbcdacaaddbbbbbccdacaaacadadbdabddcbdcdadadacdbaaabbaadccdcccacabcaaaddccabbbaddaadddbbdcccabcbbcbcbcccbccbcacacdcacddddcbdadabacddddccadcbaccdbcdddccaccbbaabacdacdaabbbaabcaadcabaddddddddbcacddcaaccabbddaddacabaacbcbdddadcdcddbcbdccabcadcbadadddacabccdabbbcdcdcbaacddddcddcbcbddabaabbadbcdaabdcbdbbaacbdadabbbaaaacbdddacbccddccacbacbbccbdcddddcbddcddcdadddaadaccbbcdacabdadbcbdababaadbabcacacadcdacbbcbcdcddddbaaaddaadbaabbadcaacaacdcaacaddcbcaadbddaaccbcabddcdcacacccdcaabadbcaadabdcbbabcbbdabbdabbbabcdbdaaaaccbbccbcdbbbbbbcbaadadcabdcbbdddadcbbbdbcdbddbddaabddbbddcdbdbbdbdcadbcbcdabccbcbccadabcbaccbacaaadacdabcdbabbccdaddaabbaaccbdcbbdabadbbdbabbabcdbaababdccdaacbcbbcdacdadddacbdaddbcdcdbdadbaadddbbbccbbbdcbacaaabbcbdbbdacbadbacdcdbccdcccaacdadcdaccdaaddddbbcadacccbbabaadbdabcbbddccddaaddadadacdcbccbdadbbbabddcabaccccdbbbddcdacdabddabcddbcbdaccccbacacaaccaaccdcadaacbccbaabddcbcccdbadccadbdcbabdcbbcabdddbacaccccdcacacdadadaabddaaabbbadcccbbababbdcdccdabcdcccbccdcaacbabbbcadbddbdadbaacbcbcdcdcbcbcbcaaccdaacdbbbaccbdadbdbbccbdbcaacacddabbccabccadaacbbccdabbdbbcacbcddacadbccbabdcbabcddcbadcddddbdbacaddaabdcddccdacdacaaadbbbcdaacdbbaddcbbdadbcaabcbcccdbdadcbdddcdccddcaaabaaccacddbabbccdddbaabbbdcccdbabdbbdbabccddaaaacadcddcaaabbadabbbcddabcdbddaaabdccbcbbddcbcbdbaacbadbdccabdbbbdcbccbaacaaccabdbbbccccbddbdcddcdbcdbdcadabbbcaabdbcbbbbbcaabaadcbddcdbddacdaadbadddbcacadacabbccdcaadcbaacddcbaaadcadbbbcbbdaaaaababaccbbbdcabcacdacadddababdcbabdadddcaadcccbbaccbdadccaddadbbcacacaaacdadcaabccbbdcabaadaadbbcabadadbacaadaaadabbacbcdcacabdcadcacccbbbaaaadbbdbcbbbaadbbbcbdbbdcbdccacdcbabbdaaddbaddcbcbcdcadbaaaadbcccbaabaccabcdcdbabbbaddbabcbaabcdabacdcddabbbacbbbacddcbaadccccdbadbdaddbcbdadcbdbdcadacdcdddcdcbdcbacddcbbccdabaabcdabacdcdbddaddbabadadddabdcddddcccabccbdbcccaadcdbacdadccadaccacacbddcaccaaacbdbaaccabadbbbdbcbdadcbccbcabbbdaacbadaccadcaabadddbdabcbdbbdacdaccaadadbdbdddddccbdbccdbaadcdcaadadccbbaabaadacddabbadaadbabbaddbbbacbabdacbdcccbaaddcbdbbcdaabdaccbbccbdaaadacbccbddbcdbccabdabddabcdbbabbbaaddabdcbabddcbaccdaacabcdcccabaadbaacabdbdbaccbbacacddbdaabaacaccaccadddaacdadaddbbcbbdcbcadacadaaadadbbcdadccadcbdbdcbccbbdddcddbdcbcdcacbbbcbbdacbabcddcaaabaadacaacbbabbcaaaaabcbbccbaaddddaccdbbcbbcaddabcdaaaaddddcbbbacabcbbacbdbbdacbaccaadadcaddcbdacbccbcacadcbcabccccabaadadcbddcccbbbccbabdbbdaabdaddaacadccacdacccdcabbbddccababbbaddddccddcddaaddcbdaacaacbccbbabbbcabcabadabbdacabdaddbbdcadcaabdaaaccdabbcddccdaaaccbcaaddadcdbadadcbddcdaaadabcccaccdabdbcdaddcabaabdacacaabbbcbcadcadaaddadddbcaccacbdaabcddcbccdcdbdbcadbaababccabdcbdaababcdbbbbacabccdccdaacaddaddcdccdcacbcbdbddabcbcdacdccdbaddaaaddaddbaadcbcccabcabcdcdacabaccccbcdcaacbdabaadabdccaccaacdbbccdcdcdbdcccaddabaaaddbcdbacabcbabcddbdadcadddddaaabbbdaadabbbacaabcdcbccdbcadabacbadbbadadadcdaacccdcabccadbcbdcbbaacadadbaddccddbaacdbbcaadbadbbbababbacdaccbaccdcdbbddbdcadadacbbabbccdbcddadbddaacacababadddbdbdddbaaddadadcccddbdddcdadbbabbccdbadcbbbdcbbdacadabddacdcdcbcbbabbbcbdcdcddbcdcdbccdddcdcaababbacbddbddacbdadbdddaabbcdbbabdbcadccabdcccccbaabcbcbabaddccbbbabcbaabacddcbcbcbbbcdbdbadcbaddbcacbbbcaadcdaaaacadcbbcacdcaabdbbcabacaababbaccbaacdacaaabcbddcabddaabbbdbbaddcdbcdbdbcbabbdbadcbbaadbdcacbacbbdbcccacabbcdbacabbbdaabaabbdbdaccdccadbbccbcdbbbbcdcaddddcddabccccaddaddcaadcbacbdacddabbdbcbadddacccdbccdccaadadccacaccccdbddbcdaccaaaacacaddcabbbaccbbcbcbcddbabdabaddcdaadacadabbaabcaacccbdaacbaccdccaaddbacdcdcdadbccaacabdbbcaccdaddcbcbbbccbbddbabaadcbcccbdbdadadcbbdacabcaddadbbabacbcadbadabaccbccddbbcbabdbcbbadadcbbbdddcadbbabbadccbabaabcbabadbccdcbbbbdacdcdadbbdcbabcadcabcabbbaabdddaddbdaabbbaaaaacacdacdbcacdbadbadddbadccbcdbdcbccbddadabaccdbccbbcbdaccbcccdcbcadcacacacdaabccccccbcbdcbcbbaddddacbbbcdcbddbccadcacbacaadddadbcdbddadaabbdbcdacabbdddcbcbbacbbbbdcacbbbddccaaadaccaabbbaddcdcdcdabdcbaccdcabdcaaaaccabddcbacdbbdabdaaaacadbbabaccdaabcdbabcdbcbdbbbddbdadcacbdcdddcbddcdadccdbdbabbdcbcaaddaccccaddcdaadddabccbaabbcabbcbcbdcabadbbadcaadcdcbbdcabdcdbbbdbadaabbaadddcacbdbdbcaacdcdacbdbddbaaddabbbcbadcdacdcbccccbdcbcaabbdddabaacdbdcaaddcaacbbbcabdacccdddaaacadbabbaadccbbdabbccabaacadbcabdaaadbcaddaabddddadddbccabcccdbbacdbbbcacadcdcbcaaaddadcbcdbdabcddddcdadaabcbadcdcbbcccdcbbcaabdaabcbdadbddacadabbbddacdacdacdcaadbaaacaddaacaaaacbdbaaacdabdaaddabbaacccadbcadacaaabcdcccccdadbdbbbcddccacbbaaabcaaaabdababcdababbbdbdcbaadbdbcabbadadcbddccbbcddcbadbbbbadadcdbbcddbbbbaaabcbbbdbacabbcdcdaccdcacdcdbdcbcbaaccaacaabaabbadbadbdcbdbdadabaccabbaabdaddbadbcbcbdcdcadbdcabaaaadbaddbaabbbdabbddaddaddbcbbdccdadddacccdbdcacaaacccddbabcbccdccacaccccabcbccacdbdaddadcdcddbddaacabbdadadabaabaddadadadadbbbbabccdbacbacbbcbbccbdcbccbababdcacababbacaddbdbdaddddacdabdbcbabbcabaabbadcaccdaccbdccdcdbdbdcacccdadacdbbdaabcaabccdddadcbdbdcbbcdbaddaccbaaccaccacaccbbccdadadbbcdadbbaabcadcaddbcacbcaadbdcdcbadaaacbbbdcaaddccadaadbbcbacbbbcdbaabbddcaacbcccdcddccacddabdbcababddadcbaaccabdaaabbaabacbddddaadabcbbcbcdccddbadccdbbdcacbadddddccbbcabddbdbcacadabcadcccddccaaabaaddcdcabbdcbdacbddcdbbdabbadbbbabdadcacbdaddddaabdbcddbdbdabcbdccadabdbcdbcdacddabcaacccbbabddcbadaacdcaccccbcbbadbcbbdcdcaadacddcdaacdbaaabddcddaabaabdddadaacadcacabbcbcddbccadbabbbdccadbbdbdbdbdcabbbcacddbdaaadccaaaabcbdcbadaabdaabcddcdbdcbdbcdacccacaaaccbcdabbccddaccbcccbcacbddbaddaaabbddadacbcadbddaabadacbbacbcccdcccbcabcaaccabbcbbabbacddacdbddddddddcabcccdcaaddacdadbbbbdbbbddcaaabcdbadddbbbbacdbcdbbcbdbcdaabccdcbdccacaacccadbbccaaadcddbdadbdcbdadbdbaddcdbccabaabcdbbadacbccbaabdaadcdbcddaadcabaaacdcabacadacbbcbcccaaacbcdaddcacbcacdcbbcddacddabdccbdabcddcaddbddbcdcabdbaacadacaddadbcadadaccbccdbccdabaaadaaccdcbcbbbcbdccdcbacccccdbbaabdcbcbdcabadcdcdcdbccbdcdddbaacdcdbdbbdbaadacbbabdaccacaaacaaddbdccbbdaaccbccccbbdcdbcadcddaddacdaaccbccdcdaadcbababaabccdaccbdccbdbbdbaabcbabadabcddaacaacbacbddaccbbdddbabacabbdddddcbdbacdaddbdaddcdbbcacaadbbbdcccbdcbaaadaaddbdacccbbacbcdcaccbcccbbbcbbdaadabbccbaabadbadcacbddabdabcaabcbdcdbddbcdadababbaacbbbaddcaddcabccabcacbcddccbbcacdcdccbdbdadbdbbdbacbddcaaabccadddabddbbbcaacccdabbbadbdaddbdddbdbaccbbdbaadddbcdbcdcababbbaddcaabbaddbdcaaabaacabdbdbdccdddbcaaadddbaadcbacdaadccddabcccaacadcbbcbbbbbaccbcddccdbdbabbbcbdaddcacdccadadcbbcddcbabdbbcccccbbbcdcaaabcbbdaaaadbdccbddadabaacdcdaadbbccdadccddddbabaddbadbcbadadabdadddabcddbdccbdabaadacaaabcddaacdbdacddabacbabbacadcccacdbadacbdcbddddaabdcadadcdaaacdcadcadbcaccaaddcbaccadbabbbbadccacbcdbcbababdaccbbbcabaaadcccbaaacccaacbcabdccaabdadcacabbbdbaacbdcbccaabbbbddacbbbcbcdbadabbbabddbdbbbbdbbddabdaaacadaacbdabacaccddddbcdaddcaaabbbddcaddbcdabccbbdcaadcaabdcabbdcbbdbaacddcccccaaadacadcccadacbcaacbccbccbcdddcbdccccbbdbbdcadbccdbadbccdbcbaccdcdcbadcaacccdccaacbadbbcaadcbdbdacacabbcdcadccadaadcadcadaddabdcaccbbccacdcbccbcccaadabcadbababbdadbcdbbdaabbbabdabbcbacddbcaaaaacacbcaaacdadaddadbdacbdacaabdaaddbbccbbbdddbbddcadddcabaccdbbadcbccbdcdaacdacdbdaadadbcadbccadadadddcccdbbbabaacdaaacddbdccbdbabddcaccccccddcdabbddddcaaadbbcdbddcacbcbddcdccadcbadccdaaadabdcddaadbccabcbcbcddbbbbaaaabbbdbdaccabaacadabdbdaacaddaabccaaddbbbbadccadaabdddcdaababaddccbcddbdabddcacccccccabacadabbaabcdbdcdccdabccabddadbadaaaccdcacacdccdabbaabbbcdaaacdaaabddaddacdbacbaabdddbaaaacadccbacbcbaacbbaacababbaddbbccdbabadcaaadadcdaccbbdbbbbaadcbdabadbacbccbacdaccbdcacbbdccdbcbcbbacddabcbdcadaacdcdaddadcdbcbadccccdcbaaddbccdaacbcbacbbabbacddbbbbcdcbbbdccabccbddbdbdbabacbabdbbbcddadddabcbbcbdcaddbbdcdddadacbbababadbdbaaddbbbabbabcdccbddacabcccdbddddaaccdabcdcdaabaacddcdcabdbbacaacdbdcbcbbbadadddbbbddbbbcdcaddcdadabcdbcbdcadadddbaddabdabdcadbddcdccbdbabbcacacacdacabdadcddcaaabaccacccbdddbddbdbaabbdddcbbccbcacdcacbaaabbddcadaaabbacaacdbadcaabdcccbdccabbadabdccdbbaddaaabcaaadcbcdbccdcadbcbadbddbacbcddbaccbccdaadaacddcbabaacadcbadcdbdbacadddaabbacbbbcbddcbbbaabddbaaabbdbddbcadcacacbcacbccacbcbcaaddabcabdbadaddbadadbbbbcacbddcccccabcadbabbdcabddadacbacbccaaabbddddadabbcaccbdbcabcaabbaabadcacbdcadbcabaaddcaaadbbadababaadbdcbdcadabacdddcbcaabcddbddbadcbabadaaabcccdabcccdbdcdabdaadabcaccbacdcddabaaabdbdbccbcbdbbdcdcadcaadacdbabcbcaacaddbcacaddadabacdcdabccabccadddbcdcdcbadadbbcaadbdddcdabdadabbdddcdbdabcbcbdabcbdddddabcaadcdbabbdcdbbcddccbddabdbccbacaaadacdaacbcdbdbacadbdbaacccddcbbdadcaabababcccbddaabaaabcacbddbaddadbcaddcdbadbacabdcdbdccdbcacbbbbcccacaccdbdbbdddadbdccbbcaacbaccbadbdcbabcdcacdcbcdcdbdacdddccddbbdccbdabdabcaacdcdbdcadbdbccdbbbbadcdadbbaadbbaccbacdbcbcddcbdaabcdcbdacbababcbbbabdaaaccdaadabcabccbaacbbdcadacddcbcccaaddacbabdabbdadbdabdabababdacbcabcddcadadaadccbcbbaccccaaaabdabacdbcadcdddcbbbacaacadaacabdbcacddcaabbbbdabcadbaadbddcdaacbbcdcaabcbaaaddbcdbaadacaabbcbcdabcdcbcbacbdbdbddbdabdacbcddadddcabacddbabbcbcccdcacddcbdadbdbdcbacccdddabdacddcbcdbdbcddacdacabcabbcccacdabccbdddadcacadaaadabcdaaccdadbbcdbcbdcdccccbcadccdadccadbcdaadbcccbadbbdaacddddcaccbaaabbaabbdddbdcccabbdcacdcaaddacdccbbcadacadcabbbbbbddcdddabbacccbdddbbddbdbcadbdddcdacbccaacbcaaadccdbddabaddccadadabdacbbbbbbbcdcdcddaadacbabcbbcdbaacaadaaabbbaadbdadddddcddbacdaacaadbabcccbbadccabadbacaacbbbaabbbaabbcacbabbaabbaaadcccacbbbabaacacaacdacdcbadcdcbaaabcbccbadcbaaadcdbcbbaaacddaabcbbccbbadddbdbbcdccccbcabadbddcaaaadaaadcbcaabacdbaddbabcbcbcbdddcaadcddabcabbdbbdbbaccccabcbaaabacdcbdadaddadccaacaaaabddbddaacbaadddbddacadcbdcbdabdacadbdadddbaaadccdcabbdcbccccdcaacdddccbacbaabddbcbdcdcacacaccbdbdaaaccaadbadbcacccbdcaddadbdcdaacdbbbcacdcbcdbbbbbbacaacaacbddbbcacabbacaaccbbacbcbadaaccbddabadbbbdcbbbbcbdbdbcaadcdcabddacbaacbdbbcbdbdcbcabbbdbaccbcacdcbbcadadbdadbbbcacaabcacddcaabbdabdadcbdcdcacacdddddaabcaacddacbbbddabddaaadabcbdcbacbabababdbacccaaacabadababdaddccddcbcbbccccacbbcccbcdcaddccddcdddbaddddcddbbabcbcadbdbacdaadbdccaaccddbadcdacccbacbcaabccbaacddcbdcdcaddccacdaacaabbbababbacdddccdcdadaddbbbbbdbcabcdadcbcddccbbccdcabdbabcabdddccdabaadbcdaabddabdbdbdcadbadaacaddbbabdcdabdddddacccdaaaccacdbbcbcadbccabaaadbcbbacbcbbbdbdaccdcabdadaccbcabbabdaccddbcabdbccacbddadbabbbabaaaddbaadddabbbcacccbdcbdddadaadacdddbaabbacbcdadaadaacadddcddccabbabbddcbcadbbdaabaaccabaccabbddbaaadbabbbdbcdcccacbcdcacbcccbadccaaaaadbacbdcaadaddcccddbabbbcbbbbadcdacbbbdbdcbdabbcadccccbbaabdccacdbbdaccacabbccabccdcbdaadcabddbcbcbbcaddbbacabcaadbdcccbcdccaaabdbcddbabaccabbdccaabbcdadbdddbaddcaccdddacdbdbbddcbbabbddcdcaabbaacdcaacccddaccacbcbddcabccdcbacabccbdcddabddcadbabbcbbdabbaadcabcabcdacaadabdadacccddabbdddaacbbbdbacddacbbdccbbdcaddbdbcdacaaabbbbcabaccdabacbbcbbbcdabccdcbbcdcdcdcabcbaddbacdbbacdbcaadbbcaddbdbacdaaccadabccbcdcabcaabdbaaaaddabcdbdbbadcadbccbcdccdcdcdbbbacbbbabcddadbaaadbbacbaaabdcaadabbaacdbccdaddbbccacadabcbcdacabcabdadacccdbbccbdadadaddbbbbddbadaabcdbcdddaddcdcaabacdccbcdcdcddcccdddcbbbbadcadcdccabdbabacabddaddccdaacabacccababdabbcbadadabcbbbabadbcdaccaacbacbaaccadabdacaccbbcbaddccddccbcdadbccbbdddbbbdccbbabcacddccdaddaaccacaaccaaddcdbcbbcbdcdbdcddaddacdcaccdcdadcdacbdddbdbccadaddbadcdbbbbaadaddadddbcbdbacacccddcccabaadcdddacddbdabdcbdadabbdaddaabdaccccbbcbaacdbbbbcbbddbcadacabacadccabababdbbbbdddbcddadcadacbbbcddbbaddacaadadaaabddbbbaddbdbaabcdcddaabacddcdbdababbbcacdccdaaaaaaaacadcbbaddaaccabdaaacbabdddbadccbccdccdaacccdaddacdabcdddcbbacdadddbcacadaabccbbdabcabbdcbbabaadcbbbcddbddadcabacbccbcaaccdabbbbdaadcdbdbbdcbccbcabdbdbcdcaacbabdbcacacdadaabcadabababaaaabdccaacbcccbcbcccccdacbcbcadbacddadccdcacabaccbcdcaabcdaacbbdcaaadcdadbcdacbdccdbbacbdbdddccdbcaabacabacaabacdadccdadacdbcccccbbaacadabaabdabcaaacbdbbbbbbcbaccdadaaccdbcbbaaaabbcadbbabaacbbacdbaaaacbccacabddabbdadcbcbbabaabacadcadbcbcccdbcaacacdcddcababbbaccbbcadddcdcdcdccadacbaadadbbdacddcdbcadbcaadbcbbabdbdddbcbcadcdcacdcdccaddbacabbbabacddadcbadacaaccababbcabaadadbcbddcddcadcabccbcaaaddcbbccdbababcdcbcbcacbddcddcbabdbdddbdcdacbbbacdabccabaddabaccbabbcadcabdbccccbccddabbcbaacdabdcadcdbdbdbcabdcaaddcccdbdcbacadabdbadacdadabccbcdcdcbbdddcaaaacbcadccabdccacadddccadadabaddadcddcadcbccddadcdabdccabcbbcadcbabcddaabadaccbdaadbcdcdccdacabcabbdacabccadbccbccccbdcadcbccddcbcbdcacddddbbacdbdcddbddcacbddcbbdcbdadbbccbdadabadcbbabcbabdcbdaacbbcbaadabdcaddcbbbcabadbaaacbbbbccddcaacbcaccdabadabcdaccaccdcbdcadbbdcaaacababbcddcdcbddaaacacbaadbabcaadcdcbdbbbdcbbbbacdcbbcabddbbccacbaddbcbabaddbdbadbcabbbccabcacbadbcaddabacdbacbcdaaadcdddccbcdbcdadbaabdcddcaacdaaaaaacdbdadccbbdccbaccacbdabbddddbcbccdbdbcadabbdaacadaacaaaaabadadcadccdabbdccdaccdddbccbbccbddbbbacabccccbccdaccadabbcadbddaccddddaacaadabaddccabaddaaabddaccddbabadcacdacabcadcbbcdaaadccabbbbcdbcbcbbadadcbaabdddcddcaddacbbcaabccabccaaaccbacccadcadbbaacabadababaabccddcbddbccbdbddccacbbaddcbdbbcdcccddcacbadbdcbbcbdababddbbcdaacbbdbabdcdbbaabdddcaaaabaacbacdadababbadadddbacdcbdbccccacdabdccddcaaabcaaccbbddcdddbdabcdbdcabcaabcbcaacabccccaadcabbccaabcdbdddadbaaccacbbacbdcaabdcdbacabacddcabdbdacaacacdbcdadaadacddacabacddbcddbbaadccddabcdadcbbbcaadbacccdbdcbcdadbbbabdbcbccbaacdbdccbdcadbddaccbdcdcabdccdcabcbabdddaaaadbabbcdacabcacdbabcdccbacccdcbcdadaacdbbdcbacddcdbccaccabcddbcccccacabaccabacabcadababccdbbbdcabbcbbbbababadccbdcbdcbdbddaadadcdddcbcdbdacdabcdadcdbddccbddbdaddabcddacdcdccaadaccabdacadcdbaadbbdaabbbbabdbcbcaacdaccabcbacadbaaddbbdbadbababcdaccadcdaccadabcbddadbbbadbbcacbbbaaaadacbaddcdccddcadbcbcbbbcddaacbcacbddbdbbcdccbaccdbbabadbacbdadcabaabaabdacbacaaabaaadccdaaddabcbcdaddabcbdadcdacacbbcbaaabdabacddadcdabcdcdcbbbdabbddddaccdbbabbbabcbdabacbcdcdbbcbccabdbdccbdbcdcabcdcbbadbdaadacadbbcbcbbbdadddddaaadabcbbcdbdaabaadbdaabbaddbaaacaddcccadccaccacdcaacacadabaddbacccaaddacdcabcbbcbdcbcdcddccbbcaaaccddcdcbddddbabdbaccdbbbcbbccadccccadbbccdcdbadadacdacadadbbacdcbaadbccadbdabdddbdaabacbdbbccdacddbcaabcdddbdcbcdadababcdaddabcdacccbaccbadcaacaabababaaadbcccddadccacaddcbcabdbbbcbcacaaaabacbdaddacadbdbddbdbbcdccbdccbacbdcbcdadbbacbaddbabdbdaadbacbababbbccdddcaddaadadbacacddddcadadcacdcabccbadacacbbcacbbdaccdccaacbadadcabdbcacdbbcdcbdcbacacaacbcbdcddbbacaaaabaacccddcdbbbbacabdddccbadccbdacbddcabaaaabdacaabdbcacdddaddbaabbdcbdddcdcbbbdabaaaacbdaddaddbcadddbaabbabbccbadaccabaddbabddbbadcddbbdabadcbcaddbadaabdbcbddadadddadaaddbddbadcbddcbaaacaaaaacacccddcdcccdbadbdaddccdabdbdcadbdacddcababacdcccadccabbcdbcdcdabbdacbdbaaaadbababbbccbbdbadbcababddbcacacdccdcbbadbadbdbacbbdcbbabdbbcabbacdcbacbdabcdcabbdbdbbbadccbbaaadbdbccacdacdcbcddddbcabbdadcbbbbcccabaddacbcbdabdaaadbbdccbbbbabccccaaaacdcbddbdbdababaabdcbcbadabddbdbcadaddabcaaddacdbbbbddbacbaaabdcbdabcdddacbbccadacbcaadcbdccabbdabdcaddccbcdacadcbbbacdbdaadddaabbbcbdadcccdcbcdcdccaabbaaddabdbcbdaaaabdabbcdaacdcbdacddacbddcccbaabadbdaaadacccabcbcbcdcdcdddcacdbaddcdaadaadcddacdbcbcbbbbcaddaadabdbdccdcbddcbddbbbdaaadcdcabadbaaccdcdaaccdbbddabddbbdcbbcddaabadbdbcdddcccbcbbaddccaabdddbcacabcbccaadcdbcbabdcabbadbcdbddabaabbcbababbbcacacacabcaacadddbccddaabddbabdabdabaccbaccdddcbbaaddadccabaccbcddaadbbbaccbadbbabbabadaccadbadabcacdaabbcbbaaaaaccaccaadcabbccbbbbbccbbacbdccbdccaadbbcbaccdbadacbcbadaaccbdcdbabacadcdcabbddaaacaddacbcdbbacadccadadddacacdabbccaaccbddacbaaddbdddabacddcddccdacbdcbcbbdacacccadbbacadadcdaabddcabccaccaaadcccbddaddcbbdbdddcbdbabbaabadbdccbdddaaddacbbbaddcddadcbbddcdddbbcbbdbbbdabbdcdbbbcbdbacdabdcdddbcdcbddadcbabdbdaadaadabbaadcbcbbacacaddcabcaacabbccdcdbacdbbdacdaacaabbccdaddbddbdcbddadadcdabbdabcdbdddabcacdbdcabcdcdbcabacacabdaaadaddadacbdaabdccbcabcabadcbcdaddddcbdabcdbbacacbdbbddbdbbdacdacdcbcaaaabcbaacbbbaaadbcbcadbbcaddddcdddbbcbdcdcddacdcdcdbcadabbabbdaddadddbbacabbbbbabcdbcabacdadacabbadabbacdacccddccbcdaaaadbbddaaccbadcabbbdaadbbdcacaaabccdccdadaaaddbbccacbbbbdacbccbdddaccdabbcadbcadccbbbbdddbdbcdadccadbccacddcdddddccdddddcbbbbdbaccbbdbabdadcbbbadbdcddbaaacdcdcbcbdcbbbaddbddbdabdcbdcadbbccdddbcdbccdcdacbaadddbdcddaddbbbbcdbccccaacdadbabddbcacbddadcacbdcadddbaaacacdabccddccdccadcdabaaccacdadbacdccbbcbbabdadccbddabacadabcbddaababccbcbccadaabcabdccacccdbdcdcbbccbadbabcbabcacccbcdcdddbaaaadddacaabdcdcadadbdcdcaabddbbddbcccabbdacdadaadbbcbbccabaabbbabbcbcbcdbacbdabcdaabcbabacdbdddccbaddcdcbbdcbbcbaaadcacacbabcaacabdccbbadcadddabbaabdbabbbabddcbdcdaadcbdbbbabdbacdbbacdabababdbbacdbbacdacacdbcacdbdcdaabcdbbdaadadaddacbacccaaabbabdaccbdbcbaadccabbcabbdcabbccbaaabaccbdbdaabcacbbcccbdaddcabaaabacddbcabcabcdcddabaabaddbdddcacdccddbcbcdbcdcdacabcabdaaccdbadabdddacdacbaabcbbbbdbcbdccddacdbddadacccbaaaaccbbbbdcbbaaabaaddaccbbbbacddbbdbdbbacbcddddabaaacdcdbcdadbabdddaaaabbcbdccbbaccdcdbddadccdabbccbaaccbdabcddbbaaaaaaadababacddbdaccacdacccbbabccdaccbbcabadcddaccbabacccaccbcccbddcadbdbbcbcbaadcaadabbbddcdaccdbccabadddbcadcdbdbadcbacababccccbbbcddaaaaadbbcdbcabdcbbcddaadcbbbaccbccdbbdbccaacacbbddbcdcacbbabbbdadbdbaccaaadbbddddcbcadaabcccbbcbccacdbaccbddcdacaccdccaadadabddaccccccddcdbccaadbbdbaddcdbbdbbaaadddabddbabcdaabdbcccbaddbbacadabcbccaadbbcbbaddaddbdddbcddcaaccccbbabcaddcbdcccaacbbdddccccbdcdbbddbddadcbabcdcbcdaccdcbdcbcddddddaadbbbccabdcadadadacbacccabaadbcdcbbadaabbbdcbcccddbcdcddaaacbaabacdccbcccbddbabdaaadddcbdbbcabadcdddacdacbbaacadacbddabdbbbcdaadadadcdbcccaacadacbbcdcaabbdaabadcadaddcabccdbabdcabaababdcccdddadcdaadabcadbcadaacdcdaccbbbbbddcbbbbbcacaadcdddaacacbcbadbcddacbbccacbcccdadbcddcbadbbabbcccdcabbcdcdddddacbcdcbbdabbdcdcbcabddccacadcbbccbbddbbaddaddabbbabdcbabccbdbdaaadbadbdddaadaabbadcccccabadcbdaddcdbccacdbbdbbabcccaacdabcddbbdddbcacbdcaabacdddbaadacaabadbbadadabdddacabaabdcdcabddacddbdbadadbaccbacccbcbbdbcacdbcbdbddcbdaadcdbcbcccbaaadadccacdbcdddccbaabbdcddbadaacdbcbdaabdcbcaadbdabccaabadadadbcccdccbdcdcbaddbcdcaadbaadadcbadbbbcaaadbabbabcbddabddadcabdabacddcdadadcacbdcababcaddbdaccabaddbcddbadadbdadccdacdaddabcccbaaacaadabaccbdcccbbaabbbdacdddbcaacaccabdcbbcaccccaacbddacdbddbbccccbdbcdbcddcacbbccadbcaaadaddbaaaaaadcdabccbbbbdcccbabcadbccbbcaacacdbbbbdcbccbcbbcadbacbdccbbcacbccbcdacbcacdccbddabacdadddadccdbbadbcabaaccabcbabdabcadcbbadbdadddddcdaddddcddbdddabdbbdbbaccdbdbbdbdabdbdccabddadddddabcadbacdbdcbcadbdccdaaddddbadcbcdbcaaaacdbadaaadbddbcccbddbcdddcabdcadcdcaaabcbdcddacbdaabdcaadddcdbdaadbccdaccabaaccbddbccddadbddbdaadccabdbadbbaaabddccaaabbbcacbbdcbcbcddddcabbcabacadbdacbacdbcccacadccddbbccdbaadbbbacabcbcaacaacddcbdcbcbabdabbccbacdbabcbbadaadbaccdddcaddbadbdbbabbddcaddacdcbcaabadcccbaccdbbdccbcdccaccaaaaaadabddabddcdbccacabbdbddccbbdcdcaccaccbdababbdddaabbbcabddaabadacccbadbdabddaccdbcdbaccdcbccaaabcddadacbdbdcdbccddcbdbcbbabacddbbdbcbdaadbbcbcaaaacacccacdcbddbaaabcabcbaacbaaadabadbaabdcdbddaaaacacdcbacbacacdbbabaabdaacbddbacddccddccdbaacbbcbdbcbbacccabcbabdaadbbadbcdaabbaddbcddcacbbaccabdccabbbcabdcabdcbaccbcbaaadbdbbadddccabccabcdacddabcbcbbcadacdbcacaaabbdcbdbbaacbcaabacdbcdaabdabbbbadbcdcdaddcddbcbabbcdcdbccbadcddbcbbbddabaaadabaddddacadcabdadbdccbbbdbbadaccddcccbbccdacaaabdacadadccabacadbdddbbacaadadbbbcddbabbacbcddbadcbcaccddbcaabbbdddbdbccdccbcccdcbbcabbcacbdcaaaccbdcaccdbdcadaaabbbcddbdabcdbdcbdbcbbdabbabbaacbcdcdbbcabbcabddbddbcbaddcccacccdaccddadcccaddbabdaabdabadaaacbbcacaaabddccdbcccaccababbbdabcdbdaacabddbabdcbccacbbccbbdbbdcacddacdcbacabdbdadcdcdbbbccddcbbcccadacabcabdadaddadcadbbdadddbcbddcacbaadaabcbdbcadbbcbcadcbbdabbbbdadcbaacddcbacddcababdcabccdbadbdbddcdccdadabcbbcdaaccadaccabbddbadabdcbbdcaadbbadbbbddbdbabdccbcdabbbacdbdbadcdcdbbddcdaacbcabaabdccdaccaabcbdbbcddddcccababaadbcccdcbbcbbdadabcbbdcaaccbbbdcddcdbbdbbadacaabdacddcabcaaabcdadccdabdadaaddaabbacadcacbadacdcdadddbbdcdaaccbbaabbbbdcdccccabbdcccbbcaabaacacbbccdaddcadccbcbcbcbdbaaddcddbabcccbdaadcaddccbbcbbcdccbaccaddccdcdddbdbcdaccaaadbbadabbcccacdbbbdcdabdacadbddaaacccdbdabdabdccabdbbdbaccbacababbcadcbdddcbdddccaabccbdbcccdbbadbbbcdbabbdbcdbdccdccaadabcbbacbaabdddaabacaddbbaacaddababadacacaacaaddddcdabbbddcaaabcaabaccdbcdcacadcbabddbbaacbacdbcaabaabbdaccdabdddbdbbadddcbdacdacdaaccdacdbcabdcddacccdcdcdbcdbdaacdbdddcadbdacabcacaaccabadbbdbbbaccbbabaccbcacdcccbbdcdbacdbcaccabaabcbbdadbcbbdbbcbbddabcadcbcaaaacbbcaaccbabdbadbdadbabadddabcdabddcadaaacababbaadacabbbaccababcaccabbaacabdbaddbacbbddcdaacdabbccaacabaddbbdcbdddbdbcaaccdbbcbdbbdcaddbcbbbdadcabddcadadbdcacdbaaabaacbcabdccdabcccdcadbacababcddbbbddaaacacdbdbaccbbadadcbbdacabbddaadddbaaddaddbcdbbcacdaabbbbbbbdacbdcbcdddcabdbcababccbbcdabaaaadcbcddcbdaaaddacdaabbdccbbadaccdbdababadbdcdbccadcdcdadcadcacbdddbcbdcbbadaadcadbbcabdbbcdacabacbdccabcdcdbcbdbddadcbcbdaccaadabbccdacbcdcbbccabcbadcbadbbddccabaabaaacacdddbacabdaadcdabcbddaabaccabbcdacbddcbdcdbcaacbbcabdadadcdccaadbcacacdddbcbbbbcbcaddabdbabcadcaccdbbcaadcbaababadadcaabaabddcdadabbbccbbdcadbcdacbaccdacbccbdbcdacdbbcdbcddadbbbbadcadbcbdcdabdadaaadaccbadddcdbbcbadcbbcaacbbaccacbddbabbcdbdbbaadcabcbdbdcbbdcbcdcabcccbddabaaaccaaaadcbcaddabdabdcabcbbabbcbcbcabdcccbddbbbcbbadaababbbacaabdaadadbbbbdbdbddabbcabcdabcbddbdbccaadbaabadbdbbccacabbdcdddabdddddadbccacdddcdbbcbdcaacadbddddcabbbdaaccdbdbdaaccbdcdbaccbdcadcdaddaabdcacbbaadbabcadbdabcdccbacacdcadbdcdadbacbababdaddcacdcddcdbacbabbdadaccdcaccaaabcacdaacacacacabcbaaadbccaaaabcdacbadaccbbabcbdcbbdbdbaaacacdacbcabbcadcbbccdabdcdabbcabbddddcaaaccccbbbbaddbbbddbbababdcbadccdaacbadcdaccabdabadabcadddbbcbbabddbabcdabbaaaadbddbcccbcacdaaabbaadbcadddcccdcbbdabbaaacabdaaabaabacaccbababbbadabaddbcdbdaacbcccdccaaaacdbbdacaaadabbacacddcadbbddcbabcaadacdaacaabcdcacbabcddaabacdaccbcccabbbabbbcbcbbdbabdbccdbbbaabdbdacabaaabdabccadbbcaacddcccbbaccccacabbdcaacccaadbabbbcddcdbbaadadaadcabddaaabccdddcacdadcadcadabbabadadbaaabdccadbccdcdabccdcbbadaccdbbcbbddbdcccdccabbbdcbdccdbabddbbdaddaaddcccbddbcadcdcdcbccccbccbabcddccbbcbbbcbddacaadcdcacdbabdbadaacdcdadbddccbabaadcbddacbccbdbaaabdbcdbcdbaaacbcddaccbacddbcbcbbddacdccacbdddcccdaadabaacccdbdbbccdabccccdcbacdbdaaccacbcbcaadcdabcbaacddccadadbdaadcadaabbbccbcaaadababbbbacdbcbcdcacbaddbcddcddacbcbadcbdcadbcbdccbbddbbacbabbcbdacadddabbcbbdddcbabdbcbaaabacccbcbddddcabdbccddcbabbcacbbbabcadacadcadbaadccadaabadddccaaabdbadbccdccbdbdabbcaabcaaaabbcdaccadaaaccadcaddbbcacbbacdadcbbacccbcbabdddbabcacbdbcabaaccccdaadacdccdcbacbdaabdbacddadcadbbdddcacdcddbaaccbaaddacbdacdcbdabaacbacaccacbcbdcaaddbaaaacacadadcbbbbadccbddabaadbdddabacadababcaabdaaddccabddbcbbbcaccdcaacddaddaacabbddabaacdacbcbabaccababcabacbbcbdcdaaacadadcadabdbbaadadadcdacdadddaabcbbadbdbbcbacbcdbdcdcaccbdbabdcbabaaddccdccabdbbdcabbbdbddadbccadaabcccddbbbbdcdbacdcdcbdcdaacbabddcddaccacaccabcddcadaaaaaddcdabadbdbababcabcadbdadbadadacdaaaabbacbdaacccbbcdddacbdbacbaabacbadbaddaddaadbaacdadabaaacbbdcdccccaacdddbabbdcdbcbcbdcbbacdcaddddbabcbbdaaabbaadacbddbbaabaadbbdabdbdcacaabbadbbacbddcbacbcbaacddbddbcbacdadbadacacaacbcaccdcdcababbdcbdccccbcbadbbadbadbdddcdbcccadcacabbcdabbdcbbddbdcbaccabaacdaccdbabcbacdcaadaddcdabcadaddbcaadacccaadadcbbcbadacddcabcbbacaabbbbcbcbcaabcbcadbbcbcaaccbaacbacadbdaaddabababccddbdccdcabbaccbcaadcaaddabacabadccdaabaadccbbdcdbbcbbbccdbabcccadbbdacaaabdcdbccbbcbccbdbdaabccacbbacacdabaaadaadcbcacdacbccdccdbadbddcdaaaccdabbdccbdacdbaccbcaabcddddccccddcccadcaaddadacabdbcbbddddccbdaabcaabdabaacabbdadabaaabadcaaababddbccccbdddabbcdadadcbcdadddbbdccaadcbcbbddcabbcacbdadcaaacccdddcaaacbcadbaddbcaccccabccabccddadcddbcabbcaddbcaabbbbdcccbacdbbbabbabaaddcdadbbabccddcdacbcdbccbbbaabaddadbddaacaacadccbcabdacadbbadadabbcaacdcacdcbdcdabbdbacbbdddbacaabaddcddcaccababbdccadbdcdadcccbcdaaabacabdbbcdcdddbabaaacdbccbcbccbbdabadadcdccbbadbcddaddbbdcbbbbddcbcdaacdccdabaaccadaacaccccccadcadacaacdadbdbccaabdabcbcbddbbcbabcbacdcbaacccbbcdaccccbcabbddcabaddacbbabbcababaccdbdbadbdbaadbdabdbccbcdabacabaacddbacdbcddbbddadbddabadbddbbdcbcdccabacacbdbbaabcaabadcaaadcaaacacdadabcaadbaaabdddbcaddaacadbddcccddddddbcbacabaaaadbaabcbbccddcdbaddddbaddcbcddcddabddbbdbadcccabdcbdcadcbbcaacabbbccdaccccdccdcadbcdacacbbabbcabdbbbdcaaacddbdaaddcdaaabcddbbaacabdddabbccaccbbcdacdbadbcbcddaaababcacbadcccbcccbabbaadcbbaaddcdbbbbddccabcabbdcbabacbdabdcdbdacbdbdcabcabdbccdccaddcaabcacaabccbcacddcbbbcaccaccbdddaddddacdbaadcabbccbcdbabcdbbdaccdcbacacddcadacdddbdabcaccdadbdcbcdddcbabbdaacbcababdcddbbadbdbacacddaadadbbcddddccaadbdbdddcacbbaddaddbbaababccddccbdcdcbaccabdbdbdaccdddcabbcbdaccadcbcbbaddbaabcaccbcbddbdabacccadbbabbdaacbbdcbccdaddcbadadaccbbbadddbaadcbcbadacdcacadadbbbccdddbccbcaddccbacbcbdadbcccdccbdddcbcdaabcbddaaacabaaadcbddccacaacabaadacaaddacbbdcbbdaaabddccbdacdaacdbdcabbdabaccdacadcaddbbacbdbabdddbbdddadbcbdbdcaacaaddbddababcbbdbbddcdcacbdccccbaadbcadbdddbdccadddddabaadacaaaabdccddaccbcabbdadccbcbcaabccdcbccdcdacabdbbacbdaaccbcbbdbdddcacbabdcdcaadcdacbdbaddccbaadcaddaacaaddbddccddbbbcdcbabdddbccacacbdadcdccadcadccddcdbccbcbabdaabbbadcbdbddbddbdbcabbbdbdabdcbacdcbbcdddcaaabdbbcdcccdddbbccccddbbdaaccddbbdbdcadadcbaacabcbbbdcadbbbcdcaddbabbadbbdbccbbaabcacdcbcdcbabbcdddcdddccbcdbdaadaaabdaddaaaabcbbccdcbbacbccbdabccaccdbbbccbcbaacbcabdcdbaccabbdacbdddadbbaacccbadbdbaaacbaadaadabcacbcaadabaddcadababcacccbdcbacbdaccaaddbccdacadbaddccbbbcaccdbdbcadadadccaccddadbacddbaacdaabcacaddbcbaabbcbbdacbbdcdbdccbcabadcbddbaacbcaabdbdbdabdcdbabadbdacadcbccbbbacbadabdccbdadbdadcbabadaadbaaddcdbdabdacdbcacacabcbaddacaadacacacacbabcdadbcdaacbaadcacaddcaadccdbcbaaaccbdcaababdaddddacabbaabacadccdbdccccbabacaccbdcccccbdccdabcaacacbdabcdccbaadbbccacdcccbbcbdddbdacbcadbdadddddacacabbabcbbdaaadddacbacadccddcccacaccdbadcbdbaababbbaccbbcaacabbbbcbdabdcadbdbccabcaaababcbddcdcbbcbacdccbaadcddbcbaacbbcbbddbdccdbaaccbacdadcacdcddbbaabacbdabbbcbadacdacdabdaadbcbabbdcdbdccbacbbbdaadbaacdaadaadadbabcdbcdcbcacdccbaddccdbbcbcbacbddcddcbcddcadbcdcaacabaabcdaaccbcbccbcbabbabdddaaabdadcbdaacbaadadacbbddadbadcbaacaabcccdcbacdcbaddabbabbcdacadaabcbbdbddcdcdbcdabcbadadaadbddcddbbcacbcbadcddccabcbbcaababbbbcccbcbbabadbdbdbdddddbaaaaddacabcddbadbacaacabaddbbacadabacdcbbaaadbdacddcbdbbddaacdacbdacbacdbcacbaabbbbbbdbadcbcaddccccbacdbaacabaabbbbbdabcbacacaadccbabadadbbbbaabccccddacacbcaadcacdacbdcdddcddaadadccccccabbdbdcacacdbbbbcdcaabdababbbabbadcaadaddabacbabaddcdbcaacaabdabbdbdbbdcdadbbbabbbadbbcbdaaabcbacdddadbaabaaadcccdbacaadccadbdbdacabdabcacbcbadddbbcdccaadcbcccdcabcdcbcbacddcddddcbdcdcadbdbaadccbddaacacbbcddcbcccbaaaccacdcbccbdcccacbbddbadcaabbaabdaabdcddccddcdaaabcdbdaccabdbdccbcccdcdacbbabcbababacbbdcbbbbaadccaccbbbccbbccdcdcadcbdcbccbdcacdbaddbbbcdcdccbadbabccaadadbabbcccbcdacccdabddacccacddccdacbccdcaadddddbcccabadaacbcaaaccbdbdadcacdbacbcccdbdbcdbdbcbcabdbaacccbcbabdccdbbddcbabbcccdaaddadcdadbdbdadbcdaabcbdcadcbcabdbdabcbcbbcdbdcdbbacccabdbdddcadabbcbabdcbcdcdccbaacbbabaacabaaadaddbadbadaddbaacdbbbbdbbcabbccaadbcaabbababdbcdadbbcaadbabcbaaacdcbbadbcababcadabbdbacaaccbbbbcbdacdcaacbaabbcdbacdbaaadcacbdaabcddcccdbbaabdbdaabbbbaabccdbdabbdbbbbcddabbaacccccdacaabacbcbbbcaaacdadcdcadacdcaccbcdcdaddadcbcdccbccddcdbdbadbccdcbcccddbccabdadcbddaacccccdadccdcacdcbacccbbacdadbdddcbdbccddbbacdcaccaddaacdbdcacabdbdabcdbbccbaccdcbddcadcabaabcbccccdcdbacdbacdbccadaacaccabbcadbaadabcaadabbcdbbbbaccaccaaaacbbdddcdaabcccbcbccbdcbdbccdcdccdcacdabdddbcbbdcaacbbabcdbbbcdabddbcbccbcdbbbaabacdacdabaaaaababccaddbccdbadcadcddbdccaadaccdbbccaabdcccaaaaadcbacbcddddacdddcadcabaacdccdcdccadbbcacaddcbcdabccdaacdbaddbdaaacdbdadcadbdcdadadacdaccccadbaccdaadccdcbddcdddbabcdacbcabcabcccaaccbccadabdcbddacdccbacacddbadccacddaaadbbbcbadbddbaaadcaabccdcabcbbadcdcabbaacbccbbdddddbabaaaaddbdbcbbbbdbbbacbdcbcbbbcdacababaadabbdaaacdaacbdccddaadccbdccddcdabbbbcabcbddaaaaaabdbabdbbaccbabadbaacdbbbdcaddccaccababdcbbacbcadccabdcaccdaacbaddabcaadcaaaaccbdcbaddaddbcbacdccbacdbdcbbbcdaccdaddacaabbcdcbadcdabcbdbbdbaaaabdbacaabdcbaacbbabacaabcdabbbbbccabdbdcbddbdadcabbbbdcdcacbbcdcbacaababccbbcbbbdbcaddcaacaccdcbbdcdacbcbdaddbccaccdbbcaabdadcbacaabddcbcdcacadbbabbaccadacabccabccabacaabcabdabcabbaddabadadadbdcbddacbccbdbabdabaacdbacabaaacdbbcbcacadabdcacdcacddadabddacbbaadaaaaadbbbcccdcbbcdddbcbacdacbdabadcaddaaabbcccabbbcdbacdbddcbacaabbaadcddbcdccccdbbaccccabccaddabbcbbcccaccccbcacccccaaacbcaaadcdcddaddcddaacadbdccaaababcdbccccabbabaccbcdacadbbdcdcdddcbddaadacaaadbbbabcdbdbdadcdccbaabbcdbcadbcbbcbdcacddddbbddabdadcacabdbdccbbabaddbbcccdaddaddaacbacdbaccaccaabdcadbadddbabccabacddbdcbcaabccdbabcbbaddaaaaadcacccbdadaabaabddcbbdcdbdcabacccdaddddabdadbccbdddccdcdddacbacccccbaabdcdcabaabaccadcaaaddcadacbcaaacabdbcddadbabacddcbdbbaaddadabccaabdddcabaaccabaabbadbdaadabaadbaaacababbabadcbabdccadcabcabdabcbdbacdbcbcabadadcbcdbcbdccbdcbaaadbacababaadbdcaccbbdaccbccacddacdbbcddcdcaacaccdabcdacbdcdbcccabaaaaaaabbabbcbcadcdbddcaacdaaaddddbbaacdaaaaddabaabbbccbbabdddadbacccdacdacccdabacdbbbcabddcacccbcacbacdbddcddababdccaadddcccabbcabbcbcdaadbadacbdaddaabcddbbbbcbdddaaaadaacbddacbbaadacadbcdbdadaacbddcdadabadadcdddccbddacbdacdbdacbcacbbbdcaababbdcabdbbaddacddbadbdbdccbcbbbdabccddccdcdcbbdbcdddaababcbcbaacbaaaabdaabdbbacacdddccddaaacccadbdcacabbcdaccbadcabcdbcbabaabbbabcbccdaaaddbdbdcaaddabdabbaaaaabcabbbcbcbacdcdaabaabcdaabcdadcddbbdadabccbacbdadabadcaddabacaddddabbbabddcadbacbddcabacbbbbcabaaadcbbbbaabddabcdacaadbbdacabdddaddaddadcabdaddabacccbbaabccbbbddbddbbdcdddaacccaabbaababadbcbcdddadaaddccabccbbabddcbdbdbbcabdcaaddcbcbacdbccbbaadcdcdddcbbbabadbaaaccddaaacbdbbdcbdcbacddbcbdbadabaadcdbdbdbdbbbbdbddddbcacbacbdcdacadaaaadabcdadcbadabcbaaadbdaccdcaacbcabbadccdbacadacdaabdbabcadabbabdbdcdadaacacabadaccddbaaababcabcadacccdaabadbcdcbadababdbdaabcddbaddabcdbdbdbdacaabbddbdcbbaddaaadbbbacdbaadddabbabaccdddadcdabcdddddbbaaccbcbadcbaccdcddbdadccddbcadcdcbaaabaabbacccbaddbddabdbbcaddcbccdbcbdccaabbaaadcabcbcbbabddaddcabccdbabdddddacdccabcacccbbcaacbdabcdcccbdbbcabbcbbbdbccddbabbcadbdbcccdddccaadacccbbababcddddbdddcbdbdadcbcdbcdcbbcaacbdcadadcaaabcabcddccaddaddacaadaaccddbdabdbcaadcddccbaaccbddddcbddbdcbbacacaccdaaadadadbbbbdbdbbdadcbbcaaacbdbbbaccddadabaaabdbcdbdaddacbababcbaaddababdbaabadcaaadaabdcbbbdadcdabaddacaabbbdabadcbaddcbbdabdccbacdcdccdbbdadcdadddccddabddaccbdcdbdcdbbaaddbdcadcaaddbbabaddbcadccaaabcdbaadcbacdbbacaaabddbcbdadccbdabdcbbcdcdccccccbadbaadbabccbaadbcbcddaaaabdbabcdbadbabbddbcaabdabbdcbabddacddccccdbdaadbbccadcbabdbadcddbccdbdabbabbcbadababaaccccdddadcacdbbddddbdaddabdbbdcbbdcdaaccbbcbdcdcdacddcbbaacbaaccbbacadbbcbcaacadaabcccbbcdddbacdbaccddcbbbcadbadccabccdabacaadbdaaacbcdadabbaaabadacaccadbbdcacdcaadaaccddbacdbbacdaadcbaccabcadcaacdcdaaddbbddccacbdcbdbbcdaccbdbbdcbdcaaddbadaaddbcbaabadadaadcbaccbacabcaacdbddaccbbddaaccbbadbddaccbbdbdcdbcdbcbddaaacbdabdcabddacddcdcdbaaccbacdbdbaacdaacdcaacbabdaaaabacccdccaacdadbbdcbdbaabadbabbababaabadcabcddcbbdbbccacadddabbaadbccbbddbcbccdddbcdbabcddadcbdcbcccaaccdbbdacbadbcbaaaabccbacaadadabbbbcbddbacaacbbbcccbdccbddcdbbccccbdcadadabcdcbbdabdcabddcacdcadabdddbccdaaadabdcabcdcdbacabdcccdbcdcaddbbbaddddbdbdaacbaccddbcabcddcaccbbbabdccadbcbacddbcbdcbccccdbcbbdddbadcbcddaacbbdbbcbcbcdacaacacaaadbcaaacadbdcdabbdbdaaacdabdbabbcabbbdacbbacbdadbdaccdcdcbccbaabaccabddddbacacaabadccbbbbdacbaccbdbbacddcabbabccccbabbcacbcbbdddbddbcddacaddadadbabadaacabbabdddcadcacddddcdccacaabcccbbdabaaabdcbcccacbdadcabcdaabbbbaadacdabbdaaddbacdaacbabdcbaabbcdacabdbdaddcccaccdaccdbaabddbcacbadacaabdbcaabcddcadbabcadabbaddddcacbbcadababdcdcbacaadcccbcbdbcbcccbdcddacccaccbbccaddbcaadccdccbaaaaaadcbcaddbbcadaccbbadabbdcbcdcaacbbddcbcdacddcddcacbbacddccabbabddbacaaadaacdcdbabcabbcabadcacadbbccaadaacdcabbdddcbaacaacbacaadcbdbacddbbcaaadbbdbdadbadcccacbcbacccddaacccabbacdbbaddadbabadccbdddabcdbbccadbdbbcaccbbddcdccbacbabacdabcabbdabbcdcacaabbadabadbadabcdbcabbabcddacabdbcacadcbbbcccabcdbcacbddbbcaadabacdadcdbaadcdabcbdbcdbabbddbcabaacabcddcdadacdccbcacaaaddddaaacbadccdaddbbaddccbdbcbdcdbcbccaabdaaacaacdabdaabbdaddaaadbdcbcdbadbabcbcbdddaadadbbdbbbbbcccabcabccbdacbcaabccbabdcdcbacabbccbaaccbbcadaccdcadcaabaacbadcbcaccabbbacccbaabbacbdbbcbbccbcddabacaccddaacbabbbdcaacccbcbccdcbadccbaabbbbcbdcccddcdbbdadabddbcdbaaacbaddbadbcadcddbdbcdddacbbaccdccabdccadcdbcbbcbacdddddbacbaaccacbcdddbbcacddababdddcadadbaccdddabcdaadcdcbabcddabcdaabcdadddabbaaababaabdaadcacaabbddcdcddddbcdadcbaabaacdbbdddaaddabaaaadaaaddddbabbdcdaadbdbacccbdabbbdaddcdbabaadcdaabadabbaaaccdadbabbacdadbcbbabaaadadcbdbcdcbbabdcacccbacadbbaacabbaadaadbddddacbcbdcababaddbbdbbaddadcdcacddadbacdbccdabaadcabadcbcdbbddacabdadaaadaaacacacbcbcbbdbbbdcbccadadacabacabddccbdabaccadcacddccacadaacacdbdcadccbdbcbddacdacdbbaadcccbdddcabbacdbbcccabcddadcabacbbabcddccddbcdddaaadcddbdbcccbbbcadaabadcacaccaababdcabbdbcbbbacccbddabcbacaaadbdbdbcbddbcbcaadcbadddccccdccddadbcadabccadbcbaabaaaddaacdccdadcabccaabddadcdcbcbccbbacdccbabbdaabaabdcdbcddddaccbadcabbbacabbccbcdbdbbdbcabaadbbcabbabacabbacbccabcdbadabcbdccabbacdcabadcbadabccbabbbcadcccacbabaadcaacadbdcdabdcacccdbadbbbbdacdddacacbcccddbbacccdbaababadaabdbcbbdaccbcbaadaacadbdbbbdbaaabdaadbcbacaddbadadabddbbbdcaadbdcddaaabddcbcccbccccabadbabbcdcbbabccddaabbabdbdbaabccdaadcddbbcaddbcccabcdaabadcbacbaabcadaccabdbddabadbdbaadcacdccbdbbcaccbbbddccccbaddbdaaabbddcadacbccdddddcaddbdaddddcdaccbdcbacbbdbcabcbcabdabbbbcabddbaadbbcddbcddaacbabaadbdddcaacdcacccbcbcbdbdddddbadaddbcadbdbccacdddadddbdcccacbbaaacbbdbddacbdbbdcdcdccbdddbaaacbbdcbbccbcbbbdcaacbbbbbcdcccbbcddbdccdabccdacbadddcdbccccbaaccddabbbbadcacacddabbadddbbadaddabbcbdababdcdbccddcabbccdbccbcadbdcaaabadcacdddaddacabddadbadaadccdddabddbdccdaddabaacbaddadbaddcaddabbadbbabcbbccdaaaabbdcdaddaadacdcddbadcdaacadabdacdddadcdcddabcabdbcbcdadabdcccccadacdbdbadbbcccbbbdbdbacddcddcdbdccbdcdabcdcdacdcddcdbaaacabaddbcaddcbbcdbcdadddababababbcadcabadcdcdbcdcabcbaadbdacddbcacbdcbaabbbccdaabaddaacadcdaccddcabdbbabdcbcaddadcccbababcadcdbbcadcdaabdbaaacdbccbbbdcabcaaaccbbaadbabdbacbdbbdcadadabdaddaadabbbbcbbdddddbdbdcbdadcadacabadaabcccccabdacaacbddcdddaacadbdcbbbaccbccbbdbaacacacdddddacbdaccaccdcadccaabdbacaabadbbcaddbabccacbabcdbcabacbdddaadbcbbbaacccccacaabddacaadccaddabbbbddbaccdddbbdaabacbdaccdabddcddaadcbccacdaacddcbddcdcbcaaaabaccbcacdabbaaabdcbcdcbbbbdbbcadabaaccacdddaddcabaadadbcbbcacbdbdbdcbbcacddbabccdcbbcbbbbdaaccdcaddcaddaaccdadaadccbddddaadaaabdddbdbbcbcabdbdcdddbabbabddcdcbabbddcbbbdaaadaddbbddabcddabdcbddaaabccbddabbdbbdbbcdcbcbcdbbadbbbcbcccaaaadcbacddacdcdbdbabbdbabcabaccdcaadbbcaadabddcdadcddbcdcbbbbaacdbccbabdbaccbaacabcabcddccbddbbbcbacbddcddddbbabdbccdabcbddcdddaaadaaacbaaabddbddcbaabdcdcbccbdbdbcdccbcdadacccbaddbbcaadddbdddcadbbdaccbbbccdccdbaadbbdcdbcddbbddbabaabddcbddbcbabaddbcacdccaabcccadcbbdbdaddddbdbdacabcbbaaaabadaabbabddcccdccbdbabaccaccadadacdaadaaadbbbabbddaaaabddadaacbbaadcbddacacdbdcdccdbcaacabdbdddddabccaddcdabdabdacadcaabcdbbabcddcdacabdabcacccabdcbbbaadcabaddbcdbacbacbcdaacaaaccbabbbdaababaacbddbaaabbdacadcbcbccabaabaddcacccbbaacabbdbbdcbcbdbdbdcacdcdbddcacdbbaaabccbabbdcbddcacbcacdadbdcaabbadccdcaccbabaccbbcdcbbacacaaaddbcaccddabccbbbbdcaadbacaabadacadcbacbdadcccdcdcdbabbdabdabcbadbcbaccacdabcdcacbbdacdcaaaccbacdcaddbccbacaddcadcbbddcdddaccbabcccdaddcdccdcadcbcccbcdbdbbdbacbbcbbdaaaaadbcdadaaacdcccdbcdbaadddcddbcbddbcdabbdbcbbdcdadcbdddcbdaadbddbdbacabababdcaccdacacdacdbdddbcccdbbabaaccbabcdadcdbdaacabcabaaacccddbaadbabdcadcccacddaaaccbdcaddbdadbabcdcdcbbbaaccbbaadcccdddbabccabccbbbbbacdaddcbbacbdaddccabaabbbadcdbccadbbbacbaaaddcdbdcaaddabadbbacbdaccacbaadcbdbdccacdcaabcaaabaddbacccbcaacdccdaddcaaaaabacbbbcbcbcddababcccbcacbbcdadccdcadcadcccdcdbacabaabdcbdbcbbdcbdcdcbcaacbabdcaccdbacdaabcaaacbbcdaddcbcdccbdcdadabcdcbcacdbcccaabddabbbcacdbabccbbaccdaccddccdacaabacbbbcbbabdbcaacccbbaabccadacdccbacbaabdddbbbdbbadcabbbababdadabddaccadddcaadbaadcdbabadabbcaadcbbadbcaadaadccadadbbcadbbcccdcaabadbacddbaddabaaadcdcccdbdbacacbcbaadccaaabbccbabcccabdcbdccbaccaccdadcabcddbdddcdcdacccdcaaabddddcaacbabaccdbcbbbadccaaacadaddabcdcadcbddbccdbdabbbabbbcbaabdbbdaccdbbbdbcbddbcdbacbbdadaaacbcdcabadbadcccbbadcdbcddbcbdabaabdddbbddddcacdcaabddadbaabbbdddbddbcbdbbbbaaabaaacbdaccdbcdbbdadbbbddbcddcbadcdccddadadbbcaaadbabcaaaccdccbcccbadacdabcdbcadcddcadbcbbcbcdaaadcbdacdadcbdbadacdadbabaabacbccabdcbbbbcccaaabdbbbbdaddaabdaacdbacbdcaaaccaccabacacacacdcaabbcdaddcaddbcdccabddaacbcbdbdbccaaadccbdabacddbbdbccdaacbdbcdacaddacdaaccddbadcbcacadaadcaccacaacdbdddbbdacadaabdccbbabdcaddbcbbabbccabcbdbbccaccaaacabccddcdccdacacbcabcaaadccadddbdbacbccaccbbcbdcbadabdacdbaabadbbaaadccabdbadbbccdccaccbbbaabacdacbcdbdadcbbdccbdbbddbccaddccacbddbcadbcdaadbaddadadbadacabbcddbbabbbbddcccabdacdabbdcadbcadcbbabcadacbaadddcaacbbbbbbbcabbacdcbbbccccdcaddaccadacdbbaacacbcbdcaddcadccccaacdbbbcdacbdabdbbcdabdbacaabbdabdcdcaacdcdccddcaddadcbcbcdddacaabccbdadabbcddacccbdacbbabacdcccdcdcccccbadcdbbdbbadddacaabcdbaabdbdaaddccccdbabdbaddabadcbbcaabaaccccabddcbddbbddabdbbdbacdacadcbcadaacdbdcabcdaccacaacadbcaaccdaacbdbdcacaabcaadbddcdbdcacabbbdbbaabaabaddcaaabcacadbccdaacaccdcdaacdcdbcabaaabbccdbdadddacdbaacdcabbbdcdbcaddcabbcaaadadbdcbdaaacabddbbcbcdacbbbcccdbdddaaadcbdaadaaacabaaacbbcbcdbacddbddabdbccadbddcdbddadacaadddadbbcccdddabaadddabcadbdbcbcabbaadababaadbadccdccdcaadaccbadccacddcdcdcdbddccbaaaccadbbdbaadccbaddbabbaabcaadbdacbdcdcadbcbbdcaacadcdcaababacabaabadbbdcddccbbacacdcccdbdacabcdbbacadbcaddaddddccabbacdcaadbaddaddcccbabadacbdddabcddbaacdddbbbdaaaadadadababaabbabcbbdabcababdbadaadabcccddacadbcbbabadccdcbaacacdcadbdcacadbdbcdbbbcddbcdbdacdcdcaaadbdddddbcdadaaccaadadccaacbbabdadbdbdbddaaddbcaacddaaccabdabbccbbdbbabccbaaddaccaaadaaddabdccaadbaaacbddcadbbaccbcabbdaccdccaddaaabcbaddbcaadcbcabdabdddacaacbacbdcdccaaabccbacbbaccabdcabdcccdbaaaccbcdcabcbababcabdcbccacabbdcdabcccdbaabcadbaabaddccacbdccbdddcadbdcbbcaababcadabcdccbddddddbdbacdcbcdccbacbdbcacbddddbbbacadbdcccbacbadccdbbbaaaacddcccddcdbdbbacbcadaabbaabccdcdbadacbccbacbdbdacbcdcadaddcbaccaadaddbababadbacaaacbbcdcabdddbcbbccadcacaaacbbadcaabdabacaabadccacdcbbbadadbbbabbcdadcdcadacccbdcbdddadbcdcbababcdadcbddbdbacdaaddcbbcdcbcaabccaaccabdbaabddabdcbdcaaadbbdbbaabcccaabcddbacbbacabdbacdbcaadbdcbdbbacaacabcaaababccccbdbaaabcacdabadacdcaccccacddbbdadcbaccdbabdbdbaccbdccdbccacacacdbabbdbbcbbcacaccbdaddcbddabcbcddbaddaaabbbdadbbdaaddcacbdcdabdccdbddcbabdbdcdddacddddccddcccabcbddcdcbdaddaabbdbadcbbddacabaddddccddaabbbdbaddaadacdcbacdaccbabdbbdccbacadadddcdbabcabbaccbcccaadabbbbbcbcabcbacbbacdddaacbbaaacabaccddabccbbdbccaccbcbbcbddbcaaabbacdabbdbdadbabaadabcbdacacddcabccddabdabacbcdddabbddbccddbbdadbbbdcbcdcadcccbabbcaacccdcbcbdbabaaaccdabacccdbbdbabcacbacbddabcddbabcddaadddddcacdcdcabbacababdbcbabcbddcccbbaddaacadaadbadabadbabdbabbabacdddcaccbbdccccdbdaaabdbacaabababddcbcdbcabaabdddbbbbdabddddaaadcbabbbddaaabdbacdbcacddbbbaacacdbbccbadadcbaaccdbbdababdbabdbbadadbdadbdcddabdbbacdbbcdaababcdadbaccaabbdadbabbcddbccbbdaddbadbbbddccacdbcdadacbabcbddcbabdbbcbbbcbbccbabdaaacbaaccbdbaaddacbacdcbdcbbabccdbdbadbcababacbdcccacddcacdabdddcbdcadacbbaacaddbddacbbcdbdcaaddddccbaabdaabccaddddcaacbddaddbacbadbacbbdbcbbccbbdbbbcbabdddccacbdccacdcbdadbcaababdadddbcbdcccaacbbbccbabdbbbdbddbddacaaacdbbdadcdbbcbabdcaacbccdccabcadabadbaacacacaacdccddcaadcacccaacdccacacbdcdcabacacbdbccadbbacddacacdbcabdccbccbbddaddbddbaaaacaaddadccbccbacbccdbcabdbcdacbdcdaadcbaabadacabaacaaaddbdcdccbbddaaaabcddbdddbadbaccddbccbcaaadcacccabadccdbcccbbbbcbcdadcbbcabdcadadacacacacaadbcbcdadcdabcabdaacbcbccaacaaaaddbbacadaabacaccaabbaccbdaddddbbabdcbbdbddaaacbcdcaaadbdcaccddacdcbabdcabcccbaddacdcacaddbabaddcacdddccdcaddbcddbdcadabaaccbbbacabbdbaacdbdccaddccddcbddbddcdaddbacdbadccbcbcbdacabacbdbcdbccbabddbbbaadaaacbccaccabddbcdabacdcbadaadacabdadbddbccacaabaadbaadccaddaabdbbabdcbbdbcdaabacccdaaaadaccbbdadcaadccdddddbaccaacdacbabdacdbbaabdcbdcccaacddccdabdacdaabadccdacadcaaacdddacabdbdbddabacdcdabcabbdcbadbdbbbcddabbccbdacaddbdacadcabcadbbaacabccdaacbdcadacabdcacbddaadcbbcdaaccabccabddcdbdacccdbdaacddccababbabcdabadabbdcaabacbbdaccbacdcabdbaacdacbccdcddddddcaabdbabdbcdbbdddacccdbbdbaccbccaddacbccddcacbaacacbadccaaccdadbabcacddbaaaadccdbbbabcdabdcaddcbbbcaacadaccccbddaabdbcaaddaacabcadcbdbbddbabaddcdbbcbccbaaabbaaaacadaaaddcadcdbddaddbdbdcdabcabaabbbdcddbdbbbcbccccdaddbcddccacdbcccdbccbbdbcbcbdabacadaacdcadcdcddcaaacabdacdbbbdabdaddddabababcdcccbdacdbddadcdbdbccdbbcabbdaacddbaccabdbdabddcdaddaabaadbbdddcabdcbbadbdbdbddaaccdcbdbcabbcdddbdacadcdbcdabacdcddcbdccccaacbccdcbcaadbaddccaadaadaadcadcacaddbdbbcbbbdbbccbababcdbaccdcadcaccdacddaabaccdcaadcbbbbcbcabadcccaacdccaacccbcdcacdcadccacbdddbcdaadddadbadddcdbdbddbbccbcdcbaacabcdcdacddbabbadabaccabcddbcadadcbbbdcaaddcbccccadbdacdabadcbdabdadaabbddbbccdcbbcbdaddbadbdbdbbdcdbbdbadacbcccacbdabcdacbccabdababcdcacaaadccbdabacbcccdbcbbddbacdcbbacccabbadadddccabcdcadcbdcbdacacacddcaababdddcbdddcbacaabaaacddaaabbdbbddccdbadddbbdbcccadaaacbadbaadabbdcdbbdbccbacdcaadcadddbbaabcccacabaadbbbacbacdbddccaccccbcdaaaadccbbcbdbadcbbbcddaadbdabadcabcdbbcacacabbabacbbbbbcccadcbdbcbbbaadbbbdccdbaaaacbbbabcddbdabbcbbcdcdccdddaacbddcbbabdbdaacdcadbcdadbabdddbbddbdbcbbadaabdaabdbcbbaabacbaddccbddcdcaacababcabcacbdaacacdaabcbcccddcabbbcdcaabaadccdcaaabdadadacacababdcccaddbbdbddbbbccdbacbcadacdabacbdbbdbcadbabbbddbabbdcdcacdbaccccbaabacbcbcacbabdbadccabbabadddcabddcdddcbacbddcccbbabbcaccdbaaacbabcbabaaadabadbaddaacccbdadcaabaadddabbaccaaadcbbaadddaaacbabbbdcccdbbbacdbaadcddbbaabbadadbbbaacbacdcdcbbbcbcaabcccbcdddaaadbdccaaddbbaadaadaaccbdbadcdbdabbddbddaddaadccddcbbcadcaabaadbabcdbbcddbbccbbaabacdbdbaacacbcdddccdcaabccdcddadcbbccdcaabaacbdddbbaccddcacbadbbdddcabcdbbddaaabcccbddbdacbadbcabcccbbdaccddcccdbcbdbbcaabbdaacabbddacacbbccbcabaadbcdddbabacdacacddbaaabbacbaddabddcdabdbabdcccadbaddcbddbcabcdddddbbbdadcbddbbadcabbacaaaacadbcbbbacabbccbcbddababbcddbdaabddcdacbaacdacbadababbdcdadcdcdcabcbacadbcaaddbccccabcaacdcddccaccccbbdcdcdadcadbbcbcaaacabdcaabaadbbbddddbacbbcacbcacaddddcdbacaaccdcdbbbcbcadbcbadacaccaddcdddcbaadacdcaadacdccabcbccacabbcacadddddbdcdbdcaacaacbccbbbaccccbcbabbdcaccadbcaadabcbbddadacbcdccbdcbabccddbaadbabbcbdacccccdbdccabbbbabbcdabaaacdaaadddcccdaddcbbccbccbbbcbbaaaddbccbaacabbdddcbadcbddaccbcbdbbbdaadaaddbaccdddabbbbabdbadbcccbbcdbddcadadccbcaaadbcdaaabbacacbccacbdaaccaabddacaaadadcdadccdcbbdbdddbbcaaccbdbabdaddaaddaacacccabbbbaddbcadcbaddbbbbcbaccdabaaddadccadcbdbabcbabdadaddcaabbddadaddcbbbccadddabcbabcccbcdbddddabadcdadaaadbcdaacdadcbdacbcbdcdccbaaccdadcabdacbcdddccaaddccdddbdcbbcbacdcccaccddcabdaccdddabcacdddabcbabdcadcadcaddbcddcadcbbdababdbdadbcdcaddbdbcdabadbbbacdcdbbdcaabdabbaacadacbbdadcdaccbcbbdcbddbcabdbcbcaaddcdadadbabddcacadcadcddbacabddccadaaadaccddcdcbbdddaabcdaadbbbdcbbdddcbaccbdcabbdccdcbaddabbdbdaabcaabbccdbccbaccaadaddaadbbbdabbcbbccadbacddadbacbbdcdcadcdaaaaacbbcbcacdbcccdbcdaabbadaaadbddbdcdaabdcbbacaddcadcccacbadaccbabbdadbbbcdddadadddadabaadacbccdcadcaaccbbbaababbabaacbcdbcbdbcbcbccbbdddbcdaddacbbbbacdaacddcabbccbcbbbbdacacdbdbbacacbcbabcdaaaccacacdcdabdbbcdbdaaccccddaabdbaddaacabcdbaabddcdbbbbacbbbacabbcabbacabbbdaabccbcdadddaccabdaabaddadbcadbbabcabccbaadcbcdabacdabaabddbcaacaadcddbbbdbdbcbbbdaadbacbcacbcdbcbabccabdcbcdbbdbbbccdadddcacbdbcddbbbaacbdbddabacabcbbcddcbdadbbacbdcbdcacbbabdbababdcbcacdabcbcbbdcbdacddaadddacdbdcccdabacdcdddadaadacaabcdbcaddaacbbdcacccbccbddaccadbcbaccbbddddaabdbbaccdacdccdabddcbadcabbbadbccccdbbdcccbdbadbcacdababcbbbdcbaaadaaccbddcdcaaadcbabbdddbbbdaddbcbbbbbdacdcadcabdcbbdbdcacddcbcdbbdbdccaadbaadccbcbdbbbcbdadcdcbddcdbbbabacccacbabacacdddacacdadadddbcdcdcccccbdabcdbcbcdcaabadaacddabddacbabbddacdccbbbccdabcccbdccdacccdacbdaccddaccbbcdbcdaaddaadcaddaaaaacbcbddaabbcddcdcbdbabcadbccbaabacaccabadcbacabacdabcababacbabdabdadabacdcddacbbbbddcdbbadadbbccccbcbaaccdcddbaadbbaaaacaccbacdabcdaacddcbcdbbabadddcbdcbadddadbbbcbabdabacadbdadddabddcabccaddaaddcadaccdbadaacddbddcadddddccacaabbbacbcddcbccbbdcddbabaadbcabcaadaddddcdaaabbabddcadaccabdddccadbccdadccccbacbcdbdaaddbbabccabccbccdbdbcdcccccdbdadbabababbcbdbdcbaaaaaacdbaddccdbdbbcbabcdaadbaaccadaccdacbbbdcccbcadadcdacdcbcddacaccadabcdcbbbcbbabacbdccbaccccbddabcdcccbccbdccdcbbbcaddcbbcbbbaaacdccabbddbbbbcdccbbdcdddadbcbbdccaacdbaaabbbadacdbddaacccaadbcdcbabdddbacbbbccabcacccabdacaabdbbbacaaddaacacbabccddacbcdddbadaacbdabdbbacdcdadcbbddcabdabbdadbbdbbcbadadccacddbbcddbadcadaadcdcaccababbdaaadbcdadabcdabdddddadccdacdcdcbcadcddcbaacaddabbbaaabcacdbbccaabbbccddabcbaacdbcbcacbddbbcabdbaadadcaccbabdacdcbcaaadcabcdddcaddcabadcabbbadabdbacbacabdbaacadbcbdbadabaaccdbdabcaacccdabdadbbddbbdbcadacdbdbcccdadacdabacabdbcbbcaaddabbaadaddbcbacabadcdababdcaacdbbcbaacbdaddbbcbdddbdccbdcbdccddaccadabbaaadaccdaabdaddcbcdbdacdccbbbdabbcbaabddcccddcbaabcdddabadcbbccddaadcdcbdbacdbbbddbcacdcdcadccccdcdbcbcdddbaacdabcabdacbcdcccbbbcabcaadbbbacbbdaaacddaabaabbccbbbccbdabdccabccacbaabacbddbaacdaaddaddcdadbcbdbccabccbaccacacabbddacaabbccddbacdaaadddbbdbdccbaadbbbaabdabcabbaddcbddaacbbbdbbcdbbdcccbdbbdadbbbadaababbbbcbcdcddbcbdcbbacdbacbbccdcbddbcbbcaabcaccddddbdaadabdbbacabaccdaacbcadadbdadcdcbbaddadbdbdddbccbdcccccaadccdbaddadabadbabadbbdbabdaacbbdacbaadcdcdcaaddaaaddbadddbdccdccdbddabbdcadcdcdaadadadcabadbacbdaaaaabbadbadadbdbacabcddbbdbdbbcddccdbcdcbdbcacbaaccdacdcbadbacbbacbadddaddcabcddacdcddaccccddbacbdccccbabbbcaddcdcccadbdcbcabdaccaadcbaaacbdbbddddbbcaaddabbabbabadabccbbbadcdbdbbbdacdadcbbdacabbbaaccdcddcabbadccabaccbcabaabdbdbbbbddbbddacbaccddcdcdbddabaaacdacbdddcdabaabdcdbabbcbcddbbdbabcdbccddabdacbacaccdbdbdaacbcdbbbcabbadcdddabcddcaddacbacaabacdddcddadacdbbbaacdcaababdbabdadbbccbccdabbdccacadabadcabaaadbcabddbdbcdbaaaabababbbbbdbcbbbbbbbabdcddbdddbbdcbbcdbddacbdbbddbdabadccbdbbddccbbacbccbbdbadaabbacaccabdcaadbbadcbbccdababcddbacddbbbddccabbdacddabdbdbcdcdcabbacacadaacdaabadacabdadcccacbacccdcbcdbdddcbdaadbacbddbbcbccbbcaadbdaabaccadacdabccdccccbcbccadcbdbcbccbdbcccbddaacabadacacbbddabdcbabcccbdddcdccababdbccaccaccbbcbcdccbabccdcdaaaaadcddadcdbdaadcbbbadbdacbbdbcabadbccbadbaadcdabbccbddadcbdddaddbddacdbadbabdddcacacdcaacdccdbdadbdcaccaddadacddcdbbbcddbbadabcdbbddbcdbaabcdcdbadddbbaabacdddabdbaddabcdabaadcbcacbdbbbdccbdbdadbabdabadccdbccbbdadccadcbaacddccbabbcabbaabbdbccbdddbddddbbbcdbaacbcaadaaacdbaccdcbdcabddabcbadcadbabaaadbcaddbaccabdccabcaadacbcdbccddddcacacbdabcaadacbdcaaddaabbbabbcababaccdbcbdabccdacccadcdbbadbabbdaaadabdbcabdbbdbcdbdadabadaaaabdaaababdbadcabacdbacabcdccadbaadcdaddddccadcdcdbacddaccbbdcdcccacacccababdabddadddbaadadadadbcddadddccbabdacdcbbcbaadabbaaababbabcaadabcbccbcabbaddbaadadaddabacdccbcaaabbbdcaaadabbcbabcaabdbadaaddaaddbbbcaaaaadcbbcbcccdadcacbcbabdabcadbcddaaadbadabdbabbaabaccbbacbcdcbcbdcdbaaccbcbbcdbacdbabcacdcbbcddddbaadccddbbcaabacaacbbacaccdcaacacaddadbdcccbddbcccccbcdbabaabdaabdbaabaaaadbbbadbbbbadcddbabdbaabdadbdbacaadcdaaabbcbadbaaddcaaabcbbdcbdabdcbccbccacdadddabbacbbdabaababaaacbabdabaabaabacdbccddcbccdbdaadbdcdcdbcdccbddaadbadadcccadacabcadadccadbbbbdbccdcbacbbddbcbcacabcacacdcdbacacdaaaacdcccdcbdacbbcdbcabdcbdadbcacccbaacddccaabddaaadbbbcacdadbbadaabdcdabdbacdbcaacacbadbbbdddbcdbdddadbbbddcaabcbdcbadbddbdadcbacbdbabcbccbcaadbbabcbaacdddaadcdaddbccbdbdacbbbcddddaacdcdcaacdcccabddbbadddddadddbababcadbddabdbbadacdbcdcbdcbcdccccdabdcababbcdbdddccccbcddaacadbdabaddacdbabcdccacdcaacaccbdcddbacdbdccbccddcdaadbdbcdcbdbabaddadbaabbbccabbdabacdababcaddbabdbcadbabbdacccbbdcabddddadcbddacbabdaaacbbdacdcacccdbdcdaddcabbabbddabaadaccabbbdccbabdccdccbaccaacbdacbabdacddaccccacdccbadcdacdbccbdbacacdddbcabcdabbdcaabdbcbacdbbabbdadbaaadadabbcbbbdbaccbdaadbdbdbdbabcabdadcaaacbcdbacbadbbbbacdacccbbbcddcbccbdccddabbdadbccdcccabbadcdaddacdadbdacccabbdccddabaabdccdbbaadcbabbdcbdbaadcacadabcddaacadadabbcaadcdadcacbdabccccbbcadabdabccabbbdacccdbcdbdbcbcbdaaccbaacdbbcbbaccabacddddcdbabbbbccdcdcdbdbadaccccbcadbcdabbadababbcccdcadcddbdabcdabddacdabcbbaadbcaabcdcaccbdabacdabdbcbcdabddbababacdacadaabddabdbabaaabdbadcabbabcdbdcaccdcddddbbadcacbabbbadccbbabcabbbdabdadabccbbabcababacadddababdcacbbabddacdacdacdcbdaaaaccbdbcddabbcdcbaaddcbccddcdadcbadbcbbababbaabccacbccdcbdcddacbbadbcaaaccccabbbccbdaabcaaaacaaddccdddcabbddcaadcbddcbccbcddcabdcabbbdbccdcdbdbdcddbbbdadbabcbbcdcccbcdabccbaccddcbcdbcdbbcbcddacdcbdcaabcabcdbbdadcaadcbbcbcdabacadaaadaabbcacbabcabbaddcdcccbdddbaabdcbdaadaacaccbaaaaabdbaabbaaabbbaccbdabdaaccbddaaabcddabdcabdadbcbbdadbaddccccdbbdbcddcdacbbdccdadccddccbddcbddadbdcddcacccaddacadabacaabccbcdabbabacadbbdcdccddabaacabaddbbcadcdcabddcdadcdbdbcdbaaacbdcaabcbdddaacbbacddbaabbbdacadcdadacbcccaacbbaaddbbaaacbacddcaacddabcaddcccbadacbaacabcaabdccacbdadcadcbdaacadaddcdaabcdabdccbccbdbaddbbabaaabacddabcdbdaacacbbccbcdbbaccaabdbcaaaccbcaccccdabbcabbdcadddcbcddbbbcadbadcddbbbcddbdcaaadbbdddcabccacbdddbcdaabbddccbbbacddccbcacbccbabddaddaacdcabbaaadbacbcaadcbbdcbbbbbbdbccccbdacddcacbadbbbbcbccaaacbdbbbbccbdcacdbaacabbadabbbbbbcccdbcbcbddbbdaaadcbaaaadcacdddaccddcddcdbdcabdaadbabbcaccabdbcccabdaabdcbdbdddbadbabacdbdadacbddabdddddabcbbbaadbaabddbacdaadaacaacbbabbadbdbdaadbadddbabbaddddadbadabcbababaaccdabbdbbdaadcbadbbcacbbccccdacdcadcadcbbdcdbaabcbbbbbdbaaccadabdcadccbcabaabdacbcdcbdabddabaadccdcdddcddacadcacdaaaccaabddaabcddddbdbacacabcbdcbdcaddccaabdbcbdbddbbddddbdaabaabacaaabbadccaddbbbbbcaaaaccdcdcaabccccdaadcaaacadbdbacbaacacdabcbdcdadbdcdcbdbaccdcbdaddbbbdbbcdbbaaaccccbcacacadbabcadbccacacddbcdcdaacbccbaabdabcbcdabbdbcbcdccbadbdbddcaaabcdbadabcabbbbdcddacbbcbaccabadbcdadacabdcdcabddbcbbddbbaddaabbddbccaddcacdccbacccdacdacccdcbcddddcabaabacbacbbdcabababaaacdcdcaacdccdaaaaccdabdbadbdadccbccdcaacabdbadadcbcadcddaabddaabddcbbabcddbcdaadccaacacdacdccdbbcaabcbbaacaadaaaadaaccbaccaabbbddcdbbbabddcbadccbabadddbadabdccbcbabddcbcacdbdbbbcabcdbcbacabcbdccbaaadbbaacbcbaddabdcadaccabbcabbdcdabdccadcabcbdbcccbaacacdccdcdcacdcddbcdcabcccbbddcdbadcdabbcadbbbcbcccccdbcccbbddbcbaabbddabacaadcdcbbddaacaabdcbabdadbdcbcbdbcccddbddbcdabbcdaabcacdccbabdbdbdcdaacbdadbccddabccdadcacbddbccbbdcaccaadcacddcbcbacacbccdaddaddcccadbccbadabbbdccbbabbcbaabadabcdbbaccdabbbbbbccbdbbcbddabdccbdcbcaababcacdbbcddddccdaaddbcdbacbbdbbdaacdcbddaaadcbddabadddacabddacaabdbcacdcdaaadbbbdcbaadcabdaadbbabcbbacacbaabbbbccccabaddaddddadabbadabbadacdcadcbbcdccaabdcacbadcccaaddcdccbddddcddbbdadbbbdaddabcbdbcbcbcaaadcdadcccaddcabbbadcbadbddcadddaabbdddddabaacdaaaccdabbcdbddacaaaaddbadbaccaacadbbdccadaddcaacbcccbccdadbdaaaccdccaccadabccdabcabbcabcbbdaacdbbcdcbdcaddccddddcdaaddbacdabcdaddbcccbdacbdaabdadcbdcbdadccbcbabaadcccdcbadadadbadbddacabcdccddacaabbacdcdddacdbdcddbaccaaaababcdbddbccddcccadaddaacdccdccbbdcaccaaabcadbdddbdccbdbcabbbbdbcdacdacccaddabdacbdadaaabdccdbbcababcbbabccbbabddcbaabaccabacadcdddbaaadcbdbdadaccdbcdbdbcddbbbacbdccbcbababacacaddcdaaccccdaadaadbabdbdcdcabdbabcdbaadabadbcccbabcdbccadbdacbdabcccaacadcdddacbcadcbdaacdabbaadabcaaabcabbdbcddaacddadcccdcbbdcdabdbbdcacccccacbabdbdaadddbcacbdbcacbaabbbcaacbdaadbdcacddacbdcccacdabcbbcdadabdaadabdbadbbaacbcaccdcdaacdcbcdbcbcbabaacdcbbacdbccdccddcbadccabbccaddbbbdadaddddacadbadccdddddcdacdbdacdbacdcdccbdbddbadbddcbddbadaccdaccbadcdbcddaccddaaacbaacddcabdaccacbbddabccbdaacabbddabcdabcdbbadcddacbacdabcacabdaadbdcababccccbadddabbddddabbcbccacdbbacdbaadcaccadbacdabbddabdbcaccddbadbbbcabacdaabdccbbaaadaabaccdccababbaabdcaaccdbdbacbbdadcbbbcccbbdccccdadbdabbcbcacdbaabdabdacdddcaabcddbddaccdcdadbbacabcaddcacccbdadcdbdcdcbcbbcbccaacbbcbccbbdddcbacadcbcaacbccccdbcbcdcbadabadaaaabcbdcbcddaadacdcbacdbcdcbbbdacdadbbadaccacaabaaabbdcdcccacdbbbaddcdaddcdabcabdaacacddadabaababccdacadccdabdddbaddcbbdabbadabdbaabbacdacacbbcddcbcdbbdddcabbbaabbcbbccdacbbbdcaacccaabaabdbdadcabcbcaabddadccbcdcaccaacaddacdabaabadcddbdaadcaadbbcbbadcbddbadbdcabbdadbdcccaabaccaadacaabcacbbacddbcbbadadcbabaaabcdabcabcacccccadcdccbcdabcaadccaaabbbbdcabcdbdaddbbdcbdbadcacbdcadcacbbdababccbacdddaaacacccabacacccbcaacdcaaadcccdcabbaddacccacdabdaddadddaabaaabcbbbbbbbabaccaadcaacbcaaddcddbcbabbccccabadaccccdddabaabcdbcbcbadbccbacacbbababccdddcdaabdccdbcbcbabbccbcbadbdbbabbdabbdaacbbabcacdacabcdccbaaadccdbdcbbaacadddacacbdbddbdbccadabbdaabacdbabadacbbdbadbccadbbaadddccdaccadcbbdbbabdcbccbdccababbbbdadbaadbcbdabdbadccbcaaccdccbacdabcadcabccbdbcdadbbbacdababbdadcbbbdcddbadadbbaddcdcdadacadccaabdcbdcadccaabbcdabaccadbbbcdcacbdbbddddbaaabdaaaaccbcbcabcadbddbcacdaacabcabdccacacbacaacbbdcbaaabbbcbbbdadcbdcdbbcabbaddcddcdcddacbbcbcabbacaddadbacbcabaadacbdabdcacdddbdcdcaadcabcaaccdbcbcdcabdaababdccabcaddccbadbabaaccbadcacbcbaccbbddcbbdbcbcacbdabccdabdaaacaddacaacdabbdcbabaacbdadbbdbdcdbbaccbddcddccbdabccccdcbcbddbacbddadbdcdbadcbbdacbbacbdcbbddbcacddcabbcbcdadaabcabbaaadbacbaacdaacdcdbcaadadbabddbacbadaddbaaadabaccacbaacdabaabbbcdbdbacbdacaacacdcbcbdbaaaacddbccdcbbbcbdcbbaadbcccbdcbdacdbaccbcaadbcaaddcbaabaaccddbdcbcbccbabaadddbcdcabcccdcaadccbaccbcdaadccaadcdacddcacdccdbddcdcdcaadbccacabdbbdacccacbadcdcaddddaccbabbccbccbbcbcccadcbdbcbcacbccdddcddddcabaddcdddbcbccbbcaccbdbaccdbdcbdbbccdacaaaacbbdadddddaddcbabdccccdbdbbccdabcbcbbbddccbadaddaabdcbcdccdcbccdbcdbbbcbddbdbadbcdcccbcddcbbcbbddacbaacdabadaacdbadcdabcddcababbacbadbddcaddbdcbdcccacdacdcddbbabdadddbddacaaabaaaddabcbbdccdbcdbdddbcdacadcbbddccabcdccabbcdadcbadbdbccdadbdacbbdbccbadccddcbddcabccbaddccbbbaaadcbddaaaadcdcaddcabcbbbbdabdaacdcddcdbdbcacabdcbacadcabaddbdccddbbdabadabcdbbbabdbabadaccabbccbbdccccbbcbbbabbbcbbbaaddadcadbcabdcdccacccbbcdaccddabccdbcdaccabbcdbcbbcabcdcaabdacbdddcdcadaabcabbaabbcdcacaaddcdbcdabcdadadadbdddacbadabaadbcbdaacaacbddcaabdbdcdcbacdbaabbadddbcaaddaacadcddbdbbbbdbdbadccdcdddaadadabaacacbdaacaabccbbbdabaccabbbaabbaaaabbdaadcbadacddbcabcbdcddbdcbbbccddcbcabadcdcdaacdcabaaaadcaabaaddababadccbabddbdacaddcdbbadcbdccbbccdbcbbbbaabaadadcdcbcbcbbacdabacadcbcacbccbbccbacacbbdacaddabbdcddaccaaccbdaccbdacdadbbadbccacddaaaadaacabadcbadadbabbbbccdadcabbbbadccdcbacdbcccdcacdcdbacbdaaadaacbdddcdabbbbbbcdcdccbccdbbbcbccdcdbdbcacdcdcbbcadddbacbccbdcdbdadddccaaadbaaaaabddbaccabcbadbdabbaccacadadcacadbcbcbaabbdccdcdcbabaaacaaaacccbcadacacbdbdddaaabaabddaaadaaacdaaacbcdcacdacbddcdcdbccaabbabacccabbabdbbccadcbbbadccdaccbdddddccbadabbddccbcadddaaabcccbaadbcdbabcacdccdcacabdbccbdadddcbddddddbaabccbbcbccbaaadacdaddbddaaabdaacbabbbadcdbbbdaaabbbcccbdcbcbadbbcbadaabadcaddabcccccabdcaadacbabadcdadbbbcbacabdadcacaabcacdcbbcccdbbcabadaccccadbbcdbcbabcacbcbddddbbaccbcccaddabddbbdddcdbcbadddcccadddcddcaddbadbbdaabbdbcbbaadabdddbdabbaabcbbaddaacaababdcbdbdbccdbcbdacdadddadcdbcbdaabbdcdacadbabacbdcabcdcbbbdcddddddbcaddaacbcaadbdbbdcacadabccbcaaaadabdaccbacacddcdadddbdadccdddbaadabdbdddaabacaaaddcbaddcabddbdadaaacacbbaccbcdbaabbadddbabcadcaccdccbbcbcbccaaabdbadabcbbcadddbcdbabcbbcabcccaacdddcaddcacaabbcadaddacbddccabbbddccdadddcaaacaccdaaccabcdcbadaaccdcbdbaddbbccbcabacdccccbabdddcddcdadbbcbcddcbdddcccbadccdaacdbcabddbbaacaabcaaaddcccadcccdbdbcdddddcdadaaacadbbbccacaadcddacdadcaabcadbccadadaadcdaabababcabaabdcbdcaabdadbbaaacabcaabbbabbcddcdccadddcdcdbadcabbdcadaabbbbddbaaabaaccbadabbddbcbdabcbdcbcbdacaacabcbdddcabacbdabcbabcbdaccaabbcbbbcaccdbdabbbcdaadcbaadbcdabccdbbaccdcdbdcaababbbcbbbadcdcbdcdcdadadbbbacadaacdddaccdbaccadbddddaabcbacbdacccdaaccacababcbcaacbaababbbbaddbdccdcccddccaadbaccbaaabcbcccbcbddacbbdabcbadddadccddddbaadabbcbabbbcbbdbdabdcadbcbaacaaabdcadddadbcdbdbaaaadadcddaadbbddabcadbccdadacdadbbdcacbaadbdaabadcaccbacbccbdadcdabbdccababcababbbaccddadbbaabacbbbbacabcddaaaadcdbbaddddaacbcbbddcbacdcddcbabdaccadbaaabaadaddbadbdadddaadccddabcdbbdbcdabadbaadddcbdcbbcdcacadbbbdccdddbabdbcbdcdccbccadbcbacacadbcdbcdaabbdbbbbbbdcccaadcacaabcbbbbacaccbcbcbbcdbbcabcbbbaaccacacababcbdaccccadbcaabadbcdbacddaacadaadaddccbdbdcbcbdaccadacbdcabdcaadcccababbdaccdbbaccbdcdcbacadacaabdccbbccbaadcccdbdabbcbacbbbdddbaaadbbcdabbababaacbdbaacddaaacccccdbcbdabadcdddcacddbdacaccabdccdaccbcccdbcbdccdabadaadaaabccdaddaaccdaaacdcbcadcaddbdddbaababcabbbbcddaaabbdaabddbaadbcbbaadcdbdcddccabadbacbcddbbaccaabcdddacddbbbbcbcbadbbddacaccdbbcbcadbcacccbddcbacdcbdabddbdcdaaabaddccdabbabdbaabdbacddcaaddbddcaccaccbcbabccbadadcdaadbbacabadcabcbacacdcacdbdcccabdadaacbdcdddaabacbcdbcababbbbadadbcdadaaccdbdabccadcdbcbdbdcbbacbdddbbccdbadacdcdbbadaaccbababbdcbdccddcdadcbbbbcacdbcadcbabbbadcaaaabcdadccdbacaabbbdacacadaadbddbccdadcdadcbcbbabaacbddcacddcddcbacabddbcbbcbaadadddbadacadacbbddbbdbabdbbadadcdbcbaccddadbbddacabdcaabcbacbcbdcaccddbcaacabbdacbbcbddcbadaddcbadabbbbbcaaccdbaaabdbccaabdbcddaadccdbdbbcacabcddaddacaaddbcabbbbdbdccaacaabdcccabbcaaccbccdddcccaabadadbbbadbcbcdddbbddabcbcbcabccbcbabacadbdcaaccbcaddbcbabddcdbbbadaabbdcdabddcdbdbccacababcccccbcaaabdbbdcccdacdbbddadcbbbaadbbabbacbbdbddadaacadadabdbaaacdcaabbacbacbddccbcadaccaaddabbcacabacbddadbdabbbaccaaaacbdbcbcabcbdbcbaacddaadbbbdbddcacabbddbbddabcbdbacadbbdcdccabacaabcddcdbdddcbadaabcccdcdcdacbbcabbabdbbcdacbacadcbacdddbdbbdbbabcadcaabbadadcdbbcdabbcadcdddbbadaddadbbacbadbcabcaaacaaaaccdbbabcaaccaaccdbcbaddbcaabcdcabbcbbadcbbbbdabcdbcadbbbaaababbbccabcbbcadbdcadddddaadbcdabbcbbbbcadbdcbabdabbbabdcaacdabbbccdcbdcdcbcaaaacbcccbacbdbabcdbdaadaddddacaaacbbabdadddcddbaaccccacbbacabbcbadbcccbbdbcddccaddcddadccbdbbcdbdbdddaaaccdcdaddccbbcbaaadbcccccdbbdcaaddaaacabbcbacdbaaddddbcccaabdbddcdbdbccabbbbcabdbcaadbbcccadadcbaccaacacbddddbdbbdbabcdbdbbacbabacaaadccddabddbadaaaaaddacbdcbdbbbcacbdaacddddaaadccbbcadcabddcadabacddcbdcdbaabcbbacbbabacddaccbbbbabcabcdbacadcdaaacbbddccccaaddccdcbcabdcbbcbbcccdddabdddddbbbcdadabdaddabbdcddbdcddaacbdcdabcccadbcddccccddcbddbdccaabdbcbbaddbccbcaaaddcbbdcbccbdcdccccddcaddddabacdccaacacacdacacdddbcbbacbadabcbadcdbbcaabcbdcdcccdbddacbcdabdabcddacccbbbcadaacdabdcddddccdadaaaaaacbbdccdaabaadcbcccdbadacdcbdcbdbcbbddabcccdbababcadcbacbdadaaccccaaacccabcaccbbdbcdbbddbbcdcadcaaddcbabbcacbcaddadcccaabccaacadacbcdbdabcdcbddbbbdabdcbcdcdcddcbcbabbccdccccdabbbbadddccaabaadbcbbadbaaaccbcbcadccbccadaddaaddabbacadbddbbdbaccbccdccabcdbabbcdaaacadddacdbdacdabdabbcdbbcdbddcbcdaacadcbabbcbbdbbbbddbdbaabdcbcbbdbbbbccaccdbdacdaaccccdddcdcdaabbddcacbacadbddccabcbdaddaadabcddacccaababbabbadcbbbddaabbabdaddcdbbaabbbddabbbdddddaadcdabcabadbccbabcdacabdcbabaddacdaabccaacacddccdaacabcddbdcaddccdbabdbbabaccdcdacaddbadbccbcbaadbbdaabadcbdbddbcccadbdaabccdcdabbaaccabccbccacbbadabdcddcbaabaacdcbddbccdbccdadbdadbdacbdbcdaabdbdccbabcacbabadcdcbbabcbbabdaadabaccacababbcacbbadcaaaabbcbdabcbdaaabdaacdadcdacacaadcdbdababbdacdbcbcdcccdbbdaacbddabcdddaaaaccbaccadabcbbdddadaccadababdbdcacddadddadddcacbababcadabaaaabacacbdadbbbdcbbbcacbccbbddacdadbcaadacadaddcdbdacadbbcddabdddaabbbbdaacbbdadcddcdcdaccbcacdddabdadbbadbbaccdcddccdbdcbbaabcabcabbabcdddbcbbadcbbdccadbbabdcbdddadbbdcdbabadabcdbcaddbbcdccdcbbdcabcaccbabbaccaabdbaacabcadbdaaccdaaadbdbabadbaadcbbdcacdcacabbdbacaccabaddbbcabaddbbcbddcdaddbdacabcdcadbcdcbaabadadabbdcbbccbcdbccdcccabdbacbbbdadbbbaabcacaacddaaaadbcbdabadccbaadcaadcadbdbbddcbbbcbcddaaaadcaabcaabbbccddadaddbaaddacacccabcbbaacdbcbcccdcabaabdadbdabacccdcbcdcaddaacacdcaccacdddabcdadadcbddaadaacbabcccbdcdaddcbaaaadbdaacbcdaabcdbddbabbddbaadaccdabbbcadccadcaaccdcababccccadadacbdaacadaadabcbcdddbbdabcdcbbddbabdcccdaabaaaaddccdbcdacdccaabcbbcdddcccdbacdabccaacbbcadacddbbccdddcacacddaccdadabadaddadccddccbdcdbcdbcccdccadbcdaadcdcaabaacdcdddcccadabbcabbdcbbbbbacdcbcddddcbcbaccccdcccabaaddccdbbccdcaaccbbcdadadbadbcbadbccdaaddcbbbcbabbcbbcabdaacdbddbccdbbadbacbacccaadaccbadcbbacdacabbbacacacabbadbbcddcadccdddcbdcdadbacdbcddddcbbbdcbdacccbbcccdadbdacacdaadbbbbbadbdcbbaacdbcbabbdcdbacdccdcccdaacdbcadcacaddaaabbcdaaacddcabdababdbabbbacbaaacbcbcbacdcacbccddadbdbbddadddacbacadccdbcbdabbbbaaaccaacdaacddadbbacbdcaccbabcacbddcbbaccabbbdaadbcabaaacbacdadabbddccdabcabdddacaabcabcccaacacdcbdddababaccacaaaaabbadbcdcadaadbaaabaadbddccbdcccaabbaadcbbccbbbacdbbabbcbcdcbbbaddaadadcacdabbcdbcabaddccdccabdbacdcbbddbcdaccaabcaaaccdbbbabdcccbcadbdccacdabccacacaadddabdadbababbaddadcccadadbdbbbbbcdddabcbbbdcdabccccdbbaadbdbcdbaaacddcacacaacdacbbadacccabcadcbdbddaabcdbcdadabdaccabdbadcdbacdbdccabdbbcbdcbbbdccdddccaaddbcacdbdccabcdaaddbbbaaddbbbdadacaccdcdbbaacacbacadabacbbcbbbabddaaaaaaabdccdbdbcacdccddadcddcbbaaddbacbbbabcaccacacabcaabcaacacbbcbdbdbacaaabbbadcadbdabaacdccacdbdaccdadacabdabdccbbbadcabcacadbdaababddadddadbdcbbcbbcddcdaaacdaacdbadcaaccdabcbdcdabddbdacdbdbcbcdadadbdbdbcdddbccadabcdacddcaacbbcaadbdcbddddadaacaacacacaccbbddcdbccaccaddcaccbcdabdddccacdabbbdadaabdcccbddcacbbbcbdbcbaaccbadbbdcccabdbdbacccbcaadacbabaccbbdcadabbcaacbaabababcdcbbcdaacdbbbbbdbddcbbdaccdbdccacabbdabcdcacbaaaabaabadbacdabcbabaadbcadacddcabdbdbaabcddbdcbaaccdcbbdcbcdddbbdcbcccacaadbdbccabadddaaabbbaccbcdddcbaadbcacdadcbaddcccabbaaddbdcbcbabcccdcccaccdcadbabadccbbbbbaadbcbcbbdacadcbccaacbbdddbbcbaadadabcbbbabaaddccdbbacabcaacbbbbdbabcdbaaacdcaacdcbbabaaabccbdbadbcaabaaacbccbabbacdbddbbbdddadbddbaddbcccddbdcdadadaadbdbdcacbabbbccbbacddbdccccbacccacbcabcbcbdddaacbbcbbaaddbbcacaabdcbbacaddcdccbdbbabbccdcdbbdcdbacbdadcdabddddcbdcdddbcbbdcdbbcdccbdccababdaddacbcdacdaabcdcbbdaabdcbccddbccdbdddcabbabcbabbaccbbcccbccccdadadabadacbadaaacabadaabcccaadcacadcaccadbdbbbadbbccacdcbbdacddbacacaacbbbabdcbcdaaaadcddcbccddcddbbcbabadaaadcadabcbccddcbcadddacbadcddbbdddbdddaccbdabdaacaadcbcbbbccaadbdbbaacaabaaababcbdcadaacdabacacdbbbbacbabddbaccbdcddccdaadbbddadccccddadbaadaddabbacbbacbadcccaabddbdabdccbbcbbccbbcdbacccaccaacacdaabbaabcbadbdcaddbdddbabbabcddabcbabcdcabddabaadbbddddddcacbbddccccdbcaadadadaaacdccdddcdbaadbacdcdccbaaadcddaaadccaadcbdaddccadbbdcabbadbaccdddabcbadbdcbaadcabdbbaccbccadcdcbacabadcbccbaadbdcbbddbaabdaacbbbbbaadcdbbabdabddddbdccdcbcadccdbdbabdaccabbaccbacdbadcdbdcbaadcbaaddbdbbbccbcbccddbccdaaddcdbbccacccbbaaacdccadabadacdddccadadbcccbccaddbcaaacbbcdababacddddacbaaadccaccacaabddddcaaddbbacbabacddcbbcbddacbcddadabcbacabdccdacddbbbdbcbdaccdcaacacdccaabcadcabdbddbbbdcdabdaccadcdccabdabbbaccababcbabdacacccadcbcadacbbcccddddddccbddccbcdbdcccabbcaaabdccdcbbacddbbcbcaadaddddbbadabcdbbddbbdbcadaacdacdacbbbdddacaacaacbacddaababddbbbabdbdaddaacbdacadcddaaddcbbccbabcabdbadaadbddcccaadabdcbbbacaabcdbcabdcccbbcccaadaadaacaadbbacdbddbbadaadadaddbddcdbcabbbacbcbdbcdcaddacdbcccbbadccadbccacbbdddabccaaddddbdcaaabbcabcbbcdcccbcbbbaaadabacaccccaadaadbbbccdbdaadbdacdbcbbccacbaccbbcbabccbbdabdbddbccdddcabadbdcaadacaccacabbbaccdbbbabaabcbacbddbacbdbbdbcbbccbdbbbaacbdcccbdabbcdaaadacbcccbbacddbbdbccaabbcbccaadadbdbcadbbcaddccdbacccddacacadabbbccadccdaddddccaacdadabdcadcadababbcaabcbaacabcbddadccdaddadbbadaccccccddbbbcdcdcdaaaddacbbcbabbdaccdbabcbbdcdcaabddcacdbaddbcbbababbcdacdadabddbabccbccbccdbaadcdbadbbadbdbbdbcaabdccbbcbdaddcdaacaddabbaaacbdaddacbadcbbcbbddbacbddaccbcdaaadacabdbcbdcbdcdcbbadcacaddaaddbbdddaaabcdccaacbcbaaaccdaddcbbdcbdadbcdacdcbabcdcdaacabacddbbcccbdbcabaaaddcbcabbadbacdbbcabdddcccabbbcaaacbbddcdcabadbdabbbdacacbabdbdccbdbbccdbacbbacbbaabbcdaacacabcbacabcabdbcbbabaccabdabdacabcdcaddcbddbddccbcdddacbaabccabdbdbcaaddaadbabbcacdcddbadabdcbacadaabdbaccacbbbdabbaabaaacaabcadbbcbdcbaddadbdabaabbacdadccbbaccbcdacabacbbadbdccababbaacbcbdadddabcbbddcbaadaaddbbddbaadabaccadacbdbcdacabdbbbcadaadccccbdccdbccadadbbdabdbbbdababcddcdacbabdadabccacddcabcbccaacdcddbacdcbdbdddacbaadcdabbcdbaddbcbacadddbddbbcdaaabadbdabbbacbcccacabdcabddacbcccacdccacabdabaaddadcdcbcbdcbddcdbbcabcddccbbaaabddbddacbbabdbdbbacdbdadaddadaaddddbdbbcdbcdcabbadbdcbaabaaabbaacbacdbaaabaaacacbcccdbdabbdbacddaadacdadbdbabdbbccadaccdbdbaadadcaabbccdbcadbcaacbabddcdadacbbdbcdcbbcaabbbbcdcabadaadccdacbcbcaacdcbdcdbaddacadadcadbbcaaaccaddaccddccbdcadcdbaaddbddbcacdadcadaddcbcbacbbcbbdbccddabadbacabcdadbbcaabcbddbdbcccaddcccaaccacddbcddbadcdabaccdcccabdaddccadbbcdcbbdabddbbcaccbbbdacddccbbdacaccaabdabacdbaadaddddbbbadacbaccdaadbccaadbaadbccadabdcabdbcaaacdddcbbddabbcadaacbacadcddabbdbdcabbbcddaaacdcacabbabcacddcbdcacbbaddbccbaaccdadaabccccbccbacadcccbdaacabccacbaabcdccdcbbcacbbbbccbdacddddabddbcbabdddcbdbdacabdbbbcbbcdcdcddbbdbddcccbdddbacdccbaadcbdaadaddbadaddccdbdacdbbabcbddcbabcbaccbccabdcbcacdcccbacaaccadcacbccabbddcdaaabbaddaaadcbdccddcccaacdcddabbbcbadcaaacabbdbbcaadcddcbbcddbadacddcbababadbabddacadacbcadaabcbcacacbababbcabadaddadccbbacacabbddabcbacabaacdcbcddadaadaacbdcbbdabddacddabacaddabddbcdabcccbacacbcacdaccbbdddabaaabdcdddddbdbccaaacabdbbbddcbadabbcdaadbddcdbcccbadcaaccacadbbddbbccabdadddaccbacccadadcdcdcadacddcabccbcbabcccbbadbaddadbabbbdabaabadbdcacbaadcbdbddcbdadcabddcacaabcabdbaaabadabbabcbdadddadbcbabcdbdacbccdddcdbbaacddddaaddcacaccadbcdcdbccdbcdabaacbbddcacbccacbdadbdcadadbcdcabddacdaababcccacaacacdabbcbbddddbdacacdacaabbaacacacdcadbbbdbbacbaacccdbcbadbaddcdbbacddbdddddacbacaadbdbaacdbaccbdaacaccabdbabbcadcbdbadabdcabbbdcccbadabbacabaccdabdcdabbacdcbdacdacacadbacdaaaabdabdcdbbdcabcbdaaacdcbcddcadcdabcadddaaabcddcccaabccaddacdcdccbbaddaacbbcbabbcbbdddcbdcccdbdcdbbdbbaddbadccdababdacabccaaacbbbbcbaddcababbbddcacadbadacdacbdaaaadbabcddaccbdabddddbabaadcbacabadacbcdbbbaadcddcdacccdcaababcabdaacabddacddbcaddadaadccddcaaabcdadadbbdaabaacacdbcddacbdcaaabbbcddbdbdcbabbdccdbdcdadddcddbbcaaabcbcbbcaabdbbabdadaabcaaaadcbbaccccadbdabaddacabdcbccaccdbbdcbddbcadadccabcbbaccbdcbccdddaaddaabaadcaadbbbdbabdacbacabcbcdcbabddcccbdbabcadbbcacbbdccbaadbbcbbbabbbadbabdbddbdcdcbdbcadddbadcdacdaabdccdabbdbbacabdcbdbccbadaabbcbacadaadccaaadbadcaddbcccadaacbcabccdabcccbcdcdabbcaddacccdcabaadcddbdcbaddcdccbdddbabcbcddbbbbdbbadaabdcbccbbccacdbbccaadbbaacdcbdccdaadcbcbcbddbcbbabcaccddbcabcaddbdcadaaadbcbbdcbdddaadadcbcadbabcdccbabbccadaddbaadacbddadbbdcbbdabcdcbbaddcbbcdaacaabddddccbddccaaddabbcdbccdcccaadbdadaabadcaadbacbaabcabacbadbdcadbdbabdbdcbbdaabaccdabcbdcdbddbabccdadadbabddabbbabbadcdaabcbbccddbaaaccdddbdabacbdadbcaabacccdcbccbcdbcbcbbcbcbacadabbddaacbadbcbcbbabbaddddabbbcdcacabdacdaabcdcbabbbaabaacddcbabcacbdbdcccadcbcaddddddddcadaacacacdcdcddbdbbdcdcdcabdbcaacadddbcdabadcbadbacabacccbaaacaabacadbdadadddddcadbcbaaabbdcdacbdbadbdccbaccccddaddbccabcaabbadabcbbdcbcddabcbcccadabccdadddbaacacbadcbdaaabbdbcaaaaabdadaadccdbccaaaddcacbccbcdcadacdabbdbbcdbadcbdbdccacdcaabbcdadbdbdcdababbaacbadcbcbbccdbbbacbbaaadcdacbbbccabdbcbacdabbadcabdaabcdacccdbaadbacadacaaddcbccadccdbbabcbabacbdacaabacbdacddbcbdaacbaacabbbcdbbaaacacbadbabaaaacddacbbbccabdaddabdbccadddcaacacddbabaabcdbabdadacdabacdcbbbdadbabcbbbcabcbccbcaabbccdadcaabdcadbbdaaaabcbdcbddbdabdadccddbccccbcacbdcadabccdbadcbdaaccbcbcbcddddcaaabcbdcdbadbcbbdcbbddbbddbdaadcdbcbccaccbabaacccdcbdcdacabadacbcccbdcdaddacbccaacbdaaddcbcaadbccbdadbdccbadaaabccdadbadddabddcbadbbadbadadadcaaccaadddcdbdabdacbbcdbbbbcbdbbcddbaccccbdcbaaccbcdccacddaadaccdcdadabcbdbbaacaddabcbdbacaccbdaddddadddaadbcacaaaaaddcdbddabbacddbbbbdbbdbbacdbcbdaadacabdadcdcdcdbcdacdabbbdbcabcbbadbccddccdababcadcdacdcadccddabdaddbddacbcacbccabcdcdadadbacbcdddaaacbccdaacbbacdbadbadcdbdaddadabcccbcdbddbbadddacbaaabdadbcbaacbdbdbbcccdcabcabbbccdcadbdddadddbbbbcbdcbbacacbdaabbcbccadddadbcadcdadbdaadbcaddaaadcacdacabcadbaddacbcccbccacdbcddcabdbcbdadbbccbbabcbabddbbaadaacadaadaabbccbccaccacadabaccbdadcddccabcdacacaaababbdcaaaacbdacaacddbccccadacdbbacbdcaadddcbcbbdacabbbbdbccabddcabccbcabadcbdbcbabcdddabbcbdcdbaabdbccdbddabbadbdacdcccddbaadabdbdcddccdcdadbccccaaaaccabcbbaccbccacacadaddbcdddbbdaadbcacbaddbabddcabaaddcbaccdabbdabcdddcccbdaacdbbbcbcdabaabbdbddbddbddbacadbbbbcddcbabcdccdccdcdbadababacdbdabccddcbbdbbddccdccbcccdcabbacddbadabbadbcbdaabbccbcaadaadcddbadccccacbaadbdaddaddbcacdbdcaccddcaaaabdcabdadaccdcdcaaaddacdbbbacdddbbcdddcbccccadcabccbcdacdacaacacccbabdadcbbdbcbbccdaaabacdabbbbddbcaddaadcacdadacccdbccabbccddaacdadcbddccbcccadacbcdbadddcddacdccdcdbdbadbbbaddbbbacdacdadaaaddbdabcaabcabaccccbcbbacdababcbcadcaabbdcddbbcaddbbbbcaccbdcaccbacaacbcddcccdbbbacbaaccbcccbbabddabbbacdabdcdcdbadcdbbabdbcdbabbadcbddcccbcdaacdbccadddbadabdbbbaacaadcaababbcacbbaccdcbddcdbdbadbabacabaccdaaadbbbcacbadcdbdacbcbbcbdcbdaacbbdaddcddbabadbabcbddcdcaaadadcdaddbbdbdcdaadabdbbcbddaaadcdccdddddddcdbaccccdddaaccdccadaaabdadcaddcdbbbccbaddbcaadbbbdabbcdcaaccabbaaddabcdaabbcddaabbbbcadbadabcddbaccdbbbacabdbabbacaabaccabdcbabbacacadcdadaaacaaacaadadacacccdaddbdcadddacabbaddbbcdabcddaccbcdaaccaabcbbadcdcaaccdacacbcabaddaccbccbbccbbaaaaacccdaadccccdcbcbacdbabcdbbabddcababbdbddccabaadccdccbdbbabaddabaabbcbcbabcbbacddcaacacacacadabcbdbdbaaaaadaacccadbcdbdbdccddcacccbbdadadccddbddbcbaadcabcbdcbbadcadadcacdacbcddccabdabacbcadbccdadadccbccbbbdabdbbcddadccbdadcdcdddcaaacdbdcccdccaccaaacddbddcdbcbcddcddaabdbacacabbdcadddcbadbacbabaadbdbcdbadcbdbbdbdabdccacdaadcadbaccabbbcdbdabbbaccdacbddaabddaddcbbccbbcbbccaaccaccacdcacdcbddacdcdbdaadacbaacaabcccdbcddadcbcacabddbbcdcdcccbdadadaaabcacdddbadaabbdbdbaabbaccababcaabaaaaaddddbadabcaadcaadcdbbbcdccbddbbdbabbccbaacaaacbdccaaadcbbadbabcdbccadacbaccdbdaacdcadaaccbbcccccaaccacbbacdddbbcaabdaccdadbbbbdcacadaaddcbbdddcabaccdddabcdcdacdbccdcabdcadcbaddbbaaabcaadcaadcbdacbbdacaadabaadbddabdabcbdcdabbcddbaadaaacaadcacabcabbdcbbaabccbaddbdcbcccdadbbaabacbbacadbdcbacccbadcddcdaabaacdcdbbdcbaddbbabababdbbdcdddcbcdbbccacdacaabdddccaaabcaccdbaddcbaacaaccccadcabddacbbcaccbbddbcbcdccdbdbadddcaaaadcdddabcbacadbdcbdbcdccbbdcadcadcddbcdadbbaacadcbddaacdbbacdcddcbabcdcaddbdaaaddbddbabdcbdaacbdccbdadcbbccacddabcbaaddcabccabadccacbcabcbaacdbcbabbbaabbcddaadadabdcdbbbaaabccaadbbbabdbbbbacddaadadcdbbbbddcbbabcacabcbabaddccabacaaadccbbdadaccdcabaacdcdbbddadcdbbdacbcacaabccbabaddababaaacdababacadccbddbaacbddacbcbddbbdccdabaaddbcbbbdcbcbcaccdbdbabcccccdacababacbadcaabcddbdcadcacbabdcacaccbaaccaadaddacaadababcbbdcdcddbadcddadaadbddccabddbbabcdcbdbaabbccabaddbcaddacabbbcbdcddbcccddcbcbaabbccacbcbabdbbaacdcddabdbbacabcacddbadbdbadadcccbbbcccabddccbccbccdaddcbdcbddbbbcbcbcddcaadbbbccdbdcaabbabdddcdccdadaccbbbbbcdccbcbbdaaadaadcbadacdbcdbdadcccabdcbaabacaababddccdcaadbcadccccacbbcbbadabbccbdddcccacaaacddbacbdbbaddddbcdbcddaccbcaabbabddbdbccdaacaddcabdaccaadddccbabcccaadbaadcccaccbdcacacbbacdadacacccadaaadacbacccddcadaddbcccdcabadacbbacbaddabdaddcdaddcdabdabbbccaddbccccddaadababdacdccbdcbabcaddcacddacaccdbacdcdaadcbdacdaccdabccbbdcdbdcbaabcaccabdbaaadcaaaaabbbbcdcaadbaadcbcddaabbadaacbacdacbcdadaabbddabddabdbbacdacaacabbcaddbbcadbbbbccdbcdcbadcbdbbaadbcddbdabaacdbbdbdabdadacccadcdbbccdcbbdddbdacbdcdcddcabcacacccadbcdcdbadcbbadabcbdbdabbdacabddacadbbdadbabdcddadcaaaaddcabaaccdaacbacbdbbdbcddaabcdbbcdababbcdaadcaccdbcddbcbcacdddddabaabccaaadcaacdbcbdbbddcaccaabccbaadadbbbccbdcbbababcbbadcaddbbdabcacddbdaaddddbdbcccaddcacccccaaadcacaaabababcadaaacdabddbbcaacdacdbabbcdcadcdaadacaadcaabcbbbcdbabcabcdcddaaadbabccbdcaaabccbdbbdbddcbccaaccbabdadaccaadabbddbcdabddbdcbdbaabbacabbacdcbdbccccbbbcdcdccaabbbdcababbddbacbbcacbcadaddbaacabccbbdbddbddcdcbcabbcabacabaccabcbaadddbcccbbcbbddcaaaaccabdddcdcdbdabbdacbadbbbabcacacacdbbbdbdaddabcdacdaadbdadbddccabadaaddcaadaaaccacddbaaacbdbcddcadadcdaadbbdcabdbdcccadbbbcdaaadbdbcdbcdacbabcbacccbacddacadbadcaccddabbddaccddcacaccccbdacaaacaaddaccdbcaccacbccbbddcbcadcadacbbdcabbbbacabbddadcbdcddaddaabbbbdbbbcadbdbacbccadbaaabaaccabbccbbacdaaccadcbbdadadbcbacabccadadddcdcbdaccabccadbdbdcaddadbddcbdcaadadcbdaccccbbcbcaaaaadaddaacdbddadbbcbcdbabddbbcdbddacacdbacacacbabaadacadacbadadbcdbccbccddbbbcabcccdcbaddbaabbadadaacbbabbacaacbdddadaadadaacddcbdccbcdbcacccdcadababdcacdccccbdacaddabacbdbcaacbbccbdbaadadcdcdbcccabbaabcddaaaddbbabbaabdcbbccccacdccddadabccbcdbbacbacabbcdddbbbcacdadaaccbabdbdcbbaddbccadddbdcccababcddbddbdaadbbabdabadcaaaacbcbdaccbcabdbcbbaccadcdabddaacacdaddaaccadcddcaccdbccdcbcaaacdcbcbacadabacccadddcdccbadcabdacdbabbbaaabbcdcabbabcbbdcddbaccdbaaacbdaacdddacbcadbabdbddbcbcdaacabcccabaddcadddcddbabadabdcdcddbaacdabaadaccbdbcacbddbcdaabddcaabdbdbcbcacadaacacabdcbddcdadcbcdbbdddddddacabdbbdbbdbdddaabcbbdcadaaaccbaadbacaabacadaaccdacbcccbdababbadcccabdaacbcdaccbadbcdcbbdaabaacdbbbbbcaadcabaacaddaaadcacacabddcdddccabbdabbaaccbcbdabdbdaaccbbddadddbdbcdcdadddbbaddbadbbcabaaddbadcccbcdbcbaddacdcbddacabbacabdbdcacbaccdbbaadacbbddcccdcacbdccddbbbaacadabbdadcdccaccbddbabddabccdcdbadcbbbcdcbdaabbaaaccdadbabadbabcbddddcdcdcbcaaaddddddbcdcdbabbbbbaacddddacdbbdddcdcdcbdbababddcdaaacbbaddaabdcbdccccdddcccbadcbbcdadcccadacabbcaaadabdaabdaabbabcbccabcdddabbbbdacbdcdbccdcdbacdddcaddaddccadaacdbbbbcccbdbcbbcbcbdabcbccacdbacaadaddabccdcbddcdcbabbcbbdaaaabbcaabaabddbbcddcdddcbbbcdaacdadadcdcdacdccdaddbabccddacbbaaddcdbdcaacdcbbbdabdaccabacbaaaccaccbcbdddccdcabacaabcbcbcadcbdcdcdbdaaaaabdabaadbacbdaddcdbacaddcdabcdbccabdbcddbdccabbdacdbdbcbcadbcbdabbaabbaaabadbcbddbdaccdcbcabadddaacabddabdbacadcdbaddcdaaaccadbabcbabbabbdbddddbddbacbddbaaacdacaccbdbdddbadacbbdcbdddbbccacdadadaabbabddaadabbccbdcaccccbbcccaccbdcbcdcddbdcbbcdbbabadacabcddbcabcdbaaddccdabddcbbdabbbdaaacabaabcdaddcaadaabacaabdccddcaddcdadcbabdcbdbcdccabcadbdbaddccaabccccbaacaacdabaccabcdcbadabbcdaabdaacccccdccadccaaabdcacababcdaacdacbaaaccccbacbdddbabacaadaaacbbddabaaacadcdccaabdcbbabbcbbdcdcabdaddbabcacdadcbcbcdcadcbbccabbdccbcaaabdbcacbbbdadacccacababdccabcaabdcabddcacccddbaadbdbcdabdbcbdcbccbbbcaadcbbcbbabaacbadacaabadccbbabccddacbbbbbbbaaaccacbbdababdbbccbbbdbadccdabdacdcdbabcadaadcadccdaadaadacddaddbcadacbbbcbbdababddddcccddcccbaacbbccdccdcaacdbdbbbadcdddadcbaadcdcacacdcccbdabbabccccbdbcbaddaaaacdaccacdbbaccacadcdadbdbbdacbacdbbaaacaccacdcddccaddbbaacdcccbccabbbbcadabaddbcacdcddcacadcadacbcddadabacddaaddbacacaddddbaccbdaadbddcbcbddcaaaadcacadabcdabaaacbadaddcddbacdccacbdcbaccbbabbcccbcdbdcbabdcaadcbbdccabdaacbbaddaccacdccbaadacdaadabbbcbddbbcddaacabdbccbcaadbcadacdddddcdbabdcbdbacbccbcacddccdcbddaacacababbabccbcbabddddbaaabdddacdbaabdbcdbdbacbaccdaaabccadcbdcdabdddabbacbbacaaddbddccdabaaddaaaacabaaadbbbbdddaccbabcaccdbbdcabbabbaaaccccdabcaacadbbaccbadbdadaabdccccddbbaccadabbcaabbbacaacddadddcbdabaddcbadcbcbbdbdbaadccccbcbdcbbabcdaddcccddcaaddddddcdababddcddcbcddbbbddbcbababadbabbcdabaaaacdbadacdaddcacddccdadbdbadacdddaaacaaabccbacbdcadbdcabacadcbbdaccabacadbbdbddbdaaccdccbcdacddaabddabacbdcddbdddaaabdadabaabbdadbddbdcdbcbdaaacbdadbadcabddbbdcdbdbadbbccccdbcacbaccaabdddbdacdbbaddcbcccdbdccabbcdadddbddbacaabcbaccadabdcdaccccdbbddbbaaccbbaacbaaaccbacbcacbababcdcacadbcdabaabadababdddbccdacdbdbbcccaccaddaddcaadaccbbdcbccabbaacbdcbadbaababccdcbdbddabacdacabbddadcdbcaaadbcddcaabdabbadacbbbbdaacabdbaacdddbdccacdaccabbbadacbdcdaacaccabbbddcbdddacadbbdcdcbbdbadbbabaddbbddccbbacdacbdddabcbabcabccabcccdcddbddbaadcccadbabcbddcbbdaabdcbaabcbbbddbcdbdddcbadbbccbdbdbdbbaddbdcaabbabddadbbccadbddacbbdaddcbbaaabbcbdaddabacadbadacdaccbacbbacacbbbadbadccccdacdcbbbaccdaccabaaababdababbcbdaacbcaacadccabbcdbdbabacbaabcbcddaacbccbcbddbadaadcabbabbcdbdcabcabddcbddbaadbaaacdbcdbaadcdbcacbdbdabcaddacacddbdaaacbaccaadbbdddcdbbbcbbddbaadaaddbcdccdbbcdccabdadcbdbcaccdcdcabaadaacdacadbbbdbcacbaddabdcdcdbacaabdabaaaabcbabddcabacadbaabddadbcdacadbadcdbacacacccacadcbcddbddddbaacbccbabaabadcbbcbcbdaadabddbdadadddbabbddddddcbdaacadcadaabbdcdddaacaccbcbcdbabbdaabcbddbbdcadbacccbddaccadcacabbbaddababddbbcbcdaacaadabbccbdaddaccbdcccbbaddcbaaddacbaaaabccbcdddbcccdccdccadaddbcadbcbabbabdcdaadabcdacacccaacadabdcbaaaaccacdbadabddbcacdcdbddaaaaacaaaacddccdabdbdbbdbcccadadadacdbdbbdbabdbbcbcadbdcacacdadadacdbcbbbcdaadaabdbbccbcbbbbdcbdbadbadbbdcacdbdcacbbbccdabccabababadddbddcabbdccabbdcccdcaabcbadcbbabadbbddddbcadcabcacacacacccbbdbacdccbaccaacdcaddcdcbdcddacdcdacaddaacdcabaabcaacadadccdadcadadcacbddccccbbabdaaddabcabaaaadbcdcccddaabaddabbcbadabddcbabdabaabbddacdadcdbcccabdbbababdbdaccdbbccacdabcacbddaaaddbbbcbdbdadddcabbbdcabbbdcaddcdaaadaddacacadbccdaadbbdbbccabdbcbddbdbcbbcadabaaacccaddaaacbaadacbcaccacbcdaababdaacdccbbbcddabdccaddcbcaccacaddadcbaabcbcdaabbdbbabbdddbcacbbcbdadddacdababbccacaaddaaddddbddcbacbaadaabdbbdaddaadabaaccbccadcbbdbbcbdbbcacbddabdbbbdcacaacdadbcabddaadccccbcadbdbbacccdadbccbccbadbcddcdacbbacdbadbdcddabdadbdcbcabbbddcbacddcddbdaddbbddcadbbddbdcdccbacbaaadcdaabbabbdbaddcabdabcddcdbccdacccddcccababdabccdcacabccaddcccabababbbdadcccaccaababbdcbacbcabdadacbaadbcaccabcaadcdddaaadbaccaadcaddbdbabbbcdbaacdabdaabddcbbccbdcbbbadbcaccbbbcadbdbccadbaabcdbbdacbccbcdcdabbcbccbbcdbdbcbbaabaacacacbaddbbaabdcccacdddbcadccaacdbaacaaadbdcdbdacdcadddcbbbbcddabcbdddcdcacdcdbbcacbcacabddbbabdbbbabcccccdbbbaadcbacbddabbcdadccdcbadbcadcdacbaaaadddbababbcaccdcbcdaabdacdbccbdabaaacbdddaddbddadcbbcbccbdcacccadddbadaaaaddbcbbdaccbaabdaddcddbadddabccacdcddbbcaccabcbabbbbaaddababadbcdcabdcdacabaccbaacacdbdbadaabcabccbdbbccbccbbabccacccaacbcbcbabcbaadbbddacaaacdacaaaddcbcdacdadaaaadcbcdabdbadacabcabdcacbddaaddacaccccbbcaabcdbcbaabcaddcbadacdcacccadadcddbaacdcdbccdabdaaaabbcabcccbdbbbbdcddcadadcdcbbdabddccbadaadaaddacdbabdcaccdadbbcacaaadbbaddbccdcdbadaaaddddddbcdcccccabdbbacbbdccbacbbcdcdaabbcccabdccdacdacacadcacbbddccbaddbccdcdcacddbdbdccabacbccddbcddaddcdabaccabcbbdcabaaaaabddadabbddadbbcaabbdaadacccbbdbbbbaccbdaababbbaadbcdacdcdabdddacccdddcabcadcdbcdaaccdacacddbddbdacacdaacccbcbacdbbdcddbbaddddbdacdadaddabdaccdcbdbabaababacdccdddddbbacabbbcabdcbbcccbcbdcaabddabcbccbadcacaccdacbccabcbdccbbaadcabacadbadcdcaccbddbbccadddcbbaacabacdbbbdbdabbbdcadcbcdbccdddcdddcddcddbaadbbcdcccabdcbccbddbababcccdabbaadddaadabbcccbbcadcaccdbadabdabdbbbdadbcadababadbddaadbbdadadacdadaddcaadbcbacacbddbabaabbaacbddcbcbaddabdcdcbbcddaadbacdadbdaddccaaaaacbaaccbdabdbbdabaabdccdbbababacdcaaacdaddcaccdbcdbaabaaddccababadacaaabcdadbbbbadadcbcddacababaddbccadbddcdbbadcbaabdcbbbcddabbddcdaacdbbdabcadaaadaabcadbacdcddabdcbacdadbababcbbdccbacbbdaabcaadddccddcdccddddbcabcddadaaaabdaadbbdbaaacdccdbdabadddcbadabdbcbbcccbcacccddccaaababacbcadcdcadddbabbccabdbaacccbdacbccbbaadddddddaadaccccbcaaccbcbbbddacdababddbdcaabadaabcaddcaadaabbcdbbdacabddbbdcdaddaadcacaabdaaaaddcddbccdaccaccadcbdbacadaabacaadcdcacbdbdabdcbaaddbbcddacaadaccdbcdccdaccbccbbbaadbbbddbccbdbdacbbdbdcbbcaadbbbadaabdbadadadbbdccdddadbdabadddcddcccdaccdadccbddbcadbbdadadcbacdabbacabaabdbbabdbcacdadbcdddcababcddbbcacdbdaddbabcbcbaabdabdddccabadacdddaacbbbdbddacdcbbccdcaaddcdcdcbbbcbbdbabbccdbacdddbdbdbabcbabbdadccddbbbaddcbbddcadabcaacdbaacadbcbdbaddcddadacccabcdaabddbbadddbbbbcddbbcddcbacdddaacaacdcdcdcbabacbabbdabddadcaccacdbadacbccdcbbcbabbbbcadacbdacabcaaccdbabdddabbdabcbdcbdbaaccbdaabdbddddbbadcaccbcacbbddcbddcaaacdaaaccabbdbcdacbccbbaaababacbcabddaccbbdabbcdcaabbbababbbccdadcdabbdaaabbddcdbddcaaaacbddabbdcacaddabccdcbacdcdddcdacabdabadaabcdbadccddbccbccabdbbacdcbbbaadddabbcdcddacccbbbadabdacacddcddbbcbaccccbcaccacaadaccaddbcadbddcdccdbdcacddacdbbbabbdddcdcdacbbcaddbdaccdaaaacbabdaadbdaaadbbdcbadaccddccaaadbabcccbdaababcccdddcacbadbdbbddccdadcbddcddbdaacabdbdcdbdcdabbdaaabcabccdaaddaaacbccadbacbbdadcbabddabccaacdcadbccacaaadbbccddacbdddadbacdcdcabaabcadddcddababaccdacccbcccbddcdcdbaadccadaabbcdcdadbbadcbaacdccadcbcdacbdacbaaacaabdbbcdcadaaaddacbaccdcadaddcaaacabcdabdacaaccbabccdcdadbdbbdcccadcddaacbdbddaadacbdbcbadbbdcaccdaabbdcaabbcbbcbdabbadbdccabadabcbbcbcdaaacacabaabcbabbdcbbdbaccaacabccbcabbcbaadbaddadccaddabadcdbbaadcbdacaccacdbddaabbddbaaacccaabadbabbbddcbcdbbddabaaccbdbdcabbcddcddaabdbaabbdbdabaddacaadadccdbcabcacabcacdcadabbccadbacacaabbdbcacbbbcbdbdbbcabdcabbdacddbcadbcacdcddacaadccbcbddcaacbcccbdbccbddcdbccadbcddbbdabdcdaaaabcacccacbbadbcabdcbbcaccadbadbacdadcdcbacadcabbbbccacddcdacaadadccadaabccbdccabdaddccbabdbacdcaaccddacababdcccbddaabcbdddcdaadbbcdcadbbddbddbbcbbacdadcbacbbabaaadaadacdbbbdbddccbdcaddcbcacbadbdcbcdcdbbcaddaacbbcdaacdbcbdddcccabcbdabccbbbaccbdccbddcadbaabaccabdadbddcadaacbcaddbdbddcccdadcaaddccacddbaacabdcccadcabbadacddbadbaaddbbaaabcacaabacaccbcdddcadcddbccbbadbbbababadacdbdbbacacacaabcabbcaaacdcabdbcdaacabaadaabbdcbddbcbccbdbdbbcddbabbbddaaabaabacaacacdaacdaabbadacabcbcccbccdbcbbddaacdddbbccdacaaabdbcddcaaabdadaaccbccbabadabddbdbdabcabbabbccccacbbabbcdbcbbabacdacbcdaddacbdcdbaddccccacaadbcdddbcbbacddcbcccdacaadadddcaacacdabbccbacdcdbdaacdcacdcbabbdbacddadcddddaacccacbdadddcadaaddcabadddaadcbaadbdaaadaabbdacdbcbccdcacaacaaabddabbbacddcbddcadcbaddcbacabbacbcadadacadcdabbadcaacababcdaccbbbbdbddbdaccdbabbbabddadbaacaacddcadccdaabbcabcacdcddaabbadcbdaabaaadbbbcbbbdccdbcdcdcbdbdaadbcbbbbdbaacdbccbbdbbcdbacabadbdabdcadcbaaabdcbcddadbbaabadbbcadadaacddbdbdaaadbdccdabcdbdbacbaadcddbbdbbbddccbcbcacacddbbbacddadcbdaccdddbddaabdaadaaacdbdaadbacbdacaaddcdcdbdbcbcaaabbbbbdbaabcbcbbbdaacbacbbddaadcabdbccdacbabbaaabcadabadcbabcabbdabcccbaccbccddcacabcaddbaaacacbbbccadccdaadddbdacdbdacbcbabaaddaccdbbadacbbccabacddabadaadaabdaddadccbccaccccccdbbbdcdcdbacdbcbdaaccacdcadccaccbbbdcabcbbddbdbbbdaacbbbaabbdccaaabccaaaaccccbdaccccaaaabadcadbdbaabbbcbadbadcabaadacbbcbacdacbbcbccacaccaabddcdddbabacaaacbaacbcdbddbccccbabcdbbacdcdbababcccbcaadadbbaabadcdaabacbbddcbbcbacccbdadbbbbbcacddadbadadcbbacacdcacacddcdcdbdacaddabaaabbccaadabaaabcaaadddbccbbadabdadabcaccbcbabcbccacabdccdaaaaabdbbcbbdcbccbddadabbccbbacbcdaababbccacdaadabcdacaabcbabcbdcdccccbccabdcdaaddcdbdbdacbacdabdbdaacaadadaadcddabbbcdabdbbccbdacbdacadadcbabadcdbabadacbbdaddbcddcdcadbdcbdcaadbadddddbbcbabacaacaddbabccbcaacbabdaaadacddacdadcbdbacddcadaddbbcdaddcadaacdadcdbdabbbbabacacaacbcdbdacdcdcabadacdacacccbbddcdbccbcadcdbdaacbbacaaabddbbbadbabdbcdccaaddabdaacbdaddcabdabdbdaaabdcaddacccabdbbbddcacdcccadbcbabcccbcabbcadccdcabaaacbdadbbcacdadbabcabaaadcacbcdbadacbaabcbbbcaccbcaadcddbbbcbbdcbaccdcddabdaddcbdadccbbbddcccdbdddcccacabbbdbcacdadbbdaadddaccacbbdbcbdcbabadaadcdddabaaadcabcccabbbbbbdadbcbbaccabdcdbdcbdadbbdcbacabdddbbcadcbcbabbdabaccbcacacacbadcbbcaddccabcbdddbaabbddcaadabaabcadaaaccaadcbaaaabbddbcccbddcbcdcdabbbbbcacdadbbccbbbbbadaaabadbbaabdcbabccbddacbddcbdcdabccacbdbccddaccdbdbaaabaaaaabadcccccccabbdbbcadabbcdbbcddbcbbccdcdbacabdbabdbbcacccbdcbcbcdacdadbdddabadcbacacdbbbbbcdaccbdbbcdcacbdcadbbbcccdccbbaaadadaccbddcaadadbcbbcabdbcbbddbdcbaaccdcaadaaabbcdbbdbdbdacbbdabdcaacbacabaaddddbddcbdcbdbdbdddcddcabbbdacccbacbbdbbdadcbbadaccbcacbbdddcabcbaadcabcabaaccddbcacbbabdaacdadcbdacaccdcbbbadbdbddcbbbbacbbdadbcccbbcdaadaadaaccdbbcbbbacccbdccabccdddacdababadaccccbdacdaaacbcdcdabdcdbadbccadbbdaccccabbcdadccbbbaacbdaaccbbddcbabacacadbbcdaadabadcabdbacdcacbccbddddddcacbbcbcbcabdbcaacbbdcbbcbdbadcaabcadccbaaabddcdabcbacbaabbcacacdadcadbcaccbdaabcabadbcbbaaadacccdcabdacaabdbdabddaccbdacdccccccddcabcabcddbacdaadbdbdcabbdddcccaaadcdabadcbacbbbaddcbcbaaacccadbadaccaabadbacdbcbaaaacacacddbbdacacadcabaacabdcdddcdaadddabbbbbdadbcbabaadbaaadaabbdbcbabadaccdbbabdaaacbacdbabdacbdaaacdbaadddbdbbbdcadadcbbacacdccabbbacdadbdcccaddaabacbbcabcccabcbadbacbabaabdacacddddabcbababbcccddddcbbacdbbadadaabbabdaababacdddabccabadadacdccccabaabcaccdacadcabddccbcabdadbabcadcbdcbbbadccbccbdbbacccaaaabccdbccccbbddbbccccaadcbcaabbabcaadbbcdaabbacacccaddbdbcabaccbbadcadcbcacbabaabcbcaaaaadccbabbbaabddcddcccdbccbbccdccdbabbddacccbcbadbdbdccddcccccbbadbbabbdddabbdaaccaccbadcaddcbcaccbbbddbaaddddbbbccacdaaabacdaabcacbdabdcccaaddcabcdccbbaaccabbdaccdbccbbadabacaaccbbabaabcaaabdbdbadbdacdbdbbcdabbbdcacbdadcdaabbaddbbdbaaddaccbabbbbbbcbcbabcadbcadabbddddbbbbdcbaababccaddbdcaaaccccddcbbdbcbcbaacdcabcaacbacccccccbddbdadadbcadbabddbbdacbdaacbddbadadddbadcbcbddcbbdbcccdddabccbbccabdcdadabdaddacbdadbbdcccacbdbcdabbddbbabccdbcddcdcbcbbbcabcbdaabbcddbabcbcdbaacbccadcdadcbdaddaadccbdbabaaacbabdaaccaaccbabcccaadccabaccbabdacccbccaaaccdccaacababccacbcaadcbcdcccabbdccabdabdbcccbbcdbbccbbddacacdcabdbabcbccbcdbabbabdcdabbcaabdaacdaccbcdccdcbdcaccadadcbaaaacbdabdadabdacbaadaabaaddabcccddcccbdddcddddcbddcccdadccbdcadaacaacbccaacbcbcdabdcbabccbbdbdbaddbbdbccabcdcacbacdddcdcdadbbacbccacdaaabcaabacabaaddacbacacbdbcccdabdccccdccdcdcddacbbdabcbccacdbacbccbadacccdabcbdcdccabcadbadcbccaadbdbdddccccbaaacadadbcaabbabcdabcbabadddcbaadaddabbddccbcbccbacdadddacdabababacbbacdbadcbdbddadcbdadcbcdaaadbcabbccccbabdbddbacbbaaaddbbdcdbccbdbadcbdaababccabdbbacadcbbbaaaabcbddcbcacdabadacdcabdabcbdadbccbbdcacabaadbdaacbbaabaccdaabbcbadddadbdcddbaabbbbbcabcbadcbbabbbcdaadbbdabbbbadbbacabacdcbbbaddddacbbdcbcaccddabbdaadbbbcbbabccdcbccabaddaacdabbbabdaadbcaabaddabccddbcccaabbddbcdbdbdacbdaabaddabbcdacdcadabdaddcaaaabdcbaaabcabbdcbadcdacccbbbcdbacdacddaacdadadcbdbbadaaadcbbbadbdcbbabcccdabcdbbccdcbabdbcccacacabaacccbcaddaabacbbcbacabaccdadabacdbcabdadcccdaccbbdabacccaddccdbaabacdcbaaccddddcdbaadcbbdacbccbaccbaadacccddaabbbdcaccbccdcbddbdccbddbcbaaacbadcaacabadaabcaccbccdbbababbcdddcbcadbcdccbcabdcbdddadaaccbbaaadcdbbadcacaddacdddadcddbbbdcabaacbbdaddcaccdadcdabcbcdaabdaddbcacbccacbcacdababcdddcdcabddbdacbdabbbdbaadcbaacbbbacdbcdddbadbadbdabdbaaddcababcdcdcbaaadbbcbdaabaaaabbaaaaaabcaddcdcbdabccbaacbccccdcacbdcdbbbcbcbbdcbaccaacbcaadcbacddaccbcddacaaadaacdbdadbcababcdaacaddcdcacadabbaadcaaabaacbaaccababddbbccaaadbbaadadadcddabbbcbbbdcacccadaccbdcdcdcccacdaadcdddbdabccadbdaaddcccdacdacbadacabcadcaccddcdbccaccdbbbdacdbdadbbccccbdccbabdbadacdbddaaadaabcacadcbcabaabaaddadacabcdadccddaabadbcdaaddcabaaacaadaadadcdabdcbcdbacdbabdaaabcddddacbdabbabdaccbaadacdabaadaddabbdaacddcacdbbbcbbccdcababbccaaaccdcdacccdcabddcaaacadaccccdcbaacaaadbdcbdaabdbabdbacacacaaadcbdccddbdcbaabdbbababcdbaadabbddaabacbbbbbccaabdbbccbbdadacadcbaaacbbccccbddcbaddcbddaabbbdddbcdacadcdbaddbcdcbcacbdcdaacdccabaadcadcaabbcabcacacaacaadbdacbaaacdcbcaadabccbdddcdbacaacbabaacaabcbcaadccacbbcdaacbcddbccdbcbbadaccabccdcbcadcbbdadcabbcbbaddabccaccbbabdbabaabbcbbabdabbddbadddcbddabbdcdaaaaaadaacadcdbabadbccbbbbbcbbbabddbdcddbdbcabcabbcbbaddcdbaddaddcabaaddbadbddccdccdcbbcbdacaadcbaabdcccbacbbadaabaabdbaacbadccaddbbaaabcbaadbcccdbaaddbbadcccccbababccabdcaddddbdbccadaccbbabcdaabcddccccdacccabadbbdbaccaadbdbdbaddacabacacbbcbcbcbabccbbdcdaacbbddacacbdaddbdbcdaacdcdbddcbddbdddaacbccadbdababcdcaccaddcaccaddabdbbadaabbacdacbdadadabadbdabddddadcaddabbbddbdabdcddcbbdcbdcddaaadcdcabcdaabbbbbcbbdbccabcaddbdadacdbbbbbcbadaddccbbbbaddbbadbbadbdabcabbcdddcdcddccdacadbccddaaacbdcdbdcddacdcccccadddabacccacdabbddddcadcbbbbbabbddddcacdcbcbbabddcabcccdadbdbdbadddacddadacbbcbaadcbadbacbbdaacaabcdbdadbddbcaaaaacadbbddadbabccbadcaacaabcdbbcbbcdaaaaadaccdccdbbababdacaaadbbaccadbdabacadccadabbdaccbdccbaaabbcacbdacacccaacadbbabaaababbbbacbdcacaddbdddbcadbbadabcbadaacaacbbbaadbcbccddadaadbcdcbabddcabddacbdcdccbdadacbbdccbacdbacacddbdcacadcbadcccdcbaaadbbadacabbaabaaccacddcbbdbcdbdcbddcabbbbcbcdbdccadbcdbdaaaccdbdddabdcdbababaaaddbcddcbdcccddccdaabdbbaccbddcbdbcccbdbaacdbdcdcbaabbcbcdbdbcbcabdbdccacdacbccbdaccbdbbdcbbbdabbbcababababaddabddbbcddcadcdbacbbcccaccaacdcdbabddabbabbccdadaacadadcaabaaaacacbbdabdbbddcbbdbbbaccdaabcbdccdaacbaddccacdbdacbbddbaabaacdbcdcbdccbcbacbcabcddbabcabdddccbddadbbdcdabdbbdbdadcaadddcbcbcbccbcbcbdcbdacbbccbcdaabdacaddccdbccacdcdadbbdaddbcababdaadabadaccababbdaabacbabacaccbabbccbdcaccddbadddacaccabbcadacaacdbdbddadcaddcbdaabcdbbdcadaddbbaaacdcbdccaddddadcbbdbbdbddddbbbbbbbacbadcbccbaacabcacacccbcbbabdccbaccaacabaadbcbcdddcbacadbbadabcddbdaccdbcdabccbbbdcacddddcbbbbacaccadcdacddbcddcdbbcaacbdaabcdadddadbcbcccccaabddcbabaddabcdaabcbabbadbbdbcdccddcbddadabbcdacaadbaacabdcbbcbdcbdbaabcdcadbcccadbabbdaadcccabcabcacabbbdbccbcbcacccbccacddaaacbbcacaccddcbacddbdcdaaacbbbadaaddabdbcbacdccacaadbbaccbcccabcbdbcccdcddaabadaacaacacbcccbbbabdabccadabdaabbddbbaabcdaacaadcacdcdadacccddbcdcccdacdabdbbadcdcaddcbadadabadbdbadcdadccdaddadcbbddddaccbccaccccddcaaccdbabcdabcbcbaabaadddbdacbaadabbbcbbcbdaaaaacbdccadcbaacadcbbacadaaacdbdcccbacdaaacdcbaddbddcbaddaabdadcdadaddabbddccccbbaccdacdaaacbbadadbcddacadccaaaabddcaaaaabbddbaabccdcbadbacabaabcbbaaabbbabbacaabdabbdbcbddaacaaadbdbbcdcdaadacaabbacbcdbdbbadbcdbccbaddadaabcbcdcbdcdadcabccddadaabdbaabccdddcdaaabdcdbbcacaaabcdacabbacdbbdcbbdcbbdddadcadcabbcdbbddbbddccddddccbadcabaaabbbabccdbdaccbabbcbbcbcdcabdcbadbcbddcaddacadbabccdcbbdcbbdbaddbdddddcddcdaccababcabbcbdbdddbddcbddcbbbbcdacabadddccacdbbadcaccaacaabcbaadcbbcbcdccabcacdaacdaacaaccbacaadbbcbdbbabdcaabddbbcaacbcbadacdaabcdcbcdaabdddcabcabbcbbbccbbbdcddcbacbcbddcaccaaccdddbcdabbabcccaccdbdacdaabdcadadbbdccabaacdadabccaaacddacadcbaaadbbcadbacaddaadadbabaacaccbcabcdbdacdadcbcbcbdcddddcccdcccbcdcdbadbddccbdacbcacbbbdcaadddaccbcabdddbacdacbbcabdcbbbbcdababacbbbccccdbacaadccaaaaadabaccbdbdadaacbbbacdcacadadbbdbdcbcccdcbbaabbacdcccbcccaccaabcccbbddaadcacccccccbccbacdbabdccdaacccaccaddccabbadacbacdbdcaaaaccdddcccaabadddacddaabbadcdbdabdacdabdaddadbacbdabbdbdcdadacccaacbbcbcdcbcbcbbccbbabcdbbdcdabcdaacbcaadbaadbdaababbddbcccaccdbdbadacdcdcccbdbccacaacdcccbcddbabbbabccadbdaddabdddbcaddcaddaabababdbbadabcdaaddbdbdadadbcabcbaaabcddadcdcbdddacbbdccdacabddaaaddcdbbaaabcaababadcdcbcadbcdcbdbaabcbbcabdacbdddbccaddbddddabdbaaacabcdaaabacdbbcdddbaabdccdbcccadbddcaaaabccdcdbacaaabbcccadacdbabdcdabcdaadcadabbcbcaddadbcbddbdbacddacccacadcbcdabcddaacddadcabbdcbadaddaabddaadccccbdddcccbdcadcdccaabdbdccbcbdbdbcbdddcbaadcacabadbabbcddddddbdbcbbddadbccdcaacdbbcbbabcccccabcadbcaddabbcccabbcccabccdadcdcdcddacaabbdcddadbdabbbadaadccccddcbbbcabbcacaadbcdbdcaabdddcacdacbaaabccadbddbaacabdbbbbadbdccaccdbaacadabbabdbcbdcacdcdabdbbcdbcccbbadaaadbadbacbacbcbadbddbaacbaacbabccddaacdadaacacadcaddbcdcbabccdadddccccacbadbaddccabbdcbbaaabcbcbdccabcabdadacacbacddcdbadadcadcbcdbccdadcbbaccbdcccadcadbccbccababdcbdddabddddcdacadcacccccdabdcccbacdddbabbddcacbcabbdcbaddcabcdacddbddaacbddaadbbdbaaadadcdbbbbdcbacabdabcadddcdbdabbccbacabcdbadddaadcadcdabdabcacdaacccbbddbdddbaaddadccdccbdbddbccdaddbbdddbdccabaabdddadcdadcbccbbadddbbadccbdbcaaaabbcdbaadbccbdadccabbdabcbaddcddaaadbabdddbdcdadbcbbcdcbdbdbdcdaaddbccbdddadcdcadcabacdbdbdcbaddbdbacabaababddbcbdaacaccbcdbcbdadaccbadbaccbdabccdbbaddcabbdabcdcabbbbdadaadbaaacdabccbbaacacbcbbdaaabaadacbabaabbbdcdcccbbbbdccadbcbcaacacdddacabdcacaadcadddbbcaddbbcbbdbadcbdacdcdabdabdddabcddbdcabbdaadabdaaabbbbdbbbcdbbcaccadabdbdaaadbbcaadaadccaadadababaccddadcdccbcbcdcddaccabacdbcdbcbbabbccaddcacbcadccbdbababbccdddbbcbdaddcdbbbbbddcbacadaabbbbdcdccaaadbdcdddcbbacacbacdbccdcdacababbcadbdcbdccddaaabaabaadcccccbbbdcbaabbcdcddddaddbbaaaaddcabdcadbdbacbbcaccdccbbbcddaacccaccbabcbccabcaaaccbbbcbddababdccabbcbdbcabadbabadbcddacbbabbabbbbdbabaacabbbbdabcdcabdbdccbdcadccdcdbdaabbcabdcbccbdabaacddbbadcadbbdbbbdbdcaacaadbbababcdcacdacabcbdacbbdbcbabcaaccacbbcdadbdcaaacdacbcbadbbbbccddccbabccaadddbcbabdcdccbcddcaabcaacccaabdcdbaccdbcddcabdbbabaacdaabddaadbdcdccbacbdddadbddcabddbcbcccadbaacadbbdddaccaccdabadddbddaacbaaadcacacacacaacbbabcdcdbadadacdddcdcabdabdcdcacdbbcabbddcdacadbbdbcabbaaaccbabcbdaacadccdcaacddbacdaddadcbacccbcdcddaadaaadbcbdbacbbcaaadbadcbbcbcbaaacbcadbaacdbdbbaddababcddcadcbbbccadabbccbdbadddbddbbcbaadbbabdbacdbbdbaabbbcadbcdbcddaccaaaddbaccdabdbdbddbcdaacdcdadddbdbdacdadddaacbcacddaccaddbbcabbcddacabbbabdbdacccabddacdbaddbcadccdbbaccaccddaaccbdccbbbcacbdcacacdaadaacdcadbaaddbddaacadaacdacadcbbcaacbaaadbdabbcccacaabbcaaaaacddaacccbcbcccddaadcadcdccdddbdadaadbaccbbdaaaabacaacdacdcdbcdbacbbcdddcbccadcbbbaabaabddbdbcbaddabddacbcccddbbcdaddccdababdacdaddbbbccddbcbbdabddcdccdccdbaaabbcacdbbdaacabbcbabbdabbdbdddddbdaabbbcddddaaaccdbadaabdbbcccbbdcbbcbdbdddacdbadcabaddcaadbaddcccabaccdcddbbdacacbabcdcabacaaaddcaaaaccbbcdbcacacacdaaadcaaccadcaadaaaacbacaabdacbaadaaadabaaadacdadaccabbcbccccacbbbcadbbbbddbccdaadbbccddddbdacbcbadbbccbcadaaccaabcabdbcadaacaaccabdcccacacbbbbddddbaacbddbaacbadbdcacacccccbdcbdcbbcdbddcabaabbcbaabbccdcbbacbacadacccbbdaaddbcdcaadcddbcdcacacaadcbbabbdaacaaacbbcaabaabdacdbbbdcaaddbccbaccacdbbabdccabbbbcaadaacdadcadbcdcaaadcbcbbaadcdcdbcbabababccbbabddcbbadcddbdabcdbcabccbdaadddccbabbdccbcbbdabbdaabadcdbccddabcdcdaaaccaaabbccbbbaaccadacdbcdbdddcdcadadddbdccdcaacddbbdadccddcdbabaccdbacbbabdbaddcdadcdcbdbaadbaaddcbbbddcbdddccdddbccadaccaaacacbbcaaaacacdcccaabbddaccbcbbbcdcddbcadcbaddcddbdbdabbadcaaacbccbbcdddccacddbadaabcaccdbaccdccaddacdccdccdbdccdbcbcbaaacbabadbbbbcabdabaddbbaaaaddacdcdcbdcbcdbbcdacccbbbaccbcaaaddcadcacbdbbbdbacabdbcbdacdacccbdabaddadcbadccbabdbcccccddbbcdccdbdbdccdcdbdcabacccbacccbcdcacdcacdbbbbcbbabcdccdddddbbbacbadcdddaaddcacbbcbcbcacccacddbacddcacaacccabaddcbbcddadcdbbadccbcdbbbdbdddbdcaddddbacadadacbbbcccdddcbcaabaabdbadcccbbdcabcacbddddaadaaaaccdbbbbacbbddcabcdcdbcddccabcbbacdabdbaaadcdaccdaacbbbaaacdbabacaaabcbaabbddbdcbaaddcabcdcdbdcbbdcadccccabaacddcddcabccccadaadbcaacbabaabdcbaccbdbadbbddaacbaacadcbacacdcabacabdcaabbbbacbcdcdbbdbddbdababaccababcddaadbbdccbccbccbaddbbcccbaabaaabcadcdaadaccdaabadaadcacbbbcddaaaaccdacacdbbdbcaabcdabdcadaddcabbaddbccbdbddbdbabdcbbcbadaaaddcdaadbddbbadcbccdddbdacbadbdaadacadbabcbabdcadbadbabbcdacbdaabcdcbadcccbbaacdabcbaccddabdccbcaabbbbbadbbcadaccadccccacbabdaabdaccbdccaccdabddcacadadbdcdacadbdabbbbabbbdbbbbcbccccbabadadcacbbcdbaaabccbdabababcbadccdabbbcbbbdddccbdbbcaacacdbcadccaabcaacdadbddaccdcdabadddacaddabacdbbadababbabaadcaadacadbadabbdabdadabcdabcdaccdabcdaddbbdcaaabbdbabbcdbadbdaacaacaabdccdcbdbbcaabaabdbabddbbdbbbccabbaacdbddcabdcbadbcacddcbdcaccdaccbbbbbcdcccbdcdaacbccabcabdcbdbbbcddcbcadccdddbcadcccaabbbbadbdacdbacbabcbbcdddcacbccbbcbcbaaabbbacdcaddaddadacccdbbbabaccaabcbcbdbddbdbdbaacbaddbbaadccdcbcdbcccbabbccaabbadacbabdddbabbdbaddcdaddbaaccaccdabbdcaaabbcbbacddcadbdadccaddcdbddbcdaacbbbddcccbdcdcdadaacdabacaaadbdabaaacbcacbccacdccbabdbbadaacadddbdccadcdacbdadadadbdddbdaaabcdaacbadacaccdddcaacabaadbbdcccabbabccbdbbbacaaadcaacdcbdbdadccdaaddbcbdbbabbacaacabaadaaaabcdcbabcbbadacdbccdcddbdbaabbccdbbccacddddbddadaccacbcdccccbdbaabddbbbcbbddbcbaaaabaacbccbaddccdddcdcbbacddccbbaccbbdbddddbdcdcacbcbacdccdcbccbdacbdcbaaddcadbbaabacbaaddccbbcdbccddbabacddaacbacdcabdcdabcccccbcbabdcabddcbbbddbbaaadabccbcaabdcdcaacaabadacbcdacdcadbdbddabbdccbdbbcacadaccdccaabdcaaccbcbdbcaaaaddaddacdcdbdbaaddbcbcabdccdcbcccabcadcbaaccbbbadcacbbbaacbdccdaaabbcadbabdccbdaddcdbddbbbbcbadcdbabaaabccdacaadbdbcddbcbbbcaacaadadddbacbdacbddbbcaaddbaabbdbdcabbaddaadbacbadbcdcadbbcbcdcdcbdaaabaddadaaaacbacddcbaacaaaaacacdaccacaacbbadadbabbbbadaadddbbcacacdddabababacacadcdaadbbdbbdaadadcadaabbaddbcdcabccdcdcabcaadaabddacdabbabcdbacbbbbbcbdbbdddbcbcccabcdccbddddcbacdbcadcddcccdaacdacababdaacbdabadbdcaaadabdcdadcdccbbbabbcbccbbcbbaaddaaadcbabdabbcdbaacdcbdcacbdcbbdcbbdaabbcabbbabacbdccdcdcccdcdaadddbabaccdccdbcabcacbbcccaddcaccbcbaaddbabccbabdcbabaadcadaddddddcbcdccbdabbcbcadabcaccbabbcabdcbcaacbbccacccddcbbacddbccabdcbabdabbdadbabbccbbadabbcccbdcaaaabcdbacabbcccdbbddcddcadddbdadaaddacacaddbcabcdddbcaacbcaadccacccdabbdbcbbacbadddcadbbbdbbddbaaaadbdbcbdacccdddbcccbcbbbbdcbbbadbcadaddcabdcabacadbcabbabccabaacccbdcaccbadbdaadaadcaddbcddcddcccdbbdccbcaddbbdcdabdadacbbdcaacccabadbcbadccadcaaacddbaadbcbccaabdabbcbcdbabdbdabdbabdbaaddbbdaddcdddadbabcababbadccddaabcbcbbdcadbbadaadbcbadbaacbdadddcadccbaaccbbbdddcbcacdbdddabddbbbddcbaddddbdbdccdaaccccccadadadcabadcdbadaadababbccbcadbacadaaccbdddabddacabdbbacdabcacbacdccaadbbababadaddcadbcbbcabcadbbbcabbbabbabcddccaccdaababbaccabdadabdaccaddbcabdbdabaaabadabdadcadcbbaadbddbabcbabcdaddabdbdaccccdabbcaaaadadcbadbbacadccdacdbbacdacddbbbacdddadabacacddaadbbcdabaabbcadbabccddcbaabdadbcaaacddddcbbbccdadbaaaacbbdcabdbdaadaabdbcdbaabccbccbacdacadbaaaadbdbaabdaadaadadabbdabdddabadbcddaabddbbaccdbccbdacbbcabadbccbbcbdbacadadacadadaabababbbcdbacddacccddcaacabdabaaabaaaddbdddbdcdddbdcaccabbddddbabacdaaabaadccacdbbcbabbbabbdacccaccbababbadcadccdaacbabbddadcabcaddabbaaabdbbaabcababddbcdbdcbcdbadbcbcdddaaddabbdbaccdabbbdbaaddcdcaacdcbaaaccadacdabdbcaabbbbcccdbbcdcbaaacbbacbbdaacbbdddaaadaacdabcabbcdcadabcabdbbacacdacadddcdbbaaaccbbcbcddcbdbdbbbdbadbccdbdcdadbbcacccdcaccabcddaaadccbbcaacacbabdabbcbaddcddcabdcdccccccdcdadbdbbdcddabbabcccdacdadcacaadcaacadabbbdaaadccdaaaaddbbdcadacdcaaabdddbcbcdabbadbdccbbbcbccbacadbabcadcbdbddbbcabacccadaacbdcbbbbdbadacdcdcbdababccabcccbaadddcadccadccadcccddccacbcdaccbababaddbcdcbbccacbdacbcbcbcbaddcababaddacadddaaabcacdcdbbaabddbcbcdacaabccacccbbddccaaddcadbccbacdcbccdbcadabbdbcccbaacacacdadccabdcdaddcbadbbbbdbbababbcaddddccddacaddadbcbdcdcddabcbcbddcdaadddbbcbcbbccdcbdbddadadcddbccbaddaddbacccbccabcbaddcaabcdddbadacdcaaddaacbdddbaddcbddcbbccccdaccccbcbbdbdcccaccabbacbdabcdbcccacbbcbaaadcbbcdaadcbbadcaaacabddcdcdbbadaddcbbaaaadbcdaabdbadddddabbbdccaadcdbddddddacddcbcbadcdbbaccbbcabaaadacddbabccabdcbdcbbbccacbabcccccbccccdccbcdaccbabdcccbabdbaaadcadbddabdacddaccbdaaadadccccddbdcdcaababacaccdccccbcbcdacaccddbddbddcbccbabdbadabbddbbbbbdacaccbadcdcaccdadbcdacddbbcacbcbaddabbddaccbaacaddbccdcdcdddcddaadcbbdcaadcbdcdcdcaacaaddadacbdcdccbccbaaddadcadccbddababccbccaacaddcadbbacdaccdbbaadadccbcddabbcabdcdbbbadcdccccbaadcadcbbbccdbadcacdcacdbbdcbbdcdadbdcabbbaacbdbabdadbbbabababccdbdcccbbddddacabdbbaabccaadccacdbbcbdcdadbacbaddcdbbbbbacddaacbbbadacbdabbaccdcaccadbbbcbbdbacadacaddacbccdcbbadaccaabacacddcddbcadadcdcbabddaddccbbdbaddbbdddbdddbddadbbcdbdacbddcbccacbdccdbbbaacccbddaadacbabcadacabbababcbdabcccdabddbbbbbbccdabcabaddabbddaacdbacadbaccbacdccbacbbaaadccbbcbadbaaaccdacacddddaaaddcdadccdacddbacdaadbbdcdacaccbcbbbddadbdbaabbabccbbaaaccaabcbcdadbbcdddadcbbaccbdcbadaaccccdaccdcdbaadbcddddbdacacacbbddacdbccccdcabacddbacadcdbcaccbdaaccbbacadbddddcddcdddcacbabdcabadcdbccbbadddcdabdbcbacdbababaaaabdcdaddcbdcccdaacbddaabbacccbbdbdacbbcaabcadcdacdadbbaacdaaddcdcabddacacdabddccadbccabbabdbdaaadcbbcadcddaacbabccdbabbbbbcbaaaacadcddbcbccaaaadbbbaadbadaccccdbbacbdcaaadcabbbccccaccaabaaaadcdbddadddbcbdcaaabaaddaaaacddddcbcbaccccbbaccdccabbaacbbdbbbdcbabdcbbcdadcbcbdacbcbcbddddbdadcdbaddccdbddcbccabdbdacabcadcccaadddcbcddaacabbbbacbbacbbbdbddbddddccdbdddddbbbcbbabdbcbdbddcdcacbadcacbcbcbbbddbbccddadcbcccddcbadddcdcabbaaaadcbacadbadcdbaacbbdccdcdbbcccdadcdbcabcacbbbdcddbbbadbacdcbbddbbcaccacadddbbcbabcbdccadadddcabdaddbcbabbabbdbadcdbddcabacdacddbbcaacacabbcdbbabdbcbdddbdbbcddabbaabdbcddddadaccbaaabadddabbaadadaddaaacacbccbbcadbddcabbdabbdccdaacbbbdccbdabadaaddcdaccaddaddaadaccccbcacaabcbccbbadadbcccbbcacadddbcdcbccdccbbabaccdbccdddadbabaadcdababacccddbdaabcddaccacbdaaadcdbbddbdcbcbdacbcdccbbcbabbaccabbacccccaaacadbadcbbacdbaaccabadcbcaabaaabdcbdabaaaabdbcdbbadaadbcadadcbbbcacbddbcccbccccbbbcaaacaaccabddbbcdadaccadabbaadabbdacadbaddccdbdbbaccdbdbcdbbbbdcabddbdddccabbbbaddcaabadaabacdddadcacdadaacbaadcbbadbcbdddadccaadabcabcdbaddddcdbdbdccadbccccabbbadbdcadbbcdcbcdcbccbacaddbabdcabcdbabddcbcdbbbcacdadddaaddadcbcdbbdbdddbcdddbbbbdbdcccdacbdadacadaacacdcdcacdbcbddcdbccadbdbbcddbaaabdcbcccddcdacbdbcbbccbcbdbcbababaccbadcacabcaddbaacbbdaabbcacbddccccbddccbcbacdbbdadbccaaddbaabbadaaaaababccbaabcdbdcbadaccbcabbabadaddabdcbdabccbdbaccacbabcddbdcddcabcdccbbdaaaaaddaaccadcbbcdaccdacbaccdaaacbccdcbbcbbaccddddddabcccacabaaccdacdabdacccacaadbaaddadbdadadabadabbbaabdacacadbbdadcababdcdbdcccdacbdbbcdbcbdccddabbabcadcdcbbcadaabdddccccacabdcbcadcbaaacaaaabaaacdbccbcadaddaadcaaacbdacaaaabaaddabdbdaabcbacbddabcdaaddddddbabdbaacbaabccdbccbdddbcdcadadcddddccbbbacdabcdaddabcadabbcccabadbcccbddbcccbccdbadbdaadabbbbddcabdcbcadccacccbbacdccaccbdbdcdddcdccbacbddcdbbbccdcdaadadabbdbcaacbcdbcdaacadbdcccaddbaaabbbdacbcaacaaaacbdabdabcadbdacbdbbdabadcddaadbaadaabcbacbadbabbccbabbcaacbbcdadbccabcdcadadaccdddbcdbccbbbddaddcadadcaabdbabcddddbacdaccdccbaabcbabcbaaccaadbdabaaccabcabbdabccbcbaadbabaabdaaacbbbcbccacaddbcbcbbdbcadababacddabcababbbaacadadaaaaccdcadbddbdcadaccccdabaabdadbbdbdcbbcdbcdbcbdddcacadddbdadbbacbaccaabccbacdadccdbaadbbacdcadddabcbadbbacccaacdabdcbdbbadcccbdcabbcdbacdcbabacdccabbbbcaaababdadbdabbadbcaddcddcaababdbcadddabbcaabdcbcccdddbdcddaddcabdacaadbbbccdcdbadaaccbaababcabbadbdcddbacbcbdcbdcbccadbadcbbbbdacaabbdbdbabdcacbdbcbdabacacbdbdbbacacbbdacaadcbcbaccabbdcdccaccacbcdbbdbcddbcbaaaadcdaaccccadacbdcabddccddcdccaccbbdcbcbcadddaabcdcbdbddbadbaaabddacdaaabbddddaadddabdcaadaabdacddababacbbcaadbccddbabdaccdaadcbdadccabaadacbabccbabaaacbaabddbcadbbaacbcbdcaabcdadbcbdbdbcbdbaabcdcbbadbbbadcabdcccdddbabcaacdccabdddbcbccabcdabbdcabbbbaaaadbadbadcbbaacaabbadacddabbcaaacacbdbdabdbbccccaacbcadaadabcacabcdacbdccbbbacccdabbccaaccaadcaccbccccabcdbddaadcccdadcbabdbccbcabaaaacddddaabcadbcbbcdacdbcdaddbddabbacbabbcbbcdbbbdbdbaabdaacdbbbdddaddbbdcdddaadcbadbaadcccaddabdabcddcddbaaadddaaabcadbbcbdbbdcbdadcbacbadadbcacadddbaaaaaaacbbbdbdcbdacddaccaadcbbdaaccadabacacacaabdbacacdaaaacaabddacbcaabdadadbaabdcaccacaababddbdcaacdddcdbaabcaabbbadbbaccdbdcbccddaadbcdacbbdaddaacacdddccaaddddbaaababacadbbdadbcacddcdbbcacddddddabdddbbbdcdcbcbdcbcdaaabbcddcccadbdddcabddbcacccccbbbbabacccbcdcbcdacdcdadabdcdccaacbbbbbbacddcbcdbadcbcdadbbadadcacabdbbcdcaaaccbcccbdacaacbbddbaaadacdcbcccdbddcbbbcbabbdadccddbdcddcbbcdbabdcacbdadcacddddacabcbbbdaabababdadaacdbcdbaacabaaaaaacdbcaadcababbaabdaacbbbdaaadcbadcabdcbaadcdadddadbaaaddadbcdacaacdadbabcdbdcabcdbcbadcbabdaadcdbcbccbadddbddbbddccbdcdccadabbadccdbbcacccbccabbaacbccdaabccaaababcaabdbcddaccbbdaddbdcbdabacddccbddaaadbaabcadcdaaabdcbcababdabcdccdddbdaaabddcddadbbdaaddacbadbdababcbddbcacdacaadbdccaccbbcbcabbbabdaabaaddbdabcdbdccdbdbabdbaabababdbaacdbddcacbdbddcbabcdbcadacadacddabcbabdbccbacdadbacacbcbaabbdaadabcadddbcbabdddcdcdbcabdacddbccaaacdbaabacaaacdaabdadcbadabdbccbabaaccabaccdbdbddadbaccbbbdaabddcabadcbcaacdaabcbcabcbccababcdcbdaabdddcaaababbdaaaddcdddaccadbcddddbdddcbaacadacdcddcbcbcdaddaabcdccdcdadcdaadbccaacaadaaacabadacabcaabcadadbbddbaccdabcdacddaccbbabddbcaddcbacabbadaacdaacaccdaccadacacbcdaaaacddbdcadabbbaccddbdbdcdaddbabcdbccbaacdbddbbdaabdbbbbcabadcdccbdbbbadbdbdbcabbaabcbbbddabcdcdbaaabcacbccacbcbcdabdbcdcaccddcdcdadbccbabcacaabdaacbbdcbadcddccbacbbbaabcdcadcdadbcddacdcccdbdacaaccadcccacdbaaabbbcbbdbbbdaaabbdcbbbdcdbaacbcdaababbdbdcabacdddbdcbcacacaaddcacabdbaabbbddbbadcdababcabddcaadbdcccadadaabcbbdbaaccdabcbacdaaabbcacadcbdcadcbcbddbccdbaaaacdabbbdabadccdddbaddccddbcccbadcabbdcbaaacdccdcddbddbcbdcacddbdabbacccabbcadbcacdbcadadbbbaddbccdacccaddaaabacacbacdabcaaabbabbadaacdccabbaacacbaaabdaadbadcdaccbdbccbabbbbcbdaccacdadadddddddaccacbdcaaaacdadddbdddbccdaabddadadcbccaadcdbccdcbbbcccadbcccbacdccdacdabcdaccaadddbcaadbcbcbaadcbadacacccabbbcbcacbbabadacddddaadddbdaadbdadbcbacbbbdcccaddcdaaaacacadbccacccaabaacacdbcddaabaabbdddbdbbbbadddbddcdbddbbbcccddccccdbbccbddababddcbdaccdacccabbdccadacbccaaccbacacccabdbaadbaabbbddbbccddcbbcabbdcadbdcbaaacaacdbdcdcddcbbcadbadccccadbbdbcabdabbbcdadcacbbabcdabbbccadbbaaabaccbbcddbdbcddbddbaadbcddbcdcbcacbdaacddccdacbdcbadbcbbcbcbbabbdabdadbdbbcbcdbbadbdcaacdababdababbbbaadaadbbdacdadacabdabadcabbdaddacbdccabdbadddaaaaacaacccdcdbccacdbbdabadcbbbdcddbaccbdbdbddddabdacbddcbbdacdaadccccadbcccdbdddabacdcaabdcbcabadaadbccdbbbccdbadcabbdccdccacddadcdbbdcababacacdadadbabdbccaccaccdaabdbdbcdacdacbddccaaccbcbdcbbaccaaddccbbbdababadbcabbbcddcbbaaccdbdbbacadbccdacccdadababdbabaaccbabcbcaadbdcbcdabbadcdacdddcbcddbbcccdabbbcadcadccbbcbdcdabbbbaabbcbabcddcaaaaadbdabacdbadcbddcccdbddaaacaaccacadabdcdcbaccdddbcbcacddabdcccaabccbacdcbcadcddccdccabbabacaadcbacdcaaacaacdbabaacabaadddcdcabbdbbbdbcaccdbdccdcbabcbdacdcbbbaaacacdbdddbacdddbbacaaabaaaabdddacadbbdabdcbcaccbbbcdabddbbadbdadacaccdaaaacbbdaddbcbbadacabbacbdadddacadaccabdcdbbabcbaadcdcaddbbbdaacddacbbaadabccbbbcaccacbaabaccbdcbbdcddddabadadccdabacdddbabdacbadabadabaabadbbcccdddbccdbbaacadacdadabccbcdbcddbbaabaddcbccdcbadcaaacdbdddbdbddbbaaaaabdcaaadcadccccbcddadbaaddddbdbbcadcddbaccdabdaabbccbbbadbacbcbadbbdabccdbcadbabbcbdabacddabaaabaccdcddbbcacdbbdddbcbcbaddddccbddbcaacadacdaabdaabaccdddcdbcbcdacbcdcdbabcaddabaacadcccaabadddbcdaaddcadbbcadcbabdacdcccbcddbdcacbbdbadaaccdacabcbbbccaacadbbdcaccbcbbbdddcdaabdccbadcbbcdbbccbdadabadcdbdddaabadddbcccdddacaacadabcdaddbcddbddcdcabddbbcadbaadabadaddcbdcadcbbdacddbacbbbacacdacbaaacaadabaaccbcabbcbccdcbccbdbcbcababaaacccbdaadabccbcccaadbbccccddccaaacabbdcdaaabdaaacdccacbacddddcabccabcabacbabcccdccddbcbcbdcbbbaabcbacbcdcbbcccabaadbdacdbcbabbbcdbcbddadbbcadababbcddababacaddbbacbbbbdbabcadbbdcdcdddbabbaaccacacbabccbccdddaabadabbadbddadbababcaccbcbbcdbadcbcbbbadadcabccdbccdbbdcdabcaccbcbccddddcdacabaadddbdcdaacadadaabbadaddccadacbadacccbaabadaaabaabaddbadcbabacbdadabbbbcbabaaabbdaccabdccccabbbcbccdbbcddccccacaddbdaacbdaabaddbbdcbadddbadaccbaccbaccdddbbaaacdaaaccbbaadcaacacaaabacbcbcadbadcabdcaddcbbaddcdadbdabcbdccdabbbadaabdcdbcbbacccddddbcabdbcbababdcabdbaabcddbccabbacdcbdbcddaacbcacbbabbddadcdbdbbbddccddaaccacbcbabacddcadbcdbcaabbbcbccdacacbbdadaacdbabbaabddcbcdabaaaacbadcccddacccbbddccabcccacaadbadcbdbcbabcddccbddcaadcbaddbbccabdabbbcbbcbdcbcadddcddcbddcbacdbbabccbbbcdbddbcdbbddaccadbacbdbcbdabacbbddacadaaacaaadaaddabcadabaddbbabaacaaacacabdcbcbbcaadaaadddaadcddbdadcddacdcaacababcbccdaabbcbcbdbbdabcccdaadaababdbbbdcdcabbcdcaaccaccdbcbadbbcdccbdddadcdacacdbaaccbdabddcbabbdacbbcbadbccdbbcbcbdaabcadddcdabacdbaacccccbdddacbbcabaddcbdaacabddacdddcddcbbdadcdbbcdbacbbacbaaadcbbdaccadbbbaaaaaaddacdcaddcacddaddcddaacdcababdbbbbcbbddaccdacbdddbbddbabdadcadaaddcdbcddaccaabdabcbddcacbabadcacccdabcacbbbbadabcccdaaddbadcbdadcdbaaadbcadccabacdcdbaadcadabbbcbccaaaadddbbadccdcccabaababbacaccdcbbbbddaaaccbccbdbacacbbaacabbaacbdbcbccdadbcbcdabcbbabcabbadcdabbbbabbdbabdbbcbaccbdcbaacbcbabdccbbadaddcddacdbdcadadbbcbcbcddccacbcdabcbabddddddacaadcabbcaccadddadbbcacabdbccdbacdbddddcdcdcdbaaaadcaccacddbdaaadbbdadaddbcbabbaddadadcbbbdccdbdcbadacaaadadcadbcaaddccbacacbadcdaaccacacdbbbdbcbaccddcdbbabdaccdccbcaababbbbbabbbdcddcdcdddcbcaaaabdbdcccdbdbadcadbddbabadcbbbbbaabcaaadcbccdcbddabbcdbcbbdcbdbadccbcadbbdbaddbbbbacacadaaadacdbcaddabbaddccccccbbaacbccdccaadbbcdbdcbaddadaadaabbadaaccddbdbaabaabccabccbddadcdcdabdbdabdcacabcbbdbcbbbcdbacddbccbdabcbbabacbacbabcbadabaaddddaadddbbccdbaaaacdcccaacbddccaccbcdadbaacdbbabaadaddcccccdabddacdcbacacdacadbbabaccaddbcbcdcabbbbababcbbabbabbdcdbcccccbadaabcadddddaccbbcddadabbaaabcbcadbaddcbcdbadacaacaadbcddabddbdbabdaddbacdadddadbdccddddcaccbbabcccabddbcbbbadadcdbdacaacbcacbdacdbbcdbabcbacccabdabbcdcabddacdacbccacddcabddabdbdabdbacbdccadcdcddccababdadadcbaddaccbbcbaacadabdabcaccccbabcaddbdaddcdcccadadcabadbdacbdbccdbbaccaccbabbadadddcbabcadaddbdaccacabbdaabaabacdcdabbabdaddaddbdcccaabbccaabdbabcccddacacabbcbcddadcbddbabaddcbcacaacdccaaaaaddbcddbadbbaddcbaadcddabcddbcadddbbddacbcadaadbadaacdbcdbdaddcdddcbcbdabdcaaddcdbbacccccdbbaaaaccdbacdcdadcacacdddbaddaaccdbdbddbccbdddabbaccddbdcdaddabdaddcdaaadcadbdadbcadcaccbccdacacbdbdababcaadcaccdccccbbccbccababcdcccaccccddcbbcacbdbcbcbabdcddbdabdaacabbbcabacbacbcabcdccbddcabbcdcdccdbcdaabdbbdadbadcbdadbdcdcabdcacbaaabaabadccdabadabbdcaaaadccadacdbcadbdbdcdadbdcddacabbabccdaacdcddbadcadcacdbabdcccdddcccbddcbdcbdbbddabbdcbddabdcccdcbaabcaddbcdbabdadacdbbbdddcbbcdadcbbaadbcbddbacaabcdccdaabccccabcadbcdcccbddacabccabadccdabbcdaddadcbcbdacddccbbdbcbdcabcbbbcbacdaaaaccababaccddbdabacaccaadcdcbdbcabcacbdddcddcacbdabbcdddabddcbaaacadbdcaddddbdddbddaadabdddbbdababdcbdcadaadaddcdbccbcaadddadadccacbaacabacaccccdcaddabcbbccaaabddbcabcdadacbbcbaaddaabaadcacacadacadacdddabdccabdddbcdabdacbbbcacadbdcadcdadcdbdadaaaabcdaaabbbadcacccbcaabacdbccaacaabdbabbcdbadbbcdccbadacbcbacdabcbcbbdbbdcdaaabcdbdbaacbbbcbdcabcaaadcbacbdbabacddcddabacccaacbaddbbcaddbdadbdbdcccadcadbadcbabaadbddbcacabdadadacbaabcabacbcbbadcdbdbbdacdaacbabbaaabdbdbbcacdddcdbbdabbdbcacbdaddbddbcbbcccabbdcabdcabbccddccdbaddaabacaccadbaacadcabbbbbabddcdcdcdbdbdcaccbaaaabcdbdcbaabbadccddadccdabdcbdddbbaaababababbcdccbaaccdadbbbcbacdacbabbcdadaadaddabdbacdcdccbdaccdbcbcbbcbacbddadddbbcadbbcdccdcbdaddadcbacbcaaaabbbacddbaaaddcbaabaabcdacbdbabaccddaabcaaabcbbaddacccababacdacbbbbddbbbbbadcddcadbccaabbabaaaaabaaaabadbdabdaadccbbaddabaacaadaaacabcccaabdabddacdbaccdbccbadbbcdccbbcabcbcddbddcccbbaddacdbcabbdbccdddacadcdddbcbcbdbdbaabbdcbdcdbcdaddcdbabccbcccccdaccadaccccbacaadaacadabcdcddbbdacaddcdcbadbcdcaddccdbcccccbbcabadcddaadbcbbcabbaddcdbddadaadadbbdbadddbdddcabaddcadacbccbadccbcabbdabcbacdbacaaacbaccadacdadcdcdacaaacaacabadabcccacddcdabababbcdcbaacdaadbabcccaadcddcddcbbaccadacacacbdbdbcadbcabaddcbdacccccdbababacabaddbcbcdcacddaabccccbccacbdacdaaaddbdbcbbdbcbbcddaaaccbdacbdccadbbabacbcdccccadcaddccbdddaacddabdaaadbdccabbabaadddbcbcdabbcbdaccdaaadccdccbdbcadbdccbcbcaadbaababdccabcacdababdcbacccbdbabacbbbbacbcbcdadbdcaadaccdabcaabdbcdaaddaddcbacabaaacbacbabbbdccbbdcddacaaaadccadbdaacabacbabccbaddbcdbabddbcbdadbddcadbddadacadacbdbaccbdbdcdaaadbbcbbadbcadcbcaccaabbdddadcabacdcadbdadbdaabcbbdabcccbaaccdcbbbcdabbacdcbdcaadcdacdbaaadbddbccbbaaddacdbccbddbddbdccaaccbaacaaabcbdddcabaaabadcdbdabaadcdcbdadbbcddcbccddcddacccbcbcbbcaadadaacbcbbbabdbaddaccbdabdaaabdaccbcaccdacdbbbcdbccccbacacabdadbccccabadcdaabadbbdaaccacdaddababbababbdadbdbccaadbaabbbdbbcbcabdcdcdadaadbbcaadaccadaabbaabbacbdcacaacccbaccaabacbccdddcddcbabdadacdadbbdacddbacdabdccddacaaacdbadcbaddaccdccdccaccadbacdddbbdddadabcdbcddccdaaadacdddcacaccadcddcaabbdaadcbbdabacaddaabbaaadaaaccdadbcabdadddddddbbccacbdaabaadaaaabacacdaabcbbdbddddbddddabdadbdddadacacbbacbaccdbcbdbcdcdadaaacdabbbccdbadbbddbacdabbdabdccdbaaadcbdcacbbbccdbdaccaccdbdadcddcbcbdcdcbdbbbacabcbccdcbbdbdcdccbccdaabbcbaadbdccbbaccacadabccbdcbcaacdbcdbccdaaaabaadbcddcccccadabddaacdcccdbdbdaaaadbacdcacdbaaadadabcacdcbcdcdacddadabdaaadaddbcbcdccabccbcbcddaabaccbdddddaccdbdabbbdbabacdbadcbbabcbcacacbbcdbaabcdcdabadbcccadaaabaccadadaccbadacdabbdabdbbbcdadbdbcbbcbbabbabcdaadddbcdabcbbdddaabddcdbdbabaddddbcbdaadbbadcbacdbdcdccddccacacdbbddaacdbadccbbbbabbacbdddcbdccacbcaacccadddaaccbcaadaddacddabcabacaddabbddabcbccacbbcadbddcadbdccddadcbdabbcbcdbcdcddcdaaaacbdaddacddbcadcdbcbaaddddcaadaaadaacccdacccacaaabcddadbcbdaadcbcdbcddaaabcccbdbdccddaccbdddacabbacaccddaadddccbcacbdccbdabbbbbaaaacaaaddaccdabaaadcdcaadacccdbcbdcdccbaaadcdaaaddbddcbacbdacacbabbaabcadcadbdbdcbcbbbbbdaaaacacabbcdbcccddabbcadcddabcacdddcbdacddddcbdcdaacdbaaccdcbdbdcbadbadabcabcbacabcddccdbbddcccadaccabcaabacabdbdbaadccbbcabbbcdbdcbcccbcbacddbdbddbddcbadcadcbbbacccaaabaaccbdacadabddaaadccbbaadcbcabacbbbcbaddddacadcaaadacdcdacbacbbcdbaaaddbacddcdbbcbddcbaabdbdadabddadaaaadbbacbadacbcaaaacaababbaaabbaaaabbacddadbabddcaaccaadbbccdadbadbadaabdcdcbbccbdddbbcccdbdbcabdcbcbbbcbbbbbbcdaadbbcdcddacddccdccdcacbcabbdbdacddbbaddbcaabaddababddccadabccbcdddbddaadccccbcacdadbcdbdaccbbbbbadbcbcddacabcbcddcaaadbbadaddbbcabcabcccaccbbccbcbdbccbccabddcbdcdcdcdabdcdccdaacdcacadaaabdacdadbaadbcdbbcdcaabddbcbddacdaacdbbdcdddcabddabcabaadcdaaacacaccbcbaacdddacadccbbbcbacabbdccacdddddbaabbacabbcacdcccbadababdddcdbddcddbabbcadccabcaabdbbcdababddaccdacccdabbbbadcabacbbbdddcbdbbcddbdadaaabcdacdbccbddabbddbbbdccccddaccdbbadbddaddcccaaacaddcbadbdbdbabdcaadacdcbaccaabcddcaccbabcdabdcadbadccaaddcabcbbcdcbadbdccddcddcbacacadddbdaaacaaaaabbbdabcddbabbddaaddcaddbcadccdabaacabdbccadcabcacaadbbcadddbaadaabdbcabadadbbdcdcbbbadbcbabcadadacbabcdacacaaaacabaacdbdacacbcdadddabdbadbdabbddbbdcabcdcccdaddddbaadacbccbbdcacaabddddbabccbaddadccaaccacaadadbbcbcdbbbbdabdbcabddbcbbccbbabadddcbcbabaadcabbddccbacadabcccbbcdaddaccbdddabbddbaabbcccccbcacccaadbcbccbdcccbbcdcdbddbbbbbbdbbbbcbcadcbbadbcccabadcbdbdbcbadcbddbaddaaabddaaacddadddbabdaccaaaababadcabbaadbccdababbacbcbcbacdcdbbbacadcdaaaadcacbcdbcbdacacbacdbabaacbdbbadccdbabcddcddaacadaadbbbcdbbbdcdbabcbdbcbbbcdcbaadababbcccddaccaabaaaddaacacadbabbaadcaaababaccbabdcddbdacabcacdabaaadbbabbadccaddacddacdbcdabcacdcabdbdacadbcaaaabacbaababdacaaabbabcbcbdcdcbbbbdaaddbbaccddcdccbdbbcbdccddbddaabacdddbacacdaddacdaacdcdbcacdccdcadabbcaaaccadccbdbbdadddbccddddbabdbddadaadcacbacdcbdcdaddcabacdabdbccdbbbbbcaaacaaacacacaadbcbabaaccdaccadadabdcabdccbbcdddcaadcaddbcddbbddacbabdbbdcaaabdbbcbbbacbabaabaaadaaccaddaabbbcaabddaccbbdbccddccbbccacdddbbabbdaabdbdcbacdabcaabcdbaabadacdccbcbaacdddcadcbccdcacbbabadddabacacccdaaaabbddbbbcddccbabdcdacacadbcbbddaaadddbaaadcacbccabbadbdaaaadadcbbddaabcbdcdcbabbabdcbdbcbcccdaaabcabdaddcdaaabdacccacbcdbabcdcbdcacbaccbbcccbbbabbbaabdbdbcbadcacdbbbbcbccabbccbddaadacacacddccdccccaaabcbaabcdababacaadccbdacadbdabcbddcdcdaabbbacbbccadbdbcbbbaabbaacadcccddcdddddacbdcbdabbadddaaabdcccdbaddcbccdcabcccdacdbacaaadaaaadcadcccaadbddbddcadaddbbdaabdbccacbaadbddbbccacdacccbcbbbacbabbbdccddaccacbcdbcdbcdbcdbbcadcccdddaccbabcadbcaccccdcacdabddcbbcbbacccdbccadbdcdddbcccddadaddcabcabccdbdbdcacbbcacbababdadddcdbccbdcbbddaabdbbbdcbaccdadbbcccadaadbbccbdaaacdbaabddbaaaabcdccdaacbcacccadcdbcbccacdcbdacacbbdcdccadbacbdadaaacabaabcacdddacbdacbddaccdcabdbcaddbddaadbcbbbdadabdcbdbacccabcabbabdcdaadaabdcbbcccbbcdcbacbaaaadaaadbbcbbaacdbbccdbbdaacdccabbcbabdaddcbaabcacbccbbbddabdcdabbdccadaacadbdbdcabaddacdacdbabcaacbabbadcbdbdbdabcbcccdaaabaaadcdaaabacdadbccbcacdbdcabcdbbbdcccbbbdaababbadcccdbddadcccacacdbcdbddaddbbbcdcbdcdcdbddcccdadaaacaaaacdaacacacaccbacdadcadaabcbabcdcdabbcacaaccdabacaddcccdacdccacccdcaacacbaaacdbbccccdddcaddbcbadaaabbcdbcbdacaadacccaabaddbdcdabdbadadbcadbcbccdabaaaddbdbdbcdccdaaadbbccdabadabcbccbbbabdaadcddccacddcdbacbaaccacaacaccadbbccccadddbbcacdcbdddcdcbdcdcaccacdaadcdbdcdadbbdddbbddadcdcadbadbcddcccabacaaaadcbcbcbdbdddaadabdaadbdddbacbabababcaddccacdbcbbdcbdcbccadbcbdaacbccbbadbcdaddacaddcbaadbbbbacbcbabadacdbbdababdacbcccaaaaccacacdaddcabbccbccdcdadbcbdbabbacbcabcdbbddaddbbcbabcdadbbabcbdbdacddcabcacccaabcbbccabbdddababaccaccbcbaacbdbaadbbdbbbbbdadcdcccaadbaadaddabdbbbbdaaaddadcdaccddaabacdacdcabbdbdcaccdacbccbbdbbabbaccabcacadbaaacbbdbcaccdbbabbbdbbacdbaabdddcdadbbacbabcbccbdaaaccdbacdccbcbdacdcbccbacaadbcadaabaccababdbbaacbdacdbcdabbbdadabadbcdaabbcdbdbbababdadcaacdcdbdcbdadccabcbdbccaddcaabadcbdabdcaaccdbdabbdccccdbbadccdccdccbbbdcadcacabdbddbdbbcbadbcabddaadccabccdcdccccbbadbadabababbcdccacdabbcddcaadddcbdcacbabdcddcdcadccbdaaabcabdddcaddccdcdbcdadddcbcbaabdbbcccadbbdcbcadadcaaacdcbbcdddcadbbaccadabdccdcaaadbdddbcccabbdbaabaddaccbbabcdbbabdcaabbdadaccdbbccacccbbbcacbcaabbccaaadbacbccdbbbaaabbccabbbbbcacbcbacdabcdadadcbbcbcacccbabbcdccdaddbdbdbdccdddaccdcddcbacdabddccbcbacdbacaacaacccccabbcbaabacdcbbcacaaaaddacdaaddbcbbdddacbdaccbdddaabaaabdacbdadbbbadbbbdacbccacdcacbdbbabbdaadccddbbdabdabbcadbcbdcabbcddcaaddbddadcaccaccdbcaaddcaadcababbbaadcccadcdcaabadaaabcdbdacddcbbbddcddaaacdbcbdbbbacbaaabdccaadcacabdbdadcaaadcdccabcccdaaacaaddddaabadaaccacddddbbaabcdbbbcdaccccddcbaabadaddddadbccdaaddcdddbbbddadcbaddbaaccbadcbacbbdddcbdadaaabaacbcadddbdacdadddbadacddcbdbdcdcdddcdcccbaacdddabdbbaabadabdaddacdcacabccbbbcaccdabdcbdadcbdcdbbcdaddbcaadacbbbaddccbdaddbaddddcddaaaddbbcbddacdcabdbadcbaadabaddcccdcdacccabbbacaccbcbdcbbcddadacadabbdddcbbcbabcbaabbbcbcbdbcbcbccdbacbdbdcdcdbdbcacdcbccddadbdbbdddcadddcdcabadccaddcbdcdcdccdccaacbabdadaaabbabcdbcbdcbdcdcdbbbaabcaddbcdbadccdbadadaaaaaabcccaaccccaaddadcdcacadcccdbdbaacdabbcddcbbcabbadcadbcdcdcbaaadddabacaccdaaadcaaabbdcdcccccadbdabaacbdddbcbcbdcabbcabcadbccaaadcdddabacaddaddbdabbccaacaababcacbaddbdbaaababbbdacbaabdccbcbcdcdacccbcaacdabadccaaddbbdbccdddcdcdbaabdccbcbaddbcbcbdbcbddcdcddddbcbbbbabaaccccacacbbbcaaadcacadbacdacdcbcdbcaacbccadbddabcaddbdaccdbbbbaaabdcdbbbcddcdddabcdccaaddbcdcbcccddcaacacdacacbdadcbcabcbbaadcbcdddbbbcdadbbacdaadacccabbdbaaabbaacdccbbadadcccbdcccadcbdbbaadcdbadcdacdccbaadddbbacdcadcdcacdbbadbadadcbddbabbdbaddcabdbabbbbadddbcdbbdccbcaacadddcaadbdcbcccaacadbddbabbcdcdaadcccbcbaaaddcbbbbabacdadcaabdabcdaccaccaccdbaccabddabadbdccdcadbdbcbcdddccbacacbcdbdaddbcdaabbbacacaaaccbcdbaddcdccbbbbcdddadabbdadabcabdadcddbaacacdcdadbcbbdcdadadabdaacbdbbbcdcbdbbbbcdcaabbddcddddcdbdcdacdbcaacabbdbdcabbaacdbacaaaaddccabccddadbabdbcdbcbaddbccbcdbddadbacadaaaacbacadababccabbdadaadbdaaabbddaadadcbcddbccadccabbdabadabcabaadddcacbbabbdcabddaacbdaabcadcaabdcbbdcabddcdabcaccbacacadcacdbdbcbcdaadbccbabaaadbddcbdbcdbcabcdabdbabbbbddcdcacbadbcbdabaaacacacbdaccbbacabdbaabbadcabcccbababbdbbcbbdbcabbcbcbadcacadddcbbadbccacabbaddccaddcbadbacbdbcbdbbbbbadddccbcabababdbbcbaaaddbcbcbdbabdacddbbbadadbdacdadcdccdbcaccdacdcacdcbabcabbdacbcbbccaddaabbdccbaaccaadbadbbdbabaadacbdbaccacbcbdbcbdcdddbabdcddbcbdbbbcbabcaddababcdddadbcddbbbbcbbbaacaccbbaccbddbabcbcaacdcbdadadcbdbbdbabcdcdbddbadaabccabcbaacdabcabbaddacaaadcbccaccddbdbdccddadabdcaccccbadddbabbbabadacdbabaabdaddbbbcbaabbabbddbcdccadacaadadbdbdbcdccbbcbbaccabcdcccabdaabdaaacdaadaadbdadaaabccbbadcaccccacddcacbaabdbbadccdcbbddccbbcbadcabdbcabbbcaccaadadadabaaddbbcbcaccdadcadbdacdaccddddbacdaaccaaabcbdbbcbbacadbdbdbadabadbccbbbdcaababbdabaabadbcdabcddcacabdcccdcadaabdbcbcbadbacdadcabcbdcdcabbabbdadaacdcaaacddcbabbddbdcaabbcdaaccccccabcaacbddbcdcbbcdbcaaaaacadddcbaaabdaaddcabdddbacbddddcbccaddadcdabbadbdcadddadaaccdbacdbdaaccabbcccabdbdbdabbbdbcdbcbaacccdadacbddcadbabacddbdbbddacdddacabdbcdcdadaccadaddbadcdadadcadcababcdaddaadbdaaabcbadccbbccbdbdadcdabdaabbdcaadaaadcaabadabcccacdacdcbcddddcbbdddbaaaddabbabddbababadaababbacdbdabdbbccdacdadcacccbaddababcabadacbcdacdbbbaaabcbaabacbdbbaacdbdbbbdadaaacbdbaacdddbabccbdccdccddabbdbcbadddcbdaaddaacacbcabacbcdabddcbdaccccddbccabdddcabbacabdabbbcdbccabacaabbabacdccaadddcccabcacaaacdbaacaaddddccaddcbadbdccdcaaabddcbdcbddcdbbaacbddcbcbcacbbdccdabbdabccbbcbadacccaaadbbacbccdbccaaaabbacddadacdadcbbdcccbdaacdbcdddabdbcdacadbbabcbbadcadcdcadcccddacbaccaabcdcaaddbbcdadabbdaaabdcabcdcdbabcababcdacabcabdbbcbbdbdcdbccdaccabcdcbbbdbaaaacddbcbbaabbbacccdbbacbdadcadcbbadadacadccccdcdcaaaccbccdcddddbbbcadbabbbccbccacbaadaccacddaadcbabaacccaddadbbaddbacacbddaddcabcaaccbbaacacbccdbdcadcdaabaaaabbcbcbddaaddadcdddbdbcabdbbabdbbbbbadcabcccbaccabdacccbbdddcbabacadbccdbdabdbbdacbdbdadbabcccdabbdcdcccdccdadbbcbcccaacabbcbbdbbbccabdaacddcaabbadbcddccdcacbaaabcaabccacccbcacbbcdbbadabacddabcbbddbbcaadbbdcccacabcaadcbbbadccabcccacbcadbcbaccabcacbbacdbcdabdaacbabbadbddcbbaaaccdacbcbabdccadddbabdcbccaabbbccdcdbadaaadacbdbbbbcaddaabdcacbccbbbbdcabcabaaddabcddabcbdbacccadabdadccbcdaaaabcabdbbadadcddccabdddddadddacdbacbbdccbcdacccbcaadadbcdcddcbcbbbcdddcbdccabaaccccaabbccbcadbccadbcacdbccadcbddaadddcdbacaacdbbadaadcbdcccabcdaddbcddaababadbbdcdabcacacccbdadaaacbbabccddadacdcaadabbabbacbbdcadbdaaacdcbbadabadcadcadcbbbcabdbbcacbdcbdaaddadaacdaaabacbcbdaacbadbcadbdadbddaaadbbdabaadbadddbddabcbdbdcdcbcdcdbabbdbcacadddbacccadcababcbbbaacccdccbbcacbdbbcdbddddcdcaccdbdcbddbacaadbaaacadcaabccdcbaabbcdcaacdabbcbcaccbcdadcbaaadbccdbcaadbbdddabcacdbadcbdaadbcaaadbdcccabcbcabdbbddcdabadabdbadbdaabccbcbccbbcbbaccbdbdddbdacdadcdbabdadadbcbcaddddadddbdaabcdbcdbdbabdaaaccbbadddbaaacbbbadabcabccbbdbdadbdcddabcbcddabbcdcadbcbbccbcbcdbdcbdddacdaabdbacbbcbdbdbbcaadcbbbcbbadcdcbdddaccdaabadaddcababccdddbcbbbdaabdbccccddccbbbbaacdadddcdabbdddbcdaacdabdbacaababdabcbbbbccbbdabbcddbccadaadcbacbcbdbcdccbddccddcaddadaddadcbbadadbdcbacbcabdcbadbbdacadacbabdbcdcadccdbbbcbcbcadddaacdcddbddadbdcabcbddcdbbdbcabcaddcadbbbcadcadddbaaccabbaadabdcaabacdaacadbadcabbcdaabadcacdccdbacbdcdcdacdcabccdcdddcdcabdddabdaddbdbabbcbcdacabdbbbdbcaddacdcadaccdabaaabdbdbadddabbddbdbdccbdbbaccacdccbdddaadccadcbcddcacdabbddbaaadcbddbbbaabdabbdbbcdbdbaccdbdbadbdabbabaaabacbbddcdaaaddaaaaabacdcdacbdbdbbbbbaddbcdbcdbdbbccdabbcbadcddaadacbbabccdbbdacccccbccadbcabcbbdadcdabccbbcadccbabdbbaacadabbabacddabbbadabdabbdccaccbabdcccdaddaacbacdbabbdcabaacdccbacabddbbccdccaabbcdbcbcccabaabbbdcbaaaddbaccacdbaabcccaacccadabcdcdbcdabadcbcaccbaaaaddbaadcaccbaaadbbccccadaddcadddacbbbdcbdaaadcbaacadcdcadacaaaadabadaabaacbaccaabcbcdadaabcbbacdbbdbbaababacdccbbddccccaddddddacddabdccabbdcacddccbadabbdcbabacbcadbbbcdcdccdcacccddcdaaacdabbcddcadaacdbdcdcbbabbbabbaaacbcbcbadddcccbdcdbdaabbbbbaacbdcbbcbbdbbcacdbdddabcdbbdbcacccabcbbabadccaaababbcbddcaccbbaaaaddbdbccbbccddabcbaaddadcdcadbcabbbadaddaabdbccadbcbcbaccadcaacbdacbbdaabaaadacaabddcdddaccdbbaadcddbccaaaabdddbcababaccbabaabbabbcdaaaadaddbcdcbcdbddaddbdbbcacdccadbdbbddcbaacacbdabbbdccabaaaaaadabaacbccdadddcbbabacaaacddaddcdbabdbbddacccaddabbacbbcabaaccacaabccccabcbadbabcdbdcbaabcababbddadaabdcdabbacbdddccaaabcbcdaaccbadadadacaaabbcbcccbdaddcabbbcacdabddcdcbcdcddbbcabdddcabbcdcbbdddabdabbdddaabdacdbcbcbdabbbacbaadcbadcbadacccdccccddcabbbdcababbaabdaddbcdaccabddccbadabadbacbcabcbadcbdcdddbcddbdabaacbadddcbdcdacabcacdcaaaaccdcdcabbccadbabbbcbbacbccdcbbbbbacaaababdaaadcdcdbacbccbcaadbdbcaddaaccadddcabdadbbcbdacdbcdddbbadacadcaddaddbcbdabadacddcdcdbccdbddaddbbbaaaaadddbacdccacabdccbcccbaadddcbcabacdcdbcdbaaacadddacaddaadabccbdbacaadbcbdabdbcddcabcbdabdabcaddabaccbdddadcabbcbbbdcabcbcddbbaabdcdaccccdacabbddccaddacadddbcaccccdcdacacbdbbcabbcbabaccadaaccabbbadbcbabacbaacbbcccbdabddaaabaddbdabaacddcdadcdbaccdbabbaaacaadaddcabddaabbddccdbabbaaccbddcadcadadddcdadabbcaadacdabcacaacaccddbdcbcdbabaccaabdbdcddacbdddcddacdcabbadbddaccadbdcbadaacabaccbaccbdacaacdccacddbbccadccabcacdbdbcadacdbddbcacccdacaababdbbaacaacdddbabddddbcaccdaabdabccaaadbadddadcbccbdbbbaacaabdcdabdbcbbdcacaacbddaddaaababcacdccddddacabdcdcddddadcbbbdcadcbccbdccdbdaacacadddcddacbacdbaddccadaddcbbabccdabaaccbbcaddbaccccaaaaabcaadbcbbdabdabaadbbbbacbcbccbaaacddbabdddcadcdccbbdadbaaabdbacaddcabbaadbaddaddabacbabbabaddccabadaddccdcacaccaddacbadcdcabdabcdbdacbbaddbccccabbcbdcccadadbcdddaaccdadbdbbbdadccabbaacabbacccdddbcadcdbcdccccbbbccaccaacaadbdababdabddaacdbbbabccddcdcbcdacbcdabadacbbbdcbdbdabccbcbcaacbacccbbddcbabdadcbabbcccdcdacabbcbacbcbcdbbbcbbcdcacddbaaaddabbabdaacbaaabbdcdbcbbcabccccadbdadcdbcbbabbabccacdabdcadcbbcaadbbddbbcaccabbadddbdcbacadbdadccdddbadbabbdbacabdcaccbdaadbbdadcbacdddcbbacacbabbaddbbbacaaacbbbddbaddbaddacddadabcbbbdbdcdcaadbabdbbdaabccddccaadaddadaacbaadcdcddbbbbcbbbaaaddddcbcbababaaaabdddbdbdddcbabcadbbddaabcbabcdaabaacbbaacddaccddbbaccbbcbaaadcaabacdcdbbabddcdddbadbbaacabccbacbddbccabccdbacabadbbcbbbccadabbbcbabcccddbaabadcbdbcdddacbdacaacbbaabcccddcccbbcbcbbccabcbdccbccabdcaccdabbcbdbcdbdcdbaaaabbcdaadacaabddbacbdbccbcddcccdabdcacbbdddacbbaabdbdcdcbdccabbdacbcbdbdaaaadcdbdadbdcabbbdadccdbcbbcabaccccbacdcbdbdcacaaddcbbaccacddbadabddcdbcbcdcbacabdcdabacdbaacddabbcdbabaaccbcacbbbaadcdadaaadcbdacacbcbaaddacddbdcdbdbbbdbabacaabccdadcacccddbaadbaaacaccddbbaaadcbacababbbcaccbcabdcaabbbadcdccbcbababbcbabbdbabcccdccdbbbdccbbaadbaccbbcbbbaadaabdbaadbbacbcdbbadcccccdcbbbdbadbabddddbcadbbbcdbcbdaadadbdaddaadbaaddcdabbbdacadcbbbccbadadbacbbbaddcdbacdddbdabdcbbaacbbbaadcbbacaacdbbbdcbddaaabdcbbdccbddbbadbadcacaccbddacabdcdccddcbbcabdbaabbbdccdcdabcaaaccdaabbadbdcddbbcdbcaacddbaadcbbdccbcacbbbbdbbbacababcbbdddcccdcaacaacbccacaadadbcbaadccdcbdaacbccbbdbacaccbbbadbabccaccbababacbabbcbbaabdaaadbdabbabadbaaacbbaccccdacdbacdccadddbcbdaaddccaddbdabdaddcbcadacddcabbaddddbbbaaddcdaaabcdabbbdaaacbbaddddadabccccddddadddbdcacbadaaddabdbcacdbdcdcbabaaacdddccdbabdabdbbacbcbbbaaadcdadcccbdbbbdcacacdacccdccddaababdddaabaadcdbacacadbcacadbbdadcbaddaadbaddbaabcdbdacacccbccdbadbbddadcccacbbaabaacbdddcbabdcbdccbdadbdadddaddcbbccbddcdcbcbabdacbabaadbacdacdbbddadbbaddaadbaaddbdcadcdcdcbdcadadabddddaabddbddcabcddcbaadbaacaccbbbaaacadbaccbbbccaadbabdbcdacdccabcdccabdccaabdddddcbacabccaabcbaccdabdcacbddcaadbdbabddcbcdacadcddbcbaabbdbaddadbcdbbaaacdaaacddbaabdcabaacaacdcbccacacdcddcabadcaddadbbaadadbbcabdcbccdabadaabcbbacdaaddbbdcbbbadddabdbabdadcabdbddcdadaaddacbaacddbbadacaaabdadabcaababdabdddbdbaacabdadcddacbddaaadccdbabbbaccabbbcdababbbadcbbddacdcaddcaaaaadddbdadbdcbcdcabbadccdabacbcaacddadbbccdacbabcddadbdbadbdaddcacccdacbacbaabbdaddabccdbdadaacaddabddcbdaccdbbccdaacccbaddaddcaacaadaaadbbdaaadaabdcbdcdaaababbbdadcaccaddccdcccaadacbdaaccbcbacdcadaccbbabccbbcdcdddbaddaabddccadbcccadcadacbaadabaaabcadaadadccdadaccdaaacccdbccdcdbaabddcdcccdacdcadacaccdddccadcacbbadddbcbaabcaababbabcdddabcbdbcaabbdcabddcccbcabcababadddcdcbcacadaacadcddabccdbcbbacacbabddbdbbcbbccadbaddaaccdaaddaadaacdabbdadabcdabbaccaabbcaacbcbcbaacccdacbccccdbdcabdbdacbdddbddcaabbcddaccbbcaccacadcabcacaadbbcdaacdbabddaddbbcadacdbcaabacbdccbcbbbbacbaaacabcacbaccbdbbbacbadabcdbdcbbdddddbbbcdbabccbcaaacbbadbbbbaabbdacccdaadbdcdcdaddcdbaabacacaabcabbaaaaddbaaadcdcdccdabdbcacdcbadcabccbabbdddbdcbcadddcbdcdadccdadcdbbbbbbabaaadaadccdbabaabdacaacddcbadddcddcabccbcdbaddbcccadaabddaaaddcdaabacababaadddcbacddbcbdbcccdaacddbdddcbbaddbabddacadddcdcbaadadabadabdbccabbcccdaccccabbacaacaaababcddcdadcdaaadbcacdadbcbbbbabbdccdaadbdbadbbddabaddbddbcbadbbabdcacdddcabbdcccdbbccddadaabaabadabbdbcccdbbababbcadccdddcddcccacaacbdbcbdcacddaddaabcadacbaadcdbddaacdaaacddbadcbcccbacddadcaaadcdbdccabadaccbbcadbadbcabdcbbbaddbadbbabaccdacbdddcaccdbdabdabcaaacbcbacbadbcdbdbbbcbbbdbdbbcbcadbccbaaccccdaddcdaaaccacddcdddbdcacdadccdcabacaccdbccdcaabacdbdbccdcbacccadadaaddbdbdbdbddbacbaadbbbbbbdbbacdbcdaaabcabccadcdbccbbaaaddcbccdabdbbbdadbabacbaccacbcbdcdbadcbbcbbacaacccacdbcbbbdadbabdbbaabadadaadcbbbbbaabcbbdbdbdcadcdccdbadbcaacdabcbabaccabdcdcacdacdcdcdadbabbbcbbabdcdcbbcccabdbabdaddcdadccadddccbabbaaccaddaabbccadbadbaddaddcddbbdbdbaaadccbacdcbcaaacdddadddbcaacaddbbdcbbccadbbaabdadbbabdbcbcbcbdbbcbadccbccacdcaadaccdcbcababbccbcdbadbdcdccccbdaabcaddcdaddabccbdaddcdabdcbaadbbcaadcdbdcbbccbdacddadcccbbdcbdaadbbbbcadabbabdbdbabbbadbcbdaaabcbdbaacacbbaddbcbadbbcaaccccbdbbbcdbbacabddaacddaccdadddaacdddbadbcdacacacdadcddbaabaaabacdbdaabccadadbcdaddacccdcdccacabcbbcbabdbacabcbcaadbadacbbdcabbdcadbcbacdbcdcdaddacaccddcbdbabadbcaaccdcbbaaadaccacadccaadbcacddaccbccbbaadabbbdacdadbabdcaabbbddabdcddcaabadcaddbdabddabcbabccadcbbbadcabbdcabcacacaadcabababbcacccacbdcddabccdbbcbdacbcaaccadaaacdbcacabcdcdbcabcacbaacabdadcbbdcaaccadbbabbdacddcddcadccabccababdcccabcbcaddacdbbcbbddcaadacdbcadcbddcdbacaccdccaadcdbaadcbccccbdbcadabcadabcbbcbcdabcddaacaaddddcdbaacbcdbabaabdaaaadadcddddaaadbddbbbdccccbcadbadcdabdcbdaacdaadbcdbcbcddcaccabbccdbdbaacbcabbaabdacaddabcabddbdadbdbbcbbcaccbbdabcbcaacddbbacabddcababdbcbbaadbaaadcccbbacdcadddccaaacdabddbddccabbddbddabbbadddbacadbacadccacbcacbdcbdcccdbbdcaabdaddbcbcdbbdadcadacddacbcaaadbabdcaabbcaadaadddbacbbccddcdbdcbcbacdbbabbccbbcbbcbcbbbadbbcbdacdadddacadbadddbadbcdbdbbaabddbaccbbadcdbadcdbabccacbacdadcaabdcbbdbbdabbbabdddaaabbbaccbdbaaccaadbddabccddbccbbbaacbdbbcabddbdcadaabcdbbadadadddbdcbdacabdbbacbcadababddcdadbddbdcdcacbddcdbdccdacabacbbbabbdbabacbabacabccbcacdbabddbadcbdddcadaabbaccccadccaadbaaababaabaddcababbcbcacbdcddbacdabcbcdabdcddbbbbcbddbabdddbcaddcccadcdacdbccdbbdadbbcdcaaccacddccdddddaabcabcbdbbbbaaadddbbdcddaccbbadcdabcccbdccddcbaccaaadddcdabcddabcdccbbcdbbcbccdcbbbacacbcaaddcbbcbdababdadaaadbbddaacabcbdcbaadbabacbbddddbcbaadbdadadccadcacbacbbacbcdbbbaacabccccbbacababccadabcbaacacddaacbabbbaaaddcaccdbabaccacadddbdbdcdbccacdcdbbbdcbdbdccdbadbbdbbdaccdcbcadbadaaaadbdcdcdbacbaaacacbcbcbcbaddcbbbdbbaccbcadccadacabddbcacdbcddadbddcacadbbdddbbdcbdbbdddabdbcbbdddbbccbddbdcdddaabcaddcddaddabacbdadbcbdcaaccdabbddbbbaacdabcdbaacbaaddabbccccddacbbcabadaaccbdbcbcdabbcdbbabcabadccdcbaacabadacdbbbabdacdbdcbbbaacbcbadaacdcdacabaccacadbccaaadaadbdcbccccbbcdaacbaadacdaaccacccbcadaccbcbacadadbdcbcaadaddadbcbdbbdbdacdbdccbbccaacadabbbbbacdcbbcdaadbaacacbbdaddcdddddccdcbdcccdbbcabcabccbdbbbcbcddddbadcaacabbcadcbcdbdbbadcbbadbbaddbaccdabcacbadbbbcaadacaddaddcbadbdcbcbaabcbadbdadbbcababdaabdccdcdaaabdacaaccacbdaddbcaacdddaccbaccaadbcbabdcbcbbcacbbabcaaaadddccbdbadcbbcbdaddcababddacdbbdbbdaabdcbbaaabcdadbabdbacccacdbddbbcabddabbdadcacadababccdddbcdacaabdcbdcabddbccbdddbacbcdbdaaccdbababccbccbdccccdabbadcadcdcaaddaaadcabbdadbbcdcbbddadbdbdaaaadbabadcbdadcacdbbbbcdcccaabacababcaccbdccadadabbcabdcbdddbcadcbabdbcacadbaadaadcabcacccacaabcaadbabdbdcbaaabcbdcdacbdabdabdadaabdbcdcbcacdadabddddbcdbbccbacdbdabccaddbcbbadcddcddaabaadaccdaccbcdcbdacaddbdcbaabacaabdaabbbdaddbadacbaadcccadbadddbaaaacaabccabddbcdbaaadbbbabbccbbbcaaacbaccabacaccccccaddddcbaaddccdddaabdcbbcdbdacddcccadbcbabcdaaccbcdbaccabbabbcaaababbcdbbbcabcaaccdcaacbbcadcacadbcaaaadcccdaaaddaadbbcbbbacbcbcbaabcaacdadaabaabaaaacbcbdaccbbdcadccbcccabcbdacdcbcaddaadbdcaadccadcbbaacbcbaaccbaacddcdabcbabbdcadbadcaacbdaddbabccbacbbcbbcaddbaddbabbdbdddbddbbdabdccaddbbcdccabcaaababcbcbadbdcadadbcbdcbaccddddaaacdbcaadccabacadbbbddcbbdbabdaaacbbbdbdccddacdacbbacbbbdbbcaacbdbbcdccdcbcdadcbbadadabcddaaddbddbadcbabcacadcaadcbacbdaaaccbcdbdccacbacccbdbbaddcdbbcacabcadaccbbbbbabbcaadcdbcbccbbbaaadabccbbdacdbabdbaddabcdbabdcadbcabbddbadcdadcbcaabacccabbcdadabbcccbddbaccdccdaaacbcbddacaaaccaaaccacdabacbdacbadbbbbabcbbbbdcabadddcddcbcabaccadbadbbddccdbccbdccbdbabccbcbdabadcbdababababdcbdcabbacccbdddaddddaabbcddbbcdaababaddbcbcdbcbdccccddcbadaaaabbbabdaaccbddcadadcbdcabcabccaccbbccbccabcdbbddbaaddacdcaddadbbabdddbcdaabcccdacbbabcdccbbcaaabdddbcabaabdbacaacaabbcdcbdcddcdcbcbdaaaaaccdadbcdcdcbdadabdabddaccbacdadcdaadbcbdbbdcdbbbbdbdcccaadbcbdbdcbabbdabbacabcccababdbcdaaaccdadbcbdbbbbcbddcddbdcbdcdcbbbbbdbdcadcabbbbcaddcddbacddbbddbcbcacadacacdbbdadcbaacdddabaccccbabadcbdadacabddbaccdacadccddbdbddaddaacdadcdaccdaabcaacbbcbaaabbabcdccaacdaaababaaabbbcdcbddbacdcbbbacabdabacaadddaaadbbcadbaadcaacbabcdcbaadddbaabcabdadbcccdcdcadacbaacdbcaadcccacacbabbbaacdcadaabdbacbdddbbaabcccbbacddcaaccdbbaddbaabcdbabaddbaddddbacaaabddbdcaddcabdacaadaccbcabbccdbadaabccbcaabdabbdacbbabcbacaadaccdaabccdbdbbbccacdcbbabdadcababaacbcbaadddaabcabdabadccadcdccdbdadabaddbbccbaadcdcdccddbdaddccbbabbcabdbcdabdbcdabaaaadbcaaabcdbaabcbcaacddabbacbaaacbbcbbcadbabaaadcbdabadbcadacbccdbadbbababdbbaddcdbddcacbacbcabacccbcdcadbcacdcddadaaaacbbaacbadcdcbcdaddadcaabdadcbcdbcabdcbbdbaccabbccbacacbadcbaabccadabcacdcdccadcdbbacdbbcdcbacdabcdccccacddaabbacbdcbbaccdbbcbbccabcbddddadbccccaaabacbadcbdaabbacbbdccdbdcaabbadaadadccdbcccacbbdbbbdabcacccadccabadccdcadbadcbccabdbabccbaccbacdbdbbbcccdcbddbadbdcaddcdccccdacdbcababdaaddadadadcdacdcabbdccdcabbbacaaabdadbcdacbcbcdbbbadaabadbcacadbdcccacccdcbccacbcdddabbacddaabacdabddcaacdbdbbbbbcbcadacdcbacdbabcbcbccbabbccbbabadacbbcbcacccdcbadccdbcbbdbbbbbababadcbacaabaaccdcababbdbdccddadcdabdaabcdbcabcbddabcbabcaacbacacababbdabacdacbddcdbbddbdbddbaaaacdcdadabaabdacccdacddccbabbbcbbcbddcbaabdcbabdbaacbaaacacacadcbdbabbcccbadccaaacccdcdcaababaaadadbcbaacaabdacabaaacbcbbacbddbbabcbaccabbdbcaabbaaabbadcbdabaddddaacccccbababaddcabdabacbccccbcccabbaadaccbadbcbcbcacbcdddbadbabcdddbdbbcbdbaadcaadabcdadbdbddbabaacaccabacbdcaacdbcacabbccddddbabbdcbabaddcdcccabbcdbbbadbbaccddbbacababcabcdbdccdadccbaddabcbccacdacdbacaabcaadddabcbbbddbddbcbcbadadaadabbdbacaacadbdadcbdcbbbdbcbaacbcaabaaaccdadbccdcddaadababbbaccddbcabbbbccdacdbaabbadcbdcabbcaaacbbdacbbbaccaabbcbacccdcdabbbbabacbccdcccabdbbbdaadcaababbadcdbcbbdabdadcaabbbcaadbbcadbdcbcaadaddddbadaaacababdbadbdbdadccdccacbaddaaabaabdcbcdccdccbaaaccdacddbbacdbaadcdadbadaddcbababbcddacbcbdcbdcaaabdbcabacabddbdaccadaabcbbcbaacaddcbadcdbdadababdbdaadbaddabddacaadaacbaacbadbdbbbbdcbcbaabbcacacdcdaddbcdabadcdacabbccbcabdcbbccbbccbadcccbaaaccdabcdcddadbbbddabaaccbdaaaaaccccadaaabdbdcbacccadbaadddaaccdcbbaccaadcdcccccddaccbbababcadabcccacabcbdacdbbcdacccadbdbbdccdccdadcaccaccbddccbacbabccbaddadcdbddddcdddcddcdcbaacadbdcabaacabbbbccdabbbbddcbbcbbbaaabadbcbdcbcbddcbcaadcbbdaccdbcacdbcbbaaacbcbbdbdcbccbdacadddacdcdcaadaacdcabddbbacaccccbcaaabcadbdabdddddcabdbcadcdcdcdbccdbbccdaabbabbdbdccbcdcddddabdccbdcbddccabcaabacdaadcaadcccbdcbdcbddacdabcdcdbacbcaadbbdccbccadaddcaacdcabaadbabbcdcbdbdcddddbacbabdcabdcadbbadbbbbcaaaacacadcbcabdcdbbcbcddcacdbdacaabcabbcaaacaabaadadbadcbdcbdababddaddabbbdaadcddccaccadbddccddaccbabdabbaabdbbddcbcadccdbbbadbcdbbdcbababcdcbcaadcacacaadcbdaabaacbacadcdadaacbbabcdbdbadcaddabcaaaacacbabcdbcacdaadcbabbbbcbdcddddccbcbbaabcbdacdcdbcdcdabdccddbabacacddcadbbbadcdccbadaccabaaacbdbcaddbbcaccccabbabddcaaadadbdccabbabaabcbbcbacbcacbbaacbbabcdcccbabdbdbadcddabacabcacacacdcddcbbbdddbdcdddadddababbbdddcbdadaddbddbbcdbcbbddacaadbbbaaacacacababcdddcdabcadbaadcbcadbbaddddbabbddabbdddddccdbbadaadbbddcdcccdcccdaadccdadcbbdbcbaaddbbacdbabdbcdacbcadacacccdcddbabcccbbcdbddadaacddcccbccbbbdbaacdddbabddbccdbcdcdadaabadbaabdcddabacaaabdcddcbaabdcbcdcbaadacdacccdcabbcdbaaddbcdccdaddddacdcadaacaaaddbbddbddabcbbcbacadbddaadbaaaaadbacddcbcadacccadccccaadbcbccacabcaddbdbcddbbddaadbcddddadcadcbadcaabccddaabdabcdbbbdaddbdddbbbdadcaccbbcdccacbbdbabdcbdbbaaabdcdbdbcccccacacacdccccddaabbdbbccdddbbcbdcccacacbadaacbcabbbcbdacdbcadbbcbcdbccaacdbbdccbbbaccdabdaccaddbbbdadbccbcdbcccabdcbdcadbdccdacaabbcbadccacbbdbaddacbcdbcdcbacdcabacddcccaacdacdbbaabcaddccccbbbacaddacdccbbbcbadddcddacdbdacbbaacdcabaabdbbbdbcdbdadddabaadabdddddacdabdbcddaaabacbcdabdbacddadddddcdbdcddbadbbbcbddcaaacdddadddccaaadddadbddbaacacbbbcaccdacdacdcbdcbabdcdbbcabcaddcdbccbcdaacddccdbaaddbbadbbaccbcabaabdcaaccaadddcdccddabacbdcbdaaabacbaddbcddacbdcdbbcbbbdcccccdccadacdbadadbaaaccbabddadaacdddccdbcadcccbdbbbbcaaadaacdbbddbcdcacdaaaaadbaaacbbdaddcdcbdccddcddcccdcadddcdcddaadcabcdccdbbdadbdcadcacadddcacccddddbcbccdaacadabdbbdddbcaddcbccaddcdbcabaaddbbadbcbbdcdabaaccdadbcbcdcdcdaacbabcabddddaaabacbddbdacdbdcbdcddadbdaacbdabbcdcbccdacabcbbabbacdbdcddddbddadcacacaddabdaaccdabbbcdbbcdabaddccbcdaaccdbdcbabbabdcacdccccadcabddbccaaacbccbdccbccdcbbdaaabbdcdaadabdaccddbccddaaadacacacbcddaadddcdbbabdccaaacadccbccddabcaacbdbbcccdadaaddaadbcbdcbbcdbdbcbbcbcdcdcdcaabdbcdcdcbcadaaadccdbaccacdddbababbacdacbdbdadbaadaacdbbdacabadaaccdcdcaddbcbcbacbaabcababaddaacdcddcaadacdacbbcaabcdadbdbacccbadcdbbbbbaadaabadcccdbabcabdaabcbaabadcbacdccbdddabbddbddddabababbabbacabbcadbacdcccddcacbddacddacacaadcaccbcbbaabcccdababaddabaaaacdacbdbdbcaadaaaaadbbdddbbdabdacbbbbdacbadcadbcdcbcbabbbcabadcaacbadbaaaddcabbadccbdcbddbabdbacdbddcacccababbcbacccacdadcaadcbccdddbaddccbdaabcdbcaaddddbccddadbdbdccdababbcbcabbdaaddddacbabbbacbdabdaccbdcdadcbcbbabbccaacaccabcbabcbdadaabcbcaacccdcacbbbdcadddbdddbbaaddcbdccdbaabbdbdcbddaddadadcbadbbcacaabcccbbbcbacacbdaddcbabbbacbbcddddcaaadbbdbbcdbbacbdaabcbbcbdbdabbadbdaabdbddcadcdbddbdccdadbacbcaddbccacdbaacacacacdabbddccbdcdccabdacacdcdbddbdcaabadbbcccdadaccbbddbdcdbadbcacbaaaaabacaccabbcccaaccbcabbdaadaaadbbdbbaabbdcabbcccbbddcabaaccdbbacddcddaadaadddcaacabdabbbdaccbddcdbdbdbdaaacabcccbccaacbbabbabaadaadbbdbadbaaadbddbdabdbcaddcaadddddddccdcddcccacbbdbaccbabcbcdbaddabcbbaabdaadabddabcbacbdadcabacabbccbadabaaabbbdbccadcdabcddacdddcabccbabadcccaaddccaabccacbacbbddddcdddcacdbbbbacdddbbbcbbcdcccbddcdabbbdddbaaacbadbadbcdbaabaadaddbdbcbaacbbbadabbaddcbbdacabddabaabcdacaadddcddbdbacabdaaabcadbbbcdadbccdabbaccbcacbcadddabccabdcdadbddbcbaacdcbabaddddcacdcabbbbdabdddbaddddcdadbbbcddbadcaccdabbabaabdadbabdadcbcaddcddbcccbdacaccdcbbcaacdcaacbdcddbbcccaabbaddbbbabaaddbbdbccbdbcadcaabccbabcdcaabbbadcbdbcbdcaacdacaadcacbdbbddcaadbcdccbacbcbddddabaddddcaaadabcbabacccbacdcacddccbbaaabdcbabaacaccbadababccdabdddbaaaddcbabdbdabaacccabaaabcabdbbabcacccbbbbcddbbddccaacdbacbaaccddbdbabbcdaccddbbcdcbccaaddbcacdadadacadccddaababcdcccadccdaadcbcbdbadcbbbdddbcbaaadadcaccacbcaabcdbacdcabcbccbaddaccbcbbbdbabdaaccbaabababcdcdccbadcbcccbbbcddabbadcbbcaaadbbdaadacabcbddbbbbaddbcddccdaaaabdadaadadaddcdababacbacccdccbbdabdadaccaaddcdccccbacbdaddabcacdbbbcdccdabaddaabbaccddbbbababcddcacbcbdbabcccbbbddabcbcaadaacddccdbabababdcdacacdcbcbbbcdddcaadabbbdadbdaadccccbacabbdbabbadbadddabcdbbdcdccdabdddaacacdcbabaccddbcbcdddaabadcbaacdbdcbcabdbbbcbcdbdcbcbbdbbdbcaabbadbbccbbbaccbdddcbcbabacbbbdccabddbaccaaabadbabdbdcddcbabbcadcbdbcbbcbaccacdbadddcacdbaabbcbcadaacdcdadbadadaacadcdbaabdcaccdddbbcaaabcbcadbccacccbdbdcdccbacbacadabbddddbbbabcacdccabacacbcbbbaddbbdbdddbcacdbaaaaddbdbadbbdcdccccaacccacaaabadcacbbabcacaadacbaacdbaadacadaabdcaddacabcaddbccabbbcaabcbcdcddccbbddbbbbcdaddabbcdcddbbcbdbdccaababccddabaaaaaddbabddacbdabcaacddbdbcddcaacdddccbcadbcdbddaaddaacabbbbcaadabddcabdabcbddcbbabacdbaddbcdcacbccacddbdbbcbdabcbddccdddacdbaaadcbcdaccaabbcbcabbdddadabbabbdaccbccdbbdadcbbaabddabbccccdcaabddcbdbacddcbdbdbaadcccbcdbadaccacbcbbcabdbdcbaccccdcadbdcccdaadbbcbacabccaccbabcddcbbddadcbcccaabdccdcaabababdacaadabbaacacdcbccddabbddbbbdaabaadbaccbcbbdcbaabadddacabcdaadddabdcbdbdddcdbcdaaaccaddaddcadacbccddcbdcdaccbadcacaccbcbdcdccaadbddbaccbbbcdbaddbdbddacbabaddbaabddbdbbbbcbbbadaabbdddcbabdbadccaacdccadadaaadacddadbddcbcddcaccbdbcadadabaddbdbdbcdcaccbaaadccbdcacbadcaabccdbadcbabaabcccdcaaadbdccabbabbbcabdbcddddbcccbcbccdadaadcbbcaabcadadacbcddcbbaddabadcaaaaddcaadbbabcadcbbdabbdccadcadccddbccdbdbcaccdabdaabbaabdacdbdbdbdddcbdbaccccbcbadbdddbccabdbbcbccbdadcdaaabccbadcbdcdacbcbdbacbbbccccdbbddccbaccbccadcdcdbacadcccbcbddcadccdccaaabbadbcdaadccadacadddbbcddddcacaadbbdadadbbcdbbadaabdaaabadbdacaadacbaaabdbbadddcccacbaaabdacbccdadbbcdccabbaadccbdbdddabbdbbabccbbadadcbdacbbcababbcbcccbcbcaccbbdcadbaaadbbadadacdaaadcbcaabdcbdbadbcbdacdbbbdbbcddacdcaacadbcbbddbdabacabbbabcadabdbadcdbddbaadbcddcdaddaaddcaddcabdbdadcbdbdbdaaaccaacdbbbbbccbbbbbbbdbadabadadabdcdadacadbdbcacacbcbcbccddadcdabccbbbbadbaabdadbbbbcabacbadadbbbcbbcdbbdbdbabbbcbcadddadbdbdbbbdcdccdadcacacaacababbdcadddbdcdcdcdaaabdcddcacadbaabbdadcdaabbbdadadcadacddcadbdbdaabbcddabdcddabcabbbacccacbbbcacdccbabddccaddababdbbacdddccbcadadbdcabbbabcdbadbadadbbddaccdcabdaddcbcbccbdcccbdcacbabbbadabdbcdbccdbcacdccccccacacbbdcacbaccdcababcaacbccddaddbddabbcdbccccbdaaaccdbcbdbbadbdabdbdbcbbbdddcaadcdbcccdadabccccbaaaacabccbcaadcbdddcdadacbaaddabbdcccdccabdaabbacbadbdadabcdbdccaaaadbaabaaabaddcdacacbddcadadddaababcccdccbaacbccbacdcaddabdddaddaaddbbbcdaddcaadaabbacbadadcaccdddadcddadacbcadcbdaabdcababdaccccbaccaaabaacbacddbabaacccbbaddddcbcbdddddbbacadcbcbcadbdbddbabcaacdabbcdbcdcacadaababbdaabccbbdccbcadaddbdcccccaaabdcdcdaadaadbccadcdccdcabcbbbbaccdbbcddddabcadccbdcbccbacadbbaaccadbccdcaadbacdaaccbbccdaccbadbdaccbcccdbacaaccbaadbcbcbdcabddbcacaabcbbccccadacbaabddcbbccddaaacbaddcaaacabacbccdbcdcdcaccbbaaaabcacadcbbabdbaaaadabbcbbcbacabacadcddacacdbadadbcababdbcbcaabbaababddadadaaabbaccababcddccdcabdaccbadbccbadaacaacbbacaabadcddbadcabcacbdbabcbccabcbaaaaaaacdcbbabdcdaccacbddcbbcbdbcddbdccaddacabdabdcdaddcbaaccdbaadcdabcbbcdacadcddacacddccbdcabadbdccbdabbbdbdaccdcaaadbadbdcddbddbbbbcacadddadcaddbbdccdcddddbbacdacabacdcbdbacdcdbdaacabacdaccbcadcabacbbddcbaadccbcaddbdaadcdabddadcaddcbabbacbdbbbddbbbcadddbbdbadbcaadcbaabcbadbcddcbcabcadddbadabdaddbdbbbbaadaddbabdcbbadbdbdbadabbbdacbadcccbbdaababddbdaaadcbdccbdccbdacdacdacabbcabacdcbaadbbadddddacaabcdabbadccbdcdcdcabbcbabbbdcbdbdbbbacbbbbbcbcbdcaccccbbabcccaabddadacaabbbdaadcdddcbddbacdbdacabccabacacbcbaccdbcddcadccdaacabdbbdabdbcacbaacccaabadacaabbabcdbcbdbcbaadbdbacacccccdacbaadabbddcacbaddcbcacadacddaadcadacbcaccbbacabddcddabdcaddadccbccacdacacccbbccbbdbaacadbbdbbadcbadabbcabacabdccdbddbbdaacdbaddddcbcdddaabbdbadadaddbbdccdcadddcdcccddbcaacdddabcdadabacacacdcbbcbaddccaaacacddabcbdabdbaaddbbcbbddcbbcaccbdddadcdbbbcbcabadaadaadcacdadaddbbaaadabddcadacadcabcacccbbcdaaaccbcdcdbccccbabccbaddbabccaabdccaccadbdbbbaccbcbaacdddcacbbadbacbbaddcbabcaabacadcaddcdccabcdbacccbcabdbcdbbbdcdbbddbacaaaaacdaabadbbbaaddccabdcdabaacdbdddbddbabcdccdabbabcdadcbcbbccadaabadbcadcbcdcdccaaddcadbcdccbaccacddbbdddacbacdbbadbdddcabbaddcabbdbbccabcbbbcdcacdabcdbbcbcaacbbdabcabcdddcbcaacaaddabaaabcaaaaacdabcdcaabaabdaadcadddbdadcbaaddbaaddcadccdabaacccccaacbadabdadbdbcbcdcdaaaccdbcdababcadcddbbacaadadbbdbabcdaadccdaabbabbddcaabccdbacacacdcbddbccbacdcadcdaaaccccacbbbbdbdcbdcbbdabcdcddbcbdacaabdacdadbbcbabcbbaadbccdcdacaccbccdcbbabdabcbacacbacabadbcdaaaadbcbbdbcbdbdbadaaccdbcddbdbaccbdccddaaddbaacbacaacbbdaddaadbbdcbbbccacaadadcaccbbaabbcbacccdaabdaccabadaaddcddddbbbddbbaaaaabdcddabbcadadcbcdaadcbadcbbbaadcdaadaaadbbadaaddadbccadcddccdaabccdbbbbadbacddbacdadabadadbacbcbbbdacacdbbbdacdbccdacaccdccdbcbbcabdcbcbacbdbadabaaadcbacbbcbadadabcdcbadbbdadadcaddcabadaaaaaadbcbacaddabccacacadcaacdcbcbcbbcdabbccdbcdacaaabddadbddcbcabcdadabacddbdacdaacdccddcabbdbdbddbbadbcbacdcbdcdbaddcacacacaadcbdabbbbcbddacddaababacbbbcbbacbabbcbbcdbaaadbdabccbabaccccbdabddcaddbcbdcbddadacaacccdcdaabbdcaadadcbadcaaaaabadccaddcdcdaabccccccbadbbaddddabccdccbdbccbbabbbddbdcacdaaacbaadbbccbadbbccddabdbcdacdcdaaccbbddcadbbbdccbabaadbcdddcdcbddadbdabbddbcbaabacddaaaaabacadbcadcbdcabcdacbdadcdbdcbcbcacdaacaadccbddaaabacdaaabdbcdacbbacdcdcdccbdaadadbadcaabddcbddabaabcdaacbaacadaaadcadadbcdadbcdbddbccbbbdabbddaadaddbdaddadbccbaadaabdbdddddadcdbccbbccdadbddaaadbbaabdacabcdcdadaabdbdcaccbdadaaddcdcdbcababbabcadacbbaadbcbddaddbdccdbccaabcdaadccaabddbdcbbabaadbaabadadcbdcbdaaadcadadaabadbccdcaacaaaabdcadabbbbbacbddabaddbdbcacaaaacadcbadddbadccbacbabaacbaabcabaadaacabaddbccbbbaacaddddbaadcabdbbcbdbdaadaacbbbcadbdcacbaddbcbabcccbbbcbbadccbbcddcdcacadadabaccabdddbcbbcabbcccbaddaadcbaabdcbccabdcdccacbbacddacccacddabcbcddbdaaddabbcbbaddbccbccaabbdabcbbbdadbbaababbaabbbcccabaaacdbbabcabbaaaddccbbacbcaacbbbacaababbcdaaabadcabacbccbdaaabddcbcdbcdbddaacbaaccdcabbdcadacdadadbacdcaabadbdcacdcaabdbbdacdbcbdacbccaacdbbdcbbddaabaadbdcccabcbcabcdbcdbaccdaadcdbbcdbbdacdcdddaaaddcaccadbcaadccdaccbaddacacbadbcacbcbababaaddddccdcbacdabbbbcacbddbcdaaccbcabacdbbacbaabbdcbbbaadbbdddaacbadbdbbbddcacdacbdbabddcadadbcbdddabadacaaabcacccbacabdaccaacabaadcbaabadbbdaddabcaadbbaacdaccbcdaddccadddadcbdaacaaacddccccdbabbdaacdabdbbabcbacadccbaacdbddddccabbccdacacbabbbcabcbaacdaadcbaaadbadcbcaccbbddbaccbacadbcacdddbcabcbbbbdaddaacccacaccdacbcabacdbccdacdccadbbbacabbcbaabaacacbbadbdcaaabcdddabddaccadcdddbddcacbddbcacccdabcdcbabcaabadbbcabcbababadabbbcbdbbdabcaddadcbabcccbabdbcdccacddcbbcdcbaaaadbdaadcbccdacbaccdaaddadbddbdcdacaddacccbbaddacdcbcddccadbdbddbcdbbbcaacadababdbbbdddbddddbcbcbcdaddbcdcbcccabddbacdcacabbcdbaccabbbacbdbdabcbcdaadbcbdcbcaddaccaacdadabdcacdacabdbdaaacccadaccccdbbcabbadaccbccabdcbbbddacddacdadcacbadabddccaabcbdccaddabdccbacabddbcbddacbdadbdaacdbddacbdadbbdddccaabbadbbaabbbabaccacbbaacbcbdacddbaccdacbbadcadaddcbddabccadbadaddccacccdddcdadbabadddbdccbbcbbbaadadcacabdbcdbccdcdbcbcbdcbdadcaaabdaabdbdbaadabccbcbbdcdccbdccbbbcdcbccbbdbdaaaacdcbdbaccaaabbaddcbddaddbbdaddbabcadcdcadccddcbcbbddbcadabcabbcbdcacaccadcddaaccbbcaabdccdabdddbdaabaabbbadcdddacccdbcdabbdbdbcdcbacbccddadcccdccbcbcdbabcdabbdccbccacaddccdabdbdbadaaabdddabdaccabbacbcdcccdbbabdbadaacbdbcaccbbcddadbbbaddbccdbbdbadadcacddadcadcdaddccbaadabaaadcbbabddccbabcdbcddabbabddcbbbdadbbccadcabdbbddbbdbcbdaadadcdaaababadbdaccaaaabcdacaddcbdcdcdcadcddadbaccaacddcabcbbcccadcbbbcddadbbddabadadcbbcacdddbaaacbddadcaddbbaaacacbcabdbadcbdbaddcdcdcadabbcaaacbacadbacbdaccabadcccaccdbdcbdddacabdcadbcbdbacaddbaabddbbcbabcaaabbdbaabbacaddbcabdccddccddbdddabcaaabcdbdcbddabddbddabbabbdbdbbaaddbbdcbaaadcabbadaabbaaccbabaaccbbbdabcbadccddcdcaacddacdadcadbcbdaabadcdcbdcacaabadbaccdbdcdccdadbcccdbccccbddbdbddbbdaccbbcaabcddbcccbcdadbddbdbaddcacacdcbabaabacabadabaddaddabdbabdbbadbcbcadccdcbbabdbdaacaccadccdcbaddbdaacccdcaaddcaabcccdbdadddddbcacdbdbcdbddddacaddcaaaabbddbdcabdbcddccbdaabbbabbddbaddadccadcaccdacabcbbbbcdbccbacaccbabacaaccaccacdaddcccdbdcddbcccbaadaacdcaadabbddacadcccddccabdccbbaadddbadbbdbbdddbcdbbcaddbadcdbcdcaccbbdcccbddcdbaaddbbacbbcbaadcaadbbdcabacacaddcbbabbdabcbbdccbbdcbdbaaabaacacababccbbadcbacbddabacaaaacccdcababcadcadbdccaadbdbbabdccdaadacccccbacaacddaddbadaabbbbbbabcddbbdaadbbbddcbbaccccdcdcdabccadcbdbddcaabacbcbabadccbcabbaccaacddbccbadccdcbacaaaaadadabdcbdcaaaaabcdaabccbcccbbdcbcdccdabaaccbcbcdcaddccaabbbccdcdbdccdbaababbaabadccabdabccbcaccddbbaadaacacdaccdddbbcdadccbaacbcddadcbccaccddadbcbadbcdcaccabbbcdaacbddbddaaccdcaacccbdddacabddbabbbbbdddbdccaaacacacadbabdadccbbdbcaadcadbbacbacdccbdbddbbcbcdabdaabbcdcddbcbdcbbacdcbdbbdddccdcabdcbacacbdbdddacddccdabbabdadbdacddcddcaaaacccdacdcccdabccbdcbcccabbabcadbcaddaddbabdcbdbccacbaccbcbabaabcaabcddcccbaddbaddcaddacabdacbbccdbabbdaacbaccdadbbcbcbbdcabacabcdaaadabddaccbacababbadbcddcadccadcbbaccaccddcdcbccaadadabdbbabdacccaabcbcabbbaacdbddabadadbdcadbdadbcdabdabadccbcadbdbbadaaddcccbaacbcdddaabcbccdccdbacabbaabccdadbadadabcadaaaaaacaadcddbcdcbdcdbccbbdbbccdbddddbbcbccdccabdbcacdbacacdaababccbbcacddbdccdbbccdaabcbbaccaccdddcdababbcbcbadbcccabcaabcaabacadacdadcacabcacaaadcaccddcbaccadddabdddcdcdacadacacdaaddacbdddcadcacdbabacbdbcbabdcbadbcccdacccbdabccaadccdabdbcdcdabadbcdaadddadddacccdddaadabbabcdcabbbbabdabdaddabbccbbddaacdcabdacccdbcdadccaaaaadacdbddcdbbadabcbdcdcbdbcdabdacbbbcbcacbccdaadbddaaabbdaadddcddccddddabcaaddcadbaabbadcccdacbbdbaadbdbbddbdddcbcddcbbddadbacadbbdcbcacaaaacbabcdaacdccabdaaabacbaddbbdadcabddcddbcbabbcadabacbabaabcabadcbccbdbacbaaadaaacaabbddbabdccbcacadabbdccadaadcbabbadbacacbbadbabacccdbaabddaabcbcacddbaabacaadcbabddcdddaadcacbbcaacdbcbdbdcccbacddcdcbcdcacdbcbcbdcbbdcddcbdaaacacbabdaaadaddcadbdbbabdddcbcacbdcaadcacdaaddcdaddcdbbcdcacbaadcbcdbaadaaccbacbacbccbabacdacaabccdababcaaddccbbcccdbdaaadcbccbcdacccadcddcdababccadaabbcdbdcdababcbbcabddbaabbacdcabdaacaaddcddcccbcbabcaddcdacdcbddcabccaadcdcadbadbccddabcddcbadbcbadbbcaddbdbdacbaadcccdbbbbacdbdacdbcaadbaaccdacaaacddacbdacacacdbbbdcbbaccbdabbcdbaacaabdccdabbcdaadbddacaaabcbbcdddbadccbdcbababddbbcddbdcdbbbbbdccddacdbddbbddabadaacddcddcbdbaccaabddbbcccddbdaabbaccdcccbaaccbacdcdbcddbcbbcdddacbbbddcdbdbabcddbacbcbddcbacdaacbabdbdaccccccadabddccdcddabbcaacacdcacabddadcdbcdaddccdadcbadcaacaccadbaabbddccdcccaaaccaacacbadabdbcadbdcdacbdacbbacdbaabadacdbbaaaccaddcdbdaddbaddadaaaddccaddbdddaaaabcaabcdbcbdbdaacdbbbdaadcbcbcdddbbaabaacaaababdbddcacdbbabbbbddbaabadddadbaccaaacdbcadcadddbcbaaaddcbccacdaadddcadbdabcaaabddaddabbbcddcacdbbaaacddbacbbcbdbcdbabbcabdcccbbbaddbcbdaccdbcccddbcddacaddbcaadaccadcdbbdbbcababccbdcbaacbbcdbbdbbdaacdbcacbbadbddaacbabdcacabbaddaadbcdcaccdaadddcaaabababdaaccdabdcbcbabcaddbdcccdcbbcdccdbccadcaabbabbbcccdadbcbdbacccccacdcdbaabbdacbccdbbaacdbbbaaaabdcccdddddddccdbaadbabbacccbdaccdacdaaaddcdbdccabadbbbbcadccbdaabaacdcbbcddccacccccbdbacbbbabdcdcbadbaabbccbaadbbadacdbdcbcbcbcaaaabdbbcddaaccbcbcacdbbacddcccdbbdbdbaabccaadbcacccbbcbddaacabdbacdcabcbcbddcdcbbadaddcdadabcdbddbadcabdbaacddccbcdcacdbbaaaababdaaacabbabbcaabdddcdcaadadddabbadbddbaabccbccacbababbabddaddabadacadacbabcdcbbccbcbaacdccadcaaabbcbdbadcdcadbbbbaabadaabaaddabdbacbbdccadcdcbadcbdaaaadbdcadddbccabbaaddddcccbddadabdbcbbccacbccbadabcbadbbbddbdabadabdccbbbadbaaabcddbdcabdcaddaaddbcaaaaaadddbcdaddaacccbdbcdbbadbadabdbbcdcabdcadbcccbccaaacddbabcbbacaccacdbbbdcdabaacdbdbdadcaddbaaaccadddbaddbcdbcabddbcbdcbabbbdcbcadcbabaddbdaababbcddbddcdcaabdadbdcbccdbaacdcbaacbbbdcdcccbbdbbabadadbaadacadbcaddadaaaaccbccadcdbddcacccaaccabaccabbacccddddacbccdddcdcddaaadaccdacddbacbdbbaadcdcacbcbcdbddcddccaccddcbccabaacbbdbcbccadbddbcbabcbcbcabadbddadcabcdddacaccdcbbaaacdbaabccdbcabcdacbcdcbadacdcacaaddcaaacddbaccadcbadabdacacdcbdbdccabababcbcbccacccbdcddbdbadcbcabacbbbddcbbadabbdddcabbdbdcaaddccbdbbaadccbabbccbcdccbcccdacadadbcbadaabdbbaadbbdadcaccdcdcabadacccbdaacabbbbcdacbdadddbbabddcabdadbcccabababccadbcabccbdbdddabaccbcbccbdbdbadcccacaadadcaaddbcacdcbcacdbddccdadcdbdcddbabbccacbabaaaabaaabcbccbacbdabdcbcccdbabaacbbdccabddbcbbcdacbcdccadaaccdabcbbadbbcbdcaddddadbbdaacacdcacdbbdbbdcaddcdcadcacaacaccadcddbdacbdaadacddbabdbcbbadacbbcaabdbbbabdbdcdaccccaabadabacddcadbcadbccdadcaddabbdddaccbcaccbcbccccdcbbabcdaccdbccddaaacacaacdbcddcdbdbcbbcdacbdadcccbbbaadccdcdbbbbdcbdadcbddaadbacbabbcadcbddbabbcccbaacaddbbccdabadccaddbadbccdcbdccabdcacddbccbaddacbccadabcdadabdcbdddadabbcbcbccbcdccbbbbbacccbcabbbbbbadddbbdcbaacaabddcddcabadbdbbcdddcdbcccdbcaaabaadcacbcbcdabbaacdcabaddddcacbcbcabbdcbabaadbadadbadcabbcddcadaccadbccbcacaccacbbddcbadcdbdcdbdddccccacddcaaacaadbbaccbaadccaaaacdcccccdcacbbcbaacbbddadaaadbcacdcbcddbdcccdbcddacdbdddbddcabddcbcabbddddcaddbccaabdbdbdbbdaaddbabdabdbbcccaaacdacbaccdbbcbabacdcacbadabadbdbdccbacdabcadcaaaaaaacadaabbcdadcbacaddbabbaaccccccbbbcabaaacaadcbabccbdacddcdcacbcaddcdbbdacabadabbbadcccdabbcdbbbbbbaaddbbdadcacacabbbaadcadbabbcbbbdcacabcdddaadddcdccadddcbdbcbdddaabddabccdbbddbbacacddbaccbabdccccdacdacbadacdcbbcccbdcbccccadbdcacaadcdababadbdcacdbbddaaacabdaddccbdcdaacdbbbbdbcbabddacdbcdbadbccdadcbadbcddcaaabaaddbaadbdacacaabcbbbcabdcaccdadbdcbbbcddccbbdbcdbabdacbcacbdbadbbabaacabacccddaddadbbadacaadddcacdcadaabacbbbcccccbabdcdccdcddcddadddcdacbadcaaaaaaadcdabbadcbacacbaccadccaabacdadbccbadbbcbdbdddbacacadabcdbabcdacbaccbcdbdddcbbadcbacaabdcccddbbdcdaccccabcdbcbdcabcbcacdabdcacacddcbdcbddbccdddacbddaaddadbcbbdcddbbdaddcbccaaadbaaccccbabaabadaacdadbcdddcbdaddadcbcbabcadabbdbbdddadadcdbaddcadcdddbbccbdcdbbcbcaddadbaadbccaaacdabcbdaaccdbdbccbddddcaaabcdcababccbaddcbdaaacdcadcaadaaddcacdbaadcdddccdddbcbadcbbaaddaddbbcaacddccaacbcbcabcdcacaccbdadbcdcbcdaccabbcdabbacaaadbacbdbabbaadccbbabbbcbcadbcacabdbdadacdabcddcdadbbdccdacdbdbacbdbdaabaacbaaabbbbddcaacdddcdacbaacabcbcdcbdbdadaccbccdadbabaaabaddbcdccbcddbcbabbddcdbdbbcbabbbaadbabaccbacabaabcbaadcdbbbdbccbadcccddaddabcacabcaccccddccdcaddccabcdadddcbdaadcacdaadbcacddcdcdcdcaabcdbbcadcbbaadaabdcbcdbabbdddbdabdbcaadadbbbdbacccdaccabbbadabdabcbcdccccadcbabcacacdbabcddccdcbbaaccdcdcdaadcaabadcaaadbbadaaaaacdbcdbaaacaaabadbdbdadcccdbdacdbabdacbdcadcbaadabbcddabcaadddbaadbabaccacbacdabbaadaabbaadcdcaccdbbabbababcbbddcddddbbaddadaabcabdadcdbdccbbaaaaaacdbaadcabdcbcdadccbbbdaadddcbadbdbbaabbadaddccbdacadbccaaaabbaaadbaabbcddaddcdbddbbbadbcdbcbbcddbaabbcacabadaacaddbbbcddaddbcdbcdbcbdabdbcddacabdcbdaabcbbcababbaadaacdacabdccacbaaccadbcbbabddbbcacaaabccdbbdabdabcdbcbbaaddcaacccbccaccbbbddabcbdbcbaddadbcbdacbbddbbdaccbdbaccaabccdcbacbcdcaddadbbcdbcdcaabacdbadabdddbdbbcbadcdabcdaacdbbabbbadaaaaaccaaaccdbccadccadadbcccdddcbcdbbcdddadbccabbdccabbddabcbdaabacbdbacabdbdbacbabbbacdaadabbdcbcdccbaccbacccbdcdbdbbbacbdbabaccbacdadbbdbadbbddcadadcdbcdcccccadaadaabdcaccbcacaacabbabbadddcbbcdcdbabccccdcdcbcaaacabcadbccbddbdaaccdcdadaddacccbccdaabdaabbbddcccadcbcdadcadadddcdbbbabaddaaaaaabcdadbaabdaacabdbdcbbcabacdcbdcbbbadaddabbdccdbabcdcdccbadcdaadbcabaaaabccbcdbdacccdcbbdbdcbbddcaaaaaadbadbcbdbcbbbbdcbbaaabdbacaabcdddcbacbdaddbadacdadbcbadacbabcaacacdbdbcdccaccdcbbaddbcdbcccbdadbdaddbcccaaacaacaadbcdaaadbdaababbbacdbcadaaddcdbbbdbbdcbdbadbdcddbabacdacabaadadabacdbccdcbbccccacccacaabbbdbdccaddbabbbdacbacaccdbdddbccbdbaccdbdaadacaacbdacaaacabdcdabbbbdbaccaaabacdddbcdcabbdbdbcbccbcdaadaabcbdaadcccbcabbabcacaaabbdbcbbaaacdccdbcdacbadaadbabadcddcbcbddbbcacaacadccbbacbbcdbbccaaaaaddddcdcacdddbccdabbabbcaaabcabadbdaacadcbbabbadaacbddacbddbbccacacdcdddccbbaadadabccdbbabacbbccddddcdcdccbbdbdcabcbbaabbccccacbabdddaddaddcdaccbbcddbdabbddaacdccdbabbaccbdcdadcabdbddbcbcabcaaadcabccacdbbcdcadadbbaadaaababddadddaaaacddbcdacdacaadcaaabccaaccdaccbbddbccabdcabcdbdaacacddcbbdbaaacdababadabbdabcddabdcdcdcaacbdadabaaabcbbcdcdbcacabdadbadabacbbaaadbcdddaacaaadadbdabdbbabbdaccaddbabbcbbdddadacaaddcdbdbaaabdccaccaaaccbdcdcdabaaaccddbbacbccdaddbdcaaccbabcbacaaadabcbbcacbbbdbcccbbbacacdcbcadbcbcccdaabcccdacbcccaabdcccabaabacdccacbbddaabcddacdaccdcddccdccdccbabccababcacabddbcdccbdcadcbbbaccbadaccadaddaddbacbbcbcccdcbddcadaccbaacbdbbdbbaccbadaadadcccbbddddaaddcadbcacaadabbcddccbcadadbdcbcddbaacbcaadacaaaabbcccbddbcdabaabcacdcaabbaccdcabcccdddbacbbacdbcadbcaabdadcccbbaababcaabddddadbbbdaaababbbadcdbabdbcabbdacacacbdabbbbdbcadbabababbbabcdcadbbbddbdbdcdccdadcccddacddacddbbacddadbcaacabbbbdabdabcdcbadbcdcddaaabadabaaacbacdabccdbcdcaaddbacdbcdbdaaabbccdcabadabbdddabaddcaadddbdbccdbbddbbbbacbbbbcbacaadbabdcdacbbbabdcbadaaaddcbdacdbcaaadabccbabbaddcbadbcbaaabddaacdbdbccdcbbbadcdacdbabcdacaadddbdcaabdddccdacdbcdcbadabaddcdacbacaddcdcdccdccacdbdccccdcdacadaacacaddabbaccbdbacbacdabcbcbbaacacacbdddabacadaaaddadcccbabacabacacacdcccbbabababaacdbccccbbbbdddbddbddcbbbccddaabdbbaaccdccbbaddcdddcdddccccbadbaccbdabdbaacdbccdaaaaabbaccccdcacbdcaccbcdadcbbdbbdabbbcdbcddbadaabbcdcabcacbddabbacbdadbcbbabccbcbdaddcdcddbdabbacdbbddaaaabdccbacbdcddccbddacaaaccbdbdddbabadadddadbbbbccbacdddaabdcccbbbddbabcbbcabdcaaddcddddddbbcbaddccadbdddcccdbcaadadaccbdbdbbacacdbbabacacabacdbabddacdabaacdaabbcdcbadcacdadcbbabdbbbbbbccbcbdcbdabbbbcadabaddaacdbbdddbbaabccaaaabbbadcabcccadabbcddadbaadddddacdbbacbcbbddbbabbcdbcddaaaddbbadaadacdccabbcbaabcddbcdadddabbddcdccbacdcddbddbcadbcbdbbbddacadadbbcaadcbbccdbbdcacbdcbbdaabbcdbdcdcbcbbdbdddcbadadddacddbbadbddaacbabdcbdbbcdcdbcbbcadaabadabbbaacbcaaacbadabdbaabcdcdcabbdaaabcaadcaacbadcbdbaadccddbaaaabdabaaabcdaddbccdadabccbdabadbabbaabadcabccbccbbdbcddabdaacddaadcadcadbbacdcadcdbbadcbcaadbaabbabcbcdadbcababbcccccabbbaddcaaccabcdbaccaaabcbdbbbadbbcbbaaccdaccaccaabddadccaaaacdbabbaabdbacbcbbbccacddcdbaaacbbddcaabcaaadbacacddaababdacadabcaaacaddcaadabacabbddcdadabaaaadabbcdddbbdaaadbdabccabaddbbdcadbdaadddbbdaaddbbdbadbcbacdcbabaaadadccddcabbdccbbdbaccdcabccbdcdddadacadabdbcdcaddbdadacddcacaadbccdbadcbcdbcbbbbbccabdbcbbdadacbbdacbaabdcccbccbcdadacdaccbcdcbdbabbcbddcdaadaacaaddccddbbcdccdaadaacabaabdcbdbdadadaababaadbcbddcabbbabcddacabcbdcbcaaadbbccabbdcbacabdaacccdccdbbcddbdabadcccbcddcbadbccacdabdcccabdcababccbaccdbcdcbbadbccccdbcbbabcbacddaabadbabaddbbabddcddcadbccabcddddddadaacbcaacabdcbccbcacdcaacddbcddbcbcaccadddbdaccbadddcaccacddcdadabdbccdccabddacbdcccaabdbdadbbaddbcccabdcdaddbbaacdccddadbdacbcbbbcaadbbbbcacdcbacdbabacaaabccdbcaddbdbaaabbbbbabdaabccdbbabbbbbaabbaaadabacaacddbddcbdaccdbdadcbbdbdaabdbbdbaabbdccadcbdadaacadcdcdbdcabcadbcddadaacbadddbbadacdbbacbdaadacbbbcbdbdcddaadacbcbaadccdbaacaabddbcacdaabddbddbabdbdbdadbcbdccadccdacbbccdddcbacbcdcbbadacadcbcabacdbbbddcbcadcdcaabdbbaccbcbbdcdaaddccbcaacbcbdadadabdacdacdbdccbdabbcbddbdacaddbaaccccdddcaddcbcabbcdcbdddbcaaddcabaaccdababadaadabdbaaddadabaddbdcadabaaaaadadbabdcbcbbbdddbbccccbcaacdbbbbdbaabcccbabcbcdcbdddbbbccccdbcbccacccaabdbbdccbadbcbcbbcdcabccbbbbabcddcbbacaadacaccacadaccaabbadadbcddcabdacadcbacddbcdadbccabbddddbdcabdbcbaddddcddccbcaccbacdacbcadadabbabccaddcdcaaacdddbaadccbacabbcadbccbbcbaccdaddacccbcaaaddabdcdbbcddaaddddccbcbcbbdccabdcacccccabdbdbbccacbcaadacddcababbcaccbcdcabcbbcacdaadadbbbcbbdaacbbccdcbaacadbcdbbcababcdcacddcaaadbbbbbddcaaccbdbbbadaaccccacacbddaccdcaaadbcdbacdbbbaacddabcabababdcacaacdabadacbbcbadddddbcababbdcccaaddacabccacbcacdbbadcdcbbcdcadcacbcbdddaadabdcadcdaabdcdccdacbdcabbcbcdbcbdbcdcbcabdabcaaaabdcdcbbcadbdcbbcbaadcbcadadadbccbddbcbcbcdcbcbdbbbcacdabccbddabadbacbaadbdcacbbabbbcbadaabaaabccadadadaccbbccddddccaadbbaacbaaabcabccdbbadbcacadbbdbcaabaaaccacbbdcdcdabadddbaaabbacdbdbabcbdbdbbbdbcbbcddcbaacdbdcdcddcddccddddcbbddcaacbbadbacdbdaacddcdabbabbbcdbaccacaddabdbacbbbcabaaaaccccddbdcadaadbbaddcdabdacaccaaabbdbdcdbcbacdbbccbcdcdababbaaaddaadcdddcbdbddadbddbcaabddbcccbadccbcdddbadacdcbddbdacacaddcdabddcccbdaabccbbbbcabbbaaadabbaadacbcdccdccbbcdabbaccdabdcbaabacbcccddcacdaccacddaaadbbbcdacacbdcbbdcdcccccbadddddbbabcdacaadbaacaacababbdccdcdbdcacbcbaaaaacbdcdcbaccdbaadcbdaacdcacabbdaacabbccdaadddacbdaabaadbaabbbcbabbbcdccbbaadaabbddcacadcdbdbcdbddddadbbadabdddaacaacddbccdcbaddbcacacbddbaaacddbdacaddbabddabdadbaadcdccabbaacaadbbcabccccadabccbaddddcdabdbadaabbcbccababcaadbbbbcbacddacadddacabaacbaaaaccadcaccadcdcabdabcdcbaddbaabaadbbbdbddcbdbcbaabbbbbbbddbbbdbbccabbccaadcbdcdcbacdbaadbaabacaadaacdbbdbabadcddaabcdddccdccdbdcdcddacbabacabddadbbdacbabdcaddcaabccbbbaddbdbacbaababacaacdcbcacddbbcbcbbbcbddcbddcbbaabbaadaadbdcccabddddcdccabaabcdbadaccccddcadcccdabdccbaddcbccdbcbdccababdccbdabbacdbadbccaabddcbaaddbcbdcbaacbbcabddcaacaacacacacdaabcbcddbcabadbacacbbddabaaabccddcbcaadccaabdbbcabbdaabbdcbcabddaabdcdbcdabacbcdccbacacbcbaccddbcdbadaadaabccccacaaabcbaacbbaaddadbcabbadbcdcbcbcaadacbcccdbabadcbbdbdcadbccaddcbbadabadddbabacbcacdacdbbdbbcdaabcbadbdcbcaadccaadddcbbdbabbbdbbaccdcccbabcbdbddddcbdaacababbcdabadacbcdabddcdbdadcdbdaaabacbcddaabccddcdabcbcdaabcadbbcdadbdbbdcbacdbbbbcdcaddddcbdccdabbabcdaaddddcddcbcdbdcbbccaccdcadcabdbaccacabcadcdddabcabdacdddddabacdaadbbbcaadaacdbbcbcdcbacbdbccdcabaaabcacbbbdccaaacbdcdbcdabaaddcdbcaccaaacbcdaccbdbaccaddcdcdabdaccaacdacbddddccacdabcacdbcabbbbbacdadadbcdadcbabacddcdbdcaaabaababaaadbdbcccbddbbadbbacaaaddacdcbcccbccaabdaddccddcdabcdcadabddbbababddbcabbbbdbddaaacbcadcbddbdccdbcdacbaccbbbcacdbbbbccacdcbdcbccbbddbabadadddbdcdbbbadabbbbccaabcacaaacacddbcdaaabdbcdaccdabcacacacbabaadcaacddcdbccbcbccdbacadcbdbcbcadcbbbdacdbbcccdadddcadbbcadaaccddbbdabcbacabdadbadcbdcddbcaaacbdacdaabbddaddbdcaacacbabbdababbdacdccaadcbdacbdaaabaadcbcdbbbacdcdaacdcabdbaccbbdddbaadadbcadaacccdabdcdcddbcdaacacbacaddabdcbabdbbcbdacbabacbbcdbdacaabcbdccbabbbddcdddcccdccdbdacccadaddcddcbdbaaddcddcacddcbccaabacdcdaddbaaaabacccacbacadbaddbbdcabddcadbdaaaaddbdcbbbbdcabbcdbacbbddacaacbccbbadbaacdabbbcddcadcbaaabdcdddbdbbaccadaadaabdcdcdddcbdaddbcdbbcdcdadbddcaadcaabbccbddcadccabcbdddabcdbdddccccdccbaaabbdbcadddcaabadbacbbbcdcddbcaacddcbabbbaabcdcaacbcddaadababccacdcccdcdbabadddadadabbcbabadcddabdcabbcdbdcccababcaacadcbcddcbaddbcdaccbdbcdacbcabcbdccdabbcdbbbcdddacbacbaddacdbaaadbdbbdadaacdddddddcbadbabaaccdbcdaabbdabbcbddcadcacdbacbddcabdacddacddccadabbbbddbbcadaabbaabcbacbdbbddbabaccdccbccaacdbdcbdcdcdbbabbccadbabbdcdacdabcbaccadbcaccdddccacbbcadbdddadbddcadacacbcadcbcdbcbcdbcacaccdddacdbaacaddbbcbaabdaabcdbdaaabaddddadccbbadaadcbbdcdbdaabbaaaaddddcbcdcbcdbaacbddbcabacddbbaacbbacacccabcbccdabbcdbcdbdacabbaacdcabbdbdacdbabcabcadcadbdcaccacacddcbdabbbddbbababcbdbacbaddaaccbdabdbbbacaaddbcbacbaabcbcbcbccabcabdbcdadcbacccbcddbabaadbddcabaadaccbaadaaacdbbccbaccbcdbbcabbaaaaacccdcdcabdaabbaaaaacccdcdbdbcdcadbdccbbcacbcdccdbdabaabddbddbbcdbcadbbadcdbbcacccdbdaddadcdcccdbacccbdcbddcadcdccaccdbbbdddaacccbdddcabaaadbdbbbdaaadbbaaccabacdccaaccbabadbdbcacacbcaaababbbdddcdaaacbaacacbaaccdddaaacbbbcccddbaadaabadbaadacbababdccadabcdbcccbbaccdadbacaabccccccddacccddaacacbcbadddcadbdaccaabbccbabcaabacbbddcabcdaadadabbccadcbbabaabcbabcbcadddcbcabadbdddddaaacddaabbcabacaccbabbacbccbbbddcdabbddcabadddcbdadacdaaaaaadbcacccbdacdcccdadcbacbbbadbcdddadbbacdccddaddadabdaaaadcbcaddbddbdbcdbbadbcbdcabaaacaaacdbbbabcbbdacdcbbdbbbdcbabbccdadacadaddcccabccccddbcadbadbadddacddcddbddcbcacacccbaaaaccacccccdadbcacdddbbddcddcdcbbdcdaaabcabbadcacbcbaabcdacabbaaaabacaadddaccdacaccbbbccacadcbbcacdbcdbcdcdabdadccbbcaacabcbbdcddccabbbcdbcddbadacbadacbbbcddddaaaaaddbdadaddaabcbaacbbaddacbacbbadcccaadbdcaccadcccabbaddcbcbbacdacadbbbcbddacbbddadbbbabbacbabbcabcbacbbcbddadccdadcbabbdddbcbcdaacccdddbcccdbcddcdbdddbbabcbaaaadbaddacabdddccddcdbadcbcacadaddddbadabbabcbbdbababbddcadbccdacdbbaddcdcbbdcdaabbcdbcccdccaacdbdabbbdcbdcdcadadddbbaccaaadabbaddcbcaabbbdaadbdcdcbddbcdadaacabccccacdbcaadccdcbbcaacdccadbdcdcabdabaccddacbabbcbcbcbdabacadaddcadcddaaccdcaabdbdccbbbdbccbdcacadaddbdbddcdabbdbadbadcadcaaddabcbdbadccdadbccdccacbdbacbdbdbcddaabbbddbbbbbdaddbdccbddbadaadcadddacbadbdbcaacccbabddbcbbcbcdcadadadddbabdadbcccdcccaabacbdababbcdaaabaadbabbbdcabbbacacadabdaadcababbdcaacabbcbbdadddbacbbddaabccbacbbbbabadbdcbbaaaaaabaaabcbcccaabcbadcdacabadddbccdbacacadbcccdbacabacccabdcbdaadabacabdaabdcbbdabcababbbaabdcacabacadacaadbbcdcddddcdcbbcdbcbaddacbbbdbbadbcbcdaabbaaadadabddddababbcdddacaaaacaddadaddaadbbdcaaccbcbbcaaadbbdcaabcdcdcccdaccccaaaddadabadcbcddcaadbadbccdddacabaacbdacbcbabacbcacababbbaccbdcddbcabbacbbabbadccacacdcacadabbbacacdcdacddcadabaddbadcbcdcabccddbcacdcdaabcacbccadadbacccccbbddcdabdcdcbbdbbdcdbdaabdadddadcacdbadcddbdaabcbdddaccaadabcdccddabcdbcacbdbadbdbaaacababbaababadabcadcaabdabbcddcdcacdabbbdaddddddaddaddcdbaddabcaddbcdacbdaacbdcadaddabbcbbaadcaddacacbbccbdcdacddcbcaacddbadabcabbbcbabadbbadbcbcccdbcdabbdbbcdaabcadcbaaddddcdcbaaadcbcadbbcbadbabaaaadadabdaddbacdabcaaddbabbdcaadacdbacccbbbbaadacabcbcaabbcaddbdcadbabdadabdacaabdcbccbcadaabacddbddbaaddbadcddaaddbacadbaccabbbdabccbaccbdacddccacadbbdcbbdccdddadabdccababbaabbdaababbcdacdacccdccbcabdbdcccbcbacdbbdcabdcdaddbaddbdadabaccbbbdabddbcbdcdcbdcbaaaddcaaccabccacdabcbddabbcacbaacaacdbaccdbbcaddbcaadcbcccdadcdbddcacdbbcdabbdabdbcdccaadaaccbadacadbbaaaddbbbababcdadabcdaaabbaaaaabdbdcccacddccbcdbcaaadacddabcdbbdbbabcccbcccdaacacbbdacbaacdaddaaddddcbdbddbccdbbaddbdababdbddbacabacdbbcdadcdabadacacbadadcbabaabbcdcbcddbddacaaccdbbcccdcbdcbdabcdbacdcdcbcaaabcaadbdcbadddcdcadcacacddccddbadccddcccbaadabbcbcaccacabcbcbbdcbcdaaabcbbddcabaaddccababaadaaaabbdcbbadabbaaccbcbccdbbadbdcdcacdcbdbdbbabbddbaabadaaabadcccbaaccaacbcdabcdbcacdaabadbababddccdbbbbbcdacbbccccbbcacdcbcbcccdcdcbbaccbadcbbdbadddcacbcbadccbddbdbcdddcbabadbdccacdcbaaddcaddcbbaacbdccdcdcbbcccbcdbcaababaddaacccbcdbbcabbcaaacadcabcbabccdbdccdddaddbbdaabcccdcbbdcbddbaacbdbdddcbbcaabdbdaadcbadccdddadcabcdbccdcdabcaaacaabbbcdbbdabdbaaadbabadabcbbcabdbcabbaadabbbbcaaacbbcdacbcdaacdbccaddabdbdacbcdcddabcaaddbabcddcdbcbcdacaacdcdadbccbaccaaadbddbabccccabbdcdabcbdccddadbcacbdcaabbdcabdabcacddadbddabcacacdcdcdbbcaccbacccaaddabcacaadbbddcdabdbdabbcdaccbbdcbbabcabdcccaccaacbacbacbadccbddccdccacccdccbdddcacaccbcabbcaababacadbadaadbdcaacdaadadadadbacbcaaccbbddcdbcddbabacdbacccadbbdabddbabdaaccdaabcdbacaaddadddddadcabdbbcccbacaddddbdbcabcdaaaadadadbcbbabcbdddcaacdaaabbbdaaadbdcbbabbbaccbccdabdbbcbcacacdabcdacdbcabbbdcdccaccabcbdcdbacbbbaaaabaadcbabbbbddcbabcbacdaabbdaadababccaadbadaaacaccdbbbadbdbaaddaccbddabccabcbcacabbdadcadbbccccbacadaacabdbbacaadaaadddcdbcadcbcabcdababcbcbdcdaacaddbbdddcbcbdaddabccbbcddaadadababaabaabddccadcdaaddcdaabcbaccdbacdbcdabbcdccdabccacdaccaacaacaaadabbcaaacaaccaaadcbcaccbddcdbdabbdbadbccbbdaaabdddcddcacbabdbcbbdbbdcdbacdaaaddadabadddcdbdabacdadcabbbdcdcacdccccddcacacbbcaabaaccdcbacbbacabcbbcaddaaccadbdabdcabbcabacaacdcdbcbacbcdbbdddbdabdaadcdbbcdbcbbcbbaaacbccacdcbabacbbacdbdcbdabcadbbcbaabaaaabdbbdbbbbbacadcccdbadaacbbaaacacacbdaddaaccdcbbaddbccddaabaddabbdabacbbbbccddbcdabbddcdaaabcdccdabaaaadbcccacabccbbabaadcddacadabbcbbbcdbbcbddbababccbbbacbadcbdacbabcaddbbacbddcaadbdcacadddbbaadaaabbbabcdcdabdccbcadbddddcabadaabaaacbacccdcbbbccbccdbdadadbbcbcbdbdabcdaaccccbbadcacdababcccabdadcacbaadcabbaadcbcbdbcadcccbddcdbcdcadbabbaaaccbddabdaacaddccbabbccacddbaaccbccbdccacddcbaccabadbacdbbbdaaadaacaccdddaddabcdccbdddcaabcccbbbdbabbcaacdcbcbbababaadbcbbbaddaadadaddaabacbabcbcccbddadbdbdabdcacacabdacadbcbdadaddadcbccbcdbabababdcbcdacdccabdabddadbdbbcdcdadbdcacacadccbbabbdbbcbdcaddcaccabaccccacaaabdadabddbccdacaadcbbaadcabbaddacbadccbcacadaabcdbcccacacabbbbaddadbccbbcacaddbbddadbabcbcbbaaadbadcdcccadabcacddaddabdabadaabdadadcadcacdbddbaaaaaabdcadaacddcccddcdddadccdbbbdabcdddaccccaddabdddbcabdddaabcaabdadcdbdcadbdcadbacbdbadcacbbaccdacabcdaabdbcbadcaaaddccbcccddaacaaaddcddbcbdaacccbacddccdbdacabcdcabbaadcddadccdadbacbddbcaaaacbaacabbbabccdbccadbbadabdddabcbaaacaccbdcaabbacddbddbcdbbcddcbdbadcabaaacbcbadcadcdadbddabdacdbcddadbbbcaaadbaabadcabaabbcbbbcbcadbbdbcdcabdaaccbbcaadcabbcdbaccbacdcdcbadcdacdbcbaabdcbdbabbdbbdaccdcdaadbabdadcadaadaabbbacdcccabdadadadddabcbdbadabbbcddadcabbccccdacacaaadaabcadcccaababcbbacbdabdcacbaccbcddbbcddbbdaddcdcadcdabbadabaccacddbdddbbddaabdabdbbbbbbddcccdcbcacddbcddbbccbcaaaaaaaadabccbdccaddcacbabbcabcadadbdbdbcdcdaaacbbaabdacddbdbbcaccdaadcbbcacbabcacabbbcaaccdcacaccdbbbdbbdccbbababcabbcddcdabcaccbbdcbbcbdaacddcbadccaadccbbdcddddccdabadabadabccdcbaddccdacabbcdcbcdcbacbadadbbcaddaccdcabadbbaaaabaacadaccbcdbadcdbaadcbddacddcbdcaaabbcccaacbaaacdbcababcdadbdbcdcbaddabcbacbadcacdabdaaaacbbccbcbacbdcabbbcccbbccadbadbdbaacadcaddcdddcabbdbddccdbbbddacdacbdbcacdcdacaadabdcbbadaccadbbaaddacdbaccdbdbddcccccbaaccbbaacbcadccbbdddcbaddbccdbacaaacabdaacaabdcadbabdacdddddcbbaddbbcccacabddbabcaabbbddadcdbbaadbdacadddacacddbaddaaaaacdbbbabadbbadccbcdddbaccabdabdcbcbcbcbcbabbbcbbbbccdabacdbdadbdbdbddbacbbabacdcddadcbccbccbdccbdbddacacdcdcdbcdcaccadbbddacccbacdbdbdddbddcdbcacbbdddcdabccadbbcbdbcdddaddacbbdacdcdadddcbbbcccabddaaabcbbcbcbcabcabdbccbdbdacdaacacacaabcabaccadbaaaadadadbbacddcaabbabacaacddaabbaadbbcaaacdabbaacbccbccadacbaadbabcdcccbaadcdcbdacbbdbccadabcdacacbaabadabaddbbacdbacbcbdddbccccbbdbbacaaccaabdaacdccbdcdcabbbccababbbdccbacbabcabcdadddabbbaccccbcadcbdaacdcdbbadbdddadcdcddbbcaccccbacadbbbbddbacbbdddbdbaacbbdbbccdbdccaaababdbccacaddbddcaddcdbdbdbccddbbcbcadcbdacdcdbccdcbcdcdccbabbadbabdcaaaaadaabccdcaaadbdaddbdccbdabbcbabccbacdcdbaacbdccdbcaacdaddccbaddddacbcbcaaaddddadaabacddcdbbbbbddaaaccbdccaddbbbabbdadadcbacdcccbddddcaacccbabbbbcccbbadabaadaaabccddaaacdcaddcacadabaacdaddabbddabdadaabbbddbdbbccbddacdaaacbcbdbcaacccabdbbcdbdbadcbdacabdbdabddaddacbcddcbdcccaccaabbdabaacdaacdacabcddcbabbbabdbbccdadccbcddacdcacbcdcabdcdabaaaaaddbbdadcdbbddbabcbcbcdddddcadacaadcacbbdccadabadcabbdbcaaaccbabbabbbdaabcbddcddccddbbddcbdaddddcdcbaabbbaaacdccccccaccaaddadacaacdbcbddcbcdcdabcbbcbaacdaadabdbababdddbcadcdbdadcdadbcddbabccccddbbddbcbdbcaadbbdbdabcacaddcacbddcbaacdddccacbaacaaacacdbcbdacbaabbcadcccabcdacbbbcaadbbccadcaadbabdabaadcacacaadadcdbacdcdacabaccbaccdbcdbcaacbbadbdcacadbaabbbdccbcdacccaadbbaccbcabaaadbbbabccadaabcbccbaccdbdbbdadccccbddcbbccdaaadcddbacbabddaabadcdbacabbddcbcbdddcaddcbdcacbdcbaacadcdacdcbcdaabacadabaacadccdcddcccbdddaadbabcbccbcbdabdbacdadddbccbddaccbdcadbcacabcbcbdaadccbcdbbccacdcbdabcbacdadaddaabbcbdddbdadcbdddcdccbdcbcadabadcabcbaacacbacabbcadddbdbbabbacaacccdbacabadbbcccdbacbbdbcdbadbacbcaccbdccbdcbccbbaababccbcaacabaacbbadcaadbdbcddccacddddccacddaabbccaadbbcbaabcdbddbaaadcbbbccbadbadaccdbabdbdcadcdcdbaadaacddacbbccdcbadcccacbdbaacbbdbcbdabaacdacadddddbaaddddcadbcacabcbadaccdabbcaadcbbcaacbcdcdaddcbdbcbbdadcdbbaccccdcacdbdcbbaddddbbaddbacdddadbaabaccaaabbcaddacacbadabdcdadbcbdcaccccddcccbbacabaabcdbbcdcadbbddadddbacddbabbacbabbaacdadabccadddddabaaabcbdbdbcdaaaacbdbdaabacbbcbacbbdbbabbdcddadabbbdcbbcbbcabcdccbcccabcccdadcabacabddbbbbaacabbaccabbdbbbaddcbaddccabbbbcbdcaaabacccbccbdcccdbbdcacdccadbccadadbcccddabadaabbaacbcbcccbdabaacdacbdccddcbddcadbbbaacbcbdcdcaaabddcaaccdaccbccddcdacbaabbdaddadadbdbdcabdbaaabaacaccbaabbccdadddbcdddddcbbbaabdadcabbaccadbdcdcbaabcbdbbacdbaccdcacaaaabaabbdabccadbbacdcabbabbadbdbbddccccdabbccbccaaadddbccababddcbddcbbcadddbbcabcaacaddadcadcccdccccbccacdccccabadadabcacdbdcadbbccbacddaacabddbbcdcdddbccacabcccdbcbbdadbcbdbbadddbacddcabdbbadcdcdccdabcdcbddcdabdbdccdbddbdcbdacbacbbccaadbbbdadbddddbcddcbbbacaddaddcccdaadbabdcacbbdbbabcbadabccacbbcdbcacacadbabbddbcdcbcaaabddcbbbbabaddcbcadcdbbbcabbdcbbdcdbdbbcaaacdcbdabacadddccdcdadbddcbaccaccaaddaadadbdcdcacadaadddccbbbabbcdddcbabcaddddbaddbddcabddabbcdbabbdbbaadaddbadbbdbcbabbbcbccccababcacadaaddbdaacdddcbbcaccdcbbcbaacdcbcaacbacbcabbcbabddbcabccbdaaaadabacadddadadabcacdaaaabdbddcbdccccbdadccabdadadcbbbbdadbddcbaabbbbdbcbdcbddddaccaddbbdacbdabbcbddbcbccccadcbadacabbdaadbbbbabbcdacdabccbcabddbaddcbddacccdcadccddbcbbacbbccabcaabcccbcbccbdbcabbbcdcccadcabbbabbbaabbadacaccbdbbaacdbcbbbaababdbccbacbdcdbcdbdcccbdddcbaabacbaaabaadbaddcbabdcddbbaccaddbbbbbacbdbdaaacadbabaababacddbbcbdbbbbababdabbbcadddbbccbccaaccaaddaadabbadacadabbcaadbbcbcaadcbcbdaddddcbcacbcaadbcbaddccccaadbbccacdcbbdbbbacbcaadadcdcccabbdaadcbabaccbccabddcbcdabbbdbcbdcdccdadcadadcadbaddbcabccdcbcdbcabbcdcaacdbbbdadabaaddbccbdcbcccbbaadbcadbdbcbdbcbcbdadbccddabbbbdbdaaaccbddacdbbccbaadbaacdccdababbdaadcdbabdabbabbdaaccdabbcbbdbbaabaccadbcbbacadbdabbcddbccaabddbaddabdbbabdccbbdcbaaddbbaaddabbacdbcbccdbabdbccbbcdacccabaccacbddcaacababdcdbaccacbccbabcabaddaabdaacababdabbaadadbabdbabbdbbbdabadddaddabcaacacdccdbaddbbabdbdabdaadcbbaddacdcdcaabcdcadcbaacccddbdbdccabbcdbabbaacaddcbddcdbbdacaabbdccddadcbbcbadabddbdbbcdccadadbaadcaccdbdbadccababdadadcaaacabcbabacbdababcabbccdbbcdadddbcadcdcdbbacaacaacadbadbdbdbadddbbdcdbddbaddcbaabaaddcadabdbcabcadcddcbcbbbcbadbaaabbbbdabdadaddbababdadcdbbcddaddacabbbbbacadbcdadbbabbbdbdacdcdbbdababbaaacadbacbaccbabdbdabddbabadabcbdbdbacaccbbbdadcdcbbddadcadccadaccbaccbabdadabacdababacababbdcaaacbbaacbbbaccbbddcadaddcabadcddcccdcbaacbbdadddcdbdcccdbabaaabaccdccdcccbaabadbabddbadddcbbabdabaacddbccbbcbbacabdadacbbdaddbaabcbddadbdddcdcaaabbacddcdcdaaddcdcdddcddaddcbacdababbdddabcdcacdaddcaaccbabdaaacbabcdcdcccbbbccabbcccddaabcbaaacddbadccdcccbdbbdcabadcdbbcacdbccddadabcaaabcbcabdbacacbaaaabaacdbddadcdcddddaaaacddcbddddddbdbccbbbbdccbcdcdabdddabcdabbabbdaacaadbcdabbddcbdccbbdbddaabdcabdbbbadcdcabdacdadbadabbaabaacccdaaadcbabaabadcddddbacaadbbcbdbcddaacacbbddcdbcacadabdadbcdcadbcdbbcdacdabbcccaabdccadadcaaccadbddabbbdcaabbccdadaaddbaacbacdbccdbadbaaacccdbcdcdbcccccbdabaddbaccdbccccababbbdaadaaabccadadddcaddacabdbdccbadbccddbbaabbddbacdacaccbcbbbaacdacaaaaadcadcbcccbddbcbdcbdddccddbbbccdbcaccacdadbccdacbcadacdcbabacbadbaddbdddbaddbadacbcdcadbbbcdabccaabaddbadcabaadaddcaabadadbdcaaabbbaddccbddddcacccadcbbdcacbbbadaddccaabbacacbccdbddbccdcadbcdbabcbbcabacadcaadccaabdcdaccdcaaaccddbaabcabccccadbbaabbaadbcacaabdcbdbabddadcaddcbaccdbdadbcdcbbbccdccdaadcadacbbdcbbbacbbcbdaabadaaacaddbbbdabdccdddacdcbdacbabbacbcdcbdbaadcabacdddbbaadbcddcbacbbcbbacbdbdbcbdabbadbbcabcacdacdccddbacaabdbbdbbccbdcadbdacacbcbcdadbddadbbbdddaccbabdacbdacbbaabbbabbcbabddddbdddcbcadcabdadccccbcbdadbdbabcdbcdbdcacbbadadbcdcacbbaacccacdddcabdccbdccababaaacdaabbaccbddaccbbcdaabadbaaadaddaaccccdcbbaadcdadaccdddadabacbcbddbbdbaccbbbddbcabaddbadddbcddcacbcbddaacdadadbdbadbdcaadccadcadabdacdbdbcddbcabcdcbccdcdddcbdabccdbcbbdcaacddacddadcabcbdbaabbdbabbcacbbdadbcadabcccbacaabbdcdcccaabaacccbbadbccabdcdbacbdcbaacaddccbddcdabcccddbabadaacacdddaabbcadcaadabaaccaaddaccbbadbadccaaadbdcbadcccbacaccdacaabaccccbccbccaaadbcdaabcabdaabdcaddabcbabdacdbdbbacdaadaddcccbcccaabcbccdcbdaddbadbdcacddacbaccdaaccbcccdcbaddbcdacaacdabdcadcaaabbacbcaabcadddddabdaadccbcdbcbddbbdcabbdcbdccadbcbdcbbccbcdbbbadcdbaccaacbadbdbabdacdcbcbcaddbdaacaacbbbbccbdacaadacaaaccdcbccdbcdaadacaccdbbabbacabcbacbabbcbcbcabccbdbbaddbaadcbbdccaaddbbdcdccdccdababcbdcdaccbcbabdbbbaccddccdbbcbaadabdccdbaabdbdccaabbbbcbaadabddbdaddaadbadcdbadccbacddcddddcbaacbbacddacbbadbbddbccacaaadaccbbdcddccbbbdcdbbdbcaadbdbadabddcbadbbcdbbddbbaaddbcdaccdcdccababbccbdabbcbcbacabcbcbaccdaaadccabbbcddbbbcaddcdbddaaabadabacdadbabdaadbdbabbdcadbdbaaacccdacbdbccddddbcbbcdaadadaadddcccddadbcccdbadbcdbdcbabcdaadbddaddbcbcbbccadbdbbbadcbcabbbbabddabccabccbdbdbacaacaddccdcdbbdcbddbaaabaaaabcbbcbbdccacaadacddacbcbcaaddbdcababcabbccbdabbabaabddaccdcaaaabaddcbcaabbadbcdbaacbbbaccbbadcccdabaaacbcbacbddbddaaabccbbaccabbccaccbbbcbdacacaaccdadddadadddcbbcdbcddaadcadbaabaadccbacdddaaababccddbadabbbabadabdbaacaaacbcbaabcbabaccadcbccabacccbbadbbdccaddbdddcdbaddabdaddcbadcccbbdaadccbcabcdcdcbcbbbcaacadcbcbbdacbcbcccdcbbddbadbcbcaddabcccddadaddaaccdbbababdbbaaabddbbaaddcdacaaccbdadcbacdbdcccdcaddaaddbdcbaacbcdbdaacacaaabacaaadbbaacbaaccaddddadadaccdabdbbcbdaacabccdcbddcaaadabddacdbacbaacadaadbbccadbbdadaabadaddbdcdbdadddaabbbabdadcabbcdaaaabbcdaccabbcadddcaddccaacaaabacddcdddbbbaacaadabbdddababaabcacbacccacbadddcacabccdbadcacddababcdddbdcdbaacacdabdddbcddaccbbdbabaddaccaaacadabdabbadcbbccdcdbcadcdddbdaccacbbcabbdccdbcaaaabbcbccacaddddacbdadcadcbbcdcbcadddaababddabbbbdcdadbcccccacdcdcabdcbbbbbaabbabdccddbccabacbaabbcacccdabcccbabddcddcdddabcbbdadbabbddacaccdcddbbacdaddcccaadbdbabbbcbabaadbacadcbcdaccbdcdcbbbbdddbddbadcbbcaabacaadcbaccdcbdaaababcdabcabaadacbdcbbaaaadcdbcabcdcdbaccbcdddcdabdcccbcaddccaacdbdcddbdbaadddbcaaabdaaaaddbdccbbadabcdacaddccbacbbcaddabccbddccdccdcdcadcccbacdddccadcddccdbdcaccbddcdacdcbaaddccacdbacbaddbcbbcbdbcbbaaabadbaadcbaababdbabaadddbcdaacaddbcbcccccbacacccddbccbccbcbdccbcdbabbdcbddadcdbccbdadbccbcddacdcbdabadbacbccaabcadbaddbbbbacaddbcbcadcbbdcababbcbcbbcbbddbddddacadccdcccabaaaadabadbdccdbacbdbcdddbaabdccdbaddabdbcdccbdbcdbdaacbdbbbaadadcdbccddadccacbbdbdcaaaaccacdcdaccdabacdddcadbdbdaddaadcdbacabacdcbabcbababdddbaabdcdaadaccdddbdaadcdcacacdcbadcaaccbdbdbddaddbaadbbbcbadbcbdbbcabaabccbdcdcabddddddcccacaadcbbcdbaaacbaccadcdbbabcbcbbcaabdcddadbcbbbdcababcddbbaddbccdcdaadacccbcbbcbcadbcbadcdddbdbccbccaddaddaccdcbdabacaababacddacbbaaacababbcdbdabddabdadabbaaaddbcaaadcbbddbcccbacdbdbadddddbabcbdabdddaabbcacddddadbdbcabcabbdcbbbbbcdacccababccacadcdbcbcacbbbdbcdcbcdcaaccadccacddbbdbaddcbcbbacbaabdacdbdabcabcddcdbcaabcdacbbdbaddbdabbcbdbcddcdcdabbbcaadccacbadbbcaacdbcaacddbddbbdabdbcaadcbcbcaaccadaddcadbdbacadbcaacdbabddaddacdcdcadbbcaaabacdcbbbdbbaaacbbaabdbdbacdbcadababddbdccdbcbcbcdbaabadaadabbadadbadbdbbabacdcacaccaabbdccbacacadaadaddbcabbcdbccbccbaddcbddcaaaacdabcdabccdbbcbbaccadcacacddcccdadcdbadbabbdadbbcadcbcdcaacddbbbccdbbbdcdcabcdbcbddabbdabcdbdddacdaacdddadaaabddccadbcdaacdcbadacbbcccbdcbacadbdabdcadddcddbcacacbcaacddddccabdaadbdcdbabaabcddbaabcbdccbccbdbdcdbacaddcacddbbcdacdadaacaabaadcbaacbbbbcadacbbcdcadbaadcdadcdbaadbaadaaadddadacacdaddbdccbbdccccbcacbddcadbadacdcbbbaabbabbadbcdcdccddaacadcbdcabdccacaaccbdadbdbcccbadcbbaaacbaccbaddbabdbdaabddcaccabbbadbcbbadcbdabbbbcdcbcaadadccddacdbbdcbdbaddbacbdcdabbbaddcaabaacbbbdbddbadcabddadaacaaccbcbcacaabadabacddcdcdaddddcccabccababcdccddcadcbabdbbbdbddcacadbdbacbdcabdaddccbcccaacabaaadaacdcdcbabdcddddaaaabcabcdcdaaaabdacabaacbaacbadbcbaabbdccbcabbbbaddddbdddabbadbabcabdbadbccbddaabbdcdaccdbcddaacccccaaddcabccdcccadcbcbaaabccbcaaabbdcccbacdbadbcaabadcbaadadbcbaacacdadbbaddcccbadbdadaaaadbbabadaccbdcccbdaccadbddaaabdaaabacacaacdbcbbbdccadadbddbababcadaabdbaaccbbaacbcccacadbbadddcbbaccdbcabbbcdaabbcdcdaccdaadacababbbbacbdddbdccacddbcbbaacbabadbccababbdadcbcbcdabcaccaaddbcccaadccabddccacbacbcadccacbabdaaddcbbbbabcaaacadcaabdbdbdacbdcadacacdadcaacdaccdbabccbdabbddadbcaccbccadbbbbcacaccddbaaddabdccdbccabadaccdadbdcbadbbdcaabadcbbdaaabaacdcdcbabaccadbbccccdaaccdcbddbbdadcacbabcacbcbadcadcadccdbcdcaaacaabdcabddbdcddcdbacdbddcbaaacbaddcccdabcdbdadcacaccdccbdbadbcbbdddccaccaadbacccaddaaccabaddabacccdbddbacadcbabadcccbadcaccdcccddbbbaaccdbacaacdcdabcacdabdddcbcaaadaddcbcbccdaddcacbadddbcaabddddbcddbbaacabbabcddcdcdbddcbbcbccabaacdcbbdcacddabbcdddcdbbbacbdbbabdbdbcdbdccaabdacdaaabcbbcccabdaadbbcdddbcbbaaacdadddacccbaccdcdcdbbdadddaccaccacccdabcaaacacbdaddcbbdbcdcdbbccbdaabbdbcdcdbbcdbdbdcccadcdaacadadccbdbcbddcbbddcddcbaababdbdadcbacabcdddadbbacddacadbbbbcaccbbcbdbbadddcabccdaccbdcddababbaacadbaadccabbbabcbbcbcbacabdccdbbccabcababcaaddddcccaabdbdccadcacacbaadacabaaaadabbdabcccbcddcccaabbacdccadabcaabdbbbbbabbdacbacbbcabaabaddbdacadacccddcabbdbddccbdbabbdabacacddccccabcbcadddccdbcacbddabbcabcdddccaaaaaaabbabbdadddcbadcaddbddbbbbbcacdcccbdaddacabdbdcaacdddcaabccaaccbccbadacbbabadbddbaaacaddcadaadaababcadbbbabbcccdccbcdadbbddaacabccdbcdccabcdcadadbcccbbabbcdaabbcddcabbddaabdcccacbdddcabbbbbdababddcbdaddaabbcdbcddbcadbbbadbacbbddcdbbdccbbddbacdbbbdbcdcadaaacdddadcadcbdbbccbbbabccbbdadbbbcbacdbbacbacdcccdcdcadadbcacbbccbadacdabddaabbccbbddabbdaabcacbcccdbadcbbdbadbbdbacaaabcacdcaccadadbacbabbbcaccaaabbcaaaddbcacbccddaabdcddadcdbccabbdadcdbaaccbcdcadbadaaadddcbcccdcdcdbabccccccdbcccdbbccdabcacddcaccbbbbacbddddadaacbbcdadacacdabdabcaaacaaaddddcdbbaadcacbabbcbdcdcdddddbcabccbcadacdcdaaabadbbccbabbbcbdcccdbacdcdccdbdbadbabbbbbcaddcbaadbcaacdbaadccadddbdbbaacbbbdbadcdddcabdbbadbadbcccdbccdacdcabbbddcaacbccbdddbcbdaabdcaddadddbcabdbbadcabcdbccdcbdabaacadcddacacaacaaacacaabdcccaddbaaadbdcacbcccbddbadcdabaaacbcbdccbbacabdccbdacadbccadbabdaaadabbadbcacddddacbbbbbccadcaacddbcaadcdcdcbdbdadacbaaddcccdcadadddaabcdadbbaacabdbdcaaabddcccdbddcdbabccbcbbaacabbdcddcadcdaabaacdcdaababacadbdcbadadbbcaadbcabaaaabdbbbdacababcaadbdbbcbcbdcbacccbccbdddbcbbbaacdaddcabbccbbacabcdabacccbddcbaadacbcdbabdbdaaadddcbddbbcdcacaabddcaadcaddadaddbbdbabdacaaddddbbcbaadabbabbccdbbdcdbabdbdabbcdbbcbbabcddacbbbdbdbccdababbaaaadbcacdbcadcbdccabcddaacddabcccdcbcdabcadbddcaabbbaabbacbbbabbaaadabdaccbbbaabcdabdcabbbddbabbaadacbaadaadaacacddbcbadcbdbcabcccaaadbccbdadcbaabcdcadcbdadbcbaabcdcdbbbcadddddccaaadddbaddcdcababdbababdaadbccbdddcdacdbdacccccccbabddabcdcbdacccbaadddcbaadcccdcaddbdbdcbdbcabacaaadddcbbcacbadbabbaacdcdcabdabcacbcbddbddcbacddbbadaccbaccabadaadabdadaccbbcbdcadabdadacbadbdcaadbbbddcabbdbbbadacdccadcbaadbcdbbcbcdadacbcbacaacababbbcdabbbbbacddbbbdccbcbdcddcaaacccbadcbdccabcaaaddaacaddaccdbcadbccccbbbadcabaacabbbcdbabadcbcbcccacbcadcbbacccbaabddaabddbbdabbddbaddbbbacdbbbdabccbaaccaaabdbbcbcadccbbacccbcdddabdbcccacadabaabddadcbcaadadcdadccdbbacdbbbaaccaaaacdbcdcabdaaaaccaccabbacdbbcacacdaaaadbbddcbdabcdaaddacddadbcdcdbbdbbbbcdaabdbacbdadadbbaaadbdbbdaaabcbaaacbadddacacdccdcbcacdadabdacdbcadcddddbdacaddaaabbbcdbbbccbdabcbcccdbadddababdbbcbcccddcdcaddbdadbcabacdcacdbdbcddbcbcaadbcbcdbbaaaadcabaabcbabacbbdcabbccaadccdbbccbcbbcdcbbaddbbbcacdaaacaabbcbbacdbdbdbdacaacbabdbcabdcabdbcacaccdbbbdbbcabdadcaadbbbbcdadacbbbdcdccbdbcabaccbdababbbbcaabbddabadddcdbddadaaacbdbdabccaacddbdbaadccacaccbbbdddacdbcdcabbddccdcabaccabdbacbbbbbacaddaccbdabadddbdadaaaccacdbcccddbaaaabdccccbcccdbadcdcadbdbdadaabcacacabbdbabdaddbccbadbacdaccdbacbadcdbacdcdbbddbbcddbdaacdccdadaaacdacabacabcdcbddaacbcdbabcccabdbdcbcdabcbbadbcbadcbbccbaacadddbcbabaababcbcaaddbabcbdbbabdbdddbacbdabaccbdbbacbaabdcbdbcacbaadccdacbaadcccbccdbcdcadbadcbddddaadbddcaaccbbbbadbdaccdcaaccadbabbacadbacbdcacccbbccbbcdccadcdcbddbcdbdaacabbbdbbdbacbccccdcbcadabccbccaabcaaacacbaaccbbacabcdbbcbabdadadaaccbbcbaaadbcbccbcabdbaddcbacaabcaababcbdbcbbddbadadcbddcacdccdcaabcabacabaaaaacdabcbdabacacddabcdacdcdbbdabbdbcdbcdbdbbacacbcccbcbcdccdbdbcbccbdabaaabddcaaadaacbbcdbbacabcdcbacbaccbbbabbdcdaddaccbbdaccaabacbddcdabaddbcdccbdacaddcabdbbbaaacacaddcdacabdcbddbbccacbcababccbccdcddaaadbccaaccaaaadcdcdbabdbcdaadadbdbaddccbbdddbbacbadcabdbabccccdacdacddaabadaddabaccdacddccabdddaaadbacaccaccabbcbcdacdddbbabddbccccbccadddbcadbbbdaacdbddcdabdddbcbcabcdbbbddcbabbabbcabbaddbbbcaabadbdbbabcdbaadadbbccddcabcadacbbcabacbbcccaabdabdcadcacabbabcadaaabccbdccdbcaddadbaddccccacaadddcdcaadacadacdddbdbcccdbaddcbbbcaabddacbcadaabadbdbbcbbcabbdcadccbbdabbbaddbddadabcbddcdadbbcaccddccbaaacbbcdddbadbdcddbaadcdaccbcadadcbcdaccccababdadbcdcdbddaaddaccababbadbcbaacddbcdaaadaabaadbaaadadbadabbabbadaabbbdabbccbbbacdddbacddacddaaccacdabaabdaccacdddcaccdbcbacdbdddacbacabbddcababcdcbbbdbaadbabcbaabaaaccadcaadaadcababdabddbcbbbaaabdbadbaadacccbdaccacbcabacbbaaccbcaaaacddbdbddabcccbaadadcbccdcabdcdcadaaacacdcbddabdadbaaabcaddaadddbcbcdbdddbcdbacdbbcdcccaddbbcbbdaabdbbdadadcbabaccacbddbaabcaddccacadbdacbcdaaaccdaaaaadccdaacccdddccbdddabaabdccdbcabcaaacccdaadccaccacddaccbbabacddcdbdacaccbaddcbbdccccbcbaabadadcbaabadccbdadccbbbdacbbcadcabddbdccbbcdcbcdbbcccbbcaabdcdccbdcdcccbdbcdbabcaadcbddabbaddaccaacdbacddddcaadaacdacdbccacdadcbccaaccbcabacdbbbdccccbabacdadbabdcadcbddddaadbdacdddaabbaaccbadcbcdadccbbaccddbddccdadddacadcbbbcdddcaccccaccabbcabacbadacddaaabadaabbccacacaddbcccacccacbadcadbaccdcaacabaccccbdccadaacadabdcdddadaaddcccaabbabcbddbbaadbbbadaccaadabccacccdcadbdbbdbbbabcbddccaaaadbddacbdbacddcbdddacadcbacdbadcdabcbaacacddcbaabcdbddbacacdbbadbdbbcdcbdabbdaabdcddbcabddccabdacadbccacbdbcdbabdcdbcabadbbcabaaddccdbbccbabcccaccbadcccadbbadbcddcabcbdbbbbadcbcbdaddcdcccddcadcbacccbcbdbcbdbaccbccacddadddbbdddadbacbcabdbbadbdcccdbaaacaadbdddbaaabcacacbcddcacdaaaccbdaabbcbbccadcdabdabcadcdbcacdcdbddcdbdcddacaaccdddbbabbccaccbbbccdcaabcdaacbacbdcbdbddabbaddaacadaccbbabcbadacbbbcadaccdacaadaaadacdaaacddcadbaacaadcadbcbccbbcccacabdcaabccbcacdbbbdddcdaccdbcbcccbccdbbaccaadbdcbdadcdcddadcdbcadbbccccbbabcbcdbcdbccccaadccbbcdcdaaaddadbdbbbccacadbcbdadddcaabdadabdcbddaadbdbddababbdbccbcccadddbbaccddacbcbaaadacdabcabcdadcaddbcaacabdcaabbaccacadacaddcddbddacddacbbadcdcbaadddbcaadcbadbbdcabdcdcacdacdcdbbcadacdbcbdbddccdccbcddadabdadddcccadcdaccbaabdabddccabbacacbdbcdcacbadacdbccbbcbabbbdadababdacdaccbacaaaaadcbbbabcbabcbaacdcbcaaaccccbcaacdbcbdddaacadbaabdaaaaccacddaadbbddbccbbcbabddddbbcdacabcdaddacbadbcaabaaddacdbccbcadbacddabccdaccdccdbbdaaacbdbdaccdcbacdcacabbdbccbaadcabdccbcdabadcbbdbcbdccdcbdbdcdcddddacbbcbddabdbddadaaabacbcdbcabdbddccdabdcbdaabcdbcbacaddbaadddbcaddbdbadaacacbaddacddbcadbbaacdcaccacddddddcdbadcdbdbcbadacbaabcaadbcbbbddababdcadccdadddadbbddbbbabdcddbdacacdbdbcbcdbbabcaabbdaadaadbadaadbbadbaddaccdaacbddacbbdbcbcadbacacdccbaabcddadacdcacbbbbdadbaabbbdcdcaadbbadbdccaccaadbbaaaddaacbcbdbbdabaabaaabbddbbaccdadaccabcbbdbcddcadddbddaaaccbcdaaacdcdbcacabbaddccbadbbbbbdcdbddadddcaddbcbbdcdcaaadcacbcaaaccbacbbaaaaaaaacccccabdbbcdccaaacdbbdbcbccbcbbdcbdaccddacdbdbbadcacaabbdbbcbdbbbcddbdaddcbdccdbdbbacaccbccdaadaacdaadbdacdbcdaddcbaccabccdadadaaccaacdabbbdbdcacbdcdabdacddbcaccabacdadccbbbcabbacbbbdaabacdbdddcaacaacbadcdbacbbabdcabdbbbdcccdaabcbbbdcdacbbacbbccccbcccacddccadacaccaabacbacdabbccccaadaccbcbabdddadbdcaaddcbcdaadcacadabccccdbaccbcadabbcbdbbccbcddabbdbadacbaaabacaabacbababbdbbdddaadbbabdcacddabaaababcccdcbaacbdcbabbbcaacbdabcbabcbacabbbbcacabaaacbdadcabcccacbcaddcccdbcbddaadcccdaabccccacdcbaaaaacccbdcdcdacdcbcddbaacdccabbadddadbdccdbaaaaaddcbadacacaaadcbbbcaddababcaaccadbabbdbdbbddabbacbddccbbadbcbadabaaddabcdbbddcbcadadaabdcadcdbccbcccaadcaddacbbdddcaabacdadcbbaccacdbdbaadcabccbcadaabdbabbacacaddaacacabbbbcadbdcddbdbddaabddcaaaaccdabbbddbcdbacbcccabcccdabadcdabccdbdbdaaadacdabaabacdbbacccdbdcdbddaddaddbdbdbcacaddbdbaabbbcabccbbacbbdadaabacabadbddadddaabdcadaaabbbadcaacdabbbbddcddbabacacdcdcbbadcbcdbccabdccabdbbcacbaadababdabddacdcdcdcbbdbddbbcacdabddddcbcbdcbbbbccbdaacadcdadddcadbdaabdbcacaaabadaacdacbaabdabaaabcabacbabddbbbbdcbcdbccbaabdabdddacaccadaadbacddcdbdabbddbcbccbadcaddcbdcdcddacbaabacbadbbcacacbadcbcadcddbadbacbcabadbadcbaabdbcbacbaaaadbbdbcccbadcddcadbabcacbaccaacbacacdbadacbbbabaadcadbabcaaabcdcbcaacadbcbcabccbbdcaacacbddbacabaccdbbcbbadbacaccbdacaddcccbaadccdcccdaadaaccbaaddcbaaaabcbaadaddadddbccbaaaacadddcbbacbcbccdcbcbbcaddadbbcdccbdbdccdcadbddabaadbdbbadadccaaaddcdaccadaccbccaacbccbbdcdaaadabccabdaddddbdadbabddcadbdcbddcadabbdadcbdbbdcaacdddbbcbabacabddabdabdbcdbaadddccbcdbdaaccbddbcdbaacbbbacdbacbaaacccaabccbcdabcbdadbdabadaabbdbabaabdabaddbddacdadcaabddddbdaaddabacaabbbbbbdacddbcacacddcccdbdbcbddddbcbbccdaababcbaddbdadabcadbcdabbbdddacaaacaacbbabddcdbbccadbabbbabcbbdcdabdcdbaaccbcbbcacccbcaaacbaccadcbccccbcdaccabddbaccddabcbdcdcabadabcbabaccaabcddbdbdaaadbddbadbadaadcbbcdcbddbdbabbdaadddbdaaaddcadadadabbcccccbcbbbbddbbacacccabddbcbaacccadcbcdbbadaabcbbaaadcadbccadaaddbcaccaabbbaacbdabbdddcddcdcadbabdbbdabcdabbbbdbbaddbdcbadddadcbbdacadbaaaacaaadadcccdbccbbcdbbacbcaddadbcabdacbbcbbdddabdccadbaaaddcaadaacbaabdcabaacabdabdacbcccabaccbabbadaabadbacdcadddcbcbbabcdbdbdbbaacbacbacddbccaacbddaddaadadacdbdbcdbbbcababddabcdaadcbbabcbdbdcdbadddcddbabaacbaaababbbbdcaadbdaccadadbdbdcbddcbacbcbacbcbddbaddbdddbabdcdadadbadbbadcbcbbccbabdabadbdcabdcacacbcbbacaddbdbdcbabcabccacbdcabccccddddcdcaccdbdaacbcdccdabbbcdccbdbdccbaccacddbaaaababaadcdbcbaddcaccddbcaaadaababbcacbbcbcdbdccbbbccdaacdbcacaadbddbdddbbddcbadbdadddacabdbcaaadaacccccaabbbcdddcacbbdddaacbacdbdddcdcdbbaaaabdadccbdcbbaccbcdbaabacbaaacabcdadcddcddacbbcdcadadbccddcddbcbbadbbadaadacabaabcaaccadabdabbcbacdcccdcabbaaccacddaaabcabbdcbbaaababcdcdbbabcaccacacacbacbabbbdadcdacddcccdacbaccbbabadddcacaaababcbdbdccbacadbbbacaabbdcdbcdbdddccabdbbdcdadccccbdcdcdcbabcaacdcdcccaccdadaadddcddcbccaddddddaaaaacddbdbbcbbadaaddccddbddbacddbdaaddcabadaaddbcbadcbddbcbbcdadabbdbadbaabcdcacdadccaacccabbdbcabbdcabdadcaabccccdccbcbbaacccbadbbbabdbdacbcdaddadbaaaaadbdbabbcbdbcbbcbdccadcacdccaabccccadccabccbccdbcdcbcbdbdaababcdbabccabadbbbccabacaadcdcabbddcacadbcbccddcbcdcacdaaccdcbdbcbbcaacbcbbbacbcbcaaaccadcabacdcbadadacacaadaadccabaccdcccddbcddabdcbccaababcbacdaaacbbacccbaaccddccbbbcdddacbbddcadbadabcacaddddabbdbcbdcbacaccaabadbbaadaacbaaabbddcaccdcbadacaaacdadbcddbcbacaccdcabdaddcadbcdbdcacccbdabbbbaccccdddccdddbacadccdcbdbadabddcddbaacdbdccbbabbabdadcabbbcdcddadcaaaadbdcacacccbbcbdaaccddbaddccdddccbcccdbbadcacdcdcbcabacadbacdbaaacdbdbbcbcaaadbaaacaacbbaaccdadcddbbbbddcbdcbcddaabbcdbccbccdadcdaaadadbdbdcaaccdcdbcbaacccdacdbcbcddcbbcbbbddbddcadcabadadbbaacbcaaadbaccdbcabddabddaacbcdbddacbabaadddddbcacbaadaaacdbcadccdbadadccbdcbacbbbbbcdaddabdbdcaddcacbddacabdabbbdadccbcdbddbbcdadbddbaddddddcddbbbdaaddbdcbaababadaabdccaabcadcbdcabdccababaacdabcccbddcadbaddacddcdacbcdccdbbdcdaabdaccacbabbdabcaadacbcbbbbcbacdbcbcddbdaccdcbadddcaaacdbabbbcdabcacbdabaaccaacbabcdbbdadcddcbdcbdacabcbbcabadcbbbadddddabaaddadbacbaaddddbbbaacdabcdacbabcaabcbabcdcdbdadddbdabdccccccaabaaacdbbaacbdddadbbccbadccbdcabbdcdcabcbabbddbabaddccabccccbbbcdbcaaddbdcbadcdcbaabbaddbadbccddddbadccaacbccdbbdbbcdaadbbbacdcdbdbcacbadbabbabadaaacbdacbacaadaaabbcdadacacbaabaccbabacdcdacacdadcacccbbbbbadbbccbdbcbdcadaddccccaddadadbccdddccaabaabdbdddbbacddcbabdcbcabbbcbbdcbabcadbdddbaddbddbbaccccbddddbbcbbdcdbcbabbaccbaadddcdabacdddabadbcdcabbcacbdbabdbdaacddbddcdacbcbdbdacadcaadbaccdcbaddbbaadbdaccbcdcacabbaadcddbabcdacadaabccaddaaacbbabcbcbabcaabacacdbdddcabadddcbddcabaaabacbddbadbabbbaccaccbabcccbbdcdacbbbacdcdcbaccacaadacdcdbbabacdcbcaddbccadbbbacabdaddbaacbbdcacaabcacdbaadbddbadabbbcdacddabbccdadacadcaaaadcabaabcbbbcdbcacbbbabccabcdadaccacaaabaadbdddccbcbbbacbbdabbaaddbadbcbcdbbadadddacdbbacabbbaadaaabdccacbdaddccaaabbccdcbabdcdddbcdacbcccdccaccaddbcabccddabbddbddddaaddddcbdbbbcdacacbdcddcdbdddacbcddbcdcdcbdbdcacadabbbbccbdadbbbbcccdcdaaddbcdabcdbccbabdbccddbcabaaabddadccdddcbacbbaddbbdbbaaaddccabbbbbabcdcdbcdabbdacdbaddddcbabbbabadacaaccbcdabbcaabbaadabaadbcccddbccbcaacdddaaabdbddccaacacbdabdbabadccacbccdbaaccdddadbacacaaabbddacccdbacdbdcabcbdcdcdbadabcdadcadabcdaccbddccdcbddcccbbcadddaadabdcdbaaccbccdbacadaabcdbcccadaabbccdbccbcabdbcabcabdadcdbccddcadcbbcddaabdbccdadaabdcddbcbabdabccbdaddaabddbbcadaaddbbbccbbcccabdcbaabbacbdbbaccacacdcbbabbcbccaaaccddbcadaaddaabbaaddbbdddaaacadaadbbaacbcbcdbababadcdadcbbddccdcccbadbdadaabaadcabadacbddaccadccbdbdcaadadcacdcaaaabddcdabcaabbdadacdacddabcadcbccdcddaadbabcabcbccbadcaacaababadcaaaddbaaabddccdbacdbbdbbcccdcacabbcabdadccbabbbdaaddcbbabccaadcccdabcbdabbbbcdacabaddccdadacdbcddcdccaadcbbdccbbbddacbabbabdbbddcbabcbacbcbabbaababddcddabcacaaaccdadcbdcbbacdbdacabacabdcaccddbcbacddadacacbdadcccbccdaacdbcbbcdbddbdbddacdbdaacbdccbcacccaaabdbabbcabbcdbabdcdacababbccaaabbcdadbcabdcabaccddcdcdabcdcddcbaddddbdcaadcdddcbbccbccbdcdcadcbcaabcdcaaddadbcacdabcdddbdcccbddddcbbcbabdcbcccbddacadcccbbcadddbdcbcbbccbdbbdbcbccacbbdbbacdbadadabddcadcdcbdacbbdcbaabdcbdbccaaddddbbbdccdbadbdbdbbadadbbbbddcbcdcaacaaccabadcbccbdcbddabaabdcaabadcdcdbcbbacdbadaacccccbbdabcddbddcaababddcbddadaadccddcdcbcbddddadbcadadcbbcbdadccbacbaddbaacaccabcccdababbddbdacbdacbabaaabbbacaddcbadcbdbabbabacdadadabdadbbaccdcddadbdcdcadcacbacbbcdabbcddabbcabbddccaddbaacddbdbabdadaadbcbdcdbbbddadbbbcdcbababdacacdcbcdcaaaccbcbcbbabccdbcacaadababccdcbbdddbccbddddbddbbaabbdcadbacacabacdbcbbaaaabdadadbddacdbbddabcacdaddccdccabcdcbbbcaadabdccaccdccacaaabccddddddcaddccddacaadbdbbccddbdbbbcdaccaaacbaaaabcacabcccbcbbbbcadaadcbbcdbabddcbcccdabbadbdaadaabdcdbcacacddbabbbcacabdcdbabacbabaadadbddbacbadddbddbbabaaabdbdaaaddbcdacbdddbbbccdaadccbbbcbcddbdccabadbcdcaaadabcaddbcababcaccccbdcccdcdccacddbcdacbdbcabccddcabbddabdbcdcdcddbbabbcdabcdcbdadbdddccbacbcbbddadccdaaaacbabcadbadbabbcbdddddabbdaabddcbdaacaabddaccbbaabbacdabaacccadddaabacccabadabddcdadbaaacdacacbbccaccddddbcadcddccabbbdadbdbbbddababcbadadbbdbddcaaaabbdccbcdaddcdaacadcbaccabadccbddabbdbcbbacadcdccaaacbddbaabbbadacbadddcaacbbabbbccbabadcdcbcddadbabbcbaaacdcbaacacacabacbdaaadabdacdbbbdbccaadbadcbccdbdaddadbbddddababdbdcaaaddaacdbbbddcbdcdcbcdcabbaccaabcccdadcbcccdccddddacdbdbbacbccabcddbbcbaabbcdddcaddbbddcbbddabbcdaccadcadddcdacdbdadaddbcddabcbdbccccbdcdcabddddabbaaacdacacadbaaabbdcddaaddbcabdabacaabdbbabbcdddadbcbdccbacbdacadcacaccbaaddbacddbcaddacadbddbdadbbbdaabbbcdcbddcacccdbcadccbcbdbcbabadadabbabaaadcbdadadddbaaacdacaccddacdbacdcccbbcbdddbbabbbaaabacabbcdbcacccddbabaabacaaddcddcbadcccaccbbdcdbdbbdcbbdaacbbcccdbcbbddbddbbcaadbcdbcccaaadbbbcbcbadcadaaddbabaddbaacddbbdcbbacadbcaadaacdadbaddabadabcdbaacbbbddbadabdbcbdabaaaacabaaabcaadbdaacdaddabbccdbacbdcbbbaddbbdbbbbbbadabacdbbacccdddacbddcdaabaacbcabbadcbabdaacaccdaaadabdbccaadcacbaacbaadadccabccddccadacdbaaadaabcbdbccbcaabcbbdcacbadcdadcdacabddbbbadcaacbbdabddbadabaabaadcccaabddcbdacdacbbcabadbcccddbaddacdcbbaddbcaacaabcbaabdcaabbcbddbdabcdcdcbabcddaaacbdbccbbbcdabcadbabbddabcbdadabbdcadabaccdbbcadacddcdaaadbdbaadbddaadaacdaaacbcdddaaabdadcddbdbbccddbccbcaabbbacaddaddbdaaccacdbabaccccaccbaaddcbabddbbabbdacbbbaaaddabcddbabdacddbbaacbdadcadbdabdbabcdbabbcdbcccddcabdaadbaadbdaababacbbbcbabdbbdddbbdbcdaabdaccddcaddcabdddbaabbdccbcabccacabcdabcdcaabaccaabbaccbbacaaadbddabdaccddbbabcdbbacbccccdddcbaccababcbbadaaadbaccbddddbcbddcadaacaaadabbdacbdadddcacdadaabdccccdcccddddbcddabdccccdbcaabaaddbdcdcacdcabccadcaabcbbbbcbddadccbdabdbdddabbbdabcaabccacadcdddcbdcddcbabdadbbabdbdacaadcddcbcaddcdbcccdacabadaccdbdbddbabddaadbcddbdbaacdbbcacdbbadabbdddbcbccbbbdccacadaadcbbabadaaabbcabdbcbbdcdddbdbaadbddcdcbdacbaccbcabdbaccbddbbacccbbcbcccbdabdaaaaadbcdabaaadaabaababcbaadabdcddadbcaadabbbdbaaadacabccdbabdbaaacdddaaccdbabdddcaabdbbbcaabaaadabccbccdadcdaaabbbbdaacdbacddaaccbcbcadbcdccbbcaddadadabaabcaabadbabcbbdcaaddadddbdbdbdacacabbdabaadbdabdcaadbbacadbddabaaddbaddddcdabbbcacdadcbaabacabaabdacbbaabdccbdbddbcccdacdcddaacabdcbbaaccbaaabcadcadbbbcbdccbbbbcabccacadaabbcdccaacbcdcadbccacbcaaddddacddbbbdadcdadbddbbababdbadaddbdcaabcbabaadbadabbabacaababcbdcbcabbdaacdddcdaaacbbdbbdddbcbbcbcdacbdabbabaddabcdbcddbdcccbbcabddabaddcddbbadadbbdcbdabaddddddbaacbcaaaaaabcbcadbdbbdcdbbddabcddcabbbcccdbdabaaaadddcaaddbccbcbcccbddbbdcdbdbdcadcaccdbdcaddadacbbcabbacbbaabbddaadbbbccacbaaabbdcdcddaddadabbccddaddabadaadcdbcadadababcddcbbacdddbbccababcdccdcabccbbdbccaddccdccacadcacdacbbbcdbcdacdaaccaccaccacdcdccbbacdcddadabaabadbcdddbaaacdcbcddcbaadcadbabbbacacaddbacbccbcbdaabaabcbaadaaacdbaabbbbadbadbddbacabdcabdacbabdddaabacdadcdbdbbabddbabbdabbacccbaacdcdbaadabdabcdcddabbbcdbdaacabcdbcdbddbcabaadcaddbacddbdbcacacacdbaabcbcacdddccaacbcbdbbbcdaaaaddbcabacbabcddbcadbbccdaddccaddddbcacbadcdbbddbbdcaabcadcdbbccbabdbaccbaaadaaddbbcadaadddddcbdabdcaccdadaaddacaddaabddbcaacbbbbbabdcbbadccdabcbbcbcdcdccddcbbcbccdaacddcabdbcdbadbddbaadadbddbcdabdabacadcdcdbcbacaaaccacccbdccbddbadbddabbdccbacbbadadaabbbaddabdbbcbddcaadbddbdbdadcbdaccbccaccacdbcacbddbabbcabacdbabbdcbbabcbbacdcababdddbdbbcaabccddcdcaccbaadcdbcdbbadadcddbbccaadaaaadbadbdcddcddbaadccacacaabdadddbbbacccadabcabcdcbbacdbdcbdbdcdbcbcdabddbbbdbcbccdbbdaaacbcdabcddaaccbbdadbacbaddaaaacbbaaadbbbdbacdaddcadbaadabacccdbaddbbadcdacbcdcbddaaccaaabbadccbccdbcdcccbadcbacdaddaaabbcdcdbadaccdbaacdcaaadbdbcbbbabdbacbccadaacdccbabccdbaaacacadbaddccadabbaabacdcbbcadbdcbdaadddcaacddcbcbcacdbbcbbaadabaabcbdabdbdbcbbdbacddcbccbdcdacddadadbbadbdcbcbbcaccbdadacbcaabbbbbdbbbdccdcababaccbbbdcdbccdcddcdcadbbcadbdabcdaabbdbbcbdcbbcaddcbcdacddbddabcbdaaadaddcbacccbccbdbdabadccbbcdddadddbdaadcbadccdacdaddcbdbaabcbacbadaabdcabcbbaabdbacdabcbdabdbbcadadaaababaabbbdacabadbcdcdbabcdabdabdcaddcbcdccbaaacabcaddbdbcadaacbcdcaacdadbcdddacdcaddcdaacacadabaabdccaddddadcdbcabccbddccdaadbdbcacacaddadcdbccbcaaadddcadbacdccccdbadccdbadcdbbbbbaccccbcaadadbdccadbbbdbccdcababccacccddcaabcaaacacdcdbdddaddbbcdadadcbcbabcbcdaddbdadcacabbaadccdcdbbaadacdabadccdbdbaabcadcbdddaaaaacbcccccacabaabcdddcccbdcababacacdbcacbbdcddaaddcdadabbaaaababdcdadcaddbabbcbbddbdadcbddaabadbbaadababdbbaabbcdcabadbdccddcdbddacaccadcaaccdaccaaacbdacabbcccdaadbdcbabdaaabbaddddcbbcccdaaaaacdabbdbdbbdadaddbadddbccdcaabcaabcadbacddbbbababbbcdcbcbdddaabbabaadbcdcdddaaaccacabacbaaaabbaabdbababcdabdabddbcadacbabbcaabbbdddbaadcdbcaddbcabbadabbbacadadcdbabcadbbbcddbbdddddacdbababcdabdbadbddcabcbdacdddacdaadcdbbbaacbbcdbbacaaacddbcdddaccbcddcbdaadbddaabbcacadddadadbbbacabcbcdadddddacaacabaaadbdaabdadbaacacbcdbaaabcbcbbbdcadbcaacddbabacdcbcbccbddbadadaaaaaaadbadabacaacdadccacccccacacaabbbbabadcbaaabacacdcbaacaabdcadccaacdbdbdcdbbcdbacbaccddbddacdbdcdddcbabccadbddbdaddbaacdbbbadacaccacdbdacddbbcbdcccdcdcddabcbbabcdccababdacbbbacbdabdcddbdaabdddbbcbaddaaccbcbcdbbcbdbdbbcddaddcbadaaaaddbaabdcadcddcbcabdddbadcbacacdbcbdccadacddabbbcbcbbcdbdcbaacdadddcbcbdbacaadddbaccdbabbaabcbcacdaacadcacbcaccabbadcbdabaddccbdcaaadcccbaaddbdcbcabcacabcbcccbddacbaaddaaaadaaaddbbcaacdadbbabbccdbbdbccabbcdaaaaadaadbcbddadabdcbdbdcddccadbdcddcddddacccabccdaacdbadddcaadbaadbbddccacbcabbbacdadcadbcddbaabcacdabcdddcbabddbcbbdcbddaccadcddcdcddddaadaacdaabbbaccbcacdddbdccabccacdcacabbbbabacddcacccdbdbacddaaddcccabbabcdacbccdabdbacadbddacbbdcbdabacbaccbbaabcbdbccabcdcaddcdbacdaaccbcdcbccdcbacbbcbcdbcbabbccbcbcabdcdccbdaabadbbaddbdccaacaadbbbaaabcbbaaaabbcbacdbdababbcaddcbdbaaddbbdcddbacabacacbdacabddbcaadbabccabcbabacbbdddbcbbdcbdbcbdcbadaabcbccdccacdcbcbdabcdacacdbbdddccacccacdcbdcabcccbcabaacadcbcdddcdaadabadcdcdcabaaadabcddcbcaacccacbbbaadbcddbcadacaccbcdbbbbccbdbdcbccbccccdccddddbbddccbbaddadbaaaddabdabbaabdabbcbdbccdacdbccccdddaddaddccacabbcabcacbaccddcaaaadbccdcbdddbdbdcdbddaabbcdcaaadabdaacdadaabbddadddbbddadacbadcabdbdaccccdcadcbdcbcbaaacacdcbcadadccccbccaabbbabddbbdaddaabdbddadcccbcbddcadbcabcdcdacaaabcaacbdbcbbccadbadcbacbbdbdcbaccbbcdacdcbcddbbbadcbbccacbcbcacbccccccdbacdabbbbdbcddcdbdcadacdcabcccabcadbaddaadbbacdabcbcdaacacaddbddaddacdcdacaacddbcabbbccdbddbaccacbccacbabdbdaadbaddccdacccccdcdbdaccdbccacacdcdccdddaaacbdacbbcbccabacaccdcbdaadcabbcabdcacbcaadadddbaabadabbbcccdcdbadaacccbdcddbcaabaacaddcbcdcbdbaaccdcadaaddccdccdacdccadacccadbcdabaabcaabddcbdbaccbdadcdcdcaddccaadaabaddccaadcdddaddcaabcbabdbcaabbdddadaacdcdcbcdcabcbabcdcdcbdcdbddcabbdbbaddabcbadbbdcdacadddabaaaadaddcbcadbccdaabaadaabadaacadcbacaabbadccccdadadaabacbacbcabcaccbdbabdacacbbbdcaddcdcbccdacddccaaaccabcdddcbdbcabbdcdcabcbcdcbdbbdbbadabbdbcaabbbaadbcbbbdcccdabdaacdcbdccbcacdacddbaabcddbccdddcaaaddaabadbbdcababcdcaadbbbacbdaddadabbbaccbabacbccdcacbaadbbcaddbdaacbcdabdcdbaddbabbbabcbcaabdabdcacdddcaddbdcdadcadabbbbbdcabdbdcdcbddabbaacdacdcbacbaaccaaadaabdcdcbbddbacdbaddcabdcaaadbbdbabddddbcacddbabacdbdcbdbccaaadaabcbdccddbcdacbabdbbdbdccbcddddbcacaaccbcbacabbdbccdaacdccdddbdbbcacdabaadbcbdbabdbadadcddabdddbaabdddbcdbababcabdacdbbdcdbbccdccbaaababbdaacdccdaccbaadabbbcdcbadbbcdbaaccbadbcccbbacdbcbcadabacdaadabcbbccdcaabaacbbbbcdaaddaaaadcdcdbccdbbdddacabbdcdcaabcccdbbcdbdbaddcaaadababcdcdbdcdabacadbbabddbcaccbadaaacbbacabcbcbacaacbbbbbdbccdddbcdabdbbcdbbcabccdcdcabbadcabbbabcbddaabbdbddcddaadacadccbdaadabaddcaaaaacabacdcdabddcacbcbcccadccacbdaadaddbbbabccdcdbddbaaaddccacacdbdcbcacabacdbcabdbdcaccbccaddccdbbaddbdccabaadbdbcbaadddbcdbdccdcdabdbcbccdddadabcacbcadadaddccaababbcdddaacadbacccdabcdabbbbaacbcdcbdaaddbaaabcccdddcbbcdacadcadcadddacabbadacabaacbacbbcbccabacaddddbdcddbacabbabccaacdbabacdbcbcbddaddcacdcdbdbabcdbbdaaddacdbaabbcbabdaaddcccaccdbcccbabddcdbbaadbbdcadbddbabbbdabadcbcdbddbadcbbddcbacdddbacadccabddadbcdbcbcbdddaccbdcdcdbcabbaaddcbabadbbdcadbadcbddaaddcddbcabcdbbacbcdaadddadccbabddacbdbbcbddbdccaccdddccaccdcbababcdabcaacbddbcabdadbdabdbdbabdaddaaddbbbadaaddccdbaddbccbcddabbdaacbcbbbdaaadbdbbbdcddaadaabcacaaccdadbdabdcaddaaabdddbbcbacababcbbcbbbdaaddcddcddadbbacddbbcabacaddddbbbaadbdbbbdcbbdbbaaabcdacbaacabbdbadaccabcbdccbdbdadacdadaacadccbcabbdcacdbccbbbbdddbbcadddcaddbaabdabadaadcdcabdcdabcbcccbbcaaddbaaacdaccaacdcdcacbddbbbdaccbbabbbcabcacdadcdbbdaadddbaabadbddcadaaccddcdbabbccdabcacbacabbaacbbdddadacccddccaccddbacabcabbdadaddbddadabababcdcccddaabdacbadbdaaddadacabdccccbaddddaddaaacddbccacccbcddddbadaabbdcadacabdbadaabdbddbabadccdacddccccdbccbccacbcdaadbbaadbbbbdcadbbadcddcdadaaddcdadbbcddcaddacdccbbacaaacbccbbdcacddbbddbdbdbdbbdacdacbbbccacdbadadacadabdaabcadadcdbddbcadacabdcbaddaacbcdcdbabdabddadcddadbcdababdbcadcacddcabbababbcccadaadddaccdacdaccbdcacbbddaacaddddabddabdbcaadccaaabdabbcbbccbacdcdacbdcddbbcacadacddaadcdaacadcbdbdccacabddabcdddbadddacadaabdabbcaacdacadabadaabdcabaaccdadcccbacadccabbaadacbabddcdaacaccdcbddcbdbbacababbdbdbbdcccdddadaccddaabdcdbbccbbccddbdbcaadbbabdbbcbbbddabbccdbcbbcccbbbdabdbdbaddcadaabdbadccccbddcbdcddcdbacddbabbbcddbacddbaccdababdacabcabbdbabccbbdcbddbcbadbbbaabdbabddccababababcdddbdcccdacbddadbbbcadcccadcaacbaaddcddaddadbbdbadaacdabbadcddbaddddddcbbbdcccbacaccbdbdbbbdbcbcdbbddbbdcccdbaabaaaabbccabdaacbbacbcabbddaaaadadbcaddddabddbbdccbcadbdcdbacadcccacadabcbbabcddaccdaadcaadbdcbabadbdaaaccabbdbbdbabcacddbcaacbaadbdbcccdcbabccacdcdcacadcbdaacbdbdcddacdbabcdcabcdcbbcdbdcaaaababcacbaddbdcbadbccadcdbcacacaadabdaddbcddabbcaaddcbddbaadcbdbdaaaddccbccaaacabacbdbabcacbdcbddbadcbddcababcbbddbdcabdbacdcaaadaccabbabacbacddbaadbcdcacbabbddadccdbccaccbbbaadcacdadadbababddbdccadbaadddbbddbbabcadabcddbababccaccddcddbbacaddaaaadacdabcdbabcbddadcbdadbacbacbbbcdcdacbbddbaccdcaadbbddbabbccdabacdcdcaadbacacaabdcddadbaabaaacacbabdbdaacdccbcbcccbdbcbbcccbdcdcbccdabcbbdddcdaacabdacdcdcdabababdcdbbabcabcdbcdacabccbbdaccababdcbadaacbaaaaabbdcdaddbdcaacbdbadbcbcdcbddcdddccbccdddaabbbbcbdabacabbadddacddcccbaacaddccaabcadadcbabcccadcdadcbbadcdcdcabdaadccbdaabdcacbcdacbdbbcbbacbcbcdcccdcaccaccbdadbdccbcadadadabacbbbcdcabddadacacdbbabcadcadbacbabddaaaaddccdcbcbdddaddcccddccdddbbbaddccccabbcddbaddbdccacaccdacadbdcdabccacdbadcdcdbcabcdadabddacdbaccddccbdabdadbbbbdaacdacadcdcbabccadabcdcaadccacdbccbbccadcbbacbbcacdcaddbcbcdbdaabddccccdadbaabdadbccbdcadccbdbbdcabdacbadaddbaabadcbbbbabbcbaadadccbddbcdbaadbbaddcdbadaaccbdbccbdbccaccadaaacbcadddbbddabacbaabcbbbcbcaadabbdcbbcccdccbdaccbbabdabcadadcbbacccbcddcdacdbdcbbabdbccbdaadbccadccbdccdcccaccdbabcbccabdabaacbdcdadddaaadabdccabcdbcacdbdabbbcbabacbdbbdccdbbccababbaaccbcbcbaababbdddccacdabadcdbcdadaadbdcdbcbbdbbcadbbacadadbdabbddcabdbacdaadbcaadbabacdaaacccccbdbabdbccccbccbcabadcaadaaacabcbbdccdacdadbaabdabbdccddbacabbcabcaacadaadbdcaaddcbccdaacddaacbcbbcaabdbbbbbaacbddcccabdcbdabaddbaacbbddcdaaadbabbaaacadaabdbaddbdccbdbdccbccbbbbadcbdacbbbdadbbdacacbbaddcabddbdbdcbacbaaccababaddccaaabcacdabbcacabcbbbcbdaacdabadbadcbdcdbdbdcabccacaccddabbcabcabbcccdbaabbdcdadcccbcbbcbaadbbbbbbaccaacdacdcdcbbacdccddbaccbacaabbcacadbadaacbadcddcbbdbadccbadbcabadbbccbcbdbdbdddababddaabdbbdcddbbbbdddbcbaddcdabcacbddbaaabcdcdcdabcacdadabdbbbdcadacdcabacabddaabddbdcbbcababdbcdabddabaabaabcdabcdbadbdadcdbcaacabdaadacaadcaabbcbadabdbbdbacadbcccdddbbbcdacdacdbdbbcdcdaaacdddbbdbddddddbdadbcdcbcbccaddabddbcbbaacbbbabdadadbabcddadacadaacdaadcadcaabaaacabddddbcbaabadcdbdbababacbddcabddccababadcdabdacbbbcacdcdcccbcabdbaddacccdcbdddddadabbaaabcdbddccdaabbdacbaaacaccddcacbccbdabcccabbdcdbaacddbddcbaabbdcbacddccbbbdcdabbadaaababcdddabdbddbbacdccaabdccbabbcabddbbaccbdbcaccdadbdcdbdccdbccdcaadbacbbbdbdbbbbbadcabccccdbadabcaadadbdaddabaddddbdccbdbadbcaaccadbdadabcdabbbdaabdadbcdcddaadcaccddddbcadbdcdbaddcbdacbcccadabccccbbcdcccdcbccbbbdcccdcbcbcaaabdbadabdbbbabbbbbbdbaccacdccbddabdbbbbaaccaccbaacabdbcbdbbadbcdccaaddcbbcbccaabcddcccbdabdcbccdabadcdccaddcbbadaabdcabcaacccdaaddcbcdcacdbcdcbcaaabcbdbbdabcadadbbbacbbdccaaacaabdaddcabdcdbdaadadcbbddbbdccbbdacdaddadcbdbcbacdcdabbbdbbdbbbccdbccdbbbccdaaadbcbadacdbbcbcbdcadbcadcbcaddcbbdabbbaddbccaddcbabddbdacddabbbbacdcdabcadccbcbcbcabcdcddacbbdbdaaaadbbacbaccdacdbcbabcabacdaddbadcaddbcabaaabbaccbcbbbbbbcdbaadbbcbabcccdcdbaaabaabbbaaddcabaadbdcccabdababbdcdbacdcabaccbabaabbcacddadaaddacacabaaabdccdbdababbbcadbdabcdddccccaccacddabdccaadbbcbcabacbdddcccbcabaaddbdddbdcbaacbcbbcccaababbadddcacdbdabacbcdbcccdabcbdbcbdacaadacdabdaadacaadbcacabcbadcabbbddabaddcddbcbcbcacadaddaaadcdccdacacddaccaddbaadadabaddacabcacdbaacdaddbacbaacbadcadddaacbdccbdbcddddcabdbacbaccdaabbdabdccdaccaacdbbcbbbaadcbdbdbdacaddccdcacbbaddbccdacbcbdccbdbdcdcadcadcdacadbcdcbbdcccdcbacdbbdcbaabbbddaddddbcabdadccdcbacacdbbbaabdadbddbdcdbddbacbcbdcabbaaccccbdacadcabccacbaddbacbbaaadddcddaaabdbbdbaabccccbacacbcababcbcdbbcbddccccbddbbdddabdcdbbabbaabdadbacdbdbdddaddcaccacddbacbccbbcaacaacabbadcdcabbccbacabbccabcbccadcacdacbbaaaabdcddcbdacdbbcadcdadabaabddabbacbccbabdbdcbccdcacadbbbdccbbddbacabbadbabdbcbabdddcdacaaabcbccbcdabcccbacddaabbcbcccdbcbdaacdacdabdbaaadabcdddbacabdcdcddcacadcbcdbcbabbaadbbcabaddabdccccdbccdaabbcccabbaccdbddbdcadabcbbadcddddbcdddddbbbdacdbbabdbdbacbdacdbacdbbbbbdaccbbdabdacddbabbaacdacddcccbabccbbdbbdbcdaaccddabacbccdbccbddcdbadadcdcaadcbaacdcbbbaacbaadcbdadcbdddbacadaccdbdacccdccdcacdbcaaccdabbcdbdcccddccadcabacababddaddacddccbdaabcccccadbdabdabadacbbadabaaddabbdacdabadbbcbbcdbdcacdcacbdbccadcbadbbacddbcddababdbcbdacdccdabdcdbabcdddacbbbadcaadabddaaaabbabccaabcbdacdbbcbcdccbdcabcdbbbcbcbdbabcbcdbbdabdbadcbaabddadadcabdcdabdcabcbbbcdabbbdbaadcbbbcdbaabbdbcdbbcbaabbcabdddddbbabcbdaababacbdbddcdbbcabbccbdacabdcacbdbbbacbacacaacdccbcacbaccaccdcacdbaacbbdcdbcccdbdaccaacadddacbaadbacccbbbacaccdbcaaccadcabadccccbbacbaacaccbbcaccacbbadaaaccacbcbbbacdccaadcddbccdcdddcccbacdbaacdcbcbadacaddccbbabacbcaddcdccbccbacacbcadbdcdbcdbabbadcbaccccacbdabbadddcdcacbbccccdbcabadaabcbdcaaccdbbcabcdcaaaddaccbdadaacacbcacddaadcdbaaabcacdabcaccbadababcdbdadacbaadcdaacddadbcacabdddacabcaccdaadaddbcbccabdbadcabcbcbdbddabcdacdacacdacddccbddaccbbcacbccabdbddcdadcbbacbcbbadabcdbcbaddbbabddccbdcbdddbadacacdbdcaadddadacddabdcbbdabcbdbcadddbaaadbdbdcbcdbbbccbdddacbbcadcbcddaaabbddabcddcccdbbcaabddcaaaaacccaccacabcccdaccccaddacbdcdbabdbcdcdbadadcbacbbaaddadbdddabacbadadacdbcacbdaccbcaabdababacdbaaddbccaacaadccabccbdacadbdacaabbdddcccaadabcbbaccdbbddadbbcdacbbadadaaccdbbcaaaacdcdbabcaccbdcaaccbcaaaddbcabdadbaacddbdbabcdabbbdbdaaddacdcbbcabcdcabbdaacbabadaadcacaacbbaacadcbbbcbabbaaacaabdacbddccaababcdbcbdbbacbdabdcbbcdcabcdbcdbbbdadabbababddbbdabccadbdbcbddaacdcdbacaabbaadaaacbdabadbabcbbbbacacbabcabbcddaabbdcbbadcbaaaaacbbdacdcacddbcdbdddcbaaccacdacdadcbdbdbabacabbabdaaacbaccaadcbbbdbaccddcccbcbdacddacbabdaddbabbdcbdbbadaabddabcbdbdcacdbaccbbaccbabacabcbbaaaadddcbabbadbdaabcbabdaadaddcacacbabdaacdddddadaccddbddcdaabdbaabdcddadddbdddbcdaabdcbaabdcddbbdbddccccdaddddbcbdcaccbdbbbbaacbdacdbabddabcccadccaababddbadbcccdcaabdcaadbdbadddaabababacbbabdccdbbadddbbdddaaadadaabccdcacdacbadbcdabadcbddbddbdbccccdbcdbcbdaaabbbcbbddcbadcbadcabadcbbbabccdbbcbcbbabbbddccbaacadcbacacabaadabcabcdddcaaadbbacadbbbbbdbbdaadddcbdabccdbdadabcbdcbacaacbadaabccddaacccbddaabcbaacacbdadbcbdcdbbaabdabccbbabdababcbdabdadcabadaabdbcbbcdacdadccacabbbdbdddbdbadcbadddbaabaddbaddcabbbbbdcdbccacbccaaabaacabbdadbabccbbadcbbabaacdddacbdcabdbaacdaccdaaabdcbdaddacdaccbbbdcbbdbdccbdcddcdcdbbbcbbdbcbddbabddbbbcdcdbadcdbddbbacbbbcbbacccddcdcadcabbbdbabbacdcdddadaaaaccdcbacadbccdcaaabdcaccdacbdbaccacdaaaddbdabbdcacccdcddccaccdacaaadddcbcdbadcdbabbcddbbadaaaaaddaddccaccacadcadbdbdddacddcdcacbaadbccddcbcbbccbcbdcdabcdbacababbbcdcadabddbbcdbbbbbbdbddcacdddccbaaddacadcabcadddddcabdcdddcdbabcaacbadabccaccaccbbcdbbbabddabaababdbdddcabbbbcdbcbdbcadbcdccccabdbcccdaadabbdcbbaadcbcdbabacaacadbdcccacbbacaadaacabcbcdbdaaadcacaaadbdacccaabbcacdcadcdacaacdbbdadbdcccdcadbbcaacdbcbbccbdacbaddcddabdaabdcbbcbbaabbcddacbaadadaaccbdcccaadddbcaaacbcadbadbddbacbccabadbabcacddadbdbcbcaadcbcaadbbcccaadbddabbdabdacbbcaabcbdadcbdcadcbcaababacbdcabbdadaabaaabbcccdacbbddbdacdacccaabababcacbacdcbdadabadbadadadddcbaabbdbcacdcddccbccdabcaaabcdbdaabbbadbcabbccbcdacdcbbacabccdbadadbdbcbdadbbcbcbdaddbdadbdccbadbcaacddcbdabcdbdbdcabcbcbabccdaadaacddcccabbbccccdccbcaaacdaccdcdabdbdabdaabbacacbccabacbaddbdbabaabddacadaccdabbacddabbdcbbbdaccbacccdabddcaccabadaabadacddbcbdabaadcacaadacdaaaddabdbacdbdcbbddadcacabbdabcbaddcaacdddabdcdcdabccdaacbadccdcbdbadddacbaabcbbddcbabdcdbbccdcdacabbaadacbcccabdbdcabaccbcaaacadbcadcdabbbbadcccadabaadbddbdabcbdaacdbdbccacddadccdddaccadadaaaddbadbacdddddbdcccbaadbcdbcdabbacbabbbbdbadbdabbbcaaaabbbaabaaaaddababaddcbcccdccaaddcbdcdbadbccdacbdadbdcadddaaacbdaddbcdaabdcadccaddccdacbdadacdcddccbdabbcbacbdccdbbaccdadbcbbcdcddcbbabcbbcccaacbbbdcaccaaddabcacbbbbdbbccaaabddaababcaacdbdcbaacacdbcaabaccadbadbdadbaabacacacbcdcddbabbdbcbbcdcbcadcadbdcacdccdbacaaabdcbccccdadadadbaaccdbdccdbbbabdaaccadbdaaadcddcbbddbdaaacddcdcbbcbcddbdacdacccbdabcdadadcbbadacbaddbbddbdcabadaddcbbddababccacdabbcbcddccdabbccadacbbcdbdbababadcccadaadbcbdacaabcbdaacdcbbbbdbddbcacbcdbbcadbdcbcbddbacdcabadacbdabaccbccacaacbbbbbaddbcacacbdbaaabbdaacdcdbbabddcbbacddabddcabdccadbcbabdbcdbcbbbcbdbbddccadbdccbcabcbacacccbcdcbbcdabdcddbbaacbcddcdbdcddabadddacabdadbdbccababbcdacacdcaadabaaddabdbdcdcddccddcabdaaabccacdbcbddbabababcaaacddacacadabaaaadcabcdcadacaadacbaacbacbbabbdabdddcabddadddddbddddabdcabbdcdcaddadacababdbbbadbacabdcbacddabddbdddabdacbbadbddbbabdbbaabbcbaadbaddbcdbdcacdacdaaddcdcdadddddbbcacddaacacbccbccaddabbdadadbbadbdcccbbdadabcddbadcdbdbbdaddacddbbaaccacbdcddcdbbaaaadadbcadaacaccddddbddcdcaacccdaadcbabdadbbdaaaaccddccacbbacdadddaabdbcdbdbcbbccccaddadbdcaabbbdcaaddbacabccbcadaacbcacdbbcbababccacabdcacddcdbabddcdacdbdcdbddcdaddabcdbccccbcbdbdcacadcadbabbabacbabbadbdabdbdbdbdcbcaddcbdbbabcbcaabdadcbdcbcbdaddcaacbbbabdbdcdbcdcdcbababdacbaaaddcdbdaaacccdcbaccdbacdcbacacbbadbaaadbabbabdbcdacdcbabacddcacdbaadadbddcaccdcbbadccaabdadadccdcdcdcdaaadadbcdcaccbdbdcaadaadbddcbbcdbdbbcbaddaacbbcdadbcccadcaacaaadaddbdbcdcadcacddabdbbcadbbdcacddbccddcdcccddcaadaabbddadbaccbaaabaabcdcccccbadaababbdccbaaccdbcbccdbdbcbcabacbdbdbcbaaddacdddcdccdbaccbababdabbbadbccbdcadcddcacbcbbabcadbabadabddadddadcddccdacccbbacbadaccbdbacdacbacccaabcacbdccabcbbccbcabbcbaccdaadcaadbbcbadbcacddbbccdabacdaccbbabbaddbbddabcbdbbcadadcbbccbccbddcdacbbdbbddbdcdabbbbbadbdddddadcabbdacababcbdcaabbddbbdcaabcaababcccaadcddcabccbdccdccdadabcbccddabddbcbddbbabdbaadadaaadcbcbbcddbbcbbddbdccbcadcbcabbacbbacacbdcdccaadcbcbbbadabccbbcdcdbaaadadaabdaaccaccbabbcbababcbbccadbadbaabaccaabddcccdbdcddbcddbbacccccccbcbdaadcaddbdbadbbcacaccbccdaabcaaccaaddaaaadcbabdadaabcacdaaaabcabadbcbadadbdcdcadddabbbacadaadbdddbadcbcaadcccdbdaacbbbbbcdcccccdbcccbadbdccdcdacacbcbbcdbbdbdbdbcbccaccddbdccbaddbabdccbbcadacbccdcdbbcdacadacddbccdbcdddcabdadccdcdbaadddbcabdacbbdcadbadaddbcacabbacbbdacddddadcdbdccdbaacbccdaabaabcaddccddacbadcddbacbccacacdbddbdcdbbadbadacddbccbddbdabaccbccacccddcdbbaadadbcbbaccadbbaddaadbaccbbadddaaaddabbcacbcabcbbbacadbdcbdacbcacbadbccaacaadadbbaaabadccadcbabdcbadabbdcccdacbacbdbaccbcdccdbaacacdadbbcaccccbaabccbdccbcbaacdddcbdcbacbbbacbaccaabcbcbaaddbaaccadcadcadacbccbbcbbccabbadddbdabcbcccacaacddabbcccabcaadbbcbbcbaabbcbcdbddcacaaadccddabadcdcacaaacaaabdcbbabaaadddbadcbdbbaacaddaaccccdcbabacccdabadaaacdaddbdccbcdcdbbccddacaccbacbddbcdddcabbcddcdbbaacacbabcbcaddcdcabdcdbcbacbbdacdaddadaccacbcccccbabcdbcaacbbcacbdccdacbbbabacbcbcaabacaaccabababbaaccaddacacbccbddbdbbddbbdacdcaacbccbadbadbbcbbadbadccacbbdbdbbaaabdaadddbdaabcbccbbdbcbcabddcabdcbcadbaadbadcdbbacddabbdccadabcadcddacbbdcadadacaabbaacdccdbbbdaadbbbabcddddbdddcdccbaddcaddcccdbdaaddbbbabbadaaddbaaaccaabccaaccabacacdddcdbabcbbaccdccacbadacaccdbbacaadabadbcbbdcbccbccaccadaacccacbccbacbddadccbadabccaaaabdbbcabdcbbbddddccccbdcacbccdddbdcdabccdcacdcbaabbdaccdcccdadbdddcbadbbdbabbbccadbbbcdaddacbdcbbbdbdacabccaadbcabcbbbbabbdabcdccbdbdcdccdcdcdbbdcdccbccaaabaaccabdddcbbbcdadabdbcaacddbdbdcdcddbacdaddcacacdcbbdcbdbaadccdcbdcbbadabdcddcbcbcdadcbbcdbcccbccbbcdbbbbadcbdaacadcddadddccccccbbccbdadcbcccccadcadbaccacdccbdadddccbbacdbdcbaccaaabdddbabdbcddcdcaddddaaddbbdbabbdbbddadaddcdcaccadababbbcddccbbdaddddddbbdbbcdadadabddacdbbbbdbbdcabcdcdcddcadabdbccadcddacdbdcbcddbccacabcbdccccbacbdddaadcaaccdcccbabcbdbcbbcadcbcadbcbbaaddbdcdddbddcdcbcaaabdbbabbacdccaadbbdadabdccbccccadaabdabaddcbacddaccbbbdababacdbacdaabccdbbccacbdabcddbacadddaacdabcadcacbcbdbcbbcccaaadccaddcabdcaadddaddcabbdabdbddaadbcbdcdcabddcccdddacbadadabdabbcccbaaaddbcbdabcdcbcabddddbadcaabbdaaddbbacbbaddaaabbbdbadbcdacacdabbdabacbaccabdadabcaababaabbabdcdaaacadcbdbbbdacbcabaccbabdcddaacbdbacdabdcdbcaacddbcaabacdddcadabcadbbcbddbacabdabacbabbdbadcacdabccacbccccdaddacdcccdacbdcdaadddbdbbccaddbddacabbcbcabcddaddbacdcdbdcbbddaacdccbcdcbcbccaadadacccddcdabbbdacbdabcbdbdcbddbdcbbbcaddbdabcbcddcabcbbbadcdbabbabccdcdaddccdbcbabdaacddddddbdaddbbacdaabccdbdbdbadaacdbadccabbdcacbbabbcddcdbacdcbbdadbdacccabcbacbbcacbcbcaccdcacacabdbcdbcdbdbdcddddddddadbbabddbabbbaaadaaabbdccccbcdacccbcdccbcdccddddcbaabaabadcadcdabcdddabdcadadddadacadbdbbdaacbbdadcccddacaccccabaaaddaadadbccbbdacbcbcbddcdaabbbdddacbcadaadcaabdcbbcdadddcaabadbbcbbcbdabbdbcdacbcacdcbaaccabadcacacbdddcccaccaacccacbcdbbccccaddadcbadbaabdadcbcadaacacccbaacddbaccccabbdaddbaacacbbabdadbdbccddcbbbcbcbacddbbadcbadabaadbdddaabdaadadcddbdbbcabdbdcbccacacacaadcddbacbbccbcaddbaadbbbcacbdcbddbdbbcdbdcbaadcbaccbccadddcdbbcababbabddaaaadcbcbcacbadadddacbbbccccaabbaacadccbcadcdcdcabbadbdcccbcdbababadaddcdaadcbbbbccbcabcbcabdbcbadbaaadbdaaaaddadadadbbcdcdacbbbbdbcaadacbbabdabbadadbdcacbcabccacabadcaccabbaabbdbdaccadccdbacdcccccbbbbdbdcbbdabdacbddaccabadccababbccaaabbcdddabbcaccadbabdacadbdbcbbbabcbccacbccaddcadabcadcbabaababdddabbaaaaabbdbdaacdbaadbabdcddcdadbcabcacdbcacdcdbbadbcacaadcabbabdbdbaaaaabcbbaabdbddacbcbcacdcdbcaabdadacaccadaccdcaddcaaccaaabbdcabbcddcadabcdbccbcacaacbbdaccadddaadbbacdbaaaacccbdbbccbdaddaacbcddccbbcadbbcadcbacdbbabbaabbcbadaadcccdbcccccbabacbabcdddccdbadaddccaadaabbdcacdbacdbdddbbdddaddaadbbbbddcbbabcbdacabcbaddaaaaadbacbcbcbdbcaabaadcadaaccccbcacddbaddbdcdcbbcccbdbdcacdccdababaadccabdcaaccabccaddcaccbbdaaaddcaaacabbbbbbabcbaccbdadccdbcccccadccccabcacdcadddbdbdccddacbcaacdaddacaabadbbdacdabbcbabbbcccacbacdadcaccacaddbccbcdbcbdababdddbbbabbadbaaccbdaadbdadbbdbbddbdabdbccacdaabacbbdadbbcbccbaacbdcbcaadbbddabdabcaacccacddaccbacdccccdcbadbbccbdddadcadadcddbacadcccdacddccccaabaabacddaccaabcbbaacacdaacbaacdcdbaadbabbabcacbdadcbbdddadcbaabcbbdaddadaacdddddcabbabdbbdaabacccadbabdadbbccdaaddaccbdddabadddaabddbdbcbcdbcccdcddcaccadcbaadbcccbddcbacadcdccbccaaacdbcabcdaacbcdccdbcdacbaabaabcbababbcbbbcbccccccbcabcdccabdbbacdbbddabdbdbbcadaaaabccdcaadcabccccbbccbdbbbcdddbbddabaacccbadcaacadaacdcccadadadadbdadcabacddcbbaaabbcbadadbddcdddaddbaacadcbcdacaddccaacdadcbcddabadcdbdacdbadcdcdacdddadbdbacdbbaccddbbacadcbdbaddcaabaadacacddadaacbbbadbdbcbcbcacacdbccddbbdcbcaabbbcdcddcdabdadcdabcdcdaabdaddbbaadacdcdaacabbbadbdabbddcddadaaacbddbdddcbaaccbadbbaaddccddcbddbadaadabbcdccdadadadcacbccacaaadbacbdbcddddcbbbbdaadadcccacabbdcddbccccabcaacbbcbacaddbcadcbacdbabbbcaaabbdaabbaacbddcacbbabcbbcdcabdcbaddabcadadabaccbadddcbdcaadccaabcaccccdcaadacbcdbccdaaccbddcdccabadcabdbabcaaabbcbccdcbcccacdcdbacacadcadcaadbabcdccdcaaabbddcdcbdaccadccdbaaacbccabaddbababddbdcbacdddbcaacabdccaacddcdabbdbaccadbbaacaadcacbccacadbdababdacaadabdcdacaadcdbcbabdbcadbdaddadbadabbdaacabcacccdccdaadabacbddacbcaccdbbcdddbababdacbcccababadcaddbdcdaabddbcddacbacbabbabdbbcccdcccbbbaddbdddccbcbdcdabadddbcaabccadbbadacccccddbadddcadcbdcbaadbdaccbcdacbbbcdacccdabddaadbdabccaaccadbabaacadddcadbcbdcadbacbdcaddcbbbccdbbcbbbbdbccddddbaddbadcddacbcdcbccaacdcccabccdcddbaadddcdbbcbcaabbbcaddcdacccbbdcbbdacdbdbacdbcbcbaadabbbbabdacacabccabcccccdabbacdccbddcbdccccbdadaaaddadcaabddcbcddbbbaaaabbdbcdadbabababcbcabbdcacaadabccabaaaabaddcddddddaaddadbaccdabdabbcabddacaabddccddddbabcdbcdcccbbbdbaabcdcdcddbbaacdadbaddddddbbdbcaacbdcbabbbbdaabccbaaccbcdaaccacdcbadcbcbcddcaddcbccabbdaccbcdadbbaacabcdaacbacdccdbaaaccbdccadaadcbadbdadcdcdabdcaacaaaddbddadadcacdabcddcaadbcabadbcadacbacbbadbcbabbaabbccdaccadbacddccdddcdbacabbcacdbcbdcdbbabbadaddcabddbbccbcbccbbbcadbcdadabdccabccdadcdacbccdbcabdbcaccdbbaccbddacaddbabccbdadccabbadacdbbacdccabccdccbaddccabddbdcbdabcaacaadcdaadddcbbaababbacddbacdcdbbbacbcbadbbaaabadcdcdbbabccdcadadbbcdaaccbdabbababdccdabdbacdbbdabbccddbccccdcddbababdddccddadbcdadbcdcadaadadbdbbdcdaccabccdabcbcdaacacccacabdabccdbdbcddbcbbcbbaccdbbabcaaccdaabaacbdadaadbbddcabdadcdbdacddcbddadacaacabcbacdbaabadadbbadbaacddcbdcaabccddbabccaabdccadbdbdbdbbabbbccbbbdcddcdbacbbacddbadbcaabbcdcbacddddadbdddacabccbdadbbccbacccddcbaccabbcdddcbdcadadbccdacabbdccaaaddabadaaacdcddacdbaccbddccbbcdcdbdbadbccddddccbbdbbbacaaacbaddaadddcccdddbbbcaaabcbacbcbbcdbbcbbccdcaabccdcdcdaaadacddcbabccbdaabdbccadacdacddcbbdcbbdbdcaabdcaadbbcadddccddaccdadcdcddaadcdcbcbadabaddcbbbcbacadaadccdbbdbbadaccabcbaddccaababcccaadcccbccbaaadbaadaacdabbdbcaaddadbcbbbabadbbcababcbccdbbdbbbcbdbaacdadbbaabdbcbaaabcdcdbcbdbababccdbcdbaadddbcaacdaaadaccdcaacbaacdcddaaabdddcbbbdcabaabacbcbadabcabcadcbdbcbbddbcccbddbcbaaaacdbadccbcdababaaacccccdbadcbadbabdbbcacbabdacadadcbccddcbcadacaaacdbbbbacdadbabbaddbcababdcaadaabcdbadbdbcadbbbcbcdcdbdcbdabdcbcdacbbddadbbddbaababadcabcdddaddadccddaacdbbdbdddbbaaaabcaacdabcddaaaaccdaddbbcbcbdccaaddadbdabdcabacacaccaacabccccdaccdcddccbacdbcacbadbbdadccccdacdcbdadbabddbdccdacadacbcbbcdcbdacdacbbbcdadacadcddaddbdbbbdabbadddbcadaddbcbcbaadbbbcaccababbdddbbbcaddadbacbdabcdddabbbccacaddcaabdbbbccbbbadccbdbcabaabbbcdacddcacdacccacbcbbbaabbdbcdbcddbbbabdadbbdbdcabccacbdcbcabdaccbaacabdbabcdbdbdcdbcabadccacaddccaddaaccddddacdccbdbdccccaccddcbdbbabbdaabdccdbdaddabbaacdadcbbbbadaabcdabaacbcbacacbacbacdbbadadcdbbbadabaccdcadddcabaabbddcbcbccbbcadddadadbccadbabaddcaccaaccdcdcddacdddccdaabbbddbbdddaaddbabccbddbcaddbcddcadacdcbdccdadcdccabdcccacbaabbbabcbcdcbcccdaaaabbbdbaccdadaddbcabbccadcdbabdadabacdadcbbdacdbacdabdabdcdadbcababaabccddcdcddaabdbdabcccacdbacddadddaadabbbbadcbaaacccabbbbcbdacbbddbaccdacddabcdaabbdbdbcdbddbbdbcdbadcbaccdabcddaacbbadadcaddbbcccaccddadaccbbdbcbbacddabddbbcaabdcccabdaccbdaddbddacaaabaaaddadddbbddabccbbdbaacabdaddbdbbdbdbccbccdbcabcacbccacbbaacabbccabcdccbbabbabacbccaadacbbbdbcababaacdbbdbacddcccbcabdabaacacdbaadbbbbcacdaccddcdcbdcddcaabcdbacaadbabdadabbaaababacdccddcddaccccbacdadcbdbdcadccaccdbbaaabbbbcccddcaabadbdcdacbabdacccdadcdacbbdadaadbadccdccccabdcdbcabacadacbbbbbcbabcaabacbaccadcadbaadcccdacdccbdbaccdccabaadcccbccbbbbdacbdccdaaaadbbcbbdaadccccadbacbcbcddbcdcdaacabaaadcaddbddbadcdbcccdbdabbaaccdaddadcabbdcaacaacaabcaccbddbacdddcabcdadcadddccacccbabccacdcacbbcabcabbadabdbdcdbbdbbaaadccbbcacbdbbcbdbdcaccdbdddbbcacccaaadadcbbaacbbdbccbccdabcaccbcbcbcbacbacbcddbbbdbaccaaabcaabcacaddcddbabbadacbcaaacababcdababbaddacdcbdaadabadcbddbbcaccadaaababacbcbcddbccddcabaabbdaccbaaacbadbaaccdbadabcbbbaccdcbbabdcaddcdaccdcddadaadabcbcbbddadacdcbdadcdaaacaddbcadadbabbcaacdadcdadbadaaaaacabbaabcdcbaaaadcbcbacccdccbcadaccccbbcdabadbccccbdcabbcadbaabddbadaaabdcadbddcabdbabccdbbcdccaadbcbbaadacccddcadddccbcccbbcdacadaaabacccbadcdadcddcbccaccdcacbdbacbdbbdacdadbcbcbabadbaacccccbcbbcdbdaaabbcbdcdcbbaccccbbdcadddccbbbcdbdccabdbbddacccdadadcdaccdccdccdabadbcbadbdaccaaacdbbacaaaccbaaaadcdabdabddaacccdbcbddacddbaacddacdcacacdadacbccaaacbacaadbdbacdccabdadddcadddaaacdccacdacbabdbddccbcaccabcccabddccbaabbdbabdcbdacccdbbcbccadacdccdcbcacccadacbdbcdccbadbcbddbddcaabbdbbbabadcaddbcdaacbacaaddaddadbddbacdabdbaddcbdadcadcccaddadacbcdccdadbcacdbcdcdaacddcbbadcbdbdbbbdaddabacaaacaacaddabbccbcadcbbadbcbabdddbcadabaddbbcccbaccbbcbccabbbccdccdabcdddcaaaabcbccabcbabccbccccbcddcdaacbcdaccadcacbbbcbababbbacabbdcaadcccdddabbddbbcabbcbcbcbabddcdbaddadbdadaddccbbdbcdabaadcccaaacabdcbcabcdbcadaddddcbdcbcaacbddababdcacbdacadddadbabcacdbcbdccbcdcacacadcdacdddcbdbbaccdbcabdcbacabbcbaacdbdbaabacbaddbcacadaadababbbcbdccbbdcbdbbbacbadaababcbcbadccaaaccadaccccadabcdacbcabcaabddadacdbbddacbabbdbddcccaabaddabacccbacddacadaaadccacdcccacbabaabddcddccabbadcbabdccdddbadbdbccbcddacacdbdbdaaabcbbaaddbdadccaadaaacbabcbcdcbbddccadddcddddacacbababaccdabacbcadacaaaddbacdddcdadbbadacdaadbccadadadcaadcacadbcdbdbbdddacadcabababccdbacccbdabbbbbdbdccdbcbbabbacaabbadabbbabdadcdddcddadbdadcabdadcbdccadcbcbddbcdcdccdddabcdbdadadbbbaabbcdcaddaacddbbcdabdcddbccbaccdadadcbbbadcdadabbdbbcbabbdbddaaccacccabdccbcdbcacbbcbdddbbaaabddcaaaabacacbdcbddacaabadcbacccbdbbaabaccaacaacadabadcbbdbadbbabdabbadbcdcadbcadccdcbdcbabaaacadaabbddbaabadcbacddbcaacbccabddbbddacdbbaacaddcabbddcababaccdbccbdcbbcacbbcbcddbdcaaabcdddbadabdcbdcacccccddadcddaacbccccdacacbbabdccccdbbabcccbbaaddaabcabacaccbbcdbcadbdcaaacadbbabdadcbdabcaadcbaccdacdccdcccaccbdbdbddadbbacbdaabdbcdbaadddcdbbbacdadbcabaccaadbdcccbbaaaacacbabcdbcacddddaacaaabcdacbdcaabdadaabdadccddacbcacbbddbbcabdadccccadbdbbacabacabcbccadbbbcccaccadaadbddbbabdbbddbddabbaccdbaacacbcadaaadaacdbddcabddbadbaacdacccbbcdcacbccdbaabbadacdcabcdcadabccdbadcddcbaacadccbccddacacddcabccabcdcbbcabdbdcbbbacbbccaaabbacddccacbcdabcbbdbdcbdbbcdbacacaddcacbbabbcbbbdbdbbabcdddcbdaccdccbddabdacbdadbbbaaabdaabaacbabdbdcdadcbbbbbbbbbcdcccbaaadbaabddcccaaababaaddccbcbcdbabaccbdccbdddccabacbbbccababbababcdddcabaccbdcadcccdaacddacaacbddadcbbbadacdaaadbaaccabbabdbbbdbbdaaaabbddcadcdbdadcdddbcdbaabdcccaaadcdcdadcacdbdcbbbaccbacabcacabddbabaaacadccccaaadcbaaaabaccccdcadbaddcbcbbdddaabdbadccabcddccdbcbaccdabcbddcabaaaadbbbacaabcbcbabccbababaadddddcaaaadbdbaccbccdbdbddbbccccbbbbbaadcbcadcdcdcbcddadbbcbadabbdbdbbadbadcaabdbbdbddbbccbbcccacbacbccacaadddabaadabcbdaccbbdbdbaacddcdbdabbddcaddccaabadadbddcacdddbbabbabcccbdacdbbbcccdaddbcccbdccacbabadcaabddadbdddbbbdaccabaababdcadcbaddcccbbcacbaddcaadcbaabdccbbadcbddbdcdcbbccdcdcdaaababdacdddabdbcaccdbcbdbdddacbcbbbcadbbcaabcdbbaaccdbaadbaacdcbaadcabacccbbaaabccbbacaadbdbdcdcacccccdddbcbcdbdacddadcbbcbadbbabbbacbcdacbbdbcbbaadaadcaddadbbdcadcdadbbabdabadddcdcbcbbbcdcbaccabdbbdccbdadcbbcbddcccdddacacaddaccbaabddbcdcbadcbabcbdbbdcbacbccbddabcabcbddcccccabdcadcccbddbdddabbccadcbcddaddcbccadcddbbdadddaccacbadbbbbbabbbbacabaddaaacadbbccccbdabbcccaadbaaaacbbacbdacacccabcdbcbbadcbabbccdcadbddcaaccddbdddcbbdbccccdcddaadbaabccdaababadacabadbacddcbdbadabacabdacacdcadddacdcddbdbdbcdbcccbcaaacabdbadaadcaddabdbaccdcbdabddcbdccabacbcccddddcbdddccabdbccbcabbacddbbadcdcacccadaabbbdadcbdaabbbaababbaddcdaaaacbdbcaacdbbbcbbcacbbdbbcdaabdddcbddcabbcabbdccdadbdcddcdabccbbbacdbcbddccadaacaadbdcabcabcbbcbaaabdaadbbdddccdaabbcbddbcacccadcdccbcaaddaacabcdccbbbcbdbbdbccbdccdddbaabddabbbaddbbcaabcbcddbbdbdbabadbcbadcabcbbcdaaaacbcdcabcbddbdbababadabddcdbcccdccbabcbbaadccabdcdadbbddadccdacabadbcbbabababbbcacddcbbccababacbbcdddddadcadbccacddabadbaaabaddbadaaaaaaadabadadbcdddbadcabadaccdcacddadabccaacbbadcbbddbadcdacdadbdddddbbabacdccbadcbbcadaaabbdddabdccddacabcbacadbbacbcbccdadacabacaadcaadacbddaddcaadbcdabcbbbcaccaaccdcdabacbdcccabdddabdbadcacadabbdacabcaadbdbbccbaabadacdcdacdddbbaabacbacabbcbabaabdcbdaadadbbcaaddcadbaaaacdbbadacabdacdcbcaacccaadbcbbabbdcadadddacabddddacdbbcdcaaabdcbcbddcbbdbdcdcdcdddcaaabdacbcccbddaddacddbaccadadacdbabccbcabddbbdbccababdcaadacaadacababbaaabccacbadbaabacbbccbabcdbcbabdddbbabbdbcbbdbaadbabbcabdddbdcabcaadbaaddcabbbcdcacbcbcdbbaadabbcdcccabadbdacbdccdbdcaadbbaaddddbcccbadddabdabaaddabcbcaddbcddadababcbaadbbbdccdbdabbcbdccdbabaadacbbbcdcdbdbbbdadaadcdbbcbbdbadbbdaadcdacaabbacdaaaaaaddcdcbbcbdbdaccddadcadbdbdbcaaabacddbacabbbabaacdbabddbdcbbdaccaacaabdcdbcdbbcccdcbbdcbcddaccaaaddbdbcdbdaabbaddcbbdbaacadcbcbdaabccbacbcddddabbcddbbbcdcbacbdaddddccdbbbcdaccccdbadabcbccacabbabdaadbcacbbaccbdddcccbbcbbabaabcacdcdbdcdacbcabbdbbbaaaadcddbcbbdbbcbcaccbabdbacabbcbdcacddddacdabdabdacccbddbcddabdacdabaddadcabdcadbdacacbdaabcddbcacdbdaacbbadbcbcddcacadbbbbbbdddbdaabdccbdcacddbbbadcbabbcbdbaacbcccdbdcddcabddaaaacaadbcddababdaccabdddaddbadbcaccbbbbbdacdccccabbdbdbdcdcdddbcbdbbbacbcddbadbbcaddcacbcbbdadbdbcabbacddcbaaabbddadcaccbcbadccacacbacadddcddbccddacadcccaccbbaddbdbbbadacaddbaddcabddcdcbbadcdcadacbdddaaabdbccdddcbbaadacadbdbcaddbaddcacbbcbdcadbcdabbbbbddcbdcdcddccbdbacbcaabccbcbbdbadbccdddcdcabcbcdaadacbccaccbddadabcccdbdacdbbdbaaaddbccbacdcaabcaabcbccdbbaccdacbccbbcdbbdcdbbdaddbbdbbcabcddaaccdaacbadcdbaccdaddbccacaddadadbcbcddcdacbbbabbbbbccbdacbaddcdbdcbdccdabcbdbccdbabcdcdcdacbcccacadddaadadbddcdbdbbbdbbbaadddbbacccbabacddddbdcbddabcaaccdbdcdabbbaacadacdbdbacdcbbcddcbadddcddcddbadadddcbaddbdddbddaacdddcdaaadcbbcbbcabadacbdbcddabdbaccdbcccadcbaddcdbbdaccbcddacaddabcacbaaadcbbddaaadccdddaabadabdaaabaaadadbcacbbdbbdadcdddddcbcddbccabacabcbccdbbacabaaaccdadbbaabbdabbccbdaabcaddcabadacbadaacdbcddadaadbaddbbbcacdccddabacdaddcbaacbdbddcdacccbbbaccbaacbabddcaccbdcadaaddbbdcaccdcaddbabaccabcbcbdbdaadccbaaccdcdbacbbabacddcbbaabdcccbbdcbbcbddbaabacaacaabacbacbbcacbddbdbabbdabbccaccdabaacdcbbcbbaacbcbdcadcbbbbbdcdcbaadcacbcbbdadaacbcbabbbcccaaadcdbacddbdadacddddaadacadadaaabbbcaabdbccabbcddccbbacaaabaacdbabbaacaababbddcaadbcadcaaccacbacbaabddcbccbabcadaddaddcddddadcdcbaccccbaddbdaaaaddbbbcabaaacdbbaccaccdaddbadbaadacddacddbdacabcdcbdcccacddcccabcadddabbbaacbdcabbdddbcbbbdacaababbdaadcdcdaacacdcbdaabdbdbbcaaabacabcbbcabcbbaadadbbabbaadaacbccddbcbcbbdadbcccabadcdabddadabcbcdbccdbccaababdcbdcabbcbbddabccaddcaddbadcacaabacdbbbaabcbcabbdadbdcdbbcbdccdbcccaaabbddcdaddaacdddaaccadbcbabcabdbacbbadbcacdabcabaaabdcaadabcddbcbcabadabcbdabbccbbddbddbdcccbbdbaaabbbbabcddbadbbdcbcdabdadcdcdcbccaaabaacdddbcaadbadadabcbccbdddaacdbcbbbdacaabbabcdaacdcbcacbdbabdbcbdbacbcabddcdadbdaacdaadadcacbbbdcdcdbddccccccddcbdddbccdcabadcabbcbcddbccaccdbadacabdcacdacdacaccdcdaacbbcdaaccbccbdbbdcabcbccadadcccdaccabdbaaadccbabaddddaabdddbaabacaabbcbccdcdbbcbcbaadabdcbdcddbccbbcdbccdbbaaaabdddbbbadbacbacacadddababcdaddccddbcddadcdbdbbccadaacbaddccadbdbaabbbccbddcabacccdadcccadccababadbdaaadcbadababaccacdcbacddddaaaabddcadbbddcddcacadbaabaaddbdcccccdabcccbaaccbdaaccdbdcbcdbcdbcdadbcbbdccbdcacadabddbbddabddcbcdcbccddbccbbacaabadcaccbbdbbcaabbdccbcaacbcccccbbdcccdcdcdabacbabdadabbdcbbabbdccbcbbccccbbbabcdbadadcddbbababdcaddcabaaccdadbccabcadcacadcdcabdccbbdcddcddbbccaadcabdbabacbaadabcdabdabcbcbaadcbabcbacdadbbabacbdbacbdbdcaccabccadbddcdadacabbacacdcaccdbacddcabbbbcdbcdabbddccdcdbbddbdacccdbccacbdacbbdaaaabcddbcccabaddaaacaabcdaaadccbbdcbcccbdaaadcbbbbbdadbdcbbbbaabdbbbbcbaaadabdacaddbbadbcbdadabaddcbccacbbadbbcabaabaddacacdcaddadadcdcbacbbddbbdcdbccbdacbdbbbccabbaccbcdbddacadbccbdacabcdabcccabccabcbdbbdcdcbcbabdaacbabaabbdabdadbacaddbaaaaacadbcabcbadbdacbbcbadbbacbbccbbbcdabdbcadbacddddbdadddadbbdcddaddcddbbbdcacadbcbbbacbdcdadbdcacccbdaabcdaabcdaccbdcabcdaaaadabbbdbadcadacbdbbbdabccadaccaccbddccaaccdaddddbaccbcacaaaaccabbacbaabcabcccdcdcbaadcdadaddcaabdbdbacdcaadabacbdcbcdabadddaaacdadcdadbdbbaababaacdcddbdcacbdabacdcbcbaaabcdbdcdccdbcabcabacccdbdaabcccbcacbcdccacdaaaaccbadccadbcdbbdacdcbcddbdcacaaccacacbbdadbbddbbaddddcbbcdadddcdddbdbcdadddbbdabbcbdabdadccacadbdbcaabbdadbcdbacbaacabbbbadbcadbbadbbdbdbcbbcadadaaaccbadcadacabcbddbdcbdacddbacbdcbddadabdccadbaabdddaadaccbcaaadcbbaababdcbbbbaaabcdadaabdcabadcaccacbadaadcdbabdabbdddcbbbdadcabdacdbabddaababdaddbabaadaddcabcadbaababcdddddcccccdacabbabcbccadaaaadbdcabdcaacbddacdbddcaacbccabccbdbbcdccdabcadbaaddcaddaadbbdbbaadddbcaacbccdddabdabbacbadadbadccbacbcbabddaadbadbaabcdcdcdababaabcbcbaaadcbbcabbdbdcccdbdbbddddadcbbdabdccabbbdcacbdadacdaabbaaacddabdabcdabddadddadbccadbcbccdbbacbaaaadbacccaacbcbbbdacbcdaccbccdbdcadbcabbdccddaadbbdbbcdcaabbbcbddcdcbcbcccbaccdbacdcadaabdaacaadbbcdcabdddacbadccdbacdcbbaddbadaaadcbdddbaccabaaddccaaababcacbcabcbcaabadbcddbadbccdbcdccddacbadbcbacadbbaddadcabddcbdcdaabaacbacbbddadabddadcaddddabbcdaccaacdbbbdddcbbcddbacabaaacaabcddccdbbbacccabcddacdaacbcacacdcdcdadaccdadccacadcdaaacdbcdabbcabbccbcbcacbcabdcbbccdccbcdcdcadabcbaaaddddabccdbcacdddcbdcaababbdbbbbcccbccccccacbadbdabadaadbdbcaacddbadcdbcbbabcbbbdccadcbabaaadcccaacadddbbcdbcdbcddbcdbccbcaadaccaabbdaacbcaaddabdccbacbcbcacccabcdadbaccababbdcbadacddbbcbdaadabcbdbcabccacccdcdcdbabdacdabbcbacabbadcbcdabadbbbdaadabddbbaaccaddabcdbdbdadbbdabbcbdcbccbccbabaabdcbcdabbdbccbdbaadcddaaddaaacaabaccdcccbcbcccdddbdabbdbbbcbdbbcbaccdbbbcdcdacaacaaaaabdcbccabcbcdcabcdcdccabcdacdadcccbccdacabaccbbacdbdbcaacbccbbbbbdaccdddadabbdaccddbdbdadaacbaaadbccadbadabdadcaadaddbbacccadbbacbbcacdbdbabdaadcaadaaabdabbddacccbdacbbbbbcbbdbcdcaccacacdcddddabbbaaabdbdcabacadcdddacadcdabdcbdccdbccdadacbabbdcbcdcacbcdccaacaadadbbdadbbabdcbccdbbbcbdbbaacdddbcddcabbadaccbabcdcbbcabadabaabcdabcbbdccccaacabbdabbccbcdcacbcbcadbabadddabcbdbdaabcbbbcacabddbbccbdcacccbdddbadddcdbdbbdcabbaacbadacccddccdcabcbdbcabcaacbccdadbbbcbbcadbbddaaddabcadadddadcbaadabbbbadccadabaabadacbdabbdbcacacdabdaddabbabdadabccaaaacbacacbabdbbbcdababbbcddadbababbacbddbccdbbbdadacabcccbdadbadacdcdabbddbbdbcacbbcccaccaddcbdabaabbaccaddcccbbdbaacbcbdbcddddcddabddaccadcdccbaadbdadbaadccabadaabcbbddacabbcddabbcccadabaacddaabcbacddbaaddaaaadadccadcbbccbdcddcbddacdcacbdbadacccabbdcbcbdadacacccabcbdcadbaccbabdbbbdcaadbbaadbbaaadbbbccdbabcdbbcacaccbdbcabdccaddccdbbdabaaddcacbcabbcacabdaaadbabcdbdbcaaddaccaadbcabdbbcbdcdadbcbbcbacbbadcbabcdcbabbaaabccbacbdcdababacbaccbbdcaabaddcbdaacbbcaadacdbcdaaccdbadcdddcacbbbddccdcdccccddddbbcbdcdcbcbbdcabdacdaacddcbdddabacbbaccdaccccadddbadaddbadbbbccacdadbdcadabbbaacabbcbbdbcbaccaacbdabccbdadcdabdadcbddcacbcbbacbcdbdcdbbaddacadaadbadaaabccadbbbabcabddddbaabbabccdcdddaddddbbbccdabbacbddccadbcdcbcabbcdbbdadcddcccadcdaaccddbabcccaabdcdaacabddadabcbaccaccbcddcababccbadacddadddacadcdaaaacabaabbdabdbcaadddababbabacdabcdbddbccabcbdccbbcbccbcccbadcabdbcaadababddbdddddcadabaccbdbaccacbbbacccbccabddadbcbdcacdbdcbadacccadcbaacabcdaaaadcdbdccccadbccbbdabbbadbbacbaadaacabcaaaaaadcbddabccbdaaaacadadcdddbcaccacccabadaacccdabbcbddcaabbdaccacbcbcacaccdbabcaaabccccdddccaabdabcccbbbbbdbbcaacbdcabddbcbdadabaadadaabbbcdabdbdabcdbaaaaddbadbcabdcbcaadaabdbaccbacadcacababdccaacbaccccdbbaaddabdcaaccabbccbacadabadacdcdcdccababbabacbdddccccbaddcbbddccdbcbbdcdbcaaaadbbdbdbdabdaadbddbdcccbadaccdcaaabcbdbaabaddbcabaaccadbddccabaaddbacdbcbbcddbcbbaadbcddbcdbdbbcaddcbadaaadbdaddcccddaadadadabbaccbbcdacbcddbaacabbcabbcbcdcccbaaccbadabdbabbccbcbcaccdddcbbddcadcaadbddbdbdadaaacbadacacabdbadcaddcdcbccbbcdbadcbadccbabaccaccbbddddaaccdbbcdbddacbaaddabcdbacccdcbcaabdaaddabbbbaababcacbcaacdbcbbcabbdbbaccabdcaabdcadbaddcccbaaadbbdcaabdbddabbcbabadbabaddcbdcdabdcccccacbbbaacabdaabdbdddbadbddbcaabddbcaaaddcdcadddcbabcdbbabbadbdcaacddbbcdabaabdbaadbdacaddbbbbdbbdcaddddbacbbacaadbbaddddbddcaddbabcbadbacaacbacdccdbdaaddaacabbdcdbcbcaaccaccdccbaaacbbccaccdaddabccabdabddabaaddabcdcadcaaccccbccdabbcabbacbabdcacbacbddaadcddadbdbacaadbcadbbddddadddccccbbddbcccbcdbabcbabcabcdbacccadddacdbbcaabaabcadabacbdcbdadaacddccabcbdbbbcccdabcaaacbddbadcaadaccbbddabbddacdbdbcbdddbdddddaddcbadadccbbbdbccaacabcbcbcaccddabbbdbddacadbbbaabadabcadbbbcbbccccadddaacccdbadcdbaacccabaaddacbdabcbbabaddabaaabccabbbdbdcabcbadadaddcabcccbaddcddcbaaacccabdcdadbbdbdaddacbdbaaadddcbdadcdcdcbbcaddababdbdcdacbdbbcddcddccbccaabaadaaccbbcaddbdddcdbacbadaacdaaaaacdbddaabbabdbbbaaccdcdadcbddcaadccbcadabaadbcbcbcbbbabaddcbcaacbbadcdcbdcbcdcbabbdccdbaacdadabacbdbaccbbabddbaaaaaaadacdbddcacdbadadcbacdbadcdaccbbbdabddaacdccdabbbdcbbcdddabbbdbddcdabadbddbaaaacbadbcbcaacacaaddacaabdcacbdbdbdcabcdcadcddacdbbbdbcacdbdbcbbbdcabddcbcdcaadbaaadcabbddacdabdacbdddbbcbcacbddacacbcddcdabdcbabdadccdddbbdaadbcbabdcddccbccbcdccacaccbaaacacdaabddacbbcbddadbdddbdacdbdcdcbcbcbbdadbaacdaccaaacbbbccaadddbdacddaaacccddabcbddbcbadcbbbbddaddcacadbccbdabdcddcaacccdbbcabccbdbdddacdaccbdbaddddbadbcacacaaacdaacdbbdbcabdbbaabcccacbbbbddcbabcbdabdbcccccdadacabacbabadcddbadbabcbaddccbabbbaaabaabdcaaaabadaacbbcaacbcbbdbabccccaabcddcddacbbcbbacadaddaacacabbabbaabbbdcdbddacdcaddcbacbacadaddbaddababdccadadbbbbdabacacbdcaadcbabbcbccdcdddababcccdabddccacbaddbaacbcddbdbcaaabbaccbcacbdbadaabbbbacdcabaadabbbdabadbaccddbbbccdcbacccacdcbcdbbdadadacddddabdbadcddccbdbcccdcbabcacbadccddcccbdccccbbbbacbddcbddacbccdcbacdbbbcdbabaccbaaabbdbccaaaccdcccbdbbbaaaacbbbacdcddabbaabdcbabdaddbaddabcdaabcbbdacdbdddadccaccccdcaddbaccccacdadccbbdbcacbcccaccbaabbdcddacddbcbdddaadddbacddbaccdadbbbbcbbabbdadacdddadadaacbbdbbadbcabcadacdbdddabdbbbaccdabbcabbbddcbddadcadabcaddbcbdbaccaabcbbdbccacacbdabbbbcbadbbabdcadaacccdcdcacdcddcdbdbbbdcdcdbbacdddcdbdbcaadbbdcdcbccbabacacbccbbcadcccdaadadaadacddbdddcbcccadbdabbbadadbdbbadabcbbbdcdddbcdadbcbbbbcbcbdbcbbaddbccaccdaccccdaaccbccbacbbcdbbdadddabadbdacdcccdcbbbabbacbbacbaacdddabbbddcbddacccbdacccbacacdcadaddaabacaaddbdaabadaacccaccbccadaccacdcbcdbbdbabccaadabbdccbaabdcbdadcbbdacccbacdcdbcabaddabbaddbcdcddbdcdabacdadbaacdcacadabbabddcaaddbbccadaabdcdbacabdabaaaccbdabccbddbcabaadbccabcabadcbaabdcabdbbbdbcdabbbacddaddbbcaacbadcababcbdbbacbdcddaacbacdadcbdabbdaabcbdddacbcadcdcccbcdaadcaabacadacdbccadcaddcbabbadccccadaaaacbdbacbababcabdbabccbbdddcccbbaabbddbbbaccbaadabbaacbccdabdaabcbaabcacddbdbdcaaadaabccdcdaabcbbaacbabdadabbdabcaacbcadabacddabccddbcddcaabccabbcccbadbbddbcdcdcaddbbcbdabbadbcacccbbcabbbcbbdbacbdbbcdcddaabcbabbcccdddcdbdaccaacacaadadbccdadacaaddaabddadaadacccdaacbbabdadbaaccadcbcaacabcacbcbbddccaabbdababadcdbabdacbdbbbbcdbcdcadadaababdcbddbabcdbcbdcacdddaacdcddabcdcbbdcdabaaabcbccbddabacadcabcdbbabddbccdadaccbbabdaacdbadbacccddbabcbbdaaabcacbadcdadddbcaccccabddaadacccaaaaadadccccbaadddaabcbdabbabbbcbabcdaaccdddccbdcdbbdbcdadaccabcbacbbdcbbcccbacdaacdcaaaabdbddcaccadbcbdbaccdadbdaadbabdcadbaaadabdaccddbbdccacacbddbacbcbdddbaaccadaadadcadbacbdcdcacbcddcbcbcdcccbdbbcacdacaddbcadbbcacabdabccdccdddcbbdababaccaadbbcccabbcaadadccbaddbaabadcaabacdcccaabaddaaadbacbcccddcacbbbcdacddcaccccbcaabbddaabbaaddddbdcbdcccccbcbabdbdddcaddccbbaaddaddbcadababdccdccdbdcadaddcabadbcabcddadbabaadcbaaacadbcbcadabaaadcccacbacddadcccbcddbdcbdbaccdbcbbacddadbcdaabcacccabcbcbcbccabacdbcbbbbdaddacacccbcdbcdadddabbdabdbabadcdcbbaaaaddccaccbadbababdacbcbcacacbbbbdadbabccdccbcccdbdbbccadcdbabbdcacbbacdcabccbddcaabdbdabdcdbccccdbbbcbbcbcbcbdabccadacabcdbdcdcdcddacaabcddadcbdabcaaddbcabcaacccbcabdcacaadccdcaaccaacddcdaaddbabababbbcdcbabacccddbcaadccdabdccbbbccddcbbddcadccbbcbcdbdaacbddbbadaacacccadccbcccbbbabcccaddabbdabccbdbdadcacdbbccaaddababdaacbddbadbadbaddcbcbddbbacdddaaaabbdcaadbbcddbadbcbcddbdbcccdcbaccdcbdbbacaadbddcdacadcaabddadbccababcadbccacdbdddcdccacbadccbbbbdbabbababcbdcccccdbdabcbcdcadaddcdbcbcaaacbaadabadbadcaabbddbbcabbcdcdbbbccddbbcdbadbdabccbbcdabcbaacbccdabdddbaddcccaacdabbbdadacbdbcbbbcbaabbcccadccdaddaabdbabbcccbdbcbbbdcddaaabdcadcccbdbbcbbcbcdcaababddbbbcaadcdacbdbadccaabbaddcddaacabccdbcdcddadcddbdbdabddbcabcdbddccdacadcbddbddcdcbdccadacaaccbccabccadbdddacccabdabbddadcacacbdbabbddabdadbdbbbbacccddbcacddcdbbadbbdacbbbbacbbacdcbacccadaadacbaaacbcabdbcabaddddaabcbadcbdddaabcddacbadbadcdbcaaabadccdabdbdacbdcdddadbdbbdbbdcddccabbacabbbdbbbabbdbbabddbdadcdcaacbcacacbbdcddbbadaacdaacbbcdbcdbcddcabcdcccbdabadddcdaaddbcaddbcbcdcdbbaadaddabbbbcbbbcccacaacbacbbbdcaabaddacbcbccadcabdaaabcbdcbccdaacadbdaccdcaccddbcacbabadcabcccbbbccbacdadbddbaacabbcdbcdcbbdbcabbaadcabdbdbacacccdacddcccdbbbbcbaccbcbdaadabbaddddabcbdbddcbdccbacadcbabaadbabccadbbbdaccacdbccaabcbaddabddaadcabcbcadcaccabcccaaaaaaaacbcacaaadaddabababbdabcbdcdabbccdaddbadbaabaabbcdbbccccaaadadacbdadbdaabacaaadadcdbbcbcdddcbacccddaaaabdbabbbaabbbacacdddcbbcdbdacccdbcaacbcacaabbdccdaddacaddcadacaaacbcdbcabadacccdcdbaadcdccdcdddcdbbbaacbadccadadbbbcbcdcbdccadbbcdcccdccdccccccccaccdcabcdbbddbacdcabbaadabcabcdcbaccdabddcbccdacdadcbadbbccccbbadabcacddcadbbbdccaacaababbbbdcabaabbadbabddbdbbadbbbaaccddddbbaacabacacdacadccadcbccdcaabbacbddbbabdcbadabdccaddaaaddbacdbbcdacbccbbbccbbdabbdcdccdbbdaddbcbcdabcacdcbadcaddacdbdbacdcbadbcdacbbbdababacbabcabbbacbcadcacdaabccbbbadcdbadcdcddbcbaabdcaabbbacabdcadcabcdcccbdcadbadbdcbddbabbbdabddbcdddabbaabbdcddabacdbccadbcadcbaaaddaaddccacabadbabcbadbcbbbcdccbccbbdcabddddacaccbaadbcdbcdaddadcdddbbbaacdbbdbdcbdabcbddccaaaaadddbdccbcaddbacccbaadcaddcbdcdddaaabddabcbcadcadccbabbcbcccbadaaaddcddbcddbacadcbddcdbdddcdcdbbccacdaacbbdbacbcbcccbdcaccbbdddabacdcddabadcbababdacdccabbdddcdbcabccdcacbcdbcbcbddacdbddccdcbdabaccccbaacdbdcccccaadbbaabbcbbbbdccddaaadbaacbbddbadbccabdacaadbcccdabccdbbbdacaaccbcbbaacacccabdaadcaadccdacabddcbdbdbbacbddbdaddbbadbdddabdbdadcdcbaacaadcbbddcadcaacdaaccabddbadddbbabddbdbccccacabaccbcabaaadbbccccaacadcdacdaadaacddcdbbcbbbdadddaccccbcdadadcbddcadcddbbcdbdaadcadcdadbabbdcdadaddacabbdccabaaadbdcbddbdcdbccacbbadbcbadbdcdccbbadbadcadcacddaadbccbdbddaddabaccaccdbdbadbabccbdaaddbdbbcacadcaadacdddbaacdcdcbcdbcdcdcbcbccaabdbdddcdcdbdababdabdbdcbbbbcbddccadacccbdcdddbacdbbbdbdbddbdcdddbdcaddddbbdcdbdaddaabcbdbbabbadbcdcabababddbabbbcbaadddabcaccbdccdbcaddabcccbbdbadcbbaddcacbcbdbddccdabdacbbaadaccdcadcbdbdcdaaaadcacdddadbcdaaccbdbdcddcdabacddacaababdbcddcbbdadcbbdbaadccbcaacbaccdabbabcbdaacacddbadaabcacddbabaabdbdcadcbacaabdbbcbbdabcaabbcdddbcaabdaaccadcbaccddcadbcadacabbcabcbadbdaadbbddddacaadbacbdddccacdcadacdbccabbcaddaacacbbabbdbcdbbcbdbdcbccdabcaccabcdcbbddadddaacacacaddbcdadbbaaabbaadbdadaabaccaabdbccabcddabaccbaaddbdbbabadaddccbacacbdcccbcdcbbdddaabadaacdbbbcaaabbdbdadabbbbddaadcacabddddacbadcdbabbbccacdbaccdacbdccaaacdddadacbbdbdacbaddadbbabaccaacbabcacacadbaccbcdcdcadcacbddddbbcbbbaacccadcacacbcadababbdbaaddddabcccaddddaabcdddacadacacbbdacbbdcaccacccaacbcdccbcbcbcacdcdbacbaaabaacadcadbabcabcbcabcddadcdabaadccdadbacaccddadcadcacdacccbdaaacdcabcbbcadabadaacbaacdddcadaaabcaadccdbadcddbbcbabdbcdacbdaaddcbcddcccadcaacdbbacbcccabbacdbcccdcbdaabdadbddadabdaddadcccaddbbadcbabcdadabbdbdcbcdabbcddbdbaddcbcdbaacaaaaaadcddbbdabdabdacdabaababaaccbdbcccddbddbcabdbbcbadccbccbacbcccbabadcdacdabacbcbdcdadacadabdbabaabaccbcbbaccdcdccbcccaacbaabdbdbdaccaccdabaccadcdcbddcccddaadcaccadacacbbdbdacddadbadabddbdaadddacaccbddabccccabddacdcdbcdcabbbdaacaadcdaddbdcbccaaacaddabadabdddbdbadddabdbadccadadabdbbbdbbdbbadcbacbbbbdbabdcbabdabdabcacbdbdabcababdcadadacbbadbbacbbaaaacbcddbabccacdccbadccccbbbdcdbbaabbbbbcdbaadadabcbdabdbbdbbdaacccdaabbdbbbdbbcaccaabddcdcaadcccdbdbbccdbaaaacacbcbaabcdcddddadbddbdcccaaccabccacddcaacbabaaadbccdacbdbdddadcbbacdbbcbaadbbadbbcacadbbadcaddcdbbdbdacbbabcbcadacadddaccacadadbabbcadcbabbbbaddddadcacbabcdcbabcaccbbdaadcbabaabbddbbddbadccbdbdabcbdaabcbabcdccbcacbdabcabccccadadcabbaccbadbcaabadcabdcbbdabdaaacadcbdaddcbcdbbadddcaccaabaabcbaabddadcccdcacccdcbcabcbccddbaccbdaadacbcccccbccbddbcbcbabbaccbccaaadaabcabbdadaaaadbdaabccadbadbcbaddccdbadaccadbdadcacbacbadbcbdabdddaaaacadbbdbaddcabbbbbaaadddddcddaccbadcdccaacbabbaddcdaabcadbdacbabcbcaaccdaaaacaabdcbcdcaaaacdacbddbadbdadcddbcbacaacdcaabbddabcdbaccbcabdadcbcadcddddacccccccdbaadabaaddbacdabdbbcbbbadadadbdcbccdadabdbbddaddcddbaccacbccbdccbdcacbcccbbccddcbabbadcbbcdcaadbdbdcccddacbccbdadbddabcdddcbcddacbbdddaaaaccadbbcbcacdccadacaddabdbccbcaadacadaadadbaddccbdcbbabacbbddabdabbcbcadccddccbdaaaacdbcdacbaccaacdbbaacdccccbaddbbccdbaaacbdbbaadadcaaaccbaadacaaabdddadabddbbddbdddddcbabdaabadbdddaaabacdaaadacdadabbadccabdaddcaaddacbdcdcacaacacbbabacbbbdccacccbbadcdbdbcabdbdccadadadbdacdaadbaadadcbddcdbddbcabdacbdcdcacacccdabadbdcdcaaccadcbcddabbdabadaabbacaacaacdbbdddaadccdadcacbbabdbddbabcdacddcabacdaaaccdaacabbcddabaddbdddadadacadbdcabcccdacbccacddcacacddbdadcaadababacbcdcccbccabbcdacdcbcdccdaccaacbadabdccdadcdacdbcdcabaadaadcbddabcbcbcbaadaababdcbbbcccddccddccbcaadabdcdddaadbabdbcbdbaabacadcdbcbbcddaaaaccccdbdcabbdaaabbbaabbbdbadadbaccbaadbccbbbdccdbbbadbbcaacabbcddadabbdaabcddaacdbaaabbcdcbcaaccdcdcbdccbdccccddbbabdcabddbcdbcaaacdaababbcaadcaccbbcbadcaccabccbdcdbdcdbbccacdcdbcdccbbbcacbacdbbaccbdbdbdcaddabdbbaaabbbccdbbcaadaddacaacaadbaadbabaaadddaabcbdbacabcbcdadcaababcaaadbacbaaaacccbabadcbdbdcbbccdbaccbccdbbcdcddcbaadbadbdbacbcdadbdcbdcccdadccddadddbcbaaacdbcbcacdbcbacbaabcacbddaacdbacacdacabcabddaaaddcbabbbbadadcaaddbdcacbdbdcccdbcdcabcadacbcccbaabbcbabbacbccaaccbaabdccbbbadbdddaaadadcdaaddcabbadadaccccbdabacddbcabbbbcdcbaaaddccaacbcdaacdacbabaaadababacdbacddcbdccddbdcbdbcbdabcacadbadcbdadcabaaddbbbdbadacabbdacdbcbdcacabcaadcccbdadaabaaddcaaaadcbdcaccbaccccbdbdabddcdccaaacabdbbbcbddaacccaddcabbcaadbccbdccdcdccdcaacbbbdcbbdbbbcaaccbbdabaabaccbddaaddadbcaabcaacdccadacbccbcaadbaadbabcaabdaadcaccdcdcaccbbcabadcdcdcdaabbbbaaddbbcdaccdccdbcddcdddabaaacaaddddccbaabdbbbdacadccabcdcddadccdbbccaddcacbadaddaaadddbdaacdcbccbdabdaccbabdbabcccdbaacbcabadadddcaadddcddadcdbadcacddbbacdbbbbcdaacdbccadbdbbdcdbbbadbddbdcabaaaabdbbaabaccabadaaabadaddbbdcccbdbdbabbddbcbbcacccacadcadcddacbaabaccbdcdbcdbdccacacacbbbbcacdacaccbaaaadddadbcddccddcacbadcabaddbbaaaabadbcdccdadbcabcaaaaadbadbcadcddbabcadcddabdcabdbbbcaaabbababcaaadcadddcbbacdcdbaaaaaacbccbaaddcdadadddddbdbabcabbadabdcddcabbbbdaacbbbbddccabbddaccbcdbbababddbadbcdcaacabccaddddcdccdcaabdddddcdcacbadbadaaccbddcddddddacdcadbddcdddadacdccbcbacccdcddaaacbccddabbbabacaadcdacbbacbbaddacccbcbdbabddbbacccbdcaadcaacdadbcbbdbdaadbdcbdadbcadbddabcbbacabcadbcbaaaabaabadcbccbcddbdabababcbccaaadccaabbadcaadccbaacdcdbddabdcdbbacdcdadadaadaaadcabdabbdcbadcdbacbdddcbccaaadcbadcddcbccdbcddaddaddccdcadadbaddcdaccdcacdcaadcbdadbbccaabbdbabcbabcdcbadbaadbacbdbadadaabaabbdccacbacddbdbaacdccdbbaababdabaccacbdbaadcdcaabbdbbcddcdcbabaabcaddddadcbacabccdddabcbbbbbaddcbdccbbcbbdddcbbcdcddaadabadbbccdcaaabdbadadacdbdbdddccadbaabdbbaddacbbcdddabbbccbccccddbbabaaacabccabbbcbcbbdbdaaabbaddadddbcabacdacdcddccbcbbddbcaabcabbcaabccdcbcacccdcacdcdbdbabcdbabdbbcbdddbabaadabddbddbabaaabadcbacacdbbaacbdabadabbbdbbaaadbbcbdbdacdababdbbcbdadddcbadabdacdbdacbdadbadaacdcdddbabadabdbacacdabcadddcbacddcbdccaaabaadaabdbadacadbaaaadbccdcddcaccabcbdbdbbcadacdcabcddaccbaddcadaccbdbbaabddcdaacddabdabddbdaabcdbbaadadaddbbcbddcdcaacdccbddbdbddbdbdaddbbddcbaddbdabcadbbdbcbadddddbaabdadadbaacbbabaaaaaaabbdaadbdccbbdcadaddbccababaaaacdaaabaacabdcbbbaabdcabdadbbabaccbbbccddbbdbcaabdcdcbacabcdcdaadccdbdcacdcdcbaadadcbcdaccacacdacbddbadccddbdcacabadcabddaabaddcadbcbdabdcbdddbcbbddbdcdaaccbcbaabadbcddaaacbbcdcabcabdcbaaabcdacdbaddcbabcbcdcadcadacddabcdcccababbbbdabcccdabcadaacdcbcbbcccdbbbdaddbcccccaccccbadaacabbcbdbbddadbbdaadbcbddbaadabdbdcbbabbccddaaabdbbcbadcbbadadcabcdbdbaaabacdabdcacdadbbadccccdbcaacacabddcaccbcadacaddcccadbccacccabcabccaaacddbbbacbbbcbaacbccccdcbcdddbcdabaadbcddabbaadacdbadcdcaabadabbdcdccadcbddadbbccacacccccadadcdbbbbddbdacbccbdbcbaddddbdbdbddbaaadbbcbcbcaabdbbdbabbdabdbbbacbaacdaddbdacaaabdbbcddadcdccbdccaaadbdacdabddbdcdcdbbacadcbabccadacdaddccccddddaabddccabbabccbddcacccdcacaadabcbaaacbcaccabbbaaaabbcccbdcbccdacddbcddbdcbbaabcaabbacdcaabdbcbababcbcdcacdadbacabbddbabbddddbcabacbadbaccabccdacdcdacabbcaadbccaabbddccccdcddcadadcccbdbdcdbbbaacadccccabdbdbdcbcbdabbcaddcdbcadabaaccadbacbddcbbcabcabadacbcbbacddccbaaddacbdbaadcbdcaddabbbccdbcbcbadabacbacbbacabdbdbcccaabcbdcbaacdcbbbadccdbcabccbdabbccbbdccbadcabcbdccccdbabdcadacdbbaacccbdbadcdddcaadacbdddcbadcccccacbabaccccccdadbddabacbabbbadccccdcddcdadadbadbcdabababbddccbadcbaabbbababdabaccbdadcaccdcaddabccdabdacddbcbdcaccdadcccdcbddaccdddabbdddbcbbaaadbaccadccbadcaddcbadacbbcbcddbdbdcbdbccadbcaaccbddcacdadbbacaacbbddcadacdbcaddadbbbddcbbcddabacbdabbdbbbbdbaaaaadcadcdbcbccdbbddccddacbdbdacbaaadabdcddccababbbcbcbbbccabbdcbcbcccabdcbdbcacacadadcbbbcddbbdaabdbddbdbbcbcbdbcddaccddabcbbdbdcbdabcbacabdaccbdaabacbccdcabcccdcbaabccbdcdcaadabaaaadbbcbbbbadcdbdcdadbcabcbdacdacbaaccbbbddccdaddccacbcdadccdccbabddcacbccbccabbcaaaabbcbbbcccbbccdccaaddbaaacdcbaadbbcacbdddbcacbcdbbcaccadbaccaaaccdabdbddcbaaccdaccdacabaddaadbadcdcbbcadccbdddbbbddaaacaddcaddcccddcdbabbacacbdcdcdddaddabacccbdbbadbccccaabacdaccccbbdcaaacabccabbdbcbcbadacaacbbdcbcdcaaabaabcbcddcdcdbcdadbccdbbadcadaddbbbcdabddddaabcabdbdccddbdaabcbbcdcbcdcdcadbacccdaabaccbacdbacddacbbdaaabbcdbbcddbcbbbbcccdcbaddabccbdbcbbbcccccadbdcaabdcacbbdcdcbadbabcbabddccadddcdcbabccbcbdbaddcabcbdbdadcbbbbdbaaacabcaccaaabaacbcabccbcbaadbadcaddbbcdccbbddaadcdbdbacacbcdadbdabdadbdbbdcccddccbbabcdaaacaaabcaabadbbcdcdccabbadbdbddbbdabdaabddadacbdddbdaacacccbaccaacbddcbbcdcaacadcacdccbdacabdacaabbcbcbbbbabbacccbacabdbaadbcdddbcdbdcbbaaaabdcacdaccbcaacccbccdcdccbdcdaaaddddacbbbadabaaacbbdbcdacabcbadcddccbbbbdadbccacdadddcbcadccbabbdbacbdcaccbaabbdbdacbbcbcbdbcabcaaacacbbbdaaadcadabcdcdbabdcdacbccdbabdbbbcbbdccbcbadbadbababaddbdacbadbdacbbbbdbbaaaccbbccbbaabdbbaddddccbabacbdcbcbbacbccbacbcdabdabdbbaacdaaadaccaddbdbaaddbddddcccbbabcbdbbabacaacccdcaccdabaabbabdccbabddbdbdbccbbdccddcabaadbcddabbdcaabbadddcddddbaccdacdccbccadcaacbbddaccabddcbdbadababacadbdabaaccccaacacbcaddadddddadddcdccbbbbadabdabbcdddabbdaddddacddccdcbcbccaabbddccbbccccddacdadbddcbccddcccabcddcaddcaacccbadcbcdcbdbdadbaaadbbdcccbaabdabacbdcbdcdbaaabbcdcdacbbadadccbbdbbdadadbdcaacdabcdaaabdccbbbcadcadbdadbbcadcbaccbdaacbdaababcadcaadaabacacddcbbddccddabcbcadcaaabbdcbbcbcbbcbaaadddaccacccbccccdbbabbdbacdccbbdcbccbdbdbddbabbbddadbdddabdcacaacbcbbbdaacacababbabcccdaccdccacbdabcacaabcccbbaddccbcbaaddbcaaaddadcabbbadbbbadddacabdadbabbbbdcdbadcccabcddbaccaddadbcdcdacbadcacbaaabbdcbdaabcddcdabddaabbcaccabdaacdaaddbaacabdbaaabacdaaacdadaadbdbacaccabcacbacbabbdaacbabbdaaacadaaccdaddbaaccadabddadacacabbaacadccadddcdccadcbdaaabdcdaacddaabdcdcdadaacaaabcabbbcbbbdaddcccccaddbcdbdbaadacbbdaadcabacaaaddbbdddaabbdbbccdcaddabdacadadcccdaccddddbddcbdbbcdbdddddaacdabbabbcddbdccddabbbccbaadacccaddadabacbacddbabaadabcdbcaabbdbcddadacaccababdaababbccdccaddddbacbabaacbaaccdbadccdcdadacaaacabbaaaadcccaacbdadbdbdbbdcaadacbbbbabbbbbacdcddbbaacbdcaaabddaacdbdacacbabcabcaadcabaababcabcbcabdbacaacdbcbcacacabaabbadadbdadaccacdaadabbdbbadccabbcadddbcadabbcdbbcccdddbdcabdbaddcdcddaabaddbcabadcccdaabcbaddabcdabcddbdcccccaadbadbacddddddccbcbaababdbdcdabdadbdccadcadaacddbdcbbadcdabbbcadcbcbaccacabdccbcbbccbcbcabbbdddcddcbdcccdccbdcadbacdcbccbcdbdbbdabccccdddababaabbddbcbcacbbaacbddccbdabdadbbcdbbaddadccdccdbabccdbcdcddbdcbbabdbaacaccacdcdcabdcaabbccccddbdcabaadccacacdddaddababcdcacaddcacabcbdacdbddbabbcbaaaccacabbbcddaaaaacbacdcbabbbbdcbaabaccadacbdbbcdaddcdcdbabaaacdabdddcdcbdcaadacbbaccbcabaabddacadcbaabbbbcddabdabcdabdabbdbcddbdcbdcacdbddcdbdbcdccadacacaadbccdabaaaccdacbbdadaabbbdbcadadabaacddabcaacdcdcddaabcababcbbacbcbcbdccdbcadccabccbabadcabadbcbccabbccbaccdccaaacaddaacdbbdcaddacbaacddbdaaaaadcdccdcadcdadcacacbbaaaccadcdabbbaaccaadcdbcaaabadabdbaadbccdccbbbacabdccbdadcbaabacbcbadccdddcaacbbbadbaaacabdcbbaddddbcdbbdabdacccccbbabbcdabcdadabaabdabbaccddcaabbcacadbdabadcbacadbddddbacbcbbacadcdadaaddccdacddcdcaaaabcccdbaabdacdacbabccdcaddcaadcdcbcbabcaaabccaccabcacaabbcaccaddcabbcdcbcbadbbbdadbccaaccdcccdcddcbcaaddbbbacadccabdbaddbddbaadddbbbacbbcabcbdbacdabcdacdcabadcdabbcaccbaaadbbbaabdbaaabccddbcabaadbdbbbbacbaacaaacdcadadddcdcaabbdddcdcbddbcdabbbaacdddabbbbbdddacadbabbbaabbbadaabadbcddddcaccdaaababcdccbadddcdbbabdcaabaabbdabccbadadcabadacadcaaaadbddabaaccdcacadcdbabdbbcdcaaacddcdccdccdcabadcdcaaaddcadbcbbccbdaacdbccbaddcacaabdadabadbdcbcdbdaacccdcddacbdabcbacdbacabbaacaaccaadaddabbbadbbdcabdabadbbcbcabcccbddbdcddccabdbaccaacbbdbadbcacdbddddacbcccdcbbcadcdcdaccadddabacdcadbbbaccddbdbcddbbdadcdcdabdadbcbdbacacbadababacbdabcdaadbbadcaaaaaadccbdcdcdbabdbddadccaadaadaaaacabaacaacacdbccaadadadbccbddbbddcccbcddbbcddadcacbddadbadacadaddddcbbdbccddcbcdbbdbcdabcacdadddadbcabdaaacdadcbbddbabacbbdcbabaccacbabcabcbdbcbbcdbcbddabadaaddbaabacccccdddabcbbbbcacdcabdadbddacdadbacabcbbddbcbbbdcddbdcabcbbacacbdabccdabddccddbdbdcadbcbadaadabadaadbcaddaabdaacacbdcbcdcabcbaccbcdcbadadbabdccadababbcdcbdaadcaccddbbddccdadabacabdbabdcccdddccddacaadaabccabcdbcbcddcdacacbadbcddccdaccacadaadddacaddcacbddaccadddcbdcbbbccadccdbdddaaccaacbcdbddcabacdbcdcbdacbadcabaddcdadccdddbaacacdbadbdddccacdcdddaaaabcdaacbdbbddccaabdbadbbadacaaccdbbdbdababbcddbcdaccbcabbbccaddacbaaaaadaccdbddddbdbaddccdaacadcabdbabbbcbbadcadcadcdcbcaddcdacaacbcbbddcacaddacbbaabdcbaaabdbcdbdacbbbcbaccbaadcbbdccadbcdccbccadcabbbcdccbbdabdcdcbacbcaaabaacdadadbbcadcbabaddbabcbabbaaccbdccadbbbdbcabadaaccbbddbcabddaadcbddacdbaaaddbdbddcdacccccbbddcadacbdccbbaacdbbcbbbbadbcdbabcdacadddaaacdcaccaacccbddabbdbaccdbdccdbcbcaaaaaccddaccdbdbbcbadcaccbcdcdadabcbbadcddccdbaaaaadabcaccbbcdbddaccdacccdcaacdbcdacaddccacccdcbcaabaaccadaccdcbdcbbcadaadcaadddcabdddacbbbbaababddabbbdbcbaadbdccabdacdcbbbcaacaaaacddadbbababacddbdacbacacccddbbbdbcccccaaacccaaccadaddddccbcbcbdbaaddcbbbabcbcddaadbbbdcdcdaaddbabbbcccbdcbcbcdcbaddaccacaaadcbcccbdacbaaadacacbddcdccbdbcbdabddadcbcacbcaadacdcabcabcdaadaaacccbcbcdcddbccbdaaccdccaddaaccbadcababcadddbbbbcaaddccacbdcbacbbbabacacdbbacddadcdcddbabdabaccaccdbdbdacdacadcdacdacaabcdcaccddbcabacbabaddabaadbbddbccbabccbcaccdbdcabbdadcaabdacaccdadcccadaaacadbbbadcccbcdbdabacabbbcbadcdabaacaadacaddbbdccbbacadcddadaabcadbbcaaddcbcaacacdadcaacccadddaababbdabbbcdcbbaabdabccdccbdbbdbcaccbbdddcabcabdbdcabbbddcbaabcdaadddacaacbbdadabbdacccbdbcdaabdbaaaddbaaabbdabbabbbbdacabccbabbcbcaddadddccbbbbbcabacaddbcdadbdaadabcdcadbbadaccbccadddabdcbadcaadddbdaacaaabdacdbaccdbdcaabdcdbaabccbcaacdaabadadacbdbadddcbbbdaaadacdcbaccccbabdabacddcddcdbdccdcbababadcbabcdcbbcdcaaddabdabcdddccabbcbbabccaaaddbaadcbaacdbcacddccacbaaabbdabbddcbabcabadccdbcddbaadbccbccdadcadccbbdaddaddcacbdbbdbcabadcbbdbbdbccdbbaaaadbacacdbbaadcbcbaabadcabcddcbddbbbabbcacddbdaaacccccacdcccdabacdcdaadbbaadacdddbcbcadabacdaabcabacdabcdaaaddacdabbaacaacdabcccdcbadbdaddddcdaaacdaddbdcadbbabddaccabbbdacabdaabdbcccdbdbcdcaaaddbcdcacbabdcdcabcabccdccaabaacaaaaccccbdadcacdaddcbcabddccdccdbabcbaccbddaabbcabdcbabccacbdbdbcbbbbdbacbcdcbddabaaaadbdcdbaacbcccbbdcbcddbbdacbbbbabcbcdbadcaddbbcbbcddcdcbbbdbccccbccbcbbbbbbabdadccbbbbddcccdaacbdbcdaccbcadabbddaddcbdbbabbabbcccbdbbababcddadbaddadbdcacadadaabdbccdabdabccaddcbbbbaaaddacccbabbccdbaabddbadaacbacbcadcbdcbaacdccbdbaadadacccbcadcadabaabcacabdacacccdbcabbcdbbbadaabbacddcaaddccccabcbabbbcbcaddcaadbabcaddbadddaabbddacacbcbccbbaacdadcaaddbadaccdbdbcabaabaacddadcdbacaddddcbbacdacdbccdccbaabbadadbbaabcaccdabdacbbbbcbbcdddcabbdcbdbbbbcaddcabdbaccddcaaadbdaaabccddddaddbcabdadabdcbbbdddcbbbdbcccddababcbccdbaaabacaccdacddcabadbcddddacdadccabacbcadbadbdbcbbadadaabdcabacaaadccdaaacaadaadacdbbabdbdadccababdadbcbbbcccabdcadacaabcaabcbbcccbcbcdbdbaabccbdabdbacccbdcbcccdbccbccbaddcdaacaadcaabbccaccabbaaaddbcddcddaabbcaddbdcbcddcbbdccabbaacbdbbbadbacdbbbdbbcabaadcbdbabaddabcbdbababbddbbcbcbbbbbcacbacacdccddbbabadddacbcdbdbbdaddcadabdcdcadbcbdbcdbaccabacdbcadccbadbdaacccddcaddcabdcbccaadcbdbcdbccadaddabbbabadcacdbdadbaabdaaddcdabccbaaabbbcdddcdbcddadadccdaacbcdcbcdbdbaaabbccdaabadabcdadaabacdaabacbacbbacadaaddaaddaadbbdbaadbaccdbddabbbcdcadcbcabdcaaccdbacaccdacdbacbabdaabddbcabbbcacdadacbdbdcabadbcabaadbdabcbdadcccdcdacdbcacbcadddbddacbdbbbcabccbddaaddaddccbadaacabaadbadbdcacbddcbcdcccdbdaadbbcadadacacbcbcbadcbdacaddabdbbacaaaadcadbabdcbaddbabadcacbcbbcdbcacadcbbccaabaaccbbabbcabababcdadbbcbaddbabdacccdcddbccdcbcaadabbcdbcbcbdabbaadacdbbcbabdbacdddcbbbdbdbadcccdbcbdbbaaddacdaaaddcacbddbaaaddaddabcccdaaaabcabdbdccabbdbdaadbdcbcdcbbaacaaccbcddcbcaaadadacccdcdaabdaddacbcababdabaabaadcbadbadcdadbbadacdbbaadaddbdbdabccdbdcdadadbaacddbbcbdccbbcabadddbaddbaccccdadccdbabaddcdadbacabdadadabdaddacccbdddacddaaddcadaccdadbaacdbbacddaddbdabbbdbbcabbbdbcadacbcaaccddadddddaabcaccacddddaadbdcdcdcbccbbddcddbabbcdacacbddddcdccdcdcbcbbbbbabcdccaabcdbcadcaacabdccaababccbaabaadbdaadcddbbbdaccadcabdcdcabcbddcaabaaccbabacbccbacabddcdabbccabdcdacbabdbaadbdbaaccbdcbcbbadcbcbddaaccccbddcccadbcabcccccddccdabbbcbcbbbdbdcbcbdcdcbabdbcdbabaacacadacabbbdcdaddcabdbabcdabdacbccddcbccdbaabadabddbacdaacdcaaddbddddbbbddbaabcbdabcccdbcabdadcbddcccaaacacdabcbddcddccabaabacdabacabcbabadbcaaaaadadcabaadabaadacdccaabaadabdcbbdcbcdbcaadbddbbabbcdabdbcddcbbdcadadccdcbdcbadbdabcabacdddcaabcbababbbbabcacccabbbcdbdbddcbddcbabddbcbdacaaaccadcdcbbabddaabdbbdbccccbadadcdabbdabdbbdcccabbbcabdadcadaccbbacacbdcbabdaaabcccacbccbdacbbacadabcabdbaabdaddbbdabcdabadbcbbdadddbdcbadcbaddddaabdbdbcbbdcabcaacdbbcacacbddddddabaddbdddbaadbabdbcaadbdaadbadadddbcababacdabcddcabbcccbbcadbbabbaaddadbabbcbacbaccacaabadacadcabccbbaacdaacacdcbdaccbbdbbbbdabcabdabaddbaadcabbbabdcbbdbbcbaaaadbdaacddcacbccbbcdadaacaccacbbbdadcbbbbdbdabdbabcccaccabbbddccccbadabddcbcbdcccdadcabacdcccaccdccdbbabddadbaccabbbcadacabbbaddcabccadcaddbcacdbbcbbdaaadadaaadcdaaacdaabbbddccdaacdabdaabbdaabaadddbdacdccbaccdcbcabbbbadadacddbdbbcbdaacaccddbdddbadbbcdadcbbaccacbcddcdccdabcdddcdcabbdbacaabdbcbbdabcbbdabcbdabdacabcdcaaaaccdbdcbdadddddccadacbaabbdbbcaaccbbcbcdccdcdcdabaacbdbdbcdbadddddccddcbdaabccbbacaadadcdbbcddbcccddbcbbbcbdbccccbbabaccdaaddbcadddccadbbcadcaabaddadcbccbddbababbdbdacccbaccbcccbbdccdcbcdcbbdacbbbadcabcacaadcccdbcdddbddaccbcaacadbddccbcbaaacdddcdbaaabaaabdcbadbdbdabadbcbbcbccdacbcadccacccdbcddddbbcaacbddadcabcdabcadabcbaaabdaacbcabbccddcdbaaaabbcccdcacadccbacccaaadbacbbccbdcbbdadacdabbcdcdaccacddacbccabbcaddcaadbbbaaadacbddbddbbabadabbbcdbcaabbcbdaacaacababdcbdacbadbcbcbbbaaadcbbbbdbaadbcdbacbbddbddcaadaaaccdbcbabadbcbdacdddadccdccddcbabbcbbcdcdadacdcbcaacbbcdddaccaddbcabccdbacccbabdacdcccdddddbacaabaadbacaddbcacdbccaddcddbdcbdcbbbbadaccabdcbccaaadaddabbdbddddcabbcdaaccbdaaabccccddbdaacbdddcdaabbacccdadbcadccbdddbadddbadbadcdbabaabdadabddddbbbbdabcbdcdcdcbdbcadccdadbabdabbbabaadbbcbdaddbbcaddbabccadaccadabcaccbbddcdbcdbdadacaaccacaddbaccdbbaddddacaabcbbbbdcdbcbccababaacabaaddccadabadbaadbdacadcbcbcdaabaabcbbccbbabacbbcdaabababcdbbadddcadccabdacbadbdcbcddababdccdcddbabbbbdbaaabcbcacbcabbccbaddaacdddbccdacbddabccabdaadbcbddcacdbaddaaabaadbccaadaaaadddddbcbbbbaaddddccccdbacaabdcbbcacaccbbdacdcbaccabcddaaaccdddaacaaadacbccddbbbcdacdacddbaadcdcaddaccddcaadaccdcccadabcbbaccaddbdccddbcbabadaccbbbcbcdcbcdcdddabbccdccbaaabcdbcacbccbdbbbbcddbdaadbaaaabdbcdbcdaadcacbacbadbdcacbadddacadbbdbcddcdbcdbcbdcacabdcdcbbbdcddcdbadddabacccbcacbbddabcaddbbbbdbbdaddcbaaabacaaadaabbaaabbcdddbabbbbcddabcbccbccdddabdcaaaacddcabccadddbbcaaacacbadbccadccbbdbccbccabdbdbbacdddabdddabcdabcaaadbcbaacaaabbabcbabccdddcdccadaabdccabbcaccacdaabdbcdaaddacdbcdadbdccdacaccdbddaadbbabcbdbdddbdbdcdbdbabadbaaabdcbaababdccdadbdaaacdacbcdbccdccdacbbccbdcabcabadcabdbacccaaaaadbdbcdaddabaaddbadbcdadccdacdacbcbaadcbcbddaadbbddcdccdcbbcdcdbbcddaadacdbacbcadbbdbabcccdddaccbcbbbbcbdbccabdbccbbbcdbcbcbadcdaadcbbaddcddbccddbcdaaadccacbacdabbccaaababcdbdaacdabbbaccbbbcbaaddaaabcdcbbacaddddcddadcdabccacdccaacabcbdcdabacdaccbdcbcddbaaddbbbcddbabdbccbabcacdcbcabcaaddbdcaccacdcdabacaaadcadccdcadaadccacbbaaadcbaadaaccababdcdcadabcddabbbcdacddcabacaddddaabaddccacbdcacdabaccccbaaabdcbacbbbdcdccccaddcacdbadacdacabdadccdadbbccdbcbadddcacdaddaadbbdabbbadaaddaabcdbcbdbbbcdaabcbdcbdabbadcdcdbbccbcdcbadacbbcabaadbdbcbadbbbcdadbccbddbdcaadcbbcadccdcddbbdbbbddadabddccbbddaacadcddaadcbdcbdcacccbababdaaadaadccaddddcbccddcaabccccdbadcacdddabbabcaadbdadaaacbbbacadbddddcdccdbbababbbaadaddabcbdccabadbdcadabcbcdcddcdcbaaadacdddcdbbcbcbdbcbdcabbbcacacbcbaddccdadcadaadbabcdcdcabadbcaabdbdccccddcbacabbbabcdddcdcbadadaabdabdcdbbadabbdacaabbccabdabddbacddcdcbdaaddbccddadbcbabccccdbcababbaabbdaacacbcdaabdcdaaadbbaacdcbdbbccaaccdcdbaadbdbacaaabbdaacddbcddaacaacacadacbdaabddbdcddbdaadcdaababbacadabcadbadbcbabbdaccbaccbdcbdbcdcddbdbabdadbdbcacabcadcbdaccbbcadbbcddbbbcbbacadcdadcdaaadbadddadcdcadbcddcdcddabbcdcabadccbadccdacadacacbbdcaadcaacabbbdacdbcadbabcaacddbbcabdbcaabbaabccbaccadbabadbbbcbabdbcdcbcccdacbacbcbbdbbdcbddddcaddabdbaddabbccddadcbabcddabacdcddcdccbcbbdacdcbdcadcacbacbcacdcccbabdabbaccbabbccadcbadddbddadcaddaccdaddacdbaabbbcadcdccdacaddcabacdaddbdaadcbccaabcbbdddcccdcbccbcdacbbddbdcadcdadccbdbbabddccabcccacbccdcaacdaabbadcdaaabacdaabdccabcbcaccbabcbcccddbdbcdbdbbccacdbbabbadacbcbaaacdbbaaaaadcbaabbdcccdacaaadcabbdabadcadbdcccbcbaccaaaacbcdbdbdccadaadabcbacdbdcdacabaaabccccdadccdbadaddadcbbaddbbadcdcacdcabadabcdbbbbcdcabdadbabdbddabaacdcccbbbaabcbaaacbcaacddbdddaaabadcdddcbaacbdbbbbacdabcdbbbdbddbdadbcbbdbbbbadcbcdcacdbdbdbbdcbadbccbadbbbabbbbcaccadaabdacdbdbbadcbdcbcaddcbaaddbdaabdbdcdcbaadbbacadbbbcacacabbbbbdadcaaadccbdcaadbdbdbdcadcbadbadbdcbddabbcbdcbbcadcdbccaadbbcbbaadddbcbbacadcbdcadbbbcaacabcbadbaccbcbababcbbcabdaacdacaccccbaaadaaddaadaadbacaddccdcbcacadbddccdddcacccbadabdbdbabbaadcadcbcbccdbabccaabcbccccbaaaaadddccbabcbaaacadbbbddbacddbacbcabadbddbccbccadcdadacaaaccacdababaddacbdabbbbabdbcdcdaaadcccdbaaddbdaccdcbbcaaccbacabdbddcacbbdadbcbaaacbdbccacadcbbacdcdcdcddbbbbadcddbacacbabcdbadaccddcbbccadbccdbcdcabbdaccaaddbdbaadcaaaababddcbababdcabdbcbdddddcbddaaddacccbbaacaabbddaccbdbdcaadcbaccbbacabbdbdbdcdddabbddddcdacdcacbcbbabaacbbbbbcacccaddcbcbbacaddcbbdbbbdbaabdaccdcaabddacbcaaacbadabaaabdacddaddbdbcdabadbadacbaddbdddabaaaaaccbcbdbabdacacddddbabaadcdbdaddaaccbdcdbccddccccbaadaccaddaacbabdbbadaadccadbdcbabccddaaacababdcbadacabbadbcccbccbabbdcaabbdadadaabbbabcbaabbbccbbbdcaadcbccdabbbdacabdabcdaabdabadbabdbdadbaccbdccbaaccaacbcdcbddcbbcababdaacbbdcabdadccaadccacaacddbcabccdbaabbcccadddacbdabbdbdcbddbaddbcadcabdcdaadcbddcdddabbdacdddadacbabcdbbbdccbcabacaadcadddaddabbcddadccbcbddacabccadcbcddabbbacccbdbadbdddacdbdcacdcacaccaaadadbdcddcabddbdbcbbadcacbbdbccabdbbbcdddbaddcdccdccacbbbcccbbaccaaabbccdbdbacbdacdcdbdccdcbcbbdcdabddcdbddacdcbbddcbcdddaabcdaabbaddadadbcabbcadadcdacbdcabacdbdbdbadbdbdbbbbccdcbbaacdbdcacccabddacccbabbcaddddadadbbdadbdababbbcacbbddaaccddccacdaddcacddcadbdacaaabdcabdacdacbadadabacbcbcbbadcacacadcbaabdccdbcbbbbcbcbbbacdabadacdcabdabdacdcbdcdabdbccdaccbcbcccadbdadbaadadbdccaabbbadbdaccabdbdbcabccccaddacbbaabdabbadcddaaacbcbdadabacabcbcdacaaddccccdacadbacbcaacddaadabdccdbdaaaabaddcddccdabdcadbdbccabaddabbbcdabaacaacacdcdbaaadadaddcbbbddacdacdcabcbcadaabaacbadbbcadabaddabdbcbdccbaaccabddbdddcdaadadcacbbddbcabadbcbaadadbccacaaaccbadabbabdddcbdcdaccdbbbdcabdadabdbcccaabdbdbbdaabcadddbcbbabbddaaacbaaddbdadccacbdbdcddabdbacbddcbdadbcaccbbbaaacdaacdacbaaacaabccaddcbdbddababdaccbdaddbcaacdacaddbcacccbcacadddaabdbdccdddbbbaabdabaddbdbbabaddcaabcabcddacbdbbdccddcbdcccacddbbccdbabcbbadcaabaccbccbdaabcddcbaddbaaadbaacbaacdabdbcdccadcacaaacabbbdddcccabdabdcaccadddbcdbdbcbaaabddaddcbabddddcccbcbaaacadadcbbdcbdccabcccbcbcabddcccbddadccaadbbcbaaacaddcccbcbdcdaadcccdcccdddaaabaaccbacdadacacabcacbaaaabaaddacccdaddadcbbadacbdbbbadbaabcdccdbdacacadbdaaadccaadbaababaddaddbbbdbdbccacbbccaddbbcaaaadadbdcccddbcdbcccbccbcaaccadddbddcbbbaaacbcdddbdddbdbbadbcbbaaabbadbbdcdacbdabacdbddabdaaabdccabdcccacdaaaaccbdadcabbacddcdcdcbdbaccbbacddbcddcabaadcbdabdacdcbdddbacabcaadcbbcbdaaccdbacbbddcbdcdadaaadbbadccdcbaddcdddababbaabaacaadacdbacaabcdbcacaaddabdadbababacbdbbabbbbdbdaabdacacccdababbbdadddccbabacdcdadadcdcadccdbabccaabdddabcdcbaacadadcbcbabaddccccaadcabadacacacbcbcdcabcbcbcbcabdacbcacdbdaacbddadcbdcccbbcdcdbdbacdbbcaacbabadabaaacdabdbbcddbacddaaabbbdbccdadabaddbadaacacaadcbbaaabdbdbaabbddabdcccccaccdcbbdabbcbacbbabcbcacdcdcdbdbabdbcbabdcdacdadaadbcaddacdbdacdaddcbcdadcbabcdadbccbcdbadaddcabbaacbcbdddcdaccbaaccabcaccbaccbabaacadaaabacdbccaadaddcadccbadbdabbcbcdccaadadbccbdadccdabdbbbddbccbbaaaacdcdccddcdacadccddcaaddaabcccccabcddbcadbcaadacacbbaabcacbbdbcdabadddddbcaacccabccbdbbabbabdaccacdbcacbaabdbdcbaccdaabbdabccbdbcbcdbbaaabacdcbccabbcabbdbbbcdaacdbbbbddacaddabbcbadacbcccdcdcbcbabdbaacaddbdcabadadcbadcbaccbcabbcdaccbccdbcbdbbdcaaddadbadcbccbcbacddaadcdbbdbaabaccaccbbcababdbbcccabaaabcbcbbccacbbaddbdadbacbacabbcabcbadacaacbadaaccddcbcdcccbbabcbcaddddbddabdaacdccdddbddcbaadabbbcdcabbdcdabbbbdcdbdcabaabbbadbddbaaabadcadccccccacbabadddadbcaddacdcadcdacbcdddbcccadbcdcabbabbbbbdbdccaaccbdadabdcdadbcbbddcacdbbccbadbbcadabadbdccbcbdcdcbdccbcdacadbcacbcabbaabddcbdccbdabcaacbbbbccabcdcbbabbcbbbddbbadacaaadbddaaaabdacccdbcabaccbdbbbddcbaccaaddcbabcdacabbcdcccbdddadcbccdbcacdcdaacbdcbccbacbdcabaaacbcadbacadbabbbcdacbddaabaaabbddadddbcddacbbcabbaccbbcddcaddbcacdbdbaaacbbdacaabbcddaacbddadcbabdbbbbdbadabbdbaadbcccacbbdcbadcbbcaadcbcccaaccbabbbcdabacbdbbaabdcabcabbcdccdbccddcabccdaacacbdbdbdcddaacbcadbbdabcdccbacbacabbcacbcbcbdcaacccaabdddddaabdacbdddadccacccaadcbdbabcbdcbcdcadbdaaaddaaacbcbdadbcccbadbcdbccccddabcdcadcacbdbacbbddbdbaababadbdabcbdcdadacdccbdbaddaaabbdcbadacacbaabcdbcadbabbcbdddbaaabadccbccabdbbbdabbadbdbbbcadbcacccbacbacdbdcadbcacbdabdadccdbaabbacbaaaccbddaccaabcdddcbbdbdccbdbccbaccdbaacdbbbaabdccbbcacabbacccacabcbcbbbcbbdddaccdddccbbcdcbacdcdddcbccdabaaacccdcddabcabadcaccccacaababdaacbaccdabacabbbdacbddcdbadadbaccccbbacdddbccaadadbadacadbbbbabcbcadcbadbabdccabbacbacbacacaaccbadddddccbbbaaddbccbddddabadbbcaccbadcdbacdabcdcbdbdbacddcccbaacacccabbadcaddadcbcdacccdcccabbccdcabbccbbbabbbdcdcdacbbabbdadbcacccbdabdacddadcababddbacccdbdababbcbaddbbacbbaaacbabdabbbdddcdaaddccadcacbadabcaddcddccccdbbccddbcdddcbaacbcbadbcddbcadadbaadcdbaadaacaadaacbaadbdabbaaaaacccdadbadbabcdaadbaddccdbadbbdbaacdcdbaccaccdcbdbbbbabaacaddbcacdaaccbbcabadadcabcdcdccbcdbddbdaddcdbaadacdbdbcdccacaadddabccabcdcccccddbbdbdcdaadabbaabdbdcdbbbabcbcbdbddaaaacdccabbcbadcabbbccacbddcababbdbddccdaaaacddbdababccaddaababbadcdacabaabbcaacccdcdacbdadacbdbacadabbbbbcccbabcbbcaaadbacdcccbabbbcacddaacbbcadccaaccaabbcdcadacababbcbadddbcadcdcadbacccbdbaaabdbadaacadaaadcabdabcaddcadacdcaaddcbdbdbddcadacbdbdcccaadbdcdaddbbbacbcdabaacacacabbcbddadacacbaaaabcacdbcdadbdbacbaaaddbbddbccacbdabbcaddcbdaadbdabcccbbaaabaaabcbadcbacbabcddbdcdaaacdccbdaadcdbbbcbacbbacadacdadbbadaadaccacccaabcdabcadcdbaacdbdbbcdacdbdbcbddbbaaaacaadcbdccbacabbddbaaadbcddcbacbadddabadcbbaacbbddcbdcababcadbaaabababdbcabbadbbbbbabcaaacbddbaccadddabdddddbbacccdcaadaaacadacabadbcacbbcacadddcccccacacccdcdddcddbabdaaccacdcaaccdbbaaaabcdbdadaddbdadccccdbcaabdcdabcaaacdbbadbcdbaccacbababbcddbbbdacbacdabddbddbdcddacdcdcadbdadbbacbcdddbdadccacdbbdaacdccaadbcbdbbaddbaadcdabdadbccbcadddbabcaaaadbbcccdbccabcadaabababdbcddbbabcddcddadcadcabdbdbcbcdabbbdddabaaabdbddcdbbbbbadabcabbcaadbccdbcbbcaaadcadccccbbcddabcbbacdaaddcdbabbbccaabbccdbcabaaaacbcccabcdbbbcddadbcbddcbaacdcbbcdabcddbdbbadaaaaddadabdcabcacbcdccdddacddbdcbdcadbddaaaccccadbccbdddcdacbcddccddbdaddadcccadaadbbcabdccbabacccccacccabdaaaddccccbacbcbdcdccbcbbbbadbcddddcacbabdcbbbddadbaadcbacbababbabacccbabdcbcaadacdbcccaabbdbaadacdbdaabbdcccddcbdbdddccdbbbabdbdddbaadccbacbbcacbcdbdaccaabddaccacdddbbbdcdbdacaadbdabcacbcddbbbcdccadbcdbcccbbddabdcbbaabbbcacabbccbcaabdbcbbbbdddcbacadbabdddaaaccdabddbdacdadcbbbbbacdbcbbcbacbdaccaaacbbbccbcdabdbbadadaaacbbdbddcddacaaadcbcadcaccdbaacbbddddbddaacdbccabdbaacbcbbabcdacacbbcdbdaddbccdbbdbacaabbccccbddacbdcddbadbaabdddaaccbbbdbbabacacdaacdadddbaddacaababdbabadbcbcaadaccdaccabbbbbcddddaddbcdbccadcbcadccbdbcbbdbcaabbbdcdbabbdacabaacbcbacabadddcbcdcadacabddadabbabaaaabaacdcccaabbdcccdabcadbbccdcacbabadaddbcaaacbddadabbadadadacddccadcddabbbbcdabdccaacadacbcbacbcaacddbdaabdabdbdabadcaaabadbacabaaaccabbdabcacbbbdddaadaaacabadbadadabbdddccdbadccadcacdabacaadbadadbbdbdcadcbbaabadbdabcabaaaccabbbbabcddcddabaccacdcddadbabdbccacdaadbbdaddaaabdccadaacdaabbdadccabdccbcbdbacabcbbadbddadacadcaddcbdcddbccddbdcdbbbdcbbbbdcbdabcabcbbcbddbbbccbcadabbbcbbacdccbdcadaacadcacdcbdcdaaaddddddcacdabccddbcacbbdbcdababbcdcbccbcaaaacdacbabdcbcaaaacaababcaddddcacadadacdcbcbbadcbdbdcccbadacdcacbaccbbabdcbdacbbabcbbbbbbaccaaacdcdbbacadcbcddbbbabacacbcbddbacbcddaadababcddcbacbaccddcdbdcbadadaaaabccbddabcacbdbadcccbacdadacdddcdcbaacabbabcdaccacbcbadbcbbdddbacbccabaddadddaccbbcdabcaababacbaaddaabbbdcabdaabdcaaacbcadbaabbdabacaddbbbdddaadcabcbccccbcbacdcbdacccacacccdabbbdcccabaaadbcdcdbcababddcacacbbbdbdcbddcdcdabbcbacaacaacaaddddbcbabcbacdcddabcbdbccdcdaabcccdcddddaacacdacdadaaabcddbabadacacadadbbcbcaaaccdadcaccbdaababdaabbdcbcbccccbcdacaacabbacbadcbdbcbabbcabcddaadccaadccbdcbdcbccbbdcdbbcacddcddddcaadcdadbbdcabcaccadcbcbbdccbbbcadcabdcbdccbdaadaddaddaacadbddabbababbdaaabdaabcdacddabcdbaccaadddbdbcdaccdaacdcdaaadcaabbcadcbadbabdccbbbbadbdddccdadccadccddacbcbcdcdaabbdbacbbacbddbadabcbdaaadabbbaabdcbadabccacdbbccbcbdacbdbcbccabaacbddbcbcbbdbbabadacdaabddabdbbababdccaacacbadacccadcbbdcdbbdcadaaadbaadbabcccbaddddaaadcccbcabcdcaacbbbacbcdbbaddbacbccbcdbbabcaadbaadaccdbdcccdabbcdaddbadbabcdadcdacdddadccacbcdbcabaadbabcacdddbdcbcabbccdbdddddabbadacbddbcccabcacbcbccadcdaabdbbdcbcaabdccbddaaccaaabdbdadbaddcadbbcddccdcdcadccdcdaaddcddbdbccdcdaacaccadaaacaddcacadadbcddadacdcbabcdbabbabbbacdabbbdacdbdbacdbdcabadabaabbbdcacaababcabbbcccabdaccdadbaddbdbcbcccddbddbbccdbacddbabdbcadadabcaabccacdcadcdbbabccddbbcbaaaaddabbaadbccbdcaddcaaabcbcabcacbdabbbabdadbcbbdcbccaddcdddccdaacdbabacdddaacbcabaddacdbadbacdddaddbbaddcdcaccddbcbbcbcadccbacdcccdaadddbcaacaddadbbddbbbbabcdadcbcdaaacaacababcdaccbabacccdbdbcaaaccbcdbbdabbabbdaaabbadbaacccbcbadddddbcccabbcdbbdaacaccdcadcbcccccabaddaddacbcbaadbddcdbaabaaccbbdccbdcabdcccbcbbaabdabaccccbdacddacddddabdcacdcaadbacabadaddacccdbbdddadcacdadccaccbccbadddadadcdbacdacddcacdabcaccdcadaadddcbbbbbbdadacaccaaabbbadcababcdbccbaaddddbabadddbbcddddbabcaadbbddcbbccbcacbcbaadcbdcbdddacbddadbdbbdbcbccadbacbbcbcdacdcacdbadbbaccabcaccabacbccaaabbcbaacdcaddabccdbdcabdbdbbbcbdccacdbbcabbacbdbcaaccaaccbcdabddcccaabcccddadbcbaddbbbcdbccddcabcdadcdabacadadbbbaccdacddbcdcabddbcdcbabcbbbdcbbbabbccacdbcabaaacdccdaacbbdaaacbbaccbadbdbbbdadaabdbbbbddcdbacadbddcadbadccbccdbdcdbbcaabbdcaaacbabddbadccadcadadabbcbcbdcdbacbbcccddcbbcabdbbacbbacbcdabddadbdcacdcdcabdbabbcdcbcaababcbacbcdbcdbbdcdbabacdddcccdadddddbddbdabacaadcbcdbbdccbbbabcbbdccdbadacdadaddaddabcdbdbdbabaaaaccdcaccbcdcdcbadbabcdddcaaddcacacdaddbabccaaabadbaabdccabddccadbadcaaacddacadabacaaaccacccdacccdcdaddcbcaabcbbcbcbadbcdbbbcdadccccbdcbcaababcdacccbdccbcdcbadcaacabdaabcaaabcbdacaadbddcbdddabaddcbbbbdcabbcddaacccbadcbcababbcdcbabaadbaaccaabbdabcdaadbaccabbcadcddbbbccdaadccbdadabcdcbbbddcadccbaabbcbdabbccbcaaaaadbdcabddacaadcdddddcdbcaddbaabdaacddadacacddcbacbcbbdbbbdadbcacbabadadacdbaaddcdbcaacbcdbaddbbbdbdcbbdadbbaadbcbbbaabccaacdbbcaabacbdbbdbdbcbccadcadbdbbaaabcdacdbcbbdadcbdbccacaabbbbdccdcdcbbcacccacdbabcbacacbaccaaabccdadbdcbddabcdaaabbccabadabacbaaadaadadcdabcabcabbbbbaacbcbbddccadaadabacacbcdabaadbdbbacdadabaacdbcddabadabadadacbdaabbcadcacdcaabdabccbabbbcdccabbcddcbbaadbccccbcbabcdbaddbaacdcbcccbbabaccabdadadcbccbbabbcdcbcdcbadbcaccddddccccbccbbaddbacdababcbbadbdccacccaabbccddaacacaaacdacbaccddbcdaddbbddddaacabccadcddaacdcaabcaccbdbadacdbbdbdbdacdccdabdaadbbddbdadcdadadbdddcbdbdcbbdacdbcdabcdbbcbbcdbbcbccacccbadcccccabdcdbcacbcddbbadaaabdacdbddcaabbccabbcaacacdcabcccdabcdbbdacaacbdbbccdaabbcadcbacbadacdbcccddcdaccaadcccabdbccabddbbabdcdcdaccdbddcaddaaaacbbcdbbcccabcdccbcacbbacdadcddbbacccbacdbcaaacccdadabbdcbabbbdaccaaccdbaabddcbadadbdbacddacaccdbccdacbabdababddbcccdddaabcabcadbdaaccdabdbbacabdddabaaaadabbcccbcaaaabaadbadbbabcdcdccbddabddcbdacdcdcdaacccbbadbbaacbdccbbcbadbadbacccbcadcbbaacabddcbdddadabadbdbddccbaddacccdaccbbbdacdacbbdbcadaccdbcdcaddddcdbbcbabbcdaccacbbbcacacbbbabadcddaaadacbdcaaccbbcabacbdbadadbaabddbcdabcbdbdbdcadcabadcbaacbacdddacadadcbbdddcaddcaacdaacdaacadbdbcbaddadacadcbcbbbadacabcadbcdccadabdcbcacadcaaabcababdcdbbccdabbbabdddbaababcaddcbaacbcbdaabadaddaabacbcbcddbdcbacccbdaacbdbbbcdabdaacdddadddddcddbdacaddddbcdaaccddaabbdacccbddaabdbcbcbbbdcccabaacbccbcbabccdddccdbdcacccdbbaccadbcbdbadaadadacddbdacaabdbaaddbadccabbdbcbdcacbccbacdcaaabdaabcaddcabddadbadcdbadabdbcdbccbadadacbcdabbdcacbccabadbbaaabcccacccddcddaacddaacddcddcdbbbbabcadcdadccadabaadabcacaddccbcdaaadaaacbddadabadbbdcdccadcccbdadbaabacadcadddcaccaabdbdaacbaadacdddaaadaadabdcddcadadbcbdcccdddacdacdabaacabacaddccbadbdbdaaaaadbcacdaabbcaacdabbabdbdbbdaaacbdacacacaccdabbdcccbdcbdbaaccaccacadbcbababdcbbaadcbaaccdcabddcacacdcdadbaaddccdcdddabcacbbbaabaaddbbcbcacadcbcbdbcaababdaaadccbacbddcdadccbaabadbcdbaaadbacaadbbbadabacadacaabccdaddabcbcbaaabcdbdbcbaccacccbbdddbcabddcaaadaccdbcaaacbcdcbcababcccaabdadaacdddbabaabccaccadadddacccdbabadbddabcbdaaddddcbcbdcaaccddcadaacbbcbaccccbadbabcacdcaaaaabdabdabadcdcdcabaacbcbbbcbdcaacacbdcbccdcdccadcdbbccadbbcbabcbccabdcbcbbababcbbdacdbaccdbbadcacbdbdcbddddbddccdabbccdddaadbcacbbadadaacbddbdbbbbbcdddadcdaddaadcbbabbdadddddadddddbddcbaaadadcaacabcbccbadcbcdaccdadbddbbcabbbaddaccababdadbbdcdbbdbcbaadddbddbbbbbbacbacdacdaabcbbcabdbbbdadbcdbabcdbcbbbdcbdabdbbaccabcaaaadbdadcddbadadbaccbddcaadddacbcccbdcaacbbabdcccdaddabcdcacdadacbdbbdcaadcbabcdcaccddbbddbabbbbcdbadbbdccdddaaaabddcadaccacadbcbbababbbcdaabcdcbbcdcaaccdddddbaadcabbdadacccdaddbaabbccabbbdbdaaccdcaabaacbdbadbcadacddbccabdbabcadbabddaabbbbcadaadcbdcaaabbddaadddccaadbdbcbaabbbcaadcbbadbabcccbabcddaddaadccbaabcbccdaaaaabcdadabddadbadacacbaccdbcccbdccdcdddcbcdbabbcddadbbdcdbbcccadbbbcbbcdbcccbcadcacdbcddcbacdcaacabbabbdddacdaabadcccccadadaaacbdacacacaccdcacbddacdddbabdbdaabcacbccaaaccbddbcdadbdcbcaacbbddbbbcddadccbbdccaacabaabbdbbaddbaaaaabbbdcdbbcaaddcaacacdcbcdccdcaccdbcadcdabbcabadbdbdabccdacbdaddbcddbdcdbdacbaadcacdbcdbabbacacddbacadacacddabbbdcabdccbacdbcbcacabbcddaaddcacaabdbdcbdcaacbadbacbdccbccbcadacddcaacdabcbddccdbddaadadbadddabacacdbdcccaacbacdadcaaaabdbaabcabacddbcabddcaaadbdacdcdbddabdabcbababdccaabddcabacacdbadbbcadbbbbabbddcdbccaacdddcaababbddaabcbacbadbbdbccaadaaccababaacaddcbdcaccbbdbbbcbbcccabdbcbbbbdcabbabcdbaabadbbaadbbcddddabadaacabcdaadadcbbccaddaadbccbccdccbaabacbcbddabddddcdcbdbdddcbccbdbdaccbaddcddadddacdbcdbbdcdbbcdccccdcdcbadbdddbdccdabccbcccccbcadbddacdacdabcbaaaddaddadbbbdacabadbdcbadcabaadbcdadcaadbaabbdcadbcddbdbbbcbddbdcbbaacbcdabbdddccdccdcabbcadaadacaabdabcbaaacdadbacbcbccbacbaaccabaacabbbadabdbcaccbaacaadabaddaaccbbbcddaddababdbbccddabbccbccdccaaaabbccbbdddddcbbabcddbabdaadabcabadcddcbaacdbbbccbcddcccdabdcdadaddcdbaaaabaacccbdaaadddbcadcccdadaadcdbaacdbcdadccaddcdbbccbcaadcaaadacdcdcbbdacdccdddcadaabadbaabcaadbbaabbdabcdcbccdbdbdbcbadaddddbbaaadbcbbacadbddacdaabdccdaccbcdacaacbcabcdbdcaaaddbcadcbadccdadbcbbcdabdacabaccabbdabaaababbbdabacadbdcabdabdadccabacccacdbaacccdcbcddaddcdbadcadaddbdddbdbacdbadadbabdacdbdcaaccbdccddbababbabadadabadacbdddcdccaabaacacabccbadadbadcabdddabccdbaddccddaaddccabaabccaacabcbacdcabbadacdbcccbbdadbdcccbdcccddddbccbdcbcbcdaacdbbbbacddcdabbaccbbdcdaddaabdaadbcdcccbccadbccbcbadbcdbdcadcbbcdaddbabcdadbdcbdbaacbacbbacdcbcdacbccddaabcabcabddccbcabbaddbcbadddcaaaddacbcdadcbaacbbbcaaddaadbadcddcababbddadbbbcccdccabbacacabbdddaddddccddddacacdcaccdcaaabbbacbacdbdacbbcaaaadcdcccbbdbddcbdbbdccabcdbaacaaabaabaddacdbcdbbdaddaabdbabbbbabddbacddbbcacadcbdbaccdaaadadadacabaadbadddbbddddbaadaaaadbcddaaddcdddcacdbcadbdcdcbbabbccbacdbddbddabdbdcdaaccdaadbcddaacccdbbdaabdcdbbbdbacacadacbdacadddbcaaabdcddcaacaabacccbcdbacbadbaddbbbbbdcbacdbddbcadbbdbaaccacbccdccbbaabbabdbcbdacdacddbdcaccbbdbacbabbabbbdcdccccbdcabdaabbadcabcaacdabadaddabccbddccbdcbdaaabbaccaabdddbcbabbccddddcdbbbcbdbdcdcadbbaacbabaabddddaabdbbdbabbccbdccabbaddbaaabbcabddbacabdddbbdaaabdbdccdccbbabcadbacbbbaacdabaacdcdcadaddbccbdabdcddacbaabcbababaaaaacdcadcadbadaadbbdcdabacbacaabbbacdcabbadabcbbabddccbdcdacccddabcabcdcdcadbbcbdbabbacdbbcdcbdbcbdacadbbbdabccdadbdbdddcdccababcaaabbbadacdbcadacadbacabdcbbcaaaccbddbaddbbddcdcdaccdcadcbbadcdbabbbadbaccabdbdadaadbdbbbacdbdbcabdabaadbbcdccdbdccdcbdcabdddcaddcadcaccabadabbaadbbdccbbccbbbccabacbaaacddadcdddbdbaabcababdcbbcbdabdbcdaddbdcdbcaccddcbaddcbdbcddabaaaacacbbcdabbddbcdcddabaacdccbdbbcabdacdccddbbbcbdbdcaacbabdccbdcaaadabadddcbbdbaabcdabdbaabdabadaabcaadaaabdacbbbbccacacdaaccccdbcdcdbbdabdbcdabdbbcccbbdddcbbadadcddabcdccdbbbbbcdbacabcbdbddaadacccbabddcaaabaadbbabadaabaabbddbddccddccaccbbbacaaaddabbcababbbcadacbdbddbdbdbabbddbdbbdcaabddbdcadcadadadbbcdbacdcadddaddabdaaddcadadbcdcdcabaaaaaabbdbadbacccdabaccddcbababbbabbdaccacdcbcbddcdbaacccbabbcdbcbbdcccdcadbcacbbccbcadddbdbddcbcaacbdbadddbdbadcadcadbdcabddcbababbbbbccadaadcbbdabdbaccabddccdaddcbbccbabdbadccaccdddcccdccaabaaddddcadccddacaccdadaddcbadcdaaacabbdbabdaacdcdaaaacdccbdccdbaddbcdcabadadbbadbdbbcaacacadbdbdcbbabdabacbbaabcbbbbdbaabddccdcccacbbdddbbabacccddddcabbcdbbcbaadcacccaddaadccdbcbdbdaccdaaddcaccdbdabbbddbdabbaaabbadaddcdcccbdbacccdaabdbbadddacacabcdbdbcbacdadbdccaacccbdcaaccbdbbddcdbacdcdcddacbaaaaddccadccaabcbdadcdbbbcbbaccddaccaccccacbdbcbcabbabbcbbbddbddcaabbaaadbccbcbddaadbcdcabdbbbaaadbacacccbcbbadddbaaaccbdcbaaacdabcbdabdbdaddcccadacbbaabcacababbdabbacadaddabbcbacbddcbcbcdddaadaabbcadabccacdbcccacacbcdabadcbcacdabbbdacdccddccdcbaacacbbddacddcaaaaddcabbdcdcddcdcacbadaaddcbddabccdbddddacdcbbcadbccbdccabdbdaddcaddddadbcdcddbdbdbcdbccadaddadadbdbcddbbabcdcbaadccacddcaaccbaacbdbbacdbdabbcadcbbacbbdbcbcdbcdaccdbacddcbcabacadaacadbabdabadbddcbbadcbacbcddacccbddcaabacdddbddbbbcbdbccaaccadccdbcabbdadcacbcacaabccdbadcadcadcdbdadaddaddcdcccdbdaaccadcdaaadacaadaabbdcabaacababdaabacaadcbbdacacbbacbbcadcdaddccaaaadabddadccadddadacbddcbccbbdbcdcccaacacdaacabcbbbadbdddbbdbcbcdaddadcaaacdadcbaabdabcdccbcacdbbdbbddbdabdcddaaabbdabbdcbcaccdaadddbccaadccdbabaccaddbbdcaadbcdcabaabcbaacbcabcbdcbdabbcbdcdbcddccddbcdbdadbacbccddacdbbdccdddbdadacacccdcdacbddcacadbaacdcddaaddadbdcccdacadabcacdbbbabbaddcaabcccddbabdcbbdbcababddcdabccabcadabcdbbcdacabdabcacaddaaababddbadabbdcbdccdcbccaaaabdabccacdcbdbdacbcdcabbacbbdaaccdcdaaccaccbcdcccdccccbbcacbcbaddbbdcccaabdbcdcacbcbbdcbddbdaccdadabbcddaddabbcdbabaacbaddbdadacccdbcdcbbbccaacbaddddcabcccdcdcdccccddcdacddbbaccdcaccacaadaddcdbdcaabbddccaacdcdabcdddabdabacbcdddacddcaabaaccabadbadddadadadcddaacdddabbcaacddadbacabbaacadbbadbaaaabcaacabdcbaadaaaddbdaabdcdadbabcdbbcbbddccccaabcbccbcddcdbdbccdcbacdddbacabccdbbabdaccadaccadbccdcbdddabbbaabcbbabbdabdcbcadcccdbbdbcadcbabbdabbabaacdccddccdbcbbcbbcacbcccbbacdaacacbaabaabdbcadcbbcabbabccaccbddbccbddcbdcabaabaccabbbaabdbabbadacbaadbdbdaccccbbbaddbbcbdcbbbacabdcbcdabcdabadabaaccdabbccbccbdbbbaaadadbabdabcbcdacdbdcabbdadcbacdbbdcdbaaadadbbbccbabadbddabccbbbbadcbbcdbbbdbdcbccabcbdaaadcdccbddacbcdcadcaaaacbacddbbdbbdcdcddbcbbccbccddddccbabacadcccdaadaacabcdabcbcdcddcbbbcddbccccbcbacaddbbabcaabccbdcabdadabbcdccaddcdaabadccacdcccadbcbbbdcdadcbdaabdcbddddbadbbdbdcaacabbddaadcdaacccdcdcaaaccccbbddbcbcdbcbbdbbdbbddbaacccbdbdbdbccbcdddcbaccbcadaacbaababbbbbdabdbdccabbddddccdbdcccbbabddcadadbbbadabacaddacbcdcdabaaddbbbdcaccacbbabaaddacbdcadccacaabbabadbbcaacaadbcdddbcdaaaccddcdacbdadadacabccbadcadaaadababbbbbdabbaccbabcacbbccbcaaccdddacacddbccbdaccccacdbacbabbdccbaacbcadddacdddadcaacdacdcdbcbbdcbbadcaaddadbdcdaaaccaccbcbcbaabcacbbadadcabdddcbabcddbddcaadcbddcabaddbbdbccbdbbcbbcbaabaaabbbabcbdadabcccbcdddbbdcbddacbdbdbcccdababaacdbaaccbdcbbadccbbadcdccabaadbdaadababbcaacacddabdacdcdcaabdcbdbcbbdadcdbdbbabdbacbabddcddcdcdbadaadabccccbcbaabacacdcddccabbddbbdcaabbbdacaaaacdcdcaddacccbcadccbddddbdabdbddccadcbbdcabbcaabdadacdcaaaddbaddccbccdcdcdbdcabaadbcadcccbdcbdaaaaaacbdaacbabbbbdadbdbddcbdcadccdcdcbdaabbabcdabcddccdcbccbabcdabaccacbcabcbdbdbacbdcdccbbcdcccbacababdcabcadadcddcadadccdbacddaacdbdcabaccadbcdaadccaabbdddcdbbabaabddabacccdbadcacacdcbbbcddbbbcdcbdaadacbcdddcbabcdbcbaabadddaabddddabcbcaaacdccbcbbacaaacabbaacdcbcadccacadbcccdcbbaacddbddabcbddbbbbadacccbacccbadccbbdbbcbbbabbaaddacbdcaccdadabaddbdbbdcaaccdabcbaabcaacccdcdccbabccbccabacabcbadbabdadabccccdacdbaaaaccabdbddbaddcdacbccccadaadcbdcbacbbcaacbabdccaabbccbccccdbaacdacbcbddcddadcdaabdccadbacbdccaadcadacbdabdcbdbaadabcabbabdbbbaabadbccdcacccdccddcdaadaccbdacbccddadcaadaabbdacdabaccbadccabdcbddbbaccdaadccadbdccadbdcdaddbadcdbccdaccbcbbbacbcccadababcbabdcbbcbddcdcbdadaacadcdaadbcabdcdbacbdbdcdabbbaccabcbdbaaccdacbadaadbbbdaacdcacccadcccabbccdbcadbbbccdcdcabcadbdbbcbdddaddbbddaacdbabbdbcbcccbaaabcacabcaccabadddaddccabaabbcdccdcdcaabbccdabbaaddbabccdaddcccacacdabbbccadbabaccbbbbcccaccbddcccbcdbbccbdbdaaccddcbbcbbccaddabdcddbaaaddbacaabbaadaabacccacabcbdbdabcdbabaaddadcdbbacaadaaaccaacabaabdcadbacacdccbbacadaaccaccbaabdbadacaabddcbadcbabcccbddbcabdcbaddcdccbcdcbabdaadabdcbadbacacbbcbcadacbcccddabcccccababacdaacadcdbccdbdacccbdbdcadacdbacbbacadbacbcdbadabcdcdaadabcbadcbddcbbbdccdadcadddcddacdcbdbaadccbcdbbcddcbcbddbccaadaaacdcccadabcbcdadccbbdcddbdbbdbadacbdbcadabacabcdcaaaccdbacbdcdcddacdbaccbacbcccdbcddadccdcaadcbaacacbbccbcdcdaaaabdacdaddcdadcbcdcddbbbdaddabdbdabdbcdcdbaccbaddbdaddddbaaabadbabdadcbabdbaddbdcacdbdbacacbdcdadbadbbdaabcbbbcabbdbccbadaaddaabbbadcdbcbdadbadbdaabcdcbcaacacddbacbddabaccabbbdbdbccbaadaaabbccaccdacdbccaaccbdcbbbcbccdacdcddbdcabaccdccbccbcbcacdacdadcbbadcbacaacbaacaaabbdbddccdccbaadbbaccbdbadcbddcaabcaddabbcbcdacbbbabdbbbdacbbacbdadabdddcdcacbbadbccbadddbdcbbbacddbbacdcacadbacaadcdadaababcdbdcbccbababbbadddacbbdbccacbddbdcabaaadbabbcccabcdaadcabdccabdbbabcdbadabbcbbdddbddaaabcdddadcddbddcccaabcaababdabccacbadadadbcabbacaaabadbcccddbadcacaddccdabdabbaccbdadcccccddcdcbadbcabbdabccbaabbcaadadabaabcadccbaccddcdacddcbddcbaadcbbabadcddcabbdbddabaabddadcabbdabbccdaddcbcbdbdddcdacadabdcbabaccccbbbaababbbdddcaacacabadcdcccaddcbcbcaccbacaddabdadbbbcbbbaadccbdcaddaccbabcdbaaddbacaddcbbaacbbaccdbccbacaaaacacadcbabcaadbbcccbdcdaaaacbaccccdcccddaabdcabbacbcbabcbdadabaddbcbcdcababdabccbbbcdbbddbbaddbddaaaaaadcddbccccbaadddaabbbdbcbdadccacaacabccacbbcbbdddbcbdccdcccbbabbbacbdabddbbcbdaaabcabcbbbcaccadbadbdddbaccdcabbbaddabbcdddabaddcdaccdacabdcadbbaacbcaddbaccdbbaadbbadbbdbcbccdccddbbabdbdccbcbabdabcdcadcacbbadbdabccacabacadbcddcbbccbcbababbdacbacbbbcdbbdbdcbdbcbbaddabbddbdcbbabdddaadcababccdddaccbacdadcbcbccdacccbaadbddddcdcdbddbaddbcdcbaccdaacdcbccabbdacacdddaccaaacabccbcbccadbdbbcaadcdaadbbdccbbdcdbbaaabdadbbbbbccaababcaabadbdabdcdbaabdabcdbabacaabcdabaaabbabaacaadccccbbbbccdccaddacdcdcdbacdcbacdacbbbbbdaddcaabadcacaaabadcdabccbbabddaccabdbdaaaabaaacdbbbbcddcabaadbcbbcbbccbbddaaaddddabcbabcbbaadaadccbcadbabbaddbccadbaabddcdccbadccddccdadaabcbdcddbdabbadcddddccdbbbcdbbbdacdcaadbdadddaccacadadcdcdaccaacbabcdcbaadcddabbddbbabaacccddbccadbbabbbdcbbdcccabbdadaabaaadcdcbaccbadbccddabddbcbadcadbccbcbdcdaabcbadcabdddcadbabbbcbcacacabbcbaaddabcbcabbbccccbbbcacadaaddacabdcdaaadccddacbcbaaddbccbdcddcbabbbdcccddccaddacdcadbbcaadbddacdbcbddacbcdddacdaadbcaabdcaadcadddadadccdccbdacccacbbaacdbbddbbdbcbdcabcbbabcddbdbbbbbccdddddccbcdbbadababaccacdbdddbcbcdbcdabcdaaadaaadaadccdbbbaccadbbbbbdaccbadbcbbadddccdbddcdbbcbababdbdcdabbccccdcaccbcadabcbbbdabcacdddaababcacccbddcbacdbcacbcdaadbcccabcaacdabcbbdcdbcddaddbbcaababcaabbaaadccddabbabbacaddaadccbdbdcbddacbdcababbddbbaddadcadbbdaacbbddbcbbbccaccbcacaabbabbacaddaaaabcdccdbbbbaadcdabacbbcbdacbbacbddcbdddcdacdbabcbbaddaacccbcaddaaadaaacaabdcabdcaabaaddabbdddcbaadadcdacaababbbbcaacabbcdccbbcdbcbbacdcccadbbadbacacdabccdabddbbddaaabdbaddabddbdcbabbbaccadabcabcbaacdcdacddcdcdbcbbddbbbbcddaaadcddcdbcccaadcddddbaccdbbcbdbbaccddadcaadadbdaccbacaabaaababcddbccdabcbbdbadbacacacabdbdccdaadbbccdaaadbacbdbbcadbcddbbdcdbabbddcaaacdddabbbdbadccccdcddcdbdddcbacbbdcacddccccbbcbbcbdcbcadbcccbbabcadaaaaadcbabadbdcadaccadaaabcbaccadbddbbacbadbdbcccacaaabacdcdaacadabccaaddcbcabccabbdbdbdccacbcdaddbacacbbdcdaacbbdadacbcdbccccbbaacacbbabacbdbdccacddcbbabdbaadaaaaaadcaccdabdddacbdcabdcadabbcbddacaddacacdbcadddcdddddcbdccdadcccccbdcbcdcdacddbbaacbdacabcaaaaacdbcadbabccbadcaacdbabddddbdbcaadddbdacabcccabbacdbadcdbcbcbdcccacdadbdcbdcddbbccdbabcbcaacddbcbcbcbdaacbabdbddacbdddcdaddbbadccaadbddbcbdacbcbcccadaabbdddaaabbbbbabddbacbcdbdabdcdbccbcdbbcbbbaddadbcaaaacbbcdbbdddddbbccbbbcadbaddcbaacbadadbabddadbbbcabbdbabccccbadbbadddbccbddacaaadcddadcdacbacccacacaddbabcbdbaabbddadcabccaadcaccbadadabdababacbcdcaaadccbccdabcbdcadadaadcaddadaadcdbbcaccababcddbbdacbacccaacdaddddbdbadcdabccccdabdcacadbbadcdbdccbcdaabccacdcadcaacdcaddcddababdbabbbbccdddcadcacddbabdbacbaaddbadadccbacdaadbddaddccccdbdddabddbbbbbbdbdacdccacbccabaadabcdaccdacbcdddcddcbcdacaccdbcbdccdaaaccdddadddcccdabacdcdabbcadccbdabcabaabcdaadabbbcaacaadbddccbbadccccbbbccddadadcdabcddadbadbbaabdccadbbbddbdabddbabcbbbcbdaaadbbcbaaabbcadcbcdcccdaccdbdbcadcaadacbadacaabcddbadcdbbadbbdbacaaaabccacacccaddbcdcaddddbdbcdaaabbbddcadcbddcddaccabcccdcaabddcdddbbdddbccadbabaadcbdddcacdaacabcaccccadddabaacbdcbbbdadacababdbdcacbcdadababbccbdddbdbadcbddacdcbddccaddadccabbcdcbcbbbcbbbbababaababbdaabaaacccadadcbccbcdabcbccbdababbcaacbbadddccccaccaadbbadabddbcccbdcdcdcacbabbbbabacddbdbcbbabddabbbbbaaabbdcbaddbbbbbabdaadabdbccadaddcbbccccbabddcccddcbdaadbbadabbadadbdccdadcbabbddccdbdabcbdbcbcdaabdcaddcdaacdcbbbdbddcbbbddddddabcccddccbcddbdbdbbbdcbbabcacabcdddaaaaabbaadbdcadcdabcbadadddbbdbcdddbaabddbdcdadaacbaaadbdbbaacdaddcadcbddcaacdaddbabccaccddbabcbbbcbbbabbccacbbadabaacadbacbacaaaccacdccabdccbcdcbdcddcbbadbbdbbdccddbcaabbabbccdaddcdcccabbbdbbdbabddaadadabcaddddacaccdadbdcbdddcdaddabcdadddacccdcabbaacdcccdddbaacdacaccbaaaabaaadbddcbaaabbaddcabccabddbbbbdaccbbbbddcbdbcaacaaacaddbcbbcccddcadcbcbbbbdadcbbbbbbbdccabbaacbacdabbbddadababaacbccaadcadaddaabcabcbacadabbbabbdbbbcbdacbacbbadcbdaaccaacabaadcabadcbbcaadcdcbcccdadadccbabbadccdcaddccaadbadabccabcabdabaaaacbaabbddabaacbcaadcbdcacaadcbdadbbddcadbbabaaaabbdddccaabbbbbbdbacdccaccaadbccddcdadcaaaccdadbaccabadbcaacbcadcdadccaabaccccdadcdcbdacdbbdbcddcadbccbdcbbcadaabaacaaabbdbcdddbbdabccaccbacabbbbccbcdcabcdbabcdddaddaacabcbdccbddaaaaabccddccbccddbbacaabdcbdbdcbbbbbacbccdacabccbccbbaaddaddadcdbabdcbddcabacbccdcaabddbabddbadbadacabdcccdbbdaadaaacbadadaddddcbbaddbaadabbdddbcbbccdabbbddbaddacbacaaccacccadcbccbdbdbbddcabcbbadbacabadddbddcadbacacadcadaccddddbbaabbddaacdddbcddaabdadadcbcbadccdabdcacbcbaacdbdadaaaccddacdadbbcabcbcddcdadaacacadddcbaadccccbcdadbdbcaccdccccdbbbdaaddabbcbbbddbcdbdaccdabadcbcabacdcaaabcbcbababcacacbcdddabcadcabbcbbdbcbbdadbcdbbccbcbbcdcbbcaaaddacaabdadaabcbbddaddbccbadbabaacadaadbdaaddbddbcbaacbbacbabcddacccaadcbdbcbcdacdacacabccbaddccbbbaaacadbbcadaadabdccadacaabcdaaccbdccbaddbdaabaacadcdadbadbdbcbccaadddaccacdbbcbbbcddccdccacddbdaaddadbbbddacccdddcacacacbdabbdaadaacacaddbddbbdbacbbbcdddcadbcacadcddddacababaddcaacccbcdadabdabadaccccccacadbbacabababdccbcaaddaccbdbadcbadaaccbcccbcaabcddbcdaaddcaabcadcbcbaaddbbbdcbccacbdaadaacccadbbacbbbcabbadbabbbcdcccbabccabacabddcdddccadacdacdcddbdadcdcbcbaacbbdbbbcadaacacabdbcadcbaddaacddcaccacacaddccadadbbcaabbdbcbdbdadcdcbadbaccdcdabdabccbababbbadbabdcccabdcbdbbbadcbcaccdcdddccacbcccdcdadabcbacaddbccdbbbadcdcdadcbaddacbbbadcdbadcdacdadaccbabdddacccbcccacbbabccaccdbcccbabdcbccdcdcbdddbbcbbccadaddbbccbbbabcddccdadadbbadbdbadbdcaaddcddabddbdcaccaddbcbccccacbdacdcabcddacadbabbbccdbcdabdbcadcaaadcaadbacabcbcbbdbbadbbcdaacaddbdbdaaabacccadbcaaabdcccdbbbcdcddcabcdbdbbaacbcacbdcbddcbddacadaadddbaadbadbdbbbcbddddccabdcbcdbbcadacdbdbdbdbbddaccaaddaccadbcaadcabbacacdbaccdbaacdcdacadccadcaccccabbddabbadccadbdadbacaadcbadcbaaccbddadccdcacddadaadcadabdddbcbdcdbdbccabddcbccccadadadcaadcddddacacddbaabaabdadcdcabdcdaccbcccacccadacbacdaddaddaccdcccdccacdbadabddbbbbaacdbcdcddcbcacbdcadcaacacbccacccaaacbbaaacdccdcdbacacdaadadcbccaddddbcabddddabacbdcdbdcddaacacadbddcbdccdaaaccddbbbbcaccbaccaadcbdacdbbaababaabadacddbacccabbccbcabaaddcbacccacdddbcbcbcdddcdaccdbcdbbbbbadbbadbbacdabdbdbabcbbbbccddaccddacddccaaddbbddaacdccadaaddccdcbbaaacbdcaadccdbcdadcccdbccdabbabdcdddbaabcbbbbcdbbabdacbaacbaddadbbcdabacacabaabadbbccbcdbbdaadbcaccccddabdabdcccbdcbbbcaabdabaaabddabccdbbcbaacbcdbdadaccdddddcbbbabddaabcdccccabcbddbbdbaacbcabadbbccadccdaadbdadcdbbbadbbadadbacaacaacdbadcaccccdbbcaccccbdcbbacccddcbcbcbcdddacddacddbabdcaabacbdcacccaaccbbcddcacaaaadddbdabbdaacbcbdbacaccbbadaabdbabaabaaddddddcddbdabdbacbcaccdbcbdcbbdbbddddddcdaabcadbcdddccccdbcddacabdcdbddbbdccdacaadaccdcbaddbddcdcbcabbcbdbccdcbacdadaaddbccccdabbadbadadccddcadbcddadbabbacabddcaabbabccbdcdacdbbdabcbadccbbbcaaadddabaadcddcdbabcccadaddbbacaadaaccccdbcaaadbdbdababccbabcbbdcabdbbdbacbccabbbabdabcdbadaaccbbbddaaabadacbccddbcbbcacacaccbbcbacdbaddcbdaddcbcdcacadccaabbdbdccabccddbbcbcabadcacbacaabbdcdccdcabcaaabcaccccadddddccdccbbaacadcbabccdcaaadbcdbbdcabacccbadacbddccdcbcbbaddacaccadacadcdaabccaaaadbdbbbbcbcbdcaabdcdcaaabdcadcddcdddababbbcdaaddadcdcaadddaddbcdadbaccbbaabacbdacabdcacccabdaccbabddbcbcbdbaccabdcaacbdccbcbdddabddcddcddadccbbbcabbdcacabdaaaaccabcacdddcccabacbacdcaabbdabaddaabcdacaacbbacbabcadcaabbaddcdbcadadadadaacccbdbadaabaadddccbababdcdbabcbdbadcaddcbcccbdcbbbbccddaddbadadaddbcbcabbbccdcdddbcbbdcdabccdaadadbabadcdacccddbcbbbacadccacbaddacdddcbcaaacddbccdabccdbdbcdaddbaaadddcbdddbbcabbcadacddddcbcbdbaabdbcdbadcaacddcdbbccaacbcdbbbbccaacdabbdbbcddcbddbbdccabddaacccbcadadddaadacddbddadadbbdbbabbacaabdbbdbaabcdacddcbcdddbbacbdcccdddadddcdbadaacadbbacaabccdccdcbddbccdaaacbcccdabddbbcdbbbabddcbbbdbcbbdbdaacddbcdabcddcadddcbbcddbacbcaaaabcdaadabbaaadacddddcadacbcccdddbcdacccacbabbdacdccddaabadadcddaabadaddacaddabaacdcbdacdcdaaccabbbbcddabacddccdaaabddbabddcddddacbadaaacabbbbbcdadbcddcbdabbcbcabccaaabbadcdabadddcdcbacabdddddbdbaccabbdbcdabddbcaaabcbaccababdddbcbdbacddbccbacabdbbdbbcadacbaccdaccdbacddacccaadabcacadacdbcacdbdcbaadcadacabdaddddabaddcbdadacbaaaadbabcadbbdaabcbbddbdbbddcbdcaaddaddcdcdcddcaacbbadcdcaacbcccddbcbbddccdcaadaaadbaccbbcbdccbcdbacbcccbbadaadaaababdaabdccaaaabcaaaaadbdcdacdcaaaaabadbbcababcabdddadaccbcbcbbdacbbbcabccccbcdadcbcbdddccdaccabdaaacdaacbadccaacbccabcaacccdbcaccabbdacbaaccbaadabaddbdabdbcdcaddcdabbbabccbadccacadcdddaccbddcccaddddadbbadcdaabdccdbdcccdbbddccadcdbcddbcacbbdccccddbcbccbbabbcadbdcdacaccccadbabdbccabdbcabcaacabbcbbcbdcbdaadadcddcacabacbbacbbdbcaabdcbababbddcdcbccadccdbbddabcaadcdbddadbacaddccccddccdaaabadbacadaacacddacdcdbaaabdcbbbbccccbcdabbddacddccbacbbaadbdcdbdbdbcdbdaabccdcdddcacadcbdcaaabadaddbabbdabcbddbaddbddbcbdcdabdaccdccbddaddccacabbdaaaaccbdcacaaabadbddcaabdaddcdddbcbcacddbaaacdabdccdaccbbbcadbbbdbbcbddccdadbaaaddcbbdadcaddcdccdacabbddbdddbccccbabdbbcacbcccaabbcaadaacdababcdbacdbabddbdcdcccaccbbdbbbdcdabcdacccbaccbdbabaaaaaaddcaaacdaccddcbccddcbacbbdddddacdcddabdbaabaaacccccadbbbcdabcabcadbbaadbbacbcaaacbabdbddbdaaaabbbdbabbdadddcbbdabdbcadadabacdaccbaabccddacbdcbdcddabdbddcdccadacdcbbdabdbdcacbcccbaddcccdacabcddaabdcacdcabcdaaddcbdadadbddddcabadcdadbcbbdadccaabcdcadcdbbdbdabbdddcbccbabdaaadcdaacabdbddaaabccaabaabbddaaaacbdabadbbbbacdcdbcacccddbadbdcddbdcddabdcdcdadcdbbdccaaccacdcddbadbdccddcdcdbcdacbaaadbddcaacbdbcdbdccadaaccccccdabcabcacdcadacbaaccbdcdbdbddccdadacbaaacacbddaddaadabcaddaadddbbbdcdaabbbaaaccbbbddbacabbbbbcbcdbacdbbcbccadddcacbccacaacdabadccdabdbcdcbcdbbddaacbddcddbcaaccbcbcdabcacbaddddbcbccbccbdcddabaccddbdbbddadaaabacbbccdcdcacabadbdacccbabbccaabcdbddaaabadbbbbdcabdaabdbacbdaaccbdabddacadadbdadbdbadbbddaddbdcbbaabaadabdcbadabdcbdaaadaabcccbccdddadccaabbaadbbdcbabcbbcbbbbbccdabcddcadbaacddcabbbcbadbbbcaadbcacaabbbcbddcdccdccddaabccadadccdcbabcbabbcdcabaacccdabcbdbabdccdaccddbaaabadcabdabccabccccccdbcadcaddbcaacaabdddaacdaaabcbbacaadabbbaaccbadcadbdaadcacbbbdcbcdcbbbcccbcaadabcccddcccdbcaaabadcbddbdccbaabacaacbdbaababadadbddcbabaadbdbacddbdaccbadcdabccadbbbdbcccbbdbcaddbcbcddaabcdbadddaccabdcbaabddcbcbbadbadcaaacbcacccaadcaabbcddcadabbbccaaddbdbdacdcccdbadacadaddcacadddacbabdcbbddddaacddcbccaabcdddcaccdcdaabaabcaacaccdabbadbdbacccbddaaacdcacacddcabacacdccbbddabaaadcddccbccdddbabcbdbaaccbbaccbdbcdbbbbbcbbdcbbacdbbdaddcbcdccabbcacdbbacbabdccaaabbbaaaabccabbadadcdddaddcbbabdddadbadbdaabcdadcbcccdaccbcbcccbddaabacdccbdbbdccaccccdacbacddcbbbcabdcbccabdaaccbdbbcccabdbbaaaabbbaabcbacaacdccabcbcaadccaadbcacacdbdcbcdbcdbdaaccabbbcbdccacddcabbdbccbaadddcaaccdbdcdcbdcdaadacccaacbcccdabdbabadbababaabbaaadadabdbbbccdccabbccbbaaaaccabdabbabbdccdcacdbdcdcdbabcdbdbadacabcdbddbbaacbbbdadcabbbdbaadccbabbbbcdccbdcaddaabdaaadabcdbabcaabcddcbdaaacbbacaabbdaabadbdbcabdcdaccdcbabbbdbdcbdbdcdaadabccabbdbbdadcccdbbadcaacadbadabcbcbaadcaacdbcbadadcdbdcdcdbcbcddcbdabdbabbbcabbabbcbcbbddadbdadcccacbdddaccbbcacbadadbdabaaddabcbbcbbcddcdddccaaadcbbdcbaaaaaccbccbadaccccaacddaaaddaacdddddcadbdaddcbdcbcadbbcdacbcbbddabcbbdabddbdabccdcddadddbbbcacdacddabdcdabbbbbadcdbbbddddcbbaccbcadbdabaaccabccacabdbaaadcaccadbbbdaabadbaadbbaacadbadadbcabcdcabddaaabcdcadabbcdacdabdcdadbbaaddcababdcdbadabadadbbdbbcccddbccaccabdaacddddaddaddcaabbcadaccadacddbacaabcdcabbbdbaabdabaaacdbcbcbbaaabbabddcabbabadaaababdcbcbbbaaccbbbacbabdcbacaddacbaddaabcdabcabcbdbbbcbdabbcaccabbcbbdaabcbbabcdbccabbddbcacaccbdddddbacdaaccdbbbbdbbabaabdcabcddccddccbabbdbaadcabbcaabbbabbcbacdcbdccaadadbbbbdcaabddadcbcacabdcabdacccdbdbcbbbbdcaaadbbaacbbcaacadbaddabaabbbcbdbadabdcacaaddbcacacbaadbdadcdabaabccabcddacddacdaaaddcaaccbcbcccdcbabaadaccbdddbddbdcdcdcdbdaaabadccccadcdaaabdcabbcaadbddbccdbdcbaccbcdcbccdcdcdacdbdabbabcbbaddddcdbddcaaabdbabbddbddadbaaaacddbbdaaaaccddbdbbaddbdbcdacabcacacbbcccaacaabbcdaaaddbbccaddabbacddbabbcaddaddbabacdccbcdbbcaaaddacabaddacadddcccaccccdadddddacbddaaaaacdbbddbabcbdbdcaadadadaacacdaccbaacdbbaacbabdcddccbcadcbbaabacbbbdabdbcdcccbdbabbaaccbbadddaadbdccbbbcaaaccaaabdbbacabdacdacbadcccbccdbbcbadbcbcdbbcbacdbbbbacabadaccbdcbdabdbcccbdcbadbcdbbcaccddadcacbaccbddcabacbdadaabbccabcaabcbccacbdabddbbcdbdbcdccdcbccbaddcaccdabcbddbaaddaccacacbbadabddcbddadacddbacadadabdacdadbdcddbcddcaddaaddcbcbbcdbabbbccabbbdbccabcbaadcdaaccaccdbabaccddaddcdbcadacbbcdaaaaabbacbcdbadabadbccadcccbaddcacdccdadadcabbabbacbdabaccacacdbbcdccbbcbbdabdcccbbabdacbbacbbbcbddbadccdbabcddbcccadcaadadbdbcdaccabaddadcbdbbacaabbabbbaabbddcccabbbadcccbccacdbcddcdbcccdacdaccccadababcbcddabaaadcccadcadacabaabbcbcacacbbcbaacacabcccdcbacccbcdbbcbacbcbdddcccadabadbadbdbbdcdadbddadaaccacddddddabdcdbabadaccddbadcaccaadabbcdaddaacaadadbdbbaabaaadcaabcdcddbdaddadcbdcdcdddcadbccbdbcdbbdcbacbadabcdbcdbabbcabdbcdcbcbcccccdbadbdbcccadacdbdaccdcabcaccadaabacddbdbcdcbcdaabccbcbcbadbcddbabacaaccaddbdabdabadcccbdcdccbdddbcdabccacdcbcbaadcbcbaadabbddddccdaddcdbadcabccabadbabdcbdabcbbdcbaaababcbccacacadcacdaccddadddccaaaaaaccabbdbaddccbadcdaacbbcbdbdabccaadaabbdcbadbcccabcaccacbaaccccdadcaacaacdadddddcbdcaadbcdcaddbdbcccaaccbbaddaabbcbbaabadcccdaacabaacdaadbddbacddacdabcabaabbabcbadadacbacaabbccddabadadabaccacbacdcdbbbcabbaccdbcbdaacadaddccaaaccadaaaababbddbbdabadaccbcaccdbadbadbcccbcaccdbdcccacdabaddabcdcdcaddbcdbcdbaabbacababdcddddcdcadcbcccdbaabacddbcddddacdacadabbcdddabbdcbccccdcbdbabdcdadcaccdbdbddccddbddcaadbbaccbbacccccbadabccaacaccbacbaaabcbbcbbdcaaaadcbaddcdbaadddcbaddbccbbabbbaacbabbababbaadbcddaaadacdcdddaacdbbcdbcdbccddcbcacbdbadbdadcdcbcccaaaaabadbccadbbacaadddddbdaccddcdbcdbdcdbbbdcbaacccccbdbaadccbacaddddcdbdbbccadaccacadacddcbcddcacdddaddadaabbaddacbaaabdcdaccddaabbbcdcbaacdabcbaaaabcbacbbacdacdcbbadcccabddccbaadbacbccdabcddbbdbdcabbbbdbdcdbcbdaaaadbbbdcbacdbbdcbadbddcdcaccdbbadadaccbbccbcaadadccacbbaacdbdcbdbaaabcbabdabcdccbccdcdaccacbbcbdbacadbbdcdccaaccbdbaccbdadbabddabcacdddbaabcdbabddcbbdabadddcbccccddcdaddbadaadcdbbaacccacdadadbcadcbbadccaaadcadccbabcaccabbbdbacccdbcaacbcbbdbbddacdbaccadccaabbbcbabbcacccdadcddadbbcdcabccdcdbadbdbaaabcdbdddcbbdaacaadabdbddcddabbbcabbccabbbaabacbcbdcbbbcbdbdcdcdcaccdcabdbdbaccaabacbbbcdcdacabaddababcdabdbbadbaaaadcccddacbcadabcbdcdcbdbaabddacacaccadbaccaddacaacadaacadbdbadbcabacddbddddddaaaaadbbdaadbdcaabbcbabcbdccadbbccddaabbdcdbddcbcdbdcbbbdddddacaaacacdcabbdaacdbadbdaaaadabababdcdaddcddbadbabccbabbddaadbbcbbbdbabcabcbbcababdbbddacdbdaadcddbacdbaddbaaaaaabcdcacdcacbbbaabcccdccdddccacaacdbcaadaabcadbdbcbcbcaadcbddaccabcccdbbaacbddcbccddccdaabddcdbcbabbcacddadccacbaaacadacdaabccdaacdadacdcdbbcdbcabcbddcbadbdcdddbabcbbbdacbdcdbdacaadaabacdcbaacbabdbaabdbbbcccdadacbccccabcaaaabaabbcdbccddcddccabbcbabaadcbadadadaabdacadacaadbadbbdacadaddddabccddbddccbadbabcdbdaaaadcdadabbdcdddcbadaddcdcdabdddbdaaaadbcccdddcbdcdbaaabbcbccbbbaabbdcdacabcadaadbbbbdbbcacbbdadcadddccdabdcabacddbaacdaacdabccaaddaacddccddabacdcbdcadcdccadcccbccaaccacaaaaabccacbcbcdbddcdbcdabacababdcbbdcbdadadbaadbacbabbbdbcdcccddadadbcccdbccaacacbdbcbbcdbdabddaccdbaaddaaddacbbcbbcaddddccbcdcddbbbcacadbacbdabdcddddbcbbdaaddcddaabadbbbcacdcccdbaccacdadacadadaccdbbbabcaadadbcdaaacdbcabdbcddcbdddccbbabaccacacdcaaabdccbcdbdcaacdbadadccdabcbdcbdcbbcdcbcccbadaccddadcdccdaadccdadcacaccdcbdbcbdbbbadaaddcbcddbcddabaacddbcdccbdabacabadcabdadcdcadcdbcabbcbdccaddcbbdbdcdccadbadaccaaadcddbdbdaabcbabaadaaacbadddcdddddacabccbbbaadcadddadbcbadaadcbcacaabacddbbbcadaccaaaddbcdcbadbacdbacbcabbdadcccddbcbbacaaaaaaadcbdccdbacababadadcdddcddbaabaccaacacddcbdcbcdbccdbaaccbababdcabcbdacdcdbbaddcbadcdbcbcababcaaaacdaadcdddadabbbcdbbbbbbaacadbadaadcadddcbcdabbdadadacbddacdcbcddacbdbccaabbccdbddcdcacadadbbdadccbdbcccddabaaaccbcddddcbdccbcbcdacccbcbaaabadcbdcbdaabdcdcaaddaddccbdacbdbbdbcdcddcdaabaaddcbdbdcdaadcdbbbacbbbccdaccccaddaaaddccbaddbdbddbaccbdcabcdbbaadcdcaadaddbdcddcaacabbabdbbbacdbcbcccdaacdddbdaabacadbcbacdbbdbdbccbdabcadbacdaccbccbdbddddbacdacbddadaabacadddcabaaacbdbbdbbbbbcaaadccbadabccbcabdcaacdbadbbaaacbdcdbbccdaabadbdcaadccacaddccdbbdbbbbbaddccbadcbddbdcdcbadaacabcdccdcccccbbdddaabccdbddcdcbdbdbcacddbdbbcaddaaaaabddcaaaabacabcddbdbaccaacdadccadcbacbbabdbdcabbbcccbdbadacbdbbbbbabcbaccbacddbacdccccbbbbbdcbdbbdadbabaadbbbabdcacbcddbbcacdddbdaccccaccdcddacbdbccdaacacdcdbaacccaaabcdcaaadadcabdadaadbccacdacccbdabccdccdaaadccaaacadadadadbdcaccadacccdcbbbbaadcabdccbdccaacdcccccbbdaabdadbbbcacaccbccaddccaabbadaddddbabaabcacbbdaccacdbabbdcbbdabadbaadbaccddbaaacabccbbdbadbddacabaaaccbdabbaacccdbbcddcccdacdbcbbaaacbdbadbabddaabbdbabcacadccaacbcacadcaadadccaccbcacbcaadddababacdccdadaadadcadcbcdacabbdbcbdadcadcdbbcbbcbaccddbbcddbbddabcacabcaabbacaddccdbbddabcdbaacddbdcdcdcbbdacdaccdacbbcccddbddacdbcadbcaddbbabbbdbcabbdacbcaaabacbcaacdbdaadbacbdbddbddbbcbbdcdcbcacdccabdbdcaaaaaaabcddbbabbddcbacadcaccdccbccdbbdaacdcbbacddbaacbcbbbbbaaadabacddbcddcbcdbacddadbddcbbcacbdcdbbddadcabdcbacbbacaacbdcacdadbaaaabbababdbcdcabaacaadbdcdabdaccbbacaaacbaccdcbcbcaddcdcdabbaaadaaaaddbabacdcccadadaccabdbddddddbdddbddddbccdacdbcdcaababbbabcaababcacdaabaccbdccabbbcbaadccbcdccdaadbbccbbdababacbdaaaddcbdddcdabcccabbdcadaaccccacbbccdcbdaaabdcbdbbddddacbbcdcccccbccbdbccdcddacddcacaaabbbaaaadcabccdabbccbbbacaaccdddcbaacdacbcbacddaaaccbdcccadcbcdaacdcaadadbacaabbaacccabdadddcbabcbbabbbadbaabbabbdbccdaccdacabacadcacabdccbcaacddbcadcccbbbddaddadbdcdcccbbddccdaddcaabbaaabdadaaaabbbabbaaaddbdaababcaabdcbbbcaabcacdadcbadbcacadcddbccabbdbacbcabcaaadcdaaabcbabbdddbbdbbacbaadaddcdccabbdaaabddcaabcacdddcdbcbbaaddbaccaccccaadcaddcacabacbbbbadbbacacddcacacaaadcccbaabbadbbaaddbcbdadcddcbaddabcbbadcabdaddadccbbdaabaaacaccdcccbdbcbaaddddcbabbcadabadabbbdbbabaaacadcdbdbbcdccabcaddccdbcdbbabcadaccbaaaaacadacacacbcccacaaabdacdbcbadbbcdcbddadabbdddbdcdacaacdddbabcdbdadabadabcbdadaadaabcabbbabdadbcacbcaabbaacbbdbaddbadacbccdccbcbbbbdcbbcdcbaabdbbcaccbddbadcaadccddccadaccacccbacabadcabbbadcbddbddcddbadabbbcccadaacbacdacdacbacbadaadcdcbacadaccdcdaaadcabbaacabaaaababdacdabddcbadbcbadabcccaabbbcccaabcdbacddbadddbcccbcaccbabbccacbdcbaadbbccbccbbbacbaaadcdddddacdaacbcbdbcbccdabcdabbdabdbacabddcbabbacdbadbcbdbcddbabbababdacccdadcddcddccdbabcbdadccbdcddadddddadadacacdbbbbbdaccddbcddbdccddaadabbaacccbdcacbaacbdbdbdccacacaadbcbaddbdcbdbccccbaccbbcbdbbcbaabbaadacdddadaaddacbcdbaaddaddababdccbaddcddbabcdbdbbaacadcbccbdabadcbcbcbddbabadaadcbbcaacacbcccbbdbcaddacdcdbbacdddbccaaadacbdaacbabbadcaacdcdcadbdccdccabdcdbbdaccbdcdbbdbcadacddcbdadadcbabaddbbcababdabccaaccbdbdbddabbcacdbacacddaabdabaadddaccadcacabcbbaacdabdbabcdbccdaacabaaaabbaddbdaacccccccddbabbbbbaacbacaabaadcdcadcaabcbadabcadcddbbdcddacacbcadcdadcdcbaddabadbacdcdbabbbbbccbdacdcccdcbccddbddabbbcbaabbdcddcddcdcaabaddaaaacbdbccddbdccddbcdccccaacdccdcbccbdcabbbadcddcccccadaabddddaaaabcdbddaacbdadbbccccdcddbbdbdaacbdcbbadbbdddaaadaaaaadcbdccbacdccddaaccdadddcadaddbddccdacccdbdbbacddcbacdbacbccdcabbcdadaaacdabaddaccacbccabbaaadadadabdadcdaacbdddaababacbabacbcdcaabdbbbccdbabcdbddadabdabcdbdcacbaacddcaaacccabccbddcadbabccbdbbdadddbcbbacadddabacabdbdcdaabbabcddcbdddbbcdcbccbddbbcbcadaccbaddcddcabadddbbbdcdbcdbcacdbdbbddadbacdbbdcacbcbcbaacadbadccbadcaabcbcbcbaaadaacdaacddadcdbcbbacdaddbdbbcadbcadaaddbbacdbdadbdaaddaadbdcbddaadccdacaaadbbdbcbcacaacccdbbcacdaddccdbdaaddbdcccbbbddbdccadccbabbcacbacdbbaaccddcdacacbadbbdacbaaddddcdddaaabcadbdaabadaaadabbddaabbadacdadccbddaabccdccddddaccbadbcdddbdacdbacaabbdabbbadabcaddcbabbcabcdccbcdcdcdcdcaadaacabbccadddccdbcdbacdadbbadbcbbbdabdcdcacbdadbcdccdcbccbbbaadbbbaacaabacacaadbaddcdaabbbbbbbaaaabddaddcdadabcccbbddbacbdbcdddcaabdaddbaacbacddadcbbbdbbccdadadbaacddbcaccabbcccbdcddcbbcbdbcbcdddadbcbdacdacaaacdcbaacdbcabcadbcabcdccaabcbdcdcadcabacaaacdcaabddddacbccbadabdcbadbbbadbcbacadccdcbdcabbaaccbdccaaabaaccbdbbcdddddbadccbcaabcacaccaadcaaabacbdbcbadcdbbcdcabbbcbbabdaddcbdbddcaacbaababadbbabbcadcbcdbccbdcaccadbcddcccbdddbdcbcddaacdbbdaddddcccbcaaaccdcdacdddcaaababcbbcabacbacddaaabbdcdcbbcccadbaccdabacabdaabbcdddcdbaabadabbbcbdddcacdabbddcddaabcadbadcdbdaaccddcdaadcaadbddcdabddaaaccdccccdcacbacbbcacdbcccacabbbdcbbabadbaabddbcbaddcdacaacbacbcdbcbbdbcabdcccddbdcbdccaadddacdacaddbcabdabaaacbcddabbaabcabbbaabacaadacdabdcadaccccdabadcbbcababdcdaabcbadcbaddabbaaddbaddcabadccbabaabbcabddacaaddbbcddaacbbbbadcbccbdbcadabdadbbaaadbadacccddabcabdbbcdbbadabacdddabadccdcadaccddbdbadccdbdbdbadbccdddadaabcdadaacbbbcabdbbbcaddaacbccacdbaaadbaccdbaaacaaddbbcbdccdcbaacbddccaadcaadbbddcabbabaaddabdadaacbadcacaccaacbbbdcadbbbdadabcdacdbcdcaddadddbaabdddcbcddddabcbcbddbdccddacdccbadcbdbbcbddbdaaacbdcddbbcddcaaccaddcadddcdcbacaadaaddcbdabaaaabddabacaddbbdaadddcadaddccbdcbbbcadcddbbdbbcdacaabcaccdcbbbcaabdddacdbaaadbbabdadaabdacbdaadbacbbcbcacbaacddabcaacadddbbddcbadbdcadbbcbacbaaaadbccabbadbbdcdcabcaddcdcbdaadcbbbbcaddbccaabcdbaacaaaddbbaadcacccabbbdaddaacdbbbbbbbbadccdcacdadabcbaddccdbadcbdabbababaacdabadcbacaaacddaadabdcbaacadabbabbdaddcbdacacbdcbbbdbabbcbacddbabdabaccabcabaacabbadaccadabaddcacbabccdcdbbcbbcdcdbaaaabdcaacdcbbcbcadabccccacababadbaaddaaaabdcdddcdcadadcaababaddaacbbcdaadadccbadddacdcdbaccbabcdbcdbdacdaccadcaadbadaacddbdadcdddbcbccdcaabcdbaacddacdaccabcdbadbcaddcadaabbdadaccbaacbbcabdbbabccbdcabdadaabcabdcaccdbcdbcaaccdbcbbbabbcbaccddcabbcbaccbbcbadacbbdabccabccdaabdcadbaadbdbcdbcbddcbddacdadddabdbcdabaabccccabbccbdccbacbccdaddccbbcdacaaacabbdccccbccdccbcdbbdcaacaabbdddbdbddcdaaadddacbbccdcadbbdcdbbdcddaabdcdadddcdadccaacbbbadabadacadcdcbccbbdacbcdddaabacbadcbbdddabaddbbcccbacdccaaaccddcbdaccbdbaddabbaadbdbbbacbcdbbbcbcadcdacbccdcbbaaddaadabcdcadacbcaacbccacadacbcbcdaddcaacaabacccababcdccdbbadbccbacbcdadabccadadbdddaacdddbacabcbbccdcacbadbcababcbcccaacbbdbabcccdacabcddbdcbbccadbbbabddbddcbccacadcdcccddcbbabadaacbdcbbddcbacdcaaccbbdbcbbdbdaaacdbbbccddcbaccdbaadccccaaadcdddacaccaabacaacbddbbbdaababdddcadddabaabdddcbcaccbbbdbdcabcbdbbabbccbbbacdaabbabcdadddbdaccadbabdbcdbdcdadccabbddcaccccbdcdbcdabbacbaadbbbcbaabaabddbbdcadcddcbdccdbbdbbdacdcdbcdaadccbadbaaaabbadbddaacccbbaaabdbcacbbbbabcbbcccccccaddcddbcbcbdadaadcdbabcdbddccdabdabbdccbbacacdadacacddccdcbaaaabbdaddcccbbccababcadbabdddccdbdbcccdaaddbdbdcdbdadccddcddbcdadbabbdacdccddbaaacdbaadababababbdccbcbbccbdacdcbadcaacdcbadbcacdbbbbcadcadbcbabdadddaacacbdacaccdabbddddcaacdccdbcdcbdbadaabbaccbdbabddaddacbcbaadacaacaddcbcaacbcddaabadcbccadbcadcccbacbcdaaacaddcbcdcaababcadcdadcbdaaaababaddbbdbdcaaadcabcdabddbbdbccdacaddbdaacbbabbcccbddadbbdccabacbaadacadcaacacdadcdbabcaadacbddbccbacaccbbabdcbcbcaabbaadacbaabcbdaddccaacddcabbaadcdbdbacbbdccabaabbdadbbcacccbbadcacacdbcbadcadcbbdcdddddcacdccbabaaacccbdcdddaaacbcbdbcadcacdabdbbccdcbadbaddcbdcbabbabacccdbcacacccbabadcabaddabacdccdabddcdbccdcbcbdddaccbbabdcbddccdaadbcabdacdbddddbdadadccdadbcdcbdaccdcdabbdcdddbbddbdbdacacddadbbcdabadabacacbcbbdaadbccbdadadbadabadcdbcaaccbdbddddddbbdbbbaccddcbbbabbaadccbacabaacbbcbddbccbdadddbdaacaacacabbdbdabbbbcbcbcaaabdcdbdcdabdaacccccddcaaaaacbcbcddbabdabdbcdaadcbbaaacacbbbccbdcaabaaccbabcadabcdabcdcabdbacbbaaddbaaadaabccababcbbddddcbbdcdccccdcdcadcccdbdbbbabaddcbaddbcadcdaaaccdcbdabbadbadbaadaaddbaadcdbadaccbdaadcbadcdcdbdacbccccdddaabcbdcccbccdaaabacdbcccaddcaadbdcddcbbaaacdacccbacbadaababcccbbcbaacdcbcbbddcbddcdcdadacdbacbacaacadddcbcabdcbdcdcbbddbdbcbcbcbadacaacbadabadbbadadcdadddccccbacdadbdcacacbcdbcbaacaacabcbccddbcaaccacddbacbdbabbcdddddacdbcdabdbccddbabbccdaaadbccbacccccdcccbacabcdcbadccaccbcccddaabdcccdbaaccdbbacddcdcaaaaaddaadcaaabdcdddacadbccdabcadcbbadbcdccaabdbdaddbdccccdbcaaabadddbbccbbbbbcdcadacddbcacbdbddacbddaccacbaacbabbadacdbbaadbbbcbddccbbaaadcbddccddaddbbbaadbdabacdcdbabdddbacdbbaaaaabddaadbbabcddbcdaabaddcbdcdcbbcbacbbabdcccdabbcddaadcaacddbbadcddbbacccbcbdddbabbcbaacaaddbcddccbbbbdcbdabcbdbccccdbadcddacbcbcbcacdcaddbbabadadccbaddccaacdcacccaaccdbdccabaadbbbaddcccddcaadbacdbbaddacdcaccbbbbbcdbadcacabdbaccadabaddbcccacbaaccddddadccdddadbcdbdddddaabbdcdabbdddacddbccaddcbaddbadcacbbdcbaddabcddadadabbccddadbdaaaaadcbbcdadbadacccddcacbdcabdbddbdbddbbdcdccbbdabdacbdcbdcbadaabccccbbcacaacddbbbacacbcbbbbddacadcbccdbdcbaccbaacbdcaaddadcbdccdaaaddadbbaacdabcabbcdddbadcbccdbbcadaacadcbcdacdabaccabdabbbdadaadcccbdcccbaddccaddabbbcdcddbaacabbdcadbcbaabccbacdbcdaaababaaccddadbaadcddbacdcabbabccacaddacbbabbccaddbbaddcccddacbadbdbddddcdcdaddbcadacbbccdcaddbcdcabbdcccdbcbdddbdabcacdbcbcbdbbaacacababbdbbaddbdacadbbaacbdbbabbdcdddacbcaddbbacbacbaccbbdaadbcdabcdcbbbbbacdcbabbcabccbbcdbbccdbbaccdbabbbadbcbdadbaadccbccccaaabccccbdddbbbcdbaabaaadcadcbccabbbcdbbdcbdabbadaadaddcacbbcbbabcdacdababcdbadadaadaadcbdaaacadddbacdcccbbbaadabbadacacddcabcccbccdcdddbddaacbbbbbdcccbacbbcbabcbbacdcbdaacabcaacbbaacbdcbacdcbdcadcadabaaccacbdbacbdcdcbbcdccadaccbccacaaddcacdddddbdabccdabababcadabdabaddbbbcaaddcadcbcdacadacaccccaadbadbabbbbacddccacaadacabadcddccddabbccdbccdaadbacdbbabcbdaacbabdcbbacdcacaacdbabcadabbacdcabbacbdbaaadddbcbdbaadbcabadcdbdadbabbdcddcabbbbdbcadcdacbdbdccbacbccbcbcdbbdbbcddacbcbbabcccdbbbbcbdadbbbbdcdddabacbdbdadddacddccccadcdbcbbdcdbccbddbdccbdaaaaabcccdacbddccbbdaacdcdccdddcdbdacbbbacdaabcaadbabadddadcaccadadaaacdacacacabdaaacdbcbdadadccdbaccdddbcbbabdbdbdcadbacdabbdbaadbacbcbbdcbcabbccdbcacbacbbdcdaadbcdcbdcdaadbaababbacdcbbdcabbbcbcbbcbdbcaaaadcccadcaabaccccaabadccabbcbdaadbcbdbacbacdcdadcabcaaadccaccbaddcdcadadacacddccccdbdaacaddcbdcadbdcccbbcbdccaabaadadccacccbbcaabadcacdbddddbdadadabaabddbabbccabcacabcbcdadbdbcccbacbaacadbabbadbbdcdbdabbbadbaaddbddbbcbbaacbaadddcacaacbbbcadccacdbaaabaabccbabddbabddbacdcbbdacbbbcabadabdadbbbadbbaaaaacbbbadbccaaddbcaacbaadcaaadaaaaaacaadacabdabbcddddbccdbabbaabcdadcaddcccbbcbbcccbcadcbdabcacadbcdbbccaccdaaaaddcacdbbbadabdbbdddcacbdadcccbdabbcdaabdcdbccadbdccdbbdaacdccdbbcbcabbbcdcddadaabbddbcdccacaabbbbaaddaccbaabbdccaabaccdbdbdacdcdbadddbcdcbacbbdacbdcadbbbbadaabcdccbaddcdcabbcdcccabaabbcababaabbaabadbaaacdbcbdbbabcdabcdcccdcadadaabdcaaddddcdaddbdccaacaababddddabadcadbaabcdadabbbbdddbdadcccdbcadbcadcacccaabdabcabccadabcdcddaaababddcccbbcaccacdabdaadabdbaacbcbadbaacabbadddadabbcbabcbcacbcddbdbacdcbdbcccbcdbacbdcddbdababdabdaddcddabdcdbdcabbdbdcaabdacaadaacddaacacacddddbcabbbacbdaccbcbaccbcbabccaddacbdcddcccdabadcbcabaacdacdddcbabbaddcabccccaabacccabbccddddaadcdcddadacddbcccacdbdbbdabdaddbbaacbddccadacaccbbdaabacccdddadcbadcbddbcabadddabcddbccbbacacabdacacbcbcabcabcdadcabcddccbdcddccdbbcdadccdbdaaccdddbbcadcdabbbdaccdcaddbbdcbbdddcbbbcbbdaaabbdcddcbbdbaddcadcbdaaddcababadbbcdcadcabbabcbcbdcabcaaadaadddbababaaabddcacbdccbbdbdadccbcbddccbabcbaadbbbacdabcdccbacbdabcadbbbcbaccbbbbabbdbcadababcbdddbbcbaccabdbddbbcadcdaddddacadadbabddababcdcdaaaaacbcaacdbcadbdabdbabdbdcddacbbadbbdbabbcabcdbccdbcbbdaacaaacddabcacddbcdabbcdbbacabdbbabbbabadcbccccbcaadcdcaddaccccadbccccdcabddbcaacdbadcddaaabddacbbcbcbabbddbddcbcaccabdadabbbcdaccddbdcbbcdaacadbdacbcbbaacdbbbdadcbddccacbbdbdacabdabddccbdcbbcadbbbdadbbbcadaacbaadaccdadcbbbbcbdbbabaddddadcaadadbbbbbcccbadbcaccddbabcdadaadaccadaccddcaacabddbddadbcabdcaddadabdddddbdddcccdbcaccbbbabbdcdadbdbcbdabcbadbacbbbadddcdbabcbbabbbcacccabbddabbcaddbaacbcbbdcbdbaccbcaabaacdbddcbcacdaddacacaaacdcbacdabbcabadacdaabaccdcbcadbbdcdbcdcbcbcbddcbbdbdbbddaaddddabcbcacccdbbbcaaaccbcbccdcccdabdccbdabdccccaddadcddabbdbbbccdcbacadacdccbccdaaabcbcdbaaacdcabbcbacccbbbaabdbcbcabdabdaadabcabccddcabababbdcccddababcccbbddcbdbccdabdcdbcabdbbdcadbbbabcbbbabbddadbbccacbabbaaacdaddbdbddabbacadcdacbaabddcccbcddccbadabccaabdbaaaddacadcddabaabcaaddbaccadabcadcadcbbaabbdaddddcdcbccbcccdbcbdccaacadbdbcbbccccdcccadbacbcdbdbcdcbccddcbacdbcaccdccaaaccbdabcaabdbaadbaddaaacbacacdccadabcdadaadddabacdaabbbdbdcbcbcdababdaddccbadbbcddbaddbdcddcbcdaabaabdbcabcacccddcbaadaacbdbdacbddadacbbaacbabdaccdbccbcbdcbadcabaadabbadccddcdcaadadadabadcaccdbbdccaaddadddadcbcbacabdbcccbabcccdabcdbbccabdcdcccdbaabdacdbacacabddcccacbdbccbcaccadadadbcdcacbacbabccadbcbbccdbbadabbcbbcbcaabccccdaaaaacaaddadabbadbcdabbcaabcddabadbbbdbbbabccdcdbbddcdabdabbabccadccbdbbabaacaccadbddccbbcccabaadadababbdbdbabbdccdbbadddcbcdddbabcdcbcadccccaadcccdccbdaaccbddcddddbdaabddbcabbddbacccbbabbcaacadabbcaaccdbabcabbdcccbdaabaaacdaacacbbacdabccabacbacbdaabcbaddadacccdbcacdcadbbaddabccdbdddbccdbccadbaacbbccbdccbdacbacdcdccdbacabcdcbcbadbadacdbcddcaddcdbcbbdaadbdacbdbcbcdbdcbaccacccaadacaadabbccdcadaabccaaacdbdbdcabbacccabbbbdaaccccbcddcdabbcdaabbbabdbacbbcaddbbddabccdbadadcabdbcacbdcbbdcbccbaadadadcbdbccdabbbadccaccaacbaddbbabddacaccbadcdcbbacdabcabacaabcbacccddcccdbcddbcbdccaaabbadbdaadbabacbcdcdcbbdbdaacdaddbbcbdbdbbadbacccddcbdcbbcbbadddbbccbcbbbdbccabdcaadddddbdbdacadaabbbcccaaaabccbddababcdcdddaabcbaaadabbbdcccbcbdabcdccabddcbcbcdddaacacbaddcbaddadabbbabbacbcdbadadbabdaacdbcbcabbdadacdbaccbbdddccbcabdadcaacaccaadacabacaacadcdbbccdbaacdabbcdddbbddbbccacccdbdabacdcdabbdcaadcacccbdabddccdbcabcadddddccabaddbadcbbbddbacdcabcbbcdbaaacbdbcaaaddbddccacdddbcbcabdaddcdcddbdaaabcdcabcbbaacdaadaabdbdaadbbdddbdaacaabdcacbbdcabddbacaaaadbbddabbcdccdaccccabacbcaccccdaabbadddcbdaabcbcaacbdaacbadcbaaddbcdcbabadbacdbcdcddacaddacbccadbbcabbcaaddbdbddabbaabccdaaabbbdbbcaabbacdbcbbadcdbbdacdbcdaadacdaacbbcdcddadcaccdddaccccccdcdcbadacdbdacbadbadbaabcdcdbdcdacdbdbdabbdddcdadabacbaaaacdccaadbddaabaacbdbbccdbbcdabbdbddcababacbddbadbbdbadcdcbbbdbacaacabcdccdabccacdbbcddadbdabdacdbbdabdccdcddcdccbbdbcbdbbdcccabdbbccccacadcccabcbbcdadcbcccbadbcadccbabcbbbdbcbbccdbddaaadbcdcaadaddbcbbbcaadadacaabcdbabaacdbabbacddbbbdadaacabddcadcdadddccaadbdacddbbabdcaadbcdaaabbabdbddbdcacabaabcaacaccacbbccadcdddcabccbdcaccbdccbdddbadddaabbdabcaaaacabbbdadccabcaabcdbbdcacdcaccddbbcbacccbcabbddbdaddcdabacabddcccbbddcddaaadcababbdbdabccbbcabdbbdbcbaabbadaadccddbbcccbbccbbddaadbbbccadacdcdcccccdbadcbdcacdabcabcbdcdbcacddddcccbddabaacbbcdcacbdcccabbabbaabdbacacccaccaaaacaabccbbaabbbbcdcabadbddcddcddcbabaabbbabacddaadababdadbabddcadbacdbcdabbccdcbdddcaccadabdcdbacaccdabddabdcbacbaabaaabcbdaaabadccbbdbbacdbbabbdcbadabbddbcdbacacbddcdbcadacadbcaaaabacabccdbdbdddaabccccaaacacbbbadcacacaabaddddacabcccddadbcabbbabacbcccbadccccbaacabacdcbddbaadbadcaabdddaabdacaacacaadcbdabbbdddbcddbcabbbdddcdbddccccddaaaccabcbdcccdcdddcdbbbbbcbdddadbbababccacbcbcdcaaabcddabdcbdbcbcaaaadbabbdbbcbbbbabcdaabdbaaadcaaaababdaadbcabbbccaccaccdbbaddabdaaaddbddcdabcdadabbcaaccbcdadaccdbadbabbcabbaddcdabcadcbcbdcaacbcaddbdccadadccbccadaaacabbcabcddcababddacacbddbcacaacdccbaabbbacdbaadbbbbadbddacaaccddddadaadacdccacdbaddadddbabbaadbcdabcdcddbabaccdababbbcbcdbbcaadbadadbdadaacbdabccadccbacabacbbabbddabbcccccdcaccdddaccbbcddbbbddadbdbaabbdaadadbaacddbddabbdbbcdaaaaddbccaaacccbdccadabbbaaddaddacccabbbaaacccbdddcdbcdcaccadbccddcaaddbbccaaccccdbbadccdddbcdccdabcbbadbbbbacbbcdcbcdaabccaabbdbccaadcdacdbbacbccaababdaabccdcadcaabcccabaaddddbadcbabbaaccccdacdbacccdaabacadcabcbbdaacadccbcacdadccdcaacbabbcbbdccdbccbccaadddaddcbbdcabbddbccccbbbaddbbcdbdbbbbddaadbbccdbbdabddcdbccdddddccabacbbaacadcddccbcbccaabcabbbdacdababacacbdcdcacddbbcccbaaaadccabcaddbabbdcaabcdbbbcddabcadabbdbccabcbddacbcaabbdcaddadbdbacbabadcacaacdabbacacbacbcabadcbaadbaaabdbdaaaacbccbadcbbbdbcacacdacbadabdbddabbaabaaabcbbcbddbddabcaabbbbbaccbcbcddbadcdcbdadcdcadadddbadbbbbaaabcacbbcdbddabcaaaadbbaacadabcddddacdcbcdadadcbbddabbbacbbabaacaadbcbbabbcaacaadadbbabdacabccdcbacaabbcabbbaadcbadaadccdaccaddcbdbbcdbddbccbdcbcacbdbdbcdccadcbbdddbaadadacbbaacbcdddabdcaabbddaacbaacbdaccbadbbacbaadbbadbaadbcdccaadabdbadabcbcaadabaddcbbcdbdabdabbcddbcbabbcadbdbabdbcbcbacbcdaacbaaacdbacabadcaaaccdbcbbacabcdaadbbadddacbddccaddcdadadadcccacdbcbbacdcdcdcaacabcbabaddadadbccbbddccbdbbadadadacdcccbbcbddadacaabcaacacbadddaaacaabadcdbacacdcdcbdcaabccacccdccaddbdbbcbdddccabbdbdaaabdacdccdabacacadaaaacadaccbcccdccccdbbddabdadacdcabcaaddbbcabddcbcccbabdbbcbadccccabcbdabcdcbccdadabdcddccadbbcdcaacacddbbdcaacdadcdaddddddddddbdcbadccbadbadbdbdaaaddddccdbcccaccdddacacdcbdcabadddbaccaccabddddabaddacddbddbabddcdaaabdcaaabaaddcdcaabacaaadcbdbbbacdaccbbcddbbcacaddbdbabccdacdbcacdbcdccaabccbbbdbbdbbdcaaaccadbdcdaadbcbbcdccccdbcdbccdddcdadcccadcaacdccdadaddcadbcdddbdbabaadaddaadccdbbdcbbcbaacaaaddccabdcaaadddcabddcdcadbcdbcbcabadbddbddabbccbcbacdaddbaadadacddccdbbabbbaabbdabcbcaabcbcddddabccddbcdadacaacbacabaabaacdacdbcabbacbacbdcdddbdaadddcbbadabadaadcbdbcdbbabdcbdcbadbabbcddbbdabbcbabcccbdadbadbadbacabcdaabacabcddaabbccaadddabddbadcddbcbaddccbddabaadcddbcccdadcbaaadaadccccdadcacccccbdabbbbcdcadcaddcbddbaacdbcccbbabcdadbccdbdaccbdcbadcbbcbabbbadbaddadcaaacacbdadcdadbddcabbcdbddbcdabcacddcddbdabcadbbdbabdcbdccbddadcbddcdbaddadcbbccaddddadddbdbdbbabacbcbaadbdbaabcdbdaadcbcbcaccdbabadcabbdddcbabadaacabaabbabddcadcadaabdcdadacadaccaabaaddcdcbabbcbbbbabcdbbbcbdcccabbdbddbcacdcacdaddabddabcbdcdcccbdddcdbbbcdbbcdccdbdaddbccdabbdcbbbddddcbdabddbbdbddcbcddcaaaddaabacdaacadbdddbdddcaacddbbadabccbaacdbdabcbddccbdcaddddbadabbcccacdbacccdbbcaabddbccdacaadddacdbbabdcdadbaaabaddaacdaabdcbbadbadbbaabbbacbcabbbbcbbbadcddbaadccaadabdcbdcdddcdbbacbdaaabbbccaaacbdccdadbaacaaadaadddcbbdcabddccccbcbaddadabdadbbbdcccabccaacdacdcbbcabdcbbbabbbaddbcabbddacaaacdbdacaccaaddaaddccbacdcabbddccacaccdacabdadacbcdbaddcdcdbcadddadadcccacaaabcbbbbaabcdbbabbdcadbacccababdbdddaddaccdddcadbaadddcdddcbcacdaadbadbadbccabaccbddbcbdacbacbabcacaccdcbacbddcbbdadabaacdcbdaabacdaccbbdaacaadcbdaacccccadabcadcacabbaaaacacdbcdddcabdadadadadbdbddaccbdabdbbbdadbdccbdbdadbbbbacbddbbcbdcbdcdabbdbbcbaddbcdcdbbdaddcaaaddcadcbccabcbbbbdabcddadaabdcdadbdcacbbaacbcddbabdaddddcbcdccdabcbcbbbcacabcdcbbbccdbcaadbaaabdcccabadaddcbcadccadabccdbabcadcbcaddabcabddbbaccdcdaaacbbbadcdbddbdbcabccaabbabdaabaddccaabbcbcdbcdbcdadcddaacaaacacabdaaaccbadbdbcbcadcddbbbdcdcbbacdaadccbdbbcbccbcbdaacababcabdaabbddccacbabcbacdabccdaaadbccddadccdcbdababdaadcaadbcbaddabdddaadcdbababadcdadbcbccdbddbdbacbdbcbacbddbdaabcaabadcddbcaadcbccbaccacccaacaabbdcabdcbbcabccabdbadacddacdccbdbaccbbaaacdabaccaacdbdcbccdbabccababdcbadccdcdcddadcdacdbcdddacbbdabcbcababbccbcbdcbbbddcdaddacacabaacccdbacdacbcaddcbccdcbdabaacdabbadcbccbbbcbacdadbbababcbbbabdacadbacbaaadabdcabbbacdacbdcaabcabdaddaddbdddabbabaaabaaccbacccbaabdaaddabbbaadccddbddbdcbcbcabbbdbadcccbbdacddbdbbbdbcdcccacdbbbdaaadbdaabdabbdbbbccadcbcbbdabcddcbcccdcbcaacaacabcbadcccaabbbadaabdcadcaccdbabdbbcaabdcabccbdbdddcacbaacaaacbcdacbcacccabdadccbcccdbdbbdadbbccccaaacccccacdaccbbdddbaccbbbdcdddcdadaabdcbdbcdddbcdbaadabbbadddcbddabdaadcbaadbbdbbabdcbcaacbdadababcdbaabcdacacbaddabdadddbbbdbbbddababaabccddaddbabbadbcbcabdbdabbdbbacddacdbadaacbadbcabbccddcccabcdbdacacbadccdabaacadbcdbccccdacbbbdccadbdcdbbdcbcadcbccdcbcccadddabbabcaddcadbabdcdbbccbdbbccabddacadbbcbddbaaaacdbbcaddabacbcdbdddcadbaacbdddacacdabbcccbbcdaabcdacbbacdddccddabaaadcdccbaaaadcbdcdbcadacdaccbcdcdbbdcbbbbbacacdbbdddbaacddbbaabccbabaccbadacdaadccdccddcdbcbccabaccccdcabcbcbdbdabcbdaddbdcbbcccadadadadbdbabcaababdbdcbadbcccbbccaaccaddabbaabccdbdcbcaadbdaccccabcadaccaaccccdbddbbcdcdaadbbcdbbcaabaadcddcbcacacbacdbcbacdbbbdcdcbdcccdbccdbaadbbcbbbdcadbbadadbcbaadbdccdbcbdcbababddaaabcacbcabbbdcdbccdbcddcdddbabaaddacabdaaadbbcbbdabaaddacabacbcdaacddabccbbdadbcccdaabccddddbabcadbbdbccaadcadbadbdbcbcadaddbababacbadaaadcadaccbbadbcabbabccdcbbbaaaddccddbccbbdbaccbacadbaacdcadbcdcadbbbdadbaaaccbddadddcaadbbdcddadbbaaaabbcbccbbdacdaddbddbdaddaaacdbdcdbdacdccddbcccacbcbbbbbdccacdbccbbbdddaddacdcccdaabadbbababacabccdbcaadcacbdddddcccbaadbbcbaddcbaaddbabaddccddabdbbabdabcdacacccdcaaabbaddcaacbcadacdcddbabdbddbbaadaadcadcacdddabbaabaaabadcbcbdbcabbdcbcbbddacddbdcdabbddcbaaacdcaadbabccdadbdccbbacdddbabdcadaccddaccbcbccadcddabadddcbdacbcdcdcdddacbdcdcaccdbbcacbbaaaadcbddbbccbadacacdbbacadbbacbaadbdacabddbacdcccabcdccbaabdbcccccabbddabddabcbcbddaacdbbbdabdadadcbdacdccdacbaddccaacacabdddcddbacbdabdbabdaacdabbbddccaccddbdddbaacbcbbdcdcbdaddbbbcaacdddacacbaddadbabcccdcddadbcbccaabbcbccadaaaabbabcdcaccdacdbbadbdbbbcdcbcaabdaabbaaabcbabacacdbcdaabbbdbcbaadddacaaabaacaccbaacbadadabccdbbcdcbdcccaacbbadcdadcadadbdbbccbadddbdcdcbbbdacdddcdcacabcbdbddcbdbcddccadbdbacccbdddddcddaadcacbbaccbaaabbaadbbbbdbbbbabcdbcbbabacdcbddaaabcbdbaccdabccadacbcaaabbcabbcddbabddcdbabdadcdbadaabdccacccbdbdcdacdabbddadbbdaddcbbaccbadcbdaacaadcdabcabaabddaddbccababaddbcbcddbdbbdabdaabacddbabdaabbaacbaadbaaddbccdabacdbccbbacbbcbbbcdbdbadccbbabbcbddddadacdccdccbddabacbdcbcbacdcbbaddaabccdaabbbdcbdbbccabccaabbccabdadadbbbbbdadbacbdadadacdadcbbbdbdddddcaacdadaacccacbadadbddbdcdcaccacacabadbaadcabcabbbaaacdaaabcabbcbcdacbbcbabcccdadcbbdbabcbbccaaacbcaaacbacbcbbdacbabdbbddcbcabcbcaacccbacdaaadcdcddcdbdcaacbbccadadbcdbbcacaccdcabaaddbbccabcccadbaaddbacdbcdcabcacabbabccdabbdabaabbcaaccabaacbabcdcaddbacacdbbadcbbbbdcaccbcddcccddbaadbbcbadaaaaaaaaadbaabaadddaabdcbbdaaacacddcabbbababccdabadbadccbdaadcdacaadcaccabadabcdbbbbaabcaddbdacbdbcbdbcdbcdccddbdddadccbaddcbdaadaadddbaccabbddccdcadabaddacbdccaaccadbabcddccddcdbddadadadacdbcddaadaddbcacccdadbdbbccbccdacccdbcddadaaabbbadcbcbcaddbbadbbccbcacbdddadbcadcacacadcadcdacdaabcacdbcbcaaabdacbccccabbbbbccdccbdbcddddbabbadcacadcabbabddcbcadabcbcccdaabdcacccaadcbbcddaacdbcbadbadaadaadadcccbdcdaacbbccbdcabbdcddbddadacbbbdaacaacaacdbbdcaaabaabdbabcababbbcadaabccddaacdbabbaaaadddadddcaddcdbcbcadddbcdcbdabcacaccdbbcabddacdaddaaacdcbabaacddcdadabbdcbcabccbccadcaacdbdbdbdbcadcbbbbcaadddabacbbdbaabaaaaabdcccbbbccdcbcabddcdcccbdcdddadccacaaabdbcccabcabdaaddbbcdbddcbadacbaadcadadbacdaaacdaccccdbadcdcddccacdbaaabacacdcbbdccddaacbbadbbaabbadabadbcdadabcacdadbcbadddabddddaaadbdabaaaaccbbdcacddddbcadbacdacbbadaabbcdaababbcaccbaabdaccabaddddddcbbddcaddabddcbbbccbaaadcbddaabbacbcdacabcabbdbcdbaacbddccadcaacccbcbabcaaccbddcccbcacacaabdbacbddbadbadcdbcbcaabacdacadbcddbcdbdadaddcaddcdbdadccbadbacccabddbdacabbbcddcadbbbaaabbccbccabcdadacbaaacaaccacaabdcbcdaccabcbdbacbcbdbcbdccaadbabadcdcdcadbdcbaaadbacbaaddbbcdbadbbcddbdadcdcdaaacbdcbdaddacbadcdabcaddadbcbcaacbcaabcbddbadacadadcdccdbcacdcaadcbadccbddbbbacabccbbcbcbaddbdadcbcdadcdcacbcbdcbcccbcdabaadcbccdbbcbadbbbadcddbbcdcabbbacdacaabbccccbcbadddabbcbccabddcbbadbaadbcbddccabcaabccccddccadbdaacbddaddabdddabbacabdacadbccdbdcacabdbdcdbdccadbccacbbbbbcddccddbccdacaccbcddbdcdbbadabcbdddbdcbabbbcacacbdaaabdcdbddbabccbbcabbbbaabadaadadcdbdbcbdcdcbcbddcacabcbddcacaddabcbbbbbcacdbcaaabbaccbaaacacaacabbbcdaadacccbaadaabbcbbbaaacbdccdbdcdbbadacbdabcbaaddaabbadacabcbdcdddbadccbbbabadcaccdcbababcdbbccadcdcbdadaaadbdddadcbdabdbdccdcacbbbabdbabccadabdccaaccbbbbbadacdabdddcaaaabbbdbdaabdbcbdccdbdbdbdababcddddadbcdbdadacbdbadddbcbccaccbddbcaabbbcaadcadddddbdacabadaabaddcbcadddaddacadcbddddadbccabddbcaaacdbbbccbbdcbacbadaadbddaababccdbdacaddbbbdbbdbaaacaaccbabbacdaaddccbaaabcbabacccdcabbcccaddcacabcabadaaaaccdcaabbabdaabbdcccaadbbcaacccbbcaaacaaabbdcbbdbcbabaabbacdcdacbdbbdacabacadaccbaababccdddcabcdacabaaaddddbdcccddadababcaacdabaddcaabbcdabcdaabaaaaddabaccaaccbbbdbcaccdaabdcacabbbcaacdababdaabadadadabcbbbbddcabbabdddccbdcdabddbabadbbbdabcabbcabbcdccdadcadbabaccbdcdddcdccdbcabbdcaccabaaadcddadcbaacdccbcbdbdccbcadddcccbdbabcacbcaddcbdcddacababddccdaabdadcddbaabbdbdbbcccddababccdbbacdbcbbcaaccacbcadadadddbddbddacacaabbaccbbdbdadaaacaacabdccccdaddcacddbbbabdcaabaacbacadaddbaadddaacaccbbbbaaadbabaaadacadaadcdaacdacaacccdbddabcacacccadaabcdadbcbdbaadcdcbacdcaabdaabbbaccccacbbcdadcabcabcbbacddacabdddaddcbbbaccdcabcaaaaddbccbbdbbabdcbcdaabddaadbbddaacbbbddbccadbccabadaaadaccdacdcdaaaaadcaccbbccbbcdccdacdcdbdbaabdccbadbddcdccccdcdadbdadaadcaaadcccdaddaccbcaadbbbdbabbadaabbaaadcdcdccdadbacaadbbcdcddbcaacddacbaccbdcdbddabcbaccdccacbcbbadaaddacadaabdddbcccdcdbddacbcadddcddcadcbdbdcbbaccdbcbcbbddbababcaadadababccdacacdcaccadccdaacaddcdbcbdbbcbccbaddcadcacdbdbcbcacacadaacdacaacadbbdddcaacbbbbabbabbcacbcbabbdacbcaddaddcdabbacabccbcaacadaaacdadccdcddbabdcccddbccadbcabcccbbdbdcbacadadadcbdcdcacacadbcdbcccdbacbdcdddbdbccddcbcccabadaabacdddcccbccbababbbabdcbbccddaacddabdbdaccbbbdbbcadadddcbcbaadadadababcdbacaadadbabddbddabbcdabdbacadcbaadcddacadbbabccbcbaaabcaadbdaabdcaaabbbdaacacacbcaaabcabcbaddbdadbabccbdbaaadbcdaabacdbabddcbcddaccdacdadabcbcdacabacccadbbabccdadadccbdbdbcaccdaddaccbcadcbbccdddcbbdbccacabddbccddabdabdbdddcbdbbabaddcadacbbaaddcdcbbdcccdbbabbbddaaaaaabcdddcacabddacbcbbccbccacbddcddcacaabaaccbbbaccbaabaadcadaababaddbcbcaaabbdbdabaaacaadbaccacacbbdcccccccbaddaacbadcadabbabbdbdddaadccabbdbbcbaddacdcaabdcdacdddaccbcbccabcddcbdcadcdaddcabdbbdbdccddabcadccadbdacdbaacadcddbcadabcabccdcbbabbaddaaaccbbdcbacdbacbaaaacbacbacacabbdcabbcbbabbcaabbaccccbcacdaacddaacbbdddcdddabababacdcdcdbaaadbcbabddbdbddbcdabcbabdabbaddbbdbdaacddcbbbdabdcdbdcbaadcbcbadadadcccbbaabdadaccaadadccbbdbddcbdadaabdcdacbbbddddacacccdcdcccbdacdbabcdcbcdaacccccdddcccdbbdbadbbbadacbddcbbcabbabbdcddcabcdbdabcaaadbaadcabccbaaaacbcabcbaacdbacbccbbbdcbcabdccbdcaadddcdcbabcacbcdaabcbadbccaaaacacbcdbdcabbcdbaaccabddbcbabbdddbdcbdbdbbbddbbbbbbddbddabccacdbcabaddbcabbaaaaddbddabaddcdaaabcccbdbbaacadbddadabaabdabbaaddbcbbdcbcbdcabdbdcbbcdbaccbaaadcdadcdcbacdcaadadabdcaadbcddccbbccaacbabadddbcdabbdddabbacbbcbdbbdaadbddabcbbaddacdacbbcbcbdcadadbdcddcadddcabbaadcdcbaccabbdbaabdbbabcadaaccdacdcdadcabddbdabbbbbcdabaaabbdcbddcaadbcbbacbccdbacbdddcdcbbbbcbacbdcdbaddacddccbdcbcbbdddcdbcabbbadabcdccddcadcccadadacbcbccddcaccdcddbcbbddabbcbbaabbcbdcccacdbccdcddabcdabbacbcccabdaacaabdcbbdbccacbcbbddccbdaaccabddddddcbbccdbcccadacbcccbcdaabbabbcbcababcadccccbaccacbabaddcadbdbbadacbdbdabbcaadbdbabbadabbccbcccdabacacaadadacbdacaacbabbdcbabcaabcbcbbcaccbaabaddbccabbaabcbddabcadccdadaccccddadcaacdbabacbddccaabacbcdababcccaddccacddcadbaabdbcddbaacacdbcbddbacdcadbbbbbbabddbbdbdcdcccacbbacdabdadabdaddacacaacabcaabcbcccbbddbabccdddbaabdccacbacabaddaaacccacaadbcaadbabadddacdbabcbbcdcddcadaaccaabadbdbbcccbdddcacbdcbbcaccacbcccadddccadcdabbdbdcdaccddacccabdabbcdabbdbcadcddbdcdcbbaacbacacdbccadbcbdbdadbbadcccdaacbcbadcbdbcbbaddaadbccdcbccbacadbacbcdabcbaaaddabdacbabdbbdcccbcdbbdddadbcabccdbbacadacbbbdaddbcbaccbbcdcbacadcdccbcdddddbabacadaadcaabdbcdaacabacbadacbacabddacbabdcbbdcbabbdbdaacacbbdbddadbaaacdbbabacbaabdcbaddcbcababcaccbcbbcccaacabdddbbabddcddbadbabccdcbadacbcccbcdcbdbdbcabdbbcdccdbabbcadbacdaddacccbdaabdaddcbdbbabacddddcdcdcabcdbdcbcddadaacccaaaabcabbbcbbaddbcacadaabdabcadbdcddbbaaabbacaaaacbccbadaadbdbaaddacabaccdbbdcdbbbbadadbbddccaaaabddcadccdbbcacacbcabaccadddadaacadacabbcbaccbcbaaddcbdabdbaabccabdaabaaabccacaaababbbddcaadababaaadbaaccadcaddaabcdacdbdcbcbacbacbcdabdddadaaccaabacbaddadbabaaddbddaadccdddadabbabaacabcaccbddbcbdaacddcdaadbdabcacbbdaabdadccdbcacdccbcdcbcabaccadbdabacbbbddddbbdbcbcbdadbaddcabbbaadbcdddbadabcdbcabbaacbbcbaaabdbabbddababacabaacdbddcbbadbcacddaadacacabbddacdcbabccdbdababcddadbdcbbabbdaddcddabbbcadddbcacddcbcdcbdcdddbbabbbaddaabbcdaddddbbbcdcbbddcbadabbbbdcdababadcdcdddaaacddcbccccdcdcdaacadcbbbbdacacaaccddccccdcacabccbbbdbddcacacaabddcbdbdbcddcccbdaabbaabbccbcbadaccadbaddddbdbbacababdbadcdbdcacaabaabbcdcaaaadbaabacdcddcdcdbabcacaadacbccddaccdcdcdaddcbbcbbddbdcdbacadcccaabdbbacddaabadccbcabddaccddcaacdadbbbbbdddbdbdbbabdcaaadbbbbcdadabbacbaadbcddccabbdcaaaddbacbdbdcccbdabbadcacbabdbadbacadbabadabacdacbbbcddaabadaabdccadccaaddccdcaaacacaddbcaacdbacadddccdbccccdbaaabdbdbbddacdcbdddbacddbccbadabdadddcdcddbadabbbcabddacbdadbdaaaadbccdbcccbadbccaacbbbcbdaddccbdcddccbdcdabaaaccabbdaddbcbcddbadcaabacdcdabddcccbdaacdcddbacddbbcbacdcdbaaacaaacdbcbcdabadacdbbddabcddddccbdbacbaadcccbacababcccddabbbaddbbcdbaababddccdbccdcdbcbcddbadcbaacccbdaadcabacadbbacadbabaabcdacddcbaccdaaaacddbbaccbdacbcabadcbabbaaaacaaabcaddddbcaaacbccdabaaaacdabbacaaaddaaddcdbbcbdcbbbccabbcadcdddaaacbadabdbcdcccdcbdcdddadaddaaaacccbadccabdbdbbbabadacacdbcaabbbbbdcbbbcddcacbcbddabcadccbacaadaccbabababdabacdabbaaccccbadcccacdbacbddadbccabcabbaacccacdacbccbdbabccbcdddadcbdccccbbdcbccddcbaccbbdcdbbcbaabaadaddddbcacbddcacddccbbdbcbcabadaddccdabbdbdcbcbbaaacadbbacabbcacadbcddbbdddadabdcddcddcdaccdbddccadbbbaddbaababdbbadcadacadcacbdadccbbdbacbcbdadcdbcdacacdadbcddaccdabcacccdabcaddababccddabcbadddaabdbdbcbaadaacddaccabdcbcabdadddbdcbbbbbdcdcbadbaacbbbbcaadcdcabacbcabdbbbabdcbbbcdaacaddbaaadadcaaddaccdaaabaabdbbbcaabbcbadbdddadbacdccbabdabccbcdabbabbbbaaddacdcdddccbadadbcaadacbdcbabdbdcadbaaaadbccbcbaddcdccddcbbadcdabdbccccabbddbbbcbaacbacaddadacbdccaacccccbaacdbdaadaabdadadbccdcddbdacbcabbbbdabdddcacbacaadcddaccccacdacabcadddacccbddbcbcbabdcbcacdabdccacabdadcdbabbdbadadddabdbbdaddddcaaacabacdcdbababacdcacadacabdaccabacbcdadcaddcaabdddaddcabacaaacaaabdadcbccaccabcdbbddabbdcccdbadddacbaadcbacdbcbbcdcabccddcdadddabcaccadaaadbaaabcbbdadcbcababdadbcabaacdabbbbdbadbddcbdbaaccbbadacacacdcbdbcdbabcdaccaccbccacbacdbabddacdbacacabaaabccaabbbbddbbbdbabddddaaccbabbdbabdbccddbdbdaccbccdbcdadaabcbbdddaacbdcadccdabacdaddbbcbbbbbbdaaddbabbadacdabdcadccabdadacbaddbdabcbbddddccddabcdbbabddaddddcbadcabbacabaddbadabdddcdacaabdbaaacbccaabdababcdccbdddabbbabcaddadddadccbabcabacacbccadcbdddbdaddacddaabcbccadbccaacccddabadccbbadaddbbdddccccaaaddbcddbbaddcaaaddbddabcabaacbaacbdbcdddbccbdadccadbbcabbaadcdbbddadadbdddcbaadbaabbaadcdadabadcabdcadcaacbbaadccbbcaadacabadccbbadccadbdbaaddbaddccbcdcdaaabddbddbdabdabbbabdbcbaadbaacdcadcdabdcbccddacabdbbcbcbcccdacbdbadaacabcdcbcbbadacbdccaaadaabadbaddadacaabbdabbccdacadcbcdbcbadaabcdccadcdccabdadbacadddcabcdbccccdcdadacdaddbbababacccaaaabacbcbdaddabcacbcadadcbddacaabddaddbbdbadbbccbbaacbcdbcabbdbabdbbbbabcdaabaaababdccaacabbcccddbadccadbcbcbccbcaacbaacbbcaadccbddbcbbbbacaccdacddccabccabdccccbbcdcbdaaadabdcacdaaabcadcdaaaabbbcacbdcaabcccbaadaaaccbbaaadbccabbaabacccdadcbbcddcacddcabadbcdcbcabbcdacbdddaabcdbcadaababbadddcdbbbacdacadddcacdddccdacaadadaccddabaaadbcaddaccadaadbbbcabdaaaadbabddccaadcccccdaabdacbcacdbcbdaadbabbbbdcadabdcabbacbcdcdbdbacddddbdacdbcacbdabbbcbabbaababcbacbbaaabdadcccabbcbaddbbaacbabaabddccaaacbadbcadbcdcaaddbdcadbbacccbccabdadaddbcbdccbbccadcbcbdadaadcccacdaadabcbaaabdbddddcaacbadddcccadacddccbdbbcdadbadbcbddadcdccbbdabacbcdbcbccddaabdbcbbbbaadaddacdbddcbbababdbaacbbcccbcabbcdacaabadcbccccaabdbdadbbabbbdbdacdbbaacabaacadbccabcabcacdaadccaccabdbccccbacaacbdcaadcbcbbdadabaaaadaabcbdcabaaccbbabdcaabdaddbaabbbadbdabddbacdbacbbabbcbbabbaadcdaaaacacbbcacaccbabdabcddadcbdcbadbaababdacbdbaccccdbbcbacbadddcdcabbabcdccccadbbbbdbcbcccabbcdbccdabbcccbbbbcbcdcdaabccdddadbacdbcbdbcacccdadadcdadccdbdabcacdacdcdbbaddbadaaaadcbcaadddbaacdcbbdacddaadadcdbdbccadbacbbadddbcabbbddbabbbdaaacbdaaaccbadcdcaacdcbcccacdcadabbdcdbdacbabdcdabacbcadcdbbcbacaadcbcbadbbdccdbdcaccdabbccbcdacbcaadbbabbbbdcabcaabbdcadabadddcabdabaabdbdcbbaccdaadbdbcbacbacbccddddacacabddabdabccdddacbcaabaadbdcbcabaccbaaccaabcacacdcaccabadcbabdabdbcdaabbbddababcdcddcdbbcdacbcdaaacbbdcbdaaaacacbbabcbccbdbbcbbcbcabccabddcadbbcbcbdddcdccdadabdbacabdcbadddaaadcbdbacdabdabdbdcdbdcdbccaddcccadacadaaccaacbbddabbddccaadbadcacabccaaddcabaacdcadbbcbabbabdddccbbdbdbcbdabadbbdabcdabddcddcdcccacbbdcdbddbbaddabddabacadbcbadbdbadbdbbcdaacaaababaccbdababcacbbabdadddbacccdacdcaabaddaaadacbddbcdadccacabbbaddaabdcddcbaccbcbccaddbbcadbcdbbccdddadcbdcaabbdccabadbddccdaacbcbdccaacabbabbdccaadaaacababaaacdabcddacddbddddccdddbcabdacdcbbbccdbabdccbaabcddbbcbbaaaaabbacbadcabdcbdaabbbbbcdddddabddbbcbbbaaadbcabdadbadbcdcdccaccddabbcccdabcadcabadbcbcbbcdbdddbbbbacccbaddaaaacdddbbbbbbcddccabbbdbdcaacaabbcddccbaccbaacdbaccdbddcbdadcbcbbabacdbdacbadbcbcadbaaabddccdbacccdcbcdacaaadacaaadbcdccdcdcbdaddadcdbabbaacccdcabacacbbcbcbddadcccccbbddcbdaaabadbbdbbadadbaadccaacadbdddcabcbdaacdbcbcdddacacbdbcdcddacadbbdbdddbddbbabbdddcaaddaddaadccdabaabaaaacbdbabcbcccddacdcaddacddcbcacccaadccddaadcbadcdcddabdddacbbcdbdddaddacdcdbbbcaabcbbdacdcbacaddcbabbaadbbadcbbabbadaccbaaacbcdabacdabbabcadbbbcddbadcbcdbbcbbbdbccccadbcddddcdccabcabcacddcabcdbabaccacdddccbccaaddccaacddabadbbdddacdddabccdaaccdbddcbabdcccccadcdabbcccdcbcacdaaacadadaadacbbdbbdbbacccdcbddadcbbbbbccbbbcacdadbbcacbacdbbabcdbdcadbacaaccddbcaacdcdabdbabdcbabcacbccccddddabbdaccadccdabbbbaabbdaadacbaaddabdcabdbccabacdddacdaacdabadbaddaadbcbadadcdadbbbcddabcdddbdbcbbcaacdcacdcdbacadabacabccbbabddaacbaadabcbacadcdbbdddcacacbddbadbddabaddbddaababbbadddcdbbbcdbaaaadaadabacddbaadccdcbdbcbddaddaaaaccbcbaacbbadddcbbaaadbddacdcddacacacdbcbabababcdaabcacacdabddabdccdcbaccccbbcccccddaddbbcaccabcccdababcbacbbcacdcdcaaacadaccdddccaabbbcddaadaabdcbaddababbbbdcbbddadbacacbbbdbcabcabcaadddcbbcbbaadccacddbdccadcbdcddccbbbcbbbbbccbcbdcbdcddcdcbaccaccbaacdbaadcabcdbdbdaccbacdbdcbbcaaaddabaacddcddaccdcdaaadababbdaabcbcbacaddbcdbcdbcbdccbadbbccbcbdbcadcddbbbaadbddbbacbaadabcbcddbdbccbdcdaccbdcbbbcbbadddcccdbbbccbcacdbadacddadcdaadadabdccbbdcbdcccaabdccbaaddbcacacdcccdaabcbacccbaadabcaddbabdcadaacaacccaadccbcaddabcaabbbbadabdaaddcbdadcbacabbbacdaacadabaabdaddaacdbdaadbccabacbbbddacddabbccccdadcdcbaaddcbdabdbbddbbaadbacbbdbccbdacbdcdcabcbcbdabcabbddbbacddbabaabaaaaddcaabaadacabcbdcdccbacbdbdadbbdbadcadcbdbccaacbcdadbcbccddddadabdaccdaddccdcabaadaccccdcbbbbcadbbadadabaaabdabdccadbcdcdcbacbdbaaccdccdbddcccdbcddcaddadbbdcbbcbacbbbaaccababacabdddaddacbcdbddbdcbcbacbcbabbcdbccacaacabacabcaddaadbdabccadbbdbbacaadbbcddbcbbddacbabcacddcbbaabaccbccbadccbadadacacbdacbddbbaacbbcddbadcacdbbcadbdbaacbcdcbdcdddbcccbdccdadaabddccabbdaabbcbdaabbcaddadcccbacbaabdbccbbadddcdddbdacbbbcaacabbdaacdbddaccbadcaddcbcacbaacccadcaaddbccbbcbadcadbabbddabaccbdacdcddddddacaacdcabccccbadbbdcbccbddbacbcadbaddbcbcdbcccbaaadbcdaabbcdaccccdcdcdbbaaddcbcaddacbadbccaddaabadcacdaababdadbccbadbbbdbbabccaadbdddabdddbcaccccccccdcadababcbdabcccacabdaadbdccdbbbadacbcdcbcaddaabcbabbacbddbdccdbdcdcabcacaddaacbcbaadddbcdddabbbabdbccbcbdacbbdadbdcabcbcdbccbcdadaacbbdbbdcdabaabacbdccbdbbcbacacdbabddacbbddcdbcaddaddccadaaaaabcdcdabaacbcabbdbdccdbbadbdcabaabcdcdabaaadbdcbacacdcaacadbabdccdbcdddccdbbdcabbbddacaadbbbbcdccbdabcdadcaabbbcbcabaadcabccbcdadabcbcddcaddbdbabbbcbbccbbdbccdabaadbcabdddbadcdabdbacabaaaadaddbbdddbababdbbcbbcbadbdadcddacaaaddaadcbccabcccbaacabacbcbbdcdbcabacbccddacabcbcccdcbbbbbadccbdbccbbddbdbbdcdbaaccbbaabdacbccabcdacbcbddbadcdbaccbadaccbcdaabcbbdbdaabbdcbbcacabacbcdcabbadacabccbbcadbcdcdaadacbbbcbddccbccdaaadcddddbdcbaacadabaabadbbbdacddbdccabbaacdbcabadabbddabbacccaaacbdbadbaacbbbdbcadacddababcbdccaddaccdbddadcbcbbbdaaabbadbcbcdcbaabcbbcdbdbabaaacddccdbabaabccadcbdcbbdbdbbcbbdabcdccdadcbddbbcbaaccdbbbddbccbdbdbabdbdadacddcbabacaabdaacbdccddcaaaddddccddbbdbcbbbacdabbbbcadbdacdbbcacdadbcadadbdbdbccabacbcadacddabacadaddacbaababccdcddacadaccabcdacbbaacaabdaabcddcbdbbcccabbbbdaddadaddcbbdddabdcbacabdcdaddcababdaccddccbbcbbdadcabdccadbacdccdcadbbadcaaacccdbbacbdabcbcadcbaaddbacabbcdbdacdcdcbcaaacbbabdbbbaaaaadabbcbbdcaaaaacacbddddbbdbdbbddcddcbcdddbabdbdabccbbcbabcccabcadacacabcababadbbdddbdacdcbdcdbccdcdbdbcadbbbaacdcaddacabdcaaddbbccddbdcdcbadcdddbaabccbaabbcbacdaaadbbccbaadbbcddcaaacaaabaadabdbccaddacabdbdcdabcdadadbdbbbaacbbddaadccdcbdaddbadcccbbddbaaccaabbddababaabdacdaabdcbccacbbabdacdbcabcdcdbbbadcbaabbdddacbdacbbdbcbbabadacdcbdadaddcdcaccaddacabddbcdbbccccdcbcaabbbdbcbaccdaabbabdcacbbbbbabacabadbdbcdbcccaddbcdbdbaccdacdcdcbddacabcadbdaabbacadcdabadccbccdaccaabbcbcbbbaccbabaccccbccadcbcaabdcdcbbbbabddaaabccaabaabaadddbcccdaabccaaadbdabcbccdacbcbdcdbccbdccddbccdaaabaabaaddabcbbcadbcbadccbcbdbbddadadbadcbcacadcadcabbbbcdcbcddbbbadacdcbcbdacccdcdddcaaabbdcbcbcddbacbbaabbdcdbcacccdadbcbcccbbcdbdddbbdddbccdcaaaaddbbaccabacbdbbdbbaabbcccacccbdbdaccddacbdbbbcabbacabbccacabdddacacdccacabbaaaddddbcbdcadcbddbaacbadcaacadbcdacbbabdacdabacbaabbbcbcbdcbacdbaacaaddcadaadcabbddadacadaddcbccadcadccbbcabbabcabaccddcbabbccbbdccadaccbcbddabadababbbdaddcabdccdacddcbaddcddacbcdbadddacccbdbaccbaccbcdbaaacccadbdbadcddbccaabdcadddcaabadcdcdbaadbcdbcbbcccabcbbbdbdaacddcbabadaaacabcdcddbdaddbdcabcbbddcdcbaadadbdaabacbccacdaccbddcadabdbdcabccdddcbccdaadabbdacacadcbaaacacbacbcdbcddcbcaacbcacdbbccbbacdcddccaacccdcbbcddbdbcccacaadddbcdcaadadbdbdcdadadddaaabbbcbddacaaadbacdbdaacaacbdcbccdaadddccddcbadbdacbaddddabccddadacbcbdaaccdcdcbcbbcdaadacabbcdaadcbdccadcbdaccdabcdacbaadacabaabccacbbbcccaacdadccaacbcaabdabdacbcaadcddcbadacbacaaadbabdcadcbaddccadaabbdbccbabaadcadadabdcbdccdadcdacbdbbcdddacccbdccbadcbcdcbabbabadbcddbbaacacccdbdabdbdadbcbbaaaddaaacccddacdabacbdbbbbbadcccdcadacaaaddcadbcadbcaabcaacdacaddbadaabacdddbbbaccccccbbcbcadcaadbadbcaabddbbadcadbbaaddbadbbadbacaccdbaaddadabdcbadbdbbbcabcdbaddbbdcddbdbdbdaabdcaccadabddadcbdbaccdabcbddcacabacdddbbabccabdaabbdadaabadccaddbcddbbadbbabbaababcbddbdcdcdddccababddcaacbdcccaadbddcdabacaddaacacbcbdccabdbdadbcdaadbcbcacbdbbdbacbbddddabbbbdccdcbbcacddcabacadccadcddcddddacbcabdddadccbcdccabccddaacbabdcbcccbccabaaacdbabcdcdcabcdbdddcaabadccbabbcdadcdbdddcabbbcababbdcabbccbddcdbadbdbcbcbbbadadbcaabcbaadacacdbdbdcbabddadddbbbddbcacaddcbdacccdacadababbbaadccabcbadccdcdbbbdcbadbccdcbdbbdbbbdbcabcddabdcacbababcbadaabcabcddbaccdaccaadcbcbcddbdbddabacaaddaacccadcaacbcdadbacdcdbdcdcbddbdacadacbbbaacadbddddaaaadcbdccdcadccbabacabccbbcdaddaabaddcaadddbdbbaadcaabababbaddddacaaadbaaaabcabbaaccacdddccbaccccbccbcbbbbcbaaaabdcaccddacbddccbcacbadcdbddcacadcbccabaadddacaccccaaabdbdaaddadcbbaaaabcacbadbacbddbaddbabadddcddccadacbbaaddcdbbdddcddbbbcabbadababbaacaddccccddaabcdbdacacdbbbadcaaabdacdbcbcccabddcdabccbddacccdcccacbbbaaacbdaaaabaabdcdaabddacacaadbbabbbbaddcdcadcacdbabcbcaabbbbbabbbcbdbacbcbbbbcccbbddbcdbccdacccccadddaddacaccbaaadabdbaaaabbababbbcbcdbadbacaaacbdcbbccdccdacddbbddaccacddadbdbdccdadaacdadadaaaacddaccccaacaadaabadcccbcdaddbacbabbccdbccbcbabadcccdbccbaacdcdcbacaaddcccadacdbcaacdccdbcbbddbbadbcbcdcbaadcacbdddccbdccbbccdcbbdbcdacdadcdbccbbbabaaadccbcbacdadcddbdbbccadcaabcddbcacbccabbbbbddcccdbcbcbcbdbbccbbddcbcaccdddcaacaaaddabbddaddcabcbcabccddaadadcdbabbaabcadbdbddbacdcbcbadbabbcbdaadbcbbdbcbaddbcaddddbdcabacbbddcbbdcacbacdaababdaacdbcbbcdbcbbdcdbbbabcacacbadbaddbccbbaaabdbbaabcdcbbbbaaaacddbaaababbcdadcbcddaabbbcdbddbccabbbbabbbdcdaadbbacacaccadcbbcdcdcbcadddccccabcbdbbcbcbdcadbdcccdbbdabacaacddacacbbbcdbcbcdaadbabddadbdcbabcacabacdcbcbddcbabdadbacbadbddddcbdddabbbbbbabbcdadbcbaadccaddbcdcbbbdacbbcbbabbaaddaaabdaccacdddcbdbccacabccdbddbcbcbadabbbacdadddcaddbcbcbacbddccddababdcbadccbabdacdcdbbbbcdcdbbbdacdadbbbcbddbcbddbdddcacadbaddaaaadbbccbcdbbbabdbdbccbabcbcaabcabacaaabbdabacbacabcbdddbcabdaacdcdcddaddbaaabbbacdccbababbbcccccbdcdbdcacccddddbcdcdbcadccbddddbdbacabbbaacadcbdddcadbbaadbdbbbbddddcddcddbbcaadbdbbcdaadccbaaabacaccbdcaaddcaadabcdbcbccbdbcdabccaccbcbbcdbccdbdcbcddcaaccccbadadbadcbbacbbcadaaaadcddaaacbbabbccaadbbaaccccdabddbbccccdcadadadcccbccdcacadbcccccbdabccdcbbdcdbcbaaabdbcbccacbabbdbccddbbaabaabccbbdabcdbacccbdaccabcadcbdcdcbcbccabaccdaadcbbcbdccbbddddbbcdaaddcdacbdcdcdddadddcdaadbccbbcacdddbbaaaadaabbbdadaddddcadaccaddddbacddcddabcdcbdbbaadacdacdadaadaaacbdcdddbbcbdaaccccbdccbddccacccbccbbbdddacccaccccadbdadaacbbabdbccbbacccbccbdbdcbbadadabdddcbcddcabddcbcdcdabbdcaadbbdcacaabcbbacdddbddccbdbadddbdabbbdbdbabdbacacaddacaabcbbbdbdabbccdbdbaadaddbbaaababdcdbdddabaccdcdcccddacdadcadabbaabadadbabbabbccbcbabdddaabcaadcbdbdbcaabddbcabdccaabaaccabbbcbdcbcbadaabdcbaababdaddcaccbbbaabacdcaabaaaccbacababacacaadbbdbdadbbbccccbddcbcdbbccddbcabbbcabdbadddadbdaadbcbdbbdbbacdaccbcacdddcbddcadcccaaaabcadbaaccabacccdbabbcdbadadcbdaaabacccbccdabcabdccbbaccbddbbdaccbdbadadcacbacccdaccdcbabbcdbdacbabccdadacbabbaaadbabbcacbdacdabdbcabaabaababcdccbbddcbaaacaabcdccdcaccbddbbdcbbadccbcccdcdbcdbadabcdcbbbaadbbbdabddaacaaccbacddaddcccbbcdcccbabbbcccdbadaddaabdbcabbcdaabdaabccbaccdbdbbbcbadadbccbcbbaabdcbdbdccbcdbcabcddcccabadababddaaccdabcaadbacbaadabccccbbdcdabcbababddcccacbbcdbbdbaaacbcbaaabdcbddbcacacdddacacabcbcacbcdccaaddcccaadacccbacbacccdadbaabdadbdadcaaddddccdbbcadaabcabcddcdbcbdddadcacddaaccabdbdabbdcbbdcdabddadaacbaabdddcbddaabbddbdddccabbabadaaaadccbcadbdcadbcdccdadadbbdacaddbbbbaaacbddcacaccbbdcbdbcabacabdcdddcccadadadadcbdabadaacbadacaddbcbbbdadcbdcacacaccbabaacccbaaabcaaaacdddcaadbabbbbaaccdcaaddcccaccbddbacbdcdaacaadcdcccdacbadabbcbbdbdacbabcabdabbacdddbdadccbdcbbdcdbcbdbdcabaaadcbbbdddaaddadcabddbcbccacccadabaacbccddbaacacdaddccbdbbacdbdaddbccadbcabdbaacbddcaacbcadddcdbbbacbabbabaaacacbccadbcdadaaaaabdddcbadcbbdcaccbbadbdbbcdcababbddadacbcdacaacdacaadcacabccdaccaccdbabcaaccbabcacadacdcbaddddcbbcdbbabacbbbdcccbbabcdbababdcccdadbacaacdabbdabdcaaabbddaabddaddaabadcdbcddccaaadcacdccbcadccdddbdbbccbbacaaadcadbcddcbadcababdbbddddbccbbcdbabacbddccbdbdacbabbbdcdcabcdaabcbcdbbccbbdccbdbbcbdabcadcdadaadacdcabadcccaddcbbbbbbbccadaaaccbdcdaccdadbcdadabdccbcbdcbcababbbcddacbdbaddaccbdddaccbcbcddcabaabdacdcdcaadbdddcaccabdbaaddabcabbacbdcbbccbdcbaddbcdacccbdabcbdaacbbdddbaddabdcddcdacddcaddbdcbcdccbdccdaccbcdbcaadbddcabaaadbacdcdaaddcbdddbaacccbdccbddcdababbbcaddbdbbddabbbacbbabbcccbcacacabaccbcbcdabcbdbcbdddbdbdcacbbcdcdbbbcbddddbcadbcdaaaaadbbabbbdcdbcaaccdcddadbddbadbdbbbdaadbbccbaccdbbcbaccbcdcdbbadbddcabaccabaadcbbcdabdccccddcabbacdaccbcbcacdadbaabdcadcdacaabdabcbdbcbccacdcbbcaaddddccadbddcdacdbcdbdaddaccbbbdcbcbdadabbbabbadbaadadaddbadbcbaabaadabcdbbbdadcabdabcabcbcdbbdcbdbbaaabbcaabbadadcddcbbdcaddbddccbdbbdcbbcdbcbdbdacbddcbccbddaacdbbbddccdaddaaaabbcddaddcdcddadabcabcdadbadaacbcbdabdccadbdcbdbdbbbbadcbbcaabaaaaccbdccbabababdbccaadcbaacccccbdcdbdcbabbaadcddbccbabddbcadbdcbcdcadcacaddccabbaadbcbbddcbccddbcdaaadacdcdaddbdaabaacbacabaabdabcdbddcbbcaccbaacccbaaabbdcdcdbcdaacdbcabcacaccbbabbacbbabddababaabddaddddaababacbbcccbdddcdcdcaaacccdcbbddbcbddbddabcadbabdcbdaaaccdbcbbcbabacbcbdcacbdcaddadcdaabdcacdabadacbacabbcaabbbcaaaccadaacbdcccacbadacdaadccddcbccabccacccbdcbbcddddadaddbbcaacdbdbdbbbcdcbbaccdacdcdaabacccccbaabcdbbabbacdacacdabdcdbdabbccacbbdacccbddaacbaccacbcdcadcdabaccdcccaacbacacbddbbdbcadccdcdbdacddcddcaaabdbddccbbbcacddbdbbadccbdccaaccdbdbcccbdaacacabbcaacdcabcddabaaacbadbbabcaddbdbcdaaabbccbcabddcbcacccbbcaccdaccadaaaccbabdbbccdccabaadcabdbbdbbddbcddcabaacbadadabdbaddccadbddbdcbdcdbbdaacbbbbbaabadbdbbcdbdbdadacbababcbdbcdaaacadcaddabccaccaaadcdbccddabaddcadbadabadcdbccaccacdcbaadadccbddbccdadacacadbdccdccbccbdacdcabadacdabbcdbdbddcacbddbaaaccabccbbabbdaadacdadcdbdbdacaacdccaadbdbbdcbbddabdbbbacdaacddccdbbddbbbddbabaabcaddcbdcbccadbbddcabdabcbbbdadaaccbbacdadaacacacacacabbdbaaddcccaacdcacabdaccaacacbdddccdcbcbdbcabaddccbcdcaccadbcdaccbbdbacccabcddaaadbbcaaccbbacadccbadcbdcdcabaacddacccddcdcdadcbdddbddcbbdccdcadccadcbbbdcdcbbbbbdbdbcddbbabbadbdacadddbbddaccdcadbbcadbbcbbdbaaadbaabcbaaacddacdbcacbcabbdcacbdaadbccbdccdddabacbdacacbdbbbaabdbdcdadbacaadcccbadacaadacaacdbadaddcdbbcbadbacbcbbcddbdbadbdaccbcaddbdaacababccccdaccadaccadcdbdcccabddabbadacabadcdbccccadcacadbacbdbcbbaadabdacacbcbadcddadbbdbbddbcbacccbdcaacabaaabdcdcadcdcaddbcacadacbbbaaabddcdaabbcdcccababadbccabcdcbabbcbbdcacddddbdabdcbcadcccaccdbcccabddbccdbdaaaaccaadbdaababdacbddcadabbcbcbbcbcacddbbcadabbabdbdabacacdbcbaccdcdbaadbdbcdabdcbbddabccaccaacaacddccadbaabbacbbdcccadacccdabdbbbccbcabcbaacaddcadbcddbaacaaaacbdcbcaacaadcbcadabddababbbbdddbbdabcaccddddacbccdbccabcdddadcddccaadccaacddadddbbccabdbddccaacadbcbbcdabcbbbbbadcaaabbacacabbabbbccdcaacdddddabdcaadababbcbacdbcbcdcaaabdccbcccabaaabaadbbcadbdbbdabbbcddacddabbdbaaddcbcccabcaddabcdaadaaadaaaacadcadaddcddabbbccbcdabdbdaaabcbddccbacbabbbdabdacbbaacbaabdccbdcbcaadcddabdcbcdaabaddddacbadcaccbdacbdadbdaabddacdccbcabdadaddaadbcbbbacbaaaabccdbbcccdacbababdcbbdbabbccbcdbbcbcbdbaacbcddbadbbabdbddaacdcddbadbabaccbbbbbdaacbabddcbadccccbcaccbcbccdbcabbbacbadbaadccddcdabbdcaccbccdbdcccbcadcbccdbbbadddbadbaacdacdadaadbaacdaabdadabdccbcdccacdbbbcabbbaadaabaadaabadbaaaddbadbcbcacbbacbddccadcdbddbdaccbcaccbbddbbdcbcddbbadccbacdbabbdcabaaadbbcacdccabaabcbdcdbadbbdbaaacbbbabbbcadbdaddcdbaadbbdccccbbacbcddbcccbbadbaccadcabbdcccbcbbbcbbbbcccadbccdabacbdbddbabbadababbaabacabccacdcdbacbcabaaddbaabcabccbdbccbbacbdcacacdbdbbbacddcaabdbdddcbbcaccdbbcaddcdbabacbcacaaadabdcdacbbbdbcdcdbbccddbdcdaccaccbdadabacbadccbcbadbcbacddaadabddadacbbbcbbbbadcabccccbccadbcbaccaacbcbaccbacbcbcbcdbddcdacdadacbcaabdaddababcbcaccbccaacbcbbbdcaccacccdcabadbcbacdcacacbaadccadcacbbdaacdbdbacdaaacccdabdbbdbcadccbcdbacabadbaacbabdbacbaddcddadaddbacbcbbbdbbbadadbdaacbadaacbdbccbcbddcabbacbccbbcaacaddacddcaabdddcdabcdbdaadacdbdbdcacbbdddbcdacbaccbaddacbadbcbbcacdaaccdbdcadcbaddccabbbdbdbbddcddbcbbbccbccdcdbbbdddaaabcbbaccadcddaaaabbbaabcccbbdcdaccbbbbaabcadaabbababacaddaabdddcdabbbbadcacaabdbbdbbbdbaaaaacbddacaddddccdddccddbbdccbcadadbabadccdcdccccdbbdbcbabbaddcddddbbaacdbabcccbbbadaabaabbdddddadcbccccbdadcabddcacbdbacaddabbabbbabdbcadabcdbcdbbabaaccbabbcbcdccccdcabdccaddddccacaabcccccbdbbbdbdaacdccabcbbbdcbbabadbcbaddcbbaddacaaaacaabdccbdcadabaadbadbcddabcbcaddcababdbabddbcabbcccbadabaadccdcaababcaaababbdbabcdbdabbbdbbacbccccbcaacdcadbcddaccddcbaabbbcdaacddabbabbadddaccabddacdcdcdabbdaadcbbbcbbdcabacddbacddbddabbaabaccdbddccbdbbdddbdbacadbaadcaaaaccddaccabaccbaabbbaabbadbaddabbbbdddacbadcdaccbbdadaabadbabdcdcadbabcabacbabdbabaabcacbbaadcbcccdaccacbacadbadbaaacacacbbabaddcacbaaacbaaccabaaabbddddcccccabdacdbcdadddbbbddddcbbcadbccbbaccdacaadcbbcbadcddbacbdcaccccdaaabbcdbbdadabbaacdacaaaacccacabcccaabbdbddccccadbaabccbaaadbdaddbbbcaadbcadbcbabaccacacdaabcadbcaaadadcdcbcadcbdccacdaadabcbabcddaabcdbbbcdbadbdaaadcccdbdbcadcadcabaadcacacddccdbdaccdbbcacccaacbdbbbbbacbcdbbcbbdcddabccabdacccbbbbcabacbacddddaabbadccdbaacbbbcddabacbcddbbaadabdccaddadabbddaabacdccccbbdaadcaaaddadcddcacdbcdcddbbdbbbcbacadaacaccaccccabbacdaddccdbdcdcbcacabcaccdaccbcdaaaaabddabccdcbbbdcbdbbbdbaaaadbaabdccdaabaaacacdbbddabdbaaabbbacdbdbaccdaaddcdbbabbdaacaacbdbcbdccadbacbbdbcbccbbbbdbbcbbbdbbabdbbabcdadcbcbaadddbbaacdbbbdbcbbdacaaaadcadccadcbaddbccbbcabbbcbcccccbcbbcbbacddcdacbabddabbbcdcddcadaacbaabdcaadbbaadddbcaacddabadbbadcacbbcdabcddcadcddbcabccabddccdacabdcacbbabbdbcdbbbdcabcdabcdbbbaaddccbdcacaaababccacbcdbbadddccccbbabdaccacbaaddabdcacddcdbaadcaaccaddcdcbdcacbdddddbcaadbadbcdcccdacaddcacddbddadbcdbccbaddadbacadccdaabddaccdcdbcbbbbacbaddadacaaacdaababcbbcbaccccddddccbbdabcdbabddbccbcabdacbdaddbbcdcbcbaabcccdadaaaaddcbdbdadbcbdadaabbabcccabdbbdddadcbaabcbcbadbcbddbbcbdcdaaaabadbcdcabbdabadccbbababccabbabcaaaadadbdaabbcdabbcccbcbcacddbcbddaacdddabcbbdcaddacbbcccdbbdcbabccccbddccdabbbdbcacbbcabbadbadbdcbadabcabaabddbdddacdccccdbcaabbcaaacbaddbbccaacdadccbcdbccacacdbcbaddbbdcbbbccaabdabbbccccadabdbabbbcaccbddbdbbcaabddbbcdbbcbbdbcacdcabacbcdccaddabdddcbaacbabccacabaadcacbddcbdcacdcdbcaacdabdbcbbacadbbbdccdcdabadadadcdaaccababcdcaccaadaadacadbaccccadcbacaaccadbdbdbccabbadbccdcacbabbbabcacacdaaabdcccbcdcdbacdadbcbcaacbdbdbabbbcbcabdadddbadbdbbadcdcadbcababaacacabcaacdabbbdabdcaabdbdacdacbccddabbacddcacbdabcabcddaccdbddcadabcacddaaddbcbaccbabbacbbcdaddbcddbbdddbcdcbcacadbcbaadccbdbbdbaabadabbcaabbadbdccbdcccadcbdddccbcccbddccbccbbbddddbccbbbcacbbdaabaadaaaaaaddabbbbcbccdbdaccdbabddccaddccdbbdbabcacbaaacaacddcadadbbadbddacbbdddbcbdaccaaacdbacadbdbdbacadcdccabbcbaacbbcdadacdcbcdaccabbbcaadacdaddccbcbbdcdccdaacdacaacdcadadaaabccabaaddaacaddbcaccbdaadcdccbdadcbcacbcdbbbadadcbbdbdaabababdddbddaadaabdddadcabccadcdaaaccccbacdcaadbbbbcbdbdbaddaaadadbcddadbccbcbdccbbbbcacbbaccccaaabcadddbbaadabaaabbdcbabdccccdcacdddaadcdcacdddcbaaadddaddcababcabdbcddddcdbbbbaaccacacbaacdbaaaabdbdcdbcadbbdabaaabcaaddccabcbdacbddbadbcdcdabbbdbcbaadbaadbbababcdcbdadcbdbcddbbcbcdbdadadadadbbdddcaaadaadaacacabcdacdbbcbcaddcdcdadbdcaccdcddbacaacbcdbcaabcdbacdbcdaaaadbdcabccdbcbadddbcdaccaaacccddcacbbdbcabbdbbbcdcbaaddcdcccbdcaabdcdcbdcacdcbcabadadacdabbccaddbacdacdacbdaabcccccdbbcabababccbcabbbdbccbbbddbdcdcdcccdbaddabdbcdaccabbdabcbbdbacccacbbdaaaaabdaadbbacdaddcdabddacccadabacaaaaaabdddcdcabcccacbbacacdcdaccccdbbcdadacbcccbbcdccaadacbddbacbddbaaadadcbabbaaaaddbaabdcbacbaaacdddddbccadadbcdaabacacdaababcbccbcbdbabababcbdadddbdacaccacaaabccddcbdbcccdcabbabadabddcdccdddadcbcbdcadbdaacdbcdccacbcbcccddccddadaddaadabaddbdbcbcacbbcabdadbdcdcabccaadacdbbbbbdcdbdacbdcadaabcabcdbcdcdddacbcbacdcababdaabbaaacaaaddaabdabadbccdddbabcddadccacbaddbcdbccbdaaabcbcdcaabcabdaddaabaddccbaadcabbccdddacaaccbaadbacbadcdcdcadbaadbdcddbaddadcbdbdabcdcaadacdbccaabdacbbcccacacaabdbbcdabddabdcbacccaaddaccaabaacabcbabdacadbbddcbbcacdbaaaadacddccdddacbaccdaccaadcbbabccdddbddddbdcccbbbdbaabacbbbaadbabdacadddbcadbbddbcdbdaccdbdaaccdbabcccdcccbcccaacdcdbbadcacbdcacaacdaadcabaabcaddddddadbbabacccacbbbbaababccbacaacdcaababbcdcabdabbcaacbbdcdcadbacdcdbddbdbdabbbaccbdacdbdadcccbacdacdaaacccabbacbaadbbcddcbcacdcdbbdbabcbaccdbaadabdcccdbcbdacaaabaabcacabaadbdcbcdddbcaaabcdbdcbcbaadaabddcadcbacbdbbbbcacadcbcccaddcbbcdbbbcaddbaadaccadabadabaadbbddddabddddbcbaadddaadacbbcccaaabdabdbbabbbcbbbbdabbcabcadadbaaadacdaadaadaabbcdabccabcacdaaacbdcdadcbcdbdbacddacdacbdbaacdadccabddddcdbcbaabdcbabdabaabbdccaaddaccbcccdaacbaddbcadbddacaadbcbbdbbbcccaacdabdddadddbdcbacccbaadbcdddaadabccbdcdabadaabaaadbdbcbadddbaaabcbbccabdbdadabdbcbcddabddaaddcdbbacdaacdabccdbdadddddbdcddbaabacbddabdccbcdcccacbbbccaabcdcccadcdbdbdddacdabbdbcdcddcbcdcbacaaaaccbccbccadddbcbdbadabddcabacdbdacddcadcbabbcbabdddadcdddcdbcdbcdccbaaacbdbcaabbdacccbbcaadcdbdbcbdbddcbcbbdbbbbbcbbdbaabcacdaadccdacbbdbadddabdbabdbbbaaccbcccabdcbaccabbddbbbaaaacddacaaabacbbacabaaccbbdbbbcddadddbabcbbccaabbbcabddaadbdaadbdacbcacacbcccadabbcabbadaccacbabdbdcabdacdcdbbccbaaddbcccacbacbdcdddddcdbdaadcadcabacccbdbaacbdbdcdbabbcbacacaabbadaaddcbacddaaddacaacdddbdbbddccaacdbbacbddcaabdabbdcadaacaacaaadbaacbcadbaacabcddbacdcdcdabdcabccdadbcabbabdbccdabddacddddbabdaccadbbcadabddadddbdcdcccdabccadbdbbabccbabccdcbaaaaaadbddabcacacdccbbadcbadbbdabcbbcadbabdadbbbabaadaabccccbbcacbaadbbddddddbdbdabcaababdabbcacbbccbddaccaadadbaccdccbcbddcbcbcdacdcdacadbbdddcdaddaddadabcbcddcaabcdcababdbbdabaabacddabbcaabbddcbcaabbdbadbcbbaccadaddbbaaadddbaadcdadcaddbaccbbcbcccccbaaabbcdaccadabbccabaadbcbbdabbadaddcabdcddaccaaccabbaaccbaabbdbcbcccabcadbbdaabcccabcababdabcddbccbacbddcadaacbccdcaddcdcdaaabacdcbdbddbabbbdbdbdadddcacddacadaabbdbacabcbcaaadcadacdbbabbaabcddcdabadccddbdabcdccacbcaaaaddaadbccbdbcdacabacdbddbbbbccdcdbbbaacbbabcacdcaabadcbccdaccacbdbbdadddaacbbadabcabcccaacddaadbdbccaabdabcdbcacaaaddabadacbcdcccaaccdcbabbbabbbbabbabcccacdaadabaacbdacdbcaddabdcdabccdcaccbbdbbbbdaaaaaabbcaabdaaccbccadccdcdcacbbdaaaabbaccaacbbacabbacccddbcbcdcbabbaaadabadbabadadcbbbbcdbcaccaacdcacdbddacdbccccdbadcbcabadbcddcdaaacdbccdcabbcdcaddcccccdbbaacdcbbacaaadadbcdccdcacdcdcaadcaccaaababcbbbaaaccbacbcdaddaadacabbacddbbbbbadbaddbbbddbbbcdcaccbdcdcdcabdacbbcbcabdcacbcddccbacddcaabcbcccdcabccabbcacdddcdaddcbcbdaabcadbabbaadcdbaddcadcddbccbdddddbbbdddabcaccdacabbcaddbcbcbdccdbdcddbdaaabdbbbaaabdcbdddddcdcdbcabccdbcbddbcabaabcdadccaacabacacdbacacabdcdbbbaccbbdadcdbbddbcacdabdbcbcbbccabaabdcdcabcdcaaacaacbcabcbbccbdabbcdcdadcacacbadaaabcdaddaadddacbabbaccbaaadacddaabcdaaacabbbabdaadbddcccaabbbacbbdacbdaacbcbbaadaddbcbadcddccccddadcbbdddadaddcadccaccdcaabddaddbdbdccccbcddcacdbddbabbcaacacdaaaddacabcbddddcabaddaaacbabdacbbadccddbcbdbdccdcaccbabdacbcdddbaddcdbaaccddbbdbaaabadbdbacdccdcbdabccbcabcbbcaaacbbabdbcdbdacbaddcaabddbcdabcddabcdcaadaddcacdbadcdcddbddaddaacdbacccddddbbdaadaccddcabacdbbadbcacbaacadacababcddcabacbcbddaaabddbcbaacdcdadbacdccaaddccaaaadbdaacdacdcbadcdabbcddcdcccdcbaaacaababacbdabbaabacdadbabcbcdaddbbbaddddcbbdcdcddaabcacaaccdadbdbdddddabbbadcdbdadbbdabacaddbcdababbddacccbaabbacbcdcacdbbbdcabdcdbacacabccadacacacdbcaaddaadadabbcdbbbdbbbbbacbadddcaadbbddbdcdccdcacdabbabdcddabbaddaabbaaadcaabddcddcdbcacbbcbbbddcbacdbaccddcadccccdbcbdadaccbdaabcaadbdbacdbcbaccdddaccacbaaaaaacddbbbbdcacbbcabbabbbcddbbacabbacbbccbdabddaabcbaaddaabdcaaaadabcabcbbddcbddabdcbacbaccbdcbbcdcccbcaacddccdbbadadcbccabbdccadbccdaabaddbacabbaadbdbdcdadcbcabcdcadcdbacccadacbcccdcbccdaacaaddcdbcaabbdcccbbdcbdacbbbcbbbbcccdcabdddcaaddccbacdddccbdabbabbcaddacdcabaadcbccbcbbcbcadccabbcaccbcbcbcadbdcdcdabbbcabaaccaaddbcaabbaacbacabbabaadaadddadddaababbadcbaddbaabdadbabbbacbdcbbbbdaacdbadcbbbaccababaccbadbdadcaadbcdcacbbccbaababcbccaaacbdccbcddddbdcdcdbaabdccbaacdbdbccdaaaadbdbcbacbcbbabadacbbbdcababbbddddacacdbcbccabcbdccbdacbaaacbccbbaabaabdabdbbbcacadacacaaabbbadacacddaabcbacdacabccacabbdcacddadabbbdddcbadacdbaddbbcbabbaaddbdcdcaccbddaacacadbaacdabcaababaddbbbdddcdbabdbbbabbdccaaabbbbdbabacbbbcdbbdccbdbdbbccdadccddbdaabdabbaaadccddbdccbdbbccaacacdcbaaadddcdbacccccaaccadccaacbdacdddddaddcbcbcbccdcabbbbaacbbbcbbaacbdddcadbadccbabdabdbabbcdaaaabddbbdaacccccadaacdbbbcaadbcccdcabbdbddcbcdddcbbbcccabbddabadabbddcdbabbcdacddcaadaaaadadadddadbabacbdccaadccdcdccbcdacddaddacbacaacaacdaccccdccaabbcadadaabcdbcdaaddcddcdadddbdcbdcbbcacdbdaabcabdbcaaaabadcbcdababcbbbddcccadcabacbacdadcabacadadbbccacdbcadadcdabbcdcdbbaadadddaccbddccaacaccccbadbdaccbcbdaaabbbbaabddcbbcbcdccabbdaaaaddcccbddadbddbdabbadbdcadccdcbbabdbadddbcabdcacadddbcdaadabdaaacaabcabbccbabcdaccdcbbaadbbdbcdbdbabcaabdcdbdcccbccadcdbdababdadcdabcbdddcaadcabaabdccddbacdbdccdcabacdaddabdccabcbaddabcacbabadaccbbccadcdbaadcddbbadabcdddcbbdadbbbacdacacdddcdabdaabaabbbbabbdabdcbdbdadacaccbdbabadaabbaababcbdaadaddcaabcbaaccddcadaadcacbcccbbbbdcbbacbbbababaccdbddbcabccbdbbabbdbdadbbbbbdbbdbbaacdcbabcbadddbdcbbcddadddbabbbccaddddbcacadacbcbcadbbbccadacabbbbacbacddacbcdcdacdcddbcbdddbabcaaaccacaadaacddabaadaabdcbaccadcdcccbdbadcaaadddabcdcdbbbbcbabcaababadacdccbbcacdcaaaadadbabdbbcdaabbdabdabbbaaacaaacbacddccbcdbaabbddbcbbcdbdacbbadaadcdbbabbdadbabbdcadacbcaaadcabddbabbbdcdcacbcadacdcabaaddabaddaccaddaaabbbdacbdbdbdacbadbccacdadcdbdbacdcababaadccbbcdacbaaabcccaddbabccdaadcaaabdcdbbacdcabcbccaadccbabbcbbbddcddadbdaabbcccadddcbabcddbbadbaabacbdcbadabdaabdadacbcdbcbddcdbcacdadcbacddcdbbbaddabbbdbbbbbbdcccdcbabbbbdcbcadadddacdaddbdddaaccdacadbddbabdbcadbdbdbdbccddcccbcbdaacbdcdabadbcabdacbbccaacabccdcdaabbcdcccdbccbaabaccbdaacdbaaabbcdbcbcdaacdaabdcccbdabccdadcddcddbbcbaacccbbdcababcabbabbcbbcbcacbadaddccbadddcdbdcdbababcaddbbcbdaaddbcacdbbbcdbccccdddadcacdbbcdaacaccadbbbbbadbdcaccbcdadcddbcccabadbadddbcdacbbdcaaabaaabcbcdabdbbcbadbaabbdcbbcbbaadbabbdddacbdbbadacdcdcbbabcbdacbdadbbacdcacddbbbbabaaacbbaaaaaadbccadadadcddacbaacbdadabadbbbcaaaaccbccccbaccbccddcabcccdbccdbaaaacdadcdaaddcabbbcbabaacacbdadcdbadcaddbdaddbbdccddabddcbdbaaccacbddaadcdbacadddccdaabbcbcacdcdbbccacddababccdbbcccbbdcdbcacddcdacbdadbdabadacccddbdddaaaddbdbacbbcbcacacddccbbccbcaccadadcdcbadddaabdcbcaacaddddaaddcadaadbcabbdcbaccaabbdcbddddcdaddcdbdcadcdcbddbdcdbcdcbddcbbabadbbbcacdacdaacdbdddbbddbcaadbdccccdbbbdcdaddcbbadcacaabbdbdcbdababccdaacbcbabdccbcddacdbcdcaccdbdaadadbccadcdbccdbaabcaddaccdadbaaacdbbbdbbcdbabdacbccbbadcbdcbaccccaacbbabadcbaadbbccabccddabaddbbadbcccacdbabbacbdcbbacacbdabaadbbbbdccabddcabbcdccddacbcdbacbcabbcdabdccacabcbdcbbdbbbabcddbbcadcaaccccbbbcccdcdababcadaaabccaababbdbddcbbdcdcbcddaadaaaaadaabcbdaccbbacbbdcacdaabadaaaaacccbcbacccdabadcbdbddabcadbbadabccaddadabcabbccbbcddcbcabccdacadcbddabdcbcccdbcbdabaccccdcbddadabbbadcaabdddcddbdddbadbcbbdbdaaccacdabbbdbbbbdddcbcaabaddabbbacbbaaaadacabdcbbbbbbdabacaaaaaddbdddbdbaaccddacdbdbccbbdabdcdbbcddddbbbcacccaaddccaaacdabadccadaddbadaacababacbbdbadbcccbbabadcdbabaadbaaabcddadccdbcbacdacddcbdabbaabbcadacbccaaaccbbddbdcbcddccadaadaddbbccbcacbdcabbacabdddadccacdcbabccaddcbabdcccaddacdaddccdcdcccaccdddddbbcdcacccccbcbdacbbcaadcadbbbaaaabdaccacaddcadccbdcddacddcbbbadbdaaabdacaadbdddccdcbcbdcccabaabcdbbdbbacbaaabbddbbbdcbaddbddcddabaccdcadcadbcdbdcdcbccbdbdcabbaccccbadcaccdaaddcccbcdbaccaacbadcbacdaabddbcddcdbcdbdcbadbaabcbbdbadcacdadaccbccadccbabaabbaccdbdadaabcabbcbbccdcababadbdabbbbaaddadddacaadacadbbbbacdbdaadcbacadacbdacbabccbacbbbadbddadcbbadccdaacbaaaddcaaadbbcdbdbcbabddadbbcaaacbadddcccdcdbdcbbcdcbbbdcaddcbccaabbdcddabdabcaadbbadddcddbcacacaaaacaaccdcaddacacacccabacabbacbcddadadbcbaadabdaaddbdbabbbbddcbadacdcacdbcdbddbaccdccbcccbdacbabdacaadbacdabacabbbaacbcbadddbbdabcdaabbddbadccadaacabcaddcdcaccccbdcbaacdcabdababbbaaccbabacbdacdbadcabdbacbacdbadababaaabdcbcadacbcadbbdbdcdccadcaadcbcabddaaccdcbdddcdcdaaadacbcddaddbbadaaaabacdcdadaadcbdbaaacaddbaabccdccccaabdaabbdbaacacccccdbbbacaccddbcdcddadcbaacddddccddccabaacdcaadacacacccbdacaabadbbabbdcaaddabbbbcdbaacbdddddbdbddccbdabdcacbcaadbacbcdcbbcacaadadcacbddbaddbcbcbadbdccdccacacdbccdacbcacbcaccbaaaddaabcadcacbacbddacbdabddabbccaccadacaadadccbbddcdccccacdcddcabcbadacacabdacbdcddaadaabcaabbdccaacbadbababbddcbbacababcdcacbaabbcbdbdadbbbbadcdcbcbccbadccdadddabbdbdadabadddccbabdbabdbaccacacdbbcbcacdacbdcbbcbdcccbbabdbcaddaadbcbdccaaacdacdabcbacdaadacddbcbbabacccaacbbcaadbdddadcaaabccddaabbaacaaadaadcdcbcdbcaddbbbdccbacacbcaccdbbbadaabbbadcdabbdcdbddcaabdcacadbaddddaababcdadbbadcacbcbdbaddbbdbdcbddcbdcaaacaddccbcddcdaddddbcbcdacdcadcacaadccbddaadcaaaaacbabacdcbaaccccdbaddabaacdacbcbbaabcdbcadbacaaadcbacbcddcabcdcdddddaddcbdaaaababcdbcbabaddbcbcaaacabccbabdbacacbcbaacdbccbcbdaadadccbcdcbcdaacabacadbdbbbbdccadaaaccdabadbbcacdcbdbadacbcdcddccdaabcacaddaaabcdddbcaacabbbbaacacbbccbabbbbdaccaddcbdabbbaaabdbadbaaadddbadbabbdaadacccabdcccbbdbcdcdaddccbdaadacccdbdcdadbabbacacabadbabbccabaaadcbabbdcccaaaabcccbdbdcaccadbbddaabdbbbccadcdabbacacdacbcddbaaacbdaccbdcdaababadbdbbbdadbcadbccdbbaaabbdbccddbcacaadadbddbdcacbccdbaaccbbbbdcccaabbbaadcbcabbbcadbbcdcddcaabccdcdddcaccabcbcdcbadaabbdbbabacabdbdcbbcbdaaacbacbcbbdcdcbadbadacdbbcdcbdadbddacadaccabbccbdabcaacdccbabaddbcacddacacccccbaacddbababdcdaadcdbabbdadbaabadbccadcadbcbcaadccdcabbcabcbabcdbdbddbddbdabdbdaaacabddddacbacabacacccadbaccbdcbaabacbbbdcadadcabdadbabadddacbbcdbcaddbdcddbcacdddbacdadacbacdccdddabcbabdabdacdadabdaddcacbcdbcddcadcbcddbabbbadacacdbbccdbabacaabdabbbaabacdcadbaabccbbaccbdabcdacccdacadbcdcdbdcaccbbbcbccccaacdbdacbbdcbbcdcbaccdbacdddccbcdabccdcabcdcdacdaddbdcddbbdbdacaacadcbaabdaddbddaadcbababbcdadbddccbcbcbbbacccdbaccdcdcadbaacbdadadabacbdbcaabbbbddcaacbbaddddcbdbdccdadcbdbacacbbcccdcdcacaabbcbabbdddcbcdadadcccdccaccdccdddbbaaabbcacbcaddbaccaadcaadabccdaaadcbcbcbbcabccadcacddddbcbbdabbacdacadbccdcdcdbacbabcdcddcdbcdbdadbccaadccbbabadadabbbaddbbcdbcabacbabddcbbbddbbdcaadacacbdcbabcbddaaabddbabacaacaadbdaaaaadadbdcacdcbdcbbdacaccaabcabdbdccbcaabdcadaadcaddddccbdbddcabcccbdabbbbbbcdacadabbdacadcaadcdbbbdbccacdbcaadadbddcbadcbdadadbacbcbcdcbdccddccadaaccdaabddabbcbcabbdacbbcdbadacaddacadbdcabcdbbcbbbcabbabacacdddadbbcabdbccdccdcaaccdbdcadbacaaccbacdbbbdbbbdcacacdcccdaccaaacbccacdaddabcccddbcaabdacabccadaddbaddbcbcabcbdabdbdcacabbbdabdaaadcdbaaabcbccbabddbcbdcabbdbdcbcbdbbcbbcdbcdbbdbdaddbaacaadabddbaabcabcbdbdabdcbdbbbcddccbddcaabdbabbbcadccddaadacadbdcadbcccbddaadbbccbdcbcbdbdabadaccdcaacdabdcaddabbdccaddcbacbbabbddadbadcdbccaaaccaccadadccaccadddaacdadaaadaadaaabcccbbdacbddcdacbabddccdddadbadddcbbabdbadcccabaaadbaddbadadacdbdcaaaddaaaaccbaaddbaadcbbcdbbbbdbaaddbadccddabdaaaaabbdcdaccbccccbddacacaabbadbcbcdcdcbaaccbcdcadccadbcaddbcdbbaacacbbbbddcbabcbdcabdddaadcadaaaabadadcccbddbddcabbdaacbdacabbbacdacddabaabbddacbabbdddcaabdaacadcdaadcbbdccbccacaabdaabbccbaadabcacccdcbaaaccbcdbcbdbdddacdcaabbbdadacaaddccabaadaababcbccacbccbabdabacbabccdcbbdaadcacbbdbcccadddadbacdacaddddbcccdacbabdcadcabbdaccdabbcdadaddbddaddccbbdadcdaaababdabdbabadbbbbddcbabcbabbabdadcacaacccababbdadabccdccadcdbdccdbbbbbdcbbbcdcdcbcbaccaadbaddaadbcabadaabddcbdabdcbccdcbcdccbcbbaccbabdbbaccbcdbaccdcdcddbaaddcccadbdcbaacbddbaacbabcdbdacaddccdddbbcddbabccdbcbcbaaaaadcccbdcacbabadcadbadddaabdbcdbddcccdbcdbcccacbbbccdbcaddddbbdccdbdabacdaccbdcbcacdbccbcdcbccddcaacbaacbdddbaabcbbadaaddddcbacbbbbccbcbcbddbbaaaadcbbbaadcccabccdddadcccddbcdaaccdcbacbcdbdbdbbadddadbcaccaaddadacbbadbcbccacbbddadbadbbacbdcddacdaadcddbddbaddabdcbdbaddbbdbcaaaaabcaabacbbadaabbdadccbabcaabccdcddddbacbbbbccdbddaabbcadcbcdbdcdaddadbaabddacddddccacdbaaabadcbdacadcdddbaacbcacadacbaaacccbaaabdacababccdbacbdbcbddcbbcbcdbadddbdbbaadbbbaaacdbdbdaddcbdadaacbdacbcadcdddddcaabbaadcdabccdcabdbadcacbbbddbbbcabadccadadababbdaddccbcdcbaccacbdddddcacaccdaddbadccccdbaabbadaaabbadaaabbbbdaacacabbbccdbddddbabcbbcbbbbabacbaacbaabbaabdadddccaacdcbaabdcaabadddcbbcdddaddcdbaaaaddccadcbcadaccabdaddbcababaaddbabddaaaababcabaadbabdacbdcdcaaddcbbdacbaabccacccdbccbbcccbbabbcbbdccbddadbcdcccadabdabdabcbabcdababacbcbdabaccddaccccdaaaccbccbccbcbadbcbddcacccdbccadaacdacbddcadcbacacbdcbdacdcadcbbbbddaddadcaaacdcbbbabddabcdaaadcbbcbacacbbbacbadcdcdbbbdbbbabcbadcaaaabcdcdaddddbabccdcbcdbbcdddacbabbccdaabdcbdadbdbacdaaaddbcacbcabcdbbacbdabcdabcacadbcdabbbabadcdcddadddbabdbaaaacacabccdbbaccabbdaaccbabadaaabbcabcddabaccbcadccbbabbbcbddabbbdbdadaccbdbdacdbadbdbdbbbccccabbdcddacaaccbaabddadabbcdddbcdcdcdbcdccccabacaacbbadddaabcabcbcbacdddaaaaaadcbdbbddbdcccbbcaaacacbacaddaadbacaadacdbddcacddccbbccdaddabbcbadacbbacbabdcaccaddadadbcadabccbddabcbddddbacdaabbddcaabccaadbdccbbbdaccdabbddccbacbbcdccbcbbcacbbaccababbbcabcddbdadbdaabcbaadcabbacbcddbcdbcccabababbdcdcabacbddaabddbdbdcabcddbdbcdcddccacddaadabddacaaadccdbdbdadaddbcabacbbbbacacadddacaaccdadabadccdcbbbcdbbdbcddadbcabbbcbadacabdaacdbbdaacadbababcbdbabaadccacccccaabcbcacdddbdbbccbdbabcaddcccccacabbabcdcbadddadaaaabbbcbcaaadabddcbcddbbcabccbbadcdabccbcbdacabddcbcdbbdcaabbcbdcaaccbdaacdbbdddddbbadcbadacabcbccbcbbdcaabbaaddbbbabccbabcdacddabdddaccadccbabacddcbcddbadbabbcadaadaaaaaddbabcbaaccbdbbbccdddcbabddcabadbbcccadcdaaacdabbbcbdbbbdbdbcaccbbdacdccdaababbbbbdcddadadbbdbcaccbccbbcaddbdddcbccbbdadcacdccdcdcbcbcaddaaccaccaccccabcadcabdaaddcccaddccdbcbddaabacccbccbbbaabdbaabbcddccbcbdbbcccdbbdcacbcbdbccadbddababddbaabbabdcabcaddadaaccbbadcbdadadcdadbdbadbaadbdadccacddddaaaddacadbabdcdabcddaadbdddcbadbbcbbcdddcacbaabaccacdddcdbbaaabdadabbbbdcbbacbcbdddabdbaacdbacabdbdccbabcddaccbdccadbababddaccaacaacbcacacddbbdcbdbabdaccadbdcadcddaccbbbaddcbbccaadcabbbdbbbcacbacbaaccacdddbbccdaacacdddcabcccbdbbbcbabcdaadbaabacdddadccababadcaabbaadbbdccbcadddddabcbbbcabbdcdcadbbbcbbadbaabbdacdcbcabbcdaccbaddcbdbdacbadddbdabbbdbbabbdcaaddabdadaadbbbbadbddcdbcdbdcbaccdddbcdaaaacddbbccccdbacdcbaadbcadcdcdcdaabbbacadbdcaddcbcdadcddbadaababaccdccbddbdbdadaadabcdddbbcdaadaabddbddabcdcabbbcadabbcbddabcbdadabcabcbccdcdbdcacdbcbaaadaadcabddacbbadbbdbabdcbbdaaacdacdbbbbbccdadadcddcaddccacbcbbabcbdcabbaabdaaccbddaccddabcadaaaccdcccbbbdabbdabbcabbabbadcbddcbaddaabdcdcabdcaabdadcbdccbdbdccbbabacdcbadbddcbcbaccddaccdbdbbcaabcdccdcbacdbcabccdbdcdabdbbadabcbcacddcddadcdbccdbbdddababdaddcaccccdbbadabcddacadaabccaabbaddbbaddabdbcbdaabadddbabcaaaadbabcbdcdddbbbbadbcaaddcdbcbddcacdddbdadbdababcdddbbbbadadddcdbbddcaadbaddadadcbbbaaadcdaacbbcadccbabbdaacdcbadaccaaabbaabbadabacacadbacaddaaabaadaadbccacbcbdccccacdbcdcabaaccadacabbbdbdbdcaabbabdbaaccbcbcabbccbcacabdbbdbddacabaaaabadcdcaadaaacbaacaaacccccdcadcbcbdcadbabcbadcbcdacdbbcdabaadadbdbdcdadbdddbacdcbdbbcdbbcaddacbddbbdccddcdcddbbcacbaadbcddddbaabdcadddabccbcaacaadabacbbaaabddabaacacabdcbbabddadbbadacacaaccbbddcadbaacaaacbcdbcaaacdaccdcbdbcadbbdabbdbdbaddcdccdaabcbccdcccbbabbcbbccbbbddbcaacacabdabccdcddbccddccccdbddcdaabdbabaccbbabacaadbdddcdbaddaaacacaabcbbcacbbdbdbcbdddcbddaabbabccdcbcacddacdcbcdbcddddabddddbcddbacddadccdbbddddabdccbaadbdadadddaaddbdcddddbacadcaddcacbdccaaddbbaaddbbbadaaadcdbabcdabbbbcdbbccbdadababacbdaadbacbddabaadacddbacbbccdacdcddbddbdccbaddcaccdbbdddabddaaccabdabacdacadabbaaabbcabbbdcbdcadbacddcacadacbbcbcddcdcacbaddbabcbdddbbaadaacaabacdcdababadcddadcccbdaadbccddcdbdbdbaaaaadacdccabdbcdaacaacacadabcbcabccbbabaccbcaacddcdcbddddbdbbacddbbdccdbdcdbdcabbadbbdcbdcccbababdbbdabcdadcdcbcdbcadbdcbaddcccacbbccaacbbbaacdaccbbadccdbdcdacabbcaabcacdadcbadddabbbbcccbdadaaccdcadcdbaabbadddacbcbdaadbbdddcbbaabadcacdbdcaabbdabaaababcbdbddbdabcadddccdadbaabcadacdbaccddaacccadddbcacccacccbdcabaaacbbccabcbbdddddbaabdddaabddccabcbdaacbcaacbbcdbacaddbcbbbcbaaabbcdaccddbaacbbcacccbcdbcdbaaadbdaadccaacbbbddaabcdccbcdccbdddcaaaaaaddcdaddddbaacdddadcabbaadadbadabcccdbdcdcddabdcdcabbcdbbbcabccddbbbbcbbabacdaaddbbbddddacdbddbdccdcbcdaddcbbccbacacccbbcaacbabdbbbbbdccbcdbddaaadcdabbadcbbcdbcbccbbdabaacacadadaddcbdaabddcadcadabddabbcbcdadacbaadacaadadaadbddadaccaccabcabdbbabddcddbbdcabcdccdddaacbbbbbbacdcababaabcdccccdcddadccdbbabdcacdadacddbaadaabdbacaadbaddacaabaaccbccbdcaddabdccbdbddaacabbbbddddadbbdabbcbcbccbbaabdbdbcaccaaabbbddddccababdcdbacccbadbacdbacbaccaabbbccbbdddadbcdcbcdbcaadaaccabadacbcdbdbacabaddcaddcddbbabddadddcaadbdcabbabaabdadcdacbbbbdaaacaacbbdcaddcbdcdbbcaadcbcdabbbcabccaaabdccdbddaadabaddabcddadabbacaddcdcbdbaaabdaacaddbbbbaabdbabdbccadddbcbdadababdddcacdabbbaabbadbdabbcddacbadbcaacbaacbaccadaacdcaddcaddbbbcaddbdcbddbcbbaabaadcaaabdcaacdacdadbdcacaddaabdacdbdcaadbaabcdddbddcabbbdbaadabccccbacbccaadaadddbbabbadccddbbbabddbcababaccccbacbdbddbcacadcabcdbacbdbbdcbbbbbddbbdccbcbbddbbbccaaccddbcbdbcababbaabddbbbcbddddabcdbdbacaadcdbdcccbddcbacddaacbbddbcabadababaacdbbccaacdbcdadbddacdadbddbdddcbbbbddbdbdcbcbbbabaacdbbdaccdccbdbdabcddcbabaaadbccbacbbadcdadadabacbbabdaddbbcbaabbaddcadbaabbdaccaabddbbcadcadaccddbbbcabcbacbdcbbcbcbbbccdbdbaccadcdaddbccbabcacbdbbbcccacccacbdbbddbcddabbbccddababaccbcdbcdbaadccbacdddcabdcbbcdcbdddbcdccabbdbdcddbcddbbadcdadacccbbbacaddcaccdddabdccddccbacddcabaaccccabcdbabcadbbcbacddccdaddcbdccdacbddcdddbacadbdadddcbdccddddbdacbddbdaaaabcbabddacccbbdbbbdbabccbbdddacadcccbcacbaaabddccacbaddbcbccbbdacdacbdcbacbadcbcbbbacabaaaabbcbdcdcaabdcabdcdbddbcacccbddcdbdbccbbaadbccbbcdcacdcbddcdddbabbccacbacbdaaaadddbbbccdbccbaabacbbcbaccabbdbadbbcdddcdccbdacaddddbbbacbcccdccccbdbbaddccadbbcadbdcabcdabdbbcbbbbbcdbbdbdbdccdaadccabacbaccdadddcdcdcacadbbdddddbbbdacbbcaadcacdccdddcddddbccdadbaddbadbaacabbcdcbdbbcbaccbbadaccabacccbdadcaddbbdaaccdadacbcdabaabdcbbbaadddbaababcbbbdbbaaadbdadbdbbcdccbdacdcbddaabddbccdcccbbdbbadacdadbcbaaddcdcbdbcddcbcbdadbcdaaabcadadadadabaabbcdbbdacaccddbabcccaacabbcaaddcaadbbbabbdcbbdccbaaddabcdbdbcbcdcbbdaabbdbddbdcacbcccddcbbacadbbcbdcabadbddddacbbcbcdcbcdacbbdabdcbcaabaddccabcccddacaadabddcbadbbcdadaaacbcabdcadbdccaaadccdcbcdbdacdcdacdbddcdaddbdbbddacdaddaadbcabbadbcacdcdacbdbabbaacaabddcaadcaabbbdcccdddcbacaadcdcabbccbaadbbabbdbaacdccbcdccbddabdaccaaddcdbbaddccdabadcbacbdabbbcbacaaadbbaaaaccbccbaccbabdacdaacbdaaadcdcbccadabbbacaddabacacccdcaaacadbabcbdbbcdadababdabbbbccbbcbcdcaabbddaaaabdccdbababdbdcaadddaaddaaabcbbbcdccbadcbcaaabbdcccaccbdddadacadcbaaabacaabbcbbadacdddaddccdddaabacddcaacadbdcbacbdbaadcadcbadbdcbdbabacdbddaabbbdaadbbbbcbbdddadbcabdaaaadccdbcbbcdababccbbbadabcbdccadcbdbcbbaabdcbaacdadbddbabdcabdcbaadbdbcaaacbacdaaabbdcbdcabdcabdabdaabdcdccccaccbccddbaababdadabaccbdacbdbcccbaacbbdbcdbdbccaaaabbbcaddccbcdacdadbccdccbaadbabdacddaaacaaccaccdacbbcacbbbdbddcabbaaccaaabdbcabdbbabadcadbdaaccbbccacdbaabcaddacccdbcbcbdbbdbccacbdcbdacbadabbdbbbcaaaddcbdbbdbcbcbccaaccbbbdbbbdccbddaacaaccbdccacbbcbaccbabbbbcbacacabaabacdbcbaacdbadaacdbbadbacbabadabdabdbbdccbcccbcccacddbccaadbdbbbacccaacacadbbbdcabbcacbaabdaccabbdbcbabbddaaccdbbdaacaadcdaccbbbdbdcadcdcaccccdabddaadacddaacabcddbacabadbcccdbcccddcdababbcacdacddcbbaaddaccaacdcacbabbdcddbdbccdbcaadcbacadaddcbbdbbaaadaddadadbadcbddbbdccbdbbcbdcbcbdccbabadbccdcdccbcbcacdbaddacadacccdddadcbabbaaccadbbdddbbdbbdbdbacadbdbddaaddabdcdcacbabcaaccdccbbcacdbdbdcabcddccdddddccbabaabacadadacaadcbababbdcdabcacbaabbddcdabdcbcacbbbbdadaaccabaadaabbdcccbbababbbbbdcaadcaaabdbcabaccccdadadcaddccdadcddcbcbbdbadddcddccdbccabdbaddccaccccddbcaaccbdcaacdacbccdabbbccadaccdbbaabdddcdcbbddbdadcbcdabaddcbbacdcbbadcabcaaabadcacaabbacaddbcdbcbacbaaddcddacabadcbdbabccbbbbcddcacdabdabbadddbcbbddcbadddcacbbbbcaaabdaadabaaacaacabacbdcddbbddddcccdaacdcaaadcbccdbbaababcdabaacaaacaaacdbbcdbcababcaabbcddabdacddadcaaaccdcaaaccbbbadbbbbacbcabdcbabcdcaaabcdbcdccdccbbdcacbcabaddbbcaccbccadaacdcadbdcbadcbbbaccbbbaccbbbaadbbbdadbcdcbccabccacdbddcdddbacdddaddbaaacaddccbdadbcaabaadbabadcdcbacbdcbdbbccbdcdcadcadacabbbcdcacdcbcadcbbcbcaccabdbdcbccabaacacbcdabadabdadddbabbbdcddcacddcacdcdbbdbddcdabcadcdcbbcdddddaaabdddbdccdccdcabadcabddcbbacbabcccdaaabbcbdbacdadaabcdbaabbdbcaabccdbdaadacbdbbaddbadbacdbbbbddccdabcacdabaabccbacbdcccdcdcdaacccaadadaddbaaacdcadcbdddacdaacadbadadbaccacacaddbcdaccacbbddcaabaabbbdbddbcdbbaabccbcdbadcbadcdcaabacbaabcdbdccddabbbdadcbaaaaddccdbacacabdbabbccdbababcdadbabbacbcacacbadccbaaccbaaacaacbccaccbabaaccadaadcbabdbcbcabdaabacacacbdbdddbaaddaddabbbbdcaadccddccababcdaaabacdaaadaabdbabdabadbcacbbbcdcdadcdddcbcabcaabdbadabcccaadcbcbacbcddcbbaccbcccdadcddcababccaacbacbaabadbbcbccabbbcacbbddcdbbaadcbadaaacbbddcddbdcbdbabbcbaaaaadccbaccbbaccdcccaddbbabababdccacdcaadcdbcbdacdcdacdbadabcbaabccdbacdcabccdabcccdcbabcabdbbaccccbcccbdccabaadabbadccdcaaabaddcccdcacddbcbdacacaabcabccdadbbaccbbacddbabccbbbcacdcbcdcabbbaaccbaaddaddcccbdbadbabcdadcaaddcdadbcddbbdaabaaaabcabbabaddcadbacddbbbcbbdbdbcdadcddcdababcbbddcccbdcbbddaaadcdcddcdccdbccacdacabacccbcdacabbddbbbcdbbcbddacddacbbdcbbdacccdcaddbababcbdcddcbccccbacbcbccabdbadbdacbddaabbadcccaababccaaadddbddbcbcabbbbdcabdbdaaacadcdcaacbbaabddccbabbbcbdbcadbbbbddddcacdcdbcbcdbdbabacdbcdabdcaccdadabbbabacbcacbaadbaadadabbbacdddcabdddbcaabcdcadcdabbdcbbbddabbbccbdaadddaaaabddcdcadbbbcacacdbacdcdcaaaadadbbbaacdbbcdbbdadaaaabbbddadccdbacadadabaaaabaabacddcababacacbcbbcddbbdbccddbcdcaadacaacccbbbdcaacdababadccbbccccdaacdbbadbbddbadabcccdbbdcacbdbaadcaaabbdcadaabbbcbbcdabdacccbcbdbadbacbcbaddabacacbbdbcbccddbcbdbddcdcdddbbdcbbaadacdcccccbbababcbaacacddbcabdbcddacacbcbcdbadaaacabddadcdddccbbcbddaadcbadbccaccaacbacacdaadcdbcdaaccbcbcbdaacdbbcaddbdbbddbcacddcccbadbcacbbbbdabdcbccacbabbccdadddadbdcaabbbacbccdaabaadcdbcdcddadbddadcadcadbcbcdbacadddabdcbadacaddbaddacbcaccdcdcaaacdadccdabcacadaaadaccadddadcacbdcdcdbdacabdabdcdbbddabcddabdcdcbcadcdcdcbdccbabbdcbabaccddddcccbcbbcacdcdbbdcadcccdbabcacbbddaddaaadbcdcbdbbdbcaadddbddbdcabbddbbccacccadcbddcacacdacbabbdcdaabcddabababdddcaabaddddbaccadcdbbdbccdcacccbcbbaaabdaccbdacdddccaacdcbbdcdbbcdcaadcabcabbdcabcbdbdbccdbbbdcabcbabbcbcbcddcaabaadacbdaacabbbdbbbcdbacdadbdcacadbccccbbcdacdaadacdbaccbacabcdbdbdaacbabacdaababdaaddabaadabdcdbadabcaacdaacbbdcadbcabacdacababdacadbcdcbcddcbadcdbbdbdabccdabcaddacbabccdbdcaaacbcbccadbcaddcaaabbccddbbdadbbdccdacddbbcaaccccbcacbaaadbcdcdbcdcbadbdacacabbbacdaababadaaddcdbbbdbdabdccbcbdcadaacdbbccbccdadcdcaaaaabcadaccbcacbbabbddcbbdcaaaaaacabadccbcbaccdadadcaccdbabdabacaacaacccddcadaacaaaaccdcdbdacabcbabccaadbcccaccdcdbbbccadccbbaadadbcaacdaaccbcaaabaacbadbbadaaaaabaddbdcbadaddaabaabbcbadcdddadbcabbdadddbdabccbdcdacabbbcaaaadccaabdbdbaadcadcdabcdabbabaadbbbabbddcdaadaadabdddaabbddcaccddadcaababccbdcadaacbdcbacdbbcddcbabaabacdbdcbcbadabdcbbbdccbcccbdbcabdcccabbcaddccddcbdbbbabdaadbbdbddadddbabdbadcadbbdbaacbccabadacaccdaacaaaaddcbbcbacdaaaddaabbbabccdaabbdacdabadbacacdadbcaadcccbbdbacadabbdcccbdbaaaabccddcbbcdcdabdcbadccddadccccdacdcbdaaaccbadddcccdabadadaadbaccdccdcabacabbcbdbcdcbddaccadbcbdbcbbbadaacadabdabcbaababccacbbbddacddccbcddddacbadabdcaaaabdccdcaaaccbcbbbcabcbacddcdbdaddcbdccdbbdcbaddbaabbddaccbcddcadccbaabdcdbbbcddcdaabadcdccbababbcbbdbdbcbbaccdcaadcdacdbddbccccbcadbbbadcadaaaccbcbbadcabacdccdddabbccadbcadabdabadcbadbbabdddabccadadcbcbbaacbcbbcabcacadbdadabdbbbdadddbadcbcdccdbadadddcdcaabcdbbbccaddbcddabddabcddbbbdbabaabacadbbacdaabdccdbcddddcacddcbbcbaacbdbacbbdcccdbdccbaadcccbaaaadcdbdddccddbdaaddaddddbdcbcabbddbcaabdbdcbcbcdbbadaacaccccdbccaacdcabcacdcdabadcccbbdcdcccaccaadcadddcddddaabaabccdbbcacdbbbcaddcdbcdaaddccbabacbdbdddabbbbbbccaacbdaddbcbaadcdbbacdccababddbabaddadaaadaaabcaccccdcbcbcabcacddcdcdcbbdccaacccdaacaacdaacaaadbcbdbcbcbbacbcccaacaacbcddbddacbbaccdcbaaacaaaaadabccdcdcaacbdcbabbaadacadddaadbacaacbbcdccdbadbcbccccccacddbcdccccabcdcacacaaacacbbbadabbadbcacaabdabadbaadcbadacccabcbbadaaaabcdccbccaadbcaadcaabccdacacbcbbccbbdbabcadcddaaccacacbbddacbaaddcacbacbdacacbabaaabaddbadbbbccabcbcadcadcbabbaccdccaababbbabbabaadddcadaaddbbbabdbdbacaacbbcabaddcadbcbbdbbcbaddccbdacacaccabcdcbcdcdcddbcaabaadacabcdcabdcabddaccadbbdddadcaaddbdbacbdbacbcccbdddddcaacacbdcdacacdcdbcabcaabdbbacabcbdbcdbdbcbbcabbdcadccccacbdaaadccbcdcaabdcadbaaadcacbcaabadabbdbbcbbaddbccccadcbccaaddacadccaabbadaaddaddcaccbbddcdbabbbdadbcbbcaadddcccbcababacbbadadbbbdbcbdabbbaddabcbabbdabbbbacbccaadbacacbdabbbcbaaacbabddbccaacacaadbdaadadadbabddcbbcaccabdcbabddbaacccaacdbaddcbadbbacdbabccbbcddcdbdddbdddaaddbbababadcaaacbabadadcbbaaabbcadcccacaaccdcaaabddaaadbacaabbaaacccacbacadbdadacadcabbdabcdacbdababcdbddcaaaacbdcbaddababddccddaacbdadcaaccccadacdaaacdaaadabdbccaccdbabadbaaabcaaadbcaadcaaddcbbcaacabccacccaaadaddbcaccadddabcddacbbadaccbccaababddacccbbbbcdccbcdbacbcaabbcdbdcbcacbccccabbdcdaddcddcbdcabcdcacbacadbcabcacccdddcadabaddacdcbcccbadbadbacdddcddbabdcdbdabbabbcdbbabdacadcdcbbdabdbddacbccccddcdddbddbaddabbdcacaddddbcadadcbcbbbbdcddaaaaabddcdaadcabaaccacccacaaabdabbdbabbcddbdbcabacdcabbbcbbbacabcccddcbbbbccccbdacdcabbdbdacaddaaaacbcdadccccddcdcccbabbbaadcbbccacacbdaddddacaccaccdcddbaaaaaaabdadacdddabbaccacdcabadcadccbbabbcbdbacaabdabbcbbcaddaaabcdcbaacaaadccbacbdccbadbacdaaacbcaabdbdaadabdacdaccdbdcbddbbcaddbbcadbbacbdbababcdcbbaddbbbaddacdbadabdacdbdabccbbdbbbabbabcbbdbcacacacaadaabddbbdbbcacdcdbabbdbaadbabbadccaadabcddbddcbcddbbaacdacbbabddcbdcbacbabbddabcdaaabadcaacadccdcbbaabdbbcadabcbcbbabbbbbabcbdabbcaabaaacaabbadddcdadbddddbdaaadcddacdbccccccccddbbbdabccabacadacbbdbcaddadddbacaadaadbaddbaacbdaacaccbdddaaacdcbadbcabdbcdcbbacbaddcddbacddcbbaacaccdcdbcbcccbcdbabadacbdcaccbadbaacaccaccdadababccdbcddbacbbacdcbddbcbcdbdadabbaaccccbdabbbaadbabbdddaabbccbdbdbdcdbdccdaacacacbbbcabcaccaadadbcdcccdcaacbacbddacbacabdbabccaaaadbabbdabdcaccaccbbbaabdcddbbccabacbbdabbabcbddbbdbbdababccddbbbcdbccadbddbbdabccdbdabdbbddcbcabbbcadbccabacdcdabdddaddacdccdacdddcaddaadcbbdaddacabbcaaddbdcaacbabbbbdcdbbbdaaaccbbccbbabdbbcaddadadbdbadabaadccddbbabcdbdcbcacadcaacbacbdccadacaabdaddcdabcbabbdcbddcaacbaacccacabbcacbbacdabbaaacabacabbaaabccabcdbcddccadbdabddacdbcdcbbdbccccbdaddcddbcabaddddbdaaaabacbaddbbbadbaddccdcdbcacacabbbbcddabcdcbdbadbbdcbccddaacdccababbdcbdcdbccabacdddcabddbadabccdabaadddacbcacbbbccacadbcdabbcbddbdbcdcaababbddaacdcbadccdccccabddbbacccdccbbccdadacdabdbacdacbaadabdddbcbdcaabdbabdbbcbddadddbbbbbbaadcdacaabddbddabddabbaacdcbabcdaccbacdcdcabbadddacdcaabdcbdcccdccccddcccdbcdbddbaaabcaacdcbadaacaababacbacddacbbbccdbaaddcbacbaddaabacacaadacbadbacacbdbaaddbaabcbaacaacabbcbbdcadcbcabaacbdbacdacdadbdacacbaccabaaaacaabaccbcacacdbbbacaadaaadccbdcccbccabadbcbdacadccccacacabacdddbcababbcbadbdaabadacaabdcbadcaabacbbdadaabcdcccdbbaccddbabbdabdddaadbdbcbbdccbdbdacadcbabdbaccbdcacdbacddbcacadcbdaaabaacddacccabadacdaaccaaadddbdbbdccbabdcadcdbdbaabcdabdbdccaadbbbababdddcacdddbdccdbdcbdaadcbabadaabaccdaaddddcdaadcbbddadbabbadbdbaacbcacdabacbcbadbadbdbadbcbcddbbdbcdcbcccbcacdcdcbaccdadacbbaccbbbbabadbbdacbddacacbcdcdadccaabcacdbadbdadbbbdcdddccaacdddcbcddcabdadcdcaddbddaacacbabaabbaadbbdbcbcddddbddaddacabdddadcabcdbdcbacdaadababdbddbaccaddabadbcababcbddccdadcdbbcbdbbcdadadddbacbacaaababdbaadbadabbaccbcdbacaabacadbbbcabdbbcddbacaddbcadcdabadcdacbbdbacbacbadddcbbcccaacdbdbcccdaaadbbdcabbbccaacadcbdbacdbcbdaabcccbbaccbbdcbdadadbcbdbadbabccbabccbbbccabcacdbbbbbbbbddabcadbacbcbccbabcadabaaadaadbbcccbcdbdacddadbbbbbddbbdccbbbbcabbbdbcdccaacbadbdbbadbacdaaacbaddcbdbdaacacbaacdcbbcbbcddcdbddcdcddabcbdcdbaacaaaabaadcbbacbadcdbbcbadbbaaadbccdbabbaadaacbaccabdcdabdbdcddbbcdddadbbaddcabacadadbbcbdaaddaabccababbccbbaccaacdacacdbadcbcddcbcdddcbacdadaccdbddcaddcbdbaaccbcbbadccdcaccdcbbbddcaabbdaacaadabaddabbdbccccbbbcabbcabbdabdbddbbaadcdccbdcdabcbccbaabcabbbabbaacbcddcabbbbaddbaccdccdcbacdaaddcaccbbcbdadcacddabbbabaadccdbdabcdcabdaddcdcdaabbadacacdabbaaadabccddcacbccadaaabbcdbdbcccdbbdccbdaaaccdaabbdaacbcabbdbdccbcddbbbcadbbcdadbcdbcbaadbbbaacdcdccdadcaacaadaadbddccaaccacaddaadaccbbadadaadccbdbcadcdaadccdcccabccbdabbbbbbddcacddbbbaabccadacabcaaabcdddbdddbddaccdbcbdacadcacccbcadccdcbdaadaccbccdbddbdcaabbaaaddcacbbcbdddcbdbcbadaabcdabcaaadadbadccbadcddbcbdaaacbacbbddcaadbacdbabccbdabddadcccabcddcbccdddbbbcccdadddadacabbcdcccdccaacbaaacbddccbcbdcbddbbaddbcacabbdbcaacaaddcdbcdbccbdbaaddabaddbcaccadddaabcadcbccddcccabcddccdadbccacdadbdccddacdacaddaabcbdbbcddcbcccbcdbbbcbdcacaadbabbadddaabbaadaacaddabcddaacbdaaaaadbdaaccacddaddbcbcdcbccaadbaccdcccddcacdaaaadbdadcadbbbcdcddbbcbaddccaccaddcdcdbbcaabadbababdbbabbbaadcbbaddcddbbaaadaacbcbbdbbdadbcbbbbdcbaccadadbacbddacdbbacccacaacabcbbabbdccbcadcddadcdaddaaccdaddbaddbdadbddcbbdaaaabbbddcabbbcdbbdadbdabddcddbdddaddcdcbdccdacdacbbaacbcddabbcccdcdcabaaadaabdbccaacaacdcaadacbcbccaccaccbdcdbdccbbcbbaabcadbccbdaaabcabddddbadabcbbdabccabdaddbdcbdddaaaccddcdaaaaacdaccbcbdacccdaadbbbdcbbdbbabaaaacddbbaababaacdabbbbdaaccbccbaaaadbacacaadddbabbddddadbadcdcdbcbbdccdcdaaaccbbcbadaaadabdcccbbacacadbbddbacddcdcdcabacdccbacdccbcbaacdbbadbcaaddbcaaccadaadcddacbccbcdcbcaddabccaddadcaadaababdbddcabcbaddaaddcaacabacbdddbacaccdacccabbacbbcdbdcdabacaabcadbddbbacddddddcdddcadbbcccadacabbbccbacddccddbadccbdcbbdccdaaadcaaddadcdcabbdcabcdaadadcbbddacdbcaddcdcdacbbabcabaddacdbcdbadccadbbbbcdcbbbcccabaccacadbdcbaaabbdcbbadaccaaddbaabdababcbccdcabcccccdacaccbbadbdddbdcacadcbdabdaabcabaaacbbabdacdcaddbcddabcbbcabdabcbbddcdcaabdacbbbcccacdbbbcbdddcabccbadccbbdbacaabbcdbbcdbcdddbdbabbcaabacbdacacdbbdcbbabbdadddaabbaaddccaaadbdbabadadcdbbdbdbcbcdbacadaaaacdcadaadcbdbbccccbbadacbabbadabbcdbcbdcabddcadcccdccaaaadbaccadcabaaacabdbddbbaddaabcdbcaccdcdbcabadaabbccadaacbcdbcbbdcdbdbcbbaabbaaabdddcbdddacdddbccaabbacdabcbccbcbdcdddadbbccdbdaccbccbddcbdabcbbaaacbdccdbcaaddbdaabccccccdababddcdbdcaacbdbacaaacacccdddadcbabcaccabadcdaccdcbdbbbcabdbccadcdadcdaddabdbabddabbcabdbabbaccbbbcadacbaacbaccbbcdcaabdaabcdadddcdabdbabaddbabccaabacbdbbbcdaccddcbddbcbabbcbabcbdabacbbcdabbbbabaacaadbbaddaaadacddaabdabdaabdcdaabdccdaddbccaddaaabbddbaaabccabbbcbcddcccdaccabbcadbbbabbcccaadcddadadbbaabccbabcdabdbdbccdbccabcadbbcbaaddcccbdadbbaaabbbcddbacdabacdbbddcdcbdaccccabbacadbccbdacbdcdacdcaccaabbdbcdcddadbaadddadbdbcdbaaaadcdbbddaaccabbdadabcbabbbdcaccbbbbadcccbcbcbcdcabccccbcbdddbdddddddcbcdcbabcbcbbbccbcccccbcabdaadbddbddccabdcaaddbddacaaddcababbaddabcacabddbccbddabbbcccbacbacaabcadcbdbcaabcccddccdbadaababdaadbdabccccadbdcaacbaacbdbadacbcbaabddcbadcdcbbccbdbdcaccadcbbaabbbddcdbbadcbadbbbccbadcaaadcbddcbccbacabdacbbaaddacacdcbbdcbdbaacdbbdbaccacaadadcdbbdabddbcdabdbdcdcabdbacbcddaaaccaadbcabbcdbaabcddaccdbaccbbcacabccbdbacdacbdcbacdddcdcdacbccdcccaddddcdcbddcacbcdaacdcbdcacccabaaadbddbbaabadbaaaadbcdddccdabddbdbacbcdadbbcbcbbbbdcbddbbcabbddbddaacbdabbdadbdaaabcdaccdcdcbaaabaacacbbcbddbddbadcaacbccbaacccabcbccbabdaaaadcdcbababcdcaadbdbbbcaabcdaacbdbcbbcccbbdadbdaaccbcbdadbbaacdcbdbdacdadaddddabdbcdabaadacadadddccbacbbbcbabddccbccacdbacbddadcbdccddbccbaacdadbcdccadbcdddbabdbccbcbcbabbdbcacbadadadccbdbbddacbcbbadadcccbaacccbadbccbacdaadaddbdccbbaadccaaadabccbdddddbabadcddbdddaabaccaccbbcbbddddcadadcdbcdcabadacdabbcbbddbcbccccbacbdcabbdadcbbdcccddcabbbacabbccbaddcdccdbbabdcdaadbcdcaadacabcdbadacadabbbcabbdadcbbcbddcbbddadacdcbbaddcdccddddbbacdbcdccaabcdbaabbbaabaaddcdbabcccdbcbddcdbccaaacccdadbcaabddacccbabbaaddacbbaccbccddadcdbbddabdcdaaaaddbbcaccadaaaddbbccbbbaacadbdaacabdbabbaccbaabccaccdddadacaadaadddacabbbbacaaddaccdadccdacbbbacddadccaacacbcbddccbadadacbcdcbbcadaddcdabbccbdbaaccbcaccdcddbcadbcacccdbddbabcbbaadaadbcbddcacadbabcbdbdbcbcaabdccababbcbbaccddaccacacdddbdcbdcddccccbaabacdbbbcdaabaaddbcbcbaabcddacabcccacdabcabcaaacdaaabaddcbaddbbacbcbadbcabbadcaadcdadccbbaaabbcdadbbacddcdadbbdaddcbabcababcbcadbbbdccccdddbacabbbbacdcdaacabdccacabbddabbaacaabdacacbdabcabadaaaaadaadbbadccccaddbcacaaaadadbddbcbddbbdcaabcdadabdcacbcaabcadbbbacdadccddddacddbbbdcdadbaaacddcccccbdbbdccbbddaadcbdbaabcabdadbdcbdddabbdadacadccddbabcacdacbbcbdbccadddcacabbdadddcacdcbccbaabbdbdaddadaaccdadbcacaabdccdaacbcbbbddacdaccccaadbacbdcadbbbdbdcdccacdbddbcadbbadcbdadbcdcbaabdcabbadadbdbdbdcaccdcccddccdaadbbdadadacbdcbaadbbdccddcbbaadcaddcccbcdccaddadaccdadcababddccbbdacbbaaddadddbdcdcdbcacbccaccbcdbbbdacdcabaacabcddaadbabbbdcdacbabdcbdddcaabdcbabaabcaddccbdbbcbbaccabdcacabaaaaaddacddbbddbdcdbcdcdbbdbddaccdacbcddbcbaabddaabdbaaabbadbbcdbbacdaccbdaabccabcacddddcabbcccabacbdabcadddddabbcdadaadbbdbaccbcbdcbadccbdabdbbdabccdcacdbbaadacacbbcccaadabbdaadccaaddcaddbdbbdadbddddbbdbaaaccbcddcacaaaacbabaadadadbdaabcacdaccdddbbbcdabbdbccdbcbacdcbddcbcdddbbdabdbbbdbadaadbbbbabcdbccbcadcabcbcaabbaccabcbaddbadccdcdadcdbdddabddbcbbdbcaacbcbaadbbbbdbbddcdcdaadddbdaddaacbabccddcabdbdcbdbdacbddaacaabcaadabcbcdcdcbcbcccbddaacddcbcbcdabacbddddbccdadcbadccadccdddbbddadccddbbabbddabcdccabaabbabcccdacacbdbdaabbbaadccbaccddabcdcbdacaccabaccaddccadcbccacdaacaccacaadcdadacbccdaabbbbdcccbbbbaabaccabacdbbaaaaadcbaddcbbdbadbccadbcbddbcbaaaaccbbbbbacdabaaaaaaabbbcadbdabbdbaccbacdbaaccdcaccabcbcddaadbbcdcabbccaabcbdadccbcdbaddabaadccabdacbaaaddbccdabadaacccddcbccdddccbcbadbcddcbdadcccddbbaabaadcbdacabbbcccaacbadbacbdddcccdaabbcdcccacbdbbdacaddccdcbdbbaabbdaacabcacdbdbadcbccccadabacccbabccbbcdbcacdbacaacadcbaacadabbdcbacdccccbdccaabadcddcadabdabbdaadbcaabbabadbcadbddcccbddabaddaabacaabaaddbbbadacbdaacccdaaaccbcddcdbadccdadddbdbbbcabcddbcbdcdbadcccdcbbbbcdbddbaddcabbdadaacdadaabdcadaccccbabbcbbdcdbddddcadcabdbccdaaccddbaccdadbbbdbcaabdbdcacabdcbaadadbcdcbbccbcbadcdcbdababddbcccbbddacdcacbbbbcabdddddcaabbbaddcabdcdbacadadbdabadcaadccdcbadbbacaabddcccddcbbcabadcaadbbbdacdddcaaabdaadcadcbababdacdbadddcaadcbcaccbcdddabdabadcccbccbdccabadacacdaccadccabcdbdaddaabbbbcbcbccacbbacdccaccccccbddcacdcbdaaacaacdbbdcccccddaacbadabcccccddbccdbbccabccdbccaddaadbccbbabdcabdabcdabcbcaaacbacbbabdacacbacbaacdbcabacdbadcaccccbaccabbdccbcbbdcbbcdbcdbdcbaccdddddbccccddcbdadcbaacaaddbababbcccbadccabacbcbdddcbcdacdbdbbbaadaddbcacadaaaadcbbadaddcbddacbccaaacabdddddaabddcbaaddcdccbaccbaaacbcbaacaccbabadbabcdcccdcbdcbdabacaadccbaaaacaccaabbbdcabacbaddcccbabcbaaabdbcbcdadcccadcbacbbcabdbbccdcbddbbbaacddaadacaddadbdcdcdbcbdadacbdcccdddaccabcbccdaaaccbaacbaaababdadacddbcabbdcbbcabdabccbcabdadcababcbbaadbbabbddcacdaaaabcdababddaddacbbaadabcddbcbdaaabbabacacaaaccddacadbbadbdbbbddabcaacabccbabdcdccdccbbbaccabbdcbdbadbadbbdadbbcaaddadadbadcadcdccaccadaabbdcaccccadccaabcadccdbbcbdcdaadbcdabaabbbcbbaabdcacdbacccdaadaccdabdbcbbbcbcbacccacbddcdddbdbabbcbbcaabadaacbbbdddbbdaddcacdabadccdaadacbdccbdcaddbbcacdadbbcbcaaadccabddcbbaccaacddbadbaaabbdaaadbdcdcbdadaaadcdbdbddbcdcaccdbccadadcdabcbcdddcaacadbbcddbcadbbcdcccbcadbddccdabcadababaabcbdddbbddcbbccabddcdaddbcacaaabdcdbbcbadacaaaadddcababbdccdadbcaabaadcccdccdddbbdccbabbcbdbcbadcbddadcbcbdcacbdbccbbbdbaabbcadbbccbddabdbaacbcaccddbddaabadacbadcaababcdcdbbbcbdddcdcbccacbcbccccbacdacddcaabccbacadacaaddabdabbacccbdddbabbaaddbcdcaabbabaaaddbdcbabbcddbccbddcdddcabdccdbdcccdbdbaadaddbdddbabbbdcabbaadddcbacdbadbaabacccbcbbbaadddbcacbbcaccadadbaccabcdadacddabccbbaabdcbbccccaaacadbabdaaadaccaddbcaaadbcbddcbdacbbbdcbccccbdcadccbdbcabdbdcbddabddbcbcaacbbbadbcbaaaadbddacadbbdddbaaacdccdccddbcaddaaadcadcdcabbdbbdddbbdacdcadcaadccbbbaacdbcbccddcdcbdbddcdcbccbbabddbbbddddcabccabbdbcbbdacbababacddabcadbbddbaabdbabcabcaacdcacbabacbadbdddaddbabdcdacadbbbdaaacadabccdcacacbdcbbcdcabbbbabdbbaabbaadbdbcacdbcadaacccddcdbdaacdcddbcadabaaaaabbbdaddbcbaacbadcacccbadaadabcbcddcacaabbcbacdcaaadaacdadddbdddcbcdbcaddbacdbccccccddcacabbcaadbadcdaaacdcbdcbdbbddcdaddacacbacccabddcaccbcdaddcadbdaaadbaacbbadcccbabbcccabcdbbdcbcbbcbbdbcbabbdddccbcbbdddadbbaccacddacbaacaaaaaddddadbcabbccdcabdcccdbdbcbabcdcbdbdcdaaabbbbcbdcbdcdcdcbdcdbccabcbacdcdbdacdbabbbcbbbbacabcbabcbaaadcbdbdcdbaacdadacabcdbacbadadbdabcaaddbbacbacccbbbbaddbcbbdddccbbbccdcbdbddaccaddddbdbbdaacbccacdcddbcddadcacaccabccbccaaacbccacddccdccaadbdbcabaabcabcdbdaabcaaaadacbddbdbadcaccadaddbaaccbdadbcccadccdacccadcdbdbbcddacaadcccbacabbabccadccdbdccabddacabdbabcccbcaadaadabbabcdbdbbdddaabaddbbdccaadcdaadbabdbcdbdcaaaccacdccabacbddcdbbddbbacbcacdccbbdbbadbcdcccabcbaadccdbdbcbdcccabddcaadcdabaacdddccddbaccadadcbdcdcbacdacdabacdcbdacacbbadabbbdcaaadabbddddbacbddbaaddccccbdacccabaadbcaddcbbbcadcabcdabbabbbdcdabbcadbdddddbddacdabcabbdcdbdccbccadddbbbcadbdcdadcbadabdddabbacaadbdbdbdaaaaabdcadbddcabdbdbadaaacddccbcaaabaacbcddddcaacacaaabaabbadcadbbbdcbcccdabcdadaacbddbcdcdcadcaacdbabdaccadcdabdccbaabddcbacccbababdccbdacdbbaccbddbdbcbccbbabdaddaccbaccdcdabaadbcbcadbadacdcbacaacabbbcbbdbbdadaaabccadcdbaadbadcdacbabbcacbaadcbbbcdbcddaabacabdbccdcdbdaabadabacbcbacbcdadabbdcdbacdacbbdadacaaaaabddabcdcbcbddcacbadaabbdaadcbbacdadbaccdcaddcdacadacddaaabccacbbccaabdadbdddcbbbaacdbcbbcccaaabbccbcbadcaacdbccdbbcccababbccbadcdbacdbcababddcbdbbadabacbbdddcdacbbbabbcdcbdcaabdbcdbcdbabbabaaaabddbdbcadbbdddabbbdbddadcbddddccccdacdabacbbcadabdcbabcdbcaabbccdbcbbcabdbbaaacabccbcdacdadaccbbdadbabbaaacdcdcabcbbbacbbdcdcbcaccdccdccdbbadcbbddbabcbbdaaaddccdccdcadacbdbddabbddabdbdabbcaadbcdadacddbdaccdbaaadccbddbbacacdaadcbdbbcaddbbabdbcaabcabddaaaabaabbacdadcccbbbdaacababaabbbdaccdaacbdcaaaddcccbaaabcaddcdddacaaacacccabbcbdbbddadccdcccbcadbbccbcadbcdabadccacbbabdadbadddcdcddaabacbbdacbacaaddacbcddcdbddbaadbbdbbbddcabbbaccbdccccdccdcbcbdaabbccbdacbdbdccbbcadabaabbbcdddccddbbcbabcdbbdbdbacddbdbbcabbcadaadbaabcccddacbaddadbabbcdabcbabdabcdbdcdcdcaaddacadbaadddddbbcdadcadcbccbcaadcbdbabbddbdcdccdcccccbddcbdddabcdbdaaabadbdcdcbbabaacbcddccbcdbdbcbbaacabbbddbcdbddcccabbccadbbdbbbaabadababcacacadbcaabacccdbabbaaaccababbaddddbccccadcabccbacdcaadddabadcbbbbbacddabbdcbabcbbabbbccdababacaacdbdacbdaabdaaacbaadacbcbccddaaacbbdcadadbaaccaadcbccbbcaaaaabbbcddcdcadccccdcbcbcaacaadcabbcddcbdcadacdcddcababaaddadabbacdccacbdbbadcdacddbbddccddabbdbdcacbdbcaddcbaabaabccdabcbaaccddcacbaaabbaacbaccddbdcaaadaaaaacaabbbadbdaaddbccdadbdaacdccdaaaccabdbabcdcadcaaddaddcdccbccaaabdbbbdddadadcadccdacbdcdcbbbaadabcdabdabcdacadbdcbbadcddabcbbacdacbdaacdacacddddaacaadadcbbddaddbacaccdbbbbacdacdacdbccabdcbacbbccbadbbadaaaabbadcabddbbacadadbccaccdbdbacadbabddabcabbccabadacadabacbcbaccacbbaaadddcbdaadbdbdcaabdcbcabcbaccacddcccbdaccddbccdacbacdbcaabbcacacabaccbabdaaaacbadacbaddbcabddcdaaddbdaabbdbadddaabcdbaaabbdbdcaabdcbccabdbdbdcaaccdbadccbcdccaacdacbddcdbcdcbcbacacaccbbcbdbdbdccdadaccdcdddabdcabddcacccdabaaaddaddacaccdcbadabbddcdbaacbbbbaaccddcaacaddcabbbadbaaadbaaccabbcacddbdcdbaabbbaadaaacbdabaabbaccccdbbbbcddcaddcdccbbcadddcbccddaaccdcbadaaccdabacabdbbccdaccbccbddbcdbbcbbdcabbcbaccabbacdbcacaaadddddccadddabdcdbdccabbccbbcdabbddabbbdcacaadcabdcddabcdcdaadbbcbcccbabacccbccbaaaaddcadaaccccacbcddccdbdadccdcacbccbabccddbdabcdbdddcbdacbbdbcdbbdcacabbbdbccaadcabbacbcdddadcaaacdadcadaddccbadabdaddccabbccbabcbbcabcccdcbcbacbbdcacdaadaccacaddcbbabbacbbbabcabbddbcaabccddcbbdbcacbdddcbabcbbccaadcbbddbbadddcdaaccbadaadabbaabaaccbcccdcdcdbddcdbccbaaccbacadbabcbdccccaadadcddcbacdbaaddbdadadabbdabdbadbbcdbbbcdacababdbaacddcbbcabccabacaaadddbbbbdabdcdddbbdacdbcabadbdabbbbabbabccdadbcbcdccbdbdbabbbdcbadcbddbdcccdcbccaadbabbcacdbbddcbccbbbcacbdaccbadaadcaaaabbcaaadbbcbddadddacccddacdbbbadcdaccbbbdcaccaadbdcccabccddbbdddcadcaabcabcadccbbdbaaababbcaabdaaacbdcaddcddbbcddcbabdcbdbcdcddadcacaccaadddacabccaadcdcaadadcbdbaacaadbbbdcadbadbabbdaabadbabbdccdbddcbbaabaadbdbadccbdacddcddbdbaaddaacbdbdddcabcbbdbacdabadaccdbcbccbbbbcacacabcccdabdacacddddcbdddaaddcacaadabdbcbdbaddcaacbbdabdbbaabbbddcbcaacaddddaaadadddddadcddbaaacdcadccbaddabaaacdbbcdacbdbdbbdcdbcbbadaadcbccaddccbdcaddcacaddcdddcbaabcbdcacbbccbbcdddbdbdbcddbccaadddbbccccbbbbbcabbcbdbcadcacadacdccaddcabbdadaadcdabbdacdbcbcabbccdddcbadaabcbadbcdababbcaabcdcadddbcbdbdadbaccddcccaabbaabcdbababcaaaccddccaadcdadabaccabacaacdcddacdacaacdcbaddddacbbbcdaadbabadbcdaacbcbaccbadccbddaacabacabdddcbcdbcbbbbdbdcacababbabdcabbbcbcddbccbccadddadaabbcbdacddcaccbbbdbabcdbcbdabcbdbdcbccbacdbaddadcbaccaddcbcdcbbdcdcdcadcbbbbccbcabdccccadbcbbbdadcbccabaaddacadbaddbddbcbdbdcdbcbabcdacdbcacdacbadcdcbbadaacbaacbccaaccabdaaaabcbacdbcdcacbaabdcadbbddccaabddbddccdaddddcbbcdabadcdbccacadcbcaabbdbddabacbbbcdccddabcdbdcbadbdddaacdccacdbdbcdadaadabaccdbaadabdbabdccdccbbbcabbcbbaabacbddbcacacdacdbcbbcbcbbdcdcccdaccaacccbadccaabbacdcccdadbcccacbbaacbdddaddcdadbadbbabbdaacddaadddbbdaabdbaccddbaadabddbdcbabaaddbcbbbbdcacaccddacddbacabbbdbbcaddddbdaddbbbabaaddcacabdadccdbddabdbbaaacabadaacdabdaacbbbbdddbdcdacbccccdbccbccbddbbddacbcaacdcacabdddddbadadbddbddcbbaaddacadadaaadcdbdbaaabdcccababbcdbdaaccbdabdcaadaadbaccbbddcbddcbabbbbdbcdbadabdacdacbabaadabbabcadddddacbccdbabaaadbcdbcbccdabdabddbcdccdcaaccacabdcaacdbdbbcacbbacbdccaabddddcbaaddbcdcddcaabcdacdacdabbcabadcbbcccbdabadbdddcddcacacdbaaadadbacdadccdccccacdadacdbbbcbdddcbddcdaadacdccaadddbcdcbabcddaacacdbcbdbcbbaaaaccdcdabdcbcdccccbcaabbbbccbaddbdcbaabdbbbbabbaabcbacabddaabbaabadcdbcdbccddcadaaaaccdccbdcaabbdcbabcbadaabadbcdddddcbccabaccbabacbdabadbacdcbbaabdcccdddaccdaadbdbabdabbcacdcccabcaacdacaddcbdbbabdbdacbcdabddcdabcbdabaadcccdcaabcddaccaacbaaadcccadcabccabcadcbbdabbdbacccdcdcaaacccaaabdcacbddadcdacdaddbbccadbadaddadabcbcaadabcddcadbdacccadcddcbbabcacbcdcbdaccbaabacdacddacdbbcddbabdbbdbbaabcbaaccadbcdadbcbcdcbcbacadccacbabcacdbacbcddbbcabbdbbddadddbbcbcbcdddadddbddbddcbcbcbcaabbcaacdcbcbdabcbdcabcaacdbabbcdcdabccdabdccaadbadccbaacadaaddbdcbcbbcacbbabddcdddbbbdcdbccaadbccaadcdbaccccdbdcdbaaadccddaccddadcccbdddcacddcbbdcadbbbddcbdddadcdccaadbadbabdccbbaadbcdabdddddcdadaaccdbaadcdbcacbabbaccbcdbdccbbdbaccabcaccacaabbaacbccabbbccdadaaadcbdbabdadccdaccbdccbbaacbabccaddbaddaddcbbaccdccadaddcdcbcddcccbaabbaddbdbddbcacbabaccdcdbbbacbbdcbddbdcdccccbabdddccddaddabadcccbcdaadaddddabcaacabcbcbadbaaadadbdddadddaaaaadbcadddcdcabadbbccccadaaadbbbcdaacbabdaadddbacccaaacaaadbcccbbadcaadbadcacddacadaddaaccbdccbdbcaccdabaddccdcbbaaabcdcacdbcdadcbccdccaadacbcabdcdabdcbbaaadcbadacadabcbccadbadacabdacdcdbdbadbdbdccccaadaababbdddbadcabbcdcbddbabaccccdaaccbaadacdcaadadbadccabdabbcbbdcdbadabdcaccdcddabbbcaaabaadacbddcbbccccbdcdcbddbdcabbcaccbbdbadabddaaacccabccbabdbdadaccddbbaddaddbdacccbccabdabdbcccacbaddbacacccbcabcaabbbbbadbaddaacacacaddcccacddcddbaadddbdbbadcccaaacbcacabccdcddddacccbacdcdcbabbaaddcacbdaadaddbdcaccbaaddbddbbcccdddbacbcdbbcbbcbdbacbdbcaaadbabcbcbdbaccabbcbabababdcbccbdbabdccabccdaccacbbcbaacbcddaadcaaddddbdbdcdbadcbcbcddcbcccdaadbaadaacdabbacdbdcccccbdccdccddbcbbcbcdbdcddddadaabbbcaabcdbbdccdadcdddbabaacdbcdaccadabbdcaacbbcaacabdbbcbbacaadbbbdcdacbdddaccddbdadbaadbcbbcdabcdcacbdcbaaacdccbbdcdccbdcaadabccbbdabccacacdbadcaabdadbdcabdbcabcbcababddbcdcadacbcdabdbcaabbcaddadddaacdbdccbacbdaacbccccbacbcabcabaddcdbbabbbbadbbdaccacabbbdbbbdbccdacddaddcdcdadacbaabbbccaaadadddaabdcabacbccadbddaadbccbcbddbacdabdabcdccdababdbbdbdcdbcdccbbbcbddbdababcbdaddddbcdcdcbdabaddbbcabdbbcabdcdcdadadbcaadaddaaacdaaabcbdcccbdadbdccbcbbdcbadaccddcccdbbaccbadcaabdababdcabaccaaabbbccdadbdbddadccbdaccbdabcbcabcccdcccdbcaabdabbcdaddbaddbcaccbacdccdcadbbacadacaacddbdddacdcbadaacaccdabcaccabbcccdcccddddabdddbacaaadcdaabaabcaabacabddbacdcbaaabadacbcabbccdbcbaacabaabbaacdcbaddbdacadbccddccaaddcadabbcbaccbbacbddadcddcacaccccabbcacdcdcddcbbbcbdabbddbdbbacbccddbabddbdddccaaaaccdccadcacdbdccdbadaacddbdbdcdcccddbdbdaadacadddabdcdcacdbbbadbddddabbadbaaaabddcdccacdabbdcbcbcabdacbdddabdbbdbbcbdcbdcdbcddbdcdbacdbdaadbacbbcdbbcbacaabbccaadbdcaababddacdbbbaccbdbdcbabdadcacadccabaddcbccabccadddaccdcbbcaaabcbdbabacadcdaddabdabbdaacdcbcccccacdabdcbdabacdacbbbbbdcbdaaacdbbbcbaabacaaadacdbdbcadcabdcaaddbdabadadacbbcaaacdddcddbccbdabadcbddcdaacadddbdcbdbddcdacddacabcadabacbbdddcacadaaabddbbaadabaccabccabdbbdcaddcacdddccddabcadbbaaabacddbdabdbccbddccdddccdbcbdcabdbddccbbbdbcbbddadddddcbcadddacdbcccccccdbabaccdbcbdacbbcddbdbcbadbddaabbcaabddacdcabbdbdbdabacbbdadddbcbadbadcbaddabaabbcbbddaadbbcaadadaddbddcdcaccabccaccdbdacbbccabbdabdabddbcdccaabadbcdddbaadcbcbcddbddaabcdabbbacbaadadabdccdcdaabccddddbdcccaacddccacdbbccdabcbbdbaacbdcbddaccbcdcacdadbbdaaaabcddbbbdddcddbdbdaaaaacaacbdaadbacbbbdcaabbacbacddcbddacddddbabcabdbcdbaabcadccabddddccbccbbadadbabbdadbbbadaaccbddbaabbabddddbbbcdcdcaddaaccdadbbbaadadaccdbacbbcdbcdbdaadbdadbcdadcabdccabdaabddcdcbbbabdccaacbdcbcaaacaabcadcaadaaaacddcbdadcddaddacaccaddccdbccbbabddbcbbbbaabdcdcbccbadbabdcddcdacccbdcadcbdcbcaddcdbbabaadbbacacbbabcdacbbbcbdbddadccadbdcadddbbdaddcdcacbdbbdbddcdddcbdcbadcabbdddcacbdbabadaaddadcdabacdaadddddcbddcaabcaddcbaaaacbbddacaaadbbccadddbbcdcddbaccbcddbbacaaccdbdcccbdabddcadacccaccddddbcdcacdcababaaabccccdcdacdbdcdddcacdddacbcdcddcdddcbabdadaddacdcbdacbacccbbaabbdaaaddcdbddbacabcbdabcdcbbcbcabdccdbbddaccaccadcdaadababdaaaaacdcbaaadbcacdaaacacadbbbadbdbaadcaddaacadabcadbaddaaadccbbbbdaabbcbdcdabbcbdcbaadadbabacbbdabcddadbcbbaacdadaacccbbaacdcadabbcaccbdcdbbbcdaababcacbcdcbcaaaacdacaccdbaaccaadcdbbddccdcadcbdddbcddbdaaccdcbcbdbddbdbcbbddacabcabbdaadcdabcaddadddadbcdacddaadbadbcaccbabdbaabadbcdddbabcbbdcabbcbbcabbcddabbccbaacdbbbcdbacdcabaaabbbabaccaadddbdddbdaababaadcaaabdacddcdadcbdbcabddcadaddcaaadbcacadddccbbcaddbcbbbcbccddcccabbbdabbddadcbadcccadcadccdbdccbdddcdacdcdcdbddabbcbacbbbbccabbdadccaaccaacbbcbdcdbcdcccdddbacaddcaddaddcbdccadddbbdcccdbadacaccdcdbbdcaaccbddaddacccdaabcbdccacbbbcbaaccbddddcaadcddbabaaabcccaccdadcdcbbcbccddddcbcdbdacabdddbdbbdacaadddbbbdccdbdacaddbdbcbabaacadcdcacadcbdbabdbadddddbbcbcabdcdbdbdcdbdbbcccbdaccdccbbdbababbcbaadbddacddbcadaaacdabacaabcdbccdbbaaddbacbdaaabacdbaacbcbcbdacdccbccacaadbdbcaadbacdacbdaadccccbaccddcbadccdcdcbbbbaaccddadabddddcabdcbbdacccbbdbccaacaabaacddabbdcaabdaadacccacdccccccabcddabaccacbccbcaddbccbbdbdbdcdbdacacabacccbccccddbcadaccbbbcddcdcbbbdbdadbbadaaadccbbcdcbaaabaacbdaddccdabaaddaacabbbbdcaaddaddcbccccabbcdbcbadbdbcbdbababddcbdbdccaacabbcdcdbaababdacabcdadbdbaadddccbcccccdbccdbdbcaaabbbccbdcbcbdaacdabbbcddddcdbddbaccaacbbdbabbddadcddaaaaadabcaccbbacccbabbbddcaacdbddabacdacbcbdbdbbabddbcacddccdcccccbaacaaaaddcdddadbcddcdddbadadaccdabacbacabacacccbadaccccdbabbbdddccadaaadacdaaabdacaacaddbcaabbbdaadddcacaacdcdaccacbcdcababccbcaacccdbadabbdbdacddcccacdbdcccbcbcbdbddbddaadbbbacbacacdadcaaaddbbcaccacddadabdacbabdcdcbcbdabacccabdbbbdadacbdbadddcddbaaacadcdabcdcacdacdcdabddadcbbdcaabbaddcdddcabadccadbadccacaabdacbcbadadcccaddbcacdbdccdbddcdbdbbaaaddabbaddaacbaadbbddcaadcdbbbddbcdabccacbddbadabbccdabcadaaaacaadaabdbaaaaabdbdbbdaacbcbbcbdccbdddbbcbbdaddaaddddddbdbaccaabdbbbdabbcaadbdcbbcbccbdbccbdccccdaccacdbbaabbbacabaaacddcdccbbcdadccdcaaddaddcabcdccbabbcddacabacdddcaaabbcaadcabbadcdcdbcabacbdbabdcacddadbadbcccaadbaaacaadddbdcacdcbdadcbdccccbddaaaacbcadccbaacadbbacadabbdddbdbccccbaddbcacbacbbbcbcadcabdbddddadbddaabbddddcdaababbcbdbdadcccbcdbdbddababcbbbccdcbbcacdaaadcadcdcdcccdbbabcddabccaacabcbadbbadbaabcdbacbaddccadcccabbbadcbcdcacabaaaccdadbaccddacabbabdbcdbcdddcacdcddcdcaddccbbdbdabdaaadbbcccaccbabcbacadcbadcbdcdacbccdacdadbadacbdcbbcdddcbddbddcaacdccacbdccbacbacadaabbbcddcdcdccaadcbaccbcadbdbcaadccdbbdaadacaadbbbbbaadccacabcadaaddbadddcdabcdaaddcbcddbccccdbdabcabababdcdbbabcdddcddbbbcdacaddacbccadbccdbdbdbdaccddabbdccdbdcdadaadbbcabadcbadcdbbcdccbacdcbcbbcacbbddbdbdaccdacbccadcdcbddbbddababdbdadcbbddacadacccdbbdabbbdbcdabbbaabdbbbadbcbaccddaadccdcccbddacaaaaacbcadcbbabbbdaabdabaccddbadbcbacddbbbcaddcadcccdccddcdddbdbccbdccccbcdcacddcdbccadbbbbbbccbbabdcbddccbdcbccbbdccaacddddbaddadaaadaacabbbbcbbbaaabdbcddaabdbbaacadcdaccbdaaddababdbbbbcbabdbaddbacaabbaaaadbaccdbdcaadbbcbabcddbdadacbdbccbdaabbddcdbabadbdbadbcbbaabdccaddacdcdbdacccdcccdbaacddadbbcbcbbbbcadaabcbacdbacaaacccabbabaddccccdbaddbaaaacacdbcadadadbbacdbbcbccddadcdcabcdcacbdcacbabbcbacacacbccacbdaacbadbddadccadcddbbadccbcdbdcbadcbccccddcbdbbadbcbcaddaccccbccdbcbaababbbcbdadcaacabbdbdcacacadacadcdbaabbdccadcdcccbbabdacaabadcbddccbddabcdcddbaaccbcaddbaaaabcbcdddacdcaabcadacabdbacadbcaadaabbaaddaaabdcaacacbccccaddcbabbbcbdcbbabcccababaccaddbdcaccbcdadcdccadbcdddbdcaddcabbaacacdabbbddddabbbadcdddaaabaccdbdbbcbaaaaccaabdbcbaabbbbdbcaacdbbbdcdabdcbaabdcbabddbabdddcaacddddbbadacbdddccadcdbaaacddcbbdcdcaacbcbdbddbccdcdcdbbdbcddaadcabdcdabadbaaadbddcdcbddbcaaabbcadadcbaddbcdccbaddcacbaadccaaaaccaaaaababadbcdabbbbbddcaccdddbcbbddcadddcbcdddbcccdaabcddacbbbadbbaaddbacdbdbcacadcdcdcdacacccdbbaddbccdccccabcbaaccddddddcbbcacdaadcccbacabdaabdbdddbdadcadbaadbbbccddccaddbaaadccdaaddcdacdbabcdbcaaddcacdbbcdabcddabbaabbcbabaacdadabaacdaadcdbdbcdacdaddaaadbdccbadcabbcbadbbaadbadddcdaaadacdbbcdcbccaaaaccaadcbbabadcabccddbdabcbbdabcbdbcaaccbbaadcadcdbcbdcacdadccadddbcdacacbaabccadccdcbdcbbccbdddcbdbccbdbabbabacddccbabbabdbccadabdadddadbabbbdaabbdbcbacbabcdaccabcddaccadabdcddbbccbcdcaacddadccabdbbbdbddcbbabcbcdbbbbccabaadaccdacdadbabdccdbcadddacbbacbcaddadadaddcbddcdacccbdccbcabacbdcdcdabbdabcbbccccacaadbbddccaabddbcaaacdbdabcaabdacaabcdaabbcbcaabddcaababddcbadaccdcbaaaacccdabaabbbbbaddbaddccbbbddccdbdadbaacbddcbbabaabdbddbadabcaccdbaadaddacdabcadddbcbbbbccccddcbabcbabdbbdbbbabcdacabbcaacacadbcdaacabddccdbbbabccabbbdbdacdbbacbbdaddbbdcbccaabdbddabaddccddcdabddacdacaacbadbabaddbbdcdadcabbbdcbcacccabbcbcdbcdacadaaccaccacbcbdadcbaabcacaaddcddabbcabcbddbbddaccbbcacdbcbcabdabcaadcdbbdbbacbddddadcdacdddacbbacdbabcdcddcdccabcddbcbccdbabccbcaacddaacccdbdcaacdcbcdcbbcdacaaadacbdddadcbdcaddabbcaccdcbacccbcccbabddaabaccbcddcbdbcbcadcbcdddbcbdcdddcabdbccaaadbaaacddcdcdadaacadacccaddcccdddddcaddcdacacacccadbbacaacdcaacbcacdbdbdcdbabbcdccadddbbbaaadbadcaddbbddcacabbaadbcaccaddcdadacddbdbcbabadbdbdaccbddcbbadaaacdcadcbcccdbbccdbbbbdbdbacbbddaccadcaaddcbcddadccddcccdccbbbdcabacdbdddbddbcdbbbdcbaadcdacbdccdbacdccbdbbddacdaaccbbaccacabcacddbabbdddbcdcdddaccddbaabbbdcbabacbccbcbaddbacccbcdcbcdddcaaccbdaddabddbdacddbadaddbdadcbdadaaadcdaadacaabccacbbcddcacadcccddccaddbdddacacdcaaacacbbacacbbaccccaddadbaaacabcdbbbaaaacaadbcdababbbacccbcbbcbbcbdabdcdbbacddbbadcbdacbbbcbadbddbcddbaddcbacbbcddbadbdcbbcabccdacbdbccdacaacccabcddadbddccacddbbcabdcdaaadbadacbdbbbbbbcbbdbccdccaadbdcbdcdaaadbadacaacbccaadccbcabdbcdcbccdbccccdacdbbdbcaadcbdbcdbbcbccbaadaabcadabdcdaaabcdacadabccaddbaaadbdaddaadaddaabdaddcdbcaacabddbbadaaabbbcbbadccbdabcacccdccdccbddcddaacdcabcbabdcdbcadbbdcacccdbbdbbcbababdacadbdddbbdadcbabaacdadcacbabdbddbadddbcabcbabcccccdccbbbcbcdaddbabcbadbdaaccdcbabacababbabcaabbcddacbcacadaaaadddacaccdcaaccbcadddccbccbdccbcdbdbbdcdcacdbabbcbadbddbddccbacbdddbcadaabbbcacbcbacccbcdcdaacacadbcabdcacdcdadabbdaadbdbacbbcdacbaabdaaaddacdbbdbcddacbbcacdddbdadbcadacababdaaadbbcaaaddbbbcabaadcacaacdaddcbadcbdcbddcdbcbccdacbcbccccbaadbdbdacabdcabbddbdbdadcbcbbbcbacbaaabaacddaaddbabcabbbdbbabbcdccbbacdbbcdcaabcdccdddbddadbbbcadccabdbbdcccabbdbadcaabccddcbcdbcddcbdadadbbabdadbbbbcaddaabbcbcbbbdbbbaacdbddcccacacbdcbcacdcaaccbbacbddaadbcbaacbabcdcddbabaabdcadccbdcdacccbbdccaaccadadadbbdadcdddcadcdbccbacddbbcadadcbddbbaabbacdccdbbacaadcadcdabdcccadbdbdcbcdaddadbacddcccdbcbccbadaadcaabadcababdbacdadaaadabbdaddcdadbabcbdacdcddbbccccbbdcaccccdadaabacdacbdcbbcccbcdbbcdccdabcadddcdbacaddddaacbabbdaaccabbabccdcabbdcadbabdadacdacdcbadabdbdabbdabcbdbcbbccbbdbdcacccbdddbdcbbbcddccbdbdbbaaadbbcaaaadabdabddbbddabaacddddbdadaacadbbdadcbcaccdcdcadbddabccaccaabdacddcbdacbdbdabbaaadabddbddbabadcddaabdbdcddacbcdcadbbacbcaaacbdcdcacacaaddaddcbadbccbdcbbbcccddbddbdabdcbadbccaadbdbbbaadcdccadcdaadccddcbbccddbdbabaccacccbbccccbcadcabbcacadaaccbdbbbabbbcddadabcddddcbbdcccdbadbaaccdccabccbbcbcbabbccababacabadddcdbcddcdaccaadbacabcbaabdcbaacddddcdbcbcabcccdbcbdcdcdcddcbcbaacbdcabbcabcddccaccdbababbcddaacdccbcdacbbbbbabadbdabababbdbdcbaaccadbdadabacccbddbdbadbcbbdcbaacbabcccadaaacddbbbcbbbadadcdbdbdbabcbddcacbddbcccabacadcbbbdcdacbdccabbdcaacabccdacddcbbcaaddbcdaddddbaacbcbacbcccbdcccdcabddccabcbabcccbbabcbdbcabbbddbdddacdddccdcadadbacacdddddbcdaadcbdbadddcccbbaadaccddcdbccaadaabddaaacaabaadbaabdbccadcaddbbdcbbcbaddacbcddadddddaaacdcadcaacaddbddadadccdaaddbaacdbbabbbbccbdacacbbdaccaddbababddcabbccdaddcccaadccaaaaaaaddacbcccbddcdbcdcaccabcbdbcdccacdccdbbccdabbddbacddaabbbbcdccdaaccbababcdabdcbdcddabddbadbbdabccdabbadbcbdbbdddcbbdacbcbadbcbbaadbcaacdadadbbaddbacccbbcabcbdcdbccdcabccabcdbbdcbdcbddabdbadabacbaaabbbadcdcbadacdbdadbdaaacdbbabccdbdccbbddabadbbcccbadcaccbbbacbddbdbaacdcddabdabcacdccbdcdadbcccaddccacaddbcabaadbadbaaadccabddddbccccadccbadcdddbcbcdcdccccdbdaccbbbbaaddacaccaadccdaabbbccdbbdcabcdcddcabccbbbccacbcdcdabbddcdddaabcdacaacadadaadacdaaccbdacccabbbbaadcbcccaabdbbbcacdacdadcdbccacdbcccbaccaaccddabdabdccbacccdddccaaaaabbddccaabcabbcdbdaacccabccdcabccccabcadcdbddcdabdcdcdcbaacccbdcccababccbbaabbacccbcbbbdabcabdcabdacdadaabbbbbbadbaacaaaccdccacbcbdbdcdabdbdacaabddbdbbcadbaabadaacdbcdbabcacdadacdaccabaaddccddcaabcdcccadbadcdcbbcddccaacdbaccdbaddacadabaacbababcbdaabddbbcbbaadadcaabcdcadddbdacbaddaaddbaacacdadccaacaccaddbcaaadaababdcabcbbcababdbadabcdadaaabdbddaaaaccbbcbbdcabdacbdddcabcddaadadddccccbdabbddaaccbcdbdadaabbbddbdcbdcbddaacccaadaddccaccbdadaadcbddacdbaacaadccccaabbbbdcdbdadbabbdbcacdcaaddadadddaaaadadbadbbcbacadadadabadcccacaadccdaaadaaacddabddccaaccdbccccddcabbddbcaddbcdabbdcaaabaabbcdadcbaddabcbdaccdcdacbaaabaaabadaabcdcdabdddacdddbaabdaabbcbcccbddbdacacccdbddcbdddbddacdcaacbdbccbdbdcbcdabaccdccbccacdcdbbdbccadcccadbaadbddbcddbdabaacbbdcbadccadbdabccdaacbabbbcbaddcbaddddccdbbdcabcaacccbbcdacabacabbaabdddbddddabcbcadcbbdcdbdbcabdacbbbbadbbddabbbdadcdbabcdbccbaddbbdbbbacdbadbabbdbbdcccbdacddabbabbccababdccdbdbbdacbbaddbcdbbdddabbadaddabdbbaabcacdadcbbadadabaabcccbcaaacdddbaccbbdbbbbbaababbcababaacdbcbbbbdbccccabcccaaddddbdbbbacaadadabccdbcbaacdacdccababadbbbddcdcabcbaddadccdabccdcddcbacadcdbbcbabcdbddbdbacaacddbaadabdcdaabbaaaabacababdbbcaaadbbabdaddaaabdabbcaadacddddcddbaaddadbbcdbbcdadcbcdddbaabaaddacaddcdcddddadabaaacdaaddbadaddccbbdabbdbbdcacacbcaccddbbcbbacbdcdadabbbdacadcdbcdbacccbddababacaabcdaadaddaaadcdadcccbacddcacbbddbadbbbdbcaadbdaddbcdacadddaccdbbbccadabbdbdcccbdcababbdaddbcddbcddbbcabababbdbaccbbdddbcbacadccbacdbbcccbbaadacdacbbbabcdbdacbdcbcaadcbbadcdabdcdacdaddcbdaddcdddaadacaadbbdcbbacbadacbcbbbdacddcaddbbcbdcdcbdaddcdddbabadbdccbaddaddabbabadadababacacabaaddababcabbcdcccbccabccdabaaacdabcabdabbddacddadbbbcadcaccaccbcccaabccccaadcbccddbaabdabbdcbdbdcacaaacacaaadcdcdbccadcdcaadddacdbcadbccbabcdcdbadccdbdabbbbabdabbacbcdadabbaabcabaccbaddabaddbbadbbbbccdcbdccbbbcdacababcacadbcccddbcdcdbddaabbcdcddabddccddbacddcbbddaacadcdcbadbdaabbdacdbdbbddbdcbcdacdacabdbddbabcdacabbcbacbacacdcaccbccabbaccdcccacabdaaadbaaaabbabbabaacabaaaacbddbcbcbbadbdcccddcbacdabdbddcdabdbdadacaadbadaaaabdacdbcddbbddaaadcdaabadaabbcbaaddcdaadabdaabbdbdbabacaacacbcdcabbdabbdbabacaddcbaddcaadacddadaaadddcbcaadaccbadbadbddcbdaaadabbcbbbbccababcabcccaaabcdccbaaccdbbddbcdabaaabdabcdabcddadbdbdcccadadaabbdcacdccaaaccddaaacacddadbadacaabccaaacbcbddaccddadbddacabbabdccdbddbaabccdacdcdabbccdcaccabdbcbacccacbdabbbdcdbadbccbbbdbacbaaddddcacdbddcbcbccbabddcbcdabcdacdabcadbbccccadddccbbdcbaadcbcaaaaaababccabaadccaadbcaabbacdbcbaddaabaaacaddcdbcbabddaabbcdcccabaacdaacccabcccdbdcacbcbbcdcdbdcbbdbbccbcdacaccbdbcbdbcbcbcbddbabcacdcbbadabdcbabcbbaababaaadaccadadcccaddabbbddbbdccdbcdabadccddbacdabbaacabacdcbccadbadcdddcddddaaacccdbccbbbaacbaacbdcdccdbcaadcbabbcacaabdcacdbdcdcdddcdabbccbdccadcdcbabcdadbcbbddcddddbaccdadbcdbdbdcadadabacbdccdcbddacbacacaadaddbadaababdcbbcddbcddbcbdbacacccdccbddbdcacbbacabaabaacddadadbcbddacdadacccbabbbaddccbadacadbabcccadcbadaabaabbcdcdcdccaabadbbaacdbbcaabacadccadcbadbbabccbcdcacddbdcacadbadcbdadbacbdcbbbabccaddbddaaabdadadcacabdcbaababcacdadadcddcabcbcbdddcdbbcaaadccbbcddadaacbcddabababaccaacdbbaddadaabcbddbddcdbbcdcdcdbcabababdcaaaadacccabbaacdacaccbabdcbabccaabaacdcdcacdadaaddccccbcbbbcacdacddcadbbdbcdcccacbabaccbabcbdaabcdbccadccacddacdcbddccdbacbddbbabbdddccbaacbcdabbdccbbdadbbddbaacaaadacdadcbdcaccccdbcbadcdaabdbbbbadbccdddcabdcddccccccdccbabcdcbaaddadaaacadababaccbacadbbbddccdaccccdcdaddcbdbdbadaaaddddcccaacbdadbcddababadcdddddaadaadddaacdabcdcbbddbaccbbdbaadacacdcccbcbcdbaaddcadadbdabdcdbcdadbccdcdccddbabccbadbbbbdacdabdcaaddabadacdbcbddbadacdabccdbdbaaabaddbcdbdbacbdcbdaddabbdcbdccdcaabbdcadcacbbacabcddabacaabacbabcccbdaccbbcaaaadabccddacdbabadcbbaadcabcccbadadbbbdadabcbdadaabbadddccbdcdbabbbddbadccabbbcdbdaddaccbdabbabdcdcbadbdccaddadcabaacaaadacdbdccddccaccddabbddcddaccbbdbadbacbaacacbdbccaadcbaadddcbaabdcdbbcddacddbbaabccaabdaacbbbbddbddabbbccadddcaccdbbdccbabccbdacadadbbbcdadadcdbcbbbdadbbadbbdcbbcddddbdbbdddaabdacabaaadbacbcbcccbbcccbddaaccbcaacbbaddaaddddbdbcddaadadccabbabacdbbcddbdddbcddddddccdacdbdccbabdddbcddcdddbbddbaacabdbdabbbabcaccabcbdcaaddccbaccdacadcaacdcabbccadddadbcbdabbddacbbbdcbbdbadddddcbddcabccdbbbbbcdcaaadddcbccadbcdcbbbaabaacabdcbdaadadddadddabdcddcadbaddadbddbbcacabdaccadacbdbbcdddcaaadbdcbbaacdbddccaaababcaddcacddabcdddcbccccbcbddcbababcacdbdcccbdcbbbdcadaabbcaccdbbbcddaabcabcdadaaaccdadbaaacbdbdaccabcbddacbdaabdccadabdcdcbcdbbdbaadabdcbabccbbbbcddbabcadcdbcdcbdccaaddbadbbadacdccbddacdbcdabbbbaacbcaacaccccbccdadcaadcccbbddabbdddadbdbcdaccaabdbbdcdccbacbcacbbcbaabacccdacaaaacdadaddbaccabdbdaaaadcdaadbbcbccababcabbdcdacdbbddaacccbdcacadcccccdadaababcbbccdbdbdccdbcbbabaaadaabdacaacaabaccacbdbbbbdaaabcbbcddacddcbdcaadcdcadddabbbaadbcaabdbdabbbaaabbdddaaabccdbaaddcabccacabbcdcccdbdbacbadbcbaddaabccbbcdbabcbcddacbdbbcdaacbbbbcdbacbabacbdababcbdbabdadbbbccbccabcbcdccdcadbdcdabadddcdbbcccbbdcbcddcdccacbdaabbcdacdabccaccabcbbaadbbabacdbabdacbdaadcabbcbbbaabaacdabdaccbccdbabacdbaacddaddccabcddaaccdbdddcaabcbbacbbcaccacdabccaadabaddaaddccaabcdadcbbbdcabbbcbbbcaaacaacbacbddccaadadbdaadcabbddadadbcdaabbddcaacabcdbcddbabadadaccadbbcbaacabbdddcccacbdbbcacbdacdcaccdaaaddaddddcccccdcbbcbaacbbabadcddddbcdbccacdbacdbbbddbdbbddcbabcaaaaadccadcbaacbbcdabadcddbdcbcaacbddadbabaacaccbbbadddbdbcacccdbbacbcccddaacacaabaabcdaaaaadccdadacdadabcbdcacadacaddbbdaaccacababaddddcdddabbdcbabcdcccaadcaacbdddbdcdbcdcdcbaccbcaadadbacaaaaabdcbbdbcaccacbdbdaacccadbbcdcadddaaccbabaabdccddccddbadacaabddcadcbbdabdcadcbdbbcbacababaaaddaadacabdacaaabcdbccdadbdcabbdbcdaacaccaaabbaccdcbadbcbccdddcaccdbdadbbaacbcbbcacdbddbdcabcccdbaccbbbbddadaadcccccbcccbaccddccacdacbcdbbaaccddcacbaacaddbcdadbbaacdabbddbbacbcbccccbdcbcccccddbabacdbaaacababbabdcbbddcdacdbccccccdaccccbadaccadddaadbbcccddaababddabddcbbcaddbaacbbcbadccbbcbdcbddcacddabbdaadbdacccccbcbdabbcdabaacccbcaccacbabababbbabcaddabbdddcbabdddababbcdadacdaccdbdcbcbbccbcbadddadadbcdbacaacadaadabdacbbbadcbdacdcbaaaccccadaddbbacdcadccbcbaabbadadacaddcdaabcdaaabbcacbbbbdcbadbbbadcacddccccdccccadaabcdccdbbcddaddddbddaddacbcbacaaddccadccdddaaaddadcaacabbdbdddbccdcacacbbbaaabddcdcdbddbadadbbbaabdcdccbbabcbacdaaabbddcbdcbabdcbacbbcabadcdadacacbacbbdbdcacbcabaadbacdbbdbdcaddadcdccdccbaadbdcddcaacaabdccdaaadaacadacabcdcbbcabdcacabcabcbbbbdacaacbddddcbdacbabcacbdadbcbadddccbadbdccaddaccbbaadadbadabadabcdddccbdddadcbcdabbababdcbbccdccadbcddbbcdadcccabadbdcbccabadbadcdcbbbdcaadcbddccbaaaaaacbcdcadabdbcdcccaaadbcdbbbbbacaaaaaacccbbbbcddbacacdaaadbbbacabaddbdbdbbabdccbdddbaadbaccdabcabcaaaacaaabbcccbbcacbbaadcddbbccccbddbbbbcbabcdbbbbcdadcccbbdbadbbcdbaaddabbbbcdbdddabbdcbbbabaacdbbbabdcaabaddacacdbcdbbabbcadbacdbcdbadbbdbddcdbabddccdbaadacaacbbabaaadcccbacbaadcaabccdabddcaabaacacacdcbadadcaabcdaaadacadabcbabcbdadbbbcbadbbcdbccccbdbabdaabcaddbdbbbbcbdcccccbadbccbdddbbdcbbdcbdbcbaadcbbbcccabddbbbcdbcbbdbacdccdabbbdcbcdcdababdccdabcbbaadcdaacddadbcbddbcbddbddbacdbbcbacdabbcccdbaabaababdccbabcdadacabcadbbcbdccbcaacbadccbaacaaabcabdbcabdbbcbadacdbacacabdbcdcdcbcccdcddccccbdaddccadbbacbcaaaacbabcdbdbdbdddaccadaabbcadcacbdadadaadadacbbbcbdcacbcddbbbcabdaadcccaacbabadabacaccabcbcbaabadacddcdcccccdbacdcddbdbcbcbbdbadbbddbdbaabacadccbdbddaddabbcbdddbbcbadbabbcbdcaabdaabdbcabdadcbaaabcdadbdbbdbbcaddaadabacddcccabbdccbcdbacabaaccbaadabcccbddcaabcccbbbabaadacbcbdccacabbcbaabbbdacabbbbcbdbbbcaaaacbadabdbbddabbadddcacccbccdccabbbacabcadaadccdaabdcbbddacdacadcaadcacbdbdccbaacdabccddddbacabddcbacccacabcbddabcdcaabcbcddacddaccbadcaaaccdabdacdacddabcdbdcddcabcabcabcdbdcadcdaccccbcddcbcadabdaaaabdabdaccddbcdbbdaadbbacbbcacdcacaaccaddcabbcbacddddbddcbbdbcdcccadcaddccaabdaadabbcdcddababdbddacbcdddcadabcacddcaccacabbbdddcbbbbdacbcdcaabbcdcbcdcaadadbbaddccccbbccaabadbbddcdccacbddddcccbcaabddcddbbadbbcbacbddadabdbcdbadcccbbccdcadcacbdddcdaabcbdadcdbdcbadabccdbdddbdadbdadcbbbdbbcdbdbddabdacadaccabbbcbddbddcaacddcaacbbcddacccdbddadabbcdabcabcddbadacdbcdcabdcbcccdacdabcbbcbdcacbaadbabbccccbcbbbacbcbbbbbadadbbacddcccdaddccacccbaccccadcccaadbdabbaaccbcddcdcbcdccabdbdbbdcccbdabdbdcaccdaadbdccbdbdcacabbaddbddbaadbdbdcaaddbcacbdadddddbaabadccdadbbaadbdabaacdccbccccbcdacbaaaadbbcbbddbdbcbaabdbdaacdabbbccddadaabcbdbdccaabadddccadccdaabdbbdadcaccbbbaabdadcaacdbdaaacccbcaddadbbdbbccbcbbcadbbccbadcaccababdbdcdbccdcbadcbababddbaaabcdcacabbdaccadbacdcccabccbddadcbadbadddadbdbbbdcbaabaadbbcaddbdbabdcbdddbccbbcdadcabccaaaadacabcbcccbcbcbbcddcdccadddaacbaddccbabcdcccaacdbbcccacdacadaadadbabdaddacdabcdcddbbdccddaacaadcaccdadabcadcbdbbdcacaabcbbdabbcddabbacabbabadaabcbdbbbdbabdcabdababacccadbcaaddacbadcacdacbbdabacbadbdadbaaabdadacaadacbdbdcdbddacdcbaadadadadbcbaccdcbaacaacadcabaabdbdbaacacccbbcabcaccbadddaadacddadccdbccdcbbcaacaacadbdcbdccccbdbbaadaaaacbcbbcdacbbadcdccadbbcdcbbabbabdcdcdadbbdcaadbaacbadcdddcdaabcddaadddbbcacdaabddadbcaabcdabdcdccccabbdbdacbdbbccaccbaacbabdbaabababdbcabaddacadaadcaaacbbbacdbdbaabcccbcbbdccadbccaabaabaaabdddbdbdccdbdcadadcccadbbcdbabccbabdcbcacbcccaacbdcbcbaacdaadbabcdabdccbcdaaddcdacbacbdbacbbdaabaacdccdddbdbddbbdcdbdabbcbcdabcacdadbdadddcababddddcadbadccacacbacccaddbcbacdcddbcbbaabddacdbbabbbcddabaccdccbcadaaddbdcdbaabcbbabbdbdccdacbcbcabaddadcdbbaabccddcaddcbcdcbaaccbddcddaadbdcabdbbbccabcddcdbbccbdacddbccaaadddddaccaddcadbdacadbaaaccdcdccadbacabcccbcbadcbbcccabcabadcbadbcbaabdcbbacdcadccdadaabaaabbadadbcadabdcbacbacbcdcdcaacdbdcdbdbacababbccbbadcaddacbbbcabcbddcdbbaadbcbdccddcccaadccdcbbdbbbcdbbcdbdcabddacdadababcaccdcbdaabcdbdbddbbccacbabddbbbcbabcbbbbdaddaacdbcdacdabdbbbbadbcbdbaaccdccbccbbdbabbcdddaaaacbadbcdbcbccaccdacdcbcdbcdbcbdabacdcbaacbdacbbdddcbbabbbadbdabdbcddbccbdadadacbbcdcdabbaacdbdcdbcddccaabcacbcaabbacadcaaaccddcccbdbddaaaacbcbcdacabaabcbbccccacaaaadbcabacccbcaddbadacbabaadcbbdacaaadbbbddcccbcadaaacdcdbdabdbaadabadacbbdcabbdcbdaabccabadcccdddadcccdccdbdccabbacadacaabaacaddbcabaacdbbddbbdbacdbbcbacaabdccbcaadccccacdaaccbbdadbaaddccddaabaadbbadccddcbbccadbdaabbddddabcdabcacddaddddbadacbcbbccbacccdcbaddbccdbcbbbddabbdabcbcdbcacadcadbdcabbbcacdabdadddbaaacccbcdcdacabbbcbcdadddacbdcdbbbdcccabaabdbaddcbccadbbdacccadabccdaadbdddddadaacadcbcdaccdbbabdbbcaddccddbbddcddddbccdbbddcdabbdbcdaadabcdcdaaccbdcaaccadbbcbbdcacbabbddcddadbdcbbbabccbcdbbcbbccbbbdabdbbbbccdacbccaadccdbddbdbdbbcbbbaacccbcaadcbcabdbaadaaccdacdbbaaacdbabcccacaaaaabbbacbdcbcdccccdcbaadacdbcabdcadbddadcdbccbbbbaadcacdadcbadbabadccbbbdbcadccdbaabbdabdadcbdcaadcbcdddcdbbdddddabcaadcbadabdcbddcabdbbabbdbddbadcbacccaaaacccbdcdbadccacddacbacdcbbcdbdbbbdbabcddabccbcaadddbbcddcdadddbcabdcababaaacabdbcadaacdcdadbccdcbbcddaaabcaabbbbdbcccacdcccbddbaadbadbacddbbbacacddaadddcaabacddacbcbddcadccbbaaaacbdadbdabcccadbacdaaccacdcacdacdccbcdbabdcbaadbcbcdcaadabcbaddaaacbcbdcdcbcbdacadaadaadddacaacdcabcdbadccdcbcbddabaccbdbacbcaabdccbbbcddbbccccdcbbadaaadcbdaacbdcccacabacbadabbbbbcadcbbcaabccddaabadcbdbadbcdcabbdcbdbbbbbcdddabccdacddcbbbdddbbcacdadabdbcaaaababaaddccabcabdcbccadacdaaddabaaaddadddbdaddabacbabdaaaaccaccbcddbcbdbcadaadccdccbdbdadadaaabaccccdaaddbcabbbaacdaaadccdbcbdcbaaaadbcdcbdbaadadbccadabcadbabaccbadbaaacdaabcaccbccaaddbdbaabbbacbabbbbdadcdbcdaccbcabacdacdbccacbbdbabbcbbccbdcdcbccadbaaccbdcbccadcbbabcddbbbcbcbcadaabddcbcdcdbdcdbabbadbdbbcdabbbdcddaaaabaaccadbcdcaadaaadbabbdddadcacacdbddabccabbbabcacaaddacdccdccbbcabaaaccbbcabadabbadacddbacabacbcbcdaacadccbbddbabbdadcbcbcccbcadbacbddadbdddadbbccdbcccdbacccabdcabbacadbbdcabcdcbcbadbacbbadccddadbdcabcadbdcabdbbacbaccaaadccccbdcbdbccadcaabbdccacaabaaccddcbcdddcacbdcdaddccbabdacccaadcdbadbcdacacddcdbaaabcddaabbbdaacccdcbccacabbadabbaabadbcdcadbddcbbdcaaadaaaabbbababcadababacbdcccaccbabdcbbbbbddbccbbbacdaaaaacaabbaacabbdbbdacdbabddcadbbbbbcadccdcaaaccbcabacbbbdadaaaaadbbcdbcacddddcdccdbcdbccdbaaddbdbabbdcaacacacdbcbbbacdcacccddbdaccdcbcadabdcaadbdabaddbbabbcbdbaabdddadbbacccccbbddcbbdcaaabbbcddcbbcbdbadbddaacdacdcdddddbacccacbcbdaaabacbbaacadcbccddcbaaabddadbbcbccaacadbaabddcbcabcbadaacddaddaddcbbdcacbacdccdcddbaaddabcabcdcbbdbddbdbdddddabdccddccdccdaacdababdaabbaddaacacdaddbbabcdbccacbbabbbddaabcaabbcbcbccaddcdbcaabbbaabcadabcbadacbbbadcdcacccccabbdbabcdaadbcdcabdacdbdaacacddcdbbbcdbdcbdaaabdbabddabadbbacbabaaabbaaadaacaadadacdccdddddccbcaccadabadcacbbbdcdbcdbbaadabccddbccadbcddcdcbcbaabacccaacabbcbdcbcddadbbcddcaddcbcbbdcbdbabaabbaabddcacadccbcdcaddcabddbbdcadbaacabcdacdbaddbbbadccdddadcadbaacddbbacaaaacabadaccccdacdacdbbbbdcdaabccacaaadbcbcbcbdcdcaadcadcbbdacadccccbcbacabbbbddaadcccbcadbaacdbadacdabacbcccadddbdcddccbacabcbabdabdbddcdcbbcabadccadcbabbbddaaaccadbaabbabbccdaadccbcacbcaacbddacbcbbaddccdabdbdbcdabbccdaadcddadbacbbdbabddacdadcaccdaabbddbbbcdabacbbacbcbcdcabaccbbabacabaddadccdabbdcccadabbaccabcadadbddcabbcaaccdcaabdaabdbabbacbbdccbdcdcdcadddcbbabdcdcabddcaacbcbccddcbadabcccbcacbcaadcbabbadbadaccbadacbbdabacddcbabaaccbcadcabdddaaadaadbcaaaaaaacaacdbcdccbbbbcddbddbbccdbccbbbcabaadcbcadbbcbbabbbadddbbcbcabbaddbccbbccaccdaddacccdabdbaaccadddcdbcdbbaadbabaabbdbbcdcacdaaccabdddcbcbaacbcbcadabdcbddaccdadabbbdbdbaabdaacacddddbaacbccdbadcaccbdbddbbdddaacadcacbccbbbaddadbcccbdadbcdcdbbcadaacbdddbccaddcdbadabcbbcddadcbacaabbadccdbadcdcacdbcdddabbaacabadcdcbbadbbbdcadcdadbbbcbacaddbacdabdcbaddcbaccbccdcbcdabababcbadadadabcbababbaadbacbcdaaaadbcaabacdacadcdddbdbccbbcdcdadadccdcddcbcdbcaddcdccdbbababddbaaadcadbbcdcbbadbdaabcacaacadcabaacadabccddddbabdaabababcbabaddbdbdbbdbaaabdcbadbcbabcbbbdbdddaccdbbcccdaddbcdbabacadcbcaccccdacdbcadcacbaaabcdbdadacdcbcdadcdbdcbadabcbdcdbaaacabdbcbcbcbbbcbccababacadbcabbdacbaccbacccbbbdaadbadabcbbbbdccacadbbccbdddbcddaaabccdaccbbddddbaacbdccdbacdbdbdcbdddabddcbdcccbdbcacaacdbcccabdcbcddbacdaabadaaacbcbdcacdbbcbdcbaccbcccaddccabaadbcaccadaddbaadcccdbbababdbbddcccbbbaacdbcbbaabdabaabaddcdcdcccdccadaabacaaccbacacbbdabbbdbdddadcddcbbcbddcbbbbaabcaadadbddcdabbaabbddaabaccacdadbababdcbcbcadcadadadcddababbadacadbdabbcaccbcdbccccdccbbbbcdabddbbacdcbcaadbdcbaccaadcbadcccdbdcdababaabdaccdcabcaaccdccdabdccbbbaccbcbabdddcbdcbadbaccdccdcbdcacabbccbbbdadbdabdbdbccbaaaccaabbbbcacbcadbadadbcaacabacadcaababccbabbdbcaddbdbdabddbadacbaadbddbddcacddadbddcbacbbdcdbbbbaccbbddacdcdbdbabbbdabdbbbdcadaccabdaddadbdccbbccdbbacbbdddadaacbaaacccbcddcdacddadabacbdbbaaddbcbbdbbcbabcdababacbbbdbacddbbbbbcbcaacdbcadbcddbcabbdaaadabcccdadabbbbdddacaaabdcbddabccbcddccabbaacaadacabdcbcdccacdbcadbadbdcbdcaccabbaaacadabccaccbadcbcdcbcbdaadcbadcdaccaccdbdacdccccbbacacaccbdddaaddadcbbdbbacbddcccbadcbcdaaabcdbbcdccbbaacbaadabddabaaadddbbacabbaabdcbddbdcbcaaacdbcdddbddadaabcbbcbabbcccdddcbdbccabacbdacdddbabbbbbdcacdadbabcadabbddcaabcdacababbadabbddbdcbdcdaadbabbdddaacbcbcdbdadadaabddaaaddbbaabddbdbcccaaabbdcbcdbbaaaacbabcdadacccbdbccdadaddacdadabcabbbaabcadddcbcaaddcdadabccaadaaccacdaacddaddabaccaadcbbabacbdbadbabcccaabbbcdddacabacaadddbaacdbcabdccaacdaaddbbbddcbaaacdccaaacbdcccbdadbdbcbaaddabacddadcdaadddcaacbbabbdcbccddbbdcaaacbddadadcdbbadacbdcdcbdaddbddaabdcabbdccbdbaaccccbdbddcbccbcaaddbacbbcabdabcbbabcccacdcdcacdaabdadddbddabadcadbcccaabdddbddcabddcadcaaaabcbabcaadacacdabddaabbcddaddaadddcbaacadbdcacbbcdacdcdbddcbacaacbaccdccbcaaabdcbcadbcadcdbcaccccccabcbbcadcadccbdcdacbabcacadbadbdcdcdbcddcbdbaabccbddbacdcbdbcaabbaccaabdbcdabadddabddddcaadbacdaacaaddbddddaaccdcddbcdbbaabbaacbbcdbcaddccdbccabdacbbbddcdcbcbcdbbadacdabdbbbcbdddccdccbaaadabcdcddbddccbaccadaaabdacdaddbcdbcbacbbacdbcacdadccdabadabcaabaacdcdcbbcadbaacbadbabbddacadddbaacdcaddcbbaabbbccdcdbacbbdbbacbcddccabbccbddcabbccadbacbdadabbbbababbcabbdbacbbdcabadcbaadbaabbaddaadbcbdbcacabdabcbbbddbcacccbaaabcddadaaabdcabacbdcdadbdccaadaccbcbdabccaaccbcaabaacbdcbdacadccbddababccaacbcaccabacbbbbdcbddbadcdbcabdaadbbaaccdcabacacdaacdbdbdaaaadbacddadabcdcbbaaabdadcdcbaccccbbaaacbcdbcbdcbabcbacbcdbbaacaddbbcbbdbddddccaccddadadbccacbdaabccbbdcadaddacbdadcdaddaabdaabccbadacdcbcacbdccdadabcacdadabccdadccdbcdadccccabdadcbdddbacabcbdabbaacbadaccddabcaacaccbcbdacdbcbdadbbaabdabcabdbdbdccbdbcdacaadddbdadcbcbbddbbbdbacccddbddcdadcbdbdddbddcdbbabbcddaaabcccaaabbcdbaaadbdbcbcbdbcddaccbcaddbcbcbcccadbcdaaadababdbdadabbbdabdacdddacdddaaaacababbddcacdbcaabcdcdcbabbcbabbcdcabdabaccacabbccbbbccdcbbbbabaaaabaaaccacbcaabdabbabddcacbadcccbbababcbacaccaaccbcabddcddccbabcdcabaaccbaccdccdcdaddbaaccdcbacabacbbcbacababdbdddaaddcbdacabdaaadadbdabddbbcaababbbaccbdcaccacdacabcadcddbbbdcabdbccadabcbaccaaddcaadddddbbdacddbccbcadbbaabdddbdcbdcdacdcbbdbddbbaccbacdbadbdccbbcadddcaddddaddbbbdcabbcccaadbcdddaaccbadbacadadccbcddabbadddadbabcdbcddcbcbcdcccdcaccabcabdbaaabccdbdddcaddadddbadbdaaddbdcabaadbbcdbdddbaadbabcccdadacccadbccbddcdddabdbbaddaadcaaccabbaadccbbcaaabcccbbbdddbbdccdadababbbddabbcbbcaacbdcbcddaddddbdaabccbcabdabaddcaaabbdadcaacccdadadccadcccaddbddbcddbccbccdbacbbcccbccbbaccddbabddccbdcdcbccabbaacdaccacadcdbdaabdbbcaaadaabbbdcdbabcddaacaccabbccadddbacdcdbadcdaaacdbbaabaccacbdddddbcccbadbadbbbdbcdadddcacaddbbcccbacbaaaccabbacbacbdabdbbadbccbdbbbdbdbddbdacbbacbbddcbbccdbcbdbbcaadcbadbdcbadcccdbadacaabbcadddbcbabddabcbcabcdaacaccabbcdbcabccacdbadabccacbbcdbddbacbccbaddbabbadaabbabadddcddbccdbdcddbcdbbdbccbbabbabdbabaddabadbcdadbbddbaddabbabdabcbabaaddcdaaadadaadbbdcacbcdaaddcadccdabadacaabbabcdbbdaaddccbacddbcaaabbacbdbdbcccbddabaababddbbadabccbcbadbadaddcbbdaadcbdddcbdddbbabdccacbccdbbcbcdcbbaaaacdddbdbddbdcccdacdbdacddaaaddcaaaccdcacbcacacbabcbbcaaabbacddcdbcbcadccbdccbadccbcabbadbccacdbaccbaaabbcdcbbbbddcbddabdcadbcaccddabdcdbcdbbdccdbacdabcccdccccadddcaadacabdbacaaabbaaccdcccaabdbdccdaddacdbdadccddcdacbdaabcbcacdbcccddcccbddcbcabadabccaaabaddcdadadbaadddcadacccabbcdcccaaddcabacaabadaacbdbdabbadbacddcacccbcadcabbabdacbadbddcabacbcbdacddddddbcddaabcabcdccdaaccddcddbabdaddbccbdabdabccbdcacdaddacddabdbadbdcabcccdacdaddbbaddbdbbaaacdbdbabaadbaaabccdcbcdcaacabcccabccdcaabdabadddddbdddabacbbcabcbdaccbcdbaaaadcbdcbccaabadaabcddcaccdccabbbbcccabbacadddcbaddaaaadacbaabcbabcbacacadacabcbbdbaccbadccabbcdddbcdbbdcabdbcdcdbdddcabcadbcaddccddbabbdccdcddbbacaabcacccddddccddccaacbdbbccbcdbdcadcbbbabacccaaddabcbbbacadcbcaaabccbaacdbcdbcdadbcaccaccabdcddcdacdbdcdcdcadddcadcacccbadadcaadbbddacdbadbcaacaadbadabdabdbabcbbdaacdcabdccdacdaaaadbcbcdcbbdbccddacaacaddaabddabbbddacacaccadadcaabdddbdcaddbdcdbddcdddbaabbcabdbdddcbcaccacabdbbbaadbabbbaabacabdacdadbbcdbdcadaccdbdbddbcdccbbcabddccbbdbacccadccdcbbbcaaaaabadabdaccbbbbdcbddaddcbcaadacdadcbbbdccddcccdcabdbbdbdcbdbabcbacbcdcdbbdbbdccdcdacddccadbaddbdaabadbadcbbcaaacbccddabaadaccddbaccbdcbddbbddaccbcdaadbabdcbbbcbbdadcccbcdadacacdcbdcbddcbdcbbabcadbddcddcbdabbbadabdbbbbddaaabadbcabcacabdabbdadbabbccddcccaddddaabacbcdadcdbcbbdbbddcababaacddbddbcacbbdbdddabcccbbdddbadbdbdaccacbbccdbababbcbddcddabadabbabcacaaaacabbabbbdbadddbbcbcdaabdabbccbadbdbababbddadabdcdcabbbabccccbcbdcccbabadacdabcaabdcbadbacacaaddcddadcbbcbbdbccbbbbbbcbddcdacadcbcbdacaabcdbdbdcccacacbbcccbcdbdbdbbdbdacdabaacadbcddcdccbbabbacdbababcdcddcadbdcdcddbbdbacccdaccbdcbaabacbcdbabdadaaaadcacbdbadbcbbadbcabcbddcbbbcabacdbbdcdbdccbaaccbddadddddcbcdbabbabcbbacdababacddcaaaadbbadbbcccadbdbdbdddddbdbacadabdacdaddacdbadaaddadccbddaddacbbaddcbdbcddcabbbadddcaddcbaacddcaacaabbccabaddabadaaacabbaadcadaaacadcccbbcadacdcdabbadcdadbdbdbaabbabbcbdbccdcddababcadcbddabdaddcbabccdcdbaccacaddbdcdbbcdcccdadabddabdcdadbcbdabacccbdbddabbaddbaaaacbbbcbaaadcbaaadacdbdcaaadabbabadddddbbdcdddbddbcaccdaaacacadadcabbdbbcaddadcdcbcaacccadbbaccaaaddbdaddbcadacabdcaddcacddbccbacbbcddcaabdbcacbcdbddbcdbdabbacccdacbaabbdbacdcadbbdadbbdabdbcdccdcaacddcbdcabbcbadaadbdcadacdbdbcdcbbcacccbbaccacdbbbccbdacdccbacccddaaacbbadddbacbdabcbcbcacbbbcabbaadcadadaabdbdabdaddccdbbdbcbccddcaadcddacddcdccaaccddcdcacbdaccdcbcbcbcbabacbdcabadaadbcadbcbcbaaacbcbaddddcddbcaacdbcabccadabbcdaccbaabcdccbabbabccddcaccddddaabbbaddbcbddcdaadcdbbdbcaacdbbccccaacbdaabcbcdccbabcdccbacbcccdacadabddadbaababccbdcbdbdbabcbacdbdbbbdbbdcccdbcddddcbacdccaaddbadabcbabddcaddaabcaddcdbdcbbadcabddbdaacbadccbbacdabddbacbacabcadbcadcccacaaabacbcccaabdbbaccbcaabcbdaabbdaabbbdbcddcaccbddbbccbbacaaaccabaaccbddccccdcbcccbcdbdbddcdabbbbdbdbdbacaaabccdaabdbbbbbaaabbaabdabdabbaaddbacdcadcaccaacbbddcabcddcbbccdcbdcdbbbbdbbdbadaadcbbadacbbddbacbadcdbacbdccdcbbcbcbbbadadbcddcdbaadcddbccccabadadbbbabbdcaccbabbbdbbcdacadacbcacddcbdadddaaadbaabdbdbdbccddcbbbdccacdcbacabddaacccbcabcbdabccbbaaddccdaadcbdbdddaadcdbaccbcaddddabddbbdcbdacddbdbcbadaccbaadcadaaadaddddadcdacadcdbabdbcbdcbdcbaadccddbdabddbbcbccabdbcacbdaddcdcabadbbcabcdaddadbcacbbcabccacabacaccadbdddbcacbbbdcadbddababacbbbbadcbdaabbdaabbcddbdbbdddadcddcbdaaddbdaaaaaaddbbcddbadbcddacbbddbabdbbccbcdcbdbaccadcbddddcaacbbdccbadaacabbbbaddcaaabddbbbbaadbdbdbdbaaddbbbcacbadddcddcabbabbcbdcddcddcdcbaadbadbddacdacddddcabdbcccbddddbdacbbdbbdbdcadbbdbddccadbbdcdcbbdbaaaabadcbadcbcbbbccbddddaabbdabbacdcbcabacdabbdccbccaabbcbbdcacbbbdbbaacacbcdcadcaaabcadadbaabcbbdcbdbabdbbccdbdaddcdabadbadacdcbacaabaddbdcbcdbaaacdaccddacaaacdaacdcaadcdcbaccacbbaddcacdaddbadbbcddabbdabccdbbcddcbcacbcdaaaddbbbdcadaccdbdaababbcbcdddccaabcdbcdbccbdadddbcbacdaacbbabbbcaadcbaacccbddbdbbacaadcaaaddbbbababcdbcdbabdaabcacbabaddcbacaaddcbbcdaddbdabadcdacdacbdbabccbddbcababcddbbcddadadcdddccdcabcdadcdcaadbaccdadbcbcdccbddaabcacbbcddbacbadbddbbbbabbdaaaccccbabbdabdaabadcccbddacbbdcdacbdbcdbabdadccbacbbadccadacacacadcdcbbccbcccbdaabbcacdbcabdacbcbcabacbbbcaadbcbdbcdbcccaabcbdabdbacdcbcacaccdbbaaabbddabadcaacbdccbdccbbaabbbdcdacabdcabdacbacdbddbccdbdadbaaddcbababdbccbccbaddcdbbcdbbbbabddddbacacabbacaaddaccabaabacabacbbcbcdccdadadcddbcdcacaabbcdcdabdadbcbaaaabddadcadbcdcacdcbcbdadabcdddabcccabdaccdaabcdaabbdbacdccdbcbaccabbbaddadccaacadcacdbbabdbcbccdaadccabcbadbdaccbcbccccddacdabdabaababccbabcadcddbcbccdddddccadacccdbdccdabbabbbbaabacdbacacaddcbbdcacbabadccdbbadbddcdcdddbbddbaabdaaabdaaddcdabbcadacabccccbbbadcaaaaccbbddbaababbbccdabbbdcbbaacbdcbacddbddcabddddbdcaaadbdadbdbaadabbdaabbdcbbcccdabbacbadbabaccccdaaccbdadabbdabbdcbcaddcbbbbddbbaadcdacdadaababbdbcdcbbacdcacccbaabaaacddbcddbbacbddddbcdbdcbbdcbadabbadbbbdbccbbcabbcdbccccdcaaccbddcaaabbabcdbcadcdcadbccbaacbadbbbacbadabaccadbaadcbbdcdadacacdaaddcdabdbccacbdaacbabbdccbcabbdccdbbbdbabdccbaabcbadbcaacddcaadbbcaccccaccdabdcaadbbadcaacabacdadacacacdcdabacadacababaccbcadabacabdbbdcdbcbabadabbaabcacbdabcbcdacdcaaccbdbabddcbbabbdbbcadddccacbcabcbcaadcbcadaddabbbdacdcccdabacabbdcbaacddcadbadbdabddbbcaaddccccbbbacddacdcadcbddccaacdbbbcccababbdddbddabbdccabdbcccdccbbcbcbcdabdcdbcbbdbbdadacdbbddcdaadccbdbacaacccbcbaddcdbbbbdbacbbbaabbbacacddaadcabcbddcbbcdddbabacddabacdbdccdbaccddbcaacbbdcbccdaabdbdccbcbdbdcaabbaabcadbcbddadddbadbadccdddcacbcccdcbdbaabacacaabbbdccaabdaadbbbcccbbbdadddddcaacbdbdccdccddbddbcdbcdbaabdaccdcabdbccbabcddcddbaabadabbbbbbccaccbdabbabbaadcaaabcdabbcdbddbcccbcaadbccdbbabacbabacdbbbcddbccbcbddbbabccaadbcacbbadaadcbcbacdaccaabddaabdbcddcaabacbdbabdbddbdcabccdbdbcabccdbdbcccbbdcdbbcdbdacabcbcccdbccbdadbdaaadcaadbcdacadccbcbccaabccdcbadcbdbcccabaaabaadcbdbabbcdaaccbdbbbdbddaaaababbccacbabdadccaddcaccabbcdadbbbbcccdaaccbcabacdbddadddcdcddbacaddbbaabcdbbccdccacacddabbbbaabacdbccccdcbaaddcbbcacdbcaccccbcddddaccbbccbbdbdcdbaccdaababacdddcaacaabcdcbbbacdabcdabccbcdcbddbcbddbddcbdabbccbdcddccdbbadadccbcdcdabcbcacdccbbccadadadccaccdcbadacbcbcbadacddbaaddddadabbaadcdbccccdcaabbabdbccabdddbabaccdddcaadcddbdbcbccadcbccbaaaadbcbdacbaaadcadcadbdddcadbabcbbdcddbdacbacaadaacadbabcdaaddbabdcaddbaccdbabaabdabbbcbbacadcacdaabdcdbdadcccddaacdcadcaaadaadbbcacbbcadbadccbcaabacddacdbcddbcaaaadddddcaccdbdcacabdabdbdbbbaddabdaabcbbadabdbcddbcdcddabbbcadadabcddacbcdbcaaaddaadabccccaacddacdadbddcdababcbbdcaddcdbdcbdbdbdcabadcbdaddcdadcabdbbcbbcacbcdbabcdcddcbdcaabdbbcbdadbbcbbabdbbacabdaddcabdcacdcabadacbaabdaacbbabacccddadccdcaaacbcaadcdccdcbbbbabddcddbdbbadacbcdbbbadccbdddacabadacadaacdbbdddbdcabccbcbccdccadcacaaaaddbdbcdabdabdcacbbcbacacdaccbcaadcdccabcbdcabdccdaaaddcadcbbcddddbacacdcacbbbddaaacdababdcdababbaccbdcbddbaacaccbdcbbdcdcddbbcabddbdbbcbbdbcabadaacdcbababaaababaacbcbcacaadbdaadadbbbcdbdaabdbdaacabdbdbbcabaddaabadabcbacddccdadabdaaddcbcaacddaabdbdbcbdcacadcccbabaadcabadcddabddccabdbaacccabaacadbdacbccbccabccabbccdbdaabbdabcdcdadbcbcdabaacdcbadbabadbbcdbcbcbdbbaccaddbbaababbddccadccdcaadcdcbabadcddabbaacaccdcbcbdccbcbcaddacdaccddbdcbbcdccbcaaccaccacacbbabbddcaaacdacabadddaacccdbacaccaddcaddbcddbcbbcddacddaacdbbdbabbdabadbcdacdbcdcacbddddaadbccbaddcdcccadcbdcabcccaacbadddbdcacbdcccacacddaacadbdacccbaacbdadbaabbcccccaabcbdcbcabccabdbacccaacbcbdadabddcbcaddcacbcaccaadccdbcbaacdcdacdaabbbaddddddddbdbbdbbaaaacddddabcccccbddadccadcbcbdcddabdacbcabbcbcadcdbdcaaabdcabdabdabadbaddcbacdadbadcadcdbcdababaddbcccaacdbdacabccdacabdacadadadcadaccbdadabcdccabbdbbdcbaabbbdccbcccabbbcbdadadaadcbccccbcbacccdacabcdabdaccaddbcbdcccaacbddadadadaacbcbcccbdcdacdabaccbcbbccabaacdabbadaaaacacaadaabdccbbdcdcdcaaddbdccaaaccccdaccbcacaadadcabcdacccaccdbbcdbdbdcbadcccacbcabdbcdddabbadbbababbdcdcaabbdbcbdbbbcadadbacdbadbbcabadbdbaacdbbdcbcddaacaccbcccbbccdbcaacccdadabaaccbcbdaadbbaabacdadcdaadcdaadaacbdbabcccaabaacdccdbbcdcadcdcaaacbacaabcdcdbcabdaccbcaaccdcdcbacacbdddacabddbabacdacddaaabdcdcdacbdbbbadbabdbbadcbbccabacdbcbbdbcdcbaccdccccaabaddbcadbaaabbddcbadbdcdbbbddbdcccadbadbdadaabcdadbbdcccbbcbcbcabbcccddbcacaadcddabdbaabbbbaaabcdbacdaacbabdadbdcbbdccbddbbbaddabcbdcddddcbccbbbdcacbbbbbdcdabbdcbbdbadcbbdaadbaabadbbaacdacadbcacbabbbdcddccddbbdadbcbbdcbdddacadccabdabdcdbcbbacacbadcabacbcddaccdcdbacabadcaaccacabbbdacaccddcadaaddbcbabcbaccaacaacbdbdbbcbbccdaadababbdbcbddddcbababbddadcadbcacdbdcdaacbadbbbadddabccbbdcbbcadcdacadbcccdcabaadcdbdddbcdabcdcbdcbdbdaadccabcdbdadcdaabcbbcbdaacbbbddabcadddcbdcbcbdabbcbcddacaabdbababacaddccbbddcbbcacbbbaabccddbdbdaaddbbcdabccaaaddbcbaabbaadbcbbdababbbbdcbacbdadbbdcdacddcccdadbdbabdcbcdcabbbbcadbabbaacdcbabacbcaadbaaabdddcbaacabbbbbddadbbbabbbcdccaabdadabdcaadbbcdabdbbcdacadcbbaaadcbcbdbadcbcbbdbaaddababcbbcacabcbdcddbabbabccbacaacdbaabaaddccbdabaaaacccbcdddacadacbbcbddbbddcccadbdccbdadddabbbbbbacadcadbdcbcdcaabcacaabbadabdadccbccbacdbdddadddabcaddadacbcacbcdbadbdcdbdccaccbbdcddbdacdbbbbbdbabaccccddbabdbdababdcaddacccdcabaaacccdbadbdacbcbbbbbdaacdacaabcaddaddabddcabbdadbababbdbaddabdaaddddabaabbdbadabcddbccdcabdcbaccddbaccabccbddddbbadbaaabcbdaabbbddddcccdcdadcbcbabcababdabcaddabbcddabbcbcdcbdbcabadbdbdbbbbcddbacbbabbbadcaccccabcdacbdcddcbbbaadcccbaabcbaacaddacababddddaadbcbbdaccbdbbadabcdccbdcadcaddacadacaaddccabbbaccbdacbdabdddbcbbbddaddbdadbdbcbdacacbaaacccbbbacacbdcbdabdbbcbcdccabbcdccddbccbcadabcabbcbccdcaccbccbcccacdcdaddcacadbabaadaadcacabcbdaaaacadcdcbadacdcaacdacbdbabbbadbbbcdcdddbdadcdcbbbbcdcacacbcadcaadcbdacabacbabbabbaccccadbbbbbdcdaadcdddbabbdbbdbaccadabcdcbdaccccacbbaacddccbcddaaccbdbbcabbbaddaabcaadddcababcccbadbdbdadbcbababacdccacabbbdaaacdcbcacbbaccdabbbadcbadcdddadadcdaacaccccbcdbadabdacdbbaabdbcbbbbacbbaaccdbdabdbdaddccbddacbbbcbdacddaaddcbabddcccdbcacdcbbbadcbdacbccbbbcbcbacdcdbadaacdcddbacbdadbbbabbbbaabcddaaabccdcdbbbdcabdbdbabdcdaacdbcadcbaddabbbcadcacacbbbcddcbaadadcccaacdbcaaaccdaacbbabbdcadaabaacccdbcacadddbbdddcdbcdadbddabadbdbdabacaacbacbdddaaccbcbcbbcaccadaddcddadccaddccbadacdbbdbdbcaccdbcbcaabbcdabdbbbcdbbddbbdbcdacdadcccadcdcbacccdbbcdbdcdbcaabddbccabbdcbcbadcccadbcccdcdbdadddcacabacbdbbcdaaacabaadbdadbacccdbbdadcaadacdadbbbacdccdcbdcbcabbcabdacacbdbcadabcddbddbbdbbacbcdcadccbdbbadbdccababdacdbdaccdbcacdbabaadbaaddaabacdddbcdbcacdbdcdcabbacdddbbabdabdccbbbcaaaabcaacbbbcabddcbdcbadaacdddaacdcbbbdbdbcaddcdbbacdcccddbcabdbcbbadacbcbbadabbbcadbcddbcdadbdaabdbbccadaacccdaadbbcbbbabbabcdabddadcadcdccadadcdbdbbbbccabcccadcbcbaadbcccabacadbbcacacdaadaabdcacbcbbdccdccddcdcaabdbbbadbcdddbdcaabdadbdbbdaaccccdbadbaaddccdbdacdbcddaaaccbbcdbabadbddadcacdcdaabbdaacdbccaabbaabaccbcacdcccdacbcbaadcaaaabbbcaadacbabbbcdbdcdbaabacbcbdaabddcbadbdadddbccadbcaadbdbccabcddbacccdccccbabbbbccdddcdddaadaabdccabaaccaabcdbacadaddadbbabcabbcbbadcaabdababdaaaddadcccacbbdcbcacbaabdadaaddcddbadbddaaacbdcdbabababacbdccdbbbbaacababaadbabcdbcbaabcdbddabbbccdddcdccccccdbcbacacabccbddbbdadabccccbcbcdacdbdbcabdaccbddbabddbddbcaaabbcabdaaaccacdccdbdbdbcdcdcbcccabbbbdcdccdcdbcbbbcddcadbdaabcbbbadcaaaaaacbbbbbddbcdaaddcbadcaabbcddaabaaacaaccabbcaabdcdbaadbccdaaacdadacadbdccaacddbaaadbcbacbbbaacacbbbdcbcdbacccbdabddaabbdbaacdddbbdaadbcccbbcbbdaabddbcabcbabcdcaacadcacadaabdacadbabcbdddcdbbcadcadaacddddbadcababaccdbbbabcbcababacdbdbacbbaaabddacdbdabdddccccdccacacbadacbcddacadacbcbdccdaaaababaacbcbdadddaddaddaadcabddbadaacaaddaacadbcacccabaabaadcbdaccabbcdcaaccdcbdaccbabdadcccbaaadcaaddacddadcbabdcbccdcddacdaddcbdbacdcdadadccccbdaaddcbacabddcacdaddacdcbdbccdcdacbcdacacabbbdbcbdbaadcaacbcdaaaddbbaddcaccccaacdaccbadbabbccbcbbddccdccaabcccacccbacaddaddcdcdcddbcadddbdcccddcacbdcddbbdbccacabbadbdbbccaaabcbddbbdccbaddcbdabdbaadbcabcdbdbadacdcbcbbadaddbdbaaddadddabccdddabddacdbdccdbbbcccbbcddcdcaaadbcdcdadbdaaddabcdbcdccaaccdbbdbadddaaaadadaccacddbcbbcccdccbadbadacaaaaabcbdbccdabadbccdaacbbddbabbbcaddcbadcaacacdacacdcdcaccdaccbdbcaaabaaaacbaabbddbbaaaabbabaaadbddabaccbcadcdbcbdccdbdbddbdaacbaabdbbdcdcabbbbdadabdcaabdccddcdacbbddaabcadcbdbbadcddcdbbbacdbbdbaaddddacbbacbdbcddbadbbadbbdaacabcaaacdabdbaacaaddadbabbbccbbdccacbbbcaacbccbacacaacbdaccddbbaabbcacdbdccaadddcbcbcbbbdcbdabdbbababcbabdacabbbdbbdcdcbacaaccdaadbcadbddadcbbbadcadcadcacaccaabcddcdcdbcbcaacbaacbcabbcbcabacdddaabdbdcaaccbacdbdcdbbcccaadbcdababdbabbdbaacacbcaabccbccccaaacdbbbabacbacbdacbcbdbddcacbccbdbbdbdbddddddbdddbcaacbcaddaadbcdcccbcadaaddbaadddadbbdccbbaabcbdcdabdbcddbcacdabadcccaaabdbbdcdaabcbbddadaadabbcdbddacacabcbdddaacabcdccbcbaadccdcdcbdcbabadacbbaaddaddaaaaabdadccdbbbaaaaadacdcdddcbbcbbacaaaacbbbdbdbdbcbbdcbbccdaaaabbdcccbabdcdccbdaccbbdcbbabccadcdcdccbcdcddccbccddcadbadaabacddcabadbdbccbcdccdabbbcbbadcbaccbcabccddccbdaadbcadabacdbbbacaadcccddbbcacddaccadaabacbcadcbbbddbddaadddcbbbcacacccbabdbabaadaaaabaddbaacaabbdcdbdbabbbabddadcaaaacdccccaadcdccbcdcdcabddcaabbcddacbddaaabdddbaacdcabbbaabcdabdbdaadcdccdacaddabcdabacdbcabcadcbacbbdaddaadababdbddcaaabcdcdbcdccabaadadabbbbcbbddcbcadbccbbadddbdcacadabddbcdddadbddcdcadaabcbbbcdbbabcaccdadccdabadccbcccadbcbcccabcacaacbbbddbbaabbddbbcabcddcdcababbcbacabbdbabddbdcdccadbddabdbcdcdcddabdaccddabbcaadbabbdaacaccbdcbdddabbbadbcdaabcacbcaadbdbcccaadbcdddbbbcdcbddcddaacabdaddbbbbaadccaababaaaadddacadacccdbbcbcdddbdbcaaccadcdbdaccdcbcdabbccbabdcaaaaadbdadbccbdaaadcddbcccddbdbaacbbbacddaddcabbbcaaccaddcbbacacddcabbdcaabacacacacdcdbcbaccacaaadcadababdcdbcbadaabadcabddbbbcddcddbcdbccbccaaccdccbcabaaccdcbaaaadbbdadddbbacdacddacdcbcadbadaabaabccabdbabddbdcddbbdbcdacaacccaaadcbbdbcacbcdbabbbddcdcbccadabccccbddabccaccccaddacbdbdcbccdcacdabadcaaacdcbadcdbbcdbcccdabaaacadcbbcaaaadbbddabccddbadccccaabdddabbabadacaababdbcadaadbbdcaabbbbbbcdaaabbbcbcaccaacaacbddaabddabaccaccaadbaddbbacacaacacbabddccaabcbcbacdbdbbcddaabadccaabdaccacbcbddbbbcbbccbaaadbddaccabaaaabddcbbdbabbaabacadaaddbbacaaadccacbbbadaccaadccacbaaadddcdcacdcadaddbbdcccbdbcbdcbacdbccbadcbcadaddddcdbabaacbdbcbcccaaadacadadcdabdacdcbbddcabaaabccbbdccdacaabdcadbcbdbacbccbaccabbddcbbddbbaacddccacdacdcbbddcddbaabbdbddcadbacadddacaccacbbbcabbdbccaccbdbcbdcbcddbacccdbbdbdccddcabcaabcdbccdabaaadaadbbcadbabdcbcdcbbbcbabccccbdcbdbaaaacdabbdbbdcbccdcaaadbacacabadccdcdbcadaddadabddbbbabbabbdaacccbbdcacdbcacdadbbdbdcbbbbdcddacbdbabcdbcbbadbddadbddacdadddbbddaccacabdbccdccadcdacaadccadcbbbccaadaaacbbbbbacdddcddbdaadcabcccaabbdacacccbdbcbcbadaacbdadcdaabdcbdcddaccddaadaabdbdbbdcdbdbbccabddbbddcaacdccbcbddbdabcccdbbacaaadcbdaddbbcdababbabbdcdaabaadabbbcdbbcabbbddcaaccdcabdddccddcbcbbddabcccbbabcaaaccdacabdacaacdcbbbdddbadbadccccadbadbcccccdbcddbacdcdabcccabdcbacabdcbcbdaacdbbadbcaccbcbbbacbcccbadbcacddddcdacadbaccbcbdabbbaddcaccaaccdaabbbdddbbbbcacdddbdcaabbbcbcdadacabccabbddbabcbccbcdaabbcabcccdbadccbaadbddcaabbdcbbcdaaaacabacdbdddcaddcdddbaaaacbdadcdadaccdddabadaadccacdcddadaaabcccdaadbabacbcabcacabbacacabdacbaaaacdadcdddbcbbbbadcddbdcdaaabbbcabaaacbbbcaddacbccdbbdabbbdbcadbabbadaaacabbbbadcccdbdbbcbbaaaabbdcddabadbaddbbbdcddcaddabddcaccdcdbabdcddbdccccddcacdcdbacacbadaccbbbbccdbaacdcdabdaaaccbabdabbbaacaaccaadbcdbddcbdccacdbbdadccabadbbacdcdadbcadcadccdcbabbdadbadbbaddbdcbbcbcbbddbdccdabbdbbccddbcadbdaccacbdbbdbbcadababcabdacccbcabbdbdacacdabdbcbddabdcbaabacdbadcdaadadabadacbdbaddabccddbdccadaacaadaaabcaaddddacaacccbadcddcbdcbccdcacbdbdccdcadacdadccbbcdcccbccbabbadadddbdadcacabdcdcacbaccaddadbccddccbdbccbdadaddcacbaaaaadbadcabaacacbcbbddadabcccdcdcbdbdcccdbcaaccdcdcaaabbccdababbccadcbdaccccadbacbbdddcdbbacbdbbcbcccaccbbbcbabbddaccddbaacbdacbdaabcbdbccccdddbcdbbbccaacdbdabacdcdcddbccbcaddcddddacbbdccbacbacdccbdaadabcbbaaaccbadbddbccdaddbcbdcccdcabbcbbabbaccacbbaadbcdddcbacdaaabaccbcbcdcadbdcbcbacacabababbbcabbbdddcaddbcdabbcdaaacdcacccbcbddacbadbdaaddcbbadbccadadccbbdbcdaaddacaccacdadadacaabbbaaddbddbaacbacacbaadabbccccdcccccccdcdaddcccdbdcabdbacbcccbdadadaddbbbcdcdadddddbdacdddadbdcdbcdacabbcaaccbaaaaadbbdbbcddacccadbbcaabdaadcdddcabddccdaadadbaadbcbccdcbccbcbadadcbdadabbdaabbdacaaabcaadccababcccabdddadcdccadcbdbddbacaaacdbbbaadadaadccacdcaaadbacabacbdbcdbbacccacbbdbbbadacabdbcabbaacacaddbcdbbbadbbaadccbdacacdddbcadbcbabccbcbdabaadccadbbbdbdcddcbccdadbdabaaabbdacaabbbdddcccbbdabaabdaabbbcbccadabdaddbbdcbddacbadbadbdcdadcdaacbddadbdbddccdaacdbbcabcbbbdaadbaabbdddabcaabcdccbdbbbcbdddbabbdbddccbcbbacdabcaddcaccbcadbbdddbccddcccbdcaddbdcaacdaadcddabbcccbbacccbdcbdaadaabbabbbbacacacbaadaaabcbcdabdddddbcccaccbbddbcabbbccacbabbbcbdbccbbacbabaccccaccdbdcabbcadaddaddcbddaddaabbdbcaacabdddbccddabaadaabdbdbdcadcacdacaabdacbbbcbbdaabaaddadcbbcbdbbbacaacdcbabbdbcbccababbaadacabcacadaabadbdabdbdbabcadccabacadcbcabdbbcaacccbdacabbcaacddcdacbbbbdbdccddbdbdcbabaadadbbdbccacaadadaadadbcdbbddbabaadabaccdbcccabdcdcacacddabdcdcdcbcbacacdcdccaabbbbaabacaadcbbaaccacadcdcadbddcdbbadaadbabcddcacbaccaddbdcdacbccabbcadacaadcdadadbaacadbcbdcbabaddbbababcbaaddbcbccbccdababcccaabcdaddbdddccbabdbbbbcbdcdbdbbabbcbcbdbdcaccbdbdbcaabcaddabadabbbdcdabacaaabdcaacdbcacddddcbbaaddacbadbdccadabbdadcbdddddadbabddacbadccddbddaabccadaabcdcbdcbcdbcacabdcdcbaaddcddacbbabcdacabdaadccccaabdcbbbbcccdabcbdddadcaaadadcbcacdacbaaddbdadcbcabacabbcbbbbccccdccdccbcbdcdadcccccbbdaabcadaacdcddabbaccbccbaabbddbbbdcddcddcdaacbbbdacabbdcbcdaccdcaadcaabcdadabbdaadcabcaaaaccbcbcbddababdccbdbbadcdbcdcbadaaddaaaacacacbdadaadbaabbdbdadbbacccaccacbabbcdbdbacbddccbcdadbaacdbdbdbcacbaabbcccdccdaccddcabdacdbccdbdacbbacdbabcabbcbacadcabdbbbcdaaadbaabdddacadabbdbdcccacdacdabdbcbccbcabcbacbdcdaaabbccdccbdaadaccddcddddcccabcccdcbbabbadacdbdccbcbbcacbcbcdcbacbddcacbcbcabcbdabbbcaaacbbbdccaacdaccadbbddcbcbaabadccbdbcddbddddbcadbcdcddcabbcbadcbbddcdbcdcdbbadddcdccabbcaabddbdcdbcccadbbaadabaacbaccbddccdacbbdcdaabcbcdbcdadaadcaacabbddbadddddcbdccacabccaadcdcaccbcbbcdadbcbdbdccbdbadbbcddbdbacbbdbacdaadcddcaaabadcbcbcbccaaaacbaabcaccbdaaacbcadbbdbcbbccadabbbccdcdddbcdcddccbbaaddbddaddbabdbddcaadadcdacaddbacdbdbbdccdabadbababccdddadbaadacccbcbdaaccabadbdbbabdbbabcaadbcbaabadaabaababcbbdacbdadadbabdccdacddbbabcccddbacccbdadddbcdcdbccdbdcbbdabcadbdbabdbdabcbcddbdabbbddbadaaabcccbcdbabbacccdbaacbbcacbbdcaccacccabbbbbdcdaacdddbcaccaabcbcbcbccdcbabbaadbbddbbacbbbadcacbcbabcbbdddcddbadaaccdbdacbaadabcbdbacbcbdbaddbaaabccbadcbdbadccbbcdddcccabbaabbacdabacccbaaccabadadbaacdcadddbbdbbdcabdcabbdcdbcbdcbaccdbabbaaaaaccbbbdcbacdaacdcabcacbdacccaaccdddddcbbccbbbaadcaadabdcbdcddadabdbdaacacddbcddaacdadaaadbadaccbadabccbcbbbcbbddcaabbcacdcbabcbacdcaaccddabadadcbdcabddabacdbdddacbadddccbcccbabbcadbdcaaccddcccacacdbaddcccbdcbdaaabbddcbadbadaabacdbacdbbabcacabcbbcbcdddddcadacdabaaccaacabcaabddaaabddbcdccbdacdcaabcacdcbbaacaabcbbcaaaccbacdaacabccabbacadadaccdadcadcdccdddaacdcbccbbdbbbbdbcacadaaacbbdcaddbbddbcabcbdaaccacacccbccbacdadbdadcbbcbaadbaaddaccacaacdcccacbcabbdabdcdacbbccadaabadbcabcadbabdcadddabcadabbdaacbbcabcababaaacddadbaacdcddbcacbddbdcaacadbbcccdababaabbdaaddbbccacdbbdadcdacacbabddbadddbddddbacdcbcdbcbbcbbccaccaccbbaaddabcaaaddddbbdcccdadbdcdacbcabcdddadbbadcbdacbcaabdaadaccddbccbdbcabbdbcacbcddaaacadacdbbaaadacccbcdabcbdacdacbcbadaddcdbddcbcdadcbdaababadabbdcddbdcbddbabdaddacbbbaaccacdcadbbdbabacbdcddddcadccabbdabdabaddcabcdbcbacbdbcaddcabdaccbcadaccccaddaaabbcaacdbbbdbcdbabaabdbbdadbcdddbdbbabccbbbcccdcdbacdcddbddcbbdbddbdcddccbaccaabdadadaccaacacbbacdacddcaadcaddbcaadcadadccbcabdadbcbacccdbcdadaddbcdbbaabdbdbdcbcbddcdbdccabaccbcacdaacbdbdccdddadbdddbbdbcdaaadaabcbdcbcdbdabadbbddadbaddccbdaacbcbccacbbdbabdddaabddacdaacbdbdccdbdbcdaddaadaadbbddbbbabdbdaddadcdcccbabbacbbcbababaacbaabcacaacababcacdccdcadbbbccdaaacdaaacdccaaabcbaaddbcccbdadacacbcabbcdcbaadbddadbcdadacdacabddcbbabdccbddcdbbacdcadcdbaccccacacbdaadbbcbacbbbbdcddaaaadaddddbddbcaddabaababacbabcdabcbbcdddacaaababdabbacccdabbcddadadadcbcadabcaadbdacacabcdcacccbbccccabbaacdcaccbbbaaabaaddbbbcaddabcaccddabaddccbaaaaccdccbddadadaaaabcdbaddabaccdddadaaabacbbbcadcaabbbccbadabadcbbabddccaacabadcdccacabddccdaaadabcdadcabacbbbcdcbdbdcddacbabbacbcbdacabccdddddcccbbcaacdaccdcadbcbadbbbbcdcbbbcbcdddddbcdbdbcbbbbcadbbdadacbbaabdaabbccbcadacabcacddbbcbababacabccbdbbbccddbaaadabababccacbbbcdaabbdcaadcbbbaddbccccbdbcddabaadabababadbcabdaccadadadcccabbdabbaacaabbdcbdddbbbdbbbbbcacaabcdcacbdbcdbadacbbbcabdbcbbaccccbdbabbbdaadcdcddbdacabbbddcbbbbadcddaddbbbbbbccdbabdbcaabddbbdccdbcacbbcdbcadbaaccaccacdbbdbdcaacbccbacadbdacbcdbaccbdccddbbcbadbcaadcdbaaddbadbcabccadacccddcddcbdbdbabcbbccbabcbddddadcdabccbdcadacbcaadbbcbbdabbcdbacaddbabbabbabbabdcaddabbccacccbacbaacdbadabcdabbbdadadadcccbcdddcdadddbcadddaadaddacbbdbdacbdcddacbbbcabcbdbddadcdadadaabbaabbdcacbdcbbccccacbcbaadcbaaccdbbcdcbbcacdabcbaadbdcdccdcdbadcbdbcddccbbbdbabbcbdbaabddddabbdcaadacdaacbabbaacdcccaabacdacabbbddbbcadbbacbbaaaacacadbaacaddddcdacdabbbacbdcdadcdabcabcacbaddabccbcbdcadcdaadccdcacabbadadaadacaadbcbadcabcacadacbdccbbbbbbaaddcbadcbdcbbcadbbccbabacaacaddacbbdddddccbcccdddcaccdaabccadadbdadbdaabbcadcadabccbaadaabbcbbbcbdbcdaababacabaadcabdcabdbcaadbabddabddabdaccbaadccccdabbdbbdddacddbbcabacabbaccdcaadcabdbcbddbbccaaaccbaabcabccccddabbaacbadadadacbadcdcaddcbacddadaacaaadbabaacadabbdbddaacbdbbcaacccaddcbbbbbabccadcdabbdcddcbbcdddadbbdcadbaccbbadbdabdbcbbbcababcbabaabcdcadbcadbbaadacdcdbacacccccaabcdccbaacdcbbddbccdaddbaaccdabccbadadacbadcaacdcadbdcacdabbcabbabccaacccaadcdacacacccdabdaadcbaacdaabaaadbabdccdabaadcdcddcdbaadacaaddbdbbcdcbccdcacbbcadadadcbaccaddbdaabdcadaddabdaacdbbdbbaaaababcdcdcabcaacbcbdaaddaccaaacbacbbbbacdbadcbcadacddbcdcadadddcbbdaaddbaadcccdbdacbcbddbcdadcbcdbacaddaddadcdcbbaaadacaccaddbdccadddbdacbcabbddcdaabdbbdabddcbcddbdbcacdaacbcabdcbcbaaadadcdcdddbccabcacbaccdcdbcbdaabdcdbabbcdcdbaaacccabaabcadbdabccdbbbdddbbcddaacbdcabdaacbcaaabaddbdbbbdaddcccbcbadacdbbdabbbbdadddadabccacdaabbaadbabbbbddccaaccabcdcdbaaabbbaacbcadccbbacbddddbbdabdccadbadcbacdddbdabbcbccbbadbcdabccaaabdaaaadaddabccabbcdcdcbcbbcddbbdccacccdcdcbbacabbbaccbddabcbdbbbadccbdddadcbbbdcaaadaaaccbcbabcddbdacabdcbcaadbdaabcdbbcdbcbacacbbdbdbacdcacddcdcbcabbcbcbbdbbcaaaadbcaabbccababccdbcbbdbabbcbbddccaaaabbbdbdbacdacaddcddacbbdcabbabadabbbdbbaccbcbdcdbadbbbadabacdbbaddcbbacbdaaadbdbdbbddddccabbabdbddbddccbcdcaabbbacbbbdacbaaabaacdbbaccabdabacbacbbabccddbbdcddadbcdccdbbdbaaaadbdccadbaadcdbabdadcdcacccdbbcbdcccabadbaaaccdcdabdccccddaddbbcbacacabbccdccbbbadbccccdbddddcddbbcaadcbcdbacbccaacbbadaacddbaadcabdbacdadcbdcdbbdbcccdcadbdaddcaddabbbdcdcbbdaabdcabbdbdcbddbcdbbbabdbbccabcdbbcdddadcaabcbbddaaacbacabdaaaadcdaddcaabcbdcabbacdaabbcdbcbaddbcdcaabbaacabbcddbdcabaadddbcabbcabbdabcdbaccbabcbbdcdccdbdddbdadcbcabacbabcddabdddabcddbcacaadaaacdddbdbabcccadcabaccbaabccbbddccacdbcccbdcaabbbbcccbcbccdbdbdabdcbbdbcabdcaddcbaaaadbaddbabbbadcacacdbabaaaabcbbdddbdbdcbcbaaacdcbddacdbcdcdacdacadcacbcdabadacacabdccdcdcdacbbdbacdadbdbacbbbdaababdaddaddaacdbcccacacababbdccadccdadbdcbccacdaccbddbcdcdadcccdabbabdbdcbbdbabdbbbddcddccaccbcbdbddbbaaacadaabacbbabaaaadbccbccabdacadabbacdccaabdcbaccccddbcdbabdbbbddcadddcaccdccbbcaabcdbddbcadddbbacdaabbbbbcdbaabbcbccbcadacbbacadacdacadcbaaacbdbbbbbaaddcdadddaccabacccddccdbcabdbdcadccababbbcaacbdadbdbcdbaaabacddbacbababddcbabaabbdcacbbdcadccdbacdbddcbcabaadbadcdacbaacabcacbcbaaabccabbacaabdcacacbbaaacccccadcddababbdcaaddaacbbcddbcdbcccdbdadcdbbdbcddacbaacbabbaabbdcaaababdbcddddcdbadbbbacbaaddddbdcccabcbbccbdaabddccabdcbcadadacddbbbbbacacdcbbadcbdccdbbaadccdabdccabbcaacbacaaaccaabaaabadacdcbdaccbccadbabbbbdbcdcbdabdcaaababbbadddabbdcbaccdaabddcdabaddbcccaaabcacbbdcaccbbbbddaabdddbaacbcadabbcbacddcbdabbcccbdcbbdaacaadabacddbaaccdccddbcbdbdbdbcabcbbcddcacbacdccdbacbbaabcccccdabcaadcadcbabdddcabddcabddbccabcbdddabbabdcbdccbaaddcccccbdddadcadabdabaacdabacaddbbbcddbddaadccabbdbcdbaacdaccabddbdadccadaccdadcbadcbdaabbdabcdcacbddcccbbcbadacbbdbdaaabbabbdabaccabbcdaccbcaacdbdcbbcadacaabdcaadbacbbdacdbdcbbbcdbdcacabadbdcbaaddaccaaddddacddddcccdacccbbacaacbcbdabcbddabaccaabbaaabccaabbabcbdbaabdadaabdaadcdccccccbdadaaadababddbabdbdabacbadddbdbdbbaaabbddbabccaaaccbdbdbbcbacacdcdcaacdcdaddcabadbddbddbbdadbbdcccadacacdbdcadacdbadcbcbbabcccccabccdacbdaadaadacdbbdadbdcdbbacadddadacdacdbacdcbbdcbbaabbacdaaccbdbcdcbdacccabddcacddbbcbbdbacbbadbaddadbbabcaccabdccbcadabaaddaadcbdddbaabbabccbcbbdaabdbbdbcdabaacdbabdacacbabcaddcbdadcabccdbdbbaaddbbabdbdcaaddbbdaaacdaaddaadcbbccccadccaabadccadbbacaaddbacbccdddddbdccbdadbdcbabccbabacbcbdbcccdbbdbdcdddddbaaddbabcddbdbdcdabcbaddabddabbcacbcbdaddaccbcbdcbacdacbdababbabddddbcddacdabaacaabadaccbbcdbccbcbddabcabcbbaaadcaccdcdddbadadaaacdacaddbcbacabcadadadaaccacadadabbdbbadcdcccdbacbaaccbbbccddcdccdbbddcbccddcacbbdcdbbbbcadddcbabcaacddcabcaacdcddcaaaabddccbdaadcddbaabbdadaccabcbdcdcaaaabaddddbadacbddbdacaabcbdbbbadcbbccacccbacacdaaddacddbbbcdddcdccbcabcacbcdcbdbacccccaacbaccbaaaaddbcbcccaccdbcdcabdbcbdcbbdcdcdadabdaacbacbccbdbbdcabbddabdddcbcdbbcbbdbbabdbbaaabcdbcdabccabadabacddddaacbadacdbacdcdcacdabbdacdbcbadcaaabbabdbdbaaabcaaabacaaacaacbaadbbbccdddacbccbdacaabdbbababcdcdaccbccabcbcddbaacbcdbbdddddadcbaabbcdcccbabbdacdabaccbccdabdaccbbddddcacdccaaacdcabcddccabcbacddcdaabbcbdcccbaadadcdacddbacbddcbcdcbacdcdcabaccdabcaadaddcadaacacbdacabcbaaabacdbdbbabbbcacbaacdcdacdbccbdcbbdbdcbdbbcacaccbbdaabacacaccdcddcdbbbadacbbcdbdbcdcababcadcbccddcadcabbbcdcbdbbaacddccadcdcdddcadcaaabbcabcdccaabdaaaabadccbdccdcbccadaacbcbaccadcbbcacddbcccbaddcbaaccbcabaaaddccacabddabadabbaccdcacbbaacadbaacbaaaacbbdbcdcbcacdddcdbdadcdacacbcdacdcacdcacacbcaddbbdbbddddcbadbccbdabbcaaacdcbaaacbbbadbacccabcdadcabdcbbadbbbdbbdbaabdbcacbcddaabccccaddbaaaaabbbbdabbdbadddcddcbdddabddaaccdbdccdcdbdaadcdaabadbdabddbcccdabdadbabcbdbbaccbcaaaacbbbcdaabbacdbcdccdbcadacbbadacddccbbbddcdbadccdaabdccdbbdaccdbabcabdbadadbdababdcdbbdbccbcdcadbdcdcccdbccababbabdddaacddddbccaddaadcaaccbddcdcdaaadcdcaaabcaacaadcababbcdacaccdbdbddcdcccdcdcaccaaaacbccbbacccdccaaaaccaaababaccccbbdbbabbaccbccdbacbdbcdcadbabbabbbcadcbaadccacdadbadddadbdaccadcbcbccacaaddbaddcbccaccddadbdaccbdbbbaadcbabccbaaacbbaaddcabdcbdabbbddcdadcbdcdabbbddbbdddcbabcadcdbcaacdadbbaabddacaddcbabbadcdcddbbddaaccaccccbdadbbdacddcccbbcddbbacbcdccddacadacbcbabdadaabccdddcdadabaabbdbabdcdabaaaaadddcdcabdddcbaddbbcdbcadabbccddccaadcdcbccadaccabcddbbadbcccaddbacacaadacdbadbddbbaaaabaaabbbaaacaddddaccbaaabcccbbcaacdbbadabcbccbaccbdbccbcdadabbdcabdbcdcadbcccdcdaadaccbcddcddccadddabaccaadbbbcadbddcabaabdabdabacaacccdcadbbcbdcdddbddbbaaaccddcadbbabbbbcbadbabcaaaaabdbcbcabaaaddbbacacabadabcbdadabcccdacadcbbddaccadcbdacdcddcaabdcdabccdcbcacabaddacadbabaddbddcddbaadddaaaaadbccbadcdabdabcdcbbadccdcccbbadcdcbccabdbcdcbabaddcbdccacadcbacaababdbdcdccbccbdcdabbcdbcbddccdcabdbddcdbacdbaccccdabbdcabaccdddcdccdadbbcbcdcbdddbabcadcababaddbdbdaaaaccbdaaadadacadbbdbdcddcabbbcadcdddabbbaabbdddabcaddacdbccdcbbcdabcbbddddcbcdbdccddaadaacabbcaadbbdbddbdaaadbbcbbabdbccdadcccdbbbcdbcbbbdbbadccbbbabcdaddaacbcdcaabaccbdbbacdbdbbacdbcbcbdaaaadaabaaaabcacaaacccbddbbabdbddbbabaaaabbcacabbcadbdcadddbcdbbddbbdabbcbcaaccdcaabaddcacdadaddcaabcdaabbbaaaabcdddddbaaabaadbdcddcdaddddabbdddddbadbccccdbbdbaadacaaabcbbbabcbcbabbcdddadcbdcbdaabdaabcbdbdbcaaacacabadaddabcdabbdddbdcaacddbabaccdbccdbbbdbabdacbdbdcdacbcdcbdbccaccacacaccaccbdbbacdcccbdbcbbdadcabdabdaaabddaadadabcaddbbdaccbdaacdaaaddcacbaaacdbaaaacacacdaadbcdaccbcdcabaddbdaacccddbddbbabbaccccabaabdddaacdbabaccbabaaaaacdccbcdabdaabcdadccabcdddaaacacddcddbabddcacabbaddcacbaababaacbbdcdcbdbbbaadddcadabcbdbbccdcbbbbaaaadbccaccccbdcabdcdcdaccdcbbadabdddabdbdbaacbcdcbbcbbaccdcddcbddaaadccbccdaacaaccaaddacbccaaabbdddbdbbadbbddcddadddcadaacadccbaccbcbbbcdaaaddcbdabadbdcadddcdbdcdadcccdcdaaccbaddcbbbbdabacdbdcbbbadbbccdaacbccdbbccdccdcbabdbccdabadddaccdcbdbacdbaadbdcbadbbcdaaaadcbcddddcaacadcabbabbadbccacddddbbadaacbbacddadaacabdbaccacdbabaacbaddcddacadcadbcabdccaaddcabdbdbacdcdadcdbbdcacbdbabcdbdcdccddddcccbcdbabbdaabcdcbcccadccaaabacbbbadcdcadddabcdcdbbbadcbbbdcbbadabbbddbbbaadddcaccdbbdddbbcbcabbdcbdcbaddbacadabcddccdcbbdaacababdddcabcdbcbadacacaabccabcddaabccdcbacbdadcadbabccaabbcdadbbbcbbdcabadbaccdabaabddbddbcdddcbbccadbbadbcccacbdadcdabbaabbbaaadbaadcbacdddbbdddccbdbaaabacaaabdcdbccbbddddbbbddabddbbddbacdbabbcadbccabcccacbdbccbddbacaccbcbaadcbcdcdddadcbbcdaabbbbbbdcbcbbbccbcbcdbdddcdddccadcdbbacadabacbddccccbadcbbadcbbdbbcdbddbbcbbddcbdccddbaabbcbbcccddbbabbdaddbabdcbcccbdacddbabcdcadbcdbdcdaaadcddaacbaaabaadadabaacdcadcadcdcaadcacdcbcaccacbdaddabcddcdbaabcdbbdaccdcdadabcdbdbdbcdbbdabadcddcdbdbbbbadbcaaccaababcaabbcbcabbbcabaddcdddbbbccbdbbdaabddbccbcddadacaacbdbbdadadbadcbddcdbcaacbcdaaddcaacbabacbcdcdcaaddcddacdbddadbbadbbbabcaacadbcdbcacacdcbdcdabcacbaddbaaacbcdadccdabcdcccdbdbddbbacddacaadccdbadbabbdddcdcbbaadccbcbbbbbabbbbaaadadddbacbddcdbaccacbdacdddbccaddcccddabacabcdbcacbadcacddcabcacccccbccdccccbaccaabcccbdadcbcacdcaaabdacacdcddbacbccbcbabcdcdcacdbbbacbadbbcdaacdbcbadbacbcdccbdbcbddccccbcbdaccbaadabaaddbaaddddccccadbcdcbbababccaaddabacaacccbadadcacbacaaddbdcbadabdcaaaadccdbcabaccdcddabaabacdbcbdcdddbbadadaaacbcbbcccccaabbabdcdbcccdbcabbbbdbaacdaacababccbcbbbaabacbccbcaabdadbccccbdaccbabdbbcadcbbdcdcaadbbaddccaabaabcccaddaaacbadcdadbbbbcbccbacdaacdaaabcdbbadadabbbcaccdddcbcbdcbabbcbcadaabccabbbaacacbaaddbdcaadacbdcdddbabcbbabcbbacbabbacdcbaccbadbbdacdbacccabcbaccacddddcbaaacdcddaabadccdacdbcbcbdccbaaaddcaadccccdcddccdabaabadcbbadbacaccbaadccaddadbbbabbcaccdbdadaacacaddbcadbccbadbdadccdacaadbacadcbadddbcdcdccbaaadbbddcddddaacddaccbbaacdbaaabbbdaacacccddcccabdcdddbddcabcacbbdcdcddddaccabacacacbabcdcacaabddcdbaadadaadbcdcbacaacccbdddbcbcdcadaacdbdccdabdacbabbbbcbacdbcbdacbbbabbdccabbacbbcdbcdaddadbbadcadacaacbbabdacddcbbbaccddbdbddbdbbccdccdcaccbacddccbdbadcabaccdcbdcccbcdcbdbacabacdadacbdbcabddccccdaccdddcdcbbbaddaddbddbbdaacdccdcbbddadbadbbadaadbcabbdabdababbccdaadcdbacdacbcabbbdabcabddccdcaacdddacabcbbaddaccbadcabbabbcbaddcdddabdbaabdbcccddadbabcbacabadbaacaacdbadacacbddaacdcadabbadbadadcddabdbbbdacdadbadaadcacdcdbdbabcacaadcdcdcdcdbacaadcccaabdacdccaadbbbcacdcbdcdaaccbaccbaaccbbbdbddcccdacdbdcdaacdcccadaaccabbdbdddbbdaaacccadccbbcdbcdddcbdbbddaadccacabbaccccbcababbdbccaddcbddcaabcadcdbcdcdccdaabbaaacbabccdbabcddaacabddcdbbaabbcccaacabbccddddbcdccacbbddaccabddcbdccdbaaacdbbcbcddcbccbcadbcacabbcdcccaabcbaccaabaacccbacdcacddabdcbbbaaaaaccdccbaccacddbbbbbddbcbacdcbdbcadccbbacaabcaabcbadaabcdcddbacbbacbabadbcabbdaadaddbddbdccdbcbcdccdddbcdcdabcbdbbbbcacacdadaaacbbdddbbcacbccbbbcabccbaacbdaaaddcdaacdbbddcaaacddacabaddcacbdbacdbcbcbcaccbcccdbaabdbaddaacdacbbdabdcbdbccbbcabbbdbcbabcdcaacabdcbadbabcddadadadcccbaddaadbabccbcdaabbbacbbbdcccddcccdbcdaaacdacdaddaadbdcddbcddbbccacbaacbcddccadaacccdadcadabdbccbcbbacdcabdbabbabaccabacabcbccdcdcacaadaddacbdabccdacccccaacccdaaaacaaabdcaadcccbdbabcadaddbbcbbccaaabddbbcbdcbdcdbbcabcddbcbdbdddabbcaccdbbbdbbbcacabbdbdbadcacaabbaaaaacacdbbadbabccdbdbacbcbdabacccdddbaadbacbdbcaddacbbccbccdcbddacabcbddcaaacbaaacdbcacbbbbbcacbbdcddcdcdbdcbcdaccabdbbbadcdacdadadbccaadcdbbbababcdcbadaacddacdbcbabcbcbddddcaddaadaacbadccddbbcccdbddcadcadbbbabbacdacdaadcacadddbcdbbbaddabdcabdbbaabdcacdddaccdaccadaaadbadcadbaccccdabdccbcbaaacddcddbcbacadccdbaddabdabcbbaadbdadcdbbababcdabaadabacbbbaddcadbdbccbdbcaabbbbdbcbccdcaccaccdcbccddbcbccaaadcbbacdbcbdbaaaabbdbacbcabadacdcbaacaacacaaddadbcccabbcbabcacbacbaabccadaabadbcbcbbddccccbdbdbdaacacbdbdbacacaacbccbbbccdadccbacacddcdbabaaddbbcaadbdacddbaccbdbdcdaaabdadcdddcdacdcadccddbddadbdabdcbbdbcbbbacaadcbaabcccbbdddaacdbdbabbdadcddbcaabcdcabbbdcdbbbbaacaccbcbcccdabadccddcadaaaadaadbabadbdbcbbaacadcdcacbbaaaacddadadbbcbbaabaacacddddabbcbbdcbbbcaaabcdbcccaaaaabddbaacdcadbcbcdcdddabdbcbbadbbdbcaddbabcdcbaacbbcabcacdbabccaaccacaccbbdccabcabbcababcdacddbbadabdddadcaadcdcaccddcccbdabbdacbcacacbccddbcababccccaaacddbdcdaabccdbcdaacbaccaccadbcdaabbcadcbcaaddbcdbbadbdccacdaaacdbaadccbcacadccccbcaddccacbabadaaaccccbdbbdcbadbdcbaacadcbbdbbcabbacabdaadbdbabdaabaaddccbddbdbdcbbadbbccacaddcbbdababdbcdaddacbacaddacaacaabbdadbbcbbbadddacaaacadbccdcddacddcccbbaabbcccabdadbcddacabdcbdcddcbcbdcdbdcdcdbdbbdcdaaacadabaadabacaaddaacbcdcadbababadadccbcdcdbdcbdbbaddbabcccbdbcbccbdbbdddbccadcdcbababbcadddcbbcbabdbddaacaabdaccadbddbdddbcddbbababbdaacaaabbabacddadcaccadacabaabdbddadbcddcbdabaccbadbdaccdcbbbbabdabbbabadaddbabdacdacbcdaccbcbabcbcdbacbaaadaccbabcdcdcadbcccbadddbacdabbbbcdbdcdaccbabcabadbabcbbdbddbadadcbadbaacdbabdbcdbdcbacacbdbbdbcacaaaaccaaabcaacaacbcccdbcddccbaabddcccdcccadccadcabababdbbbccbbacdddadcabbcbcdadadbbcbccbaadbaadacacdcaccaaabdbdaccbadccdbbccadadcdddcbccacbdbdcdccdacaacbbbcaadbacaabbdacbccbcaaabbccdabacadbabdbaccbdbdccdbabbdbaaaaaaccbbacaccadbbabaccbbddaadddcabcdbabcbaadcbbdcbccdcbdbcbbcadacabbaccabdddbbbcdcccccaccadaabbbabdcdbbdbddadbccbdddcdbbdbcbcdbdccbbbabddaddccdbadcbadacacddbcdbcccbccbadcccaadabbbbbbddbddddccbbbdaadbacbbbcddbabcabdcbacdbabbbaaadacddbdadbdcdadbcccbdcddddbbdbdddcdbbcdbccbcbabccabbcabbabcdbabbcabdadadacbcaabcdbcdabdacbcbdcbdcbcdadcbbbdcabcabccabbbaaccbaabbcbaaabdbddddcbcbdbbadccccabcadcdbbabcaabcaaadaccddabcadccccbaaaaaacdaccdcddbbaaddbcbdcbbddcdcacdbccccaababdcbdcbccabccbaadccdbbbcdccdacdacbdddcbddccaccdbdadcadcaccddcdbdccbcadbcacddcbbdcdbbcdaacbddabbaddacdaacdacddcdabcddddbdbaadaadaacacdddacaacbdbadcdabcbbaabcabdadbcaaacabcdbbdadabcaabbacacbcbdccdbddbdddcbddacccabadabbdccccbdbdbcadddaadbcbdccaabaabdbbcabcbaacddadddbccdbabddadbbabbdbbdbcaaddcbdabadbcdababaacbcddbdcddbbcccdddcbbbddbcacdcabdcbcaadddcbccdaacddcbcaaccacbdcaaddbdcbddabccbccadbabbcabaabbcabdadbcacdacbdadbdabdbdaddadaaacddddcdaaadddbddccacccaacdbabdbaabaadddbbabcdcaccadddaccbdabbcacdcbdbbbddccbabdcdabccabbdaaaaadcbdcbdabbbbcbacbbcbddcdabadccbcdddccbbbbccabcdbabcbbabbccdcdbccdaadbccdaabbdcbcacadadbcdccbdadbdcacbadbdcaacddddbbdbbbdbaaabcdaabacdbdbcacaacdcdbbcbacabadbdcbacdadaccacbcbbcbdabdaadaaaabcbaacddbdaaaacdbbbccdacaccaaadabcbabcadbcadccadabdccbbbbbdbccdabdbddbbaadddbdcbbdcdddbdbdddadddbbddbdddbdabdbdabdbaababddcdcbbcddbdaddbcaacbcadcdcdcaddddbdbdccccdbbbacdccbbdcddbaaadbddccaaacdbcbcdbbbddcbcabdabacdbddcaadcdcaccaddcdbdaabacaabaccbbddadbddbdabcdaaacaaaabdcbbadcadaaccdbccdddaddabacccacbdbbaadcbbbabcabababcbddbcdccbbacbabaccaccaddaaacdaaadbccccddcdaddcbcbddbcbbdacbbdadbadabbaababcddcbadbbbcccbbdbcacadaabdccbddcddbdbcdacbddbdbdcccaadbccbbbbcbbcbcdabacbaacbaabacbbacaccdadbababbaaddabddabaabbcddbcdbabaddbacdcbcdbaaccadbddbdcdadaddcacbcddcaabcbaddabbdbbbccdccddbdbddbcccabcdbbaaccbdbbddbcbcbdbdbddacbbaabbdababaaabcccdbcaddbbacbadaacbdbcadbbcabababdacdbabccdcaacabddaabbadddabadabaaadadddddccccbbabcaadcbcacadbbdbaababbabbaddbadcaccccdcdccbddccaaacbacaaadbacbddcadbccdbcddbadcdbbaadabdacdacdddcbcccaaddabcbabdbdccadcccdacacaccccaabdababcaadcbdcbaababbcaddbababdcddcdbbddcddcaacbdacbadccadbcdbadaddcbdcbccaacdcbdcddcaaaaddaacaabddaadcbbbcbdadcdbbacdaaccdbbadcbaaddacccdcdcbbcddabddbbaccddcdacdacdccdcabdddadcabbcaabcbdbabcdcbacabdccaaacddcaabaacaabbadbbdbdbcabcaadbdcdbadcbdbabdbcddbadabcbdacdcdcdacdaaddbbabdcaccacbdbaaabdbcbbcadadacaccaccdabbacabaabbcddddabcbacddbbdcbaaabdcbbadadcbadaddcddcdbccdaccacdccadcdcdbcbaaccccbaacccbcaadabadaddaabcdbccabdbbabdadcdbaccacaababcdabaabccbcbaadaadcdbadddbcbabcacabadcccadacdccacbadaaaccacdcbbabcbdbdbcbaacdddbdbadaadacbaacccdaaccaddbcdabbdaacbabdacbcccddbbbacbdbbbdddbbadbddcdacadbcadabbbddabaddaaaabdabcacdddccccdacbbdbcdccabaadbccdcddddadadacdcbadcccaabdaadccaccdaacadccbaadaaaaacbdbcadbccbccacaddbbddbdbcdadcacbbbccbbcaacbdcbadcacbacadabadabdcdcddaaadabcbaacbbbacbdcdcccabacabdbbaccdabcdbdaabacabbcdbdcbbcadbbbacacbdaccbdaddccddddadbcdaccbccbaadccdcbccaccabbdcacdcadcacaccbadacbcbccbcbaaccbdcbccbadbdbbbcacbcdadcbdccbbbddacbbcbdbaadbddabdcddbababbacdccbdaaacbacddaaabbaabdcbcdbcccacacbbdbcbcdbabacbdcdbcddcdadadcadbacdbabccbdbabbbbdaacadbbaacdddccdacdadcdbadaddcbaddbadbbbadddadcdaabcccccbbcdbccbacdaadcbbbaadadccddbcdddbddabccdcdaabdbaabdbbabbbacddcaddcacacdcdbaaabaacdccdbccabdadccabaadcccdcbccdbbccbabaabcccbabbdbcbbdacccdcadaaccadcabaccdacbdccacdcdcadadadbcdacaabaaaccdcbcdddccbccbadacacbadbdbddbdbbaababcabcaaaabcdcddbdcacbcdbacacddddacbdbdddcbabdabcaabddbccaabbdcbaacccbadcadcddbaadabcdbcaadadbdcccbbbcddcbccbbdddcabbbdcabbdbabcdabcbccdaccbcdbdcacdcccbbcbcadaccdcaaaadbadbcbbadcdabddcbdccddadabddaacddcbcbccabbbabdaaccdadaddcabdbdccbcaabcdabadccaaddadcacdbddaacdcccdbccdcabaccacdbaddbacbcaaccccccabbddaccdbbadcdadaddadccbbccdcbccabcddddccddaddcbbdadadcddbbdbbbccbaddabccaabdcdbbabddacbaaabcbacbdcdadacdbdaccabbadbbabcbaccccaabbccccdddabbbbabacaaccacbaacdddcdbaadbdbabcdbaadacacabadbbacaaabadbacbacccacdccbcccdaaaaabcabbadabaacbdbdaabbabacdcacbcccbbcaabbdcdcbdddbadbcbbcdacbaddbdaabccccabcbdccabcdadcaacadbcbabbbbcdbcbbdcbbaccadcbababbbbbaddddaadadabaabadcabdbddcbccbdbcbcccaddddddabddaabccaddccdadcdabbbacdbcaacadabbbadbcbbdcabcccbcadcbadbbacdaadbaababdbacddbbddbdbaadbbabdcbdaaacabbdbbbaddaaadddccacdacabacbdcaddacbdddcdaacaabddcbccadccdaccaabcdacddbddacabbacadddaacbcccadccabcabdacdaddccdccdccdccbccacabaccbdcdbdcabbcccbdbdbcbdccdcbaccacbaddccbdadaadaadddbacdacdacaacdbbaaaaaacdddcbcbacbdadaaaddabaccaccddcdaacaddbccabbaccbaaadcdabaccbdddbbdacdbabbddbccbadbddbaaaadbdadccdabbbbcacadaabdcbbbbbccbdbbcaddadcacdcdbacbabcbaabbadbbbddbbcaaddaadcaadbdbbcaacdbdccabccdbcdcaacbddddccbcaccdcbacbdbdbddadcccccacdaaccbadadddcacaadbdbbbbaadcdbacaccddadbcabdcdbbbdbbccdaccaccdcbaadddcaadaacbaccccdacabdbbcbddddaddacbbddabddadcbadabacdbdbbdbbdddbbadbbcdcccbbddcdbbbdcaaabdcbbcaabbdcbdabdcacdccdcddbbccdcacbacaccbabdacadbbcaaadcabcbdaabacdaaaddccbdcbbadababdcadcbbdbacaccbadcbbadccbaddbaadaadbcdcdddbadddaabdbacbaaaabdabbaaddcabbdcbbadcdbabdabddaccabcdabbddcaaaadadbbcddddacbabcdacdbdaddabaddaccaabddbadbadddbcdbaaabadbbcbbbbdcaddbadddbbbbcaadacdcbccabcdcdbacdcdaaddddcadbcbcdcabdbcccbcaabccaadbbcbacbacdadabddaccabcaacbdadbcaadacaaadcddbaabaddacccccdcbdbcdbcacaacbdbddadadbcccdcaabdababcaccccbbbccdadcbadaaacacbcbdcacbbcdcccadacbbbacbaadcbdcdbdcdadcdbddbabbaacaabaacdbaacbddbcdcbcdacbdaaaadcdcddcaccddccabdccbcddddbadddabbabdbbdcbabaabbbbcddadbccdbbaddbbbbdcdbcccddbbcdacdacacbaaabbbdaaccbaacababddbbbdaadadbbbddaabdbdacdbdbcccdaddcaccdacbbdbcddbdaabcbcabadbcdbaaacabdbcabcbcdadacbbbdacdadddcbbabbacaaaddaddadbacabcaaaccccdcddbccddbaadbdabdbabacbadcdbaabdabccadddbabbacccbdcdabaaddbbadbacccaabdcacabaaadbabcdabbcacdddcadacacdbacbbbadaadcabbccdbcccabcacbcdbaddbbacadcdcaccddcccdbcbccaaaacbbdccacccacccabaaaddadbdcbabcbcdcaadbabbdcccbaacbbbdddddcccbadbbabbdbabcccbadadcadddbdaaadacbbdccadaadaccababdcaabdbdacbabccdcacccdbdbacbccdddbbcdbcbccddbbbacbabcdcacadbcbabdaadbddbbaccbcdbbdacccdcaaaaddbbdaaacaccdaacddbcbdbdabbdaabbbdabdbbcaddccdbdcbdccbcabbbdcddcddabacdbadaaccadcaaddcbaccbabcaaadadadabdbcaaabcacccddbaccabbccaabacdcbdbbbcccbcabcbabcadabdacdbbacaabaccccbdcdbbbdcacabcabcababdddbddacddcccaabaacadacbbaccdcddacccdcacdbcdaacccabacbcbdaccdcbabcdcacdcacdaabccdaacadddbccaaadbbddccadbbaddccbcacbdbcdbcbaadcccaccdabbddddabaacbcbbdbacadbaccbdcabbbddcadabccbcccdcdaaacbbacabbbaacabbaaabcbaaacadcaaddbbdaaacbbdbccdaabdadbbbabbbdaacdcbadcaacddbcadbcbcacabddcacaacbddabdbaaacadcbcaaaaccadaacbcabaacbbbbbbbdcbaadddaababdbbacabdccdcdacbbacadddcbbaacdaaddbcdcdcabddbcbcdcddacbbaaccbccbbdbdaabbcddcddaccdaccdaacabbdaacddbbccbabbabacbcdacbadbadabcaaccaacddbabdbaadaadccadbbbddbcdabdacbadbddbdbbdbaaabcddcdaaacacdadcbbadcbdbbdbddcdaadccdbacccddabbbdccbbbdbbbbadcabacaacadbdabdabbcdcaaddcdddaaabadcccbbdbcdabadadbbaaabbbabbbcdcbacadddccdbcaabcbccbaaadbdacddccacaabaaacdbcadacaacaadabaadccdddaabdadccdddcbddbbaaaddadcabccdbcbbdddcaddacadabcbdabbccccbbaaabdbddbddacdcbdcdcacdcbcccbcdbccbddcbdbbbdbdbddbcbaadddbaaddaddbcaaacccacdabcbccbbbbbccadccccaaddaaaccbddadccdbabcdcabccadcdcdcdbbacadbccbbcccaaaaddbadddcdcdcddbdbdccdcaaabbcddcbddabdcbcbbbadadcaaaadcaabccbcaadacbcadccbdbcddbaccaacabcabbbaddbaacdcdcabddbadadbdcbbbbaadccccaccdaccbdccdcbbbbcaadaabbcbcabaddbdbbdbbcbddcaabdddacbabaabdbbbadbdabbbdbdbdbcdcabdaddbaabbcdbccdccbddbbbcadcaacbaacabbccbddcccddbabaadbcbcaaacdaaccdbcbddddacadccddddcdacacccacabdbddcabbabcadadcdcbddccdaadbcaacdbadbbddcbcdbababbadcccacbacbdccdaccdbabcaabccabacdbdcabbddcccbdcbddadbcadabbbbabccdcbbdcbdddcccdcdbaddadacbbccccdbdcdaacbddcbcccadacbdcbacccaacbaadcadddbaabbbbacbaaaabddddacdbbddccabcdbdbaccddaaccacacbabdcdbaacacbdcddabdbaaaadcccdbbacadbaaaacbcdccbabbdaaaacdcacbbbacbddbcdbcadaaaaaaaadbadbddcdcbcddbdccbadcbabccbbbacbcdcaccddccccadbbababcbccaddaacccbbdbbdaabbdddccbcbdbbbcdaaabacaccdaccbbbacacbdbcacccdbcbbdcacabadbacbaaabddbbacbddaabacadadbbdbcdddbdccadcdabcccdabbbdcccdbddaacaadbcacbbcadaccacabbcadaadccbadccbdaacbbcadabddcdcccbbccbabccdaabdcacccbbdadcccaccbcbcabaabadccaaabdbcadacbdddbadacbbbbbabdcccdbdaadddbdbaadbaddacadcbccddaacaccbbdbdddbbadadcbadbbddbacacadcdacdbdccbabbccdddaadaaacadaccdbdddcdcabcccadbaddadacacccccccabcadbbdcdcaadacbabcbcdcdccccabbcaacdbcabbccaacddcbccddbbdbbdcadadbbabcbdcaabacaacabdddcacdacbbbccccdadadcccaadddadacbcddcdabaaccdbdbaaccadcdcaccadcbabccddbbcbdcacdcabcacddcdcaabdadbdbdbadbcadbcbbcbdbabdcabccaadbcdbacdbdcbbbbcbbcddcaabdccdabbacbaacaabcddbbbbcdaccbdcccaacaccbaccadcdbcccbcacaabbdcdbcacbdaadcdbccdacdcdddaddcbbabbcaccdbbaacabcbdcaccaabdacacbcbacdbcaccadbaadbcacbadddaaaaacddbddbcaaabbccdccdbdddbaacdcdadaddccaaacdcbbcbbbcbbaadbdabcaabadcdcbacdaccbaabdbaadcbcacadaaabadaabddacbcbddbccdddbcbddadcbcddacadcccdbabddbacaddcadbcadbdbcdbadabbcdcddacbadbbdaadabbadbaaadccbcbadcdccbacaadccaaadabadcaacadcbdcccdbbcadccadbcdbcaadaadcdcdccdabcddbdcbcbdbbabadaaaadddaddaddddcacacaccbbbaacdccbbcbcbcbcddacbdddbcdcdcacabdabcddadcbaabddccbcdadcbcdcdccdbabdddaaababdbacabdbdbdcdcbcadddbcdddbccdbddadddcccaababbcaabdadbcbdcddaddcdacdccabbabcbbccabdacacddcadbbbacabcbccbbcaacadcccdacccbdddaadddbbacaddcdccabacabbbacdbbdddcadcbaaabadabbccacdbbcaddccacbcbacadbacbdadbcabdbbcabababdddccccadcaaabddcabcbdabcabcdcbbbcdabbabbbbdccbcbaaadbadbacabbadacbdaacbadabbbacababbbaabddcabddadbddbdabaaabbccaaddbbabdaaddddadacbbcdbbaccdcccabbdcadbdcccbcdbcabbcadccbbbdbcdacddacbbadbaababdabcbddaaccdabddadadaadccaaabbacccacbcbbccabacdadcdbdbbccddacccbabdacaccddcbacaddbbcbcbababcadcdcbbcdbdabcdaadbbabcadbbdbccabdcddcbcdddbdbdaccddcdabbacadcaadbccbccbbbacddbadbcdaacbadcaacdcabacbbbccabbcdbcddbcdbcadbdbcddcbddcacadcacbcdacacddcadbcaaccbcccccabcdadbbcbccacbdcdaaaccabcccaccbccdabdbdacacadcddadbcccbacbcadccdbccdbdbcbbabdccddcaabddcababcccbdaaaacbbccabbaaddcbacdbddbbbccdcccdadcabdcaddbbbbababbcacccbcbaacaadcadbbdaddcbbadadbdaaadbcaccdcacbcaabbcbabcccacbadabaadbdaadbbdacccaaccccdcabbbdcccbcaaacacdbdccdbccccaccbcbaddbadcbaacbbacccbddccdbacadadcbddaaadaabadddadabdbcbdcbbdabcadddcdbbaadadacaaddabbbcdcdbbbdcbabbbbdaddbcbbbbabbbcababbdbdcccaabacbdcadbbbbcaddddabdadabdbcdacdcbaadcdcbdbddaddddcadadcdddacddccbdcbcbdabacdacdccaddbacbacdcbdbbddaaddcddbabbdddbdcdabacbaaddbadcccccbbbabacbacacdaacbcccdccacddccbadaaccccaaccabaabbccdbabadbdbbbbdbbadcadddcdabaacccdcbdbbbdddbcdbbaddbdcbcbdbbdadcaadcacccabcddcdabdcccdcdbdbaabdcbbbdbbbadaaaddccdccaabbdccbbbabbcdcdccdcbbdcacaccbbaddbbabacdbaadcdadbddbadabaabbbddcdabacabcbaadbcbdacdadccabbbdaccbcbaddacbddbdaadadccabddcddbbbaababdbcbccdaaabaddbbabbccabbbdcaabcadaadbdbcbabaabaccdbbadbbbabbadbcbbdabadccaddacbdcddadccbcbabdadbaacbbcbbdadcdabaabbcbbaccdcbadcbcaccbbadaaaabaadbccbabdcadabacbbccdaaacbbccbbcacdbddbadcabdbccbdabaadddcdbadbaccbcdaacdaaacbbabcbcbcbcdbacdaddbdaaddcaddcadbcdabbadbabadabdbbcbbadbbcbbccdcbcdcbddabdbabcbdbcdcdacaacbdaabccaddaaacadabaccbcadcacdbcaaaadbddbbaadbccaddacccbacdbcbddcbcccddaadcdcdacadcdcbabcbddaccddbabcdcbdddbabdcaadbdbcaddacabdbccbcacdbcaabdadbbbbdaaacbdacaaabccabdccdccbcbacbccdabccbcbbbdcccbcdcbbadccbbaadacaaccdabadabbbcaaaaacdbcacbcadcabbcdabcbcbaabbccbcaacbabbcabaabcdbdcdcbadbaadccaacddccabaaadcdbcacadbbdabacacccdabadddacaabaacbaccbadbccddbbbbacdabaccacdcacbcdccdaddaadacaaaccaccaadcdcadcddaabddaadcbdcdbdbbccdbacdcacabcdabdccbdbddaadcbccbbcdccaabbbbabcdcaabbcdccdccbacaadabadbdcadbdaaadbbcadcdcabadbcbadbbaabbbbaaadadbabacbbdaabacdbcabdcaccacbaccdcaddbcaccccccbbadcbcddcbccbcaadcaaaacbbddacdbaaadaaaddbccaccbaacaddbbbdbdabccacadbcbdabdbdbdacabddbabaadaccadbbdbddbbbbdcabcdccdcbadcddcccccbcbadcababcabcbbacbbaddabccbacbadbdbcddcacbddabbbcbccddcbcaccdabaacdbbdcaaaabbcbcddacbadabbdbccccbdddbbbaccdbccccbbadcbbccbcabbbdddadcabcacabaadcdcabbabbbacacaaaddacababaddcdddbcdbdcabaddbaadbadccaabddcdccaccdddaabcbbaaaddddbabddccbadccddbcbbbbdcbdbdbacdbcaddccabdcdabacadcccdbaacacbccdcbabcdbabddcabacccaacaccaabdaccdaddcbcaadbbbdaccbdbbaccacabcbcdbbdadcdabaacbbadbabbdcbadaaacbadddcbdacabbadacbdaccdcadadbdabccccdabcadbdadadbbcbacacdaacddcdcdaaddbdcdbaaaccabbdacbcbddccbcdcbdbbbacbcdddcdbacbabbdadbaabadbcdcbdbbabcdcbcbdbdccdcbbacddaccbcddcdbbddaabbbccbaaccbbbdabaaccbaaabdbadaaaaaddcabaabadbcacbcccdaccdaadddcadbacbadacdcddaaaaadcbaacbdbccabbddabbbbdcbdbbacdddcbbcdabacccacbcabdbcbbacccbcccbccbabacacacaacbacdcbadbbadbdaabcbcddabaaaadabcacacbabcabbadaabbcccbdbcaabcbcccadbcabaabccbdaabaaadabdaddbcbcbbbbbcdbcdbdacdbacdacdaaabccccaacadccaddadbabcacabcbaacddaddccacddcadbacdabcbdcdccccdccbbbdbdbabcdcabbcbbddddcbbacbdcacdaddabaccaccdbcdabaaadbbbadbbbdccdbacccababcabadbbccabdabbccccaacabbcbddbcacabccdabaaacdadaacacbdcdbbbbdaccddcabacaddabdaabaccdbbbcbbadabaddcdcddaabbdddcaadbcdcadadaadadacdbaadcdaadcccddbbaaaacbaabbdcabcccbddcabbbaaaaadbbcbdacbdacdccbcdddbbdaaabcddbdbbadcbcaadcdbcbbddbbbcaadcaabdaccaddbadcddaddcaaccbddacddcadcdbcdaadcaabcbbbddcdddbddcddaddbbadddbcbcbacaddadbdababaddcadabddbadccdcdbcdcbbcadabddabcbaadaacccbadaabaadcdcddcccaaccdbdccdabccdbccacbadacbabbabbcdcccdcbcadcbccdcababdbabadbcacbbadcaabccbddcadbdccddbddbcdbaacabcadcbccbcadbadaccadbdbdaccdacaaadcbaaabbdcdcdbaadbabdbbcadcbbbdddbbabcbdcabdcccaccaaadbabbdacbaabbbcbcbaaabdcaacdbdbabacaacddcbdadacbabddadccdaaadbdbbccbcdcabbdbdadbddacadacccabbbccabaabbacbbadbddacabbaaccbacbbdadaaccadabaaadadabbdbbdbbdbacdbbcacbdabddadbbdddbcabadbaaadbcbdadbbccbddddcbacbdcacbddcabbbadbdacacbddccadacbdaaabbbddcdcddaccaacdbacacddaabbbcaabaaccadaabccdadbbdcbddcaddacbbdbdcdbcaabadbaabbacdaddacaddcbadbddcbcdccdbacbccdbdccdbddaaadcbbabdcdcbaccacbdcbbdbbbbddcdbddcbdaccccaabacabadcdcabbadcdbbdbabcbcaabbaccdcabdcddbbabccadbbbcdcbddaadbbacbcddbdbcaacdccbddababbcacbbbddaddacadddcdccacbcbabdcdbdbbcaabbdadbabcadbdbcaabddaacbaacabcacacadccddccdbdccaadbccdaadcadbbcbdddbdcdadbccadaadcabdcdcbdacacbacddbccdcaabcddacbcbdcbdcbadaacdbbbbccdbcbbbbacdaadacccacabcdcaaaacdacacccacdbbaccaadaabccbbbacbacbababcaacccdcbabadccabcbdabddccbbbbadcbbbcbbaddaaccadadccdaabbbcdcddcdadcaccaddadcccadcccbcbbddabcaaccbdcccdcbdcccbbbbaadaaddacdbcdbccbbdddcdbdbcdddbddbacdacbbdbbdbcbbcbbdacddacbdadaababbaccabcdccacdacabccbcbdabbcbcdacbdadbcaaabbcaaadcbcbcadcddccdaccbddaadacddbddbddcacbddcbbcaaccabaddcabbcacdadabaacadcbcbbbcbabcbdcbdaccbbcdbacaddbbdcccdcccaaabdaaccaaaabacbcadbdccaddcabaabcacdcabadadcbbcbdddbcdbccdbacacdabdbacacbadaaacaadcbdbaccdcdabacddbbccbcbdababbbcbbacadbadcdbbdccbccdacbcddcaaadcdbbddaabbcdddcadccdadcdadcabdbbbbdbdbddbcaadbbbdcbdddddbcbccacbabcccdbacabddbdcccaacbcbbabdcbaccbdbcdbcbbbdbdddbadbcccdbaaabdcacbacbdabbbadddaabadadbaccabdcbacbdcaccbadcdadbbcdcdccbddbddbbbcdadbdcbaccddbadbabadddabdcddbdaaacddbbadcbaabdcdbdabcbdaaadcbdacbbadbcddbcbabdbddaaabcbacdcbdaacdaabcdadcbddacbdcdbdccdaccdcdddbddcdadbcadaadccbdcaabacbadbdabbbbaadaacbbcbdbbdabcdbbcbbdcbcdddcbabdbbcdddddbcdcabacdadadcbacbacdccabcbdcdcbdabbccbdcdadbdcddddcdbcacbdcabbddadbdadddbabcabbddadbcbadabbdddddbdbadbcdaddbbbdacabcbbccbadccbdbaddadccdbacbcadcbcbabdddababdcdbcadccdbacdbabaaaadbbdccdcdddaaaddccacdccacdccaadcbdcdcbcccacabcadcacbcdcdccbbbcbabcbbcaacbadccacbcbbbbadacdddbacdcdcddcdbdbdadbbccbcbaaddcbccbcdbaadcbdadabcdddacdddacddbabbdbcbacddaccbbbdbbacbcdadddbccccaadbdabddacbccdddbbcdadacdcbcbcaadabbdcbcdaacabddbcdacadadbcbbcdabacdcadcaadbddbdbbccacbccdbaacbaaacaccbabacbbcabccaadccbbcaacdadaabcbdacbddcddcbdbabdaadacabdadcbbccddacdcccbddbbbcbabbacabacbbbaccbcbbaddccabdcbabbdcaccabbbdbaddbaaaaccdcccbaddaddcaccddcacccdcdccccbbbdcbbaacdbbadccccadacaaadbcbbabdcbbddadbcabdbacaacaadaaccbccddbbacbaddccadabddbdacaadcdbaddccdddcccbcdbbddbaadaacabdbbcdcdaabacaacbddbdaddcbbbaabdcddbbdaabcbdccaadadcadacaadaaacbbbbddacbcdcbcadbbccbabcdcdabcdcbcaacdbbaaadaadacbdcabcdaacadbcbcbccaaaabcddabbcbdacadacbabaabccbdabbbbdaaccdcabadbadbbabacabacadaacccaddbaadbbdaadcdbcadabcddddaacbbababccacbcbacdbbabaccacaccaddcdcabaacabdacbdcddcadacbbcccbdaddbabbcbccbaadddadccbcabcbadbbcababcbadbdbcbcbaadbabbaccbddbaaccadaddcdabacaddadadaacabbcaabacabcccbbccbbaacdbbacdccbbcbaccbcccbaacdbdbdbcaacacdcbacdacacaddababbcdabacacbcadcbcdbdbcbbacadcdcdbabbcbdaabddabaadcbbdbcdddcaabbaaadacbcbbcabcdbcbddbdcaacabcbcbbaabaccbcdddbcadbbaacddbdcdddddbdbaababacacbdabcaacbbddbaadcdcdbddbcdadcbdccadadbcbcbbbacccaaccdacbdccbabaadaccaadcbcaadbacbaacbcabbcbbdcaabddcdddcabccdbcccabcbcccdcbddddaadcbbdccaabbdaadbabdbcbdcdcddabbbdcbdbbccdaadadbaaacdbdccccaadaaadcdbacddccdbdaadbdccdbddbdbddbbddccdbccccbbbcadcbdccacbbccddaacaacacdddddbdbbcbddbaddbdcdbbabbadabdaaaaabbddddccbabbdddbbcaddcdadaacdcaccbabaddbbcacadbccdddadbdcadbccdbcdbacadddccddbcabcddacbddbabdabcccbcaddabaacbcdbdabacbbddadbbbadbbddbabbacbdacccccadcdacbbccdbabcbcabadcabbcaacdbbddcdbbdbdaaabcbcbcdadaccbdcbddaccbcaabdcaacadcaadcccbdaacccadaddddcdbaabddaacaacaccdbdacbbcbabaddcababadadddbdbabdbbdabdbbbabbbccbbabaabdbadcaabccbadbddcccabbdbbabcacbbbabbbadbadcccdcaaaababcbcdcaacacccacbdbddddbacabbccdcddbdbbdaaaccadcdabdcaaaacaddddcabadddbaccadbcacbbbadbcccdaabadaaddacabddbaabdbbdadbdaddcaabbbbcbcaadadbcccbcabdbbaacaaccddaacbdbcbddbaaccdbdcdbccbcbccdbdbdcaddbbcbddcaaaacacbdbcabcadabbbdcbacadaacdbacaccadabdbaadacbcacccbcccdbbbacbbabdbbadccbababbbddccaddcdbddcdcdcadddccaacadacbaddacbadabbadcadbcdcbbdbacdbddddcacdbacbbbacdaaacccbdaddbbadcadaacacadacaccbcaaabdbdccccabbbdcdbaabbabcaaadcabdcdbccacddbacbcbacadbbadccddaaddaaabbbcdcccbcdbacdbcbbddcbdabaccdabdcddabbbdbbaadcadabaddbcdddbbdcabbdbbabddbabbbbaaaacadbabdaddaacdbbdabbcbccacbddbadbdcdacbccadddcaabdcbacbcaabcdcbaacaccaadbbbcdabdadcddaaadddccdbbcbaaacabaccdcaadadaadddcaddaabbdccdccdcaacaddcdaddcbdcbacdbaabbcacdbabacaacdcbdabbaadcbbcbdbaddaadabbdadcacddcdaadbadaddacdcaacadccdbacbacbcdbcadaacbacbdaccaddadabdbdacbaddcdcabbdcccdbddccccaabbcabdacacdacccbcbdabcbadadccdacdbbbadaaccaabaccccbbcdaaadaccadbbbadbbbdcdacabcccbdddbccabcabcdabdbbaabaccdcaadaabcbbcddaccbbdbcabcbdcdcacbdcdbababbaacdcdabdaaacaccbbbdcbabcaacacdacdbbaabbbbbdcaacadacbddaabdbbbcbaacaadcdbabbacddcbabddadddadadcbcaacdbddbabacbcabccaabdbdaaabaadbcaacbddabadbadcccaacbdcdcdbcbbaabbccbdbadadcbcccacbbbbdcdacacdcbbccbccaaaccadacaadaabaacbdbbadaaabddacacbbcaabcabdadbcddadbabbcabacabbdcdbbcaabadcbaabacdddbbbdcdbadaabccdccdabcddcaddcddbaabbdadbbbadcddbabdcacbbddbbdbbbbcbddddcdcaaadbadddbcaadcbcabccdcacdaddbacccbaaaccabcbcbdcbcbadaccbbadccaabdddacabddbdcdbccadbdabaddddbcbcbaadccbcbbbaaacdacdccdbadbccadddbacaaaccbbaccacabaacabaadcadbbdddccddcddaaccdccaccdcddddbbcdddbbcbaaabaccddcdbcbccdccaaacdddcacbadcabccbbccbbadbcbdcdcabcbcdcabccccdbbccbabdadbdbcbdabbacdbccbbbabbbbddabadbddbccdddacbcbcbdabcbaccbbacadbddacacdddcbdbbbbdaccdcbdcbddcabdcbcbbcdccbaddcddbcacbbacdbbbdbcadccbacdbbbbabaadbaadbcbbccbbdccdbbdcababadccbacbbbabaaddbddccabddcbabcaaccbabcbbbadacbaaabccadbcaabadbbcdacdbcaaddbbababcabcabdaabdcdcaddbccbdcbdabbcbbaaaacadcddaaababdabddbdadaccbcbcbdccbcbccddddcdacabaababbddbdbcabdbcbddcadacadcdbcbbcbbcbdabbdbacbcadcddbaacaaddcccbdbddbaddbbadcddbaadcadbaacdddbdacabddcbcaccbacccbabacdddacbbdbbdccbdcbbdaacbbabbdbcaaddbcacbcdabdadacddcbddacdbdccaaccccaccdccadabbbcbdcccdbdaddddabdaadbcccccdadacdaabdacaaadddccdcbadbacaccbccaccbcaddbdcaacbadabadcccbbddbbbdbbccdddcbaacdacdadbbcbcbbcbccbadabddaadaaacbabbcbadaaaadaaaadcaccdaacaacccbadbdcabddcbcbcaadbdacdacbdddabbdbaaadabdcadadbacbdacddbabaaabcdaadbdadbcaaabdbcbdacaabdcbdabcbccadacabbababdababdcbaadabddcdadcdbaaccbdcbbbbbcbbbdcdccdbddaacdadbccbabccbadbddaadbcccbddcabdbcdacbdadabddcabdabdabadabbdcacabdaacbdabbbdbcbbacabadadccbbbcbadabbcadbadccddddacdabcbcdbdcdcbdbcbbadbabcbabdcabbccdabcddbcdaaccacaacbcabcbdbbbadadbabbacdbdabbdcacccbdbcaccabccababbdaabccaacdacdcccbcacbacbbddcbbddcdccaddaadabacadddaddbddbacbccddcaacabcadadbabcdbdabdcaaadbbbddaaadbaccdbcaddbcddbdcbcabbacdbcaabdccbcbbddaabbdadbbcaadcbbddcacbabaaddbdaabadadbbdaacaddbbdaadbbaccaadabccdabaadabcddaadaaaddaccabbacaacabadaddcccbbbabbddbdaacacacdccbaccababbccdbbbdbddcaccabcbcaaaaaadadccdccbacdddddaadddaacbbaddcccadbccbbcbcaccadcabaccdbadbcabbccdcabaccaadabbaabcaccdbdbcbabdadcccddccdbaddadbcbbdcbacdbbddadcaabdcbababcccadccdccadacaddaddaacddbacdddaccdddcbbdcbdbcacddbdbcdcbbdadcdbbadbabdadcdaccbddccbbbbdcdcbdabccbbbdabaaabddccdabdbdccacbadccdbcaddabaaccabacacdbbccddaaddddccadddbdccdbcddabdacbbccdcbbacbbbdbadbabbdcbbaccdbbdccadacacbbacccdbddbaddadadbccbccddadbdcabcdbacadccabbdcbabacacddbcbbaacbccadbcadbabbbbabbcbadddaaddcbabdbdaaddbbdbadbbdbaadbcccaaabacdcbcdccddcccbacbbcdcbcadadaaabbabcdbadccdbdbcbbcdbdaddcdcddcbcbdbcddcdacabdcacacdddadcabdadabbabcbcbdcabdcacdacbbaacbdddbacaaaccccbbdaadabbbabcdcacccbbdabddcccbbbbbbcdcaaaadaddcadcbaaaccccdbaabdccacbdcabaacdbcddddbccacadcbbacacdaadacdbaadddadabdacaaddbadcbdadddbacabdcdbdcbdddbddbcbdbbcacccbdabdcddbabdcadbcaabdbbbbbaabdbadaddcbcbbcbdabadcbcbcdaabbccdcbcdcbcccccddddcbbdacdabcbacabbbccdcdcdbdabcdcbcdabcdaabddccbaabdacaaabbccbdddcdbcabbaabcddaabaaabccacbaccbabbbcdacddbaabdcabdabbabdacbcbcccbabbdacddccaddbdddcabcaacbccadbdabbbbdabbccdabcabbacaabddacacacddacdcadaacbdadbaaaddaccdccbdcbdacdadaaababaacbcbaacacabbbcaacaaccababdbaadadaadccbcacddbbddaddacdddbaabaccdaddcbdbdadbbbcaaddacadbcabadbbaacccaaadcddcbcddccdbbdcaacacbadddacdcddcaacdaaadcaadacdcacddcbbcdbcaddaaddccadcbacbbcabbbaadbcabaddbabdbcbabdbdddbaddcccabacdcaacacbdccdbdaabcddcacbdccbbbcabccccbadbdccbccdabadcbdddadbcbdaabcccdbaccdacbbbbdabddbdccabadaacbbbcccadbcabdbbbdababdaddcbbbbcdacadbcdbbdbbcdcccdaddccaccdbabaadcabdaddacdcbaacdacbabdadcbcdabacabddcdabbbcbbcbbbaaacdadbabbbdcaddaadbaacbcbdcaaddcdcadacddcdddcabdbbbddcdcbaacacbaabdddcaadcaadbbddbccddbabcacdacdadcccbdcbbddbabccababacdadabbaacdbcdddabcabbaaadbbdcabccbccacbdaabcacdcadbccabcbcccadddcccdadddbabdadadcdbcbaddabdbacbcacdbdbdcccadabddbbadccccbdadabcbbbdbdcabcdacaaabddadddcbdcbbbababaadbbdcadabaabdaabccbacddbadadaadaacbdaacdadbcabbdacadbdabadbabdabdcdccbabccbbaaabcddbbbcddbbdcddbacabbbbbcdbacbdadbccaaaaddbabbadbcadbdabcacdaabdcbbdcdbdabcbcdcbbbcaacdadaacdcbcbdddcbccbcadbdcdcdcdaabbcccacddddacbccdddadccdbccbcaccbdcbcbcccdabdcbddcabcbaabdccabaaddccacadbdbcddacccacdacdddabdbcbbccbaccabaccdcadbadbbbcabdbdcddacbcdadcbbaabdddbcbbbbbaddbbcaabcbbcccbdabcddbddcddaacbbbbabadbccdbacaacbaddbcbadbbdacaaacbcbdbdbbababaabdddcbdcbbccaacbaaddcdbcabcbcabdadddabcdcccdccabadddaccddaabcbddaadcddcaaaaccdddbbddcccbccacccddcadbcbabbdacbdaadcabbcdcbdaabbdabacadaadaddaacbcabdcabadababdaabacadcacbabcaaccbabdacbaacccacadbabaaadcccbbdbbddcdcaabdddbcdcbdadcdcbcabcacdabcbcabbcbadbbdbcbcacadbbcbdddaaaacbbadabaadbbdbccbaddaaccaaabbcbadbcbdcbdaacdbddbadabcbdcdbbcdbdddadbbdacabdbddaabbcdbbcbdddccdbbdacbddcbcabbcbbacaaccaabcacdbabcddbbaddbcddbdbbcdcbaacaddbbcdcaacbbbcbaabdbdbdcbacbcbabacbabdabaadbcbbdcabdccdcdadbcbdacdcdbdddadcbabdbcaddcacacadcababcaacbbbbaddaaaacbaaaabbccadaaabadbabddbcbcaadadddaccccdbbcaadaaabacbdadacaaddcdcdcdbbcbbcadbdbdabdcdcaadddcbdcacababbaccabdcaaaadabddacbabdcdbaaddacabaddcbdaadbdcbdabcababbbcacccbdbdaacdddbcbaadddcadbdabbbbdcadcdaaaaccdbcdadbcdbccacbabbabaacbcbbcbcbcdccaabccbdbcbbabbdadbcbacadcbddacdbdbcdacdabdddcbabacbcddccbdaaadbcdddacccdbddbcccccbddcdacbcbcbacbbcadcbcbabadabdcaccadabadaddacaacdcddadbcacdadcadbaddacdcccacddcdccdbdcaddababbdaddcacaddbdcddabbaacaccbdbabdcddaadbbabbadcadbabbcaabcaccaabdbbbbdbccbddadaddbabbbccbbbadddaabbbcdacaacaaccbbcbcbaddccacdccabdaddabccacadccddbddbabaacbcadbabccdbcbadbcacdbcadbabadabdcdaadaccbadabdadbbbcccdaadbcbabccbcbbcdcccadadbddacbdcccdccdcdacadacbddbbcacabaacbdccbcbcbbabbabcbcacbcbdcdbbbbbbddbdcbacdbcaabbcbcadaaacdcbbdddcaaabcbadaabdccccbdcbadcadbcadcabcdbcbdccdbabcbbcacbcdcdbbcdbdabbcbbcabacdbbcbddcdccadcdcbdcadcabbdaaaadcdcbdabadbccaadcbdabcbbbaccaddacbcaddcaddbdacadadccdbdcaacaacadcbbaacacdbbbcbdaccaddcbccdcbaabadbaaacbbbbcdbbccccaccddbdabdcbdbdbadccbcdacbacccdddccadccddbacbabbacbdcccabbccdccbdddddcdcbcadbcdcbaddcdabdbbabbabadbbbdadadccddbccbdccaacbddbbcbbdcdbccdaadbdabdadcacccdcbdccbbabdccbbbdacdbbadadcdcdadcdbcbdcddbcbaabbabcdcabbccbcaddcdccbdaabadbdadddbddaabbdababcbbccccacacbacdadcbacaabaccbbadccbcddccabcaaaacabbcbcbabddacccadbacadacabcbdcccbcddcbcdabdddcbacccbaaaddbdcdabbacccdbcddacdacaccacaacbabbbaddccbbdacdbabcbddbddabdacaddbcbbccaaccbdccccbcdbabccabcadbadabdbaacbdabdabbababaaadccbddabbbcbacabcbccbdcbcdbccdcbdcaaacddaccbbcabbcaaaabccbcbcdadbaddacdbadabaadcbbbbbbdcacdbadddabccaabacbbccadcbbaddadbcddadbaddacddbbaabbacabbabacdddddbccdbcbbabcdbdaacabbbadbaababacaccabacdcabccddadbadacadabdadcbddaaaadbdcccddbaaddcbddbdcadcdadbcadccdcbbaaddcaaabbdccacaabbbdbabdacaacdadadacaddbcabcacbaadbabacddaadbbcbacbcbddbdbddaccdaccbdcccaaabcdbbbddcabdccbaadbcacabdadbcbaabdbadbcabbabcbccaadcbbbbdcbbacbcbdaddcccbbadcbbbcdcdacdadbbabbacdbcadaacaddbaacddbdbadacaabaaaabdcacbdccadbabcdaacaddacbdaaacdacdaaabdcabddcacdbcbcdcbddccbcbcddaddcbaaadcddaccdcaccdbbacdabbbdacdadaabdabaabdbbbcbbccabdabcabdabbbbdccbdacccbbbdabbdcdbbbdacccbcdaddcaaaadaabacdaaadabbcdbbbacacddbcdaddacaaacbdadddbcdcaabaddcccbddcbdacbdadccccdaccabbddbbbbcadcddadbcbbacbbbdcdbbdccabcabbbdcddbbadccabbaacabdaddddddbbaaadcabcbbaabbdacbbabbdabbbbadbcbdadcabdbcaaacdcdbcababccdbbabccdbdacaacdbcdccccdcbdbaddadbacdacacbadcdcbacaabccbdccabadcbabdbaabdccaddbbbdbbbbabbdacdaacacccbabcadcdadabcdcdbccbabcdcabcddddbcbababadabdccabdbaaaaabcbdddbcbdddcdabdaacaacdabbcddcbabccbcbabbcadaadaccddbaabbaacabdabbbdcbcbaadadbabcaadacaaacaabcacabdccdcbdacdaccadbbdbdacbcbaaacccabcbcbbbcdcabcdcbbadadcbbbbcbdadabcccacbbdaadadddcbddaccddacdccacbcbcbcabdcabacadacbdadccdadaccbacbcdadabbabdacddabddacbacccdbddddbddbcbbabcbbdbadcabbabcdbbbbbdcaabbabcadbacbccdcbabdabddadddcdbabddcdcabdbccacabcacdacadabdaacdcaacaacbbcaadbbcdaadbdcbacacaabbcaabcbcbbdbdbcabcbbcbbaaaaacabbaaadbdbadcddbbaaaccaabbbcccaaaabbbdccbbdbbccabcabbddabbacdbdcbdadbaabddadbadaccddbadcaddaccddbbccbddadbccacaaabaaccddcbaaddaadcdadbcdddadbcdadbdccddcdcbbdbbcaaddabacbbdcabadadcdcdbbabccabcabdcbbbcadddbaaacacbaaddbbdddbdcbadbbcbdaccadbadbbccbcccbdcbccddaadbacdaadadbdcbbabaabbaaccabaaacacdbcbaaacaccdddaaaccbddaadabdbbcbdadbbacbbcbcdbbdbbbbbbcadacdccdbddacdbcaabccdcdbdcbaccbacaccbbddcdddbadcbbcdbdaaaabbabcaacdbabbabdbdadbbacbbbdaadbaaacdacdddbabcabbddabddccadbaaaaaddccbacababbdcadcdcabccaddbdaaadcccababdadbcbbaabcaaadbaacaadaccbcbdcaddccaabddacbbdaccbdabbacacdadaaaccadaadadbaaabcdccaccccdbacddaadacacdbacbabcbbabcccadadcdbaddcabbcacacdbddbbcbdcbcaccacbbaabcabcddcbdaccbdcddbbaaaadbdacbaccaabdabbdcdaaaddbbbabbddabcbcbaadbcbbcbbbddbbabbbbabcabdaabcbbdacaabbdaadbbdcddcbdaadcbdddcdbaadbccccadbcbcdabdddaaadabdddbbccacadbaccbbbbbbababdbaaccadbbbcdcdadabdadbcbcccbbbcdabbcabaadaaacbccbabdcbdcccaadbdbdddaadbcbaadddadbabcabbdacbacabccdbbbdabdabcbadbdddcbdcbcaabdabadcbadcaaadddbccccacddbbbdcbdccadaccaaacbacdadadcbadbadddcbcabdbacbbcbcbcabbcbbbbdacbddabccdbdaddcbccbabbdcbcbbccdcadcaccadacbbdaabcdbbaadcabcdddcbabdcadbcacbcbccdddbbadbbdcaaddcdadadcdaaaacdaaacbbbacdbbabbaaaabcbbbdbbdbabddcbcbbcbdadadcacabdcbdcdaccbaaddadbddaaaadcbbdabdddbbcbbabcbdcdbacbccaaabbaacdaabdabcabdcadabdcccbbdaabbcdcbacaaccabbbdbbccbdadbcdaacbdcacacacbdaccdddcababcabbddbdcccbddbcccdcbadacbbdbbcadbaccaccaaddabbcdcaaacdcbcaddcadbdadacccdcdccaccccdbadccbaabdcadcbdacdcdcaadaddbdacdbabbcabcbdadabcdaccbdaacbbdadbdbdaddddcddabbdacbdbcbaacbddbdacbbdcbdbaddadddbacacadaaacbcdadacddddbbdababbcdbddbaaacdabadcbdccbabbbccbbbdcdccbaadbaaacdcbaadadbbdbcdbcbbbbdcaacccbcbbadbcdaccabcbaaacccdbbdcdcacbbcddcbadadccabbdacbcdccdcdcaabcacacacbabaacaddcaddcbaadaadbdbbbcdcaadcdaaaaaaccbacbccbadcaacdbcaddacbbbcacbdaddcbbdcdddcdbbdcaadbbcbccbdbdbdcdcbcbbbbabacbdcccdbbacbaaddabddbbddbcdbccdbbddccaabccaadcaddcacacccddccccbdccaccababddddaadbaddcbbdcbacdabbaadbcaadcccccabdaacbacddcdddbdacdbbbbcccaddabccadbadabdbdabbcdaaadcccaabcbbbaccbbcbbdddbaabbcadcbcdaccbdadaccdacccabdaaacdbcdbacdddccbcccababdbdbccabdaddaacdcccadcdbccbbddbcdddbbbadcabdbbddbbbddacabddcaddddbbcccdcbbddddcdbaddddcdbcbcacbccbcbaabdbcabdbdbacabcaaadadababdbbacbddadadbacadbabadbdbcbabadbdbddbbdcddccadabdbabcddbddbbacdadccdbaccabcbabadacacaccdbcbcbcdbdcaccbdabcbdbdbbdddcddbdbcaabddbdbcacdbbacabcbbcccbacadbaddcdccaaccbdbbcdcaabbdddbbdbcdabcaaccbcacadbccbdabbddaaadabccabddccbaacbadabaacbbbccbccdbdccbbbddbaddabdadbbaabddcbbbdddcaadddccbdcbadadddcabcadacddcbccdbdcaaddddddadbbddcdcabbcdcdccdbabdaddbddaadbbabadcdabadcadababbbbcabddbaaaaaabacaccccccbbdbbbdbabdadacbcccabadbbdbccbcdaabdadcdbbcbadbcadabadcbbbcbddadbdcccdbdcbabbbbdbaddbbbbdabccdccbcaababbbcbdcdccbbdaacbbcccbbbcaaccbdcbbbccdabdddacdddaccbaccbccbabdccbabaaaaaddccbcaacbacddccacdacbbbcdabcdbbaacbbaccdaaddddaababbcccbbdbdbbabaccdabacaadcdcadaacdaddaaaaacadbccacdaacccbbcbbbccaccaddcddadabccacbcbccadbadcadbadbccbdcdcdcddccabaccbbabddbbbadcbcbbadabcbcabbbbbdaddababccdabdbcbbccdacaabdaccddbcccdbadacacdcabccacbcaccacbaacbbaaddbadaabdaddbaacbabadcddbbcbacacacdbcaacdbbbabbdacdaaacbcadbcdabdbddcdadbadaadddbbcacdcccaabdacbcaabbdaddbcccadbbcbcdadaddcababcdcdaadadaacbdbaddcaaddaadbdabbbbbbbcacbabdabbdbbcdaddddadbdbcddbddbaabbabbdbdccadcdbbdddcaacdbbcaddbdcaabccbcbdbbbdbbadcbbdcbbcbddcdabdbdcdbdacadccbcbdcadbccccbdaaaadcaaccabcbccaddabcacdadbddadbdbaccaababcdaccddadbabbcddccddbdbbdacdcaadbbbcaadaaaaacdabcababdadadabaabcccdccacaaaadbdbdacadcdddadabaabcdabaddaddccddbdadaaaabcdcacacacababccbbcbbdbdddbabccbbcbccbcabacabbdaacabbbaccdbabdcddaddadabcaccabaccbcbbabbabcadddbcabbaaabbcbbdccbddaabbbbaadbdaaaabaacabbdcbbbdaddbaacbdcbbccddcbdbcbabcdccddaaaaabddadbbcbdcdccdbddcacccaddcddacaccaaddddcdcbbcbbcacbacbacbbccdcdcdcbbccaacaadaaabddbcbddadabbdbcdddcbcdcabcbddddcbbdadaabdbdbdaacdbaabcacabdadaadbbdabacdcccdcadbaacbddadbbdccdcdbbacaddccbcdbbccccdddbcddaddccbbbbdaccdccdaacdbbbabbacdcbbdadcdbacdbdaadabdaaccccacbaacbcabdaadcaaadbcdcbbadddbdcadcddbdcccdacdacabbaaaabcbbcacabdbbabccdbbdaaccdcacaddccbdbbbcadbabbadaaaacbbdbbabaadabdadcadbcdaacccaccdacdbdbbbbaddadddaacacabcddbdcccaccbcdaabcccbbaaadbaacdcdbcadabaaadbabcabadddadcddcddbdcaabdabbddcaadbbcbbbcaddcaccbcaccaccdadbcdccaaccabcaaaadccadccddcadcabcdcabdcdddbaccccdcddccdbadadadbcbbdababbabadabddbcaccdabdabbadddacbabdccdddcaabcbcbaccdccaabddbddabddaadbaacdadaccbdaaaabacdddddddcbddbabddbdbbccdaadbabdcaaccaddbacdcddadcbbaabddabdcbbdabbacaccbabdddbcbbaaacadbbbaabcaadaccacbbaddaaababacbadbabbcdadcbbccacbacdddcacaaaabddcdaabbcdcbadadbccbacabbbdbcaabacabcaddcddadaaaddbcdbdaaddddddbacababdacbaddcacbddddaddbaccabbcbaaddccbabbcadbbbdddcacbbbabaddabbcdbbdcbaccadbbbbcdbbdddccccbcacbaaadcaaccabddabcbcdadcdaccaadaaaacaacacbbdccbacbcabacaacaadddbccbabbbacabcccabcdbbdabbabddcccccabbddadabbadacbbcbbadcbcdccbbbcccbbadcdaddbadbdadcdaaadbabddccbdacbbbacdaaccaddcdcbbacbcbbcaddcdcdbdbdbacbbabacbcccbcdbdcbbadacacbcbaadacdbdcbbaabdcaacdaaddadbdccaaacdcbdbdaaccaccbcbacbcbdcbcaccbdccbcadabbaccbccccacaabccabacddabbcbaddaacbaacccbadcdaabbbcabcacdadcddcaddcaddbbaddbcacbbdbcccdbbbdccadcabbcdcccbbccacbabddaccbbcdbccddbbaabbabdddbbaccadbabbabbcacbadbbcadaacaabbaadacdbbacabbacdcabbddddbcacdddddaacabbdaccbcabaaaabbbadaadcaabcdcdaabbcbbadbdbcadadcbcaaababddbbaaccbdcdbcddbbcbdbcbdbccdacdabbdbcbcbccaabdbbbbbdccbcbadbacdbccabbdcabccaaaaaaaccbcbdabbbadddaadbcbcabcababdcaddcdcacbdbdbbdddbbbaccbacbcdccddbbdbcbdbaadbcccdbddabaaadccacdcbbaabaadddaacddcdacdaabaaccbdaacaddcbdcacdbacadbcaaaadddcccdcdaabdadbdcbabbbdbaaacaacbbacdddcbbdcccbbcdacadbbbaaaaddbbcdcccdbbcdbdbccaddcdbabbaccddabadbaccbacdcccadbbcbdbbacdaabdccdccabdbcacacaddacacddcbdacabaddbdcddabdbbddacbdbdaabdbbbcbcdcdaacdcbdcbbdcdacbbdbabbccbcbbacaccccbdbacccbccabbabbaccdcbabccccbdbddbababcadbdccdabaadacbabbdcbbcaaccbaabbddccbdbabdbbdaacccadadddbddbdcbdaabddabcdaabbcbccdbdaddcbddbbddcdbbbabaddcbbbdaabbdaaababaabdbbadccadbbcaabbabaddddddbaacadccdcabadddacddaabaaacabbbcddbdaabdbbbccaabddcabababbbdccbbdddacabdadbbcdcacadbbabadbbbaacdadddbdbddcabdbdddddcbbdabadcbddadccacacddbcbacdbccabbcdcbaabcbbbadddadcaddcdcbdbbcaaacbbbbcdadacbbdcdaddccbaadaacdacabadcbcbcbabacdccdbbcdcdddccabdacbcccddbaddaaacaacdaacaadccabbdbdcabbbacbabbbdddaaccaddadabcadbabddcaadbcbcdbcabacddbcbbcbdbbadcccbdddadbbccddadbabdcaddcadcbccbcacacbbcaacdbbcaccabadccddbdbcabbbbdacdbccaabcdaaddccdcbbacbbbcbaccccddaaddccdcaadddcacdcabccaaadbcbadbacacddccbdaaccbccbdbdaadacbbacccbcbdddbdcabadccdaddccadcbdcabddbddcaabdbbadabaacdbbbbbcdbdbbcabcbaddbcccbcdcbdaadcbbbabdbbccaadbdaadcbcccaadcabddcddbadacbcadbccbabaddbadcabbccaaaaabcaadadaacdbbcbdabcbddccdaccabdaadcdacbdcabbdcadacdccccaadbbaacbdabbadabcddbbcbdbdaaddddadaaddaaacbbdcddadbaacdcdadccabdbbbbcacbacabdadbdaddacaabdbbbcbcadacdccddbdbabdccacbbbccbaacdcdcddbbbdcadddacacccabacadcacddbdddadccccadbbabdddbbcabbbdcbcdbacdabcacbbcbadbddbdbdbbbbbbccadabdbbbbdadbbcdccbcadaccdbbaacdaaacadbadbadabdadcbcabbcababbbccbccddbbbccdacdacabbcaccbaadcbbbbddabbabcacddcabbdacbcdcbddcdcbcabdddadddcbbaabcbaabadbdbbcabaaddadbbdadbbbddcabcccababcdbcbdaacaaacacbccccbabbdcddcccbcacbabcabcabbccaabbbbaacdddabccdcbacaabcdabaacccbcddabcaadddcaaabdadacdcabaccdbababdcbbccbadbdbaacbbcbbadcaacbaaddaacbdaacdbdbbdbabcacacdccdaddddbcdbdaccaddcacdcdcbbdcabcabacccddcccddbdbbcaaaccccabcbccdcdadddcdbcccbabccaddaccbdaaabbbccacbbcadabdcaddcbbbabaacbdccabbbdcdbadabbadccbbadcdadacbcccaacadcadacbabacacabaabdbbaaddbbdcddbdbcadacbadcdacdabacadbbcdbbdaccabaddcbabcabdcdcadccdddbbbcaccdcdbbdaddddccabdcbbacdabbdaaddcacdcbabbbcbaaddccbcaaddbcdccacadddbadbbbbbbbddabaddbbbcbdcbbccaabdaabdccdbcddcabcdbcddbcacbacbddaadabdcdbcadbabcabaabaaccdadacdaccadaccdcdddaaddcbbbcdcbcbcaaaadcacccaccacdaadccccdadddaacdaaacabacbdcccdcbabccacdababdacbaacbcddaaabacaacaaacbbdddbabaaaaacddaaccdacccccccadaccdbcdcdacdadaacbaababbbbcabaddcdaddcdbddabddbbddcadbaccdcdbadacdcadbcbaadcdccbdbcbbbbdccbdcacaacdcaacdaabdbbabdbcbbdcbdadcdddabcdddcacdabddbabdaaabacacbbcdbabbbdddcbbbbbdcddccbbddcdbdbacbbbaddbadadacdcccbcbbccbbbbdddcddacddcdcddcbbdbccabdadcbbdcddacdabbcbdccacadbbdabcaacbbbadddddabccccaabbbbbbbdbaacabdaacbbcaabbcdcbdabdcdcadbdacbcbaacacadcadaddccddcabbbabbbdccabbbaaaaadabdaddbdaaaddabdaccbbbacaccadbddbabcbaacaaaaabdccadbbbabbbbdbbbaccccdcbcdcacbccbdbddcbccacdaacdbaaadbbdcdcbbccbdabcccdbbdaaabdabcacacbcdacdddbbdabadbaccbccccaaddbcaadaabaaddbcdaddaaabaddadadddbabacdaccaacdaabcbcaccbdaaabbddaccbbdbdabbccacbbdccbdcbdaadbcaddbbabdcddbdddbaabadddcdbbbaabcadcbbabbcccadccbadbdabdacccbccbaccbcbaabdcdcbbcaccdaabacacacabaaaddabcccccbacbaacabccbbddbbcccadaaaccbacdddacbacacadcdcaddcaadbcaabcdadbdcabcbddcaacdbcaabdcbcdcbaaadccbdadbdadbdaaabbdcbbdaccddbaadccacddddbaaaaaabcdacadbadaacdcbdbcdddcdddbacdacccdabdabaacccbcdcdcbdabbddadcaabdccbcdcdaddddcddcbddbcdbacdaabddabddaaccdcdccdcddddaddadccdaadcbbdbccbbbdddacddaadbbdddbaacddbabdbadcbddbbdaacbcbdacaabacdbdaddccccaadaabadcbcdbcdcbcacbbcdcdccdbddbabaacacadaaaccacddcaabaccbcabbdbabcbdabccdcdbccbaddacaadbddbbddbaddabcbccdcaaabcdcadaadaccbbddddbdaabbcccadbadbacacacdbccbccbaaacbcccbbdcdccbcbbcbadbddcabcccacdcdddacaddcacdcdaddddcdbcbbacabcbdcbacacadaaadcdddacdacdbadbbcabccacacadadddccdabcdbbcccadaabdaaaddcdddcdcdcadacbbaabcdcccccbbccddaaacbccacddccccabcdadbcbdbdcaabbcacdcacdababdadabbaacaccabacccabbabacddccbbbdcacddddcdcdabbbddcabbbcbdadbbdcbacdcbcdabaacabaddaabdbadadadbadbcbcaadadddaccbbacadbaadabcddccbddbaacacacadccbdcbbbcbaabddbcdbbbbcacbaabbddbbbaccccbaacdcccabbbccddadddacbcddccaaaabcdcaddbcbdbbbbacbddbbcacacbabccdacbbddbbccbbdabdabdadbbccdbcadbdbdacaacbddaccddcadccddcbccbdacdbaddcadacadcbacbcdabacbbabaabcacabacdacbadcdbdccddbdbcddbbbdabacbbaacbcbadaddbbacdadaddcccdbdddcabcddaddbdcadddcabccabbaacdcbacbacdcdaacdcdcbbcabbdacbaadababcddbacbcaacdabcaacbbbaabcdcbdbaabccbaaaabadddbcabbbdbddabdacadcbdabcccaacabaadabbaaddaadcbdbdbcbdacdbccaddcdacbaabcbdccdbbcabacacaccdabaadaaddacadddaaabaccabbbbaaaacbcaaddddabdaabdababadcdaabbabddabbbdddcbabddaababbbaaaaadadddbccaaadbccdaddabbaabcdbbcbcdadcbdacaadbdabdacadcdccabbadcdaccdcabcbadbccabcacacbbdabddbdbacaadadcbccadbaabbbbcabbadccbbdbdddbbcccabdcdcaadaabcdadbcdbaadcdaacdadadbdcacccccacababdaccbcdacbadcbdbcadacabbbbdabbaddabadbdcccdbadcbdcaabadbbabcdaaccdcccabaaaccccabcadadcaadcacdadbcbdccbaddcabcdbdbabdbbbabddbdbbbbbccccbcadaccdbbddccdcacbdccbcaadbdabbbacdaaadacdaddbaabcddcadabbbbdaadaadbbddddcdadcbdadbbdddccaccddbabbdbbadbbdbcbaaacbdbdcbbabcaaccbcdcdbabddbcbcaaabaddcddbdcbcdcddcdabdcccbabdaabbcacababadabdcababddacbabdbdbccbdddbadacccaabdacbdadbaaabbdadadcdbbbbaadcdbcdbcbcbdccabcddcaaadbbbbdcaaacdcdbaddbbdbdabdabcabaadccbaaaacbcdcddbcdabcbbcbdbbabdadcbaabbabddbadabdbdcaddcadaddcaaabaaddaaddcbcbaadaaacbacadcdabcaddcbadddddcdccdaaacccbdacbbcaacabdbdcaddcbbbadbbbdacbdbdcccacddcccdddddbdbadbcbdaccbadbabbdbcabdbddccabdccadcccdaaaaddbaccaadcddddbbdbdcaaacddbaccaabccdcbdcabacdddcbdbbaddbddddcaaccbdaaadcdcddbdcbaabddbaabdadbadbcdbbdcccadbdcdcdbdddbbaccabdbcacbadbbaacbdbbbbcddaadbacaacbbaccbdbbccaddbaaadcdadabbdaddbbaccbacaaaaadcdccaddabadcbabdaaadaaacdbbaadadacbddcacccbbcccadaccabbabaacbaccacbddcbadcdcdbacbdcbdcdadaccbddbdbdaacdddcdcdcaadbbbbcbbadcbaaddbadbbacbdacbdbaccabddbbadbbbabcbacddddbadabcdcabdbddaccdbbdccadadabcacadcbcddadcdbbacdbaddababaddbbdbdaaddaabccdcbccbbdacabcddabbcdbcdccdcbcbabbccadbabddcdaabdbabbaccabbaccbbabbadababadbccdcbdbccbdccdbabcbbdccdcaabbddddcdcbdacdccbcbccdaccbcdaddddabaabdcbdcdcacacdbcdccbacacbdccddbabaabdbbaababbbbabcdacdbadbbcdadaadcaadcdcccddacdcbbcaccdcdadbbbccdaaaaacadaadbcdccddcbaabaabdbcbdbcdbdaddadaacabcdacbabbbcabbbcacbbddbcaadcadbcdbadcbbacabaddbadcabbabdaccdaccdccdbdacabbcbcdaddcdacddcdcccccbdadabdaaccbacbbaadacbaacbbdadcdbbbddcacbdbacccdccdcadcdbdcbdacdbbbabbdcabcbbaababdadaacddadbaabbadcacaccbbcadabbcddaddddabacbacccacbdbbbcaabdcddcbdacbcaabdcacbddaddbaaadacdcaabbdddcdcddcdccdacbbbcbcdddbdccbadcddcccdaaaadcadbbbdabddbcddcdbabaacbbbbdcdababbcbcdadadaabbaddddbccbdbbabdaabdadcbadbcdbdbbcaaadbdabcddcaadbbcacbaadcadacbaaaabaaadcbcdaabbcdcdbcbcdcdbcacabccbcaaacdabcdabadacbdbabbbdbaadacdadcacdcbabdbbbcdbddcaccdadcdcdbcaadcaddcdcacbacbddbbbbadbbbbadcccadaaabbdbdddcbbbaaacabdabcbcdbcdddadaddcdcbaaadbcdcdddccdbbddcddacddcdabdbbadbddddabacbdddbaacbabbaddabdcaacabbbddbadbdbaacaacbbcdacbadcbdbbbacbbbacccaadcdbabbadadcbabcddbdbbadddbadaadcdabdbbdcabcbbabaddcbbcadbbcbbabcadadacabbabcdacadcccaccbcbacadcdbdccdcbcbddacdbbdaddbcabbdacdaddacadcbabcbdcdbcccadababdcbcbcbdcdcdaabcdccbbaaabbabcbbbccdabacdababdaddbacaaccdbbbadddaccabbacdbddbbdacbbacbdbbbdadcacbddabbbabbccccdadcdacaabadabacabbdcabdddcaabbbddcbbcacadcbcadacbbcbccdaddcabbdadadcbbddabbcaaddaddccaddabbdbbbadcdacbacbbccdadbdcababccdaddbaabdbacddbacddbdbcbdbdcdddddbadccdbcacbbdbdbbdbbcacabaacbdcbddabdbccabdacdaaddbbdbbbdabbddbbaadcbbaadadbcbcadbcacbdcabcccdacddadddbcdacdaabcbacdadabbaddacadbcdabdacccbabbabbcccacadcacaadcdcaccbabcddacacadddadbcccdcadacbddaaabaabdbbadcdddccbcadccdcbadaabbcbbbdabdcbdcbcbcaddaadcaabcdaccaadaaaddbdadbbacbdcadabcdcabbdbbbaaccacacbdcdbaddabadccbcdcacdccbaabdbbadccccdcdbbddbccbbdcaadcddaadcabdaccadbacbdcbdbdcbaaddbdbdbbaddaabbbddbabdcaaddabdbbcabdaccbcddddbbbddbdbabbabbcdaadcbddbdccbaccdaabacdbcabacdbaadabdcabbadaaabcadbacbbdadcccddddbbcdacdbadacaccaadbdacdbabbddcdbadbdbdbccbdddcadcdcccbbdbadccbccacbadaccaccdadaccbbbdacadadcdbcaddcbdccddcaaabcdddbbdcddbdcddbabdaacabdbacbdadadbdddbbdabbcbcbbdbdbccaaddbddaccbbdbcccaadbdbcbabbdbbdddcbbabadbdaacbbaddacbcaaabcadbbdbdcabaabcbaabccaaddbcdbbbdbcccbbbdddabadcaddbccddcacbdcbcbcbdbaacacaaacadacccbdacbcdbcacdbabadaadcbddcdcbbdacacbacbbddbbaccdabacbbccdccbaddcbcbcbcccdcbddbcadcbbdccbcddcbaaacccabccbddaaacdabbccbdacdadbddbddddbcaacccccaabdcadddbddadadacadaaddcdcaddbaaabddbdddddccdcadbbcdcdcbbbcbcaabccdcbabddbbadccbaabbabdaadabbdadbcbdcbdcdbcaabcbddaccaaabcbdbcaabdabaaaccccbaccdcbbbddcacaaadcabbcadbaadcddadbddbabddcdcbbacacaddbcdaabdcbcdcabaaabdddbcdcbccddbbcddccdbcbacbdbbdcbacdcdcddadcdcabbbadccacbbacacbdddbddababacbbdcdacabbdcaddcaaaddcbccabdbddbccdcbdbdbbaadadcbccacababadadbbbdcbaccbdbcaacacabbadcdacddaddbcacacadddcdbbcdbddcadccdddccdadddbdabcdcbadabdbbcdabacbacbdbbcadbbaaaaabdbcddabacbaacccbcbdbacccdbdddbdbcdcdcddbaacbaccacddaccdddddbbababbdbaacbacbbbcaddaccbabadcbadcdabaadccdcadaddacacbcccdbcbbdabbadaaddcbaabdbdadccdbdcaccddabcddccaaacabaaddbacadcccaddadcccdbabcadadcabcaadbdbcacaadbadcbcbccdcadcbdcaacccbbbacbbdabdabbdddacaacbdbababbbcbcbbabcddcbdbbccdddaaabaccadaccbdbcaadabcbbbbdaacaaadddbccbbacdcbbcbbdbaaccddababdbdaaddaaacabcaacdcabcbacadccabcbdcadbdbdacbbbbbdbdbbacacaabbaccadaaaaddcadbaadcadddbaabbadbdaaabcbddbdddabdbcdcbdcbbcdacdbdcbbadabdbdbbcdbadcdccdbaaadcbccdddcbabdddccbbaddcaaacabbcbbdbdbbabcbbdbaacbcbbbdbccdbaaabdabbadaddacadaaabbdbaacbcdabdaccdddaaabdbaadcbcccdadccbdcbddbbabdccddaaacbccbbbacdbbccbcddaccbacccabddcccdccbcdcaabaaadadbcaadacbdcdcbbdbccdbaabbcbccddbdbdcaadbcabdcbbdbccaabdddaadbcbbdcaabdbcbccabbdabbcbcabadabbbdcdbbbbacabbadcccdaabdbcdbaacdabcabaababbcbaacdddbcddabbdddacbabddbbdddbcdcddbaadcddbccdacdadcdbbabcbadbcacacacadbdbccbdadabbdaccbcddacbdcccccacdccaddbbddbdaaaaccaabbcddcbcbccdcbcccbacbccbbcaabbbddaabdddcbbbbccadbbcababadbacdaabccacbaccaabbcddbcaacabcdacccacdcdcdccdcacddaccaddbbdaaadacaacadaabacbdccbbbcadcdcbcbadcccacbdbcadbbbcbdbbbdbadadbddacbdbaabbdcbbaaaabbabababcbbdaadddaacabbaaaadcadbdddcbcdbdcdcdbccbdbbddaabccbbbbdaabddacddbcbbdbbbcbbbdcbcbccaddcbcdddaaabbbcbcdcbbdbaacaabbccbbcbcdaccbcbcddacababdacbcacddaacdacbbbbabbbccccdccaabddbadacbadbbbaabbbbdbadddddabbaabcccabadcbdcdbadbcacdccbbbcadbacabccddabddabbdaadcabbaacacdbdaabbdcadcabbbbcdbcccadbbdbcbcddaadadaaaddccbaaabadabcbbccbbddbdbcddbdcadcdcaacadaccbdaadcbbdcadbbaacaadbbddcbccaadcbaccabaacbccbbdcbdbaacacbbcdcacbaaaadcabbcacdbbbdadcacabccbcdaaddbdbadabcaabccddbdadacaabacccabccadadccdaadcddbdccbabadccdbccabcbdbacacbbcdabdbbaddaacbdabaabcbdcbdccabcdaccabaddddcbbbbbdcddcdbbaacdabbbaababcdaadaccacadccbacdbddcbcdacacccbdddadccabadddcadcbababdbaadbaaaccbacdbccaabbbaddcadccbbdaaabdabcabddbadbcbcabdadcabbaddbbabdcccabacaddaacaaadabcadddaddbbacaccaccbcacccaaabaccbddcddddccadbabdbaadbdccabbcaabdabbbacbbbddabbacbdadacddbaadaddccaabbcdcdbacbcdabaccbdaddddacaadbcdddcbcbcdcdddcabcbacbddddbadcbccbcdadbabccaabdcbccbddcbddaaccbcaccacdcdbccdbdccdbdcbcbbddccaaadcdcbbaaaddaaddcbddbddaaadcddaddcbdcacccdbaaaadbbcccddccbcdadcaabaacbbcddbdadadacabcbbccadababbddcccbdcaacabcacacdaabbbdbcbadcddbcdaabbbcdacbddbdcacacbacbaacacaabcbbcdcadcaadbdadbdbccdddcbadcdbcdbddccdbddacadadbcddccacacdcabcdcabbabccaccddcabddadcbdbccccabadbbabbbadbbacabbcbabaaddabddaabcccdddbbcacdbccddaddbbcaadcdddadddbbacabacadacccbabcdaccadbabbddaabbadcdabcdaaacdbccbcaccacaabdabbccccabaadbdcbadbdcadbaddacddcadbdabddbabddaacaacbadbadacadbcbdcccacccaacadacddcbdbcbcbaccaddacbaabaadadcdbdaccccaaddddcaccadaddddacadaaabaaddccbaccbccbadacaabacdacaaabcccdababaacbbddbccddaacbccbcaadbbbdadbcdcaaddaddbdaacbbacdbabccddcacbcbabacbbabaadcbacbacdbbcbbbbabbaccdcbdabcacddcbaacbabadbcbdbabadbbdbcdcddbddaaaaccbadaaaccdcabddbcbbdacabbaccaaccddbbcadcabcddacddabdddacbcddcabdcabdbadddbcdbdcbdcacdaccbaddbaadcbcbbccbcddcacabbbdaabaaacbaabdcaccbadbcbacbbcdcbaadaacadcbcadcbbcabdabacacbdabbccbacbbbdaabcdbbabacaadababaaacbadcadcaaabbbccdccaacbdabcbcbdcbbdabcacdcdabaccccaabcbddacaabdabaacadcbadddbbaacddcbacdcbbdbdaadddcbbbdcbbbcdccbdaddcbacaacccbddbabdbbdbddddbcbabadabbacadccbabcdbabadbdcaaaacbcbdaaaccabacdddaccbbbccddacccdacdaabaabadddbdadbbadcaccbbadcabdcaadbcbabcbaddabadbdabdccacadccdadabcadacddbbbdcdddaddcadadacccbccbabdcaaacbccccdbddabccdcdbdababcacbcccbcacdccadddbcdabbcabbcabababcdbbaabdddcbdaabacdcdcdccaadbccccccbccdbabbaadddadcacaaabacdbccdbacbcbaddcdcadabbccbddadbccbbbacdbcbbcacbcbdbccbaccbacaccdbbbccdbcbaabccbaccbaacbdadcbccdbdadaaadbdaaddddadbcadacabdcaaababdbbdcdbddbacdaaaadaabcabcdbbadcccbbcabbdaabddacdabcdddcdddcbcdcadacaabaccadcccddddcadacacabdbcadacddaccbcbccdbbdaabcdccbcadddbacbacadbdcbbdccbbdaabbababccdbdaacdcbbabcabbcddbdbdbbdcabdcbabaadddcdbbbdbddbdcacbddacaddbccacccdbdaaadbcbdadabdacbddbcbbdadadbccabddcbdbcbbbbccdbbdabababdbabdbbbddaabcccdccbaacdcaacbbdcdbabdacdbdaabddacaadbccccacbacbddbdcacdabdbcdaccdbaabbccdaccdacbbbbdbcbcdacdaadacbbacabbdbacddabdbdddbbdbbacdddcbcaacaadbaaddcccccaccbabbbccaaaababbabddccdcdcccbccacbbbacaaacccdbaababcacaacdcbaadcdaddacbadaabbdaababaabdcbadaabbaaadbcabaabccdccabbaadcbaccddaacdaccadbabdbdaabdaaadcabacbcdcbbdbcbdbccccdacabcadcbaacdbaaccbaccadddccbbbbdbcbcdcdbbbbbdabdddbbbabaaddadcaaddbdcaabcabacddbcdcaddaabacabbbabbbaabadbaabccabadccdcdbddbdbacdaccbabaacbdcdbdbdcdadbdddcdddacbdcbdacdaacdbdbcdbccdcbdcadaaabcdbabaabaabcbdacadbabbbbdadabcacaadbadbbcabdccdbcdbcdbcccbcbdbdacbadaccdacabaccbbabbadcddcdcbabcdadbcbababaadcdccacaabcddadcddcadccdaaacabadbbabdabddbdadbbacaabbdddbabbbdccbabbbaccbbdbbbdacbabcacbddbbcdabbaabcdacaadacccbcbdcbbbbcdaccbadddbcdaaddbbcccbadcabbaddcaacdddaadbdbdadbbcddcacadccaaccaaacaadcdbbabacbcabcbaabdcdabcbbcbdadbcaddbdbbcbabddaabbddadcbcccdbbbcbcdccdacaabbbcaddddbcdbcddbadbbabbcdccbaaacdbdbabbccbddbadbdcaccdcbdaaadddadaaddbacdcaabccddbabadddcbbdacccbcddccdbdbadabbdaabbbcdcdaaaabccacbabaabcdcabaaabcaababaaacccbadcdacbbdbdabcbdacdacccdcaabbdbbacabbcdaaabbcdaacdadcbbabddbcbacdddbbbccdcabbaccaabadbbadbbcaaacadddadabddbabbddcccdccdbacaaddcdcaaacabcbadabdbbcbacacbbbbcbbcdbbbcadbacccdcaaabcdbdbdacccaacbddbcdcdccbcacbcadcadbccadaadcbadacddacbcbdbcabbddaaccbcddcdaccbaabddbacadaaacacadbbdcccacacbccabbdcabbcdbcbcbabcbbadcabbddddcdaaaaadbdaacaaadcccbaddaddaddabadddbcdaccaccacadbccadbdacbaaabbadabadacadabdbcbbacbbacdddcadaccaadbcbabdaddbacdabdaaacdbdbaddcdddbdbcadcbaaccddbbadaabdbbcdadbcdbbcbcaabcadbbbadccabbdababccbddccbcacaddbcdcadbcbadccdccacbcccaadddccadcbccabadadccbbaabcaddadabccddcddacdcadbdcdaddbabcbbccdbbccdcbacaacddacdcdbcbdbdcdaadacadbadacdadabdadbacdcdcbcbdcbabadaadccbcadaaaabaddacdddbcdabbbdcccbaabbbaaabcccadaabdbdcddbbdadbcbbaccdcabadcddbabadbbcbaabacddcbcabaadddbbcadcbdcddacdaddccccbdacccccacccbadcddbaccdacabcaddbacabddbadbbdbccaddacaccbdbdcccbdbdcbccbcdccacdccaaaabcbbdbcbcdacaaabcbabdbdcbccabbabcddcdbbcdbbcccaccaabddcabbadbbbddbdbbcbbdabdaccabdaaaadaababcbbaccaacadaadacacbaaadbccaaabccbccddbdcbcabddbabcaddbdcdaaccdadbbbdbaadcdcbdbcdccddcbcbabcbaccaaabbabddacbbdddbcbbcbbbbaadddbabdadbbbacdcbbacadbcddaabcaaacaadbdccbdcccbacbbcabcacbbcdaddbbaaabcaaccacdacacaacbaddcdabbbcddbccdbcdaccadababccdabaaacccbcaacbaccaadaacaadcdbbaaaccdaabdacdabbddadbbcaacbcadabcbbacabddaacdabcadaadcbcccdbdccaccdaacdbbcacdcbdccbdbdcdddaaddadbabbbbdaadbcadbacaaacaadbbdbaccbddbbabbdabadddbcdddaaadbddcbaadddbdaddaddbdddcdccacccbbddaadddacbabababbbccaaaacabdaccacdcccbacbccbdcabbbddcddcdbdadbbbccbadcbdcdcbdaaddcdbaadbcbbdcdddababcaddbdbcdbbdabcabbccdbaadbacaacdaccddaccdcdbbdaababdcababcacaaabbdcdddccdaaadacbdabaddcacdbbdadbdbbaddbacddabaccbcddccbddabbdbbccabdacadcbbdaccaadbcbccdaadddcccbabbadcbddbabcadbabdcdcadddbadcddacdbabbdbbbbdaddccabcacaadccdabcaadddabaaacddcaabdbbbacbcddaacbcaadcadbbdcaddaaadbbbcdccaddabccdaacbcaacaababccccddabbcdaccdcaddcdbcabbaaadaadcddcdbbbabcdbcddbcababbbcacdcdaacabacbccbaadbbdbdccacddbababccbddcbdbccaaaddacccdbcdbcdbdccaabdadacabddbbcbcdbdadbcaccbddadbbabddbabbcbbdccdaaabbdbabaddddbaadaaccdccadcddacbcdcdadacdbddcabadcabcaddddcbcdbaaabcddbcbbdcbbcdccbabbbbdcacbaaaaabadddcbaaabdcdadbdacbbdabacbbcdcbabcabdddbbabacbacadcadacabbabddabccacaacdcdcbbdcaddadccbdbcaaadcbcaccbadadddddccbaccabdaacabdaaaccdacbcaabdadddbacbbbdabaabbcdccacbabadcbabbcdcbcccbbacbdcbbddddbdddbbbbaabcabbdbbccdcbcbadcbbbdacaccdabdabbbbbaadbdbcbbbcbabacaabacbdadbaababbbcaccdcccadbbbcadccbabbcbbdadcbddcbaadbbbcadcbabacdddbabbdbabcbabcaacccbdacbbdacdbdadcababbaacddcbaabcbacdcccdabadabcacbacbabbabbdbadabbbcababdddcdbbbbbaddbcddabdcbcddacadcbaacbddbcdcdcabaaabdbbcddddbaddaaababdcbcbaddacacdbdaadabdadaacbdadbbbaacdadcadcbaadccdabacdbbcaddacdbccdccbcadacadcdabdaabbababdaabbbdbddadcadbcccabdbdccdcaaaacbcdadababcbdddcaabbccbdbbcaaaaddddbdcaadaaaaaaabcdbdacadcdaddacdcccadcccbbaccdcbcbdabdaabdacdbbabdbdcbcbaababdcabbcdcbbcacdbcbbdacaaccacabbcdbbdbaccdddccccdbaddabcddbdcabaccadbcdabddcbbcbacaadbccabadbdddcadbdbbabddbdacddccdbcccabcdcdabbaddbabdcbacabbdbdbddabaabbabcbabcdbaadadacbabdbcbcaccbabbddcaaaaccabacccadadddbbcbbddddbabdcaadacddccccacdcbbdcddcaccdcdbbdcbdaddddaadaccbadccdccdcabcbcbccdddccabcaaaddcbbbdbacbbadabbabadbbbbbdddcaabdbdcacdbbadadbacdaadadadccaaacbadddadbbdcccdbccdcabcbccacbbababbddbddacccccbbcbccdbdbbacdabbbcacdcbdddabddaaddbbbcdbccaccdcdadbccdcdacddacdbcabaaaadbdcbacbacdddcdbcdcbacdccddbaaddabbbdcddbddbbcabaaaadabcdcdbbbdabadbabbdabdbdbcabdbdcaabbddabbbbaccdcdaabdcbaadccbddbbabcacaabdbbcaabcddacaaacbbdacadbbbbacddcbdbdbbbdcabbaacbddabdddadcdbbbadcccdbdbcdaaadddaddcccbbdabbbbacacdbabaadcdccdacacdbaacdaddbcbabcaccbaaacdbcddddcdcdacccbbddbbaadccacdababacbcacccbdddddbbccbacbacddbdbbcbbdddccacabdaadadadbdcacdddcdcbbdccdbabdcbcaccccacdacbbdcdcdaddaadacbabcccbacbcbcbbcabdcacdcacbcdbcdadcbccddadabdbdbdbbbbdccadabbbbccbbaababadccadddbcaaccbabcbadcdadcdaccccddcbbbcccadaadbdcaadabbcdcccaadcbaadacbabbbcbdcdddbaacdbddcaabcdbdbccdbbbadaddbcbcaabdbddbbdbddbcdbadbccdccdcadbcdadddbdbbaaadccbccdadccbcccadabcbaaadbbadccbaababbbbcaaababdddddaadddaacdaddbaccdbbcbbbacccbddacbdddccddabdadaddbbcbbbadbcccbddadabcbdacdabdcccbaaadddaacdddacbddbacdabdbaabddacbbcaaadacdcdcddaaadaadccaabdacaadbacdbbdcaccaadbcbcccbcdadbabdacdddddcbccadbcdbabbcbcacbadbbbadbccbccbdbddccabdbbaccbbadadaccccaaabacccaadadaabaccaaccdbacbddddcbbabbdabbccaabadabddbdcdabcabdaddbbcdadccaaabcaabbdbcdabdcdaaaadacdabaacaadbbcccccdbddbbdabbbaddadaaaccbabbbbdaddddcaacacdabdbaccaaacbbcdaccddbcbbadaaaccaaaaaaabadaaaddadbccacccbbcaabcccdbdbaddcdccababcbccbcddbbbcadbabbbabacccabdbdbbadcbcbdbacbbdddadcbcbddddbcabcabbdccaadbddbcdcbddcdabcaabbddcdcababdacdccaadbcdbbaccacaaaaccbbadcddcddbcdacdccadccabbdbbddccacbbbadddcddcbcacdcdbadddabbbacdbdaddcdbcdcddacbdacabcbbacddcddacabdaaaccddadcabdbdbabbddbbbcbcdabadaadadabbdcdbbcbaabbacbcdaddaabbcdacaccbcdbabdccaaabacdbacdddbcbbcbbdacddbababccddbccbadaacdbabcacacabdbdadbcdcdbbbbbaccbcbcaabcadbaacbcbbdadadaddadbbaccdaaddccaaccbbadadaadcdddadcbadbcddcacbbbdadbabbbccaacbbbbbbdbbbcbdcacdddbcacbdacabbbcbdcacadadddcbbabbbdcbacbcdabdcaddccacaabdccccbbbdcddbbddcabcaddccbdbdbabbadabccaabaccbdbacabcaccabaaddbcadaacdadcadddaabddbaaddbaadcaccbcaaaccaaabcbadcabacaaabcbbcbdbdabdcdbadadbbaaddbcbcacbbabcbbadddbabbadcbbdcaaccaddbcccadddcccdddbcbadadcbbabbcdaaadbdcbccaddbbcdbabccddcbbbdcaccaccbdbbbddaddbacadccbbbcddbbaaabbaacadabbcdbdbbddbaaabdccacadcdaaddbdadccdccdbaddbdadddbadcdddabbddbdddbaadaaacacdcacddcdbcadbaadcdaccbcaaaadbbdcadcabcaddcbbabcaaaddccbdbdccbbccaacadbcddaabcbabbbaabdcabacdacaaabbdbabdccaabaacbbbcbcdaddadabddbddaabadbdaddcaaaccdabddbbbbcabbacbbadbdccbadbacdbdddabccabbbbabbdbadcddddbbcbbbcadbdaaddabdacddcabccddabcddaddbbcbacdaaabddcddbcbbacccddadabcacdddbcddaaaabbcdcbdddcdbbccabbcbdabdcabdbadcadcacaccaccddbbbdadabddbdaaacadbadbdbadadcbbdcbddbdababaababcbbbaccdaaabdbcbbdadadcdbbaacbccaaaadccdddcacaabacdcdacadcdcacccbdbbaadcdbdaaccdabbaaccaacccdacbacdcacbddabcbccbdbaadcbdcbaacbdaaddbbcaaddbcdaabbabcdabdddcbccbdcbbdadcdbacdbaabacddcdbcaabbadcaddacaadbbabcdddabdbccacdcadcbcbcbbabcacbbbbadbdabbcdbaabbabdcdabbabadcbacbdbbbbacddbdadbbddddbbcdbdcddddbddbcacacbdacadcbabbcacbcdbabaccdddbcdcbaddcadababcbdbbbdaadacdccccbbbbaaabbabbaabbdccdcdacbdddcbdccbaabcdaacdccbcbcccacdcaadcccdaddaddcdddacacbaabbdcbbabcaaaadadbdcccddabccbdcccaacbbaaddaabcbacdadcccdddacddddccdacaaadcdaadbadccadcaddaaabbcbbdccbcdbcadaaaacaaabacbbcaaaadcaaaacbbcddacadcbdcadcaacbbaaabacccaddbbacadcccccabccacdbbdbcabcbcdbabbcbdcdcbbbcccccccdbcbbbddaaabdaaccaccaacadbabdbabcabaabdcccdacdddadbbcdcbccbddddcdcdcbcccbccccdaadddbcbcbccbbbacaaacccbaadababdbdcabbdbdaaacbabbcccdddbbcbbcddcbbcadacaacdacddaaaadacddddadaadabcabcbadccadcdcbdacaaadabbababcbdcdbadaacdadbdaabbbaddbbbadadbdbbabbcdbcbcddcdadadbbdadbddcddbaabdadabcbaabdcbbbddadbbddcdbabbddabdaaaccacccbdacbabbaacdbacbaaadaaaddcbabdaccbccabaaabcadbbdbcacaaacaabacdbbaaaaacadbbbcacacbcadbbdbabdadadadbadbccadaddccbcdadbccbbdcdaadbbdcbdabbbccadbdadbadcdccabacadccbbbdccbabbdacbbaccbbbdbabbccaaabdaccaaacdabbcadccadabbbaccbbbabcbcabdcdabacbccbadccbadcbacbdabccaccacdddbbdaadadcdbdcaddadcbcacdbbcdbbacddbaadaaadcccbcdadbcdbadabddcdcdcdcaccddadccacccddaddbcdaddcbbcddcabdababcddcabadccbccccdabcaabcabcbaccccacdcbacabbabbadcbccddacadbacdbccbbddcdccdbdbdccddcbadadcdaddabbddabbbbcdcddaadcdabbcdbbccddcbbaddddcbabaddaaccbbbdbddacaccacacbdddbdaccdcaabdddaccdbcbcbcaacbccdcdabbddadaabbadbccbbacacbdcdbaacdbbcbacdbdacadbbddaacdddaaabbcaddcbddbabddbbdaccccaabcbabaabcdbbdbccccbaccadcdbcbcaabbdbbaabadcaadabaaaccadcdbcaccdcbaaaaadbadbbcdddbcbcccaabdcacddbdaabdcccaaacdcbabcacdaabbcacdcbbbdacdbcbacddccbdcdbbadbcbccadaadaccbbdbcabaabbabcbcabdadcddadadabdadddcbdbabbcdcdbccabbcaabcccadcbadcccaccbdbbcbabcbadbbcdddddbbaadcccacacdacacacbdbbddcacbaabbabddcaacdaacdcabacddccdcacbbaabaaddbdaaddcbcabacbcadabadbbbbadcdacdacabacdadbacbcdcbadcddaacbcbaadbaddbccdcabadabcabacbccbacbddbcbdacdcddbcaaaccbabacccdacbaacbdbacbcabdbaacbadddaaaaacbcdaabdbbbdbbbaacabbaabdcdaaaacbdcbabcdadaaaababcddcdabdaccabcbcdadaabdcbddabddddbcdcadbcaccdccbaadbbdbaabacadacaaadadbdabccbdadcacacabddbddddbddacbaccaadcadadaadbabdabbaddddaaddccccdbddbdcaaccddbabdcddcdbaaaccbabbdabdcccacbdcbaddadcddcdcccacadabcdcdccccbbccadcdabbcccaccaacadcbaabbdabbdbcddaabbdcdaaaddacdbccdabdbcabdadccaaccabdbcbbdddbababaddabacbbcdddabbbcabdccbbdbccdcadbbbcbbcaaabccddbaabdbacddcbbabdcbbcbbdaacbdadadcbddcbcbdadddadddcbccbaacaaabdcccddbcddbdbbbcabbdaaacdcdbdaacddcdbbdbccaabaddbcbbcbcbccdbcdaabdcabacadcbdbdaadabdddcdddaaccdcdccdcdcccddbcdddcacddbbdddacabdcadccccaabdbbbaacbcdabbaccaaadacbbbdbbccbadcaadbacadbcabaadaadddbacbdcbadbcdccbaccaadcdbcddbccdbddabddabadadddbcccbbcdcdbcacaddabdcbdcbddaadbbdbcbdaadddbccccbdabaaabacaadcaacbadbdbbaddcbbbdaddbbcaabccdcbddccbbbabdbaacaddddabbcbbbccbacaacbbcbabbaacbacacacbdcacbadcaadaddcbccacbccadbcdcdcdbbccbaaddbaacaacadbadbcdacadbadcbacbcabccacdcdbbbdbccbbabbdbaacbcacabbbddbcaddcdbcbcddcbabbbbcdadcaaaacbdcbadbdbacbbdcdadbdbadaaabcddbdaaccbbcdaacaaabcddabcbcbbbccdddbacdcbcdcaccdcbbdabcbddaccabaacdbdbdbdaacdabbbbcddbaccbdbdcadadbdabaacbdadddbddacadbadcbcccddbacbacdbbcabdadabbcccadbcbccabdbbccbcbdccdababbdcbaccbabdbacdacbcbaadcaaccabaccddbdaddadcccaccadbacdcddadaaddccbcbabbddbcaadccbabdadcabaadcabddcacadcdcddbbdbddbbcdaababcdbcbdaabadbdbcbddbdaabccbcabdaaadccdaacaadabdbdbdbaacaddbadacbcaabcacbbbbbdbcacbddcbcbaddbcdcaddccddcabcdbbaddacbdcdddcdbdbcabbbbcdbabcbbbdbabccbdcadaaaadaadcbcaacbdacaccdcbcabcddcbacbbcacdbacadadcccbcbaccdbadccaabdcaabcadcabcccdcadbabbcbaccabaccdcbccddababcadcbacbadadbcbdbaadaaddabddcdbadcbaabcbcbbbbdacdbdbcabbcbaabaddddadbcadaddbbdbcbbbbbabbadbcbadbbaddccabbcdbdbcabcaddddcbdbaaadbcdabdadcaaaddcaabdadaddacbacdacadacdaadbaccbcddabdbcabbacbbcddababdbbbcabadccdadcaddbabdcaababdbdbddcbcdbaaaabbdabbadcacdcdaaddabadcacdccddcbdbcbdadabacbaababcdccbaaaaacdcdcaccbdbcbaaddccbcbcdbcbcbcaddddcccdcacbbbccabdcbbdbdadbbaddcdcdadccabbadddacdbadbadddddbddbbcaddbcadbdbadbcabcdaccbcdbccaabdcdcbdacbacdaabacddcbbdbdaadddbadbadbbcdcababcadddabdbdcbbbdbccddcaccadbaacababbccdacadbabcccdabddcacdbcdcbbbbcdcdaddbdacdbbdcbcbacccdacaadadaccaaabcdbdcdbcdacbcddbdabcabccdadcbcdccabadaaccbbdcbdbcbacbabccdadaaacbccabcbdbcbccdabcdbacbdcbbabccddaabdddbbccdbdddbbcbbcbdcdbbaadbaaddaddbddacddbbaacdbcdcccddccbbccaddbbcccccdcbbcacccabdbcaadadcbddacbcdcbccacdaaddbbbaccadcbccaaaacdaabdcaaccdadbdccddadbaadababdaacdabcbbccdabdacaccbdbaaaacbaacbabaddabcaaabbbcabcbdbbdaddaaddbacccbbdacbacadadcbdddabddcbbddbccdccbcbbcbdbddadbccbcbbbcbaccabadacacaaadacadbcbbdbaadbababadbbdcbcabddbdacdddccaadcabcaccbbdbbabbbcaaccacdadbbaadcccddbccdadacddbcddddbacaaccaddccbadbcdcdbbcdbabcacabadccccbbcdaddbcbbdbcbcbadddcdaddbbddababbcdacdbbabdbbdbaacabbdcdaccbcbadabddadbdccdadcabccaadbccdcdbccdbaacdbdcabbcdcdaddabdaabcbaccbcdabaabbccbadbccbaadccaaadcadbabbaadcabdccbabcdbbabcabddbcadbbbbaacdabcbdcaddbabcbacccdadcadbdabdadacccbbbdcabaccdbacaddcacbcbcccaaaaddcbbddddcdcdadddccccdabcdbaccbcdcbbccdcaacccadbddbcbdacabdccccddbbdcaadaabbdddaadbaadacaaabbbabddcddbddbadcbbdbbcacddbbbadacabcddcadcccbcdabbbacaaaabbbacbbddbaddadcacaaacaabadbcbccbbcdcbcdabaccabddddbabaacccddccacdcabcabcdbddcacdabdddcadbabaadadcaaabbccacaacaddccaadcdbdddcdbbddabbdbccadabddddcbdddccbddcddacccacbcbdcdbcbbacbadddcbacdcaaacccabbbbaaacaabdadcbabdbbaacdcdccdaaaabcaadacccdcadccabcdcccacddcbbddccacbaaaabdddbcabaacbaddbcbdadbcbcbacbddacacbcbbbdbcacdabdaccccdadddbadadcdbadddcdbadbccaaddccacadababcacdcbdaaddabcbaadaaccdcbabbddcbcdcacaadadbddacadddbcbdcbcdcdbccdaadcadbbaadcdabdacdadccdcccdbcdbaddacadbbbadbcaadcadcccadbcbaabadaacbcdacbccdbaccccaadbbaccbbcccabcbddccdccacabddbaaadaccbbdbdaabbbccadbdbddcdbbaadaadbacbdaacaccadabbbbbbdbbbcbccbdabcadabcbdbacdacdddbaacccabaaaccadadccdbcdbabdbcdbaaabcacbcccadbdabaaddcbabadccdadccbcbaaadcadbdbabadaabbbbadadccaabacacddbbcdaadbbcdccbccbcddacacbacbcbbdcdaddcbabdaaacbabcdaacdadcbadbcaaaabbcabdaddcdcddcabdaccbddcabcbccccddcdbaadacdbabbbdcaacbcdaddccaaaadcadcccdccdccbdddaabddcbadbcbadcabcdabbcddabbcdcdcadacbaadccababadcdbdbbbbbcdaacdbabcdddbacdbdccaacabdbaabbbdaccccacdaacbacbdcacabcbdaadcacdbdcbbcaaadabdaddcbaacabddbbbbbcdbbdbbddbcbcdbdddadcbcdbdcdaadcbdcdccaadbbbdbbddacbbbbacddabccacdccbbdddcbccbdabbbddcbbdaaddcbdbcdbcddacabacdaaccbddadaacaccbaccabdbdcccbbabaaacbdcbabbaabdddbabcddbbdaccadbbdccdccdbdacabcaccacabdcccbcccccbdabdcacadcbadccdcbdadabcbbbdbbccbccadadccdbdbddddcdaabbadadabcbdcdcdcaccbacddacbcdcadbaacccbdacbcabdabaccaababcdbcabcbbcccbdaadcaccaaacbdabadccdbdbbcdbaacabbacdcbddbbcabcddadbcdbdbadcabcaccadbaaacdabcdaadbdcdccdacdabccdbbccccddacabbaabbdbbddbccddcaaddabdacadadacabdcdbaacbbdddcaadcacbddbcabadabcdbadadccabdbdbcccaccabdadadadcbbcbcababadccbddbabbcaacbbccbccbdcbddacabdcaacddbcdbacaddaccbaccaddddbabdbdbbccaccbdacdbcbdbacbcdcaaabcdcacbaddccabbdabdaddccabaddbddaaddbaaabbddbbbaccbbcadaabcccdbacabcaadaaadddddaabdbccdcbbdaccabadcdbbbabcadaddccbbbdddabbbbdababbdadcacbdcababbcaadaccbbdacbbaabdaabdbbbdaccbbbaabbcdaacaaadbcdcbcbdccdcbcdbbddbbacdaabcabbdcbdadbccbadaadcbcacabbccdbbadcddbbccbbbbbdcdbaddaaacddabcdacbaaccbdadbdcccaddaccabdcaaababcddbddcbaabbddacbbabacabbbaacccbababcaddcbdbccdabaddaacdbbccadadcbbaaaddbcababacadddaadaaabccbcdaacbdaabacdcaaaacbccccccdcdbdcbaadaccdcddbbcabcdddcdddbdcdcbbaccadbcdccadcddbbacdbdacbadaccdbdbcbaaabdadbbdcacbddbcdbddbbbbcbacbdaaddbbdddcbabdcaadbaaacbaaaacccaaaccaaddcbadccbcadbadcbdbdcdbbdddbdabbdccaaacbbadaaacacacbdacddaadccdbacdddadcbcdbacaadbacaabaabadaaccdbccdbbdaacbdabcddbcbccdcdaaacaccdccdbdddbcddbccdabcdcabccbcbadaacdddddbacbbadddbdaccaadadcabcccdcdddbcdabdaaaabccbcbaaccacbdaaccacaaccbaaaacbbcbaadadbbdaaacaabcdcccdbaaacaadcdadbabbdaabccbccddaadcdbcdcaddccbccadaabbbcddddadabacccdaabbcdcaabadcdadcdcdddadaaaddacdadacccddaddddabcaccdbddcdcacadccdbaadabbbadcbcdcabccbacabbbabccaadcbcabbabddabddbaaccbbccdcacccabcdaddcdcdddbcdaabbccddcbccaaddaabbaabaabaabcddacccbacaddcdcadaccdccaabcdcaadaadbdddbadabacabcbbaccddcccdaadddacbdcdcdaddbdcacadcabbaabdbadcdcdcdbdadcadaaaccdbcbbadcccbacbadcdabcdcacbbdbbbbbbbdbbdcdcdabcbbdadbdcadcddaaaaddacabdaaabdcdbdaaacbbaacdbccacacabdbabcbadaabdbaaabdbbdcdcddbdccbdaccababbbaabddaabcdccbadbbdaaadbddbacdcdcaddaaccabacdaaddbccbbbcaabbbacdcdadcbcccbcbbabacbdcdcababbbaaabbdaccaccccdaacdcbcdadaabbcababdddbdbcadaabbabbccabdbcdbdbbabddacbbccbbdadcccacbacadddbbaaccaacadcccabdcbcaacdabaccdacbdaddacbbacdadcccdbdcaaabcdcccbcdbdacdcdbdddabddbaaddabddacdddaccabbbdcdaddbccddbaccbcabcacdbaaaabbabbdacabdaaaaabbdbbabadacbcabbbaabccbaacbadcabdbacbbadbaabacddccccbbcbaddcddcccccbcabdcacbcbddcadddababcdbdcbddcdabdbbbbcbdbbbaabcdbdbddabbbdbddbcaacbdccdadccacaaaccbadbccaababbcbaddbbcbddbccbdabdcabdccaadcbaabaacabbbdcaaccabadccbbcccbcbdccbbddbdccadadbabdcabaaaabbcdcaadacdccacdbbdabbdaddbbdaabccaaabadbcccababccdbdbccaddccbacdadcdcdbbaccaadaacaabbdacccacbbddacccadaababbcadcababacccacabadabbabbcacadcbcadbabadccbdaaadabaddbaadbccdcbcbcbddacccacaddbdacdcdbdbcdacbdaddaddbacbcacddbdbaaaddbaacbbbdaadcbaccdacdbbbabacbddaddddadbcbdaaccabaddcdcdbccccbbddcdbcddcbcbddbdddcbbdbaaaccddcabcddccbddcddbddbcdcdbbbdbdaaadacccababcbbdbcaadabdadbcaccdacadbbbcddaddabadaacbbcbcdcdcaabbdddaddacacbcbabdbcccdcdcabdcddcdcacacadbbabdabcbcccabcbbddcddaddbbbbbbcdabaadbcdbadcdadabbbddccabcdccabdaacbbdadacabbbbdbadcababddbdbdaacccdbdbbbddbcdabadbadddddccabddbdddadadbdcddcbcdcdddccbbcaacccadbbcbbdcaadcdcdddddadabddacbcbdaddbabdbddbaadcaccbccdbbcbbdbbbcccbbbbabaaccbbcddcabdbdcbbcccacbddacddcacabccbdadabbcbcacccaddcdbadbcaccccbcabdbbacddccabbbabaddcaacdabdababbaacbccbacccbacccddbdbbacaadccaacbbbcbcdabbcbaaddbadbababcbabccddaadcabcaacabbacddddcacdbcccadbcddabbbcabbbaabcadbcaccbaccbbcacccabaacdccabbdbddbbdcabbbddabbdccdacdcdccccbcddbcadcbcadbbbacdabababacdadaabccacaacadbadddacabdddbadddabadcacaddaabbcaacdbdccadcdcdccacadaddccacacccdaddacbddbccabddabdadabdacbbbdadbabddadadaddbabaabadbdaacdacbbbacbbcccaddbbbaacddbbccacdabcadbbdccbabaccddaabccadaabbcabbbdaccdaacdbddcadadcbdcdbcaaaaabaaddcbbacddaababaaddacbcbdbdabcdaaddcacddbaccbabaadadcbabdabbdccdadabcbccdbcdbcaabcaaacdaacbcbdbabacbabdcaabadbbcacabbbaadbdcaacbccabdabdaddbbbccccbaaadcdccdcdcbbdacacadddabddcaaccacbdddbabcaccacaddccdccdccdadddbddbbdbaaaccdcaabdbcdbbbcdccacdcbdcaacabbcdbdbadbbbbbdbdabbcdadabcdbcbbaadcdddccbccdcbacadcdccacbadabaacbddddbbbadacddbcdabcdabcbbabadcbabcdcaabbdcdcbdbaadcbcbbbcdcccbabacbdbccadddcbdabdaddbcbaccbbbbcdbbaabdbbcbdcabdbcdcbddaaccdbabccabddadccacaccdcaabdaccbbccbaccbadcbdccbddddcdbdbacaabacaadacdacbacbdccbadaabddcdbababadcccbcadcaabdcbddccbacbcabccbdbbbabbcaacdccdbaacabbbdcdbacbbbdbabaaadaacbcdddaacbcaabbdacadcbacacaacdaaacddaadadbaacabcddadcbbacdadddbddcaaddbcbdbaabdadabbacbdaabdbcdbcddadcccccddacdddacacaaabbbbddcadbbacdcccccdbdbaaaadbcaaadbddbacabaccbbbaabacbcbbbcaadddbabdadacdcddddddcbcbcdcabcaddadcccadddadacaabbbdbababbcdaaaacaadbcbccdccdbdbcdcdddbcbdbacadddccabbbbcdccbddbdbdbcadabadaddacccdabacbddbcbbbbdabbacbadbdaccddcbdcbdccaccadcadacacaccccacbaaddcacbabbcbcdabdadaaabcccaaacabbaacdaababdddcadaaddacddcacdbbcacbcabdadbbcacdddcdcbacaababaaddcadaccbbbadbacbccdbcdbddbaaaadddbabddcabbbbdbadcbcdcccddaacdacaaadcdcaadaacabcdabaaadacdbbdabcbbdcaaabcbcbbadacdbcbcdabacdaaaaadccdcddcbcaaacdbddababbbadcadaaaaaddbabcaacdacbaccabbbdaabbbacbaabcabcddddadbddbbddbcdcaabdbcaadbaacacbacacdbdbccddcccdadabdacbaddbcdcbaadbcccdaddcadccbdddababdaaacbbcacddccdccbbddbbdbdccdcbcccaddcacaaaabdacbbacdcaccddcbbbdbdddacaaddbcaabccabaccdccdacccdbddcdcaccaaadddcdacaababdbdabddcbddcacdcccdcacdaddbbbbbacdacabbaccbcbcacbdbcdbddadaaadcdabbbcbdbdabddcccadacabbabcdddcabcadaddbbaddbaddcbbacacbdcdbccbdabbbccccdbbbadccacdbdabcbdbbdaadcbabdcccbdddaccaabcaddaccaccaaadbabcbbbccadacabaadbbbabcbdaccabccbcbdbbbbadbaaccbbcdddddcddbbdcdccabcdbbbcadcaacdaccbbccbccbccbcabdadacccddadaacdabcddbabbdbbadaabddabdcadcabbcbdaddbbddcbdbcbbccbbadcbbbcbbbadcbbdbdcbbadddbaddbabcccadcdddcbbcabdcdccdbaccdcdddbddacaaccdaabcabadbdaddbacdcbddcaabddcccddcbaccbdcdbaadcddddabcbadccddcadaadbbdcddcacacdacccbbabbddcacbcacdabdcaaabbcacbdcdcdbbaddaacdcdabbdcccbccaabaacbaadbcadbdbcdcbbdddbcadbbbcaccbddbcadbcdbaaaadbdccddaacbdaabbabcdaddadbccdccadbabccccbbcdddcccdccbaadcbdadabdadadaadbbcaccbacbababcaadaadbdbcddbaddbdbdbbabcacacdaddcdbcaadaadaabdccdbbcccbdcdacaabcddbabdbaaadaadbdbacdcadadddbbcdcdcacdbbccdcacadbcadbadcbbabbadbcdcdbcbcaddbcdacbcdacabdabcdbaddcaaabbbdccadddccdbaaaccccccbdddbbdaaaaaccbdbddcacacbccbacaabbcbadbaacaacaaabbbddabcbcdcdccbbbadcdbddadcabcdcbbbabbdddabddbdbabccdcabdbadabdcbbcbcdabcccdbacbcacabaccacbababdaaacacacbaadbcdcabcccabbbaadbbddadadcbcccadbbbadabadcaccddadcadcacabaaddbdbbbcbbddbabddcabbbcacbcdccdaadccadbddcacbdccccdbdcaacaaabcbdbbaccdabadadcaacbacbaabcdcdaacacbccbcaaaaadaabbdadabaaaacabaabcacbacbcbcaccabbbcdaccbcdadacbbaaabbccbbacadaadccddbaaabccbcaddbbdabaaadaaaaadababcacdbbdddaadaadbaddccadbbcddccdcbcbaccddbdadbcccbacabdadcdcabbbcadbaddcccabbcddbbaddddbdadccaacacdbbadadaadaaaaccacdcbbcbacbabdbcacdccddbabbdaddbacdcabdaaabcaacaabdaadbdddcabacaaacdbacabddaacbbdccdcdbaabdccbbaaacbbbbbdcadaabcbcaacccccdbcbcbcadbcabaabddcdcdbbacaaddaabbbcbbdbbaaacbcdbccddacabbacbbbacbbddbbdbdccbaddbadadddadddaddaaddbadadacacdcbbacbcccdcabdcdaadacdddbcacdbccdcabcdaacdcbbacaacadbaaacbdbbccadaccccccdbddcdbdcacdaaacbddadcbdbaaaadaadabaddcbbdddadcdddcaabaacdbcdadcaccbbdcacabcbdaaaddadaaccdadabcadcadbaadddbacadccbcbcabbddadcdbadbcccdcbbdbbbdacccbdcccdacaabaaaacadbababcababacbdbdbaacbaaccddcbccbdadbcbacbdbacaacadcddabadaacddabdcbcadcbbaaabcdbdaadcabdabbaabaddacdcdcbdabbcbcccbddadbabbdccacabaacbdbaccadcbabacccdcccacaccccdaaabacbdcbbadadaddcaabbbddbcabbdcacdccbadddbacaacbccaababdbbbaaddacdadcdcdcaaabbcddbabdabacddcbbabcdcccacbabbcdddabdaaacddbbdacabaabddacdccdadbcdbcbbdcdbaaddaaacbbabbdcbdcccbaacacbbccaaaddababaaacacabcbddcabacdbcaccaaddcbbccbbdbdabcdadcdcbcaabdacdaadcbdaabdabbbbcadcacbbbcbccaadadabbccdddbacccdadbdccbcddcaddcacabbabdbcdaaaccddcdabdadadcbacacbacaddaabdadabadababcbdadbddadbacbaccdcaaabddbbcccdacbbdbabbcbbbcbdadcccacccbbbbdccbbccdabcccccbddaccdadccbdbbccbababdbccbddcabcdccdcdcbcddcbbcacccaabaddabacbddaaccbcbbbdbdacdabacacdcbbaccbdbcbdcabaddcaccabbbbdbbcbbbaadaccadcacacdbdcdbbaacccdadbcacabbddaabccdcbdaaabaaccccccbadadbdadbacbdaabadaadccaccdbdccdacddcacababccddcdbcdbdbcdccaadcbadbddaaccdddadbcabcbcbbadbabbbcadbcbaadacdabdbaadddccbdddabdbdbaacabdddcdcacdacadacbcdcbccbabababdbadbbaaabddbbbcdcadaacdbadbdbddcdccadbaaaacdbdabacdcbbdbabdadddbaddddbbbddcaabbdbbbdcddcaabccbcccccaadbddabdbbbabdcaaabacdbadbccddddbbadaacdacbccbacbdacbccccbabcdcbcdcdcbaccabcdacbdacccacdddbdcdadacadddbbbcddbaacbacdaddcabcbaadacabcdaacccdbbadaaadaadbacdbbcaaabddaabdbdbdbacbccddacbbacaabaacbcbdcbbadccdcbabbbdababbadacaaddcccacdccbbdaccdcdbdacadaabcdabddbabbdadcaababdaabacabcdbbadabccaacbdcccaaddcaabadcdcdddbcbaaabaccbcadcaccccabcdcdacbcdcccbaabcbbaddbccbcccabaccdaaaaaaabdcdddaabcacacdaaddcaabaacacdbcbbdadbcddacbcadabbcdcabacdacccacddcdcccbcccaaddabbcaaddaccbbadbaaabbbadadcbacbcaabaadabcbacdbbdccacbbbaccbdbddadddbccddabadcabdbaccabcbbbcacccdacbbcdadbabbadcccacaabaadccdddcbacddbccdaacadbcdcdccddacacdacbcbadacddccaddadcadcaabbcabcbbbcabddcddabbadcbbbddacabddbcbdabadcddbabcdbddcabbabbdadbcdbddadccaacaaaadacdbccdcaabbcabddbdddcccbccbcbbadaddbabddbadabacdaabcbabbbcbdddbddabcccbadbbdaccbcbbacacaadcaabaabadbcdddbcbaabbcdacbdbcdadaaaccbdcdabaccdccccadadddabbadadcabaacadcbabaddcaccdccbddaabbdacaabbabccdabdacaaadbbabccadbcbaaaacdbcacaabadddbaccbdcaacabbaabaadbabcbbbcabdabbbdcbbccbbbabacdcbcdaccbadacccbabddbacadbabcbadbaddddbaababbdabaaadbbbdcacbabccdccbacadaacbadcdddbaacdcabbcabdbccdaacdcddcdbcdaddddccabccdddcadadbdddbbababddbaaaacccccccacbccbabadadcbcbdbdbbdacdbddbaabcabbdbcbcdddaacbbbdbbddbadcbcddcbbdbcadcabcdadbcadcabcabdaaadcbcdbccabbbdddbbdadabddbdcdaaaabdacdabdcbadcbddccbdaaadcdbbbbcbcbdbcccbcdabdacaacbaddbbcbbdcccccabcddaaccbaadbdadddccbdbacabbcbdabcbdaaabcacddbcbcccbadbbdcdcaccbbddcaaacdabacbadbbcbaacbcdccadcaaaaccdabdabbbccbbdcbcccbbcbcdbdbadbadbbcbdbabaaacbabbcadbcacaccdcabdcaaccadcdaadaacabdabdbbcacdcadbaacacbaaaaadacabcdbbbdbcacbaacdbaaaaabbcbacbadacbddbaddbbaddacdbbbaabcbcbbbaacbdcbdbddadcabdccadacaccdbdadaacccabcdbbcbdbacabcbabbabcabbabcbddddbcdddaaccabaccababdabbddacacacaaccdabcbcdaaaabcbcbccddbaadcdacbdbbabcdabccdcbdcbacbbbbcdcbdcddccbccaaccbadbdcaadabcaadbbcaabcdddddcbbdccdaacbbbbcbcadbddabbdadadcbacddcdbcbcadcccddbcaabcdadabcadcccadccbacacddabddabbcabdcccaaccbbbabdbbccbadbdccacdadbcddbdaaabcdbccacbdddbdacaadabbaadadaddbbbbbddccadbdbaddaaccabdccbbcbdbbdabadabcbdbddbccbdbdbaabbbddbbccbdccacdcabacbcdbddcddabbdddcddcbdaaccddcbcacabbadbaccbaabaacddabbbccabdbcdcdbccdbbbbadddbacacbadcdaddddadccbbabcdaaabdbdbadcbdbbaacccdcdbbddcdccaaccbcbddbccdcdbcddaabdacabcdbccccbaabdbbdacaabcaabbdaccdacbdaacccbcccbaaadadccccdbadccaddacbddccbdaddbcdcbacbccdbccdabcbabdbbdbdbadacddaccddcddaaaaccadcdbbddaabbaabdbbcbdccadbdcaddcadcdddbcbddcbbbaababccbbdaabdaadbbdcdddcbacaaddaabacdcdbcdaccbcbbbdbccbaaaaadccaaccbbccdadcddadbaabbadacdacdaacdaaddddddbbaacabcdbccdbabbacababcdbcdccabddadddbacdbcbbabadccbdcbccacacdabbdbbbabdbdcdbadbaccadadccdadcddacbddcbccccddcccadbdcddacdccdccbbacddbabbbdcbbcabbccadddacdacdcaaddddcbbbbdbdadbdababacabddbbadbbadccaabddadaaaddabcabbabdbcaabdadabccbbcbbbdcbccabcddabbdbcbaacbbbdbcccaddbddcbcbcabcbacbcbdbbbdbaccbbbacbbcbabaadcccccbbacdbaaabdbdbaccccbabdaccbdbcbdadbbbaadabddbbabdacacbabadabbdbdabcacabadabbbadbbcdddadaccabdbcdcdccdbcaccbdbacacbccabbccbcdaddbbadcacaacabadaddbcccdbbabadcaadcdabbababcddddccdabcabbbaadaacccacdaabbcdcadcddbdbaddacbcabdadbbccdbcadaaadcdcbccddcbbbcbccdccccbaddadcacbbdbcadcddddddaddabacbabbabdaadbbbcbabcdcbbbbcbadcabcbadcabccadccdcaabbdacddddaabccddaaaccbbddbddbbacadbabcdcdabdcbbcbcdabbabccaabacbddbcbcbddcccaaccccbddadaabcbbcaabcbbbbacbabbcdadbdaadbdabcbcbdbdbaccdacdaacadbcbccdcdcaabcaabaaabdddcdccdacaadbbbcdbdcbcbbcaababbdbddccbbaabbbdbdadcbbaacaadaabaabdcbdbdabadaabcdbbaacdcaadcbbccbcacadabcabbadaccacaaaaddcbaddacabcbcdaaaaaacbddbbccbbbbadaccdcdadaccbbacdccdddcaacccadababdbacbcadabbddacabdbbbccccababcbdaaadccbbdbbdddbddaaaabbaaabcbacddcccbdcddbacbdaccdaacddcccbabbbbbabdaadbacdadaaaadcbacadbbadcddbcaadabcbbbaaabdcaacbdbbddbbbbdcabdcbcddcddddbbacccbcbbabbdadbcbdccdcccbbddbadcddccaabbdbbadaacccacadcbacddddcbbaaabadbdcbbccdcdcbabadbdcaccccbcbadddddbdccddabbcddabbdadacaccccdbaaddacbbcacacacdbacbdbabccababbabccbcadddabdbcdcaadbdbaaddccaaabaaddccbbaadcbdaadddaaababbbbaacddccbcccbcadbbacbccbaddcbaaadabdbbdccdddabbbbbdbaddcbcbcdacaaabadccaacbaccdaadccbdcaaaccaacaacaaccadabcddadcadcbdbcacaaaddcabdbdabcbccbadcaaadbbbacbacaabababcbbbabcabadbaadcbcabbbcccaabacbbdcadcbcadcdacaaacddcaccdbdccbbccccbdcaacbcddcdbabdbcbcbcdcadbabaddaadcdcabbdaabdcbdaccdcacabbcaabadcadcdddabaaaadbcabdabadddcaabdbbddabcbdbdcabaaacbcdccacbcdcddcddcbddbdddacbbbacdbcccddcdcacabdaddabadcdccabddcccdcdaaadacddccabcdbbcdacdcdabcadcbbcbbddbbabdddbaddaccbadabdaabadaaaaaaaadbaacadbccdaddcbacacbbadbbdabadcdccaaccbbacadbddcbddccdcdccbcbdadcbbaadbdbbddbcaccdbdaaacaccbddaddddadccdcbdcabadbdabcdbcdadbddcdbbbccccdcddccbbbcaacbbddbdddabdaadbaddccbaadabdbadddbadbadbbbcdaadcbbdbddabdcaacddcaacdcdbcdacdbddaccdacaaacadabdcbdaddadadacadcddbccabccdbdaacaabcbacbcaacbcdcdccaabddaddaccacdddccaccdaaacacacdccbdbabcbaaccacbaabadbaabaddaaddcadaacbbadcbcacdadddbccbcbdcadccacadaacccbabdcdcdadaadaaacbaaadcdcaccddbdbddbabdccabcccdacddabdbddbabadcacaadccbccdacbcacbddaccaaccddbbdbcdaaddbddbbdababcadccdacbccaacbaacaabcddabddccabcbdddddcbbcdacddbacbababcdccbcaddccaaaacaabbbbcacdadbdbdbbabdddccabbddccddacbcbcadbaabddabacabdabbddccdabdaabbcdcdbdbbbabdadcbaadbbcabadacaabdbbacbdcbbacccccddbbaaccacdbdcbaadabccdbcbcadcbbcbcbacbcdabadccabccaddcdddcbadddbcdbdaaddadcabadabdbcdbabbbcdbddddbadbcdddbadabccccbadbcbcbdaddaadabdddaccddacbddcdbdacacaaacbcbbbabdadacdbacbbccdbdbcabdddcdacaabcbdaccabacadacbadbcdabddcbbdbcddcdcdbababcbdcbacbadbcababdbbaabbaccddacbcaabcaabcddbbdbddabddadbddadcabdacdcdbcbbadbcacdcbbcbabdabbcacadbabcdbabcccbcbbbcdbdaaacaacabdadbaaadaccadabcadbdcbabcaadddbbcdcbbdccbcabbadaaaabddcccbadbbcbdadcdbbdbcdcbaabcaddbcbddcabcdacdccbaaabbcdbaacbababbddaadbcacbdbcccccaadcacdacabbaaddcbdadcdccacabdcabcdcddaadacacbcbcdcbadacbbccacdddabbaabababdddcddabdabcdddbbdadbdaddcacabaacaaaaccadbbbadbcabbaaaabaabbabaadadaddaaaadbbbaabbcadbbcabddcbacadcbdbcdadabbbddccdbccbcbaccbbdadbbcbccabacabddbddaacabdabcaabdbcdcaabacdbaaddcbcbabaacaccdcdabaddccacbabcaccddabcdcadacbdccacaaacbccdcdbccaabcddcccaabcbbdbaacdadccaaacdbabbbdaaacbabaaaccccdcdbcacbaaacbddbcbbcacbcddabbdcaabdacccccccabdccabccbbbabaacadcbbbcdbbdbdabdacddadcadaddaaadccaaccbaddddaabaaadcccaabcabcccccbacaabacddcadccddacbadddbacdabbccdccdbddcdbdbbbaddbbacbcddaddcaddaddbaddbdbcaaadbcbdbbacadbbabbccabcabbccacadbaaaddbadadccbdbbacabddababbddbcbcdddddbadccbbaacbaadbdcdbacdbdaabddbaacdabacababcbcbbbcccadddacdbdbcdccdbbbbcaccadabcbacbdaababbbdbabcabbccdbcacdbdbcaccaabbcbbabaccbdcddcbcccaaaaabccccdabcaccdcbccaddaaabbacbbddbccbbdbabacbbcdabdbdbcbcbddccadadabbcaadcaaabcbacadcccacaaaadacbbbccccdcddadbcdbabdacaddcabdadbadbabbaabccdabdabbbbdbaacbdacababacacacbbcdacccacaabdbdabbdabcdbdadbcadadbddccddcbcdcaddbcbbbcabbacadaaabdacdacadddddcccdcccccaacaacccbdabccbbdcdabaaabadbabaaadbacbdcbdcaadbadbdcabcdcdcccdcacccdbcacabacbacdbadddbacbcdabcdbaadbcadadadddaadaacdcccbddbabbdcaabdcdcddabdcaabddbdabdccaabadaccbdadbbcdbcbcaaddcccddadbcbbaacaccabcadcbbdcdccacabdabcbdcabbdcbdacacdadbacbcdcccbddcbbdabaaaadbcdadcaccdcddacbbadcccbadbaddcddddcddbbddbbdcddcdadccbbcddbbbbadbcbbbdcbcbcbcddacccbcbdccdaaaccccacaddcbcacccabbadacbcdaababdbccbdadbbbcdbccbccbddabdddabacaacabbccaabdadabadadcdddbcacaccccdbbcdcabacbbdbdbcdadcddcbbddbcdcadbbbdcabdadacadcbdddbccccbcbcdcbbabaadcabbcbcbaaadbabbcdbdcbcdbbdacacdccdacadbcacbdbcddaaadcccccdbadbacddaabdabdadbdbaadbbcdcdbddcbccbcbdbdacdcdaacdbadbddcccaabdbabbcadcbcccbcddddcbdccbabccbdccabdbacabdbcbaaaadccaddadcdcabccbabbcdcabcdabacaabdbbccbbcbdcdcabbaabacaaacdcdacddcccbcddcbccdbddcdcbaabadacaaacbcdcaaccccabadbcaacaccbaccabdcdadcddbdcabcbbdbcdddbadcbabdcdabbddbbdcdbdcdacadadacddbcdccddcbcdbcaddaabdcdbbaadabdcabcbacbbaaabdbdbbdbbddcadcccbcadcccdcbdcaacbadbaabddbddccddbbbcacbabbcdabcbdccbacdacddaabaabaacadccdacacbbacdcbbccabbaababdcccaadcaaaacbacbdaabababacacacbdbdcccddacbabaadababbbdcaadcaaaccbdabadbacbdcdaaabdcbdaacdddacddcccccaabbdaabadbcbbabaacbbcacdcddcbbadcadbdcaddbaacaaaacddcbdbaccabdbaacbccdababbbaabcbcbccabcbbdaccbbdadccdcadddabbbbdcaadabadbaabaccbbbaccbccadcbdbcaacccbcabcddbaababaaabddcabcdabcbaadaacabbdcdadbbbabdbddcdbdcccacbacaccacbcbabbdcbbabaaadcadaccdbdcbdbaccdbdcbaabccdccabadbabbbadcadababccbddcccacddaaabddbcaabbcabaccddadaccaabbbdabdabdcdcbdbdddddbdadbccadabbdcbacdbacbadacabdcbbddcbcbdbbdddaddddaabaddccdccaccbcbdccbddacdcddaccbbcddbadaccddaddabcdbdbbccdbbcabdbcdcbbabacccdacdcabacccdcddaaadabddabcaccadaccbddbddababacadaabbabccbabcddcaddcacbabbccbcbbdcdcdacbbdabacacdddabadaaacbdacaabcdaaabdbbaabbabbcdddcccdcabcdabccccdcbddacabdbbdabadcbcabdadacadaccccadccacaabbbdcdbbbcacabcbaaaaabbadbadaddbdbbdbdbcadbbcdbcbbaaadaadacccacccdbbdabbaaadcbccdbdccbdbaacbcdddbaaaddaaddbadbddbbccbcaaacbccbdccdbaacbcddbbdddbbcbabbdbacadcdccccadbbdbbcbaddbcbcdbdadcacabdabbdcccaaaaaddbddccadaadcbacbbdcadbddacdbccdaacdbbadaabccccdaadcababdaccbbdcccabbbbdbcaaaaaabbababacacbabddacdccadcdbbbcabccaaacaaabbbdcdcbbbcdabddaaadacbcbcbacccdacdcdbcbbbbdacdbcbacbdcbdbcbaaacbadcbcbcdcdacabbbcacabcabdcadcadddcacaddddccbbddddbdcddbdabdcbcbbacacdcdbcbbdaddbaadcacdbdcabcadaddbabddccaacdcbcadcdbbabccbaacbacccdcbbaaacdbdbdcbccddabbaabbbcbcbabdbbadcdbddbddabacdcadbbbbbccbacabbcbdbccbdabcacadbbdacdbaabddaddccbdccdbcbccaccbcdddbbcccbcaaadcccdcddacbaaadbdbcadaddcabbbdcbdbcdbcadbaabbcddabadbdccbbbbbaacddcbcdcccbadccabdbddacbcbcdccbdcacbababaddcdaabbccabbbdcaabaaabdddaddbaaaacbbcdcbcaddabbadddcdabdaabdbcadacbcaabcacbccdbcdbbcaadaadbbcaccbcaadadbdbbcabadadacaddbacadcbccdadbaabdddadbccaabcbaacbddbcabcbbdbcdcacbbbdccdabaaabbaabcbdbaccbcabbbdaabaddcdacacbdbcbabbaacaabbcddbdadacabcbdbcadadcdcbcacbcdcadcdbdddaacbdbacdcbddadccabcadacbccbdbccacbbaaccbbcbbdccbbaccccbadabcaddbbabdacaccacaabdaccbdccccacddcbddbdcdaaadccdbacadadcdabadabbdaddbccbcbdccdbaadbcdcacbadadbdcaabaabccccbdbcbdbdddbbbcdcbdbdaacacabadaddcbcdaccaacaadadaccdbabdccbcacaadacdcdccdcabbcbdbdcbcadbaaadcadbcdadcbaccdbacddcaadbaacdccabdccaccdbcaccbdaaaaddbbcaabaaccbcccadaccbcdddbccacbcddbbbbdbccdabccccdcacaadbbcbaadbcdaabdbccaacababbdcacdbcbabbaccdaadcbdaabcbcbdadccaaababbdddababadcccbcbabacaccddbacbccdacccddcccaaaddbacbaddbdadbacbbadbbaaaccccadadcdbccbadcacdcddbccdbbccddbdbdbcccbdbacbdcccbcbbdbdabbabaddbcaacadaccdbdaabbcbacbcaaabdbabcdaadcdbbabbbbabdbbbdbabadcaccbabdcdcaabbadaccaccaabbdbbdadcdddcdaabcbdddbabcacacadbcaddcbaacabbdbabaadaddcbdddcdbadcddbdbcabcbccdaadddcabadabdcacdbdbdbcdcbaabcdacbdaccacddbdbbcabcccbdccdaccdbdaabaadcdddadcbadacaaadcdbcdcabbcdcbbcdaaaccbadacbdbabdbabcdbaccddabdbcdcdacdbcabcbbdbcdadbaaaaccdaaadbcdbbbdaadaacabadcbcdaabcadbcaabaabbdacacdaccbbcbdaddddbbaaccaaacaadbdbddcadaddddcdabdcddcccdaddaacccbaccbdaccbcaacbabcbacabadbdcdbdbdcabbbdbacbcadccbdddadbdabbbadcbbcacdbdcbbdbdbbdadbcbdaccdababdadcbaccdbcbaaaabccbdbabdaaadcdccdbdaadbbbdaabbbccbdcacadccdbaccdcccdbdcabdcdbdcbcaaaacbbdbdcadbcadaaabdadcdbbabadddbaadbdccaaabaacabddaacaabadcccaadcdccaadcddbcaabbcabdbbaaaccddaddcccbbabbaccadabdcacabbddcdcbcbcbdcdabdbbabbbaccbbbbdaabbadcbbacacbcabcbbdbadcbcbaacddadcacbcabacbabcabccdcccdbbacadababcccbbcbacbdacdddadbcccbabdcbcaabbdbcbcabbdbcbbbdbdbbdcdccbcaccdaacbcbcaadadaddbbdbbbadbacbbcbcbcdaacdbabdcdbbadbadbacdbdbcabcacaadcbaaacbcbdbacdccddcddcbadbdababbcccdddccabdcbaadbdadaabbcbbccaadaddbdbdacdcabbccbdaaabcadddacddddbcabcddcbaaaacbcaaadadbbaddcadababddddcabadddcdbbcbcbbababdddcbcdcbdddcacadadbcbcdacbaddcdaaddacadbcbacddbcbbadcbbcaababcdcdcbadadcbabacdbcdabcdbcbcdbcbdbcbadccbbbdaccdbcbabcddbacaaacbdabbcabbdddddbdccdddbdddaacabaadcdadaabdcddcdbcaaccabcbccdccdabcccccbcdcaabbcaccbadccccbadcddcaadccadabbccdccadcbddacbddcabddadcddabccdbcddddcddabbacabbaccbbdccbbaddacabddacabbbbbbdbdcbadcdadacdbdbdbcbcabdccbcabbcccbbdcbbdbbddacdbdbdbadcddbbbdddaaadcadbcdcccadbadaddddcdbadbabcbbdaacaccbaccbacbadcaaabaacdcbadbacdddcbbbbaabcbdbbbcacbaadadaabadadcddbbbbbacddddadaccbaaabccbdbdbbbdbbddbbacbabbdbdbdbbdddbabddbdabbdcddbdbbabddaaababbddccbdcddbbabacdacabccbcbcddbcadaddbaadacbdcacbaddcacbbabacdcddcabcdadbdcadcacadddbbacabcdabdaddbabcbbcddabbcdaaddacdcddadcaabcdbaddcbbbcaabcabbadcabcccbaacabacbabadcbdbcadcdabaacdbdcbdcbdabccdcccdcdbbacababdacbdadcddcdaccbabccdbdddcaccabbbadcdabadaddbdabcdcbaccdabadcddbacabdcdaaccddaaddcdbbdaaccdacdadbabaacbbbbcbaddaddbbbaabcdcbaccbaddddccddcaccaacacdccaaabcbaaddbbccbcccdcaddaabbacdccccbddbaacddbdccdcbcaabdbaadbbbdbddbabcbbadadaacaddbdcccabacaccabbbabbbcadacbaccccdccabbbdadaadabbddacddababcbbbccaacdaaccabdcbbdabaaacbbddcbdcbcbabcbccdcddbdddbabadbdcccaaddacdabcdcddccbbdddadccdbdcbcaacaccaacdabdbabccaccdbbcccbabdacadddbcdccdbbdbadadbddaabadddabdaacbcbaacbddbbddaccbaaadcadabacdabbcbccaadaaccdaaadadaadabbcbcdcddadbbaaacbccdaccccbaaacbdbdcdbbddbbdcacbababbbccbbaabdcbaaabbbcbcdcbbacdddaccdbdcdcddbadabadbdccadddacbaadaaaaacbdddddddacbaaddbabdcabbbcaccbbaddccbadaadbdabdabdddccaaccdadbadbbadbaccdadacdbacbbcaaabbdacaadbaadbaacddccacbcbccadabdadadbcadcadbaabdcadbddcdcbbbaadcdbbbabdabddabdccabadddacabbaadddbbaaabbbaabadacabdbccaddaccbccaaabdcbccbcdcaadabcdaadcdadacdddddbddadddbcaaccdacabdbdddaaddaadbbcbddabcadcacbaabccddcadacabcbcdadbaddbabdaabdaababcacbdaacdcdbabdaadaccadbaadcdcdbdcaabbabdbaaacdbaadcdcaabdabcdddacaadbbcbdbcacacacdbdddcccabdcbcbabcbbaddadcbacacdcbcbdcaacdcccbcacdbadbdaccaddcddcaccbbcadabbdcbbaacdadacadcaccccdccdcabdbdcdbcbdaacaccabcdacabadbaadcddbaadadaabbcdcddbabdadbacacdadaacccbacbbacadbdccabdadbdbddcddcddbccacddacdaaaaddcddcbcbdbabacbddbdbbbdcddabbacacbcbdbbadaaabbbddccdacacdcaaaccbdcadddadaababacabbdbcbbcbddbadbccadbdbbdaadbadbccaddbdabadcabdbcbddacaddadcabccdabcbcbdcdcacdbadaddbbcbbbcbddacdddadbdabaacbcbacccbbacccccadbcccdccacadcdbcaabcbcdbdbdcdcacacabbccabccabadbdbbdadbcbddbaacadcddbaabddadcacbcccbbacabcddcddcbdbcdcbbdbdbdadadadbcdaacbadbdaaacbddababaccbccbabacacbaadbaddacdbbbacaacdcaabccccdabaccaaddccdcccccacaccbbaacdcccdaaadaddbbdcbacacbaadbcbaabcbcdaadbaadbcdccbbdaabadaccadadbadbddccdbbaddccaacbbbbbbbbbbbdcdccbdbabdbcadbcbdcbabdbcacaaccddbcaabaabaaccbcddcacdbccacdbaaabdcddcdaabdbacabdaabdcdaaabcdabbcdbabcacdbbbaabcdaddcdbaabcabbaadbdcdcacddabcbdcdacdbdabaacaddccbbddaaddaacbbbbdabdaccbabcbbcbcacadcbadcadbaaccbddccbbdbbbccbbadcabcaadcacabdbdbbbacaabdddcbdbddbdbaddcdaadacabbaabdcadbbbdadcbccacacbcadbbabdadbcdbaaddddbcaddcdcdcbcdbdacabcababccbbacadcdabbcdbabbdacdddcddabbcbdbadbcaacaaccdcdcbbadbabaaaabdacccbaccbcdbacbbadabaaaaacacaccbbdcbadbcacaaadddbccaaddacbdcbcbababbacdadcbabaddacaadccaacbbbcdacabacabbcdabccdbcaabcadbddddadddccdcdccdbcadabdaddcacacaaaadadcbcddaddbbadcbcaccbdbaccabbcdcdabcacabdbdccbccdccddbcbdbcdddacdcdbbbaccaddddbcbdacdcdbcaccddabdbbbdbaccbccabbadccdbaaabadbaaaacbcbbdcacdacacdbadcdbcbaccbadbadccabbdaaccaddcbbcddcdccdccacbcdcddcabbddbbaaabbdadbbbaddacccaccadcbcccacdbbcdcccccccabcbddbbddacabcabccbcaaaddcaccddbbcdbcbbddbdcadacbbcbbbadbcbbbacbabccbcdabccbdcabcbababbcbaadacdcbbdcaddbdbadaaddabbbcbadabdcccdbbaccbabccbdbcadbcacdccdcccadbdbaddbdacbbaabbaddcdbdbdadadacbdbcdacbccbccbcababcbcbbbcabacbccacdcadbaabcbacbabdbcbdbbcddaacdadcdabbbaabcdbdddcccbdccbbadbacadbddbaddadddaacdcacbadddaddabadacdcbacaddaddddbddddcbcbbbcbdbbadabbdadbabccdbabbddddabdaabddbadbdcdcdcdbaabbadbddbdccabdcdadbccadbaadacadabcadabaccbbdcbabdcaccaaaadabdbdcdddaddbdbbccbcbcbdabbcacbcdcdbdabcabbdbcccaccdcccddaccbbbaabcbcbacccdbbcdaccaaabcaddcdadbcacbaddaabdbacbbadcccbacadababcabacddcdcbcbcdadbaddbdcddabacccddbdabdddacdadaccbcaaaaddbbaacbdcdaddbcabadddcaadbacddcccaccabdddbdacbbddbabbcbadabddabdabccbdabacccddadadcadaacaaacaadcddbaabdaabddacbbdbadbacdabccabccabbcccddaaaacccbcdbdaadaddbddccaacdcbdcaddcdabdacddcacbdbabaddcacacacaabadadcbbacabdddddabaccccdbbdbddccdaacacbababdcdccdcacbccbbadbcabbbcabbcbdacabbadddbbaacaadccaaadabcaacbdbbcadcaaadcbbddaacacaccabdbdbddcddabcabddacdababbcbdddaacdaadddbcbbadccbbbdcdbaaacbbdbddbdddadddbaadccacbcaccbcabacabdbccdadacabccbaccbbdcadcaaadddccdbacdabbdbcbadabadabaabdaadaccdcdbcabdacacdaacbbddccdaccbdbacdbabbcbbdadcdcadadbbdbaccabbbdbdcbdcdbddaccccdacddaddabdacbbdabccaccbbdcabdbbadabbdbacacdabbbdcadcdabcdbbadbbdbdddaddccbabcdddcbbacbacdcaaaaccdadbccdbbbbdbacbbbababccaadcadaddcccccacabaddcbbcaaadcbabcddacacbdabccdaaabacdabddbabcaadbbadbdccdbdbbcbcbcaacbcccaadccbbaddaaababdddaacdcbddbbbbbbdcbdaddcbbdbbcddbcbabdcddbabcbdcdbcbdcdabcdaabddcabdabbbcacacddcddcacaadbccbdcadcabdacbbbbdbbbadbcddcabbcacdcdabcbdcccdadbbabbbbabadcccddcbcbaabddbbabbdaaacdcdcbdcbabaabbaabcdbcababbbdacbdacddddbdadbcbdbddacbdbcaacdadaccabcdccadbbdcbccdadddaccdbcdcddddcbdccbbbabdbbcdbbabcabdabbbbccbdbbccacbdbccbbdabacdaadddaabbccdcaccbbdadacbddaadbdddddcbbaacabcccbdbaacacbacaaadbbbdaccdbadcabbacadbadcacdbdaababcbcbbbbaaadcbdacdaddbcdccacccadbcaabdbddabcaddcdadccaabbaabbbcacdaaadbaadadbbadadcbdcdaddbbccacdadbdccacdcaaadabaaaabaadabcddcaacbbcdcaccddcaababaacdbbbdaabcccdbbccccdaccaacabbbadbddbadaaaaddacdaadccdbbccababdababcccdcdbdcabaabbdbbdbdbdaacdcadaaabaaabbcbaddbabcddaddabacdacbabcdccababbbcbbdccaabbabbcdbbccacdddcabaaabddcdacbcaaccbbcdddcdbaacacaaabbaadcbddbdacaaddbcbdaddbadddbbcaaddddbcdddaddbabadbdcbbdacaabdbcdddabbdbcaaabbbcbadbdaccbaadacacbcddcabdaddccdcddbbbbbbcaadacbcdadbcccdccbbbbacbabadbdcdccaabbacbccabddbaaabdabbbabdbcaccbaadacdaabdaaabacaaccdbdacabacbacadbbcbdbaadbcabdcadbccddaaacdcbdacdbbcdadabbaddbcdcbdbadbaadaaaccbcacadadbcaaddcdbbdbcbcdacdbadaaabdacbdaaccbdacbbbdccdddcababccddcaaaccddcbcbdbbdbbadccacddccccdadbacaccbccdbdccadddbcadaacabbbdcbaabbbdcbdaaaacaccbccbaabadcbddbcadaaaddacddbcbdaaaaacacddaccdaadcacbdbcbccdddccccdbcddcaacabdacbaaabdcdbbdcacbbcdacbdaaabdbaabcdadacabccadcbbdbcacacacadcdadacdccddbbcaccdaaabcddbdbaabdcdbcacccdcccdabcaadcacaabcdbdabcadcaabbdcbbcbbabbddddcbccddabacbbcdcbadcaccadbdacbbbcbcbdcbcbcbabdabadcbacdcbabadccdbaddcddabdcddbcbaaccccbbbdaababcbaabdabbbcabdcdabcadcacadbdcbcacbaabacbdadcbadacabbddaabccdbacaccabcbadcacdaddcaacdbdcbdbdadacdcbccbbbaabcdcdaccacdadbdddacbabbadbdbabdcadbdcabadcdcdbabcacbcbdbdaaddcacdddbbdcbdbaddbdcaddcdabdbadaaddbdcbdcddbadabbbdacbcddabddcddbcbbacabcbbadaacdccdbbcbbbbbaddaccacaabcdddbbacabcbdcccdabdcacdbcbbadabbbdcbabddbbdcacacadbbcdcbaaddbabdcacbaaccbbdaaddcdacdadddccacddabaddbbbcaabadbbcbdcbbddaabdadbddcdacbbbcbdbdcddbacddcacbaddacdddaabccbccdabbddabbdabbddbaacdcdaadbacdaccbccbadcadcdcacdcabbadabcaaaacbdbabccdbacabdaabdcbddacdabbbaadacdadbadcdabcaccaacddbaabdadddddacddbcccbdadaacacdccbcbabadacdbcddbdabbcaabcabbccadccdbbdaabcdcdadbbcabbcbcbaabaadcdddcadbaacbdaccbcdbadaddadbcaadcdaccddccbacabbcccabbadcddaacdabddbccbcaaabdcdadcbdaaabbbcaaaddbcdabacadaabcccbdabdaddcaabbbbcbbdcccdbadbdbaacbbdcabddaaaaaaaacbbbccaccacbccadcddbbaaaadccbadcacbabddbdbdbbcadddbbccabbaaaddcadbbbaccbddadbbcaddbcbbdbcabbdbddcddccabadbaaddaaabdcbcbbbcdbaacddccaaabbaabbabcbaccbdbdddccadbbdaaccdccaaacbcdbaaccacaddbaddacdccadacdcdadbabbdaabdddaabacbddcddaccaccbdcaccdbbcccbcaadccabadaaaacdbbdcaacbbdbcdabddccbdbcbbbdcccaaabbbcdcdcbddcbbdbdaaccacdbbbacbcaabbbbcbbabbbcabbbacddababbddddabbbdcbbbdbdaadbcacbbdacccddcdcabbbbccbbccabddbdcdcabaaaadddbaddbaddaddadcbbdddbbcabbdaaabadaaaacbcaadbbdcadbaccdbcadcaabdaabddccbcbacdbcadcabdabaaadbcacbbcadcdcacdcbadcddabadcddaddbbcabcacdcdbacddaddcdbaccdcbdcbdcbddbdaaaaaaaabdacbccbdddbcbdaccdabdcbcdcaadddcbccbacbcabbddabddcabcaabbdccbdadabcacdbcbccbaaadcdccadacdbcdbcdacbccdaccdaaaaaccbdbcaddcaaaadccccdbadcdabacbcdcbdababbaabbbcabdddddcdcbdababbcccbbddccccdcddbbbabaaabdcadcaaaaaddcacaddbcbaaaaccdbddbdbbabaabaaadcddddadabccbbdbdacdbbdaddbababaddadddadcdddbccbbdabbaaacabbababbddbadbaaccdaadbdcaacdbaaaadcabbcaaaaaadabbbccaabaaabcadbddacbccacaaccbdbacbbcdbbbdabacdccacdbdccbcabcbdacaacbddccdabdcddabacaccabdcbbabbcdabbcbcbdccaaacdccdbaacadbbbababbdbbcbdcddadbbcdbcababdcbdccdaccdbcdbcbcbacdacadccbbbcbcbbaadadaaadbabaaaaabaadaacddabbcaccdbbdacbbcbabccbaccacacddccddbaaddabdbbccbdacbccdddbabcdccabcaadabbababcadbaccddcddbbadcacacdabdddbabaadbcdbadccdbcccaabcabbaaaaaccaacbdbbbddadcddacadaccdcbadcdddcacbdbcbacbabacbcacdcddbabacdbcadcddcdcdadddcdaccbcddbadabaabdccbabaddcdadadbaddcdbddcddcacbadccbaccccddabcbdcdbaccaabcaacaddddcbadabcabbcbcdbaddcbdadadacdbbdbcabbbddccdaacabaaaacccadcadcbcadbdbdcabcbabcaaacaabaabdabbacdaababbbbacbbbdaaabbabbddabcdddadbbadabaabdddcacadcacbdcaccddbdabdbcbcaaabbadbaddddabbbbadacbcbcabcaadccbadacaaadaabbaddcaddcaccbbacadcbaaadcadabdcbcadbccadccdaaddccabddccaaadbcaccdcabcbdcccbcbbaadcacaaaabdabcaadaaadaabccdcdbcdccaccadbbbbbcadbbdacbccdccbbdcbdaccadbaacbbcccabcddbcabbcdcabddddccbdbbbbbdbcbcbaaabacdcdaadbbaacddccabbcbdadcaadbdccddbbaadacaccbcadabdabadaabdcacadaccbcdbbaccccbbbbddaacccddabdcdddaaacdcbadaddcadaaabddaacbdabdcabcdabacbaabdbdcdcdbcbbbaaccdbcabbccadcbabccaacbddbbacadadcccbcbabdccbdabcbcbbbdabddaccaaddccdcddaacdacdaaacdbbcccbbabdcbaacdbbcbabaacdadbbaadcdcdaabababddacbaabbccabcacbadabdddbcabdcdbdcbddcbdbcccbcddbcabcbbdbbdcbbacbbbcacabaacbbbabcabbddbdacbdccdcdaaccbaadbacabcdcbacaaaccccaabddbdbbccbabcbaacdcbcadcadcdabccbcadccacaccbdbaaddacaacbbcbcbddbbccadddbacbadbaddccdcbacbcddaabadddacadcbdbdddcabbbacbdbbabcbacaadabdbdcaddadbbcbcaadccbadaccabcccadbcbccaabcddcacbaccdbbacbbbcbbbaccccabdcdbdddacccccccbabdbcacbaabcddacdadbddcccddadcbaadcdbababbdadaacbccacbcccadcbdabcdabadddbaccdaaadaccbbdcdbddbacdcddcddbcbadaddaacabdddddbbdcababdcdcbdaabcdcddacbacaccdddbcdcbcbdbccbdadcbabccbaabcddbcdbbcbbdccdbadaccdddabbcabbbcbbbcbbabdbcbcdbcddcadbbbddbddcabaddcdbdcdbccdcdadccabdddabbacbddacacdbbcdaadcbdcbaabaadaddcbcbcccddacdbbaaadbcddcbdabbbabccadbadbbbbbccdccdbbdadbcacabdacdaccddaaaabcabcaabaaadddccaaaaacbddcadcaddabdaacdcbcaabcbbbcddcabbbdbccdbadcabcccbcdccacdcadbddcdbcbaabbbabdabdccdadccabcbacabdbbddbbbccbcdadddbbbcbcbdaacacabbbcaddccbbabcbabcccadbbaabbbdbcabacabbddbbbadccdadcdacaabbabdacbaadddaaadbdabcdaddbdbdbbddcbadbaacbcbcaaacdcdbdadcaabdcacabbabcbabadddcdbbddcaadbdcddadbbbbcaddaacaabdddcbabdbdaccbdabcbccbacbacaaddbbcdaadcdacccaccbccdcabcdababcaaddbcdcbdcacadadabbcabaaaabbacdbbdbdbbdcdbadabaacdbbacbdbbaddddbaaccbabababbdddadbcdaacccdcccabbbdcbdcdbcadcdbdccdadcacabaadcaadbcaddddcadaddbacdaadbdbdbaabadbabaabdbdcaabbdbbcbbccbcddbbacbbbcaccaaabcdabaadcbbcbcadbbdaddddcdaacadbbcadccaccacaacacdccdcacaabcbbdcabcbadddacacbbaaddaaaadcddddcdbbddaaddbbadaaabcbadaccaccdabcbdbadbddccacbabccadbdcccaadbdbddaacdbcaababbadabaababccbdbabaaacaacbbbcbcbccdcadadabbdcbacddacbacacabaacdbcbadacaccbabddcaddbccaaabababdadcaccdbdbbbcbbccadcdcabbcbbcacbaacbccccabbdccdbbdbbcdbddaddcccddbbaabaaacaacabcbcacbdaadacccbcaccbbdcabccacdcbabacbcaacacbadadccbcdcdaadcaabbacdbabdcadcbbaadbacabdccabcdcdcaabbaaaadbdbcbaadbccdbdaddadbadacdaaaaddabdcdddabccdadcaabbbdccbddadabcabadbddbddbaadadbacabbdbbdaddcadbacbdcabdcbcbcdadbdcbdaadbacbdacabdbadbcdbdcddcacbcaadcdcbbaabaaadccbadbbcbdbdbabacbcaddbcdcdbacbddcccdcbacacdcdaacdabcbdbbdddabbbacdbacdadcbbdacdacccccaacccddbdbcaadabbcdbabadbabcbabcabbcdbcddbbacdbdbcbbddbbccabbabbdddcccacbaddbcbcccdbabdaacbdccbcbdaaacbabbcddcbbadabcbbbabbdbdcdbcbcdabadcddaaadddbaccaadbccadadcdbdcaddddbccbbccdabdcdcaadaacbcaadabccaddbdbbdbbbbcadcdcdadaccaacdccbaccbccddabacbcbddbcccccbddcacdbbddadbabccacadaddddcbbddbdcdbacaaccdcddbdbbbcabddaaaccbbbadbdddaccabdbbdacabcccdadccdbbcbbcbbdbacdaaddacdcaadcbdbcdbabadbadbabbabacbdbaddcccdaacdbddbabbbccdccbccdabaaacdccbaaadbdacbbadbbdbbdbbaaddaaaddcbdbcdcbadabacddbacdccdddaaaadccbaaababadcaabdccbdccacabdbabcbaacbdddadbbaaddabbdbbdbcdcdacbcbcbbcdbabdaabdcbdbbadbdbaccaccbcbbadbccadbbaacbdabaabdccbcdbdcbdcbcadadaaaddcabdddbddcbbbbbaaabbacaccbacbdccadbbbdddbbbccbcbcaadccdadacdddcddcbbaddddaaabbcbdcbbbccdcdbbdbbacccabdccbbddaabddccbcaacabbddcddcacdbdbbbdbcbdbcccaacdbaddddbcbbabbcccbbabacdbbdcaddaadcaddbdccacdcbbbdbcbcbacabaababbcbcddcbbcaaccbccacacdbabbaddbbadcadbbaccacdbccaccbdbbcbccbcccbcdacbccbabdcbcaabbbddcccdbbcccbbdadcdaaacaacabaadccdadcbadcdcaadcbbbdddcaaabcddabcddacbbdbacaccbcdcabdbcdcaaacadcbbacadbcccdccbccbcbddbdcbcaddaaaadabcbcdbbdbdcbdcdcaacabbbcabbabdbcdbddbacbbdabacabdabbdbdcbcabdbacaaddcdbacdcadccbcbadbcbcdbbcaaabdcbbcddbdcbbcabbdcbbaabcddaaabaddbbaabddbaccdcbdaccacbcddbdcacabdabcddcdcddbdaaabbdadadbdcbcddbacbcaaabaabbabbacddccbbbccdcddacdaddadaaddabacaaddbaabbcadddccbaadbacccaacbbccadadaccabdbbdbadadbbaaababbcdacbaccdcdbdcbbaccdaadadbccddcddbdcccdbbacdaddbcbcbbadcacbbbbccdcdddaddcaddbdcbcdacdbaacadbbcbcdbcbaaaaccbaddbdddbabdadcabbacabaddccdbcbacbbbaddbaddbbaadaccdbcdaccbddccdccbdcabadcaaabacbbccbddbcbbaadbbccbcbaaccbdaaddadbdbabbdbdbcacabbacdbcdabadadcdcabddcabccdadabbcbdbacbcaccbababccbaaadaddcdaaccaacabcbddbcccacaaccddcbddacdbdbdcbbdabbbccdacaabbddccbadbcbbdddbdcabcaccbdabbdaaaaaabccdbdabacbdcdccdadbccdacdbaabbaacbbadbbdcdcbbdaaacdbabbbcaccdccbacddaccbdaddbbcccdccccdcbdccdaabbcddadcbadbbccdacabcbccdccaabbacdbadbdadadbcbdabddbcbabbddbbcddbbbabbcbadbcabbcbcdcccaccaaaaaaaaccbbcbaaabababdaddddaddcaaddddcaaaccacbccbbadaccababdacbabcdddabcccddcabbccbdcbadbbbbadcaacaddcdadbdcccdddcadccdbcccbcdccabacabcaddbdcadabdacaddbabaaabddbdccacbcacdabbdcdbbadbaadaabcbaacbbcbcbcdaaacdabdcaddbaaaddcddbdcdaddadbcabbbdaacadbadccdcbdabcbadbaddacccacdddbaddbaadbacbbddacbaadcddcbbbaaabaaaddcbaaaccddddbbdcbbdaccdcabbbaaccbcbcdadcbccbcdacdbbacdbaaddccaddacabdabaddaabcabaddddddccdcdbdccbdbadccdcbacdcadaacddaddddabdbcabadbccaddbbaaccdddbadadddadaaaacbcccacaddadcdcdadccbaabadabdbccadcccbdbdadbdbacbaadddddadacdacabaccadbccbbccbdaddcaaabaababddcbacabdcddbbadccbbccccbccaabdbadcacdcdaadbaccadabcacbdbacbbcccaccdcbddbabcdbdddcabcadbaabdcdcdbdbbadddaaaaabbdbcbadaabbcdbdccbddbccdccdbaacdcccdbdadcccadaabacbbdbdabbcaccbacccdbaddcacbdabcdbaddacccdcbcccbbcadaaccaadccabddbcaaabaddddcbbbcdacddadadcabcbbbccaadcdcadcdcdaabbccddaabdcabaccbadcbdbadaaccadcccbaaddbbdccbcbdadacdcacbbaadbcccbbabdabbddcbdbcccbadadbcddcdbdcadddcdcaaaddbcaabbadddacabaaddbbbbdbbdcabadcabdddcdcaacabcacdadacbabccabcbdacdbbddadcdacaaddcbcacbbcadcdaaddaadadbcacdcbabdbabbbaabbccdbacdcdbcbaadbcdccabcdbcbdcbacaccdddcbacaabddcdbccdccbdbaadcaabaabbbacdaacbcbbbaaddbcdabbdabddbdbcaadbdccbbdabbadbccbdddbaaabacacacacbdbbbaddababbdadddcabdbdbdddcaadabdbbbaaaaccacadadccabccdabacabbaaccddcdaaabbcdbddcdbcadbdbdcbddacbcddbabbaddcddbcaacccccdaccaddbddbbcbbbdddbbddbaadcdcdaaddcdcaacabdddbcacacbcbadbddabddcaaacaadcdbacdbbdbddaccbdaacaaabbbcdabaabccaaadbbbadccbddbccabbcbbbddbddbcdbbdbbbcbcaaabddddcdcddbaabcddadadaddadcdaabcddccaabdabbcabcaaaaadbbbbddaabaabddbcbcaddddcdcbadccbacbacbbadaadccbaadbadacaddaccdaddcbcddbbddbbaddbabbddaccdbbaacdbadaabababccdccbaccbaabaabcaacadacaadcacccdddabdddadbaabacdbdbdbbaaaacbcbdadabcbdbdacadcdcdbddacccbcdddbddcabadaaaddccacbaccacbaabbbbacbbcacbaaaacdbbcbcdcbaaaaccacbaddaacaadadacbbdaaddbbadaabdabdddbdadadbbdbcbcdcbdbcadbdabbccaaddccacaaabbcdcddbcbccaddbcaddbabdabbcbdccacacacabadacaddacaacdaaabcbbdacdadbddcbacdbdcacdcaaaddaddbbcccdaaddbaccdddaabacdaaadbccdbccbbacdadcddcbccaaccdbaccccaccbabcbccccadbbadbddcdaddcbcddaddcbcadbdbacccaccdcbcddacbaadcaaabcddcadccacdbdbbbacabbdbaddabbdccadbbaadcbadccdaababaccaaadacddcdbadcadadcbaacdbccdddbbccdcbabdddbaacabdddabcccaaadddaadaddaaaacbadddcddacdabaaddddaccaaabddacabadcaaaaddcdbcbdcccbdcaccabadbcbcbdbbccddccbbccabbdcbbdddbdddadaaabcdaaccaddccddaaddbbddacbabbcacbdabbabcdcbdbacaaabcbdbaddbdcabaaacdbccdbaacbdbcbdaadbacadcaabbcaabbaacbbaaabdabaddcdacbcadbabddcaacacdacddbcabddbbdddbbcdadbacdddadaabbdddbabbaaaddaabbcdbdcadbaabdbddccdaadcadacdddbbaddbbcdcdabcbadabbbdbaacbdbdadcabacabaaccbcbdcbdbabdddbcabbbdcbabccadcbadcdcbdcacabbcdabdccdcadaabaaaaacbadaacababbcdcbcccaabbbddaacddaddccacccabaddcdcdbdcadcaadbcbdacaacdcbacaabcacbddacaabdbadbbbadcacdadbbdaadbdbacadccbbbacddcaaaaccbdcbbdcabbacddcbcbcbabadbcaacbccabcadcbbbdddcdccadccccdaddcaaacdccdcbadcacbdbbccdbccaadaccbcccccbdadcbaacbacbabdcbaddaaddabaaadbacacbbbbacbbaaddddacdcccbbaccadcabbaadacabadbdccadbbbdcaddaaddddbbbccdbbaccabbacbcdaddbbacbbdaadcdaaababbaddadabdccdaabbdaababaaacbdbcbddcacbcadbbadbaaccabdbadabcaadabdbbbbdbacdcbcdcbbabbabcabcbccdbddcdbcdccddddbcdbaabbadbbabbaadacbcbcababcbbaaccadababdaabaabbcaacacdcaacddcdbdbdccbbdbcdabbbbdcbcddbbaaddaddbdccdbadbcddadcdbcdcbadcbdbabdcbcdaacddbbacababcdaadaccaaaaadcccaddcddacddcaccadacdadcabbcdbbbcabcdadbaadacacdadadccdddaddcccacbdccdbdaaabddaacbaabadabbabbbbdcddacbddcadadbcacadabbaaabdddcddbddaaabbabadcdbadacacbcadcaadadccdacdcadbababbdcbdbaaabcaccaadccbcdadbcbbadacbcaacccdacbcdcbabbbbddcaddbddddabcbdabcaadbdadccbbddadabcaddababbcdacbacacbbabcbdadbacdddddcacaabdccabaaadcaccdabcabdbabacacdbaccccaadacadababaacbcacdbdcdccbdcadcbacbabbddabaacbccccabbcacaddcbcddacabdaddccabdcacddcbadadbadbcbaaabcaddacbacdacbcbdddccbcdddcaabbcadbaddbddbbbbabbaaadcbbabaccdacdddcadacbacacabdbdadcdacdbcbcbdabbabccbacbdbcacbddbdddbcaabdacaaadddbdbbadaabccbbacdbcbdacdbdbabcbcdcdcbddaddaabddcaccccdadccacbdcbccddccddbcdbbaacaadcbcdbdcdabddccbcbcaddbabcdbbdcaadadddccbcdcbbcabcacaccbcaacdcbdacbbccbcbadabaccdaaacdbbbdcbdaadbacbabdcbbbdbcddbacbdbcbaaacbcbcbbadddcbaaadbabdabcbbdbbabdbaadacacdaadaabdcbdccbcdcdacdcdacdbdddacdcbbbbdadbacaaacaccbbacaccdabccabddbcdadbadddbdcdaaacaddbcbaabcdadbbdadacdbccacadbacbccdbdccddcdaaabbaccabbaaaaabcddddacabbcdbcadcddbabcdabdcbaadbababdcbdbdbacbddaddbbadaadbabcdcadcccccbbddadaaaaacabcaacdccaaaaabacbcccdadabaddcbbdbdcacbabcccbaabdbdbaaabacccbccddcdabadaaacbabccabbaacaaccacddaadcddcadbdbccdbbacbdcbbbabbcabdbcbcdcddcbabbbbcbdddbaacdabadadddcbcacdbaabbabdbaccaccccbacdaaaacaadabbdcbbcbddacbabcdacabccdcabdabdbbddaabcbbdcbaadaadacbaadbddcabbaaaaacabbccbdcccaccababddadcbcdcccdaabbdbacadddcacacdbcccdacbccddbccaddbdababacccacdacdbaabddaaccbaaaaaabbcbccabcccabdbcadaabcbbbbcbbbcbbcbbdbcbdbbccaacbbadadbbdbbcbaaddbccbbddbacddddccdcbbcdcaaddbbaadbabbcdbcdbccabcddaacadaabadaaaacbdacabaddadbbaabcbdacbbdaacdacdccdcdacbdcdacacacbbccdcabaddacaaacbdbacaadcaaababadabcccaabaacdbbabcdcadbadcdccaabcbbbcbccddcdddaddacabdaabadbdcbabcbcadacbcababbacdbbdcbddcdcdaacacdcacaadacaacccaaccdcaacbcddcabdbabbcbddcaadadaabbddcbadbbdddbbccadacbaabcacbbcdbbbbddaabcbacacdbdcdaacdbbbccaaccdcbacaddcbdcacccadadbacbddacdabddbbdcdbdaccdddcdaaacbccadcbdabdbbcccabaaccabddbbbaacbadaaacdcadbcdddccacaadabcaaadabcbdbcbcaaadaaddcbccbbaaaaadbcbbbdcacdbbbbcbbadabcbcacaacbcdabdaaaabdadddbbbbbdbddcaacdbdbabcbcadddacdbdddbbcbcdacccbcbbcadacbabaadaaaccadaccacaaaddcbdcbadbabdaccbcabbdcdadaddcabadbaadaabaaaccccdacdabddaabddabacbcabbbbbbcbcdbcacaaabccccddaccdcdbadbdabbacacddbdbdcddaacbcdadbaccaccdaacddcdbddcdadaccabbcdaabcaacadaadcddcaaccadbbdcaccadddbbabdbcacabdcdabbcbcccabbdbcaaadcdbaabdbacabcdbcdaabababdcdcbcbbdadaacaccababacdabaacbcccbdbdbadbbccabdcdabcadacacdbbbcbdaddbccaddcbcadadcdcddcacdddccbaacaddacbadabbaaccddccbbdcbcbcddbbbaaddaadaccaabacbadacabadbaccbbbddaadbbbbdcdcabbccaacdbdcaacddbcaaabacddddbdaddadaaaacbccccdaabdbaccdaabccaaaabdadbbacadbdcabcbbadbdddbadcbcbddbcdadbdcaaddbdcbaccaacaacbcccccbbdbadbdabdcccbdadaddaaadddbdbbcbbcdaadcdacaddaabdccccabacdcaaccaabbabdcbccdabaadcccdbccacbabcddabddacabaadcbcadbbdddccbadabcdbdaacabcdadcbabcbccbcaaabddccdbcbddbdbcbadbccddaddbaddbabdbadccaddabbccbaabcdccabbcdcdbbcaacdcdbbbacbcdadcbbcacdbcdadbdbdcbadbadadbacbabddbdcddbbbccccdadcbdcadbbcdabbdbacdddaadcdabbacdaaccadadcbdccbcbaddbcadcbbacdbaaddbdcbcbdacdddcadbadccdbaabdbdcddbdabbcdccbbcabbbdddcdccdbccbbcccbcadabbdbadaabcbdbccbacbaabcdbdabdadaccddaccccaacdcdccccbadbabadcccadcccbcdbddadacccddccccbacbdbccdbacbbcbacbdbaddaaadbbddcacbaddcdbbbaccaccbbcbabcdbddcddabbcbcadbcaacdbacaacadcbbbdbadbccbcccbaddbabaaddbddccdaddcaddaddbbbdadcdabbdcbcccaadbbacccaaabdacbddbbdbcabbbdabdbaabacdccdacadbcaadaabcabdddabdbcabbbcbcaadbbcddbcbacadcccbdcbdcdccaabaddbabbadacbdcaacddbaabbabcdacaadbddbbbbddcbccacddbbcdddbcabadaabbaabcacccdcdbddbbccdccddaabaadabcdcdbdbdbbbabdccadbcbdacdbccdaadbbacdddcccdddabbadcabcacdadabaacbabadbadddaacadcaaddcccdbbdcbabdabcdbbadcaabccaadbbddbbabcbacdbbdabbcdabcbbdcadbdbacdadcaaaccaabcadbacbaababdcdcacaacccdcdccdabccccacbdbabcbcbcbacacbacdabdbabbacbabcdcabcdbaadccacdcdadbabbcadaabcabbbddaccccddaaadadcadbdacddcabcddbcbdcbbccdcaaddcdcdadbbcccdbdbccabbbabbbdbcbdbcddcdcbcbbbddaadbaadccdbcbdccbbcdbdaccdcdabdccdcdaccdbaddccabacbcdabdbbdaaccbabcdadbbcbabdcbadbbcaccaccbcbaacdbddbaacbadadccabccdccadabcdbcbaadccacdaacdbadabcbcaadbdabadbcbccaddbbcbdbbbbaaddacdddddccbdacddaacdabbbbaabaabcaaabbcddcadbddddcbcbddcdcaabbcbcccdcadbccdbbcbcabdabaadaccdadbdcadbdddbaaabbccdaddaaabbcdadbcdaaaaadaccdbdcbdddbbdacbcbaaddacbaaccbabbdaabbcbdcacbccacdcbbdacdaadbbdbaabcdadbcadbbcddbcbabddabbcbccccacdcbbbddbcacacabddbcdbcbbbccdaadccbccdccaababcbaccaaadbdddaadcbcbbdadacddaaccbccabdbaabdadbaaadcccaabddcddbadcabaacdddababdabcaddaaaababdddaaaadbaddcbcdbdccbaddacdccadaacacaacaacbcaccdcbdccaccdbacabadabddaaaabdabcbdcbcbaaadbcacdbabaabdbdacbddabaabbdbbabddcacdbcdbcccabdbdcbdabadaaabacbbbcacabddcbcacdcddaddbaacabbaabbbdadabccdcbcdacbdbddadabadcacbdbccdcaaabdcbbcbbaccaddababdaabcdbacbdcaabbcbdbdbabaacbbcdacccabdbbaaaddccdddabccdbdaaadcccadccdbbabcbdcbcabbccbacadadbdcaccabccccdddadcbdbbbacbdcadbdbdcababacadbcbccabadabcdddbccacacbbddaccbcbaacaaaaccaadccadcbbccdcaaabaabbccdadbdcdcbaabaaccbaaabbdddabbbcdcacadaccadacdcaacbddcdbdcacdbcbcadddddddddaabacadccbddaababbadbbdbdccaabbbccdbdcbdbbcabddaabbacdabacdbadccbcabcdacdcdaaacabcbbcbbddcdbdbdcbbcbcbabdbdcccccdcbdddaaadcbaaaddaabaaabdacabbbccdcbbddccbdcaccaabdbddbbabbbabacbcadbcdbaabcaddcbddaabbddbbbadbdcaaaaabcabdccaaaabadddaaddacacdcdbbacaabcdbbbcdccdddabbbdbdabcdaddaddbccacdadccbdddbbcaaabdbbdbddbdcadcdabadbccadddcabccbccbbdcaaacbabdacbbabbddbbbdbcbdbbcdacdadcccccdcddaddcacccbdbaddcaaccbbddcaabdaccccbbacdadaacaabcdbbdddadaaccabbbdcbabcacabddcdacdddaacaabbbcddcabcaaacbbccbbadbcbcadacbaccdcabaddaadbbcdbbbbbcbbbdcbdddbbddbcdbcdbabbdbbababcacacbddabdccdbccadbabdcbbacdbadcbaacbcaabddbddccbcadadbacbadbbbbdaddabdadbcaababdcdcadcdbcdcdcadbdacacdaccddcddabcdcacabbadccadaadbcbdbaacabbbacdcbdcaaaaacbabcbbdbdcacbadbcabbbcbbbabdabbacbacdaacdcdbcdcacadbaadcbbdadbaababdabdbdbbcccbcccdaacadbdccaccccabccbdaabcdbdbdbbbbbcaadcdabbdbbabdcdcbdadadbdacabaaabdaddddbadcbddbcbcdabccaadcdcccaacbddddccdcbdbdbccbacaaaccdddbdacbaddbdcabacbabadacdbccabdabbdbacdaddccbccabdaaadaddabbcabbbadaacccbbbbabacddcdbabbacbdcbadccddcddbaddcacdbabddbaaaaabbaabbaaaaadccbccdbbadcdaababbdbdddcbccabbadbdbabcddddcbacdcacbbaccdabbcdcaabcabbcdacccbadbbbbbaddcdaacadbbaccacccbbdcdcdbbdbdbdadddbaacccbccacbddbdbaaacbdddcbbcbabccaaaabbbbaddaadbddaaacbcbdacbdbbdbdbcbdaadcccabddbaddccdacddcabbaacbdbabbddddacbcdccabcccababaaaddbbdabccdaadccdcdbdcccaaacbddabbdddddbacacacddcdbadddbbcdcdabcddbcadaacddddcabdddbbcbcbaccdcacbbdbcacccacddccbccadaadbcbcabcbdcbaaaabbaaacbdccbddcccccccbcaaccccddcdcacdccdbbaddaadbdddbbabdcdcadcdbdccaaaabdccadadcdbccacbbdcbcdabacacaddbabbaaccdcaacacaacccbbabaddccdbabcbdcdcccccdadcaadcadccababccdaaddbdcbcccdcbdcdbaccddbcadacbbacbbcaccbcdbdbdaddbbdccccacbaccccadacabacdcddaacadcdcacababcbdcacdacabbbbaaacbdacabdcdbcbccbbcdcaddddbcdbacaaacaaccadcbbcdabdcdabccccbcbcacbcadcaaaadddddddbdaabaddcbdbdcabbdbabaacbbdcabdbccacbabadbacdcaacddcdddadcdbadbadcdccaddacaddbbadaabcbcccbbacbacaadaacaaadadbcccaacbdddcabacdacaccbbdaabaaaaaccbbccdaddbbcaacddccdbacabaadbcadbadbdbbdacccccaaddacdabbabaddaabcadadacadcdbabbdbbcadadacdcdcaabccaaabbddcdbcddbbbadabacdaccdcdcdadcdcbccccabbcddaacbaccbacccaabcdbccdacabcbcaabbbdbadadbabadadbbabcdbaabcddbcbbabaddacddbadadcdcbcacbcbcbdcaccdbbcbbdababbdacbccdbdaccbdbadccadbcadadccbbdbdcbacdabdabaadcaccaccddcaabaadaabbacdbdcaadbabbbaacbadcddabacbdcbccbbcbcdaaacdcdcbdcdbabdaccbadbddcbbccabbdbdcdbdbadadccadcdcdcdbacacacbbadbdabaaaccaaccbaadadbadbabdbcabddbadcaaadaabdbbbccbabcabdadcacaadcbacaaaccbcacdcdbccadddcccbcdbbbbbddaddbbdbbbcdcbdbabbddcdcddccbbccabdbbddbacbbdaaaabcbdbadbbbadbdbabacbaaaacddbaacbbbcabdcaabadcddaadbcaaadcbabcbadcbdacdcbbadabbdcbdaaadbaaabbbddddacdbcddcadadadacbdcddcdcdcabdccabaadccdcaccdadadacddaccabadacabbcaaacbdcddcacabadbabbcacbbaadbabaccddddcdbdbcaddacaadbbbdaaccdaccaddbdcdcabcbccacbcaadcddbdaddbbdabcbbaddddcdacaaabcabddcbaaaabacacadbbbcaadbdbccacaaadddcdcbbccabbbabbdadabadcaccdddadbbccbcaddaddbbdddaacdccacabadbbcadbadadbbbcbcdbbcccbcadcadcaabadadacbaddbdadcdcbacdddbddbacabbdabbcabadabadadcdcbaaacabdabadadbbbbcbccccbdcdddcdadbbdcbbcaadaacaccbbbdbbccbbbbcadaacbbbcbddbbbcadcbdaacdaaabacccdcdaaccdacaaacbaacddbdbdbabbddabcbbadbcdcaabbbbbabddcdaacccdacacccbccbbaabccaaaabdbbddbbbbdbabbacaccbbddbdbdadacbcaddcbbccbabbaaaccdddcacdcaaaabbbcdacbcadccaccbdaadbabccdcbbadddcccabbbcddccabcccbcabbccbbdbcdcabcbccadacbabcddabadbbccddaabddccabddaccdcccacbccaaaacabbaddbcdbadcdddcbbdbcaacbbbdcddaabbbcdbddabaddcbadbdbbaccaaadcacddcbbabdcbcbbbcdaccdacccadabbabcabaaadbbbcaacbadbbabbdaadbdcaaabdaccddadcccdcdadcdbddccbadddcdccbddaacdadddabbdcabaacaaaddccbccacbbdbaddabbbdddbbccbadacbdcccabacccdcadaccbacadddcabbcbddabcacbcccddabacdccdbadccbdbdadbdcdacabbcadccabbaabddcbcddbcabbbabbcbcacbbdbabcabcaddacadcaabaaaaccacbbdccccbccbbdbbdcaddaabbbccacbdacccdabcbdbbaccacccabbdacadbabcbaddacddbdcaacbcadccbadabdddcddcabadcbcdddcacaaacdbbaabcaccdcadbccdddccdabbcacaadadbcacaabbbbadaacabbbdbaccdaddcdacbabdbcbcdbccabaabcbdcdcdbbddcbdacbddddabcdbacadcbdcacdcaabaccddabcacdbdaacdddcbbaabccbbbcbaabccbbbddcadcdcacdcbbdbbcbcbbbdccbccbabdaaaaaabdaddaddbdbaaccdbaacdbabbcbaaccbadcaacaadbddaabdbbcbcabbddabadbbacccddbddcdcaddbdcdcdcabcbbdacccbcdaabdabcddadddddbcacaaabdbbcabbdcabacababdddacbbadcacacdcbbdcdbacdccbbdddcacdbcabdddbabcddccbccbcccabbbddbadbdbddddaadbaddccbaaddccbbababacadbcbbdbddbaccabcdddcccacacbadbabbbaacbbcdababcacbdbcaccacbdddcdcbcdaadbacccbcbacadddaabddddcadabbdbccdbabadaadcdabbdbaccdbdcddbaadbbaabccacabaabbadbccdcdcbcdbbbdcddbdcdcddbcdccdadbbdccbbdccdcaacdbbabadbcbdaddaddcaaadacddcddabcbdbbdcaccdbcdcbcadcbbaaaaacacabacadadccabcbaddbcdaddbccaccdddcaacdabcaddcddbcabcbbaabbaadcacabbddbacdcdaacaaabadcbbcbcdbcbabcaabcacbbbcbaabdcaacbacdcaccdabcdacbddbdbadccadadddcdcbcdaccdbcaadbaddddcadddacdccbbbccacabbadaccacdadcdbddbaddcbcabcbccdbabdcdbdcdadbaacdcddcdcdadaaacccbcdcadbbdbccdaaddacabdddaaaaaddadadbcabcaaacbabdaaabaacbddaccbcdcaaaccbacccdbbdabbbbcccacddcbcdadcacabdbbbbcdcacddaaabaacdcadaacabbacaaaadadbadacbcccddbcbbcbdaaccddbacbddcccaccccdabcdadbdaaaddabaaacaaccbdabbdbcadadaddbccdcdbcbbaacaaabdaaabaadabdccbdcaaaadccbccbdbbabbacdadddcbdbbbacbdddddacbbacacaadacdcbdacbabbbcacbbacacdcbabdcdaabbbbaacabcdccbdbdbdacdcdadbbdccbdbaabadbcdddbbcadbddabcacacdbaddaddcdadbcaaaadcdabaabdadcabadbbcaabbadadadaaaabbaaaadcabdabadbbddaaabbdaaabdddbcddccddcbcbdbbdacbcbaacbccaadcbddaadddcabdcabacddadcbdaccbcdaabbcaaacddaddcaccacccddbdbdcbbcbaaabbdacbcadcdaccaaadccddbdbddbcadadaacdcddbdadccdaaabbadcaacacacbbadbdddcbddccdccddadcbbbdacdabccdacdccabcbdcdcddcaaacadadaabaaaddabdaccdbcccbabaabbdbcdbaaacddabdbdacabdaabaacbcbcaccdbcdcdbcdcaacbaabbaadadbdbabaccdcaccbacbaabbbabccbcdabadadbccddccdaccbdcbdbdddbdadcdadabbabddbbbdaddacbbcabdccaabbccbbccbdddccabdcbbcdccdccacbadaaabdbcdacbadbbacbcadbdcccdddabcabbbdcaaccddbcacdbcddaaaadaddccaadbacbddcdbbdaaddbbabbccdbbcbaaacbaabccacabdcccbcbddacdabbadaaccddcabddabbcdddadcbbbdacdcbaacccdccbdddccccadadadaccaadbbddaaddcdcadcdaabbcdccdbaabccbbdbcddbbcddcbcdcacbcadddcdcbdccaacabcdddcbdcdbadacbbdacddbccdaadbadcadcacadabcadcdbbbadbbcdbcddcdcddcbccbddbaddcacdbcacddbbbccdadbcbbdddacdaadbcbdadcabbbbbdcdbdbbdbcddddccbabddcaaaaaaaaaabaaabdbadabdccbcabcdcbcbadddadcccddcadaabdbcccbbbadadabcaaddcddabbdcbaacbbaadcdcbacddccdcbbddaadaccbbaabadcdcccbabdbbbcdcbdbcbddddcabdcbbbacccabbabacadbbcddddcadbcbaddaaccbcbbbddcbcdbaacbdbadadbacbbadabcddcbcbcabaabdcdcbdadaabcdbbbcdcaadbaabdcaabadaaabbcdbdcbaacaadcbcccdddbadcbdadabdcddcdcbbdaabadbbddadabbaddadadcbbbddbaadcdcdabccbcadccbbddcbdbcdacdaabdccccaddabaabcddccddabadcddddcdccacabddadbaccadabdccdaccbbbabababdaabdbddbcccddcbcabbbaccaaddcccaaabdbbdcdbabbcdcbbcbccbcacaabdaadddbacbcbbdbddbabddabdbacbabddcdcdbdbbbaabbccaaaaaaadcacaadacbbdcaddbcdcabdcbdbaddabacdcbaadaadaaccbdddcabbbcabcbcbcbbbddcddbcbddbcddbdbbaacbcadcaaccababcadacaccdbbcccdcdbbddbbdcbaadddddbacacbdacbbccccbcbddaadbababdcaababaddcbdabdbcbaccccaccccbdbcadbdadaabdaaccdaabcbbcdcccddbbcadbcbccdabcdccddddcbabccaaaacbaddcdbaadbacbcdbcbbdadcabbacaaacccbddadadababaabcacabcbcaadbcbdcdbdaaccdaddbdcaddbdbccbcaabcdccbcdabaaaddcabdaaabacbbbccbcacdcbabddbcacababcbdbbdbccbddccadcdccdcadaaadbcbababbbcaaddadccacdcadcbbbdbdcadadaadccadccdbddacabddbabbdbcbcdbcadacbaccadcdcbcadbbbaabbcdddacbaaabdbcdcdacaadadaabbcaabdcbaccdbdccaacbbcbacbaacaadbabcaabdcdcababbcdadcaddaccbbaabaabacaacbbdbdabacbcaacaadccabadcdbddbaadcddbbddddaadccbcdcabbbccdabcadddabadbdaccbbadccaccbcdabcdcacadacdbaddaaccbacdddcacdcacbbcbdabccaaccbadadddcbdacaacbbcdaccacabcdcadcdbcadaacbbcaaadbbbbabcadcaabccdcacdcacadcacbaccbddadbcdccbccddccabbaaabbaddadababdddbdaadccbdcbaadcaacabbccacbcbcdbadcaccadabbabcddbbdadadaaadbcbccbbacdbcababcdbcbbdbcabbddcaabcaadabacbddbdaccbaccccccbccdcdadbaabcabbcbbadcaadbaccadcabadcccdccddbaccdbddcddcbbaddbbdccaaacbcaaaacbbbdadcacaadcbddcaddbdbddcbcabbacbddaadcddbbdbaadddcbcdbacbdabcacdaacadaabddacaaadcdbbacccbdddbaadccbdcdbdaacccbaaabdaabccbabacbbcccbdacbcccabddabccabcbcacbdacaccccabacbabcbcadcdaaabadabadcabdcdcdabbacdcdbbacbcccdacdbdcabcbccddacccbbcacadccdabcbdcddcbcaabbccccdacbcccbabadddacbbccccbcaabbccbcaadcdddcdbaacdbbcbcccdbacdaddadadddbbadbddbbdaadcadaadbabcaaccabbaacbddcbcaacdbabbcdcbdcdbbdddbcddccdbabbbcbbccbdccbabcbcdddaacdbddbddcccccbbbdcbbabacccababcdddccbcdccdbacbcdcdcbcccdadcdcdcacbdbacadaadabcdcbcbcaadbdcdddbbbbbbccaaccaaccbcadbdcaabdaaccdaccccdccacbacbcdcdddbbababbdbbcddbdbcbdccddbdddbcbabddcbcbdbbcadcddcadadadddbdadcacaaddbccaacadaddbbdaddadaccbaacbdabacaabbccdbcabbaaddbbdbdbbcddabaccaadbcccbcdccaddbabadbdabccdcdddbdbddabcaadbdbbcdbcabcccccbbccbdabbbaddccdbcdbbcdbbcbdcdccabdddcaccbadaccadacddbcddbadbbacaabbbbbccbdbaabddcadaccadabbabbdcbcbdccccccbdcdbbdcddcbbbadccacdcdcabbdadcabcbaddddddbcaccaaababbabcadbbcbdadcadcacdcbccdbddbbaddcdadbbbddacbbbaccdabadabbcdacbdabcaacaccdddabacbabdbaaacabdbdacababbbdaabbbdbacbbbddcdaddcbbaadcbadbacbbbaccdcacbbcbaacabbcdaabbabcbadcaabdbacbbbdddcdccbcdcabacbddbbdaabccccadabdabbbabacddbadcdcbbaaaaadbaaadcdadddaabcacbbdbdcdabcdbaaddcbaaaddbbcadabddabcbbabaccbbaddacbabdcccaaaadcccbadccdccdabacaadbdddddccaddbccdbacdcbaabdadaacababdbbdcdbadccaddcadacccbdaabdabcbbdaabaacccacbdbdccaadabcbcdccbaccbccbbacaabcadadcaacaacbcaabdcdcddccdcadbcbabcbacbccbaacdbcacdddccdaadbadcacacdabbdbcdaadbabbbaddabaaabbcdccddcbbcabcaabbacddcbdbbbbcabacbbacbcacccadcadbddbabcbccabdcdacbbcdacadadccbcbbbbdcaadbaadddabbdacbcabbbbdbbccccbbcbacabaaaabdbbdbbdcdcadbdddaadbdcaccaddbbaabdccaaadbbbbccccacddabcccdacddaddbbddacaadccbcdcaadcbdabdccbcdbabbddadcbddacadaaccdbdadcdbbbccbddacaacdabbbcbbaddbaddadadadcdabcaccdbaaccdbadcdcdcddacbbbabcbddccdcabdbdddbdaddbbabbbbaacccccdadcbadcddbbcccddabbbcbdadddcbbbdbccacaaaaaacbdddbdccaadcbaccccaadcdaaabacdaaacbbcabcaacbdddadddcadbaacaddacdaddaccadbcbcabdaacdacabcacbccbaadbacaadbcdabacababcbdccdabdbcdcdabacadcccddaabbacacddddacdaabbdbdbdcbbabddaaaddbaacacacdadcddbbacaaddbadaabddbdbacaabcddcbccddbddcbaaaaababdccdcabcbdaadadaccccdbacdcbbdaaddcdcaccaadcdbccacaccdccacbaaccadadccdbcababddbcbddaaabadddadaaabbccbbcdcbabaaccabccaaabbdcadcdadaacbbccbccbaacaadcbdbcddabdbcdbcccccaddabcaabdcbabbdbcadaabadadbcaaccbdddaabacbcbacbcdcbbcbbabcaabdbbbcbabdbddccbabdbdcaccdccaccccbbdbbbdccaddbdbdcbbdbcdacbccbadcdbbbacaaccbacadaadddcdabbddcadadcacabbcdacccdbdbcbdadbdcacbbaabdbcaaabcbdddcababcaaccddbbadacacdaadaccdadabdcdcdcdbcaacbaaddaabcacbadbcbdacbddbbbbdbdcbddaddbdbaddcdaddabbbbbdcccabbcababbababbaabcbdddbdcdcadaaacdbaaacbdbdbcbbbbdddccbccccddbbbacddaaacabacddccdadbdbcbacaddaccacddbbbcbbcddabadcabcabadcccaadaabdbabbdbaaddcaadcbccdbdcbbbdadacacbbcdbbbccabdbcbdaaaaccababdcdbcabdadcacbacbcababbaaccacacccadbadcdaacdadddbadbcadaaacbaaadaaccacaaabdbdcdaccbdddbadccdcdcdaddbbbadbcdbbbadadcaabcacdadacbcaababdcddbcdcdbcaccacaccaadbdbcabbbbbbdddaabdcbccaaaacdbdcaacccddaaaaadaccacaabcaaccdaadbdbcbcadbaccbcbabdabbbbbbbdbbaaacabadccacaadbdddddabadddcaaabbabbdddddcaddbacbbbacbdacbcbacdaabccdcdddabbbadaddcbacdcdddbcdbdddabcacdaaaabcacaadabddbdacddaddbbccbababadbcdcbbdcdccdabacccdddacacbacbcabadacdbcbbcacdaacbbdadddcdbbdbaccaddbcdccababbcccdbddacdabaccaabbdaadbbadddaacabadbdaddaacdcaddbaddcdbadcddaababcacdcbcdcccabdbbbbadbcdbdbabdbccbccbcdaddcccbdddacdaabbabbdabacdccaddcbabcdbbdaaaadcaabbcaddcbaaddbaabadcbacdbddcccbddcbacbcbcdcbcbcccabcbcaddccbbbcdcabdbbbddcaacabaaccccbccbabcaacddbdbaabcbadcdbabdcacacbbcababccbadcaaccccdccdaaadcbdbdadbdcbdbaccadbccdadbbadccbdcabcbddcaacccabbdcabbaacddadccacacadcabadcaadaaaccccdccbcdcacdcdcbbcaccbacacadabacdbccbddbbadaabaadacabdbbadabdcabcdccdddcacbddbaadcbdadbdcdbbcdbdbadbcbdcddacbddcbbacaaadddcaccbabadbbbbcbadbadaabdbcaacbdabddcccdbbababcaacccabcddcbccbcdaddabdabccabbcaabbdaadacabcacdbcbaddbdbbdcbcdaaccddbabdcbcacccdcacbdbaabcaabadbabcacadaccbdbddbcadbaaacdacdabccdaadcadcbadcaccddabcbddbbdbddacaacabdcdacdacdcabdabdbabbbadcacdcdbacbddbcadbbabddddaabcacbdabddbddddddbacadadaacbcacbabbadbdcdbadacdbbadbcbcadccbdaaacbbbdbdccbddaaaadaabdbacabaabccabccdacbadddcdabaabdaddababacacddbdaaadcbcddddcaabcdcaddbdbdbaabdcadccacdbdbdbdcbdcbbbacdcddbaaaaacdcacdddabcadbabbcdbabbbcadcdbabcacdabadcbdbcbaabccdcbdcdbcbcabbddacdbdcdddbaabaddabdaadacccdccbdddcdbbababddadaaaacaaacdcdacddadaadbcbaacadddacaaacaccccdddadaaddcbbcbccddddacbbddadccdacdccbcdabcbcbabcddadbcacabbbbbaaaadaddbcaadcacdcaddabaacbbccadccdccbbdcbdaabcccbcccaaccbaccadbcdcabdacdbbaccdbbcacddcacdacaacaaacbadcaddabaabcbdabbccacdbcbbdbcbbacdccaddbcacbaabbdccbccddbcaddaabacddbcdbbbadcaccbbbbcddaadacabcaaabcdabbcdabcbccbdabcacadbcaacbdcbcbdacbcdadacbbadabacdbacddacdcddbacdacdcddbdcdcddaccccaadbccacabadbdbdcbbadbbcdcadaacdbbdbbadcaabdcccdcbdabdabdcacdbbccaccabcddcccdaacaababacacadaadcbddabadbbadddbcdbabcdadbdaccdcccbcbdadbcadcddadabbbcbbcdbbabbabcbcbacaddddddbaaadadacacabbddaddcacdbbbdbcdcabcaabdabdddaccbaadaaaccccdbaddadadbcbdcdaaadbdcdcddcddcdacbbdcddacccccbcdcacadcbbbaccdcacdcdbbbaacdbcdcaadcbcbdddabcccddcaacabbdabbabacbbaddacaabbdbabacccbbddbdbadbcccdbdccdabbdddddccbcdcacdbaabdcdcbdddddaaccadcdbacdbadcbcddbacdddcaddccddcbddddbcdcdbcaaddddadbdddbdbddcbaaadddbcccdbddcaccdddbdcdacbdddbaaaabbacdcbbaadabadbdddbdbcbdbcdcdccadbbdabdddaadcadcabacadaacacddaacccbbabdacdccabadabdaddbacddcaacbbdbbcacaadcbccdddcadcddcccdddccabadacdaddcdbddcabadacbaddcaaaccdabddcacdbdcddbbccbcbdcbdcacaddbcbbbdaabddbdbddaabaabccbcabccabdbbbdcdddbbbbcddcaccbaadbacbdaccbccadabbadbddcabcabaababbcccdcbababdbccbaacbdcdaacaccabacaaabddbbbaadaadacaaabdbdadcddccbdbdbacabccaadbadbcdaddccccccaacabbcccabcadcdbcccdcdacabbdbadadbacdcdddbbbabdabaadabbddddacaaabdcacacbbabdabccaaaabcadbcaacbdcdddabadbbccbacbbdbbdbcadddcdbaacbbaddaaccbcabdbcaaabbccaadabbcbddacccdcdcadcaccbccdcdaacbabacacdbbcbaacaccbaccacadbcbaabacdcabaaaaccdddacbbccdadcdbacbdddbccbcabdbbabaaccdabccbccadbacdadddadbddaadcdbccbcbacacdcbbbdabaadcabbbbdbbcbddcabccdcadaabbccddddcddbaadbcccddccbacabadccaabdcbdcacbdddaccdbbaaabcbbbacddbbbdbcadcdcabbcdadacbbdadcadcdaaacbcdcccdaabbbddddbdcaccadbdcdbbddcbddccdbcadaddaadbabaddacbdacbbadacddcdbbadadaacbbdadddabcdcaabbadbbbbbcddaadaadacadabcacbdaaccbdcbdddacdcbabcabcbcbbdadaadacdbabaaccbadccbcdddaaaabccacccbcdddccbadbbbcccbcddddbbadbbaabdcadbbacbddbdcdabbdcbccccdddcbddcdccadaaaacdacddcadcdabaabcaacbbbcbbcdaccdbbadbdddacadbbaddcadbaacaacadbdcbaaabcdcbcdbbddaaacbddaaccadcdaddcabdddbbddadccdcccadbccdabadbbbddcdbdabdbabdbbcddacccddadddbbdabdcbadddcdcaccbccbdbbcddcaabccaabdbdbbadabcaddadcbbbddbccddcadacabbacbccbaccbabaccbcaaccbdcacdddbbbcdbccdbaadadaaadbbcbacacddccbadabaabdaaabaacdbbdbbdabbbbacadccdabadcaccaaaabcaaacbddadcdcbdbbdcdddbdbacaccbcaadbabdaacccdcbaddddcbaaccbddbaccdaadbddbaccacdccaddbaccddbdcddbaabdcbbbcacccbdadbccdadcccabcccbdcadbbdacdadaaccdccbbaaabcddbcbabdcdbdcabdbbbddcabdcabbbcacdcdcadabddcdbdadcccdcaaababbbdbcdbabcabbdaaaccbbccbacddcbdbcbdabacacddbbdadbcbdcaddccbdacdacbddccacbacccbadaabbbcbacdbbbabbcdcaabddbdaddadadbdcbcccaccccdcbdcabcbbdacbddbbbbbdbaddaccdccaadbdcbddcaabbbdbbddbaabbaddddaabbcabcdbbdadddaccbbcdbaabdaaaadbaddbdbaccdbdadcbcadcbbabcdcbabbbdddbcccdcdcccbacdcabccdbdcbdddadcdbabddbadaadccbadbcccdabbbdabbcbcadcabdaaabadbcdacadadccabaaadacbdcbdcbccccdddacbbcabddacdbcbabcbacbdacaccaacaadddcaccbcdabacaccdaddbcabbcdacdbacddcdddbcddbdaddbbdadccbaddddccbbdbbbbbbddcdcdcaaadabacdddcaabbbacbbdccbbbcabdcdccbccbcabddbacbbbcdaabdbcacccadbcbdbbdcbacdddbadbacaddccabaabaadcacdbdaabacdbbddcabcbaabcdabbccadaabdcddaabacdddbbddbdbaaabbabbdbabdbbcdbbdbbccdabbbbaacadadadbcbccccdcbbbccbccaacabbdcdcbccdcbdbdaccdbaaaadbdddcbcccbacbddacacaadcbaabcadcdbadaddcccaadadbcabdbdcdddcacbadaaaabacbdacacaabcbdcabcbbaadabbbdbbbdacadccaabcdadddacbcdbcdbbdadacccddbdddacccddcbbccdddcbadccddcbbcabdbcbcbdbbdabacacaddcddccabcacaddddcbdacbcdbacdadcbdcbcdddcbbaabdacabacddbcabacbdcaabdcaaaaddbdaaddabcddcbcdcdbdacdddadcacdadbbadadaaabdbcacaaddaccdbbdcaabbbaacbddcbacaabbdaaacabbabcadbddabbadbaaaabacbddabdbbbcccaaddcdacbccadbdccccaaabcbdbbaadddacabbabcbbcdcbbcdaaaaabadbacccbcaadccdbbdcbdbcdabaaddcacacdadbbadababaabccdddacccaacbaaaadabdabcdccbcbcbacbabbaddbcddcbbbcabdddcbaddbcddcccbbcdcbaaccccdbdaadbbbcdabaddbbbacdbbaddccdbadcdcccdaddcaabbabbdbcabaccaadacaccbdabcccaccabcbaaccbacbddbdadadcbdddacdbbbddaaddccbbdcdaccdbadbddbbccbbbaabaacdbbcdcddccacadbdbbbdcdaabcdacbaacaaccaccbdcadbababdbcabdbaccbbaccaaaccacccdbcdcccdabbbccdcdddabaaaababdbccccacacbcaacabacabbbbccaccbacababdddcbacbabccabddcbbadbdaddaccacbcdbbcdcbcbbbdbbcadddbbcccbddaccdcdbdacacabacccbcadbdbbbadacbabdbdbcadbbccadacdbaddbcaccddaddcdcaacbdddabdcacadadcbccababcddcabacadaadbaabcdcadcacbcccbcadccbdbaadcaccaaabadcbaddcbcccbccbdcbdabdadbaabcadadcdaaaaaadabbbbdabcacdabbcbcbacccdbacdbabaabacabdbcbaadbadaacacacddcbdadbccbabcbccbabddcbcacdacbbdadbcdddbcccdbccabbaaacabcccdacabbdcacbbddacacacaddabaacdcccdabadcaaddcbabbccdbbacdbbbcadaadccdbaddcdcdcaaacdbbbbcacacbdddcaadabacccddcddaaabbcbbbdcccdccccbacbcbbddcabbaccbbccbbdcdbcdacbdccbcbbdcaadacbbdbcccacdbcccbcbbbaabbbabcccbdadbacdbcdaddcbabcaccddbacaddaabdccbabbddccbdcdddbbaccbddabadbbbddadccccacdbddbdbcddccbadcccadbabcdbaccdddaaacddcbbbdcdcccdddcadcbadaccadcaaaabbdccbdabbabdbbdcabbbddbcccccabacbddcaaabaaaddabaadcbcabbdabbddcccdaddddbccbdddbaacacddcabdaabbdadcbddbdbdcccabbacdbbdcbdcddadbbdaabaaaadbdbdbbabaccadbcbbcbdccaacdcbcaccdabbdbcbcdbbaaaaadaadcbdacddbcbbdbacddcbbddddbbdacabaaacacccadaddaaaddbddcacddcdbacccabbddbdcbbcccbcbccadddabcdabaabcccccbcdcbcbabacbdaabccdabaccabaacadccddcccbbacbbbcbcbcabccdcbdcacbcabaccbbdadcdacbdaaacbccacaabdaddbcdcaccddbaddcddaaccbcbddcacabacabaadbbcbaabddcddabbdcbcddabbccdccddacbcbddaabdbdadccdbdaabcbdabcbaadbcdbbacddccdcbddcaabcaacbbbaadabddababcdabdbcbcbbbcbabccdbdcaccadabccabbdaccdccbcbddcdbabccdccadcdbccbbdbabbcbbddbababbdabcbddaabdaccbcddcbdbacdaaddbdbabaadacabacbdadadccbcaadcddbbcccddbbdddadcdcbdcbcacadbdbdcdcaacacbcabaadddaddcbccdcbbdbbccbadbbbcccbdbcccabcdaddabccbabaaadbbadddaddbccbdaccccdadadbbbcaabadbdbabbdadadbdabaacdabccaabdbadcbccacbaabccdcaddbabadcdccaadbcaacdaddaccdcddbacbdbdbcaccabcabbabaabcacccbcdcbcdcdaabcbcadcbdaaaccaddbaaccbcbcdabdcdaacdddbcbabbcadadaaadbacbdbdcdbddadaacdbbabbaaacaaadacbcbaaddaacbcdabdacabbddccbcaacdcbdbbbdcabacddcdbbaaccdddacbcddabcdbaacaccbaddcbccdcaacabbddadbcbbdbbcbaaabaaacabcbdaabdbdbbccbbabbbabcddacaabdcabadbcdadcddcdbacbadcddacbdacbabbcbacbdbbaabcddddaacbdaccaacabcbadabbbcdcabccbbbdbcccdbacaabacdadddacdcbacbabacddbddbbcdaabddccbacadbbdbdabdcbdaacbcbcbbccdaacdacbccbdadbaadbbcadacdabdadcadacaaaabbcdbcbdabaccabadabcccacbabaadbabcabdaaabaddbcdadadbcdbadcdadacadcdbacdbccdbcdbbbabaabaadbaabacdcabcbcbbcbaabddccdcbcdbacdabbccadabcccbbcacdcaacdadcbcbbababdaaabdabcdccdbdcbdddbacadbdddbcadccabbbacbbaddbbdacccaaabbdcdbdddbaadcccdbcbdabccbaabacbcbcdcabbcbddbccddbbdbccbcbaaccadbdababdcaddaacdacccddadacbcddabaabcbcddadacdaccadacbdacdaaacacbacadcbdbcbaadcccbdbadddcbbdcadcddaaccdbdbadcbaccdbadacddbdccddddcacccbbcbababdabaabdacbbbdccadaadcdbbaddcdacccadcccacaabbcabdabacccdabcadaccbdcaacadddadaababbcbaccaddbdbccbddacbddbdbaddcbddacaccadbcabdbbaaabaddaddaabcccdcbccbcacbbdaccbaacbdaccabdbccadcbcacbcbdccbbcdcbcdabccbcddcbaaadabadddbdccabdaaacaddcbdcbdccabdbdaaadcbdbddacbddccbccacdbcdbaddddbcadcddbaaaaaccdcadbdcbddacdbbacbabdbaaaacbcbaacdbddccdbbbdbbbacbcdcdccabcaaabcaaabcacabaadcccadbdabcbbdbcadcdadbdcacdbaaabcdabbbcbadaaabcddcadcccbcabaddabdbabbbcbdcbbbaabaccdadbdccabacadaadddbbdbbdddcbcabcaaddbcaabcbdadaacadabbcadccacddcdbacdadbabadbadacaadacadcbcbccddddbbbbddbbccdbdbaacccdbaddaddadbabaadbdbacabaccdaabdaabdcabbbcbabbccccbcbdbccadbbacacadbcccaaacdbdaacbdddbaaaaccdcaadaacdadbdcadbbdbcacccbacdbbbbcabdcbddabddbdbcbaaaaabadaaddccdcdbdcadadbbadaacaddadbddcdbadbbbabacddabbddaccacbaabadabdadccdaaacbabaaadcddcabbddaccdbdbbddbcaaabdbcabcbbadabbabacddbbbcbbcbabcabbabbdcdabdddaaaabdcaddacaddadbbaaacccadcddaaabbcdcbddbaacabbabbbacbcbbaccaabcbadbdcbbccdcbddcbcbcadadaabdbbadccbabcbacdbadcbbddaadddccbadbcdbcabdacabadcccdcbaccbcbaacddddddddcdcbddbccaacbbcabcababddcacbcadbadacabdaddaadacbccacacdacddcdacaaacabadccccdadcbbbaddccbaadbabbbcbcbccabcbaaccdadaadccccacccabbdacabbcdaccbdccbadcdcaaccdaaddcabdcbdaaacbbcddcdddbcbabdadbaaaacdbacadbcddaddcdcdadbaaacdccaacbbcdcdacbdddadbcbbabccdbdbcdcdcdccbbaadbcdacddbabdcaddcdabbddaacdbaccadbdccbaadcaabbddbbdcaaddccdacbadbcbcabbbbcaadbdbbbcabddcbcabbdddcaacaccbdbdbbcbcdacabbdadddbaccbacddbdacccdadcdccbdbcabdbcbaabaddadabcbcdccbdbdbcaacabbdacadccdaadbaadbcbabacaacabccacabcddbacbcabccddabccaddbccbacdbacbaabaddcbdaddadcddbcccbbacccdccaaabccddcabcabcbdcdcdaddcacddccaddaacdacdccdabbcabbcdcbbaaccdcaabcaacccbadbabcbbdbcaadbdddabadacddbbadddbdbdbcdbabddcdbdbabacbcddbabcddadbcbacdddadbddddbbbbcdbbdbccbabcabbcadbabaadaddbcbabdcccdddbcbaddcbdbbaaaddcdbdabcbaadcbabaddccbbaddadcddccbbabccddbaaccacacddabbbcbbcbaccabcdacadcdbcacdacbaabdaabaadcaacdbdbcadbaaccdcbdbddcccdabccdabadcbabbcbdccdbccbbabdbcbbdbacccadabddbbcdbdaadaacccadbaadbabadabcdbacddaaaacbdaccacccacaccadbcccdaddccbcadbcdaddbdbbbcccabacbccdddbadbbbacdcbadbdcadbdbaabdcdbdccdbabbbdabddabacaaaaabaddbccaaddcdacccbdcabdcaabbdbdaabbdbccadbbcddcadadbdaabbcccbaacaacacbccabbddadcabdddaabccdadbbaabddababacdababbccbacbacbdcccbbddadbaabbbaacaaddbaaccabcaadaaacbdbcadaaabcbbabdbcbacbbabcacadbdcdddbaddddabacccdabdcabcdabcdcbaacbcbcbcaddaacadcddacbbdccdadabbccddcbbabcabbdcdababcdddcbadbbdbabdddbdcadbcdcacadcacdcacbbabacbcaaadbdaadbdccdcaacdaaaaadcccbbcbbaccdbdccaaaabcddcdcbdabcacacdcbbccacaabcdacddcdbdbddcbcbdbccacddbabdccadcabaccacbababdcbdbbcbcdcaacdacadbaccacabbccaccdcbbdbbbacbcbacbdbcdbdabdadaaadaccdbbbdaaadcbbbdcabbddadddaabaaaaabbbdccdadbbccacbaacdcddacdabbaacadcaacbbadadcbbcdcdacbddadbaaaaaacccdbdbdacdaaccbbdbaddbcacaccaacbbcabaadacabcaabcbabaccbcbadddbdbddcbaadddcccdbccbaacddcaaacadddbcdbdacbacccadddbddbaccaaacdabcddadcddbcdacbbdcbbbdbdccdcbbcdbcbadbbbbabaabbaddcbaaaddadddcabbcbadadaddbcbcdcccbcbcbcdcdccddccbcdacaadccccadcabacbaaadbbcbdcacddbdbababdcdccabccbddadabcdbacbacadbcdacbdcdbbdabcbdacdbbabddcbadabccdacdabccbabadcddcdadaabaabbbabdbdadabdcdacdaacabbdabbbcdddbcddccbadaabcabaadcaabddaccadcbcdccdabbdadbbabcbbadccaabbdbdababaadccbdccabcacbadbaabadaaadcdbbdbacddbddcbbaabcadabcaccbdccbadcacaacbccccbcadaaabdddbbdcbbacdbdabcccabbaacabdaaccdcbbdddbaabbcabbcbacadadbbccbdccbdcbccdcccabdccadadcadacaabbaaaaacdbadcbdaacacabadbcccdbabccdaabbbbcbbdacdddddbbbbbbcdbbddacdacbcacadbcdaaadbdcbccbdcccaaacabbbcdaaaacbbcdabbcccaccbbacbccaabbdacdabadababcbddcdccaaccdbcbdaaabadbddbbaaabbbddddacbdaadccdcaadcdabbcdbdccbdacdaabddaddbacbbaaadcbaaabcaddaadadbdacbbacbbdccaccabadcdbcacaddacacdcbbdcdbdcbcbdbcdacbadcbdbbbcdddacacdcdbcccdaaacddbdbddabcbcbaacaacdabbbdcdcdaaccdbddcddcacbbcdadbddaccabbcdaccdbacbabcadcbdcbbabcdbcacdbcdbdbadcaaababdbbbadbaccbbbbdcdbacabbddbcbdcbdcdabacacadbdccccccdacbaadabddaddbdbadbacacdaaadbadbbddacaaaaacddaddccdbabadcdbdbabacdaacbbdabcaabcdaacbddaaadbcdacbabdaaaddcdacabadbcaddaabbddcccdcadbbabbdbbacaddcdcadccadcbaabddcaddcbcdcddbdcbaabdbacbcadcdcddcccdddaccddcbddbdbabcbaadabddadcbcbbddaacbccabddccbacddacadcdbbcdabababdcabdcdbabbbbcbaccbbbdaabcdadabcdbdcaabbabdbdbabbccbdbadccccacaadbababcbddbacadaabdacdbcddaabbaacaacccdacddcabbabccddaaaddddbbdbacccbbdbcaacbbddaacdcacbbddcaabadacbaccdadbbadaddcdaaddbcbdaddaabaaccbbacbacbbcdddddacdaabaaabaadabbabdbdacacbbabcaaacddbcaadccbbcbaaababadacdbabcbadabbdaddaddacaddcadddacacccbbdbcccdcbbbcbdbddacdbabcdbddbcdadbbcdcabcddcdbaacaacadadadadccbdcddbadcbacaaccabaadabbbcbddcaddaadabbaabdbbaccdbabacdbcddddbdddaadbdbdddabdcabcbcaddbbdbbdcddcdaddddcbabdbaccbaababbdbdadcdbbdcabaadbadbbacdbaccacadbccbddddccbcbdddacacddbdbabbbdaadcbdddcacdbccdcaadbcbcddcdacdbdbbdaacbccccbbadcaacddacddddccabcbabdccdadabdbbcaabaadaddcababbdddbaccbacadabbcacdddbabbdadacddbccbaccddcdadbbaabbbddcadcbdbacdbadacdbadbaabbcbbbbcccbbbbcbaabbdcaddadcdbdcdcbabdcbbbacdadbbaabdbccddddbadcadbccdcaccdbacbcadacdcadcbdbabdbbaddaadacbacdddacabdacbdcdbacaacdadadcddaabcbabbccacbaccbabbdbcacccacdabbdcbbcacdccacdcaabcccdababddbbccabbbcdcccbabacaabbbadaaaadcbdbddbcbacdccaabbbdaacaacddadbabadcccaaacbbcbbcacdaadddcddadddddddbbabddddcadcbdcabdaddbbabbacddaccbdcaaabdcddcaacdbdbdbaacbadadcbddcaadcdaddbdccbcdbadbbcbacdddcddaacaccdbaccbcbdabaacbbabacdddadaaadbabaabcbcdbbadccaccbbcbaccdbabdadbdddcacccddacabaddbbcdabaabaadddbcacababcbdacadddaabbdbcccbdabdcaadababadabbcccacabbbbabdcbacbcadbbacacabdcaabaacdadaadacdcdddaaacccbadabadcbaaccdbbbbadcaaccbadddaadcdabaabbaacddaaccbacbacaccbccccacdbcbcddbdbaabdadaadbcdabbacadccaabbbcdaaabbcadacacbccaadaccdddccbbabddacccccaabcabbbbcccbbabbdacdbcbbaccadcacdccbdbbaadaaadcbacacccbbdcbaddbbcbbcdbacbaccadadadddccacccbddccdbcddabbdaabaadbbaadacaabbdccaacaacbdadadbdccdbccbabdcbdacbaaadbbacadaccdddcdabbbbacadcbbbadacbbcaaabacbaccbbccaddcbbdaabcabdcdacdcdaacabbccbaacbdcdbabdbdbbbddccabdbbcdbdbadadbadbdbbcdaddbdbdccaaccdaccbccbdabccddddaadcbbadabcddabaccaacdabaacdbbcdadacbcaaccadbbaaaadacacddadcbcddddcaccddcaaadcbdbbdacbbdcbadccbabbbbaaadcabcbdccccbbdacbdbaadddcdcdbccbcbcdacbcbdcbdbcdadaddcdbaacddbdadadcccbaccccbcccdbccaccddcabbddbcddbaacddddcabcbbdacdcbadadcbdadadbcbaaabcccbaadccbcdcabcccbaadbccbbdbccdcccdbcabacbadcadbbcaccdadcacbbaaddcccabcbddadcabccacbbcdccbcbddddcadabcadbdcabbabaadadadcdbbabddaacdcaacadbdaabdadbbddacadbabdddcdbddbaabddddbdbacabbcadbadaacccddcbdbdbbdbacbcdadcccdbababddcbcdaaaddcbadccbcbdddddbaaacbcacdcacbbcbacbbbbdbbabbdcaccabddcdabdbccbacbbddadadadabdabbbcbbbaaaadbdaaacdaadadcadddadbbbcbcacaadccdbbdaccaacdbbbdbbdccdbbacbaddcbdccadadcbbabbbddaccbdaddbdaaaabdbabdccdddbacacdcadbccdbbadadcdabdcbcbdbccdbabdaacaaabdbbadcbaddbcabbbadaadbccbcbadccadbbcdbacdadcdaacdddbaaaacaccadbcdcdccccbcacdbbabccbbdadbdcdbccdccbddcccaabacaabacabbccbbcccccbcabdaccdadcacaccaaacdbaaacacbabccbdcdbbdcbcdaabddacdbcdbcdccdacaddcddddacbbaacdbdbbcabdaddacbcbcccaadbabcddbbccaabbccdaaadcaaadabcadaaaddadaacdbbbaabbdcbcadaccdbcbcbbdbdbdcddccbaccddadccdcbaacabdabdbdcdddaabbdbadaddbbccdbaaacbddcdbdabacdbdacabdcacaadaacacdbdcbcdcdcbdbdbabaccccaacdabbacaddccacbbdadcdccbdaacddcacdabbbbcabaacaaccddccacaacbcbcdadbbccacdccdcdadcccdaddcaacababdcaddabaabdbccaadbddcbbbddcdbaabcaaacacbdbbaabaaadcbccbbcbbddabdabdbbdddbaddbbcbdaabbdddddddbbacbadadaccadbbadaabaaccadabadbcbbddbccbdcbbdcbdddaadabaccdbadddcbdadadcbcbaddacdbcbabadddbbbdcdcbbccbbaadcaaddcabbacbadacabddcaadcadcbabcbdcacdaddcabdaadaabdbdbcdaccabccbcbbbaccbadcdacbbbabaaacabcadbadbadaadacdcbbcaccdaaccbbdbdcdbddadadbcdcadcdbccacdcbbaccbbccdcbbddddbcaddaabcdbccabdbbadacbcdbbbddcdaccbbbcbdaaadddadbddcccccabbcadbdbbbabbacbcabbaadbbdcabcbdacdcbacdcdaccbddbcaddbbbdcaabadadbbbbcdcaddacdcbdddccdbbddcbdacbdadbcbdcccacabddabcadcdabcaadbdbacacbdbdadbaabbcdbacacaaacbaccbadaacbcbcddcabbbbbbacdccbccaaabaadcddbaaaaadcaacdcabbadcbbcbcdaaccbcaadddbbcaacacacbacdaacdbaaacaaccdbabdbbbcdcaabbcddddddccccddcdbccbaabdbdcdbdaadbcdacddbbdacbcbcdbccbcbadddbabcdaadbdddaacbbacbbddcdccdcdbadccdcabdabbbccaaaaadaddbbccbabcbadcbbbbbacdbdbbdbaaddaaadbddababacbaaaccbcbdbcdddcbbbbcaadcaaadaaaabdbbcdcbbbdbababcccbdcbdbaaacbaddbdccdaacccdbcccadbccadccabacdaabacacbcdacadbccabacbdbabccadccdaccdcbabbaacaabacacbbaccccdcdaaccaadccccabdbdbddcbcbdcdcccccacccbdddadbddcdabbcababdaabdcddcdcaadbbddadcacaccabaddcacbadbbcbacabbaacaccdccdaddbcbcabbdccddcdacbbccbcaaacabbbdaabadabdcabdbabcdabbabddbdadadbddccbbddaacacccabbbcdabadacddbbbdbdaccabbddddddcdbbcbabacadabbbabacadddbaddbdccbcccdbddcbbcdbcbbbbcadbaacdbadaadcbbaaccccdcaccacbccddbabcbdbadaddaccdddddbdbabacbacddabbbadcadbabdcbbbaabcbcadabbabcbbadaadcabacdddcdaabbcdbccaaadacdcddbdacdadccdbacbbcbcccccdaadabbdabadddcdacaddbbddabbcdcaaabbabbbcbabaaabcbadcabbbbcbcdddaaddabddbabdcacddddacbdbaabadcbccdbdbcdddcababcaadcdbcbdaccacbbbaadadbbacdbdcdcdbadcdaacdbaddadccbabccadbdabcacbababccbccbaaabdcadddcdbddbadcadbdabcbcadbbcbadbbabcaaadbdabdbdcbbcbdbaacaacaaacdbcddaccbcbabdcabdaaabbcadabbcdadabbbbddacdbddbabacbcaccababddcddbaddddaccaaadcccaacaaadbaadbbcbacbadaccbbccdaabcddaabadaacadcaacbbaddbddddddcbbcbacbabadaddabdddbbacbcbdaccbdaabccdbbcdcdacbbdcddabcddcccaaabdcbbdcaddaabbcdcdcdadccacadbddbbabaabbcdacbacbcabbdcbcabcccbbaaddcccaaccadccdbbddddcbccddaadbaacdadcabdbcbabcbbacbbcaccddadccccabbcbadcddcabdaadbbbcacdccadcbcaabcdcdbcbdbcacbcbdcabcdbaabaddaababbdddaabbdbaccdacbbaddcbbccaacdddbdbabdddbcbcdbcbcdbdbbdbddbcacdacddabcdadadcadacbdbddcabddcbcdcdaabbcbacdcbacdbdbbaadcddcdcccdaaadacbdbacacaaddcaaaabddcadaccbbadbdcaacbbabbadccaabbbacaddddacdcccbccaccadaccbbdbacbbcaabbcbccccaabdaddacacbcbdcaaccbdbbbbcabbbcbcbdbbdaabdbadbbaddcdbccddadcbadbacacccbdaabbbbadddbacddabdbbadbcdcdbbaabbaaaacccabdadabbcaddaadbdbdcabdbababcaaaacdbaacaddcadadddbabcabccdadadadbcdcdbcdadcbcdadabbddddbdcdaaaabcdcbbaacbaaccbababacbdcbabcbadbaabdaadadcbcaaccdcbdacdbacaadbbadccbcbcddaabcccbcdcdcbcbcddddbbccaabbaccbdbcbcbbcdcddaaccdbcdccaaacdaaddcaadcabddcbbbdddccbbcbcaccacbabbddbbbcbadaacbdadabacdccbcacdcabaacadbcacdacdabbdbcbcddcccddadbbcadaaadcdddbbddcabcaabadbdadbddbbdbdccdbbcadddbbbcdddcacaddbbbcdcaababacbcbbaaacaaddcdcdbbaadccabbbadcdaacdabaaddadcddcabdadbdcdadacaaaaacdcccadccabcddcccdaabbdbcbbadcbcdbcbddcbdabddadccaaabdbbbacdaaccdbadccddaccabddbdbdbcdbbbddddccdcabcdccbbabacbacbcccddbbbbbdddbbdcacbccdcbcabbdaabbdaaddddadcccadddaacdbbcbdcbddcadbbdacbbbcdbaddadcbbddbbbbacbcbdcabbbccacbddbbccdbdacacbcabacddcbdadbaddadddbdacbaacaccbaababdbaaacbabacdacabbadabbccadcaccbcaddaddacdbdcccadaaccdcacdbabaccabccaccacccbccadbaddadbdcdccccadadacbbbdaabbcdbcbcadbacbaacabdbbadadcacacccddabbbbcaadccbddbdbddabbccbcdbbcdcbbbbdbdabbaabcdaaabdaccbaaadddababadbabadcbcbccdcbdbdbcabdbdacabbacaacdcdaaabdcacdaacdddcbdbaabcdbbbadcccabdaabcccbbddcaaaccbabbadaadabbadddddddcdadaacbbccdbdcccabdbcbadcddbbaabbdbddabbacabaacbbdaaaccbadbbacdbcdbbdcbbbcdccbcadbacdbcacccbacddabadadcbaaddccbdbaacadbaccaccdbadabcadadadcbbcdaabadacdddbddaadccddbdadbbbdcacddacbaddabadbabdddaabdbdadaabcdddbbbdbcdaacdcbacdcdccbbcccddcbdaaaccdcbadacddbcccaaacadbdbbbcadbcccadddcbdddabaaacabbcabaadacadbdabddbdaacdcdbbddbdcddaacabccbcbccbdbacbcaddcdabbcddbbcbddccbbacdabbcacaddacdcdcabcddbcaddbbdcbaaadbdcccabcaabbbbbbdadcdbddbcdaddadbacdbbcbbabcdbabcdcddbcbcbdbddbbadcbddacdcbcdcdbdadbbdbbdcbdbbdbdbbcaadacbaabaddadcdccccbdcbbaabdbdabaaabcddbaddbbcaaadbacaabccddabacaabacaddbbccacacccacbbadbadabdabddbccbcbcddbabdbaddcccdcdabdbcbbcdadcdaddddbaddbacabbbdaacddcbbbdddaabccdbbdaadacaaccadcdacbbdbdbcaadbabbcabcccdddacddacbcbbdabdadcbaadddaacabdaaccdbbdacccdacbadacaaccadbdbbdddaabdcbcbbaddbacaccaddabdaacabbadcdcdccbcdaabbbbdabdabccadaaaccaddccaadddaacdddbadcaacdbdaaccbbcddbddbabdbabaaddbbdbbabbabaccacdddccbdbcdabbcaacbdbdaabcadadccdaacacaaaabddcabcddcbadbdabcbddcadbbcbdbdccddbdcbbbccbbbbccdbdabacbcdcaabdcbbccbbccddcaccddbabdddcbcdabbcbabccccdddcaacdcabbdbaaaacbccaacabccbcbdacdccdadaaccacabadddcaaabcccdcbbabbbbddadcdcdbdddddcddcabdbdbbacbcddbbacbcaaccabdbbadcadadbcccabbcbabbdadcdcbbdddcababdabcbbddcacbabbbabbdbcabaabacddcabcdcbcadbcaababdadccbcabcaacaaadddccabcddcadccbaadbcdadccdccbdccdddbabacdadcbcddbcdccdbdcdadcbbbcbccbbbaaadbbadccdcbdadbadadadbbddcaabddaadaadcbcdaadccbaddaacdaaccbcddddddacccbbbccdbaccbdcbdbcdbcbdccbbbababbbaaccdcdabdcccbdbaddaadcdcbccbdcddadddabbbbdcdcaccacdaacccabdadaccdccadbdbaccaabddbddddcccabcbdcddcbaabbdcacdcabdcaccdbbbdddddadbacadddabbbabbaacdcccadbccdbbddbbbadadcdddbbccdbcacddaccdabccbcaadccdabbbdccabbaababcacabbddbacabbddbbdcadcadbddcddbcbdbcccacbdcdbcaddddbcddadcbbbaddcbbbccbcabbbaabcdacaaabbbcabacdbadbccbccccdbcbbbdcccbbcdaaaccccbbdccbbbacadddbddbcccdbcbcdcdcbcccadbcdcabdbabbddcdcbdbbbdcdaabdbdccbbbbbbbcbbcadcccdbbbbaadccdcdbdccabdababcdaadddccacadaabdbcdabccacaddbacabaaaddcbbbcdadabdccaaddbacbacbdaaacbacdbbcaccdbbdcbaaccbcaaabddaabcddbddbbcaababdcababaaacddcbcbbcbbbdbbcdbccaaabcdcbdcbbdccddacacabdababcbbbdcbcbcabbdbacdcadaadddcccdcbdcbbbadbdabbbddaabcdadabacddbaadadbcdddbdbbdbdbaacddbddadcbbbcbadabaadbccdbbabddbbbccdcbcabdadabaaddcddbbaabcbcacbcbdabdddacabcaacabaccadbbbbdaadbdbdcdcaabadbdddbadcdcacbbabdadbcbbcbabaacaaccdbdabbabddabadcdacbcabbadbdddddaccdadaaddaadabcbacabbadcddbccdaadbbadabddbaaaaccaabadccacacabdadbaaadbaddcdadacdcabacacdcbddababcdacaabaccaacbcbcbcaddbccabbcdaadccddaacadabdccdccadababbaacabcacbbbcabcdaddccdcdcbbbbbdadccadaacaabbbdacddbacadddbcababaaabcbaabcbdccddbdcbdabcacaaadabbcccadbdbccaadcacacdabdddbadcddbadbddadbdabcdccaacbababaaabababcdacababccbcacdacddaccbbbcdacbdacacabbccabacdbbdaccabcbccadbcadadddaddbbdcbdbcdddcdbaacacddabadbdcbbcdcdbcbdacbabdddaabbddaddcdbbbdadcccbbbbcccdbddcabcbcaadcbdcdbaaadbbaaddcacbcdbdbcbaccbbaadbbcddbaccaddddbcdcccabcadbabbbcbaaddbccbadbadacddbbaacbabbdabcadccbbaaacacddbadaddbbabadbccdbbaccbaacaabbadcabdacbadcdbaadcaddadccccbbddccbcddaabcddacdabaaccddcaabcdaddbcbbdadaacdbbbabbccdadacddadcbbdbbabadcbccbddacccdcaddababcdcaabdadbbaabbdbdcaadbbdabdddacbabacbdddaacccacbbaccbccabccddbabcbadacddccdbbdccacddbcadbcdabadddbacbabcbccdadbccbbdcdcaddcacabdbdcdaccaacbadbaadccaabdabdcccccabbdbccacadaaadbbbbaacbbcbbbabddacaacbddccbcabccbaaabadaddddcdbababdcccddbbdcabaabcabacadbbcaadabbaccddbcbcdbbbcadbbaccadadaccddbcbbcadacadaddaadcacdddccdddddbcdddaddcccdbdadcbaaadcdaddaaadabbdbdbddcbbddbdbabcabadbbdcbdbddcaddcdcddddabaccbbcbdcaccadaacacddbbccadbcccabdbdadccbaccbddcaccbbccbaaaabddcabbbaaadadbdcadadbcdbcabcdadcbccbdaadaabddbdbbdaabcadababdcbbdbcdbbbbcacbbaaddaddbdbbbbaacdbcacdcabbcbbbcadabcddcdcaabcbabdddbabbdcdadaddccdbcaccbcacbdadbccaaacadcdccabacaacdccdbccacbabcaacaaacabbcabcbaaacabcbcbbcacbdccdaddbdcdaabbabbcddaabcdbbbabbbccaadbdbdcdaadcbbcdbddbaccbcbdbabdaabbbcddcdbcaacdadacacacdbdadddcbbbabcdaccbadcdbcbadababacdcbcabcbbcaadaaacbdcdddabadabbcbbdcdbabbcdabddbaddbcbacdbacababbdabdddcbdccadabcacbdcdcbcdcdadccdaccaccacaccbddbbbccbdadaabbadddcbaadbdaccdbddbbbdbbdcdddddcacabbcbabbbccdbcadcdbaadacdbaabcbcbddbbdbdabacdccaaddaaaadadcabddcbbbdcadadcdbdcbbabbacbacadacbdbacbadddcadbbbabcdbcbaabdcbdbcddcabbcbcdabccababadcadddccccdbabbbcbabccaaacdbdcdddcdcaadabcaacadbdbcbababcbbbbabdbadbcacbcadabcaaccabdaddaabbacbcacbccbbcaccbcbaaabbbabcbadddaddbadaabcaadcbdbaccdcccbdddacbdccccaacddbccbadbdbcbbccbaccccabbbbbbbcdccaaaadabcdccdbcdadddccbcbcbaacbabbaaaabddbabdcdcbddcccbdcdaddabdbdcabdbdbcdaadbdabaadaacbaddacacddbcddbacbdcbdcadaddbbdadcdbaabadccacddcacdcaacbaaccddcddcddcdbccdcabcadacbdbcddddcdaddadcdbbbcbbcbacbbacccdcaaccabacabbcaabddddbabdabaaacbdbddddddcdaddddddbccdbddbcbdbcccbbaadcccdddcdbbadbdbcbbbbabdaccaadbccaadbbccdabdbdaccaacacbcdddcdaaaabdcaccaababbaccadabcbaabdbccacbcabbcbddcbdbbaaaadbcdcdbdbbcbdaccbbbbaacaaaacadadadaaaabacddbbcddbbdbabdbdacddabaadcaadadcadbaaaccbbcaccaaadcaaacbcabdbbcdbdccbddbbcdddbabdabacddddbbbbbbcccdacdacbdaabccdddcdaadbcdaaccbacbdccbbcccbbcbbbcacbcacbadcbcacbcbaccbdacddacccdbbbbcccbccabdddadcacdcaaabcccadbdcbbabdaadbabadcbacbcacaddababbddcdbbbacdaccabcddbcacbcabbcdbdbbdcbddbbadadddddbdcdcadbddcbababaadcdddddcdbdacdacddbbacdddcaabbddccabdbcadbdddccadabddbccadcbaddcadbdddbbaccdabccbcadadcdcacaaccabbcdccaadbadcdbcdccbbadabbbaccdaccaccbbdcbcbcccacdaabdcdbaccdabababaaadddbdbbcacddbaccdacdabcdbdacaccbdddaccdbabdcbacccddabcbcddbdabadadccaddadccacdbbabdbaacbadabadbcaacdacaadaabaccadcdbdaccbdccbbcaaadadccaddbdacbbcdacdaaddaccdbdcbbcabadbadacccacbdcaaaacddcbcccdcacddbbdcbcbdabddadbcbcbccdcdddccdaadadddaaadcaaaabcaabdabbadccdbbbcacbbaacddccdccbcddbcbdccacddddaaacccdaacdbdddbdbaacbbccbaaddcadacdccabcddcacbaddcdbbbaacdbababcbddabcddccbcdcccdcadbaadadccaacdbcbcaadbdbdcdabcbcdbacbcbdabaaaddbbdcbaddaccadcddbccaadacbcadacddbcdccddacaaacaabbdcaaadbcddcaaadddbcaaddabbaaddbabcbccaabdccbddccdcaacabbbabdbdadcddcbbcbaaccabbaadbcddcccabdddcdacbdbccaaabadbdacabbcdbadddaaccdccbacaddadabacdaccaaaaccabcabbabbcbddcbaadaadcadccdbddcdacadadddaaddbcdadadaabbcdbaddbacbaccdbdbcbcdbcdcacdcaabdcdcbbabbbdbbaccbdbcbdbccacbbccbbdaaddbcbbbdabcdabccadbadddbdcdccaacabbbbdccbbadbddabaadbbacccbaccdaccbadbbcaacbdcbaccdcadbaabdbccddaabacacdcaccbbdddadbacdcdccdbacdcabaabcbcaaddbbbcaacbccddccadbdddbdbbaddbddbbcabdabbbcccccbddccbdaaddbdbdddbabbacdcbadcdddbcaccaacacdbdbddbadbdadacdddbaadddbdadbbdadbdcdabababbdacbcababbdbaddddcbcacbccaabaabdcdababddabddcadcdadaadacaaaaccbbcadbdddabbddcbdbadbacacabccaaacdddacadaadccddcbadadaadbcaddcbdbcdadabcdccddbccbaadcccbcccbacdcdddacacacbdaacddbdbcccadaddabcacdcbcdddcbdaadbccccdacaaaccaacabbcdacbbbdadbcbacbdbabacacabbbadaacbacbbaccbcddbdacdadbccbdddccacbaadcaccdbabbcdbbbabaacaabdaabcddddbcdaabacaacdabcabbbcbacbcdcccdcddbbaacbcdbddcdcadbbbbadbccddaaddcbccaccdaabadcdbcddddaabdaaabaabcdbcaaccbdabbcaccacdcdbdaaacacdddcdbdabbadbddbadddbbbbbadcbdacbadaacdcdcadbddcabcabcabbcbbdadabaadbacbbbcccaddbabacddccacbbbabdbbbbbdbbbbdcacddaadcaaabbacdcddddccaaadddacdadddcdbdbbbdcadbacdbdbacbacdacdaadbdcdcbdaaaacccbabbadcbcdadabbcbcaabbabdacbbbcbbcacdbcddbdcabcbdacdadabbddaaabccdadbcabdcadddbbcaabadaacacacccbdcccbaccdddcbcddbaccaacbdabbccdbcaddcadcdcadcdbbdbcdbcdbabcbbacabddcccbcbaabbddcdcbaacacbcadccdbabdaccaacdaabaadcaddabaccaaaddbcdbababddadaabdcbcccbbcdbdbdadbaaabcabccabdacbcdcbcdcdccabbdaadaddcddcbadaaaacbcccdbadadcabcbbabcdbbbcdbdacaacddabaaaccaddbcabcbcacbdbcaacddbadaabbbcbaadadbbdbadacdcbdabcaccdcadccbdbdaddcdcaccbacbccadaccdccacbcbcbcaacccccababaccddcccaadcdcbbacccdaccbdaddbccabdcabbcabdcccabbaaabbbadaccabbabacccbdadbcbdcdbacdbcdbdaddbdabddadccdacccbacdacdbbcbcddaadcdcadaadabcdacdacadcdaccadbbdbdbbcacaddbabdacdacacddaacdddddacbdbdccbdccbbabdcccaccddbbbbcbbabbdbbcbccbacacddcbdacbaadacdbaddbabcabdbcaacdcbacbbbcdbbdcdbbabbcbdadabccbbadaacccbcabdabcdbaccddbcaaabaabbcdbacabadbaccaacdacdcbccdbbdddadcbaabdadbbbaadbaaabadbabdcbcdcdbbdadccdbdbbdbacddacdbcbdcbccbdcdcbcaaaddcadcdacdbcdbbcdddabbbaddbbabccccabababbadcadcbddcacacddcbbbabddcbaabaacadbbcccbdccaccdabcbaaadbbdbbcddcaaddbaabdddbcbddaabdcabbdabdbcdddaadaaabaaddaaaddddbababdddbcbcdaddbabacdcbbddddcbccdbbbdddbadccbbaddabddaddcdcacbddcdbbbcbbdddbadcbccacdcbdcbbaaccbcbcbabbbcbbdbdcbbbbdbcbdcbdbdbacabbcbdbcccacbbcabacacabddddbdccacbbcacadcacbadbccacaadacaaadaadacabbdbccaaccacaadbcdadabcbcccaccaacabaddccddcbcbabcaabaabaabddbdbdaacdacbdacddcdadcbbbcccacbcabddabadabaadddddbbccadcaaddbdddcadaaccabdddcacacbacbacbccdadadcccacbccdbadadbcdccbcadaaacbccbabacccdbccbdcadadcabccbddacbcddbadabaabddadbcdabcbccdbadccadddccddbcaaabdbbddcaddddddddacdacccabdaddbadccabbaadadcadbdbcccbaadcbdbdacddacabdcccdccaccddcbbbabaaaccbddacbddcbcbcdbcacccbccdacdcbcdbabdcdcacdaccddabadabcbdbaadacccccccaaddddbadcddbbdabbacdcbccdbccacabcaccaaddbaaadbaabaaccaccbcccabcbacdddcabbaddbbaccbdbacdcddbacdbbaaadacbdaddbcdcbbdccbcddadacacaacaaadcccbcdcdcccddbaacdcbcabcbbabddcadbdbaaaaabbbaadbacbdaaabacabcbdddbdaccacaababbdbddadadaaadabdadadbcdbddccddadaacbddcacacdccdaabcddbcccdabaddbdaddbaacbcbbadcddacacccdcdddbacbdcdbaddbddcabadbcddbcbcaacacadcaaabdabadaddcacddbaddbbcacbbaaddcbaadbabcbbccbacbacaadaaadcdcddcdaddaddabdadcabdcbcabbcdccbabcddcbbccbcabaadccbcbbcdcccabccbbccaabdbbabadbcbacbabaddaacacacbdacdcadccdbbddcbccbdbbbcbccaddbdcdbdbcddcabbabddbdcdabcabcddabcadbcddabbbadcccddccbcccbcabbacbcdbccaaabcaabddcdabddccddbaadcaccacbcdbdadabbdcccacbcdcdadacbdaaaaacabcdbabccdaadddddbdbccdadababaadaaabccdaaaabcbbdddacddacdadcbacdcbccacacbbbcbcddbaaccdcaccbaadcabcabaccbbdcbddbcbaaacacabaaaacaccababbbcdddcaccdacbdcaaaabbdccadddadbaacbbdccdbdbdadbacdcdcdcddacabdcddbadaadaacbbdadcdcbcabdcababdbbacddcbadadadaddadacabcdcdaccdbcddaacdacdbadabaabcdaccbdbacaabdaddbddbbadcbbbddbddddacbdabbabcaccbaabddcbddbcaacbbcacbcdcbcbdcabdbdaaadadbbbdddbcccddbddbacabcddcadddaccbcaabdcabacbbbadaadccddcabbbcaaccaddabadbddddcbbdcbabdcadaaaadbdcbdbccdabadacbcdbddaccaadcadddacdcccddcaadcdcbbbabdcaacbdcbacbbbddacbaacacdcaadadddabbbdbccdabbcacacddabacbdbcacbadcbaacdbdabbdacddadccacadbbdbbbabbdcaddacabaadccddbcdcdbdabcbcbdacaacaabdadcbdaaccbaabbbbaabddcccdadbabbbdbdbccccacccbbdcbddbbcbcdbccdbadbbaaabcbdaabccadaccacbacbdcbdbadcdaadadcccbacacbbaaabddcdbdacdcdabdbbdbccacbabbaddaddabcadddcadbdbccbccbbbdcaddcacaabdaadcadcbdcddcdbadadcbbdcccdbcdbdccbbbaaaabadcdbdbaadcddcbccabadbdcadaaaacaadbcadacccccabcdadbbdacbadabddadacaacddccccbbbaaaabbdbbdaabbabbadbdddbaacdcbbdaabdbacadacbccbcaacbbbacccaabbbdabaacddbbabdcaaccdbbbdbaacaacaabbddcddddcabbcacadabcbadadadabbdcacacddbaccdabaaacababadcbddddcaabbdacbdcaddadddcbadbdabbdcccacdddacadcccddcccccabaacdbadcddddcbdcbbacbbadcabcbabdcbdbdacddbbcabccccdddbdabdbccacabdcaccbacadbacddabbddabbcacbcbaadacdbabaddbdbaaaaacdaddadcbaadbdcabbbbbaacddbbccdcddbbbcddbacbdacccddccbaabccdabdbcabbccbdaacadcbcadbcbaadccaacaddccdbcaaccdcaddcbbcadbdcdadacaaadbcbccdbaddcbbaadddccabcdacdccdddaabdbbcbabdccadcaccadcccaddbccdbcdcdddccdabbccbacadbcadadaabddabaccacbabdccddcadcbdddccabacabddcaacaacdcbbabacdbdcbaabcbcbdbdaaabbdacdbccaabaadabcaabcdbccbaddaccdddabdcacdaaddbaddbdcacddbacdcccabccaadccbccadadbbbabacbdddabbbcacdbcdbcbbacdcbdacbbdbcdbbcdadcabdbdadbabaaddbabbbdbbabbdbcddbaadacbacaabbbaacbdcadcdcbabaaacbadccddbadbbbabcadadcdcaccbbbcbcabcbadbdcbaadcaacdccdbdbbcbbcdadbcbbdbcbcbcdbbadaaccddadccdacdacdacccaabadbbcdbabaddddabbaddccddbcacbabddccdddadcbaacdcdccddcdbcddbdcaaadcbaccaddabadabddbcaddacabbcdbdcdbbaaadcdbcbbdadcacdcdaaccbcbcbbdacaadcbcdbdcadbccaadcdccbcaabcbdcbacbdcbbcdabbdddbcbadcacbdadcadbcbdacadabdccdbccdcdacacadbbbcaacadcbbccccaabcddcbaaccdacbcccabdbcdbbdcaabacddacdbdccddcbabbcadaaadccddbaaabbaccaaacccbabddbddbcaddbcabdadcabbbdacadabdccdccdacdabacdabcdabacbbdabdbadcaabadbdccdbbbbbacddaabccaacaabddabaccaaccdcacababccccbadddccdccdbdacdabbcbdbadccacccddbdbcdbdcaacccdcaddabdaababbccddcdaccdddacbbdcbdcdbcdaccdcbbcbbdcbdaaddcacacadacddbbaaccacadcadabdbaacacbddabadccadcddccbccadbcabccbbcbbdcbcdadaddabccabcacdbaacccdbddcbbbcaaccdcdccadaddabacbbbbdbbcdbadbbdaaaabdacdbcdbcabcddabdccbdcdbadddbddaaacbadbbccaabcabdadacddbdaccdbdcccabdcadcbacadadbdcbaadaaddcabacbabbbcadbabaadacbcadacddadaddaadbdddbbccbbcacaaacbdbbaccbdcbdaabbcaccbbdbacabdccdcdbaaaaddbbcddccacabcaddcccaabacdccbcaccbbcdcbabdccabbdcbbcbddccdddcacabcbcdcbdadaccddcadccaaaadcccbbaddabcaabbcdcdaabaacddcdddabdbbdcccddccbaacdbcadccaccdbbdaddcccacdbcddcbabcacadbbcbbbdbbacbdabdcbdabddbcdbcabcacdacccbdaccddcddbdcadccadcbcccdaddabdabddcdcdcddcdbaacbdcdbdbbaaccdcaddbddbadbcacdddbccdbbdabcbcdbbabdaccaaaacdcbbadbcdcccbdaabccdbcbabacaddbbdcabaacdbcadbddcbacaccbbcbadccaadbcbbdbbcbcddddbcaccccddaabacddcadcbbccdcbdcdaabdccbcdcadbbbdcdddcbccdccdabbacddccadaccbdabaadbaabcbacaccbcbbbdabcacabcbdcababadbdaabacdbabbbbdadcbdaaadcaadbbaadcdabddadaaaadcaacabbbdbbadcdbbaabdadcbbdaccbddbacbcbddccddaacbdbdccddcaacdaccacbbaadbddbdcccdacabcbaaabbbcacbbcddbababcbdddaacbacbdccdbadbddbbddcacdbbaaabaddbbcccccbbdbdcdaddabddacbaaacacdadbbdabcdcbdbdaddaddbacbcdcdbdbbaabcabadcdaaacccdbddabaaddbdabcdadbdcaaacdbcdbdaacccdacbadadaadadddcaddabdbbcdbaabaaabdaddcddbbababaabcdcadadbcbdccbdadbcabcdddcccacdcdbabddabdbdbadadccbbccdabdbcaccdbabcadbcbdacaddcbdcadbabaabbcbcdaacacdbcbdaabdcddddcbbdbaddabdaddbcbdddbdcddbbbbacdabdcbcbcacccdbcbbcdcbcbbdaacdbbcddccdaadadcacbdcdbddaacdbadadbbcaccbbccdcbbdccccddbacabbbcbdbbbbbabccacabcbccbdabbccadbabbbcaadacccadddaacadaabdadaccdbbbadbbcbbaaacabacaaabaaacabacbdbdabcbbbbbccdabddddcdabaccbabdddcccddacbcccdbbbbbbccdddacbbacdcddadbddcbcbcbabccbbbbcbdcaacaabdadaacbdadcdaadbdbdbbabcbdbcdcaddacccaaacccaababadabcccdbdacabbaabadcddbcabbccdccaadbaaacbbcabababbbcbdacbcbddaabcbaaaabdacbbdcddcbbbcdcbcbdddcadbacdacdbccdcacbaabbcaababbcabdacddbcdbbbcdcdaccbccbacaadcccacdbdcbcadbadbdbcddccccdaaadababcddaadadadaacbdbdddccabbacbdbdbddbbbccbddaadcadadbcadbcdaccabbcdbbadcbccdaabaaadcbcccccdadacbbddccdcddaaddcaabbabcccbdbbdbacdccdababaaaaddcaadbccbdcbbcbdcacbbcaaddcbcdbbcdadadbabdbcdaabbcbbdcabadbdccdccaabcaaaaccdbbdabadbacddacbcccbdcdaddbaaaaaaacabcdadcbddcdbbcbbaaabaccbcaaabaccdcbbbcbddaacdbccdbbbaacbdcdbccdcbdcdbcbacbbcccbbbaabdccaccddbbdcadbcacdcdacabacbdcacacdbcccbcaaccccdadbbdacddbacddadacbcdadaabccadbdbcbcbbdddddaabcbdbcdaabbcbadababdadacabdbcbcddbacbdaddbbdcbabbdccccbcdcbadabacbccdaddcdbcddcbcacacccbacabbcdadcccaacdaaaaaddacdcccdcddbbbbcccdbadadcbabcbdccababbabacbadaabbacbbacddbbbccbdacdaaddbdcdbcccaabbdbbcacabcaccadbacacaacacacbbddabbccacaaddabaadcbdaadcacbacccddbbaddcbdcbdaacbbbbcdcabbabccacadaaddacbbcaddddcddddccdbcabccdacbcacbbacbbbccdadbaabdabbaccbcaacbcbdcbabbbcdbadcdcdcccdcdabbbdcdabbddbdbabdaccacbdcdcadbbbbdccbabaabbcbdadddbbabcdddddadcdabdadddcdddcddbcdadcdacdabbaabbddadcaacddadcdddbaabbbbcacddcdabdcacccdbcabbdcbddacadbadddaddabcddbaacbdddbccccaabdddddbaddcbcaaabbcadcdcaacbbdbacacdadcdacbdcabcaadccbddbcbadcdbabaddcaacbbddcbcdddabdddadbaddbacbbaaaccbabbaccbccdbdbddcabbacaccdcbdcabcdcccdbaacbadbcddccabdcbdddddadcbadacbbacabacdbdabccdcdabdcbcbadddbdbdbabccbacacdcaaaaabdaabaacaddcdbcddcdccdacdacbadbabcaadababcdbaccbacdccababcaaacdcdabcddadcdaadbcbdadadcabbdacbabccdbabdddbcdaabadbccbadbbbcaadbbbcdcdddacabdccbcbcdadacadabbcacabadaccdadbbadbcdacdacccabcaaacbcbaddcdddcbcaddbbdcddbdcbcbadadbcbababddcdcabdbdcabbccadadbbdbadcdcaddbbcbaddadacabacbabadaccdbabbdaadbbbaacaaadaccbacaabccdddcdddadcdbaadddadcaabddbbcabddaabcbcddcbdbaabcbcddabdbdaccbaadacdabacdbbaacccdcddbbdbdccccaaadbaadabdcdcbadddbbdaadacaacadcabacddbabdadcbbaacdbbaadbacddacababbacdbcbbdadcdbacddcdbbcbcdbdaadbcdadaccaabdcdaaaccbdabaabadbabcaadabadbcdaadcbbbcacaaddadacccadcbbdddacaccbadcccdaaabddaccdacccaabcbcabadacbaaddccacbcacddccbddbacbdcabaddadcbccbdaccabbcddbabcdcdbdadabadbaabdcbddabcddacddcbcadcaaddaacadbcdaabbbbcdccddbddbbacdddcacacbabdbddadbcaaaacbbbddccdcaabaaaabadacbccdbaaacaabacdadcacdacbcdcaaccdbcabacbaadaddadccacaaccbddbbdccdccbcacbaddbcaaddadbadccaabadbdaacbddcbadbaaaadddcccaddbdcbddbbcadabababadcddabddbcaaddddacabcadabbacbcaddacddadbbcccbbddbabaabbdadaddcbccbaadcddabccbcadadbddbbccdbaabbbcdaaaaccacddbdcbdbcbbcbdcdcdbcddaccbbaddcacbcacccdcbbdbdacdbbbaaccbcdbcaabdcbcdccddacbadabdabaadaabbbcaaabacaacaaabbcddbbddbbacaddcddddabbdabadbcaddabbcbabbdccacbddaadabdacbdccaaaadccdabbcaddbbbababbcbcddbacaadcbdaddccccccacdacbaadcacddacdabdcdcdbcbabacacadbcaadcdcadcddbcabdcbdcbdabaaadbdcdacdbadddaaaadcbdbdbcabbdbaacbaabcadacadcbbabdcabddadacdcbbdcabadddbadbbcdcaddbbddaaddadbcbdcbadaccadbddadbcddcdbacbadacccaaadccbbbcaacddbdbccccbbdcdabaabdcdbacdbcdcbcbadadbbdbcdaaddcccbdbaaccbabcabccbbbbcdbdbaaccdcdbaabdcaabbabbadcdbcdbdcdcddbbacdadadbbcdcbddbdaddadbcddadcddbaccaaccbddccddadddbbcabacdaabcdaadabbabcadccabbaaccacccadaacaaccdadcccccbdbccbddbbbcadaaabcbdddcadadaabbabdaccbabdacaaacccbcbdabccccbbdababbacccbddddbbcbbcbdccacdddbbbcccddabcdcaccccabbbcacabadbbadbcbabcddcbbabdbaccddcbadbaddabaaccdbcdbaadbcbbcacbbdcabbbbccdcdbbbbbdcdddabaabcbbbadbbdaaddbcccabbdddccbcaddbbdbaccdddbbddaccacaccbdbbccbccadcabcbbdabadaaabbaaaccacaaacddbcacadbbddabbbdbcbdcbdaaabcdccdbacbbcacddcccdaabccccdcddcdddbbccbbcbaaaaaaaaadaacacbbacdbddcbabadbcabadbddcadaacbbcacdbbbbddbbccbcbdbccddcbcbbbbbdcabcbabacdbcacdbbdbbcdbdbccdaacbcbbdbabcaccddcbbdbddddbadabacbaadadcbcddcaaddcabcdcaadacdcaacdbdcabddbdaaddccbacbacbbccdabcdaadadbcccbbbdacaadbccdcbaaccbbcdccbbaadbabcccdbadcbccadbdbddcbdcdbadddbaacdacaddbabacdbdadbdadabcbddbdbcabdabadbdcccccacdcdbbaaccaddbabababdcbbcaaddadcbbacddbaabbdbabccbadcaaddddbcaadcbabacadcbaadcacbadbccbddddaadbbbcdcbccdccdbcdbbaddaadbcbbccacaaacdbdabccccaacbdadbacacdccbcbcccbdbbdcbbbaabdcbcaddcbcdbadaaabccaadaaaabbabcbadadaabdadbbbccacdbdbdbcbbabcbabcadcdadbcdadadddcdbcdbdcbaadbbbdbbacdbdadaaddabbcbadabcddabadbbbabdbaadbadbdabdbbcdaabdcbacbcbababaadcbbbdcaaddccadcdcabdcaacacdadacdadbaabdaddbaadadadbddcdabbdcbaccbddcaccadcdaccbbcabddbaabacbdcdaaaaabbbbdbbdaacacddabccbcbaaadadaadbcaaaccbdcbbddbdcbcbbdbcccccbcdaadbcbcbabdcdbcbbbcbcaabadbbcccbdcbdcabbbbccccbadcabbaacacddbadbabbbaabccaaaaaabdcadadccdbbacabacdcddddcbdadbaabccaaccadcabcaadccdaadadcaabaadbdbddababcddbbcccadabbaabbbccdbdddbddaaabcbcabdbaccaabdbbacbabacacabacbbcadddcbdbddbcbbaadadbddbacdcaaccdbbdbaabcdbdddcccdbadbdbbcbbbcddcadaccbcacadbdcacddbdccbbaccccbbbabbddbdbadbdcbccabdaaabdbadbacdcbbbabddacddadabcbbdcbccbcddcacabccdaacacbacacccbdddbbdaadcbdddcdbdbadbcdcccadbcbadabcdbacccdacbddabadbdaccdcaabccbcaccacdaabdbbabdbadcdcabdcadcdbdcdcdaabaddccababbdcbcacddabbcadaadaadbbcdacbdadaaccbcdcdcbbbdabcdbaddcaadadbcaccdcadadadddbbbaacbcbabacabcbbbadcaaddccaccbddddccdacaacbdaacdbadcaddaaaaadccadbdccadbadaacddccaaaacbddbbbaabccacadabdcaaaadcddddbccccabaacaadddddbcbbbdbcaddcccccdcadbcaaaccdaabbcbdabaccdbdadcddcadcccaadbcccccbdabdbcdcbadcddaabdaaabdbddccdadbbcdbcdbbadcadccacacdcaaaadadccdaacbdbbcdddddaabdbbcddcdcaddbbcdbaaadddbddaaaaaabadddbcbdcaadcdaddadacaadabaccbadbcaadbaaaaaabaabbabdbcbbbddccaadaccbbaacbaccbaacdddaddbbcaadddddaccdcccdbbbabdbacdaccdbacacdcdbaccbbabadabaabdddbdadacddbcadcdddddbbbacdccaabbaacdcdcaadbdbdccdcdddacdbdbcccdccbcbcdccadbdaccbdcacbbbabaddcadddcbbacccabacaadcbacbaabbbcbaabdbcccaddaccbcbabddcbaadadbddcaabcbdaaabcaddbcbcbbcdadbcddaddccdcdcdbaddcabcbabddcaccabbcdccdcbcabacabdaddbccdacdcbddcabbacbddadcddadcbcddaacbadabcccdabbddacddbcbbbbababbcddacbcbcaddcbbcbbddbdddbbadddcdbcbacabbbaddbaaddcacbdcdbdabdcdaccbabdaadcccaacbdbaacdcbacccbaabcadaabbcacaaaccbadaddcdababaabcbcacbabddcdbddbbccdabcccbbabcbcacbbddbcbaacdaabbbbcdabbdcadbccbdcbcbbbaabbcdcacdcbcccbcabcbbbddcdcbbbabcbaabddbcabcbacdadcdcacbcacacaaacdcbaababaccdbbbbccbdbccdadcbbbcbcabdaaaabbababbccddbabdbdbcdacdcadbabbddcbbaaacadbcabdcababbbdbacdadbdcdddbaacddacbccbaadcddaaacdbaaacbabdacddcadbababaacaccdcbbbcacaddcdacdbcdcdbdcadbdbcaacadbcababaabadacdcbdbcbdacdcaddabccbadacbdabbaccdccbbcabaaabdbccbbccaccdcdcacaccabcabdcbadadddcacbacdcdccacdcaadcaacdccbabaaddbadcdaccdbacaacdabbbcccdccaacbdbadcdbadbbcbacdaacccbabacacdababdccdcacbadabcbaccdccdaacbbddbabbcddbbbabcbdbcbadaccdbacadaddbbddbbaaddacadbbabcabbbaacbcaadaaacbabcdccdcbcddddddaababadbcdccacaaabddaabcbdcbabccddcdbbdacddaadaabbaaadcdadcbabcbaadcdaaacdbdcaaaddbacbcbabbadbbdacabbabbddbcabbadcacdaacbaadcbdcbdcccdbdaabbaabadbdcbccbdcdbdbcddcddbbcabbddddcacdaddddaccddccddaacbbccbaababadcdbcdcdddccdcdcdcdaadcaaacbdacabdccddccbaadaabdcbcddbbbacdbabdccaacabcbbcccccddccabcdcbdddaadaaadadcbacddacddadbbbacbaccbdcaabcdbbaccadacbcaabaadcbaccacbaacbadbbcbdcddbcaddabdbbdacbdabaaabaadbbbdaccadacccddbdaaccdaddcacdccdbcbcddccbcbccdaaaabbdcbaabbacbbaaddaadaccdbbadbccabaabbcbdadbcadcccbadaaddcaabbabbdbacdabddbadabbdcbdbdbacccbbbadabaaadadabcbdaaaaaacaabbaabcddababdbdacdcdbbaadcadbddccbbaaadcdcbaaacdacdccdbbbccbbaacacadbadbdddbdbacccaaadcdddcacacbacbbcdcbbccdcdabaaccccddccddbacccbdadacaabcadcdcddabdadcbbacbabcbdaabbaabcaddddbbdcdcbbdadadadaccaccbbdcdabdadcccddbbdabccccadbbdbabbacbcbbbdabcaaddccbdaddcadddadbbbcadaaabbcdbcdbcbabcacdddbbbdabcadbcacbcacdacdabacdcdbdcbddccaacbaadcdbabadaabdcdabdaccdbccdbaaadbbddaccadadcdbcdcacdacdbbcacadacddbadbccadcdabdcdbdbdbbdabdbcabbdacaabbdcadbdbdcbabbbaddddddabddadbbadbaacbddccbacbdbcbadccdbbbaddcddbcdaacdccbbadcdadaaaabcccdbdbcbcabababbbbabdbbacbadbacbbddccaccabbacadddcacbabcaacdbbbabdbccabbcbdaadddbcabbdbbcccdddcacabddadbcabccccaabcbdbbcbbdcdadccbdcccadcacadcddbdcacabddaacadbdaaacdcdabacbcdcbabbaacadacaabbadaacbbcbcaaccbdcadbdcaddbcbddcdcccdcdaaadbbbacdaccdabaccbbcbbbcaaaddbbbdcababaadbbcaaadcbbccddcbdbadabdbadabccdaccdbbbcbaaaacbcbcddcdbabbdbdcdacbddbcdadbddccaabcabccdbaaaabacbabcaacbaabcbadbadabadaadaacbabadcacaddbaabdcbcbbcdddbbaccbdcbbacbccbadbbadbdbadababadacdddcbbcdacabddbdabdacababdabbbbbbccdcbbacdbadabddddbbaaabcdaccbacccccacdbbaadcacadaddaadcddadabcaddddbabddabbbcdddbcdcbdbccddddcbbbcbcaadbdcdaccbacaaaacadbcbbcabbacbdcbacdabaaaacacacdadcbabadaccddbdbdaccdcdddaddbcbacabcdaacbaabacaadcbaccaccabbbcdaccbddcdacdabbcadacdadaaaabcdddbadacbbcaadabaabbaccaacdcdbddbbbcabcbcdcbcdcbbcbbacbbbbddaabaacbcadddacacdbddccdadbbabaacbccdadaabadacbcbbacdcbabaabadacdbbaaddcccdaaabccbbcdbabcacddbaadccdcaaabdabdbdaccbcdddcbbbaaddacdcddddcadbcdcadcdbcdaadbbdbccbdcddbdabadababdadcddbdcddbbacddddcbadbddddcdcbdbabacdbbbaccacdddbabaaadcabdacdbadbcabdcddacbdccbbdacccaadbadcabbdabdadabdabbadadacabcacabcacbddaacaaaddadcaddabcbdbcabdaabaccbbbbcacaaccdabddbbdabaacdcacbabdaabbaccacabcdccbcdaacbbadcbcddabacbabbadddadacdcddaccadbaabcbadaabaabcdaaacbbbaadcdbaaaccbdbadbcabadabcbbddbabaaaacdcddcddcddddabdcaabcaacaadbbccbdcbacacddabbcbccaadbbcbaacbdbdbbbbadbaaccbbdbbbbdcaacaaaacbdaadbcdaaddaccbabddbdaabacbcbaabcccdadbbdcbbdcbbcbabcbcabadcbcdbcbacaccdabdbaaabdcccacdddbbcacaddacbbadccdadaabbdcabdbcbaaccbcccdadbadaddbbdcbdcadddbcbbdaddadadacadddbaababbbaaadcdcbaadbacadacaccdaadddcaaacbbaaabccbbcdcdbbddadcbddcaacaddcbdccaddcccdccbddccaccccbababacacacdbbaddaaddbbbbbbadabbacdadaddbbadaadbdacacdabdbbdccdbcaddaaacdbdbddddcdbdbbbccdbccadcdbbadcccabbdbabdddabcccbdcaadbdaaccbdccdcbabccdccdcdbcbbdbaacccdacaaabcbccbaadcbdddcccacdbadcbccbdcbdbbbcbbddccdcadadcddacbdccacadbaabdabbbaddcbbdccbbddbaaadabbddbdbaabaaddbdcbaddacacbaccccabadcabbdbbaadcadadbdacdbcccddcdcdccdcddadacccbcddcdbaacaddbbdddacccacaaddbaabdadabdcccaacdbadabbabbabbdcbadaccbaabbbdaacccadccdcbbbbbccdbcdcdbdaacdabcdbbdaacbadbabbcbbbcdcccddcaabaccdcdbbaabdabcaacbaadcadcacdcbbbadcdcddcacacbcccaababcbadcabbaacdcdccbcbadbcddcdccbcbbabdcbcddcaadaacaddbdcbbaccacdbaaaddbbccadbdcacbaabbdcadcbbcbaaaddcbacdadadddabbddbdcccccdaadbaddcaccdbadbddbcbaccdcabddbdbcbdcdadcdaadacbadbdccadabddbaabadaadbbadbddabcdcaaddaddbdcaaadcccadadbcdacdbbaadbccddacdaabddcaabbbcdcbadcaadbabddbcddbcdbdbdccbcbadbadcadcbaddbcaabaaabcbcdcacaaadbbdababbacabaaccbcbdabdbccddccacdbcbdcdcadbabcbcbbbdccccccaaabbcbdbdbaccabcbbcccaacdaaacccbccbdbabbccdccacdbacbdadbccbacacaacaddddaabddaacdcdadccbbcbbdddccadcccdadcbabcbcdabdbbabbdadabcccaddbdaaacbaaaadadddbcbbbdccbddbacbdcabacdddcddaabbadccacdacdabbabadbcbbacbbddcbacaddcbacddbcbbbadcaabcbdabdbaaaccabbdcccadbccaaaadddabcdcdbbcadbbdaabcbaddccdacbaaabcbcacbddcadadaabacbacacacdbccdbccdacadbbbbbbaacbbbbabcbdbdacaaccabadadbdcabcabbcadddbbdbdcddbcbdaacbddbbacbbbcdaddcacadcbccacacdbadcbdbadcddbcadcbcdaadcdbaaccbddbbdaacabbadcadaacbabccadadcbcdbaddacdcdcacccdcddaccbcccaabaaaadadabddbadcbccdababddacbaabcccdbcdaaacaaddccabdbaccbbacacbcdacacacadadbcdadcacbdabcadadabdcbaaabddaadbbbddcbcbbbbccdcdbabcbddacdbbccabddbabbaadcbbcaccacddcadddaacabccaacaddbbddadbbabddcaddaddcdcbabcdbdbcbadacabcdbbaacddaddddaaaacdcccddaccccaabccdddbcbadcbdaddabccdcacdbddacabcdbaacabdbbdbabdabdbabdddcaacdddbddbcbababaacccbddbbdcbbabdcacadadabdcccbbbadacbddbacdbdbbddaaaadadbaadcaaccbaacccdaabaaccaccbcbdabbdbbbbacbadbaacddbacaacddbccbacaabccbdccaabadacdddcbbbabacacabcbcbccaaaaabbbacbadbcdaaababaddaacbdcbddacacacbdccadbcccbcdbdcbbbdcbdbbdadcacdabbabdacbccadcbdadbdabbbdcaddbbaaaacbaaddbbaddddccdababcdbadbdddcddddabbcacbadcbcbaddcadbaaabdaddaaadbdcbaabbcbdbbdcacacbbbcbdcaabddbbbadbadbdddddccbcabcacacdbcaabcdcaabcabccbcacddcbcdabbbcbbadbccbcbabaccdbccddaccbdbbaaabccccbadaacbbdcbabaddbcbaddddacababcdbadbcdbdaccbbdcadcddabaabdcbddbacbbcbcdbdcdddadccbbcccccccdbbccbabadccccddcddbdcccacbabdbddbbcbaaaabddcdcbaccbacabbdcdbaddaddcbdbcbbabcdabcdbbdbdacbdcbccdbabbababaabddccabbbadabcdcccbcbcdcbaaabcccbbaddcaaddabacabdbdcdbbccaaccacdbcdbcadbacadcadbccacbaaddadaccaddaabddbbabdadcbdbcbacabcadcadbbcdbddaaccbadbaadadddccdbbadbaacbddadbdabcdbbaadcadbbcddadcdaabbcbbddbadabcaddccdaacbdacacbdddbabbcdaacbbaacadbaccbaaccbbabbdccbadddaccaccbbbcacbadadadabdbdabbabdaaaacddccbbbacbcacbbdddccdbdcaddbbdaaddccdbdcbcdbacacbcbabcbdabbcadbacbaaacbbbaaadbbaaddccbccabdacbbdaaacdccbcaabadaacbaadadbadbdabbcaabacdccbdadbaabddadbddbaaababcbbccbdcbbcadccaadaabdabbcacacdbacabbbabdabbcadababdbdbdaaacddaaacaccdbcdbdcacbdbdddccaddbdabcdaddaaaacdaaddcabdacdbdcdabcdbcbdabcbcdbacbccaabadaacdcdcbdbccaabaabbddcdaddaddadbdaddcbabbcbcbadbbaccdbbddddbdcaaadbbbacabcbbcddbbddcddbbacabcddaddbddbdcdcaabcccbdcdcdccbcaabaabbcabdccbbcccdaaaacdbabcbccbdccaaccacbbcbadcbadbbcadccbcdddcdddccdccadaaabddbacbdadabddcdcaccbcdbbcbaaacaacbbacbdaccdabbbcbdacabdbdccdbbbcdabdbaaacacaddadbddddccdbabacadddacbcbbbabdbccbadccddcdbdbcadcbdabdbaaabdbacadacdccccdbcdaaaacbdbbdcdbdccdabddddcddcccdabcaaddcbbbdbabddabdbddbdacbdabdacbcbcacbcbdaababbabbcbaaccacbdababbcddabaabbbdadbaddcbdccabbaccbddacdabadadcdbcdacbcaddccaaaaaaccddbdccacdaababbdcdbbccdcbaacccdcbbcdbdbdcbcdccdacbcaaccbbaccdcaddadacadaddcddbccdcbbbcddcababadcdaaddcdbbbadadbbaddadbbbdcaccacadadbdcbaacabbaccccddcbcbaccabbcacbadccdcdbcbcddccbbdbadcaaadcdacadaaddbaaaacccbcaaddabbdcccdbaabddabbaddcdddcadcaddbdcdccacbdbadacdaabdcadcadbbcdbbccbbcbbbbbdddaccbbcccbccdbdbdacaabcabdadddbabcdcbbcaadabbcbdbcbcadadacadcdddabbcdcdbdbaabcbdacdcdcbddcbddbccbdbdabbbdccddbbbbadbbccaadcdbdbccaddabbdaccbccccbcdabcdaabaacddcacdaabbbbcacadbbdbdaddadabbdcbddcbddabbbcbbcbcaaccbabbbdddddbcbcbbbccdbbbacacadbbbdcacdccdbadcaacadcccabcdbcdbabbdcaccdabaadabcdbdabbaadbacdaaaccddabddbcbdbacaabccbbdadbbcccabdcbaabdbbbdcddcacbbcacbcdcadbaaaaadbdccaaadacccdcadaacaddbabdcbdbcabcdbdbcdaaaccacadabbbbcccabbaaccbcdacccabdacadabcdbdabccdaababccadacabaacbaabcbcdcbdccbaaadbbbbbcaaabcacbadbcaaabbacaabaddbadcbcabaaddbdabadcbbdbcbcdacadbcadbadbdaaabacdabcaddbcabacccaaacabbcaadbddbcbcbbacbbdadbdabdbbdbadcbbdbbddabdcdabcbbbbbdcaaaddacbacdbdcdbadcbcdbddddabcbdbabcccddbdccddadcbdbddbccbdbdcdaadcbcbaadcddacacaadcaaccbadbddcbcadadaccdacbdbcaddabdcaacaddcdcddddcdddadbbacbbcdabdbcaccaccaddccdbaacdadcabacdabbcbabadacaabadcddaddbbcdacaddbdcdcdcccdcbcdcdbcbbbddbbaccbccadbdabdccdacaadccdbdcbbadcdabbdbdbdbabcbabbdbddcddbbcdcdccddbabbacccbddcddbbcabddcbaacbdabbdcbbacabcbacacdaadcabcbccbdccdddcddbbdbacddbaccdbdbddcbbabbcbbcdcddcacddcbccdbacbbacbbacadbcadaaaccdcdbaabccbbabacccbcacadaabadcbdcdbadabcbabbccbacaabcdaccbcbdccdddddbccdadcdbdcbbbabbdddbcdbccbdddcadcbbacbdaadacccbabdccaabcadbadadabbdbcddbcabbccdbddaabcdbaddbadbdaaddacdbbdabbcbcbbbdbacbccdccbaddcbcddbbdbcdbdcacbcbcccabccbbddcbcdbbacdddbaabcbcabdcadcbcbcabdddcccdadbdcaabddababaccaddddbdcdcadcadccbcaacdcdbcbbbcbdbcdbbddaadbbddbaaddadbbcaaddddcbdaabcbaacdbbbbaabddddddbabdddcbabbdaaccdacbccdcbdbdbdcbabaabbaadaadcbabcaaadcddaabccacdcaabbcdbbbdcddbddadabbcdddbabbcbbdddabccbcadcbcbbabacaaddcbaaadababcacdaadcabcabccadbbabcaabbbaaccabaadbcdaacbbdcabbabdddbaacaadbddaddbdcbcacdddbcabbbacddaccacdbabcabcadaacbdaacacbacbbbbccbdcbdaacdcadbbbabbdbadcbaaccaabdaaacabdaddbdaadadaacddaaacccbbcbbdaddbbcbdcaadcacbbbbdbacbcaddbccdcbdbbbccabaaaccadacccdadbbcacbaadbccaacbcbcbaccadcbcdadbdcbcbcddccbdaaaaacbbbbddaadcdbacabdbccdcdadbbbaddbbcacabbdbadccbccddcddbbcabbcbaccbdcdbdcabbaddbdcacbadcabbdcbdbcaddccaaadbbaccaadbddcabdbaddbbbaabdcdddcaacacbadbbccddbaadbacabdcaaaccddcbabaaadcddcbbbdbcadbcabcbcccdcacbacbddcbdaaddbbddaaaaaadbaacadcbdddbdccbbdddbababaaddddcaccbcadddddcdcccadccaaaacbaaabaabcddbcccbadcddacbbbbacbacdaccccdcacdbaabcdabdaccabddbaddcadccabdbbbcbbdadccccbbcabdabacacdbbcaacaaaadbcddcdbaccdacacacdddbdabddacbdcdbaacabbdbdacaadccddcbdcbbbaaaaadaddbcacddaccbcbcadddcdddccadddcbcadcbbdbccacddaddccbcccbdccacdaabacdbaabadadadddddadadabbbbdcdbbaacdbacadaaabccbdbdcdddcbcdacaccbaddaccdbcbaaccdbbcbabbaacddcdaacaaabdbcbbacccddddbdadabcacbabcbbbadacbacbcdadbcdaadddbcdbbaabadbcbddcbbdadbaaabbadacdacbcadabbdddcbbdcdbbcbbacacaaccbabcdacabbcdaccbdddcbcaaacadcacccaadbcdadbbdbcaabacaaccabacacbbbbacacbccdddaaddbabcbdccbbbccbdaddacdbadaddadccdaccadadbacbdacbacddddbacccbacbacbccaacddddcccabacacabdadbddcabcacdbbcdcaddcacbababbcbccbbdabdabababadbbdddbccdbcccccbcaccbbaddcdddbdbaacddccdaccabdccbbcdbbcacacddadcbdcdccdacbaccbdccdcdaccccacabcaaddbcacdbdacbbbdaaaddbbdbaacabccabbadcbbcbbbbcbbaacadaabcacabbccdcaabaabdaabbaddbaadadcaaabcbabbbbabdadbbcbaaacbdbaabbcaddcabddbdcacccabbbbdddbabcaccddbdddbabadcbcdddadadadbacdccdcaccdbddabbcbccadbdccdbacbcccdddcbbdaacdccabbddbdbbcdbacdaacaaccbdcddacacccbdaadddcabcabbcbadccacdddcbbdacccabadbbbaadccdaaacccbdaabcddaabcdddbaccdcccbbdbaddcdccadaabccadbaabadbcbcaacaacadaaadcdadccdcdbaccababddcdddabbbdcbaccccbcddddaaadccbbbbbcbbadbcbdacbcdcccbbaccacacacccdbdcdbbcabcbbdbccbbccbadbdcccdddcdbdcdabddacabdbdddcdbdbbaddbaddbdadbaabdaccccabadcbcccdbcdddbacbcbdabbadcbddcabdddcccbabdcbcdbdcdbbdaacdabdadbcccabdddbaaabdabdaabbdadabdccababcaadaadbacbdcadcaadaababaadabdbcacccabcddbdbcdddbbdabaaddbcadaddaacdcbaddbcddacacadcbdaaacbaaaabbcdddaaacbcdcbdddddacbdaddddbdcbccdbdccacdbacdadcbcbbddcdbbbcbddbabdccdcbbdbcdbbccaacbbdbbacaaddbbaaadcccdccdcddabdcdcbabdcbbcbbcccabcddaacbddbbdcddacdccdbabaccbcdbadbaabababdcaaacbcadccdcbbdcccdcaadddcaccdcbabdadcbbbcbbdacbaccddbcabcbcadcadcacbdddaddbcdbaabdcdbbcdbcbcacaaaabdddbdaaadbcbabddaadbdbacdddcdacbddcdbdcdcdaddcbaaccbaaaaaaccbcddaccbbdbcbbaabbdccaddacabcbbcadcccdddccbacdcacdbcacddbbaaccaddcbbdbdcacbbcdcbddbbcdcaabbcaaaaababddaacccbacabcccaabddabdaacbddcddbbacbdcbaaacacdcdddacacaacbcaaaabacbaddabdbbbdabaaaccdcbacbcbcabccadcacdbbccaacdcbaacacccbbddcadcaccdcabcddbdadbcbdcdbcccccaacdbcdabdbbadcbbdbbcacaacdabbbcabcabadcdacbbabcdacdccbcaadbadbccdcdadcdcabbbdaacbcacbadabcadaacadabcdcdaabccabcbaabdaddbaaacdabcdbdcabcdbbdcbcbacbbdcabdddccadcdcabdcddccdbaaaaadcddccaabbabbbbbdbaccddbabcdbdccdcadddabaabbbaadccbcdaaaaabaababbcdbbbbdcddbcdbbddbcacdccbacaadadcacccabdadbbddccdcdaacadbddddbbdbcaaabccacdbbbddbbbdcaabadabdccaccadbbcdddccbcaabddddadccadadaddcabaaaddcbaacadbadcdbcabdbabcdcaaadbadcadbccaaccbcbbcddcbabcacdbccadbbcddaaaabddbcabacddaacbbbdaaccacbadaddbbdaccbbabbcbbcbbbcdcbaccbbbcbcdcbdbcaabbdcbbcabccbabadbdabccdaacddcadcbbccadcbcdcccbdddaaadacbcbcabaaddddcddcdbbdbaaabdbccccddddadbcbaacacdaddbcadaaddbdccdddccdabcdddccbabccdcbbbdbbdcbddcbbaccadbdccdaabcbaaaabaddaadcddaccbbbbbaddadbabdabbbadcbbcbadcbacdaaacaabaaddadbabaaddabcadadcacbcdadbcaaddccbcadcdaaabbbcbbbbbccbadddacddbdbdcbabadabdcddabdcacddcdddccbdabdbcccbcaaaacaabddbdbaaaccbbbcabdbdaaddbbbcddbddcdbbdcbaaddcbbdadcddccacdbddadbbdddcbdbbadbdcdccdbdaacadaabdbcabdccabbbbbdcadbbcdbacbaccdcdbbdcadabdcbdabbbcaaccddacbbbadbddacadcbadcbcddbadadcccabdaabcaadaaacddbbcbadcbbbdccadadbbbcbcadcacddacbadbccabdcdacabaacdabcbdcdbaacddabcaaacabbaccdcaadbbbaccabbbbbbadacbabaacdabadbcdbdabcdbdaaaabdabbccddadcdcadcbabcccacdbaabadbbbdddabbddcdddaabdbbcdabdcdbcbbbdadaadbcdbbcbccacabacdcaabddcbdcabaddbcbbaabdddcdbbdccdcccacacccbdbbbdcdbddaacdddadaacacdccccbddccbdacbbcbcdcadcddbacddbddbbacdcdaacadcadaaaaddabcdbcacccacacbbdbabbdcacbbbbdabbcaddadbdabadbaabbcbdaddaadabdcaaaaaabdbadbdcdbcbdcccaadcbcbbbdbcaabddadcabdcbcabccacdbdbdbadcdabdddbcacbadaabbddbaacabbbcabaacbdbcddcaddcadbcdaadcdddbcdaaaaacbdbbcdaadbddaacbbccdbcadbccabadbddcdddbabbbbddbcbbabaaacdabcdadccacbabdbcddbadcadabcbaacdbaaddcdcbcccadadadadddcbbcadcdddbccdcdbdbdbdacbcbccabbdaddbbadaadaaddccaddbbabaddabcaabcacacacbbcdabcbcaaadbdcbcacbcbadcddadabbaaabbdababaddacdbaddaaadbaaaaaabacacabbcadaadcacdadbadcaadcccbbccbacdcddcaadbbbcadaddcbadbabcadadbadbcdcbccddbdaabaababcccbbcdcbdababcdbdcaadddbadcdacddbccdabbcdbbacaaadaccaccdadccdddbabdcccabadddddacdcdbcaaccbaddcacddacabababcdddabcbacbdcadbbdaacadcbbbdadacacbdddbccadbcbbacdabdccababbaabdccdcbcbdccbdbacccdbabdaccadcdcbcdcbbdbdcbbaddbbcadccabbacaaddbaddaabbccdcbdbaddacdbbddcadbaaaabadadbdaaddabacdadacbacbdbccdadcddcddacacadbbccadbaddaadbccacacdcbbdacabaadacbcdbaccadddaddaadacaabaaabaaabdadbbcddccdadcbadadabadadcbccacdabdbdccbdadbacaaabaccacdbdadddbccbcabbabbdadcddcbbaddbbccbacbcbbbddbbdbbadcbdccdccbacbddcccaccabbabbadaabdcaadccabacdbbcbcaaddaccdabdbddddcacdddaddaaabacadbbdabdbccaaabbbbbbbabccbabbbddaaaadbbcacddcdaabbcaabccacdbaacbbcbaaddabdacdbacddcbacacaabcdbacaacddcbddaabaddbabdccbbccccbaaaccdaaadcddbbadbbdcbacabdcbbdddcacbabcadcbacadccbabbbdbaabcabdadbadcadcaccbdcaddbbcbbbbbbabddaadbbcdabcdbcaabddbacadcddbabdbdaddbbdacdbcabddaacdabbbdcddcadaaadcadbabadcdcacddbabcdcbaddcdabbdaaaddbcbadddbbddaadbacdbbdcddbabbccabcdbbcbdbbbbaaddbcdabcaaddcbccdbddabbbbcdaaaccdccadbbcccacbbbbccadcbbaabbddadcccaddcbbdbdabddbbcadabdbcbaaabacdaabbacdbcdaacddabdbddbddddbaddaaccaacbabbbbdccbcadbddbdabaccabbddcdcdcabaddddacdddcacabcbaadddccdcbdcddaaadccbcbadaccddcdbacabdccdbbabdbbddbcbdbdadcaadbbbaaaacbdcdccaabcccaddcabbccadbabdddcdadbabbdacdcabcababbadccbccbdcabdbbccababbccbbadadcdcbababcccacbcdbddbaaaddbddbbbdabdacaabbcdbbbcdabbaaaddabadbcaddaabcbbbbcacaaccdbadbbdbccadbdbccdcabdadcbddbbdbbacddaddabdaabaabaabbbbdbcadacbbdcbdcdcdcccbcdadcdddaaababbbadbdaaaccbaadbcabbaadcadadccddddccaabadcacdbdabadccddbaadddbcaaaddbcbddadabbacaacdbcaacbadcbcdacaaadcbcaddbacadaacdccbaabaaaaaacabccbdacdaabddbbbbdccbacabcddbbdcaabbdccadabbdbcadccdbabadbcacabaabaccccdccaacadcdbccdddcdddcdadcdddccbcbbaabcdaccbababbbdabadaaaabdbccddcbcbbdbadddcbcabdbabdaacdbbbbdcccbcabbbbcaaddbdbcccbbdaaddcccbddcaccdccaaccdaaadbbcadbcbddbaddbadccaddababdcdccadbccacdbccdadaccaadbdbbcabbdcdbaadbcdcabdbdbaabaadcaabdcdbbabadddcbbabaccacccbabddbddddaadbabdccbbddbdacbcbbdbbbadbabcaaaacabacdababdbdbdacbbbdbddaaaabcdbcabdbcbccbcadccbdacaccdaacaabccddbbdbdcabdbdddabdadbabcbdbcbcbacbaaaaacacbbdcbccccaddcdabdcddabdaabcdacabdcbdaacadcdbbbddacdaadaccaccacdcbddcbabddcbbbcccbbcdbdccacbacaddbdbbdcacdbcabadaadcccccbbcddbccacabdcadddbcdaddbccbacabcbccbbaaddaaaacdcacbadbcaabccccbcbbdbdccdbddadcdcbbaaaccaaadbbadabcbdcbbddadaccbcaabdbbcababbdcbdccbacdbccddbbadcadcdcbddbbbdbbccdcabbbbbbadaadbadacddadadabbadbdccbbcacddaaccdabaadccbabdccaacbddadcbcbadbdaabdddbabadbdabaacddcbaaabbbbdabddbaadcbdbaddccabababcbddddbdabaddcdcccbdbcccdbaaacaccabcddcdadadbaddaabbacbdbaaacabbdccbaabbbaadabbdbbcbcbacccdddbcdcdcbbabbbdbaccacadbdacddaadccdbadbcabcccadbddbccdbdbaacbcccddacbbdcdbcbcbcadcadbcdbdcaabcbdbdcdcdbdadcbbddbdbadcbadbbccaacdcacababdbacacaacdcccdbcdaccdcdbabcacaacadabbabcbdbabbabccdcbcdaccbdddabdbdabdacdbcacbbaabaaacbbcdacbaaccccdcbcacccccdddacbabbdadabcadbdacdbddddacbbbddccabdcdbcdccacadbdbdbcccbdadabaccddbacacdabbbcbacbdcbacdddaabbccdbdcddacccbcaacccbadbcaabcdabcacabbcbadadbdabbbbbbadababbdaaabaaccaadbcadbbaababdbadaaacbacbcbaddcbcccbcbbabdacdabdcddadbcbddbbddbcddbcbbbaaddbbacacdbcabaabdbdbdcaddccabdbdcbbbacdbbabdbbdadbaaaabbcadccbdccdabcacacbdcaaacbbaaddaccbddcadbcbabaabcadcbbcdccdaaaadcabadaadbbdcbcdcadcaadacccbbadbaddbdcbddadacbadbdddcbbbbcdcbabbdddcdcddaddbddcaaadcddccccbddabaadbddadbcbacdadcdcbcbbadaaabdaddabdaaaccdcccbbbbbcddcdcbddaadabdbaabdddacdbadaddccabbbaaacaddadcaaddbacaccbcbccdcaccccaaddbddccbcaaabdcacbcddccacacabdbbadcbdbabcabcdadcabddbadabadadaccabbdadcadabcdcaccacddbcdbacabadbadbbabacdadabaccbdaaadabddccdcddbbbddbbcabdbadbbcbcdcbdbbdbdacabbabacadbbddddcbddacacaabdababbdbadcddbbddbadbabcccccdddccbdababcadabbcddcbdcdcadabdddddaddccbbcdaccdaabacabdbacbbabcbdbbcacdcddccdbddbdddcdbdbaadddcdabadbcccabbadcbdccbbcddaadbdaccdbdbcbbbcaabdadabddbdbcbbbcbbdddacacacdadcccababaccbcaabbdddabbacdaaaabdbcaacabcaaabbaadcbacccbccacaacbbcadcbbbdccbcdacbcacbbacadcdccccaccaaaccbdbcbcbadadcbbbcdccacadaabcbbbdaadadcdbdbabdaabaddcadbcaadcadadabbacaacbccaccdadbdcddcaddbcbbbcbaabaddbadcabcdaaacacbacdcddccdaaaaadcaddaacaacaccddcbbaddaadcbcbaaabbbacdddbbabdabdbadbaabddcdaabbcdcabbbcbadcdddcdcadcabdcadcadaccbcdbcbbbaadabdabdcddccaddddcbcabcccababcdbcbccabcbddbbcbcaacbaccddacdadbdcabcaacadbbabacbdbddcccaccaacadbbaadcbcbbcddccccdddbabddbbaadacbcbbddcbbdaabbadcabdbcbccbdbacdcabcbcacabcabcdadbcdacaaaadacdbacaddbcbcdcdacbbbcbadadbaaccdbabbdcddabbbdabbcabaaababdcbaddcaaaabddaacdabcdbbdcbdbdddbbcbddaaadaddddabbccadabababcadddbdbabaaacbcbbddccbdcdaddccadabbdbadbdccaadcccbaaadcbddddcbdbbcabbacbabbcbddbbbcadaccbbdbadaabdaacbcccdbbdacacbadcbbbcbdccaddbbcbdbdcadbcbdbdaccabdbcaccccaccdcdcbcbdcbaadddcdcaadccbbaaddadbdddcdabbcddaaddacdbbbaadbbaacadabbbadbbabcbdababcadadcadcaddabbccbbabbdbdacadabbcadcbcccdbbbbadcbdaccabdbaddbccabbbcdadacdabbaabaabacbadbdbdcabbcbbdaccbacdddddbcbddaddaabddccacddcbaabbcbcbaaadccbdcacaddbdacdcccbbdcbbbdcbacaddacbdddddbccdcadbadcccdcbccbcabdbbdaaadaadcbdccdbddabadcdddacabaabcabdbaddcdccabdbaaabdbccddccacaccbdddbcccadbaabddaaadbbcadcbcdcbcaaabbaddaababbbccbddcbbddcdbacbdaaaadbadddcdbbbcaacaccaacacdcadabbcddccdcabdbaaaaacaddaabbccbbadcbcadcaadddcbdabdcadadacbbccdbbbdaaadbbdcbdbcdbababbcabdcbccbcddcadcaabdcdbbbdcbdcccaacbbdbbaddacddcbacabcccbbdaddddcdccdcccadbacadbcbdcaabcdbdacdaadcbabbcbbbddcbabbcccadcabdbaaacddccdcaccbbcdbdcccdcbaaccccbaddbbaababdccbdcacabaadbabccdbdaadcbabdacccdadccbbdcbcaaaabbcadbbddbccdddaccbdddbdcbadaadcccddbcdbbdbbcabadddbcabcbddddacdbcaabcbbcbbbaddbbdaaadadcbcbcdccaaddcccadbcacbbddcdcbabbbdbaaccbabdcbbbdbcbaaaacdaabacdadaccbcadbbcdbacbcdcdacdbcabbcbacdaadbbcaadaadbabbbdacdbbbdbcccabccddbadadacbddadbcbbddadbadadbdcdcccdadcabcadabbacacddbbccdadcbdbbabbaabaabddadbbbdaccddaabcbaadbbaacbcdcbacaadddbccbabaaadbdabcbcdadcbaadbaacddabadbdbdacddbdabbacdabcbabdbabddbddaadabcbbdacbcdaacaddbdaabcabbaddadaabdacaaddaadbcabcabddbbaddbbabdcdadbcbbadcbbbaabaaaabcbcaacddbdababaaabddbacccaacadbcddcbcdabbdcdbbcaadbcdbaabcabbabccdbbaaabaccaacdbbcddbacddbdddadcddbabbadcbcadcdbcbcdacdacbdaabcdcbadbaccaadababcccdabcacbaccaadaadbbbacdabbcdaddbacaaababddaababbbddccdabaacaadadcaccaccdbaaccdbacccdbbccbccbccdddaacadbddcccdbcbccdbdadddabdcdaadbbbccddbaaaacadbddcbaddcdddbcbdbdbcaccacdacabacdabdcddcccabddcaddcdabccbbdadbccbccbdbbccdccddbdabacadccdabcddbadbadcaabacdbaadacadaaaadbdcbabddbaadcdaddcadaadcccccbcdcacbabbcabcaaabcddcadcdddcdcdddabdcaaacccbcccdcaccccddddcbacabdccadbcbcdcabdbdbbcacaacbbaabdbbaabaaddadbbaabccbabdacadddcbabaadccbadcabdbbbbbaddcccccaacdaddcdbabadabaadcadcabaabdcacdabaacbdabdcdcbdaadcdbacdcccdccdacbcaacababaabddcbcbcadcacccdaabcbdaddddccccddaacaacacbbacbbbdbbbaccdbbaabacacbacbccadabdaacbaaaccacdbcbddacacdacbbbaabbdccdabadcbbabadbcaddcddddbcaddbcdccadabcdbbbddcccacaacabbdabdcbacbabbaccaaacdcacddcdccabbbccadbbbcbcbabbdbdbddacadcdcbdcabbdbadddacadaddddaaddabbadddddbbcbcbcccccabdcbcaddadbbdccaacadbbaadacddcabbbdbcbbabcdbcbabbababaaabccbdcdadaabadbccacdbabcbbaaabbbbdccabaaaacccdabdbcbccbccdaabadaadabdaadccaaacdaccbadbdcdddccccadcccaaccccddbbadbabdbbacdcdbdadcbccbdbdcdbddddaccccbdabcbddccbacbdbacbbdcdabcdcadccaacbbabbadcbbccbdbadccabcbdaddacadbdadbcaacbabcadaccabbdcccdcbddddcbbdcdadabadabbdbadcccbacddcbbccabdbcddcdcdbaaacdbddbbcdbcbdbddabaccdcaabddaddbcddcaaaaabcdbbcbdbcccccaabcbadbbbdbbbadbadbcbbbadcadcbccacddcabbcaaacbddacbaabacadabdbbaadbdbbaccccadcadbdabcccccabbdbdbdabbcadbbbaabcaccbdcaabbaaacabcbdddbdbcbbbcbdabdadadcacbdbbbbabcadccbabaababbbaacaccbdaaaaacdbbcacbccdcdacadccccddcaadbacbdbdcaacccadddcccacdacdcdaaadabcabbadcbaabadccaadacaaaacaacdaadbbbbaaccdaadcbacdbdadcdbcddcaccbccddaaabcccdddaabadacbaccdcdbdbacadddccadbaacdbabcabbdcacacaaaccabdbbcbcddbbdabaacbabdccddbdaabdabaadbddcccbbddbaaadcddaabadabbbdadabddccdabccdbaaaaaabdccccaccbccdcacbcccbabdbbbdcdcbbdcabddadbccaacadabadbcbdccacbbabcadadccdbaaddccabdaddcbaacbcccadcbdabbbabadbddadcacbaaaddabcdaadddddaabccbcbcdbbaaaaaaaaabcbbccbbaaacdaddccbdbbbbcdbcdddbdcbaaadcbaaacbabbbabadddcbabbddcdbcbdbddcbbacddcbbccdbdccdabbcbdccabbddadcbcdbacdbaddaaaabdbacadcddcacdcbcbdbbdddddadcadccdccbdccbcacabbcbabcabdbdacadbdbabddbdcdacbdddbcdddcdcacdcbccdaccaabbcbdccbcdabacdcdacadaddcdccaccbababbbdbdbccbacabadddcabaadacbdbbdacdbbabbbbbccaacbadaadcdabcddbbaabadcaddbcddcddcccdbdccbacdbdabddbbcdaddbbbbcaabdabcdabccbadbaaddcccccdbddcbbcbabbaccbbadddababadabccaaadacdbbbbbdcdcdbbcabcaddbcddbbbcdbbddccaacabccbdcaacabddddaccaacaddbddacdadbcdbaccbcadddccaddcdcdbadcbbacbcadbaabddcdbdccdaabdbaaddaaccaabcbacaaddcabacdccadbacaddccacdbcdccbddbbbbdaaccddbcadbaadcdddabbacaabaccccddddbbcdcdbddcbdbbbdcdcdadbcbcbddcacbbbcbbdccdddbbbbabcccabbbcadbaacbcdcbbbcadaccacdbaabbccbdaaabccacbccdacabccbcddddaaaadadacccaabaadbdddababbaddadacbbaaadabadbbabaccbcbcbabdaccadbcbdcdbaaacabadaccacbbdaddddcaabcccbbabdddcbadabdcaccdccdbddbadacbccbdbaddcdaabbccdbbbcdaacbaacaaaabdddcacccdbddaabbdcdcdcdacdccccbdacbcccabbcdcaacabccdbdbccccdaccdaaddccdcbdddbcbddadacbdcacdbdcaadbabbadcaaabcacabcdcccacdadbcdccbabaddbbccbccbabcdcabbacbacbacadddaabbbbcccddcddacddbcddcabbdcbdabdabcbadcdddbdaadbdbadadbbdcdbabbabbdcccbcdccabcaabcacddbcdcabbccdcbcacdabcaacdaadddabbabbabcbbcdbdaddbcaacbadcabbbcddaaccdbcdcbdcdbddbabdabadacbdbbdaacabcabdbcadcbdaddbdcaabbdddcdbbbdbdaccbdabddcabbddbdcbdcbabccbababdcccadcbadccddadaacccdaaccddcbdaacdddcbbaddcbdabdcddaacbdbcadcdbbccabccddcddcdacdacdabbcaadcbabbbdaabababdccabbadadcdddddbddcddacdbbcabdabaccabdaaaadcdcbbadabddaabcacacddcdbbacadbbacddababbbaddbadabdbcaaccacaddadaacbdcdcabbaaaccbbdcacdbdabccaaaaddcaddabdcbcaabcababdabdbacdbadaddbbcccabccaaaabddccadbbacdadbbacbbacdbcbacaaabdbbdbdaacbddbdadbdbcccadaccacbbaabdcbccbacaacdbabaaabccccdcadcadcabcbccdccdddbbdddccbdcaaabdccdcbabdbabbbcdabdabddbacddcbbcbacbbbbdbddabbbdbbbabddccdcbcdacdadaaabcdbbaaadccbabcabadbdbccadabcbbbadaabbdcccaccadddbdadbbdbbbbbdccdbacdbcbbbadddadacdbdbbbbdcabdcbdcbacdbadaadbcdbbaaabbacbbddcdbcbcadccbacbcacabbbdcdaccbdaadcdbcadcdbbbcbabdccddbbabbcbbbbbccbabaddbabdadbacccadbabaacbaabcdddbccdbbbabdcdcabbaccbdddccbdbadaadaaddbabdcabbdadcacccaaaabdacadaccacadddadddddaabcbbbcddabcbaadbadcaadacdaddadcabadccdbadbddcdabbadbcddbababaabbcadcdbbcabaccaaddadabddaabdcabcdaacbcdccbbabaaccabcbcbbacbbadddacddcbccaaaababbbdbdbcbbcbadcabacccabaacadaacbdcadccdbccaadabcabcacccaacacdaccaddbccadcbcdaabaaaccabdcaabdbcdadbbdabddbdbadbbdbccddaacdddacadbadcdacabbadabdcbcdadcdcdccbcabcadcdbdbdadbdccdbcacbbdabaacabdacdcdbcdacdabbdaabccdbaccabcddaaabccdbaddddcddacacbdacbadabbaddddaabadbacccadcdaaaabdbbbacbddcabcbcdddbbcbbccccdcabadcccbdaacccddddaadbaaadadbdaaabadbcbbdaddaacdccccbdbdaaacbcbbcdacbdbaacaddabbbcdbaddbbbacadbbcbdcbbbabcaacdcdbdabadbcdcabbbbaddcadddccacddbdabcccbdbcaddadacbdabdacdcbbddcbbadabdbcabbddccbabacbbaddaadddbcbddccabbabbdcbccabcadaadbaabacbdadcccdacbcaacdabcccdbbdbbbdbddbdcccdaaaccdaacacdddcdabcddccbcdadabdaabaccaacdbdbacddacacbdacccadbcbdbabbdccbbdcdaabdcacbdbbbbbabcdabdbbcacccbbcccdabccddcacdcbbbcbaaddabddcbaaabdacadabdacaaccddaacbddcaccbbddabbbacaddbbadaacdbacdcbbbbdcbdaabdbccbaaadbbbdbbcdcacadaaabbdbddccacbabcdbaacbadbbcadcbbabcdddbbdcddabcbaccadddbbaddccacccbbcbcbcbabcaabbdccccacabddabacaaadcbdadcacdabadcbdbcdcaabddcdcaccdacacacacbdcadbaaccddabccacbbddbcdadabaabdcabdddbccabbadbbcdaaddbbacadccaaaadacabccdcaadacdcdddccacbacdbababadaaddcbdadcddcabaabcbdcddbcbbccbacdacdbbcdbcadbabdbddcaaddababbcaccbdacacdabacbacabaddbddcbdaddacbdcbdbdabaacdcabddaadbdcabdbdcbbabacabdaaaddaadcbccabacbadabdcadabcaabadbdcacaccdadcdacdacdcadbddcacbabdbdbcbbdbbcadbbddcdccccababbbcdaacbbdaddbbccdcdcdddbabacabdddadddbcbdbaadcdddcabdaabdddddcdbaaaadbcbdadcbbaabcccdbacdcdaaabadabdcbccabbddaacddcdcdcaccaacccbdcabddbcbbdaaaadbcacadabdbddbcdcadbdbdbadddcbdbaddadcaccdbdacdadacabcabaabccbdbbabdabbdcadbdbdddcbbbadabccdaddccdbbdbcbcdcdaadabcacbacaccdcaaddadbbbbbcadadbbcddaaaabacdabbbbadaaaadacaaadbadbbadbdbbddcdccaccddcbcabaadddcdaaadbabdacbcacdcbdbccbcbcbcccabcbdbcadccbcdcacdcdbaacbbccbaddcbbdbdadcbaccaadbcbcdddcbdccbabcaaddcbdcccacdabbabaaccdaadcbaabacddacdcdbdbbbcabdbdcbcccccaddcaddcacbbcccddacacaaacacbdaacdabbbdacbcabbddabdaabbbdadcbdcbaccabcaddccabcaababcbbaaaaccbddbdcabcbbbdacbdbbdbacdadcbddadbbcdcccdcdabccaabbacbcdbbcdddcabaccaabbdbddccdccdbbcbdccbdcbadccbcbcbdcbcccccadadadabbabbccabcdbdcabbabcabdcdccbcdccbbbdabdbdcdcdacbcbcbacbcabbdcdabdbbcccacaabcdbacadddabcdcababdbaabaaacadadcbdcbbabcadcbbccdacacbccacddbdacbbdbbdcacaadbbdddbaccbabaddcbddaaccdcabaccdadbacbbacdaddabaacbaddadcbddcbbbddadadbdbdcbbbaadbaddabacdadcdaccaabbcaccaacbdacbcaababbadcacadadcdddaaacdbddcbbcacbcadbbbadcacabbdbdcbcadbacababbadabaddadbbcaaddccbcddcdcbbcbabaaaadaaacdbccabcabcdbbcaaadcaaadccaaabaaadbbabbcbbbacccdcadcccbcbdbdadddcdadbacddbaacabcbcbddddbbabbbbcacaddbdcbaddbdcbcbddcbcdcdadbbbbcacbcacabcacddddcacadadbadaaaaddccabcccbbbdbacbbbcdcadcbdaddbddbbddbabcdcaddacaabbacaacdccbaadcaccbbbdcccbdccbabbabcdcababcaaadddbdacccabccccdcddcbbddabdbbbcbdadccdacbdababbcddcacbdbbcbcbddccddccbbbcacdccbcaddcdcdcadbabbbbabcccccadabdaddcdcbaccdccabbabadcccadcabbabacbbccabbaaddbacaccdbcabbacddccddcbadcadbccbcdbbddabbabcdbbbbaaadbdabdacbcbabccabbacabbacccdcbbbdcacdabaaddaccbabdcabdcbcdacccdddacddabbdcabdccdbddccadaccbbdadaccacbcddadadcddcabdbbdcbcbacbdcaacaabbaddbcabbdccadcaaabcbcdaaccacaccaabdcabcacccdcbaadbdbbdbcaacabcadaddaabbbbcdabaadcacabdcbccbbabdadabcdacaabbcbbcbdabdddcbcdbcaabdcddcabccacdcaadaabbdaaddaddcccadbbadcbbdaaaddaadcbccacabbcbbccbcbadaadbccbbcddcadaccbbcbdabadabaddaacbddddaadadabdbabcaabdbacbaccdbbcddccccbbcacacccaaccdacdbccdbddcdabccbababcdcbdadbbddbcdadabccbadbcbdbcabbaacbdddcabdcddacbabaaadabdabbdaacccbacccdbbaacdbdcaabccbdccdccacadaddaadacaaabbadabdccaddaaabccccbcabccddabbaadbdadaaaacacaadccbaabdbabbcbdacaadbbbdccccbcbbabdcddcadabcdbddccbadcbadadbcbcdcabbbbadddbaaaccbbcdcdadccccbbaadddcbbdabaaccbcdcbdcdcaaddabcdcdbdbcdcbadbadcdbbdccbabbdbaccdbddacadcdacbdcadacbbdacdcccddabcdbbbaabddbbcbabdcadaddbabcaccbccbbcaabccccdcbcaacacbcabbdaddbbcaacadadbabbcbadbdadadabbdcacdcabaddaacabbdaccaabcabcaabbdbcdccbabbcabbaccaacabbabbbbbcddcabaadbdadbcaaadadddacabaaabadccacdadcabdcdacdbbcacaddbcdcbaddbdcabaaaaaddbdacaaabcdbcddbbaddbcccaaadcddaabacbcbdaabcdcddaaabccbaccdbcccdbdaccacdaddcbdbaabcdbdbabdcdbbcbadadcdbaccddaaabdcabcadccddcadcadbbccbcbbbdcbddcbccacbcdbcaaabcdbccabcbbcbadbdbddbcbdbbcdbacdaccabccdcbadabadaccbddbaadadcaaaaddaddddcdcdbadacdcbbdacabbdddacabacbddcbcdbdabdadcbcacdaddddddcddcdddacaacbbadbcbaabdbaabbabacbadddbbdbaccdbdbadabbdddbbcdababcddadcbacdcbbbacadcbbbacacaadbcdcbddbdaddccabbdacdccdadacacddcddbacadcadcbbdbbdaacbadbbcacaadbabccadabcbcbabdcbcabbdacababccbaabcdbacdccbccbbbbbcacacdcaadccbdccdaccbdddbbbabcacbadbcccadddaadcadcdcaabcdbaacadbcbcabacbdddbcaaccbccbadbdadcbcdaccabcccbbacaddaccbbcbbcbdbdbddadaabbbbaabaadcaaadcdcbccdcbdadacddcbbccbddaacdcbbaabdcaaccdcbccbbcabcadadaabcccbdcbaabacacdacdbdcbbcaaccabbbcdabddadbdabacbbddbaadacbaacdaacbddadbaaadbdabdcbaabaabcddcbbabaccdcdcbaaacdadcacaaacdaaccbddacdadaabbbbbbddbddbdbdcddbccdcaddaccddabcdaaabbbacbdabacdcabddcbbabbcbddabddbaddbdbcbdcbbbaccbabdbbdcaadabaccadbbccccaadcbdbbaaccbbcbbbdcbabcabcbcbddddcabdadbadcbbdccdadaddadbcddcbbacbdadcdbbaadcadaabcdacbddadcdbaacdcdabcbadbdcdcdcbdcabbddcbdcbadcdbdcbadbcbcdbbcaacccbbabdabbcbcdadcacccadcdccabcdbbacadddcccbbddbddccbbcdcbcdaabaabcaadadccaaccbccaadcbddcabcbbcbacdcbbcbbcbcccdabbcdbcbbbbdbcaadaaaccccccaabbaacdcdddbddcbdaccddbbbbbddadbbcdbddbbdcacacdcdcacdacdddddcabcbacadacbdadabdbcacbacadadddddddbdaaddbcbaacbaabbcbcdadababcbadccbdabdbddccacbccbdbbddbbdbabddaadccdabdaabcdbcccaccababbcbdcadddbcdbaaaacdddaddbdcabbaadacdcbdadcacaaddbbccddccccadaccdbcccddcdcaccbcaaaacabaabccbcddbbadbadadacdacccaccdbbbdacdccbbcaddaabcdcdddbbdbadbcddacccadadcaabbdbccbcaaddbcbbcdccddcdaacbbdacddcbcadcabadbbabdbddbadabaaababadcacdbdcbcadabccacddccaadaddadbaadccabbcdcabbcdaaccdbbbdbbbbcdcbbabdacdcbbaaaccdaabcbaccacdaabcadcabadddbbcbacdadbdcbbbaabbccadcacddadabcacddbddbaddaadcdcdcadaddcadaddaccccbcbcabdabdbcccaadacdbbabbbdbdacbbddababbdddbaadbbdddaddddbbdcbaacdbbbaaaccaabbaadaabdadbadccadddabadaaadddadbacacbbdaabadaadacddadcbccccabbcabdbcbabaaabddbbcdcabdbabcababbbabaadccdaadabbcddccabaccabddacaddbcacacacbccadadbbbbcccbddccbdcbbacaaaacaaadccdaddacbddbcbbcdcdbbcdcdccbadadaacbcbbabacdddcabbcbdaacacbddbddbcacdbccaabbaababddcbbaadcbdadaadacccaddcabdbbdddcadbacbcbcbcbbbdccccccdcdcddcccdcaccadccbdbabdabbcbbadbadaacccdadcccbbbbdcbbbbcdddddbaabbdcdcbcaacbbddcdbadaddcaaabcdcbacccbaddbdaabcacdbaabbaaaaadcaccdcdbaddacdadcacbaacbcbccdabcbbbbacaabbacbdbbccaddacbdaaddbbcdaabcaadcdbccdbaadadbabccbaabbbcbccbccccdaddcccbcdbbcdadcbacadcabbcabadcacadcabadcdcadaaabbbbcaabaaaabaaccdaabcaaddcbcaaadcabcdbdbccbbaacabcddadbbcbadbbcdbcaacacbcbadcaacacbdbcdddaadbadcacadbcddbacaabcdaadddddccabddccbddaddbbaccccccacccbbbadbbcbdabccdddbcddcccdccbacabbccadcdbdbbcbccaacabdbaaddcbbbbdadabbddaabbcddabbcbbabaddaaddadcdadbdbbbbdaaddccdbadaddbcbababbdddababacabaaaabdcadbddddaaabcbadbdabacacbbabdacbcdbbccadccacbdccddcccccadadabcdcabdcbdcbcdbccdadbccbbddbbbcddddacbddadcbcddddcabbacacdcbbdcdccadcccaaaacaccbddaababddadbcbbcdacbbdabdaabccdcddabadccbbbddcdcbabcddddbabdaababbbbcddcacdbcabdccddbbcdcbbbdbcbddcbcbcddadcadaccdcbaadddabaccacdbdbadbbcdcccdcbcabcadaaddcddadacbdcccacadcdacabdcbcccbcdababaabbcacaababacbccdcdcccaddcdbaccabadbcdaacacdbdddbccbabcbabbccadddbacabdddacadbbbccbacbacbccadaaabbbccccbccdacabdcabdcabbcdbbdabdcbabbacbdacccbdacdcdcadcadabbdbbdadaabdcbadcbcadabdbccbabaabdabddaddbabbdabcaaacbaadbcbbcabddcdbcdcdababccdbbabadbcdaaccababcdabbdbcccacbdccabaacdabcbbbcdadcadabdaabccbbbbdcdaaadcbabbbcbacaabcddadaadcdccababcdbdbdbcdcbbbbadcbcdcdaacadbbadaacccbdcbcdbdccdbabbddcaddcabaccdacababccccdacdcbcacdcadbdacdddaabbdbdcabaaaabaabdadcddcbddcdaabcaabcaccbdddcbbbadcaacbccdbbadadcccdccadacdbdcaacccccbdabbaadcdaadbacdcaddbcdbcdbabcbdadaddbbabddbbbcdabcdbaaaabaddbcaaacbaacbcccaadddbdcbddcaacbbbdbabbbccabbddadabdbadadcdbbccabacacacbdadaacadcdddaacbbcbcbacdcdabdddbbcbdddddbbcbcddabcbdddacbbcabaddccbcbdbbddddcccbaddacbdddcbadbdcadddadbcabdabdbadbbdaccdaaaababdcddccbcabddabdabadadaccccdacdbaaccdcddabacbdddabbadbcdaacccaaabcaacaccdaacdacddacbadccbbbccddaaadcbbdaabbbcabacbddacdccdaddbcdbbcacbcbacddcadcddaaccbdcdccdbdadcbcabaacadadadbaacbadcabacbdbacdcacaadacbaddbcddcacadbdabbadcbbadbbdccacadcadbbdaccaccaabbcbccbcdaadcdbdcabdcddcacacbadaadabcdbbbaccdacbbbbdcddbbacadaaddcbabdcacccbbcaabcbdabcdbdddbbabaaccadaadccbababacbbaaaacaacccacaadbaccdabacdbccddcbcccabcbddbabdaaccbdaadabbccbbababbcbbdcdbdbbabaaaaddcacdcccbbcdcbacddbcccdaccabddacabcdddcdbdbbbabcbbdadcdcadbbcdaccbbcdcbdadbdccbddcaacaccdbbbaadaaaaccdbbcbaaddaddbcdbcdcdddaaaaadbaacaaabdbcdaacaaaaacbcbcbcabcdbabaddbddcababdcbdbbbcbbccdbddccdbbdcccbbacdbccccaccbddacdabdabdccbdabacbcdabcbbcdccccccdabacbabcadadbbbbaccdcdacbaaaabbcdcbbdacbacbacbbdcadabbbcbabbccbaddbddccbdbccabaacbdaacdcbacdbdbcbbbcbddaddbaddacdabbbadcabbaddcbccacbbbdcdddbddbdcacdbbbdbabbbaadacaaabbacaacbbadcccadcaacaccdddacbdbcacaddbbddaaacdaadbcbdbbbdcabacdddbcdaaabbaacdbdcddcddadaccdcadaabcababaabacadcaccdddddadbdcaaaccbcbabcdaddbadcbbcadddadcdbcabbaadcdaddcdcbadccbcbccacdaccbcbbdccdacacddcdcaadbccdcabdbacdbdbbbaacddaddbaabdbabaadbccdcaacacbbcdbbaddcbbdcbcbbdabbccdbdddbdbddaaaabbcdabbaabacadbaddbadcbbcbdcccabadcdbdbcadcdadcbccbbcaddbbdcabaccabaaaddcbdbcdcabdbcbadcccdababccadadbbdbbaadcbbcdbddbdabddddcdcdadcabdbadacdccdcacabacddcbadbbdbcbbcdbbddabadcaabdaacbcbaadcbccabddccccdddcaaabdbcacbcabccdcabaaabacbbadbcccbdbcaaddcccdbdccabdddddcbbcdcaccabaccbaccabbaaccbaacbbcadabdbbaccbabacbaaadcbcdbddcbaaaadbbcdbdabdbcaadacabdadcbbadacbdcbbdbdabbaddbbdbdbccaaccdadcbaccbaacbcdbbccddcddccbadbabadcadcbcddcbdcddcaaadbddccdddccacdaaaacadadccabadbbdcbcbacbcbcbbabbbaaaadacaadaacacbcadbdcabdbcaadcadcbbbccccdddcbdcdddccbcccbbcdccaabcbdbdbccbcdadbbcbdbbddbcadabdbadadcbadbbcbcddddcbddbcadabcadccdabbdbbdbdaabadadddbdcabdaadaacabddaacbbbaddbddbaabdcdacddcaadbcadbcadddbadcaaadcaccbacabbddcacbccacabbbcddbabdbcabaddcbdcbbcaaacacdcaaddddacacbcccddcbbccccbcabcabccdbdcdabddabdcdadaabbbaaaacbbdadbbbbdcbabccbbabcbcbdabcacabdddbadadbcbbbbdbbbcdbdcadcbbdcbadddbcabcbdadabcbdbaacdcbcacadddcabdbdbddacbabbdccbaccaabdacbdcabccadccacdbdcaacdacaadccdbacabbddbabaaccdaadcbabacdbabccadbbbbdcdbadbdbbdabcdbacaccacccbaabbdbacaabcbbbabbcddbadbbbbcccdadcacbbcdbcadcabbadcdbdcbcacaacdcbabaadacbdbccaadddbabddaccbadcbdcbcadabbdcacbaacbadccddbcbdbdbdddacdabbadbbcadcbdabcdddadcdbaadcaddddbcdbacdccdbacdbbcadabdcbbaddaacacaddcadcbcacccaacccababadcadcadcaabcbddaccabbabddcdbccbbbbddddacddbaccbaaaaabadccadadbdabbdcaabbaccdcacabaabcbbbcacdddbdccddbccbcabdcdbcacddbbbdddabcbbdbabaacddccbccbcdadbcddbaaaaacbcdabccdabbdaadbbccdcbdcbdbddcdcbcdcdbddbaabbbcdddddbbbaddbccccbcdbcbacddbddaaccbbdbdbbddacbababbbabddccbbbacacbcdadbabbdacabcadadbdaccddbabdcacaadaaaaabadbcabcdadbacabcaaaccaadaddcdddccccbabbaadcdddbadbdacacbcccbcadacadcacdccdddacacccdcdcaabbadcbaaddbaccbdabbdaadacacbaacccbbadcbdaabddadabcbbdccbdcbbbbbaaddddbcbdabdbbaaaccadaabdaadcdaaddbccdbcaabdaaacdbbcbcaaaabbbaacaccddbbcbcbbabddbddcccabbdbadbcadadacccccaadaddcbbcadcababaacadacabaabacacdbcdbdbbbcadcaadbbcbcbadbdaacdadccadcdbaccdcdccaaababcbbddaababcdbbcabcabbbdacbdbbdacbdcccadbaadcccdccdadcbdcacdccbdcadaaabbdcbabddabbdbddabccddbbacadbcabdccaddacdadcaddbdddabbcabdbccaaababcdbaaadbacaabddcaaddcdaaaccdbbbcadcdbbbdabcbbdcccabcbcdbadccacbcddcddccbaaaabbcabcbbddadcbadbbadcddcbdcadaaddacbcdbaccccaadbadcdcddccbcdbbbccbbdadcddbbaddccbcabdabaaacaddbbbddcbaabadbdaddbaabcdbacddbcabccbacaccdbcccabbcccbacbdadbbdbbdcdcbdabbcbcbbadaabbdcbdcdbadcabcbcbaccdaaabccdcdcccbababccbbcadbcbcabdaacadadabcbadddaacabaacbddbcccdacadbdbbaaccddadbdabcccadabdddababdddcaaccdcadbdddccadbbcaacdbbdaabdaaaacccdaadcdcdaadaaadcdbbabcdcbdcadaaacbcccbdcaabaacdcdddcbcccadbbacddaddccbbbccdcacabdbaccaabcbddcccdaccadbbdcabdcdacddadcaddbccbccdbdddabcdcacaaaadabcaccddddcdaddbccdaaabbcdddbdcbcbbcbbabbcbbddcadcadccaccdacaadcdacbccadaacadabbbbcacccadaacdbadcbcccbcddbcabcacbdcbbddaccbadbddcdacaddbcccabcdabdaacaaacbaabbdddbcaadaaaabbcccbdcccbcacddcbddcbdcbdbbcbddabcccacbcccccbbcaddcbabcabcbcbabccddbcbbacbdabbacaddbbccdacdcabcdabcabdcbbadbdacdbbbcabbcccadcdcaddcacdadacabbdccbaddbdbcadadadadbcccdbadcbbbdadadbbbbbadbabdbaadcadccaabcdcbcdaaacacdddbacbdaccdabdadbcddacdcdabcbdbacbcdbdabccacaddbadddadaabcababdbcbaabcddababccabdcbddadbdbccdcbadcbcdbadacbcbdacbbddadbdccdabaccaabcaabdabdadbccadcbcdbcdcddabdabcbdccddcdccbacabadaacdaabcbadbadadbcadbcbadbdccbcdddababbccbdddbadbabdaacababbbdbabccbbddabdbcacddadddabacccbbbdacbdabcaaaddcabadabdcbdcacbdaaccbabbdbdbddbccbddbcabaccbbbbbbbdcdbcacccacbabcbaaabdaccadbacbbadaddbabcbddcccddcccdbbdbaddbbddcbcddcadcdcaadcacccaadadadadbabbabbdacacdaaddbcbdcccaadbdaabaadcdacabcdcbacabcbcabbacdddbbddadcdbddbbcbcbcaabcbaacdacbdaacccbadaccbbbbbbadbabaacdababdabcddadadcbaabdbacbdcacbdaacadcdcaabcbdbabbbbabdabbccccaabbdaabaaccbbcaabddcaaaabcacabdbbcbaadddcaccdcacbcccbcadaaddaabdbdccbdbccddabaababbbbbcdadcadbcabacbcccaabbadaacdaadbbdaddccdaccabcbccdccbddaaccaabdaccbccdbdccaccdbccbaaddabddabcacbbaddaabaabacacdacdddbadccbbcbdbaadcdcaabdaabdbaadddcdcbbccdcbacdbaaacbdadadddcdddbcdcdcbccccbadabaaacabcbabbaacbbabadbccbaddcbdcaddababaccaaccdcaabadccbcacdaaabbbbdaacbccdaccaacdacbddbccddccacadbbdaabccdbcbdbbaabccddbccadbcdddbacdddddabdaaddbdcdcbacbdbbdaabdaadacdcaddababcacbababddacbacdcadaaddbcdbabdcccddcdabcdcbccdddcaaacbccbcccddbbcdcccdbbcabdabcaaaabbcdbccdaccacbbacbddaddabcbacdcccbdadabcdcbaaccadddcabaaacbbcbcacdccbdbcdcdccdaaabacdacadabadbcabccdcaadacccbaaaacddaabcbabcbcbaacdacdcaccccdbcdccaadaddbddbaacbaabcdddbbbddcbbbddbcdaabccabbdaadaaadccbacddacbcdaacdbcbccbbdbacacaaaabdabaaabaddabdcdadcdcacabacdddcabbdcbcdccbbadbbdbbcdbaadccddcbcadaadabcacabccdaccaccaacacbbcbadacbdaaacdbcdaddadbadadacaaddbdacdadddaacbdcddbdbcccddaccaddcbccaaadcdcdcaacbcabaccacddacbdccaabdccccdcdddbcaccabdacaacbbdbbcaacdaabbabdccbcbbbbcdcaabbbcdccbaacccabcbbcaacdaacbccccdddccadaadabacaaddabccccaddcaadacbcbbbabdcdbbdbbddaadbdcbbbbadbbdcdaaabddcdbacdadaaabdcaadacaaabaddbcdccbbdcbddcccbcdcbbccbaddbddababddbbbbabdacbaabcccdddacbbadbdcdcbbcbabdbacadbbbbcdadabbdcadbcadbadabcacabaabddbddbabbcababaaccdbbacbcacaaddbdabbbdcbdaccbacacbbdbadbdacccbccadbdaaadbacdcdabdabababbabbcbcbbdacabbbbbacbcaddbbdacaddbcdbadadbabcddabbccbdbbcbbccdbcccbacacbbbabacbddaaddddaaabbbdcdacadcbaaadadbadacbbcdbadacbcaabaacbccacadcaccdbaadacdbabcaddbadccbdccdababdcbadaccaadcbabdcbbbddadcdcacdbbcbacccbaddcdadbbdcdcbbdaaaacaabbcadbadadabcdbacdaacaabbbdddbdaddbdacbbddcbdcdbcaccbbbbcbacaacbaadadaabbcdbdbaddbcbbadddcabcdccbcdadcddcbacbaadbaabbcadacdcdcdbdbcabcdddbabdaccadadcbacdcabadcadababcdaddabbaddbadabaababcbbacabddddaaaabbababbadccabbdddaccdcbdacdcdbcbadaaacddcdcacacdbdabcbcdddbacabaadcbccdcadbadcbcbbdddaaccacdadbcddcbabdbbaaddcaccdcaddadaacdbcaadbcbaacbcdbbadacdbaacdbadadbbacbcdddbdcaaaddcccbdaaddcaacadbccbabbadbbbaaacaaaaadabbadbbcabcdccddcacdcdadbddccacbcacaabbbccabadacddadbcaadbabbcadaccdcddcdbaaacdbbcacdcbaddacaabdacabcacababdddcdcacbdbcdadacbdcdccddaddddcabbdacbdcbbbcdbccdbdbddabbabbbcddbabacbabdabdcbcccbdcccbcacaadabbadbbaddbdccbacbbbdaaabdcaadbbaccdbadabcadabdccdbcdcacadcacbbadabcadbcbbbdabbbcbcdbccabacdbddacbddadbdacdbacacaddacaadcccdacababdcccbdcbbcdddacdbcaccadbadbbadabdabdbdcbbaaacbbcadbdadabcaaaacadaccaaacbcabccaaabbccaccadbbdcdcddacadbcdcbaddabbcbdcddccbdcbbccdcabcdabcbbbbbdddbbbdacddcbbaadbdcdcdbddcabdadcabdabdcbcddabcadccbbdddabcdaaacbddbadcacacdbacbabacdbbabdacddbdbcbbbbadbcdaadcdcabddbcbcdacdbbaaacadcdcbcabccaadbdbabcbbcaaaddbddcdacabcacbbadacbdadcccbbaadabbcbdcaabcdbdcddbcaadadcadcacaabdbdabdccbbacdabadcbcbdaadccbcdadaaadadcdaacaaddbadadbbdcdcbcbadcbaacdcabcccbbbaaaaabbbaadbdccadacdacacaccbadbcddcdbcaadaccacbbbbdddabdcdcccbdcbdbbbababbdbbbbadcaccddddcabcdacbdbdbcccacabcbabcdadbbabaaccbbdcddaadabbddacddbbaaacbcaaabbbbacccccbcbadacdacbdddaacbcbaabbdbaadbabdcbccaaaaaddadddbadacacdaccbbbdbcdbdddaabacacdcabccacbbdacdacdbdddbcabababcccadcbcdabcddaadabaaaadbdccacccbdcabcbbbcdbaddadccbbacbdacbaccadbdbcddcdabacbdaabcabbbddddcbbdacdcaaabcacdccaddcbacbbdadcabcaadcccadbcaabcaaddcaaaaaabacccabcbacccadcaabcccbcdbdcdbacdddbbabacdccbcdcacdddcdaccddbbcadcbbabbadcaccccddbcdaddaaadbcaacbcbadaddabdcccbaccadaabbbadaacddcbcaddacbbaaadacaadadccbdadaddbabbacdbbbcacaccbabaabdcccdcadacaddaddcddaabdacbbdccbbcdbacacdabbabadbabbcaaabacacdbcddcabacccaacbbbadbccdbbbbdacacaabcbdcaacabcaccdcbdddaccdbbabbbabaaddbcdccbdaaababbdddaabdccabbdbbbacdccdaccdbaccaaabaaabadadcbbcbcacacccaaacdabbccacaababcddbbcdbaadbbcdabdbddaccaabdacdaccdddcbbdadbbbdbaacbdbccabdadbabadcdbbcabdacababbacccbdddcdbaabbaaddacacdbcccddabbbdddbdddbcbcdddddbccccbcadbbcbccdcbcadbdcacbdabbdcdaacabbdabdcaaaacabcaababdbcccdacbadcdccbcddaacbadccadcbdacdaabdbccdbaacddbbccbbcbccaadadcbbccbaabcaddbccdbacacbbaacabdbbbbaabadaadabadcbcdbcdbcaabdabdbbcddbbaabdbaacccacddabaabbabdcdbacddcbacabacaadcaabbbcaccdadaadcddadacadcdbcacaadbdcadabbadddabccddadbaddbddaccdcdbbddadaaadacdaabccadaaaabbcbabcdcdbdbcbbacddabbbaddbcbbccccaacccababccbacbbcbaabdbcbcaabccbabbcbcbddcdbccabdcbcdcdbcabccacbbcaacdccbabcaabcbdccbaccadcdacbcdbbdadcaadcdcdabcaaccbcdcdccacdbcdbbcbbadbcbcbcadbaadccacaacdbabadddccbaabbccaccdcdbccbcbcabbdcabcadbdcacbbbabbcacccdaccdccacccbbbabccdcacdddbabcadcdabccaabacaddccbddcabcabbdaaddddbbdaaadacaaccaaadbadccbbdabcaaaabdccbcdaacaadbaaccbaaccbcccacdcdbddbabdcbddaddbabcdabdbcddcddddacdabccbdbaaddaacbdcddcccacccabdddbcbadaadcbaaadbbddabbcbdabadbdaabacbddbbbbcddbadbbcbcdbaadbcbdddaadddbdcdabccbcccdcaabacabbdadbcdadcadbacddcbdcdbbbccacbdbbabbaabdacccdadbabdbacabcbbacaacbaccadbddbbddcabbbcaabcadbadcdbaacabacaccddacaaccdbdbcdcdbacdaacaaabcdabaaaaccdbbcadbadbacccaacdccbbcbacaaacdddaadcbbcbdbdabadbabaccbbdaabdadcaaddbbaaaadbbdbbdabdcabadccdbacdddcbcadabdcaaaaddbdacaadccbcbcdbbbdabadbbddadadbacbbadccdcbadacaddbcbdcacabbcccaaabcccadcbcabcaaaccbddcbcaccbdadddbcaaddabbbadaabccbcdabddbabaddbababcaddcdbbaabccddbaaaaababacccaaddcbbdcbadabaccbcdacddbaabacaabbbbcdbdcdbbadaacdbbbbdcabadcacacabacccdccadcbbabdcaccabcbabbdbdbbbdcaadcbbaacccbcadacbabddabacdcacacdabcacabdcbaaabcdaccacaacdacbbaabbbdcdababbdbccaabcdbdccdaadacdcdbabdbacdccbcbdddbdaccdbccbbacbcdcddabbacadbabcbabbccacbcbdbccdbcacdbadbdbccddbaaaabcdaccbacbccbaacacbcabdcbcddadcbaddacdadcdbbcbccadbbccbaabadcbbddcdbdcaaddddadabbbbdacaacabcdadbdddadbbaaacbccacccbcacbaccdaccacbabbdddcbccadcdbbddbbacaddbcdcccdddcaadadadcacabddadcbcbcdabadccbbabbdddbdabacadbaabaaaaacadbdbbbdbaacacdcdcbcabbbddaacbddbccaaacccaadcacdbbaadcaddbaaadbadbaacccdbdccbbcdacbbbdcbcdbbdabbbabcccbbbcccbacbacdccddbadcddbbdbbbbaacbdcabdbdabdbccdaabdcddadaadabdccbbbabdaabccdbacbdadddbddbcddbddccdcbbacbbccdcdbdcdbdddbbbdbcbdbcaaaadcccbbaccbcdadadbabacbbdcbbbacadcaadcaddccaddcacabcabaaddcccdadabbbbbbadccdaddccaadadacadabdcacccddccdbacbaaabccdbbaccbdddddbcaccacdacbabdbbbbadbcbcbbbcbaadbdcaaabbccccccdacabdddcbccbcbbaabbcdcdcbbcdaabcccccadbbdcdccdcadadacdcbcadcdabcabddacdcabadbddaabdbaccccbdcadbabaacbbddbbcbbabdaaccdddcbcaccdbbcadccddcbacdcbddaaddabddbcdaaccdacdbcabccadddadccccdddabaccbbaaaabbcaaadbcdccbcabacaddbccacbaaccabccbadaccbbcaabbbababbcaddadcbcaacdabbdddbaadcbaddcbbbbbaddbabbcababdbacdcdbdbcdbadcdcbdabadadabdbbbdcacccdbccdabcdaccdabbbcbabdabaaacdaaacbbbdbdbadacdaacaaaccdaabccbbbbddbadddbaaaadbddabdbbaadbaaabddaddbbdcabdaadddbcdbcccbbaabacccadaaabdbacabaaaacdbbaacbcccabbdbbacadbacacbacdbdbccabdacbabdacbcdbbdbdaacaabaaaaabcdadaccccddbaadbcdcaadbcdccdbacbdcaadcbadbddbbbddbddcadabdadcadabcbccdbcbcdbabbdcabaadbbdabbddcababbccbabdbcbbdbcacabadcbcbdbdcbdcaabcbccbbdbabbabcaacdbddccdabaacabbaddcbbccddacccacbbbdbccbadcaabadbbcdbbbadcdbddccdacdabddbbdaaadddddddcbbddbaadacdaacacbddbbaabacdaabadaaadddaacacaabbccdcddbbbdddcadbcdabcddbbbccbddbbddcacdcabbaaacaddbbbbdbadbdcaabadbdadbcacbdbcccbbcabacbaacdacbbcdccdcdddcaaabaabcdbadcbcdadbabdadbbbcadcbbccacdbacccbdaadacdcdacadcdabaccdadbbccdaadadbabcbdcddcbbcabbabdacdddddaaabbbcccaddcddcdbddccbddbaccbdcadcddddccaccdababbadbdabcddbaccbbabdcdcadccaabcbadcddddcdcdcaacdabccbbddbcccbaacdaacaabbcaabcacdacbcccbaaddadbbadbbbabddacccdaccddddcdabaacdaabcbccadacabaaccabbcabbaacbddbadadaabcbbabccaddbacddabccdcddcdcbbbbbcadccddcbbdcacacbadbdbbabbdbabbccbcabbaacbdadbdbabdaddccbaddbdcaddadabbccdddcdccbcbcddacbcbcdabddaddcccdcdacadbacbcbccbbbbdabcccdbbddcaabacdcbdbacacdabdbdaadcddcaddbcbbadbabbabdbdbbabcaabadacdabaccccbbabbdcbbaddbabbaddabadaadbdbbabdcbbdcbcacaabccdbacaaaadbacadabcbabadbccdccadbbbcbaadcbcdcdbdabbcddddcaadcdcbbbddacbacbbcdcbabbcaaaacbdaabdbabdbadabaccddadabdcbaabbdacaababdcacddabadadbadcaacbdbabbccdcccdccaaddccbbabcbadcaccdcddcbddcaacdddbaadacccababcbabadccdadbccbdabacaaddbcbbbdadaababccabdabbdddbabaaccaaaabddbcaddddacbdccbadcddbabaadccccbdbabddadccacdddadcbcccadddbccabdaacabacdcdbdddaabcacdaacaccabdabddcdacbaccabcbacddbcaadacaabdddbcdbcacacaccdccbbaaababaadddbdbbdddccbbddcddbccccdabbabacbadbabbccdbccbcdabdacbcccdcbbdaccaddbcaabadacaccdabdcccdacabababcbbbddaabacabcccababdbaabbccccdddbadaabbbdbcadbbadccabccbccbaabcdbacacacabcacaacadbddbadcccadbcdccaddbcddaaadbddaddcbabcadcbaccbcaadcddadccaadbacbcdbbbcdcbbbaccdbbaacdcbddbcddabccbccccbdcbacdbabdcdbbaadaabcdcbccddacbaaabccabdbdbcddbcddcbbdbccbbdccbdababdbbbaaabdababbcdcdacaabbddbbdaddccbcaddcbcadaabcdddbdbcaccaadacabcbcabccccdbaabddbcdaccddcddccdbdadbabdbdbdcacdcdabdbddccaacccbddbaddadbbbcbabddddccdacdccbdbdbacaacdcccdcadbdbbaccaaadaadcacccdabdadccbcddbdddbcdbaddbadbbbadbbbbadddaddbaaaadadbbdadcdcbdacccaabacdaccabbdbbbbbaccabdababbbaaccdbdadcdabbdccaadaaabcccbcaddbbbadddbcabbbcbbcadcacbbddbbabdaccbddbbbadbacaabccbbaacbddccbcbdaabdaaaccdcbcbbbdbdacbbaaabbbcbcbbbabbcccbdcbadaccddaabccdccabcacdcaccaaadcabbaaacabccccaadaabccbacdbbbbdbbddddcbabaddacccbdcdbcabacdacabbcacacdacbcdaadbcbcdbdbaabdbdbdcdacccbaddcaacaaadbbaaaccddbcacddbaaddccbadccacddddabcccdbababdbddbdcbccdabdaadabadaccbcbdbdaadbbcbdaacbaacdadaaadcaccbbbbaaabddcdccddbcbddbdbccddacabbacdccaddbadbbaaacccaddadbadaacbddbbbaacbcbdacbddacacaccaaaaacdacbdabccccdcdbcdbbddcaddcbbbadbdcaadcbbbadbaaccdcbdadadaadcccbaacdcdacdcddacbbbbdcaabddbdbadbacbdbbcbbdbbcaabaacaadbccbbabcdbaaddddddbacaabaaabacdccbbbbdcbcbcbdadabbabbcababcdbddddcdcbcdaccdddcbbcddbadaabaacadbdcdababbacdabbdccdcbadcbbdbdadcdcbbcbbcacbcbcdbbbdbaacddbcbcdabbcbddcbccdaccaccaddcaaadacabdcbdccdbcaabaadadabbcdbbdcacdbccbbbaacacacbccdaacadbcabcbaddcbcaccaabccaabbcbdbdadbdccdcaaddbaaaccdbbcddbabbccbcbabccbddaddacadccdcabbcbcdcdbadcdabbbabcdccbccadaadcbabccdddbbdcdaccbcdbcacdddcacbbabdaadacacbdccbdddbabbbaacccdaabaccabbdbdcddbcabcdcdbcdcbcabbbaaddaabdcacbbbabacbcccaacababaddcccadacbacadccbcbcdabadbdbbdddbbadcbbbcdbbddaacbbdbccadbbaaacdbcbdbbaccaaadacddaabccbaddacccbabdccbdbaaadacbabddcbbbabbdabcbacbccccdadcbdcbdddbcbdddcdacbdadabcbcdaabbaccdadbcccbdaddddccdcdddbddbbcdbccdabaddabdabdddcdbbabbdacaaabbabaaadabdcbbbdaabcdcdbcdbaacdbcabaddbdaccdaacbbccbbbacdcbcddbdabbdcbdcadbbdacddcacbcccbcabbbbaddcdaadbcbcacbdcbcccadcbdaacadbbcdbbaadaaadddabbddccdcabbbcbabbaccbbaaadcdccadccadaddaacdabdcddccdcdbdcddcacbcbabbaabcaacccbbcaddbbadacabbdbdccbaaadbbcdcbdddbbcbbbaddacdbacdcdcbabcdbbdaadaddcbaacaadbcbcdbbbababcdbacddaabadaddccccabcbacccacccaaadcaccbbcbbbacdbbaacdaabbaccaabccaaabaabcbddcacadbddaddbcdadccdacadadbbdcbabcaddcdbbcacbccaaaacdabbcbdaaaabaaddccbdddcadcabadcbcdaaddddaacabaacaccaadcaadbdcbcbbbbacacdbccabccaacdbdbaababbadcadcdaabccabcdcbdcdbddaabccbdcaaaaccaacbbbacaaaccabbccddcbababadbccdddbbcaaabdbccbacddcacbdabadcbabdbdcccddacaabbccccdcacdaccabdacadcdadaaabccaddaabbdddcadbcdbaadaaadaabdbcbbdbdaacbadbababbbdaddcdbadcaacdcdbdacbdbbaabbbcbddbdabbabbaddadbbaccdcdaaccdabdddbbabcaadbdabccadacaccddaccadcabaacdcbbbccbaadcbcddabdcdacccdcadcadbddabbaadaaacbbccbbdbbbacabbbdadaabccadabbaaaaaccddabacadbacddcadbcabddbcbaacabadaaccadbaabbcaaccaccdcaabdcacacdbbbacbaaacbbbcdadbbacdddabdddaacbaaacababcdadbbbccddbabacdacabdbddbcdbdbbbcbdbabcbcdaaabbbdbabbcabdcbacadbcdbcaddbdbadbbddbbdddacabdcabcdccbacdccaccdacbbabdbdaddaaccbddcdbcdcadadacbbdbbaccbccababcdcddbbccabcbabadbdbaccaacbabbcbbdacaacbabadcbbaccdbadccccccacacddaacbaaaabbacaadbbcaaabcccaaabaabcaccabdddabddbdddacddcbdabbcdadacdabccddcdacdabaaccaaccbcbdcdbcdbddbddbdcbdabcadccddddcdaddbcbadbcaadbbcdacddabaacadbcbdadabdcbaabadddabbadccbadadadccabdadddadcddbadadabdbacbddbdcdacbadcbdbabbbbcadbabbdddcdabcbddbcddbcbacadcaabccabbababbddaaaccbcdbbbddaaabbbaccdbbddddacdbdcddccdbdcdbcdccaaabdcacabdbadbcdabdaddabadacadabacdbaaabcabdcaddbbababacaddbbdcaccbccbbcadabccaabaacddacdabdbcddbdbdcaadbdcbacacbbbabcbdcbaadcbbcbcacbbbbcbdbbcdadcddccbcdabcdcdcacabdcdbdabccbddcddccbbadbdccdbadabadccdadddbcbbdabcdaadcbcaccdbaaddaabacdddabaacccccabacdcbaaacdabddddacdcdadadabdbcccbbddcdadcaccaaaaddacccdbbaabdcdbdacdcacdacbbdaaaaccabbaadaddbbcbdcaddaabcadcdddaacdacddcddaccadabcccabaadbbbaddcbabcadbdcbabbdbdcbbbabbabdddcddadbdbcbdbccdcadadaacbbcbdacbaabccaccdbdabcccaddaccbcbcdbaddadbcabbccadbaacbcbdccbadbbacbdabaccdcdbdbcdcbacacaaaabadcbcccbadcadcbaaccbacbadcaadacbbcaddbccabbcbadccbabcaabbbaabddcdddaabcaddcddcacadaddcadbdabcabbbbacbdaacbaddabbabdcabaaccbbbccacbdadabdcacadaacccdddbbcbbcdccbcbbccddadacbcdadabddcbcaadaadbabcdccdcdabbbbcdabbbababbaabadcdcddbdaadadbccbbbbddaacacaadadcdddbcacadcbbaabcccdccaadcbcacdbaaccdbbbbdddcaabcbdbcbacccccabaaababbdcbcabaadbdbacabdbdbccdacbccaabcccbdbcdabbdcbcdbbccbdaaadcaabcabccccddccabaadcababdbdcaadccccdbaccdaacbdaadcbbdcdcbaadbddcbbbdcabddcdbcddddadbcabacacbadcbcdacaaadcacbadcdddbcdacabcddaccabccccacdbcbadbaccbcaacaaaaccddcbabaaacdbcbabababccaacdcadcdcbcdcbabcccbdddbbaccbdbabbacbdbcbbabccaadbcabcbcdcbaacacadcddddbbaddcbcdadccbccadcdadbcdaacdbbacadccaddbcdbbcadcacacdcbddcbdccbccabadccacddccacaccdcddadcdbcddccbbaccbbddbdcdacadabdddbaacbdcdbbaccaaaddcbdbbcdcabbcbccaccabbbdabddbcbbcdbbadbddbcaaadbcdddadcaccaddbbbcdabcbbaddcacacadbdacacaccdbbadddaccdadbccdcabadcacdbbddbabbbabcabaddadcdccaacbcdbdcbbbabadbdbbcdcaddccbbacdbccdbcabcabacbaccabddbdadcbdddaadacdabcddddbccacddabbcbacdbcdabaaadbaacacacddaabbddcdabdbaaccacdadcbabbbaddadababaccaccacbddabbdabbcccbaccdacddbcdbbdbbdbdbadabbbacdcabaaabdbdbcaaaaaacbcaaacbcdcbbcababcdabcacacdbdacacaddccdbadabbbccaccdaddcbbdbdacadaddcbcdadbdbbcadcdccdadcadbdaabacacddcdbadbcbcdadabddaadbcbcdcdbcdadccccdaaccaccbcddbbddcddbbbdbaaddbdcbccacacbaccbccdabadadbbbbabadbddadbbacadbcadccdadcabdaccbbacdbbdbdaabbdbcaacacdbcdaaaaccbcccacbcadbbbcabaabaaaabadcdddadcaaccbbcdaabdacadddadcdccbdadcccaacbcddbbccbcbcbdbccdadacabdaaabcabdcbbbddbccacabcdccccbadddcbdbacaadababbcbdbabbccbcbadbbcbccadbadbacdbbadadcaccdccbbcbbdcbbaaddbccaddaaccaddcababaadcdcbabbddaabcbaaaddadadabdbcbbbbcaccbadccdcddacbdcccabcbcdabbacbcbcbbdabdcdacddaabadcddbcdbdcabbdddabaccddcabcdcdacbdbdbddabcbacbdbcbbdbcdabddbdddadcbadabdccdddabdbdcbccbbcdcdaacbddbbbdcadacccddadaaaabbcbdbaccddaabacadddadbdccabcccabcbdaacbadbacacadbbcbaaabcdbaccacdabdbaacdacddddbabbaacbadacaaaadcccbbabaccddcbbabbaacdbccddcacaadadbccabbacdbabbbbbddadabcacaddbaaacbaadbcccddbababaadaadddacadaacdcbabbcbacadbddbcadabbacabacdaabadaccbcadbbacddbbcdbbabbbbadcbcddcaaacbcbcacccadaacaabcbddcbaacccadaadccacccdbbbcdadcddcacccbddbdacaddcddadbbcdbbcbccbcbcaadcccdbaddcbabddcadcccdadbddcabbdaddabbcdcdbbdaacbddccadbdbdadcbacdbdccccacaccbbbbccdcbcddccbacabaccdacdbdbbabcdcbccdccddbbcdabaacdabcacbcbccdcbbaddadadbaacbbbdbbbbcdabbbdcdcdccdaaaabdadddbbabadbabdcdccdabcacabbacaddbbcbdaadccbbdbcddabaccbdddcccdacabaadabbacccdabdaaaabbdccaccadbbdaddcacacbddbabbccbdacbbdcbbcbdcaaaacbbcdcdadabaaaadaadcbccbdadbbcdddaabdabcccaccbbcaddbabbdddddcababacdaddcddbabdcaaaabcbadabaadbbadccadaccadabddabcbaaacbacdbcbcaacacadadcdadccdcdcaccbdbcabaacbdcaacdabacdcaacbadbadaacdbccbdcbcbcbbbaddabbdacacdbcccdcaabbdabbadcabdabdacaabdcdaddcaacdcbcbdcaaabacbabdddccdbabcbabbcbbbacdcacbdaaadaccbdbbbaaadabbbdacababddcabcadbdadaacdbadcacdddbdaaaccdcbbadbcbabbabcacadcacdcaadcdddcbdaadddaadaadcbbccacaaadbaadadbcacdcdcaddcbaacddabddcbacdbdcdcbccddbcdadddbdcccbdbdbacabbddaddbbcaacbdccdbbcabccabccdbdaaaabdabbaabadcdbdddcccbcbdbbcbdbabadaddbbbdbcbbcadcdcdbdbadcdcdbadabbdbbdabcdadbdacbccddbacadddabaacbaadddcabddaccbbbdbcadbaadbdbccbbdcacbaddaacbbabaabdaaaddcabcdbcbabdadbbaccadcbdcacdadddccbaccaccabdaacdbdcccacdcadbaadacabdcbacccacbdccdcaadbcacbbcbaacabbacddbbaccaabaadcbbacbdabbddbbabadaacadddccdbdcdacddcabcabcbcbbbdbbbcbacccbacdaaccddddbbdcddababdaccacaabacbbbdcabbbdbaadacdabbabcacbdaabbbdccaabcbdcbbbdcaaaccacbcbbacdcdcdbdddaacbaacdabdccaacccaccdaaabdbdaaddcccccbabbcddbddacbdbabdacdbcaddcdcdcabcdcbcdabaaccabadcbadcdabdadcdbdbbadaaccbdacdabbddcacbcbadbadddacbddcbdcababadddadaddbdadcaddccabaccdbbcaddacbcdddccbcccacbcbacaccbcbacabadbadddabddccbabdcbabcdbdbbadacbbbcdcaaccabdcaccddbbdacbaaaabdadbabcaddcbacbddcacdbbabddbbcddccbcbbaaabcccccbddbbcadbbaccdaababbcbcbbddcbcbacdadbbcabadabbcadabdcdbbdbcacddccdcbcbaabbacbbbcacccbbddaacadddcaddabbabbbacacccabdbacaacacccaccbaaddacccaabadadaabdccdbaadcbcaddcbdcccaadabbcddadaaddcabcbbcaadabacbdabcccdccabcaadcccddcaabbdcdcadbdacdcdbacccbdaddbcbcdbacbcbbadcccdddcbcadcdbbaacbbcbacadacbddcaaabcdbddabcdadcccccacbcdcadaadadbbbbdcdbabadabcccccccbbdadbbdbdbbcabaaabdcabcbdcdddbdddbcbaddbaddbbcadcdbadcbcadaacbdccacbccbacaadcaabacbadccaaccadbaabbbcadabbdadabdbdaadbcaacbcaddcdabddcbcbddbcabbdbbbbcababddcccccccccddcdccdbdbbadcbdbcbbcaaadddaacabccddbdbaabcccccabdddbcccacbadadcabcaadbbbbaccaddadaaadbdaabcbaadabcccdcabcddcaddccdccadddbcbdcdccbdcadbdccabcdabbbbadaaccaaacddadcaadbbbddabdaabacdabccdccadccaadcbdaddaaabadbabdbaaadacdbbbdbbcabbbbbbdcacbccbdadcbdaabcabcccaccacbdcdcdcccaabcdbddcdacdacbadcaccccddaadcbabdabcbabcdacbacaddddabcbcbbdabaccdbaabaaabbbcabcadddaacbbabbbbbdadcccbaacdbbbcdddddbddbbdbcccbbcdaacadbddddddbabbdadaccaacdaaabaaddbdbadbddadbdcccddacadbbdbdabbcbcdddcdbbcdbddddaaabadddcacaacbcaacaddddcacdbcbdcccaadacdcccadbccbbdbdadcdadcddcaddcdbaccaccbabadbcddddddabdbddcadbbdcabbcddaacddadcdcadbdbabacdbcaaccdcbdcdacdbccadabbcddabcdcddaaaddccababbacacbdbccbbcadbacbdadaccddaddccccadadcaaddcbcdcabcacaacdadcabcaddddaddccdaddcdbabdaadabbcbabababdabbdbadacdcadbbccdacdbccadbbabcddcdadadabdabdabacaacaabbbbcbcabcdbbbaddbbcdcdbacdbddcdaadbbbadaabbcaabdbbabacaccaabdbadbadccaacbbaaaccaadbbddacbaaacbbbaabaacdcccbbdacbbbdbaccadddcdadbbbbdbabaccccbbbaabdaddcdcbddcadccccddaaadbcdabdcaddbcbccabdbdadaaabadadcdcddabacbaddabdcbccadacbbacbdcccccadabcdbcbabacbcdccbacdabaccdcdaacdcbddccdbbdabcddbdbdbdddcdbccabcaaccacbadacbbbadbaacadacadcacccbadabbccdaabbaddccdaaadabcabcddabccaaadccaabadcbcdbbbabcbabcabccaacccacdcccbadbccbdcccaabaaabbdcabbcabbbdaddcdccccabbbdcabaaaddbbdbdabbcbabbbcbccccccbadbadccdddbbaacbbdbabbacdcdcbabcccccdbadcadcdaadabcccbabaacadaabdccadaddbaabaccddbcdbbbacacdbacdcdcdbdddabbdbcdcbdaddbaddbcabbcdcbaacaabdacabdcbbccaacbdababaadbcaaddcacaacababdadcbcbdcaaacadcdbdadbcabacbdaabbdcddacadabccdcaadaacdadcaaccbddbaacaddccaaababcaddacdcdaccddacbbdcbbabababdccddcbaddbccbcbdcccabcccadaccbccccacdbdbabbbbbccabdababcddaabcdadddbcbcdbdcbdadabbabddcdcdbdcbdbcddddddbbcdcdbdbabadbdcabdcbdbccbbabddacdaabccabbbbdddbddcdbdacbddcabcbadbaacadabaabbcaacbaccddaacdcbcdbddddadbbdaadbcbbdbcdadbcdbbaccaaddccbabcdddbabdabccbbadaacbbcbbcddaabdadabdbcaaddccdbdbabbaaaaaddbdccbbdddccaabbccbccbdbcbddccbbbaaacaccabbabbdddbdcacdcbbcdccbbcadaadddbaaaaccdcbcccdaabbcddaddadbaadaadddbcdbdabbbbdbdbddacacbccbbcdbdccaddbbccdccccbcaadcabbabdabcbaddbaabdaababcbdcdbacacaadbcbabbbdabaadccbcaaabdcccacbbcbdcbbbdbdbabccaccbaaddadbacbbcbcaddcaddcaabaacbacddddadcdcdaaccaaaccbbddabacbaccdbddcccdbdabaccbbabadbbbddcbdccacabbddbadcdadbacbbbabdbddabdcadcdacabddccdbabbdcaadbaacbcbccadcaabbdcbbabdaaccabbacaacadcabddcadacddccbbbbbaababcabddbbdcbaacaaddbabcbdcdbdcddaaacadcdbbdbcbbacccdbcbaadabcdbcaabcabccabbdabacdccaababcbaaabbddaacdddabccbbabdbaaadaddadbccbcadbbccbcdbcbabcddbdcdcdbcccbdaccccadbbcccabddbdccaadbacdcbcbbdbcaacddbadccabbccbdacbabbcdccbdddbccaabcbadddccdbccdabbcadccdbddaacdadaabdaadccadbdbdccbbdddbddaacccdbbdababbcbbadcbbadbbccbbcdbcabbaccacddccdcbadccbcabacdcccccadadacdcadabdadaccacacdbddbabdcbdccdbbbaddbbcaddcdaaacadababacbcbdbddbbcbdaabadbcbdbccdadabbacdbadcabaaaaadaaaddaaabdcccaccacbcbbbacababcbdddcbdbccbccdadbbcddcccccbbcabdbacccaddacaccabbacacacdacbaddaccacdcaddcbbadccabadbacdbabbdbcbcadadcbccbacaabddaccbdcbcbaabcbddabccaacbaadcbbabdcbbbdadadcbdbbbddabdacbdbcbcbbaabcddaaaddbccbbdacdbddacbaaccaaabacabcadcaacdadcddcbaddbdbbdacbdadbaaddbdbddbcbdcbdaccdbdcdccdbbdacddcdcacbdcdbaabcddbccccdcadbbcacbbbcabaacabaccbaaadaccdabccbcdccbaadadabbcdcbabaddabdcccdaabccdbcacbbdbbdddacbaadbdaccaacbcaaadbadcabbdcabdcacaabacdddddbccbbcccacacabbdbaaddcddbddcccdddaaddcdcdbbbbbdcadabbbdaddaacbaccbaabbaaaacddbbbacdbddabbbbbbabbadcdadcbbbadcdaddbabcacaacccdccccdcbcbaabcdacdbadadaddaccccdbcadbbbddbadcababbbdaadacabdbbccaccdbabddadccabbddaacdacaddcaaababaddbaadcbbcadbbbdadaadcabddccbdabccdabcbdbbacbbacaabbddbbbcbcccddcdbbcbbcadaddadbbbdaacddcdcabccdbcbaabbcbdacbcddaaaddcdacbbddaacdaabcaaddbaababdccadcbadacbbbbbddddcdcabadaacdddcbaadadaccbcdacdcbbddcbaacdaaadadabdabdaaddababbbadabbbdbcabbddacabcbccabddadadadabdaddddbaccacbadcdbbdccdaaadcdabaaabdcabbcbbbdbcacbbdcacbdaacaccaddcdbcbacbbbbbaaadcbdaccbdaabdbdacdcadaaaddaadbbdbaadbacaaabacbaaacddbadccbdbdbbcbcacccccdcbcbcadbdabacdaaaaccadaadbbacbdacdacaccdadaaabcaabadcbdcabaacddabddacaabdaabbacdcdccccbddbabadadddcccabaaadccbdadadbcbddaaccbcabadbcaddccccbddacccdbddcabacbcdcbbbbccddaacaaddbccabbbdacddaabbdbdacbcbacbcdbbdabadabcbbaadbdadacbbbaabbdadbdccbdbabdcdcdcbbcdbcdaccddccacdddcdcadadbddadbcabdabcdbbabbacccbbaddbaaaabccbbdcdacbaacabbccbacbccdadcabbbdaadaccdcdcdbabbcacdadcbccabbddabcdaacdddbbdbbcadabadbcdcacababccdaaccdbabddccbacbdbccccbbbaaadddcdcbbbdbcccbbbcaabacbddbcabddbddbacbcabcdbcbbddddbbdbdcdabaabaabddaddccccbbddaaddddacaddbddcabbbcbddcabaabcbaccbbacadabaccdadddbdcaaddbbcdcbacddbdccbcabdddcccbbbbddaacdaadcbacabbcbdccdbcaadbdcbbdacaddbaaaaabcaacaabdccccacdadbaadbddbbacadddcccbddacddbbaadbbaabcaaababddaddccacdcacdcbbdbabcbdbacdcbbdcabbacbcaadbadbbbdbdcddbbadcbddabcaacccdddaaaddadbdcbbbcccaadbbbdcabacccdcdbcaababdbaaacaabdddbcbbadacbccabbdddccbbccdbcbdbcdcbdcdbcbabcadcbcdcbcbbaaccbdbcdbcacabacdbadcdbbdbabdbccdadbadadcddaaadbabacabaddaaddcddbccbdcccadaaddacbdcadddddadbccdcbbbdacdcdbdbbdbdacdbcaacdbacbddacbbbcdabbbabdcacdddddcaaacbdcddcaadcaadbacdadaabddbacbcbccdddbbddcdbabdddadcaaabcbcadbdcaadababdadddbdcdabdcdcbacbcaddabcccdadbdcbabbdcbdccbcbcbdabcaabcababdbbdcabbdbcbcadabcdbabdccbaaabdcbccbdabaaaacbbbcabcadaddcdcbaccbcaadbbcaadcddadaaddacadacdcabddabcaacaacdaabbdacaaabaabbbadadbbbddadccdcbbdadbbddbadddbbbacdaadcaaacdadbddaabcaaaadddbacabadbbdadacdbabccbcdadcabddbcdddbcbabccccaaccadcdccababbbacadcabcabddbbbbbcddabaaccdcddcdbbadcbbddcccdbbcacddddaaadbcdaddbbdaadcccbbabbcacbacbdabadcdccbdbbcadaddcdaaddababbbdbaaccdadacabdbcdbcdaacbbdbcccbaaaddcdbdccbbbbbdabaabcbaccdcdccabcababcaaaacdddacbaaaddddbcadddcaccacccabcaabcdacbdcbaaacdcaaaacbbbaaccdaabcbdabdbcddaaccabcaccbdaaccbabdacdcdaccdcbccacddbcaaccdccaacdaaccbcbbcdccaccbadccaaccaabdabddaabcaadbbdaadddbccdbcdcbcbdbadbbaccccdacdabdadccbcbdbdadaaabbdbccdbdbbbdbaddbabaccababccdabbcccbbabadcbcdababbbdddbcbbdddbbbccaddbcaacdbcbcbbcdbdbacdbaaddaadcaaaabaadcbdbaaadadccdadcbcdbaabcbddbcbdddddbdcbaaaaaaddbacaaadbaadcbbccabdcbababadacabacdcaccabccacacbdcbbadbdbbaccdabbcccabacaddadacccbddcbccbccbbdccabcdbdbcacddabbcdddbbdbdbbadacccacbdacadddcbabaaacbcadbabcddaccddbabbcbbcbbbacccbacabccaabcddbccddbdcdcbdaadcadcbaddcacbcacbdcccdbabcaaccaccbcbdadbababddcacbbcccddcdcdbbacadddacacaaadcbddadccbdbabcaaddddcdacdacbacbcdbdabcabcdcdccddaccadbadbccbbbdabcddaadbcdbbddcbaccdcbbabaaddcaadddabcddbbcbdcaccadcaaacdaacdbcccbdbdaccdcadcbbdbdbbdccbbaacbbdcadacacaaaccbccacadcacbaabaadbbccbdacadcabbbaaabacaaabacdaadcadbdbdcbbdcdabdccabcbabccbabddcbcaacbdbddddacccdbcccccdbbcbaccadadbaddbcbdcbdcaacaacdcbadccbadccbcababdccdddcddbdbddaaaabbadbadccbbbcdbabbddbddabbaaadaadddabbbcddbdaaadddbcdadacdaadcdadbbcdcbdadadbaabbaddadccabdccbbcabacdcacadcbdcbbcdbbdbcabcabadbcdbdccbcbdcbbbbcbddcbbccbdcbcacccbaacbdbbcdadbdbcbcadcbbcdcdcabcddbcdbcbccadcaacbddbaadbbdbaccacbacadbdddcaddabcbdbabbbaaccaabdbdbbcadbccaaadcddccbcdbbacaacdbdabacbacbcaabdbdbacdcbaacbbdaababcaccdbccbcaddabcbcddcdbcaacdabddbadbbbbacdbcccabbacabadddcabacdbcccbbcabdbdacbbbaacaabbaabccdcdaabbcacccbbacbcabcdabaacbabcddcccaaccacaaccaaabaacbaadddabbaaddcdddcddacdabcacdabbbabbcbbbbbddddcdbdabaabadcdaacabbbbbabbddaddbcabcddcaadacaadddcaccdcbdacabababacddbadacdbddddaadaacacccacabaddaaaccdddaddaddbdadddcdddadcbacbabbaabadcabbdbdabbddadadbabbbbadcaadcbddcaaabcdbbcabcdcabcdbcbabcbbbdddccdddabdacccbcadaaaaccddabadbddcdacbaaccbaadabccdccbbadcbbbbdbbdabcbaadadadbbaaacabaabdaabacaaaccaadadbccdbaddbcdbddabddcdcbccbabadcadbccdacbaacbcbadccdcddcacbddabbcabbacbaabcbcaaaaadddddccaaaabbccddddadbaddaabadcbdadabacddcadcbbbbbcadbaccdabccbdaaddbaaaaccbccbccbcdddbbdabbbacbcabcadbaccdddaaaccddabadbbaadcdddaacddbccdccdbbbddccbbababbccdabbcddacdcbaadcdbbcbdbbaddbdcbcdacdccdcccabddabdcdabacbbbaabcdcddabddbbcccdbdbddddcddbacadbddbbaccccccbcccaabbbcabcbbdacadabccbbdcaacdbadbabcbadbcbcdcbccdddddbadaccbddcdddabacdbbcdacaabbbdbdcaadbccabbdcbdaaccdcbacbaabbcbbbcabddddcacccbddaacabdbcacbcddbbbcaadbcdcdcaaddbcccdbbcadbcdbdacaadccdadbdacdcbdcabccabaccacaacbaaabcaadcbbdcbdabdcdbadabbaabbdadcacbadbcddcacddabdbacbccadbccdacacacccaadbbddccccccaddbabadabbbaccabbaacaababdbcaccdccaababadbadddcdcdbbacddcdcdbdbddccdaaddbcacabccabdcdcccbaaaacbcbbdbcbdabdddabcddbadabcbbadacbbdbbcccabbacabcbdbbdacdabccdbcabaadabbdcdcdbbbabdbcdbacacadbcdaabbbdcdbadddabcacbdaccdccaabcbadcccaabbcbbbdccbaccbdcbcddbddcacadbcaacdcadbcccabcaddcadcdcbcbdbbacdddddcbaadcdabcbcabdbddabaacadcadbbaccdbddbcdbadcaaccbbcbddacccbdabacbcaacaccbbbbababbadcccddddbabdddaaacaaaaddcaadddaacacbabadadbcbaacabbccddcabacabdadccadbacadbddbbddbcbaacdbccadcabddcbadcaddaddadcbcdccdcadcaacabccabdbdbddddacdcbcbdbbaccdbccaacadacdcbadcaaadddbcababcdcccadbdccbbdbcbccbbccacbcacabcddbabaabcbcabadcadcdddbaddabdbacacddcaccababadaacbbcacaadcbaacdbcdbacaacbcbaabcbcabbcddbbcadddaadddddabcbcbcdcdbbdbccabbddcbdaddcacbdcdcaccacbcdbdcbccaabccdadbaaabdcaadacbddbcbcccbddcabdcdbabcacbaccaabdddabcaacdaacdcdcdaccdbddbddbabbddaaabcabdbcabbacbccddacaccdccdcbccbacaadbcaadabdbbcbddddddccbddbdbcacddbadccabdaddccabcdcaabccdaddcabaacbaacaddbadabdabdcbbabaaadcbdababbbadabcadbbadabcdccccdbadaadbabdbabcbacbadddbddaccbcddacaddccacdbadcdcabbcadcbbaaaaadbbaadadaadcbcbdbaabdcaaadaabbbcacbcbcacabbdcdcbcdbacddacaacbdababddbdbcdcbaadacadcdbcdcdcbcabdaabdcbdbbbbabccbadddcacdbdbbadbdcabdccddaaaadabadacdcbbdbbddaadadcacdcbbdacadcaadabbbabdaadbaaaaacdbabbabcdbacaacacadbdcabcdcbbcaaaaacdddbbccabaccacddbdccbdccadbdbbacddddccdccdcbaacbdcddbbadccadcaabcbbaddbaadcabdbbadcaddbcaacbdbaccddcbabcdbdbddcccbddcddcddabbbaaadcbcabbdcbbcdcbcbaabdacadcaacdcacbaddcacdacdadacddbbcabaaadbbabbadaabbddcacdbbbcdaccaddddcbcdbbacdcabcaddcbcadcbacbdcbccabdaabbbddbcbcadcdccdcbccbbbccdaadaabacbdacbcdcdcabcbcbdbaccdbccdccaccbadcadabdcddbddcdddacaaaaddabadbdbddabccacdbbdbdbbbdbddcdaccbcbdaddbccbbabccabbcadccdbcbdbdbdbcadbdacddbaacdaddbcbcabacbbddaaacbadabbdccdbbaccdadcbcdaadddcbadaadcadacdadbcaaabdbddcdacbadcdbbbdcbbcacdaaccdbadbabcabdcbbcddacdccacadbcadcbacdccdcaccddbdbadbadaaaadaabccdaabaabddcdcacadccdacbadbdaaaacddaccadbaadcdddbacbcddcbbcabdbdaabacdcccaddbdcdbbdcdacbddbbcabacbcaaaaaddbdbddacbbccddbababccbcbbaaabbbaabbcbacdacadccadddbdabdccbbbabbdddaddcdbacdcdcacbcbbddabbacadacabddcbcdccaadcdcaadbaddababcbddabdaaaabdbcaaabbdabcbdacadbdbbbcbdaadbcbbccbdccbdbbbacbcbcdadbdbdaccdcadabdcacbbaacadcbdaacbaddadcadcaacaaadabadaacacbdcdaadddaccbdbaacddbccacbaabdcadbaacdbaccbcabdcbacddccadacbbaadbccbacbdacbdcbcbbdabacadbbcdabaccbdddbbcaaaddbcbbcdabdacdcabddcccabcdbccbbdaacbccabbadbdbaadcbbabaadacadaabacdcbcaccbcaacababaabccdddabbdaabccbabcacccccbabacadaccbbbbdcabbaadbaddacadccbadcbcdbbcdbbbaadcccddbbccccbaddbacaacbdccbbacdcdababbbadbcbbbacadadbccdabdadddbcbbcdaaddacdabdaaacdbacdabdbcbbdacdcdbabbbbaadddadbabcacaddccaabdcabbcddaaaabddbcaacbbddbacdabdbbdcccbabdaaabbcddababbbcabcabdbbdcdccabdddacaacaadaacdcaaabbabbbcdbccbaadcdcbcacdbbbcabaddbaabccdbbcdbbabaabbbaacadcacdcbddaddbbdbbddaddbaddddbbdbabcabccbaccbcdcbcdbddbddcbbccabbcdcbaddcbdbccadcbccbbcdcbdaadcddcaadbadddcdbcdaadaacadaaddddcbcbbbcccdcbcacaccdbcbabbacbbdacadccccbdadcacccadbbdbaacdaacbabdabdaaadbcdbcbbcaaaaadaabcddabbdcccccccadccbacdccbbdcbbcbddcabbadaacbbaabcabbcacbcaacccadcaacadcbbaddaabbaadaadadcdddcbbadcbbcbdccbbcdcdaaadbdbacabadacbbadbdcbcdacbccdabacbaabdbbdaadadacacddcddaddacbabaacdddbadabbaacbddcbaaddaaddccabcabbdcbcaccbbccdccbcdbcabccaccdcbdadbacdbaccaaabcccaadbdbabbabcbdaddbcbcadbcdbdcbdccbdababbbdbccdcddcaaaddacdccabdcdaabcaccdcdbcdbdcaddaabdabdacccbccaabbddcbcabdccbdbbdbacadcbacacdbddcabccadddbabcdcacaacdcdcbddccdacadbdabcbaadbacaccacbbaabccbccbaccdddadcabaadbbacdadbddaabcaadcbcbdbbabddacdcacdcaccdacbabcddcbdcacbdddbccdbdaacbddbddbdacaacababbadadcdcbcbbbbbdbacccdadadcdbdcdbbdbbcadccbcababccababbdcbaacbcddcaaacdccadddbbbbacabbbddadadbdacdacddbbdaaddbbdabdaabaacadccbacbcbcaaacaccbaccddbcadcccccdcdabbdcbbadcabddddbacadbbbcbdbcbabdcbdbacccabbbbcbcaaddbbabddddccdcadacdbbaccaccccbdcbddbbcbbbbbdadacabbcbcdadbbdbbaddddbdacbcdddadaccababaccabcddcdaadaaabaaddcbadadbaacaddcbccdcadabddcbbbccbbcdddbdbddcadbcabdccdddbacabcdacdaaddbcccacbaabcbabbbdcabddcbaadaddbcdbdbccbdabcbcdcacdbcbdadcdaacbcddabccdcbbcddcdcccacdcbaddbdccbdcdbbabcacccdacdbdabdcdacbccddccdbaccbdaaabccaaabcbaacddbdbdcbcdcaddccbabdabbdcdaddcdadbdbacddbaabadbacaaabbcbcccbccdbcbbcdbdbcbdbdbbbcabcdadbbbcdaaccbcacdadaddcccbbcbccaabdaccddabdddbadcbadbbadddcccdcadcdcaacbaaabbbdababddabbcabbabaabdabbabcbbcaacabbdbbacbdbabcddacbaaacbcddbbabacbdcdbbcaddddcddbdcbbbcbaccdcccdcbabbccadcdcccdcbccbbabcacdaddddbcbdcaabbadbbbdbdcbcdbacacddbccaabcbaccbdcdccdcbcdbdbadccccbababbdcbdbcbbbccdaabcacdcacccaddabdacbccdadddcddabccadacbdabaddaaadccaabbbbddddcadaddcbaddacdbcdacadddcbbbbbdccdbcdccdaadadaacbbddddbadaabaadddabbddddbcccdcbdbdbcdbdcaddcbcabbdadddacbcdccdcdaddbadabaccdbdbdcaacdababdbbccdbddbdccacdbcdbbccaacccddddaacacaadcdabadcbababccaaadabaacaaccddbaaadbbacdbbcdaacabcbaabaabdbbcaddcbcdbaababcabbddcdabcabcbbadaabdddacbccdaadadcccdabcacbabdcacddbcdcbaadcdadabadbdcadababcddbbccdacabddcdaacbacdacaabcabacbcaaccdbdcbcadddadbabdbbdaacddbbbddbbbaabacaccbdbadcacaabacaccdaacbccdabdbbdabaaacdcbcdadaaadaadcbccaabacdaaadbcbbdbdcabdcdcddbbacbbdcbdcaacdabcdbbccaddddadbcddbaddcacadcbcdddaacdcdabcbaabbbddddacacddcbaadabbdddccdcabaccacabdabbdbcaccddacbabcacbbbdadccabdcdcbdabdcbbaaddabdbbdbbabacabcddcabcddbadbddcdcddaacabadadabbddaccdbbadaddcdadcbaccdcdaacbbbdaacdabcadbababcbbacdabdcdcdabbbbccdcbbddbbddddabbaaabbdbbcbaadbaccddcccabbaaadccabdaaddaddcdabdaccdbcdadaaaaaddddccbbabcbadacacdadabdcddcdaabbddcccdccabddddbdcdbacbccddabcccbdacbcdcdacbdabcbaaadabdccdadabacbcbabadaddaddadadaabaccbdacbcdbdbacbacbdadacabdccbadcbbccadcbdcccdcbcbbbbdaddaabbcaddbdccbdbaaaccdccbcacabccbcbaacacdcccabbabddabdaadbdbcaabacccdadbdadcdcdcbaccdcdaaadcaabbcababaadcddbdcabbcbddacacbaddabbdccdcdaccabdbbddcadcaccbabdaaaaccabacaaaacdadacdccbddddacddbadaccccacbdcdbcddcabbcaccaaabaacbdccbabbdbccadbcbcaaadddcdcbadbdccccbaaddccaccccddddcbdadccadaacabcabdaadcbddcacbccbcddaaadaaacadccbbacbcbaddadbaadcdacdddcadadcdbccabdcccacdcbcdadbdcaababbbcbabcddcdacddbbbcbaabacacbaddacabcddbabccdddabbbcabcccadacddcababdabadcabdcdbdbbbadaaadbdbbabcdcadadcacdcbccddddadaddcbdcccccaccbccdbacdbbbcabbdabbcaccbcdacbdcdddddabcabaddcdddaddccdddabbacbaadbaacccabcdddbbdabbdaddbdddaddacaababddcacbdcdadbaadababbaddbcadcdccbccabbaccbdcbbaacaadababdcacbcaccaaddccbabdbdabdccccdbcbccabbbddcdbaddbcbcccddbcbdcdddababacbddbadaadbcdcabbaadddbaaccddccabcdcacdbccadddbdbdbcbabdbcbcadaaaabadbdccbabdbdabaddaabcbcdccbbbdcdababcaddadbdccdcddadcddddcbdbbccccccccabaccacbccdcbccbccbadbbbbdcdabdabdbdbdcddacbaacbcbbbdadbcddbaacaddccbadabdbdcdcdddadacbdbaadcccdcbbcdadbcdbbdbdabcacaabbbbccbdbccbdcdcccdbbcdacaaacdabbaaccdabbbbcaddcdbadbbddcacaacdcbdbbbbcabbabbbaddbbdaabbdbdddbcbdabdbdbcddccdcbcbcbbbbbdddccabcbcbbadadaabadbdcdadacbaabadbdcabdaaaaccbbbcccbcabbacddadbbbcbcadccdcccbdaadbbabcabcbbbcdadbbbcdbacbbcacbaabddaccacdddcabccdcccbabdccacaadacacacadcaaccdadadabaabdcbcbacadbdbbbbadbdacbddcdcdcadbadcbbacbccbbadccababccbcccbbdadcbbdcbcaaaccdcaacdbdbadcbddabbbccbabcddbcbbbdcbbbcbaaabbcbcbabaccbdcccbcccdcdbddddbbcdcbdacdbbbaddcccccbccccbbddbccaaccbccccddbaaaddcbbbbddcbabaabaddbabaddadcacbbddbbbddcabbdbdadccdcaabcccdcbadccbacabbbdbdabbdbadbcdadabcdbbddadadcbdbabccbdccdbddcbbcddbacddbaaacbbbcdcbbdaacbcbabbdcdcddbcbdbbcdbbadbabcddbbbdbddaaaaccbaabbaaadbdcdacacdbbbdacabbdabddbdddadcacccabdabcadcbcbddbbbbdddddbbcdcdaddccbddcdcbcbaccbbccaacacdbdadddcbabbcadcdcadbdbbccccdbcacdbdabccccbaaabddcaadabdaddaadccababcadcdcccadbabbdcacbccbaaddcbddabbccbcdbdcdbaadbbbcdbacacddbbbcbcddabdaaadbcddcabbcdabcdcacbcbbdddbdaacabbddcbabbdaadcabdcaaacbcdabdacbdcbabddbbabcddbccdddbaccaabdacdcbaaacbabdadbbbbccdabadcadbdcbdbabbbbacabbbbbaaaaccabbcaaadbdbbacdaabdcdaabcbcbcdddccabaacbbcdaacbbadadbdcbcbbdacacbabdcadcdadadbdbbccabbdbddbbdbdacbbdbcdbbbbcadcbdbbacddcaccbdaaadbcbadcddddcccdcbadcbabddbcacaddcaccbaacaacdadadcccdcacacbbaddcadccaabacabcaaaccbabaddbdacaccaaddccccaadbbbaaabbbdaabbbbdddbbcaccddccbddabdadacddddccbadcbbcdddadcdbddbbaadcdadaccadabaacbadcccddbbacdadbcbdddacaadbadbdcdccccabcdccdbdabdacacbdbabcdacccddbabddabbbaaaadcdcddaaddbadacaacccadcbbdaddbdcdbbadccbdcdabcddabdbbadcdacdddcbbbadcdabacbdacbabccbddadbbbbacadacbdadcbcacbaabdaabbdcddadaccdababbadbbbacdbdaaacbbabbaaadcbcdbbdcdadcbcdcbcddaacaddbababaaacbdcdadddbbadabccdddddabdaabacaacacabbadccdcdbcccbcdcabbdaaadacbddabcdccdbdaaaadcccacbcdbabaacacaadbcdcadabbbcacadabbababcabcccdbabbbacddcbacbccbccbddbcbccaccaaddcbbdcddababbbbcccdcccbbabbabbccdbbcdbabbcdbccddbccdabbaddcdbddabdbddccbddbdbcdbcbabbaccacdbddadcaccbcbababbbddddacdcaaaabbaaabaadccdcadcaddbaddbbdcbaaddddcdccadbacbcacddabacabbaaddaabadcaadaacacbbadcdacbaddddaaabbcbbbbabbadbcdbcaaddbcadaccdbcaddbdabcbaadccccdcbaabdbcddccabbddabadcacbdbbbdcaccabbbaccadcabadccccbcdddcacbbbabbacdbcdcbccaaababddddbadbbcccaabababddbbddbbcbabcbcccccbcbabacadaabccadacdbddabcdcaddadccdddcddcbbdbacdccbdcbaccdbaccdbbddaddcbabbbbbaabccbdccadccdbcdcdbaacdbdadccdcdbbccbbbabaddbaacaaadadbbabcdadcaaabbadaacabcddadccabbaaccabbdbbddbbbbbcbabdbcabddabadddacccddcccbabcdabbdddcadabbdcbbdcdbbbabcddcbaadddadddabdabcbcbddabbcdacadbbaacbddcdcddbbcacccddabdaabbbccccbadbcaadcbbcdbdbdaccdccdcdcbdacabbbbacbddbdaabaccbacacadaabcbbbccdaaccdaacdbbabbadcbbbbbcacaacddddabdacadaacbabcdbabbbaacbdbdadaabbbacccaaabbacccabcadcacdbbadbcdaadcabddccbadbbabccacbcbdaacdacdbcbdcbcbccdabbbbdcaccdcbacccbadcddbbabbadccacaddabaabccdddccacacdcdacbcadcdaaccaadbadacdddddadbdbbdddbbbdabbdbcabdbdddbbcdbcaadbadddabcccaabddcddbabbcbcadcbcbbabaacbadaccccabbbabdaabbccabccbccddadcddcdaadaddccacbbbbdccadacdcabdbbdcccccaaadcbcadccddaaccdbbabbacdabcbdacbcdacccabacbadcacccacdddbbcadcdaacdcbdcabbcbdadcbcadadcbdbcadaccaccbbadccddddddccbcdcaadcbbccaacccbaaabcaaabdadaabdccacbcdbcadcdadaababbbbddbccbbadbdaaddddcbadccccbcadadccdbdbbbdadccdbdadaadbcdacadcdacbbbbdbdaaabdacbcbcadbaacdcdaaadbaababaddaddccaaddbbdbcbaddbbcddcaddbbaadbdcdaabdaabcdcacbbcbbcadcdbdaddacaaccaabdadddccadadcdabdbbdacbbaabdabbccdadbaddbacacbccadbcbcccbddcbddcdbaadbbbdcddaabbdbdcdcdccbbcaadabcadbcbdadadcdcabdccaadabdbacdcbadcdbdbbbcaaaaabbcdbcbbdcbadbbbabdccbdccddbaaabbcbddddccbcaccbccacdbaadbcccadbbcacbcdabadbdddbcccbdaaaaadddccacdbbadbaadadbdabcdadabbddcdcbabbcadccabacbabbdbbdcdcaadbcdbcbbccabbddabdcdbdacdbcdacbdbaabbacdbcadbdddbbbdbdaacacbdbccacbcdcbabcbbcadaccbcacadbadbcdbccdacacddbccadbcadbabbdcadccbccaddbbddcdcacdcdccbadacddaacbcadbccadccccbbcdabccacccbdcdaadadbaacabaadaacccdddabdaccbdbaccdcadddbdddcabdcbccabddbcdcbbbdbbbbadacbbddbacdbbbaacbcbbcbbdbaadcbcaccadabddccdccaddcddbbbcdaabbaabdaaaaaabcaccdbadcacdbacddaadaadcddccbadddccabdadcaaacbdacaccbccaccbaccdbdcdbabdccacdcccbabcddbaccbadaddcccdcacacbadcddccccacacdbccbccdbcbcbbaaaabcaadddadbdaabaacddacbaccccbabbdbcbbabbadbbaabddbdcaddabbcaaaabbbcdcadbabbdccabcdbccdcdbcaaddbcadbbdabdcbdabbdddabbbabdbcdccdbdacdbddcbbcddadcbbaaababbadbaaacddcccdadadccacccbbacaddbbccbcccdbaccbcacacdddacbdbbbacbabadacbdabbcaccbddbacbdbaaadaadcacbbdbbbbbcbaacdcabccddbdbcdbccbddaccacdaaadbdabaacacabdacbdccdbadacddadcabccdbbcbcbddccbbdacacadbacdcddbbaadbcbbdadbadadbcacdcdddacdcdbcadbbbbbaaddccbbacadddcddacacaadaabaaadbcbcddbbdcadbbadcdcacdbcbacbcbccbcdaabdccccadabbddbcadabdaaadcccaadbadcdadbcaccdbddbacccaaadbaadcaabcbccaddaabababddaccaddcbacdcbdbdddcadbddacdabdabbadaccaadbbbccadddacaaaaddacaaadabbbdbbbbddabdcbaadacdccccacbbdbaaaabdbadbabcadcadababbdabdbbacadaadcdabcbcccdabccabccbabdcabcbcbbddacaacdbdcabcdbacccbbbdbaccdcadcaaacbbbcababaadcabbbcbabbbcabdddcaabddbdddddcbdadcbbbbacaaacaddacccacacbacbcadbabadcdddccddccbbcddccbcacabcadddbccdaadbcacdbabcbcbbccadbbacabbadaccccbccdbaccddbcbcdddabdacaabddddaccacccbaccabccaaaaadbaaaacbaaddabdccbcaaaacaabcddbbbddadabddaaaaaaacabcaadbadbcdaaaddbbacbdcdddaaddadcbbdaaacdbbdaddbbdcbcabbbdbbdbccddaccdbaddacbbcdddacbbcacccccbdcdbabcbbacaccdbdadcaaaccaacccaacddcbdddccdcbaacbcdcddcaddbaccbddbbaccbbdbabbdbccbbcacbabbaabacbaddaaddbbbaddcddcdbdbcbdaccbdbbacccbbadccdcdbbcbcabcdccbbcbadaaaddbabddbbcbdcabbdcbccbddddccccdcdddacadcadcdccbacbacbaacaabcabbbcdcddbbbabacdaddbaddbddaddaabddaabbcbadcbbbdcacccadddabaddbcaccacbbbccacbcddccaacdcbbbababaadcdbacbbaccddabbcacdbcbddbccdaaaaadaaadcbddddadcbccaabbddcdcdcadcadbbdadddbddcbbaacbbbacbabbbabcdddaabaadcacaaabdabbccddcbaadccddbaddaaaaadcdacbabaacbabdadbcddddbadcacabacbacbdbbabdacbdaacacdaadddccddaacdaccdbbdcadccddbbcbdcbdccabdabaddabdadbbaccbdcbdacdadbbbaabddddbdaaacdabadcbaadccdaacdcddabbaabbbdaccbdbcabbcaadbcaccabaabaddacabaddccaacccaaabcacbcabbabdaaaabdbadaccbdddbcabacaaddabbcbcbbdcdadcdbdabdbdbabbdcccddddcdbbabdbadadcacaaaadcbcabdadbccacbdccabdcaccacbcdcaddbcadddbaccdacaacacbabaccdcadcaccaacbcbbdaddacccaccadabadcabaacacbabdcadcdbdbcddcbbdbbbdadbbdcbdbbbacbbcbdcbcdddbdcabcbbbbccdaccbbdcdddaaadaaabadcacbdcabcdaacbcbaddcbbaddbcadddccbbbadcadadadbacabccdddadaaaccabdaacbccbbdbbcdcbbbcccaccaacbacaabcccdddbdabbadbbcaccccdccdcacbcdbcbcacadccbaacdaccdbcdcddbdcbdcccaddadbcbcccdbcbbbdbdddbbdabdaddcadbccdddabaaaadaddbabddbcbbbaacbabaadbcdcddabbadbababbbdddbcbcaabdbaaacbbbbbbcbcabdbadbadbadcddabcddddcccddcacbdabbbcacbcacacbabdcbbabdcbbddcbadacbbaabdcadacbcadabadcdddbbcaabbcdaacdabcabcbdccccbadacbddbdacddaaddaaabcbcccabbdbadcbaadabdccddbddcdbdcccdbbabaddbdddcaabccbcabcbaaaaddcddcaccaccccccccbbbabddbcbbddbccaaabbccaaabdcbaaaccacbcccddacbdbbaaddbacddcbcacdabbdbccbdcdcdaccdcaaccbcddbcbddcdacdccdbddbdbbdbbaabbbcdaadcacdddabcbadbbcacabbdaabdcadcbdcccbcacdbbacdcbdbbaabbaddbbaaaabaccabdcdbcbabbccadcbcbdabaabaacaccbacdacbcaadcddbbcadbacabbaddcbbcdabdcaaabbcbdcbacbdcdcbbcadcbaabdbbcdabbcccadadbaadbbdbccdcabbcacaccabbaaccbbcdbdabcdadabbdaacdbddbdadbbccddbabbbddbabdbaccddbdccbdcccacbacddbadaadbaacdaccdbcabadcbbdbbcbccbddbbbadddbbdbdccccbccbcabbabbbbdadcdadaddadcbccdddddabcbccaabdcbddaccbdbbdbbbdcbcccdbbaacdabcdaadcbabbcbdbacbbdcaccbababbddacbdcdaccbdabbbbcabbacacddcbcacacaddddbacbbcbaccbaabbdaabdbbdcdabcdaaccdcababdcbbdcabdbcadaabdcbbbccbdabadaabdadaddacddbcbbdaaddbaccbccbdabbcccaaacdaacadadcdcddacbdccdcbcbaacaacdabdbaadddaccadbaaacbbbabbdcccdacdbdadddaacddadabcdbcdadcdadadcdbacbbccdbdcabdbaccdbdddadacabbbadccacbbaadabbbabaadcbcddbdcbaadbcbacddcadbdcbdacbdbdbbadccbccdaaccabccbbbdcdddcddcacbdbadcdbabcacdbdcbaccdbbabccdaadaacbabdacdbbcacdbcaadbdbbdbcddcacdcbccacadaccdccdaddbaddcabbadadbbcadbbdacbccdadabaacccbadcbaabdbbccbdcbdcdbddbabbbdcaddbccdbabcbdbbbccddadaacbdbdadaddddcabdbccbcddabccabdaaccbadadcbaccdbdadbcddcadbcacddcdcdcbbdbacbbcaaaacdbcbacbbbdbcbbabcddaaacabdabccdbaaadbbababccdbcdcadbcabcdabcbbbdadaabacbcaabbcabbbdbcbccdabdbbaabbcccdacdcaacbacdbdcddcadbbccacbdcccbbdacdcaaaacdbadbccccacabbdccaddadcbacbcaabdabdcdcadadadbababdbccccbdcddbdacabcdacdacaabdbacbdadbdadbbbbccdadacadcacadcccacbaddbdabbbbbddccdddcabdadabaacabbabcdcabbdacdbabbabbcdddddaabddcbbbdddbbbdaabbddbbbddcbdddbcabddaaccdbaddaadbddbbdbccdcabbcdacdbbbdbadcbaaddadaadabbbcbdcacccadbcccddaacbabdccddbaaadcdddcbabaadcacddbcbcadaaaccbadbcbbaadadbcbdaaabcaabbddbdbaadcdcbbaabdaaabcdbcabbddabbaccadacacdbbadcaccdbdccdaccdddbcddbcddcaaccbcadabbbadacbacbbaadaaacdcabdbacdbcbcdcddabcabcdcbaabadccbaaabaaaadbaaabccadcadbdbaaaaabcacacdaaabacadbcbdadacccdaaddabbdcdcdbdcaaadababaacdabbdbcbccccbdbdcbbdbababadaaadcccbdcbcbdbbabdabdbcbdacadcddcaacdcbbabcaddaadcaabacaacccbcdbddabbabbbababbdcbbbcbdbbadbccddcdbbbbbaccacdbdcccbcaccbbaabbadcadcdbadadccadbbaaabdccacbaadbdadddaaccdbbbbddcbcbbddaabadbddacbaabdaccacdcbdacdacbcbddacacabdcaccdacdbddaddbababaadacdacbcbbdcacabbdcdcacabdaaaddccdccbbabdcbdabcbaddadbccbbcdadbcbcdccdaccdabdabcdaadbadbdabbbdacdabddaadadabdbdacbadbacddbbbdbabbacdddaabbcdaccbbbdaaabcbaadadbbbadbdbabbcababdcaccbdccdcababdccbbaadbbcbbabadbacccadbbbddcabccdcdaddacdbcbaabccdbadbdabddaddcddcadbdabdacaaaaadcddccadadacdbbccaaddccdadbdabadbadcabadbbacbbbdddcbbcbdacbccabbcdcacaaccbddbcbcadadddcbbdaccbbabdddcdbbcbcddbbaacbcaadddacbdbaabacacbabcaccddabbabdbcddddbbcbacbccaacdbbccacdadaaaaaadcacadaabbbbbbddbbdcaacdacbabbbdaabbcdccbdaacdbdcddddcbccbadbbdadaaabdcdccabccbcbcbcccabdbdbcdacbcddadcddcbbadaabdabaabdcacbcaabadcdacabdaaadaddabbcdbdbddddccddadbdcdadccbbbdbbccbbddabcaddbdadaaabbdccaaaaddacbdadacaddaabccbbcaccadcbcdcddbddbdabdcccdbcdaccdcdbaddccacbcabdabbacdcddcdacacdbabdbbcccdaccdacbbcccddacaabacadbdabacacdbcbccccbbabbcccdabadbddddbdaaddbbdbccdddcaabdacaabaccdccbcacadabbacbabaaaddbdcbcccabbcaaacacdddadbbadcbabaadcbdcbbaadcadddbcbcccbcaddadacccdbcaaaaacdabbcbdbadbdbadadadddaadccbcadcaabacdcdcabaccdadbdbdbaaaccdadbbcdccbbbdcbbccbbcdddadccabadadcacdcadacdbcaacadcdbbbdcbdaaacabacbadaacbdbadbabacdaaccddbbdaabcabbcabaadacddbaacbbaaaaddddbddbcaaadbaaabbcbdbdbdbcbddbbccdbcdbaacbdcbbbcdbabcbcaccdccaacadbddddaadccdbbbdddacababaccbbcddccacdabcbdddcbdbacacbdbabcccabbdcbdaccddcaaccccaccbdaacacaccbabccbcbdabdcbbabddcbbbddbdaabcdaccaaaccaadcdcdcccdcddbcabadabdddaaddaacaaacaacabcabadbddbabccddcccdadccbcbdcdcbddacadbcdbcbdaaadccbdaddbaadcbadadccbdadaacbddabdaaccbdbdcdcbcbaaabbcddacadbacacbccdacbbdccaabbddadddbabcadbdcdbcdabadbadbdabaabacababccadaaccbababccababdcdadccbacdcdcdbabbdbccdcaacaadcccdbdddbbcbbbabadabdacdbaadabddcaaabbcdcbcaaabdacddbaacddbcdaaccbdaaddbbdaddaaaccddbcacbbbbcdddcacbbbabcdbdcdcbddbbaddcdcbdbcacaccddcdbddcdbdacbddbadddcccbbabadbcccbbabaaabbdabbbcbdcbaccccaabacabcbbbcbdaacbababbacaadbbdaacdacbcdbdabdcaaddabdacddcbddbbdccbaaabdaddcdbbccbacdadbcbdccddbbcacdcdbcbbcbcabdadcabdbacbcbacdcbdadcdccadbcbabdccccdabacccccabdbcbccaddbbcdcaccddcbdadcbbacddbdcddbbbaccaadadbacddbcbcbaccacbcadadaababbdbaaaddaabddaabadbdcdabbcccbbadbccacccacbdacaddadcaddbaabbddacabcbdbdccadcaacabadaacdbcbadaaacbcdccadcddbcdcdaaadbccdcbcddbbaddcbcabddcabddcdacdaccbaaccadcadcdbcbbbbddbdbcacddacbbbaabcdaddbcabbbdbcdbbcaadaddddddaacbbdbdcaddadccccbdacbdcdcbbdbbddcdddcadddddcddadcabbdcaaddbadadbabaddcadbdadcdcbabadbabcadbbabbadddaaccdcddbdddadbacdbcdbcababdbccaadaadbbbbaabddbcccabacbadcbbbadaddbacbbcbddbbcdddabddabbbddddadbbadadccbcaddacbaaaaddcbaaadcbdacdbbaadcadcdbbadddbcbcbdaccccbdaaccacddcbaddccaccbddccdccbcbabddddbcdddccdddcdbdbbcddadbabdacccabcabddbcadacdcbacaabaccdaaacbcddadabbbcbbabdacaacbdaabbdadcddbadbcadccdacdaabcbcddccbbcbcabddabbdcbddbcbaacbddddaaccbbbcadcaaaabddabadaaccabbadacabcadbcbccbcbbabdcaaabbdabaaabddddadcbdbccadcaddcbbdcbaadcbdcaacbdbddcadcbacdcbdacaacbbcccdabdbacdcbbdabcabaccabbaabccdbdccabbccdacbaabddbaaadbbdbcbadadadcaccbbacbadbdbacaadccbccdaaddbaccddadcadcdbdcccaacbbdbbccadadcdabbdbdacacdddaaaccccbacccdbbaadccdbabdabcbaccbbcdbcbabdccdaaaaccbcaadaadccdcdcdacacdabbdbdbaddbcaadadabadadcdddbbccccccaccaaadccccdbbcbbabbdbcdbbcbdcdadacdacababadcdabdaacdacabbdacbccbcdbcbbdcbbbccdadbcccbabcacdbbcdadbcdccdbaddccbacacacabcccbbddabbbccdbdbbdaddacaabdaddcacaaadbbbaaacbbbdccadaccdbcabcbdbdcddaadbcddacdaccadbaaaadccbacbdcddbcbaddbdbbbcababbdbadbbbbdaddcdcbdcabddbccbacaddddcadacababdcbdcaacabbcbaaadacaaaabddabacdcabcadbbacadbcdccdabadbcdbddbaadaabdccbdacdaabccaabbdbacadbadbaaddbabbdcbdcdcaddaaccabddcccaacccaabbdacaccbcdbcaaabbbaaacbbbdbdbabbcddcacbadaabcddcdcabbadacbcacaddbbbcdabcabbdccdcaaabcaaccbbbbcccbccacbdcaddabcbaacbdbcbcaccdaaacbbcdcbcaccbabcaaccbacacadcdbcacabbbacaabbccbacbcabbcdbadbdabdcdcadbccbbbcdbddddcaadaacdadcbcddcddcaacabcabbbacaddbdaddcdbcadddbcdcaddcaacacadbbcaabbcaabacdaddadaddaddcbdddababbbbccdaccdbdccbcccdcbddddcbadcdccdacaacabcbdaddcbdabcddabaddacdabaadaaabccccdbbcdbbbcabaccbbcacdabbbdcccdcabdadcadbddbdcdbbcdcbdaababbdaccdaadaabddbcaabbcbdbaddaccbccadcaccddcabacacbbcbdbcabddbaaaddcbdcbbcbacdccdddddcddccbdccdbcadbddccabbbbbdddcdccaadbdaabbbddcaddbbbdddabcabcabdbdabdbdbdabaccbccddbdcbadaaabbadacdacdbdadddadaddcbabaacbcdcaddcddadcacbcccaaddabdbddaadddbdcdcaddcbbbcdbcacacbaadcabcccbccabacdbacdccaddbcbabcdaacaaccabdbdadacdccdabcdcbaccddbbddcddbdccccdddcabccdcdcadabcbdadbacbccabbbdbcacbdbcbbcaccaacabbadabaabdbcddabadabbdabcacdcdbdcdcbbdbadabbcadccacccaccddcdabadcccdabbadababcabaddcacaaabbcaaadcbdbacbdcaabdabadbacabcbcbacbaabcadbcbbbbccbaabdadabcdacdbabbbcdbcdbbdbcbccbcdcdacccacbccbdbbdaadcdbcddbcddbaaccdbdbbddbcbddddadcbbbdcbcddcbccddcadcdaadcadadbdbaddcddbdaaacbdcbdddddccdacccaddadaccbadbcacccabbddcbcabcbdcaddcbdbddcbacccbcdbaaacbaadbdbbdbccdcadcdcbbdcaccbcdadacaadadabbcbadcdaacaabccddaccbccdabcdbbaaccaabdaadbbcbbcdcadacdbddbcdabcdbdadccadbbaccbadacdbabacddbabdccdacaabbabcdddabacdbaadabbddacdbdadddbbaabcbbaacabacdddacbdaabadbcbaaaacdccccbabbadcaaddabdbacbdbcaccccacdaccbcccbbadaadddbadbccddaccdcacbcdccacdccdbcacbddbaddaadcdbcaddabaacccccaabacabbcacabddddccadbdabacccdabaadccbadddaaddbcddccbacaaacbbcbacdcacbbcdccccccddcbccdadbccabbbaabbcbbddaacbabddcaddcdbdabcacbbddddcdababcaadadcddcabacacbcabbadaaaadcdbdccbddcadaabcbbacacdbaacccabacdcdcacadabcccddaddcbabdadadadcdaaacbdcddbdbddccbcadbcadccbcaddcbccaccccbabddbdccbbcbbdccdcaaadabadcbbcabaabaabaacabccabcbbccdaabdcbbdcaaabcdccaadabdcdaaacbcadcbccaaabdbcadbbcccbcacdaadaabacacdcaaadbcabbddcbdcabccddbdacaadcadbddcccabdcdcaacdbcbbdbbabbdcadcdddcdbdacdcabdabacdcdabbbbcbcccacdabdbaaaabcccdcacbbbcccabaccacdccbabcbbdcabddcdabbbbdcbcbbaddbcaddddccbdbddccbdbbdacabaccabdbbccdbccadbaabaadbadaadddacacddabdbdadbabaabcbdabbddacacdbadbdbabdacdbdcddccaabaccbccdcabadbcabdcadaadbabbdcbbcdacdababdaabbddbccbdbdddbaccaddaabaaaaabdcaadbdaacdbdcdbbbbcadbdaacdbbbdacbdaaccbacddbadbdcabaaacbadcdacaacdbbbdcbacadddcdcacacabaddcdbcacdaaacdbbdbaadcccdbdcdbccccababdacddcbcdcbababdbadccbbdddbdddcccadbdddccdcbdbcddabadabadbcaddcdaabbdccbabdcbadaadcabadabdabdbcddadbdaaaaabbaccbaddcadaadbbaaabdbcbaadcbccdaabbccaddccdbbdacbaabdcbdacddacbdbbdcdcbacbbcabcbbadcbddaaaadadbddcdddcbccdabdacbaaccddadacdbdacbddcddcdcbdabccbaabadbadbbcaababaadcbcadbdaababdbcaddddacdacbcbabadbbcddcccbccdabbdbabbabccbbccbabacbdbdacabadbaccadcccbcbadaabbdaadcccdbcbacacadacdbccdcbdaaacbccddadabcccbbbabddabccadcdbdddbabcccaabcabdcbdaaabcbcdccbbbbddabacacbdacaaaadbdbccbbcadcddbbaccacacbcdccbaddabdabcccdcdbacddabcadaddccacdcacaddbbbabdbdddccaabbccadadababbcacdccadaccabddbdcacdbbdbbaadacdbabadbacbdbdabcbcbadbddadbdddbccccaccbdcaacaacbcdbabbcdbcdcddccbddadadbccbddbadacacdbbdbbbabaddddadbbaacdbbbadddcbdbdbdcbbcddccbcdacaabbbdadaaddccddbaaccdbbcbbabcadbbdcdbdbbbcdabadbbbdddadbdcaaaabdabdddcdbcbcbbbbadaacbabccbdaabddddddbabcdaacabadcadddddacaabdaabcdbbbcabbdbcbbbadbadcddbcbdbdadadabddcadbbdbcdbbdcadadabacaaadbbadccbacbadcbcdbacccdccaaabbdcdcaccbbdcabbcabddadaabbadbdadcdbadbcdcaaccabbdbbcbcbbbcddadddbadbccddadacacacccadabaacdbbbddbcdccacacbdccbcabbadacdbdabbbbacbbacdcccccbadccdbcdbcdbbccdadcbcddacdcdaccaadcccbaaccdadbbdaaabadbaabcccabcbaadbacdcdbbcbdacddcadddabaaaadbdabacbabbdcdacbaaacbabccabaddacbcacbcbdaaadbcdcddbaabbcbbbabbcddabcbccadcdcddcdbdbddbcddcadddbcbdbdcccbdccacdabaddcbcbadbcaaddbaabcdbcdcddbcbcdcdbdadbadbaabbcdaccdabcbbdadadacdbabbbaadbcacacdddcabcddbcdaadaddbdbdcbcccacddaadcbcaddcabdccdcaddaaaccaadbddcacadadbbcddcddbddadadaaaadbdcabbcdcbbcbbdbbccdabcaacdcbacdcdbbddbbabaaabcbdabbdbaadbdcdddacdabdcadcbbdbdbaddaddadaababbaadacbdcdacdbdaabbadcacccdaddcdbcdbdbcadcbcdbcbbddddddbcccadacadacacdbbabbacbcbdbbcdaadacccaaddcaaadabdbaacdcbbcccdbcabdacdcdcbccdcccabbbaadcabcdaadcdacbdbacbcacdcbcbacddcccbbbbadbaababbdccbbcdadcdbbcbccdccbdcccacbacdbbddbbccdbdacabdababcbbdabcddadddbbaadbccacacabdccdaacdcdbbbadbaabcdbbcadccddcdddbadcccbdcccadbababaacbadaddadbabadcbaabcdcbddbddabdabbcabcbdabcdcaaabddccdbddcbccbbabcadccaaaaacacddbdcccbbadabadcddabacdbbcdaabdacbadacbbdbaacaabaacbbcddadbbaacccdbbcbaaaabadaacbadbcdadaddcbdaaccdcdccdbbdddcbbdabdbcdbbbbbbcbaabdaccdcaaddbbacdddbbdadcbdbaacbccacbdabdcadbbdddabdcdcbcbdbaacdcacbdbdcacddcadbccaccbabbdcdcdbbdbdcccabdbccbadcbcbdcaacacadabbcccaaccbdabcbaadcbbabccdddcaadaddacaadbddcdbdcccbacaabcababdcacbaabbabdaacbcddbaddbabbacdbaccbbbcbaaababacccbddccadbdacdcbaaacacdabcdbbcadaaadcaadaccdaccdabbddbbdcbabdcdacabcbddbdcbaabccddbcaaabccdbaabbcdaccbcbccdadbbcbcdacdbcddababcdbbadacbaabcbbacbabcacbcdcaaaaabacadcabaaaabddbdbadbdbaddbcccaddbdbdcccdadddaccaabdccacdcabdadbcabcbcabbbbccaacbbcddcbdabcdcaccdbbbcababdcbbcbcdbabdbaacbcccbcbddbdaccadadbbbcbdbaabbadaadabbaaccdadaaadadacbdddadbbbabcccbacddbbbdbacddcbdadbdcabbdadacadbdccdcdbdcbaacabbacbbcbcbcddadccabddbadadcbcabdcbccddddbccccaaaacdadcddbdabcddadabdddacaccacdddbacdbcbdaadbadcdadcddadbcbbabcadaadabcbbbcdccaaacbdbdcdcbacaabaaaaddccbabbaabddadbaddcaacbacabaccbcccccbccababccdbdcabdcacdbdbbccbddcbbbcdcdcddcbdcbcadadaaddbdbdaddcdacaccbddcbbdacdddcbcdacaddbabaabadcacacabcaababbbdacbcdcbacbbcbabcdddddbdcccbddcabcadcdccbcdddbdccdcbbacbbddcadddcdcdcccbacbddbddcacdbadaaadbacacddadcbbcdddccaabcdbcccdbdcababcdbbbcdccddcababcacbddbabcbcbdadddabbaacaaacacbbdadcadadaacacbaaaacaabbcddaabbabadabbbdaaadaadbaadcbacddabdccdbbdddbacdadabbcdabaabadbaccabdcdbaacdbcabdaabaddbdbabdaaaacaaccaabcdbabccbbbaabdaaaddbadadbbaabaabcaacdbcadcaabacbcabddaccdcdddaccdcbddbccbbacaddccccdcbadaaddbdabbbdbbbbbaaccaddbaabbcdcddbbaabaccadacbbcccadbbacdbbcaacccbcbabdaaddabadcdccdbdccdcdbddacddcaddcbbdabbaaabdbaaccadccccdbcdbcaccbaccdabaacdcddccccadbcdbbdbccddccaaabbabadcaabdadbccadbdbcbcdbcddabacbddabdbddbbbdacaacccaddaabaaaaccddbdaabdbbdbbadcabbadaaacdaabdaadaabddddccdbbdcccaacbadcccbbdbdbcdcbdbadbddaacbaacdaabaaababcadcdbbcdacaaaaaabcbabdcadcccbbdabdddbabbbaadbdbbbdaaddaaabcdddccabaacdbaabcbadacbdcdadbadbddabbacbaacbadbaccbbbbccbcacbcababaabbadbdccdbbbbabcddadbdaabcddccddabddccccdcdcacaddcadbabdbbbbadccbbcbacababbdbdcbcaababdaacabacdddaabcbaabddabbddaadddddcabacdaacdbdaddbdaccbdcccdcdaccbacbbccaacbacabcccbcaddbcdadcbdbcbbbaacddbdddbdcadaccaadcbaabbdacdbbbcbccbaaabccccbbbadaaadaaccccddcdbaabdadcdbbccccdacbbbadbccccdbcadabbbcdcccaaddcaccdddbdbcacbbdddcbbcadadbadcbacbcbdabcdacbbcabcdbaadcbcdcbdddbcadcddabbcbbaabccdccadabcaaccabaaccabcbbcdbcdbcbdbbaabaaabcdaddabcbbdababbbdbadaaddcbabadbbacddcbcaabdccddbaabaaaadbcbbbadcdddccdcdcacdabbdaaaacaddcbbcbaccacdccbacddccbddacbbacbcadadabbabcbbccbbdcbadcdcaabcbdbbddbbcccacdbaacdcbdccbbdadbacdabacccadbdaaaabccdbacdadcdbcdcbadcaababcadddddbabbabbbadbacccbdcadbcccaaddcabcbacacbbdcbbcddbadaddcbbccdbcabdadbdbbbddcbddacbbbbbbcbbacdbbabbcaaccdccbcaaccbbbcbbcbcdacacbccacaaacdbacdcdababcbcbdbddcccdaaddbcacaacaaadaddabacdbdabcadcadcbacaabbadcddcaadacbbdbcdbddbbcbcbacdbcccddabbabbdbdabcdbcbabdacacccbabbbdcaddcdccacaacdbdcaacdbdbdaadbcabbbdcddccaaddcbbacccbaabddbcaabbcadcaccbcbaccccaacaccbbdddbcabcbbaccabdadaddbbabcaddaaadccccddcdaccdbccdcbddaabddcaaddbddcddbccdaddbbbbbcbdaddabdaaabbbbabacdcaadddddcdcdaaacddccbbcdacabccaabcacbcbcabbcabbcdbcbdbcadcddbbdbbadddbcddcbacadcbcccdbabddbbdbdccaccdbbcbcddcbaaaddcdcacaddacbbcdcaaabaabadacddbadababdccbbbacabbabbbcbdcddbdaadbaacbccacdbaccdcbaabacdbbaaacbdcaccccadabbabdaadcccaadddadcabdcaccddabccbccdaacbbcdcbdcdddbbabcdbbaabadcdbbbddddbddbdcadcbcccbbcdcbaaabccabadbbcbbcccaaaabcdcadccbabbbbcadcdccdddabbacaccbcacddbddacbcdaddbcbcdadbaabaccbcdcacbcaccbbcddddacbaaddacadabaacbbbddadcccccaaadcddbbaccaccbcdcaddcacabaaacaabbcdcdaadadcacccdacddcccbdddbcdaddcacbadaabdcbaaabccbbcdcdadacbacabbadbdabdbdaadddcdacccacabdbcddbbdbaadcabaaddcccddbbbdcbabbadbbbabaaaaccccccdadbbccbabcacdacbabdaadccbbbcbcddddaaccabbcbbabdccbddcbcabcccbdbcbbbbbbadbbdadcbdbabcbbdadadabaaddcabaabbbabcaadbddcbdccaacbdcddbbaadacaaacdacaadcbabbbbbccacbabbbbabaadcddcdbbbddbbacaaabaaccacbcaaaccccccdaaadddbbcacaaadbdcacbdacdbbcbddcdccdbdccccdddccbdbacdbaccbdbbadabcaacbdbbdcbaaadbcdcdbaabdacddcdcbacacbddbbcaaaaccdacbbccaddadacbabddcdbcbadcddacddcdbabacdacdddcdbccbcdaaccdddaacdaaaacbababbcdabcdcbbcdbbacaabbddabcacdacabacaaabaadbadaaaaacdcdaaccaccdddbdcddccabaadababbdcaddbbbabacacbaaacbbadbddcddcdacabaaccdccacccdbcdddaadbdcbabdcadbbdcdacadcaababbdbccbdaacbbbacdcccccbdbabaadccadccacbdbbccbcccbdadbbaadbdbdbacdddabcbabcccdbcbbbacddbbcbbbdbdacadccdbccdcaddcaacabdadbadaddabcdacddcdcccccbbcacbdacdadcddabcbdbddadabbcbaddbaacdcbcabaabcdaaabbddbdbcbbcbabdabaaabdaadcbdaabcacdbcdddcdbcdbcbdbacacaddbaddbadcbcaaddbadbaccadacadabddcbbacccdbababccbaddbacbdbaaccbbddbcdabcbcbacdadaadcbdbbaccdddcdbbabbaacdbbdabbbdbabccbdbacbcbddcabcddabdddbdaccdaaddbaabcdadccdcabacdccaadadcbcadabbaccbcccbdcdccbdcabbbcaadabcaddccabbdadbcacdcdccdbddddcaaaccdaaddbdaabacabdcbbbaddadbddbcdbdbdccddddcaababaabaababbdccbacdddbabbabcaaaacbbdaacdaddadcadaccdbaddcbaaabddcdbbdbcbcaacbcbbcbbbadaccbbbbbcdaabdddbcbdbbaadbbccbcbcccbbcdcbdbabaabccdaccaccaacbdbadacaaadacdcdacadcdbccbaabbccaadbddddcdabbcdbaddbccccadbbdabcadbaabbbaddabddacbcdcdcacaabdcccdbbbaccbdabbabbdbddbbbcbbcbabdaabcaddccdcdcdcbadbaabadaadabbccacbcbdaaccbaddaaddabaacaadabcbbdadcbdcbbbbcbbaccddbdcacccacacccbdcbaabcdaccdcbdcbbaabcdbabaadbdaaccdcabdcaddabbabdadcccbacdadbcabaababdbcddbdabbabbddbabcccddabaabcbbacbdadbbaabadcabacbbbcdbdcbcabbccbbdbccdabcaaadaaddaadbbdbdbbcdcbbdbacbcbccbdbbddcbaadbacccbcdadbaadcadaabbcdbbcdcbcdaaaadbddbacbacdacabccdbcacabdbbaabcaaababbaaaacabbadbcaccadbddadaddbbdabdabaddaacdcbdccabddabcacbadbdaadcddbbddaabdbbbbcaadcdacadcacabddcbbacddbccccbababdabdaaabacddbdadcbcbbaddaccddbadbadbdccdbaaabadadbdabaddbdccacbbaabcbbcddacdacbccadcdbbbaccbaabaaddaddabaadcbcddcdbdcabbcbddbbaacddaadccaccbcbcadcadaddcbbddadbccbdddbcaddcddccacddacbaaacadcabbcddcaaacccdbbbcabbdacadcaaaabbcabaddacbbadcddaadcaadbadcddabdbabbdaadacabcbccabbadadbdbcccbccadcaacdbcaacaabaabcbcbbdcdcdaaddaddabcbbbbdacbababcddaaaaddbcabcccabdcbabcbccadbdbdccddadabcccbadcadcdccdccaabaccbacababbaaddcbcbbdddcabbbbcdbcdcdbaacbbcbcbdcaccdaadacdcdaaadcdcddbaadcddaadcbddbcdbcbcaacddcddddbabddcacaddabcdddbbdaaccddcacdacbddbccabbccdcdcbbabaddcbbaadcdaaabbbbacbcabbccbbcccdabccabadaaccbabcbabccabababdcacdbbadcbccbababbdccaddbcdabccccbcbdcbacccbaccccaaaabdddadddabdcaacbcbacdbbdbbacbdbdcaadaadcacadbcbcddbccaddddbcaaadbaddcbacadabcdbacdacadbdabdddbdadccdbaccdbccdacdbdbdbbaaacdcbaacccccbdcadccbbacaddbccddcaabdbabbccdbcaccbbcbbababcdabdcbbcddbcbccabdacbddcaabdadccaddaaaaaacbadabddbdbbcddabcbcbbcdacaabbddccbdaabababbabcccdaabaacbaacbbdadadadbcdcbccbdadbbbddbcbbcddabaabaddcdaababadcbcbdbdcdbdcadaababbdcababacdcacbddbabbaaadabadbccabbdadccddcdbdbdabccabdbdbadbdbaadbabdcaaccdacaaaadbcdbbccddacbddcabbccccdbbdbbbdaaaddcbaacddadbdcbbdbaaaadbcbbaaaadcadaccdacbacaacaccaabddbbdacdbadadbcdbbadbdcbcadbbcadabadcdbddcaaacccadccbacacaabaadbdbdaacbbdbddadbabdabdddabbabbdcdbaddbadbcddddddacbbadcccdbbcacdacadaabaccbacaabaddbadbdbccdaacccacacabbbadbaccccaadaddccdbabcadabdcbaccccbcbbacdbddaaacabbcbcddcacdcddaabaaabcabbcadbabddacdbabbaddabdadbccadaaaabdabddcadabcdabccdcdcaddcacbbdbddabddbccbaccdcbadbcdbcccdbcbaadadbcbaddbbaaccccdccaaccaccaccdbabcbccabdabcbdcdcccacbddbbbdccabcbcbdcbdacbaaacdabbbbdaadcdcbacccdbdddbdddaaccdadcbaabbabadaadbdbaaacadbcbbdadbacdcbccaacddbddababacccbadcccbdccdcabadcdcdcbbcadbdaaacadccadcdcbcdcbcbbbdaadbcbadddddaabbadabcbddcabdcacdaddddddaadcbdacdcacdbddabccdcddcbcacbbbaabaacbbdcaccaddadddcabadbdacadabdcbbcddbadbbdddccbbdcccbdaaacddbdcccdddcaddccabbbbcbcddadabcacccdbddbddbbdcaadcccacacddcbabbabbbabcdacbbbabcadcddbaaaadaadddcdadcadadaaadacdaccdabcdddddbcabdcbddadccdcaaacacbdcdbbbadbdbdaaabbaacdbabadacadaccbbdbcbbacdadbbbcbbabcbcadabcdabaacdabcbcbddbcddaaaccabcdcabdacbaddcdcbddcdabbbdbcacbcdabbddaacddcabcbcaacdbddbddcbcbadcdcccbadaccbdacbcccbaddaaacbabcababccdcdadbcdbccaddcbddcddcdbadadbbbdbdccbdacaccdacabbdbddddbbabbbaddbcdaabbbcdccbdababbbadcbbacabbaddabddaaccddaaccabcdcdbddabdbabacddbbdadababdaabdbdcabcbdbddbbdbbdddcacbdabdcbaaabbbcdddcddbadbbbabdbbabdccbbaacddcabbadbbadddaaacaddcdddbdabbaacbabaddaabdadacdbacaadaadadcaccaddacdbcbdbbbbcdcbccccbdabacbcbcdacadccbadcdbbaabbadcccdaabdbddacadbbdcddabdcdbcbcddbaaabbcbcbdadabcbbdbcbcdbdbcdabaadbdaaabbdbdadddbbadbbccdcbcddcababcccbbbdbcddcdbaaabbabdcbabacddabcbdabdbaabbabcccdcadbcdddacbccccdadacbccdcbdcddccbacabdbdbcdacbccadcaccbdaadbabbaaaddbcdcaadbdaadbcaababadbcbaabbddadbbddddacdbbbdbbdcbbababbbbaaaddcbcdbcadadcaddcccdbdaddcccdbcdaabbdcbbcdabdbbdcbdbcabccbbbdbbdbbcdcacddbadadbcdbadabcaddbcabcbdccbbacdccaacbdddcaaccacdbddcaadcccadabddaccbbbcccadabdbbddddbdaddadcbbbacacaadacbdaaadabdcdcbdcbddbbdbdcaddbbbcbbdaddbbaabdbabbbdadcaacbddaaadbcbccbbdbdccabcdccbaaaacdaabbbddddcadccaaacbcdcdacadabcdcbadcbccdbbbbddbdbbbdbcdbcdccbcbcdddddabcbabdcaaddbcbddadcdaaddcccabbcbcadbbcbaddabcabcacbadcbacbbbbcbbbcbcacadcbccabcabdacbddbdabcbcdcacbbacdacaacdcdcbbabdccaadbaacdabacbacddbaddbddacccacdadbcbcdbbbbdcaccddacacadccabdbbcbddbcccbabbbddaaddbddddccddbacaabadadcddbcbcbddcbdbbdbcccddcaabbdcdcddaacdbababcbdbaaadadcbdcddaddbdddbccdbdbdadbcbaabacdaaacddbabbdaddbbdbacbbaabacaaabaddbdbcbdacdddddabdbcdbadccdbbdbabbccbaaabbdccccbaadcdbbbadaacccccdcbbbdbcabcbaacbcdcbdaccabdadbcdcaabadbdcccacdcaddbbcabcdcdddadbadcdcbccaadadbaabbdaaabadccabcbcacdaababbccbcacbdbdabcaddaabbbdaacccaccadabbbddacddcdcadadaacbabbccbacbcdadbcdcbdcccbdcbddbcadccbbcadbdaaccdaacbddacdbbbbdbbcdcdddbcbadbbbdbddaabaaabcbdbdbccccbbdcacaaddcaaddbbdaaacbdabbaabcadbabaaacabbdbbddbabaccaaaadadcdbadcdacbcabcbacbbccbdcccddddacdbcdabbcdddccdddddbbbbacbabcddaccacadaabadabccabacaabdbbaababccabcdaacbdacdbcabdbbddbbcbddacacacdbababdaadaddadcdacbacbcabcacaaabddbbddbadbcdbaccaacadddabbbbcddbddbdcaaddcdcdddbcdabccabdcdadcaacbbacdcacdcdbaaaabddadddcbbcacdaaadabcbaddccccccbbbcccdaacbabacbdadabadabcddbddaadbddbabbccbbdcdbbcdadcabbaddcaadabaabccaccabdaabbaacccddaccdcddbdacddcdbdbddadcaaabadaaaaaddacdbdaccdcbdbdbaabacddccbaabbbcabdacaadcadaaacacaacbcadcdbabccbddaacbdcbcdddacbaaadadaaacddcccbcdbbacbaaadcbcdaabbcdbcbdcbbdaccbdccbdacdbddcdcadaaacbbadbbddbabaddccddcacaddacdaddabbdcaccdaccccbbcdaabdddacacadcdbcdcacaddbbbdcadbdbacbdbcabbddbcbddbadcbcdcacbbbbcadbdabaddadbaaabdddcacccccabdccadcddadbcdcaccbbdcdcacaabcbaddacddbaacadbccbdaddbcddbccbbdababdbbdacaaddbccbddaccbaaacbdbbcdbdcbddbacaaaacbaaadcbbacadbbadcbdbbaaddbabddbdddaccacdcaacaaabbddbdacadabaccabcaccbcaadddbddbcdaadddcdadcabddbcbbbadcddbcaddabdaddabdcbdddadcbcdbabbbaaacccbaddadbdccbbdbaccabbdbcdcdbacddcddccaddcdaaddcbccdabdcddbaccbacbbcddbccdbbbaabacaacadbbbabbbbaabcabbbadadcbcddddcadddaddcdcddcccbaccacccdabcaddccdcbcdaaabbbdadaacdaabbddbdddaaabacaddddccbabbadbbbcabcadbcbcbbabdbadbbcaddcbbcdccbccbaccbcabddccdbdddaaddadbbbcbbdadbcdcabbdcbdaacdcdcbbdabddcbcbdacbbccacacbababbdacaaddadccaacabadabbdadadcdadabadaabcdbbacdccdbdcbdcbccdaabdabaabcadbaadddbabbbcbddbdcbcdbccababddbddcbbbbbaacccacaddbbdcabddbbdaabcdcdbbdccddccdbdacbddaacbddbdabdababdcddcbbddcdccbcddcbdabacbdaabdbbdddadcddcaabdcdadcabcbddddbacadcbabddbaaddbbccbdcbbabbcbdbbabdaacdbdacbdcbbadcbcacccbacdadbbbbdabaaddaadcabcdcccccdaabcaaadaaccdcaaddacaacbcdabdcccccdaacbaadadccbddaadbdadaadcaacdcdcaabacbbdbbbabadddccabcbcbbdccaabcaacaadddcabcccddcbbdbcbadabcdbcbdbbabcdacadaabdcbabdacdbaadbaacaacbddbdcdbddbbdbbacccbdbdabadddacbdbccbccbddcbcccccdbaabbadbacdadbbadaddcbadbadbcddbdcacdcbcdabccbbaccadabdcccbbcbdacacadadcdaddadbcacccdbdaddcdddbabcabdbddbaadbbbcbcabccadbdcdbabaadcacdbbaaaccbadbdcdccdacadbaccacbcbdbabbacccccdddcadbddacdadbcaaddcddcdcddbdbbabddddababdcdaaabcbddaddbcaccccccabdcadbacddbcbaadcabddcabbbcbbdbbdcbabcbcdbdaaccbbadccccccadbcabaacadcaaddcabcacabcaadcdaaabbdaadbdbcdbcdbacabdaaaadcbbddcdcdcbccbbabbccdaddaacaacaddabdddaacbaacbcccaddbadbccddaadacdcddababbccaabccacabbdbdbccbdabbbadacddacbadcccadddbabccbddabbcdcdaabbcbacdabdbcbcdbdddbdacabbdcddcbacbddacadcdbcccaaddaaacbcccbaccdbdacbdbbbcbaddcccacbadbaddbdbbaacdcdbcabcadaadabaddacdadbdaadabcbbccaaccdcadcdbacbabdcdbcbbcbbbcdbbbdcbccbacbdccdcadbdbcdaaddababbaaaddadadaaaababcdbbcaddcabbbbbacdcccdcbccdaacddbcabdbccabacbddaadcaddaadcdcbcbbdcccdcbcdbdcbcabdcadccdbdcdbcbcbcdddacaacbacbdcccdbdcbbcaddbbbcababbccbabccccbdbaadbcbcddccadabbadabddbcdcccccccdbaacbdbacdcbdbccacbcbcccbdcadaacbcbcbdddbaccabdbbbdcbadabbacdacbbbbcdbddbbdcbbdcbbcbbaaddaacbdbcccccddaaaddbbdccbaddaaaccdcabbddcadbababcaacddbadababcdbdccdaacaabcaabccabbbbbcabdbbdbadddcdbbdccdcbaadbddccddbcbdadaaaadbadcacbaabdadabbabacabccdbddcdbccccbabbddadcbccccdbcddccccbaccabaadbadcacdcdaddacddbcdacaabaccdbbdcddbabbbcdbaabddccdaacdcbcaabdadadaadcdddbcbdaabaadcdacbbcdbdbcccccadddbdbcdcacdadbdaaaaaaddbddcbbaddcacaacacdcccddcadcddcaaadacccadcacdcadcbdcabdcaadddbbcbdaabaaaadbbdaaaaccdadddcccadcbaadcbbcdbcbbacadcbccabdbacbdcabdcdcccaadbddbcadadadcadaddcbccdbdbdbbacaccbbcdcbdbcdaccbaaaabaccbdbadadbdddaabbaccbcdbaacdaacdabbaaabdbaaddbcbdabadcacabaababcddbbddccbbddbadcdbcdacadacdcdcdbdaabcbcbdaaabcacccdadbdbcabdddcababccadaaccccbcbbbbbddbdbcbabccaccbcacaccaaadbbaacdcaddccbdaabdbaadaccbbbdcbbcbcaaaddaacacbbcbaddaddbdbbabacdadddbdccbdcbbdacbcaaaaaaaaabadaaabbbddcbbcddbbbbaddcacdabdddcdaddbbccbddccbdcaabbbbbbcabcccaabcdcdbbdcbdddabbaabdcadabacdcbccdbaadbcadcdcaaaaadbbaccdbddaadddbdddaccbbbadabbbccdaaabbbaadddbbbabadbaadbbdbbdbcdbaaacacdacadcbabcaaccaabbbbbcbbadbdaccccabccdaabbcaaddacbdccdbabdacbcdcdaaacbcddbcbccacddcbaabccbccdacbcbbaaaadcacabdcdbbbadaabbcbacacdacacccadbdcbcdcababdbbcdcddbbcadbdcbdbdbaccaababdadcdcbdcdaaccacddbbdbdddbbcdddbdacdadaadbdcacccbadccbdcddcadddbcacdadcadbbbcbcabccbccacaadbbcbacdbccadcbaabbadaccdddbccbbcabcbbcadddccdbbcbacabbaaccacadcdccacaadcdccbdacdacbddaaabccdbbbabccabcccdabcbbacbaaabdccadabbccdaddabaabbadcdabdaaabccdbcbdadaccbdbdaadacddbaadbbacbdabbbadadbaccacdbccaddcbbbbddbdcadadcaabbdadadccdcbaaadcbdabbcbabdcaacdcbcacdcaaadbbaaabadacabcabaccabaabdcbccdcdaadbaaadbbaacbcadcbcbacddcaaacadbaaaaabdabbabcbcbcccdabdabccddbdabdaacbabbdbbadcdabcddcdbdcbbccadbcacbbbcdcddcaabbdabacdadaddbdbacaddbdcbbadccddbbacccabcbbcdddcbcbdcdcaddccbdbbcdbdbbdabbcdbacacccdabacdcccacbadcdabbaadbcbddcaabcddbaabbcdaadcdbabcbbdaadbccbcabbbbbcdbbbcbbabacadbdbbaddccdddadaccbdcbcaaaccdcbbcadbddacddacbdbbacddcccbacbdacbccacacbddaddaaabdcbcabccbcddabadbdbbadbcabbadddbcbdabdbdbdbdcadbdbdbcdcdbcbbabadcaacacdbddbbcabaaaabddaababadccadcdddddbdcdcbbaaabcdbcaddbabaadbdbdddcbcdabbdabbcacdbdcabaabacabcddaacbabbdaabdbccbcdddbdabacdcbbcccbbbbcdccaccacbbdadacaaadbcabcbdadbbbdbcdacabcdbbdbdcbbbbdbddabacddcbbddcbdacaabacbacadcddcdbacccabbdadabbdbaaaabbbcadadbcadbbcabcabcbdadccbdcddacddabddbaddccccabacdcaadcbbbdcabdbaadbdbacaaacadadcdddaadaaadcabaaadabcbadcccbaaddcacdabcbcddddbabbcbddcdaaccbbddcbcaadabccbbadaacaacbdcaacdbadacccbabbbaddbdcbdaccddcdbaddcbbdbdcaacddbacbdcddcccaccaadddddadcbadbbdbcbacbaddadabddacabbcdaacbcccdbcbabbdcacabaaaddabdcdcdbaaaacadbcbabdccdbabccbddccacbddadbbbbacddcdaaabbdbaadccadbbcdbbcbccadccbaaadacadcaccddcbdaaaccdbbadcdbcaddddbdbcdcddcbcbdaaaccbabaaddbaabaacbbdabddbbdcccbbbcbdacccadbcadcdddbbbcdabaddcabdcaadbbcbbcbadcbddacdddaabaabaddcbddddbcabcaccccddddbadacaccbabbadacbbdcbcbbadccddbddacbbdbadbcaaccaacabbbbdaabbcdacddcaabddbcaaadabbaacaaacccdbbacadbcdbbaaddcddbdaadacadcdbcabdcdacdabdbccdacaabdbbabdcddacababdabdbccabcacbbbccbdabdadcbbabddbacadcbabccadbbbbabadacccdcddbdccdaaadbbabdbaabbbaadaabadbabbdbcdbdbabbaaccacbacccbbbbaacadacaabbbdcabddccabdcbbdccdcadbcbbdcbbddbbbdabadabdaccddbddaadcadaabadbdadcaddbdddbacdcddcbdddcdadcacdbbcbcabbddccaadccdbacdcaacacdcabcbbbadaccbadabadbaadbaddbaccccaacbadaddbadaabcbcdadabcaaabddabadcbbaadbacbcaabdcdabbbcddbcabdbbcbacbbdcbccaddaaacdbcbacacccdddbcaabbacbdaabadddddacdaaabcacbcddcbdccccdcbccadbacbaaacddbdddcbdabbcaabdaadccddaacccbaddcabccadbdccbccadbdaacbcbbdccacaaddbccdcbcabaaccdcaacbbabdcbcbaccaabdddbccccccbbbbbdbdabacbaabbcdcdbcadadcccacbbcbccadaaaddaacacabacbbadcbdacdcdbdcbaaccabbbbbacbaddadcbcbaccababcdcbccddbcbacdaabddabbbdddabacbdacabaaaacbdadcddacbbddbccdadbacbddbbddbacddadbdbdaabbbdcbcbaaabccdabccdacdddcbbbdcbbdbbabaabdbaaadcdacdcabbbaaaccdacadaadbbaddbaacbdcdcddadabcbbadcccccccbbabdbbcdbdcaaadcccdcbbadcadaabacabaabcbbbdbbaaabbcccbdbdbadbccdccabdcdcddccaddcdaaccbaacbccccacacbdbbcbbdddcbacbacccbddcaccbbbbabcdabcbccaddbadddcabaabdcbbbdbcbaaabadbccdcdbadddcaacdacadbacbdbdabddadbcaccdcabcbaabaabbcabcdcddcdbadabbbdadcabcaababaaccacbcbddbdabddcaccdcdbdbbdbcdadcdbdadbdccacdababcbbadaabdabccdccabadccdbaabbdcdcbacabaadadbcbdaccdcaacacdadaddbcbadcddcaacaabdcdaacaddadbacabddababcacabcbaacbdbdbdcbadcdcbabccabdbbdbaaadddddadbbabcbabdbcaadaddabaaaaccbabadbdbcdcabcabaddbacacbdbddaccdabcbccdbbcccddaccdbccdbcbbbadcdacaacaacdacccdbbcdbaadccaadacacdddbbbdabcbccbccbccadbccdbccccbaacbaaadcadbbbdddcdcbcacccbcacaabacbadbddaadddbaccdbbbddccdbbdcaabbdaaaacaadbcdcddcadbcddbcbdcadcdbcbccabcdcdddacacbbcddccccbabbacadcbcaaaaaccdbabdabadcabaabdbbcadbddadcdbbcbdcbddaaddddacdbacdaccbbacabdacdacacbccbbccdacdabbcbdbdcdabcbabdaabcbaacabbddaccabbdcbdadaabcadbbbdabccddcdccccbddbadbdacccdbdadcabadcdcbbddbdaabbdabdbbacddbcdddcacaddcbbbbadbdbdcaabbcabbacdbdaaddbcaacacbdddddabdaccddddbdbdbccaddacaacaabccccbbcaccacacbbdcbdcbbaddcaddadacdacbacbaacdbdadaccabccabbdbadccddacabccdcaaabbaaacaaddaabcadbbcddadbcabbacaaddcabbdacbdbdddcabcabbbabadcccadcacdcdbcabbdbcdabaadabcaaaacacdcacddababdcaabdbcbbbdbaaddcadddabbabccaadddbccdcaabbccaabbabadcadccdbbccabbadcdccacccbbcdaccacacbbccdcccccabdacdadcbdaabbbbccabdadbbbbcacabcbcbddbacacabbcbadcbccddbbabdccbcadccacdcbdcdaaccbadbbbbbbbddcbccacacacbaabcbbcbadabdbabacacddcbacbdcccbabadabbcabaaadacdaadacdabccbccbcabbcbddcbdaaadbaddbbdabdaacbcbdbddaccaaacdbacdadccabccabaccacacbcdaabdcddababddadadddabacdccdadbdbbdabacbcbcdcdcbcadacddbcbaacdbdcdcabdcbabccadbcccdcbddbbbcabdacbccbdcabcaccdccadccbbcbbbadbddcabddcbaaaabdbcdaccbdddbccdbcdacacbbccdbcbaccbbbdbcdabdddcdadadcdaddaabddccbddaaaadcabddaaaddbcaddcdddbbaadcbbcccaaaaabbcddaadcbbabdabdcdbaadcdcdcbadadcaaadbddcaaababdbacaaaaaaaadacccbbbccdcadacabadddcdcddacbabbbdcacddabcdcbaadadabddabcdabbcdbacadaaacdabcabcbaddaadacbbabbbabdadacaddccbddcdbccccabccbcadcbdbaaccdbcaacabddbcdbadccccbbcbcabbcdddcbaacdbdbcdaccbaaaabccdbaddacadbaaadbabaccbcacaddddaadaaaddbaccadccadccccbbddbaaddbcbbadcdbcabcccbbccdbdbccddaacdaadcbccddddababdccacbaccaabbaddbbacbddacbbbcdadbaddcdccdbcbccdbaabbdbdcdadcbadacbbddccbcdddabdbdcaaadbbdbcbbddadabbacbdcaadacacccddbdacbabbcdccbdddaadcbbcaaabbadbbddcbbbbccaabaacbdbaacccdbddacdabdcbbdbadddadadcdbabcabdaccadaabddccdabbaababdcccdbacccadaccdcdabbcaccbbcdddddaccdaadbddabcdbdcdacdacadbcdaccbaadddcbccaccababdbaabbbadacaabadcdaaadbcbaaaddcacddbcacccdadacabbcadbbadbabdddddddbbbcbabacbbdabbcaaabacdbbcbdaacabdabcbcccbcaadaaabacabaabbcdaaadbdbddcccbbdbdddbadbdbcbbacabaccdcbdbacddbcaabbdddbbabcacbcccacccccadbbcbbbbdcadcadbbbabbbdccacdaddabccbddbcdbdaaccabbccdacaacdcbbaaddaabacbcbcdcbaabcdcbdcccdaccdabbccdcdadbdccbdbccdacddaacacbbcaacacbadabaacdbaaabdbacbacdadbbdccadadaacaacacbacbaccccbccbdccbacabbccddacbdabbdddabbbdabaccdddcbaabdabaaccbaadcbaddbbbcbbcaccbccbbbaccdcbbcbbdbcadbdaaddcdbbdcadaabdacdabcaddcccccaaddabacdabbddabcddbaccadadcdadaacdbbbcadaddabbcdcaacbbcdbabbcdcabadcabadccddbdcccdaacddabbabdacacabbdbbcbaadbabcdcddcdcbdddddbcbddcaccbbddadbddcdcbddacdacdcbbcabadccbacdbabdcbbcaaddcddddccaaccdddcbcbbaddbcbccbcdbdbacdbbabaaaccdccdadbbbddcbdaabddabddbacadcbbcbdcbccabbcacdbaddcdcdadcbcabdddadbbcdabacaccbacdbbbcadbadadcacccccdddabdcbabbbcdaaabadaabaaaacdcacbadbdaddaabbcddaaabddcbacdaabcdacacdaccbabcbacccbabaaadbadddadadbdccaaadbbaddacdccacccdbcdabdbbbccbaababdbbcaccdccadddcadbdbbabaadccacbabdbabdcabaabbababdccdaaacddddcabaccacdccaaabaaddaaacbacbacadbddbcabbccdcdccdbdbdacbddbbdabccdbcbbaddcacddcabcadcdadadabdbddccdddbccbdbdbbbcaabbbbcdaddacdadadaaaadbcbdbbdaabbbbbbcbdccdabcdabbbcbdabdbdddaaddcbccbddcbaacddcccacadcbabaaacadcbbabaaadcacaaccdacabcdbabadcabbbcbcabccabcbddbcdacdbcbbccdbcdbadacbccadacdaccabbcddcdcbaccccaadccbabaacbddadbcacbabdcdadcabacabdcaaadadabbaacbdcccbddccdbdbbdccacdcdbcaabcaacccddcbbddddcbdbaadbcccacdabadcadbbdddabacdcacadcddababbbccdaadcbaacaddaacaddaaadccaabcacddabcbabacddbadbbbadadadbadcadaccbcadbbbcbadcaaccacddcbbaadbbbaadcdbaddadcbccaadcccadbbdcccbcacbadcddacdcaacaababadbccabbaaccdacabcbadbaadadcdcbcdbacccdabcaadbbcbbddbbccbdadbdadbbdabdbbbcbcbadddaacbdadcccdaadcadbadcccdbdadbdbdbbbcddabdaccaddcabbcddbcbbcbbbcaabdccdaccbabddabadbabcbddbdaabaabcdcdcccddcdcdbddaabddcddaadaacaaabaaaabaaadcddddbabdcbccdcbacbacbbccbdbbcacbdadccdbbabdddbbaaadacddccabdacadababbcacaadaabbddbcddcaaccbbaacbdddcbaacdbddbccadcdcaddcdabbcccddcbcdbdbcacbdaacaaaabdaacbdbaccbccdddcbcadacddaadbcbabdbdbccaadbbddabdcbdbaaaaccccddaadbbaaacddcccaaacacaaabadbcdbdbacccacbbddbadccadaddcabadcddbcabcbbbcdddcdccadbbcadbabdbbdddbadbacbbcaadcbbcddbccbacadbbccaadcbbcbdaacaacdccbaadccadcdcbabbbbabbbdbdaddccababbacdcbaacccacbaccccdbabdadaddbcccacdcdddddaddccaccdbbbddbbadbaadbbcabaabbaaadcdcbacdadadddbacdcacabcadacbdaabcdcdccbdccabdabcaaaabddbbdbacdccddbbabaabccbcdbbaddabadcbdcaaacaadbaaabbdccabcbdbccdcbaaccacdcabaabdbbababacbbaabdbcdbbacabcccccadacdbcbbdbabadbccaacddbabbbcbaddcdaaaddbdacaacbaabcbcaabbdcccdbaacbaccdccbdaaacbdbacbdcccdababdbbcadbdbbdbcdcabcabbcadbacadbcadaaaaabbbacbbbcaaaaddbcacaaccccdbdcdabdcbbacdbcaabcaacbddcbbdccacccddddabcacdbbaabcbdddcbcabcbaaaacdbaccdccadbdcdacaabdcbcaadacbddbcbcaabbaccbaccbdddbbbdaacddccdaddcabdddadbcadadddcddadcbdccbaddcbddacccbbbabaabcabbbbdcdaaadccddbdbcbdacacdadbbcbacdaacdbacdbcddadaddccaabdaaacaccbccbdcaaadaccdccabdcadcdbababdbbacbbbccdbdadddcbbacdcbdaabbddaaccbddadabacccbaabddbabcabbbabbddbcccbbdbdbdaaccdabcbcaacdddcabdcbbdabadabdabccdcbccaccddaacaacdbabbacccaabbbadcbdacccccabbbbabcdbddbccdcabcacbdacadccccacbcbbccbdaaaabbddddbdabbacdcdccccbdadadbbaabbbabcdcdbabbadaddbcccbabaddcaadbbacbbdbdcbdcdcaabdbccbaccabdcaadacbadabcdbacaaacadbaaaddcabcbccadcbcbabcddcbdbcbbdadcabcadcbbaabdbdcbcadddacdbcabcccaadcdaaadbdabcbabbcccaacdcddbbadbbbaadbaaacbaaabdccacbbdadaabcdcdbaacabbdabddcadbdbaabbddcdadbbbacdccdaadabacbacdcbdaaabdadaccdcaddbdbcdbabaabccdadabdbdaacadabcbadbcbcabcbbaddddaabbbaadcbdbbdcbbcccadbadcbabcadadbcddddbabbcacadccbcaddcadadaadbcabcbbbbbbdbddacaccccdbcbcddcabaccadacbbdbaabbdcaddacbbddbdaaabaabdadadaacacbddddbccddcababcdabacdcaddbbabccacdbbaccdcbcbadacbabcaabdcaaabbcdbddcbbbdacbdcbccbdbdbdbbbcbccdbbbabcbadddacbacdddaccbdddacbaaadadccacbddbabbaacdadadddccdcaddbadabacbdcadddacccddcbbcbbcdcabddabbbbdcbddbcbadadbabbcaadabadacaddadddabaabbbacdbbdcdcbcbacaacbdddadbcbbdabcaacbcdcaacbacaaacbaadbadccdbbbdddacbacaaccadcccccaccbabccbbaabdbddcbcdbabbacbdbbbcaadbbcdcccadddbaacccabbccbddcbcaaadaaaabbbdccbabddcddadbcddbbcccbdaaccacbbccabadbdbabbbabcaaddccdbabbcabdbccddcaaadcbbbbdbadcccaaacbbbadabadcdadcccdbcdbbdddbbcdaadababbdabbbbabbabdccacadcaaaaccdabacddbddcdbcddbacabcbcdabcddaaacccaaabdbbacabcdbbbaaccbcaacbbdcddddabaabcbbdaadbccadcdacacdadcdbbabbdbdacdabaccccaaacabccbdddbaaaccaccdcadbcccaacaabacbbaacaaaccdacdaacdcddcbddbcddacbccbbdbaddcbddbaddbabcdbaadbbcacaccbabaccbdcaaaaddcddccdbabadabcddacbcbdcbbbdccadbcaacabccdddcadbcbabdcbaccbbbdcdabcaaddbcadbbbcdaabdccdbddadcdccadadcbdcaaddadccabcaccbbbbbdddbaabddcdbccbcacaacbaaaccccaadabbcdbbccccccabbacacbcbbacaddddbbbdcdabbdaaabddabbdadaacbdcacbbcddcbaaabadcddacbacbbbaacaacbccdcadaadccccaacdcdbdacaabbbccaabdadcaaddcaccadcbabcbbaaadbcbcacdcddbadddbabaaacdbdbbbbcacbcdccdddbbdacabcbcccbddcbbcdaacbadbbddacaadddcbdddbccabbdabacbcbccdddaccacbcbddabddacadabccdbcdaaaabcbadcdbddbdcbdaabdbbbccdbaccbaaaabbddbdccddcadcdbddbcdadaaabcacdbbdccaccdcccbaaaaccabbdabcdadcddbaaacbadcbcbccbaccabaacabdcdbabdaaccbdaaacacdaaadbaadbdcdccabdddbdabddacdabadaacbdddcbdcbbdcbcdcaacbaabaddabbadacacbbdbabcdbcaadcdccbddabcacdbccaccbcdaaddccbccbdbbbacbbaadacdbdbaaccbddbbabbabdbaabbadacdcdbacaacbacdcbcbbdcbdccdbcabdbabababbcabbcdbacdacdacdaaaaaccdaaccbbcadbadddcaddccbbacddaacadbdaaaabcabbadadcbccdcadcacabaabbabdcbadddcdaddddaaadccacbdbcddbbbcabcdbbbaccaadaaacabdabdbbdacacddbbbdbccacdcdbacaacbbbabcddcbdbcdacaacbcbddccdacabcaccbbdaaadbadcbdcaabbbbacadabccbddbbabadabbccbacbdbddbcdcbaccacddcacaddbccbbbbcaccccadcdcabcbdcacaddbdbacbcbacaacdcdacbbdabcacbcccbacaccacdbccabbbaccbacdabbbccdcacdbdacaccdabbddabcdacdacacdaccdccbdbcadbacaaaacaacabbbbbabbaacdcdacabbcbbdcabdacdabccbadacdbaabababdabaabbadcadbccbcabbdacabaccbdbcacdbcddbccdcdbdaabbdbddccaacbddcacacaadaccdddabaaababdcdbacbcabbddcdabbdbaccbbdbdcdcdbbcccabdaabbadbdbdbaaddcbcacbdabddcdcabcabaacccaaaabcccbdccdabbcdcbccbcdaaaaabddaddbccccdbccccbabbcaacbababbdcccdcadabbaddccbbabcdadccccdddcbbacdaabaacddccbaadabadddacbcbcdbadcacaaaaaaabdccaacdbaacadcdccbdbcbbbdbbbacccadbdaaddababbabddcbccbadadbabbcccccbcdbadadcacabdcadbbcaabdddbaaadcbdccbbcacbdbdcdbddabcbcbbddacbbaaabaabbabdaccabbcdbbcaaacadcdcdbbddbaccaacacbbacbdbcdadabadddbcdbbcbcbbdadbbabbbcdacbbacbdadcabbaacdcdbdcaabcbccadbaaccaaabbcadbdddaabdbdbaacbddcacaccbacdcbacabbdacabdbcccccdbcdccdcbabbdbaadadcdcacbbcadacdaccaaddabbdaaaaddaacacdbbcacabddaaacbdcbdbcbccbacabbbadccbbbbbdaddcbcabddbacacdbddaadacabadbddabacaadcacbccabddcdbbbbccbaaddccccadabdccddbbbbaccaaabbbcbaccbbdbabaadddbbcbbbbadbbdaddcbcdacbbcbbddadbdddbdcaaddaadacdcdcbaccaadbaabbadccacbacbbcbbccccbbddbcddabadbccbdaadcbaddacaacddcacaabdaaaaddcaaaabcabdcbdbcdcadbcccdbcbbbccaddcddbcdbacbcaabdcbadbdcbcdcdcdabbdddccbbcbbcababddccaccacbccaaccaccbcdaabdaaccabbdcdddcadabaacddddbbccabaacdbbbbacabacadddbcbccbbbbbaaacabaccdcabdbbdccdaaddabacbabdcabdccaacaaccbcdaaaacadccddcccdddcdaadaadbbaaaabbabccbdbbccdbadcaabdcacadaddcbacbdcccddadcbcbbddccaaabdcbaadadadbcacadaccdddbdcbbabcddcccdcbdcdbcdacdaccabadbdcdddbcccdacdcabbaacabccddbdddacabaddcdbdbacbccaaaccdacccacbdbdbcadbcbcdccaabbdbacacadcbbbdbcdbbabbacadbabdcbbabcacccacdcdcbccacabacadabcbddddaabccdcbcdbdabcabdcbccaadcdbdbbbbcdcbdacacbaddacacdcbdbbacbbdabdbcbcdbbbbaadbaadbbdbddacabdaaabddabaabdcdabcdddbdaaabddaccdbdbdbccccaacdccdbddbbacadbbaddaabbcaaacdacbdaadadcddbdabdbcacbabcbccacdbcbbbbbbcddbccbdcccccdcdadbdccbcccaddadbaccbbdcabcccbcdcaaccdbcccbdbabcaddadacccdcabccdbbadddacadddbddddbcabcbcbcdaadcdacdadaaccbddbbbadaacaadaaabdddbbcabccddacabcddbdcaddaccdbabcbbcabccbbcdbdbacdcabcaccbadbcaacddacdccbdbbbadaaadbbdbdccccdbdbaaacdaaacadadabdaccdcacaddbbadddcbcdccacbabcbadcbbcddbcaabcadacbbbbbacdbcdabddcadcbaabacbbdbcbccaadbbcdbadadbadddccaaaabadadaaccbaabdbbbbbbcadbdcdbbbaccdabaacdcaacaadcdacdacacbcabaaaaadcdcbcbaaabdbcaddcdcccdddabdbbccbaddbbdacadbdbcddbadddbbccaacbacdaaaabdbbcdaaababddbdcddcdbabaccbabdbdcabdccdcbbdacbaaccadbbacadccaccaccdaccbbabbabbdcbbadabbbadbdbdabaddbaabdcddabaabdabcdbbabaddaddbccbabbddadcddbdacbbdcaadbcdcacbdddbcddbdbcbbdcdcaccbbbbdbccbaccdacbccddcdbddacbdbdbccbcbddabdadbaddbcaaccbcaddcacabbadaaaddbbaccdbacbabdcadbacbbbbdbaabdcaaabccbdcbcdababacdbadaacccdcddadcbacadccbacbbbdaadaaabcabcdcaccdbcadcaacadbccaccbbdbbbabbbdddcccdcbaddcccacdbacbdadddacbcabadacabcbbcdaddbdbcbbbbaadcddaaadcccbbabdabbdccbccbacdabdcaacaccdcaaaadcddbaaacabacdbadbdacdccadddbcdabaaaccacccdcaccdbbdbabbdcbcadcacdbdaccaadbcdbadbcaaaddccabdadbabbbadcbdcbcacbcbdabadbdaaababbacbcacdcddbbacbbcadcbdcbabaabadadaddddabdbbdbaabaccaaabbaddccaaadcbdddccbbadcdbccbddbdcabbabdccbccacacdbcadcbdcacdcbbbdcaabdcdbccccacbcbaadbdbbdcbaddbcabdbbbacabacaccbcbcccbcdbddcccadaccbabaacbdadaabdadbcadacabccddadcdbdbbcaabcccbabdacbbacbdbbbadcdadcbccabaddabacaabaababbacacdbdcacbdcbadbcdaaacabadcbbababccbdbabdabcbcaddaabddcbcbccbcdbdddabcbacaaacbccaabbddcbaddbadcabdacbcdbcbbccbbbddabbbcadcccdcdbcddcbaabbbcabaadadcbbaaaccbabcbbcdcdbbdbaddbddadabadbdbcccbddabccbdddbaddccbadcadcccdadadadccbbbccdabbbaccbbbdbaddbcbbaddbdccaabdccabcbddacccbaaadbdbbddccbcbbbbddbdbcbacccababbccadbdcadaddcaabcdadacdbdccbabcdaaadccbacbdcdbddbbaaaaaddbdacadccbadacdbdadadbadccbdddcbdcdbddddadcacbbccbabbcdbabbcccbaaadbcbdbcdbbccbdcdcbdcaabddbacdaadadbdcbcabbaadcbcbbccccabcccdadaacabaabcddbcdcbcdddabbabcddacaccacbdbbccaaccbbacdcdcdbcdcdddbcbcbabaccbbcacbddddddadabdcadaacccbcaacbcaacabbdccddcbddabdbbcdbabddaadcdadbdcabbbcacbddbbbccbdababaccabdaaabaaddbcacdaacdddbdacbdcdaabbbcbccaccbbddbcbcaacdaaadccdcbbcbcaacaadbacdabbcbbddcadbdacccbbbcdbabbbabaacbbccbcacbbbbbbcabcadacabdbbbadcadbabcddaabababbadaddbbaacddddadcddccabbddbabcbdbbccbdbcaccdbddbbadabdadccbbbdbddddadbbbaadacacaadaccaccabdbadbacaabcdcdabcdcaccadaaaaacddbadcbddbcdbaddcbbcbaacbababbabdabbaccacbcacbaacabddbbacdaddabcdbbcbccacdababacdabadcddbdcddbbcbddaddbbccdadddbaccdcdddbcabbbadacbcdbbccdbdccadcbabbbcbabaacdbcaaadcbadccbacccacbddacdcbdbdbcdaabdadbdccdcdabaaaabaadbdccccbcaacbbbbcadcaaabdcbbbccdcddcbcacdbbcaabbdbccabaacddbacdcaaacbcbabddccccdbabcbccdacaccdadbdbbabdbddbcbcbcdaadbdbdabdbddcccbdbdcbddaddcdabbdddadaabbbadcadbabcdbdccbbdbbbabcdbbaadddcdddababcbdddccbcbcbaaddbdadddcbdaccabaaccbbcacabdaacbddbddbaddcdbcddbbaacbcbdbbdbdabbaaadbbaadabdddccddaccccdabdcabbcdabdbaabcccdcaadabbdcaabacbbabacaabcdaaacaaaadabdbdadddaaabbcabddabdddaccbadbacccdcdcdadbadcddbccadcdadaaccdccccccbcccacccaaaccaacdacdbaaacacccbbcbcbaacbdccaadcccdbcaaaacdabaadabbdccddcccdbacdbbdcbabbdcddbaacacdcbcbdbdabdccaddcccbdbbdaaaaccacdaabcdadbddccccabbacbabdbbdcaaaabaccaacdbddddcaaadbcbabcbbcccabddadadacbbaadbdbbadbddabadbcbacaaadbabbbacccdacacbddcccaadaddaaccddcbdcaabadabcbbdbdcaaadcbccddbbdcddbcbbcbcaadbbbbcbbbcbabacbababcbdcaccdbabdadccdcbccdaabaaaabdbddcabbbbcbacdddcdadddabbdaabcbaabadbbdddbccacbadaccadacbcccadaddabdadbcaadcababbbacdacbabcbbabacbcdcdcbdaaddddcddcccdbdcabddbcccdcdbcdcdadadadcaaccbddddaacdcdcacdbbdbabaacccdbbbcbadbadcaadadcdcaabacddbbccacdcddaadbbdbbddcddbbcdcbaddabbdbdbbacbadadbaccadabacababbcdaabcdacaaddccacdcacdabbaabdddcccaacbcdacccbcbddddbacbcbbcadaccaccaacccaadbbbcdcddddcccddacdbbacadccabcddcaccdaddcaaddacadbdacccdbcbacbbbcadacdabcdbdadabaabcdbbdcacbcbcdaacbccaabcdaaddbbcbbbdbdbababdccdcbdccbbaaadabdaadbdbdaccdccdcbccadbbcbddbdbadacdbdadaaacdbcccdaaaacdaabdcaaccbcadaddcaaccaaacacbcadddddabdaaddcddbcaacdbbbbbbdbbbcdcbdaccdcdaaadcbbadbdcddddcccddbababcdbacbaaaaadcacabadccbdadcdcccabbbaacbbaacaabaabbbbaabddbaabcddcabcaccdcabdabdabcdaadcddbbcbbbcbbaaddbbbcabcbbababaabdaadcdbcbcbcbcbdddadbcccdbbacbdabbdcddccadcbbbdbbdacacbbbcdacbdcacbdabdbbcbbdadadaabccadbbbacbaacbcdbabcaccbddcaadcbadbbaabaacbadababadccadbccaccabcabcbccbbadbbabcdabddbbbcaabbcabbdcaaccdcaabacacabcbbdcbbabababaacdaadacbaaccbaccbcbcadbdbacdddacaddbdacdacaddabbabcbdcbacaaadabbcdbccccddabbbdbccbdbbaaaadcabbcbabbcdbdbdbbcbbdbbcdcddcddbbdbbcacabcbcbddccbbaccbdaadcbdcdbbaaacabbdcdbddadacdccdaabcbdbdacdaccbbdbacababccdacdbaaacabbdbdbdacbadcdabcbabddcbbcbccaaaccbacbdaabcccaadacaaadcbabddadbbbcabcdcdaacbdcbcbbbdddabaabadcbbabbbbccdaaaadbaacbbbbcdacccbccdcacbabaaaddcdaddcdadccccaacacbdddbbdccccdccbccaccddcaadbdaadbabcbbcaadccddcdcbcabbbcdaddbbcbdbaacdddaccdbdbbdadbdcccdabdcdbbcdcbddabbbbbacabacbdaddcdcbccbbbcbcadddbccaddbaddbbacacbabbccdbdadcccabcdccdbcbbdddaadacaabccabcaadbbabcbddadacabadabaacbabdbcddaccaadcddaddcbbacabacaccabdacdbdacaadbcbaacaabacbcbdbccbabbcccdcdcabbaadbdcdabdaddbcddccbbdbdccbcadaaacbbcaddcccacbccaaaabadcbbbbdbaadbaddcbbacadbdbcabadacbbcdcaddddddddddccddaaddbcabdbbadccdaaacddbccdbadccbdbadbdccbcaacdabdacacbdaabddddacbcabdacabcbccbccbabcaacbdadabbabacadbdcadcbbdcbcdababdddbddabddaaabbddabbcacbbbccdddcdaaabcbdccbabcabbbdaabaadccacacdaabbdaabbdcbbdaadcabdcbaabbadddccaddddbacdcdabdcccaacacddaadbadcdaacbdccbbddcbbcabdababdacbccbbbbdbdbbdbaadbacbccaacdcbdbbcbdbbbbdbbacabadbbdbbdcbddabdbaaddddabcbacadadccbbcbbbbcbcdbcaaacdcaabcbacabbcadacdbbcddbcdaacbdccaabdabdcdbabcabadccdbabbacaadaabddcabccccbbcdabbccbadcdbcaadaddabdbabaddddbababcaabaabbdbcaabcbbccddadcdccbddddbdaabcaaacccdbbdbdadcaccddbbccbdadddcdccdbdbdbbaacabaaacadacacddddbabaabccdcdaadcabbdaacccbacccccddcdadbcdcbbcacabbdcacbaacacbadbdddbaaccbabadccacbbacdacacbcdcaabcbcaccbdbacddbbabbbbdaccbaaccadcdccadddadcbbdadcbdcdabaadbbcaabadbadaccdcdabccbabaccdcbcdddabccbcbacabbcdcbdddcbadacaacdcaadccbddddaacacbcbbddbbadacbaacbccddaccbbcdabdbcdbdbdbbbaadbbcbdcdcdcacbdbdccaacdaccbbacacbdacadddaadcdbbdcddbabcdbdaadbdddbacbcdabacccbbdbacdcadccbccaddcbadbddccccbabbddabaabaabccbaabdadcdacddaabddbbbabdacccdacbbcdadaaabbccdadcbdbadbadcaacdcadbaadacaacdabdcdddaaaacaaaabbcbddcadbbbbccbdaaccabbaaaabacdcddcabcddbaccccdaaacdccaaadbbbbbabdbcbdbbbdcadbddbddddaacbcbbcbdacacdaddbccbabccdaabcaacbbcaabaaaaccaacdabcaaabcdcbbbddbbcadaaabcddccadcabcadcabbdaccbaaddbddaddccdabcabbccdabadcbcccbcbcdcaaabcdcbdacaaaabbcadccbcddcadddabdbbccaddbbcbcdbcaacdadadbcbbacccbcaccadbccbccdcdbbbbcdaabbdbcabdabbcbcbdacabacdadbdabbdacbabdaabdbbbcabbabbadaaabadadbdaaddadabbbcbaddddcbabbdccdbdbacbdbbdcadbabdcccbacaacbcbcddcbccbdcabbdddaacbababddbbacbbaaaaaabacbbccbdacddaacabdccdbabddaadbbddcccaaaadcbdcabbbbadbdabacbaaddadaacbbdbdcbbdccabdcbdbaacbabacbadccccaacacddbaccdbcdcbdbdbdbbbbaabbaabadccdabcbbadbddaddbabbadbcbddaddddaabbbbdcdcbabcddddddaabaccdbbbddaccabcdbabbbcdcccaacabaadbabdabdbaaacbdcddbbcaaccbbbbcdbbcbacddababcdccbdbddddaaddcbabdccaaccbacbcbaadcbadcbbabccacddbbbcaddaaddaabccdcdaccbdcccddbbccbaccbcdaddcdcbbbdddbbbbddcdccdcddaacccddcdaadbcddbbdccdacbadbdcdacacaddccdddbbbbacdbbcbddaadcddcaacdbacaaacbccbdbbdadccdbabddaccddcdbccddcbdacdbdbcaccaadabddacddadabdaabcbcaddacdaadcccaaadbabcdbabcdcccaccbcadcacadcccaacdacaaddabdcdbadbcdadbbddbabbdcbcdcdaccdbbdabcacbccbacaccbdacdaccddabbaadbdbbcbbaccbddcaacabdbaccdcbaddddcdcbdbcabdadadddbdcdabddacaddcddbcdabcabddccdbddabdbbadaabbdcacbaccdcdacddbaadbdddddabacbcacaaacbdbddcbbcbdbcddcdbcbddabdcaccdbbbabdbabaccaacadabdabbadadbbcbcacaadccdbcbbcbabdbcbccdcadcdacdbdddacbabcddadaaabbaaaccabcccacdbbdcdcdbbdacbbacabdbddabaccdaaabaacabdadbccabcbbacadadabbdabddbbccacaacddbbaaaaddddcdcdacdacabbcdabbbdbadbcbbdaccbbaaaabbdccabdaaadccacbdabadbbcbacdaddccbcabbbcaaaacddbcddbaddadccbaaaaaacddbdddaadddcabbaaabadadacbdbddabbcacccbcabadaddbadddddddcbdabdacbbaabacbddcdbcadbbcbdaabdcdbbabdbabbbddacabbcabdabacacbadabadbdbbcbddadacaccdacdadbacabbaccacbddbcabdacdaadbbcbbcbaddccdbddbcadccbabadccbbbdacdbbcdabdcccdabbcdbabbcaaddadccbccacabdccdddccacdbcdcccacbccacaabbcbbacbacbbabbdcbddcccbddcaaddabcdbcadcadaaabdcbdcaadbdabdadbbaadccacbdcadadccccaddabadbbcacdbbcadaadcabbabacdddbdcbddbdaccddbccbbabcccddccdacddaaacbcabdbcbdcbbaaaddaccaccbbcabaaabaaddbddabdbbaaacbbcacbbddcabdcdabddaccababbadccbbcabcaccdcdacdbacbbcadbbddacccbbbbadbcbbdccdbbacbdabacdcaabacdabccadaaacdbdcaaccbccddccdcbbbdcaadcabcababbbabbcacbbdccadbaabcdcbcbbabcdbbbacaaadadddabaaaacaacacaaadcbaadcabcbbddcdadadabbbbddddadabbdcbcabddddacdcbdcaabdccadccddddaaadacabdbbacdbbadbdccccddacddcdbbbcbbbcddddbddbccbcacbccbddbccabcccabcbddaddccabaccdbdddbdbbdadcabcdbbacdbabcbdbccaaadbadbddcdbbdbadbdbbdbabbbaababdaaddcdaccbcddaabbadaadadbaadbbdbabcdcbbabddbddbcdadcccddcdbcdcdcbdababcdbcabddccdccbaadcddabdcabdcaacaaaccdaabcbbbadadbbbdcabcdccbadabbcddbacccccabcdbcacdcabaddbdbddbabaddadabdabbbdabacacdcbdabadacacddabacdaacdbcadccbacbbbabcbcdcdccbabcbbdcdbdbcacdbcdacbbdbcaabbdbccbbadccadcaaadaadbcdcdaadbcacddabdadccacccaacacbcdbadadbaadabadbbdaddbbaddddcdcddabdddcbbcbcbbbbcbdddadcdacdbcaccacabbbcaabcdadccbaadacccacdaddcdcbababcbcadbbdaadabbadacdbaadcdbdbbbcaacdbaadaacbbcbbbdaaadbdcdbbdadcdbaadbdbdbbaadbaaabdbadcbbbdadabdaccbbaccdcbbaccdcbdacdacbdddddabbdcbaccbdaabdbacaddcccadbcbcdbddacaaacaacddddacdaadddddbcbddcbbdccbbddcdabadabdbcddcabbcccaabdcdbabcabdcabdadbccacdcddccddacbaabdbdacbabadacdabdbbadbdbbccddabdadbbccaccbcbcabadddbcdbdbabcabbbabdcbcacbcdccbbdaaabadcbbacbcddddbadaacdababdacbcdcbdaaccddaababbdcddbcabacdbdaaabdbdbcbbabcaaabbabcddbbdddaababddacbddbcbbcccbacbbcdcaccbabbaababbbcabcddadacddbdacbdacdbaccadddddaadadddcdcbbcbdccccccbbbacdadcbddcdaccdabbaaacbddabacbbdaccabdcacaaacdcbdcdbbdcdabbcabbadabdbdcabacdacbcccdadcbacbbccbdbcdddbaacbccbcdcdbabdbbddbbcbbaacdabbabababdbcbbcbcbbddaaaadbbcbbdaadbdaabbdbccdbdbcccdbbccbdbacbdaaddcbbbcbcaacdbcaaaddbdbdddbadddaaccbbdadcbdddcdccdccabccbbccbcccdabdbaccaadabdcaacccdbbccdaaacdbcdccdacbdbdaadbbcdbaaacdbabddaacdcadddbaccbbdaacbaaccbbbbabcbbdcdbccabacbbddadccbcdcbacdabdccabddbcacabbabccabbdcdcbadbdbcacbbcdccdbbccdbbacabbbbccbcababbacbdabcccccabcbdbbacadbbacbdcacbcdcacbdcccaddcadaadcdabcadbaddbbbcbcdcbdbbacddadaadaaccaddaacbdccaccbabcccccdbcbdcbbacdbdacbddabacddbaaaadbbbbdadbdcbcdababdcadcdcacdcaabcaadacddcaccbcdadbdccaccabcccdadccbbdbabbdbdbdcbbabcbdcbacdccadbadbcadbadbcdbcacbccadadbaabddaddabdababadacdbacbcddacddcdcbbcadbdcdacdcdabddabccbbdcdbddccabcccbbcadbcdcbabddabaacabcdcbcaabcaccabaadccdaacdadcbbbcaccaaabcbbdaabaaacbcaddadcdcdcabaaadacadcadddddabdbdbcbdddbbbadccabddbadcddabbccbabbccbdaccbaadaacbcaccbdbddbbaabdccbbddbabaacadddbabdcdccdaddacabdaccccaabdcbcbadbdbbacadbcbaddccadbaddcaacdabbcdcdccacbdddbbdbdcbccbbcadcadbaabddadbddbbbbccbdddbabaadcbbadadabadadcccbadccadabaabbaabcbcbdabcbcccaddcacdcdcbddcdabcadaacccbcacadcbdddccacddabcaabccbccaadcacddbdbdadbadaaaaccaccbccbcdbadababdcbacdbddacccccbdddccdacbbbababbaccdcbbcccbccbddcbaaddbdbbddadddbccbccdcadabbbdbbddacbbaaccdbddddacadabcdbabbddaababacddbcabdcdbcbbbbcdbabdccbcbcaabbadbdadbabcdcadaaabbbdcbbbbacccabaddbdbcdbdacdcdabbbdadabadabcddbdadacdcacbdaadabadbacdddbaacaddacabddcdccabbccddccdbbbdbacbddaaaddaaacdaddcdbcacccddbadcabbdacddbabaadabcabdcaccdabbccdbccdcaabadcaadbdcabacdcbbcadadaccccacbbbcbaddbcabdaaddcbabbbbddcdcdacdcbddabbddacdabccdbadccdcbcacabbcdacbaccdcdabcddbababddcbbbbacacaaacbddabddbadbbacdaddcaadbaddadabaaacacdddcbabbdccbcbddabacdbbcbaccbbdcacaacaccbddcacadacbaacdccdaadbdacdcbdadcaaaaccbbcdbadcaacbabdddddaacaacddacbbbdabdbcbdcbcdcbccbddacdabbcacddaabbbcadcccbdabaabdcdcbbdddcdbadccbaadadcabccddcbccccdbdcddbabaadccdadbdaddacdacbdbddbcdadbbcccadbaccdacbcbaadbdbabdbdcadbbdaacaccccbcadbccaddbbbaaddabacddabdcccccdaaaccacbcbbdcbcdcaacdccdcdacdcadbdbcbdaddbacdbddabadbbcbaaacbabbddcbdddadccdacccabbbbadcbdccbdddcacabcabacbadacadbabdcabaadacaaddcbbadcacaaabccbbdbcddbdcbdcbbbdaddacdcddcbdaaaaaaabcabacbddbacddbddbbddacdcdcaddddadddcababbbacbdaacabccaacbaccdddacdbccccbbccadddacbcabcaddacbcdbabbdddcdacccbdbdadcdddbcddbcaabdabbdcadcdcbcacddabadccbcacabdcdddbbaacddbdaadbabdccdcbdddaabdabdcdabddaabbcbbabdacacbbccaccabdbbcdbbddadcaaaacccbcddadbbdcbcbbdddbabbdaccbadbabcbbbdbccccabcbdbbcbdddbbaadaaccdacddddabadbcaacdbabddcabcbdcdcaaacbbacbbbbcaabaaacbdddbabdacdbacadcdbbabdcccacacddcbacacbcbbddcddacddaccbddbbdadbbcbcdccddcdcaabccbaacaadddabcddabababccbbdcbcadadbdcdabdaaacbdabbacbbddadaaaabbcbcdabbcadbddcaadbaaadcdcdbadabccadcbbaabdbdbdbbaaadaaacacbddbaabdbdbcccacbbddacaadabcbadcabddcabbcbacbdcccbcbdadabdbddbdccccaddbcdccdddcadbacbbddadadccbadbcccabbdaddabaadadaabdcaaacaccbdacdcdabbabbdaacbaacbcbbbdcdcdbbdbadaaabacacdbdddbbdacbaaacbddbdbadddddbbddadbdabadaadabdddacdcdbdccbcadadbadababcddcaabacbaabddbdadbdbbdcbaaaabdcddbacbcdcdaaadabcadcadabadcdbaccdbadcadcbbcdaddddcabbdcdbbddaccbcacccdcddacacdadddacdccdbacacbccbdbcbddbabadcdcdccccbdacbdabbcdadbacdcbcbbaadbdaccaaccbcccdcdddccbbddbadcacccdbddccaaccadaaabdabaaccaacdcaabbddcabcbadddbdbdbbdbadddcddbdbcbadbbbbcdcababbcbaddcccbbccccdcbcccccbbdccddbcbbdacaacabcadbabdacaccdbbbdabdbcaaddcdbccdcddaccddcabdddaaddaacbccabcdadcaccbcbdcdbbbbabdabbccaaccbabdbdddabbbaaaddcdcaadbcdbdcccaddbbcdcdbbddddbbcdddabcbdbcbbccaabdaccbbabbbbccaccadababddabcdaabbbdbadbaabcddcbdbbaacdbbdbbdcdddbabbcbcaacbcccdbadcbacdacbbbcdbcdcddaaccbdabdbbaddcbabccdbcabbcacaddabcdadadacddbdadcdbbcdbdbdcddaddcbaaddbdbccbddacaddcbbdababababbdcccdabbccacccdccbdabadadcabacdaadabaaddadababbaddbddccdbcacbbdacdddbcabbbabadaadabacdaabacadadddcdbcddaaddbdbaddcbdacbcaacbaccdddbbdcdbdddabaacbbadcaccdabdcdaccbdcacacbadabadadcbcbcccdddacddbadabcbdbccadbcccdbcaacccddbbcccccddadcdccbbdbbcacadadcadacbcbaaaaadccbdabbaabdaadadacbbcbdcbcaaacacccbccadacadbddcadbbcdacbbaadabdcbadbaddcbdddcbccaacbdcaddacbadcacbbababddbdcdabddaccaddaaabbcabcacbdadcbadcdbdcdbdacbdcbcbbbdabbddacacabdbbaddcdcbcbbadddbcbbaddcdbaccabbaadadbbdbbacaddddaacaadccadacabcbccbddcadcbcacddcdcbaadadaadbcdaabccaccabacaabcbbcadcbcaaaccbabaabadaacddcbcabaddabaabcdcbdcccbbbdcbadadcabcccbacdacccabcbcdaaaaacabbccbbaddbadbbbbbcdbaddadddadcdaabcdbcdaabbcddccdaccbbdaacdadaabbacadcdaaddabcdbacacabccabaadadadcaccadcadbaaabddabcbcdddabdccdaccdcdbdbddbdacdccaacbdbbadbbbdccbdbabcddaaadadbbddcacadccccddadbcdbaaccbdccadcbcbbddaddbcbacdadbcdbddcacaadbbbdcabcccabcbdbbdacaabdabbababcbcbaddcdabbbbbaccabbabdcbddbcdabdccbadccadddbbdccdbddadbbacabdacbcbabccdbadccabcabccbbdbdacacdcabdabbaaaabbaadbdcbdccbdcaccacdbcacbabbacdbcbdabbdacabbdccbbbdcbccdcacacdbcdccccdcbdabdddddabadccdabbddadadbccabbddccddacccdcbcdbbacbbaaaabdddacdbccbbdcbcbacabacdcdcdcbaabadadbcbbadacccbdcaabaccbaadccbccacdbdbbacddcabcbccccdbdbbbcdddbddcccaadddabddccbdadcdcbaabccbdbccdaaccdcaaddcabbbbdbccadbcbdbbdadcdbbccaddbbbbccdddcdbdcdababcbbaaabaabdaadaccdbdcaababaabdaabbddccbdbdacdbaacadabaadadbabcdaccccdbdcaacbaccdcaddbcbabadcaadbbbdabcccbcdbcabadaaccdcbccbbddbdddadbbbdadacbbaabadcbabdbbcddadbdccccddcabbaccabbdddccbabcabadbbdcaacbdcbdcabadcaacaadcbbbdddccdabbcdaacabdcdcadcdcccaddbdaabddbdbdcbcbbddcccaaccaacccbccddbacdcccbdadacbbacbcdbcbcacbbababcbbccadcdabccaacddacadcdcbadbbcdcbbbcdddbdbbbaacddbaaadaaaccbdacdccbdcaadadbcaaccacbdbdbacdaddcdadbbbaccbaddadddadcdcbcbabddbdcacadbbccccdacbbbcacdacddcbbbdacabbdbddcaddabbcdadcbcabdcbccaccbdbcdcbcbbbbddbabbabbadcbddaccbcacabdbbbdcadcabbabcdcbbbcacadcdadbbdcdadbadabcaaddcacbbbaaccabacbabccccccbdddbdbbccbbbcddcbadcddcddcdacddaaccaaabaadbcbcbbdcdbbbbdddccbdccdaaadadbbadcdccbbacbbadbbddacaabbcbbabdabbcaacdddbdacbcacbbdbccbbcabcdaaacddbbabaabdadcdcadacddbcccbddaddcaccbaddddcddbdbdabbdacbcdbcbbcdbabcdbbbbdabadcacabdacaddaabbddaaadbcdccdbdadaabcababdcddbadcbcaddadcbadadcddbbdbddaabcdaccccbbcdacbaacdccacddacccbdbcbbbddabdccbdadbdcbaaaddcadccbaccbbdccccbbbbbacbdcdbcddadcbbcaaaababbcbcaabaaaacccccddbbbdddabcbbadbcbacddbaabdbaaabbabcadbbdccadbaabbbbdbcdcdadcabdbbaabbbcbaacdccdccacabbadadbdaacadddddbccccddabbbdcbdcccbbddcdcbbbacacdaaccdacdadabcbcdcaddccdcbdacccbcbaaaddddacddcdcbbccbbadbbdaadaccdcabaabdbbdbdabbcdcacbaaadbdabcaadbbbcabdaaaadadacdbcdacabdbdcdbbbcbddabadddcaccdbcbcdccabdcbcbdbbbdbbbbaadadcabdcaccdcadaddbbdbadbcacaadbaabcddcbbdbcaabdbbcbcdaddabcdcddcbacbddcddccdbadbdbccddaddaacadddcbbacbcccbbcbbcdddbaaadadbaadadbabdccaaccabdcdabcaccacbdacbdbdbdaadcdcddaaacccaaababdbddacdbddddcdbacababcbdcdcdcbadbdcdddcabbcdbddaacbcbddadbccaaccabdbaddcabbabdcbcdccdccdacdbadcdbbcaddadbadaddcbbbddbcbaaaababbbbbdbdcddbdbcabddaabacabdcdbbccdbccbcdddccbcadabcdbbaaccadaadabbcbcabdbbadbaccdbaaccabaaccadccacabdbabbcbccbbcdddabbaddbadbcabacaddcccccacdadbdcbbddaddcacaaddccdcdbbacddcbacdcaabddddabcdcacccdabcaabcadbccaadcdbcbbcbabadabdacbdabacbcbbdacacddadddaddadcabdbabdcdddacdbaabbcdcdbcbadbcbbbabcbccabcbabadbdaddbdcccdcdaadaccddcdbdbbdbcabdddbbabaaacbaacbbacdcccdbcdbbdaacddbaadcbdbccacbacaadddbdbbddcbbdaacacbcaaacdbabdacdaabacbdbdbcdadadbbdccacdacbbabcbccbadaddbabdacbbbdcddbacdbdbbbcaadaabdddccddbcdcaaccdbcbbcdbbdcdbbccbdcacbadccbcccacadadccddcdbcabbbcdccbdcdaacaabdaaaccbacbdddcbabcddbdacbacabadddcdcddbabbcbbbacdbcacccdacadacabcadbcbdcadcbbcdbdaccbabaccaacbaabdcbdaaaaddcbcccaaacdbcdbacdccbcbadadadbddccdccaaabdaaacddccdabbbcbbbdaaaddcbcababadbcbadaaaadabaccbddbcacdadcaddbdcbbdcabacadddabbdcadabbbabaccdddadcdaccbcaadbdabdaacbccdcabddcdccadcdbdcccbddddccbcdadadcbaccbdcabaacadbadbaaabbacbdacdbcdbabbbbcbddbbdadcbabcbddcaccbaaabadcdbcbcabaacccbcdcbdcbacdacbccadabccbcbcdbbccdcbbbaadcbacacbccbbacaabbbccabbadaacabcdbccccbcccdbccdccbabccadbbaaaacbcadcbdddaabadbbdadddcccbccdaabadabbbbbbbdcddbbbaadcdddadcbbddcdbabaacbbacdbccdbbcdaddcddcbbccadacbcbabddddaaaddabbcacdcbbbdcbddbdabddcbaadbcdacbddaddbcdddbcaababbcbdddacdaaccbddadcdcbdccdabaacbdadacbbbbcdccdbbacaaccdacddcaadabbbdbcbacadbddddcaabddbabbcbdccbadddccbdcbddacddbcdbdccacccbaaabaacaccbbdadbdadcbacbddcaccbddcddaaaacbbbaaabbbdccaacbbbdabaaadbacacadbdaaacaababaadadcccdbacaccabcbcbcacbcdadcbbbcadbbdabcacddcbadbbaacacbccaaccabadbdcdbcbdacbcaccabacccbadadbcdddddcaacddbabababcbcbadbbddbdabcaacdaddcacbbbcbddabbddcdbcbbccbbbcaccbbbccbdacdbbbaccaadbbbdaacbddccabadbbddaccbacbadddbadacaabaddbaabcbdaccbcacbcacddbcbcbbdabbbcbcdcbabcadccbcdacbaacbccdacacbbcdaabcdcdacbbdbaacdaccdcbccbccdadddabaccdaacdbbcdaddbabbcbaaddaacaccadacbabdacdabaabaccccccbcadabacddaaaaabacadcadaacaaddacdbbdbbbacddbaababddabacadaddbacadccabbadddabcbdccbdcaadcbcadadbaddbbdbdbcdabadbcbdbadadbacccaaacbcdabaabcdcbcbbddadcacdaadbbddbbdccbbcbddbccdadcdaadccabddabdaccadbcdcbacbbabdaccbcddbccdcaddabdadcdaaaccbcaaacccacbadcbbbdadaccbddddcadddcdbccaabcdabadbbdaadbacbdadbcdbcccacbbabadaddabbbabbddcbcdaccdcccdccdbdabbaaacdcdabadbdaadbccdccccddbcbabcbbbaacdacaaccacbbbccabcbaddbbbcaadbbbabaaccdadccabadadcaabcadcdcccbabbbdbbdcbaadccaaccbbadcbbcaabdcaddaadbdddbbddbaaaddccabdcddbbcbadbadbdaaccbcccacddbacaaacadccbdadbcaababccdcbddbbaacbcaadbcbddacbcaccddcdaadcbbbbdcacdaadacccadbbccdcbdcacabadccadaadccdadcddbcaccccababccacabadbcdbcbdacabcadadabbddaaccbdbbbaaabcadcbdbbadaaccdccabbcbbacbacdcaabacacccccbccabadcbcacabaacccdacbbaddbcdaaadcabbbbbccabccbaabdaabdcacbabbdabccdbcabcadccdcdbdadbddcddcddddabcddbadbdddbbcbddcabcacdadbdccdcbadbadaaabddbabacbcabbbbcacdacbadcabdaaacddbbdaccbdbdbdcaabacccbbcabaadcccbaaaadcdccaaaaddddbbadcadadcccddbccbaccbbbcaaddaaabcabaabccaaadcbcdaddbbacbdaabdcdccdbcddbdbdaadadccddbadabbaaabcbcbbbadbdcabbcadcccacaddaccbbabcddcabbcdcbacacbcdccabcabbabcbbbaddcbcbdddaddbcbdcbdcbcddbcdcbbbccbdabdcbdcabddbbcacdbdcbdabbbaabbdacabcdbdbcaacdbbccdcabbcbbabbcaabbcbcadaccbabdcaaadcccdbdbddcaabdcabbabdacdbdccdadbcbcbbcacadcdbdaaadddabbcddccddbabddbacbabbddbbdbacacdccbcdaccccddcbaccaabddbbacaadbcabbadcbbcdcdaaaadbdbdaddcdbadbabbcacadcbcadbdcaaabcddbacbbabacdbadccdcddccdacbccbbbbdacdccddbbbbddabaadbbadbbccabaadaaddcbaccbaddcbacbdaaaccdbcdacabcdabddacdbbdacddbbdacddaaddbbadbbdaabcbbcbdacdabdbaaadbbdbabcdabbdacaddcdacbcddaaddaacbdbdcbacbbabcacddaddadccbdbcaabbdbadabaddabbaacccdacacdcbaabccbacbcacbcadaaddaccdaaabbcdbcdcdbbdcdaadbbccbcddccbcdaccdcccdcbaccbcacdbcddaabacddacccddadcddaabcbccbbdddcbbbaddaadbaccbaacdbbbddaccddcbbbcacabbbdcbbdddabdbbbddbbbbaccbdcdcadaccddadadbdddaaabbbbadcaadbbdbbccadababaaccbbbcadbbcabbdabbcbbdabcdbbadadaaacddccadbaabcbacbbccbadaccbcbbccbbcdccdccbdabdaabdddbcdbcaadbdcdbdadbcacdacacddcdcdbccacacaccaccbbaaddcdcadcbabdddbcacccbbbdcbccddcadabbbcdbccdddbdcbcdabdbaacddabbbcaddbdcdcdcdbacdadbdacdabdacdbdbdadcadadcdbcbdbbabdadbbcdcbacbdbacaabdaddbacabdbbaaaddacbcaaddadabbbdbabadcdaccaccbadcaabaccacbacccabcacadcccacaacbaacccabbabbadaccabccdcdacbbaaddabddacdccccaccbbcbabbcdbdcddcadbbbdbcaacadcbaccccaaddcdaddacdcaccbdaddbcbdcbcbadddcdccdddccdcbaabbddaadcdcbbdccaaacddcbcaadbcbadcbdadbadcdbabbdcbbddddcdbbcbabacbbbccabcabbcabaaadabaddcccaccaddacaaccdbadbcdacbccbbcbacadbacdbadbabdabbaaccabcddababbacbbcccaaacaddcacacadbbbbddccdaabbcaabdccbbddabccaaddcdcdbcdcbaacdaacbbcdbdccbddbddcbddaacccbadabdccccddccadddcaddadbaaddbacbdddaaacadabccdddcddccbbdcbddbddcbbacaaabaadcbacbbddcccdacdcbdbbdadacbcdccbabbdacacabcddadcccdbdaabdbabccccbddcdddaaaccccbdacbdbdaacaaabaadbabadcabbdcbaabaabbcabcdbbababddbbccddcdddcbdbcccdbcbcadddddaaaacbddacbdcaddadbbbbcbaddbcbddadbccdbccaccdbbdacadcaddbbacbcdaacacacccddacccacdcdbbbabccbcddbbdaabdabbabadacaccabdddbbdaadacabcdbaddaabadcddabcdbacdacadcadadddccdacbbcbaadbbbdaddcabcabdcacadbdcbcaaadcbabdbbcdaabdaccdcbdddaddcbdbabdcccaabadddddabdbddbaadccbbdbbcccabaaaabdbbdbcaacaabbdbbaadbbcbababdbcdaadcbcadaaddcacabacdbbcdbbacbddacacaaadccbcdabccacccdcaacbababbacccabdbadddccadbaddbdccdbdabdadacccbbccccbbccbbbacabdaadaabcbcdbdaccddcabbdacacacbbabaacbcbbcdbcbbbcbddabaacdaacaababcdabbacbdcaabcbaaddcbaacdaccabddaddacbcacbccbbbcadacaabdabccdcbcddccdbbddcdabbdabacbdcdddcdacbbaaaaadbdaaddcaddacacabbdbacbbdbdbddccbacbcdccdabbcacdacdcaaacccdcadbbbbbbbbaabdcbdccdbdaacdadaddbcbabccdbdabbcbbcddbbddadcdbdbdbaabdccbdcbdcacbcddacdcabbaddcbdbdacabdddbadadabbdbaaaadabaccbaaccabcaacddbdcbdacadcabaddcaadbcddbdbabcddcddabdabbcbaaacbbbcbabcdcacbdabbdaccbdcabbbbccaadddcbccbabdddaabcdcbacadbcaacacacbadcabaabdccdcbdbccbaabcdddbabdcabdbbaaaadcabaaccaabdbabdcaababccbcadbacadcdcdaddaabbbdccacbbcdaadaacdcabbdbbccabdbbcdcabbdcbbcdcbbaaadcdddcaabcaacbcdcccaacbcdcacddbccbbddcabacddcacbdbbcdadbcbbacadccbccccabdadbbcaacdcadcdadcbdddcdacbccadabbaadccbccccdabbaaabaabaabddbaaccaaccbbacbdbcbcbcabbcddaadbcbdadaccccdadbddbadaaacaabbadbdbabdabcdbbdbcbabddaccacbbdbbdaabdcaabdbdcdddbbabbbabccdddacdcdaaabbdbcabaddbdcbaadccbbdaacaabcdacadacacbadbacaababdcdbbacbaacdbdaaabdbdbdcdbdcbbddcbcabccacacdddbaabacddbbcbcaaaabcbdbbddaaaacdbcccbcccdabaadcadcabcbdadbbbaaddbcdaabbaabbbaaacdabdccbabcbbcddbbcbabdaaabbcbabbaaaadadaabadadcdcdacdddbdcaacbbdbababbbaabddcacadcaddcdcadddabacbddcdbababdadcbddcbbaaddaacccbdbadcdbdbcacbdcbcabcaacbddacaadbdaddabcbbcabadccaccbbadaabcacdadababccbadbcdcbdabdbbaaddbaddcdacddbcbcdbcddaacdbacacaacbbccaccccacbccccdbcbdabcbabccbbcacdabdaabcbdbbdabbccbbddadbbccddbbcadcacbcacdadccadcbcaacabdacdcdaddadaadddaaacdbaacbcabcbcabddcbacbccabccadabcacabdccddcabddcabddcdadabdbcbadcbabbbacabdcbcdbbbdaaccacbcadadabdaccaabddabdbbacbccadadbdcaadbdcadadadbccdddcbcabadcacdbdadbaababddcacbacddadddbccbdabbabcaaccbdaadcdddcbdcadabdadcacadcabdacbbbbaccbabaccbcbdcdbcdbbdcdacaaacddacadbaacaacbddddcadbbdcdbcbdabcdbcabcaaccbaadaabadcabcaacdbdabcbadddabbbcddcbbadacbcbbaaaaababbccdaadcdbdcbdddbdbdaacbbcbbadbabcadcbdcdadadccdddabcbbacabaaaccccadaccbbaaabdbdbbbaaccababcabddbcaabbadbabcccddadadbbdaddcbbbcadbddbbadddbbdcdcdabaadcbddbbcdcabdadacbbdcadabadbdcaddbdcabddcaadbadcadcbdbcbcdbabdcbdbadbdbcbabadcaabdbdbcdabcdbcbcaddcacaaabccaddccddabbdcccdcdcdabcdbcdadaabaddcdcacdbcbbdccccbcddadcabcaccaabaacdbacbcdaadbdcbdadbbdaddacdcdbdadabddabadcddbadbacaacbacabdbbccccbcbcbcadbacddddcabadcbbdbabdbdbbcccbbabadbddbcabbdadddadccacbcdaddbbcacabcdcdacaaacdbdcbccdddbacdcdbacdaabbaaaadcccdabcccbbdccdcaacdadbaddcacaacacdadcbddbacdcbbcadbbaccbaaadbddbbacacaaaabbbabdabdcbdcddcbaddaccaabadabbaaadddcbddacbacdccadbacbbacddcbdbcbacacdddbacacadcadcabbadcbddbcbadcdaabbaaccbcbddacddcbbaaddadcdbbaddcaacdbcbcbcaacdcabaaaadbccdaadadbbcdcbbcbdbcbdccdacacabcbacbbcacaddabacdbcdcccbcbacccbcdaaaccbbdbcdadbbcaacccdabdcbccbacbaacabaadbccdddcacbbccddaabbddcbadacdcbcdccbcbabbaaabbddcddcbcdbddaacbaaabbdabcdccaaadccadcadbbcdaddaaaacadacaddccdddcadacdcabcdacccbcacabcdccaacdabcccdcdcdcbbccdcababcddabcccbacccbacbdcdacccdbbdacaaaccabbbbaaacccbbbbccdbcdbcbdcbcdbbbaacdacddcbabaddbacacbabacddbacababbbcadcdabbadabcabadacdacdabcaaaabaddddbbacddcabdbaddccadcbbbddccbcabccdabccbdbaaaadcadabbcdbcdccacdadcddccddcabdaacdacbaaacbabdcdcdbdcdabddcccaadbdcdadccbcaaccdacaadcdadadccddbaccbdbcbcdabddbcababaadddabbcdbcbddabdaaacabbdccdadddccdaacbcddcdddaadddcdccadddcaccdddbdaccbbabdcaabcadcddbbbadbabbcbacaddbadacacbddcccccbdddabcddadcaababbccbddcdcaaddcccdcadbcacdcbbabcdbbdcbbcaaacadddabdacbdbddbadbaabacccacdadcccacbcdbbccbaaddbbbdacdcaabdccadcbbcdcccacbadcdbbdaaacdbcbcbcaddadcadddbbacdcbddccbaabdcbbbacdccaaabdbabccdbdbabcdadddbbdcbbdbccdbadddbdacbdcddddaddaabcaddabdcccbbcacabacbbdbbbbdcbacbabdbcccbbdbbcdddbbdacdaccadbcacbadddaaabbddbdaacabbdacdcbbcbabdbddcdbbdcabadddaccbbcbccdacdbdaabccababbdacbcbcdcadaaddbcdddbcbcabacadbdacacbaaaabadcdcbabadcbccdbaacdaaacbbccbacdcadcacddcaabdabdcabcacabdaadbcaabcbccddbcdcbcaacdaadaadaaabaccbbddbddddddcccbcaddcbbbdcccacdcaaccdaabbabcbddddacccacbdbadbaaadbdadaacadbcaabbdaadddccdbbcdaadccbccaabccbaddbcbddadbbbadbacbbbdbbbbdbbaaaddcacddcdacaddabdaabadbbaaddabbdabcadabadcbaacddaadddaccdbaabaadcbbdccbdcbcdacdcbdacaccbbaacaaababbdccccaacbaaabcacdbcbcbdaaaaaabaacadcdacbbdaacdbccadacdcbbaabbbcbacaabcaaabcabdacadddccaabdbccdbcbdddbcddadaabbbbbbdddcaabcbbaaacdcacdcabaacadbdaaadababcacacdcdcdddaacdadadcacbbbdcdccbccddddcadccaabcadcdccbcadbbdadbadbdaaabaaaabaccbbabbbbaabacddcadaddbbdacaabacdabadaaabbabdabcbadcaabcacbcdbbcdcbabcbabccababbcaaddbcdddcdbaddabbdcdbacbdaabcccddcaabdccabcabbccbbacbdacbdbccdcbbaddbbaacdadacabddaccdadaabcccdccbcbcbcabccbdacdbccacabdddacbabbcaacacccccbdadcababbaaddcdacdbabbaaacdccbcabbddcdadcccccbadadcaabdbbccaddcaaabacdaccbacacabccadcaccbaacababcbaadbcaddaacabcdaadabcbdaadcccabacccaccbcaaacbccdbdddadbbbdbbddcbbcaaabadbadaadabcdbbbadcbadbdddcbccacabdadbbabdaacbbabaaabcabbaacbdabadaaabbabcabadcababddbacbbdaacdcbbdbacbaaddbcbcddcddccddabadabdaaabcdcaaaacaabacabbadaaacbddbadcacccbcabdcadacdcaccdcbcaaacbdcbcbdabbcacdcccadabdcaacbaadadcaacdaacbcdcadbcabccabaabadbcacdadabdbcddabddcdadcccdbcbbcccbbcccddcbaddbcdbccdccadcadacacbdacdadbcdbbbbabdcdaccdcbcadabddbdcabbcbcacacddcabadaaacadabaadbadcdabcaccbcbcdacabbdbbabcbacdabcabbcababcbbdcdbbbbdbbbaaadabbbbbabddccccbdddcbcccbbaaadcdaddcdddacdaabcdddbabcbbbcdbcbcddcbdabcabbbaadcacdbbccdacadbbdccbbbaaddcacbccababdcdcbbcbabbbabdcdbdbadcccdbdcacadbbadaaaabbbcdbccbcddacbddcadacdddcdaabbdabdbdacdcbcacdaabbdcbdbbcdbcdbbcddbdaadcaadcaaccdcbbdccaddddcabbccbddcdaaaddddacaadacdcbaacaaabcdaddbdccbcaacaadbadcbbbdcbdcbaacbcbcdbcbcddabbcaabdccacbabdbcbddabbadcadbadccaddcabacdacacbdcddbcbbcbdadcadabbaccccadbcdbadcaccddacbdccabccadadcddcbbdcbddbccddbcabcbccbcdabbcacccaabacadbdcbbdaadaabaddabbcadbbddbcbdcadadabbdbaabdcacdcccabdacaaacddabbdbddcdabbcbaddbdcbcbdbcbbbdadacadcbdadddababcabddbbccdcacaccddabbcbbdbadaaadcaabacccbbbcdbcbdbccccabdbccdccddcdaabbccadbbdcddacadbababccccacabdaacadacbcdbbbbadaccccddcbbdcbddadbbacabbadddcbcdacbacccccbcbdbbadddbcdbcccdadaccbdacbbbcccaabcacaccbabbcdccadbacaaadbdccddcddaadaacdacbbbbbbcdbbaddccbbbdbdbacddbdbcbddcdacabcacacdaaadabaaabccdbaddabcdbccdadbadadbdacacbacbacdacabbbdaadcdcbacbcbbdbaadabdcbcdccbcdcdacadacbdcbdaaccaadbdabacccddabbaccdadacdadcbbddcbacbbacbcdbccbbbadccacbaabcaadcabdcbbdaaccdcbdcaaabdabcddcbddbacdadccbddbddcddbbbddbabacdbdbdbacbccabcadaaacabbcbcacbddcccababaabdaacbddacacacabccdcdcaabccccddddcadcdbccbaabcccbaddccbdbdabbabccdcacabddaaaabcbaacbbcbdbcacbdbbccdbbccccbabbaccaacdbbaddcddbddbcaabccbbbcabaadabbaadcacdbdcaacdccccbdadaabcbdbaccdddcccdcaacdbaadcdbdcdbbccccacdbacbdcdccdbddbcacccdbabdbbdbcdabdbabdcabcbcdcabbcaccdbacadcbddbddbbcdddbdaabaadcbdccbbadbaacbbdadaacdabdaacbdadbaaddcdbcdacdacbbdbdadcacaacbbbdaaddddbdbdaddcaccddcddabbccaaddbcabbabcddadddbcaabaaccdaccabacaacadaccdacabbaacdaddaabcbcbdacccaaabdcbbdaccbdbacbabdbccbbacbabddcaacbaadcabbdbbadadbccccbbacbbddbbabbddacacccdabddabbcbccabcacbdacbdbaaddcbadcccadaababcbbcdacbccdccaaccabccbdabaabdbacdaddbaadbaaccadbdadcbaaaaaacbbdababadacbcbadaacadcbbcbdabaaacdabbcdaccacddaadcdadcbcbdddcdcadbaaabbcaabbdccddbccacdcdcbcdbbadacbddadabcacacabacabcabcbcdbdcdbdddaabcacaadbdbbcabadaccbcdabcccddccdcaacccddcaddbbacdacbbadcbddcbbbacabbcaaaaacbabbdabbcccdcbcadcdabddbbbacddcdcdbccbbddbbddcacbbaabaccdabdccabcdacbcdccbbcdaaaaddabbdcaabcdaaabccabbbcdbdaddcaccccadcacdbdcaaabbbabacccaccaaabdcbabcbcdddcdbccdcddcdcdacdcbbdbdaddabcbdaadadaabdabbcababcdabadbcabbbdcbcdbbaadcadbcabbacdbadcabdcabadbcdbadcbbbcbbcbdadaaabbaacabbbdddaacbbacabaaadccacbacdcbaaadbcdcdbdaaccadabbacddddacbacdabaabadccabcaaaccababdbdcdcaacabbacdacaacaaabcbabacccbdcbdabdddbabdaccacdcabdaaaabbbaacacadabccadacababcdbbbaccacbcaaaabbbdaadcddcdaddcbaacbcbdadcdcddbccaaabadaccbacdaadaaddbcaccddcbabbbacbaaccabdcdabdbcbdbadabaddcaccadcbdbcdcadaccdbdacbdaddcbccbacddaccbbdaaabaaccdadcaaaabaccbccddddcdbcddbdabcbacbaaabdabbdcaacabadbcbbcabccccdcbdabacdbcadbcbabbcbabcdddabacabcddddacbccdcdacdcbbbbbdcacccccddccbadcadbdbacacbddcadcaacbacccabccdcadacbbadbbbcadcabbbdcdddbaddccdcbaadbbdbcbbaccacdbaccacabbaddbbbcbbdaacaccadcacbcbdcbdbabbabadbacaaadadccadbaadccbccdcdacadbcacddababacbdbaccbcaadbcddacddaddbbdbcabbbbadcdbadaccbbdccddccbdccacadbbaccbbaadbdbdddddbcbdacdbdaccacbdcbabdaccbabdcdaaddcdcbddabddcbcbadabddaabbdcdcaccaaccccbadddaccacabadcbaccaccdaababcbdcccaadbbcaaabbbaccbacbbcdbcbdcbcdccdaaabaaaacabdbddaabdbbcaabccbaaccdcbdacaddacbbadbdacbccadbcaacdacbbacccbaaccdbcbaabadbdbcbabdbbdddaaabdcccbbbdbbcaddaaaaadcbaacaaaaddabadacbadaddadababcdccabdbaadbbbbddacdddabcacdcbaabbddbabcdaccbaaabacdabbbbdaaaabccbccabbcaddbddddadaadabddaadaacbdddccacddbcadadcaaadcbccabdddcbabaabbdaaaadbaddccacddbabcaccadadbadbcaacdbabbccbdcbcacdcadcabbdaacccaccaaaaadccadacadccdabccbdacbbcbcaabbdacdcbadddcddbdbdcbbccbabbbcbdadaabcacccdbbbabaaddccccdabddddbbdcdcadbcbcdcaacaababdbbddcbcbccdddcddcdcbbcaabcbadabdcaaccaaccdcdaaadbccabbadcadabccdbaaadcbadcaacbccbcbdbaacddcabcbbadcacdadbdcbdbddbdbbdcdcddcabbaccddaacdbbadbcccacabbbbdbababdbddccaccaaabdcdbbddacaaacbbdbbdddbcddbaaccbbbbbabacdccadbabcacaaccdddbdbbdcdddbaacddacdabbbdbccdbcbcbdadcdaccacdcaacddacbdbdbacccabadaadddccaabcaddadccadbaddcbddbacbddcddddccacbbdcddddcadacbcbcbdbbbcbcbdddabccbccccabdabcbabbdbbaacbabcabbcbbbbcbabcbbabadbbdccabdddbbbaacddbbccbdbbcdbbbcdccdcabdddababcacaaacacccadbcbddddbacdcdbaddaddacdcbbdcbaddbadbdabbabcbbaaaacabcbabdcacdcdcacddcbddaddaaacdaddbacaaacbcccccddbdadadbaddadddccbbbdabcbcadcddcbccdbabdcccbcabdcdcacbcbbcadccacaacbbbbccaaddbdacaaabdcadcdabbbabaaadbaddccabcabdbbbdccbcbacdaddcbdcacbccccdddcbbcacdaadaaabdacbaaccaabbbbcbcbcccddddcbacdabdacddbdabbacbdabaadbdaaaccdaacddddbccdbbacabbdcabddcdcacccddcbabdccabcddbaddbcdcbccbcadbdbcdbbbabdcbdadaccabdabbaaddcdbadbdacaaabccccddcabbbbbcbadcaacacbdcaabcdacccacadaacdccbcaddbcbabbadddcccbcaabbadabccabbbdcacdbcbbbccadbcbbcbabadaaccddadddbbcccbdadddcdacdddacbdbaadddbaacddaccadabbabbcbbddbdbdadaccadbcbbacacbbabbcbccabccbddacadbcccabdbbabaadaaacbdbbaacdcbccadadcbbabdabcaabdbabcccccacdbbcbacadadcdddbcabbabbadacdbcbbbabaaaadbbcdddbadaaabcdbdbcbadbcbdcabbabbdbacbbddbdcababcbddaaddcbaddbbbddddcbdccdbcdcbbadacdbaaddcbbaacdcabadcabababdadadbaabbaccdcabbcdbbbacdbbbcddcdbdddacaddcddcdbabdacbaddadacbcccdbaddbddbacbcadabaadcbbadcbbcadddbddccacccbabadcbbbbddbadbbaccdaccdcbacbbbbbdacabdacdcdabbdcbcbdaadbdcadccaaababcacbcdbbdccdbabbbcbadaabdbadbccbddabbdcddaaadabaacbcdddbabbabdbcddbccdacbdaacddbbcaddabbbaadbabcadbbadccdbbacabbcabbdcdcccccababbcdadcdaddabcacacbcbbcacddaacbbbcadaddadcdcdacbabcdbadabdaaacddbadbbbdbddabbddcbbabaaaaadaababdccadadbacddabdacddcbdcbbaddbdccacbdbdacbbccccbadaacbbcdccbdadcaaabdbbbcadddadbadcbdccacdbdbdbcbdbaabbcadcacbaddccacdccacdcdacaddacdbdddbabdadabdcbabadbdcbcdaabdacdbbddcbacadaaacccaaccbaadbcbccbcccbacbdbbacaaaabdcdadbaaabdacdddbddddaaccababbaaabbbcabcccdddbdcbbdcaadcdbddcdccdadaaadbadbaaadcbcaccddbdbdbddbdcdcdbbbacbbcccaddddaadcacdbddddccbcdadcccccbcaddadbddaaaaccccccaadacbabadbddbbcddcacdcdbdcabdccbadabdaacbcdaadabccadbacbcbadbcbadbccbbadcdbcbcadccbcaadcaccdacacabacaabaccadabcdbbbbbbdaacdbbddcacdaadcccadacdabcdababaaabccabaadccbdcddbcabbbacdadbdcdcaadabcdadcbaaaababaaadcbdaacabdcddbddbcabababdcbbcaabdcbaddbdcdccdabdbddcacbaabadbbbdcacbadbdaabddcadabbbcbcaacabbcabdcdadbaaccacdbdcaccbbcdcdbbadbdadbcaaddabbcccdabdcdbcbdbbdabacadddddabccaaadbaddddabdbddbdcdccbadddcbddbcdaadbadcadddacccadcccabababddbdbccbdccccbbbbdbdbcdcdccbdcdacbabddbddddadbcabdbddcacdaaabbddccdcadaccabcaaccdcbabdccabdcbcbadbccbaddbcdcdadcaabaabcdabbcbcbdbbaabbbdbddcaabdcdcdaccbcdbbbddbaababcaadaadccadadaabddbbabaddddbaacbcbbaccaccddccacababbcacaddaccdbcdccbdaacbaaaccaaaabadcabcabdddabcdcdcdcdbbccccadbcbdbdbbdcdabadddcbccbdcaccbdccbaacadaadaccbabddcdbbdacbbddaddaadcbaaabaabcadaacbddbccaacaadbcdabdaccbadcaaaddaabbbccdbbaadbbcbbabbcadcbdbdabdaaacabccadbcadbdcacbdbcccaaddcabbaaabdaaacbdaabbcacbccccbababdbdbdcdbcbccdbabcddddbaaacbbdcdbbaccdddabdbadacbadbcdcbcaaadadbdbdacbbcccbcddadccdcbcccadddabddabcdbbbcdddcabbbadbcdbddbdcccbcadcddaaccadbabbaccddcadbbabdbadcbdccdbbbbcabadcdacadcabadbdaddbcabbcaabcadacadddddaaccabaacbbccbbaacdaaacbbdbcccccadcdbdadcbbbaadbbdccdcdacaadcddbbcbcdddcbbdddaccdbdbbdaddaababdbabdaccdbcbbbaadabdcacacbaaabbadadcabcccacabadcdddacadbbcdccacdbacdbaaabdbccdbcdaccbddcbcbadcccacdbddddcdabbcbddccaabbaabdddcbbdddbcdcaaccadacaacababcdccbaabbabacaaaadcdddddbabbddcbccddbcdacadbbdcbddadaddddabdcccddabddddbdbddcdbcddadcbaddaabacbcaccdccbadaaacdbcbaababcbbadbdcdaababadccacdbaaadadabcbdbabcabbcaddadaccddccaadbbdaccbabbcdddabddbdcaccaadbdabadabbdcbcabdbacacdacacddbbadcbdddcdacadbbcddcadbcacbbdcccdcaabcbbdaacdcbbcadcdbaacacccdcaaaacacbdaadcdbcdddbaaaabcbcccddabcbadcdabccdbacbbdbbabacacadadacddbbbddbcdcddcdcbcdcdaaabcaabadbcbbdbadcadbabcaacbacdaadcabdbddbadbccabbcbcadcddbcbbdabddabbddbdcbbcdcddbcdcaddbaccdaacbcdcbcabddcccbdcdacbcdddaaadaccbcbbddddaabbadacdacddcaaddcbacbaccdddbddcbcdddbcacbdbdbbdacadcbadcbdabaaadbbccabaadcacababcaabaadcdbbbdbccbdddbccbccccbbdabdcacacacbcddabcadbccdccbbaaaaabccacbdacdacabdbbaadccccddbaccbdbbdacacdddadaccaadadaccddbcaabdcbbcccbdcdccdccacbbccbbcacbcbbdabdaacbaccdaabdbdcdadbaaacacddbbcbadcccbbcbccbdabdcbadcdccbbcbbcbdbdbaddcbdbbdbdcbcbbaadabbdbddbbccbcccbdcdaccbbdacbdabcbbadbcbbcccbdccdcdaacacdbbdddcbbbbcdaabcdaabcabcbddaddbbbaaaadaccbdbdbbadbadbbbcabbcabcbaaddddacacdaaabbdbcbbccbaaaccbcacdbaadaaddbaadcbcbaacdcdcdabaabbdcacbbdcdbdaccdcbabccdaccabacbdddbadabaaacddcbbcaccdbccdcaddcdabcdbccdcbdaccaccdcaacacbccdaddcadcdcbddaacbdacdcdcbcacbdcbabdcbddbdddbcddddccacddbbdacaabaabcbbaacdcbbdccaaabbcadccdbcacddccdbadcacdccbcadcbabbdaababdacdccdbccbadcdaadbbbaabbbcabcddaadadcabbbbddcacbbdadaacaabdbbcaacdabacdcdcbdcacddabdbddabdbacbddbbcadbaacbdabdccccabcccbdbcadaabcbcbcbadbaaacbdabdcddcbadbaaddaacacbbdbcdbccdbcaaaaaccdbaacbacdaacadcdcdadddaadaccabbbbbdaccdbbddabadaabbbdcbacabccabdddacdaadbaddbdddabdccddabcbbcbaaccbbabcbccbdabcccbdddaadacabcddbcbbdbbaacaacdbdcbbccbbacccccadaccdbbcabdbcdadadbccadbcacabcacaaaddbbdacadacbcaddbbbccdbbcdacbcbbdbcbdbacdcadadbbbcbcaacacdbdbaaccbbaccacccacbdccbddacbcdadcbdbcdcdbbcacabacbdabdbadccbcbcdbbadcbacccdcaccaacadcdbccddcbbdaabcaabbcdddabacabbccabcdddacddcbacaddcdcbccdcbadcddcdaabcddcadadaddddcbaaccbbdddaccaaaabbdcdcadabcdacacccdacdaacacdadbddccdacdcddcbbcdbbdabbadabcbbdccadccbdcabcdcdabaacbabbbacccabbacbbccbbadddddbbdacdcdcbadabdbdccdcbccbdaaccbbacccbbdcacdddaadbbbaddbcbdcababcdccabcbcadbdcccdbacccccadaabbbacbcacdcdbdbaabbddcbcacdadcacbccccdaccadbacacddbcbaabbddbabbbcddbcaacadccacababddbaddbdcbbbaddadbbccaabdadddbbcbbabcbbdaaaabdbcbcaababbcbdbcaabbdbabddbabacabcbdbccbbbacacbbaaccbbadbabdcbdadbdccacbcdaddbacaabbdddcdcbdbdddbbbccadaaccbbdacdbdddbbddbcaccbaadcadccadadbabbaccabadbbcaadabccadbdabbdbbbdabadccbcccdcaabbabcacbdbacbdcdbbcddacbdbaddadacaacccacbaccabbbadccbddbccbadccdacbddbcacadccdcbccacbbbadabcdddbabcaacdcbbbbccabcacaccbcaddacaadcdbbcdcdcbdabdbdcbaabbadacdbbcbbcacaddadabcbdddacbddbbbcbcacadbbbcbaaadccdbcbbacacbdacdbadcabadbdacbcccabcacbbbcbbddaacdbbddbdddaaabbdadcdababbbdccbcdbdcbdaaabbcbbbaabacacbabdcaabddbaababadbbcabcacdbcdbdbddbbdcbcdaddabcbbdbaabcccdbaadacaccabaabaabbdcdbddccabdddabdbbadbaacdcabbcacbbdaddccbdabdaabacaddbccacabcaadcaccbbddacbabcdcbdaadaccdbbcbbbccadcbdccbdbdcdaccdcbdddcdbadbcbccccdcbdbddbacbadcacdbadccbbcbbcccbabdacadbbccaabcabbacbbddbbcbcdccaabadddcaabdbccaabbcddaadacdccbaaadddaccbabddbdadabcbaadaadadcaabdabadbdabdcbddbbcbbcaddbcdcdccdacbabbaacbccdcdcaccadddccaaaadabddcdddadabcacdcabcbacdcbabcdabbdaaaacbbcbabcbabaadccbbdacbaaabbcccbbbcbdcaabbcbabdbaaabacacbacdcbbbbbbdaacddabdcbdccbcabcccbcbbbdbdcbddadbcdabadccdcbaaacbcddaaabadbbdbcadbacddacbbbacbbbacabcccadccddcbaaacbccdacaabacdcadbadcbbbacdacbabaabbadaddccdadccabdacddbbbbaabccdbababbbcbdcbacbaaadadcaaabbbddbbcbcbdaadaadccbaadccddadcadcddbabcbdbbbdbaaaaacdccaadcddddabbaacadaaacbbcbcacaadbaaacbccdbbbadbbcdddcbbdbddddcdcdadcacdacaabdddadbdcddcaddbaabdbaddbbaadbbcddabbaacbdadacdcdbaadaccacadddcbadacabaadbdcaabdcbdabdddcbdddbddcadcbbbdbdaacdbccadddddccccabddabdccccdaccadcbaddcdabadbaaabaddabcacadaabaadbadbccbcaacabbbaddbadcbdcaacdabadbdcbdccdbcbdaabcbcaccbaccabbbcdcccdcbcdccbbcbcbbdcbdcadbdcddcacdbdbbbdacdcdcabdddaabcbabadabdaaccdcbdccacadbacaadcaadbbbbbbabcdccdadcabadaddbcdbdabdbacadadbabdbadbdbcadbdabbacababdcccdcbcadabcdcbabccaacdccaacbdabadaaadcdbcadcdbddbadcabdcbcdcdbbdbadcadacbacddcabdabaddabcbbaacddddaccaddbcdddcabadccaabbdabcdbacddabbdcadbbcacdbabcabbbbccadccbadacbadbaadccababcddbdbcdadaabacccabddbdcdbdadbbcacacbcbbddbdbaccbdcadccccddddcabaaacacaddbcdabdaabadaddccbdcaadccddbcdcdaaaddaababacdbbaccbdbaacbdcababcccdbbdbcbcccdababdbbaadbccacaacbdccadbaabadbcdcdabbdcdcbdbbccddbdcacbcdbddbdddcbadccdbbaabcababbabdbdbdbbbabddbcddbcdcbacaacbbdbdcdbadcacacbaabbaaaacacadadaccbccaccdccbcabbadbacdbaacaaddbccacdcccabdbbaccbbcaddabcdacacacacadcccdccdcbbaccccdbdcdbdcccacdcbcbabadabbaaabccdaabacccadbbdaddcbaacdaadacdcaddaacdbabdcbcaabbcdcbacabaacbaabccccbabaccdcddadadddaaaaacddbccaabcaddcbddbbdacaadbadadddaccacbdccbdcbbcadddcbdbdddbdcabcacbbcbbddbaadccbdadbcbccbaabaadcabcbcdaadbadadcbccdccdbddbbbdbaddacbdcbcbacbacdadbdbccaaccadcaacaddcdcccbacdcdbabbcacabdddddbdaddbaaaabbccbbdcdcadbbadbdcbcabbbbdaaabccccccbcddcbbdbcbcadbdddbbadadcddbccbbcadaddaccbbdbdcbcacbbacdaaccddbccdcaaaccacccaabcaccbadddcaaadbbabdaadccdadabbabcccbbbcaadbcdaacaccacddadccaaccdacdabcaadcccdcccbbcbcdaabccbaaabdabaaccadddddcbaabaadcccddabcccdbcaabcbcbbcdadabacaccaccbccbccddbadbbbacdbbbdbbaccbdcaaccdabadaddbbccdccbbaabacbdbcccdcdbbdbdacccdbccacacdddcbabbbcdcddabbddcccdbaccacdcddabbbcdbbdcddccaabbcddabbadcdbdbcbadcbbccccbbbdaabbccddacbadabdbbcbaddacbbcccdbabcdbccdacacdbbadbaadaddadcbacabadbbdabdcabbddaddbdbdcccbcbbccabdcdcaadddddbacdcdbcdcbddcdababcaddacaddbbdadabcabdbbdcddbbdcdaddcddbdaadcdbcdbcaccdadaaddcccbaacbbbaabdbbbabbdbabbabbcaddadccdccabdabbcaaaccbbdcaaaaacacadacccbdcdcbabdaccadacddbcddddadccacddddabadbcbcdbdbaabcddbcdcdbcbcbdacaacdccbaadabbccbcccbbadcaababbacddcddadbcdbacddbbbbabcdabcdbddbdcbdaacaabaabcabdaabbdaabdcbacdddbabcdabcabacbcbacabdcddcdddccccbacdcbbbcbdcababdcaabddddbcacdccacbdccacdcbaccdabccaadaacadacbdcbbddbcdddbcdadcdbacbaaacabdadcddabdbbdbaccabcabcdbabcdbdbbbdccacacdbbbcbbccddbcccaabccdaadcbcddacdbcabcaaacbbdddbacdddabbdbaccadddddacaddaadbccbddcbcaddcbbbacccdbdbaccbddadaaadcabacacdcdbdadcabdaaddcabacdaccbcabdadbbabcdddbaccaacaacaacadddaadbadcdcbccdcbbddcbacbadccbbbdcbcccdbdcbbaddcbacddddcccbcadaaacadbbacdaadcabdddabcbbcabbbabcbdaadccbbdccdaddaddddaaaabcaabccdbdaacaddcaaccbaacaccaccaccabbdccccbbadcabbcccbcbdaabdcdbdacdddcbbbccdcaadcbcccbdbbbabddcabcbcbdbbcaadccccaddbabccaadacaddbababccbbcdbbabddddacbacbdaaacabdcadbbdacccdbdbcdadddccabccbdcdcbabdcbcbadbdcccacabcddbccabacdaddddbccadcadddcdacdacdcbaccccbdcaabdcbdbcbabcdabdcccbaddaaaccdaccdbddbaddbacaccdcbacdcbdbacbbbdddccbbdccdbabbdcbcbbdabbddbcdbbadddcacbaadcccaacdaccabbbbcaadcddccbbcddacbdcaccaacdbbccbdcdaaaccbbdadddaccdcbaacdccdacaaabbdddabbbaacbdcbcacacaaacccabadadcacccdbcbcdbacadbcacdccaccbaaaacdbdadbabbaabcdcbddaadccdabdcbcabadbcaadbcdbbbacdbdaacbbacdcdaababccdbdbcaacddbccaadcdcaaabcbcdbdbdccabcdccddbcacadcaddbdcacdccaabddccdaaaabddccbcdcbadcababacdbbdbdcbddaaaccbccacdddcbaddacadddbcdcdabcbdbaddbcabdddbbbbccdbdabcaacabbacdcdcdbdbbdccdbbaabbadbabdddabdabbacbdcbbddbacccdadacbcccdadccbddbccadbcdaadbdccddcdbcdaabaccbababdaabcdcbbddcbbcaacbbabcbcabcbbabdcadcabddcabbdaadbadddcadcabdcbdddddbddcdabcbacbadcbccbdaddabbcdaadcabcdadaddacadbdbacdaadbcbccdaabbbaacbbadcbdbcbbbcbadbdccbdcccabaccabccdbabbadadabbdcabaacdabcbaabbcadbbadcadcddcdadddadbaadbddadadbdbbabbddbbdbcadaadabdcbdddbbbbbadaacdbcbacdaccbdbdccdaaadbbbbdabcbbdaccbbadbabdaaddacabacbdbdccadadcccbcadacbdabadabddcdbddabddadabddbdcaaaadabadaddbcaadbbbdcbccbcbbcbdcdacabababbbcbdadbacddadcaadccbcddbaaadaacccdcadaabcbcdaaadbacccccaaddbbcccacadcaababbcdddbabcabbbcbcabbdaadbaaadddddaccaadbdcbabadbccdddcaddbabdddaccabcadbdabcacccdbdbccaadccdcaabbdccdcbbbabcbcbcbcdcabaadbaabbacaabbabbdababbbadbddcabcadcadabcccdddadcabcccacbcbbbdbcadadddbabddcdddbdbadaacbccaddccddabddcbcaaccdaaddbbbcbddaababadcddbddbcabadcbcdbaaccbcbacbbadddacccccbbddabbbcbaacdabadbbcddadbdbbbccadaadcdadccdbcaddbcddcbcbcaabcacdcababbbbdaddccbababcbbdcbcddaabababddacabcbbacdaabadbcdbaddbbaabdbccaadacdcdaddbbaccbccbccbdddbddacddadacbdddbbacacaaaabacacaddddabaacbacdbbaaabdbcaddaccddabccbcbabbccabdbbaccccdadbdadcccaabbabcdadbcbdacbdbadcabcbaacdacaadbdabcbbbccbaadacaabddaabbdaadbbdbccbaabcdbbccbabbcbaccbcdaddabccdcbbaaaadbabcababdcddcbbcccdccddabbbabadbbaddabdbccbaddccccdaccadcabadaacdbcbdbadddadabbbbdcbbdddaddaacbbadcacddbaabddacbbacbcbdbdddcccaabbbacdbabbcccbddcbcbadddbcdaccbbbdbccdcbaaacddacabddadcabcbdcdbdcccadddadbcdccdcabdcccccbccdcbbcdadabadbbaccbacbcdcbaadcbbaaccbadaccacdbacdabacddcabdcbbbcccdcacaadcbcbbbbccadbdbbcccbbadbdabcdbaadcbbcbbabacbabcbccacbdcabdabdaadbbdbccbbadaabdbdbcbabcbdbdbabaacabbdbcaabadddcaadacbadbcabcaddcbccbddaaaacbcabbdaccbcdbcabcbcbcbddbaaabadabccbccdbcbbddcddbcdadcaadcdbadcdbaabdddbdbdabcadcccaaaccbcaadaccbcaccbcaddcadadbcdcaccbbdaccddabcdcbdabdaaabaadbccbabcddddbaccdddbaccdbbcabbbacdbacadabdcdcbcaaabccababacccdcddbadaccbaadabaaaacdbdbdbacccabacbbaaaacbbaabdcccbcddabcdcccaddccbdccaaabdabcbdaacdddbbddaaadbdbcdcbcaacdacacbbbcdbadddcaccaacdbccaaadcbbcbcabcadcbbaccaaddbdadcbaccbbabdbadbabbddcaddabcbccadccaaadcabadcbbbacbbbcdabbbadcbcbcadcccdcabcabcacbbdcaabadddaddaacbacaccccaacabcacabaddbcbcbcadbcabaabadcdbaaabacbccdadaadcababbcaddcbccacdccabdadcbbddddddcacadcbcaddcbcadadcabddcddcbadbdaadadabadcababababadcdaadbcccdcccacacaaaacbaadcbadddccccccbacbcdddaadbcbdbbcabdbacbaacadbdbabbbacacddcadcddbaadaacaaaabdbadbbdccdaadabccddbcabcddddadcdbbaabbaacaccdabacccccadcdaaadabdbadcccabcbddbabadadbadabdbcacbabcdcdbcbcacabcbaccbabdcadababbccbadbacadbbdcbdcdbcaccdaaccabbbacadcabdabcabbdddaaccccabaaaaccdbabbadbdaccdcaadbcdacdcdaaabcccbbccabbdddbcddcddadddbbdddabdcbbacaddcccdddddbadbcdacbddbdacdbacdbbbddbaddcbcadbbcaadbbaccacabbbbbdddddcbaddbabcdbacacccabbaccadaacaaadbabdddabcbcadbcacaabcaabcdcdadadcbbdabcadabcbcbcdbbaccdbddcbaccbbddbcdcabdcdbadcdabccddddcbcaaddddbbbddaddcccabbbdabacdccbacaddbbdccadcccdaaaabacdcbcbacbbcdbdcbdcdbabbadbccdcdcdcdaddbddcbacabcbcadbcdcbddbbadcdabdabcdcabcddcbdbaacaddcabbaddddaccddcaccccbbaaccaadacaabbacddbacadadbbcbbbcccaddcdaacacddadcccdcbddcacdbdcbdacabaadbcadcbdcbddcaacdccbaaacdabdddddcadadabaaccabdbdcddcdacbbcbabbcdaaccbdcbdbbccadcdccdbdacabacbbdbdaabadbbdcabcddaabaabdbdccaabbbcddbaadadbddcacdaabdcbcbbaaabcadcccadbabcbccdabbbabcaadcddcacbbadbcdadabadcadcccacdccbdadbbbacddccdbbccabacdaddadcabdcbdaabbbcccaccdaccacbbddbcabbbdacccbdcadbbdbaacbaaabadcacabbacbdaacdcadaaaaaccadcbddbcabddbbdacbbaccacdbbccdacbbbdaccabdadddacbacadacbbddbbdcbcaacbccdbdccaaddbabacdbdcdcaadcaacccdcaabdbabbcacdaacbdaccdddbbaaacccbdaccdddcdacdddbccdaaadddacbdcddbdbcabcccbbddacbdacacaaaaaaabcdaacccaccddbdcaddddadbdccbcdadbacacccbbcdbabcabaadadaacabbcdbabbcddcdacbdddacbcabdcccbbbcbdcadcccdaacbcabcbaddcadddbccabcbbbdbaaaacabccdcbaabdcbddbcdbbaccccbdbccabbdabdbcbaddcdbddccdcdcbabbddcadccbbdadaddbcbbbccbaccbdbbabbcbbbbacbadaccbcccabbadccddacdbaababccdaacadbcdcccacbcacadacddccbdabadcabddcbbccacdbaddacbbcdddbccdaacadbdcdcbadbdddbbdddbcdabadcbbcdcddcaacbddbdbbabddcdccdddbbabbcccddcddbccdaddcbcbbbcabdddbaaaddcdbacdbcdbdabcaccadaadadccabdddcdbdbaacbbdaaaccabcdacbddbacadabaccbbccbdaacbddcabadbbacaadbcbcaddbbdcaabcbaaacbbbabbdadbccdcacdaadadbcaddccccdbcbbabbabdadcdadaddccdaabbcbcbbdcbdadacbdabbcadacaccaddcdbcacbadcccaadbbbdddbbacdccacccddadcdbccdaabdbbcdcddcddcdaaadcadacbabdcacbdbbadbaabdaabddacdbabddadaaaacabbbbaccbccdbbaabaabbbadbdaacabaaaccbbbbacaddddddadadcaccaabbcdbcabcccaadaaabbabccdacacaadaadddbbccababdaddadabbcaaacabadcabaabacbdbdddbcdcdadcadddaddaacabdbdabaaacbbaabdacadadabcababbdacbbcbbacbcccaaabaddbddbadcddbababadaabadbaccccddbaadbbacdbdacbcabadaabcdbcbacacaadccdcbdaccadcdbbbbadabadbddabacccdcbabcddcbcabacaabababbdcbbabaddddadddcaaadadcbadddbccbadbcacaadbaaadbaacdcbabccadacbddccbbaabcadccbbbddbbbabdccdccdcacbccadaacbadddcbcccacbdcadcdbdacdbcaabdaaabcbacdbdbbddbddabbdbacbccabcddbdbbabccdcdbcccacddccaaaccadddacdddccdaaddccdaacbdcbcbcacdcdddcbdabacbbcddcccadcabdbccdcaaabbdcbaaadacccbcaabaadcdaccccdddcabcbdcabbcbddccdaacdddcaccaddcadaabdcabcbbabdddcaccdbdcdcbabaadcbababbbdabbddbaaacbacccbdccbdddccbcbbadbdcbcbbabdadcbdaccabddcccabdbacacaacddbcbdadcddacdabdcacbadaddaddccdaadaadababaaadbbcaabbdaadddcbbaabcbcbabbadadcbacccbbabbccbcbbdbaabdacaadadcdcbccdcccdbcabadbacbaaddabcdcdcbacddabcdbcbbcdbadbcadadcbbbbddacadbaabbccaaaabbbdcddbdadcacdbdbddacaabdcdcacddccacacbdcddbcabadcaccbbabddcbcadbdcbdbdcbccaccaacbbdbbddcbdcabbdddccbaddaaabdaacbaccbadcdadbabcabaaaacddcdbcdcacdaccddacabcdcaddaacbadcddbadbbbcdbcbbdcabcadcdabaabdbcbaadbababbdcbdcadccdbdddabbcbabbbbdccbdbbaaacaadacbccbdabadcbadaabdbabdcbaaccbcbcddabddcdcbaddcbbaddddaddbaacabadbbcaabbacddbdbbcbaaabdadadcadddddabbdcccbdbbadaadcdaabdcbccdcbbcdbccaadcabbaaccbcccbbcabbaabcbdacddaaabcdccbccbdabadadaccbbacdadccbbacccbbccdabcddbadacccabdadbddacaddddbddcadbccadaadbccddccdbadbdcbccddaabbccbcbacbccbbcccdccbdddbbbaaccccdcddcbabadaadbbdcdabcaccdaccaddcbcbadabcccdacdcdbdbaabbdaaaddccbacddbbdadbcdbdcdacacacdbbddbbdbbaccbbcbbbccdacdadcadbddcbaaddbcdddbcabbabdabbbbcbaaddbccdcbccddacdcaabacaddaccaabcacacbbdbddabcbabdadcabcbbbccbcdbccbadabaacbcacccdaabaacccdbaaabcabacbdcadcdbbdbbbaabbcaacaabdabccdbababbbdcbacddcbdddddddcaabbacabcbcbabbdbbbabddddacdaaabdccbdcdbcccaccacbacdcadcacaddcbdcadbcabacdcbccdaaacbcdddbbbcaccdacbabbccddadadbbdadaddaccadbbdcdcbcdaddbbacddbdaabddabdbaddabddcdbdbaaccbbccbacbbcadbadbcdbdacbddbaabbbbcbbbbaadaddcdcdcaccdacdbdcddaadcbbaaddbaabcddddbdaaccaaaddcaacaacaabcbccbcdbccadadbddcdbabaaccbbdbadbccbbdaacbdaabcbaaddcabacddaabcdccaadadabcaacabcdbddabcdcddbcbdcbcdbbcdbbbbdadbcbddccaaccbbbdcaadbbdcccacddacdcabddbcdcacdccadddbbcdccdaabaddcdbbcaaaaddbdcbacbaabcbbbdaaaaacdabbcbccbcbdabaabacababbacabcabbccacdaaadaadcbbcdcbcdabbbdcabacddcaaadadddaddcaacdabadbbbaccbdabbabdccabdabaadaabbcaaddabcbabbacdacddbacabbdcdbcabbacdaaadabaddddaadaaabbcabcdcbccadccacbcddddddbbbbaaacbcdccdbacddcbccacacbcbbddadbdbcadcdcadcddbbaddabbbcdcbadcbcccddadcccbdcacbbccdcabcaaabbabbbcaaaccabbdcccabbcdcabcabaacdbdcddaccdcaaddcbbbbabdabccbaaabadccbaabbcbabccccdbcccdaadbbbdccbddddbabccddcacdcdaacabddadcadaaabacaccdddababbcbdccbccddcaacbabdcbbcabbbaaaccdcbacabcbaadaccaaccddbbdacdddddabccdbcdbbbbbdcbcbdcccddbddcddbdccddcdbbcbccaddaadabbbbbbcdbbcadbbcdaadbacddaabcbabcdacbcbbcbbcabddcadaccdbdaaccddbbddacacdbaacacdaacbdbdbaccdbbaacaacdacccdbbcbbcdcdddaddacbbaaccdacdddaddcdabbabbbdbbbdbbcdcdcbdbbacbadacacaaacdccbcdbcddcdcdbacdbbccbcbcaadbaccadabcdddbdccaabacacbabbacaabbaabbdcbcbbdbbbcdbbbccadaadbaaaacaaacabcbadcbcaaadadbcccbababdcdcacadacbbdabddabcaabbaabccabdcdaadbaacaaabbbdaacbacbccabadacacbbccccbbaaccacacbcccddccbddcbdaadddcabbcdbccdccbccdcbbdddaaddaadaacddaacddbcccacbbddcbccbcaacbdcddcdbabbaabcabccccccbccdcaaaaaabdcbbbcdbdbdbabcadbdcacbbccdabaacbdbaaaacbbbcabbabbddadccaacadcdaadccbbcbcbbabddddbdcccdccbbacdbccdbcbdbaddccacdcccaabaabbddacbccbbadbabbbdadcacbdbaaaabdaabadbcbadbcbadcbdaadacbacbdcacddbdacbbdddddbadabdbcdaddbdadddacdddbcdbcdbccddcdcacbbcdabdacaadbabdbdbacabbcdbdbbbdcbdbdbaccbbdbbdbaaabbbdabbbdaaccbbcbacdcaccbcccbacddcbdadcaadbcdcbbaacccbccababaabdabcbdbbaacbdbbdbbadbdcbaabdacdcdabadacdabbbadbcdadcbadcdcabddcccabbdddddacabacaabcbcabdbbadadacdacadcdccbdcbbabccbddbabbdcaaadcadabdacacddcadaabdbbdcadaddcbbcbbabccbbbbddcdbcbabbadaadaadacacddaaabcdcadacbdaacdcaccdacbcbdaccabadbbbabcadbcdbcbacbcdddbabdcbdacbaabdcccacacabcbbbdaddbabbcabbadbacccadccabdccddbddabdbcadddbdcbccabdbbddddbbbacdddcbddcbcdbdadababaacddcaadbddabacbcdbadcdcccccbcbdcacccdbdabcddaccbabcacdddbbcdadbadddcabacbdbdbdbdbbbabbddcccbdbacbdcbdabbcdbdbacbdaddddcaaccbcbbabbcdbcddddbdbadadcacddbbccdcdabadcbbaddccbcbdcadccdbdcbddddbbbbbbbbadadccbcdadaadacbbdcdcbbbddbcdddaabbbccacacdcbcdbccdbbaaacacbddbacbcbddbbdcacacadbabcabdacbabbcbbbdacbababdccdcbdaadccbddadcbbbcaabcbddbdcabcddabccdadddaaacaadcaccdcabacbbdddddccadbcabaaaadbdddcbaaadccabcabbbbdcdddbaddacadcdacccdddcaaddcabacaaabcbbcabbaddcaabdcccadaabdabbdbdaccacbbbbaddacadadaaccadadcbacbdcdaacaabbbacdbbacacdcbaadbacbbdadadaaaacbaaadcaabdbbcccadcaabdbbbbbaabbdaaacababcaadadddbbdadbbcdbdcacadabbcadccabaccbbdddacccaaaccaacaadaaadcddbbbccdbcddbddcbbaabaabdcbcdaadacabddbcbdddbdbcdddcbccbdbdbdaaabbdbdbbcdaaabdabbbcccbcddcbaacadbdddddcacdbcdddbbbdcdcdaaddbbdcadccddbbdbaaabacdcaaadaddacabdcdcdaaddadcbaacbdcccbcdacdcbdaabacdabbbdcdbcbdddaabddbadabbbddddcbbbccccaadccacaacbddacacbddcaadaabcadabdcbddcdabdbadcdbaaddbaddccbabbdbdbdcdbaacbccabcbbbacbccadaaabbbdaadaacdbccbbcdacadddbaadbdbdcdaabacbacdcbdbadccbcacabbaddaacaaaacddcddbacddacdbaacdbdbdbadcbcadacbbbbbcbdadaaabcbacdbdbdaadaabdcbbcdaddadcdbcbbcbbabdaabadbdcccbbdabaadadcabdcdaadcdcbdbddddbccacbdbbbdcbddbbcbdbdcbadabcbdbbcccbdbaccbcddadbbacbbbcbbcaabcadcacbdaccccacbdddaccbdbdacaacbcadaddadbcdbcccaabcccadaaaddabbddccbdbcacacbadccacbcdccdbcabcaddabdcbaabcbccdbbadcbbbbdddaabaaacdcabacaabaadbbdcddacababbaaccdbbcbabbbbbbbddddacbbadccaaccdcbacbdbcccadbaabadbadacabcabacdddddadadbdbdacabccddbbbbbabdadcdaddddadccbdcbbacdaadacaaabcdbdcbccbacabdddddbaaccdcccbddbddadccaaacdacbdaadddaccbaddcbccadddbaadcaabddcbddcbcdcdacbcdcccbcaacbdcbbbaabccabaacccdccbdbdbcbdbddaabbbcddcbbaabbaabaabdcddccdcbcacddaccabbbdaacbadbabcaacbcaacadaaccabaccacccbbacababcbacacbdcbabbbcccddcbdbaddbccbcacbbdabcbabbaaababdcbaadbbdbcbddbdcabcdbddadacdaabbbacdadcdaadbdbadaaddbacdaddbdcbccaaacbabdccbaaacbddcbcbbbdbdbbcbbbcdccbabcacbbdacdcadabcbcabdccdcdcdacbcaaabdcabddbdcaabbcacdcdaaabbcaddcdbbadaddcadadccdbbadbccabdbaaddddcdcdcbddacadadcaacbdbbdadbcabcbddbdccdcabbabcdbaabbcdbdcbdddddcdcbadaaaaacbaacdddddadcdacbdbcaddcbaaabbadaabbbdcdbbabddbddcabdabadcacdcbccdabdcdabccaadcacdabcbcaddbdbcbbaacbacbbccadbbbbdbabadaaccdabddcdcaaddcacabdbbdacbdcbbdcbcccccabaaddaaaaaaadbacbccbbbacaadabddbabcccccbbadabbdbcbddcbaaabdaccbbcbdddddabcdbadbaddbdbbbbbdacadbbcddbabbcadbbacdabbabbbaddadddcbdbcbcdcacccaabdccdabdbdbcabbbcbabbacbbddcbcbcbacdcbaadcaaadbcbccadbcdadddcbbddadcbdbabbcbbbdaabdccdbcbacacbbbccdaacacaabbdaaacdbdbbcaadcccaacbdbaadabcacbaabbbddbdbdbcbacdbcacbdbdcdcbaabddbdaaccbaccaaccdbaaadbdbdbcdbcdcdccacbbbadbcddbaccdadababdcdbbddbbbbddbadbcddaddcababacadccbabbdacacdbaccbdccdbbbdddccaaabdabdcaacbbaadcdcbcabacdaadcddcabbabdbddaaaadadaabccbdaacbddcddcbccccbddaacdcbbababcdbaadbcbbbadaadaababdccaccbcccaadcdcdbabacdcdccaabdddbccdbdbaacaadabcdadcabdadacadddbcdcdbadbccbbacbcadbacbaacaddacbaddacdcdbddcacbccbbcdbdcccbbddaccbaaabadacdddcbdcabbcdbcccaadcabbccabbaacbbdabaccbaaaabccacddacabdabdbccaacbbadababbaacaadaaaaabbddcbdcabbbabcaacbadbacdbcabcdbcdacccddbdadbabdadaddbaaaaacbdaddacacbbdbbbaacdcbadcabccdddadadacbbbccbbcbacbababdaddabbccaaacbbcddbbacacdbaabbcdabbabaaadccbabdacacabcdadbbdcbdabacacddacdbdbccbacabaddbaabdccbbaadcadbbcdbdbcddbbadcaadddccddcbbdbdbdbaacbacbbadadaaacaaabaabbcdabccdcddbdccddddcccaaabcdcbdbaccacbbcabaddaddaadcadcbadacabccbabcbcdccbcaaacdcacaadabaacacccacbabcbddcbdddbdcaaadadacabcdacdbdacdbcdadbaaabdabcbbbbccbcadacdabcbbcbbcacdcdbddcbaccacbcdddddbaccdaacbddacccacdccacdbaddbaaaccddabddccadacdccdcbcbcdbdacdcccbcccdcaccdacbcbabbbddbbaddaccaccaacddaadcaccbaaddbbdbaabdbcbdddbaacdcdacdacacbbacbdbcdcababddbdabcbbccaaaccbadbcacdaacaacacacaaaaadcacdabbaacaacdccbbacacaddadbaadcadbbcaaddaacddbccdabbdbdbacccdcbbabdcadbdcabacbdaccccddbbaddbbbdcbadcbabbaacbacbdcacaacdadcccacbaadddcbbaadbaaddcbcbadcbadacaabdcbbabacbcbaabadddddcabdddbbccbaccbcdddaacacaccacadadcbbbddcaddacbcadbadacbadacbccadcbdacccbcdbaccbcbbabccaacccdbdaaccbacbbdacabcddcbdbbccaacdadaaaddcccdcccbdbbdabadacacdbaacbccaabbdacbaaacadbdadcabccaabbacddccbadcbdaabaacaacacdbcdabbcabcddbcacbbdadaaaaccabdbacdcbbcaaccaccadaddaacbcbdcadbcbabadccbccadddaaaadbaddacbccdcabbacdcaabcbacdadcbcacdacdabdddccbdaddbcbadbbbadaabaddadbbabdccadabdccbbcccbdaabcdaababbdbbdabcbbbaccbacbcacbdccbaaccbcdadbdadacddcbadaaadcaaaabddaddbcbbdcbaadadddbcdcbadccbccadbacbdbdaacdaabcbccdacdabdccddcddccaddbbcbabbaddddacddbbcacbcabdaaabaabacbcadacadbaabdcadccbbbcabcddacbcacadacdaabcadabadaadddddddacbdaabdbdbbbccaaccdbccbcdbcbbdcabaaddabccbdccbabcbbcaadaadbcdddbbdbacbbdbddbbdbcddbabcabcbadcaaccbadcbcbcddccdbbdadcabcbcdcaacbacbdaacdabdcdcbbcabbbdbdaaddcdbaaacbbabcacdccaaaabadacbdadaaacacdcbadbadcdcdcabdccddccaaaabaddabddabbccbbbaddcbccaddadbbbbbcacddcdddacaacadcabbabcdbacddaabaabdabacadaabcdadddccabcbbccbddcdddabbccddcdadcbacadaddaddbcbabbacadcdbacbabbccbdddbbdcbabcdcbdccbdbcdccaaacadcdbcaddacdcadbaababbdbbdbcddbcdcbdbaaadbcaaabbcbabacaddadcbcbacdcbaabcbadcccddaccbddadbcdacdbcdcabbcbcabddbcaccaaabccabbccadbaccadcdbadaddbcadcccbbbcbbdcbddbdddbcccbadbbabbcbdcadccdaadaadbbddbbcddddadaaacacbdaabbcbccdbcabbdccbccbcbbdaacbababbadcbddbdabbddbcbddcaddcaabacdcadadaabcabdddadddbdabbbabadcacacacababccbabcdadabbcaadacabbcaccabcbcabadcdcbcaccabbabbcabadddbacdddaadcdacadccaacdacccacabbabddacbcccbdadaddcbccbdaddccdbadccbbbdcadcbcbabdbcdccccdcabddadcbdbcbbcbbddcabccabcdcbdadddadadcdaaabcaddcddbddcbbcdcdccbbcdacbdbbbaacacabdbbadcddddcaabcbdbcaacbddcaaacadbdddcbbdacbdddbdbcabbcaaacadccbdcaccaaacaccddbdadbbcdcbcccbdbcdbcbbababcdbbaddcbccddaccacabdcacadbcccbabbddcbcabadadccbdcaaccbdbbaadcabcadbdcbbcbdabcbcbcabcbdbdadcacdbcdaccdcdabcbdcdcaddcdccccaabbadcbbdcdabdbadaaacddddbbaaddbabccdcccbabcaddbacadbacccbabbacdbbaabbbcadcccdadcacacdccbdbadcaaadacddbacdbccbddcadadcdacbccddbdcbcddabddbbcacdcbccddcacbaacbdacbadcdaddcadcaaacddabddccbdcabcbabdbbacbcccaccbcbddddddcaabbdacbbcddcdbacadbbdadbaabcdcccbadadcdcccabacbabddcbabbaccaaaabdcdcccaaacccdcdabcdacadccdbaddabaadadaaddbacbdaccbdccbabcaaabbcbbbccdaccabddcbdcbcdaadcadbabcdaabbabcabdadabacbadacbdcbbcbddbddbbdaadbdbdbdbacbdcaaadabacbacaacacabaaabadaabcaddbabcabcbddaababbadaabbdabbddaabdbccabcddccdcadddbdbdcdddadabbaaacdabbcdbccacdbbbddaaabcdbcdbdcdacdcdbbabcbcbdabcbaaaaabadcaadddadabcbacdaabadbbdbabaabadcdcbbadaacccaacacdaaddacacccccbdddbdcdcbdadcdacadaadbddaadddbcddaccddbbcbbbaabbbcdaabcbaadccacaccddadbddcdcaaddbdccdaddacacbbbabdccccdacbddabdcbabbabadbcacdbdddbbdcbbccbdabcbbdadcdcdabbccbdbadbbcddadbdcbacaabcbddaabcbaaadcdabbdababdbbaacdaacdcadbcaadddbddbbcdccbcacacdcbbcbbcbadddadabadbccbcdababbbaabcbacbccbcbcbdbbbccdabdcddccdaddbbcaabcdbdabaabdccbcbdcbbddcaddbacbabaccddacdadabccccddacddbacbdabadbdaddcdacaacdaccdbbbbadddcbcccccbcadbcbccbdcaccddaacdccaadabadaccabdaabdcbaaccccacacbccbdacbcabbdaccbdcdbadaaabbabbdddcbcacadcbacbcddbbdcddbacaadcdabdbdcbcacabcccadcbdaadddaabccadccbcacacdcbbadbddabbcccaadbddadccccdaddcdbdadbbcaacbaabbdaaaaaabadccaabbaabcbaadabbcaabadcaddbdddcabdccbcdcadccbbdabccadcccbcbcaccbaaabdddcdcadbbccdcbccdbccaddbdccbbcddbabbaaaaadacccbddcbcadcaadaccdaabadbbbcbbdbdaddaadbccdacbacbccaddbadbdccbbdddbcdddadcdacbcadccdbccacddaaccdcdbaabcddcabbbbabdbcbdbccacabbbaaddcbddcbabccaadabdaacbadcdabdbddbbdcdcadbcbdcbdcbbcbabddbbbdbddcbaadccacaacbbbbcddcbbbbbadccadbddadaadaadcabdabcddcbbcdbdcdbcdbbadaacdbdbbabaacbbbcdaabbbccaddacabbccddccccbddbbaaaddccadcbcdcaddcabbbddcbdbbcdcadcaaaadacdcddbdcaaaccbacabdbddcbbbcbbcdbdadccbadcaacbbaabcdabccaadbccddacaddaadbdbbbddadaddcaddbbbcdccabaadacdcbdddbabddcbaddabbddccdabbcddaabdaacabacaacdacbcaddcaacccdcccdbdabccbaacabccdacbacbddddccacbbabadaddddddbaccdaddbddabdbbadabacdaddcdbcbccdcadcddbabaccacccbccbcaddadbadcccddccddcacdddcddcacacbbdbacbaacbddcabdbdbaccabbcdbbddcaabcbadcdddccccbcacabaadadadbddabccbabdcacddbbaaaaccddccbcdbddbbabdabddccdcbbaadbddbcadbbcbdbacccccdbabbcaadcbcadbbddcabbbcdcccbddccbcbbbabdcbbdcbccddaccbcbbbccdbdcabbaccbdbdccdddcccaccbbdbdddcbdcadcaadccbddcbddcccbcbabdbbacaadddcddccddaaabacacdacabcddcdbdadacadbcdacccbdbdcabbaaccacdccdcdcccacaaadacaccbbdadcbadcbabbbcdaaadaaacbbbcdbaadcaadaccbadcbadbbdbacddbdaddcccdbaacaaabacacadabbdccabdcbdbbbaacaadcbdbacdaadbdbaccddbbbcbcabbcdaadcadbaccbabbbcbdbcacbbadcaddacbbdbaaddadcdbacbcaaaadcdaacddddacbbacbaacddaacabbbddddccacbbabdabdddddbdaabacbdbddcdabbbbaabbbbaddcbaaacbbdadbbdbdcadacdcbcbdccacdcbbccbddabacaacdaadababbbcccbcccbcbdccbbcaaccaaaabdbbdcbdaadccdcdddcaacbbcdcacbddabadaddabcdacbdcbbccbddcccbbacacbcddbddbdbdbcccaccbbbadadaadaadcaaabddbcaaaabcaddcbabcdabbdcbbbbccabdddcbadababdcabbcaaaacdaababbccdbacacdbabbcaddcbbaaacacbcacadbdacaabdddabadacadbbddabddacdccbbadabdabaaaabdbcccbbabbdabdbcccdaccbbcdddcdacdbabdaadabbdddbbdbabcccdabddbcabcadadacabaacdbbdaaddacdddbcaaaaaccdcaddbaadddbbbdaadadbbbacddacbaaaabbdcdaccbacdccbbcdcdbdddbaccbddcccbbdaadabccccaadaadbbaabadabcdbbbcddbcdaccbcbaaadaadbcddaaaddaddacdbccbcacbcdaccbddcccadacddbaadbcbabcdccddcbdccddddacdaacdddbdababccbcbdbbabaccbdabdbbabbdacabcdcbbcbdadcbbcccdbdcdcdbdcbabadcadbbaabdbbaaacbbdddbdccbbdaacbcbdddadbbacdbbccccbbabbcdbdacaaabbdaccccadcdcdbaaaabcdcbdabcdccaaaddbcbbacdbbbdbcdccaabddbcadbbcccadabbbdcbadddaccdbadcbacaddcbcbcbbbbbdaddaadccaaabbacaacdcabadabbcaacddccaaccdbbaacacdcdcddbbdbdcccadadabdaddcbcbaadabadbdcddcdcabaccadababcdababdddcdccbbdabcadcaabbddbaabbcaaaaaccabcacdbbdabbcacdabdcacccdabcbbdacaddaacccbaabaccdabcbbbaabdbbbbacadaaddaccdbbaacdcbababdbcbbddcacdaddaadbabacbdbcdcbaaabaccaccaaccaacccbadaabddcadcdbcdcdabcccbdddcabdabdbaadbbaabbadabccdaadbcbdaabbadddbabcacccbacaccbbaccbacacddcbbbbdcdcdccdbacddcdccbddbaacaaaabdaaaacababacdadcadcdbcaadcdadbdddcbdddccaddcacbabbdbcbbbacbbccabaaaaadcdcbaccdcddcbbccdabddbadaccddbcdccdccbabacdaadbcaccaddaadcdcbbcdbdcddabcdbcaabbbddabcbdbbcaacbcdcdaadabbdbcabadcaadacdcbdddbcbadbccaccaabadcbddaabbbbcdbabdbdddbbccccbdbcdcadadbbcccabbcabadbccaadabcdcdbdaabbbbbccbaaacaccaaabdacbdcbaaaabddcbbacabbadcaccbcdccdddcbcaabbdaddabacacaabaacaacdddbdcbbbbcadcacacccaacdddacbcacbbddddaccbcaacbbaadbcbddabadaabacbdddcbccbbcbddcbabbcacbcbaabdcddaaabdbdcbaabadcdcbdaaaddacadcbaabbadddabcbabddcbcbcccbddbccccbaabbaaaadbbadaadbdddcbcbdcadbbabcabaabcbbaacbdbdcacbbcdbaddaabcabdbcdaccaabbbcabdadccbabbcbadbdcbddbacccccccbccdbadaaddddccaadcabdaacbbabacdccbcbcaadcbadccaaacadcbbcbbaacaacaaddcbaccdbadbabddcaaaccabddadaddbbdacdbadccdcddcdbadbbdccbbccabbaaabdaaabdabdbabaaccddadddbdcaaccbcaabdcbcdcaccddccacadabcadbdcdaabcbaaaadabdcbbabdadcaccbccbdadccaadcacaccdcdacdcbaacbddccadcbdbbbbddbabdcabdcadabddbccdaddcdbdcdbadbdaacbbcabbbaaaadadadbacacdadddddcabcdbbddaaaabdcbbcacbdcbdbbbbabcdabaccdbdccacababcdccbaaaaababbcbddcbdabccbbddbabaaaaadcacbccbadbdddbbdadacbbbaaaadddabdbdcabcaabddcbdbbdaddabbaddccbcdbcbabbbbbcbddccbdddcbcbadbcbdbabcbccaaccddccacdabadbcacdacdabdaaccbbdbdacacadcbcbabccbdbacdccddbabdadccbcbaccccdccabdaabbbabadbdddbabbcadacbbaddbdcdddcaacabbddcabddbdcbacdcabbccccacccdaadaacbcddbcddbbacadbabcacbabaadbabcbaaccaddbcddabdbccbdaccaaaddcaabcbaabdacbaddbacbbadaacbabbcdcbacbccbddacbacadbccdacdbabbcadcdaaccabcddbdddabcccacdabdccbabcbbabcdcdbabcadacaaadbbbaddcaddcbabbcaaadaccdbcabbdacaaccaadacabacdbcabcdabccaacbbbbbbaaaddabdcbcbabbabbbdccaddbaaaaddcaaccbddabddddcaddcacdbbdcdadbabbacabcdcbdabbabaccbdaccbdcccbdbcaacdcbcbdacccabdbdcdcdadacccaddddcdacacdbdccabbaddadbabbdbdaddacbadddcabcabaccadddcccdbcdddcaddbdcabcbcacbbccccddbbbbbbbabcdbadaaddbbabbacddabbadcccadabdcbbdcabbadddbddcbdbccbbacadbbbacdccddbacbaaaddbdadddcaabcbdddcbcacdadcdadadbbddbcbdadddabaaccdcbdbbccdbbdbabaaaacdbbcaabbbbbddbddcbabadccdaacdbacbbbddaabbacadcddbdabdccdbbbbdacacdcdcddcbdcacaddbdcddcbcdcdaaacdadccddaccaabccbcbdacbcaadbacddadccdbabcdabbbcdcddcadadacadcccacdabdcccbbbcccbdcdbbbcaddbbbcadaadbcbcccabccbabcddbaddcccbcabddddabbaacaddaccbabccaccbaaabccaaddbcbacbaaaabdcdccddaddcbbdccddcaadabaccbadbabcadabbdcaabaacaddbacbabdccccccdcdbbdadaadadcadaabdbdbcdcabadadbdbdcdcacdadacddbbbabbdaddabacaacddaacacdddddbbcaacaaacbdaaabbcbbbbaddbcbbbbacbcdadcdbadbbcddbbbcddcbcbabbabcbbcdbdadbdbcbccacbcbdddcbdabdccaabdaddabccddcdbcbccddaacadbacccbdcabbbaabcccaadabbaadbbbaadbadbabaccabcccdabaacccaadbcacdddcdcadbabbbcabcbbddadcccccbccdabadcdbdddbbbcdabdddbabaabcbdadcbddbacacadcdbbbdbadbddacbbcaaccbbdaddcaacccbcbbacaddddadccddbdddddcdccaccdcaddabbbbbbbccdadabdcdbcddbcdadbdbbcdcacacbddccadccaccdcacbcabccdcadabaccbdbbdabddcacbcaaddbcdbaccaddcdcbdcaaaddbddcbbccbcaadadcbaabacbacacadddabacbcbabbbcdbccdddccacdadabacddaaadadacbccdccbdacbdaacacccaadbdccdbdcccbacbdbbcaddcaaddbbcdbbdacdddccbdbdaccbabbcbbbbcdaabbadbaaabcacdbbbdaacadbbdbdccdbdbaaadbdbcdbdabbdcdddccaadaadccdbabdadadcaaccbbdcbcdabcdddbbdccdabdabccccdcacdabcaaccdadbdbccbcaacbddbaaccdcaaabdcbbcdaaddacaaaaaadbaabbdabbcbaabdaabbabccaccbdddbcdaabdacabaddaadbaccadccacabbcbababadaddcdcbbdacbaccdacbcadbaccdddaaacaadabcadbcaaadbcdbcabcadcacdadaddbbacadcdccdbdbccbadaccabddcdbdaccddcdbbadbdcbbdbbbbbadadbbaabababaccabaaaccadbacbcddbabbccdccabdbcdbdbdabcbadcaaaacbaaddadabccbaabdccbbaadbadbdadabcbcabaccbdabbdccbdbdbadabdaccacbcbadcdcbccdbbcaccdcdcaddbbbcdaccbbbbababddbcacbdcbcdbbcddbcdcbbdbcbcabbbadaaadbbccaadabdbabaaddaadacdacdccacdadbadbbaccbcdabcccdddbcaacdbaccbbbadbdccbcdccbbcaabbcdccbbbddabdaccbcdcddcadcadcaaacadcaaacadcdabbcbcbcdcaabadbdacaadbcdaccbccacddacaaaacdadcaacbcbbabdbccbbbabaabcbaccbbdbdcbadaacdcbbcbbdbaccbbcddbdadbabbdaccbbdcccdccabbdbacabacadadadabcdcdccaaaaacaabddccaabbaacacdcadbcaaacadddcddbdadcccdaabbadddbbdcbcddbcbdaacbadadbcbccccaddacbdabaaabcbccacdabdbccccdccbdbbdbbdcacaacbddcccbaccdcadcbbbdaaddacabccbadddaddccabbdbdccdacbdcdcdcbacaaadcbbaddcadadadabbdcacbbccabacbadbbabdaaacbbbabbaacacccbddcdbcbbbdcdddacbabaddbabbbdbadbcbcccbbabdbcdcabadaccdddcddcbdacadbdbcddcadbbcdacdaddbcdcdadadcbadcaaaacbdcaaddcdddddddcbbccbdcbbbddacabccaacacababdbcdbbdbaacbcdddccacdddaaaabcddcbacbdcadacadadadadcccadacdadddcadcddaadddcdacababdccddabdaaccdacbadaddaababadcdbccddccabcadadacabcaaccdcbacbcadabbdacdbcdccdacdaabdbcdabbcacbbdabbddbbaacbbbbdcabbdcdccbcbccbbcbbdbbbcdddaaccdcbabaadaabbbdabddcbdbdddcdcddbdccabcacacaddbcaccbadbbcdcdaacdcddaacdaabacbdbddcabbcacabcddbcbabcbaacbbcadacbcbdbdcabbbdacdccdabbadbcaaaacdbcbdabbccaccabcccbbbaaddbadaacdcaddacdabcabbbaadddaabbaaccabcaadaddccacbabbbdddaaddcbaacdcdcdcdbacadcacbadbbcbadbcabbbcaccdbdcdbcbdbabbbddbcbbaaabadaddbdacabbdddbcddbccccabddbcdbcacabcabbbabccdbabcbabcbdaaadaddbaabcaddbabcabcdbbcbcdabbcdbcbbcdcabcbbdddcbccbcdcbdbbaadccacaadaaabbbbacaacaddcabdcabddbababdcddcdbabdadbadbbacacbcbdcaabddddbdbbdbcacbccdbbabacdccddcdadabdbdddccdccdcaadbacddbabcddbdaabdaccacdccabccdcabbdbabadcddbbbabcbdbcdcbdcbbcbbbbaccadadbbdcbbcabbdcbdbbcaccddbbccccdddcddbccdbadbacdcaccbdddbbcaadbbdacabdcaabcdadcaabdcbadccabccccaddcbdaadbdabcdabdaccbacccbadbaddbcbdadcccdcacdcccddbadadaabcbbadbbbdcbbcaadcabbbccacdacbabccbbcdbdadbacccacccdcaabcbbadcdcdbacccbdbdbaccccabdddbaabacbadcbbddaadccddadcabbccacdbacdcddbbaaabcdabbadccccdabcacbbdcdadbcbdcdcabdacdcddabbcaadcdacdccabdbdcdccabcbcbbbbaadabacabdacababcaaacbdaadbdbccbabdccacbcdbdadbcbadadbdadacccaabcbadbbdbabdddcbbabaabddcabdadbccabddbdacccdcbdbbbadcbaaccddddadadacaaabbcaddbbdbddbcadbdbddbbbacabdcbbababdaaccbcbbdaddcbababccbbaacdbacccccbaaaaadccdaadbbbadbdbcbcadacdcaacbabddbadcacdaadbaccbdabcbdccaccbddcbccccaacdaabaaaccbdbabbacbbdaddbbccdcdbdabadbdcbaabaccdbadbaaababaccdcbaacbaadcbadbdcacaccddabcdbcbbddaaddddbdabdabdcbcbbacbcbaacadaccddbbcbbabbaddbdbadccdbbcaabcdcccbccccdacaddacbbaaaaabaabbdcdadcadbcaabacbacabdaadddbbbabbdabdcababbabdabdcabdddbcdbabdaadcdabbcbcaadccaaadaccacccdcbbcdcccabaccadaabbbabadbacbaabbbbacbacdbccdadcaddbbccdabdacdaadddbcacacbbbcbdbaabbbddacadbcbaacdbacccccaabddabbcbabaaaaccadadbaadcdacbbcdadadacadddaccddcbbdbacabbdccbadbbaaabddbacbdbdadabddaddbabbdaaacadadccaddbbcadcdcbadddcdbbbbadcbaacbccadccbaacbdcacabaacbabdbdccabaacbbadabccbcaccbdbdacaaadacdadcaacabadcbadcbabbdbcdcbabacdcadacaaccbaabacdbdbaddcbbadadaacbaadcbcdbcbcbddacccadbdcbbbddcdacdcbbdabbbbdcdaadaccaccaadbbddcbbcacaddabbcdbacdadabbbabbcbbcdbdbbbddcddcbadbbadcbddbccdbccdccbadcbbdddabdacdabcccadbbdbcbbcadccaddcbccbcdbcbacacabadacabadacbcaaadcbbccbccacccccabdbaaaadaaaddcaddbcadaaccaabdcabbdcbdababcaadbbcbbbbdadbacddaabbbcbacdccaacbdbadddccbabcacbdcabbbbabddcbbaadccaacccccdacabccbabcadaabddcbbbaaabbcaccabdbcacbadbdddbcaabcacbcbdacbbadacccacddbdaaddbdbabcacccbababdabddcbdcdccdadcdadbadacddacddddaabbacdcbdbbbbcbbccbccdbdabdbdbdcbcbdccdcbbaaadcbadccccbcbcdacccdddbbcdccdbbbcacdccadcdcbdcdabaadbbcbccabcaaabccccadaccccacaabdcbbcccbcccbaacbbabcdcdcbdccadaacdccccacbbaadbaaacadbdbccabadcddcbadbbddbaadbbdddabcadbabbcabcaadacbdadcbbdbddbcabddcadddbcabdcabcadacbdabbbcacaaaddbbaadadcdbabbacacbcbbdcbbcccbbbcbabbaadacaaddacdccbcdaddcdcbccbcdcbcbcacbabbcadcbccabcacbaabbccdddaaabbcbbdccccccaadbabbaccabbdbdbbcddccbaaaadcacccbbcdabcccbabcddacbdbcabbdadbdaadbbcaaaaddcaccdddbdbdccabcdababdccbadcbadaaccccaaadbbcaccbbadabcbabcdccdcaacaadcdcdccabaddacbaaaccdacbbadbdcbcddcbacaccdcaccdaddabccbdabbbddccccbcdbacbbcbabbdcadbcdcabbdaccbcdbabbdbbdcccddacbdbcbdcdbcdcdbdbdacbabdacaacbadbddcdbabaaacdaccdbaddcaaaaabacdcbbccbbcdcacaadadcbcdbdcbbdbcddccaddaabdaaacadacdbccbaccddaccdbbabdcdcccdcdadcddccacdacabcdcbbdbdcdccadbddacaaadbcdcbdacbbcbbacccabcdabcbdbdbdccabbadccaaccdabdadbdcbcabbbadccadbbadacbcbbcacababcdcadcbadcdabdbacadbaaddacabacacacddbadbbacbdcaabbbdcadcccbbdcdacacbcadbbbccbdcbabcbaccbbcccabddabbdaccdbbcaadcbccaddcddaddcdbcbbbcccaadccbadccdddbdabcaacaaacbadbaaccbaabdcbaaccbccbddaccccbacbdccbbcbdcdcbaccaabdacdbaddbacadbcdadbccbbaabacaacbddacbdaccddaabbddaabdbbaaddbdccbaacaabababaacdbddadabaaddbccdaccdadacccdcbcbcdcabaccacdcdbbaacbbcbccacbacbcbcbbccacdbbccbccbccbabdbbabdbcaacdbdcdbdadccbaaabbdcabdcbabadcccadacbbcbbadbabadccacadbdbbabaadbccabbbcdcbddaddbcbcccdccdbcaadbabbbbdaacadbccaaaaaccdbdacaddaabbcdbcddbbbaddbdccadcdddbdadbdbddbbcdcdadcaaccdbdbaadbabbaaabcabacdabddbdabdbbcaaaabdabbcdbdcbaacdabbacaddccbdcadabcdddcdcbcaadcbddcbdcbbbbacdacbabccbadcccdaabddbaacadccbbdcdabddaddaadddbcacddaddaadddbbadbddccaabaacdabcbaccccacdabddddddbcdcbbddbbcdcbdbaacdbcacbdcbcbdabcdadcbaadaacaccaacdcdbccbddcdabcbaccddaddababbcabdaaacdacccaaccdadbdcdbcaaaabdbaccdadaccadacdcdaccaddbdbccdccdddcdddbdaddcddbcdcddcdacbaabcacaddddbddcbabbbbdabbdbaadbadddcccadccdabcdcbddbdcadccacabbbbdcacdbdddccbcdbaaacbccaabcbcddadaacdcabdddcabdcaddcbbbcadcccdacbbdcabacabdadbccbddcbbbcbadddcdbaadacbdcbbcdcacabcbbcaacaabccbdaaaddacdcbabcccbadabbaccbadadcbccbbbdbddbacbbbdcaadbdcdaddccaaaabcccdcbdbacacdadcbbdacdbbdccadbbdccdccbdbdababdaddcbddadbacdcadbddacbadadbddcdacdcacacaaadbbcaddcadcdbbaaccddcadccbddacdddcccbdcbdcacbdddcdbbcabdcaacdacabdababcbcdbbbcabbbaaccdcbcdbbbadaadcacbcdacbdddabadcccadccccccaacbadadbccaadcbcdddaccbdcaacdacacbadbcdcbdbdcabbbacbccaaacccdbcaaacaaddcabdbdaddbccadcdadcbadacdbbbdaddccddaabadcaacdbdbdccbbacbabccdcbcddcbbabdadaddbaaddcdabdabacbbadadbccdccdcddbacddbbbaadccccadcbbdcbabacdbbcacddacdabdddcdadcdcddbbdbbbabbbadaccbdccabdabadcbcacaccccbaacbadbadaaddcbdcbdcdacbaddabcddaabadcbcdcccacdaddbadbdaaddacdadccaadbcbabdcbdbabbabadccabbabbacdcaacbaddabdbbadcbababadbdacababccddddaccbcbaaacbdccadbdddbccdadbababbcbcbddcbaaabdaacdcddcbbbbdcbdbaccccabbadbdcbdaacabadddbdbcccaddbcacdcaddadbddbaadacabbcbaaccddbcddccbcbcdaaaaaadaabacbcbcabcabbaaaccccabdaaccdccbcbdcbccaaadcbdbcbabcbccbacddadbccacaaddbabbbbdaccabbbccccdadaccdaaaabaccddbcbbcbdcbacdddbbdaacdbddccadccbcdbadabadbcbcbacdcbdcacdabbdbcadcdbbdddbdadcadacbdbaddbbcdccccdadaddbdcdaabcdbdadcabccdabbdabcccbacdcbcadccadbacdcadbdddbcdcaadcbcbbbcadacbbddbdacbddcdbbcacddabcaabacabddbddbcaddcdccadabdaadaabbcaddcdcbbabccdcdacabaacabdadadabbbbddabbbdadcbbdcbadbbbcacbdaaccbbdcdbcaacbacbbababaacccbbaddcadbaadabaabaabdacaddcbababcdbbccbbadbbcdcbdbdddaacbaabacbbcbbaadbdcbcbadabaabddbcbbaaacadacaababdcdacaadcdcabdabbbccaacbccadcbbbcabbcbbbdbabbccdbbcdbabcacbaccccccccdbacddbdbaabbdababbbbbccddcbcccaccbdbcbcbccdabadddcbaacbabacaadabdbaadbcdccccbcdabadacabacbbacddbbabcacccbdbdcbbbaddabccddaabccbcddbadabdcbcddaadabbdcbcdbdabadadbcbbddbaadaabdbacccadcbbdbabbdaccdaaacbbdbddccccbaabccdacbdacabcbbbdabadbbaabccababbbccbdadadbbdaabccdabcbcbaddcadddaabadabcadcadbabccbdbbadabdcbdccdcbdaccadbabbacdddabacabaababccabcdacacaaddbcbcdabddaddcdbcdbdddbcccbbddbdadcdbcbbbabbabaccacbacbcadcaaadacbddabdbdacbccccbbbcdbadaadcddcdcbbadccbccbdaacbbabcaacdaadcbdadcabbcadbababddccadadbabadddccadabbcabcdbbbabbbacccdaabddcaddadddacbdbddcabdaddabbbaaaaacdbbaacabdacccacbdaaaadabdbdccbaddccbbbccdabacabcaccdadddcdaccdbabbcacaddddaabadcadcdcdbcabbdccdcbabadbdbccdcacbcccbbdacddcdbbababbddcadbaddadcdcababaaccdacbcbadccdddddcbdccacbdcddadbcbdbbabdbbccbbbcacaadadbccbddcabccdbaaddccbacccdbbbdcdcdbaadbbbcacbcdcdabaacccbbcbbddbcabddccabbaaddbbccaacbccccdcccbaddcbdbbdbdbbaabaaaaddbcbcddadccacacaaddabaabaabadacaaaadddcbbbccbccbdbdabaadacacabbdcdcbbccbcdccdbcbaccaabddacacaccbaccdabcccaacbaacbddaacdabdccccddddcdbdadaadaadcbdccabcccccbddbbbcdccaddbdabbacddbadbcbaacaccadcdbdaacccddabccdabdacaaddcacacaacccabbbcddddbccbbadacbbaadbaaabdbcaadbdcbccaabdddaccdbcbdacbcbacaadcdbbaadcbadccdccdcaddbadcddbbbaaadccbbbbabacadcccdacbadbddccadadcadaccabdabdbbcbdcaaccddaddcdbcaddccbcdcabccddcaabbddcadccadbbabbcabcbdabadcdccabdadaaadbdbaaacbbbbaabcbaccacbdddacddaccdbaddbcabdcdbddaaccdabacababddcbbadaacccabdbacbcabbcdbadbabacbcdddbccbcdcdbacccdbdbabcacdddaabaaadcccdacccbadcddddbbdbcbdbabaabcdddcacdddabcddacbcacdbaddddaccddbbcbcbdaacbcdbadcabdccadbcdadcdbcdacddacadbcdddcadcddbadaaacbccbccbddadacdbddabaaadadbddadadbbbdbbdcadcaaddccbbaddcabbcbbcdbddabdcabdadcbccabdbacccbccdbbbadbdaacbbbbdacccacbdababdbdaddbaadbbadccbcbbcabcbaddcaaccccccccddccddcdbccdaadacaaddaaccdbaadabddabbbccdbbbacaacbaacddacdbbbdbcdbcaccdbabdaddaccdccaacacbccddcdacadadbdcdabbddacbcbcdbabaccdcddacbdbbdcdabadcddccacdbbadbbdacbcdaadbbbccbadcaacbbccabbbbdbdacdacbccbacaaaddabaabacddaadccabdbaadddbccddccaccabccabadcbdbcdbcbdcbdbacbdcbcadcbaacdadbdcadaaaddcccccdaddcbdbadaabcbaabddacabacdcaddabddcdbacdcacccadddbbdcacbddaabacbccbaddbbcbbddbcadacadacbcdccbbdcdcbadabbbccacbbcaaabbcbadaababbbbdcccdcdadaabaccacadcacbdcbdbbaccbdabaddaabbaddabadabcadccddaacbdbaadbcaccbddccbabdddcddbbaadcddabbcabcccbcaaacaadbcccbbcacacccaacccbddacaadaaabbbdddddbabcdabbccccdaddddbbddbdaaccadcdcddabbcacbaacddbdacccccbababadacbabdababbcbabababaadccbcaaadccacdadadacabaaaabacdbcccabbddbaabdcdacbdccbbadcabaddbaaacaacaacbbcadbbdaaabdaddacbddadbdbdaaccaddddabadcaabdbadcdbbbcdacaabadaaacdaddacacdbddadaaadbdbcdacccdbdbaccaaaabadcdbadbdccaddcadaddddcddccaddbadabddaadcaabcdbababbcbbdbdcbbdababcccbcbbddbabcacbcabdcbadccaadadbacbcbadcbcbdacaabbacabbabacdacababdacdadaacbacadbcdabcbdaabcacbcdbdbabccdcabcccbccaaddcadbddacdadddaabadbbaadcbbabcabcbabacddddaccbccbbaabcaaaaaabababccdaabababcdbdcccddbabdbbacdcbcabacabdcbcdddcccabacdcbadbbbbbddbbdbdcbbaccdaacbccbbbbcccacaddabdabbdbbaccbcbdaccbccbcbbdbcaabaabddbdbddcbbbdacaddbaacbbbcabcadbddaabacaddbbbdcdaadcdddcbbbbdbbdcdabbbbdbdaabccabdcababcbadbcbadccbbcdadadbbaadaaaabcacbabaaaabadddddcbbaabcbccddadccbddaabcdbbaaccdcbcbbadcbcbabdabccacbdaccbcbdcbbdbdcacdadddbadbbcaddcccbcaddbdcacaadcbdbdadcbbdcaadbbacdbdbbcdaabbcabdabddddacbacaacacaccadcaaccadbcccbccccbcbbabbdbcbcbbababddbaccddcacdaccadbbcaccdaccaccccdadcdddacccbbcbcbdbabbbbaaddabdcaacccccacdbbacdbccaacabaadbaccbddbabbcaaabbbaabdacddbcbcaaadbacbabdbbabcdddcdcbdacbadadbdaaadbbbaddcbdaacadbbcccbdaacdbccabdbdaddaaaacbdddbdcacaabddcccaacbabcccdbdaadcdcadaaabaacbadddddaccadbadddcdccdbbbcadacbabdbdadbaadaacadcddbababadcabbacbadacacaadacbbcbccbacdadbcdabdcdaabadccbddbabbccadacbdaacadbbccdacdadaacbdacadaaacabcdcabdbdcdacacdaccdbcdbcbabacdcbbacadddabdbbcbcbdcabbacadbdcbacddbadbcdbcacbadabaddbddccbbccbadcaabbcbdacbbdadbbcbbcdcbaadbcaadadcbadcabcbdadadcdcabdadcbcbcdbbaadcddbabaddababadcbcdcbbdccbbccadaccbdaaabddaaacbacdabbbbcababcccddbaaaccabaaabacadcdbcdadbbcddbadcdabbcacbcccbcbcadcbabbdbcaddcdcdcdbbaacaaabdacbacaccbbabbbcaaaaacdacbdcbbbbacdabccdbdcadadadabdabacacbbadacbdadbdadacdacadadbaaccdbdbdaccadcddadddccaaaaccbccabbbccabddacdbcdbccbcbbcdbbccccdbbaccadadccdddaccacbaacdadbcbabaccbdbcbcdccbbbccaacbbbadcccbaddcaadbdcbdcdbdccbdabbcabbcacaccccadccacdcabacccadacdadcbabbaabdbcbdccddbcbacbaddadcdccaabbccacbaaccacaccacbaccdcbacacdbccabababddaaabbababcadccdbcacdcbccababaaabacdccabbabdaabbadabaaddccdbdcbbcaadaddaddaaaadbcdacddbaaddacbcccabbacacddbdbacabaaabbabddcabbaaadacdbaabdbddbddbaacddaddccdaaccbaaccbaabdbadacaaaaadbabcdcbbaddbbabcadaaaddbabcbaadccacdccbdacbbbacaaadbacdcbdaacdacacaaaabbabaabdbacdcbaccbcabbaabcdaadacbdccdaccbdccbaaabcadabacbabadcddcdadddbcacabdccbabcdcbacdadababdbcccdacacadbcdcacbbbabdddaddaddbddccaaabbacdbadbaadbbaadddbdcbacabadaaadcdcbbcbcdabddaadaaddccadbdcdbcbdbaadadcdadbabadaadcdbdcdaaaaacaaddbcbddacdaadadcdbbabaabbdcadcabdaccdbbddcbaaaddcadcbcacbaaccaccadbdbdcaaabdbcdabcccdbccddbcaadcbccdaccbdbbcdcdcccccaaadabbddcbddddaaddacccddabcdadbadacbcbabbdabaacddaccbdcddaadccbbddacacdbadbdbacacdbcbbccccbcdccdccdcabcdadadabbacbccbbbdccdbcaadcddadbcbbbccacdbbacbbccddaccbcccaabacaccaaaabcadacdbbddaccbdbabdaaadbdabbddcaabacbccdadcaaabcbaddbcdcbaccdcdbdbdbdccaddcbccddaddccdbbddaacaabaadabacdccbbadddccdcdbaabdadbaaaccbddbdbdcaabcbccabdaabcdbaccbaddabacdddbadbbdadadadddbdcbcadbaddbbacccaacbacbccbabdbaaccacdcdbbcbdbbdccabdbcbcdbacbddabdcccbdacccdacdabbaabbacdbcabbaccaaadbabdcbccbacccdcdcabbcdabadddbbbbdaaccabbbddbbadccdbaabaacdabbbbbdacdcacbbccdbddbddbcbbddbcaacadbaabdbbcacdabbaadddbaaadaadbcaccdbbdddccdcadcacdbcbbdbcaddbdaaaabdbadbaccbdddbcdabcdbabaadbdccabdcbcaccadddabdcdadcbaabbacdaabddaacccddabbbbccdbddbdccbdbcddcddaadacdccadaadbcccaabbbddcabaccdbdbbacbacdbccdddbbcdaacdcaccddabcdbcbbccdaaacacdbbbbcdcdcaacbdcccdacbdabdababababccdbaccbbcbadbbddcccaddcdcbcbbbbdabdbabddcdbacacbdcaaccbdccabcddadabadadaccccacbcaabbcdacaccaaabababcdbdccbbbdcadbdbdcabdacababcabcabbbbbccdccbdbbadcabacbccbcbdccdcacacbdbdbddddbabbcbbbdacddcabccadaabbbaddcbcdddcbadddbacddccdcdddabcccdcccbdcddcadcbccddddccddcbdbaabacbbbbacdddccaccbdddccbcdcabdacaaccacdaaacdcabaddcdbcdbcdcbacaddccdbdbbbbdbcccdccccbdbcdcbacbbacbdbdacadccadbcacccaccdcadcdabcdccdbbbbcaddaccccdaadcaaddcaaaccbbaaadbcaaaddcbdbbbbcadcabacbbdaabaabcbaccdbcddccbccdbcbacabddccbabcbdddbadabadadbbaadbbdbbaaaaaddddcbbdacbbacbdabbdbcabaabacbabdaaccccadcadcaacbcbcbcdbabbcadcbaadbacabadddcaababbbabcbbdbddcacdcdadddbacbbbbbadbadbdbbbadadadbdadcdbcdbdabbcddaabacdbaddaccaacbadbcbdbcbacdcbbcccabdbcdddadaddabdabcacadbbaabdcbbbcdbcccadcabdbabccbabaddacccbddabbbbbabdacbaadcaabcbabadadcccacaddbbadadaaadbaabddbdddccbbacddddabccdbadcddddacbaacaccabdaaccbbacbacccaadbaacaadaccacaaccdbaccabaadaccabcbabcbcaadcccadcbadcbccccbcbbacbcbdccabddcbdcabdaacababdcabadadacdbdaabaaccbdabcbbaacacdcccaacbabdbdabbccccbcbdadbddcadaaadcdbcdcccdbbdadbacaadaacabbcbaaabcdccadacacdadacbaaadccdbabbccdccdadbabbdbdabaabcaabadabbccabdadaccabcbbbbbcbccbcdccbbaadccaabdcacdbcbccbadabdccaabddacacacdddcdabbbaccbbcbbbdbddbbcbdabdaaabaccdccbadcadbbdcadbbaccdcadababadcbaadcdcaabaaddddadabdaaadabdacccccddabbcdccbccbadaadcaccdaacababadbbcbbbccdacdacacccddcacdacbcaaabddddcabbbbbbbcacbadaabcababcaccaacadcdcbbaabdadaddcdadbdaababdacddbbdbcdccddcbbdabdbcccaacbaccbdccdbacaacadcddccacddbadcabcabddbcabccbcddadcabdcbccccacaccaadccacccbdcdbdaccdbbcbbaabdabababbdbabddadadcaddcbaacdacccdabbabbabdbbbdcadcdbaacbbbbdbcacbaaaacbbbddaccadbcaadddccccddaabcbbaadaaccdcaadadacdbdaddbddddbddcbccdbbccdbcdaddbdddcacdbbacccabcbdadcabcbaaddcbbaaaacbdabdadccdabbabadcaccdcabccdcccbcbcdaadbabccbcadbdbcbcbcbaabaccacdaaaabdccbcbcacdaadaadcbdcbacbabadadaadcdbbccbcdbacdddaddaabaabbbbabdbacabaadcdbdaaddcbdbbdaddccbddcbbaadcbdaacaaaabcccdcbaadbccdcaddabaccbbababadacccaabbbbbaaabdbbbaddabdbdacbdddadbaccabddcdbcdccbddacbadbcbcaccadaadbbbacccccbdcdbdacaadacaadaabdcacdaccddccdbccdaaccbdaddbcbacabadcddbbabddaddabbcdcbbccdbdcadaddacbabcbdadabccbdcdbabddddddbdaabdbdacadddbddcccaddcbadbbbdaccabdddccccdcbcaddabdaaacbddbacdbcbdcabdccabdadcbcabadcdcbcaddbcdaadacbabcbdaddcdaacbdbbdbbacdacddcbadcdcddacdbdbcddabdadbdddbaaabdbdbbbadaaabbbabacbdadccdcabbcabbbdbabdacddaaadbcbddcbcadddbadcadacadbdadcabdcbccdddaaadaaabccaadbbacabccaaadbcdaaabcdababdaaaacabbcbcabddcccbccdbdbdabcdbddbdcbccbdbddbadbabddaabbabbabdccacdcddadabacabcadaddcbcacadccdcdbaccaaaabcbcccbadbdcbbdcacdbdabbbdcabdcbcdbcdadddcabaabcbddcddaacdccabbbadaccbacdaacbbdcdcdacabdadaccdddbcddadaccccacdbaacccdbbdbdbdbdccabadcccadaabcbbdbabcbcdbaaaddddabddadccdbddcdbaadacbdbddbbacacbbbaccbcbbaccddbdcadcdcccdddccaabbdaaadcaccacadbcccddbaadabdadddcddcdaadbcadbdabbdbbabbcddaaddbabddabbcabbcbcbbbabcabbbabbcbcabccadddacbcdcaaadadbcadadddccbcbdcdadbdbbdcbbdcbdbdccbdadbbcdaddcdabdadaacbdbaaabbcccbcddccaadcbbbaaaaacbcdccdbbddacccbacacdadbbdcabbdbbddadacdadbddaabaabbdadaaabdbdbcccadcbbccbcacbadccddbdabdccdacaadbacbaaacabaaaadbcabaddcdcdbbbbdbadbcadaacacbdcaabbdbabadaadcdabdaabccdaadcabadbacbaabdccaabcdbccddcdcdcbbdbbdcbbbabcabcabcccdcadabdcdddbabddccaccadcddddbabbbbcbcbbcdcaadcdcdacdcabcbddbbdbacbccddbcbcacbdcbcddcaaacbcddababacabadacaaacbbdaadbabaabcabcbccdbbabcadbddacdadaaccdcdbdbbdccacabdababcbdbdbbcabbabcababdcdccddbbbbdccadacdddcabacbbcabdcccadbabbccddaacabbaaaaacdbdcaaddacbbcccdcdaaabcbbdcbdcadddbabdcbcdbbbacccdcdcdbbddadbbadccacabacdaaadcccbdbbdbccacbaaddabdcddddadbbdadadddcbccbbdbcddccbbcdaabdbdabaacdcacccddddcbdbccabacaccdbcaabacaabaacdcbacababbccddbcbdcdbdccbbdadbabacbdcdddbdbaacdcdabdbcbaccabbdbcaddcabcdadabdcbccdbcbccabbbcabcacdbabaabbcabbabcbdddcbcbcbdbcdabdbcbccabacdaabbcddacbdaaadcdcccbbbbdccccdcdccdbddcdbdcabbaccbdadadabcddcdabcadcddccaabcccbdabcbadbcdddcdabddbcccaacbbaabcbadbccdadbdaaccdaadcacadbcbbbabbbabdcbdadbacccbbbddaaaaaacccbcdcddabaadcccadabbcaaadadbbcbabbbbdcbdddabcdbcbbcdbbdcddaaccbaaccabcaaaaadadbdbdbdcbacdabcacbbacbccacdcaaadcabbdcbcacbdbbbbabcbdacacabcbbbacbbccabbacccaaddcdbdbaaaacacdababbbacadadaaadcdcbdcbbddbcadbbacdbdbddcadcddcaabadacbacbccaccdaacdddacdcbacbdacabccddbabcacbadacdbccccbbbacdbcdcacddadbdbdbddcbcdaaaccdabbcbaadadbddbacaacacbcbcbabdaabdbdccadddacabdccdddcbbacadccabcbaaabbdaccacbcbbcacabdcabdbaadbdaddcbaaadbcbbdcdcdddaaddabcaaddacdadaabacbabcdbbccdacbbbdabdbcdacbdcbadddcdbbabdcbaaababcadcadadbabcdbbdbacadaacadcbdcbcbbcdbccdabbbbdcdcdddadcbccdadabbdaddcbcbdaddcddbbbcdcacdddaabadbcabacabaabdbababbddbabaacbadabbaaaadcabcddadaaaddabdaabcadddbddbbbbadadbdbcadacbbdcddabbcadbccabcdabdacccdcbbaddadcbacccdbbbddbbccabdaadacacbbbabbbcdaddcbddcaaadabcbdccbddabbdbccadbcbaadbbabcabdbcacdddbddbbdbbdbccdbbdbbaaabcdddadbdcddccddcaddcbacdbcccbaccadcdbdddcccbcddccdabbacaacdadcbadaddacdccabacaabbbacbdbdbbadbdbabdcacadbdaddbddaadacdcaabacdbdbddcbaadadcdacdaddcaccaddbccddcccdaacabdadcbccccadabacbbdcadccdddadcacddabddaccccadbadcdbccabdddbbacddbdbacbdddadbccbbdabbacbdcccabccacabcbddcbcdabaaaababcbbbbbbadbdbbdbaaabdcaddcbddaacadbcddcccacbbbcbcbbbabbcddcddcdcdacaddbaabdcbabadcbcdddbbbddadabcdcbddaccdaadcdbcccaabbadbdcdbbddcbbbddbabccdcddbdbaccbbadabcabaadacadbaaaabdbcdabcbdadaabaabaabddabdbabdcdabcccaccacbcdcbcaccdbcabdabbaaaccadcaabaddacadcdbacbcccbdaccaacadacbbabccacdababbcdcbcbcbabababcabcdbacccbbbddcbbadabababadbabbdbccacbbacadbbacacccbcbbdddcbbabbbddbcccddbbccbbbacbdccadcdbddcddccaabadcdbcccadabddaaddaaabadacbbdaacdacabddbccdaddccbacccaccbbddcdabbaacddbdaaddadadabbccbacdcddcdbbbddabbcbcbdcdbabbdddcbbddccbcbdabaccdbabbbbddaaaaacbcddddadddaacacabcdaddbadacbdccbbcddabbdacbbcadabccdbdaacccbadddbbddacbdaacbdccccaaababdacbdbbcdddcdcbdbabddaabdbcddacadccbaccdabdcbbbcdccbcddaabcccbabccdddabbbcdbbdabcaccaadaabbdaddaddccbdaabcaadbbdbcbdacbddcbcbbbbbccadbdcadaacdaaccaddadcbbcbcdccaacbbadbdbcbcbbadcbcbdbcbccbcccdcbabdbabcababdaaabbdbabddbaaddadbaccdddcaccbacabbdaadbcccbbcbaadabdbbdabcaaacadccdbdbabdaababbaabdcccddadbdbdbbbbaacadbbabdbcabaabddddcdbbdcaddacbdbbdadcadababcadccccbbbacabbdbddbacaddcadacddaadbcddbabababbddbabdbcbbaaadbaaadbaccbbddccdbaccdcdbabbcccaddbcaabdbadcdcbadcaaaddaacadadcdacaadabcbcadccbacbcadbccdcbdaaddcacbdaccbccbdacaccdaaacbbbbccdadccbdadbbbdcdcadbdabdbbacadbdadcaaccaadadcabddacbbbadcbbbaaccdbdbdcbbcbbdbaccbaadadccbadcbcacaabaabbccacacaaacacaddaabccdbcaaaadcdbdcccadacababbadaabdbdbcdbacddddaadbaadccbccccdaacdbcacddbadccadddcbaccccddacdbabbddabbbcbadcdbbbadbbacaacdccbcaaccdbdccacabacbdcbbbaaaccdcddacdbabcacacbdbbdddbcaabadbcdacbdabddbccbabccbbabddaaccdbabcbbcdbbbdbdcbdbddcadaacbadddddabaadcbddadaadbcccdccababbadadcbbcbabcdbbdaccabbdbaddcdbbddacbdbdccbbbddadbccbaccacbdccbcadacbddccbbbdbbbcdcdcbdbbacadccdbbadcabbbcbcdaddacbdcbcccaacddcaabddbcbdbcbdbcbabdbaadcdabcdcaadaaabbaccddcacabaddaaabcbcadbbdadcdaaddbdddcbbbbcbabccdacababccaadcbccaacdbacaddbcabddacdaaadbbdbaacbacdcacabdadcbbcdcaabcdcaabcdbbbbaaadbaadcaddadabdcabcbbdcaaacaadadadcdcaabcbabaabadbbbdbcdaddbdbcccddbdbcddaaadaaaabdabdadacdacdcadaddadcaadbbabacaaacbbcddbbdbcdbcabbddacbcddcacaaccbcdbccdbcbdaaacddcdbacbadaadababcccacadbbdaadabacaadbbbccdcdbcccbdddddbbdcbaddabdcdacbcdccacccbbcbcddaccddcdacdcddbcadcddbbcbbcbbbacacdbdbbdaddadbbddacbcbadacadbccbbacdabbbaabdabcdddcbacabcdaccddacabdabbdbcabcddcadabdcabaabcaccabcbdaddbccaccdacdabddddacaacccccababdcadacdbaaccadcabbdccbaccaacdbabcbbabdbacbabdbcbbccbcdcbdabbadbbacadbcbdadbcabbabbddbdddccdcbbdaaadddbaabbdcdbbccbdccadcaddaccdcaadbaabadcadcdaadbbdcdcbbdabbdbabcdbbccccbbcadcbbdbbdcbbadbcaccdaaacdbbddcacadacabbccdddaacacccabdbcccbbabadbdabdbaacbdadcbbbccaabaddacbabbdacabbbcabbaaaacbaabddccacaddacbabdabbbdcbdbcddbbccddddddacdacdaddabddbdbbcdabdcaabbcaddccabbadddaabcbddcdcacdddccddcbabadcbcbcbbbbdabacdaadcaabaaddcdbdabdbddaadbdcadcacccdcacbabdadbddabbdcbabdadddbdadcababdbdcbbcbcacdbbaadcdbdaaddccacdbacabadbbccdcbcdadbbcacacbdccabbaccadabacdabcbdaabcbaaaadadadcbcddbcabbbcbaacadccbacadcadcacbdbcaacacbcccbbaaabdbdabddadddaaaddbacaaabbcbbabddddcbbcabbbbdacccacdaacadaabbcbdcabdacbacdddcdbacbbcaccddcbbacadcbbbacdaadcadddbbacbbbabccbbccbbdbccbbbcadcaabadcacdccbcadbbddcbadbbcabccdadadcdaddcbdadcacabbcaadabbcbaabadbbdbccbbbbdcbdcddcddcbddbddcabdabaacababacbbacdcadcccbaadbacbaccbcdacccdccbbbbbadbabadbbdbacdbacbbcbabddcddaabacbbdbacadbaddcadcdadaaabccbcdacbdcbadbcbbcdbbabaabccabccbdcdbaddbdabaacddbdacdbdddacdbbbbdcadaabddbadcbdcadddaabddcaabaaaaaacadbcccbdaabcdddbcaccacbbbbcdacadccbcdabbdbdccacaaadbdbcbacadacbabbdcccdbbaabcadcdabdcdcbaaaadcdddadbddabcbbdbbbbdcbcbaccacbaaadaaddcddaadbcdabbbacdddaacacddaadcaaabbdddbbcbcdbcdbddbccbdcbbbacbcbbbaabaaabdadcccbdddacacbaccdccccbcbcdcbbddaacabbaaddccdaaaaddaacccdbaabcbdbcbabcabdccdabdaccbcbbdddaabbdacdcbddcdaabcacadabbabadddcccbdaddabdbbcbdccdacaaaddbbbdabbbaabdbbdbdcbcddcababbcccdabbbbcccaddddadcabacbccaaabbcbbaacadbcddccdabdccbddcbcdcdacbcddadabdbdbbcbbdbcbcbdbbbbbadbdccdbaacbbdbaddadcabdbadadabbabbadcbbbcadbbcbdccbcacaaddccdaddcacccaacbbdcdaacdaccbbbdccbcbabbdadcdbbdcddaadabacaccacccbbcdaccbbdabcadcbbcdaababacdbdcaaaaaaabadacdcadcbdabadbbcaadcdcbbbdabdcaccbdbaacdbcdacbbbdcbccabddacbacbbbbdbacbdadbcbdacdbbaacdcdabaaaaacbbbaccdacdcacaacdccdaacbdcdacddddbaaabccdcbbccbdccbcbbaaddadbacbcdabbdadbcdacdbacaccbababaabddddcbdaacbcbadccbcaccdcccdbbcbdbaddabcbdbcbdaccccccdbadaddccadddccdabaccacbcddaaaabbaddbddadbccbcbddaadcdaccadccdadbabcabdcabacbbaadcabacbacbcaadcacaacababbaadbbbddaccadadacbcdaaacbdcccbacbdadddcacaabbdadcbbdaaaadbdccaadbdbdcadbdcdacacbdcbbbacbcbaccddcddaabdabaaaabdbcdabdddabcbcdacdbbcaaacddcaabbaabbadbccbbbcdaacbdaaddbbbdbbaaababcbdaaaacccbbcbaabbddabbdbdcabcbdddbbaadaccabbdadcddaabcccadcabdcbdabcadacbccbacabdcdbcbadaccdababacdddabbcdcdbdbdbbdbcacdacbccadacbbacddcccbdbbcbdcdcabbddbaaabdcbdccddbdbccccabccbaabadddadcccbdacabddddbadbdbcbbabbcdbabcddcdadbbccbadbadadbcababdbcdbcdbbdcbbccddbbdbdbccdacbbddcbacdddccbcbbacdccbaaabddcabaaabbadbabdadbadbbdbbbdbacbdadbbadcdabbaacddcdcdadabbcbccbbadbcbbcabbbaccbacbbcbaccbbaadadadbacbacadbaccbacabbbcbdbadbacacaaaabbdaaaabbbabdccddcbbdbdbbdcdaaadbadbccadddaabccabbdcddacadbbdbddddbcaddbaaccabbaddccccbbbbbbdadabdcabdbccaaadbdabbdccccdadcccbaabcdbbdadadcadbaacaaddbdbdbcdccabbccddbccaccbbdbbdabccacbbdcddcddaacabaaccbdcabbddbcadadaccdaadcabddcddcadabaacaaccdabbaacacadabcddabbccbbacbacacabaadbcaadccdcddadbbcdadcbbcbccbbabaccadcaddaddaabacddcdcadbbadccacddbabbdcadabdbbbdcaacbbbcbdccdbdddbdaaadbaaacdbddbbdbaaabbbdbcbbdcbdccccbaadbbacccbacbacbcbdcbccadaaacabbdaadabbaadcabddbaaddcbbaaabbccdcdbdbbabdbbbbbcbbaaddbacdbddcdbabdbabdabcababcaaadbaababbcdabdbdbbbccbabddacccadbbbabdcbabdbcdadbdaddbcdbcaaddcabacbaccbdcacdbbccaaddbdcaaaacccaabdcaddccdccddcaabdddbbccdccdabdacbdbaadadbabadabccabdbccbcacbdbcdacbbacccdcaccdaccabcddcdabdddcdbdcddaaccdcdcabbadbacabdababcdbbaacdabdcacaabbbcdabcdabcddabccdbcbcbaacbcacbcddadcbcdadccccddbcadcacdacddbdcbacabdbccdaaabcdccccdadcbddbbacabdcbdacdbdbadbddadabdaddcbcdacbaadaddbaadadbbbbbaddcbbabbdaddbaabdcacabddaaaacaacaaabdadbbbabcbdaadacadcbbbbabadcaadbdadbdbabdbdbbcccaddddccdcdbdacaadacbabccbdaabacbadbacddcbaaaabbbdacddbbccbccccacddaadbabaabbadcbbcabbccdbcdcddcbbaccccddabaddbbdbaddabadabdcdcdadacaadbdbccadbabdbdbabdbcccabbababcbaadadccabaaddacdacbbbcbcddbadadcbadaaccacbdbababbbbbbdacdbcdcdccadcaaadbdcaadaacdbcccddbaabadcbdcadcaaaccbdacccbddbccdcbacabbbbbacddbabcaabbdababbbdbccaddabdddacbdddabdaabaacccccbdcccbdcdadcbacacccababbcaababcdacbbacaabcbabccbbcbcabbbbbaabacbbdabdbacabccbdbababdccaddcdcddabddcbbcbcbaaacbabdaabddcabccbdaccadaaaabdcbcdcbbacadabddccdcacadcbacadcccddbbbcaccadbaccdbbdbabbcaddaabbcabbaabcaddacdacaaacdbdccbbbabaccdcacccbbbbdcdcaacaacbdddbcccbaabddacccbabdabaaaadabadbbccdccbaadadacdaadbbdcadcbcdaadcdacccadbddadacdccdbbbabcabbdabccbddacabaccdcaddbacccddcaccbbdcdcbacddccccbddbabadacaccccddcbacbcababcdccaabdcdadcbccbdacddabcbdaddcccccacabbdcbadbcbbcccbddcacdccbdccdaadccbbddcddacccacdaddbcadacdacbadaaadabaabaadddddbdbacccccbacdbdccbdcbaaaaddcdcdacccadcccbbbabbcdbddbddbabcdbbdbdacddadcdbaaaadbbacabbcdccbdbcaabcccbaabdcbacdbcadbcacacdbadcaccddbadbcaddddbadbacccdacdccadadbacbdcabbadcadaabcabbabddccdadaccdbbbddddbddabacdcaacbbbccaddbccbbbccbacddaadbdcaabcabbdadacccaaacdbacdacabadddabcdbbbbcdccbbcbacdaadcccbbadbbdaacabcddadbbdacdbcccabcbdbccbaaadbbbdbcaacbaccbbabcbdaadbbabcabdcaddaabcdbccbcaaaadcbcabdbdadcdccbadcddbddcbdcddabdcabadcadacbcdcbbaddccddaacdadcabcddbbabcabcdaaccdbdacbccbdaddbadbaabdcbdbbabbbbdddbcbbbacadcbacdbdbbaccdbdacdccaadddadbabcadbdaacdcbaaabaaaaccabbddcacbbadacdbbabacbbdbcddbcbdcadbbcccdcabcddcacdbcaddddbbdabbadbdbabddaaccccabacccadbccacddbbcddbaadbcbcdbdaddcdddbcbaddccbbdaacbdcababccdcaaaadccbdcbccdcddbdcbbbabcdaacbabcdcdcbcadccdcacaaadbabcccbbdbdccbdbaacadaaddcddbaddbbdbdbbcaabdcacabcaaabaabaadacaddcbdddcbccdcbacadaddbbbaacdbcccabaccaadabdacbbcdcdcdcacabdccdbbdcacbcbbadcddddbacccddddadbddacdadbadcdacbdcbcbdcacacdbdbacbdbccaabbdbadaccdccabadccccbcbacccbbbcdcbdbdabdaccaacabbcbcbccddcbdacbddaadcabdcbcdaacbdabbacabccdddaadadaaacbbbcbbcabcbccaabbbdbcbbbababdacdcabbdcccdcdbcdbdcacbbbacdcccdddadcbcddcdadbbabdcdadbdbdcbbadcbadaabcbcaababbdccacbadaacbdbadacaddacdabbddadaabacdcbabbadaccbddcaddbddbccaacaaaadcdcdbcaaadccacabdcdadbbaabcdbbacabcbdbdcadccddbabaabdaddaaccbcbdcddbacbaaccbddbacdaccdabbdbcdbbbacaabcdabbbaadbccdcccaddbcbaccbacdadbdadababbaddddaabddabddabcbdcccbdadbbaaabcbddacdadccacababadcbbddcdbcbaabcbaaacaaccadcabacbabdabbaadcaacbdbdddddabdbbadacbbccbadccbaccacbaccdcacddddcbaadcdcacadcbaadcdabddbddbbdacbadaabdccabddabbbdddcbbdacabbcdbdccdddcaddcadcbacadcaacaaacaccccccaddcacdddbadcabdacdbbbbcddbcacdcdbaabddcdadcabcbbdccdaadbdacbdbcdcaadaaadbabccbccdadcdcdccdcacbcccbabdaaadaccdacbddbdcaddccdcbbbcacbdcbddbaddcadbacbacdaaaddccbddcbadaaaccdcdcdcabcbbbbcaccccaaddacaaabadcbbbcbabbdbadcbabbacdaadbababacaccdadcbdbacacbcadaabddabbcdddbcdaaaddadbcaddccbcdaadcacaccacbaacddbadcabcacbbdbcaccccbcdaddccabdcbddaacdabcdaaddbcbcabdccbdbdbddcdbdddbbcacdaadbcabdcddbcbaabadcbcdbddbcabaddbacccccccacbdcbbdccabcbbabcadabbbaacbcbbdbbcccdbaadddaaccaabbadabbcdccdadadddabcccbcbacadcaacdcbacdabccbabbcbddaccacbcbabdcdbdabbabbaddbcdbbbdbbaaaacbbbcdcabdcbdbaccbbdcccaccbdcabdcdacaddaccaaaaacdbbcdadcacdbadbccadbcaaddcacdaccdabccbdcccbabbddbcbacdabcdaddbcacdcdbbabbcdabcbdcabaabdcdddcbacdcccdcdbcbbcadaaaaddabdddabdbbbccbabdccccdcacbcacccbaacddcabdcdbbdcbdaabaabcacbacabaccddcaadccdddadcaacdbbdabcadabcddcbadadabdbabacccbbbcbaacbddadbbadcacaacdacaadcdbcdbadcabdcdaaadddcbcadddcaabaaccddcbccbcadccacbbcddbcabcccdaddcadacbbbbbddbdbabcdacadccdabddddbaaaabadccbadadbcacbbbbacbbbabcadbbddbdbacadccbbaadaadcaabcacdadbdbdbaabcaacaacbcadccaccacaddadaabddddacdcbdabcdddccabbabbbbadbadcbcdbbbcdadadddbaddcddcaacbbccddcadaacccbaaabbdaabbccabbdbaaaaacdabcacbccbcbacaccbaaabcbdddbaddaabccbbbbabdccbbbdadbaadbdddccbbaddcdadacccadbaadcccbcdccabcbccddaaacbbcbdaaabcaccbbdbbabdcbbaabdbcbabdbdcdddacbbacccaaccbbddadaadcaabdbcdaacaacabdbdabbdaccadbdccccaddcbdcddabcbadccccbdcbabacaccdacadadbbbcacbbaccbbbdaabddadaadbaccacbccbabdabbdaadaccaaacbbbbdbbbdbddadcbcccabbbbacacabdccccdddbadacddaaacdbbcbbbadcdabbadbabcbcdcacbaaaabbabdccaadabacdbacdacccaadbcadbbadccdaccbcaccdddabbccabadbcdaccddbdcdbdabbcdcaadaadbcbcccbbabaacdddcdaadcadaccbcbbdccdbadcdababcaccbdabbcccabbcdcddcdccdcbbadaaadaaadcccaadaadcbdbddcacabaaacdcbbaabcdcbadcbdcaaaddbaadaccabcdabbdbaadaddbadcccdccbbdccaccdcbaabdbcccaacacbdccdabbcdabacbcabcbabbbadbacadccbacabacbcbbbbaabbaacddbdcbcaacbbdbcadcabbbabdbbbdacdcbdcbcdacbbaacccdccdccabbcbabdcbadbabbcbbbccddbdbdcbccadcbbccacbdccdcbabbacbaaaccddadbddbdabbdaaabbbbadcdbaabbcdcdabbbabcccbcaaddbaaccdcaabadacaabbdccbbbcaadaabbbcbdacdbcbaccacdabbbddbabcdcccdbbcbcdcbdcdcbacccbbbcadbcacadacdbbcabcdbbabacacdcccbbdcacaadddddccaadcaadcaabdadcdccddddccccdcabbcdbcbbbbababdddadabcccbdccccdbaaddcadacbcadcbdbcacccdbdadcabcaccacbdbadcabbddacbcadbccabcbcbabdbccabadccdcdbbbdbdadacdcaaaaddddbddbababaadbabadbabdbddcbcbcadaadbabbcaaccadddadbdbdadbbbdcdcbbcbacccdbacabcdbcbabacbccaaddadcbaadabccdacacbaabacddcaddacbbbaadcaddbdbadcaadababddcabdadcddbdbacbdadcdabdcaccddacccbaddbcccdabdcccaadddbacaaddaaddcadacaddbcdabbacacadddaabbcadbabdddcaacacbdbabcccadccaabacbcabbcbcbcbcbdcacbcbcbdacccdadbcadacacdbbbbccabbdadcaaacadddbadcdcddbacddadbddcbbcbdbccbdababcdddaaccbacbcbcdabdccbaacbbdbbcaccaddcbbadbbacaccbccbabbacdcdadacbadabcddaacdcacddddcacdccccdabdcdcbdbccdaccabddabcadcaaabdacbddadbcbdbbdcbadcddbbadbdbcaaacacadcbabdbdcaacbabbdabaabacabbccacbbaddcbdacacdadabaaadbdbbacbabdddbcabcdcacbacacbccbcbbbccdcddccccdadbcdcbbcaaacddaadcdcabddbcbbdcddadadccdcbcdaddacaccadbaabaadbccbcbabcbdbbcbddbaddabcbddcbaacdbaccddddbabccdaddcacbbadbaddcbbadabbaccdddbcabcdacbaccddcadccdbbaaaacaacbbcdddbdadcbbbbcdbbdabdbdcbadbddccabcdbcdbabcdcccddbdacbabbcbccadaddadabdcaacbdbddaadcdbcabdbdabbbbaabdadccddadcccccacdcbdaacabcbdcbcbdacabbaddbaddaabccaaabdcdacbdaccdabcbacbacbbddabccbcabdbbdbbbbccabccbcbcacdbbcbcdcaccdcdbacdcdddabcbabdacbabcaaccbadcabdbcaccddccabdddcaacadcdbcdbcaaaacdaacaacddbccacabcacddbacbadbdcdbbbacbbacdcbbadcdabbcbbbaadbadcaaccbdcccdccccccbcddccbbbcbaaccdcbbdcbddcccadabacdbbccbabacdaddcdbcacdbababdabcbacbdcdaacdbadcbcbcdccdddcddbcacdbdaddccbdcdbbaaabbcbdbcbaadbaaaacacddbcdaaacadddbbaaabaacbaabcbaabcaadccacbcbbbcadabdabcbdbcaccdbaaccbcbcddbdccccbdaaccbcdcdbbccdbadabacccacadacaacbcdbacbdcbdbccbacaacbddcdabacadacaddbccdbaccdabddaacaacbdadcdccbbdcdadacacdaadabcdbccaccbddaddbaddbcababbaaccdccdddcdbbdcadadddcaacabacadacbabbbbdbcdcccabacdbccbdddcaccccaccbbcccddccbcacdcacbdcaadcadcbcccaadcddbbcdcbdaddbbdbbdcaadacaccdbabaccdbdaacbaababbdbcbadbdaaabbbbdadcabbaaaacbaccdcdcdcbdcddccbcbdcdabddddbababcacbdaababacdddaabbbcaacbadaacdbacddaddbadcbcdbbcbcdcccacccdcdbccaadbaadaababaccadacbabcbaadacaaadcaaccbdaaccbcdddabadabddbdddcdcbbaaadccadcdbcaaadbdbbddacbabccddaacbccccaaacbcabcbcbbcdbabddcddabaaccdcbbddabaccbddaccdbaaddccbccbabdacccaaadccddacaabaabbdadcdaccbcbcbddcbabcdbbdadcbabdbaccdccadcbaacbadbdbdddadcbccbaccabcdabdaacacddacbaaddcbddadbcbadaaaaddacbadcaaaacacbcbbacbaadbcdbbaacaddcaaccdbacdbdddcbdbaacdaabddddbcadadcadddccbaadcacbbbbcbdcabdbdaadddddcacdaddaadabcdbcadbbadccacaabdadddadbaacdadcccbcbadcacacbaaccbcbdcdbaccbacbddbcacbdacddbacadacacdbadddcbdcdbcddcacbbddaddbcccaabccdacabbbabaabdbcdadadabaccdadabaacacccbbcbccaaccaccaadddcbdaadadbaadaadbbcbcaabcbcddbaddbdabccccddcadbadbdcbbccdbdbccbbabcacdcabadbadcdcadccacadadabbcddbdcadcbabbbabacaaadbbbdbdbbddbdacdadcdcbdcccdacbbbdbbcbdbdcdccdcbcdaacacbcccdbdccbaabbdbbaddccdaabcbacbcdddbdacaccdbdddbaacadbaabdaacbaaababccbdbddcdccdbcabbacababbccdacadcadbcbbaccbbdccbabdbcbacddaacdcbbdbddacacaaadddddbaacbadbdbaacddaddacbbcdccccbdaaccabaadbaacacdcbadaccadaadacdcdccccbadbbdcaaddbdcbacddaadabbabdcbadabddbdcdaaabacdcadbcaaabaabaaccadcdccacacadadacddcacaabdbcbaddcdbacdddcbabaddcbaadaddcdbbdddbddbcccccdbdccbdcbbbbbccabaddbcddaaaccaadccaadcaddbaaddddbbcadbdadadacacabaadbbadbdbcabbdabcbacccbbbbbaabcbaacdacdcddcbcadcbadcddccaadccdaddcadbabdbddcbadbabdbdabcabdbbdaadbabbddcadbddbbcddabcaadbaccddcbdccbaadbbcdbddcddbcbbdbcdaddcbdccdcdcadcccbcabbaacdbdbbccdaccbddbcaccdbabadaadddacacbacdacdcabdacabacbbdbccddaadcaacbddadacdbdadacacdccaaacddbcacbcbddaabadccdbbadcbbababaaaccdadbddcabbcbdcabdcccbbabdbcbbbabbcddcbbbcadbbaddaaccbadcbbcbdbbddcbcabbcdbbccadcabbccacbbabacccadddabacdbcadcdcacaabdabcbddccbbdbacddabcdcaacdddcabbbcbcaaddddbbccdabcdcdcbaabaaddaddbadbdbccbabcdcabbccbbdabbcbbabaddaddcbbbcabdcbbcbbdccddbaaaadbabbcddbcbbcbacdbbbcabcbacbbdabadbadadcabadbdacababcbadbbbbbbddaacdcdadcdbaaddacdaaadbcbdcaabadaaddbbbaccdccccdcbcbdbaacbdccdabbcbdacabcabbcbbddcdabbdaaccadcbcacbdabdbcbdaccbcdaaababddaadcbaacbdbbbaccbcdbaaccbccadbbdabadbbbdcdabbaddbbbdbddbabddaccdabbdcbccccccbddacabcbdcccbcaadcbbadbccbadbbddbbdbbcacacacdbcaabcacaaacaccacabdbabaadbbdbbccdacabacbaabbcdabcdcddbccdaabdcbdcddbdbacdbcbbababbcabbdbcddbaadacbbcddbcaaddadcdbbcaabdddbccccccddcadbabaacbdbbbddbdaccddcbcabdcddbbccbbadadaacdaabdcdcdcaaabcdbabdaaaaccaaacbdccadaddcbdcdacaddbbcbbdabcbcdacccdcdccabdcbcdabacdcdaaaadbdddbabbdcaadbdbbcbcdaacdaadbdcbaaccdaadadcddacbdcdaadcbdadbcacdbcbbbaadbbdabcdcdcadddbabbbbcbbbcdccccadcaddaddccdacacbbcbbaababcacaacdaacbbdadbdcdbadabdcdcdccbdcbdcadbaadaacaaccdddddaccbbbbdadbbdcbdadcbababddcdadabbdcabdaabbdaccabadadcadadccbbcaddacbbbadccbadbaabbddbbdbddacdcbbacaadbbbaaabaadadbadbcaacabdcbdbddcbadbbcababddcaabcdcbdbacccddddabbdddddbcacabdaddcabccdbcabcbbcaabbbbdbcabbaddccbddbcbddadbdccdbacbdadbacdacabbbbadaadcdbbcabcdbccadbdcadabcbababcbcdcbccadbdcddddddbdcccbacaaabbdddbccacaadccbcacbaadacabcdcddcbacdcbbbaababccdcdcbbcddcdabadbcdbcaccbaaacbadabcdcccdbcddccbddbdccdacdaccbccbabaddcbcbbcbccbbdaabcddaaccdabccadacdbbbbacaaaaacabaabcddacdbacaccaddbcccddbbbaaacddaaddacbcdcacbbbdaabbbbcadadadbadcbbaccacbcbabdcccbcbdcacabcccdbdbbadcaacbcbbaaadcacadccadccccccddbacbbabdcccaabadbdacbadbcbbbabdbdccddbdbcdcdbbcacbdbadadbbbcaddaddcbacbdddcacddbccadaacdcdbabbdaddcdcadcadacdccdaadbbdcbdbbcdabdccadbabacdcbbdcacbddbdbaacdbbcccdddacabcdcbdbdcbcdcaadababcbaccabddaadabbcbbacacbddbdabacbacacdabbbbdddbdcaddadbccbbbcdcbacaaaacbbaacaabbcccdcbccdcbcadacccbaccbddddbbabbcccdcadadbcddbacddbbbaacccabcdaccdccdacdaddbabdbddcabddccdaaaabdbacbabcaaddaacadccdccdbaabaddcbccababbdbcadbdcbcaabbbcabddcaabaabdbdcdcbdddcbdcacdcdaaacdcbbdccbdbcdccbdcdbadcccccdcbbcdadcaddbacacdbbcbdcaccdccdddddbdbabaaccbaaaccddcadcdcaddbcbdcbcbbdaabcabcaaddbcccbcbbbcbbacddbaaabccbaddadcacbcccadddccbdcdaabbdcbcdadbaadaadcabcabcbddbadccccbcadcacbdcbacbbacaaccbabaccaaccacbdbcdccdcdcccabbbbccabccaacadcbaddacaacccbcacbccddcdbbabdaadcadadddcdcdcbadbaaccddbaccbdccaacaadbabcaaabbdcbbdaacadcababbccddbdcbbcdddccaacccdddcddcbbdccbbdbbdbbaabbcbbcaacbadacbbdcddcacccabcaabcddacbbaadcacccabaacdccacaadacdaacdddcbcabbddbddadddcaaccbcadccbccaccbbcbbacdabbdcabdaaadacbbcacaabacbdabbacdcaccaddaaaacaabaadbcccdcadcbdcbabcaddaccdaccddcbccbbccddcddbdbdbdadbbadddbdcbdcdbdaaaabaadbccaddaacccacbbcbdcdbcabdabbccdaabbddcbbadcbcdcdcadcdbcdadabbcccbbaacabacacdadadacbabbccbcadbbcaaddbdcadcabcabbdacddbccadbcddccbbbdcaadbadddbbdcbaaacdacdcdaddadbcbdcbacdddbadbbbddbadaacaabaddbcbdbdaacdbadcbbdcaabbbcbdbbdbcdbdccdacddcbddabbcaddccdbdaddcdcabaaaabaaaaccdddbbbdcbacbbcbbaabddbddaadadbcbbcbadabcdcccabcccbddcdabdaccdcdacdddbcbbadcdcadbcccbaddccabbbbdacdcdacbdbabcbcacdbdabacdabacdbadbadddaccdbbababcbbbabdaadbcbcadbcbdcaaadaaccbcbbabacdbdcddccaadccabaacdbbcdadbdaaacdacdadacbdbaabcdbaacbaddddbdabcbcaddbcabbbdcdbdabaacbabccdabdacabcabadbaabbbbcbdadabdcdcadaccdbdbacadcccdbaaaddbbdbddacdccabbcaddacbdcddaaacbdaacccdacaadddcdbddccbbacdcdccbdcccbdbcabcbccbbabcbacabbbbbdbdaacdcdabaadbdcbbabbdbdddadcbddcbadcdddbccdcbdbbdababcbccddddbadbcdbbacdbccbdbdbabbabacbcdccbaacadbcaddacaababdabcdbabdbddbcbbaabccddadcbcbccbbaccabaadbcdadbcdcbacdabbdccdcbcbcdacdabbcddcccddbccdbcbbabcbccbccccaaddadcadcbacbcdbbbcddabcbcbabccacaaddaadddadcddaddcadacdbdddabbcbacdcaacdbcaabaaddbccbdbdcdcbaddddacbbaadcdbbaddbacbbdaaccdcadcbbbcadbddcadadcccacbcbdadbcabadbdbacdaaaadccbdadbbcacdcaddaadbdabdadaabdbbbcdabcaacbdcdcdcdaacaadbacbdadcdddbaddabccaacadabdccbacbdabbcbcaabbccccabcbbdbaaabddabdbdcabdbcdcdacaaacccdccababbccbddaddabcbcbdcabadbabadccbadcaadbbabbbbadccdbbcbcaaccbaaadbdbbaacacddadadbcadbadbcaaaacddbbaadacabbabbbadcbbaadadbbadabbabbbcdcbbdccbbdbcccdabaabbbdbadbaadbdabdaabbdcdaabadbacdcddabdadacbddcddcccadbcccccdaabdadacadcdddacbbabaccabdcddddabbabbcccbcbaaaddcabdabbdaccdadcdabcbaadddababdaabdacabdbabacbbdcbcbabadbadaacbcabdaaccbcdacaaadcbbbdcbdbbcbaddbaddbdacbbccddcccbbdcbdcbacbccbaabddacaaaadbcbadbcdaadaddbaddcddbbddabccaabcbdabdabacdababdacbcadbdabdaaccdaacbadbadadaadabbbbdcbacdcdaccccccbbdbddbcaababdbaaaccabbbbaacdaacccbcbcbababacbccbacddccbaabdbdacbcdbcacadbcabbabacaaaacbdbcdaadcbacadbbbcabddabdacaadbacdcbcccbacbdadbbdcadacdabcacaadadbbadaababbdabcdcacbdbaaacacdabaadabcbdabdcdddcbdbbaaaacacbcadabcbbcddadabcabcbcdcbccabdbdadbabbaccbccbccbcaacaacabdacbdbdadaaaadcadddddadbddacdcdacbaccddcbddddabababbdcdbdbaaaacabdbdccdddbcabbacacdadaccdbcbcabacdbcccacdbdaddacbcaacadbdbdabadbcbdbddcbbbbcabdcdadabbdadddabbcaabbbcdccdbdddcbbcbababcdaacbacbdcadccadcdbbcbbbdcdadbcbaaadacdaaacababbcdccccbabddbacbcbbcaccbdadbcccdbaadaccbcabdacbcabddbdcabacadcadbcbdbbddbbacccddaabababdadcabbcbccbbbbccbdadbdcccdbdaadaaddadddadbacaddddbbdcbcdadcacaccdbcdbdcbdaaaadbbcababddcacbadabddadcdccbbddaaccababcaccbadbacadbdcddbdbbbcdabbababdbdbcddbcccdcadddbbdbdaddcabddbddbabdacdbdbababbcbdcdaddbcbbabcccccaabbddddddbddbdacadcacbadcbdbdcaddcbcdccabbadcaacabbdcbbbcdddcabaccbccaadadbcdacbdcddccdcbaadbddbdcccabcccdaacbcbcacaccacdabddabbdaaccabdacccbbbbbbadccaddacadadcbcdaaaaabdcabdccaabbbbddcbacdbabddbaadbcbbabddcaabbaccdacdbbbabbbacadcbcadccabdcabbaddbcdcadccddbdccdccbdcddcabbbbdbadcccdbadbaacbbaaadadbccbddabbaaacdbdcdddcbbcdcabcdbadccbdbbcdacaccddaacdddcbaddcbdcacccccdccabacabbcaacabbaabacdcabddcbbdcacaabdddacdacdadabbcadddadbdadacddabdaacbdacabbaccdabcddacacaddbaacdacbccbabcdaddaaabbbbdcbcdaddddbcdaddcacccdcccbcdccaadcccaddcdcdbccdddcdccccaaadcddadbddabbdbdbbcbcddabdcaddacadbdcdacadaccbdcddabbbbaddcddababbcdccbdadbadccbddbccbbdabaaacbcddbdbbbccdcaaddadbbabadaadcaaddcbaadbdcbbdcaacacbcadbccbcddabddbaadccacdbaacaadabdcdcaadaaabcbdcbadbbccadbcbadbdaabcdbdcdbcbbcabaccbcadadbbcdcccdadaadbadadaadaaabbdacaddcdaadbcbaaaaddcbdcabdbadddcadcbacbbabbbbadaccaacaaddabcbcbabcaccccdbcabcabcdcaccabbbccbdcddbbdcadbcaabbbcdcdccaadcbdabbaddabdabddabdddccabbbbbddbcacbbbcdbaabdccbdbcdbdbbdccdbddbcdaccacaacbdccbcbcdcccdcbcadcbcdbbacdcaacbcdaabdadbcaccaaaddcadadcbbbbcabdaacdccddabbbcddcaccbcdaadadbcdddbcbaccbacdbacaccbabcbbbacacaccccbcbdbbccbcbddaddbabccdbbbcdcdcdaaabcbbaaaaaadadccdcdddddacabbddddbbdaccaadaacabdcacbdcdabdbdaccadadcdbadacdbcabbcaccddaaddddbababdaaaacccbbacaacdcabccbbdbacadbadacbaabccddcababadbbcdbbdbddcabdcacbcdbbbaaccabbadabcbcbcdddaaaccbdbdbdbdcbdacbcbdadacbddbcaaccadcddbcaabcbdacddcbbcdcbaddababaaadcacbbbccdcaddadccaddcdadcdbcbdabdacabaabaaaddcccabbabdaabccbaaadbacdaddccbbacaaadcdcdddcbcabdcaaccbdbbdbdacacdcbbccaccadbdccccacaadcdcbaccdcdaadbccadcbcbbbabbcddbbadbacbdbabacbcbbdcbbacacbdcccbaccaacbbdcbacabddcbcbcabddcdabccdbdabcacacbaddbbadcbdbcdabccdabdacacabaccbbbdcddbcbadcbabcaaddccbabcbbbaabbdccbdbdbadcdacbbddcbcbbbabcabcdccbadcddaadbcaacbbbbdcaaddcdcbacbddbadcaadcbcbcdbccbacbcccacbcccaddbdadddcbdcbbacadabcbbccbddcabcbdbaabcabbaabadaccdcaaaddaacadbdcacdcccaddbadabbcbcccccacddcdddadbccddbcbacaadaddccaacdcbbdcddbbdddadacbddcdbddbbbcccccccbbcccccddcabbbdbdccdcddcaacddabbacdcbdcdcccbbccabdacdbdabddcbcddcddabbcaadccaabbaddcbaccbbbccdddbadcabbcbbbacbccacbccbccdcacdbbdcacbdbcbadbddbacbbabaddcaabbaddabdccadbcddcbbdcdbdcbccbddacdbbcadcbabaadcdabaddcdccbabcdbbcaaacbaaccccbbbbbccadbdbabccbadacdddcbdabcdadbbbaadbbddbdabbdbbbcddddcbacabbdbaacbadcdaabaadddadddcdcbddacaccacacdbadbaddccaddbdcccbdcacdbddadcbdbddcbccacdabcbdddccdddacadbbcacccdbbdbccbbacdaadcddcdadabaabacaaddadcbdccdbabdacbdbdaacbacdacdaabdaacbddbaabbccadbbcddaabbabcbccbdcabbbacddaaabbbbdbdaddddccacbddadcbdbcccaddddccbadddbdbdacabbcddbaacddaadbddcddbadaaadcddbbcdacaabadadcacbaabbabbbacccbaacbcbcabdbadbcdccadcddbdcaabbacdddbcabbdadacbddaabacbdbcccacddbdaddcdbaabbabdbddbabbcbdcadcccaadcadbbcddaaccbbcbddcbdcacaabadacdababcaacbbaaabcabcbadbababcdabaccaadbbdccccacadadccabcabdaadabbacbaacbbabcccacbdabddbcdbcbcabdcacdcbcabcacabcdcaddcabccdcdbabdddcbbcbdbcddcbdcbbdbadcadcdaddbcdbccbabcddaaccadbaabdadcdddcbbbcadbbbcacacabaacdbabddbaaadcbdbcdbbaadacdaabbaddcdcdcdbbbadddcdaabbdabacbcbcdacbabdbdbaacaccabababbadbdbcaabbbadcddcdcdadaddaacbdcdcabacabccabcdcdbaabdcdacbacbaccbcbdabdccabddbbdbadbbbcbcbbbcdacacbbabaababacdcdcddadbdacbccacdaabdddddbccbdccbcacbcddcddbacbdcddcbcbaaabbddddaacbaddabcccabbcdacdbaaccdbbabadcaabdaddcbabccaddcbcacdadacacdbadddadcccaaddbbacaadbbbacddbbbaabbccbdabcbdbadabcadbbaaaadbcadcaccdbddcddbababcbcaddaacadbbbbbdbcbbbccabdacadacccccaccacaaccbaaaaaaadaadcdccbdbccccbadccccbbccaaabdadbcbaacccdaaccbacddbbacadcbaccdabbbacbabcccdcdbdbaccaddaaabadaacbabcdaaaccdadbdccdcdddcaccdaaabdbdcbbcacbdbdcccddbbbccbbdbbbcccdaaadaadcccacdcdaaddccccddddcbdccbccaacdacabcdccdcdbacdadcabcdcbaadaacbbacbcdbdbbccaaabdcbacbcbacabbabddcbaaacccbdabbcbacbdbaabbbaaddddcbbdbcdcdaaaadbcadabbaabdbcbcbcddddabcddadaabbdcaaabbbbcbccbdccacdcabcdbcbabbddbbbdaadccbdccddddacabbcccbccdbcdabdbdcdbcdbcadbbdaaaaddacacccccddcccdcdabbcbbbdbbbbdbaaabdbbdbbbcdbdadbcdcbbdaaaaabbbccddaacdddaccddddbbbbccbccacaabaddaccbaccbaaadcbbacbbaacbcbcdaaadbbdbccaacadbdbcddbbcacacbaadbdcbcdabadacadbcbdbbcdaabdaccbdadaadbddccbdaabbbbddacaaabdbaabbbcbdbcbccddbddacbcbaaddddcdaccbcaadcddbbcabdbcdbbbccaabbcabcbabbcdabdcccbcaaabaabadcadcdcacdbacadddaacbbbddbdaadcbacddaccbabcbcdacadbdcdbaaaddacacdacadbdbdbabbdcadcdbddbaccddcadacdcbbcaabcacabdacbcbdadbaacbcacdbdddabdbcaccdbccccdcbbdacdbadbadcccadbaaadcdabbbbcadcdbbccdaabcdcabbbabbacabacdcddccbacbddaabdcdbcbddacdbcbdcadacdcbabbbbcbcdcdddadaaababddbcbadcddabdcabbbdcdcbccaddbaaaadcbddcccabaddbaacbcadcacccdbcbcbdcdcacdbcaacaddaaaadcdaadcaccdcacadaccaaadaabddddbcabcdaabbabddddbacacaccbdabaacbdcccacbcabcdbadbcabdabaaccddbcaccdadcdbbcacdabccdbbdabddaaacccdadcbdaadbbaccdbbccbdacbcadccbaccdbbbdbcbccbcbaccbdcdbaccabcccdaddaddcaabdcabdbdcaddcbabdbcbdbadcbbabadbddababacdccbbbcdddabcccdbcbcccbcbbcacacdbacacabcbcdcbdcaccbaabcdddaadcdaacddadacdabbaddbadaaabaacbcddcdbdbdadabcbabcbcadbcacdabbbcbcaabccaddbbcdabcadcccabddadacbbdbdbbcbdcbbdbbbdacdbdaadbbbdbddcdaadddbdcaccabdbcadccbdadcdcdacddaaccdbcccbbaaabbcdcaacbcbbbbaaddbccddcdabbbbdcdbdbbbbcbbdaadbbcbccbbaaccddddbcaadccababbcdbbcbdbbabdcdbcacbdcccbdcbbadddbdddddcacbbacaabcadcbdcdcccbbcdddcbadbbdacabbbdbbababcdbadcadccdddcdddabcabddbccadcdbadbbacaaadadddaabaabaaadccaabdbddbdacbadbbcddddcdcdccabbaadcabaabaadddbbdbccddbdddcdcdacdabdddddbacbacdcaabcbdaacaccacbdacbaabcbdaccdaacbadccaaadaaadbabddbcbcccaacdacbaddaaddbbbcabbaabdcdaadbadcabbbdbdcbdbbcadcdadabcbcadcdaacbacdcacbaddbcbaabdcbdccdcbaaadbdbaccccadcbadacadcbdaccbabcccbaadccbaccacabaddbcadddbdcacdaadbadaccbcbbbcacbcabdbacddbadaaacddacbcbddabacddcdcdcaaadbbcacacdccdbabbcccccaacccdddbabcccdccabbccbcbcacccdcbdcaaccbdaacaababaaabbddbdacbcdcbbbdaaacdcccbdaadbbbabdbadababbddadbababaaadcbbdbbcbadcccbbaacdcbdbbddacbdcacdacadcdacbcbcaabcbcbddaabcddcbdddbabdccbdbcaaaadbcdcaabaaaadcbbcbabadaaddbabbdaabdcbabbaadabbccdaaddabaddcdcdcdbddbaccbdccdabdbddacccdcbcaaddbddcacbabbbaabbcdddcddccdbdbcdccaadcdabcbcddbdbadbdaddcbabcacdbabbdcaadabccabbacddbaaaabacddddbaaccdcbdaaabdbbbaccbdaaaaadaccddccabcbaaaaabcbbdbddaccbdadddddadabaaabaadcdbcbabadbabbdbdbbbdabaabcdcccdcadcbbcbdabadcaadaaaaddbadacabbccacaccdcddbccadcddbdbcbcbaacaabbcbddbddbcbcdcddbccabbbddbcccdabdcbcccbbbbbcbbbbdaddccbdcdbdcabbdaacbcabbcbadacacdbddcbbcdacbaccacaacdbdddcdcdbbdbbbccacdadadcbabcacdddaaaaadbacdbdabaaaadbdbbdbcddbdcaccccbbcbaddbabddcbdccbcdcdddaddaadcddcabcbabaacacaacbdacbbbdaacbaccadcddacddcbbadbacdbaabacddbdcabbdadbbcdbaaacdadadcbaadcbcabaacacbadacaccaaababcaaadaacadcdabcbccbaadddbcdcabbdbabcacacadacacddacddadadcadcccdcbccadbdbdacdbdaadbcababbacadbdbcaddccabbbdcbabdbdddbdbdaacabaccadbabdbbabdcdbdbbacbbdabdadcbdccccdcabcdcccadbcaadcddbabbabdadbadddbbcbbbcdacaccbbaacdabbdbdcdbcddacaccbdbdadacbabaadcaacdaaaabbbaababcccdcbbdbabccdbabcabcaabcdcabaabdbdabbddcbddbaadbbadbbaddbcbcdaccdddcbcccbcdcbabccdddbcdcbaabddbbcacdadabaacabcaddaadbdddcdbbcbbcbccbabcabbccdaabcbcbdddccdddcbbabcaacbdbaddbcbacbdddbbadadcabcbaacacdaacbcccbabddaddbaacdbcdabbbdaccacaaccdbccbdbaadbcadbbaddabadadccdcaddadbcddcdbdcbcadccacaadbdbbdccdacbaacacdacbadacaddaddcdbbaddadabacaaacbdddcbabccbddbdabacbddcdbcababcdbcccccdbddbbabaccabaddabcbbccbaabbccacbdcbdcaaadbdbacaaabcaaacdbcbbcabbcdbcbdccddbcaaddbdabbdaddabbddbbddbbdcacdcadbcdaaabbbcdabccddabdaaababcbbddccbdbcbcbcbacbbbccbaaaaccadbdbadaabbadcbcdcaaaacbbbabaaacddabcbdbcdabbddabcabdccaccacacbbcbdcbadcadacdacdcdadbcbbbcacddabdabbbdabbdcddddbcbacadbcdabbbddacdacccdbabdadcdcadbdcaacbcabdddaccaaadcaadaacabdadabccbdcddabadadcdaddccaacbbaccacbdacccdcdddbbabddadcaaccbadabcbdbacbcccdbdadadacdabcbdcdcbadccdcddadabbcacddacabbbadcdcaacadbbadbdbbddbbadddacaccacaccbcabdcacddadcdcddaccbdbaaccddadaaacabadcbdbacbbdadccbadaabbbbbdadbcbcacdcccbcbadbbbdbdbbaabdbcdaccbadabdbbdacbadcbcbbdbccdddabbabbacdcddabdacddbdcbccbdbbacbacddbbdbacdcaaaddccccbaacdaddbddbaaaabcddbbbccdadaaacabacdadbaacaaaccdcaaabdbbcdbacbdbdbdcaadcacbdcbabbabccdddadadcadcbdbcbbdabcacddbaabbdbadabcbdbbbbadccbdacacbcdaccccccdccbacacdddcdccacdadbadcddbccaccdccccbaacaaaadbcbbaaadbcbddcbdabacabbbddbbdccbadbacbccadbcbbcccddaddaaaabddcadaabcadcdacadbddbadcccabaacacccacacdacacbaaaabaabdcdadaaadadddddcbbacccdcabdacadccbadcadaacdcabdcadcaaabdcbdbdccbcabacacadabbabbabbaccdcdddddcabacaaddabaddbbaadaabaabadcddadbcabdbadbbbbcbbbcddbabbabbacaccbdacbdcaabbcadbddacdabdacbacdcddcadbadddcadbcaaabcccbcaddcacbaccaacaaadadaaadcabcaaddbdccbacdcdddacdcdbcccadbcccbdbbadabadaddacdcabbdabadbbccddadbccccaddcaadcacccbaababcbcacbcaacbabbadcbcacdbddcdacbbbccbcadbbabadcbdaaaaaadabcccabdacdbbdaaadbccdbcaddbbccdacacacadaddadbaaacdadbabdccbaacdbdaccdcabbcaccbaabbbdcadddbcddadadbdccabddcdbddddacbdabdbadacbacdbbdbccacabdcdbddadddbaaadaabbacbabddcddbbccdbdcdaacbcadbcddbbdabbadccadbcdcadcabaccdbbabbadcaccabdadbccabaccbbbbabdccaacbddacdcdbccbdadadbcbadaabcddcbcabaabbddddcdabaddddaadbbabcdbdacbddddbcaacabcbbbdddbbcddbddbaadcbdcbcdccadccddcdbaabdddbcdddcabbdcacbaccdbadacdacdcabcdbbaadaacbcddadababcbcdacdaccccccabbddcdbcabaadcbabdcadcbbaaddcadccddacdaabbccdccbdbaaaababcbaccacdbbbcbdcdbcdcddaaabccaabdbadcdccaddbaabdccdbdadabaabbcbbcdabaaddcbcdbdbadaadcdacaaddddbaaaccbcdaccdbdacccaccaacdcadbcddcabdbddacbacccaadabbcaccbcbdbdcccddaabdbbbcccabdbcaacadadddbcdcbdcdccadaddbaababcdbbbdadcaddbcbbcdbacbbabcbbaaabbbacccbdbacdcccbbabaccaabaadaaabbadbdbbdbccdabbabdacbacccbbcaababadcdbadbbdccbadbadcdbbcccdbabbccdadaaaaabaddccddcadccbacababacaadacccccaadabcacacaaddbdadcabbadbcdcccdabdcdbcaaabdabcdcadbddbdbbddddcdaadbbadcdacacdcacabccaadabbdbcbaddadbabbdbbcbdcddcbadcabdacacbbcbdbddacbdabaabaadbcdddcdddcbbbdddcbdccbcbdaaabddcacaabacbccabababccaabcbccadbcacabcccbdbabbddbcaacbbaaadcbcbdbcbbaaaabaabbacadaadadabaddccbadbacbdaddbdbdbbcaabcacabcacccbcbbacadbcbcdbddbadadcccbcdacbacdadddcbaddcdabbcbcaccbbcaddbabcddcaccbcdcccbbaaadcdccbdcbbaaacccaabcbaadccacadccbcbbcbcaddccadacbdaddbdcaadbdcacaccdcadbababbccccbcdcaaaaccbccccadbdbbbbacaabdbccacbaabadbbbdccbcdccaaaaaccdddbccdbdbadadbbddcbcaacadbabddcacacadcaabdcbccdccacccdccbbbadddbdbbcddddadcccaddcacbdcbdcbccccbcadaadccdbacabbddcbbcabbaacdcaccddcbcaaccddacbcdccccbdbddcccacacdbabddacdbababccdbcbdbcaccbdddaabaabbdacdbbbddcabcadbcdbaadbaabbbddbaaaaadaaddadabdccacdacddaaacbcccaaddbcdbbacaccadcbabacdddcddcbadcbdaaccdbccadbbdbcacdcbbcdbdbcbaadcdbdbbcdcbcadddbddacdcabbaabcbbdaddabbbcdaccccdadbcaadcaaddacdbcbdacbaccdaadadcddccabdadaacddbaadcbbdbcbaadcdaaaabccdbaccbbdababcbccabdbcbacdabcdacabbbdbabddcbbaaabcabbbaadbdbcbcabbbbcadbaadcdbadccddaccacccccaabdaaadabadacdbbcbcbbbcacddaaddbdacadabcaacdbdaaaadcaadbccdaadbdbbcbbddbcbbcbbadbddccbabcdbabbaaccbcadcdcbadcabddcdcdcbcbcabaacadbdbaaaaaabaaddccbaccbcdcdcadddbcaaddbdccdcbacbbaccbbaaaccbdaaaacddbddcbcdcbbbacdadbadbbabbdcaccdbaddcbaddbadbbcabcaabcbcdcccaadcdcabcccbcbccdbbadccbbabbaacdadcadbcbadaadbadcabccabadbccadbbbcacadabbaccbddcbdbaaabaabcbaaaccbbdcabcdbbddacbdbbdabdacadddcbbbdbabcbbabbccbcadabddaaddbbadbaabddbacacadbccabcdabdadddccabcdcadbcaaababbbcadacadbadadccaccaacadddbdabadadbcddbdbddbbccddcbcadbdadaabbcdcbbddcdbdbdacbbaabdcccdabddbadbcbcccbccacbacdbbbadcbabcddbbddccdacabadddbabbcbcccccacadacbbcadbabbbddabdaabccdcbbdabacdbcddaaadcadccaacdbdcddbcdbcabddddcdcbdbccdadccdaaadbaadcadaadcdddcbccccdcaaccadcdadaabdbccaadaddbcbcbcbbaaddabccaadaacaadcadbcdaabbadbbbbddbdaacacbccdbbccdbabaddadbbbbadbcacbbcadaabcbbcccbbcdddccbbcabbcaadbdbcbbddadbccccdacdbdadaadacdcbccbadbccdcbdbdcdcbacdacdcbbbbbbccabadadbddcdbbcbcaadbaaaddcabbdbbcbcdcabbaabbdcdcacadabdbddbbcddccdbcaccbdbbcacadccdaddacbbaccbcdcadbbbdcaacdadbaaccabbdabcacdababcaaadacbdccddddaddcbaabdaabbbddcdbbbccabdbcadabcaabdccdacaadcdcaddabbbdcdacdddadaacadaddaadadcdcdcddaacabbbcbabdbaaabcbccdcddadbddddcaacacaabdddccddccacdbabdaabbabaaabbdccdccdcbdaabdddbbddccccddcacaccbcbabcddaccdcbbbddacdcbbcacbddcddadccbadabdabddaaacbcdacdadcaccbbbadcbcdbaabbdbdddaccbbbaddcbdacbcbaddbcbaadadbbcccdaadbbaabdaacaabadcaccdbadadadabadbcaaacbddbcacbdbacdbcdcbdddbadcaadddbcdcdbcccaacaababccaabbdcacabbaacaaabadaaccccdbbbdcdddadbbdadcccbbaaabccdccadbddcccdcbaadaacdadbbcbbbccdaccdacadacdbacbbdddcdbbdcaadbdbbaabacaddbbccdcbddabaccbadbbbabaadccdbcddadbdadbabacbdcacddadcbcbddabbaabccabacdbdaaabdacadcbbcddbcbaacdcdadaaabdabdcbdccdbdaacdacdabbccaabbacbababdbbbdcbabcaabcadbbcbbbbaddbbdbbcacacbdbbdbbcddaacaacaccdbbaabdbadcbaabccabccdbacdbcabadbbdbadcaccbbaadcbccbadcbcbacadadcbadaccdcccabacbaababaacadbcbbbbbcaccdbbcbdbcaacbcabbbcddcccbbddaddcdacacdbbddcdbcadbddbcddbbcaacbacabcbbbcccccacacdcbaabcdbbabbbaababcdaadddbabcdacaacabcdbacdcbccabcdadaddbadbdbcdbacacadbdbacbcdaccbaccccdacdcdcadccdaabdddabacaabcbdaddacbbdbcbcbcaacbbbddbacbcaccacddcadbbbbddbabbabaacdddcbacaaadabbbdbabcbadbcabbdcaaaadcacdbaaadcdaaacabcaddabaadcccdddaaaabbdacbdabdbbacbabaddacbcbdcaaaccdddcbaddadadbadabbbddaaddadbcddadcbdbadbbbdacdcbddbaaccbdaddbadbcacbbcdbdbcbcdabbbbcbcdcbaaddcbabcbaadbcadbaacacadbcdaacdacabcabdbcbdcdcaddbabccdaabbaccbbadabbbcddbccddbaccabdddaabbaabaaaabbcdddacadaccbbbbcdddcdbdbdbcacbbbbababbcddcdbcbdcdcddaddacdddbadbcbdcdaaacbcdddbbdccbdadcbadbbcadbacacbdbdadaacadcaacbcccdbcdaadabcccdbcdccbcdddaabaadbcdbaaccbbddacabbdbdbaacaaaddbaacccadbcadaadcddaaadbdbddddbbadccdbbdabdbbaaacccdbacbcdccbdbdaaabcccbcccbcbacdaababccadbaaaadbbccdabdbacabcbbababbadccbbdcaadadaddddbccadccacabccadcdacadcbdadbcdaabaddacddcaadcdabbdbcaccbadbacacabbdadbcaccaaadbddbdbdabbacbdbadccbaacdaaccbdbdbcdcbcccadbcbddcbcacbaadbdbcacbddadccbddbdbccdbbadbbdbabdbddbbddbadddbcbbcbcccacdccaddaaaacbdccdbbcbcbacabbdcdaadabbcacaacabbccbddcdcbddbbabcbbdcbbbbabdbccabdccbbbdbbbdddbbcbddbbdcadcacababddddaadabccdbabccbcdddddbacbdbaddbaaaaabcadddaaaadadacabcacababdbbbbcbdbdcdcdaacbdcadaaaacccaabdbdadccddccdcdadcbbaadbadacdbdabdbababbbadcdaddacbbdadcbbaadaabaddbacccabbacaaacdccdcdbdbbcccbadcddcabcadbcbcbbdddcbcaacaddbaddddddcddcdcacabcddaaddbadbbabdcadcdacaacbbdaaaacbdbcbbbbdacbaaddcddcadbbabaabbdccbaabbdadadddcbccccddbbcbaccbdcbbbabacdadbccbddcdbadaddbddbbdccdaccdbccadacbccbabdcdbcbccbaadbcadccdadcdaacacccdbbdbcdbccdbbcdbcdccdcaccacbaaccbcdddadcccbdccbdcdacabadcccdbddbadcdccdcabadbabdcaadcbcdddcaaddaddccbdbacadbaccdbaccbadaacbabcbadabccbbcdbccbcbcccdcbaaacdaccccddcacddbccddbaabdabcdcbccadbbcbdbbbdccdcbacddcbbdacbdbdccdaccdbbbcbbabdaddacdaacadbbacdacdacacadbaaaadabacdadadadabaacdccaaaacbacabaacdaacccddcadbdbdcbcacdbcddbabddaccbaaaaabaabaaadddccbcddaadbbaddcaacdbdcacabaacbadaaadbddddcdcaadbdabdcbabdbbcaabdcaaabaaddbbbacdbcdcaacbcbbabaabacbaabbdbacdacddddccabbbdccaaaaddbbaaacabbdccaaabcbbcacbdaacbcbbbbbcaccdccadaabcbcbbababadbcddabdbdabacacbdadbbdcddcacbdabddabdcccbdddbbddadbcbcacdcddacacabcaadcadcbacbcbbdcacdaacdacaaacbbbabcccaacabdbdbacbdabdadbaabdddddbabdadabacddaabdbccbdbbcbacdabcdccbacdaccacddabcadbaaadaaaadddccdcccacccacbdbaabbcaccddabadcadbadddaacccbaccaaccdaacaddabcbdddcaacbcbcaccbccdbcddbccaadccaddddabdaccdcccddadbdacabcabbacadbbdddddadadcbccbbdcdabcadcaabcddacbcabcccbdacbaaacbaabdcbbacbddbddaabacaaaccbbdbbbbdaabaddbcaaccddbbabbbbabccadbddbaacbcdbbbcddacdbdacdbbdacabcaddcaacdadaaddbbadcddbdacccccdadcbababdcbbadbddcdcabbcbadbccabaabccacdaacbadbdadaadcdccccdaababbbaaccdddddbbaacabcccacbcaadcbabbdcbbaccdbacbccbcdabbbbdcccbcbccdccbabcbbddadbcaabbbaaababbbdacdcbaaddabccabadabaccdbbddbbcdddbbccdbacdddabbaddddaddbdababdcbbbcccbddabaabbbaadbdaccabbaabbaabbdcdacdcbcbccdcddadacbdddaccbaaaaadbadbaaaadcababadddccdccccbcbbbcabbdadacdbdaadaacaadbdadbbdddcadadacbcaccabbaaddbdadaadbccadbadcaacdcddbdaabbabdbdcbcbcbcdbbdcdcbcaadddbdacbdbdabdcacbdbacabbcbdcdddacbbacacaccbdaabaacabbcbdddacabacbbaaabdcccabcdbacadacadbdbabacaaaacadaacdadcbcdcbabbaacaadbddadbcdabcdbbdbcbaccdabacacdbcaabababbcddccbbaabacadadaaddcabbdcadbcbbdbdadbddbcadacccacdccabcbbaadacbacdbbcbbdbbbaacaccaaddbbcbbadbbdbbdacbcbbabaddcdccadccbbabbcddcdaaabacacacaaacabaaaaaadcbabccbabcccbdaabccdddabcbcdacdaabdaadcabbabaabcdccdcdbccddcdbcbbbaaacbadadddbbdbbddabbdaaabaaacabcdbdbcddddabccababbdbcadddcbabadcdadaaadddcbbdddcabbababbbacbdaabbcacccbdbbadadcbadcdabbadbddaccddbbabccaaddcbdabccbbdccabbaccdaaadbacddbdabbcdbbcddbcdaadacbbddadabdbbacccaaabdaadccadcbbacabbdccbcccdbbbaaddbadbbdbdbbcdaacbbddbddaaabdabaccdbdcbcacaabcaddacacdcbcdbaccbadddddadbaddabdacadabaabbaddcadaccccaddddaabbaaccccbadadabbdcccdaadbacbbcccdaababcabcdddadcbcbbbccdddbdcabbcccbdcddddccdbacadcbccbcdabdccbdbddadabaccbdcdaabacadbcaddbccaacacabbcdbaaaaabcabaaabadbabdcababdccbadbbccdddbdabdccccdcbdcabddcbdacbddacaacccbcabdabcdbcdabbbcbcdcadcbaacbcacdbccbaadddcdcccdadcbcdddcddadaacdbcacaaddbccdccbacbbcaaaaaaddcadacaaccdcddacbadcbcabacbdbdccbbdaabdaadcbcbcccbaacabdddbbacacbbabbcddddcdadbcdccbdcbbcdcdcaccadcdabcdadbabcdddacbbdcadcbbaadbaaabadbcbaccdaadbccbadadaaddbcddaaabaabcccaddccdcaacbbbbabdabdddbbdcccdddacbbcbbabddbdccdbdcbbdbcaaabddcadddabbbdcbbaadcaddcccdcdadbdcaacabbaaabcbddccdddccaacbddadbcbcccabcabcabdcbccdcddbacbaadddcabbdcdddabbabdacabdbbddabddaccbabccaadcdaccdadbbbbdcadbcdbbadbaadcccdbdcbdbdccbcababdbdccaaabdcaadadccbcacccccccdaddbcccadddcdccbbaacbaaddbcbcbaaabdaabaadaacadcbabaacacdbaccbccbddddbcdbcdababbadcaccdacccbbddccacbcbababadddadadccbdcdadabbaadbdabdcdabddaabdbcddccbcdbacccbbcbacdacbcabdbbaaccbdabadacaaaccdbdaddaaababbcdccddbadcbdbaadcdabcbabacbcadcdcaabdadcbcaabdabababbcabdddbcbcbbbcbcdcacdbadcbacadaccbcdadbbcaccbdacabdacadcaadbaacbcccbdcbdccbbdccadadbdbabbcabcacaabbcbbadaddaaddccdabccbacddcabcdccbadddbaaddaadbcdaadcdbccabcbdcbcbbdbdaddaadcccbbabaaadaaabcbdcdcbcbddcbaadbcbdcdaccabacaadcaddcdacdccbcaacccadaaaddbcbacabcadccbbbaabaacaddbaadbbbaccbcbbbcabcdcaddacaadbcaddadacddcdbccaadcbaccadcbdaabbdbabdaacbddbcbbabacadbdbabbaaddabcbddbcacdbcabbdbbabbabadabcdbdadabaddcdbcdabcaaadbdcbadaddcadaaadadcbbcccaccbdaabcbbdadaabbdcaacacccacdacadcccdbccbacdcddaccbcbccacdcbacadadbcacbaaabbccccdbdacadabdbaaccbccdbcbcbdacbbbddcdadccbbccaaaabacddadcbccaacacddadbbabdddabaadddbaababdadddbcdbcabdbddbbaaaccdacabcdacdccadccbcbdaddcbcbccdaacbadbacabbcdcdcbaadddcadcddddaccbbcbdbbcbdacaacadaaacacaaacdcaadcbaccddddacbacccabbbdcabcacdbbaaddddaabdcaccaccbccbbdbbbdbccbadccbbdbababadaaadaddbbdbddcddcbacdbbbabccbcbbadabcabacdccbbbcadcbdbdcbccadaadaddaacdabcdbbbbbcccbbdccbddababbacbaaaabbabaadadaccbdaaacabadacddcccbdaacacacbbadadcbbcbcbacdcadbaddbcaacaaaccacabbacabccddcaddcbabcaaacacdcaddabbdacacddddaccabdbdbbabbbbbddcbbcabdaaadcbaabacababbbaccadbccbccabdddabbbdbbaacaabbdaaddbcdccbadcabcddbcbaaddbcdbbdacdbcdbdabbabcadcacbbbcdcadbdaababccdaaabbaddbccdaacadcdcbbacbdcaabacbaacbacdddbadaacacbbadcacdaccacbdbdbdbaacabcdddbadbdaacccbaaaabcbcabdbcbabaabacdbcbcaadbcaacaddbabdabaddbcdcdcbbcabdaddaadaaabdabccadaccbaddcaacaaacacdabaabadacbbdcbaccbccccaaacbbcaadadaacadaadaabbbbddddbdcabbbbabdbaaaabcdcaddaabadabaabdcaaabdcaddabdbbcbbacdddbdbabadcacbcbaaadbabbbdbbdbdbcbdcbccabcddbaaabbabbdaaabbbccbcdcdcbbddacbdccdbbaadcaaabdcddabaccddacdacccdcbdbddbcdbcadbadbbdcbbadbccdacbcabbccdddcdddcabddbcccabdcdccdacbdbdacaaaabaadaadadbdddcabddcbccbaaacadccddbccccaabaabccdcdbddaabbacccbbcccddddcdbddabdbdbdbacccdcbacdbbacbccacdbddaddbccdbbaaddababacbbabbcdddabdabcabccdcabddbadbbbbcaddccacdcbacbabdddcdaddcdccdaccaabcaaaaaadbcdadcacbcaabbdcabdbcbcbadabbdcbaaaccdccbbabbabdbcdcdacabdddddaaddbbcdbacbbadabbabadccddcabcbabadadccbdabbacccdadaabaacbacabbacbbdcdcccccdbbbcdabbcadaaacaccbbadabdabcacbcddcdcaadccdbdbaddcdababcbcbaacabdcccdddadaabdcbababbcccbccbccabcdbdcabbcbadbdbbbdcbcccacdbacdcabdcbacaabadbccddbbadacdbcdbddabcbaabdbacdcdccaabcbbadcacbcbabacabcabccacdacccccdcaddcdbbdadbccbbbadadaabcbaaaaabcdddbbacdadddddddbacabbcdccddbaaacbcdbdcdbbccaacaabcdcaababdbcbadcbccbcbccdcbdddabaadabadbccbdccbbabaaadaaacaacbabccadabccbbbabddaddabbadcbacdabcabaddcdaadccddddcbcababcdbbcabbdaacddcbbbacdaaaadbbaadbabacaabdaabbcdacdccadcaddcbbcbcdabcddbbccdaababdccdbabaacbadabbdcbdbcabdcbcacadbacabcddbdcdcddcbbdacdcdcabbadaaaabdcaaccdbdabccabacbdbdaadabbddccabcbaddcdbcacdcdbbdddbadbabbacabcddaaddbaaadcadbdcddddcabbbcaccbbbabdcabbdbdddadcadbadacacaaddaddcccdaadcccdccabaabdbaaaacdbdddaccaadcbbdadaddbdddaddcccdcccbcdabddddcaadbdaddacccddbacaacaacdddaabacaadaadcaadccaaadadabdbdcccabdddbccbbbdaacdacacddcdadbbdbdadbdacaccabdbacdbdccccccdadcdcabdccdcacdaacaadacacacddbcbbcbbababdabccdcbbbcdcdbaabbdabbabaaabcaaaccbacdcbbbaacddbdbaabcdacadddccabdabadcbadbcddaccacacddcadacdadabdccdddacdddbadaddababcaadaaaddaccdabbaaaacbacbccbaadcbabcabdcadcacadbbbabaadbbbcadacdbbadccaadbdcadaacddcdaadcddaaddbdbddcadbbddbbaabaaddabbcbbbdccadaacbcadaaabdacaabdaddcacbcadadaddbabbabddaaadaaadbbaababdddcddbacccababdbcdadcbcdcadbaabacaaaadddbabdcbaadccaabcbadabadaccccbaddbdababbccddcabdbdcabdaabccbddcbbdcdaadcacbdcbddabacaadadacdcbddcbdcbaccadacbcdacdacbadcbccdcccdcbcabbaaabbbbbddcbbaccdaadaaddaaabccaccaacabcbcbabbaccdbabbcadaacacabbabdcabcbbacabdbaaaaddbddaddcddbbaadaddaacadbbddcadcbcddacdbcdccbddddcaccaadacddbadbcadcdbabbdcddacdbdcccaaccdcacaddbabacdbbdbcccacbbaddaaabadbadbacbadcacdaababbdadcdaadcbabbcdbbcdbdcadccddaaadaaaadcaadbdddbddabacadcabaadbddcdacdaaddcadabcddcdadddadcbaaadacbcbbbdddaacdccddbbcacbbdaccbdabbabbcdbbcccdddbdbdbcbdaaadddbbbdbcadcddaccdadccdcaabbacdabcccaabbdcbabccaccacadbacacdbdddbcddbaddbaaabcdaadbbcaabacbddddddbdaccbbaccccbbcccabdcbcbadddadbabcdacbdbabdcdccbbcaaadacaacbdbdacdbdbaaabaabbdbdbabbbacacbdbabccbcaaacbabcaccabbccbbccacdaacbccbcdadbabaddccdaccadcaadcbbaddbdccdccbdadbdcaaaccccacaaadabcacddddacbdbdbaccbacbcbacaaacaaddcbaaaaadaaccabbcacbadcdbbdcddccbbcadaacbaaacbaccddbdcddbbdbdccadcbbbaabcdadabccdccacadbccacbbcaccadacbaaabaadbbbdadcbdcddaaadbccbccdccbbabaadcacdddcbdbbdcaacbbccbdccbcdaaabcabddadddcdcbdaabdaccdbdccabaabdaaddbcccdbddaaaddbbdbdbabcaddcccbbbdadddcccddcabbcdbacadccbbcddabdacbcdcbdaddabadcbdaacdcdbddcbcbccdccacbaccdadadbbacdccadcbcddaadddadbdcaadbadbbaaaadabcdbdcdbbbcdbbbddbccaadabaacbbcaadcdcdcaacbabaaacaccaddcddcdbcbbdcdddccabbcbdaacdbabbadccccbcbcbaadaddaaddacaaddbacbcaddbbcbbcdadddbdbddacadbbbcaababbbbbadbdcdddcaaaadaadccacbdcbddbaddabdaadaddbcaccdababdaddddbdcaddabbacdccccaadcbdadabadcabdbbbdadbdacddaabdaaaddbbdabdcbabadadbbaabacaddcbaaddbdbabbcdcdcabacacbabaacbcddabaacddaacbbbbdccbacdbbcdabddcacbcaacaabaccacbaaadcdadbbddcabbcddbdbbaacddbbcadcaccdcabbbcbabcbbcaabcadbbabaccbcbcbcaddcacdcaaddbbabdcacdbdababdcbcdabacdcbdbccaccacacdddccacbabadddccbdcdcdccaaabdbaacacdcccbdccbcbbbaadcadddddadbbbadadacbcabcdcabbdbccaddcbaccadcccabdadcbbcddddabdddcbdcccdaabacbadadddbcbddadbcbcddcaabcadcbbabaaadbcaddcddaabcbbcaddadbbacdcbdddbbbdaaabaccdadabcababcbcddcbaccaddbaadcbbcbcacdcbdbaabcbdacbabdcaccbabadaabdacdcccadccdbdaccadbdcdbdcdabcdadcdaaacadabadadaddbcbaddddbbdbddddbdbaabdccdcbdadbdacbaccababddbaddaddcdabdabdcccdccdbdbcaccdabccbccabbadccbbcaaddddbbbbcdaaddbdacccabbcbbabdbdddaddbdadbccdcccadacbadcaccdccadcccadbccbabcccadddbbdadddacabadbaccdaddaddcddbbcddcccbbddcccacacdcccdacadbddaccbdbdbcbaccaadabdddccdaddadbcacccbcaabcababccdadcadacabadcaadcbbacadbdadbaccbbdcdddabcbbbabbbcdcabbacbacbcadbcacdddaacbcaaadccdbcbaaacabddaccdbbcdbabdbdccdcccbacddcbdaabadacbbbbabcacaadcabcbaabcababbbbdbbbcdcdbbadaddaadbddbcadddcdadcabaaddddadabcbaadddcbadbaabaacbdccaabdadabbbbdbdddddbbacbadbaabbbcabbccaccbcbbcbaddccdaaddacbbaadbcdccdabdbdcdabdbcbbcbaacbccabcdcccdadddadadcbbbbdaadccdddaaaacaadabdcdabbcacbdcdaddcdcbbdcaabcabaabbdabadadaccccccccdbcbdcbcabbacadbdbabaddccdbbabbdbddadaddcabddbabcadcbaadbcabbdbbadbaddccbaddcbabdcacabadcabddbcbbbabbddccabcacddabcaaabcbdababbacabbdcaadddaadbddaaacdabccaabdbbdcddcbaacdcccddbbadaaabacdbdcddbbabbcbcddacaddbcdaadbacaadcabaabdaccdaddabcdbbaddbdbccdabbbbaacbaccabaacadbbbcbcbbbbcaacddbcddaadcadadddabccbddbabbabdbbcbcacccbcabdcbddbadcdbabcaaabcbcbadabbadddbbdacdcdcacabbcabbcaabbdbbbcdadaaadbdcaacbdbcbbadcbccddbcbacddcbdcbcccaacabaddddcadacdcdddbadaaddabdabdaabaddaaabadbcababbabccadcdaadcadcbcdabdbddcddbaaadddabddddaababbbabbaaddaacdcacddccbadcabdbcdadcabdccdbbdabadabddbbddbacabbcdbaadbdcdabccbabcdadaaacadacbbcabaabbbbcabaaaccccbbccabdbbbacdacbdcbbacdbccacbcbbddabddbbabaddaaddabbacbcadbcacccddadbdddacbbbaabacbcbaaaddbacbababdcabaddcddcacddddaccabaaaabbdaaccbdddaccbbcaabccdccabadbdabbbdbaadddaacacadaddccbdabadadcdbdcbadbaccaaccbbaacaacbbddccccadabcdbdbddabddbcdacaabbcccbcdcaacccadcacdadddcbddbccbabbddbbddddcaccacdadbddddadbdcacbaccbcdcdddcadbdbabacdcddabdcccbdbcdddaaadacaccabaaadcddaacaacbdddbdbadbadbbbdcdcaaadcdbbabdabdcbcaddcdbaacdaccdacbbbcddcaabcddbacaaddbbddbcbdcabddaccdcacbabbbdaddabacaddccbdcdbccdcacddccbaaddaccbcacadcbabaddbadbadccadacddabcaaccdccaabdccddccbcbbbaaaaadccadcdadabdabcdadaaacdbaadadadddcaaddbbdccbdddbaaabbcbdbdcdbdadaaadbbbbbdbbcababadbbbccdabbacdddbdbabcdadabbdbabadaccccbbccadcbbcaacdcbccbacddabcbbaccaccddaadcabcaabbddcbcbbabbdccaadbadccbccbadcdddaabcbbbcdbcccddcbadadabcaaaababddacaddcdcddcabcbbcbcbbbcbbbaaccdabdabbdbadcdabdaabaaaccdbcabcccdbdcacaadccbccaccabadaadcbdabadbdadcbbbacddadbddbdddbdbcdbcbccdadcadaadacbbaaddcdbddcddcbbdbcadddacbabddabdbaadbdbbbbadbaadbadcccbadccccadaadbcbbaddaccabdddbabcacccadddddaddcadabadbbbccbadcccbccdddcdadcbcddababcbcdccacacaacaccacdabddcbdaaddbacaacbdacddabdcacabdadcbccbddddaadcdaddddddbadacbbcbdadaddbbaacaabbdadbadacadabdbdabdbdcdcababacbcddacdbbbbdabdbcdabbbcdcadbacccdbccbccbddbddbaccccbcbaabbdabbaadcaaccdcddcddbdbcabdcabddcdcadabbdaabdddabaaddcaacaddbdbadcdbcbbcddadaddbbcbbabadccdbbdcabcaaaddcbacbdcbabbcdaddbaaadbcacccacdbbaacaabddbcdbadbbaaabadcdbccbdcacbbadddabababaadbabbabddddddaaadaacabbbacaabbaadbbbadbdddadbcadbdbdddbdbcdbaacbcacdbdacabbdcbbbdccbaadcbdcdcdabbbacbbcbdcdcdcdaaaadcbddbcccbbcbaaaaabbcaaacaddcbcacbaccacbbbaaccbdacabbcbaaadcbccadbbdacababdddaabddddbcadbaaaddbabcbaccccdbdaddcbbcadbcbcdcccbcccbdcaaaaccdcbdbcacdbadbdcadccacaccaabbccdbabbdcccaadbadcaacbcdabbddbacdcdbbdbdbbbadbdadababacdcbdbdcbbbddbdccbbaabcbcbbacdcddabcbbadabdccbacddccdadccadacbbaabccddadddadddbaadddcadbaaaddabbcbabbbcadaacaaddccbcdddddbdcddcdccdbabbddbdcdacbcabdddcaaddbccbdbdadcccacaaaacaacabcddaacbccbacadabccaccbcccbbbbdcabdcbaccaababdcddabccbabccbcddaabbdabbabbbcddaddbaadddaaaaadaadcaabdddbdbbdbaabaaabadcbbabbadadccaccdcdbacbdcdadddddabdbdaaaabcccddaddcabadbdbdabaacbaddacabddddccacacbadcbbbdcdbcbdaacabbadabbdacbcccddcabddcadbaadbbdcadbbadcaacadbdddcbdacccaabdcbbccbcccddcdcdabbcdaccaddadddabbcaaddadbcdacbbaacddaadadbbbcbbababaccaacdaaaccdcdbadbbcadccabcbbbdbdcdbdcbacdcbaabcccbcbaacbcbdccdaddabccbdbabdaaacbacbaabbcbdaccddcdcaabaadddadbccaaaadddcdbbacdcaaddbabcdcbcdacddacbabddcbddcbccaddccacbaaccdaabadccddaddadadacccddabcbaadcbcabbbccbbadccddbbcbdbcbbabdaadbcaabccccdcacaabbadaadabcccbcadabcbaacdcbbbccabddddcaccadadbbacbdbcdacdcddccbcbbdddbccaccbabadbbccccaaadbbcdbdbaadcddcdcdddbcdaaddacabbaaaacbddacdcbccbcabacdbabcdcdadcadbcabadddbbccdcddbbbbaabcbaabbbbbdbbdccbdabdbcdddbbacadcddcbbbbcccbdbcbcbddddaddbcabbdbccdabbdadadadccddddcbaddaadbdadcdadcddacccabdccacdacdacdbacbcbbbddbaacabddddabdbababadcbcaabacdabbbddbcdbdcccdcddabdbabbdaddbdcdccaaadcadbdadcccdcccdcdcbcddcdcacaaacbccbccdccddadbdccccddbbbbcacdaaacabdcaaccbbadbdcaacdbbcbaadcdccdddbdbdaccabcadcbabaddbabcadbdddbdacdbabcdddcbcbaacdcaadabbcccdbddcddcdcbdbabccddadaadbccbdaabdbbcdaaddcacaaccaadaacbcbcdbcbaaacbcdcbacabdcdcaadacdddbdcbccababbbddbdadbcdddbaaacbbacddaaadcaccbbdaabbdbdabdbabbbdcabdbcabbdaacabcbcbbcdadaacacbaadaacadddaadbbadbbdaaddcbbaddadcadaabbdcdadbbacbddcbabaaadbdbccabdacaddbddbbabbccabbdbaadddabddadadddccdcaddcccdbdcacaccaaddcccaabbaccbdbabcdadcadaaaddbcddddbbdaaadccababdbdacadbbccdaddcddbccbccaacddaabbdaaadbdcdddbcacdcccdaaaaaabcaddaccacabbaadcdbbdccdcabdddbabdaddcdbdadababcccaccabdcdaadbbadbbcbabaacacdabdaadccdadcabbcacddccbcdacbbbccdcdcbbbbcccddddcccbdaadddccbdddbccbaccddbdabaccacdacbdcbccccacbddbdbadaacbddacaddddbccdcadcdabcddbbdcabbbddaadbbaaabcbcbabcdbcbdcdbbcacdaabcabacadccdaddcdcccadabaccacacacaccdbbcaaadddcdcaacbcaabbbadbbaaccadbddccccbbadccdccaccaadbccdabdaaaccbacaddaddcaaccaacbcbbdcbccbddbbcbacdbcbababdbbbcaadbdcdccdaaabdbccadbcbcdddcaacacbbdcaaaacbddacbdbacbddbcdaccacccaccbbdaaaddcacbbcabbdccaddccddddcdaddbadbbdaddbadbaaccbaaddaccbabadbcbdbcbccdccccbdaababdccbcbadddbddcdddacccbacadcbaccaaccacddbcbbcbaddabcacbdbccaadbbaccbcaacbbbaadccdbacbaacbbccdaaaccaabbccaabcaacccaabbcdcdccbbbddbdbcccdadcbbddbaabdccabaabcbbbabcadbdbbccddbbaabbccdbbaacddaabdbabbcaadcaabbabacadaaaccbbccaadcadbadcdacabddabdcbdababdaabcdcbabcaaacababdadbbaaddacdcccbbcacaaacddbddbcaacdccddcbcdbadcbaadacbabbaaaadbcdcacaddadacdbdcbdcbadabddacddcbccccdbccdbccaccdacccdcbcdccabcdddaccbccdbcccadbcabbdbacdcbaacdaddddbaadcaccdadcaddbadcbcadaabbbddababbdbddddbabcdbccbbdacabdccdcabcadcdabbbaccabaabcaacababbcbbbbdbbcbabcabcadccddcbddbcdadcabaddcddacbbcacddacacaaddcdbaacbcdbddcdbdbcabaccacdbddccaccaccaacacacbbadcdcbabdbacbcaadaaaacbaaaaacaacdaccdabbdccaacaddbdaabdcbaaacccbaacaaadcaabcbbbbdddbdbcbddabbbabbaaaaccacaaabcdabdacabcdcbbaadcdbbaacbadbacdaccbaabcdcbdcbdbadbbbbcacbcbcaccdbabccacbbbcbabacadacaaaaaddbacdccccdbbcdbcacacaaaadbabdabcabddadccddabbdbbcbadcdcbcbdcdcabddbbbbdbbdbadbdadbdbbdbbaadadcacdcaddcddcdacabcdaccbcddacaacabaadbbbdbdaddcdccadacadaacdcabbdcacdadbcdbcbcdcdcaaadacacdbccacabcadccadbdacbcaddacdaaacdddaabdbdcabbdbdbdbadccacdbbbcdcdbbcdcdbbbacbbbcbbabdccddddddaaccbcccbdbdcadbbcdbbdabbaacaccdcabdaadaddcadcacacddcacdaddbcdacddacdbabbcbcdadabadccddaabbacbccacbcacbcdcadddacabcdaaabadcaddccbaccaabccacbadbdaccdaabbaaacdaadddbadccaabdaccdbdaababccabbbddadbcdbddbacadcaacddcaadbdabdbcdadbbdddcddabaadaaadcabcaacddadabddcdcdddcdbaabbddbbacdbcdadcbacbdbdaaccabaadbbcbadcaacabcddacdaacbdbbdcdbcdbdddabcccadbddadcbdbdacdbbdbcaddcdaaccbdaaacaccaccadacbdaddbdaccabddcbdcbbcbdabbdaaaccdcabddacadddcbbdabaacbbbdadddbddcdbbacdcddccbadcddabbccbacbccbbacccacaddabbbbbadcbdbdcdcaaddbdacabdddadddabbbcababbbdddbbaaaacabdacdabdcbbbaabcacdcaccbaaabcabcacdcabcbcccbbacdaddabcdcdbccddcacdaabbccdbdacbacdbcccbdaacddbadbbabdbdaddbcdcadaaadbdcbccbcddcdacadbdcbacabdaddaabbbaabcbdbbbccdbccdccbcbbcaaccdabccbccccdcbbaddbcdacddadccddabaacbadccddbcaccbbaddacadbdbcdcbccaababaddbddbbadadcaadbbcadbbcacacbdcccbcaabbabcacdccccbacccaddadabdcaccdccbbbccbcbddbcdbabdbbbccaddcabbcbcbaabaddaddbbdabdbdbbcbcabdbbdddcdabdcbaccddcaabaaaccaaabdbddddccbdbabadddbaddaccbcacbdbdcbdacbbbcbbbdaddcadccaabdcaadbadbbcddcdddadcdabbaddbccdcbababccadddbdacbdcddaddccddbbbbcbdcbccadadbcdccabdabddadcabcadaaacadcaabccdbcdbbbcadaabbabcaadabccbddadddaacbadadacbcbaabccbbaccccbabadddddadbacbbbaacdbcccacccbbbacacdabdaaadbdaaabbaadddbabdbcdaaadbdacacabdbdccbdccabaacdcdddbddbdabcddbcadabbccbcadabaacdaacbdaddacdbccbacddbddbcdcabcdabacacbcbccbdacbbdccbbcdccbabbcdbcabdbdaaaacadcdddaadbacdbacabcacddcabaaddacdbdaddadcddcdddbdbdabddccabcdbdbcddacbbbadabbbdabaddbabdcccbccbacbbcdadccbdcdbdabacdcdcabcbbbcdcddddabbadbcaddbdbbccdabcdbdbcbcbabbacdddcaaaccbaccdddddbcbbcdbabdcabcaabaccdaddbcaacbcaaccabddddcdcddcaddbadcdabccddcccabaddcdccabdabdbabcbdaddbbabacccbddabdaddacaacbccddbbcbdabdaccdabbaacdaadcacdbacdbbdcbcddbacddbbbbbbdabbdadcbaaccdbaccbabdccabbccdcaccbadbcbcddaacdddcacbccbabaabdabadbcadcabcbbbcccbddbbabbbdaaacccacccbadcddadccaabcddbacdaddbdbccdacacabcbdadbbcabcccbacbbaaabcbaacdbbbcbcddbcadcaaadbdccbcdcbadcaccadcbcddacdbbcccbdabbaabdcbbcccdbaabcbbbaddcbddbadddabdadcccabbacaddcabacdacaddcbdbdbaacbacabdcddcdcacbbbbcbbbababbbdaddabcddbbccccbdadbccdcddaacbaaabadcddbdaccbbbabdaacbaddcabbcabacaaacabdcddaaadaacbcdbcccabbdccaacbcaadddbcbbdaabcbcabbbdbdbdcbbcaaadddbdcacbbdcbccdbcdccbabdbdabdbcbbdbbadacddbddccddbccabbadbbabdddabddabbcbdbdbcacdbbadbabaacddbcadccacabcdaabcbdcbbbcdaaaabadccddacabdaaaccbabdadaadddbacddbadcdcbbdcbabccacddabcadcacacbdacccccdbddcbcdaabdbaaabdcbdaadbdccbcaabccadbbadcadbbdadddbbaabccdccadbccbabccbadaacadcbaadcdccbdacccdabcddbdabaabadccdccdadacdaccacaadacbdddacaccbdcdddccdbadabccdcddbdaddccddbdbbacaacdbddabaaadabbddcbdabaccdccdccbdbbccabacacdbadaacabdbcaabcdbacbcbcbbbbaadccbcabadbcaabdcbbcbcdadddcaccacccddacbbccbcccacaacacbcbdcabbbdcbbcadababababcaddcbcabdcadcadadcbdbbbbcbacbaabdacbcbcccbabbdaadccbddccacbaccbbdcdcbaaacaccadbdadabdcaccdcdbcacabaaaadddaccdbbcdbababbadddaddcacbdbdccbadbcddbbdbadccbbcbcbcbdaaacaacbdacbbcadcaccacbcccbabddcccabbcdacdabcbbdbacacdabddcbdbacbadbacacdcdaddbacdabaacabaabbcabcabdddddbddccbcdddddcbddcaaaaadaccacaacaaddacdccbcacddcadcdaddadcbaddddddbaabdbdbbdbcadabdbadabcabdaaddabbccdbbccbdbbaadcbaacdddddcabaadcaacbbadaabcacdbabcbaabdbcdcbcbccaabbabddaacdbbdcdcdbdcccddbaddddcabcacabbdacbbdbabcbcdadcddbaaacbbabadbccdabbaccabbccbaacccdaabdabdcaddbccabdcacdabbcabdbbdaddbdbcdacdcdbbacbaabaddcacdaabdddaaddccbcaaacadbcccddacdacbccaddadcdbdcbadacdcabadddaadcbcbdcbbabcdbcbccaaaadcbbaccbcbacdbdcddbbcbbbdabbcbdaabccaccddbabdcababbabaacccaabddbaaaddbdcbcbcabdccabccbadddadcbbacbdcabcaccabbbccdaddacdcbadcccaadbcaaddacddabcdabbbaabcabcaacabcdbacbbabbcbabbcdaaaabccbcbcbbcdbdaaabcabcdcbdcbcbdcdaaabbcbdadcabdcabdcdbccbacdbdaddbabbcdbdcdbccacbdcbdbcdcccdaacbccaaadabbcbacbaddccadbdccddaabcbabbccadadbcbbabcddcbbdbdadcbabdcdccdcabdadbdbdadcccdcddbadbbacabbccdabbdabdcbdddaaaaccdaaaacbccdbbccbdcbaccabaaacdcacabbbddbbcadbcddccbcadbdbacdddbcbdddacddccdcdaddddcbcdbdcdabadabcbccdcaccdbddbddacddacccdcccddcddcddccbdaaddacdbbbcbaaabdbacbadbbddbdbadaddbddaadcadacdcccbdccccbcdbadbdbbabccacdbbbcacbadbadadadcdbcaabdacacdabcbdaabccbdbdacbdbddddbcddbcbcbcbadacbbdcdbbcdbdbddabdabadcaaddbaaadddabaacdbddddcaacdbbaacacddbaacdddccdddccabbadacbdcabccdbdbbbaccadbccdacbbbdcabbccbcaacccdabdcbcdabadabbbccccbcdaaacddbcbadccbabbbdcbcbcabcacacabcccadacddadaddaaadabbdbbcbaaabcbaccacbabbddccbdccbdbcdcacccdbcdbadddccacbdaaabadcbdcabcabadcdbddacbccbdddbbaabbdcabbcbbbbdacbbaacabadaacabdddaaadccbadccccabdbaababbcbdcababdccaccbdacdbccbdcdbbbbbcbacadcdccbaddbccbcbbbcdddbccdbaacdbbdbdbdacbabbccabaaaacacdcdcadcdddaadabcbbdbbaddbaadbcaabdcccbbcdacdaaaccdadcbcbccbdcbabddcabcbddbdaabbddcdbbdcddcbcbdcddcadbcbdcbacdadaadbbcbadacdbbacbddddbcccdaabadabadcdabdccacbccacadbbccbcddbbdbadabbbcccbdaadbcdcddadadbbdabbcbabdbacbdbaacdbaaaabbaacabdbadbbdbdccdddbdccbaddbabccabccabcabaddacbdaaaacbdbcbadcbbacaadccdacdbdacacdcccccbcacdbdaacbdbccbadddbadaabacddbdaccbabdabdadbdddcaccbabababadcbbcdcbbaadbddbbacaddacdadbadaacadbddabaacccbcabadacaacccdbccdaabcbacaccbcddbaaccbcbccdbdadcddadbcbdadbdbcbdaacacadcddaddcccccdbdddccccacbcbaddbdabbbaaddccbcdadbbababdbdadcdaadbcbaccbdbadaabcdddcccaabcaadbdbdaddadcabcaaaacddbbadddbdddbbccdabbbcacbbcadcddbdaabdccbaaaddacdcbbadcccdbabdcabacdbcccacccbdbcbbacddbddacaddcdbcdacbaccbabaaacbabcadcddbacbbabdabadcbacaaccdbbadbcaacdcdddbccbbcabadaccdbcabbbbbbdaddbdcdaadddbcbabacccdbcabdbaddccbdacbcbbabcacdbbaccbbadababcdbcacbdbbbdbdaabddddbddbccdaadcacaaadddbdbaacacbdcacbabcaadbdcccdacadbddcdcbabdcbdabdadacbdcddcdbddcdcccaccdcccaabadbccbdcbdcacbcddbbadcdbcbaabaddbccbdcbaccaabaddddccaaccdcbcadbcccacaaccdbdadbcdabdacccddcacbcbbdaabaabdddbddbcdabddbccdcdadbacbcdacaaabbcccdbcbdbaccbaabcabaaccbbdadccdacbddcacbbcaccacaccbbcbbcadadcadaacdccaaabddccaabaadccbccccdddadbacdcdacadcabdcbddcdbdadbcccdcadcbabcbaccacbbcabadaaccabccdbcdbdbaacaaaccabbbdbdbbabcbbacbdbaabddbbbddbcbabdacbcdbadcacbadbaaddbabcadaadbccacccdadbddcbcdcbaadabababcadccabbaabcbcabcbcbbacdbcdbbcbaabadbbddcdbadcbaacbcddddcbaaccddaabbdccdccabbcdbdddbaccbddbdaacdddbbaddacccddcaddbdaabcaabcbddcdccdbdaabdaadbdddabcacbddcaabaaadbdccaababacaacabbabdcddbddccbbabcbbcacacabbabcaaaabdcaabadcdbadddcdcdaacabddbddddcdbbdaaabcccadcbbadbdaaaacddcbdabcdabcdcbcbdbbadabdddbdcadaabbaaccacbdaacabddbdbbcabcabdacddccabdddccbcdccdaaadcbccabbabaccdccaaabbbbacddccccbcbcbdcbcbbcaababcbbadcbdcdabcbbddcbddcabbbdbbadcadcacacbbbaccbbbcdbbdcacacabdbccbacdbaacddbbbddbbdacbbddadcdaaadcaddaaabdccbacbdadaacacabbbddacbacaaabdcdbdbacaabbdbacccbcbcbdadabdccbaddacccacbaacabcaddccbadcddadbbbbcddbdccbaadbddccaadbcccacbcbcbcaadbcbbdcabacdbbcabbaabcacdadcdbbaadacdccacdacabdbdbcacbbadabdccddcabacaaaccadacbddbbdbbdabcbbdabbadaadaccdadddadabaaabbdbdddaadbddbbcabdadaabacccbadaabbccdabccdadbddccbcdacdcacbcaacaccbbccdacaaccaadadcaccdabccadbacaddabdddddbbbacabbacdbbdcbbdbbbcccdabbaddcdabbbbdacaacbddbbaabadbcbdcadbbdbbcddabcbbdccccccbccaddddaccbacdaacbdcacacdcaabcbdbabbcbbbbaadabadabbcacabbabcddaaabaadaddbcdcabbcaddabaaadbbcccdbabbbbbccbacbbabcdcbbbabbcbbbcbddccbbdccbcbdcaaddadaaadadbdadbacccbdcaadacdabcabbaadcaddbdbddddcdbccbbdabdbbcbabababacdaacadbcdbadddadccaadabcdcddbcbbbbacadbbdcdbacddddbbcdcbdbaaacacbcdaadadabcaaaabbbcdddbbbabcbabcdabdcddcbaabadbadcadccacabdbbcddbababcabcdccbbcbbcacbaabacccdbcbdddadabcbdcccdbdcabdadaddbbbdaacbdddcadcddababbcbbbbbaacbaddcbbadadbdcbabcbbcccaccbbacddadddaddaadccadbccababacaccbcadabbcbcdcddbbacabdccbdcdbacdaabcadccbcbccccaadddcbbcaddcdbcccbabacddcdccacbbbbdacacacdacaccdbdabbbdabddcadaaacbbaaddababaddddacbddbccbcaccbcccdbbccdbdaabdbbcccbbdbbccacabbbcdcbddacddbbaaabbcbacacbaccdaaaddabaabacabadddccbdbbbdcbbaaddbcadcdaadbbabbbdaddcbbbadcdbdcaccacdddcdcccdbcaabcdbcadcaaccbcddabbdcdabddcadddacdcccccdbacaccccaacbdbccbbddadbbcdbbbacbdbbaaaadcdadadcdaccbcccdcbadbcabcbcddabdacadcabaadaaccaabacaaacadaaabadbccbdbbddcccccdbbaadbacbdbcbdbcaaacbbddbbbacabdbddcadbdbdbdacdbbcbdadbbacacaddddccdccbcacadaccadbcacbbbaabcbdcaabcbdbdbaabddbdcdacadaaacdcbbaaabcbdcbbbcbdbcadabcddbdabcdabcbbacccdabcaadacbadbdbccccbddaabccdbabcacdbcadddaaaacdcacddbddbcdbacaadddccdbdacdadbddacdadddbbdcbbcbbcddcdddcbdcacdbcddbbababcddacbaabbbdbbdadbdbcbcabacccdcabacddbbdacbcbdbabcddbdbcacdccbbbbaababdbbcbbadddddcdccdabcabcdaddbbdbbbdbadabacddddcaabaabddbddbdbcdbadcbdccbaabdbcbccbaaacbcacdaddcaddccddacabcaadbdcaaacbdcabdcbaadacbcbcbaaadbacbbbdadcdaadaacccbdaaaaccddcbdbddcaddadbcaabaacbdcbdadcdcbdaabcdadddacdabcccaabadcaaccbdcdcadccacdcbaaacadcccabaccababdccaacdbcbdcdddbbdbcdacbaacccabbcabbcdcaaadcdcbdabcccbddcdaadcadcacbcbbacbacdadacaabcabbddaddcbddcccabddbddcacdbbcccbbdadbdbdaddccabdbdbcdbaaacbbcdbaccbacabbbcdadddcbddcbaadcdbacbbbbdddabdaadbcdaadccdbdbccadbdbbcdcbbdaaaccacbbccadbbdcaccdaadaadcdabcaaadccbcbaddacadaacbdbcacbdaadcaababbdbdbcddadbbbaaadcaccadbcabbcadcbadbaaadcdcadcbbabadccaddbababacdacbdcbcabadbbddcdbcbbbbddaadbdcacabacbddaccdacbacbbdabdbdacbbcaadacbabacbcdcbaacddbbbacdcccbcadcdddbaacdccaccaabaabdbcacddbccdadcadadbadddadabaaccdcccdababcbdabbcaadbbcaddaddadadddccbacdaccaadbdbaddbcdadabccccadbcddcdbcdbdcbbaabacbadadcadbcbdaaccbccccbdddcccdbbaabbaacacabadbddaadadbbdabcddacaacccdcbcbcddddccddddccaabbbbaaaddbbbcaaddcdbcbaacdbdaacbadbbbccbaacbbbdaabcdbadaabcacaccacabcdaccbdaccdbadaaddadacbcdacccdcbbccbaadcbcadabbaacacabbabcccadcabbbcbabdddabbbbbcbbbbcdddbcbdbaadadacdacabdccdbddcaddddbbdbcacaddcbbabddcaddcaacadaadbcddadddbcaaabbbbbbddadddbcaabcdbaacdcbdcdaccbbdcbbdddacdadadadabddaabdcbadccaaababdadaadccaabdcccbcdacdabddbccdbabcbabddcbaccdabdacbdbaadbccbaacbbbbcacccdcbccbddcdcaabcbbcadbcbddabadaccbcbdabdbbccbaccddcdaddabcdacdbcdbcbcbbbcbccbacdbdaddcbdbcdaacabcacbdbbcdbcbcdbbcdbdbcdcdcdaccccaaadaccbadcdabddbaddbdcacbccabcbacdaaabdbbaaacbadbcbbdaadbbadcbdacacdccbdaaadbbbbacdcabddaadbadddadabbdaaaacadaaaaacbaccacdbddddddaaacbbcdccaababaababdbdbabacaabcabddccadbddaabdbadbbaaaadbbddcacababcdcbccbcaaccbaaabacbdbcbcddddccdbacdbaadccdacdcbbdaacabdcaaacddadcabbabdaaccdcbdbdbdbcdbdaacbcdcabcbbddaddacccddcbbbaccabbbddbbdcddcbabbcccbbbadbbacdacbbbaccdaccadcaadcbcbbabdbbdaabadbdacdcbaadbdaccccbcbbddcdbcdbbabdbabdacabddadbbbacdccbdbaababbccbbbaaaadadbabcdabbcddadbbdbaaddbabaddacdabdacccbdaadcccbbaaaaaaddcaaaaabcbcccccdcbadcbcaacabddbdbdbcaddacaabdadcaaddaaaaaddccdbcaabcbcddbdabddccabbcbcdccdaabdaadabbdbccdcdabaaadaddbbdcddcabbdacaaacdcdcccbdcddcdbddbabadacaaaccaddddadcddddcaaabdbbaccadbbadbdcadadcdaaaaaadabdababcacabaccaadcbbcdcdbadcbbadaddddaddddbbbdbadababbbabdcdddacccdbbaaabdbdadacccabdacaddbbababbacadadbdccbcdddddbccddabccbaacacbbddaacbadcbcbdcbabbdadcccbadadbadddacbacdabbddbdabcaacdcdbcdcdacacaddadacddaadcaccadbcabcbacaaadbdddaccaacddaadaadbdcdacbdddbadaddddabccaabbacccbcdbbdbbabbdabdbcdbbacaccdbbdccdcbddbbadcaaacabcbaddbabbbbbddcccbddcbbbcdaadacaddadbbccacacadbacdcdbddcbaddbacdbcbbbcabbbdacdadabaababdcabaadcabadbbacbabdccbdbbdcdbbccbaabdabdbbbcbdbcbcaddccbddcdaacdcadddcbdaacddacacaabbcbdaacbabaaabbdbccabcdbadcaaaaaabdcdcbccbbbbacbddcbbbdbaaacdcdcdbabddcbabbbcccdabdccccaadccadccbcadbccaddabcdbdadcdcabbbcdabbdabdabadbcdbcccbaacbaccbbddaaaabbdcccbccddbacbdbdcdcdabaadbcaddcaddbaddadcdadaddbaacbaadcccbcbbcdacccbccccdadcbadabaacdacaabcdbcadbcabcacbaadbacbacccbacbabaddabdddcdbbdadcbdbdbcbbadccdcdbaaabaacacbadbbddadcabddbddacbdacbcdcabbaacababcddaacbbdbcabcdbbbbaaddaadbdddbaabddaddbddddcbdcdaabcddcbabcdccdbddaabacaddccacdbacbcbbaaaacdaabbdbabbabcdcbbbcbcdcdadbaabbaaaadbabdaabcbcacccbbbcbbabaccdbdcabbabacaddddbddbdbddacacbbadbaddacbbdadcbaddbcdbacabbccabbaadcbcdbbdaabcdbbbcabdadddadacdbaaabdacbdbddbbaadbcdcacbccddddcccbcbbccacbbbcacdcbbbcabaaaccdbbadcbcbabcbdccdddadabbdcabadaccadccbaccabababcaccabbadbcbdadbdcdabbcdbdddbddcbcaacaaacbddcabbcdbbcbacddcacbcbacbdabcadacaccadbadaccbbababddbdcccbbddabbcbdadabbcdddabacdcdcbaabddcaadbbccbbbccbcbcabdacddbdbaadcdbdcddcacbdbbccccbbbdbbbbcdbadabbcccddaabcdddccabcbccdbccacbadddaacbabadcbbadcbcdbaabdaaddddbbbcdabbadbccacadcbbbdcbbccccadccabcabacacdcbaccababaddbcdbcddbccdddadbcabbaababcbdddccbadbdbbbddccdccacbddbbdddaaaadaccddaddabbdcaadbcdbcdcbbadccacbbadcadcbdccabdbbbbdaddbbcbbcbcccacbcdbabcacbcbaacadccaadccbabdaaabddadabcabbaaccaddaacddadadaddadcdbabdbbbbaadcddabacadacdcdabdcddaadcccaaabcccdbdbddbaabbdcdbdbdbdbdabadcbcaabacbddaabacbdbabccacccabbcdbbdabbbabcdcbbcccbaaddcbccdaadddcdccdabaaaabddabbdbaabaadcaaacdadaacabcadccdadbccdbcdacacdacbcbbaaaaaabaacccabcaadbbabbaabbadbaabaababdbadbcaddabcbbccccabbddcbcdcccbaadabdadababaadcaabdcaddddccdcdcdbccaccdbcccbaaccadaaccbacbcccdbccabddadadaabbcdddbaaaabacbcbaccadcbddabbcdacaadbbabbbcadccdbaadbdcdcbdcbbdccdcdabbccdacdcdcaacdbcbccbbbaddcadadabacaaacdddddddddaabacbdccadddaabbbbdbdbbcdaacbdabbbadddcddcdbcadccaadcdbbdbbbcbdcbcbdbcdddcdddbcadddcaccacbbbddadddddbcaddddcbbbdddbbcbcdacdabcdbbdbadadbbbdaccdabcddbaacbcbcadcaabbcbddcdadaaacddcdbdbdbdccbcadbdcdccbbbabdacbccaccadbadcaacdcdccbcaaaccbadcccdcaacdabdcdacddaccccdaadaddaddccbadbdddabbdbcaabcbbdbcbadbdcdabddcadbadabaabcbcbdccdacaaccbbddaaddbdbcaacbccadcdcacabddccbbbacdcacbcaccbdabbacdacaacacaddadbbdcabcbabbcaadbdbaabcddadbaacbcbbcbacadcdaaacacacdbccaaacdbdddccaaaaabcdacddbbcdabbbbcbadbdbddbabddbcdbadcbdccbdbbddbcaccdcbdcbbcacdadadbdbcbbbbdbabdbcbbdaddadadbbaacadabadddbadcdbccacbbdcddcaacccbdcbcdacddcbabbbbdcbdccbaacbccbcadbcdcbcabdddddddaddabbccdadadbcacccbdacbcccccacccacabbcdbabcbabbddaaddbadcbadcacccacadacdaadcacdbcbabcdacccdcbcddaaacbbacdaccdbbbcbbcbdbbacbbcbcbabcabaaaabbdabcdabacacbdddbabdacadccbddbcddcbdbabaddbaadddaacacadaabcbaddbdcacdbbbbaaaddabcbaddcbcabbdcdabaabcacbcccbcdbdadbcadcbbbbcdbcadacadcdaabcdacababdbaccbaaadddbdcdabaacbbaaabdbdcdadadbdcabbcbddcaacdabacbaccbccddbbbbdccddcdbcbdabcdacaacdcdaddcbcabdbdcccabcadabdcbcdcabbbcacaddddadbbacdaacddccacbdddaccdcccdbdccbabdaadadbcddddacaacbadddcbdbbcbaadbacbbdacdaddbcbabcaccaabbadddaddaccddcdaaaabaacbccdcbdacacdaabbdbbdbabaaccddcadbabcaacccaadaacaadadbdbdbcaaaadccaddbacbcbccadabbdccdaaabcdabaccddbdbdacbdddbbdaaadcaaadadbdbddbabacdbacbabcdaabdddaccdaddccbaadbaddabdacacbbbbccdabadcbacccbaacddccbabcbabcacbccabbdbadbbbabcadbaccdbbcacadbdbbcdbbcacabcccdaabcdacdcdccccbadccaadddddacccacbdbbaacbddbdccbabaadbabababbbddbacaddadbcdabaaccdbddbdcbdbddbdbdcabaaccadcdbcbacddaaabbdbcabcbdccbabadcadddbccdcbbcbcbacbabadadacdbdcbdaacddcbcddacbddaaacbccaddddbdcccbbdbddbcddbbdbaadbcdddaadacbaaaccbabcccccaddcbbdacbadaaaddcaacaacaccdbaadccbcacbdacdcddacdcbacaaddabbcdacabddbcdbbacddddbacdababbccabcadbbbcbdcbcdbacccabdbcbdaddadddcbadaaabcddadaabddddddaddbdcdddaaccdaabdcaacaadaadaadaddcdbbadacbbbdaacaabbcdababdabdaabbaadacbcbdcdbaddddbcbabcdcbcbacbdbababbcdbdbbaccdcbdbacbacbdcccbbcddbcdcddbaacabcddccccccabbdccaadbaadbaadccccacabbbcabcbcdddabbbddbdbbbcbbcadcacbbcbcacdbcdacadaabaddbaadaadbccbddcccdbddbadacccacaddcbdcdcbbadbbaaabbbbacbcddcccddccdacddccaaadbabdcccbcccbcaddbabcaccbcbabdacaabaaccbbdababdabccdababcbbcccdaaacccccadcdadacdccabbbadbccdbbacadadbcadbabbbacaabbbbabaddbcdacbcdcadcabaadaacdcabdbcbadaabcaacadcdadabddcaaccdaadaacbddcbdccbaccabdaaccadacdbddbcddbcbaccbcbcaabccbbdbabcbdbdcdddcaacaacdadbbbacadddaccdddcdbadcaaaccadbbbdbbbaaadcdaccacabbacadaaadbabdcadbdbdcdadaadccacbdbcbcccabbbcdbbccbadddaaaccdacabbabdcdbcbbcbacdabadcbddbdbcaacbdacbaaaabdbcaadddbddbdacbdbdbaaccbdcccacabddbacaacbddadcbdcccabdcccaacdddadacacadcacbaabadbbababcccabbaacddacdcccbcdcccbbbbbdaacdcadababaddddcdaaaadcabbadddddbbccaacaabdbcdabdbbcccdcddddcdccabcdbcabacdacbacdcabadbdbcabbaabbcaaaccbbadddddadbacababaabbbdadccbbcdacdccadcbbaacababccdcbdadcdaadccabaacbddcbadbcdcdbdcbabdcdbbcbcddcbcdccdadcbbbbbcabcbcccccbbbababddbbbdcdbabaddcaacccddabacdabbacbdddddaabcbdadbcbacadbdabacdcdddcdccccaccaadaddbcbdaddbcbbdcaccdabdaccadccabbcdddadcdadcbbaabbadacbdbdbdcbcadbdcccdbbabadcacbdcdccdbbddacaaacdccccaddcdabacdcbddcbacaaacbccbcdbcdcdcbccdbdcabdabaccbccbabcbbdbccbcabcadaccbcccdbdccaadadcdddbcbdbbccbccbbddbbbddaddddbabbaccbaadabcbaacbdddcdddcdbbbccdbcbbadabdcaaccbcadddbdbaddaaacddbcaaddaabdcaabaabdadbcaaccdbcdddbbbcacbdbdadbbabddacaadcaddccddcaaddcccbcbaaaadcacdcdadcddbbdadabbaccabcddabaccabaddbcaacdaacabbabccbbbaaaacbccabaccdcbabaaddcbdbabdbaaaaaacbababaadadbacbcadccdddbccdbabdbdabbacbcddcaaddcbaadadadbdcbbbdacbaadcdbdbcdbcacbdadadbbdddbdadbcabccbdcdbdbaababcdccccdaccabdbbacbccabdbbcbcdadddbbbcccacbbcccbbdbbdbdcdbccabcdbacccbbbcbbabccabcadcbddaaaabcaccdbdcacdcbbbaddaaabaccdbadcbbcbdabcbbcbdbbdbdbddbaadbdadabdadbcddcddddddcdbcdabcdcadbcbabcdababbcbcaddaabccdccadcdccbdadacdbddcdadbcababcabccabdcccabddbbdccdbabbdbbbacbbaccdaadbcbcadcadbcaacadacccbcabadcabbbababcdcbadcbdaababdcbddbdbdcaabdbbaddaddacbcadcbbadadcdcbcadbaddadacbabdadcaaadbdacaddcddbcccbcacdacddbbdbbbdcabccccaaaaabbaccbddbadbbbabdbabcdaaaaacbddacdbbaadabcacbcdddbdcadbcbadbddaadabcbaddababcbdabbabdddccdcabccdabdbdacabccbccdbbadcaadabadaddcddababcaaaacbcdadcccbccbdcaddbdbacdcbdadaacccdaaaadbabbaabaddcaacadbbdbbaaabbacddbbaaadadacdccaacdacacdaadaaaaacabdabbbbbbaadbbadabacabaccdcbddbdbbddaabcaaadcadaacbbcabbcacbaadadbcbbcdabddcdcbabbaddccddadbacdbacadcbcbdbbbdaababaaabadaccbcdbcbdbbbdbbdaccbabccdccaabbcbddabccacacdcdbaccdcccadadacdaaaaddabbcdccbbddbcabdacaddbcbcadacddabddddbccbabbcddbccaabdbdbcbdbbacbcddbacaabdcdcbaadabcdbcacddadbcabcdbdabbabcdcaccbabbcdcacddbbcbdacbbbddcacadabaaccadcbaccaabbcaabbadcbcbcabddaabdbcbdcbacccbdadbbabbbbddbbcaaabdcbcdccddbcbbabbcaadcbadddbabbdbcbccadcbddbcaabddabddadaadbdbdcbcbcbdabccabbaabbcccbcbdadcacbbbcdabaaadccdbcabbdccddccddbacaaccadadadcadddddcabadcdaddaadababbbadabdaaaacaddcbbbdbdbaaacbdccaaabcdababdbaccdabacdaabaadddbcbabdcbdabcdddaadacadccccadddccbcbdcdabcabdbdcbcccabcadabdbbcddaaadacdbbcadccdcbccadcdddbdcaacbbbddbcdabbdbcabdbdacaaadbbaccbdddcabacdddcabcdacccddbcaccddddcbabbdacacbddaadccadbaaccddbddaadddacbdbabbabdbdcdddcdbdaadbbbcacddbdaaaabbcbbaaadacadddbbaacadabadbcaabbcbdabdabddabdaddbcdaaabdacbaabcabcabddaaaabaadacbddbccdcbcbdaaacdbabbbdbdcadddbdbcddabdddbbdddabcadbadaadcdcaabcacababbbdccdcbccbdcacbcbbcbdcdbababbacababbaddbbcaaabbdaaaccbccbdbbabcdccbabaadbcabadddacadbcccaccccdbcababcabadabbdcccaccabcaadcdcbdcbadaccbbcdcacdbbdcaabacdaabbaabcbddcadcaadbbaddabcddbaddddbcbbbbbddddaaaddbabbccdbbcbaadbdcbbadbbcabaaaadbadcdbabccaddcaabdbbacbbdbdcaacbcacdccdbbbbbbadbddbadadcabdaaadcccacdcdbbadbcbcaddbdaddbbbdcdcaccacdbdacbdcbadaccaaccdaccdbbaabdadaaabacabcbddaccaabbdddcbbbdacaadccbcdaacccabbdbccddbddcdbabbdbcccdbabbcbdbddacddcdabdacdbadadddddcabccddadcccadbabcbdbdbaabbacacaddaddcaabbacacbabcdcacccbbcbabccabbabadbcadbcabdbcbbbbacddacaaaddaaccbccdcdcbbcbdacddbadbaddcaadbacccddcdddccbccdbdabadcdcdbadbaccdcdbcabdbbacbdccbadbbccddcaaddbcbbddcbdcbabdbdaaaabdabcdccdcaacaabbddcabdaddbdcbdddbdbcdddaccbbbbabbbbdcdcadcacbbddbdadabdcdbcdccacbaaccccdbdacbdbbcddbbacadabbbbdabdacacbddbbdcbcaadbcbdbdddcadbcaadcbdabdadbacdaaccbbbcadabddadbabaabbacddbbadacbcacbcbbddaaddcdaccddddbbcdaccbcbaaccbdcbbbaddcaaccdccaaddcbbdaaabacacabdcdcdddccadbccdcaabdccbbdabccadbbabccbababdcbbcbcdbddbaaaabcbbacabbcadbbdbddcabcabdcadcbdacbbcaccbcaddddcbcabcdddcabccabcbbdadbdadabcacdccccacddadbdbdbcdbbdccdadddbbcccbbadcddcadccddbddcbdbaaccbadbdcdbdbbbcbddcccccbbdcacbcdcbcbacdbacbdbcacbaabaaaccadcbaadcccdbbabccbbbcabbccadabbaacbcbcaadbcbacadbbadaacbdcabdccccdaacdcdbdcbbccdadabbbacadaacaaabacccbadaaaddadbddbaaabdaadbdbaaccaabdcbbbcdbbacbcabcbdcbabbbcbbaabadbacaabbdadadbcbbaacdbaaaacdaaaabbbddcdaadabdabbbcbcbababcccbaabdcaaacbddccabdabbdcdddddbdcaacaaccabccddcbdbdcddaaadadadbccdaacdcaacdaacadbbaaccabcdbdadccdbbbabdabaaaaaacdadcadcdcbdacacdabadddbcdccbbcacacccacbbdbacadaddcaabdbcabbcbadaacbcdacbcbcaacbbabcddadcbbdadbdcbcdcddaacbcacdbbdaabbabbaaabcabcacbdbbdccccabcdadcddddcababdcaccbbacdacdcbdbdcdbcadcadcadcbbbdbabcbdbdcaabadbcbccacbaadabddbdacbdcabbaaadbabdaadbbcddabacaccadcbccddbacdbadadcacababaaccdccbcbacacbcaccbdbcddbcaacdbbdbdbdbcdadcdddbdbcabbccdcaadbacdcaddaccdbababbcbcdacbadbcddddcdaaddbcbabcacaababccbbacdbabbcbcbaddbabaccadbabcdcbdbdaacbbbcddbdacaddbacbdcdaadaaaccaaadbaabdacbabbcccdaaccabdabaacbadcdbadbcddadbdaabaacbdacbaccbaaddbcaabdbdbacdadbcaabadababcaabccaadcbaaacbbccdacbcbcdabbddcaccbacdaabccaabaaaaccccabdddbdcbbdddbcacdcdbcbbaaaabccabcddaccbacabdddccbcdcbddcdcadaadbbcabbaaccdcabbadaabcadcabbbabcddadaddccdcbdccbdcbaabaccbbdcdadcddccdcaaacacddcaddbbbcaccbbbccddbbbaccdcbddcaabdccbcdbccaadcacdcbcccacbaaacaddabddbcdabbddabbcabbbbdabbdadcacdaccacbbcaadaadabbddcbdabcdcbbdcddbcbdabdbdbadabdaadbbcaacaccddaccbadaddcaadabccdccdbbdabadccdaacbabbacbdbdbccdcabcdccccbbaaddbccbbcdaadadabdaaaaadbcbacaddbdaaabdbcbbaadbaadcccdccdbdbbabdbdbdacabcdccbcdccddaacccdbacdadcdacbadbdcbaaddbbddcdcbabbabdccbdabcdaaaabcadbccdcabacccdcdadcadbcabdbdbbababdbbddbdbccdacaccbbbcaaadddbbbddbadcabbbccbbdcbcaacccaaccbbbbddbdbdabcddcddabdcdbbabacbdccdbaccacbdacdaabbcbabbcdccabcaccbdcbbaaacbdacbacdcaadcbbaccabddcbaddbdaaabbabdcccdaaadababcccaaacbdaababcbdbabddbdcccbacaabaccddbcacbadcccabacdbcacbccccdccabccbddbadaabcddcccdabcbdaabdbcacbcbadbdcccadccdadddbbadbbbacacadbabbabbccbdcdbddadacbdabbcabacdccbcddccdbdbccbbbdaadccaccbacdbdcbbbadcbcabacabaaccdccdbbbcbcbddccbdccbadaadbcbccbbbcdccbdbbcbdbcdddbabadbacbcbbdaacabacabbcabacdaadbcdbbacbcacdbdcddbdcdbcbbcacdcaacdaccbccbdcadaaccaccdabbdbadaacdabdaaddddbaaadaaaacaaaccaccdbadbaabcddddbcaccdabcaabbbabcdaddcbccabdacdbcdacaabacdddbbbbddbddbddcacbcdbbdbcdbcdbbdddcbadccbacbcccadbdaacbddacdadcddbaaddbdbdcbddccbbcdbdbdadddcaaacbbabaadddabdbabcaacdddaacdcaabcbabdaccbaadbbabbcccabdbbccbcaabccdcabdbbbcaccdbaaabacadcbdccbbcdbdbacbbcadcaabaabddbbacddadadccbddaddaadcdacbcaddbcacabcccaabdadacacabbbcaacbbadccbbdabbdacbaabbabdaaabbbabdcbbcbbbaacdbcadabbcdddbacdddbbaabdadbcddddcdadddaabcadbbdbdddadbdbcaccacbcadccacbddbbccccdbdaabccadabadbdbbaaacbacdddcbaccdbddcaaaaacabdbcabbbbdcbbbbbdcabccbccbbbacbdccbdcbbaadaddbcdcbbdadacdbaaaabccaabacadcccaddccadcabcbaadcdcdccdbccaacdadacbadddacbdcccadbdbacaaadcdabbdabaaaaabacadcadbabacabcaabdbbadaaccbbacbccababaaabcbddacbbdcdacdbbadbcabdccdbadaadadaabccdbabbccbaccdbcaabdcacabadddbbbdcbdaadcbaddabacacdacbbcaaababdcbcabaadbbbbddcbdcddabdbcccdbcbdadddbdcaaddabaadabdbbcccbcaacdaccaabcbcaddbbdddacbcabccddabaaacdccbdccdcadacabbbbacbbaabbadadacdadaacabacbaacbcacbabaaaccdbccaaacaacacacdcbbdbbddcaccdabaddbadbccdabdaaadbddbaabadacbacccaccabbcbacacccadcbbcadbaabbdbcddccabcdccbdabcbaaccbcacacdaabaadacdbaadaacdbbadddaaaadbbdbcaaddccaaacbcbacdaaddcaadcbccadcbbdbddadbbcacbcddaaccdaaaacdabcdbddacccabbbcdcadadddaccdacbdddbaaacbadadbacdbbccaddcbbbddcdbdadbadbdcbbddbbbcbdccadccbcadccaadadbcccbdaacabdbbdccccbbddcddcbabaabdbbacaccdccbbbbbdbabbbcccadaddabbddbabdcadaacbbaaaadbabacbbdacdcbbcacbccbbabbcaadcdcaadacaabdaddbdaacbbcddaabdbcbbdcacabcbccabbddcdcccaacdcadadcbcabdbacacacccdadcddcbcdcababddbbcccbdcdacaadddccbcccbddcdcdbcacdbbaabccccdbdbdaaddbbcbdbcccdcbbddbdbcdbbbcdbcbbddbccccbdbbdcdaadabcbbcdacbccdbaddbbaadcdcdbdcbdbbdbcaccaacdaadadabaaaacbbbdaadbdcbcabcdadbccbddbbbbdaadcbdbdadaadcccccacbccaccaabbdbbdacdbcabbbbddcabccdadaabdaabcaddccdabcdcddaadaaabcddbaccdcdcdbdbcbcbbbabbacbaabcddabdbaaaddadbacdaacbacbcddcdaabdcdbbcacbdbaccccaaccdbbbcabdcbcaaacbdbadcacadadabcdcbddbdbaaaaaaabbbbbdacdacabdcbbbddbcdcaadacbaabbdcbdbabbbbdcbdcdacbcbdadbcabdabbdbcadcbacccabbcdddadccddacdddccbdbbbbbbacaabcaccbadadcbabbaababcbdaddddabbbaabcbcbabbcdbdaddbddaacddacddaacbadbbbaacdaacaadaabcbcbbdacbbbdddbbabdabccbbaabacabccbbcdadbbbccabddcbbdacbddccdcccaaaaabdcdacacbcbbcbaabdbaabdbaaaadddabdbacadbaddbacbbcacaacabdcababbacdacbabcbacadabbbadabaddcdabadcacaabdbaacccabccdddcbdcbdcdcdaacddcaddabbcaccabaacdbbccaabbbcabadbdaacdcbdadcbcbcddcddaabddddbcaaadbddbbbcadcdccabddbcdcbbdacccaddbabddaaccabadadbdbabbdaacabcdddbbbbcdccdcccaddacdbdadbacdabcbcbbcaaaaadadcacdcbbbddacbcbadabadaadcaabdbdcdadddbcbbbdccdabcbacbdbdcadcdccaacdccdbdcaacbdcddacabbdcdcacabbcdbacbcbdcdcdbaacdbccbadadcbadbbabcacbdbccdaabbbcdacaabdbacbdcbdbcdaacccabaccbdddbcbdcdccbaadabbdccdcbddbabccdddbcbdbdacbdabdabcbdacddccbddbacbcdbcaddaaaaabaddddcbcaccaaadaabbbbabcdbacddccbdcccdbbcbdddabacaaccdbdaccccdaccadaaaccccaacaaddacdcaaabcbccddcaccbcbadcacbdcdbdcccacbdcabdbddbabaccddacddacdddcadcababbcbbabcdaadbccbccadcdcaadbbaacbbaadbcbabdbbbacdcdbbcbabbbbdbbaaaaaacacbacabcbcddadacbddcdcacadcdddadccccbbcabdaccdbbccbabbdcbddbcbabaaadabaddccdcbdbaccbdddaaacdabcbdabcbbabccbbcdcbbacbadbcadaacacddcccbdabacaabdabddbababdaadcbbabcbdaaccccabaadbbdaaadbbbabaabcadaadaacddcdcacdbbcdbdabbdacdddcadbdbcbcdbaccaddcabaccaaaacbddcaadbcbbbdacccbadadbabadcadcdacabcbccbbcbaacdbaacaadcbdabbcbccadcbdadabcaccacbdabaacbddaabcadbccdbaccbdabaaccdbddbdddcdbcbaadaadbbdacbbcbaaabbabcdbcbacdabacbadddddcbcbcbadccbdbccaabacadddaabbdacbaacaaaadbaadcdaddbaababaccdacdaaaccaadbabaabcbbdadbaadadbcadaaaccbbbaadcbaabacbdbbabbabcaadbbabbbabcdcbdcbbccddccbcddddbccabdbdcaaaddddcbdadddcaccacbddbbccdaabbacbbdacdaadddbbcdabccccadcdcdcbaddbbdcdbbbcaddcacabbbbbbaabdbbadddcbbadcbbdacaadbaadddbbddaaacabbbcaccddbdadddbdabbddcbbacdabdaddbaaaadaabccddaabcaaccbcdbabccbcddbaddbcdddcababacbbcbbccdcacabdabdcbbbcbadbbbacbdacddbbdadbdacdccaaddcddadccbabdbcbbaacabbcdbaabadabbabdddddacdbbdbaacaacccaaabcdbbdbbbabcbddadadcdcbacabbcbacdcddadcddbcabadbbdbadadbbacaaabcbbbcaaddacdcdbbbdadbabcdbcdaacdaccbabddbdcccdaccbcbbcbbbbacabadadcabbdcaddcadccaccddddbabdbbbaaccbdbddbdbbdbcacdccaacbdabcdcacdadaaaabacaccaabbdcbcdadbbdbbdabbabccacbabdbcdbddcdbbbdcbdcbdccbcabbcdbacdddbcbdbcbbaaabdbadcbabcddacacbdaadcabdabababbbadccccaadbdbbbcaddaadbabccbaddabaacdbabbdacadbdcabcaaddbacbbbdabcaddbaacaccbcdacaccbbccbadddccdcccaabcdbaadbaacbbcbbcbaaacdcdcdbdacccdcdadddacbdbcdbccdbdcdbdbcdacabbbccacdaadddaabcdddcabdbaccddcdbdddcbccdddbaadabccdadccadcaccabadcaabccbadaabadcdbaabdadcabdbbdddccbbbcdbcccbacccccaaaabbdacbaccbcdbddadaadcadbabdcdaacdbcdbbbdbccbbdbdaacbcdbacabbcdbdaaccabcaabccadadcbcadacacadbcdbaabdaaaacbabdcdcbbccaacacdacaaddcdabcbccbabdaadadcadbbcbdbaacbdbbdbcacadcbabdddabbcdbdacdbaacbaacdddbbcdcadaccbbdcbaaddadaddccddbdaadbaccbdbcbabbccbcaaaaacbdcadacbdacbbadbacbcabbabadadbddacbbaaaadccadbdbaccbbcdbccdbdcbdbdbdacbbadbccbdcbbbdcbbaaacabaaadbdcbdcabcbacbcaaadaddbacccdaaadcaccddcdcacbdbbacbabdadddddbdccdcdcdcbdddcbbaddaccccbdcadbcbadaabbabadbacccdccbbccdddcdbacadccbbcbbdcaadbcbbdbbdccdbdbcccbcccaabaaabdddaabadacbbdaddcaddadabdacdddcabddacaabcabbbdbbbcdacdbbadbaabbcccadbadbdacabcaacaddbbadbcdddcaacaaadcacdcdcdaaaabbbbacbcbbcadbaababdbabcdcdacccccaabdacacadcabdacbabbbbbbdbaddbcacaabbbdccadacaddbaabdbbcbcbcacdcbabaabcddccdacacadbbcacbcdadcbacddcaacbbcdbdadadacaaddddcdbccbaaabcbabbcccbddcbaaccbccbcdaacddccadccdcbcadbdabdcabaaddbaaababdcabacdbadcabbcadaacddbbaacaacbddacdaddbcccccabbbdcadaccdbdccababbdccaacdbdabdbcdbcadaddbdcdbcaccddcdcdbdccbbbcbdadadabcccdacddcaabaabcbdccdacccbbbacacdbcbbddcacabbbdbcadbbcbdcddccbdbdccadaadccbddddccbcbddadcbadacdcbbacacbbcccbcadbcdbaccbaacadbbcbaaadbadaddacbdaaccccbdcdaadbabcabdddbaddbdddaddddcdbadadabaddadaabdddcbbdabaddcccadccbdabdccddacbddbdcdcbdbdbbbadbbcbdcdacdbbdabbaddcddadaacbbbdddccbdbbabadacbcbabbabddabbaaababaacaabbcddbbbdbbddcbdbdbadbbabdbcbddbcadcbdddbbbbdacabacbbcbaacbbddabdcddcdbadccbbcddcbdddbddbcdacabdbdcdddddaaacdcaaacadaaddacadaacdbacbccdadaddddcacddbddbaaaacdcdccdcacbbaccaaaacdadbdcabccabcabdcdcdacbcccbbcdddabdabaabcabaacdbbbbadcbbcaabddadccacadaddbbabdadbcdcbcacaadaaaacadabdcacadbccccadbbadaabbddbbcabbbaaacadbddbddcbddbbdcabbdcdbcbbccccacdcabdbcaadddbcbcacbadcbabbcaccaacbbacdbacbacaaddbbadaccabbcbbacabbcdcdbcbdddddabacbacccbaabccaaddbdcaabaddccccccccdbaaabdcaadcddbdaacdabcbdacbdadacadacbdbdbabccaccdbcaaccaabbdcbdabcbbaaaacbadadaaaacaabcddbdbcabacbabadcddccbaadddbaddbbbacbccdbdcadcbbbcaabbbcabcbcadbccddbbdcadccbcbcddcaddbdadcbcbddbcdbbddacbcdcbcbdbbcbcbabbabcccbaadaacbbbbaacabbbcbcaccaadbbbdbbcaadcddacadadbacdddaddbabdabadbabaacdcbddcbaacabdccddababacdbcccdbadacacbddcaacaadcccabbdabdbcbccddbbabbdbadaacdbdcadddaddcddddbbcbdbdaaaacacccaadabaaabddccaddaacddacabcbbaacbbbacbdbccacdcdacaddddbbbcccbabdddcdcbbbaccddaccacccddccdbabbccaaacdcaaddabdaccbcbcabacbadbbaadcadaddaddcddcdaabbabddadbadadbdcacbdaacacacdcbaccaaabbcadbdbdcacddacdcaaaddcbdaddbddbabddbadbabdaddcadbcdcabbdaacbabcccddcbccbaabcbaabddbbaaabbdadccbabdcbdacacdaaabdcdcbdccdadcbbabdccccccdbdcccaccddbccbacdaabcaacbbadcddabccdbbbbbacbcaacbccdbacdaaadaacbadadbabcbbbdbabadaadadcbacbdccbbbcdabbddabccacaadbddaadbdbbccbdbcaacbbadadadddcdaacddbbcdbdabbacabbaddbddaaddaccdbccdacbaaccdccdaaaadccbbacbaddabcbaacccccbddcdcacaccccaccaccbacdbdcbacacddaddadddcadbdcacbcbcadbabadddcddbcdbccaaaaaaaaddcacddccabcdabccdccbcacbbcadbbcbddcbcccabcaacbccbbadaaddbcdcbbbcadbdbcbdcaddbaadadbdbbabbbabacdcbbdadcdccaddadacbcabcbcaddbbdcccaccccabcbcccddbbdcbcdcdbccdaddbabdbbbcdbaadcdabccccccddbbbcdbccddacabddbcdabdcbddbadcdcadbdbcaddadbddacccbcbacbbbcbbadababcbbbcdacbdcbdbcdaacdacababdcbadbbacbbbabddccccbbddbcbbacdcdacadaaacdcacbcbcadacddbbcdbcabadabaddddaadcbabaabaacadabdbcbcbaabbaabababacaddabbbabaddabbacaacadcdcdcbcbcbcacdcaddbbbdcbbbcdbbbbbcaccadacabadcdccdcaccdabbadbddaacbacaddcdbdabddbcadcdabbadddbbccaabcbbacabdbcbcddddaabdbcbbdbaadcbbdbdcdbadcbcccabbbacccbddbbcbaaadbacaacacddaddbbcbdcaabcdccbcaabcdacdaadbbbbdcbdbaddbbaacbdcbaddacdaacbbccbadbaabbbbccacbbbccccbccaaaadccccccccdbbbacabcccbcdbcdcdaadbdabdbbadaaacadbcccaddabbbaaabbbbccaadcdcddcaacdcccdcdabcbaacdacbcdcaaddbbadbadbdddbddbcdbccbdbacccaddaccddacdbaddbcdaacacddcabcdaaccbcacddabdaaccbddbbaabaaaabadadbcabaaaaaccdddbbdddcadcadccabbbcacabbbcbdcadabadbddbdbabcdbbcdadccdddbcbaddbddbadbacbabdbcbcbbdcddccbbbbccbaabdadcdcdabddccccdababccadcdcbabadbdcccbbbdacddacacbbccaccddacacddbdcaadcbcdaacdccdaadccdadcbcabbbabbcdbdbdbabbcaabaaabddacbdaccabdbdcddcadcbadcbbcbacbcbadcacbdbcdcbdbbadcbadacbddccdbbbcbdcdbadbaadabcbccccdadcbbcbcdaadcabbbbcbabcacccacbabbacdbddddcaaaaabcddddadbdbabbaadcacddaabccacbddaabcbadadabccadccdbddbdccdadadddbcdbdbcadabcbcbaadaabcccaaabddaadabcbcbdcbcdcbbadaddbddbdcbabcbccbbdbaccacdbababcccbadabacacbdadcdaabcbdcabddbbadbdbadbadcacdcdabcacdaacdccdaabcacbadbdccdaaabbbacacdaaadbcaaababccdbdbcadacabcccabacdbcbbbadcacbddbcaaabbacdacccaacaddddbcbcdacabbcadcbacbdbccdccbcabbbabbddbadcbcbbabbaacdcaaadbdcdcdadbcddbcbadcdacbabbccbbacbaddbdacbbdccbcaaccbbcadbacaababbadbbbcdaddccdbcbdcddbbbdcbcbcabadacdcdccbcaabcdbdabcbcddbbacdbcdacdddcbcacbcdaaacdbacbabbacdcaaabacdcbbcbaccbbbbdbbaadcabbdbabddcbcbbadccdadcadbaacddaddbdabcbccaddbaacbcbbdddcdadaabdbcdaabacdabdaaaacbdbbcaacadbabbdacaadabbcdbadbadcaccaaabcdbddcddaadddadcddaccccdadbbdcadabcadadcacabbacbbcdbabacbbadcadbacdacabccdaabbcaaabccbbcbddcdcadbbbdaaacaccccaccdbdccabbcabaaadaddddacdcaddcbaacdccacaabbcaadbbaadbacdaccbddadbddcbbdcbddbaacdadcbbcbabbaadaabcddcdbccdadcccbdcdddaacbcbcccbcdadbabcbcddabcbcbacaccbbbcdabbbdaadccacabcabccbaccdddcddbcbaddddbcdcabcadcbaacaddccaadabcabbaadcaaacbdcbdaaddcaabdddcacccabbbdacbbccbbadabbabdacdbabdcbdcadacabbabbaadabdaccbcbaaaadbcccadcbabbdcddcbcbdbbbcbacabbcbadcdccbddbbbbacacdccbcbbbdcbacbbacbdbcbabdcabccbbdddacbbdcbabddbdbabbdadddcccbbabbaadaddbaccdbddccacdbaddabcddbddcbcabacaadacccdbabacdcdacbbbacbaccadbdabdbbbcabacacdbccaddcdbdaabbbbdbbacdbbadddbcbdbcaacdabacacbbcdaaaaddbadcabbbdbdddacbcdadbddabadddaaddbabdddbccddacabcdbaabbaaabcbccbcaaccaadbddadbbabccdaccbabccaacabbabcbbdabacbacdaabcabbbdcccccccaadacbbabbbadbbdbaaabcbcddadccbacbabacbaabbaddabcdcccabbbccacddcdbbdadcbaddcabdcbdcdabbbdddacbdbcbccbdcacdacdccddccdbcdbdadbccccbbbacdbddbbbbdbcadadbcbbcaadbbcaaaddbdbdccaaaabcbacccbbbabbabcabcaacddcbdabaaacdbbdccbdcdcdcbbdabbcccaaccbbbaadadddcabbaaccdaadcbbdbcdbccdbbadcdbbdddbbddbabcabdcbdaabdcbbccddbcddacabbccdcadadaadababacdbccdabcbdbdabbaabbbbbbbbcdadddbcbbddccdbbcbbdcacdabdcabdadbcbadccbdcdddccdbaaaaabacdbccdaababdabbbbccaddbaccdbddabaacbadddbacbddcadaabbdcbaabdabcbaaabbdcacbccbdcbbcddcbbdbcadacabcbcdbbdbddaaadaddbacdbbbddaccdccccdcabaacddccaabccabcadcdcddaaadbbcccccdbbbaaabaabadcaaadcbaabddcccdadddbcbbaabbbadddcddabdbaaacdcbdbdddadaddbcbacdcbcacacbaaccbdbbcdccdaabbabbadcacbbddbddccbbddcacbadaccacdbcbdcddbbacadddabddddccdbbdcadbadaaabbccbdcaacaacbbddadadadbcadcdcaccbddcdcbcaacdadccdadcbacacddbddacbbcabcacdbcaccbcdaadcadcadcdbadbbbaccddddcacbcbadadbcdbbaccdbbabaacbbccaadadddcdcccbdaacdbaddabaddbbcdbaaaacbabbddaaadbbdbadaccbdabdadcbadbcadadcdcadaccacdbdddbcccbcadabaacbcccdcadcbdbdcadcacbcbdcadbaddcaccbddbddbdaacdddcdbaacabcdcadabbaacabbcdabcdbcbaccbdaddbacbabadcaadabcdbadcbdadcacdadbcbacdbcacaccdabadcacaadadaaccddbcdbccadbcddbaacdacabbdcbdacadbaaabddddbaaaccaadccaaacaabccbdcadadbbacccdddaabaabccdcdadaaacaaaccadcdbcbdcadabccdadcdbdadcdadbddcaabdbaaadcacabaddbbadcbcbbadcaaddababdaaddcabbbbbadaadadcabcdcabccdccdddddddcabcdccdbadcdddabbddabaaacccaaadabadcabacbbdabbadcdccdbdaabcadacadbcadacbdbaacadccdaacacbcabacdcacacdcacabdabdadbccdbbcbdacaccdbbcbcdbbddbcaacdbdcacabdbcbbcdaadcbdcdcabaacbcadcdcccbccbcaadaaadbabbcadbbcdcdadddccccdbcaaaaaacbabdccaaccaccbddcbabddabbdcdcaacbcaccbacbadabacbbdaddbaaabdcabbcbdaaabdaacdcdbcaadcbabbddcadcbddcbddabcdaadbcdbaddbbacdcddddbdbcdbdaacdadcbbabbdadabbcdadddadcdacccadddcbcccdccbabadbbddbcdcaadcbbcadddcaddcdbccccbbadaacadabbcabcbaccabacbbaddabdbbcabcadaaccbddcadadabbacdbcabaaacbcbcbbabcccbbaaaaadababbdcdccabadcdbcaabacaaabbcacdbaacababacbaaddabccaaddacabdbaddcbabadcdbbadcbdaddccdaaaddccaacbdbbdccbbaddbbbcadbdbcbcbcbdbdcccddadbbdbddabdcabcaccbdadddbbcbddbabdcabdbcbdbbbcdccbcaaddcbdbcaacbcccdddbbabbabcbccccbdcdcdacdbabbdcacadccddaaccbcdcddccaacbabdddbadbbdcdbdcdaccbcbaaccaacbbbaabccbbdbdddcddcaddcccabbacadaaaddbcaaddcdacdacbaaaccddbdccccabbcbdbadcaccabddaacdbacbacacaadbddaddcddcdcdccccbbaacdaadbccadbcaddbcccadcdddcbdcadddcacaabdbbcadbbaddcbbabacaaddbcabbabddbacaabdcccadabadbdaadbdacadcbdadbdcdbdaacabccaddbdcccaaaacbcacdbdbddbdbcbabbbaddbcbcabcddcccdcccaadbcabcccccdbbadccabbdcacbacdaabcdacdadcdacccbabdbaaacabcddbadcaddbbcacabaaadcccadcddbabbcdbbdcbdaacaddbbdccdbcdccbddadacaddcccbacdccbbadcbbadcabaccbbabdcdacbcdccaaadacbbdcacddcddbdaadaaacacdbddcddbbcadbaaacbcacacbdbccdcdacadddaadabddcbbadaddbdcaaddcabbbdaddcdabbadcdccdacdbabdbacabccbaacdcdcdabdaadcadabcdabcdacacbbaaaadacddcbddbcadaaabdbdcbdddddbcdbabdbccabcaddcabcdacdddacbbbcacdbbabadbacdccdbaaabdbdcaddabcaaadcbadcadcaaadabdabdbbacbbbcaaabdbbcbaabdadbabbdbabcbacaabbcbdaaaaacccbdccbbcddadddaadcdbddbbcabadcbaddbdcdccbbddbcddaccdadcaddbdbdddaddbabacbdaadcccadaaddbddadaccdbbccdacacbdcbcabccdbacbadacbcbabcdbbcabbdbacacbdccabdbadadbadcdbbacaaddabbdbabbaccdbbdabdcaadccbaddcccaddabcdaddabcacabbbabacaacdadcaddadaccaaacabacbaaaabdcdbcbbccbbcaabbcbaacdadadbaadddabcbcccdacabadbdbbdabdcdcccbcccbaadbadaccccbbaabdbdddabaaddcbbccadaababccbbbccdcbcbaaccbcaaadbbbddabcacdbcbbcddcddddbccbbaccddaadbdbdcacbaaacdccadbcacbddcaaabdbacadcaacdcaacdbcbbbcbbaabcaabcaccdabdcacadcabbacacbcbadbccbabbddcdbbcdacdacadabddccaabcabdccaaabacdbcbbaabddacddacdaccbadbddbdcbddaacacadabaaadcaadcbdccccabcaabcaadabadcbbaabdbcaadacdbbcacbdbbccabdaccabddaabcdacddddadbbcddccbabbdccbccdbccbdadcaddadadaaccbcbcabcccbadccbddbdcaddbddbcacbdccabcdddabdaaccdcdabcdaddccdccdabbcbaccabbababbcaacbcbadcabcddcadddaacabdbadacddcbabdcdbdbcabcdddbdccdaacddbdccaadccdabcabdcacdbddbdacbbbbccbbbbdbccaccbacbadddacadbbbbadcaaadacadbaddbdbacccabcaadcdbaadbaadcaddbdacdabdbbadcbadabdcabcddcacbccdcbadcbccbaacacbbcbacccddabcdcdbbbabadacaaaadddaccbddcdbaccddbbcdaaaadbddbbbaacdbaadccbbcccbddbabaaddccdccdbddbadcbdbcacbccabccddbabdcabdbdaabccadbdcbadbbadddaddadbbbacdadacadcdabdcaaccaccdaddabacaadbadcbccabbdaccbcbcbaacbcbdbaabbacddddcbbadcbddcacbdaabcbddbbdadabbabdcbdbbcdacaaaaabbdaddbacbbacacbbdbdaaaddcabccccdadcbacbcbadabbacdbbacbbbcccccabddcaabcdbdddabccdbcbbdccccabdabbaccaaadcabbdcccccbbcbaaaaabdbdbcacdbddacddbdabdccbabacdbbcbadcbcdbdacddccacdcbccdaacbcadcccbcbdcbcacabcabcdadcbdbdddbbabcdcadacccaaaacbdcdbdbbaacccccdcdddabbbcccdbcaabdcdababaacdbcccbabcbbbddddcdcbaddcabcbccbdcacddcdabbccbbcbccabacaaabbaccbcdbcdbcbdddbacadbdbadbabdaabbdddaccabaccccdcdadcacdcaadbcbaaaaccccbcabacbbbbdadcdcdcabddccdbccbcaabdbcdaaacbcabdcdadcbddbbbaaaddabcddaadccdbccacdccaadcacbabdacddccaacdaacaabbdaccacdccbacdacaadacdaaaddcbdbbaccbbacbaddcabddacdcccbbbacaacdaabdbccbcabacbdacaabcbddabbddcdbaccdcbdbaccbccdcdaadddbbcdddcaaacccaacbdccaccbbdbbacddbacbdcdbabaaadbccbdccaccbaccdcdbdcaccbaaacaaabdccaddcdaacddddbdabbcbbcddcabbcbbdcdbccacadaadbacdadbbcbaadaadaccadddcdaadaadabaaadadbcbbacddaabdbadcabbcdaaacbcdabdcdbbacbcbaabbbaccacbbcccdcddcdcabdcdcbbdabaddcbadbbdadbbbbbdbbdcbbabbddbcaaacdbcdcdbcadbbdcacdbdaccdbbadbaadccbacaacdbacbdddbcadccabaddddbbaabddbccadddbcabbadccababccacbcdcbbaadabbdcacbacadbabccdcbddddbbdaadcbcadccaaabadacddcabccbbcbbddbbdbcdabaababccabccbdbcbcdcdcbdcbccabccadbaadabdcbaadbbdccbdbcaacbdbabcdbddcadabdddddbbbbcadbccaabacccbaddcccdbdaccbdaaabbbcdbaaacdbcdddaacaccbaacdadadadacaccbcadbccdbddcdddadacbacddbccadcbcaadddbdaaaacbdcadbacacabacdcccabcdddcadadacaadadaacdccacbdabbacacccdcddbbdabbdadcbbcbabaccdcbdaaabaadcbbdabcdccdccdbbdacbdbcadcddaddacaacbddbcdbaaaccadccacaadcdddcdacbbbbccaccbdadddcbacddcdcbaaaaaadbbdbbaaacdcdcccbdbabddbaabbccbbcaddcddcbcbbdadbbbcbdcdcaacbcddddcaabaabaccabdacbdcbcdcbaacacacabccacadbccbdadbccbdaabbcbbbbbccabccdcbddaadadcaaacadaaddcbabccadabadbddbccacddaabbaaddbdabdddaddcbabcccbcbacbdcacabcdccddcbcabcddabacababbdbbdbcdbcbdcdacdaadacccdbbcbadbcaabbbdcddbabcdcccbaacddadcbabccdbaaacbbaaaabdddbddbccbcdcabddccbacabdbbaabacbbbcbbdabadddadbaddbbbccaadbcabbacbbbaabdddcacdbbdccaadcdadbdccabaacdaaccdaacadccabcccdcdadacaacbcababdbdcaaddacccccacdaaacabaacbbdcadbbbacbbccbbbdcddccdaccbccdabbacdcddbcdbbcdbadadabbbcdcabcccdbcdbcdcbbdcdbcadabdadbaacccbcbbdaaccdaccdcadadaadaaaacbbaabddabddbbbaadcbbaaaaacabdbcadaaaacacabbcaddcbddbacddbcdccabbabdcbbdadbccddaaddbcaccaddbbdcdcbcdbdbbacddaacdadaaccbccdbabbadddccdcbbdddadadcababcbdcbbcddbddbacccbababddbcccddbbbdcdbdaaaacbdadcbaaabbacccbabcbccadabcacdcbbbbcbabbdbcabbbbadddcccbadbabbadcbdbcabdcccdccbccaaacbdaadcddcdadaabccdddccabdcccdabbcbcddbdbcbdbdbdaabcdcdbcaacbbbdaddacdcbdaacbcacdaabdcbbbaaaaabadbdadcbabbcddadababdaaadcdccdcbadbabcddbbdbaaacbccbbaccacaddbcbbbbacdbadcddcbababdbbdcdbcaadbbbaabbbbbcbbccabbdbcccccabcdcadbabddbaaddcabbddabbbdaaccddbacbdcaaaaaddccbddbcacabaaacaaaaaadadccbbcdadbaabccdaacdcddbacacdcdadaabbcbdbdbbbdaadcdabddbccdbdbbcccbbbacbabbcdbbabcbaccdbacbcabdaaacdcccadadadddacabdadddacaabaddddddbcdbadccbdcdbbcddcbbccacccabacbbabcadacdbacdcdacbcadcbbdcaadbcabdbbbdddcdaadbabacadadcadcabcccbcdbcbdcbaacabdbcacdadabaaddaccaacabcbcaaadccbdaadddbbbaacbbdabacbbacacbaadddabdabadbdabaabbaaacbdadbbbcdcbadbaccdccbcdabbdabcadbcbbbbccddddcabdcaddddabddddadbbababadaaadbaddbbcccbdccbaacdbbaddbabbcaadaaacccccdadcacdbbdbcbbccdbbdbcadbacbcaabbdadaadddccadddaacadaddabcbddccbaaacbbbcabddcbdacccddabbcdbdaacababbdddbaccacbcdbddcdabadcccdbcbabbbcddccdcdacbbbccdabbabaadbabaccadcbbbabadaccbbdddaababacdcabcdddabdddcaabaabcdaacbcacdcdbacbcbddbcbbddabbaabbababcccabbbdddbcbcbdbaadadaabbaaccbdaadbbadbbcbdabdbadccbbabadbcbddaabbbaccadbabaabaaaacdbcacbbaaabbcdbcddaadabcacbdadbaddbdddbcaacadcddddabccbdbbabcddcacccbddddbbdcbdcaadacdbcbbcccbdaacbdaaaacabaacdaabcbbbcbbdccbdabcadadaadcaadbabcabcaabdcddcaacdcacccabbacbcbaaacadcbbdcabddabacaaabdccdbadccabcadcaadcaaadbacdbaacadbcabbcaaabcbdcabadbbaabcadbbccaadadccccdcadbdaccbaddbdbabbccbcbadaaddccdcabbbdabccacbcbdbadaadbaadcdccaccaacadabadaacdbbbdbcdcacdcbaccbbcdddbaacaaccbdbabdcccbbcccaacbbaabcaaaccbbcdcbcadbaddcbbabacabddbcaadbcdbbbbacaaddacaaddccbdbccbbadbdbdabcabcbbcdcadbbaadaaabdbbacdbcdbacabdbdaabaaacbabaaaacbdbabbabdcbacbcdaadbbcadcabcbdccbbbcabbbccaaabaddbabbaacdcbcdcbcdbacbbcacaabcbabcabacdcbcbcaabcbacdadabdbbbbdcaccbcbdacacbaccbdbccacbdaacddabbadcabbabcddcbcadbadcbaadbbcbabbdabbccadddbdbcadcbaccbbdbcdcaaacccababbdcbbabddcbddccbcbabdabaaaabbdbddcdcbcaadcdddbcaacbdcdbcdcccdaccddbbbdbbaadadadaaddaddbacdaaacbaddbcccbccddbcbcabcdabbacbcdaccddaacddabdabbaaccddadbdaadbcddbdcdabdabbdbacddbdaadabacbadaccabcbaacddddacddcaddcbabddabaacabbccadddadccabaadddcaacbacdcbabaccdabbbaaaaaadcbbdcabaabcbcbddcadaaccacbcabaccadbdcdddaaaabdbdbdbdddbdbbdabbddbdcacccaadbabdbcaadcaabaddcdabbcadcaadcbccccabacadcbbdadcacacadcdcabbaaaddcbdbaddbaddcbbbacdaccbaaaacdcbdbddadbabdcadbdccddbadbacadbbaacccdcacbcddcbaaccddabdccacccbdcadaccabbacdcabbddaccccdbcccdccccdaaddddabacabccbdccdccabcdbbacacaacdbcadccabbbcbdaaccbabddddbdbbaabdabccaddbadcbaddacdaaaaaabddbdcaddddcddadbcdbbacaadacdcccdaabcaddaccaddcacbbaadadbcbcddcbdaccbddbdbbaddaacbbbaadccaabadbcdaaabaabdabbaabdcdaddcacbaabdcbdbcacccbbdadddcadddcccabdacaabddbcaccaccadbbcbaacabadbaaabbcccdaaabcdcdcdabadacdbcaddbcdacdbabacbbaacaacabddccbbbdccbcbcdddbbcbabdcadbaddabbbcbbaccdadcdacaacbcbacbccabbcccbbcdbcdbbdbcdcdbcdaabccddcadbbbcbbcdcdabbbcacddbbddccbabdcbbbdccbaaabadaacbbadcccacdbccbabcddbaaccbbdbaaccdcacbbdadbcaddcbacaabdacdccddccdbacdacdccaacccdacaadaddddaccdcbabbbccbdcccdadcbacccbddcaacdaddbabdccadbcccacbcdadbaabbdabcccdcaccbbccadabbabcaabdcbddbbbdaadddbdbabcbcdccbbaaaabdcdadddcbcbacdcdccdbcdbcbabcdaaddaabcccaaddddbdabbacdbddabadacbccabaccdcdabbbabbbaaccbbdbdcabbdcbcadcbcbbccaaaddbacbacbddcbcadcaaabadaccddcdcbdcdbdabcddaacdaccdbbbbacbcdaaacdbccdccbcacccccccbdcbcbbcccbdddcccbcababcaacabcacabbdadbdbddcbacbdcdabbbcbdcddabcccbbbdbbddcbdaadcbabdcdabdccbbabbacbbdbdbdacdddcbbdcdabcbabcddbdacbbabdccbbacadbaabdddccaacbaaaabcdacddaabccdbdddaaaaddbaacdacaccbaccccaccadabdcccaccbadabaadacdbdbccabdcbcbacccbcdcdcbbabbadccbcdacccabbcccbdcaabdbaaadbdcadbadccacbadcabdacdadbcccdcacdcabdaaacbdbabccdaaacaacbdbdcaddaadbdacbcdaaccdbaddbacccbdadaabcddabccdbdcbadbabbaddcbbbbadacaacbccddbbbabdccacacacabcccabcbccddaddacdbcaabdbabdbbddbdaaaabbcddcdcdbdcbacddababbacacbbabbdbadbbabadadbcdabbbcacdadadaaabccbbcbddcbdcdacdaadcdaaadbccaccdaccadbbccbddbdaadddbbbaddbddbbacdbbcdadacdcababdccccaaaddcaaacdabbcdaaaacdaaddadbabbaabbbabaabcbbbdadcbdadbcbbbddcbdaaabddacaabbcaccaaacadddcbdabdcacdbccdddbbaaccdcddcdbbbbdcdadcbaccbbdadcbbdcaacbbbabcdcacacbcadcaadaccdaaaadcdbdadcacadacddadbcacdccaaccbcdbdddcdccbdcbbdcabcbacbdddbcbadcaddadbbbdddcdcadabbcbbbadcbaaabbdcaacccabddadcddbabbccdacacccabbcbbdabccbadcdcbadadcaaabadcacaddbdcbbdaacbaabbddcbaddbaccbbaaccbaadbabadcabaaaaadbaccbcccccbacbcdddddadcacacacbcdaddbbdabadcabaaabbaadabaacbabddbdccdaaddaaadbcacbdbdbadabddcbcdacddadaacabbccddbcbabbadbdcabbbacbddbccaaadccdaaaacbaacaddccbdcaddbccbadbbaacbabbadabbddbdbdcbdbbcdbbddabaddbabcdacdadbaccaccdbdaddaabdbcccdaccbdbabbadbbccdccbcbcdbbcbddaddbcbacdaabacbabdbddddcabdacbcabadabbacaabcbbcabbdbacdcabcacbbbacbbddbcdcbbdddbadbbbadcbccddcadabddabccbcadcddabcabdcadaaccdadddcbcaadccbdbbdcdcdaddaaadbddbccbbbcbbdccccdabcbbaaddacdbcbbabacbadacdcdcacddcbabbbaaddbaabdadcbdbaabdddcbacbaacbbbaadbcdbccdcdacdaccbdcdbabadbcabbbcdccdcdcdbcdacbcbbdababacacabdbadcccdaaadaabcbdaabaabcddbabccccddbaaddbaddcabcdabbdbdbccabdacabdaadaddcdcbadaaaccaaccabcdadbdadbddcccdaabaddbdcbbccaaddbdbdaaccdcccbdacbcaddbcbbdccbcdacdaaabbbcabbcdbabadaddcddabbdaaccdcaabbcaaccacbdddbcbaabbcdddacbbdaadbbbdcaadcbbcabaabbdcbcbbbdacccdcbdabaabcaddbaaababcbcdabcccdadbdccdccbdbcadcccddcacccabdcdbaacddbaacadabdddbcbbaadddbcdbcadadaacacbcabdbacbadacaaabacacbddacdbabbdcabccacbbdcdcbacbccacabcabbcacacbddacdadcabcbdabbbbadaacacddbbdbacdadcacddcdaadcabcaddaababccbdaabbccbaddddaaddcbdbcdaaccdabcddcdbcaadccbadcacdcccadccdadcbaaccccdccdccacbabccaabaadbdbacbcccababbdbccddbbccacaabacbdccaadabcabdbdbbabcaadbaadbcbabdcccdadaadddbcdbadacbdcbbbadcbdacbcadbcadaabacaadbcdbcacbaaabcaadbadbcddcaccabcabbbbbcadacbabdacbcddbcdccccdcbdbbbdccdcbcdcddcababcadaadabddbcbdcbdbccbabbbddbbdcadcbcdaccdadabbadaddabdcacdcbccacdadabdbbdcbccbdbdabccddbaacadccbbabdcccdbdccdadbccaacbbdcccdcbbaadabdcbadbdbccdabbadcbbdcdcccaacbdbcbcdaccacdacccbcdbdbbbaaacdabcdcccdacbcaadcbcddbacbddbacbbddaadbbcbcdaaacbdbacbaacaacbdbdcbcdbdcabadccdccbcbccccdadbcbdabdabbbdaaddbdaadbcbbadcacdbabbbbdbcbaddcacadbaadbbdbbcbcaadbbbadbddabaccddcaddcdabdaaccdcabcaaaabacddcddabdcaaacdadadcacbcacaddcbcadbdccccbcabcdbabbdbbbbbbacdddbdddbcbddcbddaaaccddacadaabaadcadcdbcbdbbcdcaabdaaccdcaaabcaccddadabbdcddcbdbccacbbabbaacbabaddbdadcaddcacaadcbabdbdbcbdcaabcbabadacdaacbdddbcbaccbaaaddabbbdddbbbdacbccccdccbbcaadcbabbbbbbaabbbbcbccbdcddccbcbccabacaacaadcbbdaccacabcbcaaacdbcabcddaadddcbabbaabaabbcbbbccbaabbadcdbbbbcdabdbbaababbdbbcaadaacaacdadcddcbbbcdbbcaabdcbbbbdaabbacacdccccabddbcbdabbccdcccaaccaddaaabaccdabbcdbbaadaaabccbbbcdaacaabdbcdbcbddbbbdbbdacccdadbcccdacdadcbacbcdbcccdbddddddadbadcbdbcabaccdadcaacdaabaccccbbccbbcaadcddaccbadbbaaabdddaabcadadddcbaaaabaacdbcdbabbcbdccbdbdabccbcadcddabbbbdabdaaddbdccdbccbaaccacdacbdcbdccdaacbbacbcbdacaccbdadabbbaacbdaaaddbdacdadcdbbabdccabbcdcbaddbbacdbbabcaddabaadabbaadbbadadcabcaabbdbaadcdcacdddbbbaacaddcbcdcbbcdcacbcdcbaacbabaadabdcbdbccbddcdabbbaccacaaacbcbadacabdbabddbcabcaddacabbbcacbcbaacddbcdbccdddbdbaadbdbabccdbccdbcaadbabbddaccccbcccdaacccccaadbaabcbddbdaacbdcbccaacccacddcaaaddcdaaabcbdbbbaaaacdcddbcaacbacabdcaabddcdbabcadbaccdabaacadddabacacbacabcbbcacdcacdcacaccadaadcddbdabdcbdabacadcbabddbcbaccdbaabcccdcacbbbaadadddddcabbcaaadbdadbbbacdacaabadcaccadccbcbaaaddadbbabbbccbdcdcbcdcdcddabaaccaddbcacdccbcadddadcbbbcbdadacbaccdaacdccbccdbacdacacbabdbddacdcaaccacddcbbdacbbcdcadbabdcacbcaccbbbbbbadadcdabaadabccdbdbbdbbcdaaaddbacbbacbbddbccacdddacadabdbbcdadaddadbcccdbbbbcbcdaadbadcaddcbbcabccadabcbccadcdaccdaadaaadcacbacaacbdaababddabbdaabdcdccaacbdcbddadacabababbcacacbaacccadbcbbbdbabdddbaabdadbdabdbcdbbdbacdcadaddccbabaabacbadaccaabaaabbadcbbbaccddddcbacdcdbbbdbcbcbaaaddbacdabbbbbabbdacabadaadbbbcbabbccdbddbadcbdbcadccdbccdbdccdadbcddbcacdbdcddbacabcdbdcdabbddcadadaabbccccdaadbdbbccacacdcaaddaacddcbacdcdccbdddbccaabcdcccbbcdcddcdbcabbbcadcdadbbaacaaabbdcbbdbdaddadbadcddbdbcdcdccaacdacbaacaaaaacacbabdabdabcbbdadcaddbaacbbdcbccdbbaadadbcbbadbabdacbcaccadacdccbbcadcbdacabadcdaccbadaacadccadbbbcacdcbddcdccbbdabcacdadbdaccddcccaaddccabbdddddbcbddaddabbaaaabdccdcacdbcccbcaadbaddddbcadcacaabccdacbcccbccadcbcddadcccbcbababaccdadacbbbacddabdcaaacdacacdcaaddccaacdbdaccbabdaabcacadcaacaacdbbccadabaacdddaaaadccaacacbdcaadcbabaacdbbababdcdcaddbabdacaaabcadaaabababdcabdaadcbbadbdbcaaabaddadcadbbbbacbacdbbcbdaaaacabbdbcdababaccacbcbbbbbbdcababacbdadacabbcccdbcccddddbdbbaaddcdcdbabbbadcdcdacddccccbbcdbbcccdacaabdaacccbadacabbadaacadccdacabbbdccadcacdacdaaabccbbcbacbcdabcdabbccabccbdbbdabbaabddaadaacdcdbcadcacaacdaabdaadcaabaadadbbdccbbcdcddccccdaacadddbcaadabbdbdadacadbccaddddcccaaacabcdbdcaabdcdadbbcbdcbaccddaaccaabcabdbdbddccbaddacbbbacbbdbbddcbdcdacdabbbdccaaacbabaddadcbbbbbddcbbdaccabbcdddbddbcabadcbaaccddcdddddddbdabdadcdbcbddacdddbacdccbdcbaabccdadcdbccdacababdbcabdbdbadddbdacdcaaadaddccdddcadcdabbbcaddcdabcbadcabbaccbdbaabababbbabbbddaabdaaddcbdddcbbcacabbabaacadbcababccdccaadaadbdabacaaddcaccbdcaaadcdbaccccabbdbabcccddbdcccddcbaccaaccbdccbcdcacdcaadaaacadcadadcccbbaadacaacdadbdcbadacadbadacabaaabcabbcdcdbcbbdacbaadddbadcbadccbaabccccdddacccccbccccaaaabbdcadcdbddbdbdbbdddcaabbddccdcacdcdbdccccbaaacddcdaabdddaacaadadcbbaaabcdacaddbadaddbcdcbaaababbaaaadddddbbbbbddbcbadbcbcadbaaadddbaadacbbcabbdbddcabbadacbddadbbbadccaaddbdbaadcaabddacacacdddddcddcaddacdbccadaccccbcddbbdcbcdcdcbbcaacaacddadcbccddbdcbbdcbacdacccbcbacaacdbbabcccaddabadcdbbddbaadddbdacaccbcbbbcdcbdcdccabaabdaaaacacdabcbddbcdcbbbaabacbdaababccadbadbbcbacbbddaabccdbcdaccacdaaaccbdbcdddaaddcacdbbcabcbaadadaaccadabbaaddadacbcadacddcbccaccabdabccddbacadbdcbdaaaacdabbcaaaadbababbbdabdacddccbdddababcaccabcbddbadbcdbbdabbaabacbcabcadbdcacacddcbdbdcddbddcdabbbdaaadccbadcbddccccccababddcacdcbbcaadddcddaadadddbacbaaadabbcddcadcbddbccbaacabbabbbccdcacbabbcacaacddcbadddcdabbccccadccdbadbbacddacabbcacdacabcdcbcadadabdabdddddcbddabcacdcbbccacbcccbcccdccadcddbbabbaadacbbccbbbcaddcacbcdbbdacdbcabcdadcbbddddaccbbbbcdcabdacadbacbbddbdddaaaacacbbaabdaaadaacbbcbdabdcabdccaaddbabbcdbdaaabbaddbdbcbcbaacccdbbadcbddbdadcbacddddbccabbddaddbcdbcdabdbbbcaadabcccccbdabbddcaadbadcddcbabaaccbcaddbdbaaabcadaacabadbbccbddbaaacdaadcabaadbdbaaadacbbdccbcabcbcacbbcadcaddcadaadadacbdaaaadcdccdcaaacdcadbbdbbaccbccbbbcbbdbadbadcabccdbdbabbdaccdddccbdbcdbadddcdbdcbaacdccaabcbaddabbdaaadcbdccacabdcbabacbcddcbbbcaccdaabadbbbddbdcaddadcbbcdcdbbaccbbcbdbdabacddcdcbacbdddcabcdcdadddaadddcababdaabccdacdcaccbbddccaaabdcabdcabdcddddabaacadbcdaababdcacadbbdabaaddcbbaaacaaddbabcbdcaaadbcadaaaabacaabcdbccadbddddcdcacacdaadbcdcbabadddaadbbaabdbabaddbbcbcdcccaabaacaadbbadacbcbabaddcabccacadbddaccdddbcdacabccbdcacbbcbabcacbabdccbccbbbdbbdadcbbaacdcabacdddadbbddddabbbcbaaadddcaadabbbdcaacaaacbcdcddacdcbbcddbababdacddbabdbdbbdabcdcdccdaabcdcdccdcdaabdadccaccaabdbabcacdccabdacbccddbbdabdabccaddaacabdcbddcabacabccabbcacdbcbbadbadbabdbdbccdcbccdaaabdccadabdabcccaadccabcdddcdcdbbbccdccbbaaadcbcabdaabcacdbbbdaabadcdbddddcaadabdacabddabcabcbcddacabcbcdbddaadccbcacbacdaacdbabdbabadbdabaadabacdccbbbdbdbcabacabbcdacbcbdabddcbbbcacabdbdaccdcbbcccddbcbabbacbdbbabbcbcadaaaaaccbaadcaacdcdbdaddddbcdcabddabababdaddbcdaacddbabaabcbddddbbbcabadabccdcccbaccbadccdaacabdaaccbcccbabbddbaddadacdbadddcbdddaccccbacbaaabcbdcddcaccbbbbabddcacdbcbcbbbccdbacdcddbdbdaccbcbdaacdacaabddbabcbadacdadcbccbbadbccccaaadddbdbbcdcdaacdcdaaddacbccdcddcadccdbddabccdbbcddabbabdcacdcbcacabdcacaccbbcdbbcbbaacccbddababbdaadcacdaadcadaabcbbdddbbbbabdcabbadcabcbbbabccacbbcdddbbbbabccacaaccccdabdccbcaadccbcbaadabacbadcadbbdddccbbaddaaadaadbacdbbaadcbaccdbdacccbddabaccccbddddaaddcccadaccdabcddbcbccddacbcbbcbbacbbbbaadabdaabaacabbcbbbdbdabdcdcabcdaaabbcccbcdddcaddacdbaaadccdcacdadcbcbddcdbaadcbddbcbccdccbaccaabbabcbccdcaabcadbccdcccadabbcaadcdadcccbaccbcdbdbbbddddcacdaacddaaaaccaaacbaaccdabaadacbccbcbbabcaabcadbccdbccbcaddccdadadbcccbcbadbbbaabbdaadaadaccdbddccdcbaadacbcaaaabaaaacadbbbadacdacacbcaaabaaddadccbdabbccbcdcdacdbbabdacdbccaaaadaccdbabdabbacaadbacbabddcbccddadadbcbaabbcadacdbabdacdcaddbadccdaaacccbaaacbdccacdcbddaccdbcdabadbaaadbdbcbadbccbabccdbacadbddabdabaadcbabdadaccadbccdadbabadcdbbcbaaabbbaccdccccddbbdabdcaaabbcabbbdbadbccbcbbabdcbacddacdcccdacccabbdbbdadddcddbcdbabbddbacadaadccbaacccababbdccdabaabdddbadbbadccdddddcbcadabcacdcbabbbbdbbdbccbccddbdaccaacbcbccadddddbdabbdbadaabccbadbbcccbcbdacbbcddacdbdaadacccbbbbbdddbdaddadbaadbabbbcccbbabcaccadadadbbbdbccaacacbbdacdcdbaacbdcabcadaaacbdddbcbbababdcbccccbcbcabcaadcbbccabbbcdddaddcacbbdacaababddbcacdbcccdbbaadadabcbccbaacdaccddacdcbabccbaaccdddaaabcdcbcbdcdbbbddddaccadbccdddacdbbbcdbcbcadaaccbdcabbaddadcaccbccdaadcbddabdadcdbabdcdbbdabddadcbcabddbccadbbaacbdddabdaabbbdadadcdddccacbcaacdbbbbbaadacbccdabadccdabbababccabadaccbdcbbbaadccccbbbccddababdddcbccbcdcacabcbccccbbbacbdbdcdccbdbabcdababbbcbaabacbcccaabdcbdadcdbdbabbcaabbbcaacaaaaadccbabbdcdcaaaadcdbcccdbcdbbaabdbcbccdabccdcbdcdbdcbdccdcacbbdcdbdaaaaddbbabcacbbcdbaadbdbbacddaaadbbcaacbaabbcadcdcabbbbcdbcdbbcdccbbbaaccaaabbbcdbdabdbcbdbbbcabbadbabbcabbdccbdddddbbaabbcccadccacabbabaadccbccdbdbcddbdacbddbccaddcdbcbcbbdbcdddbbcbcbbcdddcabcccdddbbbadabbcbaacddddbbccbcdadbcbcbcdacabdacdccabcaaaaddadaaddbdabdbdbdbbaadcddbbadcdacaccccdabbabbcccdacacbddbdbbaabdcbaabbbdcbaabdbdbccbbccbbdddcbaabbbcadcabccccbabbabcbdaacbaabaaabacddbabbcbcacddaabaabbabaaabbbadbdcbcbbcbaaabccaaadbaddacdbabbbdaacdaadaadbdddcacddcadddbccdbcbccccabbddabbbbaabbcbcbadacabcccaadadbbcbabcdacadbaacdbdacdabcbbaaaabdabadbcbcbacaadbdcdaabbbadbaadbccaadaccabddcaacdcdaddabbaaacdacdbaccabcacdbaaddaacabcccdbdaabadbcaaaaddbdcbacccabddddcdaddcbbaccbadacbbddbbbabbadbbbbddddcabcadcdbbcadcabbdcaabdabbcdadadbdbcbbbcdddbddcbccddcbdaacbccdcadbbbabccdbbddaabbbacbdaabccacbacbccbaccaacbbbdbadcbacbadccadbacddbddaccbaacbadbbcbbdacdbbdbbaddbcaadcadcaaddccbbbbcddcadcbbabcccadadddabbdacddccdcdbaccdcddaddaddbcbbadcbabbccabdbadcbbddaaacabdcacbacaddcabdaabcabaadcdcbcdcadaccdbbdcabccbcdddcbdabadcaaadbabbabbbbcabbbcbdcdddcbccacbadbbcccdaacddaadcccccdbcdbbcbbbddcbccbbacaddccabdbabbdaabadcccbabdcabbababaacbccbdadcbbbdacbacaabddbaadbbddbbbdadaadabcadcbcddbcacccbcacdbbdbcccbdabdaaaaabbcabddacabbabbaacaddccabccdadbbddadbdabbdacbddbccbdccbddbaddbbaadaddacabdccbabadadccbddbaababaacbacacbbbaaaacabaddddcabbcbcccccaabdcbabbcbaccbdcdccbdbcacccbdbabcbdcdaacbdaacccbdabccdbbabbdaabddddcccbbbadbbcbcddbbabdddcdccaababdcbbbbbbacdbcbabcbddbddcddcdabdcbacaabcbddacbdacdaacdacaabbbcbaaddbbdbdacbbccdbcabcdacdadbdcdbbddccacacbacdabacdccddbbabdabbdbabccbadabdaaadacbadabdbaacbcabdbdaadabcacbcdcbbbcabbcdaaadcabdbdadbbacdcdadcdbcbaaddcdcbcdddaaadaaaaddbbdacdbabadcbbddcbbacdcbcabdadccbcdcddadacabbbbbaabdacbcdcdcddcaaadccbaaaabaddbbcbaabdacdcaadadccbbdcdbbcddaacccccdacbdaabddcdccadaadbcddacbcadabbbcbdacadcaaccbbbabdbcacdbacabadccbaadcbbabdcabadadcbccbcabdacadbadbacabdddddccdaddddccccbadacabdcdadbbddaaacbaddcaacdbccccccccbbbaabdcadbbadacdaadcbdccaabdaaacaccdbccabdabccdcadddccbbdbaacdbcaccbcdbbbcbcbcdcddbdaabdabdcaddcdcbbcaccbbbbddccabddbccdabaacbadcaddcbbcacadaacbcbdcbdbcaaacdcbcabbadcddacacaaddacdccbbbacbcbabacbbcbdbabcaccdaadaaabcabababddbddabbcdcbdabdcbbcbdcaaccaaaabadabbdbacaccbbbacdadcbdbaabddbadaaabbcaccaadcbcbcaabcdcdcacbcdcdabbbddaccbbbabacadacdccbaacccaadbdbdddadaabdacbcccaacddcbdbcddbbccbbcdababccaabddbdbabacdaddbbdccadabaccdddcbdbccacdabddaccbadbaddbbdbdcadadddacadbaabbbdbdcccdbcbaaaaaccbdaaccbddbddbccbdacbbababbbcdaccbabdabdcdddbcbbbabcbdcacacacbbcaadbddabdbcbdabacadddcddddcdcdbadaaaadcccdbcdcdcadaabababbccbdbdbaaadbdcdccbdbacdaacabdcbdbbdcddaabddaabbbbbaacbacbcadadcbcaaaccbbbcadbdadbabbadcadbddadbdbcaabcbdadcbacaaccabdaaadabddbbcdbcccbdddbdddbccaabcdacdddaabadabcadcabcabdbbcbddcadcbdcdbbdbacdbacdbdadcccdbbacaadcadbdbacabccbadbcaadbadcbadbdbcabddcccccbdabbdadbbcdaaccacdbddaddbbadaaaabcaacadabadbadcbdaadbbbadadadaacccaacbacbbdaaadccbbdadbbbbbaacaabccaaaadabcdbbcacbabcbcbddabddccadcbbcacabcbbcbcdbdcabbccdcddddabcabcaabdcccbdadbabcdbddbacaababcccddddbdddacaaaabcddcdacddbacadbdddbcababbccaacaccbbcadcaacbbcbdcaaddcbbcbbcbcddabddacbdaaadddccbcacbbdaaaabdcbdabcadddcdacbadbdcbadacabccbddcbbbadddacbacdbadddcbabcccbbcddddabdcdcdcbbddbabcabadaabacdbadddcbadcaddcdbcacadacacbcbdcdacdbbdbdcbaccdaaaccaddbaabbcccbdccbdadcbaccaadbbcdddcaacddbdabbaaadadadacdadadadddbccbcabaccbacaacabbcaddbcaddbcbadcbdccaacaaccccbcdccdadccabcacadadadccaadcddabaaadabadcbcdbabadbcabcbaaacccddbcbcbcadddaadcabbaabaabbdbdbbdcdbbabaadadcaacabcbacddababcbdacadbcbdbcbcabbddcbcddcabdaddaddcdcdabdccdaaadbbccabbadbbacabcabdabaaadcddddaddcbaddaadbddabbadccbabdbaccbddadbdbacddbdbaaacbabacdbdcbcddbcadbcbdccdbbaaabdcadcabccbaabaddbcabbccbacbaccaaccaabdaabbdabccaaccacdcaabcccabdbababadabbabcadbaaddcaacbdadbadabcdacccbccbbbdbdbbcbaadcdccccdaacaaaadcaadcbbacaaaaadcaacbacdacbdbbacacbcdddadcddaaabacaaaddcdabccdddaabbdccccbbcccbccbaaabdbcbbaacacacacdabbdbdaaccaddddacacbaadccccbadbdccdbccdddcbabbdacabaddccccdbcabddcababbdadcacccddddbcacdccacccbdcacbacbdbaddadddccabdcdddadabacadcddacaccccddcbcccabbcbcaabcdccaabbbddcddabcaabdadacddcddcbcbcbbadacbcbcaaacaadadbcbdcadbbcabcdddbcaacabaccbbaddabbabbbbaadabcbaddcdabbdadacacddcabccdbababdadacbcbccaadcdbabaacbdcbbbccadbacacddbcbcdbdaccdbaccdabcadbbccbdbdacbaadddddcadbdadbddddabddbddbbabbabadccbddabbdddaddbaadabadbabdaccbdbdbcddcbdacbcdadacdadabdadbdcaaadbddcbaccbadadabcdddbaaaccddaabcdcdadbbbbadcadcdaccddcaadbaddacdbbbabcbdddbaabbbddaaaabdbaccdbdbbadbdaacdcbbcabbbdbddcbacaadadabbbdbdddacbbdcabbbaddccbbbdadbabdbabcaaabaaaddaaccaaabcabbdbccdadabcbccddccadbdaccadbbbbddcbacdccacaabcdbbcadaddcdbacacccbaaddbcccaacacacacccdbdaccccddcbaaadaaddccbddcabbbdbdbbbddcacdcaccbdaabbbbbacbaddcaccbbacaacdbbbbbaddacdbcdbcccadbadabddddccaadcbddbbcbabaaaadcabaaddacbddbaacbadabdccdbacbbadbccacabbdcadacbbddcbbbcccaadccdcccaccbddddbddaaaabbbdadcddddcdbdbdacadccbbddbdbcbbbbdcacaadabcdaacccdbadcbcdcdcbccdaccdaadbabaabaccacbcbadccbddcbcdacbdcacbadccddbcccabbabcadbcaccbabbadccabddaddbdcaccbcccbacbabbcaccaccbdbdcdbabccdccbbbbcdbaaacbacdaabaccbacaabcdbaaadaaddcbbddddacbabcdbdaababdbabaacaaacaabaabcccaaabddcdacbabbaccacdbdacadadbcddacbdcacdaadcacbadbcdabbddadbcdbcadccdddcbabbacaccaadcacdcbadaabdaccbaadaaaaccaccaaabdaadaccddbddcdcdbdbbadbaacdcaaaccbadcdadcdacbbdddacdbcabdbbbddbcbacccddbcddbcdcaaaadcbbaacacabdcbabbdcddbbbbbbbabcdcdcadbbbbcbaaabcdcabdacddcbccdcdcddcadbcbbcbabaccaacdcccddadbdaadcbdacbcaaaabdaccddcabcdbcadbdadadbaaacdabbdaadccccddbdacdbbaadacaaddbaadadbbcddabbbddadaadcddbbdbccaadbdbdabaadbbcdbdcdcdcdbdcbccccbcbbaddacbbabcaabddadadabaacddddcbbccacdcaababcdaaddcccabbcbdccadccbccdabbacdcccccadbabddddabacdbbcdaccbabdbaabadccaddcbccdbabbadbbcbbddbbaadcbadddcddacccccaddaabdddbaacbaacbccadcadddadcbabdbdcadddbcbbcabdaadbcdccadcaadbbddbdbcdbbaadacbdaaadacbbccbaaabdacbacbdcbdccbbdaccabdacbdaacaaaddcbbbddbdacababcadbccddaabdabdcacdbbdcdbdacdbaacbdaaadcacbbadbdbadacbabcbcbdabbccbcbcadacdccbcdcdadbcdaccadbadabbabddccddaabbbbbddcbabcdbbdbbcbadadcaddababddcacbccddaacdcccbcbcbddbadacaddddbbbccddaadaaabbdbaacacdbbacbcdbdadcdddbdbbbcacacaadbdbacabdbaabbbaacbcbabdcaabbbaabdaacbbaadcccacdcddddbdbabdacdbbbcadddbccaabcbabcabcbcdbbaabcdadddbbcabaadcdbadcdbdcdabdccdccaacabddcbbdbcbaadadbdaabcdddbbdcdcabdabcadadcccdcadbcccdbbddcdabcbdadaabddcdabdddcbdcccdcabdbcdbdabcacabcdcabdbcbadadccababaaaddddaacabcccdabdbaaadcccbcaaacaaabaabdacdbdadddbdbbbbaaacaacddcdabbcbbdbcbbdddbddcbdaabbadbacddcadabbcbbdaaadacbccbdcacbbbdcbbabcdbacbdaaabaddbdcbadabdcbcabdbddabdcccaaabcdaccaaabdadbdaaabaabbdabdccdddadbccbbbddbddbddccabdbaccdbcbbaddddbcabdadcbabdabacbbaddcaaaaacbcdacdaccdddbdbcccbcdcbabddccbcbdaaccabadcbcaadabdccdbdadaabdabddaddddccdcdcdbcbacbacadacdbabaccadbadbbcdbccbdaaacaccdcbdbcbbdcdbaddabbabcacacbadddaabdddbdcdaaabccabcdbcacaccaaddabadddbabcdddbbbaaabccbbcdaddcacaaaccdbddcdabcbddbbdcacaadadcbcdabbacdbccadcbabdbcbbcabbcbcbccdccabaccdccdaddbbcacbcaacdaabaddaadcbabdbcdcbadbcadcbbbabacccdcdbdbabcdbbddbbdbcdcacbbaaacbbbcbcbdbcbbddccdbcdbcdddcbddcabdccdbdcbbbcccccdcbabadadcaaacabcbdbcddccdaadbbdbcccabbcabacccabadcddcccbcdbdbabbadadadcbddaabbccbbabcabaaaacdbdbdaabddacadbadccaadadbaadbdaadbcdaacacacaaaacddbcbbbbdbbacbddbdbbcbdbcabbbbacbbdacaadddbaadbbbcbadcccdccaaabcacabadccccacdadbdcaaaaccddaacbdbabacdccbacddbdacdddddcaaabbcbcaadcccdccdcbadcdabadbcdaddcacabcbadbcdbcdccdbdcaccddcaccbbaabdadcdbddaabcbdaccabdcbcacccadcccdcbadcaadaaaaccabaadacbcdcbabccadbdcdabcbcdbdcbacbdbaddbccadccdccbddbcdbcccccdbbbaabbdabaaabdbadcdabcabadbcadbdbdacdcaaadcaabcbbcadcdaddddcaacddbdddaaabcccbdaaacababdcbbdddacbdbdadcaccccabbabdcdbabbbbbdabcbbacdcaabbcbacdcdcbbaaddacabcaddadadcddaabdadddddcbbbdccdbbbccacadddccdcdbddaabdcacbdcbadccaaacbbadbbdccaacdcabcbabcabbddbbdccdcbaadadbadaaccddabdabbcbbaaadcdcbddcdcadacacdccaddccacddbcacccaaccbacdacbadcacabbdbcccccabdcdcacaabdcacbcbccacddadbdcdbbcddddabbdbccdaccccbbbaabbabdaccddcbbdbbdcccaabdaacccaacbbbbdcadbcabbdcdbbdacbddbcdbbcddcdaddccdccacacabcdbdabbabdcbdcbbcbdbbbacdbadaddddabbacbcddddccccdacbddabcdccdcbadcabdaabbcadadbddacccacadbabbadabaabcbdbbcbcabdcbbbddcbcacbabcdaaadadaddbabbcaaacbaabcbbdaabdbcbdabddbbbdbadadbdddbaaadabaddbadadbadddcbdddabccbdcbbbcadababacacdbdadbcadbbacdaacdcbbaabdccbcdaabdbcccacacbdbaaaccdacddddacadbcadcbacdadaaabdcddbdcaadcdacdbcbaaccddcbadbdddddcbadcadddcbdcadbbcbdbaacaddddcabdaccbbcabbbbacdabdaddbadbccaabcabbbddbbbcddbcddbdabcbadcabcbcaaacabdaaccacdbdadbabdbdbcbcbdacbbadcaaadddacadabaacdabcddbaabdaddadbbdbdcabacaaccaacccbddcddcdcbddadbaaaddabadcccdabcdbdcbabccabaabcdabddbcacddbbcbdaabdaddacdbbacccdcaabaccbadbdccdcbccddddddddbdcbcdbdbddcaababbacbcababcdbcabbaaadaacdadcacaaddadadddadadbbbaddcaccbaadcbddbdccadbdbdacacdddcadbbccdcabddbbbaccbaabdbccdcdadcabaccddbbdbcabcadbbbdcbdbdacccddaabdaadbbbbcbbbdcacdbbadadcdaaadddddaabdbbddbbaccdadcbabccbbccaacaccaadcdabadccacacdaacaacacccaccaddabbacbabbcbdbcaabcabbdcbcbdcbbaaabbddacbdccddaabdccbbbbadcacdaabaddbaaddcabbbdcdbcacaabbbadccadbccabacbaccdbabbbbabbdbdaadccdacadbabcaddbdabadbbdbdcaaddcbacbbcdaacccaadcbcbcccaacbddaababaacbaadcaabacbbcddccbaccdcdcbbcdddbbdacaaacdaabcccbbaaccaababbabdccabbdbadadccbadcadcdbaaadbdbbabbdbbcabbdbdbaccabdabcaddbadabacaababbcacddcadcbabdbbcdbbccccdbadadabbbaaccbaacbdaddbaaabdcccdddadcbdbbadcbdadbbbdcbbddbccbacaaddccbbabcddbcaccaacdcabcadddcaadcbcbadbcabcdbdcdccbbbdbbacbbaacabacabcadcaadadaccacbdbdbaaacbbadcdbbbdcbcbbdddbdadbbcdbaadccaabdbddcadccbadcabbadadcbaddabbbacadaadbbaacbadabbaaccbcccbaacdabbccccadbaddddadaaacbdbdbcbaaaadcbbacaddcacaddacbadacbdbacabcbbacbabdaacdccccdccbdacccdbcddcddbccaddacbabadcabbcdadacbaacabdaaacadbddcabdcbadddadaabbcbcdbdaacdbaacddcdcacccccccbdbbaabccbbddbbbccadadbcbccbcdbcaaadaacdcbbdbacaaaadccdbbdddddbdcabbcbbaccddcdcdcddabcadbdcbdbbacacadddcaccdbcacabbcdabdcabaacddbabbabbaaaadddbcbadadddabbbdaadcbdacbbbccbdabccdaaaacbcbccccbcdbcdcccddacaccdcdbbaadccddaabbddbacaaacacdddcbadbccacbacccbccdababbddbdadbdbcaaddadbbadbcdabcbdaabddbcbacabcbdbabbaaacaaccbddbcaabbbdbdbbcdbabbcdcabbbbbcbccdcbbcbbdabacbddbdadbbdccbdcacaacbcccdcaaccbaadbaccadcddcdcacbcbbcdbccdacabbbbbaacaaadabddcbacbaaccbcbbbaccdcabcdacccdcdbcbdacbabaadcaaabdcadcadcdcacdccbabaadaddbdcccacdddcdabbabaadcbddbcadddbcabbddcacaadbaabbcaadcaacbbcdaadaacbcbcbcbdbdadccaddabacbccadadcadbbdcccaabddabdbacdaaacccaaaddddcacccbdcdcdaddabccbacccdcbabdabdadcaabcdacddccdcacdddcdbccdccddaadcadcdddccbbadcadabdcccabdcdadcccacddbdacbabcadcaabcdaddaacbcabbacddaabbdcbbbcaadaccbabbdbddbcdbbacdcbbaaadabbabdbbacaabbdaaabcdddbacaadabdcababbcabbaadcdddcaabdcdaddadddbdcddadaccacadbcabbdbcbbcadaaaadadddacabdacaabacdbaddcbdccbdaadacdaadaaabbdcbdbdcaaddcdddbbdabdacccdbcbbcddcbacababcbddddddddacaddbcdcadcacadbdcbdcadcaaadbdddabdbabbacddbdacacaaadaccddbbcbcdcddbcbabacddbadabcaacacacacddbadcdcccbbcdcbbddccdddcadabcdabdcdcadbcabddbbbbbadbccdccccccdcdacacccdbaabdbbcbddddcbdbbbbddbbbbabcddacccdcbdccacabdcbbbdabcdbaabdcbbccabcbadcbbbbabcdadacdbaaaadacdcdabdbaadbaacabbdccccdbbccbcaabbaadaccdcbadbbadadbaaaacaaacaccbdaaabcadccdbdabaacbaadcdbdcdcacacbacdacccaacacaadaabcccddbcbcccbbcbbadacacaddaccccaccabdbdcbbdbcdbccdaccdbcacbdadabdacdccccbacdddbbbbbbacbaabdacabcdacbacccbddbcbdccccdddabdbbdaabaabddadaaccdacdcaaabbadddcabdbcacdccdddccbbccbaabdbadcabbadbaadacacacabbaadacddbdbddacabdcbbabdcadaccaacccbacaaacacadbcaabdaccabdcbcddbcddadaddbacdccadaadaaccdcccadcdcddccabcccabddbdaadbbccdbabbbbcadabdadcbbbcacdcaacdccbcdbdccadbccdcbacacdddabdcadbddabbabcabddcadbcdcdabccabdddbbbcabaccbdacddacbcabbcddacbdaddbbccaaaddcbbbccdddbdbdacbcbcdaaabaaadddadbcdbbbbbbddcaaaacacdbdbcbabaddbbccacabdbbdacbdabdbdbdaccdbaaccbababcbcccbccbdcaddbcabbcabbbdbbdccddcccabdacbcabdbadccdacadbdbddabcacbcbaccbcbdaaacddaabcbdbacbbddcaadaccbaadadcccbadcadadcdababcddacdbcbacddcbddbcbdccbacacddacaddbccbcabdbbbabacadcdcadbaabcdddccaababcbadcaddbbdbbcacaccdaddbcaaaccabbacabdbcdddaacdabacbdcbbadabbaccbdccadadddcdbddbddacacdddccddadcbbacbcbdacddacbadbbdabcdcaabbbadbdaabdbabdccabacacaabddaacdcbabacccbcadadddaaacacbaaabbacccadbaddaccaccdcabbdddacdbbaabddbaacbaaaaacddcdbadaadaaddddbddbcadaabacdadbcbcdadbbaaabdbacbcbbbacabddbaacaccbdadaddcdcbbccccaabcaababbbaacbdbaacacabcadbdbddddddcbabaaaaaccaabcdbabdbababaadaaccdcdadbaddaadbaddcacdadcdbcdcbbdcacdccaabbcbacdadcbdabcbabdaaddcbdcccbaddbdbbabcbcbadcaabccccaaaacdabbcaddbcddacabbdbdbbaabadacdbbdddbccdbdbcbdbdccbaadbbbaacbccaaaddcbcaccbdcaaaddbaababcbcddcdccaddbaadcddbcacacdadabccbccbbbbaadabdabaadddcddbdccdcddacbbcdabbcbbcbbbdbbbdaaaaccacdbacaddabdcbbbdadbadaddccbdbbbbddbbdbdcbbdbaccbaccabadbdbcdbcdadcdaabadcbababdabdaacadacdbccbcababbddababaddcdaccbaabadcdabaabdbcbbccaaaddaddcbbbccaddbaaddaddbaacbcabbbdcbabcccbaababbcdacabddccbbdbbcacdcdbadbcaaabcccdddcdcbdabcddcbdaddabdabddabddbadaaaddbbadcbcbdbabadcbcadbbaccccdcdcdcbbbbabababcbdadbdcbbbbbdddcadadcabbaaccdcbdccbcdbddabadcdccbbaaacaaacccbbcccdcddbdacbbcdbababccbcdcbcacdccacaddacdbadaacbadcddcccccddcabbaccaacdbbcbdddaacbbdcbacbdababbacdddccccaabbddcdbcccbdddbcbacdbaabbbdccbcbcbaabbbbabcaaccdbabcaabdbdccaacdbbbaddabcbbbddbdbabacaaddbdcdaccbabadddcbcdddcabdaaaadaadbacdcaddcccbcaaccdbdbcdcbdddccbcaadcaddaaacdbaaaadaaacdddcbbbcdabcdadaddcddccbbbdaccacadccdabbcabdbbaaabbaddcabccaacddddaabddadccadbabaaabcccdacaadacbbadcbbcaacbbbaabbbaaacdbaacbcadddbaadaccabdaabdcaaadbaccbabababcdacbcbacddbbdabcbbdcdacbcbdaddcabcccabacaabcbbcabcabbababcadadcaabbddbdccdbbdaccbadbaaaaadabddabbdcbdaacbdaadcaadccdabccadbcddaccbbbccdcccdacbcbbbadcbdccbabccaddabadbccddcccbcbdbcbdababbbcdacbbbddacccdbcaddcabaddbdcdcdbcabdabcbbcbcbbcbadcbcacbdaabaadbdaabddbdcdbaabdccacadcbbccbadbadcbcbcaaccabdccbdddddbbdadadcccadacddacbddcccdccccbaabdaaaccbcccaccaaddabcbddaabacbadbabdddcdbacadbbdbbcbabadbccadbdaabcbccbaddacdcbaacaccacdddbbdcaadcbdadccdcabbadbbdddddaacdaaacccabbdacbcdcacccacbdbbaacdcdabdabcbcdbbcbbcbdcddaadcacdbabcddbbabdcaccadaacbdcacabadabbccabddbdcbbbdbabdabcadbbaababbcdccaaaaaccacacccadbcdaccabbbbabcdabaabadaddadccabbbdddccbcdabbbaaadbbabddcdcabcabdddaacabbaaabccdbacbacdcadccabccbccdabbacbcabadbdbbdababcadbadbdacadbaadbbaaacbccadcdaaaacabcddcaddababbdbabdcaacdcabcbbaadbbcccccbccddcdbdbcccbaacdbdbadbccdbbaacccaddddccabddcbadbdbdaccbdbbdacbdccabccdacabaadbcbccdbbcdacdaadccadcaccbabcdbcdacbaaaccbcdccbcbabccbabdcabccbcacaddabcadaccdcbadbbbbcddbcbdbcdbaaddabbabcdabdacadabdaabbdbddadbacccbddbadaddddbcaabcdcabbababdddccabddcbcdbbddacddcabcbdddbdabbaacbdbdcbbddbaaacddcadcbbdcabdadabdbdabbdcbaadacddcadaadbaabcccbbaddadcdcdbdbacadbcbdacddadacacccdaccdaaaabcbcddabdabdbcdaddcdadcbacabdacdccbadcadcdaaacbabcbaccbaadbacdbdbdbbaccbdaddbababcddcdacccddcdacabdcdcdcaacaabadbaacadbdcbbbcbabbbcabdadbabcabcdddacadbbaadcdabdacadbddabbdabccbabaadcadabcbbbcbcaaacdbdacaabbdbacbaccdccabcdccbccbdaacdbdddcccbddddcdbdbbdddaaddcabadaddadacdbccdaadcabbaadbdadadaccdcaccdcdabdccadbacdcacbbdbcabcdbabaabacbbdbcddcbcbddbdaadddabdabdbaabcddddaacdadcbbbbbcccdcccbcaddacbccdaddabbdadcccccdbcdbdcccccbbbbdcabdbaacaacbbacccdabdaadabbacabcbddcabdaaacbaaaabbdbadaabcabcdabbdcacbdcaddabadbccbdcabdaacdcaaaadbbacadbdddcdadbacabbdbcccabdaccadbcbbddacdaccbcbdbbbccaabccccadadbbacdcbbcbcadddbbcbcbcacabdbddbdbbdcbbcdacbcbdbbcbdaccaaadbadaddcdbacdcddcabcdaabbcddbaadbacbadabbdcbacdcddbaabcbabdddcaacbdcdddbcdbdbcdcbdaddccddabdcbbcacdbbddbabcdabaabbcdbacccbbbbcaddcacbccdbcabbbcdbbcaddcccbacddbcdbacdbcccdccdcabaadcacbbabcdbbcdbababcacdabdccadcbdbdaadadadbdcbcdadcdddabdaabcaccacddacddabccccbcaaabcaaacadacdcadbdddddcadcdbacccdacddcaccadcabcbcddacdaadacdadbbddcdccdacdcdbbaaddcdbbcdddacaabbddbaaabcabbccaacdbaabbcacbaaacbaadacdbdcbbcdcbbcabdaddbadadcaddbaaaddabccdcdbddbddadccdcbaccadabbddcabbbddbabbdcacdcacbadcabbcbddbcdacdbdbccbbdabcacbaacdbbcdbbcbbababcbbdbadacccddbdaacababdadadcdcdbdcbbdbcbccbaabccdbdaadaaddbcbdacddcbadcaccaaabcdbbaaccccdaacdcaddabaabdaccabbddacbdaabdbcdbbcabcdcabcdadcbbccabbddcacaccbdcadcddaccbacbcbbcabbcbdaacccbbbacddcaacccbaaaccdcadccddcdddcdbaadacbcbbabccacbcccabdbaabcbdcabcabaaadadacbbccbbbdacaddbcccdccbabaccdcadcabcaabccadabbcbacadabcbbccbdaacddddccddacbcaaadddaddaccbddaccdbbaadcabaabdcbdbabaaaaabbdbaadcbcaabacdcdabdbaddccddaababbbdbbddbcdbadaddbdaddacbbcabccdbacccccdbcacccdbbcabbbddaacbdbaacaccbabdcbcddbdccdacaabccbdbdddccdccbaddcdbbcbabddddacbabbabbaaccdadadddababdbccdccdbcdddcdbabaaaddbabdabcbddbadddaadcbbbcabadcabdcccdaddbccdaadccddccccacaabcdaaabdbdcdcaddbacbbcadddcbdbcdddadabdabccbcdabbccbcaccdadacacdacbadacdbbdcdbacaacddcbadbdccbaaddccabbdddaaaaccabcbccccbdbddbdbbbdaabcbdcaaadcbbbbbcdcabdcadcdddaabbacbaccdddcdabdabdbcadbbbbcacaabcababbbbaaaaddddbdcdcaaadadaaaabccdadcbadabaabcadcabdcbccbccabcbdcabbdaddccadadbabacaabdbdcaadcdcccbbcadadcddbdddcdadddbcbcbbdddadddbdcaaabbbbbcaacbadabdddaaabccbcaacbcadacdadabcababddbddadcadbaccddbbdcabbccaacbacbbcbbdbccddbbbaabbacadbdcdaabacbccbcbdcbcbcddabccaccaddbbbddcbbddbbacdaccbbbcbdcaddbcaccabaccdcacdcbaadcbbadbcadacaccbacdbaccaaabdbcabdbcaaadaaacbdccbbaddbdbcbacabacacdcccaadababdcaabbadbdddbccbbaaacadbaaccadaccbcdddadcaabbabcabddacacbacadcbcababbdcaabaabddbccadaaddddbcdbabdabbacdcabddbccbdddbdddacabdacbbcacdbbbdabdccabbdbbdbcbbdbadbacdbaddbcbbbadbbdaaaadacccadaacdbdcaccccbcadacbadcccabcaaccacddaaabdccadacdcadddbddbdabacdddcbbcaabddddabbacccdbbdacbcadbdbcdbadaaddaabbbacdaabddccaddcaccacccabaccccaaddabbdcdadbabdbdbdbdcccbabcdbbbcbbaadadaddabacccbcacdcbaabcbcbddddbaddddabbaccdddacdbbdddadcccdabcdaabcabcadcacabaaadbbddccbbbacdcaccacbddaaabcdcdbbcdabadadadaadbdddbdcccdaaaccacabbdbdaddbaccabacbdcdbdcdcbacaaadbcacbcbbdcbddbbcbbbdaaaaaadaabddaabdabaadcbaacdbaaccadbbcbccdbaaabcbacabddcacabcdcdcbcdcdcdccaabbbcdcdddcdbbcbbbaacadcbacddbdcacbbccadaacababbcabbbbacadccdcdbcdbcbbcaaccdadaabbdcacddddbabcddbdacccddbcdbbdababbadcaabdadcbcdbcadbaddadacdbbaaacadbacabddacbdcbbbacddbbaaabbbcaabacbbdacaaacbbcacbbdabccaddcaddcadbccbdddabbbbaacbdaccdbaddcbcddbddddaccdaaaadbbcddcabadadabdacdddcadbcddbdbdcaacabdcdcdaabbcaddadcddacdcabbdcddcdabbcdcdbdcdbdadcaccddadacbdddccabadbccaaaacbbdcbadcaccbcaaaaaadadbbcdabdacbcdccdcacbdddadcabddcacdabbccbbdabadacbabacbdbabadbbdabaddddddbbacdddddcbdacbccccaddbddaabccdbbdacadadbadbadcbacbdbaabbbadaddbbdddccdcdcbcacdbcbdbcaaccdabdbbaadcaacdddcdaddacabbaacacddbcdaabdcbbacbacbcbcaabcbabbdcccccbdbccadcacccdbccbcbbcbdcacacadaaabcdcadccbcabdccdaabcccbccabdbddbcbcadadbdacdaabaaacdadcaaacbcdcbaddabccbabddbaaccaabcdacdddccabcadbbdacaadaacbcbdccbdaddccddbacdbacdbcccabdaaddadaabcbdbbbbbdabdbcbccbdcdcbbdddcbcbcbbbaabacaaacdcbbcbadbbbbabccdcddbabbcbacdcbacbbaddddbdddcabbdbbdaabbbdcccbcbacdcbcbaadcbcadcdcbdabadaaddbcbdaddcabccccadaacdddaabcdbdaddabdbbcadcabdadcabcdbbdcacacdacabccabbdcabdcabdbacaabccabbaaadcdcbaababbccacdbddbabdbbaddddacccaabdaaaadccaaccadccabbdddacaaccbadccdbcdabbadcdbccccaabcbcbcadbadbabadcdcbadabacccccdcdaabbaccddbbddbaacdbccddaadddcbbdcbacdbcbdbbababbdcdadabbbbcdcaadbcabbabbbccdbacdcddaddbdadcbacadabbabdbadcbcaabbaccabdbdadcbdacabbaacbdcacbadaabaccacbbddcccbacbabacabdcccadcccaadcdbaadddcbdcbbcbbbaabaabaaabcbbcabdcacbcbcccaaccaabadcacdcbdacadccccdacbdaabddcccaaaadbaacdcadacadabaacdadbbbdcbbdcddaadcbbbbdabbdaadddbadacbbbdadddddacddcaabddaacdcbaadacadbcdcbcaadddaaccccdbcaccdacabdcabbbddabddbcccddcabdaadcaacdccbbdcaadcadcdbcaabdbdbdabacabbbabbbbdacaccbaacbbdddcdbdcacdbbdbccdccbdcbaacadcaadabdcdcddaacbaddbbbdacdabccbdabcbdacccdbddcbbdabdadacbbbbbbcbacaccadacadcdadcbcdddbabcdacbccdbdbbababacccddaacabcdbaaabacccbdbbbdadaccaacbdbdcbccbdacabadbdccbcbddccadbacaaabaaacabaadbcacbdddbaabbadaccdacdbabbcccbbcdadcbbcbdccdcbcdacaddccacdadddbccbdccacccbacbcbcbcdaddabaccdabbdcbcbbaacabdbacccbdcaddbdabaccbdcdcbdbacccbbddbbccaadbbcaadadccadcdabbdcdddccbaddccddacbcbddbcabddaadddabababdbcacaaaaccbbadaabaaaacccddbcacabbcbdaaacccccbccbbddaabdaccccacacaaaadbacddbbdaadddaaacccddaabbbddcbcddcbddccdccddadbacadadaacbbdddabbdddcbccdccadbcaaadabadcaadaababcbaacbaaaadaabadacacacbdccdcdadaddabdbccdcadddcbbcdcacbbcbaaacccaddbabbdcdabcbadbbdabdcacccaabddbabddacbcbabbbbbdcdcdacbdbaccdddcbaacdcaddbcbcacaaadcbdabbdacbdccacccaddbdadbcacdbaabcdcdbdbcadbcbccacacdccddccaccaabbdadbdadcdadadcbbbccadbabcababbaacaaabddcabdbabddcbddcddaacddacdbdaacabbcdabddaadccccbbaadcadbcbbbcaadacaaccadaaacdadddcccccdddcadcbabdaaadabdbbccbaadcdadadaadddbbdbbdccbbaabdddcddbcdbacbabbcbbbcddbccbabcacacbdaaaaccbbcdccbbdddadbcaccccaadadbabaaabcdbddbddacdbbcbacbadcacadacadbbddaccbccbbabbdccbbdcccacbdbacbddcaacdacadababadabdddacdbababdcddabacbcaaddcdcdbbdbdacdaadccbcbdaddababcdabaaacaaaccbdcbdbcdccdddbbcdcddddcbcaabccdcaccbdadbbaacbccbcacdccabdcacbaaababcdccbbbdcabdaabbcdcabacdcadbcacbccbaacaddbbabcaccddccadcbdbbbdbdaaadcdaddbaddbbbdcaadcdccacdccadbbbacdddbabbbdccdddacaacdcbbdbcdbcacdccacaaabddbcabdbccbaaabbcdaaddadcdcadcadadbcabbbcdaccbdcdcccabccabbadaacbdcadadccdbcaacdddaabaccbbaccdccdcdbaababccabbcadbadcdbabcdccddbaccacdacacaccbdbbdbabddbdcccbbdbaaacbaacdcacacdbacbbcadbbaaabaadcdaabdbcbbadbdadcbbdcbcdbadbcbbbabcdbcdbaabaaaadacbadcbcdbdbddbbdadbddaddddcbaadbdabbcbbbbddbacacdacbbdbbccdbdccdcdbbddcbdbdcddbabcddadcadaccaadaaddcbbbacabcbadcadcbdbcbcbcdcaaaabbdcdcabcbcbbcabcdcbcabbaacdcbdabcbdcabdaccbcbabcdadbbcdbddcadcbcdcaaaddbabaccadabdcbdabdbccddadbdcbbcaacadddcabccadddabcbdaadcddabdaaccbddbdadbdcdaddcbbdcccbdacbadbacdaabdacaabadaddaaadcddababccbabaddddcbbbbdbaacabadbddccdccbcddbbabbcbdcdabdaadbdccdbacbadddaabddaccabbbbcacaacccdcbcbccaadbbdcccbcdbbddaadcacdbcbdaacbddcdcdbcbcabbbdcaccabdbabdabdbaaadbddabcdacaadabcadddbccaddbadbddbdbccadadbbadaaaadbabdbbbdbabaaacbbccabbabdccabcbcdabcdbacaadbcccacddbdccdcbacdbcccaadaadcbdbabcaaadcbabadcacbcaadabadbbbadccbbdccaabdcbbdadccddcacdccdaabccddcabdbacddaddccabcadcaaccbcdaccacadbacbbccbddddabacddbaabaddaaddabbcadbdbcbaaddcadccddacbbbbcbcadbccccbaccabbbbaabcdaccdcabcacabcdcbbcacacbddbadcaabcbaacbaddcadcbcdddcbdcdbabcabadaabdcadbbcbadbbacdcabbddbacbddabdabcdbbcdaabcabdcdaabdccbbacbbbdccdbccdbaccdbbaccdbcdbcacdbcddccbddbbddcbcabbbdbddaddcabadbcabcbbcadadbdbcdcbdadcddaddabbcaaaaabdacadbbcddbbbbdccadcdbcacadbaacbdbbdbbaabbdaadcdadddadddcddddbbbabbacddbcccbcacbcacdadbbadcbacacdddcccabacbabbbcccdcabcddbadbbaacbccbcbcaadaadadbbadacdacdabdacbbccaacbbdbdcddbcbccabccccabbcbcbcdbdcadaabbbdbcbdcbddaacdadbbcccacacdabdcdddcddbbccaacdbcddabccccbddcdbbccacbdaabadbdbbcacbdbacabdbccdbdbdbadaadaacccccbccbbbbadadaddadaabacbdcdddbdbcdbbadcaddabaddabaaabdacacbbabcdcdddccdaddabcbccdbcbdccdbbdbcddbcbccbdbdaccbddcdbdbacdcbdcdaccbcccaaccdbdaaaaaccddccabcaaabddbbdbadadbbcbbdacaabcbaaccbdacbcaddcacbadbccaacccabdddacbacdbbcccbbdbaabcdbdccaddddbddbcacbcdababaaddbacdabddbbbbdbbbcdcdbddaacbddcbccccaacdbdcbaaddbcbbbdbcdadddacdaabbabccaddddccabdbbdaccdcadaabaababaadcbbadbaddaaddcccbbcadddcbdbbaacbdadadddddacbdaabaadaacabaddbaccbacdcbbcabcabdaabababccadadcdbcacabcadadbabddbbabbacdcdccdbbaacdabdbbdddcaabdbdcdababcbbabcbdccabcaaccddadddcddcacacdbdbbdcdabdacadcddcddaaacbacbbabcaaacadbbbbabccaabaccdcadcbdcdabcabbcbacabcabcdbcdaddddbccccdaccccbbcddcccdcbdbbbcaccbdabdcddabbacaccabdacccbcacbbabcaacdcacadcacabaddcbcdcabbdbadacccbacbcdacacccddbcaddaaadaddababcdcdbbcbcbbbcbdaddbbabcbbcdadbdcdabacaccacdddaccdadbdcdaddacaabbbabcaababaadadcbbdaddbdcbaaaacaacadabaacdbbddcdcadacdcccaadaabbaacbbacdadbddbbbbdadddbbdacabdbcababcdadbbbcddbabcccaadbbdacbcbadacdbaadadadabbaaddabdadcccbabdbdaabadcadcaababccabadbbbcacbdcbdcccacbbcdcaadcbaaadabdbcaaaacdaaddcccdddcdacdcaddabbbdbdbbaacccbbcdcadababcccaabaaadddadabccaadcabdaabacdbdcbacbdbcbcabbddddccbbdddddacccadbaacbabcbcdbcbacabbbbdabbcdadbbdbbddccbcdaadabcdbcabdddbccbabbaaccabbddbaabbbbdbdabdbcadbdbbcbdadcacaaacbbadbdbdbddcbdddbbcdabbddccbddcdddbadbdcdcaaacaababacabbcbdbdccbdaccbdbabcdbcbaddbcbadbaacaaabbcbacbcdbacbbbaacababcbbbbaabbabbcdbcbbdccabcddccbdaadbccbcdccbaddacbabbdbbdbadbacbccccbcbbacddbbbabdbdbbadcdccdcbbbccdddcccbcadbbdcdbcaddccacadadcbcacbabdbabddaddbcccaddcbaccbcadcbbcacbccaddbdddaddaddacbaabadbbacddacdccccadaaabaacadcdacccaacdaabacdbbdbcbdcacaabbacddcbdbbcdcbadbddabdabacdaaaccaadbaccddcccadadddaacbddbbddbdaacdbbcbbacbacbdbbdcbbdccacbcdaddbbabccbbdcbaddbdabbadcddddddddddcccacdabaacccaabcadadabbadbbaaabbabbacadbabdcccccdccaacbdddcddbaccccdcbccacadbddcaaacddacadbdacbabcddccdbbcddbccdcadbcdccddcaccdabbaddcdbaddccdabadbcdcacdadabacbdbcbcccbbcbbbdcbcbdcbcccbdabbdcddbbcacbbaabccaabcdabcbddabbcdadcdcccdcddbadcaaddaadddccccbadcaabcaadddacdbdaaccbdbbcccabadcacaaabbacdcaabcbabbbddbddbcacbbbddabcddcacdaaacdbddcacadccaabccacdcccdadcddbdcddbacdadadaccbdaaaadbbdabaadcdcaabdcbababcbdcabadcdccbcbaacbdbcdbbacbdbddcacacdcccbddbbbcbdcdadbdbcdacacbdddbaaccaadbbcdcbaccbbdbbdbdacdbcaaddcabbccacadaccdabdbdcdadcbbaacbcdbaaaadddccdccccddbdaddcbcbccdacddbdacbcaaddadaadbabddbbbdbbbadcdbdbcdbbccbbacdcadccbcbdcacbcdbdaacbdddaaacbbabdcbbcbbcdacdbcbacacaccbccbbcdbcbbcdccdcaabbadbddadbaaccdbbacacdbcbbdccaddcbaddbdddbbdacdacdbdaccbaabcdbaaacababdbacbbcdddccbaacdbbabcabaaddbdabcdbcabbabbadabcddaabdabdcaaacccbadcacddbcbbddcabbbdbcdbbcacdccccbdcbaaddcbccbadccbabbcbcacbdacacdadbcaccdcccbcbcaccacacadcdabcbabaaaabacdbdcaadccbccbccbcaabcccdaaaabbcbcadcdbddcacadacbbadbddbccbcadcdcabdcbcdcababacbdccdadbadbaadbaaccdccdcaabcbcacabbcabccadcaaccdaadccaadaaacadaaccadabaddccbadddbcccbadaaccacbdcdcddcdcbbaaabacaaaccbabbbaaaabadcddbccbbbbbdddacaccacabccccaaaaaadaaaacddbaaabcbabccdbbadddcdbbacddbdccbbbddcddbccdaddddcbdddbdcccdabacdaaaddcdabdaabadbcccaabbacbbcccbdbdbcdbbcadbdabccabbbacadadbcbbdbcaccddddcadcdccdcdbabbdaaabcdbdacdacbdbaaddbbdbaadbbdcbaabaddaaaaaacaacadabcddccbbbcdbddbbdaaabcbddccbbabaadddccccbccccaddbbccbcbbddcacacacabacbccabbcbccaaccbababccbbdaaccdacdacdcbcdacbccabccdaaccddaddcbdddcbcbdbbbaabbcbbbadbcdacbdcadbcbcaccdbbaabdbbcdabccdacaaaabbcadaaaabdcbaaddbccdcbdabcddabccbabcdbbdcdcbccacbcbdabdcaacbbacacdccacbcbcabddbcaacadbbcdcccdcdbdccbbcbbaacacbbadacbadddcbaacaacbdcacbacdbabbabcccabbcaacdbadbddddabdcbcdcbccdcbabddbadbdcbaaacdcbcbbaddcdbabcbaaabccccacbddccdddbcaaddbbaabccbacbacadcdbbcdccddcadcdbabaacaabdddccdbbcddacdbdacdcaccdacbbbcdcaabbcadaddcadbdbaadbaadadabcbbcbaaacabbbdbdbacdadcddadccdbcddcccdcccbcddbaddacaabccaaacacaabaaccdabdcacccdddcccaabdbcaadbdabbcdbdbbdcdbcccdacaddbbabbaadbbdcddbbbadcadbddadaabadbdcaddbadbcdbccdacbdcdddddbbcacdbdccddcdccdababbbdbcdbaadacabbddccbaaaabddcdddbcaddcdacdbbbdbbccbbbacbbacddbddcaddcccbacdccaaaddcdbbcccbbdcabbaabcbbcdabbabbcadcadabaacdccabdcbdbdcacdbbddccddcbcdbcaadddccaaadbcaacddcddcaadabdaacaacbcdcacbdacbbbbddbadbbdccababbcbaadcbdcbddabadadcdcbbddbccdccddbdabdadcacbcdbbccdbadcdadcbaacdccbaddccacaccadbcbbbaadccdcbccdcbabcdaddcaccaadcdacaddbbbdbcaddaadbdcbbabcbdadbaddbbddcaaacbadadbcbabbbbaddabdaddbbaacccbabdcdbcdcbadbcadcdadaddabaabccdbccddddccbacbbdcddaaaabcbddaadaabddbccdccbadaacccddcacaaddbdbcadbcbdbdabcccabddcdabbdcacdaabcdddbaddcbbabbaabdbabdccdcbaacaaaddcdcdbcccbcacbdddddbddbabbcdabdcbdccccbbabbccadcdaaacbcbdccbbcdbadcacddbabddddaacadcbbdccccabdaccdccbbdccaddcbcbcccbcdacbccdbcbcadaabdadbcabbdbaacdabbcccbdddacaacabdbbdbacbbdbddbadcdacddcbbdbbdcbbcdbbaddcadaacaaaaaacdbbbcdadbbaadadaddbadccacaaadbaacdacdadaaccabcadaadcaacbabccaccdbccbcdbaaababdabbbbdabdbbdbadacdccbabcbdcadddcccacbcdbaacaaababbddccadbbbbccbcacdcdbaacbccdaddabbabbbacbccabaabcdcbdaadbddbabdaaaabccdbbcbddccacdaadbabbbbcbddbbddabccaacccddbaddbccadddcacabcdadcdcbdadcbdbaaacbacabcbabbaddbdacbdaadaaacaabdcccdbdaaabdabacdcadabcdcdbbdcddbbaadbddbcdcbccbacaadcacbbabaddaccdcccacdbcdddbccbbdbaadbccdbbbacacadbababadccabddaabdddddbbbdddbcaddcddabacadccdaccbacccaacbabbbdbdabbaaacbbaccdcbdbbbcbccbbbcaddcbbcccbdddccdbcadcdddaadbdbdabcabdbccbaccbbcbcaabdbbddccbbdcddbabdcacdacdcbacdacdadacddccdacbadbdaaccadcdadaaaacddbdacbabadbdaaccdbdadbdcadcbbbccaaaddacbcbbddaddadaccdddabcdbcbaaddcdbcbbddacaccdacaccbccbcdcdacdcdddcdadddbcdbbdddadbbccdcacabcabcaadbdcccaaabbdcddadaacbabdcdbdadacadcaddbcddaddaadcbcadabbbacaacccdcacccacccdbcabacccaaaaaadaacbcbdadcaacdaccccdcabddbadadcddacbcdcccdadbddcdbbbbcbccdbdbbdaabdbdbabdcccbdddabcacbbcbbcadbcaadbaababaacdddbdabdbadadaadbddbaddaabcbdccbadacadcbddabbbabcdccbdddaabdbadbbdbcabcadcbccddaabdcbaacaacdaacbdcbaccaccddadccddcbabacdaacdcbaddbdcbdcadaddaaccaacbdbcbacccddcdabdbcababbdadadabdddcdbbaaaccacbacadccabbcaddbabacaccccabaddcabbdbabdbdccdbdcdccddbbdbcdabdcdbdbabdcbbdaaccdcdcaaabbbddbccabbccdaddcbdadaabdbacbbccdbbdccabaccbbbabcbabbdbcabdcbdaccabccdacacddbcaddcdcddbcdcdbcbaacccabcddcabdbacbadddcddbbdcadbbbbabcddddbbbcccaaacabadcabcbadcdccbdbcadcbaaababcbcabbcadcbbaaadccbdaabadadcdcadbcddbdcbbdbddbcbabacdacbbdbaccacddabccbdabcdcdcadadacabbccbbcadcddbbdbadddabaddcbbddabaccccddbadbccbadaabaccddddadbcaadaaaabcbbadbcbcdabbaaadddccdabaaacabbccdacaaadabccbddbbcdcaabccbcdacdaacddaabcdbdbdcacdbacadabcbddbcdcbcdacccddbbbbdcbadcdabacaddccddcbddabdacbadcdbbbbdccddcabddacbdaaddbdacabdddcdbaadcabcbdcbdadacccdbcdaadccdbdddcadcddbdbdadcddcaabdbcaabcdbaadbabbccbaacdaadccbaaadadababdabccacccbadcccbcaddadadaaacdbddbbbbbbdbbbdbcdacdaaaaadacdcabadbdacbbdacbcacadadccdababaaddbadcbbdbbdbddaadacddbddaabbbdbcbacdcaabcbcbaabadaddbbaacdbdcbbdbdaaccdaaaabdcbacbbbbadbbaadcbbbcdccbbcacdcacdaaabacdaacabacdddcadcddcbcbdcdbddadcdaabdabbcbacccabdcaadbbbcdcbcbdccbccaaccadaccbacbdddaabdaaacdcacdcddbabbccdbdcbbcddbadbccabcdcccbbbccbbaadacccbbcaaababbbccdbbdcadcabbdaaaabcddadbaddcbccadaadabcbaaaacbbabddddaabdbcdcdbbdddbaadbdaaccddbddbabbcddadccbbcdbcbdcdcbacccacaacaacdccbdcdcbddcabdccdbcdbbcadcdbcaaacccaabcdcbadabdcabcaaabdcacabdddcbacdcaaaacdaabdcaadbbaacdbcccbbabccdbbdbbbbdcccaaddcccacdbcacccacdbdacaabcbdbabadadaaadacacadbddaacccaaaabcddcadbbbbbbdccdcbaabdbabacacddcacbadcabaadcacbbdccbbabcdaacbbcdcbcbbdcdbaaccdccaacbbacadbbddadcadadaccccdacccdbddbadbbbacbaabdacacabdbbacdaaaacacbbacbdcbcddcdbdadcaccdbacbbdbcdcdccadaacacbbbdcaadadcdbbccccdbdcdbdcdabdbdddacdbcaaaccaaaaacdbccdcacbccdddcdaabcaadcddcdbdbbaacbabaccbcabbcaaddddddddcaacddbcaadcabcdacdabaabbbbaaccbdcabddadaaccddabdbbdacbbcccccbcaddbdabdacbabdaddcabcadddcccacbbdcabcabdbdbcbdccacbadbdaaacadcadbbdccccddbabdaabacbbcaacbbcbdacabccddbddcaaacdbcbcbdcdcddccacdbacdcbbdbbcabddcdbbdbcbaaddabdcdbcccabacbbabcabddadaccccdbabaaddcddcddbabbdaaddadaddbaacaacccadbabcabbbbbbbbccdccbdaddaaabacdbbcbddaabbacddddaacccddbbabbbaaccdbbddbbaadcbcbabddbdabccbbbdbcbcbabbbbadbcbdccdaadbcbcdabcbcdaacacbbbacbcccabbbcacccacabcacaadcdaabcddadbabdaacdcdcadacddadccbaccdccbadcdcbdaccdaadcbacbabdadbbdbdcacbdbbcccdaabccccaddddbbbcadbdcaaadbccadbaaddbacaaccacbcacdbbdccababaccabcadcccdbabbbcbabbaacbddbcbacbdbacbabcadcbcaddaddcadabdacccbccdabbacadbbacdccaabbbbacbcdcbcbdbccdbbbccdadcbdabcbdabdacbcaadabdccddbcdbbcbdacdbcdbdcdbdadbdbddaacadbcbbbadadbbbcbacaacbcbccaabbaadccacdcdcacbdbbcaacbaddccadddbaadabbbcbadcaadaacdddacadabbbcbbbbdcdbabcaaccbaccaaabdccdbdddcbbbaacbcdcabbabdccabdcdcbabadcdabdbadbbabddabddbaaaddddadacadcdbcccdbacaaccacabbddcadbbbdcbbcdddddbdbbcaaddbccbbabbbcddccccbdbbdbadcdacddccaaabbaddabdcbcabacdbdcaaddbabcddadbcaabbbdcaaadadaadaaddbabbdcdcacaacababdadbcbaddcccadcdbcabaccdbddcddadbbdbcadbabcddcbcdbcbbdccdacdbdadddcccbbacaacbadbcbbaccbdcbdbbcdcbabccbbdabbdabddbdbdddddbdccddbddcdcbddabcdcaadcbcdcabadcbdcaababcbdabbcaacddaabddcbbbadbbcccbdcdbaadbbacabdbbdcdaddbcddaccabcdcacdadcbccabacaadddcadbcabdaccacdcaaadcdbdbcbcbcababcccbdcbadadddadbddbaadcdcbadbacdcacacdbbdabddaabccdcbbaaaaaacdbbdcadabcccdbdcacabcadadccabacdaddbbdadabcadbbbbdaadddbdbdadadbccadcbcbccdbcccddacbbaccabdbbcbcaddcbddadbaaddacdddacabadcadcbcacbadddcaabcdaabbdadbddcbadbcbbadadabbbccaddbdbbcdacccadcbaacaabdcccdbdbccaabdcdabaaabcbdbddacadabbabbabdddaccaddcabbdcbddaccaccacccbdbbbcbccdbbddbdbccbaadcabdcbcdadcbdabdcaaadbbbcdccdacbcadcdaadadabbccbcbdbbdcbdcbaabcdbadaccdbadcdcddddbccbabcdcddbcbbbaacaabcbbdaadaaabccdbdcdacbaacbabbdbddbcdcadbbccadaaacaabdabddbcddabadbadacacbdcbacbbaaaacaccbbcabbabdacabacbbbaadbbabacccbdcdbdaddbaacccdbcdaaabadabccddcaacbcbcccabcbcdacbddddaabbccccdaddcccbbbbabbdcdbabbdbcdbcddcdadbadbbdaabbdbdaddbcaabacdddbcdadcbcaccdccbdcbaadaaaddcccbbdddcacdccbbdadbbababcdcdbcdcccbacdbcadbadbbadcaaadaddbbabdccbcdddcadbcbdaacacbdaacacccacacabcdbccadababddbaddccaacaadbbdabcbddadcdaadaaaabaccbdbacddcbababddccbabddddabcdbcbababbadaacdbddcbcccdddccbadbdbaacbdccbdccdbdacdcbaabadabaacbdddcadabccccbbaaccccccaccaabaaaddbabcddccaccbbbcdaabbddcadcadadccbbcbbbaaadbbcabbbcadbbabddccbdbadcdbcdcdddacabaaacaaabbaaadadacbabdbcbcbadaabdcbddaaabcddcccdabcdabdcdaaaadabbadbdacddccccbbccbbdacbcbddadabaacadacddbdbbccadbccccdadbdcdbccccdbbddbdadaadadabdddccabaabcbdcabccdbbaaaddacdcdddcdccdbdcbdcaabacaddbbbcbdaaadbabdcaccabccccadccbcccdaddbbbcacbbdadbabaddcddbabacaababdbbccaccccdcccbcdbcbdcbdbcbacaddbaaccdccaabaabbaadcbdbccaaddadccdbddddaacddcbaacdbbbdaabacdcaaadcccadcddddcacbcbabcccaabdbbabcabbaaacadaccacddbbcbdbccddcddbadabbcbadcdacacdabacbadcaadcaadabadbddcbddaadabbccadbadabbabaaabbacdabbbbcdacaddbdacabcdcdccdabcdcabdcaabcacdbcaaadaaacaaabcbadbdbcacababadbbacdddabdcddbdaacacccddcadbbbdaddabbdbcdcdbaacbdcabbaababbabccbdaaadaddbdbcddbbbadddcabddbdbbcdbccacbcdaadabccbaadabcdaddcbbcbdbaddadadaaccdcbcdadcccaacdabdcdcabadcacbacacbcbddccbbbbadcabdbbbbaaacadddabccbbdabbcabbcabccabddcbbdabdbbacbbadbadbcbbdcbbbccbabbbddbdcccbabbaabaacacbaacadccbdbdcdaacaccbaddcadcdadcbbddbaadadbcadcacbdcaaccbbbccbbabcaaddccccbcbcbaddaaadbacbdbabdaacabbadddaacbbccbcbababcbcdadbddbdcaddbadbbddaadcbcdbddabbabcabdbbbdbdddbaabdacaaacdaddcbcbdcbccdadbdaaacabacbdbdcdabbacadddaadaaaadbcabbddbcbccbbbbcabdcdccadaabcaabbaccdcabcaaaacbdbababcababaadadbccddcbbdaddcadabaaabdbacbcbadbdbbadacbacdbdabaacdcadbabddcccabbacbdbabbacdcadbacaaaabbbadcaaacaabdabaddaacddadabcadcadbccbbaccaddbdcadadaaabccaabdacdadbddcacdcdcdcdbddbbcdadbcaabbbbdcbaaaabcdccdbdaacbcaacaddaddcbcccbbabbcbadbbbbbaaabcbdcadddadcbadbadabbcbdabdbbddadcabddbdccabccaabdcdccadadbbbdbcadbccabbddacbddbaddbbcaccbccccaadbdcadddbbdbbbdabaacbbbdbabbcdcddcdcccbccbbcadaddcdacdbcaabcacdcadcbaabaddadbdaabbbacacddbcddcbdccabbbabbdbaabdcbdbaacbccccddccadbbacabddacdbaccdccaaabddabbdcaacccdccaccdbdbbdabcabdcabdaccdcbcaccbbbbcaaacbdaabbbdcdabdcabdaabdadddddadcdadbdbadbdbccacacdbcaabcdcbccbdcbacbbabababbdaadcdddabdcddbdbdcbabdddbabcbbdabcbdbdcbaaaabdaccacbacabcaddcdaacdadadcddabbcccccbdbaddabbbbaaadbacababbabaabadbddccdddcbbadabbcbdccaabbadaccbcddacdaaacdbbcaccbdcbadadadaddcaabaadcdacdcddadbaddadcaccdcbddacbdccaaaadbbdbccaacacacddcbccaaacbddbddacddacdcbabbbcbbbbaaddddacdddbcaadabaadadbdcddcdcccbcdcdcdabbcbbbaabbbccbccbdbdcdccdbaaadbbaccdadbaddbddddaadacadcdaccccaaabdddcdcbbcbdbabbbadcaadbbdcddbbcacbaddcaabaddcbbddabdcaddcaaccbdcdddaccdadbaacbccaccbdcadacdcccbacdbdbdabbacabbbcdbacdababdacaacaddcbbdcdcbcadcadbbadbbababbcabaaaddddbbcddcbcbccddcabacaaabcbbcaaccdbbabbdacadbbcaaabccbbcdbdbbcaadacdababcbadddacccbdddddbbddcadcdccddcabdbccbbbdbbddcacdbddcccaabbdaaccbddbccbcdbddcdccbccbddbddbcddbaccadadcbaaaadacccddddadbcaacdbadbabaababcdbbadaadabcabcbddccacdaccddabbdcccdbbcaadbccbabccaadcdddbdbabdbdaddaccacbdbbcdbcbbabaddcccadcababdabbacdacdccaacbaaddcbcbaabaaaadcabbacbadadabaddcaadbcbdddcaccdccbbacbcdabbccbbcabcabcddacddbdcbcbdbbdababcdddcabcdcdcbcdbbcbcbcddbaaccdadaabccbcaacbccbdbccdcbacacbbaaacadcabbdcaddbcbcabaccdcbabbddadbababaabbdbdccaadddcdbcdbddaaaadacabaddaabdbbabacbdabcdadbbbdddbccdcddbacdcbbcdadbabdbdbccbcacdcacacadbcaddccddaacbbabbdbadcaaaddcadababcbabcaccdaaccadadbabaccbcadbdadccacddddbadacadbddaccdabbbcabbcaadbcbacdaacbadaadbdcaadddbdcdccaabdbdadcbadbaddccbbccaadcbccbadbdaababaaccbabbddacadccabcbbcacadcabbddbaabcdaaccdcdcdcdacadabacbacbcdaacaabcabcdaccccbddbbbdadcaddbdccaccdccabbcdbbaaabbbcbcbbcabdcdbdddbdaccbaddadbdbbbadbccbbbddccdbbcabbdaddaccbcbccaaddacaaadccbabcddddcaddadddcbcacbdaaacccbabbadabbdbddbdcaaadbbaccdcdbcaccbddcddaaaadbbccdbaaaddbabccccbdccdbccbdbbbaaacacddbdbbbaccbacdabdcdbcdbbdabadbbadabdacdbbccdccbcbdabcddaaccdcdbadbcbcccbbdcaacbaccadbcdacdbcbacdbccbdcbcdabbdcabaababbcdcbcaacbcddbcbbccddbccdadccadbbbdadcdccdbbbcbbcdcdcadcbcadbccdbddddaddddbbdabacbabdbbddbdcaacdadbccdabbdcdcdcbbdbadacadcdacaaaacacadabcaddaabacabbdadcdcacdaaabacccbbcdcadabcdddaaabcabadabdcacdabaccbccabaccbddccaaddadacccadbcbaaadcbabaabcdadacbaababbddbcdbccabcdddbdbbcddcdccacabccdbcdddaddabbbdbacabcaddccbaacadcdaddccbcdccbcabbccbcdbcbbdaababdddccccabcdbdcabcccdbaccbccbbbbdadaacbcadbadacaabdddadcbcdbdddbcddcacbdcabdccbaadabccdcddacdcbcbaadccdbaaadbdbdaadddabdcabcddbccbcadddbccaadaddacacdaccbadcbccbdaacbbccdddcdddbdbdddccbacbcbdddcacbcccdacacbcaaddabcbdcbbabdddcaaaaccbcdccddbadbddbbcbcdaaddadabcdcaacacacdbbadacbdcbacbbdadcddbbddaaccacadcdacaccaddccabcbdccdcbaaadacddadddaddbadbacabccdcaccaddddacddcbdabaddbdbdbaacdbdacddcddcccaaaadcbdacaacbdcacabbacdccbddbabdccbbbbbbaacbcadbabccadccacbaaacbaddaaacddabcbddcabbdacbccabcbadcaadabbbaaacabbbdacabacdacacbacdcabddabdcaadcdcdcccdccdaddaabccaaaacbbdbdcddbdbbaacabdbdcbddccdcacddbdbadbdbbcadadccbbddabcaadaaddbbadbcbdabdbdbcabdcbcbbdcaacbcbdadcdacccabcaabcaaaacccabcaabbccdcabbcdabbcccadababdbabaaacbbabacdaabdcdcddcbcdddbcbbababbbcadbdabbdcacdcddcaccbaaddadacbabacbbbbbddccdcdcdccdbbacccbbdddacddaadadadabccdadcaabbcdcbcabaccbddabcacbddccabbcaadabddbabbcddbbbcbcbcddaabcbdadacdcddaadcabbaccdbacabadbcdcbdcaaaaaacabbccdbdcdaddbaddbcaaadbdddabdacbabadcaabbcbddddacbcdbacababdacbaacaacbdaacdbdbdabcbcbcdacabddccdcaaccaaabdcccacbbbccbadcddccdcacacdcabbcbadbdbbaaddbcbddcbadacabdbcddcdbcaddccddcabdbdaaddcdbbadbaccdcdaaadddbaacbbdabacccacbbdaadcaccbbacccdccdbadccacacdbcbbbbdccbbccbacacbcccbadadacccaccbbaacdccaaaadbccbdbadcbabcadbccabddcbabbbababccbddbbaaabcbcbbbdbbaddadcbcabdcbabdbabcbaddcdcbacbaccadcccbaddccdaabbdbdddabbdcaddbcbdbddaabdcdbcadcacbcaddcabacdbbcbaaccccccbabbdddaddcababadcbbcaddcbcdacbadbbcdccbcccbbbbcdbadadaaccadbddcdaaabddcdadbaadacacadbddcbacbdcaabbbbbbadccddbaaadcbcdaaaddddbdcbcabcadadadbacdcbccdbcdbdbabbacdaacbbddbdaccbbddcbcabcadadabcbcbadbaabcbbbcadadcaabbbbababbcacbcbdccbbddbbcccbadaabbdaaaaadbdbbdbccdcbbbdccacbbdbbcaccbdccbcacbadcbaccddacadccdccbaaaabccdbddabdcbbbbaaaacadddbcdbdadcabbcadabdaabbbdbdacddbbddadbaccdccdabadbddcaadaadbcadaaabaadaaccacccdaacdbdadacccdbabbccadcacdcbdcbbcaccbcacacaadbacadababdcbcaacdabbacdcababcaaadcabcbcacddccadaabcabdbdbcaddcbbadbbacadadbbacdabdbcdbacbcbdbadbccadababbcaaddaddadccaabdaccccbbbbbdddcdcccaaadacbbdbbccbdcbabcbadddcabddbdcacbadaacaaacadcadbdcaddbabacaaccadcbddddbaaaaddccdbcdcbcaaacdcbaccadadcadccdddbddcdbbdcdbaccddcdbabcdccddddcabbbcaccdccbdbdbcbccadddbdcaabacaaabccdbddcdabddbabacabdacdbbbbabacaadbadabcabccdbdadcaabcbcacddbadbbdbbdbccbbadcbaccbacdcccdabababacbbadddbbbdccdbbacdccdcbcaccadbdabaacdbabbccdababdcbcbacaccbbbcacdbcaaccbaccdbaccabdacbbbcbbddbacbbddccddddcaadbdaccdcdabdcdbbddbcddaabababbdcddcdabbabaabccdbabbadcadacbcaacdcaccdabcdadbaaacccadbbcadadadcbcccdaabdcdbddbabbdaaaccddabbcdaaabaddaaaddcdabadaabbaaadbdbaaadadaccbbadbdcaddbababdbdabaddaadadbcdacddcbbacbbacccaaaacabaababdbacdcbbbbcdcdbbadaacccacadbbdbabaccaaaaddcdddadacaddcddbcbcadaabadbcbcbbcbbbaadabbdbaddbacbbdabbcdcdddcbdcbbcdcccbadddbdbcdcbbbabcbadcabdbbbdabdacbbdbcacdcbcabdaadddbdcacbccbbaacaadcabbdbcdaaabaabbbabbdacacacddddbdabdbdbdabdadcdacddbbaddcbdcbbbbcbcaddccabacbabbbabcabaadccabadadabbbcacdbddbbcbcadcdbbacdddacaaacaaaddbaddabbaaaaadbcaabddcdadcadaadcaaddadabbbdcbabdcdbddbacdadcacdcbabaacddddadacbdccbcbadadcdcbabadaaaacdaddbabdbdbdbbbcdbdcbbdbddbadcabcccdcabdadddbddacdbdadbbbbcdbaabadaccccacaadbbaaddbaadcddcdcccadccdbccbbcacbddcdabbabcbcdbcbdddcacddacbaabbcdcacbbbddbbbccddcdbbdcdcbcdbadcdbcaacdbbbcadbdadcbadcbabddaddabbadbdcdbccadcbbcdcddcbdbccccdaacdcddbacadbdaddbdccdbcccabcbddbababcadddbaaabbdacacddddbacddcacdbbabbdbbdbbacacaaacddadbbacdbcdbddccdacdbddcabbddccaddcaadbcddacaababbdcaacaaadbcadbccdccbdadcdaaacbbcddacadddacbadbadbabcdbdbdddcdbbcbccadbcabddbdccdcbacbddacaabacdbbbcbadbdbcabacaadacbadaaacaababddbcdbcbbdaabaacbcbabbaacdbbdacabdabcdcbbbaabdcbabacdddcddbcbcbdabddccbbcdddacccdaacbaaaabacddbcadbccadddadacccdabaaccadabbabccdaaaadcbddcabddcbacdaabddcacabbdcabdabbddaaddbcaacccaddbacaaddcbcabaacbcdbbcddbaabacbdaadadababbadccbbbdadbaccccadacccaaabcdbbcdccbacbccdddddabbcadabbccadbaaaadaadbbcdaccacaaabccacbcdcaabdcdddaadbbcdbcdddbbdabadbcdcbddcdbccadabdcdbabacbcaaaabacbabcbcbcdacdadbbdbbdaccdddcacdadadcdbaabaaabdaddababbdbdaabccbdacbccbcccbbbcdbddabaabaacaddbcabababacccbddcdccdaaadcbcdcaddaabbdbadcbaaabdbcdacacbccdcaccbcbbcddcdbdccbdbadaddcbbbcaaaddcddcbaacabddbbbbababcdccacbcaddcccddbabcddbabcdadbaddcabbdbcaadcccdcdbcacdaaddcddadddddcbaaacadccdbcacbacbbabdaaacbacccdccacddaacbdbdacbdcbcccacbbcbcadddcdcbbbaadcdcabbcdaccbabddbcbcdadccadbdcbcababddccaadadbaaacccbdddaabcacabddbddabdbadbddadbcdddcaaadbdcadccbbadddcbdadcbacdbdaadbdcdacccbcacbbcaaadaabcdccacabbbccbcbbcabddbcaddcddcddaddbadaababcdccabaaccbdacbaabcbcbbcbddabbcbbabaabaddadbcbddadcabacadddcadaaacbbcaacbbbcdcdcdcbadabddcdbcbdbdbbbbccdadcbaccbdbbacabbdbddcadabaccacadaabccdcaacdbdacdabdbaadabdcbabdacadddacdaaabcdcbcccdbbcacddbacabadcddcacabbdccadcadaddcbddccdacadbababcdcccddbdcdbcbbdbadbddaccdcbdcdcdbcdbbbdbabadabaadacbcbdbdcacaaaaaadacacddbcaabacccbdbcdaaabbbbbacbddbdbcbbccdabcbaaabdddbddbbabddcbbcddccaddabdbbaacaadacdadaabbbaacdbcdabcdacdacbdadabaccbabccabcbdcabddccdabccbdacabadacbaccaadabaaacdabddbabbaacacbcdbddbbaadabacccdbddcbaddddacdadacacdabddbdbbbccdbccaacddbbdbbbacbdbdbdbdadbabcddbcddcaacbbbabcddcbbcdadcbdaddabacadbdcbacacaacddccadabaacaaadacdadacccddbddddbdcbbdcbdcabadddbadbbbdcbdcdbcaadbcdcbcbdbcdbcacabbabbacdcdbbacddccaaaccddccbdaabaaabcccbcdcadcbaacaabbcaaacddccbacaadadbcdbdadbdbbbcddddcbaddcdbdaaadccaccccdaaabdbacbbacadddadaaccdbdbacbadabbcbbcdaddcbccbdbaddacbccaabcacaccacddbaaccabbaaccbdadbaabaaacbbcdcbbaaccdbcdaccdcdabaacddcdddddaadbbcbbcbdbcbcbbcdbcbabbacaabdbbabbdacbacdccdcbbbcacbdddaadccbbcbbdddcbcadcdcccbcaadbadacbaadbdbcaacdbabacdbacdadabccacccbadcaacbbdcaccddddccabcadbbbbbccbddcacaadacdcacbcccdacbcccbadcaaddbbcadddbcabddbaadacacbadadbbbdcdaccccdcddaadbaddabcbcadcabcdabcaaabcbddadcbaaaadbdcbacdaacccaccddbdbdcbdbdcacbbdaabccbdbaadaadcacbcbcbadabbbabcbacbaddbddaacbaddbcddbadaddadbabcbddbbdcbabcdbcdaaadaaacbdbcbbdabcacccddaacddbbaadddbbdbaaaacddddbbbadbcaadccabbdbcbdcdbbadbcbcdaddabdccccaabbadbaadbaaaacbaccbcacbcdabadacbabdadcdbcaadaadabcdbaccabdcabacacbbdbabcdbcddccbbaddccdbacbdbbbbcacaaccbaddbbcdcbbbdbbacabddabadbbdbdbdaacabdddbbcbdbcacccadbcbaaabaadddabaababaacabdcbddbcbaabcdaacbcdddcbbbbacccadacdddccdababbabbdacabdacdcdabaadabdcbcbcaacaddcccbdadbbcddacbdaddabdcddbbadabbdcadbacadbdbdcddbbbdccbdbbcbdbdbcabcdcbbaddcabaadabbbcbcbddcdcdabaddcbacdabccdbbdbabcddaccdcabdacadbcbbbcdbbbbbabcabbcdcbacabddbaacaaddabbdcddcddbacadbbddbcaaccadbcbbbbcbcbdbdaabdbadddcadbddcdbabbcdcbabcdabdbbddabdbddddccbbdcdcbaabcdbdbddbaacaddbabdcbcabbbcbbbcbbdbbbccaccccdbacdcacdddaabccddbabbccdbccaababbdadadbbadadaccaabaaadabdddccccaddadbbccbabbbaaadddbdcbabdccdbbaacacdbdcdabddacacadcbadaaaccddcdddabbcccdabacaacbabdacbdbdddccadddbdbaaaddbaabdbaccdacdacdadabacddbadcbccacdadccbbabaaccbcaacdbcdddccbacaacacbcbacbabddbadbbdbcabacdcbbbaaaabbcbbacacbbaabdbdcdddcacccbcababccadadbacccacdcababddddabdabbdacadaccdbddccdaadcaccbabdcbddabcaabcdbaacdabadbdbddccbcabaacbcabaaddbacdabaaaadaaddabbaabbbacadbbdcababacabadccdcbdaaaaacbcbdbaaccdccacdbbcadbbddadcabdabbadacabadaabcbdcacccbababddacbccccbbdababbbddaccddaddbbbadcddccddaaadcbdbbbccddabbdaadaddabbdaacbdaddaccbaddcbdcaaadcbcbaaddaaaabbcaaacbdddbbdbaadbabadbbaaacacbbadacbadadbbadaccbddbdcabcbaadbbccbdbcaddbddadccdcddbbbcbadababcbbaabbadbadccabdcaabcbdaacbcccdabacbaaddcbbabcdccddaccacdbdabbcbbbbaddbddddbbccccadadbdddbadacbcdddcacaabccaaaabddbbbacdabbbdabbbabdbabbacccacbabcbdccdadbdcbcddbcbcaaccdcccbdabdccdaccdcbaacccbccdccbcadbbaccaaacdacdabaddbacccbdcadadacdaadcbbbbaaddccbbcbdbdbbaaadcacaccaadbbbddcdcdaccabdbcbacadacbadbbabcdaaaaadbdbccdccaddcbbbbadcbcccbbbbacaddbccadaaddaadcabbcabcccbabdacbdbcaadabddaddbbabaaadbbbbbbcbbcbddcddddcabddbdcdaacdadbccbccddabcdbbddcbcacdadacbaacadbbdcbcccdcadcbdddcdabacdccaabacccdcaabacdddaaacbccbcbbbcdcdbcaacdbabbccaaabadabaabacacbaacccdbaaccccbddbadbcaaaaaacabcccbadbbcbabdbdacbdababdbabbcbbdacbcbabbacbdbdccadcdabcdabcddabdbcdaccacbcaabbdabcbabcaacadcabddccdccaccbbcddababbcdbbbaaaadbcabdbabbbbcbbdccaadddacbacbdcccbcacddbcabbcaccbdccbbbbcabcaccddaabccadaaccababdacabdadabddcdadccdcabaccbadadcbcaaddcdbbdabaddcaabdcdaaaccbddacbcccbbadcbcdbcbdabccbbdbdadbcbbabaaaccbaaaddcdccdbcdbccbcdacdaacdabbbdaacdaadbadccabbcbcadccabbdaaadbcacdccddcbcdcbdadbcdccbabccdcaadddaadbbcdbadabacbbbaddcbccbccbbdbbbdcdbddbdcbdcdbabaadaadccdccccabdbacbddaccddadbdcaabcbcababcadcbbbbcacdaccdacbccabdaccdaccabdcabddcdbbaadcadbbbbdabdaabbaaccbbaddcbccccdddbbdadddbcccddbbcaaadbacdaaaadcacadababccbbcdbbabcddcbdaddbbadadbbcdddbdbabdaaacabccbcccbcdbcacadddddbdcbaabacdbbcdbaccbbadccbdcadacdbbabadabdbcbcabccdbbaacaadbacddbbbdbcadcacacdcdcacbbbbccabccdcbbbbbabddcdcbbbadcaaaaadbcbdacadbcdcbdbbbbcababdcdbaccbadbabacddddddbcaddbddbcbdcddbacddbaaadabdcbdccddaacddccccaaadccdacadbbbbdbaccabadaabbbdacdbcabbacdcbbbccbacacdacabdbbbdbbbabbacacbabbaccadcdadbadbacbabbcccabcdadacccddbdcdccbabddaabacccacbbbdcbbcdbddacddccdabaabcaddbcabaacdbaabddcdacacdabdcacbbbcabcdcbccdaaabdbdddcbdadcbccbaddbbdcbcddbaaaabadbbbcbcbaadadbcdbababbbdccdbacbcdaabbcdccbddadcccbbaacabcbcdaacdddaccaadbabdccdcbcadcabccabababdcbacabbdbbadbadddcaaddacbbddcdbcbcbacabbbdbbcddbbdbaacdcbcabddccaddddbbbcdbdaaccadabdbdccbdbdcaaaccbcbbdddbdabcdbdcccccdbaddccabdbcababcadcdabacdcabdacdcccbacadbbccabadbdbbaadbaccacdaabaacddababcbbcdcdbdbcdabcbcbcdacbdbdcccadacbccdcaddddaaaacdccdcbbdabadabddbdadcdcbbccaddadcdddcbbbdaacadbbccbacadaccdcaabbcdacdddcbbddbddacabbbdadabdbdcadadccbdccaacacdbdcdaccdadacbbdbcbcbaadccadbcaccabacaccdadadcdddabdcbcbdcbadbdcacbbddacaabaaddcbcddcbccbcaabdbaacacdbdacacbdddddbdbcadbbacbdacbaaacadbbaabdaabdcadccdcdbbbdaddbccbaccabbbbdbdacadcddcdccabdcaaddabbbaddadcbcdcabbcbadbddadbbbddbdbbcbddcbbcaacccadaadabdbaadbcdccacdbcdddadabacbdcbcddaadcbcaaddcdadcbcddbbadddabbcbdcdcbcbaddcccdadcaadcabbccbdccbcadadccdccbccaadddcacdbddabbabdacbbabcdcaadbcbddaadcdaacbbcaabcbbbabcadcdcccdaaaacaadcacbcacbcbacdabcbcaaacdcdbdabbcdabcbbbaadbddacadacdddaaccdbddacadcbcccbdddddaadaadaddaaadadacddccbdcdacdccdbdcbdbaccccadabacaddbabcaaccdbddbadbcddcbaadbbbcdbdcbdacadbbdbdbcccacaccbcdcabcdbccccabdcacdcbabddadcccabdbbdbcaaaacbddbdaabcbbbbcdcdcdacbddbdaddbabdaadbbbbabcbbbdbbcccacaccbadbabcadbaccabaabcdaabdaadbcdcacccbdbacbdbbbadabdaddaacdbbacababdbcdbbbdcacdaaadaadcbbbbcdddcdcccccdadbdacabaadbddddbabaaaacbababadcaaaabbccbcbcabcdccbccdcbddcccdbcacbcccdbabbdbbbdbcbcaaadabdaadbabadacdbbdacccbaacdcdacacdacdcabacdbadbdbacdadcacaadcbdddadbacddcbcbccbdaadbcacdcccaddcdacbacdcaadaddaaabbcdcbcbcccdcbdbbccccaaabbadbbdcadaacddccabbabbadcddcccaddbbabadcddddccaadbabcbbbdbabddacbabbabcdabdaadbccbabcdbbabacdaabcabdcbdabacaaaccbdaccdcaacbbadccddaadaaddbcaabbccbddbaaccaaabadacbbcccbabdddadaccbabccdabdadbdadacddbcdbdbbdcdddadcdacdcabbcdccdcacabdddaacccddbdabadaaaaaccdcbcccabadbcdbbcacadbacbcbbbccdccaccabccdcbdcadbacdbadbdcadbadcbaccbcdcbdbcdadbcdcabacdcdbacbddbccadcaadbaadadbdccbdddccdbcddcdcacdcadcbccbbcbcdbadbdbdddadaaacccdadacbbbcdabbdcaddabdbbadcbbaadbcbddabdadabbbbbcddcccdababddcbdcbdaccdbddaabcddbadbbbbabccbaabcdbcbbbccaaccdbacabaabadbdbaaddbbdddbcdcbdaabccabcbcaabadabccbdaaaabacbbbadddcbccadcdcaabaabcccbcdadaccccaaaabcacccaacdcdadbaadbbbdacaaccbbcdabdccbbdbdddddbbccbbcdcdcdaaadcdcbbbccabdbdaaacdbcbaabdcbbbcccbddbacdaadddbcabcaddcbadcaabaaaaaabcddbbbcacaaacaccdbbacddcbcbacbdbcdbbdaaddcdccddababdcadccbaabbdddbbbbabdaccadabcbacadabadddcaacbcadabdaaaaccdbcbddcaaacacdaddbabacaddcabbbbdbcbdbaaddcdbdbcbbbddaccacbbababdddbdcadccacaaaadbcdacdacadcadccccbcddacddccbbbdbcbdbababdcbdbbcaccbddcccdaccacbabacdccccadbdccbbdbabbcabcdcbcdccbcbbacbacbdacaaaaccabdccdbaacccbbdbbbcbdbaddccbcdccbcbcddabaaaddadbcbadbaacdccdabdaacacabcbadbbcadadcccbbcbadbadcabccdbdbbbbbbbbbcabdcadcaaaccbddbacbabbcdacbbcbbddadbcdaacbabadaacabcccdabbcdbadcccbdccadccacbdbdbacdadbabbbcadcdbbddaccabcdcbaadaababbacacacbddabdabbacaabadbbdcbbdbddcabdbaababbabbadccdcacbdbcadcccbdabadcddcababbbbaabddbadbaccbcaabbbbcbcdadacbcdbdbcabbdabdbdadcabcbaaacacaabcdadaaddccadacccbdbdcbaaadbbaabacacbcabcdadbabdbbbadcbdddbdacccacdbbddacbbdcacbbdbbddbcacabdbacbdbacacbacbdbcacaadadbaabcbaadccbbcddacaaabdcaadaacbdacaabcaddbbacdccadcabbacbbdbabbbaabadcbbdbdccdaadaabbabcaaddbcbbbbcacccddbcbbcbbdbcdaccbcababbbbdbdbcababbaccaacdcddacbaccaacbcbdabdbabbdcaaadababdbbdcbaadabadacccbaddadcbcaabcdcaacdbcddcccbacadccccbcccbaabccdcdccbbbcbdbacbdcddaddcbcbbbdcbddbcbacbcccbcacdbcbbdbdcaccacdaaabbbdbbacbddaaddbddadbbbddbdcbdbbdacbbcdcacbabaacdaabdbcddccbadacdcacdccacbbaabbccaaaacbdbcdcbadddddcbacdcbaadaacacababdbdddcbcadcaacacabcbcacbdddabcbaccbcccdcdccaadbcaabadddcaababaadadcacadaacbcabbbdbdcbbcdddaacbcabcbacccdbacccabcbbbcbcabbcbdcabbbdddcacddcabcbbcdbcdcdbaccbbdbaaabdcabbacacacbbcacdaddaadaaabcdbbdabaadaabdddccbdcbaabcaccbdddbabcadcdacadcdbabdacdacbcaacabcdadaacbdbacadcddccdcdabbccbabdadddccddabbbbaabadcccccddcacbdbbacdaddabdacbbabacdacadbabbbcddacccccbdbddaababcdcddbaabcbdddbbbbaaacdcaadbcdddadbaccdacddbbdbccbaaddbbbbbccdacbdcbadbbbbdccbacacbcbbbacadcabdacdbcbbcbaadbdcbadcbcadbcbcaddabcbaacabbcddbababddcacbddabdcccbaabaacdcccbdadccbcadcaabdddabdcccbabdabdcbdacccbbbcdadacabccabcaadccabccbaadbbcccbcadddcbbdabbdcbcaacbbcddbbcbaccdbaabddccccabacabacbdcdaacdbaddabcdbdadaccdddbbaaaccdabcdadbbcbabbcbcdccabdcbbdacadbcbbbcdaacdaaddabdbadadccaccaaddacadddcabbddbbadcdcdacdacdbcdbccccbccbdcbbdcdddcccacccbdbcbbbabbcabddccbbbaaccbacbdcccabadacdcdbbadadaadacddabacdbadaccbccccbbcdbabdacbddbbdcbcccabdbbbdccddabddcbcddccbbcacdcaaccbbdbbbaccdbdcbaaadcabbcccadbcbbbbabcdcababdadcadccbdbcaaadbdcabbbdbdbbccdabcbcbabcaadddbacdaababbaaabbdcdbddbcbaddabbbccabaccabcdadacbadcaadbdbddadbdcdddcacaaddddcdcbbddaaadddbbdcdbddcbdbbbcddbadbcdabbdaacdaccdccadbdccdbbddcabbccdcacddbabadddddbbbcccdddcadcdcccccbacccbbbbacdaacddcabdbaaabccdabdadaadbcabbdddcdcadddcbddbcabcdaabdadcabdbbdaddabadbadbccbabdbcaaaacbababdadcccbbaadcdddccccaacaccdbbbcdbbdcbdacdaaaabdcdddcabdcbddcacbaddcddcabbbdbdcbbabacabbcdacdaaaddccbbabaaadaaddbcddccbbdbcdcdbdbcdaabbacdcadcacccacbbcbdbbbbccaccbdadcaabcaaabaadcabdabdadcdcbdcacddbbaadcdbcddabdcddbdcbccdcddccbddccccdabbccddbcdadddcbcdbbbcabbdcdbbdabbdcbdcbaddabddaabcdbdaacdadaababdcccaaccbabccbcbdcabdddbaaadddcddcccaaabbbdbbccaaddbabdcdbdcadbaccacbadaacdacddccacadbddacbabbdbdaaadbdcccdbadacbbdccbbaababababbadbccdcccddadbbaccaacaabadabacdbbbcbaabddbccacaaddcbdaabddbdbcdacbabcaccbcbdcbaddddbacaaadbdbcdccccbcddcacaabcacdbdbdacaadabcbcdbbcaabadaddacbcaabdcddacacbbbacbbaacadbbabcdccccdccdbdbdbdbdbbbaccaabcabcaadddbcdcbacccdcbccacbaccacabbdabddddcccbabdbaaccbbbdddbaddcbdccccdcabbdbacacabccdcabdabdcabcdddddcbcbbdbcdcababdacbcdbcbbcdbbaabdaabaabbacdcbdcdbcbbdccdbacdccbdcabddcdadcaacbaabcdabdcdabccbababcddcadabcabdbabdcbdbbcdaadcbacdcdbacdaaadadcacbcbbaacddcbcddaabccadbbccaccdaacdbabcadbdcdacbbabbaabbadcbdcbbacbddbbbbdacdbcbcdccadadcbcaddcabbbbdaacdbdbababdcbccbbbdbabcbaccbdcdaadbbbdaaaddccbcadadbcccdbabcbbbbcdaadcddcdaacdcbaacdcccaaaaddbbbaabccaccacddcacbadddababcaaddaabdadccaaabdabdabaaabbddbcccbacabdcbdbccdaaaaaacccaccacbdcccbcbacdbbccbddcdbbaddadccbdacabccbbaaadcbaadaccbabcdabddbcadbaddadcacbddbdbaadabcbdbaddcbcdcdadcbdccdadaddabccbcccccacbbaaaaabcdbddbcaabbcdcbbadcabcaadbcddbcbdadabdddaadcbcbcaadddcdbdadbabcacadacaacbcdbbaabbdabaaabdcdaabbbdadbadbcddccbcdcbbddddbbdaaddbdbddadddcbaaaccbbddcbbccdccddcadbcdaacaccabddccdcdadddbbcabcabddcaddbcdadcadcbcccdcbaaadbcbddccbccacccaabbcbabdddbcdabadbaacddadacdcabbbabccbabacdbcbabdccaddaabcacabbcdbcccbdddccdbbcdcdbacdbcadadacadbbbbbcaaabdadcaadcadddcbdddcddcbcbbccbacbcddbdcbabaccbdbdccacacabbdbbdacdbbaacabacbbcbdbccaaadbccbcacbdaadadbccaaacdbbcaddccacbbdbcbdacbbcabbdabaadbbbcbaaaabcbddbdbacddcddcabaaccaddadcddbccddcbcadadbcbdaaaccacabbbabbbdbdaabccddadcddbccacbdbdccddacbbbbbcbaddddabdbddcabbacbbdababdbbdaadcdaabacabcbbbdadcaacdadbdbcaaabaaadcbdadbaadadddbabcadbaaaddabccbbabbbcbbddcacccccdbcaddaccccaaaadcacaadbbadddbddbbdbccccacdbbaababbbcadacccaadddbacdabbbccbdcbbdbccdcacbcbcacabbcbddcccbdabddbcdcbdcabcbddaadcddbcaccdbbbacbcabaadbcdddccbaabbabaccdbccdcbdaacdbddbbcabdcacddddcadcbccccadaacbabcddcbddcdcdcbccbacbddaaabbbccbcadabcbaabaaacacacadbcaabbcbbdcdbbacbdbbdddbcbabcacabaaaadcdaddcaccaaadcbcaccdbcccdbababadbcbcccbaabddccbdccdbaaabdacaaacdcaacddbccbbbddbddbcbbdaadccaddadcddcccccadcadcccbdbbacbdcdbdacabdbdabcbcbcdcadabcbbcdbccaacbbadacdacdaadcccaabbdacabcbdaadbaaaaacdcddcadabdbababccbbadcaacacacbbadbdcacadabbbcbddbdcdddddccdbaccddbaacdacabbdcdcbadadcbbabdcddddcddcdabbabcabaaacacbdcadbdbcbdacbccccbdbaddabbdaabcdcacdbcdbddaddabccaddbbbabddccabdacccabccdaaaaccbcabdabcabddbabdabcabaacdbbaaadbddcadccbabababcdbdacadaaaacdbdabdacabbadaaacbaaadcababdcbdcdcabdbddbbcbbcabbdabdadddaadcbdbbbdbcccabbbadbcaacbabdaddbaaaabcbdaadabccaaaacbdbccdcabdaddcabcbccdcdccdbcdabdbddbcbbbcbddcbbacaddcdcaadaadcaaaadddbdcccdbccdcbcbdbcccbcccbbcbdcdcdbbbdbbabdaadadbbdcdccadbccdccdddccbbdbbdbcbbadbccbddddcbdaddbadadacaabcbacdacaacddaaddbcdbcbababccbadaaaaabbddcbdcbcaadcaadbaacddbbbadaddadbbcabddadddccdcacadcbdaabdacbababccabacdabccdabcddaadccdaddbaadbcbaddcccdcbaadcbbbdbdbadcbbccbaabaaaaadddaadbcbbaabbbcdbcdaacacbbccadacddbddaadbbcbaabbacbbcdcbcccdcddccdadabdbdcdbccdcccbbdbbaccccbbbbcccccdddcdabacacccadcbabcaaadcbcabbddaddbbbcbaabcdabddabaccbdddbabcdcbbadabbbaccacbdbbbcbbcacbadaacacabdccdbabaccaabcbdbddcbdddaadddbcdadaccabdaaacccbbabdbbddbbcddadbadbbaabaadaddcbcdbcddcbdabcbbdbdbdcddddadcccaadcaaddcacccdcbadbccbbabcbcccccacdabbabbcadbcbccbadccabddbcbbbacbddaadaddaaaacbbbdbdacadcdcdcadbddbccabcaddabacacdbcbbabccdbbbdbabcaddccbdadccbcabbacbcbaadbaddddacbbbbbdcdddbabcbbdcdbcdacddcbbbddddadbaddbdcbcaadcdddbabccdadaddbbcbcbdcacdbccdbccdbdcdccddcbcbdcadbcaccccccdcbbcbcacdddcabbccccccdcdbacacbbabccdacdacacdbbddcdcbbcccccabcddcccdabcbadcccababbcaababdccaabdcbbdccbabacaaccdbcadcaddcbcbccddbcdbbdcabaacaddbbccdcbacdcbadabbacbcdcbbbabbaccaaacacadcdabaacddcacaccbcababddadccbaccadaacdbbccadddabaaccabbddddbaddabcaccccacbddbdbbcccdcaccdbaccddddabacacbadcdcbbddddcacbcdabadacadccaacbcaccdcdcadbccbddcdaacacbaacbcabadbdbcbbacabdbdcadcccdbaaaabcacdabaaacdbbdcbbaaacdbacbcabbbcbdaabdaccbccabacccababababdcdbbcbacdbbcbaabdcbccdcaaabcdbcdadbcbddbdcacbdcdadbcdcdabdacaadacbcbbbcbdcbababcbbbacccddacbbacdaaccbdccdadcbabcbcbadcaaaabccdaadbadbcbdbbdbabbdbdcabcadacccbccaddaacdabbcbbbddaaacbcdccaaababaacabcdcbcddbcbabcbbbcdbaabcaaddbbaacbdcbdbadcadcbcdcdaccbadabcccbacbdbabbdcaabbdcbbbdcaacaacdddacabadbcaccabcbaadcdbbcccdbbcdcdcbbcaaadddabababaababcccdcbcaddbbcbbbadcabcbaccbddbdcadadbacdaddbaccdccdbaacbdbabdcabbdccbbaacacabbccbadcadabbabacdbbabdabccdbaabadacdaaddbdacaadbaaadcbcddbdcbabbbbaddbadbddadbcbbdbcbddabadbdbcaccbadabaabadcccabadbadaaaadaacacdcbccadbbadaaadbdadcbbdcbdcccccbcacdcddaadbbcbdbbbadacbbcccdbdccbcddccababcaccbbabdaaacdbdcddadcbdccbcddbacbdbcaaccaadbccdddbababadcbbccaddadcbbbadadbdccbbbbbcdabaacdbdacabdadadcdcbdaddaacbcbccdaabdcabdbabcddadabbdbddcbccabdcdcbadcbcdbbaaccbacadcacbcbcbcdaddbdcbbdabbccbbdadaabcbcaddcadbcbbabacbddcadcbbdcaabccdcdadaccdddcdabddbddcaaaaacbcccdadacaddddbaacbcbcdadcccdbddbbdbacbccdababaaabaadabcccaaccbcacccbbbdcbcabbcbbdaadadbdcadccddcccbbdbccbbaadabbbbacacbabdbbbacbdbcccbacaccddcadabbbddacbbcbcdcadbddcdcbadadcbcacacaddcdddacdddbbdcbadaabbdaabdbdadabdccccacacacadccdccccaccaddbdddadbcbaddbcdccdabcbdaccaaaadbdabddbcbacbaaadbdbcbaadbcccabdacccbacacdacbcacbacdddbadabaacdbdcccdbabdbbbdcbcdcddaadcdacdcabdabdbadccaccddadcbbcaccaccdabcaacccdaccbabbbdacdccdabbbcaddcbddacbbddcbdbadccabbccbabaabdcbcbbacabacaccacbcbddbacbadaabcabcbdabaacacdbdacdacbabbccdcbaacaabacabbcadccdabdaacbbcadcbdcdccacbcbaadbcdcccaacbcacddacabccdcbcbcbdcdddacabbbbcbaabdbadcdbccadacccdbbddcbddbbbcdadabbadbdaddbcbddacbcacaacbaacccacddabbacdbcdcabcaddccdaabaabbbddbcbdacaaacabcbacdbccdaccabccccccadbddbdbabcbcaccdbddbbabdaacaabbadacaaabdbbacbbabddacacbbbadddbbdabaaabcdddbbdabdbccdadcbdacadabdbdccdaccaabcbababdccbdacbdcdaddbddabcbcdcbcabdaddbcdbabacadbbaccabaaacdcdaaddccadbbdcddbdbbccabdaaaacdacbaabcccbcccaaabdabcaaadbbdaacdcbdbabcccabbbddbdddddddcccddccbbcbdadbaabcbbdcdbcddcdaccadddbcabbdaabacbcbadbbbdcbdabbbcbdabdacbabbacbcaddcbdcabbbbbccdcbbdddccbaabbdaadbcbbcdaccdbdbbbaccadcccdcddaacbaaccdddcacabbdccbdbcabddddaaccddababbdabbccbcbbadbbdaabbbacdbdcadddbdabbabccbcbbaddbaadaddabbcddcddbcadcdaccaadbccaaaacadaacbccbcdabbaacdcddcbdcdcddbddbcbbbbccadcaabadbabcccdaabbddbddabdddbdbaddcabcdcbbacbcacddccaccbdcaadaacbddaccacbaddaaadccbacbddaddaacbddbacbddbccbcddabdddccbccabaaaabbdcadbcdcbbdaccbbabcbacdacdcddabadddccadddddaababdbdbcadbaccbadddcbabdbdabbddcbaccdbcadadbccaddbdbdabcbccccbbcbdaacbabacabcccacaaccacadabbddaccdbdabcbabaabcccaadbadabddabaacccbabdacaadcbbdbdbccdcbcccdaabbadcbcdbcadcacdccabacacaabacaaaabcdcbacbdcbdddaaacaabcdbcacdcbbdbdcccdababdaaddbbcaddbabdbdadbcdccacccdddabaccddbabcabbddcbabcbdaabbbadabaabddbaccdabaccccacaccbdcaabcddddbaacbcbddcbbddbcdacdadaabbdbacbdaacabdabcbaaaaabdbabdaddacaadbdccababdbaabaaccbdabcbbcccdabbdcccdadbccbbadbabdbbccbcbbaacbbbbbadacabccbacbadabadccbaadcddbbaddabdccaacabaaacdbdabbccdadbdacbcbbabcdccbbaadddccdaccbddadbcababbdcbddcabcbcbdbdcadabcadaccdcdbcbcdbbbcdbcadcbabbbbbcbcdbcdbaaaaaacccbdabcbdbdbbcdcccdcbdcbcbbaaababddbcdaabddddcadabddacddcccdcdbcbcaabbbcdabddbbcbbabccaabcaaadbbaaaabccbcbbadcabadcbdaddaadacadbccdcaddaabcdbbdcddabbcbdbbdabaaabbacdcaacbddadcdabcccdabdadbbdbcaccbdbcdcbaaaadcdddbaccbbbacbcbdccccbcbdcdaaacdcdbcdcbcdbcaabdddcccbddbacacacbddbcbcddcacccaacadbbaaccaacdbdbabbdcaaaaddbddacbdcccbbacdcddbbdabddddaddabdbbccaabcdadcacdbbaaabddbbbdacdcabbacabbbdacacabdbdacbacbadbaddabdbccccbcdadccdacccbadcadcbaddddcdbdbdabacdcbdacccbcaaaaabcababacddcabbacbaddadccabcccbcdcaddadccadbcabdcbabdaaddddabddabdcacdaaacabdabcdaccaabddcbadbddbdadddaacdcadbddaaadbdaadcdcbdbddadbdccbcbdaddddaaadacbddcaaccbdccdbbbdcdacddbacacbbdababbbbdcadaaaccabcdadcaddacadabbddacdcaddaacbdbbddcbdddbbbccddacabbbcbdbbbccddabbcabccbbabadabbbabaadaaddccbacadccadaccbdbbcdcbbbcbccbabbbccbddbcdbdcccacacbcbdcdcaadaadbdaddacbbcbcccbadddacdbdbdccbdcaaddddddaddbbdddabcaabdbacbdcdaddcbbabbcbcbaccadabadcacbacbbbbccacadbaadcbcdcbaacddccddbddbbbddaaacddbcadbadacbbacbbacbbdcacdbdcbbacabacbaaabadcdbdaadacddbbbcaacdbbdcbdbcddacababcdbbcdacbaacabcbcdbddbccadcbbddbcddddbcacdddcaccdddbdccacadbdacaadbadcbaadacddbdbcbccdacabcacbddccddadbabddcadaacdcaadaccaddabababadcbababdcbbdabbcbcdcddccbbdcdaacacadaccbcdacaababcdcadadccaacbbddaabcadddccacbadbbadcacdadaabcbbdcdaadadadbbbdacdbdbdababbccaadaaacbaaabbcaadacdbddbabaaaacdbcacadccccacdddddaacadcdccdcaccbbbbcdcbaababccbbccccbdcabccaaadbddaddacccbadbaccbadaddddbacdabaadaabcbacdddbbacbbcddacdacdbabcabaacbddcabcddbacdaacdbbaaadbaccdcbdcddcacaaadbaaddaabcccccdadbcbadbcbaabddcadddcabadbcbbaadadaaaadbaababccdcddbcdcbbdccaadccacaaaadadddddcacbbdcddcdbdaacddbadccabcadcbaabddcaddddcaacbbdbbdcbaddabaacdbadbdbabaababcababcacdaddbbbaacbdbadcbdbaacabdacccdccabdbbbbbbcdacdbcbdbcadbdcdadcdbadbdaddcbbbdbabbbdcabcbbabadbbbaddcbbcbdacbbbbbcdbcccdcdbbbbcbaaacbcccdcaaccbbbcabbbbdaabddbcdbcbabbbbbdddacbbacaddcddccaabccdbdcaadcdaaaacbadcddaccbcabccbadadcabcdccdbacacdbdbbaacccbbcaaaaacaadccacdcccdbcdbcddbaccadcddabbbbbbdcdbcbaaabdabacacbddddcadaccdcbdabcabbbbcaaaacaacdccdcdbbcadcbcabbcbcccacabdbbdaaadbdcddaacaaddddddddabadbcbccaaaadbddbaccdccbdbbdbcbdcaabbcbdbdcadcddddadbcddadadbdabdcbcacbcdccbcbdcccdaacbacdabdaaaadccaccdcbadaabaabaaccdaacbadbdbabcbcbabcbddadacccacbcbbdabcccdcbbbdbcaabbdcacbbadaddcddcccdadadcdbdacaabaadadacddabdbcbcacdbcadbcdcbdbccbaabaacdbaaaccbccdbbdbdbadabaadbabcdabbaaddcbbbccbaacabdcddaddbaadabdbcdcaabbcaacacbccaabdaddadcabdbcccdabdcabbadbbbadbadccaacdbddddcbdcaccadbdccadbabcddddbacaaaddcaadadcbadaccdddbcabdbccacdaabaaaddbbbbddadcdabbdddaaaddcdbaacadbcbcaadbcbdaabdacddccdcdddccaaaacaccadcbbaaddcdaadadccaddbdcacacadcddcbacdcbdcbdbccabcbcbbabaacccadcaacabdabaaabcaadbbddcabbcdaddccacaacccacacbaabcbdabbbaaaadcddcaadaccaadadaadabaaaacacdcbaaccddbbbadccdaabdadacdcdcbdaadbcabcaacbcabccdbabccddabbccaadccdacdcbbcdccdacbaadacdcaacabdbcdaccbdabaddaabdababcaaddcddcdccbadaacbddabcccbaabdbadaaddadbcddbdadcbddbbcadbdbdbbbacbbcadccbcaabdbcbbbbccaaaacabcbddcbbccccbadcccbabdcccdabdaacdcdaabcaadbadcbddcaaddbdbdbdcacdbcadddbdbbcdbdacddbbcbddabdabbbddbaabdcbbdabbbcbbcaacdadabdacadcbddbbacdcabcacdadadbdcbababddcddcbddbacbbdababccdaddabdbaaddbcbaabddbdadcccbbcdbbbbbbbabbdacdcaadaadababcbcbcddacdcdabbbcbbcdbbacacdbaaaabdbaacabdaadbdadbaabdccdaddacabaddbabbbbdabadbabaccdddbddadddabdbabdcabcbccaaabdbdaddaacdcdabccadccdaacbadddcbccbaddbbcbbdaadccadcbcdccbccbcacaacaddbcadcdcccbacbcadddacbdacaaaddbcbccabacddbdacdddcdadacaacdccbadabbabacaddbdbcbadcbbddabccbdabdbadcbcbdcbccbacdaaacdcbcaaabcacbadddbbaabbdcdbbddbbccddbdaccdddbdadbdabcdaaadbabbcdccdddbcccdcdadacdcbdbacdcacaaddbadcacddaabcddcaabbbadddcccabcabdcabbabbabdcdcbcaddcabcbdcbcaaadbcaccbbcbddaddadbcccdcdcbaabcbaadbbaccdadcdcbbcdcaabcabdcdaadbdaddbcdaabdbcdacccabdcccbbbabccdddcbaabbdcddabcdabcbaadddabbccdbadcdccddddabbcbddaccdcbaddbdaabccbcaaddccbbbddddcbddcdabcbabddcacdccdcbaadbdcdbaddcccaacdadcaddcababcaaadbbdbaadcccbcaddcddabccccccababaccbbbddbdbbaabadddbdbcadcbaddddcacacadacabbbddabdabaaabbdddddacbdadcaadbcdcdbadbddccbaccdaacaddacadbcadaaccbbbcccdbbacabcbcbabdcddccadbbcbdadbdbccaddbcbabaadacdbacdbcdbbabcbdababacbbbdbddbcacdadacdaabddbaaadabddcbcbbbbdaddcbccbbbdbaadcacdbbadbaaaddccbbacacacccadcbaddbdcadcdbddbbbacbbbdadaccdaccdacbbcacbbcabdcbdbaabaaabdcdcdadccbccdcadadbcbbaddbcbbbacbcdcdacdbbcaddacacbbadabbaacbbdbddaccbdadaaccbbaacbadadcccbacacbaaacdaacddcddddbcdbdaddbbcbaabccdcdadaabbdccddcdbacdcacdddccbabbddacadcaddcdcdadcbbabbacbabaddddbabaccdddcdbddacbbbcddcadccbbddadabcddbdbccaabacdbaacbdaaddcabacccadccddbcbbaaaacdaaaddbaadcadabdbbbbadadbcdadcbbbddddabacdccbadbdcbcabacddadcacccadbaaacacccabaddcbbabadaddacddadcccdcdadbbbacacccbabbbabdbabadcdcabcbbabcdbbdbdacadbdbcbbccdbddddbdababdbccddaacbcddbbadaccbaadcdbddbcbdbcbbdadcaaabcaadccbdabaaabdcbcbcacadaadbddddbdaaabdbdbdbbbcdbddcbbcabddaacadabccabaddadcbadcbbcddcbdcdccbbdbabacdcaabbabbbcbbbabaaacbbddabddcccbbccbdcdbbddcadaccbadcbbbbaddbdacdbccccbdbbdbabbcddbcbdbcaaaddcadcabdbbdadacabddbabcbbbbbcaaaadcaccbacdbcadaaaaaabcdbbcccacbbdbacdbadbcbddaabaaccaddabbcdcddbbccdaddbaadcbcbdaccacbdaadacacacbabadadbcdaadaccaccbddcccadadbbbacaaacdbdcbdddbdaabdabbddbcdaadbbabcbbcadcbddbccadbddcbbdbaadacaaaaccddbcddaaaddaccbbdacccaddbddcbcaaaddabdadcddbdbdbbccaadbadbcccbbbcaacdbbdacbdaaccbadbbddcbaaacbccdccccdcdbbddacdbdbccabaaacadbababcdddccdbadaaadaadacdcaabcbacdbbbbdbbdcdccccdccaacdacbaaaaacddcccddbcccaccbcddaaaddbababddabcbdbcaaaaadadabcadddadbdbcccbbbdbcccaababacacaabbadadadccaaadddccbcdcdadabbbaccdadbdabaccadddcbabbdbbaadcdcaadbdcbabbadaabcaadcacabdacbaaabbaadbdabadabcdcbdbbccbbbaaaadadbbdbccdacccbdcdbcdadaddcdbddaddddccddccdacbcbccbdadccabbbdcccdddabbccbabbdabcbbbbdcdbcbbdabdccbbabcdcaaccbaccabadbdcccddadadccdddcccaaadbbccbdacacddbbccdadaddacccbdbdabcabaccabbccaddbbcaccabcbabbccaccdacdcdbbbbbddcdddacadcddbbabdbacbbbacacbbdbdcdcabcacabdbacdbcdbcaddcbddddcadacdbdcbdacbacabacbcacddabaacdaabbdbaaacbbccacdcdddaabdabbcbdaaddbadbaaacdadbabcadadbaacacacbabddccccaadcbcccdabdcbaadabdadadabaaaabccabaccaabbdcaacddacadadcdbaccaabaaabbbabbbcdccacacabccababbcdacccbbcabddcaaacbccbabbcdabbabbacdacccdbbccabdcbdbcddbacddbdcaacbdcdcdbbabacaaacdabbcbabcddaabbbdcbbbacbbbdaabcbabacaacdaddaadcbbbdbddbcdabcdbaabbcdaacddadcacdcbbddabdcdbddadcaabddbadbccabddbaccbdacaacacadbdbbdaaaaaaacdcbccdadabcbcdadcdcdbbdcdabddbddcaaabacbabbbabadcdcbadbbbdbbaddbabacdddcbbccccabcdbdccbbaddacbdcccbcabbcdcbaacbdbabdacdadbbcaaacdbbbbccddcacaaabbcdcaccbcabacbcbcbbbbadabacacdadaaadbaacadcccbdbbccabbcdcddbcdcccbbaacadddbabacbbabdcdaacddbcdbcaacacddcabcabccbdbbbcdaadabcdbcaabcadddabcaaabdabcddaadabcddbaddddadcacccaadcbbdbdaccdbaaabadcbabbddbbccdcdbbddbbbabcbbccacacbdbbdabaddbbdcadacddacbdbcacaabdacdbdaadcccabdcccbcdbadabaacbacbacacbcabcbacbbcdaaaaccbacbdcbccdbdadddacdadaccbcdaccbdaacbacbacabbabacadbcdaabbdcabacaadaacdbbbcdacbacbcdacadacddbcbacccdbbcbabbabacacbdccbaccaacdacbddcabdacccbadcadaadbcdadbddcacccdcabcbaadcbbacdaccbcbadcbddbdcdbdbbabcccbadcbdabadacabccbdbcdbdadcbcddaaaacbadddaddacadbdccaccdccbcccdbacacdaadaccadbcbdcdddaccbaacabdbcbadadbbccbbcbcddcabbbcbdbcddadcbacadaddaacdcbcbcaccddcacabbabdbbacdbbcddcaaaacaccbdbadacdabadbabcdbacaadcacdbbcddcbbdadcbddadbbadabcbbcdbcbbdaabbabdbcdaaddcdbabaaacaadccdcdabdaddabbdbadbdbcacaaacbcaabdbaaddbcdddcaddcdaaccadcbdcdcdcdaddbbdcacabdabaabddbbbdbacddadbdbcbbacddccbdacdccaaaccabcdbadbaabbbcaccbcacdcdcbbbabdaaacababcaadbcaaacbadccaacbcddbacadbdcacccababbdaacbaabbcbdccabcaacacbcdbacaaddaaacddadcabddbbddddcbaacabcbdbbddadadbadbdaabccadbbcbccbddacccacbbcbcacbbaadbcccddcdadbdcdbdadacbdbadcdbbddcabcbbbbaaaabbababaaadbdbcacacdbcdbdaacbbcadcbdcbdcbccccacacbbbccdacaacdadbdbdddbbaaddacdaabdbadadcdbdaddbdcbbadcddacabccdbbcdbcbbabccdcbdaadbcbaadbbcddbddbababdcbddadaccdbbbabbcccdcbddaacaaadcaddbcaacaadbdccbddddacdabadbbabadddcddabbcdcaaacbdacbacaadacabbdbaaabcdbbadbcbabcdbaadacccbcaadccccdacabdadbadbdbabdcdcccbaacdcaabacbcdcccbadbbbaadbbbcabbcabcbbbdbccaaacbcbaabdadacadccadcdcdbbadadbaddaadcbccbbcabbbdcdbcbdaaadbbabcbacbdabdacbbccdbddbbcdbcbbccadacdcdbdbaabbaabbddccadaccddabdccbbadbcabacadacbaaaddabdccbcdbacdbdcacddabcccbbcaddccccaadbacadbdddaadabcaadbcbbdccadbcabbcdddbdddacbcbdcdbdbaabddadadabdaaacbcabcdbabaaababdcbdbcdaccbccbddbbbabaaadaaadaddacadccddaacdaddacddcdbbabaccbdbcbcddbcdcdcaaacbddcdacaaadbdaabacbcbabdacdbdabbabccacadcdabcaacbdddbabcbabccacaacdaddcbaadaadcdcacacaabbcbabbdbdaddabcdaadaabdcaddcccdcabaabdcbdbccdababdcdabcabcdbccdaabbdcdbdcbcacbdcddaddbddcaaccccbdcaacbdcacddbabdccddabcadbcaaabddcadbbcbaddcdbadddaadbdcaabdadcccbcccbcdcbccbcaabdcdabadabdbbabacadbbaaccacbcbaccaddbcdddccdaaadddaabdcdccdabcbcdbabcdccacadcacbdadcccccbdcbabbbccacdccabbbdabbadbdaaccbbddaccabbddbbdcabbbbdddbabbadcdabdacddcbccabaaaaabcdadadacdacdcbcccaabbcdabcbccababccacacadbadbcabacadbbbdbdbdcbadcadbcdbbcdacddcabaccbabcdadcccbbdcddaccadccbcacabdbcddcadccabcbbacabcbbbcbadbbbbbcabdcdadadcccdaaabccdcabcaadcababddbbdabbcdcbdcabccdaaccccaabdbadacbdccddbcbadadacccdccbadaccadbdddcaacaaddddadbcbdcbacddcdaabadaacacababadbbdddccaacdacdaaccacaadcdbdbaaddbdbacdabcacdbaadaddbacaddbcbcadbcbaabbbddccddcbcccbbabaaadabaaddcaaacdbcbbcccddabccdcaddaccddcacbadcccadbdbabdddacaddbadbabddaaccbacbddcddaddcbbcabccbbcaaaccabadaddcbdddaabddabdaaabdbadaccbbcadcbccccbbbdcdaadadcabaaadbcbdbdacdbdbddcbbdbdbcdbcccdbddbbccbbbcbdbcabbbddddcdbbbccbdcabdabcdbbbccdadcccdbacddcaddacbcadbbbabccacdbbbbbdcddcbddcddacaacbacababcbcbbbbbaddcccdadabcdadcbccabcaadaddaadbbdbabddbaabababacacdcbbcddaddcdadcbaadaaadabccdbbbabbcadadabbaccdcacbbadadcdccadcababddcddddddaccdaaddbdbdacacababbdcacdcdaadcaaadadabadccacbccdcbaababcddaddcacadbcaadadabdbdddbaaddcdabdcbddccabdcdadaaddabddbcabddadbbdccabcbcbbabaabcadabdccaadbbbabddbdabacdbbbcccacabdccdadabcbaaaddbdcbbbbdccadbcdccacaadbaabbbadbabadcdbadadccddabddcbcdbdaccaacacaabdddaaabadcdcdaccdbadadbcaaacdcdccadadcdaacbbaaadcbaaabdbbccbacaccbbadddcadaddcdcbbbabaadbadcdcbdcbddaddcbdcdcdadddbdcadadacbbccdaacdddbddcdaabbdbbdbacabbaddbcdacbddccddbacbcdaacddbabdacbddcbacdbbaaddcccaacbdacdadbcbbcbdbcacdbcdaabcbddccdabacdbabadcdddcddbbdbadddadcccddaadbcaabdacddcdacabbaddadabdadaddadbdbadcbdaabdabcbccbbccaadabdabbbdbbbcdbdcbcdbabdabdadadcacddaabdcdaacacacadcddacaaaabcddababddabbddbccddcdddbdcdbcccdbccddbacbcbadbbcaddcaabacbbcbbdabadbdcadacbdaadaaadaaabadddcbbdcbbbcdccdccadddcaabaadaccdcbaaaddacdcbbdabdadcbdcbabbbacbadddbadbcadacbadddaddababbccdbdaddddbbcccdacbddcbddccabaaacdadcacabbbbdbacaadcabbadadbddbdcaadccbcabdaddbbaabaaaacabbacaaaabadcbddcccccbcccdacbdddadbdabcadcacadccbcdabdbdadccbddaaaabaccddcaacabadacbbbaaccccbbdbbdbacadbccbdbbacaaccbbcadbcccaaabbdcabcbbcdddabaccdbaaadbbdacbdcacddcaadaadabbdcddbdabcacbdbdaccbbcbaccbaabccabbbadddadcacdbbddacddbacaadbcccbabbaacacccbbabbadaadbacdabadcbcdacbaacbbcdddaccddabacbccdcbababadccdbdabbdcddaaabccadbacccbdddadbdcaabcccbbdbcccdbcdababacbaadddabbabccadcaadddacbdadbacadddcdddbbbdbdabbacdaaadbdadbbdbdcadadaabbcbabcbbaaaddcabcacbabcdbaaaadcddadbbcccbabddcddabadbdaacabcbcdcdbcdcacaadbdaddccabdadccddcddadbaadcdcbbbdaadacbacbdbdbdcddccccdaaaabccdddadabcbbbbdccabbcacaaaabadaccdcbacdabddabbcdaddcddacdddaacdcbabcbaddbbcacacdabaabdbcdadaccccbabbdcbcabbdbccacacdabdbddbcaadccacaaaabaacacadbaccacdbdddaabddcddcbcbadbcdbcdaadcbbdaddbcdabacbbbcbacacaccbcacbabaaddddcabdaaaddaadbbbcccdccbaacaadcaaddabaddabdabbbadacbbaddddbdbcdcabccdbddddbaababdcbcbcabbacacaaadcdbdacdaccdacadcacabadccccdaadaddcdcacaaccdddbdbaacaaadadcbcddadbccbbbcbcbacccddaaaddccdbcccabccbbbcbabccbcddccadddcacabaacdcdaaacbabbbadbdadbdccdddaccbaccbabdcdacdabcababcdccbdbacdcbbdaabdbcaadaccdacddabbbdccbabddcdcacdbcccdcccdadbbbcdbbaddbbbbdcbbcdcdaadaacbdcabdbbabddcaadcaacabbcdabccdbbacadccdcbbcccccbabbadcabcddbbcdadadbbcbbcacaacdbabdcdbbbcbbdacddbbaaabcadcdcaaaabdabddcdaadaadcdcbaccababadbaabaccdcdbcdcbaadbbbdcaacadcbabddcacdbccddbcbdabadcddccbdcacbaaddcbcddddcdaccdadbdcbdcacdadbdcbcdaaadadcacbcbbabbabdbbdcdccadccacdbdbdddaccbbacabccbcaacabbcaaaabaaddddcbdaccbdcdcbaaaccdbbcccbdaaaadcbdccadbdbbdddddbaaadcabbdbddcbcdcaaadbbabaabcaacbacadcbbaccaaaadcaaaddbacacddadbbdcdcaadbbdddbacadaabbdcdcaadbbddccadadbddcadaaaaccabdcabcdabdbcadbcabbbabdbbbcadadbcbbdddaacbdbadbacabaadbdabddacacdcbadaaacadbcbddbbaddbbdbbcaddbaaacacbbbabcccdbabdcaacacaabcabdaaaaddcabdaadcdbddcddcbcaabacadbcbbabcabbbddbaaabbdaaddcbcbbdccbcbaddcdcbaddbdacbbbcadbddadbbcdbbddadbadbcdaddcbacbcabbbadcaddbacabcbcaacccbbcabacabcbdcadacccbaccddabcabdadbabacadbdcacdbbdbababaaacabdbdbcbbabcacdcdaabcdccbadcdbadccdbdcbbdcabacbcaacaacdddbcccacbdabcbccaccccdbdbcccbbdcacaaabcddacaadcdbdddbbbaadcbcbdadcaccbbaddabdcdcbbdbcccdbdadcddcaadcbcadbadddcbccdacddbddcbdcddbdcdbdcdabdddcacadcddacbccabaaaddcbddaccbdcbccddabacbbdcbaacdbadbbadabbbacbbaabcddabbddcbabbbdcbccbaabdaacacbbddacbcaaabdcdbacbacaaaaacabcdbcdbcdcdcdddbaccdbbdaadbaddbcdacaadacdbbbacdcbaccccdddcdcdadcccabcaabccbaddddddddadbdcdbbbacdabaddabadacaadaaddcaadddcadcbdcaadabcabdcaacbbddbbbcddacbadaccbaadcacdcaaacbdcbadbacaccbdacdcbddddadbbbaccbdbdcbdbdaacbddbbddcbcccacaacbddbdddccadbbdbcabbbabddbdddcbabcacaccbcddabcbdbcadbbcaaacbdbcbcbbacadbcabbbdcdaadabcabbcdbbddaacbccddadcbaccdbdadbdacdabaabdacabdbbcddabbbdcbacbabcabbbdcbacbdccbbbacddbbdcddcddcbadabddccddbcacbaaaddbdacbbbdabcdbdcababbcbabddbdbdbcabaacbaadacadababbcacaadcbdaaabbaabbdacddcbbabcdbbbbccbacbbcaddabacbcdbbbccccdccdbadcacacaabbbabcadabaaabcdaacdbabacdccdaacbacacbdbbaddbacbaacccbcccbcdcdbcbbccabaadbcabcdcdaacbdcbddcaabaccddccaadaacbbccbabbbbcbdadaddaabcdcdcdbcdacaaccaacbcbdddbabbbcdbabbccdbaadcdddaacccacdddcaaccbdcbacaacdbbbdadbcacbdbbabaabdaabbccdddabdcabdabddccbbbbaddbbdabaddcbccdabaabddaccacccdcaaabbcabbcacaddcbdcdaadbbaccbaddccadbccdcbdabbbdbbbcbabbadbdbadcaaaddacdadbadcdddabdbbbbddddbdcbcabbabacddcdcaaaddcacccdcdaddaaccadbdbbbddcccabbaaadacbadaadcbabbadadcbabbaaadbbbabdbadadadbbcacdbadddcaccccdbdcabacabdccccbccdbbdaaaabaabccbcccccdcbbbbdacbcbcbddbdbbbcdccbdbbcdcdcbdbbcadccaadbdbaaacbadcadbaccbccddacbdbcaadcacbaacbabadcaacbddaaaaaabbcdddddaababbacbcabdcccccbaaaddcacbbbdbddabcdcbaacdccbdbcacdcbacdcbdaabdabbdbcccadcbbccaccbbddadcbbcacacddadbadaabacabddaadcadbdddaadadcdaacdddccdaaabadcddcdbcabcbabbdacddabcdbdacbbbbabbdbcdddddabcccdcdbdbcbdbddcacabcdababdaadacbccdcddbddddcdadadacdacdbcacadbdbbbcbcabcaabbaddacacdcbdcabcddbddbcddcadbdbddcdbcadddbaccbbcdbddabaaaccbdcdbcbdbbadddabcbbdcaabcaddcbdabbbdccbbbdaaaccdcacbbbacaccbbcdbdcabdcaccdbbbbbccdabbdabcddabdbcbbbbcadbddaccabdbdbcdadcdcdacdaccadabdbddcdbcdabbbbaccadbccabcaaabacadbabadcdbadaabaacbdadaadcadaaddacbddacbabaaaabbdcbcaacbdcaacbacdddcdbcdbcadaccbcbbdcdbdacbccadacbbadbacabaaadccbdbddaacabdabcbaadbaaacdadcabbacddbdacdbbcdacbbdcbdabdcabbdddcdbccdacbdccdacaaccabbaacdbcacccaddadbcbbbaabaabcadaaccccadbbdcababbcbabccabdbbbcbccddccbadbcdbdbcbadabdabdbbdbcdaabddddccbaabbcddcdcabbacdadddccbcbacaddbdcbdcbbcbbadccdccacbbdbaacbccdbddcdbadbddbdbaaccdbcdaaacaabcbdbbccaabbdccdbcddacdbacbcbdbdbcdaadaabacdacacacdacadccbabadaadababdcabdaacdbbcdbabcbcdcbbddccacbccadbcbdcbcdacdbabbddcbbcdccdbcbdbddaabaadacaabdaddaacdbdddddcadbddbcdbdbbcccddbcbadacaaadcbccdbdacdcbcadacbdadadbdcbdccdccbadabbadcbdaddacdcbdadcbabddabadbbdaaadababbddaaddcbcbbacbaaabcbdcaadbbabbacacccbadadaaccbbdcdcbbaacdcbcbbacaadcbddacbbbacbcadadbbaddacbbcdbdaadacbadcdadbdcdbbbbacacddbdcdbbacbaaaabdbdcbaddbbccdbaaabadacdacccaaadacacaadcaacdcbcabbbcbddbbabdcacbcacbcddbbddddcadccdcbcaacadccadbdcbdbdcdbacddcbacbbaabbbcddbddaabaaccdbbbcaccdaddbadaccbbddadaabdbbaacaadadddabdddcdbaadbbccccadddcbbaadcbbbcbccaaddbdbdcaacdacababbdaaccbdacbacacccdcabaaacbacaadcdcdacdaccabcbcaaababadbbaacbdcbabcbbdbacabacabbaaddacadadabbaaccdbdabadbbbacadbcbcbcaacdcdabadbddaabdddbaadabacdbdcdbccbaaccdaaddabccbcdbdbcdbbbdcaacbbdababccccbabaadcbcdddbadabbadbccbbabbaccbdccdacadaaddbaabaaddcabdbacdcccadbcdacdbdbcacbcbccbbcbaaaabacbdcaccbacaacdabdbaaddcdbddaccbccabcbcbdaabacadddbabdacbdaacccabdadbdbacaabccbadbcbadcbdbacbaadbdccdabdadaddbcccddbdbbacacadcbbbbdbcdaaadaaddcdddcbcacacaabcdbcadbbbacddbaaddcbadcbabddbbbcacaccdbbccddaddacaddbcbdabddacacdbbdddbcadaaaddbbdcbbacbacaaaccbcccdbbdccdbcbcadddccdccabaacdbdcbadcabbccaacaabcbdaacabdbbaabbbbaadbddddccbbcaaacbddccaccbcdddcbabbddcadaaadcdbabdadcaddbaabbcddccdaacdddcccadcddaadabdbccdabbdcabacccabbbadadcbbcaabccadbdbcddabddbcbbdbaccbaacbdddbabadaacadbdacadbccabaaadbdcdaccdaaaadcbbcaadcdbdbbcdacccdbbacddbbccabdaacabaadbcabcdbababbbaadaadbbbddcdacbdbbabadaacbdabdbbadacaabbccbdaaaaadbcbcaabbdddcaaacccaccaddbdcddbbcabbadddbbddabadbbaacddabdddddadcddabbbababcdbccbadaaacbddabbccacabdacaacccbcdbbcbbcbcdbcacdacaacabbbbcbabdcbccadacdbbbadddcbbcccacadabacbbabadbdbabdacdbdaacdcabaabddaabbdcabdbdabbaadbccdaadacccbbcdcdbbccabddaaacbcbccbdcdcabadbbddbbbcbdbabbbacdbacacdcbcdbcdbccddbcbdbcacadbaadcaaadbddaccbbdcaadacacddacaadacadabadcbabdbdbddacdaccadcbdcaabbdccaccaaddbbaadbdabacadbdabcccdadcbcccdadcdbadbaadbdcdbbdcacbbacbcadcabcdaababbccbddddacaadbcdcaacddaadddbccabbaadcdbbbddcddddbbacccccaadadcbccaabccbadbaabbcbcdcbbccbadbabadaabbcaadacdddaddddbdbaacadbbaacbacacbcababdbdccbbcccaddbcbaabaccdcdbcaababdbcdddbcabbddcacabdcbacbbdcbddadcacccdabcadcbcabcdaabbbaddbaabdcccddcabbaaadaddaaacabddcabaccbbdadacbdcbababcaaacdbbbabddcdcaacaacbcbaccdadbcacabcbbacbabacacbcdccbacbcbcbcaadbadcacbcdabadadbabcddbaccbddaaaacbcacbabbdabbccaadbcdcdcacdccccddbaaaabcbbcccaaacdbadccbacabbcdccabadaccddadabadbbaacbcdcdcaaccdaacddadcccacadcabdabcdbdddcdddbdccddabccacbccccacadbadcacdddcbcdbcbaddcdccdbbbadbcbaabcbdccdbdaadcacbabdbddbbcbdabccccddbdcdddcaacdaaaccbbcbbbbbbdbbcaaaaadadcdbbdaccdcbbdddcbcbbdadbbaadbbdddbabbababddcabdbcccbbbccabaaaccaadabccdccbaabccaabcbbdaccadaaddddcbdbadadccdcddbcbbcaadcacbddbccccbdcbcacdabbbbbacaadcabbacbabcdbcadbdacdbccbdccaccbbddabbbcadcbcddbdaabadcacadbbdbaaabcadaddbbdaabdbbabadcacddaddacbbcabadabbabdadbdbabbbcdcbdbcdabdbcabcbaddcbcadddbbacabacdabdadaddbccbcddcccccdbabbacbdacbdabbacdacacdacadcdbbacdcadbbcddbdddadbbddbddccbaacbbbdbbddcdadcddbcdacbdbbabdbacaddcdcacbcaabbaabcacacbddbccdbbaadacdacadbbcaaabbbddcdacdaadcbadbdcaaaacbbbcbcdabaacaadbaacbccbbbcccbbabcabbdaddbcdbdcabbbacdaccbcabaccabbbbabccddcdbcdacbbddcccbbaaccdbcaabcabcbbdbbadcbbdaaabccbdbadbdbdbcabcaadadcbbaabbdcbdabdaddcddacdaadaabacdacdcaccadcaacddbccbaacdddddcdbdbdbaadcaaaabdadddadcdadbdcbdcbdcccddbdbcbdbdadabcdbcddaaacacbdbdbacbbbadaaccdccbdadbacbabdabaaccbacaacbdabaadbbcbdcbacdbcbbdabaadaaaadcdbbbccbcbabdcbadddaabacbabbdcdcddaacbcdabbbcadddcdacbbbaccccadabddcabdbdccacbbdcbcbadccdbbbaaacdbbaddbcaddacaccdddacbbbdddbaabdabccadabacbabdbabdadcabaddbbbdacdadcdcbdcbabcbbdcccbcbaaaadcacbbbbacdbbcccdabaacababcddbaabdbbddbbcadcaddbdaadcdcbacccbaabdbdbaacadacbcdabaacbabdbdcdcaacdaaaddaadbacbbaabababbcdbcaddaaccbbdabacbcadbbdcbdbdacbaddababcbbbacbbbabcabcdccccbaadbdbccddccbcbadccaacadaabdbcdbddadcacdcdaabcacccaccbcacbacbbdbbcddbdbbdcbacacbdacbdbcbbbdbadcaaacdcbdbacadacbbcdacaabdbbcdcabccbbbcbadbcaaccabbabbaddcbaccadabcdbdadbcdabcdadcbbbdcaacdcdabddaadbdacdaacacabaabdbbbbbbbdcddcbbdabccbdbadacaddddbcabbbddadaabbdddddcbaccdbbacabaaadcaabdacaabbbcdaaacdbaaadacbbaacdacadbdbbadaccccacdbbdbdcacdadbacdbbaccbcbadbdbadccdcbbbbbbaacbbdbaaacbbddcdaaddacadacabacbdbbdaadabbdbbaaabababcababccadbdcabdbabbdabddcabdbbabddbdcbdbcccddbdbabaccbbbdadccadcabcacccabdbcadbdcabccdbbcbcbbdcacddbddbbaabbdbdbddbaddcbacdddcbadddbaaababcbcaabaaddbdbaacbacacdabcbabbababdbcbacabdccbcbbcbcddbadcddaccaddaccbcdbadaaaaddcaaadabddabdddacddadbbddabcadbdddcdaabacbdabcbaabddccbdccacdcaadbaacbabadacbbadabcacddaccdbbdcbabbbbaadbdbacdaaabdaadaaacaabadccbcbdccddbbcdabdcddcccbaabbabcaccadadaadabddaddddbbdaccbccbbcdbbcddbbcccacabcddbbaacababadadabdbdbbabbbadadbacbbccacaadbdddaadbdaadbbabdadcdcbdcdabadaaadaadbcadbaabaddccdddcaababbdcadbdbdcaccbcaaadcdcdbccbadbcbdbdcdcbdacbddddbdcabccaacaadcccbdaddcbaccccccdddddcdbdabbbddbbbdaacdbaaabaaaadabdddccacaaaddccdacaccbbcbbccaababcadcbccdccdaaacddbdaabbabacbabdcabbccdaccabddbaadcadbcbabcadbacadcabcbddbacbbdbccbacdbdddccadcacbbcdcdaacddaccbcbacbcbaddbabdababdcbbcddaddacbadbcbbadddbbdcaaabdbccccacacacaadcbbdcbbcaacdddcbccdaccdbccbcaaccdddbababcadbddaaaccbddaacacdaaccbbddabddccdbccbadabcbddacdbccbdddbdcccdcadbabdbcdaacaccbdabbadaacacdcccdcddcaccddcbaabcadadbcaadddcdbcadabcccaaabbcbddcacacadcabbaaaabdcaaadcbabccddaddbccabbdddcaabdccbaccacbdcbcbbacadabbacbaddbcbababacccacbcddbcdcabdbcdacbcbbbcbabcbacbccdabbcbdcaacaacdbcbbbcbdbbacabcddbaadaaabccacddacabcacbbbdcabaabbcaaadbdcbbbbcabacabdcaddddccdabbaabcacaaadcaddaddcccbacbdaaadcbbabbacababbbadbacdacddaaadbaddcbccdccdccabaacaaddbccbdcbdbbcdabdaabadddbadbdcacacaacbcddcbdddccbccddddccccbcaddacacbbdbbabcacdcacbabcabddbaaaaaadcbaaccbbbabadddaadcbabacadaddabcbabbcdacccbabbdddbaaccabcbbadbcbbcdabcdccbacacacacaadcbabbbbcacdddcacddbcbddcdcbacccbadbbcbdbabcabddcacaacdadbccaaaabccbbbbbbdacaacbcdbcaabbacbaabcbdbbcadabbbbdccabdadadabaaaaabcadacdcdaadddddadacbccdccdacdbddabcadcaaaabdaacbcabdbabbccabbbdcbcddbaccbabdcabacbaabadbcbbbacababcbcdabbcbbbbccabbabdddacdadadacbdccadacddcabacdccdcbcacbbdbabbbadbbcdbadcbccbaaacbbabbccbddadadacbdbccccdcbbbdacacdcbcbbcdbccaaccbcccbacccbbdaccabaacbcdbacbdaccabccacbcbadabdcdcaaddcacadabcacbdccbbacacacccdbadcbaacaacbdbcbcbddccdcbbdcbaccccaccbaabddcadddbbcadbdcdcccadacbdacadbbcdaadacaaacaddbdbbbdadbdcbcbdacbbabaddbddbdbcdddbabbcbabcacdbacdcbaccbbcaccbbbcaccbccddcaccbcbacccbcbaaaccacaabbbcdcdacaaadddaadbadcccaaababbddaaabcddaabbbaaccadbbbbdcdabacdcbaaaddaabbbbaaabaadcdadadbbcbdcaaaddabbbbcaacabcccbbbabacdcdbdcabbabccddbbdccdcadbaaabccdadcdcbddcddbdcabbcbabaaaddbccdddbdccbacbacadccdaaaddbdddacabbcccbbcdcbaabcbabddaaabbbddadbddabbdaddccbdbbdadddbaabdbadcbdbddbacdbbbbcddaadccdcccbadbabdadaccddbbaabcadaddbbbbdaabadcadabbddddccbddbbdcddbdbdbddabbbdcbabdcdccaaabdbddabccdacdcacbcadcdcabbcacacacddcaccdaacacadbcaccdbdddbaaddcdadbbccdcbaabacdbaaacbaccbbaaacacdacdbacbbdbbccbbddbbcacdbdddbbaacddccdcadccaacdbaabbadddabdbaddcaaacdcbbbbcbacbdddaabbabbdaaabdabbdbadadaddbacabaadbaddbccbcdabadbbaaccabdacaaadbbcccdaabacddbaddddbadcadacaccdccdccbccddbbabcadbbbbcaddbabdacacdcbcbddbbdbdaabcbdcbbdbabccaabbaddabdacbbaabcddadadbbabbbcabdbbaacdccacbbacbaaacbccdcddcdabccdaccbdcccdcaccbaddaabdcbbdbcddbbbadbcaabddbdaaaccaaaadabbcaaabbbaaabbccbabbbdccadbaccbcbcbabdddbccbccaacacaddbabdddadcaacdbbcccbcadadacbdcbaacaacdbccbadbbacbbdbabadcdaadbddaacdacbabbdddddbcbadccdadccacbaaddddbcadbbcbbbdbdcaccccbabadaddadccdbaaccadadaadbbacbddabaaddbcdaccdcaadcabcdacbbdbcaddcddcaabcaccbdacbdbcdddbacbcbaaaddbabadadbdcadddbccaccbddabcbdbabcbacdbcbcbabddaaccabdbadbcdcdaddbabdbcaccabadccbccaaaabdbcadccdccddabcbdabccbdcdbaddddccbbbbabaabaadbcbcacbcdcbcdadcaddbbdbbaaaaabdbcbbaaaabcbdaddcbccccabbaccdaacbdabacdabdcddcadabdacbdcaacacccbddcdbbdbacdcaabcdbaddcddabcbcaaddbbdcdddacacadbaddabdddadadaacaccaabbdadabdbbbaabcacdbcbddabdaaabbabccacccbbccaabbddbcaadabbabcccdadcacdbbbadaaddccdcadaddababbddbccbdaadbbdbcabbcdcaabdaacaddcaccaaaaccdabdcbadcdbdccbbdabbcacbbcbbaababcbcacacccbcacabcbcabbdadddcbcaddcbccabdaacaddbdbccdaccddaacdaadaaccbcdbadddcbcdbabcdbdddcdaddbaccccbbdcbccbccabbbacccbabababaddbbbaddabcbbbcbbbaccccaadbaadcaabccbccacbaaaccadcbaccbdcacbbaacadddadaaabdacaadddddbdcdbacbcddbccababbbbabdaadacbccccbdaccddaabcbcabcaabaddddccacdadacabaabdccbadbbacbdcbbdcacdccbdccacbbbddbbdcbbbbcbbcbcaddbdcdbccbdddabcdbabdccccbbbdcbadcaaddcdcdbdbcdbbcbbbadadadabadcaabccadaabcdaacccdbdcccaccdaacacabdccdbbaccdbdcdcddaaaccacaaccdcddbcddadbcbadabdbbdddadbbbbacddaccdbccacabbcdcccabbbcaddcbcaddcaaaabaaddcbcdcacddbbabaddbcbdbbbcbcbcaacbbbabbaaaabbdcbaddccbdcbddbbabadddcabcdbabddadcbabbdbbdbacbaaadacadbddbbbdaacabddbbcbcbbbbcaadadcaadbbabdbbadbadadabbacadbadcaabcabdcbbbccddccadddbcabaccabbcdbdccadbacbdcdaadcbabaabbbbcacbcbdbbdbbccdcbdbbcaacaaaaadccbcdddaacacaaadaaddcdbaadcdcaadbddcdabdbcdacbbbadabacccbaadbccbddcaddbdadbbcbdaaaccabdcabbbdcdcdbcbbccbcbbbbdabccadcbcaabacbbdabdddbbbdccdbbcdccccdbcbbdbabdbaddbdbacdcaabcaadabdcddbbdbccadacddacdadaccaadbcddaaddbabadabdddbcbaadbdbcdaaacbbdabdcbbaabbbbdaccdabbddaccadbddddcaadabbabdbcddcdaaddbbbcddbbdacabdbbcaddbccbbadabaadabbdccdaaaccacbcbaabbaaccdcbcadcaadcdddcbbcbacbbaaddcabdbacbcbbdadddabbacbcadaadaabbcadadbcddcbbbbcbacddddcccccbdbdaddaabccaaccdcdccacdddddbcbcbbadbdacbabaabacbbbbaadddabcdcccdccaddbcdacaccdaacddccdbbbaaddbaaddccdcabcbacabacaabcacdbadbddbddbaaddbcbcddabbcaacbaccbacbbadcdbaaabdacccccbbaaadcdbddaabcddcdbdcbabacbddbbacbbabdbaabcaaabcbccdbaccdadbbacbaaddcdcacdcaaaaadacadabcbacbbabdacaddddbacbdabacdddbbddaddcbdcabcbcacbaccdadccccabcacacbccacadbdbdcbaacbcdcdcbdcbbcbdacdaabddaacbdaaacdaccacaabdcdccccdbbcdcabbcbbbbadabbbbbcbdaaadabddcdabadcbabbadacadabccbdddbabcadacddacccbabcbaccdccdddbabadbadddacacbbacbabcaaccaabdccabdabbaccabddcaaaaddcaabbcdcaaacaadbdbabcbbcadbccadbbdcccdbaadddabbcddbdcaadccdcdcddcddcdcdaaadcbcaaacaacbcacaadbdbdddcadbadbbbcccbaaddddcabdbbacddbabcdaadacadccdacdbdbddbcbdddabcabddacdbcaccdabdbdddcabccbcbcbadcbbbacaadacdabdddaddabccacddbaaccdbcadcccdbdaaaccadacdabadbdabaccbcbabbdbadddabadccccacdbccadbcacbaadcaacabbbaadadabcbdbadccbaabddcbcdbdcbbccdbbccaddaacadadcdcdbdddcbaabdbabbadbcbbdacbabcbaccacdccdddccdcbbcccbdacdaaadbbdacabbaccbcaccbcddddbdbaccdadbbcbabbabcaddbcbcbdbacaaddaacdadadcaabbbbcaacdbdbabcdcccabdcaccdaabdcbbacddaadacaabadaccddcababccdaacbaccddbcabacabaaddccbacbbbaddcdbbcbdadbccdbdabdbbacacbccadacdadddbdcccaaabaddbbbadbcabccccdadccdccdaddcbdcaadaccbbdacadaadaddbbbbcbdacccacabdbabdcbadaccbdacadadbbdabbaabaaddcbdaabddbddaabacabaadddddaabcaacaccbbabbaadaaacbcadccadcbdbcddcccaccaababdabbabbdadacaaabbdddabbbabbcdabddaddcaaccdadcaacadddcddcbcaacbaacdbacadbdcdbaacbcaacbadbbacbababaadbccbababbbabccdacdbacbdbaccdcbcdabbaacbaccabbbdcaaaaabbbcccacaccbdddadbcbabbdaadccdbccbcadcabddcbcdaccdbcccadadaacdbbbbbbdaabddaacbcaacaaabdbbaddcdaaadaabcbcccbccddacbabbaabddbbbbcabdbbadbadcbabbdccdbcddcbacadadddcbbdbcccddcbbbaabdcabdbaddcaadcbaccbacaaaabbdacdbcccbddbbbbcdbbaccddcbcdddbdbcbcdbdaddabbbaabccbbabcccddcabacdbbadadbbaabbadacdabdaddcbddacddbadaaccdcbbcabbcbcbaccdaabccabbaddabddcbdcbbdadbdbddccddcbbbabbcbbdcbabbbacbaacbdbcccabdcbdadbcadabdbcdbbaabcabadaccccaabadaccabccbbdcbcabdbbdcabbbccadcdccaaadcddbbdbdcdddbbbddbbbdabbcccbdcadabbcacbddcdcddccabbbdbcaadbcdcddbaccbadbddbbadbdcabdacbaddcbcbbcccdbccbbdcbdbaaacaacdbbdcbbcccddadccbdbaccaddaacdcaabbccbcddbacdaccbcccdacccbbdacababbcccdcbccccbbcbccacdacbcabcdabddcadcdadddadaababbacdcbbcacabacddabdcbbddbbdaaabaabadbcabbabdaadbaadbdbacacddaadddacdccbccaddacdadddabbaacbbaabaaabcbbbbdadacbddcdacbabdaddcbbacbbbdcdcccdadbabdaaacaabccbccabddcdcbcbabdacaadccadcdddacbadbadccbccaacaabddddaadcdcbbbddabadabcbdbabdbbccaaabbddbdcbcaccdbacaadbbbbabcaddacacdadcbaaacddacdcabbbbdcacbdaabdabaadacadcbbcccbadccccddadabcdbabaaabccbacacadcddbbcbaadcaddabdbaccbabcaaddcbacccbadababddaddaacccdbacbadddcbcabcaacadacaaddabcddacdcbbdacccdaaabccccaccadbddbcbbaaddbcdcbbadaaddcbbaaccacadadbccdaadccdbbdcdadbcacaacddddabcdabbacccbcaaaaaabdccbcaababccaaadaadcabdaaaaaddacdcadcbbaddadccaadadcacabaacaabcbdbbbbdbaaccbabbddcdaaabadcdaaaaaabcacbacdbacdcaddbabadabbbbcddddcdbcbdaaccbabadaaacccddaaddbaadddaaddbccbbabbccccabaaccbbdbdacabbadbcaadccddaccddbcbcbbccaadacbdacdbbddbbaaccbbcbcadbdcbaddcbcaabcbcccaabbcccdaababbcacabcbcddbabcadbbcbdacaacbbadcccadbdbacdbacddaabbdadccaacdacbacdabacaadaccaacddcadbbbbbcbbbdcadcdbddccbadacdaddabddaabdbdacabbaadbbaccabadbabbdbccabcaacdbdddaadbccabdccbbdcbdcbbdcbaabbdcbcccdacbbccdbcdaabcaddcbbdadccbaadbcdabbbadbccdbdadbdddbccbdcbcdccdbbcaabdabaddcbdaddabccddcacbdcddaabacdcacaaaacaadacdbdbcbcdaaadbadbaadcaaacbcbaddddbbcbbcaabadbdbcbdcacdabbabcbbccddbdaacacbdcbbccdddaababdabadbaabcbdcaddabbbacabbabaddbbbccaddbabbcbddadcbcccacbacdaaddaadbbaabbdcbbcbddbbacbbddbccdaacaccccbcccccbcddaccccdbcdabcbbcaddadccabdadbcdcdcbbcaccccddcbaabdbcdbbcbabcadcaaaaadbbcacaaabcdababdbcacbbacccdabdbadccabaddbabacccbcbcbaaccacbcbdbcccbdbaddadacadaabdcbbbdcbabddcdbccdcbbaaddcadabbaadacdaadaaaabccdaabcbbcbcadacdadcdaccdbabbaacdabbbcabbcbadcacddbacabbdbcabcbcdabcacdadbdbcbbcdcacddbbdccbbdbadaccbbcdbcbddcacaabdbcadccbddacdabdacadbbaacabbadacacdabcbcccdabdcbaaddadcbbbacbbccadcbcbaaaaaadbdbdcbccbacdbcaadadddabbadbacacaccccbabdabcbddbabbdaacbccbdacadcaccdacacabdabddbbabcdabaacacaaaccbddaadadcbbbbcbcdddbacccccacabdaacdadcbcadbcbabcccabbbcbabacacbbdadbcccdcddcdadcbbbcdacbbadacacdcdbddaabcbcadccccddcaadaadcbdddcbdacaccadcdbcdadccbbcbdcadccccdddbbbcdbbaacdcacadddcbccdbbadcbbbccaabbcdaadaccdbccacdaacdadcdabadbacdabdbcbacdabcacccbdbdcdcccddddcbccbcdddbabbcacbcccbdcddcabaabdaabaddcbadbaccdbaacdaadcacacddbdababadcddbbbabadbcccddadadbccdcacbdadaccabddcababaaabbdbacdaabababdaabcbabcdccdcdbcddbdadbbbdcabacbbbbdaacbdaaddbcaaaaaddbaccadabddcbbaddbddabcaddaaacaaacbcbdbacdbccdcadaabccbccddcbaabcccabcdabacdabbacaadbbbcacbbaddbddaccaacadbddcacdbdcbcbdaabbdbddabbdcabbccdbdddcbbaddabaacbaabdbccdbadbdbcbdadbbbcdcdbcdbdcdabaacbdcbadabdbcbdbddbdcdbbddaccddbbacadccbdbcbdcdaacbadaddaddcbcaabbaacadcabcbdadbccbbbacccbcdbccaaadaadbdcadaabbdddbccbbdaacacaccdcaadbbcccdbacdacaaaabadbbbdddacdacabcbadabcacbbacaabddbbcbbcbdadbacbaadacdabbababdcbbbcdaaabbcadcbcdcbdcadbdcbbddcddcddacbacabbadaacaacabacbacaddadcddcacaadbcbaccdbddabbccabcdddcccadbdadccacbbbdadccbdcabccdcdabbbababbbbbdbcadabaaaadaccdccbccacbcbbabacdcaddbabbbadaadccdcaacacdabcdddddbdddcdcbaccacaaaacbddbdaadcdabdcdadadbbdbcdadaadcaaadccabaaabdbcacadcabdddccacbaadbbcbbdbacbabcacacaddbbdcaaabdbccaddadbbcddbcaadcabccabcacbaabdbadadaccdaaddbbcaadcbaacdddbcabbbcdaaccddcbcbbdbcbcadaadcaabdacbbdcacbacabcacabcbdddccbbbcaddbdaddacaddbbdddbacabbadbcddaddbabbdbdbcbaacacdcabddcbdacbacdcabdcdcacadcbbcbdabbaadbabbbdacbcabddbccbcbcccaabbcccbddbccabdbadbdabcbdaddbaacaabbcbddacbbabccbcccddbaaddbaaccaabccbbadacacacdbcadbbbbdaacababdabbcdbabcdabdcccdbaadddccabbcddcbabcbbbadcabbccacaaadaabdbddcabbddddbbdcccbbddcabadbdcbacababbabcadbccbbaadcccabdbdbbbcbadbcabbaccdababccddcacccbcdacbcdbcccdccbabacadbddcbdcddbabddcbdaabdcaadbdccacdbcabddaadddddbdbccdaabcbcbbbddddbaacaccbcacadddaadccdbdbcabdbadddcbbaababaddddbdcbbdbcadccbdccdcdbdbdbcddcddbcdaadadbbbabadbdcdbaabacaababbbbcadbdbbacddbacddcadaababcaabbabbbcabddddbbbcacbcdbaddbbcbcdccdcdbdacccacaacbdbbbcdddabbabddabddabbabcacbacddabbbcddbdacbcabdaabaaacdccadcdcdbdcacbcbdaaabcbbbadbabbabcddadbacdbbdcddcccdbdadcbdbcaddabbcadcbcdabacadbcddbcbdabadbccadabbcaddacbcaadbbcdcbcacdbbdaddacccabcbdddcdaddcbcaddcbbdadbcccacbcaccadadbacbababadddbdbdccaaaaddadabdbdcabbbbcdcbbbdbddbdbaccccbcdaaaabbbbcddcaaddcccbdcdcbdabaacccbbcabbdabdcabaccccdcbbaabcbabaaacdccdbaaadccadaccbccdcdccdaaabaadbddbcbbcaccdccabaadcaabaaabbbdbcddabddcdbbbdbbdcaacacbcacaadbdadbbccabaabaacadcaacdbbcaaccbabaddcaaccbaabbdaacbacdcadbdbdbcdccadcdcbadbcccaabcbcccbbbbbddbacdacddbabcdcaabcdcccbcddcadcbddaccddabdaddbbcdaaccaadbdadaaaaacaaabaaadbccdbddbdbaddbbddaadbcbcadddaaccccddabccbdabbbadcacbcbbbbabbcdaabdcbcdabcdbcdddabaabcdcddabadddaaccddbaddbbdbdccabcaadbabcaaaccbbcdddcdadabcdaaabcccacaadccabbddacbbdaacbcdababbcbddadcbcabddcdaadbacccdadbdbadcccbaccababcddbbdadcaccbdcdaddaacbcaddcdabdddddcbbdacbaaadcaacbbdcdcddabbdadcdacbaadbbdbcdcbbcdaaaaacbbbcbdccaacdacacbddbdcbcadaddcabbaaabbbaababacabdabbccaccccdcacbabbdbbbcacabccabbcdbbbaaddaddaabacadbcdddabdaadbcbdbaadcaacaccabdaddacaddddcddbadddaadddbcabaaddabdcdbcaabaaaadcbccabdabdcccbbacaccbcdbcddbbcbacaadbccacadccbbccadcacbcdadcdcbbdcccbbdcacaadbcbaacbccbddcaacaadbbabcbbcadaabdcadbaabaddbbdbdcdadaabcadaabdddbadbbdadbbababadccdbacccaaadacddcdbdabbdbabbcbaaacabdcddcbbaacadcdacbbdbddadbcbdbaacdbaacccddccabbcccacccbcacaabddcdaddbbdabddcdcacbdbbacaabaccddcbbdcaabdccacadaddcccacdcadbaadbdaadcadbbadddccbcadbbaccacddabbcadabadcdcdcdddcdcaaddbccbccccbcdbdddbddcdbcbbadbbdabaacdbbacdccbdddadbcabdbacddcacdbdcaadadcbcdababccbbcbcaadddbbccbbaabaddbaddbdddacbadbaacacddaaadcbccadaddcaaacbcbadaacabbabdbddcbddcbaaacdacbdcbabcdabcdcdadacbdcaadaacddabcdcbcbaddacacddbadbdbdcadcddcdbbdddddbbdcaaaacabddcdcdccbdaacbabbdbbcadadbabbadbabbccdcbcaaaabdbdabbdbccdcddcabaaabacddaadbaadacbdcacbbdddcddccddadcbcdccadbbabcccdcaddacccaadabbdcbbcdcdaaabaddcbaadbcbbcdcaaddcbbdbccaddbabcbbdddacccbdabdcbdddcadccacbdbacbddcccddbcbccddddaadaacadaaaaaacdcdbddaddbaccacacacaaababdbcdaadadababccadbbcdcbbdbbaaaacbacddcbdaddaaccdbcbbbcbdcbbcabbaaabdbccaacaaddbcdaadaaaacbaababdcbddaddcbabcabdccbabdcddabbccddbabaaaaaabbccdccccacbbbaccddbcaabaacbabbacbccbddbbaacbbbbadcccabbccbbaaacabccdcdcbcbcdccbddacaaabaddcdabbbadaddbadacccdcdcbbadaaadccccbcbbddadbbcbddcabaabddbccdcbcdddccdbddcccddcdcccaaacdacccadabddabbddbcaabcddbdccaadcabcaccbbccabdbbacbdcbacbdddbdbdbcacaadbbbccdcdaacbdabcaaaacbadbadcbcadcabdbcbbbaabbcaddabbdbbabacacccbcbccbdbbdcaaddccbbcacacbddadbbdadaacabaadaabdaabcaaaaacddccddcabcdaacaabaaccbcacdaacabcccaacabaadadccacdccbddacbcbacdbcddcbccddddbdadddcdbbbccabcadbcbaccdcdaddbcdddabcbcadcaadcdbacbacbcbacbcacaacccddcbdabdbadaaddcbacdbbbadddbccbdaccabddbcdcabadbcdbdabbdacdddcaccbccccddbccdacccabaabbbcdaabdabdcbaddadacbdaacbcddbdbbbdcdbadcadbbbcbcdccdbbbbbdcbacacdbabdbbdadadbacddddbabddbddacdbbcabbbdccdbdcdddacacdcbccdacbabddddcddbccbcaaccdbbcdadaacddcdbaddcdccaddcbddbccacacabbaadaabddccddddcdbadccabbdddacccbabbbcbddadacddbcabdbccddbddadacbdcddadccdbdbaaaadcbdaccccbdccacbdaddabbbacbcdccadbcddddabbcccbbbccdaabdaabbddaadabbcdacdabaaaddbdbbddabbabadcddcadbccbabadbbbaddabcbaddaadadcbaacbdbbcccbabdcdbadcacbccdaaacabababccadabdbcdaabadacdcbbadcddaabaaacdcddcccdaabdbadbcadbdccaacbcaccbaaaddacacdacdccdcaaaacaadcbaaacbbbacbddaaacaaabbdbdcaaccbaabcccbdaacaddaabbdbabcdbcbdabacaccdccbddbddbacadccdacabcbccdbbbdbabbdabbccdddddaababbabcabbbcdbdbbcdbadadbddabbdccccabdbbcbaabdcaaadacbddbbacdccabbbdccbcabbabdabcdbbabcbabbcbbcabacdccddadbbdaccdcabdcdbcbcdccbaabcaabccaabcdaacabaabbacbadaadaddaacdadbbacdabdcaadadaaaabcbbaadaaaddabbcbcbcccddbbacbbcaadcadbdcdababadbbccbdaacbacbcbdbacadacabbbccbbbdbabadadcbaacbbdcbdcdbdadcbaccddbbbcddbcbbdbddcbcabbcdbdaadcccdabcbbccccccacabddadacbdaccbbbbdaccdddddcbbdbcacddcdbbdcacdddbdabddbaadadadacddcbbdacadcdbbbabcdbabbdadbcdcdaddcdaccadbbdacdbbbdddcdadacdbbacdacbaccdababacbacabcdacaddacdbcabdbbdcacaabcccaacadccbacaabbdadcdcadabacccabbcbaabbabdcabaadbcabaaddcaaadaddcbbbcbcabcbdbdacaccdaddbacdaccbcbacbddccbcacabcadddccadccaddbdbcaabdacbdcacabddbcbddbcadccbdcabcbbabbccccbdacbdbdccbdbcbdbbccccdcbbdaccddccaaccbdcdacddacbdcacbacaaacbbbbcbbccbccaabcacdccbcdadabbbcbbadcbabacdbbcadcdbbcbcacdaadabbababdbcbaabccccadcbccaacccddcbcccabddcbbadbddbdbbaabacabbaddcdcdacdcaaabdabddadbdcabbcdaacdbadaacdbcaadbbadaaadddacddcdbadbdacdbcbbbcbdcccdcabbabdbaacabdadcdadadbcbdccbcaacbcbccbcbdbbdbbdcacabdcadacaddbdabcdcdddbddbddcdacbabbbdabcdcaccaabbccdabcccbaabdcadcbcccdccaacaaccdadabaabccccacbcbcaddbdaaccabbbaddcabcddbdaddbdbcadbabbddacbabdcadcbacdcbadcdbcddbaacdbabdcaacaaccbdaaacbbdccbcacaabbbbccadcadccdddbadcacddadcabaccadadbddcdddbccaacdccdadaccddcbadbbcdccabcbdccaddaabddaadcdbabcbbcdcabacabcbacbcacacbacdcdbaccbbdbacbddadcdadbbcbdcbcbadcbbcaaddbdccdaaddaddcdcccabaaacabdacbaaabcbcabadaadcdbddcabbaacbdbdbdabaccdaabcccbacbacbdcccbcadcacddcadbdbaccbbbccddbaadbbadddbbcadccdccddaadbbcdcadcabaaadcabccaccacbcabcabdaaaacabcdabccbbdccdcadddcabdbbcdbddbacbcbabdcddbcabbababccdaaabacaccaaaababaccdcdadcbabdbbadddbadcdabbbbaccababdacaddbdaddacacdcbbcbabcabadcaccadccdbcacabaaadacaadddbabddbcdcbaabdbbaabababccacbdbbcadabcdcabccaabbddcaccadacaccddcadaccbbbbbdaabcaddddbdacadbcddacddcabaadaadbbaacbbdaacbbaabdaabbddacabbbcadacacbcbabddcabdcbadaabccabcbbdccbdadbddbadbcdadaccdbbcaaadbccaccdbbadcbdbcdcadcbaddbbcbabdaaccaacaaabbdbaacbcabbbddadbdadcadcbcdcdaaaddbccacdadcbaddadddddddbdaabccdaddbbddcbbdccdddcddccbcabadbdaaababbcdcbdcdcbddccdcdabaababacbacbbdabdbaabbaaabcccdcadccdbadadaacdcbbccbbdbbccdcabdaaacdaddbccadbaaddacdabcadbccbdaaaabaaccbdbcaadbcbbdaddbdbddaacdacacbcdacababcdccabdccbcbdddcdbbdddacaacdbbaaccaacadccdbddcaabccbbbbdbbddbdbbbcdcbdadaddcccdccddccdaccdcaaabbaadbdaacbccabbbbbcaccdbabccadbdbbcadadaabaaadcbbcbbbaaacdcabcdacbcbdcaccdddbcaadacbaabcaaddadbbaddccabbacdbadbcdacccaacdacdbbdbbbdbcddddbcaacacabcbadddacbadadcaabbcccaadcaaadbcaabbbcacacaabdaccacaadcdabccadabcbbabddbdabdcbadbacbdabbdbaacbccddccccdaccddccdaccbadbccdcbbdccaaaadbcabbcbdabadbadcdbabaaaabcaadddcadabbdcacaabbbcdadcaaabcadaacdbdabcddbcbbbddcdccbccadccacacdbbadcbacdbcdddcaadabcbcbbaaadbdaadbdaadaabcaccdcdccadddbabacaccdbdbcbbacdacabddcabcadaadccbdaccbccbddcbabbabcccbccbbbcaaaabbdcbdbccdaaabcccbacdbbcddcdbbbbbbddcabaddbcdccadbaaacdbabcdbacacccbaddaadbcdccbbbbdaddbccdcbcbcdabaacbdbabdcbdddbbbbaacbddcbcbdbddcbdcdcbbadbbddcdabdadccaacbadbcbbdcccadaacbaacacbbacbdddcbccdbadccccaabbbbcbdddccbbbbaaccdabcbcdbadbcaccbbdcccdcccbaababbcabcadcdcbaccccadabccdaddcdaaacbaabccacaaccbbbddadbacbdabbcabcbbbaacadababbcaddacdcabdcacbddbadabadacabbabbabbcdaddcccbbcbddcaadbabbdccdccdacaabcbbdbadacdacabbbcddabddcbbdbbbcbccaacabcdbcdbaddabdcaabbbadaacaadbccadaccbddcaadcadabbbddadcddcadabbbbbddabccccddcabcabdbdbacadcabaabdaadabcbccdbbbbacacdcdaabcdaabadbbbbcbdaaacdcacdacbaaaabbcbbbdabbbdccdccbddabbbdcdcdbaaabbccddbacdabaabdddabbbacbbbdccbaadcbbabbdbcabadaadbbbadcadccdabdddbdcbacbdddbbcabcbbacabdaabadacaaabcaaaddcaaddcdbccbdcadcabadcccdccdcdaccdccdcaacdcddcdbccadacdcccbaadcaabcaacaabbacaccabbcbcadbbdcddbabaccbaabacbbcccccaabdacddaddabccacadaadbdbbcbcccaaacbaaacdcabdbbaacbadaadbadaadbcababcdcdabcdaabadabddbdddcabccccacccdddcddcddbbbccdcaabdcadbaccddccaacbdcdbddcddaccddaaaaddbbdbbdbabacbccabdbddaabddadbcabdbbacabcabbabcdbcdbadabaadbabcaadcaabccabbddadbccaacdacbddddbdcdadcdabcacddcddcaadcccbabaadddaadbcddcdcdaaadabbbccacdacadbdbcaadabdabababadadbbdaadddccbbcbddcbbabcadcabccbdcbdacdaaacdcdbcddabddbdcddacabbbabcbcdbacacdbbdcdcaccddcadadadcacbdccdadbcdbacaccbdaaabcbacbaaacbdddaacacaddaccbbdabbabbcdacbaabcbdbaddccbcaaccaccbcbcddbdaabacacabcbadcddadbccabccbbabbcaaacdadaaabcabdcdcdccdcacdccbccdddbdaabbcccbcabadcadcdabadccccaabbdaaadcccdabccbbddbadaabbabbdadbcacaccaaacaadaccbbdaadcddcaddbabddbababcdaddbccdacddacadacbddccadbbdddddccadccdbaaddabbbddcbbcdbbddacadbdaaadccddabacdadbacacddbadccbadacdaabdabbcdbcdbccbdccabbdddcbdddcabbdcbdbaddaccabcbdcbddbcaabcbdddaadbddbbaccccdcbaabdbcdaadcbdaaaddcabcbdbaddcdbbcccbbcbadaaacdbcbacdcaacbbddccccbbcbcdacdcaabaadbcaadaaabcdccbcdadacbacdabbccaaaaccabdcabadcdbddaacdaaabccdabccaacbdbadbddadacacbabacdbccdcacdbbcdcddacbaddcbbbbddaaadcdcbacbbdbcaddadaabcdddbcabbaacdabcbbacabadcaabbbdaccbbdaaaababbbbdccabbcbdbabdbcdbccadccdaccdccddbbbaabcdbddcabdccdddcaabacacaabddaabdccbbdcaccdbddcdcdccbbdaaadabdadacabdbbdbabaccbcbcbabccabbbaabccabaabbaccdbaaabbbdcabcacbbbadcacbbadacdbbbbdabddbdbbadaddaadbdadcaddaacddbbccaadaccdbadcdcbbacdacdddbbdabcabaddbdbadadddbdcdadabbcdbcdaabcaadbbdcdcdcdacccdbaabdcabdacccbcddbdaddacdcbdccbddbcbbccbddcadabbbdbcbbdbbacbaaaaddbdcdbdabadcaabbddbbbcdbddabdcbdbacbbbddcbcacdabbacbccbabcbbdababaabdabccddccbcbddaacbdabdcaabdacbcbdbadaadbdbdbdddbabccbddbcddacbbbcaabdacaddaadbbcbacdbbbdacbbdcddadaaccadbbddbcbadabbdcbdbaccdaadabcaaaadbadbcaaccbdbbddaddadcddccaddcaadcbccdcabcbddadabdbbadddadcdbccacbbddbccccabacbaacddbcbbcdaadaaccacdaacaaacdcadcddbcadccacabcaadcaccaaacbcccdccadbbcaadcaddababbdbcdccbdaccbccbbcbbbbdcbbcdbadbccdbbcdcdbcdbaccdcccbbaaabbccacccacbacdccbbcdccabbdbadabaabbacbaddbdaabbcaacbdcabdcccdbdabbbbcadadcaabbcdcadccaabdbbadbbbabbcddcdccdcdaacccdcbbbbdcdacdbbdbbdbbddadddccccbdbdbdbdaccdcdcacdbacabddbacdcdadcabcdaacbcbdcaadccdcbacdcbbbbbacbbcccddddcbdabbdacbbadabbcbccbcccacacbdaadcdcaabddabaabadcbcdbabdbcbddacadaabbaddabcdbabcdaadcbdbabacbabdbacccdcdbbccbcabdccbccaabdbddaaaddbcddddbccbababaaaaadcdbdcbbaadadddcbdabacaaaaacacadbbacbdaabbbccdadddaddddaaaccaabbddbacdacbcbbccbddbddbbbbccaacbdbacdadbdacbadbdbacacaadaacbdbbabcccbaccbdddcadccacbabcadadabcaddbcbbdcbbbcdcccdcdaccdbdbabadaaabaadbabbcaddcdddbdcaaababddabdbbbabaddbaacacccdacaacbdabbaaaaccbcaaadabacbaacdddbccdcdcdabbbcaabbdbccbbacdbdcabbcacdccdabbbabbdbcccaaccbabcbcdbcbbabdbabadabaabdcdabcdcbccdcacccbdbabbabdcddbbdadacbbbbdddcddbddbcabcaccaadcacbdcdacaccdddcacbbbaddccdbbccbaacadadcacccaddcdaacadabddcdbdbdbadaddacccbbbddacbbbbbabcbddcadadadbdcdabbaaadcbadcadcbbadabbabdbcbaabccdaacdbdadbbbcbcdcdcacdcbcccccccaadacddcbdabdbdadccabccbdadbddcdbbabbacaaabcbcacbabcdaacaaccadccacaacadaddcaaddbaadcaabddadbddacdabbcddcdcbadacddbbbdbbaabbdbddddaddaacbcadacdddcabdbdcbbddddaadacbdcabdddaddbdbdabbcabdadcdddaadbabacbdbbbbcccbadcbaadbdaaddccaccabdabcbdbdbcbbaddbbbdacaacaaacdcaacaccadadbbaddcabccacdaacaddabcccddbbdddcbdbbdbbbbcddbbaadcacacbbcbccaccdddbdbdaaccbdadddabdaaaddbcacddbddaacdbdcdaaaacdbbbdacaaccadaddabacdbdbbdacddacbdcdadcddbadcacbdccadadcdbcdbccdcbccbbcddbbbdbcddccdacaadacdacddabadaaaddaaadcaacbdbdcbcbaddbaccacdbbbadbdbdccabdadabbdbbaabbabbbcdcbddadadbaaaabcaddcacbacabadbabbaacdaaacdcdccbcbcdcbbbddcaddacbaaccdacbbcccabbdbadbaddbaacaacccaaacbdbadddbdcdaabbbccaccbccbccbbbdaddaaaaadabbcbcbbbccacbdcabadcdcacaaacddaadacdadaaadcbcbaaaabdbddcdacdcbcaccadcabadcbcdacbccbddcbdacddcadcdcabcbbcddadaabaabbcaadcbbcabbdcbdddddaacbbbcbbdaacddaccbbacbbcadcccbbadacaaacbcdadbdbcabddbdbbdbbdaadcaabcbaadddcabddabbaabcdabccddadaacbcabbccddbbbcccdcaabddabaccdccbadbaacbbcacbadcbdcdabcadcbaaababdcaccdbacbbbbbaddbabcadbcccaccccaacccaaccabcaddbbdbbaacabcbdbbdcbddacbbbdaacaaabcaccbcadbbbbdbdcdadcaaaddcbbbdbbcdbadacbdddaddadaccbbbdcabadacccddcaddcbdadabcdddaadbdddcdbbbbbdabccbddbcabddcccdccdaacaacddaaddbabacabdcadabdbbcccacacdcdbcaabcabcabdacdaacdadbabcbaddbabbcccadbdcccbbaddcccbcdcccbcbcbbbcbaaddbbddbbdccbcbddcbdbbdccccbaabbdcadacdcacadbddaabddaadadaccdbbadddcbdcbadccaddabdcccabcabdbdaccbdaabacdbbdcdaddbddbbabacbcbadbdccdbaccaccdaadccccdccbbadcddcbdcaaccbabdaddbcbbdbadaadacacbdadbabcdbdaacbcddccdaaaaddcdadccdcadabcbddddadcacddbcddadccdaddbccbbaacbdadccbdadcbbdacddbbdcaadcdaabcdacbacbcbddcbddadbddaccacdadcabdacddacabbdccbaabacdcaddbcbdaddcaccdcbdbadccccbaacbdacaddaaaaccccdbbadacadabddbcbacbcaabcabbdbbbdcdbddcaddcacbbdabdaabccdaaaaadcbdacccdaccdcbbacbdadcaabaaaccabbbcaccccbadcbcabdddbbacdddcdadddbcbbabcbdcbdddcbaaaaabcdbccbaccccccabacccbdccacbadddacdcbcbdbccbdccbddcdbddcdcacccbbcddbdddbbaadbbaccaaddaccacccacbcbbbabaabacadbddaccdddbbdabaabadcddbbdaacaddaadacbdccbdaaabcaadcddbbacababcdcdcabbbabcadddccaabacccabccaddddaccabaabcdcbabcbbccacdccbdccbccbcbcadbaddccdbddbbdcccabccaacbdcacadbbbadaacaddaaccccbdabdbbcbbaabadcbddbcbcabccababbbbbdabddbdcddaacacacadbcdabbcbdddbadaddbcdbdaabcddcbbcdaabdcabddccaaaabdadccbcccbbacccbcbabdabdcdccdcdddadabbdbdccaabaacbccaaddacadcbbbabdacdddcaacdccdaddabaaaabcdbbacbacabbbdcbaacbcdbadcaadcacbdbdbbccacbdbcaddbaadddddbdabcbbbcddadccacdddadcbaacbbbcddbabddaaddabdcaaacbdccaaaccdadddccccdbbaddcbcdcbaddacbcdddacdcdcbbdaabdcdddaccdbdbcdbdcbdaacbaaaadcdbcdadadbdbdbcbcdbadbdddbcbbacbbdcabddbaccbccbddbabbbdaaccadcbdcbddaacbddaaddcaaccaaaabbabdcbddadcccaadddcbcacbcacaddddddabadddaabababcbcbbcdcddbcddabcdbdbadcdcbcdbbcaaaddbccbbcacdbaabcacabbbdcddaaccbdadddaaabdabdadabadddadcdbadcdcbcabaacdaddabcbbcddcdbdaadbdadaacbbadcabbbcabacbcdcdcadcbdabbabcaabdcccbbbdaccbddcdbcacdbcbabdbcacbdbabddcdddabcdbdadbbdbccdccdabbddbcacddcddcbbdcabbdcdcbdadcbdaadcacbbcdbcdbdbabbcbdddaaddaaabcacddaaabbccacaaaddcbcaaadbdcbdcdacbacbaacaadbabaaacbbaabadbaddadccabbcccbbdbcbdcdcbcbcccacbdbbbcdbdcadaadabbddbdadacdcbdcacbcccacacdbbcbdbaaadcddbcddcddadddaaddbcbddbaadddbcacaacddacbdadababdcbcbacbacdbbcabdbbbadcdcadbadcbaccddbdadddddcacbaadbadaadbcaddbcdbbacdbddacccaaddbbabcbbcbdaadddddcaababbdabcbcadacbbaabccdbbaccdcbcdadbadddddbbdcccbddbadcbdaaacbbbcaddacdbaabbdbabacdaccaacbccdbccabcbabbabdbbbbacabaabacdccabccadbaadcdcdaadcbaabcaacdcadcccccdaccdbacbaccdaaacddddbbbccbcccaadadddcadbccdcabcbabdddabaaadbcabbdccdbadddcbaaddcaddcdcbbcddbdccddddcaaabdabbcdddbddddadcbbacbbbdabcacbbcabdcdbcabacbdbbabdababbbcbddddcadbdcbccbcddccdddaacdaaddcbdcbbbadbabccbdbcbddddbadbccddbaabcbdbbcabcadddbcdaddbdcbbaaaadbdacdadcacdbbdcabdaadddbcbacdadbccbacabcdcddccdaadcccabbcddcccdbcbacbaacdbcdcdaabbdcaccacadcbdabbbbdcaaaacddbbdccddbddcccdababcddbbdcdadcacdddabbabbaaddccabdcbaacaababbcbbababacaabadbbacdcabdaccbddbadddcaacdaaccbbbbaccccbababdbdcbaccacbacbbdbabadbcbabbdcdcdaacbbbbddbbcaaccddaddadacaadcbbaccacdccacbabaabdbccddcaacdabdccabacabdcdddadacdcaacacaadbdcacdbcadccdddcbccdacabbabdacadddcdbcccdaabbccbbbaabbccbcadabdabbbdadacccdaaddccacbcdddabdadbddcdbbbabddcbbaddcaabacadbcadcacdccdddddbbbcbaabbdbccadbdaccdadadadddddcaadbaadccaaadcdabdbacadddcaabadbddcddadbadcacdacdacabdaacdbbdcacdbdadcdbaacbdaaadcbdbaabbbaaaaddddcbcadadbbdbabadadbdcbbbddcdcbbbaadcbbabcccacdcaaaddaadadadbacabddccdccaaabccbdbccbccacccbdbdadbbbacabdacacbdbdcbddbbaaacbdcdcbccbaccabaaabdbcdacbbcdddbbdddcbadabdbbdcbdbabccadabddbdbcdacdbcdbbdbbdcaccdacabdbbcbbdcbaddbdddcbcabddacddddaaaccbcccccbdadcadbabdabdabcdbcbaadcbdbbbddaadcbccbcbbdcdbbbcbcbbbcbaabdbdacccaadbcbccdcdbbcbcaaacbdabdbdacdbcccabbbddcacdacacbabadcbadccdaddadbaaaabccdddabbadcdbbdcdddcbcdcccacddcbbadcacbaaabbdadabcadbbacbdabbcbbadcabaaaddaccaddaccdbbaddcbdccacabaacbdddadccdcaadbaadaaacdcbdbbabdddcbbcaabcbabccdddccbdacadbdadadbdddbcabbbddbadddcbcaddaddcdaabadabaadcbcdacdbaccaadcacadacccccbabbabbddbabddcdacaddbdbacbaddcccaaacbddbadbdaaadcddcbcabcacccbccbccdaddcccbbaadacbddcbaddbcbbbcadccaddaaabababcbaaacaacbdbdddabbabddbaaacbdbbddcbbbaddacadbaabcbddacaaadcbdaccaaccbddbbadbbdadabbdbbadcabddacbaaddcabaadccddbacacaacbcabcdbdaadadcbdaacbdadadcdcbdadcdabadcdcadaadcccabaaacdaaddbdababccabbaaaabdbbadcaabcbccddaaddcbccbacaababbacbaadcbadacccbdbcbdbcdacdcdabcbbcddacabbbdbddacdbddbabbcccabdcddcddaaacdcbadadbcdadabaccdcbbabdaccabadccddbaaccbadadddabccbbcdabbaabcbbdcccabcabaddcccabbccadcdccdaccdddbccabbccccddbccbacaaaaccdbcbdaadcaaadbbdcbadbcdddccbdddacbacdabdbaabddaaadddcaaabdcaccdcddcbccdbabddbaadcdcdacdccdcdadcbdacbccddbbdabacddbbbdadbbcdababaaadadbddaaddbbacddddcddcacaadcaaabcdabdcbbddbcadbbbbdacbbccbbbbbadccaccdcbcccbaccbbccddddbadbaaaabddcddcdbcdddccadcaddaddcadaabcdadbabacdddcddabadbdadcbdbbaabccadcdcadadabbabadbababbcacdcdccbcddcadcdacabaccdbbaacacccacbbdbdadcaadbdabbdccbbddbacbcbcaaddccaacbdddbbcbcdddbbddabbdcdcaaaacadcdcdccdbddcbbdadbaaccddbcbddbdbbddacadacaaddbabbbdcdacddbcacabbcdcdcbbbdbbadaaabdbbcccabadadacabdacaddbbabdabaabadaadbdddcddaabdbdbbcddbaacbdadbbaadbbaaabbaaccaabaacacdbddcbcadcbccbcbacdcdbdaacabddacdbbbddbdddcddbbbbdaaaadbbcbbaccdacddbdabcddaabaadbdaadacadcbdbbdabcbcadcadbacacbccaabcbdcdcbddbacdbdbdbcdbccacacaaacdadcbcbcbdaddbdccadbcbcadcddcdddbcdadcbcdcdcaabacbbacddcdddaadcddbacdccddcbcddacaddbbbdbdacccbbcbdabbbcacbaccbbbccdccaadcbaaaaccdacbadccacddccdddbbaaddccddadcbcdbdacddbdbcabbdcbcacdbbabadcdadbaacdbcbdcabbddbdcacdcbcccbcdccccbdadddbaabdcbccbadcadcaaccacbddaadcdaacbbcddabbdacbcbbbccccbaababaacabdbabcabbcabcabccdcacddacacabbaaccaaacbbdacaaacaddbdccaccdcdcddcbcaadcaabcdcdddcaabcdcdaccdaaababcdcababadcccdddababbaaadacdbbbccdbcabbddcdcbbabdcdddbbbdbacaadbabaaacdacccdbcaaccabddbcdddbcabbdabcabbaacbbbbadcccabdcddcbcdbadabadacbbbbcdbacbcdadcbbcbaaaddcaabbbdcdcabdddadcdcdbdaadaacabddabddacdadcdbdccdccaddacbcadddbacbbcbaaadcbdbdacbabcddbbddaaaaaaddaadbdbcabacddddabacdcbdddabdddaccaaaabcaacabadcabccabdccdcccacabcbabacacaaabadcdbdbdacbcdadbcabbbdcdcbabdaabbaababccddaddcdbdccdabaaabacadcabacdddbadcbcacdabaabbabdccaaaaabbcdddcbbdccbbacbbcbcbcbccacaddcbcaacdccbccaaddabaaaccadcccaadbacbcbbddaadaacccbacbcbbbbbaccabbdcaacbcdaddcccaabddcdbbbabdcdbadcaaddbbcdcdabbacbccdcacdbbbbdacdacdbddcbdcdbcdbbcabddcabcaaccdcbadcbddacdcdacdddaddabccbcbacaaabbbddacdbbcbdcabaaddaadcbcaabdcdacbdadadabaaabaddabddcaccbdccddacacdbdaabdadccbadacccbacccdacbcdbccaadddaacccbabccbbcdbadcadadbabcddbbabadabacaadabadccacacbcabcdcbbacbaacabaaddccdaccadbbbacbddbddbabcccacacaacbaccadcccddbbbacbbcbdadddddaddabcdbbbabadaccdcdddcbcdadadcbbaaccdacbcddcbadbbcdbacabcbabaaddcabcacabdcdabcdcbabcbbbcbbccbdbdbbbdbcadcbdcbcdaaadbadbddbcbddcccccabbbdabacdcddbadaacbdaaacacdddcdcadcddaccbccaabcaabcdbbcbacabaacabadcbcddbabbabdddbdbcddaddcacaaaaacdaaacaaacdaaccbacbdbaaccdbacbdacccdcbbbbaddcbbcbcdcabbdadabcadbbbdbcbdbccaccbcabaaacbadddabcaccdaacdbaaaddbaabddbbccbdcddcadabdcdddacadbdccaabcccdcdbddcaccbcddcddaddbcacdabdddaadbcccbdccdddbadaccbcbcadabbbaadccbacaaccaaccdccacacabcdbcbcbddbaadbbcbbddcbacaadcbbcdbbcbbcdcacdbdbdddabbddcbdccacddcccdbcacbcccaacdcdcdbbbcbdcdabaadadaddbddabbdadbdabcacdadddbbdddcbaaadcdaccddcbdbdbbcaaadbddbccacbbbbcbbbbbcdacbadddaddbbdadbacdcbbabdcbaccbabdaccbdbdcacdabccbbadccdaabcabdbdacccccdddabbacbbcdddcccacdbcabdbacdcbbaadbdccbbcdacbadcdabdcaddadccaaadbcbbcbddaabacacdcabadaddddcdaacdcbcddcdcccaacbdcbdddddacbdcbbdbdcbcccbabbadddbadcacbacaaadcccdcaadbbdbbacadabcccadbdadcaacadacbbaaadbadaadaddaaccabaddcabdcddaadbadcabaaccbcdddbdaaaabaabdaababbccbdbddcabadbdbcbbacababcadcccbdabadbbdbaacdcbaaabbcaabbbacacdccabcccbccaadadabbddccbdbbddbcbdbaddacdacccbdaabbcaabcbadcdcdccbdccdabbccdcddaccdbadabdccadacbabdaadbbccdaccdabdadabbcbacbdcccbbbadcdbdbcacacbbbaadbcadbbaadaaacdaacdbadaaaaabdacbcbcbbcbbdbbacacdaacbccbddacdadabbaacacddadbbbcddbcdaaddbdcadcdbcaadcdbbdbdacbbcdaccddabbcbadabbbddcdcbbcdbdaddbcbabbabbcdcdabbbaccaabbcdcaabbcbacbbbbbabaddcdccdbbcadccdabcddacacadabcacbbaacdadccabdbcacdbbdbadccaaaaabcccbdcaadabdaccbdddcadcbddbabccdadbbdccdccdbacbbaddcabbcbdbcbdadaabcddcbaacbcdcbcacbdabdadcdcbcddaabaaacbcacaccadacadadbccdcbcdbacaacccbabcdaccadbccaabababcdaabcacdbbcbbbcbccacaacabadadbbbdccabcdccdcdbcdbaccddddaabccbdbadabdddbdacacadacdabdaddccdcdbcbcadbdccddcbcabbaccaccabacabcbcabddcbcdbcacabacdbbddbcdbaaabcdaababdcdcdabbcdcdabdbccdaadddcbddccabcbdbabbbbdaccdddcbbbcccdcacbbdcddcdbcdcdddcdcbbaaabbdadcabdadddbcadabadbbbcdbaaabcabacabdddbbbdcbbcaaddaabddcabaaaddbbcbcbdbcdddccaddaaacccddcaddbacaacdbabcacabcaabbbabdbccacaacaaaadcadacbacacddaaababbdbddbacdadccddaddabbbdacdddbaaacadbbdbbcddddbaacdcabcadbadbacdcbdbbcbaabaadacaabacbdbbdcaacbacdbdcccabbabccadcdadbcbaabababcacadacacdcdcbbbccbcadddbaadbcaabacacadcddbdaadcddccbdcaacdbdaccbdbcacbbcdcbdaabdddcacbacaccabcdcccbbdadcabdbdcabdadbaaadbadabbbddbaabdccaaddcabcdcbbcabccdcbbcadcaaacbabadbcdaaabdabcdcbacbdbcdbcadabcccacbaccadbacccdcccccbcaaaabbdaacacbbbdddadccdacccddacbdbacaaddddcdcccccaacbcdccadabccbacadbbdabdccacadccabccaadabbcddaccbacdccdbcbadacccbaadbdacacadbdabdbdadcbdacadacabbdadcabdddbcaacbacadcdabdbbddaddccaddadccbddcaddcdcbcbddbccadabdbcbdddcbcccbbbccabcbbdcbaccbaacaddcddbaacaccbcacdabbacbcdbdcdbdcaabcaacccbaabbcdcbadcbbadabbbdadbabbaadabbacccbdbccadbadadacbaabdcddbbcdaaddddacdbacaacaabaadabcdcaabddcbbaabddbcbaddbaaabdadccbcadbaddcacdccddcdbdbdbdaccdcacadbaadabbdcdcdaadacbcdcbbcdadacbddbabdadcaabbadbcdabdbabaccbbdcabbaaabcbcabaaaaadbcdadaaacadcdcbadbaddbaccacdccbcccbbaddbbcdbdbccaabdaaaaabcdbbbbddddadabababdabcdcbddcdaaddbddaccbdabbacaccccdaacbaddaacbbdccadccdcccdabddbdabacadaacdbbbaacccbbaccdaddaddcbbbbabbbbcdaadcbddbaacacdacbcbaddabdaabdcadababdbcccacdccbaacddddbbbbacaadbaacbacbccacdbabcddcddadcbaddbcbbdacdcddbcbadaacdaabbbabbcbadcdababacaadbbacbbcbaddabdbbbbdabdbabcccdcacccdcdcbdddaaabbdbddbaabcadbdbbbddababbbcdabaaaccaadcdcbdbdcbdaadbdacddacbacddacaaacbaccbbbaadbccddaaaadbdadacabdcbbdbccddbaccdabcdadccbbddcbbabaaabbadabbcbaadaabacbccadddddbaabbaacbdaabbdadcddaabcdaacaccaccadaadcaaaaacdadbaddbbacbbadacdadaabdacccadddabdcaddcabcddacdcaaaabdbaadcacdddddcccbbbbbbbbcacdccadccbbbaaaadcabbcbcddacbabbdadabaadbadacdbcbcdcaadcddccaacbcbcabbdbccdbabbcdbccccdcaccbdbbaddbbbabacccbddbcdbacdcaadbcadaabdbaabbbcaccaabacbdcbaddcabaababcdbaabbaccdddaabbcdbdacabccdddbbbdcbdbccbcddcbcbbbbbbccadbbadbbadcbdbacbadacadacacacdbdccaadcacdddbbbacdbdbdbcdadaacaadadddacdbddbbbcdbaaaaaabccccddccacdaadddcbccaaccbacbcbbbddaadcabdbaccddcbadcacdbbbcaccabaadccddcbccaacaddaadbdabdadaaaaabbadccadacacddbbcacbdbadcddddbdabaccbbbacacdbccddbbdcadabddbdcdabbcdaabdadbdbdcaacdabaadaacbcdcabbaddadcdcaabccabbddcbbbcbdaaddadadbdcabddcadbcddcbdcdbbbabbdbacadabcddbabcddddccadbbcdcccabcabbaadadbcdccbadbdcacccccccbadabaaacaadbbddaadddabddbcdcaabaaccdbccaaacbcdbbdddacaacbbaadbaaacdcaababbdcccdaccbdcbbcacbcddadabbdccbabaddaabcacaabbbdbddabaabcdcccbdcacdcbdbaabcbbcbdddbaacadaaacdcaddddbcdcbcabacaddccaadccadbccbcbabdacabcbccdccbbdddbaaabbbdcbdadcccccbaaaabdcbdbaacbacbabdddbbddccdaadcccacdacdaaccdaadaaccbccbdabcbccddcaccdadddccbccadbbbbccbaaaacdaccbcccbddadcadcaadabcdddbdbaaabcabdccacdbdadcbcacdbbdaddaccdccddacadbdcbddcbdaccdddbdacaacbcdddaaabcadbcaccdacadbbabcdabdbbcaccdabcddbcbcbabacbdaaacacdccbdcddcdcacdcdccabcdcddbcdabddbadabadccddabccddcdbbaaadbcdbddccbadbaabcbdaaabbdcbbadbbddacdabddcdbbdabdddbccadcdbaacbbccddacddadcbbdbccbaaddacbdbbacbcdcbadaacdacabccaddadbacbccababbcbcbdbbaabdbadcdaaabddabacbaaddbcbaccacdaaddacbbaaddcaabbadbdcbcbcbcccaadcdabadabbabaaabdddcaaadccbbdcacddabcbabadddccbadacbadcdcdbcabacccadcdbcdcbdbdcccaddaaabbddabbbaaaadbaacaccdacbbdbaacdddbccccdcaaadbcdacacddccbabcadddddaccacadcdaaaccbdacdcdbdbabdcdccccabdacababbdbcdccaadabcadadaddcbbbdabaccacacdbaccadcadcddcbdadcacdbbccdaaddbdccccbccdaaacdadddddbcbabccdcbadbcdcbbdbcaaaadaacaaaaaddddddababbbaccbbbbaadcbdccccabbaabcadbccbabdbbcbccaabddcadcdabbccdddbcadccddadccdabbdacbddbdadacadcbbbdbccdaadbbcaccbcdbdbbbacaacbcbcdabacabccabccacadccbbbdcbbdcbadcbcbdddaacadbcbbbaddbbdacdddddcdadcdbbddadcccddabcaacbbcdabccdadaaacbbcddbcacbccddcbdacddadcdaacaaabcbddbcdbaaadadadbccaaccadccbadcdccddddcdcadacdccabadaaddabaccdbcbcddacbadaaabababcacbbcbdccadbbdcccacadbcaddbdadabbbbaddbbcadadcbccbbcaacdcdadcaaaacccddbbddcbaaadbacdabcbdaabdaabaabdbcbbbcddcbcaddaaccdadddaababbcabbabbabbcbaababcadddadddcdddcccbdaacdcbbdadaaabcaacbacbbdadbcbbaddccaaaaadddadbaaaabbdddaabbcbaacdcbddacccadbcbadacdabbbccbddcdcbbdccbbbabdaadbcacabbbbdccadbbdcbccccbbabccddaddaadbcacaaccdddccdbaccabcdaacacbcbcdaababccdddaacdccbdabcadcdcbaacbaaabcacdccbdbbdccbcbbacccbdccbbbccbdddcadbccabadccabbadcadcabacababdacdaacbbbccbbcbacbaaaaacccddddaabdbdacadadcabbadccbaabacbcacbdccaacadcabdbcbbbccbabdbacccbcaacdaddadacacddadadcccacdbadbdbdbdbcdbccbddaddcdabbaabaacbdbdbcbadcdccdaababacbadabbcbcadcbbcdaabadbaacccdbccbdbcdcababdcbacbbcacabccbbbcdbdbddbadaabcdbbadcabaadbaaccbbbcaadcabcdaddcbadbdcdacacadddaccdabaccdcbbcdcaccadaadbbbdadcccdaabccbabcdbdbbcbcaaaacabbadacccaddccabacbdadbbdbdbbbdbdabdccaabcacbbacddaadaaaadbdadbbbacbabdddbbacbabacbccbcabdaccbcadbadddbaccacaccdbcababdcaabbddbdabcbcccbacdaabbbcccbbaccabaabddaadcacaadaaddbaadaabbbcadbdbbbcaabdcaaacdccbdaacbdababcbbaaabacbbbdbbdbabcbcdacdbddddbddccbcaaacccbddbccdbaaaaacdbcdcadccabbccdacacdabccccbdbdacaddaadddabddbbacaaabdddabcddaabcbdaabbccabbbbcbbdacadbaacabbbddddbcbdbddacbadabaaaddbdcdaccdddcaabcddaddcdbbaddcdccccbdddcaadbbabbcbbbcdbabadbabcbbcdabbbabdddbdccddabccdbbdbbdabacdcaaabbdaacaacaaababccdaccabadadaabacaabcbacabadaaaddcbddbaacdcbdbdddbddacabdcdabaaaaddaacbccacdddddcdbbcaabcdabdadbdbaaacbbbbdddcaadcccccabbaadcaddadcbdaddcdcaadaabccbdddaaabbaaacbadbddbbcdbdcadaaccacaadbacaadaabbdbdbbabacacdabacdaaabcbcaabaaabdbdaaacadacddbcdacdcacacabbcbabbddbacdccbddadbbcabbccaddaddccbaacaacdcdccdacdabdaccabcbbccdcadcccdaadcaaccbdcdddacbdacdddbcdcccdccdcdbbcdcaccdcccabbcacadadacbabbcccaaaadabaacabcbcbaaccbacbbbddbbaabadccabdcdbbbbbaddccbbacbcbddbacaaadbaacadcabbabcadccccabddaacabcaabaaadbdacbdbcdddaaaaacabbbdaaabadbadcbaddaababcbaaacbcaaadbcccbbbadbbbdccbaccdacbabbcbcbbbdbccbbbadcbacccccbcaccdcdbcabcdabaaaadacacdcbbaaadacabdbcacdcdcaddbacbdcdaabddcadbadacdabdcddbdacdcddcdcddcbbcbcaaacbdbdddadbaccaabcdadbacccadbccbcdcccacddccabbdcbbbadbcdcdcdbaadabccabcbbadccaccdcbbaddcbbbbdaabbdcbbcacabbbdcdccadaabdbddcdacaddacabaaddcbcdbdddbbbaccdcdcccbdccdcaadaaccdbcddcbbcdbcbdbdadbddccabbabadacddbacdadbaaddcadbaadddadcbdccdabbdbacdcdaccdcbaccbbdbdcbccbdcacbadcaccbccdcaababdadbcaddbcacdcbdadcacacbacddcbadbbbdcabcdbdcbaaaddbddbbbaadadabacabbcbcadcaadacdbdaaccdbcbbdaacddbdaacdddadcbabcdbddbcddbcbadbbaadabcbcabcdaddabcbddccbaccdbbbabcccbacdabdabdbacddaccaabadcacacaacbaaccddadbadacbbbbabaadaabdaddadbaadcbcdbabbdcbadcadddbcacabaaccacbcdbdadadbbddccacbbabccacacbcbabcabccacbbadccdcabbaabacccdddddcdacaabbadbacaaaadacdddbdcdcdcccabbcaaacacbcacdadcbabcabadaccbdabbaacbccbdddcaddcbcadbcaccaaabdbdccddcbacaaabbbdcaadadabbbdcabbddcddcbdadabbccdbcbcdaccaccabbbdcdcbcbbcdcdcbcabdbdccadaaabcddacccaacbdacaaccadaadbadddbacacdaddbbbccdbcbdabcbcddccaadaacabdaccdbdddaccbdaacdbbabdbdbdcbdbcbaadbacabcdbbdcbbbcbddbcdbdbaabdacacadbbacdccdbdccbddbcbdddaccabdddcaccbaaaddaaacbdddccdddadccadbabccdacdbccdcbbddbbbabdbbcacbcacaaacacdddcdbbdaabcbdddabbcacdcacdaccaabadacaaaaccadccadbbbdcdbdbbdcaaaadadccbbbdcabaabdcccbadddcdabdbccdaacadccbbcbbbdbcadadbcdbdaadaacdcddcdddcdacbacaddcacbdadabcbaababdadccabcbccabbbbccadacbcbcdcadabcbbdcdcbcbaccdaaabcbcbcbcacdbaabbcaabacaccabcbaadcdadcdbacbcbaacccdaadabdabcadbddbacacdbcbcdcaddabcacababbbacadaddaaacbbcdbdcacdabdaacaadbdcaddcbaaaccaccdccabcbbacdabbabbaacbdabdccdadbbacdcadaacdcabcbdacabbacbbccdbdabddadbbbcdddacaacaacdabbccaabadccacacbbdcdbadbbbdaaddabbccbdbcadcbbccbccdaaddcdacddccacdcaacdbabddbdbdcacaccddcadbaccbdadcdcaadaddbddacdbdacbabddcabacacddcbaaadabadaadccccccdcaadccdacadccbdacabbcbcadaccccdbdddabbabddccddddcbcdcbbdbdcbaadaadccdabbcdabbbabbdabbaddbcdaacdddbcaabbbdbadbdbbaacbdcabccdcbadbacadddbaadacaaaddbbcbdcccabdcbdbbbaacabbbddadcbaaccacbdabaacbbccabbadadaccccbabbcacddcddbacdaccdcdbcbbbbcbaaadaddaddcbaaccbdabcddddaacdddddbcdbadabacadcdddaddbddbcdadaaacdacdaacbcdccabcbbcddbcdaadcccaacddcbaddcbccbcbcddcabccdacdacdbcacccbabbddaddabcadddaadddbdccdadaaacabbdddaadcbddddcdacdbcddacbaccaaaacdcbcbacbbddbbccbdaccaacdcbcbababbbbacabcbacdcbabadbcdbbbacbbbbbdabbadcbbccccccdbcabaccaccbbbaccaabadcaabaabbbdcaacdcbdbcdbbbabbabbaddbdacbdcaacacdabbdcacaadbbdcbdadaccddaacdbdaddbadcddbcbabbbddddcbbaadaccbcdabbcbdadcbdaabdddbcdbaabccddaaaaccadcacdcdabbcdbadabddacaabaaabcbcdccdddbbdaddcdccbbbcdbcdadbaccabcddaabdcccdacddcccbabadabacbdcccdaadaaacabbacbdbabaccdadcdcadbbabdaadccccaddcabccabdaddccdddbbddbdadadabbdacbabacdadbacdbacababcccbdbcadaccdddcadacabccccadbccbdddbdaccdbadadbcadcbcdbacadbbbdbaabbdaddccaaabaaabccadccbddbcbabacbbaabcadbbabaccddadacdabacbdbcbadbabddcddaabddabddacadddabaccbcdbadabdcccbcbdcbbcaabdcacbdaacdbcddcbddcbaabacbbbdddacdccaabcbaadbdddbddadcadaacddbadadbcabaaabccdabacbbdcabcbbbdddcdadaadabadddbadcbcdcaabdcabbdcbbdadabdcddbdadcbccdabdbcabbbcbbbaabddabcdcdcbbabcaabdaccbbacdbbbbdacaabdababaaaadcbbabcddcbbacddddcdddabaddbdcccddbacaddcbadcbdcadbddbacdddbabaadaaccadbaabacdaddbbcaadccabacaddbabbcbaccbbbbbccbcbcdadbdccadbcdcbcabbbdbddabcacbccaacbcbbbcadcdbdcbcdbbdcddaddbadbdaaadabbbddcadddbbadadccbdbcbabbbabcabbbaadbbdadddccaccbcbbdbcdadbaacbacbcdbdcccbaadcbcacbaccddaadabbabadaacbbddcdbcdcbccaacdccacbabcbdcaaccbdcbcddcabdcccccdabbcddbcdcbbcbbccaccaadabbaadbcdadddabadcabacdacaaccbdabababaabddcadaddddccdccbcddaacabbcaadcacdabdbaaccbbababcacccdbbdacacbabcaaabacddccbdcbadaadcbdccddbbadcbabbaabccacabbdbbbadabccbdcdcaadcbbcaddcdbabacbdadadcadcaacacbacdaddcdacdbaaabdccbddbbcacacaaccbccbcabcabbaacbbdbdbadcdbbccbaddcbaadcaccdbacdccacbcabdcaacdabdabaadbabcdddccddacadabbdcaddcdddcaddabadcabcdaccdcbaacaadbccaacdcacacabddacccddcdcddacbaddcdaccbcbdbcddcadbadbccdcbaaaddadccdbabdccaabbdbcacacbcdbddbacbabbbabbccbaacdddcadacdccddadbdccddbccaaccbbbacbadbcdcbababadbacccacdbddcdbcaadbcdaadcaadcbbbbadbcbcbcbddbabcdcbccbdcdcabcddabcadbabbbddcbbbadcbbaaaacdbadacdbabddbbdacacbbdaacbabbddddabcdbddcdbbdbbbbcddaccccbcabbcbabdbcbbdabaaabdcdcbdcdacdcbccbcaabbacbbbbacbaacddacacaaddbdddbabcaaddccbbabcddcadcbdccbadbcbdbdcbbbcbcaaacabadacdaacbdbdaadccacbaaccbddcadcddacaddbccbcbccdddacabbdaaddaacbdacbddcadcccdaacddadbccbaddaadacabcbcabdbadbcadddcbbcbdcadcacadcbcbabccbbcbcbbdccbdbbbcccacdadddbabdbccabdcadacbaaddcbbddbaccdabcaddccacbaaaaddddbddaaccccdccbcbaadbdaaacbcbdcdacdcdadadcbddaccdadcccabadbccdcddacaaabbbbaacabbbcdaaabbabccbacaddcaaaccccabaadbadabbbadddcdcabdcbaabddbdadcacaaaccadcaaabcdbbdcddcdcbcbccbbabcaaaadadbcaaacdacadaacbaaccccdcdcaaadddddcddbbccdbaddbcbadccacabcaaadcaccdacddccdbaddbacadbccbadadaadbdbbcccdcbcbcdbbdadcccaababdaacabacbdbcdacbbdcbdacbcbacdcbdccaaddcdabcbacbdddcacadcaabaabddacdddbcdadbddbddccabdabcdddbdadbddbbbaaaacacdccdcadddcdbddaaabbdadcdcbcaabcbbaadcdbaaddbbccadcbcbcddbccccbbddabcbacbacccdacbdacdcccdbbbaadbbbaddddbaaaccbdcabadbdcbcdbaccabacacdbdbbbbadaaaabcdbdbaacbdacacaadcbbaccbabacbabbabdbdcbbbbcaacddadacdcabbaaacbabdbbdbbddbdcabaccbdddaabcdaaacaacddadaddcbcddaabccbbccaabadaabdaabdbddcdcaacdddcbcbcdbdccddbcdbcaaddccabcbcadabbdaaaccbbdcbcdbaadcacabcdadbbadcbbdccdaccdbacbddbababcbacbcbdbcaccbcacadcccbcbcbbbbccacddbbbaccabdabcbbbcbcbcdcabadabbbbcddabbaacdbccaaccccadaadaabbdddddcbbacabaadabcdaddddbdcdddcbcbaacbabbddadcdacbbbbbdbdbaaddaddaddccabbacdcbccadbdabddabdcdacbcaacaccbdbbcddabadbaddbbdadbaacbbdcbbccbbbdcbcaaaabbccaadaddccadbbdcadabbcddccdcbabddcadcbadbbdbcdcbaabbbccbdbbbbdabdababddaabcddababacbbdabcdadcadcabcacdabdbddcbabbcdaadaadbddbabaccadcacadddbcadbbcdcdbdbcadbdcbbdbaddcaadbcadbaabbcdbdcbdddadddadaaaaabaaadaabdcbdbcadddadcaababcbbcccbbbbdbabcacdbaccccabcdccadbbbddbaadbaabadbbbbbbbacaaaaadbccdcbdacbbccbaccadccbdadcbcbdbabdbdcabbdcaadbcabdcabdadadbcaacaabdbbcccaddccacbbacbbccdbbbddccacaaabaaadccadcdddadbdcddcdcabbbbccabcbdccccdbdcdaddaaadbcccdadddaabcbcdbbdbbcdbbddaddcddabdbddcccbdcbbdabdbacbaaababdbcbadaccdccdacdcdbdbdbdbdcabadadbdcbdbcaadcbdbaddbcbaababcdbcaccccbaabbbdddadcabcbdaaaaadadccadaaaaccdcacdbddbccadcaaaddbcbcbdbbdcbabbaccccaabbbbdabdabcbdacccccdaabacaadcbaabbcbcadbadcabcdbdcaaacadcadcdcddbadcbacadcbcabbadcbcadddcaababcbbbcacccbddacdddddcddcccdcddaacadcccacddbbddbcccbbcbbbcbcbccdabdcdbcdcaacadbcadddcbadbbddcbaccabadacbdabbbbdccddcccbdbcdabddcbbbabdcdcadcacdacbdbacddccbbdddcaccdcddbdaccdacdbdccccacbabddccdaaaacbdcbbdddcabcccbccdabcadccddddacdcbbadcdacabcdccacabddcacbcbabaaddbdddababbcdccbcdcbaadbcbcacddbadbddccbbdbaabdadddbcaacbdacbbdccdcddbddbddaaccbddadcacabddddabdcacaccdbacbacacdddacbaadcccbdcdcbdaabdaddcacdbbbababbcdbaaddabdcbccadcbbbbcdadabcbddbbdbaaaccdacbdcbacbbccbacdbdbddbbabdbaddbdbdbadbabbbbaaddbaaccadcaaaacdadbdbccabacacaccbddbcabacadbbbcabdbabcddccaaccdcabdbdaabadabbcbadcadabdcdadcbaabddcddabcbbbbdabcbbaadadddcbddbcacabbaddadbcaabdccabccabcbadcbbbdbbcabcaccacdcbbabcababaaacbaadddababcbcccbbadcabaadbcdbbbdcabadddcadddddccbacccdbaadbaddacadcacadcbadccadddcccacbdcbbdbbdcdcdabbcabdcbdacbacbabcccbacacadadbcddcdbdbacbabacddbadbbacdcbcbbcacabdbbaabddcdbdbdbbaadbcbaaadccaabcbbcaddaacdbccacaaadaabbbaaabdbdbabcadabcabbbcbcdcbcadbbdccdbadabbdbbdabbdbcbddddccaddadcabbacacdbcbdaaaccddabdacaaaddbdccdabdcaaaccababdadcbbcdcdccddddbcaddcbaabccaaccadcaaacaadbbdbdbcadaabbcdaaacaaddadcbcbbacabacbbcadcbccabaccacdccadacccdbcbacadaaaccadacacbdacdccbadabddbbdcbaacaccdbdcdcbcddcdaadadddcaabdacabdbcbcdccbddcdabbdddbabcdddddaaaaddcdcabdcddbabcacacddbacaddabdadaacdaadcbdabbdcbabddaccdcababdaacdcadabbbacdacbaabdcaddababdadbbdaaacdabcabadddcdddcaabcdabbaacaadabbadcbbaddabccddbdcabbdcddcdaaadcdcbcbdaadbaccdacadcaaaaaccdcdaaadaabccbbdbabcbcaabcccdaaaadbcccaacddacabdcccaacabbdbbdaaccaddccbaccaccdddbdabacadddabbddcadcccaddacabbddbdbcbabcbacbacadbbddbdbbcdbdccacbcccbacdcdcdbcbdabbdbcadbddabacddcbabadbbadaadbddcdacadacbacbacbaaaabbccdcbcabbcdaaddddcddcbabadacbabcaddccbbcddcbcccddadbcbcabaccdbadbacdbaadabadabbaacadadacdbabbcdcccbcbcbcddbbbdbdccdbbcacdcbdcbbbcdddcdccaadadcbdabdbdcbadacbcbbcdcbbcaadbaccdcdadbdaacdbbccdccabdadccaababbcacdddddbabdbbabaccbaabcdbdaabddabbdccdcbdccbbddbbbcbccdbdbbdaadccddccccddcbbadcccbabbbcbdabddadbdbddbdcbaaadbdbbccccdbdbadcaddbadbcbabcddccccbddddcdcbbabdbcbddacddddbdbdadbadcaadadaaadbbacabaaccdaadddbcbabacdcbddcaabccccdcadddccbdccdcbccbdbadacbbdbcddccabdbaccbccadadabddbccdcbaddcdbdaabaadcbbacbbbbcbbbadaccdbcdccabdaadbddacdacacbdacdddbdcdadbbcabcddbccbacdadcacbcbdbcbaaaadcdcbdbbcddaddccdccabbbbdcdabcccbbbbdcbddcdadadacdbbcabcddcdbbbbadacbabcadabccabacadbcaaabbddddabcbadacdadbcddbadcdabcdbbbddbdadcacadacdbdaaacababacbdcdaacbdacccbaabdadbdadbcaddcdaddadbddabbcbdaaaaddccdddccdadcdbccdbcbbaacacccdadacbcccadbddcabddddcdabbdbadaabbdbbddccabbcbdccdabbbdcbaccacdacbdbdbbaaccbaaabaddcbdaabcaaadaaaaccacbcdabcddcccdcabdbbcdcbdcccddcacdcaabdbaaadcbaadddacccaabbacbddbacccacbbabcbcaccdccdccbbbbabadbccdddcbaacbdcdaccdbdcdcccdddbddcabdbbdbdadabdbabcbdaabccbdcbbdaadaddccababacacbabcbabcdcdadccdbbbadadadbcdbcdbdaaacbdbacbcbbccababbdddadacdccbbdbbdbabddabaadcdbbbccdbbadaaabcdadabdaadacbbbcbcabacadcdbcadbbabcaaacaddabdddcdccbbaadadaadabdbbbdaadadcddaddabdbabbdacdbdcbccaadddabbdbccbababcdcdbacbcddbdbcbbabbacaddabbdbdddbcbcbcbccddccaacdbbdcacacbdbaacbbbaabdaacdbbcacabbaadbbddcdaaabbbccadbcdbdcbcccccdcaadcdbdbccaadacbaaadaabaaaacbbabbcbadaccbbabaabcaddccdadcbcbbbcdcbcaaddaaadbcbaacbcbdbdaaaddccccbabdddbaadbcaadbdcdbadacbaadbbccbcbdbaaaaddbcbbabcaaaccadbdaaaacdbbdaadacdcbabacaaaccbbcbbdabbbbbadbcaccddddcaacbaccadbccaddcbcdbabcaacaabdddbcbcbdcabaddcbdddcaadbadcabbcdcadcddcccaddacccaadbacdaddadccbdcdddcaaadaadbbabcdacbddcadabbdbddddabaabaabacdcddbbbdaaccbbbaaddddddadbbacddadaccaabdcdccccdbbbabcbcbddbddaaacbcdcdbdadbadccbddbcbbdbbdabbaacbdcbadcbccacbcbdccdabccdbbaadaccddadaaaaabbdccaccaadcbacdbccdcacacddababcdbbcddcacdbbcbaaddbbabcdddabddbddbaccddccbdbdccccacbcdddacbdacadadbbaacaaadbcbaabbcbccdccbcbacddbdadcbccbbbdacdbbbaaacaaacdbdbaadbdbbdcdaccbcbbabcddccbaadadcbdddadbcbcacadddcaccaabdbbbaabddcbaabcbdcbcddbddbabdcdbadacabccbccabbdaacccbbbbdbdcbcbcabcbbcddbadabcabdbaadcccbcabcdacdddabdacccaacddbbbaccbdcbadacadbdabddaaddadcccdbdbbbabbaccbabcabdcbbddbddcaccaadbabbadbadcbccacbddabbcbdbcbdddbabddbabcaabbdadadabcadacccbbbadddbbdccccdaacbbbcdcdbdbbaaccdadbcbabbbacdbbcbaabdadadccadbabdadbacadaacdadabccaabdbbabbdbdddcacabacabcaaccaadadddbcbccaaaddacbaaacbaaacbbbbacddacbdccaccddbdcacdbddbddcbcbabbabaaccabddadbdbadcabdaadcaacbcbacdddacdbcdcdadcbddcbbbdcbacddbcabcaaadbdaddabdcccdcddabcbcbaacaaaddcdccdacbadacbadccccdccdccbdaaaccdcaabcacbcbacaadbabdbcbbdbbdddddbcbacbdcdbcadbccabbbabcabdbddbabbadccaaaabbbcacabacabaddcabbbbbababaccbdbacaadbcdbbcaacacdadccbccdbdaadadacbcadbccdcaddcaaddddcccdbaabaaacaddccadbbdababddaddbdcdbcadcbbaaacadacbdcbdbabdbccbdbacabbaabbbcbdbaddbbdbcadbbddbbbacdbdcdcaacdacbabacbcdcdcbcabbadccddadacacbabbdaaadcdcdadabcdccdcaadacbbcdccccbdbaadccddbcabacccaabdbcdaababcdcddbdbbadbaadcdbcadcaabdcadcdaaaaabbdbcbddbacabcaddcdabbddadacbcadbcbaaccddccabaabcadbcddabcccabadccbbbbcacaacdcbaabddbbabbaabadbabcbdbcdcbdbccaccbaacaaabadcbbdbabacbadcadbbbddabbcbdbacaaacaabcaddcddadbaaaadbcdbbacbadbcbdababdaaadcdbbcbabbcccadddccbbddadaabdcdbddddbbcccbabbabcbaccdccbbdbaddcdcdbacdbdccadbccccdbcddbbddbabcdbdbacdcacdcabbcabcdcdbbabddcbcbbccacdbdaaadabcdbcdbddcaddaadabacacbabcbacbdabacdcabbbcdcbbcdbbcddcddbadbbbbccabcbdadcdbacaacacdcbcbcbdadbcbbaaadcbcccbacccadbbbcdcbaaccdbabdabadddacaddabcabbbddcddabdabdcbcbbcaaaaaddcaccbacbccaaadcbbcaddcacccbdadabcccbcccdbddcbdccddbadbdddabcacbddcddcddbdacdcbddcabcbdcdbbbcaddadbabcdbdcbadbdcdbabacbaaaaddadbcabcadcdbacbccacbaccbaadaacdddccdabbbdbababbadadcabdcdaacbccabbbbbccccaccddcbdbbacbccbaacadaddaaadabcaaabcddcadbdcdbdbcadcccbbcdcdcbcbaadadcbcdadcacbcbdaccbdacabadacccadbdacbacbbdabbcbbddaaaabbddbbcdacbaadcdbdbbaabcbbaacdcddbdaabadddddbdabbdbdbadbaaccddabdcacadbacddcabbbdbaadcdadabccdbcaaaaabaadcdbabacbbabadccbdbcbbaccdbbccbbcbbbbbbadbbbcbdaadbcaabbbdddadbadbdbdabacbdccbdaaaddddadbcabdcdccabdababdacacbaddbddabbcadbdccdaccbcbacadadbaacaccacdbccbcabaadadbcbcddcdbbdccdaddccbdacbbcbcdabbaabcdcdaadaabacccaaabdbcdbbabaabcdbbdcccbbcadbadbacbbdbdddaaaacdbaaaccbcbdabbbbaabacdddabacccaaacbccacdbaacbcacbdbbbcdacccabbacddcbbbbaccdadabdddbdcacbdbabbcbdbcacbbddcadabdbdbdabadbbddcaacdabcccdaccaacbdabaddccdcacbadbabdcccbaadadccbabbdcdccbcbdcdbcbaaccbbdabdacdababdcdbdacabcdcabdccabddbadbbbdcaccdcdacddcddaabbaddbcddbdabddcccaabbccacacaaadcbaccabaabbcbabbdcdabdcadaccadbbcabdbabacdbbacbbbdabbadabdadaadcbbaaccddbdabadbddbbacbaccbdaaaacabaaadccbbdcdbbdacbaaaccacabbdbcbccbdddcdddccbaaaadadbdbacacdcdbbbcabcddddabacdadbbdddcbcdbdbddddccdcdaaabcccaabaabaacbcaadcbbaadddaabaaddaaccacddcabacaddbcdbcbcabcbdbdbcabaaaddaabbdacacdaadcdbabdccccbdcccbabcbbccbbcdcacacacbddcbaaaccdbccbcadcaaddbcadbbaccbacdcaabbdbacabbadaadadacadddabbaabbaaaccbadbcdddadcbabbabdcddcdcdadbbacdbbacadadbacaacbcddabbbadcdddcbacbaaacbdcdcbbdcddaabcdcbaccbacabbadadcdbcaaacdcbdbbcbcacdddbacdacdaadddcbcdbbadbaacabdacbadbddbacabcdbdcbacccbaddacbadccbcdcbbbdbddaddccddbdbbacdbcdcbdcaaaadbcddbacacbacbcdadbccbabdadbabbaabccaccdaaccdcbabbbcdbcacdcababdcacdbacabdcccccdbbadbdcadbccabcdcbbdcdcccdacabacabcaccdbbadddbcabadbcabdaccddddddddcabadbdaddbabdbdbccacacdcdbaddcbbaccccaddaababaddbdacdcaabcdcadbadbcccaadcddbcdcdddcbbcbdddddaccdbbbabdbaabbccadbcaddbcadbbaacbdcdcaddabdbcaadddbdcddbddcccdbaacdbbbbbacabdacabacbdddcbbdbdacaaaccabbbacabcacabacacaaaaaaabbdbddabbbcbdcabadbaacacbdddcddccabdababddbbcddcccccadbcdabcbaddcaaabccbdacdbabaacbbdcbaccdbddcdbdccbdbaaabaccbcaaabdcdacacaabbcdcbcbcbbcdabdbcdbdbbccbdcbdcdcaaacddaaaabcabacdbdabacbcabdcdbcabaccaccadbcddacabcccdbacdcbdaccdbdddbcbbbdacdaadacbdcbcdbaaaddaddcbcccaddbccacdaccabbbcadcdccadddadccdcbcbabbbbcbabdccaddaadddbcaacddcadcacaadcabdaddacdcbabaccabcbadbadbcddadbbbbadacbddbbbbbdddabcdbdabccbcbdaadcdcdbcbadbcabddbbadaabdcbcacacadadbbdcaadbdbbcdbcdcabbbdcaadcdbabccbbbddccbadadabddcdccbdcabaadaabcddcbbbccbcaacccadacbcbcacacadacdbbdcabdbadcdcabcdbababccbadcdbacbacabaadbaaadbababddbabbccadcdaccbbabacacbbadbabaacdcaddadbdabdbaddcadddcbdcdcaababddadaaacdbbbcabadbdbdcbdcabbcddabaddbdcbbacbadabbddcbdbddcdbccbbacbadacbcdbadaccacbdbdbddbcabbcdadbddabccbacbbdabdaadcbccddcdbbccaaabaadacccbcbaccadddbadcdacabbabdbbbdaacdbadacbbdbabcdbcbdbcabcadbadcccdbabbbdabbbdbacdaaddbccbccbbbdbdaaadaccdabdacacabaacccdcdbabcbdcbaaccbdbddcbabacabcdccbddbdcabbddccdaccbbcbbcbaddbbabaddccdaacdbccbcbccbbcdbcaaadcbbccccbacacbccadcbbddabacbaadbaadbcdccbccdcbaddbcbaccbcdcacbdbdddcbacbadcdbabbaaaadddddbacbbadbaddadcbdadcaccdaabbcdccdaaadccabadabaabdbaaaacacbcdcdbaadcbbcbaddbdadadadbbbdddcadaacdaddaddbccadbdbcdbbaccbadabdbddbcdaddbbadccbdbaaabdadcdcbbbbaaabdbacccddcadbaadbadcbddddacdacaaabdbbdabadbbaccddddbbccaaaccbabdcdddaababbbccbbaacaacdbacaddcbdcdccaadbaacccacccdbbddccccdccbabbdbddcdaaabdabadcdbbcdbabbddbabdddcbcbbadabaccbbaabaacdacdcddcbdadbaadbdcadcabadcbcdddadddabddaacbadbaabcadcccdccacbcaabbaacbccadbadcdcdaccacabaadaabcbacabaacdbdbbbbbaabadabcccbcbddacdcaacacdadddacccacadaabdcbbaadcdbcbbcadaaaaacddcccaddadcdddcacdbbccbdcdacbdacbdbcacdbbcaddcdacbabbdadcbdbaddddddcddccbccddacbcaabbddaaababadcacbbcbddbadadddddcccabbcacbacdcddadcaacbbacdabaadacbbdbcbcabaadacadabadaccaaaacadddcaccabaaddaabadcdddcabbdabbbbbadcdbcaaaabbcbcccdddddaadbdddbabbaacbabcbcdcbbadaaddacdbcdaaccbaabbaaabbbacbccabddabccbacadcccacccdbcabcbbdcabddcacbcdcbbcbaabdabbccdbbbbaadacabaddadaddddbabdcaabdcbabacadadaabbbacacdaadacabbcdbdacddbcdbbadaadcacccbacaaccddcabdcadcdacaddbbddbbdadcbdbccdcaddbbccacccacbccadacdbbcdccdacabbdcdacdbacacccdddcabbaddaaaaaadabcdbcbcccdbcdaddbddcaabcaacacbbcbbcdaacdaadabbbbdcacdadccaaddcdddddbcbcbabbbdddaadadaaacdbaabdbaddacdccaccbcacbbbdadcddaddbdccbadbbaaddadcaacccccaababcabccbdcabddcabdddaaccbdacbcdcaadccdbbcbdcdcacbdababadbdaabbabcccbbddbadbdacdadabaccacabccbddbdccbcacaccbacbaacadcccddddbddbaabddccccaaadccdccdbddaacccdaadbdbadccddaaaadadadccdaaadbbadcaaacbddacdadccbacbcddccbcbdbdaaaaaadddacaaabbdbbaabbbbddabbabccadbdbdccacbaaadaddacacacaacdcbccbcdccbbabdbcdcabababdddabaabaacbcaadadadbadabcdcabccbaaadadbadcbaacaddababbdadaaacdbbbddcadadabdcabbadbcbbaacdadadbddacdcbbcbbdbabbcaaccabacabcddbbababbbcbcdbacbcababadacbcbbdabbbdcbabbbdacdbbddacbcdcadaacdbdbcdcbccbaddcdddacabcbbacaaddbddacddcabbabdcadcbdcdabdcdccbcbaddabdaadacbdbdabadcdcabbccccdadbcaaccaddccbcbabbadcacccccbdbacddccdddadbaddabaaaaaccaddddcdcadccdcbccddaadbdddaaadaccbabbbddbbcaddacaaaadadadcbccccbacccdadccabddccadbdcdbdabaddacabcdadbbaddbbcaadddbdcbccabcbcddcdbbdccadbbdadcccccdabdcadddadacaaddcacbaacbdbdcbabaaabdcbaacacabaacdccadcbcdabdccdccdbbdacaccabadbabacccdbbbadbaabccbdcdbddbadaccbaadddbdbacadcaabddcacccbacbdacbddbcbcbcadabbbacdddabdbadcccaccdbabcdddcacdccdbdbdcbadbadbcbcdcbadacdcbbaabbbcbabbdbbdddadcaaaabcabdbcdbbddccdadcbacdcbbdddcbbbbacbbcbaacbabbccbbbdcccdabbaaacdacdaaaabcabcbaddcbbccbcdddbddccdbdddcdcdcabdadcdbbbdbccbcdddccdcabcabacadbbccbcdababbdbabcbcaacacccbbbadcbddaadbbdcaabaacdcbcbdcacdbaaabccbddaccbcdccadacadcdbadbdbdbbabbddcaabbbaabdaadaabbddcadacdcacdabddbcabccdbbcccbdcdccaadcaadccdcadcaacccabdcadccabadcdddbbcaccbcdbcdbaacddbabdcbbcdbcbbacbbbcabaaaacdccdaccdbbbbacabaaadcacabdaacdddbddddbcccbabbdbaaaccbadcaacadcbbcccaadadbbbcbacabcbdcddbadcbdbdbbcddcbbbdccbbbbaaaabcdcddbbdabdaddcbbccdaccbbccbcbcacbacaddddbabdddbcaaccdabbbbbbaddddbddabbcacababaadcaccccbbdacdccbadcccaddcbdccdbdcdbcddbccababadaaadccaacbacddbcbdcbadccaadcddcbabbcaabbcccdccddaddaddcaabcadaabbababdccacbddacdbbcadcccdbccbbbdbacabcdbaccabddddaabcbcbbacbccbbaccaccdbaaabcabccaaccaacabcdaadcbcdbaabdcaaddbadabdbacaacbbbcaccddbdcabdbcdddbbbcdbcdbaaabbaaccbdbbdabcdcabcccbcbcbdaabbbddcdacbbbcccaccbdcdddcddccbcddaabcaadbbbcdcccadacdbbcdccdcaabccacbdbbccbccddaacdbbabaababaabcbabadcbadaddccadcbbadadaaabcbadcdaaddcdbaabddaacdccdacdccddccbdcacaacdbaaaccbcbbadbcaaabcdacccbdaaddbdbcdccabcdbcdaaaddadabcbcccbddaabacccdccaccddcbddcddcdcdcbdabaccadbabaaaacbdcddcdcbadccdcabbadbbbccdababcdddbcbdbbcbcabaadcdabcaacacadddaabdbbcbcbbabdaddaaccdbdbbcbadbadbcbdbadabbccbadaaaccdcbbbbddabbdbacabadcddabdbbdcbcdacaddbbabdbabaddbabbacabcddccbcabccddbdaacccbbadcddcdcbcdbcabbcbbbbbdccbaddbabacbddccacdadbbdbaccbbcbbabddcbdaadaccaaccdccbaaabdcbdbacaaddadcacdbbdaaacbbdbaabacbaabdcadbddadcacacbabcbabccccaadddadcbcacabdaaaddccdcadddccbcaaaabcbcbbdccccdabdbababcaccdbacacdcbcccbdadbcdcdaaabcbbbcdbadaccbabcacbdaddbdbdbcacabcccadbacddcdaddadadbdddabaabcbdccdadaaaacddbdbbcadbcabbaadddcbbbbdaadaaaccdbdbbacdaddcaddacacbdcabbbccbcdcbccbbbbddcaaccbbddbddddbdbdacadacaddacabbcababdcbdbabcadddbcddabbabdccbadabaccabdcccbabbccbcbdbcbbdcdbccddccddddbdddacdbdabbdadcdbabbadbbdaddbaddbdabdbacccbbdbaccbbbababacaababdcadcbbdcbadcbdaaabadbcbabaabbabdbdbaddcbbabdcbccacdbdccbaadddaaadccadbacbabadbcaaabddacdccacabccdadbaacbddbcacaacbcdadbdbcddbcdbcdccbdbadacacbabadbbbdbcccdcbcadcdbbcaccbaaccddbbbabacbbacaabcaccccaccaddacdaacbdabacadcabdbddcbaaaccaacbdddbabccbacdcddacbbaacbcaabdcaddaaddcbdadbbbdacadabcadadaadbacdcadbdabbdbadaadabadbacbaadaadcddadcaabbcdcdbbdbdbcdcbbccacaddbbcaaabcdccabcbdaadbcdbccdbdcabddcbcababcdadbbbdcdcdddabdbbddabbcacabcaaabbdbcaabddbabbdddcbbdbdbcbabdaccababcdccabdccabbcccbcdcbaabccdbdaacaaaddddcbcadbcabadddaaaacadacdbbabadbbdbcaccbbbaabdaccdcccadccccbbcdcbaabbdbadccdcbbadbaadbcacdadbdbccacdcacaabdcccadcbadcdacbdbdaacdcaadcaacbcdcbaadbccbdccaacadaabadbaccdaadbdcdbdcdbbbcdcbabaadcbabbcabccdcdbbabadababcdadbabccdcdddcbbababbbcddcbbcccccacbaacbadabcdddadaaccaaabacbbabdadcacbcdcabababbdbdbaacbccccbbccabbccaddbddbdaabcaabdcbdddcbdcaadcadcadccbcdbbbcdabdbcdabdddbadabbaacaaccbaaabbbddbbdbccdcaadbddadacddcdbbdacdbadccbaddbbabcdadbdbcbbbacdbddbabcdadacdcbbabdccadcbbddcbdabccaaacdbdbabacabcaabdcdbcdaabbbcdbaacadddcaddacddbdbbadddacaccaaaacaabdbbbdabcdbdabbdbcaadcacddcbbaacaccacdcacccbdadacaccaabcdddcdaabbcadcbddcabbbacdaaaaddbdacdabdcacbccdabdadcadabdcccdddadbadccbcdddbcaadabcdabdbcdaccaadccaaddabacbddabcdcdbacadaaababdcabcccadbbbbcaacadddcaadbdcabacabcabbacdadcdaaadbabaaaabbaccbbdcbbaaadddccadacdbbabacacdcbdbcabacdcdcaccbdaddbddacbdcbbbbcadcdcaddbabbbbcdabadbddbaaaccbdbcbdbabaaadcdadbdddbbacdacdccbabcdbaacbbdcddccbcdbcaccaabadcddadcdbbcccbabcbaaabadcaabcbcbcaccdcbbabadcacddaacdddabaadbdbbbdcddcdaabacdabdacbabbcdbdabcaabadbcbaccbdcacddaabbcadbcdbcbdcaadccbadddaaaccadabccbaacbaddbabdcccabbbbaabddbabadbdabcacaccbbbdcdbaabddbbbadbaccccdacacccdbdccbbdabbcbdcbdcbdabddcddbccabcccbcddcbbadbaddcacbacabdabcbbcabdcbabccbaaddbccbddbdccdcbacdcbcdbdcacadcdbccbcdccabdddcabdabbdabadcacdbdbcdcaddcbdabdddaabcdddaddbdccbbaabbcbabbbcddadadbadcbaaacbcbcacdabdbbaaadbdaabdbaadbdadbaaabbbbaddcddabacdaadddabaacdbccbbdcadbcccdccbddbdbbabacbdccaacacaccadabdbdccdadadbbaaacbabbaabacccdacbbcdcccacabcabbdcabcdbabbacbbcdcaddadcbdacbcacbdbdcaabdabbbddaccdaaabadbbabacccdbdbabbaacbacbcddcadbdadcccabbbdbcbbdacdcaddadbbdaadbdacdcbdddbcadacababadcbaacabddacdbaacdabbbddcbdddccdcdadccbbdcbcacbcbbddabcdccdcdcdcadcdcadbbbbbddabcccccdbdbdbcbbabdcabbdbcbbccbbdcdababcaaddddbddccabcaccbbaccbdabdbdcddccddacbabaacaddcdadcccbcccdbbddcdbccddadbbbdcbddabdddbacaaaccdadbcbcdcddddcacccbaadadbdbaaaaabbcbdcaaaaacacaccbdaabcdcdadccdbdbabacacdbbaadabaaaacdbdabbaccbdbdddabcacbcadbabcabacdcaabcccbacbccabcdbabccbbcddbadbaaabacaacdbcabcadcccadbccddcddddccacbbdcacdaddbcdbddddcaaddbdababbbbcbaacaacadaadddadddbdcacbbaaacacdcdcaaacccbbacdccdaaabccccccdcbdbcbbaabacdacabcdadcabcdaddabdbcbdbbbddcddaacbddcccbdbcddaadcbaabdbcaacbcacbacbdcacddccbadcccaccdabcdbacbbbdbdbcbcbbbcacbdccabcbdddbabcbbadbbbcbdacdacdcbdacadcddcdccadbbddabaccdaaaabadbbadcbabaaccbcbaabdacdcbbabbdacadbacbdacacddcacdcdcacaaabccccdabbbbbdbcaddaadbbbdaaadabdcbabacabdccdcddbbacabaacadaadbcbcddbcbccaaccbcaabcdbabaaabcadacbdcddbaaddabcadcbacdddcddabddcbdaddbabdadadbcabddadbbcbbadbdbdadcaddcbbadbbcdabdbdcabddbdccbcdbcbbdadbcbccdcbcdcaabdbaababdddaccccabcbdaadcdaacbddbbdbcbaabadaaddcabacddbbadcabbdacabddbcccabbacbadacaaabadbbbdcbcbadacdbbabbdcdbcbacabcbdcaabddcdaadbbcacbdcbbcaddcbabbabcddcbdcabdbaabaacddddcccbcacdaaaadacdadcaccbbddccabccaadaadabaccbbcbcadcbccadabcbadaabbcdadbbaaacacabcbccaadcbcccddbdaacdadacbcbddabdcbbccadcaccdbacaccacacdbddadddddddbcccacadbbbacbbcdcdddcabbdbccdbabcbcbddacbababacbaabdbbbcaacbaddabaabbdbabadbacddaabbbbccaacbccdbcccbddbdabbdcabdbddaabdadcbcdccacbbbacabbddaaddadacbdbdaadacbdacaacdccadcacaccbbcbcddcdaacdbbaaaabdcacccbcbbccbdabcadbaabaacbcacacdbbdaddcdccbdcaacaabbcacdbccbdbccbcacdddbbdddcacbabbbababcbabbcddbbcdbbccbadaabbbdadcabadcbcbaccabaddabcbadbddccacbaadcadcdadddacdbcdacbddbcdcddbbdcaaabcaccadccccdadabcdadbdbcbadcdccdacdbabdccdccdbddaaddbcbaccabddddcabcaadcddbcabcaacacabcabbaddbcddadcacaacdbacbdbabaadbbadcdddcacbcccbbaddacdcdcccbcdbadacdcbbccaabbdbabcabacabbdacbccbbcbcbdacbdcacacbaadccbabdabbbdaabcddcabbcccbaaaaacbbcbbbbaadadcbabcccdbbaaccbcaabdccdcddcbbddbabbbbccbcaddaabbdbccbcacbdbcdbdabaacbddcabaacacdaaacdbaadabaabdcaacdcbddccabcaacadbdbabddbbabbaccbadbcabbcabbbbcbcdcdaaaacacbdaccadaaaddabdabaddddddabaddcccddcaccbbbadbacaddacddcddcbbdbdabbbcbcdcdcbbdcbbcaaacdccbabdbdaaadcdadbadbbdcdadbbccabddbbbbdddcdbcaabdadbbdbbdacddddbcaabcddabddadaaabcaadacaccbcbbadcdbacabbbabcbccadcdadbbadcaddadaadadaabadcabadddaaccbbccaabadadbbcbbabcdccddccbddabcbcbdccccaacbdaaacbbdccdadddbddaabaddcbddbcacaddbbacdacbbdaaccccabcbadcabadbabdadadadcdcccbadaaacabdcadaddaaadabdadadcddbabdabbdccbbdbbbcbbdcdbabdbdbcdbcabbadabcddddabcaccdaddbdbdbbbdbbddddbbdabddddaddcabdbbbbaacdbdcddaadbbaddbaadacacccaaddccbaccddbbaaabacdbdcabaddcabbabbdcdcdbbdbcaabcccbbdbabbcababdaadbddacddcddddacacbcbddddbcdabbaadadbddbaabdaabdcdbbbdaccacdaccbacccacbabcabcbbadabddcbbcddcccacccacddbaabbbcacbacdbcdcbdbccabadbaddaaccdaccbddcacdaaabbdcabcdaabdadbddbcdbbdcdddddcacaaadcdbdbbbacdaadccdaacdabdcaadaaabdcbdbdcbcddabcdbdcdcadcccdbcdacbccbddacdcdcdaaaaaadbaabbdbadcadbaabadadcbddabcaddcaadaaaddbadbcccadcbdcbcaccdcabcdcacbccbaaaddabdbcbdaddbdbacccaccadbdaaabadcadcdadaabcdcdbabbbdcaaaccdcccbdcbcbcbbbaaccdbbddbdbdacdbbddbbabcbbabbbaadbaadabdacccaadbadcbdbacbdcdcdcbbacbdddabdcabbdacdacaacadddcddcdacacdaaacbacabdaaadcdadbdcbcabadbdaabdccbdccbddbdadcdcbaaddcdcdaadbadbdaabcdccddbdddacadadcbcbccbdddcbcddadbabaaaadadacbacaddacadcdaccdcccdccaaacbadbbbbbddbcadccddcbddcbabdbdcddabcadbcbabacccacbacdadabcbbbcccddbcabadbcddcdcdbbbdcbdaacdbcaadadcbdddabbacadbdcdcccacbbcbbbdcbcbaadadbdbbddcbadaabcaacdddcdacababdabacabcadbdccabaabbcabadbacabdbdaabcdaabddddacacbdcbcadccbbbcddadbdbbcabcbbabaaccdaccaaddcddccbbcbddddababababaadaacbcadcbbbcaacabadacdcdbbddbddacdaaacbbbbbdcabbddaaadadabbccdcaadbcdbbbbdddbaacacccacddaadcdacaddabbcdcdaadccbccabbcdabbbcdbbacaaacaabcccbddaacddcabcadbbdcabadaccdaaadbdaabbacadaabbddaacbbcddacbacccdcdabbaadbcccaadbabcbbbaaadcaadabbdcadcabdacdbddabccccdbbbbcbacbbabdbcdacbcbbadbbacdbdacacdcccbdbdbdbbdcbcdbccaccdaaacdcaddcacbddbddbbdcbdbcaabdababddabddbadaaccbaccdbdbcccddbbadddaadaadabaaacbccccabdbadaaddcbcaababbbaadbddcccdccbcbbcacdcddccadaabadbbdabadbaadacbcccccaaaccadacbdbcaaccddbadbbdaccdcccbcdbbbabacbdcaacabbbbbcddcbcdbbcababbbbbaabaaaacdcbadadccbcbadddccdadadcbcaabdcaccbbaadcaccdbaaabcdbbdbbbdbcddbccddcaddbdbbbcdabddddcdabadbcbccadaddaccabcbaaaadaccabdbbcadadaacdddcddcdaddbcbdabadcddabdaacbdcccacaadbdadadbccacdccbdadadddcccdcaddbcddbbabdbcaadbbacdddbbaabcadabdbbaaadabcdbabbababdcacdccdcadadabbbcaaabdacaacadacccccdbbbadbccbbcacdbbddbadcdbdbacbbababdbcdbddaddbaaacbdddcaaadcaacccdcabcabddcbddcbadcdccdbccbcadcdbbbcdddcbbabbbbacbbddadbccddbccaaccacadacabbccbadcdcbacbbaacabcabcddcbbcbddcbdaccdbadcbbbbcabbcccbacbcadbaababcddaaadbddcbabaaadabbabdccccdcdcaccbcaddbdaccbbbdabbccbcadddcccdbaaaabbddccbbbcdbdaacddcdddcdcbbaaadddbcdbcbbabaaabacbcbddabaaddacdddccadadcadcdadbdcacadabbcbbaccabdcdbbbdadccddccdbbacccaccabdcbccdbcacbdbbaacaacdabcbaadadcdbbcaccabbbdacdcccbdaacdbabcccacbdddccbbbdacabcbcbacaadccbbacaaababbcabbbdcaddabdbccdbcadcabdccdabbbcaccbcaccabccbdcbddadccbabdcdccdbdacccabbdaabacaccbbaadbcaabbbcbabccbaddbbbacbbadadaaaadaadadbadacbccdbabadcbaddcdddabcadbdbccbdcbbbdccdcbddacbaacabcabacabaaacdacadaddddbacdabddacacbcadcccbabdaababbbdbddcdaaadbccabcbacadabcddababbabdcabbcdcbdbaacacdcddbccbcdcabcccbdabdadbdadbdcbcdadabdabdcaccacaddbbdbdabdacdddbcadddbcacdcbabcdadadbdcbcbcabbcccabaabaaccaacadccdbdcdaabcaadbbabcabbbaadaddaadcbadbadaddccacbbccaccddadabaccbaadbdaaabdcaabbaaadbaddacadbcadbbadaadccabbbbcacbdbbbcbabaacddadaccccabbbaabacdcabdddbddacbacdcacdacdbbdcccccbdadbdbadabaabcbcadadaccbaccbabacadcccadcdcdbddccccbaccdaacbccbabadcbadcdccddaabbdaccbbdbbdadcadcbdbcdcacacdabdcccbcabcdbdcbcddbbdbdbcabaacabbdcadabdcaadbcbadbccaabccdccbdddaaadaddbadbcdaddccbaaacadddbdcdcdcadadcbcddbbdaadadabaaddccbbddcadcdadacbddaabaacbbadcabddabdacdaaaaacacadbdadbddbccbbdbbccbacadadabcdaaccdbaaaadacdacbddaccdbdacaccdadddcdaccdbbadbcaccacccadaaaddabccacbcacbcbbacabdcbdcaaabddaccadbadcccdbabbbabcacbcbdabaccbabddcabbcbabdbacbbbcdacbadbbdacccbdcacbacbcdcbbadccccacaccdaccdbabdccbddbbccbadcbbdbacacaabaccacaacaddabbddbccaabccdadaaddbcacdcadaacabadcaabbabcaacdadadcddacadbddaadccadbdddbcdaacbaaaadbaaaadccdacdcdbcadcaddbbcbacbdbbbabadaadccabdcababcaadadacacaabbacbcdcabaacacbdcdbbdcccaaadddcdddadbccadaabddcbdbcdccbbacdabadbbbbbbcabbdabccadccaddbabcaadbdaddbbcaaadcbaaacabbaccdcdbadaabbcccabcbadcaadabdadcdbbccabdaddcccadbcddddabadbddaadaddacbababbdbacbadaadcdcbddddbcbbaddbcdcdadbdaabddcabdcabcdcdbdbbdbbbacdacccbdcbdbcacdaaadadbddbaaabdcacacddabcccbbabccdabaddbbbcabcdbadcadbbbacdbcbaaabcdbccdccaccccddcdaababbdbcabdcdccaccbcbacddbdbccccdbccdccbcabcbdadbadbacbdaaacbaadbaabaaaccdddacbbaaadcbacabcbbddbabdcdcccdbbbbdadaabdcccaaddbddcaaabdcbabbcaabbcaadaaaadabbcddddbbaadabddacccdabacaadabbaadbdbccdbbcabdccacccbcbbbcacacccbadaadabbbdcdbaccbccbddaacbbbdaacddcdacabddaaaccbddbdaadadcacdabdcaddbaabddcbacdcdabcbcadabbddcbabacabdbcabdadaabbccdbcaacdccacaaddaacbaaacacdcabdadaaaabccddccaccbcdbccdabcccddbbaaaccdacadbbbdcbbcccbcbaadbbbbabadbcdacbbcdadcbbbcbbcbacadadbcddacdbbbaccbccddccaabdbdbbbaadbaccccbcabbccbbbcbbadcbdcaaaaddbbadcddacdaaddcdacbcbbbddacdcbddbaaaaabcdbaacddbbbbbaacbdaaacdbdcbabbaabcddcbbdcbccbdbcdccbcdcbdaddabdcadadbacddcbbbbacdaccaadbabaccbbbacbdcdcdaabdcacadacabbdbacabcbdacdbddccccddbddddcbdabacbdbaabacccdadbbcbadadaaaabaccdccdcaaadaccbbbacadaabcbbbdcabddbadddbaddbdcbdbbcbbadcccbdcdcdbabaabaccaccbcdaababbbcaccacbababcadddbaaabcbdadccacdacbaccacbaccccadbccdcbccbbacbcdaccdbbdbdcdbcdaaacdacdcdbbddcaaacdaddbdbcbaadddbdccdcaaabcdaaddbbbaccbaacbcdcdcdadadacdaabaddbcbbddbaaaaabbdcaacdddbbbabcdbcbdadbdababccbdbadbacbccdcacabbadbaccdacbaadccababbcbcbacbdacddddcdbdacdbbdacbdbcaaadaacbdcdccbdadccbadabaddacdcdccaabadbcdccccbacbccccbddaabdcbdbdacddbbdbdcaacbadbbccbbbaaabccaddcacbcacacaaaccacaaaccadcbcbccdabaaabdadbdbaddbcbabbadaaddddcbddcaabcbdbbbcaddbcddadadbcbbaabcdcddcbdcabaacaaddddbcacdacbdcadabdacaabaddabdacdbbcccbcdbcbcabdcaccaacbadbcbbcbcabbaabcdcddcabdcabcdddacacabadbcbcdadcbdacbbabcccbbbabacdaddcacadcbbcbcacdabccaaadcbcbcabbacbccbbaccbdcadbdbadcdbdcabcbccccadbbbdaddcddbbbbcacdabdcdbacccbdacadaccdabaacbcacdbaadbbcdddbccabcddbcbbabdadaaadacbacdbcddbbbbdaaddadbcabbcddcadddccaaddaadbddbbdccaacbaacccabcbbccdabdbcbaadbcbdcccaabcacbacccddcbcadcaabacbbbbaddaaddcacbacbddabadcdccaccaaccbaadcdccadbddcacccbccbbcbcacdbaaddcddbbddaaddcbadcbcbcbbdcdddbadbbdabadcbabacabdabdacdbcdbbadcbbabcbdaddbbacacccddddcacdbdcbabbcabccbdaccdacacbabadaabbcccbacbdcbdbccbbcdaaababccdabbcacddcbbcbcabcdaccccdbadbddabbcdcdbbdaaaadabdccdbacbacadadbcbacdcbcbdccaacdbcadbacdadcdabbacbccbdbcdcacdbcddcdcbddacabbccdcacbbdbbdacaccacbaacdbdccddcddacdcaddcaccbbbbdbbaccdabaabdcbdabbadadbbadbbbadcacaddabdaaadbabadbbbaddacddbcaabdcddcabdbbdddcbbbbadbabccbadaabbaabdcbcddcdbccdddacaddacacaaabdbabdcddacbaaadadbddaddbbcbbbccbaaaccbcacccaccacaabaaccdbbcccbbdaddaddbabcdbacddbbdaabbddcdbcbacccaddbdaacdbadccccdccdcbbdbdacabdbcaadbdacbbdbaaccccbbadabdbbdcdabdacdcababbdbcddbaddcbcbdacdbbdcddcdbadbddcacbbcccdcdddcaddababbadccadcdccbdbddbdbddbccdcaaacadbbcdbabaabdcddbdadbcabdabdababdcadaddababaaadabadacadaaaaaacdaabaabcadcccbbadaddcdcdaddccccbabddbbacbdbcabcdadbaadcaaacadbcdcbddbbdccbadbdbdaabbbbababdcaaabdcbcabcdaccbbbbbcabbcdaabccbdcaabaacccbdbbcddcabdcababacccacabdbcbccaccbabcdddcaaaabcbaaaddaacaaaccaccccaacdacdbbbaaadaacadcdacdbdddbbdccddcdddddccbabaadaacabddbadbdadbbabdccddbdcccaaacdbccddcbaabbdcbaccbcccadcaccacbbdbbbbcbddabdbacaaccbbaccacddacbbadcaddcbaaadbbadbdbdbacaabcaaadabdddabacdbdcbadcddddaabaddadabdabaccabacdbdbdbacdbcabbcdaacadaadbbbdababdabdbdddadddaddcbdbaacacddadccccacabcdcdddbdcbcddddcccddadbbccadcaabccbcacdcadaabacdcbdccacadcacbcddaccbcddbcacadbcbbbbcbbdbadbdbadccabdcbbabccabdcaccdbbcabcdbdccabdbadadcccbbcddabcbbbacbaacabbdaaddbcbbdcaaabbcacbdddbbcabcacdadbaddbdcacbdcbbbcacdbcabadcdacdbbdddcdaacabacdbbabdbccaadaacaadccddcaacddccccdbccbacbaacdbbabbcccadddcaccbbaddabcdbdbbdabdacababadcbccbdbcacaadadcdddddcdcabdadaaaddddabbdbaadbaccadaabbcdcaabababbddacdbcbababcdcdacdabbdbccbaaaacabaacccccabdaddabcdddccbdddbddcabdcbbdcdacbaabababbbdaacaacddcaddcbadbaddbacccbdaabcdbcddcbabaabbdadabdabadbdbcadbabacbbbbabbbbacadcdadbcbbbabdabbbddabcaabccbccadbbadbbdabcbbdadcbacdbcacadbbbcacabcbaadadddbdadcdddccdccbdddbdcbbcbcadacbbdbdbcccdbbcbbdaadaddbdbcccdddbbbdbdaddaddccdddaaadccbbaaddaacbadcbbaacadacbbdbdaabcbcaabdbdbdabaaacdbacaccaddbddaddbbcadbdccddbbcbbddcdbccdbacabbbbddcbbbdaddccacacdbdbcadcdcadbadbdaaacbadbacbadacdcacaabdcbcbcbbcbddbcdbdbbadbacbaabcbbdbdadcadcbbadcdbaaacaddbbbaadbddacacdbabccadbccbdabccccbdcbacabdbcdadcbcababbbcdadaaaccdbcdbcaaaaaaacbbcadbaddbbddaccccaacdcaadbaabadddbacdccadcdaadccbabdcbbcdbccbdabacabcabaccddccaddacbacdbdabaacaddabbccacaabccadbdccdcdbabcdacccbaaaddabcbabacdabdaadacaabddbdaddadaccbadbadcabccddbbbdbcddbbdcccbcaabaacdadaaabbdddacdaaccbdbbddacdccdabdcccaabcaccdbcdddcbdaddddaadaddabdaccdaddcdacdbdbcbbbdcadabccbcaaabaabbbbbbdcdcdacaabaaacbbbabcaadcaacaababdbacdabacaabbbccbbcabaaabdbcbbbabcbaaacddaacccdaadacdbadacbaabcbcaddbbbbababdabcccadcbbbcbaddcbbdcabdabcbdbbbbbaabddcadabdacaabcdcccbbbacadbcabcdacabdbdbaccdbddcdacdbaccddbadbbcbacdbacadbaadcbccbdccbacddccbcbbcadcdbbdbcbccacdcbdcaadbbabbdbabbdbdadaddbdaacabaddbdcbdaccddbcbcbccbababdaaabdabdadbbcadccbbcbdcbdcddbcdcbbbadacbcadaabcdcddcabaacacbddabdabddcdacbbdddbcadbbcacbdcbdcdcbabacdcdcccbbccbdbabcccdcaddaccddbdbcddabcccccaddaacdaacbdbacaabbabcbccbcbcbcdbbbaacbcbabadcbacbccccabaaddddbacbddbaccabcabadaabcadaadbadccadcbacabcaabcdcdcbcbadbbcabdbddaadbcaadcdabacaaaaaddaaccdcbadcdcdbaacbbbacddbdaccaaacbbaccddcddadadadbbaabbabccaddabdddacddbddbadddcacbdcbbcacaabdccdcabccbdbaadcbdcaccdbdbaabbbddadbbdabcdccbadbaabacbdaadddadcbabbdddcacddccccdccdaacdaadcbaddaacadccbadaacbbadaabdbbccdbbcdbdcbaacdbbacdaaadccadddabbbccbccdcdddaddaadaccdbbdadcaadcddbbbbdbbbbdaadccdacaadcdaacadabdccddbbdddbddcbaaaaaaaccacdccadbabacddbdddbabdabdccbcaacdabbbddbbdacdaddbbcdacbadbcacdaabddcabbbbaadcbdacddddbbdbdaaadcbcbaddbcadaccadabcacbbbcadadabbaadcbbaadcabbdcaccaaaadaabaddbbdbadbcddadbdaacddcbcbcbbcdbcbccddcdcbcdbdababdaddbacbaddcbdbbaadcdbaddcdabadcacacbdbbddaaabbaaccbbddccbdaddacdacacccdacbdccbadcbbdcadbdbbaccaabcdccbdaacacdaaadbcdabacbbddaaaabcdaacdddcbdbbadabbbccdabcccbdaaddbbcabcabdcddbdccacccdcdaaabadacdcddaccddadabbccbdccbbabbbbddbcbbaaccbcabcbadddabcdabdcddbcbabbcadbddbabaacaacadbdddcbadccbccaddbcacaddccdcabcbcbdbdbabdcddaacbdcccdacccbbbabaaccbbbbacaabbdccdcbdbabbabcddaaaccacbbcddbaddaaabcdbaababcacdddcbccdccbadbddddacacbcdddcadbcbdaacccaadabbaccbccddcbaaaabdbddddacaccaaacbcccbacaabadabcbdacddaadbbccaacbcacdbaabbbcddcbdcddaabbaddcaabcbacdbacaaabdcacdacbddabacdcaaadbbddccbdccbacdabcadacdcccdacaddbcaaacbbddddbbbcdabbcbdbccbadbccdaddbadbbabbcdbdbbdabbdcadcdadbbcaaabcdddbadbcdacdadabbadddcabdadabddbbcbacbaaadadbddddbacdacdcbcaabcdabdcdadaacdcbdcccccaadcccdbbcdbaaababcbdadacadadbccdaccdabddacccabdacadbbbcbabbaabadbcadcdcdabbacbddbdaddccbccbcdcdadbccdadbcacbddacbacccdcbaaaaaacdcdccdacbaadcaacdbacdbbdcbaccbcdcddcbccddbabbabccbdbbcdbccbdabdadbdcbbdbcdcdbabcabbaadabaacddcdabccadcbaacadcabdddaaacbaabbacbaaccbabcdcbdbbdadadadabbccacdcadaaacaccacbaadacdabcaabbbcabdbbadddbbdddadcddacbdabbabdddddcbbacaabbcaddddddccabbacadaaacbdccaaacdadcbdbadbaadbcdddcbadbcabacdcbcdbcdadabaacacbdcbadabbacbcbcbdaccdbbbdbaddadcdcbaabcacbddccbdbbbcabadcbdcddccdcbacbbaddcbcadacabbccdddabdadcabbcbcdcabacaddbdabbdbdbddbdcdddbdcaadcababcacdbabbaaccaddaabbabbbddcadcbdacbbdbdacbaabcbcaabcdbdddcdddacdadcdddadbacdcaabbddaccbdcdacabadabcbbdbdbbbbcbbadadbabadbdcdabadacbdcdaddaacaacbcbbddbcbcccadddcbbccdcbddadbdccdbcbcbcdbdbdadadabcbccadbdddbdccbccbbadbdcdbbbdcbdcbbbbadccbbdccccdbddcdaacbcbabdaaaadacddcdbaccdbbdaacabdbadccbbdadcbdcbaadabcbdbacbacacdcbdbccbddddadacbdabcdabbcdccacdbbacdabcccdbcccdbdbcaaadbbdbdbabdadcacbaaaadcdcdcbbcbdcbcaaddccaadaacababcbbcadbcbaccbacabdaadacacccacddbbdadcbcadbaadbdbcbdcbaabdadcacadaddbbabaaabaccccabdcdbaaadcaacadcabcbddddbacbaabcdcaadccabcbddbacaccbbbbddaaaaacbdaaacabbdddccdcccccdcabcbbcacaccbdcdbccacdbaddbbacdadcccddadcaaabddadacbcdadabbcdccbaabbabbdbcbabdbabdcbcaacdabbbccabcadaaabcabbcddcbcbdcdacddacaacacdcabbcbbcbdbadabcdbdcabbcdcdadaccacddbaddcccccacdabdbcbddaadadbcbccababdddbcbccbbcbbcbbbdaaccbbdccacaadcbdcccbccbddccdacbaaadacadddacaabcaacdbcbacacbcbdcdcdbadcddcbbcabddcccddcbddaddabbccbabbccacaacdadacdbddaddbcdaacbcbdcabaccdccdbddbdacdbadcabccbcaddbbbdcaadcddcabdadadbbcaddbadddabdabcbbbcbdbbcdcbccbbbdbcddaadbddacbbcccdcdacbdcbbbcbbdccacccbcbdbabdadbadcaaacbcaccbbccadaddbbcadabbdbaccbcddbacbdddbabdadbcaabcbbddacabbcbbacdcdbddbccaabcddddcdaadbccbcbbbaacdacdccddcbadbcbcacadbdcbacbabdababbbbcadbdddbaaddcaaaadcddcaadcacdcacacabdcbbbdddddbadaacaaaaccdacbdbadaadddaabccbccbcddbacbcccdbdddddbbbabccdabcbbdbdacbbbdddabdacbdacdbabdacababccaaadbcadbbcdaddadccdbbccacbdbbdccabacdddaccbbdbddbddcdcadacdabcdccbddddadabdbccddbdcbdcdaaadacabaacdadabadddacdbabbdddddccadccadbaaddbabbaaabdcbccabaccbddacdcccbacccccbbdcacdbbddccbccbccabcaccdaccbdaccaddbdcbdcdbddbcbdaabbdbcabdbdacbadabcbccbaabbbcdcaacdabcacdcdacddbcbbdbdbaabcaddabdabbacaabccdbcddadadcadbccddaababcabdabdaabdccacdcabbaacddabccaadbabbbbadcbcbcabdcacbcdccaabbccbadaaacbdcaaaaccacccbadcbdcddcdcbddcdcaaaaaaccddbbdacdcccbcaaaaccacbdadcbbcbdadadddbbbccddbccdbcabcddcbdbbbdabcbdadaacbadaccadaaababadcddaacaaabcdccdabcbccadcbcaddcddbcdbdaabddccaddbadabcdbbaabdcdbbddaacaacbacdbdacaaaaabdddbccccbcddadadaccccbbcbcaccbbdddbddddcdddabbbacbcaaabcccacbbdcaabbabacabadbbdbdcacdcababaddbccadcbaddaadbaaadcaccadbcdcdabddbbbacdbdacacabaaccabcbdbbabbdabbadccacbccdbbdccaabccddbabbbcbcabbbccbccdbcbdbcbadbaccbccbcdadabacdcdddcbcadcaccbabddaabadbaacacdbbabcddbcadbdbbbbcdbbbcddaddbbccbaadaadadccbcbdccadbdbacbbbcbcadaacdbaacdcbbdadcdccdbdacdabbddbcbacbbbbcabcbddadcbacbcdbbcacadbdbcbdbbdababbaabaacbbbabcabcaadbcbcddbcadbbddaacbcbddcadbaabbbacbdbadababcacccbddddaadcdcccbadbddcbdaaabddacdbddbabacbbddbccdacdbabbdabbdabacaadbcaacaabbaddcbdacbbaddccaabbdcddabdbbcbdabadabbbdaccdbacbdddcbcdbccaabbbbddcaddbdbccbaaacbdbdcdbacadcbbbacbcbcaaddbbddbcabcbadcbccdaabbcbccdbdccacacdbbdbcccdbaacdbddddaabbbdbccccbcbabbaddadbabcabddacccabaacaabbdcbbcbcabdaadbcbbababdacbbdcbcdccdcbbdcdddbabbcbadbadcabdcbbdbabcdaaabccadcdbadcaadccccadacdbdcabbbcdcccccdcbbbccbabacdcbbacdcdbddbabadcdacbdbadbbdadadcdaaaadbddcbdbbbdabcaadddbdddcddacaaaabccdcbdcdcbcbabcdaadddabbddacbdaaabaabcadddcadcaaaaacbdcdcbdddbdbcdbacdadbdadabbcdcdcdddbaadaddaabbaaababddbabddcddbbcbdbbcddaabdcbcbdcbcadacadcbdcdcbdabdbacbadabbaccaaabadbadcbccdaccddadcaddbdcdbcadccadaaccbbbcacbabbddadbacbacccbbcadabdbabacbcdaaadcccdabdbcdbdbccbdcadbdbcccdabdcbcdacdaccdcdaccdaccabccaaaadcbddabdccddaaaccbdcddcacbdbbbdcdadcdcaaadaadccadabbcbbbbdbdaddbaacacbacacacbbaaaacdabbddaacbabddadbadcddbbddcabacddcbdbbbcacdbdbacadacabadcaddcccbbbcadbcddcabaacbacddbdbcabccaaadaadbbdacaadbbdadbdbddacabcbcaaacacbaabdbdcbacbbabbacccabdccdacbbabacacbddbbacddcaccdbbdbaabacdcaaccdbabadcbbadbdbdcdadbccdcccaabbbaddcbcbccddbddcbaccadacacbadcccdddaddbddabadbdbadaaaaaddacdcaaabbcdbccdababbcacdbdddbaadaadcadaaccdcbcdddabccdcbdadcbddacccabadddabccabbcbdacbbaccbdadaacbabbdbabbadbcdabcddbddcadccbaabadccdcabdaccabddccdddbabbbadabdbbbdaddaaddccbbdbdaadacddcadacbcadcdbbadabbcccdcacdbacaccbdaadcdbabcdcabbcacaabddabdddcbddacbddbaadcaabdcbdddbdcddddbaadcaddbaabaabdcabddacbcdbccadbcbdcabdbcabcbcbbdcbacabbcacacbaabacacdadbdadbdcdccdadcacadcbccdaddcaacbcbdaadbacadaabddccabbcdcbdcacaaabacadaacddabdbcadcacaacbbdcdbabbdaaccdaadccdddbbaacabadacabdccbccbabcddddcaabaaadaabbdabaacdcadbbccaadcabadacbadcabbcacbabcdbdddaacbacdadccddacacbddaaadbccbcbdddaabaaddcdcdadacbacaabbbdbcdddbaccddddacaaabbbddbcdaacbbbdbccdcbabcdacdbadcdccbbdbbacbbcbddbdadbcaabcbbdacdcdcbdbdaabbadadaacabdbbcccddacaddacaabcbdbddabdaabcacddcbdabdbcbadbbacbcddccaadbbcaacadccacbcbacadaadbcdcdadbcdcbccdddcadacbbbcbdaaabcbccaaabaacabbadbdacaddaacccaddddadacaaadacabbcdcaaacdaccbcdbabaadcaccccddabbbdaadbcadaccabccaadacbacbcabdbdbdcadbddcbaddcabcabcadddccbcadbdbabccbdaacddadcbdbccbdaccabbdccccaabacdbadbdbcdadaddcaddcdcbbabdaacacdbcbbbadbadccdcdacababcbbccbadacdacbddaacdbccaadaacadcabdbccbbcdbaaacacdaccbadbcbbaaacacbdddadbdbbbaababdccdacaacbabbdddcdcaaacabcdbbabbaddabbbbcccaddadaddcaaadbcbbbaaadabcabdadababddabbccbbadbbdbdccbcaadcaadcacbadddacbcabbbcbdddbbaccbabbabcdadccdcaadbdcdcbdcaabcdcacdddcccbbdcbbbcdbadcbbdaddadcdddbccdadddaabdddcabbbdddadcddcbdacdaccaddcbcdddaddcbbdbdbbabccaabadccdcdacccdcdacaabadbbabbddaadbdaaacbadacabacdddcdacabcdcaacbadaddaadbbbdbbdadccdccbadadddbdbaabddbcddbcdbcadcdadddccdccbadabdbbdcdadacacadddbdbcccdcccbacddbbbbcdaacccabbaabdddbbabdcdcacbdabddacdadaadcaadbbaaccdcacabdcccbcbbbdacacdcccaacdaaacacdbdcbcaadcabaccddcaccbbbcbddacbacabbadaabbccdcddcbdaaabcbbbacccaccdbadbcdabbdcdcababacabadaaacccbdacddbdddcdabbacabaccddacbbbddbcbdadacccccccbdbddddabbacadbbdbdcacccdcacdbcdbabbcacccbbcabdadcdacbbacdddaaddacbcddbccbcaadabacadccdcddadddbcbbadacbdccacbdddabdddaabdbcdbbccbdbddbdaabccdabcbccdcbbcaaadbddbabcabdcbdbacdbdabdcbbdcadcabdbbcaaddcbbbdcdcaabdacddabbabacbbcacadadaaddacbcdaaddbcaaddacabddbdddccbcbcadbcaccdabcacacacbccadcdcdabadbcbbbbadbaabdcbbabcbdabacacabbdcdbaacadbdaadddcadcdcaacbdbbdccbdbcaabcddbabdabbcdabccacdbbdddbbabaacbbaabbaccacabdcdcbbdaabdadacdbaaadcaddbcadcbcccbdbbbadbbadadbabcdacacccdcddaacbccbbaacdcaadcbbbbdbdbcadbbcbbdbbdcaabdccdadcccaadcadddbbdadaabdbabbbbbcbdcdbbabacabaddccbdadabbadbbccccdbaaadcacbbbcbdcdacccbcdbaacdbadbdaccbbdccbababdbaacabcbcbcaaccdcbacbbdcbbbbdbdbbdbcddcbacbcbacbdabdcaaccabaaaabbaddcacacccdbddcacddddcbcccbcdbaccacaccbabcddaabdcadcbccccbacacbadcbbcadbdcbcbddadddadccccdcccaccaabccabcdbbbdbdcccaaaacdbdaadcbcdccaccdbddbbdabddbdbcaacdbbbcaaadbbbbadacabaadaaabadabcbdddbbdaadccbdaacadacaabbbcdadbccadcadbcdbdbbaaadbcddcdbdaadcddadcbcadcccddbbabcdcbbbbcbacdcdbbadcccbadbacbdddadaddbcbbcdbcddddaddddadbaddcadaacdbbadccaabbccbadcddacabcabdabccabdbdddaaabadabcbcddcbacadbaaacabddadacabdbddcabbabdacdbcbaccabdbbbddabdbcbbbabdbccddcdddbcdcdbabccbcccdcdbccbcabcdcacdcbacccacabccbbbddcddaacdbcddabddadddabdbbcacdabcaddbcbacabbbcaddaababbcddddbadccbcbbabadbcccdaabcacbccbcaacdadbabcdbbbadbbccbaabccaddcbddcbddaacdabaaacccbdadcadbccadbadaadcdbccdcabaabbbbcaddcccbacddabddaacbaabbbccbaadcdbbbddcbbbdcdbbbbaccaddaadbbbbcddbcacdbbddadccdccdcdaadbbccbababcdacaabbccadbdcadabcabdbddccccababbadaddccaddcbacddbcdacbaccacbdaddabddbdcbadbbdccbbcbdddcacddbbaddbaaddcdbbabcdabbbbbdbaccdaaddbdbbbcaadabadbcbcadccbccccccadaaccdbccbaddabdbdabbaadcbddadaabcacaccddacbabcaabcbadabcdbababbadadbbbaabddbcbaccbcbccdbdacababbcbabacddacbbbcacaccbdacaaabbabbdaaabbaababbbdbcccadbccaccaddacdcbcbabcbbbbcccbdabcbdadbadbadccccbddbcbdcbdbbdbcbadcabcdbacbaacdccdacdabcacddaacdcbbbdccbddbcdbadaccbcdbbbddaadcddaccbacdcdadacbccaadabdbddbaabcbccbbccacbcdcdaadadcbccccbdcbcbdaabcbbdacdadddcaccadaddddbdacccbdadabbbcbcdcbcbbccdabcdcbbdadbaccabcaadccbbbcaabacccbcbcacdadbbbbabacccbbadccabacaaadacdacabbcabbddccbdacabcaadacacdcbbccdabbccdbdddacbbcdbbdaacccccdcdbacbccabbadacaacaddccbddbadaabbbabaadbddcbbadbbddbbdaddbdadaacddaacbacacbcccdddabaadcdcbadbadaadabcdaacdbccbdcacbdbcddabababbaacdccadbddcdaadbddadaaaaacadbcbcbdbdabdcdbdaacaabcaccacabaadbcdcadabacdaacbdbbcccddbbaccaacdaccabccddadddabcccdcbddccbcaacbcccddbcadbbabbcdacdaadacaadabddacbdcbdcbdabccdcaccaadaabbaaaacaadaaacdbdaaacbbddbbacbcbcbabcdcdbcdcdadccccabaadadcdabbaacacbdaadcacdbbaacccbdddbcabcdbacdbdbccdbcbcbccddcbbabbdcdcabddcdbbcbccdcddcbbcaaddcdacdbbdbaddbabdbabbaababbcbbabcacdabbbbcadcaaaaabdaccccdbbcbcbaaacdcdcccdadaadcaaadacdcabccbbbaddabbaddadcbdbabcbdabdcccdcddaaadbaccdacdccbbacaabcbaacdcdbbaadaaadcbbcabbbaadbbabaabdacdbdddbccadbaddadaccdbaccdacabccabcadccdcdcaacbabadadccccabcabdccccdacbbbdbabacbdabdacbddadcdabbdbaccbabcbbbdbbdcbdcacbdadacdcdcbaccaaccdabacacdbcdbcadbcdadddbdcaadcadccdbcaddacbdbdbdadacadadadbdcacbabcacbbadccdbacaacddbbcbaccdbaccbaaccababacbadddabbacdbdcbcbbddbbabadaadddcabcbbbcddbabbcdcabdbbbcbaabcdadccbccabcaccdbbdaccbcbccacbbbcacabacbddcdcadadbaadbbddbdcadddddcdbabcacdadccbcabadcababababccadabbccdbbaddbbdddbaabcdabcdcdbdabbaddbcccdacdcaababaacaabdbbbcbcaddbadcccabdcbaacdbcbbadddcadbdcbabccacccdbcbcadddccbdcaddaadcbbacaabbaaaccbcdbcbadbbcdaacdcddbadbbccaacbcbdcdbccbbcdacbdaadbacccbbbaaacbacacdbdacdadcaacdbbdccbcbdacacdadbdcccdcabbcbcdbdcadbaddaacccabbbdcdddddadbdadddabdabdbaddcbacbbcdcbcdaabaabdaacaaaabbcddbcacdccaddcbbacbbabdbcabbcdcaddbcadacacbdaaadbbaabcadbbcbadbabbcddaaabadaaaacbbdbaccdaaccaaddddcacabcaacdacabaddbdccbbbbddcddabccaaaaccbbbddcaaabbbbbcbbbdbdddcdbacddbddcccdbdbdacaddcdbccccadbcdcddabdcdbaaaabcabaccbcbcbadaabacccadaadcdabacabacdbbbacaadcddcbbaccbcbcaccdbdaaddcbaacdacbadabbdbccbaacdcbaadaaacaacbdbdaacabcacdcaaadbdbbbadddcbdaabaacbbdadbcaacabcccbaadabbabadbbbabadabddbbabcdbdbdbbdbddaadbbdaadababaaaddabcbcdddbadbbbdcdabaacaddcaccdaccacbcdbddddcabaccbccdbbdacbcdaaacaabbbcacbdddbaccdacabcbdacdbbccddbaacbdbcdacbabaaacdabdccdadcadbdbdaadcabcaaacdccadcdcbdccbbacaacabbbddacdcaddaccbdccacbcdccccabbabcbdcaabcbadadddbcabcaaccbccaddbbbbacdbaacbcacccbbbbcbbddabdbbdcabacddcdcdcadbacdccacccbbbbcbbcacccbddaadabdddddbcbbaddcbabccddadbcdacbaaaaaddbbadaaadaccbdaddacbbbababacacaddadbddaaadbccdddaabaaadbdcbdcbbcbaabdabaaabcbdcdbadbaaaddbbdbabccbbdcaacddbadbddbdbadaacabdcbaabccbbadadcacaacaadbbccadcdcddbbdbdbcbbccaacccaadbabdcbbbddaabdccdacaadbacbdcabccabdabdabcaccdaaccdcdacacbbddbccddacbcbbdbadcaddadacdccbaadbcdcccaabcadbccaacbdbbbaaccabbaaccccacbddcbdcdddadddaaaabdacaddcccdbadcbdddacadacaacbddaadaccbddaabcabadcaadcdbabcbdccaddcbbddcbabcbaadbbcaacccdacbdaadddacaaaddcdbabbbdaacbbdaacbcddbbababaccbcddcbabcbccabbccdaaccaccddcdddcdaaddabddcdddbdbbbcdbacadcaacaadabbdaaadcaabdacbbdadcbbaccdabcbaadadacbbcabbababadbbaababcddbcccdddcbbbbbcdbdbccaacdbcdcddadbabdbbbbdbbcabdbabbbbaabcbbaadccbccadadbacdacadddbcddddcbdbbdbcdbacdccdcdcccccbcacdddcccaddbbbccabbccabccdabcdbaddccabdabdacbadcbdadcaabddccccabcdbddcddcacdaddabbdadbbacaccbcbdcadcadacaccddbacdaabaddcadcbbbdadddaacccdacbbcaaacababdbccdcdbacbcbdcdadbaddccacddbadabadacabbcacdbddbbcacccbbaabdddccabacaabcbdabddabdbcdcdbbaacddaccbccabdcbbbaaacdbbaddcdddcddaacabbaadacaadddaacdadaacbccadbdaccababcbacabaacacacddbaadbbbcdcacbaaaadcdbadddcdbabdabcdcdbbcccbbcaabdbccaddcacdaabcbcddccccbcccacbbddaadcbdbcccddaaabcdacccdddadabcaabcacddccaabbdacccbcbccdcbdbcbdacddcccacaadaddabdacddbdcdbaabdacaabadacbbadcdaabaaacdcccabbaadadbabaccccbadaaacdcdadbddccbaaccbcbabcabbdccbddbbdaacbcbcddccaaccbbdbcddccbcdcdcbcadbadabadcdacdcccdccbdddbdabbdaadccccbaacabbdcdccacbcbabadaaccadcdddabdbaaaddaaabdbaccdcdbdacbdbdcbdbbabadabcbbdaaccbcbaabbaadabcbaabdbbddabbbbddabbdbaaaabcbbdbdcaaabcccaabbadcbcbcccaddabaaddabccbdabbccadccdabcccdbcdccbbcbadcdcdccccbbdbaacadcdcaabcddcdbbdcdaaadcdcccdcddabdcccadacacadcbabacdbadbbdcdbabcbbcaacabcbdbdabaddcdbcddddcacaccaddcdcabbbadcbabdbccdcbcdcadccccbaccacadaabcccdbaddbddacbdccbadcdcbdcadabbdcdbbadcbcdadccbdcdabadaabdadcaadbbdacddbcdadbddcbabcadddbdccadcadcddbbbbbddcaababdabaaadcddaddbbadbccbcdcddcadacaaddcccbdcdddaabdccaacdcacdcadcaababbadcbbdbdadccaddbdddcdabaabbacdbcbbddadcacacacaacdaccbdbabddaaacababdbabbbbadcdabbbaabcdaaccabbaaccbbacdbaaaabcbcbbcddaccacdddcbacddacabdcbcccacbadcbdbddcdddbbdcdcbcdbbaabbbabcdbaaccdbadbbdadccbacabbbaadcbdcaccacaddccdcbabccbcbaacadbbdaddabdbdcdaaaddbdacdcddacbabaddddabcaabcbaaacaacbddbbddccdabcbcdcbcabbcbadaccdacacbddcabdbdcabdbbdacdadbbdabccdddcddaddbdbabdcabdbddadbcbcdababdcddacddcaadcdadbacddbcaacadabbabbddbbbcaccdcadcacbcbadbacccadbabaabcbccbbbaaaadaaacbccddbbbdcdbbabddcaacdbbbccadddbacbabbcaccdacbaaaddddabcdcdaaccacabdcacccbbaccdbabdabdccdcaabadddbaddbdbcdddbbbacbdcbccbcbbbbdbcbdbbcdcdadcbcbdcbbcadbaddcdbcddbbacdacdadddabdaccaacbcdbbccdddcdbacbdbaadbbbabdccbaaaddacabaabcacbbadbcbbbcdddcdcdbdacdccadadbdadaddddcadacaaabdcdcdaaccbcbcbaaabbbbbbdbbaccdadbdcbdccdbaddbbbdaddacbbdbddbbdbddddaadcabdaadacadbcacacacaacccccacbdccbdcadcdbdbcbdccdaddcdddbbdbdcdbdcbabcacaaaacbcbcadcdcadcaadbdadcbcadacbbbddbcdbbbdcdadcddbaaacddbdacbbadbddbdbbbbbaabbcdbaaaabdccccbdbbdacccdaacaabdaaacbbdadbabbaabbababadadbcbdcddcdadcbbacdcbdcdbdcdaccdbbcdbcbbbcbcddcccacdbdcaaccdcddcdcdacbcbcbdaddaacaddddaccbddaadabddbbcbcbcacaacaaaacdabbcbcbabaaacdcbcdccbbacadabbbdcbdddadadaadbbdcbacdadacdbcbdddbccdbabaadacaaccdcadabaddaacaabdbadbcbdaaaaaaddbbbcbbdaabaadadacdbadbbaadaabbcdcbbcabcadbbdcadcaddcdcdddbddbbdcbbdabddcaddabcdbbcdcddcbacbbbaacabbbaccdbcaccbdadbddaabaabdbcbbdcddccabadaccdcaadbdaabaaacddcdcdbdcdbaacdbcbbcddadaaabdbbcadaacbcbdaadcdcacbcabacdbcbaddadaacaaaaccdbcdadacadcccbbcbacbbdddaacabccaacadcadbdadbbcbcccdcdbdccddbddbdddcccccbcacddbbcdbdcbcdcbdcdbdddacddbbaaaabacdcbacbccabbadddccdcbddbaaabdacbddadddcbcacadcbdabbdcdaaadbacadcddbacddcbaabdcabddaaccccaddbacddbacdbcadadacdcccaccbcabccdadabbdabccbdddaaddcacdaacdcbabcdcabadcaaadcbcaaacaadbcabdcdbbbcbbdcacbddabdddaccdaabddcbccccabdcadadaaacdcadabccabaabdbcdddcbcaaddccdbbcdabbccdcbacabbccccbbbcbddcdaadccbbcbcabacbbbbbcdbcccdaaabbbdbcccadcaadccbcdabcbbbcaabcdabdbdddbcddddcbdddcaadababccdbacbbcaddccbdaaccabacdcddcdbcaaacddabcbbabdadadaacabcbdbddcccbaaabbdbabdcdbdbabbbdccbccddcbcbbcddaadcdbdaadddacaabddacbccbaaccbbbdbdaacbaacbdadacbbcacbbacbdcdbcacababbbcbbbbbbacaacacabccacacccddacdbdbbaadaabcddbabcadbdccdbccbadbadcadacdbdbacdbabdcdadbdacaaabaaabacaccbcddcdaaacdcdabaadbdaacbddcbacbdbdaddadcdbdadcdccbabaaccddbaacacabdbadaccbccadadccdbbaacadcccccacabaadacddcaddccaccbbbcbaadcaabdaccdccbdcdccabaccbcdcaacbacaddabaddacdadabbcdabccbabaadddbabddabdabdddccbadacabccadddcddabcaaabacadcabacdccbacbccdabcbbabbddcbabbbdcbbbdbbddacbcacdbaabddbbaaabddaacaaaadadbcdadbdddadbdbdaaaadcaddabacbaacdaababababaccdbcbccbddadddbcdddccdadaadcddbdbaaadaaddaccbddbbabacdbaccdcbdbdbadcabbdbabcabbbdbdccacbbcccdbdacabbbbaaccbbddbdbabacacbccdcbcbaacaacabcdbbdabdaadadddbbacbadbbaacdcbccabaadbacdaabbdadbbddaadccadbacbabdbdaaabdaddbddbadabbdcabbbbcdddcbbcbbcccbccbddcbdbcadcabbccadcabbccdbdcaacdbacbacddbdabbacbabdbcbbddccdbcacdccbcccadbccadddcbdaacdadcadcabdbddcbacbbcdbddaacbdaabadabaaaabadabcbbbababddddcbccbbcbbaacaabadadaacddabdcdabcdcbbcdcccbdaccdbdcbdaabcaaaadbbaaccbbbbaaadaaddbcabccabadaaddadbcadcaadabcdacdcbaddcbacbcccbcbccdddadbaaaccaddddbacddacbbbababdacbbbbabcdbbbcbadbbcbbdbbbaddccccbbcccadcabbabccbdcadabbabbbaddcccbadbbdcadbabbddabdbabaabdbcbddabadddbdadccaadadbdccbababaccddaccbbcaabbcbbdbcaccdacdbcbddbaabccadbbcbcdbbdaabcbbbaabdababcaaccdbddaccccdaabdadacaadbaacddcdbaddcdacdcbcdabcdbccacacbccbccbddcbcbbdccddcdabaccbbbbccdadcbbabccdcbcdbaccbababbdcacbaadaccadcbcdcdacdddbcaccdaccbabccbbbabbcbbbbddbabbbcdaadbaabaabaabdbdcccadadcadbccbaaacbbccbbbdbdcbdcdadcdabaaadbbbcacdbcaaaadcaaccdddcbaaabaccacbbbbdccddbddababdddcccbccdaacdaccaccadbdcbaaabdcbaddbbacadbcdcdbbdaaaacabadcdadbddccbbaccdabdbbbabdddbcaaaacbabbdaaaccadcadcdaacbcbdadcdabbaaacddddcddacdcbbaadbdcbcbbcbbcbadcacdccadacbbdadcbbbcacdcacdbdbdddbadcbabdadbbccadabadcccdccaddadcbbaacacdcadbcbdccbcaaaadddcbbcddabacccaaacbbddadddbbbbdcdbccacadccddbdbbdbddbacaaddbbaccaccbbabcdcdbdcabdadbbbcccacaccaccdcaabaaabdacdabaacabbbbbdbcabbcadcdbacdabdbaddccdddcadaadabacdccdcacdccdabbcdadaabaddbabdcacbdcbbacdabccabacdacddadaddbaacadabaabdddbcddcbbbccbdddcabaaaccabbdbacccaddcbaccadcbaaddbccbcbddcaacaddaabcacccbdbdbcacddbddbbbabcaadbacbaccacbabcbbbadaadcbabacdabccbbdccdbbccacaadcbddaddcbdcdbbbbbdbcaadbccdbcdaaddbddbbbcdddcddadbaabcaddccacbaaddcbabdbacdbcdcdbbcddbaacbcdadaaacaccbcdbbabaaadcaaaabcaddcaadcdcddaacdbddbdbddccaaddaadcbaacbaacdbbaddbdabbacacabacaaabdaacdabacdcaddbacbdacdccbaabcbaadcacdbdcdccccbbbcaabbcaaaabdaadbccccbcbacbdcccadcabbdcdcdcdbadccccddbbcbddacbdbaaddacbcbadadbbcadadbbabbabbdddcabcdbcdbabddcaaacaaabddbdcdaadaddadddccadbcbdbadbaddcadacbadccacaadcaaaccdbccdbddbcdaddabbbbdadbdccaabbcbcbdcdcdddbcaadacddadaaddcdcdaadaccacbbddadbbddcbbcbaddbdaacacaddbbbcbadbdcdcddbbacdddbdccaadbdbabcdadbcacbbdcccadacbcaccbdaacdaaabdabbdcbdabcadbccddaccbcacdbbcdbbaadadcbbbbabacabaabbcaadbdbdbddcbabdaabadddacbabdccaccbdbccaccbaabccbaccbbcbdccbbdbbbdadbbcacbcaaddbababcabaadbdcdccbbcccddbdcbcdcbdcbbbdbaddccddbbadadaccacbaabdaddbdadcabdbccddcccddadbdaabbbccddadaadacbcabbabbbaaacbbcddbbcacdacbaacacaabbcabcdcbbcbcbbdbdabbbbadaacaabacabaccdbbbdabdbacbaacbcdcbabbdcccbbcdcbabadaaaadcbbacacbadabdcbabbabcaddbdbbacabbccdccdbbbaccdbbccdbbdbdaddbbdbccdbbdcbdaccabbcadbbcaadccbcabcbcabddcaaacbacadabadcbcbabdaccaaadaddbdcdaacdaccbadccbbbadccdbaadbcabcaacdcbcaadaaabcaadbacdbbdddcdacaccdbdcbccacaabddbabbcabdbcccaccbcabadccbdcddaadbacaccccdaddcacdbabdccbcaaacbcaddaacabaddcbbabdacccccdaaaccabccdaadcbadcabbddcbccbccabddcdddbccdcadacbddadccbdcbbcbabbaaadcdbbcddddcdbbaadcccadbabacaccbadcaddcdddccbabacbdaddccbadbaacaaddaadacacabbacccaadbdabcadcaacdcaacadacbcdcdcdbbdbdbbaddbacddbacacacbadcbcabaccabbabbddcadbbcdabababcddcbccaadabdbbbbccddbcbacbbcdbbdbdaaaabdbbcbccabccdcbaccdcbabcbdcaaababbaadbadcbbcbbcabccdaddacddaabcaabcbcaabbbdcdbbcdcbddbdbdcadaaaacbbdabadccbdacdaccdbaabdbbcaadaadbcadbcbdddccccbbdabacaadcdcacbabdccdbdaaadacdacbcddabbcbdabbadadbacadcdcdbbabaaadcdcdcabbaabbabcccadccddacadbaccccadbadbdcdcaddacaaddcddbdbcadcbbbcbdacdaabccabcaabacddcdadcddaddaabaacccdcdccbbabaddabdbccabcaacadaadccbacadadccbdcacabbcadbbabaadcdadabbcdbcbabcabbddcdbdbccababcbabddabbcabacadacddacccdbbdbaacdababdbacbddbdbddabcabdbdaddbcaddcacadaaccdcacbdcdccbbaadcadcbdbcadddbaccbbaaaaccddcadbadbcbcbcbdabbaacdcdaadaabbcbdcbadcbddbcbcbdcdbbbcadadbcbcbadbdddadaaddbbacdccadddddcabbbdcdbdbbcadacdbbbdcdcadcbabaadcbacbabdbcdcadbbaacbabddbaadccbbdbdbcbbababcabcdddaaaaddcbbacdbbacadcddbdcdccbdadbdcccccdccccaccdcbddbddaabcdcddaccccdbbdddbaccdbdbbbdaabcbddcbaabddcccbcdbdccbdaadcacdaaabacdcbccadacabbdcabbbabdcdaadbccbddbbaccdcbbcddadbabbcdddacccaabbaddbbcdcbabacdacbdbbabbcccacbbacadbaabadbbccddaacbbdadbccaaddaddddcaccbaabcabcdcccbabbbdadcdddbcccbdabccbbacacaababcadddacadbbabaacaddcaddbbddabccbcbbbbabacdacabbcdbcbccacbabcdbdddcdcdcdccccbdacadbddccaddabdacbdaacccaadcbabaddaacddbbabcdaddcaaddbcbaadbacbbdcdaabdbcbbacadaabdcccdacddbabacaabdaccbccdbbcacdbaddaabbccbacbaadcbdbdaddbcaddbadbbaadddcabdcdcacabaacadadaddcbdbbcdaacbddddacadbcbbaddaccdddcdbcdbaddbbccdbabcaacdadadccbbaccaabcaddaabadcccdacdabdccacacbaadaadcbbdbdcdadcdaaababdabbacaaadaadacbdbcabdcbaacbcccbbddddbddbaaccaccacddabdadaccdddcdddaaccadddabcccaabcbbbbbcbdaacddcbbddacccdcabbddaaacbbdddbcccabcdddddabddbddbbcacdbaccbaaadbcdbbbababcbdaacbadacabcdaddadbbdabacaaadcbaccdbbccbdcbabcccbccccdbccbbccbcaacadccdcacbaccabbbcdbacccddabbcabbadcacbcdbccabcdacbdbddcdbaacabccadbabcacbddadabbdcacdcbdbdcabbdadbdbcabbdccacbcaddadbacbdddcabaacadcbaaadcddbbbcaabccccdbbdcdcdccccacaccbdddabaacdbaabaccbdacddaccddcadcbdcabbcbaadcccbbaaddaacbcababcaacdcaaaacbacddbddcadcbbbdabbbdacbdcbbccaabdbdbcaaddadabaccdaccdcaddbabbcadadadcaacbabadcbcaaaddbcbdddcddbcadcacbadbbacdcadddbbdbbaaabdabcdbabdccdccccaacacbacddbccacdabbccccdcacaccbcabdccacbcbadcacaddaccacbbcddabccdccdaadcadacaaacbcbcdccadbabaabdabcdccdadbdaaadcdbaacbdacacdbddcbbccdbdccabbcabaaaaddcbaaddabbacbbaadcababdccccdbddbcddbdccaddacbabdcddbddcdadbddcddbddcacabcaccddbcdbcbbcccabdadbcaabdbcddaccccdadabadaabaaacadcacaaddcccaddcbcddadbaaabbaddbdccbabbcaaaaddbdcddbadcbbdbdcbadacadbabddbcadbaddabdcbaccddbdccdaabcbabaabbadabbcbbadbaadaabccbddccdacdccacbddcbdbacbbabacdbaddccbcbbccdbbcbbdbdbaaacbbcbddbadcbdbbdbcddadbcdddbdabcddcdaadcdcdaacacadcadcaabaadccddaaccccbccccbdaccadbdabaadbcdcdbadbcabadbbacbadddaccddbdbbdbcabaaaacacdcddacbdcacbbbdcdaabbcabdddadbadcbcaabaaaadabdcccaabbacbcabdcddbbddcabacacccdadacddaccbaabbaabbcaccbaaaadbaaacbbbaacacddcccdbbdacaccbbabcdbddcacdcaadcbaccdddaddcccadaadaabcdbbdacdbbdbdddacbccdcdadcbcbacabaccbdddccbbcbcadbccddddcaabbccbadccacccdbcbacadbdcadacbcbabbbdbacdcdcacdddbbabadccbddcccadacabbadbddadaaacdadcdcdbbbcdaaccdddcdcdcdcacddbccddababdaddaccbabbcccaabccadbcbaccdccaacbddacdbaacacbadcdacddbabcabaaabbadaadadadcbacaababcbabdbacddacccacbcccbadacaccbdbbacdbccbbbdbbdbbccddcccabcabbdbdcdddaaacbdadddccbdddcdbdbdbadacaaababababcbcaaddcabadaacaddbbdcadabdcadcbcaaacbdaaacadbddcbcdccdabcbcdcdadcddcdcccadaacbacbcdbccabaaabdabdbddbcadbadadbddcbcdddccbccbacabdaacbcabddbacdacaabaacbdddadbdadacccadbaabcadacddcdbbbaabacccbdabacaccadbaaadbdddcacccddcadaadcdbdddabbddbccbcbabacbcddadacdaccbdbabdcadacbdcaddccaaaadddaddcdbdbddadadbacaaadacdacdcbddbbcdaaccadbadcabbabbbaddbccccdabccbcddbdcabcdabdbdbccacbbcabccdcbaacddccbcacaaabdbdccdbcbaacaabdcddcacbddcacaaccabcacaacabbacddbacdaabaddaaacbbcaabdabdcccabdabaabdcadbbdbccdddbacbadcdcadbdccdadcadacaaacbdcdababddbccdccddbbcaacadcdbacdbdcabddacdabadcadcbcbbdaaaadaaabddadbcbccbadbbbababbddbbabcadcbbabddddaddabaccbcdcdaddccccbccbdccbaaddbddcdbcbacdacdabcbdbcaacdcccdcaabcabddadcabcbdcabbabacccdbddbccaadacdddabadbbbcddabaabcaadadbbccadaabbbdabbaccadcdccaaaacbccdabaddadbdadccddbbacdadadbdcdacdacaabcbdaaacdacaccabbabcdcbdaddbaccdbabdbcabdadbaccdbdaaddbbbdcadaadcdbccdbadbbaccacadddcdaaccdcdadcbdbdbadadbdaaacccbbbbddcabcbccacbdabdacacdbcabbdbbabbbaddccbdadddcbbdddcaddbddababbcacbcdbbbcccbcbcbbbcbbaadabccdababadbdccbbbbdbcbdcdddacbacdddbadbbccacbbddbcadddadacacababdbaccdadcaabcabbdbdbabaaaddaddcaacbbcdccaabbdcbdcdcbcbaddbcbddbbabbaddabadbbdccabcdccacbdcbbbbcbcacbdaccbcadbaccdacccabdaaaaacbaddcaddbbbadbbdbabdcbccaaaadacbbbbddcabbbdabdccddaaccddacdbbacbaadcdbacaadbbbaabdacbccbbddcccdccaadddaabddacdcbadcbdcbcddbcbadcdcddabdbadadbaccbdbbcdaaccdaababdacbbcdbdacaacaddbcabcdabadaddddcaacacddbccbdcddaacbcdbaaabbacdcacaaadbddabababdbcbbaabaccbbdbbcdbcdddccdcaacbbbdbdacbbcbcababbcbdbddacdbbcddccdcacbcdcccdccdbdabddddaabaddbdcbdcaccabdcdccddcaabdbbcacadcbdbdaaadcbaaabacddddbcccbbccdcbbcaccacbacacaaaacbadccabcddcbaccabbadadcbbabdadbccaabdacaabcaddbbbccdabdadcaaacbaaadaccbbabcaaccbbbbbcbbabddbddaadccccbbdaabdbadacbccbababdbbbbbadbddcdacbcddcbbadaabbdabcabddbbcdddaadaaabdcbdabddcdbddccdcbccacddbbdbacdbcacacbdadbddcdbdbdbbcbdacdcaabccdababcadadacbcbccdbcbacbcdccbccdbbbbaaacddccdabddabcdccaacaddddcccbbdbcbdddbacddadcabadbabcbccbacbbddacbdbccdcaccbadbbabbabbbacbbacadadaadcddcabbcbcbbaacaabcbbaacbbcccacdbbdabbbabbbdcbabbdbddabdcabbaddaabaaaddcbdbcbcdabacadcbbcbcdbcacbdbbdadbabbacbdbbdcaaddbdbcddccbccadabbbdbbbdcbbbbacbaacddadbadbcacdccaadadacaaccadbbaaaadbbaccacbaccbaaccbadababdcacdacbbadcbdcdcbabbdacbcacddddccbcdcddddbaccdcbdcacbdabaacbbbdabdcdaaadbacdcbababadcacaadddbdcddcccbcbdaddabcdbcbcdaabaddcadccbacddadbdcddbcdacdacdaaacabbddacbccacdbbcadadddccadcacdbbdadbdaccacbbbdadbacacdcaacadababbaaccbbdacbadabdaddcbabddcbadcaaccacbacadbacabcdbaadcbcbcddbdddbadbabbaabccbccbbddddcaabcadaabbcaabdcbbbdbbbacaacdcdddddacabbdcabcbcbcdcbdadadddcdadbcddcbbbbbbaacccdbdbbacbcbbcccacacdbabddbcdbbcadccbbbbcdcaabbbaaadabadacabbcccacbbcabcdddaddcabcdacbddacdcacacdbabaaaaaaddaacabadaddabcadbabddddccddadcbcacaadbcabaaadcaddcccdddcdcbaacbbcaaddddcaccdccdcbbddaaccdcbccacbdbbaaccacdadbcbbacdcdcaacadacadbacdabcccbaccabaacdccbddadccbdadcbdbbdbdabbbbdadddaababbbabacdadcadcdbbcacadabcacacadcbcbdcacddcbbbbbdcadaadccaadcbdaadcccdcacbabcdbbddbdcbdcacababdcbbdcbabcadcdddabababbcabcdddabbbddbdddbbbdcaadcbbbdcdbbccbcbbdbabdadbdadcbbcdbabcdcdbbcddccbcccdabbbdbdabbacbdadddcdbbdddcbccaddadbdcbadcbacadbccdadbaacbcacaabdbbbccabdaacbcdbaacbbccbcdcaadaacbbdcaccacbbbdcdbdbdccbbaacabacaaadaaaccddbbaaaababdbbadbcbbbaacadaccacdaccbbcabaccbddacacbdbddbbcaaacbcabcbddcaaaadbcaacaddbabdbcbddadbcaddbaacbdbdadccbcbaabacabcbaacaabcccdccaaadbbbbbbddababcabacadcbbcddddbbddaadabddbbdbccbadcbcacbdbddcbbdcbddabbaacccdbcdcaacbccccaabcaabcdcabddccddbcaacacbbbdbaaacbbbacbddcccacbddbababdabaadbbdaaaaddbacbdacbcdbbdbbbdacadbbdaadabbacaaadbaddbbccddaabbddbaadbdacadddadddbadcacbbddaacbdccdbdaadaacbbcbbacdcbccbdbdcaacadacbcdcadcbbdacabaabcaaacacccacaccacdaddcddadbbccadbaadaccaadacccdabacdaacdbacdaacddccddabdbbdabdcccbbcbcbcbdcddbccccabacddbcbaddcabaddbbadbadabddbcabdbadcccaadadadcbdabbdbacccdbbdbbaccbaabbcaaaaacbabdbadabbcadbbccdcccbadbdabdcdacaccbdbdadccbbcdccdbaadbbcdbbcbadbdbaddbcaacdbcbabcaacababbcadcddaacbdaddacbdbbbccadccdaababacdbdabaadababcaaccbbabbcbadcbbbbdcbdadadddcbdcadaabddadbacbdddcbccaaabaddcadbdcbcbadaadacbcacbbabadbaacaacdcbbcdbdbaabcbcccdbaccdbcabcbdabadbcacabcbddccacdcbbbabdbbadaaccdcbaddbcaddbcadbabadbbcabbdcdcddbcabbabddaaaabdccdcbbcbcbadbcdadbaaccadbbabbababdcacbacadbdaddddccddccbdbabcadbdbbacccdaddbabaccabcccbabdacdabcadbbbccccdabbcbbcbacddababcaadddcaccccadbcabcdacddccaddcadccaaaaddaaadddbdddbbbddbdcdddcaaaadbaaadddcaaabbcbbddbdacadacabcdabcaccbdcccdacadbadacdaddbbdcbaacababbccbddbbbadacddaaabacbabcacdabadadadaadbaabacacaabdbddabbcdabccabadcadccddadacccdddaaadcdbdaaaaabddbdaccdccbcdccbddcadccaadbcaaccbcdcacbaaadabaadaacaddabadbabbcbddcacdbbadbdaaaaacaadcddadcbbbdddbdcadcaabbdddbdccaadbdbcdbdddccdbcdadbbaabbbaaaaabcaacddadccaccbddbdbbadabcadbdaddbbddaadbdaddabcabbcbddbcbdabdcbbabbdbaaccacabadddbccadaadcdbbbcacddbacadbacabdcbdbcccddcbcadcaabddcbcaadbbadbadbdccacbbdbbabbbabdadbcabcbdcddccabddacdbbdcacbdbbddababdddbbcbaacadddcbadccaabbdbbdacddacddacdadaaaadccbcdaddbcbbddddbdbcdddbadadccbdabbdccdbccddbbacdcadbbdaddcdaabddcdbdbdcaababbdcdbbbdcdbabdcdbcadddbaadccbbdaaaaacbdddaddbdcabadcddbccbadcacdbdcbbdcbdbccbbbadadbadacaaacdcadaacccbabdadabacbcacdcdcabdbdbbadccbcddcdbbadcaccdccccacdbacdcdaccbbabacbaabbbdabadbacdbdadbaadbaccaacbaabacdcbbbaaabcbbdbdddadaababccbdbdcdcdcbadadacbbadcbdccbadbbbacbdabbabacbbabaccddcddacabbaacdcdbbbacaaacccdacacabddbdbbbdaaddcadbddbabcbbdadaaccdcaddcbacdbbbbaabcdccacbccccccadbdbcaaddcddbcccddccaacdcadadacccdddaabccaabbddbabcadcadddddbbbbbcddbccccdacacddbaabddbcdcddabccaddbdbbbbadcabbcddccbdbdccbcccdbbddaacdcdacbcddcdbccacbccaabaabcabcaddcdcacbdbbcaccccdbbccbcbadbdcdaabbadaabcbacddabbaadddacdcdaaadaababdaccababbbdacadcddbdddcbbddbdcbbdccacbcdbbdcddbaddaddcdbccdaaaddbddbdcbcbcdbbdddbcdbadadbdadcdaacbccbddddbaddaabdcbdccddbcddccbdbddbdaadbbddaccdabcacdcddcbcdbbbaadcaccaaccabacdaccdcaadccbbbddcdababbacbbaaaabcbbbabcccabadaacbacacdaaabcadbccbddacbdaccdbdabdbcddbdcdbbcaadaadbdcdcbccbcdcacabdddcbacdbbdcddddcacdcbbbdaaacccacaddcadacbdcbcbbabccacbcaabddacdcabdddccdabcccadccbccbcabcdaddcbcaaabacadabbccdcdadcacbcadabaabbcddbadbcdacaaabbddbacddcbcadabbbabadcbcacdbcccbdbbddaddbcbdccabccbdbcabadcdccbcccdbbadcadbccabcdddabbbacdcacabdacadcccbcdcabaddbbadbadbbbabdcbdbadacdadbcaacaccddbdbcbccbcbbbadaaacbadbbcadbaabcacbaadacccaccadbcdadbcbabcbbcaaacbdbabcacbcbacabaabaaccdbcbbbbbadcaadabccbbccabcccbdbbabcccadaaadcbccdbabaabbabadadaaadcadcbdccdcdbbdbbddbabacbaabadcadcdcbcccabccccdcccbaadcccabccbcccabddbccdadddabaddddcccadbabaabbbdcacdababaddaadcbdacaddcdbbccbadacaadcabcdaabbccadabadaaaacbcccbcdbbcabdadbdcbcbbbaccabbbccbbcacdadaaccaacdbabcabbcaabaacabdcbbbabcdddbcbcdddbbdcbdbbabaddcbbbbbdccdcadadddacccabbabcccabacbcbadbbadacadddcbddccbaacaaabdbcaaccccaabcacddddbdbabdabaaabdbccacadaababbadbdccccbabccbcdcccdbadcabcbabcdcabdddccddabcdaacdacaadaaccdbabcbbacacbccdbcdbddcdbdcbbcadddccbdabacbdaaaabdccdacaacabcaadbaaddccbabaabcbdddadccacdbabcbaadbbdcabcdacadacbdbddcabaddcaabdddbbdbcbcbddccbdbaaccababacabadcadbcadbbacdcccadbccccacacbdcaaabccbbbabaddddccaadddcacbdacbbdbadabacdaacccdbddbdbdbbbbaabbcbdddacbbccababdacadddadacbcbddbdcdcabcdaaadccabbaccccdcadaacabbbabbaacbddcddbbdcbbbbbabbbaaccccbdbdddaaaaababcdacbbaccdcccaadbcdcdbaaadababccbaaaccbaccababcbcabcbbcbdbcadddccadacddaabbadccbdaaabcdcbbdcddcdbdbaddbacbddcccdbbcbdbabbababdbcbbdcabcbcaadcabbdbabadcbddbcabacbbbdcacdbcdcdcaaaadccbbdcccbdabdacbaabbdbdbdaabccdddaabcdaddaaacaddacbbcdadbbcadbbdcccbbaabdababbcddcddccbdbdabcacdcbdcbcaddcbdacaddadddcaaabbcbbcbcbccdccaababdddccdaadaabddacdcaabbadaadcdabddbcbbbcdaadcaacbadadbdaaabdccabbcdcbccbcccacaabadbdabccabcccdaaaadabcaadddadbccaccbaaaadcacdaadbcdcadbadabadaababbdaccacabaabbacaacacabaababcdbcdbacacbcbbcadccbdaccadcbccabadbaadbbbddcdbcbcadcccadadddcbdccabbaacddbdcbbbbaccccdbdbbbadddbbaacdbbcacbdccdddabcabbcdabbcbdddbdaaabbddaacddddcbbcadccddbcdcacdaadaadadddadadcdbadaacaaddcddccbdaababddbbabbaddbdcdcadbddbbbdcbabacddbadbddaccdbdccdaddcbccbbddabccbabddbbaccacaadbccbacacadbbcbadaaabbbacdbcbacbbbababbbddddddccdabcccabdabbccbabaadccccacadccdabcadccddcdbbccdbcddaadcddcbcbdadccabdbcccdbadcdbbdaacdcaddccccaaaabacdcbcacbadadcddcdcdccabdbaddbbdcadbcdacdcababaccaddcabdcbdbcbcbcaccccaadacaadccccdadcaaddabcddbbcadbdbabbcdcbbcbdaabbccabcbdbbdcdcabbdddbbcaaabdbcdbbaccbbbcabacddaaadabdaaadbadaadcabcdcbbdbdacddadcabaadbcadcaccabdcbbccabdadcabbdadbaddcdbdbabcbbdadcdcbcccccdbdabadddacaaaabacdcccccaabcacdbdacaabbdabacdacaaacdbddabccaabcdcbabcbdcadaccbcdddbbacbbbabcbbdcbccacaaaccdbadacbaabadbccdadacccbbdbbdbbbcdccbcdddaaaabaabdbddadcacccbcacabaccbdcbdadcdddbbccdcadacaadbaaabcbbbaacdcbbdbddcddbbdbbabdbccadbcaadcabdadbddccbbcdcacddaacdcabccbacaacbcbdbabcbbddaaabbcbabbaddaddaadbbcbdbccaccbbadaaabdbbbbbaccddabdbadbbaabbccadbcdabdcacbcbbcadacbbbabcadbabbabbddccccdcacacbdbccbcbdbacdcdbbdccabdaaabacdbcbbdcaddcabcbacdaabcabbccbdbdacccccabcbccbdaccbbcaabdcbdccaccbccdcddacdcbbcadadbdaccdaabdcbaadbdaaaabcbbccabcdbadadbadcdabcdbbbcadccbcaccccdcdaaababadddcadadbabbcadccdcabccbcddabbdaaadbcbbbcadabbabadccdccacabbaccdaabdddccdaaacbcdbbaabacccbaaaccdaabcabcccacabbbbcdcaabaacdbdaaaaddabaacdcdbdbbcdccaaadbbcaadbdbccbbcbbaabaadbcbbdaadbaadacacbadcbaadcaddcdcbcbdbdbbdcadabccbdacbbbaaadaadabdcbbbbacbbdacbbadcbadcaadabacdcdaddacddbaccdacdbcccbaaddbdcbaddcaaaaacbabbbabddbdbbddacabcddaabcaaacaddcbbdccccaaacadbabdaadbccadcabdddddddcddcacbbcdddaadabadabddcbdcbaadccbdcdcdddcbbadcbdacbdaccbdaabccbaaaaaadaccdaabcddcacbccacdcbdddcccbdcbbaabdabccbcdadbddbdbcdadbccbcdacbaaaccbabacdadacbcacdbbddbbcbbbbaadadccaabbcbabbcaddacdbcddbdbdcbbccadcbbccbdaaadbdbcdcaddbcccbddbddddaaddddabadcacadbcddbbdbcbbbacbacacbaabbbdbaaccbdaddbaadddbbdddabacdbdbbbadcabcababadcbbbcdccaddbbdbdabdadadcadcddcdcaadbcccabccbddddabdbabcdcdcacdbaddadddacacacccddbdcddcdcbdccadddddbdacdbbbddaaabdddabdbcdbccdbcbacdcabaacacbcdacbcbabccbbbbbacdaadbaadcaaadaaabacbbbdbbaccbabadaaacccbbaaddccbbababcacacdcaddbbcabdacbbcacbadacdaaaddbdcccdbbbcccddaaccacbbacbaabcbcbcbcaabbaaaabccaadcccbcddadacabddaddbcbddbbcaacbdbdccddacdcccdacbdddadbbbbdbcdbadbacdadbdaddaacdccaacacbaadbdbdbdcacbacbdbacabddaacbaadcddcaadbcdbbdddcdddcbcdcaaaddddbdadbddcaadabdacdcadaabcbddbbdaacbdcdbcdbcbdacccccbdccdcadcdaacbaaabccadcbddcbbdbdabcbbbcadadcaaabddcbdaacbacddcdcddaabaabddcbddaaaddbddadacbbacadabaaabbbabdcacaacddcabadcdcdbbddcdccadddddbdcdcacbcbbbadccdddaabcbbbaabaddddcbcccbbabddbbcdacbaaadcbacdbcabccbddbdccbdccbbdbddcdbadbbdcbddcddcbdaddbaabacacbabbcabbacdcacbdacdadddacdcdbcdcdaacbacdbdadbabbccaaadaadcddaaddccddbacabbcbcbcababbddcaccdcacdcabcdacddccacadcdccddccabccccbdbcddaacdcacbcbacbcdcddddadbbbaddadcbaacdacabcbadccdadbaaddbadcbbbaaddbdbcadbdcdcdcabadcdabcdabddbcdccbacaabdcccdbabdbabbadbbcbcbbcaabbabbbacbbadcaaadbbbdaddbdbdabdbdabbddbadadbaccbcaadacaaadccdbcbbaaddaddddaadcaadbbbcaacdbbdccccacacabbaaacaababaabbaadbbccbdaccddacccbacacaccbddcdcabaacaacabbdabbabdcacbbbcabdcacbadbcdabcdccaccadaaddcaaacbcbccbdcbcabdcdcaabdcaabacdbbbbaacdcdddcacbcccbbcccdaccbdadccabbcdbaccaababccbbacddbaddcbbcbbbbccddbdabcacbbccaccdcadadadbcddabadacddbdcacbddbdbbadcdcaddbcdbddacadbcdbbbbdaaacbcdacdcadabbcccdcabadbbacccdbcdbbdcccbccbdababcbabcabaacdddabbdbacbdcacdacbbccddabcbaddbcdccbdabccadaabddaaaadbbacbcbbbdbacacacacacacdaaccdbadddabadaacbbababcddabadcacbdabcbdbcddacabacccbbaacacbbccadccacacaaaaaccacbcaacacacbddaacabdaabadadbdbaddddbaddacdcbcddabbaaddbadabaacbbabdcddbddaabcbacaaddccdacbdcbdcbcdaaccbdbadbcddacaabcbcbcaddbdcdabdbcbadbbaccdaaabaacdabbbdddbbbcaaabbaacdadbbdadcadadadcdaabbdcdbadcacddbaacadcaabbabdbbddcbaaabcdaadbccbacbbcbaccabcbaaabaccccabcbdbdbcdccddddbcddabadacccdabbbdcbaabbaaadbdddadcdcaadbcbbcaacadacdcdaabdddaadababdbcaddcdbadadbddbdaccdcabadbddadabbcdadabbbdacbabcadbbcacdbdccaaadcadbbbdddddcaaaaadadadbbddadbbadccbdbcdbcbcadaacaabddbadabcaaaaacbddcdcdabacaccccdabddabdcdbcabdddddbbcbdadbdbcdadaabbbdcaddccbaadcaabccdbddacccccabdadcbcdbdaadbabbacdcbbdcbbcaabbbaccddddbbdaabbadbcaadbdcaccbabdcadadbaccabccbdbbadaddabccaacaacbbddcbcbbcbbcddaddddcdcbabcabdcdddbdcacbdabccaacaadabbbdcdccccdbbbacaabdbcbcadaadcadadcccdcaadccaaddcdcbcdadabcaddcdaacdacbdcbadbaaddadaaaaabbaaccbdacbbbbaadcddacacbdcabdbdbbbbcaacacddaaabcdabdddcadacddcbccccddadbdabdcbbaccbabdcbddbcbcdccdcbbaccbdcaadccdcdbccabdabbddbacaacadbcaacdbddcddbdabbbadaaaadacdbdccbabcbcadacdcaadadacaccabcdcdbdbbdadcaddabcaadbbadccdcbdccbdbbddbdacdbbdcbbbdbdaacbddbcbaddccabbbabdabbccaadcdbcbabdcadcaababcbbdaacddcbddcbcaddacbcbccddcabdbcacdaabaacbabcbcaaacbacdbbdddbdbcbcaabcbcdcaacadddacacaabbaababbbbbbbbdacbbaabbbbaaddadabcaadacabbaabdcacccbdcddaaacbacadbccccaddbdcbacaadddacbcdaadcddadcaddcdbacabcddaccbcbdbcdbddabcabcccadcdbdcbbadcabbbbdcaddcdaadadbcddcdcdaddaabaaadaddcaabaacbdddcdddbdcadaddbdbcaadaadbadcbaddbbabbadcabbbbddcdaccacdacadbdadbbaacaccddbcdddbccdbbbabbbadddccdcbaacbaaacdaddbdabbdbddaabcdbdbddbdbdcaccdacaadbccdbdaabacdbcaabaccdbadcbccabcdcbbdaadcdcacddbbaaddabdccdcadcbbbdddaacdbbccdbaccbcbcabbabcdaddbbdcdcdcdcaacbcdbbabbcdbcddbddcdadbccbbdbaaabacbcabaabdcbcddccdbdaaddadaaacabcbbbdabccbcdcddbccdacabdbcbaccaabbcbcacdcadbdbcbbbdaddabacddbdabdbcaacaccdbcdcbcacdacbcbdacdddaababadccacbacaddacbdbdcdcdddaccccadbccbaaababbabadbaadddcbaabbbdbadcaaabbcbddddaabbddcdacddbcacacdabccbacdacbbccaabbadbacdacbbbccadddbacccdbaddcbabaddbccdccbabbccacabcccbbbbabbdabcadbbcdddacbdacdadbabadcddacdcaaacbcbcadacbbcabdddcdcadaadcdabdcabbacdbdbbaaadbacbccbbaacaaaccbbcdccaccacbacccaabadcdbddaabdbddcddbbbdbcddcdcdaadccabdcacbcbdabbdaadcccbbbabbcaaddcbbbaccabbbbddadcdadacdbbaccadccbbdacabadacbdabaddacdbaccaccadccbcdbdacbddddbbcdacccabccbcdadacabdcbacbbccaccccacabddddbaaddcccdaddcbccccbabcbdbccbadbbabccdcddacbacbacddcacaddcabddbbcdaacadacdbcccbcddccdaabbbcddbacaacccddddddaccabddaacadcbcabcdcdddbbcacdcdcbccacadcacddddcbcbaaabddcdddcababdccbcbdcbbcabbcddddaadbdbabdadbdbaabcbbddaddacdaacabbbacdabcccadadcadbdcbadbbacacccdbacdbbddaadcbdcbababcbacaccbcababbbbbcababbabddbcbccaacabbcdadcdbbdbcaadbabcadcabbdbbdbcccdbabbcaddcddabdbacacbbabcabacdddbbdcaddabbbcddddddaaabcacdcdcaadbdadcaadbdccbbaccaabdaddbacccaadacaacbaddabdddbacaabacddbdaaaddaaccbbbbbdbadacadcccddbacbaacdabcbcdaadcabaaabadaacaaccdacbdcdbdcbacbaaadbaddacccdcaabcabcbcdaaadccdabdaddadcbaddaacabdaabbbabddddadacabcddcabdddbbcbcbdbdacbdcabacdadbcdbbdadaaddababdbbddddbaddadbdddbbcacacbacaaddabdcdabcbdbabcbaacbbccaccadacaaadcacbbbacacacbbacacbbbbdbbacccbadbaddbccbcdbabdbcbbccbadbdddddacddcabdcccadadccadcdccccbdddacdaddbddcabcdabccdccbddccdadbacacbaacadbdcbccadbadbdbdccadacbdcccdbacbdcbaddccabcdcaaddaaabbbbbbcbdacbccadcdcdbcbadbdcdadcbaddccaddcdacbdaadbbdcabbcccabbddaddacdbcddaccdbbbbabdbaabbdbaddcabdacbcbddcccaddcabbdbdbccbcdbbcabaaaadccacaddaccbaaaacaadddbcacdcbabcbbcccbcbdbbdcdccdbaccbacaddbbbdaadabcbbaabdbddccadabdacbcbdcccccddcbcacacbdbdbdabcadaaabadcabaaadaabacdadadccdabadcabccdddadcdddaccabbbacdabccabaadaccddcabaaaadcdcadccbaadaccbadbbbbadbccbcbcbccccaccddcbcbbbcdbadaabbaddbbbbbbacbbcdccbcbddbcdcdccccbbbaacaadbcbdcbadbbaccbcdaddcdbdacbbadbccdadbbdbbcadaacabdcacbabcaabbcccdaccabcdddcaadbdabbccbbadabbacabdaddccbdaabaadaaaadbaddaddaddaadbcdcbacdadaacbbbcacaccdbdcccddcdabcbacdcbcdcabdcbcdbcddcddccabbcdbdabadddbdbdcbdddcbbaadbbabcbdbdcbaccdbcddcadddaadbdaccbccbcadbddcbcbacddbcccdccbddbbcbadbddccdbdddbddaaaddcabbdadabaccbabccbadcddbbaddddadbcdadddadddabdacbcbacbbddaccdaabdadabcdbdccccbdbdbabbcdbdcbcddaaccdabbadbaaddcbacbadbabaadbccbdbddddbddcccdcccbcabbcadbcbacdcbcdaadbdcbdbbdbdbdbbcbdccbbabcbcbdccbaacdbccddbcadadcdbaddaabababddaacdbcaddbbdcbbbcbdbbddabbbddcabaddaabaabddabbdccbdcbbbcabbdaddddbabbbbadabdcabadbbbcabbbaaacaacdbdcabaaaaacadbabcdaabaabbbbcaaabdcabbbabdddddbaabbdbbcdbdbbdcaddcacbabcddcbcdbbbcddbdbacdcacabcccdcadcdcdabaadacdbddacacbdaabdcdacacbdcbbcdacaddadbddbdcbccccbadcaddbdbdbddbabcaabcbdbcbdadbbabdcadbdacbbbaaaaacbdbcbacdacdddbdbaddabbadcbbdcdabdbaabccbbcbcdaabcbdacbddabdbdaabdcaadbbdbdcdaaddbdbbdbbacdddbbcabacdbdbbbbbbcddbdddbcaccbddbaddcbbbacaccbcbdddbacbcaccdcaaaccacabcbdbbababbaddabdbbbcdcadaabcbddccacdcaacabdbcdaadaaadacacdaacdccaaaaacdccbadababdadcadcabccbaadbaddddadbadcdbbdbbbdadcbdddccdbaacdcacbacbcabcaadaaabadbabbaacaadadadbadabdcaabacbcacbcccadaadbabcaaabddbaaababbbaaacaadbcddcbbaccdcdacdaaadcaccbdcbdbaaabacaadbbacbcbdbaccaaaddbddacadadaaadcbddbacdaaadabdabaadacdddcadccdbaccbdbabbbbbddaabadaddcdccdcccaddacbcaabcddcdbdccadddaabdabacbaccdabaadabaadcdcdabddddadbcdcdabaabdaabcbdcabcdbbadcbcbaacbaacddaacabcabcdaabcdcaccaccadccadbbcadaadccdaccbbddbcdbbbadcadbbabcddbcaccbdaacadbbbabaadccccaaccddcbcbbadccccbcbbaababdacaacacdbcaddaaaddcbcbdcbdaccdabacbccacaddacaaaadcabaadccdaadcdddcacdcccadacbaadddbcbcacbcdbbdcadabdccdddccabbadcbacbcabaaaaacdbaadaddcbbccaaccdaaaccdbabdddccaccbcabbbacdddacdbcddddbcbbdbddddcbbdaabbdccbdbdcacadbaacabcbbdacbacdcdcdaccddacdabbdaacadaaaabaaadbddccabcabddadbcabacccdbacbbdddcadcbcccbdcdcbbdccbdbccbcddcbbbabbdadbacddcbbcadcdcaacaacbdbadaacbbcdddbdadadcacdbbacdadccabcbbddbdccbddabdcdababbaadccccadabdddcdcdbbdcaadcaaabaadbbdababaaddccbadaadbadbcdcbdadacdcabaddccbbddcddcdbacddcbaacbbcacbbbdcddbbaabdbbcbdcdcadbababaccaabacdacbcbabbaccaaacbdcaaacaddbcbcbaadbccccacbacddcbabbdacacbabbbcdaadbdbadbacbdbcdbaabacccccbbbcbccbcddadccabacdcdbbdbbbabdabaadddccaacbbcadbcdbdcaaacacbccacbababbbabbcbdadadacbccadcdadabdacaccadbcbbcadbcdcdbdccdbcbacacdcdadddacadcddaaddcbdbdcbaadccaadcdccbccdaadcaabacadcacaddcbaabcaddaddcaacddcccbdcabcabbbdadaaaddccabdbbababbcbbcbadcacadabcacdaacbcddbabcadccbbadccccbccddaccbacabdbdadadccbcddbdcdabdbcadbadbbcaadbbbadabacadddbacccdddaddaddccbddddccdaccaabdbcaacdccddddaaaabcadbaddddcbcacadadbcdcabcabbaddbcacddbdbaabcadcabbcdcdcdcbabcbddaacccbbdcbdccdbacacccabbdcddcbaccabdbbcaabbcdaacdadccbdccabdbddacadadcddbddaccbcaaacdbadaaadaaadcabacaacdacdababcddcaaababbbccbabcbdbbcbcaadcddbacdbaddcbaacaaacccbacbacdaadcdcdccddbaaddcbbababacccaaabcbdbdabaccbbbcbcddaadccbcbdacdbbbcacacadccaddcbaacabccdbdacdabbabacabcacddaacbdabcbdddbdacbcacbbacddcdcbddcdcdcdddbacbccbbcbbbdcbdcdabadcddadddadabdccbaaacbdaadcaccccaaacbbbaddcbaadadbbabddbcbdbadacbddccccabccdbaacadbbcbcadddcbadcbcdcbbbaacddacacccdbccabaabababacaabccaadcbbaacddbdcadcbcdcdcbdaadccbbbcdadddcdbcccddcaadbcbabacbcdcdbadacdbbcdbbbbdaacddcaacbabcbdcbcbcbbdababbabccdddbbadaddacbaadcaaadbbcadcbcacddabbcccadadcbbbaaacbdcbbaababadabddbcbbcbdadbbcbaacabdadacbddccaaabcddcaadadaacababdabdccccdccddccbdaaccacbdbaababaadacbcbccbacdcbdbccbadadbabadbdddccbbdddbacacaccbbcbaaacdacdbacdccdbbadbacaabdccbbbdaacdabaabbbbcacdddcabdcbbbabbabcccbcbdadbdbccbacacbbcdcbbdcadcbcdbcacbaacbbbbbdacadadcdcdcccccadcabddadbadcddbcdcbcbddcdcdddabccdbcbdbddaddcdabbdcddbcbbcaccddabbacdadccbdabddaaabcaabaaddcccdabddddbdcdcbbaaadcdbabccdadcacccccddbaaacdddccdadcddbbcaaccdccaddcbbbacbaccbdcbbadacdadcadabbccabdaabbdadabdcacdabbaadacbbcacbaaccabcaddbbcacacbbaddacbadbabbbabbaddcaddcbdbbbcdacacabdaabdcbbdcbaccccaaaddcbaccbabadcbababcdbdbbccddbcacacdadbdabdbcbdccbddbadacddbcdccdcdbcdababcacdcccadbaadabcddaddadcbcccbcdcbcbcacaddbccbaaabacaddbccabbcbdaacabddbcdabbbdaacbcbdadadbcaaacacbaadabdbcaccadbcbbbadcdaabbaadbdcbbcdccadbbccdbbdaaccababadccadddbadcbcccbddbdacabcdbadbaabbaacadbaaccdcbacbcbbddbbcccccdddcaaccaaadbabaaccdbdddbcacaadabdcddddadbdcdcacdabaccccbbaccbacacccbaaadbcdbcdacababbacccccccbaaadbcbcdbadbaabacbaabcdaadbacccbccadaaabdbdcccbdabbacdcccacacacabbbdcbadbbaaacdaabbdddcaadaabcbcdacccbbbbaacaccbbcaaabcccbaddaabbcaadcbabbcbbacadcbddaaddddccaccbcbbdccaadcccccddcbdaccabacabcbcbcdddcccabdbcbdabdaddbcdbacdacadbddcadacabcdcdadacbcddddcabcdcdbabdcbcbbbdaabdbcbaccaabccdbdccbcbcccbaaaabcccacbbcabbbbbbdacbcddacccccdcbdaddaccbabccdaddcbdacbabcabdcdbcccdabcdbbdabdbccbadbbdbdbaccdadaaccdcdaaccdcdcbbccdbbdbacddbcbbbddbbbbdddddcacbcdcdaddcaddbcdbcbdbbccaadaaabcacdabaabbdcaddbcbdccccccbcbadbddacadababbaababcdbdbbabcbddadabdddacddabbccdcacaaadcbbdadcbaaccbacbddbdddddbbbbbcbaaabbadbadbaaabbbcdabdacbbbcdabcabdccbbdbdaccaddccdaaaaaacbdddccaccbccddddabbbcdddaccdbbdadbbacaacbcabbcccbacdbdaacdaddcbbbbdacdddadabddbaaccccacacadcddddbaadddbcaacbcdddccbaaddacccdbcaadbbbccbcdcadcaacbaababdbacacbdaacbcddbcdbccbddcdbaaaacbaadccdcdcbdcdacbadadddcaabdbabdcccacacaadadadcaddbaddacdadacabbcaadadccaddcdadcdabddcdcabdaaaacdcdddadcacdbcdbccdcbaccabcbbbcbbcbbbcabbcabbddadbbbbcbdcabacdcddaabdbcbacbdcabbdddaadcbcdabccbcddbccdabacbabbcbccdddcdcdacbadcbcacbcbaccdbbadcbdaadbcabdcdaadcadbacccdcadccadbabcdacbabaadcbcbbdaaaadddbcdbcabdaabbacbbdbddbddcdaaaadacdcbccadaadbacabdbdddbacabababadadaaabdbbbbaadcddbcadcdaababbdcacdbbbddadcadbaccacbbcabddcabbaacdbbccaccabacaaaababbadcdddbaaacdbaadcdbdbbdaccbdddcbbaaacddaaccaacdcccaadcbdddbddabdabdadccababaacdcdbaddcdaacabddaddddacacccaabacdaacddcdcacbdbbbccadbabdddaddddbabddddbcbadcdabddadccbaaadbabccdacdacaaddbdabaccabcddaaddacabbacabdbcdbbbbadbdbabbadaddcdaaabddbcdcaddddbdacacbaddbcbbbbbbdbbccdbbdaacabbcdabaaaddbdddaaaaacbcbcddcdcdaaadddddbbbabbbbbbcddbadcbaabaaaadbdcabcaddddacabadcbcacbbcbaccbbdbbbcbbaadcbadcccdcddcbcaacbbcbaccccdadaddbdadaadacadbcadcaaabcaccdcbccbcadbbbadddbddbdaddcadadbbbbdabcbcdccadaacccbbacccacadbdbcbdacccbcdbdbbbcbddddcaacacdabaccbdcbdcaabadadbdacdcdbbaccbdcdcdddadddcaabcbacacdddacacbbabaadcbbdcadcbacdbcbacabbcbdbdaccbaaccbabcaaddcacbdadccadbdbcdbddabcbcabdababcadcacdaacabdcbdbbcbadcdadddacddcadabdddcaabaacbdbcdcdbccddbbbacbcdcbadabaabbbbccddbddcadddcddaddcbbacbabbabcbcabccccdbabdddbbaddcabbbcbdababbccccccadbdbbcadabbbdcdcbcdacacbdcadcdddaddacdbbddbcbbbcdaaacdaddacacaccccbccddabbaabbbaaacbadddddcbbdbaddacbbbcbddcdbdbbcaccbbdbddccdadcdcabbcdcadbadbbcbcbacbddabdacaababadbbdbcadadbadcbcaabbaabbcdabcabddcaaabcccabbaaaabcadacabaabccdabdadccadacacacbdaaaccccaacacbdaaadcbbcdbbadaabbcacccdcaccdacbacbbcacdccaccbabbcbcbbcadaadacdcccddacdadccbdbbdadddadaaaacbacdbbbdcbaabdabbabbbbacacdddcdbbbcbadcaabccadcbaacdddcaabbdbcabadacaacbdcbaccaabdaccbdaabbdbdcbaabcabaabcbcdacdbdcbdbbaaadbdadbbdcdaadbdabdabbcaaaaadccbbcaaabcadcccbcbbacbbacccadcdbcbdbbacbaacccacbbddbbccbbaabccabbacbbcaaacbcccadcaccadaabccacbbabbdcdadbbccaabadabdaabadddccdbcbddacdbcacbcbbaabbcccacabbacdabbdaaacccabccabcabdabcdcadabbabdbadacabdbdacdbbbbdacdcddccdcacbdbbdcaddbddbaacbdddbcdbddddbbacaacdaccdaaacccccaaaaaabcaaacaacdddccbabbcbacdaaddbdabddbddbadbabcddadaddbcddcdabacacabccbdbbaabbbdabbcabdcddbbcdadbbddabbbaaaaccdddbaaaabbccaccbaccadababbdbbcdbddccbabadbcdccbbaccdddcaccabacaddabaaccaddabcaddbdacbcdbccabcadcbaccacbdbdbccadccdacbaaaacabcaddcdbdddbabdddbcbdbcaacabdacbddabcdcaccacbdabaabccacdccbaddbdbccacbddaccabdcacdcbabdaaabcaadbdacdaacbccabaadaaababacabbdacbcbaabcccddbdcdcdaaaddcadccdbcdcdcdadcadadacdaacbbbcbaaadacbdddaacacaaabbcdcabcdcbccbbccccdbaacdabaadbcbbabcadaadcdcbcbdbcaccadbcdadcbbaddccbbbcbccbbdbdbbabdabbabdbdabcaccacdbadcdddaccbbdcbaddddcbaabddcdababacdaaadaccacdbddbccccaabbaadcbccacddbcccacdaabbdbdcddbcbccaccacadbcaadacccadcdcdccdacbbbdacdbdbdcbdabadcaabaddacacbdcdbcbcdcaddbcdbabcbccadababacdaddbcaacdadccabcabdccdbbacddaaadccbdaabcabcdaaaacbcbcddaccadbaadddcdcccaadbacdbccddbcaababbadabcdcbcadccbddabbabbbccbbccbabcadbbacdcacaaaaabcbadddddbdcdabddadaddbdaacccdadabdcdcababadbadcadbbaccdcdcaababbccacabdaadacdacddbbbbbccadacbdcccabdbddbaadbdbbcbaabcaccccbcbdcdadbcdbddcabbadcbdccbbbaadbcdaaabadadbdbaaddaabacaabdcbcaddcababbadbbbddaddcbdadcaacbcdaadbccbabcabddbbcbddbbacabcdadbdcaadaabcacddcaaaabacacabaaaadadcddbcdacadaddbaacddbbbcddbacdbdbbdbbaddbcbaacdbcaacaccdccdccaadbaababbbdcaaaccbdbcbdbaaadbaadbccdababcccdbbacaddcbbdcccadccbaaacccdcbbcddbadbbbcacaacdacaabddccabdcddcbcbcacacaddaaaddbacbbabadaddabbbbccbaacdbdabdcccaacadddbddcbbcbbdbbdddbabaaaadacaabacaabbddabbbabbbbbacdbacadbdbaadabadcbbdbcdddacbdadccabdbddacbaccababbadccdabbdaaadcbbaaacdcdbabcbdbaadcddaabdcbaabdbbcabadddbdccaaaacddbcbdacdacdaabaababcadaaddcbdaabcaadcaaaabcbdcbbbcbddacdccbcbaddbbdaddddcdddcbbbbcbccadabacabcddccdddcbbaadcdcdddbdbcbabcacdbbaabdcccbabbbadabcbccabcddbabcbdddaaddadcdbccccbbcaddacbadcdbdbdbbacdadbccbcdbddbcabcaabdaabccaabbabbccdaacddddbadbbdccddabcbdadddcbabbbdcbdcbacbcaacbdacddadccddbbbacbccdcacbdcbcccbddbcbcccbbcbbcaaadcbdadacbdddcbcabcbaddddbabbdbdacbbacddadabcbddaddacccbdddbcadcdababcbccacdcdbdcbaadcdbaabcbaadcdccddcdcaabaddbaabbdabccdccadadbdbadcaadbcbdaddaadbdcbcdacbbbbdaccbadbbdcbdaacccabbcaaccbddbbbdbbddbcabdbdacadbcccbdcccdcbccabcbbbdcdbdbcaaccdbaadaaaddddddbddddabbdaadbdcbccdddadbddaaddcacabaaabadabdaaaabdadddaadacacdcaaacbaaadaccacdadbcdccddabdadcbabdacaccdccddaaadbdbccbcbdbccaacdbdbdbcacdcdabbbcaabcadcddccdcbbccadbabbaabbababadbcdcccbbaccaaadacccddaaddaddbdadaaabdddbdcbdbbbcbabcdacbccbaaccacdacbcdbcbaabddabdaabaaccbbccccdbacadbcccdadcdccccbddaccbddabccbadaddbcaadaabaabbaacbddcdcaabdcababacbbdddadccddacaabacdcbaaccbdaccbdbdddbddcdbabdbcaabbcbbdddbabdabbccabdabdbccbbcdbddcdcabcccbaaaddbbccdbcadddddaabdcbbdcccccdbacddaccababbabbdbdcdcaaacdaacdabbcbbbacdcaccbcbabbdbbddccbaadcacacadbcbbddcdcaabaadbbdbabcbaabaadadaababbbaadccacbbbbcbdccdcadbdccbadbdbdaddddbaccdaacabbbdcaacbddcbcaadbabbcdccbdcdaaadcbbcbdabbddaabacadacaacdadcbdcdadadcabcbcababadbacabbbccbdcaaaccacddacababbdcdbcdaaddbcaaaccddaccacbdbbacacdaddadcaabcccaaacddcacbbdabcdabbdacbcbaccabcabcaadaaadabccdbabcdaabaaadcaabdacbddcaccccbccbacacdcaaccbacabdbddaccdddbbcabccbacccaacbacaaaabdcdbacdbaddcbddaaaaadbaacadadcadcdbabddcdbaabbbcccbcbadcdadbaddbbcaddbcdcbabcdbbcbbdbdcacdccbdbdbbbcadcccbadbbcdbbbabcbcbddbdcdbbdbcddbaaabcaccaabdbdbdbbbaacbddbdbccabdcddcbbaccbcbdbcbcbbbbabacbdbcaacbdbddabbbaccddbddcbddbcacbacdbbabbcaadbdbacbbdcbcacbdacacdcaaddabacdddcdcabaccccdabdaacbdacaddababdcacbcbccdcadcddcbcaaccacaacccbababdacbbddacaabcbdbbabbcbaacbacbcacdcdcbbddcddacbdbcdabbddbbbdbbcaaadcdadccdaadcaccdbbddcacbdbddbccaddaaabadcdbccdcdacbdcadabbadabdbbaabadbbbdcabaddddbdabddddacbaddcacbcabbbcccadcadcdddbcadccddabdbcdcbcdaacacbabadabbdcdbacacdaddadddcaacdcbdbccacdbbdcaabbbddcdbacadbacdcaddcabaccdbdccddccbabdcbcdcadaacbabcadaccabaaddaacdabadabddadbcccbcaaabccacdbdabaadacabbcacbbcaddcbbacacccadaacacdabddccdcabaadcccbadbbbddddddacadbcbdabbbcbcccdaaaacdcaaacadbbbadddcbbabdddddaddbbddbabdbcadddabcdddcbbcbcdcddccdbbcbbbdbcdadadcbcbaccccacbaaabacbdbdccbcbcdbbddbaaacbdbdcdddacacababbaddbdcbdbdcbbabbbdbbcbcadbdadcccaccbcadaadcabcaadcbdabcdddbacaadbacdcdbabaaabaabaacbdabcdbacabcddadddcabcacbababcadabdbdbdcbccdbcbddbbaabdcaaaddddbdbbddbdbddcccccaccbcbbbbdbbcdcbdcadcacaacccdaacccdcbbdbdcddddccdaadbdadcbdcdddabddabdadcdcbcabbbacccdcdbaacdacdcdcaddddacdcbdabdcdaababdaddbdaabcaddaccbbcbcbccdbcdabbbddcbdcaddbcabdcdbcadacabbcabbdadabbacdabaabbddabddcacccdcccbababbccdacaabdcbadabadaacaaaccdcbdbdddacdbcbadbdbadccaaadcbbaddabdadababacbacbdcbdddbdcdcaadccbdcacbadcdaccaddadabcbcdaaddacdddacaaabbdbcabdcdbbcbccccbcccbacadcabbacddcabcbdcdddadcbcacdcccabcaababbccbaddbcccbbadddabdbbaaadbbbbbbdbbdbdaabbccaaacabdcbcadacbddbbdcddacacccacbadadcddacdbcdabccccaadbbccdddddbcdaadcdbcbbabdadbbcdadcabababbcaccdbcbdbbcbbdacbbacbddcabbdccdcdcbcbcabaaccabcdabcdddcabcacbcaaccdaabdcaddbbdddacdbbddadadddbaacdccaacbcaaacbccccacccabccccabdcdbacacccdccadadaabdaddccbcdcaadadcabbbcdcddbdddcbadcbbaacdbcdadbacdabdbbcddccccdcaaaadbcacdaadabacdadaabaacaaabbcccbabacdcdabbcaccccaaabbdcdcdaabbddaabbaaababcdcbbdbcbaabdacbbacddcadacdaccdbcaccdbaddcacdcdcdbcbcadddbaaaabcbbaaddadcccdcaaadaaabadacdabbbaadcddacabacabdbbbabacbabbdbdcaadbbcbdbcbbabaaacbccadcbbcabbdacaacdbaccbddaccdaccccbcddddabccaccddcdbadcccbadbacacdbcacdcbcadcbbccababbacddccabccccadabcabddaabdcacdbdbcdaadbcddcabdbbdbcddbcaadcbadcadcbaabbababcccdabcaadadddbcacdbcbddabcdccdbbcdbbabdaddbccbadabcdbadaadaddbdabccdbdbccbcddccccbbddcbbaccaaddbcbbdcbbdddcbcacbccbbdaddbcbcabdbccdddabaaacbddbdccaadcbdababcbddcadaadbadcadbbdbacbadcdbddccabcbacadabdcccddddccbdababcabcddaadaccbddbabbcddcbcbbbbdbbdadcdaacadbdbabdcacdadaacdaccabdbadbbbaaddacddabcdccadbbadadcbdcabbdacdcadcdbcdccaabdaccddacbccdcccdadddcbbbbbdccdacaddbbbbdcaaabbcbaacbacbbcabdcbbbcbacbdadbdccbbcbbbbacbcddbbaaccdcbcacdcadbcdaacbddbbbaacbbbbdacbadddacbbcdcaabbcabaccbbdabcbbcaaababbdbbdccdacabbbbcaadbbaacaadacdcbdbdbadcdddcbabadabcdddabcddaddcaadbccaabbbabbadddbabaaacadabbddbcadaccbbababbaccbcccbdadbdabaacdbabdbbbbbdcadaccbbabccdadadaabbaddbdbbccdbaccdacacdccdadbdacabcdbcdcbdadcbaddbbbdbdababbcbdccbcdcdcaaaabbabccbadabdabdacabacdcbcacaadbbbbdcbbbdabbcdcacbccaacddccbaabaacaddacbbdddddbcdadccdbcbcdbbaaadbcadbdadbacaddbccdbabaddabcbcddcdadddaaacdcdadcacabbcdaaadcbcaadcbbdaaabaaaaccaacdadaacbbccadbadccdaccbdddbbdadadacbddcbccabdbdacaddabdddacbdaccabbdabbdbcdccbdcacddabbbcdaadcabbdcabcaaaaaaadbdaddcbaccdacdabadacdacddcadbcdaddabbbadccaadbcbbaacadaaacbdddabcadbacdddaddbbdaabddadadcdbcddcbaacccabbdddbbddbabdbdddcaacbadddacdaabbbbbadbbcaccbcadcbcccbabccaaaaccbaabbbaacdadaabcabcdabccacdacbadcddbacddcbbcbbadbdacaabbbdabadabacabbdbadbaaadbabbaabddaccddbbdabbcaddacaddbdccddadaddbbadaacddcbbadabddabbabcabaacdaddddadcddcbcaaaabaadcacbbdadbdcddbcdaabcdbdccccbadcbdaddbdbcabcbdbaadadacddbaddcadbadbbcbbbdadbbddcbbbcaadcacbcbacadbcdbbbcaddcaddbbbdbdabbbdabdcdcabdcaadbaccaddaddaaddcbdbaacdacddcdbcdcdcaababaabbcaaaacccbcdabbbdddbacaacbbadadbcaadacdabadccdccbbaacdcbcaccbcdcdccdcdbbcdcbddbdadbccbccadccbdccbcabccacbbcbddccdcdcbdddaabdccabcbbabccccdbcabbaaccbbcbcbaaaabbdbccadcdbcdddacbbacababbcdbaabdbcdcddccdabccdbabbacddbdbaadcdbaccbdbcccabbbbcaabcdabcbdaadbaccdadabcbbcdbcacbdbadbadcdcdaacacccaabdacabaadbcbbaadcaaabdccbdabbbdaacdcdcccbabdadcccbbcbadccaacadaadbadaaccdaadaaabaadadbacabdbadddddabdcacbcccacacaaadcdddaadadacbbbcaadddcadacdabbdbaccccaacbdaccdddddbcbdaaccdacbdacbbddbdccbacdabddcdadcdccabccbccbcabbaccbdabbbcddcaacbbcdaacacdbbdddbbdcdcbabcabcacacbabbbadbadbadbdbbcbcbbddcbbdcdbaacddddcaccddbbbcadacabddababcbabdbdaacdbbbadcdbadbdaabddcadcdcbadadabddbaaaddacccbddbbbdcdccabccacabaccaaabbcbcabbcadabdddbadbbcbbaaacbbccdcbdadaabbcadcacbdaccaccabbabdcadbbbbdcaadbdaddaadcaaddcadbaaabdabbcacccacddaccccabacdcaabcbcccdcddcccccadddcbbcbdccabcddaacadacabdadbcbbadddaadbdbbbabcbadaacbdcacdbacddbbdababccadbaacaacbdcbabdccdbdcbaaddcaccadccadaabbcbabcdadaddbccddbcbaadbdacabddbabbaddcddabcdcbabcaabaaacaadcabcbdccababcbcdcabbbdccbbbcbbcabcbbcaddacbbdacdcccbbaaabdccbdccccdbcbcadaacaccacacacabcacaabdcacbddbbddacaadcdbbacacdbdcbcbcbcdcbadadbdcadcccacacdabcccbbdaaababbabddcddacdcbbcbbdcdbccdccbbdddbbbddcdbbabadacbadbdbabbbcabacbbcccdccddcbaccbdcdbaaabbbdadabcddacadbaddcacccddbcbccccbacdcdcdabbddddbcdbdbbddbcbacdccabbbdbbbcbacddabbcabacaadddbaaaaabdcbcbdabdcbdadbbbbaacdcdcbaaacdabdacdabdddacdaacddaaccbdcdcbbccdbbdccdcabdcccacbdbddadbccaccacaadcdbcbdbacbaddbcbdddcddbdccaccbcdbaccbaadbadcbcdadcbdbacddaddcbcccadcabdbbaacdccaababdcabbacdbbccdccdacbccdcdbabbdaacadaaacabadbaddaacadcccbcbaaccdddcaddddcdadacccbdaaabdabbaadadcbcdababbcaacbccddcdcdcbdbabcbabddacbabdcbbcbccdadbcabccdcadbabdccabbdadcadcacbaaccccbcdbddccadacaaddbcdbbdcbccbadabbddbbadbbbaccdaabaddcbaacdccbbcacaaacbddaacdabbbadccaaaaccaaaddbcbdbccdcddbbcdcdaaaacadacdcbdcdccabbbbcbbddcddbbbbacadadccccacabbbcabaadccccdbbadcdaacccbccdadbdccccccbbcddbbabdbaabbccbcccbcbadbadcdadaadbdccbbbcdcbbaabbdbcdbcbadcbdcabddcccdadabdcaaaabcaddccccdbbbacabddcbcdabadbddbccccdcdcdbdaaccacaccdbbcbacabcdbcbcacbacdacdbccdccacbccdbbaaaaaacddbbbbaaddccbcabddbccddccabbcabccaccaccddbdddbccbcaabcdacdbacdddbcbaaadaccbacdbadadaaccaadcdbbaaaaddbdacbdacdcabdaaacbcdcadbabcaddbdcadbbaaddacadadbdadbabbcaddbabdbbacaaddadbdbbdbdddbcdccddddcaaaacabcacbccddadcbdcbdbccaabcdcbdccdbbabdadbdababcddabccdabcbadddcabcccacaaaddabacddaacaabdbddadbdcbbcbdddccbadbaadbcdbbdaabddacddabaddaaaacdbcbddddadbbdaddddccaabcacbbcdbbdcddbacbddbacaabcbbbdadccadbbbcbccaddbbdcdddddbbaaddbdbbccdcdcbadccbccbdddacabdcdbbaabdacdbcddbbddbadccdcbbdbbcacddcbcabddacbdcaaabdddadaadacaababaacddbccbacdbdbadbdcccacbddcbbcccabaabbbdaaccdadbacdbddcdcaccbcdbbacdacdcabcdbdabaddaaddbccbbddbdbbccaacbdbabbcdbabbaccbbcbaaaaaacabaadbddccaccababcbbcaadddcadaccbcbdbddcdbdbbaaddadabdaadbabacbbabbdcadcdcadddbdcbbcbabbcdadbaabbabcbcabaddcccbaccbcbbbbcbcddacabdaddbaaaccddcdcbdbaadcdadadbaddcddbbbcbabbbcdadbaaddcaadaabacbacbccbacddbbbddbaaacbcadbabbbaababdddcabdadcabcadcaccddaddaddddadbcccabcbdcacdbacbddaabaaabdbddcddcadabadccbbadabcbdcacbbdbddbdcbcbdbcdbddbadadcdbccdcdbacacddbdcabdbaaacdaaccbdaccabbbccbdcccbcccaacbbbddcbabadcbccbcdcbcccadadacacbbccbccbaaadcbdcdcdcdcaccbbbcdbdabacccbdadddadbaadadabcaabdbbadccbbadbacbddccdcacbddaabaddccababdbbcdabdbacabcbdaadaaccddacdcbcdccbcbbcdabbdcdcbaaddbdbbaadcadcaadadaabcbdaaccabddbdabcbbcddccadaabbacddddbcadcbdddaaacdccddbdbccbbbdbbadaacdbaaddaabadaddbacadccdbbdadcdcbadcdccccadcdacdacaadadaddabaaacadccbbcccddcdddadcadbbbcdcaabadabbabbbdccaddcbaacdbaaaaacababbdbdddaddcbabddbbcbbadadbabcdcbdbdbddaacbccdddbdabdbdbaaadaacacddccdabbdccbdadbacadbadadcbaddbcddbaadacabaaaccbdddbccbdbdabadcdcbdbdcbadbadcaccddaacddddaadcbccacacabbcbaccabcadccdadcabcbacdddbccaacabacdaadcbaabcbbaabbaaddaccbadcdacbbcdabdbddbaccadbdcdbbcabdcdcacbadadcabadbdbbddddaaacdbaacaadbbabcabcadbcadccadabdcaccbaacdbbcaadcdaadcababdbaabdaccddbddcadcaddcdddaabcacdcbbdbbbbaaaadadadaddbdacddcadcaaaacccaaadcbdcdbacccadcdddbccbadabacdabbbbdccdbcacadcbbdcdaaccbcabcabcccaadbbdbdadbbcdbbadbcbaaccdcabaccddacbdbcadccccaaabbcddbdccaccddaccdaccdaacadaabcdcdbadccdbaadcbdcdbdaadddaaddcdbbdabcadbcdadbbdaccccabbdcccabadacddbbdbcbcbdcdbbcdcbcbccdcabcdaaddabdbbbbcddacaaddbadadabbcccabacaadbcadbcdcbcabbaaadcacdcbadaaadbdbcacbaccaaddccbabadbaadbaadbacdaccbaacbbbdabcccbbcbadcdbdcaacabdcccccacbccacdaadacdacadacbcaddcbdbdbcbddddcdcbcccbdaacddacdcaadaccaaccdbbcddabbcdcbdcaddcbaabdcdcdbddbbbdaddcbaabbdbcdbccdcbdaccdabbccabcbdcabaaddddadbddccddccabbbdbadabcdcbcccdbdaccdddaacacbbcccdabadcaadaaccacbdbcabddaaacccacbbaaacdbcdddcbaddacddbbababdacddddcccccbbccaadaaaaaddccdabbbdaaabbaccdbcabaddbddddbccdcdaadccdcbbbaabccbbdacdcccccccbbdcbadcabbbabaaadaacdcabcccaabcbcbdccbbbddccbbbabddccabdaaacdaabddabadcbabbabdaaacbbabcdddbdacccbdddbbcaaaaccbdbbdbbacaadbcdadbdbaddbdadadbbbddbaadcdcdddbbabbaaccbddaabdddccaadaccbbdcdbbcdddccbacccdbaababadabbacaaccaacbbcdcbcbcaabdccdddbcbcadcabaddcdcbacdcababdadbbadacddcccccdcaabcdaccbcccadbacdbdbddaacdcaccdbadbbbcdbdbdbdcabacabddcacdcdccbdaaccdbddbacacddbccacacdbbdbadadbabdabdbbaacbcababbdbdbddbccadadcadcdaaabbcbdabcdbaacbbabbdbccddacdcaabcacdaccbcbdaccdcdacaaaadadadbbacbaaaccaacdadaccdcadaddbacdcadddcbcaddbccdddcbcbddbadaaabdbdcbdbaadbdddadbbbccbaaacdbdabcbdbbddcbcaaacaaadbaabbabacdadbccbdccdcddadcdbaddbcdbdbcdccacaaabbcdbcaacabacbccaaaaabacbbadcbddababbadddaadbcadadcddabdbacacbddaadcbbabdccacadabcbabaabadbccbcccbbcbdbadbccbdccdcbccccaaabcbbcabdbcdabaaacacabdbcbbaaabaaddadddcadcabbccccdaabdcdcbacccccdaccbaaaddccdbcbbbabaabadabaadacaccacaccabcabddcccaacdbccdcbbabcdacaabbcdabadadbdadabcdccdacdacccaabdbcddbcccbaacacadcbcabddcaaccaccddbcaccacdcadacddaaacaacbabacdaadcbaabbccabcbabbaadabadcddbbddcbacabdbaadcbbacadaccacadbdcbcdabadcacccdbbddbabcbaadbbddacdaccaddcdcaaddbdcccaabdddadbaccdbabdcaccbadabacdbdddccbdacaadbbccbaaddabcababcacbbdbbdcbaccbccacbadcbdaadaababdcadbbdcaabbabdbbcbbdccbbbcbdbbccdccdaabccbdadbdcbacccbcdadcdbadbaabcdcbaddcdaaacddaacccdccbdddabdacaaababaddcadacbcccdbccbcdbcdbbacbacaddbcbbcadccdbbbbaadacacdadbcddcacbccdaabdbaccaacbcaababaabbdabddcdbddccadaaaacdbacaaccbbcaacdabcadcbabaccbaababbdadbccbabcbcacadcddcbbcacccbcccbbbabadddcbbbccbbdaadddddabcbcbdbdcbbadbbaaacadbcdbddbaddaabbbadbbadccdccbacdcdacabcbdbacdcaccbabbdcbdabbacbdbbccbbabacbaacadaadcdacbbdcbccbabcbccabaadcbaabbcdaabbdcdbdacbcacadcccbbbacabddabbdacbbacaadcabbcbccaaacadacdcacbbbbadccbcbabddadcbbcbbcccbbdcccabcbbadbabdbadcacadadbbadacacadaddccbccbdacacbbdbaddcaabaaccdabadbdaacdcdbcaabaddabcadbaabbdbcdbdddcdccacabcddabdabdbcccbcaddbdcacccddddbbcadcccbadddcabbaabcbadbdaadaccabcdbbabadbadaabcacddabbdbaaadddbcdaacddddadddcdaaaacddcaabaccdbcccaccabbbdcacacbdbabcbdcdcbdcadddbdbcabdbbcdddbadbcacadcbcadabbbaccbaababaabdaaabdabccabcbddadadbcbbabcddcbbbcbcdabbcbabcddadadaabaddcadcdaaddabbaadbcacababbbacbabddadadcbdbacbaddbcdacadadbaadaabacdacaaacadbcdbacbdbcbcaaadadbccbcabdaabbbdccbaabbbaaabddcbbbcdbbdbcbbcadbacbabdbbcbbbdaccbcbadcbddbcacddcbacbcdccdbcdbadabbdcababccddabaadccccccdacccaaaacdabccacbaaccbcadaaababdabdbdbbaacdadcaacaacbbbcaaabdbcaabbdabcabadddcabdccabbddcdddddddabbabdacabcdbdbbcdbbccbbabdbbbbbbccaddcdbbcadaadabddcccccbddbbbabcaaaaaddbadcaabbdbdabbabbdddddbcdbcaaacacdbadcadacdbbbcdcacaddbbcbbcaddccbbbabdcabddbcabbdbcdcbdbccbbdbbcadcbbbbaababccdadbaddccabbbaaabadcdabbcdcabbbcddccadcdaccbccabcbabddcabbcbbdacabdbbbcadddbadaaaadabcaddccdcdbbdccadcccaccbbaacbddcbacadcbddbacddadbddadcdabaddaaddbddbadbdbbdaaabbdcadbcbbcddcaccacacaacdabdbbddbabaccbcaadbdaaabadaacadadcbacadaadaddaadaabcbadbbbddabacbddadbcadbccababaddadbacbcddbadabbdaaacadcabcdbbabdddccacbcdabcacbcdcabcdadcabcadbadacbdcccdacbdcacabcdcbbcbaadccacbdaabdabcbddbbbacbccbcdadbdcadcacadbcbaadcadcacadccacddcbdcbcdbbccbaaacccacbadcabaadacaaaadbcdaaadbdcbcbccaaaddcbcadddabcbdaccbaaabcbbbaabdbccdbdcdabbcddaddbcbbcdbcccdcacbcdcbcbddaadacddddcadbbdcbbbdbbcddbadbdcbcdacdcaaccbaaddacbacabdadaaacdbdcaadcbcadbdddbcaccacbbbddcabcbbbbdcddcdbaccdbddcaaaabccdbcbabddcabcddbdadbcbcdbcdacaaaadaaababdacbdaadbaacdbdddbbdbacccdccdbccdacbadacbcdcbbaaabdccaddacccdcbabbaaacbdcdaccbbdbacbdbcaaaaabadbcaabdaddbbcdacadccbdcabaccaaacbdbdcbbbcabbcbcbbbbdacdcccacdbdccadbabcdaadcacaacacbbaccaaacdcccbdbdccccdbadcaacbdcdcbbdadcdcbcaaaaabbbabcdbdbabbdababbdadacdababbdcdddacdcadccbcdbcbadbbbddbcddddbabbadacbdcbddaddcaddddaaabaaacabadbbbacaadccbabcdbdcdcdabaacaacdbdcdabbbabbabaccbcaddaccabdbabcdadabbdabaaddbcbbcdadacdbbcbbdbaacabcaabddbadabbacbbcdbbcacaaaacaabcdbdabcddaabcbcddcdbccddcdacccbcaacbdddbbbadacbbdcbbbacdaaaccbbaddcccccdabacdddbdadcddbacaaabdbccbcdaabacacdcdbcaabbbacdbdaccbaddcbcbcdadbdbabcbccabcbbcddbbacccdccaadbccdccbbcaccadabaddcbacbcbcdccbdddbaddabcbadbbabcbabaccabcacddacbdddabcdddabcbcddbaddaccbadbcadaaabadccadcbccbbdccadbcbdddbaccbdcabaaabaaacddabaaadbadbbcabdbdabbbdabaadcdcdccaadcbababaccbbbddabacaddcbdadaddacdabadbcacddcbadbcadbcdabccdabdddbacddacbddcdbbdbadbdbdacdaabbabdcadcdbaabadddcaccccabddbaabadbccaaaaaabbddbcbcbabbbdacadabbdadacdcbdaccbcddacbdadabbbabdcbdbcdcadcccdddcbdadccdbaaaaaababcabdbabcadbcbbbaacccbadabacdbabbdbbbbccddccdabbaabbbbddadcdccbaadbdbabbaaddbdacbaacdddaabbacbcddadbadddccdbbbddcddabdddbcdbdaccabcdcaabdadcddacabdbacdacacbcddcdcacacabbdcdbdbcdbacddbdddabbccaccaccababcdddcacbbcddddaabdcbdcdbbdcadddcddcdddacbdbcaddbdbacaacdcaadcdaacaaaddbabaadacabdcdddbddabbbdbabdcbaaddccaabadbdbcaabccbdaababaacbbdabdadacdddbaccacadcdcadacbdbddcabcaabdbbdcaabcbdaacabaddcdadbaabbbcbbabcaabdcdddbbacbcbbcccaabcbdbbcccacdadabaadbdbdcabadbcddacacaadcabdcbcaadbbcbdaaabbbcbacddddcabdbcbbddcdccbddbadadbbcbbcdccbcdaddcbbdcbadadaccaabcdbdcbdbdbcaccbdddcdbccabcababbbdaadddaaabaddadaabbcbcaadccddbbbbcdbdaadddadddbbbaadcaccbdaccddacaadccbbccaccbdabcabccaabbcdcbdddbdddacbccdbddbacbcddcaacbbbcddddaddcadbcaacdccacbcbadabcbadbddbcabcbdaacccabdcbcabdcbdabbbaadcdacadbccdbabddbdbaabccbadddaddaddbcccbadbbdcabddbcccdadddadccdbddacdaccbaadbdbabdaabdbaddcacabddcacaabddaaccadbdabddacbdabcbccbcdaabbcbadbacdacbaccbbbcbdcdddcccccabacccbcdbcadbccabaadaabacaddddcbcaddcdccbccdcbdbabacacacccacabbcaacccbddbdccccacbdcadbdcaccabcbddacccbbccbdcbbacabadbbddacbadcabdbdabdbdcddcbaccbaaccadcbadacbbdababbcaddbadccddcdccddadbababcacbddbddcccbbbbacbdbbbbaabbbaddaddccaabaabbccbabababbdaaaddacdcadccdbcaaadbddbbbadabccccabdabbdccdabaabbaadccadccdacccdbaadbbaccdbadcdadacdababcdbbadccabddaadcdadcbcdcccbabadcddbbdcdcaadcadaaaddaddaabaaccbddbbaabdcbacabdabbdbccacccbcaabbdbbccddbcabaddadbbcbdcdabaacbdbdbaaaadabadaabccbabdbdaacbbcdadcdcacdcdddcaacdbcbccbbdbadbdbadbdadbcbabbbdadbccbbbdbacdbbcddaccbabcbcbcdcaacbbdadddcabaadcdaabacdcbcabdbddcccbbccdbcdcdcbbddbcbcbdbaccaaadcacbabdbcbdbcddddcdbadcccacdcdabaccdabccbbcadcbadabadccbddbbcbbacccbaddddccbccaccbbdccabdcdccddbaaccbbaddadabcadbabacaacadaaadccaccbaadaccbcaacbcdbacccbbbcbacacbcccbccbbbccbabadbbdaaabddddbdbcbbccacaabdcbddbaddccddbcdddddcbdccdabaaddcdccbacdadacbbbdcacacbbcbcdbbbdbcccbdacccccccabaabbdbbaaabdbddacaaddaadcaccacdcdacacaddcbccdabdcccdcaadaaaddddbabccbcdabdccdbadadadbadcbddcaccddbabbddbacabbddbbbcabaabcaccdcbabbcbadadaabadcdbcbbbccbaaacdcacbbcbdaaaabadbdabbcdbccdcdcbcbcdbcdddcdcdadbacbdddbdddadbbbacdaabcdbbbcacbbcbbbbbcacdddaccbaadbabaddabcabccbdbddbabbcbadbbdabdbbacbdddcddddbbcbddcbcacccdccaccddabadacdadcbabcdaccddadddabbcdababcbbbdccabcacdcadbcbcdabcdaabcccbdbdbdbbaaadcdaabdddacbaaaacddbbbdcabbaddbbacacaaaacddacaaddcbccddaaadbcdcaabbbdacabaadddbacdcacacbddbddcaccabdababdadcccbadacbaababbdbabdacaaaaadccbbaddbdbaadcddbaaaddaaaaabaacabddccbbabddacbdccbbcacbbbaddcdaddcdaacddbcbccbbbaadabbddcabcbccdddbcadddabcbddcbadddaddbbbdbcbdddbacdaacadbdcbcbcdbcdcccdaabaddaddbcccdccbdaddccdbacdbddbadabacbbbddaaacbadacaabbbbbcdbbdcddbccbcacdbdbdcabcbccddacabacdbcdabdbababbadacdadddadcdbcbaabbbdabaabaaccdcbabbcdcdddbbaddbabdbcadddbbabbdbaacaccacdadcbabdbadddddbdaaccbbdddbbbdaccaacadccdddbcabdcdaaddbdacacbcbadabbacbacababbcdcaacabdcdddabbbaabbbdccbbdcbcccdbbccbcbabaaadcbacbbcbdaddaadcdbcabadbaddcbbcabbaccaccbdbdddaadacbaadabcddccdabbbdcabdababadcbbbaddbaadbdaabdbccbacabddbcddbdadadcbccaccbbdbddadaabdadbcaaaabdaabdbcdbdcbdccabdaddacbbabccbadddbbcdbaacdbdcacdacbaccbaadccdbddbcdbaabdbbcddddbcbccadcaaabbadddaacbddbddccbacccdcdbbdaabbdbccbcacccbababacabacccadabbdcaabbacdbdabcabacddcaddddadacacbbcdbbdcaaabcbbaadbbbdcbdbacbcdddacdbdbacbcacbbaabaddadbbccdbacadadbddacbadacabdddadddbccdaacbccbdcbdbcbdadbabacccddbdabadabdabadcabccaccabcdcdcdbddbdabbdbaabdabbacbdaadabbadcabcadbaadcdabcdddbcadbbacbbbabbddbabcacbcacdcaddbcacaadababbcabababacacbbdddaaadcdabcabddaaaadbddbddacaadddbabadaabcaacabddabaabaddbbabcdcabddaadaabcdabddccbcbaacbbbddadcdabdadcdababbcdccbccdbdacbdcbdadabaccdbaadbaaadcaccccacabbcdccadddbbbabbdaadadcdbdbadabbccdcbbbbbdcaddcdacdbbbdbbacacccccabdbacababdbdccccdbbddcabadacbddccbaccaddaacbccdddbcadcbadddbbdcdaacdaabacbcbcaaacdcaacdbbaaabdadcddabddacbaccdaaacaccccdcccccbaaacbaabcbccdbdcbaccbdababcdcaaacbdccccccdcdcaddbcddbbccddcabddbacdabbacddcbcdbccdbcaadddbdbbadaacbcddacdbbdaadcbcbbaddbdacbaddcaddaabcdbbbbddaacaabdddccbccbdaacbdaaccbbbbbcdbadbabbadcbdccdddccaadabbabdbcbcdccaccddddcdddbbaadbdabcadcbdcbbbbdabadcaddaababbcbddacdbccdcbaadabadbbcbabccabccbdbbbbabbadcdccabdbaacbccaddbbabbdaddcccbdcbcddbcdbcdcdcbadcacbaadcddbdacdadadbccabacdaaddbdabcbbdabbdddabcdbbdaaadcbacdbcabaccbddccddccccabadcadbcdbcabadcacdbccabaccddcbcadcccdbbacbcdabadacbacaabbbacacbcccddaaddcacdbbaabdcdbcccdabbccdcadabaadabcdbcbcbcadcdbdbacddcddcabccdbccddbcbacabdacbdcdaacabaacbcddbabdadcddbaacbbccdcadbdccdbacccabacbdacabaadbcbcabcdbdacdcddddaaabdbcdbabbbaaacabdbabbcaaaacacddcbababcbadbcaccdbcdacddbcdaadbbbbabcccdacabbdccddbdcaaddbdccdabcaaaaccacdddbaccccccddbaaaaddaccabcddadadadbdcbaabdacbcbcccdcabdaccbccabddaaaabbccdddacccbccbadadabaacbcbcbddaaadbcdccdcdaadccdbbabcdaddcbcdbdbacbdbdbcdbacdcdddcbdcccabcadcccbdbcdabacbaccbccbcdcdddbbbcacbadbbadcbabcabcccddcdbcdbbcbccadbdadacbddcbbcacbcdddcdcccadddabccdadaaccbdaacabcddaddddcdacabcdddcaadbbadccdcadbdcbaadabccaadbcccdbddbdbabcddbabdaadadbbbdbbdadccdbbaccbdaabadcbaddadcdcbadabababdaabcdacbaabdcbbdbccdcbaabacddabaabcbcdbbdbcabcadaadcdadaacbaadcdaccbcbdbbaccbabbdcbdcbdcacaacacdcdcdabadbbdaadcbcbcdcaadbcddaabaaddcabdbadcadcadacbccddbbcdcabaacbbdbccbdcbbdbccddbcbcadadcadacbbbdccdcccbbcbbacabccaadcdcccbacaacbaadbabaccbdcdaadcdddccccdcccbddbcbaabbaccbdabcccacdbdadbbddaaacaccdbbbdbbcdddcbbcdadbbadddcbcacdbacccddacababdbacacabbaddbcccdbbbddacccacadbccbbcaacadcbaaaaaaddbccbbcaabaddbddbbabdbadcbdbcaadbabbcbaabaabbacabacbccbccccaaacdadccbbaacabcbddcdbdcabbdaaadcaaaaacbcdbbbabcccabdcaaccbaadcadbccacabbaabdcaadabccadddbccaaadbbcabacabbbbaccaacdbdbabccaacbacbcadbcdcdaabcdabaacadbcdaccbdaadccaddcdddaddabbacbcdbccbcbdcbbbccbdaabbcccababdbdcbbbbddbddcbcdcadbdcaabdbabababbcdbaddacdcadbaccdadbacddbdbcbacdcddccccaddcbdbbddabdcdabadddbbcacbabcaddbcdabbabbcaadbdcdbbcadbcbddaabdadcdcddbacaadcdaabbadabadabcccaacddddbcaadacddccacabddccdaccadbcbbcdddcbbbdadcdaabadcbcccacdbdbbcdcdbcdbcacadaadaabaacdbdabccacadbadbdabdddabcacdbddcadabbcbcbaccabbdcaabbdcdbdcbadadcdddbbbbbabacddaccacddacbbabccaaacbacccddcddbddcdddddaaadddbccbcdaddbbaabddbccacacbabdaaacbcabcbcddabbaacadcdbaccbcaabdacbaccddbbaaaaacbccbdaacabbaaccbdaabcccbbbacdabaccddadbcacbbcbdbdcbbdddcbccdcbbbaacdccccbaabbccccddacabcdbbbabacccbcbcdaabbcdabccbcbbddacdaaacabdcddaadbbadbdcccbdaabddcaacbccbbbdbdadbcaddbcacbccbdcbaacdddbdbdbdbcbabbcdcdaaacdadcbcccbdacaabacadbdabbbbcbcbbcbacbcccccdbbaaaccbabacddadbcddabdcbbbddaacbcbdccbdbaddbddddbaaabcacaacbcdbdcacddbcdcadacbcaadadcbdcdddbbccbdaaaabbcddbdacdabbabcbcdabccbbbacccbabadaabcbbaddcbcdbaadaadadddcadcbcdccbabadccbccaadbdcbbadcccabcaccdccddbdcbddddddbcccbbcccaccabcadacaacabbccaaadadbbbabbabdbabddbdddcbdbdaabdcbaaddacdadadcdbaacddccdccbaddbabdddcabcbdbabbacabdbababcbcaadbbbbaadcddcbacddacabccbcdacdababdbcacdddcccdaccdccbccccbbddbadaaabcadbdadcdcdcbbacbabbccdbcbdaaccdbcbbcbcaadaaadccdadbbdcabbddbcbacbdcdcababbcbcadcdcbadddddadbdbacbdaadbcbbdacacbaadbcccbdbdacacbbcdccaddbcbcaaddabcdabacaacdadcdaabaabaabccbcacbdbbccacabbaadcccacacbbdabbcbabcdbcddcbcbdbdbabdbaccadcdaadbddcbddcccacabdaacbdbcacddbccbbcddcbddbaacbcbacbdacadcddacadcdcbcdbacbadcaaccddacabdbbcddcdcadcccdacdaadccbbdccabacaaddbddbddabcdbcaaacdadaacbdadbbbbcbdbdcacdabcabadcbcadcdddaaccabcadcddaaacdadabdbbacabdbdbdcbcdabbbdcaaabcbaabdabacadcacdbbddbdcddcdacbcddbcacbccbccbbbabccadbdccacabdbcacdbaaabacbbdcacdcddaabdcdbcbabacbccaabaadaccdbbdcbcdddcbbdbadccbdadbbcddadadbcadbccbaaccdcccacdaddaaaadcadbdaaabaacbaabadbabcccaddadcacddccbacdbbcdbbcbbcbcbbdbccddaaacdbbdcbdacaaccdbbacdabacdaccdbdddcadccadcbdbddbabdbddcabdbbadbaabbacbbdcbcacaacdcbaccdacacbabdcadddaabbaddaccccadcccabdddcacccbbdcdbbbdaadbbdccddbccbaddbcbbcaccabacacddcadcacdccbdbbbcbdddadcbcccddcdbaacddcdabcdcdacdaddadcbbcccbbadbacacddaadacbabcbbbbdcdbbcabadcbccadabdbdbacbabacbacbccccdddbcdbcdadddcdddadddadcbdbccacdaddadadaabcaacbbbabbcbacacbbacdbacacbddadacacdddbddacbacdcadcddbdcbccaddcbacdccdddcbdbdadddbdccacdaacdaccadbcccdabaccbbbddaaddbbdaaacdababccbbadaabdbdaaacdadcdcadcacddcbabdaadbbaaaccabbcbaaacaddcaaabbdcabbabdcbbcccacacbbcdbdcddbcaababdcadcaacbcbadbadbdabdbacccdaaccaccdbccbbaaabddcaaabcdcddccbaaccaabaacddccdabbddbbaddbabccdadccacdccbccddadaabdbcbdddbbbcbdaccbddcbccbaaaacdabaacaccbdbbbcdbcddabcccaaaccabababdddacbabbbcaabddaabdccbcdbacabacbabbcdbbcddcacdabddddddddbcbababacaadbbccdbbaccaadbcbaadcbdcbaadbbabcdbbcbdbacbcadcdddadbbbdcdadaccaabbbccbdabbcadbccbccdccdbadcacdbbbdbccbbddbcbacadbcbbdaccccdccbbbcbbbdaaddcbdaaabcdccbbcbdccccbadbbbabaacacdbdcdadadbcadcdcaabcbbbccbadabbbadacbbcadccdaadaabaabbbdbbaadcabbddabbdbbabcdadaddbdbdbdadbdbddcbcdbdcdbcbdbdcaabcacdddcbabdddacbdaddacccbccacccbcddbbcbcccbcbaddcaccadcdcddbbbaaaddcdabdbaadccabcdabaacdaaddabdabcdbcdddddbcdaabbddcbcabdadbbbdcbaadbbcaabaaabdadcddddcddddbbdddbdcbcdaaccabbbccdabcabaccabbaadbcbabaaccdaacbdabdcadbbbcabaadddbcbdbdcdbddadcbcbccbaaddbadcdaadcaaabdbcccdcdadcdaaccccddddcdcacbabbccaacbbbcabbdcaddaaaabdddbacbbdddbcaacaaabadcddddaccabccbdccabacdcdacaadaccbdcccabbdbaddaaccaacddcbacdcbcbcbaccbaaddcaddcaccaccdabadbddaaadccaccbccabdbdbdadddabddacdababbcdacadaaacababbadddcaddcbcadabacacdbadadbdbdadcdbbccdbcabcbddcbcbcddbabcdabcaadcdcabaadccdbabdabcdcbacbccdbcddaaabadacdaaddbaacddbdcaccbbaabdabadcdcaacdbcbdbaacbdcbcdabbaabbdaaacbbabcddacdabadaadaaddbacddaacadcbbbaacbdacccdabcdcadbaadbabcaacbacacaaadbbaabdbcadadbccbcdccbdbcccbbdbadbbddcadcbcdaddcccdbcdabbadaaabaabadabadadcbccbbadbacdcdacbbbcbcdbabccbdccabccacccacbabacdabcdabacddaddcbcaaaaabcabbbababcabccaabcbabbaddbabbbdcababbdbaabbcdbdccdccbbccaaaacdbbbbacbabadcaaaaadabcaadabccaabdacdacdbbbddddcbbdcadaacdacbdcaaddabaddaabbcaddaccacdbdbcdccbbbbcbdcdacabdbbbbabddbcaaddaacdbacaabcaaddbbdcdacbadbaabccbcabcadddddcaabcabcccbccaabdbaabaabbacbadbadacbddcdbddccbcbdbabcabcbdadacaacdcbbbaabadddaddacbdcbaabdcdaccbccadbaccdaabddccaabaadbcbdadcbdddcccaaddcbcaababaddcaccdcbadbbbccabcdabaaddbabdaadddcadddbcdadbcccbbbdccabbdaabaabbddcabddaadccbcacbccbcbdaccaacadacddddaadaaddaacdaddaaabaacdddbdcadcbbdddbcddabbaadbcccacddadaddaabdcbbcbdcbbadbbbdaabcbbdbbcdbcaadbdbdcbcaabdbdcdccdaacdbccbdcbcacabadacdcbabadadabbbddaddcabcddbabcaacbadacbdbddbaddcdbabadbdcaababbbddcccacaaaaccaabddbbcdcaddbbccbccbdcaddacacbaccdddaccacaaaccabcbdccaabdcdacadddbbacbdbbcacbcccacbdcaabbbcbdbbadadbbcdcaaaccbcbddcaadddbdccdbddcccabcabcaaabbaccadadbaaacdcdaabaabddabacdadcdbacdbadbddcabcadcccddddacadabdbccadbbdaaaabcdcdacadbcdcdccdcacbbcbbcdadccaddbbdcddcdaddabdaaaacbaaddbbbbdaabbadbcbbcdbcbcacddbdccaacbbabbdaaadddacbbccdacadaabdaabcaadbdacbdadaabadcbaaabdabcdcdcacbdddbaccbaaabadbbdbbbaadcaaababdbacabdbcbadbcbdcaaabdbdaaabbadacaabbdaadbccbbcbaabcacbadcddbdcbbcaabcaddacabacbcdddcdcaccaadcddcacbcbbdcdbbdddbadcaddbabccccbbaccbbdadaddbcaddbbbcdbbabbdacdcbbcabdacdaabdacbcbdbaccaabddcbaabdcddcccadccbddabaaababbacaaabdbdcccbabacdabdaaabcabcbbcbcacdbddcbbcaaadcbbbcaaabddcadadaddaaadcacbaccabaaddbaabdbbaccabcbaadbadddaabdadbcadbaadbbbcbbbaddabcbbbdbbbcccdbbaabcaddddddabbbcddbaaabdcadacaaadcdbcaadbdddadbdbbbccabddbbbcaaabdccccbcccccbcaaaccdaacccdacaadcbaadbaaddaddabdadbbadcbddbacbaaabcabdddabaccadbdbccdccbccccccbbcbabccccdcdcdaabadccdddaadbaabbcccbcbbdcdbbccddbaddcabcaadaababcddcccbabadcaabaaabbccbdddddaacddcbdacccccbdddabbbbbbbcbdcbbdbdbcababacbdccadbcdadcadddbccbdaabddcdbccdadabdcaadabdccbacddccaabccbddbdbdabaacababccccaabadbabbdbadaacbdcbdadacacdbaadcdbcacbabaaccdbbbbccccccddccacadbadaccadbdcabcaacbdaaabbbcbadcadcabdbabadbabacccddddadacdbbacabdccdbbbddcbaacccaddbbdcbddcabbdcdbacdbcbabdddbabcbdcadddcadddccbcdabcacbccaabaaacaccacccaacaabbaadddaabbdcdacaaadcdbbaabcadddacbabddccccaadadbcaadbbbdacabababdcadadbadddcddabbccccddddcdabbcdabbcdaabccdbdabacdcdbabcbbaadcdcacabbabbbbacdbdadbdabcdccdbbacabdbccbadacdbdccbadabadbccabadbcddadacbabbaadadbaacccabcacbbbddbbdcaddaabddbbdbaaadccdacaadadcaadbadacdcddbdaccbdcbcddbbbacdddddbadbacdabdcbbccaaddccadcdbdbaaaddbabccbdcbccbcaddbccdcbdaaaaddadabacaccbbbbaaaccdbdccacdbcdbbdbdaacdabaaccccacddccdcdaddbcadcbaabcbbdcbacadadcaabcabccbdcadaacaadccacbccacbaabdcbcccbaddaddbcaabcdddccdbdbcbbdadcbcdabbaacdccddcbacdddddbbabcbbcdbaaadabcbddcabccbddcbbbacaaaadabaaabaadbcbbdbbbddbbaddacbacbbdccacaddcccccabcdcdcadabdcabcbbbcbbcabcadbaabdcbbccabdabaadabcbbbdcaabcaaaccdcccdddadbdcdbdbbbbacbddcbdadacbbbcacadacbbabbaaddacdddcdabdbbbccacdabcbdbaabdcdadccdabdacddbbadcbcbdadadbbcdadcaccadadcacbacbdabbacbaabddccddacccbbdcabcacacaccdbbcddabdaaccdabddbdadbbadbcddcacdbdacdcadbacccbbdabaabdbbbddccbacbdbdaddddccabcccabccdacddcbbcdcbacaacdaadcddabcaddacbddddadcbdacaadabcccbacdacdadbabadaaacdcaaddccacbddbabbdaddcdcdcddaaaabbcdadbdcaaabddaadddadcdddadcccbacbcabbcdabcbbddbddcabbbaaccacbccbdcdbacbcddcbabdaaddbcccdbbdcdbaddcdcabddbddcadcadbddcbddccaabbddcbbababcbcaacbcddbaccbaabbdabbacaaadddaccadbbbdddcaacadbabcbbcadacabbcdcabccbabbdcbdabacbaacbbabdaacbdcbbdcdbcaddbbbcdcdadadcdcdccddbdbabccdbbcaadbbabaacbdbdaddbbbacdcbcbcbdcbbadcaadaacacbcabbadbdababbaacccbcddabbbcbdaccbdabbcdabcdcacdcdcaaccaddddaacaddbdbdcadddbaabbadbaacdacdcdbaaccbaadabbaabdabbaddcddccbbabaaababbbcdabbaacbaddbaaddccbdbccbacccdacbcadbacbdcdaaadadbcbbbacdddacaadaaadbdaadddaaabaaddaadacbcabccbbcbcdaccacbaddcdbbdaabbccbcdcabdbaccddbbdbdadbcbadaddaaccbbbaccadacdbbbacabdbbabacbdaaddbbabccbabcbccdcdddaabbadbddbbcbacddcdabcdcacaccadcaaabbcdccacdcccdbcbbaaccacccabadabadabaccdabcdbbaaabbdccadcbacacacbddcaccababaadcccdccacbbdddbddcdaacdadaaaadbadcbcdddcdcdccaabdbaccbcaabcaacdbbababbdcbbdcddccbdcccddbabcbbdcbdcbddcdbaadaadbccbcbadcaccdbadbddbcdaaddbcabcbdadadbddbaacdabccdccbbacaacbddbabbdadbabbccbacdcbdbcdacbdddddcaabaddadbcbbcbcbddcddaabddbaaadacbbacbbacbcbaaccabbcccaaccddbcdacbaccacbaaabaabddcaddccbccbaacdabddbaddcadbabdacacacbcdddacbabcdcdbcabbaaaccdbaabaccacacdddcdcbabaaddaabaaddcbcacacabbaccbbbbcbcadcaabcaaccaadbabbacbaadcccccbdbaabdabdbccbbbdccdacdccccacbccaaaadacdbdacddbbbaadabdbacccbadaccdddadccbbccbdcacbdcbabbcbbadcdabbbcddacaacbbaccdaabcddbbccddcddcaacaadbccbadacdacbccbaddbddbbadbaccddcbcaccdcbdadaccccacdbdacabacaacbabadadcdbbdcccbabbdaaabbabadabbcbccbdacdacdabaccddbaadccbbadcddbbbbcbddbcdccbdbbaadacddaccadbcbbbbddadddbbdcbccadcdadabdadacbcbcaaddabbcccddcbdcbcadbabbbacbaadadbcdddcabbbadbdcbccdddcbcdcacaacdacbdcaaabcbaadbdacddddbdbbcaacadaddbdaaabacdcbacacabbaadcaadccdaddcbbdccdbbbadcbadccbdbbaacabbcacacabdccbccddccadaaacbbaadaadabadcccdcbbcddccacacaddabadaabdadaddcbbdbbadbdcbbdcadbbbdcbabbdccdabadddbddcdaabadcbaaddcacbcbbbabadacbbacdccdddcbbbdadaadacaddcdcbcbdaabddcadadabacaadbcbabdcbdababcbbacaaacbabbacbdaaabbcbacadcaaacabdbbbdabddbcacdadacbabcabdcdddaadcacbaadcadbcbbaadcabbccddbbabaaadacbacdccaccdcadcddcddababaacbccaacabbccdaccabbacabdcbcabdcddbcdacbccaccdcbbabaaddbaadbdacdbdbbacabdbcdcbbdbaaabaabbaacacbdaccdcbbbadabddabccadccdbbbdcdbabaacbbdcadccdaacbccdcabcabccacaacddadaacbdabdbdadbcbacdabaddbbbdcbdadcdbabcdcdbdcaababcbbbbbccbcaabbbcbcdbacabddcdbcdbdcbdadcbbbdcbcbddbdccabdadbddbbdbbcbdadccdbcbddcbdbdcaccadbcbaccdbdbaaabbdcdababdbbadaacaddcbbddaccbcdbdbbaabdcdbabadcbbbddcbacaaaddaccabdccdadcbbcbddaaaacddcbbdbbabaaaccabbcabccddadabcdbdbcbbcddadbdabccbdbbabdbcddacadcdacdbcadcacdabddcdabacbcdbcaccadccadacdadadbdacbcabcabdaccdcdcaacaccbcccbbaaaacbbccaadbcbccaabbbbbdadccabbdbccbbcabdcbabbacdaadcdbbdadaabbbbcbaaaaadcbdaaaabaabbbddacaacbadcdbbccbccbcacbaadbbdcbcbabbbcddaaddcaaabcbdacdddbbdaabbbdbbbabdadcaacbacddbcbbadabaababaccacddcdacaacbddcaaabccdcbcbbdddcaccdadabdccabcbbdbdadbabddadacadacbacaadbbaabdbbdadaabcadaaaacdbbadaabdbcbabcababbdcabbbbbdcaabdcbddccddbdacbccaacbcbcaddacddcbbbaaddbbbdabcdcbddabaaaccbbcadacbdcbbdabaabcbacabcacddbbbbbdccccdacdaabddbcabcdcbbdcaddddbabaacbbbbcdacacbdbdcccddbdccdcdaddbcbaaabadbcabadddbbcababadbdccbdcbdcbdbbacaacaccadbcbdcbaccbcbcbbccdadcbbddaddabadbadbbbcabbaadacbdabcbddddabcacaadaccbdbdcacddcbbacdababddcacabbcbbdcdacdcdcacbddbbdbaadbcaddcbcccaaaacdabbbacabcbddbbdccbcdcccacbbddcacdbccacccddcdaaaaaaacadccbbdacbabcdcadadddbbbbbbbacdcaaddcbbdcacdcaccbbbbbbaadbbddddadcbcbacbdacbcdcddbdabcbccbbcbbaaadbccabaaccbddadabbdaadabdcdddddddcabdddccbcacdbacddcadbbdddcadbaadddbabaacaaacadbbddbccaccbbdcdcdddbdbdbaacdbdbdaccaddcddbaddcabcaababddaaaddbcaadccdabcadcabcbbdaacdaccddacbcaccbabddacacaacdbddcccdacdaaccbdbbcaadbbcbbabccbddabbbacadbdcbdaccdccdcdacaccbccbbdabbdbbcddcdacccadbbacbdccccbabdaacbbacbdadaacacdcbbdaabdbcdaccdbdcbabcddadcadcbcbdbcdcddbdabdcddacaaddaddcbbbdbddaddddccdcdadadcadccbaaddccbdcadacbbabddcdcacacdbccdbabbdddbaccddacbbbcbddbdbddbcdabcdbccbaabadcabadbcbbcbcdbbbbcbdcdbdadcabbabbcddaddcacbccbcbbbabaabbdbdcbadbcdbbacdcaddccbdbbccccdbcbbdacdacbdddbbddcddaaccacdcbaaaabcddcaabbdddabccbbdbdbabacdcdbbdcdaaaabaacddddaddbbcddcaacacdabbdbbdaadaddbabcacbbdddcddbdcbcbabdadbacadabacddabcccdacbcdbbabdadaadddddabcdbdbacaacccabbbccadddaacaaacadacdcbabddcbccbabbaddbbadabddbaabacabbcacdabcbbacdcbaabcbbcbcaacbcaccadcabddaabcbcdaddcadbcdddcccbdcdaddabbcbdbcccacbcadadbccbcbbbdcacdbdbcccaddadccbcddccbcacaabdccdcabbbbadbdacbbdcacdabcdacacddcabcbaaadccbbddbdcbdcaadaadaddccdacaddcddaadddcbcdcddaadcdcbdbacbbdbacbbacbacbdcaacdabcbabccabdaabbdcababbcaabbbbcaacaacadbadccbbcacdbbacbaaacbaabbbdcdcbdbcaccbcaddbdcabcaddaccabbdbabccdbdadbbdadbbddacbdaaaadbdcabbdcdbddaddbdbddbabcdcdbdbaaddadacddddabdbccaddaacbbadcbadacbccacdddbaabbaaddacaccccdbbccbcdabdcaddbbcdcccadbddcdbadcadaaaabbdaacccddcaccaabbdcbbccbdabbcbcdbacbcbcbbdbcbddbcdaabbcbabcabccaaabbbaabbaaccbacdbbacbabcccdbdbbdaaabadaaccadcabddbbcbacabcdadddadaddcacabdaaaccccdaaacaccdadcacbccddcbbadbddadbdbadaaddcbbaddabbddcbddacbbbadccacbdcdaaddbbaacaddcddabbabcadccddadcbdddcacddccacddcbdbbbccddbacdadadbabddccddaaabbcabadcdadddddcccbccbaadaccbcaccbadacdbabddcddccccacccdbaaddccabdaaaacaacaccadadbdacbcbcbccadbccbcaabababacdbdbdcdadaccabcdaaddadcacbdccbcbccdbdbccdbdbdacdbaacbacdbccbbcaadcccbdaacbdcbbabbccaaddadbaaadbdbcdabadcbbcbcbadadcdbdabdddcaabddcdabddcdbcacdbbbabccadaaddcdbadbcdcdbbdddcdcadacbbbcaaabdcacccdcabbadbaabaccabadccbdcaacdadcadadbaaabcdcaaaadcbcbbaabbcddadbbbabdccbadcbdccdccadcbdccaddbbbdbabccabccbabbabcacdaddcadcdcbbdddddcbadadbabddbdddbbbaaaadaadbdaabbabdaacaccbcbcbddaddacbbabdacdcbbadacbdacdccadcdbabadbcddccdaacbacbaddacbbbcbabccacdbcbdcbdcbcdabdaccccbbdcddacbbacacabcdbaccaadcaabbbaabcdccabdacdacddbacdbbddacdbbbabddbaddadbbaacdabddcabbccbccddbcbcdaaabcacdbcbbcdbcddabddadabaaadbbbbbbccddbcaadbddbbcbdaacbdabdbdbaacdbaadbdcaacccbabbadacacdcbdcacbdabaaccbcbcddabbaccdbbcdbdcdbabbdbccaaabcbddbddbabbadbadcbdcbbbcdcddcdcdbadcdcdaabcbacadbccabbcaabadaaddabcdacdcdaaacbabbcbccccbddaaadbcdccdadbabbbcbddcdadbaacacbcbdddabbbcddadadddcacddabbcabbcacdccbdabdabaababcdaddcdcccbcaacdccdbdddacbbacdabaddaaacccaabbaabcacbdbaddabadbdbbbdadbcccbbddbbababdbacabdaacddbcabbaaabbcadbdcabbbcbdbacbcccbdbbdcdcbcbacbdbbbdabcdacbcbdbbbbbcddbcdbdabadcbcdbcaaacadbdcbcddcdbcccdcdccabcababaccbbcacddddddcbbbdcbacccbdcacbdbdaabdcaddadabdabdbccccacbaddcdaddbdadadaabddcbdcbcccbbbdacbababddacbbbdddcacccadadacabaaddadbacdaadbcbdaccccaccaabdbadadbacccddddcbddcacdccbcdcabddcbaacdbddaccbcdcdbcdcbdddccbddaaacdcbccbbbccdbcaabddcadaabdcdaadcaabcbdbccadccacaadabccdcabdbcadcccbdaddbbbbbacccadbbaabcbabcbaacdcdadabaaaccacaaabaccdabacadcaabbaacabbcacdbdbacdbccdbdbddbcccaababcacdbbcacdabacbaacccdbcbccdccccbadbcadbacaacdbddbcadadadabbabccbbdbcddcbdcbccbabbcbacccdbdbcacacadbbbabddbabbdbadbcbacabbdadabadacdaacccdcabdacbcdcccddcdbadccbcaaaabdddadddddaccdbccbdbaabbddcbccbbabaabadaabdbdabcaccbaacaddbacbcabcbbcbdccacddbdcdccacdbcbbacccacaacddddddcaccabcdbcbbcccbadadccdacaaabbbcacaddccdbadbaaadbcadaccaddbcccdccbccacdadaccbddaccadbdbdacbbbcabbdcbcdbaadbdcaccbcdbbbbbadccdbbbdadacdcaccdbcdcadcccdbaddabbbaaaacaddacbbdadaadcabdccaccdabbbadaadcadadbcacbbccabadacdcdbdbaabaacaaaadcadccdbdbaacddadcaddabdaddcbbaabbaabaccbbccacdbcaddcccacaaddaccbadbabcaadccabdcdcadbcdbcbdbdaaadcacabdbcbdacddaaccdbdccdccacbbcacbdddabadccaaccbbcabacbbcbddccbabbbdbcbdcdabddaccadadbddaacacdbacbacacddacdaddcdcdaccbdccdcdacbddcadcaccdaddcbdaaaabcacadccadcaabcadbacddcbdababdabbdaddcbaaabcdddbbcbcacddcacbbdaabaddcaaacbdbdaacbcbddcbcbabbbdbccddcadbcbcddcbcbbadadadbacccccbdcaabacdcbaabdbbdbcccacbbbdcaaddddcabcacdbabdbabbbacadabdcacccdccaccacbbcdcbbcacbdaabababdcacdcaddadabcbdcbbdacbdddbcdabcdbcbcadcbadbadcbbcbbdabdbcbbaadaddcbcbaddadaadccdabbddbabcabcdbcdddabacaacddaabddddaddcacbabaddbdaacdcddcdbcacacaddbacbcbbdbbdcbddadcbcbcbbdaccbcdbbabbcabccccaaaabddbdbcbcdcccdbdbabbbbcbababdccaccaccdddacccaabaaaacdbababcbaadcccadacbccaacccbcbbaccbcbcccbbccccbcacbcaaaacaaaddcddcddddacbacabbcbacacabdacabbdccbbbbcdabbcbdbdcaadaaddacadcbcbcabcdadbabcadbacdaddbaaaaccdbbadbddbdcacabdababbbbcbaacaaccbbccabdadcccaacdaaaadaaaabbdbccbbbdccaabcbcbcbcdaadacdbdbccaaacbbcacdabddcddbcbabadcaadabbdbddcdcdbaadbacadcbdacdcadccbabcbbcdcbadbccbabaacacbaccbbcbdcddbcdbabcbabacbcbddcddbacbccbcabaddabacaaadcdadbbdacbabaddccaabbccbabbacaccacbdcbabddbacbdbcccddadbdcbbccbcbaaabbdadccdddbbbaabdabaccaacdcdbdbdcddbaabaabcbabcabacacaaabbcbbbaddbbacbbadcccbbacdacccbbaacbccaabcddcdcbbadcdbcccdabaabcbcdbbabaccccbcddcdbaabccccbdcdbadaabdabccadbababacbcacadbccaadabadbcddbbdbcdcacbddcabccbdccbcbdcccbdcadbbcbbcaadbacaddaddddcaaabddbadacadbdadccabdbdbdbacbbcbcbdabbabdbccaabbdbddbdaccdadcbbbacdacabbabacbcbdcacabbadaccacbbbdbaccabccdccadadbbbccbcccdbcccdbbadcaaddcadcdcdccbbdcbccccdcbdccacaacbbadbccbbcbadbbacdcbbdacbcccdaadacabaaaccbbbbaadabdcbcbdaddabbddddbaccccddbcdacdacaaccaaabdbccdacaaaddcbddcaadbabddaaaadcbbcbbabcbaabaadccbaaadbbcbbbacbccaaaccadcadbddacccacbccbbcadbccbcccaababadabdadcbcbcdddabacabbabbbbadacddbaddcaabcaacaddcddaadababcdbdcdacdbdbdcdbabccabdbddaacbddcacadaacaccbdbbdacbcdddaddabaccccdcabcbbbaadbabcbabaaadbdcadbadbcbdaabbdbcbacadcccadcdbddcabdabbbdcdaaddacabcaabadccbcddbdbbaabcbcbabccccbddccabcbbaadcabbbcdcccdabbddaabdbabbdadabcbccbcdbabacdbaabbdddaccdbccccdbccdbabdbcbdccdabcdbacbcadccbdbbbdbbdbbdaadabbbbdcbbdabacdcbadbaddddaccbabccbbbbbcdabaacdaaccaabadcbddbddcdadbcacacddabbcdacdcbdddcaaddbbabdaaacbccaadccbbbadbcdacdccaccdaccbabcdbadaaaababcbaababbdbaaaadbcbdadccabcdaccdaccbcabbdcdbdbdddbcbaaccabccbbaaccddbdcaadaabacdbbcdadbabaadacdbddbcaddcdbacbdbcadcbbacdbccdddccbaddabbadbbddddaabccaacbdddbadabdbbcccdcdbacbddbabdcaddcbcbaddcccddaabbdddcabaddadbcadbaaabdcbbabdcacbadcbaacaacacaadaabcccdcdaabdbcaddbbccbcbbacdbbcddabadaaaddcabcccbcaabadadabdccbdbddbacccdaccbccdcdabbcdcdaadaccacbdcbdcddccacacdcaddcdacdbcccaddbddadddcadddcdcdcdacccdddddddaccdcabaaaadabdabbbadabcdcddaccabdaddddacbbcaddbbcaabddbacdcbbbadaadabbbcbdcadcddcabadbdacbbbbbbadcbadddabbabdcddbadabcdadabdacaddbadcadcdcdaccaabdcdbdbbcaaccbbcdcabaadabacdadadcbacbccbabdbadadaacdaabbdbdcdbadaaaccbccdbaddcabacdbccadadbcdcdcdabbcccdbcacaaabdddcdabbddcbdbabdddcdbcabdcaaddbdbdcbacdaacbdbadaaadddacbdcaadcdccbdadbddccbadabbacacdcccbbdcbadcbddddbbadacbbbcabbddcaccdadcdbdcccaaabacccabadacdcbddabdbbadcccadbcaabaacacbbabaabdbbbdaacddcbdbababbacdddcbbccbaaabbccaadaaccdbddaabaccacdabacbccabaadcdccadbcdbdddccbaabadcdcaabddaadadbcbacdaadbcdbddccbddddbccdcaaddbacabdbdabcabddabbcaadbcbbddacccbbbcdabbdbaaaaccadccdaadccbaabadbdcdcabbacdacabcdacddcadadbaabdccbcabcdccbbbadbbcdbbbbddaddacbabddccaabadbcbaadaaacaaddbabadbbbcaabcbdccacdbbabbdbaacccbcadddddddbdbbbddbcbaabdddcdcaddcaaadbbcdacdabbdddbccacabcbcccbbcbabcbbabdbacdadbdabacadaabdcacbbbcadacdaadbcbcbdcabbddcaddacbdcccaaaaccbcbcccabadacdadddccbadcaabcdabdadbcdbdbccddabdcaadbddbddccbbdccbddaaccaadacadddaccadddcdbcdaccccbababbbadbbbaaadcaaabccbcabdcacacdccccdbcdddbaabcbbcabcaacccaacdcaabbadbbdcdbbddabdacbcdaaadbdaddbbbcdddccacdbdccdbbcdabcaadadbdddababdcdccacdcdcacdcbababbddccaabcdbadbcdccbdddabacbccddcacbbbacccbcaacdbadabdaddbaabcabdbdabbadbbbbaddddbbcabdbabccadbbdaddabccbdbdababcccabbdbcbadababcdbaacacdcbcbabbddccbcbcdacdacdcabcacdbbadabaadadbacdcbadcbbdccacdaaadacbbcbdaaaaadabaaabcdcccdadbacacbbaabbadbaadacccbacdbcbcccbdddcccbbcacdcadaccadcaaaaccaaaddbcdaddabcdcdcddcaaadbcbabdbccbcbadbcbaabaddddcccabdccbcaabccacccccccbbbbdabcdddbbabadddbacaddbccacdcacccddbabacadccbcdcaddaaddbbcddaaccdadccdaabdccdadbbbcbdadccdadabbacabdcbbbaabccbbcaaddaaccadacbcbdcaaadcbccacbcdcaacdcccddacbbdaabbaabbdbdcdcbcccbcbbbdddbddbcbaccdbdabbacddcaddacbcaccbcaaaaddacbaddacdabcbdaadaccbdddabacbacdaccddabbcbddcccbdbcadccbadbabbdababccccbaacdaadddccccaddbaaddcbccccdccacbdcccddbbcabaabbaddcbcaccdccbcbccbcbcbbbacacbbbdcddaddacdbaacbadcaaaaadbacddbbbdacbdaddbdadccccccbaadadbabbadbabbcbddcabdcccdbbadddaabbbbddbcbdddbaaccccccadbccbbdcccbacdababaaaaadbcbbddcdacdcbabacbccaccbdcdbcdadacabccdabbdccbcdbddcadbcdccbbacbadcdadbcabaadddddaccbdacdbbbaddabcababdbadacabddabccbacbdbccdddcccbbdbdaaaacbdcdadaaacdcdccbddbbaadbdadabadccbbdddbdcaacdacdaccacdcdadbcbdcbdcdbcdbaabdbbabacbadcccadbcdbdbdaaaccccadccddbbcdadabadcdbddacdcadbcacabaddcdaaabadbccdcbcdbdcaabbccbdcdbccbaabadacbddcbcbbdcaccddbabdcddcdddbabacbabbbacabcaccdcdacbdddcdcaadaccbbddddbbaadcdbaaccbdccbabcdddabadbdcacccdaccddbddcaaddbabaddbaabccdcadabaacbcdaacbdbcbabadcdcdccdddbabadbbacabaccaacdbadaccbdcccccaaddadbdabdbabccbbddcadcbacbbadbaabdaccbbdddddbdacbacaccadddaddadbddabdaccddccbdbdbbaddaddcdaadabddaacadbbcbccabdddbdaacbddadaaaccacbcdcaadcdbcdbdbdaaaacccaddabdcbbdaccaddcdadaaaabbadabbddadbbadacdbdbddaaababdabbccbbdbaabaaabaabcdbdbbbabdadabbcdaaddddcbadacbdccdcdbbcccbdcbdbdcadccdcacdcdbabcaddacacccddacbcccddccdbcadccbdabdbcdacbdacdabdacdcbddccdcdddabaacbbcbdbbccaaadccdddaaaaaacadbbcbcaccbccadbdacdccbaacacbcadbbdaadbbbbabbcbaadaacdccacbdbcbcdcacdcaababdcbcabbaaabcacbcdcbbdbacabdabbaccbbbdcddcbadcaaacdbdabacbabbacbddcdaacbdcabbaccaddaaccdbaacbacdbbcddadaaabbcadabacdacbdcacbcdbbccccddcbdaadddabcacbdccadacaaaadbbbbbaddbdadadbabdadccabdcdaababdcdccbbddabbccbdadacdabdadacdcadbbdddddbccbbdcaadbbddcdadcabcabbaabbdccadddbbccbabbbddaddadaacdbbaaddcdaddcdccaaabdabbcaaaadbdddcdddacdbbadbcacbbbbdbcadacaccabcadcadcbacbbdccadacdbbccccccbcaacaaacadaabbdbbcdcccdddaabaccddbccabbdbcdbccaadbacbbadddcbddaccaccaddadabbdcabadbcdaddddabdbdabbcbbabddbbbcbacbaabdbacbbacacccdbdddcdccccbcacdddbdacaccccdcacccbcbdbccdaddbddbaadbbbbaadbacabcadddccaddccbbbdbcddccdbbaccaabbdcbdacdbbbcdabcabcbbdcdabbdadddaadbbcdccdccbddaccdaaacddbdddddabcacbaaacbbbaaaddabcabddcdbbcdcacdccbabbcbbacbdcdbddcdabaadcccbbdddccbcbbaabaaabbccdaacbaccdadaabdcbddaaaaadbccbdaddcdabbcaacacbabddcdbacdacbcdaabbdaccabdddccacdbadcbbcddbcbadaaddcdacacdacacddbbcbabaccdadadcbbcbaccdcaccdbbabdcdadbdbdbcbddbdcdbcaddbccddbcdccdbcbcaadddccdadccacbbdabaaddccbacdbcaabbabdbbdadaddcbaddcbabdcdcdbcbabdacddbdcbbaacccbdccdcaabcaadcadbdcdbaddbcdacdbadabccdacdaccbbbbcdaddcccdbcddcbcacbacdddaddcdccdadabbadadaabbcbdbbcbccbccdbcacadbabcddbaacbaccddbdbcbcdacccdaddaaadbbaaaddbaaacdccdcbcacdbbaaabdcadcabacdbccdaabacdabdcccacdababdccdcadbdaabadbbdaabbadbbadaddcdccdbdadcdbdbcbdbcddbddbbbaadabbcdbbbddcbccddbbcdcaccdcabbbbddabcbbbdcccddcacbdadacacccdbbdccddaaadbdbaaaaddbbcaabdbcaadacdddbbbcbcbbcacbbbbcbccadbcbcdcdbaacdadadbaadadabbaadddbaaacbbdbcaaacdbaccdaadbcaaaacbdcbaaddbbcdaccbcadddaccbbaaadaabcadbaacbaabaaaaacbbdcacdaddddadcbacbcddddaccdccabddacbaddbdddaddbdadcbabbaaabdaddabdbadaaadcacaddbadcaccbdacabdadcbaaccacbcdacccdbbdabbcccdbdbdbdabbbbdbdcbdbcbbdbbcccacccddbabcabbbbbacdaacccbaadccacbdabccdcdcabdbcadadacdbdcaacabadaccddaddbadcdcbbcbbbaabcbabbaccadacddabccbbaaacaadddbabbaddbdccddcdcacbbddbbddcbdbaaccbdaddbcacbcbcacdcdbddcdaadcacbdbdddacdcddbacadaacdbcaaaacbbadbdabcbcbbddacddbdadabacadddbdccdcdcdccdccaacbddacdcccabacbaccddbaccadcaacdccddaabbadaabcdabaadaaddbbbadadcdbdaddbabdaaacadcdbadbcccbaacbbdbacbcbccdcccbcccdaadadbabcbbdddbbabdbaabdcddbabcccbabbadbbbcdcbaabaaacddacdbcbcbddabacdbcbddcdaacdcabddcbbabbbbaddcadaccdabdcbabbabbacdddbaaaddcdcaddaddbbcbaacacaacbcadcacdabadccdabacbbbadccdbbcabcccddbabcccddacdcbaabbcacdbccccdaabacabbdbaaaaccaccabbbbbabcbaaaddacadddcdcbccddcabbacaaabadacbcbcdacabacabacbdcbddabdbbdddbdcabbdbbddbbdcdbcbbddddcaacdadcbccbdccaadbadbabdbcacdcaaddadbadbdbabcaddabdbbdaababdadabbbdabadcaddacdbbadabddcdcdaaaabbaccdcdccaaaccdcddbdccbcdcaaddaaadbacbbbccaddadbdacbbcdcacbbbcbccacadbcabbdabbabbadaaacbaacbbdcccddaaabbbbbabbaaabcccdaaaaaabbadccdbdaccbabcdcddbdbdacdcbbabcbcaacbccbbacdaadabaaaaccbaacadbbacbabbbbccbbdbcbbcbccacddbacdcabcdddcccccdcababadbabadcccbccabdbbbbdbaaddbbcabdcaddbadacdcdabbbdbdcabbdbcaabddcccbcadacaadcadaabbdbddbcacdcdcbacdaababacadccbccadbbbaaccdaccbadccbcadaddbabbbdcbccbbbdbcccadbdcbcaadadcdbacccddadcacdaddaadccbddcbbbcbccbaaabaadcaddcbdbabddcdcaabbcaaacbdacbcaccbcdbbbbbbabbabcaababddcbadddcdbdaccbaccdacccdcacbddbdcadaadaadcbdcdbdddcbddbbadbbcdbaadaadabbdabacaadbdcccdcccbbbababbcacdabcccddbaacaaccadbccddbacdaaaccabbadbbacbbdcbddbbabdbcddcdbdccdcbbaddcbddbadddccdbbcbcabdcaddddccbbbccbabccccaccbcabbabdcbdccdcadabcaccdabaccaababbaabbadaabccbcaddabcddddbbacdbccbbbbcbacacbbbacbdbaaaabcabdbdadabcbcdcbbdccdabadcacabbbbdcbbacdbbbbbacddcddbdbbaacbabbdbcdcbdaabddbdbdcdcacdaadcdaccbabbabcbcdacbddacdabcbbcadaaadbbccddcdcaccaabbaacaccdcaaddaccbdccadddcadbbdbccbaacdbbdddadadadadccccaadccccdacdcbddbcadccadccbccbadbcdccadbcacbaaaaaccccdcabaacbbacadbcbdbbadcbddcdbabcdbabccccacbcdcadccbdbcabbcdddbcbdadbdccabcdabccabadababdaabcddaccdabdccaabdccccdcaadcbddbadcaccdacbdacaddbbadbadddccacbaacdcdbdbbdddcbcccacccdcbdbdacbabcdadbcdadadaaddcacbadcddadcacaaabbaaacbcdadacccbdaabdbabaadabcbdbbabdbbddbabdcdccdcdbaacabcbcacccbbccddbccbbdbaaadbdbcaccaadabadcccababdaadadabdcddcbaabcdcdbbdaacdcabacdbbdbbddaadaadddddccadcacbcbaccbaadbaaccbdbbbbbdcccbccbabaadbbcbdcccbbddddbaadddbdaadbbaacdadaababadddcdaccbbbaddccdacbbbbdcbccbdcdbdaacdabbdcbddbaccbdccacbddbbdabdcaadbdddbacbcaacabbacbcaddaabbadabbaaadaabacaacdccbbaadddacbbddccaccadcacbdabbbbabdacdbbaddabcaaadaaaaadabcbaabbbbaddccdbbabcdcbdcaadcdbddddaacdacabacdcbdbbccbabcbcbaaacaccccbcaaaccccaabbadbcaadcdcaacdaaaacdccaccbcaddddacacdaabbadcaccabaacadbcdcbcbcbcbbacbbaacddbaadcbccbdddcadbaaccdddacbcdbaadddacaccdaddababbddbbdccdbcbbadbdcdcdbadabbdbbccabddaaaacbdcdadacdcdacccdabbcbcbcdbadbdbadabdbbaccababaddadcbccdcabddbbbdbdccdacccbadbbcbbddabcbbacddcdccddadbbbccaadaacccaadacdbbdbaaccabbaccccccbaaaabdbcbccddcdddbdbcccaabdcbbbcccdcbbddbcabbcccbddddcaccdaddaccadbabcbcababbacdbcdabcdbacabbccdbdaaadadbcdcdccabdcdbcbcdbddcbddbddbcddadbbcdcadababdbbdcdcddabaaabbcdacddddaccbdbbdbcdabcadcbcacdcdbbacdbdddaacdcadbaddaadcccacdaddbadbddaadddbdccccabdaadacdcaaabacdacacacbbcccabdcccbdaddacaadbabdddbccadaacdaacbaacabcaacbadbbabcbabcbbdbcaaabacdbdddaccccdbbbdddaabdbdaddbbbbdddbdcadcbdcbdaabbacdbabdaaadcdaddddabbddcacaddaddaabaddabdaadddcaacdadcdcbbdabcaccdbcccbcdabbdbdbbbccbcbdabdaabdababaacbdbdbacbbddcaabcbbbdcdbddabbdabbcacbbdbaabcadadbbddcdbabaaddcdaadbcbdbdcdcaadddadccbacbbabccadcabcbbdcdababddcdababaacbbcaadabbabddbabaccacbcaababadccacabaabbccabbcbcabaabcdddbccaccdabcacabdbccabcccdcbaadbcaadbcbaaccddcbacdacccabaadbdadbaddadcbdbdcabdcaddadaabaabcbbccdddadcabcbbbccdbbcdcabdabccaadadaadcacacbbbaabdbdcadaccddbccbbddaccbccacbcdbddbacdbbbadcbaadbdbacaadbdbadddaabbcaaacdcdadaabacbcdcacdbabcdddabdcbbdacabdbaddddbdcdbaaaaacacacbdacaacbbadddaabcccdbbaaadccabbbbdadcbcbcdabbddabaaadbadbabcbcbdabdcdaabccaaadccabcbbbcbabbcddcabbbbcaacdaababdbcbddbdddddbbaacccccdcbadbdadacbbadcdadddbcbaaabccbdccacdadbdcbcaddcbbdbdbbbabcdddadaaadcdbaaacacbadbaccbdcbaccaddddbbacadadacbaadaabccbdbcadbccadcaddcddbcccacddbdbdadccccbbdaadadbaacdcadcbdaacccaacccccbadcbbabcdccaccacccaacabddbdaddbddadbbbbacabdddcaaababcbaaddccbdbabcaddadcaddbdabbccaabdbbbdccdbababbbabbabddcbabacdaadaabacbbdcbbdaddcbadddaddbacbabbcadaadbddacdbcbcabbccbabacdbcdadaaacddaacdcbcdabadabbccccdddccdddbaccdaaacbbcdaaddabacdbbdcdccacadcdadbdaadaaababbbcdcdccaaabcdbcabdaadadbaacbdcdcdabbdaaddcdcbcdbddaabcccbacccbdadbcbaccddcaaabdcbdaaabcdccdbcabbcabaacabbabaadcdbaacbbdcacbadcacacbdbabdaabcdacdcdaccdbdcadcbcababdaacdbbbdcbadadcadcdaadcdabcbdcccccadadbbbcddbcdbcdbdaadcdaabaabddccaadbbacbaacaacbccadcbbbacccdcacbccdcadaabdbbdaabadbdadcccddbaacdcababbbbddcbacacaaabbcbccbbdacacabbddbacbdbbbabadddccdcbcddcdabdacbadababcbccdadcbadcdababcdacdbddccadadcaccbcaabdaacbdcbabbdbdaadcacbabcbdddacaddadacbdacababacdbcddbbabbcabdbabcbcaddadaccccaddbaccdcadcbabccdbcbccacaabdcbccaacbbbdbdbadbdbbbcadcbcabacdadbdadbbbcddabdbbacdbaacdbdccbabddccadbdabbbadcadcabbbcbbbcdaccddbaccdcdddccbbbdcbadbacbdbaaaabbcbdacbacbcdcabadacdcccbadabdddbcadcdbdcbcaaaabbdcdadacdaabcdddbcaabcabaaddcadddaadbabbabbadccbcabdcbbbadcadbabccccadbdbcdcaadddcbddbbbdbadccaccdbabdabdcbacdbbabbbddcacdacacadacddbabcdacabdadaddaaacacddccbbccbaaaddababaaccaaaaaaccabdcabdbccbbcbccabdbdbbdabaadbccbdadabbdbacbcaadbdbcdaddddccbcabbbbdaddaddcdadbdaacacbdacaccadccdbdddaadbcabadbdbaccabbcabdbdbabdacccdcbadcbacbabdbcaacbdcdccdcbbaadacddbccddbdbbbdbaddabdcadcddbccbadccdddcddbbdddccdcbdacbccaacbbcadbabdbbcddadcdcccacdcccdbcddcacdbbdbacdadbbddccdbabadbddcbdcddccdbdadabbabadaadccdabaaacbbccddcbddcdcbbacbacdcabcbbcaccdddcaabbaaabcdcabbbdbabdadacdbcccdbcbdbcbcbbccbdbbabdbbabcdbcdacdadacdacccbacbacadcabdbccabbbcacdcbbbbddddaadbbaadcccaadbbbdcddcbddbbdccbadcaabbcbcadbdadabccbcaddbbbadbdccadbdabdddbaababbcddbdabbbabbbbcabacadccdcbdbabcabaaaadccbbdddcbadaabdccaacacbddcdcdcccacaccddbbcadbbbcababdbbbaccbcddabbdcaccddcacadcaccadadcdbbcdbcbbcdadcdcdcaaacbdcaabcddcccdcacbcadddaddccccacddacbcdabacabbbadbaaaabdccabdbdddcaddddddccccbbdbaaadcddacbcaacdaaddaacbababdddbdcccdaababdabcadaaadbbacadbbcbcdaadcbdcbabdbaadbcbddcddacabccaacbbdccaaadbadccdcdcadcdbbadacdcbddcaaadaadaccabcaabdbdabcbbdbdabbbdaacdcabccadcadcadbcbaaccadbcbbdaabaaaabaccaccbcdccdbbddbcdacadadbadbcdcadacbbadabddbbcacbcaacbbaabaaddabaccbadddddadbbbdddbcbdaadcdcbbbbaddbdaadaaacccdddbdbaaaccdbbacabadbbbdbbccdccbdadbaddabbaaddcddbbcaaccadadababadababbddcaccdcdbacbbadbbacbcbbdbdaadabbcacadbadabcbacdcbcdbabcdaadacaabccdbdbbccbbabadbcdadbbbbcaabdbcadbbdbacadadbddccbccddaadabdabdaaccacadddbdadccddabbcabccdaadadcccbccbbacadbcbbdacabdbadccdccabcdacdaacbbddadbcadacbdbadacdbacaccdbcbbdbbaacbcdcbcdacbbdbbbdcdcbdcdcdacbbccbdcaddaaccdcdcdbbbdadccbdbdabbdcadbdadcabacbdbbbacdccdcabbbdcaacdbcdbccbdccbaaabcddcbaabadaadbaddcaaddbbabcbbdaccdcbddcddbbbdbdabdcdaaddaddbdadbdbddbcdcdadbdabcacacbcbcbcccdbcbbbadccabdaddcddcdaadaaadbddbbcddaabdbdcddaabdacbaadcdaddbbabdbbacbbabbadbcadcaddadbdaacabdbbaaaacbaacdcddabddbbcccdbaaacccccadbacdbadbbdbcadabdadaaaccdcbaacccaacdbddbcbabdddddcddabccbbcbcacbbdcbcbbabccadacccbdbaaabbdadccbaaabaadddbbbbbbabcaddcabcaacbdbcccdadbddddbcaccbdadbacaccbbcdabdbcabbaaaccaddcacaccadcadbacaabadcccabdcacdbadccbdacccabdccccdcddaabdcacadbcccabdcdcaddcdcccbaababdcbdcbbacabbababbacbccbabaaadddadbcaacbcdbbbcbcabcdadadbcdccadacadddcdadbbbcacacddccbcaaccddabcacbaddabccdcbddcbbbddbbcabaaadbdcdbdbcbdccdddbdadbccbbdbdccadabdbbbaddcbbabcabcddbcaadabaabccaccdbddaccbdabaaaaaadbbcaddbbcbababdadbbbccdbcbaaccdbbccbaaccadbcdbcbbbddcdcacdaccaaccacdbdcccdccbacacdcdcbbddaaabadbcdaacbdadaaccdcbddaaddacdacdbbacdaaccdbcaacdacadabbababbdccdaababbaababacccaddbacbcacbbdbacbaadbcbcddddcdabadcccbcdacaabbccacbbbbcbbabcbbbacabbcadaabacabdbaadbdbcaaadbccbdbdbcbaabdcacdcdcbcdaccaacbdadadcbabadadbaacadcacabdaabbbbddacbddbcadabcdcbccddccadaaabdacdcdbbcdddadacadbabcacdacdbaccdbacbbacccbddbbaabaccddccdbdacccdacdcdddbabdcbacaacbcabcbcdcabddcccdabcaccccbbabbcaacdccabbbdaadbbbcdadaabcaccbaddbdaacbccadbabdacdbdcabccbaddcbadcabbcadbaacdccdacddbadddddbdddddcdabddbddbcddcacaabbbaacacbdcbabddbbaaadcdbbaaaabbdacaabbcbcadcdcbbcbbcacbddbbcccbcbbcacbdcddddcdbcadccbabcdadbbbaacccacabdbabcabaddcbccadcbbddddcbbacdbcbbdbbcddacddacdabbdccdbbcbbcbcadaabdacacdbccbadacbdcdbcbddcbccaddbbdccbaccccbcbdcdddabacbdcdbaacdcccbcdbaddccdacaadaddcbdacdbacdcadbbcadbaacbaacacdbacbaadacbabbaacaadccbbddbdcadcabbcdcbbdcadcddcaaacadbcaadbbbbadaacadddccbdadcbddbbcadaaddabcaddbdccaadbcbccbbcdcbbccbaddbcdbcdabddccdccacddaccbdbccaaddbbccdccdcdddcdbbdaaaaababdbadcdccccdbadcbdabdaddddacdaabdbdbbbdcbbbadacaacddcaaacdbcaccadbaadadabdbccdcbacdbaabaacdadcdccbcdabdcbacddcddadabddcbcbdcdacaaaabbbaccadcdacadaaccdabbdbdddcdbcaacadacccbbbbaddadcdccdcdbdacacabcadbdbabbbaacdabaaaddccabaacddccadbdaacacccddbbbaadcacaabccdadaaaabdddccccdadbbccbcddddaddadbbcbdabadababccbaddccbbcaaacabbabdbbbadcbaabbcddacaccddcdddabcdadabcdadabccddcaaaacaaadbcdddadcbaddbaaacdbabdbdbdbaaddcdcccacccdaacdcccbdbbdabbacdaacbadacbbddbbddacbadaabdbcbcdbaadbcdbbabacccdbaabababbbbdbbdcabcdddabcccdbbdcacaadcaadcbdcbcadccdbdbccacabadabddddcabbbacbdabbcdacbdcbdbbcbdbcbdabbaccbdacbccddddccdbbbcdacdbdbcbccbcbaaccadcbcdbabadddacacdcbddccbdbaaaccbcbabaadbdaaddbcdcbadbbdcbdddcdabdcdcacabccdbddadaadcccbbbbabbbccbdcbbbdaaccdccaccaacbdaacbcdadcaccaacacadbdaaddbdbbdbadcaccdcabdbbdddbcabcddccccaadcbbdcddccabbcbdbbdddcdbacaccbdcbbbbddbcccbdacccdbcbdddbabdaaaddbcabbdcadbbacaccdaccbcbdacbabcddbaaddbbddadbcbddbcbabdbcccdbadbdcbdbbaddbadbdaaadaccadcccddadbadccbaaddbaabdbabdbdadbbabadadbaacccbcbcdaadabccbcdaacddadcddcaccaccbaabcdaaadababbcdbbdaabdddcdabddcaadbbdaddbadbacbbdbcdbcdacacaaccbdcdabcbaadbdcadcbbccbddccdaccacababcaddacabcddcbccbaabdabbbaddbdadaaadbabcbddcbbbcccccdacddcdacdbdcdddbbdbbacaadbdaadaaccabccbccbbaadacdcdccacaacbbbcabbaabdaaccbbbdaabadbbddcdbbcdabaacbbdbbbccddddccdcbbacddacacdbbabadcaddcbaabaccdcaccbacabdccddcbbdadacccbabccaadddbaaabbbcdcaccdbbdcaacacabcccabcbabdcacaaacdacccabbdadacbaaaddacdddadaabaadbcabbadccabcbdaddcadddcdcaaacbdddddcababbcbccbbbdbacdaadacbbbadadddcdaadccccdabaddcdbacdcaabacddcdcddadcbbcbdabccabddadbbcbabcddabdcbdacdddbacddbcaadcacacbbcacccdcccabddacdccadbdcdabbbdbccccdbcbbadbcbccadadbabbadaabbcaabbdcddcbcdcaabbabccbaaabadbdbbaacdcddcabddcdcacacbcabcaabbbaaddbdbdcaccbbacacccdddcdbbaadadaaabdcdbdaaddbddcaaaabacdaccacabaabbacccaddcbbcabcabaadccddaccccccacacbaadbbacdbdbdddcadbadbcbdbadcabbaabcbcaaccdbdadcdcbcdccccdcabaaccadadadbbdaaabddadaccadbbcaadbaabdcacdbadcdacdcddacdaadbbabdcbadacdcadcbdbdbbbaaaaddcacaddbbddbdaaacbbabadbdaddabddabbcaacaddacccccbaaddbbcadabaddcbbccbbdbcbdadadabdcdbabaaccabaccccdbabcbccdbacdddbdddbbacdbdbcabdcbdbaccbcacdbddbbbbbcabbccbcdcbaaadcdbaaaabaacbaaaccddacdadcdbdacacdbcdbadabbaaacaacdbaccabcdcaaccabadbaabaabddbabdcaacbcadaabaabaaddddabaabaddcbcdbadbdaadcaccabbccaacbababaabcdcaddbaccddcdcdadcdcabbcadbcddaaccacabaabaadbaccdacaccdbaaaacbbabcaaabacccacacdcdabababcdcdcdcdacaaaccacbcacabdabddcbbcaabddcccddbccdbcccdacdbdccdddbcddacdbcbccddbdcdbccbcbcdbcbbccbdabbcddbcccaacdcdcdbabacdababbaabbbdbdbabccabbccacbcbccadaacbcdcbaccadccadcbdacbcabddacdbdccdcaddddbcadbdbcdcdadcdaccbdbacabdabcadacacaabdcdcdccabcbbdcbdbccbdabadbcaaacbacabcaacbdbdabcddabaabdabddadbcbcddbdbcaddbdbaaacdaaabdbdddbaacdddadabcacdbbdcbbcbcacabbcbdadbbbaaccabacdbcdacadbccbcdabdccdbcddbdaaaadaccdabddabbdbbcbcbabdbcdddadabcadcbbabcccababacdbaccacdddaccadcdadcdbccabdccaddbcdcbcbaadbbbacdbabcccadccbccddcbdcdbddabaaadddadcacbbdccaacdcaccddadcbdcdddbdaadbacbdbccacabbadccbbaaadddadbabdbaaccabccaacbbdbdacaacdadccbdbbabbbbcbdabbccdccdabbacabdaabcaddddccbbabddacaccadcbdcadbaaaaaaadacacaaaadbccccdadbdcbbcabdbcbdbdadacddbbdbbdaaaadcbbbacbcdcacbaccbbbdbdabbadcbcaadabbcbadbabdddbcacbadcdbbbacdcdbddcdadddabcabdbcddadddaaddccdacaaaaaaacdddadcabcdcbdcbadcdabacddccaaccbcacaaddaaddbccccdbbdabdaddbdbaabdbadbcdccaacadbadaccaabdbadcbddadadbbdbaccbcdccaabccccabcacdadabbbccabbdcdcadbddacdcacbadcadacabaddddbbabddbadaabcdcaabcccddadbabadbabdadaccbdbcbabdadaadaacbbddcbcbccdcabacdadbbadbdbcdbbdbdabddabacbbcaaaacadbddadbcbcbbbdaababbbaadaaacadcdadacbaabbaacaaddcabddbcadcdddcdbcddddadcaddcaadbddcbbcbdddbcbcbbcabcdccdaccccddadcbadcdddbadccccbabbbacddacabcabadaddaadacddcbbcdccdaabdddddbaaaacabcddcbccabcdaacbdcaccbbdadadbaadcadadcdadcdccdcacbcbbbaccbabddcdcabdcaaacaabaccaaacbdbdccaaadacbaaddcaaabbabbcdcdabcbdbabcbdbcadddbcdbdbaddaacdbbdbbcdabddacbdddccddbdcdadaccdddbdbddcaacaadaabbdacccbccabbadaddaddaadbaabcdaabbbcdacdabdddbbbabdbbadbdbbcbcdbbcabbadbdaccababccddbccbadddacadcddbdcabbadbcdbdcbcdaaaababddddaccadcbdabbdccbcbcbbabcbabccccbdbcccabdcaacddabbaaccddbdaccdabaccdcccdcacaddaccddcdcbdcddadacbbabcacdccddcbcdbdccddaaddcaacbaacbdcdbccacccccdcabacabbbcaabbcaddbbacbcbbbabbccdbbacdbcbbacbbcdddbacccadbadbbdbdccddddcdabaaaddadbdbacbdcdbdbdadddddbaacbdcbddccdabdbddabadddacccccdbcbbaddcbabddacabbcbaccdaccbcdccbccadbdcabdbdbaacbddcdccddddbcaaaccaabaaabadaccdbdbbcdbcbbaacdcdaabaaaacaccaaccbbcadcdcacadcccacdabacccacaddbdbddbddcacadbaabdbadcbadcbdadcdaadcbacbbaabbaaaacadcccccbabcdcddcdbbacbbacdbbbdccbdabacadbcaddadacabccbbbccdaabbcababbacacbcacdbabdcddbcbcacddbabadbbbbddcabdcacccdbabcbaddddcbadcbbaddbabaccabcdadaaccbacabbcbcabcdccbcbcdddaabbddbbbcbbacadddaccaabdbddbcbdcacbdcdbccbbbdaaaacbdbabbcbabaddbbcbaaabbccaadbdaaaaaabaaadcabddacdabbcabcaacadacacbddccaacdbcbcdccaadcdababaaaccdadaabbbdcbddbcdabccbabaabcdccbdaababbaaaaaddbdbabdddacaaddcacbbddcabdabbaaabcdaacbdadabbbcbdcbddcaaaccdadbbacdbddddacbbcddcdcaacbcbbcdcaacdabbdbcdabcccdaddbaaaabdcbaddbddacdcbdcdccdcdcabcaabadccdbbabdcadaccdbadaaddabdbbaababadbbadbdacddddcbcbcdbddcabdbccbcbdcacaadadcbdbdcabbacbddbcdbcadcdbbbddbbcccccbbcacaaccdccabcddbbbdbdadbbbacddbccadbbcdcadbbddbdddbcabbddccbbbdbadbcbcdadaadbbaccadbcaaaaadabcbadbdddbdcbabaaabbdcdccccbbabaddadadccbadcbaabcaabcbbbdcdadaadcdcababdbddbcdbacddadbbacdabbbadccccdcbdabdcaacabadcacbdcbcccdcaaccddbcaccacbcccdbbcddcdcdbbdbcdacdcabbbacacdbabbabacbcddbcbdbbbdcacbccdcaaaaaddcddbbcccbcbcddcacbdcabdbdccccccdaddbcaaabdabdabcbddbacbcababbcacdadaccacbdabcdbcacbbabdadcaaccaadacdaddcccbcdbbbddcaabacbcddcbaddbdcaaccbccbabdbaadccbdcdaddddacbdbbbddabbcdbaddbdcabbcdddcddabccddbcacdbbcdacccdaddbaccdabbacbbbdbbdcbccbcbdcacbdbadbaaacbbcdbdddbcbacdacbaccccacadcdcbabababcabbdaccdbdbddccaccbaaaccddabbabaadcdcacdbaacdcdcadbcdbbdbcaccaabbdccdadbaaacdbcabdddcdbcbccddaacdcdcabacadcaacabaddbcbdbccbcadcdbacdddabbbdddbdabcccadabccbddccabddccacdcbaaddcccbddabaadccdaaaabbddcdddaabccccdbdcccaabbddaacbadacbabccbcccdbbbccbddabbaaadabaaadbccdcabcdbdbcbcbaccbbcaabddccbdadaccccdcaadbacbaddddcbaadbbbbddddabbadcbcbcbacbbccccbccddaadcccaaabdbddaddcaccbbbdaabdddbbbccbcdddcbbabbdddddddcabdbdddbcaddbcadbadaadabbcdbacbadddaabbcccbaaaddcddbdcdbabcadddcabcbcccdabbcacbacdddbbdccdbabcdadccbcacddbaacadddacccdbddbddddbdbaabadcbadcbbdabcadcddadbbddcdacbbacdcbdabcadccdadaaccadbcddcabbbbcdccbcaddabcaabdaaddadccbbddcbbcbbaddcadcacdddcccdbbdbbbdaccdbadacacaababbdddaabbcaabdbcdadcaadbdcdcdadccddcacaccdbadbddbadcdcdabcbbadcadbbdaccdacacabcaddbabbcbbacaacacaadbbacccacbccaadccdbdaaadddcbcddbddadcdbaacdaabccbdadcaccbcbdaabcbdbcbbcabbcddacbbbdddcdbbbcbcccaaccddcbdbabddadcdcaddcccdcbddacccacabaccaaaaabdcbbdddccaabcbaabdacdbbbabbccaabbdbabbcdbaccdcaadcbdccbcdacaccdacddacbaaaddabbabadcccaccbddadbddcabdbaacdacadaacdbccadadacaaadddabcdadabcbcbdacdcabbacbbabbcbcaabdcbccacdcbcbbcdbdbcbbbabdbdcbacccdddcabcadcbcccdcaabbcbcbadcbadaddbacccadcabcadddbbcddacbdaddbaabbcddbacdbcacddaadbccdbaadcdcccbccddbddbbcbcacabdddabacbccccdbaabaadddbcbdccdbcadaadcaadacacdaadcdabbaccddadcbdacadaaadbaadddabdcaabccbdbdbcaccbdcaadbabcacaacadcdadcbaddcdddccddadaadaccbdcddcbdadcaaaadbcabdcccddacdbaabcbbdcbdccbacdbaccaddcbaddbbcaaacbadbdccacaaadacadbbcdabdcbcbaabbdaacdbcdbadadcddcccbdbbabdcddacaadacaabbdaaaabacacdadbdcccabccbadcccbbcddbaddadbabdabdddbbaaacaddddacbadaaacccacbacbdbddabaabcbddaaadaacdbccdcdcbdbdaadcdbbddddbadaccddccdacaababbdbdbcddaaacdcdaaadcbbdcacdcacacbcdddbdddbcaacbcacdabcccadaaacccbcdbdbcdaacbaaabcbbaadaaccdbdcdbddaabddcadadacdcbacdbdadaaaacabbacbaaccccddaddbaaabbdcbbbdcbdbcbabbcababbddbcbcaaaddbdcbcadacbadcccddccbcadbcaddabbbdaddbabdacddabbbdabaccdcbddbdcaaacadaacbbbbacbbcdcabbdbbdccdadcbcbaaacdddbcdbbbccacaddbcbdacabdbdabcdbbdabcadbbadcdbcbbaaacaadddcabacadcdcabbadddcbabdadcdcdccaddbbdbabcdbadddcacdbcdaddbaddadaabbdadadcbccabbcbdadcbcadaccdbadddddbadcdbdaacbbccbddbabcadcdaaabbcabdacbcbadcaadbccacbdbdccbacaadaabbbabccabbadcdcadaadabccdddbdccdbcdbdddaddccaadbbccadaababdcbccbdcaaaaadcbddcddbdcdccdbcbcacadddbccbdaaadbcbabcccbacbbdabcaadadcaccdaddbcbbdbcbcadaddbdcbbacddadaadcacdabbcdabddaaaabbbdbdccacbdacbdadcbadcdcdbdacaadcdbcddccaadcbbdaaddbcbacacbacbbcdabbbbddadcbacccaabccbaaccbdbdcaacbddbbaabbaccddacaaccdabaacbaacacbcdcdacacaaaaaaaadbacdbaccbcdbdcabcbbbccbacbbdbcbaaabdddbbdadbbbcabadcaccbccdaaadadacbbcacbbbbbdabaddcadccabccbcbadabdbdabccbcbabbcacddaddabcddbabcbbdcccbaabbcbbbcbacccdcdbbaaddaaaabbbdbadabcdabbadccbabaaacdaccbdcaacddcadccbdacbcbadcdcbbdabcbbdbcbaacdaddacbabcacdbccbaccaaaababbaacabccacadabbcdbdbcabadcbabaccddbbccacaadccbcbbabbadaabdbcccbcbaabacadaabcbdbadcacbaddccbcbbdaddbdadbcaabdcbcdcbcbdbdbbcacbbcdabbcccbbaaadbbaccdadbddadcaaadbbaddbdbadcbddabcddbbbbbbabacaddaadabccdcaababaacccbbabacadcdabcdcdadabbdaccbdaddcbcaddddbaaccbbdaabaadabccbdcaaccbbdbacdbbadcabcbbddbbddaacbdadbdbddddbbcdcbbadaccacbdcdcbdbdbaadacacdbaadcccbbbadcdbabcbcaabdcacdadbadbcbabdabaaddbbcbbabacdbabaadcababbacdddcababaaacadcabaddaaabbccddabbdabbdaaabdcccddbabaabdacaabbbcdbadacbaacccdccacdddbbbbacdcbdbaccaabacaaadcdaaacacccaadacdbbbcccbaacaadcdcdbbbabdbdccacbbcabcababdbbaadcccbcbbcbbabbcbabacadbdcbcbcdaddbdbacdadcbbcdcbdcdccaacdacdbcccabacbdbdcacddbbddcaaabcdddbbdaabdbaabcdbdbabacdbacabcdbbdbbddbdbbcbdcdadddcbcbdddbbacddbcbccabbccabdcbaabbcdaaccaadbaadaddabbcbbcbadbdbbddcdabacbbabdacbccccabaadcadbcbdbbcdacacbcacdbdcbcabdbccadaababbcdbcdbdccdbaaddcbdccabbcaddbaccdcddaabdcabbdacdaddbabcccccaddcaccadaabbdbabdabbdbdddcbadbabbdccbacccbabcdabcbbacbcddaaadabdbdacabcbcaadbdcadddcbbdacaabcdcddbacbdbdcadddbcccaabaddcbdcddbabdcbbbabccbbadadaccbccddaddbdbbdccbbdcccdbcbbcddcbcbbbcaabddadacacaabaabbacabdcdccbbabcddcabacadacddcadcadbcdbdacbbcbdbbaadddacccdcddccaddbdcddacbbdcccbadbcdcbacaabdddabbdaddadacdbdaadbbbabdbddbbdcdbdacaccddcabcabbbdddadbaddcbaaaadacbbadbcdabcabaaaccabcaccccadcaabbbaaabdddbcacbaacacdbadacdaadccdcbdcbdbcddbbaaddaacacbaccbbcdcccabaddbbcbcdddcadbbcadbdbcbbacddaccbabbdcbabddaadabddacbbdacabaadcabcbdcbbccaccbdcadbccdaacdaabcaccdcccbddcdbccadddaabcbaadabbdbbccdadcbaabadbadcdabbdacbbcbdabcbdbdabbdaccadacdcdacbaacdcddaaddaaaccbdbaabcdbadbabcbcaadccdccaacdacddbacdcbabdcadbbbdcbadbbccbaaddababccadbabcababbadabdcacacabaaddcbbbddacbbabddddbbaadaabbaccababcadbadacacadccddbdaabbcbdcaaabcbbbdbddaabddaaabcccbcbabaccdacdcdabccaabcccdbccbddcdbaccddddcdbacabbabdabdbabbcddcdddcdcaadcaabdddabcdcdcbbdcbdbcbcbdddcdaaddaddbdbcaacababcbcdcbcadcdbccdbbabdcadccacbbcbcbdbbcabddbabccadcaaaaaccbacaccddabcccadcdadbbcbdddadacbaacdcccbcabaabcbaccdbcabababcccabaddbbaaabbdbbcdacdcbacbacadcbddcaabcacddaacccaadcbbaaaccdbcaabcddddababbbdcbbabddbbaaadbcdbbcbabccaadbdbccddaddbbcdadccaaabaddbabbadcdacddbdccdbbadcbdadacbcbcdacbbcbcacccbcbacbaadbbcccccddacababcadbbddabcabbabddbddcdccccdcbddaabdccdacbaadbbdbbcdbaacddcdbdccbdcabcaadcabaacbaaddcaaddadcbdbcbaaaabaccbdcdadbbdadadddbddbcadccabbbcddabcbcdcbadacdbaaacdccdbadbdacccadccdcbbbadcadbdddcdadccdccdbcbdddccdaddadbcbaabdbacbdccabaccdadddcddddabbcaabcacbbadddbacdcbdccddbdcaacddbbdbcbbcbbdcbccdaddbbadbaaddbacdbaccccadacaddbdbbcccabdbbcaadabbadcadababbadacccdbdcccadadacdacbdadddbdcbcdddccbadaabcabddcdbbddbcdddadcdbbdccbbcaacbabddcbbccacaddbcabdbdddadaaadabaaccdbbabdbadbcbdabbbcddaaabdccdabbdacdacaaccabaacddccdbaabaacbbdacbaaddcbadaaaaadcdcdbbcbbabdddddacbbababddbccdaabcacbcacddacdadaabcbdaacacbcccdadbdddccddaddadcbcbdbaaaadbdbccabcdabcbcbcccdcacbcbaddbbcbaaabdaccbbdcbcccbccbbbdcdddbdcbddbdbcacaccdaabbdcbdcaddabcaaadbbddddacdbacbbdaadabababdabaddcbbdbcccdaddbbbcdbaaacaddcabaccdddccbbccadbacbacbdcdcacbadaabdcacdcbaabcddbbdadbbaabbbaddbddaadabdcabdabadbbdadaacbadbaadaaccadacabdddbbbdabbbddcababdcadddbdcdabcdbaabbccaccdacbdaaccaddbccabcacbbcdaabcdadcabdbbcacabbcddbdadbdacacaabcaaddcaaabdccccbdbcccacbcbcbaccdbaadbdcbcaabbcccdbcddbdaacbcbbacaaabbaacbabbdcacadabdadcadccdbbaadbccccccadbcbcdccbadbcbadccacddcddbddcacdbcdadddaaaddcaadbbaabcbbddabbbadddddcadadcadddabcbccbacadddcdbdcbbbcabadaaaabacaaaabdbddcadabaacbaadbbbdbdadaabdcacabddacbaadbbdcabbbdacdddcabdcacccacbcdbdacacabdaaabcaccabaddbbdacdbaacdddadddcbccadbcdbcbbdddcdaddcdbccaabdbcdcbdaaddcacddbdbcdacdcccadaacdbcbacabccababbbcadaccddccbccbabddddcadadaccaddaddbbbdbbbdcacccacbdcacbdbbacadcbbdcbbdadaabdbdacbdcbbddacbacdccbcdcddabcdbcbcdaacbcddcddddbbbbdbdcdbaccbddcbbddaaabcdcddcacabacaadcddacdcdaabccdcadacacdcdabacddabadcdabadaacadabccdbbcabcacacbcbacaabbdacbacccaaccdaacaabcdccdadacbaadddbcbbccdbddbcccaabbcbacabdcccacddababbcbdbdddcacdbaabbbdcbddabaddcaabdbdaacdabcaaddadaadcccaccaacbdbaccabdbbabbadbcbbaddbaaadbbacdabaaacabccbabadcacddaabbbabbbaaddacdcddadccaabadbbcdbcadacdbabdbbdbbcabcbbcbaabaabdbddcbbdcbaccacdadbacbcccbcbaacddcacdbdbdcddaccabbcabadcaaadabbbaadbabbdddddaaadccccdcaaccaacbccdacaaacccbadaddbccabdcccabdaaacaacdcdadcadaacbcbdbbbbaadcabacdbcddacccdcdbdbacddabbababdacaadbbaacbdcddcbbbdbdccdbaaadccdbdabaabccdadddddaccabcdbbabcdcaccaaaaddbaacadccaccbabdbaaccbccdabdcadbdccbdddbbcbddcaabbacabdbccbdbabbdcdacadcaaaadbaacccdddddcabcccddaddccbdcbbcbdbabcdacaabcddddacddddbbdacdcbbaaabcbbabcbcacbbcbcacccabaacddcbbdabbcaadbbadbbabdcbbddbaadaaddcdabacaadbddccbbbadadbacccccdadbbdbbcaccccdcabdbaaccabbdaddadcacacbddbcdcbdbacbcaaddadccccdaccacabcadcccbcdbacbdcbbdcaabccdbbbccddcddacdcaabaadcbadbdbccdaaadccaaadccdcbabbddbcbbdabadaaacbdbbbbdcacaabdaccbcbbbcbabcbccddaaabdaabdbbbbbccccddacacbbadbdaddcbdaccdcdccbaaaadcabadabdccaadbcadbdbbcccabaddcbcaccccbcabdaaccbbddcdccaaabaaacacdadcbdccbaabbacbdddcbcdbbcbabadbbdcabbccacbcbaaaaabdbadbdcbdbdcdbcadbbbccdcbabdaddaadadbbcaccabadcaabbbccaddcdddabbdbddbdbadddcbdaccacabcacadbbacadabadbbbababbbddadcaababdbdddbcdddcbacbdbadcbbbabcddabdadcdcdccaaccdcbbbdbbcbbccdaaacaacbcbddadacddbdbbbbbabddcadadbdcacddacacaaddcccadacccdcdbacdbdadabbcccbadbdbcbaddcdcaabbbaccdaacabdadbaddddcaaaadccdcadddbdccbdbcbdcbddcddadcaadcccdbbbcbaaababbabcbacacbcbcadcdadddbacbdadcbabcaaaccbadcbdbdbbaabbbbbcdadbabdcdaabbddaaacbabddcdaadcdadacbbdbcaadcbabbdcacddcdaadcddccaaacadcdaccaabaadcdcddadcccdccbddabccbcddabbdcbcdddddbddadcbadcadcabdcdbbacbcddccabcbabbdcdaadccddcbbdbdbcbbcacdbcdbdcbcdcbdaccdcdcadcadacdacbdadcabbbbaadbcbdacccdcbbbdddadbddbbdcacadcddcdcaaaaabbcbabadacbbdcadaddddaadcddcaababbbcbbbbcccbdaadccbbdbaabbcdbddcdbccbabaaddadbdbcbbcccbadcdcadaaabdcacdbddcaccadbdbbabaaacbddcdadccdabababdbdaabbdacdddcabbaacccdadbaadcbbbbdaddbcdddacabadcdabdbaddacadadabcdabaccabccabbcaacccadabddbbbbbdcadaaabdacccbbabccbddcacddbdddaabdcccacabbaabbadcadaacadbbcabcdddaddcdacaadcacacacabbaccbaaabddbbbacdbbcdbbdadddbdcacdaaccbccdcadbdcaaacacbaaccbbbacdbacdadbbddaadcdaccbdcabccccaacdbaccadcaadccbccdbacbdcbbaddbcaaadbbcdbddbcdcddbadcdbbadbbcbbcbbddbcbdabcdcddaabdbadcddabdabcabaddcbaaadaabcadabdadcdadabdcdaacbdaaddaadbcbdbabdaadddccacdddacbccadcbbadcdadccaabddcdcdddacbaacaacabbcbaccdcacdcddddbcccddccddbcbcacdddadbbcdccdcabccbddcbbcdadacdddcdddacdacadddcdcaddbbbbcaacbcbccbccccbaddabbaabacbcdcdaacaddaddcadbaacadadadadbcbcaddbcddbddbbbbbdabaccccacccaaccbbcdcdccadacaacbbdbdcccaddbaddacccabbaccccabadbbbabbdbcdaccacdabdcccddabbdabacbccdbbdadbddddccabbadacacccddbbbccccccbcbabadcaaddadcacdaaccabcabbadbaadccabadcdabdddbcdccdbaddbcbaadaddbaadddbccabcddadcbbdbacabdcdcdbacdbaaadccccdddabcbcccbbdbbcadcdaccabbcabcaddaddababcacdccdabdcacaacbacabcacbbbdbbcadcddbcaccbbbabcabaabccdaabaddddacdcbddcbccdacbabbdbbabdbbcdbdcdccaabaccdabbdbbbcadbdbddccdbacadddbadccbaccababddaadadcbcadbddabdbbcdcbdbbdaccdddbacbddcbddcbcbbdddddbcaabdacbcadbbacabbacbacbdaabbbdcbaccccdabcaaddccacdaddbacddaaabbdbcaadcbbbaacdabadaadabbcaaabbbcbbcdbdccaacbcbbdbbaabcdcbadccaddaacbbccdbddabccbaaaddbdcddabcdadadaccabbbdccbcbcbdcacbbdddcdcbadddddccbbdbbbdadbabaabacabdaabccdbcdbabddaabbaaddbacbdaccdacdaaacdadabdcdcdcbbcacbcabbacbbabccccadcaaacabcbcbabcbdcdbacaacddbaddabdbcbbadaabbacdcadabcaccbcccabdacdcaaabdbdadaaccdcccabdabadcbdcacbdbcabdcbbcaaddbdddcadbdacbdcadcaaadbdbcacbbadcaadcbbdcbbaadabdccbdabcbdbdcaadbacaabcbccddbdcabbdcbccdbdaadbdabcbabbbcadcbacbccdcadbddabaaacbccaadbcadcbaacaadacdddbacaacaacaadcaacdaddcabcdddacddbbbdcacddbbcddaabbbcbabacabcabcabdbacdbdccbcadaaabcbabbdcbdbccccadbbdcacbbddbdcccbbbdadcdbacdcbabcadcacccddaddcbbadaaadbbbaadbbcaacabcbadccabbabbacaaaccddabdbdddacbbbcbabadddbacacaabdcdcaabccbaaaddaccdacaaddbdbbccabadcdcbdbcabddaaacaadaccadcccbbcadaddccbcbabadcadabddccaadbabddabcabdbaabdaaadadbccbdcdaacabaabcbbdccaabbaaccaaccbccbadbababcdbccdaacaadbbabddbdabadabbabaddacacdbbadbcdcccccbddbcabbbcdccadadabdcabccdabbcdbaadadbbdbadcbabcaddbbdabdddcbacabbcdaddbcaaddbbabbcadccbbdadcbcaccacdcccabddbcddbbdbaaaddddbcbaacddacabaabcbdcabbacabaaaabcbdcdbaabaabbcdcdabdcddccccdadacdbccadcacddbadcbbadadadccaacdccdcdddcabaaaccdcbadcbabadbbdcaddddbdcbddcbdbabaddcdcbcbbbabccbdbaccbadbccccbdbadccbcccbccdbbcadbabbdbccccdabaacdbcacadaccaabcdadcaddcdbcdcaccaaaddbcdcbacdbbcbcbcacbabacabbdbaccddcacdadadccabddbdadbdbcddbbdaabdbcacdbbcdcbdbbdbccbaadccbadabdadacbaabbbacabdddcaabadbcacbcaabdddbdbaaacacdcbcababaadbbdbcabccdaddadcaabbbaabadcdcdadbccdddcbaaacccbcdacabbdbdcdccddaabdbacacdcdbaabbaaccbbbccddaacabbbbbbbacdbabdacdadbababcabaaabddbbccdcdaadcabccccacbaadbacdaddacabcddaabaccbddcbdccbcabccbadddcbbcddabbcaadccddcbadaacbdcbabcababaddabdabdcbcbcbdbbdbcaddadccaabbcdbcdcdadbadaaaabcbcbccdbbcbcbacbdbabbcbcabdccdaabdacbaddbabcadacadcbcaaaacbcabdadacbbdbccbadacbccabdcdbbcbbaaccbddbdaaacbcabcabacbbddcabcbccdcddddabdcabaacdababdaddacabaccacdbcaabcbacdababcdcdaabaccacdbbbddadccbcbacbccdcbddcdddcddadbadaadbaddbdaacdbbbbcddacbcddadbdbaacadabadababcdbdabccaccddaaacdcddcbdbcaacdacbdddbadaacccbddbdcabccbabcbabbcdccaacdadaacacbaababdcacacabaacccbcdcacadaadcbaccbacdbdcbaaccdccdcbccadcaaacbbacddcddbdbbbbbcdabbcdcaccaaddaaacdcbaabcdbdcbccacadcbdcbbbbbababccdbcbdaacbdadbdacdbacacccbabcdccdacbdbcbcbaaaadbcabcccbdaaaddddbdddbdbdabdcbaadcbadcbdcdcaacabdccaaadcdaadababddcbacdcbcdadacbabacdabccbccdbadcbdbaadddabbbbdbbabbbddadbdcbabadcddadbcdaadbaacbbdcadadbdddbcccbbdcccdcaadddababcdbcdaadaddaccacbbcccddacdcdcadccacdcbbdcddbdcaadbdacdacbdddcaaaddbbabdcddcbbcbaccabadcbabacdcbbbbabadcdcddabbaabdcadaabacbadbdcaacbcbdadccbaaaccddcabadcdbacaabdcbdaccbbbcbaacaacbbacaddadbcbadaddcbbccabaccbbbbadcdaccccdbdabbbdddcadddaabaaabcdcacdddddbbcccddccdaaaacdadaacdaaccacaaabcbcbddbcdbdabcaaabdabcbddbbacbcadbadcdabbcbdaabacbcbdcbbbddbddbaddddbdbbcbbabcacbacacacbcccaccdbdbbbacacdcccbbbabbcbbaddbcbcacdccaccddadaaababdcabbbccbbdaccaaddccadabcacdccccaddadcbdbbbcddabdacbabdabcdbddaaaabaabbcccbdcbcbadcaabcacbddcbabbcadbcdccacbadacadabdbdaccdabcabbdadbcaaccbbacdbbaddcdbccbccdcbbaacadccddaccccadbaabaaacaaabbabadadcbaddbaccabcbbddbdabcddbdacbacccaaadcbcbcdadcccacdddbbbccbdacabbadbcddddbdaadbacdabadbacacadbdacdccaaadaabbcbbacdbdccddbbdcdcadbcdaabbdccbbcabddddabdbcddcbaadcccaddbadbcdcadacdabcdbcbbcadaccbbaddcdcccbdcbbdbccdabdcddbdaaddbcdbbccdbacccdbcbcabdbbddcabacdaddbaabdbcdbddbbaadddbabbaddddcbccadaccadcdcbbccdcbbaddcadbaadbaaabddbcacdbbcdcdacbcbaccabbacadabdcccabadddbbaababdaccaaaaaabbcacacdddddacdadcbbaccdaabbdaddaabbacaaabcdbcdcbbaaaabccbbbaccbabccabdaddbbdbcabdaccdbdcbbcddbbdacabaaabcdcdddbcabccababdccaddcddddcdcbabbccadbcbcadcadcaaaccbbdcccccaaccddadbabddcacdcbccadacbdaadbadccadcbabccbbcacacabcaaabaabccbcaadcbdabacadcccccccbadbcaaaaddbadadacbbaaaccdbabbadbcdabdbbaadbdaaacbcabccdbacdcbacbaaccdadacdbdadaddddaccdabdbadacabcdcdbabbdaacacddccbbcdcdcdadaabbdbcadadbddcdbabddabddbabcbcacbcbacdaadadadaadaacccdbbadbacdcccbddbabbdbbddddcdcbaccdabdcdddcaacbbadcabadbaccbcddbcdcccbdaacbbddbbddbdaccbdbadbddabbadbcbabdaadbcdaadbbccabaddabdbadbddcddbcdbadcbabcbdbbacdbbbdcddcbcdbcccbdbdadccdcdddbabcaacddaacdadbacadbdddabdadaccacbaddccaccbcaadccbdcabcdbcacaacaccbacbcbbdadabcabcabdddbbccaddbddaaacabdcabdbaaabadcaacacddacbddcbaabbccddddddbccbcddaacdcbcbdcbcbcaddacdaaccdcbbaabdbbbdabbdddcadccbcbdbadcaabbbcacaccdbcabddbbbcdcadcbcccbaccbabbbcaddaacdadabdbbbccbbcdcacdacabaacbddcbbcbbdacdaadcacadcbdacddacdcbdacaaddcdcabbacdcddbacaadddbcbbaddcaaacbdcbdcaccaaabbacaaabdaabbaaabbccadadbababbccabadbaadbcadaccabcadbdaaacdccaaccaadcbdccbdbdaaabbcbbadadccaabddbdacaadabbcbddaacccbbdacbdccdcadbabadaadabbddaaddadabadbbbabbbccbadcdccdbacccadaacdacbcaaccdcacdcccccdbcddbadcbdabadbabdcbadbaabacabaacabdabcabcdbdcadadabaccdbdccbcbccccbcadbadccddddcdbaccaccabbdadaacdbbdbcacdbdbabcdaddcccdbcbabbadcdbcddadbbaabdbbcbbadadadabbdaabdaabccdbabaaacccddacdbacabacbabbcccdcdcadaacdbadacdcacadcadadaaccbdddcabdbcddccabcbdcddbbabbbadbacdcbbdcacbacccdcccbbdacdbccabcccabadbcbddbdcadbcdcdbdddbaabccddacdcbbdcbddbcccccbaacbbdababcdcdaacaccbbddbaaabccdcbcddabccaddbabbccbcccacbcaddaadaadbccbabcdacadbbadccdddbcaccacbdacbddddaacabaaacdadaadaacaacbdbbaacbadddbcabbbddbdbccdaacacbdccadbdbbbbacbbcaabaccbacaccddccbbcaccdccadaccddbdbabbddadadcacabdabbbcddbcaacbbacaabccdbabbaccbbdbcaadbccbbdcdacbaadbccbdcdaaadacbadbcbbbcddadaddbbbdacbbabbacbcdbddcddbabccaadbaaacbbaaccdaadbbdabccdddbbdaccdbacccbaccbddbdaddcaacadaddacbdbcdaaacbacccdcbbbcdacaaadbddbbcdbadadadccbaddbaaadccaccaccbabbadaadaabacdadddcccdaacdcdbdbbbdbbddcaccaddddcadacaaabacbbbabcbdccadbddcaadddbaddabcacdaccbbcbdcbcdaaccdbbddccdbadbacccacaccbbcbcadbdcbdcacdddabaaadcdddddbaadabbaaaabdddcabccbcaadbdcdbdcbdbacdcaddbdbdacccabaaabbdbabababadccddbcbcabdacbcaccaccbdadcbcaccdcabcbabbbbcbbdccaddbaddcbadddcaccbacbdccabcbbdcdccdbaddcbcbbcbccacddbadbabbbbabdabdbdbdbdbdaabaacaaddacccccbcdababdcccadacaacadbdcdabacacdcdababcabdbcdacacaccbbcddacdcbcadccaccdaabcdbacaacadddabbccaaacdbccbcbacbacbdbcbbcdccabdbaddcbaccbbaabaadbbacddcaaadbddccbabddacabcdabaabadaadbbcaccaacbaaddbcbaabaccbacaacbabbddcaddacbdcabbdbccbddcacddbabbddaccbccddbccaaacbabcbdccdcaaccadbcdccddcabbbaccdccbadbccbacbdcbbbaaacbaacbaaaccdbccdcdbdddbbdaddcdaadbbadcacabdcbdccadcbbadacdaccaaddaadabbdbadcaddcdbcacbbdccbbbdccbadbcbbcbbbbaddcbadaaaddacbbbacbacdddcdcbbddaabbabdaacdddbbcbbbbbbbcdababccddabdbcbdbcbadbdbadbabcbbcbcaacdbaaabaabbdcdbaaccacacbdcaabaddddcbabcbcddbabacbcabbbbaadcaadabddbddabcbbaddaadadacaaadccccdcbdbdbdbbbcbacdbbacccaabadbabbadbaadddbdbaabbdddaacadcacdcddcbdbdbdddabdadddadabcabaabaddccccacbacaccdaaddbdcdaccdaaabcbdcbbbdbdbabaaddbabddadbadacbcabacbbadcccacdbcddbdbaababacbdabacbcccacacabbbcbcadddadcbccaabcddadcacbbcdbdcdbacbdbbcbaacaabaabaaaaddcbdcdcbccbcaabbcabacccbadcdbbbdadbcdbddcadddadcdcdabcbddbcbbccbcccdaabccadbbccadbcbabaabcdacadcaaabcbcdcbaddabbaccdaabbbaccdcaaddcbbabbccbaaaacaabccbadccbbadcacbaccadabcbaaddcddbcdaadddadcccbcbdaadaccddddbccadddaaadadbbcdaaaaaddbdacaaddcbcdacdccaddcdddcbaabbbcdddbddcaccddcabdcdcabacbddadcbbdcdcdacabddbabbcbccbbbadbddaacaaadccbbaaddaabacdadadbabbccaabbcacdbadbaccbabccddadbdddbdbbdcaccddaabddbcbdadddaacbbcadabbccddddcbaadbccaaabbdbcdcdcdaddbdcabbbcaabdadacdacccccbaccbbddabbdbddcbbacacbbcacdbacbcbbadaabcbdabaacaccdbadccbadacbbbbbadbbcddadcdbbcacbadcccabaaacdabbcbaaddbabbbdcdbaddbdbabaacabddadccdcdabcbbacdcdcdbccaaaadbbaaaddaababdcccdcaccabbbdacbbdcacbdcacbdbccdcddbadaadbbddbddbdcbadaadacaadbbdcbbacdacbabdbaacaacbadacbdbcdcdbbbcddcabbcabcbdcbddcbcdbcccadacddcbabbbcabdabcbabdbdcaddddadbddcaddcadbaababcbdcbcabbbaaddadbbcaabdabccaccaddaaccabadaaccbdcdbabbdbdbadcdcbabdbbbbbabdadccaacdddbaacaccabacbcbaacaabddbcacbadbcaacabbaaddacbaabaacdabbaaddbcabbacadbcaabdbcdacbaabcdabbaaddccbdcddbcddbdbbbdddbcdacadadccbdcadbcbdadacbcaccbcddaccddacbcdabaabdbabacccddcccdddadacbaadacdccbbaadbcdaccddbbdcadddbadddaccdccdccdaabaacbdadbadbbcbddacdcacbdaabdcddddccbccdcbbdcbcdbacdbababbbaccdaabbdcdababdcbcdadabcabadbddacaacadbcabdbbcbaddbdbcaabbabbdcaadcbbdbcacdcbccabaadbaccbabbbbbdbbbdcdbcadcccaaacdcaadbcbdabacaaacbaaccbbdbcdabcacbabddcbddddbbcbdabaababcdcdbabcddabbabdbcdcaddccaccbddddcbcdabcdbacaaadddacabbdcdcbbccadcacadbcabcddaaabaaaaccbcdacddcdbcbbbbcbbbadbbdbddbdaabaddcbadbadcacabcdadbbdcccbbabddccabdcbbdabbbacbbabdddcdcaabdccbdcbcdbdbcdbcacadbcaaadcbbbabbdadcbcdbcdbbabcacdbdcbacdbddbadcbcaadaccbbaaababdacddadcbbbbadaabdcbcababacdbbdadddbdaaadabbccbccdaadcddaacccbdbdcbacccaadbbbaacbdddcaddddabdbaaabddbcbbdababaabdbbcbbcaaacddadcadbbdbabddccaaccbddbccccddabbcccbaadaccabaacbbacdbabaccbacabbddadcbabddcccbaacabbbdadcdcabdbcdbccabbbabdcbbcbbadcccdbcbabacddacdcaddcaddacdbbcbbdadddbcbacaabadcbacdcbcdddbdaaddbbaadccdcbcdacbababcbdcadccdadcddbacdaccbbccabcaddbacbdabcccbbcbbacacbcbabacabadbcbaccbdccccdacbdbcdcdaadccbabcbbbabbcbbadbdaaabdddaccadbbaabcbcabcbbdbacdbbaabddbcacbbbabbaccadadbbacbabbcbbadabcbddbacbdddbdaabaccbadbcdaddcdcadcccaaadcdcbcacddcbdcabadcccbdcabbababbadcbbbbddcacabbcdabbcddddccbcadcabcabcdddcdadcaccbacabcbaaaabaddbddbbabdacbcadbabcaabccacdaaadabaccdaacbaaaacadaccaadcabcbbbbcbbdddcbbdbccacbccadbdbabdbdccbbbacababcbabcdadbaababbbbdbdbbcdddcacddaaadcdabaadcddccbbcbdbdbdbcdaddacabdbddcdaaadcbcdbcbbcadcbcbcccddabbbdbbadcbaaccacccdaabbdcaccaaadcccddcdaadddbdacabbdbbcdbbcdabbacadacdaccccaccdaccdcaacbaadaaaabdacabbbaadbbdccdbdaaabadadbadabcddaaddbbdbabaccccbbbabbcddbdbcbdbcabcbbddbddbbaababcdbabdcddcbcccaacdabacaaabbabdadddbacdaccdcccbbabbbddacaaddcbcddddbddcbbaacdcccccdcdcbcbacbabbcddddbcaababdabcbbbdacccbbdbbaabdaaccdbdbbcadbccbaccddbccbbacacbadabdabccabaaccddcabaacaddcdacbcabadbbcdabaadcaadbbabcbcadaddbbcacccbaddbbaabbccbbccdbddbacdbcdabccaabacccbadadabcdddccbcdccdaaabdccccabdcbcbdabcaddbcbdabbdaadadadcacbbdaaacacabcabbadaaccbcadbdadbccdbadcccbbabcdbbbaadaababdbdccbdaaddabdbcbdbbcbcbaddadadbdcabdddacbddbbbdacddbddbcdbddbddddccdcaaaabdbdcaccbcadabbdcaccbcddbdadaaddbdabbbabbcadddddbabadabdddbdbaacadadaddcdabbccaababaaccddcddabdbcbbaaabbbbaccabdaacdadccdddddabbadbabdacabcbcddbadbabccdbcdcdcdbbcbdcbdbbddccdacddbbacdabdbacbacbaacbccacddbcdddcadabacddabdacbdbaccaccccacaadbbcabbdabbacaddbcdbcdbcbacdbaaacdddabbdadacdccacacabdbbcbdbcdccadcacccadaddcadacaacccadcdacdbdabbcbacdaacbadaaaabdcaacaabcbccdcddcadcdbddaacdbbaddaaccdaabbdadadbbaddccdaadddacadacbbdabcabbddbbbbbbcdbabbdadcacccdbbddaabacdbaaccabcdabaacbccdacaaabbadabccabaabadaabacdbddbacbabbbbadaaadbbdcdcadacbdddcbcaacacbdbbaaccacbbbabadbccbacabbadacbadcbbccacdaccabadddabdddbadabadacbdccbccbbcbabcdbaadcbaaaadbaabbdcacdbaabdcbacacddcdacdcdaadddadbacdbdcbcbabacacacdaddcccdddbdcdacabbaaaadcccbccbaddcaadbcabccddcadacdcacaabcdaccbccadaadddbcdbddddaaabcaaddcddaaaaaccccacddbccadcbcbdbabbdbabcacabdddabcdccbccddaaccbcabdbabaacdbddbdcacdaabcbabaacbabbdbcbcbbdcbccccdbcdabcabcbdadbbbdcccddbcbdbbaabbcbcacbcbcacbccdbbddaaacaccbdbcbcbbaccbdaacadbbcdbccccdacbcbaaadaccabcbbaacdcbbacdcccaabbaaabcdbabcbcdaabbbbbcbbcdbaacadddddabacdbddbdacdbdaccbcadbadbbaabcdbbbdcbacbcabbbcccbbabddbccccdddbaadacddaaabdaacbadacdbacbccddbdcbdcdaabbdcbbccdaccbbcabdccddbbdcbddcbcbacacdaabcbabcbbadbabdcaadbbbdbcacaadbbabbcbdbbacacbccabaadaadabdaaaacbbbbaadababdbbacdccbbbbaababbabcccbcbdbcdddadcbcaccdddddbaadbbabbaaccacbbcacacaadccdaacbcdbddccddbdbbaadabbadcadaddabadbbcccadcdbdddcdbaaddccdbbdaaaccbbdddbbaaccbabdcdbcbddcbacccacabacdbdacdcbbdadacdcdbdaadbacaadadaacadbdbaacacbacadabdaadbcbaacdccadabcabbabbbabbccdcbbbddaadacaacddabdcddbbbcdabcdcbadbbbadcdddccbcababcbcadcbbacabcbbcbddcbadbdcdcbbdbdabcbbcbcccaabbbdbdbbbbbcbcadccdbacbdcbcacccaadabacccbaabbcbddcbcbcaccccdbdddcbdabcaabcaacabcadacabcddcbbdbcaddbadbaadbdcadbddaacbaaaacbaddddaccabcbcabcbaabcdccccdccbdabdbadccadaddcdabbdbcabacbdbabbdddbdbdacbcdcbaacdacbcabdcabccbadadabbacbccbbcbdabaabaadbcaaadddccdbdcadddaaddbcbcdaaddadcdbcaccdccdcbaaadacbaadcacaddabccddccdcacaddabbabcbaabaabbcaacbaadadbccdcdcbbbdddcdabcbbabaddddcaccccababcbbcabcdddcbcbdadcaccbbccdddddadcdcbdbdaccddcadcdaadccdacdacaacaadaabbacbdaccabdcccbaaadcbdddcbbbaabbabdcacabcaccbcbdcbbabcbcabaadcdacdacadbbdbcbdabddcadadbabdddbdcccbbaccbbdcdadbdcadaddbdacbbdaaddabbccbdaabcacbacccccdaadadccdbbbccbacaaadcbdabcdaabcaccaabacccccdacdddcdaaabcacacaccbacddbcbbbbdbadbcbaaabcacabdcccadcacbcccbdcbbcaddbdccbccadacaabcaddbbbaadcddaccddcbbddcbdcbabbbddaaadcbaabccabdddbaccdcbddaabadacdabbdddacbbcdbdabdbbcbbbcbbbdbdacbdabcababdabacbdbdcdcccaaadbbddaccddddcdcbbcbabbdbbccdddacbcbdcaccabcbcbacbcbdacacbcadcabcbdbbbbadaaaaabaadaacbadccacdddaadbbcccbaddcccaadddacaadbbabcdaaddbcadaddbbcbddabbbaddacdbdcbddcacddbccbcbbbdbccbaccddabcaaabbdcdadcaaddbbabacacdabcabddabbadabdddacdaaccccdabdbbacbacabccdbabdcaabaccadccaadddbdbcbdcbddddbbdbccccbaddcacccbbcaadbddbcdbdccadbdbccdbbadbbaabcaadddcabcbbdbccbddcabaaadcacabbcddabdbccccbcaabaadcdddcccddddaddcdcbaabdbdddbacbcbdcccbbadcadbaadccaccccaccbabccabaadadbdbaacdaadbdcaccbcdaadcabbdaaadaaadaacbbccaddbdbcaabbbdadcccbdacabdddcbccacdcdcbddddbaadbabdbabccdcdcdacabcbbddcbabaadbdcacacbccadcbdadabdaaadabcbadbdddadbcbbdbdcadabacaccccbcbdddccababdcadccbabddbdbacdacdbdaabccdaacacbaaaacacbaabbbacacaaadadbcdccdacabacdbadabdbdcdcdcbabdbaddcbbadadbcaaaddbabdbbbbddcdadabcabadbcbbcbdaacaccdabccbccadcccbaaabcddbbacbdababbbddacbacbaaadcacadacbbdcdccbdacbcbacbabbabcadabdcbccacabadbbccbdcbcddbcbdbcbcbcbcdbcbccdbccbccacaababdbcabddcabbddacbcdbababdddbbcadccccbabbbbaacdbdaadaacadacabcdbbdbdbdbbcaabdacdcdccaadcabdabadbbbccdddbcaaadcbacbbbcbccdbabdbbcbaacccadcbbadcbddbbbbbaadaabdcaddcbcabbbcbddaddccdccaddcdbcbababbaccbdbabbababbaabacadadbcadccaaacdaadaccbaddbbbddddaddcccbaacabddcbbacdadbdacbbcdcbddcdadccbbacdaddababadadbdaccacddadbdaabcadddbdccdabbabdbddbddccbdcdccdadccadadcdacbcdddbbabdbabbddccdbcacdbaaaccacdcdddabbbbabbbccbbacbccbbaabacccacbdcaabadcddbaaaccacccbacabdbbdccaaaddcdadababccbaadadaabddccccbacbcadcbccbabcbabcacaabbcbbddabcbdbbaccbbbbcdcdbbdcacacbcdcbcdbaddacbcccccdbdabdacccaaabcdcddacbbddabddaadbdcaaaadcacaaacaacdadcdcdacacccbbabacabdcaaabccbccbdcdaccdbdbbdbabacbcbbbdacbdbbcccbacdacbadcdabacbadbadbbadcaacdaaddbdcccbbbddbcacbbdadddddbbcadbaadababbdacbacbaaddbaaddcaaadcbdabbadbaddcbdccaadbbaccaddcbabbacdbdbcabdcacbdbcbbabbabcdddbbddacdcbadacdbcbbcabadabdbabbdcabdbddddbbdbabaaccacacacbacbddcbcccccdcddcdcdbaabadbccadababbbabbccadbccdccabcbdaacadabbbbcbbcbddbdccbdccabadbccabcbcadacaddaacbcbacdbbbcaabcdadbbcdadccddbadbadbcbbcadabbbabaadddadbdadddbadbdcdccbdaadacdccbcbcbcacdaaaaadcaddaddbcbdacdababbdbdbbccddaabbadccdadbcdbcccadaaababddadbadcbacbdbdbaacdcadcbbbabcdcacdcbaaccaacccbbdbbbcdaaaacdccbbdbcccbbacaabbacdcdbabcabaaccaabdddddcacdcbdbdaaacccccadcbacbbdabcaaddadcdcdcddcdcdacccdcdbaacccddadccdcdbadbaddddaadccbabdbddcddbbdccabcdbcaadbccaddadbbbaadabacbbcddabcccddcddcabbbcdacddbcbabddccacdddddbabdccbaabbadaaccbaaaacccccabdcbbabbccaadddbdccdaacbdabbbbcaadadccabdcbdddbbbccdcdacdadabcaadaddbadccabcbcdcbcbaaaaccadabbcdddbacabcbdcbcbbbdcabbcdaccacbddaddbabadcbbbdcccbbdaaddcbcdccdccdccbddcabbcaaccbcbdbbcaaaddcdcccadabbabbcdbabaabbcaaadcacbabcbbcbbbbabdacaacaaadacabdacbbbaaccaadbadcdbacbdbbbaddcbcbdbbccdbcbaadcdbadabcbdabdbddadaddcacaadccdbacdcaacabcadbdcaacaadbcccbdbcbdacdddabdddddbcccaddcacddcaadcaadcbdbbacabccddbbccbadddcbadddddccdcadbdaacdcaadccacdddcdbccaaaacbdccdbdbddcbaacdddbdddcdcacdccdbcabcddbbdcadbdcacacbcdbabaaadbcdacbbbadadacabddbaabcbdccbbaabaddbcddcbddbacdcaddcddccdccdccdbcdabbccdbbcddaddbbabcadbaaccbcacaacbdaccbadabdcddacbbdbddbddacbccdddaadbbcadbccaaccbcdbaacdaddadabadcbadbdacddcacbdcadadddccbdbcbcbcbabdbbadabbaacdadbbaccdcacddcbdcdbbaddabddaabdaacdbacccdaddcbadaacddacabbdcaabdbcdcdaacdccccbabbacdbbbdabcbccdbadaccbbbaccaddacaadaadaadabcdcddabcccaccbadabcbcddcdbacddcabbdabbdacacabcbcdbccbbacacbcaaccddadccbbacdcbdbdadcbadbdacdbcaacdbdcdaaadaadccdcbabcbaaaccdacbbcdbaddaddbadbacbbbcdddaabccccbbaababcbbcbaddcbbadcdababaaacabaacaabcadaddcacabacbddccaabccbcccbaaddababaabbddbcdacccbbbbbdcddbbbccacdbcdbcccbcccbdbbccdabacbcbcbbaccbbcdadcbdbaacdabadbbbbbbcdbabdcabacbbbcddccdadabbbcbaabcbadccabbabccbdcdbcacbabadbbdcabdccbddacbdabbaaadcbcdcbbabdadbbbdbcaccacdbaabbcbdacdccadaadcddadddbaccbaadbcadadccdcdcdbdbcaaaaaccddbdcdabcbcbcdbbbbccccbabddcbcacaadddadadbbddccbcbcabccaabcacadddddbaacaadbdccdcccadcbcdadcacadaaaabdddbadccdcabdaccdbcddbacaadbcbbadadbdcbbccaadbacdbdcccababdabddbcdbdaacdaccaaacaccaaccaccbdcbccbbaabbaacdabccccadaabcddaccdcbddaadadbaddbccdccbaccdbaadddaacccdbbccabbadcabdbdaaaccababbcbaaaabcbacadddccdabcaddcacbddcbabcddabcacdabdabcbccacadcdabcbbcadbcaccabaccbcacbacccbacdcbdbccacacbcbbdddcadcbdcbcabacaccaccccdbabddbcdaabbdbbacadddbaccacdcbccbbdbaddbacbcabcbccabacdcdacddbaaabbdbaccdbbbbbdbbbbdaacbcbdcddabaabcccbacdaaadccbbaadbcbbcdcaccaddddccbbcadbcbdadaabdaadccdacbadcaacdbabadabdbcbcbaddbbdaddabdabcacbacbadaabbcaadbdccdcbbacaccadadbbadbdddbbadbbcdbacaaaadaaccdddcdddaccdddccabbbbbdddcdaabdcccbcddaccabbdaccbaaacbabbcdaacaacbcaaccdaabcdcdbcbbaadbcbdabdbdbcdccdcbbcdabbbdcdacddcdcdccbddbbbaddacabcbcbcdacbbbaccddcacddddcadbdcdbcbcdbbacdbaadadcdcbcddcabbacaababbcabbbabbccdccbaccaacddbacbcddbdbabbadbdcbbbadacdcdbcbdbddbcacccaddcbdbdadccaadbcdadabcbccaaccabbdcaaacbdcccddadbbcacacacacacadcaaddbcddaadadcaadbacbcbccddddcabbcadbadadbaacdabbabdbbccbccdadbdbccccdcdcbbdcddbbabbddcbdadddadddbccaddaabcddddabccdabddabacddcddadaddcabdaadababbdaabdccadcbbcacdacbccaddbbcdbbcbadbdcadaaaacabbcbcccdadacdbbbdcaacbdabdaabddccdcdcabacbcbbbbdccbbcbcdaaacddbaadcbdaadabbbadccabdccabaaadddbcccaadbbbdbbcbbaabbdddddcacbdcdbbaddabcdabdbcaaccbadcdcbcdadcddddaacbadcbdbdadbabbcbcaddbdddddaacacbbbbdbddcbdaddddbbdbdabbbabdcbccdbbbbbacbcbdbdcdaccbddbcdcabbadadbaaddbcbcbccabdcccbccbaaddbaccccddbbcdadcdbbadcdccdccccbdbabaabbdababbadbcbdacabccaabaaabcdabbcdbdddbacddcdccbaaccccccdcbabaaabdcabbaddacbbbcaccabbadadcbcababddadaadddccdbdccaacccbabbdaadcadaccbbddcddaaaadbdddadccddcdbbbdcbdaccabccaccbdcddaaacbdcaaacacccbccccbccaadaaadaddcbcbddcbdaaacabcbaccbbcbbdcadadcabacbdcccabcbbdcacadccbcacbddbdbcaacbbcbddbbbdddbcbccddbbdcccbaccdbababdabddbabddabdbdccabdadbbbcdccbaacdbcbbaaabababddabbaaabdaddaacabdccaacbddacdacbabaacbcbdcbbacccabdcbdcaddcaccdbcbbccdaddbdddcaabddadbaadadbdccbcbbabbdcabccbccbccaacdddbadbcbccadbdbadccbbdbbadcbdbbbadbcdcacacdacdbaddccaadcaacdbcccaddbbddadcbadddcdcdcabbcdaccdadddcdadacaaadddcabdddccccbcbdabdaddccdadbbaddacdaaacdcbcbbdbbcdaccabbaddbdccaadaccacaabdabacbabccabbdbbacccddbcbbcbdcacdcccaddbddcaabadacbcaaddaaaccccbcdcbcaacdccdabdbadbdbaaabacadddcbdbcbcdcacccbcaadbddcbaadaaaaccaccdadadacbabdbbaabdbadaddacaaccbabdbdbcdabccacaacadadcbbdbcbaabdbbcddbaabaadcaacbbddbbdddcaccdabbdbcaabdbadcabbabdadacbcbccdabaacdddcbbabcdaddcddbadddccadcacbbbdcbcccbbbabacdbaabbdadadbbdabaccaababdbaacabcadcbaaddaaadcacccadbcbccbaadaacbaaddcddcbdbdddcbacbcdbbabaddbabadacaaaabdabacdcdacbccbbbddaacdbadcdaccbcdcddddbbccdbcccaccdababdccdddcdbaccbbbccdcbbcaacbbaccaddbdbdcccdcbbccdcadccdaacddbaabdbcacbbbdbcdbdaaacaccbadbbcabbabbbbcaabbcadcabaddacccccbbcbaddcdcdaccdbcacccaaddcccbbcbcbdacbabcbdabbdadcbbbcabccbbdcdbccacadbcadaacbdbddadacbdbdbacccccdccabdcdbdbdabcbbaaccdccdbcbcaccbcbddbabbcdcdbcadaadaadacbdcaaaaccbdbdaadcbdcadbdcbbccacdccbabddcdcddbbababbbaabadabaabbdccacbbcbbbcddaddddbdcadbbbccacabcdbcdccdbccbcccdbacaacbaaadabadaabdbdddcaddcbdbcaccacddcbddddbcdcdaadbcbdbabdbcdcabccdcbccabbdadbddadaadddbaacdabaaadbbabaabacdcabbdabbbabdbacccdcababadcdababbbaaaacadacaabbcbaaddabcccacdcccaaaccadbabcbcadabccabddaabcdbbadadaccacdbcdbcdbdbbbaaccccbddcbbdaadbbdabdccaadbbdddadadbcbabadaacdaadacdbaacdcaaddabdbbdbcbcadcaaccddccbaabcddbddcdccabcccbbaaaddbbcbdddaacacbdbdcdcddccbbaaababadddaacdcccdaadadbbbdbabacbadddcddcddbacccdaadcccadcaacdbbbcadcdadaaaadcaddbacbcacacaddcbcddccdaddacdbdbcdbddacdadadbcbaaabdccbacdaabacaacacadcdbddaaddbdadbbddddaaacccddabaaadccabbcdacdddbabbbaaccdcccccacbdcdbbacabaccdbacacdddccdcadcaccaaabaaadbdcddcccbccbacdcdbbaaadcbcbcbadcbcdcdadcdcdcdcadcadcbbacdcaccadccaaaabccabbaadbddbacdcbdcacbbcccaaacbcaaabacadcbdbccdadccababdcadbbbacbadbaabdbadacacddadbaaaadccccbcaadbcdaddbdccaddabbdadabadbbaddbccbbacdcadabdcdcbadbcdbddadbbabbaccdbacbacddabdaccbcacadccdcbaccaacbddaaadabccccbbbbbacaacdbddcbdabaaccbcacacdcdadababcadcbccccaaaaadcddabadaccccdddbdcbcdaaaccbccdabdccbcccdaacbcabcadcbbbbbdabccaddccaddaabdcaabadcbdcbcaabddabdcbabdcbabcddddaaacbacacbdccabbacdbdaddabbadaaccbaacbacccdacbadcdcacddbdccaddacccbcbcbaabdcaadcdbbaadddbcabccbabdbdbbdccbbcdccdcaabaddcdbbbdbaddcacdbdabdbcaabdaabbaddbdbbdbadcdabdbacdccccbcddddcabacdcdbbbabdbaaddcadadbbdaccaddcbdbdbadbbbacdacbbcccabbaaddadaabcdabbbacdbbcaddadcbcbdbabdadabcdcacacbcbcdaaabcbbbbdbacbabaccdccdbbbbdacadbccdbbdbbabacdabdbddbcccdbadabbabdddadbcdbcdabbbcaaacccdddacddaacccddacaacbdaaccddcadccdbdcbdbcbcacdbcadcccbbbdcddbacbdbbccdddcbdbbadccabbbbadbbdccdcbaaaabcaddcbadbacdccababdcaacdbddccaadabdbdbacbabcbaccaaccabcbbbdbccbdddbccababaaacaadbadadbdbcdbabdaccabcdcbabbdccdababdbbadbdbcadbccbdcdaacacddcdacabdbaabcdcaadacadbcaacbadcbcbdadaacadbcacdabacacaaabdaccdadbcdbbdddcaccbddbcabcddabbdabdbdbbacdbbbbcbdabbddaddcbbbdbcbdbabbbaaadbbcccddabcdcbbdbdcbdaabadacbcbddcdacdacbdacbdcbddcaddcbbddbcacacbdaaaacbdddaabccbcabcbccccabaaadccbcbcbcbdbacdaaabcddccdbabbbbbbbcccaadabadaaabacaadaccdabbadbadaadcdddbbcbdcdcdaddcbabaacacdbacbaadcbdaabbdacdaabcacbdacbdbaabacacbcdddbaddacadabcbbabaadadddacaaacbabbdaaabbbdcccdadcaddbdaaaaabcddbbacacdadbdacdababadaacbaaadddaabdaccabddbcbddcbabcbbaabacbbdbccbabcbbabaadccccbabbbaaadacdcccdbddcddccdbdcbbcbcacdadbcccbcdbadcdbacdabdddadcaaaabadacddaabbbadbcbbbaacddbadddbbbccdddccaaabadccdcbcacabadbcdbddcadabcbbabdacaacdbddacddacbdcdadcbcdbcccbabacbdbabbcdddccdbcdbcbabdbaaadbdabdaddaccbbbcbaaabcbacabaddcbcdabbdddbbddbaccdaccdbbdccadccdbdabdccabcbcbbaddccdcbabcaddbacbdbbdbacaaaadaccacdabbdbdcabaaaacccabbadaddadadadbcbccadadbbbbdaacbcdbccdbbbacdaadccbbbddbaccbddbddacccdaccddcdccbdbabadbcadaacbccccbadaaccdabadcdbddacccdddaccaaaabcdccbddcabbddbdcbdadcaacdbbababdabaccabbddbdbbabaaddcbaabdbadaccbddaabacdbcbdbdcbdcdabdadcaddcacbaadaacbbacabaabdacaadcadaaaaacdacaddadbdabacccbbbaccaabbdcbcbdbbbbbbaddddbccaadbadccaabccdbbccabdddddcdadccdadbcabaaadbdbacaccadccddcdcabaabaadcdaccdacaaaadbaabddcaacbbbdbccabdbbaccdcdbdacdcccbdaadccdcccdacccabccaaadcaabcadcaddddbcbbdbddcccdbcaaabcccccabbdbbddaccdbcdbaaadadabdabbadacaddcadbaddcaabdddaadcdaabdbcabadcadccbaababbdcaddcdaddcabcabcadbaddbbadbacdaccabbaccaccbccddcbaddbddcdabdaabdaadccdbcacbbabccbcdcbabccbbabdbcbadddaabbbdccbacdbcabdbddcdbaddbdaadcdabdadbbddaccbdaadabcbcababbccabaccbdbabbaaabcaabcdccbdcddacadbcadbcacddacdbaccbbcbdcdcddcaacdabccacdcbccbbccdcbbcdccbbbbcddbababbdbbcbccacaaadacbdbcbbbacbddbbcdabccdcacccbdcdaaabbaaabbdaaaccbbadcdcbcccbdbabdbaddacdccaadaccddccaabcacabbcbbabbdbbcccdacdccaacbbbdbabdadacdaabccaaddcccdbddddaccdbacdcaadcaacbdbbcabaddacdcacbcabcabbdddbbddcbbcacaaaabdacdbdacdbbbbcbdccddaccacccbbacddadcacbabdcacaacacddaadaaaccddbcccbaaabdbdccdbbddcaaddaddbacbbddddddaabaacaacdcbdaddacadcdbddccdbccdbdbabbbdddbbcbdbccacbacaabadaccddddcadcbbbdabbacdcbdabbcbccabacddacbdbcdabadbddcabdaadabccadcabbbbcddbabbbdbbaccaacaaaadbdacbbcdddddddadbbdadcdbcbcddbacbcabadabacbcdaacaadaabbdcdcdcddbaabaadabaaccabbcdbbcddcbddbbbaaabaddccccadcdbaaaaabcdbaabcddadabcdabbcbacbbbdcbcbabbddabdadcdbbcbbaddccbcdcbbaccdbaccdccabddbbaaadbcdcbcbccaaababbcccadaaacabcacaaaaaddadbddbdcdcccaadbaabbbddddabccacdccabcacbabbddaaaaddbbaaadcabbcdbccacacdbdcdacdadbbdbaaadcbbcaaccccdadbdabdbbaccacbacabdbdadbbababcdccdacbcacacdabcdaaccdcaabbbcbdbadabaddbdddaccaadbbcdcdbbcbaacabdccaaaddcbcdbacdadcdabdacdbbcbbabdbaddadccdbdbdcbdbbcdbabaddbdadcabbbdadddbcacdddbabcbccdcaddadcccaacbcbbbaaacbbbcacabbaccccbbbbbcddcddcddabcddaaabaabadccdcbbadcbccccdbcbdcccbadbbcddacdabbaaccaddcabcbabacbaaadcadadbccddadcbdccdbbaccaabcbcddacaaaccbbacbcdbcdddabcaccacddaabaccbccabdadaabdcbdabadcadbdadacbcacdddadcdbcaccbabbcbbbdbdcaacbbbbaaadbadcbbadadcdbacadadcacdaddccabddbbadaadcbabdddaacadbdbccbababccaadacbbacddaccdcdcdccdbbdabcbadcadbcbbaadbbdcbdbbbdaccacbbcaabbcacacabaabbaaccabccaaaaaddbbbaaddabaadcbbbdbacadabcaadbabddcadccddaabcbdcccbaabcaabaabdaaddabbadcdaddcccccdcdaaaccddaccbdcaccddadcaadbcccdaacaacdbbddabcdabdacddbbbcccdabdccddaaabbdbbdcbaadcdcdbbabbbdddaddbdcabbabbdbdbcbdbacbacbacacdbdcadadbccddbabdaccbbdadadbaabdabdbcaddaabbcdcdaddbdbddbbadadaccddabdccbbcadcabababcbdbacbbdbabdcdbdcaaabbccaabadcddadaadcbdbbaacdddcdbbbbcdacaddcdbbcbbadcccbbaddabbdbddbcbcacbbcadddabaacdacbdcdcadbaacbbcadcbdcacacbcdcaadbddcadcacbccdccbbddacaaacccccbddacadbddaaaccbbbabbcdcbbddaaadcadcccdbbdddbaacccadacaaabdaddaccbdbcdcbbcddabdbcddcccddaadcdacdacbcccbacbaaccbbddbaccdcbbcddddddcccddcdccdbbcbaadacaaaaccbdbabdabccabadbbbdccdacdcbababcbabadaacbdbadacbddcbdbdacbaddaabdbddbddcbccdccddbdbacdddcddcbabacbcbcdcdcaddabcacdbaabbbddbdddabbadabccccdbbddcaacadbdbbaccdadccbbbaacccdaccccabbcbccbcbcaddacdbbdbccadbbbccbdcacbdbbcaddbcdabccbcbcbccadccacdcbcbdbcadccdcdbabbcddbbadbdbaddacddadccdcabcadddcbbcabadaadcadbcbbacdbdaccabcdddcdbcdcddcbabbcbbabacaaccbababcdddabbccacbcdddcaadaabdccaddaddcabbaadbcbcbbabcaaacbcaacdacdbddcbddacbccaabcadddddbbddddaadcdbddddbbadabcdccdcbadaadbdcbdaccdcdbacbbbccbbaabcdcaaabaadbbbdccabcccacbabdbcadcadcbbbcddaddbbcccbbbadccdadbcadbbbbcdcbabdcdcbadddbabcdaaabcbccbdbcbcccccddcccccadbdacdaaacdcddccdccadadacddcdaccdabaacbcbabaadccabdcdccbddcabbabcdcddabaadcadabdabaddabbdaccadddaaadbdacdabcadcddbdcbbcdbbcdcaabdacbabbbcdddbbddccdabdabdadccdabccacbddaddccdabcccbabbbdabacdcbdcbdcdbbcbacccbdbabccaacbaadcbaddaddddbdbaacddacbbdddcbadbbdcbcadabacdacddbcddcdadbdccadcddadacbbbcdacadbbdccbbbdcbbaccbdcdbadbdcaddaadabdabdbbbcbcbbdccdcdbbcaaaacacadacdbccddcbdddbdabaacadddcdbabadcccbcbddaadddddcadbccacddddadbbccddbbabcbdbadaadaabbbbbbcaadbacdbbacaccacbcdaaaacccabdbcadbcdbbbaaaabdbccacdbbcbbabbddaacabdcdcdccabcbccbccddddcadddaadcbdcabbdbcbdacddccdbbabbcbaccabbdbabddacdddadbcccdccbddaabbbacadaddddacacbcbacbbdcdaaacaaacdabddcbbbbbcccdcbdabcbcbbdacbaacdcddadabccbcdbcbabdacadcbabdbbdbcbadddddcaadddaacbdddaabbdcdcdddbacbbaadddcbbaadcbaaacdabcbdddddbcaaabbcbabdaacaadbcdccccdcaabacaacbdcdcdbcbbdabcabddbddbdbcacabdabadaaaadacadabbbabbdbcbcaabadacdacbcbbcdaddbaaababdaaccaaaabacaaacdacadabbbadcdcdabcadbcbdcbddcaaaacddcbcdcdaadcbddccacdabadacabcbbcaadcadddadbaddbcacacddaaacdaadcbddcdadaaccbddcabdcddcccacbbabdbcdabcdabcaaaacbcbaacccbccdbccddaacbabdadacadbdbaaacccbdcdaaddcddaabdadcbabcaacdddbaaadababbbacbbddbcadcbcddcdbbadcddadcbbdcadbbabdbcbbcbaccbcdaccccaadabbbdcdacddcbddabadbaaabdbbbdbbccbcbdbcacaabcbddbadbbbaaacccdadacacadddacdcadaabacddbacaaacbadbbccadbccbabaaadddcdccdbbddbbaccbcdcccdbbacdadacdbdcddacdcbcbddbabaacdbbdcdbaadbbccbaddbcdabcccdacaacdcdddcbdbbccbbaaacaabcaababababadcacbabbabbaaabccaacccbcdbcbbacdbabcccdbabdcabdbcddbbadcddcadccccaacbaadbccbabaccadadbadbcbcaaddaddddcbddcbcabcdccdbdddbcdbadcdcbbbddcbddacdbccbaaccaaaadddcaadbbcbcbadcadbccbacdabcbbaddbdaadaadcccbaccabdbdddbacbdacbdcdadbacadbdacbabdacaadbaccbcdabdcadbacbaddddcabadaadbaadbdaadcbdadacbcadbabbcbaaccadcbdddabadbabbaabcbacdacacacccbdbabccbcccadcdadadadabbadcacdccbaccccdabcccdabbcabccabccbdadadacbcddabacaccaccbcbadbcdbaccadbcdccbacbcaabdcbaabacbacdccabcdacdccadbadddabcdadbabddbdbaadccdcdcbbdcbcacdcbbcbdcddbbdbdbacccddacbadcdaadddaacabbccdabdcacaddbaacaacadbbccbdccdadaccdbdcabacbbdbdabdabaadcddcbcacabacaaccbddaddccbbbdddbadadadacacadccbbbcbdcbdaadbacbccabbaabacabbbacaadcbaabccaabccacaddcdcabadadcdaadaacbcabbabbdbbdbcbdcacdcdadbdbcadacaababdabcacacabcdaccadcdddbbbbdbadbadccbaadbcbdccbabbdbbcadbbbaddaadacbddbbdcadcbaadabdaddaaaacddbabbbcdcabdaaabaacbdddbcbadbdcbadcbbaacdabbbbbddaddacbbbcaddbdbbdbcacdbdbdcbddabbbaabdabdbdcccccdadadddbbbabccbbaddbdcddbdcbcadbacaddaaadbacdcdbaacbadadbbadaddaabbddacbdbdcdbbaaacddbccacadbcddcadccabddaddcabbdccaaddbcdbcabbcadcbaccccdddbcbcdddbacbaaddacccdbadbbcbcbbcbadacacbdabadaacbadaddadaaabdadddbdccacdddababbaaccacccdbbbbbddbbaaddacbccbcacaadacabccbdcbdbcbccadbaaccbcbbbcadbacbadcbbbdabdaaabbcbcdabdbdaabbdacbcbcabdbcdabbabcddbcbabcdcdbbdbadcddcbdcbdccaacdcbabbcbbcbccabbcdbcabaabccbacaaaddadcbddaaaddbccaccacdaaabaaabcbbcdccdaccbcdcabcbadcbcabddcddcdabddbdbbcbabbddabcdadbcabaabdadcbaaadbcaccaaabaccccaaabddbcbcdcccdacbddcaccadcbadaaacaaabbbcadbcddbdabbbaccaabadbaaaaacbadcabbcabdbccadbadcccaabdbbdbabbddacbaccbaacabddcdcbddbcccddcdcbccdccbaccbaccadadbbddcddabccbdcdbdadabcbaaacaccbbcacccaadaabcdbbddccddbadbbcbdcdadbbababbacddaccccaabbadcaabddadabcdcaabacaaadcbcbddbdcccdbbdbcbddcdbabcacaaacdcacbcbadaabadbbdcbbaababcddabbcccccacaaababdbcdcdddcaddacaddbccabbcacdabbdbaabbcddbdcdcddabcbbbaabbbbdbabcadcbcbccaabaddacbbddcdaacadbaaacdbbbdbcbbbaabbaaaaabbaacccdbddaaabcaaaaadabdbdbbdadbaadbcadbbdadbdababacaabcabbcdcbdcdaddacdbddcadbddbcbccdbdbbcdcbbabcaccdbddcdcbadaccaaadcbaccbdabdbbdaddbbadbaabdbaabaaabbcbbdcbdccabddacdcddccacbacadaabddbdcdcabdabbdabbdacdcbdcbacbcbdbcabbacdbdddcadbabcdccbdcdddcaaaabdcbdbadabbdcbdcaadcdadcddadcccbcccdbcaccbcdaacaddbdcaccbcbcbddbdaddacaddcbdcccacdddcabcdbaddccaabdcbcdcbbacdadcaabbaadbddbabbdbcbbdcabcddcabbdbdddcdacccdbdaccdbabbccaccccaadbcbbbdcbdabbabaccddababaacabcbbabaaabccddcadbabddddddcadbabdcddccaabccccbcddbaacbccbdabddbcdbaddcbcbcddcdcabbaacdcbdabdbdbbaaaccddbddcacdccdcbaaaaaabbcacdcabababcabcbdcddccbdcbadddbbdabdaaddabaabcbaacabcbcaadcbbddbbbcabdccdcccaabcbccaadccabbbadcccadbbddcdbddadbbcaabcdcbcabcadaacaaadcccbabbabccbcbdbdcbcbabbcdbcbcaaabbcadadbbbadcdabcdaadcccdbdbaccdbdadcdadbddaabdabacaaacbccbccaacbabcddcdaaccabaaccaaacbdbdcdbabadaccdbcddabaacdcddacdbcdcccacbdcaabbbbbaacbdbccaddabcbbaadabbddbdcdddccbcbbcbcdaddbbddcdaabcdcaacccaacabdbbcdbabcaabdcdcbdcdabdddadcdbcbadcbdbcadcdacdabaacaabdcabdbbabcaabbbdddaaadacddbaacbacddbcdbbadccbabbbabddbcaccacdcaaccccbaaadcdbbaccaaccdcccadabcddaddbbaadbabbbccbbdbdbbbbddbbcadadccbabdabdadbbbaabadbadadbabbddcacabdaadddbdbbbbadcaabdabcbcadbdaccacdddbacaadaddccdddcbaacaabcbcabdadaddbbccbcbdcccdabdacacdadbaddcddcdbdccababadcabccbddcbabbbaaadcdcabaacbbcdcacbcaabcbbadaddabcccdacbacdcdadbbcabdcaccdbbdcdcddcdabccabbcddaabccbdbcdbaddbcdcdbcabdbcdcdcbdadaddabdcccdabdcabdbcbbcddccbaabacbdccdcacbadcabcacaacdcdbdddabcbdbdbbbabacdbddbddbbccdacacddacdbbddadbdcdaccadbcbbdbdbddbabbddcddccaabcbdbdabcaacdbcacbddddcbbdabccaaddccaabadbdbdbadacadbbbdbcbcbbdacbabaababadcdabbadbcdacbabddbdbdbdbddddbccaccacdbabdaabadbdcdcbddccbdcacddcacacbabcdcbccadccccdadbddcdcaaabacddddcbdcabbadabadbbbacadcccbbbcacbccdadacaddcbbadbdbcbcdbcbdccbaddbbddddacbbadacdaabcadacdccadcbbdcccbcaadcdcbccbbabdabacdcacababdbaabddcdddddcdbcbaadccaadcdbacdbccbcdcbaabcaadbbdbbbaddbbbcbdaadaacbbaacacabdcadcacddacabbadadaacccccddbcbdcdbaccadabdadbcddcabccaadcbdddaddcccbabdcbadbadadadaccccacabbabcdadaaddccdccbcdbdbbcaaaacaaccdaccbcaaddbbbcabdcbddaabdbcdaacadadccadbddabcabacaaadcabacadacacddccddbddbccadbcbdccadbcabbdaaacacabcdbdbabcbaadddacdddcacadabcdabddbbcaabdcdddcdcccbcbacccccbacdcddaababaaacdccadabaabdccbbaddcbdbbaaadaccacbdddcbabbbccdbabcabdcabdcadcdccadabdadcadcacaddccadbcdbbaadccbbadbdbbbaccbaddcdaccbabcbcbdbdccdaaaabdadbdcbbcdbadbcccdcccdabcdbbacbbdbccaabaddbbbcadbdcbaabdcaccbbcacdbdacbcbcdabbcabacbdbbdaddcbcddbddadccbabdbdadbcbbdbbdcccadbdaabbcdbcaadabcdaccdbcabccadcadaddaddbabbaadbbacadbbadbabadbadacbcdbdacdbbbcbbbaadbdbcdadaacddcccdcacbccdabbcccbacbdcbadabcbddaccacaccbdbcddcbbdddcdbbbbdcdcddadbccbbacdcacabddbcbbbaadbbbcdddbdaaaaabbdbadbabdadcdadcbddbabdbdabbddaaadcccddbcdabbdacadacdcadcadabdaddcbbacbcacccdbadcacaabddccdbbdbcbadcbcccabbcbdaccaddadbcddbdbcadbabcbbaccbadabbbbabcdcabdbadaadbacdacacccabbdaacdcccdccddddacdccbddbdacccbacacccabbdadcccbbcccbadcbbbcaacabadbbbccdbcccccdadbbbbcbaaacbadaacdddcdbacdaaadbcbabdbacbdcddcdbdcdccadcacbcdacddbbaacbcbaadcdbbadbbacadcbccbdcbdabbdbbdaccadbcddadabcdccdcdabdbcaaddcaababdbccacddbbddaadbcadbdbcdacdadbadaacdbcdbcbbbbbcbcaabdccbcabbcdbcaccabbabdcdacccbababbdcabccaaaddccadcbbdbaccacdbababddcbddbdcbbcacccddbcabdadcbcccabccaccdabcbacdbadddddbdcddabdcccbddcbddccdcdbbdcdbdaddaaddaabccbddadcbbdbaaaabacdaccdaabadbbdbadddadbbcdbaddbabdbbcacdaacabcabdcabdadbbcacbccabcadcbababcadcddbdaacbadacddbacdbcaccbccbcdbbcdcbcdbbbbbcbababcddccbccdcddcadcaadadaadacaabddbddbdcbadaacadaaabbacbbbadbbcbbbdcabdcdaaccadddddcaacdaaccacbcabbccaddaddccccbaacddcdccbbddacbababaabbabcbbacbdcddcababbbcacabaacdbbaabdabbccbbcbbccbddbccadcbcaabddbabbadbaacacabdacbcdddadacdadbddccabbcdadcccbdbaaccbcbcbcccdbbdbacbbabddddaabcccdcddbbaaacadadacbaccddbacbdcdbddddcbaaccaccdaacbcbcccacddccadabacdbaadacdabdbcbadaadabdddbacdcaacbdabcababcbcadccdcdaaaddbbdcbdadbcdddaababcadabacdabbcaacabbaacadadaadaabcbaadabcbcaccccaddbcbdbdbabbcadaaddbabbdacabbaaacddcdbdbdabbacbcbcaddddaacaabaaadacbddbcbbacdadcccbcabaadabcbcabbbbbabbcbdcadbbbaddcbadbcadaddbcaacdbadbdcdbccadaabbaadbbdadaacccaaaabccabccbcabdbacdcdcdddcbbdbdbabdcabcaadcbcababbdabbabcbaacdbbadaababdabbbcaacabcaadbcdcaaadbdbcbcabdcdbabdaabaddcacbadaadaaacdddcbacdccbabcbcccdccbaccaaaaccbdcbbdacadbacdbbacbdcabaadcccabaabddcbbababbddacbccddccabdacaccbcbdadcadbcbaddcbdddabbaaaaaacbdbadccaccaacabdbacbcadcacdacbdacdccacbbdabccdabbddaccdaadbbbbdccdcdcacdadddbbabdabdbaaaddbdbdadbcdbddabaacadcbddababacdcdddcabbbbbbabcddbabcbbdababdabbbcabaabcbbbccdbabcadacddadabbaabcbdbbbabdccdaacabbcacaddddbacbccbdaabbaaacdadcdbadcdbdbbaaaaaacccdcccbcacbcabdddbbdddbcbbdcdbacbacacacbbcaddaddcabaababcbaacadbccbdcdbcccabdabccdddaabcdddddddbacadacdbbcbaabdbbbddcbbdccabcbcaacdaacdbcdbbdcadbbddacbbbaddbadddaacacbbdcbdbcbbaabbabcbdabbdbcddcacdbddadcddccdbbcbabaabadddabdcbbdadcbbccacdcdcbadbacbcdbdabdacdcddcbddadbabdbbdcdcbacdacdbbcaaabcbbcddcaadacddcabdccadcddacacbacdbaabcacddbbcddbabaaabbadaddadccccccddcbbbaadbbdbbaaddcaddccdcdddaabcbbbcbadbdcdcacdbcbbcdcddcdaacdadaacccbcbdbdddbabdcccbccdabaaadbdbaccaaccdbcabbcabcacaacccbcbaababdddacddcabcdcbbacdbabbabccadcbcddbdcdbdbccacabdbcbdcaddbdbdccadbccdaccbcbacdbadacbcdcdcbabcbbdabbdbcdacabdbaaadbccaaacbbbacdbaadbdcddbddbaabaccabccbaadcdcaddccbaaccabbacadcdaabaccaadbabdcbbacbbccddbaccccbddbadbbcddadadaabccbddcbbbabaaabdbccddacdcbdacbddddccaddabdaabccadaaddccbddbaacdaccccaadbbaadbdcccaaddcbccabbcccbcdccbdabcbdbbccdacdbddbbcdaccacbbcadcaccaaacbcdbdcaaabddcbcdcdbadcbbbbabbdbcacdabaadbcdddaacacdcdabdbaaadacdddadcdcdaaadccdccbacabacccccbacadaadcdabcbacaddcbbdbabbabbbbccccbbdcbadcbcbcacbbcbdadbacbbacbdaadbbcbbbdacddcdabcddadbacabccadcabcddbacbacbddacdbdbdbcccaabcbaaadabadaabadcdacbacabaacadcdbacbcbbccbacababccccabddadabddcbdcccbdacadccddbaadcbdddbbdbddadbddadccdcbdacddccccbaccaaaaccacdcdbacdabcabcdbdabdccbddbbdbdabdcacdbdbacdbaccaadaccdabccaabccdbbccaccbbbbacbabadbadaaddbacbdaaabccdadcdacbaaccadcdbdaabccdbadcacdaccdacdcbcabdcabcbdddccbdaccaddbacaabcabbbadadabdaccdababababacabcccdcbaadbdddcccabadacbdabcbadcdadcddcbbadddcbdababdbcbcaadbddcdbaccdbabdbbbcccdcabcdddbcccaabddacbcbacbbabcbabbdcddcdabbcdaddccadbcbcdbaadcdababbbdaddabcaabccdbbadbcaaccbbcbcdcbbbdddcbbdcdaddcdccbbcacdcbacaaddabdbcbbdaabbbbbdacbbacdbabcbcbcabacbcddabcbdacabadbbcbbdacabcbcddabaccccddbddbccaadcdaadcddcacabccabdbcccaadbabaacacbacadccabbccdbcabbdbdaacadbdaccbcbcdbcdbdbbdacbaccbccbdcdbaabcaacddadadcddcaaacdcdaadacccdacacccdcddbcdbaadcdccdcdbccbcbadadaadbbbbcaacccbbadaccddaddcdbbdacbaccadbdcdbbbabbabbabccbccdcbbaacdcabddddbabbadbacdcaabbcddcbabbdcaaacdadccbcbdcddbbbaaacdabbdccbadbbddcbabadcaacdcdcbadccccdacdbbbacccddcddcacdabbdcdcbddddbacacddccbbabcddaacddabdadaaaaabcccdbbdadbdaacdacdadddbacbccdbbdbdcddbddcbabaabadbcbbaaddacadcbcaaadadbccaacdacddbbcdcbaadbbcabacbddbdaaadcabcbadbdccccbdaccdcbdbacddabababccacbdddcdbabbacbdbbcdbcbccbbadaacacbadcbbbbacadacbbbcdadcbdcbcacacccabccdacabcaabaadbcabbabdcabcbbacaabbbacbbdcbbbabbdcdcdadcdcdcbbacbaadcdccacbbdbabbddcdccbccbdcbcccbbdcacaacdadbdabbaabdacdbdadcbdacddbaacbdccccbccaacabbdacddadbddaacabdbdabaaaadddabacaaaccdaaabcbabaddbdcacaacabcdaadacdacbcbccdbcbdccbadddcdddddcadbdaacddbccacdacdcbcbdcbaaccbcbacacadbbaddbdcddcccabaaddaaddddcccabaccbdddcaccdaaabbdcdddbdabddccaaaacabdaaddccbbaadaabbbaabdbdddcddcabacacababbcdcaccabbcbddadabcdcbddddccbcbbacaddcdcacaabbdcacaddddcbcadccdaabbbbddaabdcbaacaaacbbabcaccdbbdbbcdcdaadbbbcddddbcbdcbdadbcacdbbdcbcbcdbdbaccddccccacbadbbcdcdbcbbbbcbbadcbccabacbdadbdcadbaabbcacadbabdcdbbacbcbabdadccbbdcbabccdbbabbbbbdacbbdddaddcbadcacacdbccadccdaacbcaaadaddaaacccbbbbaccbabbccacccbbacbdcdcababbcaacddcdcadabcacdaaddccdbbdabdbacccbbdababbadabddcbadcabadacdcbdddaddccabaabcadcadbcdbdbcccbbcbddcccbbbcabacbcccbdabbdcddabddbbbdabdcdacbbcadcaccccccabdbccddddbccccbdccdadacacbaacadadbaacaddccaadacbabadacabacbbdabacdbcdbccbdddabdaccdbcbacabbcbdaabdbcbdcabcaddbcbdbabccacabdbbcdaadaaaacdbbccddccccabbdcabcddbaabdcbccbdbaacaccbdbbacacdcdccababdcddbcaddbaddccdbcabadaadbdbdcabaaaddcbabcabcbdcdcdbadacbaabdbbdaaacdcacbbbacbdbaddbdbdbadcbccdccbdaaacdbcddaddabdcbcddbacbbcdbbaaadcdcadadddbabcabbcdcbbbabacdcdbdacaadacabcadadbdccbdbdccaaabdcadccbabdacbabbdaddcccaccbccbbbdbdcabacbccccbccaabbcddadbcabadaabbabdbcdccddbcacdabccbcacbdcddddcadbcbcabaacdcabdbaacadabaacdaabadaddaccdbccbadbcaabcabdbcacbbcddccacdaddcdccaaadcadcbddabbcabadbbddcdacdcbdbccbcabcaaddacdacbdbabcadaabbacdacdddddabcbaccdacccacdbdbbccccbdbbcdbbcaabdaddcbbcabddbcddbaabbbaadaacccbadcadcbccbbcdadccddccadbbbbadbaadcabbbabdbbaabdbaacaadaadddaccbdddcdbbdbcaccaaabcccdacbacadacbccdbdacccbbcaadaddcdcdddbadccbadbaaabcddbbbacbcdddcbacbdbdcabbacbbacaccbddbdcdacacadbcaabdcbaacbcbbcbdddcdbcddbdbddcbabcdaacdcccbbbcccbcdddaaabbabcabcaaadacbbbdbabbcbbdccbdbdcbdbbddaaaccbbccaadbcaabbddbdbddccbcbbaaabaabdbbbbdcbddccbbdbcabbdacdcacaacbdbacddadbcdccadaadabbcdcccccbbdbdbcdacbbbdbdabcacddddbababadcbbbdabdbadabacdbcdcbdbbacaddcbccaddaaccbdcacbcadcaaadcbdbbcabcaadadaacdbddbcbbbbadacadcabbcacddaacbccbaccbcdbccbaacdbaadacaaddbdddddadacabbcdbbccaccbbdbacdadccdcbaadaccaaababbdadcdddabbdbaddadaaddccadcbabccacdcddabaaccaddbcbdbacbaccdcdbaacaababdbabcabddababdcbdaddbbbcbadcbacbaacbdcbbcdcbaddcdbabbacaddbacabdcdbddddadbbdcdcbbcbddaacbdbcdcdddcccdcabacccdcbdddbddbbcccaadbbccbddcbcdcdddcddadddbbcdbaabccabadddcbbcdcbaabbcbcddabdbccdaabcbcdabdbabdbdaacaddcbbdbbcabdaccdadbaddcbddcdabadadaccadcbaacabbdadcbddcbcaddbbadcdcdcdbddbccbbabcdcdaccadbcacdcadacddcdabadbbbadcbdabdbbbdbddbdcbabbcbccdccbddbdcaadcdacdbbaacadbdcaddbdcabaabdaaadbbdaadcbbabbbaadcdbdacaacaacbbaabdddcbbacbbabbaaccadbdbcdddcbbdcbaddabbdbacababaaacaaaacddcdaaabdadadcdcaabbbaacbbcbdacdbccacacbaddaaaaabddbbcabaaadabacbdcabdcccacbaccababbabccbacbabbbddadbdcdadaaacddcabbbdcadcabccaacccaddbacdcdaccacccaacdccadaccdcbacaccddcdbaadcdccccdbbbccdbaaccbaabcbadddadcddcbaadcbbdcddbbbbbbbdcbcbdddababbbadacddddcacdbacdbdbbbdbddccbdddbcdabcacddbcadcacbdaaccacbcdbbaacabdddbadcdaabaaabbcbacbbcbdbcdbddaddcbdaddabcacbbddbdaccbbccaaddcccdabbbabcadbcdadbcddcabacdcbabdddddbbcddbaccdabdccdabbccbddbbcdadcaddbbabbbdddccbdacadadaadaabcddaddaadbdcbadccaaddabdbadcadcabcbcbbbdcaddbbbddbbadabbcdaaadddddabdcadbbaccdadbbbcbadaadbbabcbabccbbcddddcdbccadaadadbdbabbcabadccbbdacdcacbaaadacaabaabcbccaccbdacadbdcabcadbddaddcbacdddcddcddccddaccabaaccbbdbbabbcacbddddccccbcdcacaacababbcbdabdbbabdacbdadcdabbadaababddbddbbabdbcacbcbaaccccaacaacddacbacdccdbccbcadbdbddabbdadbabbcbbabbcbccadbccbadcbdcbccbccdbdccbcabaacbdbbacbaddabbbacccdaddcdadccdaaaacdbbadcbcddbbbddccbabcbbddddbdaabddcbcddddbdcacdaaccbabcadcdadcbaddccdacdddaddbdbcddacaabbddccababcdccdccbcccbdacddccbcabacdadddcbcbcddbccbdbcdcacacacbaacadaaabbdabdccbcccaacbbdbbbbabaababccaacabbbacaacbabcdadbaacacabdacbaaacdbabadaaccbdbbbaccbdaddbadadcbababdabddcdccacdbccbdadbabcbbddbdbcddabddadcbabaaaabdabcdcaabdbbddbbdbcccacbddddbbcadbbdbddaadabdbdcabdbbdcdabbdcccabcddabdddcbbdbcbbbbadbbdddbadaadadbbdadabdcbbddabdbcbcddbdbadcbacddcbabaacbcccdadbbbcbcaaadcdabbadddbdbbadaccabddcbdbccdabaddbadbbdaccdbcbdabdbbaddcdccacdbacbddbaadbdbacdccbcbcbcccdddcadacdacdccadbbdbcbccdbddbdbbaccaaacacabacadbbbcacbacdadccbbbdbdaaccdadaadbccddcadbdbdbcdbaccabdcccbdbcadccddbadbbbcbcdcbadddbacdaabcbabdccdcdadddcababdacadadbdababddbcaaadbcbadcbabcbabdccdcadacabccbacdbacddaababdbbcdaacccdbbabbaacdbbccdbdbcaccbaaacbdbcadcacabaabdabbaabcccdacaaddcdcabbbcdbabbcddaabbccadbaaabddcbdbdbddbaaaacacccbcbcabbacccdabdacbbdbadddabccddaacbadbcdddcbabcbccbacddddcaadbbbbbabddbaabddabcccbddbbaacddbcbaddacabdadbccaadbbcdddcbbccaababcddccccdbbccabddaddacdccdcadacdddacbddbdaabdbcdbbbaabadbbbcabdddcabdcbdacdcbacaabdccdbdbabdbccbaccaaaaaabddbbcabdcabbcdcdbcabcbdbcaaabaadaaabaaacadcdbaccbddcddccbbdcdadcbcacdacabcdcdbcbdbabbdcdcbaacadcdccbcdaaaabcacccbbdbabcaadacbbbddadcaaacdbdbdbdaaacadddbaabdddaaaddbdbbabdaacccabaaaaadabbbbdacbaaaabbbbdabdccbacabbcbcdcadddbdcdababdbabacbaccbbbabbbcaabbdcaccbddccdbbccbcabadbaadcbcbdadddaaaacabbbcddcdaaccdbbcbabddacbdcacdacacdadabddbadddcbddbdaaacaaabdccabadacbdcabcdcdddaddcaddbcacddcddaddbbdcdcbcdadabccdcccbcadbddcbaccacdaacacaccdcdbcbccccbcadbdacccdbbaabddcccaadbccaadcdcbaacaccdcbabcadbbbbcdcccbdcaadccccddbaaabddaaabbcddadadcbdbcdddadccabbdbcbcdcabadcdaabbbbacacdbaacbbdddcddabbbdbdcbbddaadacacdbaccbbcbaacddaacbccdadabbddaccbdabcccbdbabbdcbdccdadadcbacbdddddbaddbacdabbdcdbbaadddbbbbdbddbcadcdbbcdbdbcbadacbbaadbabcbcbdcacaacabbdbaabbcdabaccdbdbbddaccacbacabdcaaaaccdaacdcacaccbacdabbbcbdabbccdddccddacccbbbadbaadbabdadabdadddbdddabadabcdddcadbccbcbcbbdcadbcbbddcacccdbadacdbcdcbdcadabdbbbcccaccbdcddcbdcacbacaacdbabbaabcccdcadcdacabcbccbdbcabacbdcbcdabbbcbabbadadaddacaadcaaccbcddbcaccdddbdccdcabadcdacdbbcdcadbbbadccddabadbdcabbccdcdddabdbbbbcbcbaabccabdbadbcdaadbdaabdbbbdbabdcdbdaddabbcbdddadbccacccadccabbadccbccaadbbaadadbcbdcbcdcbcaaadbbbbabcbdaddcbdbdabdcdaadddcbaddddcbbdbcdbdcadbaaddcdbabccdcdaccabbacabdccaadcdbcdacddbbabdbbaadbcaaaaaccbacccddcaccdcdcdbbbcbacbbbbddbbbcadbcbbbbaacccccdddabbbadabdabcdbddcadcdddbccaccbabcdccccdcbcbcabdcbcdbadaaabddcdccacabadcbcdddbabdbddccadbaccadddbdcaadadcdbbcddcadbcaaadaadcdccdbaabddacdbaccabaabadcaacccddadbaacdbabdbcdbadbccbcdccaccbabacbadcbccdddabcddccdaddabcbdbddddabdbcdccbdbbcdddbadaacccddabaaadcacadcacdbbbabbddbbddbccbbcaadbaabaddddccbdbcadddcdaaaadabaddbccbcbaabcddbbbdbccddadcddaddbcdabccabbacbdcacccaddddcccadacaacddaccdcbadcbdabdbbbddddcadcbadbcccdcabbcddcabacdabdabccacaddbdbabaadaadadaaaaabdadcacbdbccbbdccacbadacdadccdbccdbaacbbbaabaddaccdacbcaacddbbccccacbacccdddbccbacdbdddcdaaaadabaabdaadabcdcaaacacaadbbdccdccabbddccbdbccdaaadbcbacbaacddacbdccaacadbdccabcadcddcddccddabcdabcdbaccacbdbbbbbdaaabdadcaaacbaddabcdbabcdccacaabbcdabdaadabcbbdcbacbcddbadbadaaacdddcaaccaabbabbbcacdbbbcdbbccdcabbbaaacbadbaabdcdacbccdbbdcbaacbacaabdcadbbcabacbdccbbdcadbcdcaaacbdaddddbaacadbacabddcdddcadadcabbabddcdcadababbbdcaaacabbbabdbddbdbbddadbcabadcabaddddcacabcaacadaaadaacbbabddcdcbaaddcacbcdaaaabccaaddacabdccadaaacbcdabacabdcdbbbbdbabbbdadccdadabcaaaddabbdddbacddaddcdcdbabdaacbbcbcacaaccbddacbbddbdaaacdbdabacddbdcbdacdabcbddaaacddbddcbbcddccdbcbacbbddcadbbbdcbcccccbbdaccbccaddcccbacdbbcaaabdbbbaddbbbbdbcbbbaccbadacabdbbbaaadcdacbcacddbabbdbadcacaacaddbcabdbabdaabbcbcddcaadbdddcacacaaccabadabccaabddaacbcbcbdcaabdbabbddaccdddbdabbadddbaabadaabcacdbdbcdbbbdbdabbdbdddbddccbdbccccdabbdbcbabbcbbdbaacbdaaddccdabcbaabdbcdddadacaaddddabdbdabaabbbbbcdcddaccadbcacbbacbadbcddccbddddbcbcabbababbddcabddcbccdddacddbacdccaadbbadbdccbdccacdbcdabbcbabbcbaabcacadaacadcabcbabbccbaddcacacababbbdbabdbbcbdaadcdcdbdacbdbdacbcddbadabcdbaaccacabacddcadccdcdcccaadadacbdbcacbcbbccdcaddbbbdcdcdbbbdbbdbbbdaacdcdbcdcdcaabcddddbabbdacacaacbaadccccdacbbbaabbacadbdcdadbbbabdddbdcbbabbaadcbcacddababcbdadbcdcabadabddacbaacddadcdbacdbabbddddacdbacccabdadbddbbacdccacadbababcaddccbdcbcadcbaabdbababbaabacaabadaabcccbcaddbcdbaacdacbaacbcdaaaacdccbadcbdaacbdababbbdaadbddddaddccabacdaaddccaaccbcbbaaacbacaadbcdccddaabdddbdbadddbadbbabcabaaabddadaccdbcadadcaacabbcccdcbcdcbbbcaacdcaccdcadaccddbabdadadccddddabbcaccdcdadcaabdbdbabcbbdacbbcbcabbbcdbaabbdacdaadbaddbacbdbccabdcaacbbbdddaadbcbbdbccdaacdabdbccadccbbdbadcbbbcdcbaaaddddcbbcacabadabbaacdccadbadabddccdbcbbbacbdcddcadcdccababdbccbbbdabbdadadadbaaacccabdccbdcbadbbbcccdaababacabcbcdbddabbbcabadbdabdabaaddbdacbcdddbabbcddcbdcbcbdccbdcadcccccadbabacbdddabcbcaddbbcbcacbbaccdbdabdaccbaaaddbddaccdabbbadcadbaaaddcacdddbdcaababcadddcdaadaaddcddcdddbbabbcacbccccbcbcbbaccbacddccbcbdddccacaccaaabcddadbbaadabcadabbbdaabcdcbcbabcddccdcbdbadbdcbcbcabbbdcbbbdbacadccdacababdcaccaaaadacddbcaacccbcdabaaaaadccbcadcbbccadddaadadabcdadddbbbdbdbadbbabadcdbacadbdccdaabbaabdbacbdaadaadaaacddabbcdddcbccabacbcacccbdcaaacabaaabcbddadcaadcaaccbabdacdddbdaaacbddbbbadcacdabcbddbadcbcdacdbaacdddcddcbcadcdabbbcabdccbaccdbcdcbcbaacccbcabcddccacddcaabdacddddaabddbddbacdccbbddddbdddcadbadabcaabbcbbaccdcbbaabcdcbbcaccacaaabbcaaddbbaabdbbcdccbdbbdcdadbbbacdacacacdbddcddbcbddababaccababbbbdcabdcbadcdaccbddcdabcdcacdaacabadacdccabadadabdadaacaaaddbbcbcdccaabdcaccbbbdcaccacdbaacabcadcabcdbcbdaabccaddaacbbcadcdcbcbdadcdbccccdcacdaadaccbcbcdcbabdbcdaccbdcadabdaacbacdbddbbaddaacdccaccccdabbdbbabaddcdcdaddccbabacccacdacacdccbdbcdabcbbcaaabbcccccbadabcbbbdbbdddddddaabddccaaabadbbcdbdadccbbddcdadcabacdabaccddcacbabbbcadadccdbaabacbabccbbaadcdcbbacbaaacbdbbcdddbdbacbbbabbabcbabdbdccdaddbbcdacdcbbdccbbbccabcbacccadcdbabacddcbaccacadaaddbbdacdbdaabdbdccddcbddcbcbababbaaadcabaabbbdbbbdbaacacdbcacbbcadccbacbbaccdcabbaccabbcbddbbdbdccabccacdcdcbadbbdcccaabbbacabccdaaccaadacddbcbacbcaabdcacbdadabaabaaabbddcddacdcccdbccbdbddccbabadaccbaddddaabacdabbddbabacdadabcdacaacaacbdcddbcddabaadbbacadbbbdbdcdcdaadbccddbdcdbcacbccbdacccccdaddcdbabadbcddcddadbcbabacbdaddbdbbdcdccbdcaccccccabacdaacabcdddbdbdcbbcdcdbabccdddcadbcbdcbaabaaccaaddacaccbcabadadbbdcdaccadbacddbdbbacbcbcacddcaaadddccbcacdbdccacdccbadcdbaabcdabbcabbccacdadcdacacdcddabccabbdcaddddcbbdaccbaabddacdbbbdabcbddadbdbcbbddbcadbbbbaddacbcdbdbcdaddddcbbcdbccddbacbddaaacabbabcabacacccbadbbacabddcacabcccddcadadaccbdccbcbaddabccccadbaadcdacabbbbdcaaccddbaadabbddbcdcdbacaaadadbdddcbcabcddcdcdbcbdbbabcabacbbdccbdcbcddacbabcadbcbcbddbbcbbddaaabccccbaaddcdddcbccacabbcbdcadaddcbbcddcbbacbccbadadbdababaacbadcadacadbabbacccaddacbdaacdadabbddbabcdbbbbbdacccccdcddbbdccdbacbadaaacaabcdaadbccdcdaaaddabaddbcaabddadbbccdbacaaccbdcbbdddccdbacddbddcadccdbddccdadcddcabbdabaadddcdaabadadbdcabadcbcbcbcdbdcbdddbaabadcacddaabadabadcddbdbccbabcbcdacdcadbabcdbccdbccbbbbcbbabaccbabbacbddcbbcccbcbdaabccadddacadcbcdcdaadbaddccccdcddabcdacacaccdabbaacaddddbbbdbccaacbdaadcbaaabaabbbabbbadaacccabdaaccdadcdbdcdcdddcbddcdabcccaabdabcacbdaddddcdcdcbaadccadaaadbcabcdacbbbaadbddabcacaadbbdbccccddccdddaccbbbbacdbbbacbccaacdcccbdabdcbaccaacccadbbdacacababdcddbabddcccbcbcdddadccababbaacabccbcaabbcbbacabbdbcbcbcdcbdaacacbdbcbdbadbcadcaadcccacabcaddbbcdccaabcbcbdbbaabdcdaacabcbdccacdccdccaccccddacdbbaaabdbcbabbbbbadbcbccbdbdbacbdabbddbccbaabbbdbbcdaddaabbbbbabbbbabddacccddccacbaddacccbacadacccadcabadbbbabdabaabacbabccbccccaaddbacbccaaacdbbdcbdbdadaddabaadabdddbabaaacddabdbcbcbcadacadaabadabbbcadcadadbbdbabcacdcdaaccbbbdbaaabdbbbbccadadbcccaacadabbcacaaaabccdabcbcadacdabbacbbdcaabcdbaaabcdcbdcabaaaddccdcdbbbbdcaabdaddcdabcdadddbdbbccbbcccccddacabaaacbdcabaabdbacbadbccdacacbbcbabbacccbacddbccbbdcdcbbdbbaaacdcbbcdbbdcacccbaacdcbcbdadbdddbbbcabddcbadccbcdcacdaaabdaddbaadaccabaabdcdddccacdbaaaabbabddaccbdaabbaccbdbabdabbbdddcbdaaccbabaaaddbdbddadabbaaacbaaddcaaddacbacddacaaadacbdabbbbbbaccaccddcaadacbcadadbbddcbcddabdddbaddcdbbbcccccdbdbcadcacbcacbabacddccdcadbabcaaccbadcbbddbdabaaaddaaddccdcbacbacbadbdddbbcbddbccbccccadddcdbcbaccabdcaabdbaaccabcbcdbbcdbcddddbbcdadbcaacbcbaccccbcdbbcdacddbcdacbacaddcccbcbcbdabbdbccbbdcdccdadadcbabbacacdbabbaabdadbaccacbbddcbaddaacbcddaccaccbdccdbdbadbdadabcbaacdaabbcddaabadbabaaabcadbdccddbcbaabdabbdbcdcdcacbacdcaddcaabdcbabbdbdacbaacabbcccdbdbdbabddaddcbabdcaccdbcadbcbbdacacaaaddcaaaddccabcaddcacbaddcacbdbacbcccdabacbcaaadaacdccbbabcaccccdabacccbbcddaccccadaaadabbcaaacabccacbacbcbbacbcdcbcaadbacccbddabbdcbcbdadbbaadacdcccdbcaacbbaadbabbbcbbabcbabbdcbbddccaabdcdbbcdaadcacadbbccdbcacaddbabbabdbabbcbcbdbdddccbdcaadcbaadcabddaabdcaadcaccaaadcaccddbadcaccadcbabacbdbdccadcdbaabdbdadbcbcccdccbacbcbccbadbbbcadacdbddcccacbddddabbccbacaccabaddacdccdbbdbbdbbcbcacabacbcddbcbdaccaaccacddccddbcdcddaddbdddbabdcabbdcdcdbaaabcbcadddabccbdcaddbacdcaadaaaacacbdadadadbbcbcbbccdbdaadcccddacdadaacdcdadcacaabdaccbcdccbdabccaddacaaaabbcdbdbdcadbcadabbadabaadababcaddbcbcddacabddcdcdcbcaacaabbdbaabdbddccdddbbccacaccccabcbcdbccdcabcdbababaddaddcddbabdcccabbcabdbbdddbbcbbbbddabbcccccdbdcdcbccaacbbaaadcdabbbdaaccaadadccdcbccbacdabcbaaaccccbbbadbcddaddcadbaaadcdbaaabaccacdbbbbcdaadcbcdaabddbabbcbcdbdaaadabcbababccaabcdacdbcbcccdbddcdbaddacddbdadbadcadabcbacaccdaacbaadccbdacddaacbbdacacbcdcaddccabcababdddabbcaabdbdaabbcdaaabbcacdbaaccaabddbbccdadacacdacbadddcdaadbacabbdadcbadacdabcbabbddbbdacacbaabcaaabddcbdccaddddddbdddbaaadccababadcdacdcbcaabbaabccdcaacdbbaabbbaccbbcacaaccbcbdaabadacdcbbcdcbaacddacdcbcdaabadcbccabdacdbddadcdcdcbdbdbdacbbbaabbabdaddbacdcbdabdcbdddacadccbbddaaacababacaddbbcaaabcaccadbaccccbcaddadcabdbccbccbbacbdccdcdacbccbcccddaddacdadbabccadcbbcbdacadbdabccbadddbbcbcbbbddaddcdbddbadcacbdccdccbbaaaccbaaaacbadcdadacccddbbcaaaabcacaddadcbdabddcacbddbdaacbaddcbadbaaabbbaacdcbbaabcacbbcdaabbcbbcbbcdcbaccddaabdddadacbbddbbbacbbbccaaaccbbbaabbdadaddbcbcdbdcabcddbbbadbccbbbbadbcdbccbbaddbaddaaaadcaacccaacaacdcdccaaddacdababdcaaddaaccbabacaaccaabbaadacbbcbbbabdbaabbccddcacccdcdabcbdccccbbcbdbabacdadaadbadabbbcbabdbcdaadcbdbabacddcdbccccdacaacdbcdbaddbdbcccccadcddccbbcdbdcbdbdcdabddababdabddabcccdadcabddbaddccbacccdcdbdccacabcdbaaddacbaababbbdbddcabcabdadddadccdcadacbaddadbacaabdbcbbdcbbcaacabbddadbcacabaadadaabbacdccddcbccaaddcadccadbdbbdbaddcadcbdcabcacbdccdaddbbbddcdbaccabdbdadccabbbdabbcadbabbabbcbcacbccdbddcbabbadbbabadcbbbaaccacbadddbbbaadadbbddcdbaaacaaacaabdbbdcdabdaaaabdbbcbbacbaacbcccbacbaadccdbddaddbacdbdddcbadabadadcccddcbddcddbadccbddbdbabdacbbbccbdababdccaaadadcdacdadcddabbadddbaabaaaaaccbdbaabadddaccaadabcccdddbdbccbcaaddacdbdcbcdddbbcabcbbaacddacabdcbbbbbacdbdbdddbcabbbdaaacabbbcbadbccabdaddacaacdbcdbcacaaaddababbdbdbddabaaababbbaccdcdcdbdbacbcabdabcadacaccdbdacbbbcaccabdbcccccbbdaababadbbdccabddbabaccdaccadcbbabbbbccdcbbcccdaadcbabadabbcdbcadbdcccbcccadbcdacdbcccadcacaadacdabdccddbdddbdbbcdcccbaddcbadddcacabcacbbdcccddbbabaacdbadcdcbccacbacbaabbdaacadcabbcabbbaaddccdbbdcacbabdcbbdcbadadbabbbbaacbdcdcdbdaddaddaadbacbdccaabbabbcaabbcaadaacacdcddbadcdbababdaccaddbbaccadbbadaaacbcadcbcbbacbadbaaaacbcdababdaadbdaddabacbcadcacdcdcbacbbcccbddabbbcaccadcacdccddaccaaadcbbccbbbbacdcdadaddcbdadcbbdbadbbabdbcdcaadbcacabaaccccabacdcbaccaaaadddbcacacacbbabaadadcdacadddbcdbbbcdbdaabbcbcbdddcabcdabcaaddddadabdaddccacacdcdbdacddbbcddbabdcaadbbcddcccdbaddabdcbaccccdacbcdcccdacaadacddcabaddcacaacdaabcddadbacbbdbdcdbcdbbbbdadaddbbddbdaccaabdcadcaccdaddcabcaaabdcccbdcacdababdaddadbbcbbbadadbcccbbadbcbdacbbbcbccaadacadcbdbbbdcbcdbddccaaaacbbcabaabcdbddbcccaabcabbcbddcccabcbcdbccdbdbdbdadcccdbbcbcadbaccaccbacdabadcacddbbdabdadadbddbcdddbabddccbddabdacaacabadcdcdaacacdcdbaddaddaaccddbbbdcbbdbbacddddcdadbcaadadbbabdaadadccdcdacdbdccccbcdddbddcabbbabbcbadacbbbacbaaddcdabbcccabddcbdddccabbcdcdacbcbacbcbdadbdcaadabadbcaacbaabdcadbbdbcdcdccabbbaabbcaaacacaccacacdccabcbcbcbabcababaaadcacccbbbdbabddadcabdadaccacdabbabaaaddabbcdbcddbbbccdbcbabbacaadaddbdcadabdbbacabbdacbadccacadaaccdccacacbcdbbddcdadcbaaadadbbbcaacadbcacadbaccabcdbcdacadbaabcdbddcdbccadbcaabbdaabccbcddababdaddbdccbddaccaccacacbbbbbdccabaadcacacccdcbddcbdadacdcdcdadabbbbadbddbddabbacdddadaaadaabdadacdcdbaabbddddccaacdabcaacdcbcdcaddaacdcdcccacaacabcdabbbcacaccacdcbcbadaadbdbcdacadaaadaaaabccbdbdbcdaacbabbcadccbbbbadbbaccccaabcdcddddbabdbadccdcbbdaababcbaabcabbdcaccacbbaaddbdddbbacadcbccbdbcbbdbddccabcbadcbadacbbbcabbdabbaccaaaccbbdadbacabaabdcccdadbddbcbacbbcacdcaaddacabdadbdcabbaacccaacbdaabbbcbbacaddbbacaabbbbdbabdbdcaadbadddcabcdbbccabaccccadacacaabaccbcadacdaabbbabdadddbbbdccdcdaadbbbaabcdaddcaacdbbdadcbdcadaccacbaaadddccaadcdadbcccadddbdcdabcbdccccacbdcddabdbbaddaadbddbbdcdbbadcbadcabcdbcbcabdcacccbbadabadbcddbcadcacababcbcadcbdbcababdcdacdabdcdbaccbdaaccdadbddabddadbdbdcbdccaacdbdadbbcbcccbbbbcddacbcbbcbabccdadaacdcdcdaaabcadbbccadabaddacabbdddcddaadbbdaabcddbbadaabaddacdacccbbabbcadcdcaddccabddaccccbabbddccaddbaccddcabcbabcccdbcccacbcdadddadbdcaabcdcdadbcdabbcbdbdaacdbdccaabadbdbaccaabaaddbbdcbccaadbdacdbadcbabbdcbbabcbaaccaaaaabbbccabadaacccdddaccbdabacaddcaabaddccbaadbcdcdbadcddacdaacbadbdaddbabdddbbdccabacadbdbccddabddacdcacadccaadbcccaddadabddaabacbbacbdbdccbbccdbabccbaaccdcaabbcddbbbabbdbbdcbdbbbaabbdbabbcccccbdcbabcbacbadacbadccdcdadabaacdabccdcdadaacbcdadcddddccbcdddbaaabbbaaaaadcacaabdaaaadbbbaddcaaabdccaabccabaabaaccadcaabcbaacbabaadcadccbabcbcadaddbdacadcaaababbabddcdddabaddccdbbcbdbadbdcbbdccaadabdaacdbabcbccaccccdacabaabddadbdaccbbdbcbacaadcbcccbdccdaabbaacdadcababcddcccaccdcdcbcdacdbbdabaccbccaadcbbdabccdbaabaabbbccaacdbddcdcbbadbacbbdbccbbdbacbbdbbacdaacbcaaacabcacbddacdddacdcabcccbdaabbbaddbcdcbaabdbbcddabccdcdaabddbcbccbcdadcabaadaabbdaabbaacadadddddacdaabcabcbdbdbaacdbcabbddccddabddcbddabcdbadbdbdcaaaaabadabaabcacddbbbbbbaccdabbbdbadcaabbccbadbcaddcaddbabcbbbdbdcdcbbbcbccabbacdacbccabcbcaddaccbdaadcbbbbdbdabbcbdbccadacddccbbcddbdbcbbccbadaadbbdcadbabadcbaaaaabbbdbcaadabbababdabbdcccbbdcbbaccdbacbccdaccdcdacadadccacadcbddbaaccccadcabbdadcccccaadbcdbadddabbaaddbbaaccabddbbdddaacdadcccbbdcbacddaabacaadcbaaacbdadccacccaccbadadddaabdbcbbdaddcbbdbdcdbadbbbaddbdccdabbcbacbaccdccccbdcccbaababcabdbbdcdaadbdcdcadbabdcacacddaadacacbacbdadadccbabdbbddaddbddbaccabdccddcabdcbdbdbabbddccdddaadcccdbbaddaadbbcdcacbcbddacbbdccaddcddddbaaababcbdcaadccddbbacbcbdbdbabdabcdbbdababcddcdbdcbcbaabcbbcbabaccacddabadaabdccddababcdccabbabababddaadaadaadacbbdcadcdcddcadabdcdccaacdcdbbdcdddadbcdbaccacccccccabbaccbaaabdccbdbdcadaacabcdbcdcaabbcacabbbdaadadcbacdddcabcaabaaaacdbaccdacabbcbcbdbcddcbdcccaaccdbbcdadaccddcaadcadcbdacbbaaadbacdddaddabdbdbcabbcbcbbbbcdccbbccbcbbccaaccabddccabbccdbbcdabcdccdbabcdbbcabcadbaaabaddababdbaabacccbaddddcdbccbbbacbdbcbcbcddaccbadbbdccdbbdbdbacbcbabcbcddddcbbdddcacccabddadadcbdcdbaacdacacdcbacdccdabcbadddaacabbacadaadbbbabdccaaaaaccccbacdadbbdbcaccdbdbabbcabbccbbbdadbbdabddcdddacbdddaabbabcdbaadacadcdcbadcbbcddadbadaccdccbcabdddbdaaabbaddaacacdcbccaaabdaacccdbdccacadcccdabdbcdcbdbdacbcacccbbdaadaaddabadaadaaabbabdbdddabbdaacdcaacbbbaddbabdccabaaacccabacbadadbbabaccbdaccacbaddacacbbbbaadbcbdaaacabadacdadaddddbbcddbdcacadabbdbdadddaccbcdcddbabbabdbabddcbcbdbddbcddcacccbccbaadbdadbacadddcaddbcadcadacdaacaadbdabcdbbdcddccdbaccdbcccddccddbccadcdcaaabcaaababcbbddadcaddcdacaacbcbbdddbccaaddbdcdbcdcdaccbcdaabbbdcbcbbccdadcabcadcbcddbcaacbbdaddcccadddaababccbcadaddaccbaddcdcacbbcdbccadabcdabaabcbcaddbbbbcccababbbddadabdabccaadadcbdacbcdaaddccaddcbcaaccaaacbcbaccbbbddabcadbbdccbdadcacbdcdccdabcdaacdddbdaabdddbcabccdcaccbcbabccbdbdabdbdacdcddbbcbcaccadcdacbadacdbbacdcaacacbdcadaddbcccdabadcbbcdbbdcbbdbabacabcabbcbaccbdaacaabbbcdcdbbdaccbaadddcaacdcdccbdcaaaaaadacbabbacdbdabddbccacaccdbcbdacdadbcbbdacddabaacccabbabcbdbadddbbbbabaaaaccdbdcbcdcbabbaacdcbbddbccaacaddcddcbccaacccdaaddcadbcbcabadaddbacccbdbccccdcccabdcadcadcdbbdbdacacacccacdadaccdaadaacbbddbaccbaaadbaaacdaaacdccababdabacbcbdabacbadabaaadcaadbacadcdacdabcdcbddaaabddccbbbccddcdbddadbdcbbadcadcdcadacbdacddadcdbbbddddbbcbdaaabacaadbcadaccccaaddcdacdddcdbadaaaaccacdaddaaacbcdbddcbbdcdcdcabbdbccccbbaaccddddbacbadcaddcccdbcbaadbbabccbddbbcaaddbdcabbaaaaadbdbbcaacccbacadccaabccbabadbdadccdacadabdbbcbadabaabcbbbabdddcbbdcbbbcbccbcdaccbacbcbaabacdcaacbccbbbbbccddadaadcabddcbaaaaddccacbdcdccaabaccdcdcbacabcbbbcbcbcbabaabcbacbdccbbccaddadcbacbdadccccdcddabdabdbbcdbadbdadcaddcbbbbcccdcabbdcacdbdcbadbcbbbdbdabbdacdcccabcadbbacbabacdcddbaddbbdbababdbaccacdddbadcdddcbddbcabcccacbbdbcccccacbacdcdcdadcaccacdcbdaadacbccaacddacdbadacabadbbadaccdbdaadcadbcabdcdbbddcbabdddbbbababccacddaaabacadbdcddbaccaabccbbdcbacccadbbddbbdbdabcddbadcdcbbcadcdccbdabcabdabdcdbcdcdcccbbdddabccaaaddabbaaadbccddbbcdaddbabdabaabbbdcacbbacbcbcabcbbbacacacbcacdabdcbdadcdcdcadddddaadcdcaadbcabddaddbdadddbdcdbabbbacdcaaadaaaaadabbdcadababcabdaaadaddbddddddbcdadbadacdbaccacaabbdbccacadbcdbaccaadababbcbdbddadbabbdcccbcdcadcdbaaddbbcccbabcabddcddaddcdccdabcacdacbbcababbdcaccbcccdacdcbacddabdccacabcdbbbadcabcbbcbdcbcdcbdbdaddaabaadbbacdacadbabbcabbcdbadaccbdaddcacdaddcdcdcccadbacbddcdbadcacaddabbcacabdacadddbaaaaabbdbbbcddbadcbdcadcaaaccadadabdabccabbcbbddbababaccdadcdcbabdcababdadccbbbdddcdaacdabbbcadaaadbdaccadddabbcddadcbdaababaccbdbccccdacdaaaddabdaaaaccacacdcbccbababddaddcacadbacccadabbabcccbababcdbbdbbcaacababcabdbcacadaaaadacabbdaadabdadbcacbdaddcdbbabccbdddbdbaabbabbddddacdcacbaccadbadcdbbdadaaadcbaacbbcadbaababcbdaabaacbcaddbdcccbdbbaddabababcdbaacbdabdabcbaaaaaadbbdacbddddbdaacbdddcbbbbddaabbbaaccddcccacbbbacbaadcbdcbabaabccbccccaacacaadddcdbaddbccbcacaadbcdacabdddcddbadbcddacaadcbdbbbdcbaadadcbabcdcbbcabbbdddcdababaacabdccdcdbcccacbddbdcabcdcbaccababccccddcdcccdbabcdbbcdccdaabacccbdddaacadbdcbcbdbdadbbcaaabbadbcdbddabaaacaddbdddcdadcbdcbbdcaaaabdacbdccdcaabcaabdbcbcdddddacbbaabcacbbbaadbabaadbdadcbcaaccaabddddaadbdadccbababdcabbdadacccdaacbdccdcdabddbdadcbdbbdbcaacddbdcdcbdddbcaabdbbbcbadcbcbbabadaaccadddcaccadbcdcbdccaabacdacaddcdbaaacccbbbddbdabbbbcbcccbbabdbaccbdcdabdbababaaaccbbabadcabbabcbdcdddadadbaaddcaadcbdbcddbaccacdacacadcdcaddaadbdddacaaacddbabaadbbdcdbcacaccbaacbabbddddcbcbdacaadcbccacccbaacdadcbccabaabbcccbbcbcabadcabbbcccacbbddabcbbbbbdabdbdcbcaaddbbbddddadbacdbadddbadbbabddcddcaabddcdadcdacbbcabbaaacabcbacbaacbbcddacacbcdabcadcbabcbaacbcbdcdcbaabbccadabaadadccdcdaaabbbdbdcdaddabbcdadadccbadcdbddddadabddccdbbdbbacdccdddbaacdabbcbcadaabcacbddbcdddaabdbaadacabbbaaddcddaabccddbaaddbcdabdadddacbbadacbccacabcbcdccdccaaccdbdabbdbadbacbacabaddccbbdacbacbdcddcaacbcaddcaaccbbadbcdcdababadabcdbbbbcaacbbabdadcdcdaccdacbcbdbddccbbccbaccdbadbabcbdbccaacccabacdcaaadbcabbdabacbdccabcaadbadccaabbbdcdaacddabbddacdababaaddacdbcbabcbddabbbdaddccacdabadbcbaadbbdaccbdbadbdccdaaccbdccdcdbcacbcdcdbdbdbcabaaabccbbcbdaadabaadcbbcacddabbbaaaaccbdbabbccbbbdbbdabdabdbbcddbadddcbdcacccbdcccccacdaabbbdcbbbbdcaadadbadabbbbcddabdbbadaaacbddacaaabcacbdbdbaadbaddbcabcabadcadaaacdccbdabadabbadbcdbcaabacdddacacccadadccdbcdababdbacddadbacddbabbbcbdabcccacdccbadbdcccacacccbcbbbbcacdbdcabdacdcadacaddcadccaababbbbbddbabadccbccdbcccccccbbdbbcabcdbbaddbcacccacdcabbabcbbcddccbbcaaaadbddcdabcaabddabbadcacbdddcdcacbdcdcdcccdcbbdacadbdbcababccbddbabcbbbabbabacaadddcdbbaacaaacdbadbadbbaacabbdccbdadbbcabdaacccbabbabadcdbbcaaccdacaccbaaccdaccdccbbcabdccbdbbbcbcabccacbadabdbcbcbcdcbbacbccbdcddacbaabcadccbbcaacdabccbdbaabadcccbccaddbdacdcbdcaabdadbbbbdcccaddaccdccbabdbbbaddddcaaaacadbadadbccbbcdbdbdbccbdacacacbaaccbaacddcddaabccbdbdababcdcabdbaacbcbdacdbbbddaddcddddaaabbabbbaddbcbbdbaaabdbbdbadcbabccadcbacadaccabaaddbdcbbcbcadcacdadddccadcbabdccbbcccccadcbbcbdbdacbbccdadbaaadbabadadccaddcabcdbddbcabadbdcbacccdbdbdbccacaaababbccccbccccdabdcdabdcbacbdbcaddabccadcccdddbaaddcddbcdacdaccbacdaaddcaddadaabaabdcabbacbaabbcdaadcbadcabababdcdbbaaddcaddcacccccadccaadbbbacabdbcbcdabbadadcbccadbcdadccacabbbbbcabbcacbdbbccdbabdbbdadbaaabababdddaccbacaccabacaaddcacbbbdbacabcdabcaadacadacbaddbdccabdcaabdcdabccbacbdcbddcdbcddacdbaaaccccadbdcdaccbaacadbbdbdacdaddbcabdbccaccbaabdacdddaccbacddadcabcbccbacaabdaaaddbdcdccbbccaadbcbacbbddccbabadcbdaabbcddcbdddcadcdcdcacbacbcddabbdacdccadbbabcbcbababbddacbbbaccaaaadddaaadcdaadbddcbcdcdacbbacaccbdacbdaaccbccaaccabaddddbabacacbaccccdbcccabbacadbdcbdbbdbcddddbddacaddabdcbaaaacacddcbcbcbbcaccaddcaabbadbccbbabcbdccdbdadacdbbcdbadccabdabbbaddcaaaabbbcbdbabdaadaabbaccbbdaaaaacdaddadaacabdabcbccdcadbabdcccbabccdbaadddcddaaadabadaababaddcbccdccbbdbdbcdabaadbaacabcdacccabaacacbdccadabdabdddbdbbadabbdbdddbdcbcddaddccbccdccdaddaccbcccbbdbbaadbbbbcbcacdccdaccabcaccabdbdcbbdaabbadddddbbacacacacdcbaabbbacbcdccddbdbbabccdaaabbacacaaaccdbccacaaccbaacdccaaccbdadacdbcddbacdddbccaadcdbccbacabaadcdabcdaddaacbddaaacdbadccadbdaabacdadadabacbacabacaabdbbbdacacdcddbcbcddacacdbaccddcbaaadcdbccaaacaddccdabbbdbacdcaabaaaadbbdbbccdaaadaadddbbbcbacdabddacdabbaaaadbcbacaaabbbbbbcabdadbdcddbaadbcdcddddadbbdbcdaccccbccdacadbbdddddaabaacdadccadcbadadbbbdcadbdbbdccbbaadcbadbbbdacdbbccacbbabcccdbaadaaadacdcbbcddccccbbbdadabacbaccbddcbcbaddbbbcbaaaadcabbbabbdbbadaadbabdccccbadbcacddcaaacadabcacdcbaddacbbcddababcadccdbdbaabcbbbbcbcdbcccbbbddaaddaaddbdabcdaaabdadaacababdccbddaabddaacabdbcadbdabdaaadaadadbccbdacdbbcaacbdccadccdcdcabbcdddbccaacacbacbccadccdbdabadbddbbaacaabaadccbbabddbbbcddbbdacbadcbabdbaaaababbcabddabdcdaddadaaaccbbdbdacdddacbdbccbbdcbccadbcabdcdcdccaaadcbccddaadbcaaadbbbdbbcbadccdbbaacacbbbadccdccdddbcbaabcdacaccacdabaacabdaaacacabddcbcbbbabbcbdccccdacabbdaaacaadaaaaabcadccaccbddccdbccabccddabbadcdabcacdcdbacccdcccbcbccdcbbdcccadbdacbcadbdaccccbaaccdaddacdbcabdbacbdbdabbdccaadadbbdaacadcacabcdddaacadcadcccbabbcdbbccdddcdaaabdccacbacddcdbcaacdacdddcdacccaddcabcbbccccddaaacadaddcbbdabaabdaabbadbcbcbaaaacbbcbabbcbccddbccdccbaddcaabbbcddbdacbaacdcdaccbacdbccacdacbbadccabbbaadccbcddcacbddacddddcdbdcdcbdddbabdadcdccdcbbbdbbbdccbaddbccaaacbbadbbdabbdcdadcccadcdadcbbbbbbbbcbcdabbdcabbdbcdaacdbbabacacdbababbdadbbccbcbbcaaabaaacadabbbdabcbdddcadbbdcdcddcdcbbaacdcabdddcccbaaadaaadbbabcdccdbadcddadaaaddcbabbcddbacdbdacdbbddabbccccaabddbaccacdcbdcacadbcbabcabccbaccaaabaacabdddbdabbaabbbaaaaadbcdbacdbdcdcbddacccaddcabbcccbccdacbbdbbbadabcbabcbcdcaadbadbdcdaadbcabaaabbabcadcdbabacbcbdaacadbcdabaaddbacdddddaabadcdcbacccbccdcaacddbdabbcdcddaadbacbdacbccababccbbcddbabdcdbcaacaaaacdcadbdabcbaadcdcacbaabcadabaccccaabbcadbaaddbdccadcaabdbabbcacdaddbdbcbcabaccbbbbddcdbbaccccaabcacabbbdaaadaacbbbddbbdadabbccdabbdccdabaccacaccdcddacaaadabbbacacccaacbbbbdacabacbacbcaacbcbdbbdadcaaccbccddbbccabbddacbbdabacdddbaddbddcdbdcbadaadccbcacbbcadbdaadcbbdabcbccbacadbdabcaaadadbbaccababbbcbbcbaadbaabcbcacddccbbbbddcccabaaaccbdccbdcadaadadbcdccdbcacdddcbdbcdccbabbbddcddacddacdddcabcabcbbdbaacacbcdcaddcddcdddddabbacadbbcdbacbbcdaccbaddccccddabcadabbcdcacddaacdacbcddddcbcadcabaccddcccdccaccbbccacdbbadddbdbdadadabadaddcdababdbddccaddcbaccbaacbcadddacaaccbdcaabdddbaddcaaaccbbdbdddcaacdccbbbbacccacacddcaabbbcabcacaaabdacbddaddacdbaccdaabddbccacaccacdaadcadaddddaaaaabbbcbbbdababddbdbbbccdaccdddccdbbaaddcaccdcababaaadbcacacadacddbcdadcddabaabacbcccdbaccdcbaabacadcddcbdcabaabbcaddddaadbdacaccaddaadcadbddaabdacbcbcdbaaabbdabacccbaabcabddbbacabaadadcdaddcbcbdbbbdddbbcbabddbbdbadcbadabdadadcdcabdcaacdaddbaccaadbacaccdcdabcbdaddbbbddaacbdbcbbbcdbbbccccccadddcbdbbacccddcdcdbacabacadcababacbadcbdbdbbaccdadddbdadcdaddcdcdbabababccdcbdbaaadbadbbbcabbacacbacdddbbacadaaadaaaacdbdaccbccbccbbdacbabbcccbddabddcdbddcddaabaacbccaaaacabaacbabacbdcbbbdcbbbabbdaaaddacccacbbadaabcbccddacdabddabbacaaddcbcdbbbcccadbacddccadadadbbbacdcddbaacdaaaccdacddbacdadcdbbaacbbbabbadccaccdaaabaabacdcabaacdddaacacbbdbdccabbadcddbdcbcacbdcadbaacccddbabcabdacaabbbacadcaacaabcccabbaadcdadcbbcccdaaadaaacacbabddcbbdbccacdbbaaccaadbdbabaaacbabddadaadaabddaabcbbbadccabbddbdbdacbaadcbcbaabcacacdcaaddaacdddbbcddddddaacdddcccadbabdcdcbdcddcaaaaadaacdaadaaadcdcbacdbdacadcaababadcbacacabbdcccbadabccaaddbaacbcbcbaddbbdadadaadaadcaaddcbccddcdaccbcdacccacadcaaacadcccddadbdbaababbccdcacaacdbdcaacdbdbdabdbbcdabcdabcabcccadcabaadaddbaabcdacbccdbdcddbcdbbaccddcabbbcbdcacbcbccdbbddbbcabcdabdadcaccabbdbccaacadbdcdcbbbbaaacbcaddbcddaccbbacabccbddabcbbbcbcbcbccabaabaaccacaaabbcaaccaadadaccdcdddcbdadcaadaaabddabbccbdccdddbabaaaaabadccadbadbcddbcadccdabdbdbddabadbdbcbcdbabdacdaddccbdccddddbacbbabcbcddcaccddbbdaddabdbadadacbabddbcdaadccddbabdcdaddbcbdcccabccdbacbdaaadaadadcbdaaaacdacbbdbbbcbabcdcacbbbcdcdbadadcdcbadaaadaacdbcdbcbaccccabaacdadbabbcddaaddabdcddccccabaabdcdcbacaacddcbddccaccdcdcbbdcbcbdbddbdababcdcacabadbabdcaabaaaabbbaacbadaadcacbadcbccdddbabdaaaabbcdcbcddcbcbabacccdadaaacdcbccabddbaccbacabaaccbbadababbbcbdabbbcdbbcdcbabdcaddbddccdddaadadbbdadcddcacccbabadabcdaacbaddbcbbabadcbdcadccaccdbdabaabaddacacaddaadadbbdbbbcabbcbdcbbaabbcadbaabbdaddccadabbcadcabbdddacacdcaacdcbcbbbbccbcccaadddacdaaddbccbaacbccdaaccaacbcbddcddcbccdbcbaaddbcadcdccaacddabcbdccabacdcaaaacccbdbaacbbbaaabacccdacccadbdbbaacaddcdaabcadbbdbccaaabadacdaccbdbcbddaccbbccdaaacdbaabadbbcacabdcdcbbcbdaaacbaddcbdbaaaabcddddbbadcabadccddbcdcbadabdcbbdababccdcaaccdaadcddabcbdbdbdcacdacdcabbdbaaadbbaadccbcbadcccdcbacacabcaccaabdbbbbaaacadabaacaadacdbbbbbbcccbcbabbcabadbcaabccddcdadccbdcacddacbbcddbaaccacaadbdccdbbdbddacbacdcbcabcbcdbcccdbadacdcbccccdbabcabdbdabdbaaadbdbdabababdcabdacdcaaadcccbdabacdaacacccdacdaabcabcadcccddabcddcbddcacbcacaaaddbdabccdddccdbabcaccbcdccadcacbbcbcccdacbddabacbcddacdbdadaadbddaaaabbddcbabaccacbcbcdbcbdbabbacdbdbcaddbcdccabbcacacccddbccddcbbcbbaadadcdbbccbadcbdbdabadabcaddadadccaabcccdcdcbabcbacbbcaabcbdbcadbcdddaacdbbdacdbaaacbddabbcdbaccbbbddaadddaadaccddbbbbdcbabdacbbcdcaaabaddcaaacabdadbbababdcddbbdabddcbababdabbbbbbbdddcaabbcdbbbaaaaaaadcdabdddbabdbacddbaadddccbdadadbcabcccabdcadaccbadccacacbabbdbdaaccbbaccbbaadbbabccaacbdaabccadcbacaabbcdcbabcaccbbbcbadadcdcbddbbdcaadadcdbaacbcbbabbaadccdadaaddbabcbadacabbddcaacdcdcabdccbccabbbadbbcacbdaabcdddacacdababbaaadbbbcbbbccbcdabdbbdbaddcdabcaddbdaddcbdcaadabcbdcadbcdcdcbdcbdddbcdaccbdbcacabacabbcdcccdabadbbbccdadcdaabadbcdcccbcdacbaabaacddcadbbabaaabcbdaadbacbaccaaccadbaddcacddacabadcccaddaacbadacaccaccddbacdbbaddcaaaabdddbabdbdadccdddbdddccdbddccabbdbbbcddbbacdabbdcbbbcadbbbcbabdddccaaababccdcbcccdbbccacddbcadcddaadacdaabbbbbcbaddaaaaabaaacdddbbdabccdadadacadacdccdcbcbcdccababadcbaabdcddbcdbdaaadcbdddcadddcbabbbcdccddcbdbabcbaaadbbdcaacaababddcdabadccbbdaaababcaadabbbbaaacabdbbadaacdaccdaaccdcbdabadcccccbbaddbcbaacbdbbbdbcbcbdbccacdddbdabdbacabbabbdcddaacacdababbccbabadacbacbaaacacdcbadabbaddbdcacddaccbdddbcddcdbddcabcabcbcbbadbadbacdbbccabdadcbbcabaacccbbdcdbcdcdcdbcbddcaabadadddcabaaaabaaacaaccdaddadbdcacaabbaadbdcddadabdbcacdbddbbdadbcabdcdadaabdddcabdcdccdaaabdabcaadadaabaaaacbbbaadaaccbadddbbbaabdaacddacdcbdbbbdabdbabbddaaddabccddbbdabcbaacbdbacadbcadbdcacccdadddbccddcbcdcabcaadbcdbdabbcacacddacccabaddadadbbcdadbaabcdabbadacddbddbbacdbaaadbcdbcdacaacdddbdccababdaddacbaacadddcdadcbcbacbaadbaddbbbbcbcaadbadcaacdcaddcababaacbbcddccbdaccdbddcaaadcdadbcbccbddddaddabcadbabbcbacdcddbaacbadadaacdadddcddabddaacdaadddbdccccdaaaadcdabcbcdacbbcdcbacaaacccaaabbdbaabdbabcbadaabcbbdcabdcadabcccdadcacbadbbdcddddbdbbdcdaabccdcdbccabccbbbaadaacbdabcdbddaabbdbacbdbabbbcdacaccdadccbacdabdccabdcaccbdaaabacdbcabcaccdcbddbbcabccbbddbaabdbcdadcbdbcbbadbdccacbcbadbccadbbcaccacdaadbbbbaaaccacaaabdbaccbcbcbdadadabbaabcadaadabbabdbcddbdccccbdacaaddccaaaaaaaabaaadddaddcbaaabacaaddcbcdbdbdbbccabddddcabddddbcdaabaddddcaadcdbacddadcaaadccddcbabcbcbcdabdcabdbdcbbcbdddbcacbcbabdccdcbbdbadaabcbdacdbacacadbbddcbdabaacbcacbaacdbadcdccbdaddaabbbadadbbbadadacdbdcbcacdbdacccaccbdbbbdcbcdabbdadccaddcaadaccdabcdccbacadcbcddcdacccacabcdcdabaaccaadccddcdbbddddddbabbbdcddbbadbdaddbacdcaadacadcbdccacdaabbaadacacbccddcacdbdbbdabcaddabbbcbcbbcaaddbbbabbbdbaadddbcbbdddbbcbdbabdcdccddaadccadbabdaaccbcabaabaacbadabbdaaccaccbabcabdaabcbcccbdaaccdbdacabbbbabcddddcccbcbacbccdbbcbbbdcbaabdcccdccccaddacbadddadddbaddabcacdadabcddbacbdbddcabdcdbabdcdabaddcacbddadacaccbbaacacacabcadcdaabbabbdbcdbabdcbbabdcddabaaadaadabdbdadbbddcccdbbbabcdcccadbdbcaadccbcdabaadaccaabccddacdabbccababaaaacbbccabadacaabcdabbdaadbadccacacdaaddccbcadccccdcccbccccacbddabcddbcdbaaaaccbdbaaccccbcbccdccaddcacbcdcbaddddcbcbaacdabbaacaaddadaddbdadaadadbbbbabacaddadabdddcbaaabddabbcbacacbdbdbcaddcdcaabbbaaacdaddcabcdbcddbcbcbbcdabcbadbddbabdcdbbcabdbbcaddaabbbcadbbcbbcabbbbccbaddaccbacabacdccbdabdcbcdaccdabcadcbabbcbdcbbadaddbddcdbcdadcccdbcccbadcadbbbabbdcdccacadaccdaccbaacddbbababddaaadbcbcdcccbccddaabcbddacaddcdadacdbcccccaacccacacdcddaadadabcbcaccabddbbccdabcaacacdddbaabbabcbcbccaabbdbdddccdbabaacdcaadacdbdadcbddbaaaaacbcdbadabbcacbdbdcbcdbcbbaabcaaabddddcbccadccaadadddadcadddbbbbcacbddabcccacbbbadcadbdadcdaadacacaccdddbddcdadcaccbcbadcccbbcabdcbdabccbcbbadacacdaddbcdccbbacdcbacbacbccbbbcadcdbbcddaacdcdabdbbbaacaaadaabbdbdaacddbdccbdabadcabdadaddcabadcddbaddacadaccddabbadbbacbbaaabdacdaccdadddbacaaddccddbacbaacdacacaddcdccacdadadabcdbbbbdaadaadccabbdbbcdbcbcacadcbcaacdbccaadacaaaddbcbacabdababdbbcbdbcbdcbddccccdcbbccdadbbdacddbbbacdcadbadbbdcbabbdacbdcdaadbdbbbbaccdbdaccdcbcaacdacaabccbdddbabdcadaccdddbdbcbccdadabdacccaadadcdaaddbbdadbcccdacdccdbabcddadbbbcbbdbccbbccdaaadcdadddbbcdbbabacddbabdbddbdcacdbbcacaaaddabbdbbabccacacccacbaacacaaaabdacadcacacdbcbababcdabdababbbcccbccaddddbcaacccbabbdaddbabdcdabdacdcdbbcbcaabbbabbcbdadddaababcadddacddaddadacccdabadacddbddabbbcdacaddaaacbabacbcbdbdbbdababbdcddbcdacdbddcbbccbbdbdcdbcbcdccaabadacadbadcbddccbbaadbaaacabacbaaababddababaddcbbdacddbdbdcbbdbadbddabcdadbcbcddccdddbbabcdabbccabbbcdcbaddaaadbdbdcccddbbacccdcbcbaaadacdaaddddbacbaaabadacdcdbdccabaacdcaddcdcbcccccdadaaddbddbdbabcdbbdbbbacbccbcccaacacbdcccdabcdbababccabccdbadcbaadadabcddcaddabaddaabbaadbaccbabcdadcccbddbcbbdbbdbbddbcbbcbdaacabbdbacdadcdcaadbdabcdbbbadbaacbabddbaacdaddcadcddabaccbaaccdbabdddcbbcaaacdcdaddbcadadccbcdbacdcdadbcbdcbacbdbbddcbccddbcccabbbcddcacabcdbadbcbccbdcbddacbcaddcaadbbbbddbddabcbadbbaaaadbaaddbdcbbacbcbdbabbbdabaacbbccddbcababadbdbcdbcdddadccbddacdbbadbbcccaccdcaddcbdcaacccddbacaccdccbbcbccccbbddaccddacdabadacbaccbddadbbcaaacbaadacbdadddbbddcdbccdccddbcbccdcdcaaddacbdadcabbcbccbcbcbcbabacadbbdcdbabbbabaadaaddbbbdddaadcdcbadbdcabcbaacdddbcabcbcbdcdbcbaccaadcddbcadcacbcbccddaadcbabcbcdbacdcdbdbaabcbadaddcabbaaacaddbabadcddaadacdbabddccbdbabccabbdbdabcdabdbadacccbadcdcacbbacbbcadaacbccaaadbcacccacabadaddcababbabddbdbbaccaaacaacacdbbaddddcabdaccaddbabdabcddccbdcbddbdbaddcaabdaacbbdcadddaaccdcdcbdcdabccabccaaadabbbbcbbadddbcbbababbdbbdabbdccbddbbaacacdaccbdbbbbbbbacdacaaaabdcdcbadccadadcdabaddbcaadaccdbcabbdddacddccccdbbacbabbdbabdbdbccbabbbbdbcdbbcacaabcbdbddbcaccacbdcddddcacaacbcbbaaddbdabadbcccabbbcacbbddcdcbbaadccdddaccbddcbcbabacdcabbcbdadaabddaaadbdadabacaaababcbbdaaaaabddcbbacdbacccdaadacdbabaddbdccdbcbdaccacbcbacadbbbcadcbcaaccacababcbbacaacdaacaccabbabddcddccbddcdadbccddbdacddadbacdcddbccabcabbbdbccbdadacddcccaccabdcbacddbdcadbcaaccbcccabcdaaccddbacdcaadbdcaddddddcabdbabaadddcddadccdccbcbddbdcadbacabbdcccabacbdaacbdccacdccdaddccdccabdaddddabacacbaaadabbadcbabcbccbbcadbacdbbdcbdaabcabbcbabccdcddaddbdddbbddcdadcadbadcbababccdcadcbaabadcbacdaaabbdaadccbcddbaabcdaaccaadbbcbdbdbcaddabccbcabaacacacbcacdcddacbbaacadbadbddbbdddcacaabdaaabcbabbacbbbbcbbbbadddccbcdbdbddacdabbaaaaaaaacdddbdbbcccccabcdcacddddaccdbbacaadbaaabcdaccbccbcccbddbdadccbaaccbaabbaddbcbdbaccbddcbaddcbbdbbddcaccabbcaabdcbdaaaadcbbcabcbdcacdbcbccdcdbdabcaaddaddbbadaacdddbbccdbbbdbcccacaddbcabbbcdbcabccaacdadbcadabcdcddadddaaddaadccddbaddbaddcbadcbaabcaacbdabbabcddbdbccbddabbdcbacdacdcbcacccbadbaadccbabddccbadbcbbcaaaabdcbadbdbbdcaabbbbcabcaaccdccadccaabababacdcdbabdabcdcbddcabccccccbcccdcbaccdabacbccacccbbabdabdcadddcadcabacbdbcccababcbbddcabcbccccdbcccadbcbdddacadcdbadbddaadaabbddcdbddadacdaacbdcbbdadbbacbaacdcabbbddcadcabdcdacbbccbbccbddadbcadbcdabbbdddbccaccbaddbddbdaaddccdcbbcbcacddaabbdcddccbcccabbabacaadcaacbadaacbadbaccdadbabdcdcddaabacbccbdaaaadaabdacddbbbadabbdcabccaaddcabadcbcbdbabbcacbcabbbadddcabccdcbdaadbbaadbdbabacdcbdddaadbcdccbaddaacabdacbcdddcbcacbadddaabcbbbaadcabccbdaaaabbaaddcdcbdadbaabcadcabcbccbdcdcdbaadcdabcddddcaccddccacbacbbbaccddaddcccbddcdaddbcacdcbdbadcdabccaadbdabacdabbdbabbbcdccbbbaccbdadcccbbcbaacacbdaacdadcccdaaddadbaadccaaccaddbdcbbdabddbacbbaabdbcbdabccbdaacabdcaddcccdcbcddacbbcbbdcbcddbbaabbbbcdaddabccddbbcbbccbdbabcbccadacbadadbccbacdbbcbbcbaddbaccccadddacbdadbdabcdadabdaabccbaacdabcdadbbcacbcbaccaaacdabdcddacdacdacbacbbcbabcaddbadbdabbacddababbddacbadcadabcdcacdbbabdcdccbaabdbdbcbacabbbaacdccdddcddddbdbcaadbcdcdbbdabcbabdadccbdcbbaaadbbadbbacccccaaaccdacbacaadcdbdacaccbcbadbcabaddcdcbddabdbadccbcbdaabacdcaabccacbddbbabbbbbdcccbbdaabdcdbdaacccbabacaddacaddadbcbaddcbcbbcbdcabaddcbbbbabdadcdaacdacbdccdbcbaadcbbcbdbcddcbbcacccaccbdbdadacbddcccbcaacccccbcaddddcdddbbbbcbdddbaaadcbcacaccadaadcbabcbcacdcdcabbcabbaadccbcadcbbdbabdacbbccdbdbbdadccabddabdbddbdacbcacababbddcdbbbababcdbdcdbabbccbaaaccbbccddbbdcaaccddadbaacbaacbbccccccdddaadbdccdbbaaacadddacbbacbdbdcaaabbadadbdccbdaabbcacdbddbababbadcbbabbabadccbcbdbdbcbcdbabcddbcdcacccbbbacaddcaabaddabbdbcbabccdddbadbbacbcbacbddbdbdbbbdacaaacdcbcdccacbddcadacbcbddbabdccacbacdbcdddcbdcacacabadcbabdbdbadbcaabcbdaadccdcbbdbadaddabcaabbdaacadbbccccacdcbcadbdbddacbabdccdcdbbbdbccddbbaaacddbadcdcaabccaccddcbcddbaabcbdcbaaadcdbaabdabacccacdbddaddcbcdddadadaaaacccabdbcbbccbabccdacdbbdbddbbaabdccabaaaddabdcbacccdcaddbbbbbbcddbddcbbacbdcddcdaddbdbbcbdbacdbdcdadcddcbbdacabdddbadbcaadabaabcbbbacabcdbbccdcbbbdcababdababadccdadbbcbdcacbcbcadaaacddacdcacabdaacdcbaabbbdbbabbdcdcdabccddbbcbdddcdbddcddbbcdbaabdadadaccacbbadbdddcbbdddaaadbccadbdbbdbcbcbabbcbdacaababccbdcaadcbbbdddabcadccadcbbdbdcbdbdababaaadaacbdccbbdcdaabccbbcbdcabdacbdbbaaddabccdcadbabcabbdbddbbdabdcdcccaacbcddcdcbcdbcdaaacbbcdadcbbddaaababcadbadbdcdcddaccaadbbabcbbdabcbcbcabccdbdabdbccbccdbdadcbaaddaccaccbcddcaadbcababbabcbacacdacaaddabdcbbbdaccdbabbdcdbdcbcadbadadccdcdadcacbdcbcabddbaaadabcdcddbcdcaccaabdaadbacadadbdabdcacadcaccaacbaabdcdcabdacbcaccbccaaabbacddddaccbadbcbacdadcbabbcacbcbdaaacccbbacbbccaddbcadadbccddcddbbcbcbbbdcdbdcbdcdcdacdadaccdcabbbcbcdcacbbacadcabaacdbbbccbddcddacddaaacdcabbadadcaabcaacaaadccacbcdaacdcaadbbdcaabadbcdcadbabdadacaacddcddbaaacdadcbcadbcbbcbcdccbcbbdbccdcdadcbdbdbbccadbaddbbbadbacbaabdbcdbbcdddbdcbadacbadbdcbdccabddacdddadaadbaaccddaacdbacddcabacacbcbbdbdbbdcbbbcacbcadcbbdcdcbbbdbbcabaaadabdcbcadddcccbbaccbbbbbadaddbcadcacccaaadddabbaaddcdcabaddccbdddccccbaaddbdccbbdbaacbdcaccdccbdbbcbcdbcdddddbdcaddcbaadcabcccccbadbbdcbdbcbcdcbcabccaaacbacdaccacbddabbdaadacdadbabcadccbdbcbaaacadbdbbdbddccbabacacbcbccaacbcabccaabcddaabbbbdccbcacbbaaabbbccbdbccbbaaaaacccadcbbadadcbbabcbaacadddcbadccaacbdddccbcbaadccacbdacbdaadcdaaacabaddaccdcdaddbadabbbdcbababdaacaaacddbdcbadbdcdcbcababacbcacabcaddbabcccbbaacaacabdadaccbabaccbbdcccdccabcdacdcdddbdddabbacacaccabddbbdcccddcdacaacddbadaccccddacaddcdbacdadbccbdccdadcacccbbdcdaadaaababaadcbccbbcaabdbadaabcbcbdbbabdccadacdacdaddbcdabbddacaaabaacccccddcdcadbcddcbdcbbcaabdbbcadbccdbdaaccdadadcbaaadbcbcccadcdaacccdbdddcdababacddbcdccacccbadbcabacdacacbdbbabaabaacabcdbcbbadbaacbababdcbdddadadabdacbdaacbccdabcacbcbdbbbcbcdbaadacdbcadbbddcbabcddcacddadbabdbdccdbbbdbcbcbbadbdddbbbadbcdcadaddbddaacdaabcdbbdbabadabadaabdbadcdacdbbdbcbcccacbaccbdadadaadaddbcddccbdcabbabbaaddddccddddbcadacacdadabacbbabacddbaccdcbaabbcadddbacabaabcdcdccdcadbcabaadbbcbbdbaadccccdddbacdddbcdaacacbaccababbaddcbdccbacbcadbacbacbccccbccdbadbccdbcbccbbbbbadbbcadcbcacddaccaadbaabcdbbbaadddbcbcbdddaadcaacbdbaadcdadcdbdaaccdddddbadaabbcaadbcdacccbacdddcddabbdcbcabccdbbbdbccbdbbcabbdccacadacaadabaabcbacbacacddbdbdacbbdbadcabadbbddcdaabcdbdbdaabdbcbdcaabbccabcbccbdcaacbdbabccadbaacaddacdcbddaacdbbccddabcdcaddacdddbbbdadcccbbacdababbdddcdcdbdddddcddbadabdacbadaacbbdbcbaadbadbddcbaacdabcbacacaddcaccccbddadddbaddccdabdababdbbccbbaccccaabbccbabddcbaccbdbcbdcdacdababcddcbabbdaadbabaacdddddbacdabbccaccbadddcbbbcddaddbcbcaacdabaadbdbccaddbbdcbdddaababbaacabdcbdbcacadddacaadddcdadbbcbbaddabdcbdaddabcbddaabdaccdcaacacdcbaacabbbadbccdacddaacbbacbbddccbdacbacbbddddbbddcddbbbbdbdbdbdddbbadadddbcdaabbdbacbabcabdabcbbabdacbcdcbcdcacadaacaccacbbdddcdbabbcaaabcaccccbacadbadbbcccdcdcabacdadbccaabbabadcabbbadbdccabaaabddbacbacdabdabaddacdaddcbcaaabbddaaadcbcdcdadcacbbacccaaabacacacadbabaabdaadbbbabcdaadaabdabcbbdaacbbbacbbaddbdadcdcabbabbbaadccdbccbdcaddbabbcaaaabacaadccddadbbaacbcbccdbdbacdbababdacdbddcbdbaabadbdbbbabadababbaccacccbdabbcdccadccbdbddddcbcbcccbbcccbbbcbddddbcbcaddcbddacbadcabcccaaadcddbdcdaaababaddabcadbcbaabbdbabaccbccbdcbaaaadbbcaaacaadcdcbddaabddddbddbbabbbcbbdbccabdcbbbccacaaadddcadbaaddbdbcbacddabdcbdbccdbdcaaccdcddbadcacbbdbdbddbdccbadcabacccaabbdabcabbaadabbdbcbdccabcabbbbaabbdabdcababccaabbbcdcabdacdbbcadcbbdccaaabaccaaddccddcbbbddbcdddccdbaacbdcdcadabbddadbcacbdccaacccabdddacbbbbbadacabdccccbbcbccbaccdddbcdacdbbabddcccaaacacdaacacdabdcbcacbbbababbbadababbdbcdcaaaadcbabcdbcaadbcbddbbaadaaacddbccaccbcdcdcabbbadaaabcaabbbaadddcdbcdacbdcdabcadccabbbbbbadaacacabcaacbbbacaccdcdadbacabbbcbabcaaddabadbcdccbacacaabcddcbabbabcbdbddacdbbcbdbacccdccbdbcdabdcccccacabddbbacbacdbbabbaadacdacaadaddbdaaacbcbbccabccdadbcdbdccaadacbcbabbadadbccaabaabadaaadbddbbdbcddabcdbbdbbdadcdbccbbaabbbbdaacadabadacaabadacadbabadabdbcbcbddbdbdadaacabcccdabaaddcdabdabcccbdabbaadcabdddbaaddbbbadcabaaabacabccbcaaadbcacbaacadbbccaadbaabbaaccddabddacdbbcbcdbcccdbaadcdcbaadbaccaabacbdaadcddbaacbdccaacccabcabccdaccddddbacbdcbdadbcabbcbaaaddcbdadadaabcbabdbcabdacadbcbcbcccbaadbadddcbadcdbbccdabbbcccbcbaacacddccdaaaabacbcddacbabaaddaccadcdbddddcbcdaadcbdabbdcacdddbdcdbdabadbabadaadccbccadbbbaadccddbbaaacdddaabaadbaaacddcacacbcadccdbadaccdbdbcccddcaabcbcdccbaabcbccdbccdababcbaccbddbbbaccddabacbacadcadcdacabcdbcccadcadcdcbdbcccccaddcabbbdcddaacdbbdaddcdabcbacacdcbbccccbaaadcbdacccbbbabddcbcadbddacacddcadcdabddcdcacaabdcdddcdccbcbcadbadccccaaadbdbabacaddabbcbbddacccabddcaaacabbcabcbcccabbdabdbabccbdabbadcadddcdacdcaaaaaaacdcacaaabbcbcdcccaaaadacbabcabcbccdabdbcddadadaddadcaabbbdaccabbabddacbddbddddabdabcdabbbcbddcbdbbcdcbbbcdabdcddabacbddddcddcacadadaaccbcabdbaddadcdabbddbcbaabddabbcdbdcabacbcbbaabdaccbdcdbacdadddaaabcbacddcaccbcbcdabcdacccbbdbbacbbbdbbcadcadcccccabdaccabcdbccadcacddabbccdcdbdbdcbbddcababcbdddbdbbadaaccdbbdcccdbacdcdacbcccdbcaaaadbbaaaadadadadbdadbbcabccbaadbbacaabadccdaadcaccdaddacbababbaddddbbbdaaddcabacdaaabcbdbdcbacdcacddbcdddcaaaabbbcdaaababbddccbccaccdbcbdbbaacdcababcadbdaabcaabdabacbbccdddccbbdabbdbbcaabaccddddcbddacabbdbcbbbbdcaaaaaaccacdaababbccbbbabbcabdabaaabaabbcdcdbcacdddadcacbdcdaabdaccabcacaccdbaaadcccdaaadadbbdbbcacadcdddcccaacdbbaaadacccbbacbdbdabdbcbbbdabccdacbbbcadadbacacdaadaacddddbdcadcdddcccadacddbbdbbabadadabccbaabcccdabdbdcbbdabdbcbddbdabdbbdabdbbaadcdadaacbdddadacddccdabaddcdbddacadbdbbbddbadccbdabacddccddcccbabddbcabbaacacbbdcbaabadadbccaabcbcabbddbccdaacbbaabbaccbacabddaaaadbbcccabacbabbaadcaadcccddddaaddaabadaaaacbaaadaabbacadddacccdabbdcdccabbdbaabaaddacaddbdbadbadccbadaabadbcabcdadbadabdcabaabdadcddcabddacdcdbadcdcbbaccaaaadacbdbbbacadcccbdbdbaaacacdddbdbcacdbabcabacdcaaddddbcaaacbacddcbabdabcdaccccacdbcdacccaacaddbddcbdaccbbaabcaddddbccdbdddabadcdacbbabbabbdacccdbcbbadccbabcbcbdbdddbaaccacddabccacadddddbbcacabcabdcadbbdabdbbacdcadcbccccbdddddcbddbbcdbccaaccaacdadcccdcbbbabbdbdabadcaadcbddbadcdbcabcdbacbbdbcbaadcacacccabccbcccaaccabbdadacdabdabaccdabacacadabbabdacaadabacacadbacddabdaaadbcbdcbacaaacadbddcbdbdbdbcdbadcbaccabbbdaadabbbadaacbdadbadbacbaabcadadabcbaccabcaadacbdbcadbbdddcbbcaaacddddbcabbdccbdbabaacdbbcabababdaababbdcadadaccadbaadbbdaabdbbcdcdccacadbddabbaadcdcdabaccdbabcdcdaaaaddbddcbddaacadadabdbbdbdacdacdbadcabaacdcadcbdaacabcdadaaabcdaccaabbbcbcbabbccdcbcacbabdccbcabaabdcbacadcaadcdbbdbcddadcbbbccdadcaacaadabbdbaccbbbdaccabbdacabbcbbdadacddbaaaabcadbbabdaddbdbdabcaacccdddbadcbaabdccbccacaabcbdabadabdcdccadbcaacbbcdcbabccbccabbbbbdbcaaaddaaabaacaabbcdbdcaadbddbdcdbcccbbacadcabdacababaddadcabccddbacabccddabccbcadccbccdbabadababdadbababbacbaaaaabbdddbcccdddacbcdadcbbdbbaabaabcacbdbcbaaddabccccabccaabbacbabbdcbabcdbbabbccbddabbbabcbddcaadbdcbbcdaabcaabadcacaaadddbdcbdcbbcbcaddcbbddbadcbccacbabcdbdadddbaaaabcdcbaaddacdbcabcacdcaccbabbdcdddbbbcbbddadcbccbccaacaccbbddabccdadacbdbababdcddcbaacababbccacbdaacbcbabaadadbdcacdccccbcddbcbadcacdabcbaccdbabccdaabadadcadbbccbabcbcdaaaaddbaccbbcabdabbbdaadcdcdddddbaccaaadabbdcbcdacabbdbbdaacdbcdcbacbddbabdbbadcdbcbacacbbcdabcdaadccabbaadaabdddbcdaadadcccabcbdbaacabddbabbdadbbdcaaadbbbcbbbddccabbacacabdbabdbccbdabbddbccabbcaabdcbddabbddcaccdabdccabbbbcdcadcadcdbbcddddddcbacdcbabdccbddbadaababccdaddcaccdaddddddcbdaacadabdbcacddbccaaadcdaddcdccbddbdddcababcaccbdbbcbcdddbdbbddabbbadcbcabccdcccbbdcbadccdddbbbddbacabaadbabdbcccbccdcbaadadadccacdcbcdcdcacadbacdcdbcdbbabbdaacadabcdacababcacccbabdadaacbdcdddaacdbcdaadcbccacaccddabbacaaaccdcacbcabdacbdcabacdcbcbbdbcaadcbadcddddccbbbadbcdbcadbdadbadbdaacdbabbbdbbbaaadadacabcdacbcccddadacbddcabbbdbcbcacbbacdbadcdcdcbcdbbdccaddcddacbabaacaaccbadcdabddaadbabddaacdaddcdbbadbcbcdddaabdcabcccbdbbdadddccdddbcbaaccccddabacccdacadddaccdcabccdabbabbdcdacddddacadaadcabdccabcbdaaabcbcdcdaaccbdbcdabdacdabbccbdbdbbdbbdadacbadbbccbaadbcaadbaddccadcccccbaddddddaccddbbacdbddbaacacadacbabcbddbbbaddadcbdddcdabbccdcddbaccbabbddaadaadacbcadacbccdaadcdcbcaaaabccdcbabdcbccbabaddbaadaadabbaddaaadddbbdcdcccccdadccaaccddbbabdaccbdbbaadbadbacdcdbacdabaaadcbcabcbdbaabdccadbdcdcbdabcbbddccaaaddcadadcabdbcbcdcdabdabadcdbcbabbcabaacaabcddaaccbcaccdadddcabbdbbacbcbdbcdbaddadcabdaddccbdabacabdcdadbacdcddcacbcabacbddcaababaddbbccaabbcacddcbcabadbbdcbcabbdccccbadbcbcdaacdaadaaaadadbbbdabddadadaddadcdcabccacabacddbcadaaaddaabacaddacdadcccabcabccbdcccddaabaadcaddadbccacdabddabacbbcabbbdadcdddcccbddbacaabddbadbccaaabadbdbbabbaacdccacdcaddbcdcbbaabbbcddaaabbadccdbdbaccbdbbcbcbadabdbaaabbbdcddbbddcddbaddcadcbcdaddaabbbbadcbccccbbadadbadcdcbddcbacbaabbaaccbdaacdddacbcaabbdbccbccdbcacddaddcdbcbaccadbabbbbadcdbabcaccaabdcaccbaacbdbdabbabaccbacaaddddcaaccacaadddbacddcdcbcdbdacacacbcdcabccacaddccbabaabacccbadabcaabbbbdbddcccdadccdadabbadccbcbbacababccdbbdbcbdbdddccabccacbcaddbbbcadddabcacacdbdcbcbddcabccdcbccaacbcdbadbcdbdbbacbdabbdccabaabadcacbdbddcbbddcccccdaaabdbdbaddabacbcdabbabcbbadccccccacabccddcbbadbdcbaacacddbabdbdcbcddbbcdbdabcdccbcdbccdccabcbbcacbddbcadbaddcdadbbdcbdcaccdabbdaabaddbadadacdcbabacbbdadabaacbbabcccabacaabaaabcbcbacadbaaacbdddccdaaccbcabbbcccbdbddcdbcdcbcccbcdcdacdbcdbbdddbabdddddadcbccacdbdbdbbcbaabddbccbcbacbddcbcabcbddabacdbabdcbacdbdbadcbabbabdacaaccddddcdcbddcdbadcbbabcdccaadadadbdcaccbbdccdcaabcabacadbdbaccbaccbaadabbabccccacbbadcdccbccaaadcdccbdaaacdacabababaabdaddacccccaddbbbcaaadadddccdcacacbddbacdccbcbacbbbbddbacaadbaadcbddddcdcdcabcbaabdcadccdacabcdbbadbbbbddcdcbcadbabddbbbcccdcdbcdaabdaadabbbbbccbbcdbcdbacbbabccadbddbcbcbddcdacbabcdcbcbcbdcdcccdcdbaadaadccdbdbddcdbcbabadccdcbaaddccdbbaaaadaddbabaaaaabbddaddaccbdaabbbabbdcbbaacdaabbdaadddadbcadadbbababacbdaabcbbdcbbccadbababadbadcbdacbabbabbdabbbadadbadcbcbaadddbdddadcdbbccdbdcaccdacaadbdbdaccdbaadaaddbbdaabccdadbcdbccabdaaaaacbaacdaabcdabacdddddddbddaddccbcbacaabcadcaccdabcabddadbbcdddcacbacabddccabacadbaabddbdcaaaadadadcadcdcbcdacbbdbabbadbbbdabcddcdaababbcdaacbadadaddccdbdbcaabbddcbbaddacbaacadadddcbdbdacccbccaaaaaaabdcbacbcbabbdcbdbadabadaaddbbabcababddabcdddcdcdcdabddddbdadccdcabacdcbdbdbdacaaccdaddbbacbbcacbbcbbcdaddcbadadabacddacabccbccdbbdbbcbdabdcddbdddcabbaaacdcdabbdbccccbcadcaabdaddcabaacabaacbcdcacbaaaccbcccbaaccdaddccbcaaddbccbabaabdddaaddabbabdadccdbcbbccaadbdddcaaaabaacccddcbacbadbcdbaccbaddbbcdbcbdadacbdabddbadddbdcadaddbbadaaccccabdccbdadcacbdacbadcacacaacbaaddadcbaaabcdbdcbcaabbcbbbdbbbacddcbaaddadcaaaaaccabcbcddaacbaadbbacdbbdaddabdbdbdaabdaabaaaccdbbcdaabdcdbdcabdcaacbcdbbbbdaddddbcbacdddabcbcdcdddbbdaaadcdcacbadaaabcadbbcbacaadbdbbcbbbaacdbaaacdaaacabbbdcddabdcbaacbdbdcbbccadabacbcdddacbaddcdcdabdcabadbcbddabccccbbaacbdcbdcabbbadaacdababddaaacddcbacacdcbadbdbaadbdcddbbacdbbacdbbcbabaabdbbddbbddbccdbabbadacdcdcdddccdabcadbdcdabdbbbaccdabcaddcdabaacdcaccbdcbbdacdcaaabbcaaaaaaabaddaacabdcdddacbdadcdbabcbccbcdccbaddbccabadbdbcddcdadcbcbddbbabaddcddcabbbcbbcabadcaabdaadbcbadbbbcacabdacbddabddaabbabadccccbdcacdadbadaaacdadbcbbdbbdbcbbcbabaaadabbdbcaabccbcccdbddbcbbaddaccbdbbbaadcbaabdadadccbddbdddabadbabcdbdbadadbababddadcddbaadbcabadadbcccddbcddcbdddabaacdabbbcaadaacbcddcbbcccbddddddadccbbacdcbcccaddaaaddacabddbaddcbcdaddddbabacbbbdbdaddaaddcadbadadbadadccbbacacacdaddacdbcacabbaabbcabaacbbadddcaaabcdabadbbbacdbcdcacbcabbcdbbacabaabbaaacaaadccbccdcaadaccbdbdccbaddacbababbbbbbaaadbaacaabbacaacbaccadacccaabdaabbdaddabdcbaacdccbddaaaadbbdccabddbcbddddbbdabbadcbbccdcabcbdacbcaadccbbcadabbbdcdcadbbddbbdaabdbbddbadcbbadbaddddadcdacaadcbaacdcddccbbaccabacbcbacbbabdcddabbdacacabdadcdaddbdaabdccccacdcabbdcabdbdcabcddcbacdcbabaacbbabadadaaacabbddacbdaccaadacadacadacaadbdcccbcbcababdbccccdabacdadabcdaccbacbcdddabaaadbaddbcaccbddaabdabcbcdbdabdbaddaaabaadbdbbbccadcbccadbadbadccbbdbbcbaadadbabcccadacdddaadbdccddabcacdbbccaaaaccbcccccdcdbdcbcadabaacabdccccddccdccdddcaadbcbacddbaccccdddbcacbacdcbbbaaabaacbcbbccddacdddacabcadbabddcbaddabaabbdbdcabadbabdadcdbbcdcbbbcbcaddccdadddbddaacdcdbacaaccbcddccddbacbbdccaccdbdbbababdcdcdcddacdcdccbabcbccccdcdabbdadacdddcdcaabbdbdaabccbcbdcdcabcbaaaccbbbbdadbccadcacadccaabacadcdcdacacdbcbdbdbdddddbcbacdccabddcaadccddaabdbacaacbddabdabbdacadadbddcadbbdcccccddaaabbbdcadadadbdabdabcbcbaacbdbbdaaacdbcabdbcdaadbccbddccadacdccddbbdadbcbcdcabccbadacababcbacaaccadabcabaabbcdbccadcdbdbcbdabddcccddababbbacccbdbcdaacbbadcabcbbbbbbbcacbbbaabcdcddcbacdcdcbddbdabaaacabbccdaaadaabaaccdabadbbbcddddadcbdacbbcaabcdddcddacddbabdbdbabbabdbcbbadcaccbdcbbacacabaacdabdabccccddbbbbdacdcdddbadacbdaccabcbcdbbcddbbccdddaaacbdcddccbcbbbdbccdaadaccddbdbcbcaddbdddcbccbbcccddbadbbccdbcaabbaccccbadcaabbbcdcadaadcbdbaccabcbabdbabcdaccadcbdaccdabadacabcdbabaddddaaddcccacdbacaaaabbbcdbbdbaccdbcccdacbdacddbdddcdaaabbabbaacccadabdbcdacbbacbaacbabcbddbccbdccabcaadabddcbabacddcdacbadbbccccdcbadccbddaccbbaacccadacddbcdcabbadccabbcdddabcaadbadbccbcaddccaadaccdbdccccbadabaccdadbacaabbaaccdcbccdddbdbbbdbddbabbdaabcccadaccdcabcbcabaaacbbcaddcccabbccbdabccacdbdacbdabacccbdabbdcbdbccbdacaccdbdbcdddbaccddabbcbcccaaaddcddaddcbabdadcaaadccccaddabbbddbaababbcdcaaacddadddbcabcdcdbddccdbcbbbbdccaacddccadabbcbcaaabbcdbcacbddbddadcaadbbcdbcddadabbdabdabbacbacccdadbccbcdddaccdbcccdbdbbbdcbbbcdbbbbdcaababbacbadbaabaacdcaccabbcddcdcaabbdcabcbbdcbccdabbadcdcccacdacadcdcddbcdddadacabdabbaacdcadcabbabdbdbcaacadcdcabbbbdbbbaadadcaaaacdacabbbbbddcccbbdcabaacadcccbbdcdddddccacbaabbbaaaccdbcbdbbdbddbdaaabcbcdcaabdbddddacccddabbaacbcbbddcdaddaabcdaababccdbddabacdadabbdbdbdbbbcacddacbaaaddbaabcaddaadbbbcccabdcdbcbccabcbdcbdbaabbaadbacacccdbbaacabacacbaaaccbbddcaadacccbbcdcdbacacbdbdbcadabdbaddbbaacbdadacaaadaadcdbaabdbdcbdbdbacbdcadadddcccbcccdaaabcacddaddaccdbacdabcbbbadcccbdadcadbdabdccaabcdacabcbabbcbcbadbdabddaddbdbddcccadcbdbccdbbdadbcddbbdabadbcdacbdbdaddadbccbcdcacdacabbddabbbbdcdabbacdccccbdcaaacacbdacccccdcabcccddccdbcddbdcbabbbdbcaacadccaabccdccaaccaddadcdcabbdadcbcaaaaddcccddccddaacddddcadbacdbbacbaadddaaaadcccbabaadabdabaacaadbadccbabcdcdbddaccccabcdbadadbcdcccccadbaddbdcababddccdcddbcacddbbaaabdaaadbdcbbccddbdcdadaccdcdadbdcaaaccbaddbddbbdadcaddbcbccabbdbdbadbbbdccdbbbbaaacdbdcbccababddcbdcdbbcbadbbdccbcccbbaacaddacbaccabddadbbbbddcccccdccabdcbddcbcbaabacbcacbdbacaccddbaadaadcabcbaaacadcdbcdabaadbbdbbcddadddabcaadcdbdaaabccddcdddacbaccbbdaacbcdbabcdaacdbbddbcababadabcbcaddddadddcbdbccabbbbbbdaaddccbcbddaaabbcbccddbdabcbcbccbaaaccacbdbaaabdadadabdbbaaadacdbbdccaccadaacbacadccccbbccbdbddccdcadabacabdabbbbdabcbbbcababcdacbdcaadcbdcdadacabcaccbccdbdaaccbaddadabdaccccdcaccdaaccbbcabccbdabacabaaabcbdcbcadbdacbbaddbcdcbbcbdbbddddabbabdaacbadaccadbaccdcaddbdaaddcbdcaccbaacbaacaacacacacacacdbddcaadacadcdbaadbcaaadddddcbcabcdccdaccbacbcaccadcbacbcdabcbdcccbbbcbdbdcabbbadbadcbaccbbccaacbbbaddcadbccdbcbcccbdddccbbcaacdaddbdcadbcabdbbaaccccdbddadbcccdaddbbbabcaaacacdccbbcbadababcbcdccbaadbacbaabbaadacdbbdadcabadadacabaacddacdbbbdddabaacabbbaccabbdabbbcdddbcbcdbaadcdcdcbbcbcbcbdbabadadadaccdbcbddcaddbcbdbcadbaddaaaddaddaacdbdaccabbadbbadabbcdccdddbbddcbbcbcddcddabacabdbadaaabdbbcdaadbdcabbdcbbcadcddacdcdddbddacdaaaacaacdddbcabcbaadbbbdbbcaccccbdabbdabadabcbabcadddaaaccdbcdcbbaadbbabbdababdbaabddccaddacdadcadcaadbcaaadabcccdbcabcdbddacdacbcbadacbcbdddacaddcabbccdbaabaacdabddcadcdbcbddcaabaabddbcaadbbbaaddcbdccccdadcbbdcbbdddacabcbddccccbaacddbddcbccabbbcdaacddabbacbbcaaddbaaaccbaadabdacaddcddaddacbaddcacdadacbcacacccbdadbababbddcbacadadbcacdbbacdbdaacbddddcddaaacbcadaacacbcdddbcabcccccbacaadbdcabcbbacacbbbadcadddabcbdcccaaadbccdbddcdbbaccbbdcaacbcaadddddaacabcbbcabaccbacbbaccbdbbcbbcdaabdaddacddacdacdabbcdacbdbbadadcdadcbcccdcbcaccaabdbdccbcadadcdbbaaacabdabaabcadbbddaccaababdcdbdaccbdcbbbddbdbacdcbbccbabdbaacdbbaddaabdbaccbabccacbdaccbabbdaaaaccdabdacddacbbdcdbccbcacbdcacacaadcbaddbcdcaaccdaddcdabaccccabcdbbbccbbcbcdddabddcdddcdbbdbcaadbddcaabbcabcaccbbbdaadcadabacbdbdbcaaadbaabaccdbcdcccbdcddaddcbabccbcabadcddaddaabdaddcbacaabbacadadbabadddacdddddbdbcadadbaddcccacdcdccbdcddccabcadbbbacbdbbccadbcdbbabbabddbbaaacdadbcdcaaaaaadabccdaacacdaaabccdacbdbaddaaadadbbbadcbbbbbbbacbccdcccbaabdcbbcccdabbdcbaacdaabbbcdcaddbcadcbddbddbbdacdcddbbaaacdabddacbdccbcccacaccbdbdddbbcbddacacaccbcdccaddbcbcbddbdbbdacbdbddcdabadadccbcddcaabdbbadbbcbbccbcddccdcdacacadbaacccbdbdbdbadbacbcabbadbdbbccadddcbddcaacabbabbddabbdbddbabcbdcbaacbaababcaccacbcbbddbccccdbaccbbdbbbcccadadcdabaabdaabbbcaacdabaabdddccccbbaaaadcccbcdbbddabddcccadbdbcaacddcdbcdadaadcadbaacbbbbcacbaddacbcbddccbbbdddccdddbdadbbcdbbbdbcacdacdbaacbbcccaccacbbadbdcacaabbbadcaaaccdccccdaddccddcacbaacadbbaddaaadbbacdcccadccccdadcdcbadcadaccdcaccbcbbbdabdabbadcdcddcaaccdabacbcadaddbdbbbbadadaaccdcbadbdbdbaaaabdabcbadbaddcdccadabcbdddbcbbcdcbaacddabccdbcddadababbcdcabbdacbbdbacaccbcaacdbaddccdbcbdcaddabaacddddcccbbababddbaddcccdcdadbccacbdbaddacddbcadaaaadcacdcddcdaababbcaadbbaccacccbcdbcbbcaadaabbdcdaacbbcacdacadaacdababadabbdacdbabcccccaddabdadadadadadaccabcbadacdaabccbcaabcbcbdaaabacccbbdacbcaabaccdadbdbcaaabbaccccbbcbabccddbacbdbbbacddbcbbcdacbadadaaaccdcabccdcdaddacccbdcbacacaddbadbabcbababbdaacdadcdbbccabbbcadaababddbcaaaabbacabdaaadcccddabdabaccddabcaccdabcddadcaabadaacbbdbcdbabbdbcbbdbbcbbcdcabddbccbdddabdcdccbcacabbaaaaadbbdcdabcbacadadcbabcddddbbcdbaacbddccbccbcadbcacccdcddbbdbabbbbdddbddacacdaccacdacacbddbbddabacacbbbbdccdabcdbadbdbadccdadabaadcaadbbcdbaaccbcdaaddddbdcaabdbabbcbcbcbccbcdcabaddcdbdbbbacaabdcaccdbacbdbccbcccdbbddaacbbcdadbbacbadcbabdadbbabcbddabcbdbbaccabbabdddcccbacccdabadddcadbcddddbaacabdbdbacccdbccddabbddccdcbcaadbcaccdbccccbccabbabbdabaccdbdadacbdaacdaaddbdadbbddcaaddcaacddcbccddbdacbdaabddcacdbccddbdcbacabcbacbdbccdaaacdcddbccbaaccababbbabddbadcababddddccccaaccbcdbbabdbdcbbadbaacbbbaacdbbdcacbaccdaababcbbddbdbbdadbbabcbbbccbbbbcddbbbadbcdccdcdcdcdabdaccbdbdbdaabaaaddbdcbaacbddcbdabdaaababccddcaccadcbbcacabbaddbaddcdbbbdbacbbaadbcddcabcaadbbdbdbabdcdacaadbddccaabcccccdabaadccccccaaacbaadadabdcbddadbaccdddddbdaabadcbddccaaabbacbabcbbacadccdbcacaabccbdcbbcababbddccdcababdcdcbbbadaabcddddcabbdabdadbcaaccabdababbabcdacaacbbbdaadcbcdcccbcbabbbdbaccccdcabbdcabbadaaacacbddbbacdaabcbddbccdddacddcbddcaacbcaaabbabdcbbacbadbdabdaaadcaacccadddbcdaaacaccdbdabcbbcacaabcbbabddabddcacbaacddbdcbbcbcacdbbcdcaddadbdcbdcbdadbbcbbaddbdadbdabacbdbabadddccacbaadbdabadcaaaaadbbbaacdbccacdcbbdcdacaabcaabcadccaaaadcbccadbcccadcbbbaccdbcabdcaabbdcbcdaccdcaaadadacaadbdabbcbcaadddabcabcbacbaccadbcacacbacacdcdbbdcadbcccbaaaaddcdadabccbdcaabcacdcbaccaaddcabdbbabccdbadadabcbbdbbbdabccbdccdcacdddddbbbdbaddaadcbdbcddaddaacbdcaccabdbcbdadddddcaaaadcddbbbbbbdcdadcbabcadddbcaddbddaddcdbddbbcdddbbbdbbacbbbcdbbdbcbdaaacacbacbcdcdcbbacccccccdcdaadcadbcbbaaaaacadbbbbbbbddddaadcdcbdbdddccabdadbccbacdacbcbbbdbbcdbcccccbacdadccbcdbcaccccdbbadaabaaccbdcddbaaddacdaddcadadbcdbcdddbabcbcabacccddbbcaaadbbbbdcbaccdadddaabbbdaabbdaddcdbdacabccbcbcdccbaacbbcdddabdabddaacdbabcaacdbaacaccbdbccddddbbcaabbaccbbdcbabcccddaababcccccaacbaaabbaccdbaccbcccddbcabdcbbaacaadddbaabacabccababdabbbaacbadcbdcccadcadccabdcccddbbabdadcabbcadbcdaaddababccbddcdcdddccdaadcaccadbdccbbcaacbcdcaaabbcdcbddcaaccbcdacbcabadbcaaadacbddbdbccaaadbdcdadaaadaacdaaddbadacdadcaccccdbbabdbbccbdabacaccdddcaaccbcabdabddbdccdbabbaabbaadcbaacaacccaccddbacdbdabcadbdbbadcbacddbccbadcacccadabaadbcabcabcbbdbcaacacaadaadcbcdcdcbabbcaccbccabaccbdcbbbdccaadaccdabdadcdbdbabdabcbbbadaadbbdcbadaddbbdbdbbccaabccdbbdaacacadadbbadcaddddcdcacccddabcbcdacaabdcaddccdacaaadbacbabcbdabcacababaddcbddccbaadcabdbcadabadbbaaaaadcddcdcbacdcadbcbadaaadbbcdabdcabbdcddddaabdcbabbddddacdbddbddcdbbbabcbaaccaccabaaaacdcabbcdaccbcccbddadaddaccacddbaddbcacdcdaccdabacabbccdbcaddccccdabcbcaabddddcdaadaddccbcacdabdddcadddddaadadcaacbcacacacacddcbacbcabccbcaabdadbdadccddbddabcacdbdacabaadaaabbdcbacdacadcbaccbcacdcdacbcbdcaacabcdcccdbccadbcdbcadbbbdabaadadcaacddabcbadcccddddadcdbaaccddacaadbcaccdacdcacdcdadbabcacbbbbadbbddbbaabcacabcadcaaabcddbbccbacdbaacdaccdbcddacccbccdbdcbdbddbacdbdbcbadcbbdcbbdacabccbacbadcadbcdabbcbadbcdccbdcaabaaddbabccddbacdcabddbdacaacaaadbbcddaccbddccdcdcbbbcbddabcdddabaabdcbdcabcbbaccbccbadbbdabdddcaababdbadcbcaacccddcbcdcbacbcdcbcdadbdacdbbbbaaabcdbdaaccabaddcacccacaadadbacdcdaaaabaccaabdcbcdcabababacaabdcccdabadbdcbccbdcdaaabcbbcaddadbcdabdbdadadccbacbbcbaccdcdddadcdcccbacadbcacdbbadaadcdbbaccbdbbbacdacabaadbcbdccbcdcaabdbbdcbdcdbacdacdcccaadcddcbadcdcdcaccbbcbdbaabdadaaabccccaacddbddbdbdacadddbcaccadabddaadbcabcbbbcbcbcadbaadbaaabdaccdacbdbccabbdaccaaccaddacddbddcadddddaacdbadbdbbcdaadddadcdbcdacbccadbdbababbbbdbaddacddabddadcddaaadccbdacccdddacdbdaacddcaaddbcccdbaaaccdcdccddbbacbaadbbabbcadbbdccbbbbaabbaccddbbcadccbdaaaccbdcccbcadbddcbcabadbdacddacacababbdcdcbdcdacdccaddcdabbbddcbcdbcadadabcdccaadaabcacbabcaccdcdbaacbcccccaadabbddbddbabbacbbbadbacdddacaaccadccacdddcbcaaadbcdbcbcbaddcdaadbccacacbbbbbbaddadadbbbdacdbadcaccdadbcacabcbadbacadabadacacacdabdbcdddbbaacdcadcccdaacaabbddddddcdbdcddcbbddcadadadbbdabcccadabddaaabbadcbcdcabbcbdabcabacbccbbcacddadcccbbbabddbabdabccdcbdbbccabbbbdcabaccbcccbbcaadcbdaaabbcbdadcbdddaaabbbdbabbddacccaaadcaccbdddaabaddcbccdabcbdcdbadadbdddcddacaaddaddcbcdadddcbccaacadcdababcbcdbddbccabddacbdbcaaaccbaccbacacadcbcbcddccbabbbabbcbaaaddbcaabadcccdcdbddcbababadcabdcddcbdbaadcbadcadaaaadaabababacddacaadbdbcabdcdbbaaaadccccabbadbdddbcbabaaccdccdcaabdddcadbdbadcccabcdacbdbbacdacbaddbadbbacbccaddbaaaccdcacacbdcadddbbaaccaaccadcbabcadbbbccbbddcdcacaadcbcaccaadadadbcabdabbacdbbbbcbdaacdccdbdcadccddcbdadaaccbddaaddbacaabdbbabcabdccbbdbdadaadababacdadababbbaddadccdbaacdccbddaabcbbdbaacacabdcaccabdaadbbddddddbaacbdabaaacacacaccbcadacabadbbbdddabaaccdadbbcacbcabacdbddcaabbbdddbbcddbcacbcdaddddbcdbcdbabbbadbaccdcccadadbcdbddcbcbadacaadccccaadcabdacbbdbaaacddaadadbabaabbaddadadbcbddaccabbaaccaacbbdcbadadabdaccccadcbacdbacbbccbbbaaccaadcadcadbcabccabcabbcbcaadbdacbcdabdbdccdacbadacccbdabadbbdddcbcdcdbbbabcdbcbadaabbdcadadbbddadcaddaacddcacadcdccdadaadbccaacdadaacbdbaddacdbcbccdacdcbddcaddbbdddcbabbaccdadadbdcbcabadcdcbbccacaabccdbdcacdcdcdcbabdbbaccaabdbbaabcdcdbcabbabcbbbadccbbdcddcbabdaacdbabdddbbbdbabcdddcabbbcccacdbcbcbcbbbdaaabdcbbccdbabdcddbababbacdcbbacbcaddddabbdcddbabdcdacbadcbdbcdcbdacaddadacdbbdbbdbbdccbbcdaddabdadcbadcacacdacbaddcbbcbddabcddccaccbcddabdcdadbdcdabddacdabdddcdabdcabdcccacadbaabdbcaadaacdccbbcbdbbaabadcbbdcdcbdadaddccabdadbdbbacdcccbabbbcddccdcdbbbddcbdbbacbdccdabcaabbbccdadcacaaacccbdbdcdbabbdcbcabbdadbddbdadcbcabbadbccccbadacdcacabdbdbccbbbcacdabcccbaabaddaabbacbaacdbaadbdadbbdcacdccabbcacbbabaacadbcbcbadacbbdbabdabbbcbadcdadcbbddbaddcbadaacdaadcbcccbdbccadbbcdadbbaaadabacdadcccabacdbbccababcccbddcdbabddbdccbdbbdabdbdcabcaccccdccbccaaccadddabbadbcdcddabcbcaaaabbccbaababdbccaaddbbabddbacbbbaccacccdcdbbccdbdaddcbdbbacddbcbdabdcbddacbbcadabbcdbbabcbcbccbbccaccbbadbdacabbdbbbbcdcbabadadbdbcddbdbddbdccbdbadbacaacacbcdaccbcdcaacaaaccdbaadbaddcdbbcdcacbaadcbadaaabdadabcdcdcacbddbacbcddaadacaabcdddaccbccbaadaaadbaddbccdcadadccaadccdbddbccccabbacbaadcccbbbdbabdbcbbcaabbabdbdccaaacbdbcddaccbddadcaadacdcaabddbbbddbccbccabdcdadbcccadbcbaccccbdbddbbccbaddccdbadbdaacbddddaacbcadcdbdcabcadcadcbcbcbdcbdbcddcddcccdaadbadadacdbddccbbcbbcbcdbddbdbcbbbcacbbaacdbbaaabcddcdddbcccacddcdabdadabbacaccbcdaacbcccbcadbddaddbcadacabdddbddaacccabbbcadcaadcbcccdcabacdcccbdbababdbbaaddbddabdcdcdacaddbdabcdbcdbabcccdcbaddddaddacbcdddcbbdaacdaabadcaadbbdaabbbadcbaddaabbdddabcacdabcbbdbdccaacabbdbcaadaadddacbcccababbacbbbdcbbbabbbcbdcabababbbddccadbbbbcdaabbcaabcbbabdcbdcdbacacddddcdadcadddcdbcbbbbaadbaaabcddbdddbdaaddbdaccaabcbcdcdbaddacdcccadadccddabdaabbcccbddbabcbadbdadaacacdcdcbcdcdddbadbccbdcacbbbbddabacacdbcabbbbcccbdabdbadaadbaadaabddbaadbcacbcdaaabbcddcaddacadaaacbdadaaccaaacbbcbddabcabacdadbadadbdaddabaabbbaacdbccbdbabadbaaddbbbaadbddcaaddaaacbdbbcaddbaddbbbcbcccbcaaaccbaabbbcaccbcdadbbacdbbcbcbabbcbadcdabbaacaadcbbadcabdababacdcccbaccdadbbbcbdccbcacbcdaadbadbbadacaacacadadbcbcbacbbcaccbcddcabaaacbccaddaacdaaccdadadacbbcdbbccaccdaadbccbaaccbbcccbacbccbaabbbdbcaaaabddacbdadcddaaddbcbbbababdbdadbccbdcaaabccddbdaaaccbddcdbcacaadcbbdddacdbabcdcccbadcacdcdcddbbbaadddbaabaacdaaccabdcababcbcbcddbdbadcbcdadccdadddbdccddbcadcacbbbadbddbdbbdcabcbbbbdbabbbcdcbcddcbababcaacadbaddbdddaddcbcddbbbdddbcdddbaccabbcdadabbccdbcddbadccbbaabdcabcbbdcddcbabcacacdabaaabbccaaddddaccacbcacdddccaacadbcccdcbccbbdcabddcadddbdcbbddadbbacaaabbbbaddcdcdbdcaacbbadacbccdbdacabbbbadcbcabdbabacacacabbabadcbbccddddcddbbdcdbbaaadcbddcdbbabcabbcbcbccaddadadbbdadbdccdbcacdbbacbbdaddbaaacdcbababdcddbadbaccdadcbdacddaddddbbcaccdcdcaccbbacbddddbbcadabcadbadbbddbbaaaabdbcaacaddaabbbdcdadadacadaaddcccabdadcdbdaaacdccddacdbcadadbbabbbababbacaccabababbcbbdbbbccdababdbcbbcabdbabcaabbcacdadaabcdcdabbadcbabdcdabbadaccaabdccdccdbbdbabdddddbddbacbcddbdadcacacdccbbcdbbdbddccbdabadddccbdcbcdccdcdcddbddbbcbabccdacbaaaabbadddccacdccbcbcbabadbdabdbdadacbaadadccaabbadbdcbaadbaccacbaababbbccbbcaadacbadaacbaabadcabbddcbcadddaddaacbadbdddcdcadabdacadcaaadcddbbddbcbbbcabbcaacadabdabbaacacdbadddaacbcbbbdadbddcadbcaadbacdbdbacacacbbbcadbadcbcbabdaaabbcddacbcbbdadbcdacddcbcdbccacccdacadacdbbaddcbccccaaaacaaaababccbcbddbaaabdbccccdcdbddbcbadcdcaabccbadaacacbcdcbdcdbdaddcacaaaadcdbbdadaaddbadacbcddcbbbabddbacabcccbdadcddcbdabcbcaacaccabcbacbddabdadccbaaaabddbddbcdadbadbbcabadaabbbdcaddbaacbccbdcaddcdaacdcdccadaddcdaacbcdbbbdaccbbbabcaadccbbadccdabdddcdbccdccdbdcdcaddbadaddcccabbcdcbcbababdcdbcbdadcbaccabcaccbcdbdbcbdadbacbcacdcadbbcacbdaccabababcacbddcccacaccabdadaaaddacaccbcdcacbdcaadccdccbbdadcadbbadbcdaccccddbbcdaaacdababccabdbaadbabddadaadccdbadbdbdbcbcaacbcdbcdbbdcddbbacddacaccbcdcbadcadbdddcbadacbbdcbddacbadcadddabdcdaddadcdccadcadbaaadabccdbccaccacccadcadaccbdddaacabaddaabcdaccbdcdabcddcabbaadaaadccbcaaccaaaccaddddabdadcdacadcddcdbdbddbccaccdaccccdabbaaabbcacaaabdacdbdaaaabaaabdddbbaaccbdcadacaddaabccbcbdabacbabbacbbcaccbddabbddbbacbbdbdbbcddbcbbabcaabbaaadcdcbddbdcdbcdcbbabadddbaadaaacdcdcabbbaccaccbacbadbcbdbdbcacbdababbcdcaaddaadacdaadaaaddccddccbcccbacddaabbcdbabdbaacdcccddbdbddcacaaabcdbacdacaadadbacdababcaacdcadadabdddcaacdadadaacbcdbcdcabdaacdccaabddbbadcddcaaabdcdabbdbccdbcdaabccddabaaaacbabaddcdcbddbccccbabdcaacadbbcdddbbdabccabbdcabadcbabdbdbbbadcaabbbcbbbbcbbaacdabdabbbaadacdcdaabddbbabadaacdabadadbaccbbadbbdaaccadaabdcbaaadbbcdbddbbaadadcdbcacadbaacbbbaaaaccbcbdcdccccadbaababcccbcbababaadabccaadaddaaccddaadadcacdccdbdbdbbadbbbbbadddadbaacbabdbaddadbdbcacabdcadbcbddcddcbdbbbcbbcdcdcdddacddcbacccbbbdccaccbddacdacccaaaaabdcadccabdbcaadabccabdbbcadbddddabdadccabdbcbbaacddbcdbccadaacbdabacccdcddcbddabbacdacbaaccdbacaacccbdabaccdbddbcddccaabdaaabaaaacaadccbcdcbbcdbcdadaacdcbccdcaddcbcdcdbbcacbdcacbdadcdbbaadbbaacaadabcaccababadcbccbcbbdccdaabbbcdcddddccaacddbacbaadabbabcbaccbcbabdbddbabdaadddcabdbbadcadadddbddbbaabbbcbdbbcdaabcbadbcabddbcccabbbdcdbccaadcacccaadaaccdaabbbbabbbdabadcababadcaccbcadbddbacdadcbbadadcbbbbbdccbbabbbcdbcbaddcdcddabdbddcdbdccabbadadbdcabcacabadaadacdccaadddaaadccadabbbdadaadddcacacabccdbadbcbbadbabacbbdcaccbaabbbbdddcaabbbacacdbaadabaddbcbcbacbbcbcdacacdaddddddccaadbaacbddbbaddccbbacbdcaadbacabdcacabbddddbbcabcbadcaaddcdccccbbcbcaacaaaabdaccccbdbcddbbdddcbaabacdaabcbdbddcabcabcddcddcbadabbdadbbdbdabbabbbaccadbbadabbdcdddaabadaacacddbaadbbbabbbdbabcccbadbadbdbcccbaabcccabbdbacbdbaadcdcbaabbbdbbcccbbdaadaadaadddbcacaaddcccbacddcdddadcdaaddddcaaadadcaabdaadcadaadbcbcabbddcbaabaaabcdbbdddabdbaabccdadbdbbbbcdaddaaabbcdaccabdbdcabacdbbaddbcdbccbdbddcaadadcacacaacadcdcbaacabacdbbbdaaadcacbcacbadadcabbcdddadabdadacaacdbacbbbcacddcddcccbdacccbccabacbbdbadddbbadbadadcccacdaadcabbaddbddabdabbaddcdcdcdbaacbdbccbbcccdbbdbddacabddddabbdddaaccbddccdaadbccbcabdcbdcbbcddccdaacddcacbbdcccaaadacdacdabcbbbdaadcbdbbacdaccbccdddbcdbddddbcaddddbdcdbaacbacabaabbdbdccaddadbbadaaabddcbddcaabdcbbabcbbcdabdbcddcdbabacbdddbbacbcabcacdbaadbcbbaabcaacaaaccbbadcabcbaabcabdadbbbccdcadbabcbacdcaaacbcbbbabdaaccbcacddacccdcdddadababaddabcdabdacabdcbcaabdcacdacdbbadcadcdbddaaadcbdddaabbddbcccbdcbcdacacadcbaddacddacdbbadcbdcbcadadcbcabbcbdadadaadbccaddbdbccbdbabcabcdccdcddaacaccccbaddcbacccbadcbbabdaadbdbaaadaacbdbacccabdccaaddbdabcbcbcddcbdacaadadbcadbbacbababaaabbbadbbabaddddacacdbdbabbdccccbababdacbacadaabddcbacdcadbdcccbbdbdabdbdddaacadaadaadcdcdbdadddbdaccbdbdbddbbbcbbcababdaacbcbcccbbcabbbbcbdddbbdcabccdcbdbdbbddbdaaacaaacbadbadbaaacbcdaadcaddcadbdaaaadbcccaddbbcddadcddccccabbdddbabccaccaacbddbadbccddaadbdbdbbcabaccdcdbbacadcbbcadbcdabacdabccbacdcacdbbcaabcddadddbacdcaabadbaacbccbdcaaabcbbbdadccabdbbddbbccdadcdadcdacbacdcbdbdadddbdcaaadccbdabddacaccadbdbadaadbdddcabbbacbbaaddcadbadbabcbacddcbcbcdabaaddacaabdaaabbccbacdbccddddabdbadcdccacacacadbddacdadcccdbdaadbaabdccdbdbbbdaccadccbabadbadbdabacdaaccdadddbabbdcadddbbacdaaddcacabcbcdbcbbbddbcbbddcdabacbcdcbbbabacaacbdbaddbbacadadaddbcccabacacaccdbbbacdbdababcabbaaadbcdacccbbddbaacaadbdddabbdadaddbbcbcdabcabdccabcdadacbbccacbccdcaaaabbddcddadbbbcabaaaabdcdbbbcccadcccbabaadbcaddacbaaacdcdcdbabcadaacdcaaabbcadcccadaacabcbabadabccabbabbadcddccadabbcacabbcdaddcacbaaaadadbbbcacbacdcadbccbcbdbacadbcddadbdcdccbaabdaccdcdbbbddacaddcbbbcbcacdbcbcbddddcdcbbaacbaacacddacabaacdbcbbdabadcbaacacabcacadbcaacabcbbbbcaaacbaaabdaaaaaccbdcadcdcabbcdbccaadabbaddabbadbbcbaaabaaaadadccddbbbbadcdccdbdaccddbcaadddbaacbdcdadbbdbddbdaddcaacabbacadbdbdbaabbaaadddbdacbcddbaaabccddabbcbdcdddacdcaccbcbdcdddbdbaadbcdbbdcbbbcccadbbccbcdcddbcdadcaddabcbdabdcbbcacbcbcbaadacccaabdbccdaadbdaacdbbcccbaacaadbccdbbbcaddcaccbbbdbcadaaacaadcadadcbbcdaaadadbabbcdccbdcadaccbbaddcbacadaaccbcaaddbdbbbaaaccaccaadccaccaadabccbcdabddcdddabacbddbccaadaccbcddababbaddcadcbbabccabbbbdbabbccdddaccbcdcccddbcdabdbcbdbabaaccbdbbaddbcbdadddadbababbadaccbcbaccdbccdcdbddcbadbccddcacbdcadddbbabacbcdbaaadcababccaacdddaacdcbcbddacacadadaadcbabaddbcbaccdcdbabdbdbbddbadabbcdadbdbbccddacdcadbdcaabaababacdadbddcccbcbabcbababdbccddbddababbbcbdadccaacabbabccbaaddbbcbddadaabcddabddaddbdacdadbabbbbabbaadadaddbbcdbaaadbddbbcadbcccbcccdcdacaabdabbadadbbaaabcbbaabcaabaaddadbbdddaabbbcdaacbadaaddbadbbbdadbdbbcdaccbcbcddbadabbcdacababddccacccaadacabccaddddcaabacbaabadacccdccbcbdadadadcadabcdabaacabccdbcabaadccaaadddabbaddbadbbdabcdbacbdbbbaaaacaabbddccbadacbcbdbbadcbcdaaabddcaaddbdcddbcabdbcdadbdaaaaacabddcabbdddacddccbddbadccbcccbdadaaaddcdbcabbcbacbabddccdcbbcaddaabdccabdddbddadcdcbddbbcdbbacbabddbabddcccbacaccdcbaacddbbdbaccadddccdabcdabadcccdcdcbddaaccbadbbdccdabbbcdddbbadacdabbdccacadbdadccadbaacadabcaacdaabcacdaadcaacddacdbcdbadbbdbcabcbadddcddcaacabccaadcaddbbccbdccabacdbddbccdbdadbdaddcddaadbbbcbbaccdcadaddbabddcbaddccddaacdcdcbacadacccaadbaacdacabaaabacacbcddddbcdbbcdaabcbbbbcdbabcdcbdcaadcbabaaabacbacddcadadccaadaabcdabbabdaddabcccddabbbacdaadbacabcddacdbcaaaccbbdccddccaaccdaabdccaaabaadaccaddbcbbaccbdddabdacbacbcdccaddabdaccabbccccddbdabdaacbacabddbaabadbbdacdacdaaccdbdabbbbdcaabbbbccacdbdbddadbcadabbccaddadbccdadccbbdbabbbccaaabdcabbbbddcadaddccaadabcbbcbbacdbccdacaabbdddacadaaddabcdbadcbaacbcbdbadbadbcddcadacbacccdcbcaabbadabaacacbcdbdcbabcdbbbacbcbcacabbbadcddbacbcbdadabcdadaadbbbdadaababcadadaddaaddcdabcbadacddbbcadbbdacccadcdacdacbbbdbbaaddaacadbbdcccccdbcabbdaaabbdcbadbdacbbddabddddbcabcbcbbbdccbdacbcabaabadbcbcbaaddddbcbbcbcadcadaabdbadadbcaccbdbcbbadbbddabddbcccbbbabdcccaaaacaccdbbcbacdbadccbccdcbdcbbacaabddacaddbcacdbbbbcaaccbcddcdadbcdccdaccabdaddddcaaddacaababdbbacdbbdbaccdbcddacabaccaccbbdacdbcbadabcabbdabbbaabaabaaddccdcbbabcbbcddaadaddbcadcbaadbcaacacccdbdaabdccbabcdadaabcdcccbcaaaabbbbacbcdacaabaababcdccdccbdbdbaccdbbcababadbcbccbacaadbcddbcdbcaddbbcbdddbddbcddcbabcdacbabcccdcbbdddccbacbabcdcbacbaddcadacacdcdcbdcddacadbdbcddccbdcddccaababddcaddbccadbbcbaddcbdacaabccdbcccddbdbaddcdbaacbacdaacbccbbacacaaadbdaddbbbdcbdadacadaccacbabddcccbdbccaccbdccccaadabdbadacadcbbbabababccccaadadddaaabbbadacabbdccbdcddcaabdbacddaabbaccbacaccbdbbdbbbddadcadabdddbabdcadcdacdacbbcddacacdddcddbabcdcdabbcabcabdcccdacbadcbdbbcabbcdabaddaccbabbdbaaccdcabbdcacbbaccbddbbbacacddcbbcbdcdacbbcaabaadacdcabcccccbacddacbdaccdddbdddccbcbdbccdacbddbbdbacdadcddadaaadacddbdcbcabccbbadddddbaaddcbaccddbcdcaadadbbbadbadbaabbdcacaddbdbaddbbddcadddcbdcddacabbaddcdcbbabcadbccbadabcccabbacbdddbaaacccbbbbcadbdaccdbbbdbbabbdcccdcdcadbbcddcacdbccaccbdacccabbaaaacccbabdddbabdcadbabcadbabcbacddcaddccbcabacdccaadcbdacbabcdaaabddbccaadddacacdbadaccddcbdaddccdccbabccaddabacaabcacacabdcddbdbcddcaadcbbcbbdbacbabbabcabddaaacdbabadadaabddabadaddbaabbcccdaccbacacacaddbacaabbcbcddddbccbaccdddbcdaaaddcbddabbbdaddadacadcbdacbcbadcacddbddbcdccddaaacdadbdbdabaccbccdcabbacddbabcdbdbbbaddccddddcdbbacbabdcacdadccabddcadcdddbbdbdacdbabbbddbdcdbcabbbcbacbdbbcccdbdadcbaddcdcaacccccddcdadcadccbadccacbbcbdaadcdadaccadccabcabcdacbdacbddbaaadbcaadddccccddabbdbbddacaabdadabaaaabdbabbbcbcbdadcbccdcccabadddcdaadbcabcabdaaabacdcbaccdbccadbccaabcdcadcbadbccadaadaaccaddcbdcdddbacdabcddabdbdcacccacdddbacddbcbcdbdddcdbbcabacdaacdadbbbdbcdaddbdacadadcdbadbcdcdbcdbcadaddcacddccbcabbdbbabdbbaacabbbadaacccdcaaaabaadccbdbbdbccdbbdabdabbdadacdcbbdcabadabcdbcacbdaaddadadcdcbbcbcabdbbdcbbbcbbdbadbabbdcbbdbababdabacccdcaadbbabadcabbacbdbacbddccababbaaccbccddddadbdbaddccacabcddacabdcbccbcbbbaadbbcabcaadbdbabddbcadcaaaadaddccbbccabbbdbaccaccbaddddaddcabcbacbacabbcdcadaccaddbbccbdcdcdbccadaaaccadbadbbbcdbbbdbdbdcdcacbcdbdbcbadcddaadbcccdadaaadbaaccdbbabbccdbddadbcccccbbddbaacdbbcbcddadbdabcabbdddcccaacadcbcdcdcbddddaccacbcdabcddacbaaabaddbaabdcdbdadcdaacbcdddcdcbdbdbdacadccabcaddbbbdcdabacddbcaaacacacaadbcbabddbcbaccddaadbdcbaacbacdbccacddbadbdcccacbcdbcadbdaaccdabcbcbdbcbcacbccbbabccbccbcaadbbbadbdacabbaaaaddcaccbbdcdbbbdcadbbaccabdcdabddddacbabbaddcabdccdababbddadaddcbbacadbcbbabacbdddbabdacadcbdcccddbacbbabbbdcaacdaaacddbccdcaacdcdcabcbcccabccbcbccaddaacbdaaccbbcdcddbdbdbdcaccdbacdaaddcbbbbdadcabababadcbcdcababbdcabdaaddaacadbbbdcacbbcaddbdcdbadbdcccddacaccaccccaddcdaddbbcbbaadcccbbcdabdbccbcabacabdbabadaaabdccbdbacbabcbcbdbcdaacbdcccdadbccacddababbbdcadbcaaaacabddbdbbdddabbbabbddddaababdcdbaadaccbadddbacbcbbcbdddddddbdbaabbbbabcabcbadbbddbbcdbbbdacacbacadbccbcacabadcddcddacdbabdcbaadcdccaabbadacccddaacdbaaabcbbccbdbddabcacabdbbbcbcacadbcdabcbcbccbcbbcbbdacbbbbbcaaadccbcbbaabdbcaabbbadddadcbbabadbbacbdbbccdbbcaabaccdaacbbdcbabdbbaccdddbdaabaaadbabdabcaaabbdbcdddaadbaccabcbbbaaccaccadcdcddbddcbdcdbabaacbcadacbcbcddddacccaabdcbdadabacabaaacdadcdadbaadbccabbdbaaadabacabcadcccbbbbaadcbddcbccbbcbcabdcadbdcdcdbbddcddacdabccdbddbdadadcddcdaabbcdbdbbbabcdacdccadcddcdbbabacddcdaacbdbdaddbdcbcdaacabbdccaadaddbaaadcdacbcaabcdadcbbaddbdadcdcaabdaccddccdaadcbadabcdcddcabcdabdddcadcdacbadcbccdbddcaabdaaabbcbcdacabbbbbddcddabdbbdcdbacccddcccdbbdaaacdbadbdaccddacaccadbabdadadbbabcadcbaccdabaabbdcadccbcabbabcbbddbbddccccbcadccccbcaabbdbddabccbaaccaaccccabdacacbbabaddabcddaabddaddcdaccccbddbdaccddcacccbababccabdbdbbabdbcabddbdbbacbdbdbddadcdbdaaaacbdcdaacaabaccdddccacddcadbdadbadaabaabbaacacbdcdabdbadcbdaddabcbddabacaacbdadadbdbbccccddcabbbcdcaaabdbbccabcacaaaaadbdddacbbdbaccadcdababbbbadcacbdbbbaaacdbccbbbbaccabaccbacdbabdabaddaddcbbbcaabcbcdcbccbdcabadddcddcdcdcccbbcbcbbbdaaaacabdbccacaaaadadddaaddbadddbbdcbdcaddaadacadabadadacbcbcadacdbdcbadcdacadbdbabcdbadbaacbccdcccaabcabdcbcbacdbcdcacbaadadbddcbbbcaccbabaaaadbacdbabddcbcbaaaddabacaadbadacaccbdacaaaabbdaaaacdbccaccddcbacdabccbbaacbabdbbddbccaabcdabbbdadaadacdccdbbabddcbbcdbdcbdddbacbdbdccdddddcbbcdccddaccaddcadadcaddcdbbbcaacdbbdbcaccabdaaacbabbacadbcbaccbbcccddbcaabcacabacbcdddcbabbddcddbdabcaaccbaadccdacbdcbcabcddcddbadaadcdcbabcbbaadadabddcbbbdacdadacccbddddbaadbadbdadacdadadaaaddbbdaacaddbacbbcddbaadacddabdcccddccdcbcccadcaabbdacbbddccbacabdbabbdddabcccddabcddcbbbacdbcdaddbcabbccccbdabbbbcdcdcbcdddacdaaaaddcacbdaabcdbdadcbcacbccdcbdccacdddaccbcbdaccbdcbbaaacdbbaadbcbabdcbaaddcaabdaabccbbdccbabaadacaaccbdaabcdabdbaaddbacbddadcdbcabacdbaaccbbbbbcaacdcdcaddcdcaccdaacbaacaabbaccacadaabcccbcdaababbbdabbbacdcbdcadcdcddcaddcdcbccbdabcdddabdddcdaddbccdccabdcabcbcdcacccbcbcadbacadbaccbccbdcdaccabababcdccdcdaaddccccddcbdcbcdcccabdbabcdaabaddadadabccacccdcbcbcdababcabbcbabcccabdcbccbdaaccaabaccbbcaadaacddacabaccbdaddbbbaabcdacbbadcabbccabcbbaaacdaddddbababaacdcabccbcabcbccacccbbabddcacaabcccdadabaccadbccbadbcdaabacdbadcabdaaaacbdcbdbdbcdcaaacdabcccdbdaaabdbcdcaccdadaddcabbdcbbadddadccbaaacadbacaabbbacdaaaacdbcdcccaddcddcdbccccadacdddacbcaabdacdbcdbdcdcaaacbcccababbbcbcbaddaccabccbdbcbdabcbacccabcbadacadadcaacabbdadcbaaacdbbddccbbcdaccbbddcacbddbbabbcbcccadcbbbbbaddabccdbacbcabcdacaaacaacdcaabcdbabbcacbccbdaccbabdacacbabddbbbabdddacbddddbabcbaaccddccadbabddbbdbbbdacccdbbbcababbaddbbcbcbabbdadcbcbbbbdccadabbbbcbdbcaadccbcddcabccaababacbbaccdddcabcbacdcacbbbbdcdcdaddababcabaabbbcbcdcacdbcbcddbadaccbbdaaccabdbcbddbddcabcdcddaacaadbaadadbccaaaddcbbcaacbccaaabacdaacaabbdacbdccccabdbcbabddadddcbacadcdbaacbbcddaadbdadcbadbacbbacadadbababbbaaaaaacbbcbdcaddbabbcbcabbbdabcaacbacbcccacbbdbcadaaaabadcdaadabbdabdbbbbabbddcdcabdbdcdbbdccdabadcdbbbcbdacbadadcdbbcaddaaaaaaadcaaaabcbacaaabcdacdadabcdadddcbcbddadbaabddddacbbabccdbcaaadaadacacbbcacadbbddbbbccdacccbbaaccbccbbaacacabbdcbabdadaddcbbbbacbabacacdccabaddbdcdcccacaabbbdaadadddaabdbccabaaddbcbbcbcadcaadcbdbdbcbcaadcabcddcacbabccbccdadddacbadbacbbcdbcbbcccccadabacdcdbcaabbccbbcbbcdadbbdacdbdbacdcdcabbcabbbadcaaddaaaacbaccdbdbadcdaddbaabcadcdcbdbddcabadabadbddaacddbcccbbddcddddcbddcddcbcbcccbddcbcabdcbdcadacbbbbaadbcadabcdcabdbbcbddbcccddacbbaadbaddcccaccbbcdcadccbccbcadcccbbcccdcbcdcabccbabcbdddbbcdcccccabbccaddccbcdaddbacdcacbabbbbcbdaccccdcddaccccaabaddbcbdaddccabaadbaadcbadbcabaadadaaccdadcacbbdbaddcabcbbdbacdbdabcababbaddcbddadbacdabbabcacddaddddddddbcaaaaadcdadadccbadcacabbcdbbbacdbbdbaaaabacdccaabdbddbbbbaccbccbccdbaaccbbbadabcbaaadbdbbcddcaaabaccbabdccddcbbdacadaccddcdbacdacdcabdacbbadcdcbbccddcbcdbcadcacaddbabdbcadbabbbacabadccbddcccaacdadacdcaddbbbddabcbcabcabbabbbbacbcdccabbdcccbcaadabadabcdadadbabddabbbdadadbaaabacdccddcadbaddcdbdabcabaadaccadaaddabcbdcccbdbbbacbbdadbddbdccacbaacbddbadaacbcddbcabbddbbaccbbdbcbbcccbaabdadabababacbadcddbcaccbbbbaadbacbcbaadbacbddbdcababccacaacbbccccdccababbdcbdbbddcdcbadaccdbaddbcdaabbadddbdaaadaaccdbcbdaadcaddcdadaabbbdcbbcccabcbcabdbcdacdbadbddcbccddaccdbbddacdcadaccbababbdcbdcbbabbbdbadbacabbadacbadcbbdcabdadddbdcadddacdadadbabdcabbaaddacccdabdabcabdddcdadaababcadacdabaddbcbbcacdddcabdbcbbdacbcdbbddaccccbdbbbbbddaddbcbbdddbddadbbdcbbcbbbdcdccdcdcadcabbacbcdabdcaabbdacbcddcdacbababbabcadddabbbbadbdabcaadaacccaabbbdcbbadbbccdaaabdaacddbbdacdadbdcddbcdabaccdbcbacccbabadaacddcabaaddbaacadcdaabcdadbdbbbcddacababaadadabbcdbaabdabdacddcbbdbccdaaccabbbaccbccdadababbabacacadcdadbdbdccadbbdbcdccdcadbbcbddbabbbbcaacacbcbcddcddaaccccdbcbadbbbddbcabbdbbacabaadbdabcabaababcacacddccbbbbcbbdbbacdbdbdcbddaadacccabacbbaabddcddabadabcacdbdaddbabcadabccccbcbacbaaaccabdbacaddadaaacbcbadaaddbccababaaccdacaaacdcccaddadbdcbbdaaacabcbddbddccbdcaaddadbabcbbdbdcbbcaabbdbbcacdbaccbdcdaacadcbcdcdcdaadabbcbcbcbdcdcbdcbbcdabcccdcdacacdadadadabbdbdcdaabbdbccacdcaccacababbdacbbcccdbdcdaacbcaababaadcacdccddaadddccbbbcaabcbccbacddaabdccacbcbcbddbdbcdacbddbcddbccbdccabdcaacdadadccbbbccdaacadcbcbaaaadacbabcbddbbbbbdaabbdcbddcadacacddbdaddacbdadddadddbdbcacabdbddcbabacbbbcbcabcddccdbaacacbbbacbaddbcdacddbcdacddbcdcdcbbdccbddbccbadbbacbbcacbcbdaabbbaadbacdacaacdbaadcbadbcaadccabddcdbccaacbbcbdbcbcbadbabddcbdabddacbdadabcdbacbdcdddddadccdacacbbdaacbbcaaacadbbcbddaddaccabbcdacbbcdbaaadabbaacadbcbadcadbbdddbddbdbcdcdcdccadbaadacacacdbaabddbabcacaabcdbbcacabacdcacabccccddcadbbccddadcdbddaacbbbcbdadbabaccdcdacaabaddddbbbbbcdbbbadacaaacabadcbbdbdbddacacdbadabddabbdbbcdcdadcdcdbdbbbacbbbbbdbdacbbabbcabcbdcbbbacddaabacadbbabbdcacbcdcacaadcccdacaaacccbdcbaabcaaaccbdbaddbbbbcbabdabdcdbaabdadbcaccbcbcdddcbbdbbddcadcccbabdaaaadcccbadbbdacdaaccbbdcdcabaababdccabaaddacaabcdadaadadbaddcdacaccaadcabaaaacdcdcddccbddbdbccccadbacdabacdcadabdddccddcabbbcadcdcccbcdcdcbaadcdacabdcddbdbaaadbbbdbdcdcbdccdcadcabdbccbbabacddababcabaddbdacaabbaddbdabbcaaaadabdcaabbbbddbcbbcbcbadcdbcaccadacbbacdcbaccdabdbcaaacdccccadbbadddaddcccaaadaaabcdbbbdcccaddcbdcbaadbcdcbdaccbcbdccddbaabcadaaaacdbabadbaddaacbcaacaaaabbbcbccbacbabacabbcdbddaabadbcabcdbbadcaaadbaacbdabbbbbadcabdbbaaddaabdbddcdbcbbabddbbadbcdccbcdcccabcbabcacccaaabdbbdacbacccacddbdddddabadccccabdddabbbdacadbacaacbbcdbabbbdaacdacbbcabadddabccbbcddadaadbacdddaaccddddaaababddbabbddbbcadccbabddcdccddcaabcbbdddcaadbbaaacacabdbadcdabcdcabacccdcdcbddbbcbabcdcdcccabbabaaaabdabbdacccbaccbabbddacccbabbcaaaddbbbdddbbdccddbcbcdcdcddacdcbcdcbdbdcbabbacbbabaabbbaddcdabccdaaabdcbbdbdababbbcdddacdbacbbbdadacdcadbbaaccccbbaadaccdbcdbcabcacbcbacccdcdbdaabbddadddabccacabdddccadadccadabbcdabbddbbdddbdbadadcdcdbcdacddcdacdacbdcbcbbbcbcaaacaacdcaabdbcaacaaadadcaddbccacccbaadaccabbcbdadacaadddacbdddcbbdaaaddabadacaacddccbadadacacbbbabaabbccaaadcccadbcdaaaddccdacbbacccadbcddbdbccccdaacdaaacdbcbadbaacbccdabbdbdaccccbbbdacbbabbccbdadabbcacaddccdbbcacacabbbabdabaaacbbaddbabbadacdabdbbadbdbadaaadcdcabcadadaabcaabbdcbbccbddabaddaddabdddaabaadacacbddadccdddbbbbaddcbccdcbabdaaddcbcbaaccaaacbacbdacddbacabcbcabbdcaabdbbbbbaacaadbcccbbcdaabadadcbadbabdbdbcbbdacccddbbaaabdccdcdcbcddbcadddcbabcbcadbdbabbacacadccadabccddacdadcdcbbbbdaacbbbcaacadacabaddddbccdabbbbbaccadccaaddddabbdadbbaccacbcbcaaaaddadbdddcacacaadcdbbabccbbbbdabadccbaacccbddcacbddcaacdabcbbacdbacbaddbaddbcdcaacbddbbdbdcabaaabdbddbddabbbcbccdddcbdcbcdbcabcdacabdbddbccdbcbbbcbbbdccadcacddbddbbdabbcdaddcdcbbcbbbcbabcaaaccbabdcdddbbadcaddcdcbcdbaabddacabbbbbbbcadbcbcbbdacbdccadbbacddbccaddcccbcabacadcccbaaabcabbbbcaabdcccdccdacccabbdcdacbaccddbdbcbdcaaabaaabacaaccdbcbcbcbacadcbabddaaadadaadcadacdcbdaddaaaddacaccdbdadddaaddbbcbdcaaccaaacdacbbbabdbcbbdbadbadaacdcbacbadbbcaaaadbddbaaaacbcbadbaaadaaddbbcaddcddcbccacaadadbaacbbabcadbcabccbaccccabaadaacdbdccabddcbaabbbdbbaadccddcabbdbbcaadbadcbbcaabdabdbaaaacdabdddcaaaaaddaaaadbadaccabbbdcdcadbcdddabcdbbcccbbcabaacacacadadcddacddbdadabccbccacadbadbdadaddbcbdccabaacccdcddbabababacdcbabdbabbdccdcbddadadadaccabcabcbdadadaaaccacccabdddcaaadbdadbaadbcaacadaacdcaddbaddaddddbddccbccdccccaddabdbabaabccabdabbddccbbaaacadcadcbadabaccddddcadbacdcdaadbdacdadbaadacacdacbbaaccaacadcbbacddbbadbbddbbcadcaacdcbbadadccacdabdddababccdbbacadabbcbcbadddbbcdbacddccacbbcacbaaccbbcccccacccccdcdadabbbcccbccdbccaabbabdaadabbbdccabaaadbdcabcbddbbdabcacbdcdbcacacdabddcbccacadbadbbdaadbabcbcdccaccabadbbaaccddbccccabacbdadcdcaccbdaadbadbacddbcbbbddbadabbcbddbaabbcaabcbbdaabddabbbdbaadabbdcbbcbdcdcbaacaaddacddbbcdddcccdabdcacdadcadccdcaaccdbabcacabdacdccdadbdcbccaaadbacdbcddaadccddcccaaadaabccdabbbbbcddacacdccdbacbcbabacbadadccaaabcbcbbdddbdaaccbbcbbdaddcabdcacbbaabddabddddabcacbbadaddbdccccbbdcacacddacadcadcdaadddacdacbbdaadddaccaddcdabdbdbbdbdcadbdaccbcbbaaaadaccbacbdbddbbdddaccabcbdccccaaacaabbddcadacaacdabddcdbbcbbbddcacabbddcdaacdddaadaaaddcbbcbbbdbbddbaadabcbaaacbbcccccdbbdbacbaaddaabcabbacbddcbcaddbdbdbcdacccccdccacaacabaddadbcabdbabdcaabcccabbbcbaaccadcdbdddcbcdaacdcdbcbaaddacabadcbaddcbbddccddadcdbdbdadbbbdaababcdabcdbcabcabcdadccacabbbdccdccbcaadcdddddacdbbcbaadaccdccbcdabcadcdcdaadabccbcbbaccacdcdbadbaadabbadccdbdbadccdbbccccdaddabaddcdccbacdaaadaadddbcaaaaddbcbcdcaddacdcacdabddddcabbdbcbdcdccbdccdbcadbdddbadbdbbbdbcbcbbacaadbdabddccdacaccbdabcaadbdbdddacddccabdabccdabacdcabbdaaadcdcabbdbcbaaccdbbbdcbbcbcbbaadbadbdccdbbccacddcbaabcdcbbbcdddacdbddcbcdbbbbdcbaacbabbbddcbdcdadadccababbcdcbdbbbaabaaccadbbbcbaadcacdcdcacdcbcbaaadcdaccdacaadacccbdbbbddaaccbdadddaadadbadbcdabbadbcaccbdaaabdacbbdadbdbdbddaaccdcdcbcbcadbdbabdcbcabdabbddacbbbadacadccdddbdccccbdacbcabdaacdcbcbdcbdacbdbabaabdacbaddaadcabaadbdddcbdcbcabbbbcaccbcacababbbccdddbddcbccaddbcbdcaccdddcacdddcdcddaadccadbaabdabbccbddadabddcbcbabdccccdbdbbdcaaacbdbbdcbdabbcbbcddbcadbcddcbcdbdcabcdcbdcdbcccddbdcadcccabbbdccaaccadddaabdbbbcacbdabddbdabbccbbccbcbcaaacadacccaccadcddbbbccaaacddbabdbcaabadadabdbbabcadbcddccdbaacbdccbbaabddadbbddababcbaccacdbccabaddabbbbdccaccdcacddaaabcadcddacacbbcbababddadadadbbccdccabadcccacbcbddbabbcccbddabddbbddabbdcbcbdddcaddddadcbcccdbbbdabacdbabadbbbdbcdbaacbdbadaadbbbccbabdabdabbbabcacacadddabbadbacadbcbadbbcdcbaacbabbacdcdcdbabaddaacdabbdbbbdbbbadbbdcdbbcadbabdddbacbcbabbdbabdcdcccacbacddbdacbcbadbcdbadbbcbbccacdccbdacacddccaabcacdaacbadcdaabcadcaaadcaccdddabadcddacdadcbbdddacadaadaadbadacbdcccbadbcddaadcdccdaadabcadcbdadccdaadbcacbaaaaabdcaaabdccbdcbcbabddcdadbbadcbcaabccacdcbbdadabadbccabdddbaddaadcadbdccdadddaddbcabacaadcbddacbdcdcbacacdabcdaaaddcddcbadccdbbdcdbccabbcdbcddacbbdcbccabcaaadbddabddaabcbaccdbcdbabdadbcddabbaccaabaabcbbabadaaaddaabbdcacaddcddaabdcccdbddcdacaacadacadcccacdcbadccadddccbadbbcacbccbbdadbabbbdcdcbbaccabdddbdcabcabadbacbdcaaadacbaccdacccddabbcbbdbbacadbcbdbbcabaddbabcbaabaaabbadcadcccaddbcaacdaabbcabcaaddbccbacbdaaaddaabaaddbcdbacccdcbabbbcbcbadaabbaabbcdaabdabdaacbdaaaadaaabbcbdbaddccbbcaddbbbaddddaabdccdcadccbddabbbadababbbdcdbcdaacacacddcbaddcdabcbacdbdccbbbbcbdadbdbddcbcbaddcdcbbabddbabbbbaaacbcdbdadcddcccacbcbcdcabbaabccadabacdcaadbabbaccddcdacadaabbddddcbaacbbbccbdbabaabcddcdcaadcbdcbacdbbcacbadacaddacbcdbdcbbdbddddbaddbdaaadaadcbaabbbbddbcadbdbaacdabccdcadaacabdaccbaccbddcbbacaddbbcbbcbdcacaacbddcaaadccacdccabcdabcaabbdaabbcbcbbdaabbcbcbbacddccaabbaaabaaacabdcbdadbcabbadcdcddbcaadcbbbcaccabddddaadddcbbadcaabadcbbbaacdbcabcacdbcdcccdacaadcdaccdaddacaccacbabacbbdbaacdbcadcbdbddccacaaddcdbabcbadbcadbcaabccdacbdbdcbaaccdccddcdddddacbbbdabdabcbbccabddcccccacbdababddadacabccacbcdbdaabaabddddbacbdbbcdbdadadacdcbbcbdabcaacaabbcabdcadacbccdadadcabacaaacabdcddbdcdbaacadbaaabadddbdacbadccddaadcaddadcbbdacbcbadaaadcadaadcdcadacababaacbdbcdbcccbaacacdabcdbdabdbabdbaacbabddbcaccccbdaacbcbbbbbdcbabdcdadaacbbdacdcdabbaadccbdbdccdacdacadaccbaacbdacbbdacdcdbcdbaddcbbdccdccdbbcdaccccccddcbdbcbacbabbbdcdcaadddadabccacddadbbaccbacbccbccdabbccdbdbbbbadbbadccbbabbcbaacadcdcadcacbcdbdcdaacaddaddddaabbbccbdabbccadbcddadabbdcdcabbaaaadadabcbaabbaddaacddaddcdbcacccadcbcdbbacbbbbadddddadbdabcdacaadadaaabadbadbbbaddbacbcbaccbaabacabbbdadcaabbccccacadabaacdbadabbccadccacdbadbccdbbbabcddbcaacdababcabcbcdcbcbbdbcbcabcbcaddbabdcadbcddddccddcdaddddbbcdddccdbdcadbacbcbccbacdacbacadadbabbaacdcdbcccdaabacdddbabdcdbcbcbbaabbcdaadaaaabaacacdaccccabdcaaddddddccaddcddcadbcdaabddbbdcadacbdbadddbcccabadcdbcddcdcdbbdbcbadddcbdbbbcbababadcdadbbdccacbbaaabdaaaddbbccdaaabcbbcaaacdcdcbcaabbadadbccacccbacdcccabcababdbccbbdadbbacbddaadbcddabcdbdbadcacbacdacdbdddbcbbddbbcdabbbdabbabdbbcdabbcdabdaaadddabbccbdabbdddbbcaabbbbadbcdbbbbdddabdbadcddccbdadbbaababcaaabcdbcabcadbcdacdddcdbdccaabaacacabdbdbbdccdadaaacdcdadadddadccadbaabbbcabcbcbbddbdddcdbaddcabdaddbbdaddaadacbdadcaaadcbbbbdbccbbbdacababaddddbbcaababcbccdbabbbcbbddcbdbdbbcadbbcaaccbbdddaaabcadacabadabdbddbaacacaabaddbcdcadbcccdccbdbadabdaccbdadaddaadcbcbcdaaaddccaadbcccbacaacdaddabadcabcdcddcdbbcbdcbbcdddacbdcbdadaccddabaadacbcddddabdadbdaabdacdbacbcabcdbdccccdcdcbbdcaabcdbccaaaabcddbbcbabacacbabddbabddcacaabbadbbcbbacadddcabdbacbcaabcccdbddcaddcdaaadccabbdaabcccbdadcbbacadacadcbabadbbdcbabbaccaccacacdcaddddbcdcdbbbddadcddddadbbabcbdaccbdbbbbbcbcadccbabbdacdbacbaddcdaddbbcccbcbbbadddbdbbbbacacdcbabbbdabcaadbcadacbbdddbbcbcbbdcabcccadacadbaacdbddadadcbccbadccdbcabbabdaddcccccbbcbabbcbbdbddbdbddcdaacaabacbcdbdabcddaddbbabadaacadabbdbcbcbadcadddbccbddcadaabcaaddbcadaaadcdcdcdabdaaaaadbcadacdcaadbbccbaabadadbbcbccddacccdcdcdcccbaabadadacccadaaadbbbddacadbdadcdcdcbbbaaccccdcdabdabbbbcdccaacdbdcbaadaacddccccacaaaadcacdcccdcbadcdbdbadcccdccbdddbbcaabccbbabadacabaddbaaacccbadaccdadbbabcbbdbaaddcaacabbccdbaaaacccaacdddabdaaadbddbdcaccacbdbdbbddaddababadccbadbddcbaacabacccddacdbababcacaddcbdbccbaaaadcaabbbccaccbbbbbcbdbabbaaadaddacacdcbcbacddccdcaadabcddbcaccbccbcdccaccbbcbdacadbcadcadaddbcddbacadacbbcbccaabdbaadabcbbcabccabaacdabdddcdbbadccdccbdcadadddccdbdbdcccabdbcdaacdabdaabbaacbbcdaddaabbbbdbdadbdcdadadacbaaacdabdcbdccddcdddaddcadbabacdbadcaadabbcbbdaacddcaadbaaccccdbcdaaccacdbddabbdbabcdaaaccbcccaadbdccddadccbdcbddadadaaaccdacabcdbbbccdccdbcbbdadccdcaccbbdabbddadcdadaadbdccbcabbcdabadbbdabbccdacdbadcadaabbccbaccacaadbadbcddbdbccaccbdcbcbdaaacbabacabbbbccdbaadabbbbbbddaabcdccdabaaacaaacdddbbdcbbbdbdaadcbcadacbbcbccbaccadabdbdcddaccbbddabbadabaabdbadcdbbdbcbcabdbdbaaddcaadddbadddaabcdbdbbdabcdbdcadccbaddcdccdbaaadcacaaaabdaabdbdccabcdbcbdccaccbbadaaccdbccbddcadddccbdbacdbbcbcaaabbbbbbdcbabadadacdbbcdbdbbabcabcbcaddbbdbccbddcbcddcabcaabbcddccaadbababadbcddcaadddcaddbaddbdbcacccdcddbbbdbbbabbcbcaadbbddcbcbaaacabbcbcacacdcddacbdaacdbaddcddbcadcaaaacbcabbddbcbdccbbdcdcbdcbdacbcdccdaddcaaacaaacbdbaacdcddccdbacbacadadbcddaadbbbacbacbccbddbddcabacbadbbdddacbcccaababcdadccbccacabbdbcaaaaaadbabdbaabbabacbaccbaccddabcadaccaababdcccadaccbdbaacddddabbabbddbdbbbcbabdcddddabcaadbaadcaacaaadaacdddbbdcbccdacdbbdaabadcbcbdadccbccacbbdacddaabccadccdaabccdaaaadcaadddbdcccdbcddbcbadacaccdbddacbdccccccaabacacacddbdbadcbbcbdcbacadaddbdcdacdbbbcaabbdcdddbbbbacddbcdbcabadaabdaddabadaaabaacaabdbcbdbabdadcaadccacabaccadbccacdbccdacdadddcbbcdacdcbdcccdcbabbbcacbbaccaddbacdacbbbdddcbcddccbabcbbbcbdbababccadddadccaacbddadcddcbcddaadcccdcbccdbadcccddbdadbbbccdacdaaddbdbbdaaaaccdadbabadbcddbadcaacdadcaccacdccdcacaaacdbaccdccabbbabdbccbbcdadbccabacdadddcbdaccaaaaacbbaacbcdbccbbccadddabbcacdadacdacdccbccbacdddbcccaddbadbadabdccdbcaacdbaabaabdadcacbdcbccdaaadabbbdadcddccbbacddbbdabcdcddccddacdcabdccbaaabcdcbbbbdddccdbdcdbdbccdcaddddabdadcdcbaabababdbaccbacaddddcbbadbcbcdadaabdcdcddbaaaadccccabddbbdbbcbcbadcaacdaaacddaabdcbcbaacbcdcabdbdcdccabcadcbcbdadcbdddadbaddabcdcdbbbdcabadddbaadcbadccdbadbbdbbacbcbddaaddcbacacadbdaadbcbbdadbbdaaadbbadadbcadabbccdbacbcdcdbbabadcadadabcddbbadbbcccdabaacddcbbacbbbabbabccadcdcadacdbbcccddbaccabbdbbbbbaabadddbccbdaaaaadbcacbcdcbaddaaacbdbbbbdcaaccbbabaabdbcbabddbaadddddbcdabaababaaadaadacdbbacdccddbbcddaacacabcbdccaddacdbbaabdbcdcddbdbacbaadacabbadccacddccddabbabdcabbdcccaaaabcabcdcdaacdbbaacaaddcdcadaccddcacdddabbacbcbdcddbaddcbcbacccacbdbbcacbadadbaccbbdbaaaadddabaadbbcdadabcbdbdaabaabbdabadadacacbabdacddabaaabacbcbddbcaddacacdaddbcbbabacaacaaadbaddacadadbdabcccaaaadcaaacddbabbbbacdbbbdbbcccddabddbddabbbbdcacadabdadacacdccacacbacdbbdcdbbddaaaaccdbbadddbbcaddacdbbcababadbddccdbdacbcaddccccacbaabbdccacadbddaacbcbbddcabcbacccaabadbbbbcadaacacdcbbdacbabdcddbdccdbacbadacddbddadaabbcbdadddbbdacaddabbcccddaccacddcdccbcbaaaaadccdbcaacddbabcccccacbccabcdddbacbddddabbbbcadbddbdadbbdcacbabdbdcdacaaccbdadddbcaddbdccbcbadbaabdacaacbcbdaacdaddaddaabbdcbaacddadddbcdabdddadccacdbdcacdddabdcadcdaacabccbddbabddacccccaaddddcbabbbdbaccabadbdbbacbbbcdaddbcbacddacbabbbdcdaacaacaddaccbdbcccbadbbdcbbbdcadaaadcdddcacdbadbbcaabaacccbcacadbbdcadbabdacccddbaaaddbbccbbcddccddaaabbbcbbccdddacccabdddadcdddbcaddcbadcdbcbddacadddddabbabbcadbacddbdadadbccaadacacbabbadcacaabcdcaacbdbccabdacbcddcdabadbacbbbaaaabbdbbadbdaddacbbcbdcadbcddddcbbbcbbadbdbbacbabcabaadcbadacdbdcbabbddadcbbdcadddccdcbbdbdbccacbcdcdcbcdabadcdaddaaabacdddccdbdddcbcddbcbddbadccbdcdcdcaabcabcaaaabbdbcadbdddacababbbabbccbabbddbcaccdddcbcaabcacbadcccdbcacabbcdaccacdaaabacaadadacdccadbadcbacdadbadbddbabcbdbbdddbbabcdccccadbbbaacbbaccabbbdaaccacadcbcdbcbdbdcbcabcbbcbdadddddadccaaacbdacabaaaabcacbbcbacddbdaccddcadbdbbdccacccaddcbddacbbaabddadbbdbdbdacabbacdccabbdbdbcbabdcdbdbbcaaddaccbbcdadddbdbbabdadadbabaababdaadbcdbbaabaddaddabddaaddcbbbcabbcccccbcbaacbdacdcbcabbabdddcadababdadaabbababdacacbbdbdddccbccdccccccdbdbaaddcbccbacbbaaccabaccbbcdbbbdbdacbdaaadcabcbddaaddcdbcddbcdccbcdadcabcaccabaccbddbdcdbabcccadcbcadbdbbcdbaccbdbabcacdddadcbaadcadccaadbcabdccbdacdbaabadbcadbcdabadcbccbbccdcbbdddbdcdabbbdbadbbaddaaaadccccdccccdaddccccbbdbabdadbdcdadccbbcddcdacbbabdbcdcbddccbdbdcccbadabadbbdbabcbdccaddddcccacbabcbcdcdaadddabcbbdbadbdcbabbdbdcdcbacbacbcdaaadcbdbbaadcaaabbbbdabbddabdcbaacddabdabadadacbbcdaadaddadddddbbcbbaaddaaadddbdcbaacddcabcbabacdaabdaaabacadccbaacdbdddcbbcaaccddadcddadccacdcabddccbacdbbcabcabcabddbaaddaccaccbdbddddbddbdcbcacbdbbcaccaabdbabbbdddacddaccdacdbcdbaaaadaacaddadddcabbccbdadcbcabcbcaaaadbcbddbcdaccdccaabbbaadbbbbcaadbcbdadbddbcaddbbbcbdddccaabcacddbcdcbccbdacaaddccbcbbaadcdcdbabbbbdbcbdcddbbcbacaaaacdbcabddbccddcbbbcbdddacbccabacbcdadcdbabaddcbabbadabdbbbccbbcadbaddaccbaadbbccbaaddaadccabddbacccaaadbadabcbdcbbcaddcccadabddbbdbbbccbadbcccddcaaaddccaaaabbcababbddbbddddbcdbabdacbbabccdadcbaadaadaaccbdbdaddaadccbbdddcccbdcbdbacbccacbacadccbdcdabadbcdbcabacbcddcdaabaddaccbadccabbadcabacbaabadbcabcdabbcbbdbdbbcadabaadbcadccbadbcbbabcabddccabbaacdaaccbcabcbdaaabcbdcabbccabcdbabddbbbcadccdcbaacdacbaaaddbaacbbaaacbaabbbbaddacacdaddcbddaddbbdbcaaccababcaadcaadcdcdddbadccdccabddccddbbbccdadcbacccccadbddaccaabbdabacbcbaacbdbddbaccababdbddbcdddaaaaccabadcccacdbadcadcbaabcabbddcddcdbdbbdbbbaaabaccbcaaabbabbbaddabccbcabdbdbccbbcddbdccbbacaccadbbbbbdacbadadbddbbbbddbbdadbddbbcbdbcadaddbaaacdadbccaccbaacaaabbcabbbdcabbdcbcbdbdaabcbbabacacacccbcaddcabbcacbcbadbccdcccdbccacbacccabddbdccdcbabbbacaddcbcacbbbbbbcdadaddaadbccaadbacccbccaaaccdacbadbbdddbdcdaaacabadbcaccdcbaacbbcaaacbabaacadcbabaabaaadabadaaabacbacbbcccaddddbcacbbccabdabcabbbbbcabcbbcdbcacddaadaaaaccbaabcbbbcbdacadcabcbddabbccabdabdbbdbbacdbadbaccacbaaddaadaaccbdddcaddbbadabbbabadaddbadacdbddcddbbccadacabbcabbdbdddccbcbdbaacdcdbabddadddcbadddbcaadbcccadbaabbbbbddccaacbacabddccddddcdccdacbabdabbbbcaaccbacbccdccddcaccddbcdabddbdbbcadbdaacbbbbbaddcbaacdbcadddcabbabccddbaddbaabbcbdcaaabdbacbbbdcabcadaadabbccababaabacaabaabbddbabdaadddabbcddadbbdcbbddaccbbddbdacabddbdcacdcbcccbcadabcacccbcbcdbbbbdaaddbcdcaabbcadccabbdbadcddabbacaddbdbcadbacccbaabbccdabaadccddccdcbdccbdaccbdacddcbcbbdaaacadbababbbaaabaaabaccdacdbcbaddabbadacadddabbccbddacddddbdbbadbbddcdbdccbdabdacaddbcbcdbdcdacaccdacabaaddcbbcbdaaacccbdcdaddbcbbbbbbdbabdadcddddcbbcbbcddddddcbbbddabbabbdddaacbaadbddcbbdcdbaacbccacbbadacabbaadbaacabbdacdbbabcbdadcbdabaddbbbbabccbcbdcdacccbdbbdbadbddabddcbabadabdbcdbdcbcdbcdcbbabdcacaaabcdcbdaccccbaddcbcdbdcdcdbadccbcbacabccdbcbdddcdcabcaadccaccdbcbddadbcbcdcdcabdccaadcbccbdaddabdbccadcaddbaadcccabbaacbbdbdbdcbacdccbbabbcdbadccdddcabadbabaddcddbbaaabdbbcbaaccbacbcdcbdcddcbbcbbdbcbcadabbcbacacbacbddddcadcaaccdccdabdaaabbcddbbbaacaabbadaaabdaccbacdbdbcacbacddcdddabddbdbdabcdabacddacadacadaaaabdacabcbccacabdbbbaadcaccbbdddbdccbbbbbdccaddaaadacdccaaabdcccaaddaadacaacadbcabdcacdcabccadaccbcadbcabdbbbdcdaddcbdbbabadacdadbbbbcdcdccbbadcabdccdaddbdcdbdacdbdaabcbbacabacdbdcadcaaaadbadabadbdccdacacaacadadccacbacababbadacdbdadbabaadbddbacbadbaabcaadbdbbdbaadbddbdbcabdababdcaadbabccaaccccddcaacbcacbcdacbacdddbcabbbadadbbbcaaccabcabadabcbcdbcdcbbcccbbbcaddbccbbdaabbbbabdbaccdbaacababdbdccadccabadacbcdbbcacdbdbcdcccccdabbdaccaaaacbddbbaabadccdabdbbcddadbaabdaaabadcddadcbaabdabbadccbaabcdcabcbaccbadcbbcadabdcacdcdacaaccabdcbdcbbbcabababbdddcacdcacbcbcdcdbbabacaddbaadcdaadbcdbabbcccccbcdcbddcddbdcacadabdcbcbdaddddccbcbacaadbdbadaaadbbababbcddcaccdbaadcbcdccbaaadabdcabdbbcadadabadacaaaacaabdddadbcadcbcadccaadccdcaadaabddabbbaaaaddcacddaddbaacdcdbcaadbdcdcadccababacabbbdccdaddacccbdddaddcdbddaaccbbcddaacbacbddbdadccadadaddcbdaadaadaadddbddcadadbbdcaaaabdcaabccdbbddbdaddaabbdbdababbbdbbccddbccdbccabbdacdbabddaddcaadbcbacbbdaddcdabcccbcbaddadcbcdbbcdbddbbdccbddabbbdccbabbabacccabbabcccccbcabdbccdaacabdddbdbadcccaaccabdbdabdacaacccaaadddbddcaacbcccdccbcacdbcaaadadcaabaccbcdbdddbcacadbaacdbcadaccadddddbbbbcccabdcacabbabdccbdddddacabbaaabcddadaacdacddbdabcbbbaddcbbccbbbcccdbaccbacccaadcaccaccdbdcadbacadbdbddcbaddbcaabbdabbabcdaacddacbbdddadbddabcbabcbdadccaabbadcddddcdacbbcbcabacbbaabdbabdbbdccaaabaaddbccaadddcddbdadacdacbcabacbcdccdbacbdbbcddcdacdaacacbddcbcadcbbcdcdaddaabdaccddbacbdcbabdddddacacbacaccdbcaccbcdbbbccacaccbaccdabbaaccadabbbdacacbddcbcbbdbabdbbbdbcccdbcaaadaaabaacbddadadcddbacddcdabacbbbcaaccbacdcccdcccbbaccdcbcdccdcddcccacbdcadacbbcaababacbdddbbdcbadbdabaddbdcaddcadabadcbdbadabbabcddacccdbdcbadbadcccdccaabcababbdcadbadcbccccacbdcaddacacadaaccadbdadaacbaddbddadadadaabaaaacdaccaaccccbacbcbcbccbdbcadccbadddcaaabcbddcbdacdbaadcdddadadcbacadbaabdaaddaaacaaadcccbbcdbcdbdcdcccadbdacaddbacdbcbbcbacdcccddcadcddcddbaaadbadababbcacbbbabdabdacadacdbccdbbdcdaddbdabdbadabacaabbbbdbadaccababbabcbabccbabadaadbddcaadacaadbbccbdbadbaddcddaacdcdaabbbbdabccacccbaadcdddbcccbccdabdcacadabdadcbbdccddadbcddaaddbdbcabdcbdcbbdbbdadccbcabbccdacdbadbbcaacbadddcbdadcacdcdacaadccbddaddaadabcbcaccadcadcbcccdbcadaaaccbbbbacbdabcdaadbbaacdbabcdaaadbbabadbbadbaadacbabbddbaacddaadbbdddcabacdcdbcdbaaaadaadadbbdacadbbbabdbdbcaadaaccbabaacdadaabbcdcddacadccbcdabdcaddcadbddcacddcaccbdddaadccddcdcdadbaadddaadbbcbcdaaaaadbacdbdbbbddbddcbdbdadbaaaacdbabaaaacaacadabddacabdddbbaadacbcdbdadaadddaaccadaadaacabdacbbbccaacddbcacabbccbaccabbbcdcdacddacbabbacdcbcdacddbdacaaadaddbbddbcbbcbbdaaccddaacbddaacaddddaaaaacdddcdcccbbabdddccdcaaaabdabcdadbcabccbabcbaabcdbaabdddabbabacdcdcbbaaccdcacdcbbcbdccabadbccbbccccaddbaadccbababbacbbcbdbcdababdbadbbaabbddcaabddbdaddbdbbacacacbcaddaabcaacdbcabbcccacccdbadbdadadbbbbadcddccaabdabbcacabacccddbbbbbaaaacbbadbdcacdcddabddbdbbdbbabccccabcbacdaaaaaacbcdbcdacaccabdbbacdcdbbcbcbdacbbdbdbdaabcbadaaaccadacacbabaacbbadabdadcacbabbbaabcbadddcadbddaccabbabacdabbcbcbcaacaabbdabbcadaaabbdbbdcaccddbcdacdccaadcabddcadccdbdbcacccacccdbddcbcccdabdabccbbaadaadbbadaaaaaadcaaccbabadddbadbddbbaadcbbdbdbadcdbbababbbaabaadbdbabdcccacadaadcabcbdbbdbdbbacaddcdcbcabccaabbbdabbbdabaadbaababadcdddbbddbaabccbcdadbaddddaabaccadcbbbaacdcdaabcbbbdbbcbbdcaadaaacbcbddbbdabbbcacdbcdcbbbbadaadabddabcdcadcccdccaabcababaccdcaaccdbcaccacabbcbbdcacbabaddaabcddcbbaacaddadcdacaabdddabccddbcaabacbadaccaacadbdbdabccdcbcbbaaccadbabbbacccdabdcdcaadddccaabbdccaaabbbcbcbaaacaabdbcbdbdbccabdccdbbbccbaadabaacdcbbddbdababdadcadbdaddbbadabbaabdacbbbdccacdcbaacbdddabdcdaadcbdcbabcdacbacaaddcadbdddbdaddcbaabbaccdbccabcdaabaccacaabaadcbdbccaccbadccccdcddcacbdbabbddaabaddddadbddacacabdadaacbbaaddaababbbdbacdbcbbdaabaacaddbbadabdadbdacdbabacbbadaacdcacaddcaacdddcdccccbccabbdcbbaadccabaccbcacdddddbadcbbbbdbbadcabccacdcdcbabdabdbabaabbbbccaabdbddbdcbcaacacabadacaccbbccaaddbcaccbbbcacdaabbdbbccdbdbaddadbdcadbdcabddaadaadbabdaaaaadbddacccccbbcbdbbdbdcdaacdbcbcdabcbdccddadbcccbddaacaadcbdabbbabddabbddbaabccadbcbcddacbacaabdbdcccbbaadbdbdaabbaacaccdbbdcbadcacaddcdaccbbdcbbdcabdcbcdbbdbacdcbdcbcaacdacbcaabbaccbdcaacdcddabbcaaaadaababbbdbccbcbdaaacbadcbbdbcdbadcdacaadcbbdbdabcbdbccdaaacbcabcbccdadabcdbdbcdcacaddcdabdddcbccbddadbaabbdbbcdcbbbcbcaacbadddbcbbdbaccbabaabcdddcddacbabdadddabddcddccbdbddddcadabdabddaaaadccadcaacabcaccadbdbbcbbdcdddbcaddccadcaabcddbabcdbbdadcaabbbbbdbcddcacbccdcbbaaccaacdabdcccddcdcddbbbcadacddbbbdbcbbcbdbdcbacdacaadcadcbdadacbccaadbbcbbbcddcabacadbaccbbcdababcaaacbaaabdaadbdacbdbbdbbdbaddadbaaadbdacddddbbadddbbacabacabdbbdbdacdacdcbadbbdddcacaddbacccccbcbaddddcbcaaaaaacbacbbbaacdadadabbbdadaacabbcccbdcdbbbbdbbbdabcddcaadbcacdbbabcdbaaaaadddcdbbbaacaadccbccdbacacbcacaccbbddcbccbcacbccccdacddddacbdaaabadaabdbadccbaabdbddaabbcdabbbddcbaabdbadaaadbaaaddcbdcadbdacadcbaadddbdcbddcdcdcaaccdabcbcaacabdbbcddccbaadcaadaddcccddcccadcbbbacadabbccdbcbdcdbbbadbcaaddbaddadadcabbbabaadcdcabacbcdccaccbdadcdabcdacdabcccadaccaccbdbbdcabddbbdccdcccbcadcdaddacddabaacbbdbabdcaabcabbcbbcacccdadacabbcbabdccbacddaaaddabbcbdadadddccdccdbbabacccddbbdbabaabdbbcbaadbdbddabcdbddddaaadadcbcbbdacaabccccbddcdcbcdbbdcdbbbcabcccbbccddbbccdccdabaddccccbdbdcaabbacaddacdabdaddcaababdcadbbddadcbadbcddbdbccccbbdcbadddbcdcbbadcbbcdbdbbbacbabccccabcdaccddcdabadcaaddcadbabccdddbdcadddddcbdbddbabcdbbbccbadadcacdcbbbacacdadbbddbdcbdcdbadcbdddcbbdccbabbdaadbddccadbaaacdcdbaabdbcabbaabdadccbbaccaddacadacdbdcdcccdddcaaacabbddaacbadbbdaccbcdabcacdccacdbbcdaacacdaaccaddccdccacccbadccdbcaccdccbabadbdbdacaddacdadddddcbcccaacadbccadddddadbacbdccbcbcbcddddcaaddbabbbbcaaaaaddcbdcbbadccbdaaabdccbbabdcaccbadbcbbbdcacbabdaacaadbbcacababbbdccabbcaadcbbbbdcdbbacbabddbbcddaddaacadcbbdccaabadbaaacbccdaacdddcdbbdcbcbcadcddcdacccbcbacaccadbddcdcbbaddcddaaabddddbbcccccdbcaadaccccbdbccbadcaaccbccaababbdccdadcddaacbddbcbabcdcdccccadcadcbaacbbbaccddaaadddbcdcbdabbbaadcdaadacadaccabdcbcbdacccdbddbdbcdbaadbacabdabacbdaccdbdccabdddacddcbbadbdacbadbddbabbacacbaacdaccaccbcadcbcadcdbcdbcabbadcddbcbdbdbacacdaacadbdaaabdbcacbcacacdaaaadbbdaccdaccdcdadbddcbadbcacaaacdcdaaaccdcdddcbdbcddddccdccabcddbaababcbdadcbbaccbddadbcbbddbcbbcdaaacadadadcddccdcdbdbcbcdccaacacdcbdcabbadabdabbdbddacbddddbdadcdddcbbaabacaabacbcaddbaaadcaacaacbbcaddcabbcdbabaabaabcbbcbcbbacacdaacbacbabdaaccccdabbccbcbaabccdcbbaabcabcbdbbccccccacddbbabbdcdabdcdbcacdbcdbbbbddbbdbcaaccbacbacabddaadbccdcccccccbbadaddcccaddbbccdabcbdbcaaabdccdaacbcaababcbcbdbcabaacabbbccabcbdbcddbcabaacbaaadbccaadbbbabdcddaadabbdbbaaddccbcddcbbacdcbdcccddadccabaadcabbcccdcabbbbbcdbddbdadadcdabdcdbbbababcbadbacbcbcdbbbcbcbbdaddadcacbcbbdacaccbbcdcdadddbaccdbdbbabbdaddbaccacdccbdbbdacbcdcbddbcdddbbdaacabcaadbddaccdbabdccdccaacaddaccdccaabddbdddddadadaddddbdbdaacabcbcdccbccbbbcdbacdcdabcdaaadabbaadabbbdabaababbacbdcaadbbadaccbbbbabbcbdacadbaaccadbaadaabcddcdcacadaaadababbccabbbaddbbcaadacddbcddcacbbddccdcbadddbacacbbbaaccbaabacbadcbacabccaababbccbcdddbcadcbdbbbdccbbabdbaabddacbbadcbdccbdcdbcbdadbccdabbddadcbbcccdcdbcabcdacbdcbadabdcadabdddaccbbabbdcbccabddacccbcaabdcbddbdcdaddbcaabdabadcddabbcccccbccccbbaccdadabcaaaabddbbdadccadccccabcaccbcddbdabaccbbdcdabdabaabddabbbbddcccbcccccdbdbccdcabdddbcdcbaddcabccdbccdddbcbaabbcacaccbadccdcdbccbadccacdaaacddbabdabababbccccdddaaabaccccaadbcaccddcbcaddacccddbccaccccabccbacdadabdbacabbdadbadcbacaaacbcaacdbcacacdbccdacdadbcbccadccccacccdbcbccbbdaaaacbcadbcddadbddadbbbdcdadcdbacadcdccabddcaacdbcdcddcdadcbacacbcdbdddbbbbdccadabbdbcbdbcacbbabbcbdaddccbacbddddcacdcabbcacdcdbdddccaadadabdcabaddbadaacbacdabcdcabcdbcababccdddcaaaabbddabcdcbcdddaddbbccdccabcdcdcdbccbddbaacbcacabdcbbdaaacccdcdabdbdcbdabaacdcaaaaadcdacbbdcbccdaacdcabdcacabcabddcadbdaabddbdddbaddabcddaaaabbacbbcbaadccabdbcabdbbccdaaccaacbaaacdcbbcddbababddcddcdbdbcacccadccbdcccddacbabdcbbbddcbdddcbbccbaddacabaccddcbdbadcdacccddddcdaabcaadccbcbcdaadcbdadadabbdacaccccabccbdcbccdbccdbbbcaabaccaccabacbcbdacbbcaddcabddcccdbcccbaacccbccdacaadcabbcdabbcadcaadacdacbaadaabbadddddcdacbdbccaabdcdbddcaddaccbbbdbcbcaccadabbacdbabbdddccbaabcbbdcbcbabaadabdabddcbbcabcbaccacaaddbcdbaddabcdbabcbdbccddbaacdaadbdcbbaccbdcdccddcddbdabccabcbaacbcbcadabcbbdaaaccadaaadcadcddcccbdbcdbdcbbacbadcdbaccadbbcbdaaacabaaccbdddaadcdcccdddccadcdbdabcdbadadaabcadbdddacdcadbcaabdcccbaaadcadacdabdcdbccbadbabcdcadbccaaaadccbccacbcbdabbbaaddccbddaacabbcdbcbabbccadadaaaccbcdbddcadbcccaacaddabbddcaddaabbabcbbabbaabbbcaccbddddbddcbabcabbbbabdddabdacbbdbbbdaacadcdcdcddccabccbbdabbdbadadacdddbadacddbbdbcbabbbbddbcaabacdddcdcbaaccccaaddabcddaabdcbddabdbdbaaddaddadbdbabbdbbddddacdbccbbcbaaadcaabbbbababaddddacdbdddcbbbddcbabdcaddcadacadcdaabdbdbcccbcacbdcaccaabbbdcabccbdbcdabcdbdcddbcbcaddccbaacbabaaacacabbddadddddcbdcccdbddabcddbdcaccbcddaacabcaabbaccbcacdcabdcdbcbabcaacaadcbbbcccdadbbbdbabcbdbbdddacbcdbbbaadcdaadbdcddaddddadddcadbbccbabdaddcdaaacaccdbbadcaccdbddbbdbcaaabacbbbcdaabaaddbacabacdbbbcacabdbbddbddcbbddbcacbabddcccadcacdaacbaabbcdbdacbdbcacbacadcaadaabcacabdcbbdaabdaccacaddccabacabcbbaadacdaccacbabdbaacdcaacccbbbaddbbbcdbacccdcbbdddddaacacbbdbbaaabccbabdadabbadbcbbadaaabacccdcdbcbabcdbdbcabdaaaaddbadacccbadcdbbdabcdacddbbbadacdcdbccbbacbbcdaddbaacbbadaacdddabbabacdbcdbbaddbdcaaccdacdaacddcccadcbddbbadacbabaddaacaddbcddbcbbacbccddbcbddbadaddaaaaddbabbdabcdaddcbaadcccacbbcddbcaabbaacaccbdcbcdcaacdacdacadcbbacddabcaccacbccabdcdbcbaddadabdccadcbdadaaddcddbababdbdacdcddcabbbcdaccaabdadcccbbdccaadabbbdbccadbcaadbacaabddddbabdbaabbabddadcbbcbaadbbcdcccdacdcacbccddbcbbddbabbddcacbccacdaaaabcbccccabdabcdcacabcabbadddadccbdcccadbbdbbaabbcccadbbdabacbbdabacbcdacbcbcacabcabaacacdacdddabbdbbcaaabbdababaacdaddbadacabacaabdaaadadaddccaaaccdacdcdbaddbacbadacddacbccbdabdcdcaaaaadcaccabdbaccccdcbdbadbabbbbbdabcbaadabbcdaddddbccbbaabbbdbcdaaccbddabcadccdbcadbcbadbacccbccbacaddccdddbaaddbbbdccdbdcbcacdccadaadccaacccacccaccdbbaccbcccbaccccdbdcdbdccbcdcbbbaadacbccbccccaabaabbcbacbabababcbaddadbdddddbddddcbdbbdabdbbbcabdadaabccbcdacabbadcaabadcabbcbcbabacbddcbdacbbcdaacaaadcbdadcadddcccdddadadbdbcadaacdbaacabccbccdbabacdadcccacbcabaccddcbabbaabadacabdadcaaabbbabdaaddddadaabcaddbabdddcbccacbcdcabdbcbdccddacdadddcbadaddadbaacbbbbdbaddbbdbcabddbacdddadbdadbcbababbaacacbcbadaabdccbcaaacdccabddcacaabdbbbbbbcbbaadbdddccadabdaaaadccbdbacadbaaadacadddbbabcabbbbaddbcdbbabcabcbadbadddcbaaddaaacaccdddcccaadcbbabadcccddabbdabdadbcddcbaaaabcaadcaaddbbcacbdbadcccbbdcabcacabaacabaabcdadddcbcbacaabdcaadababbbbaacaaabcbdbcbbbdbabdcadcdccaaacbabcddcaaadbdcbcbabddcbbcabadcdccdacdbbcbbbabaaccbababaacddcabcdbbaacbdcadacaabccddcaaaccdcadabaadcbdbbbaacbdccbcacadadccbaacacddcbdabbbcbaacddcdddcdccdabcdbdbbcabddddbcbdabadaaadddadcbccbdbdcaadcdcdabcacccbdbaccbcdaacaddbbdcdadcbbbaabcdabacbaccacadcbdadccbddccdaccddbbbdcacaabcdbbabdaaccadaacacbddabcadbbbdadbadcabacbcacdddbdbbbcaadaaabcabbaaaaddaccacbcacbcadbbabaccdbdbcdccbcaaaadcbbaaaabaabbcabbbbddcabaccdcbaadcccdbbbabbbdddcddcbbcdbdbcabcbcdcaddadcadadccbcccdcbbdbadbcaadbbbcddbbdcaccbbcaacdcadbadccabdcacdaccbdcabcdbacddbbcdcbdbcaaacbdddcdddcbdabdaaaccbbacbabdcddcabaccdbaadaddddcbdaabdcbdccaadaaabdcddbaaacbbacadddacddcddbcccacacddabbbadbadabdabcadcddbbbcdacadbddabbabdddcaabacbcbbbcadddbadddbacacbaabdaadadaadbacbaacbdabdbdcccaccbbbdbadccacbdbaacddcccdabacaadbadbbddcadadbaacdcccccdabbbabcabaaabbdbbdaddadddcbddcbbdbbcadccccaccbaadbabccbabdbbbbdcbccabbbcddbcdcbbabddcacdbaaadbcbcbcbcacccbdabdddabdccdabcbaadbdcdbadcddcdcbaadcccabaabcbccbadbacdbacabbdacaaabacacbcabcdbbcccbbbcdaaacbbbaaacbbcddcacdddaacacdabcacacbacdababbdababaddddadbddbdbddddcbadaabdbbbbccbccbdcdbabbcaacbbbcbdabbbdbbbcbdacdcadbacacacaccacdaaacbaabcddadbcaaadcadcdcbcacacbdbbbbcddbbddddbcdcccdcbbadccdcaaccbccdbcaaadacbbbabdaacdbdabdaddcddccdcdcacccbdcbddcbbdcabdabbdbdabaaccaadbccbaddbdcbbdcbdbaabcbdbbabcacaabdcddddccbbdbbbdcdadaddddbdbabbaaaacbdacdcabcbabbbbdbbcdcdbbbcabddcdccbbdbcdddabbdbdababcccbccacabbbccadadbaadadcbcddcabdcacaaccdabdaaaaaddccabadcddacbbacabdbbadaccbdccdbcaabbaaaacbadbcacdadadbacccacbdaccdbcbaccdacbbcdddbadcbdddadaabdbcadbddbcabbcadcadaaccaabadcbdaadbbacdbdbcdbbdcaddcabcaaaacccbbddcaddddabdddbabccdcbbadbabdcccbbcabacccacdabbcdcdcacbcaaababacbdcaccdacdcaccddadbdbacbdaddacacddbdbbadabdcbccdacabaddaadcdaaccdabcdcaadacabacbaddbcababbdabccabbaabdaaadabbcccaabbddccdacacbdabddcaaaddcadadbcbbabcbcdbdbcacdccdbccbadcbcadbaaabadcdbbabadbcdcbddcaaccddccdcbbacbacccabaacccddbbcaddcddccbabbccdaddcbaadadaaacadabcabbbaacbaddbaabcccbddcccbabcadadcdbcdccaaabadcdaccbddcdccacaaabbcabbdcdacadbbacbcaccbdcdbcdddccbcdbbbadbcacaaadaaacbddabcdcdaccacaccdcccddabdaddcdabdbbdcabdbdbdbbbbcbbbddbdbdaccbddddacdccdcbcdaadcddbdddabcadcdcdadbcddadbaaaaadadabaadbadcbdbdbbcddcaabbabcdacaacbbdbcbabdcdadabccdccdcbcaabddbacaabbbaaccabdcbcbcbcbbdcaabbccbadcdccbaaccdabccaadbbcaaacbabddcdbccddabbddcdacdbdaddddddcdaaabdddadbcababcbdddcdcbcdddccddbdccdcaabcabcbadbbbbdbcdaccacbbbdacacbddbaccddcbccbdbcdccdcddaddaccbcdacddbacdcdccaddababbdbaaddadaababbddacdaddccaababaadaccacacccdcbcbbabbbbcbddcddddacbddcaccdaccbdcabccdcacaddaacbddbabdbddcccabbcabcdddcaaacbbbdbabbabddcaaabddcdccdbbaabcddabcdbbbaabacbccbbcddacbcabdddabcbddbcacadcadbaadcbddcdaaabbaaacdbcacbbbddddcadacbbcbddddddccacaabdaddbddccaacdddddbdcccdcaacacdcbdcdcddaadccadadadcbcaaccbdcacdbacdbdadabddbcacbaadadccacbbbabbbdbcbaadddddccaaaabdbddcddbaaccdadbcadadbcbcbbcababdcbcaabccdbdbbdabacbcddcacdbcdccbbabaaadcaaddbbcaaabaacbacccabcbdcbcccbcadbbcabbdbccbaacabbbcabbbdcbdabcbbbddccbacdccdbbcbbdabbbcbccadcdcbabbcaccdbacdcbabababacdacdabbbdadccdccbcbcabcabdbabcacdbbbbbdbacabdacbdcabccbbadccadbaaaadbbbbbaacdbcddaadbdaacaccadbcbcadaacadabbaddbacccbbdbcdccddaadcbadaddcbcbacdaabbcaddcadcdbdcdddddbccdbddacdaadbadbccdcbcccdcbdabbdacaacacccbbbaabddaaacbadbdcdcababccbcdcbabbacbdaddccacbcabcbbaabbacacccaaabbabddaaacbbbbbadaaadccacccbbdadcdddabacbaccbaccbdbdbbdbadaacaccddbdcbcdbbcbaadccbbcdbbbccdaacaabbbdaaaaaadbbbcbacbcdcdaccaddbddcaccdccbbdacaacaddbbbbdaccddddcdddaaadbccabcbadbbbbcccbacbbcdaaaadcbccaabccdacbcbbccccabbdbbacdcacaddadaddbaadccbcddcbdabbcbcbbccdcddaadddbbdcddadcbbbaacdddccdcaabadcdcccadcdaabbaaababcbacdbddcbaaddbbddabdbdcbdcbbacbaaddacbcbdacddbccdcbabcdbbacdcabdadbadbcabcadacbbcbcaaabdbdaabaabddbcddadbbababbdacbccaccbdddaaabaabdaabdcccdabccabcaadadadaabbadddcadbbddcabcaabbbcacbbcbbcdbacaadbdddcacbaddbbdacdbcadddbcbadcdbdaabaabaaacdbabcbabcaaabcbcccdbdccdcdaabbadbbabdadcdcbbcadcbbccddabccacdabdcdbdcbdcccdacdacbacbdacacbacddaaaddddcbcbadadddbbdabbdaadbcbabdaddaabbcabbbcadcbaaddbdacabbaacacbddcbaaadcdbdddbbcbcbcdddcabdacbbadadccabdcdbaadacabbaddabdcadbdbcdacdadaaaaaabbbdacddbcacaaccbadbbacadaaabcbbabcdbbdcacbbabbabaabdaccaacaaadbbabaadbbcadabaccccbddbdacadbdbaadbbbdadcadddccccabbacabcccaadccccacacabcacbbdbdcaccbadadbccacdcddbbbabaddccbcdaddcaccdcbccdbbadbabcaadccbcdbaddaddbadadaddacadbdccbddacdaaaddacabbcbbcbdcdddadcbccbacaaaabdccdbbddbcabbbdacbdaccddbaaaaabbcdcdabaadabdbcbdbccabdcabbcbbbbbaccddbdaaadadbaadccdcdbadccddbdabdcaaccabcdabbaddabcabbbaacbbccbcadddaadbbcbcacbaabaabcdbccacdddabaaccbabadccdacabcccacbdcabdbabdcdddcdbaababaaadbdbdadccbadaaabbcbaacaaaabcbacbabdccbdbbdccabadbaddacbcabddabcdbdaadaaadabddacdbbacccbcdcbdbcbaccaacbbcabdbabccaacbcdaaaaddacdaacdbcdcacdbcacabdbcdaddcbbbaaabbdacdadcaddbdbdaabaabcdbdbbdaababbcdabdcddbadabcbccbacacadaabbbdacbabbacadaccabaddbddbaadbcdddcdabcadacbdbcacababccaabbdbcdaaaacbbaabcdbadddacccaaccbbbbbaaccbbbcbbdcccaadcbabbdcaddaaabbacccbcadbcbbbbcdcccbbdbddbdaddbbcbbbbabbccdbddbccaddccdadadbdddaaabbbbcaccbdabddcaacbaddddbcddbbbddadcabaabddaaccaaddbcbdaadadabcdbbccddaddcbbbbabdadbaddaaacdbbcabbcbccbcadccdbbcddadaacaadbcacbaacbadaaabdadcdaccddcccddabdaaacaaadbcbaaddcbccdabdacacaacbccdadcdadcbddcdcdcdacdababbadadcacaaadbbacdbdcdaacaaccbccabdbddabaaabcbcaacbcbabbaacdcbbccdbdaadbdadaaadbcadddacadabdadddcbbdbbdbdcbdbdabbbbcbaabaabbaacacdcccddbbaabababbcaacacccdcbccdddbabdaadabdbbcadcdbacdcacbcaaaddbbaabdacbcacbaaaabdbdbdacbbdbcdabaaacbcacbdadcaadabbbddccaddbbcabaaacbbcaccbcbacbaddcbacaacacaabbcbccaaadacbaadaddcaacdabdcadbabdcbcdbabcaccbbacbcadaaaadabbdddbbcbaccbcabccbbabbcacddabadaccacdcbadcacadadbcdacaadaaabdccdaadbbcbdabcbddabaddacbadbdcdacccabcbbdacabdaabdcaaabcdbbcabdbacdadddbbabcabdabbcbdbcddccbcbadacaddaadadcacadbcdcabbdbccbadbadabbbdcbdbccccbacabcddbdacbddadcadccbacabcbcccbdcdcccbbddcdcddcaddbcdaabcbbccabbccdbddcdaabdacbdbaabbcdaaabcadbabbaddccabdcccbdcbadddcdbbcbdbcaacdbbcddccdcddcbabcabbccacddabadbabdddccdbabdbbdbbccbacbbaacbdcbbcdabdccddcdddcdbdbddbdaccbaaabcaccaabdcddccacdbdddcbdaccbdbcdcaccaacdaaaacddcdcdbddddacddcddcbacabcbdadccdbddccbcdbaddaadbdbbcaacdacbbddbaddadbbbacaacccbdcddaddabdabbbccdbbbdacddcabcdbabdadbabcbbbdbcbbbdaaaadccdbcaddabdcbdbcaacbbdacbcdadaddbcbababbbadbccbcccbcdbdcbccbdcbbacdcccdcdcdcbdaadbbbbbcdcddbacdacddbddaacadcabdbdabadacdbadaaccadbdbbdcccbdcdaaddaababcbdbabbdbdddddacbbabcbbbccbdadbbaabadaccbdacacaccaaddbabdacdcadabacabaabadbdbbcaccbadbdabddbcdcccaddacaccbcaabcbaadcbcdacdcccbbdbadddbbddabbabdcddbcddbccdbaaababdddaddbaabdadaddcbdacccbcddcbccabbaabccdcbcaadabbdddbbdbaccddbaabbbacddbcadcaccbdddcacaabaabbcaddbadbcdcbdbcacbdbadaabbaabdcddbdddccdcbcdaaccddcbcbdcbbadddcdcadcaabbdaacabaaddabbbdbcbbacabccadcbbbbbdabdaabbaddaccadbdcccdccacabcadcdcaabadbccabbabdddacbbdadaaaacbdbddcbcbacabbbddbcabcdadcbadbadcabadbcaaabbbbaaacacabaddbacabacbdcbdcdaadcacddcbaaadcacdcbccbcacdaacaabbdddbdcadaddbacaabbccdcbccddddabccdbaaaabcbbcdcbbbbcdabccdbbcbcadadcbdacdcddadaaadcdbdcbdababdccbcdccaacdaaccbbcdbabbddbccdddbbaabddbabcdadaccaccaccddbdddabddacbcacdccaaabdcacccdccdccbcabdaddadbcadbdabccccdaddaaaadabcadabcbdcdccccabadbdbdbdadaadbaccdacddcddcababadcbaccdcbaccbbbbdddbbddaabbabbabcbcadbababcabbcbdcbabadacaccabdbccdcbaadcccbbbcddacbddcaddaabaddacbdbdbdcbaaabadbddbbdbcbdbacdddabbbbbccaacdbbaddbccbcdcbbdcdacbbbbccddbcddcccbdbdddacaacdaaaaacbbdbccbddaabccacbdbbadadbbdaccbddcbcbbcbccaccdaccdcdcbcdbacdbababddacbdadcddadcdadcbdbbdabaadbdabadddbdddddddbaabdcbcdabbbdbabddaddacbcbdbcbcaaaccbdcdbcaddddbdcaabcbabdacdaabcbbbbbaccdaacbcdbdcdccbcbdbaaaaaccadcabbbbacdcbcbbdcbaccdbbddbcdaadcbadacacdbdaaadddcccccccbddcbadbcdbccbdbdbbcddbbccbaaabccbabadcacdbcabbabcdabbcddbcdadcbdbadccdcbadcccaaacdcbdadcbaabbbadbacbdbcadadacdbbaabacddbbacabbdacdcddbdbcbaabcbaaddbcddcbbcbcdcbcbcbddacbbbdbdabbcccbbbccbdcadacabdcdccccdabbabcaadbbcabacbdaddcdbdcbaaaddbaabaabdabcddadabcbcbaaddbcadbbdcacdabdbacaaacccccdbbcadbaddcdccddacabadbabbccdcddbcccdccabdbcabcabbcbccabdcabcddbabccacbbacbbbdbbacdddadcaacaccbbabdaabcdaaacbcccacbddaddcdcbddcccddabccbbacdbdcbbbccaddcddddabcdbccdabbdddbabaabdabdbcbcccccbadcabbdbdbaabdbbcabbbbabcbabbadcbcaaabbccbcddbadccdcbcbdbabbcdadbcbdcccccddcccdbaacaacbbbcdcbdcbbaacacdacdbbabbbdbccbddccbaabcdbdccdcbddbccdbdccddddabdbbacdaaddaacbaddccbcbddbbaababbabcddcccdcbcddcbbdcbccdccacbcbdabacaccdccbacbcabbdaccabcadccdabbbabaaccadccbdcdcadddccbaddabdbcbcdccaacadbadabcdddbcaacdabdbdbcacbdcdaabacdadddadccdabdaaabcbaaaacdccdddacddcbcdadacabadcdbccdadabadcadbcdaaadcdcacddabaacdddddccbaccacbcbcbdcdddcdbcabbabcbaccddbbbcdadadbabacbacaacdadcddbbdadaaacadcdbdbdcaaabcadccbcacbcdbccccdccabbbcbcddbbacdcbcbdcbdcaaacacccabbcdbdadaaaadccbdbcccaaaddacbaaaadbcdbdbdacdcbadabccaabdabbcabbbbaacabdabaabbadaababccccaadbacacadbadbdcabbcaccccbbbaadacddbdabcbdcdbbddcbbabadccacddbcacbacaddabdabadbbcaacbaaddacccbdbaabdbdabacbabaaabadabaaacccbccdbcdbcbaaaccddddbbcdccddaabbcddbbdaacddcbddadbaacabbccddcaaccadddccccdaaadddadcadcdababbcbbbccdcccdccbbcdcacbdabbadbabbacdddcbabccdcdbcdcdaacdbadabdcdcaacccdadaaaadbcaaddcdcadbcadcbacbbacaacbacaaabdbaaccaddadbddacaacbcababbacdacbcdbdaabcddccacbadbaaabbdacacbabdacddbaddcbbaabdbdcabddadadddbcdcdabdabbbbbbadbbccdaadbccacacabcdbdccaddabdbaadaddcbbddabddcdabdcaadcdbdaddbcbcaaddbdcdadbbbcddabccacdacadbbabdaccacccccdaacdaaabdadaccdbcddabcbcdbaadbbbcaddcbbbaadaaaddbdadcacadbdabcdadbadcbbbccadbbbbabcbaaaddccbbccacdbacadddbadacccaababaaabdabcacbabacccbcbccddcddcbcccadcbddabdcabdccdbadbddbabadbcadcccbbdcaddbabbcbdddccbbbabccbcaccccdbcbdcbbbcddbddbddbbcbcbccaaabadcadababbcddbcdbdadcbddddcbdddbddabcaccdbabbdbababaccbacbbcbcadcaccdcabddacacdcddacbbabcdadccddcdadaddadabaccbddadabacddbddbdcacdbdcddadabdbdbddccaacbabbbabcabbddcdcdddcbcabacacdcacbcbbbddcbcbbabadacccbbacddabdcbccbbdccacdcbbbabcacdbaaadbbcccdacdadabddcaaccdcbcbbbcadacdabbbcadbacddbbccdddddcabbaccadbccdaadaacbcbdabaabdbbacbbaabdbdbbdadaddcdddcacdbbbccdbbadbbaaddcbbbdcddbaabcaabcbbcbbbcbbccddbbdcaaddadbabbdbaabbdcbbabdbcdaddabddacacbdccddaaadaababaaccddbdbaaddabcbabbcccbdbacddadaccccdccdbbdbaaccdcddcbcbcdacbcbcdcddcdcbabddacdbbbadbdcdcbdbcabddccacaabcdccabcadcbadddbadcabadabdccdacbccdadccadabcacdccaabddcdaacdbdbdcdcdacbcdacbaaabccbcbbadccbbcacbdcdccacbcdbbddcdddbccdbcccaadbbbabddabdddcdcdcbaaacabaaabaddaaadcbddbbcdbbddccdcbcadcbbbaccbabcccaddadcacbdccadacdccabbcbadabddaddacaabddcacbadcdddbbcdcbacdcbccccbbcddcbacccdababbadbdbdcdbaaacbbcccbbccbdabbbbddcaadcaadaaabdaaccccddbacadbacaaaabcccbdbadcdbdbadbacbcbabdddcbcadaaacaaaacdaadabbabbbadcabcabccbcdccddadddadbaabdacdaacddccdccccdcbcdbcadcdcdbddcbbbabbabbcaaacadbbdbdbcccdaaabdbdbbcdcadbbaadbcaadcdbcdadcacadadcbcdabdcbabdbbccdbadbcabaccbacacdadccdccbbdbadbabaaaddcdadadddcbadccbcaaaaccadaabdbdcbcdacbcccccbacbadbababacbacdadcaccddcdcbacadddacaccbabaabbbadbacbaabadadbabcddcadbdbaacaccbdbaaabcdccbccbabcaddcaaadaacddacadddaddadbcbbaccdacacadccaacdddacdccbcbacbddbcaabadacbdbadddabcacbdbadddaabbbdbccbcdacdadddbadabadacbcdcdbadcddcabcdaabdddbdbaadbbdadbdcbabcdccccacdcdbccbcdadccbabadbabdbdbbddbbbdcabcdccbdacddaadadcdcacaacdbcdaabadcaabcdbbdcacdcbabbdbdbdcdbbaaadacccccdbcdbaabacbabcdcdddbabdddabccbcdcacaddddccabaddcddcbdbcadadaddcccbcbdaaacaddcbdbcdddacbbcddbcdacbbdcdccddbabcacaadccbddddcdadacacdacabadbcaaadccadabdddbccabcadccdccbdacabddddbcbdcabcddaabdaabbccddbbbdbcbbdabccabbaaabbbdbbbbabdcdaccddbdddabadcaaddddbcadddcdacabcdccccbadbbdcaaddbcbdaabaaabdccadbdbadadcccbbcbdbcabcdaadcddadacbaabdbcdcdcdccdadaaadddbacccddccdddbabbcacacabadacadbccbbdcdaabccdbbacdcddbddbabadaaaabddcadcddcddccbbbacaacdbdcddabcaaacdccccacabbbbddadccdbaaadcdddbadcdbdabbbdaccdddcbbddbbaaccbabaacbdcbbadddbbbdacddcababbaaacdbcaccdbdcacdcbabaaacaccadaacdccaccdcaaaccdbaadcabdaaadcbddbddacdacbbcdbaccbddbcdadadadbabdbcccdbcbdccdddaadccbcbcdabdadbabddacdcdbbacdadadccddddadccaacaccababccdccabaaccdccbadadcbcdaabaabcabdabcddcbdcdbdaacbddbbdabadbdbdcaccbccabbcbaccdccacaccdddaaabdbaaaabbccbbabadccdddccaadaababacbcdcccbddaddbbcabababadabcacdcbaccbcabdadddbddacadacbccdadbabdbccabbbbbdbcddaddcbadabbcababcbacbcddadbccccdcaaacdbcabbddadcbcdccabaabcdcaddabbbddcbbbcbdbbacbdddaacbddadcdbbcabdcdbccdcacacbaccdbddbaabbdbcbcddcbdbcccadbccbddaaadaadbcadaddbcbdcbadddadcabdccbcbdaabacadbbdbccdcccadacadcdbbaaddacabdccbbbdacdcbddcbcbdaadbbdbbdabccbcdcdabddcacbdcccdcacbdaddcaadaacaccadddbbdcaccbdbcaddbadcabdbcdcaccdadaabccddcbbbcaadbbbbcdccdcdabcbbbbbbdbbbabdaaabcbbabbbcacbcbadddbadadacccadadcabdcacbdabbddbacdcaaaadbacbcacdccaccaabdbcadaabacdcacddbcbacddaccdbbbabccbaddacbdabbcdbbddcabcaadbdabdadbccccabddacbaacaabbcdcdcccbcbcdbaaaaacbbdabccabcdcabccabdbcdabbabdaadccdcbcadabbcccdbadcdacbaccbcadccbccacddbcbbadabdacdaddbccbcababdccbaacbabbacbdcbcaadccacacaaccbcdddbdbbccadacadabcadbaadbabbdcdbdbdabdbbccbbcaccccdbabdcacdbddabdacddabacaaacadccbddccabbdacdcddbbcabcbccacbabcabbaabdddbddccccbddaadbcccaabcadbdacddcaacbdaabaccdabdaaabcdcaaddbdadbcdacaadabcbcddacabcbcbcdadbdabddbabadbbacbbdbbcdcaccbdadcdaaccbccdabcacdbabcdabaccbbbcddabcaaddbcbacaadcddacccccdccddacbbcbdcdcddbbddcbbcadccadbaaccadcbabaaabbdaaccdcbdbdaccbdcbcbdccdcadaacdabdaccdcdddbbcdccdcbcdcdcabcbcacaaabccaaaccadaacacadaabbcbddccbabdccabdabdacddababacabaddcbcdabdbbabdddaabdbbbddadcbadabdbadabaaaaacbdbccdbcadcabbadcabcbbcdaddabbbabdaccbcddabcddbbaaadcbaadddcacaadcabcccdacbcabacacccddccaacbbdbabbcbdabbabdcdcaacaaacddaccaadaabcaccacaabbabcbbcaddcacaadccacdbdddacdadbacdcdbdabdbaabcbbacacacaccccbbcaddbdddbcddddadacabdddbdbbbbdccccaccdacabccbdaabbdcaaacaccccabadacdcdcbcaddbabcdbbbabcbcaacaddbcaaadbdabbbdbaacbbbcdbabddacacadabdbddccbbabbdadaddccddbbdaacdcdddabcbdbbaddcdcccadbccabddddaabbcddabccaaddccbcaadbcbaadcabbbabddcadcdcbadaabdadbcdcbcadcccccabddbbacdabbdbabaadcdaddcccbadbdabbcdbabcaadbbdbcbbdabadbadcbaacabbbdcaccddbcdbcddddccbdcdbbbdaddbccbcacddbccacddaacadddcdbbdaaadccaadbbbccabbacdbaadccdbadcbbdcaccbccdbbccbcdcdcdcccacbdddddaaadaccddbbdcadcdbdaddddacdacadadacdbddbbbccdcadacadbbcddcdbabcbcadccadbbcbcddcdbbcdbbccaadcaaabdbbaccbabbadaaddaabcbaabdcccbcddbccacbaadddadacbacabacddcbaaadcadbbbdddbbcdabdbcdbbccbbbcddbdbdaadbccaabcbcbaacdddaadabbaddcbcccbacbcddabaacbcabccbacdbbbbbcbccabbbdbbbdbbcdcbdddbaadbddaabdbbcbbbdbccbdddbbcaadddacdbbdaaadbbaabcdcdcbdcbcacbdbaaccacacbcabbcbddccabaadbdcdbcbcdccbadbaaadcbccbbaaddabdcacdddadccdabcbaddadcbadbdddbdaababbdbcccacabcbdaaaabcdacbccdaacbbdcaacbccdbdbdcdcddcbdbcacddcbbdcabcdbdcacddbdcddddadbacdabadcdcbabcbcccdbaddcadcacacadbaaadbbacbabaccbadbcccacbbbcaabbadbbbcaadcaddbccaaaccbacddcbdcabacbdbcdabbbcddcadabaadbbccaabbcaacdcdacdcbaabacdabbbccdbbcdacdacdbdbbcbcdbaaaacdbaccdcdcacbacbcdccdaaccccadacdbaacdddbadcbadadbcddbccacbbaadbaadaddbabcabcadaadaabcadddbbaadaacccbdbccbacdddddbcbccbccdbdccdcbbacdabaabaccdacacbbbddbcbdcbdadadddadadddaccddacccbddddaabadccbdacccccbcaabbbddcbabacbaacdbcaccaadbdbdcacadabadccccabbdddbaaabdaadcbaaaddbcdbbddbacabddbcadccabcdaaabddbbccdbcbaabbdcbabdbdcadbcadcabbdbcccbcbdacbdbadbbbcdbacadcadbbccbdbbaccaabdadacbbcbaddddcbcdbbccbabaddccddacbdcddbadadbdbdbacaadcbbcabadbbabcabbcdcdcbcdbbbcabbdadacadcbadbdacacaacddbccccadadbaccbdcdcbabbaadcbcdcaabcdaaabcccdbaabbdbdabbdbcadcbbaaccddaccbadddabdccbdbdbabddabcbddacaabbdbbaaadddddbdacadbaabccdbadccbccddbdadddcdcadbbccbaddddbdaabddccbdcddbbdaabbabcbbddaabccacbccbaababbbcaadccbbcdbbaaccdcaacbbababdaaaaddbddbcbbcbdcdcbbabdddadbcbcdacdcdadbdadabbabacbddbbcbdaacaadccbbabdddcccaaabcdadacdacddaacdddaadaddcbdbbbbacaccbbaccbcccbcccdbddabaabaacbcdbcdadabaaccbcbdcaadaadcbacbacaabbbcabcddaabadadbbdbcbbbcadbbaccccbaaacdccdbbbaadcccbcabadbaadbdbdadcbacaccacbdccbddbcadcaabaccccbbaccdbdbbbbdcadcadddddbbdcdccdabaaaaaacdccababdcddabadcccabccccaabcbaababaadbbdcdadbddaaadabbabcaadabcbcdabbcbdadbcddacacdabcbbbddbdddcdccdaabbcaabbbaccbccbacdaccddabbdaaaccccdcbaabbcadbbcccaccdccbbbddacdbbabcdbcadabcddcbbabacdbaddcbddbbacbdbdacbddddaddbabdcbbdcadaabccbdbacbdacccbacbaaadbacabaabbbdccabcbaccbddaacbcdcbdcccdddbcccbabadadabacdcbcddaaddbacbcbaabcbcaadaacadbcdcbdaccbdbbacadbdbbcdcdbdaabdacbdddbbbcddcbdddbdccbbccadabbdccadadddadbadacabdacdcabccddbcdbacbbcaaacaabbddbcacddcbbcbacdccadacdcbadbbbbcaaadddcbcdcacadbdcbbbbdccadddcaaabcabcabbbbbbacacacddcacadddadbdbacdcacddccabbcbacdabacbdcbabbccdaacabdacbbacbbbdcbdcadcbbaaaabcbacdacbadccadbababdcddaacbcdacbdbdcddcaccdbcbaaaabaaddddacabcbdababcacaaacdacdbaabcbdddcddcccbdcbaacbdadcbcaacddccbaacccadabcbadbddcabcccccdccbcadbbaaacdcddcdbbccadadcbbdaaaaacdbbcccabcbadcadacccabbbaadcccadadcbaccdadbacaabaccdabaaccddddaaaabbcddccbcacadbcdbbbacbbcbbdbaddbcabbbadaadcbdabadabbbdccddcddcdbadbabdacacdadbadabbddbadbdaddddbbddcdcdacdaadcabccbcdbcbbcbddaadcaaccdbbccabbaadcccacaadcaadcddacbbacbbcaccdddcccbcdbbdbaaccdbabbdccdadaadbadcaccaccbdadacdbabdbddbbacdcbcccdacddcbbbccbaadaaccbcdaccbacacaccbbbcabbcbbdabcbdccdadbabcbdccdddadadcbccbaadaddcbcccbabbaacddcabbcdccbbaaabacdcabbddadacbdaabbbcaddaabaabbccabacdcaabbbabddddbccbdcdcbddcababccababcdabcbbbbcdbbacdbdaddddddccabddacdcaaabcddbabcdabcdadddbabdbdadcccdbaaccbdcadbabbcccbdcbcacabcaccdacbabbaacbdbabdacbadbbcabbcbadabcdbcccacadbdbacaadcabbddcbddbcacbabcbababababdcdcddaadbddabcdbcbdcdcbaddbdbdddcdbcbabbcbbaacccaabcabcabbbbbadcbadbaaaadbdcdddcabaacdabbdcdacdadbbdcbabccdbaddccaabdacbbbdbdccccabddbddbcdcbcdbccacccabaadcbacacbdaabacbdbabdadcdaccdabbdbabbbdbdadcbbdaddadbddbbaccdadccaccbdacbbdbdddcabcbddcbacbacbdccbabcccdacbdbbdcabdbdddcbdcbdbdbcacbabdaaccccbcbaadccbdcbadddcdaaaccaccabaddcdcdabdadacbbaaadccacbbcbcadcacdcbccdcaabdcddadacccbbaccdcaabcadccdcbadddddaccacdaadadaabbbbddbdcdbaacbccddbbadcabacccdabcbaacbbbbdabddcbcaccadbadcdabddbbacdcdabbcbbcadcdbadadccadbadaadadabcbccddbacababcbcdcccbdbdddacddbdddcaaacbcbcbccabddbaadccbadcbcababaaaaccccbcaabbabdcddcccbddbcddabbcbbbbadacdbdcdbabaacbdddddcbccadacaccdcabddbdbdbbbbcdacdbddccccacbaacddcaaacadcbddcbcdbdabbcadbccbcbcdbaaaddcddcbcccbbdccabadcaddacabbcccaccdcddabbaccbadbadbbdccdddacbcbaabdcbaccbacccacdabadacaabcccaaabbbaddbbcdbdcbbcacdcccbadacaccdcdbcababbabddcdcdcdddbcbacddabdcabcdccacdaaccdadabcacbbbbadaaacbdccdddddaccbadaaaaddddcbcadabacbdaddbdbdcacdacdcabdadbadbcdccaddaadcbddbbabacbcbdbbddcccbdbbdcbbaabaccadddcacddaccccbdaccbbbaccabbacdaccdcabdcadbccabbdcdbcacadabbddcbaccbcdadbbcddadccbddbcddbaddcacbbcabdabbcacacabcddabbcaaabaddcbaabcaddcbabbcccadbadbbabbcadbacdaacccacbccbddbadbdabcdddcbdcccaaaaabbbacaabacaadbdabadaabddcadabbdbbacacadacbddcdbcdcadcacaddadaadcadaadcaaabccdddbcbadbccdbbbbbabacabdbbadccbbbdbbcbddbcabdcbbbbdbcabdbbdcbbcbbbdadcbabbacdbbcaacaaabdcadcbcacdbbdbbcbccdcacdbdbbccbcdccabcabbbcbbddbaadcbabaccdbdddaacdabadcdccacdabcdcddaacdbddcdcdddabbacdbcbcbcadbcbdbabbcbacdddbbadacdcdcbddadcbabadacdabbbaccaabcabaaacabbbbcbbabcccabccdcdacddaaddcdccabacdaabcddbabcbdabdbbddbaaadddbbabcbbcabdbacbaabbcadaddcbcbdbabdcabdacabcddcacddabbdabcbacacbcacdaddaadccbbaabdbdcacdabbdccdcabddaaccaaadcccbaababccbbccdcbbbccbdbaacddcbaabaabcacbbbdbdccbbcdddabdcbbddbcbbcbbdddccadacbaabbbcabbcabcdabdbacaccbaabdbaabccdaddcacaacacacdddcccddcaccbdaaaaddadadadacbccbcbcadcaadaadccbddadcabcddbcbcabbdaddcacadcaabbdbcdadcdaccbbbbccbccdaacadbbbbaddacdacdddbaddacdbacdbddadbacccbdacbbcdacdbdbbbddbdabaaaacbbcbccdccacacaaadcabaacbcbadbddabdbacaaacbcdddabdddcddbbadbabccbcbdcdbbbccadbaadbddcbddcdbcdbccdabddabadccaddadddcbcdbdbdcbdbdddbdaabcdbcdddcaaaddcdbccdcdbadaaacaabbbabddccdcadbbbdcdcbdcabdacdabcdccdccdbacdcaabdddbbcbbdccdbdbdcbbdccbddcdbbbdaabddacbbacbddbdbdddccabbccbcdadbddcdddcbcdccabcdaabcacbdacdccbcbcccbdaccccbaddcdbddbccaaacbbdccccaccccacadbbddcdbbaacabdccbdaddbbbcacacabbdacdacccdddcadcabcbdcbbabadcacddbcbdbadbdcdbdadbbdaadcbbdbaaccadbbdbacbcabbdbcdbdccbbccbaabcdbabcbbaddcaccdbadbdcacadddadabbabcaaaccbdddadbbccabdccaddacbddbccbacbbccbbdbcbadbbaaabdaabbdbcdabacddbbaccbaacccdbabdbcbdbcbdbddcbbcabcabcaabdccadaddddadbcdadcdadaaaacddabbddcbddaacaabcaacabdddadcbdaabbdcbaabacbdadcadaccacbcccdbacbcaccacbbabaadcdbbbbadccdcbbbcdddbcbcacdbcdccaaaacdcacaadaaabbbdddcaccdccadbdaabcaaaaadbcdddcdabacbccbdcbdccabbbacbddcbbbccbdbcadbcabbbdcdcbaaddcaddcabcdbcddaaabbbccbbbaddacbbaccccbbcaddadcbbbdccccabdabaddacabbbcbcacbcccabdcccabbadaccccdcccdcddadcadadbacbaaddcbcdcacbdcdacccaabcaacbcadadabbabdddaaacddacbcabacbcdcaabbbaacdaaccadcdccaadcbbdbccbaadbcacccccbbbdcbddcddbcddcbccdabcacaccdcbbaabbcaacbabdadacbcadddcbbaccccbadaabdbabaddcdaabbabbbddacaacbacbdccababbabdcdcadadcbaccbdacdaadbddaddcbddbcaddbbbaaddddcbdccbbcbbbabadabcaccbbabcddcddbdaaaacddbdaabcdadcbcaddbadcddcccaaabbdccacacddbbcacadcddbabcaacdcddcbcaabcabbbaaccbbccabdcaddadcbacbcacdbdbdbddbcbbbacadccdcdbdccdcbcaccdbdadabbdaaaaabcddabaaaaaccbbabacdbbbcdbccacbcdcdbddababcadababcbaabddaddaccaabcbcacbabcdababccdaccccbbbbcacadccdbcbcabdcabadbccabdddaccacaacaacaaabacddbcbbcdababaabdabbbddcdabcadbdcadbaaaadaccbddadabaaadccacaaddabccaaabadbdbdaadabcbccabacbdcccaaabbcbaabaacaddbbddacddaccaddbcccacabccdbbdcababccccdaddcadaaacdbbdbbbcabbbdbccdbccbbcbdcadabcacccdccdcbcacdbaccdcabcbdbcacdcbdabcbdbcaaccdacbaabcadddccdadcaabcbdbbcddcdcbbaabdcccdbbabadbcdaacdbbbaacdbddabdbcddcdabcabdbccaddbaccbddcdccbdacdcdcacdaadccccbbbcdbbcbdbabcdbadcdaaaacdbdcabddddbbabbaddaabddcdaaddccbccdcdccbdcaaaacaccbadabcbbabdcdaccaaccaacbcbbcccaabbaacddbdcbdbcaddaabbacbddbaadcbbcccdddbcdcaabcaacdadcadacdabcddcacdabbbccaadcaacacbacaabbabccdaacdbcabddaaddcaaccddabdbbadbabcbbabcabdcabddbbbccbdccdaccbdaadaaccabddcccaddbadddbbcbbccacbbbbaaadbdbaadaabdacbbacdbacdccdadbbdbaaabddadbdacccaccccaacdcdbcababcdddbbaabcbdddddadabaadbdaadddaccccacaabcadbbaacccadcdaddcbccccccddcddadcaacaaddadccddabacacccbdcaccbdddccbbcaababdbaddbbddadddabccddcbdcadddddbcbcabdbbbbbccdbcbadddbdaadbdaacaccadaaaacadcdccdacabdccddbcbbbbbcdadbccdddaadbcdcbdadbdcbbabcccccdadaaacddadbccabcbcdccabbdbddcdbadcbcabcaacbbdcaccabbaaddddadbdcadcbdcadabbbadcccabddbbdaaccbabcdaccadbacccdaacbdcdaacbdccdcbaacbbcbcbccbaccadaaacaadcbcdbbbaaabcbaaabbdcaddbdcaabdccccdddddacdccadcadcabdbabdcdcdcbcddbabaccabcbadccbdcddcdbadacadbabddcdcdadaacaaddadbdddcbabbdaaacdcbdadcaacddcddbdcbadabdbabbcabccaacbaadbcddbdcaaaaacdacaaccdbbadadccadccbbdaadadccabbabaccadadbdcdbaccbddcccadbdadaddcbddddcddbcbdccbbbbacdcbdacaadbdddaddcabaabdcdcdccadababbbcbcaabdcabaaacaacabdbacaabaddccabbadbcadddcacbbbdbaabbcbdbcdaaaccbcccbcaddcdaddcbcaaddbacdaddadabddadccabaabcdcdbdabbcbbbaaacabababdcbbcaadbacaacdddacaddcdbdbbcdccadadbadccbaadcaadcbbcabaddbcbadccbaadbcdccdbaaacacbcbbcbabacddcadacacbddcabdddcbaddcbabddcbadaababdcbdabdbdbbdbacbbbabcaadbabbbacdddaaccbcbccdcddbbacdcccacbadaabdccacaaadcbcddbbdaddcdabadabddcadadcddcddccbddaadbaacabbcaaccbabdcbbbcaadaaabbdbcccacadabbdacdcddbbaaaccacddcadacccabbcaccadccddbddbdccbadbcdcadbcdbcbcddabcdbacabcbddaccdaaacdbacabbaddbcbcdcbbadbdbbdcbbccdadcdbcdbcaaabdcbbcdcacbddadaccaddbacdbccbaadbcbbccacadacbcbcdaaadbdcaadacbcbbcdbcaadddccddccadbaddadcadcdaddbddcddaccbddabbcbcabccbdbcacdadadcbcacaabdbacbdcbaaadababdcdbaccccdcbbbdaadcbaabadcddbccdacbdaddbbbbdcbccdcdacabbbadbdbcddbddddbccddbbacdadcdaaacbaadcbddddaddcbaaaacbbcccbdcaccbabcdbbddaaabcccacdcbcacbacbccbdcbbcbabccbadcdcabadddbbcadaacacabbcbcdaacccdbaacccdcbcabddabcbccadbcdabaaaabbabddbbaadacdadaaaaadacaabbbdcddcdadbcdbcabddbabcabbdbaccbdbcabcdcddcddcdadabacddbaadaccdadcdbbccccbaabbbbaccaacdaaddcdbaabdbacacaddcacaaddabccadbdbbdcdbcadbdaadaabdccbabbaadcbababadaacddcabdbbdcbdccdcbbaccabdbaaacdbbdbabbaabbccaaddabbccbdbcadcdbdacadaaddbdabcdbdabbcbaacabccaaccaacbdcaddcdabcdbbdbaddcdcdbcdbdcdbdaddccccdabdbbacdcbabbabcadcdbacccaadcacbaabbcdbaddccdabddcbabbcaabcdddbcaddbbabbadbaabdcdaadbbbcdcabddbcadbdcdabdadccadaccccadacabacdacbbacdacdaddbddaaacbaaccaddccadbdbbcccbcadacddadbcbccccdcadbadcdbcdaacbccccbcabdcdabcdcdcbbbbaccaacddbacabccbbbddbddbdbacbbcdabcbccbbbdccabdbbdbdbadddbdccdbddbccdabcbdbacabacdbbbddbcaacbdbaadcaccdbbbcabdacdbbbdbddcddaaaacbbddcdcdbabddbcadaabccccbcadbadcccdcdacbbbddaaddbdcaabbdcdbcdaddabdbabadacabcdbcdccbcbabcaababaddbabcaacbadcbbcacbdababddacbcbdbabcbcbababdbaddccdddbbdbaacbcbdbaccaaabaadbbbdcdaacabdcdbdbcbbbbaacbdaccddcacdcbacaaaaababcdddadacaccaaacdbaaadcddbacbacbdbccaddbddbadcbabdcadcbbdcadcdbdbddccaabdacdbadccaccbcaaacbdbacbcacabbcadcbbbcabcadddbddccabcbccbacbadcddbdcdadddbbcbcbdcbbdcbbbccdabdadbdaabcabdbdddddacbcadcadbdcbabcaddbccdbdabbbaabcbbbcdbcccbbacaccadbdacbcbbdcabdadcacbcaccbadcdbcbdbcdababccdacbdccadaacadddbcdcadacdccbaadcbbcbbadbcaabcdadcbadaadcbdaccdadbcbbbcaddccdcbbabdcabcdbcabacdbdbbabbaccdcdabddbdcdbbdacaaadcadadcaaacbccbbaddcccccbbaaabcddcdccdbbcbccdccdcdbdbbcbaaadcaccbccdbdabcaccbaccdadbcaadabadaabccbcbddcbcaacdaddcdbddcacdddcdbbcadaabbbcdaacbaadbaacbcadbcacdcbaadddababbadcdcbadbaadbcddbcdccbcbaddacacababdabccadaacbcdaabbccabcccbaacabdcdbaacacaddbdcadadddbabdcadccaccccccdcacabddabdbcccadbdbbbbbdccdaddacddabadbdcacdcdbcbbdbcdacdccccacdbbbdacbccbdaddcdddbdabdbaabcdccbcbcacdddbcaccdbddbbacbaabcbbdccbcabdaadbdddccbcbaccccbdbddbdcdaccaccbacbbbbcdaaddacdaacaababbccbbcadaabdbcadbddcbdcdadaddaabadcbcbddcaacbccacbbababdbcabacabdadaaacdbddbbddccbdcdbaaaacbcbbbcdcacdcabaaacaaccabbddaacdddcbdcbdbacbcbacbdabdcaaddacddcacccadabccaabddcbdabadbcddcbbcaddbbccabaaaabdaaabccdbcabdbcccacdcdbdabbcccdbadaaaccaaccdabccacddddabadadbaadaccbbbcabaaddbaabbcadbaacccdcbcaaaacbbabccadcbbbcddcabdacdccdadabaadbdbcccccadcbdcabadcacbaddabdbabadddacdaddbbabddcaadaacacdbdddcadcdbcccaccaccdaccacbbccaadbbaccddccccccaabdabadbcccbbacbbbdacdcddcbbacdabbacadaadbcbdcccdaabddaabdcacbdbcbbabbbaaadbbdacbcddaccdacccbbcdabccdacbdcacdcbddcadabcabbbcbcdbdabadbbbccabcdabcacdbbadcddacaacbbcbadbdcddddacdcbcbaaccdbcdcaccbdddddabaaabbbcdacdbcaabaaacadccbbdccbbadddaddbcdbbaaaadaadbccdaabacccdcaabdbababadccbdabddcdabcbacabcacbdcccddabdbccbdcdaccdbbddabbadcacaddacadddbacbbccbccacaaddbcbccabccadaabacdccddaacdcbccbbabadacdddcbdbbabbdcbaaccbacdbaacabcbbcddaacbdabadcbddbdacbcddcddcbdcdccdbabbcbbdbbabcdbbabddadacaababadcbdacaadadbbdccadadbccbbcddcacbcbdbdbbbacaddddbdaadabcadadbdcbcbadcbacbbdcadbbbccbccdadaddccdcbcdbaaddcabdbaaddcababcddddabbbacdbbdbdabbabbbcacaaabccddadbddcdbabdaddcbdaacdbbdcaadbcdcaddcdbcabdbddbcbbbcbaddbdbddaacddccaadaacdcaadadbdabddcbacabddbdbabdadcaaabdabcabbddbccdadbdddcacabcdadadadaddcbcdaaccbacaccbcadbcabbdcccdbacbccdaddccdcdcbaaccddaddbaacdcbaaacccbbcaabdbbcdddddddabcccdbbaadacacddacaabbacadadbaaabccbcdbcadbccbbadbcabbadaccdcdbbdacddcaadaabaccddddcddbbbcbcabdadbadaddbcdcdccccccbcccdadcdcaacacaabacbdbdbcbdbcbbaccdddcbbdcdcbbcddbaddadabbcbdadaabaadcddbbdaadbccccbdadcdabcbcddbbdbabcdbaacccbbbdadacddbccccabcdddddbadababddbcbccccabdcbbaacbdbdaaddbabbbabbccccdacadcadbbcbcdcbbaccbcddaadaadcddccadcbdbcbddccdccdcadbabbacddcaaabbddbbcbcbabdbcabbddcbacacabbbdbdbcdccddbdbcbdbbddadcccbbbbcdabbcadcbbcaccbaccadbabccdbdabdbcbcabcdccabbccdcddabacadcdaacccabccccabccacadddddcdbbdcccbbdcdccabbacdcccdaaddacccdccdaacddbdbcdcacbcdabcadaaddbcacbddddddadaccdcdbdaabbabadbadbadbbddabddaadcbaabacbcaacaadaaccbcabdabdacccaadbdbbacbdbbcadaaddbbdbacbdbbdcbdbdaccdcccbaabbbcaaababadddddadddbbcaacdccaadadbababcbdbcadaddbacddbacabdcddabccdbacdbabdbddadcddaabadacbdcdbdabbabddcdacdcacdbbabbbadadccbbbcbdbdcbabbcdbcdcdadccbaadcbbccccadcbabaabaaddabbddbadabdbadcbcbabbcdddbbddbabadaabdaababcadcaccaddcdbdcababdccddabacddbaaaaadbdadadddcabccdacacadbddbacadadcdbcdccabcdcbbcdcacbbbddcacbcbbcbcdbadbcddbaddcdbabacaaaabddbbadbdbdbbddcbddbcccbddccbbbaddadbadbaadbaababdabbcbbcccccbdccacdbdabbbcbdadcdcaacbcaaacacbccbcbcbddaabbdabccccdcadadcdbdaabcbcdbbabcdcbaaaaadaaacbbcbcaabaddacabdcbbbaadccbababbcaadccacddabdbbccdacdbddbccdadcddbcccbddabbdaccacadbccacaddbbcdcbabdcbabddabaaadcccbabdddbcabcaadddaadaaacdbabbddbdbcabccbbbadaaaabccaabcbadcaaddbccabaaacccadbcabdcdaddcbadcbbdbcdbdbadacccdcacabaccbbcdcaaaaacbbdbbbdadcadaaddbbbdacbccdabddcbbccaaaccadcbdabcbacdddaaadadbbcbbadbbbaccabaabccdabdcdbabdbabccabcbddbcdabcddacbacabdddabbacdabacaccccaddcbacdadaabaadaaacadbcdaacbcbadabbbdadbddbacaccbbdaddaaabbbbdcdadbcdabbdbbbdabcacbabcadcaacadcaddcbdbdcaacadcaccdcdabddabaacccdcdbcaadabbbbbcacdddbbbdcbdaabdaadabdaaaddddacbbdbbcabbabccbbccbcaddcbbcdadaccabcbcacbbdcacbccdacddaaadbbdbccccddaadcbbbcbdadadababbcbdabbcaaccccdabbacaacdcccddabaaacbbbbaaacacdbaacbdcdccdabccdddbcacdcbcdbcdaaadbccaacaaacdaccacdcdbacdddbcccccbddcaddbbcabaadcccabbbdcdaccacdaaaccbdabacdccbbbdaaabdbcdddcaabbbcdbcdacddcdadbdcddbddbcdacacdcacdcaccdadbcbabbdcabdcdcabbbdccccdaddacadabcbbbdcacbdddadcdbbaaccabdbadabaacacbccaadbddcdbdbabaabbcddacdbcdcaacbbcdbbacdccddcdbacdbdcbaacbaaddcaabcabbbacbbccdbabccbdcbdcacbaaadbdccdabadcdaddabbcbdaadddcdcbadbcabccaaabccbbdcbbaabbdbcdcdddcdaabadbdbdddcbcacdccbabacbaccdbbdcbdbcaabacadacbacdcbcdbbbcaadcaadcdddbccdadadcbdaaadbbdaacccbcadbbcdabbbbddddcbacddaaccaadbdcbcbabcbcdabdbcbbccacddcddcdbcbdaaadbacdacaaadabacccadbcaaabcacacbbcddccabdaacadaaabbcccbccbabdbaadbcaaabaddcbcbaccadccbaabdadbabbcccacabcbbacccaabccdcdacddbbadaddcaabddbdacdddbdbdbbbadadbbdcdbabccddacbcddcbdcdddbcbcaadcaaccdcacdbcddbbbbcadbadcdacaccbbbaddbbabcbacbcaaababadbcabdbcbadbadddddadacbddacadbabcadadabdcccbbcacadddaaacddddddbabdccbdbcaacabccaacabbbdaccaaadaaaccacbadddacadadababdcbcadddcaccbacbacaacdbdabbdccccacdcbadbdacbdccdcaadbaadcbcbaadadccbcbbccabaaccabcacaacccdccbccacdbbabbcdbacbaabdacbaacaccaddcbbbddbbdadbcbbcdabcacdccacdadbbabcabbccaadbcbacdbdacddbdcbbdcadcdcaddacaaddccbacccaaaddbbdbaddaaaddaaaadbbbadddaabaadbcdddcddabdbbccbadcccbbbdcbcacccccbadcdcababbcbdcbaddcccbbbaacbbcddbccadbdacdbaadddccaaabaddbcbdacaaacdbaabbdcdbcbaacadcaccccaddababcdcbcabbbadaacaddbaaadbcababbbcddcdabccbcbaaadcbbcbccbccabddacaddaaddbcbcbcbcbddaabcbdbabdbcdcddadbbabbdcdbbcabcaabbadcdbabdacacdadacbcdaacdbabcbbdbcabbbdcdacaaddacccdaabbcdaadaccbaaaddcddbbbbbabcdababbddbcdbbaacccacdacabaabdabaacbadddabdcbadddbdbabbccbcccccddddbacccdcdaacaaddaddcaaaaaccaaccaaabbddddccccdbbdcdaabbdbbcababddcdbbbababacacbbacabacbcbcddbdaabdaaacaccbbbaadbccdddccaaddccccddbaccbbbadacbabdbbdbbddbbdaccadcbaddaccacccbccdddcdcccaddbccaddabdbdabccdcaaaccdbaacddddbcdcadaabcdacbabdcbcdcacbababcddaccabdcbbacbdbbacccbadadcbaddbbccaadbcdbdaccaabbbcccdadcdaadaadcaccbddacabadcbdadbcddcbbadccdabdaaaaccbabbbdcbaccbbccacadbccdcaacbbdbcbbccddacaacdbcabddaabdabbddbcbdaabbbcdabcbbccabdddbbcacdbcbdbbdaaaddbbaaaccdbaadaddcacdcdddaaaaabdcaaabdbadabcbcdaabcbbbcdcbdaccaaabaaaabcdcadcaaabbabddccdbcdcbbdacbdbcabacdaacadbdcdacadcbabdccabdccbdadbbbbaacbbacdacadbdabaadbddccadadddccabbabdcbccdbabcdaacccabadabbabbaacabccdaddcdcddaddcdddbaddcbdadccbbdcddadcbbcbcacbbaadbcadcbddbaadcabbadcbbcccbdccdddbbdabddcaaadbbcaadaddbcccacdabaaddabcdbcbdcddaabbdbadbdcbdabdbbbddcdacddcbdbbaaaabddaadabccbdbbbbddbbabdbbbaabcdcbbbacbddaaacdcabaddcaaddddddccbacdcbcddddadabbbddcaadaabbadbabaabccdbdbddddbddbabbcabadabdaaccbbcabbbabccdbcaacacacbacdbdccdcbcdacccccbdabaccacbcbcbdbcabdddaabcdcaccabaadcbbcbbadcabcddadccaaaabbcbdbdbadcbdcacbbbacdccccdbddcacbbbdbbbccbadbdacadadbdcdbdadcdcadbcbbaacabdaabdbaabccabdabbcadbcbcbadcdacdacdcbdbcadbacaddbbddddadbbbccbbadaaddcbcbcccccdbddadabdbbbcadbcaaccbddbdccbdccacddcdbbcdcccabccdabcabdbccdddddacdbadaacccacdcdddbacbcbddadaddadbcaccddddcabdbababccadabdbdccdcaadbdadadbdbddadadbacdadaaadabbbacdaaacbaaaddabadaddbdadabadddbcbdabbdaaadadbadabcabcacdabacbdcbbbbbcacdaadadbbcadaadcaccaddacdcdaccdabccddddbacdaadbddcdddcbaacdbbdcccdbddddddcccbcdbdaabaddbabcbbabbddcddcaababdcbaadacdadbccaddbcdbbdacddbcdcbacdbcbaadcbdaddbdaccaacdcaaadacbbbbbbacbabaacdadbcbaaacdabcbdcaabadabccbacabcdadcbcbdcbcbacadbdaaabccaddcbcccacadbdbabcddcababcaaadaaabcabdacbcaacdbcdbddbbdabdbddbcadadbbcdcbdadcabaaacbadcadcbadddabddbcbcccadccaccdccdbadcbdccddabdccbccabdacdbddcdbaadcdcbbbbadcccaabbbbacacacdddcbdcbdadbddadbbacdbbadcddcdccdbbbbdaababaacbdccbccdabcadcbdcacdbddaaacdcbbdcbacabbaaabaabbaabdacbccdddbbddbaaddddacbacdaddbcacbbbacacddadbadbccdbccccaaaddddccabbabcbbbadadbcbdddcbdbbdaacacabdcabcdaacdaadbbdcbbbdcdabbcccdaaabdbbcaaaaabcddcabcbbbccbcadaaaccbdabbacddbcddcacdaddbdadddacbccbaaddcbdcbabbdddacabaddcdccdabcdabbdcaacdcabadadaccadadaddabcddcddcabcbbddbdbcccdababdccabadbbbdcbcbbbbddbacbbccbdbacbbbcdbbdaadbddcbbcbabbbdbcacdccbacdccbcdcccadaadddbacabadbbabacbdddcaddcdabcbbcbdbdbbdbbdccaddbaabbcdbadaabacbdbbcaadaadccadbcbaadcbcbbbcbcadccdcdccabaacaddadacbdccbdcbbbccaadaccbdddbbaadcdbbcacadaccaadbbaadbabaadddddcddbbbddbdddbacaacdabbcbbababdbcddcacdccaacbbbacabcbddaadacdccabdaacbccbcbcacccddcccbcccdddccadcabadacbddcacacaaccaccbbdcbcacbcdcbcdcdbcdbacdaccdbcbaababcabdaddcbccbdbbaacdacdbbdacadbddbdabdbbdccddbbcccdbacaabcccbdaacabcbabbcdccbbadcdaabdddadcbbaaacdababcbadabcabddabcddcbcdddccaadcbcbbadacacbacdacabcbcdbccadaaddcadbabbdbacdcdddbbbbacadbdbacabbdbcbaddcbccdbabaccdddbbcdcbccbdabccdcbbddaaddbccdddaacbcdccdbabbdcbbdddccdaacadcdadcbbbcdbacaadcdaddadaaddacbaabcddccdaccbabcbcdddbbbabbbdbadcabccdadabbdcdbccabdbcabbaabacccdcacdcbacacdaddbcbbcaadbbdccbbdcababbdbbddbdcadacbbcdbcdabbabddcdddbacdaadcdbdbbacdbacdacbaabcbabaacdcdcabbacccbcbddcacacacabbcbbbcbdbddaadbcbdddaaaaabddcbddcdacdadadbadbbaacabddbdcacadaddbdabdcabbadddcbbdaabbccbcdccbbacdbdbdacacbbdacdbbccbbdcdaddbdaccbbcdcaaacddaacabbcdabdbdacdcddaaabbcaadbabbcadbbacaacdabcbdacdbbcaaddbbbaacacdabcddacdabcaabcbdadbcdaabaadadddbdcdcccabddacbdadaadcddaabdbbabcbdaabcadabcccbcccdcdaacbdbabddcdacbabbcbdbaaacabdcabbabccdbddcaabdccabdacbccaaddcddbbdabbddcacaadabcaccddbaabbbbbdabdadabdcdbbdabdacddbdcdccadaddccccdddbddbdabbccbbbccdbbabccbaaabcaadadcdbccbcaabadadbdddbabcaaddccbdcddcbbcabdcbbbcacaacadbcacbdbbcaccbcacbbdbbdadaddcccdcdabadbbadcbaacaacadbbdbbacdcbaddabadbbdbdaddaaddbdabdddbcaaaccdaaaddbcadcbadccddddaacababbbdccacdcddcaccbacacdcabdcbbadcbbccbbccdbaadcbbdbbcbcdcbbccccdbabaccdcdbcabcdbdbbcadadccdadcbdddbdacbbbbccaabcdcadccacdbcbcababcdcdabbbbdcabbdbdbdbddaadbbdcadadcdbaabdddcccbcaddbcdbaabaabaaaaccbdacbbdddabdcabadddadaabdcbdbcbadcacbdcaadadabbbcabdcbcdacdccabcdadcbabdbabccbddacbbbbacbbdadccadaddcbcddacdcadcacdcabaccabcdbacbbaabacacacbcacbdbbdbabbccaabdacbadccccabdabcbaccaababbacbaabcddadbaaabdcdbdbbcbcccbaacbcadcdaaabddabddbabdaccabaacadaccddabacdbcadcadbcabcdcbcdddcaccabcdbbcacabdbbaadcbbadbcadcdabdcdddbbbccbbbaddbcabdabbbccbdaacabbbbacdccbbbabcbdacbddadcbbbabacdddabccdacadcbaadcbaabdbcdbbbbdaaccdbadcbadbcacbcbbdcddcdabbcaadabaacbbbaccdadabccdabbdbdbbdbdccdbbdcbdcaddcdacacbcbbadbdbadcbdcdbdcdabccaccadbdccdbdcbbcaddbccaddacaddddbcdcaabcddcbcbaadaccdaacdcbabbdbdbcdcaddacbdbdacbabadbbcdacdaddadbdcddaabccadcbdddcbccaaabaaababadcabbbdcbcdabbbabdddadcacdcababdbaabcabddddaccbcaccdddbcdababbcabccaacaacaadddbcacacdccbabadccbddccbacacaadbbdccabbadacbdcadbadbcbaccadbbdaacbcbcbdaddcabcdcabdacacddbdacbabacbaabbdbbacddaaccbadaabbddabbdacaacdaccdbdabdacacacbbbcbabbbccdabbbdcbdabbcdbdbbacaccadbddbbabadbabcbddaddbbdacdbddacabcdbdcaccdcdcccbdaacbddbcccacccbacccbadbdabdacaadbccdaadcababbbcdcabbcccacabbddcdcdadcbbdabdddaabadbbcdadaaaddddabaaadcddcddddcadaadbdddddacaaaacdacbbdddaacacaadbdabacddccadbbabcbcbdbacdccbdcaacacabadbcaaadccacbccaadbcdacabaacdddadadcadaadbbcaacdadaaaaccbabcdbadacadbcdcccccaacbbcddbaabcdadcaabcbaadbbdabbcdbabcbacdcbdaaccdacabcdcdaadaacddbacccdbdadcbaaccbcbcddcbcbdaacddaadcddccdcdbaadcabadbcbadbdbdadddbbcdcbdccabaaacaddaaaddbdbcbbabbcbdcabcaadbcdbbddccbcbabcbccacddbcbdccbabacddabcabaddccdddccccdbcdadabdddcacacccbddaacadccbacdabcdadccddcbadacbdcabbaccabacacaacbbdbcdadabacdbcdbabbcbaccbbdadbbadcbdaacdacadbababbabbddaabbbbddbcbadabbaadbcdbbdcdadcdbcccacaccababcdbadaacaabdcdacbcbbdadbcbbadbcdbcddbdddbcdcddcdbbcbacbdbdacaaaddcbbcbccabcbbcadabadddddacabadabbbbccabdbdcbbbbadadacdbbccbbdcacbadabaabbabddcadcdccccaddaadcbdaddabbdacaaacddabcbacbdbdcadacbbcdddcadbccaaaadcbcaadabcbbabddcdabcaacdaddbcddcdbccccdacdaadabacdcdddbcbccdaaabddbbaccddbcbacadcacddbccbabbbcbccbcabcaaabcdbcddcdbbdcdacabaacbdcddbadcaabcdaaacaddccaabbdadcbdbdbbdacccacaccccdcdaacaccadbbdadcddaadcdddaadadbabaddccbbadcdbbbbccadbadbcdaddaabddaaccbbacbadbccabacccabdabbcdabaacaccadbbdbabacadcadcabaddbcdbcbdadabcbdadcaddccbcbbcbabadadbaacbcaccbddaabcddbcabbbaabcbcdabcadbdacdabddcddcdcbbacddabcdadbadcdcadaabadabcbadbacdbbdcdcdbcccdababcdbdcabbcbddcdacbdcdbabbdaabaacbdbdbdbabdbdcddaabadaabcbabcbadbaacdcadabdbccadddcacbaaabababccbbccccaccdcaddcccbbabccbbcaddaabbdbbdddcdbbbbddbdacacabdbdaacdcddbcabbcacbdbbbdbdbabdddccacdacbbbddbcdbbbdadcaddbaaaaaaddddaacbabbddcdacaccadcacdabdacbbcbabcdaadccdbbdbdabccabcbdbddcadbbbddcccccacadbbbddaccbcddadabcccbadcdbbaadaabdbbbaadbaaaccdbbcdccaddaabbbbabaababbbbbaddbcadacbdbbabaaccabbddbcbdcabaadadbbaabcabddbbcbcbdcaabcaaadcabbaccbcdbdcbadbbccccccacaccacabcacddcacdbbabcaadcabdccbbccdcbdbadadddbbcdbadbaddbbbbddaacabadbdabcabacddabbabdcbddccbaccaccaadcacdddbcdbcddaabbabdbbdadcacdcdabcbcdbddccadadacdadbcbdcadddbbbdcdbbdcadbbbcbacdcbadacadbdcdbdabcacacccddcbaacacbdcaaababaddcdbdddbdbaccaccbcbcabbbdadcddbadccdbacbaabaccdaaccbcbdbbdbcbcdbdabbdacdcaddaadadbdabdbaddcacabbcccadabacacbdabccdbaddddcbcddaddcdccbacdcdadcbaabbcbbabcacdaacdcbbabaccccdddadccaccdabcabdbdacccbacccbcaaadcdbbaddabbcdcabadddccdbaacbaadbaabdddbbacdbcacdadbbbccacadbaaddcaacadbbccdbddaaacdbadddddcaaccbbbdcdcdcdddadaaadccdccaaaaaaccdabcddbadaddddbdaadcaadcaacccdcdbdbbcacacabcbbbacaadbabdabacbdcddacdbbdccadadcbdbcbdcadcadbddaaadcabcaaacaaaaadadabccbcdadcbadcdccbbadacbcdcbcbcddacddaaddddbcbccdccacddcaabbbcaadcadbaadcdacadaacdaacaaddadbbcbbcddccacbbccbcbdbddddcacbdddbabdbcabadcbbdadbcdcbdacacababbdaacbdcddadcaacdcbcbdbccdddbbadcadccbaaadcbccdbccbbcaadddadbdcaaddcacaccacdddcbabbbbdabdccaadbacbcbacbbbdcadadacaabdccddaddadaddcdbbcbdcdddbbcdadacacdbcabaacddbadbdbccababbdbadcbaacbbccabcabacabdbdbbdbdcadcaadcbbbbbbbaaabbaaddbabccbaaddbcddaabbdcdbcacbbdaacbdaacadddaaababcaabdcbbddbaacdbabbdccbabacbdbcdccdabdbcdbcaababccabacdacdcbbcaacdcaaddcbabdacbcbcaaabadcdacbbdcaadbbcccdbcdbaaabcacccdaaaaddddcbabbbdabbaddbabccddbddddcdcaaabccabccdbdcadbabdbbbddbacabbabbdaabdbaadbddaccaacabcbacaabdbaccaccccddadddabaadccccdabbadabcbdcbdcdddddbcaccccbcaadbaaaddadaaaacdacbadaadddbaaadbacdbcbaccddabdcabbbdaadddbcdaabcdbabdaccbcdcadbadaadaaaabccbacacbdbdacdbdbdcacdacccbadbddabadbdadcbdddadddcbdaaaddcbacbbcddbbbccbbccdddaabcdaabbaaaacddbddcdbdbdadadabbccdbbaddaadbaabaaacbdaccdaaacbdabdadadbbbdbbaccbaaddbbccdacbbadabadbacacddbdaadcaaacabaccabcbdbdadbdccaadacdadddcbbdcccdaacbddcabcbdcbaabcadadaddcbadcaaacabdadaaadbaddadbcaabdbadaabdadacabadbdbbbaacccdbbabadaaaacdcacbcbabbdacabdacbddabdbbcbdbacbbadacddaacbccccdbccacbabcbbdadbcdaaaacdaaadccabacadabdadaabcccabdacacaaccbddcdacdaababccbaabacdcbbbadacbaabbdcddcadcdabadbcdbacddbabbbacbbdcaacbdbadcbbcddcdacdcbcabacccaadabdbabbbbddadccdbcbccdabbdadbabbaabdbacdadadbddcddcaabaaddcdbadbbadabbdcdacdcbaadcabaababbdbbddaacbbbadbdcabaddadabaaacbddbdabaabbccbdcccccbababbccdbabaabacddbcacaccdbabbadbdbcbaddbddbbdbbcaabbabbdbbbbcdccadbbcaaaacaabdaacdbccabadaacaaacadbdabbaaccddcabbaabaadcdcbcbdaccabcdddabdbbddcbcdddacccbdabdbcbdbccdccabbdcaaccbbccccccdacdbcaabbbcaababaabcdadacadaacbddcdbddcdaccdacaadbabccbccaaabaccddcccdadbbdcbcadcbbcabacbddbabacbbddbbbddbacadbccbdbdbadbccbccbbddacbbbcacadaaddbbaaddcaaccdcbbacbbddcacdabcbcdaaaacbaadbdcbabbcdbddbcacabdbdcabbaaccdcdcaabdabccdaaadbdbbccbabdacadabbcacacdbcacdadbdaaaabddcddcdaddbcbdbcaccabbaddaaaaccbacdbbcdccdbaadbdadbdaacbccdddbbabbbadbbdcdabccccbabadaaddaddbaddadcbdcdacabcbddacdcddcbbbddcbbbcaacabcabbdbcaabbddcdddbddbcbccbadbbddabaaacadbbdbaaddcacdbabbbcbadbccddadbbdccacddaccacbaaccabbbacdbcbdacddabaadbdcbadaccaabbbddacdddddaccbddaadbacabddcabdbbdccdbacddaacacaaabababacbcbaabbacaaababacadbbccbbadcdacdddabaadadcddbdbdadddcbdccabcccbbcbbcddcabaadaaaaaabdaabcbdcdbcbdcadccdcdddcadadcbadcdadbacdddadaccacdadabccccacdaabcaadcccadccdaadbabcdccdccacdcadacbadddbddadccddcbbbccaaacbabcadddbdbbcdbabacbdcdcdacbdcbbdddbbabddbaadcdbbddbadddabbcdadbbcdaadcccbcaaccbccadbaddddbadbccadcddcccdcbbadcbdaacccdcaccbbbdabbbbabadbbabcdddbbacaadbbbcbbccbaaaacbcdbcdcccdaacdabcccdbdbabbcbadbaccddacdbbadadaacbdbabccaaacccbadcbdaccdacddabcbdcbdbbbbbaaccccbccbcabcacccbbcdbcdccccbacbacdaadbacdabdabdadabaaddadababdccbcbbcbababcacbcdbdccdbbadcbbdbddbacabadacbcdbabaadccaccdcadccabbadbbbbbbccbbdcabdcbdaccbbdcdcaadcdbabdaccdbbabdbbbbbcaaaacbccdbdabcacbdbddcadddbcabcbbdaaaccadacbbbdccccdcadbdaacbaabaaacbddbbbcacdacdddbddbabbddcbdbbdaadcdadbcaabcbbcbdcbadabccbbdacbbbdaaddbddbaccddaaccdcaddadcccdabaccccbabacabccaacbdabbddaacbccbcccbcdcbdbbdddabaadadbbbcbbadccbaaccadbaddccddddbbdacdcbcadabdcccbdbadcaadbabddbbbddcdabbdbdcabcbdcdcbacdacaabadddbddbaaaaddddbadabbbaadaaccabdddccacacaaabcaabacadbcbddbbcbcaaabddbcbbcdaacdaddbddcaaddcbcadabacbacddabbacddadbabcaccabbcabcccacccaddbabbbaacdcbcbbcaccbbdbdadacaddcdadcbabaacbddaabbdccacabddcbdacacddccbdadbacdaaccabaabcbbacdacbdbcaababbdbbccdddacacbbccdbdbdacdbbaacadbbbadadacacbdbacaacccbccdbbdcdcdcabdccccdcccaaabbdbbdbaacaccbdcabdacadbdaaddabcdbdabbdbdbddddabdbcdddabcdcaadbcabcdaadcbadbaadaaaaaddccdbcbbabaabbaabacdbccadacdaaacacabdaccccdcbcddcacbcdabccdddbaadadccbcccdabaddccdaddbaabdcabbbadddaabbcbacdcccadabadbabdbaddbaccdcbacbaccbddcacaadbbbcdbbbcaacdadaabbccdabdcdcaddaddabadbaabacabcdbcbcbdcdbdcacbdacccdbabdbaadddddbdbdcdaaadacdcbdbbbdbbbbdcbbdbdabdcccbbdaabaadbacbdacbbbccbdcbcacdcbadbcccbbccbadcabaaccdadbbbdbadbdabacadabcaccaccabbadbdbdcadbaaabdcacabdcdaadbcbcaaacccabdabdaaaaccbdddbabccdbacdbccdadcbbbcacdaddbddcdcbdabbacaabbdabaddaccbdabcbdcbdcdaadcdbdbddabcaaacabccaddcaccbcccaacbaddcaaabdbadcdbaaabcccbbbcbacdcdbbaaadaadacddbbacdbaccbccaccaaddbacaadaccaabddbacdcdabaabaaabcccdcacdddcbdbbcbcacaacdccadcabbbacbcdbddbccaaacbcbcaaaccacdadccaacaadadcbdaacdbdbccaaaaddccadcdaadaacabdacbcbdcbdcbcadbadadccadabdbadbbcabdabddaabcdabaddbcabaabddbcbbdccdaaabdcaddbdbcabaacbccbcbdbdbdacccdcadcbdcccabccbdcbdbdcdddddaddbddcdcaabccbdaaddcdcdccaaddaacdcbaddbbbaddcbdcdcadadcbabbddadbabcddbcadacababcacdcccddbdadbcacdbdacbddabaadacbaaaccabccbdbbbdcddcbaddbcbdabadaabdbbabcbaacddcbbdbbcccddbccbaabacdbcccdacdaddbdadbbdadaccccaabcbaadccbbccaadbbdbbdbcdcacdacbaaadcbdccaacdaddbbbacabbadbbdaabbcdcccdbdbaccdbaabdcdcdbacdaaaaadabbbcdacbddacbcbcadacbcdbbbdccbccbbcbdcccbbbcbccdaddbccbacabcadddccdaddcdcbaabcddddbbdcabcbbbdbadacabdcaaaabbbdadbdbaaabcadcbccdaddbcdbaacbdcbdbdccdabaccdadbcaadbbcbdddcdaaacbcdcdadacaacbbcdccccdddaccbcadbbdadcdadbcbddcbcaacacadaadbcdcdccbdbbbcacddbcdaabbdbcbacddcdbacabcabbcdbbcbdbbdbabdbdcacaacbdabadbabddbaccbdaacacdcbadcdbbacdacccaccdadbabaabccdcaaacbcaabacadcccbbadcaacabcdcbbdccbbabbddcbccddcddcdbddaccaadacbbcbcbabadadbcbaadcbbdacdbdddcbbadccbbdbdcbadababaacdcbcbaababbbbabddadbccbdcbadccdcdddccadbdbabcdcdcaccccbcadbcacdbaccbbddaaabdbaabbccbcdcaaadabccabdaadcaadadaadcadccaacbccaaaacbcdcdacdadddbcabccbcbbcdbccacdacdbbadcadbdcbcdacdabadacbaaadbcdaccdadbaacddcaacbbaccbcdbdcabbbbadbaaacbcdadbbdbbcbadccbccbcccbbbcdaadbaadbdbdcadbcbababcacbabadcbacbabdbacacdccbbacdacbadcaaccbadbcdbdcdaadcbdaaacbacbdcdddbbdbcabaadcabddacdaccbaadddcaacdbadcddadddcadcbdaaccdcbccdbbcbdadbcdcaaaccaadabdadaabccbabbdddccbdbacddbbaaabbdcddddbccbaaabaddcbbdcadacdabacaabddccaadabaaaccabbcadbaaadddcbcdbbaadaddaabadabcaaadabcccbbcddabbaddbdddabbbcbcdccaaaacaccdbdadbabcdcacaacdbbadcabbcbcdadcdcdbbacdadaaabdbabbadccadbbcbbdadbdbbadbabdabacbcbadbcaadddddadddaaaaaccbdaaabbbbbcaddbaaddcbabccdccacbcdcdcccbaadbddcbbdcccccaabbadbbaadcaddabdabadddaabaabdddcbbdcdcdbbabcbbcacddbaabbcabcaaabadbcdddabcdcadcbabaacadadcbbadddccccdaacccbcddbabcbbbacdaccaadcddabbaadadabdcdbcacdbbbaacaadbabbdcbaaddacaddcbbbccdcaaddbccddbbcadcbdacbcdbddbcadddcbbadddabdccdccccccddaddbbdbbcacdbcaccbaadadacabbbccdaadaaddbadabdaccdacaabadbdccabadddbbdcaaaacbbbaaacadacdbdbdbaacdacadcbabdaacacbddbccdadaaacddabacdddcadccbacaccdbbdcaaccacabacaddbbabdadcddbdcbdcaabacbdccbdbcccccbcdcddbbacdbccadbbbaabddddbdacdcadaacdccadaddabcaccacdcbdcbcbcdaaacbabbcdabcaaabacabaacdaaccdbcddcdcdbcbcccbcbbddbdbdacaddbbacdddbbbdcaadaaadbabccadbacdccdacabdcabadaccadcaccccdbdcbbcaabbbabdcdabddadbcdbbdbcdacbabcdbdccdccbbbacbdcaaaddacdcbcabbbcaabcdcbcbadbadcdaabbbddbcbadbccddacccddcdbbcdbbbaaabaaddbadacdbcdbbaadbcdaaccdacdacdbcbdbdaadccadbccdadaadcbbdcccbddcaabbaccddddacabdccddbdcbdbcacdbcbccbbcacccaadddbbaaccdcadadaddcdbbdcacadccabbcbacbaadcaaabbcbcdabcbcbadbcabaaddabaacbacacbddccbdaccdbadccddaddcabcbadcaaaaacbacdcbcbaccbbcdacaabadabddabbacabccddcddcbbabcdbcbbacabcdcacccbbdcaabddcadbcbcadacbddbbadccbacdadbdacddddbcacdbdbbdabbbcdcdabbdabaddcdadadbbcabcacbbdbdbacbbadacabbdbadadacccbdaaadbbadcbaadacadddccbabcaacbaccaccbaabccdcabddadbbbbbbcccadcccdcdcdadacaaddcbaaccdcccbddcbdccbdbadbddbdacddbadcddcdcadaaaacdcabbdaaabdadcdcbdbcaddccdcbcdbdaadbdddabddbdbbdddcccabdbacbcbbccdabcdbccdbbcbaadcdaaaddcacaccccddbbaccbacdbbdcacdbbbbbaddabbbabcccdcbaddccdaabaddbcbcadadcacbdbcacabddbcaccadbacaadddacaccccbabadbcdbcbdcddbcaadbccdbdcbabbaccbbbaadacaaccbdcaadabdcaacaabbbbcbacbacbcadbbbbcdcaabcabdbcdcbccbabcdcccbdadacdadababcdcaacbdcbaddaadbddccdbdacbadbdccbcacdbdddaaaddcadadbccbaabaaddacdbaddadbabaaadbddaddcccdabdbccbbdbbdbbbbccacadbbacbdcdcbbaacbdcdcacbaccdcbbabacdbcabdaabddccbabbbbbcddbcadaacbacccaabddadcdaaaabdbcdbbcbbcdadcbbddddbddcbdcacbbbbcbccbbcbbcdbbcacaacbaabbbbcddccdbaaaaccbbacbabdadbbdccbdabcbdcdbcbcdcbacbadcddbbdcbbcbcacaadbacababdccadadcaddadabdaaabddcdbdcbbabdcbbdaacccdaaccbcddadbaaccdadbbbaccbabdcadccbcdccbcacaabcbaadcbcbbccaaaacadcdcdcdbdabbaacabdadabdcbcabcbcdbabcccbbadddabbcdcbdacdcbcbaaacbdcdbdddabbbadbdcbabacbaadcadcccadcbcaccaadabcdacdcbccbbddcdbabdbbdcbcdacaaaacbcbcbbdbccdddaccabbcbacabadbbababacbbdbcdddbddbadcdddccbbcddabdadddaadbbdbbcabacddaadcadbddbadcadcbcdddabcaaccbaaacbabdbdbdbbbaabbbcabaacaadcadbbabccdddccbaacccacabbbcabcddbbccbabcbbaadbdddabaccdcabbddaabdcdcbcacaacbcacdcbaddadbddaabacabdaadaccdcbdaccdaabbbaddaabbbbacaabddbdcdddcdbbdddabddddacbdddacaddcadaadadccbbbaadbadbdcabbadbdcddbdbacbbbbbaabccbaaccddccabdcbcdbcbddabacaaabdcbbabbbbbacacbbddbcdbbbaabbbabadabadbaadbbcbddcadbbacddaacdbdbbcbcadbbacadadadcadccaaadacdaadddbcaaccaacbacdbcaabdbdaaccbcccabcdbbbcbbabbbdcaabdbadddccbaddcdbabbbdbbbbcbbddadbabbddcdaabcddaabdbcaacdbabcaaadbddbabddbdbbbbccaabdccdcabbccbdbdbdadacbdcbdcdbcacbdbbbabbbcbbcbcbcaabcddbbdbcccbcdcdccbadcdbaabbbcdddcbaabaabdaacdabddaabdcbdcacccddcccbadaadbdcdcbaccadccbcbbcdddadadbdccacbdaaccbbbdcddbbaaccacddbccbbabdbbcdcaacdaccbabddacdddbbaabcbcbddabbcdbbaadbdaccbaabacacdddaaacabbbdbbbdcdbdbdccbdacaccadcdbbdaabcbbddabbaccdddadbcdbccbbaddbdccbdcabadbbdaadabdbbbbbcbdddccddcadbddcdadaadabbbdddcdbaacacbbdacdabdddbdabdacccdabdbcacccdbcabaddabadcdcbbcaddddbbbdadbbcaccccddcaadbdbbbbacbbbbbbcbdcabbcaaacdcdbcbadbbcadadabcadadcdcdaacbcaccbccbdacdcacbacadcacdccbabcdcacbcccaacaadcaaaccbadadbdcbddcdcaacbacdbccabbdbabcdbddcacdadcbdbaddbbcbbdaddbcbccdabddbbbccdccbdbcaacbbbcadcdccdbbdcdacbcdacadadbbaabcdcabccaddcbacabaacbcaacaddbbbaacdcbcddcbbbcccaadcaccaabacaaddaccccabadacccdbddcbbcbadadacddccddbdacbbdcdccdbacdbbbcdbdaccbdaadbaaabbabbdacacddcdadcccadccbdbbaadbbaccdbcddbcdbcdadbadaabbcaabcbddacbabddacddacbccddaddaabddbbacacdbabcddacbbaabacdbcdbdbaddabbdcaaacaaaddbbbbdbcbdccabddaaaacbbcccadcdadadddcbbabdabccdcccaaadcaaccabdbdccdaccdcadbadabccbdbababadadcdddadcdaabaaabcaaccbdcddbdacbccdbdcddccbccdaacbaacdccadaaadacaccbadddcbbbadacbadbdcaaacabbdbacbccdbacdcdacacdbadccabddddcddaddadcbdbbbbbdcbddabdcdcdccbcdaacaaddabdbcadaacddadacbaccacddcbaabaddaacbadaabacbabdcbcacdcdccbbbddacdabcbcccadbccbabbdddaaccadbcbabddaacddadbcdaacdcaddcbdccccacdddbadcdbbabdaaabcddadbabaddabbbcbdaccbccbacdbdcdadaccdaaabbbdadcddcbddbdcdabbdbaabaccaacdbdadcbcadcdacacbdaaadaccbaaacacbbaadbddcabddcdadbccbbbaadcccbbcacbbadaaabdcdaadcccacbdbbabbccdacaccddaadabaacadacccbdcbbbcbdacabdcadcdcddadbaabddcadbacdbbbcaddbaaaaadadaadadcbcacccdadbaacabdadbcccaaddabddcbabbaaabbcdaddbbccccdcdcdbbdacbbbaccadcaadaadaddbbcababcdccddabaabcbaccbbcadbdbcbbbbabcbddcdbbacbaacccaddabadabdbdabcbdcacaabcbadcddacaccccabaccbbdbccbabdbababddbccccbbcddcabaabaddccbccdcdbbbdbcbcbcdacbaaacaddddcbacbcadadabbdddcdaacacaaccccadcbccabcdaddccbcdbbbaaddbdbddcbccbcdbbbdcccddaaadcaadaddbcabadccaccccdccabbadbcbacadbcbccbbabcbbcdabaddbccaaabcaaccdaccdcaddbbcccdcabdadbdbddcbbddbcaddcbaadabcacbaddcccabadccadacbacbabaaababdbacbabdcacaaddbcdbadcaddbbbbbdddcdaccdbdaabcaccccdacaddcacabaabbbdaabadaadabddacdcccdbbabccadbdababcbaccadccbbdcdcbbbcaaabddaaadddabcccddcabaaddcbadbdcabcabbbbbaaaccdcdbccaaddaabcccabaddabbdbdcccabaacbaaabcadccdbcacccadbbacdbabbccbbcabddaabbbadaddcbaaaaacbdcdcbabcbdcabcabdacdcacdcbbdacbbbabbcbcabcbcbcabbcabababcbabaaabddbcabaacdadbbbcdcdcccadcdcacccacacabcadbaaaadabcacccbcccddccccddddaadbdaaabdbbdcabbcacaaabacaadacaadcdcdbbdcacdccacacbbbbdccaabbddbdaabcbdadbdccaadbbdcdbdcaccbdaacbbdbbccbaabbcbbbaadbcaabbaaddcddcbdbdaadabdcdaddccddcacbbccbdbaddadadcccddabdcbccaacddddaacdaccbccaabccdcacbadbdcabbcddcaacddcdbcdaacdcbbddabbdcaaaababbdccdbbdbcbbcdbbcbcdccbbddadcdbcaabbaabadabbdcdddabbcbbbabacccbacacdccddccbcabbadbacaaabcbadbbababbaccdadbaadbcababbbbabbbdccbddbaabddccbacabbdbdaadbdabdbdacbdacbcbddaccdbddaabadccbbacabdcbcddccbcadaacdcacdddabbbdcdbbcabaadcccbbbbbbcbccdaddddbbbbbbdbabbcdacccccdbbbbbbbacbbdddcacabadcaaddcdbadbccddcbaacdacbbdbccbabaabdbcdbcdbddcdccbdbdcbcbdbdcbadacbbddadaaaabacdaadbccdcdcdabdadcddccdaabbccdbbdabdbdcababbddcaabbbcaacbdacacaacbddabddaccccbaabcacaaccccaabacbaacdabcbbabdccccaddadaddbaccdaaabddbacdbbcdccbbcdcabdadbddbdaaddddaaccdcbbccbcdcccbcdabbcbdddabababdcdcabccbcbbdcaacddabcbbbabbdbaacbbdbddcabcbaddcdadbddacccacadcccdcbaacbbbaddaaabacdcaacabacbbddacabddcddccccccbbcadcababdbdddacdbcaddbacbbabdcbaaddcbabbdaadaaacbaadcbaddbdbaccbdbbacbaadaabcdbdabbbccccdaadbbdcbaaadcadbacacccdbbcbccbaccbaaabcadbdcadbdcbaabaaaaacbdaabccaaacbcdaaaacbcbcaadcacdacccaddcddbacbcacbdbbbdaddabbabbdcdacaaadcbbdcdcdcccbabbcaaadadbbdbccbccbbabbadabbabdabbbabaddcdbdbdddbcacacadbaabbadbcccddcbdadcddbccababbdcadabcacabbabbbdcbbadddbaacdbdccaaddcbdcaacccacdbbbbdabccdaccbbdadabdbbaddadaaabbcbccdaddccacddccbbccddbbbdadcababdcbcbbdbdbcbaccdaadbcddadbcccaddddbcccbcdddbbdbddbadaadcddcaaaaadddccbdcaacdbbcaccbcbbdbdbbaddabaccadddcaaacacacacdacdbddbbaccccdccabdbcadbdcdcdcbcabbbcbbbccbabdadabbbcabbddcbabccdacbcadcadababbbacbaacbcbdacabadadbbbcbbccdbbcbbaaacbbacccddaacbbcabbcdddcbbdcaacbbddddbdbdcaadddbdcccdcbadbcadcddbcddcacccdadaabbdbbddbabddbbcadbbaccbdcacacabcbdbdcdaacdcaabbacdccbcaabcbcaddcbcbbddacdbabdcdcdcdbdcdbabababcccbaacdcadaabaabdddadcdddadbbdaadbadccdbadccbabcabddcbacddcbaabbbdcbdacdbbdaaccacddccabaddbcaabcddaddbacdbacddaddcdcbbdbcbcacabacbcaabacdddddbabbbaadadcdaadddbddbddadddbaddadbabacbadcbddcdabcadacbdabbdaabcadddbccabccccddcadacadbcdbbbcddbbabdabadaadaddaaacaddcddbcdcbdbdcdacccccccacddcaddcddbbaabaaabcabacaddabdbdadddbdcadbdcaadcadadaadbccdabbdbdcdbaabacbabccadacaccbcbbcdcbcdcaddacbababaacabbbcbabcbbadadbdadcdcdaddabdbdbacbdccccdcbbcbacdcdbaccbabbbbdacbbccabdadcdcadddddcdaddbbaadacadbdbcadbaccdbbcaddbdcbabbdbbacbbaaabcdccbbaacbbaaabaabdbdbbcbbcccbaddabdbadccaadcbccabcdbaabdcbaacdcbcadadccddbbdbadababdddbbdbdcdbacacbaddbddaccdaddcbbabdbbcbcccdcdbdcdcccacbadcdcabcdbaadadccdaacabccacdcaaacaacddabbdccccdabccadacccddacacabcbcdaccadadcabaccbadbcaadaadccaacadcdbadbacadadbaabaccadcdabcbdddbcbcdbdbbccbdbabbabdaadddaddbbbbbdcbcbbbbbadaaddadadbcaabaacbacababdacbcbdbcbbdcddddddddcdaaccabbcdcbcadcbbacdccdaddbcbdabdccaccdabaabcacabccbcaaddbdddadcbbbdabaaaaacacdbcabbacdacbaabdbdbaddcbbbcabdcddacddabaacdabccddccdccddcbabdbabbdacdcdcdaddaddbabdbdbbdbbcbabbbdcdbdbbadbdccdbaddadacdddbacbaacdcadbcadbbddcbdbaddbddbaaddacbaccccacabdacacdcddaddabddddaabccacbadddddccabbabcabaadacbabccdadddccdbddbcbcbcadbcddcdbddccbabcbbbcbbcdbbbcbbddbbaddcdcdddbdcbdbcdbbbabddddabdcbdccacdabdabdccdaccbbadbaccbcbbabbcbadbdccdddadadccaabdcaadcdcdaabadccdabaadaadaabdcadbadaaaadadddbcbaacbbacccdddcddddccccbdbdccccadacdacbadbaacaccddbbdbdcdaabbbdadcdacbbcaaaccbdcccdaaadabddcacdabacdcbcacabbbbbadaabaacadcccabbcaddddcddcadcacacbdabccdcccbaccbccddcbdbcccdadccccaccccbbacddaaadbadbbadcdaabcaddcbdcbbccadbadacbacaddbaaddbbbbdbddcbbdaccdbdcaaccaadbbdbadaadccdcdbcdcbcacbbdbdabdcabcdccbbcaabbaabdaaaacdcbcabbbdaadddbdabbabcccacabaccaacbdcabdabbdabccbccacdabcbccdbccabaddcacdbacdcddaaddbdacabbcddbdbacaaadcbcacbbccdbddbaddddbacadcbabaadbccbabcccaabacddcbbddabadddacdaccbaaabbbcdabadabacabbcbcbbdddccbdaddbaaaccacdbabaabbcacdbdcaabcbacaacccbdaabccbadcbaddadbcbacadbcabdcacbcaccdcdbdaabcbcbcdabaaccbbbccbbbbddddbbadbbdccaadabccbacadcaacaddcbbbbdbdbcddcdabdaabdbdcadddadcddcbbddcbabcadacbcdddbcdaadcaacbdcbddcbacabaccdcbbcddcbaacbbaaaacacabbbccbbcadabbaabaabddabcbdddcbacbadcacbdacccbddacacddccbbbdccdabdbcadaaabbaacaabccccdbdacbaaddabddcababadbddacdabcdbaccacabdaacabdcbbcaccaabdcbbdccbbddccddbadcbcbccbaddddacaabcacdacccdacbdadcccdababbcdbaddabdacccabbabccabdcdbbcccbcadcbabcccdadcdabcaabbdbccbdbabcaaccabacbabddabbdadddabddcabadabaababababacbcdbaaddbbddadaabbaaddabccaacddaaaacaaddcdbaabdadccadbdaaccdaadddaccccbdcdcadbccdcbbdbbdbbabababdaacbbdbdabbbdbdbaaaabcaaacdcbddbdbadadbadbaaacabbcbcccabddccaaccdcddcddbbaacbbbdbbcdccababccbddabadbbcadcbccdbdddcaddcacdaabcddddadcbcdadcccbcaaaabbdbcdccdcaccdddcbccbcaccdcbaccbdadddacaddbbbdbabbacccdbacbcdacbcddaaacdbddaccacacbddbccbaaadcadaabccacbdbbbadcabaacbccadabcabcaadadbabbdccdbbbbbdcdccbbddbadaacadacbbdbddacdcdbcddabbdbadbaadbccbcdbcacdccbacaddcdaaccbdcaabddcaddacddbcacbacdccadbdaabbbccbdbbcaaadadcccabacbbdccdcddcbabcbdcdbbbdabbcccadbacacdaabcddaacadcddcdadadaaaababaccaaaddabddaababccbbcaddcabcacabcbdacaadbcdccabdcccabdbcabdbbaadcdcadccdccaccdbcdabddddadddabababbcbbbcddabcbabbaabbbbdcbcccbabcacaaabbdaaddbcdadbaaccabcbaabaadbdcbdddddcabcaacabdabddcdbdbbdbcabbdadbccabddbabbbdbcddbdbdbbcbddabaadcaddbddcddbbccdcbabdbbcbdbbdaddbccdacdcdbbacdbbbbbbcbcbbbcdaababcaaabbbdcccdcbdaabcdbbaababcbccdccbaadbbacaacdcdaabcbccadaaaabcaabadccbcdacbadaaacaaabaacdbcaccbbbbbcdacbdbccdbacddbacdddbbabacaadccdbdabcbadaabdaaabbdbdaaaccdbdbdbdbabcdbbbdcabccdadbabccdacdccbbaabcbbcccbcbabbdcaacdbcdbcdcbcdcaaddbbbabdbdcdcaacbcacbdabdbbacaabcabacdcdbbcbcbddbbdadcabbbbbbcbcdcbcaabbcdbdabdcadccbdbdbaadcbbbabccacbddbddcbababcabbcbdcadcdadddddcbcbdadbcdaacadabcbabbdbcabcadacaabbbcaabadcddcccbaacbccbcccabcbacadaaacdcbaaadadcaaacdaaacbcbaaadbbbcccacacccbcccbcbbdbdacbcbbbccabcaaaabdcdcaadcacadddabdddbbbbbbaaccaccacbdbbbdcdabaddaabbcbaccadcaabcdbacabadcbadddccdddadddcbbcdddcadadbcbadacaaadcbababcbddbcaadccdddbbcdddaddccdcbbdbbdddbbbbbbcabcccdcabacbadbbcabaacbbcdcdbbaccdabadabbbccbbaddaabbadbddcccacadbbacacbdbbbaddacccddcdcdbdbbbabcccccbccdbadadddcbaacbbcccccdcacacdaadbccdccdcccddaadbbbbcabdadbcbabcadcaadabbcbddbbbaccabdabcababccdaacccaacdabcbbcabdbcddcbcbbabdbdbcbcaacacacaaddcaaccddacdddcddcbaaddbcdbababcadbdabaaaadbcdcbdbdaacadaccdacaadcdddbdaaadcabcccbcccddccaaddddbddbaacbbbdbaccdccbadadabbdadacacaacdaadbabbdadbbbbaaaabadcbbbddabadcddddccddcadcbdcadbbdadabbdabdbbbddadcaabdbdadcabcaaadbbdbcbbdbdbdadddccaaaacaccdccbdbbbbdbbddaccdabcddddbaabcbbdbcdbbbcaaccbdabbadadddccaacabdacddddddcdbbbccbbccaaacccddbaaaabacadbbbbbbdcbdaddcdccccbaadbbbbdacdcbdaadddabadaadcababbdcbbcdabddbabcaddbaaadadaacdadbdbbbacbbdbacdaacdcdababdccddcbaaadbbddddbaabcddbcbccbdcdcdcacbbabdbdbccbcbaabdaaddadddbcdcbbdbcccccdcadbabbdcdbbccbbbcccacdcdbadddcaadbdcddcadcdaaaddaccaaaacdccbdcbbbbcdcabddacadcabbcabababadbbcddcbddadbaaaaaabcaaabddbbcabaabcbbdabdddcaaddbaaadabcbaadcbdabaababdbddcbcdabbccbacdadddbabccbabbbbbbbdccbbcdccbdbcbccacdccbccbdbbddbdcccbaadddabccdbbdbaababcaddadacbcdcbcabcaabadcbbbddaadcccddcabddcccdcbddbddbaadbbbbdacbcacdddcaacaadbdacadbcacbacddaaadcbddcaccbbbbdbdabdbacabbbddcaadbbdbcbcbbdaadbbaadddaaddabddcbdacbabaadbdcccdadabddaabddcbccbbcabbadababbdcddcdbdaacddccdbbcaadabdbcdbdbcdadccacaaadabddbddbcddbdbaadccddbabcdddbaacbadccadacbbdbdabbaadbaadacdcdcababaadbaddddccbacbcbbdccbdaaaccadcacddbcdadccbcbbbbdacbabcccadcdbaccccadcdabccbabbabddacbbaabddabbddcddcddabdbdbcbcababadadaccacadddaccbbadcbadddddccaddabcbcdcabcddbdadcdbdcbbacabbaccccbbcdcdbaaabcccabacbababddbaccdaddccaaccbdbbdccaaddcadabbddddcabdaacaddcababadacadbcbcbcdccbdbcddbaacabbbcdcdcbcddbbdabcdccaacadabaaddcdbdbaaabaccdbdcdbdbcbdbccadabcdbddbcbccaaacbcbbabdbabcdddddcbcdcdbaadadcbdbabcbabbaaabdbcaadddabddaabcaccacdacadcbbdacbadcabccbcbdadadbcadcaddccdadbbccacadbbacdccacccbbbcadccdbaddddabcbdbdccbaddcbdcaddbcacdcdbddbbacccbbdabaddaaadacacbbadbaccdadcdbacaddcccadabbbddaabbbbcbcccbbdbcdadbbaaadbdccadadcccbacadadcccbdbcaadaacbcbbdcadbabdcbddbbdabcadbdbdacbacdaabcacdbccaaabdabccbaacdacacaabddabcdbcccdcaaddbbdcaccacabbdacadbcabacdbdacddcbcaddacdcdcbcbacbcbcabdbbabcbdcdccdbcdadbaadabbababccaadbbcdacdaaacbbacacadcbbbbaaadccbddddcdacaadcddccacbacaacbadadbcbabdbbdccaaabcabcbcaacbbbbaaacbacdcaaacddbadcbbccdadcdbbdcdbdbbacdadccbcccacdddbacccdbbbbbdcbdcdadbcddcbaddaccbcdabbdbaaadcbcaabbabbcbaddcaacacdbbabbaaabcccbacdabcdbaddabdadacaabccaaaaaadddbbaadabbdbdcdcabbdccbaaaddbcadbbbccbcaadccdacadabddabdcdddaacbcaddacaaacddbbddacbadccbcbcbcdacabdbcbcbccbcaaddbaccbcdbaaababdcdaadaccdabbbbbbaddbaccbdbaabdbbaacacadabaacdcddbccbcdcabcdbdabccbbacaddacdccddccaadbaabaaabbddaddaaaaabbbaccbdbdcbbbbddcaabacddbdaadadcddddcdabddacdbaaaacdcdabbacbbcaabaccdbadbdcccdccbcdabdcadbaaacdacdcaccdabddccacdddbcabaadcdcaaabbbbadbdbbcabdcbcaadbcaadddacdadbbddbbcadbdaacbbdadaccabbaddbbbbabdcbaccbabbbcdbaacdcbdcbcbcdadcccbbaddbdacdcdccbaccbaadcdcddbbcbdbdcddadbadaacbbdaddbddadbacdcaacbaabdddccccacaddbcbdaacbaccbdcdddadacdaacbcdbbdadcdbdaddbcbababacadcbabbbbacdaccaddcdbbdbccccdabbcbdadabbbabaaaabcbacbaddaaddcabbadabadbdacaddabdaadbcbadddabdbdabcbadbcabbdcbbcdbaaadddcdccddabdaaddaaabdbcbbdaaabbbbcdccdcbaccdbadbcbdaaacbcddadbdadbdbcadbbbdbaaadacbadcdcadcacbabbacadacddcacbbcdcbdabcbccaabcacdcadbacbdcabacdccbdddbbbbdaadbaabbadbcabacdccabdbcbcbdbcaaabbdcdaaddbdccdbaaaacbadaacabacdddbabdbaccadabdbcadcbdacabadbbdcaadbaacadbbcddddbbdadadbcabdcbcdcdddacccabaaacbccadabadccddabdbdbabbddacbcdcbddacacdabdadbabcdcdcddadaaabbabcccdbccdcbddddcdcccddddbdcbccddbccbcacccacadbdddadbdbcacabcbcadbddbacbbbdbacbccdddaaaacadabcaabadacaabdcaabdcddbcbddadcbccdaacadcdabcadcbbcbdcbdccabdacabbcccdcaacdbadccabbabbacbababdbdbdabccdccdddbdcdadaddadbcadbdabaadcadcabccaccacabdadaccabccaaacabbdcbacdccbcdadbbcaadcdcdbacabaadabddddbbdbbcccabdbcacccbdcbddcacadacbbdbcbdbdcdaaddcdacbdbaddddbbccbbcdddbbbddbdadbbbadcbadcdcacccdddadbdcbaaabcbbbcabcdbcdaaacbabcacdbbddbdcdcddbcbcadbdddddbcccdadacaaaddbcbdaabcaadabdaabdcbacbbccaacbaacbccacabbadabddcdbadddcddacbcbccabddbdcabbbbbbbacdddbaddcabadbcbcdabbcabdbacdbbddaaabdbdacbcaccaddcccbbacccdbdcdaddbcccbcddaacccacdbcbcccdaddbcacadccdadababbcbddcbdccaddaabcbdbacbdadacdcacadaaadbcdcbcccacdbbcbdcbabddbddaadadcdbacbcbbbbbcbccbabdbabcabcbabddbcbbbbacdcccddbddaacbabddabbdcbcdbaddcdadbaabbdabdbaadcadbacdddbbccaddacddbacbccbcaabcaabbababcadbcdcdaccbcaacdaddaaddcaacbbadccbcccbcccdadcbbdcdbddbcababbadabdccbaccaadababcaccdcbdabdacaacbdbdcaccdaacbcbcdababcacdcdacbdadcdbbaaddcbcbcbbcddcababdccdcdbdbdacbaddbddabdbcbcabbdcbaccadabbdaccddabdacaadcbdbdabdcacbcdddbbcbbadcccbadabdacbccaaacacdbbdaabdabbdcdaadbcbcabbbdcaabadaaabcbccbaabaccbcccaabdacdadcbbdacacacccbbcaaaacdbcbdbaacaaacabddbddbcdbcdaacadadcaddbdacabbbcadbdbdbbaabdbdacbbbacadbbaacddbaadbddbbbdbcadacaabcbbaaddddcdddbbacbcadbbcabadbccddcadcbdbcaadccbccdaabbabbadbacdacaccccaacabccbcdbdbadadbdccbdccbbdbbabbbcdbaaaabdcacbdacccbccddddcbaddbbcdbbbddadbcdacbcaccdccaccacdddbcabbbadbcccddadddccacdcaacadddadacadbcbabbcdcdcabbbbabcbacddadcdbabddcbbbccccbdcbbcabbaccdbcdcccabdaddcacdbcbabccdaddccdcaadbcbbdacabbbccadadccadaadadcbdabaccabdbcabacdadabcbcabbbcbabcbdcadbabadcacdaccbcabbababaccacdcacbcaddbbdbadbcbbacadcdccddacacbbbccababbbbaccacdbbcaacbbcbbcbcaabbcdcbcaaabcbbcddbbaaccdccddbddaccdbaadcabcddbbcbcbdacaaccddbadbaadcdcbbddacacddcbadccbddcdcdcbbdddabcaaaabadbcddbdccdbbcbdaadababcaabcdcbbaaaddababcdabadbaaaaccdddbccdbcbcbdcdbcdadbaabdaadcbdcbdcababaabbbbcabcabbcaabdddacccadbaacbbdbdabaddcbbbccdcabadaabcadacddcadbaadcdbadbdbddcacaccccacdacbdccdadacbdabdbabddddccaabddcdabadccadbacdcaccbbddbcaaabcbddbdcbcbdbccaadcacaccdccddddbdbbddcadabdbcbcdaacdbcacdbaccdacdaaaadcccadccccdbaacccdacddaaccabbbcadaaccbbbddcccbbabbcbdbdcdbdaabadcadbcbdbdbbcbacddbaaccabcdaccabdabdccaccbdbdccbcbdddbabdcbdadbbdbcbaaaaabbccbcaddcdbbaddaabdabdaabcadcbdbdccabbbaadabbdbaacdddcaacdcdddcabaacaadaabcbbdcdbccdcabbdabdcdbdcbccbdacdcbdcbadcccabbaccdbbcdadabdadbaaddabbcdacdcaabdbacbbbbcbaabbdabbcbccdccacdaacbcbdcdbbadcacdcdaaccddcadabddcaadadaabacdbbbdbddcbaadbaddbaaadddabadbccbbaacacdbbcaabcdaabccabdbadcaacbdcacccadbcdbacacadbbdaaaacbcbddcdbdabddbabbcccbdccdcacbdccabcadcdcccabdcbbbcaaccadbadccbddaabbdbbbccdaccddbddddddccadbdbdddccadacbabbbddddccbbbbbcdbcbcdbdcababdcdcccadcddbdaddcabcdbdddacacdcbdbdcdbbbcbcbcacadbcbdbbdccccdcadbacddadddabccbbccccbaacdcdbccdcbadaaaabbcccdacbddacccbdbddcadbbababbbbdaacabdcadbcbccadbcbbbccdcdacacaadaddcbbddcbbbcccabdaadaabbcdabddcadddaaddcaabdcdbcbaabcbbcdccaccbddacbdbaacbbdbbabdbdacabbacabcdbdaaccbdddbaddcdddcacdbaaabababaabacaacbdbdcadccbaddacacacbdbbbdccdabbadaaababaaadcddabbbdadacadbcaadbbcdbcdcbdbbddbdddbbcadadcacacdabcbabbdddcabcaacacddcacccbadbbcaaadbbadccabaadadcadababcdcadbcccdbcaadccdbdbbdabbdbcbbbacbacaddadcbbcbddcadacbabaacddcacadbbaabdcdbcbdbbcbaddaaabbdababbdddabdcabccddbcdcaadbaccadcccababaacdacddddddbbcbcabdaccadcaccbdacadbacacaccbbccbbacbcbcdcadddddddbbdacbcababbbdacabbdaccccbccaccadcadaccabbdaacbcadcdbbdcdcdbbcacabddaadddaadadcdccdccdcbabbcaddbdbcdacbaaaaacacbacbdcddadddbcbcbdbdddcdbbacabaddbcadcddbbdaadbadaccccacdadaaadcacaaabdbabbacbddbdcbadbcddbacadccaddccbcbcaabbabddacdbcdbaadbbcbacadbabcbdddaddcaaaccdacccdaddcbbccbacabaaadadcdbcdcaadadbaadbdddbddcaccadaadabcdacbbcacbdbddddbdbcabbbcabdddbddcdbbaacbadaccbbbabcacadddbdaaadaaddbcdabdbdbadaaabaaabadcdcadbdbabdbaabadbccacbbdbdadbbcbccbbadcdbbcddbbbadadaaabcbcabbccdccddacbadbaaacddaccccbdabdaadddbbcabbaccdcbdbaacbbbdbcdbabbcbbbbcabbccdbbdacaccdbabaacbbbbaabbdadcbadbdabdbcdddbcccdabbbcbdbdbababbaaadbacbdcadddabaabbacadacdbabbcbdddcbbbbdadacbccbcaacabbbababdcbabbccbbddacccbabccadddaababcbbdcdbdcbbabbbabcddacddccbbccdbadbbcdbbbaaadbacadabbaaaaadabcabbdadbdacdcbbdbcdcccaadcdacbaacbbadbbbbdadadcabcabbdcbccdaccddadbabadddbdcdadbbacabcbaadacadacabbdacabacdabaddcdddacaacaaccdadddaadccdcabdcacabcaaaacbcacaacadbaaadbbabbbbdbbdbcdcaddabcaaacbbcdbdccbadaacbcdcacccdcbaabcbcaccbdaaaabbccbdbddaccddadaaabadbbadaadacddbbcadbccdabadddbccabdcacdbababcdbbaaaccdcdcaaccacdcbbccadcdcdaabdaacbcdbadaaacccaababaaaadadbaabaddababcddbcaccdccaddaadcbcbaabaacccdddaaddacacaacaaccbbdaabacaccaabddbccbdcdcaabcbcbabbacbbdcdcdcaaacbcdcdbdcdbbdbcdcddcbbbdadadbabcbcbdbbaadddcabccaacbbcadcbaadbdbdddcbcbdccacccbaccdcabbddcaacbdbaaddbddacdacaddbbbaaddabcbccaacadddccdadbbcacccbdbddaccaccaddbcdbccbaacacaadcdabbdacddddcbacdbadcbdccbbbbbdabbddcadbcbcdddabbadbbccbccadbadcabbcabdabaddbdacaaacadcdccccaddcacbabaacbddddcbbdcdadbdacaaccadcdbbacddcddddcbdbbddbcddaccdaacccdccccddacdadcbdbcccbdcbadbcbbcbcadadaddbdbcadacabcdcddbcdcacddabcbdbcacadadaddbbbcabbbddbcbabcdbbcacdadadcbbcaabadcdacadadcadbccbbacadabbdaddaddbacccbcdacbbcdccddcdaccddccacbacaacdbabcbcdadbaadabadbabccabccdcbadccdbccababdbaaabbdcbbcccbaadadbbdcaccdbbcccddbcdacaaccbbcdddcadaabbbdcdccbaadcaddaccbaacbbdcaccacbbdbcdbdaabbcdabbcdcacccaadcdacadaacccbadaadacaabbbdbdadbabbacdbccaaabddadacbaabbcadcdbcccdacbabbabbdbababacadbcbbaabdcaaacbdbdbbdabcddcadaacdcbcbcacdbcaabacdddcdcabbbacadcadadacacdaababdabbadabdacabadddabadabaabcbdcdbbbabcabdcbadadcbbacddbbcbabcdcbdbaccdcbbdbadaadcdbddcbcbdccaabbadcaacccabcdccbccaabbdccaddcabcdcddddcdddbdcbdbdcdccbbbbbdbbaccbddadddaacbddddabadccbdadbdbabcbcccaaccaabcdabbaaccbadbdcbcccbcbccadacaddcdacbccbddddcacacdcdbbbabbdcccabccdbcaaabaadaccabdaccbdccbbccbddbdbbccbbbccbdddbddbaacadacddccabdabdccbdcbbddcaaaccbdcbaacbddbcdcbcbaadabaabcbbdabbaacdcbaabcaaabcaddbbccccdbbdccaaaaaccdacbccbcdacbbaccacdbaacdcbddaccadcdacddccbbbdcdcacdbcdaaccacddcbbabbcbcacabcddbbbccacddacaadbbacaddbacdcaadbbbccbabcdbbcdadcccbdcdbdbabbdaabbdacbcbaacbdabbaddbddcaabacabcddadbdbacdacbbcbaacddbdadadbbcbabacbdcadbabdacccddaddbacddaaacbccbbbaccdcdaccabddabcabccaacabddcaabbdbcbcacdcdaaacddaabacbcaddddbbcbadadcccdacaccaadbddcbcbcdbdbbdbacbaddcadbaabbbacadaabacbbddabbcddcacadaddadcabcddadddacbaddabddabbdbacacadcabbabccbdadbaddcbdcdcdddccbddbdbdaaccbcbddacaddbacadababbacdbcddcababcddbdccacbcadccbcbbbbbcbacbccadabacccacbcdbccccbcabaccdccbbbaadbcdbbccddcbbdadacbccabaadbccdbacababdadabcbcddbcadddacbacdcbbaacabdacdabaababddcdbbabbdbcbacbdabccdccbbbadaaaabcacbbbbdddbcbcaadbdaabbababcacdcadbabdadbcbbabacddccdcadcdbbbdcbdbdbddbbcccddbddabdccddabdbcadcccacdacbbaacbbcbdadabadcbcbcddaddbcdbcbbcadcdbbdccbacddbccaddaacbbdabccdcdccacddccaabbdddbaddbadaadbbbcacacadbbaadddacdbadbcdddcdbacaddbccadcdbabdcdbaddbccbadbcddaddcdbcaabcccbcbaaaccacdaaacbaabaababacacadbacbbcaacbbbbddacaccabcddabcccdadbbcccaabbadddaaacacaadbacdcbddcacabcbbbbadabacdabaccbcdbaabddcabbdbcbcadadaacaddcdadbddadbccbbadcbcacabaadacccaddbccaccacbcadadcdcdadcbbccddbdbcabdacaccaacdccdbbbbcabddcbcccddbccccbbccdbcbdacbbcbbdcccdccacbcdadcbaaccdcadabddddbdccdccddccaabbdddddcdbcdcadbdbaadabbabcaddaacdbbbbbacacdcdbaaadcdabbbacddbadacbaacdadabbbaddcddbcbdaccacbdcabbddacdbacaacdbcadcadcacdabbabbdbddcdabcdabcdcbbdbdaddcacbaaabaadddbdaaaaaaccbacbdccdcbcbbaadbcadaddabbcabbcbacdadddbaadbddccbcddbabddbcacababdbdadbbadddcacdbdbddcadbbdbbdcbadddadcccaadcaadadccabccdbbbaaabbbcdcddbbbbbdcbcbddbabbabdcbcaacabbcbaddddabaacddcaddabdbddababcdbacddcbccbdbccbdcbccbbadabbdbccacdccdcccacdcdbdbcaaaaacddcaaadcccbbbcdaaccdbddadcacddbaddbadaabccbdbbbabbcaaadbdcaaabcdbdaadacdddddcadaaacbcbccbdcacbbaaabbbacbbbccdcaacdacdadddbcccbdccaccbbdbacdcddddacdbddbddbcdbcbddcacdccabdbbabacabdbdbbcdcabcbaadbdaddaadcbbbcadadacbcccababaaccbbbbbbbcadccccbcbbbdcbabdccbbaddacdcbcbddbbadabddbcaabaabbcccbadbbbbdbaacbcbdababaacdcddbcbcbcabbccdccdcccdbbddaacacddbdcadcdcdaaadcaddddbabbcdbdddbbdadacbdabcbcaccadcbcccddddbcbbacbadccdcadbdaccbabdbbcadccbbddbbcbcbaabdddcaccbdccbdaaacdabdbbdcdddabcaddcdcacabcabccbaabbacdabccdbabbcdbcaccbdddabdddadbbdbadcbbaadaddcacbdcadaddbadabccaacabbbadccbacadcaacdddacbacbdbabaaadadcabbdbddbbbbddaabbdaaadbdbaabcbdcccbbdcadccabbcacacdcbbccdcccadaabadcabdbdbcbdabcadcdbdcbdbadbcdadbcbbdcccdacbbddddabcbcaacaddbdbcbdbaadcaacbdcbddcabddadcabaddcbbbcccbaccabbdadcadcbcdbadcdbaaaaadbaaaacccbdaaddacbbacaadbdaadacdcacbabcccadaabbacbdbadaddaabbbcbccbacadbbcbbcccdcdacababadadbaccccaacdaddbbabcbadddcabbbcbdadbdacbbcaddcddbcbddbaddcdaccacdddcbadbbdadbcccddcccdbddabacbbacdaddcaccadaadabadcaaccabbbdabaabcbdcdccdbbbdbdacddcbbcbdaccaaaaabddddddabaacccaacdccddadabbaacbabdaccbacbcaaaddccddcdcdbbddccdaaddbcaaddcddbcccadcdabcbdcdcccbcabdbdccddbbcbcccbdcbcbbdaabdcaccbbdaacdacabcddbababbcaddbabdccbbbdabdbacdcbbccaddcdbdcacddaacccaabbacabdabdbcccacdbacddaabcabcadbbbdbcddcdaddddcddadbcbccaddddddaacbbbcbccdaaaddaadadbbaaaaccdabcdbcacddcbacbcbbddbbcdacaadcbaadddbdbddaacacdadcadacaaddaccdbdaabbcdccbdddadabccadcacbcaaabdaaacbdaacdccabdcbbbcadbaccbbdbacbadabadabcdaddcabacabcbccbdbbaadcadabcabddddcbabbbcddddccabdbbdbdccddbcdabaccdacbbbdabddcdccdadcccbdcabaabcbdcbdbabdbddbcddabdadccdaadabbbdcaaccbaacbcbccdabadcbccaabbadcdddcaacaaadbccddbdddacacadbcbcdbacbcbdcddbadababcdcbabaccdcaaaacbdbababdbdadcbadbdbbdccbbababbcdababcdabbdccdaacdababbabddabbdbdabbcadddbdbbdbabdcaadabbaaaccaddcbabaadbcdbdbdcacaccbcbbcacdbdbadbabaaabcaadbcaaabaaacaadcccdccbbbabdbaabccacacabcddacbcbcacccdbdacddcdbccdcabbabcadadccdaabaaaaacdaaadcaadbacbbdbdcccbcbaababbbababaccacdbadbcbaaabacadabbddcadbaddccbbdcbccddaccadddabbaaadaaaacdcaadcddaadadbbacbbbddbcdaaadacbacdcbbddaaaadbacdcdbdabbdcdcaaddcabbcdcdccabddbcdabaadaadbccdbddababbddbddcbdacbbdaaacaaccccabaaaabddbaddcaadacabacccdcaacbdaacdcbdccbdbcdccdabcdabdbcbbcadddbadbaaaccadabcbcaabaadbcddabcabcadabacbcabbacbcdabadbbadbbcaaaccdccdbccbbabaccdcdaaddabddccbabcddbcddbbcaacbbadbbaccaabacccabacdbcddaadcbdbadddbadcddbbcdaaabbbcccabcdddcacaccdabcbbdadbdbabadddbbabbbadcbaaacbaaabccbbdbbddcadccdcdbdacdbcdcbdcbcaaadcbadabcccbddccbdabacccbabbbdabddbabaaddababbacddcbaabdcaaaccabcbaccdccdbacadccdbbacccbbbadbabcddccababaabdddbbbbacdbbbaadaabdccdcbdddbdadabbcdaacdbdbbbbcbddbdbaccbbabbdbdcdabacddccbbccddaababbcdaabcddddadcadbdbbdaaacacccdcccbcacdaaadaddaabcaaddacdbaccbbadcdcbcbaacabbbabacaabcdaacaacccbcaccababcccbdaccacaabacccddbbdaacbadbdadaacadabdbcbdabbaabbddccbdbcbccaccabcbacacadccbbddacabdbdbdbdadbbaabbadbdabbabbaacdacdcdcacddcdcbabbdcccbcadcccdbaaccddbdcbcbddabbbbdbdabbcdbbbaabbaccbbcdabacaaacbbddbcbbcbcaddabdaaadadababdcbbbcdddcabbdcdcadbacccbdcacbacbacadaadabdaaadbabacadccccbcbbdcdadcdbcdabacdbbccdbbaaaaadbdabcacdbacdddacdbabdbcbacbbdabcccdbcbddbbccaacacbcdddbbcccbddaccccbbbcddcbdcdcccdcbadbdccabaddccacdbcdacbcbcaabbcdbdaadcabcbccbdaccbacbdbabdbddaccaaabcabacbcdbbdbbacbcdbaaacbccbddcdccaddcbadbacbbcbbdacbdacccbbdabbcddabcaddacdbacdbabdacdcdcbdcdaacbdcabadaadccddadacacbcbaaaabddbbadbadbacdddaadabaabddddcbabadaabdbbcadabbacbaddccddbdccaadcbcccbacbddadcdbbcddacbabcbdcabacbbcbdabbabbdbbdabdbddddbabdddbdcdbcbaacabbbcabbadbbaccdcacbdcbcdbbcaccbacbacdcbdadacdcddccddcbbbddccccdbbabbbbbddbdbbbccdcdacadbabacadcbddbcdabaccbdadccbcdabccdcdddcdadbbacacadcabbabadcbcacdbdaabcacabacccdcbcabacadbbcdbcbdacbacdaccdccaaaddaaaadcabadcbaadddccbcbbdddacbccbcbacddddcdacbbbadcaccabcabcaadabdaabbdbcddddcbbdaccccdcaabacaccdcbadcdbcdcabcdcabcabbbacbdbbbbaababcddabbcbdbbabddabdcbcabdbdbdaddaacdcadddbbaadbcaaddbbddacbaddbbcbccccccdabaabddcaaadddbabacbcdddccacababdabcdcabcdcabbaadbdaaaaccbbbcacccbcdbcaadbbbdbddbdacdbcdcdbbaacadadadcaadbaaddcddaadcadddbdcdcdbdbcdccddbcacadbdaaaccddcddbbabdbbabcddaddacdabcbdbcddadbaccbddcbacbacdbbbadbadacacdbbdabccddbaccbaaaaddcbcbdddcbdbbcacabdaaacbaaadadddacbdbbacdaccacbaadcccdbcbdacdbcbadcdbacabdbbddbbbbcbbdbaddbaaddababaaabddcadaaabccbdabbcdabdbaabacbadaaabbbbbdccaabdacacabbadcdcbbbcbbcdbaacbcdacdbdbdbaddcacdcbacbadccdcabdcdbbacdddccadadccdcdaadcabcacabcccababcadddaaacbccbbdbbccacbbbaaacdcbadcacddcbaabacbaadadbdbcadbababdbdcadaacdbacabbaaddbccdccddaddcaccdcbdbcdcbcbcabaaacbdbdadbdbabaddacdcdbdcaddaccdcadacaaadcbdddcdbabbbbbdddaabdbddbbadabacacdabdadcdacbdcbabdbdcadbbababbbdabbcbcbabacddadcacdaacaabadadcdacbbcccaacacaaaaddabdbabdbabcccbccdcabddbcbcacadcacdcbaddbbaaddabbaaccaddcadcdbaabcbdcabdbdbbddaddadcabcaaadbdccccbbbcdcdccccabaadcaadcbdbdbcdbacabdcbcddbabddadabcbdaddcaacdddbaddbbabcdbabccbcacccdbbcccbabbccaacadacbbcaddbccaaddbddbcaadbcdcabdcacadaccacbbcccccbdbbcbabadadadcdadcadacaadcbacdaaddcdacdccbabcccddbbdbadaddadcaaacacccadccbbaaddbdcadbbabddccacbbcdbddbcadadabdaacabbabdbdcdabacabdbaabadcbddbabacaddcdcaaacabaddabdccabbcdaddacdaccabbabdcbddcdacbcaccacdadbdbcabdddcaacbaccdaabbcadcdcbababcacabaadbcccbcdbcccadcaddbacbadcadcddbbbbcbccdbcccdccaacbdbadcacbcbdabacacadbdabddbdcbacdbcdadbacccbcbbcaddbdcdaccccdcbccbacbacccaadcccbacaadcdcddcdcbdbbabadddbbacadcbcbdababadbabbbadddcadabddaacabbcbadbaadaadabbacadbabdcbccbbddccbabdbacddbcccabdaaadadcadadcccbbaacadbdbbdccbcabbcddabccacbacaadcdccbbbcdddacbacbaadbcacacaddccaaccdabcbaccaabbaadbaacdadcdccaccdbadaaadbbcbacbbbbddbaabcdadddbabbaaabbdcabdcdcabbccbadbacdddccabbdabacadcdadccccdaddbcbbdabdadbcbdaadbddabadbdacdbcbaaaccbadbdccaccddaabbcdcbbabcaabcdacbdccbcbcdadddccadbcbcbaabbcaadccacbcbdbcdaacadabcaaaacadcadadadbbbabdaadddbcbcdbaccbabdaaccdadbddbdbcbbdbaaabcdbccacdcbacacbbadbcddbdbdcddadbddbbacdbdbbbbabadaddbacccdadcdcdbabccabaddbabcbddaabacbadabcadcbacbbddddccacacadddacbaaacccccaddccbaaacdddccaacdcddabacdadcaadbbcbadabadabdbbccabcdbbaddcdbddbdcbdacdaccaabddacccbcddcdbdccaaccacdadbdbaabbabdacaacddddcdddcbcbbccacaabcaadcdacbcbaadcbcddabbacbddcadacbccbbabddcdbcaadddcabaadccbabcacbcadbbdcabcaabccccdccbbaabbdaddcddbbbaddcaaadbcacabbdcdcccaccdcaaaacccdcdcabccbcaadcdbddadddbacccaccabaddaadddacababdadbcdcbacbcbcccadabbdccbbbaaccccadbacddacccadbddbcadadacbddbdaccaaadcdaabababaaddbbbccaddbaddddabadbdabaaaaabbacbbddcadcbdcababbcdcbacdbaacaaaadcacdccccbabcbbbcdcadcaadbccdbbdddcadccbbabbbcddcbabddbcaaddddcbaddaddaaaadbbccbadbcaaddaaadbabdadacbacdadaccddcdbccbcdddbcbbbddcbddbbbcdbccadddbbdbbacaaddbcaacbbdcddabbbccccbdbabaddccdbdcdcdadddabbdbbddcccababacdaaddbbacddcddcdbbadddacaacbacdddccabcaaccaddabbaacdbababbcdbbacacabccacabcbcbbdcaabcabaddddcdadbbbdcadddaadcadddabdbaadcccadcaccbdbccaadbabbaaadcaadbbacacdaddcccddacadcaaacabacbcbcaccaabbbcbccbdddbbcddadccadacccadbccddbadbcbcadbdbadccaaacbadccadbacbdadadbcddbbbbdddbbbacacdabaaaacddadcaccbacacbcccdadbbcbadacaddbcadbadccbbdbdaccdacbbbdacacbdbbccddabaadcabdaaacddcbcccaaccbbddaabbacccdacdbaacdacdcaaaacdcccdcbcdaaababdcaccdabcbddccdbaadbbdcccbbcaadbcabbcdaabcccbddcbdbbadacddcbcbcbbdbbbbccacabbabacadaadbdbcddccaacaabdababdbbbbdbaccaaadbaadabbaadcaaddccabbbcbaccabbcccdcbdaadbdcadccaccdadbbbbdbdababcbbacdcabcacdddcbdaaabbdddbbcabaccccadacbcacccdabdbaaacdcadcaacbbcdacbaaadcadddcbbaabcbbdadaadadddbcaadcdaabdbbacccacdcbdadcdadbaaadbbccbadccdaccdaabdbcdbbaadaaacadddcabcddaacbbbbaaadcbddadcdccbcbbbdacbbdcbbcacccdadbbaabadbccddccacababdbdbbcbbcacacbddcccccddacdbcdbadbbacababcadadbaccbbdbaadbddcbabcdadadcddabdcadddcacdaaacdaccdbcdccabdcadcaadbacacdcacdddccbdbcbbaadbdcdbdbbdcdcabdabaadbccbcbbddbabdbdcbdbaacbcdccaacaccacaddaaacbdadadbabddadbbbbcbcacbbacabdddaadbddcbcabcbadcddacbadccabcdcbdcadacbdcabbbbbaabdccccbbcabdbbddaaacbdaadabcaabdcbabcccdcbcadbcaacbaadaabaddbcdbbcccbdccdbcaadbaadaaccaccaacccaccadcaadddcddacaacbbcbbadbbabcbbbaccabdcacbbdcbcaabbdddabcdbcbddbadaccccbcdbddbabdddccddddcababbbddccbbccababadcbddccbccbddbadaacdadacaacbacdcbdaacbdbbdcddcdddddddadccadccdadbabddbcacbbacbbbcbcbdabddcbdccacabddadbcdabdcaacdabaddcddccdbddadbbccddbbcdcdcaaddcaacbcbabdbcabcccddbaaaacadccbaddbadabdcababbcbbcbacbcddbcadbbbccdcccdbdbabbbcdaccdcadcdacccbbbbbddabdaadbcbbbbbacabbbcccaddbbacbbbbccbcbcabbcbbacaabdcdacdcddbaaadcbabddbbdcccdcbdcccabdcdbdadbbcadabbbadabdacabbabcccaccccdabcaaccbdcaddcbbbcaaaacbacbcbddcbccacddcbbddbabaddcccbddcbabbddaaaadadabbdddddddddbdaadbdbdabaabccabadbddacbcbdabdbccacdcbaccdcdcababbcbbbdadccddadbaddcbbbcbcadcbcbacdbadaaaccdababaabdcbadcccbdabaacbdbbcadbdddbbcccabbaccadcacbcdaddacbdbadccdacaaddbacccabacdcbdbbcdbbadddccbabacddabacacccdcdabcbdabddbdbcdaacbdaaacbcccddbabddcaccdbcbccccdabdcbbdddaddccbbbccacabbadadcccdbabacbbacdaacacbccaacdadbdcccdbbddcacdaaabbccdaaccdbbcdbaacccabdaccdacbcccbcacbcabbbcdadcadabbcbbbacabdbcbdbabcabdaabacccbdccdacaacbbcddacccaacbababcdddbcdabdcbcadabacbddcbcdbabcbbbbbdcbbabdacadcdcabbabbcccacccbcddbacbaaccddacdcaadacdcadcbacaddcdadaaacaadabcbddabdcababdcdbcdddabbbabbaabcabddaddacbdacacaddbccdbcbcbddaddcbbabdadacdddabdadddacbbaacdcdcbaccaacccabccdacdbdcddaddcbccdcabbcbadaccabbaadaccddcaddcacadddddbccadbadccbbbbbbabbacadbadabddcbadacddaddabbdcabccbadcdbcdddcbbdbbabbbddaadcadcabbcdbbaacbbcbcccaaacbbddcddacabbcaacadbbbadbbdcabcdddbbcdabdacabddbdcbcddabbbdbcacccabdadbadbaadbdbdccbaccccdbaaabdccddaadadcdabdbadcdbbbcbacbbddbabdadabdbdccddaddbbdabcbdccdccacdbdbccbbcdcddbbcdacadbdbbdaabdbcbbbdbacabcdcaaddaadabbcaccddcdccadcdbacabbdaccbcbccaddbbadcbdcacccaacccbdcaacdcdaacbbbadaacbdbcddddcdbbdbabacadcadaadddbdbadcbdadbdabbbdabcdcbaacdbdcddcabddcadbababaccdddcdaadbcbdccbccabccdbbddacdccdacbbcaccbcbaddaddcaccccddcdacccdbaddacdbadadaccdcdbaadcbbbbdcdbccdbbacddbacdadaabbbdbbdccbcacaaacccaccccccaabddacabbdcbcaddbcbdbdacacacbccabbdddbbbdaabbcdacbbccbdaaabcddbaadbccabbaadbdacdccdaabadbcdadbaccbcabdaaacdcaabdbcbbcdaddadabcbdcccbbbaabcbbbdcbddaddacdbbdaddadabddcdbdadcbdbcbdcdabaadcdcbbdcdbcdddbadcaccacacbdabdbcabaccdddbccaccbdbcdabbabdbcacbdbbaddddacdaadbdccdbabdbabcdddaddbdacddaacdaddacabdbcdabcdaaaadabacdcccaccbbbacabbbbaaaababbbbccdbbabadbbdacbaddabbdbabaddcadcadcaccdcccabcbdbbcbbaaacaadbdbaaccabcacdacdcadcccadadabbdcaaabcddbbcaddaccacdbdccaccbadabbbddbcdaccacbacdcacccbbacdadddbacbdadcdadbbaabdbaacaddaaadbdccaaadbcbbbdccccdadbdcddacaaacbccaaddcdadaddbabcbcdabbcbbbcabcddbccbccbbabbddababbdcbbbbcaadbddabadcdbdabddbcabcdccbdcaaabbccdddadcdccabdadcbadbbbcdbbaaddcadacbbaaabcdcadaccddababcddcbabdbdaccbcbdadddcbbdbcacddaaabddaaddbaabddaaacbddddbddddcdaaadadcdadccbabaaadabdcbadadcacbcacdabbcbbadbaaacadbcdcbcaadbaddbdbadbaaacbbccacbcabbcccdbdcbbddcdbdbaaaccabddadbccacdccacdbdccaccacabaccacbbddacadcabccaddcaadcdabcbcccdcdbacbbbacacbcccbbaaadccabbbadcdbacccbbcabdbdbcaaddcdabdbdcbcadbcdccccadccccddbbdccbadaacbabcdaababdcbdccbcbbccbdcdcbdcadaacbbbcbbbdbdbcabcacacbcbcddcbddabdbccacbdbcbcaaaccbaddcbdbbddddbbbbcaddacdbbdcccdcdcddbcdaaabbbacccdaadccbbcbabcdaadaccacbacabcabddccddbbabdbdaacbabbcbbcbdaacbdcbbdabddbadacddaccbdadcdbcdbbababbcdbcacbbacbbddabdcdadabddbadbbcdbbcbbabcdccabdadaabbabdaccbcbccacdabddccccdccdbcbaadbbcbcadddaaaaaadbcdddaacaddadbdddaddddbacbadcccbaadcdacbaabdbcdadcdcabbabbaababbbdcccadacdbaacbaccbcccdccaadbdccbcddaabaccaaadcabdbbacbacdbbbbbdbaaaadddaacbadbdcdcccadddbbadcdbacacbacabbcbdbacccbbbbadbbcadabcbcdbcbcaddbbdabbabbcacbaddccbbbacdbaadaccbcbabcabdadaaadddabadbbddabdcabddcbabbcbdbcbccbcccbadccdabcabaacdbbaabadadbcdcacaaaaaddbadbadadbabcaabdacabbdddaacddccbbcbdddaccccaddbbaacccaabdaabaadcbadbddacdbdcbacbbadaaddcddaccdddcbaabdcddbbadbdcddbccbbccbdccaabcdaadcbadddabbdbadabbbababbbacbcbadcaaaccdbdaddcdbdcdbddaaacdbcdaaccacbcbdcddbdcaddbdccbacbacaccdcacbacacbbdadbdccdcacabbccccacadaadabccdabccddabcabbabdcbbdcbdbaccaacabadddcaaadaabaabaabbcabddaaccaddccdddcdadddacdcacbaaadcadbaadcdcbacdccddaccadacbbadbaabadaaaaacbcccbbbddcaaabdcdbcbadabdcadabaadbbcdcdaaddaadcbbdadbadadcaacbabacdcaacdcdbabdcccbabcddbacaabcbadbdcdbcdbbabbadddcdbaadbacdcccddcbddcacbadabcbcaabbabacdbbdacbcddbccbaaabbdcabdbdcabbbdacddddddaaaddcddbdccbcbdcdadadbbbbcaacbbcdcccacdadaadabaabbbaddccabbcccadaabacdcadaabcbcbcabccdccddcabbbbaacbdbdcccadddbdabcabcaccddcabbbadbbccbbacaccdbcbadccaccbadabdddddbcdabbadcbcbdacaccbccdadbcabbabccbddcdcadbcdbcaabbbbcadadbbcabbaabdcababbddddbabbcdadcbdddcaaabccbcddbdaaabccccbdcbdadaacbaaacbacdacbdcdcdcddacacbcbbbaadababdabadacdaaacddccbddaaccbdddddddddbdcadbbddbbdccdcaadbadddacdcdbbdbabbddbbaabcabcadaccaccbdcbadabcdacdcbabadcdaadbcdcccbbbcdaadaabdbddcddbbdddcbabddbcbcaaaaabccdadacbabadbbdacdaddabddbcbddaddababdbabbddbdddcbbcbdbdaadcdbbaacdcbbacdbbabcabdaaacaddcabacbbbabaacacbaacbbbddddadbddaaabcabcddacabdddaddaddadabccccddcbadbcddaaabdacdcbacdabbccdcadccbadbdbddaaaccccabbcdaaddaacaadbcdbccbcadcdbddabcaabbacbacadcabdbadabdaddddbdbdadabdadbbadcccbababbaadddabbaccddaabcbabbbaadbdddabbaacacaababbcdbcadcadccaabbacdcadbdcdbccbccbacdaddddddbabcddccdabdacbdbbdddbdabacdcccaddbdbaddcccaddbbcbbdccccbbabdadaccbcbddcacbbacdaaabacdadbacbbcccbaacabcadadbcdcbacdabaadbbcbdccbadabddbccaccdbddaadcccadcdaadbacddbdabaaaddbbbabaccbcdcdbccbbcbaabcbacbdbbbddabadaaddcadbabbcdcbadacdbdddaabcdcbaaaabadcdbbdbbcbdcacbadcbdbcbbacdbacbacdbcbdddaaddadbcbdbdcbababdbaadacbdbaacbbbdababcbabacdcadbbddcbcbbcdccdbabbcbcabccccccddaddbbddbaaccbdaacbdadcabbdabbddccccbaddbacdbcbdabcbdbbddcbaacbccbacdaadccabcccdabbbbccccdadaaabcccdcbaaabdaaccadaadcdbaaaabcdadbdbddabbaaadbcacbdddcaadcdcdcabbacddadbddbcbcdcdbcdadbaaacaacabccccddccaaaacddbdbacccdabcdbacdcdbcdcbacdcdabbdcaabcccbcccabdabbdcdbbaddbccbbdcaddbdcadbbbdccdbdaaabbbbbbcbbbabacabbabaacdddcccbabccdccbdabcbcdadbbaccabcaabccbadcbbabbaabdcbddbcbbbdbbdadabbaacdbdbcacdcabacaaddadbdaabdcacbcdcbdabdcbcbddccbcacdddbbbdabcbbbbdcdbddddacdddddccbcbacbdbabbdbcbabbdbbabbbaadbdabcbdcbaaadddabdbdbaabcacbbcdccaabbaabbdbddbdddbdccaaacdbcddbbccbacdbbbbcaadacdcbdbddabccaaaabaabbcaacdccbdaacddcccabddbbdaaadddcbaddadcdcbccbcaaabadddcddbddddbbdcbbbdccacbbbcbcccbaaadbaabddabbacbadbacbcbabbaaaddacdccbaaabadabcacccdcacddbcbbccbbdbaadaabacdbdaacbcacccacabcbbadbbbdddbdcbccccdbbbbcdbcadcdbcbdbacbcbdbaaddcccaabbbddaacababdcccccdaccbbcadbbacadbbcadcbbaabdacbbcadddbbbbaabbababadccdaccbccbbbaabdabcddadbdbcababcdcaaabbbddbbdbdbaaadcbdabcdddccdbcaacbbdbcbbbbcbdcaccbcdbcbcbbcadccccbcddacadaaabdbaabbaabdabbcabaaabadaacaaadaabdcbcaaccdbbdbdaccaaccdacdcdcbdddcbaadccbddbacddadcacbccdacbcbcbabccaaacdccdbadaddbdbddcbacdbaadccbcdbacadadacaddbcdcdcdcabadbcbbdbcbabbabcdacdbdbbddababdaccbbacbdbacaccabbdadabbbcbbacdcdabcbbbbdcbdaabcdacadcbbbcabaddaccdbadbddddcdaddaabbbbadddbaabdbddbdbaccdbbbdbdbdcccabaaddadadaccbbadadcdacdbdccabbdcadbbaaabbbabccdcdbbdbcdbdadbabcccddddacababaccccbbdcdbadadbbabdcdbbcccdbabbabbdbaaccdadcadcdbaaabbdbbbcddaacdcddbdbababaaaddbdcccbdbcdbcacacdcddccadadbbbbdabcacccbbccddbdbdbcbbbddcbdbcadbdddcdacdcdbacacbcbbadbbdbacdbdabccaadcdcdacabcabbcbdbaabcbdbbcdbababcbccbcaccacdcccdbdccbadbddcbbabaacaabcaabcddcbacdbbdcbabcdadcabdadacabdaacbbdcbdabdaadcbcbcacadbbabcaaddbdbbdcbcdacabcdacbaabcddccccabcdacdccddadacccbcbbababccdbacaccbddcabdcaaabcbddbbbdbdabdadcacccdbccddddcbcbacaaccdacaaccbacaddadaacdababdcddddddaaaadbdacdcadddaadcacaaaabdabbbdcbbcacabdaaacadacdcbacbbdccbaaaadbcdaddbdccabacccdabaddabaadbacbbadcdbcbcdbdccabdaadcbdbabdaaabbcdccbcadbccaabdcbdadbbaabbaaaaaddcccdacaacaddacaddcadcaababddbcaadcadcbacccdbbccbdddbaddacabcabbabdabacbbcbacadbccacadacaabacbcaaaccbaadabbbadadddabdcdadcdbcddabcdddbccababcdccdcaacaadddcbdbdaabdbbcabdacbdabbacaddcddabbcdccabdacabbbaccbadbbbdccccaadbdacdbdddadbabccdbacccdaaaaadbbacccaddbdccabcbbabbbbbabbcdabddaabdbacacbabcbcaadacbddcbadabadadbabdcaaaabbccdcddcbacdcacbabdaacddbddbbcadbbadddddddbccddbbccddaacaabcdbddcaabbcddbcdaccdcbaadcaadcbaabccbbddcbcdcadcadcbbcccdbcaddacaddaccbbaacddbdbbdaabcdbbaaadabcadcdabaddddbdcabbacaadbbbaababbcabbcaaadddddabacccbcdbabddbdaadcaadbddcdcadaabcaabbbbadbddadbabdabcccbaaacadabdcbdadddbdbcabcdaddbbcbbcabadbacdbcbcacdadaabddbdbddbddaaabdbcddbcccbabdcbaacadbcccdaddbddccdcbbaadccabacbaaabdccdaabddbbddcbcdccdbdcdadcaaaabdbcccbbacacdcdadbdbdabacabbacaccbaaacdcbabbcdbadbcaacdccbadcdbdbcbcadcbbcdddaccdaccdadccdbabbbdbdacdabcbadaacddadaacbaccaaacccbadbdaaccacbdabbaddabcabacdddadcccbccbbccdabbbcdcadaaabaadacbddabbadbcddcbcadccdabbcccabdadbdcaddaccbddcdcacabcaabddbbbadcaacabbbbcdcdabcaacdddaddcdaddcbabdbaabbadcaabbadbbcacabbcdbdacddcbabcaacbaabcabcbabadbdacacbccbbbddbadcbaccbbbbacdbdaabbadaaccbacddbdbbdacddcbcbdaabbbcabccdbadddcacdacdbabbcbddaabacbadacacccccdddbbcbacaacdaabadadaacbbddcabbdbbdcbacabdbdcdbbbcccdabdaabcbaacbaaccaddadadabdaadbddcbdaccadbcaaddcbcccdcadccdaadcbabcaccddaccadbddbbbbdcbdabdacccbabccbdabbddccbbbcdbcaaddacbacbdcabaacdabdccbdaadbccccddaadaabbaddcdbdbbbdaabdccddcaddbdccdddaabdbdaacdaccabccddadbdbdbbbbaabacdaddacaddddaaabaadddbcadaccbbadccdadbccbdcccacddbbacadcddbcabbcadbcccccdabacbdcdabbacbadbdcbabaddacbbcabdaddbbcddbacabbcccbacaddabbaabbdaaaccbadcacaaadaabbcdcbabbbbcacdaddbbadbdbaacbbacccddadcddccbddacbdbdaaabdaaaadadbcacdcbcabcdaddcaccababcbadcdacbcdbacbabbaabbdbcbaabbacdacdccaadccbaabaababbbcadabaacacabaacccacdbbdabbdabaccdbddbcbcdabdbacbdcdbdcbacabdacaabcdccdbddbacdcbbbddbdabaaaaccdcaabcabcbacbaaacaacbcdbaacacaddcaabcbbaaadaabbaaaaadbcddcaddcdcaadccbaadccdcdbadabdbabadbadadbbbccddaddaccaaddbadaddacbbadbdcabdcdaccddbbccabcacdbacbddbcabaabadddddabbdcabdacbadddbdbaadabbdddcdbcbbddcdcbdabdcaaddaccabdadacdccdcacabbcacccbababbdcbbbcccabcbcccddbadbbcbbbdcdabbcdcdaddbcbcabbabcbcbacbbcadcdacadaadddcacbcbacacdcddabbaaabbdbbadcbbdabababdbadbcacbacaababbacbbbcadbabbbccabdbbddbbabdabbccddbcddadcadabcdcdbccaaacabcadaacdabbbaccaddccbadbacbacabbbadaaadddaccdbdccdddacddbbcadccddbcddbcccdbdacacacbbaaadaddcccdbdcccdcaddcbbaabaccbccabbddcccdcbdaddacbbbbcaacbbcadbdbcaaaabdacdcbbdcccdbacabaddcacacddbcacdaabbadcddcdaccbdbacbbccbdbdabdcbaacaaaaccdcdabadabdadadbcbacadcbcaabbadbdaacadaaddbabdbccdcbcacbbdbdccacaddaadadbaaccacbbbcccdabdbdbccbcbdbabbacbdaaadbaacbbdccabaaaadacbbcbcdccacccdbbdbbdcdbbccadbcdddcbabcdbbcabcaddcddabcdcdbcdcadbdbacdcdccacbabdaacbbbddccdbacddcbacbaadcddbcbcbbbbdcccabcdcccbcbdbbadcbdbccbbaaadbbcbdbdbcdbabbadbbdcccdbabbdbacbdaabbbbcdccbcdadbdbbdacdbcadaabbdaccaadbbbbdcbbcabcadbddaddadccadabaacaadcdaaccbddccbadbcabccabccccabbaabbbdcbaadabaaabbdbcababdcbabbccccaabcdbdcacabdccacdcdcbbbadbcdbbbacbacddcddadaaccbaaacbccababdcbcacdaadabccbdbdabdadcdbacadbddbcbbabbaaaaaddaccacdcdbacaddabbabbccccacaabbbbdbccbcbcbadbcbddccddacdcbacacbbbadccbacdcdbcbadabddcbdcadbccbaaaabddbbabbbacddcdabadbdbabaaaccaccdcbcaaabcbadcbdadbaabbbcbbcabbbbcabacbbabbbcccbacbcaacabbadaccabcdabdabaccadddccaacddbadaacdddbaccadbacdcbdddbcbbbcaaacdabdcabdacabdccddbbbcbaccbdbcddbccddadbdddcdcbddbbcaabdbdcabaabaabcbcbbccacbcbaaabddaaabdcdbdbbadaadaddcaaadcdbcaaacddcbccaaabbabaccbbabcbaccdbbbbbbbdcabccbcaddaccaabacccbbcdababdaaacabdacabbbadcdbbadcdbcabcbbaabbaacdadcaccddcacdbccbaadcddaaacadcbdbcdabbcaddabcabbbbccccbbcdbdbcdcdaccddccaadabcbdbcccbcabddcabdcdaddccbcaaaaadbdaabbaaaaccdbbbadadbcdaddddaabcbcabbbdddcddccbbddaccdbcdddaadbccaddbbaaaddccdbacdbcdbbcabdcddcacaaddadddacbaaabccdaacddcddcdaccbdddbbcbbaddbcdbacaccaabcbbaababdbdadcabdcabbadbadbacdcdbbaddcabadbcdadadcbdddccdbbacdaabdcabcadcddaabccbbadcbdbcaadbaacdbacbcbacaddddbdbdbacdbddddbccbcdcdacddddccabaaaccddabdcdbcccacbdbadcacbacabccddbccbdbadcbaabccaacababbbadddbddabbadbbabdbaaacdacdadbbcdabdbdbdaabdbaccddccbdcacddbacdaaccbdbabdabcbabadbdccabbbaabbdcaaaadcaaacbabcaddbdcbddcaccdabaaaabacdbbcbcdaacbdddacaccabdabbbbaabbcdacbcddbbdacadbcccddcabadbbcddbccacbdaccaabbbbbdaaadacbdbacdbacccacdabdcaacbdabcdbaacccadcadaaadcbcaaabcbbdaddbddabccbdbdccbadcadacbbdcabdacaddbcaddadbdccccdcbbddbcdbdcacabdaadcbdaccddcaabccdccaadacadcbdacbbacbabaccadddabcccbdccbaacdddcacbadbcbdcbbdbaabbadddaadbcaaadabbcaccadaabadadaaabaaaacbdadcbdcbcddcdbcabbdcdadacbbaadbaadcadaddaaadbaaaaccbdadddbbdaccccacccddbaababdcbaababcbbcbccbadbbcddccbabcaadcbdaccacbcdcbbdbbbbdcdaaaabbdbdddabdccacabadbbcbaaaccaccadaccacdddcadcbcdbcccacadaacadaabcadbcaccdabacdcdaabadaabddacbbcbbabadddbbacabdaadcdabababaadcdcccaaacddaaaaddcddbdddcadabccadcabaabcdddcdaddbcbbabbacdddcdcabcbaabdccbdddacadcbacddddbdcddaabdcdabdcddcccbbabdacccaabbbbbadbcbdcbddddbabdcddcbdcdbbaccdadcbaabacabcddaaabcbdbacdacccabdcbabdaaddcbcbccbccccdcdadbaabdcbacbabdcdadcaacadbcddbacabbccaaabdacacdcbbcaaabcdbdcdcddddaccdbbbdadaccabcadbdcadacdddabcdccdabbcdaadddaddbcbdadddddbddbbccbbbdcadbadcacababccabaccbbbdbdcdbcbdddadbabadcdcdcdbdaadbcdbadacbbdabdcddaaaccadbbbdadcdcabddabacaabcdbdcdcabaaaadcbabaaadaaadcbacbdbabcbbddaccacabccaaaaaaaddcaccbabbdadbccaccacdbcbbbcccdbccbcddcabdbdcbacaacabccabdcccaacaddcdddcdcbacaccccbccbbbcdacddcdcdbdcccbdcdaccaaccbcdadadbbdcbbcdbacddcaacdadacaaabaacdaacbbcbdabdaddbdddbbdadbacdacbcbbdbcabaabddbbadddddbdabaccbcaaacbbdbdbcadbcccccbdcbbaadabdbddbcdabacbcbdcbaaacbbcabccddbcdaddabaccaddcdbabbbcbbbbbcbcdbbdbbbdbbbdabaabbcbaabccaadcbdcbaabdabbdacbadabbcabcacacbbccadbcccbbdcdcdbabdbddbadccddacdcbaacbbdcbcaccdddbbcdbacaaccbcccaaaccaaccbaaaadacbcbbcdcdddcbcbaacbaaacbcbbcaacbdcaaddaaacaacdbbdbbdcaaabbadbddaadcddcdacaccadacdcdcccddcaabcccddaddcdacdcaadacbdbdddabbcccdbbccacdcddccbabbcaadbccbbdbcddababdcccaaaccabcdbbadddccdacccababddccaaccbbdbbccabdacdbaabaadabbbbababdacabababaddaaabdaccdbaacccbadcacbcddbbadcbaaadaaabcaaccddbabddcaabdbbcdabbcdcacdbcbcdabbbbaacacddcbdacaccbcdbacdacbdcabbcddbdaddacbbcacbbabcacdabddbcbccbcaababccaddcbbcacadbbdbcdbbdcbaadbdadbabbdacdbbdadaccddcbabbaddadcdacdbdaccaacdbdaccacbabccbcbbbbadcbbcddbbccbdcbaaadddaacdabcddddcacddcccdaaaaaddbdddcbdcaadaccaddadabcdbaccbcaccadbdbbacdbcdbabdccbddaaccbddaabcdbcacccbacadddbaadabdbdbbcdbadaaaabadbdcbdbdbabbcabccabdbacdcabccbaacdadcaabbddccbdaccbbdaabbcacbcccaaaabdbbadabcadccbccbbbcdbbaadcabddbbcccdcaaccdbdbbddbbaacacacadbbbdadcccadbadcdadbccddbacccdbacdcdaabdabdcabaabcbcdaadbbddabcabcbbcadaacccbcacbddacbbacaabcbaabaaaababaadcbacababcdbddbcaccddacbcbcccbdbbbcadccccbaacdccbbcbccbbdcacbbaadbabbdcbcbcbaacdcaddcbcdaaabddabdbcbabbbcdcbbcbddabaaaacaddacddacbdddddaaacdbdcbacacaccabbcddbcbcddcbdcbddacccdcdcaadbabcaddcbdadaaadccddbaabacdcdccaddacdccbbacabdaddbadcdabaadbacdddbbdabaaccdaacdacdbcdccadccabbcddabadaddcaaacabdbacddcaacdadccbacadbacaabdbaaabcdbcccabcdcdbbaaddabdbdabaddcbabddadcadbacaabacaccbbadbbbbabcbdacbcdadacdbccbabbabddcbcbdcabcabaadddabdccadbabacabbdcccccbdddbbcdabcabaadbbdddabcdbcccdcccdacadaccdbddadcadbdcaadcdccbabadbddcacaabcaacaadacdcabbdddbcccddccacaacacbcbacbcbacaccddabcbcdabbcbbcccddcbdcdaacdadbadaadaadabadbdcbcbcadbaaaabadcdbabdbadbadddaababbcadcabacdbcbbbadcacdadddcadadaabaaccaadddbabbbacbdcbcddcbcaabaaaddccbadbdbacadbcdaadbdbaadcbcadddadcbaacccdabbddddbbdbbdbdaccdababcddcabaddacbccdcdaccbbacaacbbacddbbabdccdddadadcaabdbacdbbbdcbbdbababaddadbddcaabbaabcbbaaadbbacabccdbdbabddcbddcabcdcabcdacadccaabababaddbbaaabadadbdbbdccabababdacdadbbccdadbdcbccddcbbaddaaaadbbadcaacadabccddbdcbacadbaadcbbbdcadabdccacabcaacdbdaddacdbaddaabcddddcdaabaadacccbbcaccbadadbdabaaaabbaddddcbabbcdaabbacadbccdccbbcdcababddbdaaddcdcdbaaadacddbaabcdbdbcadbcbadaabbabcbccddbaadadccbbcaaddbdabbacbacccbacdbcbabbbbbdcdddaabaacdabbbbacaacaababcaabbabaddbdccbdccacbacdadcdbcbbabcdbbcccabdcadcdcacdcbbbaaddccbadcbcadbcadbdaddadcacccaddabcabcaaccdbbdcdbaacbacdbdbaaddabccdaccdbcadddaadaacbbcaacdbbabcdcabbdcbdaabadccbdccabbddcdccabdabbabadacabbbbddaaabbdabbbbadcbccdcbcbbcaadbadbddccdabdcbcdccadbbcaacccacdcdbabcacaaaadaccabdbbdcaadccbdcdacdabdadbccbccadaacacdcddaacbccabaacdaadacbabcbdbbcadddcdbadabcddcdcabdcddbdabbdbaccacabaadcabdccbbbbddadaddbadcbacaaaddcaaaccdbdbbbccbaabcdaadabdcadbcaabbacbbbbdcdddabbcadbaabdcbbdcdbccdbccddcdaccbcdbaaabbdbcacbbbbbdbaacadcbbbbdaaddacddbdcdddbdbabadcdbccddbbcacbddcdbaabcbdacadcbddccccdaaaabaababcdbbadbaddccbddaadcddbcddcacabaddabaacbccbddacdccdaccacaadacacccbdcdccbbabcabdaddcbabcccacabbaadbadaacddbadadabadabdbcbdbdbdbdbdcbacabaaadbbbbaabccdbcbcacacdcdaacacbaacaacbbdacdcbcdcabdddacabdbddbbabadccacadcbdbaddabcbdbdbccbababcbdcdcccbcbabdbccabdccdcdbdbbaccabaabdbaccaddddcabaacbbcddccacccaabdbcdbdbabbdccabccbdbbdacccccbcaaabadbdbaacbaddbcdaddcacccdaddcbaddacbcdcacdcbcbbaccbdddabbdcdaadccadabccddacabdbcabadabcbaaaadccdacdddbaaacccbaacacdcbbbcdaadcdbdbdabdabbccaddcadcbaccaddcdccdcdccdddaadcdbbcabacbdccadcddcdcdaadccdbbdcccddbdabdacddbcbdcdccccbcdaadbccbdddbadadcdcacbadbcddaccaddccbccaacabccddbbcdcaaacaccdcbbbcadaaaacdcacbaabcaabbdbdbcdddccccbadaadbccbbaaaabccdbdaadaadbccbdcaabddbbabacddddadadacbdcadabdbbadccccdaddaddccdaaddadbbdbbaadcaacbdabcbdcaacdbbbacbbcdbaccddadaddcbbbcabddddbdadcacbbabbbbccabdcbcbddbdddbadddcacabaabddcacddbcbbaabadccabadbaddababdcdbbddbdbdbdccbdbcccdbabccddabdcbadbdadcbccdbbaaabcdaadbcdadccabdaccddcdbdbaccaadaadddaddcbacacaabdddabbdadbabcaaddbdacccbbdadaacbabcadacbcadbdabcbddbcbddbbcdacadaabcacccabccadbbbaccaabdacdcbadcddacbdbdacccacabddbaddddacaaddbbbaadabbdbdbbdccacaaccdbbbdcababbdbcdcacbcacdbdcacbcbbcccbccbacadcbdcbbbabbdcdcdadcbbbadbdcccccccdcabcaacbcbdaddacadbacbcdbcaddcddddaacaaaabacdabaacbbccbbdcbddddcacdcbacabcaadadabddcabadbbccbcbcdddabdaddabdcbddabcabdaccdcdadcbbbdbbcabbbdbaaabcbadbdabadcabbdcccddcadbcccaabadadaacdcbcadbbaacbdaacbcdcadabbabaabcaccbbabaabbbaaadadabccccacbacdbcdbdabcccbccccbdddbdccaabacaacdccadcbcbbadbaadadabbcdddddcddbbdadbdbaaddcbbabcbdcbdabbbbadadababdbbddbbcbdbacbcbacdbbaddcbcccadbbdbbacabddcadbcdabcbbbadcbbdcbaddadcabdaddbbadcbdbabcccbaabbcdcccabbddcbdbddadaaddabccbcadbbdcdcacddddaaabdacdacaadcdcdbdccccdcbbacccdccdbccbccdabcdbdadadaccaccdbcabcddaabddbcadbabcbddcdaacbbccdbbabbcddbadabddbacdcdccdabdcdbccabdacabdcadabacbaadcdcdaaccdaaacdbccacabdabaaadabdcdccbcacbacdacccbbabcdcdcacdaacbdccbabdbababbaddacbcaacbcbababddaabccacadccdcccbaccbccaabcbdadcacbacbddcaabdabdccdabdccaaabbdcddbadaacdaacbaccbccacbcabdacbddacddbaccbbbaabdbdbcddcbbbbbddabddadbddaabadbadcbbbabbbccdbbbbadcbadacbbbadacdabcdcbcdacdcdaaddcdcacaabbdbdbbdcbdddbdcdacccaadbddbdbbcaabdaacbdaaddbcadcadaddbabdbbcabdcbcacadbacbdcaabbacdaaccaddbcabdabdbdabddbaacaaccddcaadbdabcacdbbddacbdbadacbbcddbcdcdbcbddbbccdddcccddacccccbacbbacaabdcccbdbbbaabaabcbcdcadacaddaaaaabbdddcbdbccdcbbdbdcabddaabcbbbbdccdbdaddacdaacdcdccabdadcadcdcaaccadaaacbcdcbdccbbdbbbacdcdcbdabdcddcbdbccbaabddbbbbbbbbbdccabbccbacacbabadccbcbdabcddbcaacbaadbdddbdcaadcbaaddbcdbacbabdacaabcddadbcdbbcddacabbaaacdaacbabcbbcbbddcccdccccabbdbbbbcaabcbaacccddddaaabaadadbbacacbdaddbcdbbdbddbaccdbadbadabaaaaaddcdcbacbdcccbdbcdadddcdddaaadbdbcdddbcadcbbbccbbccbdaabdcaaaccccdbdaddddcacabbdcacabaabadddaadacdbddaddbaabacddccbbddabbddbdaccbbcbacdadaabbaddccaccabcbcaaddcccacacbcbabdcaddcdbaabdbcadbbcbccbccddbddcdbcdbddbacdabaadccbcdbcdbaabccddbcaababbacdacdbbbccbddadbdddccadbcdcdacdddabcabdabbdacadaadddcadaccabccabbaadcaaaabccadcdadabaacacaabaaacbcacbbdcbbaadcbcbbcbbaacccabacdcbabdcbbddbdcabbdcdcdcbccaadabcbadcadadaaadcdcacbcbabddbaabcbadbacadddccdbdcbaacadacccbcccdbbbbadbcdbbdbcddcaddbdbdaababadbaccbcdbddbaaaccabaaaadabbdcddbacbbcbaaccaaaabcdcdadbdbdcdcbcccabcaabcbccadcaddaaadbbbbcddaaabacabaccbccbbbaaccacbaacdadaccbbdbaabbccaddbdcadbadbacdcabbaaccabbbdaadbaaddbacbbcddaacacaddaabccbcacdaabcdbccbacbbbbcddbadbdbccbbdcdabbacacbcaddaccbabaadbcacbbdadccddbbdbcdcdbabcdddddcadcbacbacccdacdbabdcbadbbcaadbaccaadbcddadaadbbcbadacbcbbccdccccddcdaabaabdcdcddcabaacdacacbcaaaccbcdbdbcbbbaadadccddbbdddbbdcccaccabbadccbacadccdbcbaddbabdaccaaacbbaabddbcabbcbbcdbbcdacaaaccabdaadacdddbbaacbbdbcdacdcabacdbacbadcbabcdccacddadbbabbccbadbdcbaaaccccdabbddcdcaddbcbabcbdbdaccdabbdccddaaaabcbcdccadabdaaadaadadacbcbaadcbcabaccccbcccdacbcdbdacaccabddcbadcccbdbcdaccabbcacdbdbbcbdccdcdbdcdcabaadaadccdbcbcddadcdbdbdcccabcddaaacdaaadccbbbbbbdcaccdbaadddbadabcbddcccbaaaacbbaaaababcccadabbddbacbbbacbacbddcdcccdadcbcdbbadaddbabbdbcacaadbbaddabbabaabddccabadabcbccbbbdbcabacdababccbdbdbbcbccbcdaddbccabbdbbbacdbdbdcabadcdbacaabbddadaccbbabadabcdcdabccbcbcbaddaabdbbdabcaddcacbcadaacdaabcbaaacdabadbacccacbcbcadbcbdabacadaadcdccaddacbbbaddcbacaaacaadabdbdbccadccabddabaddddddcdcadcabadccaadcaabbadcaacccccacbadacdbaacacabdbbcbbddaabbbbdbcbcaaccdaaabccabbddcdbcccdacbbccccaccbdabccbcbadcddacbabccdaaccaddcacbbaaacbaadbcbbdcdabdcdcddcdbacbdccacddccdccddbcaadccdacbdcbbbadccbdcbcccddaddbcbacbdbdcdbdabdbddcdadcaaaadaddcccbccbbddababdaadabaadaccacccadcbadaaacababbccbbbbaaddaacddbadccacbdaadaabaccbbadaaacbddddbdbdadbaccbccbdddaabaabccdcbabdccbdaacddadcacbbbbbbadcbbddaacdcdccdadccdaaccabbaaaabbbbddaddbcdcaacbbdbbcacdacdadcbdcdccdaaabbbdacbcddccdcacabbabdbbbabdbccacdbddbaccbbccaabacaacdcdbabcbcaadddadadccbdcadbcbcacaaacddbaacaccddbbaaacdddbbbabddcccaabcbddbccaaabcbdccccbbcdbcaaaaccbdacacbcabbbcbbacdbcdaddcbbcadccbdcbbcabdbabcaadbcdcabbbacaaabbdabdddcabbacddbddadbbaaddcabbdabccbccaabccbbacadcabdbddabbdaacdbaaabcabbabbcacddddbdbcbabbacaabaddcbbbabadbacacabdcddbccddddaaacbadcbbdaddcbdcaacaccbccbddbdaccbbdbacddcdccadbadadbcdddbdbcbddbaacbadbdbdbdacadccdcbdbcdbdbbdaaddcbbbbddadddbdacdcdbdcaadacbcbbabdbbbcbdddcccdcddacbbbbcacdccbabaadaaaababdbabbbbbddbaccacaabbdabdcdcbcbbabadabccddbcacdadaabbdccbcbccbabcaaccaaccbcbbccbddabaccccabccadabadcbacbcbbdddbaaaddababaaccbbdbaccbbacabdddcbdccabbdbaabdbcadcaabbdcacadabbcddaabbaabbadccdcdccbcdbaccdcadddbccccccbcabaacacbccdddabcdaccbbababbcdbcacbcbaabcaacababadbbadbaddccbddccbbdabbaacbcddccbacabaacddaddccdcdbddacdddbcdbcddbbddaccbbbabccbbdabbbcbdcbcaacacaacaacbcbdcdcdaacbdcdaaddbbbcccddccaccbdcccadaabacabacddacbbaaaadccbdcdcdcdaabbdccacadcdbdcbbccabacdbddddabbdddacacdbbcbcdbccaabbcacbabcdccabbacabacddaaddcbbdbdccbcbadacbbdbbabcccccabdbdaabdccbdbddaddbaaabbbdbaadcbbbbccbcbcaaaabbdcddbdadaabccbbddcacaccacacadababcbadcbacbbbaabddbadaddabddccbcbabcbdabaaddcbaacdaaddacadbbabcbacaccddbcddbaccdccddbaabddcddcbaaabdbcddabbbcaccaaaddccbcbabdabddabcbdacacabcdabaccacacdcddbbdbbcaabdccadcaababbccdcbbaadaddccccccddaadbdcdabcbbabbacaaaabbdaaddbccabdadbccdbaacacbbddbacccdaccdbbbbacacbabbabdcdaabbaaddbabaabcccbbbaaadcbacabcbcddacbadcddcbadacaddddabcdaaddcdddacbddbabbccaacbabcccddabcaaaaaadcdcbbaadbbaabbabcccccadcbbbbbcccadccbabdcaacddccccdadcbcdbdbbacccbbbadadadddaadddbabcbcdcbcaadbccccacacacbababdbcbcaddbdadabadccbcaadaccabdcdbcadbcbbaccbdcdabbdcbaadbdbbcabbabdabdabadcaadaddbbbbdbacbacabbdddccaddabbadcbacadcccacbbdbdcdbbaccabbcddcbacbdaacddacdcacdcdcddadcbcaddcdbdaddbbcbacdcccacccbdbcaaacdadbabcadbbbabddcdbbbcacccaaaabcbddacabcddbbdadacaacaccdbdbdaacbdcbdccacbabbadbcdddcdcbcbabacddadcbaccbdbadcdaacbcadcadcdbabbbdaadbdddaaadbcddbadcdacbdcccaadbdbdbdcadaacdccaacaaddcddcdaacbbcadabcaccbbbdbbaaaccbcdadabaddbabdadbacbaaddccddbadbcdababbababacbdaaccddcccbbbbbabadbdaabbdacaadbdababbbacbccbdccddbddcaccccbdbcbdbdddbcbdaadcbbdacccbcabadabadcddbcbdbbbcabdadbbbdbbcdbdcacbbcbcddbcbcbacabbbbddaaabcdcdbcbbbdbcbccaababbccdcacacdaaabddcdaddcbbdaadacdcbcbabcadacaabaacdaaccaccadcabadabccacdcacbbdaadaabdccbabdbbdaccbddbaaadbdaccacdbbbdaaabadbaddbbbbdadabbdbddcabbdccaaddcdbcdbbbdacabdabbbaadddddcdbabbbacddccbbbbdaabcdadabdabbdddabcdcccddccbdbcbbdbddcaaabccbbcadadccbadbbbbbcddcaddbbadbcdabbccbcdbacaccbbcacacadaabaccbcaacabadcccaacaacbcbbdccbbccabacbacdbcbdcbacbbcabcbbdaadcababcacaadacbccdbabddabbcddbdbbddabdcaddbbdcabdabacbddaabaacababcbbabdcdcacadcbcadbcabdccddacbbbaacbcbcdcccbcddbdaadadddaddaddadcbcdcbcdabaaaddaaabdddcbbdcadabdabbcdaacdbaacaaacacbcddbcabdcaabaadddabddcabacadcbbddbbaabadbdddbcaacccadaabbcbccbbbddbacaaccbbbccddadabcaabcbdcdaddabbdcaaacdcdcdaabbddccadcaccbadaadcdadcdbdcadacbbbababdbccdacbccbcabcadbabaaddcaacccaadacadacabbadcbabbdaacdacddccdabcdaddcbbcdaabdaccdabcadccbdcaabbdbbcdacadbcabbcadcdbaaccbdbbadcdcbcdbbcabadcdcbdcaaccddcdbddbccbdddbcdabdbccbcdabcddbcbdcaccdcabbbddccdabcdcccccddabaddcdababbddacadacccbcaaaadbdcaccbabbcccdabaaacccbdbbcdbcacbabcacbdccaaccadcdddcdbbbccbdbbbabadabacbaaacbcdcddacdcbcddcbaacbadadabcddbcdcbadcbcbabccbbabdbabbbcaadbbaacbbccaaccbbccdbaaacdaadcadaadcaacacbaccaccbbdbaadaadcbbcbdabadccdacabbdacbbdbdbdabacddbcbcbccbcadacbcccccdabababcdbadcabdcdcbdcbbaaabbcbccbcdaaabdbaaacaabdbcddbaacdcbdbadabaddadbaddcaddccbdcacacbcbcdbdbddcacacacabccbdbbacacccdabbbddbdbaadcacaaadbacbabacddaaccadbdcbdbacdadbdccbacaccacbdcaacacaccaaaaadaaaccaddccadbbacaddddcadaacaccbdadcbdabababbcadbbcbcdaddabccdcdadbdddddcccdadaaadbdddbcaadccbccdbadcacdddabcdabbabddccadcdddaaccabdcadbddccdbaccdccadcaccbcddaddbbdcaddadcdabcacdbaddcdacbbcbdacaccdccddacacbbaacdbddbbcbacaabbdcbcccdcddcbdbacccdbaabcaaddaaadcccdbccadcabbbddccbcdccbcabddcbcbcccbddcdcdabbbbdddaccddcdddabcbbabdbabbaaacbabcdaccadcaaacacbbccdaabdabdbbccccbaadaadcbcadcabbcdbbdccbddcbbbdcabcaacacaaacacdcaccbbdabbbdddcdcdcdcdcccadabaccddbaaaddbdbbcddbcdcbdbdbdbdbaacdddaabbcdacbcaabccdbdadaadbdbcabcbdbbcbdddcdddababcdadccdbcabcaddcdaacbbcacbccabddcbdadbacabddadccccbdcabcabcaaacaaadddcbcdaabadddabddacaccdcbbbbaccdcdbadcccdabaadabcdabdacbcbccccbbbcdccbacccbdbaabadddccccbcaadaacdbccbdabbcacadbacabadcaddbaabdcacbbddbcccdccdccaaabadabdbddbdaddbbbddbbbaccccabaaddbaacbbbcbaacbcbbabbbcdbbddaadcadcbbcdaacbcbddcdbbaddcbdacaabadbddbdaabdcbbaacbcdaadabbbbcddccbbbcadaabcabddcadbddcdddacacbabdbdabcaacdaaddcbcaccaabaaddccaacbabccdcbaadddbdcdacddabddcbcdaacdccdcdcdcbadadacadccdadabacdaabbdaabdcaabbcdadcbdbcbadadcbbaddaabadcbccbabaadbbdcbaddbacaaabcbdcbdabdbacdbddbdbcdaadacaccccbcddcdccdddccdabbcadacacdcbadaabadddcdcbddaaaccababaacbdccababaadddbcdcbdbbcddabbcaccbcabcbcddbdbcdcadabccbddadcadabacdaccdbbacabccdabddcdcdbabdabdcccccabdbaccacdbabacabdaccadddbcaabcaaabdccccadcddaabacbaacaabadadcabbbcdddcbbdbbdcadbaabaabdbdaccccacabadadcaaabdabbbabaadbdccdadaaaabcddacbddddccbadddcbbcbbdabdcbdbcdaabdbdbaccdabbcdbcacbddadcbdccbcbcbbbbdabcacbbcabcddadddaaaccdbbabcadcabcbcdabbadbadadadaacdcababbaccaabbacbcddddcbbcabdbbdacadcbbcaaacbbcdacabdbcdcccccaabdaabadadbaaaccadacacdabdccbabdbccccacbbacbdcccdbbcaaaadcbaacdcdbbdabcdaccdbcaddddacabdcbdcbcbcbbdddccccddabdaabcacdbcacdbdbddddbaadabaddccdbddcbdbcbdacbddcaadbcbbddabcbccbccaabacadbcbdbdbadadbaccbbdbcccbcaadcdcdbddbdadddaabcaabdbdaabdbaaadcbcddabdcdaaaaaddaddccbbbbccabccadacbbdddbbadbadddabcaaddbbdcccbcddbdbcdbdcdaaddacbadcacbcbabcccddbcdbddabdccbdabdbbbbadccddcdbccaccbbcdacdcdbbcbaaacacdbbdbbcaaabddbddbbacbddcddbadcbdcbadcbcaddccdcbdadcddacbcbbbddcbccdabaacbdbbccbbcaaadcdbacaaabcabdbccbdbcadbaabcdadbbdcadaddabcbadbdbdabcbccaaabbcdaaacbcbcdbbacbbcddcccdaabcdadcdcabcaaaababcdabbdbcbbcdcdbaaadddcabcacabbadcbbdbbcadaccaaadaccddddcbabcdcaddacbdbcaadabcddbdcdaaddbbdddabdabbbcabdadbacdbdddbcdcccdaccbbcadcdabcacdcabdcddcadadcbcdadababdaddaccbccbccdddacccbaccbdaaadaadcbdbcaacbcbbcdabdcaabcccbcaccabcabcaadbbcdadcacbcccdbaaaadabdbccbddbbcbacadcdddbcddcaabacbdaacadcbcabccbcadbdbcaccbcaccdaccacdccacdcdcbccddabddcdcababcaadbaaccaacaabccbacbacbabccdddbcdbddacdaaabacdbadbabdaabdcbbbcbdcdcacdbaacaacabcbbadcbbbabaadacacbadbbbaddbbbabbcaababbacbaabacbdbccabaccaddaadbcbacbadcadcbdddbcbacdcadcdabbacacbbaacddcbcacdbacaabbbadbaddaddcdcacbaacbcbaacbacabadbadccacabccdacddcdbbcadbdadacdabcacadbabddcbabdadaabdaabbaacdbaacdccaabcbdabcdddaaacdcdacbabdabababbadadddabacbdcaadababbbdcbdaaacadaaadcbdacdbbbabcbccabdcdddaccdaadaabbabbccbadabbcdcaccdadcabcbbbadcdcdbaacddbbaaaaabaccadbcdcacddccacbbadbaaddcacbbabadcadabcabbdbcaaabbdaabddccccdcdbcdccdaabacccbcababaddadabcbcacbcbcbbbbdbbcdbdbaabaddaabcbdaaadabacaacbcacbccabacbbbadcaaacccccdaaadbbcabacbddccdacabcccacbcabbbdcdbaabcccaddcabcacdbdaaabacddbbddaddadbdcdcdacbcbbdcddaabddcbcadccdccbbabbaccdadcdbbabbcddbddbdbccdbcadbccdbdabcbcddbdacbabaadaddccbdadaccbcbcbaadbbdbbbdbddbdadaaaabacadcbccbcaabacbaadabacbacaabbabbacdcbbdcccbcadcadbcacdcacacccddcacbdaabacaadbcdabcabdabdacbbdccddbdbbbccccbadadddaccddddbcccbcccbbcadbdcdcdddbcaccbaccaabbdbabdddbadaaaadccccdccbbcbbdccacaaacdcbcbaadaabdacacbccdcbcbadbadadacabbccdacaaaacacacaacbddcaddbdadbdcaaadacdbdbabacddcbcbcbbcabdccdabadabbbbbddbcbdbbbabcbbccccbbaddaabcddbdbaccadaaabcdcccaccaabddddaddcabaaaabbbaccabcabbababbbbbdabaabbacdcaaadbbdbaccdacddbcdcdabcdbaddaacdccbcdacbddddbbadadaccdcccacdcdbbdbdcbbabbbaaaabdddbaaaaabcaabbddbcdbbcdcdbdbbcccaccbbddccdcbdcdddbbddacdddcdcababacdddcbdccbacbbddbbcaadaddccacddabbacacbadabbaabdcdacbdcdacdacaacadcdabadabdddcdcbcddcdbbdcbccbaaddaddcbcdddadbcdadaabaadbbabbccdbbacadacdbccbaadcdadaacbcabdddcdcbbdddcdacadcaaacddbcabbccacbcccabbbdacacbdcdbdbbabcacbadcdbcbabdabbcaabbaacdbccbcccaaabbcbcacbaababddaddbbbacbbcabbadcbabdacdcbdcccabbbbcdccbcaabccccdccbbacdbdbdccabacaaadcccddacdabcbccbbcbcadbadabdbadbccbcaaadadcdbddbcabcbccdcbccdbadcdccbddcbaadbaaacaaacddaabcaadbbdccbcababcdcabbbdaaacdacdcdacdbcbadccbbdbdabdadbcbcaacdbacdbbbaddbabdbabbbcbbccccbcdcbbdccdcbdabdcbdaaccbcbdbaaacdbccbacbbddbdadccabcdcddbacdabdcbbaddccaadbcabdacabadcbbcacaaadbcdacccacbdbddbdbbadbcdbabadadabaaacbccabcbbbcdbcbcbdcdbcdccbddcccdbbcbbaacccabbbcdbcbdcdcacdaaacadddcdbdbdbaddbbdaaccddcacdccaaaaaccdcdcabcbbdcbccacadacdccdcbabdbaaaadbbcdcbaaaabbaadbcccccbaaccbabddccbccaddcacdbbaadbddabbddcbcbcaabdaacdccbdcdbcacbbddbcaddaacddcbddcddbadacbadccbdabcdbaabbbbdacacbbbcdbbadbabbdcababbcbaacbdbbbbcbbaccaacdbccbbdadcacababcbcbcacadcbacbaddbaaababbaddadaabcaddcccdbcbcdccbcbcdadcbdaabdcdbaabaaadaaabcbabbcbbbacddbdddbcddcbcbbbcacaacaacccdaccbccddcbdaabdbdcaaacacbddddbdabccdcdbbcbccdcacdadccdcdabadddabdcdcbcbddabacccaabddcdacdaaaccdddbdacbbdaadbadcccacbddabdbbcbaccaccbaabcadacddadcabcbdacacbccadbdcdbaccbccbdadabcbdddadcdbdcdbdccccbcbbbcabcddcccacaddbaaaadbcdacbcdcacddbcbdccaccbdbabcdaabddaacadbbaacbadccdccabaaaccaabaacabaacaaaacccacdadcdaabdcbadccbcadcbaddddcdddaccadbdcccccddadbacbcbbbcacbadabbbcbbcaddcadcdcbbdcbabccabaaddadbaccddcbcbdddcccaccbdcaddcdddadacabbbcaabaabbacaaaccbbcabaaadacbdcddbddaccbbbacbbbacddbaacaacccbadbdaaaaddbabddadbbdddaadbacbccbbcdaddabdcbddaabbbdaccdccbdaadacabbbbdddddadcbabbdabaaccbddbbcdcbabbdaabcacaaacadacdbcaacaadcaddbabddacdcacadbbbdaabccbdacdcbaccacbbcaabccbbdcaacaabdddaaadadbabcdaaaddadabddddadbaabcccdacbbcdaccabcaadbacaabccaabbadcbbbaaabababddccbddcabaaaabcddddadcbbdbbdadbacccbaccccbbabcdaabcdbabcdaaddaadbbcbbbcdddbbcbcaaabcaccaaddbcdcbddbcdbbbbcdbcdbabcdadcbdadbbbacbdcdccccbbbacddccbccdbbaadabaaccdcdccdbbaccaabbccdbaaaccbcdcbadbcddcbdabddcdaababcadbacabdadbbbbdadccddbdabdccaaadbcaddaaaaabbaabdabdccdbcaccbcbddacaaacacbdaddcdbabaacbdcdadcacbbbbdccaabcadbcaaaccaccbccdacacdbdcbabbadbcaaaacabcddddaddcdddcdcddcabbbcaccbadacbbdbbbdbccacbacdaaccabddddaccaacdccacaadddcaccbcaccbdbbdccbdddaadaacbbaaabddadabacdaacdddcacbacbabcacbcccbbcbbabcdaccbacdaadbdacddacadcaddbdacaaaaccbcdaabaabbbcacadacaadcabdbcbabaabcccdbacaacbcabcbdbdacbcccbaadbccdcdbacbbcaaaccddbaacadaaabbbcbcdcbbbdbabbbbddbbacbdcaabddccaccbdccacbbbbacbcbbbdacdbcdacddbdbadcccbdabbbbcbdadccacdcccacabccbbabbcddabbddabcbadacbccabdccdbccbcacababcacbaaaacaaaacdbdccdacddcdbccbaacabbbbdbdbcaddbabadddbccbabcadaabcdbcdbcabbddccdbcddbccaadcddcbcddbddcbddcdabbccbdcbccadbbdddcbbbbcbadcaaadccccddbdbaacacdcccdbdbcaacbabdcaccdcbdadbdabcadbbdbcdaccbdabdcadbcacccbbbbdcdacaddadcddcaabdbaadcdacddcbcbcdcddccccacdaaddcdcdaabadbbccddcaaddbabccdccadacdaaaababdbbaacbaaacbabbdabcccdcdbcaadccdccacdaabaaaddbcabadbbcabacaddaccbdcabdbcabbcdcbaadcdbacdadcacdbccacddabbccccaadaadbdabccaccbcdabbbadbccabaadadadadbbddcbdddddddbbbadacbcbdcaacabdbacaaccdadddadababacadaadddcbabbbabcadaddcbcaddaaacbcbacacadcaadaaccbddbbacbcabbddbbccdaadadacaddbbbdccadbabddbbbababdcbaccaabcbadaaacdcdcdacddbcabacacbcdcaacbddcdacccbccaccdaaccdcababbdcbbadabbbcdbbbddbdbdbdbcabdbaccbbabacbddcadabbcbbcaadaddcaadbdadaadbcbadcabaaacacbbabddaddbdbcaddbddbaacaabaddaccaacbabadcaabadabaccddaccdcbcddccddaabdccbbbdbacabdbcdbdababbbdbddcccacdbdbbacbaaabbcaacabcdabdbccbbabdbaababdccadabaddbdccadacaaaadcacaccdadccdbcdbdabaacabbbaadaabbbaaacbcdbbabadddabcbcbaabccaacadbacbabbcdadaccbdddacdaaabccaadbbcbbdcbbcaadadbaabdbdccbddaadacddbaabccaddbcccabcaddbcaddcbadbddddbabddcbcbcddabcdbcdbdccbdbabdbcacadaacbbbbcbbadbccacddaddbddcdbbbcbddbbbdcddaabcaccbcaacacabbccbdcaaadcaabadacbddbcabbccbacdbadcbcadbbcacabcddccccddcbcbdadaabdabdabbaabcbcdbadacadaddbdcaadcbcabacccacdadbcdcadcaabddabdbadcbacdcbcdbcdbaabcddaacdbaabaddbbbcadaabdbddbddabcabcaaadabdbdcbcdacbdacaddaabcabccdadcadaddbcdbccdcbaaddcbbdacbcadbabacbddbabbaacdadddbacddadcbdbbcdddcbacdbdadbcdcbbbbbdccbbcccddddcccdbacdaadcabdaadacbdacdddbcbbcdccadacadddbaadddaaacbbdadabaaccbdabbcacccdbacaccdddbdccccccaadadcccdcacabdcabacdcacadddbbacabbdbcddbcbaaabadaddcacaccbccadccdbbdbbbbbcddbdcadcbbabdadbcbddbcdbdcdcbaccdbdbadddccaaaddbdcaaadcbddcbcbcdcdacccddabdaadaacdbbbbadadcdccddddccbddadcdbaddcacbbaccaddabbdadaadadbcdbadacccdbdbdaabccdcdabbcabdcbadcccbabdadadbaccabdacabbcbdcccddcbbacadcdadadacddadadacdadcbdacccddbddbbccbbdbcdcbcadccacccbbcdbdadabaadcdbdbcdcbddcbaccdcadcbbddccdbdbcdabcdcbdacbcacbbabdbbddbdbcccabadadbccdaaacbcddaabdbbbaabadddbcadcdbddbbaabcbddbbbbbcbcdbadcccccdddbaccbcdddadbddacaccabbdcbdbacbbbddcccdadddbbabbbaacaacdddbabdcbdacdababbdaabdccadbdccdcbbbbbbdcbcdaddbcaaadaaccaddcbbdaaabaadaccdcadadcacbbacdbdaaabcacccacdbaadbabbcaccddaadabdbaddbcdbbaadbbdcddcbadcddaadddddddabcbaaaadccaabaaabbaaddbbabacdbabaacccabbaccbcbddcbbbddacccdbddbbbdaacddacdaabaccccbddcaacaccaddacbabcdbbabdcbaacccdbdbbcccaaccdcccdcddcaacaaabbdaabdbabacbcdbaabcdbdbbabbacaddacabbdaddcdabaabaadccaacacaacbabdbcadbccaadcdadcdccdabdbcccddcdbcccbabccccdbccdcbcacddbaabaabcacddcaccbaddcddabdbbdddcbbbdacaaacdcdaacacddadababcccdcaaabbacdadbbcbaaaabdbcbbbaddbdbbddbaaaadcddbabbcabdcddbccaadcbcdabcbdcadcbcdcbbcadabbaaddadabacdbcdcdcbaacddbdbaadcaabbcbdddaabcbdccddcaacdacabacbcdbbbcdcbbadcacbaabdcabdddabcdddbddadbacaccbcacaddccbadcbcccacdcacdbacadaccdcbbaddddabacbbcaccdbdcdbbacadcabcdcadcdccdccbcaaabbcccaadcaaaabbcdbbcbbadacbdcaacbacbdcddcccabdcddbdccabacdddddabdbcabbdcbaaadaababbccdabbbaccbcaabacdaddddbbbccadbccaaddcbadbacdbbccbcdbdacddaabbbacbcdadcaaaaacbbdabcbcdcdcaccdbbddacddadabaadcaabadadcdadcaaacaddadbcaacdcdabcdbbacabdaabbddaabaacababadcaaacbcbdbcbcaaddaabcabcbbadbbaabdbbaaadaabcdbdbcbcacacdbcbccbdccabcccabcacbbccdcbbadaddaddcdbabddbabcccaabbbcccadddcbcbcaadadbdccacdcdbdbdccccadddbbcbcccbbbbabaddcbbaccbacdbabccdbabdaadabbbbbcbcbbdabbbcbbbcabaadcbbcabdaddcadaaababdaadabbdcccbbbcabcaddbbdddacdcbacccbabbadcdadaabbbddaaddbdacbccaacaacacbdacbdabbadadddbbbabcbabdcddaddccacdbcdbbcbadcccbbaaabaabdbcccadbbabadccadbdcccaadcdbabccbabcbaacdacdadddcaaaacccdcadccbdabbcdcddacabbadacbcaccdabcccddabaccdcccabcbcaddadcdcbbbbdacdcaadacdbaadbdbcaccadcdcaabadaabddaaccadbdbccdbacbdbbcbddacabdabdcabcaaadacbdaadadcabacaaadaccaaadddabcdcddaacbdbdadcbbdabdddcdaabdbbdaccbbcdbcbbadcabbcddbcaaadacccbdbbccababbbddcdbbddbdadcaaaacacdbbbaaaccbccadbcdaaadddbadcbbaddadbddadccbcccccbcadddadacdbcbbcdbdbaacbccdabbdadbbacbaccacbbdabdddbddccbcdcdaabacbaaddcbcbcccbdbccacbdccbcbdbcdadacbaacaccaabadbddabadddadbababcbbccabdadaadcbcbbbaccbddbaccbacccacacacaadcbcddbcdbdabaaccaaacaadabccdaadddaabbcbbccccddbdbabaccbaadbbcaaccddbadbdaadcdbdacbbbcbabddddaadacbbbbbbabddbddbbbacabadbcbcdadabcabddcbabacbaccabddaabdadcccbdcadcabcbbbabbcdaaaccbdbcacbabadcbacabcbcaddccddcdddacdcbcdddccbacbcbaadcddcbdbbaaacacdccacddcacabccbcbabbdbcdbcaacaaddacdddaaddbdcdbadbdccbdbcdcbbdbcacdbabbacbbccbbadaddbcbcddbaadbbcdaccbcaccdbbbabccdcbbadacddaccccccccdcbbddabcadacbdbdcdbbbcacacdabbbcbbdbcdaccdbcbaaabdddbabbcabccbacbcaddaabadddacadabcaccddadbbcabbaccadcbdbcacdadbcabcabcabdcaadcccccabdbadbdcbdcccdbdaccaaccdcaccdcbdaccdbdcbbabadbdbbbcbcbcaabbcbcadbbdadbbcccacbdabccdccdbddacaaabaacdacbbacccddbbcbbababcaadbabcacdcaccbddcbadabdbbdbdababbaaaaaaacdddccdccdcaaabcdadadddccadbcabacdddbccadddaabaacdaccbbabdabcccbbadaaadbdcdbbcaabdcdaaacabcddbacddacacbdbaacbcadcccccccccacbdcadcdbdabdbddcaaababcadbdbccbdcbbcaaabcdcadbcaacbbadbbbbacaacdabbdccccddaadbaddbbbbddabcdddccbbbacbdddbbdbcadbcacbccccbbdaabbdddcadcbddbabadacbcabcdaddccbdaccbaaccccabbdbacabbddccbaaadbcdbcbbbacadabbbacccbaaddccdbbdcdccaaddcdcdaaabcddccbcadbbbccdcbaddbccadddadbdcdbbbbbdabddccabccdbbbddbbdcdcdacbbccddbdccadbdcdaacadbabbccdcacaaacacabbdbccddbbaadcaccaaaabbdadbbdacdbccdcdccdbcabbbddcbcdadccacaabbaccdacdcdabcbbbccdccbaaccdcbbddccdacbcadabdacbbacdbbdccabbdccadbddaccaddaabadccbcaadabaddbacabbddadbcbcacbbbaabddcadbcdbabcddcdacbdacabdbcbccbdccdbabbbdcbdbccbaccdaaddbcbbcadacaabdccabccdaadabbcbcababbcdabbbbcddaacaddabdaadadabddbdacadabccdabcadcbbabbbdaacdabaadcdbaddcdaacacacabcabcdcaabcbaabbabbdddccdbdcbcadacdbdbcbacaabccbbbdbbcccdacacbadadbcaacddabccbdabaacdabaadcdacaacddbaaddbddcccacbaaddcaadbbbccdddbbbadbaacdcbbbdabbdcacdcdbbaaabccacaaaccbbcdabcaddabaaacadabdbdcddaaccbbbdacccddcccdcbcbbcaaddabdabababbbdcacdcdcbbaaacbacddcdaacddbbaddbbabddddcbcadcabbdbdbdddaccabccaadacdcbbdbcbdbdcbcdccabdbacabcdcbcabbaadddbdbbbbabacbcbccdaacdcacbccbabdbdacdcdcdccccbccaaadddbbccaaddadcacdccacccbacdbabcbbdbcbdccdccaaddbdadbdcccabcbcaabbadbaaabcbdbcdadadaddcdaabddcccbababdbddabcdbcdcdabdaacadbbaacdcdbbaaaacbcddcdaadbcadbbbabbabcddacbcdaddddcdbbcbcadddabbacbcacacbbbcbcbbcbccddabcdcacaaaacdcaabbcbbbbacdccabcaaaccdcbdbcacdacdccaaadccdccacbbdcabdabdacabadbacdcaaadacbadbcccbcddacdbdbabdccdcbadcdbcbbbacdcdbbcaccbbddacdbcbbdadcbcbadbaaccddccdbdcabbcbbbbdddcdcacabadcadadadabcdabaabdbcccccdcddaadbacdabdaabcadbbaaaaddadcdcdddddbbcdccddccbadcacdbacacaccbbbcbaabbcbbadabdbcacbbbaddcddcdddbdbacbdcbaccddbcbabbbdacdcdacbcddaaacbbbdbcdbbdcbddbbdcbdcacdbcbbccbbccdacbabdbddccbcadbdbaabaacbdbdbdcaddacddccbaacaabcabbcaabbcdcdcbddbaccbbcbccadadacdacaddacbcdbdbcacdccbabcbdbabaccadabdabcaaddcadadcccccbbbdbcbbdabbdddacbadbaaadcbacdadacabddaacddaaacabdccdadbccbadbaacddadacbadbadbbbddcbabcabbaabdddbcbbdcdcabacccdcdaabdddabdaddbcaacdbdcdaccbbabaccbbddddaccdacdbbdbacacdacdddaadcdbdbcdbddddbacbccacbbacccaabdbdccbabcbbcddbbabcbdcacccccadbcbbbbdcbacaccacadabdcabdabcbdadbcdcaaabcdcccccdbaaacacdcbabccbbdcaacdcbdacacaadccbbdddcaadbccbcbadcbadbdbdccacccadadcbdbcbbdbcadcdcaacdcabbcccdbaababcccabbbcaccaacbdbcbcbabdadaddaccacbabbbaabbcbadcabddcbcdabbddcdcdacaacabaabbaddadcbccabdabadbcccdbcdcdaaadaadaccdadcbddbbdbbccdbbabdabdcabbdbcdbdaccbdccdabcdaaaabbbcdcadbdabcbddabbacccdaccadaabcabaccabadccdddbabcdbddbdacdbccdcaacadaabdadbadadcdadbbdaddddcdddcaddaadcbddbbdbacbbacbdacccbbadcddddaabbbabacaaddcaccccadbccdcadcbacddddbdcaddbaabdcacdcbcdacbdbdcbbcacbddcbbcacabdcdaaccdbdaacdbcaccdbcccccaabbdbccccaaaacabcacacabaadcccaabcdbcdcbccababbdccabbcaabcdabbcdddcbdacdbdcbccdabaabbbcaadbccddbaaacddccdcccabbadacabbbccdbadbbccbdbbbadcddcddadddacbcbbaaacadbdabbaadccbbbbdbccdacdaabccdabbbdcccdabdaaaabbaabbaabcddbdbcbabbbcacbabcbdadbaacdaaaabdbcbbcaccddcdadcbaaaddcddabdbaadbcbbbbcdadacddcdcbddbbdccdbaabbbdcbbaadbadabacdbbdbabcbddddaaabababdadadbdaccdaddaddcadbcadbadbcbcdbcabaaabdccadbbcdcddddcdaccabdccbadddadcdaaddccbdcbadbadadcdacdccccaaabacccbccaabddccacbdaddcccacdaadbdadbbbcabaccaaddbbccdcacacdbccdccacddbacaaacbcdacccdadacbaaabacadbbbcccacbadadcaddccdddabcdbcddaabbcbcdbcbabdadababcccabdbaabdcaabdabdccaaccaacabcacabdbbabcaadacbacbccdbbbdaacdcbacbdadbcbaacdccdbbbdadcabcdabacdbbaccbacddbccaddaadcacaabbdccbccbbadabbacdcaccbbcbaaddcadcbbaaacadaabddabcdcdcccdbccabdcaadabcdadddaadacdcccacddcdbbacdbbababbaddbbccaabdacadcaddcdaabacdaacccaaabcdbbbbcaadacadddabdaabcacdcbccdbacaadaccabbbabacdacdbadcddcbcdbcbdbdaddaaacdcbdadcbabcbbaacacbcdddbcddddadaabcadabddbbabaadcdddccbbbdabdbdabcbcbccadddacbdcbcdaddcccdddbacacddbbbbbbcccccbccabdccbdbdbcbdcdddcaaddcabbaddbccbaadabcbbdcdaccdabaddcbacacbcddabdcaaaaccacaacadbadccadbcbcacdcdcabbbbddcbbbbadacadadddbcaccccdaaaadacdcdbcdcbddcbdbadacdacaaaabbacbdacbabdaabbddcccaccdcccdccbbddaababdcdbddaadccbbbcbaaccbabdcdcdbabadbdabbaccadbcdcbaaddabadbcaacdbdbaacbbacdddcbbdaabdcdddcbbdcbdadabacbbbaababdbbadcddadcddbdaadbccccadcbabacbbbcddddcddcbcdcccbadcbbbacddbbadbddbcbddcbddcabbbdababacbbbccaababcadabbadbadcbccdbdccdbbcdabdccdaaadbdddacabdcadacddbdababddabaabdbdadacdbcdbcbccaacbbacbdbbdadbbddcdbdcabbcbabdcaaccbaddaabdbbaacbabadcadaadbbdddbaccddbcbcdcacbcdaddcaaacadaaaacccccbbcdabccbdbcbcdbddbbbdbcdcbaababadacccbcccaabdcacdabaababcacddcdcacabccbdabbbbbbdccbbbdcbadabadbbdbbaddcdcbcaadbdcccdddbdccdabdcacbdbaaccbadcbbcacaccbbdddbcbcbcbaacabcacbcbcbcacdbcaacaaadaccbabbcdabdacbdadbdabaccbccaccabaaabdabccdcbacddadaaccdbbbcabddbaabccdccadbadddacdcccacbcabacbcdacdcbccabaaaabbbcaaddacbddcabcabbabdcabcabbdccbddaacdbacbdcbbabcadccbadbddbdbbddcbbaddacaaaacbcaddcdaacabadbabcdcddaaaadddbaabcadcadaddccdccbddcbbabaaacdabddcddbccbabdbbcbcaabdaacadaaddddabbbbdcacbddacdcdacabdccdacdcbadacbcacabbdacdcdadcaaccdddddaddacbdccddddccabddabcbbaabddabacbbabbaacbbdbadcbaabcbdcdcbbaababcbbcadbdcbdbadbdddbcbccaabbdcccdcbaabadbccdddabdadbddacadcaabbabcdddabcddababdacbcdacaabcdbaacdbbcdddccacdcaaabcabbcdaccadbcbbdbbaddbadadbadadcbcdcccdbdbdcbbdbbaabdaacdaacaabbcbadaaadbabdcbcaaddbcdcdddcdabbbccadbdaaabbdcdbddadbbdacacbddbaadadcddcabdaccbadbabbacaabaaaddaadcbdbcdbbbaabbcaaaccbcccabbbbadcaaaddbbadcdddbddcbcdabcbdcbcabbcbdcaabbacccdcbbbadbdaaadabbcbdbcaacdcadddaaacaccddabccacaccbadabddcacddaddcaadaddcddbcdabcddbdabddbadbbbcdcbbdaccbbcbbcabaabdabacbcbddadbbaadccaaadbdabcbcbdbbdcdcdbcccccbdbaababbaaaabcadcabdcddbcccaacdaabcdbdabdbdbdaddbbcaaccabdcbbdcbadccdabcdabaabbcbdcbcbbcdbaaccadbddcdaabdbdcbacaadcacaadccdabcbcddcdaaacccacbbaabbcdddcaddabbaccaadbcbdbdbcdbcddccaaaaccdcbaaacadcabbcbcbbdccacddcccccaccbbdadaaccbbdcbabdbcccbaadbaddaccccbbcababcbdaadbcbdcccacdacdababbdddadacdcaccaaacbcccdcbcbbbcdcbabdabbbdabccdbdccaaddadabacacbbbdcbdaadbaccacdbcadcadaaabcbcaabcddadbcdababaadbddddbccadccbdbbddccdcbbcdcdcacbdaaabdbbdbaaabbadcacadbaaccababdbcbcbaadcacdbaddaaabdacdbdcbdbddabbabcdcbadcbaddabbbdaadccabaddabadaddbcbbcabccbcadabababbadbaccbdcadccbaadaaccabbaaabccbddcbbbaaabdbadbbdccdddabdaaaabbcccbddbdadbcdbdbdcdcbbbcdccabaaadbcbbcacdbaaccbcacabacbabbddabababdbbddbcacdbbcdabcabdccabcaabbccbccccabadaacbbaddcdcbdabacddbbbdcbdacdaaddcddbaadccdbbcadcbaacbcccccdaddcbcbcadabdcaaacabbcdabbdbcdcacacaababdddbcdbcdbacddbbcccadacaaabddcaadbbbcdadcdbcaddcbcddddddaccbaccacaddcadddbcabaaaadbdbdadacabdbacbdbcccbcbbabccdbaaaccbaddbccbadcdbdaaabcddccaadadcabcbadacdbdcbcadbcdbabaccddcbabaddbabbcbbbcbbaabccdddbcddbcaaabbdddbaadaaaaacbabbcccdcbbdddccbbbabdcdbbadadcdcabcaddcddbaaacdbdaacdbdadaacaccbbaadddaccdcbddcabdbdddddddaadcbcaaaddddaddbcadccdddddaabdabcbcaacbdcdbdddccabbbaccccccdabdcddcdbdbdadcaaadbdddabbbbcccbddbbbdcadddbdbcdcdacacbaddbcadcacccdbbccacbdbbcbdcbdadbdaddbdbddbacaababbdbbdacabccdbabadacdbabadccabcacdacaabababaadbaacdbaabdccbcdcaddcacdbabbdacacbcacabacacbbaacddcccabbadcddabbdababadbaadccdbbbaabaadbcdccbbbcabddacccadabadabbbacbbbbccccbaaccbcbbbbccadcbabdaaddbcbbabcbaddbdddcdddadbcddcbacbabbcdddadbdabdcccbdbbaddcdabaadabbdbacbccbcaacabbacabdbbbdbabcaadacaddbbdacdabdcaadbbddbabaadddadbbdbdbdcacdcbdadabadbbcddbbdcbcdacbdddaababcdbcaabbbbadaacadbaaabdacdabcdcabdbacbbddaabbbbababacdacbdadadcbabadbaababdaababcbaadcdabcdaadddddccbdccdadccacbcddbbbbdcddbacddbaddaabccabcdaacbabbddbcabcadaccabdbdcbbbacbadacbdccacabcabdccabddbcaabaabdcccdabbdbaacadaddaddccdaccdacabaabbdadccbbbdbcdabdbcabacdbddacccaacdcdcbbcabbbbabddbbcbdbcccabaabcdddcccdaaabccaadcbccddabaddcabcbdbbcdbabadccdcbdaabbcdcacccaadbbcabadcaacbddbbcbcbbbbcddbabcdaacbdacabdbcaadcbacbcbbabcaddccaaadbaadcabcccabacadabadbdabaaadddddbabbdabdacddddcbbccbbccdbacdcbdaacbbbbbbdbadcdcbbbbcacbcadccbdbbaddcbdaccbcdcbabcbbabbbcadbbbbcadcbdcbddaabcddcaabadbbcbdddacdcbcadaabcadbacadcabddaacdddbccdabbddbacbcdcaabdbcccbbacdcaadaaaddacacacadaabacbacacbcaadcacdcabdcbdacccdbbadbccdcacdaaaddbdacacacbcaddadabcddbaddcdadbacddddbbccdddbbcbdcaccadcccdcdcddccbcdadcbbbadbbdddbbcdcabddadcccbcbcabacbcbbcbcddbadcacacadcbbcdcbacbcaacbbbddcadadaacdabccbaaadbbbdccacddacdcdacdbddabbdbdbbbcabccdabdbbbadbdcccbcabcaddccccbcabacabccadaabbacdabcbaaccbaccadccdabbccbdcddaacbccacacacdcadcacdaacbdcbdacdbbdcaadadbdcddbcdbdbbbbddaccdbcabbcaaacdcbcadcbcbbcbdcbcabccccdcaabacbbcdddccbcbdbaadacdbdcbaddadcdbbcdcdadadbbbbaddbcbddbbdacacdcbccbbbcacdaccbacacadccdadcbcbbcdcdbaaacadaddddaabacadddbaadabcbbacdcadbdbbcdabacdaddcdcaddccbdbdcadaddadabdcbbaccccaabbdaddbcadbdbaddcaccabdaacbbabdaaddccbaaccbcdcababaddccdacccaacbaacddddbadcbbcdbcaabdabcccddadabbcbacaacdbadbdadbbccaddcaadaccabbccacdabccccdbcdcabacbddacadaccacddccddaabbbcacbdbcdcbdcadadcddbccdaadcaaaabcaabcaaddacccdbacaddacbaaadbabbbbbdcdcccadaaadbcacbbaaddaaabcccddcbbabadccbabbdacadddaaaccbacdadaabcdbcbdbdbdccddaaadacdbdddbaddcdaaddcaaabaacaabcaabdadcbbaaccccdbaabbcaadcbadadbabdbbaddcabccdbacdababdaaadbbaacaccddccddddddcbabccbdcbbacccdabacaddcdcabcbaacacbdacbdbaacbadaadadadcbadcbcbdddcdbccccdcdddcaddadadaabbabbbccaacccdbacddaaacdbadcadccbccbabcbbccbbabbcccbaadbdbddbdbadbaccaabdaaacbcbcccbadbbdbcababccbbbdabadadcdcbbcacaaccaccdabcaaadabbcaabacccccbaacadacdbdadbabbbadaccaabdcdbabdabdbabaccabcdbbaadcdcbabaacbbbdabaddbdcbbcbadbaabcddadadbadbddcbbdbddddcbcdcaadcdcdcadabaddacdbcdadcaddcaccacaabdbacbbdddccbdddbcccdabddabcabcdbcadcbaddcbdacccdcdacbadacbcccccabaaaaacdccacaacbcabadbbbbdabaadaaddcddacacbbcbcdadddbccadacbababddcabcaacccaddbcbccbabaacadccbddcbdababdddcbbdbddbdbdbcdacddccaadbddaddccccaaadccacaabdddcaddcdccbcdcbddacdcdbadcbcdddcdaaadaadacaaaccddabccadcaacdbcdbbccddacbbbabcdcddcaacbdbaabdbadaacbcdbacddddadddcdadadaababcaadbdcaaadbbadbcadaaddbcbacdacadcabcabbdccbccbcaacccaabbbcccccdaddabaaaadddbcaaaacbdcbcddcacaddbdcdbbcddaabaabdbaadbcdccacddacadbdacdacccaddacdaabbbaacccaaadcaacbccdbacbddaaccbdbcdddcabacbbcccbbacdbacdddcbbdbbabdcacabadbddbabcccbbbdbdacdddaadcddbadccdbcbcadbdcaddcbdcdbacbdcaaacbbbbcbcaabaacaadacbbbcaacdaaabbbabddcbbcddbaddabcbbacddcaacdadabaacabcbdcdcdcababcbccddcdcaaaddbbbadadbbddcdbaacdddaccabbdccaabcbdbbacdaacaddaccbdbacccdabcddaaacdbcbabccbcaddbacdcdcdbdaddcdbdaababcddbcabdbbaacacdbaaaddbdadbbbbcccadbbcdacadabcbbdaaacaaacbbccbddbaabdbbacbccdcadabcdcbbddcbaabdcdbabaaaadcaaabbdcdaddccaadcadaccddadcdbadbaccbdcdaddbbbbdddcabbccabbcbdcbaaaabcadcccbdbcdcbdcbbbdaaaaacaaddbaaadaabadcbddddbabadabaacddbcdbaabaccdacdbdacaddabcacbaaaacddbbbabbadcdabdaabbabccaadadaccbdcbdacbadabddcabbccbbaaccbddacdccbcacdccadcbababbdabdbbacccadbadabccdaddaabbadccabbbccabbdacaababaaddadaacdbbccabcaabbaabdcabbbbbcabbadcdcbcbbdbaabadadbdddbcbbababdaadbbcaccbbdadadbcbbbddcacacbcccdbcdabacdacccbdabdcaaccacacbabbdaddbdaadbcbacabbbabaabdcccbbccdcbdacdcaabdcaccacdddcacbdaccbdaaaddcacbaabcdbaaabcadccabdabccacccabcadcaddbdcadaadcbbddbdbbccbbdcbababaccaaacacacbcdcdcccbcddcbabdbddbdcacdadacdcadbabbcdcbcbbdbbbddcdccdababadacabbaabdbdcadbdacccdbbabaccdbccdadbbbaacdaadccddcbbdaabaaddadadddbbcdbdcbadbcdddaabcbbdccdccdcacaababbdbaccbddcccdadccdcbccacdaaddaadcdcacadbaaaaddcdbbdabbaccdcaaacabcabdaacbaddccddbaaaacacbccbcbbbcbabdddacacaacdcabbcacdbacbdcbdacdadcdbbdcbdcacabadcbbcdabacabdbbcdcaaddbcdcdbccaccadbadaacccdddacdbbabbadacaaacacdbdaaadcaacccbcbbdbbdccaabdadbccabbbdbcbcbadddcbddcabbbabdbbdbdadadccaddbbbddbbcadadbccadabbccacbdabbdbcaadcbdbbabbaadcdbaadabacdabdbcaaddadcdcbbbbbddabbdabdbdbbbadcbacbcdabbacbcaadbbbdabadbbacbabdcbcabaacbdbbcdbaccabcdaadadccdabdabcbdabdcdddddbbdabaadbbddbbaabcddcbcadbcabbdbcdbababdadacdacbdcdaabbcbadbbacaadadbcdabdacbacaacabaadadbbdcbcbbacbacccbcbdadacadaacddbbbaadbcccddddcdccccabccdadaaccaadccabcadbbdabddcdacccbbbabaccbabcbdabbdadaddabdadbbacddacdccdbdcaadcdbccbbdcbbacddbaddbddaccbcbdabdaadcdccdacbadcddcbadddacbbbbdaccabbacabdacbadbdbadabbadddbdcbbacbcbadaaadbdadcbbaaabbabdbdddbbdcbcbbadaccdbdaadbbbcbbdbcabddddbaadabbaadcbcaabbacbcaacdcccaddbcacaddcacdbcccdccbbddadbdadbbcadcabcdbdddbbbddcbdacacddaacdadbaababadbdbdacabbccbabadbccbcaccdaacaacababdccabdadbcacbdaddadbaabaddcccbdacbddbdcccaccaaaadbcdcaacdacadadaadabcabcacbbcbaadcdbcddadcbdabdcdbcddcbbdbdcbadabdadabbdaaddbabaabacaadbbddaaadcbbaabbdcdbcbbcbccaccddacdbadadbdadbdbacdcccbababbdbdbbabccdbbcdaadcaaaaadcbccabaadacbdbbaddaacdcbabacbcbaabaaacddcdcccaccbacacacbcdbcdddadbdcbcacabdddacaccbdccaacadbacbddabbcaccbcacaddabbcaaacbdbadaacacbbcaddaacdcdcbabaccadccdacdabdccdadaacabdbccdbdcddccdcbbcabcbcdaaadcdaabcbcbcabdccdcbdcaadabbbbcbcbacddabacbdacabcabbdbcaaccdadbbaaccbaabababbccdaaccbbcbaaaacccdccdcdcbcacaaacabbcaabaccdacdbaabcadababdbdcdcbcdadacdbbdbdbbdcbcccaaabaacbcadddcddadccbbdccdbaacbdcbdcbbaaccddcaabcccdbdcbaacaacadadaccdcaadacaabdbbaddcaddbcdaaddaacccbdabddbbbccbcdabdacbcabcbbadcdabacdaacbcdcdbcbbdbacaddcddacbdbaabdcbaabacaddbbcbbdbbdcabacadadbbacbdbbbcddacbcbbbcadcbaadaacbacbdcdcbbadbdbaaabcaacdcdbdddacbccbcaaaababaccabddaaddcdacbbacaccadababddbdabbdbbbcabcdadabddbbbcbbadaaacccdaaaabdabbbdccccbddcadcbdbbbcccddaaccbdddacaddccdccbadbbcadbcadbcbabcdbaacaaaacabaadabbdadcadacaaacbdddaabddccddabdaaabaccdabaaaadbcaccbccdbaccaadaccacbadbadcaaaddbccddcbcabadbbdababacdcbdbcadbacddadddcadbcbddddcbacaacaaddbccccaaddcbaabadcabacadbcadbadcabbadadbcaaadcccdacddcadadabcbbdddbaaabdbbbddaddabbbacccdcdbaabcbcaabaabbddbbbdcbbccadbdbbcaadbcabadabddddcabdccddbccaabcbdddacbdbdaddadccadbabaccccaaddacbcdcacbbbbdabccaacacdacccccbbbbcbccadbdddacacddcdadaadcbcbbbdbdadbabccbdcddacacaabdabbcbdccdcdddcaadbcbabcabddccbacddbbadbbaacabacccdacdbbcdaccabcbcbdccabcaadcbdddccbddbbbcaadbdbccbaaaacbabbbcdabcbcbbdabaddbcbdbdbabcccaadcdabbdcacbbccbbaccddddbaddadaccbcdabdbccddaacbaabcadbdbddbddcbcbcdbdcdbdbdaabcbcbdcbddcdddaccbbdbcdcddcabcacddabddcccaaabdbcdcddbbddadabbdddcaacadaabcddcdbbaabccaacacadddbcccacdbcdcccbadcddabcdcbdbbacabddbbadccbaacdadccbaaacdddaabcaacacbabbdbdcacdbaaadabacddacabdbcddbbdaaaadcdbaabaadccbdbdbcdbbcbccdccaddadddaccdbdadbaccccaaddacbbdaddbcbddbdbbdbaccbbdabaacacdcdddccbdbbacadcacbadbadbcbddbdcacccaaabacdcbabadcaacccbaabadcccdbaabacdaaadabbccccacdaaaadbcbaacbbbbcbaabaabbbadccdadcdbbcacddbdcbacbbbaaabcacdaabcacbbddbabbccdbcadaddcdaccbcbbcbbddbbcddabaacaabdddbbbbdabcbacdacaababdcbccddaaccdcbbdcdcabbacdddbadcbbcdaacabbcdacdcbbabdbbacacccabcbcccbbdbbdddcaacbbcabdddbbbcbbbcabcabcbaaddadbabbabacadbdbcbadacbadddbdbabbcaddcddcdccdcccaacbdcbbdadbacadcbdddbaddbaddbbddaaccbbcccaadcdcacbddccbcbaacbcbcdaaaabcdabcdadddccabcbdcdcbcccaccdbbbbadaacaddbbbaddcbdaadabbccabddddccddadacbbddabdcbbdaabcccbcacacacdabadcbabbcdacddacddbadbbdaddbbdcddaaabacaddbddaccdcdabddccdccabbcaacbdaadabdddcbddbbadddbaddcdadbabdbabdccabcaddbcacabbbdddcbdadabadccadacbaaaadddddcdbdbabbbddcbdbbabacccbaccccadbcbcbdaadccaadbbbbbabcdaababaddcdadbdbcbbaabdcdacaaadbcbabbbacdcbbdababbdcdbcbbdbcdbbdcdaaabdbbaddbbdacdbbbccdaddbdcdabcdddadcbdbcbaddbcadbbccadbbacaddabdbbcdcbabcccaabccaadbacbaaaccdccdbcdcbadbddbcacdcaccdcbccddcacadcddbcaaadbbcddcdaddcbdbbadddaccccbdcabdbbacadccbbcbdbccdbbabcbbdadaabdadaacccabdccbbddbcacbdcaddbabddbcdcbcaddabadcdaacbabbbccbacbdbaaddaccdccbcaccabadccbadaccccabddbabaccbccdaadaaaacacbadaabdaaccaabdaacabbbdaaacacacbbccaccdbbaccadcbccaaacaaabcbdbacbdacbabbacbcdaadaabdaccaccbbcaadddbaaccbbdccaccdbcdbcacbacdabcacdccabcddcdcbcccabddbbcbbbcbdddbdaccccdbbadcbacbdaadcacdaaaccbbbaadacaacbadaddaaaacbcbcabacbbbacababaabcbadbbdcaaddadbdacbcaadcdcdbbcdcddbcbabddaddadcccbbdbcbbacccbbbbcdbcabccaabbabdbaacacacbbcaaadbdcbaaababdcbbccbddacbaadcdbacdbccbaaddcbdadbbbbbbbaccabccbdacadcccbbbbcdccaccccbaacdbbcccbcdccbcbabdcdcbadbcdbadaaaadabcbbaccaccabdadcdabcdadaadcbabbbddbccbadccddcbdacdacbddbdadadbcccdabdcaacadcdcdacbadbdbdbbbccbadadabcdcddbbadbbaaaddbdadadbaababbbbdbbcdadbbadbacacbdaadbdcdddacddbbbdbdbcababbcabdbdcdadcbbcdcbdacbdaaddbddbabdbbcdbbabaccbbdcababbbaacaadaaacdbdcdadacbbcdabcdcddbacbbcbbaacbcdbadbddbbdccccbadaabcabacbaaabcbaddcdcaccaadcadadaacccbccdcaaabcaacddddcbaaadaacdaabbcbbbdcdcdbbaadbaacabbbaabaccabddabcdacdadcbdbadaabbcabcbabbcddcabaddccccadbdacbdcbcdddabdcbdbdacabbadacccbdaccdcdbabccddddcdacbcdadaadcdabaccdaccbbacacbaaacdcdabdddcaaaaadcaabddcabdbdabcdaddabcbbadcacdbadabcbbdcaaccacccbbaacccabbdcbcacdcaabdabbbbaabbdddbadbadaaaadaddbdadddcabbacbdddbbdacbabbccdcbcdadbdbaacdcdcdccadcaabdaaacddcccbccdddddadabdccdcbdabcacdbdcbdddabaaaadcbbadcccdbcabbbddbcabdaaadcdbbbccadddbadaddccdacdbacdacdacccdbbaaaaddcbbdabbbdbbdbccdddcbadccbcbdbaadabacdddcddccabdabbcbbbdaccbbdcdccdaddbadcdcbabbadccccdbbcdaacdcbbcabdcabbaabbbbaaabbbdddbcdcdcadabbdbcdbccbcdadcacdacaaccddbbadabcbabbdcabadcaadbdcbcccccdbadbaacbaabbcabdcdcddadaabacaadcdbadaaddddcaadccbaaacbacbbdcabaabddabbcbcdbadaddddbacccdbcccdbbbbcabbdbbcddccbbcdddbadadccbcabcbacaaabdcabacbdacadccbbdadcbaccaabbdccdbacbcbabcaadabacadddcbaccdadccdccdcabadcdaddacdbdccaadddcaccaacacccbdbddacacdbccdacbbcdddabdcbdbcbcccbcccabcdcdbbbbddacbdbadcddbbdaacabcbcabdcabbbddcbbbcdbdddadccdbccddadaabcccdacaccdbaddbbddcdbddddbcdabdacbacbaddbcdbadccadacbcadcaccaabdbdbdbdcacdbaaaaadaccddddabbcaadbcddcdabdbbddccbdbdadbdcddadccbcbbdadbacccadbdccdccacdccabccccbadcbcbdadcacbcabcababaabdbaadabbbddbbccbbbbdbacabdcbacabacbcadbcddbcdabbbabbbdaddabbdcbdaaabdaabccbccdddbacabadabcdabbbacbdaccbbcbadcaaabbddbcadabacbcdbacdadcdddbdbcbacbccaccabdddbddcdbacbabccacadccccabbabbaacbdacbddbbbbccccccabdbaaacabbbcdaddbadcccbcdaaacddbbaccadbcabdddbddbadadcabbcccdbaadcbabcdabcccacadadcaaacaadcbacbcdbadcddbdaccbbaddbaadbdbccbaaacddbccbccaccbdbcbdbbbbdbcbcccadcaaccbbadccbabaabacdacbabdabadddddacacbbdaacadddcabbbcaaaaccbcabcbdadaaaabcbabbddacacddaabacccababcbdcdacaaacaacaabdddcaddacbacaccbabdddcbdbadccbcdbaaacdbbaacddcbcaaaccbbadacdcbadaabdcdadabaccdccddddbcbaddbababadaabbcadbdadacbbcaadaccdacaccaaabbdbdbaabcbdcbcbccdabcddbaabaacdbdabbbdbcdadbbcdbdcbdccdccbdadccaaadabbabadbccabcbdcdbaddddabbbcabbdbccdddcbcdaadacddabcdcabccdacbdbdbadbaaadcbadabcdcbdddaaadddbaaaccadaaacbcdabbccddcddcadbcdbcbdcbbdbadbadbdbddaddbabcadadbaccacbaddbbcaadcbaabdcdccbbdbdaccadbcdaccacccaadbabbcadacddddcddcdcbbdbcababddbdbbcbdbcbdcdbccdbcbbbdbaacacbdbaadabccaaddababbbccbcbdbbabdcabbdccbdaaccdcaddbbccbdbbccccbdacdcdcddacabcddbccabaddcbcdabdbcdddbdcdbabcdadccbbcdadcaaaaacdcbdbcdacadccdcacbaacbddaacddcdbdaababdaadbcdbdddcacacbbdbabbdcbdcacdbcccabcbbbadcabcacabdaacccaaddabaaddbdcbadcddababccbabbdbbacabcddacbdbbbdbcdcabcddccbddbbdbabbcaadbaacddcacaddabdccccbbabbadbcacbacbddcacdcddbadbcdaacbbbbbbdaacbbdddabdbbbaddabcddbbbacabccdddacbabbcaaccaccaddbddaabdadcaaddabdacacdcbddaaacdbacdabccdbcabcadcbbcadadabcccdacbcabdbdadacccddbccdddbcacbcaacbccdaddacabadacdabbbcabbaaadbadccdaccbdabddacaddbcddddcbddcdccabacadcdabacdcdbbccabbcadabadbcdbadbbcaaadaadbaccddbcdbabccdacaacaccadcadbdadccbdabbacdbbbbddbbbddbbbddaccbcbcbbaabdbbabccbabbaddcdcbcdaaabacbcddabdcabddcbcbdbaddbadbadbbacbbcaabccaddbcdbbdbdacbcaabcbcbababddadacacdbbadaadaadccbcdbbadbcdacacbbacacabdbccbadaaababbdcababbbcaddabbaabbabbcadcaaccaaddbabcbcdddcbbbabaacabbdcdbaaabadcdacbadbcccddabdcacaabdbbadcdcccbdcaadccdbdbccbdccadddacadcacddbadddcdcdcaaaaabcaacdbbacabbcbddddbaccccccbaacbddabbbabbdabddbcbbdddaabbcabdbdabbcbbdbadddbcaadabbcccdcbdcccdbbbccdcbcdaadabbcbabacbadccdadcdabaddddadaacdcaacbdddaacbabcadadaccbdbdadcdaccabdcbcacbcadbccaccccbbaddadaadcaacbdccccaadcadaabdacbccaccaacacdaabcdaacabdcdbcacacacddbdadacdaadaccacbccbaabbbbaadadbcacbadcccccabdadcbcabccdabdbcdaaddabacacdabdadadbadcacdaaddaaabacaaacadbdbbddbbcbddaccbbbacaddacddbbacdbaadddddcbdbdcdccbcbcaacdcabccdaadbbcbadadabcdbaccaabdccbcbdcacdbdaccccccacacdabbbbaacdddcbdcbabbacabbbbdcccadaadadddddbcdaadbdaaabbaabaabcdabcdabddbcabaadaddbdbaaaadbdacacdaddcdbdcdabadacabdaccbaccacabababadaccbbcdadabcbaaaaccabbadbbbadabddbdbabcdaaacabbcddcadcbdbaaaccaacdddbbcdabaaadadddbbaacbbcbcbcabcccacacbcacbbbdcccaddbbcbbbbcaabbddbbabbcabacdbcddcbabaadbdddbaabdbcaddcbbcacadbbbdbddaccbbadaacbdabaddccbbcacbcbadccdbcbdacdabdaadcccccbbaddccaaaaaccaabbbddcaaadcddbbbccabdbaadacbccbcaadacbcccbaaaccccacadcadadbdbddccddaaacbdcdadaddabacadadabcbaadcadaadbdaadbbcbabbbbabddaccdacababcbdbaccccccddacadbccbbbbccadacddcdbbabacdbbaccaabdacaabdadadcaddacabaaaddccadabacaaaddbadadcbdcadacbbaabdcacdacbaacdadccabcddccbacdcabbcdadadddacaabaacdcccacccaadbcabdbcbadaaddbbdbabaccbbaaccbaadcacbabadabdcbacbddccaccbabaadbaddadadddcbbdbdadbbbbddacadbcbadaaabbabdabaaabcbdcdabdabcaaccdacccddababcaacdbcddcbbccdabcdaacbddccdcbacbddadcaacdadbabdabcdadbbabbcbacdccdbccbcadccbaabaadbbacccabbdbaaaccbbdbbababcdcbbbdbbabdcbddababcbcdbdaababcdcabcdbababcbcabdcdbbcbbaaaaddadcdacccabbcbcbdbbcacdbdcdabaabbacadcadbdabaddaadddddbacabdbbdbbbbbaabcacdcdbcbadcbdbaabbbcdbabbbbdbcbdaaacaccadcabdbacbcaaddadcabcaaaababbdcbabcbccacdadcdbdabcdcadbdababcbadbbacadcbcbdcdccdcadbddaadcdbccdbadccaccaadddddabcccbbcbadcbbddcbabbbdadcdaabacbaccdddadcddbbbacabaabcabbabbdaaaadacddcdbaadbdcbadaadadcbdcabadbbcadddbdbcdacacdbddcbbdacdaaccbbdcabdccaacbadadadbdbdabdaadcbddaadaddbccaadaabcdcaaaaaddaabadacdbcabcdbdbaccbbdbdcdbabdcdaddddadcabbbadaacccddcbadbdcddbcccbddcabacaababbddaddbdaccdbabcababcdbcbabdcbaadaadcdcdcbadccbcddccbbdadbcaaddabbaabbdcdbbbaacaccdaabddcbcaadbacbdcaddaadbdcaaccacdcdccdadcdbccaccbdcacababaaccbcdaccaddcdbbdcbbaacaadbdcbcccbadcdbabddacbdcdcdbaaddcdaabcbadaccbbbadaaaadbccbabddaadbddbacbabbccdcbaddabccdcdbacdbaddbcdbbccadddadccbbbcbabcadddcaacdbbacdbbcdcdbbaadcbddcdbbcbbadacbbcbdbcccbdcaccccaccdbabbcddaadabaddbabdbcdcbacacacbbcddaacccdacbbbadababbdbcacbaaacadbddbccbccdbccddbcbdddccdaabbddacbdbccaddbadaccbdaabbbabdbcaacabddadadcbcdddbbbadddddcacabaaabaaddccbcaabbdcbdabbabbcdcadcbbabccddaaabdddcbbacddcacadabbdcdcdccbcbbaaacddccddbabaddcaddccadccadccbadcaddbabcabcbbbadbadcbbdaccbdcbadbdacdcacabbacbadbbbdccbaabaddddbbdbbdcacbdbdaaacbadadcbcccddadadaddbccadcaccbababdcaadbbddbbdacbaaabcdaacdcdccaccbadaccccddbdcccacdbdacbadbabdadcdbcaaccaacbcddcbabdadaadbacddccbbcbabccdbdcdbbadaccdddcaacabbdadddccbbabbccbadacaddabbbacbaadbccadbdbdcbaabccbdbdbddcdbcbbcddaddcdbadaccdbcccadbbccbdcdcbbaabbdcacaacacbcacacdbcbddcdcadcdcbaddbcbadadabdcbbacbababddcacbdccaddbdccccaddbcbabccbcadcbcbcbcbccdbbdcdacdddcbabdcddabaddaadacdccadadcacaabbccadcabccacdabcadacacaaaabdbcccdbadbcadabbdcbbcbbaacdbabdddaadacdbaadcdaadabbdcabcddbcbabdbcbdbdadbaabddddaadcbbabcbbbadddaacdbcdaacdaadbadddcacbdbcccddcbbdcaaaadadcadddbcdadababbabbabccabbbaddbddbccdbbbdacdaabbcbdcbbaaccddcaadbbcdbdbdbdbbddccadddbbddcbcbbddcdddaaaadcacbddbbcdadcaaaccadacabbaddcbddcaccacbbdbdcdcaacbcabaddadddabcacccbddcadacccbcdcbdddacacdaacdddbcdacabaccbcdccadbcaaaaaacdbdccaabbdbcdacccaccabccddbcbbaaaacaabcabcbdbddbdbaabcaacdacadcadbcdcbbacddcbaaddbdadbdcbabcababdaacbadbbcaaabdaccaccacbbadaadcdbddcdccbdcadbbccddadaaabcaaadaadbabbcdacccdaccccdadbaaadacaddccacccacadcdbddacdaccdbddbadabccdcbacdbabdbccdcbcddbbaaabdbbaccbabbbabaaddaabadcadaabdcaadadbabbcbbbdcacdadbaabdaabddacbcbabbaddcccdddbaaccaddadccccababbbdaadbcaabcaddcdcdaacacacaccbbbdbabdacbacadccaabadadbdababaaccacbacdddaacaacddcabbbabaacdbccdaddbcccbbdbcbcdcacabdababdaababcaabccdabddacaaddacaddbcaddccadcacbdddccbcdaaaddcdadaaadbcbaabdaabdcccbdbcaccbbacadadacadccbdcabbbcbcbaccbbabdbdbbddcdbcdcdddaadadcaccbdbbaacbdacddddacaccdccaaaadccbababbcccaacbacdcbcaaadabcddccaccabdcaaabccdcbdacddbcccdabbbadcdbacbcaaacccadacbcbcbdcdadbdcccdcbccabcdaabcaddaadaaadaabcacbdccdadcdcddccbbbbbcdbaaacbabcdaabbcdcabddbdddbababdabdadbcbadaabdabdcaabccbcbccdbacddbbacbccccbaabaaadcaadaaddbcaaaacbcccabdbabdcbabcdddcdccbaccdadbbbadccaaadbddabacbaabdcbadcccbbacabdccacabbcbbdadbcbadababbdcdcdbccaadbdbbbbbcbdcbbddddabaacddcacbabcbadbcdacadccaacababbcadabccbaadbddccdddacbaaccdbbcacabbabbdcaaabdddbabacbbbdbbadacbdcbcaddbabccbbccbbbcbcdccddcadbcdddaaccaacdaabdbaddabcdcababbdbdbbbbdcabaadbbcacdabadaccbacabbcddbcdcabaacbabdcbdacaccbdababbccaddddccccabaadbccdcbdabdcaaddbbdcaaaacbadabcbcbaaaaacdbbdcbbbaacabcadabccadccadcddbaccdddbdadbbdabcabadbccbaadaddcdabdaccaddacadcbdadbdacdaaacacbdcbccccccabccccabddabbbcaacadaaccdbcbcaddcbdbdbcbbbccaacbcccbabacacbacddbbadddbccdbdbbaadddaaaaababdbddbbaccdbdcbdddacdabbdcadaacaacccbadccbbaabaababaaabaacccbadaacabcabbbdcddcadcbdbaccdacdbbcbbababdadbddaadaabcdaccbaabaaabccabdbbdcdcdbcccacacdbabddbbccccbdccabcacdbadbabcaabbacbdcdcdddddbccbddccaccaabbadbdbdbabddadbdcdaccadadccbacdacacccdadddaddadabaadbcdcbaacdbadaadbbcbabcadcabdabdcbaccdcacabdcaaccaadcaabdddcacbdbbabcdbbadacdbbcdcccaabacdbaacacddabddbcbbaaabadcdbabcbcddcbacddbabaccdbabdcbbacacdbbddaddbbcccdaccaccbaccacbcadadbcabdbdababbccaadcdadccddadcdcdbdcccaadabbcacadbbbdddccaaccbcbbcadaaccbadabbbcaacdbcbcdbbdcabcaddbcdbbccbdabbdaddcabadacaabcacdadcdaaabaadaacccabacacbccdbcabbbbabaddbbbcacdbddbccddabdbcdabdbdaaccdbaddcdcbbbdbdbcaadccdabaacbcdcbcccaadcbbcbcbddbccddccaaccabbdcccadaabcaadcdbaccaacbcddddabaadacadcadcdabccabccadababddacccacbaaaaabbdbbadcabbccdaadabbdbcaccddcaabbabdcbcbabbdaabcbcbacdcbdadadadccaccacddcbaccbbcdacdbdcbbccddcdbacbadabccadcdcabacbdaaadcddacaaaddaddbbdbaabcadcbbbcbacbcbbabdcbadadddaadabcdcadbaccdaaddadcbcdcbcaacddacbdcbbaaccaacacccdbcaccacddbccdbdaacdbaacdaaccabaaadaccbbadddaddcacbcdcadcbdddbbccabcadbaacdbaadcdadacddabbcadbdadaababaabbadcbbdadbadadaaabcacbbcdabdbdccacababbbbabdabdcbddddbaadcccaccadbdccadcaadaaaaacdccbdaabadabbacccdcccdcbbdcccbadaaabaddadacadbcadbacbcbccdcdaacccdbadacccacdabcdadbcdbabdaabdcbccabccddbabaaddadbbdbbacbdccddadcdabbaccacbacaaabbbdcdccadbcdbcbaddcabbabadbbdbaababdadccdadccbbbabccdcbbcacccbdcbbbbbccccbbbdcbddcadbaadacdcdccddcdcaabccdddcacababdbaadacdbaaccbdccdabcddcabaddddbaabdbacdcccbddcbaabadbcbbbccbbacdccacabbdbccadcadccdcacdaaacdbcdbbaabdcbbdbbdabbcdbdbdcdcbcdbacdcabaccbbbdababaacdcadcdccdcabdabaddaaddbcadbdabdcccaacbcaddbcadbccdbbdabacaacbdabdbbadcdbdddaacbcdcadcdcbdabdbccbbbcdcacccacbcbbacddbadbbabcddcadaaacbdcdcccadcaabaaaddccdbabbcabbdbbcccbbcaaadadaddccadabdcaccbcaaaddbbabacccbbdbcabaadbcabcadadbbbbadcabbaddbadcbbaddacacacdccdbbddaddaccdcacdcccdcbbbadadadbbccdcadabaacadacaaabaabcddbadbabcabbbdabbccdadcbaddbbcaccaacbdabddaadabacaddadbababbcabbaccbcccaabcdbdabcdbcabdcadadadbbccbacdaaccadaaabcddbaccdacccdcccdccdbaaadcddaabacacdbbddccdcaaabbddbccabdbbcdaddbbdbbcbababaabcbbacbcabdbbabcccaddacadcbadabbbbcacabcaddcaadbbdadccbcbccbbbddccbcdcaabaababcaadabdbaabdcadcbacaddbaaaabdabdcdbabcabcbacdaccdddcbbbbcbccabcaabdbccbbabaabbbbadbcabcdbccaddaacbabaabcaddbbdbbdadccbbbacccbddaabdbcbaadcdbdcccbcddabbaccccdcdddcbdcbcccadadddcdcdaadbdcbdbdddbccadcadbbaacbacaabbdbcbcacdaaccbddabcaadcdadbdccdbbbcbcaddbbccbcbaabccdddbabdcccaadbbcdabdbdccbbcadcbbaccdabadabcbddaddbcddcaabddbbdabdacccdbaccdabbbabcbabdcbdcddcbcadabbbccadadbbadcadaacccacadcdbaabdadcdabbdcaaaddabddadbcdcccbbcddbabcabbbdbabcdddaabcdbccbbadaacbaaccaabccaadbdbdbdbdaaaacaacbdcaddddabbbbdaccccadabbadaddadbbacdadacbcccbdbacccbcabcaaccbcadaacbbddbdcbcbdcccbbccbdddbdcdabbdbbbaaaacdaaabddcbbaacddadaabaccadbabbbddacbcddabdbcacabddbadddbcdcbccacdcbdacaabbddbcbcccbbadacbcccabbaccaccbbcddcdccacadaccbdcaacbcacacdcbacdcaccccadaddbccbbdacadccadbaadbbcdaaaaaacbdcbabccbbcdcbbcbbaabcdbcdacdddabddcbbcdabaabdbbdabbdbdabbbbccbccbcadabbdabcdddbdcabdcdcabccccdacabadabbbccbccdbbcddbcbbcbbaaadcaacdacdcadbcbddaabbcdcdccabcbdcdbcdcdacabbcdddbacccadcdcdccdcdabadcbbdadaadabaaabdaddcdabcddddabadbbdcdbacdcabcdacddbacbabacbbbdaacbddbdddbbddddaadcccbdcbcbbddbdbdbbbcaacddccaadccaccaadccaadddcbcbaddcaaacbabcddbcacaccadcabddcdcaaccbaacadacdabcbcbccccaacdbbdadbadacacdadabaadcccadabbccdbbaccbdcddbcacbcccaadabaaccabbbacbddbdadcacbaabaabaabbdddcbdcddbbbddcbcdadbacbadcdbaabaadbcdaabcdcadbdbdcabacbbadbaabccbaccddcbbabadaabbcbaadbbdbcddbccdababacbbacbaccddcabdacbaacaabcdccacbcadcdcbbacaddbdcbcbaadadadccdbcdbcaadccddcbabdbcdddddddbacaadabaccdcbbacdddcacbddcbddbdcbccdddaaccaadcabacdabbbccbbbbbbdbddbbaacbcbccacbdcbdbabcdcccdcdcbaddaacdcddbadcbcbdcdcacbaccababccaacaccaacdbdcbdcacabddabcabdcbdbdcabbdaddbdccdbbbaccaabaaccaadcddcbcbcaabdcccacabcdbdbbdbcaddbcadccabccbccbcdcadaaddddddbaadcbddabdcbcadcbcabadbdadccbcbdcdaabbddaadcccdddbccabbcccdccadadbbcadcdaabbcddccdcbbbbbbddbaddbabdadcdcbaadaccabdbacddddcdaacbbcdbacabcbbbbacbbbbabadaccccdabadcabdddacdcbdabbcbcdadcaadcadaabcbbccaaaaaabbccacbbbadabdcdbddcbdbcaabbbdbcdaaccaacbaaccacbcdadbcdcdbccbddbaabcaacacbaddcdacadcabccbcddbdcccddcbdddaaddcabacabdcbdbdbdbbadcbbcdabbabbdbdbcccbaccadddabddabcabbdddccadbddbdcabaccdcdddbdbcbcbdcbcdbddcaccdcadcddbacacaacaccbcccccdcadadadddcddbabbdddabdcbccbbadcbbdacaabaacdbccccbccdacacadabccbddccaccaabcbccddccbadacdaabcdbcdacbacabdcabaaccaacdcbdbbcbbdabbccdabdaacaabaabdaabbcbcdddabbbcccacbccdcabaccdbbacdbcdaaacaabddcdbbbcccacbcacbdbadadbcdddccadaabcddacdaaccbbbcbbbbdaabdcbddabdcddacddbacbabcdcabcabdaaccaddbbddadccdadcbacbcbbcddccbddbabadbbdcaacdcbabacabadbbddddbbdccdcbdcbadbcaccadabdaababcabbaaaadcdabdccddbbdaadacdddddabdaddcacbbcbacccdccdcbdaaabbddbaccacccaaacccdddaaccccabbddddbaccbbcddadcadcddcbccadbacdccdacaaddcccadddabdddaddbbabdbdddbbbddbaddcccbbddabadbcdccabbbcdcaaabaabddabbddaadacdccbbccdcdcdaacddaaababccacbdcabcaaaaabbacadbdbcbcdcababcddbddddcadddaaababddbbdcdabbcbdcabbccbaaaabdcaccabcbbbaadbdbadaddccdddcbdbbabbaadbdddcdcbddcbcbdddacdbdbcbbaadcccabdbacdcbaaccddddabbdbaccaacbcacbbcbccdaabbddbaaddcdcdbdddabbddcbacdbdcbcaccbdbcdadadddaacadbabbadbabcddcacbcbdbccdccbbdadaaddddacdcbbacdbddbacbcbacbccddcccbcbcacaaacbcaadddbadbbccdddddcbcaaaacbdbccbdbaaacdddbbdbaaddcdddcbbbbdadacacdabbddadccbccdccaabbaacdbacbadbcacdcdcaddbacbcacccaacabdabcccdbccddbbbabcabbddddccaddaacdaaacbabcbdddabaacadaaabbcddcccbdcacbdccaabcccbabdbbcacacadcacbddbaacdcddaadcdababaaaaddbbacaabcbbabdacacbbacdbbaacdcbddcacccbbadbdddbbadcabacbbddadddacddaacddaadddaccbbcbdcbaacabdbbbcadbaaccaccbadcabdbdabadaddbcdbcbccabdcdcabadcdadbcabddbbbcbdbddcddaaaabcbddbadaacdbcccadbccdbddbaddddddaaaabcddbbadddcbdccabacadbccdadcbadccbcccbcdadcabdccddabccaabdcababaacaccdabbbdbbdabcadaabbacadacbbddabbcacacbdcdcdbbacddaddbabdcabaaadbbacacbcbbabcdbcdbbcbbcaddabdcdaaadabbcaccacbdabbaccabaadbdcbcadadcdbcbdcdcbcbcadcdbcbabcdbabcaabadbcbdccadbbbdccacabccbcaaaadaaacbdaaaaacccbcbbcbbbdddcdabdcacbbcbcbdbddddbcdbbcadbbaabababcbbabdcbccddbabbaccacabdaadbbbddccbccaabcbdacdaadccddbddbccbdadccddabaaadbcacadbdddcaccddbbccddacdbbdbcbbadcbdbcaaaacadbdbcccbaccccdcbadbdcccadbbadbccadddcaddcacbcaaaaadaacaccdcaadcdcbddbbaccdcccdbacadabcdadcbcccabddcaaccadbdcbcbcccacdabccdbadbcddabaaaccdaadddddbabaaabbddcddaabbdddbccbbbbbdbbdbccdbcdabbbcabbbbbccbbbdbcbdbdcaddcbadaccdadbbbadbaabdbcbabbccdbddccdacccdaaacdddbccbacbcdbcabdddaaccdcbdbccbcacbcbcabadaaddbcdcccbbaaacbdccbccddaaaddccaaadbcbcddbbacbbcccaccccbcbbcdabbddaacdaaccabccdccdbcbcdaaaacccdacbabcdcbdaabdadbacdaaccaacdcbbbadadadccccbbaabcdddddddaacccbccdcbbcdbabadabdcbdbabddaabbaddbbcdbbccbcadbdccabcdcccadccddddddcaccabccadcabccacdcdddbbbcbbaaccbbcacbcababdbccabcabbdddcddbbccacccaaacaacbabdcdcabdadadaddcaaddadccccacdbacdbbcbdbbaaccbdcdccdddcccbcacadbcbdbaddccbbcaacbdcbcbcdbadbacbabbbdcaadcdaaccadccabbdbbbcbddccdccbcbabdaabaabadbadcdcddadaaddbabdadabbbdbbbbbcaccaccaadbabddcbaddbbbddcbbdcdbbbacabadcacbdcadbaadabddbbbcbdabbabacddabdbabadaccacdbcdaadadcbdcbdbaaaccddbdacdbadcdccdabdadcdabbbdacbdccaacaacbbbcadadabddcbdcccacacadcbdbdddcbbdacdcddabccabadbadbccaccbdbcdbbcccaaabbdbcbabdadaaaaababcaddcdabcacaabdbaaacbacbbcdbdddcabcbdaadabcdadbdbbcccadbabcbcadababaadbdcbddacdddbdddcbbadabcdbddbbbbbcbdcabbcddccabaacabaabcbdaabccdcbccdcabdbaadbdbacbcdadbbbcdccbdcbdcaddbdbbddcacccdcdbdddbbcbddbabaaddadbdbbbacbacccddcbbbdabababaadbaddcacdbacabdacccddcddbabbdbaacdcbbdddbcbbdcdcdcadcbbcbccdcadabddadbdadcadbbadadbddacddcccbcccbaddbcaababbcdbbcaccbbdbcabbaaddaadccbdcddadaccdacbbacbddabcddadccababdccdcaddcdbddcaddcacaccabddadbdbdaaaddbcbdcdcdacdbaaabbdbbbaccbcabadacdddaddadbdbdcbacbacccdcdcbbdaccaaaccdcdccdbddcaacaccbbaabbccbcacdabdddcbcadbbccdaccacacdcddcdbbbcbcacacadcdbbcbbdcbcaadcacdaccddcacdadbdacddbccdabccdbdbaadcddbaddabbbdbcadbbcabcbdcdddacbabdcabccdbdbdbbabdcaddbbdcbadbbcbcaadbbaadcbccdbcbadbcaadcacddbdcbabadbcccadacbbccbdaadbddadcccdabbccaccbbbdcdacdaddbcdaadabbbacdbcccaadccbaacaccdacddadbaccdccdadbcaadaabdcadcacbcaddabddabddaabdbdcbdaabdcbbbdddbbabcaabdacccacbdabcdcacacacddddabbccabaddbcddabddcdabcddadbdcbdbcbbccbddadabbbbdbbddcbdccadcbdbcabdcdaabacdadcbccdcbccbbabbdabaadaccaadccabbcbdddbaabacbabdbccdbbddbcbcddccccaabcacaaaaaccccdcdbddbdcccdadcadbaababbcccdcaacabaccdbcbcacabadbabbaacccacbdaccccbddbbaddcacaaacacdaabccbabcababbdacbdaddcaabdbddcaccbbdbddcbabcadcdcbcadaabddcbcbdbacbbcccbcaaadbaddcccbcbacbacaccddcaaabbbbbcadaaddadbccbccaddbbabddbbcbbbccacddbbdbcaabacbadbcddddcbbcdccadcaabdcbbcbbccddbcbabdaaaadacbdbccdadcdadabddcabccdbdddbcbdbddbdcddabdbacabddcacdbdbbcddacbcbbabcdcbacaabaacddbcdddccabdabcdddbbdddaadabbaabbacbccabccadcbdbcaaadbdcdbcbbabddcdadddcbacaddccdbaaaabcbcadacbabcdbaddcbbbbbdbdbaacccabdddcbccccbbdaaddabdbcabbdcdbabbbdbaccadcbbabacabdbcbbcddddbbddddcbaadcbddbdaadcccadcbcdadcdacbccdbcdbbaadabddcbadcadacdcbdbcbdbcdadaccddbaabadbccddadbbbcaccabbcacddcabdbbabbaccabbbbccdcbaccbabccbacbdddadbadacaaddddabacddadbcdcdbbcaaadaccddbbbddccdccaababbacbbdccadabbdddcaacaaddaaabacbcbaddbacabcbdddcddabcddadbccdcdbcdcdcdabcadbaabdacdadacdcacdcbddcacbabbccaadddabdcacbcadcdcbccdddccdcddabaacdacdcaccadabaaabdaaddbcbbabacdabccadcabdbadddaccdadbbbaaddbaccbccbcacabaacdbddbbccbbdcdbbabacbdcbbdabdbbbaaabbcbdbdddccababdadbbbdadabdaaccacdbdbabccacaadddcbaacbadadddbbbbcbdaabdbbcdaadcdccdcbadccbcdadaddcabdbabaccaaaabdaaaadaaacbbbaddcacdacccbaaddaacbdbbccbddddcddddaadddbddddbaabadcdaacabcbdbbcbbaaacaabbabdabbbbcdddbbbdaabcbdabaddabcadaacbbbadcbdbdbcbbbdddccaaacbddabaddcbbbbabddaabddcdcaddadadcdcbccbbbaccdacaacdadaabcbbacabdadabcbbcbabdccbbcaddbbcdcaadcbdcaccacbbabdadbbdabccccddacdbccaaabaadcddadcacbadddccbacdbbdbaccbacbbaabacaddadacdcbbbbddbadcbcadccdbddbacabcabcaacbacdcbcbddcaacbbaacdbcaabbdaadcacbcdaddadbdadcbacbbadddddbdbdcacbbbcdababbddbaadacddaaddcabdabcdcaccdcbacabcabdcbcbcddbacadbccbaddbcdadcdbcbadcdcccaddbbcddbaaaacdccdbdccdcccabbbddcccaddbcbbdbbaddadaaacbdbdddbccdbbcdcddcabcbbddbadcdcdacbbaddcdbbbdbdbdbcbabccacbcbcabacddcdbabbadaaccdcbdcdbadadaababbdacdadcacbaccdabbccaacbddccbabcbdaacbdcbabdadbadabcabdcaccdcddaddacabdabacdabbaabdcacaadcdadbcdbdcaddddddddcdbccdaabccabccbcdccaddcaaadcdadbbadbcdddacabbccdbbbdcbadbcbcadaccabadddcbabddadaaddcbaadacdcbcadddaaccbbbacbadbddcbaacbdbcadbccabaadacacacbdacdabaddcdaaacbdbdaccacdbabcacbdcabcbcdbbacdaccaabddbbcccddaddbdcddcdadbabcbaaddbdabadbacccaabdddaacdacbbadcdaabacbdcbccabcdcabbdbcdaaccadaddcbccadbcddcaaaadabccabcacacddacdababcaadbdbbdcbadcaddcddddbcdcadbcadadcdcdadaccacacdbbbaabbabcdccdaddcdabdbcccabaccaabbacdbdcbbcaccddccacbabbddbccddbadbbbcbddddccaacbadcaadabcabdcbccbbcccacccbbaddaccdcbbbcccbdbcbbbddabbccbcbaadbbbdaddbabaccdacbaacdcdbaaaccaadcacaadacdaadcbaacacccbaadbcbaabcbdbabcbccdadcaadbabdbdddccaabccdbcdcbbadaabdcbabdddbdadbcadcbcabdadbdaadacacaddbbddcdbabbbbacdcaadbdadaddcbabbcacdabbdccbaddcdacbdaabbbdbcbdbbcadaacaccbdcaabacdacdbbddcdcbddadcbdbaaddacccaddaaadcadadadddaabcdddccbdbcabcdcaaabcadcdccccbcdaadabcddbcdbbcaddbaccbabcdccabccadddbacadacbacabacbabcbdcbacdbacdaaabbbbccaaaaadddbabaaddabdcabdcbccccabbabcbddbcacadabbbdbbabaaabcabaacdcddbddbbccccaadcbbccbcbcccacadcabaaadcdddaccccabbadbabdcabbcbacdcbaddddabdbbcdcddbdaabbacbdcabbadaabaaacbbdbabcbdadcacbcdcaacadccdadbbdbcbaadcbbddbcdabaacbdbdcdadbcddbdbcddbdabacdbacbadcabcddbabcbabccbcadddbbcbddbcdddaddacdbbabcdaabaacbabbcaddccdccbcbdbadbdcadccdcacddcddcbddccaabdacdbdddadbacadcaabccbcabbacaddddabddacddcbaddbadadcadaccbcdacddcadbbccddcadbdbcccdbcdbccdbdbaaaaaddcddadbacabacadaaccdddcadddbabcbcdadbddbdccaacdcdbbddababbbddacacbdcdddcadccdaaabaacaabaaadacdbdbbacccacbbbaccdccbbbcdcababbdddcbccacbdbbadaabcccaabdbcdbcdbdacddcbdbddccaaaabcbddbcdaababbbcbcaabddbacabacbdbdbadaddddaccccbddcccbaaadacdbdabaddaaabdadddcadddccacbababbacaaccdccabacbcdcdcaadddbdccbdaaccccdcdcbcacbcacbccdbddccadacadbbdcabcdbababadaccccbddcdaadabcabcdabaccaaacadacbccaaccbbaaddbdcdbdddabcabcbbaaaadbbdacdcadaadaddcdddbdaaaccadcdcdacddadadbdaabbbbbdbddcabadbdadbaadbdcaddcaadaabdcacabccbcaaaacbddbcbdcbbbaadabcdbdbcdbcabcddcdabaacbaaacdadaaadbcacaadbaddccaabcbcdacbdaccabacabcdcbccabbccbcbddabdbdbddcbbddddcbcacabdddbdbbdbdbbaacadcaabcaaccdaadcabaacacacaddbbbcabdbddccabdabdbcddddbcbaaaadabbaabcbbaaacaaccaaaababdadcaacacbccaabaabbabdbddbaacccbabccbdcdaacccbcbaabddbccaaacaadccdabcddbbadbbaadbdadcccddcdcaddacbbacadbabdadbdcbccdbccdaaabdcdabcbdaccdbdbcbdbadabdbbcdddbabddcbdcabdcacddadacbcdacabddabcdcdcbbadbacdddccadddadaadbdacacdaadcaaabbbbbcaacdcbcdccabbbddbcdaaaabcbbdbbaaccaaddddbdbddabbbaacccccddccbaccbccdaabddbcddaccbbdabdadacacabcdcbddaadbbabdddddddababadbdbbcadbaadbbabbaadadbbdddccdcbbccaddcbbabbabdcbabbbdacadddaadadbaaabbcadddcaabacaccadbadcbadcdcaaaccaccbcaadcaddddaababaaadbbbcbddcbccddbbdbacbacabddbcbddaaadbacbbcbcbbdcaddbbbabacacdcccddcbbbcaaaadbddddbcbacbbdbbaadaaabbbbbdcbdaccdbbcdccddccbdcbdcabaccbcdabaaaacbcbabdaacadccbbabadbddbccddcdacaddbaadcdcadddadbbbdacdcabbadaabbdbbbadbddacadacadabcccaaadbcdcbdbdcbbdcddaacbdcdbacbadaaadbdabbdacababcbabbbdcbacbbbddbbacabcadbbdbcabbadbaddadaadbaacadcacdbddabbcbbacadbcbbbaddcbabcadacdbacdababaabbdcdcccbacbadcbadacdbcaacdadbababacdddbbaddacddcdaaddaabcdbacdbbcababbcdbcacbbbdbccaabbbcabdadcddccbcbabbaadbcaaacddbbcaddcacdbbbcdabbcadbcddbdbcadbadabbabbadadcddcbdcccaaddbddbbdbddcacbaccadbbbdcacccdbadacadcddcbbabbabbccbdacaccdbbcabaccdbdcaacaacabdcacdadccbbacdcdddacddabbaabdbbcacbaaabbaadbccdcabadcbcccccccabaddbdcacbbcddcbccabadcacdcddddbdddcbcaaccadbbdcbdddacaabbabdaccadaabbdcbcbacaddcbcacddcddbdbbaaadbdadcaadbccdaadbcbadacdcbbabdcbbabadcbcbbaddacbbbbbddcaabaaccbbccbbadaadcdbdcaacbdcccaaccbcdbbaaddaacacddcdbcbccbabacdbcbbcaacdcdbcdcabbdbcaccdbbcdbadddcbcaddccccbacadaabdabadabbacccbacacdbbdabbadbacddccacbbdcdadacacccabcbaacccdbcbadabbacddbadaabddbdadadbcbbbdcddccadddaacaccdcababcabbdbaacdcbbadbccddacbdbaaadadabadcadbccdcbcbbcbaccabddddbbaadadbcaadbcbdcbdcdbdddcbbcbdcbbcdbbdcacbacbcdcdbccadbccadbaacdbadabcbbcadcbdcdcbccaacbbbdcccaddbdcdccddbaaaadaabbcdccbbdcdaaabccaabcbadabbabddcacacbcadbabbcabccbdadddaabbcbaadccdaaacadcdabdcacaadadddababccdaaaadccacadadccdbbabbaaabbaccacbacccdabbbdcaaadcdcddbbdabaccccccaabccccddbadcbddadcddddbbcdadabcdbacbabcdddddcddbcbcbabdbbaabaabcdddbbbbdbbbcddaaadaadbddbdacbdcdbbcbacbabbaacdaddddaaddcbdbcaaacbbcdaccaacdabdcdcccaaabccaccbaababbaabddadcaaabacccdacacaacddccbadbcacbacbdccdabcbbccbbadddaaaaabcddbaabbabdbbaaadbdbdddcbdacccdbdaaddadbccadbdbcacbbbdabaccaddaccacaddadccaddbadcbadbadabcbacbbdbccdabcaabccdddbbdcddbbdcadcacaddaacdaabbccdadcbdaaadccaabcbaaacbcbcddacbabbabaabcdaabadccacddadabbcbcdaadbdacadcccbbdddadbdbacdaaddaaddbddbabcdcaccbdcccadcbccdbbabdcdbddaacacddbdbcaacddadbddccacdacbbdbbacbddabcbcaabccddaddbdbdacdcbbcacdcbbcbcbbdacbcdbcacadbdbaccbdcdbacbbddccabdbaadbaacbaddabddcdcbaabaccaabbddcdbcbdaabdacaabcccdbdbbccdaccbadddabbdbbdccbbadcbabdbbbbddacdabcaccdcbacadcdaaadcabcaadddddaabccaabcccacbadcbabcaaddbcddcacabddbddabdaddcbddbacbbdcdcbcbacddbaccdbdcababcbdcccbaadbdbbadbdaadbbbddcadbdabcbccbcdaaacbdcbcccadbaadcaacddacadaaddcaabccdbcdbcdddaadddacbddacbcabdabdaacbcbcddddaddcbdcccbbcbbacbdcdabdbcccdacdcbdacccadbbaacccabcccccdddabacaddabcadcadcbcbbdadabcbcbbddcaabcdccaaaccabcbbabdbdacacbaccaadcbbddbbbdcbdcaabcabdbbbdaaccdabaabbddcacaccbdadbddbdbdccadaabdcbdcacdcdbccdbdbcadadcdababcbcaacacbcacbdcadbdbacdbdbccacbccabbcbaddbdbbddacbdcdaddbcdccbbbdddadcbbbbacabbbddaaacabbbdddbdcbbaaaabdccaacdccbcdccdbdacacbdbacccacddabacbbcbaaadadcacbbdadabadcadadcaccacdbbbdacbadacadcadddcaabacccbdccdaccdabdaccabbaadccaddaabdababadbacdbdccbcdbdbbbddcdcadcbbdaddadabaaadcbdcbabcaccadbdcbdacacadbcaabadacddabadadbadcadcdadababaabbaabdccddbcaaddcddcbcbadbdcbddccaaaacbbbbbbdaacbcddbbadcbccaaaaaaabacabdcccaabbbaacbaaaacaaabddcbbdcaacaddadbbaadccccaadddacbaacdacbdcacabbacdbdaacaccaaadabaaacdbbcadddabdabdcdbcdabcdcdabcbcbcbacddbcbbcacbdbcbddbabaabdcdbdcbbadaabbbbcdcbbcdaabcbcadadbacbcbacdbcccbbadaabdbaaacaaddbbccaaacbcdbddbbbccdcbdacabaccaaccadbdbaabbadadbadcddbaaccacaacaddcbcdcddbaabcdcadbaadabbcaaaddbacbbbddbaadaccccccbbdccaaacdbcccdcbcdbddbbcbbaadcdddcdadbaadabdabcbabdacabaabbdadcacbcbbddbadbccdbbcddabaccccabcdcdcbddddacabbdddbcaddbabaccbabbddaabaadcbbdddabacdbdccbbcabbdcbbdbadaacbaabdcbabddadcadabbdabdcadcdcbdcccaadcdadabdadaaabddbadadcabcbddbbabbdbbbdcadadddacabaaddaadbdcbadacbbacdadbadabaccabaabadbdbadabaddacdaddcbcaccaccbcbadbadbbbcabddabdaaabbdadbdddbdddadbadadcdadaccbcaacacbadcabdbdbbcaccabcdbcddcabacadddabddbabaccbabbbbadbaabacdaabaacdccaadccbcbcddadbcabaabadcacdbacbbdabdccbccaaabdbaaaacacdaaaddbabbccdbaaddcdbdcdabaccadbadabcbaadadcdabbabaacbdacbddbadbcadcacbcacbacaccbcdabadcbdacbbbddcabcabcccdaddcaabcabacbbaaacbcabbaabcddacbbcabbccddcdabcbbccbaacaaadddbbdbdccadacdbcbccdcdccdadbddcdabdddcabdcbddbcbccdbcadadadcbddadcbacdbacdcbbcbdcabcbbdcdadcbdaababaacbcdddcadbabbacaddadcabcadcaacdaaacbadbaabcbacbbcccdaccbaccaadcaaabdcaabcddbcadcdbccccaccbbccbdbcdcacbcdabcacbbcadaacaacacacdaacbaabbcaccdaddaccbbdbbdcadaaaaaacadbbdcccbdbcdbcddcabdabaacbbadacccdbcccacbdaacccbaaaabbbbdddccdacacbcaddbdaabbbdaccdcacaddbbdacbcdaaccbbacdcbaadddcaabaccdacddaddbadaccbaaaaabbdcbcbddddabddaadadddadbcbdaaacdcdddbccbcccacbcbbdbcadcddacbbbdbccabcbbbdaabacbadddcaaacacdcdcabcacacdbdbdccdccdbdccbcbccbdbdadadccadabbdcadcbdabbbabcdacadbccdadbabcdbadcddaacacbccdaaaccbcacacbbcadbdadcddcdcbccbbabcaadbddbacdcadacbcaacbbdacbaaddbbcbabcacabcbaddcccbbddababddddacdcbaacbccacddbbbdcccaabddbaacddaaddaabbabadcbadabdccadcadaadcaabadbbadbbdababddbcdcbadbcdadbddccbabbcdccbbdaaccbbbdddbdcaaabcacdbcbbdcbaacbbcdacddddabaacdadacabbabadadcbdcbabdcdcbcdaacdcaaadccdcaddcdbdcdacaccbabdccddccabdacccabaadddbcadbdcdaaddcbccaddcbdddacccadbbbcdddbabcaadbbaaccdbdabbbdcdcbdcbdaaacbdacadacabdabcbabaacaadccdadbadcccabcbcbccbdabbcbdbbccaccabccadddcbacacbadcdbbaaacbcaadcbaccddaddadaaabcdcdcdaaaddcdbacbcbaddbabbbdaacaccaccbcacacbacdccbacdcdbcdcadbdbadabbbdcaadbababccdcddacabcdcaaabbdabcacbcccabdadbcbcdcdcabcccdbbdddcddbcdcacccabdbcabaccaadaaaddcabbcabdddcbbbcabcdcacbacacabcabcaddcaddbcabddcdaaabbdbcabcbcbaadbabacccbcacabcbabbaccbddabdbdbddbcaddddadbcbacdadbccacdcabdbddbbacbddcabaabbdcabaccaadcddabbcacbdbddccbcaacbaddcaabbcccbaaacdddbbdacacbcdcdacbaaccadabadcccdcacbcdbdaaababdbbdbcabadcaaadbbcbabbcaddbdababadcdccaddcaadaadddadbaddabdccddccddaabbbabbcadabccabdabcbcccbcaaaddcdabcaadbadabbddbabdddbbdbddcababbacbdbcdbaaaabdaccbacabdbcbbcabdcabddcbadddaccdbaadcbcdbaacdabdcabdccacdacaacdaadcbccacdbccaadabaadcdbdcaaddbdbacaccbaccccbcbacdcaababbadbbbbadbbdcbddbdbdcbabdbdbdbaacbcbbcacccdabcbdbcbbacdccdddccbbcbdbaabbcbbddaccbdcbbcadcbacbddcbaddbaccacdbadbcdadbcbdbdcacbacbcdacbabadcabbddddabbcaababdccddabccccbccbbcccbadbacccccdbbcaccaabdccdbcacdadacdccbaaaddaacccdbccabadcbbbbadbacdcbaaddadacdacabcdcdaacadbabddacdcbbdbdbbdababcbbabbdabdddbabbdbcaadabccdcddcbcbcabadabddccbadadacddabbaccadabbbdbdbacbdbcacaccabbccddbccdbacbcbcccabaaadcdcbdddadacacbacccaccbacbccadccbdabcadbbbdaaabcbbadcbccbccbcaaaaabcdcacdaadaabccaaccbabbaccaaaaccddaabaacabaaabadcaacabacbbcdbcdbaabacaadbbadddbabdcadbcdbabccdbabcbdaacabbadcadcbdccdadcacadcacabaccacacdcddbbdbdaaabdabcdabbcadcabbaadcdcbccbdcccbacabdabbcddadccdbdddbdbcdcacbbadcababccacccdabcddacaaddcbcdadbcdbbbbcababaaccbdcbbaddbdddccbccdaaacbbdacccdcaccccdbbbdaaabbdaaabbbacbdcbadbcccbabdbbccaabadacbabccbabadbacbccbbbdcbcdbdaaacacadbabbbbabcadaaddacbbabccadababbddcdbddbacdbbbcdbdbbdacaabcbddddaacacabaadbdcaddccbdbdbdbcbacdadbbabdcbdccddbccbbbcdabaacbdbaacabcccddbabcadbccdbcabaacdadbcbcdcdccbcddcbcddbddabbcaaababddadcbaddacbabccddabdbdababbdddcdbbbaddbabcddabbabbbcadcaabaadbaccdabaadaacbddbcacddbbbcddcdbdbdbcdcbaacacccabadcbbbdcababbdcbccdddaacaadbbbaaddcadbbbacddadaadacdcddcccdcaaadcaccacdabcdbbbbaadbdacaacdddcdbbdcbdaccdddccbbaacbcdbdbdcbacaadbdccabcbcdacdacbcaabcdbdddddddbdaabdcdbaabccbccddddacaabcdcabacdabbddaacabdbabbabdddbbbacadadccdcacbaacbdabbabccdddbbabadaaadbcbacdccdcadadccbdbbbabdaadcadaccccaacdbadbcccdaccabccbbdaacaccbcaaccbbcacdddccaadcbaaddcdcaabccaccbdcdcbdbcdbdaccdbdaaabcadadabdbddbbcbdcdbdcbdccaabdabcddcddcddbbdbddcdcbcbbabbadcabcaabddcddbdaabbbbadbcbacdaddcdcdabacabadccbcddaadbcddcbaacbccccddbdcdbbcdbabbabbdaadcbcccbbdcccadccbbddccdbaddbdcdaaacbdddadccaabaaaccacdddcdcbacbabadaadbbdcacdacddcbadbabccdabcccdcddaccbdacdacbdcdbadbaddbadbbcddcbcbcdcdbdabbcbabaabbbdbaddabddcccbbaddaaccbbbbddddbababdcaaccaaacdaabdacadbbabcdaccbcbdcdcbdcccccccacbddcbabbbaacabdbdacbdbdcdaacddcaaddccbadbcccdbbdcabcbaababcccadbacdbbddaaddddcbccbcdcabadbabbaabdccaccdcadcadbcdccdbdddacabccdadcbbbdacdabbbaabbaabdacadabccaabddaccaacbdacabdcccbbabddadadbdbdbdacaabaccbbcacbccbadabacdbbabdddcdcccaaddcdcacbaabbaabadabaccdbbbcaabcddaabddcbdccdabdcabccddcabaccabbbadbccddacbdcbbabaaddadbbccaabaaccabcbaccdadcbbbacdabcacccabcbacdddcdbcbdbbbbbbdababdabbddbccbcabcaadacababdcbcabbbcbdacdbaadcacabdabdbcacccddcdcdaadacddddabaadcaaabdacdcbcdacbabcbccbaadbacbccddcdcdcdcacabbbddaccbdcadbdccabadaccccaacbadaabbdaaddbbbdacbcacdbcadaaddacabaaaddbccbddcbcabddabdadbdbccbadbbcbcaadbcdcdbcaccdbbcbadbabacabaabdaadaaccbbadacbadcadddbbaacbdaccbbdaadaacabdadbddaaacdddcaccccdbcdaaaacccaccbdbaccccabdbbdcbcbbcddbaaaaaacbcadacbdbdbacbdbadaaccccadaaccabccbdbdcaadddbdbdacddbbcdaadaddcbbdaabcaaaaddbbaabadadbccbaabcdccbcddbdcccccabdcbbbbdbabbccbbdbcabdbcdcbbdbacbcbddadcaddabcddddddcbcabccbbabadcaddadaccddbaddbbbababdcaabbdaccbddbddbacdcabdcbadadaaaaccdcdbacabacacdcaadcdcaacbddcddaddcbcaccdcddbbadcdbbabbbbbdadcbbdacdacdcdbcabddbdaacbdbdaacccabccdbcadbaabcbcdcdcddbbcabaacdadbbbabbbbabddbdbababbbadccbdcdbcccbabcbcdaadbcddacdbbdbcbbcbbabdbddcddcdaaddbabbcaddcdbdbdddcbbaacbbacdbbdaadacbabcbcbbbbcbacacbcdcdbacacabdbaddacdbdaabdaaacabdbbbbbbdabacbcabadbadbbcabdbbbcdabbadccdaaccabcddbbacbbddabacaaaccabadccabbbddbbbbbbbdaacbdbabcdcddcbcddccdccddbacabdbaaddccccaddadabadbabbadbbcccabcaadbcabacbccaabbbacabdbddabbaaaaacbbaabbbadbbdcbbddcbdbccddbcdcbcccdddaaaadbaaabadbbdababddcbbdddbdbdcbbbbbcbdccdcadbadaccbbbbacdabdbbabcbddcabddddddcccddcbabbbbcbcadaccabccaabccadadccdadaabbdbaadbcdcdaccdadbbdcdbbbdaaabacaaabcdabccbdcbddabdabcbbcadacdcdabacdbbaaaddbbbacbdacccbbbddadcbbbacacdababcbcdbbcdcbcbcadddcadccaaabcbadcabacadddddcccdcbdaadacdbbdbabbbaaacacdadbacdbacbdcccddbbbbdcccacaccabbaddcbcccdbcdcdcbcbccccadccabddaaadcccaacbcadaddaaccdaddcdbbdbccacdacddacdcadacccaaaabdccccaccccbdcaddbadcccbabdcdddccabcdbccbcbbcdbbdabddbdbadaabaccdaadbccabcabcbcdcaacbacbcbbbabbcccdaccadbdccccdddabbdbbdabdcabbaabcddbbadadabcabdcdbdbabccdcadcdbcabbacaabaadbbbcadbdbadcdaccacacadaaadbdaabadccdcbcacdcdadabdbaabacacdddadacaadbaabacccacbbcbbbcadcdacababddcccdbacababbccdacdbaddabbccaccdcdbddcabddbbaabdcbbaacacadabacdaacbccbbdadcbbbabacdcbbbbaacabaaabdcaadddcbbadcccddbcbdaaadacaaadacaadbccadcbaabddacbdddbdadcccaacccadcccdaaaacdbcbbaddaabcbbbaacdaacbcaabcadbbbaddbdbcbdbdbdbbdcbdbabacaddabdddbcacbabbacdbaccababdccbbdcbcaadbbbcbaacdbacddcdaadbdaacdadccbdcdbdaddddccbaabdaadbccbcdaabbbcbaaddccaabddaddcabaacdcadaddaccbbdaaaabbbdbaadabbbddbcadaadcbaabdbaabbbcbaadabdbdacbacaadadbbabbbaacaccadcbaaabccbcddcdbdaadccdcacdccdcdbbddcbbbdaccdcadcbbadbcaacacbdbdcddacbaaaadccddcaaaacbdcbcbabcacbbbcaabdddacacdddcadacdacbadadccddcadbabbadaaddadababacbcbdcdadbcdbacdaaacaccdcbdcbcabadccaccbacbcadacbdcddacbbddbcaddbcddcccaaacdcababcccdbaccdadaabbbbcbcdbabdcdbadcdddbbadacbcbcacdddddabccdabcccaadcadcabaccdcddbbaacddcdcccdabbcbdaddcaccaddcdaccadabcbaabdcccaddcdcbdcccadaabcacaabcbaabdabcdcbcaccbaccacccaaacbabcccadcbbdbadaddabbbbaadaaccbddacbabaacdabdaadddadacdaabddbcddcdaadddbbddcbdbdbcbbbabddaaccbdbbdbabcdddcbdcdcdcbcbdddacaadbadbdabdaaadacdccbaccdbadbcccbdbdabbccddccbacddaadccdacbacaaccccdccdccbabccdabbaccbbdddaacddaadddcadabdcdddcacdadbcadbbddaaabcbcbccbbaacdaabcaaacdcabcbbdaadccaaadcababdddbbadbbdcaaadbbccaccbabbcddcccabaaacbaacccacabaabbdbcadbaacadabdaaddbbdadadddbadcdabadbabcdbbccdbdbbadbcaabdcbbadbabadbbbcaadcbbdcbacbcbabddababddbdaccdbaddcdbcadaacbbdccaccdaccdccddcbaadabcbbacacbbddcbbbabdcaacbcdcbdcbdcbaddbdbcbbdaabccbcbaccadcdccddccbabbadcbadcbdadbdcadabaabdddbcabbbcbaadbabdaabdbadcbbccbdacbcdabcbaccadadbcbaaaadabdbbdcdbcadbadcbcbcbbbabdddbdbddbcacdcbdcbabdaacaddbcbababbcadcaddcadbaadacbddaaddcbcaaaadcbcaabccdcbddbaabcaadbadbdbdacbdccddcdddcdadabbdacdcaaaadbbddbabbabdbdbbccabddacbabcbcdcabcbcabcbcddbbcbabacadbdbabdccaabcdadbddbbacabcaacbdbadbacbdcbaccdcdadabdaccdbabacabdbbcacababbcacadccacadbbaaacccbddbbabddabcaaacbdacbcdcaacadbcaaaadabccbcddccbcbcbaadbccdadbbacaacacbaadcbbccadadcadccaaccacccaacadbdcaadacabbabbcadaaabbbccdcabaabdbbdcbcdaccbacddcdbbbacabcabbadcbaccdcbacccbcbadaacacddabbcbbbadacddcbcbcaaccdddcdaabbdccbcbadaadbbdacabccddbadacacadaaaaccccbcdababbdbacbcdbaadbbadccbbacabdbddcbbdabaaaddbaaacabbdcaabddbdbdacabcbaacbcdcabcaacdacdddbbaddbcaddccdcadbbccadcccadaaaabcababcbaadcadbabdcbadbbbcbcaaccdcbcbdcacbccbadadabdacdbbcccaacacaaacaccbcddddabdadccbdbbcadddddbdacacbdbddacdbbcdcddabbcdbcbbdcbcbdccdabcdababdbdcccbcdaacbddcdabcdadcaaccabaccaacababacbbcddbbbadcdbaaaabdbacdcbbcadabcbadbdbdbadccdcdddbdccacdcdabbdadacdbccacbaddbddbadbbbdcdbcbbababadddaacadcbdcacdbccaabbcccadabbcdaabaaacaababadcbbbcdacccddddabcbaadadccabaacdbccccbcbbcaaadbdaccdbbccdcabcbdddbbdcdaadacbbadddcbabcbbbcbaaadddabcbaacabaabdbaaaabbcaaabdaadddddbbcbdcaacabadaadadaccacbdbaabadbcaaacabbcddaaddcbccabadbaaaabdadabcabdcbddacbabbdcbacbbacabadbbdbacdbcbabdcbbcddbcbbbbdadaadadabcbdacbbdadcdbbbacbdddbbcaccccdbcbdddadacdadcbababddccdcbabadcdaccdbacaaddaddcacddcadcabaacabdcbbbbcbcccbdbdbbcacbdbcccdaabadcdccdbdcdccccbdabbccdacbcdcccabcabbbdacacabdcbdbaccbadbadddadabdcccdcdcdbbbcabcbcbcbcbbcadcddcdabcadcdcccddcddbdccbbcbccdcbdaacddddbcbbbacbcddadbdcdacbdaccbcbdbccccabdccdbccdddacddadcacccbbcabbddadccbadabccccabcbbccdddaccbaacbbbcbddaaadbdcccbabdccacccccbdcadbbabdaddabcdaabdcabccdbddbbbdbcabdbcbcabcbacbbddccbbdcddcdaccddcadddcccabcbbadcdccbabbbbaacacbcdbadbdbbdbcabbdaadaddaacaddbbaccaddadbbacdccbbcbabaddccacbadaadcacaccabbadbcccadacbbcdddddadbcdbcaccabdcdbdadaccaaadbdbdabdbbbabbcdccbbdbdaadabbdbbbbbaddcbdcdadaacbcdbaacbcddcabcddabbdcabcdbdbdabbcccddcaddadbcdcbadbdadbaabbdaaaddcdacbaacabbbbddacaddbaccbddacadcabdabbcaabcdbcbddcdbdabdcadbbbcaacccdaaddcdbcaaabbcddcbaacdcddabbbaadaadcccaccacacaddbbbddbbcdbccbbdbbaccddbacacbbddaaadadcbacadaaadddacdbbcabcbdbbbaaabcdacaabadadbbbadbadcaacaddaddccddbcadbbbccdadabbabcdadadabdcaaacbaddacccaadacaccbcaadbdbbdddbccbdcdbbcbaadabbdbabbdddcdcdbbbadacaaccbdcdbdcbdcbadabbcddbbbcbcbbbdcbdccddcdbcbdcdbcaadbdabcacbcdcbbadabcacdccdcdbccdaddcacdacbaabcaaaaaddaccaccacdcbdcacdbabadcddaaabdbabadbaadacacbccdddcaaaccdcdcdcbcbccaabcdccdbbdbabccdaaaabcabcbbbaacbcdabbbdcbbacdadbcbbdacadddcbadcadccbbdcbcaabdbbdbccbacbddbcddccbddababbabccbcdcccdddccaabbddabcbccdbcabbabdacdccdcdabadcabcadcdcbbcabaadcbdccccabcdbcabbadcdbccdcdaacbcbccddbccbdbcbabdabaddabbbcbccabcacabcaccbcabdaabcbbccdbabcdabacdbaaabdbbddccccadcccdacccbdaaaacccbccbbcabaacaccbdcbcbbdbcdbadcdbcddbbddbabaacddaaccdacccbccddaddabbdcdcaddcadcdddadaddbbcbbaaaddccbcdcddcbbbaddbdccdccddabbbdadcddddddbddddbbadbcccbacdddccadbabbcdbaaccbcdcacadbdbcaaacbbcbdbccacbdcadadabcaddbddbbdadbcdbbacbdaccaaccaabacacacccccabbcdabaabbbaccbcbdadddcddabdccacbbbdabbbbbadbabbabbabbdccddddabcdcbabdabaaaaacbdbddbbdabadccddabdcaaabcccdbacdadbbcbddbaccaabcbbbcadadcbabbdaaaadccccadacccbcdacccadacaacadcabbcddaddabcbaadbcdbaadcbaccbbcbdcddbdbdcdbaaccaddccdadadbdaacddbbbddcccabcdcbbcaacabaaddbbcdacbbbbdabccdcdaacdacbcbccccddaadabbaaccabacaccadaaaccadbbcbcadadbcccbaccbbdddcaaddccabadcccddadbddbadbacaddadbaaaaacddcacabbabdcbdcdadbaddcdbcbcddbbdbdadcbaadcbbddcaaaabadccdadabbaadbbbdabcbadcdabdbadadcdbadcbbccababccbacbccccabadaacbdacdbbdaadababadacaacbadaccacddcadbaddacdcddcdcabdbdaaabcacdbcabcadcbddabbcbcdabdccbadcdaccadabdcbacdaccdbdcddaaabbccbaddabbbacaaadcabbadaabbacacdacaccacbcbacbdcbbdcaadbcabaabcbacdddbdbaaccdabaadbbdbbddadcabbdbaacadbabbbacdbabadcaabdbdaacbddaabbdcaacdbdaaaadddaddbaddcbabadacccdacddaabacbaadaaabccaabcadbaccaddcdbdbabcaccddccabababacddaadbdccbadbccccbcabbbdadadcaadacadaadadccbcdcdcbbccddbadbaacbcadcccaaaccaaddccbbcbadbdbcdbbbaadadabaacddadabcadbaabdaaccdadcadaaddaabbddacbcbabbddccdccbaddcccbbccbacaacadccacdbabaabaadcccccbdbcadabaccaabaacddcacddcdcaacaaadbbdbbcaddaaddcadddcdcbacadccaaccccbacdcbcacbabbdacbbddcbacccdcdbaccdbbcbcbaacccbabbcadccabbbabbccdbdbadbbbaaddcbbcdddbaacbcaaabcabbdaaadccdbbababccbcbccddddcddcdcdcddacbdacdbabdbadadbdacdaddbabacccaabddbbabdcbbbdadadccdbabacccdbbaddcabdcbabaddacbbccdbdcacdccdccbbccdaaccbbbaddadcbbdaacabdaabcacbcdaabbdcaacadcadbaddcbbddcabcaacdbcabbabdababdbccbcabcaadcbbabcaabdcdccdbcdadacdbdcacbbdccbdaaccadcabcaabbadaaddadaacbcaacddddaaaaabaccbcccbaaaaaddabdbadcbdcddcccbccbcabcbbcadbadadaddacdaabdaabbacbcbdadbbbbbbacccddcbccdbababbaaddaddcdcccaacdbdaabcccdbdcdbacabdcabdaddaacbacddaddcaccaabdbbadbbabdabcdbbacdccbcbcdbaabdcdbbaabdbbdbaddaccbaddccbcdcbbccbbccbbdabcbcbbccdaaaddccdddcbaccaccdbdabcccbdbdaacbbaacbbadaaccddcaaaaccccbdbdaddbcdbbdcdcbacdadadadacadcccdbcdaddbbaddccaadabcabdbdccddcacddaccaadcbbdbdaadbaddcaabccdccdcadbdabdbbabbbcbdcaacdbcddabacaaddaabaabcbabccccddcbcddaacddcbbbaacbbcbddacaddbdbadcdaadbccdccabdbcaaddabbabadbcddbddcccbbadcdbadcadabdbcdadbdbbadadadadacbdacddacccdbadaacbaccbdabbaccddcbaddccaaabadbdddcadadbdaadbbcdddabbaabbdbadddacadcbccccbbdacddabddcaddcadaddbbbddadbaadbddddbddbaddbccbbadcdcaacacdbbdbbaadabbaadaabaccdcadbdabbdaddacdcccbacabdbaacddbbcccdadbcbaadccddacbdddcdcabacbdadacadddcaacabbdabcbcdcbdcddadbcbddaccaadbdbdaabcdacdddcabbcaacabbabbabccaddcbddcadbdbabcdcddccbbbddaaadbdbaaccacbbccbcbadabccdcbbacdcabbdabcbdbadaabcbddacaccadbcdcdaaacccdbabdcadcdaabbdaddcbcaacbccaadbbccbcccbabbcdbcbddccbdcbaadbdbccddabbaabcbdaaaddbcdbacabaaacbdcddabadacdddcddabbdabdcbaccdbdbdccddbbddcdbdcdabbadaadbcabbabbbcbcbdabbbccaaccacaaddcbabdbcdccdbbdcadbdbacaccbbcadaadddcabdcdcadddbddadbbabdcdacabcddaaabcdcaadcbbcaaddccdcabdddadcbbcaddbdbbddcaacabbccdacdcbbccccbdacddbadcaacacdacccaacadcadacbdbbbacbdbcdbcddaaaccbdabcaadcaabaacaddbacdbdbdabdbabbcbddabdcaadccddccadccdacadacdcdcdaccacdbbcddbbabbadcacbdcabcdabaaaaacaccaaaaaddddcccaadccdbbabaddcbcdcdddcbbdabddbcbcdcbaaacaaacbbdcbbcbccbaaadccccdcdadbbdacaacbccbbaccbaaccbcacaccddcdacaaabbbccbabaacaadaddcaaadcbddbadbabadaaacdcbdaacdbaaadcbdbadaadbcdbacadbbdcdbcabbdccbcacabbdccaadcdacbdcaadbcadbccaacdbddcbcbacabbbdcdccadcbabacbbdaababcaadaaacabcbdbdcaadcaccbddbbddaacbbaacacdcddacbdcbddaabdaaacaccccdaababbcabdcbcdbabbcaabbcccaabbabdbabdcdabbbabdbcaaddcccdaacccbcadaadacccbaabbacbacacbaaacdcbdacabcbbdcadaadcbdbcacdaabbdbadadbcbacadbdcababaabcbadbcccaabcbabbaadddabcbcdcadcdcccddacadaaddccccdcababcadaaaabcdddcdbbccacbdabccdcacaaabccbabbaddccabcbdbcdcadcbadaccdbbbdbdaaaacccccacbdcbbbbcdaccddddddbbbdaaaadbcdaaadbcbcbbbbbccdbdddbbdaadbccdbcdaabddacaabdabdaabdaccdccdbdbccbadacdaaadabaccbbbabbdaacaacdcccbacbadcbbbcccdababbadaadbbdbcabababcaddcabbdaabdcaadbcbcabbadbdddbbdbdcadbdadbbdadcdaaacbdcabbabaabcdbcdcdcbacbdddccbcdadddccbdcaacbbbbaddcdadaacdaaddbcbabbdbdcccbcbbbcbacbccbaccbbbdbaacdadcbbddbdbbcabccabbddbacabacacaacbabcbacadcdbdaccddcdbddadbccddccbbdacccbbdcaadccbbaadaaacadccacbbdabdbcdbacadaadbaacaacacccbcaabccbdadddcadaadaddaaabbccbccbcbccbbcaadbcadabacbdbadadbdbdddacbbbabdcddcdbadcdaabbaadbacbbcbadabadcbcaaabcbbdbaccdbdddaaadcddabdbdccdddabcaadcadadcccbcaaccdaaaabbabbbddaabaadacdadcbdccbbcbddbdadcdcbcbbcbadcababdbabccdcaddbdbbbbcdbbcadbaccdcbcacaaadbcbcbbabcabdcdccbaacdcdabbadbbbdcbacdddcbddddddadaaccbabaacdbacaccbcbbddbbbbbccabbaabadbdadbbbcbbdbadaabdaaddcabacaaacadaacbbdabaaabaccdbbcdcacdddabbabadcabbbbadabbadabcccacaabcbaabdcabdbbcabcacadbacccbdabdbdaccbbdbbbaccbdadcbcbbcbddbbccccccaacacdbbcdbaabbbccbbadaccaccaccccbbdcdcddaccaadadbacacddabdbcbccadaaddcbadbbddbbcdddbaaaddbdbbabbbdabaacddbbacdddbbdcbaadcbdbdbbdaacdbdddddaaaccacabdbbdabdaadbccbaddddcbcdadcadaccdccddaabcbcabddcbddabdbdcdbcddacbccbacdaaadcbdcdbccbbcbdccddcababbbcccbdbaacdbaddbaacaaddbabcbcdaaddcddcdabacddbddadcbbaaddbaaadbcdbcbaacdcabbaacbbabbcdaacbdbbaddaaabbacbdcbcadabdddcacdabaacabaccdccccbcacbccadaacaccacdddbabdaaababcccdbcbbbcdbadaabccacacdacbacaabcdbddadaaccdbbbbdbcbdbdddcaaddbcddddbbcadccaaaaadadadcbabcdccdbddcbccbbbaabdbadaacdcadbdbcaaacbbdbadbdddadccbaaddcaccbbaabdbbdaccbdddabbaacabacccbcccbcaaaabcdaaabacbbcdbcdcdcbbaaccaddbaccbccdcdbadbacabdccabdadadccdaaacddbadabdabacbbcdbcbbcdbadcddccbcddccddacdbbbcdddbbaaddbcdbaadacccdbbbacbddcaaadccbcbbbccdaabccaabcbcdcdadadadabdddacddbbccdbbadccdbcbaddbdcdccddbbdbdacdccbadcccccacccdcddbdcdbbccbdadaadccbbbabbbaccbdabddbbaddabacabcabbaddcdabdcdaddbdddacccaacbbbccacabacacbbaadabbadcbcdaccdabaccabbdadccadddcbcddacaabcabcabaabbddaaccddddcbddbbdaddbddccbbdadccaacaaccccbdbabbcdcdcaacdbacdcbbaadadbbadccccaadbddadccabbacacbdbccbdabaabaaabcaccacdbdcdcacaaaacadabbdddcbbcdcbbabaaaaadccdacdadccadbccbabcdcbccabbadacaabdbbabdddadbbaddbaabbaddadaccadabdbbcccccbddaabadaacdccacaddcadbaacabdacddcaccbcacabdcdadbacccccaccddccdbbdcddbbadbddaaacabcaacacacbaaadadcaccbdbddacacbdbabacdadaacacbcdddbbcddddbaddbbbacbacdbdabcacdbabadcaaabdcdccdccbcbbaabccdcdccadaccddcddadcdddcaaddbcaacdbabdbacadbbaaaaaddabddaabaabbbabdcaccdbabcbadbadacdccabbddbdabddabdbadbccdaabaccaadacbabbdcaacdbdbdccbccabaaaaacaaaadbaacbcccccbcdbdacccbdcdddbdaaabcaddbacccbaddbccddabddcdcbcbbcbabdaadcdcbcddbbddbbcdbddbcabaddbbaadcadaaaaaaddacbadbacdddccbdcddbdacdadacccccdababbabbbbbdbbdaadccaccabcbddaddabadcbbccaddacddbdcadadbacbacadcadbbadbaaaccbacbacdcacaadbacabcabdaaccacaccaccbaddbbdccaddcddbbdacddccbcdaddccabdbdddbddadadddccdcdbbcbcccdabcddbaaadccddcdddcbbdbcadddabcbcdadcbbcaaccdcaadbbabdcbdbcaccbbcddacdcaabcadbaacbbbbcacbbdbadccdbccaacaaabdbdabbdcbdbcbddaacccbdddcdddaaaaadcaddaaadcdcbbdbcddccbdbadbabadaaabddacbcbbbdccbdabdcbbdbbccacabdbddacaadcaaaacbaaaaabdaadacbdcbcdbddcacabcddbadabdaddccadbcdbcdaaadcdcdacdabbbacbbacdbbbdacbaacdcbabcdbdddaababbdbbbbcbcabcababdadbddcddccdbabaadbcaacdccbcdbadabaabcccabaadabcbcdbabbcbcbddcbdcbabbadbcbcaaadcbdbddbdbcccdccbccdcaccacbbbaaaaaabdcadbcddbbdbaaadbdacabaaadcbbdbbcbbbbdbbcdcabaabdbabaacbdabbbaccbdcbdbabbbbacdbcaadaccbdaabcbddcbbccacbacdabccccbbaacbabbccbcadcbabacbabbcbaccdaadaddbccbdbabdcaaababcacdccaadadcabcbdddbcccbbcbbaacbdacacddcaddcadcadcccbcbccbdadccdaabcbbbccdbbabdaacddcdddcabcacabaaccbcaadbbadccdaabcdbddbdcabaddcbbabdaabdabcbcbbcaacaaabbabadbbaadbcabcacaddcdbadabdddccabcbdccacadbaabdacdabddaadacaaddbaccabcdbccaacdccabaabbbcbbcbcccbbdddddcccdbdabcaabababaadabadbabbadcadabdbabdbbcabcadddddcdcdbdcdcdcbcdcdabcadadccaddbcadadbbacdaccdddacddabbabcadacadacbdbbadbccdcddcbbadadcabdaabdddaccadbaccbddcbcdacacabaaaaabbaddcbbabdacdacdbdcccbbabdbdcbcbdddadcddcaddcbbbababddacbdddababbdacbcbdabcbbdaaddcaddadaadcbadadddbdcadababdbccaabcadabadbdabaadbaabddcbbcdbaabbbaabcbadaadccdbbdabdaacdbcdadbccaaacadabbcdbabcbdacaddbccdccadbabadddbabbdacbcddcdcaaacbddcbcacdcadaaadbaddbccacbaddbaddadbdabbcaadcbbddcccdbaddaccddabcbabcaaaacddaabdbdbddddadadcbbdddbacccacdbbddbacbacacacadddbaabaaccdadaaddcbadddbbdadcabdddbccdcabdcbadaaaddacabacdcdbcdbdacdccadddccccbbaddaaabcccbabdbcadabacaadaddbccacbbacbdcddcdabdacbdadbbadaabdcdcacbadddcbdbbcdbadcacddabbaddaccadadbcddaccbaddbcadddcbbbdbddbdadadabdccabbdadbcbdbcdadadcbcbaaccdaaddbcbcccbbddaabbbadacbaddcadccacbcddccaddacacabbdcbcaadbbbbaddabdccbdcabcbcadcbcbcdaaabccdcbcbacdbbdaaddaddbcbacaabbaddbcaaccadccadbdddccbadbaadbccccaadadabadacaaacdaaaacabababccccdccabbbbdacbbadabbacbdcbadbcaadadbcbccaaaabacddbdbbcbbbaacadcaaadaadbdbbbcbbaabacabaabcccacdcdcacddbcdcbcbcaddacacaabdacccabadaaaccbccadccbcbdbadabcabdbcdabaabdbcadacacacacdbdacdadbdbbccacdcdcbdcdabcabcccdbadacacddddcdcddbdbbaabadacbcaaccaadacbbbbcaccaaabbdacdbcdcbbbdcdbadbbbaadcccccbabbbcdacbdaaddcbcdbccacdacdbdbcdaacbabaaccabcbdabacabbabadccbadbdaabdaaaacacdbddccaaadbdbadcbdabbabdcacbbdbbcbbbacccaccbcccaddbcdbcacacdbdacbbcbdbacaccaaddbbdabbaacacbbaadaabcbbdabccaaddadbbdbbbcdcadabcbacacbcddbcbcbaabdbbdadaacacccddbbcdcbccadacdabbaabbddbcdadbdbbdcdbabbcccacbcccaabbaaabbbbadcadacacdacadddbdbbcdbbdcdccbdabcdaabdadcabaaaabbaabbaaaadbbddccacacccbababdcaabcacbaadababdcaadacbdadbacdcadadbbdcdaacccaddccbdaacddcbaadcacbddcaaddaaadccabdadcbbcaabcdcaddbbcdbdacddcbbabcbdacddcadcdccbaddcabbbbabbbcbdbacabbbabdadccaacadcdcbdaacbddbcdbabccdbcdbdbdbbcdcaaccdccbdaabccaacbbabdabaabccbcadbacaacdacddacdddadaadabacababddccabbaacdbcaacdcbcdddcdaabcaaadcbaaaaadbaacdcbbcdcacaaccacdcccacbadcdbdcdcacdbddcccaacababbadaaaccbaaaddcbccaabdaacdbaabbbdcdadcaccdbbddadcbbbdcacaadbbdacdaaddabdbbdcbbdcdacaaadaccbbaadadcdaaccdcccbbbbaabcdbcabbcaadcbbdbbcacddbdadbdadbbdddccdcbbacbccacccadbcdddaacdadababadddbcbabcaddbdcccbcdadcbcdbabaabdcccccadadacaacdadbcdabababdcbadccccacbbacdaacadbaadbddbdbacdabbbadadcbddaabacbbccaabccdbdaccacbbddbdbbbcaaccbcacdbbbdbdcdddccbbddaadbbaddaddbddbddddabbbaabadddaacbbbddbcdaddaaacbdbbbddbbddddcbabdcbbaabddccbadcababadabdcdcbcbddccccbdbdcbcbababcbbbcabbcbdcdadcdbbdbcccabaddcaddbccaaccbbadbccabbabbbaacdacdaacbadabdbbdabaabdbcabdbbdccaaadddcacdbcdbbdddbbaabbbcbabdcdddabcaadddbddbdaccabcaadbabdbadcddccaadbdcaccbbadbaadcabbdadcddaddddaddaabaadbdbbbdbdabbdbadaaabaabccbbdcadddcbabbadcdbdbdbcabbaccbacdbcbadddbcddabacaddabbdbacdcccdadcbccbbbaccbbbcddcababcbaabadaccbaddcabdbbddaabbcbccadccbdbccbaabddcdcbbacadccaaabbdddccbaddbddcbabbabdbcdcdabaaadbabadbdaccabcacadbcaabcccabdbcdbaaccaacbbcdbbbbcdcbcccadbacbccbcdcbdbbcdaaccbcdadcccdbbcbbdabdbcbcbdbdbabdaaaacbabdcababbbbbddbccbcbadaabbcccbbddbcdbcadbadacadadabcdccadcdabcaccaabbdbadbdbadcbabdabaadbbadddcbabbababbdddbbabcaadbbdccaddddadaaabbbdbdcdabababcabbaddcbbddacaabaccdbbcaadbacbaadbbadbcadbcbcbaaabbbbadacbccdcdbdbcddabccbcdcdbbaddadbaacbbdabccbaacadddaadccabaccbcdaccccbdbdccccddabbdaccaaaabccdaabcaabaadbaaadbdacbddbaddabbdacadaccacadadcabacadbbbadcdabdbdcdbccdbdaddbccbdbabbbacdabaccdcbdaaacdabccdddaabbacdbbbcbdddaccbadbacbcadbbcbbcdcdadbbcccaabadddbcdcaadcbccdcbdcddabcbcbabdabbbbbbcdadcbdabdccbddbcacddabaddbccccbbaddcbbdbbbbdbcdbcccdcbdbbddbddbcbdbddacbbdaabadbbbabbcababbbccbacdbadcaabbbcabccbcbdbadabaacacadccdaacdcaccabbbaaddbbbbccbcdbabbddcbcbaadcdccadcabbcaadcbbabacbcbdababcccaacbdbcccacbcabdddcabaadbaddadabdcbcddbaabcccdbbbcdcaadcdcbdcccbacddaadaabdddaacadccdcadaccccdbbcabbdccdbdacdcbbdabcbbcbddbccbbbdcaabcbadccbaaaaabbabaaccbdabdacdbcccabccbabababcdadadddbbcbabdcdacdaaddddadbcadcdabcdcccddbaadcbaaaabcdddadbbdbdcdaaaacbaadbacbdaaccbacdaaaabcbcbcbbaddaddbdcbdadbacbccaaacabbccbdcdddbddabcdcabdbabddadbcdcaddcbabacdcacaaaacacddcddbacdbabdaccbaccbcddadcdcbbcbadcbcaddcddbdbbcbdbbcdcdacddbddabcbcaabbddcacdcdaddcdabdadbcaaabacccadcbbcaabbcaaddabaabdddcbdaabaddbcdadabcbcabddaaccbdcdcdabadcadddadbadcadbdbacadbcbacabdcccbbadbbbdababdbcdaddbddccbdcbbdccaaadcddcccbbacbaaacaddadabddabbaaccbaccabbddbdbacadddbdcdcbdadaacaabbadcbdccdbbdaaddccaaccaddabddcabbbccababcdbacabcddcdddddabbacbcbcadbdcaccbbcdbbcacccbcaadbbaabaccacaddabcbaabcababdcbcbbcacddacadbcbdccacaabdadacabaacacdcaadbabaaabddddadddcbdccadcdbabdbdadbbbcacdbbcdbdbddccddcaadcaccdddaddaadbcbdabbbacaacdabcacaccbcabbabacdadadddaaccbbdacdadbcbacccadbdcabccbcaddcccabbdacbcdbcbbdcabcbcdaacbcbacccacddcaacbdcabacdcdcabdddbccabaabbccbcdccdbcbacdcbbdcaababaaaadbcbaabbccacddbcaabdadcdcdcaacdcccddccdbcbdddabbaacbcbdcbaddabdaacacaadbdacdbccadcddccbaababcdabbbccbcdbbaccdcccabcabbaddcadccabcacacacbababacbbacdadaadaaaadacbdaabbaadddacbdadbbcccdccbacbdabddcdacbcabdcaabdbbbdadddcaddacddbcccbcaccbbdacaddddccbcccbbdaccacbabaadaaacadababbbddddcdaaabbdabcdacbdaaaddbbdabddbbbbaadabadaadbadcabdbdbdbdaaaadaddadabdbddbacdaacbabacaadcdabdcbdddbdadabcacbabbbacdaadcdcaacbbdcacdaddddaaccbccdabcbaabdcbbcddadcddcdbcadadbddadbddabadaaddcadabcccbbcaadacccaabdcdcccdcbabbbdbadadbaaadcdaddcddaaccbddcdcbcccbaadcacdcdcccbdbbbbdccacabccdcbacddcbcddbdaadcddaaababcbddcdacdbbccbccabdadaccbcdbcdbcbbdaccdcddbaaaaabcacbdcdddacbbccdcccaaacdaccbccaaabadadaddaabaabbabbcdbbaabbbbbbacdcddbbdadadacbdabcadcdcddccdaabacaddbbdabcbbdbdccbadbcbaddbaccbabdbbcccccacbbcaddccdbcdbccbbdaabbabddbaaaabaadccbccabaabbdccdbbbbdacacadcbcddddadcbcdddcbaccaabbdaacbbbaaacccbdcaccbaaabbcddbbccbdbbdddcaacaadaaabcbbbabbdaccbacbabbddaabaadcbdbacddadaadcbcaccadbbbcabccbbabcbbaaadacbcaccacbbbbdbbacacadccdbdcaabdbccdddbbbdcbddabdcdaddbdcababbcacbdadbdbadaadcdbccabcdadaaabdcadbbddbccbbdccdcdaaabaaadbdbcaaacaaccbbbdcbaccaaabbbbaabadcbbcaaadaccbcbdcaddbbcdbcccbadbdbdccdadabcabdadcbaacdbcacddcddaabccbdbadaacdacacccdaddabaabccccbacacccccccaadcbbcaccdcddaddbdadbccbaababbdbdbabcbdbcdbccccacacbcdbdbcdbabdadadcadbcbbaababacdcdaddacbaacbcabcadcbadaddbddccadbaadccddbdbacdcbacadaddbdcbddabaabadbadbccbbcdcddbcadaabcdbabcbbadbcbcbdbabcccaccdcbdcbacdacaadbbdbbbacdccdaaddbdccccbbabccacadbaaabccaadbddbcaacccccdcbadaaaccbdbbcbcdaabdcacbccacbcdbadaaaacdacddccabadcbccbcbadcacacadbcbccbcadbddbcbaababbcdccabcadcadbbbcdaccadaaabaaddaddbddcbcaaacaadbcbadcdabaccdabdcbcdbcdacabcaddbdadbcbabbabcaacbddbbcaccaddaacaaabaccbcdbbcbdacaaddaccaacbdbaccccdcdcaadabbacbdabdcddbadbababcabddaadaacdaabdaacaddddcacdbcdacddabbdaabbabccababdcaadcdcdaadabddbbcdcaadbacdaaaaaabcdcadddbcbddabbacccabcdcaacadcdacabdababdbcdabddddabbbabadadcabbabbcdcadaddbcdbcdcadddccbdbacacdbdadadbbbbbcdadcbcbaacaabbaaadbbacddbcbccdbddcabcacabcadadcabbccdabdbddcaabdcbbdaaccabbaacddcacabbdbacadcbdbadbaaabbdcabdaacdccddcddbbbaadbabbdbabadbccadaccbaadabacbbcacaadaaadccdcdbadabadbabcbcbdbabbdcdcbdbaccabdbdcdbbcacbaddbabdcdabacddcdbaacccbadcdacacaccbcacbacddadbaddccbbbdbbdabbbbdddabdcbaccddadddccdddadccdabbbcccacbdacabcbccadaddadbdabbaacbbddaadadbbcdcdadbbbbbcdcbacbcacbcbddbdadbdaddbabbcdaadbbbabdacbadaddcccabdbccbbdcaabacddaadcaccaacdaacacacabdcddbacddbacaddadcbdbaddcdbacbccccbbdaaabddccbacccbcbbddcbcdabbadcacdbddcaaadcbdbcacacdccbdaacaadbbaabdbadadacdbbdabcabadddacddbbadbaabdbbabaacddaccdaccaddaaddbcbaaabbadaddaddaaddcdbdcabbdcadacaacbbaacbbdaaaaccddcacaabbccdbdcddbdbcacddccddbcdddbcaabccadddaddaacddcbbccacadccccaaadcdbdcbccbabbabdddcbadbadaccdbdccaacacdadbdbddbdaddbabccaacdbcaabaabbbabcabacdaddaabadadcdbbadcabaaabdbbaabdccbbdacdcaaacdbadddbcddcdcabdabcdbaacbdabadddcbcdbaabcaccaabdadabcddcdcdddbbdbacdbcddcbcdbacbdadbbbbbacdaddbcbbbdbdabdadbbbdbbbbdbccbabdbaadaccbddcddabbacdbacabbbbcdddaddddbbbddbabbbbbdddabcbdaadbdbaaacadcbbdbdaabbbabcaddbcccadcabdaaaaddddcaccaabccbabadcddaacdbabccbcbaccbaabcdacabdbcaacabcbbbdacbddbddabaaaaabdaccbcccdddcdacbdabaddbabbbccdaabaccabbadccabbbbbabddaddcaadddbaacbcbdddcbacbccaadbbabcbacccaccbbbccaaacdbaacbacacacbabbdadcdcbbdcacbdbdbcadbdcbbaaaccdabbbbccccdbdcdbcdcbbcbdacacabbbcabadabdbdbcacaabdcbcbdccaccbcabbbbcbbbaccbdabddcdbcbdcdaccbdabdddbbabddcbdbddaaababdbdcbabdddadcdbadabdabddddabaacbababddabdcbcbbabbabbcddadbddbbaaaadacbbdbabdbaadbacadbacdabbdadbbcdaccadcabbcbdcddbacdaccacdaddccbcbbbbdbcaadcabbccbdcdcbabaccdbbbcbbdbcaaddaabddaddcbacdccaccabcacbacddbbcadcbddbcdadcaabcaddbabbaadbddbacadbcbadaabbbaccaadabcccbdaccacccadaadbacdbaaadabcccdbdcdbdadbbbdddbdcdaadaaacbbbacabbaddcbdadbabbcaacacdaddadabcdbbcdddbacacdbbaddbdadbadcddddcabdabbbabdbdaaacbccbabbaadacdcbdcaaacdcadaddddcccbbddabbcdcdaacdcbcbbbdcbdbbccbaaadacdbbcaddddacbdcdcbaddaaababdadbaadacacaabaddadbabdadadcbdadabddcbccdaabaabaaadddabacdddcdabbcbdccddccacbbaabcbaaccadcbaabbbdaaabbcaadbdccddddbcadcccccbccacacccdddacbcdbdbcdbbadcdccbbbbdbcbdaccaaaacbabbadcbdccaccdabcacdaabbcbcabdabadcacbdaadcaadaccddabdabdccacdddbddaadccdcccaaddadacabcdaacddcaadaccaadabdccbdbcacbddccbcacaccacaabacacadcccaaaccbdbccdadcaaccdccaccdcbabaccbacbbbbcbababcaadcbdcddadabbcbbcbcadcccaddbdbcababadaabcbacbdacaabbdacabacabababbadbabdacdadadbccaccbaabddadbcdbcdadaaadddbcacdaaddddcbbdacbccccdaaaccadbdabdadadbabbbcadcdcbbbbccabbabcbddabbcbdbccdaadadccbbabacbabbaddaaddaddbbbbdbcbcbbbbbcabcbacbcaaddbbbbdbdcbadabcacbbcabbdccaccaadbbcdbbbdcbbabcdbaaccacadacdaddddcddabbacbbbbbbcdcccdbabacdabdbdddacbadbbccccddabacaabccacabbadacdcaabaabababcccbccdaddbcdbdbcaadaaccdacacacccbcbddbcdacaaccdbbadccacddbdbccddabccdaacacccbdddddabddabacbcadcddcabbdbacabadcadcabbcabcaaadcabbcdbadcaacdbdcabadbcaadaacbdbbddacadbabcdbdcabcacdcbabcbdaabdcaacbcdbadbadbbbcccbdbacbdcbcdcaaadbcacccccdbcbdddadadbdddbcbabbdcacdbbbddcbbcdbdbacbbdbaabcdccaabdacdaadbbbaaadbabccbcccaddbcddbcbddabcacddadaabadadbdbcaaabbcbcabddccbacdccbcacabccdccbcabdcdabcbadbbbcddbddaabcbccbbddadbbdbcacbadcacddaddcdabbcdcaabcbcabbabcddbabbbdccbaacaadabbbbadbccadcaaddcbcaacbdacdbdbbbdbdcadbdaaacdabaacbbbcabdccddaccaddcaaabbbdbdadbccbcdbcbcbcadacabbcdadddbbaddacbccadbdcdccdddbddaabacdddcbbbacdbadabaaccccadabaabdccbaadcccdcbccabaadadbdabddccbdcbdbbcbbdaabcaadbccaadcbdcccadcdacaccadcdaaccbacbcbaaaadcbacacbcdcbcdabbdbaabcacbbdbcabcbcddabbbcadabdddbdcabacadbccddbbadbbdabbbacdbadadacbdacaacbabbcbdadbbddabddcdaddadcddbcaccbdcadbbcbacbbddddaccbcbacbaabcdbcaadbcdbaacaadacaacdbbbacadabccabaaabbdacaadcaaadadbbabcabcbacbddbddcbdbcbbadaaaabbacbbcaabadcaccdadcbdddbbaacdcddddbbaabcbbacdddbaadbadbbdaabddbcbcabbacbaabccacdbdbcbbbbdadbdccdcddcaacacdcdbacacdcacccadbaaadbacdcaacddcadabdbdccbdbbabddbcabdaadcccabdccddcdbccaccadaabbccbbddcabdcddccdadbaacdbdbadbacabbdcadcbdacbdbdaaddbaddbcccdcadbacaabacbbccbadcdbdcbbdcaadcbacbadacbccbbbcdbddabccbcdbdbbdadbddcdddbddddbcbcdddacdbdacbdbacdaccbacccbaacddacddadcadaacbbdcdccddbccbadabbaaadbaaacbddaadbbdbadbdbdabaabccbabacababaadccaddbccabdacacadddbaadcdbcdcdabaabdadaadbdcbcdaccadadcdcacacbcbddadbbdcddddaaabcadddaddaabdbcadccdaccdacadddacdbdddbdbbaabbadccdbbccdbbaaaccddadcbbdbcbbbbbdbcccbdbdccbccdbcaccabaababccaababcacaabbdabbbaacabddddcdbdbbdcbbdcbbdcbdaabcaadaaabdcccaddbdddddabdbdddadacbdbccdbbbbbccdcdbabbaccbaccaabacbadbabcdccacdbdcbbacdcbddcaadbdcaccdbababcaccaabbbabbbdaccbcabbdadbdbbbdbaadaaddabdabccacdcccdbadbbbcccacdcdcbaacdbaadaddcbabcdacbdcabaddaaccdbbbbbbdabddbbbdddaccdadabbacdadaabadcadcadbdacccdbdbdabacdabacccbdadabcbcdcaaacadddcbabaadcabbbacdbbdcbaacadcdbddcbbaadbcaaadbbcbbdaaabdbaacbccccacdcbcbcbadacbbcacadccaaababcaabdbababbaddbbbdaddcddbacddadcbbbaadadcdbaabbaacdadcaddddacbadadbbbdcccbcddcadddbddcdcdaaaacabdcaddacbcaaadaacaaabbacbbdcbdabbbbcbacbbcbdadccdcdcaccbcddcabaacccddbababdaadadbdccdacccbaabbcbcdbcdacbbbaaabcdbbbdbadcbcbabadbdbdbaadabbacadbddabccdcdabddabbddcbbcdbdacdccbbbbbdddbbaccbadacaabddabaccababdabddddacacdcdccdcacbbbcccddbbbcbaccaaddddbacccaddddbbadabdadadaabbbbdddabdbbbabcdcddcbcddcbacadccbaaacabcbaddaadcccbacdddcbbddbabaddcaaabdaddabacadcbadbcdaadbdccddbddbdcdacbdccbcdbddbadbbbcddadbbbdbaddcbcabadbbcaadbdadacbdcccdbaabddcbdccddbdcddbccdbcaabdbbacadbbdacbcbadabdabccaddaacbacbaacbdaaaabdccdadcbabcccbbcddacdacadcabcbadddbabadacdabadadbbdbbcddbacbbcdccacddaaacdbaaabaccabbadabbacbcccdbcddbdaacadaaabddaccdbdcdadbdcccbcabdccccabcccbbaccdbabaaccadcadddcdadadbababbbadcdacccbbdbccbdbcbcaaabdcdbccbccababbbbcdddbcaabaabadbaaccacacccbaddbccddbaabcbcbadcbccbbabdddcbaccccbdbdbcdbcccdbaabbcdcdddcccbcccccdccacbdccdcacbcbacaabddcacbdadbbcbbcaadadcaddcdcdddccbacabadaccbbadabaadbcbdcaadbabbdadbdcdcdccccbadadbddccaadbadddcdbdadcaaabbaadbbbcbaacdbcaabdcaddcbdaaadbdacadaddbccbabbcdabbbbbdcdabccdbabacddbcdabacdcacddbcdaacdaadbaadcbbabdcdadcacacbacddbbaadbaaddddaadaabcddcabbdbbdbdbbbbdbddadccacdccbbdbbacacdcdccbaadbcccdbaddcbbcccadbbcaabaacdcbbddcbcdcabdccaddcaacdcaccdacdbbbbacdacddaadabcaadaadbccdadbacccacbacaabbcbdccbddbbcdddbbcaadccbdbddcacccaccaabcbbdccddaddcdcddcadabacbbccabcdaddacacadabaaabdcadcdaaaaadbcacdcbbaadbaacacaccaccaacccdbaddbdcddddaacdbbbcbdccdbcbbacbdadcacaadbbccdabdcddbdbbbcccdbdddcadacccabacdbccdbccabdadbbdbbcbbdbbaddcaddddaacabdbccbdbbcbbaabadaacccbabdcbcaccbbdcacabcabbaccaaabcbcddaaaacbadbcbbcbbcabcdddcbcdcaddaabcbcbddaddbaaadbcccdbabbaacddbdabccaaccbadcaacccaddcdcdacdabbbaaaaccdbbbcabdbccdbcdcdbaabbaadccdbbacdcdcacacdadbcbcdcbaaabaddbdccddcadcacddbadadacbacccaccdbddcdaacdbaddbdddbcacdabadccaacbabcacbcbccbbbacdccaabaababcdbabccaaaabbdabbcbbbdacadacabbddadbbcccbbcbbdbcdacabdbcacbadbccabccbbadabcbacaddaddccacadbcdbcabaaaaccccdacbbdadddabcddcbbbbaadabbbaccdaccaadbaaacbacdbdadbcdbcbccddbbcbbccbcaaabdcabbbbabdcbbbdacbacadddaacdadbdcdacdacababbbaaddbbadaaabcacdbcbbcacbcbbabcccacdbbacaacdadadaababbccdbaadabacadbcbbcadddabacaaaabaaaddbadbdccbcdaccabbdabbcbadbccaaaabcabadcaccaddbbdccaabddddcdadcdaddbdbaacdcbddaacacadcbbadacacdddacacaabcbdcddcdbababddbadbacccacaadabaaabdaadaccbdcdbcbbcbabbbbbdacbdbbbcbcdbdcbbcaccdaabcaabbabccdbcbdcbdacdaccccbcabdcbbbcbcccacbccbabadddaccddbdccadaacbbaddbaabdadbccabdbbbcdadaddcdadcdbbababcbbacdcbbbddbcbdbbdcbbdabbacbddabbabbbbccaadbcaadddcbaabcaabbbaacabcdcabacdbadaaddccddbbcdcdddabcbbddddcbdccbddcddcadbcccdaaacdcadcbcaaaddcddacbcdccccbbcbbcaabaddaddcdcdbaddbbadadcbcddbccdcddcdbbdaadddcdabaaaaacadccccbccddddddcbccdacbdbbacbadddcdcabccdbcdabbaddaabddbcdadcaacccbdcdbddbabbccabdcbcaadbbdaabdcdbccaccdcdbcdbcdacabccaaacbacccadddaddadacdccbdabbcbaccdbcabbabbcbacdcadbbacbccdadbaadcaaadccabdcdadcbdbbdacbbbbabdbdadabdadadbdaacdbcdaadbbacabaddbacbddbcdcabcbbdbbcdcccbccacdbcadbdbaddccdcaacdbadbadcdccaacbdbdbcbdcbdbbbdcabcbbbdcbdbddcdbddababaaadcbdbddbaaaacbaccddcddbcbcbacddaacccaadcdacbdddbaddacacdbccddcdacadbdbdadddddcaddbaabaaaabcbbaacdcbdcadbdbbcccabaddbaacbabbcababbdaccbddcbadbacdbdaaadbaacadaccabbdbdcadaaaacbbcbcadaadacccabddcdcddcdcdcdddddccdbcccbbdbdacdabcacabacbbdbbbbdcdbbbabcaacdcddbbdaaadcccbdddbcdbdcaabbccdbdddcbdbbbccddbbaabbaabcdccbabccaccbabdbbbbabddcaaccdbccdddadaccabdbdcbbbddaabcacccccadbcacabccccacbbaaacacabaaaddddbabcdcdbaaaadaaabacbdadbdacbcbdaadbadbbbccaaadbadbdabbdbbaadddabccaadddbabcadcccabbdcadabddabbcaabcbbcdcaacdccabdccbaadcbdccccbbabbacdddbabdddaccbbcacacbddabbdabccddccbbcacacdcdacdbcdddbddacdabdabdcccbbcddcdabdcabcccabcbaddcccadcbccbcdbbdaaaaccbddcbcdcddcababbaacddcdabdaddabacacdcadbbdaacaacccdcddbdabbadaccbabbdbcbababcabcbabbbdabcbdaaddadbbdaddcdabdcdabdbadcbacaadcdabaccdbdbaadadbccababacbabdbcbdaacdcddcddcbadacbccccdcddadbcccaccdaddaacdcbbbdbccaabbccdbbacdacdbdcaacbdbdddbbabcabdcaaaccccdacdadccdccaccdacbbdddbddcaadccaadcdbdabcadbaaccbddbadcabaccdacadccaddccddbaadcbadbacaaaacbcbacdcccacdadbdcbabcdccadbbcabacbcbccbbcbbbcaaacbddbaddbddbdbaccabcdddbbcdaadaadcdadbaadbbdcabbaddcccddcbadcaabbacadabccdaaabdaddbbcbadcacddcaaadaadabccdacaddaaabbcacdccaabadadacccabbaadaaaaadcddcbbcdaccabdaccccccaaddbddacaaabacacdbadbbcbbadbcdbdcbdabdadaaaddaacbbaabdbaadbaabcddccaadabacddcaccaaadbbaadbabbdbdbabcbabbbabbabbdbcdaddccdadabbcbbabdcbadababccbcccdaccdbaccbdadbacbaaabdaadcdaaddbbbdbddcaadabccdbcabdbbddbbacacaaddaacacbbadadbbcddbdbccdbbcbdbdcdccdbdbaddbcbaccbcabcacbbcabcbcbdcaccbbbccddbadcdbbcdadaadaadaacddbaabacbdadbabdadbccbadbccaadbbadadddbcbabbddbbcccbbadbbddbbbdbddcbabacdabccbcddaddbacdcbaadcacdddcbbcabbbbbbbbdacabdabdacadcadcddadcddcdcbddcbdaddbcdaabaddababccbcdbcbcadabacacadcbcbcbbadbacbabbdadbcdbbadcadbcdbcdcaadacaadcbcbcacadabbcacdcdaadcacdbdabcbcbdbccccdbacabccdadaadbdbdaddbbcbcdcacacdaabacdcadcaaddcbcdbcdbbcbdabbcbdbbbbdacbacdacacbbcbacddbdcaaacdcccddaaadbbddcddabaaddacdcdacbdacabbcabbbbcdadcadcdbbdcbdcbabaacddccbacbbbbbadddbcdcbddcbdacdbcbdddcaccccdabacabbcbacbddccabdacbdabdaaacadabadccbcacadddbdbdaadabadadaacbaccbdcdabdbdacdcbcbcdcddbdcbcbdcbccacdaaddcabcacdcddcadbcbbacaccbaaacabbabcbdabaaaacdccddbddbdbdbaadbdaabdbcbcccbddbdbbbaccdbadcccdcddbbcbbdaaddabbcabdbdbdcbccacadabbdbdabbdbbaadcabcbabdcbdbcbbdcbcbbddaddadaccbdcbcabacbbcdbbaacccbadaccbaabaaccbbbcdddcadcacbaadcbdbabdcbaccbadcaddbdcdcbbacadbcddddccbdcbcccdcdccdcdcabcddadbbdddbdbcbdcacadcdcbccbaadcadacdadcabaddbcdbdcdcacaccadbbcddbdaacbadcaaadbaacaabadbddabdbbbaaacdacdbacccdcccaaaadbdbaaccdcaaddadddabcdbadcbdacdacddaadaacadcdcbbabdaaacbddaacacbddacbdaccacaacbabacadadcaacdaacbddaddadcadabbadbabcdaaccdadabccacdabddacbddbdadccbdbbbbdbbcbbadbdaadbdadddaadbbbcacadacdabdabbaacdddabbbcbaddbddcaabccacabcadcabbacccabdaabccacbdccccbdbdbdbdccadcadddccbbdcabddaddccccadacdaaddbaaaaaacddbbdacbbaccbcccdbdddcdbadabbdcbccdbacaddacbbbdbcbacacdbbdaddaccadaadbadcadcdcabacdcbbdcbabbcccaaccbcabacccbdcdbaacaabdccbdcdddbdcdccddaadaaccacdbadaacddccbcbacbcbcbbadccadabcdbbbabbcdabcdddbacbcdcbabdabacdbdabcbacbcabbdcbcbaabaccdddcbabccbcaaabbadbaacdacbbddbbacdcabcaacaaadcbdbccdbcbccddccbbaaddbacdddaaacdbdbaabbdcbcdcaccdbcaacddabcbbaaccadbcadbbbabddadcdbdadbdbcdbabbbddaddbacbcbcdcacddbdccaccacdcbbbbcaaabcdacacbccdcababbcaabadbdbcbdbccaaabcbacaaaccacdcbcacddccddbaacdaaadabadcacbdccabacddcaabddccbabdbdaacabbddcccaabadccdacbabcbaaddddbbcdbcbadbbbaabdabcbbcdddcadabbacbbdcdacbcbdbbdadbdbabdccacaccadbddababbbdbcaadbcaaadabbbcdaabcabbccadcdbcdcdcbbadcadcccdcacccbcddadbbaaabbcbddacbcbaaaadaaababacdabacaaddadcbadcbddbacdcaabdcbccdcbaccadccbbabbdabcdaacadabcdabbddadbbcaabacabacddcdacbbaaaddcacabcddcdcaaccdbdcadcacdcacdcccbbaadcabcccdcccdababbccabbacadbccabdbdaaddbcbbadaadbaddbbbaaddcadbcdcdcbdadbaacadcdcacbbbaccccaadacbcaaadaacabcccdadbbbcdadaaabcabbcadcdaddadacbdadbbacadaabcbcdababacbcabbdaccbcaccccbbadbbdbbabdbccabadbdddbbbcbbcbaabdcdbbcdccacadaacabdbbbbacaccbdabdaaaacbcadabadddcbbaaadbbdacdddbaddaabbdcdddcabbcaadbcabdadadaadaccadacaabccddddccadbdbabdaddacababadbabcbcaddbcdacbcdcccbddcdccddccdcdccdbdccddcddaaadcbdadcacabbaacacacdcdcdadabaadccdbbaacdbcacdbbcaaadbbaccaccadbbccbdbccbaaabbcadaccdaaacaddacacadadddacacddabbcccdadbbddaacdccdbabcbbaacddadaddbdacaddccabaaccbdcacadcaabcbabdbacadbacbddaadadbacbcabaacbdddcddddbdcbccccbadbabcbaadbddcaaddbbbaddcabadcbdddbaccdadcdcdcbacbbbdbbabdadaadcddcacdabbcabddcbcdcccdabbddadbbbbdcdabacbadcccdcacddccbabcccbadacbaccadadabbdcbdcdcbbadcbcacaddaaaccadacdddaccdbbddbacddbddccbbdcddbcdcbdaddddabdbcbacdacabdbbadbbbbacbbaddbccabccabccabddbcabdabcdbabababdcbcccbacbbacdcdbbcacbcddaabddcdcadadcdcddcdaadcddabbddaaaaddbbbdcadadbdddacaacacdddbcbcadadadabaadcdaacdaaabcaccbcbcbacddddbadcbddaacaccbdcddaccaadddcaabaadcdaddcbbbcdbdccbcacbbaadabadbacdacdcacdcbacdddadccddcdcbdcaddddabaaaddabdbbccbabcbdcbabccdbbcbdbdbcbcbadddaacbdcddcbdbacaddaacdcbbdbbdaabaddbbdddcbbdcdbddababbabaaabbabdcccaccbdcbcabdbaddcadaaaddccabdaccabbccaacdaadcdcccbddbbccbcbdabddabdbdccddccbaccdcabddddcbacbadcbdcdadbddabdacbbbbabcbddcdbdadbaacbdacbccbcdcddcdabbbddbcadbbdbbdbcccacacdcabbcbcaaadbadbdadddcbaccbabdccbddaacadabcacbddcbdbcbabbdbccbccabdccabcbdbdcabdccbbabddccadbcbdabcdbbdddadddadabadaaadbadddbcbcacbbdbccaddccadacbadcbcacbbddbaabbdbaddacdcbaacddbbddcdcccabbdcbbacccacabaabdbabadbdcccaaccbdddaacababbcdcddcacbcdddabbabbdddbaacacbcbddbbcdcdddbdaacdcbccbcdaabdadadaaddacacddaaaacdaddcdaccaaabcbdadcddadbabbbdcadbcdbbabaabcadcaaddadcccccaabdacbdcbddabbcbbcdcbcacdcadadadccacacdcbaaaaddbcaccdcdccacadabbdddabddaadbdacdbdaccccbabbbcdadcbcbacbccabcbcadddacbddbadbcaabdabccbdadbdcaabdcabcabcbbaddbcbbbcaadabbbbdddcdddaaddabddabbbdaaaacddbbdcabbaaddbbadddbcaddccbcddbddacabccddadbcdcadaddaaadcbadccbabbcbacabaccaaaddacdaacaabadadbddcaccbdbbaadaaababccacddbadcacdbbdacbcdcacabcdbdcbdcacbcdcdadcdbacbbddcdbcdababdcddcadddcbcddcccbcadacaabcaacdacdadbbcaabbacdbbadaacddcaabbddadcaaacccccaddabddbadbbbadddcdcccdbdcbbbccabdbadcacaadbdaacbbdaaacdcabadbaddcadbcbadaddbbdbabddacbdbabdabcbdcdbadcccdcbcdaaaccadcbdcbabbddaaddcbcddcabacabddbdaccdcdccdbdbbbdddabddcaddcdddbdbdcaaaacbdcacabccbbddadacbdcbcddabcdaccdaaccbcadbbddcdaabcddcbbcccaaccddbdabbabbbbbaaabddbdadcdbbbbaabaacdcdcbddbdccbdabcdbdbdbbaccdaddbbdabcbdaddaccbcdbccdcccbcdddbcdcaddbddacccbbcbadbdddaacbddabaaccdcaadbdcdbcbbbdcbdbbdcdbadacaddbcbacdcddaaabaccbccabdadccbbbdcacdbcaabaadddbadaaaddabacabaddcabdddcdcddcddadcaaaabbbacdadadbaddcdcaccaccbacbaabcdbdaadcbbbcabdbacddcbcbacadbaadaabaadaaaabdccbdddcdddbccabddbbcbadcbcbbacabbabcacdacddbcdaaacaabcccdcabcaabbbbaaabdabaddbabcacaccacbdcbddabbabdccccbacdbcdbdcbcacabbabcabdaacaddcdbbaadbcdbacabccbbacbbcccaadcabdaddaadcbbdbdbbacdbcbcacdcbacdacadcadbccccdbdddddbdcdcbddcbcaabbdbccadbcbbabadbacabacaacbbdddbacbdcabacaadbdaaaabdbbbabcbadcbadcdbccbdadabcdbbbcdddaabcdbcaaacbbdaaddcbbababbaadabdbbbdaaaddaddbdbdbbaadbaddcddcbbbaabbbaddabaaadaaacadbccabbcbddcdcadaccbddcdababdccbdabdacadadcdbcababadbbcbddcbddaabababccbdacbcccbaaccbbaabbcdccdbcbbcbaaccaadababcadaababbdbdcacccdbcbaddcddcbddbcdccbcbabaccdbaddcbaabbacaaddbacbcaabaaabbbbcddcbdbdcccbacbddcabaaaacbabadddbadbacdbbadbadcdccbacbdcacbdccdacadccaccdbaabddbadbcacdbaccbdbcbbcbcbcdabacddbdbbadcbaacbaccbbaabbcadcbcbdabbdccaccddbcbacadbcdddccdacabbcadbbdbbbacdcdbbdaaacbadbcbadcdccabdcbcadaaaaadbbacacacdaabdbdcaacdababaadacabdbbcdadabcbbbbdaccddbcbbaabcdbcccdbcbacbcdabbdcaaabaccbdbcdabbdcccdcdcaadcdddaaaccddcbdaadaaacacdbdcccabaaaddbcaaadacadbdcadbdcdadaaabbdcbadaaddbadbddcbbbccabcbabdddddbcaadcbdbddcdccbadcadabcdbdbbbaaadadabcdadbddababbbabcdabdbbdcccabcdccababaacaaaccccacaaaadbdddddbacddccabababbdadacccaababdcdadcdadacacbddcccccdcccdabcbcdacbaaccdcdcdabdbdaacaaccddbdcbdbccbdababaadacddddbdcabbbaaaacbbdbcdaadbcabbbbcddadbbaadbaacadadbadcadccbbaabbdaaaddcadbcdacbabdbcddacbbccccbbcdddaccbbcbcbcadacddcbbaddddabbbaadccbcddbcdacabdbbaaaccdcababaddbccdccbcddaabacaddcdbaddcbbdbaacaaabbddcddbcdacdaabcbcddaccaabddbccddadccccdccdaabdbddccadbaccdccadadaacabcbbababdcbbdcdddaaabaabdccccdbcaacccdcbadccdabbbaddaabdbbacaadbcadcaddacaabaaacdabdadcabcbbaaacadacdbadcbadcababcccccaddbdcabadaddbbcdbacaddbdddacaabdacabbcbbacacccdcdacdccccddabdaccdababaadcacabcbdaadccacddddbcabaccdccabcaddbdcbbccdbcbbddcabdaccadcabaddbbbbbdddaabbcccaaabbdcaacdabbcdbcaccccbbcbdbaaddbaadaadcaaacdbddacdcbcdbabcdacabdbaaddcabdddacbbcdaacabdbacccdbdcbdbacbdbaaadbadbcdcbbcaacbcabacacbcccccdbcddcaaacadcbdccacddabddbbcbbccaddbababcdaddbabbbddaaccddcdbcccaccbdcdbdbbadbbabbbaabdcdadcaccbcabaaaddaccbbaabddbbcdacbadaaddcccdbaddacdbbdaaccadbbbcddbaacaaacaadadabccadbccabacaaaacbadccddabbbadbddcbacbbbddaaadaaadadbbaabadbbabdacdbbccccaddbacbcbabacdcccdcacacacdacabcdccbcdbbacaaacabaabccbabddbdabaabcbcbbacbdbadcccdacccddaabacbbbaabcadaaaccbabcdbdbcaaacbadacccbdadccdddbdadaaacabbbbabddbabdcacaccddadddaadacdbbdadcacbadbddaaaabcbdadcadcbccaaaccccdcaaadacdccdabdbdbbccdabacdcccabcaddbcbccdcdbadabadcdbacacbdbdbbaddacbaabbbbbadbdbdadbacbaabacabbbbdbaaaadbcbabdcbacabbdbaddacabdccadcbadbbaadcbcbcaabcbdcadacabaadaddbdcdacabacacabcddcdcbcaabdcdacbdcbdddcccbaacacbbbadccdbcddadaccbcdcdaaadcbacdaacadbddcbbaadbacabacddacddabbccdaaadcaabcdbabcbbcdcaababcaaadbcbbcbdaddcccbcbabbdcadbdcdcdbbcbdbbbaacacddcbabdcdddddbbadbbabdcbdbccbccccccaacacadcaacdcdccdbbabbacccaacbcdbccadcbdaabdaddbababbbdcacdacdbdadcbcabacbcaadcaacaacbabadaddabdbadcadbdbcdabdcddbabbdbdadacddcccaacdbabdadbdccddacdaacccbabdbdaaadbadabddaacbacdbdbbdccaccbcbdcaaadcaaaccbcdbdccbababadcaadcbbcabadbdcddcadcbccacaadaccdaabcddbccbbbdbaaddccdccabddcbddabbcacddaccddbbacbddcdbadaaddcaaabcccadbbcdababdcdcdcabccbbdbbdbacabaaadaadadbbdbabacdabbcbabdbdcadbddcaccbcacdadbcacdaaabcdabdabbcdbccaaaaadddadcdabcccdadccddcdccddbadcaccadbbbaabbdcabbaadcaaabcdababbccaabbaacbaacabbcaabaabaadbcccabcabdcccccabddaaabbcabcdaaadacbabaacdbcacbcbdbabadcbccbdadcbdbdcdacabdcacabdaccbabbacdaacbbcdbdcbdcabaabbcbadaaadbbdcdcdcbccccbccaddaaacdaabbcbcbbdaadaadbacddbacdabdbbaddbddbcccdccadcaddbabdcacacdccdbccddadbcdbbadbccbbbbddbdbbbacacddaabaaabbbbbdadbdbdbcdbdbcdaddbbbdadbacadbccacabaaddacbddcaacabdadaaabaccacccbbccdaaabbadcdbccadaadbbbdcdcdbbdbdccbccccadccdccdbdbcdadbdcdaddabadccaadaadccbbbbdcccdbbccbdddacccbddaddbccddadbbaccccbddcbacdcbdbbaaacdabaabdbcbabdacacaadcdccdcabdcdcbbdcabddcbcccadcdaaabcdbdacbcbaaabaaddcbbaacbdbbadcdcbdcbbdadaddccaadbacadacccabcabddccdbbdbdbbdbabddabdbbaddabcbaaccaddbbbbadaaabdcadadbadcccdacbbddddaacdcaaabdddbcdabdbcbccacbdabbbdcbbcbacabccdbbdcabbcacdbaccccbacadbbbbccdadcaaacbcccccbbdcdddbdcbabbcbbdbdcbcaddabcaaddbaccbbadabadccdbbbccbadabaadcbcbaddcbbaccadcddbadbdddcaddcaadbadbbddcbbdadbbaadbbbcadcabbabdbddddacaddbacabdccdaddcababbbcdaabbbacbdadcbaddcbbcbccccaccdddaacbbbdbddcacbacbabddccccdbddccccbaccbabbcbabccdbdaaccadbcbddccbacadabdcacdaabacdbaaaccaccdbbaacbdbbddcddcddccacdabaaacacdbcaaabdcccbdbdcbbbdaaabacddddcdadaaacaddadbbbdbdcdaaaabbddababcadcaacbbacbcbdaaadbbdbcdbadcdcbddadcabcbacdbdbadcdaddadbcabddbbddbdbbbcbccacadcadacdddadcadbdbabcdbbbcaacbdbcdcdcacdbbbaaabdcdcdccdabcccaccaacadbbdbcbaacaababaccdcacbdbdaadabdbabddabbdcdabbcdaabbdbdbbabacbdbccbdbddcccabbcdcacdbbddcbdbbdcacdcbcdcbadaccbddbdbbddbabcacdbcdaaccdbdaacddbdbdddadabadcacacddadbbaadcdddacbcbcdcdddbbcbdbcccbaaccdabadadccaabbdbbccdcdabddaabcdadbdddcbcbccbbccacabcadcdaabcbdbcbbddddcaddbaacccbdcdacbbccbcbdcadbccdaaaaaacaccbccadbcadbbbbacbbabcccccabbacdadbddbdccccbbacdcdacdcbdcbacbcaaadcaccbbbcaccdcbabcdcaaabaddddacbaadbbacabccbaacabcdcadcacbdbdadddbdbdadababbbbbdcaacacbcaacdbacadcdcaacdbadcbababccabcbdcacbbdbcababcaadbdbbcdbbaadcaccdcccdadaadbaacdbdacbadabaddccddcdcdbadaabcaccabdccdabcdacadcacabadbcacbcbddcdcadbaabbbaacddaadbcbadcadbbbccddddabcbdcdbabcacbcadacadcaccbbbabdbdcabdbabbbcdbdaccdabddabbaaccacdbbbadbdbcaadbcabbbadcbbdaaadacaaacccadcddbccdbbadadaadbcccacdbdadbdcbcdbdbddacadbcbdbdbaccaddbacdacbadbdbbabdacadabbadacbdbabdabccddaaaddbbbbbadbbdabbbcacbcccccbdbddbbbbabdcdcaacbcbbaabacabaaddcddaabbdbdbbbbbbdcddaccdbcbbabcaccbbbddcdbdaabdbaddadcbabbbacbaddbbaadcbbacaaabdcaddbbadcdddcadabcaccabadaacaabdaccbdbaacbbadbaaadbcbaadadbacbcaabdcaddaccacacbabadadaddbadbbadddbbdcdacdaadadbbcbabbddababbdaaadacaaddbadddbacbacbacdaddbdccdbdadaabbccbabbcbcadbbadacabbcbcbbbaaabbbbccdcbdccbdacaaacbbadcadccbbadacaccdbbbcacccdcbbdccbdaadcabcdddaadbcaaaabaccbcbaabcbbadabdbcbacadbbcdddbddaaaacacacccaccaddaadabcdddccbddadaadccaabcbadcaddbbdacaaaadbacbaaadbbaaacdddacbcbdddaddddabcdcbdbdbdacdcabbacadcacadbdbbddabccdddcadcbbdadbcdcccdabdacdaaccabadcddbbcdcdbccddddaddbdddddaacbdbaaddbadccadacabccbcddacaadddcaacbbacbbcaacabdddadadcbbddccabacacddbcdbbbbcbaddccacaacadacccddccacdccbdddddaacddadacabcadcaccdbabcaadadbacbaccabcbccabcbcaddaccbbccaabcbcdbbbaadbabbbadacabdacadbaddacaadacbbddabcbdbabaddcddaacbdacababccbaaacabacdbcaacccbaddcabbbcbaddbcbccddbcdbbdbaddccbccdccbcaabddbccbbcbabbdaacbacdaddbadbbabdbadbbabbddcbbaaacbaaacadbcabccaabcdbdcdddbcacbbccccdcbcccaabcbadbbbacdacccabaadcacdaadcccddadcaaadbccbabcbbbcadddbaaaabbbcbdcbcbbccbaaaadcdbcacccadabdbcaccbdaacdbbcdcbcaccbcbbabdbdabddadddcbaacadbcdcdbddaaadbcbbadcccbaddbdcacdddcabadbcbcbbcccacddabacabbbbbacbabbcbddcdadbdbaaabcdbdbdcdcacddacabbbcbddddccaaacbccbbacacbbdcddbdabadccbbacbabbcaaabaadadcababdabcbccaacbcadadcbddbcabcabcacaaacdbabbccbaccdbabdbaddccabcababcacbaaadbccbacdbcbadaabaacdbbadddbacbbabaabaddccaacacbcabacaababcbbcbdabbccdbbdbcabbadbcddbacdbdbbacccbcaaadacbddcbdddaababdcacdcdddbbddacacdddadcacdddccbdccdcabdacabbabbbababbbcaadbddbacbdbcdddbabbaacaaabdabddcbabcbdacadbaacdcddbcddabacdaaddaadddbcabbdbacbcbddbddabddbdccdccddcaadacabdadcbabadacbccdddbabddcdabbdcccacaddbccbadccbdbcbddaaaacbbdadabdaddbbabdccaadadaabdacbdbdbbdddacaabadcdbdacbaddddbacbdbcccadbddbdbcababbacabdaabbaccdaccadabdbdbbabdabddccadddbadcbbddadaddbbadababdbbcddacdbdaabdadabbdbaadcabbccaabbdacddaaaccddbdbacdbadadaddacdbaaacacdcabbbdbacdcbdacbabdddbabacadddccbbdcdabccdaaabcccdcddaabbadddbccdacbbcabacadacdbdbbdccbddcbbdacddacaacabacbddabbbbcbbadcccccdbbccbdbddaccdbadbcdaccaccdddabbbbddbdccbbadcddbababbaccbaddaabdbcccbaccacbdaaabcbadadcdadaadcbcbcacddbbacabcdbacdcbbaaabdcadbbdcaccabbdddaaacbadcdddcdabcabaaacaaabdabbacabdabcdbcdbacdcacacbdddddbbabcbcabddbbcbaababbddaccdcbbacdabbaabcabadacdccdbaddbaacdadbbbaadbbcadddddbadabdcbabcbabaccccdaaccddbdabddbabdccdaddadcbcabbbdbcdcdcbcbcbadbbadccbbcabbdcbdacaddcdddbcdbddaadcdbacbcabddddbbcddcccdabbddcbdddcdabbdccddadadaadcadddcccdabbcaacdadaadaccbcaacdccdbadbdcaacddadabacabbaacacababcacbbbdaabdddbdaddbcddbbdabbdaaabcbcdcbbddababcdaaabdaaabbaacaabaccddbccbccddcacdbaadacbddbcbbcbcabcaaadbcdcbcacabcbaacadbdbaddcdabacdccabcdacdbcdcdcbadbdaaabdccbdbbadbcaddbddbdbcaacbbbbaccdddaabbcbbdddcaabaaabbdaabbddddcbcbcbaadbadbbddcbbbcdacaccacdbacacddddbaacaacbbdaaaacbaaaadbbaaabcaddbbdccabcddcdbabaaddadcbcbbbbdbcccdccdacabcbddccbdddbdcadaddadaabaadbcbbadcabbbbdbdcacbcbccbaddddaaddcbbabadbddbdacbcadbcdddabcaaaccddbbacdbcaabccdaadbadacdddbdabacbadaaaacbbbdccccbddbbaddbdaadaabcbcdccacbbcbabdcaabdacaccbadabccacacccaacacbcbcdcccaacabdbabddcbbdacadbbdcdbddbccabaccadbabacddbcddbcbcddddabdbddacbcbbbdbbabcbcbabbbdabbaacaadbbdbadaabdadcbdcaaabdccbdadacddabbdbabcaddbbacdbaacdbdbaabbbbdbdcdaadbacabbcaabdddbbccabdacaddacaaabcccaadcbbccdcbbbccaadaadacbdabcbaadcdcdcdccaabbcaddabddcdbcbacddbbccbdababcababadccdcccadddaddccadbabdcbadabaaadbdaccbbccbaadacacccbabcabcbdddbaabdbbdccaabdbbcccdcacacacccdbbabbdaddaddabbdddddddcbdcbcdccdadddcbdccdccbcdbcdaaaadcadacbbadcdcdbdcaabdabaaabcbbdaadabaadbabccadcaaabccdccdabbbabbcabcdcbcdddbaacbbadacbcaabbbcabbdcccbddbcddddddddcbbccccccbdbaabddbaaaabcdcbdbbadbbbccbcacbacbaddcacddddbcdbddaadbdccdccdcbccbcbdbbdacacaaaacabaabbabbbddbdcdaccdcacabbddbccacbdcddacbbaacbcbcdccdabdaaaabcdcdcdbdadcdbabadbbdcadaacbcdbbdbbbdcdacbbdbbbcabcdbacadbacdadabccdabbbdabcbaadbbdabbbcacdcdaababbccbbdcdcdbdbadacbbabbbbbacbbbbcbbcaaddbacddcbadbddbbaddccadaaabbbaacdbdcccbcaddcddbbcabdcabbbbabddbdbbcbbdabaaadbcbddacccdbabcdacbccdabbcbbdcbccbdaadadddbcccaccaaabacbaaaabcddcdaabbbdddacbdbbccaccdcadacdbccbdcdbcbacddabbbaacabcdddbcddbddddadbccadaadacadabbaacddccbcabbcdbcbbaacddcccacccddcaadbddcdadbaadacaaacbcbcbcabcaaacdccddadbcbddbabcdabaaabbbbdcaddabdddbdbaacdaaddaaaddbadadabccbbbbdddaabdcbabcdbadcbabddacccddccbcdbadbcaccbdcdbadbbbbdbaaabbabcbdbacbbdaabcadcdccaabdbbcdacbccbcdbddddbbcccbcccbcdbcccdcbbdccdacccacdbdddcabdadbcababbacbbbcbdcbaaaddbadacacccbdcbdbdbdadacddaabdadbdaaacdddcddaacddacdadaaddbadbaaaacbcdcadacabdcdbaaacadbbcbccacccbcbaabaadcabacbddcdacbbaaabdacdcbdbadadccdbacaadabadaadccdabaccacbcbddcabdcabacadacbcaddadabbaabbddbbabcbacabddddacaaaaccdddbabbbbbabaacaccabbbcbdcccdabbbdbcbcbabcaabacaacdbcabaaacddaaadabbdbdabddacadbbbcacdcabccbbdaadbaabcbdcbdbcddaadbadabdccbbbcacbcdcadcdddabcdaadbdadabcbaaccddbccaaccbcbbdbbbdbadbadbdddacbdaadaddabcbadadcabbaacdcbaacdcbdadccbdbaabccccbcaccbaacaaacbbabadadcdbdbbdaadaadabcccbdddcdacdadababaabbddbcdbbdbcdadcadaacbccdcdddcddcadcaaccacdabbcdddcaddcadcbcaccdcacabaaabdcbbbcddacddaabcbddadddbcbdbabcccbdcdbdabddaaacbdabbdcdbbbccadcabcabaacacabaadcbcbdacdaccabdcbccaaddddabddadaacacbbcbabcacbcddccccbabbcbdcacddccbadbdbbbabcccddcbbcbddbbcdcabcabbdacdabaaaadadcbabacbcccbcabdcbdcddddddcacbddcdbddbcdcbacccadcadadabccdcdbcdaabcacccddcccbbbddbbcdbdacbaccadacbaaabbdbbddcaddccabddaacdbaacaadbbdddacbcabbbcadccbdcacddbcdcddbdaadbdbdbcabaaadbdddbbbcbbaddaccccdddbcadacdccdccbaccbaababaddcaabbcbaccbcbbacdbbddaacadcbcccacacacdcbdddbccabdccccabcddbbdabbcabcaacdaabdabdbcacbaccdaccabadabcbaccbbabcbdcccbcbdabacadbbdcabaaaacacdbaadbddccdbabcaddbacbbbdabccabddddbaadbadabcbcbbdababdcdcddabdbcdaacdcbccbbddcbaabbaaadbbccaaaacacaacabcaddbccccbcacbadcabdabacadacddccacbddbbdadcccabacccdcbddbddbdcacbadcbbacdcbdbbdaddcbddbbdbcdaddcaacdaaccadacabbbccccbbcdaadbbbacabbccbcbbaacadbdadcaabababbabbbcadccdccddcaacbaabcccbbacddcaacaaccadacbbcdddbaababcdbdacbdcbadcbadccbaddbdcdcbdcacbbcdbdaacacbdccbddccacbaabccddcbcbbbbdaacbdaaaddcacaddabacbbbcbdcddaacbccabdcdbacdcabcccacbdbdcdcaddcabdbdacbbcdccbbbcbbabcadadcbdaabccabdadacbdabbabcccabdadbdaddacccbbcccaabcddbbcacabcbdbdcdacbccdabccddaccdbbbdcccddccacaccdcbcdcacdabccaddadacccabcbabdacdbdaabacdcdcbcababcddcdadcacabbabadbdaacdcbbddabbcbbabacdbbcbaadabbcadabddcadbdaaabcaaaddabccbcdcbccbdddbbacdacaadbcaabadcdbdbccbddcadcddcdcabbdadaadcacdbadaccdabbaadabdbbbcaddbdcacdbccdbbccdcccddbbdadbcbdddaddcdbbdbaaddcdddbacccdcabbbccdcacbcbabbaadadcabcccdddcdccacccdcccacbcdcadbdadbcdabcdcabaadbdacabdddaadcbcaadabcaacabacbadcbdbabddbdbcabcbaddbacdabbadcccaadcccdabbabdbaccdadbadcabadaacbaddaacbdccbbaacacdbdbcbdbadccbdccdcccbcabacbcbcabacabdbbbcddddddcbbcdbcababdadcbbdbcaaadadbbbbdacdcaccdccccbcbaacdbcbccddccdddcbdcaadcdbdbaacaaabbbbadaacdddcccbcbbabaacbcabccdaaadcadcdaacadbddbcbdbcddacdccddcbdbdbadbcaaaccdcadaaaabadabcaccdacacbcbbdaaabcbcbaadbbbaacaddbaaaddadcdcadbbdddadbbdcabaddddddadbdcbaadcddacbacdaaacaababdbaaccaaadacdcbbcdbbcaacdcbddabdbcabbdcccdcdccacdcaadbdabbbbbbdbdbdbcabddcaacdccdbdbadacddbbdabaabbbbdbdabddcdaadbddcdbcdbdbadcbbbbaabadccaaddbbcdaadaadbbbabbdacaaddaccaacccbcbdcacddaaabdbbddcbdcbddaaabbcabbcbccdbdcccaaadccadbbccaabbbcbbcdcbadacdccbbacbdabcaccdaddaaabcddabdbcababbdbcadcbbbcdcababbadcdcdacbbbbcdcdcbcabaabdbcaccbddaacaadccdbdcacacadbbaddcdcdbcdbcbbabccabbbdacdbdacbaaabbbdabcccdbbdbadabadcbaaaddccbadbdabdccbacdccdbbbacdaacabdbdbadbcdcdbcbdaaaccacbcddbbaaaaddddabcabdddcbabbadbbcddbcaaabdddacbdbbbabbacdcccacdbabdabcddaccaaabaadddbbcacbaddbdbabbdbbcadacccbbabdaadbcabcbdbcdcbccbddddabbacbbdacababccccadaccbcacacdcbdbdbdabacddbdcccdacdadbbdddbcaaabcdaadcbbddcddbcaadabcbbbcadbcddabadbdddcbbcbbbbcbbdcdacccdccaccddccdadacccdcabcbbaaaccbcdddcadcbbdddddcdccdaccaacddabbbadacadbdcdccdbdcacabbdcdbbdbcddcdcdacabbddcccaaaadcbbacbacdcacbcddbbaabbbbbadadccbdbcdbaddbacacdcaddbccdbdccacddabccdbbcdcbbdccaaddbdcadddccdbddaccdddbccaabcdbdaaaacaabdcadabacaadadacbcccdbcaddbbdbbbccdbcdbdccabaabddbdaddbccdadbdabcbaadbaabbbabadddccdcacadabcdbcdbabadbcbcdbdcdbddbdbcdacdabcbbadbdcadababdbbddaacabcbdbcabbdbbdabadbccdddabddacbaddbcdcccccbdcbddaddcadadcaddbcaaacabddaccbabbbbdddbcddaabacbdcbbdcddaccdcbbdcdaaacaccdacaacdabcdbccccdbacbccaccddcacbaadcdaddabcabbadaddadaddddadbbcdbacabaadabbdabccbcbadaadbcbadacaddaacbcbdbdbacdcbcbccaabadddbbcbdababdbcdbddadaaabcaacbacdbdaccadbbdcdcadbbdbbadbcbbccaabbccbdbdbbbcabdbbaccaacdccdaccdbcaccccdbadacaddacadbbadddbcdddcccbbccdbbcaddacaabcbbcacdaadaaabccddadcdabbcabdcbbcabaabcabadadcddadbbabcbaccaddbbbccdbaccbacacddacbcabdcccacdddabcbdadcccabccbbbabbbaddddbbbdcacccdddcbdbabcdddaddacdcdccaaacabbcbacbbcdabccabbcdbcbcdcdaddabadccdabcdbaabbdbdcadbdaddcdcdadddccadccccaacdbdcacaccdabacbbaccbbaadabcbcabbbaccaaabcbbaacbddbdcccdcbbabdabdbddbdbaddaacddbbdcddbacadcacadaacbadccadabbcacabbdbcbbabdbbaaadcadabccdccadccbdcccadabdddacbdacdddaadbbcabadabacadaabababbbbadabaccdcbacaababadaacabadbdcbbaadbcdbacadbabdbcddbcdbdcdbabaccdabbdaadbbbccaaababacbcadcddbcdbccbdcbcbbabccbaacaabccbbbcbaaccbadccdadaccddaadbcccdbcbaddcadadbbbcbdbddcdaaacdaaadcdbcbdaabdbcbccabdbacacdabbadcdbbadcdbdcbabaabddcacaacdbcacbacbcbddccddabcbabdcacadbbdbcddcbddabbccdbdcaacbbbcabaaccdddcabdbbacacabdcdddbcacddbadabdadbcbaaccadbcbabddddbdaccbabcbdadbbcbbadddabaacbbcacaabadddaacbacadbbadcbbcbdccbbcdcccadadccacaacccdbadbdcddddddacdbabbabaddbcbcacbbbbdcddbbccbcacacdacabcdcdcbaababdbadccabcbbbcbbdbddbdaaaaccbaadcaabadbabbaaddbdadbabbabcadabbbdbcddacdaccbdbddddbadaaddbbcddacbbaabcbacbadcdadcdcaddbcdcbadccaadacdbadbcccccadcaadcacddbdcabcacadddcabccbcaccadbbbbdbdbabbddabbaaaabbadcdacbbbcccaadcbaadbcaacdabbbabdcadbcacbdaccdaacccdbcdccbadadccbadccadabcaadbdbaaabddcacaacacdcadbbbddaaddbbcaddcdadbacddcadadbcaadbbddbacddadbdaababcbcacadccdccbacbcdadccbadccabdbbcdabaaaaaaacbaabbdaabacdaaddbddbcaaddadbcdccadadaaabbccbbcdbdbdaddcdbbadbaaadadaacbbcbabdcdbdbdaacdabaacbddabacdaadddccaccbbabbdccabdcdcabddcdaccdaddccccdbadcaacdbcaababcdbddcaccbbdacbdcdcacaabaabaadababadccadcddcaadddadcdbdccbdacbacacdbcacdcaadbbadcccccacbdcacddccdbccddabcdcababadbcdbdcbcbdbcdadcdbcdabaaabbdbabbbcbaacabccdcddabcdcacdcdabcaddaddaadbcdbbbacdacccdcddaaadcacaabacdbcaddabbbdcbccccaaddacababcbbcccdadacdabdbdaccbcabdccddaadbbbbccdccddbbddcbccdadacccbcdbcdaadcdbaaaccccdaaddbddbadbdbcabbacaccabadaddbbdcdaaabacabddcaadbdddbcbdacaabccdcacdabcdcacbddcbdabcbadcbabccdbbdbdadbaacddcabdcabbcbdaaaabbbdcbadddababbcbabccddbabcddaaadcddcabbdaccbacdcbddcdcabaacdbaaaaabdabbabcddbccbddcdddccbcdcbabbcabbacdadabbccacbbacbabdbdabaacabcdbdbcaadcdbaaaadabdcabbcbadbabddbdcdacaacacaaacccbddadccacdccadbbabadadadcbbdcdacdaadcbcbcdbcdbbccacadadaacddadbbcbccbabddadcbbbcaabcdcdcbccddddaadbccacdbbcadaadbbcbbbdbababaacadbacacbddaabdacdbadbbcabbbdcdccaccacbcadccbbaadbdddcbbcbccbaddcadbdbccdbacbbbbddcabddabcdbbdacdbbddadaaddbadadaaabcbdcdabddbabcadcaaacacabddacbaaddcdbcaabcbadabbcbbbbbcddbdddcadbccbbaccdcbcacdcaddcdcbadbcbbbbbaadacabaddabcdaaabbbdcaadacadddaccbbabbbdcacbdacbabdbaadcaaaaddcacbbdabbccdccccabacbdcabbadbcbaddbcbadbbbcabdacacdacacdccaddabcccbadddaaddbbdbbcabacbcdccdcabdabadbdaddddcbccaabbdddabdabbdbbbdabbddabccbbddbddadbcaddbdcdbaacbbdcbbdabddcdcabcabacbbccdacdcdcabadabadbdadbdadccadaddcdadbcbcdbaccaddaaacaadcdcccbbcdcbdcabccdbcabdabcadbbbacbddbdcadbdadacddddbcbdbaadcbbbdcbdcbdaaabaacdbdcdadbdadaacbbabddcccadaadcadcbaaababdcbadbdbacbbbdacbbddcaadcbcaabdccaadbccdbdcbaaaddaaddcddcadaaaabdbaadcbdcaababcbdbbdacbcacdacdaadbbdcadacddddddacababbcbbbcbccdbddcacdacadcacbbccacbbabccdddacaabbcbbbcdaabbdaabddcdaacbdcddabaacaabbdcbbbcddaacabbacdaadbdabbccbcdbadadaaaddbbabdacdcddbbaabccaaacabdcdddcabcbdbdcdcdabbdacbcadacddbbadbdbcbdbdbcbaddbaddbadcbccadaaaaaacdaabadbacbbabbbbccbaabdaadcdaccdbdcadddbdacaaacddbbadabddccaaadbdaddccddbbdbdddcabddbdadddaddabcadaaacabbbbcdcacabcddddddacadababdbdcbbabadbadbdabccbadbabcbdcddcabaabaccccbbadaacbdcadaaacbdbbaacdabbbbbdbbdbbdcdbbdcaadabdbbcadaacccaacdadbcadcaccaacaacabccdbcaabacacddddbbdcbbdaabbdbbabcbadbdcbbaabdbadabbacddacbbddaadbcddbdabbdcbbddddbabcacacacbbdaacaccbbabcddbcabbdcdaccabccdcdbddabbaddcbacbadadadababcdbcbbbbbacdcccdcdabccccdcaadacdddcababadcdabadbcdbdcbbcddbaccabcdbddbdbabcbbcbcabaccbdaadbbcdcdbadaddabbacabdbdbcbabcddacaabdcabcadccdadbaaddacbaacdaaacccaabcdadbcbcdcadcdaacaacbbddbbcbdbbddcaaacdccdbbddcccddddddacadbbbcacaddbdbbaabcddabdcaaacddbcabcddbdbbbacbcacdacdbddadadbbcaabbbbcdcdcdccabacacccbbddcabdbbbbcdadbdcabccbbdaabdbabaaaccdcdbbccacdcdadadcccabcacaccdcbbdbcdccdcaddabbadbadbacbadcbcbbdccaabdacdcdacaabdacababcadbdcdccdcbbcbdbbcaacadbcabbcaaacbbdcddcbbcdadbdccdacacdcaababadddaabcacbbabcbdbdcabdbbbddadddbabaddbdaaabdbbacdbbccbcadcbdcaadaaddbdbbcabdccbcdbddbbbcabcbccabbdbcbcaaaabbacaabdaacdcacbaccdadaacbdadabdbcdcbbbcaccabcbaaddbdcbbbaccdacacbadacbabaadbdbdacdccacbdcacadcdbcbccbadbddbcabdbcadccddbcacaabbcbadcbadcbacdbcdbabdcbaacbcababcbbcdcbcacacddcaacabbcacabdccdaaadbbdabccddabdacbdbbbbdbcacdcbadcccdaddbccdcbaadbdcdbadbcbdbdcbabcbdabcbcbaacaacccadbbcaccbabdacdcaabababcbababcbcbdcadbbbbdcacdaaaacddbaadcbccdaddbabdabcddadadaaddccdcbdcabdbadddbabacdadbcbbaddbaccbbcbbbddbbbcdddaabccddadaadacabdbdabadacbcdacaabcbbbdcdabbcabdaacdddddabdbddcadaddcbacacdabaccdbacbbbbdabcadabbbcdcbabddddbdaddbcccccddbdaaacabdadbabbabcbcaacbacbdcadddbcbbabcaabccbbdbacaccdddcacbbaadcabbcabdadaadabdddaabaacbbaccdadabbcdcdccccbcdccbbbcddcacacdbaaaadddcacababbdbbddbbbadcbbaabcdddabcdbbdcbcdcbaabdcdcadabbbadddbbcaaabccacabdccbbbcdabadcdbbbbcbacddbaddacadcacbdbdbdbcabccabbadccbcbdadcccdacbdabaabcaccddbcbbdcdcbddddcbbbabcbacdacbcacbdbdddddcacaadabdbdbdaacddacadbddabbbadacbdbccdcaddadbdabcaaacccccbabaadbccabcbcdddcabcadbaadabdaddbbdbbcbaaadbcbbadbabaabcbcdbaddcdcadbbbdaaacbcbabadcdccabccbdccabccadabcabdadaadccbacbdcacbcaabbbdbccdddadbddbacdacdddcacdadaaaabaacccbbbacadbcadcbddadddaddddbcdbdacdddcabacddbdbdbccdabaabbcadccbabcbdcadbbcddbdddabcbdaababaaaabddcaccadaadcbbddaddbddcddcdabbcccdccbdaacdabddbbadaccbaaacaadabdbacbaaadddacaccbadddacccaabdbcbcdbabdbbabdccdbabcaaaaaadabdbbacdabccddabcbdcddbbaaadccaaadbcbaaddabaabbcdacddbcbaaddddcbbcdcdabbaaccdcdddcdddadcdccabdacbcbcaadcaaadcdbbddacdaddcaddccacddcdddbbddacadbdbabdaadddbbcaabbcacadbacbcadbadcadbbdacbccbaadaadbcaacabbbbcbbcdabbaddacacdcbaaddadbbdaabbbacacadcddbbaccabbbccacabbdacdbccddcdaacddadcdbcdddcdabcabccacbaacddabdadadbdcaccacdbbbdaddbbdaaaddabbdcbbcbaccbaaddbbaabcbccbcbcdacdaaabbaadabaacacbabbbddcbccbaaccbadddcbbcacdcdbbdaddbcaccddbadcaadbdccbddbabadcdccdacddcaddbddaddcccabacbdacdacbdabdddccbbccbccadaaddaccaddaaabbbbccbaacdbaabbcdddbabadbacbbdbbbdbbcabdacadcdbdbbdbbbacadccdbdccaccddcbddacbbdbaacabbcabaadabcbcaacacdabbccbbbaaddaddadbccadcbbccbbcdabcbbdcdbbadbbddadbbacccccdaaadccdcbaadacdbbbdacdbbbcdabacabcacababdadbbdaaddaadabccdcadddbbdbadabaaaacadaaccbccdcdcdaadadbaaadbcabdabacbdaaaddcbccdcccdabddbaaaabdabcacdaccdabcadacababaacacbddcdacadcacccbadbbdbcaaccbdbacacdbccabcadcaaabdbddbacabaadadcaaccaccacbdabaaacdddddacbdbaddbbdaabcbbdaadcacdacdccaddadbdbaaadccbabaccdcacbccbbdadbbccccbcdcadddabcabdbbdabaaaacbbbcccacaddbaccdadcaccabddcdcdcbcbbbababdadcaacbddacaacbbddccabcccaadcbbbdbccaacaadcaadabbabaabbddbacabacbbcccccddcaabbacdbaaadbdabaccbaccddabbcaddbdbabccabbaaaabdacdbabdaccbcbbdaaabddddccababcbdccdbabcdccbcabcbbdbaccaacddcbbddcccbcadadbcbcbabcbbadcdaabcccddccbbbadcccbcabbdcdabcbdcdabdbddaccdbabccccddaabbbaacaccdaccddbcbbbccabbcddcaccabaacdcccccbcdcdddaccabcdccddcdcbbcccabdddabbbddaacbbcaadbdddbbcabbcadaabbaacbdabbbbdaadcccbdbccaccabdacbadadcadcabbacccdcacddadbacbbbdaaccdbadbcbacdccbcbbcadbbcddbcdbadcbdbbdcababcacaccdcdbccabbccaaacacdcdacdcbdcdbdababdbdccbaddabdbcddbcdaacdcddddcbabcadbaadbababdcbbddcadaddaababddacbbabdcdddbbbcacddaccbddccaddabcdaccbcddcccdccbcddcdcbdccaaaadddddbaccdbadaadcdacdaaaddbcbabccacbaaccacbbabcbacaabaaadbacababdbabcccaacadaadadbddaacbdbcdadbdbacabcaccdacdbbbcbddccdbdbdcabdaacccbcdbcbbbdddddaaddababccaaacbabbddacabaaaddadcdbdacaadacbbabccbdbbdcdccaccdabccccbccaaaaabaadddcbacdaadcdaabbcbccdccbbcdacabbbdbccdbacddbdacbcbbcabdddddcccbdadccbdbaacbcacbcabbbcbdcdcadcddbbbcaaddbbaccbabacddaadcdaddcadbdacbdaccacddbccbdbdccaccbccdbabadcdaabadbbddbdabbbdddbcaabbabdcacdbdbddccabacabacaaabccabdbbdcdbccbdacaabaacdcbadbccdcadabdddabdcbcacaddcadadbacbddabaacdcddccdbcdddacccdabbcbabbcaabdddbbdddcabdaddcdccaddcbcccbccddcaddadddcabacaaacbdadcabdcbbdcbcbaadcbcddbbabbaddcadcaaaadbbdcbbddbdddabbabcdabcccbddbadbbdaddaaccdacabcdabbdcacccbacadcaadbdccadcaacdcadcdddcdbbdddaadcaabcaabbbaaaccdaadadbbbdccaaccbcdddabadbaabbddbddaccbbbcdddbaadcdbccdccddbbcdabacccacddbabcbddadcdcabdbdaadbbabdbcacdaaddbccaaacdadcdaadacacdcbdccdabacccddcddcbccccdcaddaacdcdbdadcbdbbadaccadbbbaadbbbacbadaaddaaaaddbbbcdcbbadababcbdacbdcacbdbdcaddacadbdcbdbdadbacdabddacdddbaabcacaaddadbdbbddcaabcbaaccbdccacccdddccbccbbacbbbddbdaccababaacdcdabccbcdbbdcbcbdabdaccdcbbacabacbaccddbadbacdbbdbaddbacadbbacbbaaccadaabccaddabbcbbcacccbbdaaadbacdddaccacdcacccaabdcacabababadadcdbabbccbdbdacdaccabcadcbdadacdbcdcdabbbabccdcdcadbdddbbdcbdddbbdadabbcddccccbcdaadccabbaabbbbcabcacdacaccdcbabdbddcadddaaaddcbddbbacdabbcdccbccdbabcadbcabcdcbcdbbdaabbccdccacbacddddccaabccaacacbaacdcbddacbcaaabdabbbccacbadccbcdddddaccccbdcbdccccaccdaaacadccabcbccabcddcccbddadcbbdbdcdbdaccacaccdaacbbcdcacccdbdbaccdbddcadcacbadcdcaabaaabbdbabdacdbdcddcdbbddababbbaadcdbcabaaddaaacadbdbabddbacacabdaaddcbaccbacccdcadcdaadccbcabaddddabbbdddcbdbcaaaddbcddcabbdbcdbcbddcaacdbdabadbbddbbcadcccdbdaacadacdbdbadbcddbdcddabbadbcbbcadacaccbccacdbadcbbdbaccdbadbaadaccccccbcdaaacdbdbddbcdabdcadcabdbbcacbcaccdcdcbcabdaddaabbbadcdcbdbadcbaadaabcbdbddbcccdbcbbcbbcdcbcbacdbcdbdaddbcddbdcbdccbacdccdbdcccacbbbabbcabdbcdcccacaadcaacdbdddbaadacdaddccbcbbacddbbadbdadadbaacaccccacddbcdcabaccacccccdbdbcbcabbdbdaacccdbbababbacbaccdddcabadcddaaaccabddbacddabbbdaabddacababacadcbcbcadbacdbdaaaddcadabdccaddbdacadcbbdacacbaddbcacdacaddcccddddabacbacacbbddcbabbacbdbcabdbbcaabadbbcdccbbdcaaaddaaabcadaabdddaabcdbcbadcccdadcbacdcdbbdbccccacabcbddacdbcbacabccbdbbaacbcaabaacdbcdbdabaaaacddaacdbdddddababdbadcddaddbcdccacacbaabacbccabbdddacacccaabaaddbddcabcbbdaaadbdccdcadbaaadabdddbaaadcbccddbabadabcadcddcdddabbdbcdbdaadbddbcdcbaacdbdbcdbdcdbaccbbaacdcabcaaababdacbbabdcbccbddbcdabdddbbaadaddcbdbdcacdddbdbcdbbbbddadddbdaddabadcdccdcddbacbbbabdacccbcabadcddccccbbdcabdbdabbbcddcddacdbcacbacacbbabbabdbdcdbdccdcacacdcacbcddbbcdcbcacbbaaccabcddcbbabdbddbaaaacdcdadacbbdaabaaacddbdcaddaadcccdabbacdabbbccdcbcccbcbbcadbccdcacbdbaacbacbbdccadabababbbccbacbcbacdababacdabcdbcbbbaddddcacccbcaaaccdbabbaacaabcbacabbbbdbcccaabbabccbbdaabadabacddccdccdccbbbbccdbbadddcddbbddbadaaaacdcbabbdddddccdbcbaccacadddcbacbcabbacbdccaabdbbdbdacccbdacbbdbddbccbbdacdadcaadabadddabccaaabcbbbdddaccdadabcacaadadacaadcdccccdbabcdcabdddbddaacbacbbdccbdbbbbcddaadadacaccadcbbbbdbaacbbdbdbdddbbbcccacbdbabbabbccbdacbabdadabcddaccdcaaaabccacddddacdcaddbacbdbbdbbbdacbbbaabaaabccdcaadbbaccdbcbbccacdadcbabcadbccddbcbdabcccabdbacabaaadcdddccdadcbbdcdacadacadacbaacaaaaadccdbbdcdabccabbdadcbccadbcbbbacadaacbbacdbcdaaaddbdbccccbabbbaabdcadbadaadbadbcabbaabbacdcbdadbbbbbcbabadbdcadbdcccdbacddbaacadbbabbabadbccbbdaddadbbccbabcacdacbccddcbbcbacdbabcaadbcddccdbdbbcbddbcacdbcadcdbcdcbbaaaccdaacdbabddaabdbbddadaccbaacdaccacdacabbcbdcbbabbabbccaaadccadbbcdadbbdaaaddacadbbdcacdcacddbbbacaaaddbabbbdcbbabbaaadbbcaabadcdcbacdbdcabdccbccbcacbadbabcabddaccbbbbbcccabcaabcbcabdccaddbccdcbbcbdaadbdcbcbacabcadbabcaabaacdbccabbccacbbbdaabaabdddadcdacbdccdbabddbaccacbbcadddcadcccbcbccbadbdcbaabbccccbccbbcddbacdcdccdbdbaabaaacbbadbbccadacaadbbddcccadadadbbdcbbaccbdbdcbbababbabbdcadbdbcbaccbbabcccacbbddbcccabaaaccdbabacddadaababcaccddbaadbcaabdabdaacdabddbdbdcddcbccbbaaadbbcacacbddacccbcbcbdcccbdbcabdadbdabdcaaaabbadacadbdaddaccdcbbbaabdcadacbbcacdcadbdccdaccbcacaaacdbbccccadccadaddcacbdbbbaabdddbaddcccbbdbacddcbdaabdccddbaccddbadcaccabacaddbbadcbdcaccbaadaabbadddcdaacaccbdaddadaabbaabdbadbaacabbabdbcdaaaacbdbcdddabcaacacaabaabcdbcdbbcabbbaccadbcabcbcdbbacaadbbbacacbabdaccbbdbbcaaaccbbdcddbdabcdcbacdccadbddbabccdbcacbdbadadccabdabdcaaddbbacadabdadcaabdcbaccbcdccabdadbcacbabaacdbbcdaacbbccaccbaaaccccccabbaabcbbbbcacdbdadacacbdabadcabaacadcdaabdacdcabbcbbccbcbbdcddcadabbcbdadabcbdadacbbacabbbdacdcadbcbdccccbbbbadacbddbacbbbdcbcacbaddcddbbdcabccbbccccbcbbacbdaddbdadaacbdcbdadbbbccbdddadcaadddbcbcdcccdacdbbddcdbcdcadcbdabdcdcbbbcbaaaacacbacddcabcacaabacdaabbbdddccdccacaadbdbdddcacccdacddcbcdbbcbaaadabaaddbbdabadadcbdbcaaddaccbbacbdacaaabbdacdacbdbadadbdbbdbacbadadaddcddcabaaccdcdabbadddbcdcabacccbbabbbbcbbccbdacdacdadddcdbdddbbdadbadcdaccaadcddddbbdaadcbbbccacbcbacadbbbbabbbabdbdcbabcabbbcacbbbddbbbccacaaadcabccbccaacddcdaaacbacdcbdcadcaabbbcadadcbcabdbbddbdaabdcaadbbabbddcabcccdddadcaaddabdcadcabadadaddaccabaaddbbabcbdbaadcccbccccbcacadaccccbaaadbbbcbdbbbdababddddacabcbcaccdaadbbaabbdabaacaaadddadddbaaadbdcaadbaaccbdcabadbcbbacbcabdacbbdbbcdccccacaacaaacaadccacbaadbbacdbdcbbbaabbddcbbbacdbbaadacccddbdadbdbbadcadbdccdababbbbbcdccadbcbbbdcbacdadbdcadabadabcacdbabaaabdddaaaaacabbdcbcccadbaddadbabdbcaaaccbbaadcbbbadbabacccbaabbbbccccbbababbcdbbccacacbbcddbccbcdabdcbcdcddbadcbbbbbbadcdbacccaadbbdcbddbddcabcbadcbacabbbcaabaabbddaacddcdccbbbbccadcacdbddbbadcddabbccbcbcacbdcdbcbabbacbadccdbadbcdbcbabaaadbcbdbcbccdbbdaccabcccddacdbababadbbabdaaababcdccbddacbaccdbaaaabbccbddbaacdacaddccdbadcabbddcdbbcbacdcbdcabdbbcccabdbbdaacaadbcbcccbcdcdbdbdcaadccdcbaccaddadcbdabcbcdcdccdaabadbcbdbcdbbdbdcbbadadaaacaadbbdaaddbaadbbccabcbabbabacdacdcdcadcbcabaccacbcabdbbadadaadbaababcbccdadccdbabbdabcccdadaacaabcbbacaddcdddbddbbcbdabbbdbabcbadccdddaabaaddccdabcacbaccbacbcccaccdcccdabcbbababbdcaaddbdccbaaacaaaaccccabbcdbdcbcbbdcaabbcadcbadcbadbcddcacbdddcbdbabababbccbacdcbddacdddcddcdbcdbdcddadabddcaccbaddacabddbabaabacdbbdcbadaccacccbabadcdcbcaacacbdbbaddbcbcbcdaaccacdcdacdcbdbdbabdaabbdcddaaabbcbabbbcdbbabdcacaacccbabdcaddcabcaaabdcdcabddabaaddabcbadcddacaccbabcccdcdbbabbacbcbaabbbdcddabccbcdaacccacbdaaddbbaaaabaaccdccddddddbdddbddacddabcacacdcdcaccbdbbadaccdabbdbbccdcdccbbabacbddbadacaadadbdadcddcbacdaaaccbbadaaddccaabdbbcdbbbccdacbababbcacdcbcdbbadbbbcabababcabadbaaacddcbaabaadadcbcdbdcddbdcbccbdbaacbbaadaabccdadacacdccdaadccbddcbdadbbbcadcbbdcabaabbdcadcdcdddcdbcbaadddddbcaabbadbdddddbcaadbacaadbcadbccbaccaaadabcbaacabdcaadaadcbbcaaabbcdcaabaddcaaddadbddddddaaddcadbcccbccddccabcdacabccacabcaacbccacdddcaaddbdadccccbdccbabdbdbaaaadcddccadccadcbcaabcdddbabdcddcbbdbddcabddcbabccdabadadcccaccdbcadbbbbdbcacdddaddaabadbcdcdccbcbcbaccaddbdbbbbbdaaabcacbcaaadcddabaacddddddbbdcabddccccaccdacaccbcbbcdaabbddabbacacbbbacbddbdbdacddbadabacdbddadbacadcbaacdaacaaacccababddbcadcaccbacbacacccbcbacddccccbbbaaadcccdbbbacdbaccccadcaddcbaaddcbcaaaadacdbadbcddadbcaadabbaadaddcbccdcbcbdbcacbbbdadddcbcbbcabbadaaabaacabbbadccbaacdbbaacbddbbdbabbcccadcbacadbcddacbdcbadbdaaddadacdcbabcccccbcbaaacaaccaccbcbcaabaababbcadddddabdbddcbaadbdbcdaaadcdccddbdbbabaccabbcbcdbbcdbbcbbacccdabddddbdbbddabccadadbcbbabdcdbacdbaaacbcacbbcbbaaddacbbbbdbdacbabcdccadaaacabacdabcccbdbddcccbacbabacacdcadbcacacddbdabadaacbbbcbabcbabcaddcbabcbbcadacbdccbbbaddbdcacabdddacbbbbcacccbdbbbdddcadbddcdddabbcbcbccdacccdbadcddcdbcdabcbcbdadcadbdbdcddcdcdbccabdbddccdbdddcddaddbbcabbddbcbbcbbaadadaacadabccdcadbcbacdcaddccdbaaacabbdaccbdadbabaaacccacabbbddbbcabcbdacddcdbaccbacbdbcaddddddbbbbbbbbcbcdbaacaabdcbaaaababadbcbcbdddaddadaaaccbbcacbdccaaddadcddacbbcabcadbcacabccccaaccddcabaccadaabbcaabdbbabababbdaadbdadabdcdcacccdadcadbdddddbcaacbcccdbdbcbdcdaaacacbadcbadbbcdbdaaabacdacabbdaaabdcaacbddacdbaadbbcbbdbcbdbabcdccdbdbbcbabbabbdadbbabbcaacccdbddabbdadbaccbadddadddccddccccbddcdbaadabacbcaabaddbaabbadbdacccbdcbcbabdbddbcaaccacbbdcaabadbcaddcdcacabddbbdacdabdadaaacaadcddaaacdcbcabacbadacabbbdbabccbdcbcdcdddbbdcacdcbaccbcccdccccacddacbdbaaadbddcacaaaddaddbddabdaadbdaadddcbcbdcbabdadabcdccacccacdbadabbdccdcbcddabcbabadcdddddadddbccacbbcdabcdcaacbbadaacaabaccccddadddbdcaaaacdcbdababdcdcacbdbacabdacdbdbddcdaacaccdcadccddddbcddabdddcddcdaadbcaaacacadcaacaaabbaccbbabadbacabddcddcdbcbcdababcccdbbcaababbcdadaacccbbddaacddccabaaccccaaadacdbbabaabdcbdcdacabdbaacabbdbadcbcbdcaddcccbddcdaccbccbdcbdccddabcbdbcdabacbbdcacdcbcbdaadcacacabccabdcdcdadbacccdaacdababcdbccbdddbbcdbadcacdcaacadaaccbabcdcdbccccaddcabbcdccdbdccaaabadcadcdccabcbdddcbcbdcbdbddaccdcbdcdcdabcdacabdcacbddaadbadbdbccdabddcdcdbaaddcdabddabcbcddacaccdbaababdbdccdbbbbdabddcdddcadadabbbacdccdbabdaabccbbdccbaadbdaacccdcdabcaadbbdbbabbbbadacababdddcdddbaacdbbadacabccdddbcabcaccbadaadacbadccbbcbbbdbdbdaacdcadbbddadacccbcabbdadccadbbcdbacaadcbabcbaddbcccaabcdacaacdacaadcacbdcdababdcdcabcdadbddadbbadaabbcdaddccbaaacabaadadbcbdbbccbbbcabbcacdcacbdcbbaaaaaadcbaaccbbbdaacbccdacbdbccccabccababcbabbbcbdabbacccbcbaacdcdcacbaaabcdcadcabadbbbcdbdacaadadbccdbccaddddcabbcdacabdcccaaacbdcacdabbccadcbdabdcbdcbabddaaacccdbbbdadcdacaccbddbcdbbdcabdcbaacccddaddabddbabcabbcdbbadabcadddcdacabdcabcabadbcdaddaddcbddabbaacadaabcadccabddccabcdcddcdcdbbcdadaababadccbdbdbbcdcabbcdabdbbadcdabbdbdadddbababcbdbbbcbbdacbadbcccabacbbcaadacbabbdcabaccbadcbbaaddabcabdabbbbbaddbddcddcccacdbbccdbdbbbcddcaadcbcdbdbdbbddcaddcacbaacbaddcddcddddbabcbcbdaadddaaaaadcbbadaddabcbbdbddbadabcacbdadbadaabdcdbadabacbacdabcdabadcadaaaaadaabaccdaabaccbbdcbadcdcdbcdababbbddabaabcdaaaabbcccdadbbaabcbbcbcbbcabbdadaacccbabcbcdaacddacbbdbddacbababcdaacbbbddcbbcbbcbadbadcbbacbdababcbbbabbdacdaddddadaacaddcbdccddbcbbcacbdcddbaaadadcdbbbdacacccdccbcabacbcdbdbdbbdcccbdbdbbadadbbdbbadcaddabadcaaadcdadacaddccabbddacbaabbaabcadbbcabadcbbcbbcdcbdbadccdbacdbcccdbadacccccbbaaddadcdacdbcbbdcabccabbdbdcbcbabadcacadbadcbcacbbbcddaaacbadbacadccabaabadccbdbbabcdaacccdaabdabcbdbdabcaabaccbdadcadaadacdbbcdbdbcbbbaaacddbbdaadcacbbbbbcababdbcdbabaddbaacbcbdcddcbaadacbdddbbccdcbdbbcdabccbcbbacbdbdbadcbbabbabacbdddaabaaddcdabcbcabcddbddababbaabccacaaabaccbdaaabdaacababbdbcadacadddadddddbbbdbcddcbbccacdbdaaccdadbbdacdccbdacaddadcaabcdbcddcdddddadcabaccaadddcdaadcbcbacbcbcdbdbabdadcbdacadbadcbcdadaadcadbcbccdaadacbacbdbcdacbccbdcbcbcccdaaddcbadabadabbbcdddadbcaaacabadbbaaddccbcacabdacdcdcbdbbdcabacbbcdbdcbabdbdbcdaabccacadcbccdabdbcdaabacccccacbabddcacadbdcaddbcabaaadadcddcbdbdadabdbcbddadbdaabbdabccaacbccbbaabdbbcabdbbabbbaaaacbabdcdabbccbaaccbcdccbacdddbadccaaddcacbddbccbdabcdcbbbccccbaabddcccbacdccadacadcdaabcdccccbdddaacaacdcccbddadbcaadcbdccdaaadbacbcdcdcccbabcdbbbacbbccccdbcddbbabcdbcbdcacdbaacadcddbbdbdcbbabdaabdcddbacbaabacdbaadbbcccbccccbddcadadaabbbccacbdcaccacabacccacdcdbabdcbdddabcddbbddcccaccadccbcdbcdaacddbaddbabdacbacdbcccabcbdbdabcdbdbabcdadadddccaabadbdddddcacddadcddadbdcccdcbadcaccababdbadaccbadbabaadcccbbdddbcdbabacbbadbcadaabaaccabadddcabcccccccbdbbdcabcaddadcabaaccadbcdbbbdbdcdcbbcbbbdaaddbbdbdcbcbabdaaadbadaddbcbaacacdbcbcbbddbcdcadbbdbbaacccccdadaabcdddbaaabdaaababcbbbaacccbdcdbabbacbaaabcdddccabadabccabaababadcacdbacdacdbabccbcacadcbbccacdaccaaabdbaadcdaabcacacaabccdcdcbaccddbadbdcbaadccbabadcbacaccddbadaabbdddcbdbbdcdbadbaddcbddcddcaabcddcbbccddbdbbccacbbabbbcaaccdbcbccadacdcccdabcbbbbdcaddaaaadaacdbabddcddacdacbdbbbbbcbddccaaabcabbbcdcdccbbaabdbdbddccaabaacadacbaadadbbdcbdaabddbcdbcacadacbbacaccddabcdcbddaddcbdaacbddbaccbacbbcccbdbdaacbbabdccddcccadbccaadbbdcdaacaccacadacdcbdbccdbcbccdadcbcbbcdabcdaccadbccdbbcdccadddbdbcbcdaaacdddaadbbacdabdacabcacbbbddacaddddbccadadadcbacaaadbdadabbbadaadabdcddcdccdbbdbbadaacaacdbcabaccdadbddcbddaacdaabbbdbacadbddbbaaaadbadaabababcababbccdbcaaddbccadbabbddabbbbdbbccaddddbddacbaadaabdcbdcabbdbdbcdbbdabddbdccbdbccdccbbdadabddaabbcbddcddcdbbbdcdbbadaaddddaabcaaaadacbdbadacccdcbddaccabbaaccdbabcbcdcdadaacbacdbdcaabbbabbbdabccacacdcdddddaddccddbcbcbaabbdbacbbdbabdacdabaacbdbbacdbabbbadacbbadbaadbccddccdcbddcdbabaadbcadbababdddbbbbadcadadbbababcdacdbabcbacdccaaaddccccabdcaadaadaaccaddbaacbccabbdcccbcdbcaddccbdcbadbbcdcacbabdcbcccbcaddcacabcabbbdaaacaadcbaddacacbdbcccbcaadcddbbadbddbdbcacacbaaaabbcbdcddcabdbddaadabdaaabcbcdaaabddadbbcdbdbcddbcabadbcbcabbddcddadbadaadddcbabbdcacddbabdabcccbaacdbddbabbacdacadababdabbdbdababdddababaadccdcbdccbbaadaddacdcbabdbcdbcbbbbbdddaddddabdabaddaabaaadacbccadbabdcadbdcabdcdabccdcbbaadbaadacdaddbdcbbbbbcadacbcaadcbcbdabdddcaddbaaadaaabdccbdbdcadbddbbbabcdcddbddcadbcbdcddacdadbbacdbbbddabbdbcaccdccadcbaabcabdccbaaabaacdbbaccbcdddcddbabaaaccbacabdddbdaddcabccacdbcbaadbbabdcccbacadbdbbacdbbcbbcacadbadaccdbacccabbdbdbddabdabddaccbabdcbdbbddcaacacdbddbcbbabaccdbaddaabddacdaabcbacbcaadcaacdcbcdacdcabacaabbdabadcbbcdabbccdddbbbdcddaacdbdadabcbdabdbbdbabdccbcbdcccbdadbbcaaddbdaddacbccdccbccbbdccdbbcdbcbbccccccaabbaaaabbccccaadaccddbcdbdbddbbddabcaccbabbcddcbbbdbabdbdbdadcbccbccbabcdddadddbabcdadbadabdbbbdcccadbcbaabcccdbabaaabdddacdadcbccdbbbadacababddcbbaccabddcadbcaccbccccbcadbdddcbddbdbdabdbaabadcdddadbadcaabddadcbdccaaacdcaaaacacbdababacbaccbabdbadddcadbabdcbcbcacabaadddcdababadbabdcbcdcbcbbbdbcaaabdcbcacaaaabccdabbbacdcccaabbacbbddbbbbdccddbdbadaadbdbccaabbbadadadcabbcbcbcbacbdcababadddaabdbcaddacbaacdbdaaabbaaaadcadbcaccccbddcdacaddaacbbacdbdddcdacbcaabcadacacddddaccbdbdbcddbacccadccbdaddaadaacbbacbababbaaccbacbbcdcdbcabdadaccaadccaccdbacaababbdbcbcdbacdcdccdacacaaabdccbaacabddbddbcaadbdbbaaddbabaddaccdcbadcbabccacbababbabaddcccbcdbbbabccbcadadaccbbaabaccdcbdcabaadaddccbdbbdaaddbdcdbbadccaaddbbdaaccddcaabccddabbbaabdcaabdbccadbbbbbabdaaddabbaaacccdddabbaaadbbcacacdabadadaaadbddbbbdbddcbcbaddbdcbcbcdbacacccccbabccdbaddccbdddcabaddadbbcaddbddbbabcdbcbbababccaaabdacabacddabccdbdbdccabcbbccaaabadbccbcbbdacadbbdabdcddbcdbddaddbbbddcddddcbddabcdbcadbcbbaacdbaccdbaccbcdbddcacabaacaabacacacacbccabcbbbabacdbcbcacdadbbadaabbbadabbcbaadadcdddbaaddbaccbddacccbbdcbccdaacacdcaccabbdddccdbcbaabcbbbbcacabccacddabdbabacbdbabcaccccdcacccdbbccaacdbccacaadcbdcdaccccaddacaabbbdbabbccdcdadbabbbbbbdbbaaacdccbbaccddcbacbbacdabbcaaadddcbdcacdbddadbcddabcbaaaaacbcabbccccaadbdbacccbaddacadacbbdbccbdaabcacbbbbcadbcadbacdbcddaaaccdbabaacaabadccbdadbaaddcccbbdcddcaaadbbcabbdcabbcadbbabcadccabcbbadabcbcbdaabcadabdcaaaccabbcaabcaaaddcbaccbddaacadabababacddabbbacdcbccadbcdccddabbdaadbdaccaccdababadcccdbbdcbadacadbcbcbaccacdbbcdcacdbcbdbddbbdbdcbbdddbccacbddadbdbacaabacddcbcdbbcabcdacbaadbbcadcbccbadbabccacdccbaacbbddcdcaaccadcadaadabbadccbcbadabdddcaddadacbbacbdaaaadaaacaababbcaaddbcbcaabbabdccacdacaadccdadcccdddabdddbadbacbdbcacaaccbbbcdcbbbbbbbcdcaabdcbaddbbaabddbaccdacbccdbbacabbdaacaabaaabdadbadcbcbcbbaadbbabcbccaaddcccddcabadddabacdaadcbdcbbacbaabdacddadacabcacbbacbbdbdcdacdcccaabcadaacadbcbcacccadcaabcbcbbabbdbcdabbadabcdbdccadccdcaccbdabcbdaaadddccabcbcbbabaccabcbacabdbbbddaccbbcbdaabccbaaaccbccdcdbbabaadabddcadbdcbbbcabccadcdcdbaadbdccbdcdaadabaaaabbdbcadadcdabcaabbabdadbacadababbbaaaabacabbdbaddbadacbacadaabcdbbcbabbddcbbbacabaccdabcbbcbcbacbbcaabddcccaabbdbbcbaabcabbbcbcdaabadadcbbdbdccaddbcbcbdbacbdacaacccadddadddabddbaccadbdbcacaadbcccdacbbacbadabbdcbadbababcddbaacdbadadbdddaddbbaaddbcdcbadbcdccdbcddbdadaddadadacccdcdbaadadddcbaaaaaccbdaaacdbdddbcddaabaaaacacabbdcabcddccccdbabadabdbdadabaabbdabcbcbdaacacdadaacdadaacbacbbcbcbbdabbbddaabaddccbbddcbadacbdccdbbacbcdddcbbcbcabdccdbabbdbcbdbaadbdacbcacacaabcdaddaabbdaabaaacabbaddcaaacdaabaccddaadcbcdbcbbbccddbaddadbbcbaaabcdcabcabdcddaacccbccdbabcbbacbbddbdaccbaacccccbdddbaabbdccbdcdbacbdbdbaacaccddcabacbbaadccbbbbdcbdbbdddabbdbddadccdcdbcbaaccdacbbcdacacbadbdaaacdbddcbaccbcdaabcccbaaaabcaccababadadaccdadccbddabbadcccacbabadbadbcaacdbcacabacbaacdacaccdddddcbdaabbacdaddddaabbaacbccaabacadbacdabadddcdcabcdcabdbdbdbaacddadbccdcadbbcacdacaccbcdbabbadddabbdadbccbadaccacadacaaaaddabbaccaadbbbbddacdadabdbbdcccabdaadcbacbbdbbaabdaaabdbbbbdadbbcacbbcbbcbadccbcaacaccccdbdacbcabadabccbddaaadabbbbadbdabbdcabbadadcbdcacbacacacadbdbccddacbdbdddbaacbcbbbbaaaaddcccddcbbcbabdbccdaaaabcbabcddbcbdccdddabbcbbcadcbadadadcabaabbcbbcbcbdaccbadbdaacacddabdabcddbccaddbbadabaccaadbcccbddcabbcbbccbcbabbcccdadcaddcdbdadbadcbaadccabbbdaccbabdaadacdabbbddcaabaccaabcbacaddabaddccadbbabdabdaadccdbdabbbdbbadcbdbdcbdadaccdccbbabddaadcdccaabbbadabdcdcdbaccbacdaddcaadcddddcacbdbcbddbcbcccbcadcbcdcacdabdacdbccccbbbcddbdaacdcbcdacadcbbbabadabdcadcbaddddabdacccacdcdadacabcaabdbbbbaccadacadcacbaddcdcbcabbbacdbcddbcddbdabcacdabacacdacbaabdaccccabcaccbcbcababbbadccabdadcddddccacbccbcdaabcacbbddcdbbacadabcbacabbddabacdbbaccadcbabbdbcaaaabaddadaccadbacaabcccabddcdccdbcbbbcadbbacbbaccdaaaccbdadcababddbbdcdddaccbaadddddbbbbacbabbbbdcaabacddbaccbcbddcaadccccbbcdaccccddbdacdcddccbbdddccbcdabdcaadabdcdccdcabbbcbddbaaadbbbccabaddcacbabbdcbbcbcabaabacbbdaadbaaabccbbbddadcbbcccddbddcdcdabbdbdbaaddbccaddddabdbcbccbccabbcabcaaabcbdaddbdcbcbbcaadabbacdcacdacbbbaccabbbcaacaddcabbcbabdccbdcbbcaaaaacadcbbdbbdcdcabdbcdbacacbabacbbcbdcdbdccadbcccdacbcccabdccdccbcdadabcbacdbdddbbbdccbadcabacababccbbcbbdcabaabdcbdbdddacbddbdbabcbbdbddccdddcabddccbccadbcbbcbddbabcaadbdabcbcaadaddccdbcbbdcdbbccaccbbbabcdcdcddccbcbacbbccacdcccacdacbbccadbcccdbcccdbadaddbdccadcdbdcadddcdbcdcbdbabbcccbbdacbaddcdadbdbcdabbbbdabddcccccabcabadbccadaacaadbcaadaddaadddaddbcaccbdbdadabbbabdcdcbbcbacdaddcadbabbdcdabdbcdcbddbcbabacddadccbbabbdccbadcbdbbcaabccbdbdbcbdaccddbdbdabcdaabbaaacbaddaddbdcabdcacbcddacabcddabbacdcbabbcbdbdccbbbadddbdcdaacabbdbadcadcbdabcdaadbdbbcdacddbbbaccdaacdcaadbabcdcdadcabdcdbdbddaabacbabaaaaaccdcccbadcdccadcabbbbbdccdbdaccddabbdaacdcccccbcddaddcaacaacbcaccbdadbacabcdddddddddbdcacabbbbabcddbacabbadcddaddcabbbbaddbcadbcccddaaccdcabbaaaaccddcdcdbccbbbdbcdcbdcaccbbbadcdddbbacbbbacccccbbabdddcdabccdbcdacbddcbaadccdbdcaddbaddbcdbabdbaccdaadcddaaaccdcddddbbbdaabbaccbdbbcdadcdcccdabadbdddaaccacaabadccbabaddacbcabbdcbbaaacbdaabbddcacabccaddccaddaacacdcdddbcddbdbddadaabddbaddbbccacdadacbdbcaccadcbccbdadcbababbdbaccccadddddbaacaccbddbcbcbdbdcbcbdddbdcddccadcaacbddbabcccdccacdcdcaaaccddddcbadbadbdcdbbaadbbccdcdbbdaabadadddadcaaadbccbdbdbccabdbaacbcdaaaadacaabdccdcadccbdbcadccbcbbbaddcbcbaababbcddadabdabbdaabbacaadcdbaccdaaaacabbbccdacdddbbbacbcdcbbccabcbadbcdabadbacaabdacbddbcbdcdabbcabcbccbdabaddccadbcaabaccacccacddccdbddcdddacabdbddbdaadacdaadbbabcabbaadbdabddbaaaddbdcbcdccabbcbbdaacdcdbacdbdadaccdccddcdcbcdbbbcbbbadaccbddbdcadbabdadbdccbcacabbdbbabacaabbdbcdccbddbcaacbabdddaadddabaacdacbbddcabcbcccaadbccdcbcbbcdbaaaadaaaaabbaddbabbabcadcadcbacbcbdbdaccaacdbcccabbdbcacccbccdbbaddddcadcaaaabcaababdbaaadcadbcdabccdbbdabadcabacdacbcbdbcccdacdbadbabaccccccdcbddadccbddabdabbabbcababdcddcddabdcaacccbdadccdcadbcbabbbcddccaabcbadbddcbbdddaadbcccadacbcdcbaddcacbcccdccbbacacbddabbabbbccccbbcbaaaadcaabccbbcbadbacacdbbdadcbdaabddcabcdbcccbbcaacccbbcbabdadadaddcaccdccaadcbddccdbcbadadbbdccddcddddbacbaaadacdcadcddcbbabdbbcabaaddabaccbabababbdcdbbddbdabdcabdbdadaacddcbacbcaabadddaacbddbacdcccabcdaabcaccdadadadbaabddabddadbdcabcbcddacbaabaabcdbbaacbcdcccdcbadaaaacbbdddcabcbdbdbbababacbcddadbdaaaddbacddddcadaadccbabcbbabacaddccdcbbdcaabcadcddbbdbdcdacacbddcbdaadabdbdbcbaacadddbccdbdddbcdbcdcacdcbcdcdcabccabbdcddcbbadcaacdbbdaddcbdcddcadabdaadadaaadbabcbccabdcacdcbcdbcccbbdcddacbacbbdbddadbdbbaadcdbcacabcabbcbababdddcddabcbdbddddaabbccbdbdcdcbbbaacaaaacdaaabbabbcccddcacbccbaaacaabbdbccbddddaccacaddbdbddcddaaddbbdbcbadabadabbadccbbacabbccdadccbacbadbcbdcdbdaddcadcbddabacddabacadbcbddaaadacaddccbadbadaaaabcaabdabcdadbbbacacabacdbbadccdacbdcdadbddcdcccbabcaadaaddabcdbdcbddddaadaddcbbcdcbacbbdacacaabdbccccbacdbcddbaababccdabbdaddbaabbbbbcacadcbcddbccaaadbdbbbcadcbdbbcaccdacdbcccdcabcddbdbabbbdbcbdbbcbabadabbcddabdcaacbdcabccaabbcdccbcdbbaddbbacadbbcabadadbcddbacccdabbcbdbcdbabaddcbdacbdccccdbdbcbbadddcdcdbdcdccaddccddbdcbadaacaaddadabddcddcdddcdabcdcdddcabcaacbdaacdbcccabbdcbdccdccddaccdadcabbabcaabadbbbbcdcbcadbcadbaadbcdadaaacccbacbbddddadddbaaaddadcdabbaddcccddbabbcbcaabbadaaadbccdadadcaddbaacabbbcdbbbbcbcdbddcbabdbbcbcccadaadccbbdddbaadabddabcdcbbdccadbddddbbcbcdddbdacdacdabbacbabbabccaabcadacdcabcdaaaddadbacbacdcbbccbdbbcdacbcacdaaaccbdacaaaabacdbbadcbadaabbbcccdcddddadacaabdcbdbdcabbbaaaacccbbbdcbcdcdcacaaaaaaaabdcbacddaabdaacaadcbadacbcbcdcbacccadcbcabaabbaaaaadbcdddacbadcdddbababbdbcbcddabbcdaddddcadcbcacaddccdacaaddbcabadabbdbdcbbaddadccdbadaaabadbbbbbcbdcbcabadbbccdabdbabbbddbbbbcbbdaabccdbcdddbdbabbadccacbbbaabdbdbaccdddaaaadcbdddddcadabdaadbdadbadcbddcabbcdccdcbadababaaacdccbaacabaabaacbccaacacacabbbbabccdccdadbcadbbbcdcdcbcbdbabbcbbcdbbcabddaabbcdccdcacbcdabbbdcaaacbaacdcdaccaaddbcdcacdcadaabdcccdddacbacdacaccaaccdcccdcabadadddadbbacacbdcabdbadabadaddddccaccdacadbacbdacabaddbcdcbcbbacbcddbcccdbbcdbabbdcdaabbbaacbacddacbdcacdbbbdbbadaccbabccacdadbbaddcdbbcabcdbdcbdccabdcccdaabccbcabbacaaadacdddbcdbaabadccbddacbaddaabcbcabbbcccbbbddccaaaadbcabccbabcbacddddaabbddcaaccdcbadcabddabccdccddccadddbdadababbdaaddddccccbbddabdbdaadaddcdaaabbcddaabadacbcdbabcdcaabbaccacbdaadbdbcbaccdddcabaadcdcdbcabaddcbadbbcacacdbacadbdabccaccdbaadddccabbbbdcdbccaacadccabdbbbabdabbcbcddabaaadbbaaadabbcbbcdadcabbacdcdaddbcacadcadbdaabccaccdaadcddabacdcabbccacdcbdbdccdbdadaadbbdcaabaabcdddcbdcbcdccbbcbcddcdcadabcaacdbaabadbbdccaabbddccdbacacaacdbaccbbddaaccaadcdaccadabbcabacdcbabddbbdbbbdcdcbaacdcdaccccccbdbdddbdcccbccbddccdaaacbcbcbdaacddbaaadaccbbcbbdcbadbcdcdbaaabddbcdbaaabdabcabbddaacbbcbdbdddcabbdbcadbbdcddddadbbaddaadcddaacabcaaabadbdaccdabbaccaaabbaaaaddccbcbabcbbdbaababadddacccdabcdabcaddadcabccaacdccccbddbabaabcccccaaabaacdaddbdaabbddbbbcbaaabcdabccddddcccdacbddbadadabbbddaabacccdaccdacbdcbdabcddddaabccbddcdbacbddccaccadcdcaccdbaaadaabbaadbcdbddbadaababcbaadcadbcdbbddbdbbbadaaccaaddbdacadddbbcbbddbdbcacdcbbdbdccacbabcddadabcddacbcccccabccdabadbdbadddcbadddbddacbadcccadccdabddacaddcdcabbdcccbbdbdbcadbccdabbdcadcbdababcbddbababdbadcaddabcdaabbdddabbadcdccdadaaacbccdddcacddadabdcdcbaddcabaccacdddaadbcbadcaabccbcdddcbcccabccdccaaabdabdabcbbaaadadaababdbcdcdcaccadbbcddabcdbcbbdcdbccbbbadbcbdacbcbbbbbbbdadbdbcbdaabcdcbbbacbaaabaaacabacaddccbaadaddcddbdbcadccadcdbaaacababbabbbdabbcabcdbbcddbacbabbddabacdbccaabdabdaaabacabbbccdcdddaaaadbbbdbadaaabdaacbcacadcbbdbccbccaacbcbccbbbdbddcadaadbbbbbbddcbaccadcdccbdaacbdabbdbccadbcbdcbcaadbdbddadbabaabadababdbdddcaaaadcbccacacdbbbcddaaacddbbbcbaabdbbccccccbacacaadccdcabbabacabadbadbadbdaacabcabcbbddcbcadcbcbcbddcdddccaaabcabcadcdbbbbdabcdbaadbdaabcbdadabcdcacadbbdbdbacdbabccacdcbcabdcdcdcaccbdaababbacacbcbcbdbabadbcdddcadbacacaacbbbbcacddcacadbcacbcbddacbabdabbcaabbcbccbadaddcacdccdbdaabcdcaddaaaaaacccbbdcbcdcbcabccdddacacddbcddbdcdcdcabccbadbdcaaddcbddcbddcbaaddbbcdabdcbdbcdaadddccdabddaccbccabcacabbbddaccdcabaadcadbcbdcdbbbaadacbaaaabaadacdbdbaabbcbcdadbccbabccddabcbdcabaadbddabddcabaabacbbccdbcdcaaaacbcacacdabbabddcdacbddbbdabbadbabacbbaddddcccbdcbadadcacdaacbbcbcdcacaccbdcbccbabacdaabcabadbcbbbccabbcacabbcbdaadbbcaabcaadbabcaddadbbbdbdccababdcbbacbcbbabcbaaacabbbabbbbabacaccabcddaabdaaabacacadaaaccbdacddbaddbbbcacdbdcdabdbcacdbbddcbabdcabdbbadbdbaaabbcbdcccbbabbadaabaddcbcbbbbdcbcaadaccdcbcababcdbddbaaabbcbaadcbbaaaacbbcdddbdcbaaddacadccabbbaabbadcaddbabddccacbbdbbaacaadbabddbdabdbabcbbaaaadbdcaabcbcdbcdccbdaddcdcbbacacacdbacbcadbabaacdcdddabbaaaababbbdacabdcdbbcdabddaacdcabcbbcacbabcbabbacddbdccccdbdaaaaaabaccdcbbdbbcaddcdaacdbbddaadaabbccdbabbdbddaddadccbbdbcbcadcbcaddbadcaddbadbbbaacdadccbbbcddaaccdbcbcdaabddacabacbbaaddcccbbdacbacdbdbdacadbacaababbccdcdaccdbadabbbdbabcaabcddababdacdacdbcccacaddbacacabdaaddcbdbdbcdbddadcdbccdaacbacdbbbabddaabddacccdcbadbcdacdccdadccaddcddccbdbbaadbaabdacdbadadbddccabcdcabacdaaccbcdacdbadaadabbcddaaccddbbccacdcacbbddcbdcadcbcbbbccdacbacdbaaaaaaacabbaabbacdadcdbacdacdbdaaccbaabacbbbcadddbbbaddcbdcaaabccdbadcddabadadbcbabbaddaccbdbdadacbccaadccacbabbdddbddcdccbdbbbbcbcaaabacbbcabadaaaababcdbdadbdddcaaaaaaadaadbcdbbcaacacacdddbcaabcaaaccbdabdddbddaaacadaddcccadaccbccdccbacdcadccccbbaddbccbaadcaabbaccbdbcdcdcccaaaddcbccddbcbdabcbdbaaaaadbbadbddacadbbdbdbdacbacccaccdacddddcdbdbabccddcddcdabdbaccbacadcacbacbbaadaaababccbdaaacaadbcbcaccdcabbccdadacadabcdaaacdadacaaaddcddbdacacccabadcadaddbadacbccabcdababbcdcbabddcbcbdacaabdddaabdabbcbddddbbbbccadcdddbdbadcdacbcbadbcccababadaacdbbadddbabddbbcdcbcbcbdadcaddbbcbaccbadcaadccccabaadabcbabbaababadaccdbccdcbdababbbacddbcaaddcbbcabdbcdccabdddbaaaddacdbcbcadadadabcbcddbdcacdadabdcdbdccdcadcaddaadccababdadbdcbbadacbcbbbbabdccbaadbcddabdcdbbbccbadcccabbbcaacbcaccacbbddcdcbcbcabacabaadbcbcdbbababdadaadcbbbcdbcbacbaabcdbbbcbbaacdccaccbabbdbcaabddaaddbdaaadbadbbcabdbdadadaaabdbcbadaaddaadcdaddbcacdddbcbbaddcbdbbdacabdaabbdabadbcbbdabbacbabadbdcbdadccbbbabdaaccabbdacaccbaaccbccddcbdbcaaaabbacccdabcdcccbddabbaddabaaadadddabdcaaaabbacdcdcaacbddddadabbbddaccbacdddcbababaacbccbcdacccaaccccaaaabddcbdccddaddcdabdbccbbddcbbdaaabdbdddbbabaccacaccccabdbdbcdbcbbcadccdaddccccabdabbcdcbcdcacbadabcbbaaccccaadbadbacaccdbcccbdacbcdccdddacbdcdbddadbbddcdbbadbbcacadcbacccacdbdadacdcbdccdaabdddccaaddcbaddbcaadbabcbadacdcdcdbdccddadccacdbdbbdcdbdaddababaaddbcbcbdbaabddcbcabdcbcbdcbcdcbacddaadabdddbacbcaddccddacacbbbbccaddcdccbacabcdaccccddadaacadbabdaccccdcdcdbcbcbabcbaccccaabcbcacbccdadacabaabccadbdcdaabbbdbbbdcdcbbcdabcdbbbddcacccabcddcdbbccabacdaaacaabdaaabcaaadabcbdccccbcccdabdbabccbaabddcaabcbbaadcdbcabbacaccabddddbcbbcdccaabcbaacbccbcdcbcacdadddddbaddddddabacacadcbdcbccbcbcaabddaaaabcbdcacbabccbaadccaddcacccaaccbbbdccdcdddbbbcdccdddddbbdbdbdabababdacdabacdaadcbcbdbddcdbdabccaabababbbbdadabbcaccaddbaabcdccadadcccadbcdaaddbdaddaccddacbbadabbaddcbaddcaccddabbadcdccbacbbbabcaacabbcdbdbaaccccbaccabbaddbcadbcbdcdbcdabacacdacbdcddbaaddddcdcdddbcbcaadbbbadadacdaaaacbcdaadbcdaabbccdddddddabdbbbcbdcdcdaabacdcaddccadbcadddadcbccddddddcacbcbbdbddababcccbcaacdcbabbcdcabbbbccbbabdcccbcdbccdadbbbacbaaaacddbabddcacbaadbddcbadbbcdacdcacbdbacbbdabaabbbbbbaababacdcccdabccdcaaccaaacabacccbbababaacaccacabbaacddbccacdaabcbdccccacddcbdbccdacbbdcddaabdbcccabcbdbcdccdbadbbcbcddabaaddbcaadcadcbadddcabcbaccaaacdcdcacbcbbccbdabdcdcbadabddcabcbbacccddcdbddbabbdacacacbcccacbbcbdbccdacddadddcccdacbddadccadcbacdbbcdbdcccbcdccabcbcacbaccccdacddadcccbcaadaddbadcabdcddabacabcabaccddbbcaaccdcbdbbcbabaccdaaacccbaacdcbddaacbdbbcdcbacacdccadcbabdcaddcdccddaaddaccbbaadbbdbdbdbadadaabcadddcbdadddacbbdcabdacdabbcdbbdcaabddbaddccccbcbaddccaacacccadcaddbcadcccabbdacbdcbaabbdbbdcbbbbbcbddcbbaaaadcadcbabaabbbacbcddddacbacacadccbbdbbbcadbaadbcaaaabbadddcbcdbbccaccccdaabdaabbdddaacbcadbacbcabbcbacbcbbbdddcdccdcacacccabbcdbbcdbaaaadbddadbbdbcadcabaaddbdcddbddaccdcbbcddabbddabacadcbddddabcabcdabdadaddcaaadbcdbabccbbcddbbcdbbcaccbdaabdbadcddcaacbdcdbcddadccaddbbddbbcadacabdccbaddabcbbdbdbbacabdcaabadcabadacaccddbcacdadbdaaacbbcadddddaccaddddacdcbbcccaadddaacbcdacbadbcbddaadaaadbbdcbdbabacdbcbcabbdcbacbdbbbdbacbabdbaabdadaddbdddddbbaccbadcbabaadcdbbbccabbbaaacaacacbddacabbcdbbaacccbbadcadbbbbdcbadaddcccccbdbbbaaaadbcbcdacbccbcbdaccdbcdacccabbdbcabbcbcacbcbcbcabbdccdadadbabcbdbaacbbcbdbbbcdccccbacdaddadaadadaabadcbdbbaaadabdcabbbcacbcbcbccaabbcdcbbdabccdabdcbbbaabaacbdcbcdadaaadacbcddcbcdadacbadccdcabaabaadaadbcddabbadccacbadcaacccdcbaddbddadaddaaddacdbbccaccdcabcadadacadcdacacbaacdcbbaabcdaacbdcccdbcacdadcbdcdcaabdaabdbaabcacdcccbbabaabbdcbababbcaabcdbccddccdbdabadbcdcabcdcbcccbabdcabdccccbaddacaccbcbacbaaccbcbcaabaddcbdbbccddcacdddbccbddabbcbbdcabbdbabbacaaacbddbcdbbbdbaadddbdcdaadabdaacbabaadaaaaacbaccdcbdcbacdcaaccbabcabadcaabdbaddddcaaddcabcdcbdcacabbabaadccaddcabcadccccadbdbdbddcbbccdadcaabcacadbacabbbdccdcdaabaccdaccbcbbdcdcbbbbaccdcbddadcdbddbdddccbcaaacaaadbcdccdbabccadbccbdbbdcaddbbabaacdbbcdabaaabdbaccadddadbdbddabddaaaccabbcbdbdccabdacdbaacccadcbadddcdbadccbccbdbdcbcddcbbcbbbaddddadbbadacdccaaabbaadcabacacdabdcbcdcdbdbccdbadbcaaabbcdccdbcbbabdabbccdddbddccbaccbabacdbaabddabccccdacbbbbaddbdbccadcbdacbbdcddabddacdabdaddbaddcabcdabbabcccbcbccccacdbbabcbacadaaaadcdbdddcdbbcbbaaaacabcdaddabaadddcbccdabbaccdabbcccabacdcababacbcdcbbbbbcabacdbbddadabbabdabbdabdbdbdacdccabcabcdddadbaacdaaacbcbabddbbadbdccbbdccaadacbabcbdcddccbbacbddabcbbaadadbcdbbcdbbbaddcadaaabbbddcbbdadaadbddcccbadddddcbaddbdabdacbdcdaddaaaddccdadbacdccacdbbabadbdacbccbcacbaabdbbddbdbdbcdabdbbbbdcadcbaababaabbbacdcddbdcbbdbcdcbdcdcdbddbbbacabacbcbcddaccaaabbbdddcbcddaaacddddabdaacbccadcdbcdbaaccccdadcabddcdbbabdcbacccbcdcdbabbabdbddcabbbdcdbcbbcdcddbbbdcdddccbddbbdccbdbaababacadcbddcaddbbdacbbdadcacaddcdabdbbaccbcddcaddbadcdacbdcacabdbdcacdabcbdcbddcacccdabcabcabcbaadadbcaccabcaddbaabcccaaadccbbcdbdbdcacdcabbdadcacacaacbbcaaadaccabcabbdcbbdcadcabcdddcdbaacdaccbcabcdcdbaddacdbabddbccdacbccbcdddddddcdcbdbcbbbcccaadcacbdaacacadbadaacbaacacadccaadcaabbcbbdacbcaddbdacacbbadabdaabbccbcbdabccccbcbcbdcdaadccadbbccacaabcbbcbabdccdbdcbbaacaaccbacdbdcabcadcdacadbcbabaacaabcadcbbabaabdbcdcccbcaacaaaaadacbdaaddaaabbcbbbbbadabbabdbcccdacbcbadccbadbccbddcaaddadcaadcadbaccbccdbcccccaadbbbdbabcbaccadacdcbadcabdccdbdcacbdabddabddcccacbcddcddcbdacbbdcdcabccdbbdcdadbadadaaabaabdbcacccaaabdbcabcaaddbcbadddddcabdbdcdccdddcbbccadccccbbcbbbdddbabdddabdddcbcdbbababcaaacbbbcdddddcbccdacdddaaabccdabdbcadaacbdddbadccaacdccbbcadbcccabdbdcdcbddbbaabaacccddcdadddcccdddaadbcbccdadcbcddacacbdacdccdbdbdccbcddbcdbdaacbcabdcddddcbdbabbccdcbababcacadcdbbcdbdbccbddacbaadbbaacbccabbcacdcdabcdbdacbccadcabcaaacdcaaacdacdaabdaababbcdbbcdbbdcdcddcbaabcdbacbcddbbcaacaaccbddbbcbadadaabdabaccdabbbcbcbbacddbaaddcbbaabbcabccadabdaadbbabacddcabacccbbaacdadaacddbdbccddadabaccbcabaadbdbdacbbbddacbbcddadadbacbaaaddacdacabbbcbcdcbacaadaccaaabddacadadacbdacdddcbabbcbbadabbbadcadcdbcccaddcdaddbccbcabcdbdbccadddbcccacaabdbcadadbbdddaaadccdbbcabadadbcaccccaacddacdccbddacaacbddcdcbbdddcaddaccaadbbbbbaddadcbdbdacdbdabdccabcacdbaaccaadaacabcdaacbaacbddcbccbdccbcbaddcaabdacccacdacacdadbcbcdabcadcddbdbadbcaabdbbbddbdccbdcdcabcccccddadbcacdbadcbdbaadcacacdcbbadcaadadbcbadcacdcddbaccdbcabdaacdacbbcccddccbbdccdbcbbacdddccccbcdaabbddbbaadcdaacbcddacddabacdcdbdcbcbbabccbbaabcbabaabdbbdcbaccbbabbdccdcbcdabbacccbcbcdacddbccdbabcbccabdbacdbbbbbcabdcadacdaacbbcbbbbcacbdbbdaabcacabdddbddbadddababaaacadcbccbccaddaaadcadadaadabbadcaddbdcdbdaccbaababbbdcbdbdbdadbadacdabdbbccdaadcbadacbcaaccdcddaaddbccbbdabcdbbcccddbadddbbcaabababcddaddbddbbbabdbbcdddddacdcbbabddccddbbccbccbbdcaacdcddddacbdccdaddbcbbbcaccddaddbabcaacadbcadcadaccbaddaccbabddccdbadbdbbbadbaddadbaccadccdbcbcaabdbddadbdcabdcdbdbdbaadaaaddccdabdcddaccbccbbbadaacaacddccacccddaabcdbddccabcdcbacbbbaaacbdacdbbabcbcbdbcadddbddadddccaaacbaadadcbdbdbaddbcaabacbbdabdcacbadcacccdcbaabdcacaaaadccdacccabbaabadadcadaccacdadaaadcadcadaccbcbbabdadbccdbdbdaccbbbbaccdcbdbdabbccbbdccccccbaaaabaabbcbbcdcbdbbbbdcccddbacdadbcaaacbadccdadbdabcddbadaaaddadcbabcdaccbdaaddbcdbcddaaaadcdbdcdddddaabbcacabcbddbcacbbadaaaccccbbaadbdbcbaabccbbadccacdcbccdacbbbaacdbaaacccdbbcbcbadacbdcbccbdbcadaccbcdccdadcdbcbcdabbbbaabdbbdbbacccaccbcbbdbabbbcbadcbabbbabbcbcbcdabcbabcadcbabcbcdbccbacdadbaabcbdbdbcdaccabadcabacbadadbbababbddcbddcbcadbcdbababdabacbcdbbbcacacbcadbccccacdbbacbdcbacacbdbbaddaccbacaaadbaacbdddacabbdcbcdcaddbccacbdbdaaacddcdaadacadacdacdabccbdadbccbbbcadadaacadcddaadaccacacdaaccbccdddccdbacbbccbcbacdcbaacbbdadcaabccbacdacdcbccadcaccbdbaccdbaadcadcabaadcdbbaaddcbdbbcaddbabbccaaacddbbadaabcbaccdcbaabaddbbcabccbddcccdbdbbacccacdbdaabddbbdaddcccacdddbcaadddadccbddcccbaddcbddacababccdbbcbbdcaadcbcdbccbbbdbdcabdbcddddccdbdbbbccdacdcbddcaacdbcdcaccdababbdcdbcbddbddbcbbcbbddabcbbadbcddcabdbccabcdacacbbbabbcaddbdcbabcdbdabcdcdbbbcbddccbacaccbddaabcdbccbacdbdccccbdcabdbaaadddcbccacaadaaadbaacadaabadbcabbaddbddbccdcddbdadccadacdcadacadcabdbccddacbbcbcdbcbabbbcdbcbadccdbdbaacabbadbddddcddccabdabcdabbadddabbbdaadbccddddbaddddccdaddabcdddbdabbdaccaaaaadbdcabdcdbcadcaabcdaaacababddaaccadadbadbdaabbddbcaaaccddddcdbbadbbdaacacddbbabacddabbcabbaaacaaaacdccbccbcccdbaadbabcacaddaaadbddbdcabdadbbaddadbcbcdaacbacbbbdbdaaccbabcdaacdddbbddadbddccbadbacddabaddcbbcbbdabadbabbcabacdcbabaacdcabccadadcdbcadcdabccaaccdddcadbacbbacaccabdaacccadcdcdadadcaddbcdbcdaacddcdcaddaccaadbaccacdcaaaaabcdabadbbabdbadbadabcacbaacaabdddacccddbbaabcdbbabadaccbbaacdaddbcdacaacadaddbbbbdbabccbbbdbcdbddbbabaabcbadabadacdbbddabadcdabbadbbaddbbcdcacabaabcdadacacadaacbaadabddbdcadcabccdacdcbcddcadadcbdadbdcbdacacacabdcdcbabcadbaaaacdcdabacbcbcdacabcdbbadcaadbcaabccaadaccccacdddcbbaacccaaacdaddacbbcaabbbbccbdbcaccaaadabdbaaddcbccdaabcbdaabadbdbaddacdadabcdaadcacdadcaabacbbdccacabcbdbddccdddcaaccbcacabaabdababdbdddbccbadadbcdbaabdbdadbdaacdbdabbcbaaccabdbdbcbbaadcadcdcbbbabdbdabadbcbddcbdadccbadbdcbccddbadbbdcbdbbcaabcccddacdcdcaccaaccaaadabcddccbdadadbcadbcdddbbbbdcdbdcacacababdbcdddbccaacbcddaddacbdbcdddcccbccdacabbacadcccdcacdaabcdaaddaaabaddddbaaabccacacaaabbdcaadcccbbacdaabdbadbadcadcbcdbaacaddabccccbcdccdcccbcadaaddbdbdcdcdbdbbbadabcaaddbcbacbdacbcbaababacddcddcbaaccdaacccddccbdabaaacbbbdbabccdabdddcaabdbbbdcbacbcdaabaabacadbbccadbabbdbbcdcbcdccddbddcbcdadcdcabbdbcbacdaccccdcbbdcdaaadbcdbbbaddbaacbdaddcbdbcacaabacdddcdaddbbddccbdabccadaabadccadbaadaccabacbadacdaabdcbbbcccaddbacbbadbaacdcbacdcaabadbcbdbbaacbbaddcbabbcbddddabdccaadbbbddddbddcaddbadccbbadaccdcbcabbaaabbaccdccccdccdcadacbbbddcadbabcbdbcdadabbddcbacccbaddbbaaadcaadddbddbbcabbccaadbdaacbdaadadaaadcbaaacbdaaabdccddabaabaaaababcbdcccadddbdcabdbacaabdccdbbcbcdaacdddacdccddbbdadbbbbcaadcbbcaaccacccdaabcaaabccbcdddddccdcadadababbdddccadabacbacdadadddbaaccabaddacaacaddabbadcbbccaadabadcaaddccbadabdbaadddacddddcabbbadacdbdaaacbaabccadaaaccbdcccabddcbdbcacdacdbbabccbbadadababcbbbdacdadcbbbcbadadbddcbcbababbbccddcdcbddbbbccbadbaacadaaadbbbaccacacbbabcaadacaaadbdcaadbdacddcbacbbccccdabbbaadccbdbdccdcbcbbbcbcbdbdccddcadcaacbbadbddbdcabdbbcaaadbcdbddaacbcbadcadbcbdcbbddcbcaaadaadaccbcbadaabddbdbcabbddcbaabacdcbdcdcdbbdbabbddbacaaadbbabbbccabaaaaddbdadcdbdddbbcbbcdabcbdddddbdaabcdcaddaddbbcaddaacbabbbabddbbbddaaacbaaccdccbbdacadcacbbdccbcbdcdcbbddabbdccbddccdacbdabdcababadaddabadbdccacbbdacacdbdbbcaaabcaabacaaabbcdaadbadddddbbcbcabdcbbdadcbacbcbbbdacdbdcaaccbcbccbdbcacdddabaacaddcddbdcabbbdcacabadaaccddabaabbabaadcdbdbddbbbddbcadbabcbccaadcaccbdabadbcccbdcaccabcdaacccdcbbbbccaacadccbcbccdccdbdabddcbbbadbbcbcbdccabbdabacbabababbabdccadcababadbbaaabbbdacbdadcdabcdacaabadbbacabdbbddababacdbbbdddaabcbcaacaccacdcaaccdbcdababdabcccccdcbadaaabbcbcbcbbabbadbcddddddbbacabbdbbaabbadabddbbdbaadbdcddacaccabcdddbccbbbbbcaabbdbacbccadaabdcaabbdddcdacdabdadcbdbabbbaaaacbddcdcbcbbdcacbdcddbaadacccbacdacccbbbadbbbdbddcccbbacaadddcadccdbaacdcbaacabcaaaccdbddbdcdbabacabbcdacacacadbdabdcabbbdcbdcbcbacadbaddabdcbdbaacdcabbbdacaadadadcbcbaadabddbacdccdaaaaadbaddcdcadcdbbbdaddddddbdaacddcaaddcabaddcaddbddabbaacacdbdbbcaabdccdbacccdcccabdcbbdcddbdcbccacccaaabcdabdadbdadcddcbbddabbcaabbbaaacaaaddaaacbbdcdaddacbbcdbbcadbcdcacbbadacabaaaaabaacadadcadacaacbcaabccdbaccbadabacddaccbdcabdbbacbdbbaabbdacacadddbccdaccccaddcccaaacdababdaacdaabacbbccdbcdcbadbbdccaaddcccabdabcddcddbabacaddaddadcccddabbbaaddabaadbbccacabbdabacadaaadaccccbabcbdbacadacdbdbbddbdaaabcabbddccdadcddddcbdaaccbbadbcccbdacaabdbacddcbcbcadacbcadbaaaccbddaaaaadddcbbaaabacdadddaabcadcdcbacbbdcdbdacacabaadcbddabacacbcadccbadcdcddbdcbcbbbaddbddaccdcbbbdbabbdabdcdbaddabbababddaaaadabbbbcdabbdacacdabaacdbdcabdddcdbdcbdbadaddaabcdbabacdcdddaadbdddccbaacacbdbcbdcbccacccdaabccabbdcaadbddbdbbdbcdbababcdbdcaddadadacadddbdbccabbbdcbaabbdccadbadbbbcbacacdbbbaadbababddbdaaaddcddadaabdccdcdcadaabbbccbadcbdcbaaacbdaadcbbbabaaacbdaaacdcdaaaaadcbabdbabcaaaadadbabcccddbdccbccbaccdcababbdbdddbaacaaadabbbcadbcddbcdbbabdcdacdbcbadcdbdbbddbbadacaccadccbcbbdbdaacccbcadcbddcdacbbcbccddbdacadbdacdccadbaabacbabbdabacabcbacaaababccddadadabcdbcbbdbcbdbbbddcdcaaddddccadcdbdcbcbcbdbaaaaadddcdadbcbadbadcdbdcbadabaccccccddabbabddcaaccadbadaadcaabdbbacaababadabcbcdcccddbbbabcbdadaaccddcaadbbbcadcaacdcacadcbaabcabcacaadccbdddcbdccacaacbabbddccadcddabdabaaaddcddccbbcacccabbbbdddaacdaabbaadcabcbbbccdccbddcabdccccbddadcdadacbdaacdbdabadbbdcdadacaccdbccbcabdabbdbcdbbcdbcbcddbdbdabcccccbdbabdbadccbdbaaddcbabdbabbacabbdcbabccddbaadcbdcbcbcbdccdbcbcdccddadccdccacbadacaabacdbccccbcbcbdbaabaacddadcbddabbbdcadacbbcadbaaccdcaabcdcdcbbbcaaabadbcddbadbddabaccdaccabbcaddcadcadbbacbaacdadcbdddcdbaaacbcddcbaaabaabdbddbccdccbcabbbcddadbaacbcdaacbacccadabcdabccddcbbaacaabaccddacaddcadaadcabcbabbdabbacdbcbbbdabcacdbcbbcaadbabccdbdaaddadbcacacacccabbcdbaabdadcadbddcdcbcadaaadbcddbabadaaabaccacaccaaccbabacadbbbacddcdccddabdabddccdcdddabdcdacadadcbcdccbbbcdaaaadcccbaacaadbbbbabbcabcccaabccbdadcbbddccdccccdbcbadcbddccdacdbdbadddcdcaddbbacbaddbbabdcbcabbbcacbdcadbbdacbbaadcdbadabaacdbdcddbacdabdddaadababaababaddaabcaaacdbadddddddacdadccccbbacdbcbabcadabbacdbbbbababbaaadcbbdcdcccdbdcbacbdcddcacacdacaaccbacdddddabadbccbcabacddbacabbccdcadacdbdbacddcadaabbbbaccbabacddaabaddbddbbcaadadbcdaaacabcaabadcbbaaddcdbddbaccdbbbdcbbbbddcbccdabbbacdcbdcddabbdaacaccaccbbbcabcbcabcdcbcbbacdccabcbdabcacdacadacbcbccabdadddaabbcbdddcdcdacdabbadabdcdddbdbbdcacabcabcbdcdcbcbdccbdacbbbcaabcabdcdddbadbadccdacccabcdaaababdcadadddabbaddaacbcaacccdababcbbdccbbdadaccdcdbacbaccdddbdacbddcacbbbaaddcdaccdcbbcbacdbcbbcaddccbbabcbcdbacdadcaddcdaabddcdccccaadbdcabaabdbacabbccdcdbacadaccdbbabacabcdabbccbdbbacaacdaddcccaabbcdbbddadacbbacbbdccdabdbaddbcaccabaddcdaacdddbaccbcbcabbcdcccccbbbabcaccbddabcacdcbbabddabacbaccbbdccbbadccaadccbabbdddbdacdcddaabadacaddabdaccdcdbdbcbcaabddababbcbaaabbbbbccbdbddcacadddadcddabbacadbcbbbdcbcddaccbabbcdbcddbbbddbacdbadcaaccbadbaababaaacccaaabccadcbbbdaaccbadbcbcdccdcdadcacdadcdcabbcbacbccbaccdaaccddcbddbbcbacdbcaacccbdbadcdcddbabddcaccabddccaabbacaacaadcaaaccdbbaddcdcbbacddbcacbddacddcdccbdacacbacdbbaadcdabbdadababddcabacdcaabaccaaddbacbbdddccdcddcacbbaccddadcdbccacabbbdcabbadbdbbcdbbdcdcbdacadadabdccdacccdbcacccacacddcbccabdcbbbcdcbacdcbbddbaacdabdcacadabcdccbbdbddbcdbabacddbabbdcacaacdabcacdbbbaddccbddaacabbccaaddacbcbccbbdbcbddcbdabcdbcadccdbddbaaabbccdadacadcabdadabcbabcabddacdbaabdacdabbcaccaaacbdccdbcbacccaaabaddaabcadbbadbdadcdacbbdaabbaaaacddabbcdbbdbccdcbdaacbabbdbdcdbccaddcabacadddbbbdcaaaacbdabdbbcbabbcbdacdabbddcacdaadbbcabdadadcdacdaaddbadddbadbbcacaccccbbcdbbbdccbdadcbddababcdcdcadcbabccadbcccdcadcccaccacabadcdcaadbdadadbacabaccdcbdaaaccaabccdadaaaadccddabccdbcbdddaaabaadcacdaadcbdbacabcadcdddcbdbcbcbaccabddbcccdaccabbbdccdadcaabcaaadcbdadacacdaccddabdacbcadddaddbbabcbddadbdcbcccbdbaacbbdbddbbccbbbdaaddabbacbaddcbaddccdacadadbabbbcdbcaccbcdbbccdabbbdacdcabdcccacdbbadddbcaacadacdbbcabdcdcddaddbcbbcaabcadacaaddcbadbddbadbdabdadadbcccaacdcccdcbcabbbccdbbccdaabacacdacaabdbcdcccdabdcccadcdacbacccaacababdaadbddcbbbcddaacbaddccabdaacddaadcdbcadabbbbbbcbcbabbdbbcbbbadbdbbcbacbdabdcacabcccdbccdbadadbadabaddbddacdadcabbbcdcdcdcddaabbbacadddbacadbabcbbbbbacacdcdabbcdbbacacdcabdabadaabaaabacdcbbdbddcabcbadbbdadabacccbdadacbacbaccabddddbdcddccdcadcbccbcadaaabbbbdcdabdbcbbdcaacddbbabdcababccdbcddddaaadddbcacbbcabadaabbdcbbdcdabcdcdbdbadccbcccdababbacabbaabaccbddbcdaacccaadbbdcbddaacbcababdabdbddbaaccdcddcdaccdaabdbdcdbbccaadbccaacdaaadcbbaadbddcbdadccbadabdadbccddddbbbcbaabaabbcbcbccbbcbbbbdaaccdabbdbadcbdabcbcbdacbadacaddabcdcdddcaddcccdabccabbdbcccddaddccaabccbbaddacdcccaabcdcaddccbbbcacdbdacacacccdccbccdcccdcacadbddabacaacdaabcbdacbcacbdadacbdcdabbcddcbbcaabcdddabddcddadbabcadadcbccadcbcbadabbaaabbaddcadbdbacadddbbdcddcdaabacbccbabbddabccaacbcaadcdccbcdbbabdadbadbabadcbbcbacddaaabbdadbdacacbddbaaabcbbbaadbdacbbcadcbcbbcacbbbdacaabaccccacdddddbbbadaadabcaddcccbbbcddbddbbbcbbcbaaacacacddbbddccbbbbcbcacaadddbcaadabdcbcbdcccabbcccadabbaadcbbdbbcacddacbbccddcbbcdccddddaaacbadbabdabbbdaccacbdcdcdbcadbbadcbcabccbbcbcaaddcbcccdddbacbdaabdcacaadcadadbadbacbcccbbdaadbddabdaadccadddbdabdcadbbcddaccbbdcaadcdddacacacccbcbdbbabadbabcbccdbdbdbabababbbbcbcacadddaaacccacabcccbcaadaaaadbccaacdcbbcdcaabdbbbacaabcabdbacacadccbadbdaddaadcacabcbccdaaccdacaadcbbbdddbbccccccdadadaddddccdacbdcbcdbbcacdbabbaccaabccbccddcdcbddacadadcabaccaddbbababdadcccccbabcabdbccddacdccbabacbccbdacaaccbdbbdacdbababcabcbbcaddbdbbbaabaaabaacbdacdcbabcadcccaaaacbaccbadaaddbcadbcbbddbcdcdbbbcbddcdbcbbdcdcaadadcacbcdaddbccbacdcaadabccbbabcddbaacdaccdaacddadbacadacccacbbcabacdcdcbccababcacbaacdcddcccccdddabdacbddbadbccdddddcdccdbcdacddaaccbdaadbbccdccddaadcdacacbacbadaacbcdcbbacddbdcabcbddccddcbbbaddbabddbcabbcaabdcacbddcbcbaaaabcbcacabacbddaccdadddbbddacacaaababaabcabbbcadbcccacdcacbaccaadbdaabcbbcdbbbcdccbcdadbddddbccddcbbaaacdbdadabacbbccbababacbbcccdadddbadbaccbaabcbcabacbcccbbaadacbbdbdabdbcacdaaddadbbbcabccddcdbacdabbaddabbbbadbabccdaaaabbabadadaabdccaccdbaadbaccdcbbdccdbdabddbccadadcaadcbcdcbbbdbcabaccccdcacbadaacbcbbdaaccbbcabcbbcbdabbcbcdcbdbdcdbddcccaabbdbbbcbaaabbcbcaadcbabaccbacabbadbdbdadabdbcbaacacccadcacaadacdabbacbbdabcdaacabccdbacaacaaddbabaddadabccadbcbbadacdbbbdbaccbbaacdbbbcaabaadabdabcdbccdcbadddcababacdbbbbaddcbbadcddacaddadcdcbadbccbccbcbcbcbaccadbbdccbccbccabdcaadcdbaaaddbabbbabacccacabdcadacccacdbadacabddbccdbdabdcaabcabcacabdddccbdddccddddbbdcdbcdcddbacadbdcbdcaaabaddbbacacbaccbbddddbacbbcbcaaaccacacddcbbabdbbddaccdacdcddaccddbacaccaadccabdccccdcbabdcbccacddbcacabbcdbbcdddacdcacacdcaaaccaadbaabadcaccacdbcaacbccaabccbdaaccabbbaddcddddbcccdadaabaadbabbdaabbadaddbcaadcbcadddaccacaabcbadbbcddccadadcbaabcdbacdbdcabccdccaadbbaccacaadabdaadabcabccbabcbababdddccdaddbabbadcadbbdadccacadcacacbaaddcddbbbabdaccbbbbacaacdaacddabdcdbbaacaaabaddbadbcacdaddacdbaacbdbacdbacabbdacbaabcbbcccdaacdddcbbbadcbbcbaadbabdbcdbbdbcbadbddcbacccadccdcabdbcdabcbddbcddbacbbbcdbbdbbbbdcbdadcdabbdbaadbdcdcaacddddbdbbccbadadcdddaccbccbdbbcdcbccbaacbdddaabcbbbacaccacdcddbdddddabbaddabbddccddabdaddccadcaabaddcbdccadbacbdcbaaccbacdccadaccabdabbbacbbadaacddaacdaabadaaadbaccbdccdabccaadbcccccdadcacbbaddddaadaacdcaaaccbaacbddbbbbbaadddacdbbdccdbdaabccccddcbbbbcbcaccccdbadbdbabadcddcaaadabcadadaacbacdbccdcbbbabbcdcdbacccbbbddbabdcbbbdddbacbcadaadbbbcbcbbaabbbddbdbdccabbaabcaababdacaabbccbaadcdcaaabdadcdadbadababbbabaadcaadaddcabbdbbbbbcbcdcabdaaacddbbbcdabaccabbdbdcccbbbaacbdcaccacccddcaccbbcddbbdaabdbbcdbbdbddabaaccbdbadaaabcaadccabaddbcbccadbabcadbddcabbababcdbcabaccdacddcbdadadcdbcadbbdddbdcbdddbcaacabdbabacddbabddddcaadcccddacbadbddbacccddbababbbaddabdcbbaacbdabdccbaacdaabdbdbbdaadacdbbccacbddbacaabcaaccdcadaccacbbcdbdcbdbcbaaaadacabcdddcdabcccbdcaadadadcbdcadaddbcccadaadabadcdabdadacdaadaaddacdbbcccbbdbaaadbadbaccbdbccbbcabaaaabdbaddabcccdbcbddbddddaddbdcbdcbcabbacbbcababbcccbbaaaccaadcbcdacbbabacaadcabbbdbaadabbcdbbbccadadadbcabcdacdcbcabdabbcbdcbcbddbcadacccdcdcdacdcdadacaaaddabcacacccbdbbaadcbdabcdbcadacbbbbdbabdcddbdcaacbcdcddaadcdabbcbdcbaddbddddaabddaadddccdaacbdaabcbbbadbaabdbcdaadbcdcdaddddbababcabcaccdcbdaadcddcadcaaddabadcadcddadcbcbdacdacbbccddacdddcccbdcaccaddadbdaacbdcdabddadaadaaacabdbbaaaccccaabaddacbabddcabccaadcbddbabaaaaaddacdcbdcdbbcacbcdbacbaabbcdabbbadbcccdabdaccacaaccadcacdbaacacbbdcddacabaabbdaacdbcccbaadcccdcbacbbabbabaacbabdadcadcdcababcbabdbdcdccaadabdadccbadbcaaccacdcbbbcbdccbcaddbdbabadbdcbdcaababcaddbbbadabcadacdccbcbdbadcdaddcaaadbdadabadbcbdacbccbbcbbdddbdaddccadaaabbdacacbcddbacabdcaacbdbabaccccccbbaabbbababaccdaabbaaddddddccbdcbaddacbabdadaacacdcabcbddccbdabcbbcccdbabbccdbcdbddbbdbdcbcbacabbbcdccdbcbccadacdccbaacdcdddbbacbdcadaabdbabcbbbacbbbcaabaaacaccdaacbbaadcdbccadbdbbadcabcaaddaabddbbcddcddacddccbcbaddaacdadbddcdcaddcbcacbbacbabbdcbcadcaccddaabadcdadddbbcdddbaccdddbcdccdacadcddcaccaadcbacaaacdbabbdcdbcbaacabaaabcdbaabdbccbbdcdddddacabdbcdccccddcacacccaadcacbdaccbddbcaacbaaacbabbaccdbabddaacdccbdacbabcabbacbaacbabdbccccbcbabaaadcddbcbbddbdcacdddbbadbcdcccbaccdcbcacadbbbabbbbbdbbbbdbdbbbacdaadabbcacbcabaaccaabadcabaadacacbdcaaccaaadbbaaaaccbbccbbdabbdcacdbbdadcccddccdcbddcacaaaadcdbdcddbdcbcaabcbdccbaaadadcbdcdbddbcaabbbdadbcadcacddacabccdbadbaacdcaabcdbcbdaabcaacbdaddbdcbcabacaadbcabcdaaaadbbbaddcbbcbddcdacccabbbddaccdcaaaccdacabbaadbacdcddddabbbdaaacbccbdcabdcdcdbccabbbbbcbaacdcbdbabdbaaacacdcbbddbcbbaddcbcabbcbadabdacdaaaabaddddacbbdddaadbadcdcaacddbcdbcaaaacccbaccbddcdcdbaaabddaaddcdbcbccababaabbcdbbababadadcbcabcaabbacbaaccdabbccbdcadacaddbadadddbacaacbcdaddbccbaabcdbdcdabdbabcdbabddbabbacbdaadccabcdcacbdaaacacdddcabadcaadbadddcbacddaddbcddddaadddcbcdbccddabaddacbccbbbaabbdddbdbdbbbabcddbaaadcdacbbbcaaaccbcddbcccdccdaacbbacbdddacabbdacdbadaddadcccddadccbbabdddacdbdbbcdbaadaacdcbddbabcbdbabadbabbbcbbabcdabcbdababccddaabbabdcbabbbabdbabddaadbcabdbccdadcabdbdccabcbabbabbdadcbadcdcddbadbcbcaacddbbabdbdadbdcacbaaacdbcccbadddcdaacaddaddcabaaaacabbcaaaacdaacbbcbdddcdcbadcdbcadbabdadbccdccdacadcaabdbcccdaccbbdbcadadcaacdbbabddbcabaaaadbcaddabbdccbaadacddccaddbaaadadbddaddacbdabdabbcdbcdacabcadaadcacbdaaabdcacccccbadbabcadaacbacacabdaadacabdcaaadaacaacabcaadbbdddccdaddcbdbdccacccaaaccaaccbaadbbccbcdbdbdddcacdadcacbcaacccacccdadabbababdcddbdcccdcdadbbdadbadbbccbcdccabcbcadcaabcdcddcddbbadabbbaadbdccccccaabcacdabadbdbaaadacccbaadcadabdbbcbdacccdcadadccddddcccddcdcdcaacdcabdddaadccabaaabacbabaabbadabbdbcacbadcdacbdbdcaccabbcaaadabddacdadaadbacdbcdabddcbdcdcbbabbcbdcbdacacadacbabcaddacbbacacadccdcadbcddddacdbcacbadcdddadcbccbabbaccbbabbbcaadddcdbbabacdacddbaaaadcbaccbcbdcbdbccabadbccacbaabaabddcbddabcabbadacdaacbbbddbdbcaabadadadbddcaaacaccbbadbdddcdadbbddbdcacbbcbbcddbcdaadbabdddccccddaaacdadabbbdbaddabbcccabcbddbcbbcdcdbbabaaccddccbcbcdccccddbcadcabcabdcdbddbdabdabcbdacdaabdddddcadabcbaabcdaacddcaadcdbccccbdcbddbcccdbabacbccbabdcdadadbdabadcdbcaddcdcbacaadbadddbcbdbbdcbddbadccdaaabbbaabdaaabdaabcaddcbcbcababdaddcdbdbdbbdddcdbbaddcbaccdcbccdddcbcccbabcabbaabadadccacdbcabccbdacbcadcccabddcaaccbcbacdbbdddbdabcdbaaddbbacadddacaacbbadbdccaaccaaaaabddcaabcddbccddddacaabdadbcdadbdcaacbcaccababacdcaaaaadccbbcdccbcbdbaadbabcdcbcddccbcacdadabcdcdadddcaaabdcbdacaabacbcdcadbaaaaccadddcbbdaabcddbabbaccdabcbbcdadcadadbaabbdbdccbccadbadbbbacdaddcacacbcabcbcdddddddcabcbdacabbccabadbabaccdbacbccbbcdbcaddcaaaadbdddabdabadcdaaccabdcabcdcaadbadcdbcbcdcbcddabcbcacdcbacdcaaaabdcdbaaacacdaacdcbbdaccdbcacbbbaacddbabdabcbadabaacaadcaacdadbaabbbbcbadbcdccabcdccabcddaadaaddbdddddabcbbbabdbbbbadadccddbbacdbcaacbcaabacbbdccdccbcdccabaccadbcbbdddcbdccacccabacadbcabbcadadadcccaacddccccbdbadccddbdcddcbdaaaddaddaabcddcbcaccdaccacdbdcbbbdaabacdbbbdddcabaccbacacdabcdccdddaccbddddbabcabccccaadddcaaddbccddccbcbacbbbaacbdaaabaacaaccbbcbcbdcbbacbbdccabbcbbbbccdacbbdcabcadaccccadbbbcadadcdaaccbaccbdbdcddbdcabbdddddbacddaacdbaccdddbdbdbaccbcdcbcadcbddaaabadbcdcdaccbbdbcaaabdddcdcbcadacbbadbdcccacbcdaabddcabbbccaddbdacbddbccacbbaacdaaddbabcdbbcaaaabdcabdacdaccbaaccacbaccddccdccdabacbbdccabacdccabcbbabbabacddddcaaacbdacdbcbbbbdcabcadbbbcccabbbabdcddadbcabaaaccbcaccacdcdabdbcbacbabccabbacdcccbdbbdacbcbdcbbaaccabddbacccdddbcdbacdadacaabcaabbdcdcbdcccbdccbabddbdcbcdcbdcaddddababbbccabddabdccababacbbcbbabcddcaccbaddbabaacacbdcdbddabbbdacbabaddbdacadcadcbbacdbcccbdbcdbdaabdabdaacbaacbddbcbdadaabbadadccdddddcdbbccbdbcaaabcbdbacaaacbbcadacdddacbbbbaaddcbbdbdbbdbcdaabccdbdcacbccabcbdddbdabadbaccccbdccabdbcbcddbccccbcbdddabaadaababbccaacdddaabbccdacadacabcbaabcdcaacdadbdacaaadbcaddcacbccccdddcdcbccddadcbbcbcccddbdccdddaccdcacabbacccdabdabccadadbdabdccdbabdbadcbdabcbdcabcaabbaabacbbcaabadcbdddaabbddaaddacaddbbdccbadbcbbaadbdbabbacbccacaddabbbccddabdbdbcdacbdcbadcdbaabddbccdcabddccdaadabaacbbbdadbaddbcbbcddbdaacbdcdccdababdababdadaababdacbacccbabaabbcdbacbbbbbacaacaaccbbcbdbdaccdddaacdcbcadaadbdcdcbcaabbdadddbbbcaccdaacddaddabdbadbbccddbcbacbbcbaadbbbbcdbaaaabacbaadaddbcacdcbccaaccdcadcbaccaaadddaadbcabbaacaabababcbacdbdabccabbcdccdddbdaacabcdabaaabababdbcdbcbccacddbabcacdbbcbccaabbbdbadbbcbbcbbaddbbcddccdacabdbacaaadbbabcdbdadcbcbbbcbaaadaddbdaaaacdbdcbdcbcccdbddccacaaddcaaaccdbcccdddddcccddccabddbddbbbbcabddbcddcabcaacdcdbccbaadabdbcdbcbcbccbbcacdcdccbbccacdcdbaadbabdbbcacdbdbcbcbbdcbaaacdacddbabdcbbabbcdaacadcbdddaabacbbccbbbcdbaaaccbbbdbddbddccacabccabacadddbbaaabbbadaaababadaaccbbbccdbbdaabdddaabbabddaccdbdbcccdcdbbcccbdbbdbbbbbbddcadcacdcbcaaddbcaababbbbcdbacdaaaabdddabddaacadddbbcdccbbbcaccdddabababcdcbdbdbbdcbdcccbbcabcccdaadbbbadbadbcaadbdcdccabcacbbaaadcbbbdccacbacbbaccccdaabacddddccdcdaddbdbddcdbbbbdadddcdadddcbbaabdacaadccdbbabaabaadccbccaccdddbabcccdccadacbcbcadcbdddcbdbcbbabbdabccabddaacadabbbccbddcbcadbbadacdadaacdcbccbbabdacaaacbcaaabdcbccadcddadadadbcbaabadbcdabdacccddbbcacbdadabcbaaddcaaacadcddcabadbdcdcdadbabaaabbbbbcadbaadddaacdbbdacacbaddacbddbcacddddabccddaacdcadbddcbcdcadccccbaccbdbdcbbccdbbbcdcaadddaaabdccddacdcbccbabdbdddadacadcaccbcdadbbdbcddaadbddbbaabddcacaababaaddbbcbacbdbddccbdbaabcbddddadcbddcbcbccdddbdcabcbcbcddcadbcdbbaaabccbdbddcbdaccdacbdbacccaddcdabdbdcbccdbdbbccbcacabdadbcbacccdcadbbbaadccddcbadabccacbaaacdaaaabcacddccdddcadabaaababaadacdabdaddabcabdbbaabaacbbabcadcddacbddbbacbaabcdadcacadccaacccbdaabacaabbdddbacbbdbacadbcbabbbbadacbdbdcdccbadbcaaddbbcccbbbbcadccacdbacbcaabcbcbcdbccdadaaadbdddbbbdbbdcddcccbddcdcacacdcaaccdcbbdddbbcbddacbdbdbbadaadabdbbbdaaabccdbabbbcddddddcaabbdbbbaaaaddacdbbcccccdccbddcaadcaacdddabdcbdaccbcaacacccbcbabddcccdddccbcaadadacccabcaccacaaaadcdabdabccddbaacccccacaaddcbddcbadccccdaaabccabdaabadccabaaacbddabaacaacbdbacabbacaaccaaabbdbccdabdaaabccdaadbabdccbcdddccdbbbccaaddaacaabbadbbabcbcdbdadbbcccbddcdbddcaacdaabcadaaaaaddaccbaccabdbaaabbbbbcdcdadbaaaaabacbdccbdadcaabadacaadcaaccbcabbdadccadbcdcaacbdcbabacbcdbbccbcabdabcdccbcbbadbcdbcbdcddcadcbdabdbccbcbcbcbabccccccadcbbbddabadadabccbbabcbbbbcaccbabdcbbacaaabaccccadcabbaccaadddbbacdccababadbaddbdddababbbadbbcccabcbdadabccdcbddbdaccdbbbbbdabccacacacdbaccdcabaaaadcccbbcacddaddadcdddaccdbbbddccbdcadbdbcdbcabcbdddbadcccbbbcdccabcbdbdbddabbbccbcbcbdcbbdabbbdddacccaacaadccdcbadadcddcddcdbcbabdaacabaccdacadabcbbbadccbbccdcaaccddbdddacbdbbcccabaadadbbdababadcaacadaabdabaddcccaacadaadccdcdbabdbbbabcddbcbbabaccadbdabdacabcdaaadacabbdddcdbaacacbcacdcdcddddcddcacaabcbadbdccdbbcdacdcadcbcaadcdadcbabcbbdcadaaabdadddcdcbcbbdbdddaddacdcabdbaaabacbbcabbbcdabdbccdddbbadcabbabdcbcbcdddbbabcadcbbbcdbadbddcdbcbacbbdaccdbbbdcbdcccddccbabbdadcadbcaabddcddaacdabddaddbdddaacacabbccbbcdbcadacdadbabadadaddbddbbbadbbacbcddddadbdccddcddbcacacdbdaacbbdcaabcbaddabacddbcdbbcbcacdccbcabbddbaadbdbdccdcdbbbdccaabbbacadbaaabddcdcacbcbaaabccadbaccaccadbbcbccddabccddddcbddadaacaccdcacaaaaccbadaabbdabbbddbdbcabccddabbbdcadaccaaddaddcdbbaacdcacaccabcbddccdaddabadcbbbdaddbdcbbbadbcdaaababdbaddaddadbcdaccadaaababbcddcccdbbcadadcdcdccabbcbbaaadacccbbcbbbddabbccbccaadcdcaadadbddbddcaacbdcbbcbadbbbcbabacccbcbcacaadbcaacadcbbdcaacccbbbbddddcdcacadddbcddbbccadbdcacdddcdadcaacbabdbbcadaadbbcbaabcdbdadcbbdbdababdcdbdbacbaabbbccbacbbccbbcaacccbcbdcbdddddbddbdbbabdbdbcddddcbdcaacaccbcbdabcddadddaadcacaaabcabbbabcaddbacdababbbdcdadbcccaadbdacabbbcbcbdcccadacddccddccdbdcdbccbdddaddaaaadbacbccbcabbbdddabdadddaacaabbdbacaadadddaacbcbccbabbdbdbaddcaadaacacbacabcdacdadcdccdcacbacaacbdcaabddabacadbddbbdacdccbbdddaddacdabcccbabbadaacadcabcdbbdddbbaadaadcabdaccaacbbdccdbcdccdcbcdaaaccdbdabbdbdddbcbaabcbabdbabaacddbbcbbabdcadccabaacddbcbbcbadccbacadcbbadcaacbdbcccaabcbcacdcbabdbdbccbcbbbcbcadcbbcbbdaacdaaacddccbcbacadbbcdabcdadaccaaadadccccdddbaadbddddbbcccabcdaadcbdcaddacabaabbbccdaaaddbbdbdcbddbcadbccbbbdbdcacccadacdcbcdaaddabcdcaabcdddcbbacbdcbbbbdaadaabddbbddadccccbaabcbdadbdbcbbdcacdcdbcacaccdcdbadccacaaacbcbadcccacbddaaababbddaddbddbbaadddcdabbdccadcacbcacdccabbaabaaadcccddcaaddadbcadbdadaccbbcbcacdbccadbddbbdabdadcdcabcbaacadaaabdaabaddcaaabcbbbaadbccdcdbbbbbbccdacccccbaabaccbbdccddcddabdddaccbbdccddccdbbdcdbaddabcdadcbbdcbdbbacadababbbabccbaacabdbbccbdacdcaaaaaddbdaadaaccadabdbbabdddccdddadcbaccabbaaacbaacbdbddbacacdcabbdddacddcacbdbdaddcdddbacccbcdccbcadddaadbcabaacbbdbdddcabbdcaddaacdbccaaaacbbdddacaccddcdccbccadcaabbbddacdaabbbbdacadcabdddaddadbadcbdcaadbddcdabddbcbaaddadabdacbadcdccaaababbbcabdbacadcaabacacbaacadaabdcaababbcaacbdcabbacdaadaacbddbdbaaabddcbcbadacabbdccccdcdbacabdddadaabbcdbabbbcdbaddbcdbaaacadadbacddbbdcabdacddababdaccccbdbcbcbcadcdddbcbcbcddaabcbbdacabdbddabccdcccacdadcaaadcaddddcaaabaabcbaaacccabbbbadbbaadcbcbacabcdcccdabddacddcbacbcbcddddacbbdbbdadaaacbdbbdbcbdadccdcbdacddaacccabacdbcdcdabaadbcababbdadbacadbbdbbbacbaddacbbadbbbaccbbacadcddadaabcadadcbbdadabdcddddadbcbaabdbbadbcabbdcabbbdbcdbbcbacadaddcaccaabdbddacbbdbcabbcacbbcdcbdbabdadaadbacadaddabccaabcdcbcbadccaacaccabaccaacccaaaaddcdcbbabdacdbacccacccdcbbdddaddabababcbddaadaaaddbbcaacbbacacdbaabcdcddddbbcbcdbaccdddcaabbabdcbacbcbccdbaddbddaaddbcbcdcadabbabddabcdacaacbcbbccabcccacbdadbaadbbaabcbccccacbabacbbababddacdcacddcbbadacaccbaaadcbdbdabdccbabadabbdcdaccbbddacbaadcaddcaddcdabadbbacacadcadbdccaccadabcabcbacbbbdbcdabddcdabdbadaaddbbdacadbcddcbcbcdadaaddbbabdbbbcacbcdbcddddcddcabddcbbdadccbcccddcbcabccacccbcbddbdabbcadbcacadccacdcadbddcdcccccaadbcbdbbbcdddbdbbccddacccdcbabddbddcbcabbcbadabadbccbbabbadaaacacdababacccbbcbbaabcbddaccbbaacabdcacabcdadcdcabbcbbbdbcddcdadbbaccbbbcbcccbbbdbdadcbbdabdbcddbcdabddbbdbcccdbacbcaccbbdaddbbbaabbdccbacbdcadaacadcccadaddcabdbabcbcbdbccacaadbccabaacaacacddacacdaadaadabdcddcdccdaaaabbcdacdbbddbabdadcababcddabadcddbabadaadddacdaabdccbdddaacbbacaadaababcaabcbaaacdabbbbaadcbcabdacddaddabaacdbbcabaccdddccdcddabccbcabdbdccbdcacdccaacdddbcdcbbdcaaddbabbabbcbbabbacdccbcdbcacbbadaadcdbcbcabaaabaccabddbbcbccbdcccacacdcaddcbcdbcdaaaddcdaaacbcbcacbccaacbccbaaabbdaccaaacbacbddbaaddcabbadbcdaadddbacadadaabadaccbcadaacadccbaabaacccdbacadbbaadddcdcabcaddbcbcbcdabbaacaabbcdddbbaaaadbbadccadddababbcdbcddaacbabbccdabccaaadabddcacdbabcbdcdabbbdbcbcacccaaabadadccdbbdaaadcccadcdadbbbabdbdddcbbcacdcadcaacbbbbbaacbdabcbaadbaaddbbabbdadcccbcddbaaaabddbbccccacbcdaabbabbdabdaddbcadaadacbdbdcbbadbaaddddbdbabacadbadbccdcadccaadcccbbcbbdcdbadabccdabcdcbcccdadccddcbbccbddaccadbbdddddbacbbbcdcbbabcacddbcaaaabdbdddabaacacacbccddcdbccddadabdadccbdbbddbbbcacddccbdbbdacababcdaddcbbbbadabdcbccadccdcbcdbbcbdaaddcdccdcbdccdbbbbabaabbadddbcadbbbdabaddbbcadbbddcbcdbdcbddbcabdcbbddabcccbbddabcddacdcdacbdccabddadbabcbcacbadadcddabdcbbdacddaaabddcddcdaadbabbcaabbdcdcbdcdbcdbbdabdbdaaadcdbdcbdbdcbbdbcbdddadaaacddaacdbccabbcabaaaacaccbbbcddadcaddaadbaadbdcbabaddaaadccdcacbddbcbababacaaabbcbcadababcbaabdadbbccddcadbdbacbcbbbbbbabbddadccabaccdbbabdadadacaadbabbcbbbcbbcbaabadbdaddaddccdaabcdacbcbbcdcaadbacacbdabbbddddadbbbdbccdcaccaccaccccdacbbacaaaacabdcbdbcccaacdabaaccdddcddddcaddbabddbdacbbcacbbdcadbbdbdadbaaadcbabdacddbcdbabaacdccbacaddaadbbbacdbdddbdcadcbbccbaadcbcbdcccaacacdddccacbccbbcbdcbadccdbbbdadbdbcaabcdabacddadccbdbcabbdcaaaccadbbddaaddaacadccbcbabaaaccabddbcdcacccdcabadabbdccaacddcdcacdaadccbccccacaaabcbcddddaabdabaaddbbbabbbbbcbacaaddaacabaaddabbbcadccdcaaccdaadbbcbababacbbdcdadabadbcdcacaaaaaaccbcccbadadbdcdabdcbadabaadddaabbcbbababaaccbccacbdbcbddacccadbdabcddbadcaaddbdbbacbaadaacdadbdbcdaabdcadbddbabaabdddcbbcbcbdbaccbaacaadacbcbaaddbaadabbdccdcdcbabcabaaabadbabbaaadacabbdbbccacadbabadaabddabbcbccadaaaccadbdaccddbccbcabcbcccccaababcacbddbccccdadcccdabcaaaabddcbacddbcddacbdcadaaadbbccacbcdccccacdbbdbcbcbdaabdadcabadccbbaaadbbdaaabccadbcdcdcdacdbacdcbaacccddddccdbddcbbadabbdbddacacbcdbaaabaacddbcbcbdbacdabbdacaadcbcabcbbbcdbabbbcbabdddccabaadbdabcdcdabcdccaaabbacbacbdcabdcbbdabbbaddbcdadddabddaacabccccbddbdadbacaabdcbdcaaacccdcacdaadaadcdcaabdbccdbabcdddcdabcdddcdcabdcabadbcaddaadbadddbadaccbbabbcaabaccdbcaddadcdddbddacaddcccccbbadbbcbdacabbdaabcacbddbcccdadabdcabdacdbddbcadaadcbcbabaacacdaccdccddacbcdbbcabaaabdaabacbdcdcbdcdcbbddddadbcddaaddadabcacadbddbdbdcdaadcbadbcdccadabccbdbabdddabdadabcabacbbabdcbcadccbbcadbabacdacdcbccbbacabacbddccdacdacbcabaadacbbbcddacadabbabdaddaddbdbcdbddcccadcabaacaadabbcdbdbbdbdddcddcbddddbccadadddabcabcadbaadadadcdcbabccbddaaacdbdabbddbcabdacdabddadcbbbccadcaaacddbbaadaabccbbddcadaadddaaabddadbcadbadadcccaaaabbcabdacacacbbbdadddcaacddbcdbdbaddacdabcaadabbcdbaabaabbdbbdbadaddddbcbbcdadcbcdbcacdccadaadbbadacbccdbaaabdabaacdbbccbdcacdcbadbbbccbbdabbcdbcbdcabadcbbcacbdcbbbbabbbccbacbbabdcccbbcdabdbacccdabadbabdadaabcbbbcbdacddbbcaabbacbbdcddbdabcbdacacaaabdbadacadacadcdcddaaddbcdcccdacacabccbbdbcbcaaccaaabcadbdddcaddddaddbdccbdaacddaaadcdaadacaabdcbabccbaddcdcddabddbbabbddadcbadaacccccacddbbbbddaddcbacdcacaaadcbacacababdccadcaccbcabcaacaacbadacacbadccddbddaddacadcdbbddbaddaadcbddadaabdcddaabacbbdcccbaacabbcbdaaddcacbddaacddadbdbadabddbcbdcdbcdddbcbdbcddcadcbacbbabbdbbccbdadddbcddbcccddbadcadabadddcbbbcbaabcaaadabcccabbaaaadadabacaadabdddabbaddaaddccbbaacdbcbacacbacccbcadabacbabacbadcdddcbdbcaaadaacacdbccacbccdcccadcdcdcbbdacbabbbbacbaaaaddcbacdbabddacabaabbbdabcbbcbadaabbddcbaadbbdbdddbabcbdaabaabaccbdaacaacccababcbdadcaddbdbcacbddcdadbcddbaaabdcdccacdacbdabbabbbcacbcbcdabdbbddcadddcbdbdababcaaaccdacbaabcaabcdbaaaadbadbdacaabcadcbcbbbbcbbbccdbabababbaaaddbbacbbaadbbabdbaabcdbbbadabacacbbbddabcacaacbccaaddddbaabcabdcdcdbcdcbadccadbabddcddbaacbdcaaaddcabaababddddbabdabbbabacaccbcbbabcabcbaaababdabbbbdddaaccdbbabdbabcdddabcddcdabdcdcabacadadddbbdbaccdcdaabcbccdcdcdacbabbcdccaccacbdabbdaccaabbddbcaacdcdccbbdcaaddabdbcbbdcdcaabaaabdccbcbbcaaadaddcabaadcabadbdcaddaabdbabdbccccdadbddbbaacccdcbcaccbcdbabcddcbaabdbadabdbdccddadcccbabbccdaccdcdcdcbabccbabdcddbadcdbaaccdcbbaddbddbadbcddaacdabadbbabbccdcbdccdbbdabddaccbcdbaabcbbddcaccdbddbdbbdaababbabdaaacadcadbaccbcadddddbacdaaabccbabccaacacdaaadcdbbbacbdaaaabdaaccccbababcbabadbbbadadacabdddaaadcddcdcbcdbdbacdcddcdaabbdbbadaaaabcadaccbaababdcbdcacdddbdbdbacdcbbccbcbaddaacddccbdbdbbaadcbcabccaadddbcbccdadaaaccdaaabaaaccdaadddcaccdcaacacbadbbababcbbcbbdbbdacabcdaacddacaccdaaabdcddaddcbddbcccbccbbaacbdddbccbdabbdcbacdcabbbbccbdccbcacaddaaacabdddcdcbabcdcadbddadaccddaddaaacdacccddbcbddcbdbdbcbacaadcacbdcddccddcbcdacaaadcbbbcbaaaddbcdbbbcdbcbdbdbdaadcacbabbabccabbddbbccdcbadcabdcbdbdbbdbbcdabdcdcbcbcdbbbccccbcdcdacaccbbbbdbdccdbbaccaaadddcddcaaadaadddacccdcaaccabbccacdcbcdbabbacbadcadbdabbacaaddddbacadddcccabcbdbbddcaacbccababacaaaaacacdcabacccaaaabaddadbdacbbcdadcdaaddaaabcbacacaaaccabcdbccbcdcccdcbbdcaadcdddcccdbdbdccbbabccacabdabcdddababcbbcbbbacdbdcdaaaabdcdbdcbaddbdbbcbaccbcaddcdcdbaddacbdcacdcdccbbbadbaacbaadadbabdbbbbccbcaaabaabbadcacccacdbaaadadbadcdddaccaddabaddcbcaaabdcbcadbdbdcabacacaabbbccbaaadbbdddabcbadadcbadbbbcbcddadcacdbcbcadbdaacdaacaabccccdbbbbacacbbcabcdcadcddadddaaadbaccbdcacadacacdbdbddbacdbcbabcddbbdaccbabacbabaadaccababddadacbbdddddbdccdbdadaddacbcbcadcddaabdcbbbacdcbbcddcdacaccbbabbacbadcddbddacbbcbddaccabbbdadbbbbdaddbdddddacbacbacaabaaadacbabbdbbacacbdddcdcbaaabcbaddacbccabbbdccacacdccabbaccdcadbbabbcdddbabddbaadcadcbddcdbddbaacbbdadbccdbacddacddbbcbdbbbabdbcccaccaabddccdaabdbdbdccdaaacbbdcdaacccdcaabcadbbcbddcbbbddccdddcaabcaadadabacacdccddbbcddacaabbabcbabcbaacbbcabbbdcbbadbcacbbcaabaaacddbbcddccccdaaddbadccdabcbcccddcbabaccbadabadaabddbdacddbbabdccddddbbbdbacdcbcbdccdcabdadbdbdadddcaaabcbcacbdbbbcbbdcdbddabddbdaaaccccbdaccddbccaccdcdcccbcddaddadccadbbcdccccbacdcaaaddacbdacdbbdadbaadcbbdcccbdadbbdacdbadcdcdbdbadabddcbaaccaadddaadbdbccddbaddacacaacadccdcdcdddcdadcdcbbaddcaddabbbdaabbdbacddcadbadddddddccaabdcbaddbbbaaacdabadbdadadabcdbddcdaaccbbdbacaadcdadddacbddbddbcdddbbabddbaaadacdacdbbcacdacddbcadcacbdbabababdbddadbdacbbbadaaaaabadaddccbcbabcbccdcdddcabbbaacbadbbbddbbbaaccadacaccdbbabdbabaccbbabbbcbdcacbaadbddadbadcdadbddaaddccdadacaddcdccabadabcbbaadaddcbccdaaaaddaddcbbaccbcadaacaacdbdbbbdcbacadbbaadadcdaabaaabbdacdabdcbddbabbbdacbadaaadcdbdbaabbdaabdaccbdcabcccdbaadcdbcdabbcdbabdcbaddacdaaaabdbcdccdbaabdbbaabdbdaadbbcccbbbccdcabbbbbcbbadddbccddabdabbbcccddbcbbddacddcbdccbaddddbcccbcadbdcdccbcddabbbbdadbdacadcbbdacdcbccdbccbcabdbbccdcbdbbcbbaacddbabcdcbdacddbdcdcbbaadccacccabacaadadbbddcadaaccabcdcdabdddccbdddacdaabdbcbdadacdcbccadbdaacdcccddddddccacdbabadacabaacdcaabbccccddbcbdaaaaaddcacddbaddbdcbadaaaddaabbadadddbbbcbbcdcbaccbbdcdbdcddaadbaccddcbabcabbcbcbcdaccdbcccdadbaabbbdabdbabccbcdabaaddbbbcdbddcbdcbdbdbaabcabdabbcabcdbbdbdcaabdbbbdbaabaababaadbdccabdcdabdabbdbbcccbcdbadbbbacbbcaaacbdbaccbcacbddbdabadbbdcccacccccdbdbdbcbbdcdacaaacbdaaabcdbddcaacddcdaababbbbbaccdcacddcacaabbdabbbccacdcabbcbcdbcacbcdbbdcdddacbbccbadacbddddccccaacbdbbcbcbcbbcabababbaddababbbdcbadbacbddadbdddbdbdaddcbbcaacabbaddaaacadaaacbdabdbbccdbddbacbaaddabbbcbdcabbbdccabaadabbcbbbabacabbcddadccaacadbcadadccadacaccaabacaddcdaddbdaacabbacaacadabcacadbbaccbdcdaadddcbcdbdcdcaabdacbcaaaccdcaccacdbbcccddbdabbbadccbdaabddbcddcdcbbbadddbbabcddbdabbcabdabcaccadbdbdaaadcdcdcbbdcdaabbbbcdaacaaadbbabaaadcbacabaabacabccbaaaddcaaaccbbbaacdccccdcacbbdaddbdddacbbbbbcadcabdcadcdbdabaccabbbacbacdbddadadbbbacdcacbbbcbbabdcdcbbcbadddccabbcbbaccccbaccaccabbbcabbcbcdaaaacaacbbddcacbadacaadaaddacdbccbdcbaaaaaacbccadbdaabdbadbadbadbcdcbbaabbbabbadabcadbbaacbcbccabbdcacabacccbdbbbcddbacbddbbdddbbdbdacccadacadbadacacccdbdcaadbabbdbcacdacdcddbdbbacbdacbadcbadccdabadaadbaaadcbddabacbdabbaaaadddbdcaccbaabaadacccdbdabaadbbdcccbdbdadbaabdacdcbbacbddbbddbbccdddbdabacbbcdcaddcbaaabcaddabddabaccbccdaabadbddacabcdccdbacdbadcddcbadddaaaacdacdbbdcccdabaddaadddbabbadccbcacbdcaccdababccbbbdcababdbacdacaccdbdcaaaabcdbbcabcdcaabbcbacabacdabdbdaccccbcabdcccdaadbccdcdcdabdddccadcaadbbacdadadbaadaadddaadcdaabbcabddaddbdacdddbcbdcdbdacacadaaddcaabadccdcacdcddcabcdbcbcaabbdabddbadbbcaaadacaabbbccdabbbaddcddaacddacbcbcaadcbdabbccaccbdbbbcbdbdbdcabdddbbddabadababdcddabbabccdbaaaabcdccaabaabdbccbbdbdaddabdaadccccacdbcdaddaccadaadbbabcbddcdbabbdabdcdabbbabbcacccbbaaccdddaadaacbadacdddccbababacddabbbaadaabdaccadcddbdccaabdbacbadbdcddcbdaabcdadcbacabccaabbadcbcacdcadbbbdcbbdbcdcbabababbcbccddcaaabbbcabcbdaddccabaaabaaacddbcaddcaaabddabdabbdabadadabbccdabddccdaccdbddcaabcccacdaccaabaaadaddaaaadcdacbbcaadabcbadaabbaacdcbaaaaaccbdabdaccbcbcbbadaaabbaccbdddacddcacdccbcadbaaddcccbdcbcbcacaacdbabcabdbabbbaccaaadaadccbaccabcdddcddadaccdcbdbcacdadbcccaacbcccbacccabaddcaddccddadbdddcdccbbcbdbdacdcdabbacaccddabcdbdbaaaadcacdaabababaacacbacbcaabcdcacacddbbdcdbdabdddddcbbacddacbacdccdabbbcccccdbcaaabdaadaadbbaccbadabddabbaddbdbcabcacbcaaaaccbadcbdbaadbdcdbdbddcacacabbadcadbbdaddbdacbcdcaaccccabadcbbadabbbcbbadadbcacbadbdddbcbadcabddcbabdbbddadbccbabacdddcddaccbbcaccdccdaaaababbcdccabddcbbddcbdbbbbbcbcabdaddbcdcdbbaaccaabbcddbaadcaaacaaddcaabccbadddbddcbaacddaadbccccaabcadacddaadcdaabcdbbbcdabbdaaaacbdcdbdcaadddccbbbccbcadadcaddbbcbcdadababdbabcdcdcccdbdbbbdbdbaddabbbaddbacdbdcdcaddacdacdaacadbcabaccacbcbbaaacdbaccbbbaacbdadcdccdbccddbccbdaddbcdcaaadbbcabdbcbacabdababbbddddababddbabadbddbbacabdcbabcbaadbdaacdabdabdcdabaacaadccbcdccbdddcadccaacdadaaccdaaabdcadaccbdcdacdcacbcdbaabddccccddbacbddadcaabcbabccaaddadacbdbdaaaaddabaaccdddbbdaacbdababbbdccbdcadbbbbaabdbadcdaddadabaacadaccabbbadaacdadbddabdadaabacbacdaddcdbcacabaddbbaabcdcababbaddbdbdcbcdaabccaacaacdbabbabbcababadddcdccbcdccddabbabbdacaddbbdddddbdcdcdbacdababddcadccacacdddacbcaacdbacbddbadaaaaddabdcdbacdadabddcdddbbaddcbdccdbbcbcbbcccbbcdcadacbcbbbcdabacbbcbcabcacdacbdabdcabbadacdbcbdabdaccbadadccacbddccabbddddccbabdcbbdaacbcacaaaccddacdabdddbbbbaadcdbdacdaabbbbaaaacdaaddcacbcbabdbaabdcaaacaccadaacdccdaaddcccdbddccacbbdcbcdaaccbbdddddccbcbdadddbaabcbbcdbbbaacaabcbcdabccacbdacbdccdacadabbaacbcbdaaacbaabccbdcaccbdbbabadbcbbcabcbccaabbcadbaaabcbacbcbddccbddbbddbaccabcbabcabbdbacadbbaaabccddacadabdcdbddbbadcabcddcbdcdbcddadabdabbbcaddcbadbbcadadbbadbbbcdddddccbdbccbbccacbcdcaccbadabcccdabaabddbcbdabcbbdcaddabcccbdabdbcdacccdadccadccdbababbbadaddccaadcbddbcabbaacdcbddadbadcacdccabcdabaabcacbdcccbdabcccdcdabcbdbacccdacabdbabdcccbaddabdaccdcbabcaccbbadabbcbadacbdcdcbcabbddbaabdcdbdcccbbdacabccbbaaadccdbdabdaadcaddadccdacadcbbcaccaaadbdababadbdaacccaadabbcccdbabadaccdbcacbbadadaabcbaadaacdaabdcdcbdbaabdcdbbcdddbdbdcabbbccbcccdbdcacccacdbbabddadbcdbabbcdaaabbbdcccabbcdacaaadaabbbcaacbbaaaabbdbadbddaadcdadadadbbcdbaadcabcccccdcadddbcdbaaacabcbbbcbcccadaaadacdaaaddbdbbddbacaabacbccacababcadbacadacdabaaabcdaaaabcaaacbdbacdcdbadbbdbdcccacbaccacbccbbdaccabbcccadcbcdadbccacaaababdbbdbaabbdaabbdcdcdbcccddabdbbddbabaaddacbcaadcbbcdcdddccabdbadbdadccadccccdacdacdabddbabdadddacdadcaacbccbdbcbcdaaaabbbabccbbdccaabacabbbbdbbbdaababccdaccbbaccdddddbbddddaabdaacbdcddadbdbbbbdacbacdbacbacddabbcccabaadabdbcbdaaaadcacddbdaadabbddabbadddbaabbbabbaaadcdcbaddddcbbbbdadcbbbbadacddcbbabdbdddadbbcbaabddddaabdaabdaabbadbbccacbcaadacdbccbcaddcaadabdcbdbbcbdbcaddcdaacadddbdcdddccdaacccbbdbcccbdaacbbaadbbdaadbaadbcacaccbcdaabbcadabdbadcabbbcdaadbbdcbacdddcbaacdbdabbcdaaccbcadabaacbdaadddddacdccadbdabaddccddcacaacbaaddbccbcadbadcbccbbabdbccbabdaabbbcaabbdbdcabbabddbbaccabbbcbcbdbabcadabdccbcdbadbdcabdbcbbadcdbdbcaadcdacddbcadaabdbabadbabbdcdaabbbcdbcdcdbabcdacbdbdbdacdacdaabddcbddadcbdbbbbccacdababcaddacbdabdabadccdccdabdcdabdaacdbcdcbaabccddbabbcdddddbccbabadcbcbccbcbcdcabbabccddadcbcdcdbbbcbadbcbdaaaacdcbbdbccabcccbbbcddccdadadccdbbbbbbbbbbddbcbddcdbbddcddbacccdabbabddccabbdcbcdababbccbbcccacddadbcccbaadcabbccacccaddbabcdaacccddbdbbbbcbdddaaccaabdbcadacadddabcabbabdbdddcaccbacdadddadcbccababdccdbabdccccdaadbcabcbcabbdabdadcbaacbbccbbacdbdadacbcdcbadddcbddcabbdbcbabcbdaaddcbddabbbcbabcccbdcdbaaacabcaddcdaabbaaadcccdbcaabbbaabbabbaacccbabbdbdadaaadccaaaabbbdcccaddabcdbbdccdccacdcddbcaadbcccadccccbbddbbacdabdaaabcdcccbabbcddcbbdadbaadaacbaaddacbdccdcbdbdaccabbbdbbadacdabccabdbdbaadcdadbdcbbbbccabacadbbdbaaccbdbdacddaadcddbccacadaaacbadbccadccbdddbacaabdccbdacaaddababcccdabbcdacddccaabddcdabaccbccaabddbddbbcdbdaadcdbddbdcdbbcaaacddcaabbbcdddddddbbddcdbbcbbcacaddabdaacdbdcacbbccdbaaabadbcdbdaadbdbcbbdaaddaccddadbdbcbccbcdcbabbccdbbbdabdcadaddcbcccabbbddbacbbadadccccddaabaaacdbcccdcdcbcbaacdaabdbaacadbdbdcbacdbcbbdddaddccdbdddabbcdccdaaaccbabbddcbadbbbaaaababadcbccddacadccacbbccbbaddcdbdbddbdbaddcbaaadabbaacbddbbbaccaacbcdcdcabcddcdddaccbaacdabdccaabddbbbccaccaaaddcabcadddabbadadccbdbbccbbbbdbdaabccddcadcacacbbbccdabcbdbbcccbacddcbbdcacacdccbcddccccdadcbbdbcbbddbababdacaaccbbcaacddabcbbddcaabdcbcddbcabaadababadddbdbcacdabacdaabdcdcdacadbcbaddacddbdadcddbaadbacdcadcdaacbccdaaccabbccbcadddbbdbbcabaddcbaabdbccaaaddcbbbacddbabbdcaddbcaaabdddcbdacdcbdbcccddddddbccddcbccccbaccdcaccddbccaddabacadadcccbbdadcbaabcbbbadbcbcaccadadbcbabdaabcdcdcddacdcdbdabadcaaacbbcbcccbdaddacbdbcababdbddcdbcdbdaaccbcbbdddacbbdbbdcbccdababbcabdddaadbaabacccaabcdbbbdabbbcacbdcbdadcbddabbcacbdadaddbbdbbcdcaacbccacababacacacabdcdabdcabdacbabdaacbbdbccacabcddabcdbbbbddaacbbdbddcaccbabaaaababdcddbbbbccdccbdaccacabcbaccbaadbdbdcbdcbdbbbcbabacabdbdcccabadbcdddaabccdbadabddadabcdacccbacbdbdbddacdcabdadcacdadccabbaccbcddbacadadcdccdbccabacddbbcbcbaadcbcdbacbbdbbacbacbbdddcaaacbadaacdaaabccbbcbadcadbaacdadccbacaaaaccacbabaadbacbdaccddbbbacbaddbdbaadcbaddcaccdbcdbcddbabcabbaabbadaadbbbbdbdcabcacbbbdbcdbcbddbbddbbcddcbaccadbcacddbaacdbacccbddddbccacadbcccacbbacccbddcdacabdbcddbbbccabdcabdabbccbdcbcdcadbcddbdacbbdbbdbaccbccabdabacacbdcdccbbddaccdccdbabdddcbcaacacadbddcadbdaccadcbbccdadcdaadcbbbdcaccdacbcdaabdaddadcbaabdaadbdacbbcaabdaddddbbcbddbbaadabbcbcccaadabcdbbdbacabcdcadddbdabaccbabbccbdabccdbaabbcbabcabdadbdbdcdbbcbbaccdbadaabccdcdbabcbcbaabcbadcbabdabdbcacaabbadaabaddddbacdacabdaaaddabaaccbccbaaacbbcbdccaaadcccdadccbbcdbaddcddcbcbaddadbbbccbbbacdabaaadccbabaaadcaacbcccdbaccacddcabbddacdcbdbbdbabaacbababadacddcdabbcdaabdccccdccabcbccdbadbccbcabbbabcdaaddcbbdabcdccddbadcdaacaacdaacddddbbbddaacbbabcadaadbadbdbcdcddcbacacabbddddbbcacbbadadbcadcddaaddccacbbadbcdaabbcdaadbaadccaacdddbaddacdcccddcdbccbcbddbbdadaaacdcdddbbbacbbbdbcaaccbaaccbcabadaccdbbdccacbcaacdacacccbabcaddccacadbdccbacbaddbcbacdccdbdbbaabbdadcaaddadcdbbcadabcabdababdaaaddccdcddbcaaadcbdacbdddcaccacdcdbbbdbbdddbcbadddcdddacddabcccdaccbbdabbccbdcdccdcdbcbdccbacbbcdcdbaaaaddaaaadaadcaccddcccdbccdbabbaaaccabcccdbdabcddaaddcccadcdddddddbadcddaddbcccddabdcbababbbcbdcddcaaaacacbbcbabbaaccdabdcdbaaccbdccbcbcdbabbdbdabbadccccdaccbdbbdbccdcbcbccaaddaaacbddcabacdbdaacbcaaaccaacdbdaadbbdccadbaabddcbbaaabacdadbacddcbbcddcbddabbcbbdcabbaaacacabccbbccdbaaababdbbaacadaaabcbacdccbcacbcbacdddacdbddcbadbbcabaadaddcaabbcdadcbbcaabcaddbaccacbaadccccabadcbbddbabbaabacbdcbaccbbcaddcbcdbdbbbbddbbbccdcbbbacacdaddcbbabaaaacbccbdbbadcdcbdbaabdbbacdbddddaacacdaabbaabaacddccdbcbccdaadaabaddbbcddbabaaccaacdbbbcadbcbccdccdaacabddbcbdbcbccccddaaddccaadaaadbabcdcacbdbdaadbbbabcccbcdcaadcccbcdbbabadbdadcbbdadacdddcadadaabaadadbbcddcabbdbccbadaaccdcaabbbdbbabdbaccacdbccabacabbadcdcaababbccacacddddbacdabcbccccddbcbadacdacdcbcabccbbcbbaddddccbcababbbaacabbbbaadcbaacccddddcabccbcaadbadcbdbcccaadabbabacbbbdddbdbdbcbcabacccbdddacdddccacaaacdcbcdcdcdacbaadadddabddbddadccdddbaadcabbdbacaacacdadcadcbbcacdacdbdccccddccdcaccdddbabacddbddabcdbadbccdbccbaaaaaadcbccccccdacbbcddccddcaaadadbbabbbaababbdccdcacbcdddbaddadcbddacacdbdaadadaaabdcddccbabdacbdbdbddcdaaacdaadcaccddabbddbaacbddadbacbbbccdadbdaabbdbbabbaabbcdccadaabcbbcdbddabaaccbbadaddaabadcbabaddbdacaaadddccdadabddaccaadbbdccababdddbadabcaccdcdcddbdbbadcdbabcabcccbccaadcbacbcabcddbdbddcbcbcdbccabbbbdcbdbacddcaadcadbcbadddaaaddcbcdcaddcaccddbdaaccbccdcccdcdacacdabddaababbbbdcabbcbaabbadbbbdbbadccbccbdcbbcbccadbbdccbbbcbddbaadbabadcbabddacddabadcaacccccddabbcbcdadadadaacdbbccaaacaadaabdcddbdcbbbbabdaaddccbdacadbdaccdbadaccbccdadcdcaabcdcbbaaaacabcabdccdbaabadabdaadccdadabbaaacacddaaabddacddcacacbdbbbbbdacccaadddddacccdcacbbcbbdcbcdccdaaadabcbbadaddccbbdddbcbacadacbddabddaacadbaccaaddbdbcbbcacaaaccbddbbcccacdbdcddbbaabdbdbbacbaccdadbbaddcacddcbddabccaddbbbbdadbdccbddbdbbadddaddacbadcacbdbcacdaaadcadbcddccaddcdabccacbdbbcaabcbadadcbddaacabaabbddabcdadbbdbaabacbaaaaacddacddadcbbdbacaadbbadaacdbbbacdcbbbccdcabadcbccdababcadababacddabcdcdcbbbcacaabcdadbabcbcccdddcbadbbbabddabacabadbabddbccadbacbadacbbdaabadbbbacddbdaabaddbdbabdbcbaddaabadcbacabbbabdaddabbbbabdddacdbdbdadabdbabacadacdbdadaddcddddbdbcdcdddaddccbcbcddbabdadbaddcbbbabbabddbdddcabacabcbdcbcdddddcadacbddddbdcadbcabbbdbabdacdbbbcbcbcadbdbdacdcbcddbadaaabbdcccdcaaacbbddaddcadbdccbacdbacaddaaacccccaaddaddbddbdaadbcacabdadbdccdaadccccbdacbcbbadbccbadcbcaadccbbcbaadabadcbacbcbbdcdaddbddbddcbbdbaccaabcabbbccaaacddcaacdcccbbadacacbbdaaadacdcbaddaaacdadddaaddccaadddcadababaadcccabadcacacbaadbcbabdaababcccdbaadddddbccdcbaabadaddbddacdddcadbaacbdacccdabaaaacbaabbdbbbbcccaaaaddcccdbaabbcdbacdadaabdcdbdacbbbddbbdaadaabdbcaccbaabbcdacccccadabcacabdcdccbbbacbccbccacbcaddabcacbdaddadbdccaaccabdbcadaddabbcbabdabbcdccbbdcddcbaabcdaccdbbaabdcdcadcdabcbaabccdcdaaaddadabdddcbadadacddcadadbbcdbbcadaccabadddbddcbbcddcadbabcdcccaddbbabaaddbaabaacdaacababdbdbddbcddbcdbdccbdbdbcaaadbbcacdbcaddccbbaddaacabddcbbbaaacdcdadbdcacdccdaabbadcbdcadcdabccbabaabdabbaadacaaacbdcaddbcdcadadcbccbdabcaccabaddbcdcddbbdcaaacababbcddadbdcdaaabddcbbabcccdabcdaccbbdcdabdaddbdaaabdbcdcdbcbdcbadddbdddaabbbaaabdcbccdccabdbbbdabdbdccadbcbdacdadbbcbdbbbcbbbabdccbdbcbbbcaaccacdacabdbdccaabcbdcaabcadcdccadbbabcabaabcbdabdcdabbacccdadadcbcccccabbbdcdbccbbdaaabcaabccacdabbadcbcaacdcddbaddbaabdbabadcddaaadabdacdcbdddbdabaabbadbdbbbaacaddccbbaabbaddbbbbaadbaaacabbcbdbdcccbbdcaddadabbbbdcabccdccbadaaadcccacbadcabcadcacbdcdbdaabdcdadcdaadaaabadbcdccbaabdbcbabdccdcdbcbcdabbaaddccacacadbbcbcdabcaabacaaaabbbadacccbabdbddbcadddbaadacacacbbbdbaddadccdaddaabddbbdcacbcabcbccadcbdcccccdcddddcdbccaabccacbbcbcbdddadadddcadbcadaddabbaddcdbddcddaaaabcbcaccdcacddaadccdbccaadbbcdbaaddccacaaddcbbdcdaabaaccdaddadbabbabddddcaadacdbbdcdcabccacaddbbdaabdcacacbdaadacbacadabadcadddadcdacddaabcdaaacccdbcdbbcbbcdadcacabcdbdabddaaabadbacdabaaabcbaacaabadbdcbddabdbbaaaccdddaacdbaaaacbbbabbbacabacbacddcddacabcbcadcdbbbbbcdcbbadccadbbcbcbbaabccabcbdbcbbaccaaacadddbabcdbbacdaccdbbdacaaadaabbbddbbccbbdbcaabddddaabdbaadcabcdbcccbaddcbbbaabadbcaaaadaccdbbdabdbbbcdabaccadccaabacdadbbcabbcbbccaabcadcbccdbccbdaddabccacddcdbbadbaacdaaaddbaabdaddabcabcbbbcadccbbcbdaadccdaaadadcdccbdcacadbaccbabcdbddbbaabbccbdbccdcccacbdcbacbdbadabccadacabaabccbccbbccbdbbddcdbddbdccdadcabcaaccdbabdccdadadddcaddcabbcabaaabdccdddcbdddcaaadadbcacdcdcabccaddadcbbbacadddbcdabacadcdbadaddcbcdaaddbbcbdbcbaddaabcccccdacdbbbbabddcdadadccdbababcbdcbaaccdbaadcbdbcdcdbadadccccdbbddbddadaddaadcaabcaabbaabdcaacdbaccaacbcddbabbbbcdaadcababadbcccdaacabaaaabaabacaabccdabbdcadcbdcccdadacbcadacdcabdabdabbbababbabbcbbbbcdccbcdccdaaadaaaadbabcbbdddbcdbdcbcddccbaddabbdbcbdadcccbbdbadbadbcadccbdcbbdbacdddddacaabadcccdbbbbdadabbdcdadbacaddbdcabcdcdaccdcadbcaddbcaccbcabdbcdccccddccccadbacbaaabddbbddaaabbbbaccaacabcacaadbbaccbdbcbdddddcabcaddbacdccbddccdcacddbadccddbabacccbacaacaddbbbccaabaadbbddbbaccaabcdddaaaabbdbaaacaccdbcbcababbcbdabbaabbdddadcdadcccbdccacaaddbdcddabdaccbccdbddadaacdddadbbdacaccddcadcbcccdbdacbdacacdbcaaaacdbdacbbcbbbdacbddccabbbdbdcaaccbdabaaadddaaddbdabdbacdbadcaaccddaabacbadbddcaadacbcbccdcbcdcadbcdddccadbbadcbacbbabcdddbcddcadbadcaadcccbbcdabbaccbadbbcabddcadbabcccaccbaabdbdbcbdacabbaccadbdcbbcdcdcccdbcbbccdadabaccaabaaddddcacddadaacadcbbacdbdadbacabcaabadcbabacbaabdbdababccadabaacbabdcdaaacbcdadadbbbbbdabadccacdacacbdbbcddddbddbdaaabdbbbadcddcdddcabddcdadacbddaadbcbaccabcdcbdaacbadcadcabbdcdbdcbaddccacaabdcabdadcdbdbaacdddadcbadcadcccdaaadbdaddaaaadadaadddcbcbddabcdaaacdabdbcaaacacbbdccccaaccdbcdbcccddbbddbcddbabadbaaddbadbbadbbabbcbdcdbcabcbccdbddaabcbccabccaddbcabbabbaabbdcdbadbdabbbacbdbcaabcacdaabcacabbdaacbcbbbbbdbdcbadddaaaaaacabbaaaacbcdacadbbcdcabcaccbbbbcabccababcaaddbabbababccaddbbcbcbabcaaaabcdbcbbaabadbacbdabaacadabacdbdcccbbccdbcdcbdbccdcbbddbcaacbacbcbcccacbbbcbdbaaadcdcccbacdaaadabbaaabbdcbbcaadabdabddbdbcbcdaadcabcaccbccacaaddbcaaadacbcbcbacdcdbacbcbccacaccddcdacaaccdbbbbaadbccadcabbdddcbadbdcdacbadcadbdbacacabaddbdbcdcacdddaccdaddbcbaccbbbabcbccaabcbdabaabacbadadcadaacbbaaadbccdabdddcdadcdbdcdabdddbcbdcdabbbdabcbbcccabbcccbdcbaabccbbccdabcaddbcdbacaabbdbcbcbaaacdccddbbbbbbdbacdaddbddacbbdabadccbbddbcbbabcdbbcbddacccbbaacabadabddbbacccdbabbadbdadaaacddbdcbababbbbdccdbddcadcbbcabacbcdacaadcaaacdccbbabdddadabbadcdbbcaababdcccbadcdbacbdbababcddddabcdcddddbbcccdadadcbabbdbaaadbabcdddbbddabdcdbacabadcbdadadaabbabdacdcdcadddbdaabddbdcacaaacbbcbccbbddbcdaaaadcaacdacbdbbdbdaadcadddbccdddbcabbbbcabddaabaabbdabcdcaddcdbcabcbadbaddacaabbbbcdddbccaacbcdcaddbddbcddccccadbcccdacdbadcaacdcbaaddbbccadababbccbbdddbbbaccaccccdacbadbcadadbdbddccbcddcbcacadcddbbdbcdcccdddbddbdcbcadabcdbcdabadbbcabcaacaaaddabaacbabaaacbcddccadcbcdccbbcdbdaabdddbcdababdbacdcabdaaaaabcdaadddcbadcaddcadbbadbbdddccadabcdbabdadaacddaccdbbabdbcdcdbddbdacdcdaaccdcdcdcbdcddabdabcdccbbcaddaccbaacabcbbbdadcdaaccdddbbaddbdcbabaaddcaabccccccabdbbbdcdbdbbabbbcaaaadbdaccccdbcbbaadbcabcbcbabbccdadcaaacbcdbccaacacbddaacbdddacbccbaadbddbdabddbcdcbabccaccbcdcddbbdcccddbcaaccdbbdaddaddbccddadbccaacabdbabbbdcaabbabddabaabaacdbbdcddaccbacdbdabbaadcdccbaccadaccadbcdbcbdcdabccbaccddcdacadccacbbadcbadbbacabdccababdbbbdbdabcdddbadbdddbdcbabddcadaacdadcbaacadaabaadabadbacdbaadbdadaadbddadcdccbbabbacbabcabcaddabadbbcbabadbbbbaaccabbddcbcdbbbabadbbccbbdabbdcacbaccdbcdbaaaabbbccabdabaaddcbbadddaacadccccbddbdaaabdbdddbaddcbcabcbdbbbcaccdbbddabaddacabadacddcdccbbacbbbbaaabddbdaacdbdadbbbcdacacbcabaccdacdacabdbaacaaacabbddddabaabdbaddbbcaaadbdccbdbabbadbdbbcdcbacddbacabddaacaacabaadacdcddaabcbbbcabbcaacbdbbbcddacccaadddcbaccaccccbdcadbcbddbccccabbbbacabcacdbccbddcbaccbbddcadacabdbabbbdaddaddcbbdbdbdcdcaccdbbbdacbcaacaacaadcccacaccabbcdbcaddccccaacaacbabbaadbaabdcaccdaddcdcdbcbddbbaaaadcccdababaaaabccaaaccabaabdbbbdabccbbcaacdcbabcddddddccdcbadbdacdadccbbaacdbbaddbdaabadccbacdbdcacdacbdacbdbaaddcadcbdbbacbbaacabaaddcdacbcacacdaaddcaaacdabcabdcbcabbbcacddbbdabcbccdbdcdcaabdbbbadcddbddaacccdbbcbababbcbdaccdbcbdbdcabddbbcdccccbbddbaadabcddccdacbacdadcbcabccacaadddddbcabddcbdcbabdcddcbaaaddadaccddbbdcbbbabddcdccacdcdacadcadcdcadacabdbdbcdaddcdaddcababddddaaadcbacbbccdbbadbbbcdaacccbabdddcdabacdbbbaddacdadbdbadabbbdaddbacdcaddaddbbdccbbaabcbbddccdadadbbcaccddcbaabdaddbdbabdbbaccbbbcdbadbbadcdabdcccbbcadbdabaadbdbdaacccabccaabcdaddccbaaadadccacbaaddaddccccbbbaabcabdccadbabbbbadcbcadbccabacbbccadddcbdccbdabcccbbaabcaacdaaacbcccbbcabaacbbadbadbbcaddadcbcbaadadbabddccdbababcbaaaadacdbdddcdababbaacdabadaadacbddaadbdbacabacbccddacadaaaaaacaadbdaadcbbbbbcbbdacbdbbdccdcacccdccddccdddbdccbccacddddacdcbdccccacbacdbcaabdcacaddddbadccddbbcbddcdcbbdcbcdbbbdcbbdddbbbdabccdcbdbdbcdbddbbbddcbccadcabacbdccdcaacaaadadbadaadadadaacccdcbcbaabdbaccaccccaddcabaaaacabdccacaaabbddbabaabddbdcbdaaaddcadaaadadabddbaaccbcccadbddbccdabcccaabcbbaacabddbccaaaaadcccaaabdcbdcdadcbbcbcbbdbdbddabcbddadbdabdbdcdadadbcacddacccbdcbdbadaaabdabaacccbdbcbcdbadadadcabcdabaccbdcddbdaabaabcaddccbaddabdbbcaddcdccabccbacbaacddacdaacadaccaccbdbacbdbbadcddabaddcddddbcbacdbcbdbacdaadbdbbdbcbacdaadabbccddccdbbadbddbddccdddbdaaddddbdbbdabcababcaaccaddcdbacabdbabbddcbbaabdcadcaadddccadbcbdddcbccdbdcacbdcbcadadcaababbaadaabccdababcdcbabdcbabdaacccacacdaaddbdcacbbddbdbaaabcacbbdbaabdacbddaddcdaacccddababdbbdbdbccbcdbccccbdcdddbdbccbdacddddabbaaababcbbbbbcaadaabbcbdcaaacadbdbdcdbbccaadcbcbdcdacdacadccdadaadcbcdbbddbbcdcadcacbbcdbdcddabcabcbacccbadaddbcdbdccccdbacbddcaaccdaccaaadddddbcdcadbcabdbacbdabbcaabdbacdbbccdbbbaddaddcbbcddbbcddccddbbccdccaadabacbacababadccdbbaccaacacbbbbaaddbbbccbadbadcacaccdcccaaacdaadccdadcdabcaaaadccdbcdbadccbcaabcdaaaadaabadcabbcbcdabddddabbcaacaaaacbdabdcababcadcccbbddddaacaacaddaaadabcbaabdbabaabbcdbaaadcbaaaaadddaaaaaadacccaddcdccadccbababcbdabdddacdccbdddcdbddbddbbaacbdabababacdddadbbcbdcdcbacacaddccacbccadaccbaccacbbaabadadbadcacabbaddddcdccdcadddbdddadcdbbdadbcdcbdbbbcacddbbcddddcaacbcbacbbacbdcdbbabbacaaacbdabccbbaabaaaadddcccddcbbcabdcddadabddcbdddbadaabdbdcbbabcccdaaadcbcbcdabbbcadadcbbbcdbccdcdbbaabbadadbdbcdbddccbaaacaccbbdcbaadadcbabbcddcaadddaacdabbadbabadbddcbcbbadacdbbbcdaaabadbcddccccabcbddadcddbdbacbbcaadacddcdbaccddcaaaccbdbbbabbbbabbdcbababcdccdcacdcdbabacbabaacbbbcbccaacaddabcbaabdbdbacbaccdaaacdcdabadcbdcdbabaaacadacdcaaaaaddaccbdbddddadaaccbcbaaacdabbdbadcabbdcdbbdbdcdbdcbccccbacdaaaadbcbcaccdcaadabcacabccbacbbcccbcbaacddcbacaaabaacbdbaaadbbddbdbcccbccadaabbaabacaadbacabcabdaabdcaddacaabcbadadacdccccccbdbdddcbadbbbaddcabccbccbaddbdcaabadadcbaaadbcbcbabccdaccddcdccaabcccbacbbdaaaabbbccdcabdabacddcaabdaddbaddcbccbccccaabdbbdcccbcdaccbbdabbcabbdcddccbaacbabaccddccbdcbdadabccabdcdcbbbcadddbcbdacbaadbaabbbdcdbcddbaacabbbcacbadbddaddbdaaddbddbcddcaaccbacabccbbbbadcdbbcadcbaadbaddadadccbdaadaddbdcbaaaaddcaacdadbbdcdabcaaadccbcbbdcaaccbabaccdababdbcdcaddbaaddcbcccddaccdabadcaadabddbabbcaadacdccaaddabbcbcabbbcdacbaaaadbbcdadbbbadbcbbcabcccbadbbcbacccbdcabaaccaacdcbcdbbadbcbacadcdcbdddcbadccabaaccbdcbdcbadbaaadbaaabcbcbaddacaacbdbbadddcbbbaccddcddadbdcbacdbcacdadddcaacdcddcdaacdacdaabdcdabdbdccbaaddcbadbbaacbbbcadcdbbddbccdbdcabacdcddddaadcdcccbbaccabbcbdadbbcbbdcabbadddddaabccadbcaacadaddaccdbccabbddadddadbcddddadbccaaddabababcbddbcbcccbcbdadadbcdadbacbacbbbacaadaddbbcbbdcdaabbbacabbabdbacdbadbbaaaaacbdaabdacddacbdacabbdbdcdccdabdccdcaaaabdaaccadaddbccbbcaddacbbbcbacbbadcbcbdcdddbaddcdbabbdcadbcddccdbccccccabcbcdbdabdcaccdaaaadddbabcdacbcdbabaaadabcdacbbaccaccdabdabbcbdabddddabbccbbacdaccaccacbaddbaaccdcababdcaaadbadaddbabbccbacbabacbbcccdbbaccbcbbddcccabbdbbcbbcacbbdacddaacdccdabcccbdbabacdbacbbcddaabdcbaabaddaaaaaaacdcbadadaacacbbbbddcbdacdabacbbaaaadbadbccdaccacbcddabcadcaabbcadacdbdbaaabcabdabdbdddcdaabdabccaddbcdddddcabbdaabbbcbdcaabacbbacabcabcdccadcbcaadbcbddccadcdcdbbdadcbacbdbcbcdaccabacccbacdcadaaacbbacaadcdcdbddabcdcdcbddacdacaaadbdddddcbbcacadbccdabbbbdaaaaadadaacadadcbcddcaaadcacddbdbaabbcbbacbdbcbdcbcbcaaccadabbcbbddaaacdcaaaaadacbccdbbabaadacccaadddbbaaadbcdccdaababcabcddabddacaadabdbccbbddddaadacddaccbaabbdbdcdaaacbddaacaadcdcdcdbacbcadbdaadcdcbbbadcccababccacabaadbbaacadbacbcadbbacbdccbdcddcdadaddcdabbcdadccbaddacaccbcacbabcdbccacddbdacddbacdccccbcbaccbbccbbddcaddabddaadacaccacddbbbbcabadbdbbacabdaddcbdddddaddadbccbabdcabbdadabadcddccbbaabdbccbccdacdbaabbccadddbcacbbaacbbccaadaaadbdbacdcdabacdddddaadbadaabaadaaadddaabacabbbdabaaacdbdacbdbbaabbadcbaabcbdbddbcdabcbbaabcabcacdbaccabdcbccdddbcdadacdcabdbdacbacdbcccbccdcaacdddbabbdcbbadcaaccabadbdbdabccdbdcccdcdacdacdbbabcbcbacdddbdddbbacacbccabdcbdbcabadcbdbaacdbcccadabaaccddbcbdbacdcaabbcddccadcddbadbbbddacbbbcbaddabbccbbdacdddcccadcbdaacbdcdbbaacbddadccdaabcaacabbbcadcdcccdbccdcdcbacaadadddbacacbadbacacabcdddaadacdcdbbadabbcadbacdbacdddaabababbaddcdacbcdcddcbcabdcccbcdbccdadacaabaaabbbaabdcacadaababddbbdbdcbccbdbdbcccdacbccadaaacbdcbabaadbdaccddbdccabbbdabbbccbaadcaddabadadddddddcaabddabdabbdbbaccabadacaaddbacbdddcccdbcccbddadcbcdacadaccdbbccaabdaccbccaddcbabbbdccabaccaaddddcdadacdbcddcacdaddbacddaaaacbcacdbcbcaadcdcbaccdbbbdcacbaadcbacbabcbcbbacacaabacbddabbdccacdaaaacacdabdcabbadcdbadcdddccadadddadbbacbcbaaddbddbccdaddbacccaacadcbcadcdbcbcadbacdddbabbbadbcbdabadccccabbbadcbbbcdcaabcdabbcbcbaddcbbccacdcbabcbccbcabccaaacabbcccbbaacaabdbbddbadcbdbaabbbcdcabccbdcbbbcdbdcabbdcdbcccbddbcadbdcabcdbbbdddbddabddcadcadadccbcccabbdaccdcdcbaddcaacbcccbcbdbcccccdbaddbbbddcdcadcabdaababcabaacbadabbacdcccbaddcccddddbabccaccddccadaddadadccabddbdbbcdcdbbdbabcadcadbbbdcddabdabdcdadcaddbadcddbcddabaaadcdccbcacbacbddbbbacddadbaccdbcaadaadccbcdacbababddbccdbabcddbabcccddabbbbcaddbcccbcbdccadbdcaaccadaccaaadbdcaadbcadcaabbbdddcaddccdbadbdcabaddabacbddbdaadcccdbdbcadadbbdbcadaaaacdccddabbdcdcdccbabddcddabcaaaadcbbddcbadccdddababdddbbcadcaacacbbdabcdcdacaaabcbbadccdadadbbdabcadabbaabdaaccdcaacdcadbdbcdbbacabcabaabccaabacbbbbbbddacadcdaabddcbcdddcdddcabacaddbbccbdccdbacacbdadccbdabaccdcacacdbccadaabbcaaacbdcaaccdcbacaacdddbddbcacdaddddbcdcbabdbccbaccddbadcbdacadaacadaabdbdbccdbdcdccdbdacaaadabacddccdcaabaaddbaabcdcdbdacabcaabdbacdaabbccddcabbcacbdabdddbccabccbdaaaadccabdddcccbdaacbabbcaadbdbbcbbadbacbcabadabbcbcaccccdcbbddbaadcabadbabcdcbadcbdbcccdaddacaaabccddbdbbdaacddacbacadbdaacaadabadbabcaaddddbabcccddbabcbadaababcaadaaaacbcbbbddbbcbddaacbddbacddaddcbaaacaadbcbdcddacbcccdacddabbbcacbcccbbbbbcccbdcddddbdaadddbaabacdabccbacbddddadccdbcdbdbbddbaadbbbcaadcadddddcccdbadabcbadaddbcaacaadbdabdbaacdbdbaacdaaadcacbdddcdbbbbdbabdbadadbbaabdbbadadadcdabaccbdbdbcdcadddaccabcbadddbccbbdabdaabbbabdbbabacdddcbcdcdbccbbbccdddcddadbaacbbdcdbdadbdcbcbbcddbcacbbccbbddcddddddcdadcdabaccacbbaacacbcabdbdacaadacdcaadcabcbddacadcbdcdbaddacbccacddadbddddacbdcccbdcdadccdddbdbdbcbbbccdcccdcdacbaccabbcbaacbbcccddabbcdcbccabbdccbdbacddcdbaacbdcbadbccdddabaaaaabbdbbcbabaabadcabbbbcdaaddaadcabccbccbcacdacddbadacdddabcadbcaadbabccaabcdaddddabdabbadbbdabaabacbccbccabaddcdaabaddaccbdbdadcbbaabbadbabcbbdabdacdaccdaaaabacadaccdbaacbadcbcacddcbadcaabdcaabadcacccdcaddadaddaabaddddddbcccdbcbdcacccbcaacccbcdbaddaabdacccdcddacbabdbaadabadadddcbacacddcdaaaaddaccaadcdbccabdcabaabbdcdbbdccddbddcdbdbadbaabcbadcacacdddacadcacbbaddabddccabbddadaddabddbbdaabbcacddbbbddcaabbdacbbbdaaabddabacbacbcadccdacbdaaddcadbbbbacbaaacbadbbdacacdbcbdcbcbddaddbcdbbcdcbacacbdbacccaaaaccbbddbccadbcbacbbadddccbabadddcdbdbbabacbaddbcbbacbdacacbcaaacbddadabdcaaccddabbdaaadcccbddbdadcdccabbabcdcbccacbbabcbccddbbbddaaddbccbcdacaaaacacadcaabacadacbbcdbdcbdacddbdbdbcddbbdadbccddccdbaabadddcbcdadbcbbabadcacbdbcbaddbdaaacadcbdaabdaabdbdacbabbbabbadadbcbddbcabbbdcadabcadcdcdbdaccbcbdbbbaaaabbbdbaacdcababccccbadddabbabcbadccbbadcaabaadabaabdaabcbcdddadabccbcdaddababbbcabdccadbabbaadbcccdbbdcaddadadbdccbcdcadddabdadaddcddbdcdcdacdbcbbddcaccdddbdbaaaccbacaccabdadaadcccbcdddcadcbcdddbabdddacdacbdabbbabcbbaaccacadbdcabdaacddcbaadcbadcddcddcadadbddabaddaddbcdacabacbdadddcdcbadccbcbcbcccccdbbabdabacddbccabbccbccccdaaadddaacadbbbbbabbbadbbadbaacccaabdcadcdbcdbddddcbcbdbbadccabcdbbdaddbaacdabcaababbdacdccbdcdaacbbbcccccacdacdbbcacdbacacccbccacdacccbaccccadbabbdabdbdadccaadbdadbdadddcdbadbbbdaddbcddabcbcbadacbcdccbbcddbccbdabdbadcbcdcbbddabadbcabcbdbacbaabaddcbbacdacccdabdadcaacbbdcabbaacaabcadbcdbbbbddcaddaccbbdaaddadcbbabccdcdddabdcbccbaadccdbddbaaadabaccbdbddbadcccdcabcdcbabaccaddcdadacbcbcbdbcbadbcabcbcaddacbbcabcbadcdabcdddbbccdbbcadabdbcaadbcabbadddcdacdbcdbdcdbddcbbcacbabacdbbbccbdabdddcaaadbddcdbdcbcdcaaccababadbdcaaabbcdcabbdabbcbbaddacbdaabbaacbcdacccdabdbcbdacdddbdcaabdaddadbbaaaaadadccbbbadabdccadbbacbacbdadaaaaaaccadcdbddbdadccbcbbbadcdaabaabbcddaccccbdaddadbbadccccadbaacbabddcdcdbbbbcbcbaadacbcddadcdaaacbcbcdcdbdabaabcaadbbadaadbbbadccdbabdcdbadcbbbaaacdcddabaaabddcbddbbddbadcdddcbcdabcdbcbaacabdccacddaadbcdbaddcaacdcbccdacdbcaddbcbabcacbaddbbadcabdbabcbdcddbcaaadbcdddcacddadcabddabdaaabdcacacbcadcdddabcbcdcabdadcbbacccdddbacadabdaacccaddadcadababacbbdbccbccaddbddcaabcabdcabdddcaabadcabadabbabdcbbbcbcaaccccccabcbabdabbdcdadccabbddadabddbcabaabbbbcccadbabcaabcacadcddcbcadacdaaacaddddadbacbbaddcaaddddcbaabbbbacbcbaadabdabcbadacabbadddcabacbcbcccabdbabcacabdddcddacdddcccacadcbbddbcacddbaacacadcaabaadaddadcaabcbbacbddcacdacacdbddacbadbdbccadbabdcccbdadbbbcdcdbaddaacbacabdcbdaadcabcabbcbadcbdaaaacdabcdabaacabaadaddcadbcdcbcacdddcacdacaacdcbcbbabacbadcaaadcbdbbdabcacbaabdcdcdaadbabddbdcccdacacaddcccbdaccadabaadddbcdaccdacbbacddaddbacaacaacabdbcabcaaadbdbcaaacadbadadaacaacadcdaddbcbbcbdabacadccaaddbbcdcddaacaababdcdabcaaabaaacbbabbcbbbbddacddbadcdacdadcddbabadaaabbcabaaacbdbcacbbdaccdabaabdbadbddcaddbbcdbccbbdbcccabbddbbdacaaabaabcccbdcbdabadbdbaaccbaccbdcacddcdcbbacbbcbcbccadacccbadacaadcbabddcaaacbaaadcbcbbcacbbdaddcdcbcbbabbcaadcdcabcbbbadadbcbcaddcdcbbcbbcabcaadbcbcdcacdbccacddcbccdaaaccddcdaddcccaddddaaaadcddaabdcacbbbbdcdcaccdcdaacadcbcccbdababcadcadadbdaccdcddbbdddbdacdbbadcadbcaaadbcaabdcadadacbdacbdaddcddacabaadbabbaacacadbaccbdbdbcabbbbbbacabbacaacccdbbcacbdbabdaacadcdbbcbbdbdbcdcbccbdcdcabaccdaadccbabaaadaabcabdbdadababcdcbbbddbdacbbdcbbccdaacbbcbcbcdcadbcabcdabbcbddccccdaccbbadcdbcaaaddcabcaacddbacaadbbaaccdbdcbadbdbbbbacdcaaccadadabcbacbdaaccdaddaddddbcdccabcaabdbcccddbcaddcbccabcccaacbddaccddaddaddcccaccccbcccbbcabbaddadbdcbbccdcccaadbcdcdbcabcbcdbdddbbacccdaabaacdbdbcbbbcaaadacdbcdbcdadbcbadbbdcbcccbdadbaacdddcbddbabcdccacdbcbbabaddcccdbbacbcbaacaddcadadbbbcacacbdbdcdbcddcdaadbdacbccdbcadcbccabccabdbabbcbabcdbbdcdbadabbaaccadbaaaabdbdaacadacddcddcdbcbcbaabbdabdbadddcaacdcdcbccdbdcdcaacbbacbadcccaaaddaaaccbadadbaccbaccdbbddbacbacaddbcaddaaacddbbdbdcccbcabcccdbcacadcccadcddaacadbacaabdaccccbcdbaabbccccbdacdaadadddaddaabccadbaccdaacdbcbcccaababadbdbbdadbcbbdbdcbbbadadcbbcaadacccadbbdacdbdbcdbcacbdbbcbdcbbccaddaabdbdcddabbcabdccdacabdbdbdbbcaaadbaadbdcccaaaddabacacacdcabadcbaadddcdaddbdabcdadbcbccbaccacdabddbbbabbcaccaacacbdcadaadcabcacdabbdcacaddddbbdabbddadccbbccbcbdadbbbaabcdcabdddcaabdaaacaaddddababbddabbdbcaaaabdcdcaababbacbbabdbcbacadabddcdcdcbacaabddbadacdaacbaadabcadacadadabcdaadacddbdacacccccbbcaadddadbcccdaadbadbccddbaaddbcabbbcdadabdacbdbbbaacbddbddcaaabbabdbbbcdaaccddcdaccbbcbcbcaddacdabdbabaaddbbdcabaabaabcabdabbccbddbaadcccacadbacccbdacbaababcaddccaabdabcbdcddcbcddbbbaccccbbbaddbaaadcbddbdabcbdcddbabadcbbacbbbbdcbbbcbbdcacdbcacdddaabdcaabdcaadaaacbbabacadacadcdbdbcbdaaaaabdadbcddbdbcbbbdcdbadacbbcccaadbcbddcaadcabcdbdabacacdbbdabdabcccbbbabacbacbadabdaddbddbcacbdbcbdadacddbbdccbcbccacadcbbbaccdbaaddabaabcaaadbcbccaaadaacdbdabacadacdcbcbcccaabcbdcaabaccbcaddadbcdbddcdddccacdabbbdaadbcaaddadaddcdbababadbdccdbcaabcdabbcddcbaaabcbccadaaaccdaacddbdbacdaacdddabaabaacbddccddcbadcbabdabcacbdacbaabcbbdcdcdbdcaadbabdaadbcdbaaabbadbccaaccdababcbacababcbcbbcccbddaadbabdccbcdbcacacdddcbcbdbbcacbaccadbbaabbdcbbccbacbcbbccaadbcaaacbdaccbbbcaabbdbddcccdbdacaacbdcdbddbccccaaccbabdbcccabcbbbdbcbcdcaacdaacdccdcdcbdbcadcbdbdadabaddccbcdbabdbddbabbccdddbbaacadbabadabcabbadcdcbaddabacadabaabcbbabdabcdbbacbdbacdbcababcadddabacbcbbddbcddbccdbdbababaaaaacacbbababccacdbabadacdcddbcaccacccabbabcdacdcbbbacccdbcbdcbbacbbaccabdbbcbddcbdacccdddcbadbacdbbcbcdacadcccbbcabdbaabcddcdbacabbcbdbcdaacbbdcbaaacabbcdaddabcdbccadabadadcccdbbbcdadaddbbcbbbdbaadbdddbcdccabbadaacdacbbadbdddcbdbdbdadccdcabbcadbacaacbddbadcddcddcabbbbdcdcddddcadcdbdcabaaacdcadcddbdbccabdccaaabcdccdccdbccdcaddddaccddabcccdaacddabdcaabacccabcdbbdddbdcaccbbbcaacdbdccdabaadcddbbdcbccbdcbcadbddccacabaddbacdbcbddbcdbadbcbcdaccbabaacbaacbadbbacaadaabbdbadbdbdbbcaacccccccdacdadcbdccbcdacbabcadabacdbdbbcadacadaabccccbccbdcdddbcddbaaddcdcabbbababcabacccaabbcabbdcbcadabcdaabcbabcadcaabdabbddaaaaaddaddadcccaaccadbabbcdabbdcbccadcbbaadbcdcbababcbabcabaddabbadbadabddadabcccabddbbaaadbdcababdcdabadabbadcdcdcaaadabbcddaaaccdbbacbdaabdaabccbbabdbcbbdbcadbcddacccadbaccbcbbadbbdbcadcabddabcaadabacbcadcccaabcbaadbcadacddbdbabcccaabdcbcabaacccaccaccbbcaacbbcbddcbaccbbaaaacdbdddbccaccddababbbbdaddcbcadacadbcccddbacdadbbbaccabcccdbabdacdabbdbbcadbdcdcabdbcddcdddbbbbadddacbbadadbbcdaacbdcacaacdacddcbcdabcabcabbacbcbccdbaaccdbbdcbadccacbcddccdbbbccbbdaddbbdcaddbdcaaaacbabbcbcddbcbbbbdcddddcacdacbacdacbbbbbbbbccbdbdaddcddcaaabcadcbcbbdacdcbddcbcbdcdccadbacbbbbdddabccbcbdabadcdaddcccaabbcabdabccddccdcccdadcabcddaaaaadcdbabdddcbbacdbabdddbbcdcacadadcdbcabdacdccdcbdadcbbcbdccbcdadaccdcdadcdaddbcbbabdbdcbcbdccadaabaaccddadddddaddcabdbcaddcbddbabcbcbadcbdbbbabacbabcddbbacbabcdddadabaadbdaddaaabdacbccadcabddbdadddbcadabdbbccabbbabbccbdcbabcbabacddccacdaacbddcbaccbbdcadccddcdaabbdbaddcccbdcdaaddbdddbaaadccbacadcabaabddbdabdddaddccacbaacbabadabadbbaabbbbabcadcccacdccaaacadabbbbabbdaadaabdcaaaabbdbbadadbbdaacdbaaccaddadbcabaaadacacaabccdabbbbadcdccdcdabbdcddcacaabbdcdcaacddbdbcacbbbcddbdddcdacadacbdcccabbdcdbbdddbbdbcdbddbdcabdcbdcacdbacddbbdadaddbabdcaaadcbbddddbdcddbddaabdacdabbdcdadccddcdcacdabaaabaccbddcbaabadbcdaaaccabaadaaabdbcdbcddcbacadbaaddbbdddbbaaabdcbdbcbcadcbcddabcdbbacbdadbaccbdaaddccbcdbadcdbabbcabacadcacbbaaabdabddcbdabcadbaacbdbacadbbddddbbccbabdccbbbbcdbdbacdbbdbdadbacdcbadccccdacabdcbdcdbabbcccabaccdcbbacbccdbccbadbdaadcbcccdbcacabadacaacdaadcbddbbcbccacbabaccdaaaabaaadadcbcbbcbbdcbcddcaaaaaddddadabdacccbababacbcacdbaabcbcccddaccbdcbbcbcacccabadacaabccbabbddcaacabccdbacadcccacacddbabadccacdabbddccadadbbaacbabacdacbdcccdaadbdcdbddcdcadbbddaaaccaccaabdadbacabcdcdcbbadbacdddcdbccbcaddccdbdcccacdbacdbcadaabaabccadacdccbadbccbdbabccacabcbbbbdadaabdddbdbbccacdbdbadcdbbbcdacadcddbacadcaccbcccaadcabccdcbcddddabbbaadadaacdbababaacbdddcadacbaccabcddddcabaadcddbcacbcabcacbaddbdcccbbddcaaadcbaacacdcbbbacdbacbcbbcdcbbcdacbbcbdacabacdbcbbbbaaaddadaccbadddccadbbabcadabdcaddaacdabbccaccbabaabbaddabbaadddadabcdabaccdaacccdadaddaabaccccbabbcabbaacccaaddadcabdccccbbadcaccbaabdcbddaaabbddabdddbdddabcdbdbbbdadbabbabcbdcbdbbbadcacbbddcddccbabbaddabdbaddcdbcbbdbbcbbccdddccadbddddbcacdcdccaaacacabaccacddcacbbbcbcaaddabdbddaacbdaaabcacdadacdbacbcddaabdabaddabbaaaabcdbbdccdbaadddccbabbccacadadabbcbddadbccdaabcdbbacbdcbcdabdbaadbccbbbabbabdccaabbcaacddbaddaabcdbdaabacacabbadccbdacabbbdabdccccddccacbacbdbaccccccbdaccbbdaadbbacddbbcbbdadabaadadadddabadcdcaddddbabbabbaacaccbabacadbdccdaabddacaddbaacddadbcbbbdcbacbaaccbbaaacabbbddaacccddcdaaccccaadbbddcadcddcdccdcaabacdcbbaaaaccdbcdadbdaabaccbadcbdcdbbbcbddbbdaacbbaacbacccbccacbcdcadccdbdcaaacddbbddaaccbdaaaadbdaddadbdbcacccbdbdaabacacaabaacabaccdbabbbdbbacccaddbdabdbbaccdabcaadabcadbccddacddbdadbbaaaabdcdacbddcbdcdcdcadbacbddcddddccddcccaabaaccccccabcacaadaccddddbdaaaacbbccbbdcdacbbbddaadacacbabdcdcbacabcaadbaccadcabdbdcddaaacdbdaacdbadccaabdaabcdcddaaabcbdaabbcbdacaacccbbcacdcddcbdcaaadabacaacadadabdadbbdadaddbdcbdcababdcccdbacdaaadabdccdbacbdccbcdcadbbaaadbcaabaccdabdaaabdcdaadcbbdbaacbbbdcdadcdddabdccabbadcddcddaddbdbbacbdabbccdbcbcabbbabbccdacbabbcdcabaacbdbbbaadacbaadcaddcbbbddaacadbcadaacabbccdbcccdbccadaaacdbccccccbbcbdaaadabcdbddabacbdaabbaaaddbdcaacbcdcbcdddaadcddcacbaddacbbddacadbbccaacdcaacabbadaccdcccaaaaddaddbcadbabcbddacdacbbbaaacddcccdcbdacaacdacbaccdaabbbdadbbbbaabaddabccdabbacdcdddbbdacddabbaadcacadbacabcabbabbaaaccabddbbcdaddbcbddaccbaaabdccbdacaaddacbbaabdbaaccbabcdcbbdacbdaddbbaaddaaabaadccdddbdcdacdbadaaaadbaaabdbcdaacddddaacbdddcddbcccbbcdbaccddddbddcccbdbaabdaaccccdbccaddbcbdabcdddcbacadbcaccdbcabaaddabadabacbddaaabdcdcbabbbdcbcbdbbaaabdadbddaccacdadddcabaabdcdccbdbcaabdabbadaacbdcbccbaddbadbacaaaacdbadcadcdadbacaadcaaccbbcbbabcaaacccbcdadcdacabdccdddcbbccaacadaaadcddabccacbbbbbddacabccdbcbadadcdaddcdabbbdabcdabcccbcabaccdabbdcacbbadaccddcdaccccdcbcccdcdcbaddaccaadacbddbaadcdcaacdbabccdbaccbcaaaadddcbbcdbabbbbaddabdaaccbcddcdcdcddbbbacadbcbaacbbcbbcdbbbbabadbabdabaccbbaaaabacbacadbcdccdbdbdcccccbcdbcabdabdabbdddddacbacaddabbbdccbaabcbcccabddadbbdacababaccdbcbdabccacaddbadcaaddacacdccdddbddabddccccadadacbcbdcdacdadcabbcbcdddbdbbabdddccaddbabbbcaaccdacbbdaadcdccaaaddacddcdadbaccdbacbadcccdcdcbaadbcaacacbbbcccbbdabbdabadaaaccdddaccbaddacccdacacbbdddbabcabaadbdaaccacaadcadbbddddddaabaacaddbdccdaabbdbdadadcddcccdcaaadaaddddccbadabacaaadccccdbcbdccadadaadabbacddbdadadaaddbdccddbaccbcbdacacbadbaacdddabcbddadaabdadabcbbdcdbdcabcabaabcbdbbcdbdaccccdcdabccaaccadacbbdaccbcacacabcbdadcdbaacdbbaacabbccdabaddcdbccadaabadcabababcccacddcdbbdbbbdacddcaccbcbdbdcbacdbbdbacbacbbdddbdcdaddabbbdadaadbcdacabaccabddacbcabdddbbadaccabdbbccdbbadbdcdacbaaabcbbcabadcddbbacaaccbbddaacdbdcaacbadadcadaacbcbbddabacaadcbdabddadabbaaccccadacdbccabdbcddbadbadddbabdddbdbcabdbaddabbbacdcddaddbdcbbcacbaddaaacaddcaacccbbacbcdcadcbcbbaadcccaaaaacddadaacdccacaccdccacaadbcbbbcdbbabbacaadcdcdccdbbacdcdbbcddcacbbddabaacdaddcacccbbaddacaddabdadcaacbbadabdbccdbcdcdbddadcddddbcacbcddcacdbbccbaddacddacbcbdddcbadaabaadbddddbabcaabaccbacdbbadcaaaaaabccdddadbcadcdbadadcbccaaddacbabdadcdbbccddbaaaddacdacaabdcbcccbddbcacdbadcdcabdcbbccbcccaadbddabacaaadccacdddddbbcdccbcadaccddbcacdbdcbdcadabcbacabdcacdbbbcacbbbccdcbcdadababdacdddaaaacbccabddcddadcaabddadddcdaadaccaccddadbaaabcbcbccadddcbcbcddbaddcbabdbbcabadadaadbdaacbaabddcacbadaddbbbabcbdacdbbddadccbdbadcdacaaddbcbdaaaddbdddbcddddbbbabbdcdbbaddcaaadddbbddcdbabaadabcbdddacaccccabadcbbdacdcdccacababbcdcbdcacbaadddacaaaddcbbdcdadacdbdcaccaddadcbaccabdbdbbcadcbbaabbadbbdbcabddbabaaddccdcbacdbbcabdbacbaaabbbbdabccdacbcbcadabcbbccabadacdcbccabcdaccabbbcadabadabaccdcadacbabcadcbadcaaacbbaabcdaadccdbbcdadbddabcaadaaccddcdadcdbccbcdbbbdacaddccdddbdbdacddcdbbbacddcdacaadabcabcaaaabbddcaabdcdadcbdcbdccadbddbaacabacbadaddaaaadaaddaaddbdbcbbbabdcdcdbdccbcaddddadcbccababcccccdccbbbddbbcabcbcbdcccbbcdcbbaadbbbccaddbcbbaabbaaaccbdadddacbdbcdbbbacaaaabbbacaccbccbadcbdcbbbcdabdddacbaacaaaabcaccbbbcabbcbccdabacccbbacbbcbccdadbbadccddabdcbdcaccbbcddcacdaadbddbabdcdbcbbcccddbbdcddcbabdccaadadabdccacccaddbbdcddbacdcacdbbdadcccabcacbaacdcacbccdaddaadabbaddabcdadccdccdbabdbcbddacadaabcacaabbbbccdaddbcabccabccdbabbcddabcabbdadcccdcdbbbdbadaddbcabbddcbadbcdccbbcacadbdbbaccbcbcdcbccbacadcdadbbbaadabdccabdbcacbacabdaddcddcadbcaccdabbcabbcabbabcdcbdcccbbbabacdbdbabbdbdccddbabdcdddbccdbbdacaaaccdaaabacbcdacdbdcdcadcbcaaacbcdabddccddcdaadabdbbdaaddadaddacbaddaacdcccddbdccaaadaacacaccdcdbcdabddddacbdbaabaaabdadbdaccabaacdbdacabcaaabcdcaabdabdbabdcadcabaccdcddaabaddccacbccacddbcddbccacdbdadbbcccbacdddcbbbaadccdaccbdabcbaacbadcabdbbbaacbcbcabaaadacccacbaddcccbaaaccbdcaacdaacadabcccabcccdccdddddcdbdcdcadbabdcaacdcccddaadddcacabacbabccbcdcacdcbacaddadadcdddacbabdccdbbbaddaacbbcbdadbdadbdbcbbdbbaaaacbccaaccadababacbbbccbaabbaccdccccbccadaabcbcdccababbcdabcbababaadddcdcaadacccadbcdbabbbdbdbcdbabcbddabbdcdcbbbabcbdadcdcccccddcdcaaddbdcdddacacbdacbddaabacbbdbbbcbdbbbccdddaacaddccaadbccdadaaaacdcaabacbddbadabdbdbcccccadbcddaacddcabcbabaccdadcabddacacbddcdbcadacdccabadaabbbbabaacddbacacdbcaacdddcaaacbdaddccbdcadbbacaabdcabcbdcdcbdcdbcabcdccbbaaccaacbdacacaddbbbcdbbacdbdddcbaddacbcdabdbabadcaddcaddaccadabcbadcbadbcbbadcdcabaacbbddbdcadcbdccbdabbccaacdcccbcdcaddadcddddcdddabacadbbdadacdcdadcadbadddaacbbbabadbbbdadbaaaacdddbcbddabadaacbabadcbcdcaadddabcabdaadadcbcaaddabddcadadcccadbcbdcbaaaacbacddbcaadcbdcadddaddbadccddaabcbcdbdadbabbdbbdcbacacdcbacbdaaaabacabacadbadcaacdbadbdcccbcabccadcbdacccddcacaacccdbcccabadbddddbcabacacaddcbabccdcaacadbdabaabbadacbccabbacabdabcbbbccddaccbcdbccdaaaacbbacbbaddbbdcdadacdccdcadcdcaccccdcaabbabdaacabdbdbabbbcdcaaccbacbbaaacdbccbdbdcccdcdcbdbbdbbdbcabcbaaaababdbbbadcdcdcbcabcaccaccdddcbbacbcbaaccdbadcdcabdbbaadcababcdbcbbbcabdadabbabadaacdbbdacdbdbcaccbbdcccbcabdbbdcaadcbbabaadbbbccabccdbbbacbdcbaaadaccbbaabcbccbcacddcdabacabdbdddcddcacaadababbbcaddabbabcdcabdaaacdcbdcbbcbbbacadddabcabadacbbbddacbbbccbddbdaaddbccdacdaaaacaacddddacbdcabddababcaaadadbdbddccddbbcbdcaadcabbabbbbcdcdadacccbccabcdbdadadaaabcccbababdabbadddabaaddcbccbddddadbccbcdbcabbdbdcdcaaccdcaddbaadbcadcdabccbcbbdacccddddddacccabdddcdbdabcdadadabbbdaccbaabdaacbadbbaddadcaaacccbdddaaddcdbcacdddbcacabcaccadaabadadaccbbcbabddcdbdbdcccaaadbbcdadbcdadbcbcdaabaadabdbcccabcdddadcacbbbbaabdbdcbbbdcacaccdbaddcabdbcabddccadbcbddaddcdbbdbaaacaddbcdabbadcdccccdaabcdcdacdadacdbcbbabadcdbcdbdcbddbdaaacdccbdbddbbbabcaccdcbbbdbdccccabbcdbdbdccdadadbacdaccaacddacbcbacddbdcaaadababdbcbbbabdbcbaaccdadcacadacbddbcaaddabacabcadadcbcddbaaadbcdadcdbcacaadcbdaabcbadadadabcaddcbbcadbadbdcbdccacbdbabcbbbcdbcadbacabaddaccccdbabccbabbcccdcbdacdcabbcccdcabccbabcbccddcbaaabbbbacbcacddababadcacdbbdcbcddacadabaddacbbdaabbbcdadbcdcbdadcbbacdadccabbbbdaccaaabbbbbdacbbcbbcbbacbbaaaadcbdcaaaabccdbcaabddaaabcabbcccbacabcdacabdbaccdbaccdbacdbbcdddcdcbbdcbcdbbccdaaabacabcadacbdaacabbaccacdddbaacbbadcadbbdccbbacdaabdcdababbcbacbbcacadddadbcbabddbaaccbacbaddabbcbdcbabddcadbcaadbbacbcbadacaabccdabacbbbdcacadbacbbcbddacccbbdccbcdaaddcaddbbacaaadaccbbbccaddbcddbabcaccbdbcadbbddaabbbbccbabbabccabcbbdbacdddacccdabbbcddaabdcaddaacdabaccaaaacdabdddcbabdbdabdccbbbcccccabadbbbcbccbdbdabbbcdadbbabccdacbdbdcadacbbcbbadaabbbacabdddaacaadacbcabaaccdaddccbaddbddaacadacbdbcddacbabdddbbbdcaadacbcaddadaabddcdbcbbbacaadcadcaccbcbcaadbcadbcdcabacbadcdbcadccbbbbbaaaddcbdbabdcdacbcabdbccadbbbdccbdcdcddcaddbcbbacadcbadbcacdbaacdbdbabadddbaaccdcbbabbbbccdaabcbabbacbabcbdcbddacdacbcbacbddadaaadcdbcbbaabbcbadbadccabbbddccdcbaacbcccdacccadbacbcadaacbdbbabcabaddaddadddbccbbcdaadbaccbadcddbbbbdbbabaabbcddabcaabbcaaacbddcacdcaabdcdacbaddcbbbbdadcdbbaacacdddcbcbbdbabaadddacdcadabddccabbcacdabaacbcdacdadaacbbcabaccaadccdabbabccddccddcadbddbbcadddccaccdbdacdcdaddbbccdccbcbbbbccbaccdacabadddbbbccdbcacadcbcdcbdccdaabdccdadacaabaacabcbcbddbddacbcbbabaccadccbaccdadcacdabccdcaaabbcadcccddcbcbdaabcbbcacbadcaddbbbcddbddadbdbbdddabccabbabaccbaaabaddddcabcadcccbcbcbdbdbbdabcbddcbddcadadcdaaaaddbdbacadcbcddaabddbcbacbbdcdcccdccccaddbadaacbbbcabccddbbaaacdbdadbddaabcdcddcdccadadcaabdbcabdcabcccbdadabbddcaacbaabcbdadddadcbbdababadccadadaccbccdaabacdbdccbdacacaddbcaccdbaadccaabdbbcbaadcaadcbcdbbdccbcadddababbabcbcdbdcaacaccbbcbbbccaddaccddacdddbdcbaddcaabbdbbccdcddbddcbddcdbcbbbabacbccdaddacbccbcabdcdbbbbdbcabdbcbccdbbabcabbdddbcbaaddbdbcddcadcbdacdccbaaccbcdcaaaaaddabdbcdddbaadacaddabddaaccbbdacddcdbacbadcccdaccbabcccadacbaccadddcbdacdbdabbcdcccbbcbbcacbbaccbcacccdbaacbcdbbbbcaabddbcacacdbbbdabddabaddbbcccdadbababcdaaacacdabccdcddbdcacaccddbaccaccccdcbaccbdabbbdcdbcbdabbacdbcddbccacdbbbadddadccdccbdddacbdcbdbacdababadddadacdcdddccdadabbdcbbaacaadcdbadccabdabccccabbcadcdacadbbcdccbbcaabdcbbadaccaabbdbbaaacdccbccbabcbdcdcacddbddaabdbaacababdbcabaddbdccbcccacabddbabddcbdccadabdbbcdcabccdcacaddadbabbcabbadbddaadccbcaddaabadcbcaacccabdbdabbacddcdbaccbbdadccaadbdadaaddddadccaddaddbbbadccaaabbcaddcccaccdacdcadbbabdacabcaabbcadcaddcbacbbadddccadcbadcadccbcccccaddaadcdbabcdaaccdabbddccdaabdccbccadbcacdddaccabbbbbdbadbdabdacbdcacbabcbddbdccdccdcadabbcdcacdbdccbadbaabdcccabdbacbaabacdabacbbaccbbbdadadabddbbbdddcadaddaabdaaadcaaaacdcccddcdddbdbdabaacdccbddccdaadbcccdcdddcdaaddaabbccdcaaaccdadcccbbadcabbacadaacdbdbcbabdaaaccdbadbdaddbccbbcbdcaaaacbcdcbbcbababbdaadcbacabdabcabcacccdacabacccadbddcccbdabdcbcccadaaacdbccbccbcaddbbdccabbdbbcbbbbabcadcacaacbbddcaddddacdbbccddbcbcbbbbaabbcdaadbcabaadbcadbccaaadacadaddcbbdaacccbcdbddbaddabbbdddddaadbccccacaddababccbcabbcccbbbccaacbacbadadabcddacbaadababaabbbbcdddcdbcbbbccdcbaaddbbadcaabaccbbdddcadbbdcccbcccdcabdbacddcdddbcbcdcdddbccbdccbdbaccdaacaabbcddcccabcdddbcdbddaccabbddcdbccabcadacdccadaccdabadacbcacaddddbacadbbbcbbdabaccccacbcbbcddaadadbcbcbdaddbbdddbbccccdbdcacbabacbcdabdddbadbcbbbacdbacbcabbbabcbbaacaadddcbbdddbdbcaababdbabbdcbcbabdcbacbdcdacbddcddcbdccbadbaadccbddcadacabaddbcdbcbcabbdaabbbdddbbdcbadbddccacdaccdbdddcacccdbbdbaababcaaababbdabdbdadbaccdccdbbbccadddcdacbacddaddcbbccddcadcbdadddadcacacdacdbabbaccacaaddbddccdcaadaddcbccabadcabdbabccaaaacaccdacbbbbabdccdddabadbaabcdbbcbbcbcdddcdabdcaddadddabcdabddccabccacdbcadbcadccaaadcdbaccadcdbcadadcbbdacccdcacabdbddddabdbcacbdabbbcdccadabddbdccbadbbaadacbcbbcbcdaccdcacacacacdcbabdcbddccbaadaabcccccbacbddcdbbcabcaaaccbcbcdaabbcddabdbaabcabdaacadbbdbbdbdbcaadacbaadbaddcdbcabcadaddcccaaabbadcbccaddaccbddcdcabaadacaccbdcaccaaaabbdacbbdbcdabcadddcbbcccdbabbbadddbadaaacbcbacbabbadacbabcbdaadadbcbbddaaaabdccbabdcccacdbaaddacdaddbccbbccbaacddadddaaaabacbbbcbaacbddcaaaaacadccacacbccacbacadcbcdaadcbababaccabcbddcbcbcbcdddddabadcabcdbadaaabdadcbdbbccabbddadcbcbbcbdcdcbcacccabcaaacddbabaadbbabcbaacaacbdcaccccaadccabbadbddbaccadadbbcabcdaddcacccdaacdccabbabdbbcbccdcdbdbcbbcdbcadbabcdcadacadbbcdacbcabddccacaabdcddcdaabadbcbadccaadabdbcbbdbdbdccbbdcacdbcbbdcaccbcacabdbcdcabadbbbabcdadccadbdddcddbabaaaacbcbbdddbdcadcbabacaaacaccbbdddbcacbcdccdaabbabaaccddccccadbaadddbdbaaacaddcdcaaddcccadccbdcccdccccddadaadcbccccaaaaddcbcdbaabaadcddaacbdbbcacccccadaadbcdcaadbadbdadbbbbccabdddaddcabddddcacdabbcbdcddbcdccbdcddbaaababadabbccadadddaddbdadbabdaaddabbadddadabaacacbccbddacbccbdbccddcccdadddcaddabcdaccdcdcdbdaabdbddabdcbcdcabcdddcbbaabddaddbabddbdaaabbaaaaaddcaddbcdbcbbddcdbcadcacaababcbdcaacddabaaaddcababbcbabccacdcbcacacbccaabbabcaaddbccbababcacdbacbbabbabbabdbcddbcbabccbadabdcadbbcbcaccaabbaacbadbccccbabddacadbcbadaaaabdddabdcbdcdddbcbacddccbbabcccccddabcdcbcddbcddaccdbaaaddadddadaddbcdcadbbcccadbbcadccacbcdbcbadbddcadddaabaaddcddcabadaadcdbadddcaabbaccbbbaccadaaccaadccadbdcacdaadaacdddaaabbccdababacacabddcbbbbbbccdadbbbcacacdcaddbddababcbcdcdddbcabadcaadbdbdcbbdbadddaabbccadbbabcbbdbdbaabcadadadbbddddbcadbddaabaccadaacdcabdbbabdaadcddbddcddcdcbbaccabbdcdacbccdcccaaabdbabbcdacbccabcdadccaabbbadbcacbbaadddcaddcdbcadddadcbbcdbcdacadccbabaaadccabdbbacdcadccdbddbcadacbcdbcbbbcbaddbcdcaacaadcbbacacdcddabcabacaddbadbccbcdcaacacdcdbdabdbbbadddaacabcabbcccabbabbdadcdbddadddbabdacadabcdabdbaaabbacadbccbbbacdccacbadaabacaccddabdbdcdddddcacbbabbccbaadcbdcdabadbcdbdaaacbbbabacababaacacbabbcdddddcddcdcaddaaababacbcdaaabdaadaadbbdcbdddcbcddadddbbdbcccbcbbacbbadbbdbdaababdaaaabbbdaadcaadccbcccddbddacadcbccabddcadadbbcbbddcdbdcdcacccbccdbacbdccaccbdbcdcbddacbbdabbbacbabbadbacaabccdabccdaccddcbaddbccadbbdaaadcdbaadacadbbbcacadcbddccdbcabacacdbccdcbdccbacbcbdcbbdacaabdccaadbadcaabbbdbbaddabccbccbbddbdddadbccabcdddbdbaabcdcbcddcadccaddabdcddcccaddbabddcabbbddbdaddabaadabaaddbbbacbdddccdbcbbdaaccbcbaddbdcdadaccbabdddbabbabbaadbbccbdbacdbcddccbbacdcddcbbcbdadadaccaabdcbacaccaabbdbccadccaddbbcbacdbabdaddcccdaadcdcacabcbbadbdaabcdaabacbccadcdadcbcdcbbcbcbacdcdacbbaccbacccbbbcabaadabdaaccddbddacdadcdccbaddadacdcdbadbaacdcacacacdbccbdcddaabbabcbdbcadcdccbadddadbbdcbdbcdadacdadcbaddcdccbcbdadcbabbaccabacbbcccdcaddcbccdcccdcadbaddbabcbacadadccbabdbccdadddbdcbdcaadabaabdddcdaccdaacdcbbbbaabbbbccdaaccabaccaaaddabbcbacabaddbcaccddcabdbbaadbcabacbcccdadabddacadaacabbcbcbbbcabcddbcbcbdbdaabdacbbcbddcacbcadbaabbabdbccaaaabadacabcdbbacddbacdabbadbcdbcdcbabadbcacacabdaacaccdacdadcabbbcbbcbddccbacbaadabcddcabdbaacdcbacdabbabbcbbacbbbdbcbdcaabbdadccdbadbadbbabcbddbcbdcbbaadcbcbdcbdadcbbccccdbaacccdacbbabadbdcbdbbbaadbadabbdaddbabaccacbaacdbdadcbaddbcccdbcaccccbaddcdcdbdccbcbaabadbcdcdbcbdcabbdabddaccdbabdadccccdcdbbddcbdbadcbbacdcabdccbaaddbccdcadbabddddbcddacccdcdcbbacdabddddaadbcaaacbbbddbabcbbcdababcdbbaababdcdddbbabbcbbdbdbcabccdbbbacbadccabcbbdbadbaaaadabdccdaaabaccbbbdbdcdaadacbaadbbcdccbabbbadacccbbddaadddacdacabdbbcdcaadcbadbbabccbcbbbddabbdbabbaadddcaabcddbadabbcddbcaaaddbadddbdcaddbcacaabaaddabaaccccabdadaddddacabddaaabcbdbcaddacadcbdccbddadabcccdbdbbbcaacbbbcccbbdcddbdadbccbdaacaabcbddacabdacdcabbcbbbcaabdadaddadbddbaddbcacaccacdbdacccdbbcccdaabbbbadadddcadadabbdbadcacccaaddcccdabaaadabbdbaabbadcacbabdcacddaaacbbccddbccaabdbcaadaaadaabdbcadadbdcbadabbcbdadabaccbcbbbabccbdabbdacdbcbccccbabbbcadabaddbaacccbcbbcbdbcaddcdbcdbbbdabcccaddddccadbaccccbcccbbccadcdbaacddcbcdcdadbccdbdababcdbacaacababcbdadcbdccaadaadacbcaacdcccdadcbacbbddbbbacbabccbddccabdacdacadccadcdacdbdcdbdadcdabaccbbccbcbdabdabddccccbbccdacdaadddcaaadcdcccdcccccbcdaadaacbddcaaaaadcacccbdbdacdcdadcbdccdbdacbdcbcccddbdcccbcdbbdbcbbcccabdbabccccbcaddbaccdcddadaccaacdbbacdbdbbdcbdabacbbdbcdabbbbadddbddadcccacdbccdcddadcdccbbdbbdcdcacabdddcddbbcdcccabacddabcdaababcdcaaddcddbaacbcccabaaacdddbbacdcadcdbcbcdcddadcdcccdbabcadacdbbbbddaccbcbcbdcccdccacbacddbaaaccbcddbbcaaaccacbbbddbcbdddbacddcbdddbdccdabcdcbbdcbdbbcaabccdcbdbcabbacccabacdcbabdbbdbbabdccbccbabcbdbaabbbcdbbddacaababbbababaabaabcbddbdddadcbcabcbdbacddcaddddbabbcaddbcacccdcdbdaabadbabbbaacdbdbacdddaddcbdadcdbbdbdbcdaddbbadbdbccadddcbcabcbbadbdbcaddbaaddbdabaacaddbcbababbcadcdbccabaddaababdbaadbacacadcbdcbbbacaacccbbbacbbabacdcbdbddbddabdcbcadccbaacdadbcbacddbadccdabcbaadbcccaaaadcbccdbcdaaccccbbbdccacbbabaadacabaddcdccdccbcbabdbcbcdabbddaddbbcbddddddbcaccbdbadbbdbcbcaacacbaadaaacbdaccaddcacccaacdbaccdbabbcbcdcdbcdadabbcbddbacdcddaacdbcdbaccabccacbadbabacdcdccdccbbaddcdcccbbaaadabbcccacbddacbaaadcaccaadbbbabdcabbaabacdcbdbdcaadccdbbadcabacdddbbcbdaddbdbaadbbaccbaddbbdcdbccdcacbbbaaadbbcdbcaddadbdbdccbccdbbbbadcaadbbacbbadcaabcbdcabbcdccaaccbdbadddacdabacbcabbacbbdadbadddbbaaddbbbccaaadcbcadbabaabccaddaadaddaabaddcddccbcacadacddadccbcaccddbcddbbdcddaddbdcbacddddbccbabbdabdccbdaabcbdccddbdacabbdcbddbadccdabdbabaaccabbbaccdaccdbbddacbabdcaaacbbabbdcbdddaccbcbbbadcbddaadacacacbbbabdbbaababccbcbabacbddcbbdadbdbabadacdcaabbacdacdaabbbbaacabbddbcaaadcdddbbcadccdcdccbdbbdcccbdbdcdbdcdccaccddbdbddbcccdcabaabbdccdcdbacdaadadadaddacbdddbccdaccbcbaccadcbbaddddbbaddabcabdacdbbcadbccccbbdaddddddddaccccccbbdaabcacadcadbcdcdbcbbaadbbccbabdcabbcbbbbdbccbaaddddacbdadbabdddaaaddaddcabcabcddccbbdddccddaacbbcbcdccdccacdbdaadbdaabccbaacddcbbdcabcdcababbaddddbacabaccbcdcaadaacdbbaddddccdbcdabbdcbaaaabdaccbcbccddabbdadbbbbbaabacbddcdddadcbdbabcacbbaaaccbaaadcccacccabacdacadbbadbcdbddbbdbcdddbdcdcbbcbdaacdcdbbbbcdbdbbbdadbcddabaaddadddbcbcccadbdbabccdacdbabbccdcdcdadbbadabcbbabdccbabdacacdaccdaabadbabbaabdaacdcdaabdacbbdaadbaddbcadbadacadddccbaaccdadcacddbdaccdbabdddcbcbcaabcbadbcbbabccacdbaadaccdacabddadabbdacdcaabddcdacaacabbbbdbbacbacbccbddaabcbbddcdcaadabdadddbdacbdbcabdcbbdadcdcdccbcaaadaadadbdbacccdaaabaddaccaadababbadbccddaabbcabaacacbacbbabadcababddabbbabbdbbdabdcabbcbcbaaabaddacbadbdcadcabcacacacadcabbacdcbbdbbcbdbbddaabacdbbaabacbadcbdcaabdbcbaadadbbddcccadcbadabdcdaccdbbcadaaadbbabcdddacbcbbccadaacbccdcbcdbbdccdbcdcccddadbbaabaccbddbaccdbdcdcccaacabdbbadabddbccdadadbabbcdabccbcccbadbcdcdcddccdbbcbddbcabcdbababbdbbbbbbcaddcccaddaccdbdabccdaacbcccddabbaaaadacababbcbcbacacacdccdccddbabbaddddacccbccaacaabdccbbcacbaccdbacaccaaaddbcbdacdcabddaadcaccdaccddccdddacabacdcdbdbccaccbbabbbbdcacdacbccbaccccdabddcdabbcaabacdadbdaabbbcbcbabcbbabadbccccbdaddccacdacbccddbadabddddabaddbdcbcdddcccdadbdbacdbadadbadcdbbdcadabcdbcdcbdcaddbbcdcccdabbcdddddddbaccccadbbdbcacbbcbdadadbcbcbcdcbcacdcbcdbadadbdddddaacbbabbabbbcaaccdbcadcbbbcbccdbabaacdcdccaccdcbcdaacbdadabccaccbdbcacaacccbacbccdabacabcdababdccbddbccbcaadacbadbbdccaaaddcaccbbccdcaacbcacbaddabadcaccdbdaacdabbbabddadbacdabdcaddbbdbdddcdcbcaddaddaaabcabaaaccdbdcdbbbddcaaacddcadccbabbbcdbcbadacdbcbddabcbabdcaddbcabbbddbacdccaadddddbdadbaabcdbbcbcaccaddacacadccbabcdcabcdbacbbdabbcbdaadbaaccbdcddddaadbdcadbbadaadcdaacacabbdccabdcbaabadaacddccacacbabacaccaccdbbcdddddccddadaadbbabaadbcbdaabdadcdaacdbcdacadcbdaaababcaabdbabaaddbdaadabdbdcadcdbcaddbacbbddbdccbdaccabbaaadaadccccbdadbdaddbccdaddaccdbdcdcbbaccdabdbbbcadcdcbcdacaaddbdaadbadcdbbbadcadddbbdbbaaaaadadbbdabcbabcbdddbcdcacbdbdddddabcbaddacbcdcbdccbbabcacdbabdddabcbcbbaddabbcaaabbdcbdbabcdcccbdbacdbbcbacacbbcbcddaccadaacacdabdacbaaadbdccaadddcbacaaaaadbdaaddadaccbaddbcdaadcdbaadacabcbbccbdaadbdddacaaaadbddbdabaabacdddaacbbbccdcbcdaaaccccaccbaaddbaddddbadcbadbcbacacaacdcacdacdddccdbacdcadcbbcbccbbdcccdbddcacbbdcbbcadbbcbabacbaccdddabdaadabacccdaabcbcdcdbccbdddcddccaaddabdbdbcdbcadacddbdbbcbbdacbdcdacacccabccaaacbccdbacabacbcdddcddcddddaadbccccdcdbbbbaabbdccddcabacdabbcbcbaadcbbbddbbabdcbaabdaabcbbbabaabdbacbaccadbacbbccaddacaadbabcdcadcdcccbdabaadccdbabacccacbdabbabcdaccdbcabdbdcadbadadcdddbadcdbacabcaadaddcbababcaadadacacdacbdacbabbbcbbdacbcbcddcacdacdabddbbcbbbacacdbcacbdcaacaacabaabddccabcbaabcbbdcdcaadabdcdabbddacbaadaccabddccdabcddbaccdacbdcbbbddabacdccaadbbaacbabaacbdbcdbdadccdddccdccbddccbdaabbaddbacbcaadccdcaacaadcaacdddabbccaadbadabdbcaadcddbbabbbcbbcdddccbaaddddbaaddacdabdbbcadcbcbbbdacacbcbcbcadabcaabbabbabacdbaabadacaaddbdadccdbcacabadcbcccdccadccdabcdaaabcabddacdcbcdcbacbccdccabbcbadabbcdddadaacaacbabadaaadbaacbbbabdacdadadddbddcdcbccaacbabdbcdbbcdddbaddcabadcbbdbddbbcadbdcaadabdabaccdadbbccadddaccadbcdcacddbdadaaadacdaaddbbadaadabacbbdbaabdcddcdcdbbaacdcbdcadddccccbaaadcadbccbadaadbbaadbbadbdcccbcabaacbbccbacdaaaaccdaccadbdbbbbabccdacbdbaacbcccdcacdcdcbabcaccbdccadcbaadbddbcabcbbccbbbabcabbacbbddadbcccbcbbadbbacbbaacdabadadbcdddaacaccaabdddabddcbabacbddaddacddccbbcbbcdbacccabadcdaaaccadbbdbccddaaaacbbacbbccdcbbcadcccddbadadddbbaaaaddaadcabacbabbadcaaaadcabdccdadbdbaccdaccddcabdaabdbbadaabbbbdacccbbbcbaacbdcaccbdccadbaaadbaacacdcdbcadcdbcdaaaadaaadacdbdabbcddddadbddadaaadaddddccdbdabddcbaadbaacadbddbdcababbdcbbccaccbadcdabdbaddbadddbdaacabbdabccbccdcdacdcacbcdbdbbdcbabaaabcdbacbcdcbaddacbabadaadcbcdaaacdabcdbccbbabbbccdddaddccaccadadbbdddacbbcbabdbbcbdbccdabdcbadbcaaaadbcbababbbdbdaacadbdccbaaadbdbaabddcbccaccbbccbdbcaabbaacbadbcaaacccdcabcddcccccbdcdcdbabdcdcacaacccdbbdddbbbbdbacbddababbadacbaccaaddaacdbddcdabdddcacbaaddacbcabcadcdbcdcabaccddddaadbbdacbddcdabdacdbdbcdacabadbccbccccbdaaadaabddbbcbabdadbccddbdbcdadbbddcbcddcbdbadbaabccaaccdcadbaaabcbabaaacabadaacbdbcddcbbdaadcdbdacacabacaadcbbbddbcdcdacccbddcaaabbabdaaccaabcbacddbaddabcabbacdbabcbdbdbccbadcdaabddbaddcccbcbcbacadacdcbbacbdaabaadcddcddbadbadcacabcabbbcaababcdbabadccdcccabdccddbdacbbbcbcccadcbbadcaccbcdbbcdcaaaadcbaabcdaaddaabdcbcdbbbabbbadcbbadcdddcbdcbcdbdcadbcdbbdcdccbcdbccbacbdbababaabccdaaaaddccbcdddcbaacbaacbcddadddcbccbcdaaabbcbcbadaaababbcdbaacabdaddbbdccbbaadbdcacdddccacbccbbbacbdbaadbddcaddcbabcaaacabcdbbddaacbaaacdabcadbaabacdbccabdacbddddaaddcdaaacdddadacbbcdaabdadcacbdbdccddcddaaadbbdbabdddcbcaaccbcaacdbbadaabbcabbddcdbbcacacdababdccdbbbbaddbacacddcdcaddcaaccacddabcdcaadcdabbddcccbcbcbcdaabdddbacccadabbddcabbacbcdcbcbacddadbddbddbabccbbcbdccbbdbbbcacaacbaadcdadacbcbbdcbacbaadbdbbddbdbcdabdaabbcbcadabddbdbcbabadaccaaadddcaccaaccccbcbbaacdabadbdcdccabccabcdbdabadbbdcbacaccddcdabdbddadbaddaadbacbdbdabcbbaaddcbaddcababdbcbaababbdddbbdddbabaacadcaabbcdcccbaaddacddcddabbbddadaabbcaabadddabadbccbdadccccdaabaaccacaccdaddbdadcddbaacabcdcbbacccccbbaddbaaabcbaacccbcabddcdbccbccddccdcbbadbaaadbdbbdbacddaacababdbccadddaaabbadcddcddbabdaacabcaddbcacaccadddabcddabdcccadbbbbdabdcdaacbadcbbcabdcbbbdbaccacaacdbcaccaacbdaabdccaccaababdabcadbbddcdacbdacbddaaccabacddbbaaddbaaaccadcbaaaacbcabdcdabadaadacbabbcdbabdcabccbadbaaaabddbadacaaaadbddabcacadbadbbcdddacadcbaabababaabaaaaabbcbdbddddabbcababdddbddcbbcbdaadcbbaddcabbaccadcaabcbbbabcaccbdddbbcabdcbdbdcaacdcddabbcbbcdccdaddaaaaaacdbccaacdbabadbbcddcbcacacdccbdbacddbdbdbacbdddcacdaccdaccacaabbcaccadabddabdabbccacbbbcddcdcbccaccadababdcdcacbaaaacdcacccbbcccacbacacddadabdbadacdcbccbcddcbcaacdcbadacdaacbcdcccbccacababbcacdacbdbddabacaddbcdacdaccacbcccddddacacdcacbdacdcabcbcbdacbbaadbcbabbccabbccdbcdbcddddbaadbcaaccdbacabbcdccddacbcacbdbcbadaacdccabccbdbbacbacacbbacaaaabcdbcadabbdccdcdacacdaaabcdabdcbcdcacbdcdcaacbccdbaaaacabcbadcdbbccdabdcbbcbcbcdcdadaccbadcbccaddbcdcdcdbccbaccccbbcdcdaaacabccdcaaddbaccdacacdbcbaacddacdbabdbadbdcabadbdadcccbadcaabacccabcbdadbacabadcbccbbbbbbaddbdaabaaacbcbbbbcdadddabbbcbdbadbadccacbbabbcdbccdccbcadbccdbcbabddbabdbcdcadddbbdbcdcadbdbcbbaadcaaacccddacacbdcdccadabbbdcccdbbbbccaaaccdddbdcabdccbdbbbbabbabadbadcabaacdddbaabcbcbdabdaacdcdbabacbdacbdabbaacdadccaabcbacabbbbddddbabbccbaaccdcbbccbbacbbdbddbbbbbcacdbbdbccbacacdddddcacdbacbabdbbbddbdcacccaccacdacadddcbabbdbaacbaadbaccadabdacddbcbdbbcdadbabadabddddddbcdbbdbbadaadbbbdadccbacddccabaabdcaaddacbccddcbaadaaacdddbcdbacccadbbcccdbdddcadbabdaacacbcacbdcbcddccdaacddcabdccbbadbcbcacbbdcbbccbadabcaabddacaabbaccdccdbbacccdbbbbbdabddcdaabdbdabbcbddcadabbbbcbaccabdcadbbdacdbcaccaddbcabdbababdccacabddccbaaaaccdaaaadaacdadccccbbdabbbbcbdadbabbddbadccdadabbbbbdcdcabdbdbabcbabcccdadabdabdbaadbbbbbcddcbdcabccdcdbdadddccdaadbdbaccbbbbbcaddaddbdddabbacaaaabccadccccbddddbdcdddcacdabaadabbabcdbacadcaccbdccccdddacaaddbacbbbcbcdaadcdacddcabcdaabbdcbacbbdccdbcacbacaaddcbbddaccabcdadddabccdbdabddcabdddaddcaabcccddbbdaccdcabdbadcdcbdccaadbbcaaadbbadbccccadbaddcabcddbbdaccbdacbcabbcbdccddcdacbadbacabadcadacbccbadaddbabcbbbbbbbacdcabbacdbcaaadacdaaacbbdabcddcccbcaabbbaabaaaadbadaaadbdaddcdcabcdabbcabdcacdccdaababbccbbdbcdabbdbacbbadcaacbddcdcadaadaddbcdadddbaadddccddcbabbbdaadcacadcdacddddadaccdbddcbdbbbbbcdcdbcbdcabbccccbdddcbbbbbbdbabacbddccadadcdcbdbdbbcdbababacabacbaaaabacbaddacbcacaccacdcbdabcacaddaccdadbcbdcacaadabbdccbdcbcabdacaadaabccbcddcdbbddddbdbdacbadbbadbcacbbbddaacdadbacadbbacbbcdabadddaaccbddbbbbadcadcdcacacdcdaddcaacccbaddacbcbadcacadabaddbbbddbcdcadcbbbbbbdbbdcaddcbbbcbbbbdadcdddadcddbdabdddbcddaddacababcdadcddcabbacdcadbbaccaadcabdbabacbdabdabbdbbcdbbccaabdabbbabbbbacbdbcddcbbabbcdcddcaccacabccbddadacdbbcdcbddcaadcbbbbadacadcdaacdccdadaccaacaacbdbbbddbddcbdcadacddbcabbbddabdcddbdadcbdcddbccdabccbdcbdcdccdcdccababcadbbddcbddcaabccabddaacbbabddbbaadbdddcacccdbcdaddbacadcadaccdbcadbdcdacdccbbddbacccdabddcbbdcaddbddbbacdbccabbdabcbdbacacdbbdbbbdaadbbbccabaaddacccbcdacdcaddadcddccaabacaabcbdadddaabaccdabdabdcdacddbdbcacdbdbbaacabddbdddddcadbdcacdabaccbbadcaaadccbccbdcbdbabaacbbbaccadbbcaacbcdbdaaccadaccdcadbccacccbcddadbaabbbccbdacbddbccdadbcdcaaaabcccdbdbdadcdbccccdcadddcbdcbcbabbbddabdccbcabcaadbcdcdabcadadcaacbadabdabcaaabdbcccbdacdaccccdabcccddcabcbaabacbcaccdcabdbbcaabdabdcdaacbbcacbabcdabbbacabbbabbcdbacbcccabcbaabaddaacbbdcaddacbbdadacdbccacacbcdddaddcbccaaccdcbacbbbbcbacbacbaadadcaaddacbabbbbbcacabbdcdcbbddadadcbaccdcdcbbabbaaaccbdacaaddccdbbcaabdcacbbadbadbaddbdadaaabcbbbbccccacdddaddbddccbacbadcbbabadbacdaacadcbbacccacbadccddadddbcbcaaadccbadcbcabcbcccddbbcddaacbccacaadacbdaadbcacadbbdadbcbaadcddadddcbbabbdcaddbbcbaddadddcbcadbbdabddabcadcbbcabdccddcaadcbaaabddcdbcadddbbcaabdacacccbbbcbbcdbbdadccbbabacbcbbccdbbdabccacdcddcbacccbcbdcaaaadcacbdcacbcdccbcbcabdbddddddbbcddccacbabcbcaaadaacacbbaccaaabdcabacdcdbdacbaadaddcaddcababbababdcaabadadbdbcbabbdddddcddabcbbccbdadbccabaacbacbdbdccadaaccbaccccccacabcbccdddadccbcdbbaaaaaabaadcbdaaaaabcdcacccbbccdaabcccbabdbadaddbbbadbdadacadbcbdaccadaabcdaccbbcaddabbbbbcdcbababddaacbbbaacbcbabdacdaabaccababcccccdacbdabcabcabbdbdcaabaccddbbddcacacbdbabdbabcabacabcdabcadcccbabbddbbddabaccbbccbbbadbccdacdbbdbdadbddacdacdccddabacdbdbdcacdabaaabcdcacaddabddbdcdbbacbdbaadbdacabbcaddaccdcbacdacdcbaacaabadbcaaabdbdacbacadbcbacbdadabadddbaccdcddbabacaabbddcbcbcbccaaaadadbddcdabbcbacadbdddcabcbacccbbcbcdbcdabbcccccaadcdbbbdcbbddaccbddabbbcdacbadbaccbcdaaccbabbcdcbbbaababdddadddccccbbbabcbbacccbabbbbccbddadccabbbdbbcbcbadbacdabaadcbaabbaabcddabddabdadacabbdaddcacccbddadcdadcadcbacdbddddcaadbcbadcbdbddcdbdbdcadbcbcaadbdaadcdbacdcbcdbdcddddacbddadddbadaadcdcccbcdadbdaababbbbadbcbccaacbbcdadcaacadbbcaadddaacbababbbbdbccddbaaadabcccbbbadcabcccbdcdbccdcadbadbacbaccaaddacdaddbdbcbbcddaacdcbbdbdcdabbccbcaaacdbaaddccddadaadcacdddcccddddbccbcdbadbadbbccaddcdadccbbcadcbdbcadaccdbcdcddccbbdacdadaacddccadabdcdaacbdbacaaacbacddabccbddddcbaddbababbcccddcdacbdcdabcaddacaccaaabbabbdbdbbcbbabcccadcacabcadadcccacbdddbddcbbbdccdcdccabdddccbdddcdbdccbbddacccbccaadcbdcacdbbabacabdadadbdaaddabaabdabbbcbdccdccdcacbdacddddbbdcccaaddbbbcadbcdabdcdabcbbbbadbbadbcccbbbdbabbbbddbdddddcdcdbacadbcdabcbacdbbccdddcdcababccaaddcdbaabdcbacccdcdbcbcaacddaadbaadbabcadcaaadaaacadccddbcdbbddbaaddbaaacadddcbcbdddcaddaaccababbabbabbbdadcdbdadcbdcdbcaacdbabadaccccbccdadadbccbddddadabcdbdbdcbbccbadadaadcbdaaabbcbdaacdaccbccdaddccbabbaccbbadcacdccaaadbaabcdcdcbaaaaaccacbcccacadbadbabcabbbdabacacccbddbcadacddabcddcacddcadbdbdadabaaccbbcbaaaadcabcaaaacbbdbbbaacbccdcacdbbdccbdbcbaadbccdbddaadcbcdcbaddcdbcacdbbdcdbcbaccaadcbaacabacadbbdabdabbcbcbcaabcbddcbbbbbccabbdcbdaddccdbaacabbadcbacdddcdacdccbbcccdbbdbacabdbcdcbbcaaabaacabcdcabccbdcdabcbadabbdbbbdbdabdabaaacacaabdbbcdccbccbadcaacabcacaaaacadbbdcbdacdbbcccdcccadbdadaccddcccabaadcbadabacbddcbcbccccbabdbccadacadadcbbcdbabcbdccdccbacbcdcadacaacbacbbbcbacacbcddcabcccaabddaacadbdadcadcbacabcbbaaaadbdcadcddddbdcccbbaadadacdcbaddcadaaacccbbbcdbccccbacddacadbadbdabacabbabddddbacdaabcacbcdccdbddcbdbadadbddccccadddcacadacadbdbdabdabddadcbdbacdacaaddabcdabbcabaccbcbacbbccbcbbddbaaaccbbbdaaaacbaabdbcdbcdbbdddcbadccbaacaadabdcccabdbccdbddddbcccaaacbaddcacdaaddcadcdcbdcbcadcdacdcccaddcbcdbddbbacacaaadabdaddabdbdaaacbadbccbbbbcacaadbdbbddbcdaaaadcabbcbdacaccaaabdcbddbabddbdcdadabbbcccbdbabaacbacddbddcdbaadadadbaaaaabbddaddbbdcdcdababaacddccbdaacabdcabaadcacbcddcbbcbacacabbdbccabddbcacadbdaacbadbcdbaaddaacbdbcacdbacbbdabbacbcaaadaaabdcaaaabbababccbcbacccdbbdbdcbadadaccbadadbaaaabddcadcacbcabddcababbbbbadbdacdabcdddbaabcddadacacddccabaddabddbcbbdcccbccdcccdacacbbadccadbcccacbaddaadacbdadcacbccccaaaabccccbaccccbcdbaabdbbaaccaadadcaababddcdbddbadbcaacacadddcabbcbccaaabaadaabaaabaddccbabcbcbcbbcdccddbadcdcadaabbacbccccbcbadcccdccadcbcdbdddaacdadcddbdaaddbabdbbdbabcdaabdccacdaaaddcccddccdacdbdbcbdabcddacddacbdbadabcdcdbcaabacaccbabdadbacccbdcabcbacbacabdabaabdbcbcaddbcdaaddccbadcbcaabacbaabbdcadabbaaccccccbbaababbacdabbacaaccadadadabbdbaaaabccbadcaddcbccbdcababdbacdbcacddcaddbadbccbcacccdadddaccbcccacddaacdcbabcadbbcabdcbcdcbbcbcccddbcbacaaddbacbadcdbddbddabdcacbccdcbccabacdbcddcacbaccbaabbbcbbccbdddbabbbccbbbcbaacbbbccadcdcdccbcaabaadbadcadcabcaddaabbdbdbbdcdaaaccabacacacabcbdcbbddcdcddcccccbaadbccbddddcdbddacababcbcdbcabdabdadbaccaacaddbcbbcdaddccdadbabdadcaaacdddcaddbdacccadcaadabacabaaabbcccdcdbaabdaddbcadcabdadccbbdbacbdbadcdbabdbbaccaccbadbdabcabdbcaddbdbbbbdacbbbacaaacdbbdaadbccdacaacddbabdddadcdacabbacdabdaacaddccbccbaddcdcabdccccaabcbdddcadaabbaadbadcbababaadbbbaddcccbccbdacbdcddcbacdaadbadbbbcdbbbdbddbabbcbdbddcdccadbddddaaddbcccbdbbdcbcbdcdddadbbbddbcbaddcccaddaaddddaaddcbdcbdababddabcabbccdbbccacbbdbdaadabcdbbaacccbbcbababbbaacacddbabbaccaacccdcddaccbacbdaaaaacaabcaacbcabbcdcbcaaaddbaacabddcbaaccdcaadbaaabaadddacaacdacbacdcaddcdadbcccddacacbcabdaadcddaacaaabdaaddcbadbacbdaaabccddccbbbcddaccddbacdaaaaabaadabbcaadbaaaaabcbdadacaacbcdaaadacaaacdccdacabdbcadddbcaccdcbdbdccbbbbcdcdcbbdaaabdddcdabcabbdbdbbddcdbbcbdbabddbbacacdadbbacaacbdabdcadaccbbbaaabdaccbdcbbbadacbdcbbaabbbaabbbdadddcaaadacabdadaaacacbccbccdadaabcdaccbcaadddaaacdbcaabdbdcdbdcdabbddabcdbbbdcddacabdccbbabbaaaabbddbcbddbadbaabbddaaaaabddabdaacdccbdcaaadbdcdcaaacbdcbcabbcbccddbccdaaccdbbdaabbbcabccccddcabbcdaabccdbcddcaabdbbbabcaabdabbbadcbdbbaabbbbcdbadccaacacadbcdaddabadbabcdbaaaabcbaaccbddcbabaababbcdacbaadaccbcabacccacadbabbdbaddccaddbadabaddcbacbbabbbddcbbbcbbdcaaadccadabcaabdbbaadbbddadabcaaaaaaaaacdaacbbdabddbadbacdcbbdbaacaaacdccabaadbbdcbbcababaabdaacbadcbccbdaddddbbbcaaabdcbdcbbacdbcabbbadbdddbccbdadaabdaaccbcacacabddbcbabcbdbdabbaadacbcdcdbdcadbcbdcccdbcdaaaaabacdbabbacbccdbdcddadddbcbdcabaccdcbacdcaddbcdcbdddabbdcacabdaadabbabbacadcccccbcbabacabadcadccbadbacdbbabacccdcabbcddcccbcbadbdcccabbbdacacddcccadcdbabdabbacdbccbdbaccbddcbadcaababaddacbadbaacbcdacacabcacacddaaabdddccbdbbadabaccaacabbcbdbadcaabdbdabbaacaabccdcaaacacbcbbaaddcdabaabdabbadacaadadcddcbdccbbaadabbddcabddaaaaacadbaddcbabbadcaaaaacbcacadcdbccbcabdcacdbdddabdcbcccdabdcbdbdabcccdabadadcbaccbdbbddabcdaacdbacdccbcbbccbbaddcacddbabacaabacabdcccbbaccdacaddabacaacbdbddbddbddcdaaaccbdaaacdbccdbddbcddcaaadbcaabbbdcddbccadbadcdcadabcdaccdbadbcbbcdabcbadbbbadcdddcdbbdbaddacddccbbccbcccbbcbbbbccaadcacccacdbddbacacdbaddcbdaccabbdabbccdacabdaddadcadadbcabaaccbcbabddcdacbaadcbaacdbaabbaccbddcdccadbdcbbdccdbacadaacbaacaccadaaabdabcbadadddacdbdcdabcdcdaddbcbdcdbcadabccaccabdaaaadcaaadacaabccdadbcbadcdbbbdbbcdbdcaadbbcbbacdbcabaadbcdddbddaabdaccbaddabdbabadcdcccdbdbbcabadcaabcbcddbadabcddcdccacdabaaaabbbddcccdbcbdaacddabdaaadbcccaccaadcddddbbaacdbdcbbddcccdbdbaabbbcbdbbbdbbdddbccbcdbacbacbcddcabcbdbdadbcaddadcabdccdadabababbbddcbbcadabbdcbcccdccdcbbcaaadbabadbbaabcccabbddaaaddbbdccbcaaadacabaabdccdabacabbabbacdadccabcababcaaccbcbdadcdadcaaadcccdadbcadbcdcaccdadcabcbaaddcadacbbbbbcaadababdddbcddacccadabadbbdcccadadbbddddcacaaaccbddadabaaadccaaddcdaaabdabcddddbdbbdadbbadaddddccadadcdabadacdacdadaaaaadacdadddadbcaaddaabbcbddcbbaaccdccbbcdaddbcbbaabcddacdcadaacacabaaadabdaacdcccabbdbdcdcbbdbcbcdbddcdcacadbadcdacddddbbddbbdadcccbcccabdacbacdaabbbccbcabacadabcddddaabdacbbcccddabbaddcdbcbcdcdabbbbaabbccdbbccbbbacbacddaaadddacbbacdcbdcabddaaaaddadbdbdcadcadbbaadadddcbdbddbccdcdbbacdacbbcdcabbcaabcadbdbdddcaacadadacdacaacbcadcacbcdacaccbcbddbdcddbacacabcacadcbbdcbcbbacdcddbdccdabadbcbabcdbaaaadbbdcacbbcdbcadbdbabbbdcacbbbbbddacbadaaabaddcadcdbabbacccddadadaccbccadcacdbbcbdcbccaacccabddcbabccaadbabdbaddcacbcdacbdacaaacaabcacaabacbdcabaadacccbabdbdbcbcadbadcbabcbcdcdcdabbdadcddbaabdadbadbacddbccadbcbabbbdcadabcbdcbcaaccbccbadbcbadbcbadccbdababccaabcaabadbcbbcdbcbbdbccbbaccaccadbacaabdddcbbccddcacbadccdbdadabddabaccccddcadbcbddabadabbdacaabdbaabbccadcbbccbabccadddacabbcabdcbcacbbddbaacbacdcbcbbdacdaacadadcdddbdadaabbcccdbccadaccadbdabcddcabddacccbdbdacbdcccbdccaaabbbbcbcddbdaddbcddcdddcdabbbdaccdadaddaaaddaadbcdbdccbabdccacbccdddcccaacadabcdbbcaddbcacdcddbdcaabdbbbbaacaadbbadacdbccacdddbdcdddbbbcacdbaddaccddddaadbcaddabaddbacccbacdddcdbdcbcbdcdcbcccabaaddcadbbcbccbaaccbddbadaccaadcbcabdcbbbdbbdbcadbbdacbabcdbbbccabddadddaabbcbbacadbbdbcdcaacbaaaaaabbdcaccbddbcbabaccaacddacaccadabbdcdbabaababdcccddabadababaddddcbccdccaacabbaacbdcdbddccabbbadddcdaaacaadcddbcbbcdbcbcadcbcabdbccccaadbbdcbaaddbbbcccbccbaabdccababdacccdcdaaddddccbbdaaaababdaacbdcddccbcacdcbdbabcadccddbcaccbdddbdcbddcacacacddbaacbaaaadcdbaccbbbbcabadadabdddbddabaaaaaabdacabdbabbdbdcbcbcdcdcdabddbadcddbdcbbaaddbaddcbacaccaaabbcdbabcaccccbcbcbaadcdabcbdbdbddbdbbdbdaadcccacacbcacaddaacbccdadbbccddabdacaacddbcddbbcaadccccacdbdaddcbbbaacccdcacbabdcccccbacdbddbddbcabdbbcabaaaaaabcbddcccababbcdbadbbddcdbcaacddddddcbcddccaccbcbdabdbbaaacaaababdabcbaaadcbbacdbcacccbaadbcabcbbbcdcbccdaadadabaaccbabdcddbdadcccabbddaadaadbdcadabbdaaddbabdcabbbadccabddcabdabddcbcbcabadccbbdaabaadaaabcabaddbcbabdddbbacddcddcaddccabadbcdbbbdaaacdaacdbdaacdcdbcbabdaabdacaababacaacddbcabacdbbcabdadaababcbbddccdcdabddabdbbbdbccacdccbacadaaabadbacbdbabcbacbaacaaabaabadbbaddababccbbbaccabacbddcabddbacacdaaaadccbcaabdbdacdadddcacbdcbaadbddcbddcbddadcddbaacbadaacbbabadcddbbcdadddbbadabdbbdddadaccbddadbbabbccbcabaabcbddadbddccadccaaabaabdadbcccbbaccaaaddaccdaccdabccbcbbbcbadbabcccdadbacaabbcaaabddbbcadcbbdbaadbdcccddabcadcbbbaaccdaababddbcdabaaabacdbdcdadbacbbccbadbcadbaddabcdacccdbbccacddbbbbdcabdccbdddcaccdbcaccadbaaabaadcddaadcababcbcbccadbbbbccacaacbddbaaccaadaaaddbadaacbacbdcccadddbcdaccaacbddcbdadacbcbbdadacaccdaadabdaabcdbcdddabcacccdcdabddbbbaacadbcdbaadddbbdcccbacddbdbddccbbcdccadcdaaabdcdcadddabdccaabdbabcbaaaacabbdcdccaadbdbdabcabbbaddbdcacdbadbbdbadbabacabbbbcbdcbbabccbcdbbccbabbdcbccbcdcdacccbccddddccccacbdcddbdbbddcaddcdcccbccbadadcdccccdbbdbddcadbabdadabcabbbbacacbcbdbddaacbcccadadabdacccabacbbccdcbbddcbcbdbdbdacbcddaccabdcdaaacdaddbcacbbcbabbaaabaabcbcabccccdbccbcbcabbbcbccdabbaaccacdacdcccabdbbaaadbdbacacddcadbbcbdbadbbadbaaaacdbcacddbdaacdbbcdccacdbdcbdadcaabaacdddcbacbadabdddaccadcaccccbabdaadacbcddcbacdddbdcadccdbacbadcacaaacabbaabccdbbbbbcadbdcbdadababdcdabbacbdbcdbbadcaabbbdbdbcdcbaaabbdbcaaacbcdcbbdaacbbaabdcddcabcbddddcbdcdaddbabcaccbbdccbbcadaadabbadbddaadcaddbadadddacbddaaadbabccbdbdbbaccbbaadbacbccddcbbbabbcdbbdddcadbaaaacaadaabbddcccbbdccbadbcbcbbcbbcdcaacbbadbddcdcdccccbcccccabdaacacaadaaacccbdbbdccacdaccaabdcadcbbdddcdaddcbbdacbdbddcabdbbcdcabbaddaabdcccccdadbacdbdbdbbdccabacaaddcbbcbcddbacbdcddcbbcbbdbdcddbacadbcccdaaddbdbadccadbcdaddaaabaccaccbdbdbaddcdddcacbaacaadddddbbbdbdbcbacbdccbbccbacadcacddddcccbbacdcbdcccbbdbccddcccbbabdcbadbbccacbabdbcbbddbccdcbcacccaabbbbbcabdcdbdcbdccbdbcbcaabadcdabacbccbbaaadbccbadabdbadacabcccdadbddaacacdcbacddabbcbbdbdcdcacbacddccdcdcaaacdbbbdbbdccaccddacddaabdcdccbacbaadaabdacddadbccaabddacabadcaadcbaccdadadbabccbcbddacbdadddcbabbbcdbbdaabdbbaccaabcdcbcbaababaddaddabdddcccccbdddccbbdabcdcdbbdddbbaabdccdabcabccadaaaacbdccdcabccbabcabccadddbababadbbdddbaddabcdaccbcbbccaddabcacaacaaccbbacddadccabdabbccdcdbcdddbbbabcddccaadcacbddbcbabbcaadadcacddbcbbbdcccbdbccddadaaaacadbbbabccbabcadabccbddbdbccaacbcacbdcaccddbbdbadbdadacbbbbadcbbbaabbaccdbdccbccacbbabacdaacadddbdccbaaacbcbabbddcbbaaabdabcddbcdcacacaddcbccbaabbbcdadbccdaabbdccbaadbdabbabcbcbbbcababcddadbbcabdcacdcbababacdbcaabdcbcbdabbbbabacdccbbbccdadbbbbdbbdbabcdddcccdbbbbdccbbaccccbbcdbadaabddcaccbdcdbbbddacdbaabcccaccaababcdddcbbdacaccbddcacbcdaddacddbccbcacabacdbaddcdbbacabdcbccdbbaadaabcbddaacdadcbdabcddcaaadbcdbcaddbbcdcdbadbbddbcdacadbdbacdadcbbaacdddbccadbccdccdbccaadcbddbacddaccabbddddadbddbbacbdbaabbdbadbdaaccddabbbcaabbccacdcaabcababdcdaadcaaddbddabacabcdbadcdbbacdcababddcdaabccbdbbaaacbddccbdbbddcbbcdccdcbabccccccbcbadbcbdcacccbaddacacaaaabcbbcacaaccddddabaadcaaadbbbcbaddcbcccbadbbbacddbdcdacddbabacccddcdbaabbdbbcbaddabbcdbdaadbcaadbcbdbcdcbcbcbbdbdadccabbabcdabadccbbcacccdbaddabdcbdccdadacbabdbbaccdcdaacddddcbddddadbacbcdabbdcbadaccbabacccadabbccdcbbcccadacbaadbcabdadcccccdcccdbaacbcdacadbaadcbdbdabcaabdcbaabcdddcbacbacacaabcabcaaaabccbcccdaacaccbaadddaaaaaadadbcdcadbdcbaccbddcaabdacdcbaabcdcddccdccbcbaaaabbddcaccbbacddbbbddcbcdbbbcadbcdacdbccdcbcbacbbddaaadaabcdccabdaabdaaadaddbcacbaacbdbadbabcbaaaababddacbcbbacbacbabdcbccccdadcabadbcaacdbbbcbdababaabcaaabbbadcccdbcdbcaacacbcbcccaddabdccabbdcbddaabbdbbcbabbbaabbccaacbdddccaadaadbaabadabbacddaadbccddccabdbaadabadbcacaaadcbaacdaaabdcaacbcdbbdadcdcbbdcadabcccbbddbadbabcddbcdcbcdbaddccacdbdcbaaccbddddacdabadbadcababdaadaabadbddcbcaaddbcacbbddcbbcccbbbcaccadccccaddabcbbcadadadcdabccbadcbddcbadddbadbadabcdccccacdaadbdcdadbdbcbacbbbdccccacbddabacdabaccddbabddddccadbadddbbdadabdcdbdadacdcdcdbdddbcddcbbdcdcaddcbabdabadadcdbbcbbcdabcbccaabdddcdcdcdbcbbccddaadbddddadbcdcababdcbaaadcbbabdabbbcddcaadddcacbbabdacbacbabcccccadadaaaadbddadcdddbadaabdbdadccaaabacacbcccadbbaccbddbbcacdbabacbbdcbaaadaacadabddbcdccdbcaadaaadcaadacdbaabdbcbaacbbcdbddaabddcacdbdabaabbabdbaadbcdcacbcbbdaaccbbbcdacdcadddacabbbbdabaccbabbaccaacbbdbaaaabacccaaadbaabdcabbbaaadcbdbacdbdaaaddbcdbddbdbdccccbabddcdadabcbacabbbaacdbcacdbaddaacbaacdcdcabdcaddbdbaddaabccccabdaddccdccdbaccbaaaadccbbbabbacdbcbadddacccdabdcacbaaaddabcaddcabdcbbddbddddbdbacabaacabbcaabaccbaabcdbbdcdbadcdbabacdddbaccadacbabddbacabdadadaabcdbaadccdbaddcdadccaaccbadddcddddadcbddcdadbbbaacaadcccbcbdacabdbbacaadcacaddcacdadaddcdcbdadbbbdacdaabbcccdadddaaccdbcdcbdbcddaacadbbddacbbbadbdbbaaccccbadaabbacadbdacbbbacddbddaaadaacaadacddcbddcddadcccacdaaadbccdaadcbababaccdbbdcdcdaabccccdaabbbcbdbcaadacbabbdbbdcbbcbacaadcaaddabbcdadddcbbbaaabcddcbbcdbccccabddddaaababdaccccbdbabbdcbcdaacddddaabdbabdcbdacdccdddababbbadcdcdccabbcbbaddbcddccddcccaaddbdacabdaabbabdcbdccabdadddaacaccacddabcadaaabccccbadadbacadbabcacacbcdacbcccaccadcbbddbbcddbabdadcacdbbdacbacbbccbacdaaadababacddddbacadddbacbacbbccabddccdaacdbbcdbcacaabdcbdbabacdacccddccaddbcabadaacbccbbbaddaaabcbbbdadcadaaaaacadacccbcbadbdaacdbbcddadacdcadcdaacacdbdcbbbdabadbaaadacdbaaddcdcddadcdbccddbcdcabbcbbbabcbaabcdbcababdbadadbaacdbbcdbccacbaddacabbacbcbcbacabbcacacdaabcabbbbbcbbcaaaabdcbaadcdbbdbbbaccbccbaddbdcaabccadbcaadcabcbabccbacdcddaacddcdacbbbcabdadddccbdbaddcbcddbcbccdaabbadbdbcdadaabaacbddcaccadbcabbdaacdbcbbacccdadbdcbbddbddbdaacdcabaadbccddadcbccddabbcccaabacbbbaacbdbbbddbbadadcddccbbdcdbddababdcadbcdddcaabdadadabcdcabbcbccaccaddbcbcdaabbdccacaaccdbddabaddcaddaaddbabbdcdccdabcdbdadacccdbadbbbcbdcddbaddccbcadbdcdaadacbbcccaaccddabacdbdbcadabdcdcddcbaddbdbdbbadcaccbdccccabdcacdaadacccacbbaddbddacaacbcdbbcaaddadccbdababaaddbdccddbdabdacdddabcadaadaadacbbccbbaddcabbcbddbcbcacacbddabacabddabdbcabcdaccbacadccddbdbdbbabdabdddacdacadccdaccbccdccbacdacbdbdadbcaaadcdbccadbcacabcaacdcbdbbbadbdbcadcacabcaabcccadaccadacbbdbbbccbddbcacacbadcbcdbaaacbddcaddbadbbdaabadbcdddcabbbccddaacacbbaabcaccdcddddcadadbbbdacacabaacddbdcdddbaacbdabdadbdbdabdacdcabbbcaaacabcdcbabbacabdcdcabcabbcbaadadcaaaacccccdaabbcddddbadcacbbdbcabdcdcbdabcbacaaddbbadccabbcbdadcbadcacacbbcddbaaabdbdabadbddaddcadaccbdadcaccaccaabcaabbacbdddbdddabccacbbccbcaaadcddabcacadacdccacaadccabaaabaabaadcbacacbdbbddddbccdaabbadcccccdacccabaadbaaaadcabdaadaccdacbbcbdaabccadbbbaddabccccbbddccdacdcddcabadabbbbddccacaadbcbcaabbdadaababccdcabadbcabdbbcdcbbbabcdadbdcbadbdcdcdaadcbddcabcdccadbdddabcdadbcdaabdcdddcddaddbcbcabcadbccddccaadaaaccdbaaddbdacccbccdbaabbababcddadddabbdddccaacbbbaacbbcccaadcdcbacbbaadccccadbccccbdbbcbbbabcabdcccdcacadbaccadacddaabbcdcabbbdbdcdaccaaddcdcccccabaacdaacddbcadddaddbdddcbdcdcbbbdaaacbdbbdcaccdcacacabdbaccbaaacbadaadadcaaaabdccaadcdbaddbcbcdabbbbdcdbcbbdabaddcaaddabbbcbcdbddadbacddbcbbbbabbcccbbbdacaadacbcbaaccdcaacabcaacddddbbbacdabaaacddbaaccbcacdcdacbaabccbccacacbabbbddbcadccddcaababdacdaaadadbcaddbddcacdaabadcadacdddbdcadbbbadddadbcbdabaabbdaddaadcacdccdabcbbabbaccababdbcaccdadbaddcdcdbdbbdadacbbcdccccdacdddbadbabcbbacdcdbabacaacddcbdcbcaaadadacacdcdacaddcaadbbbabaaddddcabbccadbadbaddcaaddbdadbcccddaaccdbdbbcbbcccdbbcadddbdadcccdaadbbbbdbdcbdbbdcdcabbbdacaccdaabcabbacbdccbdaaabbdddcdbccdbdcdcccdcadcabcbcccadaddaaaaabccaabcadcaadbbadddcadadcdbccbdbccccdccbabbccadadcabacbbcbbdccaadbbcbbcbbbdbbbadbaddbcaacaccbbccaabcdadcdbcbaacdddbdacbdbcccacbbabdbccdbcbcabcbcddaaccdabbcdccccbbccdccccabdaddddadadbcbbbdcdcccbcadbbabbcddaaabcbbaaacabdcbbbbdaacdcbbbdcccddaaadabadacbdcbdbddcbdbbbdddcdbbcdabdbbdcaaccadcbacdbcacababaccacadadbcadabbacdbbdbbbbcdcabbbddcddccaddcdcbddaabdadbabbcacdcbdcdabbbdcacdacabdacbdbbabbdcbacccccbdacdacadaaccdcddbaddccbacdbcdabddabdaddddcddddccacdacbcabdbddbdbcabaccbadcbbcacdadbcdacbbbdbaabdcaaddcabcbccabcadadbccacbdabaabacaccbdbccbacccdacbacbbadcbdddbbcccaadabcdddaccaacbacaaccdddcdbcabcadcabadcabddddaccdcddcabdbcbaabcccdbdbdacabddbcabddcbdbcbdaddccbababcaccbcabbdaccddcacadadaabccacbabbbdabdbdbdbccaddaccbccbbdcbadddabdbdaccdcaadacddccaabdcabdacadaabacaabccbcaadaaabcbadddcaddcddcaccddbcddaacbaaaababaccbbbdcacccbadcdaabdcacccbcdcaacdbddabadddbadcddccdbcbaaabbccbbadbcacbaddcbbbbcbdddbadccaacddcbddadabbbbdcbbbdbabdbabbcbdadabcacdadcbaaabcdcbcadbdddbcdcbbabbbcbbbadbdcdcbccbdcddabbcabdcaaddcadcddabddddbaacbcaaddaacacacbbbccdabbaaabcdbbbdccddcaabddcccdcccdccddaabcbdcaddbcccdcddccacadaccccabbaadbbccacddaabaabcabcdaabbcbcbacbcbdababbdaabadcaabdbacbcbdadcadcddcccbcddadcbadcadacccaaaadacaadbbadcbbcbadabddddaabcdcdcacaaabdbabbbacccabcaacddbbcdadbbbdaaabbbbacccaaaabdaacaadbdbbbbadcbacbbadcbadaccbbbaadabcacbcbbdadbcadabccaddbdbaacddbdbdccdbbacbcacddaaabdbccacaabbabdbbccababdadbccbcbdbbabdcdbbddacbdaabdbacbdcabaaaadadaadbdacabdddcadbbdacbabbdcacbababbbbccddbdcaddbacabddadbbacaabbaadcbbbdbbbdadcaaddbddcaaabaadcaaacabdcccdbaadccddabbcacbcacaadbaabcbdbaacdccbcacadddddaccacdbcbadccabbcdcbddacbbcadcbcabcddccdadbdadbbaaaadddbbcdadabaadccaaabdabaabddaaaadcadcacdaacdcacddcbacdaadcbbcbaaacbcbccdacaabbaacdcbdbcbccdbccbdbdadbbacadabcacbbdaaabadcdbadddabbdbcaabccdbccbbacbddbadbdaddbcbcdbcbcabdbcccadaaababdcabaacacdabacaaaabcdacccbccabbdbabbddcccccacaaabbaacabaadbcccaaacbdaacddabadacabccabdbcccbacacbdcbbcacbadcbbabacacdcddaacaaadababdababdccdcaccbdcccccdddcbcabdbdcbcbcdbbcbbaaadccbcbccdbbdcaaaddbdccdacadacacaacbccdacacbabdaaacbaadbdacbaabccdcbcaadddbbddbdcabcacbddcbbcaccdcaccbbdbadccbccddadacdccabcdcbabbccadcbbdabbcbdabacddbbdbcaaacccbcccdaacbabdcacdddbdaddacaabdaacdaacddabcccbbaddaacdaaadabccccbcdadccccbdbdbaddbcdddddacbcbdadcdaabddabddbacddcccadcaadcbaccbcbcbbbccaddddcbdcbbdcbabcadadccddccaadaaaccdbaadbcdaccaabcdbaaddbcaacbdadbbbdcdbdbdcbacaaaccadaadbcccaacadcdbbadbdadabdaaacadcaddbddcdccbabdddccaacdabbacbadcaacadcabccadaaadcabbdbdcccbbbabadcadbdacbdaadabaabbddbdaaabdbbbdabbbbdbabddacdaccdadcbbbababdaddabdacbcbcdccccaadcbdacadddbaddbdccbdaccadcbbbaddcddccdcbdbddbdcdabdcdadcdbbdcabdabdabdccdcbcbbcbabcccdcaddbcbbbcbcdbcbcdaadaadcccdcabadaadcadcbdaddaaaaddbaacbdaadccbcadccacbddaacbdbbbdccbbccabdcddcdcacddddadabadcaaaaadacdaaadbdaacbbbadcbdabacdddadbcdccccdcbacdbbaccbdcbbdaddbbdaccdddababbdcaacaddaadbacddcacaadcaadccadacbababbabcbbcdacbccdacaddbaddbbbdcddbccdaaaabbbbbbddadacdaaaadacbbbaccabdacdbdabcddaddbdbbcbacdbdbccacaccbcbcbabddcbabbcabccbaadcaabdcbddbdcbadcbbbaaaccaaaababccbbacdabbabdbbbcccdccbcbcbadaacabccdadaddbcccacbbbcbddbbacdbdccdadaddaabbbdddccadacdcbddcbcdccbbbbccdcdadcabdcdbcdacbdddcadccadbcdaacbbbbaccacaadbccbbcadbbdbddbddcdddcbbdbccbbddcbabaacbcaacbaabbdadacdaaddbbaabcabcdccdcaabdddacdacacacdacbdcacacadbcdaacdaccdcddcbababdbabbccabcdddabcbdbcaadccccddbcaacdaccaddabbddbadbdbdbccaccbcccdadcabddcdbdabdacccabdcdbaacdaccadbbbaadcdbdbcdcbaabddddbcababaabdabdcbcdddccbacaababacbbacaddbddacdcaaadacbacbadadadcbadabccccbbaabbcddbcbdbdcdabbbdacbddaabcbdbacabaaaccadaabbcbbdcbccbbbcaacddcbdbbbbaaddddcdbbadaacdacdaaccbaddaacacdddbdbacddcbcdcbdaaadbcacdaabaddcbcdcdcddcdcbaaacdbcbdccaadacdadbcbcdbbbbcccdaddcdadabbbacdbddcccbdaababbcccaabcaabbbacadcadddcbbddbbcbbcccbcdbcbccadaddbabbdccbccadaaabacddbcadbddddcadabcbcabababccccabccddbaaaaabdbcccacbbbdbcdbbcaaddbabcaddaadacdbaabdccacdaabdbbbbbaabdddcccbccbacdaaaabcababbdacddabbbacaadcccbabaddcbadbcaacdacbaccdbcdbbccacbcdbadbcdabaddbacadbcccbadaadaacbdabbdaccacabbcaaadbbdbbdddbadcdbaddbdbbaadaccccbcacbabbdccccdababbbcccabbbccacbccccdbaacbadccdcdbdcadaddbcbcddbacdbbcaacdadcccadaacdcddaacddabdacabdbccabdaabacbdbddddacbccbbbadaacbbbdcaabaadadcddbdbaabaddbcacdacaccccabddabcbdccddcbdccbacaacddabdcdbcddaadddbbaadabacacbbcbdacadddabcdcabbcacbcbccadbddacdbadcdbcadadcbbabccacbdbabcbaccdabddcbcabbdbbbcdcdaaddbcbacbdaaccaccdbadccbcbdbccadadcddaddcabacaacadcaddabddabcdbbccbdadbcaadaabddcdbccdbbddbbcadcbdcdddbaddcbbdaaacbcbdadabcaccdddacacddbbdacbcbddcbddbbbacabbacadcbccccabdbdbcabbcbbdacacccaccadaaccdaadaaabdadbacbaacbadbcadcdacbbbbdddbcbaadaadaadadbcdaddabddbcbbdbbdbbcabdcdddbcadbcbbcbdaadbdadacbaddacabadbadadadcbbacccdacadbcddcbbaddcdcbcdbadaadcabcbcbdbbaabdcbccbcaccbacbbbadbbaaaabcbadadddddcdadccaaaddababdbcacbabbcccccaddcccddababdcdccacbdccdbdabccdcacddacaadabcbbdccabddcaddbcbaaddbdcddbadbcbdbbcacdcccabdabdabcbaccadbcadbbbcdaddacbacacabcdaabdbbcacbbacdcabddddcbdcccdaacbbbcadccaaccadaddcbcaabbcbddbdadadabadbdcbbdcbdcabacbabdabbbdbdaccdbabacacaccdccabbacddcadaadadbdbddaacddacacaccbadabdcbdcdadbbaccbaadcbdcaaabbcbadbbadacabaddacbacbdbdddddadccaccccadddddbcddddcbdbdbadabdaacacbaabbdaadbbcaaccdbcbadcddccdbcabdcbbabdadbcdbcaddcdccdbbadacabdbdabdacdaaaccacdbacbdcbdcbdbcddadbcbcbcbcdbbccdbcabbbaadbcccbcdabdcaddbaacdbbcdbdbbabcbabbcaddcbadcccdddcdccbcddabbddadddaaddccabdddbddacdbcbabcdbadbaacbcccbbabdbdcbdcdbdabbacaccdcadbbadcabbddacdccbdadbbbdccdacacddbaaaabbcbabbdbcbcadacdcddabddcbdddabcdacccdaccbcacddabdaadddbddbcacabccadabdccabbbaddacdabddcdaccabadddcacdadddadccbbbbbbdbdbcacacabbbcdadccbadcaadcbcccdbcccdcddcacababdbbadababbbccbbdbaacabcbaddbddbcdcdaadcdcbccbdcbccbcdddabcaabdbaacbaddccccbcddbddcbdcbbbabcdcdbbbcddbbabbbcadcdcabdddccaddadabacacdaadbbabbcbaddabbcddbadaccdddbabbbcdbaddcacbcaaadaddbaadbabccacabdcbbdbdbcabccabbbdbabacdbdcaddaabcddaabaccadccadabbbacbcbcdaaadcdadcbbdbcdadbcdccbbbdacdbacdbcddadddbdaadbddbcbdaccbabacbcddcdddbbabcdababbdcdbbbacbcbccadddadababcbabccdcacdbabdbcadcaaddcbbbbdbdbcbacdcaaaccacccbacccdabaddbbdaaaabbdbbdaddaadaccaaaacacbddadbcadcbbcbdcdacacbddbbcaabccbdbdcabdcadbacaddaabaccaaaccadddcacdcbaadddbbcdccdcddcbdaacdcdadccbdbacbbdcbdcdcaccbdaccdbaddcbdcdbccbabadccbcbcdddbbcabbaddabddccaadadccddcbddabddaccadbadcdcdddcddaadaccbbbdadbdbdbbddadcbcadccbcbccdadabdccddbacadcdabcdddacaccddacddaccbddadabbbcdabadaaaaadadabcddbadacddacdcccdccdbcbaddcacadbcdcdddcbdacadadabdcccbdbaabcccdddcabdcbbaaadbbbdaddbcbcdbacbdcdaaaaababdadcccdcdaaddbcdacbdadddbccbacbbabaadacdbdadcbabadbbddaadddadddadcdbadadacdabadbdaabbabcdbbabddbaddaaadbbaccbbbbbaadaabcbacbadcbbcbababbbbbbbddbabcbadbcaaacdccddabdcdcddcbadabadbbacdcabdbbacddabdbdbdbcacdaabdacdbacbddbbbbbbaaccddcccabcdbaaacbbcacacdcbbddabcababccabcacbabcbbadabccbccabdcadbccdacbbdbadbdbdacbadcacabdaaddddaadbbaabacabbbdbcddaddabaaacdbacddadbadacaaaccdaccbdbacbdbdadbacbcabcccbdbcbcbbcbbdbadaccbaacccaabccdbaaabaaccabdaabacbadbccacdbadacaaacaabdaadabaadcbbcabcdbbbaaadcbdaacdadbcaddbdbcbbaacdabdaabbbbbdaacababbaacccbadcbcaddbacacadcbbdbaddacddcdacdcadcabdadacbacccabbaadabbdbcddaabbbcddabaddaddcbdddcacdcbbbdabbcdbabaddccbddabbdcbadbaccaaccbbbcadbbdadababaabcdddbdccabacbbadddbdbdcacabddcdcababaccadbcabddcabbcdbdbbdbbbbabcabddbdbcbcadbdcadaadcaddabdbcdacaadabadaaabcbaadcddbccdabdbdcdaadacadaaadcbdabcbadbbdddadbddacadabcbdabddcdbbcabbbcdaaddcdaacbdccbdddccadaabacdbcddaaacddadbbaccaabbccadccdbabbabddbbdcbbbcccdaabaccaaadbcaabadaaccddcacbbcbcdcabacbaccacdabbbdabbccbcccbadacaabcaddbddadcdccacbdbabbabaabbdbadcacbaaacabdcdcdddddadadcaabbbdbdcccbcabbccaccbdddbdcbcacbbbdccbccabcadcbddbdcabdbabccccbcaabadacdabdcbdbcaabbccbabbdccabaaaaaaabdcdcababacddadccaaaacbcdddabadbaaacadaabababddcadbbccaabaadbccabbbddaddacdaaddabdbddbbbacadcddcbccacdddbabdbaaaaaddacccdcabdcbbddddabdccdcacdddddacaacabdadcdccacccddbddbdcadadacbbcddcbadbcccdcadddbaabdaabccdaccbaaaddddbcbdcacadddbdaacbacaddbdacdbbddabdcdbdacbbbcbdcbaddcbbaacbabaabdacbaaaacdaddabddbbbabaaddddbdcbcadaadddcaadbacbaddcaddbabbbdadacdacaaaabadbadaaadcbdaabaabdaabacbacaaaabcddaacdddcddaaddaccccaaabdcbdbbdaccccdabbcbbbbccbdddbdbbabbadcbcacddddcbadcbbabdccddddccdddbacacdbaaaabaddcabaabcaacddbbadabcbdcbaaabdcbbdcbabbabccbbcabbabcabcbcaddacccabddadbbcdaacdbbbabaadbbdcdcccbbbddbbdcdaadcacdabbbadcddacdabaacadcacbbdbbdcbcaabbcaccdcdaadabbdacabbcdbbdadabddcadabcbcbbccdaabaaccbddccdbaadcbcbbccbaadadbdbadccaaacaadaabbadabbbacbcdccaadacaccdbcaaadcacbdbdaddcaabddabbbabbdcbbcabdcaadcadadadcbacaaaabdabcaddcacbbbcbccaddddbdcbcdaadbcbadbcddbacccccdbabaabacdabbddbbacacdcbbcbcacddddacbbabbcabacdadcbcacadcddacdaadacccbccccbbcabbddaaadaaccabbaabacbaababcdabbccaabbcdabdabdbbbbaaacdcddccddbbcabaadabdbbdadababcdaadcddbddbbbccbababdbdbbababddadcbcdcdbbacacaabddcabadccccacabbbbbbcbbccaccdabbccbbbadcacaacbdcabccbbccdaadbdbcbccdabcacbadaabbbbbaaadcdabccbacaaccdbaddaccadcabacabadcacccddddbdcababdddbcbaddabdbabbadabacbcccbbbbadcaacadbbddbccaadccabcbdaadabbabbccbaaadccaadaabdbcdbcbbcdaaacdbacccddccbdddcdbbcbbcadabbacbbbaddaaccdabaaccadababbccbcbbdbdcdadadaabaacdadbddddcadccbbbbcbbbcddaabbbddbbabcdbabdacdbacacdbcdadadbabddacddaccaaccdacbcbdbdaccacdbabcbcbbbbbccbabbbdccdaaadbbcbdcbdcdccabbacdcaadbbcccdcdcdbcddcbdcdcccdadddabbcabdbdcbbdaaaadbbcdccbccccdcddcbaddcddbcdaacdcdadaccadddbabdbcacdcacddaabcbbdcbadbdacbbaaccbbaacdcbadbcdccbbbacdddcbdbdddcdbbbbbdbaacccaaadbcccdcaddbbdabbbdbabbcddacadabbbacbcbdaabacdcadbcabdaacdabdbbdcacddaabaccddccccccbcaaddccbcdccccddddabcbaaddddcbcdaaccdcddbcdaccaadabcabdccccdbbbbadbbcddacdcddadcccacabadcaabaccabcababbbdcaaaacabcbdcbcabdcdccccbaabbbaddabdccdbcbacccdbdbadcdcdcdbbccdbcaccbbbccaadadcddcbacbddacacaaaadadccddccacadaaacbabdccbbbdddbadbcacabadbcbbbdbdddabbbdcadddbaadaadbdcaacadddddbccdcbbcacababbdcacdabbaddcbdbccbadadbbcbddccaaadaabacbddbadbcadbaaabbbcadddadccbabcbbbcacbccccddadcdddbaccddcddcbabbdbaacccbcabccbdaddbdbabaaadcacdcacdacdbbacbcaccdbcaadaaacbbcbabbcdbbbcabcbcccbdbaaddbadacbcadabcccacbcbdbadcdbbcbdadbcdadbcadbdbbacbdaabcdddabbdcacabadbaabcaccdadacadbbcccccaababddabbbcbcdaccabbbaddcabcbdadddbaddcdbabbcccddcadbadbdadabaacaddacbbaccbcbcdaaadbcdaddabbddbbacadbbcddddcbbacaddbdcccdcccaacbdddccccbbcdabcdbccacbcaaaaccddcbdaaccdcbacdabbbaacdaaaccadcbabbacbbbabbddbdbababbcabaccccbacabdacbdcdbbbbccbdbcbbdcabccaaaaaddacacbddccbbadbabaabcacdccdabdbaacbbacbddddbabcbaadbbadacccddddbcddaccddaaaaaccdcacddbccaaacddcbababdcbdaddcdadadbacbababbaccbdabcdbcababaddcbbabcddccacccaaddccbcddbbbdbbddbbacbccbddbbcdbbdbadaacacdadddcbcbdcaaacbcbbcaccccbaaddacbbcaacbdaccdaccccbdbcddabacabacabbbddadabdbcaacccdcdcabcacabbaaabccacacdbddbabbadccabdbbdbabbcacaadbcacaadcdadcabcadadbbacbdbcbbbacbbddacbdbbaaadbccbdbccaddbacacdbdddbaccacadbadcbdbccaacabcbbddcdacadbcbcbaddbdaddaaacacaadabbdccdacccbbacccaddcacddaddbbbcbcbdaccababdadbaadcadcbdadbccbbacddbaddbccdbabaacacdabacaccacdcadddbbbacbdadbbadbbbbdbbdaacadbdabddaabbdbcaabdacccddcddddadbcadacaabbdddbcbabaaadddbadcaadbdaababbacbdbbcbbbbaabbabdcbdccbbbabbdacccbaabbdcbbdccaadbacadcaaaabbacbdadbbddccbabccdabbadabbaacdacccbadbbbbcbdabdccabacdcacdadbbbbcdbdddbcdbddddbbadcacbbaacdbdbbacadbacbbcbbcbcabcabbabbcabcacbdbdadbadddbbccbabababaadcbaccadbaaddaaabdbcdbccadbdcdcbccbaaadadabcccddcdccaddbdaddcbabbbbdadbcabbdcdbaadbdbcbcbcadacbcdbbbdccccddaaacadbacdaadbbaaadbcbbabdaaacbcdacdbbbbddbbaabbaaaaacdddcdddbbaacbcdcdbadabbbcddaaaabbdbacdbdababdbccbacadbabcaccaccdaccabdacddbbbdcbaddbdcbcccabcadddacbabdddcbbcaadcccadddbdbacddabbdcccdbbddadbbababddabdaccbcddbbbbcbbabcddabadabbacdbbbaddaaccbcdaadabdabaabbccbcddcbaaccadbcadbdbaaaacaddcabacbacbaacccccaacbbacaadbbdbcadbdcdbdabcbacdadcbdcaacddcabbaccaddabaadcdbacddbccbcdbadbbbcabbaccdcddddcbbaadaabdacccaabdabcbacacbcdbaabcbcddbbaaccbcacbbbcbdbccdbaddaddabdbddcdcdacbabadddabccdbbccccbadacbcbbccbcaccdaccdcbbdadacacddbdbbddbccacdbccbbaabcadcbcadbcabbcacacabcddadaaddaacbbcdddddbbbcaaddabacdbdddcdabccdbadbdcddcccdadbdacaabbaadcccaaacabdbbddbbbaaababbccccaabdbaddcbdcbbbcbbbaaacdbaccccdbcbaababcaddabaaabdbcdadaaabdcdbddbbbccddccaaadabbacaadaddabdbbacdbbadbdbccbadabdaadacbccdadbbcadddccbcddcccbbbcccdddbbdacadcabdbcbabcbbadacacdacbdcbcabcdbccadacdaabdbdcdaadadabaadccdaaacccadddabbbbadbddccdbaabacabbbaccddccbcadcadbcdbdbbbccbbbddabccbaccabbdabdbababccacadccddbaadbcbccadcaadcabbccbcacbbcadcacddaaacccabaccabdbdcacdddcbddcccadaccbcaabdabccabbcddaadbdbabcbccdadabcdaabdccdcbdbcbcddcdabadcbdbacabbcdaadcadcbcbcbcddcacdacadbbdaabccdaadbbadbcdaddbbaaacbabacbdcbabcdcbcaaacdcccccdbdacabcbcbbacbcdcccbaaccbabddaabaabcdbadabccbccbcbbdaabcccbdbaccbadccdadacaaabbdaccdaaadcbcdacdddbbdacbcbdccaabcaabadcdccababababdcbbccbbaccbdbadcaabaabbaabddddcbcddababdccabaaaaaacbdbddccacbccdacabdcccdaadadbabadcbbaccababcccccbbaacdddbddbbbcddbccaccaabacadbdddabdbcbadaaddcadabccbcccdcabaccadddcdadaaddcbcaaabdcaccbdcccdddcbcadadcbbcacacababbdbcacbddabaabdbbcaccccdaacaacbabdbbbdbbccdabbcddbcacccacaadbbcccbdcaccbbccddacdbbaaababaaccaabaadbcccbbbdacaddbbacbdadadcabbadddcabbdbadbbadbbcadccddabddcddbadacaadacadbddbccddccccdbcacdbcadcdbbdcadabbdacbaddadcdccabdcbcadabdbadaddcdbccdbbbbadaaaaabababcaadcddbbaacbcdaadcdababbdacadaababddcbddbddcdcadaddddaaaadddbdbbddbbcabcbdddbaccbdddbcabbddbdbbdbbbcbaacbaabadccbbccbccacbbbbccadbcbbbcbdcabbcabdbcbddcddabcbcaaddaddaddcdaabbbcacdaccbdabadbbbadbcaddbaddbabddacbcbadbccacaccbacdacabddbdbaabbcadbbcdbadcbdccdcbabbcbddabaaabbdbdcccbddbbddbcacddacdcabddcadcddabbadabccbabaadbabaacbbbddbbbbccaaacbdbddaddabdcdbddbabcdcabdbbaadacaddbadbaddbbbdacdcbbdbcdbcdabbcaadcbbdcaaccbdbcbddbdbcaaaccbdddbadbcbbadcbccadbccbadbacbdadcbccaddadcdbbbabdbabddcdadcccdddbcaccaadbacccbaccdaaaabdaacaccdccbcabbacabcbdadbbdccabbcacacaddabadaadaabaacdcddbdbacbbabdbaccdbdbcccaaaaabcbcaaabcdbbcacdcaadcacdaddbbadbaddbdadcacccdbccaddcdcaabbbdcdabaadacbcbadddbcbcbccddccacdcadaddcdccbcdadccacaadbacabacdcacabddbcdcadcbcaddccdabdadcaaaddbddadccdabcccddbdadabccccbdaacbbbbdcdbcbaabdccbadbddccadadcaaccddabccbaaabbddcbcbbccadccacbbdbccaaacdbacccccabdcadcbabcdcccabbdcabcaaabdbcadbbddbbcccadaaaaccbaccdbabbcdccbbaabadadbbdaccddaccacdacdaccbcacabbacdbaadabcdddccbaabdaddcabbbdcddcdbcdbbbdcbbaaaaddababbdcdcdbcccdccbdabcddbcdcdabbaadaabbbdcdcbcaacbbcbccdbdbbdcacadadbcacaccaaabdbcbbcbaabbbaaaabdacabccddacdcbcaccadbdaaaccabddcbacdadaccbcdbddadbabaaaabdddaadbbddcabcdcdcaadabccaaacdbbbddbccbdadababbbbadadcbaaaccbbabbdcbdcaadddcbbdadcbddccdbabbaadaaadbbdadabbbdcbccbbadcabddabcdcddbbbccaaabaabdcbccacaadcbbaccabccaacdbcbdddddcacdbdcdadbababbbadbdabaccbbbadbdbbbccbddbbcaabbadcacdcbcdababcbdbcbcbccdadacadbcaaabdcdbaabadaadabcbcdccdadbbbcadcabaccbcdcdaadbdcaccbccadacbdccbaaaccdbcbccadcddaacadcbcaaaadddacbddbcabacbcbdbddbccadcacadaaadabbcbcddbcdbadbbdaddabdaaddbbdcacdcdbaadcddadcabacdbddbaaccdbacacdcddacdabaabbbcaccdadbbcddcaaadbbdccacacbaacababcadabbcddbabcdadddccccbbdccbaddcbabdddbdabbbdacabdcdccaabccddddbdccccdadcdacdbccddadddcccabddddacdcbadaabbcabdadcabcadccdabdbdbabdddabbdacadaadddacaaaabacadacbaaadabcaadcdbababbbaaadaaddcabbdacdcaaadbbcaaacccacaacabcdbcbbccdbbdbdaababccabccadcdcdabbaacdcccbdbcadcdbbcdcdbcadcddabbcbcbbadbbbccdcacaabcbcccadbadbaccadbccdacdadabbdbdcacaadaddabbcbccadaddaaadccabdadacbdccdacabbdbbabccadcdbbaacdcccdaacdbdcbdbbccabcdccccdbdcdadbcaabcccacbcccacdcbcabcbadbcbdaabacaadbabacbbbccbadabbbbdcddabbbacbcbdcadbcddaacddaacddcccdbaacbabcbaadccdbddcabdcdcdcbcbbaaadcdcccbcbdbccdbbdacdbdddccdaaaddacaacbcdaadcbadcdccdbcabbcaabdbdbaabaadcccacbcabcabbacdabdaddabacdbadacadbbddccdcddabacbccbcdadcdbdbdcdaacbbacdcaadcbdacbaccabdbdbabdbddccaabacabcaabcddccbbbdcbdcbabdaddbdcbddccabdbdcdbaadacdddcdacabccddbcabcbbbbabaccdacdaddababbbcbcbacabbdcdcacdccadddbbbccbdbaadacbdddadbddaccabadcccabdbdbdcdcdcabaccbabddaadccbbaaabbddaaccadcaaccabccadadaaddaacaacdaddcacbbcdcabdaccbdccdacadadbababddcadcaadcaaabadddcbcbdddadbcbaacdadbcbbcddddbbccbbacbbcbacccbccccbdaadcbdacdbcaacdddbacccccccaaaacdabbbacadacaccbcbddbdcddddcdbcbdbbdbbbbcbacbbbadcdbccacbcdaaaadaccdcdabbaabdaaaabacaacbdcdacbabdbdccddddcaadbdacbbabadbcdbcdbbacacbdaaccddcdadacaccbdabdbacdbabbbbacdaadbadcdcbabbbddbbdbbdcabdaadccbbadbbabbcabcccdcabbcbdcaacacaccdbdcadcddbabaabddaaabddccdcdbcbddcbcbbbacbbacbbaccbddddcbdbbbdbdcabaacbddcdabcbbacdbbabbaacccbcacbdcdbcadcccdadcaccdbbaabadcbddcaaabbbaadabdcaccdbaabaaabbbccdbaadbaabddbcabacdccccdddcdcdbcbbcaaadaccabccbcaddaccdddbbdcadbabaccbdbcdcababddcdcaaccadccddaddcbddbadabdcdbaddaaccdabacdbddacaccaddbbdbcdbdcadcacdcccccbcdcdbbdcadbcdcbbbddbacddbdadbaaabbaddcdbbadadbdabbcbadbadcbdacabdcacaddcdccddcdddaacbdcaabacacacdcaadacdbbdccdccadabcdbdaccadcbcbabddaacdbbbcdcaabadbddbcaabcaabbaaccbdcacbbbabaccacabcccaabbadaacadbdcdabdaacbbccaccdcbacccaaabcbadaabddddcdbdbaccddddacacdbdbcbbcdcbadddaddbacaaddcacbcccadbdabdcbabcacabbddccacdbccbaddcabcdcdbdabadddababbaddadadddaabcabddababddaaabccbdccabbddabcadabccacabbccccccdadcdadcaddbcddbdcacdcdaaccbacacbaaccdadddabdcbbaabacacbabdabcaaaaddbbbabcacabdccdbbbabaaabbcaaccdbdbddbaccbbacdbcaccccbaabcbdddcdbaddbadaabbddcbaaccaadaabbdcddcccbccadaaddcacbadddbcdbdadcccdaaddddcbcaadabccbbbcddaacacddcdabbadcdacdacacbdbcdccbcbdadccdabbdadcbcadadabaacadbbadbadabbbaababdabbdddaacdbdcbbcdddaaadabdcaababdacbaddcdbacadaacaaadbabbbccbbcddcddacdbcbbcbcaddcbadbcaaccadaccbdbabcaadbbccbabcbddccddacbdaddaadabdbdcccacabdabababbcabaababcdddbaccbccbbbadcdcadcdadccbacaabaacdacbbaaaacdbaadbcccbcbdaccdcbacdccaaabdaaadbdbcadabbabbbcaccdbbadabdaccdacbadcccbadabbcadcbbdccdbbcbbbccbdbaccbadababdaacdadbcaaaaacacddaabdccaddacbccbcbbddbaaadbcdbabdbccdaaccbdbdcabddadaddcdacbcaaadcbadcdbaddaacdcddaadccdccaaadcdccdbccdadcdcddbbbaaabcdadacbacbdbbdabaddababacaaaabbbddcdacdbacdddcaccdacdcbccddccdccabbcbbadabadccddaaacaaacbbacbcdccacabdcbcbdcbcbbbbbadabdadbacdcdabdbabdbabbcbbcbcaddbbccddddcbcbdbacccdadcacdcadbdacbdbaddbcddcddabcadaaaadbcadcbdbadcababcadaaccbbcbbaccccccaccbdcacdbbabaaabdbbbbabbddbcccadcdaaacbcadaabdbbccaabbcabbcbabcdccaccadbbadcbaaacccdccdaadbbabcdbcdaadbbcdcdbcdaabdbbddccdcbbbddcdaddbdcdadadbbccbabbadadaccacdbaddddddaaccbddddababbacaadabcdcabbddaccacddadcaacdbdbacadbbddcdcbadbbddaadcdcadcddbcccabaadacacbcaaabbcacdccdbcdcacbccabbdbcbdbdcbaddacccbadadbaddbbacbcbbbadaacdbbacaaccbdbddbacabcaadccbdaaadcdcaacaaababcbadbbddcdcbcaabcabbdabcacbbcacdababddddccacbdcddbaacdbbcdbddbabbdbdababadcdbadbdbdbccdaabcdabbdabdbadcabadadacbaadccddadbdabdddabdcdcabbbdabbbbbccbbaddbbcaadddcaddaaaacbadacbdaddbbaadbcabccdbcadcdababbbbdadabaaabddabaabbaaadcbcabdbaccbcbcdbbbddaaabbaddaadcdccadaddcccbcddaddacacbbbddaccbdbcadabcaadbdcbdccbbdabdaaadabcbcdccadaddccddbababadcdbcccdbbbcadcaccabddadaddcabdaaaabbcdbabcbdcaadbacddabdbabdcdcbbbbddcaaabbbaadadcbaacadacaaabcbadcaaacabaacccaadcccddcbbcdbaaacbaaccabdcdddcaccabddaabdbadbbbacddcbbcaaaaabaddbbdadadabbadbabcbbdcdaacabbacbbabccdcabadacddaccbadcbdcdcbadaddddbdcadbcbacacadacccadbdbcdaaccbcadccbacaadcbbadbdbbbcdcbabbcbdcdbccddacaadccbbdbdacabaaccddadbddbbaadccccccccddadacbaccddbabccdacabcaadbdccccdcacbdcccdaadcdaaddaacabdacacaddbcbdacacadbabbacaacbbaaadacaddacdddcbccaadddbbdaaccbbacbaabbcadbcbccacccbacbdbbacacabdcbacadbdaabbcbbdbbddcbccdabcccabbcaadbadaabcbcaabbcababcaabdbadabddacbcddadcccccaaaddbdcdabbdddbdbcdaccdadbdbcaacbdaabaccaccbaccdbbbacdaaaccdccdbaddbcbabbdbcbbcbddcccbaaacaaccdcaccaaaccbaddbccddaabcaabbaacdbbcdddbdabdadabdabbbbcaccdddcbcabaabadcdadcdcacaacaaaadbccbdbbddbacacdabbcdccddddddbcccabccdbcddcbacdbcabddbcbcbccaacccbcdccadcbbaacabbccbacaacaacbbbccdcaadbcbadbbbabaaacbadbbddadaaabbcbdcadcbcdccbbbbcdccabcaabcdbbccbaaacccdbbbbbdcdcbadccabcddabbacdacbcbccaacdcabacbccdaccdcdacacbdacabbabdaaabcbadadbbbacadbdbbdcdbaabadadcadccabbccbadcccdbbdabbcaabcdbabadadaadacabadaaaccdbabbdaddadcdbcabdcaabcdaccbccbbcabcaacacbcccbacaabddacbdbadcddabbabdbbdbbadbddcabbdadcbdcdbbbbbbddcddcbddccdcbdcdccacadccbddbdbabccdbcaabaccddbabadcacbacacbadaccaaddbdaadacaddcbbadcdcdcbddcddabbbaadbabaadddccbbdccdaabdcbdacbbddbddaacddddbdcabcabbabadccdaccdbbbdadcddccbdadacdcbacbdbadcdcadaacbbbbacbdcdcdaaccdcdbbcaabaaccddadbbbdbaaabcadbbadacbcbdbaadcabdacbaadbddaddcbacbbddcdbbcbcaccccadcddacadbdadbabcbdcbbcddabbcadaacadbdcbbbbccdcdbabcdbbcadcacbacccdddadaadadbbbbcbcbcbaaadacddbdcaacdbdcabbdddadababaadddbbbdabbbbacdbdcccddaacddbaabaddbddcdbcdddacdabccbdbbddcddcccbdaadaacddcdcaaccdaccddbbbbabcbdbcbcbbdcaddcccbdcabccdccacdbbcaddddddbaacadcdabddbbbcdccdbdcabbbaabaddbdabbcbbcaabcbccbbcbcaaaccbcbcabcabcbbcdcbbbacddaabdbaddaccdbadcbccacdbcaadddbbcabadddabbdcadbbabcdddabdddbaaddbcbaccccdbbabbbcbdbccaccaccadabcccacbcaddabdcbdcdbbddccadabdbbbdadbadbdcabcdbadccddddacccbcaaaacbcbbdbdadcaccdcbacdddddddcacdbcdcbcbcdbaacaababdcdbcabbadcdcaadccddbdbdcbbddaaaaccadddcddbccadbcbbadabdaaabbcbbddcaacabcdccdcadcbabbcbdaaabdbacdbaaddadcbddacccddbcacbcbbacdbdabcddcaadabdabbaadcadcabdbddbdbaadbddaddccbdcccccdaaadbabaacdbbabcdcbccbcbdacacacabcaabcdadaacdcdacbacbaabaadbaaddadddacacdbcdadcbdbccbabccbcabcccccbdcaadbcdaddabcdccacdbccbdcdabcdcbbadaacaabdcbbdacadadbdcbbacaabcacccbddcddabbccddddacbcabcddcaddcdbbbcaacdbbbcaadcddbabddcacccdccccdaadaabbccbaadbaaaccdabcaabbccaddcabbadcababbddacbbcccabddcdabacacadcdcddadaabadacaaababbdbadaccdbcccadaadddddcabcbadddbdcccccbbbadbbabcddabcacdcdaacdabacdcdcabcdcabaabddcacabbadaaabcddbbadbbdcbacbcdcbbbbcadadaacbcdccdcabdbdcaddcbdbbcdddccbbbdbdaabdcbdbdcddcccbcacddabddadaddcbbaadbbdbddacadadbaadcbbaddbaabdababddcadbbbcacadcbccaaadbababdcdaddbccbdbcacdccadbdadacabaaacbdbdbabaddabddcbdddaacbacbbdacdacbabacbcabbcababdacadcddccddabbcabdcddaddaacbbbbcccabcadaaadaddcadaddccdbaaddabcbabcacbcbaacccacccbbcbcabdccabcdddabaacdbabdcbaabbbadbdcbcdbdacbadddabbcbaddacbadddbbacbcabcbdacddbcaabcdcbdcdddddcddadbadcacdcdccbdcbacaddadcddcabaaddaadbccacdbdbcdcabcabadcbacddbbbdbbdbbddcabbdaaccdbadbddcdcdbadbbcacbcbddddbdabccdcddabcabbbccdbdacbccdcbacdccacbbdbbdbaddcaaabadcdccbaddabbcbcaccbccadddbbbcaabcdbacbadacbddaccadddbcacdcbcddccadbabbbcbbbbcdcaadbcadcabbcccadbcbacbaddccdbcaabbaacbdccdcdaaaadbabadbbdaadcbcaddaccdbbcdbbcdccdabcdadbdcbcbccadcddaaabdcbaadbbcbdacdddaccaccdbbbdbdaadacdaccbcdddbaababbdddcabbacdcdabadbbddccbdabdaddcbcddaabdbbbdaadcaddabcbcbbaccddababbcbbdbdbdcbaabdcddbdcaadbcccbccabbdcababcdbbcbcaabcdcbaaacabadcdbbdcadbbddcbdbbdcbdadbbdccbdadccaaaadbbaadaccacaddadccbdddabadbbbababccbdbcabddaacbabababccdadbcbdbdbadccabacdadaabdabcaddbddcbabbbccdbdadbddbbdbdcabcacbaacbbadbdcaabcaabcadbcccdcbddacbacbddcbbddcbcbcbcdbbbcbaccbcdabccdbaddbcaadbbbaccdabdbbaabdcdcbccacbddacbdcdaaccdbdbdaccacdbbccdbababbbacdadccdabcdccaaccbbddddbacacabbcdcbcadcaccdccadbbdbbbaccdddccbcaadbccbdbbabdaacadbdaadbabcdddccdddabadbbcbacdbbdaccdbcbdadbdadabbddbadbbcdcbddcadddabdbbaacaabdbdddccaaaaacaadbacadabbabacbbbccbccddbcacaadabddbddcdacddaabbcaaddcddbbacbbabcbadcdcccddbbccabcdbbccaacaccaacadbcaaaabcacdaabdbcbacbbcabadcacabcadacbbcccccdddbacddbacbadbddbcadacbbdadcdbacbaacddbbdaddbccababcaacabdbadbaddaaabcadacdcabacbbacbdddbadaddadadbadbbaacbdcaddaaaaaddcbbdcdaddbabccbcdddcbdddacccddaccdacaaabcbccbacbdaaddbccbacdaacdbbadadcaadcadabdcdcadbcdbcdabdbdbcdcdabbbbbbcbbaaadcbaadacbadcdbbadbababbacddbbcccaccbdaccdacdaddccaccbaadccccbbcbaaddaababcdbaadbddaaaacabddbcbdabbcccbbbbabacdbccaacccddbdbbbabdaacbbacbbcdcddcbdbaaadcbdaccccababbccdadcbadccdccaadacdcacdbcadbbaccbbdadcbaaabcdbddabbadcdbbdbababdcbdbcacbcbbcccdbaabbbddbababcdabaabcbbadabdbcbcccbaabacdaccdbbdbacbccdcababdaadbbcbadbdddddcbcabbaacdbacbdbabdcadabcccaddcaccadccdaccbadabbbcdbbcbaaaabaaddddabaacdadcdaccdddabaddddbaaacbdcbbccdcabbacbbacdbdadcbdcbddddbdcbbcbdacaaadbccaddbaaacaddbdbaabdacdcbacbadddcabccccdbbaccccddcbbcbdbddbccaabbadbcaacbcbdcbcbbcdbbbddcbabdabadcdcddcacaddaadabcadbdcaacdbbbcacaaabdbacabcbcdaddbcdcdddbcadcaabddcdbddcadcddbbcaadaadcadbddbdcabbbabdbbbbdbdbbaaacbabdadcdbccacdcabacbbdcdbaaadaabbcabaaccacdcdcdccbbdbcacbbcdbcacaabccaabcdbaddccccabdbacaadacdadcbbdbbcdbabbaadabcddddcbaccabdcaaacaabddccdababcbaacbcdadbdcacbbcadbddacadbbcaadabaddcccbdabadccaaabddcaaaaddcabaadcbcdcaabcccdcccabbdabcbadbddbdbccaabcaacdcccbbbbcddddabacabbcdcbccacdcdbabbaabcbbcacacdbaadbbcbcaccaaaccbbadadbcdaadabdbdcccdadabddddabadddacdbbcdbacacdbbcbaaddbcbddcbdcdbccadaccbcbcabadacddccaaaadcadddbcdcbbaccbdccdadaacccddaccadbcaccacaddbabbcdacbbaaccdadcbcddcbdcbbcbacacdabdbccbdbdaacbaabadcccbdddcddbaddabddcaabbabacbbcadabdbdadbaaababbadabbbdbacdbdccdbcbbacaadbcbabbdbadacddabdaddadcccdbcadbbdbcdcdaadcbaadcbbbaabddccdacacbddacdbaabaddadaacbdabcddbcaddaacbbbaabcddbdaddbdddaaddcccdccdbdbbacabccaccabadddaabcabccddcddabbaabbddcbcbbcbabcdddabadcbcabddbbbddbababcabbdabacdbacacdcaaaacaabcdadcbbdbbdabadcadcdbacabdcdcdbdadcdbddaadddcbadcbabaabddcabcbabcbbcdbdcabbcabdbacdaccaadddbabccdcabbaccaddbddbcbccacdcbdcbddcbddbcbabddbbdcbcabcaacdbdcdcacbcdaddddbdabdbbdcdadadbdccdcbbdddbadbdcbbbdbcbacdcdbddbcdcbbcacaaaacabdacbcbaadccbcddcdddadccaacbabdaaaabcbcbadacccddabbbbbaabaadcabdbacbbbcddacdaadabdcacdcddacdcadbdcbcdcdcadbabbcbbcaaaaaacbdccbbdbbbbdbdcbbbcbbabdaabdbbccbcdbacabddbcddddcacbcadcccbdccaabadccabdccdbadcacbccdbcbccbddabccbdadbabccdbabbaaadcadcadbdcdcddadaadbcddbccbadbaababbadaabddacbccdbacbbbcabbcddcbbdaacababcaaaadabcaccdadccaacbdbddbdccbdcddddbdcbbbddcabaabacdbdddccbdcdddcaabcccbccabbcadccaadbcbbbddbccddaaacdbadadbaaabccddaacbcbacbbabaabdacdbbbcdadcdbcdaabbbcaaacaccccccabacbcdabcbdaabbccddcaaaaccbacbdcccdacadcbbbdccbacddcadcaabbcdbdbdacaababdadbdabdcadababdccccabbaccccaddbaaddadcccbbcaabcaaaaacddcabaddaaadcbcdadbcdabbbddbcdccbcabbabacdadbcbddcddcbdbdcbacbbbcddabadabddaaaabbacdacabacdaabdacccdbadbcaadcaabdabaddcbadbadbdbcddabdaddbcabaadcadcdcadadcbcbddbccbbdbbcbbbcdbcdccabcacccbbcbaddbbdcddbdaadbbbcdccdcbbaabaabbdaccacdbdaabaabdddadccadccbcdbbbdadabdbcdbcadccaccbbdcccbadacacbdaabcddddacdbdbcbdbcbcdbbdaaabbcdbdbbcaddbbcabbdddabaccdabbddcddabcdbcdacadbaccbabdbdabcbccbdcbbcddbcadccacaaadddbacaddccaacbadaadaadabdcbcdaadcbdbcccdacbdadaaabbacdcabcdacddaabdbbabaaaabaddcaaacabccddaabbbbbcbdbbabdbccdbbcbacccbccbdbadbcdccdbaccadbbabdaccadabbddbadbdabddddcbdacdddcaaabccbaabdcccdcbdcbbcdacaddddaddcbdcbddbbdabdddabccdcbcaadbacccdbbddbaddccadbdabdcabcbdbdbaddbbacccbcabbbacbadabdadbbacdcccddddccbccaacbdcaadabbdbdbccbaccbaabaaaababdadcdbbcabdcdaacdaadaabdccababaaccddccbaadbcccaccbdccdbdcdcbcbabadbdabccacabcdcdababddadbabdbdbdaaababacddbcabcbcbadacbbddbcddccbcdbbbccbdbccaadccdddaabbdccaadcbdbbbbabacdbccadccadcbcbcdddbacacadadcacbbababbabcbacdaabbbdacadccaadadddacabdaaccaacdddabcadabcdbddabaaccacdaccabbababbbdadcaadbabbababdabcdaddddccaaccadbbbddaaadcabaccdccadcdbbbbcbccdbbdadcddaddbdbdabacabccdabbbddbbabdbaccccbaccccbcdacccaacacdacaacaacccabbcabcdbdbbbddabbababdcbdccdbacbddbcccdcbdabbbcbdadbadadcccaaacbabcccbcddbdcbbbdbcabcbddbabdcbabdbbbaadcdcccdcadcdabcabdadadadbaabdbcacacadddbbdabbdacdbcacacdccdaabccbdbbcbadbbaddcdbbbabdbccbaacccbbbcdbbbcadbadbdcdbcdaabadcbaaadabcbdcbddcbabaddadbccadcaddddbdcccccabcbabcbbddcacbbdbcaabbbbcaaaddadacacccabdbdbbbaaacccdaadddcacabdbacddaccbdcddabbcbdcaaacdddccabbcccbbccdcbaccccddaadbbabaacdbdcacddccbddbacdaaccbbdaaabcccbbabddbdbcdabacbadbacddcbcdddabbbbdddaaacdcabaabbbdcbdcddaaacbdcbcccbcaaddbadbbabdccdacadbbaabdaccdbbdcdbbacabbdcddaccdddacbdcddcdcabddcbddcccabbcdacbbbcdcccabdabcddbbcabaacacdabddddcbaccbbcadbcaaccacaaaacaadcbdccdacdcdacdabcbadbcbaadaaccbddbdabadbdbcacbdaddadccabdbdbcabdcdcbaacddccdbdbadaddaaadcddacbabaacddddbddbdbcacacdcccbbdaaaaaaaccccccdaddcbdcdddbdcaabbadbccdcacccbaabadbccbbaccbadbdcabddacacbacadcbbabdbdacbcdbaabccabbcccbbacdccbddcdddcccbcbccdcabdaabcabbbcadcaaccdbdccddacaccdbbdbabadbbacbcddcdbcadbcdcdaaacbbaccaabdbbcdaaadbaabaabbdaacadcbbbacbbddcddddbbcacdcbaadbdabbaaabbacddccbbbbcdcadbbcbdccbbccadbabadccdaadccabcbdcacdabdabdabcabaadcbabaaabcbabcdabcbcdbddcddbcccccadaddcbabacaacdcbdaacddcdcbabbccdcbaadadcddaaadaacdcadcbbacdcbaaaacaaadbaaacbadbbccabbadadcbcbbbadbddbcbdacdcdbdccaddddcbadcdacccdadbcdcdcbdbbdbacacbaadcdaacadccaacaabcdaddcdcbdaabbdcdcdacbdcadddacddaacdbdcccaddabbbdaddabacbbbcadbddbdbdaddddcadcaacbacdcbbddcccabadbbcccbbbccbdacbabcadddabdcccbbbccaaacabaddbbbcddacdbadcadbbddbdbcbdddadbbdbccaaacddabdcbbdaaaabbacdcbbdbbcaccbbdcbcabbaaddbbdcdadaddabdddaaacccbdbadcdbdababccbacbccddcabccdbddacbabdadbddcaaccbbacacbadaaaacccbdcbaddcdbbcdbbdcbacaababdcbdcdcbcbbbaadaabcbaabaccdcadcbabbbcabbaacbdbbcbcbaabaadddcdbabcdddabbabcbcbcbddcdbaaacddcdbccacadadbbaadabcadcabaddcbcdacbbbdccaccbbaddddcccdccdaccabcacccabbcacccaddcddccabddcdcabadbbbdcaadcaabdcabaacbacadbbccadccdbbcdcdbcadcbdbbdbdcbcdabddaaaddbccdadbaabadacbddccbcaccbdcabddccdcabaaadadbdcbdcbaddacbdccdcbbaacdbbcbccdccbaddcbdcbcbdaacabcddacdadcabbaccdacdaadadcbcdaaabdadbdabacdbbddbbdcaabbbcdbdcccbbbcdcddaabbdacbccaabadabddbdadcaccdcabaaabdaadaacdaadbcdbdbcbdacacbccabbbccdaccbadcaabbaadbadaadacdbbcdccadababdaaaccdadcaabbbbcbbbbaaaadcbabbcaababcaddbcbdaddbdbccacbaaccbbdaaaddcdbcaaaccdcbaaabbbbaaacbbaabbcaccbddcdcadcacdcdabcdbbaacbcabccabcabbcdccaddcacccdacdbdcdbddcdbdddbcbacdababaaadccadbadabbdccdbbdcaabbdbbcabdadcadaaadbbbaddbbddbdbacadaaccbdccdacaaccacccccdbcaacabdbccdbbcaabdcccbbdaabcbaaaacacdcabbabadaabddaacbcbdbccbdadcacddbbddbcbdccbccaacddcdaadaadabccaabcacacaabdccbcababdccddabcabccdcaacaabbacdacdccbbbacbcbdcccdabbcadadaabdadacdbbabdcbcdabccdcbaddccbccbdbdababacaabcdcbcbcdddddbdccacdbcdabcdcbbdcacccaabaabcbcabbcbaabdcbacaabcabddbcbbdcdabcabccbabbdcacddabbddbccdddabcbddcbdbaabcccaabcbcbbdcbbaacdaaddcbbcadadbacbabbacbcaadabaccacacbdcbddcabacaccdbcbcbbbbdbcddababdacccccaabaabaadbaddaccbabaddbadcbaddabccadcbbaccbbddbbdbdcccccbaabcadaaabdbbcacbacaacaddbdaababadccaddbabcbcdadcadbcbbcddaaabcaddddabcdadacdaadcdbdccbcdcdaaccabdddacaaddaaaadcdcccdccccdbdbaabddcbabbcacdadcbdaacccdadaacaacddcabbdddaccdddbcbcdbcacacdbaaddaacaabbbcddcbabbcbbabdbaabddbadbdadcaddbdabbbdbcbaadbbacadcbbbdcccaadcddaaccadadbcaabbdbbcaaddcccdbadbbcdcbaadcadcabbcdacbdcabaaddabccaabaabaadbaddccbbddccbacbccaadabbaddbdcdadbcccdaabdacdaaadabdcdbbddcdacbdaacdcbbbcaacabdcaadbcadbbacaddddbdabaddbdcdcbccbaddabdbcbbcbbbccacccbcbcdcaddcacabbaabcdbbdababbacdccacacaabaacaccbdccdadadaacbdbaaddcdbdbbcdaabacaacbbaabdbaddabdccbacbdacdbaccdcdaabbbbbbdcccddbbabdcbacbdacdcddcdabcaaabbadabcbadabbbcabccbbdaabbbacdddbcadbdabbaacaadbacdaccbcbdcacbbcadcccbccacccacaaabdbaabcddbcccdbbdabbccdaaccdccbadcddaddadbbcabbadcaadbdcbcbdacdbaaaddacdcccdcadbabbdbdcadcdcbdbbccdcddbbaaaabdabacaacdaacdcbbcacdbaaacddcaacddbcadcaaaccbabcdbbdccccdbabbdabdcbaadbddccbddcdddabcbdacabddbdbccacaaccbccdccdbaadadccacbdbcccdacbdbadcdadccbaadbccacabccadcaccddbaacadacddcbaaacaaaadcaababbdbadacbdcbddbaaadbbcddacaadddacbdbdbabbacaabcadcbdcccbaadaaaadbdcaacdaadabdbcbcdaabcbbbaadadcddbbcbcbdaadbaabdcccddbaaadacbcadbabaadabadcdcaabcaadabdaabacdcbdcbbadbbdbddcbbbccbbacbcbbaabbabdadddccdbaacaccdcbaddddaababcbaacdabdbadcacdbcbdadbabadaddabbbbcadadccccdbdcbbbdababacdbabcdacaadddaddccdbadadbbbccaabcbadaddcbadabdbaaabaabcbadbbcddadcccdbbbacdbaccccdcddddadccdaacccbcdbaccaaddcdaddbcaccdddbbccbdcdddddcacdaacbadcbbdacaccdcbdbbadcacdddcdacbcdacdcbcccadcdbcbcdaadcacdbbdccbcabcaabdadbdcdcbaccdacdaaaccabdbcbdbbcddabdaccdbdacaadbadcdadbcbabdabcadabdbaadadaabccacbcdcccbadcacaababacbdbddaaccaddccabaaacdbdcababdaabbbcabbdcccaacdcbaddbadcdbadccadabdcaddacdbddcacbbcdcdabdacccaacabbbddbadabbbaaadcbacabcdcbcdbbbcdcdbcdabbacdbdaccdbcbcdbacaabbbbaabbccccbbddacbacbddbbcbdbdbbaddaccccbaaccdadbbdcadadacacbbacccddccbdbbabdacccbabbadbcbcbcaadaacbbddcccacbabddcabbcbbbbbbddcbdacdddadbbabbddbbbdadaaadabddbaaabbacbbcbabcdaddbccdacadacbdcdccacbadcacddbdaabbddccaacbbabacaacdddaaadcaacdabddccaabacdbcddcccdbbbbddadabccddbdbbcaddbdbbcdbdbcaddccadcaadaccbdaabbaccbbbabaabcbacdacacbabdbbdbdaaaabadccccdaacdcdaacbdddcacadbbbabbdcdabddccacbdacbadbddbcacbccbbcabddbdaabbbccadadccadbaccdccadbccaadcaabdaadbbaabcbddaaaccbcdabadccbabacaccaadaddcccbdaabcadbdcbdccacdbacbdcccdadcbdcccdcadbaaccdaabdbadbaccccddcbddddcccddacbddacdaabbbadaaacbacdadddccbcabdbcdbdacccddcdbccbabcacdcdcadacddbcacdddabcbcadbcccddccadcdbaaaadcdbababcabdacddbdbcddbadacabcbaaacbbaaaadbabbcbaabdcddbacdcdbcdacdabdcdcabcacbccacbcacbcdcbcddaccacccbadadcccdaacccaddabdcbcbadccdaadddbdcacbcbabcaabbbccabdbbbaacbddaabadccbcbdcccbadbdbbcaacbaddccdadacacccbadadadaaccbdcdbadbcadddccacdabdbdaaacbacbabcdbccbbccbacdbacbbbddacccbdccaaabbacbacdddcaababadcaddddddadcaacadbddabdacbbadbddacacadbbaadacdbaacaddaaaadcccdaabcccccaadccbdbabccaadcacdbacadabcdbcaadbbbccbdccaaaccaaacabddbaddaabbaadbdbbdbaadbdcadaababcbcadccdbdbdbadddbabdaaddaccadcaabbdcbbabaadabdcdccadcdabbdccbcddcbcdcbccacabbdadbcdcbcacccabadcbaaacaadadabcccbaaadaddbacbabdcdcabccaaaabaccacdccccddabdbcabddbbbbbdadaddccadbdbbbdacacbddadbabaacacbbdbdbcbbabdcdcccababdcbddacdbccbbcccbdabbbbcbcadabbaacacddddaabbaaccbdbadddacdbddaddbccadccbdcccacddcdbcbacaadbddabdadaddbdacaacaadadbcdbcdacaadcddadcbaadbacaaccddbaabdaacbaabaadaddccbabcadddcdadadaacdbaaccbdaddacbdcccababacbcbbbbcacbcbddbbadaabcdaaccbbccbccacbcddbcdabacdaddbaaadacdaacaaadcddabdabcccbbcdabcababdcddcabccbaddcddbdacdadadcdcbdcadcabbcdbaccccaabbcadbbbbddabdbbdbbaabadbbcdcdbcdbddcbbbccadcbcbdbbabaacccbdcaaacdcccdbbcadbdddbcacbdbaddabbdddbdaddcaadcdbdbaccdcbbabdacaddaccdbbddaaadcdbacaaaddbacddbcddbddcccbcdabaddaaccacaaaddcbddcdacdcdadccddcbdcadcaacdcccccaaadcaccdaaaacdadbcddbbcbbaaabbccacbcddcdcbddcbabdcabbacaccbbdbbbdaacbbcdbdccddddbcdbbaadccadacdcdabcddacbaadbbabbbaacddbbbccbcadbcdbcacabddabcaccbdbaabbcadbbacccccdaadcbbdbabccacddadbcbcdccbcaadccaccccdddddabaddaadcbadcbbccabadddabccadacabadacdacbcdacbdbbcddbadabcdcdbbaabcccbbdabdabaaccacdccdcdddbcaacdbacaccbcddababbccaccbdbcbdbdcdbdddadcdaababcddcbbbaddddbabcdcddabcccbdcbdddaabbcdacbcdccaadababbccacabaddadadbabcbaabadddacdbcadababddadccacacccbcbddcdbaacadcabbaabdbadddaadbccacdbcbddbaccadcdbbaccbaccddbbaacdcccacccbdaddcabacbdaaabdddcbaaddcacdbbdaabcbddddbcddcbbbdccdaddbcdabdcdadcdbabccbaacbabaccacdccbdcddadcdccbbdaacabdabccccbdbbccdabacbacabcbbabccabaabbccaaddbadadcbabdbbdbdbcbddbdbcaaaccbddddcdadaaadacaacdbdddbccccddbbbdabbcadbbcbddcacbaddbbcbdbaddbdbacabdbcabdadbbcacbcbcdbdcbacccbdabaadddacddccbdadbbbdaabbccbaccdbbbddabbbcaaadacadcdbddddcdcbabccdabbabcbdaccadcdcbdbbbdccbdcbadbddadbdaddbbcbbaadccacaababccaddbcdccadabaccaacdabbdbcbbaaaacbcdbacaaaddabdabbacdaabcbdbabbbdddbaaddaacdadbcbddcdddadcdddbcaaaaddbccaccaaddddcccdbdccdadbdbabbbccdcdddcdaacddcbbbbcaacadaacbaaddabdbccbbccaaddbbbdbbabccabaaccdabdbdddcabccccdadddadbddbdabdbacdcdbaccbddbaabbcbdbaaddaabadbcbcccbbcdcbbaccbbccbcbccbcddaadcbbcaacbdcdbcddcaabdcabccdcabdbabbbaccaddcadcdcbaabcdcaadddaacaccbbadacababdcababdcdacabdbabcaaaaacababccaaacbcdcbcdabcacbbaccccbcaddcacaaadddbaccdccdbbccbbbdabaacddccabcbbdcabddadbcaacddcdabddadabacdddddcacadcdbacbdacdcdabbabacdcbabcddaacbabadbaadacabdbbcbaadadcdbcbcdbccbcdddccbbbcbbccdbadcccdacbacdcaaabbadadcbaabcdbcdbbcbbbbacadbcbcdcaacbcbdbbacdcdabaabbcdddccacdcccbccdddadbccabdcbacdddabaaacbbadcdaccbcdbcaacbcdcbacbadbdadadbdbbadcddcabdcbcccddcaabdcaddacbccbaadaaaddacbbaadcadcacabdcdbdcbdabaaccabdaabacbbaccbdbbbbbdacdbdbdacdaaadacddddcbaabadadacbcccbcccdcccbbbdcdacbcdbbbabadabcbbcabdadcddacccddbacdddbacaddacbadaadacccbdcdcbddcdddbcbddcbdcdaabdcbbadaccbbbabbbcbddcdbddbdbbababaddaadbbacbbddbdaaabbbccbcabaabdbacddbaabbaacbdcbadabbabadaadccacabdaacdbbabdcbaaaaadaabddccdbbcdbaccabccbdbaddbdbacbccacdacbadcbabdcccbbdddbcccbaadabcbdccaaabbbddbbdccbbcaacccabbbbaccccbcaccdcacddadabccbcdbbadabdcdccdcdddccbdbcbdbaabccadadaaabacbcacccccbddddcababaddcdabdbcdcdbbaaddadbbcbbbdddbcaaabbdbcbaaddcdddbbcddbacacddabbdbdaabcbaaabcdddcbcbaacbacbabbcabbbbdabacccbbadbadbbabdbbccdbcdacadaaadddbbbccdcbcbdcbdbcdcdaacdcabadcdbcaccacbabaacaccacddbccacccdccbddcbbdcbdbabdcddbbadbadcaaccdbcddccbbdccbcdbccabcccbcbadcbbbdaddcaaaabaabcdcbcbcdbcbacadacbbbbbbdaabdcdadcdbbdccaaaddacdcacdaaaaadaacdbcddbddbddcaacccccdbcccdbbcbcaacacbbbbdbbcbbbdbabcabacdcacacccbdabbbcdccacccacacdaccdaccadbbaccddbdbadccabdddcbaddbdbabbaaaddabbbacbdbcadbdbbcadacacbabbacccbdcbaddbdaddbacddbbcbbdcddbbadaadcbaabacabccbbbdddccbdcbdccccaddbacabdbcbcbacccaaadccddcdccdaddbaaadabdcbdcbdcdbcbcdaccbbabaacdacbcbbccaaabcbdcccaaaddbaabababbaccadadcddcabcccacabababbcacaabcadbbbcdaacdcaabdbbbabccbccdbadabbabadccdaccdbdcdbbbcaaaccdaaacdcaaccdaaaccbbcdbabaabdbcadbcdaddccdbcdaaabacaabccdcdbcddcdcdcabaddcbbacdadcbcccdbcaabbccdcadbacdabbdaddbaadddaabcdbcdccabdcddbddacbcadcccacddbadabccbbcabdbbcbcdbabadaaccdabdbcdbbbabbdaacbcbcddaadbcacbccabcdbbdbdcdbaddabdcddbbcdcbacdcddcddaaadddbadddcadcbbdcdcaccbbdbadadabbddacbacddbcdbdadacccabcadabbaabcdbadcbcbcbbcdbdbadbbdddcccdcadddabbcacbbabbbcadbadabbadbdadbaabddbcdaaacdbcbbccaabddadbbcaadabadaababbcbabccaaabdbbdbacbcbbbbaccdbcdadbdbcddacabdddcabbcbaabcbddcbacabdbddcacaaabcbcbddcaccabccdbcddcdddbcddaccacbacddaaadddcaddadcadaabbadcccbbadcacddcdccaabdcaaabaabdabcbadaacbcdbdcabaccbcccacbcdccbababbcaaacacbabcdabaddaaadacaacaadcabcababcaadddadcacbadbcbccddadbcadaccdadbabdcbbcdbbdadbbdbaccbccbdbddcacbbcdbcdbdccbacdbbaadbcbdabddaacccddcbababdddcacaabdacdcdcdaacadccaabccbaadacccbdacaadcbadddaccbcbdddbdcdcdcdadaadcbcabdcacccaacbcabdcbcbaccacdacccaaddddcbdddbccaadbdcdddaaabbcacabbdaaacdcdbabbddadcbcadbdcbcddbabcbdbcabbbbbbbdaadadaadabcbbdddacacabdcdacdcabaabbbcbcddbaccccbaabdabdaabccdcdcaababdccccddacccdcbccccaabdacddbacaddaacdcadaaddabbabdcbbcdbbaaacaddbddcbbabcadbbadabaddcadbbbdababdbbbcdbacbabdcacddcccdabdacdcdaacadbbbabcaaacbbdbcdcbcdcbbcccabccbbdcaaddbdddbcccdbacbcdcbcdcbbdccacbcbcdadddadacddbabbbababbacadbbddadbaadacaaaabcbbbadbdbdcacbdbadacbbadbaddddcadddccdaaaacdccbadbacdbcdcbbabbddabcccbdabbddbaaaaddbdcaabacddbbddcbdacacbcadadabbacacdcddcacccdcbbbcaabaababdbdbadacbbcbdadcadadcbbcccabccdccdcdbdcadcdcaadaabddcbdbbcbadbbdcacdbcbbbdcbaddddcaacdddcccabbdbaddcacddcacbcacccbccccbdbdacadbdcadbcaadadddabbdabcbccaabcddaddcddcddadddbbbbacbbcdcddacaabcdaadabdacbaaddccbadcbaaccaddabccbdcbdacaadbcdadadadabbbcccbbbaadcccbcbccbbbbddaabbbddbcabbbcdddcacdaabbbbababaaccababcadbddabdcdddadcaccbbdacbaddaadadadddcccaabbadaddddadbddddcdbcbcdddbdaabcdbbbdbdddbddcadaabddcdcbcacddaddbadbdcabdcdadbbaccbdaddddbbbabddacccadabbcdbadadbaddaadcddbabacdadcbbabbaacbabbababdbcddddcbcdbcddabcbbadcadbaaabcbcabdbbccdacaddcadbadbadcbadabaabdccadcadbccbdbaadbcacadbcbccdcdcddbaabbacdaddbabcacccadbbccbbabababdcccdaccaadababbcdbdcbbbbadadcddacbbcbdbbdbcbbadddddcccacababacdccdddcbacacaaaaddcadadbababaddadbcabbcdcaccdcaddbbbdcaadacbcdcbadadcacadcbbcdacdadddaabbdacdbaabbdacbbbabadcdbaaacadaacadacbcaddbacbcbbdbdbddbbddbdadcaadacadcacbdadabcdaacbddbadbddcdaaaaddabcbbcdbbacabcbdddaadadabdadadabdcbcadccaccccbbcdddadadaacdaddbcaabababddbabdcbadbddadccadbcdacacacccaddbbdbdccdcdcbcdcccddbaacbdaaddccabbddcacccabdddaccbdbdaabdaacdadacadaadaaccabaabbbccdadbdddaccaccabbbaacabdcddabcdbddbadacaabcbcbadabcbdaabbabcabcbbdcaadcacdcaadccbcbbcdabbcaacabccdccdadcaadabddcbdaadccdccbbcdadccadcccddcddbddbaadaabccabbccccaabaadbdccbbacbcccbabaccbcadbaaccadcadadacdccbdbbadaababadaccaabccddcabbbbbbbaababccacccbababcccdacabdabbbacdddcadabdddddcabdacbccddbdcdcabddcdcdadbadccdddbadabaacbaddbcaabcbbcacadabdccacdbdcdcabddaabcdbcbdaddbbaabaddcbbbbaababccdbbbdcccdadabbababbacbbbdcbcbcabdbbdaaaddaabbacbddabaddbdbbdcbbcddcbbdccdcaacaddacbcaddaccdcabbccddbadbbbaadabdadbddaabccccdadcbacddaaddccaccaaacabccdaddadabbaadaabbdcdbdccabcdabadcdaccabdbddbaddccccdcacdcdccdcaccbdbbadbcbdcacabccddcbcdadbdbacaddcdbabaccacdbcdcbdadcbcaddccbcdaaccbaadccdaaadbcaaccdddcabcabaaabdddadbdcccdbbcbdcabcaccaccbbdabbabaccbdcbbdcdcccaacaaccccbbcbaddadcabbdcccabdadbadbcabccdcdaadacdcabaadbbcdbcaddabbddbabaddabdabddaddcbacbadaddbcddbbbddabadaccacaacacbadcdbcddcbadabbbabbccbacbbcbadcaaabaaabbcccacccadcddaabcbbdcbccccbcdaddaccbbdccbdaccbdcadbdcbcdadbbbcbaadccbcaaddaccaabdacaaadacaabaacdbdaaccbdbbacabaaddaccaccacbcdbddbbbaadccbbcacabcaaccdcbdaddaabddbdbcdcbddabdadcbacdaddadabcccbaaddccdacdacdacabcdcaaddcdabacaadbddbacccbacadccacbccacbdcdccdbbbdccdbabbdbcababdcdccdabdbcabcacdbbdbdbacdadadcbcddbadadbacdbdcccbbacddabbdcbbabdabcaaaccdbaabbddbbabdaacdbcbcbbcbdddbbaccbdaabccaaddcacacbbdbdacbcadcadbcaacccaacbbbddadbbbacbcbaacdaaddcacadbacadcdcaacdddcddcccbddcbcaccddaacbddbadaccbdcdccaabcbccddddccacacdabccbcdacddcdaadcbdbcddaacddbaadcbbabbbdbccdcbadddbcbcbccddaccdccdacacabcccdbdcacdaddbcbaaccaacbcbdaccabddaacdcabbbcabbbdaddcbcdabddbaaaddbcdacbcdbbbcaaaaddaabdadddcdcbbddbaadabdbcbadbadbbdbdcbdbdccaacbbaaccabcaccbcbaaadbbcaabcbacdcdaadaccbbcdbabbdabacccdcdbcbdcadacdcdbccacacbbbdbbacbdabccdbcddbadabdaacdcacdbcbcccdaddbaaccadcdbcbccbadbadccabcaabcaaddbacbdbdbbdaabbcbcdaabcdbaabdddcdbbbaaddacdabbcddaabcdabcbdccabcdaccdcacccdddaccccaadcbaaacdcbddaaaacbabdadbaabcaacbdccddccccbddbdcdbddcdacbbacccbdadccddcbaaabaadaabbdcabcaccddadcccabacbbcdddddbcdcacddaadabbaccddbddccccaddcabadadbadbbddbdbcdaacccbacddbdccdbbbcddaaabbacdcabaccaccccccdbcaaacadaddcdbdadcdbdaadabbdcaccacbccdadcdbddcbababdcacdabaabbdcadbdacddbcabbbccbcdabcaadbdcbdaaacdcbaabbccabccbadcdacbadababcbbdaabddcbdabdcadabbaccadcaddadcabbcdabcabaaadccbcdabbbbbdabcabdcaadadbbbbdcdbdddbacbcddbccadcbadcdbbbdaacaddbbaaacdbddcbcbaddddbdacaabbbcabddbabdadbbdcbcaaccccbbaaddbddaccabdaaacbccdcadbaddccccdccdadacbcdcadcdccbdbdddaacbaadaccbdcdbadbbdcddbacbabbbacbcccdddadcadbbdbabccadabdbdccccccdabcddccdbdbacdbaabddcbdcacccbccdabaddaabaadaabbddaadbcdccbaacbacbbadbddaaaabdbacdaaccabbbdbdcacdbbbdacaadcddddbcddacdacccbaddbaccccccadaaaabbdadbdbbbdacbbbcbcabdbabdabcdadbadbaacbbbdbabcdddcdcbcbabccacaabbabadcdbbcbcbacbdacabbdacbdcdddddacdabdddbdaddcadbbbbdcddcdbdbacdaadddaddbacccaddcbbadbabdbbacbbcadcabdaadbaaaaaacdbdbddcbdcccaaadbbbccbddacabdccbdbbbcbcdcbaaabdbdaacbbaaadadcbaacaadbaccacddcdcccadbccbdbabcbcbbdccacccdaddcbbdacbdaddbadcabcabdcbaddbcddabbcaaccaccaaddabbdaabaaaabdbccbbcbcaacddaacccaadabdaaabbcabbabbbaaaaddbcbbcabccababdaadbaddbdccdadbbdddcccbacbcccbbabcbddabbccbacdbddcdabcdacacbcccbbabaacaaababacdbbdcbccadbdbdcdcabddbcaabaabbbcdbccbabbbacbbcdbcbccdcaaadbddaaabdbaddddaabbcbadcaaacdaddadbacabbdcabcbcbcaabbccddbcbdacdbbdbbbcabccdbdbaaadcacddabdbcdbcbbbabbaabbacbadacbbccbaabaacccacdcbdabcbbccaccbbbddacddcddbdabbbaabcdbdccdacadcccbdbdbdadcbcaccbcacbcbbcdaaaaadcaddabcdddabaabcdbacbccacbcdbdddbbdadcadbbbbdaaadcddabaacbdbadadbbbdaabcbabcdbbaadddccababcdbadbdddbabbbbacadabdcacacccdabdbdbcbaddaddbccaaabaacbddcbdbbdcdbddbdbcdbcbdddcbacbccdabdbaadbbadbdccbcacddcdcdddcdabaababdabddacdccbbddbbdbadcbccdddcbbaaadbdccbbbcdccacaababbdbabdbadbcbccbdadbddcbddcadadbaccbdddaabdaaddbbaababdcccacccacddcbbacbdddcaaacbdbbbaccccbdaccdcabddbacbdadaaaabbcbadaaccccbbadbbdccbccdabcdaaddbbcbcddcacdcaaadbadcdccdbcbdbbacccdaabaaccacadcdadbcdcdbcacaaddacdcdbdbdccbabdcbbabbddccdadcaacaaaaddcbbdddcccacbacdadbbbdddbddbdbaaabbdbcdcdbcabbbcdbdcddcbabababbccaaddaabccdcaaabbacccacabdcabcacdaabcdbdcacbcadddbdbbaddcdbbdbdddbddccacadcdcdbcbddaddcccdaacbbacadaaacacbccbdacdcbbacbdbacabddabcdaacaaddacbdccdadbaddccaacdbcadddcaadadcbbbadaaacddbdaddbccddaddbbbbbbaccbabcdbbdccdcbadbadcbadcaabcdccdddcdccadbacdbdddbaaccbcdccbddacbcaadaabcbadacadddacacccdaccdddbdccadababcdbcdcbaddcccdadbaaadcdbddbadbdacdcbcbccbbddbccbbcacabbdacbcbcbabccbbbaaddbcdcaaadccddadbacdcaadcddaccdcccdbcdcdadbbbdbcbdbdabcadcaaacbbbbcbdbbddaabdddccabdcacbbbddbccbbcacdcdcddcbcddbaddddacbcdcdaaaaddabdddcaddcbacacaaaccdbaaaccbaccdaaacdbddbadcdaabacdaadbadcdaaaacbaadcdbbdccddcdbadddccdbccbaccdacbbbadbcdaccbbacaadabddccbdacbdbaadbcdcaaabccadacdaccaaccccabdaaabcbbbcbadacaabcbdddccabbaacdbcaddbdbbabcdaaadcabbadcbaccbdaaddbdaaaacbadbbdbddcdbdbdabbbdacccccbccabcdccddbbdccacabaabaccabcbbabdbcddbaabaddaccacdbcacadbcaacddacbbbacadcbcbdbcbcdcddacdccaddadccbdccabbbabbcbdbcbcadcadabdddacabbcccbddabdcccdabccbccdbabcbdaadbcddccdcdbdcccbccaddbadbccccbcdcaaaacacbcbcdbdbddacdbcaaddddacddcbddbdbcdcbaacaacabcbcbccacbabccacaacccadacbdbabdbbbccdbcaccbbbddbaadcbccddcaddcdbdadabcaccabbdaccacccbcadabaadabdccadbbddaabdcaccbdbcdcbbcbadaacddabaaacbaccccaacdbacbcbaddddcccdbcdccbadbcbbadcbacaddcddbacdaacbbaabcccabacaacddcccaabacabbdbdbbcacbbddaddababcaabadacdddbbbacdbdcadbbbdadcbaccbcbcdbdcdaccbcbccaacdccccdaacaaddaccbbbacbabbdbaddadcaaadcddcadabbdccdddcbdbddabcdcbccdabdcaccccdcbbcaacdbcdcabbbacbcacadcacbdbaccaacadbbcccdaaadcadadcddacaadbbcacccacabacdcbdbbacdbdadaadacddcacbbdacacccbbcdadcdbabcddcdbdbaccbbbbabdaacdcccdabbdaabcdabaddcabaccccbcabbcaabaacaabbbcdbdaacbdbdcbaddbbbdcccbdaadbdcbcdabdddabcacbcdcbdadbcdcdddcdbadbdbadadbccacbdadaabdbdbcadcacaaddacdacaaaadaadabcbccbababcccdcdcdadddacdacabacdbdddccdbdbbdcabbcddcccdadcdabccdcdccdbcacbcddbadcadcaacacabcbbcdabacaddcddbcdcaabcadbbdddbcbcbdabbbccbaccdddbadcaadddcddbdacdcbaabadddbacccccddabddadcbabcdaabcadaaccbabdccbcdcccabaadbcbcdbcacdadddaacabaacaacdbbddbcdadbddbdcadcbdcddddcbcdadcbbccabddcacaabbcbacbcddabbdbdabbdacbaccbdcbdcadcddcabddccabacccdbcbdcdcbddabcdcadddadadddbacabbcaabbbaaabaacabbdacacadaacacbaabdccabdaadbabbdcdbaadbccccabdaacbcbadbbabacabbadcaadbcabdcbdbdaaddadabddddcababbadbcdbabddbcbabccbbadcdbadcbddacdaacdccabaccccddcccaccddaddabcbbbaabdddcbdadddabdcbacacbdbbcbabbcaaabdbbdacbcdccadcdacbcbdcbbddddcbdadaadbdcccdbccacabadbdcbcabcbbadadccaaddaddbadccacbbaadbdddbaccacaddcddcdbbcacccbabbbabcddcdaabccdbccbadadbcaddcddacadcccdbcdaccdaabacabbaaadcabbcddccddadaccdbbaaacacacbcbbacbbbbacbaabadddcdbbcdddacccaccdddddbaadbdcabcaaaaadcbdaddccdcbacabdbaaddbcbdcaacdabaacdacdbbbadcdbbcacacdaadcddcdbddaadabdccacccdcadabacddaddbbadbbccccabbbcaacabcdbabccdaccadbcacdacaabaacacbbacccdaaadbdccaadcaacaccabaadabcccbbdaabbdacdacbadcccddbdacbccabdcabaddcbcdaddddcbbccbdcadaaabaacbdbdcddacbdcccbbccacbacdadabcabbdcdbaadcbddcaadddcbdaaabacacadaaaaacaabdabbbcdacadaddbbbabcaacbabbcbaadadbabadbadbadadaccabdcdcdccdbbcbbcabcbcdaaccdcbddadbbdcccddccabdddacccacbcdcdbadaaabaadaddaacdccdcacadbcdcdaccbacddaadbbdababccbcccbadaabadcccadbdccddacbabddbcbaabadbbbbccbcadbcdbdcbcdbbccbcddddcdbaccbbdaacdcaddbcdcdddaddbbdaadabaabdacdbdaacbaaccbdacacbaababbdccadaddbacccababbbdcaabadabacacbbccdaaadbdcacbddadaabcddcbcbabdcaaadacbdbacdaaccbacbbbadbdcaaccccbbdabbabcccbcabccadbcdcadcabdbcbdcdccacdcadaccbbdcbcbccccaaacabaddcadcacbdcbbdcdacbbabccdbcbcdbcccbbdcbbccabbbbccaaabcbaabcbcaabddaaacdaadaacdbaadbaacbaaacaabbacccccddcaacbbacbbccbdddbcdddbabcadbcaacdddacaddbdbdbcacdadadbddcddbcdbbdbbccaabccdadcddaccbaaadaccaabdadcbdccbaaadadcaacddabdadacbccbbacbdbaacccaadbbaadbadcacbbdcabbcbbdbddabaabdcdabdaabbccabdddbdaadbcdadabcaccccdcabdccbadcbaacdcbdaadadcdacdccdabaabddcccbcdbbcdbddcaadabdcbbbbaddbcdbdcdbdbbdadccacaacdabadcbabddbdbdcbdbbcaacccdcaaabcddcadbcbdddaadbbcbdcadabcdadabcbbbaddbdadabdaaabaacacddadccabdaddddddcaaadccbacdcbcabbdcdbdabcaabbdcdcabddbbbdddbcabbabcdadabddabdacbbcddaadaabbbcdacbacadcacacccbcbdcbdbcabdcdaadacacacaaadaabdbbccdbbbdcacccbdccdcadacdcbadacbacdbcddaddcbcdaddabcddccdbdddadcabbaadbdadcdaaabcdabbabacacdbdccadcdcaddccabbcbdacbbcdaaadadbbdbcacdddabcdccbadaccbccdbdaacdabdcddabcbbbbbdbcccabaaccccbbbcbcaadacbcddcacbbabbaaaaccbccddccaacacddccaabcbbacadbcbbbbadbddcbcabbdcbcdcdadddccadadaaddabaaadabddcdddcdacaaddcbcbcccddacabcdbdcabdaacddcadabdbddaadbddacdaadbdbcccaddacbcaddccccbcdddddcdbaddbdbbcadadccbbdadcdddccbdbbbdcbdcddabdcadbcaccbdabbaabbadccccddcbbadacbbddbabcaadccdbcbacdababbbbbdcbccaccbbbddaccdddcbbacadaaacbdcccabcdcabcddabadbcbddcacddbcccbcdaacbabdabbadadaababcbdabbddddcbcdddbcbbbaacadbbacbcbbcdabbcdbdcbdaaabadbcdacbccabbbacbdbdddbcabacddaacdbcdbbccaaaadaaacddddbddacbccbdbcdddbcbbdcabccdadcdacdcaabccbdbbacabcccdcacababdbbdcbddcdabcbbadbbabcdaacadcbbbddddbbadbccbabbacbdbddbbdbdbdadddadbdbdbdaabcbdaaccadbaaacdbbabdcddccbcddacadbaaabdbacacbddcaccbbabbbaccaabdbdaacbbacadacaaaaddcddaadcddadcababdcadccaaaadcbdadcbcdaabbcaadadbbaabddbccdbabbbdcdbbbcacbcbdcccdcccbabbacdddccaccdbcddcacdbccbdaadbbcbbccbcdbaabbcdbbdccabbddabaadcdbcdababbbdabcddcadacaababadcbcdcdbdacbcadadaddddabdbccccdaddccbaacdcdacccdadacabddaccbdcddababcbcbadccbaabccdccbbbaaabaaaababcacacaadacbcccccadbbadacabbdbaabdacaaadcbababdccbbdacbaabbcbbbdcdccaacaddabbdbdabbdaadcbdbadddcaaddbcbaadcabdcabbbcdbcabadccdacddabcbdaaccdacbacdacbdbadcabaadcddaabdaabbccdabcbcddcdbdcdddbcbcadddbbdcccccdbdbaacdbbccabbdaddadcabddccbbdacdbbbdbdabaabcabddcccacbdabbdaaddacdaaccddbcbbddbbdcbdadcdacbacaadbdbdaddbbacbccbbaccdaaabdbcccabcbadbddbacdabaacbabbbbdbbbbbcadadababdcbaacabbcdbdccbdcadddabbadbbdbbcbbcdbddaddcbdbacbdadbabaabdccdbaacbccdddaaccbaccadbcadbddacddabbdbccacbdababbcccddcdccccacdddddadccaddbcbdcbccddccabadccbcdcacdadcddddaabcabcdadccacbcbdddadcccbdbbaadacddabbcadaabcbabcccabdcbadddabdadcdcdadbdaccbdaaabbdacaacdadccdadcaddbccabccbdddcbdbcbadbcdcaacbdddbacdcccaabcadacdddcaddbddaabaaccabbbbcbaaacbcbcabdcbadbbdbadccadcdcbaddcbdccddaaccbbbaaabdabcdabadaaddbcccacbbbbabdabdadcbdbbdcabacddacaddbaacdbbadccaabccbbdcdacdbccddbbddcabaaddaacdbdaaababddbadbdbacadddccddcddcccaccbbcaaadbdbddbccbbcbbccccbbbdbcaacaacbaddbcbdadaadadddbbdcabdacbaaabaacadcddcbbaabdabbccdbcbaadcccbddcaacbacbaabdaaaabdbbbbcdaaacdabdadbbcaccbbcbabcdaddcbacdddddcdabcbccabaaadacbabdcacddcdabddadcabbbbccaccdcddaabbcbbdaddddaaadcaaaaaccbadabbddabacdbcccbcbcdbbbcabadccdabaaabaddccbdaccacbbdaccccbbabdbbdccbcbbcccabbdcdcaccabbdcdbbacbdcbbbbdabcbbbcdddaddcbdcdcaabadabcbdcacbcdcdbbadcacaccbcaacbdcdabdccbbccdbdcccaddacccbdbcdadbcbbdcababcccadbacddddaaddbaaaabdcacdbbbcaddabccabbbdaaddbaabcbbcaccccacbdaaacadcbdddcbdabadddabcbcdbdabbbcbbddcdcabcbccabbabcabaaccbddbcdcbaacbdacdbcdcddbcaabadbcdcacbcabadbddaabdccbccddbdbdbdacdcbbcbaccadbcdcdbbddaccccabbdaabddbdddcdbcdadabccabadbadbbccbbcbbdcdddabaabbdcacaccddbdabdcabddcbbdcdbcacdcdbddbdcbcaccdbbcdcdaddadbdbdbacbcdacbddccbacbbcddcbaabdddaacdbacbcdaabbaacbdccccddddcdccacaabbcadadabcddabddccddcdbbcbaabdabccbccccdaddbddbdabbaabadacdcbddcaabdabddacbdddbbacbbabacabcccbbbdbbcccaabbbcdddabdaddcccbbccbbaadacdbcacdbdcdacaadadbabdbbdcbcbcbcaacbcbcddabbbbbabaacabdccdabdbccaadbabcdbcaacacacccbacdbdcbdbdaadbcadccdbccdcdcbcadcdbcbdbadbbadaabbddddbabdbabbdadabdbcddabccaccdacbbccbaccabcbaccaaabccbadcdcbabbddcacdbdbbbcacaddcbddaccbdabdddacabbddbbcdccddccbcddacacbdaaddbdaccdbccbbbcbcdcddccacbdaddacbbabacdddbdddbdacdacabbddcbbbadcdabacabacaadcaadbbbdccbddccdcdadcdcbaabdbaaddcabbaadcdabcdaddbcbadadbadcbbbbdacdadacbabaacbacddccbdaababcabcdadadcccbcacccbcccabcabcaddbcdaadcdaaabadbcdaacddddbcdcbbcdaaadbadbdbcdaaccdbaadaccdaaabaadddccabbabcaabccbbbbccbcadbbbadccddcdbabadccdcaadbadbadbabdbccccaacddbdbacbcaacbcdcaaccdddbcccbcccccaddcaaacabcdcaccaadcacbcbdbdaacbbacdbdcdabdbaabbbccaaccdcbdadddcbacbcdddddcbbdcacbbdcdbdbbcacccaaccbbddcbcbbcabcdddabbdccdbcdacacdaacccdbdbcbbaaccabbbccdcdcbabbacdcbbadcdddddddcbddbaabdadbaaaacddbcabbabccdbdaaabcaddddbdbdbabcccaaacababcddbdacbaccaacadadabbdadbcacccdcbbaadacbbcadddbbdcdccbaaaabbaaabbbacbdddcdabccadabcdabcadcbbdcbbcaaabbcaadcbbaaacbaddcdacdbbadadabdccbcdabbcdcbcdaddadcabcabcaccacbbcaacbcaabdbaaabddbabdacabdacccddcbcbcddcdbabddacbccdcababdcddaadbcadbaddccacbddabdcbcdbdabdacbccddbdcccaabdcaddbcbdbabcdcbacaadbccacbbcccbdbcbdabbcccddcadcdbbbccabbcdadcddbdbbbdadacaaaaabbdaddbdbaddbabaaddcbaaddcbbbaacbcbbdaadbabaaadccbaddbccdabadddcdadddcbcaaadbddcabadcbabcbbabddacabadcaadcdddadaadadbcdacbbacccacabaaddacddccadabbaabbbcacddaddbdaacbcdbccdaaaaabdbcddbcbdacbdbaaababdddbdadbcdaaddcdbcbdabbccdccbcdbbbcbabdacdcbaccbccbaccbbcdbdcabcbcbadcbcdcbbdbcdddaccacdbddbddbadabadbdbaadbdbaccdabbbcddbbbbdddaccbbcbccadcdbcdaabbabdddcabdaadbabdbcbcbbbdbaaabaabaddacbacabbbadaadbacbbcdbcdabdacdcdbaacbcacaadbdcbbcbabcbacdaaadcddabbdcaababcccdbbdadbbcbccdbdcadcaccbbdcddcdbadabddcdbddcdaadcdddacdbaabcbccacadcaabdbaaabbddcbdcccacbccbccbcaaddbdbcdacadaadacbdbcdbbccaadaaababbccadaccdbcbdadacdcbcbacbcbaacaadaccbbbdbacdbdbdcadabaadabaadaacbaadaccddccbdabbbcccccadaddbbddbabbabcdbadbbcbbaaccdacdbdaadbaabddadadadaaccbaadacccabaadabbabcabbcabdbccccaaccbcbcaddadacdddbaddbacadcdbaacacccbbbbababccbbacdabacdbbddbcadcdddacbdbddabadcdccacdbdddcaaaadddaccadbbaddaadababdcacaccdbbabdaddcbcddcbbbcacadbbcbadadbbdbbcccbacadacdbaacbcbdbabbddddacaabcbabccabbbaadbbdcadbbaddababccaaccbcddaddcddcdbaaccccaabccccbdaaabaaabcbbdcadadcbccbadcaacdacbaacddcbaabacddabcbacaaabcbbcacbaaccabaadbccbbbbcddbabaccabacbdcddaddabccaacacdbacacabdcccbbcbddacadacbaadbbcadbdaaccbabdaddbcadbddcbabbcbcacacaaadddaaccddcccdabaaabddccacadcadcadccddbdbbbdbadabbcbadaccbdcbcacbadcdbddabccaccdcadbbdaacbdbccacccadbadadbcacadbbcdaaadaadbccbaabcaaaadbaccadacacdcbaaddcaabcaabbddcadabdcdddbdadabbacbcbbdabcdcbdccdbcadabcbcdbcabaabaabcadaadbcbbdbdbdbbbbaacaacbadacbdabdccddbbbbaaabbcdccddddcdcaccbbcdcddbcbbbccbcbcccdaadcdbdaacadbaccbccdacaddcbcdaaadddadcccabacbbdcbddaaaaddcacbaadddbdbcacbaacdcbdabacbcdcabcbaabbacdababdaadbbbbbcbaddcbdcbccadddccdddbbbdbacddabbccbddcccbbadbbbaccccdccbcccaccbbbbdccddbbabababbdcddbcbdbbbddaabbdbbbbadcdcaaaacacdddbbddcabcacdcbabaaababbdbdcabbcdbcabdddcbddaaddbcabcadcdbdadaacccbccaddbbddacbbbacdbabaadcacaddcbdaccddbbdaaacdddccbdcabbcdcadcddcbbcadbcbbbbacdcbadacccaaadcdddcdacbbdcaacdcbdcadcadaadbccacccacddbaccaaacaaaddddaaccbbcccdcccbdabacbbbabbcabcabdcbcabbcbbcadaadcdabbcdcdbabaccdbdcbcccbcbbbccbbbddddcaaadbabcabdbacaabcabcdddbbcbcbacbbadabbcabcbbcdcdcabcdcbccbaadbcbbdbaacacaaddacdbbcdbaacdbacbbaacdadbdabbdaaacdcbbadacbdddacddadbbdbaabbcadcbcaaacbaddddaaacdadaadabdcacabcdbbddabbdbcadbddcacbbbdadccdabbcdbcbadcdcbdcaacdbcbadaddacdbbadcbaccdabcbdaabbaabbabbcbddccbcadbdacbdabbababddbbddaacbcaaddddaadccdcdacdccbadbdcbabdcaaadabcacddddddddcddcdbbbacbcbbbdbbddccccdcbabaaacbccccdacbbddbcaacddbdaadbcbdadbddbdacddaaababacbddcdaadcbcaabcdcbaaccccacbdcabbdabbababdbcdccdcbdccaababbaadbdbccaadbccdbaacbadaadbbdadabbdaacbabcbdcaaabaabccbacbacdabcbcbbacbbbbdbdadbcadbbbbbaaacdcaddcacdbbacaccdbdbbcdcbdcdbbbbcbccdbccdadbcbbaaccaabcbaacbbccaabcccadabadccadbdddcbbdcbcabacddbadbdbcdcacbbabcadadcabadabadcbadaccccdabbbbadddbabcdacdbcdaacdccdbaaadccaaacaabccbcbcddcdadaaccdbababdbabcccbcacadbaabcccacbdadcaddabccdcbbddbcaabcacaaaaccccdbbcaadcdddbacbccdabdbbccadabcbaaadbccdbbdbbcdbddacccdccacdccacabcdcbdacbdadcdcbccbacbdabbaadbacccbdbdaddbdadbdbbcddacdcbcbbddaadcdcdadcccdbdccdcdbdacdcbcaacbdcadbbccccccccbaaabdcdadbabdcddccbdcacbdbaddadbacbaaaccdabcbadabbdaaccdbcdcbbdbcddbabcabdacdbccdccaddabbddadacdcdcbcccbbbccdbdcbbcabddbbdcadacdcabacbdaadacdaadbaabdabdcccddaadcbbcbdaccaadacdddcdcdacaccabbadabcbbaacdddcdbdaadbdcdabdadabcbaaaacbcabdbccaaacacbacbdadbaadcaadabdadabbbacacbbabcbdcdddaabdcadbbdbbabacbcbcbbddcdabbcddbaacbcacbadcdcddbbdcbcbcabcbdbccddcaaddddbbddbcdabdcbccaacdddbcdacdddcabacbcaddbcacdbaabacaccbadddbccabcdbacbbababaaaabdcdbcacddbadacaaddbbaccbcdaccabdccadacdcbadbbdbcdbdcdaddadaaddbcbccabcdcbbbdabdbbabcdadaacbdddaddaacdbcbdaacbcaacaacdabbcaddbbdcaccccdadccdddabbaddabadbddcddddabcdcddccadcdbbacbdbbbdacdddbaccddbdadbdababbacddcddadcabadcbcadcaacadcdcbdcbadadadcddcbccbbdccaadadacacdbdddabbadacaacdaddbcbbbdabbdcaacabcbadcabddbdbddaccddadcacbdbbacacbcadcabaabccabddaccbcaabcddddbdbcdabcdcdbbdcaabcccdbddcacdacdcdabbadbabaccababbbbcabbccdaccbbddbacbdaccacdacbbdddabbdcbcddaadbdcbbbcaddcddaabdcaccbdcadbdacadaaaabbbabccbbcaabcbababcaddccadadbbcbbddbabbaddabcdddacdcbbaccdcdbdcabaacdabddbddbadcabbacddcbdaadccddbaaaadbcaabdbbdcacbdbcaddbdabcaddddbbadccbdddcaccaaddccddadbcbababbabbdadacddbbcadccbcaabacccccdccddbbacacdbdbbbcccbcbcbcdbddbbbbbcdbdbbdbcdddbccaaabdcbbbcdadacdaabdcaabdbbdddacccaccdabdaacdccbbcbcaadcbdadbdacaadabdccadadcdcdabbadcccbdcbcaabadcbbcdcbabbacacaabbbcbbdcdbcdbccadcadcbccbccdcabaabbdbdddddccdabbcbaaacadcbaaabbbdbabacddbcccccaddddbabbdabacdabdbbcabaaddababaabcbcbcdbbdbabccaaaabcccadcdacbbcdaabdbdaabacadcadcdadabaaaddaddaadcbaddddabcaaacdacadbacdcbadababacccdadcbbaaddaccbaccbddcddbdabbaaacabbcabbcdcabdbbbabdbccaccbbddbddbdbacbccabdcaaacaabacacaacbccbccabcdaccdbbbabddbacdaaccbdcdccaccaabcbdbdcadcbccbbbabccbadcddaaaacdbcdacbbccccababccadcadcbaacdabdbcaaaaabadbcbccdcbdbacccbbacaabcdacadbdcbaabaadbdabbbbacbbbacdabdabadddbbbccaddcdaccdddbddcadbdacdcdbddacdbdaabcabcabcaccbacaccabbdcbbbacaabcdaadbaddacabacacdbbbabcdcddbbaaadccbbaddddbcdbcddbbbacdddaaadbcdbacccdbccdabdcadaababdbadbcbdcbabaddaddbdcaddcaacbccacbbdbabacdcdbadbcccbbdcbbabccccaadbbaabbcdbcbcadaadadbddcaabbbadaadbcdcaabbddcccbaabcadddbcdabacdacdadbabdadbbdacabaccdbbabddcadbaddabadaadcabdcacdcbbbcadddddabaddaaababcbabbdaccbacbcbcbcdadabacacaabbccbadabddcbdaddbbbdaacaabccbdcccdcdcbcdcccddcbddaababbadccddcbaddddacdbbaacbcdcbdabcaadbbdaaacabacaadaaacdabccdbdcbcbcdddcdadbdcbcaddcaadcabbcbbbbcbdaabaaacaadcaadaddcbdddcbdbdcdcdbccbabbdcdcdcacabbcaadbbadbbbccadbbaaacabbdaaabdacbbcabaabdabdaddbaadcabcdcbbcadbcdccabbbaaabdaaabbcabdcaaadcbddbbadbaacbcdaaaabbddbbbaadddaabccccaacdabddbbacaddadccdbdacdbcadbdbbbadddacdaaaccdcbcbbbbabdcddbdbcaaddbbcabcbcdbdbdadbddcbbcbdcddbccaacbdbdabaadbadadbabcbcabdccdbaacbbadadaddbbdabddaccdcaaccbaddcbbadcdbbbabacabbbbabbaaaddccaccdbacbdaabdcdbadbdbcdabaadddadadcbcaabdcccbccbcbbbacacbccadbaadababaccbccacbbdacabdcaabddcdddbbbabbccdddbcbdbccabcdaddaddbdbaddadaccacccbdcdcdddaaaaddabdabbdcbdddcdcccadbcacbabddbcbdddbbacaacbbcdbbbcbdcbbcdbbccccbcdcdadbdbbcadccaaacccdbccaaacdaabccacdbbdcacdaabdcdaabbaadcdbaadccbbaaadcdabbcbbacdcbbccbdbbcbdacbadcdabcdcbcbabaadbcaddbbbbdababbdcbbbaabaaacdacbdbccccbabbbccacdadbbbbbbbccbbdbcadccabaaddbcadacccabdbcaadbacdbdacbabbaccdaddddabcdbaabdbbdccbbbcdcbaaccbdaaabbbabbadaadaadaccdbcbcbbdadbabdcbdcdcbcddadcaccaaabbabcdccacccabdbdbdaccbcdcbdcddabdabcbccbddbdddcadbbacbbdddadadbcbbbcadcbbdcaadcccccddbbddccdaccbdcbbdcbabdddbabcaddbabacbcdbaddadbcdddaacdcaccbbbbdbcadbdbcccdabcbbacbccdcdbacacacbcdaabddbabadaadabdaadbcbaddbabdbbccadccdaabbbbbadcbcddbdacbccdbabbcdacdbddbcbdcbcccbbcbacdbcdacbbcbabadbdacdadbbadacdacccdabadbbabcbabbdacdddbccdbbbaabbcabcccdadbadcabcadbabcaddaacbaccdcbbcbcbbacbabdbdbbdcccccaaaadaaddbbcbbdaccddcccdddcbcbcbacccbabbbcccdaadcdacbbcbbddccdbaaaababcbaccdbcbbddccbdcdabcbaddbabbaddbdbccbaabbdadbbbbccacbbbdbcbdaccddaabbabdddbdabbbabcaadaccaddccbbcbcaabdccaadccbcddcccdbcaadcacaadbbcdbdbccdcbbcdbabbdbdaddacbbbabccacbdacbcbdcccdaacabdcccacddcdbddbbccaaabacbabacdababbbbbccadbccabbbabdacddbbdcddaabadbbadcbcdaacacdbcbdadaccaabccbdbccdcabddadabdddbbaabcccdbbaaacdcaaccdacbbaaddbdcadcbdaadaabbbccadbbdabacbaadacbdbaccbdaadddabababbcccaddacadadddcbbcaacbbadcddcbdaacacccdacdadaabccabdaacbcdccabbabdbdbcacacdaddbcbbdbcdaaadbabacdccddadbbdacaacbadcdadbdddddaddbddccbbbccaaacbccbbbddcbbdcddbaacdaaadcdadbaccaadadcbadccbbccbdbdbdcbdbdcababbdacbabbdabbaaaddbaadddcbabbbcbdcddaaacdcdddbaddbacdbaaaaabccbcbbcaaacabdaaabccdcacdbbcadccbaacbabaaaadcbadddbabadddabdddcdbcdcaabcddbdcddcabacdaabbddbddbccdbbbdbcccacdbcdbacadacaabcdcdcaacbdcddddcdadccddcdbcbdccbbcccdacddbcddabaccacbbdcbcbbaccbababbcccaccccbcddaadbaaddabddbabaaabdcbaadabcbdadadadaabbdacbabaaddbaabbbaacdadbcbdbdbabddadacdcdddbdccdbbdaaacdbdbbacaccdbdddbdcdccdbbdbadaccacabdcccbbcdddbabddaddcbcdcbbdcdbbaabcbbdcbacbaabcdabdaaaabcdccaddbbcbdbadbbcddcddbaccbbbaacbadcccccdcabdbabcdccbbdbcdbcbccbbaaacaaddccbdaccbcadadaabddbdbddadcbdcdcbbaaabaddddbcdbcacaaccdcbcadbdaadaddadaaadbbbacccbcbcacdaabdbccbdbccbbdccdadbdddbdacdcadcdcbabaabadaadadbbcaacacbdcabbdaabcdaadacacacadbdbddacadcababdacdbddddadabdcbbccddcdabacaccaabacadbabcdaddbadccdbabdabbacddbcdadbaaaddcabaadcacccbccbdabbcddabccdbcbabbcbbdcabcbcddacbacccdaaacdccdaccaddbdddbbcadbbddbbdcbddacdddadbdcddccdcbcddaddbbccbcbcdcbcddccbdcbbbbdbbddacbbacdcabaabadbddcdcabacddccbccbbdbdaddaabdaabaaccddbaccacbaccadaddcacdbbacaabdbdbbbcdcaaacbdddcddabdaadadddabdddccacabcabcacccdbcaaaacaadcabbabcdacbbbbcaadabcddaadbbabbdadccbbabdbaaccadabdbdcbaadadacbbbacadbccadcaaaddbcbcaaddcacddcbbdcddaaaabbdaddacdbbbadddbddcdcccbcaadbbabbbbdacbdddddacabdbddcbcddddcbdabdcadcabadbcbbadbbdbbacbbabbabdbbbacdadabcbaaaacdbbbccabbddcbdbddbddaadcabaadababaccbccaccacbbcbcdbdcddddcaacbdbbcadcddaddcabbcaababdcdccabbcbbbdbdcadcdabcbdccbccabbdabaddacdccdadbcddbdabdbdbaaaadbdccbdbdbccaddcbbccacadcbddabcdddddabacbbaacbdabcbbbaabcdccddddacbdacbaababdcdcdcacbaabcabbdbbbdbbabbbaddbabdccdabbbacbcacbbaabbadbdbcbdabbbbdbadcdbdaccbbddaadadbcbbaaddadacadcacbdaaddcaaaacadcbddabddbbaaddccacbdacaaacbdcabbabcaacddcdcadbdabbcbbaabbdadadacacbacbddbcddcdbadcaaabbabbbaddbcadddbacaccaabdbbdadcdcbcbdbaaddddaccacddcddccbdcbaddbaaadcaacabbcdaccdbcadcbcddaabadcabbbdbbddcbabbdbcabadaadcbddbbaabdcddbdacdaacdbbbcccbacdaaaaccddcbcbaadadadbdaabbbaddcbbcacddbcddddaabcdbdacaadcdcacbadddcbdbccacabbaccabbbcdabbcbbbaabacbadcccbdadcdcdadcbcabbabbdcdbdddccabbaddaaaaacabcaaccbcbabcaddaddaccbcabbbdbcaccdbdadbdbdbcbbdcabdbcdbcbadabbdbacacabcbabacabacbbbadddddabbbbadbbaacabcbbabcbadbabdadaddcbccadcbcbdccdbdbabdddbdbacaaccaacccbabdcddcaacdaadbadcdaaaddbbcbadccaccabaaddadaaaaabdaaacdaadcbaadcdbcccbadcadbccacbdadcbbacaabacbdacbacbdccbbbbddcbdddbdbabdbcbcdcbbdbbdadcaadacdbdcbadbabbdbdcbbcabcdaccadaddbbaaadabcbdbddcdbbdbaadbbcadbcbdccddcdcdbaaaddcbadaddcbcacbcdbdbcaaddbdadbdcddaadbabbaacbcbabdcaacbaadbcbddddbacbaaacaacdbbbbaadacdddabbddbadacbddcaacdbbaadccaddcdccbaaaadbcbaadaadcacdbdcbdcdbccbbdbbddcddccdccdadbdabccdcaacccbbdddaabadacbddbddccaddadddcccccabbbdbadadddbadabddbabcaccdbdcbaacacabbddbadbacdcbcaabacdcabcccccdcabbcdcbccbcdbdbacbbadadcdbdcabaadbbadacabdabbdbbdddcccbdddccdccaacbcdabcaaabacddccbaaabccdadcbbbabbbaabdcabbcdbccdcdcbdccbbddaadaccabbbdbbcdbcaddcddabcacadbbddbadccbbcabacdbaaddabbadacbbcdcdacddadcaaaabbcbbdababbaaacdadcacdadbdbbcacbdbdbcaaacdcccdcbbbcbcccaaabacdabdcdcdddbbbcdcacadbbacbcbdbbccbdabbaabbddbbdcbacaaacdccbbabcacbcbdbaccdbcaddacdaacbaabbcdcccbbbcddaacdbccdbbcaadbdbadacbdccdacbdacbbbcaabcddcdcbbddaacddacbdbaaaaaaddbccbabbbcdbcaabbaacdaacbdbccbbaadadcbabdcbadddbaaadbcbbdbdaaddbdbdacdbccccbcbacabaabbbcbadaadaacaabbddbbbadccadcbcaacbdccacdbdcddbaddbabdcabaaddaaaaabcbabccadcabdbdadcadadaaaadbacccdccaaabdcccdcbabddbcacdddabbacbddbbadcacadbdacdddbbddadabdaacadabacddbdcacaccbaacaddacbbbabbacdbcadabdaccbbbabddcdaaccabbdabbbaabdcdccddbdcbbdccdacaadbbddadacdadcccdbdcbcdcaaabbbacdbbbacccbcdcaddaaaccccabaabbbdcdbacbcddabdadacddcbdbaadaacbcaabaaccbbcdbcdbdbdbccddcbacababaadddbbccdddbbbabaacaacdcbdadcaacbccabbbabdbdaabbdbcaccadcbbaddbccbbbdcadcdddccaabdccacddaadcaabdadcbaacbcdbbdcbbabacabaabcbabbaccdcbbabcabaacabcdcaaabadbcdabcbcaabdcbdcaaacbadabdccbaddbcaaadacdaaaccbdccdcddccababdacaadccbccaddbcdccdcdaddcdadadbcbacdddabcbbdbbacbccbadbbbbacbdcbcadaaacdccbcdccbcddabbcabacbcdabbcabbcabbdbbdbaddabadbdcadabccbdcdcdcdadadaabbbcbbdbbadbcbdacdccaabbdcaabbdbddddcbbddbacacabacbaacdbcbaaadcdbddbdbbdbdddbdaddbbbdabddadccbcddcabadcaddddacccdddabaaabacbcbabadaaadadacdddccdcbcddbcbcabdadadadacbaaadaddbbbcddcaccdccdbbddaabbcdabcbccbacbcbcdcaadbbbadaddadcbcdadbdbcacaccabaaaaccabcbbbaaaccacdbaaabcdacabccddcccddabdcababbbdaccbcabaddbadabdbcdbacaaddcbdbbabcbccccbaabacbbddacdabdcdbcdcdadbacbcaabdbcccadbbdbadbbcdabdcacdbbcaaacabcdcbdbdbcddaddaccacdadabcdcbaaabcbabdcbcbbcadaadcacddaadccdcbadcccbdcdaccaababccbbdaddaadcdabaaddbbadbbdbdacdcaaababbcbdadbccadabcadcabadcabaaabdbddbdadbcbcdaaddabbaaabbdccdccbbbbaacaabccaabbcaaabccdadbdaabdcbccbdacadccbbcaaacbadadcccaccbbcbcdbcdcdcbaabdabbddcaccdbcbacccbbabacacbcbaddbbadbbaaabcbabbdccdcabdbcccddcabdccdddcbbbbacdadcdbbdabaadbccdccbabbdccbddddadccbdbcbccbdbddccdddbcbabadcccbaacdbbbdbaaabbdcdaccaabcccbccbaccabadcacdaacbcaabbcdbdadccdcadadcdcbdcbbbbaccadcccddaadaababdbdcdabcccdabacddcdbcbcbccaaaaaadadcadacabcbcdcdcdcadcdacacaacbcccbcaaaaddbbddbbcdbbbdbbccbdacbcddabddbbbdcdddcaababddcacbbbaaddcccbcccdbddadcbbbcdbbcdabccabbacaaaadbccccaadaaaddcbbbaacbcaccaacdcdadaddaaccdcabbbbbabcbbddabcddddacbdcccbccbacdadbbbabcbcaaddbddbaddcaacdccacddccdccbcdabbaabcbacaaadababcddbaaaddbddabcbabbcdadcbaabddcadcbdbadbadabcbaaabaccbbbdcacdbdddbbabbbdbcccabaddccdcccbabdbdbdabcabbaddadcacdbccbdabcbcccaabbcbacccaabbbddadccdaaaacddbadddaabcbaabddbcbdbadacabbcccdabaccdcadacbcdabaddacdbaabaadacddbcdababcacacbdbccaccdbbbbaaadadabbabadbdabcdcbadbacabcacbcbcacddaccbcaabbdccbabbcacaddaacacabddadcdccbcdbcdbdccbdacadbcadadbdcacaddcbdacadcadadbadcbadbaadadcadabdbccdaabacdcadbaaacbbdabbdcdcbcbdcaaadacbbcdcaccdbbacddbabbcddccaaabdcbbccbbcdbbbcdbadcadadcbdccbcdbdabddaadacdbcadababdacbabcadacdadadacddcdaccddccbabbdbdcaacddcdadaddddbcbccbbaacbdbdddaddcdccbacbbcbbacaacabcbbbbacbbbcdcdacaabbbadbcbdbacabcdbabdadaccaabcbbabcbcaacbcbdbdbbbdaaabbccdddbacbdabcbdbddacaddcabcacababcbbbbbdbacbcadccaacdbbddcdbcacdbcacbdbacddbbdbdaacadcaaacbaddcaddacccbccaddbadbddcdaacbdbdbccdcdcabbbbaabbdacbbcdacadbdddbdbdccbbdaccbabacbcaadbcdbacddacdabbaadbbacaacdddbccbaabacbccabdaadddcdcdcacbbbbbddddcbcccdbabdabcbbdbccadbbabcccabdbbcacddddbdcbcbadbaaaaddacababcacaddadacdbbbcbbdabdbbabdbbaabaacbbaaaddaabcbcbcdccdabcdadcaccaababcdbbbacbdddaaccdadacdadbcbdddcbdcacdbcbcadcdacadcadcbcdccbcaabddbddbdacbacacdcbddcdbabccbbbdbcccadbdacdaadababdaadbbcccbddbbddbbbcdaaacacdccdcadcbaababbccdabaaddaccbbbdbacbbccbdddacabccabcaacbaabaacaaaabdbccbbadbbbabacbacdcaddcacacccddccaadbcbccdcdadddbdcbcacdcdcadcaadaabdcddabdaccbabcacbccbbccccdcaabbccbdbaacbcbcbcbadaaababdacbddbabcbadadbcbaccadbabdaadcacaccbaddbccdabadcdcbcbaadabaadadbadcbbaacbdaccdbabdcabcbdddcdabbcbdcbdadbabaacbcbdcbdcccabbadddddaddbdaaababdacbbddcddbbbcadcdbdcbadadbdbbdbcccbcdbcbcccdadccbbbcddddabbbadacdbacabcccbcbdcadacdcbbbdbddddbaddcaddccbbdddccdabddaaddcccdabdcabbcbaddddcabadbabbccdadcdbdccdadcbcacdabdaadcdbdcddbdcddbaddbbdbdbdbbdabaacaacbabdccbbccddcadabacdbccdccbacaddadbacddadbaadbabcdbbabadaaacdbbacadcbbbccdabbdbaaccbacbdcaaddbdacbcbcbadbaaacdccabddccdcaaadcdccababccbadabbbbabadaddaaddcbddcbabbaccaadcaabaaddddbadbbdaddccaacaacbddbaaabbacbbdadcaaddaccbbccddabbbcbbddcbacddbbdaaddadbacbdcbdbcaccbadcdabadbaabdcdcacdcccbddabaadacccdbccdccdcbcdcbadbabcbdaacccdbaacbabcdbcbbcccccadddcbcabbaaaccaaadbabbadcccdcddaddccbadbbdcddaadaddadadbadacaacacacdaabdbcdadbccaacabbbcaddcabbddaaccbbabbddbabadbbcbbdbcddbaaabdccdcccdcaaabadcdbdacdabcddcbcbbdacbddbddaaadbcabccddabdbdaadcbcbbaacbadaaabdcbccabbdcaabdaaadbadabccaacdcdcdccddbbdcdccdacbcbacdbbccbcabdcbbadcdadadbbdbccbbaccacbcbcacccdcdadcbbcdaddbaabcaaadadcbddddcacbdddadbacabdbddddadbaacaacabacaaddbaaddaaabaacacbcdabdcabcccdddabdcabbdacdcbadadbbacddcacdabdadbaabaccbcbcacdbddcaddbcbcccbddadcbddabcddcaacaddcbaabcaaaaaaddacacdddccacababccaacddcbbaabdaabbccaddacdcbabacdcbbadccddbdccaccaccabdadadaccddcccddccbadbdcccadaddbdcacdcadbcaacbbddadbcacbcaccdcbccabbcbdbddabbdcdbcccdadcbcacbcbdcadaccacaabcbaccdbacccaddddcaadbcbddbaccabccccbdbccaccdcababbdbdbdcdbcaadabbdabbbbaaddcbdaabcbadcbadaccccaddadbdaabdaacdbbcabdadbbbdbcbbabcdcdbdcdaaabadcddbacabdcdbdddbcddcccbdcaacbadcbdbdbdbbacbcdcddacbccdaabdcbaadacbadabacadaadcdaacbaacbddbacdddadaadabbccaaaababbbadbcccdbaccbbabbccaabbbdabddccbabdccadcacdbaaaadadbdcdacaccbbddacdabccbcbdacbccbbabaddbaabdaddabbbdabcddccbcadbdadaacabadaccbcccbacdaabbbbbbbaccdbddbccddcbbdbabddcbddddddddbcabbbbdaadcbdddcacacbbbdccdccacddbccadcaaccaabcabacbcdbbaaaccccaabbccbcdbcdcdbbcdaddddaddbcbaadabbbcaccabdbbbbbbcaacbcbbdaccadcdbdbbbdbbdabaddcbaacbddbccaccdbdaabcdccbcbdaaacbadcacdacddaacdaaabcabacaddbbddcaaadcdbccbcbcbdbacababcbbcadccbdcbcabdbadbaabdbdcbbbddcbacdadabcbbdbbacccbdcacccbcddbabcddacbcaacbcbabdabdadcccdaccbccabdaaaccadbccbbdbabaddddddbaccbbddaadaacccbacaccdcacdaccaadaddddabbcaaccdadabdcbcdabbddcdbdbbadcacccccaddacbddadcdcdddccacaacdcaccbbcdadcdbcbbccdcdddadbcacdabbaddbbabcbdddaabadbaabaacabacbddcbcbdabbddbaccdbcbdacdbdaaacdddbdadbaaabaadcacacdcbdadddddcdacccadababbdbcbccabbcdbdcbcbdddaccbacabddacaccdabbcbdcbbdabdbcdbcdacccdcaccacabbadaacbdabcacdacccccbddbcadcdadbacbbacdbbbdabcacdbbddaabcbbbcacabcbaabddcccdcccbccdbcdbbddacdbdddabbbccbcadabccadcabacdbbaacccdccbaadbcdadbaddbccbdadabccddabacdbbccbbdccdddcabcbcabdcdbabccbcdaadcdccdcdacbaadacddacdbabacabadbccbbdcadaadabbacaddcdbadbbacbdbabadacadadaddbcdbdbacbaddabaaaddccdcccbddaabbdcdcbaabdbddbcacccbaccaabcbbbcaccbdcaabdcbbabbcbbdcdaadbacdbdbbdaaccabcccbacbbcdbdcdabdccacbaddbccdbdaaddccdcaabdbdaadbcabacccdacbbbdbccbaaaccccbcaddbbdddbacdbababbdcadaabaaaaaacbcbaaccbbcccabbdcadaccbcccaadaaddcddbaadbacacabdcabdabacadcaddbcccbbddadaaabcddbbbbcadbcaadbdaabbacdaabdbbaccddbdcccbbbdcbbaccddabbabbdabbcbacbaabadcdccdbcbbdadaddbcdacbdadcdaddcbcdbbbdcbddddbbdddcacccdcdabcbdcccaababadcdcdaccbccbbdccabcdddddbacaacdabcababacccbaacbbabbbcbaabacadbbccccccbbcccabbdbbacaddbdcbdabdcadacbbbabdbbbdcdbbcddcaddcaaacdccbbccccddadadbbcacacdddcdacaabaabbaadacbbbdadaaabdbcacbcbdcdddaabcccbccaccccddcbbbabbaadccabbcbababaddcccacbabbdcccddadccbacccddcdadacdadbdadcdcadcccdbbdccadcdacddbbcaaacabbddddbabbcccabadcdbccdcbbbddbcaabdcbccdacacadbbbdbabdbaadbcbcbdbdbbccbdbabbddabdbcbdaabdccbcddcddabbcaaddccdbbcdbbbadcaaadabddaddcccdcbbdacddabdaaaddbdaccbdacacbcdcacbabcacddddcccdacdcccacdbdaaaccbbcacbcdbdcbdbdcdadadbcdcddbbaddbbbaabdccbccbcaddaaddbdbbcbcabccdccccaabddbdadabcaadbbabbbddbcabcdbabdcbdbdcbccdacccdabcbcdabdddaaabcbccccdbbcbdbcddabcddcccbacccacbdcacbaacdaadacdddabcddcaaabcdcdcbdbdbddbbbcdabadaaaaaaacaadadabbddbcadcbcbccddcbbabdacdadacbcaaccdbccbacadddadcdcdbcaabbdcbdcacacdaccdbccdacddadccaccdcbaabdcdbbdcbdcdadbabcacababcbadccaaabbbccdacdcacdacbadcbdbdcadccdabbbaaacdacacddaabdbbdccccccbaaacdabcbdcdbacbbdbcccaccacabccaccdaabdbbabcdbabaadcaabdddccddabbadaabdabcbcbcdbccbdabdabbdacadacccdcbbdbbccbcacdadadccbbabbacdabdddaddadbbcabcacdddcbdabacacdadbcbdacdbdbadccdcdbbcdbddcdbcbbbdcbdacdbaacccacdcccadbcaddcaddbaddbdacbabdbdbdbdcddddcabbdddcdcadcbcccacbcddbdbaabacaddabadaaacbccbabbdbccdabaadaadcbbccdbbbdacdcddddaddbdcdcccddcadddbbbbaadcaacacdabdaaaadcdcbcccaccacbbaccadadbdccddddcabccabcdbdbacbcabcdccddaacbbaadbbbcaddccadadbdcdcbadaabacacacccabcbdbbdddabaccdccdacbbacdcadbaadccaabadcbcbabbaddacaabbdadaccaccddcbbcddbccabbcbcbdabaaabdcadbdcdbdcdcbabbcbcbbadbccdbcbdcdcbdccdbbadbabbbbccbaacccacdaaadabccddbddddcbacbdbddcbcbabdaabbcddccddcbaddbabbdacbbbbcdbcdcadbadadddabbadacbcaaacacdbcaabbcdcbdddbccbabadaabcdddcbcbcddcbddadaadbddcaccdbadbabcbcddbaaabccccccdabdaabcbbbcbdabacabadddbbacabddbcbbadacbaacbdbcdadbdddbcaccadadadddcdcbbcbbcdbcaadcbdbbdaaaddaaadbbdcdcccabbbdccccaaaabbdcdccbacbddccdbdcaacdcbaacadbaccadcbcbdadcdbaacbaacbbddadddcdbbdaabcccdbacaacaccbccabcbbccddddbbaabbcaaacacacbdaaaabbcdabbcbbaccacabbdbaddccaddadaaacadcaadaabacddcadbcaabcdcaacbbccabcdcbbadbbabacbcdadcaccbdccbbddddaaacaaacabcbcdaddaabadcbcdcbdbaccaccbbcabdbcbdcddaddcadbddbdbbcccacacbadadccdaaddaaccbddbddcabbbdbacadbcadcadcccdcdbdacaaddadcbacbcdaadaaaddccdacdccdbbccaadcadbadbaabaabacbbaabcbcbabdbbaabcdcccaaaaacdbcadcacdbabbdabaddaaccdbcbbcbbabdccddcabdacdacbbadadbadaabcbdaacdbcaacdbcbdcbdddcdbcacaddadddccdcaddbccdcadcdcabbbdaaabcdabccbaddbaabaddbcabacbbadadcdadbdbaabaadddcabdbabbbaacdabbaaaccbaddbcbbcdccddddcddbdbadadbcaaaaabcdbdcdacddcbbccccdaadcbcdacbaccbbbddbcbbbadcbaabdbabadabbcbdbbbdbdcacbacccbccbadcbacbbacdccaccddcacbcccdaacaaacaaccaaaccadaaaddabccbbbdadbcdaacdcdaababcbabaaccdbbdbcccbdbcadadabcbbccacbdbbabdbcccaddcccacbbbddbcdacdcacdddbadbbbaabacaabcadcccbccdadabdbcbdcdbcacbabbdcdaabccddcbcbcbacbaccdbbcacacadaaddaccbdaaabcbaaddddabbabcaddbabcaccbbdcacdacaacbacadbabcdaccadacbcbadaaacdbdacabddddacdcdbacbbcacabcddaddacdccadcbccacbababdbababacbcddcbdcaddcccbbdbadbddadbaaacabdccdbadbabccdadbcadaaacddaddcabcccadbabacdbbadabaaccbbbbddbcaadbddacbadbaadbdccdaadcadcdbbbdcacabcaabcbacabaabaacbcbcbbbbdcbbcaccddbdcdccdadbcabacbaabbbcbaaccadaacabccdbaaaacabaabdddcaddabccaacdbbdaaddaaccddaadaadcbbdbccabaddddcabadadbbdcdbcaccdadbdcadcbccdcacdccbdacdcaabbcbccbccddcdbdabbccbcbcdbababcbcbdbbbabcbaccccadbdccdacdadbacccdcdabdbacadcbabdacdddadbaabcbcbcbbbbddadacaadbdbadadacdcddbbdadcdbdabddbadbbdbabaabcabbbaacaddbbcaacacaaadcdccbcdacaadccbabccadaabacaddbccbdccacbbdacbcdacbbcdbabbbddcdabacbbcddcbccdcbdbbaacccbadacabbcddaddaccddbdcbbaadcdbabdabacadbacacbcddcaaaacdddcdadaddaacacdaabbcadbbaaccacbbadbcaaaddbbdcbccdadbdabbcdaccdcbdcacbabddbbdbcbdbbdabbbacbdcabdaadddccdaaddddbbdadcbbddccbccbcbcbabbddbddbdccdbcccddadbbdacdabadbddacbabaccddacdcacacddcccdbabaacbdaabbbdcbdbacabbacacdadcbaabcdadaaacaccddbadcdabdaabcabbbddbacadadbadcabacbaccaabbdbbccdcadbdaacbbddaadddbccdccabcddaccaababbddbcbaddcddbdcddcbacbdbcabbbabdccacbabcddabadbdaaabadbdbdccaabacbadacbccbccddcbccacacccccacddacbccdddaabcbababcccadbaddabbababbbdabdbcacbcdbcaacbacdaacdabbbaacddacbbacdaddbbacadcddaabcdcacbcbbdcccaadddbadcdaadacdbcabcdabbaddbccabddddbdbdcccbcdadaacaacacaaacadbcdabddcbbcddccaaccddabbbbbdcbadbcbcbdcdbcabcdbaadcdbbddcbabdbcbacbcacddacddcacbacabbaddbaabcdbadcabbdcbcdbbccccaaabddccbcbcacdbddbbccbbdcdcccccbaabbcbabcaadddbaadcbabccbbbdcaaccadabdabadbabbaaccdbdacbcdaacacdacbcabbbaabbaabbacababdbadbdbaacdbbccddacdabccaabbdadaddddbccbcdbbaaddcbbacdbbcbdcabacbbadaacaabbcdbcccccacbbaddccabacadbdccddcaaadbdaabdacacaabbdcccccadadbbbbcdbbbdbdadccdcaacbabccdacbaaabddcabbbbcdaabcacccbddbcacaadccbccabbcdadcbdccdddcbddabbadbcadbbbccdaabbaaaaaacabadadddaaabcdcadbbdadbccbcbbdcadcacacacbdbcdbadcbdbbadddabbabbbcacbbcaddbdbbddbbdccabacabacccaaccadddbabadadbbcddacacccabbbcbacadcbbdcbbbbaadcbacbddbbabbaadbacbcbcdbbaabcaacaabbacdbabbddbccddcdddaaaaacdddcaacbdcbdacdbcbacadcddabbdbdacbadababdbcdccabccabbcdcababaddcbdacacbcbdbdbbcbcbabdaccaaaacddaaccccbcaabddadbdbddddaabaadbadabdccaabcccaaabbccdcbccaadcadbbacdbcbdbcbddbcadacccdcdbcbbcdbcadbcbddadcccccbccbbbacbbaadcdabcabadcabcbbbbccccaaacaccdaabdbcbcdcaacabddbdaacadcbcaccadbaadbdcdbdacadcdddbbbcbccddbabaddcbdacdcbcbcbacabacdcbcdcdcbcdcccccdbbcbdcbbdadbaaaccbbdabbadaacacaaaddacaadacbcdbdbbabaadbacaabccbbbdaabcbcbdbcdadbcccbbbacbdbbacabddbbacaccddbadcbddadabbddbcacbcadbaddbabbabadddccbbbddcbbddbdbcbdbdbdbcbcbdcccddcdbaccbcbacabbdcbdcaabccbadcddcacbdadacaccbdbdbdabdcabbdccddacdbcacdcaddaacdbcaddababbdabcbadcabcdacbdcaacaccdcaaacbbaaadbdcbdcccadbcdddbdadabccbabcbdabddbcdbcbdbdccadacaddbdadbbcddbbabcdccadabbcabbbbadabbaacdababbddcaadbaddddbaabccadaaaacdadbaaacaddcdcdccddcccacaacbdbbccccacaaccababbbbabadacadbcdbbbbcbdddaaddcbddabccabbccddddcccdabbdccdbcabbbdbadbadadddabdabcaaaaabadbaacabbadbacaabbbbadcdcbabcdcdaabcdbaabadaacccbdccbcdbcdbacbcbadcdbadcdccbbbddbabbdbadaccccbabdbabcddacadbdddbcacabaccccdaaaabccccbbbbdcaadbdbbdaabbcccccddadccaacbacaababadbddcabdbbddbccbcddbcacdacabddaddbccbbccddbcdaccdbdaacaabddaaadbcabbaddabddcbdacdacbdbbccdaaabbdcabbdcabbaccdbbbababcbcdbdcbbbbbbddbcddaacadadcdbdadacaacadcbabadcdcbdadcacbcddcaaaddadbdbddbbaaaddcbbcdcbabaadbcdaddcdaccbdddccbddaadbbadccdddddaaacbcaacbbacdabccbdaddbcacadbabdbaaaacaacbadbaabcbcbbcbbbbcdcdaccdaaadabbcddcccaaaadadbdbdcdbbabbdbdbcccbbabcbabbbaaccbbaadbaccdbddaadbdbcbbcddddabcdbaabcbccacbbcabacbdcdabaccbcaadbadadadacdcbdbbbddddccaacdadbccbddbcbddaadbcaadaacbdaaaabcaaabbcdccbccabdbcbabbcbacccabdbdbcbbbdbdbbdcdaabdcbbbcacaabcbdcdadbbbbaadadcbaaaaabddcbbbaddddaabcdadcadcaacadccdddaddbbaddaabdadabbdabcbbaccddcacbbddbdbcbcdbdabcacaaaadbcbcacbdbddbcabbcaaaabcbcdadbbdabddadcbadcacbacaacadadcaaaabbbacdbbdadccaabcbabcbcdddcdbcbdabbdddddcbbbcddbcdccdbbbacdcbbdabadadcdabdbdcdbbbaccbaabcadacccbbbcdabacbccccaccdbcbddcdcababcdadcdadacdccdaacacdabadcabacbcdbaadbdcdabcbbcbaccdbcbbaadddcaccaaadadbddcdacbcbabdabcccdbcbbdabbbdbcbaabbbbaababddabcdadbbdbbcabbbbcababcbaadaaccbbbbacdacbbcbdcbcadbcdcababbbcaaacbccbdccadccdbaabbdabbcddcabdcbbabccbddaaacdcdcadabaadddbddbddbaadaccacabbdcbdddaccbcdbbcabdaadcaabdacbaacabcbdbabacddbddababddbcbdbaddbcdcacdccdccbbbaaadbbbbddbbdcbdcbddbabcacabdcccadccbcdccbccdadddaaaabdacabadccbbaccdcddbccdabaaabdbdbdcdaaddcccacbbadbcadaabadcbacbcddadbcddccbcbbbadcdccddbcdacbbdbcccbbadaccaaacccdbaccbbcdacabadbabbdabcbccbbdcacbaddbdcbbbaccdbccdacbbdcacadbddcbadcdcdaabcbdbccdcbdcaabdbbcacbdacaaddccadabaadababbcccaadbdadabdbdcdaccaddadbcaadccbbdbbcbcbbabdaccdcccdabcadaadcbcadcacbbbdbaacdabdccbcdccccbddddbaccddbdacdbdbccdddbdcbbdcdddcbdaccaadcabcbdbaababbccbdbbabddbccddbabaddbcddbcbbacbdbbbbabbcabcccbbadbccbddcccaaadadaaadcddaacadaddabbdbadabbbbaddddbbbcbccccacabdcbcdccdadcaaccbaddcbdcccccdaddacacccbbabaabccdccdcddcbcaabcabcdbcaccdbcbadbddadaccaadbbadbbdadbdbbcdcbbdaadbdadcdabcccbddbcbcbbbbaccbbdcbabddcbabddcbcaacaddbbaaaccadacadbdcbbcabadccbadabbdcddbdbcbcaabbadabccaacbdcbabacaabcaddabccbbdcbbcbcddaabcdaadbdbcbaddccdbabcabaabdadcabaaabcadadaadcaaaaddacdcadacbbacaaacdcdabbdcadabbcddbbbaaacbbdcddddcacbcaadacbddbdbacdbdbccdddaadbddadcbccccdbbbcdcadcacccaacdaabaccccccdcbacaadcaaacbaadddbcabdabbadcbaabdaadbdcadddacbdbbcbbdaabacdbdbbbbbdbbdcacaddaaaddcabdccaacbbbdaaacdbcbadacaadccadabababbddddccdaddcbccdddabddbdcddccddbdccaaacccdbbaabbcddcddddcdccacadbadddadbcaddacbcaabdcaababbbabdadcaaccbcbccbccdcdbcdccabdcbacbcdcaabadbbbcacdaabddbcaddbaacdbbdadacbbbacaabbcdbaabddacaccccbbdaaccacbcadccbbcaabcaccaabbababacdccbacabbadbbaaddbadcccbaddbbcbdacdbcbbcabbbcaaaadababdaabbbbaacbcbcbcadadcaabcccabddaccaadbddacbaacababbaaadabdacaaaacaaadcbabbbcdbbcbbbbbddbadadccbcbabaddbcbdcbddadadbdadbbaabbdbddaccbabbaabccbdbdaabdbbbabdccacdcaadcabadbdbbacddadacbddcbcdadadcbaccaaaccdcbcabcccdbbcbbcbaaddcbcabcdbaacdbadbdabaddcdcdabdcddadacdccdbbacccdabaaddaaaddbcdaaabcdacacdbacdacccabdbdbdacbcdbdacbdcbdcaadbdbbcbccabaddbcabcbdddbbbabccdaaadbddcaadcacbcaacdccccccacdaddadbabbabaadaabbdaaabaabcdbadcaadcbcadaccbcbddaaacaacbddbdcdcacabdadcaadccbaadcddccbabbabaddabcdcbdcacbdcbcdccccbabbdabadbcdddcbddbbaaadbbccaaaddbabdabbababcbcbcabcadbcbddbbabccdbbddcbacdcdbcacbcbcbddbabcbaadbccbdddacbacccdbcbbbaccccdacadaabdadcccccbcdbddadcbcbcadaaadacbabddabddadcccdbcdadbbbbaadbbdddbdabcccbbcababbddcabacbdaadbdccdbbabdcacbbdbbaaaddbcaccacdaaacddccbdaadaddcbddddbcadbbadcacbccdcbadaabaaccbcdccddbbbbbbbddccadadbdaaacadbbcadbabccadacdaccabdbddcacabcdaacaaaddbadccbabbdbabbaaaabdccbddaccabcacaaaddadbcadbdccadcddccccbbccbcaaabbcddcaaacbbdcdbcdadcccabbcccddaadbabcbdaaadcccabacaabdaabdcbbbaaccdbddcbdcaddbcabcaccdbabadcccadccdcbaccabdbcaadaccdabbcbcadabbbccbbcbbcbbbabcadacbcabcdccadaadcabcaacbaaadbacdbcbabbcabdcbcabbcbbdbadaccaddabbbabcddbcccccbcacddcacacdadbccadacbdadabcbdcbcddabccbdcadbcbabacdccbbbbccbbaaaacddccabdaaaaaaadccdbdadcadaadccbccbcaaabdcadcadccdccdddbbdabcaccdbaddbbadddacbbaacadbdacaabbadddbcdbddbdaadcdbdccbadccdcccbaadbbaadabadccacdbdacddbacdddbccbbccdbaaddbcdcdaddabdadacacacbabdccdabcaadadcbbbbaaabbcacdccdddadacacbbccbbbdbabbbddcccabaddccacbdccbdaaccadccdaacbabdadbdcdddabcdaabcddddaadcaccdaaaacccddadbbcdbaaccddbcbddbabccaddbbcdbcbacaaabdccdbbabdabadcacddaccbbccdcbbdcadddbbaabdcdcbbbcbdccdcbdcbabaadbbaaacbcbcbccbabccbbbcdabddbccccbccddbddccdbcacabbdbddccacadbdddaabcccaadbdbdccbcadbaaacdabaacbddbaadbcaddbdadddadddacdaccddacdadbcbccdbbdbbadcbadbcdbabddaacbbbaaabadbdadabadaadcadddbbbabdaabbddcdbcdadbbaddbccccbbaadacbcdbaddbccacbacdcdcadccbbaddddcdcbbadccaadbbdbdadabaacacddbdbccbbadbdaacbdbbbaddadbacadbdddbbbcabbdcdabaccaacdccbdddddaddcdddabadcabdbbdcccadbbbaaccdbaccbcaddcbdbbdcbdddbcdccacccccbdcadcccbaddadbbcbcbbacbcbabcbacbcccdbcbccacbddcaddadabcacbcaaabdbbaacabdabaaabaacaaaaabbcdbdbaaddbaabcbadadcabaabdbbdcadccdabdbbbbddbcddcbbddbbccccdacbbbddabbcdbdcbbcddbddbcbcdddcbbbaaddccdadcbdbbacbacabbdbbacbadbcabcdaaaddcbcccabbbdcbabacdacbdddcddaadbaccabbbdcbdcbbdccdacabdbcbccabbbccacccdddbbaddabbbdbdcdbbbbdcbbcaaadabcadbdbddccacaccdaadbdbacdbcadbbbcabcddacbcddaabddcacbbbbdbbddadbdaaabbbdaaccdcbaacdcadddcbdcaabdcacadaddcdcbdadabbddacaadbddbbcaaccaabbabbdcdadcdbddcbcdbadcbbcccddaaacaaaabcdbdcbddbaadabbcaabbbcabdccddcdabdbcadbacccdcdcbbbadaaabadcbbbbddbaabacaacccbbdaabaccadbbdabcbbdababcbdabadccdcdcdcbdbcaadacaaadadbbbbdbbaaccccadcdcddbabdcbdbddabacbadadcdacaacddcacdbddcdbadbbadabbaaaabcbcbccaabbdbdddbaaabaccdbacbaaccbbbacacaddbabcabbabbdcdcdbdadadabccaababdcaddbcbbcdcbcacaadbbddaaacadcccccabcdaccccdbacbdddddddbadbaabdbaabbccdaccbacabaabaaaccdddbcbcdccddcddcccaccccabddcadaabdbbbdcdacddbbaddbacddcadabcacddbbdacbdbbbaccdbabbcdbacbdaadabaadccccdbdaaccaddddbbccabaccaaccbdacadccadacddddbddbbadbaaccddbdccaabbacccacbcddadcddddbcadbcdbccbdcdbaacaccdaddcbccbdccaabaacadbabcdcccddccdaccadcaccbbadcccddcdccddbcadacadaabadaacdbbbabdadbccaaababadbaacabbadacdcabcbdbdddcbcdbadbaadabdcdadbbbdbcbadaaddadadababcdabadbdcacaacaaabcbdcdcacdddcdbbdbccabcacddbcdbcccddbdaabaabbccbbbdbbcbcdabccbbdddbcdbbcddbdbdaaacaccdcccdbdabdbccccccdabadcadcdcddbdbdcdabcddcbcaddbdcbbcacadacbddccdbcdbccbbcbcdbbcddabaccacbacbddadddcaabbdcbcacbdddacaddabbaabaadcdabcdbccdbcbdacabccbaacabbcdacabdaacbadbcbacabcacaddbbddccbdaddadbacddbbdbbcddbbcdcdbadcacbaabbacdbcdbcccccdbdcbddbcadcbcbabbdccccbaaccdbbbacbdabbbbdcdcbaacdcbadbbdacadccddccdcacbdbdddbcddbcaccdbababdaabdcdddbbddcddccdcacccbbbacabbbbbbaadabdacbdadbbdcabccdacccbcddbbaaaaaccacdaacdadbccddccbbabcdbacdcacdbcddbcaccbbcaddbbbcaaaccddbcdbccbabdcbacabdcdaccddbaddcddcbbdddcbbdacabbaacbabdcbcadbcdacdcbdbabbabdddbbdbdddbbbaabbbbcdacaddccacdddbbabdcaadaccadbdbadbddabdcbdcacbaadbcaabaaabcdccdaddcbdcddbdbbdbcbcdddaadccaadcdddaadcbbbbdbadcaaadabbaabbbcbccbdbabbdacabcacdaaccbadbccbbcdcacbcbcabcdadbbcadbcdbadcaadbdbcddcdccababbcadddccaaadccaddadcdcabdbadddbcaacabdcccababbcbdadcaddbdbdadadacadaaaabdaabaadbcbadaaacaadbddddaabddcaadbacddcaadadbcdaddddbbbacbccdcbcbadbbdbcdccabccddcdcbbbaadaaabbddaabddaacbcccbacdccacaabdbccaabbcbabbdcccbbcaddcbaabdacabaccddccaadcbacadbdcadacaaabadbbabcacbcddbacdcaddbdbcdbbdddacdcaaaddbbdaadccddadbcacaaabcbaaadaddbadabcdbdcabbddddcabbabbccaccadbaadcdddcabcbbbdadbabbadacccdddcabaaaccaccdcabacacbccaadbccdbcdbaaccbcadaccccacdcbabddbabdcbdadadadadbaaabbbbbaadbdbccaadcaccbbcccacbcdcbbdadabccabbcababbabacdadcadddbaadacbbdaadadccdcbabbdacdabdadcdcccbaaaaaabbbdcacccaabbaadcccbcddcbbcdbbaabababcdaddbdccdbabbdbcbcadcbabaaccabccdabdadabdbcdbbbbcdddaddbadccdcccdbabbdbcdaaddaddabcddcbbcdaadadbdddcadbbbabaabcabccdddcacddadbbcbdbcacbbabcdccabbcaccdacdcababbadababdbbcbaabbbabdadaaabdbccaaddbcdcddaacaadcabdabcbbccaaacaddbcdadaacdddccccdadbbdbccbbabaddbcbacabddccbdcaaccdacbdcaaccbdcbccdabdcabbababbacabdababbcacadaacccdabdddabbbababdddbabacbdbaaabbccbabccddaaacaabbcdcadbabccabacbbabdccaabacbcdbdcacbdacacaaabaacadbabcbbbaacaabacdcbccadbaacacacbbbbaccadabccdabdadadacdbbcdbcddaccdddabddaadbaadabcaabaccbdcbdaaabbcdcddacdbdadbadacdcbbdaaacbaccccdddbcbcabbcccacdaabddbbbacbcdacbdcbabcdccbcaccdacabdcdcabcbbdddbabacbdbdacacabdacdadddcddadcaddccdddddbaccabcdbaaddaacdddccbddcaabacdadadcadcdcdbbaccabbabcbdcbbdddcdaaacbbabbbccbcdbdabaddbaacaaddbdcbbabaacababdcbadbadddabbaaccdaadacdadbadbddadbbbdabacbcaacccdddabacbcddcdcbcdbcddddabbcadbdaddcadbbccacbcaddbcabacdbbdccbbdcbcdaacaccdcacaabbdaddacccdadaaaccabbcbbbbcccaacaadadacaabdbbdacabcbababbbbcdabadacdaaadbcbbdcbcaaaaddabaacaddcdcadaccacddabbacddbddbdcdcccdbcaddaccbaabacbbcbbbdddccccbccccdcdcaccddaaadbabbabbdddccbacacdcbddacdabdadcbbbbcadbaacabadcdababbbababddccbdbbcaddcbabdbdcbdabdcbccdcccdcdadaacbdbdbccaaadccdcdacbacdadcbbdcdabacbcdcaaadadcbadcbddaccaaadaccaadcbababbccacddcbaabbdcbdcbdcdcbbbcdcabbcdcdbdcdcbcbbdbacaaadddcbdcbaaccbbbabbdcadaaccccacbdbdbcbabdabacbbcdbaddabdddbbbccaadabcdadcbbdcbdaddcabacbbccdbaaddbcbaccdabbbaadcdddcdbcaddcbbdcaabcbdaaddcaccddabadbdddcbdbdaaddaaccddbccaaccddbcdadcbbabbdcaaccdbccadbbcaabbdddddbbbcaadaaabadcabcababbaacbdccddccbcbdcdbcbdbccbabbcbbdadcbbddcbccadbcbaacbddadbcdbbaccdccbcdbbaabcabbbdcddddcacddcbdcbdabbacbcaddadaddaacbccddcccdbddddcbabdcdabbbccbacaddbabcdacbacbabcbabccaadcbddbaabdccdbbbacbcbdadcbccbcdbddaadbadadabcadcbaabdaacccdacbacdabbaccdadaccabdcacbddcccababddddbadadacddaacacdccbbacddaaababdcbddbabddccaddabcddbbcbcbdddbbdbdcddaddcbbababacbadddbdbbbddbaaccadcabbbcbccccdacbcbbbcbdbbdcadccbaadbadcadcbadaacdddcbaccbcbcbdccdbcdadbdcaadcbadccaccbbddccdccabadadbaacddbcbcbdcbcccadacbbddcccbaabdbcbaaacacdaadbaabdcbcdcddbbbbddcbbbdccadbadbbcbcadbacdbbbcadbaadbacdcbbaccdcbbcdddbdabbccaabdcacdcdaabcacbacdddbadcadbbbadcdccacabacbabcbddbdabdbdcabcbcadbccccddcccbbbcaddabdccaacbbcdabbcccdaababcbbbaadadbbacdabddcdadcdcadacacbdaaccadaadabbbcddbcacbdcadacbcdaacccbbdbbdbbdbccccabcddbdcacbadbcbcbaabbbcaacccbacacaadaacbcddccbabccdbdbaabcbdcbdcaaaaadaaaacddccddbadcccacdddcdabcabadbcadbddcdacadbdcddcddcadcbdacacbdbcddcbcabdbddaabbdcadcdbacdcabbaddbdcbdcbbbabbcccabcbdcacdcccdcdcdbbaadabbddacddbaabbcccaccbbbdadbcbdcbaccbdbbdcdadadbcbbdaccabbdddcabdcbbabaaadaccbabacaabadbcbadabcbbbcdcbadcacbadcbdadbbbcbbbcaabbacbddaacabcbdddbdccbdacdcabbacccdaddcbccacbdbaddccdaaddbadabbdbdbbbabbcbbacbcadaacdcbbbcaaabcadddadaabbacabbbabaadcbcdbaccacdbaabddbbaabacbaabbacdddabcabbdabddcdadbdbaacaabdaaaacacddbcbcbddcdcadaabcabcccccabbadddbddaacbbacdbacabadbadbbbdadcbddbaacbdacdddcadcdadbddcddacdadcdcdacadcbacacaaaabccdabdddcdabddccaabacaddddcbadccaadcadbaddaaabaadccacaadabdccccaaddacabdaacccbabaabdbdaaccacadccacdddccbcaacaabcdacacdbbaabccbbdbcaadacdbaddaadacabcbacadcddbbaddbdabdcbbbbbabaaaabadbaaaccabccbcaabaccdcdadbaaaabcbabaaadddbaaacadbcacaacbccddcddbcdcbaabaabdbbcbbaddcbcbddabbbdbccbcddbbdabadacdcbdcdbbdabadabdcdcdbadbcbcaabadabcbdcccaadcbacbccbcddcdcaacbbdacdacbbacccdcaadcadcbcdabbcbbdcdcddabcacdaadbdaadaacadbabcdabadccdcbccdcbacacdbddccadbbcabbdabadbcacabbacdbdbbddacbbddcbbadacccaccacccdcddcbdacbcdaabbbcacacadbadccbbbbdcaccdabaccacadbcbdabdabdbabdbcacdaccbcacccdccddcbbdaddbccbbaabdcdccbdddacccaacccabbcbadcdbdddabbabdbcdabcacdcbabbbdaaacaddbdbddbbadaaaabbdcbbccbdcccdcbabbdbacacbabcdcbdaaabcaabdbabbcbbdddbdaacdbdbdbbbbababdbadacbdaaaaddaacaabbaddbbacbdcdbbdcacacdaaacbdadccbbbcccdcbabadcdcbadacdcdbcbdbabdccdcdbaacaccbacadbcbcbaabaaabbdccbdbdccddabbaaacabcacaaadaacdbdcaaadddabbcdbbabccadabdbdddcbddcbcabadbdacdabcbddbbcccabddadabaadccabadbbbbacadcdcccacaaaaabcdccaccbaabbdbcbbdaddbaaaddbcbcaaacdbdcaabaadaaacdaacddbdbdacdcaddccbbbbadcdaaadbaacdbccadadbbbcacacabcccadcdaabdbabbbaabbdaabbcbbdccccbacacabbdcbbbccadccdcbccbdcbaaacdadccdbbcacaddcdabbcbbcbbdcadddadbdbdbcadbcbcabaccccdabbbdbbaaacaccdcdbcbcbcccbdbdacaddbcbccadbdcbbbbdbcadcaccbbbbbbcddccdaddacbbdaadccddcddddadccdabaaadddbaacdbadcdbbddbbabcabdadbadabadadddddccdabcddcbadcbbaccbbbccacadabadacacbcdcbcadaaaddcbcaaaaadbabbcaccaabadadadcbdcdaabddaaabaaadcbaaacdbcccbbbdabbaaddcdddaabdcbccdbdcbbcadaaabddbbcccadbcbbcbdccddadabdcccccacacdccbaaabcaadacdbbadbaacdabbddababadabcbbcddcabaabcaabccdaccdbaaababbdaabbcadcbbcbdadcccacdbbbcacbdbbcadbcbdabdbcbcddcaacddbcaddbdacacccddccdcabdbbbccccccbddbaaadbdcdbcbbdccaabccddddcabcdadacacabcbadcbcbccbbaacbaacdcaacaadbbccadddcbadabddcbaccbcdacddbbbccbdbcbdcdabbacabadbcbcccadacdaabadcbcababcabaabaadbaddbcaddbbbaccdabcacaddccbbccbaaddbbccaaddcabdcddbacbcacacaaabbacdabbcdbadacdbdbbaabdbcccadabacdbbddbaacddcdcbacabcddccdbcbcabbccbaccacdacacadacddcadcaabcabdaabbbdbccabddadbdacdbccaddcdcacbdaccacbbdcaaddbcadadacaaabaaddbcbcbccbabcdbdbadbdbbbabcbcdabbacaaacaadcccbccddaabadbcccdccdacabcacdaadaddadcbcaaaccbacbdccdadbdcaabbcaabcadaaacbaadacbbbdcbaabcbabddaddabdddcddaabdaaabadcbbaabdaacbbdbdaabacdccabcaaccbabccabaaddccaabaadccacbddcaabccbadcbabbddccddadbdbbabaccaddccccabcddbbacbddcbbdaadaacacacaddccaccbddcdaddbabdbcccdcccacbbcbbbdbbdddbcdcdacddabcbbdbaacccaaccdadccabbbbbdcbdbcdacddaccdaabbdbdabadaaddbbabbaadcaacaacddaadcbdbbdddbdbadddccdcabaddcbbdbcddabdbddddcdcbdbbdcdcdbdabbcbbabdbdbdabbbdbbbddccbcbcdcbccaabababaaacbaaaaddcbddabdadcabcbcacddaddaccddbbbcbcbaddbabdddbcbbaabcbcaccdddbaaccbcbdacadbcccdbbbaacdddbccbbdddadadbbbccbcadbcdcadbddbbdabbcdddbbdbadabacaabbacaaacdccacbddacbdbcbcabdbccbbbdadbacccdbbdacbcbcbbcaaccddcdbaaacadcabdbdddaaddacababbaddacbcdadbdbbbabddbdbbbdcdbcaacabadbcccdcdbabddacdaacbdbabdcbbbaccdbbbcdcdbcaddccadccbaaddcdadcbdddcaaaccccbbacbdbcabacbddccbcbcabdcdbdcbaaaadcbcdbdcccccddbabaacacbcdddcacdcaaabcbccdcabcdcdcbbddabadabbdccaacbdacbdcbadcbaaacbacdbdaccbbacddacdbabbccdaabdbdbaddccaabdadbaaccbbdbdacbcddadaacbbdcbdcbccacbccabbbdddaaacbaadcadbbdcaaadadaadcbdadaabccccccbdadaddacdaacbbacacadabdddcddbbacacdbbdcaaacadbbdabccdcacdbccabcbbbbdccadbacacdccabaabbadcbdabacaccdcacdbcbaddccdbccadddbdabbdcbdbbacababdcbabccccdbcaadbcbddcabadbccdbbaacdbcbddaccbabcabadadcccdbbbaddcbbbcabcabdcdbbabdcbbcbcbdbbbcbdbadbaaadcabdbabaaacaaabacaadadccccacabdbcdbaccbccbcbabcdddcbdbdadbadddbbacdcdddabaabcacddbacbccbccdcdaabbdbddbaddcaabcacabcdcbbacdbdbcacccabcbbabcccdbbbddcbaaccbcdcabbdabccacdaddbdbdcddcdbcbdcccbacabcdcacaacadaadccbcbbacdcbbbacbccbbcbbbbbdbcababaabdacbcdbcbcdababcbdaccdacccddadbcbdccabbacbadbddbdbccdacbcabdbabddbcddabcadbccdabcabbcdcabadaaabccacddccbdbdbcadabadcbacdbdcdddcabcdbdbccaaacdcdcaddcabcabdacdbaddbcadabbaacdabddadcabdbcacabdaaaaaababdacbacabdadbaaababadadacadbbacadaabbbcccdabbbcdaabdcccadcacaddddaacabbcdcdcabbdcbcdbcbdbaccacbbcdadadcadbdadcbcdbabdbccddddddbaadbbadbdcacbdabbddccbacddaabbaaddddddacbcddcacbaddaccdbddccccbcbbbabbbbacbdbdbbdabccadddbaacbcbccadadbabbabbddabadbdadcaccaadcabccaccaacdbababcdddcbddddaaaabcdaabdacddaacccbdabaacbbdabbcabacdadbcbbcdbdcbdabccbccaddabcbbaddddabadbabcccbddbdabadcdbbdaacdbadacbcdbaaaadbdbbaccccddbcbdbabdcbdcbcdbdaddadccadacbabddddcccadbbcccbaacdbaaccdcbaaaabbdbdaacaddadcdbcbccbcbcbcddcbbddbddbbdccbdaadbbbcdadcbaabbcbbababcadbacacacadcccbcdcdbbdacdbbdadbcabadccbbbbdaaabcacbdaddcdaddbaccbcacbdcccacdbccadcddbadcbccdcabacabbabdbddbadddadbacccdbbcbdbcddaddadbadbbbdddcbbdbdcdcddcabbbbcaddcccadbacacabcacaacbadadaaabbaccddaaccacdbbaacaaddbbcabbdbbcdabddacbbcbaabccdcbabaccaabacccadabdbdbbcacbbbbbbcbccccbcaddcadbbacbddccdbddacdaaadabdacdccccbcdabacbbcdabbcccbacabcdcddadacdaabbddabdbbddcaabcdddadddaddcbdaaccccdaabcbddccbababcbdcaacacbdadddddacbacbbdaaaabcadbbabaabbdddacaacbcaaadbddabdaddacddddccbccadbcdcbadaaaabdcadcbcaacabcdbbadccbbdabbbaabbcdddadcbdcddcddcaaaadbadcaadddadcabbbbbcadabcbaadcdbaacdbddbdadacdaadccbbdcccadcaabadcddabccdcccbcacadadadcdccdbbacddacdcbcbabbdccbacbbcbcdcbaabcdbcdcdbdcdccbbacbadbdcaacccdacccddbdbbdcdbcadaaabacbdbadaaabcbdbbdabbbcbbdbbaadddbababcadcddaaaabacbcbacbbabacbaaacaaccdadbbbbcddbccddcdaaabadccabaddadaadbcaadddabdddccadbbdaaacbdadaadaabddbdaccbdbcbbdcadccabbaaaddbdcbacacccaacbcdcddabdabcadccdcdcccababdcdbddadbbbaacccbdddcbaadddcacacacbbdacbacacccacdabadaacbbabcdddcbdabdaaaadcccccabdcbadbbabcbcdbaccaadadbcbdbbddabdcbdbbabccccacaccddcbacbcbbbcaabaacbadabcdbdbabdabacabbbaddddcaaaddddddbcbaccbaadadccdddcaacaacbddbadbaaadbccbaaaddbdacdaabacdbccdddabbdccadadbbdabdcdaaabcbbbbabddcaddaadcabaabdbaaaabdbcccbaaacaacbcddaaacdcdbaabacbccbbaaaacbacaccbabaccccdcdddcacdcbdcddbdbacabaabcacbbdcbcccadccabdddddabbdddabcdbcbdaccccbcdacddbcbcadcabbbbccacdabaddaadccaadbacbdbdbbacbbbabbacddaddcccadacdbacdacddabddccdccbbdbbcbdacccdbdbcabcbcbccadbbdbaabdbccbaabccbdacaabbacbcbcaadaadbcaaaacbbbdaacdaadcbddbcbddaaccbdbaacaadcbdcdaccadcaddbbcbdaddbbbcabadbbbdaccdabddcadcbccbddbcbbbdbbcdbbabbdbbddaadcbabbcdbbbacccdbdccbcacbddbdabaaadcddcbbdccbdabdccbdacaacbadcccabaddcddccbaccadbabbddccdaadbcccaacaaccaadcbacccaadcaccdaccbcddccddcddabababaacacbbbcaaabbcaaaddcccbcbcbcaccdaabcbadbbcdbbbcdbbabbaaaabaacbbacdbdbcdbcbdddbbccbdbabacbdccddcddbadacdddadbcbbcabddcbbdcbbbadcabdadbcdcaddaabbcccbbadccbcadbaabddbabcdbdbdbdbcadccaabbdcbccabadccacacbcdacabbabcdcdccddbaabbbcdcbcbabbcbbddabccadbddbcbcbdcaddaccbcddddbbbbcbdcacababcabcdddadabacababcdbabbaacaaabccbccbcaabccdadbabacbbaddcddcaddcbbdcbabbbcdbbbbcccbbcacbdabdbbadaccacbabdbdbaddaccabcdcdbaadbdbaadabcccccdaacbadabdbacdbddbbdbbbccacabcaaddabdcdcdcabcbdcdaddaccbcdaacbcdbaddbbabdbbdabdddcbcdbdaddbacbcdcdabbcacabcdddbadabbadcbacabddbdaadbddcaacdbbadbdcaaadccbaacbdccddacacdabcaccbdaabcccbaaabcbddbabbdbcdbdabbaddbacaacdcbdaaacbdbccaacccababbaaabddbbcdbbacbdcbcddbdcdcabadcaaddbcdaabcbcddbabbadcadddcdddcbbaddacbabcdcbdbbbdddbbccaccbbabaacdbbdbcadaaadbabddaaccadbaaadbbcacdbddbdbcccbbcccbdacdaacdbdacdacdbacdcadbbcdaabbdcabdcbdabbaaccababdaabcddababbdddcabcbcbddcadadddcbcabdcddadaacbdaabbcdbacdacdcdccbdaadcdbcbacaacaaacbadcbdbabdcaccccbcbccaaabcbdaabcddacbbbcabdbcabbbabaccdbabaabadaaddabcdaddbaddddaaabaaacabdacbaaddabdcadccdcdacbcaccacbdbacabacdabbabbbadcbcccdcabdcbdbcccacabbdaabdbdcccdcccaacdbcbacccdcabbddbbcbdabccbdcbaadcdcbcacaacdbdbccbddbddcbacccdbaadaaaacacccbdddacddcbacddccababbbcdcaacadaaddabbcadbdcccadabbbcccddbbdddcbabbadccdddabdccbdaccccbdcadccbcaacadddbaacaacdbdccabbabbdcbdaaacdbbddcbbadcccbabdbacadcbdacdaddbccbdbacbbbbcbdaaacaacaaabdcaaabdddbcaddabddbdbadcadbccbbacdcbdbcaccaaddabcbabbabbbbadbdcccbacbbbbabddaaabdbcdabbdbabdacdabcabdbadcbbddacdacacdcbcdbdddadbaaadcaccacddabdbdaddbbddbcdabbacbdccbddcbbcababdaadcdcccccbdacaaaddbbdbcccbdcdbcbbbcabacbadddcaabcbdcbabcccabdcbadbcdcdbbdaacacbbcdbcdbaadccccacbacdbaacbccadabbbcaacdaddddbadccbabaddcbabdabcaddabdaaacdacbadabacabacddabddaadabccaacadbcdaadbccccdbccccabddacddaccbddbcbacdacdbdcbdccccbacbbbabcaccadbadddabddcbaccbdbaadbccddaaacaddabcacdbbacdaadcdbcbaaccbccdacdbdbddbaddbbcccbaccbadaabcababdbdcccbcbadbadaddabaccbabdccaccddcaacbadbacbdaabbaabdbadaabaccbbdbcdacdcbababdcbdcaaddacddadbadcbabbaccabcbdccdbbabcdacdabaacbbcadcaacdcacaccadaaddbbbaabaacdadabcbdcadcbcbcabbbdacccbaddaccbabcbccbbcddaabaaaacbbbabddbcaabbcacccaacbdddacdbcbcbbdcaacbabbbddcdccbabcddbdbabbdcdaabbcdabcddabbccdaddbdaccdbbdcaabcbcadadcdcadbbcaaaacbadccdbddaaaccccbcdbccddcdddacbabcacdadbcbccdbabdbbadaabdadbdaaabdcadadabbcaddabddaaccdcaacaadbbabcdbbdccccbbacdadcadaabdcdcabadabaccdcbaddbabcdabdcacacbaaaccababbabcacdbcdcacaaddbabbbbcddbcbbbbcdacdbdbdabddddaaddcbccdabbbaaadbcaabbabddcbdbdacaadcbdabddbdcbabbdddccdcadbdadccdcacdbacacbcdccdcbdbdacbcbccbbdcaadbcabdadadccccdddcaaadbccbbbbcdbddcabdbdacbaaabbdabcacadadbccccddaccaadababcdbacadbbbabbddbdaddddcdccddabadadacaccbaadccddcbccbcccdddadaaaacaccccabbbbbdcccaadbbbabcbdddaabcccbdcbacdbbbddaccdbdbccabbdabddccaaccbdbdccddacacbdabdddaabacbbadbbcabacadcddccbadcabbdcadccbaddcabadbdccbddacbdccbcbddaaabcbdbabaacbbcdcbdddaabcdaacacbbccbababdbcadacdabadbaaaaacacaccbdaccbbbcdddadbcaddcbbaaaaabddddaccbadbdbddabbbdcaaacbadbdcaacbbbabccabbadaadbabaccbcadccaacccabaacccaadbcadbadabbdabdbdabacabbbaccdbcddbcdadcdbdaaaadabccacdccdbccaabaacbcacacdbbdcdbbcbddacbdddcabdbbaabbddcddcbbbcdbbacbaaabbcccdcadbaaaddaddbccbcaaccccdaaaaadbbdbbcaddcaaaabdaacacaccacbbdbdabdacacdcdcaacccbacccbbdbaabbcaabcbaaccdcddcacaadccdaddcaacaccbabcdabdaabbbbbdbaabcabdacacaddadabccacbbdbccaddbdbdcbdadaddddbabcadddabbdcbcbbbcbdddddccabbcbddccbabbcccbdbacdcccbcccadbaccacbbbdabbbcddcccacdaccbccaaadbdccddcaddacddddaacccbdcacbcadccacdcbccadbcdacdcdcdacdadcddcacdbadccadacdbcbbbdadbcbdbbbcbddcddbccdbaaabbbaadcadbccaabbaadcbbbaaabdcabcabbbaacbdcdaabbbdddaddcacdbbdddddcdabbbccbaacddacdbabbddcadbcadccacccacbadbddaddacabdcccdddcdbbaaabcbcadcacadbabcbbdabcbadcdcadcadaacacacabccdacdabbdddddbcdadbcddbdbddaaababcddaccbcadcccacdabbddddacbadcaccacdccbcdbdccddbabbccdabbdabdcbdbacdacaadbbdbddbadaabcdcaccdadababaddbcaddcdcabcaabaaabdbbdbcabccbaababbddcbabdcbdddadbdbacbccabacccdaacddadcaccadbdaaddbcbddccdccdbdbdcbddcdbdcadabbbacdccdddccdccddcccbcddacbcdbbadcccbbcdaacddabcaacddcdabaababdcabacadacbbaddaccccdcbbbcbadcaabaacddcbacccdadcddacabcbaccbcddbddcbabdaaabcccbccccccdaddabbbddacaacaadcbbbaccdcaadcbacabcbcccdbdbadaddbcccdcdaadcacbdcdbaadcaadaccbadccabcddaacadaaadabdbbdccbbbabacabdadbdacdaaabbdccadaabbcdcdbababcacbbbbdacdccdddcdaccaabbdacdbddcccccbddcbadddddcdbcadbbcaccbdbbcdaaddaddacccadcabdcdcbddbbbdbcdcddaddcacccbbacbccadcbaaabdadddacbcdaadbbabbabacadddadbcaabadbaaacacabcccdcccdadabccdcbccadccbcaddcadbbbcabcadadcbcaaccddcccbccaadbcbabbcccdccbcbccacaacadacbcbcbdbaacdbcbdbdaddacdabcaccacbcdacacdcaddddccbbbabbcaaaacabbbcbcbdaccabcbbbbbbadddaabbcbdaaaacbbbaaadbbadcbcddaacacadbdbadddcacbddcadcabccaddbcdabaddacddbccdccdcaaddabcbcaddbcbcbdccdcadbbadbaddadddccbddaacbdcaacaccacddcdadbadbadaccdcbacabbbaaacdadcbaaaddbccabdcbabddccccbcccabdacbcaadcbadcbdbcddacbabdccccddbdcdaacdcacddababacababbddadddacaddbdccbcbadaabcacdabbdacdadcbbddabbddddcdbcabbdcdbbdbccabccadcdbcdcdcdcbbadbaaddbcdcabcdcdddccdcabbaadccadbbbcddbcaacddcddbcbadbdbadcdacbdbcbabcbaddccbaccbbcaadcdcddbbaddbdbcdcdcbadaabdbcdcddcbccddccacccccbaabccbccbbaaddbacbdbbbaadcddabccddddcbaddcbdccdbcdbcbcbaacbabccbdacddadcdaddccccccccbbddbdbdddbabccbbadcbddadbddcdbdabbacdcdaabdabccaabacbcaccbdbcdbcdabbdaddbadcbdccdbbbcdaabcdccdaacaccbddcaaddddabdaabdcdaadddbcbdaadccccdcbbdaaaddccbddaabdddacaacaacaaaccdcdabaccdbcbbddcdadadddcaacacdcddcbdbdaaaccbdcaddabdddcadccbbdcbbcdcaaadbcbcbadacccbdabddcddbcccbcaccaaaaaccccdcdabcaabdabcaccacbaacddbdccbccbbabdcdbdbbdddbbbcdcdcabdcdcdcaaddbaddcbbaddacdacadddbbcdbdbdddddaadacabbdaccadbbbdcbcccdcabdbdadabcbababdccaacaacabbaaacdccdaddaadacdcaabdacacbdcaaaabcdbacaccbaabdcdbdabbcaaddcabbaccabdaaababacbdcbaccdbbccadddbabdbccbdddbdabbcaababbbbdaddddcbabcdacbabbbbbcadaadbaadbbcacabbccddaacccadadcadcacaddaacacbcdccabdacdaaaacccadccdddcadcddcaabdabddbabcbdbbcacadcdadadddbddccdaddaddbaaddcabacadcaaccdbdddcbbddcbdbccccbaabbaadddaacacbccacdcbabcbcbdaabbbabbaacababdacddcdabaacbcccdddddbccccadbdabbaaabbcbcabaadcbcbaaccacbdbbdacdaaaaadbccddbabdcabcbcddbaababccbcacccdabbdbbbccacccbddcbdbbcbbcbbcaaaaaadcaddcbcbdcdcdcdabbcdcdcccacddddcdbbbddbdaddcaaaaabccdaabdcdddbbadaccacbddbacccbacccbddaaddabbccaacddabcdcdcbbdcaababcdbcbbdaaccbbccaabbabcaaccdbaddcdbcbcbcabbdacdcaaacdddbccabdddacbdbbcaababdacadcdbbdaadbadbbadbcbdccdbbbaabcddaddacadbdadaaadabacabbbacbdcbabbdccbdacabacabacaccacadcabccdbdacacbbdccadaabbababdbbaacaabccbdccabbcababbdcaabaabcbaccdcdacdaacdacbccdccdcaaaaadabdccacbdcbaccaabddbdcdbbccbaabaaddcdcacbadabbcdbbaaddddbcdabcacbdcabddaabcadddbcddddcabcbcddcdaddaabbbdbbdbdbcdbbcdadbabbbbbcddcbbacbbaaaaaadbcbdcacaacdacbcdbbddddbccdaabcaaaadcadcbddabaabcacbdacdacbdcbcacddadaddcaddbbbadadbacdbadcbcbdabdabcbccdddbcadbbbccddbaddbbdbbbaacdaaccdbdbbdbddbadaadcadbaabdacbbcaabcdbaabbbbdbbdcdadaddcdcdccbdccdbadacbdbbddabcccadcadacaccbdccbdabdcabddbdccbdbcdcdacbddabdcccacabcdcdbddddabbaabcccaaaccabcdcbabcacaaccaacdabacacadcccabacaccacadbddabadacdacaabacabaabcbddbdbbbddcadcccbacbaacabbdcdaacdaaaacaadababbcbabcbbcbdacadbacdcbccbcacbccbdbdadabcbabcbccdbddbdabaacbdbccaaaacdbcaddccdaaabdbbdbccbbcabaadcccdbaabdcdcacdcccbcdccbbbacaaabdadabcabbcddccdbcddaccccccabacbaacbdbbcddddababaadccdadbbaddddcaadcbbdcdbcabccccdaacdbaddcabdcbdadbdbbaaadbdacdcdddccacaabcaaaabbcdcbabbabdadbbdddcacbacabddaccbbcaadbcdabbaadccddaddbccacbbcadbacabcbbacabdadabacbdcaadbcaccbddbcdbcddcdbdbabaabbdbcbacbbbcccaadccddbddbbccccdabadbcbdacacaddacdaadccbabcdccaddcadddabccacadcbcccccbcabdcaddccbdaabbaccdcddbabacabccbcabbcdddbaaadabbdddacbbdcaccaabacbabdcdadbcbdbbddaacbcacbaacbabaddbbadcbdcdbcacbccbadbcccabcdccadcdbccccdacaddccccdaabcdbcadabcabcdbbcbbdcaccdbcdbbdcbcdcbcdddaaacdbbbdddabaaccdcbbbaacdabdcdabccdacbbcddbabaccacdccbbcdabdbacdacadadaaaabbcccacccacdbcacadbcccaacbcdabcbbdcdccccbdccbbbaccacaabcbbadcbbddbbbadccbbbdaacbdaacdbcbbbcaccdcadbbddddaccddcadadcccadbbbddbdabdcddbaacbaaabbdcddbabdccdaaadbbbccabcddacacdbdcabcccaacbaabbdababbccabbcbbdabdbddacbaaadcdabdaaddacacadbadadcddadbacdacabbaaccbbbadabbcdcaaacaddacdbdadbbbacdabcddcbcdcbcacadcccaabcbccbddcccadbdacaccdcdccdccccbdcdacbbabaaacacbddcccdbbbddacdccdbdacdaadadccdaaccacacadbdabadcdbacadddcdbdcbacacbcacaccbadbcbcdddcacbaabbdbbbbdcbaddbcbabdadacacabaacaccbadcccaaabccccccddbadaadddabadbdadcdccacbcdcacdcadddbbcadbacaccbcbaddabbcdbbcbccadddbbacdcbbadaabbcbacaaadadbdcddddbacdadbbcaaccbcaacabbabacadacacbdcacbaddcacccbdbbbccddcbdbbdbabcbdddadbacabcabcabdcabbdbbaddcbbbbcdbddddbbcccdcdaccadacbadddadcbbadcccaddcddcdddadcaacacacabddbcaacaaccdaabbcbcbadcaddccbddabbcbbabbddcdcdcbdaabcaddcdaccbdddcbdcacacabdbbaccdcdcbbabdacadbcccdbcadaabcbdcaccbcacdbabdbabbcdaddaaaadcdbdcdbbcddbcacabbacadbbcabaadcdbaabbccdbaaadbadcaccaccbdbbbdccbcabadabacadbdbabccbdcaabcbdcadcacdacaaccabbadcaabcbcbcbccbbaddbadbacdddaddddccbcbabdbdaddddcdbcdbababadbadadcccdcbdcacdbdcbadbdcbdbdcaccccbbbbbbcabadacbbcacaccbabadcacccbdcbccbdcacdbabacacdcdadbbdadcadbababdbccbddaaabacabbcadcbddccbbbcbabdbdcaaddbcabcdabcdabbdbdcdcdcadacbccaaadbdbacaabbcbabacdbdcddacababbabddbaaadbdabadccdcbbaaddabdaabdbaddcbcbaddddbbbdbdbbdbcbaccbdbcacddbcddabaadcdbacbbdcbcabddbaacacdcaccaaadacddabcdddaacaacbbdbdabaabdddaddddbcccaddacdabdbabcbbadbccacddcabaaaacaadabccdcabccacaaddcadabdbbcddbcbbacaabdcaccdccdbcbcdcadbadaabdbaaaaaacdcbcbdadccabaacaabccadcabddbaacccdacccbaadccdcdbddaddabcddbcdabdcdcbcdacbabdabbdccacbbdbabaddadaabbdaacdbcacdcacadddbddbcbcdaccacdadbccabacdbabdbaadcaadcbcddccaddabcddbbaacbdbadbdbcccdcaccadbbcabdbcbdadaaddbcddadbcbbbaabaacaddccbcbbdbacbadbcdaccaabcabbdaadcbbccabdbdaabadddbbababacaaacdabddadadcacdaadbbaabbdadbaabbcddcbaacacddaaaabbdcabccddcddbdbacdbbdbbcacaaadacbbabbaaacbdccababdbcddaaddbacddcdccadccaccdcabdbabadddacbbadbcaccccacdaacdadabaabcdadbadcaadbcbddabbbbabddbcbcbcbcacbbaddcaadbccabadcbdbbabbdbdbdbacadccaddcadcccdabddacbabdbdddacaccdcabbdcdbbdadbdadcadaadbdcbcbdccbdbaaaccbcbaccbaaabccdcdcbbabcdbbadbcbdadbddddbaccabacbdcbbaadccdaabaaabcdabbbbdacbbabcdadbcccdabcbabcdbbdabdcddbadadcdaacbccdaacbaababadaabccadaaccabbadaacddcdacbbcabadcdcbabbaddaddcaddbacabcddbbbcbccabdbaaacbaacbbcccddaddbbaaadcdcccaabaddbdbdbcddadabbdcbdcccdabccdadcdcdcbdbacbccdcdbcddcdbdcdaddacbccdcbadbcbdcadbabdcdbcddddaadbcdddaacadbddbbaccdcbcaaccacbccabbccdcccbbcdcbdacaaddaabccdcddacacadaacbaadabcdacababbbbdddabcdcabacdaacbabddbdbdbadcdccaccbabccadbabccaddaddcabdcadaaaaaccdabacaccdccddbcaccbbabdbcdaadabdbcacdbcdabaacccbdbbaccbdabaacbcccbcbcacbacbcdaadcccaadcadcdabadcabdbdabbabdcaddabcdaccddbccdbbbbcacbcbddcdacacbbcdacadacdaaacbbdaaaddcadddababadcabccbaccdbdabddcbaadcdcdccbcdaadddacccbadaabccdddccabdddabdadcdabddacbcddcacdccbdccccccbbccbbaaacaababaabbbadccaacaccdcadbbdaabbababbdcddbcbddaacdbaaabcdabddcaadcddddcabdccddbaaccaaacabbbbcbdabaaccbbaccdbdaaccccbdcdddcdcaabdbdcdaddbbadcdbdbcbbbcddcddbbbcacdbbcabacaaacdbbccbdaddabbddbaacabdadbdbaadaaaaaadababacbcbaadaccbdabaadbcdbcbcbbdadcadddbbbaacbdacdddaabcbdaabacbadaacbdadddbbbcdacdaadadaddddccbdddaacdbaaabbddbddacbacaacaccbcbacbabdaaabaaadaddacaacacaacdcbdbbcbcccbccbdcabddcbbdbcbccbacbdaadadcaddbccdcbbcddaacabacbaaccccddcdaacbbbaddbdacdcdabccabbcbabaccbcccbdaabbdbcdcaababcdaacaddacdcdaddabbcacabcdccccccbbabbaccabdcdcddbacbaacccdacdbbbbdbdbccdabdcbbbdadcbbaabbcbabdadacabcbbdadbdabddadcccdddaaaaaaccdcdbaacacdaaddaadabbbacddadddddcccabaabaddbdcbbabdccabbcbabdddbdbcaccaacacbabccacdcddacbcbbccdcbdbcddcdcdddcccbbdcbabcababcbccdbaacbadbbbbbbccccaccabdacbdacbaaccbdacaddcdaddcbcabbcaaacbbabcabcdacbcdaddccdcddcdbaabadbacccdbdcccbcaaaabcdbcabcbccaacdabdcacbbcbbbdccacbadaababaaccbcdbbcbddbbabadbcdddbabbabbabccddcdbddcabddcbabddbbccbdaddbdaccbdaadcbacbadacbacbcddbcccaddddbbcaaabcaaaacbdcdbcbcbdaaadabbddcbdaabbbcaddcdbcacadacacbccddcdbacbbdaadddacddaaaabbdaabadadbdccaacabbaccdabbcccbabbcdacadcdbbcbccaadbcadcddbdacbaaadbbddcdadabcabbadaddbcdbdbaabbddbccbcadabdacdbabccdaabadaaadbbadaaacdabdaccdadbbdbcccccdbbcbddcacbcbbdbddccdbdcacdaaccbbdbddcdadbbadcbdadbaaabaaadaadabbaabdadddccccbddddbbacdbabbdcdbaabddcadccccdabaddabaccbacdbcdbbcadcabdcdaabbababdcbddbbcdabbcaabcbbcbcbccabcbdcddacbcdccdacbabdaadcdbdabddcaaadddacaddaadcaadabbccbadbbaddaacccbcacabcddbdcddcaccdadaaadbaaaacbaabccbadcaabacdbbdcacabacbddadabcaadbbbdacabaccabbabcabcdaaabdbdadcadacbbacbdcbaddadddcccdadbacbbddbddcbccbbbcdbdddbaacaabdcddabdcbabdcabddbdacdcbdbdaccbaacabdbabaadcdbdbbbcdcbadabcdbdbbcacaadaaaaaacadaadcdabbbacdcdacbbbccbacdaacbddcaabadadddaccbcadadcaaacbccccbcacdacdbcdddbddacdcbccccbdbbcdabdbddccbdbddcacaadbaaacdddabdbcacccdcdcdacdcadbcaacdddbbbbbaccabcdadbbaaacbbacbddabcadacdaaccddacdcbaaabcbddaccbccdcaadbbccddadcdadddbdddcabadabbcbaadbacaadbaacaacadbdabddbabcbcabadccbcddcaccbcdbbcbbbbcbadbdcbbbdcdbdadacdacaacdcaadbcbadaaaaacbbbccadbbdcbcbaadbbcbcdddbcbbcacddbcacacccbbcaaadcaacbbbabdbdcacadacbcabdaadbbdacccbdcbacdaadcccabbaaadbababdbacadcbcbccabaadccddcddbcaaaabaadccdaabaabccbbddabcbacbacaadbbbbcdbcddcaacacaddbaadaadaaccbcddbbaccabcaddbabdabbbbaabcbbbcbadabdaacaabdccccbdddbcdbadadacdcddbbbabdaacacbdbaccdcdaaccdaddbbadadbcdcccbdacaccbbadbbcaaaaaaddbbaaaccabacbbabaaacddaddbadbaabdbcccbbaccccdaacadaacccbacccabcdacdaadcbbddaacbbbbdbcadcdacdcdcddbacdaadabaadacbdababbabbdddbbdacaadcbdcdbcaddadcadadbbbcbdcbbcbaaadddadbccccccabaadbaccbdddadbdadaaabbbaacaaacaccbdcabdbabaacaccccbadaaddbaadbbabddbbddccbbacbbabbcaacbdbadcadbcbdcddadcbaddacccccdabbdbddddcddaadcacadbacbddaccbbddcbdadbcdabccccbdcccbdbdcacbdccbcdabcccaacdccdbdccbdaabaaadddddddaccadccacadcddddaabcccdbbbaabbbacccdadddcbcddaadabbcdcdacbbbbdadbcbddaacaabccdbcdacbdbbbabadcbcdacbbcdaddcabcbcabaacbcddbbdcacddcaccbdcbcccbbbaddccadaacdbdcbbaddabdbbccbcabbadddabbbbcacdbadadcbbdbacdbccaddddaccbaabdcddaaccaabdcacbbbbbacddacbabdbccdbdcbbaaabccabdadcbcbaacaaabbbbabdaaddacbaadbacddbcacdcadccbadcaccbccabacaaaabdbbacbcddddbdcdbcaddcdabdbaaadbdcbbcadcaaacbdbabadaaabbcbcaddbcdcbcdaccbdabacdcbaaaadbdbdadcbdccbcbddaaaccbcbbdcdaddcdaccdddddbaaacbcdbdbacbdddabbacadcaabadcbbbbcdacbcdaddddcaddcbadbddcdabaabddaacccabdacddabdabdbadbdaddccabadcccdcdaacdbacbdbcbbccacbadddaadbdbaccddbbdbdccccdbddbdbddbcaacbbdbcbccacccccdabdbdbdccbbbccdcaaabcdcabacadacddbdbdaadcdabbacbbcccdcbaabcabbaadaaaabdabbbdcdddadabacacddcadcdbdcddcdcbaccddaadbbdaadcaaacbaccbdaacbacadacdcabbccadcdcbcbccbacacbacdbacbadddcacacbbccaaccdbdbdbdcdbcbcbcbdadbbadcbcccbdbacccbcabadbcadbbaaabcbacddcdabbdccdcbdbbddbcdadacaacdaaddcacdcbdcbbcccacdcddaacddcdbbcbccdadbbbbaabbcbdabbdadddcabbcdabdabbacddcabccaaddadadaabcbdcacdadbabcacdbaccacbdaabaacdcacddccccdaadcbbbccccacbadadadddacbbadadcaccaadbabdcddaaadcdacabcddbcdbbdabdcadadbdacddaddaaacbbbdccdabcccbdaabbadabbbabbbaddcbabbcabbbacdccbccbabcbdddaddacabccadcdbccbdacbdcbbcadaacacbdbdabaccaabadcdaddaacabdbccadddbbddddddbacdbcaddbcdadcbbbadccdabbccbcbbacabacacbccadabaabccabbaacccbdccababcbbddcbdbacbbacaaacacbadbdbaaaccddbcbacbdaadadcdbcacdabccabbccbbacbbaacbdcdbbccdadddcaccdacbbcbdbcacacbbccabddddcbacbdabbccdadccbbccbbcddcdccacdddcaacadaadaccbdabbdbbdcbcdbcdcbabbcdbcdabcaddabbcdccbcccbbadcbdbccdcadbdccabbaabaacbdbcdbabbccacaadcabaacbdbaddaaabcadbadbbadcaacddbcdcdbbbbbacbdbcacbcbcadcbacddcdaadcbbdbcdbbdabcabbcccbbcddbcbdbbadaccdabdbdabacbbaadcbdbcacbdccddadaaccbdccdccddcddcdabbdbabdccbcbababbaccbcccaadbaadaccbccaddadddccdcbaddcbdddabccaaabaccdcacdcbbaacacbacdcabdcacadaaaccacbbcaaadcbdacbbbbadcddbccabcccabdabbcadcbbbbddcccddcbbaabccbbdabbbdcacaabbadabdbccbccdddbbabcaabddbacabdbabbdcdaacabcdbdbbcccabdaaacbcaccabddccaddbddbbdaddaddcadaaccaaaaacabdbabcaacdbbdddcccbcbadcaddabdabaababdcbcacbbcddbaabdddccbcbaadbaccdbbccdadadcbabbbbdaccacdcddcdaadacdcadccbccbcdbdabbdbdcadbccbacddbcbcdccaabbcadaabbcdbbbadaccdbacbddaddbbaaaaadabddaaddaddaabdbbdadcaabbdaaccbcbccabbadcaadabdbccbdcaccddccaaddbddccbbbcaaddacaaccabcabdcacdbddcbbddddabaddcbddbdcbccaaaabddddbddcddcdaadbacaabdbcccbddcbaaddadcbdbcddbbcdcdcbabacdcadcbcdddababaccdccdcdbdbcadacbbbbdacbcdbadccbabdcbccabcbcaacccacadbdbdbdbbdaaacbbacdcaaaabccbaadcddaccccabcbcbacbabdccdadbcbaacbaaabaccdacdaaacccdacadcaabbddcababdacbaccccdcdaaaaadaacdbdacbbbcdbdaddcdaadccccdbabcdaccddaddbbbcdbcbcababcddabbcccbacbabbbcbdcbabbbccabbdaccdadacaccdaaaacbddadaadcaababcdbdadadbbcdbccdcdccbccacbdddddbccbbbdcbcbddddcababaaddbbabccddccbdabdbbccbdbdccabbddaaaabbdbdbccddacabdabdbbbbcacbcdcdaddccbcbbaccbaababbdaccacdbdbababcbcaacacaadcddcdacaacadbbabdcdbcccdacaccaacbadbbdcbcdacaadaabccbcdcdbaacdbabdbdddcaddccaadaaddbbcaacccadcbbacabbcdacacadabdbdddabcadbcdddabaaaabbdbabadaabcccbabbbddbcddbcdddbacccbabcdbcccbadcdbaabbddcaadcaaadbdbdacbcbaacabacdcbdddadadbcddbbbacbadbcdcaacaaadccdcccccadbdcdaccbbbadbcbddcdcbdccbccccbadabdcdbaabbaacdbcdbbabcaababdddbccbadbdddaccccdbdbcbdbacdacacbbcaacbcbbaccdddaabdaadcacccdcbbdbadddbcbbacbadaacacabacabcbabdbccbcbdadbdcaabaaddcbaddbbdddbbadcbbbcbdadacaccbacccbabdcbdbbacbbaaadbdcbaddbcacabaccaaddcdcbcbbccbaadaadaddabddaadbdccccdabdccdcacdbaccaaadbdbdccbccddddccaccaacbaaacdbbdbccadbcdaccabbcbcdbacdcaccbbbcadabcabdcdaadbabcbaadcabbaddddaabccdaadaabdbacaaccdbcddbcbcdbdbcdacdaacacbcdcddcadacdadccaddadadbdaddbbcaabbbdaaadaccabbbbacaadcabbddbbbbbcbcbbdbcbbdbccdacbbcddaccacadcccadbadbbccbccbbcaaddcabdccddbccddadbdcbdcbbacbbbdaabccbddaddbcbadadcdadcacddbbabddbadabddcbabcdcbcdcbbbabdbcbaabddccbbacdbacbbccccacdbdbcddbbacbccbcadbaadabaabacacbadcabbbadddccddbaabcccccadccbbacabbbcdddcdbdacacdabdbdabaaddbbcbccaabcdadcbbadbdaaacdbdbddcaaabacadddcadacbacbcbbcaabcabddbdaabcadabaadccacbdaccaacbbadbcdababbdbddddbdbcbadbddccadbbaddcbabbcaaadbddbbbabdabbacacacadaddcbabacbddddbbbbbdbabdabccdbaadbdccbacbddbcaccbaccdcaaabddcbadcabcabdcbddcccddbabbbabbdcaaadbaaccbacaaddadcddabbaddccccbbbcbdcdadaaddcabccacbdaabaadaadbcbdddacadaddcccdcbcadcbababaddadacdaacabadccaccdbcabaccdddacbadbadcdddcbcabdcddcadbcabaccbbaddcddcdcaadddcacacbbdddadcabababbabcacdadacbdcddcbadbcacaabdadbaadacdddaccbcbcadcbddbcacabbdcbbdbdbcaaaabddcadabddccbdaccbbcddadbacbdacdabbadbaccbccdabccdcdbdddaccdbabbdadabdddcdabbbdddcccddcdaacdccaddcbdcaddadadcdaddbccadaaddcbcdccbbadbaacaddbbdadabdbdcabddbacdcdccccdbabbbcaabdacdacacacacdadbdbacaabbacddbbddbcaddacbbdabcacabbabbdadbbcbbdcddddcdbaadccdcabcbdccabadbaaaaabbabdddccccacbaadcbadabadbbddabdcbdaaccdddbadbccbdbdddcbbcbdabbbbcccbaadabcbbcdbbdbbbabccacbbaaaaabddacbdcbbcbaccabadbcbccaadcdcdbcddbbbaacbbabbbabdabacddccbbdcadaabaadddbcbddccddacaaadaacadcbbdddbddccddaaacaadcbabdadcaaadcabcdcbdaddcbbcddbbcacbaaccbbbddbcdddadbdddbcdcbcbdaabbbbbdcdaddbcacdacccbcaddddabadbbcaadadccbccabcccaccdddaddbacadaabbadcccccabbdacdbbbcaadacccaabdadadcacaadccbabbaadacacbbabacdabcbccccaabcbccaccbabdbbdaccdbddaacaddcaacdacaadabcbcadaacccadaabbbcbbbccbcbbabdbbaadcbbdabdbcdbbbacbbcbcccccabddbdbdcdbbddabccadccbababbbdcccabcadcabcccddcbabaddcdcbacabbbcdbbdbcbaddcddbbcabcbabbdddbbcdbcdabadcdcccabdccdddaadddcdabbdcaabbbcbaabacdbadaadcdcdcaabbcdbbaabdadbdbacdbcabacbaaadcdbddababadaddbdbcadbbbdcaadcaadddbccdcdadcabaaaccdddbdddcabbcbbdddbcdbacaddcbdabccabbdabbcaaacdcaacbcdbbabdcaaddcaaabadaabddbcdbbdcdaabacbcbbcbadbcacabdcbadcabdacacaddddcdabdddadbcadcdcdaabdbbdaacabdccdaccaadacdbbbcaacbcbaabcbbbdbcabbccabdddbcbcbadaabddbbcabcaadbadcacdbaaaaaddaccbcbaabacacaddcbacbccccacaacdcadddaaaaabacbbadcacdbcbdaacdadaacbcccbbbadcdcadadaaacaccbdaadcaadbdabbbbcbdbcdbaaadddcddcddddacddcabacbdbadabcccbcbbcccbbaacadaddbcacbccdbbbcddcdbacccdcbabdaabaaaadabcabdbbccaabddccdacbdccccddabbbaddaddaadbaadcacdbadacccdcdcbdcbadcdbbbcccdccdbabcaccbdddacaccdcbcacddcacaddacddbbadbcadbbbdcaadacccddcabbbcbbccdcbbbacacccbabadcbabdcdccbabcaacbbbdccdddbbdaccbcdadadcdbbdddcccccbdacabbdcccbabbbbccdabacbbddabddcdacacbaadbddcccbbcaabdcdbcdbadacbdcbcccadccdabadbadcbadabaabccabdcaadacdcddccabdabdcdddcabaadbdddbdccbdcacbbbaacbbccbdcccdcaacbababcbdabcabbdbbbdabbdabccabacdbcabccbadcbabbdaccabccdbcdccddddcccaaacddcaaabddbbcabbbabddabdcbacbbddbbadcdaaabdaadbbbdaccccddbbbaacdddccbcccaadddddcddabccdbabaacabbcababcbadcbabbbaaccdbccbbdbbcadcccaadbdbccdddcdbcbbadddabcaadbdbccdbbacaacdacabccbbdabcdadbbdcbdacabcbcaaccdbddcdbbddbccbbabbbcaabddbccdabccbdbdaaacdbdabcccabcbadabcddabdcccaddcacbdcabddccbabdacbbbcbbcbccdbdcbdcadbcbbcccabcdcaaabcabcabdaddddbbcddbcbabbadbbcadbddaccbbbacbbadabcdbddcdabccbaaccacbdaaccbaabbccdddabcacabdcadddbcbdccbdbddcaaadccbdbdddacddcbcbdadcacdbaabcdcacbacdbcaadccbcdbadcbbdddcbaaadddddcddcadcbcabccaccabbcbdbbbddabadcacccabddcdbddacddbcaddbacdccdddcbbcbaabdbdaccabbdbdaccdbcbaacadcddaabdaccacdcaaacbdaacccadbaacdacacabacdadcabdbccbccacaddabccaacdbaabbdaabbddbcaacbddcbabbacddcccaccddccaccbcbcaacbdcdddcddaaaaddcadadddbbabcbcacbaabdadabdccdabababbdbdbaaababbaaaacacbbaadbbdcaacaabddcdcaabdcbddddadbccabdcccbdbacdabcdbadcdbaddabddddbcbabcabddacacddcdbcbbabdabdcbabdbbacabacddcbbdbcabacdbacaacbcadaaccddbdbcbcbacddddbcabbdccccabcbadddcdccabacabcaaaabcbddbbccdaaaaacdabaadacbcbdddddcbcdaabbaddabcbbddcadaddcadabacbdccdcbbaddacaabbcbbaaabdccbbaacabbcbcbaabbdbdbaddacbcbddcadccadadbacaabadbccbcbdcbbabddaacbdcabcaaaabcabdabdadbccccabbdddabbdadbcdcbbdadcccadbbabbbcbabdbabaddbadbcbbccbdbbbabdabbbbbaccbbdabccbcbcdabadcdbacdbbcdbcbdddccabcacdbdaaddcbdacdbbcbacdabcddbdabbaccbaaaccdabcbabdcacdacbbaaddccadddbdacbcabdcdbaadbacbdaccdaabcddaddcbcbdacaacbcabacbabcbabcababcaabbadbcbcacaaabbbdcabacbaadaccbcbdadddbcacaccdcddadaacacbaaadaacbbadaacbdabdadbcccbcbddadabcadbaadbadccbbdaacaacacadbbcaacbadbcbcadabbccbdcdacabbbddddacbabdddaabaacabdddcbaacbadbbcdbcadbdbcabdccdddadadacaacdcccabdaadcaadbadbacbddabcdbcbdaabbabadcbdbaddabcbdabdbbbacdacadcabdaaddbacbdcbcbadcbcacbacadbdbcabbddbdddacbdddcababbacbbdbcccbbadcadbbdddcddbbdabaddbcbcaddbcbbbccccadbcbbaddcaddccaabcdbabdababdcbbaaabdcbcdcdcdadcdcdbadbcccadcddabdbacacadbcbdabddccdbcbbaacaaacdbaddbbcadbdccaadabaadabdcadcaaacabaacaddcacadcadbdddcacabcdccddcbdbbbdccdbcaaaaabbbabccaabbcacadabcdcacddbccdcdbddddbcaddaabdbabaabbabdaacddaddaddcacdcabdcddbcacccddcacbdaaddccacacccbbadabbadacdcbadccbdbbdbdbbacdbcdadadcacacbdcdcdbbbadcadadadabbdaadcbddcbdaabdcadaaababcbabaddbadabccdababcbbcdccbdabddcabdddbdaabbdaccbcdbccbdbddddadbadbddddcaadbbbbdddcdbacacddaddcadbddcaaaddbbcbddacacbcacddddbaccdbaabbcdcbabcdbcddcbcbbacdadcbbcdcbbbbdadcdcbabcadbcdcbddbccaaccadcaaccadbdcccaacdddabbaadabcacbbbdddbddbdaccccdddcbaabbadabacaabdabdcdcabcccbbacddaaacbddaacaaabdabdbabbacaaaadadaadddcdcaacdcccadabdabbcadcadbcdbacbccacbccbadcbacddabcbaabaaccabccaaabbaacdcddcaacbcbddcbbdbdcaccddccbcdbccaddcdccadbdaabbdbabdcdaabcbdbbabbadcbcdcaacadccdcadcacbdadcbbbccdbbbbbbcdbbabdbcdccdaaabbccdcacacbccbcdbbdddaddddaaacdacaaacacdbccdbbacddbbaadacadbcacbdacacadcbcddcbdbccadadcabdcdadbabdbabbddbbacabaacaadcdbdcdacbadccacddaabccbccaccdccbcbbbdcacadabacbacbcbabbccccddcadddacdabacdddbccbaaaaabbcbdaacdabadbccdaccdddadbbadbbcdccdbccccbbbcdbcdabdcdbabbcaddabddbdacdabdcaababbbdbacbccaccacacdddbdcbdabbdacdcdbddaaacacabadacabaaccbbdcbccdaabcabaadaadaacbbdbababdbddcabbcdbabaacbdbcabbcbddacbadbbaadbcaadaddbbccadccbcacdacbdabcccadccbabacbdadadbcabbbdadcbaccabbababaaaabaaabbaccbdbbbdcbddcdaadbddabdddabcdcdcbabcacbcddccccdcccdbabcdacdaadbcccabadcabbdcbdbcacbaccdabacacbaadaadddccdccdcacbdccccbacbccdadbdbacacacdbabcacdadbbdcadbddbbcdcbdccccbbdbcbabdacdbdaddddddbbcbdacabdbbadaddbcdcbbbbbacbbdbbdadbcdbbacdddadacbbcccbbcbcdbdbddbcbcdcdcddcbbbacdddcdaaacabccccdcbbadccaadbccaaccadccbdccababbbbabdddcadbbccbacccbcdbcbadaccbbbbcdcbdccacaaabcbbdcdcbdbdbbbdadcbdadbbaaccbccccccbddbbadabcdbdcbccddadbcdbcbcdccccaccaccbcdacbaccbccaacbadcbdbbaadbbabaccccaadcccbdcdbacdadbcccccbcacdbbcddabdbcbaacdcdddcaacdacdddbcadbdbdbdcddccaadcaadccadacddccaacccbacccacbcccaaabdddbaaadbbcdbaaadcbabcabdcadbabbaaaccddbcccdbabacdddccacdcbbaaabbdadbbbbdddcaacadcabbadcdacbbdcbabcbacacbbcbbabcbaadbcbccaddcbbaacbabadaabcaccbdababdcbacadadcddcdcaaccdabbbcaaadaabaacbcbbbbccbbcacadcacaccdcbadaccdbaaadbbabadddaababbbccacdaaaabccbaadcccdadaccdaabdbcbbddddbabaacddccbbccddcbacabbdaaccdcbcaaddbacbdbcbbcbbbcadcbdcdaacbccbdcddcabdaaacabdcddddbaddddccccdabdddcacbbbcccaacadbdbbdadcbddbdcccbcaddddddcacbccdbcdbcbbcdccabbdcaabbcdcabcaacaddcbbbddbdbddaaadccccaccdcabdbdaccbbccbcaddbddcdbbbcadcaacccabdbbbbaadaaabdddabbccbcccaaabcbdaadcadaaaacadbbcbbccabcbbdbcddddcdbabbbbdaabdcdcbbcaadabdbbccadaccacacbbbacaacdbdcaccccdaabadadbbddcbaabdacdccaccbaaabcddcacdbdddaabddbabddcdbcdccdaccabaadccccabaacbaabddaacdbbcbacacbdbaddaccacddbbdbddaaaacbcbbcaadcabcddbbabccbacbabaccbaabadcbbdacbddcaacdaadbddcbdddccacbbcdcdaaacddbbccdabbadaabaadadbcdaaadaaabadadbadacdbabccbacadaaaaaacacdbbbbacccdcdbbdaddadcaccaccaaccbbccbbdcdbabbbbdcccabacbbadbacaccbbbaadaabcdadbddacdadaabdccbcdccddcbcdabdddccccaaadcaccccbbcbacdcdbbaacaddbdabaabbbccddddbbbcbbabcdbbabbbbaaccadddacabbddbadcaabadcacdcbcdbcbababbbcdddbbbdaaaccadaddcaddbcacdccdbbcbabdadbbabcabbadbdacbdccdcccdadabcaaaccaaddcdccdccabaaddcbabcbdcbddaccbddbbacdcdcaaddabcbaccdcbccaccdaacbbabbabbdaadccbcdaaabadcbadbabcaccdbdbbaabaaaaacdcbcddcdccbdcaaccbabbcddbdbabbabadddbbbdcacbaaadcbbcbbdbaaddcbcbadcacdbaddcbdbccabdddcacbaaaacbcbbbdcaadbabcbaaaccdbabdcaadccadbcbdcabcdadbcddbdacbbabcbabaccaaaadbbdcdaacbddcddcddcccbcaaabadabccbadcabdadacdddbbdaadcacbdbaabababaaadbbbcdcdcbdbbdbbbbacaabbddcadcdbdacdcccdacbccbdccbacbdbddbabbcadcddbddaaacaadabbdabbdcaacbacabaccccacacbaccccdbdbcddababbdcacccadbcddcdabaacdbabaaddcdbdaaccccdadbdbdbadbdbdcbdbdbacacbdbaadabdbdcdcbcdbdabcadadddddaccddacaabdddcbcaaadacdbcadbdcccdddabbbdccabdcccccdadcacbacdcaadddccaadcdccacbadbdbcababbccbaaacaaddaaddaddbbcdcbaadccdadcbbcaddbcbcdcaacdbcabaaadaadcbcddccdaaaacbaadbababbaccbcbaaababacdcbcdadcbcccbbdadbcacabddacaddbaaddddcbaabaadccbdbdbcccbcbccdaadcdcadcabbcdacbdbacabcadaabdcbbbdcdaacaddbbdbcbcaaaadddccbcdddaccdbcbcbcabbddabaabbaabadbdadcaaacadcaacbacddaccbabbdbcccdadddbddddddbdacdcccaadbcadcabdadddcabaccdcbdddcbaabccdccbdbbcabcbdbbacdabcbadabacdadaccadbddacccadddbdaccdccbdabdbcdcacdcbacacccbdbbcbadcccdbdcbdacbcaccbbadddcaacbabbdadccbdcbcbdbabbddbbaddcddaacdaacbbbccaabacddcbcbacbacbaddbddbabdcdccdcbcadaddcdaabcbbaddbcadcaaaccdbacadbabaddbdbbbdbcdcddbaccdcdaaaadcddadcbbddbbddcbbdbadcaaadccbadabbccdbabcadabcbdbdacdbbacdcbbbdaadcddddaccadbacabaaddbadcaabadcdbbdcacbbdcbadaccbabccdddcdcbaabdaadaccacbabcaccaadcbbdcdabadaaacdbbcccdacacbaabccacaacaaadabdcdaabbcbbcacbadbddaaddcacdddddacaaabcbaccaaaacccaadcdacdddcbbbcccdbadbdddcbcdcadccdaccacacdbddccbadabcdbccaccbadddaadddcdaacddadabacbdbdacabdbacabccadccbccdbdcbcdddcbdcbbbddacbbbaddacbcdcccaaabbbcbaacdcdbabdcdccddabdacacbbcddbdadccadccbcdbadcbddbdbcccdbcbbdcabdabcbddcdabccbddbadccaccacdadadaaaaddacccccacadddbadaaababdaabcbbdbcaaadbdddbdaacbababdbdbdbdcccdbcdbbcbdbcababcadbaddcaaadbcadcdcbcdcbddccadbdbbccabcadaabddccaabacbdaaaaccccacbccdbdaccbbabcadacaccaabcdcababaadccbcbcabaddbdbdacccadcabdbcdacdbdbadadbcadaadaabbadccbcadcaaddbbddcbccabcdddbbcccddcbbbaacdadbadacacdabaaddcdaaddcababbdabbddbdcadabbdaabcadbadbbaaddacddcbdabacdbcdddbdacbddaabcbdcdcbbbdcddcddcacacddcbbddbaadbdcdadacdbdbacbcaabdbdcabbbdbabdaacacdbcbaadddcdadbccbbacddabaabdcbcbadcbcbadaaadadcdadacdacacabcabdcaacbdccaacaadacbdaccaaacbcabdcaddaabccdccaddabbacbbaabbbbdddbddcabdcdcacbaacabcacbbdaccaacacaadacbcacbdbaacbaaaaccadbdbccdcddbddbcabdcabcbacbacacdbaacddadddcccadacdbadbaadcdcdbcbbbadcdaadcdcbddabaadbacdabbbddcbcccdcacdddabddaaacacbbdbdbacabbddcdcbabcbadbbbddbbbcbcbcbabdcacdadddabbdbccbdcacbdccbaccabbdaccddccacccbbccdbbcbadcabdddcbcbbbdcdacacddbdbdcbaababacbabbbaaddacdbbadabaaaadcbcbcbbcbccadcbbbbbaddbddbdbadabaacbdddacbdddcdbdadccaddcababcbcbdddabbbbcdcbcccbcdbbdbaabdbaddadbababbddacacbcbcaddaaadccaadacbdaadbbcdaaaddaadabaaacbdbbadadccdccddcbaddcbdbbbacdbdbbcbccbabdddcdbbbcaddcabcdbccbbbdcdacddddddbcdbababaddacabccdaabbcacdddcacdddadadbaabaabcbbbbbbdbcabdccaccadaadcbdbbbcdbcbdddbdcbccdcbdcdaaaabdcccdbbcadabbdbdcaddcbabaabacdaddaaccadbcacddcdcbbaadcdbdbaddccaabcacbcdadcbcbabdcdcdcddbcdcbcddbcadadddadccaaaadbdadaaadbadbcdddddaadccbaaabbcdbdbdddcdcabbbdaccadbabcdcacdcbcdddccbcbbdbcdcbaacdcddcabcbcaddcccbccbabbdabadaadaccadcdaccbdbdcddaddccadaadbaadabdbcdcddddcbadaaccaadcbbcbcabdbbcabbaabbdacdbadbccbadcacbbadabdadbcbbdacdccbdaccddcdadacbccbaabddbddadddbbcbbccbdddbbacadbbcbcbabddcdadccabdcbddbbcccbbccacbaddcbdcbcacbccacbdbaabcdaadbabbbdcacaacabbdacbadbcababbcaaabadcbabdbacbcaaabaaddbbdbcaabdcddddadaabddacbcdbcbdabcdddddaabdddadacccddcabcdbdddcddcadbbaabdcdcdadbbdcbbddccaadaabbbdadbbdbdaddacabcadcbcaabdacabbbacdaacabaabcbbaabcccbadcbbcdbcddddaccbcabbadccdccdbaababbacbddcadbcacdccdacbddacddddabbbcdabcbdcacaaccabacbaabaddbdacdbdbbadabdadcbccccaacacadcbbbaabdcbbadcabcccdacbdbaacaddbccabcbbcccacabccbddbdbcbadbaddddabbbacccdcdadccabaaccdaaaaddcbcdbcdcbcddacbdaddbabadabcdaccbccbdbdaacacbbcdbbabadbaabcadcbddccbcdbbcccccabdcdddbdcaccadadcaabcbbacbbaadbabddacacbacbbbbaddccbadcbddabacdbbbdacbbaacdaaaacbdbbacbccdcbddacccdbbabaacccbaacdcbabcbccadbdaabbddaaadbcbdcccbbdddabcddbabbdacbacbcccbccacdcddccdacaddaadcabddccccdddcdadbbbacaadadccbabbaabaadccacbbdaadadaadccbaacabcdacacacacdcbdbbcdaadacdbcccddccbdcbdcabdaadccacabdbbdbbabaddbcaccbddbbdbadbddccdbdcccabddcddacadaabccaaabaacbccbcddcacbcdddcdbddcdbdbcbccbcbcadaaccaaddddaaccdcdadcdbdbcacddbbabacabdadbdcdabbdbcacdcdccadcacccdabbddaaaadbccccdabcbcbbbdbacaadbdccadabadcbaccbadbbaacdbcdddbbddcaddbbbaaddaccabdaacbbabaacabcabacbabacdbddddadbadadbcacbacbbbdbbacbcacabbccdcaddadaabadbcaaddddbdcdcbcccaaaddcddacdbddbcbdabbcdbbaacaaaaddcacbcacbcadcdcaaaadabcdaacacbabadaccbbcddacdbcbacccabbbcdbbdbdaccbddaddcbccbdbacdacbabbcccccbddcbddbcddadabaadbddcacbbddbcadbbdbdacaccddcbdabadbcacdbbcabcccbccbbcbbddadcbdbccacaaadbbbbadcbdbdcaaadcbaabacdcbaacdcdcbdabdcdcbaabbdcbadadaaabacccccadddcbbcddadddaadaccbdccacccbcbaaaaccdacdcbcaadcbbccddabbbaadcadcccbbdccdadcdabaaccaaaccdcaaaadabcacababacbbdcbaddbdbacbbdbaacdbcbbccdcbaadcddbdabacbbdcacccacaccadaabbabcaaaddccaadcbbcbaadadbccdadacbcacababcccabcddaacbdbdcddbbcbdacbdbddaccdcddbdadccdadcdbbcdaaaabdbabcbcadbbabadbabbccbadcbcdaddaccbdcbacbddccbaabdadbbbcbaaababbcbaabbababbcbcdacaabcbbabbbcdcbcdabbcdbccbcacabcdddcbcaabaddccbddbacbabaacbcaccadccbbcbbddcdacddbabbdddbbcbdcadcdacabbbcadbcbabbadbbabcdaabcaccbdbcabcddabbadbdcbcddaadaacdbbcdabbaccccabaadcbbdddadabaacbbddbcbdbccbcbbaacaabcbccbccdccccacddcadbcabddaaaaabbcdcabdbccccadccccdacaddcdbdabbddccaadacdccbcbadacdbbadcdaccadccbccdbbddbaaacaabdcabaddacaabaadbdaaabbdbdcdddcabbaaadaaddbcdcdcbabccddbcbccbbabaacacbbbbbbbbaadaabaadbaadcbaddaadcbaadbbcdcacddaddccbccaacbbcbbcacddbccbbccbdbcbcabaccdcaaddacbdbabdccdcdadaddcbdccbaddbbcaaabbaddcdbbbcdcdbadcdbbbbaacbbbababcdcacbccdbdacabbdbdbbbccbacaabbcdcbbcdbcdababcacbabbdccadcdbcabbcadaadabbadbdbbddadcacdacbddbcdddadbbdadadcdbbccccccaabcdcccbacadbbbcacdacdcdccdbcbccadcacccdabcacddcaabcadaabcbbddbcaadcaaaccaccbcacddabadbbabcabcccbddcdddcadbbaaaabcdbbcbdcacbcaaaaaaaccadcbcdcabcaacdaccbadccaddccddabccccdaddcbadbcbadcdaaacdcbcdddbcbccbdcbdaccdcdbcdcacdbdaacdddbabcdbbaabddbdcbabadbcadcdcaacbacbbcbabcbcacdbddaddbdaddabbdccaaabdbbcdbdbabbcdddbcbdacbdbcabdccbbdcdbabcdbdabdaadddcbcbcabdcbbbccbacaadacadddcadddabddcadadaadcbccbbbccdacbcdcbcabdcaacdddaddccaaabccbcbaddddaaacdadcbdacdadddaababdbddbcdddbdaccdaddadaacbbbdcdabbabcadbbcdcbbcaddbaccdbdabcdaadacacadddadcdadccbdcacbbcdacbddaacddcabbbaabbbadcbaccbaddbcacbcbdcadcaacdabababacabdcbcbccdcbcdbccdadaccddabbdabbbdddbcabdddabaddbbdbccccbcdbacbdbcddccabcccdcdcbabcbcaaddbcadcbcdbbadcccaabbdcaacbadbbabacbdbcadbdaddcddbcddacadabdbbbadbdbcccbdbabaabcbdcbabbbacbbadbdbcbbaadcdbdcdabdadacadbacbdabbcacdabcccbdcbcbdbaacdababccdbdddbaacdbadcacaccccdbbabdaccbdbcdbaccdcaacbabbcabccdaccbddddddcacdbccbaccbcdbdbaddbdcaaacdabddcdacbcbbbdcabcbdbddbdcbacccbddcabbbdbbcddaabbdcbbbbaabaacbadccccabccaddbdbaaccaddcbcdccbabcddbbabcbddcbbbabdaddcdccdacabddabbbbbabacbdadccacabacabcbdbdcbcbcddccaddabddddbabbbdccbcbaabdabbddabcbbcccabddcdacdbcbbdadabbddccacaadbbccbbdcaaadbcbabbcdcbcbabbbbcbbcdacdddcdcabddddddaabdddcdabcdcbcacddadcababcccdacbbacbacacdcbcaacbcadacadabddabbcadbcccbcbdaaaddbaddadddabaccadbcbaabccbcadaadcabadcbbabdbcccabbaaadddbcbaadcaccbdbddcaabdcdcbcddaacaccccddadcbcaacbadccdaccacbbdbddcbddcccaaaccdacbcdcacadaacdcddcaadadbabcadaccacabcbacddcdbacaaadacbbbdadcdaaabadbbdabaadccbddcbadacadaabdccadcabbbddadcaacbcadbabdabdabaacacacabaccaddacdabdbdbdcdcbddbaccbbabaddbbcbdbaccccdcadbbdcdbdcdbabccdaadabaccdccdadcdcccadbcadabdbdacddddcabbbdbbcacaabadcddbaaccdaccacaadbdccddcccccacdcadacdcacaccadbadbbacccdccdbdaaddbdcdbdcabaccdcaabdbdcdaaddabcdaccbbbbdbddbccacbccbaabadbcddcbadcbdaccabdacbdbdcdddbcabddcbaabaccadddacbdcaccbbddccdbdbbadaacccdcbadabbacdcdcbddbbdbccdaaccbbadbccdbabdcaaddabcdbcbdcdcbccacacabbaaacbcbaaabadddbabcdabbdabcccbbcccacbbdbbbdcccacbaccabbaaaabddaaadbbdccbcbbddaccbdcddbccaabbacbbbbbcacaccbacaabadbadbcaccadaaadbddcbaadbdbddbacadbbccccccadabbbbadcadbccadbbdabbcdcdbdcaccaccccaaabbdccadabcbcdcdbccbcccdacdaaadbbddbbcbbcdbccdddadddadcddabbcdddbdcbccacaadbbddadaacadcbbabaccaabcbddacdbbcdbabaaabccbaaacddcddcaddcbdcbcdcbdbaaccbcbcbbbacadbdbbdbdbdbddccbbadcddbccacddacbdbbbdbdaadbbdddbdcbadcadaddcbacadaddacabcaabbcdaccdbccccacdcdacbabacacacdabdbdabdccbdbaacbdbaadbbdcdacbdbacbabadbdddbbddccbcbcaccaacbccababbcbbcbacbdddbabcacdcccbcadcccaaccccdadcbcdbacabaaacbbbadcbabccabaddabbcadbbcaadcbcddabcbdcdcbcacacaccdccbaabcdbcaaccaaadbcadacacbbacbbcaddaaaadcadddadbcbcdbcaabacdcabbccddbbadabdaadbdaaadcddcbaccccabddddccaccbddcbdbdbdccbadadcddbbabbdbabdddccbccdaddbaacacabddddcddbadddccdbabbdcbbaddbccddcadaddacbaacacabbbccaaabccbbdbcccbbadccddbdbdcccdddbabddaccadacdccbdacbcdcbaabdbcbaadabadbaadcadbdaabdcdaddbaacdbdbabcbbabaddadaababbabbabbaadaabbbabbcbcdbbdbadccdbcacdabbbdbcbcbdbaadabadaacacbcbacadddacabddbaddbcdddabbdbbcacacdcbbbbdadcabaaaddbbaaabdadbbcdaddccaccccbdbddadcacadaadabcaaabbcccbcdbdabaddbcdcbdddddddddadcdddcbdabdddcacaacbbdacacdccbbaadddaaaaabcbbbcbdbaaadddbacadcaaddbacabcbdacdabdaccbabccbdcabbbbaabacbcacdbbcaddbacdbccadbcacddbaaaaaacbdbbacbbddcacabbddabbaacbacbbacbcaaacdcbbbbdaaddacabdacdaabacbacbcbdcbcbdbbbbcabababadbabaababdccbddabdaacacacadccddcccbbccbbbcdaccccabcccbacabdadcbcbdccdbccdcbcacdcbbabcacddbdadaacdbbcdbbaadbbadbccdbddbdcbbcdbadbdcacbcddaaacdbddbddcbbdcbccbcdcdcdacdddcbccadcddcbddadbbadccbddbccdbccbddbddcbcbbdbaccbabcadcbbdacbdbcaaadddbcdcacdccadabbcbbbaddbbbabaadcbcbdcdaccaccabbacbaadabdbcbdadbcbbacdadbdaacdabccbdccacdabdabcddcdcbcabddbbccaadaccababbdbcbadbdabacacbbcadabbacddabaddcdadddccbcddbbdadcbccabddbcccbcaaacaddbbccbdddcacbbacaabbdccccbbcabaabbccbbddcdcbcbabdbacbacadccdacdacacbdbdcadcbabbcdbdccdbcabdccadadadaabaccddddccabbcbadcabdabbdaadcbbbaaadddcdbcbbbcbacaaadbacdbacbaccdbcabcdccdbbabaccccdbbcdaddbaccaaddaccddbdddaccdddcdaabbdbabcbabbbdacbcbaadcadcbbdacddccccaaaadcdaddadcdacaddbbaaadcdcabbaccbdacbdbcadcadbdbbcbbbbddcdccadbabadbcabbcbcccdbbcbddbcdabaadbdcdbbabbcddacaccacadcbcaddcbcabcdbadbbcacdaaabbcabbdbdabddbadacaabcdcdbdbacadbaabbadaadbabdaadabbdbbcdcbbdbdbdbcbdbacccaacdbdacdaadccadcabbbabadccdddcdcdabbacdcbccaddcadacabacccdcadbaadbaaccdcbcdcdaabdabcdcdbdcadbdbbdcbaccccdbcabdacbdbacdadcdcbbdbdcdabcddaabacdcbbbacabccabcdbcdbdbccdcaccbccccbabacacbbbcbdbcbbdbbadcdcadcdddacdcbabcabacddbbcddccdabdcbccdddacadbcaccdbdccddddaaababbdaaacacdccdcbddbcdbdcdddbabdbadabbadcacdccdcddbbdbdbbbbdccadcacbbadbbaddaccdacadbdcdabbabadcbabbccbdddbdaadaabbcbbbdccbaddacaaadcccddacddbabdadbacdcbabdcddbcccbcabdacdaccaaddabbbcdbcbacbbaabaacdbcaaacadddabbcdabdddbdcccdbcadccddcbcbddccdcadddabddccdbbadcadccdadabbabddbbbcdbcdbcadcaacabcabaddccdbbdbaddcdababbcaadbccbbbbcdcdabcadbbadadcbaacdcaaadbbdbccacaddcbbbdabddddcdabbadbcaaadcdaddcbcdcdccbbaaccdbcddbcbcbbcdcbcbdaabbbdabbbacaadcddbaacaacdcbcdaaacabaabbcccdbaacbdcbdbdacabbbcababbacdcabaccdbadbcdbcdcacbbbbbbbddbbacccdbadcabccbacbdacacdbbadacacbcdcbcbcbdbbccbbadabbacbdaabccaababbcacdacbbbdacbcbacdcaacbacacbbabaccddacbbbcdacbacadcacdcbaacbdbbcddcabdccbbabbbddcabacccaacacdddddbdbbcccdcccadbaccdabbacaaaaaadbaacdbbbdadbadadabaadbbacaaddbbdabaadbbadcacdcbdbbbddacbbadacabaaccbaccaacdbccaadbdabbaacdaaccacdbabdcbaababdaaabadaacbdccacbdcaaaaadbccabbabcbacdccbccdadcddbdddbdbddbdcbabbcaadadacdcbdbccaddadbaddabdadbdaccdadbabdbcbdcabcabcbdbccbaccadabaaabbaadbbaddadddacacdcbbccbdcbcdabacababcbbcacaaaaccbcbbbaaacccbaccaadacddbdadadccdadbbdddbbcdaaabacdaadcddaccbcdbbbbcddadaadcbcdbdbacddccbdcbcaadacccccadacddcdaacbaadadbbcdadacadadbcbcabcbcbccddcbddbdbccbabcadabadbadacddacababadacaccdbcaaabddbdccdbdaaaabbadcdcacbcadbdcaadabadbabddbcbdcbaddcbacababdaaacddcdcaaccbcbabdddbcbbdcdcddaddabbcbacddabbacadaadcdbbacdbbdcbdacdbbdacdbdddddbaabcabcbbaadcdccdbbcccaddadbcbbdccaccacaaabbccdacdbababaadaaacddbdddadcaccbbaddcbcbdabdcdaacdccbddaccadcbdbacaaabadbddcabadccbabdcdcaadbddbddcbcdddbccddbdcdccadbccabbdabdcdaaaacdcaaabcadbabbdcbcaacbbdcadccaacccbdbddbadacbcccaccbbabcbcbddbdabaacbdbbcacadbcbddddbddbadadbccbddacaabadcaadcbabddddbacddacdbbcadcaabcabcadaadbacdaccaacddbccdbbbdcdadaccbcccbbbccaccadcabcababccdcbdccadadaabccdbbddbbdbbdbcacaaaaadcdbaaccdcabcccdcbdbbccbbabdbbddbacbcbacddcbaaabcbbabaaadbccbcbccbccaddcbdaddddbbdbdbacdddddcabacacbdaadaabcbbaacadcdabcaacccaaadadbcdbdaabcbbcbdadaaaadbaacbccbbccdbbcddbccadbbaadddbbbbbcacbadabdbacdcadbbbadcacacbacdabdcaabdbccdbadbaabcbdcadaddcadbddcaacdabbcacdbddcbcbbddcabcddccaacadccbcabcaacaaaccabcbabaabcccabbabbaabdacbdbbadcaddaccdbabbaabacadddcabcacdacacbdcaadbdcbcdacabaabaabbddaaddbcbbaaacdcddadbcccccdbcbdbcbadbdbdcadacdadadacadabbbadbbdcdcabbbaacdbadacbbbbdcdccadbabaaabadbbdbabbcbabddddddbcaacdbcabccbbdababdbbdcbbbbcacbacdacaddbdababdbdbcaaccbbacdbdbddcdabbcabbadbcbacbdbadabadaacaccddbadadbbcbdabaaccbadccdcbdcddaccbbbdadabddcbdbacdaddbcddbbcabdcabccccbbaccccdbadcdbdaadabcaabbdddaabccabcabcdbadadcccddcdbabdbdadddbaddacaaccbcbacddbcbabacacddcaccdabccbaaacbacbbcddddddcbcccaaacabbbbbcaddbbdcbdcdcccbbdbacddaddaaaaddcbddcacdcbacbadcbbdabccdaddbcadcbddcdcddbdabacdccdabdbccaaadadaaadbadbccccabddbbbdbbcbaaddacbdbabddbcdccccccacbcabcbcbabadacddcbbabddabcbddcdabcdbddbccbbdabacaccccbdaabddcbddcdacdcdacbcaaabbcbacdabdbcccbaabbcdcdbccabddcdbbbbaabcdabdcacddbbbddabdacccbccdccbacbaacabadbdacdadcccdbccccbacdccadbbddbdbbaabddcabbddbdadabacdbacdbcaaacddcdddcdbabaacbdddbbaaaaadcdccaddaabdddbbcbabbaaaabadcabbbcbccbaadcddbbdadcacdadbbdbcbaadbacdadabdddddabdcdddaaccaddddcabbacdbbaadbbacbbdcaaaadbcddcbdbabbbdccbaccbcdbdaaaabbaababadcddabddbddcdabadbaabdabbaaddacbacadbabddacadcbcaabdbdddccbdccccdddbbbcabccbdbabbaacbbccdaddbbccbcdacaddcbadbbcdcccbacccddadacbbccdbdbcacacdcbcddccaabcbccddcdddcdcbcbabcacdaababaaacacdcbcddccccbbddbcbadcdbdbabcddcbacaacbcccaccdbcbbcdcbbbadbbdacacdcbcadcaacbacabcaadacdaccbabbbdbadadbdaabaabdaadcaaababaadcaddcabbaadadddacbadacadabdbadbbcdabbcbbcaacdcccdaaaabbacacabddabadcbabadcbddacdccacdbddcbdddddcaaccbacbddcccdacdbabaddcdccdcddbcacaabaabbdacadadcddcaabaabcccbaacaddccddadddcadbbdcdddbdccddccbbcaabdabddaaacdaadddddccdaacdcbddaadacdbddbabbbbbabdccdbcaabdbdacdcccaaacdddbdabdabddcdbccbcdcaddbaadcdccddccbddcccadacbcccbbcbdabddaabaadadacadcccadcbadbdabdadccdbadacbcbdccbdadbacccbdbcbbcdcdaabbcdddcbcdcdcdbbcabaaddccbccaabcadbbbadbcacdabcbcbcbcdccdcaadbdcdcabcdbcbaddbccbbaababbbcacacdaddabbdcdcbbddabbbbdbcddcadcadaaacdbcaaaccadbaaadaabaaddabacddbcaabdbaaccdbcccbdcabbdcbddabbaaadccaaccabadcbdcbcbabbdccbcdcacbdbaabaaabaadbccddddbaabadccddacbcdbacaadcccdadddcadcbabbbdddcbcddacaabdbbabdbbdaadabcdcbcadbcdadcccbacaaaddadbbcdabbacdcaddbddcadbabaabdccbddbabdbbccdadccdcbadabbbcaabcacdacabbddccbdaabbdccbdbabcdbbbcadacdadbcaccadbccbacacddaadcbcdacbdbdcccddabaadbbcbadccbabbbddcbcabdbcdabddccdbddadacbaaadadccbdacacdbddccacdcbaabdbccabadabacccacdacdbccbcdcaabdaaacadaadacabdcbabbccaacaacdcdbbaccccacbaaaaacbcabcdabbbabbaaabbabdaacddbabadcabaacadbaacbaacdabccbbbbccbbbadbcbadabbdddcaabdbbdadcaababccbcacaccbbcccdbddcabbacbbddcdaaacdadbaaadbcdbdadcbbdabbcbdaaacdddcacbabcdabbdaadbcadccbcbbcadcbaaaddbbadabccddcdcabcbcbdbbcbccabdcacadbaccbaacccbcbbbdddadcccabdacdabdcbddcbbacaccbbccdacacdabcacbadacacccdbcbcacdabbcdaadadadcbddabbcadcdbabdbbacccbdbacabcbdadabbdadacaabbbabdabbdbaaadadbadaacbcbdcdbabcdbdacbccbbabcaaabacbbaacddcbccaacdaadadabccddaaacaadaccbcbdbbcbbbcbddddbbbdccddcbcbadacacdbddabaddcbabbaaadcddcdabaabdbbdcccabcccaadcaaacdbadbabddddcacacaaadcdbbdbcadddadabacabbadbbaabadcbcbdcbcdbadcaddacdcddbadcbccdcdaddcbbadbacbcabccaaccdcddacbbbdcbbacbdbdabaaaadbcddcbbccabcabaaabcdaaaddbadacddccdadacbbccbdcccdadbacababdadadccbdbabaaabdbdcaabbdabcaddcaacdcaccccbcaacddbbdddddbbdaacdcdbacccbabbbdbabacbbcdadabddbdcacbbcdbadbaadbbdbaaddbdbabddaccadbccbdabcbbabacbbaadacccbcabdbbccdbdcbbcbbccdcdbbddbbdabcdcdabcacdcaacaddadcadadbcdaddddaabaccccccaadacddbbdccaabacdaccdbdcdabaccabadbacddcaadabbcacabdbdaacbdcdacadbcddcddacbbacdadaabdcdcacbbaddadccdacdddbddbdbddabcbcdacdcabdacbdbadbbcdcacbcadadcccdadaabdcbdcddbaabdbdaabbbccdadddaabdadbdadbcadacacadaadcacbbacbcabacdcadcdbdcbadbcdcacddbbaabadcacdddacbdababcacddbdabacddcdcbcdabcbcddcaadacbbaadadcaddbdadbccbddbbcdacccabbaddcaabdccaacccbadcbbdadbcaaddaacbddcaacababbbcbaddbaacdacddaadadaddadcabaabccdccaabbacdcaacababccddbcccccababdbdacabccbcddcbcdcdbaacdccbbddbccdcabbddadadbabaadaaaabcdcdaddbcabccbbabdbbdddcabbacddbbcbabbbcadddacdadcabbcacadddcdaccabdacdcadddddbdcdbbdcdadcbbbadbaccbacdacdddbbbbbabbccaaadaaabbaccabccabacdbadcdadcabcbadddadbdcabbaddbabcdabdacacddddcbcbabacbcacaabbaaacbbdaaccddbaabbccccbcabacddcabbbadacaacdbbdbacbcbcaccbddcbabcbddaadcbbadbadbdcbcabadaacaababdcdbaddacdbbcacadabcaddbbddcbabcbcdabbbadbabcadaabbbdbbcdbadabbbadabdbcdadccabdbdddbcbbbdbdddcbdcdbdacdcccaabbbdbabdbccabbcdcddbcbbcacdcaccaabbbbaabcbaacdccaabcbbbdccbabbbaddcdcdbabdadacbdbaacdacbaadccabdccbbdacbbdbbaaadadaabddbbddacacbbcdccddcadbcdcabbbadbadcdbdacccddccdbbaaabcdbcddbccdbacdcddadbccbaadbbcacababdbcddcdaabaabacadcbabcbccdccbddadccbbccdcccdbdddbbaccbadcddccaacbccaddcccabbcbbbdaddabacccdaaabbccdccbcaabaaadbcdadbaaaadcdcbbccacacbcbacccbcbbdabdcabadbcccddaaabbabcbadcdcccbbbaddaaacadcbcaaddabbccbcabdddaacddacaccacabddbaaadbbbdabcaabcacccdbbcabaadcbcbdaadccddcabbadbbaaadcabcbadabcabccacdcadbabbbbccddccadaddcdbccdcdadbacdbdcbcabcccccabcdcdcaaddabbcccaccbdddaddaabdbbdddcaaccbdcbbdabcbcaccccccddddadcdaddcadaadcddcabadababbaccdaddbcbdbdbbabcddbcabdabacdbdaaccbddbbabccbdbdcdadbbbaddbdcbcadccbbbcabcdcddddbabaaacadbbbbcabccddbadcdadaccbdccadbaccabacddcdacdacbcbadbabcccbdbdddbdcbddbcbadaaabdabaadbdabcdadddaacaadcddccaaccbaaaacccbcadcaabbabdbdababddbaaabbdcdabaadabdbbddcdbacdacadcacbbdcbbbcbcababcacdcbacabbacbbbbaacdcbcbacbadabccbaacdbbcddccabdcdcbcbcbcbcabdabbddbacaaacadacdacabdcccdcadcdcdbadcdcbbbccbdbbddabdabbdcaaccdbddccdacddaacbcdbabdadaddcdaabaadccbdaccbcbabadddcaabdadccdcbbadabcacaaabbaaccadbaccdcdccbaabbdaabdcbbdaaaabbccbacdadaadcbbddbdcaaacbaacddbdbdcbbabcdaccadabbadcacbabdddadbbcddaddaccbaadcbdaddacacabbccdbaacddabaabdbdccbcbaccbbdddccdddbbccaabddddcdbccbbdcdbabdaadadbbaaadadcadcbbbacbbbbabdacddcaddcadbdabbaabbaacadcbabccdbdbbcccadddcadacddadbadbbcddadbabcdadbbcccaaadbbaddacbbcbddbcbdbaaddabcdbbcdcaacccbdbacddbbaacaddcaddabcaabbdacdadabdabcdddbadadcbbacaadaddcaaadadcbcdaaddddbbcdcdadcaadbcdbbcbadbbabdcabdadbaabbcdabcacabbacbdbbddcdbbbaabaaaadccbccacddaacaadcbcdcdcdbadbaacbabcbccddbdddabbbdbcdbcabccddbadccbcdbdaabdbaddabccddabbdaccbcbbcdcaacaddaaddabdbadccbcbccabcccbbbdbcdabdbccddbddacbacdbdcbccbadabaaddddadaadaabddaabdcaccaaaaabbcdaaabbbcbbaaaddaaaadaddccbccdcbccadccdcdbcacdcdcbaaccdabaaabbbccbdbdaaacbdbdabbdbdbdaabbbdbacbcbdcccbdbdabcdcccbbccbdccaabccbabdabdbdabbddcaddbcaacabaacdcbcaabccddbcabaaadabcccaddaacbbddacbbbbddbbccacddddccbabaccacbadacaaadacabbbaadbacdaadadccbdbabcbacddcbccbdccbcadbabcbddbcadcbacbcbadbbbcaaacccbbabbcdaddccabaddbcacdcbcacacabcbbbdcdddabbcbccbbadbccacdcddbccbadccccdacabbbddbcdccacddbadbdcadabccccddadbbcbaccbdbbcdddbbcadcadaacdbccabadddccaadbccdcbcdadbdbbacaabacddaccdbbcddbacbcacaadcdddccccbcbdbaabacbdabdcbdbdbdcddbcbcbadcccddaacbccdbdcabbcbcabcdcdabbdacabbbadddcdaddacddccacaabaccbbaccddababdbccabdcacabacacbabbbcbacccacaaaaddddbabbbcbcaddadbbadabdabccbaccdddddbcacdabcabdcbbbbbbcdcbaabcddcbacacbccbadbdaddacabbdacddabaaaaabccccdbbaaaacdaddcdccaadabddcadcabbdcbbacbdbbcddbaccbdbadbcdacbaadcaddaaadcaccacbdbdcbabdaabadddadadaabbdabcadddbcdabcccabadccbacbabcddbbaccadcccdbaabbbcacbadddbbdcbddbcbbadbabdbbdadcbcbdaacacabaacddcccddddcbbcdcabdabcaadbbcadbbbcaaaddaaddabbcbaddcddbbdcbdacddccddaacababddccadbabdcbcbcccabdbddaccbcbdcbddcdbaccaacdcbbabbcdabbbcbbcabacdbdacbadaddbdacacdbcaacabbcdbdbacdbadcabccbdddbbaacaabcbaaaddacadbabccabababdbacbddccadacdbbcabcdbddabdddaaadcdbbbdbcdadcbaabccaabbaadcddadbddacbccbcdcbdbaabcccbccababcdacccdbbaddadcbddcacadcbbaababcabbbacacbcdbbbccaccbdcadbacbcadabdacadaacbccbdaaabaabbcbbdabcbccabaddadacbdbadbcaccdcdbdddbadaadddbadacdcbdbabcdacbacbdbbcdbaadddccdaddbcbccabbdbdaabadacbcdacbbdddadacdbdbdbbbbdbbbbaadbabbbdcddaaddbacabcdabdbcccbbbbdabababddabdcbbaddadaddbdbabdabdaabbdaddccccbaadccadcdbbcdabadbddcdadbcccaadaddccdcdcccabdacaddbbdccccbababccdccbabcbdcadccbbbbacbadbdccbdabaaacbbadadcdaadcacdcacbbadccbcabcbdccaadcccbbbadddadcbdbbdcdbbcdccccdaabbabaccacacdcbaacabbacdbcdcbdbaaacacaacdbccacccabcdbabcbabddaddacdcdbddbabddabddaddaaabdddabddcdbadbdcaabaacadbabcbcddcbdbccbbbccdbabbbcbddbbbabccdccbaaccaddadcbdadaddcbbaaabccdbadbdaabaacccbcccabbacbcabddbadddccbcdbcdcaacbcaaadbabcadacdddbaabcddadbbdaddbcbabcadddadbcdbcddcaacbddbbcbaabbaccbbdaaaacddcadccbacbaaddacdadbdaabbcacdddcccadddacababbacccbadcdcbbbdaaaaabbaddcbaccdbdbcbbcaaadbdbcbcaacccadbbaddddbabccdddbbcacbaccccbdbacdaabddcdadcabbdadddabcbdababdadbdbbcbbbcccadaacbdbccdddbddccadcbbbacdcbaaadccdabacbbdacddcaadaadbadaaabdbaaaadaddaccdcacbdaaaaadabbbdabdadaaadcbddabbbddddcacdacdcbbacdbdabbbadccbaaaadbccdcbadbbdcaadbdddabaabdbabdabddbbaadabdabbadadbcaaccbacddcdddcdcaacdcbbcbdbdacccdbabadbbaddabacadcdadddacdbabccbbbcabbdaaacbcddacdbcbdcdbadbccdcbadbddcdbbadddaaccbcddabcddaaadcababaccacccacccdddcdbadcbcacacccabdcdccaaabaadadaadabdcbbbbccaddcaddcbaddaccbadaaabddacdcdbccdaaccacbcabbabbdcacadcdcabcaadcabaabbcddbcacabbdadddcaaaaccbcacddacbbadbdbacbdabbddaadaabbbbbcddddbdbbadcbdbdaccaccabaaaaacbccabcaabbbdbcabdcadddbbadbcdaacdacbcdcacadabdababddacbadbddbbdddbdaabbddbcbcbcbbaadbddbbaacdbbbdcddaaabcbbbcddaddabcdccbaddcabaddacbbdcdcacaaaccbaddaadaccdcddbaadccdcaddddbcccdadcacacdcbdaaaddcbcddcbbbbbaacaacddbdacbdacaaacaacaccaadabbccccccdabddacabdadbccdcadbccddddaabbbbcabbdabbdbaabccbbbcbcbabbbcdaaaaadaccadcdcccbddccdaadaddbcbdbbdadbdaababacbcdcabccdabcadbcbdcbcadccdaccccdcbbccdacbabaabdaaccbcbababadaaadcdccaddbdbdaadbdacbccaacdddcacbdaddaccddbaadcabbaaaacabadbcdadaabcbadaabdaabacdaadadbbbaccbccbddaadcbaccbcacdcadaaaabacbbbbabdbbddddbbbadabcaaacdcccdcaddddcadbaadcabccabbadbdbaabcbbddbaddddbacacabcdcdaadbddcdbdcbabbbbcdccbdbbdaaccddbdcbacbbccdaaccdadbcbccacaddccabbbccccdabbcbadbddcbdbbadbcbcaaddabddcbcaadcdcbacdacbdbccdcacdcddbaacbaaaddbcbcaabcacadcbbcbcbbadacabbbdcadbbdaaddaddabdccdacaaccdaabdbdbbacaaabaccaddccabbbdabcdbabdddcbaaadccddbcdacacacababbddaadcaadbbaddabcdcbabadccbabdbbbcadcaacccbdcdbddadccddbdbcdacacdbacccacbaacaaacbdbbccaaaccabadabbcabbacccadcdabcdccaddcbbbccbdaccaaabbcaaaadbabccaaacdabcbbadbbbdbaaccdccadccdbbabacacddccaddbbcbcacddbacdcdccdadacdadddccadbdddccdcbbaaababaadbddbbbbdbdcdbabbacbadbacbabdbcadcabccbbcbcdaaccaddabcadddbcabacbcbabcdbabbdbcabbcbdbaacbaacdcbaabccaabccdcdbddbddcbcacabcdaabcbdcbbccbaaccdbdbbacccbaadccbcadbddadbaacdccdbcbcccaaacbddabccacbcaddbcdcbdddbbcdbacbbabcbcddbcccabacbccbcabcadaccdabbddabdbacbcdcbdddddbcbccccccaccbdcaaabacbcbbcdbcccdcdcadbcaabbdcdcadcccabcaacbcdacbcdaabdaacbcbbbccbaacbbbdcdcbcdddddbbaababbdaadbccdccdbbdddccacaacbccccaaabaaaddccdbdbaaaccbdbdbaaccacddaacddcadbbddaddcbbcddcccbaddbddbaabbbabbcdccabdcbbcabbbbbdcdcdcbdacabadbaadaddbaacaabbaacbbaabdccdcaadbbbaaabbddaaabcdbcaabaaabcdcbbadcacabcdaddbcdbdbabddaaacaacacaacdaccdccabdaddabbaadcccacbbabdaaccdaadaacaacddaabbdacdacaddaaabdcddcbcbccadacacdcadcaaaabaccbcdaadbdbdbabbccdaddbdabbccdcccadbdabdddbbdacacdcaabacaaadcbbbdabbaccbdbaddaadcdaaccccaadcbccdccabacbbdbcabbbcbcdcbaccdcbcacbacadbcacbacdcdbaccdbdaaacdcbbddcadbccbbadbdbaccacdaabdcddbdcbbdcdacdcadcbaccbadbccbadcbbabadddaabacadbdccdabbbdddabbccdaabcbadacdccddddcacbbbbbddcadcabdcadbcadbccabcdbccdcbcbccacbccbcbadbdcacaabddcbbdaaaabbacbcabcdbcdbccdaddcbdabbdcadddcccbcdbbcbbbbbbdaaccabbbacddabbcadbbdcdcaabbccacbbccabcdbabaddcbcbbbbccadcabdcadbdccdbbcacdcadcaddacbabcbabcbadabacdcabdbbdbcbdaddcccbcdadababbdccdbaababdabbdcbcccccbdbcacbbbcabaabccacccdcacabadbdcaaabcdccddaccdcbbddabbbdabdbabaddaddacaaaaddabaabbddccbbacbbbacdbdcadbdaabccacadbbcbbbbbcaabadcaddabbbbddcbcbddbccbbcbdccdaadaaaaccdaaadbcbbccacddcbcdababbdcbadaaadbdcdaddacdbcccdabdbbbdabbbdcbccbaaccadddddbcdacbaddbdbddaccbbcabcdbacccdbbbaaabddaadcaaaabcbdbdddbbdcacaddaddbadbcbddbcbcaacabbccacadbcdcaaaccbbdaadaaacbaacdbacbccbdccdaabdacbababddabcccdbdbdbdbdabdbadcddbcacdbadbbdcacddcababaaaaddccacabbcbdcacccbddbdaccbdbccaadaaccccdabbbbaabbacbbaddbdcabcbabbbcadbbcbcacbcaabcccddacbaddcbbddddccddccacdbdacacbadcabcdbaabbabcbbcbcddccbdcadaabccccbaddacacacdddabbcddbbdddddbcdacdadccddacccbbabccdbbbccdcabdcacbbaccacbdcbccabacdbbdaddabbcbbccdbbdadcbcbabadaaaadbdadcbcacadabcadcbcaddcbdcabacabadbdacbcdcacddbcbddaadbbacbbcbaacbccddbdabcdabbaabbadbbacbdccdbddaabcadacbcbbadacbdacaacddaadbcdbcddcbadabddbbbdbabcdcababbbdbbaddaccaacacdcbcacbbddbcdcbdbabddabdbadaabbabbaccbaabadbdadabbaababdaaaaccbacdacdacdbccccdcccbddccbcdbbbdadabbcddcbadcacacdbdababbdbccaabbcccdcaaaadcdbadabbbcdcaabaadabddbddaddaaccdddbbadcadbabddbbaaacdaabbbddddbcbcdbcdddcdbacbdbbacadaaddacbdcdbcdabcaadcbdddbbbdbccbabdacccbbcbbdaabaadaaddbbcbdccdcdcdaccbaaacacabacadcdbcaaacccdcdbdcdcbbcccdbbccaddbbbbadaddbcaabadadbcaaadbdcacddcddacbabdddbacdbaabbbbabbdbddacbbcddbbaaaaacbdbddccdcbdbacabddaccacbacccbdbdadccadabacadabbccdddcadcdbddddddabaacdbbbbaacabaccbadcbbbddbbcacdbdbdbaaabbbabbaacadadabbaabcabbaaccbddadcbdcadbbcbabdbcabbdbdbaaddadbdddbaabdadabcbcababdcaabdccddacdddcdccbcbcbbaacbaccdadbbcdccacdcbcbbdabcddbbbbdcdaddcddcccbdcadbbbcdaabcaccccaacbbaacdbcccaccaaaacabacbcacaadccbbccccdccacacaaabcdcaacacbbbcbaccdbcccdbacadacbcacbdbcbdbcccdbcbbbbabaabddadcacbdbbbabbdacaabbccabdacaadbbcdcccacbbbcbaccadccaabdbccaaacabdadcacbccdbdbbdabbabbcadcbabdcaddcbddaabdaabcdacddcabbabaddabdcabcaacaddacbdaadabdbcddcbaccdadaaccaccccddcdabbccbddbdbadacbbbcbabcadbdbbdabbacbccacbdcabdbabacacadaccabccadacabdbacccaddcbdbabbabcccbaaddcdcbaddddaddcdddcbccbcccdccddcbbadadcdaadddbbbccccbbabcbccabbbbcbdbaddbcacdadaaabbddddcbbaddddbddbbcdcbcddbcccccbcddcdcbadcaacaacadbdbcbaaaabbcdddbacbdadddbcaadadbbcaccbccdbcdcabdbddadbcbbbbbddcddaacdacacdbcdcabcbdbdbddccdabacbddbddcdbbacbcbadaabdcbbbbbbabaacadaaaabacccbbbcdaddbbcbdacacadbdcbddbaadbddaccdbcabbdcbbacacdcacaacccdaacaabdddbcdcdcbbcacdccccbbbaacadadaaacdcccacaccdddabadcdacbadbaacbbdcdacbcabbdbcabcccdcadcabdbabbbbbaccddbacbcbbcbcbadcaacadccadcbabcbabacacaaadaacaadbbbadcbdcdcbdccaadcdccbccbacccdacabdcdccbacbdccddcbbdaacdcccccbbcdaadcbdcabcadaccdbccbbccacabcaaabcdcaadcadbacdbcacdbbdabbaaaabddadabcaaccabdadbbbacbadddacdbccacbcbdbcbabbdaaddbcabcdcccdbcbbadcddccacddddccbcddabaddbaccbadaacbbdcbdcaabcbbdabdaadbbabacdcacbddccaaabdccabcdccddbbbbaccdbbdbcbddaaaacddcbdddabdabdcdabdbbbdbcddaadaaaaabbcabdcdadadabaaacbcbdaacaaddbccccbaaccdddacacbcadaacbabbabbcccbbacbbacbaababdbdcbcbbcdbccadddcadabdcabbdabaacdddcdbdaaadcbbbcaabaaacdabdcabbabdadabbcdcdcbbaabbadbcacaacaddbaaacdadbadadcdabaacbabdbcbbdccaaaaddaacabdababdccdbbcccbdcbbdcdcbaacacbdadcbadbdaabcdccdcaccdaaaabdacdacbcdbcdbdabdccbaadbcdcaacacccddcbacaddcbddacccacbcddcbcbaabcadbcdbdcdaccacbcbcabdcbbcacdabaabdacbcaddaccacddcbcdacbbdbbbdbdadcdbdbddaabbcbbddbccccdbabcccacbabccdacbddbbbdabbddccbadcdaaabadcddccbddcacabaaadbcccdccdcbccdcbbbcabbdcccdabbabdbacbcacdcbddddddbcaabaaddccdabadbdabdababcabaaaadccdbabdaacbdccbcaccdcbcbaaddcbcccddaaaddddcabbcbcaabbcaaddbddaaabdcdbdccacacadbcddbdbdddaddbbadaccadabcabdcadacbdbbcccacbbbaacadcadbadabcaabcaaababbabbaacacacaacdbcbdddcbddddacbccaabacdcabacabdbdaccdbaacdcaacacbdabdaabcabcadbdacadcdbacaabcdcaccbaaccdddaaaccdabdbddcbcbacdbadabbacdadccddabddadcdacacaaaabbbbcabddbbbdcbcbddcaddbdbddadbdbbbcddbacababcdabbcaabcadaaabcbbabcdbdacadddcbdbccdbbdcadadcbddbadcdbcdddccabddbaabbdcbdbdbaacbdbcccbbbadacbdbcabbddbccbaddbddacdbbddaabbabdbbdbbaabdcdababcddbbbbbccbcbbaaacdacdbddabacabccaacadabcaacddabdccbbbbdcabcabddcbcccdccddbddcbccbadcdaddcaddbdcaccbabddcddcacbdaadaaabbcaabacaaccbadbaaacbbbcccbaddbacbcbaabacacdcccadbddabcbbadcaaadabcbabbaaaadbccdccbcbdcbdabbaddcabababbaacdbaabbbddbbaadcabbddcbababddadbaccaadcaddbcadabbbaacdcccadcddcbabddacdcacadcaabdbaacdabcabacbabdcbdaddbbbdacacadbbaadcaadcacacaacbbddcdbbdbcbadaabdccbccbddaaccabcaaadbcaaaaadcdccaccaadadabccaacdccdcabdaadcbccacbcdbaadbcddcbbbcdadddcabdaadbbadbddcaaddadcdabdcaddcacbdabaaccddbddcbbcdbdabbdbbddaaabccadcdabbadaddcabdcdabadabbdcbdbbbcbccabccbcbccbcaccdaabddbcacbcadbbccddddbccdcbdcdaabdccabddcdbcdabcdbabbabadcddabdccaadadadcddddaacbbcadabdaaccbdbdcdbcadcbcccdddbdacabbcbbbdbaaddaaadcaaaaaacadbaaccbdadddbadddddbccdacadcdbaddbbabbbcadcbcbcdcdacbcadcdbdcbbaaddaabdbdddcbbbdddbaabccddbdccbcabbdbddbbdababcabbcaacacbbcbbcbdbddcddacdabdbbbddcdadbacadccabadccbccbdbaabcdaaddcdbcdcbabcaaadcbbbacdadbcbaaaacbdcccbccbbbdcdabcbcdcdbdaaaabdadadcbddacacbacdbdaacabdccadbbaaabdabadcdcbddbbbccccdcbadcacddbbcbddbddcabcacaaadabbbcdcaaddcccdcabbdacabddaacdddbaccdbddccbabdbbdbcccdccaadddcabdaaccdadccacdacbacabaabdcacdadacdccdbdcaccdcdabaccbaabddcabbddbdcacdabbdbabddccbcaabdacbabcbddacbbbddcddbbdddadbdddaadabccaadcadcacbbcdbbacbadbdbcdcdbadbbdbcaabcaadaddabccdccbdcdbdcdcbbcadbbcacaccaddbbacbaaddadabcadbbadbaacbddcabcbdbdcdcabddbdbbccdabacbdddbaddcbabdddddaccbaaaabbdbbaaccdadcacdacaccaabbaccbdbdadbbcaccddcdababddccbabdacbabaabddccacdbdcbacabaaadbbdddccdacaddcaddadbbddcccbddbdaccacdbbcccababbcbaabccabbcdddacdcdbdbddbbbdcadbcddaddbbcbdbdabadcdcccbbddabccccaaabbbcacddcdbccdabbcadbaccddaabdbabbbcddbbbaacbdcccdbdcabcdaadcddabdcabbddbabddbdcdddacbacdcbcbcaaabcadddabcbbcabaccdddcdcbaabcbcaadadaacaabdcbacbaacabbbbbaabcbadddbabbacdaccbbbaaaaccacbbabdcccbccdcddbddbababbaccbaccbaabdbadaabdbcdbdbaccaabccabaabcaacbaadbbaabcddcbcbdcbbdbcbdcddadabdaadaaacbcccbdcdbadccaabaaaabcaddaddbdbadabdbcdccdacdcdddababaacabdbbbddadcaddcdabdcbaadbadbbbdbacaddadbaaadabaaacbbabddcddaabdbbbaacdabacdaaabbadddcddbbddbcddacacabadabccbacacaabadbdadbcbcaadcabddbaabcadbdbbcacadcadbacabddacaabdbcacacdcbbcabaadacacdbacdbdbbadccdbadbaacdadadcbbcacdcccccabccdaacddccccddabbbbbbbcbddbdacbbddabdbcaabdcdaacacbbbbcaadacbaaccbaadccacdbbadaaccdbcaaacdadddbabbcbabcabacbdabbdbcbcddabddcadabcababdadbddbbacabdbbdacdcdbcbaddbaadcabbdccbcadddccababbdbbdaabddbbcdaadcabbbcabccaaacbddddcacddcacddaababcddbdcadbccbaaabdddcdcaaccbcaddadcbcaaaabadcabddbbbddcbdabadadbadadaadabbbdbcbcbadcdaacbddbdacaadcaadcacbaccbcacbaacdcabcadacabbdcbaadbaddcbdaccdaaaaaaccccccdacbdddbaccaaaaacadaddacadbccdaccddadadabdddcabcacacadcccbcadddbddacdaddcdcdacbaaababcabccaaccbbcbcbddccbbbdacadbddcdaddbbbcadccdcbdcbdbbbdcdaacdcadcdcddcacbabbbbadaddbdbcaadaaaabdbccdcababcdaacbccadcbbdcddaaccdbcddaaccdcacbdcaacbbdadcbdcccdbdbacbbddcbbdcdbdcdcadcdbaaaddaddabcdbdbdcaacdcbbbdacddcdcaaadbdaadabbaacbbadbaccdccddacbcaacaabbdbabdbbadcababdcbaabbbdbdaadbabdcdbaddbabbacdcdacbabbdaacaccdbbacaadbddbccaaaadbabacccbcdaccddabdaddadbadbcbaadbbbdbacbadbccabbaddadcdbcbbbdcddcaddaddbaaaaaacdbbbbbacaccaadbbdcbdbadbdddcdcadaaabccddccdcbaddddddcbbbaadaccaadccdbadcdacdcaccdccadcccddaaddbddcdbbaacccbdadbbacdcacbabbbddaabcabcddbdbcbbbccabadbbdbaaadcaabcbdbaabbddbadcadcdbbdcdbabcdabbdbccaabdbaaabddabacbcddabcbdccacabcbdadacacccdbabbbaaacacdcdaddabcadbcdabbbadbaabdbddcbbadbbabcdacaaaabdcababaaaabccbbdcccadbbccdbbbdbbabdaaadaacddccdacaaacbaccbdccccabcccaaaaddcdbaaabcaabbaacaddaccaccdbccbbbbbaabdadcdcdbdcdadccdbcddcdbcccadaaccbbbcacbaccacadddbbbdbdcddbbdddacadcabdbdadacabdcbaddddabacadcaccddacaccbaddcacdcabcbaacdccacacdabacdadbaddbcbccddabdcacbaadccbadadaddbcaacbdcbcbbbaaccbadcccbaadbdcdbacdbdcdcadddacdccccdbaddbdbcbbcbcddabccbbacccbadcbabdbdbcdbddbdcdcdaccbaaacdbadabbabdbcdbbacccaccdadcabbaacadcadbbbcdbcbbcaddcdaabadbabcbcccbadcabdabacadaddddaadadbabbcddbcbbdbdbbaaccccbaccddabcacdadabbacadcabbbacabcdcbdbadddccbaabbcadcbcacbcdccbdbbcbbadddddadcacaacbadbcdadcbccdcbbdbdacdcadacbbddcccbbdcbccccdbddcbbccadbcbccdbdcdbbbcbdababdabaddcdbbddaabaacccbbdadbdddbadccbdcbdbabbcdbbbcbbdccdbdadaabacdcdacdcabbaabaaddacabdbbadabbabbbbacabcbbdaadccaaacabbabcaaacccaacbccdaadadddacbabbdaacadbccbbdbbcdcbbcadcbabcbdddcbdbbcdcbabdbccaabaccbbdcadaababcdbabbdabbdabbdcbcadadcdadbbaabdddbbbacaadcbdcacddabdccbabdbabdaccbcababdbdadcdaaddcbbcbdcbadccddcdbdcaadcdddbddcaddadcbabdbbaadbbbadccddaabdadadcacbcbbbdcadbddbcdcdcdadcddcbcadcadbdcdcabaaccaddbccdcbacbcdbdcdbacddaccddddbbdbbddbacdbdbaacabbccdbdbadadbacdbadddccbcdbaccbdcdcbcdcbbddddcaddbddcbdcadacdbbcbddcdddcbdadacbbbcbadaabdcbdbabaaacbdddbbdccdcdabcbcbdaaaccdbbdcacbddbcbcdccddbdcddbddddaabbdcadbbbaabacccabdbddbcdabcaddddaabcdcaabddbccbdccaccdccaccbddbcbbdcddcbaaccaaadcdabacddcdcdabdbbdabaddcddcdacacbbddadbdabaaddcaaadddccbcbccaabdbdccdabcbcdcadaaddbbcdcddcadcbcbcbbbabbbabdacdccaadabcdadaadbacdddbcdbcadccacdacaadddcbddcdcacddcdccbcbaadbcacdabdddadddbadccaacacbbdacccccbbabababddcbbccbabadaabbdbdaabcdccbbcbdbdcadbcdbdacadcacbccabbbcbbccbddaacdbcaacdddcadcccdbaaccabdcbcbcddbccbccddabdbcdcbadcbccbbbaabbcbdbabacbddbbbdacdadcbcbbacbbacdaabdadcbacaaacaaabdbbbaccdcadadcacdaabbdbadddcaacabccdadaddcbdbacdacacdaacccadadacbbaccdbbcbcadbdbdcabcddbddacadddcaadbaabcbaccccccccaaddcccdacaabcaadcddcddbdcbccdabccabbcaccbbccbcdbcabcccbdaddbbacbbadddacccbabbbbdddbdababbaabdadadaadcdccbbcdccdcddacbdccaaacdbaaabbddddbabadbacbdadcdccbdbaadadcdbcaaabccbbccbaaabdbdbadbbbcacbcacbadcbccadbbdcdcacdbbabaccbabadabcddbaccbcdcccdbaacbdcdaababaccbdaccbbdbcdccddcacdcabbcbbcbbacbdaddabcaddaddacccbabcdaccacddabbdbdccddabcdabdbbbccdacbbbdbbccdcdadbacbabccbcadabdcbdcccbdbdbdaadadabacadcbddbbbdcbbcdbadbbccdadccdcdcbccdadbaacdaacabbacabcabacabadadaabcadcbbdcadcdcddaacbadbcdaaacbdbbbadacaaadbbabcbcaccddcdbddcbdbcdacdbbbbccababcddccaabcbacbccdaadbbbdabbcbccbadddcabbcdbdcdbbcacaccaabcbaccccbddbbcbbddaaabbcadcaaadbdbadaabcbacdcbbbdaabdbdbcabddbabadaaacdabcdacabbbabdcccbdadbdbdadadbbdaaaadcbbaacbcaddcccddddbbddcbbaaaaaccdabcbabbbbdbdaddaccaabbdadcbcddbabababddadccababbbccbbaccbcdadbbabadcadcddbccadabacacdcbabdbddbabcdbbddadbcccabcbddacbcbabbacbdbadddcbbdcdabdddabbacccccbaccabbcdabcabddccbadcddaaacbadabbacbacddcbdcbadadbacbddbaaddcdccddabcdaccdbdacbcaabbddabbcdbbadbbdbcababdabcdabbddabbddbaaccadbdcbdcaddaabbaaccbbaacbccbcdbccdddddbcadbacbddddabddacbcccddcddcacadabcdaabdccbbdadbcbadbaaccccabacdcadbbcdbcabaccbccdcbacdbabbccbbdaabdbcaabaabbdbabdcbacccbacdabbcdbbabbbddadcbcdaccbabcdabacadcddaadbdcdbaababcdcdbbcdcacdddcacdadacddddbadbadacdccdcdaabbcdacccdbdcabbacabbcbccbadacbaaaadccabaaacbabadbdaacddcadccdbadacaddcbcccbdddbdadaaadbcbcadbbadcababdcadccbbbbadacccbbacaaadacdbdbdcbcacdbdabacbdccaddbcaabbadadadabcccbbbacddbdcddddccbccccbbbddbdbadbdacadbacbdabccbabdacacccccbacdccaccbacdbccbdadccaabdaadaddaadcccddabcbccbddaacdabcbcabbbdacabcbccadabbdaddabcddcbcbaaaabdbacddadbdbaaddbdbcdcacabddadadccddbdbadbbcacddcaaacadbdbccddbbccaccdadbaddbbdbddcbaabdcaaacccdbaabacdbabbdacbcccbbadaaaaabbbbcbaababbccbdddaabbbaadbbcbbcdccabbacbcbaabcacabdddaaadababbbcbcabbabbddaacadaacdbddbcaaaaccaaaadbbbcabbbcadbcbcadddaddaabaadaadaaaabdbadbddabdbacaccdadaabdbcbadaaacbbdbbbabdcaabbbcbcbaaddadbbdcacddabacacbdcccdbccbaacbdbcaabbccaaddacdbcddccbccbbdaacadccddddcbbdccadaaabddccbadabacadabbadcdadadcddcddacadccdbdbbadbcddccddbacbddbaaadcccaabccabccbcaddddbbdaabccabadcdaabcbcdbbcadbdddbdbbdccdccdccbdbbcdbddcdcacdaacdbcddcabcabdcdbaadcacdbaaccabaaccccbdcaabdcdabadabcbadcdbcbdcbddbcbbdbcccdabcabdaadddadabcbcbabadbcdcbbdadaddaadbbabdcdbabdcdbddaaadbabddacabadaadcadaaadcbaaddabaadddaccdcacaddbdbadbbdacdacdcaadcbaabaabdadbcabdcdbbcacccbabbbcdddbccbacbbcadacbcadaabcacdddbbabbdaacdbcddcacacadcbadbbdadcadbdbbbbdcbacddbacbcccddbbdbbbacbcbcddcadaaadacdaabdaadcdbccdcccbacbdbdbaddaccbacbccccbabcabbabdaadaabcbcdadbbbbbcddccbadccbabcbaccbdaddcaabdbaccbabcbdbabacdcaacabaabbccdacdbbcdccadcaaaaabcbadcacadddcdabcacdaadddbdbbacdacdaddccdbaccadadccacddcdbaabcababadbdbbabbccbccaabdbdabcdbdcbaaddbdadaabdbbcacadaadbbadaadbadcdbdbcdddbddabddbdcbadcdbccdbdcdabcabacabdcccccadabadabddbbdadbccbaabccccaaababddaacabbbccacccccccdbaacacddbdccbbbcdadacbdbcdcdbcbddbabddccdaacadcdcdacaaacbdddcbcbdbbaccdccbdbcadbbcdcccbcddcbabcbccacbbabaaabacdccdcdbaddcadacabccdaccdaaadabbcadbdbbccaddbcdabcccabbaccabacabdddcdccdcaacdcddcaacbdabacbbbaddadcbbdadcbacdabcacbdbdaddbcddadacadbadaacbdbcdaabbbccadacbaddbcbcabcccbbdbaacdcaabbcacbbbbdbabaababaababadccdabcddbdbadadbbabcdcddcabcadbbbabdbdbcadadbbbcbaddcacabbaccaacccdddbcbcddaacdcaabbdbaaacadadcdabcdadabcaadbccacbaaccdabddcdbaccaabdddcbddbdcccddcdacbcbcdbdbabdadccbabacaddcdbababcadbadbcdadddadcbcdcbbaadbdcacdcdddccccdccdaabbbbcababdbbdbbadbaaaadbddcacaadcaaabdbcadacbcabacdabcbcdcbadbbbaadadaabaaacaaacbcbbcbacdbdbbbacaacdabaddcdcdcddacaaaabdbcdaccadcdaacddacbcdacacccacbdbdbdcacdbcdccbaacccbdddacaccaadabcdbdacbaabaaacbcaaaccbdaccbbbcddccbbbacdcaddbdccbbccbaaccdaddadbbccadbababaacaacaadaddabddcdbdadcdcadacaacdbbbcbadddaadbbbdcccaaaccbacdccbadcdcccbcadbcaabaabcdcaaacdcdbacbbdcabbdadadcbbbcdacaababbddabdbccbbcbcccaacadbadacabcbbdadbdbbbdbcbbadadabdaacabdcbccbccccaacaddddbcbbccaabbddbbababbddcbdbbacdcbacccbcdbbcbbbdadbacccaaabcbadbcdadaabcdbdaaaabdccbacaddaacbadcdbcbabaababbbaabaaabadbacbabbaaabcdcaadbbcdcacccadbcaccbccabddacbabddabccddcdbdcacbbcadbbbcbddcadbddbdbddbaadcdadcaccbddcaaabdbabbdabbcababdbbbcacccbadbcdabdcbcdaacababcbbaadbaccbabaaddbadddbbdbacabdcabccddcacbcbbaddccabbdacdcbcdbbaabcbccadacadaddcdbbbbdcacaaaabaddddacabdabacacbdbdcccccbdabbddaccacbbddaacddcdbbabcbdacadcaddaddddcccdcabaadbbadacaacdadbdbcbacacdccccadabcdcdacbabdccdabcdbbadabbaddcccbabcbcaaccccccddcbcabdcdaabdcdbcaccaccdadcdbbbaacababdaaabbdcadbdccbbcbdccaddcadacbbbdbcaacacdbbddcbdaccaacadabcabbbcbbcaaaaadbaacaacdcabacadcdadcddcacaaccdaacdacbdbacdcdbccaaabcabdcdbcaabbaddcbbadbcbdddacbccaaabdabdcbacbcacabdcbdaddcbdddadaddaddacdccdcbaccbcdbabbccdaccbcbcdbccacabacabbabbacdbacaaaaddacdcdcbbdddbbcbddcbacbcacdcbaddbcbdcdbbdbcbabdcccbbcaddcdaccbcaacdabaadadbbdbcccddbcbcccddcdbbacccdbdbcbdcbdbbacdddbdacbcccadcccbbbbbaaddbcadcaddabbcdcddccdcdbcddbdacdbccdacbcabcddacdbcddaadabdccbccbccccdabddcabddcdbaabddacdbdcddbbcdcbccdccacdddbaccdacacacbbabcdcccababcbddbbbabdbddaadadbdacbcaaddcdccabaaaddadbacaaccaadacbdbdcbbbbddddadbcbabdbbbddaddcabdbdbcdcababbdabbccbbbbcabccccdcdaacdabccabadccbbadbccccbbacbbdddccbbabdbcacadabbdacbcdabcaabacababcdacadbdaadbaaabadbccbccbcdccccbddbdaabdaccdcaabdddcdcdcccdaabcdaadaacabdcbcdacadbabbdbaddbacdbabddaaacadcbaadadbbdaacccacddaadcdbcacdaabdaccdabdcaddadaaacdaaadddbabcccaabbddbdaabbdbbdbaacddadbbbacbdadaabddabadabadccbdbbaabddcbbbccbbdddabaaadadbbacbbcdccdabcbaaadcacccbccdabdcdbddcbdbcabddccaaaabbddadccbaadacbbbbbbbbcadaddbcaddbbcbdcabdddaaaacbabbacbcaddadaaadadbabcdaabbdbdccbaaabbcbdddcccabcbaaadcbccadbaacddacadcbabbaadcbdbbbaddbababccdbdaccdcdacabddcbbcaccbdcbcbdddaaabddccdddbcddadbbdddaaaababcaadbdabacbbcccccddbbaddabdbbbccbccbdbbaaadaaaaacacabcdcbdadcadddcbaddddaacdbcddbddddacacacadaccbddababcdcbabdbbbbaccbbacdbdcabdaabcbbabdbdcabcdcbbdacdbccacccccacaadddcbaaacbcdaabaaabbbaacbbacadabbcbbbdacdcccdadddcbcadcdaabbadccccbaaadcdadbdcaadadbddbcaaabbbbabdbbcaddadcbacddbcdbbdcbcaaaabddbbdacbbaaaccabccaaaddbcbcacaabdbbdbddcdaabaccbbbdaadacddbabccdddcbaadabaacdcccadbaddbbdacaccacacdcdbcdbdadbbccabcdcaccbcaacabcbcbbcaaabbcaaaadbdbbcabbcbddbdbacdddacddddbcabdddcdbcacacbabdcaaaabdccbdaabcdcbaaaacaabcaabcdbdbdaddabababcdabacbddccdabccdbbbdbdabadabaaaccdcabbcdadbcabbccaadbbcbaaabbddbcdbbcdccacddcacbaacbabbcddbaacbadaadbbcdbacaccbcbbabdbdbbabcccacdadcbbdcbdddaaddaabbdcddcacdaacdadcaddcaabbadcddcbbdbaccbbaddacccddbcacabacaccdacbbdcbbcddaabcaaddcddddcdcbdbdacaacabaaadacdbbcdbacaccaccbccdbcacdabbbddcbdbabddabaccdddcdbdaccdaddbababababcbaaddabcabaddababacbadddbaabddbcdaacadbcdbdadaabacdbbadbddacacabccbaaabaddabababbabaddacabbabcdbcdbdcdbccccddbadccbaddcaacdddddabadbdacacdbaaacccbdcdadbadbdcacdbbcbabdadcaaabbbcaabcbbaacdcadddcacaabdcdbcdadbbaaccbbbdccdcadadacbadccbdcbbacdabdaccbcdbacdcdadbccbdddacbdbddbbddbbcacdccdcabdccaadadbdbbaaacacbabbbdcabcbbdddcccdbddbdbdaabaadbdaacbbbdacabdaacacaddcbbcdbdadabccbdcbcdbdcdbcddddddbacbcddabaaaccdadbabddabbcddddbadbccdabacdacaccaddaddbaccbbdaddddcbcbcdcbadbbcccadcbcadbdadbddcaddadabcbadbbcbbaabababacacbbdaabbbaaddaaccccdaabcdcabacbdcbbdcbcbbbcacdadccddbcccdaacdaadbaaccdaaacbbccdcbbdacdadcaaaabadbcdcbdcdbbdbacabbbdacbcacacdbbbbbddccbddbbaddccadabbadaabdcbdcbdacccadcccbbcabbdcddbbbdaccdbdbdabbdadcadcdccabbcadaadcbabccdbdabcabbcaaabcbabdcdddcbcddbdbbcbcacaccacbacdbcaaaaacbcbaddddbdcaabcaaacbcbaaadcdcaababcabbddddbccbdabbbcadacbddcdddbcbcbcbaacdabdacbabadcacccddbabcbcacdacaddaacdabbaaabbcddadacbbdbacadacdbabdaccacdcbdaaaadadbaababcbcaabdccdddccdccccbbdbababccdbbcdbcbabbbabdcbabdcbabdccdbbcaabbdccbabdddabcddcdcacdaaaccabacdcddbcbbdacabcddcdacdddacdaacadabcdadbdbaadcadabbadbdbcabcdbddaabdcddbbdcccbcdaadbbbcdcdadcaddddabacbacccaddbbbccbaadcdbdbbbcaaaaccbadddbddbccdcccbacdcbbdccacdbbcccbcbcaaacbdcbccdbcaabbcbbbdbbabbdacdacaccbcbddabdbcbadadcdcdbabbaabaccbcbdbdbdcadbbcbbcbccaddcddbacbcdbcbadabdcdcbbbdcddcbadcdadcdabdccadbacddbdabcddaccabdaadbbcacbdaadcbdddbcccbbbacdbcdbcbbdacbbdcdbdabdbdacbadbbcadaacaccdbacbdacccccccbdbdbbacacaddaddadcdcbcabacbcdcbbcbcaadbdaadbbdbbddcbbddacccabccbacdbcbaccdadacadccaaaabbddcbabbcbbadddaddbbcadddcbaccaadbcbbbbabbccdcbcdbaddaddcadccabbbaddcabdacdcacacdaaaddcdbcabddbbdaaddbdccbbadadbbdbdcdcaadddbdcccacbbbacdaacadcabbaadaddcdbcccdcdcddaccddcbadbcbdcbacbbcaaaaadacdbdbbdbddaacdbdddabadbbdcddaacaaabdaacaaaadddcadcaaddcadcdadbbcaabcdaccabbdbccdbabbaaabdcccbaddacbcbcdbcdadddbacbaabddcaabdaadcadccdcdaacadbbacdaaddaaadbcbacccbcdbcccbdacdabacbadadbbdcbaaabcabbcdcccabdcdabbabaacccbaaabddaaacacbbcbadaacbcacdadbbbbdbdcaaaadcabbbdabbcccbcccdbbcbaadcaabadadaaacdbaadcccbcaaadacbaabadddababddcddcdaddaaadbacadaddcdaaccccaacdbadcaaadadbdbdabbbdbaacdaaaddddddcadbdddcacbdbbcabbbcdbbdbbabbbcbabacbcbabaaadcbddabcbdabacdddbabababddddcbbaddcbbddbdaaaadacdadddadbbbbdaacbadbbccbdacdccdbdbdbbabbbdbdddcdbcbcdbdcddddbbabcbaadbacbdccdccdcabaaaadaccdbdddbbaabcdbccdcbccaababbccdabccaaddacaccdcdbdbddbbdbaadcdcbbadbccdccdaacccbaabbcbdabddcbcaadabbbdbcaabbbbacacdabcabddadcbdccacdcabbcbcccbccaacdaddadbadccadddddcdccccddddabdcadaacdabbdaadbaccacddbaddaaddbabbabaadddddaadcbadabaaccacbaddabadbddabbadcbcdbbbcacacddbbdaccaaabbccccbdabcbaddadcdcdcaadadbbdacccdabdcadbcddddabcccabddadbccddaaccdaccddabddadbbbaaddcbabadbbcabdcacabcccacadbcbccdaadabdccdaabdbcbcbaaaadbcdbbacabccdbbaabcbbcacaacdacbddccacacdbdccbacdcdabaadddbcacdbbcadaddacdbabdddbcccabbdccbdaccdcdbababbbaacdbcbbbccbbdccbabdaacacdabbcdddccdbdbbbdaaabbdadaaddbcadbabaaabccddaacdbdccdaccccadcdadcdddcddbbabbbdbcabbcbdacbcbcbcbcacccccbabbdddddabccdccaadaabbdcadddabbccdbacaccadcbbcdcbabbacacadbcddaddbdcadabacbddacbcccbaacbbdbbddcddadadccabddacbacdcadcbbdcdbadcddadcbcbbcacbbdbabdbdbbcbbaccdcaccabadaababcadbbcdaacadcccadcccddbacaaaadcdbbabacddbdccadacdccaccbcdcccdbcbacaabcdabdadabcbdcccdaacbaadbacccbacaacccdbddacdbacbbaabcbadbdcadcbacbccdbbdabccdcabbcadabdabccdddcabdbadacaaadabdbccaccbbababcddababbbdddbaddccdddaabacbaacccabcbbaddbbcdcadcabcccdcbadcbacbabaddbddadabdccadcbdbbdccbadcabddddabcaccbcdabddccadbdabddccbbdcadabccacbcadcbbacbbdddddbbdcbcbbdadbcbacdcbdbcddccdcbadcacaddcbadbadabcdbcddadbcacbadbcdbabdbacbaadccadcabcaabcbddbbdbbbbaabbaaabdaddddbbdcdccdcadabbdadaddcbcdbdbcdcdcacdaccddcbabdbdccacadabadaddcdcdccbddadbadbcdbddbddcdcdaacbcddcddcccbccbcbcbaacaadacdbbdcdddcdcbadcdcaaacacbbaabcabcacbcabaddcdcddbabcdccddadadbcabadbbcdbdabcddbcdcbcbcaccbdadcbbbddabaacadaaacbbaacbdbbbabacddcaaddacbddaacaacddadbbdccacbabacbddccdccdcccccddcbacabaddbabcccdcbccdbadacdabaadddaccbabdcaccadddaddddacbaaadccdbddacdbcdacbcbababccbbddbabadddcbaadcdaaddadbaaccbdccdcbcadabcbdaddadddcdabadaacabdddabcdcddabcbddbccbabbbbdcbbacbcabbcacdcacddbbcdbacbccdaabcaadbcbbccdacabbcaababdcbdaddcaaccbcbadddddbbbddabccccdbccbcadadcbcbcacbdabddaacbbccbbbbdabbbbccdabdcadbcdaabcdacbdadcdcbcbcbbdccabaadcdbdbbdbccdcdcbdccabddcdcbadbbddccbcabbbabbccaacdcdbacaddcaccbcbcaacaabadbadaddbbccaddabdcdbbadabdcccbdccdbbdbddabaadccdacdaacacccaacbbbabacdddddbcabcdcccbcdbcdcacbbbaaabbbaaaddccbbdcccdccbacabbbaaddabccacaadbbddadbbcbaddcbdccbdadacbbdccdadcbdcaabcbddbdabdccdadcdcddabbddadcadbbaadddcdbabddcabddcbdaadbbcbdadadacadcabaabccdacacdccddaacccabaabbdabdaabcaaaddcbbccccdbdacadacdccbbbcdbdbbacdabaaaadddcccbcdccbccccadacaababaaaaacaccbbcbbcbabbbdbccbbcbdaacbbadcacacadacdcbdbcbddaabadadbdbcadcacaaaabbcbdcdcadcdcbcacddccbbaddbaaaabbbadbabdaccbdabddbdbabbdaacbcbaaddadaaadabaacbacccbddabbcacbdddbccdbdbacdcaddcaccabbccbcbaaabbcadaabadcbbbaaaddccabaaddabbbbcdcbdbcbbabbccdcadccbbacbcdbaaacadbaaddcbccbdadaadadbcabcdddbbbaacbaabdacbbbdabcaccaacbddddadbabaabbdbdbcbcdcaadcbabccaadcbbcacbbacadaabacdcdcdddcbbcadccbddbccdbdccccbdbbdabdbacdcdabcbdbacadaaccbadbabbdbcadbcbdcbcdddcdadbadabcaccadbbbdadcababbdacacdbccadcbbccddadcdcbdbbbadabdcaacabdcabbaadabdcadbbddbabdaccacbcbcccbbbcdbcacdbdbdcccdacccadbabbbbccacccbdacccddcbddabdaabdbbaddabdbacddcdabbadccadcdcabbaaaaacdcbbdaabdcadaaccbadabcbaccddcbbcabdaacbabadccadbabaaddbaccacacabddddacbdbcabbbaacdddcdddcccddcdcdcddaaaddaaacdbdbbaabadabcccbcacaacddabccabdbbccdaccddcccbdddbcdddbcddddbdccdbccbcbbaccbcbbaccdcadcacdbabddbbccbcbcbdaccbcbcbadcccdabcbababccabcddacccaacdaaadaccccbaddbbdbdbdccaadbddcacccdbdacaddccacbcaaabbbbcadccbdbacdbacaccbddabdcccdbadddcdacccabbbbabdaddadbcaaddccbdcaacbacacdbbabbbcbbbdaddbdcabaaadadbcccdabddcdddbbcccccccdacdacdbadccdadccacacbcbbaadbcadbcdddadddddaabaabacdcdacbcdaaacacbcaccccdbdcdbcdccdbcccacadbaabaccacbaaaacbacacacdbdabbccbbcabbcbacdbbaabdbdaabadbdbddcdbdcdaccddabcddabbaccbcddcaccbcbddbcddadabdabbbdacacdabddaaaddabaaadaddadcaccdacbcaccbbddacabdddcbbdbccdcacaaaabdacacadbdbbccacbabadabccbaacdbddbdaddccdacbbcabacdbdbcaccdbdadccbccbdddcdcaccbacbbaaccccadcaacacbabdabdddbccccbddacbacabdccddbddcbadccbabdbbdaaabadaacbdacbaadadcdcddcdccaaababccccadcbbcbbaacdadbbdcdbbacbbcdddbdaadaaaabcabbbbdbdbddcdbdaaadbadcbaaddcdbdbbcbbcdabcabcdbadaddbcacaabbaacdcbcbcbbbdaddadaabbcbdacdabdacaccddacabccabcabbbcabccdadadbbdcddbccdcbaadccabaddbdcaddbadacdbcdbcbbcbdaaaadaccbcbdadcaababdddccaabccacddcbdcdcabbabbcadcacbbacbbbabaadccdccbbcccdccccbccddbacacbdddabbadbadacbbdbbacbbcbbdacddcacbbcccbddabbcacbcbcbbcadaadbcdaaccccdbcbcadadcadddddbcabcadcadbaacbcdbaabbcdbcdabababbbacaabdbcadbcbdbadcaacbbdbacaaddcbcddacacbaaaccaacbbdcbcadbaacdadcbddbaabbbacdcabadbaaaabbaaabcaddaaaddacacaacaccaadcbcacadbabaabbddbcdacbbbbaacacdddbcbacbbbbcbcbdcdbaaaccbacbbcccabbcbcaaabdabddadabbbbdabcbdccaabacabbdccbaddcabcaddcbdddcbcbaddccaabcbcdcacacbccdadccddbcbcdbdbdbacbbdbcbacdcacadccbbdaccbbbaddaabcbddbaccdcddbdbddcbdbdacdaaddabdbadbdaccbcdcbbdccdbbacabadbcbcbabcdabbacdacbbbacaaaabdbbbaddaaacdbabdabccddabaabdabcddcbdcacddddccbbbaadccdbdddccddcbcdabaadabcaacbadccabaaccbdbbcadaaccabacbdacabbdadcddbdabbcdddbcddbacdaabcdbbbccdbbcbdbdccdbabddaccabcdaabdbcccacbbccddbaadbbaddacabbbbacaaaaacdbcccdbbbcadabdbbaabdbcbcddbcbbdbcddcddddddddcbabacbdddbccdcadaddbdbbaabaccbcbcccabccddaaadddacbcaddbccdcdcaddbdbaacbccbaccbdccbacaabdbaadadbbbdccbdbdcbadcbdddaccacbdaacacaababddbdbccccdbcdcbddccbcbccadbbbdbdccbdccbabddacacacbbadadcacbdbabccaccbcdcbbaccdcccaabdacdbdacbacaadddbaaabdaadabdabcacbbcadddabdabdbaddaddadbabdddababaddabaddabbdbbdcdccabcdccdccbbcdaaccabcdadbaaccdbdccbcdddbacccdaacbbcdbddbaddcadccdddacaadacadadbdccbdbcaaccdccdaaaaaaabbbdbccbbcdadcbcabcdacbbabcbccccdbccabdadaddaddcdbcddaabcbadbabdbdbaabbbaabdddaadbacbcabacabcbbaccdcdcdcacbadcbddcbaaaddaccbbbdaaccdadddacdadacdcaaccbdaabcaccbccdccaabbcadaadddcaabcbcbadbbbcbabacacbbacbdabbcbadcddbddcccabadcbcbadcddaacadaccbbabcadbcbbaadbacbcbdddbdacdcdcacccdcddbacaaaaabbdbaaadcabaadbccbbbcdadababcbcadadbbdcdbcdccbcbdcddbabcdcaaaababcdddcbbbdcbccadccabbbdaababdbcbdddbdbddcadcbdbabdbcccabbcdcbbbdadbbaacaaaabcbbddbbaabddacabcacccbbbdadccbabcdcbabccacddbbacbccdcdacaadcadabdcddddaabcddbacbcbcbbccdcabdcdccbacabcaddccbacbbaaddbcbabbcddcbacabacddcccddaadcdbbdabbcccdccbabbacbdcacacabddcbacabadbacbaccabaabbbbdcdbacabdddbababbddcaacbdcdbcbccdadccdabaccabcababaacccabbacaaadcadcaccdabdcdaaaadbbcccdddcdcdaacdadcacbbbabadbddcacabacddaabdccdadccbabaadcbccadccabbaaabbdbccbbcdacaddbadccbcadcccabcabbacdcaccdbdddbbcddbcacdbbcbcdaadbddccdccdbabacdbacbcdccbbdbbdbabccabaabaacaaabacbddababccadbdcacabaabbbbbbbccdcbcabaabbcaacbadddaabcbccabddbcacbaacbbccacdaccaaddbacdcddcdddcadcdbbbacacbddadddacabbdddadadcdbcbdcaacbcdabcaacbcbcbbdadaaabbccbadaabcbcabbccabdaccddbcabacddaabdabddacbcbbdabaadccdcddccccaabababbcdddaddacdaabbcdbdabbaaacddcdddcbbcdbaadcdabccbdabdabddcadcacbaccaaabdbcbbccbbcdccbbaaaddccbcdddccddaacccaabdcdaacccddbcdbcdaddcbcadcbcdbcbcddbbdddadbbaabbbbcdddbaadcbacaaaacbddcdaadbccadabababcdabdddccbccbccbdbcddbbdacdacaaaddcbaadabdaabddddacdccbddacdcdccbdcaaadbcbaccdbcaccaaddcabdbbbbdaacdddacbdbbcdaaadadbdabcdbdbcbddabdbcdddbbcabcdcbacbbcdcccdcdbacccbbcdadbadcccdcbcbaadabbadbdbcacddbcaacccaaabbdacbdcadbacbdcddacacabbbaadaaaabbcadaaddccabacbccdbabacccbbcadbccddddaccbbcddddbddddabcbcbbcdabccadabbbddddcabddcdbdcadabccbdcbacbdcadcdcadddcacbacbaaddddcbdcbcccaddacccddcacbbcaabcbccbcbddddacbaaddccbabdcddcdbcbcdcadacddcaabcadbdaaabbcaaadbccdbbabaddabcadbdcdaabaaddcabaabdbdcaddbbbcddbacbaaabacaccdbbabbddccbbddcbabbbbabccabdacaddcaabcbbdbcbbaadcdaacdbdddacdddcacbcabababcadbdacddcdadbcbabbbbaaaccabaccbcdbddbdcadbcabccacacbcacccbdacdcbbbdaabcaacbcadaaaaaabacccaacdacadbbaccccaadaabdccdbaadbcddbacbdaadcbcbcccbbdbddbabcadccddaaacdbacbcddcddbadcbacdbaabbbdcadabddcabcadcbcaacaabaddaddacdbcadccacdddbddaddcabbcdaccadbacddcbabcdabcadabbdbacdcdacdabbddcccaadcdccbaddcddbaadbbbbacdcdcbcddccdbbcdcbacdccacbcddbdbcadcbacdadacacbcdcdabdcbbbddcbcbccdcdbadbcadbcabdbbddbabbcbcdacbbdbddaaabdabaadaddcccabdcadadcdccaccabcadbccbadbcabcddaddddcbbaccdcdadbdaccddbbccdadadbbcccbccbccbaacdbacbababbbdbdadcaacbacbbdbbdbccdbdbcccbdcdacaddddcdcdabbddadbabdbbcaabdddaabddbdddcdaaddbcaddbbbdddcdbacaccbbaccaaabcaacbabadaacddaadcdbadddcaddaaaadabccdbddbccadcaaaccaacbcdbbabcadadacbacbabccdcaacdcabcadddddbabacacdbbdadccbadabbabacbcdbcbdccbbdcbcdddbdaacbbccdddccccdbcacdddbaadabdbcdacddadbbcaaadbbcabbbcbdcdabbcaaaddcbabdcdabcdbaadbbbddccbacccbbcccbababdccacbaaadabdcbdddcdccbdcacccdaaddbddbcddabadabcdcbacbddabacbaacbddbcbcbcdbcbacaadaddcbddadaadaaaabdddaabcdabcbcdadbdcddccdadccacbcbdbacaaabdacbadacbcababaacbcdcaacdadbbdbdcdaadcaaaabaaddbcdabbabacadbbacaadcbadddcbabdaabdcaadbccddaaaadbbddcbdbcadcadcabbaaccbbddbacbabaabbadcbbcaddbadbacdddaadccabbabccbaccbbacbcadaaccbabcbaaaacbbbbdacdcdbbadaadadcdaabadcdbaadbcddbaabccbcadbcdacccbcbbadadadcacdaabbbdadaaabaccdddbcdddcacdbbccdacabdaaabdbdbbabbcbabbdadcbbcdcbacadbdabaaabdccadbacddadaddddbcddbcadcdbcbcbccacdccbcaccbadcddabadddccbccbddcdbbddcdbccbbbccddadabdaacadcccbadabbcddadcdacbcbdbbdcddadcaaadbccbbabbdaddbcaadbdaaddccccdcaadbbbbacabbbdddabcbbdcdcbbcdddcdccacdccdcbcadbdccddadccbadabcdcbdddadcaaaadbdaabcaccaaccccbbbbcbcdadcdacacdcadcbcabcbdbadcabccacdbadabcabaccaaccaadbcdbabdddcdddadcacdcdadaddbdcddcdcdcaddbdcacdccaabcdcbcacbbdacdbdcdcaadacbaccbdcbccaacbbcdbbaaaadbbcbcbcadcacbbcaadabbcabdcdaabbbdccaddaccaacbcadccccdaacaacddcdcaddcaaadcadddbacaccadaaddbadbaadccdbcdbaccdbddbabaadcaadaadabdbcbacdbbbbdbdbbabccbccbcddabdbdabadcdadaadccaaaadbbaabbdadbacacbcddcccbcacbbacabaddadaaccdbcdbbadbccaccabdddcbcdadbcbadddcdabcdaaadddcacccddbcbcabddccccbabcbcbcddbcaaaadaacabbcacbbccbbdcbcdacaacdbadcbaaddcadbddbddcdbaacbcbdcddbdcaddbaddbaabbbdccbbcbbdbdccdbaaadacbabdaaaabbabddcbcccaaccadcdacacaadcbdbaadcbcbaccacdabdbcbbacdbccaddbbacadbadabdcacdacdacdbacbdadaaaabadcbccdbaabaaacddadacbcaadbcbcdbddadcdcacbabdbbadacdadadddaddbdcbdaddcbdbbdbbcbddcdcbbcadaadacacdccbccdbacdbababbaacbacabbbdbcdccdbcbaacbddbdadcabbdccdbbbaaccbbbbdcbcbaabaacbabaccdacbadadccabbdadbacbcccbdbcbbbdbdccacacccddbccdcdbddcdadbacdbbbacdabccbaabdaacdacccdddadcbadaababaccdccccdbcdbdbacaabdaccabdcdccabbacdbaacadabcdaaadbacdcddadcdcadbdbabdadaccbcdccddccdaddacaadbbadacabbdccbdbcbdadacccbbbbdacdadbbbaddbbaadccbacbddadbacbccbbacacdddcccbadabaaaddacddadbbcdcbbbdcccacbadcbbbdcdcabaaadccacdaadadacdaadacbddcdacdcccabbacbbddcaadcccaaacccbbdaadabdabaacabcbdcddbdcaaaaadabbbbababaaabadcdbddadbbddbaddabaabadacdcdaacdabdccbcbbcdcabaaaabadbccdbccdbdbbdcccbbdccbcbabcbdcbcaabcdbbbddadcddcbdbbbdbbcdcddadbadcccddacaadcddcaadcadaccddcbdaddababcdcacddcddbababdadcadbaddbcabcadcadaddbdbbdaababadcbbbabaadddcdbadbdcdbabdabdbcdcdccbddbcdaacccdaddcdbbabddcdcdacabcddaddbccddccadbacddacbdbaccbbdccdcaacabdbabadbbdcbbdaabccabdbcdccadbccbbdaacccbbadbdbacaabacbdbcbadbcddcccccccbaacddbbdcddabdddbdccdddadbdaaadbacbbaddcaacbdbbbbacbddccdddabcdcdacadacadaadbbcbbabaddaccdacbbbcbddacdcddbbababbaadcacdcadbbcbacdabdbabdbaccbdbccaadccdddacbadcabacdbacabbdbcaaccacacacadacabcaacccbccabaaacbbcdcdbcaaddbcdadcdddbadaacdcccbbadbcbdddccccaacbadddcacbbbcbcdcbdddcaadcbdaddadcabaccabdbabbcbabcbabadabbaacdcbdadadbbbdcbcaaddbbddcacbbbdcacddaaddadbdcacdcbaacbadbcdadabcbbbbadbbbbcacdabaaccbaabcddcacaccccbcaddabbaddaacbabbcbbddcababbaccaaadbaacabacdbcbcdcddacaaaccdabaadcacdbdacaabaabbbbacbccbbcacbaaadacaabddbcbbbbcaadaddaacccaddbcbbcdcadcdbdcbaddcdcadbccacbbdacaaacacabbacbbcddbdbabdbbcbabdccaadddadaddbbdbbabaabbaadaddbdabdbcaacbdccdcdbbcbbacbbcadbdcaaddccaddcdbadccdadbccaddcaabddcaccdcaaddcacccadbdbdbadcbccabcaabddbbddbcbdbaadbbbcdcaacbddaddadaaacacdbbcbacbcddbcddddbcacabdcacdabbaacdbcbdababcbabcdcbdabccccdcbaddacdcdbaddadadaccddabdccddabbbcabbadabdbadaaacbbddcbbdbdddcdabaabbadabbcbcabcddacaababcbdcdddcbaadcdbbaadaddcdbcacabaabacccababccbcbccbcccdbaccadacbdcaccbaabacccacacbcccbcbacbcdbdbdaaccabcbdadbabbaddabacabdcdadcdbbabcccdcbadabdacbbbbabcbbadbbabbcdaaacdadbdcdacaaabaddddcaabacdbbdbadadadccadcacadaccdbbdcbcdabbabadaacccadbaadaabacaadccabcdacbcacbcaacaaddddcbadcaddaacbbddbbcdbaacadaadabadcdacabbcbadcabbdcdbddbaaaddbacaddbcdacdccdabbddacbcdabbabaaacddbcdabcdcdaccabcbbbcccbaddcacbacddccbacbaacbbabbbbadabcaadaacaaadddbcaddaacbaaacddadbccdaaabddbbcccbbadbdbbccbbadbabdaaccbbcaabaaccccbcdaaddcbabbdabaccdbbdcdabcbacdddabaaacabcabbabdcadcaccabcbcbacdcbdbbddbcddccbabccdacdbbccdabdddcccabdcaccbaaacadddccbdccbdaabcdbcbdaabbbacccddcbcbbaddbddacaccabbcbdaccbaddcbcadacdbdabcaddccdcaaabbaacbacabbbcbbbbbaadabcbdaaaaacabacdaaabdbaccabccbbdcabdcddadabdbbcaddccacbbcadcbdbddccadbadabdbaabdabacbccdbabcddcacbcbcbdadcaabbdcaabadcbadadaacbbcdcdddccbacabbbbadbcbcaabbaddacdbbdbdcdccabddabacddabcdbdaaaddadddddcbbabccbcddabcdaaacbaaabcaabdacadcadcbaaabdbdbbaddabdcabcbbbcddccaaaabcdccbcccacbcbcbdbdccacccbbbbdccbacdbcbdbcbcdddcddbbdbcababcbaddddccbaabbcccbdcdabcbdaccaadbddaabdcababcbddbdabbacdadccddccacddcdbbdbcacadbbcbbbdcadcadccaaacbdbbcabcabcbcaabbabcbbbabbdcdcbbcccddabcdbadbdccdabcdaacddcbadddcaabdaadbddcbddcaaadcdbaababbccdcdaabacabcdacacddbaacdbacbbbdccbaadddbadbabaadbaaabbaaddcdadadaacdcdbacadbcdaccdccabcdcaddbaaacbbcadcdbcbdbcdadaddddbddbabcbbbabcbbcbdbdbbccbdabccabdbbcacbdaacdcddacadcaddcabbcbcaaadcdcdabadbccbbdbcdadadabaacadcbbdbcabcdccaabcdadbdbadddbdbdddccacdbabccabcdbddbddadacaccbcdcacdbdbacaddbddacbaddcaddbddddcdcddcdbadbccccbababccacaaddaccaabacdacbddddcdcbbbbcbdbdbbaacbacccbcdbdaadbbaabaabcadaadbabcbdacdcccacbcddcabbbbacbbcddabcdddbcbdaddadbbaadbddddbcbdbccbacadacbdababdbdbcaacccbbabbbdaaabaacddadabbcbcdcbbadbcbbcabcdddaaaacadaadbaacadccbcbcbbaabdabbdaacbdbcbabddccdabaaccabbdaddabcacaddacdddabcabaabdbcaabbbbacaccdccccbdbbbbbccabbcbdadadddbdadacbacacdcaccaadabdcaddbabdbcdcddccdddbbcababaacdacadbaabcbdddaacccdccbdbbdcbcbbacbbdababcdcbbdddbdaccaaaacdbddccbadbcadbcaacbdbdaaabccdccacbabbdbcadaddcdbdcddbadaacacbdcdbaacbbccadbddaabbcbbacdbabadccdaccccadcbcdbbbadddcbcdbdbbbabbadbacccdbcaccddbacaccdacdbdbdbcbacbabcbdbaccccccbcbbbbdbbcabacbcdcacbcaaacbbcdccccbbaccbbadaabacbcbdbcacaabcaccaacdcccbcdbbdbabdcabbccaccdabdcdaccdbabbbcddcdbdadcccacacddbabbbddadcdacabdbccdadbbbdcccbddbadacccbbdabdcdaabacdbaaaaddadabbaacacbcbbacadcabacdadacacccacaccbadacdcdcbbbdbcaacbbaccaacccbadadbabcdabdccbccbcbbddcbbbbbccbabcbbcdabccdbadbcaabcdcddbcbdbaccdcacccaaabcbbbdbabcabdacaadcdadbacddddabdabcdddccdcbabddabdaadbcabbaaabdddacddccdadbcccbbabbcacdacaacddadabcacadcabbcdbccccccbcccaadadccaaaccababcddbadbabdadaddabbabacdcbdbbcccbdcbaddacdbbbcbabdbbbdcbccdcddbcbcdbdcadadcbbcadddddbcddddccabbadabbadabbaabcaadbdcdccdbbbcaaacabcbabaddcbdabbddacabbcadacccdcdbcacabcdccbcdbbbdacdcdcdaacabcabadaacabbcdcddbcbacbdaaacaddddcadcaccdaddacbdaababadadccabccacbcabdcbbcdbaaaaaabcaabbbdacbcdcbccbadbdbacbcadaacaadcbaccaaddbcbabaccbaadcdbccdccdacbcbdccbdddacbcdcdaccdbadaaddadbabcbcbabccadacaaabbbdbcabbbdaaadaabadbaababadbdacddaadddbccdacbaaddbcbcdcdbccbbdadadddccdcabcdccaddaacbbaabacbbcdcccbcccabbadaadbaacbbdccaaadacbcacdbbbdaaacacccadbcbcacaadbaccbbdabdaaaacabcdccadadddcacbbdaabaddabdcaaaddcbcdcccbccbcbbacbcbaabaccddaccbbaaadaaaddbcadbdcbbdcacbbabdaddcacbacaadcaccadbacbdaddcbcadadaccdacacbbaaaacbbbbbacaddbbdbbcaddcaaccddcababbbdaacaadadbdddbdddbbaaccdccccaabdcdbbaabcabcaabccbabccadbdcbbcbccacadacdcbdacdcacacdaacccddaddbcacbacabbcabdcaadcaacadccdbdbabdcccddacbcccdacccdcdacbbcaadcbdddddcbcaccacaccadbcdcccbadabcacdbbcabccdddcbabbadadacbaacabdcbabcbbbdccbdcbabcddbdacadaabadbbdaacbcbadcdcacdabcbbcbdcabbabcbabccacbababbbbcdcaddaacdcaaddaadcaadaabccbcdcdbdaaacbaabbbabdbdbadadccaccaaddcdabcbbdbbbbbaadcbbccabdcbadcddccaccbbbcbdcdcbdacabccbbbccbdbcababadcbcdcaabbbdbaacdbadcbcbbdccaacdaacbcabaacacacacbdbbacbdccaaddddbdadcbcaddcccabbaabdbbbabddabdaddbabbddaabbddbacdbcbcdcacaaacaaddbbdaaadaccdaabdcbabcaddabccdcdbbddddaacccaccdcacaccbaddbacdcbcbbaddbcdcbbbccbdcbdaacadcabadacdbbcbaddadcaaadbaadaccabcaadabbaabddbabccddadbaadbacacccaccadcccdddcbcbddcbabbccadacbaacbdccbdacdcacabdaaaabdcaadbdabccbdbcbaaadaaacadcbbdadddbcbacddddcbbbbcdaaaaaddcdcbdddbabcddbccdbbddbcdcdacdcbabdaabadbdcddccbcccbdbacbddbbcabbbcdbbabccbcbdccbabababaddcbbbdadcddaaaacaadaacbbbccadcbaacabdacdabdcbbcdcaaadcbacdabcaabaacaccaddbccadcddadabdcbbbccdddadadaccadbcdcbcddacdbbcadacbccabacaccacbadadcbbacbacbbdbaadcaccccbbbbdcbbabddacacacacacdbbacdcdaabdccdccacdbacaaaadccccdcbcccaacdbddcbcdbccaacdbbabdbbadbddaccbcacbcabcabadbddbcdcbdddddbadabccbdabbcacaddabbdabcadbbaadaccdcbbaadabaabaadbbdaccdabdcbdbbcdbabcdcacdacbbbbcdbcbabccaadcdbdcbbcdddbadcdbccbdadacdabcddabbbcdcccbcdacccaabcabdcccdcacdaaccbbadcbbbabbbddccadaccaccacbdbcbadabdcdcdbaacabaaabacadccbdbcacaddaddbbcaadabcbbbababdaabbccccbabbbbddbcbbcdcbbcbabdadbbaabdccadcdcaacacbcadbcadaddbcababcacadbbacbacccdccdccabadadadcbbbbcacacaadcccbddabcdcdcddcbaaaccabaacbcdbcadbbdccaadddbcddadbabdadcaddbccdacacaaaccacacbcaccacddbbcdbabbdccadbbbcadadcddaddaabdbcbbcbdadcadcddbaabdccabaacbdabcabdabbbccbdbddddabdcbaccbacacdaccdbadcacbaabdabbcbcccbcccbaaaadcbcdbdbaaacddaadcbaaddbcdaccdbabbaabdcbbaababccccbadaadcbcddabbdbcdcbcbdbbddadadbbcddcdddaaaaddbdbbbdcdbcccdbdddddccbabacbbddbaacadbaccbdcbcdbacabddadadbbdabdddbccaadcadbabbcdbbabaccbaccccbbdbabbbdcdbbcdabcbaabaaaadbdccaccddccabcadcdabaacdccbbbddbdbacadbccaadcbdccccbddcdbbabcbabbdbabcbcccaccabbdcdbbddccadbaccccbaacbaadaaacccddacaadbbdcdcdbbdcbdacbaacddcadcacccccdadccaacaaacddbadbaaaabcadacdbcbccbbcadbccaccbbacabacdcabcabdddbbabbbdbddabadadcbcabccddabccadbbbacacaddaadadccacacdccbbabcaddaccacbaddbccbadcdcbcbddabadbaabacbcacdaacaacbdddcabadcabacdbbabaaabbdcdbdbbdbddcbaacbbbacabccbbaacdcccdabacdbcadbdbdacbcdaaacbacbbcdbaaacacbbbcabcacdbbcdadbaabdccacdccabcdbbdbdacbadadadadcdbcbcaddbdacaaaddcadcbbaabcbcbdddbbdaacdddbadbddacdbbbcccbaadadbcaaaadbbacdadbbbdbccabcacbbcccbcaaccccccbcbcbcbadcdbbddbabcbbdabcbcdaddbcabbddaaddbbbdaccdacbdadbbdddbabccdbcbbbbbccddcccababaaaddcbabdcabcdadbdcdbdcdbaaabaccadbdcaddacdddbabbdbcbadaccccdadbdbdccccdcbaccacdbbbabbabcdbadadabdcbaccdbddcdabdacdcabcccbbbabbdcddbcddacabbdadbcdbdadbaaadddbdbdccdcdadbcbcdadcbdabccabcababddddaacbbcdacdcddccbbdccdbdbadbcabaaaccacacbdabcbaacaabcdbdcbbaabbaddccacaccabacccddcbdaadddadcbbcdcdbdcaabdccbbadcbccaabddabdadadddbdddaacdadcacaaacbbbdbaabdabcddcabacddbdababbcbbbbacbdcbcaacdddcbaccbacbdcacbcbdaadcacbadddacacadbacbaabdbbcdabbaddbdbdadacaddacdbcbaaaabcdabdddaaadbcabddbabcddababccdbaadbddbcadbcdcdaddcbbbbcbbccabdabcdabdcdcabddbddabccccbabbbaddbcaacadddacaddabdbbdbbabbaccbbdcacbcabcbbbadcaaccbadbbabaccbcdccdbabbbaabbcdcacdabcbadcacabbccbadcddcaabdcabbacccaaabcbdcaabbbccacbdccbaabdbdbadcaaababdacdadddaddabcccdadaaddcdaadabbcabadadadaabbbcddaaabdbacdbdadaddbdddcadbcabcadbaabbbaccaacdbcbccaadacbdaacdaaacbcdacaaaacccccddcdbabdcacabcdbcdbcddddbddbdcdcaaddcdcdbcbaaacdbddacbdcbbcdcadbaaddbdbbbaddabbdacaababdcbabcdabbaacacacbdadcdaabdbacdcacdaadbabbddbccbbdacadbcbddccaabadddabdcdaaaaddacacbbadcabaccdbadadbbabbccdbbaddcdbcacbbdccdbbbaddbdcabcbacadbbaadbbcdbbdbbcbcaadbbbdccaadbdabdddaddaccbadbbacbadcacdddbdcdaccccdbcbddcaabdabaccabcaadcaaddacdabdcdaccdcccdccabbadaccddcaccaccdcbbdccbccccadbcaabdbdbcdacdbaabddcabacccbdccacdaadcbddccadcdbabdcddcdcaddddcbbadbdddbbadbccadaaadaabcbcccbaacddbcdbbabbbbaaddabbacadbccbddaaabddcdcbcccccababbcadcbdbdbdbdabcaaaccbacdccdbadcbcdccaadccaacabbbcdacbdbddbcdaddbbddbcaaddbaccbadccaaacabaabccacccabadcccaccccabdaddcbdbbbcaaacdaabdccdacbacccacaabcdbcdacbbacbdbdddbacbcabcbdbddbdcadaaababaabcdcddccacbcddacacbbddcddbcaadbdadbacaaabaabdcbcdddaacddbbabadacccadaacbacddcdabcaddddddcdacdbdabaadcbcdbdadbaddbbabbdbdcbdacccbcacaadcdbbdabcbbddbdbbdadcbbbabcaddbbbcbdcccddbbdacccdccabbdbcabbbdacdadcbdccccaddcdadbbbbcbacadacdcbddaabaadacccdbcdcddbaadcacbbbcacaacdbabbbbacabddcabccdcbbaabcdaccdcccdcabdbbaadbdbbcccabaccbaccadbcabddccbcddddcadabdcdcbaaacbadbaddbabcbcccaccdcaacdcadacadddaabddacdaccaadadadbccdadcbcdbbacbaaddcbccbacdbcabbddbabcacdccabdaddacbcbcccbabcaabaddcbbcccbbbdabccaccdbdaccdcdbbdbacdddcbabdccdbacbdaaaadcadaadbabdaddacacabcbbcddbdcbaaaabbbaddbdbbcccbbacbcbaadcabaddcaddddbbbdcaadccaacbdabbaacdbadabdabbacbcccdddcbacbcadcdbdbbbddbdcdacbbabbcbcbdddaadccdadacdaadccbabacabcadaabcccadcadbdcbdbbcccbbdaaaaccdcaddcdbdaadacaadcaadbdddaaabadcadcccaccaccbbbdcacbdaddcbbadbbdaabacdbbbdcbdbbdabbaddcdcbaacadccbacdacdcdcdbcbabcdabaaabaadaabcacacacbddcbdacaaccdbcccaccadbcbdccdbbaccbabbbaacabdcacbdcabbcaaacbabccaaaadbbaadabaddacbcddabdbccdbbcdabbaacaddcbabaddbbdddbcccbbaccbaacdddddbacaadabdccbbadbabbcbbacddbabdcbaaaadbdacdbbbccacacbcddabcbccadbababbbcbcdbacaddcdcbcbdddccbacbccbcdbddbdccddbcbcbbacbdcabdcabbddbbcccbbdcdbdbbadcbaacdbccbcadababadcacddcbcbbcbaddbbacbbcbabdcdaadcdcaaabcabcbbbccdbaadcbbcaabbbdbabaabbcbaaaccbcbbcdbabccaaabcbcacabbdaccaabddccddcabdbbcbcabacdcbcabcadcccadddabbcbbacdbbdacbdbadbbababcdbccccbadbbcddbdddbcabdbcabcabbbbbbbbacbdbdddaacddbbcddabbdbaacbcaccbabccacdcbcaacbcadacbbdccccdabadccdcdacbcbacabccdbcddabadcdbbbddbaadccadccdaaccdcdbcbdcadcacddbbaacbdcabbcddaadbddccacddadbdddabdccccbdbdbabbdcbcdddcbdcacdaccccdcdddbbacbabcaaacbddddadacdadddadcadccdbadccbccbacadbdcabbddcaaadcadacbbabbcabddcaadcbacaccabacacacdbadabbbbcadccbacbbbcbbbddbdaadabccbabcbcdcbbccadcddadabaaccccdccbcddccbdbadcdddcbbdaaadcbcbacabaacaddcbadcccbcacdabbdadbaaaabbabbcaddbdadcdbdacbacbabdbacbcaabbbaddbacddcddadaddaabacdabbdcadbacabbdbabdcbbccbadbccbcacdbcbbbddabbaddbaccbabdadadcbccbbbbaadbcdaddabdadbbdccacaacaccbcaabdacdabaddaacdacabcacadbdadbccbdddadaaddbdbbccdcacddcbbbbcbaabbabdaadaccabdbbbbbdbadcacadaabccbcaabaacdbdccdacdddcdaccdaacccaccbdcdcdbbbdcbacbbabacbacadddbdadbbcddacdcddbabacabccdbdccdacbcbabcbdbcdbcbabdbaddcbcdddcccccccdbdbbaacadcabcbbcdbacabaacdaccabdcaaabdcbbdbcdcdddcaaabddbddbbcbdcdbdccdccbacacaccabbdcbdbccabdaaacbcccadcbbbdbacdcddadbcccddddbcaabaabbacbddcddcbcabdadcbccdddbbaddabbaddaabacbdbcabbbccbddcbcbcbcdaabcddbccbadacbcacacadbacddcadcdbbddbdbabaccdadbbabbcddbbbbabbbbccbbdacbccccbcbcdbdcdbabaaadbbcbbbbcacdadacbcccbbdcdcbcabbbadbdbbadaacbacbaabddabdbccbdaacaccddaacadccabacbacdabbaaddbacbcaddddccaaaadcddddaabccbddbdcccdacadcbddbaabbacbcbdaddbdacbcbadcbddcdabacddbaadcdadbbdacbacbbcbbdcddaabcaaccbdadddadcbaabccabcbcdbbaaaaadbbacccccababbabcbbdacbbcbbcbaadbadbddddcacbaaabccbdcacadcaabaadcccbacdbbacdcccacdcdacbcbdacaaccdcbaacbdacdbadabcabdadacaadbdbadcbdbbdbadabddbadbbbcddadaccbdcadbdbbddacdcbdcaabcabadccdaddcaaddbdcbdcddbccdcadcdcdbcabaababbcddbdbdacddcacabdabccaabbcabdcbaddcaadaabdcbacdbbdcdcdcbbdcbcadcbbccabcadaacdcaacdabdabadcdbacabbadbcadbadcbccdaadaabdabbccaccadbcddbcccbbbbbcdbcdcdddbcdcabcacbbaccbbcdbccbcbadbbaabdbdaadcacccdccdbbabbbdbaaadcbbccbacbadadaabbbdabccdbdababcadadcbabcacbaaccdcdcdbdccacaaaaacdcacbdbdabdcdbcadddcbbbcbabdbdacbbbccbdcbbddbabacbccbdadadbcdadabcadcbadcaccbddbbadccbcbabcbdabddccadbcccbbdddbdabcbacbddcbbaabbcccdcabcbdccdddbdadbaaaccbcbbbcadadccbadaacccbdcbaabbdbacdaabdcdcabcdadddacddbdddbcadcaabccdacbcacabdccbbbcdadcacccddabadbddacdbdddccccccbbcaddbaabbddabbcbaccdcbddadabccdcdbdbcccddabbaccdddcaddcdbdadbdbbaabddcacdacbdcababadbcdaacbbcddbacadddbbaccadcdccddddccdadacbbddccccaaadabcbcacbdcbdbdabbcbadcddbddbcbbdbaccdbabbdbadccadbddbddbbdadaabbcabbaaabdbcaabddaadccaadacdbdcbccbbcbaaccccddabadabbacdbbabdcbabaddbaaadbcaddaabdcacaacbcccdcbbdddccbdbccdaddbcbdababdccadcdaaccacdacabdddaaadddbaaddacbcdabbbbdacbcbbcbcdcaabcdcccdbddbaabbaabbacdcdbdbaaccbadddcabcbbbdcabcaaababcccccaadcabddaaddddcbadbddcabcddbabcadddcabbddbccaacacaacbcbaddbacacbabcdcabadbacdadbadadbccbdddccbcbadacaadacccccbbbaddccbdaccdbcdbcbabbddcadabbcbdcbcdcdacabbdbcbaddbabaaaddadaaccdcbddddbdccddaddcddccadbcddcbcddbdccbdbddbbdcacadbddddadadbabadcbcbddbcbdddccdbbcdcbbabbcddbbccddbbbacdcddcbcababdadddccabaddbaaccbbdbaacacaacdcdbabdadaacaaaacbbbbddbbbaddbbcabadacbabdaabcdaddacdbaabbacbaacbadcaabcccbcdacbbbdbdacbbcadbabdcbbbbbbdbababbdacdcbbbdcbdadaaabdcdadccdccaccbadcbdbaadbdaabbaddcdcccdcaacbccbbbdccbbcadccdbacaabacdcdddbaaadbaaabcddbcdcbabaabcabbcacbdadddabbcdcbaacbbdaadaaaabbdbddbbccadccdbadcdcaacdbcddaccacdbabcaacaaabcddadabbbcccbcdbdadbabbbabaabacbddacbbbdddcbcbaaacbdbbcacdcacbbdadbbdcabbaacbdbababbdbdaaccacbccbddaddbddbdbcbddaddcbbacccabdadbacbcbdcbbbbacbbcbcbddbcdbbacdddbaadabddcbcdbbbaccbdabdbcccccaaaacccbdcabcdcaaacaddcbbbabdddddababbdabdadbdbaaccdbddccccccdddcaacbbcaccabbdabacbdddbdbddbdaddabbacabcaccadabdadabbdaacabacadbadaadaacabcddbbdbdabdbbdadcaddababdcdbdbbdbbddbacccdabdadadcbacdbaddccaabbabccdbdcaabccdabaddadaabcdbbadacbbbadadabadbdcdcaacccbbabbddbababdbddadbbbcdcbcacdbabaaadccaccdcabbcbddbbdabbccaadcdbabddbbcaabdcacdbccbdcacbbacacacdcbaabbacbaccaaaadaacbdbabcddcccdaadbddbabdddcbaaacaaddddbddddbcbabbcbaababbcdbaaabdcdacacadddabcdbdbbddaabcacdcaaaaacbaababbbddacdbaadcdadabcadaacabdccbabdcaddbcdcccbabddcabdddcbbcadaaacbcddcadcdbaabbaddadcddabcbdcddcbaccbbbcdcbdacccddbdcbcdabcadcadcbdbbadcacaaabbabadcdbdadbacbcddacabddaacdbbbdbccdcdadbccbdbadbbacdadcdaaacdadccbdbdaddaabaaacdbacbbdabdcdddcadcbccbbaddcbccddaccdadaccdbbcacaabcbcaadbcccacbacdacbbcdddadcccbdacbcaaabcbdcdbdbcccdccdbbabcdadbbbaabccdacdadaccaddcadbbcacbdcbbdadccdacdbddbdbdaaabccaadadbaabccabccbcadcccbbadbbbcbabbcdcbbbcaabdcbbcccccbaccaccdddbcbabaddcbdbdbbdcbaabdbadcbddcabacaacbdcaddadccbcdabcbadadccdaccdbcacaabddadcbdcbcadacbaabaaddbaabdbcacbbcadaacbbacaacbabadcdadacdbbdccadbaabdbcdccdbdbccdbbaaaabcdddcbaaacaabbdbadaaddcacdaadbcddbaccadddcdcabcbadabdbdabbdccddadcacaacbddbabadbaddabbcccabdccdbbadaabdcadaabbbbaacdccabdbabddcddabdbcdabcdbacbadbdaadbcdbcbcbababaaaacdbaaaacbabbbdddbccacdddaacdcdaddbbcdbdcbdbbdcdcdbadcaadbdbadacacdadcddabdaabbdbbbbdacaaadbcaacbbbcccddabbccaccbadbaabbcadaacbcdbbccbdccbdbadddacdaadbbbabbabdaaabcaabbdbabbbcbabbcdcabadaddddcabcbdcddcaaaadbbddadaaaacdacbcbaadcdcdadcccaadaccdbddbaaacdacadbdccdbdadaccaacdbadbcbdddaadcaaddbacbdbdbdabcbdcbbbbcdacaacdadaacbcbdbababbdadbdbddbbabaaaccaacbbbdbaddcdcbadaccadaacbaadbbcbdacdacaccabdabdcbcbcdcdbabacccaaddbdabbcdacccaadccdccdbcbaadbadbaacccabcbcbdcbbcacacccbbadbbdbdcaddcccbbddcddddbbadcaccccaadbdcdbddaabdcaabbdadcaacddbcbabadddddacdddcbbcdabccbdadababbabcdbacdcabbdbbdcbabbbbaaaabcdddbabadcaccdbcaccabaacccbcdadbccadccdcbddadcbdbbbcabcdacbdcdcbccacadacccccdaadccdddbbccdabccacddaccadbdbddbabaaccabccccdaabccccbabdbaccdbddcacbdacddbacbcadcdacdccdadaacdaaacaabaadcddaaaadbdddbdacbbdcdccdaddddccababddbcbdcbcddbacbccccdadccbccaadbdbaabcdacdadcacaddccbacbdaacbccdabbbaabcaddbabaaabccdaccdbddadbbcddbaadabacbbcabdcbacccccaddbbdabdbdabadbcbacbbdddadbdaabbbddcdcddbaacabdbacbabdacddbabaabdaabbbbbcbdabdaadccaabcdcaaaccbadcbbbcbaacacddcadccaccabaadbbcbbdbacbbadbcdcdabccccdacbdcbaadabdcccdabcbdccaadcbdaadddbccbacaadccbbdcabcbdbcccbbccbdddcddcadadadddaccbbdabcdcaaddcbcddcbbdbbddbdcbaabcdbddcbcccdcdcddbbdadbcddaacbdbaccacdcbcaccddbcacadcbbbcadbcacaaabddcacdadddddddbadacacccbccaabbdcbbbacdcaaaadbacdcabcdababbaacbbdbcbdbdaddabdcadcdbddbabbbbddddababdddaaabdabccaaadcdacaacccabccdcaaadadaabddccabacbcbcddacbdddcbcccadcddcacdacdabdccacbbcbacdacbdaabacccddddaddbacadcbdbdaabdaacbbcdccdbbdcdbbaacdddcdaccddaacbccbcababdadcadcdccadadcdbaaacbaccaaddbcdaadacdcdcabbdaccbabdaacdbbcacbcbcaaacaccadccacadbbcbacdabdbbcaabbaaabcdcdcbabbadcbcabcacddabddbbdddbccbcacbacbbddcdaccabbbdbdaccadcbdbdabacddadcacabcabadbbddbbaacdacdbcddbcbdabbdacdacbadcddbdbcddcacacdaabbcccccbcbdbbabbddabdccbdccaabdabbdcdadaabcddccbdacaabbabbbaabdcabdccddadbbcabbbaabcdcacdbaaaadcaaacbccabbdbadbcadbaadbabbdadbadccccdcabcadddcbbddbdbcaacdcbbabbcbcbbccbbddaadcdddababdbdabcdddbdaaadbaddcaddacccabadbbcdcadccbaaddabcbdccabbbdbadbcaaccaadcccbddcadbdbcadacadadaccabdccbbdcdddcbbccddccadcaacbbaacaccbabbcdbcaccdcdccbccaacabbbcbcacbdbbcbdcbaddcbbbcaccbdbcbbacccdcbbcbacaaaaacaacaaaacbcacbcaddbaccabbcdaaaabaccdcadbdcbaaccabacdcadababddddacddbbaccadcbacaacabaadadbdadaacbaaadddbcacbdcccbdccbddcdadccbabccadcdcdcdcdddcabbbdbcbbddccabadccabbddcdbdaccbcadacacbadccabbdaabacadbbbcbdaacaabccbbbadabbbbbdabddaadbbdacacbccaadbcaadcddbbbbdcdbcacbbcbabbbdaddcabbcbdcbcdcacccacccdababbaabaacdacadadcbbbaddbbccdababaadbdddcabadbaabdcbbcbaabadbacaadaddccbbbacccbabdcbcdccaddbcccaddadbaadaacccbbacbacdadddbdbcdababaabbdbcbdcbbcdcacaddadbbacadabdadaababbcdcdccbdccbabdbdababcbbbbcababdbccbacdbbccdbadbddacaaacbddbbdbcadbcaccacbcadcccaccbbabcabadacaddcbbaacacddbacbaaaaaabcacdbdaaccacdaacbddddaadbacdcdadcdddadadbabaacbddcbcbbacbaacacccacadbacbaacbadbbcbbcbbcabdcdbabaaccdbccaaddbddcdbcacccbdcaddcbadacaadbdabcddcbcdaccdbdddaadddbdabddccadddbcbbacddbaccdabaccddabcbcbadcdccbddacbcacabbbbbccabbdcdaddbccdcabbaccbddddabcddcadbaddacbbcddadddbbabbdbdccaddddacbbbbbbbcbbadbcbcaabbacaccbaacbcdcbadcaabcbaddbacddaccadcdbaaabdbbcbcabbbcbabccbdcaabddcdbcbcdbdbadcdcaddbcdacdacacadcdcdbababcaaadaccbbdbadacabccabbdaacbdcddcccabacdcabaacbcacaacdbaaaddbcdabcdacddcacbbdbccadacaaaadbdaabbccaaacbacaadcacbbcddacbaacbadacbcdcadbdaadcbaaadcaddacbcbcbcdabaaacdbbabcdddbaabbbaacacbaddbdaddadabaabbcdcbdaadabaddadbacccbbdabcacaadbdccbbcddcbabcbbddcbcddcdabbbbdbcbcddddbdbcbbacadbcadbccdddbdaadaabcdbcdaabcdbbcadcacadcdadcbdcacbaaacacbcaabcbcccdccaadbcbcaaacbbaddadcadbcddbaadacaccbabcabbddacdabdcadccdcdccbadaccaabacabccbddcdabccdadcccbbaccbddbcdaccbadaddbcbcdbcdcdacaabdbbdacabaaaccdcbcadbddaadbaacdcbdabbdddacdbcccdcbabacbdbdddddcadadcbacdbddaddcbdcccbaadbccbbccddabacdbcacbcbcacacbbdbabbadacdbadacbbbbdbddaadddabbabdccdcacaddcaabdabcdbdcabcccacccaaddacbacbacaadbccbdacbcdcdabcaccdbcccbadcaaabbddddadbacbaddbbbdbddbdccddddcdcabdcbbadddcbacbbcdbdcddbcabbcaabccddbcaccbcbababdcbcdcbbacadbcddaacbacbcdbbbbbcaaaddcdddbdaabdbdadddbbabacbabcacbdadbbcbbccabbddccabbbdadbabacdbababbbaaaaacdbbcbdcccabacbacacbabccbbbbabcbaccaccbabccbbbbcaadabcbdcbccabacdbcddaaabacddddcaadacbdbddacdabdaadadcaabdbbcdcbbcbccdbcccadcddddbabcbbaaddaccabbdabaddbdbdaadcdadaaccdbcbdccbcbabaabccbddabdbccaddacdbcaaaacabdacbbacddcaaacaacbabaaabcdccabbadcccdcadcdacdcbbacdcddaddaadccccdbdbbadbddabbbdbabbcdbdabcacaccababaabcbbaabaaccdccdacdccabcadbdaabadaadbabcddacdccadddbcabccdbdddcaddcadbcdcddbbacbbbddcdcbaabdaccbaacdbdaaccbccaadabcadbbacdbdbcbcdbddbcddcaaccacdcadbccdbbabbdadddadbbdaaabbddaddbdddbbabccdacbdcddaabccadabcdabdcccddabbbadcdbbbacdaaabdcdcdcbbcdacccacccdcbadadbcaabbdbbacbdadbaabdcaaccacdbabdbcdcdabdabdbabdccacabdbacdddabcacababcaacbbbbddcabdbaababbabbdcbbbbdbcbccadaacdbdabbaabcadaddacacdcadbdddcbdabdacabbccdaddbabbddacddddbacddabdcccaddbcbcbcbdbddddbccdcaadbdccbdaddbbaadcdacbccbacddbadabdbdccabcaadacdcdcaddaadaaabccbaccabaacbcdccaacbdccdabdbbddcbcaaddaacdbdbcbbbcbaddbbaacbcacddddbbdcbcadbbcadccadacabcdbcbdbcaddcacdbacacbbddadcbccadacddabaadbbacdddaddddbccbabaabcbdbaabacddcadabddbdcadccabcdbbaaccadcadcccbcbbbdacaaaacabacaccdcdaddbaabdcabcbacbaacddbaabcbcbddcaacbaabcbdacbcbdcbbcaaaabdcdcbdccabbdcccbcbaacadcabacdcbcbcbbddadbbadbdbbdcabaabbaacdadbcaddcbccdbabdaddaadaabdcdaacbbdaadcaaadadcbdcacbbcbbbdcbddcabcabaccddaccbcadabbbacdcccadbcddadbadbdccdaddcdcaccadcdcbbdbadbadcacdcacbadcaadccbdcdbdadacdcacbbbabbcbaadcdacaacddccbbaddbdacddaccadcbbabbbbacbdadbcaccbadabbaddbcabcadbdbdbbbbbbcdaaccddbabdbbacdbddbbcbcbdcdadccbdccabdabcccabaadadacddabbacddcaccadbaadddabacdacadbaabdadabbcbaaaacdcbdcbdcbbccbdbbdcddbbacbadcacaaacdbcbaddccdddbbdaadabcabbdbccbdacccdadccdaccbaadacaabbbcbadcabaacdccbbadbcbcbcbcdbcbacbbddbccbbadccaadbcaccdbbaddcabadcbbdbdbdabcbdbcddbdccabcdbdcbdcbbddabacdddaacaddcbcabcabadbbbabddbacbbdadbcddccbcdcdbababdaaadaaabbadcccbcbdccacaadacaccdbbdaadcbdccddbabadbccdcdbdccddababbbabccacdaaacbaadcdbddcacaccdcaddbccbbbbcbbcacdcccdacabdcdbbcbcbbdbadcbdbaacbbddcbdbcbabaddbdbcbabccaabbdcdaddadbacdcacccbcabbccbbadcbbdcacaaddbbcaacbabdbbadcbbbdabbdccccccdbcdabdaaaabaccadacaaacddbacaaccaacaaaccdddacbdbabaadcbbaabbcbcdbbbbbcbddaddbbabcbbabccaacbbdacbccbbadddcbaadcdbddadbbbcbcbcaddcacbacacccbbbacaccdbdaacdbcadbdbbadacabddabbacdcbcbadaabbcdcbdbcbcbdbcaddcdcaaabcadadabbdcadaabddaabbabddddcabdacaccbcbbbdcacabdcbdcdacadaadabcaaacddabbcaccbdbdddcdccdbbadbdbbccddaddccbbdacbdcabbcaddcddadbdadaaabcabbbbbacbcbcdcbcbcbbdacacdabcdcaccdabcbcbababdcbdddaccaaadadabaddaccdbbccbacbabadbddaaacddccacdddabbdbdcbcdadaabbcdcbcbdcaccaabdacdbcdbacadcbbccabcbcccddccaacccacbcaccaaadccdaccbdbcbbbabcadaaadccdbabcababcadcaaabbcdcbddabacccbccdcabcabaaccdaaacadaddcbbaaccdbbaacbcbcbddbcbbaadbbaaabbddcccdaaadbacacbcdccdcdddcdaabcdcbddadcacadbccbbcdbbbddabddcccabcdddcadaadcddcbdacbdbadbdbddbacdcaabdbcadbdaaadcadbdcdcabdbcddccdcaddaadbcacbbdaadcdcdbbdddbadaabdabbadbaababbdbacabdbcbdccababcdaabcddadacbbbabacdbcccbdddbdacadccdcabcacaaccaabcbababcdbdcddbbcbadccbcbcdcadacadcadacaccbaadcabbcadbadcdbadadadcbcbabccadbdbbdadddcadaaacbcdadcabcadbdaabbacddaababcbcdacadabbdcddbccdcaacdcddabbaacbdabddbdbcbbaadbbbbddbcccbdaddccadcaabaadcdccbcadbddabbdbcddadbdababccccabadcabccddbaaaaabcabcccaddaacabbbcdadabaacdaacbbabdbbbabdbbadcbbbbabadabbadddadbbdddcbccaccabbadcdacdbabbbdabacbcacddcdcaaacddbbdbbbbbabcaadadaacacddadbadabbbcacdbbcaabaddbcdbcadaaddcccbadaabbacdaabababaaccdcdabadadadacadbdcbdaccbcbaccbdababadcbdacbcdbdacbadcbbaadbbcddcdbcdddbbccacdbdccaabbdbbcccbdacacdcddbcccbdbbcccabddaccabcaaacabdccbdabcddbacccddbcdaaacaccaaddcacdabbdcdaabbbcbdaadcddbcdaccdadaabcdccddabdbaddbddcddacacabcdbadbcbddcbdacdcbcacccbdcadcdcbbadccbabdcddaadcdbdcccccabadabbcabcacbccdcbccbcabababcbddcaaacbdbbcdbdadabddbcabcdcbcdaadbcddddbdaabaababadabbcddbdaaaccdcbdbcaacadacbccddbcadbbdaacddcdbcadbbdcbdccbcdbadacdaccabaccabacbbadbdcccacbaabbbdcbdaadcaccbcdabbcaaccadacadcabdcdadbbccdcabbadabcacabcccbccaaccbdbcadbaddccccaacacaddcccacbbbddadbaaccccbcbcacbddbcbadddcdaddadbdcdccaccadadcabadcccdacdabdbcbddaadacdacacabbcdcdccaadcbbbbbacacdaccdbdadbdbcccbcbccabbaaabdddbddaaccacbddcaddddccadbcaaddaddbbbacacadbcbdacaadadbaaccddaadddbcdbdccbbaaaccbbccaaddcacdaaaacacdcbbbbbdadadccbdcacbdbdddaacbdcaddbdacadabbdbbdbdcddcaddcdcdbdbcbcbbaadaccaabbadaddacddcdbaabbcbacddbddadcbadccaccdcadcbabcccdacbbbabbbdbddbcabccdcbbbabddbdbadbbccbdaacacdbaaacbaccadbbacabcadabaabddaadcbccddbbdcdbacdacbbacdaadacacbccbbccadbabccbaacadaaadacabccbaacdbddcadbcddcbbbcbcccbdaaaddddbacddbbcaddbcaadddbabcbbadabdabaaabbbadddcbccabadbabcddcbccdbbddcbbcdabdaccadabbaacabadaadabaddadbcdacccacbddbaccbbcdbbbabdbbabaaddbbdbaccabcddacbbabcbdcddcdcabcabdabbccddbabbbbbaabcaccdcbdaabdcbcdcdaadcdbcbacdcdccaddabdbccbcbdacbcadbbcaadbbcbcabdabcbbbbdcbbccbcacbaabadbaaddddcacdccbbcbbabdadbacbbddddaaadaddcacdabbdcddabdacbbdcabdddddbbacaadbaaddddbbbcbacbadbacbbbdbabdabcabadddacdcbacaadddadcabccabbaacdbaabdbcbaccaddcdbccdbaacbbabaccbaccdbddccaaccdcadbcbbbdaddddccacadddcbcabbaaccbbdcdcabdbadacdddcbbabcdabcdbcccbcbadcbbdbdcdddabacddcddcadcaadacaadaabababaabaccdadadbdbbddadacdcaddbacdaabbadbbdcbccacddcdacbaccbbacadacaccbdcabbdacaaaadcbddddabcbadbcbbadddaddcacdbcbbccadadccdaadbbbcaaabddaacccbabacddddbcdabdaccaacdbddbdcaacbccabccdbddcaaaabcdaccddbccdbaadcdbbcdbaabaababbbcabdcdcababcbbccaacadbbcdddbcdabbcbacdacbcbbdbdccdbcabbaacdcabbbbdcabbabbccdcabdbcbacbaaabaabcbbcdaacccaccaaadbaccaacbaddbdbdccbadaadabacdbdbcaadcaabddbccbdcdacacaccabbcaccdadbcddcaaccaaaccadaaaaadcbcddcbccacdcdadaabdbacdaabdbbbbacdbbabdcadadbdcaabacaadbaddababacdadaaabdbbcacbbdcbabadcacdacbdbacddcdbcdaaaaccbdbcbcdbdccbabaaccadabacdadaaabcbbbbccadbacaacdcbbacadbddbaadcbbbaaaccabbbcdbcbbcbabdaccabddaddccdcdcccdcddbbddaabccaaadbacdaabdabbccaddbadbcbcbaddcdaddbcdaacdbbaadaaaccbddcbacadcbaddcaaddbadbccaccbbaadabacaabccbbbaadaccadaccbccacadaccbcabcccbdaadcbacbadadbcbbbbacdacaccdadcaacacccaaadccdcbacbaccbaadacaccdabdbcdabdccabadaabdcadbcaaacbdccdccbdbdaabdabadcbbbaddaabdacacbdbccaaadccdaadbddbaddadbccddbacdcbdbadcbacbbcbdccadcbcbcdbabdbcadbcccbcdcbadbdbdaacabbbbabbcccbddadbaddbccaabbbdadbbbcdddbbaddcdbbdaabbdcabcdadccdacabccbcdaddbbcccbdddcdddbbbbbbddbaddadaccdddabccdbdcbbbcbbaaabbdbdbaaacccbacbcbdaabccddadaaabdbabacaaaccaaaddbaccadbabdcddcddbacadcdcdbaacdbbabaddccccbddddabaabbbcddaddcbdccbcaacbdaccbdbbcdaadddddbdcaaccbacbddadcdbbcccdccadddbaacccadbdaaadcacaadbbaddadbcddcbdbbbdaaccbadabacbccdcaadddcaadccddcdaddcbaccbdadadcdaacbbdccacbcadbcacdbdcdcadadacabddbdbcbabdcdbcaacababcbcdccbdddddaaaccdabaaabaadccabbbbacadcbcbcacbdcbcdbbabddcbabdbaabbaaaaaabaaaadcdaccabdbcbbadacddcabdbacadacdaddcdbacbcbaabbbcbcaaadbddaabbacccdbccdbbccbacaddaccdcbbadcbaacdcccdbdbcababbabdaabcddcacbcadbacdbdbbdbbcbbcacbaadbaacbbcabcacaaabdbbacaccaaddbbdcdbcbdbcaddbadaaccddcdccddadaaabcacacbbadcdcbccaaaabadacdcacabbbdabadccbcbddcbdadababdbdcddbbbaddaacbbacccddccaaadbdadaccacdbdbddbaabdddbbacdabaaadabaaddabbcbadaaacddbbdbbcacdbdcbbdadccbbabbdaddbcaadccbbdbdbcbcdbdabdbddabcdcbdaddcccbbccacabcdbbcaadcbaccccaaabbdbbdcdddbddbcddadbbbababbdadcabbacbbdabbdacbaacbbbddcbabbcdcbacbbaababcadbcdcddcdaaddbbcaaaaacbcbccabbccabccbdbacbcbcbdcaadaddcdcaaccbcababbaaaadcdddabcbadcbcdcbcabcbbabdcababcdcbdbaabdddccdadddbccabdabbcabcdaddccbcbaaadddcabcdcdcbcccdccbadadadddbaabaacbbbababbcadbabddbbdddacddaddccdcacbbdcdabbaabbbbbccbabadadabccaddbacbbddddcdcbcbbddcdaccbbcbccddcccbccbaccdcaaacadacbabbbcabbcdadacdccbacdbdbaccddcbcbdbbdcdaabcabaaccddbabbadddbabdbcbdaddcbcbcbabdbabbaabcddabcabdaadcaacadcbcabdcdbbdddaddacbbcadcddaaaddbbbdcbdacadbcacdaddabcabdabbbbcdabbdacddaddddaddddacaaabcbcbcacddbbabdccdbcabccdbdbaddddbbacaadcaaccaabbdaddacbdcababccaddbaccaccdacddcacdbbcadcaabcacabcddbdbacbdbacbcdabddbcacaabcabdacdaacdbbabbbdbdacbbcaddbbcdcbbddaaaaddbbbbcbbbcdcbdaaacddababdddbdbcccbbcdacabcdbdcbaadabbcbbcccbdddccaaadbdcccdcabcbbdcbbcbdcdadabdadbabccdcabcabdbcbcbbbaccdabadbcbbbadbdcdbdbddddbccbdbdccdabccdadcbcddaabbacdcaadbcaddddddbdaddbaccdccabdacbbabdccddcaaddacdcaacdacdaccababbdababacbdabcadcbadcdddabccadcddacbabbadabbbcacacdccaabbcaadaccdabdadcdddcdacbcdbaaaadbadddcddaaccabcaabddbbbbdcbcbcdacacddcbdaadbdbddcbdccbdbcaccbccdbaabdccccccdbacaaccacbbdbbdabacadacdbcaadaababcccbbbcabbbbbacbbaaabaddccabbcaaaccbbdabdbbbbcdadaabadaddcdabdcdabcaabdcccbacacdcacdccabaacacadaacdabadbdacddabaabccbacaccaacdcbcbddcdcbbcdadacccbdbbcbdddadcaadaabdaaacbdcdbbdacabdaccccadccddbabbbbbaacaababaccdcbdddabaddacbbcaacddccdbaabdaaaacacbccaabdcccddbbaadbbadbdaccdccbadadaaadcbdbbbccbddabbbdabacddbcbcbccbabdbcccacbdadbccdcaacdabdcbcbdccdbbcbcdadcbbbbcdadcdcdabbddadaddddccacabacddcbdcbbcbccbdbbadabcddcbddadaddddcbdbbdbaacdbcdaddaacbcdacbbbabdaadadbbdbdbcbacbacccccdbbbdcdbabcbccdbacbcabacbdccdbcbdcdbabccdcacbccbbdccdddcdaadcaddcddbbdcdbbddacaaaadcccbbddbbacdcabadcbadcbcacbcdadaddbcbccacbdbcadcabdadaadabcacacdbacabcbcccccbccccdacddccbdddaddbbdacaacdaddbaadccabbccdcbcbdbaaaccddcaddcccbbadbadadbddbabddbdbbdcabadcbcadcbabbbbadccacbaadabbcddbbdddcdaacadbddadacddbacadabcaadbbbaabcbdaaddcbccacdbbbaadccacddacadbdbbabbdccccdabbccbdbaccbccbbbcacddacbdbddcbccbbaddddcbacccaddbdccabddbcddbaccddacacabccbbbacbcdcdadcbdbbdacdcbbbabacbaadadadddbbaacacacbcbdccdbdaacdbdbddabaadcdbabdcbccabccacbdadcbbdaaddcdcabacbbcabcccbabcccddacdcaabaadbdabbbbaddaddbccaacbbcacacbbbcbcbdcdacacbddbdbdabbcdbcbbddcdbcddccdbbadbdcbdcbdadadabddbbacadbbcabddacdadaaddbcbdccacdbdbadabddbaddcdbbbacabaabadcdcdabaccaccdbbcccadbdbcaddaabadcabdbcbdcbcdcdacadbabccaabbcdbccaadbbcbadddbccadaaadbdabcdabcaddcddbababbdddabacbddccccadadbacbaabdaaaccddbbacbccaadbdcbbacccbbbdaadcddcbcbcddcccddcbacbadbabbabbabcddabcdbbbdbdacabcbabdaaaccaccdaabbaadabccbbbdaacaaaacdbbacbbacddbaaaccaacabcaccaaabbccbbdadbaacbaacbdccaaacdddadbcababdcbcabadcddcccbbbcdbbcacbbadbdaabbdababcdcccdbcabcdddbdcaddbaaadbdbbcbdbddbaaadbdaacbacadcbbabbdaabdbbbcbdaabcbddbbdbbdccdccaaabcaacdbabccbdccddacbdbadcdbcadbbacdbbabbddcdaddbcccbcdadcadaaddddcadabcbbbacbacbccacbddabacacbcbdddbbdcdbbbdbcababbdaaacbabadaacaacbdcabaccddabccdacccaadbaaccabdcdcdabdcbdabbcbbcbaaaadbababaaadbdaddddcdaaddaabccdbbaaddaccacdbcaccbdaabbaacbdadcddcaabdbddabaabcbacaaabdaaaaadadbbcdaacadabcdbbaccaadcbcacdcbaccdcaccddcacdabaadcdbbbcbadbbdabacdcbbddcbdbcdabaadaacccaacbabdabaadacbdadaadcdccbdadadbcadadbbdaabbdababdbccdaacdcacdbccacdcbaababbdaacdbcbacdabbdaccacbbdcadabcababdbccaaadcaacaaaabdabaabadadbbdaddbdacdbdbadadcacdcbacdcdcbdddbbdbaaddbbbdbbcccdbbbddcacbdcbccdcbaccaccaddbdadacbdbaaccbddacdbcdcbdbdbcdccabaddbdbcaaaaaddaacadacbdccbbbadbbcbaacacbdcacbdaacbbdddddbddcbdccbcbacbbbcbdbbdbcbadbcdbcddbdaadbdbbdaabcdbaccccdbcbdbddcbacbaaabadcbcacdaababdddcdacabcbbadabbcccbdcacbbcdbbacabbdbadddaccddacdaadddadadbccccbaddddddccdadabadbcabdbacabadccacbbabcdcddacbaccddcbdccdbabccbbabcdadbaaabbadbbbcabadabacadabcaababbdabbdbbdbddadccbccaaabdbdcbaddabcdbcabdaabbababcbcbbbdcaadacdccccacaadcdddbdcadabacaacbddbccbdabaaabccacdcadddabdbcacbaddbacbbbadcdbadbcddcaabddadbabadcabdadcacdcddbbbbcdbcabbbbadccdaddbcadbcbaaadcdababbbbdcacbaaacaacbadcbdbbbdbddcccddbaacdacddcbcdbbbcddbcddadcbcccdbaaadbabccbbddbaccbabccdccbacdcccbababdcadbaabcaabbaccabdadbbacaaddbcbbaadbadadcbccaadcdbdcbbbcdaadbcadadcddccabcbbcddcabdcadbdcaadaacdabadcccbbabbdadcacdacabdacabadbbabdcdbdcccacababbcaadadadbcbdbcdabdbddaaabdaddaabaddaaabddbbcbdaddaacbaadabcdaadccdadbdbbdadbadbbdbddddcddcbddbcbdbdadbbccabdbdbbdcaccddcaaadaddbbcccddadbaacbbdbacabdcdcdbbcbbacbccdccdccdaadbdacabaccabcccadadabdabcdabdcadcdddbaaaabbacbbbddcdddcacccbcdcbdccaddbbdddbcacbbbbccaadbdcccabdaaddaabaddcbcacadccadcdccbcccdbbcbcaacbbdbacdaabcdaaaabaaccabddaccbcaaddbccbcddcdabdddcbabcddddbcbccbbccbdbbdacddaaaddbcbdbccddcccdacdbbdddcabacdbdbadbcaccddbaacbbcdcccddcdaaccddaabacaaabaaabdccabbdbdabcdcbbcaaabadcabcdadacabcabacdbdcbdacadaadababdcccdbdccbcaacdbbdadbdaddcababdbbdacaaccdbccdccabcbcbadacabbaddcaabbcaadbdbbcabbccadaaddabaadadbbacbdccdacbaaddcaaadbcbabbaadbdaadcccaabcabbbbcdaccbdbcbdacaaccbacabbbbbabdddacabbcacabcabaabacccbcbdabccbcdccdbbaabdbbadbdbaacdadcadacacdddddcbdbbbdcdcacbacddbaddaadaaddcacbdbddddcddabbbbcdbcdadabddcbabcdacddacdaccaddcdabccbcbcdcbaaabcaddbbdbabacacbabdabdbdaadbddccabbccbdbddaacdacbddabacabdbdbdbadcacccdbddaabacdcdbacbbbadaadcbdbdddccdcadbcbdcadbcddadbdcbaaaccabcadcdcabaaaaddbccddbddacaadbabbbdcbadcbcbccbdcacaaadbccbddcacadacccaadacdcabcddddcdbcaddabaabaabccdddbddbbdbcddcdbdacdccdcdbcddbaacbbcdabcdddddbddaddccdaaababadaaaacdabcbbbbaacdaadaacbabaadcbcbdbdbcaddbabbdcadbdbdddcaabdbacdaddacccbcddcdbdbbbbcadabacadcdcbacbcbaaabbbbbadabcbdddaccccbadbcaacbccaccacadcadcabdccbdddccaccddbcdbcbacdcdabacbcbddaaaaaddbaddadcdcdacaaabdbcaccadbadbcaadcdadcacaddaabcbaaccaaacababccabacdaadadcabccabcdccaabbbacddcbdcdaccccdacbbbabcdaddddaadaddadcdccddbcacaaabbaaddadbaaadadbccdabcbdadcaaabadbbadbcdbdabdbcbdddddbcacccdbabbdabdabbabcaaddadacababcadccddbbdddddbacbdbdbccbbadbacbdcdbcacddbdacacacadccdcacbddcacdddacadbcbbcabccaaaaacddbbaaabbbabbbbbccaadcdacabccdbdcddddacdddacdacccbcbdbcbdadcdaacaacdbcaaddcdaacbcbacabcaccbaadccbdcabaaadabbbccbdbaabdabababdcddbabaacbcdcdababdcdbccacbbdbcbbbbddaaccaabadbddcdbbdaaabccddcbacbcbdadaabcdddbcdabccdddcdadcddccdcdbcadcccdbbdbcdabcabaddbcccadbadacabcccccbcaabdabcdcadaacbddccabbacccaabcadbdacbcdaaacaccccaacbbccacdcdbddabccaaccdddaacbddcddbdbbcbbcaaddcdccbadacbabbacddddaccadcdcacbbdacacbbbbdaabaddadabdcbcadccbdbcaaaaacbacbadbabcdacbcabcabadcacbbcabdadabaacbacdaacddabdbaabcdcccdcadcadadacabdbacaacbbababccccdbbbcdbbdaadbcdcdcdccbbdbbadddacacddabbdaaacacdcccabcabcaadcadadccbabccbbbcaaacbcdbbdbdaddabbaabaccabbccaadcaabdcdbabdadcdbdcdbdcdabcadaabacdbdcbccadcccbdcdcbddcbcbbdbcdbdacbcbababcbdbdaaddddaabcacbbdcbddcbdabaaadbddcadbabddcacdbabdbcbdddbcbbbccdaacadbcacaacaacaccdaadcbbbdbbcacaabbdbddacbcaddacadcbcbdbcabddaadaddacadcaabbcaccbbdcdbaddbababcbcadbadaccaccbbcaccddaccdbaabbddabbcbddabaacdbddcacadbabcaccbddabadcabbdacdcbaacdcdabcccdcbbccdbabcbddcbdaacdcbddbcbdabdaadaaddacabdbacbbbddcbdbcdbdadcbbbbbcaadadbbdcbbadbacdabdddccbbcabbcdbbaaddbdcbbaddcdcadddabaabdccddbcacdcbbcababacccabbddacdbabbcbddcdaaabbaccbbaddccaabcdacbaaabbcacaacabbaadacaadacccbdbbaadbbaddbbcabababbabacbcbddcbbcbcaddcdddbdadaacbddcaddbdbaacbdbbaacbdcaacccbdccbbaaadacadbdbaddaabbddadbdcbaacbccddcadbaddbadcccadbccabdaacabcabbcccdcacabbcccabddbbaccccdbccadcadcdcacbbbddbaabdaacbcccdbddbcddaacdbcdaacacdbdcbcbaacdbaadbdbbbbcdbcabbdcbcabccccacdcabadaddacadbcdaabdcbccacdaababbcdadcdccaaabdbabdabdccbcabddcaadabdabadbacbababdbcbdaccbcdbdabdbbcacbdabdadcbcccddbbbdbbcadaaabacccabbbcbdcdccabadbacaddcdbacdbbbacbccbacdabbbaaabdbcacbbadadcacbdaacdcbcbbacbddbcadaadaddabbacbddcabbaadaabacdbabbddacbdaccdcaddbddccabddcdbadcdcacbadcdadbbdaabdbddcdcbaaccbcbcdaaaddabdaadbdcbbcdcacbcbbcbdaabbacbcddbcacdabbadacbdccaababcbadcabaacdbdbcbccadbdaaccaadabbbcdaadccadcccddaadbdcdadaddbcddbdcadbbaccbbbccbbdbdcdbdbcbbdccbabaacddbadaabbdcbacacbccbcabdccbdddddbdaaadbcbacdcdbddcbbabcdaaabbaabbbbbaabdddddcabbbabadaccbcbadaacddbdcabdcabababccdaaaadabcbdaabdcbadcaaabadbabcbdcbcdcacbcdbabcbaccbbacaddcddbabaacacabaadcababdbcdbdaaabacacdcbddcbbadddcddaaccbbddbdddabacadccdbccbdbdbbdadbadddacadccbdcdddcaabaaaadbdacabdddcaabbdaabcaacbccbaabdacdaaadbabaaccdaabadaccdcbaaadbcbbbdbccabbcbcbbaaddbcdabaccaacbbccddcaacdaadabccdbaadabbbacaaddbcdadcabacbbbcccbdbdbbcddabcbcbacdbaccdcdbbaddcdacbdbbacccadbdbaababcbaadcdadbdabaadbdbabdcabbbcccddbbacacdcccacbdabcaddccbbcadacdbadcccaacbaaacdadcdccdaacabcbbcbdaaacdabaadcdcaccaacadabaddbbaddaaaabaacdbbdbbdcadbcbbdaaabddaddabccbcabbdcaccbdaddadbccaddaabdbdaaaadbacbcacbcbccababdaacdbcdcabdabadabbdabaacabbdcccddccbccdaacabadbddcbbbbbacbdbadbbcdbbcddcdccbcadbdbadbaacbcadcbdbbadabdcaabdcacddcbcacbaaabdccbacabacbaadcaaddbdabaaddbcccaadddcdcbbaddaacccdabaacabcbbaccddcbdaddcbaacabddcbbcbadcdbcddbcbdbcdadcdbbbbdcaccbbdddabbddbbdcaadbcaccabcaddbabdcdadbddcbdcbadacddadcbdbcdcdacbabacbdcbdadacbdbacddcdaabdcabbdccbcabaabddbcdbacaddaaadcadaaccbcbabaaadcabaaddddacdbbbbaccaadcaacacbadbabaaaaaabdbdcbddcbadadbcccdabbacbbcabbcbbdbcbabddabbdacdcdaacacddbdcbbbdcdaaadbbcccccbbccbbdbbcacdaababbddacdcadacabadacbacbbddabacaccaddbcdddaaacbdadbdcaccaaacbbdddacabdbdcadbdbdbbaccbbcbbcccdbbabaabcaaacbddccacaacbcdbcbdcaacddaacccccdbcabdcababbbabaadabdccadcabdbaadbacdcdbadaabccaaadcdacdcbabbcbdccccacdabccaddcabadaabccbabcbdbcbdbbcacbcccacbbddcddabbbcaabdddbbabddcaaadaadbdbdccbdccdddcbbababadacbdddcdddcccbbaaacabbccdcdbaaccdbcacdabaadbbdacdabddcddbcbbdccdbcaacdacabcddbdbabdbccabddacbdbdbadccccacdcadccdabadaccdbbacbbacadabdaaacdcaccbabbdcbaadadadcadbcbdaccacaccadddacbaaaacdbabdabaccababccdaabcdabccacddaabdaddaabbdbdaabcbbadacabbbbadcabcdddaddbacbbdaccbdccbddabbacacbbabccabacabaaccdaddcaccadbcdacbbdbdbbbbcabdaadacadabcbcaddccadaacabcdcddcacbaccbccdbacddadcadbcbcaabbacbccadaacbdccdadcbcdcdadbbdbcbbdcdbacabcbbdcddaababccbcbbbcbcddcbcdddbbaaccdcaaabcdccaddcbdacbadddbbaacbdbcabcdabddbbcdcacdaabacdcaaacdbadbbdbaaabaaabcaadcaadabcbcdcdcccdcccbdbdbcdbdaacdabbdddbdbdbabaccddaadbbddacccabbdadbcacdbdcabdaccddcdabdacadabbbbcaaddccbbcbbdbcccdcbcdaacdaddcdbbaddbdcbabdbdbbcdbdaabccccaabcdcdaabdccbacdaabcbddcbbbccabcdccccdcbbddccbaadcbdacbadcbbbabccbcdcddaaccdcadcdcbbbbcbdcbdccaacadabbbaaaabdccbdbbadabddabcbcbdadadcaacbbbdcadacdcdbbdcaddabacbcddcadccabcaddbdbaccddcdacaacdbabacdbbbccaddaaccddabdddbddadddbcdabaadcbdadadaadbadacdadcabdbccbaccadcdaacccdabaddabbbbdacbbcbdbbcbcccaacbdcbbdcdbabaaccdcdbdbdbabdbdabacbdabbccbddaabaaadddbdadbacdbadccbbbadddccacddcdadbaaacadcdcbcdbadacbaaccbcabbdbaabadddadaddcbaccbdcdabdcbabddbddcbdbadabcbdddcaccaaadccddbdacdaadcdcaadbbbdbbadbbdccbbbdccdaadbcbcabdaaacccdacaadacddadabdddabccaacbcabccabcbaadabbdbdbbcaadccbbcdcddbddababbbbcbcadaaccbdddadbcdbcccccccbabcadadaaaacabdddddaadacbbbdadaadbddaddababadbaabbcbaccbdaaadddccadccccbabaccbabcacbacbcbadddbdddaccaddaaacbdcdadaadaabaddaaccacaddbbbdcadccbabbcadacddaaabcacbcbdbababdadacacbdaacdaadbddccddacdacacdbacadbcddbcabcbdaccccddcacccaabacddbbbdbbbcbddcadbadbccaccbaccdbcdbdbaadaddcdcccabadddacaadcccdbaaaddcbcccbdbbdbbdbbddccdadabcadbbbdcabbabdcbbdbcbccaadcccddddadabdcccdbbaacaccbaadcbcabbcbbbdbdccabcabdcaadccaddbdbccabbccbbccbdabbcccaadcbaadbbbcccadbaadddacdccabcaaadccabbdcbddbadcababcaabbacbadcdcbcaacbadabcddcddaabaaaacdbabcbbbbabcdacaabcdddcdaadbdbdaddbdbdaacdcacccacdacaadcabccdabcabdbaaccbacbcadcbbcdbbbbbcbdcbaaadbbcddadaabddcdddaddacccbcbcbdaccaaddcaddbacbabadbbbaabcabaabacaacbbdaccccdbdcacdbccaabbacaddbbbadcabdcbcdaabaccccdabcccbaadacbbacdaaccbacaccaadccbacdbccccbbdacdbbaacdadcbdadddaacdacddaacaccdbbadbaacdbadbaaaacacbabaacdccdaccbabccbbcdcaabacbcbcddbaacacbccacbccbccdbddbbaadabacaccdcddddbbacdabcdccbdddbaaadcabaaddcacabccbcdadbaadabbdddbcbaaaacaddbaabbddddddddcdcaabbaaaccdaddbaccabccbaababbcaddbacdcccdddabbcddbabdbbacdabbcbbdaadadbaacacbdcacdbbcddcbbdaadbddaababacabbbbdaddaacadabdbbbdccaacdbcabbcdccbcdbdacdaccdbadabbabdaabcdaccdcacdbcabcdcddbabbaccaabdaddbddbbabcdbdcddcddccdaccdadccbabdbacacaaaddacddacacbcccccddabcbbddbbdcadacbbdbbbbbbbcadacbccdaaaaaaaaadabcacacccaccbaacdcabdccbacccbdacccbbddaabdbbddcdcadadcdabbcbdcdddacbaaccaacaabcbbadabcaabbbaccacbbdacabddcaaacbaababcbadadbacabcbbabbabdcccdaaabbbbddadaabdbdcdabbcccabddccabbaabadababdcaacdadbdbdddbbbdabbdddadbbbdcaabdacdcaabccbbaadaaadcccadddccccddccacacbaaabcaaacccabcaaabccdacddcabdcaacbacaadaaccabddcbbcdabddccbbdacddbdbabaabbaadadabccaabdbdcbcbadddcbdbbdcacbacbddccdbabacdbabdbbccdcbbcbbbcaadaadabaadccddacbbcddbdacccbdccddcdabddbabccccabbacabadaacacdacddabbadacadbdabddbbcbbccadddaaaccbbbbdabaaadadccaccbaddabbcccaacbcacacbbacbadcabccbaddacdabdbbcbdccaabaabcbabbdbddbdadddccdabdadddaaaadadcdcbcdabaaccaababadacbbaadabacbdccddddccbbbbbbbbddbdabbbbaaaaacbbbcacacbbbcbaadaccaabacbbdcacbbbddccdcddadabdbabdbcbcbcacddbddbbbddbbcddbcadabaadacacdddaabdbbacddbcbadcbddbdabdbaabddaddcdabcabdccadadbbdacaadacaaccdcaaccccbbdbabababbaccdcddcaccadaccbcdadbdacacbdddbdcdcdaddcdbadbdbcbacacaadcabbbddbccacacbacddccdcaddcbcbbdcccaaadbddbcdabcddadaabdddadaaabcddddcabcbbbbadbcbabacdbbbbbcdacabccdbadaadccdcbbdbbdbcdcddbccdcdcccbbcbbdaccccdacbddbbaacdbdbcdbcbbccdccdaaadcbcddccdccddcacabdababddabadbabbddabccbccbbcaccaabaaadcddbadccaddaaadddaacbadbdbcabdadccbbacbcccbbdcbdddbdaaadccadbbcbddcdaabdcabcbdacbccccdcaddbddbdadbaabddcaddcdddcbdccdaabcdacaadaddccbddbdabbabacccdccddddbccbaabccbabaabddcdcadbdcaaabdbadbaaabcbaaadbdbacbabdccacdccddabcdaadcadcabcaccaaadcbababbcacddddaadcdbacccaadaaaaabcbdabdbdacacacdbcddbbbddbdbcdbdbbccdcbbaddbcbbdddddaddbacbcaacbadbaaaaacadcdababacbadaaccadbdaabdccbbdcacddddabbdaacdbbdbdccbacdcdcdbddbadabcddabcaadcbdacadccabcaacaacdddaddcdccbcdbddaddbabaabbacbbcbbbccdcaccdbacaaababbbadbbbbdbabdbbadccaaddabaabcbbaacddaddabdcaaddccbacabdadcbadbccdaadbdbadaabdaddaacadbcdabcbbccbbbabaccdcaabddbdcadaccdcdccadddabbbbdbbccdadacbccacdaabacdcbadbdbcaaadcddadaddabcbcbaabcaddcdabadbddbcbbbcbdbdbbacaaddcbcbbabcadadcbacdbaddddbdbcbcdccabbaaccdbcadddbccbbcaaaddabcacacccbddabccbaadcccdddcbcbadbaccabaddbbacacaadcccadbddaabddacacbaddccbacbcdbabcbbaababcbcaadccaaabaadcccbaabacacacabcbbcddddbaccacdccbadabddbadbdadcdccdbccdddccbdabbcaaabacdcbbabcddbdcbdbcbdcdbccacccbaddbdcacaadcccaaccddccbbadcbadbbcdcadaaacbadacdcaaaacbccdadabcbdcaabacaddbdaadbbcadcdbbcbdcddbacdabaabbcdbbdcaaacbcbbacacabcaabdcbbcddaccdddacdcdcccbcadaaabcdbcbabaaccbcdadbddbdbabaabbbdabbabcdabdcbaacccdbbdbcdbbcadcbdbacbcdbadbcdddcaabcbaccddcdccddbcbbdadccacabadcccddaaacdaddabadcbabbdcdcdabbcbdcccbdbabddbabcdabcccaababdcbdaacdcaababbadcadccdcbdbcccdccccbbaabcdccdabbbaacbcbcdcdccbddcdacccacdbbabadcaaaacdcaaabcbdcdacbcacdcbaadbaacbccaadddabbacabbdcdbcbcbccbabbcbabdcbddcbacdddbaacbdbbccaaddccadabaccdaaddcaabbccacadccddabcbaaddbabcadacadaccdccdaacaabbcbbadcdacabccccaabcabddcdaacdbbcddddaaacbcbabcabacddadcadcdcbcccbbaadbcaaddbabacbaaaacacdcbacbdbabbdaadaddbabbdddcaaddccdacbaaccacdaacbabdbbbaddabcdcbdabcbbcccccbbccabaaaabcbcaaacbaabbadbadbadadabcadaacbabcbcaaabdacddbcbdadbdcaddcbabbbddbdbcccdcdcabbdcabdaaaaabbacbbdcdacbdbcbcbcbdbcddbbbcbcbdbaccdbcacacdbdabddddccdccaddbacaaacccaaabcccaadbcccacbabbcbccdbcccdbcddadcbddbbacbaaaabacbcaddcabddbbadcdcdabcdadcacacdadabbdabcbcbdaccbcaaadaacadbbcaddbcbaadbdbbcddbadbacbacaaacddbddcabaabdabadbdcadcddacbabacdbbcaabaacbabbbbcadcdcdbdababcbcacddcbbdaddbcddcbadbabbbcacabcaacacdacdbbabadcdaaccdbadacdcbaaddddbcdaabbccbadbdccabbdaccbacbabbbacaaaddddbaddddabdcacabbbdababbdbccbbdacacadcccbcabccaabcbcdabcbcaddadbadbcbbbcabbcdddbbacccacddccbaabbccbddddcddbddcdaabcdbdbcddbabddabadbbddbddbaadabdaacbcbbbabaaadddabdcdcbadabdbddddccdbcbcbadbbbdabccdadbadddadbadadccccddbbddaabcdaaabadbacddbddcbcbacdacbabaabbcbcacacdabbadadabbcbadddcbbabadcaaadcbcbddcddadbccdbcbcbbdcdddcbbbbcaddaaadadddaccccbdbbcbbabbabccccdaaabccabbacbdbcbbabdaaaababbcddadbabcdddaccaacdbabbcdcddbdcadadddcdbadbacaabbbadcddddabbdaddabdcbcdaacccbadcababadbbbdcdddcdaadbaaacbacabdbdbadbacdddadbaabdbbddcabadbddcbadabadadccddcddcddccdbbacbdbcdcaabacdbaacacacbabcaadcaadabdacaccdcaddbabdbbdcaabbbdbcdcababcdbaccdbcabcddbccbbbdbdcbaccdbabbdabddbcadaadbbcacbdcaddbbbbbaccdcacdabdcabcbadaacaddbdcbcbbaacbddccabdaaddbadacbdbbdcadbaaacdcbcadddccddadabdcddcacbaccbacccbccddccaadadabdcdcbcadbdacbdbccbbdbcaadacbcdddcbcdaababaccccbdadbbadadbbdadbccdcacdcbbcacbddbdbcdbdaaacbddaacbbddbdacccadbaccdbcbcaabaddbcadcddcdcbdcdbcbbcddddbacdaccaacaddbddbadcaabcdccaaccdcbddbbbbbbcdacddabccadacaaadbcaacdaadcabbabbababbbcadacdcdabaaabadbaddcdbddcacdddccdbaaababdacbabababddddacbadbbbddcaadcdcabbbccdabadcccacacaddbbbcaaadaacdaabbdddacaddbabbdbdabbdbcabacddabbaacabaabacabcbadbadbdbacdbacbbbabcbcbdbadcdbbabaacabbdcbacaddacacdaadbdbbaadccaccacdcaddcdcdabacbccdcaddcddadaabbbacdddcddddabacabbdadbcdabbccaddcaacbddbcdbbabcddabadddadcbdbddaadcbdbdbbaacbbccdacaaaaaacdacbcbcdbaacdcddddcdaaaaccacabacbbbabbbccdddcbaddcdaddbdabddddbdbdccacbdaadaabddcbcadaacacdcdbbdbbcdbdddccabbdbababcacbdbaabcdcaaadadadcabaacadcddccbcddcccdadbbbdcbbadbddcdbaddbcbdaacdcacbaadadccaaaaacbbbbbcadcacacdcabcccabbadccdbddcbaccbaccddbacdabdcaddddbcadcadccaadbabacdbcdcbaabbabdbabcdacdbcabdaaabdaabaddcbbaaaacbbadcdcabbcbbcccbbabaaacdabbadcdddaaadcacdbdbbaadbbdbccbadbbddddcaddabbccdcadbbdaabbccddbcabdccbdaadbdcddbbaccabdbcdcbdadadddbbddbcbaaccbbaddbcadbddadadcbcdccbcddacababdbaaccbccdcbbccbdcccabcabaccdddcdbdaccaacccacaacdbabcdabaadaccaddbccbaaaaabbbaddbbdbcdcaabddaabadddbcaccddaacacdcdbbcaadcbdabbcaaccbbbcdaccbdbcacaacbbbcdcaccdcdbcdacacbddbcdcdcbbcdbcadabcacaacdcbacbdbbcacbcadcaddccdbddcbadcdbddcaccaadacccddccbbbcbbabbcbcccadbcbbdcbdcdbccaaacdbbdababdcdbadbcaadddbcbbcacaabcadabcbdcacdbbcbadddaabaacddbddbbddbdddbddcccdabdadcbbcbccccbdccadbcbbbccbcddcaaacdcddaaacbadccbacdcadabbcdaddaabdcbbdcaddcccbdaabbaccbabaccdbccdcbbcccaacbacaddbbacaccabcbcaaaadbadcdabdbbdcbdbcbddadbdccadacbbcadaccbadbcbdcdabbbadbcdbacbbcbcbddacdcdbcdbbadddcccccbbcdbadbcccbcbabcacaccdddaabdcabcbccdcaccddaabddaddcaaacbacadbbaacdabaadabbddcabdbbbbcbdadbddacdcdbaaaddaaccbcdacdbcdbbcdcbacdbbababddbcdcbcacbcccbcadbbadcaaacacccadbaababaadaabcbdaadbdbdabcacabddaddacacccaccddacbabbccaabadacdddbdadaabdbbcbbcaddabbddbabbaddccdcdadcbabddbcccccadabddbbadadbdbadddbcbbaabbadcbdcadcbbcccbcdadcdadcadabcacdcaaaacccddbcaaddbabacabcbacacabcaaaabcdbbbcdcdddbcdbbcbaacbddddcbddabdccadbccdabbbcadcccacaacbaadacddacbcccbcbbdbddbddddadbbccbbdbcdcaabbcbddaaacacbbcbbabdcdacdabbcbbcabababacbcababaaccabbcaacdbdadbaaccdabbbbdadcddcaabdcbdcacdadaddcbddbbcddabcbdbcdddcdcababdcacddbbdabccccbbcdbdbbcddcbcaacdbbccbcdcbdadaadabddabbcacbcbabbaccdbcdbcbabadbabbadbdcbbcbaaacddccdddaccadcaccaaaccddbaadacbbddadbccaabcbdaaccdcbcdbbcdcaccdbcdaddcadcabbabdabcbdbabdbbbdbdccdbdbdadccdcabadccaaccdaccaddcdcdddaccdcbdccadbbaddcadbaacdbacbdcbbcadccbccadbabbaacdbcdacccbcdbccbdccbdbbdadccdbdcacdcabcbaaccdddadbbdccaacbdacdabbccbbdcccccacadaacdccddbbdbcdccbabbcbcdabdadbdbaadaaadcabddabaccbacadccccdbdcbaacaacabccbbbacccccadbdcaccaacbabadcddcadbbddcabbcabbdacbddaccdcdacbbcccabbdddcbbdbbdbaadcaccbcddcdaaacabcbbdabdddcbccccbbbdbababacddcbbaadbcbdbacddccabdadbcdaaddbabcbbacdbddcdcbdabdaadbccdbcdbcabbabbcaccdcbcddcdacadbbdbcacddacabacdbcddcbbaccbbcaadabcbbbdabadbacadbbdccdacddabcbbbadcaadabbcdccabcadcabbaabcdacabbaabdbcadcbdddccdbdbaabbcdddcddadbaabccbbbdaaddabaaaddcbcdbbdaccabadccbccdccbbcbbaddcadccdcacdcdccdcbdabcbaabbbcabbcbabaaabddacbcbdadbcaabcacbaccacccbdbacdaabccdacddadacacadabbaccbdbdcabadabadacdcacaaabdddbdaacacbcdccaaacbbbbbaaddbbcbadcddbbcdbadadddcbdabbacccdadabdcacbcacbcadcabadacccaadbbabdaaacbcabdddbaccaddbaccbacbcabcacaacbcbaadcbdaccbccbcdcdaabbdcdabccbbddbccbadcbdbadabcacabddbdbccdabccbdbaddbbccadbacbdcbbcabcabbbddadccbabaaddaccdbbddaddcdcbacabcaabbcbdddacaddacaadaccdbdcaabddccdbdaabaabacccdddddabdabbaadccbcaaaadcbdddccdcbbacaaddcdacabacccbbdbbdaaddcbabddaabbdcbbdbadabbaadddcabbdbbacbdccdbaddcaadcacddacabaccbacaaaccbdaaacbdbbbbbccacdbdbdaaddcaabcbbcbbbcaddcdbbdbaccbccddcccdaadbdbbccccddadadabcbddccadcabbcdddbacdaabacaaaabbdbcbaadcaaddbaccdacdbccbadcabcccdcccbaaacadcbcccabaddabbbdcbbbcbacbbdaabaacadcbbddadbdbcbdcbccddcaacbddcccdadabccaababbcaaabbdabcdcabcadddddabddddcdabbaaaabcdddccacacdccacddaacddabbccbccaaccdabdbddadbcdaccbbcabaadbadcdcaabcccdbabbdbcaaccdccddbacbbbabdacccddabbcdcdddaaddbdcbacdaaacbabdbbcdbdcbabdabdaabbacadbbbcbbbdcadaccddbabcdadbdddcdddaaaacdbdbaadbccdbdcdacaaabbcbadaccabdcdcdddabdbbddbacadaddbdaaacdacbcdaddddabadadccacdbcadbaacdacccdccbdbcadcddbaaadbdaabbdbabaabbdcdabddcbdbcadddbdbadcbaacdadbdbbbabbcdccbcacddabacdccbdbdaabccbcbababcbbacbacbdbdabccadcbccdcaacbdadcdbcacdbdcabcdadccacacddddccdaacabdbdccddaaadcbbbbdaccbcccbabccdcabacabbbdbcbcdddadbabcbaabbbbaddaccbbddccbcbddabbabdcaaaaccadaaacddbadaabcbbadbdddcdbdbdccbbbddaaaacccdcaccdbbcdabaaaacbbbcaacccddbdacabbcdbcadcbdabccccaabaabbdaacbbcdbcddddacddcdcbdcbbbddabccaddbacdbbbabcdcbccabaabbacadbababbdabcbcdbcdacdbbccccccabbacbbdbdadbcbbaacdddacdabdaadacbbbddcadaaccacadacbdccdbbbaadaccbadacbdbcbadacdcbbccbbbadbbdabbaadcddbdcaaddabaaadaccbdbaaabcbcadbdcaacbadadccddbdcbcaccbbccddbbbbbbcbdadcbaddbbbcbadbccbbdddddddddabdaddbddbdbcbcdbcdccaddbacddbdbabbbddaaddacdabdcbbbababcdddbdcbdddcdadbddaadbcdcabcccbddccddbabddccabdccbbdbcccbdabdbdadaddbbbacadcbcdddbdadbdaabaddabdcabccbdbdcabbdaaccaabcbbacbdcdababdddbdaacdbcbbbcacddacdbcbadccdadccdabbbbbbaadbddacbcdddccdaacccbbcaccdbccabccadadbccdaaccaacbcbbdcabdacdbbbcbabbabacaddbbdcaadaadcddddcaadbddccacbacbdbdddaacaccbbbdcabaabaaddbaabdcbddaacaccccdabbdddddcbbbcdcdcdabcbbccbcdaaabdbbddcddbdcdadbabcdbdacdadabaaabcdcbdbacddbcbccbcaabccdcadbaabccdacdacbdbbbdacccababdbbcabcdccadcaabbbacabbcbcbbdabaccbacaddbbddddddbdabbdbdadcacbcbbcacddbddadaddabcbcdbcdbdaacdadddcdcdbadabaccdcabaaddbcaadbcbccacbddbbdcbcabbbdcbcbccdcbaaddbdcaabbdbddbdadaacaadbbacbccbcbbdcdabdcaabbdccdabccdcbdaadaddbbdcddaabccdcadadacbdcdcccdbddbddcadccdcdbddbadbadddabaaccbddbcdcccdabacadacbcbcbbddaabddabbdcabcabdbddcacaabacbcadcaaacaaabbcccbddbdbadbacbcadccdbbbcbabacbacbbadcaabcbddbbaadcdadabcdbdadaccbdaccabadbbdaaabdbbcbdddccadcccdcdbadbdccadcdabdbdbbbbabacadabdaabbdbacbdddddccbbdadbbababbbbabccccabcddcbbbdaaacbcbcbaccaadadacdaaadbbbcbbddadabcdbbddbccddbdbaccbaddadbcccdddabcdadccbdaacdabbddacbacdbdddcdacbdadadaaccaaacdbddbadcbaadcdbcbabdabdbcdcbdcbbccddadaaadabddabbcccacadbddccbcdddbbdbadcaacbddcbadcadadbadbcddbcadcdacdaabaaccbbcbbdccbadbbdddccdbdadabddacdabbdbdcdacccdccbadbcbccaacddaabcaaacaabacdabaddbcaacdbddddcbcdddaaacabddbbacadddadcabccbbabbdbaacaddccdddbcabaaacbcddbdbdbdcbabdabacdbdbaadbbbcbcccabbaaddadbbdddbdbcaabcacdbdacbccccdadadaaaccdcdbbacdaaaccbacdbbabcddadbbdadbbddacbccbccaccbdddddacdbbcacbcabdaddcabaccabcdcdabbcbddccddbcaacabdbadaabcbbbaacbaccadcdbdcacabbdbdbbccadbbbbbdcacbabcdcbccbaddcddbddaddabacbccacadcccdaadcdcddacbddbaccabcacbcdcddcddaadcacaabbdabdbcdcacdabbbbdcacaddddcdabcdabbdcaddacdbabbbbdbbababadbcbccdaaaadacabcddbacdaccacdcdabacadcddacacabbdbaadbbdbdabdacdcbaabacabdbabdbdccaaabbcabdbcaddcabccdabdccaccbcacdaadbcbabdcddccccbdddcbbadcaccacbbbdaacabdacbabdcaaabcdacccbaabcbcbacaacabaccbdbbdbacddccbaadcdbdaddabaccbbbadddcadbacbbbcaaacbdacdaddbdbbadaadddaacabacacabbcdbcbdbcccdcbbdcacbdcbbddcdbbacabcdaabdaaaabbbadcdddcacaccaaababaacaabacdbbbbdccaabacdcbabbaababdaddcabaacdcddcdadcbdaabddcabcbacacbcdddccbdcadacdcbccbacaddccdcdbaadcbbcdabccadddbccccbdcabbbacbaabdcdcdddabacabccbaadadddcbaadcabcadbacdcbbbbadaccadabbdcbaccccccbccaabcbbaacddbccdddacccbccccddcbacdadbdcdabadcacadbcdcdccacbcddbccdcdbdcdabbdcdbbcbcaaccaabcccdbbdcccdcbcbacacbaaddadcaabbaddcddabcdbbdadbbcccdcbbcddabcbadcccddbadcdabbbcdaccacdadbcccbdaaacbacddbdbaccbabcccdbbcbdddcbcdbdbcabbaaacadbddbbcacdcdaabcddccdccdcbdbbdcaabcddddcdcbcdadcacbcbcabbbcbbadddbbabbbdbddabdcbcccaaadbcccdaabcddcabdadacccbcdadcabccbdbaaddaadbaaadddbbdaddacaadaacbbcdacdbadabaaadaadbcdbdccddbddacddcacddddbaccdcdbdbdbaccbaabccbbcddaadadbacaccadabbcbdddcdadabddcccdcbdadaacbaaabacbdbddaddababcabdacbddaabcaaadaaaacacdaacabcacdbbdbdcaddddcbbccadcbdcbabbcaacbaabdadaccddbcdadcbbbabbacdccadaabbbdaabaaabbbaddacbdadccdbddbbbccddbaadcacbddccabbbdccbbddcbbcdaabcdbccbbdbbcbccccbdcbdaaadccbdcacbddadbdccdbcaababdbbbbdcacaabacccdbbaadababcacbccdcccabadacbcccccdaacbcdaccdadaddbcadcdddcaccbbcbddcccddadbabbbdaabddcdbbabbcbddbabcaabadccbdcbcbacbdbcacbdbdddddcdacdbadbabccbdccabababacadbaacabbadabccbbbccddbcbddaaccaaacaabadaadcbccdacbcbcacdcaacdbabbacbabbdbabcbbdcdcbbdbddacabddadcbdddcadcacdcacacccbdabbcccbacbbacdcbbcacabcadbdbacaddadcadcbadbcbdcddcacdcbcdddbdbdadcaabbaabbbadbccbbbcacdcaabcbdabccdabdcaadcccdbbdccaabcdcacbbbbabacddacdabdcdbcbddacabadabdabdbbccbcbdadbbdbabaabacaaacaacaaaddaabcacccdddbdadaccabcdcbaacbdacbacdaaaaadcacddcbcbccabbbabbaccabbbbadcadbbbbbaccacddbdbcddbbbabadddbbbcadaadccdacabbabdabacdadaadcaaadaddcbcbaabdcbdbabbdaacddcdcdacbdddacbcbdadddabbdbbbaaaacdaabaabccacadabbbcdcdbdacabbdcdbabcddcdadddabdcbdabaababcdaddadccdadaddbddddaaaaabdbddacaadbcbddbddddcbadddcabbbadbdabddbabaccbbbaccbbbcbabccaaccbabbbadbcbdbcbaadccaadcadbadacbdbdbacabababacbbcbdaacbaccbdcbccbcddbaacaabccadbdacaacacbacdcaaaaadccbcdacadcbcdddcbaacdbbacdbaccaacbccdaacbacaddabadbdbbbadaaddaaacaddcbaaddacacadcdcbbacacdbdbddcbdbbacddbcbdbcdcccdbbdcbdabadadcccbbcbcaabdadbbaaaddcccaacaaababdbccddabbadcccdbcacbacaaadacaadbacdbaaacbaabbbdbcaacccdacaadcbbccbdbbacadaacdcabcabcabbdcaadbcdbbbaddabbcbcacdbbbccadccbdcbddccdaacacddcddcddcdbccabdaacabacddabdbdbaaabbccccddccdbcabdbacccaddadcccccabaddbcbbccddadcadbdbacadabbadcdcdcacdaaddcadcaabadaabdbbcbcccaaaacdbcddcddddbbdadbacccdabaadcbcadbacbbddccddbdbdaaabddadcabbbdbcaddabcdbdbdcacbccadddbdaccdccbdbaddcbaadcdbdaaadbdbccdcbdcabcbbacadbdaddcdccdccadddcbdaadbdcdadbddadcdcdbdabbadabdcbcaaadcbcdadacbaccdcdddcccddbdbdcdcacdcdddddbdaabdbdccabcadababcadadcddaacaaccaabddcdbbccccdccdcccbcddacdbdcccbbadbbcadadcbacbcbdbbadcdcddcccccacaacddacadabcacddcccbccbabbcbdaccaabdaadbcbacdccdbadbabddbcddbabdadbcadabdadabaaaccbbcbcbcdcabcaaadbcacdcdadabaabbbccccddbdbbcadbcdbbccdbbbbbdcacadaacbbbabbdcacddbdbaaabbdaccddddbabaccbbabbdccbcaadbacdbcbadcbdcccbcacbabdaaaadaacbabdbbacbdbabdccbcccdcadbbdaaabcccdbcbcadcdddbacacdacacabcdddadccabbbacccdabdcacaaabddcccdabadbabdcbdbacbcababaccddbabbadbbbcabacccbccddaadaccddcbdcaacbabbcbdacdccbadcddcabdbdcacaddcabcbccdcbaddcabbccdbbdddccdaaaaddaacdbacaddaaabdaabcaddabdcbaaddbbbacddbdbaaaabbddcdcdaacbdbcbddcacdbadbdcabacbacddabdcbacddbadaacdcacdabcaccadbaddbbaabcbabbbcbbdabcaadadcacbdcabdbaaddbccbdbacdabddadbabaddacbadccddcddcdaddbdcddcbcdcbcdadaabbddcaddacdaccacddcababcadcddbabdabdcabddcdbaaddbaadacbaabcadbdcdabcadcccadbcddaacdabcaadcdbcadcdcbdabbdbbbacdaddcbbcaaccdccdbadcdbdadadbaccdcdcbbbbcccdddbcddddbdbdacabccccccdbccabcaddaaaccbbbcdddacadcacbabbbcbaabcaddddbbacaabacaaacccbadcdabdddaacadcdbaacacbcccddbbbbacacbdbcdddddbcdbdbacdbbdbcbccbbaabadcacaadccbccdadcbdbdacaccaadabdaaddbccdcbaaaccdcddbbbddacdaccdddbabadbcaaabbcbbcccddcbbddccdcdbdaabcdadacbabddddacaaaaaddbdddbbbaaadbacbdcaabcbccaccccdcbbcaabccbcacccabbbcbcbddbbaccccbbacdbdbcdccabdcadbdcddcdacdccdadabddbdaadacbbbdbdabaccbcaaccccdbbcbabbbdcbdaddadbaddcbaacdacbacbaadccbdacabaddabaabbacdbbdbbaccdcaccddbadacdcbcdccbccdaddbabccaadbbabacbbbbaaddbddcbbaadccadaaacacaaabbcdbdbaadccaabdccabacbdabcadaddadbbaaaddcccbdadbaabbddbdbdadadaaabaacdababcbcaabbadcdbbbbcbadbacbbdcbcddcbabaadbdaaaddcbbaadaaaaabccabbdbbdabacaaadccadbbdbdacdccbabbcabdaaccdcabcacbdacdcbbbbbbaacbaabbcadbcacddacdabcabaabbbbdaddccdbbcbbcdbccbcacaadbbabcbdcbadcddcabbadaadddbdaccbdcccaadbabbcdbdacdddcabadbbabbcaaddccacdccabdddcdcccdccadaccccccdaaddbaccadcbdaaabcbcadbdbdcbadbaabbbaadbaccbabddabbbcadbcbadacadbacbccccbaddbbccbababcbbdaadacdcdabadccddaddcddcddcababbcccccdacdbdcccbdccdbcaacaccddddacccdadaddaacadaccbbbcaacadaaacbbadbbbcdabdadccabaaabccdbabbbdbacdacadacccdadddaabbadadcbdaaabcdddcbaacaaabbbbaaccadadcbacbdacdabaabdcccadcccabddacdadcdbabcdbbaabcddcddcccbaddbcacaacacbadabacdbcabcbdaaaabadcaddaddcccdbcabddbaabdcdadaccbcdaadadcdacbdcbabcdcdddcccccdcbadcdccdbcadacbabaccdbcbbaaddbabadddacabacddaadcdacabacdcbdabddacaacdcccabacbacdadccbbdcdccadaaababaaababcdaabccdbbaccccabaddacaacaaacccdaacacbaaaabdcabaccdcbcbdddaadddbbabccdcadaabadacccabdcbdcabbcbccaddaaddaaadbbbcdaccbbdbbddbccbdccadbddbcacddaadacbddcdcbabaacbcccdabbcdaadbdccaddabacdbccadcbbcbdbcdabaacdcadcbbacdbbddbbaddbdaabdbadaaaccbdddacbabadbddcdadabcdabacabbdcbbbbcabddacdabddabadaaadbacccbbacdaadccbcbcbcdbcbacddbbabbdacadbcacbdbbcdddacbbbacdcacaabdacdbccbbaaabcdbdbdcdbcbaabacacdaadbaccacdbddaacbdbcabdbabcaccdbcacacbabbcadccdcacbbcadaabcdcabdbcbdcddccabbddadbbcacbddcdaacccacabbacacaccabadddbcbddaccbacadabcadbdcadaadcddddaddaadabadbcbbcddadacddcacaabbdcacabbbdaaaddbcdddbaddcdaabcaacddababbccbdaddcdbcbabcccaddddcdaccdcaaccbbdaadddcbddccbddcbcacccbbabcbbccddcaaddabbdbbdbaabcabacdaaabbabddcdaadaadaacacdabaadcdabdabccddbdadbcbdbabcbccddabbaddacddacabcdccabcaaabdccdabbbcbacaacdcbacccdbcbdadcabaadacaaaccbdcaabcdaacccabbdacabccdcbaabdacadccbdbadaaabddaaccadcddabbcddbabbcccccbabddcdccbccaacbdbcdbdcadddcddbddcaabacaddbcddbbccdabaaacbddddcbdbabbacadabaddbaabacabaddcbcddadddbacbaddbabdaabbddbddacccadaacdcbbbbaadabbdacdbdcdbabaaaccaaabdcbcadbdcbacdabcdaccabdbddbbacdbbddcddcdddacaabdcaadcaddccabccbadbdcdddddabddcccbcbacabbdbacbabbdadcdcbbddbcabbccdcaccdbabbcbdadcdcaabcacdbbcacaaabcddccabbdbabbbbabdabbacacdbbbaccaccdacdbbbcbbabdcabcacdbbcaccacdabccdbadaaadcdddbbdcbcabaacbaacdbccacbccccbbcaddabcdbcbcbcbccabababcdcacbbcbbbccccccddddbdabdbdaaccbdddcaababacbdcaccaddcacabbdaadacacaadcbacdbdcccbddcabcbddaccadcdacadcdaabdaacacbacdcbdbbcddddddabbbddccbcddcdbbcadbcbacbcddacaaadbddddccbcbcdcacbccacbdcdbabaabdadccbbbaaaccaacadbccbaabbcdcdbabdddccaacbbcabcdcbbbdcaddabbadaddbdbcabcbbbdcacdaabaacaaddcdbcaaaaccabdcbaabbbdcbdddacdcbbccbddaadcbadbaaaccbbdbcacadadbddddbbbabdaadadadabdcaccdbccdccabddbadbcbdabdddbcbadccbccdddacbbacddbdbdcaadadcacddbaddabadbbbcacaccabdddcbadbcadaabadcdbdbcddcadbccbbadcbbbbcadcddabdcdccadabadcbbdcdccdabababbabddbdddcdaaacabaccbccdacadcdbddbdacbbdacbcdddaabaabadaabdbddccddaabbacbcccbbdbbbddabccccdbdccbacbaddacbcddcacbadbddbccacaaabaccdbcbdacdaaddbccadabdcbcbdbccbddbdacccabdbcdbcddbbadbbabcdbdbcaadddbdacaacbcacdddbaaccccbbcccacaddcaaddcccccacbdcadbdbcccdcccdbbacbbbcaaddbbdcbcddabccddaaacbddbaddbbddabdbccdddcbdcbcbcdbabdacabaacaabbaabcbdadadbbbcaccbbbcaadbdcbcbaabcccaaabacdcbcddabdacbadaaaabbcaacdabcbadccbbadcbbcbdcdbabdcddddcdbcbbcddbcbdadaaadbbcdcdcacabdcdababadccbbdabbbcbaddccadcdcddbcadbddadbbacacbaccdbabacbacddabcdddbcbacbacabdcbcaddbdccacabbbaabbbcbbcaabcaadbadbcabcdddbacbbbdabadbbdbabcbaddcbacbcbcdcdadbcaacbccaadcacadbbabbbbdbbabbbddbaabaaaadccdbaaaddabbccadaaccabbcababcbdddbaddaccbccdbcbbacdccdcbbcdbadddbcaaddbabcdcccacdacbdabbbadbbdcadccaadbababbbdddddbaaaadbbaaccbbcabdccaddadcacdaddcdbdaabcbcdabddaddabbdccbcbdadcdddcbdbbabbcaaadddcdddbbbdacddcdaaacadddaccabcbdacbbdcacaaacddbbbbbbccdbaaadabaddbabcbabcabddcadcdbbabbbdbccdbbbadbacabaaaadbcbdacadcddcbccbdbbccbcbaddbcbddadccdacbcaaadadcccbcdddacaacbcaabddbbbcddccdbaddacaaccdcddbbdabbbababdbddbddbbdbdccccbddcbadcbbcbdcaadcabadbddaccbaadcddabbcbdccbbdcbcddcbaccbacabbcaacddddccabbccbabccacdabddbabaadcdbccbdcdbacdaacccbbbdccbdbaadaadadbdcbaaacaccbcbabadabbbbbbbccacdcabacdcbdccbaabaabdbcdcdaaacbccddbabcbcbbcbdccbbbacdbdabbdacdcdababbccccbcaadaadbbcddbadbbbbccdccccadadcbadbcccddcabdaaadbccbcdbdadbcadddddabccdddccbcbcabdbbbdddcbcabaababddcddbdabbbccbcdbbcaadbcddddddcdbcacdbccccabdaacdccbcabaaaacaacaacbdaaaacbdabcaaaddbbdcdbbabcbacbabadcacdbbcbdddaadbbcbcccbcaabcbbbccdbaabbbaababcababcdddddabbcccbaadddaadbacbcabdbccccddadbbadddddcdbcacaccbbabcbddcccdadcadcbbadbbbbcccdbdcabdbacdabadcadadabdcbaabdddcadbacdbbaddaaabcaadbbbcbdcccdbbabddddbbabaadacddbccdcdbcaaabddbcaaabcdbadccbcbcdbbabccbdbbaddaadbcdaabcabccccaaddcbcbcadbcbbcbbddaaaadacaaddccbaaabcccbdabaaabacccadcbdcbcbbaabcacabcdacaaabbcbcbcbadcbdbcaaaddcddaddccbdadadcdaccbcdaacadabcbbddcdaadcdabacbcdcccbbdddadddbddbabbbdcaaaaadbdbbcbbdaccdddaadbaddcbbacacababbbacdccbdddbadbabbbcaabcacadbbdccabaaddaabcddbcccbdbdabadcccdbcddcaabcadbdadcdccacdbccbdcbccabbcbdaadccbacadbdcadabbbdccddabbbabaadababbdbbbaddcdbdbabbacaaaddcddcbacacaabdbbabacdddadddaacbabddbbdbdddabbddcddccddcadcacacdcccacbacabbcbcccdaccbbbcbbcbbabcdbbbccaadbdddcaaabdccdbcbcccdbcaadcbacdcbbcabacbcaaacbcacdcddbaccaabdbccdccadddcdacddbbbbdccbbacbbacdbcbbabdacadbdccdcbdcadabadabdbbcccacadcbbbcdccdbbccdcddaabdadddcdadacbcaacccbdaabadcbcbcacbccabdbcbbbcddadaadbddcabacdaaacbadccbcddbcbbcdaadbbdcabbdadcaabdbcaaddddcbbbbaddaaabcdbccddbabbaaacadcacadcaadabdadccbddddccbabacbddbcbbdaadbcdbabcbbacccccbabbbccdadcdacabcdcdbcbadcbcdaadcabbbdcccaadcbadacacbcbdbcdabcbbcbcbbacbadcdbcdadabbdcaddbbbadcdbcdadddbadcbbcbbcbccbbbadcabcabbbbcbcabcdacdbdbbbbabaaaccddabacdabdcdaaabdbaacabcbbbabaadbaddaaaabbaddbbcbadbabacbbbabbaacadbdcacaabbbdabbcadacadccaaddbbbbdbabccbccccdbacbcddadaaaaacdabdbdbaccdabdcabdacababacccaabcdddbbbcbbcbadabdcbdccdbbbbdbcdcaddaccddaabbccbbbacbbacdcbdddabccdabcabdcbbdcaacacaabbcccbccaaaaadcdcaabcabcbdadadaddcdacabccacdbdcccbdcddcccdadaabdaadcddcbbcdbbdcbaddbbaacbdbbbadaadbccaacdabdddaccbccaacacbabcabadbdacadabcaaacabcaddabdcbccaaacdbbdbbdcdcdbdacabcabdbbaccbbacacdaaccacbbadbbdccbbdcaddcdcbcabdaabdbbddbdccccbadbdbdbccbcacdaaccddabdbdbaaddcdadcbacbccbbcbbaddcbbdacdbbadacdacaaacdcbdcdbdbbcdbdbbdadcbccabdbcbcbcdcdcabcdaccdccdcaabdababcddcdaadcadcbdcaccacbcbcddcddcbaabddbdbcddddacdcbbabacbddabcdacdddacdbbadababdbacacddccddcacddabdcacbddadacbddccadbacaaadbadddddccaabdcaadbaccbbacbabbacdacdcdacdbadcaccddaaccccbbdbccadacadababcdbaadadbcabddbdabdbbaccaabacbdaadaabddadaaaddcbbacacdadcacdbacccacaddddabdadacaccbddbcbabbdcdbadbcbaddbdcdadacacadadbdbccdcdbaccdaaabcaddcaadddcdbdcbdccadbbcbacbacbaccbdbbabdddbccccccadabadacdbbbccadcccdcadaaabcdbacccbcbcdacdbabbbdbdcaabaddaacdddddadaddddbadcdaddadabbbaddbcbbcdaddcaacdadbdadadcbddbdabddbbcdbcabcdabcdcdadbdadcdcdddcacbaabbaabacdbacabdbdcdcbabbaabaababdbdbbaadcadcccaabcbdbdcadccccdaccdbabdbcccdbbbbaadcbadccdabadbccacabdadacbbbbddcdaaadabcccbccabcddacbcacdddadbddadbdaababbcbcbcbcabbabcddbdacbabdbacccabcadcccbaadbcbacdddbcaabacadadbdaccaadcaababccdacbcbbacdbaadacadaacdbdabddccccacbcdccdcdbcaabcbdcbccacbbbdcbdcdacacdabccbdbbddddcdcddacbddddbadccddabbabccbdbddaadaacacbccbdaadaaaabacdccccdcdabdbddadbbcbbbbdbdaaddbbdbbccccadcacdadbdbddababbcacbbddaddbddcabdccbaddbaaaaccadabcadddaddacadccacdcdcbddaababddacacadaacdaabaacdbcbbbcaadcaabaabdaabaddcababcabbbaaabcdccbacdccdaaddacdcdaadcacaccabbdcaddcaadddcdcdabbaabbdcbddabbcbcbdbcdcadbbdcdabdcbccddbddddbaabbcbbadadaaacdbaadcccababacdaaaaacdbbdccaddbacbbbdcbabacbacbdbaacadadcdaacdaaabcabcdcbcadcaccdcaddcadcabadddddaacabbbdbcabddbccdcbbadbadbcacdccbbabbbcbddcdccdcddaaacadbcbaacbddacabbdcdddbabaaccdabababbbddcbaccbccacbdbacdbcaadadddbcbdaaabdddbccdbadacbdacdcacccaaabaccadcadadcbdadccddddaaacacddcabaccbacbbbcbccdbbdcbdcbaaccdadcdcbabddacaccddcbabadadabbadcabcabcdccccbbadbbbcddbcdcabcbdabdbaabdabdaadabcacddddcbaacacbacbcbbbdccadcbaddddacbbdcaacddcbabcccabddadacacadadcadadcbabbdcadcaaacbaccccccbaddcdbdbbadadcbaddadbadbcbdbabdabdcdddccacacddcdaacdabbdaddccabdadaabbdbabccdbbcddddccbcccacaaddcdbaacacccdbaaddaabdcaabbbadcabaaabbcababcdbadbabacacccbdcaaddcddcabcdbaabddbbabdbbddaababdbbdcddbbccacdccaaacbdaadbddbdaccbdadaadcdbdddbbcabbbdbdcbbacbadddadabdddbcdadaabacabbacadacacabaddcacaaadcccbccbaaccaabbcbcdbbbcbaaaccbcacccbabaadadacabdcabcbaaacadbaabddddbcabbbdacacdaadadadadadacddcddccadcbdbbbaababacddbbadbbcaadadcdacdadacbbccdadcccdadaddbcadcaaccbdcddbdbbcbddaaabacacabbdddbdcaccabacdbbaacadabcacabbbbdbdbcddacdbcccbdbaccddaaacaacbbbbdaabcbadbdddddaddbccacbcdcbdcdcbcddbbddcbddccccccccbcbaccdaadabdbbdaadccadcdcdddacbbcbdacbcdaabdadaccbbbcddabccadcdbdacccbbdabdcdabdadcacbbcabbadbdabbabadbabcddbbdadaccddadacbcdcbbdddadddabbdcacdccdcbcbbaacbabdadbbcdccbbadbadccacdddacdcbacddcaddbdcddbdcbcbacaaaaccdbbaccdaabcddbdcbdbaabcdcbcbbccabdababadadbdcbbddcbbcadbddbadddcbbaccadadbbcacbbabdddaddbaccbbabcbdacaabdbacbbbcdadacadaaccbabcbcccbdcadcdbdcccddbdccbadccbadcddaadbcbdacccbabbbbdcccacbabdaabbbcbcabbbaccdadbaccbbccbbacacaabccbadbbcaddbcbdacbccaccdabcdbbbddcdccbccccbacccbbdcdaddaccdcacddbdbcdbadabddcdcbcaadbbdccdbcabadcaabdacccacdbadacbabadadacaaacdaabdabbdccaadbbbddcbbaccadabbadbadbcdacabbbbcbcdbcadacdcbdcbddbddacbcddddcabcdccbdacabdbbdbdbaaabbaddbcaccabdcdbdaaaddcbabbbcbadbaddaabadacddaaccadbbcaabcdbabccacdabcdcbaddccccbdbdddadcdaaddbdcadbcdcbcabbdcabadbcdbbaaadbbbababbbdddddabbcbddaccaadbcabbadbbccbdabddcdcacbccdccbcdaacbccccdaaadadabcdbaacddcdbbdcacccaadbacacaacdaddaccbbaadadbccddcbaaababdbdadbcdccabacdcbabdbccdadbabccdacdcdddaadbcabbdcbdcccccabbacddaabbdbccbaddcaacbdcaadbbbdabbcdbbaaddacdbadabcadbbdbbcabbdcadadaadaaababdabcdccbdbdaddbabaacbcabbcbbccbbccbcccbbabdaaabddbbdbdcabaaaadbbdddcaabcccaccaacdcdddbbaabcdcbbaccbdbbadcccbdbdccbcadbcddaccbdabbdcbbabccddddbdddbaaaaccdaacdcdbbddcddcbbabbbadbcadddcadcaacddadacbacdacbadcbbdcdddddcabbbdabaabacbaadaabaacdccdbcdcdacccacabdbddddcabdbddcaadddaacadaaacbbaccaadabbadbadddccbbbdddbccaabaabbcabaaaabcbbadcdadbadccbbcdccdddaabcadcbcccdbcbbcaccacbcadbdddbdbdcccddcaacccaddbadcdcdbbbabcbadccccbbcabcbbcaacaabbccbcacdbcbadcddaccdbcbcaccababdcabbdbdcbababbdccaacccccbbcccbaabccabcdbbcccdadddccccacbbacdadbbaabbabacbccbdbadcdccbaacaadcbdcccddcbcabaddbcbccaaabcccbcbdaddcbcccaccdcaabadbcababbbaaaaabccabcadabdcdcbaabbdbdbdbbacccdbbdadcacbbcadcabacabcbcbcbadaddcbccabbdbaadddbbaabdcdddbccbbadcbdaccacbabcadbabdddadbabcdcccbcacaadbbccbbddcbbbaabdcbcbddccbbdbacdaabddcdcccaaaaabbddcdcabcddccabaaaacdddbbddcbabcdcdbadaccccaabdcdabaddbbcacbbcccbbcadacaabddababbddbaacbcddaacacaacbcdacbbabdccdabdbcaccdddacdcbdddababdccacadaacbbbbbaabddabacdddddbababccddacdbabadabcccdcdbaacabbadabcdabcbcdcbdcddbbdddacacccadacbbcdcdcaabadcdacaaaabddcbdcadaaccabdbcdbabdacaddbbaadccbddadaaccbbbdababbaaabccaccabacbaadbcdcdcbdbbbbaadacddccbabcdabcbadababbbdacaadbdddbabbddabbaabaccccbabccbaabcdddbdcadccbcacdddcabbcacbaccccdbabbdbdcabbdcaadcdaabdbadbddcabdabacbcbdddbacbdcaacbcbadccaddcddccacdbddddccbadcdccdcbdbaaadacbcddbbcabdbacbaabaacbadabacbcacdbddcbdbbcacbcacadaccbbccacbcbcdaacdaabcdbaaabaacaaabcadaacdccccbddbcbaaadcadcdcdaabcacddcaadaabdbbacbbcaddddabcdbbbcdcacccaddacadadcddbaddadacbcacaabbccbcaacadbdadaaaadbacaccbdcdcbaadbbbaaadbcacdaabbcadadcbabdaadbaadabbbbcdadadcddacabaabdacdabaaabbddccbddcbbcbdddaccccbacbccdbbbbddcbbdaccddbbdbcccdccbbbdadbcbbadabcdcbdabbccdccdddcaccdacccaabccbdaddbbaacaddcddbacdaddbdbcccbaabdcdaaacbabdbdbdadabaacdddcbcabadbacadbccadcbabdcdbaddbbbdabcaabbbcdbcaccbdadabccddbdcddababdacdbacccaadcbbccaccbbadcdbacbdccccaaadcbabdccdbabdacacddbacbabdcbdbcddaacdccdaddcbbcacbccaabacdcaaacbcdbdbacbcabbaadcccabcaaadccccdcaabddacccdababcaccbacacdbdcddbdbbacdcadcabacacdcbadbbbcddccdcbbbadacdbbabacdddacbddbacccbdbcbadabccaabacbdcdccbcabbabbbbccddcacdddcdbcaacbccbbaacdddacdbadabacbbaaadbbdcadaacbabbcbdbaccbbbdcccadbdbbabacbcdacaddbcdccdabadabbaadcadbccbadbbdabddccbadbcbcabcdbcbabaabacbdaabaaccddcdcacaabddcdcbbccdcacdbadadabaddbaaddddabadbdabccbbdbdddcdcdbccaaccbdaaabaddddcdaddacbdaccbcbbaabbabbbcddadddbcabdbabbcdaddccdcaabdaabcdadaaadddabbbadabcbcadaabaccbacaccaaaacbbcbcccddbddcbbadbdcbbcaaaabbdabbcbccbadabaaacaadccadbcaaddbdcacdcdacbbdcbbdccaabbccbcddcbbcabbabacdcdaddcddcbdadbcadabcaabcbcabdacccddabdbccadbdcbdaaccdbcbcaccbcccdadadccddcdaacccabbabcbbbbacbadcabbbddccbdacaacbcacdbbaaacdabcaccdadbadccdaacabcddbabaabccdacaabdbbbcdbdbcdbabcabbcbdaabacbabaabddcabcbaacacccdaddadacbdbacbbacdabacdaddbbaccdbaaaccdabcddcaaddbcabdaaddcaaacabacabaaccbbcdcaccdccbbccddcabddbabacbdaaccccccbcbcbbaabadbbbcdacbddccadaadddaccaccaacddaddadbadabddddbcaccdbcdccdcdbcdddcaccbcbbbacddddabcbbbdaabdbabddabbbbcbdaaaddbcdccaddddacadabddcaaadabddacbabacdaaadcdcdadbddbdbdbbcbddbcdccbbbdcddbbcdcbbaacaabbcadacaabcbabcdcabaccdadddcbdababaacacaddbbabbabcadbdcbbdaaabddaddbcbdbacbcabaccddddbddadcabdbbabdbacccbddcbdbaacabdaaaabadbcbdabcbdacddccaacbdabbadcddbdbdbdbbabadcbddcdcaaaaaddbabbdacdcddcbababddbbacddcdadabccbdbcccaddbbccddbbcbcacddabacadbcdabddacccbacdadcbabccacdadcbdadacdacdcbcccabcbabdaacbddabaaabdadadbcdaacbbaccbbccdaaacdabbcbacadadbbbbbccdbcdbcdbdadbddddbbcbadccbacddadcddadbbbcadbbadddbbdbbbbabdabddbacbdcdccabdccbaccaadddadbabdabddaacdbadbbabadaadccadcbbabaabbddbccbaaccbbdccdcbbdacbbbdbbaddabadcbcdbbcbbacbbababccaaaadaddcbbdcaaacdadbabbbbaddcdccdcdbdbdbcddadbbabacbcbdcccaabbbababcbdbabaacdacacbabddbcdcaccddccdbbabbdbadddaadddaaddbdbbdcbbabccadacacdcccacbaabaabbdcdbdbddcddcabddbcbacbcbbabbaccbbacdccccbddbdbddbadbacccabbadbcaccddcabcbdbacaaaadaccacdccbaadbaaadcabacbcdbcddcadbccabdcbacacbcbccacdbcddacdcccaadbdcbaabdcdadcadcbbabacabccbbcdacaddcbcdadaddcaadcabbcccacadddbccaaaccbcaccdbdacbbaccddcddaadabbacdddbbbdcaacbbdddbddabacddabcbbaaddadccaabdbdbdccabdadddbaddacbcbdacaddacabadaacddaccdbbabcaaaadccbabcccbabadbabbadaaaddacddadcbddadbbdadccccdcaabbcadbddbddbbbdbdcbaccbccbbacbccdaaadddadcddacddaabdbadcdbccbdadbaaadaabdaadadbbabcbddcaaccacaccadaacacbacabccddcbdabbbdcddabcaaaaddbbbadbdadddcdccabaacabcddaabdcbddddcacddbbdacadaadabbddcccbddcbdbcdddddcaaaddadbbdcdddacdcacdcaabbddaaddcdcbabbbbcaaccabddabaadbbcbaacbcdbacadbdbdbcbcbdcbdcdcacdddbcaadaabdbcccbcadcbbcababadbcdbcbadbcaabacacdcbbcdbdddadcccaaddcaabdabccadcddaddccbccadccdabddbaacabadbddcbbccdbaabacdcacccacbaacabddbdabacdcdbabdbacabbdabaddbbdcabdddcdabadcdccaddddabdacddbaccacadbbdacaaacddcccddaddaadccbcabcdbacccbbadcaccbabdbdbacadadcaccabccaaaaabaddbcbaadcaadadcbadccadcbabbcdcbbcdcadddbcdbbccdcbccddabddddbbcaccaadddcadbadbbaaadabddabdcdacbdccdccccdcbdccaddbcccbacccccccbcbdabccbdacbcabdadbaaaaddacbabcadccabaaccbdddaddaccacbaabcbccccbbbdacadcdabcdcddaddbdabcccaaaacdcdabbacbdccdabcbbbaadcbccaabccadbddbbdacbdccacbbdababddcbbbcdcacacbdcdcbaabdaacdcdcddcccbbbabcdbcbcbacbaadcdddcadbadabcdbccdabcdbaaaaacddbdcaccdaacbccbacababbaaabcacaadcaabaacabdddbdbabcbaababacbabcdbdaacccbdcaabbdbdbcccadcaaacdcaacbbdcccbdcdacccbcabaccdbacbbbddabaabadabacacadcaacaaccaacaddcaabadcabdbbdbbcacadaadacaadbbccacbaddcdaccccdcdacdccaaadabbaabadcddbbdbbaddadbbccbdccccbbabcddaababdaccbcadabddbddcaaacdacaaadbcbdabbcadddabdacbaabdcdcaabccdcacaacacabcdcbababbaabccdaadbbccdcddcaccdddadcdcdcbcbaacabaddcbbcddddbaacdbddaabdbdadaadcacabacbdbcabccbddaabdcdacabbbcccddbcccbdbdacbccccbbbabcadbbdcddabaabbcccbddcdacabddbbbaacaacacdddadbcbccbbbcbbcbbdabdaaddcbbcdcaddbacacbdccdbdbdabaabccdccaddaaacdcbabaccccacddaaadabbbbdcaccbbabaabbcbadbdbbcaabdddcadadadbbdbcdabdcaaabbddbcabbabbcaddddcaddbaacdcbaababbdcbdbabccdbbccabcadbbabcaddccabbccdbbacbdcbadadccdcdbbaabcadbccabacdbadddbadabdacdaadddcdbabdbbabbbddddcbaaabddabddbccbccabbbbccdaccddaddaaabbbababddcbcaacbdadccbbcbacbcbbbdbaaddacacacacabdadaadbbabbcdbccdbaaccbdccbddcdabbaccbcddbabdcaacdbcdbdaaabcaddadcdadadddbccdabcdabdbcbabdbbddddbbbbdbdabdbcdabdaacccccdbaaaccacdcbdbdcbdcaadacabbbdbcddbbaddbdbdcddcabcbaaabbcddcbaccbabaddbbadacbbccdbbaabbcbabcddcdabbdbadcadccbdbcccddcccaccdbccbcccccadbaabbcacbadcacbcadbddcaabdccacdaadcbcddababbabdbdccadbaabbacccddcadbcdcaabccabbaddacbccdbaccabccacdccdddcdacbbbdadadcbdcccbcdcdacdcaadaaabbbddbdbbcaaddaacccacbbbcddcabbdbccbddccaacddadcdabcddbcddcadaaddcdaddddbbdaabcdaddabcbcbddccdcadaddddadadbaaacaabadcaabcbcddbcdcbbcbccbbccaccdaadcbaababacddbddaddcdddddccdcabcabcaacbabcaabababcaaadbbcccbabadbaadcdcbcddabcbaddcdadcbddcbcbbcdbadaaabdadcdbbcdbccacacddbcadccadaabcbbdbbdbbddbdaacbcbdcccbccaccdbbacadccdcaacadddabcbbdabbdbdcacacbbcabddbcdcacadbbcdcdcabbdbaddcbcadcabcaddbaaaabddddbcdaaadadadadaaddaacbbcbdaacadbbdbdbbcdddbabadcbbcdadacbcdcbabbbbbcccabbbdaddcbaabcbcdccbcacbbdbcdacddabbacbcbdbabddbbbbbbdaddadbabdcdddddddcdcbbcbcaccdbacadabadbdabbbcbcdadcccaccacbcbacabbddccacbdcbdaadcadcddbddccacdaddbdbabdddcadcaddadacbbbadbbaddaccacddadccbacccdaadcabcddcbaacadaacaaaabbbacabaabcbcccaadcbccadccbdbadcdcddcbbdbbaadacacccacaadcddcadbddbcadccbdcaaddcaadaccadcbabbdbddbaddcccaddaccdbabdbcbaabdbdbbabdbddaddaccbbdabbdcabdccdacabbabaacbbabcabaccddaaaaccdbaabacbccbbbccccddadcbbccdcdbbcbdbbaadbcabadccdcabcaccabccccbbbdbbbcacbcbaabdcbdacbadabbcdcdccbdcabbdccbdacccdaaaaabacadaccdcaadbdabaadbdbccdaaaddbdcbaadbddcccdbbcdcdcabbbaaacadbbcaadaabbcccaccbdbcbabbcdbbdcdbddcdcbbacdadcbaaadcbbbdddadbdddbbdacbdaacbbdbbccbdbbcaaabdabcbbaabaabadccdbaccaacbcbcbbaaaabddbadbcbcccbccbdddcccaabccbccccadbbbdcacddcbccbbdbabdbaccdccaccadaaaadcdcbbbbbbbbcbccddadccabddbccaadddbbddbadacaabdcaacadabaddcdccddbabacbdbdcdbcacbacccddaabacccbacadbdddcbbbdbdccbabcbbddcbcddaabcbdcacacdcbababadabcbadccbbddddbcddcbaaccddcaadaacaddcaaaadbbaccabddabcbbcbbaccaacddddcacdcbbdacdbcbaabbcccabcdcdbddabbcddaadaacdaadbbbdddbdaaaaccdadaaacccaccbdbbbdcacdcdcacddcdacabbbdaabddbcacdcbdabddabbadcdbbdbdbcadbcaabcaccbacaccabbdcaddaabdacdacabdccaddbbdcdbbcbbbbbdaaadbaddccabdbaacccbcdbbcadcbadcdaaccbdbdccaaabbdccbbccadcddbadaccbacbbacccbddbcccabcddadcdabccacaadcbcdcbdbadbabcbcacdbddadddacdacdabbcbddcbdbcbdbbadcabbbbccabbcbdaddcdcdbdbadabccccababbbdccacaaccadbbadcccdbbaddbcbdbacacaabbaabbdbcaccbaaaabddbbabddcaabbdcdcaccacdbadddaadacddaacbaabcbaaccbbcbcbbccddadcdadcaabcabcbcccbdccccbcaaccbdcdddbadddddcaaacccbacbddbacaccddbaccdcbcbcdcaaabbbaadccaabacabbbbcdbbbacdddbbcdcacbaddbbbccbdbbcbbcdaadadcdcdcccbbdbacbbdcbcadcdbbddabaacdbaccbccccbccaaabadccdacbadbbbbbdcbdbbcbdbaadccdcbcadcdbbcaccbccbaddadcadcbbbbdcdacbcdaccdbbbcbcbbaadbdbaccddcabcddbbbddcaabaacbacbcaadddbdaaadbbddbcabcccadbadbabbdaabbcbccbcdcdbacbacdadbadbadbacdbddcabcaddbcadbbbabdcddabbbaadccadbaadccbccccbdbadaaaaaddabcbbaadbcbbdbdaadacbccadcaabdcdcadcaaadadbadadddadccbddbcbabdaababdbbcbbacbadbaccabdacbbdbdbbcdcbabaaacacbdadbdbcddabdcaddaaaaacadbdbcbcaaacbdbaacddddcabbcbbcbcacdbbbdcadddcbbacabacdbbdbdddddbabddccaaadaddadcccbaaaadbcaaaacdaabdaadbddcbcadddddadddadcacadbacdcaaaadacdaadabbcdbdbcabcadbbddcbcdabaccabaccdcddbbabcbbcbababadacdcdabaaadddbdcbbddccdbbccaccdbcabcbacdbadbabbbdacdadaacbaaddccdabddbdddccbacddbdabccadadbdadcbdbacddaadbbbdbccdaabadadaaddbbdadacdabcacddbbadbbdbbabdbaddaacccaabcdcdcabdcddcaabbdcaddacdaccdcbcdcdaaacbcddbcbcdaabdbddbdddbcccdbbababaacdaadcadacdddbabdadabbdbabbbaaddccdbaacddddcdbccbbadddaacdddbaacacadddadaddcaaddccbacbbabbbdaadbddcbcbbbabbacacbabdadcabbaaddbbadacaddbaddccbbaacdabacddbdbdbcbacddcbcdddbadcdccbdaadbbaccdcaabdbddcccacdadcadbacddbbdbdaadadccbbbadbaacccdcbaaccbadacaddabbcdaaaadbbbabbccdabcbbdbcbbbadcbabdcaddadbaddabcacabbccbdccabddcadbdcacbdcdddbcdabacbdbdadaddbacacbbdadbbdbcdbddddabcbccbacbdcbacbccbacbbcbdbdbbdddccbacccaccccadadbabdbccbcdabbaacbdadddaccacaccbcdbcbbbcadccbbbcbbaccddabddbbabddbbcdbdbdacbababbbbdcddbddacbacadcccabdbbdcbabbddbbbbcdbbaaabdaddbaacdaabcdddcbbbdcdaddbdbbacccbbacbbcaaacaddccadaccddadcabddcabccbccbcadcdbbddcbcacdabcccbaacbadabcdcddcbdabcdabcacbcdbadaabacbadcabdddcbbdaaccaddaabacbbccbacaacacbbcbbabdadccaddaadaccbbbbddcdcdacdcccbaccddbbdadbdbaabcdbaaaaadcbadcacacbddbaacaabdaacbaacbacabdadddbbaccabbbbcbaacdccdabacbbdbdaadaacadaabbccdcdbbccbccadabadcccababaadcddadccaddbadcbcabcaadddabcdbdcabdcdddaabbddbbababacaadbcabdcccbddbbdbbdbbdbccdcbbbaabbbbdcadccabdcddbdaddacbabdccbdbcddbacbdbddccadcaadcdacbbbddbcabdbdcbcccdcbcccddbcccdbcaacdccaaddbbccbdbbcbbddbbaadccdbbabbdacddcdacbcaadbbababcbdbaaabbbccbadababcdcabdbccbddaabbbbbabcbcddccdbdbdbcdcccabcdadcdadaaaabbaaaaaccdcdacabbbddcaaaddabbcabacadccbbdccbbcdcdcbdcddcbbddadaabacabaacaacbabbbadcccbcccccbbcbcccbcaccbcdbadbdaabacbabcbadcccaadacdacacdbacbcdcbbdaaaddaadbbbabacaaddaaddbdbabdbcaacadbaabcbaaabcccaadabbddbdadadaabaabcdaabcccdccbbbaacbbdacacddbaccbdcddbcdabccdbdbcbaddbabacccdcdcaccdcbddbaadbbbccadabdddbbcaccdccddaaccbdaadcdcaaacbaacacabcdccbadbaccbaddccbacdccdccbadbdcaabbcbbccadadccccdadbcbccbbcaabbdbaccccccbcdbddabccddbccbcbbacaadcaddcbbbacbcbcdabcbbbaabbbcbaadaccbbcdcccdadabadccbddccccdbcdcababbbacbdbbaccdccabbbddadabbaabbbbabdcbccadaadbcbbdbdaadbbcacaddaaaddacddbddddbcaacbbbdaaaadbdcbcaaaabaaaccdcadaaccaccbdaabdaccaabdbbcdcaddabdadbaaabbdcabcaacbacacdccbdbaaccddbdbdbaaabacacdcdcbddaccabdbdadabdddcbbcacacccddddaaacbbdbaacdbcdbcdddddaaaabdcbddadaababcadaaddacbabbabddbabbabdcdbddcddcdabccdaacbbaabbbccccdcdadbaaddcbbbcbdbadcbbccdbabdabbacbccadbbddaccdbdccbdadadaccdbabccbdbdccbaddcabbdacdbaacaabaccbddaabbaccbbcbaacdccdcaaacaacbbacddcacbbbdbadbcbdbadbbacbbabccddcddbdccbddaddbbdabacddccabbbcbdcbabbbadaaaccbdbdbccbccbbaabdcabaacbaadcababbbabcbbbcbbacdcbbbcabbaccddbcddcaaccdbbdacddbaaaadbadacaddcbcdacacbddbbddaccdcbbabbcdddccddcadcbbaddcddddaccbddcbcbdcaaaadbadacdabccadaadaabccbcdcadcaadcaddbddcbdacadadbdbdadbdbdbaddccbbabdacabdcbbdccccbbcccdcbbabbbdacaccbdcdcaabaddbccddbabcabcbcdbbbbddddbdbbcdbddcdcbbadbddbaacccddaaccaadccaddbdcbbacabcbabbcdcccbcccdbcbbbbddbbacdadbdcdbabadbaddabbbbabdddadbacacbcccabadcaaaddacbadbbccbbcbacbabaabdaaccbbbbcbaccbcdcbdcadababadaabaacababdabbbbdcdcabadcaccabccabacbcbcdcbccbcbadddcbaaaddcbcdbcdddacbdccbcacbaacdbabccabaacbddaabccbbdcabadddabbaaccbcbbdddcdcbdcdcddbdddadaaccacbcddbccccabcbabadccbbacbaddadacbadcbccabadcacddcdcbbbacabdabcbabaddabccacaddbdacbcaadcababbdcdcdcbcbaaaacdcccbbadabdbddcdbbcbcdadccdadcbabbdcaaccaccadbacddcddccddbbcdbbdabaaabbdcdaaaadbcccacbddcdcbcddaaaaabccbdddcbdcbbdcdcbbbacadddaadcdadadadbdaccdccacabaccdcaccababacabbaccbcdbadbdcbdbccbaaadaabcbbacaddaacbcaabdcdccbbdccaadaacbcbddadbbababdbaccbbbcaabddaddcdaccdbcbdbaaccaacbcbccbbacbdbcabbbacadacadcaccdbbcbdacccaaadbcbdcdaaccdadbbcbabaacadcbdbbcdcbaccabdaaabdabbccadabadbbbadacbccdbdccddbbcdcacddcacbdbbdacccaadbaaaabccbccbccdacbddaddbadaccbdcadcccbcadcdadcabbcdabcbbcdcaabcacbbccccdaacdcdcaacbbcdbbdaaccdcddadaddcbdadbbdbacadbcdaadbbcaddbadccbdbacddcbababbdcbbcaadadcbdbbdbcaadbccabdccbcaaabcdcdbbcddbdadcddcddcabcbdcbbbcbbdcdcaaacdcabddaaadcdabcccacadbacddabaabddbacbbabcbabbdbdcccacaaddbdbabbbabadaccacacbaaabbdddcaaccadacdbacabccdbbdcbaacbadcbbabbdacbcccadcbcdbdcacbbacbcdbbcbdccddbdbcbdbbcdbdacaaabaacabddabddbacaccabaababdaacdcbddddadcbbbadddabcdbcdcacdbdabadbccbacbdccbaddacddcaaacddbadadbabbcbdcdacddbdaccabdaddcdccbdbbdaaabdccbbaaddbbbcddcaabcccdbbcaabdbabadbccabcaaacbbdbdaacddadbdcaddadcabddcaabbbbaaadaddddbacccdbddbcbdcdccadcccbbbabbaccbbbccdbabcabadcccdccdacacbcdbabdbabdbacdacbddcadbadaddcadbdabcbcdaabdcdacdaadacbbcddbccccbbbacacdbcbbcbccaaacdbaabbddcdabccddbabadbdbbdbbbdcdbcadbccddbacccdddccabdddadcbbbccbddbccbacaddadcacadbcbbabddadcdbaaaccbdcbadaacddddbccabacbaaacdbaacaccbdbacabdabccccddcbcbadacbaccccbbdddaaccacbdccdbadbdccbabbadadbcacbcbabcdbdaccabdbdbadabaaaadbccdbdaaddcddbabcbdaddbbcaabbccdbdcabbbbbbadddcdbcdadbbcdadcdddabdadadcbddaabcdbaabdbbbbabbacdabdbbcdcacbcddcbdcdccdcbdbccccbbacdadbadbaadccbbccabbdcccdabdbbbcdabacbcdcaccbcbbadcadcbaccbdddcadbccbacaaaddbcadbaadbdcacbcaadcbadbdadacdcdbbabadaccadbdbccdbcbbccccaccddabaabccccdddadbcdadcddabdbdcccdbcdbbcccddddadadaddbdadacbbdbdabdccaadabcabbcacdbaaaabacbcbdbbbbacabcbcbabbabbdcacbbbbaaabaaaaadbdcdaadccbcaacdcabadbaccadbbcacdbaccbaadcdadddaadddbbabaccadaacacccaaaabcaadcbbbbadccdadacdbcbbbaacddbabcabbdaadcdbcccbdaddcccaddbbcbacacbdcccdbddbddbadbbccddcabdcaddacaacbcbabbddbabbbcbbbbcbdbbbacadaadcddbcdbacacabdbbbcbcbabcaaaacdcacbccdbddbbdcaacbbcdaadbcbadbaaddacbdacadcbdcabddadbaabccbacdaacbbabccadaddabaadcacdcbdbaacdaadcbcdaacbaabdbcabbbadbbdcccbacccbcdcbbdcccaccbdabcaabbbabcbcabcdcadcabcacbcdacdbddbbbbacdcdccadcbabadabdabadbabccbadbccdcaddaddaddbabbbcadbbddabbbcccabbbcaababdcdbbabaacdbdcbbdbbaadbdbbccdbccbaacaabadcbdcbbadddbcdccdaadccadddadcbcbadbbdccccdcdaacdcccbaaaddbcbbaacaaacbbccdbbcadcabcbdccdcaabadbdcdccbcabdbbbcaaaadbbcccabcdcbcdcbddbccbbdbacbcdcccadadabbbcddcccdadcaabaaaabdaccaabaadbbdaaabcbddcaccdadabcdcccbaaabcdababcabddcbdbcaccbbbbcbaacdcbacdaddbbcdcbdbbdbcadcbcbbbacaabdaddabddbdbcbddcbdcbcdcabcaaccaddccdbadbbbdbbaaddaddcbabaaddadcbadcbcbddbcacbdadaabbcddaccbaaaadcbdcdaabbaadbaccbcabdcaadadccbddddcdaddadcbaabadbbdaaadacbbabcbadbbddbbdcbdadccaddaadbcdbbbadcdbbbcbbbacdaabccaacabbddbcbdcddadccacabdcccdddcabaaadcbabdbcacaaacdabacccdaacddcbcdddcdcccdabdcddcdbccbcccbbbdaaccccdadccccabadddaaddddcdcbbcdaaaadabadadacabcdabcddadbacdcaccaddbbbaabbddaabaaaccdbbadbccdcabbadcddbddaccbdbacbcdcdbcabcdcdbdbcdacddadaabdccbdccadbbbcaccabcdbcbccaddaaabcbcbdacbccdabcdaabbbbdbadbccbbddcaacacddcbbbadacdbddbdababadaaddbbbacccacaaddcdabadcdbcbdddabbccbdcbcdcabacbabaabbcacaacacccadcacaabadaaaacaabbbbccbaddbcacabadabbaacbdabaccabddccaaabccbcaccaddcddacaccbcdbcabadcaabcddbcabbdbcdbacbcaaaababcbcdccbaccaccaaadcddbdcccbcaaaadbbadcddbbdbbbaadbcbacdbdaccddbaacbaaadcbcdcbadddcacaabcdcbadadbaaacbadacdcdaaacbcccdbcdddacadadaadadcddddcaacaaabbbbbaabbcabadbbcbabcbaaadbdddbcbddcacdadcadbcadaccadaaaacaaaaccbcbdcbdacdcaccddddbcdcdbacacbdabddcdcdadbbacaccaabdbabcbdcdcadbbaccddbaacbbbbadbdabbdddddaccaababbdcddcdddaadddddcbbcbdcbdbbddabbcbadbdbdcdabdacbddadcdaccdbcdcacdacabbacdbdbadaabdccbccacbbcbbcdddccaabacaabaababcaddcbccadacbabaccaabadddcbdacadbcaddbdcdbcbcbdcbbddabddccdcccbbddddddadaabadbcbdbdbcbdbddbcdadadaaaaacbddbbdcdbdbddadcacdadddbddccabcaadbcbaaabacccaddcbdcbdcdadaaabddddcbdddabacdcdbbbaddbcdddcbbddadcabbdacddbabdcdbddbacdacaadcaaaaacadbcadccacccbdcbacbabcadbbdbbcdbdcdabbaaabbbcbbbadabddbcbabdcabbddacbbbaadadccbaaddaccbbdccbbabadcdacbcdcaadccacbdcbddccabdabcbcbbcbddcddcdacbcaacbabcdaaacbabbcadcdddaacbddcabddaddcdcdcbdcaccaadadcacabbcbbaabbdccbdcbaaaaadaacbbcdbbabdccaaaddcbbdcacacbdccdcdcbadacacadbbaabaacababaaddcdabadcaaabcdbdababccbaccbadbadbcbdcccaaccbabbcddbabcacbbccabbadcdabaccbbbcdbaabbbdbdddbacdcdacdccadbdbdbdbccdcaadbbdadbbaccdaaddbbaccbaaadabaaacabbdabdcbdadddbcaabaccbbcbabcccadcccadcdbacbbcacadddaabdadbddbcaacadadaabcbabdaacbabcdbcbcdcacbdbdcdbcdddcdaabbdbcabdccaacdccbbbcdcabcdaccacbcdbcaaaddacbcbcdabdbdabcdabdccabbcdaacccbaddcbbaaaccaddaadcadaabcaaabadbabbadbbcdadbddcaadbdbccddbdbaaccbcbddbbcdcaaddcaaabbabdabcbbaabdcaaacdbadbbcbbacdcacdccddbadcbdcdccabbdcddbddbdccdbdbcbaddaadcaddabcdaacbdbaabaadcaacddbdbbbcbdccccdbdacdaaabbbacdbbdbbbdbbaaaacbbaacdaadaabdaccbcdabddbcacbadbadacacddbacdcdaabbbcbabbbdcccddbddacabcaaaadcdbaaaacbbbaadbcddcababddbcaccaaccaaccdabcdacdcddaabdcaaddadacccbcadddbacddcaacdccdcaaacdccabddbabdaadcbdbccbcaadcbacabbcdadcdabbadcddbccccdbbccbabcdcacbadcdabcccadaddddbccbdadbcbacbbaabbcddddabcdacbabcddbcdababcbbababddbdddabddabacccabdcacdbadabbdcdccdcbbadcbcdcabcaabcbddadadccbaadaabcddbcadcdbdbabccbdcabccdcdadbbabdbcdbaccccbdadbcaabdbaaccccdcabcbaccabbbaaadbdabdbabbbabdcdcbcbcdccdddddccddbbdbdacaaddcccaabcdaccaacaadbdaccccaabdababcbabadcdbadccadcdacdbbabbacbdcdcdcbcdcdbabbadadbcaacbdaacdddbbccddddbbcaabbbddbadccbcdbaacaaabbbacbbdcadcbaadcadbaacdbcbadbadccdbbdcadbbbbdadcabdcdadccacbcbcbaacccaaadaadaddcddddadccbdabdbdabcaddcaaabcbadddadccdabddaadbaacadcddcabbcbccadaadacddbcdaababcbbcacccadcdddccbaadababadddaccddacbdacddcdcaaaacbdacddcdcdbbbbcacdacdbbbacbbaaabbbbacdaaabdcdacbdddaaaadbbbdadaabdabbcaaccbadadbbadcbbbdbdadbbaccdbcaddbdcdcbcbdacabccdbaccbbdbbcbcddcaacbcbbcbabcabccdaddcacbcdbccddaadcbbbdbbdacccbdcdcbcbcaccabaacdabdbbbcabadabbadbacbbaccbbadbbadcdbabcbccdaaddabcbcaadadadbbbcacdddbacaccddaadbddcbbcdabadcabadbcadabacbbbabdaddbcddbbcabcbcdadcbaaacbabbdbacdccccaaaabcddaaadadddccdcadadabbbadadadbdbbbcdaccadabadcaccacaddabcaaddaaddbccdacdaccbabdcacddbabadabdaababdacadcbdcbbdcccccabbabdbdbcaadbccccadbdbdddccdabddcbbdcdcbcdddbbadadbbccbddbbbddabacabdbadcabcaddcacaaadcdcccadabbdcaabaaddacdcbdabaddbbdadbccbbaaaabacccbbbaddaccbabcbddcaccbcbcdbbbcbabaaddaadbccadcaadcadbddcbdabccadcaadabbaaaccbbdbccbbdbabbddabacddcbbbcddcdacccbbccabbcbcbdabbcbaddcacaacbbdaabbcdacaaacbcadcbadacdacaccaabbaabbadccbabbcdbcbbbdabcdacabbccbbbbadbaaacbbaaacacbaaaccdddabdbccaddaccadbdacacbccdabacaddadbbaadcdcdccdcadadaaccaadddbbdddabddacdcabddcaddcdccbbadcbcbbcbcdaccccabdbacddabddadbbdaddcabaacccccbddacbacdbcadaccccbadcbcbcdbdabaadaacbcdbddbacdbccacddddcabddcadbacaddddacdddacaadcdbbbdcacdabdccbddaabcbcdadaddbadcacdbacbbaadcaaaadcbddaccdcbbaadcdadbbccbdcbbbacacababdacbcadcabcddcdaddcbdcbaddcdbbccddacaaccbbadcdaacbbbaabbaacccacbbcdbbdacdabddabbccdbabaddcdbabbbddbadbaabbbaabaddddabaabcacbddaaabbbcdccbcaadabccdccbbdddbacbccbddabcdacacbcbdbdcdbbcbcabbcbbcdadaaccbbadbaccdababbbbdbbcadabccddbcabbcbcbadbcdbabaababcbdcccdbbbbddbacdcacbcbbbbcaccdbccacdacccbbabcbabbaadcbadcbbcacccdaabccbdaccbbccdbcdaacbaaaabaaccacaccdabccdbddaddccbcddabaaadccabaacadcdcdcbadccbbbbbabbcbdaacdbcddcadddcdabcbaddcbbaaacacdacbccaacacacccdabbabadaadbdcacdaabccbdcabcbcbcaaababcdabacabbaacbddbcacbdabddbcbacdddcbccccdadbdcdcacbbdcbddcacbcdbddbadcaacccbcdacbcbdbadddbbcadbbbbacacbccccaabadbdcdaabaddaadabbddcadaabadccccbbbcdabbabddacccdbdbdaccddcbbdbddcbadbcbbddababbbbcdcbacbadaabbdbbbcdaadbcbdabadaabdbabacbadacdbababcbaadbbdacadacbabdbacddbaddddcaacaaacaccdabcbbdabacaabdabaaadccdbdbaadbddbadaaddbdcccadababbbbaadadbacbdbabbcacadcddcbdbdacdabbbbbbdadaddbadcadcaccdaadbddaabadaddacacbcdcacabdcbadbcabcdccaadabdabbbddbbdcadddacaadacbcabadcdcaabbdbbdcddbcdcdbddaddbbccbaccababccabdcabbdbacacbbcbdbdbadccdcaccbcddbddcbdaacbacdaddbaacbbaaaccbdbbabbaaddcdbbaacdababddcdbbccdbabbaacdabbddaddabccbdbccbaadbccaabddabacbaddcbbaabcdadbababaccdcdadcbddabbdadaccabcccdcbbaddaaaaababdcdadabcbaaccaccabdaddaadabccbcbcbacadccdabdddddcabcabbdbbdaddcdaaccbaaddddaabbbdccbdadcaccababcdbabcaccdbaddcbacdabdaacbcbddcbdabadaacdbaddadabdbdddcbbdcbbbbdabadbcbddbaadbbdbcabbbdddcccacbdbdcaadaaadaccaaacbcddbdddbdbabdaacabdbdbaccbdabcbaabacadacdddabcababdbbcbccaaddaccdddbcadccdbcccacbaaaccadddadacbacacaaccddcdddabacadbbadbbbbdcbbdbdaddacbbdacdcdbdadccacccbdbdcbbcccbdbbcacabcabaaaaccbadcaacdbdddbabaccdabababacbddbddbcbaadadbbaabcabacababbcdccbbcddcbdddbccdbdcbabccababbbddcadcbccdaaaccbbdaaabdacdcadddababbcabdbdaccabacccdabcdcdadddcbdbaccbbadddabdbabacdaddcbdbaabadadccaadbcbcdbdadaddcbadbbdddabbcaaacababaacbcddacaaabbbcbadbabbbbbdcbbcbbdbdabadababbdabddbaabaaccaabcabbddcbbbcdabbbdbcdaddcbcdaabdcbdcdddcbbdccabbaddbdbadcccdddbcaccbadcdabddacacccaccbddbabddcaddadadbdabbbaadbbdadabbaaaaabbabcabcacdbdbabcaacaddaaabdaadbbdacaddabbbbbbdbaaadccabcbbcdadadbbdbacbadbdabdaaddbcbbdccbdaacabadcbdddcaaaaacdaddcdccccdbaacaaabcabdadcbacabddddaaabbbbbcdacddcbdcbcddbacccddacccccdacbcddbabddaaaacdacabbcddbdbccbcbabdcccacdbbdcbbdbbcbaacdbadabbdcadcdacbabbddccdadabcdcbdaadbcadbccbaabdccbddcbbddaabbbaabababdbcbbadcddabbdadadbbccdadabacbddacbdbadaddadccbbbbbbcdccaacacadcabdddabacaaddacdacbabbbdcddccbccdacbbcaddccdddaadbddcdaddaaccccaacbabbdbbbcdadbcbcabdaadbaabcadabbcbbdaabbadaaddadaaacbcbccdcbdbbdaaaccdbccdbaccadbbdcbddbbcdcddcdcaccbbdbaabdacdccdbacadadaacddaabdcbccabacddccaaaabddddacbbddabddbcaccbabbaaabaccbadbbcaacbcccbcabcbcdbbbdbabcbcbbabccbcbcbcdcddadacdcdcabbdbddcddbadaaabcdbabdabbcccabcadcbbdacdcdaaabacaccacddaccddacdccbddbabddadacbccdcdbcddabcbcdcdbadabcaaacccadcddbadabcddbbcbaddadbbabadcdddbccbcbbbbddddcacddcabbcadcbcbcdcdbbcdcabcdabcbcbcdcbacdabbbcdbdddccacadccdabddcccbdbdadbdaadbabdbabccabbabaaaaddbccdcccabbbabcaacadaacdbcbddadabccaccbaabbbddbcdcdabbacdcbcdadbdacddbcccacabadaddcbdddbcbbbccbcdbcacaaabaddacabbdcdcaadbabbdbcdcdacadacabaaabcdbcbaaaadbbbdcccaaddbddadcdcdccadabbdbccbcbbcbcadbaacddbaaaadccbaadcaabdbbbaccdbdcbbdccccaacdaacdaccadccdcddcbbaaccbaababcdcdabdccccbaacaccaaaddccdaabadbababdbbbdbdacddbcdccadddcbbdddabccacacbcbdaddbcdccccbdbdcbdbcbacaaadacdddbccadcbcadbdcaababcabdaccadbbbcccadcabbdccdbbdbdbabccbacdbdbdaabcaabddcbdacbdddacdcbcdabdbabdabdaabdadaacacbabdbddbdadbabaabbbbcdadabcacdbbbbdbdbbabdabbcdbadcabdbcaadccdcbabdbacbcbdbcbdbbddabdabdbacbadaabcaadaaaaccaacbcccdccdcbbdabbbaacdadcabdbccbbcabaaacacbccbdbcdbbbabcbdbbcdaadcaacaccadcddcbbabbabcbaddcdbcbddbabbabdcdbddbdadcaaccacaddddcaaadbddabcbbbbaadcbcddbbcbbadbcdbbdcbcdbbbdcabaabbbdcdaadbdacacdcdcbdcaddcdcdaadbbdaddbbadaababdbaabdbdbdbcdcdcacdbddabdcadcccdadcabadadccbabbadaaacdbcdadabcbdcccdadaabbdaaacdcabbcbdcabddbadacdbbcdaacbaadabaddbabdbaacacccadcacdcadddcdaccacccaadaadaddabcccdacddcddbccaadbdadcacaadbbbaabadbbdaaaabcccbdcbdabadbcbaadbadcbbabacdbacbdcccacabacdaccaadacdcadacdbccacbacbbacdcbdddbccdbcdddadbdbdcadcbcaacddcbdacdbdacdbccddddabcdbcdcbccadadadadaabdaabbcbabbacabcaddabdccadbbbdaccdcbdddcbaacbbcddbdaacbddbacddccbcdabbacccadcaabcbbabdcabbcdcbcbbdabcdcddabcbbadacbbbbaabdacbdcadbdbabadbadccbbdbabcaaccdccabccacdbddaacdcaaabccdbabcdaccacabddadbbabcbacbcadccbcbbacdbabbcdbacdbcbbcdcbcbbdcccbcaccbabdcabadcaccddaabcdcacabdcbbbabcddcdcbbdbdaaddadcaccdbdbccccaadbbbbbdaadbaaaccaddcdcaddbddbbbdaccacdddaccadabcdbcabdaacaadcbdabaaadcacdbbcadacbcdbdbbbbddcdabdabccadbccddbbcabccdccdbcbbcdabcadbcccdbcbdbcbaddaabcbccbbdcacbbddccabbbaadadbbaababdccdaccbbcaaaccdcbcbcdcdddbbbbaabbccaccbcaadacdccbbcbdbabddabadbbbbbbbdcbbdbdcdcdbcdbacdcadbadababdbccbbdccabbacdccdbababdbcdddccbdbcdabdbdcbadcbdbaaddaccccaaaaccaaabcddabcdaccbdcbdaaddcbcbbbababacddbacdadacabdaaadbbcbadbadaacabbcccbcbacaabdcbaddbdaacccdbacacbaabbdcdddccdbcbcadcbcbbdbdddddbbbddcdaccdabcccccddcaddcccadaaabccbccccaccddcdcabddbccddacbcdabdcdbaccdcacadabbbdaccbbadcbcddcdadbbbacddaddccbacadabddbaccacbdacddcccacaadbdacbadbdccabcdccbbacaaccbadbbabccdbaccabaaccacbcdaabddcbdaddcbdddadbcccaaacdaaacadcdbdccdccdbcdbbbbaacdcadaddbbddbbccabbaacdbdbaccbbdaaabdadccdcbdacadbccdacabdbabcbdadaabcaccadbbabdadaaaaaccbabcdadaddbacbcbabbcbbabcbcdbccaababbbdcbccbdbcdcdcbaaaaddbacacdbacaddbaacacddbdbacdcbbabbaccabbbdcadabcddddabddcbbaddbdaabbdbbbdaaababdcaabcabcacacbdacdcccaaaadcbbababcbcccddcbaaaababdaadcdbbddcabbcccdcbcdabddcccdbbbacbbdaddccbbacbbbaabcadcdbbdabbdaabdddaabbbcadcabbdadbbbbadccdaadacdcadbadbbadcbacacdcaaaabacaaaabbcacbabdccccdbbdbbcaccbcbdbcabbadcdcddccbdcacbacbacdadcaaabcdddabacbddbcaacadcababbabbacccddbbddbdaacbadaccdddbabbccdadbdbaccbcccbccbbcbacbaaabaadaadbccdacbdbacdcabaaddccdcdbcbbcdbbddbacabcddcdacccbabdbccabdabbcccdabaaabbdcbcbcadcacbdccccccbbddabcddccdabccacddacadbdbddbbbbacbddbddabbbbdcaabcbcadaadbdabdacbbadbccaccccbbadddaddbacdabdcadbddaccbbcadccbaabdacacdbdcabdaabdbaddddccdccaacdcdcdcbbcbdcbaaadbbadcbbcbbcaddbacabddaaaabadbbcadaabababbacacaccaabddccabdbbbddbdadbdbbcadacdaaddaacabccabaddbcadadcacdbdadcdbabccdcddcddddbcabcdabcabdcbaabadbaabbcbaabaadabcadddbdaddbbaacabadbdccbbdccbabcaacaaaadacdbbcacadadbddadbbbcadcbdabbaddddaaddbbcacdcddbbadadaadbddbccacacbcbcaadadcdddccbbacddaccadddcdcdcabcbabdababbcdbbdacdbcacbdcbccacabbcabcdcadbaaadbcbdcadadadacdcbbddddcbadcabcccdbabccccdcabddbdacacbdcbdbdbcccdddadbadcaaadadddcbdbbacddcaccbadddbaddabddabaaabdccabdaabccbcdbcdacdadbcaccacbdacdaadbabacbcbabcbcdccbacaacabcdbdbacdcabbcdabdacbdabcdddddbbadaabdbbbaccabcdacccccdcdbadbbcbacbacacbabbddacaccdaddcadcccabaaccbadacdbaddcdcaacddbcccdaccbccaacabcdaaaddcdbbadabcabaddcbacbaaaacdbbabcbdacbbcabbbbcadbbbbcbccbdbacacbccdccccadbadbcababdcadaadcccbdddbdbaacddacacbacdddcccacacacbaacdddcacaaddaccdacccacbacddacccabdacbbbbbabdddabccacbdbbdaacbdbcdbaaababbadbcaadacdabacdbcbdaadcdcbbdaddadcccdddabaddadbabdcabacdcadddcddbbacbcdddccddddddbadddddccddbddcdbddbbbcbccbbdcacbaaadaadccaabdbaaddaccabdcbbdbcdccabcdbcadcdbbdcbddcaaddbcacdcdadddcabcddbacacadcbcbcbdaabbcbcabdadcbbbdddcabcaabccadcbcbdbadccaabbbdbddbcaccdbcdbbdbdccacddcddccaccadcababcccabdbdcbcccdcaaacabbbddaacbbacccdaabaabacbacbddaabddacaaadaacaaaccdcdbbbdacdbbacdadbcaabcccacbacbdbdcbaccbcbbcdabddabcdaababdabccababdcbcbdabbacbcdcbbbabdbcbaacacacdbcbcaddacddcdcadbcccdaccdcbbddacacdddcaabadaccdaadbaaaaddbcaabcdbbbddcbdaddbbddbcadabbcdadccbdcdddabbabbadbcdbbaadcdcaabbabdaccaadcabdcbcddddcbabadbacdcacaadbadbaaabcacabdcaddcdcbbccdacbadabdddbbdacadabcbdcbcbbccdcbddcdbbcddabbbaababddcbcddacdbdbccabcbcccbdadcbcacaccdabcdbdcdaaadddcabbbbdcdbaaaabdddaaaaccdbcbbacabdbabbbcdddcabdcbcabbacdbaccccddbddcbbaccddddcaccaccbccdacaccaccabbdddaacacdadbdddcdbcdcbcabcadadcbcadbdadacaadaaacbadcaccbdbbbdbcaaabcaadcdccbcdcbbdacdcbaacadcbaaaaccadadcdacbbadbccbadcdacbcbcbddbcdcbcdddbdbaacddbbcbbacdcdabaadbcbccdcdbcabcbdddcacadddacbccabbdcbbcdddbcbaabddbcabdadbabbcaccbaccbdabccaaccdccbdabdaddbacbbbccacdcaadcbdbaaacdbadbdcadcacbccbddcadabbbbabbdbbadbcababbbcadcbabbcacccaaaddbdaabcbabccbbcaaccdbadadcdbddbaabcacbcababbabaabaacbbbccbbddccaccbddcbdaccaccacbcdbabbcadabcdabadabdcbcdddbbadcdbcdaabacddbcbaaabbcdcbbcdaacbcbacacddcdacdbdddbcabadcdccdbbcbacccbaddddbacbbcdaadcaddaccdcdacbcbbdcdccdcbccabcbbadbadcdbdaacadddbdbdbbbccacaabadacacdcadaacdbcdbbccabbbdbcaacdacbcdbbaadcbacbcbdddbbdcbdadcddbdacababaadbdcdadadcdbcddabcdcddcdbdcbaaacabdbabacdbaaaacabcacccdacaaccacddccbcabcccacbcddcacacacabdcababdbcaddbbdbbacbbdadcddadadabaddcbcbddbaabbdaaccaddbbacdbdacaaddacbadcacbbbcccdacadddadccaddacddbbadaddbcaabdccdcbcaaccabaadcdddbdcdbbdccdcddddcbbdadccdbdcccadcabccbdbadcdbbcddbdcdcadabbbdcbbddddacddbdddddbbccbdcdbcbbbacbbacbdbadadbdacdccbacadabdcbdcaadcdbaaddbaacaacbaaaaaddbdbbabbbddacbdbcbbabbdccbaaadabaddaadaaabbcaadbadcabccdcbbddabaddcaacdcddbbbbaadddddabdabcbbacddbabbcaaacaabadaacddacddabbdccbacadabdbbbbcbabbbaadadadbcadbdabdddacccbdbbcbdaaabcacbbaccacdbaccbcaabaadccababacbdaaaadccdcbabdccaacbcdccabdadaccdcbcdbaadacbbbbbdbdbbadaabcbcaaabddaacdcaddacbcbbbdabccacaddbbdcbcdbbcabbadccbddbbbcaddadbcabcabcdaddaccdbbccbdbbaccbdacdcabccacdccdcbbaabaabbddacaccbadcdcbaabcbcccbcdaddbadbdbaabdddacbcbbaabcbabbbbcbcdcaccdbbdbcddaaccabbcddcdcadaacadaabccbdbcacabccccaacbbcbdcddddaadcbcaccaddcbdbbcdbbbdccdbcdcaccdcdaaccdabcbaddcdbccdbabcbbaaaacbbdcbbacccddacaccbbbbbbbdcbbacacaaaadacabcdbdaabdacdbbcbdbbdccdcaabacddccaddccdcaabaacadbbdbcadcdbcdbcbdacbaddbaddcccabbdbdcdbccdbaaabaabddacadabcabacadddcdcdacaaddabcaccacccbcddbbccaacccbdacbccbcbccadcbdbcdbabcabcbacacddadadaacabbbbabcdcaccbdcbbadbccaaaccbdcccbdccdcadaddbdcaabccdcabdbcccccaddbbaaaabbcadadbdcdababbcdacaabacbcacababddacbabbaadbaacccbadcdddccbdadacababdbcadccbcadcdabbdadaacbdcbababacddcabddccbcbccdaababdccacdabacabbddbdbcccdddcbddbcaacddcaccdcccaabcadabbcbddaacdaadacbcdcbdaabbacdcdbbadbdcbbcccbbadbbccaccacdaadccabbacbabaabbbcaadbdcccdabdcadbadabdabdbacaacbcaddaaaacbdddbbacabccbbcddccabaccabcbddcbabcdcbbbcbadbbcdcccaaaddcdbbaccdcdbabcbbabccdccdcdacdccabddabacdbddcdbbbcbaabddcadddbabbaccaacdbddaabadbdddccddbcaaabbdadcbabbdbadaaacdaababcddbbddbbbaacbbcabbdcbcbbbbacdccccbcacaaadacabdcbdbaabcbdaadabbbbbaadbdcccaddddcdbdbdacbccaadbaabbdacdcbdbcabaadccddacbdccbadaabacddabbccbddcbbbadcdbcbacbcdacbacaabaadccaaaabaabbbaacccbbccacbdaacddbdddabdadddcbbcdacbacdadaabacdacaacbbbdcaadbacaaaccbabccdabbdacbddadaabdaaaaddcbddadbdbdbcabbaacbdabbbbaccacddbdbdbddbaabacadabcdbcabbddadbbcababcaddcddbadbbbbcdbdaccaacbbbcadcbbcccaaaaabaabbdbaddbbacddaabcdbcaaddcbdbaddbcccbbadabaddccacbabacbbaddaaaabaabdabadcccabcccdbadbcdddbbbbabaddcdcbcbdbaadcadaddbcbdbbdddccaabbadaabacadaacdadcdddabbabcdbdbcccdcbaadbbcbdaaddaaaccbabbcccadbcbdcadbbbaaaccbddbbcdcdaadcacdacbacaabadddbcdbbdccadaabadabcddcabbcbbbaaccddcdabcaaacdacddadaabcaaddabdbccdcacccdcadbbaacabbcacbbabbdcaabcbaddadadadcaabccddcacdaaaccbdcdcdabcccdabbbbbbbdacadabbcdcaabacdcabbdaabcbaddaccdccaddabcaaabccdbdaddaabbaacadcacabacabbdccbaddaabbbbbbddadcdccbcacbddaacddacdbcbbbbaadcacacdbdccdbbdcbcababdbdacacabcccbdddacadddcdbbdcbbbadacdbacdabaadcdbbdaccbcccddacbbabddcbcddcbcbcbaabdcaaacccdcdbbcccabcdaabdacbdabddbccdabcbcbbcbccabccadcacadabbdddcddbbcaaabcbaacbdabacadbbbcbbaaaacdbacbacdcdddbddbdabadabcbbbabbbbccabcaabbddbacddcaaccdbdabddaadbcbdaaccdddaaacaacbdacaaaaacaadbccbbbdcbcaddbadcababcabbcaabcaaabddddccddcccbbaadcdbccadbcdadbacdadbdbcbbcccdbccaadadacbbcbcadccbbabaadadddcacddcadddcdcaacdbcdaaaacdabdadbbbcabbaaaabbccaabccaacaaabbdabadacbdaccaccadddaaaabbcdddcbbbccdbadcdcadbbbbcbdadacbaaaaabdbbccdabcdcdbbaaaaddddcddcbcbabbaccadddbdbcacbcbbadbddddaccdbaddabbbcbddacdbccdababbdbaccccbbdaacdcacabccbbbbaabddacdcadcdcadbdaabcaacdadacadddddbaddaaabacbdbbbbbcabcdddcdacaaabdaaaaadccbddbbaabcddadbadcabcbdcadaadacadbddabbbbdbcbaaaacbabdaccadcabaacdacdaddabdbcabdbbccadaadbaccdcabdbabddcccdcdccdccabababaabbcadccbaccdcbcadacabadcaaaddbacacbddcbbcadcccbacacbcacccacdbdbddcddcbccccaaaddcbbaabcbbcaaaadbcdcbabadcdbdbaabbacdcabcaadbbdcccbbbbbabdddbaaabbcccabdcddbdbabbaacbadccdbabaaaabccccddaabbadaadccbdbbddabbadaabbccdbdabaacbadbabdadcadbccdabbdaabdbdddcbcdbcbddadbacacbddabbdaaacccdbddbacddddcacbcdabddabdcdabcbbdccbcbdadbacbaacbdacacacdbccccbccbbadcbbdbcdbdddcdadaddcbbbaababcbbdddabccabbabdcddbbbcdadabbadbcccaabbccbbccdacdbddbddbbaacaacccbddcaabdbcccadcbccbbddacbbcdbbddbcdbabadcdabdadbccbddaabbaacaacabbbdbdacbaadababdcbabbdcbbacadabbbccdcabbdbcadccacaabaadbccbdbbccdcbadcbbcaabcbacbaadcbaadccadbdadadaabbadaadcabbbaabdccdbcccdbacdcbbcddcbdbdcdbbbcabcbcdaacdaacdadbddbccabccdddaccdcadbacccbdacbaababddbcabcbdaadbdabbbdcbcaccccdaacbbccaddabcabadccdbcdbbdcaadbadbaadacdccaacadbcacdbcabcadcabbcdaadbadcdcbcadccdadcdcadabddccdbcdbabacddbbdacdaddcbaccbbbccddbacabacaabcadbaaaabaaccdcbcdbbccabbdadacbadbbbbbddcdabadaaaccbcdcdbabbcdcdadcdadabcbcaccdccaabccbdacbdcaccdacbdbabcadbbadbbaaacaadabdcbcbbcccdaaabbadacaadbcddadcbaacbabadbbaaaaaadcbccaaadabaddddaaaadbaddadaabbccdadddbacaadbbaabacdbddcbbbdabbabdddcabccccddcddacbcacdcdbbdbbddddaacabdbabbdaacbabcdcddbcbccacabddcbcacacaadcbdabbdabbdcaccccadbacbccdcaadccadcccaabdbbcbaabadacdcccaadacbcbbdacbcdcbbbaccadbacdbcbadbdadcacbdbbabdccdcbacdcccadaccbbdbaddbccabcddbabacaaaaadbcbbbbbcdbdbbccdcbabbddbbacdaccdbbdaacaacccbbbdacccdbbbbbdbabbcdddddbdaacdabbbdbcdabcbbabcacbadcadbbaaacbbbbbaaccbcaddacacacbdcddaabccccdadaabdbddaacadccaaaccdadcdcbdaacdddbabbcbdaabbbbbcabacadcaadbaadabacaccabaaaddbcadcaccbcbbcabdaabddbbabbabadaccadcabaaacabbcabbccaaccbbdaccddddcddabdccbbabdbcddcccccaaccccbabdcdccadccddcdbccbbbccbbccdcbabdcbcbaabcbcbbddcabadcacdccbacadbbacbcbdbbdddbccdabbbcaddddddbdcaddbbdacddcdbbacabccdbdbdbbbdbcaddddadbabadacdcccaadaaadaddbbcdabccbdbcbbadbcdbcbdcdbcdbbbaddabbabacbbcdcdbabdbacdcaaaababaccadccacaadccaadbcbababaababadbcdbadddddaacbdbbaddbcdacbbdbabbcaaacaacabcaabcdcbcbadcddaabacbbcaddaaadbcbaccadbcbdbbacacdbaacacaaccaadddbadbcbbbacddddbccbadccddcaabcbabccccbdabcdaccbcdcdddaaacabaccbcaadbbdaacadbdaaabcdbccddcbacadcaacabcddcabbabbcacaaabdddbbcbacddddcddcacdbbbdbbdbbdcccdcccadbddbdbbcabaccccccdbcabddbcbccdbadabddadbabdddcacaadabbddbbbbbabdccbbdacbbdaadbdbdddbcaaccbdaabbbcbdccdcdcddbdabacaacaadcbdaabcdbcacacccaacdbbbcbbbbdaccbcdaddadadcadddcdbcdccacbddadacbaabddbbdababcabbaabdbbcbbdabbaacbcdaccbcadbcbcddacaacddacadddadcabdacbdbbdccccdccbcdbaababdbbdcdcbcacabdcbdabbcdbcbdadcbbbbbcdaccabdcabaacdbbcccdbdcadcbdcabbbbcdcaacbaadaaddabaadbabbccdadcacdddadcdcacdbcdaadbbccdadcdaddbabdbdababcaddbdacdcacacacdcbcbdaaaadbdadcdabdccbbbdaabccccbdbbdacaabcaabbadadccccaaccdbdaabaabdcdbdddcdcadbdcadcabcdacccdbadaadcbccdccdacadbaccccaacadadaaabdcadababcacbbaaaaacccaddbdaccbbdbdaadcacacbbabaabaaccbccdadaaabbcbdddbdcdbadbcaacaabbdcdababddccaaccdcbcddbaddcbbbaddcaabdcdaddcaacbdbcdcabccabbbcdadcabcdacdbdcbaddccaacbcdcddbbcaabacbdacdadcbcadbdbddcaaccabbaccddbabaaabcaacbbdcaadcdbcccaccbdacbbccdccddbdbcdadbabdbababcdaadbbcaaadddcbbdccddcdcccabcdbbcbcdadcadcadcacbbdcdcccaacacbbbdadbccddbbbbababcaaaddbadbdcddcbabcbccccdaadbcaddaacabaababbbccbbdbbcbcddbbddbbacbbccadbbbcaadbaddddaadadaccadcbcdccbadcabdadbcaacbbabdddbaabadccacabdcaddadcaadacccbcccbcabcbcccbcbcadbdcdaacbccbdcbabaccdbabbcaaabcaaaabadbaabdbaccddddaabbcbbbbbacabddbadbdcaaddabdccbbdbdbaaaddacdabdbacdacbdbddabbbcbbaddbbdbdcbbbacbacbcccdbbaddaacdbcbdcbbbddbdbaccdcccdcdbbbbaaabaaddbaccabbdcbadbbbdbdbadacdcdcbdbcbabaadbdcadbcdbdadbccddacbdccddbbdcdddcababcbdaabdacadcdbbbdbcdbaccdacdccabbcdccadabddcadcbcabaccaddcaabbcdacdddcbbcdddaaabbbbacbadaabdcbbcdbdbdababaaaabccdaadbdacddcbcdbdabbadabcabacdcdcdcadaabcadacaccbccbcabacdbdbbddadccdaaaabdddadbcbcbaddcbacabacdddcdabdbadadbadbabacdcdbabbccabacbddbbbadcbbabbccccdddbacbabcdadaacddbdbbbcaadbdbcadaccbcdaadbadddbbdabddaaaabadcbdadbcdddbdccbbbbdddddacabccaacaaabcdbabdabdcdddacbdccddcaabbabcacdaaccaabcaaabbcadbdcbbbbbbabbcddccaacbaaccbabccdadddabdcccadbccbccbcdaadddabadbbbbabbdaddcddaaaadbcacccdbbacccaacacdabdbaacaccdbaaaacadddadcbcbabdbbccdbddbaabbcdccddcacbdbacdabbbcddbbdbbbbdccccaddabdbdccddddccacbbaabccbaacaaadcdddaaaabccadcbcbdacabcdccdaabbbacabacabcbcacbaddcdddddabcdadbacdaadddaddbbbabccaabccdbbbdbaacdbdacbcaccdabbdcdcdbcadddabccadcabdcbbcdccbdbcaddadddcaacdcabcbcdbbccccccadbabdabbbdbaaddbcaccadcbbabcaadcbcccbbdcadacaddbcdacddbbccccacacddcaabcadbdbdadadbcdacddabddddddccccbabcbbdcabacaddbabbcdbaddbcdbcbcabacdbdbbaaabdcdcdbcdddadcacddbabdbbaadacbddcaacdccbcdbacbbbdbbbcbccbdbabcddabadbcccaacdbacdaabbacbbabcddacdddcdcbdabbaaabcbdbdadaaabbbadccadbdccbcabcabcabdabcadacbdbadabbcbacdcbdbdbacbbbaacbdbbbbccbdbbabdcaaadaabadbababababcccccdcdacdadcabdccdbcbabbacaaabdcbdbbadcbbbbbaacbdccabcddcbcabaacbdbdcdcadbdcbcdadbddbdbdbdcaccdbbbdacccaaaccbbbacbbcadabdcdbadcabbadcdbcccdcacbacdbdbbdcbbdaabacccadcddaccbcbcacbcbdbadbbaadbbdbababcdbcdabcaccabdbaadacdcadcaaadcdbccbdaacabbadbacbbddabbdabcabdbcacabcabcdacbddcccdcdcccaacadacdadccabaabdbabbadbcbccdcddaddbbccbabcddabbcbabdbdadccabacbdcbdbaabacbcccacbababddabcbaaccbababbaddbdbabbcdcbdacacbbcdccbcccaccccbdcdbdcbadabbcbbddadaaabacdbcdccabddcdbcdbbdacaccbbdbdbadcacabbdcdaababbcdccdaacdacadcccdbbaddbdbbbabdcbcacdabcaaccacabdacdcccdcddbdbddbbddcbcdaaadaccdbadbbcabaabccccdbbacbadcabadbcddcaabddcccdbdacdacccbaabdadabbbbcddbbbdcbaadbcadddccabadbdcaadbcadaabaaacdaacccdaccbaaabbbdaccbcdadaacddabaabdccbbdadccabcbbbacdcbadbdbcadbacbadcccdabcadabcbbbcabcaddabccdcbdabaaacdaaacaadbacdcbccaacabcddaaabdbcddccaadcababdddabdcbbadadaadabacbcbabcaabbcdaadbdbaacdcabdcaadcbdbcabbccccdaacdddaaabdcbddbcdddaabbcdbaccbcdbddaabcdaadccadcabdbcbdacdadcbabddadbacadcaacbabdcadbdbcdbdcbcbcdaccccaaacaccddbccaccbdaadbbcbdadcdaaadcdbbbccbdbabdcdbacbcccacbcbcddabdaddababbaacdcbccbddccdbddccdddcbdddbbbcdbadbaadaabdcacaacbdbdcccdaaabdadaadaddcdbccbccacccbaaddadaacddaabccdbcaaccaacbdbdacbcbcccbbdadddcaddddbbbcdaacbccdbbcbcbddcbcaaadadacccbcccacbbcaacddddddbaadaabdbdcdadbadcdccbadaddcdcaadbcbccddaddbaddccadabbdccbdddaababbbbbadcaddddbdacacacddacaaccdcaadaabdccbcbcbbbdacbdabaacccadabcacddccbbbdbdaaaaaaccdddbbbdcacddadbaaaacdaacbadaadaacaaadababcdcaddccdabcdaaadbcbbccbbcbadbbabcaccadcadbcaabcbacbcccddacdcadbbddbccabcabdbbbddbacbcacbacdddddbadabaccdddbdbcacbddbdaadcccbcdabdcddcbdddbccabccbadcdcadcbddbbadbcdabdddadbadbaadabcadcccaacccdadcdcdcbdadabddcaccdbadabcbdabadbbbacbcdccdabcbcdccdbaadddaaaddaccbbccbccccbcbdbcdbcdbacddddadabababacabbabddbbbbbbbcacadacdccbbbbdbdbddbadacdacdbcbcacbdbadbadbacddddaabdabcbdcdcadbdcaacbdcaaccaabbcbdabcabadbbaabcbcbbcaddadbcadbbbabbbdcaadddacdddcccaccabcaabbbbccccbcaddccddaccbbdccaddbdadadbaaaacdacdbcdabcabaccbdcbccddbadddcadbdcddccaaaadcbbcaabcacbadcbdaaacaccbacccbdccadaadbbccabdcbabcccaadaadadadaaaccdbbdcddabdaccbcbaddbdddccdbdcdcbbdabcddcbdacbaabbcdadccdcdbcddabbaadabaaabdddbdbadaccdbcbdbaaccbbabbbdadcbaaacbdbcbacacadddaadcddacdbdbcdccadccaddbccabcccabacacdbccdbccacaacccdbbcddacddcabbaadaadacaacaadccbbaadacbcbccacccbcbcbabbadcbacbbdcbdabdcdbcacdcdcccdaaddacacccdadabadcbcdabcccdcbbddadcbbbaacbbcadadbdcbddbabccdccadcacccdaaccacbbdcbcadcbcaaacbdaacacdcaaadbaccaaacadacbdccaaabbddcddcdddbbabcaacabbdddbdaaddaccbbdbdadbaabddccacdaddbbbabdadabacaaadccbcaddabcdcbadbbabcccbdbbdabdbcbbbbbacdabdbdacdccbbbdbadbbabaabdbbaabbdadddbdacacdadcdabbcbcadbbcdbdaaabbcadcdcbacdbdcccacdabadbdacbbbcbbdacdcbcadcacacadcbacaadcabcbdbcdbbadcabccaddacadbddacdcdcddcddcbacacaabdbccdadccbdddacdabdcacdbcdbadaabababcdadaddddacbacbabbbbdcacacaccddcdabcbcdaabaacdadabddabaabbdcaccddbbbbcbbbccddbaabaccacadbbcbdbbdbabacbddccbddaababbdccaacbccbacdaccaacacbbaccbcbdbddabaccccbbaadbcbccacdadddbddbcabdbdbccadcdbcdacabbbabbacdaddccaabccbcacdcdbcdcaabdccddbaaddcbdcabbaacaabdcdbbbcbcccadacadbabcbbddcbbdbacabbbddacabdccddccbbddcccadbcbccbdaaabaadacbbcdabcaaccacbdbcabcbdcdbbcbcbddaccaaabbdcaacaddabbbdccddcdbaccabbabaadaacaabbccaccdcaacdacdacaadbcdcdbaaddddaacbdcdcbbcaaaccbbdbbdddbdadccbcdadcdacabacdaddbcdbccaadbbaadccabbcaacdcdcbdcbbbccaaaaadbacaabdaacbccbbbadaacbcacdaabdaddacdcacbaacbcdbacbbaadbadcbdcdaddaacacacbcabbadccdcbbddbcddaddbacdcdaddcbadddacbcdaacadcbbcbdcdcabacdacaccaccbdbbdbaadbacaaaadccdbddcbddbdacababcdbdbacccbabaacbccddacaadcabbddabbdcdacbddcdbcaccbcbbdbdaaabcbbbcdbaddabcdcccdcabdaabbddcbbdcdabbdcaaacaddaabbcccbdbdaadabddadddccaacbdaaacdcaadbcaccddbdbcdddaadaaaaccbbbdbdbadbcabddaccaddbabbddbbaaacccccaabcdddbdcaaccaaccbaaccdcdccdbaabbaacaddbdaccdccabccbdcccccbaacddddaacadccdccdabcccbdbaadccdacbcdcaccaabcddddaaddbccdcdaacbdbcbadbddccdbabbbddbbaccbadaaaddcdccdcddddccccdcaadcdaaacaacddadbbdaadaadddaabcbbdddbcbbbdccbbdcddcccbaadadbacdbdbddcacbccbabbdcabcbbdcbdddbabbbaccaabcbbdadcbabcbbbcbacbacadddaaddabcddbcaddcddaccbcabcbcadbcaccccbabcdcbcdaaaaacacbababaadadacaacaccdbdccbccddcbddbaabbabddccbacdbcdcabdbabbcdddbccaaacdcaacbdccbabbcdccabbdbacddabaabbbcbbdbbabcbbdbddadabcbacadcabbccddacbccabdddbccccadaaacacdddadbababdacdacacaaadabbcacdacbdbdddcaabcbbdbccddbcabbbdbdaabddcbbcbadcbbdbcdabcdddabcccabcbbbccdbaadbbcbbdbabddabdaacabacaabdacddbbabbcdababdacdaadcdaccabcbdcdcadccbacbbcdabacdacabbbdbbabdccbadccdadccdbcdacbbaddacaabadbbccccddaaccdabcaadaaccdbababaaacccdcbcabdbaadaddadbbddbccdbabaaabddabdbaaaddacdcdacacbabddddacbdbaddcbacbdbacbddcdcaddcddcaaccccaabdddcbddaacbcacbcabdccabccdadbabbcadcabdbddddcabbccbcbabccdabdbbcabacdadababababacabcdbaaacbcacaaaccbddccbadacdcdbcdbbbbbaacadccaddaddbddcbabbabcacabbdcbbaabaaacaaddadddcdcaadabdaaaacbdccdbbdadadadadcadadabaabdcacddddcabddbdddadbacbbbbdccccbccaddcaadbbaccbaabbddbbadacacabbaccdbcaddacbcaadbdadaacabbcbdbcbbbccbbbccacaccdcbbaccabcccbbbabcbacaadbbcdcacbaaccbdadbaccdcccdcbbdbccccababaddccbacbdaacbbbabdcbdbadbcdacbcacdaacadaaadcacbbabbcadcaccdbdacbbadccdbcdcdcbbcbdadcdbcaccbcabddaddabdbddcccaccbadabbdbbdcbdcccdbdaccdababbbdcbdaadaaacccbbdaacdbbaabadbcacdadbadcbbcbdcbcdabdaababdadddbababccacbcbbcbbbbabccdcbddbbbaaaddabaaabbbccadcadcbbdadaccbcdabccdbadaabacbbacbacdcbbdcdacaccbccaabdcabbcaccbccabdadbabbcadbbccbcdcaaaabcdabddaddcaacacadcaaddbbaccaababccaacbabbbbabdadadbcccbdbbaadadbcadbababcbbcacdccaabdbdaadcddbcbcbdaadbadacacbcaacbbbcaabbaaadadbdddabbcbabcacdccadadcdcbcabbbdabbacccbbcbddaaddcbddcdbddbacacdcbbacccaacadadbdcaadddbadbadaaaabaabaacdbddccccddcdbcdacdcdccddcbcddadaaabdcccbbbacadaabaddabacdabbabdcbabcaccbaacdcdbcbdadcaadccabbbdbccbcabbbaadddcadbbcdabdadaacdbddabbdaaacaabaaaaadcdabcbbbcddcdbccabacbbbdaddbbaabdbabccbbbbccbcdacddaabcdcccbbadccabdbcacacaccdccdcdbcbbcdbdccacbbcacddabbcabadabbacbbdcdcdccabadbdabcadacacdbcddddcaaacadcacdccabbcccccbdbbcacbcacbcaccdddbabcdbacbdacdccbdbddbdcdacaaadabbcaabaabcdcbcdbdcdcdcdcbbdcddccbbdaaccdadbacdbdbabacdbbaabcdcbddcbabaddacdcadccaddcbdabcdbbcddbccddaadabbdaddcabcaacddcbbccbbbddabcddabaaccbcbadbdadcbcaccdbbbbcdcdbbcbbcadbdabcacaccaacbdcbbcdbcbaabcbacccadbcdcdbbdadcaabccdbdabbcddddacccbabadbaabddcdcbbdcadcddacbbdbdbbbaaaddaabcdddbcbddcdbbbdacbabbdaaddcdbdacdbbbbdaaccaddddbddcdbaaabdadcdbdcbcacadaaddcbddaadbcdbcabcdaadadbccabdadaccdcabbabbbaddddbaddaacdadbaccbddadbabaacddbddcacbbabcbdcbacaadbaaaabddccbacdaaaccdbabbdcdcbaabdacaabccdacaacbdcdadddaccccbaccaabacabbabacbabddacacbdabccbcddaabaacbcdbadccbdcaacabbcaabbccdbcbbbcdabddadbdddadacaccddbadabbbdaabdbcccbcabcbbcacbddcbddddadcaaabbddbdbcbdcdaadcccdcbdcaaabddcdcbdccabdbdbdcdcabddbbbadbddbaabccbbabacacdaacddadacdadabdacadacdcbcdacdadbbccaddbbababbccbdaaaacaccbdabddbccdaccbadacbbbcadabcbdaddcadccdccaabbdbbcdaababadabcabcdabaccbaacacccbdcbcbddabbbdbdddaccaacacbadabbddbabdadcdcaaddbdcbbbbcacabaacdbadabdadacbaaddcacaaacbbdaddcabddbcadbccbadcddddacdbaddcdacbbbbbccbcacddddadaacdddcdccbdaabdddccabcbbacdbbddddcddcaaabdbcbabdbbddbcdcabcadccdbcbcddaaccbadbbcaaabddacbccbacddccbbadccbbdaadcaddcddaddcaaacaacbcadddbccabbaabccbcacdbbacaacdddcabcdcacbacbcdbbaacaacdcbabdbabddbcbdccbcbdbdabbaaccbcdbbdabddbdccdcbabadcdbdcdbccbdcddcdbdcbbcaabccdbdcaaaaaccbdabdccacdbddadbabbcbdbbbdcbbdbabbcacdcaabcbbbdcabaabbdcabbbbabccccabcdbcddbbabdadaaccbcccdadbaaadbabcdcdbbabdddbadadbbbcbdcdccccabbbdabdddbccaadddacdaaccbbaaadcddcadcddcdbaacabcccdbabadaacbadbcaddcddccabbbcddadbaddbdadcdddbcabbdacbddabacbacddbcaccaaacdabcbcdadaccbbcdbaacdcdbbcbaabaaddcdacabcaadbcbadacdaaabadbacddacabbadaadddbcdadbbaaacaadcccbdbdcbdadbdbcccbabcbcbbcdabbadddcccaaaddcddbddbdbbcddabbcbabdabddaddadbbdadcbabbacdddabababdddacdacdacacaabbccddabccabccdbaadbbaccadacdcdadbbcacaddcbbbddccccdcddbbadabcddacbcbababdddbbbbabcabddbdcccdbdccdcbcbddbcdbbadbbcdadbcdbcbadccbbadbbbccdbdcaacddbbbbcabddbcbdbdccbadddadbcbbdbccabdcaccbccdcddcbcaacbbdaabdcbbbaddbccddddcdcbaddbadabbdcdbdabdaadccbacadbcbcdcbdacacaabddbadabddbdacccbccadbdddaccdacbcbdbccadaccbacaacbaaacbddbabcabbaabdacacbcadadbccabaccaabbabbdadbcbddadbbbbaacabbdcccddbdcbbdbbccbcbbccbbbbccbaabadcadcdbdbadaadbbccaadcdcababadcadadabbabbcdccacbbdabccbcacbcacdabaddccdcddccbbcabcdacdccdbdbbcadddcdacdccbbcaaadcdbacaaadabdadacaababcbabaadbcbccddaddddbdcadbcdccdbbacaabdcadddcbcdbacadcacccabcdcccdbadccacbaacbcbcbbabccdbcbcadddbbdadbbcacaabaadbdcbccdbbbcbcddddcaccacbcbcaccdaaaaddbbadbddddcababacbbccbddbbaadaabcbadadcdcbdcadcdcbacbdbbdcdadbbaaccbbdbcbabdcaddacdaabbbaacbcddddbdbddcadbccddabdddbdcbabcdbdcdbddccabbbdaaccdbaadabddbccabccdbccdccabbadaadbaaacdbaddbcdbabcccddabddcadcababcbbcacbbccaccdbbacabddaacbbddcccbddbcdcadddbbabbabacabbaabdcbacaddcddcaadbbacbdaaaacddbcaddccbddbcadcacddcbbbdacdbbadcaacbccbdacdadcbbccbccaccadccbbbadacdbdcdbdabdcdcdaccbbcaacbdbadbccdcbccaddbbabcbdaadbbaccaacbcccdcabcdcaccadcaacdcbbacbabbddccbaaaddbabaabdbdbccdacabcdabbdbacbccbcdadcacbaacababddbbccbbccdbbabbbbadbcbdadbbdbacaddddadbdcbabadbcccccabaacacaaddcbabbaadabaabddbacccaccaabbdacabbaaadadcdabcaaaadbbcaabdaadccabccaadbbcdcbabaabdbdcabdabadacdaabbabbacabcdcbbbbddddccdbcbcbbbbabbcbccbbbbcabbddbdcaacaaadccabbaaddadbabaaccbdcaacdbcdbbadbbabbabcbddabccacdaabcdbabaabddcaabdadadaaddacdcbdcbdddccadacaabddcccbbadaadcdcdcdadcdcacbcbabcccacdbdccbaabbdcdcbbddcdcadccababbbaaddadaddacbcddcdbddabacccaaadbddcdbcabdbbdbdcacadcadbabdcbadbcaccdcbdaaadcbaabbacdddacbbcbdbbbacdbbaddacdabcddaabdcbcdcdacacacdcaadadcacdbdaacbdbacaadbbbcdaabcadcdacdddccddbcdadaabcdddabddadcdcaabccdabcbdacccbcdbcaccbdddcaadbacacdbaccdcbacdabacbdbdabdcbbdabdbcaaaabccbcababccaaaabcdcdadcdbaddbbcbcbcdddcaddbccaaacbaadabbdabdcdccaabcabdbbadaccbbdabdbdbcaddbccdacbcaccdaddbbaabcbadaccacccbbdcadacdcdbabacddadaacdbdcbdbaddcbcaacbdadcbbbadcacddbddcccdaccbdababbbdbbdbacbabcdcddaddcdbccccbcdccdcabdaccbbadddbcdadaccaddacdccbddbddbccbbccabadbddcacbcbdbabddbbaccdcdabbccadbaadbdacaadbabdababcccaabbadbcbdadcacddcbdabcbcdbbbbdbbddbabcbdbdbcacbacdccacdbcbddaaaabaadacbbdcabccddddcdabdbddadcdbaabaddabbabdacabaaccadcbbbcddabcaaaddcadddababcabacdddcdbbcbddcbbccaaaaacababbdcabdacccadabaaadcabdcbabadcbdaacabbadabaaddbbddabcbdabcacabbbbcbccdcdbaaaadabdccdccacabdddcacbccbcaabdbcbdcbaaadddcdbbcbaababbbadaddbcccaccabaacacabbbdabdccdcbcdbadbabcdddddddbcccbacdadbaabdddbadcabdccabddcccacaddacdcdcaddddcbcaaadbbdcacbbabaccdcbddcdcadbbcdacacdcabdacaddbcadbaaadddbdbbbcbcdcbcabaddabadddabaddcadbdddbabddcbadabdbdddacbadcabccbdbabdacbaadcdbcaacaddbadbcaadacccbbbdaaacdaaddcbbccdddddcacddcaadadddbcbacbcdaadcdaadbbabdddddcbcaacdcbdcdadacbabccbbabdbdaabccdbcaadccbccacddacbaabcadcdcbcadcddbadcbbbddbcbaddaddababacccbdcdcadbabbddacbddcdcbddccccddabcddaadcdbabdacddbccbaaadbaddaccbaaccaadddbcadcbcccdaabcdbccdbaabdaaabcdcbbdbdddcdcccbdbabacdbaabdadbdaaadccddcdaadddabaacbdddccbaaadcccaaaddabcacabccbdaabdabababddbcbdbcbbdcdcccbdaaacacbdaccbbbaaddabcaddcadaacccdddcbaccddddcddddbbcabdccdcdddabcbddacaaabbbcbbacbdcccdaacdbddcabdbdacccddbabdbbbbcadcdcaaaccddaababbcccbadddcddcaacdbdcdbccbbbadadaaabccdaadbbccdcacdbbbdacbcbbbddacbccbbababcabdcccbadbacdbbdcadcaddbdabccdbcccacaccdbcccdcdccbbaddbcbbcbabdbdbbddccabddbddcaabdadabacccbaddadbdcbcbbbbdccbcadbddcbaddaacaddaddcbcbddaadbadaaaacabdcbbddacacdacccdbacababdbaccabdcacbbdaccdbddbadbdddaccbadccabcaccacbcddaacbacaabbababbacbaabdabdbbbddacdddcacddcdacbaacdbabdccbcdbdaddbccdbcccabbdadadaacdddacccbaadacabcdaaccadcabbaaddbbbbcdabdbabdcdcdadcdcadadbadcdbacabaccdbdabbabdbddddcacdabbabadccbdbbdabcaacccddaababbbccddaabacacdddbbacdbabccdddcbbcddabaddcadabcacdccbbbbbbacadddbbdaaacbadbaaaccdcbdbcabaadcbbbcabbaddbddabbcbdaaabbaccaccacaadccbdadcadbcdacbbdabdddabdcccdcccbbddcbdaabcabbbcdcdadcbcacddabbadadbabcdddcbdaccbddcbdadbbcdbcccdcaacdadbabaaccdbacabaacbddbdccddbcddbbcddbdbbdabddcaccdacbcbaddacaabdcbccbaacabdccabdbdcdcccddccccaacbbdabdbbacbddbbaadcacbcbaddcbccbdcacdababbbcababdcccbccbcabaadddcbcccabcbccdcaaadbbaaacbdacabbadcdbbacdcdbbbcdbbddddddddccbbcbbbadbdacadbdbadcabbcaacbdddbccbdbbadbcdaabadaccbbcacdacadbdbdbabcdacbdcaaaadbadddcbadaaddddbaadcdadbcbcbacccdcdcacaadcadcccaaacadcdbbbccbabbdccacacddbddaaddbbcacacdadcabccbbabcdbbbbbcbcbbabdddbdadaaadbacdcbcccbddaacbbaddaadccdcbcadaabcadddadddccbccadaadbccdacccdabcbddcabbbbdbbdbcbdcccadadccabdcbdcdddcadacbaabdddcdbabcbdacaddadcadddbbaabbacbdbcabddbcbbaaaddabdabddddabbaacbadcaddbbcbdcccbdbbdadabadbdaddabdbdbaacdcccbabbdaaadcbbbddddbabcdcbabddccbbbddbbadcdbcbcdbbdbbacabccbccbbbcdaddccbaacacacccdcdddbacdabaaccdcbadcdbadbbcbbbddaddcccdbacdbddbabbdacdddbdccacdcbaaccbbdddaacdbbbdccdccacdbbdaaacdbdbaabaaabcdcbabbacaabbdadbcadbcddbbbbbadddbdcbdcbadbcdbccbdbcbcacabcaccdcccaccacbddabddbdcbaddadcbbaccbbdbdaaddcacaacbbdaccdbdaaabdcaacdbdaacbbabbdddbcacbdccdccbdcbdbbcdcbcaccdcbbdaaabdddaabbbccbabaadacdacddccdcaacbadcdbddacadabcbdacaaaccdccdcacbcbdddbcacbabdccdacdcdbbccdaabcccbdcdbccbdaadbabcddaabbbabdcddbdacdcbddccbcacabbbbaddcdddbbddaccadcbbabddddcaddbaddbbccbaadbcaaccdbbccdadcbbadddbabacdbabbbdbbccdcadddcadabcacbdccacddabdadadaabcbcdabdbcaadbacabadbbbdddbdbdacdbaaaaaacbdbdcccccdbdabcdbddacacdcaabbcbbcbddaccccbcdaabbaddcaccabcdbadaacccababcabdddbcddaddacbaadacbbacaadcdaddbbdacaccacbaccbbbbabdabddbdcddddaccdbbabababbdaaadabbbbcbdddcdabbadcaaddbaacbdaccdbdcdadbabcdddbcdbbbadaaddadbaabdccdadddaacabdbcccddcaabdccadcabdbccdadacbabbddbabaaddccbabddacddcadcbbadacacdcdcdcdbdbddbbdcadacdcacacdbbdadcaccabbabbbadbcbccbbabdddbadcadaabcddaabaaaabbbbcddadbbbddcccddcdbbaccdbacaddccdbbaacbcbbdbcabbdadaadbddbcbaaccabacbdacdadbdcbcbccabacbbccbbaacdccabbbadbbdbddbdcacddbcdcbbccccddacdbcadbbccbbbbabccdbbaabcbdbbbbbdacbbbacabdadbdbcadccdcabcadbddbdbccaaabdcbabbbbcbabdcabbbbdabbaccdccdbdccabdbacccbdcbccababbaabdcddbdcdbaacccabddcdcbacdaccabdbbdbcacbbdadaddaabcacccbbcabadcaaaabcdaacddddbadbdbdabcddbabcaaadccacccaddbcadccdbabadcbadbcabdbabcdabdcababadcbadccbadbacbbdbccabdacddbddcaccccbabbcbdcdbccbccdabbdaadddcdabdacdcbcabbdcccccbacbbcabdccaaddccdcddaccbbccdddaacbadabcacdabacaadbabdddabcbdcdabacbcdbaabddaabdacdacbabccacdacddbaddbdaabdddcaaabbacbcdabaaccdacccbbbabacdbbacdbdbabaaabdabacbdbcbcbccdadcccccdadbddccdbacaaaacacabbabddcbaacaabdcbaadcbbcbdacaaacccdabcdbaacaddbbdbaaaacbabccdcdbcaabaacddcaabbdaaccbdbbabddadadaaddacaaabbbbdddaacbadccadccddccccbbabdbbdbbbdcbcbbdacacdcdbabadcadcdccdccacabcbdadbbadbbdcbbbccdbdbbdbdaabdcdabdbccbcbcdcbcbbdcbbcdcddcdddcdcccaaccccabdabbbccbdddbaabacdbbababddacbaacbaaadacadbbbccbabacacabcbddabaaadabbcdadbbacabcbabcbbacbddabcbddabaacabaabaabbaaccabdcdcacccdabaccccddbdddbccdddbdbcbbadddbdcdaaacacadcbcdbdbdbccaacbabccbcaadbcdabdbaabdddabdbabdcbcccbdccdccbdaccbbdbccbcdcacbadaddccbdcdddbbdadbaaaacdbcbbdbddbbcbacadddbcadcbbadacccaabacbaaadcabaaccdcddccbcdcaddbbdbacaaacabbdddccbcdadaaacbcdadbacacaadbbcbaadccdddaddcbcddcbacdabbbdbdbdcabcccacaabbadcdbcbdcbdcbbbacaabdabbddbcbdadddbbccbadbbaaadbaacdcbaabbdcbacbbbdaaaacabdacdcbabdacdcdddbccaacdadddacccadacddaddadadcbcabdbbbcdacaaccbabdbdbaaddcddcddbdabddccccbdbbbcbcccddaabbadcabbddbadabdcdabbbdbcbddbadbbdbbbaddddbcbbddbcbacdcccddbddcbacbaacbaabbababdbbdbcaddcbcadadbaabdcaaddabbcdddbccbcdabccaacdbbbddbbbcdbcaadcbdcabcdcdaaccccdddbcabbbabdcbbdbdccabcdbcaacaaddacaabdddddacbcadcbbababacdbcccbccdaabcabaaaababadbadcddbdbdcabdabbaaddbcccdcacbaddadaacbccbdbdaaaaacdcdadbabbcbbcdcaccabddabdbbcadcbcccbbabcdcbbabdcbaaccdbcddccacbbcaadbcaabdaaaddacdbbddadbdbdbdbcdbbbbcdacaadabccbbbbbddcbdbbbbbdcddbbadcabcbcbabacdaaacbdddabdbccdcbacdadaacadcccaacbadbacbcbacdbccbbcabaaaddaddcbacbaadadbadabbdbaabdbbccaacdbdaddbbccdcacbcbdbddbbbbaacbddabdbdbddcddccdbdadbadaccadacaabdaacdcbbbbcabdddbaddcccabaacdccbbdadddbbabddcabcaadcbddcbaacddbbabbbbbacdbadbcccccdabcabacdcdcabcdddabbcabcdbdbddcbabbbbadabaaaacdaadddcadabcdbacbbdbaddcdaabadacdabbcdbdccaddcbcabcbdbbdbbbdbaadbdcdbdddcbdcabbadabbbbcdadadacdabdabbaddccccadcdcadacccbbdbbacabcbdcbdbbdbcdaccddcbbaacbdbdcbaacbabcdaddabbcbbdbbbaddadbbdbcbbbadbaddbbdbcdcbaabbbcdadbbdcddababaccbdabaabcbadadcaccbccaacddcdddcdbadbcdbccddbabcdbbaacabdadcccacdadacccddadddcabcbaaddaadcbabbccccaaabaddacdcabbaacbbbacddbdcaabcaaaddbadacbbaacbbadccaddabdcdababcabbdaccaaacbbddbacdacdbabbcccdbcdbadbbdcbacabacddbccdcacdacacbacbcaaccdccacabdcbbdacccacbbcadddaabadadccbcaadcadcdbcdcddabcadadbdbbacaddaaacabcdacbbdbcbcbcbaadcbcacacbacdccbaaaabbcdbcddaddccddcbdbaccbadadacabadbcabdcaaabaacbddbaccbddbbcdbabdadcdccbbbcadcbacbccccccdbabddadcbbbbaaddbbddbdbdacaadbdddacaacaacdacbbadadccadddbaaabababbbadcadcbacbbbcadaaacccbcbddabdcbddbdcdabbbdcaadddaabcbcbaaacdcddadabaddacbadaaccacacdacabcbadbbacaadadbadccabbbcbbddbacdcbcdbabbbdddcbdccaabacdbcdadcbcdaacdacbaabbadacaacadabcabcbbddacdabcbbdaadcbdcacbbabdbbacbdcbbabdadbcadadaaadddabacacddcdcccdadcabcbadbbcaccbdbcbaacaabaddcbabccddccdcdbaccdbabcbdbcaacabccadacadcdbccabbaadabdbacccbadddbcadccdddcdabcdcbadbdddbcdcdcbdbcbdabcccbdbdbbcabcbbabcddaddccaabdaadcbdccdbbbbccdcdbaacdacbabdbbbbdcbcdaddcdbdbbadacbbacbadabbcdaadcdaacdbadcbddcccccbbbcdcadddcdbbaabbadabbddddadaaddcccdbadbdddaddcacaaaccabbdbbadaadcbcabacdaaabdadacbabcaadccbaaacdbbdcadbccdbdbcccbbdabbcdadacbcabdbacdcbbbddccbbcabcabcaaddcccaacdbdccccadabdaacdcbbdabacabbbcbcbdacccdbadccbcdcbbcbcdbcadabcbdcdadacbaaadccbbccacacddccddbdbdbccdaadbdbdaabddadbadbbdadcbbdcbdbbddaadccbaaabbddabacbbbaacdcdcddabdadcbccbbccadcdccbdabcbadbbadaadbacaaddaadaabdaaadbdadcbaacdddbccdcadaacaadccbcbaabbaaadbacbcbbabcaddcbccdbacadababbaccdbbdbbdcbaadbcacbdcdbbcaaacbccacbabadaabcdcdaabacaaadbdaadaadccabdabbcaababdcbcbcdcabbcabbacaadcaacbadcadcbddcabdcbdbadadadcbcddabbdbaccacdbcabbcbcacdcacacdacabdbacaaccadcddddbbcbbdbddddcccdabbccbbbbcbadcdbabbcaddbcdacdccdacadccacaccdcdccbbbdccaaadcbadadddacaaabccbabcdbbdbbdcbcbbbbabcacaadcabdacbadcbdcadcaabacdacaaaaaacbdbbaccacdacccccacabbdcbbbbbdbdcadbbababbbbdcdddcbcccdcbaddaadbadabcccbbdaabcadbdbdaaaadaabadbadcccdabacaaddadadddcaacddbddbcbbcadccbbcbaadacabcddbcddcbadcaadbadadadcdbccaabbdadcccdbabcaaaaacdbddccadbaacbcadccadacacbbbcddbcdcbbcbdbcddbcacbbaddcaaccdcbcbccbdbbdadadccacbadbbdcbadbdcbadccbcaadccaaccbcdcbdbaccbaccadcdadcddcbaacddadcabddaadbadbbaababaaabdaacadaaaaddbcaabbdcbacddabcdbcdaccaacdbcadaddcddcdbdaaddbddcbcadcddaabcccbcacdaaaaadbcbdccabaadadadcdccbbdcbdcbbaaadabbbadcbbcbdbdcbbcbabaabadbddabcbdcbadaabaccdadcdccdabcbcacbbbdadbbcdbdbcaaaabababbbddbdaacbddbaccdaddbdcacaabcbdbbdbbcabccadcaaccddbacadddadcbbddcdbddabbaababbbcbdacccbadccbabdbaadccadadabccbbcbcabdbbacddcdbaabaadbbcbaaacaccdaccdaaadacdaaddccabacddcdacaadcdadacbcbbbbbadacaddccbadbbdadbcaaddadcddbaddcadbdbcdcbcabacdcccbdcbddbbcaaabcbcadbbaddaacbaacbadabdaaaadcdabaccacadbaabdddaaabcaabdaacdcdacdbdcdaccdcaabddccdacbbacdbbaadddcccdcacddbddcdbdaacccabadddacacbaccacdcddcbbcdacddadbbccbadacbdaaadabaaddcddcdacddbbddbabaabdcabbcccdadcdbcbaadbcddddcdbaddccbcdbbacdacdadadcddcbaddabddcacbbdcaacabbcaacbcbcdcadbcddabbbdaadabdbdabbdccadabdaccdabdddbbcbccadcabdcacbbdddcbbccbabcbddabadcaadbcdbbcddcbdbabdddccbdbbaaabcdbdcadbacbddadddacccddabbcbcddcddbdabbbbbacaacdbbbcacaccdacdadbbcbbbcdbaacaaaadcaadabaabcbaadaacdbcadadcdcaadabacaadbcadadcbdbacbacccaacdadbdbcadccdadcaaaacbcbcdddadcadabdcddaaaaccabdcdcbbbdbdcbaaaadbccbddaadccbdddcadaccbbbdabaddcbcaddbbccbabacbccdcbdcccdddbdacbcdacdcbcaddadacadbdcbddddbdacaabdbcddddccabadbccdddaccbdaaccadacbcbcbdcadaccbbbbcbbccbaccbcbbdbabdbcadbbcbccabadbabcdccaabdbabbddadddccdababccdbcaacdbadbcdbbcbbabaacbbcbbadcdbadbbbbccaacabbadcadbdcdcbddbddabcadddaddddbbbdcdcbcacbcaaacdcaccbababdccacaddcbcbcaaaabaddddbdbccacdcabccbdcabddcbbccbacaacccbbbdbcddabbbaaccbbcdccbabbacbbbdccccbdcabbdadbaaadccbcbcbabacdbaddababcddcabdcaabacdddbadaadbabcadcbbdcdcabccddbdddbcbadabdaddadbdaaaddbcaabbbaadccdbdbccacbdadbbcdccadbbcbdcabbdcaababbdabdddbadcbdaabdbcacdbcabbdddbaadacdcdaabcddbdddddabbadcbabdabcccacbacccaacccccbdadbcbbaddcdcddabbabbbccadcbdbdcacbccbbddbdcddacacbbabaaadcacbccbcbdddaaacbdcaadaadcdcbaddddbbacdcdddbdcdddababacacdbcacabadbccdbadbccbbaacccabccacaddcdcbacddbbbbcbcbcdbadcbbcbddaddcadadccbabddcdcadbddacddcabaccddaacaabbbbadbdabccbabcaaccbbaaacbddabbccabdcccdacdcbacddabccdacbabadcacabbdbaabacdabbbdacabcabbdbcabcdbdaabcabcbcccdbcbbcabcccabbcacdacacbdacddbacabcdddcaddcbbbccbacdaadbcccaadcbabccaabcaadbbadbcbbdbaaaccdcaadccdbbbcabadaccddbacbbbaddccdbbcdbcaadccdbcddacdcddcccadbccbdddacaabccccadbabcaaccacbcbaddacacadbccaabdabbccadbaddaccdaccabcbacaaadbbdabacccaadcaccbcdcdccbaccbdbcccbacddbdddaacddcabccbdacbaadbddcbcddababdbdcababcdcaaaddddddbaadaddcbccaccabbcabcdccabbadcccdcccbacbdbbcddbabacbdcdadcaaacccdbbcdabdbbbdcabccacbdbcbdddadbcabbacadcacdaccabdacbbadccdcbdbccabcdbdccbbadcccbccbadacbbadddcbbcaddbbaddacbccbccdbdaccdccaaabbacdddacacbcaabcddccdcbbcbbacbbdcbbcbdaccdbbbbbdbbbacddbdaddbddbccdcdcdcadcbadcbcabccdcbcdcddbabbddbaadacacdcddccdcaacacbbbddacbcdbdcccdbcdddbdcbabbbdbdcbdcbbbddddbcaadbbbabadbcaaabbccdcdcdddabddaddbadbbbbbcbcbacdcaaccbddbbdbabaaccccadbbdaddccacccadaccddabbabbaccccacbbcbdadcdabaccdccaaaabaacdbabacccdaaaddbacabddaaaaddaadbadaccadadccbbcaacadddcdaccccdcccbbbacbdcbbbcacbdcacdaabbcaaacbbaccbdcacdabbdbcbabbcabbbccbdaabaccdaacdccdbadaacacdbcccabacccbbbccbbddabbdccbbbbdddadcdbbccaaaadbadadcbdbdccacaddbbbbadbddddccbbbcbccbbbadddbbddaaaaddaccddacdaaccbaabbcbdababaaddbabdddbddccabcbdcbcdbddaddbdaabccbbcdcdbcbdaccaacbabacbdabdaaddbbaaacaabbacbdcbdcdccdddcdaabbbdddbaadddadcabdccbccccbcadcccccdbababbacadcadabdbcbacbbbbdadbabdaaddbbdaadbddcbcdabbaaadacddcaacbccddccdcdbdaddadcdaabbadbddadcabbabdbcabdacdbaaababacaaaaddaaadbbdcbddcdcbdbbccabcccbccccccdbdcaaadbacacddadbcacadcacacaacaccdbccacccabcaaaddacdccdbbbdabbbbbbdbaadddddacadbcbccdbddddaadaadccbaadddbbddacaccabdbacbcdbcbdccdcdbdaaacccccccbaaccbcdcbcccdbaabbccbddabbcdadabcaabdacbbdbdbcacdcdcacdbabcabbccdbbdbbabaddaaadbaddacacccbcbcccacdacbdcbbdaacaddddbdcccddbbccdddcacccbcbabdbdcadbdabacabbdacadbabaccdaddcddccabbaadacccbbbccdbdbdadabddcabdbbbbabddabbbbdbdddbbbaacbcaabdddbaddcaabbbbaddabbdacdacddaaabbabdddbabbcddbbbbdcbbadacdadaaacaaaabbdacccbbacaddcbcdcabbcccbdcabbbacabdbdcdcdbbdbdbdbacbacdabacbbddcccacbdcadaccddacdbaddbdcddacbbdbbadcdccadcacabdbddbcaaadabcdcabbacbdbddddbcccddbadbabadcddababddbcbdbdcbdddadcdcdabacbddaaccbdcacccddacddbddddcaddcabccadbcadcabbabdbadbdcccbbbdbdadbbcadbccbdcbdacbdaaababdcabcdcbaccdabdcdccbbbbbadbaccbbaadcdadaabcaabbadaacccaabaabbaaacbaccabddbdabbaacdbbadcacdcdbbdccdaddcadabdbdcbbaaaadbadbabdccabdadccbccdbdddadacbcdbabaddaddcccbddbbdbdbdcadacacdbddaaabadbdbcdacddaaabdbdacbbcbbcadadccdaacaaddabbacbdacaadbaccaddbdcbbacabddcdacbdadbdabcaaacbadddababdbadacbaabbcddabbcbcbabcaacadbabbaaabbccabbaacbaaabacdccadbbbaacdabddcdacbdcdbbcbabcababdbbaadcdaccddddcbdcaadaacadaddcbddcddaabcdcaacbbddacddcbbabcbdcaadddaaadadaabdbaaadddbcabacbbcdcababbcbcbaddaadcaccacddcbcadcdbccbcaabbacdbdbbdddcacdaacbcabccadadcccdaadccabcdddababbccdddbbdcbbdaabcccbbbadcdbbbdbcdabcabbbcbbcdcacdddaacdacadbacbaacdbcbbccbdcbcbdaadaaaabccccbabadccddabddaacdbdbbdbdabdaacbcdcadbdbddbbdbcaccbabababbabdabbbccdabbacdbcadcdabccacbacbdbabbcbcaadbdbbaabcaacbaaadabaacbbddaaaabbacaadccbcdaaadbacabbbcccbccbcaaadbaabdadbabadaccacadaccdbdccccbaddbcbcaddddbabcadcddbcdacccccabcadaacdaaadbcbaaadcbabddbcadcbabdbabccdbccaaadcabdbaddababacaaadbdbbadbadaacbabccbbbddbcddcbacabadcbbccdabaaaccbddbabbddbbdbcbbcbcbdcccababcbcbbdddabbabbcccbbbacddcdaccbcdccacddbacccacabcadbbcbaadcbadbbbbacdcbccacbacbcdbbdcabaaadcaddbcbddcabdcdabdcddabbdadaddddadcbcdcdaaadaccbabaacbbdadcaabbdcadcddbbacbacdadaaabcaaabbacdcddbabdacabcabbadabbcadabcdccaabdcddcbcdaddbdbbaaccbbdddddcacdcadbdccacbbbdbdaaaadbddadacaabacbbdcbdbbcdcdbddacbcbdaabadbbddcbbcbaaaddaaadcacabcbadbbadbbabbccdbadbdbcddadabbdddbaaccbcacbacbcbcdddcacdabcdddadababcdaadacdacbccaadbcaabaabaacdbcabdbaddadadadbaaaaaccbbddabddccbdddddbcddbdacadbcddaadbcbbadcbbbcdccddbcddadcccdabbabaaaacbbdccababaaadcbabbcdcbbcadbccacbbadaadadbabcbcabdbbadcbbbdbadacbbccbbcbcadccbbbacbcdcccacacabdacdcbdddddabddacdddbdcdcdcdddacaaacccdaacaacbdbabdcddbdaacdcbbcdabdcbcaaaccaaddccdcaccddaabcbaccabcbaadabdaaddddbacdbdacaccdbcaabbaddcaacbddcdaabbbacaabdbbbcbadabcdcacbbdbcdcadadcabaacdabdcacbdbcdaabbddbcaaadacbdacbacadacaddadcccddccdcbaaddaabbdadcadbacdbaccdadddbabaaaaabbccaabacbbcdadbadaaddaaaacdbadaadacdcaacbbdccccdcccbacdcbbbcadabdcddabdaddcdcbcdacccbcbbabdbcdbbabdcabdbbcdbaaccbaacbddccbbacbbabcbabbbdadabcdbdcabbacbacccbccccdacababccbddaccccbbccadbcacddbdccabbccdaccdccadabcabccbccdacddaacdaaaccdbcdbadbcbbccaadbcabbadbbaacbcadcaadacbaabdaabbddabacaaaaddcdbdbbbaacbdacdadbddbccdabdbaccbdaadbcabdbdccdcdbcdcdbddbdbbdcccabadadcdadacccababdbacbabbbabcccdbcadbaaabbcadadadacabdcdbdccababbdadbdbdcdcdcdacbdcbcddbdbbadccdcbbdaaccddcdcdbcbbdcdcabbdcaaadbabdacaadaccabbaabdcbcbdcbbcdccbdbbadbbbbdcccaacdbbbbcaddabdbdddcbaaaccccbbabacbbcdbbbacdcdacdacbbabdcbbccbcdbcdadabcdbbbabdccbbbaadbabbddbacdddcccdcbcaaaaddcbadbcccacddcbddbccddbbcdccacaabdccdccccbbbcabadcbdbbcadbbbcaabcdcacbcdaacabcddcadadaddadabcabadaabddbbcccaddacabaacdcdccdbbacdbbddacacbcbcdcdbadcabdbbbaddabdcbbabccaaadbcdbdcbbbdbdcbaddcccbcbbcabbabaacadbdaacbaddbaddbcbcdcbaddcaaccbabccddcadcdaacdccbdbabdbacccdcdddddbdddabccabccadbacdbcbbacaddcddacccaadbaddabcbbbaddadacbccdcaddaacbaabddabbbbdccadcaadacadbdcdbdcbbbdcbdcdddccbabdcccdbcadcbcaadcbacccaccbdcabdacbbbcaccdcdcbbbdacbddbaaccaccdcdcbbaaddcaddbacadbabbdcbdabadcaacbababccccdaaddbcadcdadcacdbaacabacdcdcdccdbdabbcadcbaabaaaacadadbcaccdccdcdabdaadcabccddddbbdbcbabdbdbaaacdccbbbdccdcdddcdcadadcbbbbddbcdacdaddcaaddbdbddadbbdcbcaccacbdaacbbcbadcbaadacbdccbcbccaaaadbacbbdbdcccdbccbcdccacaabdddcddccdddbcbbccaaccddbccddbbbcddbacbacdcbbbdbadadaababccbcbadcaaabbddddbaccdaaddbdddaaaabdccbbbbbcacdbcdccaaaacacadddaaccaaaaadddcabcdaaacdcaadbccccaaabdbbcdacbddaddbdcddcdcaddcaaacdbadccacaacbbcdccaaaabcdbabccbabbbcbcbcdaabccacddcdbdbadacbabcdccbbbdbdadadbadadbcacbdddbdadadcabdaaddacacdbabaddbdbcaadcbdbdabdbdccbbbabccbcccbbcdddabdacadddacadbcccdacbdaabdacbaabacbbccdacaaaabccccacaacbcbdaccbbdbddcaccdbbcabddacdaacbdaadbbdacdbbdbbdbcbcbacbbcbdbbcbcdbaaaacbdcbccabacdbdcbcccadddccdcdaaccdabcdcbcdcbadcaabcdcabcbcbadccdbabbdcddbcadaaabbbccbadcdccbbdaddbbacdcbdabcbcbdaabababddcccdabdaddcddcccccccccaaccbdddacbcdadccadcadcacbbdbbdadbdacbbdbbddbcbdcbcddbcbbabbdabdabbccbbcdccbbddcbcbcdccacaadcaccdcdccbbabdcbbadcaadccabadddabccccdcdbbddddccdbcdcabddbccabaddcdacabdbbabbcdbdaababdddadadacdbadcbdabcddbadadbaaabcaddcaadbaaabbaadadbababdbcbadacabdaddaddcaccacbaaadcbddccddbacddabcaaaabccbddbcccbcbcdaadbbbdddcdcddddbdadcbaddaacdabaacddcbdadcdbbcabdcbcccabacdddabdabbcbbbbbdbbacadddbadbaaddbbaadabbbbcbadddbadbbcdacacadbcbbdbcbadaaadababacaaaadcdddcbdddcacbaabdacbdddabdddadcbccdadadcaacabbbbdcccdbdddcdadcbaaadbadcacbaacadbddcbcadabddcddacddddcabbddbabbbbbdcacacbbdaaadccdabcbadcdabbcccacbbdabdbcaabcdbcbabcabcaccbbacdabdbcadcddbcaddadacbacbcccdddcbcbccbccadcbbbdaadbbccabadcbdccdbabbbdaadacdabdbdcdddaaadbbdadabccbaaddacdbbdabdbdbdbddbaccdddcaadabbbabdbccacccbccddbdccbdbabdcbcaabbdbcacbabaddcdacadbddaccaddcdccaacccddcbacbbdbbbcdcbbaacaababcccdaaadccccdcaccdbcacddcbaaaadcdccddddbbcdacccbdcdadcccaddacbbaacbbccaabcddbcaaacacaadaaaabddacccdaabdbcadcbabbcbaacacdacbaddabcccadcdccbbdadaccbccdaaddacaacacccaaababdcbadbdbbcddcccdbbacaccaacddaddbdadabdbbaaabdbadcabbcacbabccbcddcdbaaaabcccadbdaadbbccdcadabbaaaacacacdacabdcbaaabdddcadbaacbdcccbadcbaababaacbcdcadabbacdbbabbcbcdacaccbcdcadbacadbdcdabdcdcadcddddcbdbadcddcadbadbddacadbddbacabccabadaacbaadadadcdcccbdcbbddccdcabcbddbcbaacddcbabcbacdbcbacddbcdbdccaccacdaabdabdacccadddbabbddbbaddcccdcccdcaaaaabacbaddbbdcbcaabdadaddcdcddbabadcbabbbabdacbbdbcadaacbdccabacddaaaacdcbacabbcbabbcadcaaaabcaaddbdcacaadbbcabccdddcacacdaabdadbbcacbdbaaadbcdcbbdccbcacabaabaabdcdbdcaccccbcbdabdcaadddccdacaccbcccaaacabcadadcadcccddddadddbcaddcaabcaabccbbcdddcbbbbdcddaaabaddbdbdccbacbdbcbcbbaccaddabcadbdbddadccbacaabbcabbbacbbabcccdbcbaacadcbdbbaadbdabbbdbbaddcbaadcdabcdbccadbaadcadddbcdaddcbaaddaddbabdababdbabacdbbaaccdbccbdcdccaadabbbccddddddbacdcabbcbcdddcbaaadbcdbabdbccdcdbddbdccabbacbcdcddadabcbbaddbbcbbdcbacbaadbdabaaddbdcbcdcaddaadcdadacaabbdadcbbcdbabbbacbdaaccbbbbbabadacdbaabbcadacaaccddaaaabdbcacdbabbbdcdbadabdacdcdabaadbacabcaaadbacdabdaccdabbdadbddbbadbbccbdccccacbdddaaaccacccaaccccaadcaaccdbabdddaaadbaabdbacabbddabdbddcacbbcacddcccdcaabcacdcbacbadacccdabddbbbbabbdccbdddcdcacadaadabcaccbccccbcbdcbbdbbaaacabadabaddabcaddbccbdbdaadcccbdddccbdaabaadcccacdbdaabbbcadbbcddaacabdcbcacdcbbbdbbadbcaadcacabddbabcddbbbcdaacbdabbababcacdcabdaadadccbaddabcddaccbbbbcacdcccdcbcbbaccdabbaabaadaaadbdbccaccacdadadbdbcacacdbdcdcdbbacbbadbcbddcabacdbcbbaaadbbdacccbadabbcbdbccdaabdcacbddacbbccdddadbdbccddabacabbbdacbdcbbdddbbcdbcdcdcdaddcbddcddbbaadbcbbccabddcdbcaacdaabaadcadcdcbacabdaaaabcccbdbcbadcbdabaadcdcccbdbbcbdabadccadaadbcbcdadabacdbdcdaabdddabbabadadacccdaabddadbbdaabcdaabcbdccbddbdacdddacbacdbacdcdddabdcccdbbcaccbacdbdaabddccaccddbacdbdaabbbaadadacdaddcddbbcacbddcbdddcbdaabbdbacbaabdbddcbacdabbaabcbbdaabdbaadabacaccbbdcdcbdacdaacabdcdcdabcaaacbddccccaaaacbcadcdaacdccddccacddacdcababbddaababadbcdaacbaadcacabadaccaabdaacbaccacdaaacdccbdccbcadadbbccbbaddbbcdadccbbddbadbabaaaaaccdddbdabcaccccadcdccacbdbccbcbabcbacddaaabacacaadcdaaadadcdadadaaabcababcdbddcdcadbabdcabaaccdcccaaddacccdbacbbcaabcabbababddccababbdbcddacbdbabdacaccbabcdaccbccbabbadddacdadaddccacadbddaabdcabaddabaaabaadddbcdbdbbddccbddcdbbcdacbbccaddaccbcbdbaabcbcacbbadbdbbbdaaaaaaacbddbadabbccccdccababbdbbcbbbacabddbcacccdbcabbcccbdaacaababcdaaacdddcccabcadacccabdbdcdccaacdbcabadbbcaaddadbbccbaaccccbcdacbadaabbacbcabdaadcccddddabaaacbabbcdbdcdbbaabcdacadacddbbbdbcbdcacaadcbbadccaaddcbcbcdcbcbdabcdcccddacbcdcadbcabdcbacdbddbabcbddcdbdaacdacbcbabdcaadbbabbbbcddbbbabcdacadbbcdaddbddbadbdbdabdbbaccaabdcbcabcadbdabababdbabdddcddbcbcddabacabbbbbcdbdcbbcbaccadbadabddcbddabadcaaddacdacbddcbcccbacadbcdbdadcbdcabbcdbbadaadabcaaacbcabdccacccddadbddbabcbcdacccbaaaaaddbbbdaddacacddcdaddadbddbdbacdbdabdbbcbbdbdcdadadcabddbdbbacaabaabcccdadbaabacdcbcddccacbdabbccacaaaddacbbccdaadabbcbabbcabbdadcbddbdbcbdaabbabddbabcccbccabcbcadddbaddbbabbdcbaddbacabdcdabdbdabcabbdcdbcadccabccbdddcbbbbdaacccbabcbcacdaddbbaabacddbdaacbcbbdbaaabdabddaaadcdadcbacadbdcacabacddaaccdcbccbaccdbaadcbbcbaabadccaabaabbdcaacdabdaccadbdbaacbabcababbdbbcbaaaddbbadcbcacaaaaacbabcacadcdccadaaadbacaccbbbcdbcbcdabbbdcdcdacdabdabbcccacaadbdcaaddbabdccbcabbadababbbacccbdadaaababbbaaadcacbccabaabddddababadbadacccabadbbbbbadcbbccbcdcabdacbcabcdcaacbbddddacdcbdbdcaddacabcadcdccadbbbdbbbddcdbadddbabadccdabddbaadabbbcacbbbbdaaabaddababcdbddabaaaaccbbccdaaaddbdcdcdbbbdbbdcdcdabcdaddcbbdacdadcdacbadbdddddbccbacbcbbdacdcabdbbadbcdbbbdacdbbddbbdbdcbcadabbabbcdcbbadadabbccadaaadddadddcccacaababcaddadcacaddbdacdcddacdbbdabacbcbcdccbcacccbabddaaacbbbacbcadbbaaadbbdbdacdcabdadaddadaccbacbcaaaddbdcbcdabbabdbbadabaadacbbcbacbdcdcdadcacacdacccdcdbbdcbbbcabadccdbbabcccbdbdcaabbccddcbadddbbbddccbdbadbbdcccbdcaccbbdcdacbbcdabdbcddddadaccdaacbdbdadbcadcccabccddaacdbbacdddacdcdcbaccdddbddcdbbabaccbcaadbbbbadaaccccdbcdbbbccdcddbcbbadccdabcbcccdbcccaccbbdaddbabcdcadcaddaadccdbdccdcaaaaaaaadccaaadaaacdbbbaaaadddacbddcbbdcddcccacadbaddbcccbbacccdbbbccddbaaacaddabcddbdbbcbcaabacccdaaaddadbcadabbcadcabcdbdabdbadddcdadabdaccccddcdddbcbdcabdabbccdcdbadcacacbcbbabbcdabacdcbcadddbbaaacdbcccddbcdbabadccdccddaaabdddabbbbbcdddadcbacdabcddcdcadadddcbbbaaaadbabadaaacabcdcaadccbdabccadadacdaccbcccdccaacccdcabcdcabaabbacdddbccbcbcaadbaabbdcbcdbaccadcbbddaabbacacacaaabbbdadadbbbbbdbadbdbcdbabdccbdbcbcdaacbbddbcaccdcadcacbcbbabcddcaadacbdabdaaabbcddabddaacabbbccddbadcadabbcadbbcbcacabbadbddcbaadcbbdcabdccacaaaadbccbabccbabdadbddababacacbbbccbbcbdbbaacbcbabdacbaccdcbaaaccabcdbcdbccadaccddcdcccbacbbcdabddadabadacddaacbdcbddadcaaccdaabaaaaacdccbaadacccdbacdcdcbddcdcbdaccbacddcccbccdbbdabcdccccdcdcbbbacdcbbabdbdbdaacaabddabaaaacddbaccacdccabbcdbbbcdbdccbacccacabdcaddaabdbadbbbdabccdbdcadbaabbdcbcccccccbcaacacbbdbdbaccdcacccaacacccaadabdbdcabbacdcbaabddcbdccabdcdacdaddddaabbcdddbcaadcdaadcbaaabddcdbbbddbaddccccbabddabaadbbbbcbbcbaacdbaddabcacbadacddbaaabcacaacabccdccbcbbbdccbacbdaabbacdcbacabdaccadadadbaddacdbdddabdaaaaabbcdbbbbbbbbdddbbbbddbbbbcacbcdaaabbcadddccacacacbdaabaadddcdcddddbddcdbddbdabdbccbbdbcccabaaddddbbaacbbbbacdabcadaabcdbdbbaabccaccdabbbdaadbcddbbbdcadaacbbbadcbcdbaadabcbabadddcdbdacaacacdbcbadddcdcccbddccaabdbbbacadabbcaacbbdcccddcbaadcbcabccbdddacdbcccdcaaddbddbadcadaaddcddcadcbcadccaadbacbbcdabdcaddbcddacbadcdadaccddacaddaddacacacaacbacdcbdddbbbaacbbdbaacadbaddcdccddbdcadbababbadabddddddaaacbbadabcbbddadbddbdaadbbddabcaabbccdbbcaddbcdacaaabbddcccbaabcdbbabadcbbcdddadbbdcdabcbbdbbdddaaaccbcabaacdcdadcbdbdbbabccadccdbcaaadcddbcabcdaadcaadddbcbdacdccdddddaadcabcaaddabbdbcbdcbcbabbbcccbcbbbbcdcbcccdcbcbbbacadddcabaddcddcbacbaabcdbdcdabbadbddccdbbdbdbdacadcbbccddbaacbcbcaaaacaaabbaaddcbadccdbddcccbbdcaabdbcdadcadbcccdabacccdabcaacccdbabbbaaccbdacdadbbcabbabbbcbbbcbdacccacdaddadcadbabbadbbcabdddbbbbcdccbcbdcbdddbbcacdacdbbadcbbaadaadbaabcaccaacbbadbdbaaacdadccbddadddbbdbaabccccabdaddaccdcdacdbdbbccccaacdaddaaccaacccdcaddbcbccdcacabcbacadccacdcaabccdcccdbdbbbaadbabccdcdaabdadcaddcbbdccaaadcaaaacababdadbdabbbbacbcacadcddccdadbaddbbabaadddbcacbbdbbccdcabbbcddabcbdbacdbbcbdbabbbadabdadcccbccbdcbadcdddbcaaaaadccacccbcbbcdcdcccbddabbdbdabadbbadbaabbadcadadabdccbaaadbacbdacacccabcddaabccdaaaaabcdabcbdaabdddcbcdbbdcaacdabcdcdcccbaacbcabbcdddddadbdbdadbadaccdaacdcbdadaddbcbbcdabbbaaccdbabdbcdbaaaccbdccadcdcdadbabaddcadadbdccadadadbddbcacadbabcaacbbdadbddbbaadacdbcabdacadbccdbcbbabcbbabbaddaddbdcdbbadadacbdacddacdadddaaacbdaccaacdccbbccaacdcaabadacadabcbccdadbdbbbdbcdbddcbdbbbbcaddadaabdbdadaccddaababcadddbdcaaadccabcddbdbcabcabaabbacbdbcddaddddcbabdcccddcdcacbbbcccddbbcdddccbbbbcbbbcbbacbabdaacbdbccdbdcaccddadbcacbdddaccbaaaabbbdcadcbbabcaaaaaccddccccaacbccdcbbadbaabcbbdabcaccdacdccdbacadbbdbcddaddcccbdcaaccaabbdacaaaddaadcbcbcccbccbdcadacbbddbddbcdabdcadccdccadadbcdbcdaaaddacabcbbabbdadacbbacdbcbcbdcdbdbcaabbdacbbbaacdabcadccdccbcdcdbbacbcddadbdacdcbdcdddbadcbcccdaaabcadddbbbcbddaccbdbdcaaddabdbddacdcdcbbabbcdaadaadaabcccaadacdacabcdddaadbdccbddacdddacabdbdccbcacbbccdcdacccdbddcacbabdddbdbccadaacacdbabcccaabbabdbbdaaddddabdcbbababbaadcabcdaaaaddccdddbadcbccabadcababbbccccccbdaabcbaacbacabcadbbdcacbbaccaaaaacccdbbdccaacbabaaadaabdabababadcdbbbacbdaadadcbcbbbbababaaacdccccabdcddbabbccdcaddddbbdaacdbadddabccdabbdcaadddbbcdddcdcbbcaaacbadaabddbddcaacadbaadbbcccadabdadadacccbdcddbbadaabcaadbacbdccbaddbdacbaabcdcdbdddacbdddbdabdaacabcaababddcbcaabbaccaaacabdbdbaaadbbdcbcddcadcbbcacabaabadaccbaabbaccdcadbdbadacbbbbddabdaaadcbcccbcadbbadbbacbbaabddbbccddacacbacaadddabbccabaccabaddbcbcbbbdcacddbbdbbdccaaccbacdbccbddcaabcbcabcbaadaacadbbbaadbbadbaaabbcbdaaaaddabdbadcbbacadbddaccbcaadbacbabcbdbdddcaacbaabcddaaaccccacbaabadbbcbddabbaaddbdacbbbbbddcddcbbdcacaddbcaadbadadaabbdcddbcdbadddbdccaddddbdddcadbcabaabaaccaacbbbbacdaabcabdbccbcbcadcddaddbddcadadcdabdbcaabbcabcadabcdaacaddaabaddbacabbdbbcbbdbacadcccddcbbccdddcbaaacadabbbdccccdccabcaddacdabdccbcaacbccccddbcdbdbaabccdcccdccabacdcabbbcccadbbccdcbaaacbbdddddddaccbcbdbbdcacbaacadcacbdbbacdaaccdcaccbcbdcccdbcbbddbddabbbabdcdacddbadbdbdaabbdbadabcbaabdccdbacabaadddbcdbbbbccacaabdbbddaacaadadbdbbbaaabaabbabbadddcabaaaadddaaacbcddbdddbcabbddbdababadadbcacbccdabddbccacaadbbcdbbcdcdbcdadadbdbcbdbdcccacdddddccbbcdaababbdbddbddbaadaccacdbdaadaddddcbcadccacdcbbbcadabdabaddbabcbbbcbdcaabbdaaabcbcacadadabbdcbdcdbaabaabadbbcbddddcadddcabcdcacaadbbbbacdaacddbabcbccdcabbadaccaaadbcdbdddcaccdcddcaabdcdbcddadaccbbadadddbdcdbdddcbbabbbbbaacbabbccdcbbbcaaaaadabbcdaccaabdbbdcdddccabdcdbbccabcdbbdbaaddaabacacdcbbaccabbadcaccacbdababcccbaabadbdddadbaadcdbccdcddaccccbddccbcbcdccdbadadddbaabdcacbdddcdcaddbdccbcdadabbdbacccbdbdacacddbaaabbaaaddddcdcabbcabaaaaccccbccbaabddabdbccdcddadbcbdcdcabbaaaadaccdaadcbbaababcbabdbcbdccddaacdddabcabbcacbbdadbdcaabbbcababababacdcbdcdcbcdddbbcdaadcbaaabcaabaaabdcbadcacaccbddcddccadccdcbbdadcdbdbacddbcddddadcacaccdcdbcdcabbbcdadaccdabbdccdbacbadbaccaabacbdbaabaadacbbccbdccadbcabacacabddcbcdbbbadddababacaaccdbdbdbdcbcacbddbaccbaaacbccdaaaabbbddaacdbcccacbadabcdcadcddddbcddbcacdaaabbcbabcbbacbbbcbcacbdbdabaaaccaababaddddbcaddbcddbdbcbbbccbbadbaaabbcbbbcadadadccdbbbccbdabcaacddbddcbaaaddadbbacacdcbbbcabcdbaddcaaaacadabbadbdaaccacbcabdccadabaaddadcdbdabcacdddbcdbccbbddcabcabddacddbacdcbbddbaadbcaccdbbbbcacaddbaabbcabbdadcabdcbcbcdbbcdcdaacbbbadadadccadbacbbbcacaabcdacdadbdcbdbabcddaccdacddbbbbbcbcaaabcbabddbcaaccadaaccaacccaaddbbadbacddbcadabcabcdbabdacaabccabaacbbcbbbabbbcdbcbbdcadccaacccaaccdddabcbdcaaccbcbddccbdbadbdbbccdbcbcdcbacadaabbcbcdbcaabaacbaaacddddbcbdbbdadddccdccabdcbdcdabbbbbbdbadcbaccabbccbbacdcbcadbdddcabcddacccaabddbccdbdcaabddddbcbcdcabddaabbccbcbccbbbaaddccbbcbbaddccdbddabbcbacbcadaddcbaddadbdbdbcdcaabbdbaaccdcbcdacddbaaaabdacbadcdbaadbdbaccacdaaacacaabaacadcccbcabdbcbdccdacdacdacdaabbbcccddbcbadbcccadddbdcbdcdbcbdcddabcaccbcaccddbdaaadaccdbacddbbbbdbcabaddbdabcdcaaadacdbaabbdcadddbaddaddccacdcccacbbccbbdccccabbdaaddbaaadacaddcbdcacbabacddadcbbacdaddcbdabbcdacbddacdaaaacdcdabdcdbbadadcdccacbcaabdacadaadacabbcabbacdbabbbacbdbbadcadacbdbbccbdcbbcddcabbaababdbdabcdddbabddaadddddddabdcbdccdaddacaacadabdcaccbabccbdcdbdcbdccaddaabbcacaabcabdabdcabdcbadcdacaddabbddbdcccddcccadbdadacddacbdbcacaacbdcababacaccddbbcbcbabdcddccadbbcbdadaadcbbbdabcdcccaddddddcaaaaadbabcbbccaabcadbacaaaddcbcabbaadaabdacadadaddcdabadadccdcbdcdcaabdaadcbddddaaccabccbddbdcacbccaaabbdbdcccdbabdddbcdaacccdddcdcdabcddacaabbdbcdbdbacbccbcddbddabaddcadacccacabcbaadbcabbddbbcaddadacddbcadcabdcdbddbddcddadbaaadbbbdaacdbabdabcdbaddbbdbdcdcbccbbbbabdbaaabcbabacdbcbbcaddbcdbdadcdcbacdccccccbcabbdabccacadcabadddbddbacadbbdccbdadacccccccaccacddaabbcdbacbddcaaadaacddaacbabcadbbcbcbacbccddcacadcbbcbdbbddaaaababcbcbabacbbaddbccbbacacadcbdbcdbcdbccdccaccbddacdddbbbddccaaaddcacbbbdadcadaddbbcababdbbadcdddbbdcdbabacbadaaaddcbaadcbccccdcdcbbbaaacaaaabcbbbcbacbabbacbabbadbacbbbbadcbbcdaababccdaaddbbabbabbdbbbccbdbbabdaddbabdccadbbdacbabbbbddbadbddbdbbabbddcbbcaabbdddacccabcdadcaaadcbcbadabaddacbdbaddbdbdcddbadaaccbdbdbabcaababbbbacaacdcabcbccacccbdddcdaaaabcdcddcbbbbbcddbdaabbbcbdaddcdddcadcbdbccabbdcdbcaaaddcabbabadaadadccbccccdcddadbdacacaccbcaccababcaaadbccbaccabcdadcdbcabaadaddcaadbdcbdaacabdabbbbdccbacadbadddcddbcaadacdadcabadbcacccadabdccaadbbabababbacbbcbbbbaaaadccbcacddcddbcabcbcbabacaabbadcdccbbcacbbbdccbdcadbaabdabacaaddcbabbbcdcbbddbdacbddcbddabcbbbbbbbabbbcccbdbbaaabbabcacdcdaccccdabccddddbbdbdacabadcbcaabdaddcddcccdcabdbccdbadcbbcbaadaacdcdabaaccacadbadabbcbdbbbbbbbdabdccacaaadacddcbbcdcacdcdbaccbcdadbdacbcdaabdaabcbaddbbbcbaadbabbdaccdccaacaacabcaccacccbbcbdcaababaccdadbcbaabddbaccdccdaddbdcbbaaabaddcbdcabdbcccacbdbbcddabbdbbbbaacddadbabdbcbcbddbdcdacbdbcdbbbadbaacbcdcaadbdcdaacccacdcbcadccadbbbdbcbabddcbdaacdddcccdbadbacbabdbdababdabbbbdbcbcbaacdcbaddbdabbcdddcdbccddbbcabbbcbaababcbddddbbabccdbadccdbabdbbdbbcadaabcdcaccbccbcbbbdbcbddcaabbbbcadcadcddbcccdcdaacbadbbabaaccaadaccbabadccabaaddccaccabdcdbacacdddadccbbaddadccbbcadcbbacbcadcaaaaabbacdcdcaabccdaddcdccbbccabbcddacabbabdddacbcbdaddcaaabddcbaacdaccabcccbaccdbbcabccbaaababbbdbccadbbabccbabbbdcabbcbacbdcabadacadadadbbcacdbbaabbcdddbddbddacbbcdcaaabcaadaabcdcaacacabdabadbcbcbcccaadbabdbaaddbdaccddaccaccbadbcdcaabcaacabddcbbaaabbdbbccdbadadbcdbdcbadcbcbbdbbabcaabdbabacabdbbbacccbadccdadcdccacbcbbbccbcaaabccbaddacbbbccbcdbcbdccadcdcbaabdcdcbbcbababcacacccbdaabbcbbbabbcaadbcacadcdaabcdbccbdababbbbcbaacbaccbcdcdbbddbbdaaadbacaacbaadbcacacbcdaadbbddbdcbdabccccdbdcabdcddaaddccadadddaddcacabcbddaaaabcaddbbbaacbcabbacbccbddbcbababaabadddbadacbbaaccabcdbdababcdabbbacbacacccacacbaabcdbcdbdcbcbdcdaaaaababddbacddccadcabdcbaadbbccbaaacbbbdabbbdbacaccdacdbbacbaacdcbaddaacacbcdcdaaaabbadbdaddcbdcbddaddacccbbdcdcaddcdddbcdcbcabbdcdacaaaabbbbcadcadbcaddabbdbabdabacaabbadcaacdcbcacccbbaaadaddadcccbcabdcaaacbdbdcbcaadbccbccabdbcdaddbbbddbccddcdbbbadddccacddadbcacbacccdcddadababbcaddcdbbdcddacbaabbccabadcadcdacbdacbbdabbadaacabbddbbbaacbaacacdacccbcadcadbdcddbbcadcdbbadcdbddacabacaadaccccbdcbcbcccbcbdbdaabbaaaadbcbddddcdacbbbdaddabacaddadadccbdcccadbbdabbcdabcccccdbdcddbbdcbbabddbdcbadabcaacddbcbdaaccbaacddacbdacdbdbdddddacbdadcdacbaadddccccddcabcacccdcdcccbddbacabbabcaddacdbdddaaaadbcddaabaaaccbdbaadcadabadacddcacaabcbccbadcddaaccabcdbddcdadacabdbadaaccdbcdabbcabddabccddcbbdacadccdddcccbbabacccaabbddadadabdcbcbabdbbbaccbbbbaacdccbddccbbaccbdbdccaabbadbacbcbacdbaadcbdacbcdbdabcdcbbaacdbcacbacdcbbadaddaacbabcccccddcdcbbdaacbcabdabdccdcdbbaddcdcccacabddbcdaaacadaadbbbadaaddaccaabbddcddaddadbaadaccaaabaaaadcddbabddbdaddcddabdcaacccccadccabcbcbbadddabaaaacbccaabaabcdddbaccccaababbaddbbcccbdcccaddccdbdbdbbaddbacbcadbdbcbbcdbacddadcbdddddddabbdacbccddddabcbddcddbbbdbaacbbaabcbabacccabbdccbcacdbaacccababdbbaadbbdacbcadbdccaacdbaacadacdaabdccdcaddcbbcdcbcacdddadccddcaadddbacacddddccdbadaddbdaddabbcbdacdcdbbadadbbcdccccabddbcadabbabbbdbbdbbbbaccddbaaacbddbddcbabdcccbddcbddbabaadabaaadaccbadacbbbabbdddaacaaabacbcacacadbdbbcbabccaaccdcdbbdcccbddbdbcdccadcabcadbbcbcbcabdccdaabdbadacadbbbbaaaaadbcbbcbddbabdbdbddbccaccbabdcdddbacdbccaacabbbccbccaabcaacadbcccbabcdaacbdbadbbdbbcbcbdbccdcacabddcaddabdcddccabbdaddbcabdadbdcabdabddbddcbacaacbaaddddddccddaccadddddccaacacbddabdcbbdbbbdcbabccdccbddbaababadaabaadaddbadbdbbbddcbcdbbcdadadbbccbbacadacadbdbdaaaaacbaabcdcbbdacbabadbddacbddaaabdbdabbcdccdbcbcddccddabaaddcaadbdaccdbbdbbbcddbdaadbddabbaacaaabccaddbcdbcaadccdccdbbbbddcaadbdcdaccdacaabdbcbdcabcabaaccaddbaddbaadbabcdcbddbcaabbabccdacdbcaaaaabaddbbadabcbdbbbbacbaadadcdbbaabcaabbdbbdaabcaadacadcaacbbdaaadaaaacccbabdddddcbacaabccdcccabcccbcbbdbbadcccadaabadcdadcadbbdbdccaaaaabbaabbaaddcccccddccddacddcbcddcdbcaabccabadbabbcabaddaccaddccbcbdccccdcbabdddaaacbccdddacacdbcdccaddcbcaaabdcdaccbcdbabcdbdacbacbdaaabdbbcacbcabacbaccbcccdbbcbcccbcddcdbacbdabccbaabddbbbaacadbbccbcbbbbbbbcacddacbbdcccbadcdccbaadcbccccacdadadbdccddcdadccdababdbbacdbccabaadcddbbabdcacccddccaccdaacdccbdacdcccddbdcbabdccdbcaadcbbddbabbdbdbabddcbaabcabaadcacbdaaabccacbdaaabcddccacdcccbadbaaaccbddaadbdaccadcaddcddbcabcbcbababbccacaadacaaabaccdadacaababacdacadbbcccddddbbdaaadaacdbaacdbcbcaadccddaccddbbbbaaccacaacaccdcbcabcbdbbbdbadcdbadccbcadcdbdcdbddddcadbaddaadabccdbbaadbcadccdcacccaadcacbcaacddbdaaabbbdccccadcdaabcdbabccbcdacaabccbcabcbabcdadadcbdbbbcddcadbbababbdbabcddcddccbdcadcddddcbddbdcddabbbdadcbcbacbcbcadacdacdabbdccacabddacdcdaddbcbacbdbccdcbacbaaacbcbadadddbddbaddacacbbcdcccbcadbcaaccaadbdaaaadbbabdaadcbdcbadbbdbaabaadbaddcadaacbddbcabccaadbaacbadbadbabacbdaaaabdbdbdadacadbdddcbddaadddcbbbadddcabbcddbbbcdbaccddbdbbcddacaacbabddcabdacaaabbacadcbaadaacbdbacddaabbdcbccadbdacaaddddaaadddddbbdadbadccbdcacccacacabbaccabbccacadaaaabcccbdccdaacadcbdcddadcdcbdddbbaadddacdadbcdadcbcaabbcadaddaadbadcdcaaacadbabaacdddacccbadddaccdbdaadcacdcdbbaaaadccaaccbaabbdcbbbddcdbcbdbddacccbbccdbcaabdccdcaabcbcbbbddbdccacbbcaccbdcaaaccdbcdaccaadabaabddcabdbbabdcdbbcddabddcdccddbbaaccaacccbdbcdbaaaddcacdcaacccaadabacddacbddbbccbccddaaabdacdbccbcddcaadcdcbdcdabdacbdcdabacdccdaccbacdbcabaabccbcacacdbaccdbacbdbcddacbdddbaadaccdcaccdacdabbaddcbdadccbbaadddcbdbadcabaddddbcbbddaabaccaabdbbdaabbacabaadadaadbbdabaabbcaacdcbcaacacccaacbcdccbcbababdacabbcbadadbaacadaacddbdbcadcbdcbaddbdddbccbadbdacbcccbdcbcbdaacacdbcdbddccacacaccacbdbabaabcadaacbddbbddaacdbbbaabcbbdbaabccdbcdadddbdddcccbadbcbaabcaddccabcdadbdaacdccbaabccaadcbcdbacbdbddacadcaaccababadbbabcdbcbcaddcdadbbccaaabbbbccbdbbddccbbcbaacdbaaadcdbababbacdadbddcabbccacdabdadabcbacdccaccbadaacbcacaddcbcdabccdcaadcddadddabadbdbcdccdacdabbadababbbabadddddddbbbccacbccacdccbdbcbabdcdccdcddaddbccabcabbdbcdbcacbbbcbbdaacdbaadddaadaacaaaddbdccaccacbbbddaaabbcacdcdccabbddcdcbadcbbcadadcadaabbdbbabaddaabcdddcbbdcacdaacbdbadcbdbacdcdcbadadcddcacacdcaacdcbbbcbbbacdadabddcdbbacbdbcbcdbcddddaabbcbdddcbacaadbddabdcadcdcdbbdbbcbbbaadbdbdcdcdcabbbaddbacbdbdabadcdaddcdbdbabccaacbbacadcabddcbdaccdcbabcbaaacbadccabcddcdaaababbabdbddbaacbbaccdbbacddbcdabdcccdadaaabcaabadbaadccabdaaccdaaadbbadbcbccbaaaddbdbaddcccaabaacaaaadbdbbaaacdcddcddbaadcbccabdacabcbcacabdcbabddddabbadabbcabbaacabbbcbabcdbcaadbbadcbaddbaaabbadabcdbcdccbcabdcaaddacdabcaddbcdbdcccbdcdacccacccddabcacbccdabdacdadaaabcbbbdcccdcbccacbaaadbdbaacbcadadbcabbaabadbaababbbdbdaabdccdcdbbdaaddcdbcbabccdcbbdcadcbcddacacccbdbadacbcdacdaaccddbccccadbcdabdaaadacacdaadbabdcabadbccaaabaaaadbcbbbaacacbcaadabbcdcdababaddddbddadddcbbadccbccdcdbdddcdaccadcdbaabbaddcbadccccdbadccaccabcddcbbbcbbdaaaadacddadddcabdadddcbcaccbbbacbdabdcabcacccdcdaabcdcadccbdccacbaabbcbbddacdddbbcbcdacaccadbbabbcadcdcadacadbaacaabddbabacdcbcddccacddaacbdbccdacbdbadabbccbabcbbddccabbcbbdbbcdbacabdbccbbcdcacddabcaccacbcdddbbbcddbcabdcdbbadbcacbbadddcaadcabbcccbadbabaabacdabdcbcdbbcaccacabdcaddabacbdaddbacadacbbddcdbadddbcbdabdcbbabadadbaaaabbcdbcaaadcdddccadcbadaaadccdbbcdaadddccadaabadacdabcacabddabdbbadbcaababdbcdcaccdcdbbdcaccabdcbbbaccabaacdcacdddbbdacadbabaccabccbacbaadaadaccabbbcccdcbaabdbbcdcddcadcdbdcbddcadbdbbdadddcccddddcccabdbcdbabadbcdcccbcabddcdddbbdccbabbacbbddabcbcaabbacabbccadddacbcabbbaabaaacacddadbaabdaccacdaddaadcbcadacabdbdbbcbbddddabcadabccccbbccbcadaaacbbbcbdaacdbcbcaacbcaccbcbdaadabccdddccaccabcaabbddcaaaaaaabcbcddbdcdadcccddaabbdcabdbbadbababaababdbbbccddaaabbcdbbbaabdaaacbcdaddaaccdaacdadabcbbadbdbbdadcdacbaddbbdabccaadcdcccbdcdbadbdbdbcccbbabcdaccbbcbddabcbdabdbbdbbcaadccadbcaadccbddbbadcabdbadbddbcdaaddadacdbbddcaccccbcdacdccbcdcdabbadaacddcbdcbcaaabcbddcbbcbbdbdcccdaaaabbaabbcddbdaccbdcbcdabddcbcdddaaadbbcaccaabaaaababaabacbddadddbbbbdadbccdacccbcdbabbcbbadabacdbbbddbdaadbcbddaddcbbdbddaddbbdbcccaabdbccdcaaccabcccacabdcaacadabcccaabbddabdacdbcadbbbddddcdccaacaadabdddaccbccbbbdbabaaaaccbaadccbbdbabcccbdcaadccabbcbaaccbaaaccbbcbbdacaabbccdccaacdaacccdcaaabdddcabdacadcadadbbcdadbcdcdbaccdbcbddddcabababadadacddabacacdcddcbdcaabbddbcbdadcbbadbbacdbdcadccccbcaacaccbabbbcbddccbcacddbbadaacaccbacbbcdccbdddacbbadcbbacbcacaadddbcdbdbacbcabbcddddddcbcbacbccbcbcdcabbcaacacadddaabadcdbabbadbdbcadbbbbacbcddcddabbdbabcdbaccbdcaddadbdbdcdadbcdaabbadbcbbccccbacddcdcabadcbbcaddacaabbccdcadcdaaaadcbbdbdcccbbdbabbdabccdadadaccdaaacababbdacdabdbabdabaabbcaddbdadddaacaccbadbdbadaadcdcbdcccdccdadaacbadccdaaaccbcacddcaabcaabaacddbdddabaabacddadddccddbbcbdcbddaaadbacbacdccacaddcdcdcaddabdcccccbbacacccbaddcccbbadcdcaccadcdcdcbddbddabdcadbbcadcddccddcdcbdbccbaccbcaaacbddcdbddbaabbadcadccababcabbababdcbabcadadcdccabdbcacdbadcbbbdbcbabbaacdabddbcccbdadbbadcaddcbabdbbabcbddbcdddaabbdbdabcdcbbbcacabdbabdcacbdaccccdbbabcdcaccdccaccaccbdcbbcabcdddabcaaabdbacabbcdddcdcbacaccacbbdbddcbdcdadabccdcbdccbcabddacbddcbdadcbbbabbaccdaadcadbcbcbbcbbdcdbaabddddcbabcddacdababbccaaddcdcbcbaacaaacccbdabbdddccaabacbaccaabadadddaaddbacbacaadcabadcbdabcaccbbdabbabcbdbaddccaaddbcabcbaaabbcaacbdcaadadcdccdbbbdccdbdcaddaadbcbdaabdddccdbcbdbaddddadccaacbdccaadacddadcabadcbdaacbbddadcaaacacbbabbbdcdbddbccbdbdcaaacaddcaabaabadbbaddddbdbccaabbcaabaddcdbbbccddbbdcdccadcddcbccdcadaccbbcadcababacaabcddbaacdbdbddbbbccbcccbabdacaadbabcdcaddddbaadcacdbdaacadbddbdcdcadbccdaccdabcbabcabdacacddcadabcabbcdbbdacabcdbabbccdbdaadaabcadabbccdabcabcacbdddddabcabacababddcbabdbbdddaadcdabaabaaaaacabbcaabddabaacdbbaabbbddcdbcbddadaaabbccddcddccacabdbadbbdaadacbddbbadaccbabcdddadcddcdcbaaddbadcbabacababcbabcabbbcbbbdccaacabacbaadaadbdcaadcddcabadaadccdddcbcacbaaadbadcbbbbaaacbacdbddddbaadbbddccabcdbabaddaddbabbcbdabccacabdbadaacaacbcbcbcdbdabdcdbdbcccdaadbabccdcabdbddbdcbbbbdcdcbacaaccaabadbbdbddccbbdadacaabcdbcadbacaabcacddabcdbababddadbdbcbdccbdababccaaabbdbddcadbdcdbbccdbccddcacbddcacbdbdbcdcbddabdddddccabadcdcdaadbadabbaabaaabbbcccadaacbccadbaacbacdbdcbabadddbbcbbccabdbcddddaccbbdcdadaabbdabcbbbdadabbcbbdbbabaaacccddcbaccabcdddcdabbbbcbcaacccdddddcdcbbcadbababcdabbdabacabbbadbbdbbddcddaacbbacdccadddbcacbdadabacbadcccdbacddddaaddbdcddbaacdcbcaddacccccadacbddaabcbcaacbacbdcacddcbdbbaddbccadacdacacabaadcacabadcaaadbbdbbbadaddcbbcbccdbccccabcddbdaccbdccdabcbaddaaabbbabccddaadaccddaadcbccccbdccdbcadddabdcdbbddaadacddadbbaaddadaadbadadcbbabcdadbcdaccbabccdbdcadbaabcacacccddadaabcabdbaaabbaaabbaaaccbcacbcbcacbdaaacdcbdadbdcbbcaaadbbdcadcadcdcbcdbcdbddccabbdbacdccbbabadaacbadbabddbcadcaccdbbdadcbabcccbaabbdcaaddbccbcccbcadbdcbdcbcaacdbadbdddaabaadbbdcbdbadaabdacaadaddccaadbbcbbcacbbbbbacacdbdabacccbabcccdbabbbdbdcaaaccacccdbcaacddccacdcbcdacbadcdacbbdcbabbaaacbaaddbbdaacdbadbccccccbabcbabadcbaabcaaaacdadacdadbaccdcbcdbaaababadadcbccdcbabdbadaaddadccabbacaccbbbcddacadcbcdbbbcdadbdbaaddcbadaadcbacbbaaacdbcdaabdaccabcaacdcbaaadaababdbdcbdbaabcdbaadcababadcdbddbdacddabaddbadbdbbaabcbcbdaabaccbbaaaddcbaaaabacbbabcbaacccbdccaabccabbcbdcdcadbcbcccaadadcaaadcbbcdbbdcbbdddbdcbdacabbdabcaaabaacadbcacbdbbbddcadbabbaaadbdbbbbccdcabcdbcbbcadcaadbbbabdacadacadaccddabbaccaaabdddbdbdbdbdbdaaccdaacbccdcddcccccdadcadbcbcdadcbbcbbccbbbbddbabdcadabadcdaaccbddbabaadbabadbabcaabacaccbbbdcacbbcdbcacdbcdbacbbcbdcbdbcaabadddcccbcdddcadbadacadadbaabbcbcddabdabccbcadcbcabdccbcccdbbdbbdcdabddbacccadbbaddcddbdaaccdabcacbabcbcbabcdcdcbbdccccdacaccdaaccbabddbcacdcbccbabbcbbbddcdbdbdcdcaabbadcabdaccdcbbabdbbababaaabbcacbdcbabcaaccddaddcbaaadcdabacabbdbccdcbacdcdcaaadbcacccabccaadaacbabccbcdababdbdbaacddbacaccdbabacaadbcbabcbabccdcbacbcccdcdcddccccacdbcaadaacadccabbcdbdddcbcdddddbabdcbcddacbabbbcdbbcbaaaaabadcdcbbbadbbcadcdaddcbbbbaabdccacbccaabcddbbaaabcdabbdbcbcbcaaddbadabdbdbddaabadacbdbaaddbdadbacdcaaaabdabdbbdcbbcaddccdbdbbcdbdcdbbcddacdcdacddbcddbccaaccbacaaddcacccdbcddbcdbadacdbdbccdccdaadbcbbcadccbabcacbbbbcbcbcababacccbccccacaddbccccbdbaccbdbddbdbabbccdabbbabbaaddcdcdbccaaccbdbdcabadaadbacdbaadbbaaacadbdbdbcdccbbabcadaaabcbaacbadbbdcbaddcbabcbbddcbbaadccacababdbabcababddddadbcbdccaacbbbabaadbddbdbadbccbaddbcaabaaccacdcdddaabcbabaadbbcdbbaddaaacddbcdccdcabadaddabdddcabcbbddadcdadacabcabcbaddddaacabdddbcbccdcbcabacddcaddabdcccbbccdaabdbaaccadbcbdccaabcbacaadbaaabccbbcdabdccbabcbabcbbdabbcacdbbccdddabacbbbdcdccdcabdabbabbbccbdcbcaaacdaaacddbbcaacdbacadccabadcbccbcbcbdbdbabbccdabcdcadbbdcaacbdaddadcddaadbdcaabbabbadbcccddaaddcccabacdcbbcccaabcdbdbdbdcaabcbbcabcaaabbbbbbadcbbcccccadacbcddcdcbbbccbbbbbcbbdcdbaadccdbdbaacdaadadacccabdbdddcadcbbccbbdcdcadbaddabcbabddabbaaabccacdaaddcbacbbaadcaabdccbadacaacbdcccddacadcdcbbddcdcbaaabccbaaadcdcbbbcddbbbccacbdcabddadcbbbabadcbadabadcadcccaddbbadabbacaddcdcbbbbacdabadadaacbcabbddcadacabcaaccbdcadabaccacadadccbdddababbddacbaccbdacdccbbccacaadaaadbcbbccaaaaccaddacbcddaabbbaaccbdcdabcdacdbaadadbccaaaddcaaddbddbdacbccabbacacbabccdbabcaadcccadabddcaddbbbdddbdcddcccdbdcaccaaaaccbbaabdbbaabcbdcabdabacbbbaaacaaaadadadcbcdbadacadbaddcdcabbcbddbadaaddddbdabcbacdadaaccbcadacdcdddbdcccbcbabbbdadacddcddacbadabbcbbacbdcbdcccacbcbaddcddcbdbbacbbcddbdddddcddabcabaaaababdcaccaabacccabdbdacddccbbdbacdbdcbddbdbabdbabbccbabccdaccabcacbdadabadabcdbdccabbcadcbbcaadadcdcbabbdbbddacbdaadbbcacbcadccbddaabbaadacdacbaddbcabdaaadbbbdcaaddbcdcccbbddcccaccbddbccbbdcbccacdaaacdcaacddccdbabaccdbaddcadbccddadbacdaadbdabdcdddabbadcdcadacccbdbbbdddbdadcabddcdaccdadadadddadbddaabdcabaadbcadcddccadacaadadbadbbbbdbbcbababaaddaabbbdbbadaacacdbbcadabbaccddcaabdabcbbbaddaacdcbccccbbbacccddaacaabbdcbbbbbbdadbdbccbaddddbbadbacaaccbaccaacbdbdacddbcaabcdbcddcbdcbbccdddaadbbcadababbbabdbbdccdabbcadbcaacddacbadadbacacbccaccdaacdbdcbcbcaccbaadaadbcdacddcbbcacaadaacacddcbdccbcdcdddbddbddcabbcdcbbbaadbdbacbadcccdcaddcccababbcbcbcbddbbbcdbbdaaabdbdaddddadbcacabcabcbddccbdbbbbdbdbbbdaaadcaaccdcdbcccdbaabddabdbbdbaccacbdacbcadcdbbadcccdbcbccddbcdcbbdcbbbabddbdcdaaadcbcbdcdbaabddbdcacaaacaadbccaaddacbcdcbddcabadccabadbbaaacbbaabacbbaadaccbadaddcccccdacbbcdaaccbcddbbadccbadbbacaabdbbbacdadbccdaccaccacaabacdbcbccabccbdabdcabbbabcbbdaabdcbccbcccdbaadbbdbacadccbbbadcdcbabdaccdbbcacbcdcadbadabbdbcacaaddbdbddacadbcccacaadacbdcbbdcabcaaadbcbabbddbabddadbacdcdcbbdbbcbcbcddddcbbbaddcdccacddbacabcbcccabcadbbabbdddbacdcabcddacabbaabdaabdaadadcddbdbdccbabaabddcacdaabcccbadaddbbcbacbdabdbbbdbabbbbbaabcacdababcbabbbbbdaababbcdccabdaccccdddbbddcaadbaacbdbbdcabdadabdbbdcdaddadcbddcdacddaaacdbdabcdbbcbcbbadcdcabcdabaabbacaadaabbbbcadbdbbbacbaacbcaccbacdddabdddacadadabcacdbddcddbcdcbbcabdcccacccdcddaabbcadaabbaabbadbcaaddbdcdcbcabbbbdcdccdcdbcdabaacddddbcdbbbaaddadbabaccacacdabccaadcacadbaccbbdaccbddabacccabddcbcbddacdccddbdaaaabacccbdbcdaadaadcbabaaadcbbbdccdcdaacccadbbcdbdbcbcdcbcdbcdcaddabbabcbddbdcdacbccdbabbcdaadadcbcbcbaaababcbcacccbbabbdbcdbddadadbbbadccccadcaacababacbbabddbccbdaccacdcdacaddbdaaababcbbdbacbcdbdcccacbddabbcabdaabdbbbbabaaacbabdacadddcadacbabaacbacccdcbdbcdcabdcdbbcdacccabccbccdddcaababdcbbdaacdcadcdbadcdcddbdbbaacbbcddcbcadcdbcbbacbbabcccbbdcbddbdcabcbccccdaacabbaaccdcbbccbaaaaadaaccdabcbaddcccdaddabcaadabbdbcdbdadcbdddcbddcdacdacbcbadacdabadddbbcccacdcbcaaaadcbccabadadcaddbbcaaadacddabbcbbbcacaadbdacacdcadbadabbddcbcbaadacccaacbdacabacbacacbcccadabcdadabcdcbdacbdbdaaabccddaaaadaacaabbacbaacbcdcdaddaabcbdccdabdbdbcadaaccbdaaccbaddccaaabcaacdcadadbabddcbdccbcabccadbccbddabbadaddbbcdaddbdccaaccdcbabadcdcccbcdaaabaddccaadcbbddadabdbddcbccaadcdabbdcdabbccabcaccdaadcdccbaabccacdabcdbdbdcdacbcaadccddbddadddadbddcdaadcacbcadddacadddadaabccabbcdadaabacaccddabbdacdabaadddaccacbcbcaabbddcbcabcdddaaaccdacaaddbccbcbdadcaaadababbdbddcbabacbbcdbcaccadcbcacabcadbdcadacbddbacaaadcbddcaadcdcbbbcbbccbabdcdbdbbbdbacaaacdaadaaabaaccbbaaabdaddddbcabbdaadbdacdbdbdbbdcbaddcbabdcdbbdccdcaabdbacbbadcdcacdddadbbaaabcacacacbbbddaaacdaaabaacacdacaccdbcbadbbaacdcbaaabcdaababaadabacabcbcbcadacdbbdaaddbdacbdcccdbdcbaabbdabdcbaabdcbcaddcbbcabbbbbbaabcaaacbbbddcdbbbdacdadcbcbcdbbdaaadccbcadcbaccabbdacabbdcbddbcbaadaacbddbdcdacbdcbaabccdaadddbbcdcbaadcaacacdddbaccbadacdbbbabbcadabccacbaabdbbdcbbabdcddabbacabbbcabdaacaaadcdaccbbdbddcbdbdddddaddadaaaccbdabddcadaadcbdbdadcaccccadbadcdaabdcdbccadcbdbbcadaacdbadbbcdcdddccbdcddabaaccbacacccadacbabcbadadddadadbddcbbbbcbdccbabdcabddbbdbadcdcbdddddabacdabbbbbbddbadaaddaacacacdbdbbbcddcbababacbbdbdbccaddaaccabbcbaaacbbaabdbaacddbabdaddbaaabbaacacaacccdbcbcabddcacbaaaaccaccbbacbbdbaadbccdccdbabcdcbbbadcdbacbdccdbdcccdcbddbccdacbbcadbbcccabbcaddbacabdacdaaddaabdacaccbbdcbbbbbbdcaabbdbaccaacbaadbacdabdcdbbcdddabcddcdcbdbdabdcbacdddabccccacdbbcbcadaacddaacccccdacacdcabccbbbbbdacbaddcbccbdcbacdbdbadcabccbdcbdadbacdaaddccdbcddadcddcdbbdabacdadabbdcaccdccdcdccccbaddcbddbacddaadbbccacddcabdbdbadbabbcdbadbdbcbddbacbaabdbbbddbdaccdcbdddaaacbbabacddaaccbabddaadbcbcacabbbcdcdbbdbcdaabaabbabdcabbbaacbadddabbaddcdddbcdcddcdddabcaccbddbcaabdabdcadadcbdbdcbdbccbcbbdbcacabcabcaaaacbabcdbcbccddacdcbacbbdacadcacabacbaaccdcacccdccccdbadabbdbbbdaabaddaccbcccaaaabbaaccbadadccdaabaddcdaacdabcbadcbbadabbacbaabdbbacacbdbcdaadbcddccaadddbcbabaadbdbbccccacaacbdacaabbccdcdcbcbbbacababcadcadbbbaabdabadcbaaaadbbdcacddadadcdabccaacbbbcbddbcbdbcacbadadccddbddbbcbcbaadadcbcacaccbdcdcacccbccbbbdabdbdddcbdbaaadbbbcbabbacabcbddbbbacbaacaddbaaaaddacacdabcbcddbcdacbcbcddcacaddaabbdacddbdddabadcdcddccdcbbbddabdbcbdcdbbccdadbbbaadcadbdbccbdadaaadbaddcbcbbbbcaacdbbdacbbaacbdbdccbababacbddcacabbdbdbddcaabdcbaabddbdcdabbccaadcdcabadacacaabdadcdadabaaabaabddacddbcabbbdbbaaccabbbdabbadadbbadcabdbbbcbabbddcddbcdaaadbbcddabbaaacbabcdaabdabbbcbccadccbcadcdcdbddabbcdadddcbdcccacdccdbcddbdccddcdcbcdcaababbacdccacbccbdcddcabdccbcbcbccaabdccbbbcabcadcdcbabbbabdbddaddabdddbababdacbcbdddacabacadccadacaccdbdbbbdbaccdaadcabadcbcbaabdbaadddcbaddbbadddbaabdbdabadcbaccdadacddbbadbaccbadbdaacdbddacbbbacbcbabbdadcabaddabbddbbaddddcdbacdbaabdabbcacccdcabadccaadbdaddcccbbacbcbabbdccdddabacdabbbacadbdbcbaddccdcaacddcccdcddcabdaabbdbcccbbbbdcdbcbccddccbccaabadbcacacaacadcdbabadacdbdcbdcdaabbcddccdddcdabcaabaaacaacacdabaaadaadadacbbdcdbdaacbdcbcacacddbcadaddaabcacbddbbaadcdbcccdbabccbacbbbbacbdbaddddddcddbacccddcacdbcccdcbbcabcdbcabbdbdacababdcddcadbaddcaddadbdddddbabdadbbccabdbdadcaabcbbadaddacccccdcabcbcaacaccacbbaaacccbdccdacbaabababbbbbbabcdbccbaacaababcbabbbdbcbccddcdacbcbcbbbaddabdbbacdacacbcadabccdcdcdaacbbcbcbbacdaabdbabcabcbaddcccccdcaccadabbcabaccabcabdaacdadcccbcdabdbcaaaacccbcbdbbbdbadbaacdbdddcdddabcaaabdacbaddabcbbdbbdacabcccadbdbdcdcdcdcaccbadaabbcdcdbdbcadbabdaddcccbaabdacabbcaaaabcbcbabcdcbaddccabccccbadbcaddabdccbbcbbbabdcdcbdcaacaacacddbdbbaabbaabcabbdccbddbaabcdaabbadbdcdbccccaacddddbcbacacaaacdcadacadbadacddbbbdcabacddbdabacbaddddcaacdacbadabbdddbdbdcadbdacdbcdddadcccddcdbaccccadccaacbabdaaabdaaddccdcaadbbbaaacbbddcdccccadacbcdbdccaadddccbcbbddabcbbbbbbcaddacdcdbddabbdacdadbabcacacdcbdabbadbccbbcacdbddcccaaccbcdaaababaabcadbdabbcaddbbaaadbaacdbacbddacbbddccbcddddabdbddcaacbdacdadabadacdbdbccaacaadcabbddaabdbbddbbbcbdcaccbcaacdabbadadbbadbbbbbccbbbababdadbaabbdbdacacbdbcbdddbcdbabdadbdbddbbbdacddcccbddaabdbdabaabcdcbdaccabdadccbdddabdadbdddcdadaccbabbcaddbbabacbdcdcacaadabbddcdccccbaddbbccacbcddaaabbcdacbbacdabaadcccaabbdadaccacaddbacadddcdbacddbdacdaccabcdadabbccabbabaacbbaccdbdbdbadbbddaabacddccddaacbccdcdbcbdbdaacdaaaabddadcdcbdccaacaaadcdadbcdccdddcbbaaacdbdaabcaabbdcddaaacabbdcabcbcbabbbcdaadaadbbacbacdacaaddbcabbcbbdadcbbddacacbddbacadccbcddadbadaabccdbabdacbcbcacdccabaabdbaaabcaaabaaccdbaaddacbdbbcddddbdcabacbcbddaaaabbbcdbbdcacdbdbccdbcddccdcbcbaacdccddddbbbbaacaddcdaddacdbdcdadaddbdacdbbdcbbddaddccddccdbbdbaacaacbbadddbddaadcdacadccbbdacaadcbbabcaaccdbacbdabdadbadddbccbbdcccccabbadcddddccaaccaabbdbbacdbababbdaabacdcabdabccabdbadcddbadcdbcbbdccccccdbaabccaaacbcddaccbaccacaddcddbcccbcdddbcddadcddacaacbdadbadacdaadddbabaabacbcdaabbdcadaadabacdcaddbbacdcaccbaaaabbabdcadcacaddcccababbaccdccdbcbcdaaccdcdadcccabddbaaabbbcbadacbaabbdcbabdaaaaabaacbdaaaaaaddabdbbadcbcabbcaccaadcaddacabccddcbbbacabddaddcccdbacdbaaaccdabbaacadccbaacdcbdccaadcddabbdcccbdcdadaddbbcdabadbdbcacbcbdacbbbddbbddabaaaddacdccddcbacabdddbdaccaadcccdacdbbcabbbbbcbbbcbabdaddaadccdbcccacaabadbaadcdbbcbbcbacdddcdcbdcccccadaaadbbddababadabbadcbabdcddbcaacadabbabbbccbaddcbadcdbbdbcbabaacdadcdbcacacaadacbaacdaabdccbddadbdbcdcadabbdcacbbadacbccadaacabcaddaacdaaabcbddaabdababcbcadcbadabdbdcdbbabcaabbbdbaccdccbabcbdaccdcbaadbabcbbbbcaccbbddabacadbaabadbcabbdadabbccdddacaabacdbdbdccadacccddcbbcaacbddcbacbccaddcabaabaabacddccbadabccaabdbdabbbbbdabcadcaacbddddbdaaddcdcbddbdbdadbddbabdaadccbbdcdbdaddbcccdddcccbcccabdddcaddaadaaacbcdbcdddbbcaadadcaabbcbcccbdddaadddcdcdbbaaaccabcbcbbcaacbabcdcadaaaccaabccadbabcdcccccdbacdadbbcdcdbdaadadbacdacaddcaccdababadacdccbdbdcdcbacdabcbddcadcdccdccbdadccbbccdaaddbaabacccbbbaccdcdbacbcadcddaaccbdddbbddcacdbdacaaabdbaaadcbbcdcadbbbbdadcdcbadacaaacbdbbbdacddcddcbcadaddbadcdbdbdbdcdcadcbaaadaaabacabcdccccaddccbdaaabaccdaacabdbdbddcdcbaabbaabcdbcabcbadbdaaabcddcddbbbdcdbdccadadbbbcbcbbccaddbbaadbdaccbcaadabdaddabccdcdbbbbabbaccbaddaadacdcdbabcacadbacbabbcacccbdadbbadbbaccdddaadcababdddcdaabbbbbcccdbbabbacaaadddcdbbdcdaabbccbdbdbabdcddcccdabbcdadaabbbadbaadbadadbababddccbbdbcbaabdcbaddccddcadadbbaadcddccbdbcbabdabddacbdadaacdcddaabdacddbbbdadcbbddddcddcdaacbacacbabadadcabcbdababcdbcacddbdadbdbcdcbadadaabbbaaaddabbcccacaaccdbdbbbdadaaacaabbcdcddacaacdcaaccabddaabdcabbaccaacccbbacdbaddaddaaadacbddbdabadcaccabddbcaacbcacdccaccadccdaddacbbcdadbdcabbacccbbcdbaacdccabddbccbbdbddbbcabaabbcdaabdbbbdbbabbaccacabbadaddcabdcadddbdabbaacaadcbddccadbacadcaddbacccdbbaadcdccbccaaadabdcdbcacbdccabbdcaaaaddbcbdadcbdddcddcbcbbaccbbcccdaaaddcdcababbcaccaadcdccbbacdbccbacdcbcbaabbdbdadaabdbadaccacaaacadbdccacccbaacbacacbbacdbbdcbbddbbbbcdcdccbcbbbbbaddcadbabccbabbaaabcbcdcadbccacbccdacbbdcbcccddcaabbdcbcdbacddcbcacbcddcbcacadabcddcdcdcdabbbaadcacdcdaaaddbcbcbbccbbbbcdddbdbbaddcccaaaaabaccccccddcadabadccdcabdddcabaaccdbadcadabbdddbdabdcaccddaacabcccbabcbaddacbcddacbdcabdacadadcbcdbdddcbbbcacccdaabcbcadbabcdbbbbbdbacbddbddcdbddcadcadadaccbcccaccccddcdbcaacabaaddbadbccacbbdaadcbaacddbbdccaaccdaaccccdccababacdddadbabbddacadacadccccacbdcaaacbbadbacabadbaaabcbbcdcabbddaccbdadbdcdddabbbadcaabadadbaabbbddcdbacdbdcbadbdbaaadbbabaacdccbcbacbbbddcdbaadaadcdccdccabcbdacbbabcacadabdddccbcabadcbaddaccbbdbdbaadcccbccddbbabaccabbcaaadcbbbbabdabbbbdacdabaadacbdabacbcacbabccdbdcdacbbdaadbcccddadcbcdadabbadbaabcdbbcacdcaababccabaaddccdcdbadbdacaccacddcbaadbcaabadddccaccdabbbccadadcccbdddbccbcbbbadcacdddbaacbaddcbcaddbddbccdccbcdbcbdaabbdccbddbadcddcccbbaabcbcddacabbcccddbbadabccccdcbdbcdbcacaccbacacbaacaccadabadcadddccbdbacadccabbaaadabcdbbaccaddacdddcdcdabdaacdbdddcdcabdbabaacdadacbdbcbbdccdccbddadcababbcbcabacaccdbadbbdbbccddcddbbcdadbcbcbadababddbacccbccabbcbdbabcabaccbcdcdbacadddbcdddccbdcdbcccbbacdadaabdcddccaacdacbcbbcaadbaddbbcaadbabababcacdcabcbaabdbdbbcabdcbbadadddadabcbcccdbccccbdaaddadddccabcbbcbabbabbabbabacabacacddaccbbbabcdcbbacbccbaaddcdaadbdcdbbbdbbddccadbccacdbcddaaaadacabdcbddabbdabbacadcaaabbdbacacaccadabcabbddddadbcdaabaaccdaddcbbaabccdbcccacaaaaadabcbadddbcbbdadbabdaadddabcbbcdccaaccbdccccbaadacadacabadadabcbbddbcbaabbbdadbdabaddcacdaacacacbacacbcbbabdccaccadbdcaadabbcaccbcccddcacbbdcdaabdcdbdbbaacbcaddcabbccabacccbdbbbacaaabbccdaababcbddccbbbcdabbcbcbbaddcacaabbbcdbdddbacdbbcbdabbaadcbddcbacacabaddccbbdbbbdbbcdcbccacccdddbddaabbdcabbbacbcdaadaddaacdbaccdaaadbdcadccaaacddbadbbacbdcccccdadacdcbbbaaddabdddaacdaaaddbcddaacdbacdaddcacddaadbaacbabdbdbdbbaadccbabdaccbcdbbccaacaabcdcdddbbadadabcbccabdccbcdbdaaddbdcbcbadccddaacddddacaaaaaddcacacccddccdddbddacdcdddcaabcbcadbaccdcbabcccbbadbbccddbdcbbddbcaaadbbcbdcaccadcadbaddadabbbdcdcbdddbdbcbbcabadbccdbbcddbcabdcbddcadcdacbcbdcbddcbdadcacbaadbabbbdabbbbcdaaabbcaccdadacabcdbcbbbcccbabdddcddbcbcaaaaaddbddcaadbaccdddbbccbbbddaccbdacbbbaccabcbbbdbcaadbdbdcddabacdcbbcabdadcbcabaddccaddddbccabdcbaaccccabcdaccbcacdbcbbcaddbbbaaadabbbcaccdacdcbcbbaaccbcdadcbadcacadadddacccdbcdaccdaccbabcbddcdbcbcddaaddaabaadddcadabcacaaadcdcccacdcbdbbaadacbbdbdbacabbaacdbacbdcadcabbbcbbccbbcccaadcdadbdadbddccdbbcadddbdadddaabdbbdcbbbadbbcddcbcccabddcddadbcdcdcaddccddbcbdabdddbbaabbdcadbddaaaccbcdbaaddccadbbbacdaabaabadacaadbbababcbababdbaacbdbacaaccddbddcdbbcbddbacbbacbdbdcadddadacbbcbccbdcacdddcbcbdcacaabdacaaaddaddcdcccaadaccabdbadbaadcadddcdabbadbaadddccbccdbcdacbcbbbadcbdabddcdcdccddacbdadbaccdabcaaddbcdbaccdbddabacadadcbcdbcbcbbadcbdaaddbbcbcbabdbcaccccaaadbccbadcaabaccacbddadcaaabcbdcbdaabcbbdadadbabdbabcaadabdbdcbbdbabcbbbcccdbaaaccbdcabdbdcdbcbacbbaccdcbdbbaaccdadabdadbbcadccbcddadcdcdacbaccdadabadbbbdacdccdcaadaaabccbbbaadacabbbbccabdaddcabbadbcdcbdaccadbcddddcccbbadcbacccbbbdddacbbdbabdaabdaabbbadaccbdadcbdbbdbddccbcbdbacaabcccbddcddbccccddaddabdbccdcadcadcdcbdadbdcadddbabbcdcbbbddbbabaadbdbccdcacabdccbadddabcabdddbbcabdddcaaddbddcacaaacaabcccdadbbddcdcbbbbbcabadbdbdcadddbbbdaaadaabdbadacdcaaaaabccbbcabbaacabadababbddaddccbcbddccbdadbcdacacabaaabcbbadcabcaddabdbcbdccbcdadcbbcaacccddcdcdcbbabcacdccccbcadbababdcdcdbdadcbdddacbadbaaccbbaabdbcccbddcdddbbcdddacabdacdadacdcdbdbbbcabdaacccdaabbcbcabbbdbcdccabdacdddabcccdcbaadbaaaadbcadbcbbcabcccbcaaabcbcaaacacbbbacaadbacadbcabdaaaddcbbabacdbdaadccdbbddbacdabbcddababaddddcbdaaabaccbcdbcaaaabcddacdbacbccdbacdabddadbdacbaccacacddadccddbdbcdddaabdacdcaacbbdbbdccadaadaacddbdabbbdacbbadcdddbbccbaabdacadaadadabbbccadbbccdbbbdccbababacdadbbcabadaccbaadccbbdcbcddbbaabbacbbcbcabaabcddcdbcbdccbaacdadaddacadbccbbbabbacbabbbccdacdbdaddbbcaaabcddbdabdcaaabdddcccaabcaaaadaddbbcdadbaabddbaccbaaabcabacaddacbdacbaaccdbadacbdbbacacaadacacbddddcdcaadabadbadabcdcbbbcddbabccdcdcadacabcaabdbbdadcabdcdbbbbcbbbbcdbcacdbcccdccbbacadcabaacddabaadbccddcdaddbbdcadccbabacaaccaddaddbdacbbacccadcacbccacdadadcadacddbbadbbbcaddbccddccbdbbdcbabddbbaadaadccbbbcbbcbbadaacadcdacbbacbaabaaddcdbcbcacdddadbbacddadcdccdabbdabcdccabbcdbdcbccbdbabddcccaaaccbadcdcbdaddaabcbaabbccdbcddaaaccadccdbdaddcbadabdbccbbdabbdbccacdaadadbcccdbdccccbaaacccdadbddcdbbbbbaabbaaadacabaaccadbbacdcbccacaddbbdbdbcdaacbabaacabaccccccaaacdaddadddaaabdbbbacbdadcaadbdbdabcdabddbbabdacdaccccbcadcbdabddabcdcacdacdcbadbdccdccbdcbbdddadadbbcdcbbdcdbaaacbcdcaccaaadadbacbdacadddacbcbabcbcbbaaadcbcdddbdcdcaddcdacbcdddabbcbcbdcbababadabacdaadadcdbcbabbcdcacbcbccdcaaaacaacbbdabaccccbdbdbbbbdbabcbdacbabbdcbccaaaabcbdabbaddbcbacbaabccdbcaaccbcbcabaddcaaddadabdbddcbbaaadaadacbabdbccaddcaccabcdccddaaacbacaabaacaacdadccacccadccbdbacaddccdddabccaccddadbdddcbbccddccbbbacaabcdbabbdabbbbddddddbddabaddbdbbdbcdcaabccbbcbbcdaabdbdcdddbdcbdbadaadbbbbbcdbbdcccbaaacdbcdbcbccdcdcdbdaabadbcbcdbaacdbaabbaabdcdbdadccdadabcddabdbddababcdcdabbcbbcaabcabbddaadcbaaadbcdadaccadcbccbadbadadcadddccadabdcbcbbcacbddadaabbdaddadadbacaabdcdaadbddbdbdcadcdbbdbaaadcdacaadddabccbcbccbdcaddacbabdccbcbddacdbbccbabbbdabcdabddcbcbacbbdbbcbdbcdcccadacdacadaacabccbccaddcadbbbdaddcddbdadbaacbbaaaadcbdcabacbccaabdcdcbdcbbcaaacbbbdcbcbbcbdcccabcbcddbccbadbbabaddadadaaddbcbdcbbcdaaabdbbaacbaadbbadbacadcbcdadddbacbbbcadaadcddbcaababaadcaadcacdbadbbcadbdaacdaddcaaccacabbbbdadddbaacdcdcbdbcacababdcbdddddcbbdccddbaaabdbadcbcdbdcacbcabaaadbbcbcabadbbabbccdcabdcccccbcdabccacdbbbdabccddaabbaacbdadaadaaddccddbdddcdaaacbabcabbcbdacbdbaabcccaadbccdcbdaabbbcdcbbdcacbabbbaabcccccdbcdbbccacacdddacaadaadabaabdbcbbbbcbbadbbaccdadadadbcdacaacabbbdbaabaddadbcabbbddacdcbabbbbddbccbdcbadacccccabbbdccadbacdddcadbddddcdcbdcdabaabdcabbcdcbbcdbbbbdaccadbabccaadcbcbcadcbabdaadcbbcadbadaacbabdbaabbdcabddbbbdbcaaaccabaabacdbccacbdcbabdbbacdbaadcdaccacacaabcdaaadabbbdcacacdcbdcbbccadabdccbdbbbacadbababaaaaaaaadadcdcbcaabbadadacbaadcababbcdabaadbaddcadacbcadabbabdabccddabcacdaabbcbcacadbadaccaaaadbdbbccaccdaddaaadbdcdabcdaaadcdcdbcbabbdccccdcdabbcbccdbcabbbcbacddacbcbdacaabdabaccdbacccadccbdaabadabcbabcadcbdabdbdccdcabbddddacdccaccbbdadbdcdbcadbdcddaabdbbdabdcadacbbdaddbbdbcadcaddaaddccddbacddcbdccdcdaaaccbaddcbdcabbbbcddcbbcbcadcacdcdadacadacabddbbbaacadbcabadddbccbcaabdacbbcddcaaddddcbdaadadccbbdbacdaacaabbdbcdddcdadcccaccadbbdcbadbbcadabdaaabadacdaababdacabdacaddddaaabdccaaadadcbcabbbcbbddbccdcdbcdaaacabcbdacdcdddcdcdaabbdddcadbddcbacccbaadaaaddcddcabdaddbabdcaabcbbbaddacbbbacbbddabddaaddcdbcdbcabcddbdbcadcaabbbdcdabbdcaabbdadadcdbaadcbcbadadbabccdbcdadbdabdddacacbbbcacdacdccaccdbaacccbaccdbaacacbbcaacdcbbcacacbbcdcbccabddaaabdddabccdaaaddabdadbbcadacabcddadbbcbcacddbaabbadbdacddbabbacccadabacabbadddacbccccbdcadccddcbcacdacbdaabbbaabbcdbbaddaacacbbbdaacabaccddcbacadabdbaacadaaaccdcdbdcdbdddcccbbdabcbbcbdbaadbacaadcbccadadccabdcaaddacbababbacaadddacdbaadbbadabdddbccccbdabdbacdabcadacbacddcbadcdccadabbcaaaaddbacbbbabcccaccbdaabcacadaadbadaddbacbcabdcbdadbadadcadbcdcdaaccddaaabcbaabcdbbddbdadcdbdadadabdcadcacdaabdbcbcdacdaadbcbcabdcbddcbdbaaddcbabdadcbabbdbdadcbcaabdbcddbadcccdaadccddbdbacdcaacaacabcdcbcacabbaaaddabdcddadaadbaadccdadddbabbdacdbbbbbacdbccbaacaccadaddabadabaaabddbdcaadabdcaddbadbbcdccababacdbbbaadbcdbccbabbcdbadacbcabbadabccdbcbbabadcdabdaddacdacbdcaabcdccccbbabcbbbdcdaccccabacbacbdcaaaaacadcadbdddcbbcbdbacaacbcdabaacdbcbacbaaaacdacacbacbcdccbddbddbccbadcaccccacdacddcaadaabcdbadcdcdbaaaacddaabacaabddbbaabbbdcbbccdacaaacbdbaccddaaadaababcddcddbcaaabacdadbaddabacdbbcddadcbadcdaaadaabbbcccbdccccdabddbcbdbccdbcbcaadbabcbaddccaadccbcadbdbbccacdcdadcabcbabdabaaadadbddbdbdcbdbddbbdacdbacbbbbdbcccacbadcbbdbcaabaadabdbbbbabdabdabbbbabaacbbdacacbcdaddddcbbcdaccbdbcadbbaccdcbdbcddaaaccbccdcacdacaaaccdabddbdccddcabadcacbdbcdbabaccbcadccbadcacacccdabdadddcddabadddcbabdabacccabcbdccbcaacbdddddcdadbaadbdccbbcdcabbbcddddcbbcabcaaabbbddaaccabacdcbccdabcbdbdadbdcbacdbcbaaddaaacbacadccdabbdbbadaccddaabcaacdddbbddaddcdcbabcbabaabdadbbbabccdcdcaccdaabdddbdadbcccccbccaabdbdddcbbaabaccdacbdddbbadddaccdbbaadcbdbacadcdabaacbbdbdddbaddbcadbdcadcaabdaadbbdbadbaccacabdaadcddaccdabcbcbbddacbcdbaaaaaccbaaccdbacdcacbdcabcaaaccaabbcabdbbdaabdaacbcbdcccbcabadcabbddacbacaabacabbbabccadbaaabcdcaaacbbdbabcbdbacaddabbdaadddccccdccccccaaadababbbbddbbacbaababdbccaccccdacdaaadbcddcbaaccdcabdacacaadbcaadbbcadbccdaacbcaaabcaddabacaccadcdbbbbddadcaaaccbdbadccdccdbaadbcbdbbdccddbacdbadabddaadcbabccabdadaaaddbcbaadbdbdcdbbcddababddaababddcaddacacddbaddadbdbadbaadcbbdadbcccbdcbbcddbcaaacdcbbbadccdcdacdddcbabcabbcadddcacbccdcbbdbcbbcdccbaadcbaaabdcdbdcdcdaaacabbdabacdabdaaabaacbcbcdccaadabdccaaacadcbdbbbbbadcbddbdababadccbabcacccdcccbcdbbaacadacabadbccbbbcabbccaccdcaddbbccbbcbccdbbacddadaabdbcddabcbaaacbcbbcbbaadcaaacacaddddbbbaccbaaababdbabbdddaaacaaabcdabccbccccccdadddcdcaabdbaaddaccbccbcbbcbcabcbbbcdaadcabadabcbbbaddadcdbbbdabbcdccbdcddddadbdbabbbcbdbbacbdcdadcacaaaabcbddccbdcbbbcabdbacdddcddbcccabbaabdbdadacabaddcaababdaaaadacbabcadbdcbbbdaddcabacdcadabaabacbcdbbdacbcddabacbabbdbdaccdbdabcabcabbddcbdcbdbccababddacbcdcaccbcbdcdadaabccbdddabbbadbcaddbdadaabccbadcabcbbdcbaaccaaddcdabdaadadcbdbbadcaabababacbacdbccaaaabdaaabcbaacaddaddcababddbdacbaabbacdddaaccbababcbaacbdcbadbbaabcbbaadcbaddbbbcabdbcaadcaccadcbbacdbbbcbbaaccdcacbcaadcbadccbaacbadcabacdbddcbabbdcadabcbbacabddaccaddaccdccaabbbbcdbacddcbbddabdcaddcddbddbccdcdcddccddcabdacacbbccbbbbadcbaabcabbdddadbbdddbbcbbdaaabaabbdddabddcbdabcaabcdabbdaabcabdbadabbabdbaacddadcccbacddbadcccdabdbaccbccacdaddbdaabaccbbbabdbdcdddaccacabbcbcdcadcbdaabddcadcadcdcacbbabbaccaadccddbdbbdaabcbbcbdabbdcbcdbdbcccabccdacbbcdbcaacbaddaaadbbdcbbdaadaacbbabacabcddabdaadabbdabadbababaadadbadcbbbdbbccbbcbbcbdcbdcdaabdbbdbbdccdcadaacdabbbcbccdbacadbcaadcbcdababadbdabcddabdabbdcdbdbcbcbbaabdbdbaaabdbbdbcbaabcbabaaaaccbbcbccaddadcdadbcdcdcacdbdabdddcccbdaabddbbbcaabbabdcacabaddaabcdcbbdacbcbabdbaaccddccadaadaabbddaddacbdcbccddcabdabcccacadcbaccdaadadbcabacadacbdaccdbbabcabccdddacaaddbababdcbabcccaabbccbdcddcaaaaaacdabdbabdababcbaacccdcddcdabbcacadabadbadaccddcbadcaccddacdbaccbdbbcbbacaabdcdacdbccdcbaddbdddbbcbbddbbdccdbbdbadadaaadbccbbacdbaadacabcabaabddbdddabccabbddbbcabbcddadadbaaacdbcacbbdaccaadcacacaabdbccccbdcaddbbabbdacbdcbccbdadaadbbcabcbadcbccacbbdaadabaadadadddadbdddbbccdadddbddadbabadcaacaaababcdddadddcadddbcaabcadaaacbbcabadbacbaaccbbaccccadbcccccbacaaacabbabdadaadcbcaaaadcdcbdbbcdbabbdcaccbcbaccadccdabadcbddbcabbcaaabccdbcaddcdcbbdacaacdbadaaddcdbdadcbacaabddccaacbbbcdbddcbbdaddcddadcccddccdcdddcbcacdadcaddacdcdccbadcbccbdbcdcdcbacdbaadddaddcadabccdabccddcbdbccacdbabbcbbccdcdddabbdabadbddababadcbbacbccbacaadcbdadbdbabadcbaccaacbdcbadcdcdacbbbabbbdaabdaaccbddadbdbcbacdadcaacbcacadaadcaaabccbbbcdaaddddcdddcdcdcbddddababdcdbcddcbbbddbddadacccaabddcdbabcdabcaabccdbbbcacaadbdccddadbdacadbdcbcdbdbccacddadbccdcddabbdcccbdbccbdacdbbcaabadbcacaadbddddaddcabccddaadcdaacabdadbacddbcabbaabbdbbdcbbbaaadbcdcdbcbdabcdcdcdbaacdddbcdacbabddcbcdbdddddbbababccacaabbbdcbbbdbcadabbdbacacacbabadddbcadcabdadcbbdaaadcbcbdadccccbdacdbacbddddbbdcccbaccbbdbbcdbdbdabbadaaaccbcbacbccbadcbacdcbccaaccadbabdcbddcccddcdbbaaaddbaccddcacdaadbadaacccdbbbcabbccccabcbddbaadccbbacddbdbccdaaddcabaccaaccbbabadbabdacbaadbbcbababdbdacdabcdcabcdabacddddbaacababbdabacbbbaabcacaccbcbbdcabaadaacbbaccbbddbabbacacbbbcdbbbabbdcccacacacbdcbddbbbcaaddbcababaabaccdbbadbddacbdadcaabdaabbbdaabbccbdaabadbccabdbbaadccaccbadadcaccddbdabacaccaacbcacbbbccaccbdcbdbcdcdadcaccbbaaccbabbacddbaddbabbdcbcaacaaddadccdacbddadcdaccbbcadbdddbadbbbbaaadccbabddbadbddabcbacbcdbaaaaaddbcccaacccbbdbbacaabdadacadbbddcacacbdcddbbddaddbddcdaadadccdccdabadbacbadadbdcdadbccdabcbbadcddcdddddbaabadccbacdddccdcbabccacbbcadbcabbaabdaacaabacddcdbbdbdcdabdaabbaccdadbbbaabbbbdcccacdcadbbabbcaacbddabdbdcdaccdbdccdbacbcdbbcabcabbdaadbccaacabaacadddccbdadcdcbabcaacadbccbdbbdbbbbabbbaabdcabddddaadddcdadccbdbbccdabbdbaacbaaadcadaabbaacdadacbaadddbabccbdbcaccaccacadaccbbabacbdcdcbcbcbabdcbabcbacdcaddbdddbabbcacabcbbdbadbaabbcaaabdbaddacaacbcbdccaaccccabbcbdccdbcdadbbdddadaddbcbbacdadbdbbacbcadaaaabddacdacdccdacaadbabbbabbccbddaccbaabbbcababbdbcbcaddbcabbddcabdacddddcbdacaddabaadbbdddccbadaaccaccdbbcacacadacadadacdbacdbabcdaccdbabdcbbacbbcdbabcaddbddcbdbbaddbacbacdbdabdddcdbabcdcacbbaabcbcadbbbbdcadbbdababdacacbddbbcbcdcdabddbcbbbcbbdaacaaccddabcbacbacadcdcdbddcdacacccbdbbbdaabddcdbbbccbbbadadcabadddbccdddaacdadadacbdbacdbdcacaadbbcbbbccdbdaddcbcbcccdcbbdbbdabdccbcdaadbdcdbdacacbadaacbbaccaaadcacbccddbccdabbbcdcbadccbabbccdbadbbcdcaaccbcddddabbddabdcadcabbabacaaccbbcacdbaaacbccbcdddbabacbbaddccbacbaccdcbcdcbadabacaadcaabcdaadaabcbbccbccacacdccaacaacbdadcdadcadddcadacbaabbacacccabcbbcdcabdabbddaabcbdddbcddbaaccbcbbababbddaccabccbccdadaccdbcdcbbbccdbadccaacdbdadadbadcddcaadacacccdadbadcdccddbdbacabcdbadcbdbacbabacdaabbabadbbbaacadacccaadbcbacbdcbcbcccbbdcbbbacdcddbbadabaabcdcddacddbacdcdcdcaccaaabbbacababdcbdaaabbcadcbdbcddadadaabdbdbcdbbddbacdaabcbbbcbcbddcacadbdcccbcdbcbdcbbbabcbbbcdbabadcbbcdbaaaaaddccdbacccbcaabbdbddadabaadcaaacbcbbbbbadcdabdaadcbccabcbccddacbbaadcbbdaaacddcccaddabcbcadbcccbadddcbcccabccbdbbbaddccbdcdaaccaacacdcddcdcbaaadacbbbbccaacbacdbbbcacccaadddcccbbcdbdbdadccbbbdbccdabbbbbaaccaccabbcaadacadcacdcdbbbccdccbcacddaabccbcbcdddcdbcaacdcdbdbbcbaccaccbbbdababcaabadababaaadacbabdaabbabbcacddddcdbacbbaacbbbdacbacabbbddadcbdcdacbcadadcccabdbcaaccacdbcdacdaadcdddbccdacaaddbdddcaccbbcccabacdaccbcaddabacaabbdabdccdbbcabcdbcbbcccdbaaacbcacacbdddaccdadddacaadccdaaacccacdadddadaadadbcaccbbbbcabbcbcddbaadccabdcdbccdccadbdbdacccacdbcadabdccbbdbdaaccdabdccbadcccbaadccaacdbdaccbcabdcbcacadcbcbbbbabbdddcbaccccaccbbdaaddbcbabdbbbddbdbabdaaaddacabcdccccdcaddadbabaccccacadcbcacbabcdbdabdcbccdccdbabbdcbcdbccbadcccbbdbaacbdcbcccdaabdaddddcbdddccbdbcdbbbdabaadaacbbaadcccacbbabdadcadbccddacddcdbbbcdaadbacbddddaacbbbdbddcbbaadddccabcbcaadbcabccadccdbaaaabdacaddadcaddbbbabdababdbabbdccdcaabdcddbacaccccdbccdbdbadbccbbacacaadcabaddddddcbdabdbddacdbbccbaabcbbbbdbdcddbbcbaaaddbbcbcacdcccadddcddcaddaadaabdaddadcdcbbacabbccbdacbbcbacdbabcaaacabaadbcdcacdbbbdacabdacdacacaaabdacddccaabaabddabbdccbacdcdacbccccabcddbadcddaddcbabdbbddbdcdcdcdbaabdacdbdddbbccbddcaaadababbbbbdabbcdbdcdcbbdccdccdacccdddadaadcbcdadcbcaccaacacdccdaabaddddaddbaddaacdaaddbadbadcddbdddcbcdabdbdbbaccdcacdcddccbbdcdcbccccabdcaaddddbcaadabdaaaaabbabaabbbbbaaccaddccddabbcbbccccbcaabadabdabdbbaaabbcddbcdcdccdabbdcdcddcaadbbaddadbacbcbbcacadcddadbdabbcccdcbccaabdbdbbdbcaaccbcaabbdccacddbacdcacaddcbbbdababcdbaddacabadabcabdbbaddbddbbcacdacbcdcdbacbdadaccadcabcdadccdbccadbdbaddbbcdaaddbdaabdbcddbdcdacadbcabbdaacabccbdcdbdcddabacbabbcccdccdcbdcdcdadccbbaabccbbaccbcddcdaccadcddccaddaaccdadadcdccaaccddcadcaaddbdcacaabdabadcddabbdddaaadaddabcbdcdabbaddacbbddacdaaccdadccdbcacadadbdaccaaacadbcabddabdbacddbabacdaccbadbaadbdabacaddadbadbbbddbdacddccbdabcbbdbcadaababcbcacccbacbdbacccdcdcdcdbddbccbccdbdaccdbdcabacddddacdddacddabbacadaacaccdbdbaaabdcdcabbdccdbbccabdcbcbbcaadabcbddbcadcaabcdcabdcdbcdbbacbaacadcdbcdacbddbcaabddbbbbbadcabdbcaccddddcacdddbbabdaadbcbdadcaabacdaacdadabaaaccabbcccbabbbcbbaccdcdbbbbdacbdbdddcddacbcacddbcdbdbcaccdacdaccccaacdaacdbaaabaaaccddababbbdddbddcbdbccbdabacdabbaadccbcbadadcdadababcddabbdcdbcaccdabcbbbbdcbddcdacbbadaddacdbbcdcbaddcdbdaccabdbdbcadacdaaababcdddbccbcaaccacadacabcacadcbadcbbbdbaabdcacdbadbbcdcddddadbddcbbbbcdbbacbadbdbcbaaacbbbabdaabaddacdbcadddacabdaadccbabaacbcdbababddcccbaaacbabbacacbddbdacdcbbddbaababbdcbbbddadbdbdddcdcdccdbcacaabaabccbbcbbcbdcbbbabacddadcbddddccdaddcdadbcbdbdadccbdbddcabccccaaabdaaddadaaaabcabaccdddcabdcdbbcaaadcacacdacbcacacbbcadcbaaaabbcbcdbbbcacacbcbacbdaabcdabbddaacabbcdcdccbaabccccccadcddadcaddcadcabccddbbdbddadcaaadcababadcdcdcddaabdaacbdabbdbcadbcbcaacdcdcbcabcddacaadcddbbbabacbabcdccbadddcaadacabbacbbdddbcdcddbdbacaccdccdbbaccdabbcbdaccacdddddabacabccbaabbcddbbcacbdbbdbdbabdaaddaadaccdcdaabaadccccccbbdbcbddbbacaaacdcccdbacddbbcaababbbddbdbadaacddbcbcdddabccaabdcaaacdcabcdadabbcadaabadbdcbbcdadbbbddbbdcbbcddccabaaabaccccbbbddddccbdcccbabcccbbdcccddbdcbaaccbdbcababbbdcacccddcabcabdbacbcddbcabdcabccaccdbdaccdaaddcaddbbacbcbacdbabbadbddccbddcbbbcbdcdabdcaadbacbcaadacddadcacacbaacabbaabadabdcbabdbdacbbaaaacbaaddadddabacabbcaabbdbaaddbcccbccdabdaaadddcbbccddaddbcccdadabddacdaddbbbabbbdababcdcccbdbaabcccadbddcbaabcccbddabcddbbbdadbbaccadabaaddcddbcccdccdbcbbcabbcdacccaabcbbaadaabaddcbbaabcbacdaababcbdbcdbcaadbaaccddbbcbcbcbddaddaaadaaddddabdcaabcbbadcaaadccacbcaaccccdaccdbadbbdbacdbddbacabbcadacbacacabaddcccbabbababdadbbdabaacdcdacabbcadbcaababcaccbdacacacbaabbdcbdbabadddacbcddddddccdcdaaccabdddddcbadadcdbdccaccadbcbbdabcbaddadbabbbdbbabacbdcddbbccdbdddaddaabadabaabaadbabacadbbdbcdacdbbbccbdccdcccddcdcccbdabacadbccabdbdcaabccadddcdbbdbdadaabcccaacabdaabbcbddbaadccbcdabaccadacdcaacbabbbbcdcbddadcdcacadccdabaababcdabdccbaccbdccabbccbbcccddadbbcbcbcaacdabbabdccabcaaccabbbcdbcadbccddbdacaaccbaabacdcbaacbacccddcbdccabccddcccbdcbdddddbabacbbcccaaabbabcaddbbcadacbabddbaccbbaaabdcdcabaabacdccacbdcabbaccadcbbdbcdacbdcddbcccbbcdacabdbabcddbdbbbbcadabdddddaabcbccadaaabcbbddbdbdcaddbabacbcaccacccccdcbacacbabcaababbaacabaabcccdcdabbcbccaaddaacaadacddcddcccddbaadddbdadbddccaacaabadaaadcaabdbccbdcaabdcabadaaaddbbccbcdcadcadcccbacacbbdcdbbabcbccaacdddcddabbcabadacabdcacccaccaadccacabccdcabdcddddcdcdbbcdbadbcaabadacaddccdbaaacaccacbabaccaabdaacdaaacdcbcdabbaccbbabbabacdbbbcdaabacbaacaacdccbadbccbabdbacbdbbdcdbdbcabbdaccaacadaccccbcbdccacbcadacabdcddaabddbacccaddcdbcdaacbabacddcabcddcadbcbcddbddbcdbbcbaadcddbcbcacbadaacbaacaaaaacdbbaadabaababbadcaabbbdaabddacadbcbdbdcaabddaaddabbbbddacaadabdcabaabcdabccdccadbacbdaaaabcabcdcdcabaadbcdcacdbbacdabccbccaccdcbddbbdacabcadaadcaadcddddabbbbaccbcdbddcadddaccbacddcaaaaabccabdcbcbccbbabcaadbbbabcbaaabdbcacddcbaadbcdabcbcbbabaaaacdbdaadbdcbddbccdcadacccaadadabcdcdacdbabbdabbcbddabaccbadbddacbaddcaddbcadccdbddcdbbaabaaabcbddccbacdbbaddbcddabcddddcbccacbbdbaaccadbddcbcbccbcdcbccccdbcdadcbdddcdcbbcdbddcddaaabdacbcbaaaadbbcbcddcdbbbccbdbaaacdcadddbacadccaaccabbcabdabdbdbaddccaaccbacbacdccaccbbbbabddaabbadbcadbbcbcbaddbbadbcdcddccacacacdaabbbacddaabbbcabacacabbaaacabcadabbddaddbaabbbdcdcaadaacadacccaabdbcddadacabacbbdcdddabccdaaddbbbcbaddcccbaadaaacacabdacacabaadbbcadbbacacddaaddabdadbbbbdddadcbdddbdcdcabbadcdcdcabbadbadabbbdabbdabaadccacccbaddccdbddaadccbdddcdcaccddadbaccadbcabcccaddacdcdbcbbacacbabdcbcabbccaccbdcaaccccccaacadcbbccbdcddbdbddcccddddacababbaaacadadbcdbcabccbccbbdbabbcadadbcdbaddcaadbbdbbbaccaddadcdcdccbdaaaddcccddccdacdababbcbcbdcdadbdaacccbdcbdaccdaacdbdcacbbcbaccbaaacabdccabddbcccdddbcccdacdcadacababdaaddcdcdbcacdaaccabccbabadcbaadbbddbdaaddbbdccbbabbbacbbaabdbccccdccabacbcaabcaadabdbaddabdbaabacdaacccdcdabacbddbddbbbdcdbdbcbbaccdaabcabdcdcbabbbdbbbdcacddadcbddcaacbcbbcadbaabbdbcaacbddbccbdadbdbcabdbbcadddadcdaababdbcaccdaaacaccbaadbaddccabdcbbdbbaadddcbdbbddccbbacbbacabdcaaacbaddaaadccddcbcccdcdcdaddbaacbcbbaacdcadcbdddddcabaaabdacdbcaaacbabaaabcbbcccacabccbabbcaacdabacabbaccbbdbbdbdcadacdcddccdcbcbbcccbbcdabadbcaabccdcdabbcccccbbddcbabcbadbdcbabbbddbabccdcaabddaddbbbddbbcbadbbcdbbcaabacddcadcaabccabdbaaabdbaacbcabcbccabcbdacbadaabadaabdbddcadbbaadbdccbbaaddccbbadddbcbcbbaadddbbcccaddbbcbcbaacbaccaaaccdbbcdbdcbacadccddcbbdbbdacbbaaacadacbbcccaddcbcaaacdacbddbdbdaddbdcdcadbdbdcabcaddddbadbabdbbcbcbccaddbcbacccbdcdacbbaaadabdbcbdcbdcdcbcbbabbcbbababaaaacaaaabbccdcaddccddcbdadcdaadacacdcbccabcacbbaadcbacadcbbcadaacdcbbcadbddacddaabcbdcbbbadbabdaddabadbdccaadabaabdcdaaaccacbdbabaabdcccacdaccbbcdbccaccdaadcacbcdcdabbdbddddabdbdbdacacaadddadcdcaaadcdccacadcaccdababcbaadaababbaabdcccccdabdcacdcadabdacdddacbdabdccccbddacadcbccccccacdbddcbccbccdccdabdacaacabaadddaabbdbcdbcdbdbcacccdccbdacabaccccbadccacaacbdbdbccdcdacabdababbdaabacabdaabbbbbdccbadbbbadbdbcacdbabdabcacbadccdbbbdbaaacbdabbcadbdbbbabbbcddcaadcbcabbbdddabbababadbbcddabcbbdcbbabbbcababdcdadbbbabadbdadbddcacdcdddaccbaaacaacdacabdbaabdcadbbadabacbbbddcbaabccacbddddadcabbdbcbcbbacacdcbadddcacbbaddabbcadabacaccaadbdcaccabaccccadaaabadacccadadbabbcabbddbddcaddbddadadcaddbbaadacbdaadaadadaadbbcabdcdccaaacbbabddcacbbbbdcaaaccacaadbccacbabddcbdcdaadacbccbacbdcaabaddbbddbbbaaccbaaacdbbdcdcbcacaabcbbadbdbcbadbbdcbaccaabbcdabacacacbbbcdcbcdcaadcdbcabaabbbccdcbdacdadbadbdcbbdcdcbcbcbaadabcbcaabbbccacababacdbdcdabbdbbaaabcadcccbdaddabcbbaddacdddaacbbcbddbbdddcacbbdbdaccbcaadabbcbacabdbcaddadbacbbacbadcdaabccdbddbbaaabcdbaabcbbcadccaacbdcccbdbccaaaaddacabbbdaaaaacdadbdbbddcddcdcdcccdadcbdacbcacbcabcacaabacacacacdbdacaacdcdabbdddbdddbaaaababbbdcbdbbbdccababbbcacabbcdcabaabbdcbcbaccbccacaccbbbbbdcbbdcdbbcbacdaacccbaabbdccadcbcbbbcdcbdbdbaccbacaddddbbcabdacaddbccacdaaadbcababbbdbdabaaabdbbdcdddcbcbadcadcbacbcdbbdbacbcacacadbcaacccaddabbcaabaaaaccccbbcaadadadbbdcabaccddcdacbcaaccbdbcdbdbbabaabcbcccbddacdccacacddaabbdcbbdbdcadddbcbbdaabbbdcbabbadabdabbcdadbcadadadcdddadcabbcdaccbccccdcdcaaabddddcdbddbcaccdadaaabdbcddabddcbdbbaaddddcbbbacaacbcbaaabbbbccabcadccbbdcbdbcbabaacabdddadcaddadabdacdcbbcbbccdaadaacbbacadbccbbbabdcaddacaacccbacbdccdabcacddccbbbbcbbddcddacdabadabddbcbbcbacdaddaacaaddcbccdbaccadcbbdbcdbccdcbabcacaddcccabaadcbcabbbbdcdaadbaadaacbdccaacbaabaabcdbccdaccbacbbacddcbbccbabcbdcbccaddcbcbdcdaaacbddcdabdaacdbdbdaabaacccaccdddbcbababcbaccdcabbcbbaadaadaddbdccdcbbacccaddadbbdddcddaaadcdadaadbbbdadbdbbabacaabbdccaddcdcdadbcacacbbbadddacbbadadadabaddbcdadbdbcbbacacadcdbabcdbdcddacaababcadcacabaaadcbcaadddcbdaddabcbccdbdbbacbaaadddaaaccadddbacdcbddacaaadabccadacccacbbddadbddddcadadcbcbdbaccccadacaadbaaaccdbaabaaaccccbcbacdbdbbcacdcdccadcdddcccbdcacdcddddcddbacbbbccdaddacccddcbddaddacbbbbbcbcccdcbbbccacdcbdbdddadabbbdbdababccadacadddbabbbabcddbcccbbdabbbbddacccdcaccaddbcdaacacccabddbccdababdddcccbacadddaccbbbddbdbddccbcadacdbccdddbacdaabcbcbcddbccdcdacbccbbaddacbdababaddbdbabbcdcacdccdddbacdccacdacbabddabddcdccdbcdddbdcadabbdbcaccccaaaabdbcaddddcbbdadaabacaabadcaccacbdccbdddcbdbadacccaccdccdcabaabdcbcaabcdcbdbddaacdbadddccaadaddcbdbcbbdbbdcbaacbabddbacbcacdbdaddccbbcbaadbcbabbaaaabdcbabbbbdbbcbddbcdbdccaddcdbcbcacbaadbbcbdbcbddcdacddacdddbbbddbdbcbcabacaaccbddaccdcdabccadcaccdcaddadbdaaacaddacdcadbcbadaacabaadbcaacabaddddbccacbcaadadaacdcabbccbbcccbccdcdbacacaacbdbbddaabbcbdabacccbaddbbcccabcdccccbbdcdcacccccacccacddccbababbabaaabcccacaadbbbdddccdcccacbadbdbcdddcacadabcddbbdcdabddbdabbdcdadcaddbaacdddccbbbaddbbcbdccbcbabbbaccdabbcdcbadcdadcadbbcbcdbcadcaddbabaddadcabaccbbddbbabdbbabbdcacdadaababcbcabbdabdabdacaccbbababdcdcbcbbbcdbddbacadbabdddacbbcadbababdbbcbabdbccbdabcccbbddadcdbdcdddcbdccaaabbdaddaabdaacabbaccbbaddbdbbcabcdddcccabacdbdadaabbdadaddcdbbabacccaddbbbbccdbbabaacbbadcdccaadadbcbcbdaabdbcbbbdccaabdccbbcabbabaadcbdcacdbcadddaccacdaaddaaaccdbbabcabbacbdbcddcacdadbcacacbdcbbbccbadddcdcababbbddacdcdbbdccbabacdddaaaacaddcacbbabdbdbccacdcbcabcadcbccbcacbcbbcdbaddaaaaaaabbabbacadbbaababccbbbdcdccabdcdbccdbcabbcabcbcaccdcbbdaaccdaabcdbcbcaacacbbdbacccbadabccabacaaccbddbcddcaaabdccdbddcdadcdcbaacdbcdcbabaddadcbdadbaadadcbabbaaacdbdddabacdcadcbcadaadbddbcbdbcbccbcaabacadabbddabcdcbcadbbccaacaabcdddddadcdcbadccccddcccbaadcccddcaadcbdbbdccdaddaadddcdccbbccdbadccacdadcdcdccaccbccbccddbbabdacccbcdddccddccddddbcbadbabdddcbdabdbabcadbdcadbcdacadcdbdabdabaccdccdbbdbbabbaadddccdabccaacabdadabbcbccdabbbcbdcbbdddccccabbddacbadbdcaabdddcbccbabbbcbbcccdbddacaacbaabbabbbabcbdccacccdbcdacdddacaacddccdbcccbabccadcbccccbcbccccccbabbddcadaaacdadacdddccbadcdaccbbcbddbcadbccdbaabadbddbaaabcdabcddbbdbccdababadbdcccdbdbadcacaabacbacadadbbadaddcbcdabacbdabcdbdbdcbbdbabaddbcbaabbdbccbccaaacadbcbccbbabaaacdbaddcbbbbdadadccabdabbcbbadcddcacbdacbabdcadcdccbbabbbcccdcdbcccdbcbbcaadbcacdcbdcbbdadccbdaddcadaaddabbdbdaadcdadbabbbadcddccbdbbdbcbdacacaadbccdbcacbdabdcccaddcbdcbbbbdddbddbadbcdbdcbdabaabdacadbbaaaadcabdddbcacabbbdbcbacbadaabcbadbdaddccdaaadaaadadbcccaacdbccbcbdcaabdccaadcaacbbabbbacbccadadbcadbbbcdabcdabbbbbbcbcddddbbbaccdbbdadbddcaddcbdbcaddcbcacbcaaaabbbaabacaacbadbcbcdacacbacddcccdbaadcbbccadaacaddbcccaabaccddbadabdbdbbaadbbcadbdabcbadadadabcdacaadaddcacbaadbacdccdddbdddaccbdabcbbbbadbdaabdcacdacaccaddababbcddacdcabdacddadadcaabbaccbccdacabccbacccabaacdcdbdaabcbdbadaacdddcbcaacbacbacdcdadbddabaabcddacdaacbaabcadabdaccbccdbbbbdcddbccaddcdbccbcdabbaabdadbbcdcccdbdaddcbddddbacbcdadaaaddcaadbcdacdbbcaaddcddbbdadcdccdaccabdabbcccdccabadabaddbacbaacbdcbacdacccbcbccabdabbddacdacbcaadcccbbcaaaaacacacdaddbddddbacaadaadbdcadbdbdcccbbbdcddcdbdcbbbbaadcbadcdaddadbcdddabadcabcbcbbcabbadbdacdcabcbdaddcbbabddcabcbdacbbabdcbbdddddbccdbaabbbadaddcadbdcbbdaadcdcbabaabcbbbdabbccdcbbcbbabcbadabcbccadcccaacdcbdbbcbbdaadcdaababacdbaacbcbaaaacaddcdadcccbadcbddadaddbaaddadbdaabbddcddabcbabaaaabbbdbbabdabbdaacacbaacbbacdbaadadbdacacbdcbdcbbbcbaccddcddbcdaddbdaaacbccbaccabddbdcdcacbdbdbcbdacaaddaabacadadadbcddacbcccdbbabddcdaacbaabcbdcbcbcbbbbaddabcdbcdaacbcbacbadbbacdcbddaddabaaacdbadbaacddaaccacabbccdbacbaaaccbbcbccaddaabcccdcbaacbdabadbddbddddbcdbbdacdbbbcabadbdacccdbbdaaaaabbbdbcddcbbddcddadbcccabddcdadcdbbcbcccbccbcacbcbcdddbbcbdbbcaacaacccababacdaccadcbadadbcabcbaaaaabdbbabcbdbccdbbabdcdadddbbbbcbbaaacaccdcbcbdcbabbadacbacbccbdcddadcabdddcaacbacacabdbdccaacdcbdbaabddddabaacdabcaddbdccccdaccdaccaabaabbdacccaaacdcdcdbadcaaccacaacadbbabdddbdabdbbbbdacbdcabdccacbaacbbabbbbbccbdbdddacdacadcbcbbdcabccabccbbadabaacbaadacdabdccbbabbddcacadccbcdbbddcddbacbcdbdaaaddbdbccabcaaaccbbcdddcaaaccdacdaabbaccacadcadaacacdcbacdcacdadbcdabddbcbabdccdadacdacccdcdbcccbcbcdbaabaaccabdaaaaabdcbcdabdbacacdabbbccbaccadadadcadbbadbacbdbdcbbcdbdbdcabbbcbaccacccbdddccdcabaaabbaabbbaccaabccdcbabcaddccacddddcaadbaabdbbadccdcbdbdbbccaccbdcaaacbcbcbcbaabcacdacbabacbcdbadaacdcdbdcaddddbdcddcbbbddcaccbcacbbbaddddbdbdbbcbdbaccbcbabaabbcacbabcdbcbbacbcbbcbdbcacccbdcdbddcadbaaaabdcdacdddcdcdccdddbcadacadaaadbbacaccddababdcbaaddddbaacacaabdbcdababcaabbddbbcadccbabdacccdabbdcddbaadccaccbacadcddbcbabaadbcabcbcababbacabbcdcbbdabdcaaddcdccacccddbacdacbddabcdcbddbccbacbcccbdbccbaadcbdbdacabbdcdddbbbbdcbcccdbcaadbdcacbcbccdddabadcdadacdbbbcacddcabacadcccbcdaaabdbcddcbdcabcdcddbddbdbbdabbadbbabbdadcdbddccddcdcdacbbaccdddacbbcbcbcaacbadbbaacdcbadaababbadabacbccaacabdbbcbcbbcbdabdadaddccdbccdbddabaaccdaccdcbaabacbadbadbaacadbbbbbbddabadaabcbaaababbbbbdbabdbbadadbadbadaaabaaacabbbcabdacaabdaaaadcddcdbdcadaaaaddccacbcabbabcbdbcabcaabbdbccbaabdddccccdbcbdcbaadcbadcabdccbaccaddacabddbbcdadbadbabdbbadccdaacbdcdadbdacccbbbaaadcacddbcbbaacdcddcbaaaabddacddddacbabcbcbbbddcbbaabbcabbbccadbcdcbabdaadcbaccdbaadabadacaddbbbadabacccbaaaacabdbbcbcdcaccdaaccaabadcdccabbabcdddcabcbccadcaaaabcbdcdcaddacbbdcbcbdababcabddcaadabccabbdaabcddbccdadadaaabbcdccaacadbdbabddcbcdcadcabccdbbdbabaabbadccccbddaabdaaccdabcbdbaddbcbadcbccdaadcdbdacaabadbbdcdcaaddbddbddabbcacaaacbcbdbbcacdadadcbddbbaaddabcacbabdcbacddadcddaadaaacbcdbbadcadcbcccadbbbacaaddcbdabdcdaabcddbacaccacdcbcddaaaadabcadaaaaccbabccacdbbadcdccabcdabddcadbadacaacccdcbdddbaadaadcccaccaadbbbccbbdbdbbbdabbcbdabdadadbaacacbabbddcadcdbaaadabdcbcddcbbdabdccacdbaccddbdbdcccadcdcbccacaccbccbaaaabdaacabdbaddbdcadabdacbccaabcddddbbccbbbaadaddcbdacdbdcaacccadcacacbbaccdcacaabdcccdddbadacbbbcbbdbbdbacdddbbccddadbdadbdcbdddbacdbaaddcbaddbcacbaccadaddbcdacbbcdccacbddcdaabbbbaacbdbbdacccccbcccbaaabacacbbdbdbbdcddcdcdbbccdccbbabdbdcadaabbddabccbdbdddbddcbcbddbadabadcbbcdbbcbadbadbdbdbdbbcbcddaddccbbbacbbcabdcdbaccddacadabdcbacdabacbdabcccbbdacdccbcacddcbabccbacabacbdcdcaccbdddbdccdbdbcbccabdbacccaacccccdcbbccdbdadabdadadcdbadddaaacdcccdaaacdccccacdbddddbbcaadcaadcdaadbdddacaadccdadabadcacccaaaacadbbdadddddcadcbccaabcbdcabccbdbadcaddbbcbdbbabccdaaababbaabbdcbcbbbdcabcbadcacabdbbbddbccdddddddcbcdbaacbbbdcaadddcbabbddcdbabcdaddbdbcdacddcbbcbdcabcdbcdcbbcdadbbddadbdbdcbbcaaaaadbadabcacbbcbdbaccddcdcadcaddaadbdbdccacabdcadadddbabbddaaabbbbbdbbbacacabcccbdcadbaadabcdacccdccbaacbdacccacaadbacbdaacbbddabaccabdbbdccbcdbdbddbbddacbcdadddabddabbbdaabcbabdacbcaabcdbaaddabddaaaaddbaabbabcbdbdbbaabadadbadabcddbccacdcdbdbadcadaabdbbdaabadaddccdadbabdcadbcbbddcbccbddcdbaacdcbcbccdacccaabcadadcbadbaaacbcdaccdbadbdccdbdbdcaacdbcbdcbadcbabadddcbaadcdbdaaadcccbbcdbdbddadbcbdabcdadcddccacddbcbaabacabccbdaaacbdacbcbbaacdcdacbabbddcbbbbacdadccbccaccacbdddbcadcaabaaddbddccdcbaacbdccdcdbdbdcdababadabcacabaccccaaddbcbcbbbbdabbabdbbabdbadbaadccadcbccaaacbdcbbddcbaccdcabadddbcabcdccaaaadcddddcdbcccbddacdabaaccdadbacbacabdcacdadabbababaddbbaaaadccbacadcaaabccababaaadcaacddadaaacdbbabaccdcaaabccbcaddadabbcbadaaaaaddbadbbacbbabbbadcddbddbbbaaabaccadddaaccacccdabdccdcdcbadaacccbaddcdacaccdacdbabbdbcdabdacddabbbbccabcbbddabacdcdcbcbddacddddbbaacbccaaccdbbdccaccbadbabadbacdcdbdacababbacbbcbccabcbdbacdbdbcdddcddbabdaaadcaccaadbabccbcbadcddcccddbaddabccabdbcccbbdcdaddbbdcddcbdcacdbbdcddcbdbcdbacdacdcbabdadabcbbddbcaaacabbdcdbaccbcabdadbbccacaabdddabccddbccaababcccaaaabdbacbdcadaabcbcacdbbadccbabbdbddabbcddddbcddbbacbbcadaccbdbdddbcdddbaababdbadadbdbcdcdbbccadbcdbbcabbbccbaaddccadadcaaccdcdcdaccadccdcbdbbddccabdccabdcabbaccacbccbaaddbacdabbbadcdbdabbbccddcdcddddccddddccdaacabcaaccbacabadbddbbcbaaabbabbdbaccaacacdacbbaadaaababddaaddddbbdcccdbbccacbccbaccaadbadcbdcbddbdaccdcccabddcccdbaccdcbdaaddbabdacdaccbccccaacdbaadbabcadcadbbbccaacaddbbddbdbbbcbbcdaaacbdcdbacbbdbdccbdaabddadbbdcabcabcadaccddddcdaadaabcaaaadaacaaaabdaaaacbcbdcdcccbcbccbdccabadacbaacbaaadcbaadbbbbaacdaacadabddacadcbbadababadbdcccccdbdcbbaddabdbbbbcdcbddccaaccbdcbdbcdbdccbcbcabbbabbabaccbdcddccdacaababccddccddcaadacddacbaaadccbdaabccbddadbcdbdbcdbcdcacbbcbccababaabaaddcbcaccbaacccbadacadbadcddaadaaadbdbdcdacabcdadaccaabbabbcdaabaabddcbdacbcdabcbaddaabacdbdcdadcbabcdabcbddbccaadbacaacacdaadaaddaabbbacbddacccadadadaacdcbdbbbaabbaadcaadcadabadcabccbaaaadccdbbbacaccdcdddcddaaabcccdcabbabbbbbabcdcddddbcdaabbcaabadabbbbdaccbddccbcbbdbbababdcaababcaddbbabaadbaaaabbbbadcddabaadbbbaccbcccadbcccaacbadadcabbbbabccacbadcaaccbcaacaababacbdacbdbdccdaadddcbdacbabddacdadbdcccbbdccadccdbcbdadbdcaacaccabcccdaaacbabdabaddadcaacbbaabddcdacbdbadbcaadbdbbcdbbabddaaddaccadababbdbbcbdbaadaccaddcbcdcccdabccdadbddbcadaadaacddcadcabdbbcbdbadacabbbcdbbaccbdaddbcaadbbbbcbccacbcdbcbaddcaacdbaacadbbdcdcbddaddccbdaacdbdabbacbadacbaaaddabdaaaacbacbdccbdddbacaabbbbccaabadabbaaacdbbdcbdcdcdbbbbdacabccddbdaacbbdacccacdcbadcbddddbdbabcbcaababbccdccccbcbdcdcbbdabbbbbcbadbababbadbdbbadcbdadacbbdccbdbbccdadcbccbadacddccddbbddababdcaadcabbcdcbdadacbbdcadacdbdddadacadacdcccdcbbdcddddadbbccdadabbdbdadaabdbcddddccadbcbbcababbaddaacbabbcbbaadddbcbacbbccbacdbddbbacdbddbcabadcbdbdbbbacdcdabdbcbbccddddcacaddadacacbddabcabdbdbcbbcbbdccadcdcabdcdadbdcbabdaabdabcdacadaddabbdaccbbbbacacdaabccacbbddabcaaccbdddbbdabdcdbccdbddcadbcbdacbabaacaddcbacaabbabccbcabccbdadddcdbbabdccddabbabbabadbddaddddbaddccacbcdccdadabcbccdddabcbbcdcbdddcbcbdbbddccaccddbabddcdccdadcbbbdaabdabccdbddcdacaaccaccabbbdcbbaddbbdabcdbbbcaccbcaccbcbddbbaddabbabbbacdcccbbacccbdcccaaadccbcdcbadccacabcdccacaaddaadcccccccbdbcdbdcbbdaddccaabddcddabbccacaabbbdacbdccdcabdbbcabdabbcacbacabbdbaaadccadbacbbdbcadbcdbdabbaadbdadbabcaddccdccabcadbacddbccbdabacaccaaddcbddcccdaddddcabdadbcbbdddaaadbcddcccdddbbaadcabadcdaabcbbaaabbdbdabccccabcddbbcabdcababbacbcbbcccbbbdcccadbbddaacdbccdabddabcddcadcbbdbacbbcbbbbdcbaadadbdbccabbbcccaacadbcdbcbcddadcaddbacbbcadbdccbbcdadbbcdcccbccadaaddacaaacdccbbdaabcccabbdabbabbdabcdbbcbdadadaaccacdbabcbadabbbbacbdaddaadacbbbdcacacadaccabdcdaccbbbacbbcbccdaccabaddddcdccbadddcaccdadccdcdccaabdabccdcbcdadccbaadaacdaddacabcbacacabcdacdcdcdacabdabddbbbbdbadcdaddbdacdbbcabcbbababdbadacddacbcbdaaacdaccaddadbdddcacbccaacacdcaddcdcdbddacbcbbabaddcdaadbdaccdabddcadcbabddcdaababbbbaccdbbcbaacaadcbabadccbdcbadbcdcbacbbcaddcabcddbdccacbbdbaaaaabccbcdbdabbcbdbaadbbccabacaacdccaabcabbcaabcbbbbacbcdbcabdcacbddaadbcdcddbbddcccbbadbcbcbdcdbdabcaacdadcaaabcbdbbdaccbbbddaadbdccddcbdcdddbddbcdcbdbbcbbcbbccbaddbddacacdcdcbcbdacbdabdcddbcdaabaaddbdcbdcbddcbccdddbdadddbbdbabcbdbdbcadabbaccdabbbbdbbadccdccdbaddabacaabbcdccbcbdadadbdbbdddddacbbdaadbccabbdddcbdadcdcdcbbdabcbaccbcbcaabdaccdcbdbdbddcbcccbcddcbbcbaadbdaddadbdaacbdaaccbcbdadaadcabdaaddcccbdbbbbbbcddaadadcbccccccaadaabbbacbcaabaddaadbbcddadcbbbacdbdccbbddbbaababbaaabddadbaadddabbbadcdcaabbadadccdabccbcddccdcccdbccbdddcbbbcdcacbacaccadbaccdcbbdacbbbcccbcccbaaadabdbdcdabbcadbaaccababbdccacdabcbccacdabbbcbacadbcbabacadaacadaadccaddadcacbbaadcaacaadacdddbbaaaacacbddbbbccddbccccaaddccddddbbdddabcbbccddbadabacaacaccadbaccccdddbdacdcddabcbcabbacacdadcdbaddbccccabddbcdbdcbcdcbcdddaaccabacbbddbddadaababcaabdccccccacbcadddabacdaddbdccccddbccdcdcdbdcdddcadbcdcbdbcdbdcacbbdcdbcaadaaabccbdbdbbccddddcbbcbbdcccdbbbdcdbabadacadccdadbcaaadccaacbcbadcbbacdcbdbddbbacbccdaaadabadcdccbdbcaacddcdccdacaadccbaabcbccdacaccaabcbcabcadcccbadbcbbccdaddacbcdccbdbadacdbbadadacbdbdadbcabacabacddaaccbdadbaacdaccbadcabccddabdddabaabdbdacadbbadabbbbdbcbbbccdbcdaadbdcdbbdcacdbdbdbcbdcbcbcddaddcbdaadddaaccabdbcbbaacaccbcdddcababbbbaaaddaaadadbbadadcdbddbadaacccbddccbaabbabddaccbbaccbabccbddbbabcbdbadcdabdacccdddbdccbbbddcdbacbdabbbcdabcaccddadbadbbdbcdbddbbabaddacdbdcccccdbccdddddccdcabbacdcacddbcbaccabaabcbacaacbcbdbdcdadabcccacacbcbabcbaccdcdbccddaddbbcadadaccbccdacbbbcddcbbcbcddddcdcadacaaccdcaacacddcddcbcbacabbaaddbbbbdbdbadddcabaaaaacacbbbbdddbbcbbbcacbcadaacabbdbbcbbadddbaaadccccaadbbdcbabdcabbdbcdcdbbdccabcabbdcbdccccbbddbdaccaacdabbdabbbdddbabadadadcdadcbddaaddccddababadddbdcbdaacdcddbcacdcbbcacaaccbabdcddadcbdccdadadddbbabbdbbaaadbaddbcdbdbbbabadacdcbbdbbcdbbbbbcacacabbaabddaaabbbadaccbddbbcaaadcdaabbadcbddbbcddddcdcdcbabadadacaababacacdcabbaaacabcddaaabbacbdaacddbacdcccbaccdccbddabadbcdbadaadcbdddacacaabcadbcddcaacadaacccabbabcbdcdcaacbaadaabaddadbbcdbadcaccdcccddbbbcbcbdbbaaabbacdcbadabbdcccaabdbcddaddaaaacdbabbcccadbccbbadcccadabdacdbbdbaababdacdcacddaabddcbbcbbcabcbddbccbabbdbcdcbdacdbdcdbabadccbbbcbdbabbdadabdbdcabdcadccbcadadbdabdbbddbcbbcccbcdbadddabcdbdadbdcdcdcdabdcaadcbcbadadcabccbcbabdbabdacabaacbbcaadcbadabacadcababcdbccbcccdcddddcddcbadbdabadabacbdaacddacabdaddcbbdcbccccdaccbaacbbaabcbbdccbacdacbadcbdccdcaacbddccadbdcacbadbbaabbcbaaabacaddbcbdbddbabbddcbaabcaaddadbaabddadaaabaaabddababadccadcdcbacdddbdcddbbddabbdabdbdbdabbdaccabdccdcdcbbbcdadacaaccbcaabcbdbdcdcbbcbbdabacdaddddddbdacbcabdacaaadbaacdbbcdcadbdcbbabbbcbadadadbababcabcbccadcaadbabbadbddbaccccccdaddaabadbddcabcccddddcbcdabdbdcadcdaddadcdaadaacabccdabcdaccbbcddbbccbccbcbdddbbcdbdcadabcbbdbdcccadcbbabdcaddbdcbacbddbcbdcbadadcddbbbabdabdddbacccadbbbddcabbdbbdcdcddbcdaaaccabdbdabaddaccdccabccccaaaaccbadbabaccabbabbabacbbbbbdbdabbabacacbdbcabcbacbcdaabbdbdccadacbbacdbaddcdcbbcdbdabbabcbbcadcccdabcdcbdccccbdbddbcccaaadadcbbccabaaaaacddddcaaccabbccaabbcadcacbabacabcbbbdaaddabcdaddbdadaaaddadbbcaaccadcbcbddacadcbababcbadabcbaababbcacbccbbcaccaababcababadddbbcbbbaabacdbabbbacdcadaabddabddcdcaacdbcbccacbdabcddcacbbcaacacaccbcabadcddcadabbacabbdcdbacdcccccacbbacbdbcabbbccbccbcdbcbaddadacbdadddbbacdaaaadabccddddddbadbadbdbaccdcadbccccdbadccbccacadddcbbbddaddabbcbccaacdacababbdcadaadcccaadabacddaabbabbbbaaaddabcacbdcccdbcdadbbddbdbdcadadbadbaadcbaadadadacabdacdbcbdabdabbabddbcbdadbadccdbaaccabacbbcddbdcabbbbccdcdccdcbadddbbccdaaacbabcbcdaadccacdbadbdadbccadbadcbabaadcbdaacbabdacaaaddbcabacccbdbdcdbbccbababbaddcccdacccaddbbadddbbbbdbbbcbaccacacdcdbddccaadbbdcbacdaaadaddddcdccbaadbcabacbacbacabdcabacbdcbccdddcbacadcaadacaddaaabcbdadabbddcbdcdaccdbadaccbbadcdcdabcccccbcdbaadadaaadbbdcdaddbaaabdaaddcdcdcaddcaccddbbaaccbcbcdacacdabddac
ddbdcadccdabbadcdcdcbdacdaddcbbdaacccbdcacdbcccabdccaaaacaccdcddcaabdccbdabdbcccdaacadadccddaadcbacbcccaaaddabcdcbacccdcccbbbbcababcbbddaddbbacdaadccabbaaaaababdbddacdabcdacccbcdcacbccbccbdacbadacaacbdbabcddddcccdacadadbdadacbaabcdbdbaddcbcadcadcbcabddadbccadababcacddcdadcaadccabbddbcabdadabdcaabaaabcbbccddcaddaacbcbbcdbaacbcddaabcbddaabdddaaadbccdccadcddadabdbcbadaaacddcadaccabcbcbbaacaadccbcabcabaacdadcdbadbbcbaccadbaadabbdcdcbadacdabddcabccbdabcabbaabdabbcabcbdacdadbcdacbbdcabadbabaccaccdcdcdcdacdaacadbddbddcacaadadaaacdddacbdaaacdbbaabcaacbadababbabcbdbddbbbcdcaaaccbbacbbabbcbdadbbdaacbcdddacdddcaabdddbccbcbdbdbacadddddaccdddbdabadcbdabacadacaaadcabdaaccdacacacaddaabbacdbbccbbccdaabbbbcabbabccbcdbbdbccbbccccddacbdbbaaabcdbbddbabdcbacdbdbdddaabcababcaadacadcbdabcbbcddcdaccdadaaabaadbadaacadacbbdbcbbabbcbbabcbacaabddcbcdbdccbccdbcaccbcdcbccbddbaaabdbaaddcdbacacdbcdcbaacdbdccdacacdcccbdbcaccabbdddddaadabddccdddddabcdbcabbabccbcbbacbccabbbbbbcbdbbcadaadcdbddadaacddbcdcadaccdbbccdacbcbdbddbccdaacccadbabababbcbdbcccccadddcbcddcaccddbcbbdbbabbaaaabbddaccbabbbcabacdbcadddabadcdbcabddbdbdccdacabbcacaaabdaccdcaddcdbadaabdcaccbcacadcaadacbcadbccadbdaacaadcaaaadbdbbbdcbdbcbaadbdcbbbacdacbbcdbdbddbcccccbdaccccbbccdcaddadaaadddabdaccadcbddadabcbaaaaabdcaadbaaabaccddadbddaaabaadabaccacabcdddabccbbababdcdaacadcabdaabacbdcdbbabbabcdcbddcdddcbbbccdbabacddaddaccbbdcdbccdbdabcacabbddbcccdacbbabbbdbadccbddddddcdcadabbbddaabaabbbdddddabdabacdddadbbbadcdacdcdabdbbddbdaaacbaaaabbdccdbccababbcccdaadadccbcdcdcbabccaccccddbcdcbabbccabcdbdbbdabbccdabcbbbbbdacaabdacadccbacbdacccccddcaacdbbdabdddcdcdacdccbddcbcdbbbbcccaaddbabcaccdcdcbcaacacddbcabcaccdbbddcacdabaacdcdcbddadadddbababdacdcadcdccbdbaccdcabbbdacaabcadcdccdcadaccbdbcabcbddaccabbbbbbbdcbbcccbaadaacddcbabaddcaacabddccabbaaccddaaccccaacddadbdbbbcbbcdacdbdbddaaacaacababdacdccaaabcbaddbdbccbbbbcadaaddddccdaacbdabadcbdbbbcbcdbccadbbcbadcbcaacddddcdcadbbdcbbdaccbbacdcabccbacacdadcaaadaacdbcdbddccacabbddaaabdbdcdcaccacbdddadaddabbacbbcaaabbdcadddbbacbdcdccaadadccccdcdaaabddabccdabdcabddaaccaaabbcdaaddccbabcdccaaaadddddcbabacbcbcbabcaccdcaacdcdabaacbcbdacadcccccddcaacaccdcbddadcdabbacaabccbccaacbaccabbcdbdcabdbabcbbccdbadccccadcccccdccccbcdcdbabaccbadbaabaadbadccddbbdbcacdacbcbaabcdddabadbbbbddbdbcbbccbbbbcaddbabbddcccdbbadbadcaaacbbbccaaabbcbdddaadacaccdddadaabcadaddadadacdccabaacdbcacdcbcaabadbcdaacbccdbccdaccadadbcdaabdaabcaccacddbadddabbbdabddcaadcdacdbbacadcaacaccadbddddccabdaacaccbbcbccbabddcbbdcccbcabdcbbcddbaabbddaaddbcbdabcadbbbacbdcaccaccdabdbbdadddddbddbbabbddaaccdcaaacdbadaacdaacbcbdbbdbdbcdacbdaaaacddcdcacbcabbabcbadcaabdcdcdddbadccdbcbdabbbbddddbadbbcbdbbbbaaabaddabcbadddbbccbccdcadbcccbdddbccdbabcbcabdbabbbaabacdbdcdcaaabaccbaccdacbccdaabbcbacadadaabbcbacaacdaaccacbcabacccdbadbcdbbbcccbdbccbcaddbccdadcaabdacdaacdcbdcbdbbdcadddcdbbcdabdabadbaababcdbadabcadbadbcbccddacddcdcdcabbcbaadaddcbdddbacbbcccddccdbbacacdcddcbbdbcbdbbdcddbddcbcabcccabbcacaddcccaabaacaadbabbabcdbdbbdabbbdabaccccbddbbabaacaccdccdabcbaaaabdbadcbcbddcdbdadbacdbcbdccdbccaabaccabbacaabacacdddadacdaaccbacbbdddbcccccabdabddbbbcadabbcdcbaadcdacdaaddabcdbbcdddbabadbcbbccaccdaabcaadcaaaabccabacdcbcbcdbbdbadbbcbacbaaacacbcdbdbdabaccadcadbdbbbdadcbdacaaadcdacddccdbcdbdababccbaccdaabddbcacdadbbdcadcbdbcbdbbccbbbdbcdbcaaadddaabdcbdccccddbaacddaddbdcadcddaabaadccccaadcdacabbbddbaaddcaccacbbcaadcbbcdcadcbaadbccaccbdbdbacadbcdddaddddbbdbcbbcdcbacdcadbbbccaccdaaddbaaabddcdadccdaccdabdbcaccbacccaaccbdacabadabdbacdcbabadabcccadddcadbcaddabbccddabaacdbcabbbacabacadbdabacddacdbdadacdcdaacbbcdabcadcbcbacdcbabdcccbcdadadaddacaccdcbbddbddbdaccdbbadabadcccacdbaadcdaddcdcadcbbcddadbabaabdbaddacdcddbbabadcacdaddcbacadbbcbaddbbabddabaadabdbbcacbbabbbddacdccbdcccddaabcbabdbbbdddbabdcaababccbdababdbbcacabcdcdbadaabbbdcdabdddaabbdadbbabdadcaccccdadcdcbbcaddbbdbadacddcdabaacddaabdadcbaaabcbabccbaadbbabbdcdadadbddbabaddbaccdbcacbbdcbcdddcbccabadddacaabcdcbdbabdbddddaaccbcbdbbbadddcacdabbdabddaaddbaacbccbdcaacadbdccbabdaddcbbbddcccbbddccdcdbabccdcaccdbcdcaabcacccbcdacdadccddbcbacadbcaddcccadccbddbbcddaabbabbabcaaccbdcddaaabdaaadadbddaabbbcdcdbccbbcdadccacccdbbdabacbdcdbacdcdadcbddbdaddbbabdaccbcbbabdcbbcaccbccacbdcbcbbdbdabcbccddaccccabdacdaaddbbbccddaadabddcdccacbcddbbaabccdadbccadbcacacdabdbadacaddcccdbdaabbcdabdaddcdddbbdccacdaaabddcddddddcbcdcbbbadaaabacaccccbdaddabbcdadbbbabbccccdaccddbaaaddcadaabaacbaabaccaaccacadabcacbaaadccdabacbccbdbcadabdacdcbaaadbabdbaaacbadbbdbcaabaaaadaacacbaddcdaabccacddaacdcdacabbbcbbdabdababbcbcddbaadadbcddcbaddbaddcdddccdcadcdbddcdabcbbccbabccdcbcaccccdcbadbbabdaaacacdbadbbdaaadbbbdcaaadbcdacbcddcaabccdbbabbabdddcbbdadcbacbacddbaaccbabbdcbcccaabcccaabadabdcabaddacadcbdcccddacacacbaaaabccadadcabbddbbababaccdaacbbdcdbdaabbcccddcabbdbababaabcaaabcdbdacdcadccbdbddbdbbdcbcccacaddaabbbdbcabbbcccbcabcadcaadddbbcbcddaaabaaacbabcbdabdbdabcdcbddcbacbcbcadcdbdddbacaaccdcccacbbcadcbcddababdddddadccdcdcccddbbabdadbdabdcbdcdccbdcbcccaabbbddabdbbdbaacdabadbdcbaaacdacaddabddbbdbacabccadbbbabdcadacdadddcdcdbbaabbabadabccbdadbbcbcdbababcbbdbcaacbacaabcabadadcccaccaabacbaddadacdcacadccbaaddbccaacbcdccbcdbcdbccabcaccccabccbdbbdbbdbbbbacdccdaadaccdccacbaaccbbcabbbacbbbbcbaccbdaacbcddcdbaddbcbbdbdbbbcdccbdadbbacbdddcaadcaacdbbcbdbdacddbaddbbbcddcacbcaadadadabbadddbcacdbbbdbcbdabcaddadbcbddcaabdcdaddddcbbcdbadcaaaccacdddbbaddbbcbdbaccbcaccbbacbddabcadbaabbcbdababcaaacbdbdccdbdaabdcbdccbbdacabcbdabbabddbcdbccccbcaabddbcccccbadbbcbdddacdbbdaacdccdbdacccdbcadbaabbbdbacadbdcbdcbbddcbbbcacabbcacaddcacbdcaaacdaabdabacaaccabaacdcbdaaabdaaabbbdaaaccccbaacbbbadacaaababdbcbbbbdabacddbabdccbcdbdbbadabbabacddbacaccbcdbbbddbdacdcaabddbbccddbdcdcddbbcdccdaadacbaccaaacdabbabccbdaacacbcdcdbbbdcccbcadddddbcbdbdbacbcbaaaadbabbcbcbacdacaabaadababccddbccdddacaddbbdabbadbddcaccabcadbdbccadccbacabbcdccadcbccaadcdabcbcccdbbbddbcccbbbacdcabcadabbacbdbadbdcdaaccbbddbdbaadaabccacddddcbdaacbbdccadcdcdcbccaacbacdddbbcdcdcbdddadaddabaaddaabcbadaacbccadbdacadadddbddabcccdccabddcdcacbaaccbdbbaaccccbcdddcbdbcdcaadcbdbbaadcddcddcbadcbbccbbbdcbbcaaddcddadbdcaadacbaadabcaabdcccbbacabaadaacdacdbdcdddddcdaadbcbdbaabdbddbababdcbbcddcaccdddddccbadbcdcaabddadccabcabccadadbbcdaccbcbdbcacbdbacbbcdcdabcdbcbcddcaacdaacabcbacccbdccdcbdadcdccbcdddaccbbdbcaddccaabaccbacbbbdaabcddbacbdddbcddbcabaacaacbdbaadbddbabcbbdcbbacbdbdbbbbbbcaaababddaccbaadcbadacadbbdcdacdcbdbcdcaadaacbddbaadbacacdabdcdcddddccdadadcdccabacabdacbabacaadacccddbdccbdababdaacbddaccbcacacdabbabaacaabbcdccdaacddbbddcddbcabdcadaaddacdbddcddbdaaddaaadadbdaaccbcabbcbacbbcabadcbccacadcaaddcbabccaaadddbcccccdbdcdbdcdaddacadbabdddcadbbcccbaaddbddcbccbacdacabccbaaaabaaaccdbccbdcdacbddabbadbbcbdbadaaaadcbdcddddabaddaacacbccdcbaacddacdaaccbabcbacadccdcacacdbccbbacbbbabdddcdcdadacccdaabbdbdbacaabdbacdcccddaacbbcbaacbbbbbbddcacbdddacbdcaccdadabadcadaabcddaaaaacddbdcdabbadacbcdcdadddbbababdabcdcbaaaaaaccdacccdbbddbddbcabacaaabbacdcdcbcbdbddcdbcdddaacbaddadcdacbbcadaabdcaccddbababaaacccdbacbbaaaaddcbabcbbcaacaadbaccbdbdacaadcbbdbcbdccbcacddbabbcbdabcdbccddaabdadbddcadcabadcadaccdcabbbbcaaccacbcddabcdbdcdbccbddbabdccadabbababacbdbabddaaabcbcbccabcabccbcdccabdbdbdabbbbabacabaaaccbacdddbaaaaaabbadabbdaaaadadbabdcdcbdacaacbccabbcbdaccadbcbdbbdccdcdbbadccddcacddbdcbdcdccbbdbaddbbbacdadccbddbccdcaddbbcadbbdbdccdabbbacbabaacdbcbcdddcbcbdcbadccabbcaaabcccadcbddbcdabbacbcadaacbdbbadbbbbadbabbaaaaccbcdbacaaacdcabbbcdabcbddacadccbbbddacdaabaaabacccabcbdcaddacdacdabccdbaccddadbacbadbabcbdbdaacaccbdddbbdacdcacdaccabbabdcbccbbadcdcacbddddbdcadacdbcadbbcbdaabaadbbdaddbbccbdcdcbcdacbacaddbcbdbdddbaadacadaddddbccccaacbbabdaabddbadbbbbdbcccddaddaaadabdcabdabbacaddbacaababbddcacddccbabbbacbabcdcddbccddddaabbccadaabacaabdcbcbaacbdcbddadbccccbbcdaddddddabacdadbbbccbacddccdcaadaccdaabcbaabcdcdadcdbcdcbbcccdbdacdbcccbabcaabdabdbdcbaddccbcaadabdbbccccbcbdbbdaadaabcaaadddaddbbcaacbbbdacdccccadbbcaaadcbaddaabcadabacacdaddbcdbaccbadbbcacddcabaabccbddbbdbbbdcbbaccdadababddbadccccbababdbbccabbcdcdaabdadbddbccdccadcabcaddadabbadcaabcaababcbbadcdabdcdbdbbccbbdaaddbdcaadccdadddadadbadbddaaddadbabbbcccaacaaaddbccacbbadbaadaddbdddcbbaabdacdcdcaaaccdabddbbadbcccbdbdbcccccadacbaddddbabbaadcdcbdbbbdccdcabbcddacaacabdcbaaacacbcdabbcaddacbaccdbaacdbcbdabcdaababdabdbccadddaabbbdcccbdcbddccaabddddbbaddcabdbccbccabddddddbdadcdbdbaacbdaddcacbdcbbccacdbacaddccbbdccddcccaddccbdacdbdbadcacabcaadccbcbbcbccbadaacbddaddbdaaaaadcabaabbcbbcbbcabaccacbbabdabbdbcccaaccaddaabdabadcdaabcddbbdbadaaccadabdcadcdcacbcdbbccadbccddccdddbcdaaacdddcaabbadbbcbddcddcbacacdabcbdcbcbdbbadaaaaddcdbddcddcccdadccadcbbcacdcdbdbbaccadaccbdcbbaabddacbcbcdaabcbbddddcddacdbbbbabddaaabbadddddcaddabbbabbcabcbcbbacdccbadddabccaaacbccbdcacdbdbdacddcbcaddcdacdcbcacdacacdcdccbabddadddcdcdbdbadcbcbcdcbdadcccdccbdbcacdccddbdccbdabcbcbbcbbabadddcbcbbdaacbdadacbbcadacabbcdabbcabaaaccadcdacbccdcbbdbcaaadbacabdbcdadcdbdbcbdddccacdccaabacaaccdbaacacdadbcdbccbcabddbcadbacbdccbbcddbbcdaaaddabaaabcccbabacccbdbcbacbcdaddbbcbdbbabadbbbddccbbabcadabbaaabbbbccddadcbaddbbcababacabcbbdcaddbbbccbcaddbadbdbbaddbabccddbdbbabdacabcdbcbabbbcbadbcbddbdabacbdddaaabcbbaadbbbdbabdbbcadabbdcbbaabcbccbcccabdbcdbcacabacdbacacbdadbaabbddddababbadbdabcbcaaabbdaccaccdacdbcaaddddcbbcaddacdcdcabbbbbddcdabdddcddabadcdbcbaaacccaadbcccdacadbaaddabacdacbdbabaadbcaadbdadbaadadcdbbabdcadcabbcacbcbbcccbaababdddbbcbdadabbdcbcbdcdaaaddccadbdabddbbacbdcddabbdbabcbcdcadcccdaadbbbdcccddaaadcbddadcadcddbbadbbdccaccccdadacadbbdbabadcbcabbdabbdbadcdcdcbcdadddbcadbbbabcdccadcbcadcbcbcccdaaaacccabbccacdcbbadccbdbaaadcddcbcdbaccbcbcbadcaaaababcddabccaabaddcdaaaaccddddbddbbdddcaccbcaaccddcdccdcdadabbcdbdccbcaabbbccbdcbbcadddcdccbcadbacbdaddabadadcbaaacbdacbdbbbdddcddcdadbaccbacbcadcdbacdbddcacbddcdadbcbbcbbdbcbddcadbcdddabbbcacabbabcdabdadbcdabdbcdadbbacacadaddcbcdbcaaacbbaaabdbbccbcbbddabaabbbbdbadcabcbdbacadcbcaabddcccddcdcacccbcddabddbcbaaaddbbcdddbcdcaacabcaacbdadcaabddbddaccbaacadbbabbbdddadcbbccbadaadacacaacccdbaaacbdddbdccddddbcdcbddabaabcadabcabbbcddaabccbcbabacbcadaaabbbdabadcabacbcacdcbcbccdbbcacabadddcbbbbdadbbabbaaccbcadaddcabdcdcccdacbcbddacabcaabbdabbdcaddaadbbdbaaddadddddaacdbbbddcbabadccbabbaccbbccbcccdabbbdabbdcdbadacddabccbbdcbaccdcdbdadbdbcbaccbbaccdcbdadcacdadadadddadaabcbdcbabbaadaabddbbaddacaaddcccdcbacadcacadcbcacacbadbdadccaabdabdbcadacdcddbbcbccbacbddadabaddabbacbadacaacdcbabbbccacdbcdadcacbbabdcabdabdbaadcabdadbacdbdbdcdcabdbdaabacbbacbdbdbaaadccbcdcacccbaadabadccbaaaabaacdaabddcccbaaacdbbaacdacdcacbccbaadccbbadcccadaddcdbbbdcbbccdbdbcccccdabbcbaaaaababddcdabcbdbabdaccabaacdbbbbdcccadaaaabacbbbdbcaccdcdcabcccacabbadbbdbccbaacddadabcbdcdddacbbbcdaabacccbbdcdcaacacbccbbcdacdcacdddbbcacdacbbddadbdabbdaacddbcacdccacaaaaacbbdacdcbcacccbbccbcbadcccaacddacddddacdadddadbbbacabaaccdbbcaacbdadaacadbadabaddbdbbddcbcddcaaabbaddbdddccaddcbbddccdabddbddcacddbbbaaacaaabcccababcbddbdaabcbcddbcbdbabdaacdacbccbcbddbbbaacdaadbdccbdbdbabbbbcdbddcbbcddccaccaddccbdcccbcbccccdaabcbacbdcdbadacdccdbcbadbaacabcbbbbaccadabbdcdabbacddbadbbbddaddbbabdddcadddbaacbbcdbdddccabbaacbacabaddcadadbdaaacbaccacdbdacacbbbdbbbcbcdddadcabbcbdbadbdbbcddccaccdbabbabbbabbcdacbbddcbbcaadbabcdbbcdbdbdbacabcaadcdaaaabddbaddaccacccccddaadcbcbaaabbcddaddaaadccdbacbbacbdadbcabddadcadbdcbadbdbbddcaaaaddbacbacaabbbcabbddcbcddaabddaccbcbadadacddcdadcacddabbcbdcbddacadabcbaadabacdaccdccbbddccacaaaccddaddbcdbbcddcacbdbbccbbbabdbdcbcaaaacdbbcacabbbdcdcadccaacbbbcaccbcdbcccdbbbbdbbbbadbddaabcbbdcdacccacddaaaacbbbdbbdbadbaabbadacdccabadadddbdbddbdabacabbdddacadadcadabccabccbddbddcdabccddcabcadcaadadaddabbdbcaccaadcddabacdcddaacccaaadcdcaaabadcaaccdacaddabcccbbcadacbaccaacdacbbcdacbabdbabdacccbabaaaaaaabcbababddcbbdbababbcbbdbadbdacdcdadbccdbabaddaadaddddbbadbcacaccaabdadddbbbaacbbbbccbddacacbdaccbbddccdcdadcdaddaaddbccbddcdbcdbcadbadddccdcbbbcaabccacbdbbccdaddacbbabacaacdbadcaacdaadbdadcacbbbdddcacaacccabccccbccaaaabcdbbcdaadaabadadacadcaccaddbddbcbdcccbcabaacaaaddbbbdadacddcbbbdabbcaacaababacbdbddcabddadcdbbdbbabccadaabbabccccdacbcdabcbdddaaccdaacddcbadcaaacaacbcdbbaaaadbbbdddccbdbcbdbbbcbbbccaccccbdbbbaabdcccdabbdbdbcbcbcacabbbcacaaaabacbadbcddbbacacdddcbaaccabbabbaabaadcddbbbacccdccadabdcdcdddccddaaaddbabcbbdbaaccdaccbbadbcddaaccccdddcaaadbddcddbcaabaadccdccccdcbccbabcaaabdcdbbadacadbbbbdadaadbabacaabdbcbcbcdaaddabcbaaccaadacbccaadddcbcaddcaadccdcdcbccbbccccacaddcababddcbacdbcbaaaabdaabbcbbcbbbccbcadcddcccadcdadccbadbbaddcabcddadabbccdddccdabccbdabcbcdaabaadbabddaccbaacdbaaaaccacbcbaadbaabcbdcbaddbadcbaddddaabdccdacbbdbdcaadabccbbdadadaadccccadccacdaabdbbabdcccddbadbbaabaabcdcbcbabddbaaacccdbdbabccbcbdccdcdcccaacaccbaddddabdcbbbacdacacbbdacacbbbdcbbcbaabbabbcddcddabbcbbbaaacadaaaabcccdbbaccddacbcbadccdbabbdbcbcdbcdaacadaaabccbacdadcdddabcbabcacabbbaadcaabaadbbbbbdccdabcaabaddaabcdcbddaacbbcaaabacbbacbddcaaabbcabbaabbadacddbaddbbdbdcdccdcaadaddbddabaacbddbaccdcbcdabadbcdadcddcabdcbcbabcadcabcadaddacbabcbdbaaabcddcccbcdadabcabadddcbcacdcaabbbbaccbbbcbabcaccaddaacccdcacbddcbabbdadcacbbbdbcaadddbaaabdaaaacdcdbbddcaccdbccdbdddadbddbdbaacdbcadddadbbdabbcdbacccacbcddcdaabbccabcdabddadaabbacacdbcccdadacddddcaabccdbbbadaccdaaddcacdbaddcdcddcabbbcccbccadcbdcdabcddaadaddddaabddbbdbabddaddacdaaacabdaddcddbadcdccacabacccdacbbdababcacccdcbccabaabacddacddcacbaaccacadbacadccccdbbbbbdddcdbdbadbdacccaaabbddcacbaacaddcacdccdadababcbadcccbadbcbcdcabaaaacaadddddbcbcacabbadabababbabbccbddbaaccacbdccbbadaacbadaaacabbadccabdcabcdbaaacccbbabbdabaccbdbbcdbaabbdbbdcbacacdabaccbacdabbaaddaddccbddaaccaccdcadacdcbdadbdddacddabdbaddcbccddbcbcccaaaadcabadbbccbdcdaaccbddaddabadcabcabddcdaaadadaadadbddaadaaddbbbbbdbadbabdabcacadbccdbacacbddccabaacbbbcacbadbdbacdaddadbabaadbcbcddabbdcccaaaddaacbdccdabcadbbdbdacabadbdaccdacacdaaacddabccbdaccbdcabbddcddaacdcbbacbcbbcdbddbcdcabbddccccdbbdbdaacbabbbaacbccaccccdcccdabbbdccddaaadbdcabcdcdccdbaccaacdcbadacdcbccbcaacbddddccddacadaccacddaacbaabbcacccbbdcacdcbddaadccbadcdcbadbdcbddcbbdccbcddbbaddacacbdabcbdccdbdbdbcbacddcaabccaccacbbbbaddcababdcddcccabdbaabcaabcbccbbabaacccacbcddcdcdddaaacacbbacdcdbdbacaabdbcaccbaddcaaccbdcddcacbbdddcdcbddcddbdbbddbadbaaadbadaacbccaabdaabcbacdbacbcbcaddacbbbbbaacdbccabadbacacdcabdcaacbcddabdcbccddaaabadbcbdbdddcdabcdaacbdcddaaaaacdbcbcbbdbbacdaccaddbbccdcdbdadbbbccdacbccbbaccccdabdadcddddadabdcbdcccdcbcabcdaddbaaaaabdccccccdcbcddbddbcacbbddadbaadabdcbcdbdbabacbbcddcaccadbdaacddacdccbbbdbbcccadbaccdcbdaadcbcdaaddcbbddbaabccdccabaaabaadbdcbabccdddaacbdabcbbacdcababdcadbbddbdaabdcbbcaacaaaaaadabdabbdbcbdcdbdccadbddacdcdadbaaddbbaadcdcdaddcdcabdacbaadbdcdabadbccbaccbabbbccdbdbbddaaadaccaadbbddcccdaddbabddadcdccaaccacddaacbddacadbddcacbdadaacadcaddcdbaddbacaadabdbdddadbbdddcbdcccaaaccdcbcdbdacdcbbabdbbbbdccbdabdaddbadabdcdbcbbbccabdcbdcabbacadacddcbbccbbadcdbaabadcddabcabcaccbbbcbccabbbdbbabbcbbdccbaaccdbcbaaadbdcbcaabcbdaddccabdbcaddaddadddcccbacdbcdddccacacacbdbaacbadcacbdabbbdccabaabaaccadaabcdcdcbbbdcddacbbabdaaddbbcbaddccbcbababbdccdabacbcddcaddababddbabdcddadccdbbddacaacaaadcbbbdbacbdddbcbcbbbaadbbdcddddbbddddbaccadbdcbcccacbbabcdcabcbacddaabababbaadcbcbdaacbaacbcdccdaabaabddcccbaacddabaddcbddccbadaacbbcdbbbaddbcdbbcdcabdbcabbdacdddaddbdddbcdcbcbccbcdbabdbcbdbadcdccbdbcdbdaddbccccbaadcbbccdbaadbaabbcabdaacbbbbabdcaaddbaadcbdbbabaadadbdddbbdacdbddddbdbbbbadabbacabcabacaababdbaddaabacbadbdcacaaaaaddbdddccabcdbbcbabbaddcbcddbbbaacddbcaadbbadabbacbbbabcaadcbadcddadbbbbdaaabadcddbbcadabbcaabaccbbdcddadbdadbbacccbdbddacbdbbcbbdaaaacbbdcdccbcaadbdbcaacaacabdcdabdacabcdaaacbccdcdbdddbcabbabccbacbdddacadadbccdbaaaacdcbadbcbcabddadbdacdddcadacdbaacacccdaccaddddabaddcacdacdadacddaddbababdcdbbacaccddadcdabccaadbacaddccabdcbcccbdadbacaacaadbdabdacabddaadbbdcdacbccdaacabdaadacdadacddcacddcaddbdcdcccaadbabacdcdaadadccdaaabbaabdbaddbddbdbccaabdaadcdcbbdcaddddcbdccdbcbddabaabdaaddabccdabcccdcaadabdcbbdadcdaddadbbcdccdabccabbaccbacccdcbabcbccdbacaadacabdacdabadabccdcbbbaacdbcadacdbbaaacccccccdddcabaababccadbbbaabcbcdbabbddadaccbbcbacdcbbddcadcbdaccbbacbdabcbbddddbdcbadabddcbaaddbdbbadabdadcabddbdabadddddcadbaabdccabcdbcbdddacdabbbbddbbadbbcaddcbaaaaacddabcbdcadabcadccddbbaccbdbbcbddcaccccaddbaabaccadaadbbbbdaacdcaacbdbbabbacacdbcabdbbbcdbdabcdcccadadbbddcbaabbadcabbcddcccbcdcdbdccdbccdcbaadbaaabdaacccaababdbbcccbbbdcdadaaddabdadadbadcaacaadaddbaabaaddddadccbdbaacdbdabdbacdbcdddbcccddcbacccbbcccaacadabaadddbbcacdbbddddddbdacbcdcadcbbddbdcbcaacacccbddababccbbacabbaabcddcccabcddbcdcdbaabbbcdcbcaaddccacacaabadaabbdabacdccdadcaabcdddbbccaacaacaacbbacadcaddddbaaabbddabadaccbdbacbaabccbaacdcddcdbaacbbbbdddaddacccadbddccbbacbacbbcbadabdddcabbcbdbcadddcbbcdcaaacabddbcaaccbccdadbcbcacadbbbccdabadcbdbbddabbcbbaaccdaacbcadaacdbdaacccacadbbccbabbdcbbdbbababcacaabbccbddddcbdbbcdbbbaabdacbdbccdadbaacddbbbcabccddbbaddaccddcbdcbaadacabcdbbcddadccdaaaaabcbcdacbdcbcaacaadccbabcdddabdaabdbcbacdbacdbbddcacccbaaabddabcadadacbaccccbcaccccadcacbaacddabbabdddcaccabccddccaadcdbbdabbdbcaabcacadbbbddaabbaacaabcabbdacacdbdbacbcbdbacccdacabbdbbbddbbacabdddddaaabdadbcadaadcccdaacccdaaacdcdddbcadaabcacdaaccbcabcaabcbadcdabcccabcbbabcacdaabdcabbacbdddabbbbadcdcddcbccbacddbcddcbdbabcabdacbcabbbdddadacdbaccdbabacaaabbabddacdbacdabadbaacacbcccbdadabdaaabbcaccadacabadadadbbaddbbdbdaacacbacaabadaaadcccddaabacabaccdbbdabbbcccacaddadcccddadcbbdacbbdaaddbbacdbbbcbbbcbaddbaaadaaddadbcbddbaabadcddcddaacccdaadcdcbddabcabdbcdacddccaddcbdaacacabadaddacccaacbbccabacbdbaadcbcdddacabdcacaadbccdcaddbbbaaabdabdbacabcadddcbdbdabdcaccdcbccdcaabcacbddddddccaaacbcaabcccabacddbcdcdaabaacbbcaddbcddcccabbadcccaaadabaadbcbbddbddbbbbcabccadaacbbcbcbadabddbdacabcdcabcccbddccbacdaddbdaddacdbdbaacbbababaccabcbabbdbacacccbbdbadaddabbdbbabddcadadbbdaabcbaccacddcdddbbdcbbdcabadadddcabacbacbddcdcdbdaabdbdaddbbcaababbddadaaaccaadbbdaaacaacacaccadaacbdacbaacbdcbdabbccdbdacccccbccbcacccdabacbacacbaddaacdcccbdccddcdcacabdcbdbbcaccbacbabdbcccccacddddcbcdcbdbbdbcacabccdcdacbadacbacbbacbdccdaccdabcdbccadbabaaccbdbabbbadbbabaccbcaaaccaccccacdccabdcddbaacdcabcdcdcdbadacbcccddcbacbbcdaacbccccddcaaccbaaacbdcdddddbabacdbcdacccbabbdccbbaaaadbbabaadcacadddcdbcadabccadadccdbabadadbaacacadcddccdcbbccbddcacccbcbacdcccbcbddabcdbbacbccaabdbadcdccbcdddbabdccbcdbbacbbbabcbdcbcabacdadddcdadddaccaccdabddcbadcbcadbabdbdaccccbcdbbcadacadddbdcbbcabaaddaacdbdddddbdadbbcadadaabaadbbdddabcbdcadcadbbaccadddaadccaabbcdbddbacaabababcccaccddaccddbbbccddbaadbbbdcaccbdabcaaaadadbbbdcbbbdccaccbcdbaddadccdccadbccbdbbbddaddccacdaaccadcaabcaababdcabcaccdcabbadacaacbcbbdcdddbdcabcbabaccbacccadbcacbaacdcdbdaabdcdbadababacbacadcbcdbddbcadcdacdcddbaadaccdadddbabaddcdcdabbacddabacbddbbaccdbcadcbcdaacaddcbadbdbccbdbcbdcbadbcddccbacaabccbbcccbcdacccccdbacdbbabbccccddaaabbaaaccbcdbcacbcaddcaacddbbcbccdaaacdcccabcbbdadabcbcaccbcccbdabdcaacbbcdbaaabdccacbdcaddddbabacaccdbcddcdcadcccddddcadaccaddcbcbccdadacdbcdbbbcaabbcdbabddadbbcdcabbacdcabcbaaabdcacaccadadaaaddadcbcbbbacbaabcbcadbdadddaacddbdbbcacbacccbbcdccccaaaadcddaddcbaaccbcacabdcbcaaaacbbcdbcaaababdabbbcaadbcbddabaaabcbcdaaddcbcdccbaabdbbabdadbadcadbadabdbcccadabababaccadbdadcacdcdddabadcbcabcbaadcbdcbdbbaabbaccacabcdbdbbaddcbbbaadaddaadaadbdcbcbcdccccdaabdcbacdccbbabacdccabbddcacaddccabdaaacbdadabcbbbacbabcaabdddaddaaabdcaadbbdcdccacbbdaaadacbadbbaddbbbcbacddbbdbdbbddcccdacccadaccbbccacacadddaaaddccddbdcbdbdbbbbcbaadbdccdcddabbdbacaaddababdacdcccccbddabaabcbbadacaaddcadaaccbcdbdbcaddbbbbddccbcaadbaaacadadbdcdaaaadbdbddbdbcaabdbdcbdbcabcaccdaadaddaaabacbbbcadbaabadddbbacdbacdacdabcccdccbdbbaababdadcdcbdbbcbaaddabddacbadadcbddbcbbdcaaaabaabbdccadabaacdcbbbcddbbcbaadcdcabadcbbdaabdcccbdcadcdbcaacdaddddcacdcabdcdcadcdbbabdddcaaadddddaaabdbbacabadcabdccdbadbabbbdbbbdbacabbdccddbaabdabcaacdadaccbdbdadcadabdabcbaaaabadaabadbbdacdcccdbdbaaababccddbadcacccadcabdbbcbdabadbcbabaddcbabcbccadccbdbcbbddaccddbdbacccbcbdabaabccbadabbadaaaadcabdacabacbcdccdacabdddbabdcccbbabaabcddacbcbcdcabcacdabaabdaaabadcaacdbaaaaacbccbddddbaacccaccbabacdbcbbabdaaadccbbbdbcbcaaccadcbcdbbaacdacacdcbcccdbbbddaaacbaabdacabbbdaaaaadcdabbbbccbadbcdbcaaadcbbadacbcbcbcddbacdabbdcbbdcbacbcaaaccddabdddcbcadcabcbbdaaacdacdbccbaaabdadbabbdbbccdbbddccaacbdbaacbaaccbadaaacddadcabdacbdbacbabdabdbdaabbaccadcbbbcddddcdadaadbdccdaaaaaacdabcaccdddccbdabaaccbabccacaadbdddbdbbbcbcbddbbddcbabbabdadabdcdabdadbdcaadbdcbcadddbcabdbabaaddaacbacadbbacbcabcbdbaaadcadaccdaddbdabcacdbabacbcdddababdddaabaccaddcaaababcbbbdbcbcbcdcbabdbbaababdcabbcbacaaccccdcacadacbdcaacaabdbbdddaddabccbbdbacbadaabcddabacccdcccadcbbacadbcccbccadacadadbcbbccbbcccdbdddbcadbcbdcbbbcadaabdbdcadadcddbbbcbcadcdddcacadbadbaabdbaadcbccdaabacdcdccdabbccacdaaaababddabdadbabbdbcbaaddcdbdcbbcbcbaaaabcbabcccdbbccabbbdcdcadbbbdbdbaddadccaaabddacaddddaadcdbacadbccadcbccabdaaabbaabcdccccabbbabbbabddaaccaadbaababadbabbdcbacacbbbccabadccadabadacdaddcdaabdbbbbaadcaaaadcbcdddccccbacadbdcdaccbabbbdddbadbaddaccadadbbcdcadbabbaddcaccdcaadabddadaacbdaccabadcbbacaddaadabaaccdaacdacbcbadcbcdbbdacdcdbbabcbbdbbbbaadacdccacaaccddbbacadbaddadcbdcadabcdaabacbcdbdbbcadddddbbcdabcccbccabcdcbdbaccbcdcbdabadabbdaacbaadbaacccdcabbbbcadbccabadccddbaabdaaacdaaccccdbbdcbaaccabcdcadbdaccddccadcccdacbcacabcbdabddbbaabcdcdacbaabadaaacaaddbbacccadcddbbcccccadaabadbbddcddbdabcccbdadbbbbddccbcbcccbdabcddccdbdadbbbcddcabbdabadbbcaaddcaddabaaadbadabbbbdbbbdcddbbbaabbcabcbaaccbdaccdacdbacbbbabbddcbbbcbcdaaaddaacadbbdcbcdacdbbbdacbdbcbbabbadaccdcccbbadbcacdbabbdcbdbccadbdcccbbcbbbaacdadbdaddaaadbdbdbcdaadadbabadbddabcccdddcabbccbbbcbaaddddcddcaabacbddaadddcadbabbdddcbdccdabbadaddadabbbbadcdabbdcdadacbcabadaadacaddbddddbcbccdcccbbabbdcaaddbbadbaadccbabdaaadbcbbbbdbcdbaacdadddcddbaccdcddbacbabdbcdcabdadbbbddcddbddabbcadddccadbdccdbdabadcbadaadcacccacacdaccdbbbbbcbbccacbabbddbbbdddababcabcaaacbacbbaabbbddadaaacbcdbccbaabcacbdbacabbaacbacbbdaadddabcbddbabbacaacbccacbdabaaadacabddadbbaacaaacbabbbaadacddcbbdccabcaaadadaaabbdadacddaccbdbbcbccdcbdbcdacccdbcdddadabbddddcdaaccbdbdacadbcdcdbdbbdddaabddcddccbacdbababaaacaaccdabdabbcbbbbbadaaddbaabdcadaccbcbdaaaadadbddbbbccbdbbcbbdccbbcdcdbabdbbccbbbbbbacacdbbdacabccdbdbbbabdcbbcbbbbcbcbcadbdbaccdbcddadddabaacadccacccddacaacaaddddbbcbaadcdbbadbbdcacdabcaacddbddbabdbddcccccddaddccadddaabdacabbaaacdcabcdadbaaabccbcbddbccbccbabcbccbcacabdadbadaccabaabccacdcdcccaccdcddbadcdbccbaaccccccadaddcacddaccadbdabcbaaacaacdacddbbcaadadcadccddddbcdbaddaacadbbcdddcdadaddabaaaccdcbdcccddbbcdacabacbcbccbddadaaddbbcbbcacabcccdccbcbacbcdbacdadbbaabccbbadbdabbcddddaccbadbdbcaaacbdacdbdaabbddadcabaaaadddbccabcccdbcacaaddbbaaddbdccabcccbcbdcdbcdcdbccbccbaacddbdabadbbcdbadacbccbbaccbbcabcbbcbdababdcbaddccbadbcbabdbacdbbdadbdbaacbdbbcaacbbcdcbadcbcaaccadbabaabaccdbdbbdbccddddacadcbdcdbaaaaacbdbabbdabaddcdbcabdcacccacbacaaaccdbdccdacdccabcdbdcaacdccababdbcccadcdbbddbcdddabaadbcacaadcdccbaabadcbadbbdcdabaabacaadbcabcdadaaccddbcddacccdaddaaaaddaccdaabacacadacbadadcbcdccccdddbacccbccbddcabdcaaccacacbcbccbcbcbaaacddcdbcbabbadbbdbcbddcbabcdcbccdbacdacddbaabccabcdcdbbabdcdbdaccddcdacbbdbbccadbdddcbabadcbdbbacaddbbabccabcdaacdaadabcaccdcbaadcabbabdccbcabacddcbdbcddcbdbddcabcdbaddcbadabaccbcadbdbbdddabbccbdcbadabacbcadbadddbcaabaabcabccacacddbbbccdbbaddcdbccdabcacddacdbbbbabacbaacdbaabcacaaddbddcbadacddcaabdbccccdbbdadcacccbbaddcbbdcbacbaaadadbbaabbcdcaaddacbbccbddcbdcbcdaddabbddbdcdcdadcbaccdbacbacabcbbdbcbdcdddcdacbbbacdaccdcbccbcacdabadbddddabacbbdbcaccaacabccdaacddcdabcbbaaaaadacdaccbaddcdbaabccaaaccaaccaabdbbbaabddabdcbbcdabaddcccaadbcddadbbabcaabdbadabcbbaacdbadbbdbacaddbacbccbbaadcdabbcaadacbdcdaadbcdaacbdcdcdbabbdaaacbddccbdadbddaacdbbdbcbbaaadcaabcacdbaadacacdaddaccaaccbdcbdbcdcdabbaabadabbbacabbdcaccabbbdabcbbabcccbcbdacaccdbcbacaacabdbcddccbbddaabbacbbcabaaadcdabbcdbaacbadaccbcaadcaaccdadcbacdcdcacadbadbacbadacbcbbacbcacbcdbacdcbddbdbbaccadbacaaabcaccabcdacacdddbbcacacabcacdabcdacccacdadaacdadacbbababaacabccdadbbdcccbbdcddbcbdbdcabcddcbacdcaccbcabccacccaaaabcdbdabbcaadcabdaababaaacdabbbbbaccaadddbcccddaabaadaaaddbadbddcdcdbcdbdcbddcdcdbaaabadccddbaacddcbddaabbdbdcbcbacdcadbbdcbcbbcdccacabdddcdabadbbacabcbadbdabaababadcacbcdadbcccabacddbaabaaabbdccdcacdaadcbcaabaacbacaaaaddbadadbdbbdacbdcddadcbddaadccbdccbcddbcbcaaabbcdaabbbbacaacdbadddcccbaadbcbbddacbabcdaaccdbbaccbcaaaccbbcccbccabdbbbddbccbcbcccdabcacbbaccbdccdbacaacbcaacacdbadcadaadaccaabaddbaddcaaadacacbdbdbaccbbaccbbcdcdbdcdcccadbcccbcbabbacdcdccbaaccabbbdbddcaaaaddabdcbdababdcadbbdcbbcccddbcdddccdbcbaccbbdcdcacbacdadcbcaccbaadbacaacabbbcacdaddbcadbbadcabbcbabbbbbbcbbbbcadcdcbdabccdadbbbdccbccacbbaddabbdbaddabbccaaaaaccadadadacccbdadbbaacbacbdacddbdacbadabcbdbacbdaadddcbbdddbbbddbacbadacdaccbcccaaadddcbcbdcbadaabcdbbbadacbdbddadbbadcbabdddcbabadcbbddbbbcbcabcadadaaccdabaacabbabdbbdccdcaccaddcacbccbcdcadaddccdcbdcccbccdbccbcdcadadaaacdccdadbcbacaacbdaaacccacacdaccccbbbacdcabdbdcbddaddcaacbcbabbcddadcdabbddadcbaaacdbbcdacbbddacdaabdcdacbcbbabdacddbacbacdaaabcdcaabacacdcbbdccbcabcddaadabdaadbabbbbcbaaadbdacaadcccbacdcbaacdbaaabdbcdcdbccdbadacabdbdabbbccdbaaabccddaaaccdadccaddcdacbddaabadbcdacaddcbacdadbcdbacabaadcbccdbaddccbcdbbdbbbcbbdaabacbbbabacbaaaaccacdabbdbbadbbdddbacdbbaacacdbcdcbaccdaccacbddaaddcdbbbcaacbcddbcdaabbbcaabbadadccacbdacabbbddbdcdbbaccbdadaaccdabbdbcabccbbaaccddabaacbdbbbbdaacacacbbdbcdbcbccadadbcdccbbcbdaababadabbbdabbbbbddbcbbdcdcadcacbbdddbbaabcabdbacbccbaaaaadddadaccacdccdabbcccdbcacbacdcdbaabbcdbbcccbdcaddaccadaddbbaacdccaadccaadcccacbaddaabbababdcbaccdbbcabbbdcbdaadbadcacbbabdccbdcacacdcdabbdaacaddadbabbddbdaddcdddcbdadcbdcccdbdacccdaaccccbbddcabdcbdbbbabdacdbdbaccccacbcacdbabcdabbddbcdadabdabdbbdcbacdbdaabdabaadcabdadcaaaaacadbadbadcccbddbdadadcbadbcadbdacbcabcbbbddcddbdaddcdadcdacddcbabadddadcdcddaaabddcbbabbbbbadddcbdaddcbbcddbbddcbccadbcdcdbabadacbbcabcdcddacdadadacabcadacdbbcbbdcabacdaddacccbdacdcadaddbdadbcdbcdbddaacddcbddcdbdccadacdadabdbaadabbaddaadbacddccdabdcdbddaadbdbadacbaddacddccdbdaccbabaacbccbcddbbaaaddbbdaaadbabbabacaccbadbccdbcdabccccdbbbcdaabaccdcbaabaddbdccaadcaacddddcccbdbacddccbdcbccdcadbdcaccacbcddabadadddbdcabaaadbacccddbcbcbdcbcdccccdbbddcddcabbcdbdcbcdaadadbbbbbbbaddadbdcbdabcbbcdaabdcacccdcbdbdbbcbacabdcababaadcbcbdbcabaaaabdadbcdacdaccddcdaddddcdacdcaaddcdbddddccabdbabcaaadcdbdddbacddadaadbcbdcdcacccdaabcccdaabcbbbbbdcbaabaadcdadcdacbcacbccdcaddaabddbbcacaadaddcbdbcdcadccddcbdacbbbabbccadcccadacaacbadadbdbccbbbcbbdbacdcdbbdbdbadddaaacdaabcbccaabdbdccccddbcdcacddcdddcadcaccdbbccddcdccbdbabcadddcacccbaadbaaddcabdbddbbacadddcbbabdbddcdaacbdadcbdcccbdcdacdacbdcabdabacddadccbdabbbcacdcbdcadacbdacabbccdbabcabbcaaaaabbddaadabacabbadbddaccccccadcdcbcaaabaaababcdcbdbabbcbcacddcacdbcacdadbacbdaccabdccbaabdcccbabbcdbaabdbaccabbaaaacabbacdcacbadccbcbcaadaacbbbcdcdcabbbadaaccaaddddabddcddcdaaabcaabdbbcaddbcaababacacadddcdbbcbbbabbbbacdcadbddacabdbdddcddccbdabaabdbbdbdadbcbbcadaadaacccdbcacddaccbcbbbbcddcacbabdbabbccdcdcaacaaadcbcbbaadddbdadbcadabdcccddbbdabbbbccdbcdbbaabdbacbaabbcdaacbddaabdcccaaaccbdcadbcdadbbbcdbaabbddcccabddbcdcbdbdbcbbcdccccaacacbadbdcaabccabcabddbdccbcccdccbbdcaaaadaabbababcdadccdaababddcabcddcbddbbccabacdabbaaddadbaabdaccdacccbdacaadbacbcbadccadbbdcddcbacaaacaacdaddcacbbcbcbcdabdbcadcddcadbbabdbaabadcaaaadcbdcaaacbbcddbadccbbbbbacdbabcddcbdbacbadcaaccaddacbabbacabddcaccccdcaccddacadcadbabdbaadbcdcadcdbdbbcdaddbddacbddbcdddaabbbbcabaccabddacddbaaadddaacbbbbdccbcabbadbbcdbdbdbcabadaddbccdbccaaccbabdddcbdbbbbdabbddcdbdaacddbccccacaaacbaaaaadcabaadccbcabddadaaccbbcccbbacdaccacdcdbabaaaddadcabcdcbbdbabcaacaabccbcddabcccdbcdddddbbdddbbddddccadcbdccbbaccaaadcabddbcdbacccadccdcabcbccaabdcbadbcaccddcdccddbadaabadddddbadbbabbdadcbddbaacdcccbcbccbbbbadcdcaacbdbbbbabcdbddbabccdbdcdbbbdbccaaddaabcaabddcbacdbcabaaabcabbcbcddbbbdababdbcadcccaaaabadaadaccbadcdbbcabccbbbdcdbdbaccabaacccbdcbbbaaddaaabbdaccdcdcadcbdacbbabbdbcdbaadccaaabccbabaabddacaddccabdaddcbabdcdaccaaacbddacadbaccaacddbccbaaddacccbadcbdacdcdacdbdabdacdcabbddddbabcdbaabbccddaacbaddcdbdbccbdcdbcccbcbababdddadbcbabddbacbbddadbcadbadabdaadadbaababbaccaaabcdabbbcbccdcbcadddbbbcabdbcbaaabbcbbdadadcdcdbabdcbbbbbccaaaaaadacbdaadaadacdabcdbcddbaabdcadcdbbabadbabaccbdcdccccacdbcddcdacbbbbaabbddbaccbcabdbbcbdabdbddcacabdcadbacbadaddddbcbadcdbbbbacabadabcddcccbbbabadacaccbdbacddaaddbbadcabbccccdacdbcabadbdcadbdcdbcbbddcddcbacacbbdaacaccaaddcbabccbbabcbbaaadbabadcaccbbbdadddabccbcbddcabdcadaaaabbcbcdcdbdcacbbcdcccbbbdccaccacbcdccbbbcacddcbacdbddddabdbabacccdbddbdbcabcddccdaccbabdbbbcadcdadbabcdadcdaabadbcacaaddadccbcbadacbddabcababadaaaaadbcaadbddabaadaaaccddbdaabbaadacbddcccbddddbabaccdaaaadaaaccaaddaccbcdacaadcccabdaccbbcbaaabcdcdabbddacdaddddabdadcdbbdcbbbdadbcbbadcaadcaacdddbbcdaacbdcdaabbdbabaccaccdaccdbdadabdcacdcdbacbcddcadaacbcacacbaadcdccbcdbcbdcccbaaaaaccabaabadcdccdbcabdcdcadcadadcadcaacdddbaddbdbdcdbccbcdccbdccabaccabcbadcccdbbdddbcbbaccabdcccaaacadcbdadcdcadbcabbdaddabadbcdbdaabccddabdacaadaadacbcbdddabadccbbbabdbacddbcabcbdacbabbabcadcdbbddddbcbbadaccbaadcdabadccabdcbbbbaaccdbdbbacddbcbdabdcbbbdbbdadbbcbbbbbbcccadcccbbaaabbabbcbdacaaadcdcaaacbababacabddabacdadadbcdadacdacbababacabadaccacdcabaaaddaabcaabcbacddbdccbbbbaccbdbbbddabadbdbaccaddcbbdacdccadbacdbabcbdbbabbbdddcbacabbaadcdabbbacaadbcadcddabcdaccbaddabbcdaddcbbbaacbcdbdbcbbcdbcbdbabdbdaacadacdbdcacdcabcadcaaccdcbcaabbcadccddaaacdadadcdbaddbbddacdbddaaacdccdcdcbaadaacbdccdbbbaabbbcbdcccdbcacbcbdacdaadcbabbbbbbdaabddabdbadbcbdbcaabbbcbcbdcaaccaabdcabadddacacddccdcbbdbdbabcdcbbccdccbccdaddbbadbbcdcacaabcadbdaccbdbabadababdddccadddacbccbcbcdcbbadcccccbcdbcddcdaccadbdacaabdadbdacbabcaadaddadaccdadacbdbadbadacbdcbadcadadadcabbdbccbbccbadbbccdddccadccbcabdadcdcabccbccddcbdbadccabbcdaacbabccbcccdbbcbccadacdabbdcbbdbbbabcaadddcddaabcdbbbcaaacccbdccdcdadddbaadbcabdcbcddbcadacacdbadabbcabdacabcdcdababbbdacacbddddcbaadcadbdbdcbcbacdbcabbbdacdcdacbcdadcabacdbabcbcacdcdbbbabbadbdddcaabbaabcabcdacaddabbadababbabbbbcdbacdbbacccaabdbacdddcdcddcdaabccbddbbdddcddccbdbabddaadbbaabdbbccababbdddcccabacbadadddcacabbdbcccadbddbbabcacbbccdbdadbaccbcddcccccabaadaadbccadaccbcacdcdacdcbaaadbdbbacbccaaadcbbcadaacbbadabbbccddcbbdaacbababdcddbccbbddbdccbcbbdbaadcdadaddadabdbaaaadbddbcbbbabdbdbcdddababdacdbdbabddbabbbdbcccdacccddddaadacadaadbcaadbccadbcabddaccabdbcddadcabbbcbcbbbdccaaacadbdabcabbacababdbcbacbbcccbcddddbbbaaddadddbdcadacdbccdcbbbaacddbcbcaabcdabdbdbdbbbadaccccbaababacddddbdababcddaabddddabcddbdddcdddaacdbddaabadcbbabdaccbcabddcbdccaddcabcccabadaccbcdcbdddcdaccdbcadbbbadcadacdccbddbbacdcbdabdaddbccbabadbacdbccbdcaacbaccacaccdbdbcdccbacddaadcbacdbbbbadcdcaaabbbcccdbcaaddacbdccdaabadbddaadbbbaabcaaacaaadbbacbbbccbddbcdaddccaddbddcabdabaabbabaaabdcdbccddddbbbccaadacacdbaaacbbadccacbcabadcaddadcbddaccacbddccbadbbbcaacccdcbccbbbcaccdabcbddbbacadbabacbbaadadaabbcadcaaacbcbcadbbdcdbdccdbdbacabacacdbbcabdaadbaddacbabbbbabccdbcbadaddcacadbcaadadbddbbddbcbccbbddcacbccdcabccdbcdabcbccbdadbadccbbbaaacaccacdaadadabdcdcaacdacdcbabbbcddcdcacadcdacabdbabcbcccaadccbcabababbcdcbacbbdbaadcbcdccccbbbbabacdbbcbcabcbacbbdaadcdccccadbddcdddcbababbbccdccdbcdcbabcbbddadddbbdaabaccbcccabbaaddddbadcdbbacacacdbdcadccddbcbbbcaabdbacbcbaacdccbbaaabdabcaddadaaabcddadacdbdbabccaadbaabbbaccccbbbdacdaaadcdaaccadcbcbcccaaabbaabdbbdcbbcabcbadbdbcbcccbdcbbcadcdbccabbdaaccbbabbdbccccacdabadabaabdcdacaabdaadcbacdabbddababdabcdaddbccdacbdccabdcddadadcadbdbbcadcadcacbbdbdacabdcbdbcadabadbaddcdccdbaaccaacaadddbdacdddacbbaaaaacdccccadbaddabadcdbccdabdadbbbdbdbdbbbccdbbbccadcbcdacdcdadbaadacccadadddcbbbbbaaaddccdcdbabcacacbcccdadbadaaabddbabddcdbcacacbdcdadcbacbddbcbdabcaadbaadabccddccadbdbdacdbbcdbcddcadcdbdbacaddccabdbbdbbccdddddbcadcddcbddcbaaabbbbaacbbdacbbabacbcaadddbabddcacaadaaadabdbbdcdacdadbaaaccbbabcccbaddaaddcbdddabccdaddcccbbbcdaacddbbaabcaaacdcddaacbcbcacacaddacdcbccdadbbadbbabdbaacbbdcbbcacdccabcdcbabaabbbbbccdbdcddcdbadadcabcadddddbbdcbdaaacabaddddaacaadadbdcccbadbbbdcbaaaaaddabcaccccbadbddaadacabbacadabbdabaacddddadabbcdbdabbbddabbbdccdadcacbbbdaaabcddbddabbdbaccaaabbddcdbdcdcdcddbddbbabdacadbacbbcdcbbdbcbdabbcdbbadaabbadbbdbacadddbdadcbbbddbaccdcddbadbdccdadaabaccaaddacdcddcdbdaadabdddbdbddbbcbcbccabbcbccdcbaddaddaadaddcbcbbcbbaacccdbbcdbddcadabdbcaadccbbabacadabdbddabdbddbaabbcddacdaaacbcbcbadacdccacddcbbcaaabbbbbbdcbdddbbccaababcbbbbbcbdbcdaabaabdbdbcaaabaabbbbdaacbdbdadbacabdcccdcadabdaadcbcbccddbcdcdbbddbaacbbdbdcccbcadadddbcacacabcbccbbdbbbcbbbbbdadababcbadbdcdcbdcaacbacbadcddadcdcbaaaabdadbacacdcbbdbdddacaaadadccbbdcacbccbcaccbaccbabdadaacddabaabadccaadbbabbbdbdcaacadadbdbaddddaacaccbcbbcabbaaccabbdcbccaadddaddbcaababaacbabcadcababcbaaccabbdaaccaaaddcdbadbcbccccbbccaabcdabcaddbcdabdbacaccbdcbacdcdbcddacddacbddacacaadccdacbdbddbbcbdcabbaddaabcdaddbadcbddcccbdccdacddaabbaccdbcbaadddcdcddacbcbabddcdcbbccbadabdabdbaaaadbacbdbbaaaacbbcbdaaaccddccbcddaadadbadaddccbdbbaacdbacbadcaacadcabdbdbcdbbaacacacbdbbaaaacccbdaccbcabbbbbadacbcbcdcbcccdccbcdabbccdbdacaabdbadcccdccdbaadcadabdccaddbdbcabddacbacacdbcdbadabdabbacbbdcccadadcdbccabdcdccbdbaaccdbddbbcbbbddcdccbbcaddcaacbbdcadccbbbddcdcadabdabccbddbbdcdabadcbbdadbdcadcaadbabccbbccacbccdcdadcdbdbbbdbddbcbdcbaacaadadacabacdcaacaaabbacaddadbdbbdbcbbdbbadbbbbaacabbcabadaadcacbbaababbcbaadadcadbcddbaccdbacbdcddddbdcddccadabbcdbcddbcabbdcddddcaccbdadaacdacbccbdcdcbdcccccddbaadddcbdcbcdcdacccbbdcccddbabbbcbccdbdbdccaccbbdccdacacbddcddddbccbdbcddadadadabdccccbbbdbcddaaabbdbcccddadbaddcadbbabbbccbaacbaacbbbacbaddabaadbdbbcdadaddbdabddcadcbbbdcbacadabdddabbcdadbddacbdcdabaccaabdbbccbdaaacadbaabdabcbdaacbbaccdcdcbabacbabccbccbacabbaaabdadadddddcdddadcdaaaaddacdcbddbdaabdbdbbdbdcabcdcacbcaddddcbccdbdabccccdaddcbaccccbdbddbbaaccadcbbaccbaadcacbcccddcbabdbcbddcbcdadbddcbcbadadcbabcdabadabcabbdbadcccdcabadbdadcbacabcbdbabdaccbcadaccdbdbddaccbcbcbdadbaadcbbadbdaaccbabaadcddcaaabccbdbcbdcaabcbabdadbdcbaacddbabbdacccbabaccdaccbadcdabbcdbbcdcbaadccbdddcacbadcaccdcadaacbdbcdbbacddccacdbccdbadccccdcbaaaacbcabcdbdccdbcabcdbaddacacadbbcabdcdbbaadbcbdacbbdcdaccabcadcbbcbcccaccdccbddcdcbabbacaccbabaadabbcdccacccbbbcdbcccaccabaabbadaddcaaddacadabbbccabaabbdaddcdbbddcbaaadbdcdddaadaabaacdccabcaabacbaaaadbaddddaacadbaabdadbbcaddbbcdbbbadcbdacddaadcabaccabbaadddcabcbddaaaaaaaabadbadadadbbcdbdbbaaacaabddbacddccbbaacdcaababbadbacbddbcadcaabdaccabbbccbbbadcdcacbacdacccbcdacddcdabacbdbccabbdddbacbaabdcdacccccbbddaccaabdbbbbbaccbcabcaaccadabccddcddcbdccbbaaabccbdcdccacababccdcbadadacacdcdcdaababadaababcbcccacabbddddbcccdbcddbcbadcaaabcbdbbaaddccdbdccdabbbcdcbbbbdaddaccabacbbbbcaabbbabcaacdcdbdadbbdcaabdddaccacaddbbcdaacadabdaabaacabacaccdcccabdcbacdcbacacbcabcddabddbdaabadbacdbddcddbbdbdabbbacbdbcbbdcdabbcaddcdbcccbbadcbdcdacbdcddabccbcbcdcdbbbddcabddcaabdbaddbbbadcaddccabbacbabdbcaabbcddcadddbdcbcdcbbaccccdadcacbccccacabdcbcadcbccabaddadbcacdbdabaabaccadabcbaadabdcaaddbbbbdabcccadacbbdacccdbcbacddbdbcdcddbadddddddabcdaabddbbcdddaddaddbadccaabbcabaccddcdbabcdadaddaaadccdddcbdbabbbdbdaadbbacbcddcccacdbaaadcaccacdbdddcabcbabcbbaaaccbbbdbcbdddddddbabcbcbaadddbdaaabaddaadbbdcccccddbbdbcdccbddbcbccdcadbadabdcdaaccbadcacdcbadcdacadaabdccdcdbccbabbaaabadcdabbbbbbdbdbbbcaaababcddcddbdbddbdacadaddabdcbcbbddcbaabdcddabcbcbcbadbdbaaacbadbdcdccdbaabbcabdccababdbaabbaddbadcadcbdacaddbcdbbacabadccaacdcbcbbbbcaabccdbcaccdbadbdabbbdababbcaabadcddbbadcdbdddbabdbcbcbbdbddbccdbabaacbbababccbabbccdbdbabadaaddaacbaadbcddbddacdacadadccaccabbccdcbdacababcbbcaaaacadddcaadbaaadddbccbddabbabadbddabbddcaddcbcccadddadabdabccaaacdddbcaabcacbbaaaccccbbddcddbddaaddbdbaababddbdccddcdacbaaccdbbbaacccdbcbaaccabbbaaddbaaccccbbcbbbbacdacdadcaccdacaddddcccacdbdbdcdcbdacacbddcdcbadbdaaddbacccdcadcbabbabadbcabdabcdbdccbdacaacadbcdcbacddaadcbccdccaadddaccbdbddbcdbabbbcaabcbbcbcdcbbddadaccbdccbabcccbbcbababddbbddaddabccddddbccaddbdbbcddccbdbdddcabbdbcbbaccabcaabadcdadcbbccacbcabcadbcdadbdbdadabdbaadabcabbddcbaddccbccbbacdccbaadcdabdbbbccdadcadadbaccccbcdacbdccbadbacdabcdbdddbcddbabbcadbbbaacbdbdcacddacabadcbbcdaacabbbccdcdccbdbaabadccdabaaadcbbdadbabbdcaacbcdcaacdcbdacaadacdacabcdacdaccbdcddcdcddcdbabadaadbddadbdadcddcadbdaabcadabcbabbaaccadaabbcabbadcaabbcacdaccabbccbaddbcbcbdadccabaccbacaabcdcccdbdaddcadcbdbcaaadccbcababdcdddccaccbaacddbccddccddabddccabdcbbbacddbcbbccacbbabdcdcbacccbbdabccbcadaccccdbdddabaddaadcadcdbdbdbbadcabbcbdbacaadbddcccbcaacbdaddadcdddcbcbadbbddddbaadcbaabcaaaddaacadbbcbcadbaddcbcbadabddcbbcbccadadaaabdcadbadbabbdbdadaacbadadbdbdadcaccdadabddaddacabbcbbbcbbdcdcdacadbcdadadcccadbbadbdabbbddabccdaccacddbddaabbaaabbcbbcdcccbbacbbbaabaaadacababcadaddadccccbbbccaddacacdcbaccdbacaacadaacbbaddbbcdbcdacdaaabbddccbabaabddabaccbbbcdbacbbbadbdbdacddabddcbacbbaddacbadbdaaddacdcaadacabcadbcdabaadcabaabcccbcdbcbbdcdbcbbcccdbdbcababdbabcbbcdcacbccdcdcdadddaacabbbbdadbdacaddbbbcbbddbadcaccbccbdbbdbcabdaabdadbbdcaadacabaadbbabcadacacbdccbbcccaabbcadaddbacbbcabbbcdcadabddcbbccccbcadccaccdabddcccaacabcbadcbbbadbdadcddababadbaaddabacbacdcbdadcbcdcabdaaabbbdaddbcbdddbadbaaacdbaacbccccacdbdbddacbdbaaccacdaadbcadbadccabbababaabaddaadddbaddccabcbdcadcdcdadccbccaacbcdcaddacdccbaaaadaabaaaacbbbabdbaaddbdaadcbaccacaaaddbcdddbacdacaadccbadbdadcbdccbbcddaccaccbbdddbbadcbbacaddbdcaadccdddccdbcaccdacccadcabadcacddabbbdddbbacbbbabacbdcdcdbdbabcbbdaacacbddcbccdccddabdabbbabdcbcdacaabbcbacccaacadbbdbddbbdadddadabcdccbbdcbbacddaacdbcbcaddabaccaabacacdcaaacabddaccbbcdcbdbcaabaadbacbabacbcccabbddbcacabcddcacabdadbbcbbaadbccdcadbcaddaaabdaacacdcadbdddbcaccabdcddcadadadbaabbdcdcabcdddaaccddadddbbaaaacbdcbbcdbacadddbadabcdcbdddbadabdbdacdcccdadadbbbcbccbbcacdadcabdbbbaadbabbdccdbdabbaaddbbddbcccdbaaccbbccccbbadaccdabddabcdddabdccddbbbaadcddbacdcadabdaabbccabdadcadcbcaccbbdcdddddcdadbbbcbddacbaaaadbcacccbcabbabbaaccbddcbadbbdacbcaacccdbddabbabaaccbbabacccacbcccadaddddcbabcbabccbcdabcbadbbaaadbcbabcbaddaadcacdbaabdbcbcacccdcaddbcccddbddbaaddcbbdcacccdddbbccaddaabcdbaacabccaccdcadbcdbbcababcabadcaabadbbabacabdacdcddbbadacbdbbbdbaacbdcccbdaacacbccabacccabbaacccadbabadacbdaabdcbababaabdcababbdbbcaddaddadabbddddcdadddcdcadcddcdcabaddbabbbdababacadabdbbbbddaccbcabcccbbbdbbaddcbdbddcabadbccbddaddcdddbdcdbdccdacbbccbcacbcabadaacadcccccaabdcdbdcbabccdabdddbacaabdbdaaabcabbddabbbaacbddcbddcbadcddbcaaaddcccbcbcdbdbaacdbbabaadddcddbbadaddbbdacadbddabaacdddbbccbcabcaabcaddaccdcbdabaadabcbddabcbbcbcabdbacacacbddaaaaadadccadacacdaacdbccccdddaadacabbcbbdbdabcdbaabcdbdbbcaabaaaddbbabacbbccaacaaccbccacaccdbdddcacbddbdcdbbababddcadadbcaaaaaacabcacbcaccddcbadacbdaaadbdccadaccddacdaccbdaccbacbbcbcbdbacacabaccddbaddaccabbcbcbddbcdaddacbbacdcadacccbcadbdaabddbbdbbdabccabcddaadddcdaaabddabbacabdaabbddaddcbaaabbaaadbabadacdccbcadbdbdabbcbbcbddcdadababcbcccbddacccbddbaccdadadadaaaacdddbabacaddcbabaadcaacbbadcbadaacdbcdacdabbdcdbbadadddcddcbddbabdbdbabdbbbadaccbaacaabbcabccccaccddbadadbbdcbcacdbbacdacaacbccddacbaabddcbaccbcaabbcbbabbadaccdccdcddcdccaadabbabcbaadddaddaacaaadcadbaaccddabbcbddbdcbadcabadcddcdaabbcdacdcacbadcabbadcbbaacbbdcccaacbadbcdddacbcadbbacdaccdadccbdbdbdbcdcbcbabdbdbbaaacaaccbaadabcadabbddcadbacbbdabbcccbadcaccabbbbcddbdbbaddddbaabbccddbcaaabddbcadcddbdbcdbaddcdbdcbdaddcbbbdabdbcbbcacaadadbbbcacccbacdaabadcccdacdbbadddbcdbbcaaacbbbdbabbdbdacaadbabdabdcacbadadbcdaabcddbccabcbbccadccddaccdbbbccdccacbabdbbbabcbdcbaaacadbccacabacdddbdaadccacadcdcdccccaacdcddacbadcaccdbcdcbccddbdbaacadcadbcabadaaacacaccaaacbdbbddadacdbadbbbcbdbdaacacbbbcadacaccdddbbcbccabdbbdaccccdcccbadbcabaaaacddccacccbadabcdcbcbcbadcbdbacccdccadadacbdcccbdcdcbbbdccdbcccacbadbbcacdcdadabccbcaaaacbdaaaadabdbabbacabdddaabbdddbbbbdadcbbcdaccdababbdadcddaabdbbacdbdcadaadadbaabbccbbaadcddcbcddbccbbacadcbdcbbbdbbbcdddbcaaabcdadaaabdbdabbbcccaaabaacdcacbbccabccdccaddaaccbaaddcbcbcbdbbccadaabaacddadaccccdcadbaadbddaacabacadbabddadbadbbbaabdddabddcbddccbdddbdaddaccadcabbdabaddbacbdbccaadadbcabbcdcdccddbcabacacaabadbabbcaddabdababdbbdcaacbdbbaacdbaccabbdabdbacacaabcbbdcacacaddaacbbddddcddbdbbcbcacddadaabdaaccadbdabcdbabbddaacccbbdbacbbdcdadaaaaddaacaacdabadbcbccacbbcdadaddadcbbddccdccadbbbbbaaccdbbacdbcaddddcdbbcddaabbccbdccadbadbbabcadcadbddbdbcabdddcdbaaddbcbccaaadcabacabdbabddbdcbabbbacdbbbdcddcdcbdcbddcccbbabbbbcaccdcdcadaabdaccdaccbdaddbabdaacddadcdcdcbbdadbbaadbbbccbdaccbbcbadcbbabcdaabbdcaacbdcdcbbdcdcadbadacbdddccdcabccdcdbdcadbaaddbbabcdddbbacdcabccdcaadbadcabdaccbcbbcaacdbccababaddabdcddcbabbacdcddcababaabbbaccbaddcabbacacdbbbaadbcddbaaaccabaaabcdbbcdcdddaadbaacbacaadcdacbacdbaadcbdaadabbcadcdcbccbdbcabadccddbddbbbcbcbcbdbcddaccdbcdccbcbcadadbccbdabadaaadcdcacbbcccabbaabbbcccdccbbddcbdabbcbddbcadcbdccaaaaadddabdadaccadbaadaadcbcdcdbbaacdabbaddbbaacbdbdbcaccbbcdaccccbccdbdadcadccbccaacdbcaaddcacddcabcbbbdbcbbcccbbdadcaabdcdadaccdcacabdabdacaaaabdaadaabccbbabaabbdadddddcddbbbbcbaabcacaabadabdbdbcabccbdcadcbbdbaacdababaacadabdacadacdcbadcbcbbabadabacbdbadcabbcdbcbbcaccbdcddccbbdcdcbbdbbdddbacdcbcddcbbcccbababcadacbccdbcbbcddacdbbbcbccccbbdddcdcbdddbcdccdacdddaacbccdcadcccbacdaadaadcdabccabbbccbbcbccadcdddadbabadacbacbaadadcdcaababacbabbcbadddadcbdbbbaccdacaabdaadbacbcacdbabdbacbddcacdcddacddcaabdbcbdbbadaabdcbacdadccabcccccdaacbcaddddadbdbaabdaabbbadbbbbcbcaabcbdccadabddbbddccaddacdccddadbdadcdbdcadbdcdbcbccbadcbdcbcdcdcdbdbcaddbabbacddddaaaadcdadcaddddddaddacacbabbcaccdbbbbddadabbabdbdcacbcdacccbbaabdcbaaadcccababbaadcaabccaddbaacdbccbcacadcaaacdaccaccacddcdadcddacdabcaabcdbdbbaccbaacabccdcdcbcbadcdacbbaaacbbdbcacabacddaacaaaaccdbdccddbaacabdacccaccadaaabcaddacadcadcacabcabbabaadabdacbabacccadcbcaabcacadbcbbcdadadaddadbbcccaaabdcaaadcadbacabadadcbaddddababdaaabddccaddadccbbbccdcddaccddabbdcdcdcbabacabdbabadcdbbbcdccdcccdabbdcdbcccaaacacccacbdbbbabbadccdcccaacadbcbababacbcaaaacbbcbdddddcccdccbabaddabcdaadadddadaadadababcbbdcbcadccdcadcddbbcabbaacdacaadbaaddabcadacacccadcddcbcddcacccbddbccdbcbdadacdbcdababaabdbbcaddcbcabaddccbbcccbdbcbaccbccbbcabdcbdbabaaababcaaacdcaadacaabdabbbaadababaabcdaccbcbbdaadbdcddcbccbbcdcacbabccdabdabacaaccbcaccdddddcacbbaccadbacbabbdaaadddbdcdadabacdcbcbaabdccdabcccdbacbdacbaccbaabacdddcbccdadccddcbcdbcddaaddabdbbbbaaadcbdbbdbbdbdcbadcbadcdabcbcccddcdbcbadbbbbbbcabccbdabddaadabccacacbbdbdbbdacdbcddccaacbbcabcdccddbbddddbdadbaddcbdbdcccbdcbcacdaddabddaabbbababbacbbdbdbabacdaaadadbaacbdcbcdbdadcbbabcaaacbbbdcbdabcaacccbccddaddabbddaabccdbdaacdbbcdaddcbbcddcdadbaddcbcadbdbcbbbbcbdaccddbdbadbbccdaabdbdbbbbaadbcddddcacbbcbdaacdbccaddabcabdacccbcadadbbccbbdcbddadaccacbdcdacaddadcdccddcbccacabdddddbddadaadbbcbbdccbbabddcaabbdacdcddbabacbbcddccacadbaacbdbcbcdcbabcdaababaacdbadcdaadddccccbbaabbccdccddbccbbdcabbaadbcbdbbacbaccccabcbbacccddbcbcbdadacbdacbdaadcdbdbbdbbdddbbadcadbbbcdcccdccccddaaabbaaaccadaadbdcddaddaadccbcbabaaabaccdacabcadbbaaacdcdbdcadbdbcddcaaabdcdcabccbcbbcabbcdbacccbdaaabcbcaabccbabcabddcdbabadddbbacccddccacabdabcbcddadbaadcbaabacabcccbdacabbddddcdddadddbaddccbbacbbaddacababbbdaadacbdbacbbbbbadccaadbacacbbccabbaababdccadddcacabbcbddbabacbaacbdbbcddbddcbccbadabdcbbcacbbcaacddbaadbdbdacaccccacbcabdacddabccbcabcdccdaacabcccabaabdccddbaaaaaabacadbdbccbdccddcabccbbccbacbdcbdaaabdbdbdaadcaabcdaababdaaaaaccaabcbabdbcadbcbcccdaadbaabdcbddaaaaadcaccacdadcdaacbcccdcabccbbcdbcbbbcbdcaabacdacaadcaaadcaddbbaabacddbacdbcbbbacdbdacdadccadabcbbcbccbcccddabbbabbacaabcdcccabccaddaaaadccbcbabadbaadbbbacddccbdcaccdacbbcddbccbbaadcdbaccbacaaaabbbabdbbbcddacddbbadabdacadbbabbbaddbbdbbbacbcabdcbabacdaccaaaccddbcbdbabbbaabacadbdcbadbbabbaddcbaaccdbabaacbbbaaacacccabdddbcaccccdddcbccdcddaacbadcadadadcccdaacbcaadadcccbbabaabdaaabbcbabccadbbadabbcbcccbbadbadcaddcacdcabbcbaaaadbcdcccabdcacbbbbabccababbbcacbadccdcabbcdbabbccaaccbcadbaddccdaadbccbdbbddcccdccacdcbdadddadadbdacdbadacbacaabcadaadacaabaacdabddcbbacabdcbacadbacadabbacddcaaddaadadacabbccccdcbccccaadcacdddccccbacaacdcdcbdcabbaaacadbcadcdaaacddbaccaabbcaadbacaaccccbbcaabbaaabddddbcaadabccaacaacacaaddbdbacccbdbcadabccbbdcabcadbababbadcbcdabdbacbabcdddabddaadddbcdcbbcdbbcccccbbdcbdbdcaabcbaaccccabbdaadabcbddacaaddbdcccccbaccdcdddcbcdbdabbdccbacbdbccddddabdbacbcdcdcacbcbaaacadbabdaadaacbcbdcabdbaacccbaabaaadbcdcabadacdcacbaacbdcadbbbbcdcaabaabccabadcaadcbabcacccacabbcdbccdcdcbccdcbbaaaabcddacacbaaddcdcaacbbbcacadadbacabdaaabbddbababcaacdaaadacbaacdcaccbacbcababddcadcddddbbacdacabdabdccbdccaacabcdaadbdabcdaaaccbabddcbaacdbadbcadaaababdadadbdbabbbdbcbbbdcbabbbbdadccbcdbccaddbacbddcbacdccaabadbaaacccaccadabbcdcaccbcddabcccaabbacdddbbcbabdaddddacacabddcccbdabccacaadacbaabcdbaddcacdcbddabdbbbadaacaddcdaacbaccadabbacdcbdaacadcbadddbdbadcbadddbdccadcacbaabdddaaaadcbacddadadccdcdabdabddcbbcbbccadbccccbcbcdcddacacbbcbccbcbcaadbdddccbabbcddabbdccbcaadddcdabdabbcabacbbcaadddccdbacbddaaddcadbbdabadaaaacddcbbcaadaaddddbabbdbbcabcdaadbaabbbbabddbdabbccadddadbaadbaaccadbdcaccacccbbaaadcabcddcbcbadbacbdbabccabbdcdbccdcbbadaddbbadaaddcabddccdabcdbadadadabcbabbcdabdbddbdcdaabbdbdcbdbccddacbbadadcbacccbcbdbcbbdabacdccaabdaccdcabccacddcbcccdbacaddabbacabbaaadaacaadcbcbbdddadaddbcaadaaddcdacccbdaccccddbcddccbabbdaaaaddddbcacdadcbacdbddadcdbbdbdddabbdacabacbcbaaccddaddcbcddcbddabddbcacdaccadbbbbabbaacadbcbdabbdbddbbcbacaacdaabdbdcdbdadddaaababcdaababdaabdaaabdaccdcddaabaababaacdadbccabbbdadacacddacadbdddbdabdcbbcaacacbbbbbacddddddbdcbcbabaddcbbacaacabcdddcaaadaaabbbdbaadabcdadadbaacaacdcbadcacacabbccdcdbbaadaaccaddcbabccadcadbccdaacbddddcacdabddaaababcbcaaccbadacbadbdbddbbaaacabadddcdaddbdcabbbbcdaacddbcdadccacacaaabbabdcdbddadccbcdacaddcbaaadcdabcdaacbdabbbcbbbaadcbbaacdaccddddbaacccdcdbcaadcadbacbdabbaacdcdcadadadadcbabcbaccbaabadcaabdacbbdbbacbbccccbddbccbcbcddbbdcdcadaabbbaccadbcbabcdbaaaaabddaadddabdbcacabaaccbdbbbacdacdbdccadcdbdbdbddcbbdadccaddacabbcbbabdcadbaadbdaaaababadbcbcadbcdbbcddbaacccabbcbbaadbdbddaacddddddccabadccdbddacbbcdaacdbbabbabcbccbacdcaabacadadadacacbbdcdadccaacbccbdacaaaacdacbadcbdcccccddcccbbbbbadabdcabdbdcadddacbbcddaabbdadaabddbdbddbbcabcacacbaddbcbbbacdabcdcadabddccdacddaaddabdcabbaadddbdddcdaabaabbddaaaaddbcabaddadbcbbccaabbacdadcbbcaacbaacdadbaaadcdbddcabdbadaaabbadabdabcbdbbaadaadaddaaaabdbabbbaadbcdacdbcaacbbdcddccdddccbcacccadbadccacbccdacddcadaccaadbbacddcbbddbcbbababadbddbabcaabdbbbddaccccaddbccbcbabaddccbdcbbcabdcabdcadccdacdbcabddcdddadabcadcdcbaddbbbbcdbccdabaacaccabccccaadbbddbdbbbccbababaccdbcbabcabaadbbbcbccadccaddaccbdadbdbaabacacbdcdcaacddbaddccddbbddaabbbabbcccadacbaddaacabdaacbaccbbdbbbcbcbdacabcbadcbabbbcccacacbccbdbcaaabdddadbdbdcdcddbacaabaadddcbadcabdcbcaaddcdacaabddabadbbbaccacbacadacbaddcababddacccbcbacdcaabdbcdbccadbcbaabdaacbdcaccbbcacadccbbadbcaacccdbacbdddadadcbdbbabaccdaadcccdbcdcbdbbbdcbdbbccbaadcbdacabccabcbbdbdbddbcdbcbddccaaaddcacdccbdacacaacbabaaabcbccdaccccdcdccabbabacdcbccdbdacddcdccaddbcadbcbcdbddaacadaaadacdabbaadddcddabbcdbaacbcbaacbddcbcbcadaddbaabbbdabdcccacbcbadabddbabbcababdcacdbdcaaabddcbdcaaaccdacabcdddcbbbcbccacbabdccbdabccbcacdcdacdbccacabacdcbbcddbabdcabdabdacaadaabddcadaaccbcbbdacbabccbcdbbbabcacbcacaadacdbacbbabdbddabaaabaadaddaabbdacccbdbacddbbcdccddcaccbbacddbccaacaccccacdadaaabacddbbcaaacdbddbcdcaccaddbccadcccacdcdcbdcdbdadcbcccabcbbdccaacdcbbccabbcbdcbbbbcabaadbcccbcabdccacccaddacccbbaacaccbbddbccbdcdcdcabbcdcdccbcdbabaaabaccbccabdcdbcbadcddadadaddcacbbcacabbabdccccdddcadbdcbaccaaaccabdcdbadccdbdcbcddccdddbcaaddddbdddcacbdbcbbdaabcdbbdcdaacccacacacacabaabcdcccaccccbdacbaacacbbddccdacbacbacaabccabdacabbcbbacbdcbddcbcddddbbaadbabdbdcbcabcdaccbbdacbcabdcbccabbbcaacabdcbdaccdcacbacccbcdcdbddbabbcdaadaaadddaccbbdbdbdadbbdcbadcabaadbddadbbdabbaadddbadcbadcbbaccbcddaaadcdaacacacabbbdaddbbcbbcaaddcdbbbcdcdbabcddcaaacadcbadcbdaadaaaccdbdbcdadaddcaddadadcddaadccaaddcdbcccddabbccdbddbbcdbbbabbcbddccbcbbcccabadcdbdcdadabdcaccdbdcbcbaddbaadbaadadaaaaaddddbcbdacccabacddbcdaccbdbcdaccbbbdcbdbabbaaccdaaccdabbbbcbdaccdbacbcaaacadccbccaabcbbddccbbcaadcdabcbcccdbbddbcbdbaababaacdcdacababadccbabbddbdbcdbdaabdbccbbdccddcacaacadadcaadccababddddccdbbdcbbbdbababddccdcbacbdbcbddababbbdddcababbdcbdaccbdccdbdbcccbabdaabbcaabbcbdacbacadbbcdcdcdbabaaabaaacdbbcbcadbccdbcbadddbccdddabbbbacccacaabddbacdaadbbbbdaccabcacdcbcbdbbcbadbbbcdbbbadcaadbddbbbccccbabcccbbcbbbdaabacaababbadcabdcdddcaacdadccdcbcdcababcadbcdadcbaccbccbcdbabaddbcacadbcdbcdcacaabbaaaabddaaacbbbdcacaccaccdbcabbbcdccbbcccdcadcccacacbddadddbcdacdadddddbbcdbdaddaadccbbdbaabbbbdbccbacbddcababdddcbbdaaacbaccbddabcdbbdcdcabbccddabbbdcabbbbcdcbbbbdbbbdbacbacddacdaabbacaabdbcbaacadaacddccabdabdacadddabbdbacacacdabdaacddbaacaacddaacbdbbacbcaccbadbbbacaccabcaddcaaaaddccbabdcdcbdccdcabacaabbcaaaacdbddbadabdbdddcbbbcddbacbaacbdbdcabddbdbcaacaadacbaaccdaabdbaaadcbdccdacaccddabcbbcddbcdbcacabdcabacababdcadcbbddbaabcabccdaacbcdddbcadacdcccbbbacdcccccdadcbbcbacacccbddcbcdcbacdcabbacdabcacddacdacdbbccbdaddddaccbcdbcdbaabbaacadbbabcbbcdacdbacbcadacbbbacdccbdaccadabdddabacdbbcbacddabdaadacccbdccbbadcdbaabbbdadbccbbcabbadabdbabbddddacdacbadbaaddadaadaabdddccbbacadcacbaccdbaabbaddcaacdaadbcdbabcbddbdbcddadaaabbbcadaadcdbbadccdacdadddccdddbbdbbbbbacddcaadccbbccaabcbcabbaadcbddccdcdddbbabcadaaadddccbdabccacbabddacabdcadbcdbabcdaabdbbdbadbbcbbcaadadacbbdacabcabdbbcaddbcbdbcdcaaabbcbbccbdabdbaacbcababdcdcbaacdddbdbcbcbcabacacadcbaadbdddaaabdcdcabddcacdadccbdbccadbbbabdddbbaaabcabbdbacdbcbdbdbadcddbdcbbadbacdcdcadccacaacbbbdcccaabaaabcabdcccbbdbccdcdbcbdcacccbbadbcdbdbacdaabbcdcdcadbcbbbdacdddbabdbabdddaccbcdabccaadaccaacdbdabcdcabaabcdaddccddbbcccdbbbddacddcbaadbdddbadcdaadaaccbadacbaaccdababbaaacbbdbcdabaccadbbdacadbacdbdbadccaabbaccddacbbadccbbddbdabddcbacbdacdbbdacdaacccccaadaddccbddaccbdacbcaacbdddaabbbbccaabcccdcadcdaacdddabbdcdcdbbbcababcbacbacbcdddbdbdbbaadcbcacbbcadadaaddababbcacadbacadbcbccbadcadbabaacbbddbdbcbcbaadaaababaaccddbdcdaccccacdbaaabccdcbcdbaaabbddcaabbdcdcabbcbbdcaaddadacaccacaadbbabaabadbdabcadcddacdadadbbcacabcccabdddcbbddbdbcdabdccccacabbcdddbaabbbbdbbdbdaadbccbcddcdbdaacddbcdcdbdbddbaabcbdcaabadbdcdadadbcadcaaaacacadddcadbaabbabbbddaadcbdaadbcaaaddcaadaacbdadbdbccaadaadbcbaacccdcadbaadcdbaaddcaaabdacbacaabbabbbccdbbdddbaabcabcbdbcabcdacbbccabbcdbbdbddcdddcbabcccdbddbadddccdddcbdaadcdcdcabddaabbacaabcccbdcddbdadaaaaadaaaacdabbadddaabcddbbccbccbbcbcaddccdcabcbcdadabbdccbbcdddbaddbaddaaabcdabcbdcdaddadabddddcabacccddcdcaadcddcccbabdadbdadbdbabcaaaacdbbcdaadadbddcaacaaacadbdacccaccabdaaaccacbababcadcbacacbcdaacacadcccbcccdcadcbacadcccacdbabaaaacadabdbddadbaddcadbaadbbbbaddacaaddccbdcdddbbbacbcccabbbbdbabbcccaaccbaadbcbddacbbacbcbddabdabdcaddbcbcbaadbdaabbccddbdadaddddcbacabbbdaabbbcadabdbdcdacbdddcdacddbaddbdabbcbdaccdbacddbacdcdbabcdbcaadaddddddbddaabbdcccdaddcdaaccdccdddbbbccccddacabbaacbddbbcdbdbdbadbdcccbaaacdacaacddcdccadcbbbbcccacacadbbbabccbdcddaacacdaccaccabbdbcccdbabddddcbdadaacbbcdbcbaabbdcddbbdcbabcadccdbdddaadaabaaabdccbcbdbdcccbcaddbadaaddacabcddaacbcbbcdcaddacbdcacdbdbcccacddadbdbbcbdcabcbdcddaadadbabbdaddccadabadacdabbbbaabddbbaaacbddacabaacbbbdcbbcbcdcdadcacadacddcbcdbddabdbcbacbdbacadcdbcddcbabaadcabcabcdadaccacdddbabacaacbbdcbbdddadbadddaccbbaccbbdccaacabdcbdadbbcddcddadccadbccabaaadcdacacdadcbdacabdddbddadcbdabbdabaabbaabcaacbdbabdbbababcbbdaabacaaadbdabdddcadcbabccabdbcbcddccbbaacbdcabdcbbddbacbcacbcdadbdacaaaaacacbcdadbacbbaccadbaabcbddaddabbcabadccbdacbcaadbcaabbcdcbcbdcddcdcadbaadabdabaacbdcaadabbdbdadcbbcaaaccdbbbbadddabadcbdabbdbcaabbabbbabcacadcdddabadbbbdaccaadaccaddddbbcbabcabadcbccbacaddacacbbdcdcbaaacbabbbdabdadcccccadddcabbdabcadabddccdbaccdcadaaabbcbddccdaabdcaadbdcbdbadaccaaabaacddddcdbbbbcacccbbdadbbdcbbabbdcdcdbbcbdabdccddbcbcdcbacbcbdaabaaddbcadcabddbbbacbddcdddcddaaddbbbcdaacdabccaabcdaadbbcbadcdbccbacbdddcbdccbaccacddbabbdacddacdaccbcbacdabaddbbabcdcaddacddcbcbabacbcbdbddcbdbbbacacacabbacddbbdaacdcbbdccccbabbccdadaaabcbadbaabdaacdabacaaaddcdabccccccaadcbcaaabaaadcdcdacddccbbcddddcdbcacccabdaacbdddcdadaabdabaaabdcaccdacbaacbaadaadbadabddcaaccbbaabadabdadccbbddacbbaaabcaacaaabaacaccbcabacccdcccbabbbbbdddbacbbadaaacaaccacaabadccbbcbdddbbaadbdbbbadcdabbcbaaabdbdbaaacddaaccbddbbacaacdbaabbcabdbcbaddabbcabaabbbccbcbbabadabbdababcddaddaadbbaccbbdcbdcdccbddaccdaadabadacaddaaccdddbabaabdacaaccbcabaccdcadadbadaadcdbadbcdcdaccbbbdaccdaaadcdccbaacaabcbcdacabcbbbdabbddcdbbcaddaaadcbabaadddaadccbdbaaadcddacdadacadbcbbbaadcaaccdacadbcdcdadaacaacccabbcbdbcbcaabbaabcaacaacacccbcdaadacacabcbbbccaddacddaadbadcabcdbdaadbaacbbdccddcbaabcccccdcbadaddbadbdbcbbdcddacbaababadbacddcdcbbdbbdbdcddbdcbaabccddcaddacddbcabababacbbdcacdcadaabdcabcdcccdbcdabcdcdcbdaaccdbacaccdababbbbaccadcdaddaaddcdcddbaccacdcccbddccabbcdadacdabbdcdcbababbccbdcbbcbacaccbbbbbcbdacadbcdcccbbcaabddbdabdacbbacdacdddacbbbbddaacabdacddabccacadbccaccbddadddddacbadcdadbadcaaddadbddabbdcdabadcbdaccadddddabadcaacdccddacabaadadaddabbcbadaaccccacbbbabddddbcddabaacdaccdddccdababacdccdacccddbaacbcbaacabdacabdbbbcdcabbccdcbaadaaaaacccbaacadcadcdaabaaadbaccdcacbbdbaadbaaccdbddaacddaabdabaccbabaacdadadadacbcdbcccabdcbdaaaacdcbbdabacbbdacbbcdcaddccacaddcbabbabbdabcbddadabdddbdbabbbacaaabacabbcdbdacabbbacbcbcabbcddbadddbadabdbdddabbcaadaacbcaabddaaddabacacdccdaaaccbabbdababbadcbbcaccacacaabcdddadcccaccbdaacdaccbcabacbacaacddbddaacdcddbcbbccbdcbabdababcaabbbdddacaacddacbccccdcdcbbbabbdbbabacbacabbcacdcbcbadbaadcacbccbcaadbaaaddbddbdbcbadcccbcbcbadbcadcbbccbabdaacbbabbcaadcdbbbbaccaddabacacddacbaacabadacdbcbccdddbcccbccbaccaccabaadbccbdcbadbdddabddcbdbaabcbdbdcbbddcaaaaaddcdcaababdabcdaaacccbadabcbccbcbaccdccbdbbadbbccaadabacaccddaacbccbcbdbbaddccddabdccbdacbbcdacdabbbbbbcbbdcacbcdbaddddacbbbdaabbcbadacdbdcbccaccbccddcbcddcdcaddcaabbcbabbccdcabcaccdbdcacadccbbaccccddbcbcbabaadddbbacdaccdcbdabbbaacddcbdcdabcbcdcaddbbcdaaddaaaadddbbccbbabdadbdabaadccbdabbaacacabbdabcbaadbdacbbdaaadccdaadccadccdbdabadadcaabddcabddacbacbdcdccdcaadbaadacacbbbacaabdddabcadaabbcccadacaadaaddbdccbabacdcadccadcdbdccccdbcbcdaddaacaccacacacddbbaaacdbcbddcdcbbcbbcbbabcdbaccabcacbddaddadcadcbbbccaacdaaacaabadaadcdacdabaacaccdabdbcadbbddacbbbbcacdccdbcbaaacbbdbbcadbdbacccaaaddcbdccabcbacccabdcbcbabbbddbcbbbdcccabcbccaddcbdbdcdbdccddccaadbdbabcdbdbbbaababaccbbaaaddddcdbbcdccbbddcdaacdcbcbaabadcccbdbbdbdadbbdbadbdadadaaabacacacabcaddcddacdacccdbbddaddddddbdaddacbbddabacdaccabbdcbcbdabdddcbbdcdbbcdbbaddcadcbbcacdbcbbcddaaabcdcdaabcbdabbaaaaadcdddccbbabadccbcbcbbbcacdadacdaacacbbacacbdccbdbdcabdbdbcacbbbacaaccdcadcccbbdbcbdbcdaaccabcdcadcadccbaabaddaddbdaaadcdccbccacbbbccdbaccdbdcaaaccaddddadaabdbbddcbddabcdbdbcdaccacacbaacacccacbccddcbbcbbabdcacbbaccccabcbabbcacacdddcadbaadacdaabdbbdbdaddbadbbabdabbbbcbdadbabbcacdcdacdaddddadbcacaabaddacaacdacbacbbccbcbccdcacbcdbabdacaaaaababbcdcbdcddacbddbbdaccbabbdccbdbbccadbdcaddcaddbbddbcdbaabdcbdcddabbbcdcbbbcdbddbdcdadbbbdacabdcdbacacbababadcdaaacacddcbabaacbbaddbcddccaabdadbdbcddbccacabbadbbdbdcbacdbdcdbbdacaaaaddacaadbabdacbcacbcdcbddccdbcdbdcbdbadacbabacaccacbdbdaaccdcacdababbadaddaaacdaacccbbccaaccaacbdbacabcbbdabbccbdacbdbdcdbbadabbadbaddbccdadcaacdccbbbacadbdcbbaadccdaabbbbbccccbdabcdabbbbaccdddbcbdabbddacdbcddcabdcbbaacbcadaaabddcbacdbdaacaadbcbbabbacaabccbcaccababccdbccccbaabadaccadacbacaacbaabddccabcbcbccbdddadbdccaaacccccbcadaabcbabcbdbdcddbcadbcaccdaddcababaabdacbabdbbcdccadbbdabccadccadcdcdcdcbbbddabbaaddacadadbabdbbdabcbbdccacdaadcbabacabdcaabaacdcbdcdddacabbdddaaadcaccacbddadbdadcccaccbacbdbcdabdbbbabcaccbdaddbbddbdddcadccdddabdcbbccadcbdbabbcddbdbdcbbcbadabccddcdccbbdadbbccccbaacddcbdddaaccdbaddaaacdccbbabbddcbcaabbbdaaaccbddcbcdcddcaddccbacdcbdbababbbccbabbcddabcaaacccddddacdcddcbbccbbcaacdccabcaddaabcaabcdddacccadbadbcbaacdddcbbdbaaabbdcbadccbbdcbcacdcddcdbdabbcdbaccdddabbccbdbcddcddbbddcaccbbcbabcbcacddacdadcddaaccacdbccbcadddbbcddcaaabdabcacdcddbacaccadcbdcddcbacaadcaabdccaaddaaacabccaddaccbcaaaacdbdcdbccbbaaadaabcccccbabdcdbccadcbbaddbbdcbabbbcabbddbbdccaaabdaabadcdccbaccababdaabddddccccacadcccacaabbccdbacdbccccacdbcdcdabddaadcacbbddbdcdcddbccdcacbbddbddcddbabdacbbbacccdadbacccacddaccaabcaabbdaacbdaddaaadbdaadadcacdbcbacbcbddddaabdccadcdacababbbddaacbabdaaddcbdbaadadbbcaadbcdcccccaccbbddaacdbdbbbacbbadcdcccdbdbabdcbbacadbabdbdcaabadddaadcddbbbddbbadcdabaccdcabacabbadadbcdaccaaabddabaccbadacacbbaaabcacbcbdaccbaaacbaadabcbaadadabcdccbccabdaaacdddbbaddcdccbcccdcadcdacabacbddccdcccbaddbddaddcddabcbbdacacdabccdccaaddddddccbbcadbdddbdabccbadbaddaddbdacbddadaadcacaccbacdcabacccaccbcbbbabdccaccbdcdbdcccdccbdbdbbbdbdacdcddbacbdccdacadbaacaabcdcbcaaaadcddbccbcbdabddabcdaaccdccaaddbbddcbbcaccaddadaacdbcbccbdabcabcbdbabbbbcdaaacdacaaaddaddbadbccdbabaddcdaddadaacbdcdcbcdadcdbadabdbbbcbbadabccbbbabbcddbdddaddbbaabbdadcdaccbdaddcdbbabdacbbddadcbbbababdcccbadddddddcbdabbddaadcdcbbdcbadaabacddabaccaddcdbbdbdbbadcadddcdcdabbaadbbabaadacabcbabccabadbdcdadbdacbccdbdbbaacbcbaccbccaaddddbcbcaacbabccdadadbbacadacdcbcdcdcddbaccbabacbdcbaddababcbaadcbdbcbdbdacbdbaadcbbcdccdbdcbcbcbdcbdbbcccacabcdcccacacdabaddadababbaaadaccbbcbcddbcdbacaddcbcdddccdbbbdcccbcccbaabbadaccddbadbddacabbbcdcadbdbdbcaccadcddabcdbdacaddbdbdaabcddacbaaccddabccbddbbdadbdcbabbcaacdbacadbdbcdbabaaaddcdcabbcdbabbacabacdcdbccbbcddaadabccccbbadcccadabaaadbabbdcdadaaddbababdbadacabccddcaaaaadaababccdacdccaaacdbcaaddbbdbabaccbddccbdbaababadaadccddcccdaaadcaaabccaacaaddacadbdaddcdabaaabbbddcaabdcadbccdbcdbbdaabbbbcccaadbaabadcbccbcaabccaabddaadbcaabbddcbbbcbbdcadacaaabbcdbaaccacbbbddbbadbbddbcacbdadcabadbdbccaaabddacdacabdbbabbbcbdcbdabadadbaacabadbcdbcaaaacdbcdaddbbcbcaccdbcadbcddbcdddcbaccadabdacadbacaccbdbdbccbabbadccccddcaacbccacccbdaadbdbadacabcacadbdcdacccdaaacccdbaabcbbacdbcdddbbcbdcaadcdcadddcaabbacbcbcdcdddcadbbcbdadddaddddbdabdaaabbcbadcadcaabdaccccdbbaaaddbabadacabbdcbccbaaccbbdbbabbdadaabccdcabbcadbbdadcbadcabbcccdbcdddcbdcacbdabdaaabdbbcbbbaccacccaccbbadcbddabaaccbabbbcaddadabbccccacacdbaabbbcabbbbbdbdcdbbbcbbcadabaadddbbcbaabccddcadcddaddbbaddcabaadccbadbacbbbdacdcccdcbdcddccbadbdbcaabcaccadbdcaabbdabcbdbaaaccacbdbbdaabcdabbcbbadadcdcadccdcccbbaacacddbdacaabbdcddcacbcdddadbaccbcddcabcdccdaaacaacbaadbcabbaccbccabdbabcdbdddbcdaabdbcbdbcccbdabbcbddcaadaccdcbbdbbadcbdcddabbbadacbbacadbbbaccbabccdcdaddacddcaabbcbccabacccbcccacdccddddcaddabaaadccacccbadcbcccadacbbdbbbaabddcdcaadbdaaadcddbacbcacdbcaacadcabaacbdcdcdbbadbcdabdabdacaaaaddabcdbdddbcaaccbaccbbbbcbbbbbdcdcbabccacdbdaaaaaaaacbdddbbbdcbcabddbaacaaabadcdcaccbddacdaabbcaabcddaacadadadbdbcaadaaacbadcabdddaabbbcbcbdcaadabbccadbddcdcbbcacbaadabdabbabbcbbddcdbbcbacadbacdbbbcdabacacddccabadddcbccaacbbdcccbcbcadbbbccaaaccdbaacddadccadbcdbccdbcdabbbaadacaabddbbcdbbdbccbdabbabbabccacccccdccbdbddcbdcaccacacbaadccccbaaaabcdcbdcddbaddcdbccaadccacddcdddddbcbddabbccabdcaaddbadbaddddcbbdbccdbadccddbbddcccbccbdadccddcbcdbdabdbaddbdbaadabadaddcadbabdddddcbddcabddaadddacbcadbdabaaccbabccddbabcbdadcbadbcbbdadccacddccbbcadcdbdacaddbbbcaddddaddabbbdcdabbddaabdaddccddacbbadaccdbabbbcccbdbdbddabdaababaabdddbcdaadababbdacaccbcdccbaabddadcbcbbadbdbabbaddbbdcadddbababcdbbbddcbccdbccbbaddbabadbdddbdcbdcaaaddcdbaabdcbacacabbadbbcbabbbbabcbbdbbbabdbbbdabcccdacdcaabddababaccabdaaacabbdcccccbdcacadcdadbcaacddccddbbdacdbaccbddacacccabcabcbcbdcbcaadabcaaaddabddbdcbdabcdabddcccbbaacaccbaddbccaacbbccbcacccaccdccbddbccbaccbcaddbadaabdabbcddaadaaacabbdaaccdabacccdcddbcdbbccaddadcddddbbbaacbcbadabdbcdcdccbababbbdbdcadbcaaadcbddcabbaccbbdacaccabacadabaabccbbdbaccdcadcabccdddacdbccdbaacbabaaabdbcabbdbbaabddccdbdabacacbdaacddbbaddbbdcaacccdbbbaabbcadabdbddcaadcaabbbbaacbacccdbaccdbaadbbcbbdbdbbcadababdbbbbdacaddcdcabdadbaaccbdabcccdbbdcbbcaaaaababccdcbddccccdbcbdbbcabaadcdddbcaddaccacddddcddbabbacadabbbbddccabdaaadcddcbacdccdcbdccddbaabadacabdddaddadacdaccdbcdaaaaccccbaddcddcbadbdacabdbabcccaababdccdbcccdcccdabdbdaacbbabdcbdadddcacccbbcdbbbadbabbacbcbccbacdbddbdabaabbcaaabcdcaabcdbcbabdbcabddbbaacbaacbaccddbcdaccccccbaccdbbabdcaaccbddccdcdacbddbcdbadaccccbcbdcdbcaadacbcbadadbcdcbccdcdbbdcadbcddcbcaccdaaddcaadbadabcbcccbdbdddcbcbbcbdadadbccaacbcabdbccbaccdaacbbdcdcdccadaccadddabdcbaabdabaddddcbaabdbaacdcbdcdddadcdcbdbdacdbbabdcacdadbbbdacabbababcbdcbdbcabbdcbaccddabbdadabaaddbbcdcabcbdcbaaddbabcbacdcabbccdddadbacddbabdcbdbadcacabdbaacaabacdadddadcadbcdabbcbbacdddcbdcbabcdaaabccbabbdcdcacbcbdaadaddabcbbbccdcaacbbcbcbbddadbbaddddddacabddabbddcaaabbdbaccbdcddbbddaaaaccbcdcaaccadcaabbbccdadabdcacdadadbaddacaacbabacdcaabadcdbabdaaccbaadcdcacdbbdbcaabadaddacbdcaccaaacbddabdbbdbbacaacdbcaccaaaccccccdbccaddbacbaadadbdbbccdddbbbcabbbcbccdccdaacdcddbbdbbdddabaadbdddbacdaadbbcbbacdcabcabababdbcdbbdcdcdcabbcddbccacdbabcbcbadabaaacaaccddbcbdcdccbddcbcbacbddabbadadabbccaadddbddbdbdcbcccbddccdaadbbcaccccbacaabacaadccdabccabbbccbdaacbdccdccbbbbbaadabbccaabacbdabbbbaaaccccaabdbdacadadbabdccadabdbadbcddaccdacaaabacddccaacccccadaacabdccddcbcbcabcbcabadcbdbbdabcbaddcbdcabaadddacccabcaaccbaddddbbcdacbababaacdaddacabbabdabddbdacdddbdccdcbcabbccbaaacbbdcdbaadbcbdabdbadaabadaccbdbbadddcadbaadcdcbcaddcabaacddacdcdcdcbddaabddaddcddadacbabddbdcacbbbcaccacdbdbcdbdadadabacbbbbcdabbbaadcabacbbaabaabdcaacdacacbdbdabdddcadccccbbacdbdaabddabbcbbbcdbbcbaabaccbcbaccdaccdcacdbacdcbaaaccbbbdabaccacbaccbbddcdcbcbcccacbaabbcccdccdcddccbaddbdcbdbdbaadcdbacbbdadaadacbabccabaaaacababcbacadcadcbbbdaaabdadccbacccdbdbbcabbadbbddadddbbbcccdcbbaacbcbcaaacacccbccababaddddbbbadcbdacabcdaabbcacccdbbcbcdccdcbdbcdcbddbdcbdbdbddacadcdcaddbaacbdbbaacabcbaaacbdcabcdcaddbaadcbdddccdbdbbadacbbdccdcacabbccbbabddaaabaacaccdcdacaddbacadcdaabbbbadbadcbbabdbabbaadddbdbbbdcabdcabccdabaadbcacbbbccabcaacacacbaaadaaccaabadbacddcabcacbdbbcaccdcaddbaabbbdacbcabdaacbcddcbcdddbbdcabcbadbdabcbacbaddbbcaadddbaabbcacccbaadacdabcbbacbbaacbbccacbbbdbdaddacccaababdadbcbdaacddbcbdbadcadbdbbcbaddcbacdddaabacdbbddcbbadbadadbcddacacbdaadacbccdaacddbcabccdbbdabdacadcbbabdbdcddbcbbcaacaadcbbbababbabbddbcdadbaaabddbadddbddcadddbadaaaccdcdbabbcddcbbbbadabadabbccdcddacabaabdaccdcddbcbddcdbaddccaadacdbcaccbdcbabdcbdccabbdbbaaddbcaadbcbabacaddadbadddccbccacbddadbdddbadaddacddcdcacabacbddcbcdbbddcdacbcbbcaaddaadaadbbadadcaddaaacabbbbcccbccaaaaacbbcacaacabbdaacdddbccdbcdbaabcbbcbaccabcbadbbaacacbaacdbdaaaacbcbdaccbdaacddaabbcbaddbaacdbcdbccdcdbaddbacbcabcdabbdaaacdcacabddbcddcacbcaaabcddbcaaaacdbbbbcdbbadcdaadcacaaddcbacdcdadbbacacdcccacaaaaaacbdaccdcbddbabbacaddbccccaddcbacaabadcbdacdbbcdddaadcbcacbdcadbabbcbddbbcbcbcdcaabdbdaadadcababacddcbabcbdadcbdddcdbbbdaadabdcdcbbcdccacbdcacbdccdcccabcadacaddccacbabcbddccccbbcdcbddccacbdddbcaadabacabacdcadbcbcddccdddcaddabcdcaabdcdbdcacaddadcdadbabdccbbadaadbcdcadddadbdabadacabaaacabbabddbaddcbcabdbccdddddaaabcacaccdbdcbbbaacccdcdacdcccbabccdaddaadbddaaadbdcdcadcdadccbddaaddccbaddccbaaccabacbdbdbcabccacbaabdbbdcbbaabddbabdabbdbbddcaacaaddcaacbcdacdcabbccdbdbaaadcbcbdcaabbbddcdcccbdbacbcaaacddacbccadbabbcaabbabccccbaddbbbcdcddaacbbdadbdcdaaddadddabcbbcbdcadaaccdbadddccddcccbadadcbcbbabbabcdbcadcacacaabdadbcabdccaccabbadddbaadaaababcddcadcaadddccadcbbbdbccaadcaccdbbbccbcbbddaaddcdcaabcabccbbdcdbdcdcbdbcdbbbdbdbcbcaddbadbabbdabaccbcababccadbccbddbbccdcdbcbadbacadcdcccdbacbadbdcaaaabcaccccdcadcbdbdbabbcddbbdcbcdddacdadabacdaacccbabbccdaabacddbadccabcdbbcaaadabcccacdbaabdccaccbbcacacbbcbbababadaaacdacacabadadbaacdcbaabbbbadabddacbcddbddaabbccbbcbbaacddcbabbacacdcdacdccbccabbacccdccadccddcadcbcdddcdaaccddbcacdcabacdbcbbaadabaabccaabdccbacccbcbccbcdbdadaadcababadbabdbadadadbbccbdaccbaadabcdbcdbdabccbabcbcbddbdddbadccdacdccadddadbccabcabbddcbaababadbbcbdcdccccaaddacccacdabcabdddacadaadcdddbaccccabdcbcdbcbbaaadaddbadcbadabbcbaabcbababadbcdddabacaaacaabdbadaccdaabbadaaaabaddbcbdbdaaddbabddcababadadbdcddadcccdbaddbbabccddccccbbddaaacadbbdcabbbaaaaccdadccacbdbbbbccbacabbdbdcaddcadcdbacadcddbabcbcbcddabbcaaacddaaccadaacbbaaccabadbabcabddabdcabdbacdddccbcadadabcaaadcdcddccdddbdbbcdbbdadcdacdbdccdcaadbbacbbddbcdbabcbdacdbbabdabaaacbdaccdadbddadbbcadcbbcdbbcdadbdcccbcddbaabaabddcbbaaaabcbdabacaddcacdbddcbbadababddbcdacdbbabdadacdbdabddcdadcddbcbccbaaaddccaacbcccdaacddabbccbcbcbdababbbcdaacacbcbcdbccbbcadcaabbcccbaddccbcbddcbcaaccccaabbaacacabdbcbcadbcddacdbbccbdcaabcbbcdbccddacdcdddaaabacccacadcabadbccbdccdabcabcbdddadabacbccbacaabbaaabcbaacbbdcdacaaaddddcdcbbdcaabdabcddddcbabdbbcbbcdbcbdbdddcbbbccbccdadaaacbbbacacdccdbbdbddababbaddddaabaaccbaabbadbabdbbdbcaddcdadaadcccabbadcaacdababacbabbdcccdcbdcbadbbadcbacbabadacbbdcabacbdbbabbdaaddbdbbdbdbbdddbcabcccbccdcadbdbabdcadbbcadbccdcabdbdddcaaabdcbdbdbdcdbabdbbbbdcbbbdbbdbddddacdabbcdadbabacdcbbdbaabaacbcbdcbdbaacbabdcdaadbacbabcbbcddccdddaddcbbcdaabacacbdbcacccdbbacbaccaddbbcbcdcabaacdcaaaabcdaaccbdbbccbadddbdbdddddacbdccaddcbddbdacbdaaabbbcdadcadbcdcdcaaadcdbbbcccdcaabddccacccbabddbdacddcaacabdababccdbdbaacacbbaaaaabcbdbbdbcaaabdccabdbcaacbabccbbacdddbccddacadcdbcccbcabadbabcbbdbcbbdcbdabcdbacadcbbadcbbdbcaaaacbccddcdaabccadaccdcdcbbababdacbbbdbdadbbccddabadccbccdbdabcbbadbbbbabbcaabddabbaaddbcacccdabcbccaadcddcbbbacacdbdacbaadddaacacaadababdacbbacdadaaccaacbdacbcdcbcacbbdaadbcbbcdbcbdaacbddddddbdacdbdabadcdbcddcbcaadbadcaddaabbcbcaacdcdbdbbaaccccddadbdcaccbabdcabbdabccabddcacddcdcbcbcccdbacddadcddaaaccdddabdbdaabdbbddddddcccdcadacabababaabcdcadbccdccbcbbdccdcabbdbcccdbdcbbdbdcbabaabacdaacbcbbcbbadabcbddcbadbbcddadaaddcacbbddbdccbcdbdaddbbbbbdbabddbdaaaddbbcccccaddbacabaddcbdbccabdadbcbbababcbdaddddaaddabdbdcbdcbccbcaabbdcabdcdddaccadbcbaaabddbddbddacaaaaaababccbccabdcbcbaaaccbbcbcabdcbdbccdccacddbbccdbbaccbdbacacdcadabbdbadcdcabaabbadaadccdddcbdacaabbccacadddbdccbaabcbbbbcdcaddacacbdddcbbcbdacbdcddaadadbaabcbdccdcdbcadcddccdbacbcbddbabdacbaaaaadababacdbabcaddadcbbcdaacabcbadacddabbacaaaaabbddaddddcadccadadbacaaccdadabcccdbacbaadcccadbbabbbacbbacabbcacbbdabdaccacbbbadabdcacccaacdddccaacaabcdbccbcacdccacaaaaacbcbdbbbbbbaaddcdacbaabadcbccbbccddabcbbbccdcbdbbbdbddccbbbdddbbabacaccaccadbabbdbccaaaaaaacaadbdddbdbcddccbdbdaccbdcbcbbccaccadcddddbcadaacbccdcbacacacbbdddaddccbdddbbadbccabdddacbdccdcbbbcdacbbcaabcccdaacccbcacadbcdbbadbaacdaadcabdcdbaddadcbdbcbdadddcdcdcbcaaaaccacdacbabcbaabacbbbccaaabcbdbdadbcbdbdbbadcbddcabbacbcdaccbdaaccdaccddacbaadbabbbcdbcbacdddcbbaccbdcbbdabadddbaaaccccdddcddabdbadacababacdcddcabaacbdabaabdcdaabdbcaddbdccdcdcbabdcdbccdcadcdabbddcadadaccccbdacdaddadcadccdccbbbbdddababccddaddccaddcdabaaadbdccbdcbcccdcddabcccdddcdaacbbdccbacbddadbabccaabacbbbddbbdbabdadbdbbdadbddaccccdcbddccaddcdcccaaadcbcccdaadacabadaabdadcabbcdcaacabacacacdcadccaacdaadbacdbcacdcadccddbdaccddcacccdbcbdcccabbababddbcbcaadcbccadddccabcccbbadaccacadadbcabadbcaadbadbdadcbcabcaaabcbcccabaadcbaacaaacbdabbabdadcacbacbbbabdbcabacaccbabbcdbbccaaddbbdccdbbcbbcaacbbcabdccbadbcdbdccadbbcbccaaccabccddbbaacccbcddbabbcacaacacacbcabddcbaccbaabbddbcaaacdbdcdadbbdacbcacacbaddadacbaddbbbcdaabddbccdbbdbbaabcccdbddcdccaccbbcabcddbbbaaabbdbabdaacbadbdbcaddaddbbaadadbcccbdbbdaaacaadadbabbdababbbdcaacaaabbbcbbdcabadcaaaaacaddaababbacbabbbcacddcacaabbcddddaaadaddaccbccbbaadbcadaaddccdcadccbaacdcbddbbcadbdccbbdababdababcbddcbdcddccaccdababcdbdaddcdccabccbabcacdadddcdbbbbcdbaabccbabadddadddcddacbbdabbcdcaabbaddaacbddcdaacbadaaaaddaaddcdbcbaacbdaadcaadcbbccabcbdbbccbcbcdbddabacdbabcadbadcaccabdddbcbacadbbaaacccbdabbadacbacbccaadbccbcdbddcbadcdcaacccdacacadbbaaadcbbbcccaaabcaaddcaabdacbbbbdcbdccdacadbaddbcddcabacabaabaabacddbddbcbbbadabdabdaacbcabdbccddbadcdcdcbdbbabbcbbbdbcdbccccacbbdbabbcbbbcbadacdacddccbacabacacbacdaccaccccbaddabbbccbdddbabcdbabbaacdadcbaccbbccdbadcdabbcbcdcdcdaacdacbdaddabccaccccccacadbcacbbcdbcbcdcbbacabddaabcaddbbdaddcbccaddccddcccddbdadbdddbbddccbcdccaddaaddaadcdbbddbaddcdccdadabbaabaccabaddccacbbcaacdccabbacbdbaabdbbdbbacbdccbacbbdbcbcdbaacaaacabcddddbabdccacbdbbbdaacaacdabcacdbdcbaacaadcabbadcbadcacdddacbbbabbcdcabcbccddabbdcaaddbdadcdbcddccdcdbadbacbdaaaadaacccdcacdbbcbcddcccbadabdcbabcdcddcaabaadccbacbdaaacaaacaaddababdcaaddcdddcbcabdaccccccccaddbaaaabdbbadccaacdcbaabbcbdcacaabcabcdccddbadacbdacddaabaddcbcabbbbbccaaacbdbadbcbbbdbbacdcbbccdadabcabdaabadadaaabbccccbabadaaccbadacdcdcabadaaadccacbdacabdbbdaccbcccccbacccccacbbddbbdcbbcaaadbbddbcdbcadcaabccdcacacbcbaabbbdddcaacdaccaabacbdddbacdadaaacaaadaaabadcaddcbcadacadbdddbccdccbccdabccbaddadddccbdbaaccaccccaacdcbddabdcadbaccaaddacbbccdaacccbcadcadabccabdccadabcbccdaddcdddcacbbaccabdaaaadddabdcacdbadcbdccaadbcdabcbbdccdacccdbcacddbbcaaccbdadadbcacacbccdcbbacdccacbcbdcdabcdabdcddadcababcadbcacddacdcaadabacbabaddbaddabdacdabaadcbbbabbbdccbbbdcddaacadbacacadddadcaabbadacdcbbadbbcabddcacbdddbbdbbcabcaadbabbdcaabdabddacbddabdbbccacabdbcbdabbcddaadbabaaadcdbddcbbacabdacdddcccbdbababbbccbdcbbdaacaabcbccdbbccaaddbaddaabbabcdcacaacbaabbabddbaccacbabddbdacccadacbcbcbddbdccaaddbacabcbddddaddabdadaacaccdddababcddadcabacaaddaddcabbcdcddbcddadcbbdcaddadcdcaccaabdddccbbaaaaaadccbcbbcaabcdaccddddadcbabcddcdbaaabcccddacdaaabdbcacabccbabddacdbbcbbbbaccadddabaaddaaddbaabbcdcbcbbadcacbdabcdbbdaaabbbabccdbabbbcdbcccadbdaadbdcbabccaddbbbbabaadadabaccbcbcddacdbbbacadbcaaabdddcabdbdcbaaccabcddbaccbaaaabdcbbbbbccdddadcdcbbdbdbddddccacccdcabcabbabbabdccbabbaabdababcccadcdabbcbaaadddbbdbccccbdbdaadaccccddddcdddabaaaddcaacacbaacbbabbacabdbacabaaaddbbaacdadbdbadcbccddcadcabcabdaacaabaadcdbababdadcddbabcbabdcbbdacbdacdbdbaccdabaacabccddbbdbcbcdbaababaadabaddbcdbbacdabbabddcbcacadabbddbbcbbdaddbdbcbcaadaadabbcdbbccabbbbddadbbbdbdabcbbdabbcdddddacccaccccababacddaaacbabdbbbcaaddadadbbacdcdbaaadccdbdbabdcdcdadbcdbababdcdbcdbbcdbcadabcddccbcaadbbdaaccaccbabddcdcdbcabaacdcdacbacbdadddddccdddddbbdbabcaabacbcbacdddbbabaacdccdacbadcbdbbbbcabdccccbdacdbbdbcbcdadaacccdaaabacabcaccbbaacaabdbabbbdcdbcaabcddbcbbdbdcdddccccabdcdccaccaccdcaaabcbadacdcadcadcabccdcbddacbbaaaaabbbcddcbbbabacbacbbdbbcaabaabcdcaaacaccbdabbcdbddddcadbcdbddadcdcdcbdccacabbbabadddacdddccbbcdabadabccdcccabdaaabbacdaccaaabddaadddaccddbadcccaabdaddbbdbcaabdbaadcabbdbddcaddaddcaabcdcacbdccbbbcaacddcdbbacbacddcabaaddadcddbbdaacbaabdabaaccccaccdaadbaacbaccaaccbdadaaaabbdbcabcbccaabcccaccdcadcdcaddbdaacbbbccadaadddaccababdbcbcbccdbcacccdcaadbbadcaaaadabddbaabbdaababdbbdcbdbdddababddbabdcbbdddbdccdacabdddacaccbcbabaacbbaaaadaddbaadacbbadccaabccacaccabcbabbcdddddadbbcdcabbdbadccbadbcbaddcbabcdbbbcbcaaabbcccacdacddbbcbcdbbdabadaabbaaddddbcddbcbabdacbaccadaabddbadadacacbbcccbdaccccddddaddaccbcddaaacdddcdacdbdbcabbddadbabdcbdcdcbabccabcaacdadcadddbbadcbbbabbbacacabddaabacdbbdcaacdadabbbdaadadbdcbcabadbbddcadaddcdcacaddcbbcdabacabdabddcdbcbcaaddaadbccbbcacaaaabbcdddbcaadccaacccabcddcccbbbddbcbbbbcccccccacccddccdbbcdacabadcaadaacabdcbccdaacbbbcabddbbbdaacbdbdbdcadcbcddcdbaccdcabdabdbcadbdcddbddbaadacaaccbcabbcabbbadadcaaddadbcaaaadbadaadbaccbadbaadaacddbdbdccdadcbbbaacaadaddccbcacbcacddaaadddccadddbddcbabadccdddbbdbccbdccbddcabddbacddddddcadddacacdbcdaabbdbcadbaaddaadcccacbcbdccdcbcdababbbabcdcaddcbacabbccdcababdcacbdcaacdbcbdddbbbadbbbdacaabcdccbacdbabcbdaaddacbccdaabcbbacdccccdaddabccaabbadcdadacadabcbdccdabccaaadacabadabddbdcddadabbbbdadcbaccadbdcabdbcdbdcbaabddcaabadbbbdcaacddbbbadddabdaabbbdbacbdcadadaddacacbcbbddadabcccccabcdaacbddaadadccccbbacdcdbabdbbcbbaaacaadaddbabacabadacaccdbabdbbcaacdbbaacdacddbabcdccdaccabaddbcbaddacababddadacdcbbccbadacbdabdaadbbcccadbbbaddbbcbbabddccaaadaadcbbbdabdabbddbabcbaddddacccdaadcdbaacaaabdcaddacdcddbcbcabdbcbacbabbbaacbacdaabdbadaacabccbddbdcbabacacdbbaaacaacddacdbbadddbaabccbdbcccdacbdcadccbdcabcacbbcdbbddabcddcdbddbdcbddbcdbcbddddcbddcbbabdbcbdbddabdcbcbcdcadcccbadcdbbccddcbcbcadaaabccbcdacdbbaadccddaaddabdacaadbbdadbaabcacddcdabbdcbddbbdbbabdccdcbaaaacdacacaccabbdbaadbdcbbccabacadddcbcdbdacccbbdcdccdddccdccddaaccbbcabccbdaaddcabadcaadbaacddbcdadbbacdddadabcaabaddadcdaadadabdabcaaccbbbbadddbdbcdddacabacdbdbbbcbabdccddadcddbcdaaabdadbcdcdaaabacaadadbddabcbccccdbabcabbcdcbadabbdbccdbdcddddbdbdcdcdaddcacbbbabaabbdadbcbaabdacadcadcdbadcbaaadabadadababddbdbdbdaadbdccdaadbbbbdacaacaacadcdaccbcbcdabbadcacbcdcbcdbbddcacbbbbabbcbadacbdcccacaadabcacbdcccadddaababdbacddcbabcdcbdaabcdbdcaddbdaacacadccdcaccabacbccdaccbaabdbdddccabbbabacbacdcacabcddccdacdbbdacbacbaadacbabcbaaacbadcbdcddcbaacaaacaacdabbdadcbcbaabcddccccccbcacdbccddbcdacadbbbbdbcadadddabdddccbacbbbbddbadcbbccdaadbccdbcdbaadbddbddbdadddadaacbcacbbccbbadcbadaccbddacabdccdcbccacbbdddaaaacbaddcdbdddccbaabacdbbbdacadbaabddccbabcaacaddbbadcbdbddccaadcbbbabdbaddbcaadbbbdcdbaabdddabdabcabaccbababbcbdbbdbccdddbdbbbbccdbbcadcbdadbcbcbdccadcdcdbccbcabdbdcadbcccaabaddddcbdbadaabadaabcbaddabbdaddcabaaadbaabdddabbaacadbdcdcbbbadbbadbbddbcddccdadadadcabbddcdccccccacbbaabdbbcdababcdbcbdabbcddbdbbcdcbbbaddbbbabbcdbcdcacdbbcdcdacdadabbdcdacdbabcacbaadbccaddcadbaccbbaddbdbaaccacdccdaddaadacabdbaabddbbaabcaadcdacbddccbaabddcadccbcddadadaaaaacbabacaabadbcaccbbbabaddccbccaaccbabadaccddcbdbddcddacbbbaaabababbcbddaaddcbccababcbdaabacdcdbcaabcbdabbdbcaccadcabdbdaabacbcdcacbbcbaadabcacdbbbbaadcbaaccdbabcadbdaddccbaacacabddbccbbcdaabdddbabbcbdabadabcbbacaddcbdccbcdaabdbbdbcdabccadddcaadcddbadbabaaabacdacdbabaaadacadabcbaaabdadcbcddbbcbbbdadbcdcdbadadacacdcdcccccdcbcdbdbcddccaaabdadcaabaccdaadababaacadbdadacbcaadbbcddbddabadadbaaddaddabaacbbcabdbddcabbbacdcbdcbbdacdadcaccaabccbdcbaddaabccddaadabccabbaddcaddadabacddcddcddaaadaddbaaabbcbbdaddcbddcbaccabbcccbbbacabcbbaabaabccbcabdcbdcbcacbbcdcbcbcbbacbcddcaaacbcdabdcbcbcacccaccdcbaacabdbcbacaaaaabbbddabbdaabcbcaabcddabbddacbdcdbbbbdabcbaaddbbbcbbbacbcbdaddacabbdcbacbccdabdccddccbdbdcbaacddabaabbcadaadbaabdabadddcbcbbcbcbdbbabdbcccbadadbdddaacbadccabaddbaaaccccbcbdadbddcadccadbccdcbcdacdbadcabbbbbcdbddacbcbcdacccbbcdbabadacabbaabcccbaddabacdccaaddbcdcbddcdadbddcbddcddbbcadbddddbbcbababadbbcacbcccbabdddaaddabdcbcbbbbddcaabccabddaabddbbcbcdbdccdbabbdbddadbddcbbcabdbdabbabbababcdddbdcbdccbadbabbcbbbabbccbaadcbccdadabbabadbbcdaabddbbaddccbdbdcbcaaccaadadaddbacacdddbababcaabbbbbdcdbacbbbbaddaadbcbddabbbbdbcbdaacaaadbcaccaaccdbbdcbbcaabcccaccddbddcacbddabaddbcdcccaddddcccdccdbdcadadadabdbdaccabbbadcbbacbabcaddcbdaadbcbbdcacacccabbbbdbadcdbabdabcabaadadddddbccbbabbddccdddbdbaaabbbccacbcdcdccdabababdccbcdccbacacaccaadcccdacacadadabadabcccccbaacbabcdcbddcbdccbddbcadcccdabbcdabcccdccbccabdbbcacbbdbabbcaccdcbbabcabdcbdacdcdacabcdbacaaadcbaadcbaadbacadaccbcdcbbdaadabcaccabdbccbdbbcbacaabbdbcccaacbaddcbdcacdbbbcaacbccdadcacbacaddacabccbcaadabbdaacbdaabbccdabcbadbaacbbbbadcccabcbdaacdcbacbcbbddbcbbaaaaabbdcadddaccadcabacccaadabbadddbaadabdbbddcbbacacaddddcbdcdadccbccbdbbbaaacdcdcaadbcdacabdcabcadcbdcdcbdbaadbdbabaccaccbbdacaaacbddcbadcddddcaadbcbadcadddabdbdbacbdadccbaddcacadbddcaaaacdbabdcadcdabdcdbdabbbadccaadcddbdbdcdcbdaacdbbdbcbadbbdbabcdbadbbdddbdabacbbbccdabbabdbdddabbdaabbacbbadabbcacdbadbacababdbaacbbaaccdacadabddcddddbdaccddcbbbbcbcccbcabcbbaccabdaacddabbadccbacdbdbdaccbcadbbabbccaaccdacdccccbbbadbddbcaaabbcaaabcdbddbcdaadaddccaacdcbadbdbcadaacdaadcdadbddbdddbbdbadccdacbcabcbcadcbcddccbbaabadacdbdbbccbdcdcaddbdcbacccbabbcdcadbadbbddcacdabadaccabaabacdabccddadbcdccdccabbcddddccdcaadcbdababbaccadcdcccdcacccadcdddbabddbccbcaaaccbadcccddabdbabaaadbdabbbcbdbbadadacdbaadcddaaaccacabcadaaabbabbadadcddbbcaacbccadaaadadbaddbcbcaccbcadacadccbdddacabbddbbcbacbbacadaaabaadabccbabaaabcbcbdabaddddcbbcdbbbaaddacacccadadabbaabcccadcabcbdcabbbabddacabdaaabcbcddccdaabacadcbdccaccbdacadadbbaccccacaddbadcacdabdcabcaddccbabdbacaaabccdcbddcdaccbccddcbacbacbacbcabccbadcdacacdacbcbdabdabaabcdcddbadcccaddccabdcabaacaacbbacbaddcabdddcdadaadabcdbdbaaaacaabcacbccdcbabdaaadabbbcbccdabbdbcbcbdcbbdaaacdcdaacdbbcaaccbbbccccccaccddaaadaaaddaddcadddacdadbdbdbcdbddcdbdbaaacaccccbdccabbcbdacabacacadcbbadddaadadacadbabbcbdcacbabdbaabdcccaadacbaaccdccdaabdbabccbadddcbcdbdadbaacbbacbccdbbccabcdddbacaabddcbbbbaabcabccbdaabadccaddcacddaadcbddcbdcbdccdbacdccbcdcbbdaacddcaaadaaaadcaaabdadcabcaabbdcdaaddacccacbdbdbcbadadbdcabdbdadbddacbbddbcacbdbdbadabdcdacbdabbdbbbcbdcbaacdcabbddbcaaacddbbabcbadbdbdcaaabcdbaaaacaaaacbdabdcaaaabccaadbcaacbdbacbdbbcdaadbaadabdacbabdddbccacdabbcaaabbcdbaacaaadaccdccccddcbcdbaabaadccbcbcacccaadcabaddbcbdcadaadbacabcdcbdccbccccacdddbacbbaadbdaccabbbbdcbdbdcaacacabbadccbccabbdbdcddbbbbdbadbbcbcdcbbcbacbaaabccaadbdabbdbdcdadbddbcacadbbcaaaabacaaabaabacbdcdbadcadcbdbddddcbbadbadadacacaccacbbcaaabbcbabaccadabdcdbbdcaddcabcabddbaddcbccbacdaaaadcaccaadbbcaccbbcaabacaaabaadabdabbdcbaaccbddccabbdbccabcadbacdabbdbcbabcbcaddcbbdcadbdbdbddcbbbbcccacbacdacbacabdddaabbdcdcacabcbddcaaddaccccbbbccdbcdadbdccaaddaabccaddccbcddababbbddccbacbbaacdaacaccaddbadacaabcdcaacdcdbbddcaabbcbcdacaadabacccddabbdbcacbddbbacddbbdacddcaccddcdaadcdabaabadbdbabaccabccbbdbcbdbccbaabbacacadbcdacccddacaacbaacbbbbbbdcbbbaadcdaddccdddbdbccaccabcccdcadcbdbdbbdbdacbaddbcaadcbbdadcbabdbabcabcdddadadcbdbbbacacdcbacbbdabcbaadcacaddbdabaacacbbbdbadbcdcbdddcbdabcaaddbbddabcbcadcdbcaddddcdabcdbacacddcacdccccdadadabcbcbadabcbdbcdaacdabbcdabdcbcacccacdacdabaaacaabbbddbadcbabadaccaaadbabddbdbbcdddbcdbcbaaabbcbdcddaabddccaddbabcddaaddddbccbbaabaabdadadaacacaabdcaaccdbaddcabadccbdacdcccbbcddabdaaacadddacacadcbbbdcbdbadbdadccbadcabcabbccdcbcadddbbabbdbcbaaaacbbbcbbccbcaddbdabdbadacdcadadbdadcddadcdbcbaabccdacbbaacbccccbbbccbaaddcdbabcdaabccbbbccbcdaaacbdddaaccddaadcacdacabccbcabdcbaadddbbbbabdbbadabcbdbcaaacdabbdbddbaabacdccbddcdadcccccddddccdacabdddcbcaadcddcbadabbdaaabbacbddcbddbbddacddcdccbbcbccacdaacaabddacbddcbbcbdbcbadabbccdbddbbbabbbaadcdbdaddcdcbacdadaadbddddddabdbcccadbccbbbddddccbcadccbdacdadaddcacbcdabbbbdddbbbabdacaabddcdbbdcadbdaabaddbabcbacbcbdcbddbaddaabdcccdcbdbcccbdcbcddbddabdcbabdacdcdbccbadbadcaadddadddddbccadbddbdbaaaaaaabdaddddabaacaacdcdadcdbdcddaacabdbabdabcabadaddabddcbdccabdabdaaacbcbbadbccccdcdccdccdabaacbbbddbccaddbbbabcacbdacacabaddabcaaadacbcacdcbbdabdaadcaccbcdbaddcdadbdbdcadabcbbdddbcadccddacbdacdbabbdcbaabdbcdbadacaaddcccbdbbbbccadaddabdbadadbaabdbcdbcbddacdaacabccabcacbbaddccdbbbadbaacdcadbadcbadcbbbddcabcccbbdddaccdacdcbcbdbbbcacddabacadacaacaddadbbadddccbbbcadbcaadaacbdddabbbdababaabddabbdcddcbbabdcccbcdbacaabbbdbcdaaaabadbcadccdbaadccdbbdadcaaacbaaabbdbacdbacddcbbddccdaacdbcbbccdbababbabcbbabccccaccccaacaccdbbbdbcacdbbdaabccdbddbbddbddacabadbddccdbdaaabcbaaacadbabaadabdddabababcabadddaabcdacadbcdabdddababbcbbcabddcdcddbdcadaadcaddcdcbbccddabaabbccadaaaaaddacbcdacdabdabdcabcbacbcdabaabaccabbddbbddabaaccbdadbabbbdcdbcbdbaacbccdadbdccbdaccdbababdbabadbadbcbbadcddacacbccdbabccdadadbacdccabbcadabcdadcddaccadcaadcbbcbacbdcdadbddcdddbccccadbcaddaccacababbbabdddddacacdbdabbaccaccacdccaabaadccabaabcbbdadadddcbadcbbdddbdbdddaddabbbcccababcbbaaabaadccadbdcadadaacbccaaaadcdacbdcdbdccdbbbcddacdaacadcdbadbbadbadccbabdddddbdcddbcbdbacabcdbaaabccbabbdcdaabccabdccacbdababccdbdaabaabbcabbcddabacadbabbdbdaaccbdcaccdaaddddbbabcdadaadacbacdbacddbbbbddbacacdbbccdcaccbacddbcbdcbcdcdaadcacdaadbbddbddbcadcdbcababbabccbcbaccbadcaaaaacbccdabddcbdcdddbcccbbcbbccadabdadaaddcacdacabccdcaaadaadadcbdadccbdccdbcbdcacabdbadcbabbdcdcccaaaaabadbbaababdbcbbabddbacddadbdbbcadabcccacdddccccadbccccacaddcdbdbdbaadcbabbbabbadcabdaccadcbcdddadabccabccbacdbccdbddcabcbdcccabbccdabadddddbdbadaddcbcdbdcdcdbcdaccaaddadabdaadcdddadddcacbbcdddbbacadcbadabbbcacaacddcbdbbaaacaddcabcdbccbbdcdbacdbcbaddcaaaabcabaaccaddadcbadbbcbaccccbcaccbadddaddbbdbdbcacadcbbcdaaadbdcaacbbdaadaddbabaaabaacaaaadacabddcbbccadcbcdbcadcbcbdddcdaccbbdaadcdadcbdabdccaabbaccacadbbaccbbdacbdddbdddcdbdddabcbbadaacbdbbacccbababcbccaccdcadadcbbbdabbbcdbcbabbddabbbaaccadbddabccacbdaaaababaadcaccddcddadaccdcbbacbbabbaadaaabcaaccdbddaabccdbcbddcbdabcbcdacdaacdbccbdacbadbbaaabdbbbbaacccabbbbdcbddaaaacdbbcbbcaacabbddcbbbaadaccddcdccadbcababcdddadaddbdaaabbcbabaadabcadbcbaaadddbaabcbacddaccdaccbdadabaaadcbdacdcddbdadcadbbcacbdbbcbabbcbccacadadcadddbbbcdcadbcdabaabbaaacbdadcdabdddabdabddcacdddbabaddcadaaaabbbbcdbbbbcdcdcabcadaaddbadadddbddadbddbacdbaddacdbbbbcdbbddbcbdcdbabaabbbacaaaccbddbadccabbbddbabbbdbadaddddbbccdacaadbadacbaadbcaadaaddabccadcaaddbddcdabdbcacdcaadccccbbabcddadcacdcbdddcdabadbbbbccbdbadddccadbcbaddabdabababaacaadcbdacbdadabdbaaadcacccaccdadbcbaabaccabddabbbaddabbcbcdccbbbcbadbcccbcdbdbcbacccdabadcddaadcacbcbccdbcdadccaccddcbcbdadcaccaaacbbaabddbbcabccaabbbbdbcbdabcbddbbdbdcdbadbacadbdcbbdcbccbbbcbcaabdabdcbabbadbdacbbddabcdcbcdbaadaadcadbcbbcbdcbabcdacabbdbbacabadddabccadaaacacaacaccddbcdaaaacbdadddbcdaddbcccbcccbccbaddbddacbddcbadbaaadcdcadddbadacccabcccadcdcddccaabcadbcbadcdbbcdbcccacabbdbcacbaacdcbcbccaccccbdacbbbcdabcadcbcdabcadabacbbacccbdccdddbccacdcdbbcaaddbccbaaadbaaccabcbddbbcabdacbacbbaabacccbcbdbbcbbbdbdcbbdaabdcccbdaaaacddccbbdbacacccbcaadabdaaaaabbabdbbcbaddaccddabbaaadddbacacbdcabccbababaabdaacdadadabcaccdddacbbdcbadcaadbcdaaadcbbdcadcbccbaaddccdacbbacdbaaddadccdbaddaacdadabcadcadbbddbbabacadacadbcbcbadacaaccdccccccccabdccbbcbdabccbccbbaacaabadcdbaccddcdbbddcbdcbcabbaccdcbdbccadbababbadbacbbdcdbacbccccbbdddbdacbbabbddaabbbcacabddbbdaaadcabbadbbccbbbdcadbcdcdaacdddaabcbccccaabccaacabdcddddcddbaccbcacccbdbadcabbdabaccaddaabbbcddabdcbbbacbbacbdaaddcbcaabbccdabbddabaabddcbcaddccdbddbacadbdbcbbbdaadcbbcbaadcddabaacadbbbbdbdcdaabcabdcabcbabbbbccccdcccdaaccaccbcacaabcbbcbadcaaddabddbcbbcacbdcabccaabbcdaadcabcdaddaacbaccaacddbccadacdcdbccbdbccaadaddabcabddbacdbbdcdacbaacabbcadddbdcdbcadcaccacdcabaaaadbbcbaddcbadddcbbcaabbbdbdadaaaccbdbdcbabbdcaccddbddbaccccccddbdaddddcccabdbbcccbbdaacddabbabbbcccbcdaaadddbcbdbacbacddaccbbbbccdaadabcdaabdabbdaacdacbdddbbacddacdcaccaabbbdbadccacbbdbddddaadccabddccbaccadadcabcbdadabbccdbcdabadcdabbbacaacdaaadcdabccbaccacacacaaadbaacdddcbadbbdaaddcccdcbcaccdbcbcdddbdbcbaccbcdbcbcbadbcabdbadbdaccdbddaacadbdccddccadadbdbccabbdcdddbacbbdaadbcacbccbabdcbaacbbaccccbddaabdbaabaddbbadbabcdccccaacbccbcccdabadcdbbacabbdacbcbcaadaddcdbabbbcbdcabdbcdaacbdbcaadcbbddaadacbbbbabbabcaadbcaacdbaabbaaadbadcbcababbcdacdbdbbcbcaddcddabbadacccdcbbdcdaabaabbcadcabbccdcbdccdcdacbbdbbccbcdccddcddaaabdbcccdaabacddcabdacacadcccbacddcaccddbcabcbbaddbddddaadddccddddaacabaccbcddddaddbbdaacdccccdddccabbccbabbddccbccccdddacaccdddbcbabdbaadaaadbddaddcdabbbccbdbbabdadccabbcccbdcdabaacbcdddaaabbaaabbddbdadbcdadbcdbcabbababbccacbcadaaddbaacabddaacdbcccabcdabaacabccbadbdacabadcddcdaabbbadabcaadcbddbbddadcbddbbbdaaabdbccbababddabaccbaddacdadbaadbadacbcddcddabaadcdcacbbaddddddccdccbdbadaaddacbbcadcbdacaddaddadbadcbdcbbdbddacbdcdbaadacbabacdbdbaabaccccbadabbcbbbabbbdadacdacdcdcabcdabbcaadbbcabaabcccbdabcabbcdbddababbbadaababdcaaaaddaaadbdbaacbbaddbaadddbdbbcadcdddadbdcdcbabaacdbdbbbdbcacdbddccddcbcdbcbbcddcacadbbadabbcacbdbbdcacbabbdcdabababadacdbddbbabbbbcababaadacacbbabcdacbdcbdbcbbbaaaaccadcdacccadcadbddccbddbccbdbbddcbbdbaddadcccdaaabcbabbccdbadbadcadcacddccdbcaccbcaacdacacddbcaaaccdbbcadbdddaddbabccabddcbdbaccddcdddabbbaccdbbdcbcbbcbdcabbccbcbaabdbddcddadbcbbbddacbadcadcbadbabacbcdccadbdabbcbbbddaaadabddaabcadbaabdaccddccbcbbabbacacbbadaadaaadbbbbcdddcbdcbdccaabdaacabdbdadbacbdcadbdcbcdaaddbcdbdcddbcccaacddaccdaacbccdbdddbccdcbcddacaacbdbdbbabbdcabccdaacdbcbabdbbbbcddaaddbcaddbcddacdcabcbacbabcbdadcaaabddbabaddbababbbadcddacdaadcbcbadbcddcacddccdacaadcdccbddcddacadcabcababaccdddadcadccdccabaabdaabdaadbbcaadccdaacadddbdcbdadcdbacdadaacdadbcbbadadabbacabbccddabbaccddadccddbcadabcbddcddddbccabaaccdabcbdaadcbbbacdbcbbdaabccadcdcabdcbcbabcbcabadaabdaabdcbccaddcbcaabbcbdbdbbdcdccdbadcbbcccdbdadbbbadaccdccabdaabbbdbdaabbadaaabccbaccbdcbacdbcddcabbbaacaaacdaaaacabcacabdbbccacdddbdbadcbadacbbdbbcaccdbbbcdbaccbccbdcacacdbacccdbdbabbcccaacdaccdcbabbcbcbabbdcaddabccabccbabadbcdbbdaacdcbbbdcadaacdcdaaccacadadbbabdabcabcacdbacbcaccdcddcabdabcdbcbbbadcaadaadddccdcabbacacadcacbbbdbaacddacdbbdacccacbcbccbaddbccbcdddaacccbabcbbdddccdbbaddccccdcbcdcddcdadbbdbcabcacaddcabdcacccdbabdbcbacacaabbacbacaddbabcaadaaaacdbcdcadcaacdadcbdbcbadcdcbdaddaaadbcacdaaacbaabaaabaadbdbcaababaadbdbcaccdaddcbadacbaddaadcddccdbabbcabddabacbbbbccdbbadcdaddcdaccbdbabdaaaaacbbcbcccbbddadadcdaabcdbabcaabbcdbbdcdcccaaccbcddacbdcccdabadcddadadaddcbdaaddbcabdcccddcacbcbbcddcddabadcaddbaabdaaabdccaaaacdaaccdabddadbabcbcacddaabbddabbbcccbcabddcadcbbcccbcbbdcabacdacdababbcdbccadcdcddcaabaaabadabaddcddbbccdcbabaacaadcbbccdaababaaaababababaaacbabdaabcccbccbbdacdbbaccdcabdacaddbdddcacbcadcadcdcaadbdbddbbdcdaccdaabcadaddaaccccaacbcbcaabbbcbbbbbdbddaacdaabdbabbbbbbccbacabdacccbdaaabdbcaacbcccacaccaabadddbaacbcabccbbabbabbdabddcddbcdccdcaaaaccdbacacabbddcabcbddcbabacaddbddcdcdbcbcbbbaccdaadcbbacdcbabdcabbacbccccbdddbabdabcbdbdcacacccbbabbbbaddcadabdaddcadbbdadbdbadcabcdaadcbdbccadcbccdbbbbccbaacbabacabcddacdcccdabbbdcabcabcbdaabbadbcdabcadbacdcccacbbbddcccdbbdcaacabcadaadccbbcbbbadbdccacbbccbbadbbcbbdbbccdbbbdaccbbdcaadbbaaacabddddacbacbcdacaadbccaccacddbccdbbccadaaabcccbbcadcdacdabbaadcdbcbbcaabcdbdbdaccdcdbabcbacbcbcddbdccdbcdcdbbbcacbaadbabcabdaddcdbaabccbbdadcaacdbdbbbabbdbddbdcbbddacdbbadacdcbbbadcdbccdbccddbbbbcddabcaacbabdbbbdcccdadabdacdcbabcbcabadaaaadcadccdddabbcbcdaddabcabcbbbbabbbdcdbbabddadbddbccbbacdcadadadaadbcdbabdabcdadadcabaadddcabcccacdddcddcddaaddcbbbadcbaddcacdcdcbabaacccddabacbaccaacdbddbcbdbdccdcddcdaabadcaaaacbdaaabdbbacadcbdabbcacbabccbacaddccdadaabdacbccbabaddbbdbdaadbdaccabdddadaaadabcbdcbbadabbddabdcabbbbacaaaddbabdabcdbdadaacdcaabcbdbdccdcdccbcccbbcdbbbddcdacccccabbadbdaabdaabbbbdcddbcbccddcdadcadbbadacddbbcadaccaadabacacaaadbbaacdaadddcccbcacacaabccaacaddadbacbcdddabdcdbdadabbddcaddcacdccadbdddcabbbbcbccdabcaadadcbbddbbddadbacbcbcdbabaaadcdaddbdcbacdbbcbaabaddddacdabbdcdccbcaabcccbbddcdbbabdbccabbcdcddbbaccdcabaccbcddbcbaabcbccdacbcbcbdadabdbaacbddbacacaababaaccdcdabcdabbbacbddddbcdabcccccaaddabdabdcabddbdaacddccdaaaaadcdbcbbbcaaabaacabdcbadbabcddababcbaaaadcbadbacbbccbdaaddabbbccadccddbcbacbaadddbdaddcccbccacddcbcdacbcdbdccbbabbbadabdcbcacaabdbacaddbcddbbcdddcbcdbcbabdbbacbdccdddddbdcdbcbabddbbdbdbaadbdacdcbccccadaadbcbccabcdcadcaaddddbdabdacdcabdcadcddbbdbbbccabcdcccaccabbabaabdcbabccccdcddabbaccccaddbccdaccdabbbbdbcbbbadbcdcababbacacacadccabdaabcbbbdbdadacdcaabcaaacbcdccaadcabaddacdadaabddaccadaadcaacdaddcadaaacdbcdadcbbaaaddcbababcdcdaaaccadcdccccdbbabbbdcdccddbcddaacbccabcadbbbbcbabbcbadcbbcdcacacccdccbcdccaaabbbbaabadbcddcbdacdbaddacbabcbdcccccdccacabcbdbcabcbaaabbcdcbddaadaadacdcacadabaaadadbdddbdcdadcacdaaaacbcbbcdabcdacccaaccaabdaaacccdcbbbcdbaacbadccdcccacbbdcaaaadabbaaabdcabbacacbccdbddbcadddbcddbcccdabacaaaccdddbdcccbccbdcbccdcaaaaabbddcdaddcdabaaccdbdacbccacbadbccbbaaacaabaddddacabbccbaabdbaaababbdaabbbaabbadadbabbdcdadddbcddabbbcdacdaccabcbdcccdbbbddcabaabbbaacbaaccdadbbbbaddbdadcdabbccbababadbdadababbdbbdadadbddccccbdbbbdaddbdddccdabbbccbbaddbccdbddbcbdccbaaaddcbdacbaddcdcdbcbdddbddccabccbadbccddaccadccbcbaaabcacaabcacbabddbacdacbbcaacbdbabcacbdbdcbbbadcddbbaadaadcbbbabbdbcccdccdadaabdadadbccddabbdabbddbcadbcddaaabcaaaaadacbbdddadbcaabdbcbbacacbacdbacbbbcbbcbcdaaabbbaaddbbdbccddbddccbaabbcbaccddbdacccadccaaacabacaabaaabddcbbcbbdbdbcbcbbadabaccddcbbbccbadccaaabaacabbddaabbcbcabcdcbdabbddaadaadbbbadcbcacbbadaccccbcdabacddccbcddaadcdbddabccbdccbababbaadacadcadbcbbbbbabcacdcdbaababbdabbccbdccbbbcaadcaacdabdcdddcabdcdababdccacdcacbbdbbcdcbdaabbdcabbaadccdbbdcddbacbbabcdcbacaabbbbdccbaaaaaadadcbcdcaababcddccbcacadadaaacadbaadbdcbbacbadbdbbbdaabaaaadaacdbcabaacbdbcabddadbbadbccddbcbcbbdabacbabacccbaddbbdbabbacbabadbddcdcbbabcadaacaacbdbbaccbddadccbaccdcbddddbadbbadbcbbdadacbddddcaddbadaaacdcdbbbcacbabadbdcdcdddadadacdbbdcaaadaaacccccbccaadcddacacdccbbbabacaababbdadcadcdcaacacabadacdccabadaaaadadabbbaadccdadabacadcbdbadddbdcdccabdcbdbcddabbbccdaaccacbcdbdcccdcbbddcbdbaaadcbddccdcbcacdcdbcaadcbbbccbaddcdcddbdbdbcddcbbddcdadbcdbdddacbcabbcacacdadcbdbdacaabcdacacbadddbadacadcdabccbbacbaddacaabbcbcccbdabbbbdbcbddabccbcdadcbddaaabbcbacddbacbddbaacdabdcabddcbccbdbdcacddddbbcdabbcdabccbadacaabdabbdbadcaaddbbcdcaddabcdaccdbcbcadadbdbbadcabdababcccbccccbabcaacbddddbbbabbabcccbadccccddacaabcaacbccbbcbaadccbbadbdbbcdcbabbacaaaaccaaccbbcccbbddddacbdbbabbccbaacbacaccbcbbbadcccaabadcdbdbdcadddcdaacbaadbcdbddbcbaabaadddadcbcabdcaabbbadcbdccabdbaabcabdabdcdcbdadcdcacaaacdddbcaabacacaabaccabdadddbbbbacdbacdcaadbadcdddcabaacdabcdabbbbddabacaacdbbcbcaabbddbbccacdbbaacddabccdadaabaabdbacccbcabcddadcdaddadbddbbbbdbcdcdddbaddcddbacbdddbbbaaddabacdcbadaddabcdcadcaaadbdbccccbdbaacbabbdabacbdbdcaacbdacabcbccccbcabacddbdaccaabcdababcabcababcaccdcaaadcdaadadcbdbdbcacbbcdccabddaccbdabbddaaccbdadbbabadbbaccacdabbdcddbbbbabbcbdaaadcacaabdbdccdaaacbcabcdbbcddacabcacddabdadbacdcdacacddbbbdcddbababbdabccadbddaabadbaccdccdadbdaacbcdcbdcccdcdcbddddddbcddbbacdcaddabbaacbdbbdbcbcbdabccdaabcadbbbbacabaaabbccbdcdbbbcaaddccbccabdabbbbcbbccbbaddabcaccddcddababacdbdbbcbbabdaadcdbaaacacddccccdbcdabdbdacbbaababddbbddccadaaaadabcddbadacdadbadcdcbddabbdabcabdbcddddabddcdbacbddbbbcdcccdbccbcaaddadcdbacddbbbbabacbcdcdacbadddabadcbbddcbacbadacbcbcabcdcdddcabddaccbddcdcddddcdbabcbbadabddbdbcdcdddaadddaaadcaabacbddbdbcbdadbcadbabadcabbbacbdddbdcbdccddabcdddbddadbcdbcabaadbccadddacacabcaadcadcbbddbcdaaadabadabbcacdcbaadcaccccbddbacbbaabdbcaababacabaddddbbcaddbacadacdbbdbabdadbdbdcbddbadaccacaacddadddabadcacbacdadbacbcdadbdbdababacccabdacbddbbdaaddcddccdccaccbcbcbacbddacdadcbadaabaddbbcdadacddbadcddbdbdadbbdddcdcddaaacabdcdcdcddabdcdaadbccbbbdcabcacbcadbccacdabacddadabbcadaabcdbdabdbaabdbacadcdcbcddccbbcccbaaaadbcbbabacdcaabcddbddcbaaadabdaababadcadcbdbdaccbcbbbadbaacdddbcaacbcbcddadbddddacbbcdbdbaababccbbacacdbdbccbacbdabacaaccdbbaadcbccabbabcbdacabddaabbacddbadadbdacccdadcbcdbcdbdcdcaabaaacbbccabddabcaccddcbbbcbcdcadcbdaccdaddaaaaadabdaddbbbcbaadbcbbdaddddabbbcccaabdcbccddcbdcadaabdcaaaaadbdbabbbaddaaadcbacacaababdaddcdacaabbbccdcabddbcabdddacacbdccbdaacacacadcadbdcabcbbadcacbabdbcadbdbdacdcbbbcdaddadabacdadababbcadadccddbabdaacadbbdbabbabddcadadadccddaadbabaddbccacdbcadcccaacbbcdddabaacdcbcbadcddbbadbabcdddabdadbabbcbaaacaaaaababccdabdabbacabddaaacaddcccdbdbcacaabddabbdcaacccacadcddccbddbadddbabadabcbccbbdbabbdaabdadcadbddbbbaadddadcbcddbbabadcaabbabacddbbdbbdbbacaabcaddcbbbbbbbddbbdaadcbabaaaabcacababcdabbcbbaadbabdacadbbacbabcdacaaaaadaabbdabddadddabcbdbdadbddcdadddcccbcbadbbcadaadcdbacddcbdbadcabcbdcbcadcbbdcccbbccabadcddadabddabcbabcdbadaccdaccdacbacddaadddabaadcabbcbcacdddbdaabbbbbbddbaacbdbcbdbbacbbbbcdcbbbaaaccbcadccdaabccdbabccbcdccacdabacbbbddcacdbdbdadbccdadcdccdddabbaadbccbdbbbcdbbcadcaadbcabdaadcbdacadcdaabbabdadbdbbaadadadcaaabdcacbbdaababbbdddcddbbcdcbaadabaacdcbacbbdbaddbacbcadcdbcbaddccbaacaddccdcbbadcadbbaacdaaacbcbddcaaddacdbbbdbcbbdbcbbbaaacdaadcdbcadbaccbbddadcdaabbbdccaaabbcbbdbacdabbbbbdddddbcbdbcbdaaddcacabbcdacaddcaccdddcbbcbadcaccadddadaaaabccbdcbdccbcddbbdbdaabdbdcadbbdcaacdbbddbcadcacadacacacaacbcdcdcacabcdcdcbadabbbabbcdadabbcddbdbdacabbbdabcbaacdbddbddcaabdacbdbdadddbdbcdaabadbcdcaaaaadcbadaccdbcabcabcaabdddcdbdbdbadcbababdbacaaacbaaabdcbbbddddccbdcabbcadacaaaabcbbdabccabdaadcadbadcccbbbbdbdacacbbdacccadcdbdbddcdbbbacbbcacccbdaadccddbcdcbcdcdbbdcdbcdbacacaabbbacaddddcdbdbaaacddaacdbdabbdabbaabbdaacbadbabbbadbbdbccbbbbbcbbaabdcabbaabddaababddbcdcdcbdacdbdcadbadaabacbaaddadbbccbdbabdabdacadadcaccdaaaaacaabdddaaaabbaaabcdcbcbccaadbcbcbdaadcbdbbcdddacaabaacbccacddddcbbabdacaaadbadacabaaccdcabcbaaaddbdddbcbdcbddccdbbcdbbcbaaaaccbabaacccaccacaaaabbabdcadbbcdbdbdddbdadcdbccabbdbaacbccbacbaadddabcdccbddcaddbdababaccbaddcdbbacaacabbcadccbabdbadbbaacadcccbbabcabbaccdbbaabcdbaddabcdcbdccadcbacacbadbdbddabbdadbadabcdabaccaccdabacdcadbbbbaccbababddcbbcadcaacaddddacccdcbbccacccdbccdbbdadbdbcaddcbcbdbdcbcbdcbadacbdbbdcdcadbbbacdbbbcdbdbdadabbaccccccbbdacbdbbadabdcdcacaabdaabcdcadddbdbbdbbbabbbadbccadddadbdcaddbcdaddbbcadccdbaababcacddacdbddbddcdccbdbbabccbcdaaaababaaccbccadccccbadbabdcdcbaccbbbcacddaddcddddcaaddbbbccaaaddbcccbdcdcccddbcdcabccdabacaabaadccdadadacbcbddbcbbbcbddbcadcadcaadabdbccccbaabccdaccddbdaababcaadcbabccabcbacbbcccbdccbcdbabcdddcbaacaaaacddabaccabdbbcbbcadccdaddddaddbbcccbacacdddddcdbbaacabddddbcdbcadbdcccdbbbbcbdccdbddaaccdcaccdccdcbdbbacbddabaccadacbcadabbabcbaabdbbbcbcdddbabcabddbdbdcbabddbbccdddbdddbcbcadcbacdcbddbcaaabddcdccadcbcbaadaabcabbbdddddcccdbabbbddaadaaddcbddbbaccdccadbcdbcbadacbcbcddbaabbabdbaaabdbdacbdaabdadbdcdddaadaaaccaccaadabddbaabbdbcaacccdbddbaddccbcddbcccbcbdbcacadddbbaacbddbcbcacbdaacccdddbaadcbcbddcdaabccccbdabcbdaadaabdcdacbbdccaadddcdadabdcbadbdbaabdbdabccdbbabacadacbcbdddcccdbdcaaabdbdcbbdccddbddcadccadacbbdcbddbdbcbbcddbcdadcbcbdcbbbacacdabbddabcaabbccacabbccdcabadcdcbccdbbcdaaabaccabdcabdbbbcdadcbcaaaddddbdddcddadbcbbcbbbcacbbaacadbacbcaddcacbbdbbcdcddabdcbadcdcdcbbacddadadcaddbaccbcccbabdacdacccccbbacdcdccabacadaccbaacbacabbccabbdaccbcbbcbccabcbddaabbbbcdcacabaaaccbccadcbdaccadbcbdacbcdccccdaaacbbbadabbdccbaddbaccdaddadabdabacaadccbdbabbaaccccdddaabadddaacaaaadbddaadbdbdbdcbcbdbdcddbbcdccddbbcddcdcdbcccdcdcbdbababadddbbadbcdcbcdcacdcdbacddbbbdacdabacadbccadaabcadbabccacdcdcccaaadccdcdacbbcccacabbdabdcddacdcdccabcbbddcbbadcacdaacddabaddbaabacbadadabcbccbccbcabcbdcdaabaaccabaccdbcaacacdddbabcadadddabdbdadcbbdabadbabdbcaaddcdbbbdddbabbaddbdaddcdcddbbcacbcbdadabbcbbcadbbddaddccbbbbadbbcdaccbcbdccdabadcadcbbddcdddbaababddddbccccadbdcadbccdacbdbdbaadaacabcbcabbcbccbdcdddbbcbbbcddcbdbdccadaaaacaddcaaabdcaddcabdcbdabccdddbbabccdaacbdbaaddddddaacbabaaccaababadbbaccbdabdcbdccdddabdacbcdabdbacacdaadacdbdccdbcacbadcddabcacdcdcbbcbbdbbcddbabaddcabbbbaccdccdbbddcaabaaaccdbbddbcbdddadccbcdaadccbdddadbbcbcbbddddcacdddbcbbcadabdcacccddbbdcdabbadabdcbdbbdabdbaabbaaaddbcbbbdaaadbbbdcadcbdbddabdabbdabdcbaabdacaacacdccbddcadacdbcccddbdcdbbcdaccdccbaaaddccdbddcbbdbcdbdbcbdcadbacaaabcbdacaddccbadacaddcbdacbbadcddbdccbccaaccacacaaacbbccdadaabaddbdcaccddcccadcbadbbaddbacdbacbdccbcbcadababbbadadbadcbddcaaadacddbbacbaacdadbdcbcdbdbbccdabdaaddcbdbcbcbccdadbccdacabdcbabcdabdbbaadadccbaadbacadacaddaccbacddcdbddabbdbdcbdaddbcccadcbdbbcbbccdcbccdbbbabccbdbcabddcaddbaabbbaabddabadaacadabcdabcbbbcdababdccbbdabddcacaccbbbddbbdaddabcbcdaaaccdcbacddadcbccaaaccacbdcddabdbbdabbcdcdcddbbcdcdccdaccaadcaabccddaabaadddacbaadcccaacbacbcbbcbcacacddcaadbbbdaadbcddacdbcdbadacbcdcddbcdacadcdddccaccaacddabdcaccddcdddbcaaaccaadcdddacdacddbbddddbbdacdcccdbaccadbcbcdaaddbccddbbbccddadddcdabbbbdbabbcdcbdcdddaabbaabadbaccccdccaaddabccaabddbabcadbaabddaabccadddadcaddbaccbdccbdbddcacaabdbcadbcddbabaddbcbabbdbcababddbcbbcbaddbbbadddcbbcdbaccbbbddabdabcaccbbdbbabcdcbabdabdcdbabbddacacabbacbaaadadccdbabaddddbacdcadacccdabbabccccadaddbacddadcdaaddbbbaacacacadbaadbacadcadbaabdcaacaddacabddbabbbdcbbabdcaaaabcbdbcaaddcbbbdcaddbbaddbccaddbbdaaaccbadccccdccdacbcaccbdbbccdbdaabadadadbdbaaaacbabaadcbdacabcbbbabaacaaaddcbaabaddcdcbdddccccdbabbacdbabacbdcddaccbdbdbddbccadcdcacdccbbdacbacbcbccddbcacadaacadbdacabbbbaaabbaaabdccddddcddddbadadccadbaabcdcbdddabcdbabbadddadbddcbcbaccdadabadaccbcbcdbdbabcdaaacdcdaaabddcdaddcadbbdbcccdcbadcdccbdabcdcddabaddcaaddadbdcacaabbbbbbacdaabbcdcbcbcaabadcaaacabaadabcbcabacdacdcdabcbddcacabdcbaabadddbcdcccddadaaadaccbcdbabcdabdbbdbcbdcbabdcdccbddabdcabddcdaabcdaccbbdbdccaacbcbadbaabbbdacadcdcdaccdbcdcabbbbddbbdacadadcddbbbddbbaaccbbacdcdcdcaaaaaaddcdcccdcdcdbdcccdbdbdaababdcdbdcbcddabdaabbcadccddccabbabdbcbbdbcacdbcbcdcaaaabdbabbbbbacbcdddbcaadabaccbbbcccbbaadabbdbdaddabdcdcddabdcbbacdddbaadbdababbaacbbcacbbdcbbddcdbbcadaaabbcaaacccadcdbccbcaabbaabbacbcdbdcdbadadcabdcbadcaddcdbbaadadbcbcdbababbcaccaddcbdadcbaadddddaccbddbdbbdacaaabcadcacadaccddabccdcbcbdcdabdcabccaababcbabbaddbaaddcaadcaacddacaccbaccadaabacaacdbbddbcdaaaddcaccccbabdcdabbdbabcdbdcccbdaacadbccdcacdcdcbbaadbdcdbddabbbccbcbbddaaacbdccaadbdadbbabababacdbbaccbdcacdaaddcccbbdcbaabaacdbdaadacbadcacbabbdababbaacdadaccbcbdaaaadbdababcadacbddacdcbdcbdccaadccbadabacdddcadcdcdaabacccbcbaadcbdbabcbdbaaaddbbbdbaaccddcdaacdbcdbadcaadbdadbbadadbcdcbadbaabcdcaaabbaccdbabaaadcacabacacadcccddcabbbadcdbdadbadbdabddbacdcdcdccabbcccbddbcccadbbdaacdaadcdbabddacdacdcacdbdadbcaacbcccbbdadbccbcaabaddabbbbadbbbcdcbbdbbdddacbaadbacdaabcbcbddbddcdbbddddbacdbbddcbdbcbcbccdbaddcacdbadbaadabbcdcaacacccbdcdbdcabbadbadadccbdabbbacccaccacabaacbdacdcbacacdaddbbbccbcacddabbbabbbbdbacaccdddcbbdbddbdbdddbccdaaadccacdbcbaccadbaaacbacaadcbcdabdcdbaddbdcccbaadcbaddbbabddadcddacbbdcccbdaacbccdaaadccbdbccbdccdddbaaaadbbacdcdcdaaccddaadbabbabccbacdbcbbddacbbccbdbddaaddcadccabadbbbbdcccdadcacaaaccccccacaacbdbababbddcbccacccacbaacdabcddcbbddbbcbbbbcdacadabbddabcbaabacacbdbdbdaadcbabaaabdbdbbdccbabbddccabbcabbadadbcacaacabbcbcdbbdbcbabbadaaacbdcbdadaccbcacbcbdbadcaaccdcdbcdaddcdccabdddabadccabadcbdbbbbddcdbabdbadabccdcccababcbadabaaddcbdbcdacddbbbbbddaddaabaadcdbcaadcbaddacbaaccacaabccabaaccadbcddcbaccbaccbccdbdddbddbdcbabcdacdbdbdcdacccdaaabbbdcccbddaddadddbacbadbabbdddddbcabcdcddcaabbcbabdaaaddbaabcaaddcbaccabcbadcbacccaddbacddaaddbcacabccaadccabbcaabcbddaddcccdcbdbdbdcdbcabaccbbcaadbaddcdcbccbdadbcdadbbddaaabadadaacdcddabdbadcbdccdbbbabcadcacdbdaadabdcbddbccddcbbbccdaabdbabaccbdbabacbdbcbcddcbcabbbddccdabddbcbbbdccacbdcabbababadaacccbcbccbcabcdddacbdcbbcbccbcaaaacdacdcccdbbacddbddadbdaccdbabdbaddcaddaacdabbbdbaddbdcbaadaccbcdadbccddcbabcbcabbcabbbadcbcdcbabcaacdbdbcdccdcdcadddbabbacddccddcabcabcbdaddaabacaacbdbdbbcabbcddbacddcbacdcdaadbbaabcbcaccacddcadabaccbddbbbbbdcddaaabddcbadbccaacdccadadbcbdbadaadbaaddccccbabacadababcdacaddbbbbaabdcbadbcddccddddcaddbcccacdaaddaadcabdbaabaccbbaabbaadccbaaccacacaabadacaddbbcbdbababccbccddbbabadacbccabaabcbddbbabbdbaddbbcddcddaccdccacdcbdcdabbbacadbaddcbcdbccddbbabdabaaddbdaddbdaccaccaccdbadddddcadbbbbdbdbbadcbddddaccbcbbbdbaccddaabcbcbaabaaadcccacbbacbdaacdbdbcddcbcdbacdccbaaaaccaadaabccccdaadbcacdaddddbccbcbccaadadabbddbabbcabbdbabbbabcdcbdcdcbdcddddaabccabacbbcdaaddacbdbacbbaaddbcddaaccdbadbbdcabaadaddccdbadbadbbaccccddabadccdaaaacddcdcdcaaaacddccadcababddabbadacdacadcaababbaaabcabbbababbdccccdcaddcabddddaacabcccbdadadcdbdbdcaabccdabbaccadcdddddcbccbbbcdabbbacadcdccaaaaabcdcacccacbcbccbbdabacddddacbcabcdcacaabaccdcdbdaaddadacdcaabbabddbdbdacdcaabaacbdadbbbacbbadacdabcdccadbbcbcdbcaabdcaaabdbcbddddcabbcbaaaadbbbaddbddadbbcdbccddaddbacbbaaaaddbddbbcaabdcccbbdbbcaddcdaabbaaadbbbddaacaadcdcdaaadaaabcddddcbdbaddbcaaadccbabddcaddaddcaaacacaaaddbaddcdbabacadbcadbacdcbdcdabdabdaccbbdcdabbcaabdcaabbbbccdaadcaaaadbcbddbadcbdcaacdacdcddacabbccdddabaddabbcdccccbcbabddbbabdccdbdabcbccbaadbbdabbcccccddbdcdcccccbbdaccacccbbcddddbcbbdadbbaabbdcdaccdabdbcaacccbacdccddabdbdbcdccaabdaabcbacbccdadccccdbcadbaabbdbabaabdabaddcbdadcdbdcbbbbabdaccbbcbdcaadbddbccacddaaacdccdbcdaacdbcbbbbbcbdacbbcadacbcdddaadccaccdaddddddadbdbdadccdbccddcbddababbbbbabdbcadddcacbddaacddadcabbdcdccbacbcadccbbbccacaabcdcacccbbdabaadaccadbccbaacdadbaddaaadddaaadcaabbbbaccccaccdcccdbddabbdabdcacbadbacaccdaccdaaccabadddbccbdbcaacbbababaddbbacbbcdabbbcdacabdabcabbbcdbdddbcadddbdaabbddbacadbbdcdcdccdbdccadccabcaaadadabadbabbcdcbcdbdcbcacbdcaaaacacabdccabbadcadabddaddbcdddbbcabbadddbbbdcadbaccdcabbcdcbddccbadccddbbcddcbddcdadbbdcccacddabbadcbbbbbcbdbbbcdbccadadbcdabacbbdacccaacbaaddddacadccaadbdabbcbbbbcddaaccccdccdabcccbbcbcbdcbbbccdccadddbadcbddaacaaaacacdadddcbdacabcaabbbddcbcdcababcacacccdacabddbababbdbabdaccdccdccaaabdcacbcbabdaacdcaaacddcccddabdccabacbbdcabbbcaadbcdadaacacdcaacbdbdabbadcaacacbcccdacdcacacbdaabdbbbbdbdcacbabaacccbbcddbddaccbdbbbcbadbcacccdaadaabdbcacaaadbaddaabdbdbcaddababcacccddccdddadcbcbcadacadddbadbccdccbbdabdbcbcacbaadddbddacaabbcbcabbbacadaabaaddaaabbdadccdbcdaaccbbdddaadadbdcddddcacadbbaaacdadabacccaadabadabbacbacbbadaabdcdcbaddcdbccacaddabadbdbddcbddcccdbbddcdcaacdbacdaddbbcdcaacacababcdbadcddcbdbcbbdbbabddcbabcdddadbdaabdadacabcbdcdaabcbaddcacadcdbcaacccddcbacdbbaaccdbbdbbbbabbddadcacbabbbbbbbbcdadbabddabaaadadcbbbddcdcbbcdcbbabcacdaccbdcbabbadcbabdabcacdbcaaaacbdcadccbbcadcabdbcbcdaabdcdabaabbcbadcabdaddbcdcaddcbcddbccabbbbabacccbaaddcdabcaaccccdaaacdddbdbcbaaaabcbdcaababdcdaaacddabdacdbbbbddcabcdaadaaabcabbcddabbabccbcbbaddacbddadadadbaaddabbbcabdddaaacbdcdbddadabbaccdabacccaaaaccbadcbabaabccacacdabcbbbccdadcbabdccdddbbcccbdbacabcbddabaaacdddcccacdacbacdbccdcdbdbcaacabddbcacdacaadadaabdccabacadcdbcddacabdacbabbcbbaaccbddbbdcabcbbdbabcadbcbaaacdbbbbbbddccabdcaaabddccacaadaabbdabcddaabbbdbaddabaabaadababdcacaaacbadddadbbbabbaccbccacdaccbaaaacdbdadccacdcdadadcaddacdbaccbbbbbadbbcbadccaaaccbacdbcadbaabbbbdabbaacbcbbdadaadccccabacdbacadaaabbcbdabbacaaabbaaddcdacbbadbdadddbdadaadcacddcaadbcacddaabddadcabcbaccaadbddccacdbacaadbbdbdacaabbacacaaadadddcbacbaaacdbbdcacdadccacadbcabbaddbcdddadbdbbabadbbaaacddaaaddbbabaadcdcddccadaaccccababadacdcdddaccbdacbabbcadbbcdacbbaccaacbbadabaadadcbbbabcaddaddddccdccdbdbcdcaddadabacbddddbacaacadddcdcdcacaccbbdcbcbaddcccdaaacbcddbacdccbbdcadbcbccbdaacdbbddbddadcacdcabdaaacdcadcccbabaccacbcaddbbcbdadacaacacddbbbcbdcaacdbcacabcdaacbddacbcbcdddbbbcdcddbbdaacbbaadbbaabaddddaadadbbacccacdbcccadabcadcbaddbbadbbdccadbadadcaacbbdcccdcbabbbbcbaaabbbdcbbbcdabbdccacbbadacaddcdabbaababbdaddccbacadbabdbacacabaacbcddbacddaaabdacabcdcaaadcbdbabdaacdaacccbabbacbabcabdbcbacddbbabccbcccdadbbcddcdccddadbbdaccaadccbaabddbabcbccbccbbadcaddadcbababbacbbbcabaaaacbbdddbdbddadbdddacddbabcaadbbbccbdcbcbaccacbbaacacbabaacbdcdcaadaddccaddcbdcbcadbababbbbcdcabacaadbbaabdbccbaccddbacddddbbcabaacdaabcbaadacccbcabbaaddadbcadaaababdaadadbaccbccabbbbcdabdabdcbdcdbcbabcdddabcdbbbcbacacbbcaddddcbbdcaababdbbbcabbcdadcacddacdaabdbaabaaaddbdcbbdbbabbdcadacbaacccbadcbddaacbaabcddbbdccbbcdbbaabbaaccbadaabbdbababcaccabdbadcabacaacbbcaacbccddbcaccaccadddacacdbaacdacbaabdacaaacdbaccdadbcbcccaadcbbbcadbcadcbbbddabdcdacddadcbcabacbdcbaabadcabacbbacccacadcdcddddddddadccaacadcacadabcbaacbcbbbbbbdcabadaacdcdadbaccccccbbccacacacaacdcdbcdbcadadacaabbcbcadbadbdbdbccddaabaaddaddcadcacbbbbcddbdbcaaabdddddbccddbbcaacdddccaaacaabbbdcddcbdaabacbacacacbaaacabddddcdadcadadbccddbaabcacccdabcbdcdcbccdaccdbdacdbbbadbdcddddcbcbcbbccdcadbbbccabcacbaabccabadabbcbcdaddddadcaaaaadcddbaaabdcbaccddbbbcacaaadbdbcdbdaccccccabdbdadacbccdbccacabcabcdbbaccbbbbcaacaacccbdaaabacacdbbdccdcadacdabcbdcbdacbaaacabcbbacdddcacdbadbcbdadaccaacacdbacabdbcadaccbbcdaacbbdabbddbcbdddbbbcbabdaadccbdccbabbadcbaabccabdcccdaccddcbdddacbaaacddcadacacccbbcaadbbadbcbabdabadccadabcbbbbcbcdaaabcdcadbdccbcbaadbcbcbabdccdcbbdcbaabaddbbcdccddcbcdcdabaacdaadbbbbacbadabaddcdbbcacdccabbcccccddabccbdbabdaadadbccabcccdadbbacccbdacbccbbdcbbdcbcadbcdccaaaadcccdbacbbcbbacdcdccabaccbcbdabccaddcabdcbdbdbabadadaaddcaccacacbaaaabcbcaacbbacbdbcbbdbdabccdbbbcdabbcdbaadaaccbcdccddaacdbadbadaababaddddcdddddaccdbddabbadadbbaccbdbacbbcdabddbcacdbdcabddcdbdcbbdcdacaccaccdccacabdcbddbccbbddbccbccdcadddababadddbaccbcaaddbcbdaacbadcdabaddacbacacbddbacbccdbbbbabbaacbaaccbdbbbdabdaadabdadbbbdabdaaabbbaabcacddcabddcbdccbbddadacbabbabaadcbdcbabaadddbdcbcdaabbdabbaddbcccbdcbddcabbdaacadaaaaccadcdaaadcdabcbbcbcbddcbbbdadbaadcdbacbdbbbdadaabbdaadcaaadababcaabcaabdacabdccdaaccbbddabbabddcbdbbaaadbadaabcaadcaadcbbdaacddbbcdaacaaaacddcabdcddabaadaabcddbaadbaacacbbadccadbbbcaabacbccaacccadbbcccabadccbcaadbbcdacdbccabbbcdcbdbdbadddabcdcbdcdcabdddaccbadacbbaddadbabcaccbccdccddcabdcbabbbdadbcccbaccacadbbbdbcacddddbbadcdcdbdbccadacacccbbcdadcbdcbaccdcabbbadaddbbcaabbddacacadcbbbcdacabbddaccbabbdbdabbdcdcabcaccbadccbacddcdcaadbdcddaababadabacacdaabaacbcdcdcbcaccbcabcaddbcdcaaacccccaaacccdcdccbabbbcbccbdbbbbbaaadbccaacbdbcbcccdccdbacccaabbddabaaaadaadcaccbcbcaddacbaadaaacbbdbaaacaabbbaacdbacabddccddbdbcdcdbdcacadabdabaababcdbcddcddcabaaadbdbbacdbdcdadadaccdbdadcabcbdcaadccbcabdddacbcaacacddbbbadbacacabcaabdccbabbadccccdaccbddbbcccbbcacabcaccacddabdcdcccdaabbcddccbdccadddcabcacadbbcadaadbcdbbcbabaccdbbbaddcbcddcbcdcdaccbccccdadbaaabadcbbcdbaaadbaaacccbdacbbcbdaabcaadddcccccaccacbcddcdcdbcdcaacaadbabacabaadacababcdcbbcdddbcababdaaddbccbdadbadddddacccbdadadabacbaacbccacdcddcabacdaccabaddbaadadbddbcdaccdddaaacdcbaacdcabacdcacadbdacaabdcadbdbbdbbcaacbadbbaaaddabbcaadbaacbddbcdaabbbcacdccbcaaaaddbccddacdccabcadddddbbbcdcdbddcabbbaccbddbbbbdbccbdaccbbacaacbbabbcacadabdcacabdbdddccdbcaddcabddaccdbdaaadabbadbdbdabcacacaabbcdbabadbdbbdaacdabdcacbbbaabbcdaabaccadbdcdbccdcbbaadaaaccaacbbcddcadcdadabcddbaaaadbbacbdacdadcbabbadbdcddcadcabccaaaddccbddbbcbbcbbaddbcbbddbdccacadbbdbcacadcaaacdcdabcdccbdcdcccccaabcbbbdccaaddacabbbccaaccdbacdccbccdadbbbaccdcdabddadbdbbdccacbbcacabdccddacadcaabbadbadbcbcdabdacbcaacaaabccaabcdbaaaabbbdcbaccbabadcacaabbbcddcadcbddcccdddaddaabaaccddccacbdbbadbdcadacdbbccbacccbdcabcdacbbcddadacdbcbbbddbbcbdaabbaaabbbdacacccdacdcdcccacbaddabcbcbbbbdacbabaacdbccdbcababadacbbdacdcaccbbbcdccdcbbadaadbaddacccbdbabcbaadbdcbaadbacccbadccaadcbabdbbbabadabbbdccadbbbbcbddbcacaddaabbdaccbaaccbcbbaccacaccadcbcbdcddbacbdadddacdbddaacdbbdbababcdbbcdabcbbaacdccccaaacdaacabcacbccaaaccbdbcddaccbdbbacbcbabcdadacdbdbdacadbdcdccadcdccaccabbaaaababcbddabdbaccdacbaaaccabbcabdaccaabdddaccdbcabddcaddacacbbbbbdaaaaacbabbdcaacbbcdbadbbbaddadabbaddcacdaabcbbddadabdcaaaaaadbdcbdbcbaaccbcacbcdbdcbabaccbdbdabdadaaccbcaccdddddbdadcdcdaadabadbddaadbcdbcccdadcabdabccbacbbadcbdacddbacbdcbbcbaaccaaacccabddccbbccdbdccadbdababbbbadbbbdaaccddbaacccbadbdcacababaadcbcdaaadadcbccadacdcddbcaabcddcbadaacadbcaadbbadbddcacdbadcccdacbcacadcbdabccdabcdabddacbadbcacccbccbbbaaaddcbcaaabbbaabbdddbbbdadbdcaabccaaaadbbbddabbadcdcbccccdbabacddadccacbacacbccacdddadbcdbdabdcababdbabaddcbcccadadbbcaaabaddcdccbdaccbdaccdddddccbbadbbacacaaddbcdabcccabbdbddbaaacdbcdbcdacdccbddbbcddcaabbdcdadbbdbdcacbdbdbcbbdbbcabbbadabacdabbbbaddbdadabadcbbaaaddbaccbccbdcdbaacbcbbaddadabbccbddddabbdddadddddadbcbdccbcccbabbdccdcdacbabddccbacdbcadadddccacadaddcbcaddcdcbddaaacbcbbcbdaccdbbdabbcccbbbdbdcbadddaaadbdcadcddccabaccbdadabbacbcdbdddacacbcadccdcaacdddbcbdcacacbcbaabaaacbacbbdadacdcbacaaccdccbadddabccccbcadbccddbabbdaccbddabcadcaabcccbccbdcaccacadacccbadbcabacabcbabdacbcbbcbdbacbddcddbcccaaaddabcdcacdcbcbbccadddddddabddddaccdcaddbbdabadbcbadccdacbcadaadccddbaacacbcdaadbdbabadcadbbdbcabdbcaccdaccbbbbbdcacbcccaacbcdcbdbcddadcdbbbdbaabddddacbadbbcdbcdabcdccbdadaddaacdbaabcbcbadbaabddcdbcaacdabdcdababcbcbdccdcdaabdccdbdabbdabcdabbbaccdbcbcabdbbdcdcdcdcdbdadcbbbaabbcabbcabacbdbaaccadbdadbbcddcddbadbdbdcabacbdbcdbcbdadaadcbdaddcbcddccccbccbbcddacdaabdccdbadcbcbbabcaaaadadcbbcdcadddaacadaabdbbbcdcadaaaadcccdcbbaadabcbdbcadbcaaadcdcddabbbbbbbdaacacaaddacdaacbabbadaacadcbdbdccccdaacacdbabaacabcddbbddaadaadcaccaabbacdacadbabddcbdbbdaacadabdcaaddadadddccdcdaabbabbbbccdbdcadddaddadaabcbdccbaaddcbdcaacbadbbbcccdcdbbdcbaaddacdcbccdcaabbaabdcaaccccadddcbcbbaaddddccbabdcacbaabadbddbadcaabaaaaabcdcaccbacddcbadbcaddcdbddbcdcabbbadabdddbaabacacbdaabaadabacbbddbddcddcbdaddccbaccdbcddadbccbccacadbbabbbbbcacbadcacacbcdccacbbbbdadbdccbcacbbacacdbaccddbbdbbacbcdbbdacadccdccdbbdcddbbdcadacbbaaaadacddbadabcddcdbddbadcdbbdabdadbdadbbbaacabdcabdacaaddaccddbddddcbdbcdbcbbcbcbbcabcbdaaaccbaacadcdbdacdcccbdccbabdbdbbdddadbbcbacdbbdcdadbbbbcddbdbbbaddccbababddabdaaabccaacccdcabbabaaddbbcabbaaccdbdadaabadadbccbdadacddddadaabaabaaacaabacacccbdbcaabdccbdccaacabbcdadccdbbdbccbdabcbdccbcaaabbdabddbdaadbdacadcaababaaaaaacdaaabbaabdacacabdbccddaadabdddcdccdacbaddadbacabdadadbccddcdacdccadcabadddccacabddaadbbaabcdaaadaadcadabdcdcdaddddbaaddacdbdbadabcddabacadaccadccdadccdbcdbccdccbbddddbcbbcaabcdacccbbaadcaaaabcabddbbdcaabddbabaadbbddddddacdacaddcbbaddbabbcccbcdbdacadbcaadaddcbcbddcabbabbbacdcdadabdcaccddaadaadabaddccdcaddbbacddbadacdcccdadbbbbcccccbcaacddacadacbcccbccbbabbbbcbcccbaacdbaddccccacdccaaabcabddddcdadaaabbaadacacabcbbacabaabddbcbbbcdbbbdcdbbcccadbdbcacbcadbbbdaacbbddbcaaddcadcaddbdccbcccbdcadadbdccbaacacbccbdabdcdbcddbbccddbbccdcacdbabaaaddbbacddddacdcadcadbadadcbcdcdcbcabdabbaabbadbbdbadddaaccaacbbcddbdbbbdcbcdcddbcccabcadaaccaddccdbddabacbaddbbdbdcacdabbcabaacabcabbcadaacbbacdbaadddbbdbcbdccdcbabdcdbbabbabbdababbbbcdcdaaacdcacaaddacbcbacdaccbcbdcbaaddbcabdbcddcaadcbdaccaacdabbccaccacacdcdcbbccdabcacbbdcbbdabcccdaaabcdcbdcadccaddcdacbccdaaadababbcacadbbaacadccdbbabbbdaadbcaaaabaddbbbacdccbabdaccdccdddddcadbabbaadabbbdcddcababcacddcaabccacccddcdcccccaaabcbbcbababadcbddaaaddcbdddccacaabccbbaabbbabdbabdbbaabbbcacbbcdbaadabddaacbdbaccaabcadccadbbcabbbcddcacbabbcbbbcdbcbadcaabbaaddaadadaddcaccbaccdbaacaccaaaabddbbbdcdcaadabbdaacdbbadbbcbcabbbbaaacabbcdcaabcbacbccdcbccabdacdcacdcbbbcbacdbaabdddbbdccadbcbbdbacacdcbcabdaccccabaddabcddccabdbcdabbabbacddcdccaccbbdbcbbaddcbcbddbdaccccccbdbddddddcaddadbdcbdacdcaacadccbdddacaababdaadcaaddbacacacdacdbdccddabadaddbdbaadccbcdcbababdcacbdaabbcccadbbabdcccadaacdbaacdabaaaadbbbdddcaddcbabbbdbdbabbdcdbcaccdcdcccddddcacaddccaabdcbdcccddbbbcacdbcbbdadcdbbacabbbbcdaaaddabccdbaacabaaadbaccdaddcbcbbbcacbcacbdaabcbdcaacacbcbcbbbbcbcdbdabadbdbbcadbddddbbadaaadaadadadcdbbdcbdbabdcbcccbcdacaadacabcdcddbaddadaacadcddddcabcdcadadbcbdccabdbdabbcabdbdccbadcdaccdbadbadbadcddbabcddbdbbdacdaccbabaacdddcabcdababddcaacacbcacbcdcbabbaaddcacdcdbcdcbbbccbcccabbbccbdabcccdabbbddbdddbabbadadaabcbddcdcbbbcdbdcdbcaddabdbadcbdbadabdcacddddadddaacbbacddadabbcdbcbbcabaaccdcadccdadaaadacbbcbaaccaddcdbbcacbdaadacbaccbabaaccadccdbdbaddcadaabaaababaacbaacacacdaccbabbaababbddddbdbaccbcccacdcacdcdcccaccbbacdbdadaaddcdabccacdbadabdabccbdccabcadddadbaddcadacacbcbdcdaacbacddbbbaddccbbcbbbcbdadbccddaaaadaddcbccdcdbacdababdbadacdcbdabbdcacbdddabccccbdaccdbbcaabddbbabdcccaccddccabbcbbdcbaaadccaadbaabccccccdbacccabaadbacadcaccbaaaadcaddddcaabdcadddbbdccbaabaccdbaaadccdcdbcdcadbaacbacbbcdacdcdbaddaccadabacbcccacbbddcdbbbbacadbacaaacadccdababddccbddcbdacbacbbaacddadabaadcbccdbabcdadacbbaacabcbadbbdcbbbccdabddadabcccbcdbbbbcbddcbbdaaddacabdcbbbaddbcccbacddcaadaddcbddadbbdbbdcbdcddabdcacaddcdbabcbcbdddacbcabcabcaaaddbcbbcbbddadcdcdddcddbbddccaccdcdcabacbccaabdaddbdbbaabaabcbccbbddcabbdaaddacbbabaddddaddadadbdbccbdbddadcaadbddaadddcdbbbcaccadbaadbcbcdbcdcdcdabcddaccabbbdcccbcbbcdccccdcacbcbdcaaaddaabacbdacddaadcacaccbbadabbdaaadacdcadabccccddddadbbbcbdcbbcbbbcdaaacabcdbadccdacbbadacbcbbcbbaddbcbbdcddccddabdcbadadbddababacdcbccdbbbcbccabacaaddcabaaaaababbdbcbbbdcccadadaaadacddbbacdcbdccccdbcdbbcddbbabcabcacadcbcbdaabbcdcabbcacdccadbccaccabdbdaddccdbbcacccbcababababdcccaacdabbaacdacdccbdabdbdbadbbaddcbabcadbdababdabcddacabcccccaaddacdbdbddcaddbddbbaccdcddbbbdbccaccbdbcddcddbcbdbbdccaabcddcbadcbabdaacacacadcadadbbdadcbbcadaddbaaccbcdaaccbadabdaaccaadacdaacaccbbdcddbbbbcadbdadbadcaddbbaadbcbabddabbdaaabaacabacabdaddccabdbddbcacdccaccbdcdbcbbccacaabcbacbacbddabbbdbacccabccddcabadcdddccccccdbbccaabbaadddcdbdabcaccadddacbcbcdacbcccbcdcbbacbcaaaaabdaccbbaacdccaacaccbcddbacbabdacbdbaddccdbcdbdacabbabdccabbbbbccdacdbcadbcacbabddbcdabbbbaacabbacabcadcdbcccdccccdcddbcbaacaadcdcbcaddabadddbdccbabbbcdbbacdcbaaadadcbabdaccaccaacacaccbcaacadbdabdcccdabcaabccaadbdbadddcabdbbdcadccbaadcbdaacaddccbabcbaabdaadccaccdabbcaabaccdddbddbbbaaddaaccddddbccdcabcabbbabccdbcbcabbbadbdcdbddbcbdadcbadbbadcbcccdabacabbbddddbcabbadbcaaadacddbbcbabaabcadadcddaabdabcbaabcbadaacbbccdbadccbadcdbaacbadcdbaadcaadbbcabacbaacadbcaacbdcbbdaadddbbadbcadabbdddcdadbdabbbbbdbabddbcbddccbadccabacdacbdccadbdcbcdcddabdcbcdcccddbdcdaadbabcccaacaaacdcdcbbbdaabbbbbdacdcabacbaccdcccaaabdddcdcaaaddbacbaddcccbacccbdcdcbaadaacddbbddcbbcaabdccdbabcbcbdbdaacbcdabbdbcdbaaabcdcaddcdcaadcdcbcaaaddbbcacaaacaaaababccdddbddbcdcbdcdbcdddabbbcbcdabbcbadabdbddacbbbdadddbcadbbcdbcdabcdbdaacbadcbbaacdcccacdcddcaaaadcaadbbbabbbaabaddaaccbcbcbdbdcaababccbacbccbdbadcbdbaaabdabcbadcbdccadaadbddcabcbbdbdaddccbbcaadcdbcccdccabbbdacdcadcacaccaccbababadcbddccadddddadccadbccdbaadadbcbccccdbdaadcadbcddbadabcdccacbaddbcdadcddcbbdabbdaacddddaaadbdcbccabddadbdcbcabcaaccacbdacdcdcddadbadacddadcabdcbbccbcddabdacdaadabddcdbadadbcdcacababadcaddbdacbbbdcacccbdddaabbdbadbbccbdcbdbdddbbabbbccddcaadcddbaddbacbcaacabbdcaacbdbcbabddddcddbadbbacadbbbdddbbccdccbabcccacccaccdddddcdcbbaabbdaaabbbcaabddbbcbbbdbbddccdbdbdbcbaacdbdabbcbcbddcdcaabbdaccbbbcbaaabcabbdbaddbddbdaadacaaadaccbdabacddcccaddbaababddabacdadcbabcccdcdbcacdbbcbacddbbaacaadcbbbbbddabaddaaccdccadadbadcbaaddcdccccadbbbbdbcacdbdcddbcdaaaadcaabddaaaabddabbcdabdaadcaabaadabbabcdccadcababaddadbdbdccddacaddcdcdadbaccbaabdbcbbbbdbcabaaddaacdacdadcbcccbcdcacbbbccadccdbadabadbbbacaaccabacbadadbdcabbaacbccbdddcdbaabccdbdccaacbddccadccdddbacbabaaadacccaccdcadadbddccdcdbbccacadbaaaddddccdddadacdcccabbaabababadcccaabcadaacbadcdbcabcacbccddbacadaacddbbaabbcccabacdbadabbbaaabcbadbbcbcdccbbccdccadbddbabaacbcadbdaddbcbacdcddadbbcaccdabbcdaaccdbbdaadadabacbddbbcabcbbccadcdbdcbbcaacdabcbcabdcdbaaddccacadaddbbbbacdbcaccdcdbbaccacbadcbddcdcadddddbbbbabdaaaaaddabcdcddacdcddacdcbcaabbadbabbddddadaabcdaccacbcadbbcdacbccaaaaadadbaddccaaacaccddbbddabacddaaaaaabbabbcaaacaacadabdbabadbbbcccaabcddacbdaddbadcdbbdadccadbcddccabbdcddddcaddcbbcaccdabaaaaddbaaccaacbbbccaccccadaaccbdbacaacbdcbddddaacbbcbbdccdcdccadccccbabbccaccaaacbdccccddbbdcadddcadcadabbdbcaabbdcbdbdadbcdcacadddaadadbdcccacadbbddccbdaabcdabbcacabcbbddcccdcabbaccaddacdbaaccdacdadcbbbbbacacacbcdaadbccdadbdbbaaccacadccccdaaaccdbccbcdbacbdddcccbacdbdbcdbbdcaadcdccbacaaddaaaabbaccdccabcdadcdaddddacdddabbdcddaadcbccbccbdaababcdacdcabdbcadbcbcacaccaccdcbdcccacbacadaacddbcdccadbacdbadacaabbbcbdacbabbcdcdccbabbcbcaddaaacacdadddbbaabbaaabaddcaabcadbcdcbbdbdbbdabadbadbdbdcabbcdbccbbcacdcaadaaacabcddbdcabcdbbacbdaaadacaadcabdbdacdbcadddbcdaacabbdbccddcddbbcdbccacdcccbabbddbacdbdbabdadacdccbaacaaacccaddbcbacadaabdaabaddcabdaccbbddbabcccbcadabbaacbbcbbccdddbaaccdacadbbadaadacadcbdaddadaadacacbbcddacaacddcbacadcabaddccdbbddcddbaabbbacaddacaabdaabdddbdbbbdabcbccdacdacddabcdbacaccaacbdaabcbabddbbabdbcccdbaacbbcdabcadadbbbcbaabddaccdaabdbacbcabdaaacbaddaabdbbcdccccbabbaaccddbaacbcadacadccaaabaababaaaabcdbdbdddcbbbcccccbbcbccbcabadadbdbcccddbddaaddbddbabbccccacbdbbdcabbbdabbaabadcbdbabddaaacdccdabdcbadbdcbcdabddcdddccdabcdbdaacdcdddaccdcddbdbdbadddbcdbcaacbbbcabbbbdcbabbbaadddcdbacbbcbcdcabbdabcaccbddddaacaaccccdcabcbccadcaccbacaabddccbcbabbadccdbacdaddabacdbbdbbdccaccdaaadadcbacbcdaddbcaaacdbabccdabcabdbaabcddbbabdaaadddccbbcadabadaaacabadcaddbaccacdaccaddcdbaddaaaaddddaacbcddcdabdadaaabcddadccbcbcaaaaddbacdbbcdaacdccdbdadcdcdbcdbdabcdcddabbcdccddcaddadbbcdabdbdadacacbdcadcdbdaababccbcdccbaacbabaccdccdadbcbddabaaddcaaaacddacacadbabcdbbcdccadcacadadabdbadccabbadbbadcccbcdbbbcdbbcaccacdaddadadabacdddadcbaaacdcdaddcaabbaabbaadccabcababcbcbbccbadaadaaccdbcabcbacdadcccadcdabababdbdcbabccbbaaacbaabcbaadbbcddbdadaabbccdcbddcccccacbcaaacdacdbbdcacbbacdabdcabacbbbaaaacdacadcbdaababadcdcaacdadcbcbbccaacbdbacdccddbbbcbdacaacdbcbaacbbbbacdccdaabacacccbbbdbccbadbcdbbcdbbcbacbbcbaabcacddadbbdacbadbaacccdbbbaacbbadcdddddacddcccdbccacaccabcdbcbbaccaddadbdadcadadcbdbcadbddbcbbbbddccaccbddcdbbbbbdccbdbbdcbdbbcbbdbdaccbcddcdbcaccbaaccabbababdbdadaccbdccadcbbdcacdbcdcabbabbcbcadcbacdabaacbcaabaacbacbbaccdacadcdbaabaacaabacdbacbcdcaabdbdbddacbdbadcadbbbbdadcdaddaabddadbbacadbdcdcbaadaadbdaddbadbcaadcdacdddbabddbdaabbabdababbbccabdcbaaccbdcbcbdbccbbacbbdabaccaabbdaacaaaddcabbbacbabbdbcddcddccbbacbabdaccacabdbdaaadacaaddaaacbbacbaaabcddddcdbdcadbcddbcbbccbcdbadbcaacdabbbdcaccaacbcdbcadacbabdccbcbcdbcdccabdadbacaabdaaadbddacdabbddbccbacbcdcbaaaddabcadbcdbabaaadbbdcbdbcbccdbabbcbcdadcdaccabbbccccccaacbbbacaadcadcdbcccadadabaccddddcdaaabdbabdbdbddacccccbadcbccbcabbcaacdbcbaccbbdaadbbcbcadcbcdadddcbbdcabdbcabcabcddabdcccdbdcbbbaddcccdbbcdaaddcdddcbaddacdbbcbdcdaababbccaadaadbaaacbcaccaddccabbcadcccaabaababacdbaddcddacbbccccaccbbdacdbbdcdcadbacdcacaccbbdbcacbcadcbbbbdcbaaabacaccdddcacacbdcadaccbbcbbccbadcdcadbcbccbbbaaaaaadbccdddbbddcbaccdadabcdadccdabbadbaaccdbcaddcbcdcdcdabadbdaaaadcadbcadccddccddbdcdacdbdbbacabdaddabdddaabbaabddbdcdaddaddbdabbdbbdabbccdbcddcbbabdacbadbdbacbaaccdacacbcbdddbcaacaabadbcdadabbbcbdcaacbbbbbbabadddbcadbbbcccddbbdbbdbabdddddbbcdabbdbadbbbccdaabcaccbdabdaaccdddacddaddcccaddbacdcdcbaacacdabccbaaabaabbbddddcbdbcdbbddbaadddcbaacccaddccacbadbcdabadadbcdbbaadadbddddacbcbbdcdcbbcadbccbbbadaadabbdcbbcdcbdbaabdbbadddbdcdbdbacdabcccdccdabbccbccbababdbacdbbdcbbccbddcdccbcdaccddaaddbbcdacaddbacddbacacabaaacadbabbabbaccaabadbbaadaadacbddbaacdbabbadcccadabacbadbaadcdbadccadabbabadaadbacccdccdccccccadaaaadacdcdddbacbbbccaaaddadbbdbcddcccddbbaabccadbccbbcccddccabcdaccbbbdbacdaccddcaaabcaabbdbccacbbcaacbdcdcbcaaddabbcdbdbdadbadbcbaabadaccbddacdbcaabdacaccdccbbcbdccbcdcbaaabdcabbbcacaaccdbbadcacdcdbbaabbcbdcbbccbacdcdbbbcccccbdcdcbacbcbaadabbbdbbabababaabcbabcdbdcdcadabaacacdcabcabdddbcbacccabaaabdddbacdcdbbabadaaccadadaabcacbaacbaadbbcacddbdabadbbddbacccddbdcbbabbaccbdbbbacbdbddcdccdaaccdaddddbcdcbabcddcdabcddcbacaccacacdcdaababddbaacbbabbbbcbdbbabaabaddabccbddacbddcabbacccddcdbbdcdaacbddadaccdbabcccdccddbdbabdcaacddcacbbdcaacddacbdbdcbdacbdccbbbbcdabccdbbccdbbccbddcdbdcdcdccdddacccbbcabbdbbcabbcbdcacbcdcaccddcccdcdddbdaacbacabccbcdcdccccacccaaaaddbcbdcdbaddacdbcbddaccbddbacccdaadcaabdbaaaacadacadbdaadcddcdcbccbbabdbcddaacbdbabaaadcbdabdacccaabbbddbadbdacdcbcaccaccacdbbcacabbdabbcadddbdcabbacdcdbbabaacaabcaddbdbccbccbdcabadaaabbcddabcdcabcdacdbcaabddbdabdbbdbbbcdbacddcdbdbcddbacbdaaaaabdcccbbccadbdacacdcdddadcbaabdabdcbaababbbaacadaaacbcbbbcadcadddacabbaadccddcdcdacdbddcbdaacacdaccccccbbbdcdbadcadddbdadaadcbbdbbadaabaabaddcccdcaacacaccabacbdabaadcbdabdaaacdabaddacdadcdcabcdbcdadabdcadbbddcabbbacdddccaaadabdbddcbdbcadbbcbaadcdbdddacdabdcdcbcdbcccdacdabdcacbdbabacdbbdacbdcbacdddbabdcacddbcdcadbcbddbdddcabdddbadcdccdccdabccccccaadaabcabbdcbdcddacbddcdcbdcbadaabaddddcccabddbbacacadbaadddcdadadddbaddbbbdbacbabbcddabdcccbdbbcbccabbcbdabdacdcacbccacaccbdbbdcccdcbbdccbbdbabadcacbabddcdacabcabadababaabbacdadccadabccdabaabacdbbbacccbababdbcadacaacadcadbadbaaacccaacabdcaabbbabdcbcbcadbdbbdcabcaadcdcbacabdcbbdcccbcdadbaddcbabbaddcdbcdbcadaaabadbddbdacbaddbcbbddbddcccdbbbddacbdccaabdcaaaccdccdacddcbcbadacaccaccbbcdbcdcbbadddbddaabbaadbdcdcbcaccbadacddcbbaacabaaaaadcccbdcdcdcbdacbbdddadddaadcbbadaaddbacccdbcdbdaccbccbaddabacaadaaacadbadbcbdbddbcdabcdacdbbbaaddcabdccdabbabdcacaaacdadbdcacdcdccaddccddacbcdbadaaddcaadaadddacadbbbdcabddacacaddbadbadbdcbbbbcaaddbacbbcabcaccabdcbdbddddacbaadbbdbdcabbddaccabcccaabbbbacabdcbcaacdbddcbddacbcbdbcbbdabcbaadbadabdbccdddaccabaaaabadadddbcdcbdcdbbcdcdbdcdbacbadcabacaccdacdaabbcdbdccacbcdcaddddcdabdcdaddbdcaabbbabddbbdbdcbaabbadcddaadbbbbadcbdccadcbccdbcacacadbbccdaaddddbaacddacbbbacabbbcdcccddacccdabbcaacdacaacbbccbcccacbdcdaabcbdddcabbcdaddbacaabdbdddcccdacaccbdccaabdbacacccbadabadaaababbdbaabbdacccdcaadbccbbadbdbccababbaabddcababbbbcdbdcbbacbddbbdccbddaabadcccdcbbcddbadccbcbdabacacbcddbcbcaaccddabbdbbcccbbbdddcdddbdcccaadddcdbdadacbddbaaaccbdddbdcaadacbccccddbbaccaabaaabdddcdacacbbcabaabcbaabaacdddcabccbbbbdcabaabbddacccccabcdcdabccaadbbddbcbcbdddbadaaabcddbbdbbabdaacbcdcbabbaaabbdcbbddbaabbbdaacdaadaabcabdcbaabacdbdbccdbcabdccdcccddcabaadcdaacbbbdabaacbdcccbaddabbbabaadbcdcaabddabdabadcbacaccbabccbbbbbaaabbacabdbabaddbbbdcbadaccdbbdbadacdcbbbbddaaadaaccdcabbbadacdacdcdaaacbddcadcdacbbbaccabaddcacbacaabcddcbddaaacaabcaacabaaddcbdcddcdabdabdabaababdcdbdcbdcbbaaadaacbababbbadddaadcdacccdddccabbadaadaaddcbabcabaddbdaccdcdadadbcdbcbbbacabcdacdddbdbdadabccaabacdcbcdbccdaabdcacdbacaadccdcacbdccadcccbbddcbdbdcbbaddcccbcdaddbccbddbddcaaaddccccaccadbaaacdbcacdabbbadbdaaaadbddbcdbcaadcbcadbabbadadbdbcddddadacbadccbadbdcaaabcadbddcddcdcaaaacddbbccdacccddddcccddcccbbddaadaccadbdadacbcddbbbbaabdacabbbaaabacdddbcbaaaccbdbccccdadadaaccbadddcadbdcbbaddddbbcccabbcddbabaabdccacdbcdcccbaccbdbcdddbcaaaccbcaabaadbdbbadacdaaabcadaacbaccacaabacddacdacadbabbdbdcadaabbcabdcccbdcbdcbddccbddcdbacbaabdadbbacdbadaccabcdbcddbadddcabdddacdcccbadcddaccaadaabaacabcacdaadbbbbabdadbacaacdcdbbccdacbacdbaddacccbddacabbbcbbbcbabbbdaacbacadbadcdccddabdabacbdccbbcdcbcbcbcadbbdbdadcdcdaaacdbbacdcccdbcacaaabbabaaabbbbdcacaabcaddacdaddbbadbaaddababbcddcacaacbcbabbacaadcccdadccdbbcbdccbabbcaabbdadddcdbbbbbdcbcdccccbcaacaabdbaddbaacddbaacadcbacbdabbddbbcabadbcaddbacbcbbbaacdcabbbdbbbdbcacadcdddaaaadcbdbbdbcbdbddcaabcdadcacbcaaaddcdaabcccdaccdadcdabcbcabbaaaccccbacaaababdbcddbcaccabcaacadcbabbbbccbcdaddbcccabddabccbcacdababbdbdbbddcdcccaaaabdaadabbbadbbdababbddcadddcddadbadbcdadcdaadcbaacbccacbbdabdbccbcacabbdacacdbbdadaccdbabbdaccddaacdbadcabbaccbaadbddbbabcbadaacadbccdacaaaabbbbdacabbcccdacadddddcdadaccbcdcbcdcbcaadabcabbaccabbcadabacabddbcbaabddbadaacddcdcdddacdadcccbcdadcaadacbcaccdcbcacabdbcccddcdcacddcbbaadccacdadacacadbbadadcaccbdcbddaacadccbcddadcabcacdaaacdbdbdcdabcdbbaacddacdabdcbaccaaccacbcdbbaabdcbdcdcdddabbdddbbadaddcccdbadadcaadbbaddababccabccabcdbbaadbbadadbddccabcddbddbacbabdaadcabdddccaaaddacbdcabbbaacbdabaaadaacdddacbdaddcaabadcacbdddadccdacadccbcdcbdbccaaacdcdcbbddbdcccbaddcbcacdabcbabddbcdbbcdcadaabbbaadbdbbbacdcabcacacbbaabcaabcdbadadbdddbbccdbcbdacbcacbcdaddddbaabaaabdadabcdcaddcbcdaadcdadddcbbabaaccaddaccddacacdaabbcddaadaccdcdbbaddcccaadacaddbcbacbbdcbdcacadcdbddbccddacaddbddabbddbadddccddacdaacaabdacbbbddadcabdbdcbcacabcdbdddddbbadbbaabbcadacacccbbbcabdcddaaddabcdaadcccddbbddcddadabbbbdbbabcdddabaddcbbdccabdcbbcacdabaddaaaacaccaaadacbbacdccddacbdbcbcdddbdadaccdddaccdadbdadbddbaddddabcbaabbacbdddacccabdddcabbcdcdcaadcaacccdbbdbccdaadadcabadbcabddcadbbdadccccaadcdbcddcbbdbadccdbdcdcabacadabbbbaacaabadbabadcadddbbdbcdbccddbcaccbabdbdacbcdccbbbdcbabbbcdccbdaaabbacacabacbddadcbdcbcaddccddcacaccdbaacddaaccddccdbcbbadccccaddadaddcbbbccbccbbdaccdacbbcddacbbcbddbcacadadadbaadacacaaaccccbbdbccdabbbdbcbbbbcbaacbdddacdbbcaadcadbbdadaaabcbdbbcdaddbaccddcacbdbaaadbacababcadccbddbcccbacadacadcdacbcaaabcbdaacbaabadaddbdbccdacaaaacaddabccdaababbbbadcaaccbacdcabaccddadbbccbbabbbabcbddbabaddbcadaacbcaaaaccdbabdbdbbadabcdabbbadaaacaccddbacbcacbacbbcdcaaddbdbbbabdadbacaacacbdcaddddbdacdbbacdaaabdcbabbdbdacbcbdacbbcaddcacdccdaabbbacbaaaabbaacaddabacbabbcadbbccdcdcbbaddddbabcdaacbadcbbbddabddadbaacdbaacbcbbaacddabdcddabadccaccccdcbbbddacabdaadcbcadaccaadcaaacabccacbcadcbaabcaabddaacadacbcabbaccacdadbddbdadbbdcbcaabbdcaaaddbdbacdcbabbbcadcdbdddaaacbabbdccdbacccaccacccabaadddcadddaacbabbbcadbcaabbdbaadbcbaaacbabbabdcbbbdbcccaaabbcabcaddccdabcbcdaccccbcbaabdabbacaccacccaaaddcaddbccabcadcadbdcaadacadbbabddabbdbcaaaabbaddcdbcbbbdabaadbbcacdbbbabdbbddaaccdadbbaccabbccccdaabcbcbacbbabadddddaadcdadaddbcbdbbdabcabaaccadaddbbbabbaaadcccddcdbdcaaadbcccbbdacbdabcddbddbbcbdcdcbddbddcaacdbdbbaacddcddbdabdcdccbababdbcaaccbaabbcdccdcdcdabbaddababbdbdababaabdbbcdcabbdaabddaacddbdbdcddbcabbcaaddccbbccbadbcdabaabbdbaabdcaadbdcadbbbbcdbdbcddadbaccaaaabcabaaadcbdbcabacdcdacddccbaccbbcaaaaabbadbababdcabcbaacadbcbbbadaccdddaabbaccacabbcdbacadccdcdcacbaabddacdabcadddcbcbabcdbabdbdbbdccdadbcadabbdddaadbdbbbdacacbddacddbddbadbcabbccbdaacbddbdacacbdcbbdcbdabbdacbcbbabdababcbbaabdbacbcbcdddcbaacdbabbccaaaaadcdbdcbdaaadabcbdaadbddcdccdacdcccadcbcccdbadcbddddccadbcccbcaaaddbadddbbbadbadcccccacaaacaddddabbddccbbacccbddddcddaaadbddbaaabdacbbadbbaabbabbddabcdddcabdccaabacbcacacdaabadabbbdbbcccbdcabccaaacadabddbcbddddbdacaadccdadcdacddccaaacadabdbdaacccbcdcbdccadcdabdabacadcbaadaadadbcbdbcaadcaabccbcaacdbbcabaabbadaaaccbaacbadaddddccacbdcdbdaaabbdadabbcbcccbbaaabddcdaabbdbdaaadcaabbdbcbaaddaacbbcbddcdacaaadcaabaaabbbadddccccacabaaccadbaaadbdbabacbcbddaaacbbbcaccbbdddbcabaadddabccbcabcddbbbaadadabdddcbbdaccdabddccbbccdcdcbacddadabbabbbaccccdbadccdddbacaaacbaccdabcdadcaaadbccbbdcadaadacdccbcabcccbddcdbbccbaabcacccbabcddbcddcadcbcccddddccddcbabbbbaabcaaaabcdcadaaadadbdccaadbcbcdbbbcaacccbccdaccabcbcdcdabdddabbadccaaabcbbdccbccdbcccddcbcddabadddcadaabcdcdacaaaddadacaabddcbaccadcabcaddababbaabadddadcbdaadaaccbdadccbcdcdbcabbbbdadbcaadbbcdcdbadbccabaadbacaccccadcdcdcbbdbaadbbcbdadaabdcbcdcbdbdbcbddcbabaaaabcdacabaaaadcabbcbbbacdbcdabcbdccdaccccddbcdacbadaacddcaadcccbcbabcdbaccaacbcdbbaacbbabbbadbbdccccaccccadcbbdadccdbbbbbddccbadbaadccbbbcdbdacbacaaccdabcbacbcaaabaddcdbbadaccaabbcbddbbdcaccbadccabdcdcaabbabbacacabdbcddbdbcbaccadbacacbacabbcaaacbdaacadaccdbccadbadbccaaccdacabcdcdcbcdcddcddaccabcaaaadddbabbcdabaacccbcaadadacadabcabadbdbaabdacbcaddcaacbabdccdcbccabdaabbacdabaacddbcbcdcbcacaaacacdddddccdbadbcbcbbaddbbabdaddcbdbdcaccbcdabdccdaabaadcbbbcbcbaddcdbbabdcbcbccdbddbbaccabacdcbccbddacdabccbdadbdacdadbdacdaddabacbbaaabadaaddcbcaddccaadbadabacdbdcabdaaabbabcdccbcacdcaabbcaddddbacccdbcaaadbbcdcddcacdabdbdcadabadcdcbccdabdadcdcadacaacbbbdbacddcdcbddbdacaddcddcdaddbdddcaacdbbcabdbccabcacabdabbdacddddbccdaacdaccbbccdabbaccbcdbaabdbacdbacccddddacbadaccdddbabccdcccbdbdcaacdbccaacbcadbbaaaaacbacbdaccbabccaaababbdcbcddbabacdbcccacdaabdcabddabadbcbddcaadbbabadbbaadabccbacddabcdbbdcbdacaddbdaaabddcacaaabcdabdccabbcbdaddabcaccbbcdcabddbadacbddcacdacdabbdddbacddaddcabddaabaacbdaaabbdcabbbcdbbadbdbdbbaccbddcdabdbcbbdbddbbdbddabadbcdaccbadbabcdcdcaaabbdbcdcbdabbacabdcddcdbababbbadddcbccaacdcaacdcbbcbcdadacbbabdccabdcdcccaadcabccaaadddcaccdddadccbdddabacaabbcdbbccacbaacbddbacccdbddbdacbaabbdccbaacdbaacddabcdacadbaacdbabcabddbccacdccababadcddcadcacabcacbcbdbbcadabdcaccccdbbbcccddadcabbbdbdbbddbabdbcdbcdddadaabdbcccacabbacdaadadccccacdddcddbaacbcbcddbbbccdbcbdbccbbcbdbccbcacdbbcdddadbddaaaabcbbdcadcbdadccadcacabcaaadadccbaadcabbccacaabbaddabdcdcbaadbdaabaddcbccacadbdabaaadabcbdaadbabbdbbdbbacadccadbdbbccdccddabdaddcbddababbdbadabdacaaddbaaacaabbdaacacccbacbbbaabbcabcdcccabdcadacdadacdbccdabbdbadadbdbbdcacdcaddabbbcbbabbcaadddaaaabdddaacdccacdcabbcbbacdddbdcacadbabadbbcbdaadcdadbccbccabcccbcddbbadbbbbdbbadcadaaddcbddcdaabbadcdaaaaacbacdadddbadaaaccbbadabdddcdccccbbbadbabdbdacadcbbdaccdcbbcaababbbbabbbccbbbbacabcbcbcabcabbbdbaaabcdcaaccabdcabbacbccadadabbacbcdaacaccbcbcaaadbacbcbaabcdabdbdccdacabbacbdbbcaccaaadcadaaaadccabaabcccdcbbaddbcccdadbdccacbcbbdcddacadbbccddcbddcddbaddabccabcadccdcbcaababdbbbabccdaacdcacbdbdbbdcdbdddcccbaadaaaddbbbbbdbabaabadbbacbddcdbcadcbcbcbcabcabacdabcbbbbabcaadcdbbcacabbbcaaadcabcbdaabcacdacbdcdabacbadcbdddbbcbbaacddbcdaddbcbcbcacabaaccdbddabbbacbaccadbdbacabbcdccccacacdbbbbdbabbdcddbdcdabbdcbcbadcacdbccadbaaaaadcadbaadbaaddcbadaababdaccabbaadbdbdbadddcccbacbcacdbbbdbcdcdcddabdcaddccacdbdbcaacbccacbdbbbbcdabaddcaabcaabdddcccdbdbabdcccbdccbdabbdcaddadadadcdabaccdccbbbdabdcadadcccccacbbdbbcbdacbbddddcacbdcbadabdabacdcdbbccbdcccddbdbbccdadcbbacdacddaaabacbddadddbdaaaabaacccdaaadbacaddcabcbdacbbdbdbabdbcdcbcbcdcccbababbccbbacccdcaacaacadbdcbbcdadabbcbacaddabbbcbbcabcbcbcdbcbdddcaaacbbcddbddabdcbdadabcdadbbdccbddacdabbdccdacaaccbddaaaaddccbcacacacaabbdbdbbaabbadaaaadddddaccabdaccadabbcbccaaccabbddbbdbbdcaaacabaaadbbbbadacbbaaadcdbaaccdbacdcdcadabadccbcbadbdcabacdcabdddaacbdbdacdaaadaacdcabbdcabcbdbadabbdcadadaabcdcbccddbbaaddbbccbabbbdbadccbadbacbadacaaabdacbcccdbbdbadabcdccbccdccbbbdaaddabbadcabdcbbbdbbadcdcdaccccaababacaccdadcccaaaadaababadacccdbddabababcddabcbcddcdaacdabbacdddcddcdddbcaabbcdcbabacdbddccacaabbabdcbbddaaddaccbaaadbdbcdabbcdcddadcbacacdbdabdbbcbdacadcbbbdbcdddcddcdacbccbcbdabcabbaabadbadcdbaddbbbdccbaabdbdabddcccacbadaabcabdccdccbabdbbbbacddddbaaabadaaabadddbaabbaacbdbcabdbbbcbddbddaabcaaaadadabadcbbabcadbbdabbbbbdcacbbbabadbaacddcaacbcdaadbdbccbddbbddcbabdcbcabdaccaddcbcbbadccddaacbcdaaddadacbdbbacddcabbdadbbacbbcbabcdbbbccbdcaddadbcddbcbdcabdcccbdcccbccacbbbbbbaddcacbddabcdcddcddabcccbbdcaccdbadbadbdcacabcdcdacbdcddccbaadadbdcbbbbcdbabdacbaddabbbaacadaccdadcdccdbcdabadbadabdddbddaabaaababbbbbbccbaacbabcaacabcadadbcdbaaaccadbbdbbbadbdcbbcccbbccbbacadbabdbcadadabbbbddcbddddbcdbbcdcacacdaaacabcadccabdadcdbdabaddcacdcdaaacbdccbbaaaabcabccdccbddbdcadcbbdcbbbdcadcbcdbddabcabbcccddbdadabcbbccccabddcdcdabcaddcccbacdcbddcddbdccddbdbabaccdbccdbbbaabcbdbacbbdbcacccdaaddbbcaacaacdbaaccbddabcdbcbbbcbcabaacddcddaddaaccdbdbabcaccbcacbcdcbdcdcaccccdbcbcbaadbdbcbbcdcabdbcddcddcddbbacacacaacdbacaccbbddbbacddcbdcbddddddabbabacbbbbcadacdaacabcabaddbaaccdbcccdbddbccadbcbbdbcaddbcddbadcddabcbccbdbacbbbbddcaaaabcdccabddbacacacabbcdddaadccdbaabdcbdbcabacbddacdddbbdbbddacabbacccdadddcadabcaaddcacdacdbbadddbcbbbdbbdbaddbcacbbcdddaddbbcbdbcdcaccbaaccaddbdacdadcdbabccdbcdbcdcdbdabbdccbbaaadcddccbdccccddbabcccdcaacabadcccbacccdddaaacbaadcddccbcccabadcddbcacdbdbbcaaadbddddcdadbacbbcacdabcbcdbcaddcbbcbdacacbcbcccbbdaabbcadadaacdddaccaabcbdcbdddbcbadddcccbdaccadabcbbbbbbdadaaccaadcbccdabbbacbbadaabcabaacbdcbbaadbbdacbadaddddcbdcabdbbccabdddbdccbcccabddacabbccdbadbddcdcdbadcccdadacbacddcbcbdaacababbddaabbdaadacbcbbcacbbcbbacaaacadacbcdbbdcaabcaaadacdacacdbaaccbabaaddccbbdcdaadbaddbdbbaddbaadaadddbbddcbaadadcabcccbbcbbcccdadbadaddcccabcdbddcdbcbbddbbacddbcaccdcbbadcbacddadcdbddcdaddccdbbddbbbbaacdbbcbcdbdadcccbbbbdccbbbacddcdddbaaacaacbdbabbbbbaacdaaccbbdddcdcbcdcdaccbdabbdabdaadddcbcdcdcabbabbbdaccdccbaabbcabdabcccaacdaaaacadddcbccdaddabddccddbdcadacdabdaaabcadbabadadbccadabddacbdacbbdccddabaadbadbbabdcacdadacdbadbcdccadccdddddadddaabbdbddccbdbcbabddaadabcccaabddaaaaddacbcaddbabdcbbcaacdadaacbdddbbaddbadcdacdcddddcbbabbdddbbbacdccbcbadccddcbbbabbcdabdadddaaabaacdbbddaadcaacaabddbacbcdcddccabcdcbdbadccabbbacabadccdbbcbbccbdcccdcadcbabdcadbdcdbcbdbdbbbcdbabbabdbbabccbdaadbdbaaddbdbdcdddadcbdaddcacbadadbdaacbdbbbaaddaacccaccdadccaccaaccadbbddcdadcdddccdcacabdbcbbabddcdcccdcdccbccdaabcdabbbbddccdacaaadcabadaaaccdbabcbdbaabdbaaabcbabddaacaacdcdacddababacdbccacccdbcdcccdaccccdabddadbcbdcbdbabaadacddddbdbdbbcdaccacacbccadcadbbdacdaacadacbbadadaabbbaddacaaccdbdbccbabcabccbcabdbdcccaccbbabbacaccabcbcacdcccacbcabccccaadbadaddbdcabdbcbbacbdbbaadbcaadccbcdadbcabcbdcccbbcdbabccbbcadddddddbabbdcdbccadbbbdccadbabddbdcccbcdbcccdcdcdbaabdbbccdbcacdadccdacadbcdcaddbbdbdabbdbcccabcacbdcbddacdababbdbaacdabbdacbacacacabcdcdacbbcabbdcaaddcdadbacdbacddabcccccaadccddcbbabddacbcaabcadbabababddbaababadcbdaabcabbdcbbdadbbccaadadcabacdaddbabdbaacaccccddaccaabbdaaddbdbbbdabccbccddcdcdbcddaabdbaccccdbbbaadbaaddacbadaccabbddcccdcbbacbbadcaacbadabbdbdaacbdddbbccdaaddddabacbaadbaaccaccbddabbbaadbccbbdbcbabbcabdbadaccdcabbdadadcbdabadbcacbcdaadcbbdcdabdccccaadacccacbcaabddbbddaddcacbcbacbbdaacbbbacdaaabdaadbdaaaaadbbccbccdcdcaddbbdcadadcacbbbaabcaaaddabacdccccadbadcaadbacdbdbccaacbdcbcacbacaaaccaccbdbbacbbbddadcddbbbaabbacacbddcaccbaabbdcddccdbcdcdcbbcacbbdbacdabaccadbdccaacacbdabdabdcbbbdbcbacacaaccbdaadddbbbbacabadadddbcbddbaddcddbbdaaabadadaabcadaaaaaabbcbdbabaabbdaacccabacabbcdcdbddddcadbdccaacddbacbaaccccdbabdcbbacbadaacbccdadbddcdcbbcaabcbbbaccaddaacabcbcdcccbaddacbaadacddadaaccbadcccdcdbccddadccaadbbbcdaccbccccadddbcdbdbdacbbdacbccddcbadcacadbdccddcdcbdaccbbacacdadaddcabdabcaabdbcdadaaacdaccbdccbcdcaccaddacccbddaabbcbbbcaddddaabdbbdbdaccbdbcdaadcbacacabddccdabdacabcbbdcdbdcbcddabcccdbbdaacdbdbaaaddadacabdcaddacdaabbbcbabddccdcabcdcbddcdbbcacddabdaaadcdadddadaaadbbccddccdadbaadbacbcbdbcabcadabadabacdcdcbcccabdbbbdcdbcbbbdacabaccbacdbddadadbababaccdadcbcdbaddadcadcccadbdadabbbbbaaabacbbbdabddbabbbcdabdddbcbbccbcaccbabcbbdcbbadabcdbabdacbcbdbdbabacaddbcaddcbcbdbbbcaccdabdcaccccaaadadddccdccacbcdbbbdbdcbdbcdccbbbdbbcbdcacddacddaacddddcdabdcdddddcadcdadaabababddccaddbbbccaabcccacabcccacdddccdbdbaddabcccdadccdadaacddcccddbaccdcccbdaaacbcbcacbccacbddcbababdbddcbcbbbccaadcaccacbacdbdcdbbcbadacdbabbccbdbacccbabcabbdbbddbdbdaaddbadcaabdddacbbbbbbcbaddbccdccacaabaaabadccccccbacdcdbabbacccbcaabcbdcbbdbdddbdbdbcdbcdaadccbcdbaccdabcddcbcdccbbbcbbdadccbddbcaacdbccbdbacbcadcaccdcacbcbccaaccaabdbcaadbdddbaacaabacaadaaadaacbdccaaabdacadabaabcbbabbdcdccabcdbaaabcccadcbcbbdcaacddccdbcbcdbadcabddaabcabdbabcdccdbaccacdddbbaadacdaabaddcdcaabcdcabccdcdbbcaabddbbddadccdbbbccdbbcdaadccbabbabdcbbccdaadbcdbbcdadcacabcccdbdccaadcabacacdcdccaaabbacdbddaabbbbbccdcaacababbbadacdaabdbdbdbdadbddacdcdaaaabccbaaabdcddacbdddadaaadbccbadcdcdbdacacdbcaacccccddaacddaaaacbdbbccaaaadccdccdcdbacdaccbbdabbdbdcbccdbdcbaadbaddcbdccddbcadabccdaabbbcaacaacbadbacabbbccbdabcbdbbdbbbadbbbbaaccbabadacdcbacbdcbcdabbddcdabbcacdddaacdbcdbddabddbdbaacbaddbdadaadbbcbbbabdabbbdbdcaddbacadaddcacccadcadcaddaccbaccddadacddcaddcbbcccddcddbdbbbcacadbbcabdcdbcbaaabacadadcddaddbccbbcdbbdcdccddbbbbbcdcdbcadaadbadabddacbcadcabdcddbadcbabbbbddabdbcdcdbccbacddcbcddabaacbddabbaaababdbbabbadabbbcadbaddddcbbdcbdaadbacbcbbacbacccbaabadaccadccdbbbaadcabcbbacadcdbacadcaabcbbbadcbbbbaacddcddbbddbbcaadbabcaaadbdaadbbaacbaccaaaabcbbadbdcbaaccaacabaaacbcacbaadbbadabadccbcabcbadccaaadcccbcadcdcddacdbaabcddcddabaaddadccaccdcbccbcacadcbdbacdaaccabccccbbcbcbdbaddbdadccabcdabbaadbdddbcbbbcdbaccabdbdabcacbdaccaddcdcacbbdbccbcacdaadccabdddcbcccbbbdcabbadaadadcdcdadcbbdddabbadbdcadbdbbcbcbbaaabddbbcccbcabadadabcbcdacbababbbbdaacddbcacdcdcaaddabacbcadaaaacaccccbdbbccbbcaccddbbcdacccbcbdbbddabbdddcdadcbbddacccdbbbdacbcaacacbcbccbbaddbdbabacabccbacbcccddccbbccabbdabcdbbaddbdddabbdcbcacbadbddbabbabdaacdcbacaacbaaaababdcccbdabccaaccabdaccdaaaadcccbddaacbadbbcdaabddadbdabbdcddbbaddcbadabacaabadcbabcdddadccaabbdacdbbbccaacdacadaaadacdadbdcccacdaaadddbcddabaacaccadacadddbcbcdbadbbdadadaddbdabcdddadadcbcdaacadcdccbacacdddddcddddcbdacacaaaabaaddacccbcbbdaaccdbbacacccccaacdcabcbccacbdaccdbbbacbcdacacbbcabdcddadabdbaabbacbccadbbabaddbdababacadadaaadddbdcdccbdcadacdbabbcabdabcbdccccaadbaaadbbacdacdcddcbdaaaccbddbbbbcbccbababccbdddbdbbaadcdadbbacdccaccbcabdcacbabcabaccdbaabdcabadbcddadacdbbbbcdbdcbcabddabaddaccbbcccaddbadbbcdbcbacabcaddbcdaddacaddbddcadcacdbcdabbaccbbacadcbbadaccacddabdbbabbdababcdbbcaccabdacccdccbbcdbcabaaaaddabcaabbbdccddcddabbcaabcdccbccbdacdcaadcbdacadcdcdbcbdcaccbcbbcdddbbccadccbbbdadccbbabbcacbbacaadcbaaabcbbbbadadddbcdacacbdbacabddcdcbbdbacbccbadbbbadccbdcaabadadadacaaaaaaccbaacdbbadcddbbbddbbddadabaaccbaaccbdbadcadadadbdccdddadccddcaadbbddbbadadabcaadddcaadbbddaabaccadaabcccacadccbbadcacdbaaabbcabadcaadabaabaadbddccadcdccbbaacccabcccbdadcbacaabbbddadcadbbbabbcbcbbdacbcaaadadbbcdbcabcdadbccdaabcbbbdccddbddbbccbccabcdcbdddaccbddbbacacddbbddbbbbcaccbdadbbbbcbcdacdccdccaddcadcdbacbcdcdcbddcdaaacbcabdaaccdadadbcbaacbabdccadcbdababbadccbabdcabbddbbcaadadacabaaccdabbccdcabbdcddbcacaddcadbcdbbddcacbdcdddabbdcddcccbaaabcbaccddddbbcaddadbcbdcaaacadacbacbbacbacaddbadaadcacadddbacaddcbdddbddcdadccbaaddcbddcbacdcddcbacaadcbabbacdbccddbaccadbaadaacbcddaddcdccbabbdccbadcbbcadbacbdcacbbaccbadbabbacacdbcbdadbcdacbbdddbacbdbabbcadccdccbdabcbbdbadbddaddcbccbcaaadbcddaadccadddabaaacdaabdccabdbddaabcadadcaddaddcdaaccdcddabbadaddccbdacccccdbbbcabddbabbbaadbbccddbadbdabadcbaaacbddadddbdbcbbbabcaddabbbdacdbaddbdcadadbdcacbdabdbddadbadbabcbddcadabaabbbbadabbacdbcccadaacdacdadadbdaabbbbcaccdbcdcbbcddccbadbdacdcaaccddcdccdcddcabbadaccacacbacaddbaddabcccbccacbbaacacdabcdbabdcabcabcabcddddcabababbdcbddabcdcaccbdadbbdddadadddadcbbdacaccddadbadcdbdcddaddacadccdaaabcbbaaacbbabbcaccaaccddbdbdaacadacbbcbbdaacddcdbabdbadaaaadadcbdabcaabaadabcacdacaabdddadaddaddbcadaaabdabcbdcbcdccbbbbcbcdcbdabdadaacacabbdcbcdbaccbadacdadcdbcdbddbcabcddabbacdbaabbbbaddbabdcccabcdaabddbcabcbadbccacbbbbacabadcbccbadcaaccddabdbbadadcbdbccbccabdacaadaabdcbbdaacacbbbdcaaccbdaacaaabadbabacbddddcbabadcbbbbdbcddddacdcccdbdbbcdbbdaaaccddaddbdcdabdbabbadcbddbcbadaccaadccbacbbadccaabdbbddbdbabccddcbddaccddbbabcabbcddabbadbcbcbbcdccabcccaadbbadbdcbbdccbdbaddbdcadccadadbdcdacadcbcbddbdcdbbadbddaddcbccbaddbadccacbaadddbcdcaadcbaaacddbccccbcaaabcdcccdbcdbddbcccadbacdadcadcbdcccadacbccdacbacabdaddbdaaccdabdabdbadbabdadddabbaddbdcbdaaaabcdaaccddddcaacaacccdccdbadabacaaabbcccbbbcacdadadcbadcadccacabddbdcadbacacbdacbddcabccdbcaddddcdaabbcabccbcccadbbdadbccacbccccdaddcdcbcabccccabdcadbddcdbdbbcddcdabbbaadccdbddaadccdcddddcbbbccdcddaacbbabbaaaccbddadabbcbddabcdacaabbcdbccbbaacddcdbdcbdcdddcabbaaaccbbabdbcbcbaabddacbacbddbdbcbdcddcabbaabadacbdbcbadbadddddbaaabacabdadcdaaaadbaacbdcbccbdcddacbaabacbcadadcaccbbcabcacccaaccbcadbddbbdaaaaaccdbccacdcdcddcddacccabcbcbbcdbccddadadbbdcbcacaabcacbcacacbbddabcdaaacaddcacaaccbadaaadaaccdcdcbcaaddcaddaaadddbdddbaccdbddcabbbacadcbccbbcdbbaacccbddbacadcdbadcbddccbdadabaacadddbcadabddacdcdddbbbdacaddcdcdcddbabccbcbaacdaaccbbcabbcbaadcdbccdbddbcddaabacdadaaadbdaaaccbbdabbddcaaccdacbaadbddababdaccacbcbbccbbcdbacbccccaccdbbbabbacdcababadcbadadababbbcbccccdcdcdabbccaaabdbaacdabcaabccadbbaadddbdccabaacdaadabcbcabdbdaccbacdbcccdabcbcaccccaccadacaccddbbccdaccbadadbaadcabacddcdbcddbcdadbcaaddcdbbbabcbcbcadcadaccabadacabbbbccdbddbababdbccbccdddbcbadcdcdaddabdccabcacbbabacbdabacbacdaaacadacacdcbacdcccaabacbcbabcdcdcdbbcdcacbabcbadaadadcabdaccdccdbbbcaaddcddaabcadcacdbcbaccdacaddcbccbaabcadbdcdbacdbabaaccccbbbaddcdcdaacbbdbdcaadabbaacaabbcabbcaaacbacdabcadcccdbbaaadcddabbaacbbcadbcbddbbdbcabaaacbabcbccaccaddbdacddadbbbaadaddddcaabcddcabaadcdbdabbabdacbbcaaaadcaadcbbbbbbbcbacbdbbbdcbcabccddcccbdccdbcccadcddcdbacdbdbababbcbbaccdadcadadabdbccacdcddcabbbcccadabccdadbbddabaccdbacacaadcddddcbddcbcbbabcdaccadbcbdbaadcbbbaadcbadabcdddaadbadbdbaabaaacbaababddadddbabdbbdccbcabbcdbadccbbbbdbdccdabdcdbdadcabcbdcabadcaacdcdaabcbadcddcadbccbccdaaccbdaccabccbbaddcdbadcbdaddbaccdadcdadcabcdbabbbbbddccabddbdabadcdbabbcdddcbaababdbbddbcdccaabccbadbdcadcbbabddbdabbabaddcaaddadbbabbbccbbdbcabcacdbbbaaddbddccccbacbbdcdacadcacdcaaddbbdbcaaaabacbbdbabddcbabdcdbbcbbcabbdababbaacadabcbbdacababdabbaddbdbcddcabadbbaddacbbdbcabcbddabccdcccbacabdacbabcadbbaaaacddabddcdcbaddacccaccbcaacddcacdabdaacbbbaabbaabaadbacbdbbacacbbbdcbdcadacbddacadbccbbdcbadcdaadcbbbacdccbcacabdcadcdccbacbbacacdcbdcdbabbdccdcdbdacbaaacbdbacdaccdcbdbaadabddbbbacccdddaadcbcddbdacadddadbdbdbbcacccdcacdabdbdabadcbadaaabbdacacadaccaacbdbaadaccdcdabcaabdbbbadacaabddcdaabbbbbaaccabacdddcadcdabdbbcadabddbabaadbadbcabcbbbccddcdcdcadcddbabcbcadaaccabadcbaadbcabacbabddcabadaaddbcdccbaabacbdccbcdadbacadcacdbabcbddbdbcbaabbaaaccdddcbabaaababbcbaacdddddbcdcbcbdaacbbabccdccbadaabddaaabcddcbbdddabddddcccacdccddccacbbdabadccabddbdbcdacbddccddcacaabadaccdddccabbdbdddcccabaddaacdcbbdadcabacabbddccaaababcbddadbbacacdabbbcaccbbcdccacdbbdaddbbddabcacacbbabdcdcbcbcddbbaccdbcabaddabcccaaaccbbdaabbcbacacadcbabaaabbaaacccabacaadbdcbdbacbadcbdbadccbcabddcddabdabacdbcaadccdbaabddabdbdacbbcabddbbdbdcbcdbdcbdbcaadccacbbadbcdccbcccdaabbacadabcbddbdbdbbdaacadadbcaaddcddbbadbbccddacbabbcddabdccdcdabdcbcaccccacbdaabdabbbdcbbdbaccdccddbacddbbcccabdcacccbcbdcdadbbcbbdadcacbadccaacbbbabadadbcabacdddadcbaacaacdbadabccdccaacbccddcbaadbdaabcdabccddadbabbaddcccdcdbacbabbcdcaddabcddbcdacbaacbadacdcdbbcdaabdadadacabdadbdaadbdbbddcdaaddabcbccbadcdabcaccbcbcbcdacddcbcabadbbdbdaddcadabddcadbbcbdcdacbccacbccdcbdcdaabcdcdcbdcddccbbbbcacdabbabbabcddcaadbadbdbcddbaddcacaabcabccabcbdaaadbabaabbadacbbaaadbbabdccadddbdbaddccaabadcccabcbbccaccabbccccaaadbbddabcabadacaadddaddabbbaacabcbabcabddbabacbccbddcddbabdccbdabcadbacccbbabdbdabaaccaadcaadbadaddccaabccacdaaaccbabacdcacaacaacddbacbddcddacaabadabaaaabcbdabbccdaaccbaaabaccabbcdbbdabddaddbdcccaddcadaadadaacbdababcacdddaccacbdbdacabacaaacacadbdbdddcaaadaddcbddaaaabcbdbdadcaadabcddaacabaaacdbbdbbdcaabbbbdbaccddcccdabadbaaabcdabdbddadadadcaddcacbcddadcbbcdcacabcbcbbbbddbcadaabcaabadaaaccdadbcdcbccacdbccdbabdcdbcacbdababaaadcadbdbdcacaabcadadadbdbbcbacbbabaabbddadbaadabcbcccbbdcbabddddaaadadadaadbdddbddbcbbbbacbbababcabcabacbddcaddbacacabaaadbabdcacaddaccacdbdbcbbcabbcbbccdbabadacdacbbacdbdcbdbdccaccadbcbdbaddcddbcaadacdaabcbdcadbcbaacaccabaaccacdaccababaddbdbbdddcdaaccacccdcddcdaadaadaddcdccbccbdccaaabcbdabbdbbaacabacbdabdbbcaddadaabdcbcabbadbcacdbdddbbbacacccbdddccabbbcbcccaabcacdabccacaaccbbbdbccdcaccddcaadaabaabbdcbbccabddcdcdcdbccbdbacbdaadaccdbdacadddabdaaaaabdcdccabadcdcbcbabddddbcbababcadbddaddcbddaccbddccdbdaddccbaaadcacbbdbccddacdcaadccabbcdcaddaacbcadccdbadbddbccbccacdcdcdadaddbccdddcccdcaaaabdbccbcccdbdabcacbabbbccaaaacaacaadccbbdaabddcccbaadcdacacdabdddcbdddbcacbcccdcccdbaadcdcabcbcdbbabbbbcacddcaccbaddbaaaaddbcacaaabccdaadbddbccbbdddbadcbaddbcaabccbbabaacbdabbbcabdbdabcbbdbcbbbcddcabdbbcdcbbdabdacaaccdbcddcbbcbbaacdcaadbcbaacdcbbabdaccbabacddddcbdbabddbaaaddaacabacdcbbbcadacbbbcbadbdacbdddaacdbabcbbabdcccdddacacbcbdabbcadbccacabaacdbbacccacdaacbdcbcbdbdcdaabdabdccacdabcbddbcdbcdaccdadbcdccabdcddababcbbaddddaaadccddcbdcccddbcbccadbbbdbdcbaddbabcabcdabbbbbaabdbcdbabcdcbbdabcddaaadcbbacababbbadbcbbbdacbccaadabbccbbbabbdbdacbcaaccaccbddcaaadcbdccdaacacdccdbbaaadccacdcacdaabccabbcacacdcdbcdbcbacdbacabaadadacccacbbcbaabddaaddcabaccbcdcdaaccbcbcbbddddacbdadcaaacccbccbaadbabcdcdbcacdcacdaccdbbadaccccdbcbaaabaadbbcdbacbadbcbdddacbcbdbddddacccbdcdbbddcbdbaddacadcccbccadbcddacaddbccbdacaccababbbcbdababbbaabadbcbbcabcbcaccccccaccacbbbbddcddddcbcbaccaccddacbcbbadbbddbacddacabbcaacacbdabadaacaabcdabadcbcddadaacdaaabddaacadccaacaaacbdacbdacddddbcbababbbbadacbcadddbadbbbcabccdcdbdcdbbdcccdbaccdccddabcdbcddbcaacbabddbbbacddaaadcbabbaddbabbadcbacadcbacbbdddddadcdcddabbabbcdddaacaaacaccbbcdcaaaaacdacdccbdcacaacdcbdcdcdabcdadbdacdabdbaacccccacabbbbcbadcddbacccbcaabcabbdcdadddbbccaacbacbabcadcdabdccaddcdcadbbcbadcbaadcbdcbabcacdbcdcababcbabdddccccacabddabcddabcabaddcdddcaabbdadbbbdacaaabcbcabbdcabbaadcbaacdabaaabbdcbacdaabbaaaccddaacbcccddacbcbcdacdaddbccdbcadacdccccbccaacdadbcbdadbaccbaadaabacbbdbdcddccccdbbacdcadbbbdcdcdbdccdaccacabdabcccdbbacccaabcdbabdcadbadcdabcddccdbaaaddaccdbcabcbadbcbdbabcacdaccbcdbbdaaaaacacdccdaaacbcbdadcbdcbabdcccbabcdccaadcdaaabcaadabccdbadccbabcaacabdcababcbcbcacbdbaadbdacdacaadbacbbdbbdcbccbadcdbdbaacbabaadddbcaddccacaddaaadccdcbdcabbbadacabdaacadddacaaccdadbbdcccaaacbbccdbcabacaaacdbbbacbdbbdccabaadcaaabbbdadbccacbbbbcdcaababccccccaaaaabdcddccccbaadcccbaccbaabacaabcdccdcbbacaaaacbbbcbacaddbbdcccddcbabaabcdaabdcbabbabaddacdbadcdacaababbcbcdcbcbcdbccacbacbdbbabcbacbbabddcaacdbcabdabbdaaaaabcbacddacaaddabcbbbccadbadabcbdadddaaabdaabbadddbcbcbbcabaacbabaadacbcbdbbdaddabdaddacbacaaddbaabdcbdcadbacacaaccbabdababdbbabacdcacddaddaaddcdcbaacdaaabccccbaaadcbdabdacbdddbbcaaaddcabbaccddcdddccdcabbaddaccdbddbdbbbbccacbcbbabadbcdaacbbcaabcdaacdcaaddbcaadcdaabcbaaaacbdbddaddcdacdaaddacabbaababadbadcaaccabbaddbdbacbcdcdaaaccabbcdaccabadaccdbdbadbbdbcbdbadadabbcaacbbbadaaddddddbbccbcdabdbdbdaacdababdbdccabaacadbabdbaaabadadddbcaccbccddbaaaccbabcdcdccccabaaddddccdcaadccaabdbddacccdbdbbbcdbbabbdbcdcbccaabadabadcccbbdbbaadacbcaadaacdadcddacbbcabccdcdacdcdacbbbbabdbbababddccbaabbbdddabcbddccaabccbabaadaacdcdbadbbccbaccdbcadbacccacabbabcdadcbdbbaccabcabdabbdccbcabccbcccbcdcadadbcddcaddddddcbdbaabbabbbbcbadbadbbadccbabaccbcadacdbdabdccbbcadabdbcaddddcaabaccccbdbdcbbcaacadbaadcabbccddcdccabaabbbbdacadbaddabcabcccddcaaacdbcbcbdbcccdbaacaddaccacbadcdcabcddcadaddaddbcdaaddcabdbcbacbdddbaacaabcbcbbcbbbddddcacbdacaadcdadcacabbacaacdddaddbddaaccabccabaadacdcacbabbcdabbbdccaaccabbbbdccabccbcddbbaaccdcabbaacdbababbdbbabbddabaccdadbadacccacdacbbccacacdabcbcccadbdabbacabcbaababdbbcbbbbdcadaadabcdbcadadbbbbdbcbdacdbdbdddcddbccadcdccbdcaddcccbbccdcdcbdadabaabcdccbcdbcaadaabdaadbaabdcbccdbbabcccadcbaacadabbbcbcaacdccddabaccbaadaacdccddcccddadadabdcdbdaaddbababcccdcbcdbaadbabdaddddbcdacdbdcccdccaddcdadacbddcacbcbabcbdacbabbbbcbaadbdaadddddcacbbcdbadadbbcabdadbbdcaaddcccbccbdabaabcadddcdacbacaadaaaccbdcabcbaabaacabddcccddacdbcababbddcdcbadcdcdcbbcadadadbbbcdbccbdcacacbddcbcaddbbdbbccbdcadadddcdbddacbbcdbadccdabdaddcdacbadcbcacdcabdbdbdbdacbadbbbbaddbbcdabcdbabdadbaacbdbddacbcabbbcabccccdbcbcdabdaaacaabccaacccaddddcabbccccaddbbcbacdabbaabaddddaccacadaaddcbddccdcdcaacddcabdabcbbbdaddaadcabbbcabdcccadcccabdbaddabddacccadacacbaaccbbbacbbaacdcdddbdddabcdadaadacacddbcdacacdbdbcdcacadccddddbdaacdcabccccadbaabbdaacbbbbcabaacbabaadabaccabcacdcabbcbcdddbcbaddcddbcadccbcbdcaadacbbaadadaacddabdcdbdcdcbdcacbbadccbacbccabdbbbbcbdcaaabbaacbddcbbaaacccdcabdcdababdbcbbdbdaddbccddcadadcbbbdaababbabbcbcbcbaccddbdbbcbcccbdacadddacbabcacccbbdabbbaaacbdcccddbbccdadababdabdbacddcdbdbcdaddbddbccbbbaaccaccadbaadaaabdddbadbcacbbccaccdbaadabbaccdcddcdadabdbcddbccbcadabdccbadcacddaadbbadacdccacdabdadcbdddcadabcdbbccacaaddaaddbcddcbbdabbdadadbdacbcacaadddacbadbbcccbbcbaadbbdbbacabbbcaacdbacbcbdccacdcdccdadaacbaaaadabadadddadcbdbcadbbcbdcbbadcdabbaccdaacccbbbdabdadbaabbbcbcbadaaddcadbdbaadacbdbcaccdabbddaaacbdbdddabcadadacabccbadbddacbbcadabcbddddbabdacbccdddcbaadccdccbcaabaadbddbabdbccbcaddbabcdcbbdccadabbdbdddbcdabcbdcbdbcababdcbacdaababdbddbbbaadccbcaaccdababdbcacadcddbbbaacdabcddbabbabbdcdbacccbbbdbdaccadbdbbbdddbddccbacdcbdddacabcdbdabdcdacabadababdddbaabdadcaabbbacbabdcaabaabbbbddcdbaabbaadadabaadcccabcbaddcacbababcbaacbcaabaacbbbcaddbbbbacbcbdadbccbdcbbbdacaacbdcdaccdbcbdaabcaccdcacbcbdaacddcdcbabcccdbbacaccadbbcdadabccaccadadadaadaaaccacbcbaadbbcdcbadbcddadcccadcdcccdcdccaacbbaadadcacbaaababdbadcdbaccbdacabdcadbdcdaacbbcdadbacdcdbcaccbcacacbcbcdaabadaadbaadccbaddbaacdcbcccdcbdddbcbacdbcbcdcbaabdbdcbdcdbbddacabbccaabacbbdacdddbddcddaddabadbcdddabcbbbcbacccaddadbbbbccabdccaaddcaabbbaababaabaddabbdcacbcbdbbddcacadbadaaddcddadbbbdddcbbcbcbbbddadbcbbbacabbadaaaccbdaabdcaabadbcdaacadbbcbdbcaddadadcdddbadbdcbccadcdabbcaddbdbdbadabddcacddbbacbbddcbababccccddacbabdbaaabdaaabcccaadccddccdacdbadcacaadddbabbaaacccdccdbdbbbddababbbdcbcbcddcdccddcddccbabdbdbaacdccacdbdbdbcdccbacdbaabdadbadbabddbdbbaadcbbcaaababdaabbbddcdcbcadababdadcaabdaadcdbddcccadcdbaabccbccdcbdacddbaccdabdddbdbdbaddbddbaabddacbadcbcabbdcdaaadbbbabacbaacdaabbcddcbccabcdbcbccdbdaccdbbadcbcccdbcaaabadbaaadbacddcdbadabbbbbddddbcdaabbddbbcdccaabdbbccccdbdbcddcaabddcaddbdabaddddcdabaaaaabcbbabadabbcabdbaabdbadcacbcdaacadcccacacdbccdbbacdaccbcdcbdbcbccbbabccacdbcbabbdccaddbdbaacdaadcbabbddabdbdcdccbdbcbddabbdcbdbdcadcddbdbabcabaaaccabaadcaaabdbacdaaddbccaaadbadadaacbbcacdaadccdabaccdbddbbaadabadbcacdadababbacadbcadaaccdcbbdadaadddcacaddbaabbcabbabadbcaaaadbcccbdbbbbacdcdcbadbbadcbcbcddcccbdddcdaacabdcbaaaacacdbbcddbdddaabadabbdddaababdadadcdbdaaabddcbbdbdbddccbddcbadbbbbdabbbcddcaccacadacaaddcccbdadcccadbddabcbbcdabbdbabbdcddaddbdaccccbcdbbbaacddadddabdbbaabacdaaadcdaabcacadcaadadcbbadbdcaabacddbcdcdaadaadbbbdcbbabcdadcdaadbadcabababccabadccbcbddbbcccdbcbbccadddcccdadccacaadcacddcadadccaddbabcaddcdcdcbbcbccbdabbcbdccbdcacdccdaddbcbacadccbbdcadacadcacbbccdddcddccdadabccaaddcaddbddaddabdbaaaaacacdcbdccaccddaaaababddbdccddbbbddccdaaabccbaacdaddaccdbaccccababcbddabcbbcdaaabccadcdcadbcadcaabdacabadcacdaccdccabbbbdbcdccdadacbbccadddcdababacbbcbdbacaacabbdbabdbdaddaadcabbdadcadbccbdabbacbadddbccbcadbccaadbcacbaddbdddbcccadcaababaccbcbdbabbdbdcaccaaccddabbbbbbcdaabaadbacbbdaaaaddadcdcbbbdddacdaadccdbbcbadabcdccbadabdadccaacdddcbcbdcdaccdacaaabadaabddbadbbbcdadaaccabbcbcddccdbcababdbdaddddcccbbcaaabdcddacacdbabaabddcbbbcbdbaddabbcaabbdaababadcaddaaadabdaabbccdbccadbcacbddaacccdabccacaadaddcdbacbacdadddbadacbcbabcaabdcdadadbaacadcadbdcdddddcccbacdadccaacdbbabaabcaaddababaaccacaccbadbdcdbcaabdbabaadabcaababdcdcadbaabbbcccccaabcaadbcbadaccaadcadcbbccaadabcaadbadbcaacacacbadcbddbaaccaddbaacababdccabcccbabaaaddddbccacbcccdbbacddbbbcaddcabdcccbbbbcddadcbdaddcacbdaaaacbacdccbdcbdbbcbcdcdddccacdbabddcdaddcaddbabdaaadcdcadbacbdcababacccdbaadbdddddbbaacbadcdddadaaadaacadabbbaaaabcbbccabacddcdaaddaabbbccdbadabcbacbbcabcbbcaacdbacbcdbaaccdcbacbdbacbdbbdbdbacaabdcdbddadabaddcbbdcbbaaababbddacdbadaccaacdacbcdcdabdaababacccaadbacabbcddcdabadaacabcbccdccdcdacbbdccdccdcdabcdbaaacddacdbcccabdabaacacdaadaabbadccddacdadaacaadcdaabacdadabdbbddccbdbcccbbcaddddbbadccaababbbbbdabbbdabacadbacccbbadbbdabbcadcdbdcdbbbacacadbdacdccaaaccbcbdbdbcadddacbcbbdbbddcccccabbcdccccdbcabcbdabbdaaabbbddababaddaddbaaaabdaaacadadbbcdbbadbccbbccbadbbcdcabaadcdbbddaaccdadbbbaaacbadabdbadaadccabaacbaadaabacdcadcaacdcbcadcddabadbcbccbddcaccbcdbddbbcbbbccaddbbbbdcdbaabaddadbccbcbbcacdaccbcbdbbdddddcadaaddcaadcadcddcbbaadbcbacacddbbccbbbddbcaaaddbbbcacbadcaddbdaddddccbdbcdbcdadacccbbcacbbcdcaccccdcacdcbdbdcccbbbcbbbdadabbadcaadcdddbccddbcbadaacbdbddbbddcadaadbbbcbcbbadcdbacacbcccbbaddbbbdaababcbadbccddacabdcdbabaaadddccdcadcabddcaccabdaabadbacaabacbbadbaabccaadabbcdacddcabbbcbbcaccbbdacbadacbdbccbcbdacabbbaabbcbababcdcccbaacbdbdaddbbacbaadbbabbddcdcbadaaacaaaddcddbadcadadadccdcbdddcbadadaacccdbdbdcdddadddcadcbacdccbcddbbdbbcdbbcbdcbcbadadcabcbabacaaabbcacdaddbdbbacabdbcaabdbcdcacdacdabbcbbdbabaaacbbcabdabcddccdddbbacaaaaacbabaabababcbacadccbaadacbccdaacdbcdbabbbacdbdbabaacbddbbdbabccabdabbddbcadaacabcbbddcdaadccbcddcaacdcabacbcaacbcacbadacadcbaadbdbcdabaddabcbcadacbcdabcdbdddcabcaaaadddddadcacdacbbaddbdbcbcbdccccaabcbbdbbbbabdcdaaddadabcbaadadacbcababdcaccbabaadbaacddcabcdbaccbbdabdaaddcbacdaddbccdbbbbaabbdbaccbaacdababbddadabdbbbabbdbbcbadacccacccbdcbcbadcaadbdbcdabaadbdcadbaabdaacdabbaadcccdadddbcbcbaadbdbbbcccdabacdabbacbbddcaadbdacdaaadccdacdbadbdbcadbabbbabddadddaaadcacaabcddadaaccabcdadcbacdaddabccdbdbabdabcdaddcccadcccacadcccccbdbdccacbcaddabccccabdbbbbadbacbbcbacbbabaaccaddddbcadbbccbacbadacdadadabcbdbaddabdbacbbdabacddacaacaccabbcbaddbdbccdbbddbddcdcbccbabdcbabdabcbccbcbaaaccbadbbcabccaaccbaaddcacccaacdbaccadcaabadabacbbcdbcccccadcbdcbbdcaddbdbbddaaacabbcadadbadcdababccbcbcdaabcdbabacdcdcdcdbbabaddcccabcdccdadbbaaccddabdabaccccbddacbbaaadacaccdacadabbacdcbbadbcabcadacccabcbdcdbbbdcdaccacddaabbdcabcaadaaabdbdadbdcbcbdadcabbcbdcccbadccbabbbcdbcccdcbddabbdadbccbdbbcdddbbcdcbaaaacabccdcabccbbccbbbdbadbadbacdddadbdbadadcbcdddcaadcbbbdddbbdbabdbabddabcdacddbdddaddaddabcadacdadabcddcddbbcadbaabdbaadddbabbadcccdaacacdbdcbbbccbcbdcbdbaacbdadadccccdbaadccdabadddcddacddccbcbdddcaddbcbadddabdcbaadbbdddddbcadcaadbcbbbdccaaacbccabbdcbaadbcdbddcadbcdbddbabbbdaaddadcadddabbdcdcbcaddddbcddbcadbccbadbbddbdbbabacbbdddccacadbaabacbddacddbccbcddbbaaaacccdcababbbbcbcdbaddbdbadaadcabaccdacadcbdaacccacabbbcbcdbcccdadcbdabccbddcdaaaadbbabdddadbcadcaaacbdbadaddccdaaaddcabdbbacadcbcdabcbdabaccdddccccbdbaadbacbccbccdacdcdbccbbaadbbbbcadbbbdacbdcbddabdddbddaabcaddacddabdbcbccdbdaaacadcddbdbadbcbdadadcdbbbdddbbbaadccbbcbcabdbabddccbcdbdabccccbcabddbdaadccddaacccadacdbadbdbdaaacabcabbcacbbdaaabdaabacbdbcbbcbacbddcdbabbdcbdbdcbaccaccdcbccacbddbbccbddbcdabdaccdcbbabacdacabcbcbbcacbaccddccbbcdaddccbabacdababadadaaccabcdabbadcaabccacccdccdabbbdbbbbdcbcadbacabbdabbbaacabdcbdddbbabadabbbbbbabcbadabaaaadcdaaaabcccdcdbbbbbccaddbbabbddbcbbcdbbadcdbccddbddaadbdbacdacbdccabaccaddbbcbcdcadcdcdbdbdbbdadbbcacdbbdcbdbbcdbccadcabbccbcacdcdbaaddbabcadacadbcabdcbdcadbaaababbddaadccdadddacaaddddccadbbdacdabbddcbbcdcaddababcbaacadcbacdcbabcdaaacabbdcbdaadaddccdadadabaccbadbdcdbbdbbbbcdadadabdcdcddacbbabbbbadbabdabbcabcdadbaacbbbabababacccaacababacbbbaddbcbbbdbdccdabccacaabdbbbdacaabddacadddcbabbcdcdcddabbbbcbdccddacabcbcbdabcdbcabbcdacaadccbaabaabadbcbcdadbdaddbdbdadabadaabcacacbabbabccbccbccbaabcbbbbdcddaacdcacbabbbcacaadcbadbcdabbadadccdabdddadababdabcbdbcdabaadadcacdcabddcbbbcabccdcbaabcaddcdbaaddbccdddabbaddcdcbdabdcaccdccbbacbdbdabcabcdccaacdaacabccddadaaaadcbcccacadcacddaabcdcaddcccccaacbdaacccbaaaadbbddabdacbcbbaadbbcdcacddddddabbacbdddadadcbaacadddacbbbadcdcaddcdaddabbcbabddcddaadddacdcdacdbccadcaabacbddddccddadbbbcabadbcdcdbbdddccabbaccdaadacbbdaadaddcacddadabcbbaadabaadbcbbabcddbaccdddaccabbbcdbbbbcdcbccacabadacbaabcbbbcdadbacdbdacbcdacacddacdcdbcddcacdbdbadbbcdbcbdcabbddcddcaaacdabbcdaddabacabadcaacaddadbbbbdadcbbadabbbbcdbcdbcacbcdddabbbbdadabaddcbdbbddbcbcccadbabccacdacdaaaaabdbbcccacbdccaabaaaadacdcdaacadbacbdcabbdcccadbdcbabbdbabddcbccadacbdcddccdcbabdbababdbcabddcadcccbddcdcbdddbadbdaaabcbdadadabcccabdaabcbddbcdadaaabddbcbbcdcabccadababbbdaadbbdbdcaddbdbacdabcadbdbbcccabbaadabcbcbbdacbbccbcbadacbcabdddccbbabcaabaccbdcadccbaddcdaadddcbaadbaabaadbcabaabdcdbddcadcadcdcadcacabcbcaacbbabbaabbcdaccacabadbbcadcaaacdbcacababbbcaabcaacacccaddbbdacdddccabadacddaaacdabdbdacaddbabdbcadcaaacbbcacadcbadacbbbbaddbcbbbccbaacdbaabddcccacdcddbddadbdadbadcbbacbbbdacaadcdcdbadbcdcbbacdbcdabcaaacbcbaadcbddbdbccbbbbdcdcbbccadcbdacbdacdcdbdcaccbdccadddcccddbcbbaddcdabcbbddaacdbdadacbadbcdcbabacccacadddbdbccccccbacdcbcababdbbcbbaddcccadddabaacacdacaabccdacdcadcdcaacbcababbbbcdaabcbdcbccaccabdbbbccdaaabcccaccaaaacbcdbcdcbaabcbacbccbaadcbccdbadcddcbdbdcbdaacaabbbccbabddcdccddbacccbacdcdcaddabcbcbacabbacdcacaaadbacbcdcabadbbaccdadcdbaacbddcbccdadacddbacadadbdbddabcccdaadcbcbbbbacabadccddaacdbddcbdccacbdcaccadcabadacdadbdcbdcbcaccadcdcbaacaaadcaccaddbbacbabbbdbcbcddcccbaaabbadcdbadcdddbbccdbbcbbcbbccbcadddacdccbbacabcaccbddbdacabdcaadcccadccbbdcbdcdaadcccaadaaccbbbabcccbccbaabcabbadcbdbcacacdacbdbcdcbadaacbcbdaddaacadbbcddcaaaadddabbbaababdcdbdbdbaabcdddbbbcdccabcbdaccacdadaadaadaadbbcbbcddaccabdcdcdbcadacdacdaabcbbaddacbcdadbbddbacadabaccbbaaaddddaaadcdaddacccbbabbddbddbddabacbbcdbabdcbdbadadcdccdaadcbcdcccadabbaacdddcacbbbdcabacacdabdadabbbbcdcbdbdcbdcdcacbabdccaadaacbcacdddbcdbdbccdabaaaabaadddbdaccdcbacaddcdddbabbcbddabbbabaaaacbcdabcadcadcbbdcbdabadadbccbdbdadadabdacaccbcbbbdcbbaadadacacabcadadccbdaabbacdbcbdcbababbbcdabcdaadccdcaddabcdcbaabaabdddcbacabcccabcacbdddbaaacaddaccbdaddbbbbdbbabcadbadbcccdbaacaaddddacdbcbabbbcabdabadbddbcdbcabcbbdbbbbcbccabacbcbbdbadcbacaddacbccadbcdaadacaadacddbbadaacbcadaadcbdbaaccccacbbbccbaddddaaccbcddddaadacdaaadccacacbabaaaabbcdcbbcacbcbddbcdadbcdddddbabcbbabcacbbbbcccdbdbdbcdbaadddccbaddbabccbccbddcdcccaaaadabcdbbbdbccacdaaddbcdbbabdabbbaadbccadadbcbbdcbddbcbaddadadbadbcbcdbacbddbabaccdddbbdabacbcdbbcbacdcdaabcaaaadbacbaabaddacdbacaddabacdbddadcccbbababaddcddbdcdbcacbbdddbacadcdcccaabbacabbcbcadbbabddcddcaadadbddbabdcdadbbcaddbcdbbdacdaabcbbbbbddacdcaadccdacbaddaccbacbcbbaccbacdaabadcadaaccaadcbbbaabcabbaaabbabdbdbdddbdabcdcbcabbdbdbddbbadaaaccaabcaadacadcccddacbdcbcbadbbabddccbabadbbcccbdcbcbbcdabccbccbdacbabaaacbdccdcccdbbbcbcddaaadabcbcdbbbbcaccdbacdccdcdabbaaaaaabcabbcddbaccccdcdcabacbccbbbbaccaabadcabdaacccdabbdbdcbadabadaacbaddccdbcadaccddbbbcbbbaddbddcdddabddabcacaaacbdaaaabccdacccacaacbbcbaabaccccbcccabdbcbabdbbbccdcdaaabbbdcbbdbacadabcccdbdcdbacbdbaabbcdbacccdbaaadcbbdaadaacadcacbaaadaadacbbdaabcdddccbcdadadbdbbbcacadddabdbaccddbdbabccdccadadcacbaddacdddcaadcddbcacdcaddbcadbdbaadacaabdacadaccdcabdaabbadcdbdaccabbcdbcdbbacddddcccacbdabaabacacabbabdbcbbbcaabcbaabcacdabdbcbdaccddabcbbaccacabaabddccdbccbbbcdbccaccbacaacdacbcbbddbdbbcabccabcbcbcdcbbccabbacbcbbcabadaaacccabbcdacbcbddcbacdcbadcadaaaddbdbcadaabbcacadbadcddbbcddaadbddacbbdcccaabcdccbadaabcacdacaabbddabcaccbbcbabdaabbdbcbbdccacabddacadcccbcdacdcacacccbabcbbccbaacdcbddaccbbaabbcadcccacadbadbcdaadaacdcccadbcbdbdbdaabdddcbdcbdbaddaabdccaadaadbbdbbadbbdbbaaabcaddcccacadacbdbbcdcbadbbabaaacbbdbdccdccabdaaccdabbddabbbddcddabcdbbcbcbdcabbbdadbbaabdcbacdbaacabaacabdaaccdbcbbadacbbaaccabbcbcbdbdbbbccdcdacbcdbdbddccacddccdadabbccdcbdcaabacdbadbbdbbcaccacccbadcddaacbcaccddbbabbaccabccbdcbaacbbdabaaccdaccccbabccbcbaddddcdbadcaadcdcbcbbcacadacaaccdcdbbaadcbcbdddddcdccacbcdbaddacabaddaccdcdaaaaccbbdaacbdbaabccbbadbcaaabdbdcdcdcccdbaabacdacbdccacddcccdcccbbcabdbabbdbacdcbcdacdddabdcdacbbdcbdcbcbaaadbdcbbdabdaaadbabbdaacccdbdaabaccadacacbbdaadbcbddabacdbcbabcccdcaccabbcbbbcdbbaacacbcabbcaacaabcaaabdccdbdbddddbcccdbcbcddbccaadcbcbbdadbbaaacabccadcaddcaabacacbbdcccabadbacabcddcadabccdbcdccdbcdcbabccdcadacbbadbcadbbaacadddbdccdbacdddbacbcaddcdcacaaacbbacdcddabaabbcccbbbddbdddbdcacadbcbabcccdcddddacbbadbcabacddacaabcbcbbabcbccabddddddbcdbdadabbcbbccbdbbacadabaccdadbccdacdaabcddddbbabdbcbdcadcbbbcbbbdbcaacdacbcbdabbbddbbccccbabbdbcbbdbdcbadbdcdabababbddcbbadccccbddaabcbdabaaabcbadaccbcabbdadaccbbcdbcabaadcabddbadccddaadaaacddaabbbcbdbbdbcdbcaadcacbddcbdcaabacccabacbbdabbacacccbaaaadacabaacbacaccaabaddadacdbacccabbcadbbdadadbbdcdbaadadaddabddcaabaaacdcdbbadbdbdabcdadbcccddacbcbbcdbabadbcddbbdccabbcabaaacbababbbcbaaddbadbabddbadcacddaabbbdbbcdbabcccddbbaaadbcdbaccccdbacbccdcabbbabbdddbcacccaadaaccaddadbdaabacbbcaaccaddaabacbabdbdddadbadadbcadaccabccccaadcaddaacacbccbaabccdbcdadbddccbbbcaccabbcadabcbbacccdcadbbbccacbcbdaacccbddcacdaccbdaacdddbddbaccbbacdbdaadcbadccbadccacdcacccacaaadaacdddccadcccdbacdbbdacabdcaaadaabbdbaadbbbdcddabddcbccabccabcadcccadabdacbcdcbbbabcdabaabbcddcbcdddccbdcbbaabddadaabcbbdbdbdbacccbbcccacdbbcacdbcbacaabccdbbbbaddabcdaadbbbbdbaabbdaadababcacbabbbcaabdbadbcdadddaacbcbcbccdbcbcbdcdaddcdaabdcaccdacbcdbacddbacbdbdabbdddadbacabdcbcbadaaadcdaacddabbbabadccdddcdcddbccacaacabdcdcbbaddddabdbddccadaabbdbbbcaababdcdaddbabaddbbbcababcacddbbbdadaaaddacacabcddbbbadbddaababbbbaabaabaadbdbddaadaabaaaccdbcbcbbbdcabdbcacdcaddabdddbccabaadcabacabcadddbaabccbbbcdddbbdaaabbddbdbabaacbcabcccddddcddacdcdcaaaadddcddcdadbddbaacacdcacbbaaddcacabccbabccbdcbdcdadccdbcadadaccaacadbdcadbdcabcabbdddacdbbdaccdacddaabaadddbbcaaadbcbcabdcbadbbadcadcbbcbddddbacaabbcdbdcdbdbdaadbbbcccbacbbbbddcbbcbaadadddbcbbaacacbadcaddcaaccbcdccbddbdcaadddccaddaddcdabacadcccadaccadaacddcdbabbbadcbaababddbccaacaddbbadcdbdaaabaadaacccabddbacbaabaabcdbbdbbabcdabbdacbddbdadbccbbbcccdabadadadbcbbbbbadbdddadaddaadbdcdbdaccbadcdbccabdbbcaabddcdbbdbdbcddbbdbacdabadabccbcbdbcaacaccdbabbcbbacacddabadacabcdbbbadddaaccbaddcddabddbdaddaadacacdabbdccccacacdccbaaababaccbdcbaadbccbddaccbacccdabbbcdcdaccababddaacaccacdbcaacbdaaccaacbaabbadadacaacbbbbdbaaccbcaddabbdccdbdcdbdbbdcbcdccbadabbdbdcdcacdadabcdccbbcbbaddbcdddccacacbabaabdadaaadbbcddbabacccaabddddbbccabdbdbbdddddbbbadcbddbdbabcdbddbadabacddcdbddaadaccaabbcddbdbddbdcabcdcadbcdbbdbadbdddbdbacdabbcbbabddaacbababddccacaadcbadcbcdaacdbabddbdbddacbdabbccbaabbbccddbddbdccddacaccddadadacbdaacccccadaddbbabdaacdaccbdcacdadabccdcdadcadcccdcdbddccdbaabacacbadcacccdabddaccbddbcabdaacacbadccddcddadaddaaaaddcabbbcccdabcbabddbcdaacacabccdcaaacbbbbabcbbacdcbcdcbcbdacabcbdaddcdaddabddabbabadcbbabbabddacbacdcdcbddaadbadcbcacaacdccbccdbabbadcabccddbaabcacccaacaabddcacbaabbbcdbacbdddccacbcaacbdbccdcdccdcccccdbdbcacaddaacbbbcaaaacaadbbbaabaacdddaabcacdacdcbdccbdaccaadbadaabcdbaadccaaddddbbdbddaddbadcdacabbaaaabaabcbcdccaadacdcbbddccacbbaaacbcadddbcccbdcddcdbaadddaaababaddaacadbdccbddbbdbdddbdaaacaccaccaadabdccdbbacdabcbabaddbadadbdcdaaabcbcccabdcacadbdccabcccdadbccbcabbdcbcddbbdaaccadbdbcccbddcbaadcbbccaacabcddacbcadccccadbdcdcacbacbbbdadabdbddcdadddbdacaccbbacacadabdadaadaadacacbddadadcbbcaabcdbddbcddadccbbaacbdaaadbadbbdacbaaddddcbabcabbdbabcdbdaaabbadababaabcbababcbbcddddddcddabdbdbdbdaaaabaadabcbdbcbaddccccbcacdddbabddacddaabcbcbbddcbcddacddddbbbbcbcbbaaadbaabcdddccbbdbdacdbbaababbbdbacbabcdbabbacbbdbadabccdbdabbcadcddabaaaaadacdcdccbbabddbddabdcbabdbddcbbaaadbcddcbdddccdacadccbcababacdbabbbbaabdbabbdcabcdaacbbcddccdabbcbbbbdaaaddcdbcbdacdbcaaabddbddaaaabbaaccdcabbcacadacddcbabcdbacbdbccccddbabccacbbbaaddbadbcbbccacbdaabcbcdddbddaccbddccddddcdabbdccadadddaabcdcddcaccadccdcbcaaccdcdddbddcdbaabbdcabacddaadbbcdbbbdaccddaacaadbaccdabcabcacabccccabcabcabdcbadccccbbbadbbabbbabacdcadddcdbacdcadcadccdaabccbbccaddacbaabdaacdbaabbcadabacdacbbdbdcaacdcababbbabddcadddbdaaddbabdabbbdcccacdacccabdccdbcdbdcdddbacdcddabccdbdbaadddcbcbcabdbdbbaadabbaababdbccadccbcbcbadcddaddaaadcbbabcdcddabcbdccccdcbabbaadbcbcbdccabaccbcdadbdbdbbdaddabdcdbbdadcdcccbdadccccddacbdaabacbcdccdaaacdbdcdadacacaacbbaadadcdcacdcabbbcbcbabdaacaaaabaabdbaccaacdacdbcddccdabbcaddcdabaabdbaabbddbcdbdbcbbccccbcdabccadcadaabbbbababbaadadadcadbdacbbbcdbadbcdcbddaccabbcddadaaccaabcbdbccbadaadaddbbbacddaacdddacbbcdadacaadcacbdcdadcacdbdddbcbcdccbadcbaadddaabadddbbbdddbbcdbaadbbdbaadbddadacacbcaaccddaddbcdcdbdccddddabadacdcdddcaadbcbdaaaccdbdbbdcddbbbadacbabcabbccbcaabdbaadbbdcababdcbcaccbddcbbbbacdbbabaaddbbaacbdbcdcbddccdacacdddbddbbdccaaaaaaabcabbbbacccacdbabadbcaaabbaaaadbbddadbaaadcbbcbbcabbcbcbdadcbbbadbcdcbaddbdabbaabaadccadadcccaaabcbaadcbcbadabddadaabdabdacddcaabaacadcdbcdcacdaccbddbcccbadbdbcdcacccccbdbdddabbdccaaadcdcacbcbcacadccdbbaccdddcdbcaacaadbabddcddadababcbcdbcccbdcbaacbddcaabdaadbdbabcdbdbdcacbcccbcbbdbcdcaaddbaaacdcdccbcbdacaacbaaccadaacbbbaabcbccddcadabababcbdbddddddcabbadabaddabbdaddcddcbbcdadadaabbbcabbadacaabacbbdadcacbaadacdcbbcccdbddbaccbbdddabdcbdbdacabaccbdddacabababbdcabddcbabdccdbbadbdaaaadddbabababdccbcabcaadcdbddacddbbaacaacaccddacdbbacddabbdbdadccabbddaacbccadbbabbbadcaaabccbcdaacbacbcdcddbddbcabacbadbacaacddbacccbbcdbcaabbddccbdcbbacaaabaadbacddbaadbadbacabbcdbaddacabadcdbbdddacaccdacddadcbbcccdccbdbaaaadbbcadadadbbaaccbdbdbddcbbccaadddbacdbdbacbbbabbcadaadacdabcbcdbcbdadbdbbdbbaababdcadbbddbbbcacacbcaabbccbbacccaacacabddacbbbcdacbbaccaabcdacdcddbadabacbcaadbaacbdbdadcbddbdadbcdcbbdddabcdcbbbddbaddadddcddadccccacdddabdcbaccabcaabcbaaddcaaaaadbacdbcddcddbaaaacdcdcaddddccaabbbcbabccdbaacbcacbddccbcdabaadbcccddddabccaccbaacbabadabaadccadbdbdcababbabaccdcacccdabdbacdabaabbdcddcadcccabcaabaddbcddadbabacaabaacbbbdcdbcccadaccadbccddacbcadacccbabbbccbdddaccdbcddaaddaddcbaadddaabddcbdadcacdabadacabacbbbcdcdaabadbaccbadbabbcadcbbadddbcbdccaacbbbcacacbcacdaccdbdaccbdddabbdabaaabacaccdaabbdaacddadabdacbddcddcbadccbdaabbadbcacbabcadcbdccadaabbcddabdabbadbbccbdcbcaaaabadbacadddddbcdadbbcdadbaddddacbdcbbaccbcbdaadadbcbcadddaadbcaadacaabdadbabdadcdadabaccbaaadbcbcabacbbabdbdacdddbcaadccaabacabbbabcaccabbcabbaacbdaaaabacccbddabacbbadbdbbbadcacbbdaabbccbdbdcbcdbcdacdcbcadbccdddbacccdcbdaacdbabccbadbacccacdbddccbdcabcbabaadadabacdcbddbcaddbcabcbcdcadbcaaacdacacccabdcbadddbababccdcddccccdbdbaccddabbdacbadcaabdacccabbccdbbcaaacddbaddacdbccadbcbcbbdaadccbdcdbacddcbabdbbadadbdaccbccccdcbbdccddddcddaadadcacdbcdaaddabaaaacbdcacbaccaabaacdabcdcaadaacacacbacdbbdbdadcadddbcacacadadbcccddddbaadccabdcabcadcdcdbabbabcbbbddcbddbcabcabdbcccbbccdbcdabdacadbccaadacbccbbadcdbaadbdcdabdcdaaccabbbcabccaddcaccadcbdaaadddacdcabcbcacbabbbdcacddabcbbdbcbaacccdcdcbcadabdacccbbbdbaddabdbacaabacabbbacddbdaadbaddbabdcccbadadbaddbdaddadaacdcdaadcabdacbdbaabcadcbbaacbcaaabdaccdadccddbddaaccabcdacadcbbcbdacbdbadbaddbadbbaacbcbccdcccdcccdadbbacbccdcbcabccaddabdccbcbccadadacbdbabaddcbbbdadbdbcdbabbadcdbcacadcaacddaadcccdaaaaabbbccdabdadccacdadadddccbdacddaadaddbadabcbdbdcdaabcccccadbbbbccbbcaacabaccdcddadccbdcbdbdbacaccbacbcbbbabdcabacadbcccbcabbddaadacadabbaccbaabadddacdaadcabaacbdaadacbadccddbbcabdcadabdbadcaaabbdaddaadcacababbdccbaacbacdcdcddaaccbdaccdaccabbccdcabccbddcbaabcaddbdcadacbcbddcdcbabcaabbcabdabaadcaccaccaddddbbdbddaacbbddabcacabccdccacbdbdabcacdcdadabccabbbdabbacaccabbdcbacccadcaabdddbabcccbdadddcadcddcaddbdbdbddcbcbdcccdbcbdabaddcbddcdbdacabcccdddbababaacbcadaddabaadcabddcbcbcbcddccaabdaacdbabdcdcdbabdcadcbdcacbcdaacbacdbdbacdbdacacabdacccbdaacacbdcbcabdabdabcbcbbcbaaadcdbdcccbacdbdbaadbdadccbbbaaccbaddbccdadccccdabccdbbccaacacbadbbdcdbaaaddacbccbabbdccbcbccadadbdbbaacdaaddddbccaadbaaadcbccdadbadbadacacdbbddbdbacdccdcdadbbacadbaaaaaaccbadbdaabaadddacabbaabaddacccaaabaadaacdbadccccbdccaaabadcaabbdacbdbabdcbadccbcdaccbbaaacdbbaddadbcadcadcabbcbabadabacdbdbcdacaabccdaadcdbccbcabddbdbadcabadbdcbddaddacdbcccbcaabdaadacbddbabcbdcbbdccbdacbbabbaabacbabacabccccbddadadbddadacbbdbdbcaadaadcbcdaaacdccdabbacabbdbbdbbadbdcddcaccccabbabdccbcdaadbbbabcdabcddbdadabbbacccdadaddabbaaabcddbadadbbacccbdabcaaddacadcbcccbbaabccdbccddaccccabbcdcdbbbdacbbbccccdddbcadbdcdddbccccbdcbdcaaabdbcdbabddbbcdbccaaaabadcddccccabcccbbabcbaadaddccdbdbbcbabdacdaaaccabacbcabacccdbabbbbabdacddccadcdbcbdbadbabadaaabbbcdbddcacbdbbddbdadbcdabaddacbdbabdbdcbdbdcbddaccaccadccacbaddbbabbddcacaaabccdbbaabbdaabaaabbdabdcbaddadaccdaaaccadbaadcbbcddcbbbcacdbdbcaccaaaccdcddabdbbbbabadabdaacccabcabbdcaadacdcbcddabddacccdbcdbcaabccbaadbabaadacacdaaabcdbbbababbcbcdcbaccaaccdadcbcabbbccdcadabbbddbdbdcbacacdbbbbabbaddacdaddabbdcddbdcbaccbdccccbcacdbcddaddcbbddaaaddbbcdbccadbcacbbdbbdacbaadbdbbcaccbddadadbaadbbcbccbdbababccddacdddcbbacbdcbddbdbaccdacbddccbbccbdaaaddbcbbdcaaadcacbbccdabddabbdbbdcbccddddbcdacddbadacccbddbcddbbbccdadbacacadadaadaddacadacdddbbbacddbcdccacbccbdccddbdcdbdcbcaaadbabacccbbbcbcdccccbbcdddcabaaccabdcdcdaddacaacdabcdbaddbababbbaccdabbbbdaccdaacddbdaddbcbdbbbbdabddcdaabcabbcdcbbcadccbbdbabccbadcccdccdcbbbcaccabbbbbadcadbddacbddbbaaacaadcdabcaaabddcaccacdaacddadcdabddacbdbbcdbccdbbbbccccddadccaddadbcadddaddbbbbadbbbaadadbadabaacadccddabcabaabdcaacaabaaabdcacaadaddccacaacacbcaadcbdbdbdbbadbcbbdccbbdbbbccbcbadcbbdbcabddaacdbbcadcdddcababbddddbbbdaadcccdbddcccdbddabcabbcbbddbacbdcccdddbcbccabdbdaadababaccbdacbacdacbbcbdcdaccaddcbbabacbaaddcaadcaadcdcaadcbccccdbcbcdccdaadcdcdcbdbdcdaccdbcdddbacddabdbacbbaaabbdcbdacccdbbbcdbdadddccacdcddccbdbadcaddadccdbbbbdddbcaacdabbcdccbcacddccabcaadbaddcccdcdaddbadbaaabbcbdbccaadcccadbcacbbcabbacdbbadaacaaabcabcdacddadbabaabccadbdbccaabcaabaddbcdbacaaacdcccdbdbcadbbaaabdbbdbbccadbbdbacacdaaacdcdbdcbcbbdaabcbbccddbaccdcdbcbcdbcdbcadacdcacbcbbacdcddcbbbadacdbadddbbadbbcbbcbddccddabbcadbcddcdbdcbbacabcddbdadaacbaabbdababbabbacacbbdadcddadabdcaacbadaababddbdbdcbbcdabbcdcdcbacccbcbbdadadaccccdacaaccbbdcdbbacdaaadbbccbddcdadcdcbcddcbdcdadabdaadabcdadcbdcadcbddbcbbdaaddcddacdddbababcaadbaddcddaddcdabadacacaddbdadcdaacbbbdaaadbcddcbdbddbcbccdabdcaaacbdabadadadcbabdcdbcdacdaccaabadbadbccaacbaccdcbdcdaabaacadddcbdcabcbcbbcbdbcddbaccccbaacdddccbcbcbacdaacbbbdbcbcdbcdddbdbbddcdaaaaaddacbbcbcaccbcbddcbdbdacdabbddcadaccbabbadbddaabcbccbbdbcadcddaddbdcdcabbbcacbbcddcccacdadacbbcacacddbbadadbdcacdcbdbdbbaacbcacddddabddddbccdaadccbbadbcdcaadabbabcbbcabcbaacadbcbbcdacbdcbdabdacdbdaabdcbdcdbaddbaabcdadbcbbcabadbaaaccbdbcabcdbbdcdccbcbcbbaacdddbbcbacadbaabbccdcadbdbdcabbcdcdcaaaccacadacdbdcdbacddcbdcbcbabbdbabacccbaadcabbcaccdcddacdbbcbaacdbdcabcadbcccdcbadcdcaddcdabcadbdababaddacbbccbcbbcdaaadddacbbddbabcdcdbbaaaddbbbbcdbccdaadcabcdadacbbcdbcaadbddbdbbaaaadcbacbbcdcacbabaaacaadcacddaadcdbacdddcaacdbbaadcbcabdcdcaabbbdbbaddacadacbcaabcbbaddaabcaddbccacdcbdabcacbaadabddcdacbbbcbcabdcabccdaddaaabaaaccccdbbaabcbaabaabaaacacacbdabddbbbacaccdbcaaaacdacbabbcccacdccabacabcaacbccbbacabccabdbdcdcbdbaabdcbbbbbcbdbdbabbbdddbbdbacacbbbddadcdadbbacbdaacddadccbcbccacdcbccdbcdbcccabbabbcbbbdcdcbccacacacdadbbdcbadddcdacbadadbbabcdadaaacabbcbbbdbcbdcbbdcbdbbcdbaadcdcdbcacdcacbbbaaccddabbabdbbcbdbbacabdbbbdbdacdadacdabdacbdccbbcddcdcccdadddbaccbdaababcdcbbaacbaaabccbcaabbdadcbabadddbabbbdbaabbabccadaadbbcaaddabcadbbbcbdbbddcdacacbcdcbbaaaaadcbccbccdbacdbcacacbcddacbaabcabacdbacbdbabcadbabbcdbbbcbbccaabccdbbcbaaaccddcbcadcdabddccbdcccbccaaaddbbcbcaacbcaccadadbcbcadaddddbbcbdbdcaababadcbdcbcabaaaccaddabdabacddcddacdabdbaccacbbcdcbbddabbddbcdacadbdadbcaadcdacbdbccddddcbbdccdbcbdcbadcaabadbccdbabcddbbdaadbcdddddddbcabbcaddbadaddcabbaabbaddaaaccbbbcaabacacdcaddadabcabbbcadccbaaadccddbaabcbcbbcbdbcaabcacbbcbdacbdccbaaacbaabbcbadbbbcabbaddcbabbcdccdcbdbabcaadbdbbbabbbccaacbdddbcdaadaaccddbabcaacbbdddadcabaaccbbcbbdddcddcdcadcadbddcadccbbdaadadcbaccdbcacccadcacccbabdddbdcaacdabcbccdaaabddcdaaacaccdcccdcbaaacbdbacaaabbbdddbbbdacadaabadcbcdcbbbcbcbbcddddcacdcaacaaaaaacaddcdcdaaccddcddcddadccadddcadacabbccbcaacaacabbccacacdacabbbdbbacababcdabcbcdbdabcbdaabacbdadddccdcbacabaadcbbdbbbbcaabbcbabdbacbcabbdaacabdcbdbbacdccdaaabcddabdccbddcccacbcbdcdbaabaaddabbdbcaccddbcabdadbdaabaacdcababbbadccadaaccabdcbcdabbcbaccbbbbcbbababcdaabdcbdbcdabbabddcbbcbbdbdadacabbcacbaabaaacadddacbdaaaabdcdabaadbaaddbdcbccaabdccdabccadccdcbabdddcbaccdbbadaadadbbabcddcbcdccdaddcddbccbcdacdcddcbaaddbbcaccdcabbadbbddaccbcccdccdadcdabbbcddaaacbdacdbabcbbcaccacdbaddbbccdcaccdcdcaaacbcbcdbcaacbbaddbabcaacbddaaaadcbaccbcdadccddccddddcbbacbbcbbbbbcbdaabddccdcdbccdaaadaaacddbcbabacadaaacccddaacbabcabcbddcccdddcaccabadaccacadcddcbabbbcdacbbaaadcaaaddcbaacdadddcaaddccdcbadbcccdbbdbdbacbbccdbdcbdbaccacacbdccdadacbddbbbbcbdbdbcbdaddcbababddabdcacacddcbcdbbadbdddabbdbccbdaaacbaccacddddadcacdcbbcbdddccbcdbabacadbcbacdabccaaacbbbdcdaadababdbbadcbddbbccdbaacbbbcdbaadccccddcdcadbacccbacacadacbccaccdcddddaccdbadabcaccaadcbdaadadccaaddccdadbdcbddabccbbccbccacbcddccaaacdbcddaabaadbccadcacdadaadddbbbbdcbaacdbbddbcbbababacadcdadbacaddddddaabacdcddbcdcdaadcbcbbdcabbcaaddbddbcbdaaabadcaacdadcddcabbabcddabcdaadcdaaddbaacbbccadacaaddbdcbcbdcdcabcdacacbdbacbcdbadddcbcbbdbdabbbaabcdbcbdabdccdadbdcbadcddcccddabcdacababacbbaaabccbdbdbbbddbccdabbdbababdcdcbbddbacdbccbcbdabcbcbabadacacdbcdacacbcaadadbababdababbaccccbcdabcabacdcdbcadcaaacdcdddcccababadaddaddaccccacdbcadbcadcadbbdacaddaacaddcdacccacccbbaacacdaacacbcadadcdddbddccdbacbdababbcacbbabbacdbadababadbccdcdbbdabdbddbbccccdacccabdccdcbadadcbabadccddccdbdccddcacbdacbaaadbcaddbdccacbbaacaadcadccbadbabacaadcdcbccbcdbbadbccddddccadabdcbbdcddcccbdcbbbcacdbcdacddcdcdaacbabaccdbdbaadabacbdabdacddbaadccbadbcccdbdaaabdbaccdbbdabacdbabcccddbabddaccbccadbdcbdabbccdbbddccbbbbaadbdcdcddbcbbbdbaacbcccdbbbaadcddcdbbbadbdadaacaacdccbbbaccddcbdcadabcdabbbcabcbbacadaacbddabadadcbacacdcbadaaaacdaacdbcadadbbaaccbddbaabccbaccdcbaadbaddaaaabcadbaddcacadbdacbcddbbadccbcdbccbcdbcbabbbdccbbbcabddcbbbaadbddaaadbabdabacdbcdabdcdccdaabddcbddbbabbcabbddbccdacddddabcaadacdcacdbdbabcaabdddddbdaddddbddbacbacadcbbbbdcabddaaadcccbdddbcdcacdcadcadadbcdacadcddbddddbbcacddccbcabddabacdbbdbbabcdcdacdcddadcccbadcaacadcadcccddccdcaaddddcaaccddbaaddddacbddcacadaccdcbdabaabcddabdbdcaaabbbccdaabcaaacdcacdddabdcdccdcabccdcaaabbacabcacdcbdccbbacdccccdccdacddaadbdbbacbdbbcdcbcdbbacdadbcdccccbdabbabacacabbccbddbddddcbdcdccddadcdbbaaacbccbbddadaadcbbdaccccbbcaacccabbdaadddaddcabbcdcabdbbabcbacdbcdbaacabbaabddccadcdbdadabdbbaaacaabccdbbddaaddbcbaccbadbdcadccaccddbbbcbacabbcbadacdcdbbcdaabddadcbcbdadddcaaabbaabdabdbabacbbddabbdabaccabdbdaabdddddcddddcbccbaadababacabdbdbbcbbccacbabcdadaadcdadadbbdbbdbacdadacdcaaaabbcdcbbbccaadcccccadcdcbbaadabddacdcccaccdbdaacaacbadbcabdccdabcaaddbccadddaabddcbbbcacddbcdbccbacdaacadacaabcccdabdcdbacdadbbdabcbadddcbbdabaabddaaacaadabbccabadcdcbabcbbbccdaddaabcddbdcccabcabaddcbcaaabacaacdbbcdbdbdbcbacaaccacbaddadddbacdcdccdaadcdddbcbbcbcbccbccbbaabacbdaccbcaadccadcbcbbabaddbabcbacbddddabcacbccaccbabacddabddcdaddbcbacddbccccddadcabcababbddbabcaccaaadababcadacdacbbccccbdddaabadcdbcabcdacbbadbabdcbdaaccbdcdadaddbdbbdaaaacadbbdaccadababbdaabaccdaccbdbcdddabdadcbdddddaaddacbdcbcccdddbcdadcccbabdacbabddbdddcabcabbdbaaddadadbcdbdbbddbcdbdccbaacaabdcabdcaddabcababdadbaccbbcbcbbaabccbadaadbadaacbbdcbbcaadbbbddcdcdbddbbcabbdadcacbcaddcaadbacaaabbdbdadcabcddcdaccbcadadacaaddbcddadabdbdccadbccddcaccadbaadbadbcbbbaccbcdcbdcbcbcbdbddbbccbcacaabdadadbbaabdbccbcbcbabdababdbaadaaadbdbabdbacdaabdbbdbaaccabddacdadacaacbcabdbabacbdbcbbdbdddbccbbcdddacababcdbaabacddcabcadaddcdbddaaabddbdadbaabdccdabcdbbccbcbddaaadccadaddacbbdcbacbabdabcaadabdbcdcabbdacccbcaddbacbacdaaccdcacaccaadaabcbcdbdadaaaaaadcddbdaadcacbcaaabcadcbdadcbbbcbccccaadccbdabdaccbddcbabdcdcbdabaabcdadccdcdbcbababcbaaabbbdccddcbcbbbbbabadbcbbcdcadcbbaaabdddcadccabdcccdcabcbbacaacbbadccadaacddbbcccacabaaccdaacbcdbcbbdddaadbaccbddbaaaadbaabaaabaacbcdacacdbabbbccbbbbdacabacccdccaadbaddadbdbcdcabadabccdddbcabbaaddaabbccacabdcacdddadaabbabddcaacaadcbccacdddabbccbcbabccdacadacdcbbdddcdcdcccbccbcbcdaddcbadbdbaddcbdabdaaddbaabdaddaacdcccccdccccadacbcddbabbdcbacdbaacbaaabdaadabcadbbaaabbaaccdddcdbccacdabcacdccbdcaacdaddbbadbadabdbaaddddbacacccabcbaababaccbcbbaabdbbadbdaacdcbaabbbcbbbddbdaaddaaacaddbdcddaacdaaccccababbcdbbbcbddcdccdcacacbdccabbcbbcadcabaaadabbbddacddbbddacddcdbcdbbabbbbadbbdccacaabcacbcccaaadbcaadcdbbcacaddacadabbbaaddddbbdacdbcdaacbbddaabbcacccbadabcadbdbcabbccadcaaabaaabaacdbacccbdcddbcbbbcabbdabbbbddbdbaadbdaababbcbccdddadcabdbadaacccddcdbcacdabbabbadaaaaabcbcabdadcdbadaacccccccaacbacaabdcbabaaadcaaabbdbdaaabddaddbadaabaadbbbcabaaabaaccdbdaddcabccbddaddacadccacdbbccdaaddccbbdcbbcddbabdbadccadbcdaababcaaacaaaddadcaddabcccddacbdcbbcdacbbccdbcadadbbddbcaabaadbcbcccdabaccbcddbbaccbcacdbaababddbababbabcbbacbccbdabcdaccdcdccadccdbbbcabccbbdacbddbaadbccdabdddaabdaccaabdbaaacabbccbacddbcbdaaadcdcacbbcccadaccdadaacbacabaccaabcdddaddbaccbabcddddbcadaccdacddbcadcdbbcdbdcaadccbadcadbdacccaccdccabddadddbdadbdcdcbcbbbccddcbdcbbdacbbcdddbcdcaabbdbccabdaaddadbdcbbabcbbcaadaacbcaddbccadbacabbdbdbbabbbccccdbaaadbcdbccbdcbdcbdcaabbaacaabccaaaaabbccbdaddabacdbacdacacaaacacdcabbcdbaadcddcbaacabbddaaababdcccdbacdcbbdcdbadbbacbdbaaacdaaacbcdbadccabadaabaaababdbdbccbacadbbbdaabdcaabdacbcdccadcbcacabdccbcababacadbbdbabccabaccaddbcbadbadcdcbdadbdabdccabcbddadaacdbcdcdcdbbbadbbbaaabcacccbabdaccccbadddddcdadbdadbcabddcdbacacadbbcdacdbccbcbcccdcbaabaadddcdacdabcdaabbabcbcabcbcbdcbcadbadababddbdcccdabbcaaccddddbdabdddcdcadbacccbcdcacdddaaccddddcbcdbccaddbbbdcabcbadbcbcdbabcdaacccdabcccddccddbccdaddabcdaccbdabbdadaababbbabcccbdbcbacbcbbbcaacddcadbcaaadbbbbccdcadddadadaccaacdadbacdcdaaccadcaabbababbddcbadadbacbaadabbababcaccbbcaccabdcadbbaddbcbcbcabacddabddbdcabdccdcbbaacdaacccbbdcccadccbbaccbcbcabcacbbcdacdbbcadccacadcababaccbcaddccdcdbcbcbdcdbadadaaadacdaddbcdcaadadcacdbbccaaacccacaadbbcadaaddbbbcbbabddabdbdbbadabacdbcaacaddddcccacacdbccbaababdabcbdbbdaccaaccccdacbdaddcccddabdccdaddbbcddabccbabbaadaccabbbccaacbccaaddccdabbccbccbbccccbaadacdadaadbbaadbaabbcdabbadccacccbdabcbdbabbcbbdccacacccbccaaadabdabbcaadaaaadbbadbdcbadacacacdddadcdbabadbbcbadabdbdbdcadabcaabddaabbabddbbcbdbbbdaccbabcdbddcabcdacbdddacdbdcabdacccadccbdddadbddcbdcbddbadbcddbccdddaaacbbbadbbdcbbabaadadccdccdadaaccaabadacdbbcdcbcbabacdadadbaaacdadabbddcdaacdddcdaacabbccbdbbdabbdcaccdbbdccbacbdcddbacaacdcccddcccdaaacabaaddcabacdcdccdbabbbcdcbbacbcabbacbcccbbaabddccbbaadbddabcdbcbaadcdaadbdbccacddbadaddbcdbdbbbaaccdbbcadaaaadacccacdacccdcaabbcbbcdccabcbcdababdacddadbdcddbbbcdddbabaaacacbcbbdaccacdbcbdbbdaaaaacbbccabddbaabbaacadabdcacdcbcdbdcdbcabdcdacabbbddaddccbbabcddbbdacdbcaaadadccddcddabacbdcaccaadbaaadcbbdadaaaacaabdcdcdaacddaaddccdacbdbababccabbdcdbadccccdadadadaccaccbacdccccbcdddbabbcababddccbddadbcbcbcdcadbbcccdbdbcdccbaddacccabcdbcbcdbcacbddaddcaccbbdaccacddcaaacbccadabdccbcdccbabbccdcdbdacaacbdbbbcddadcdadcddabbbbdadadcbdabbadcdbdcaaacddacccabadbbbaabbcababaaccbdabaccbccbcacacbaacdcabcbcbcaddbccddbdabbacdaddcdcadcaacbbbccacbaabbdbadcabdccaccdaadadaacbbdcabcbabdbbbaabdbadcaaabcdacbcdbbadbdbbcdbbdbaccadaabddcabccbbdaccbbccdddccdcccdbbcdaddcaaaaabdcdaadcccdadcdccdddbbddbbaabcbbdcdadbcdcabbcddacbadbbbacdbadaababbabdbabddaadccadaadccabdadcddabcccabadbaabcbaabbcdbaaccdabccbcdbbaccacabdadbbbbabcdacadabacabaccbbacdccbbbdccddbbccaacacbbcdcabaadccadadadccddcbbbcacacdcacbcaadbbcabacbdddaddcacddacdbdcddcabaadcdabcabcbcacdbddadcbbaadccccdabaadcacdccdbdbacadaccbbdcddbabaddabbbaadadbcddcacbcabcaddbcacabaaaddadbdbbaadddbdadbadaabacbabcabaacbabcacbccadbbaccaddddccbdcbccddcbccbcdbbbdaaacddacdadccacdbcdddcdbdbcbbaddbaabacabbddbddbcdbdaadadbaadbcabdbabddbbdccbabcabcabbdddcdbdcbbbdaaaaabacadccabcbaacbbdaaccbdccdbaaadbdccddbdbabbbbacadaaabcdaccbaddbdadbccdcbcdabaacaccbbadcddcdcbaddacadabddadaacadaadccdbbcdaadddcdbaaabcbdbccdabadadcbdaabbdbdddddcdbaacdacabcbddbbccbbcbdadddaadbaccaabcaddbacccdcdadbdacbaccbdbbcdadbdabbdabcacabadbbbbaacdabdacdacdaadccdadbaaccdadbadcaacdaaddcdabbcccbddbdaddbacadcddcddbbbbabacbabbccaccdbacccdbbcaaacaadcbbbcbaabbbccbcbccaaabddcdaccddadbbbbcdadcaabcdcabdbcbdccdbbccdcbdbcdbaaabdbcdcbdabdbbdcddbbcadccdcaacbacdbbdccbdddaacbaccbbcccabbaaadcbaadcdcabdcdddabcaccabbadabdddbbdbacbcbaacdbdddaaabbcabcbdadcddabbddbaccbcbddcbbddadcbddcaddababaacaadacaaabccadbaabccbadcaadacaddccccbdabababbacdabcdccbadcdbbaacaabadcdddabcdcbadbcdbabbbddbcbddacacdcbbdddcbbcbbddadcacaccccdbbcbdacddbadabbdaaaacdbddcbaadbbaabcacaababdbaccdabbccddccdbadddaccdacdbbcbaabcdccabccddccaaddadddabaadacdabacbcabbcbdbbbdbdbdbdcbdbaccccaadcdcbbbbcacdacacaadaaaabcbabcbacbdcbdcdaaddbabccbaaaacadbdbddabcdddaacadcddcaacaaacbcdcccdcdacdcbbadaaadddcbbbabbaabaccdddbaadbddddcdbccbbdddbdaadcbddacdcbcdacabdacbbdcccdbacbdcaaabbbcdccbacdbabaaaaacbbbcdaacbbcacabdadcdbbadcbddadabcdabadbdbaccbdbbcdabbbacdaccdcbcaaacbcaadaaaacaadcdcdcdabaaddbdcdaaaaacbccbdddadacdcddddcbbbcddbbaadbcaccadcacccbbcdcdaabccddcdbaadcdaccbdbaddbbdcbabadadcbbacddddcbacdbbbcdadccacbadcddbdacdddbabcabdadccbadddccddcdbadbdadadbcbdddbaabcababdaddcccadccabbdcbcbcdabdadbcddddadddcdddadbcdbbbbdbadcdcacccdcacbddbacdcbbcdcdbddddbbbdccbddcadbccababcadadabacbbbcacaaababcabccbbdccbbdacbddabaadbdbdcbaccacbbddbabdbaabbbdbbccbccbbcbbdbbddbacbccabccadcbbaabaccaacadddcbadaaccadcaaacbcdddbbcbdbacabcabbdbdacddcaddacabadbcbcbacaabcacaadaaddbdbcdcabcabdcdddbdbdbbbaddbcadadbaccbbdabdbacacaccadcbdbbcdbdadaddbbdccbcbaababdadcdcbbbcaadbaddbdaadbcbdabdabbddbbbadabaacbbbcadabadbdcaddbbcddbddbbdcdbaaccdddcccbcdcbcabdadddccadaabccadacdaaadddacaaaabddbdbacacdbabdadcbbdcadbbaadaadabbbbadbdbbaaccdaabccaaadcdbdbaddcdabdbbacddcdadabaadbcdccbadcaabbbacccacbbdabacdddcbdcbaacdbdbabbddbdcdbabcddbcadcbdacdbcbbbddacbdbdbadcdbcaadabaacbddbaddcabbdbabbcddaadbccdbbabaadcaddcacccbadbdbdcccdbccacdccccdcdcddbdccadabcbdbdcdaaddbccbbdbccdddaacbabdbaacaabcddbbcbaacdddcbaadbacdbbacbabaccaaabacbacdbbbaccbbdbbbaccabdacacacadddbbcdbcdcaadbacbddcadadbbaabbcdabaabbdacbdbdbccbddcacabccccdaadbdbdbcbcdccacccccbcccbddadcdaadaddbdddbbbdacadcaadabaadaacbadcacdabbacbcccbdabacbbbbccadbbacaababdabcdbddabadaabbadcdddbacadabdadbdbddaccdcbddbadbcbdbddbddadadbacabbadbcadbbaacbdaadbbadcbddbcadddbbabdcbacdbcbaccbddacacabcadadbbbcaccbaccabbabdbabbdaaccdacdbbbaabcbabccaccabbadaccbaccbcddaacdcbbbcbcaabcbcdcbdbccaaacccbbaababaacbbccdcdabaabbbaabcdaccdbddbcdacddaccdbbbacdbbbbabdcdbcaccadcabadcbbadadaaadadbbaadaaabddcaaddcccabdbbbbdadbccdbdadababdabacbbcacadbaabcdacdbaaaadabaacbabbdabcccdcbaaccdbadcdcccbccbdaabdabcaabddbbbcbccaacaadbdaacabdcaccbcccacdbdadacacccbdbcaccbcbbcccacbadccddababdcdabbacbacbbcadcbbbdcacdcdadaccacaadbccdddaddadacdbdbdbaaabdcacddcbcbdadabadbcddccbdabbadcabdacdbdbdacabddccadaaddcdbdbccdbababacbbcadcbabaddcdddcaacdddaabaccccabbbabcacdcabcbadcdabbaacbdbdccdcdadaadabbbabdcaaaaacaccabaadadaddccdbaacdcacbdbcadbdccbabcbcbccbdccaddbdbccbdcddbcdcdabaabcabaacbacbaacbcdcbdbdbcccbbbbcdddddcdddaadbbbdbabbabdacbbbbdaadcbbdcbbddcdcbabdacdccbadccdbdcaacacbddddcacabbdbbbbcccadbcaccddbacbcabcbabaadabbadbcacddbacdddcbcbbbccadcabdcdbacbcdbdaaccbdccbcddcbcddaaabaacaaacdadaaacadadbcbaaadaadbcddacaabcacacabbdcbdcdcdabcadddbdaaccbbadbaaaddbcabbdbbdaaabdcbbcdaabcabaaaadababdabacaccbaaabbcdcdddbbbadcbaaaabaaddcabbacbcddcabbacdadacaaadaacccddbbbddaaaacbdbdbbbdaabcddcdbadcadcbdccccdbacbdaaccadcbddacaccdcacaacbabadadcbdcdbaaadcaabdacbdccbbdbdaddbadcccacbdddccacbcbcdaccdcacbbbabbdcdccaddaaababbcbdabdabaabbbaddbcadabcbabaaaacabaddacddbdadabdababccbacdadacbdddcaacbcdabadacadadccdbbaacbabdcacbbaaabdcaccbdaacdabaddaddbaaaacbadccdcbabacbbcbadccccddcddcccccbdcadbdcddcadccbbcabbacdabaacdcadaabdddcbacdccdbbcccdabbcbacdcdcacbbdbdabaccbdcbddcbabdcbdcaabdcabccbdcacbaddabdddcdacbbbbabddabadbdcaabaccacaaaabbbabadbbcdaddabaadaaadcdddbadacddabcbcbabdbcacbacabbdabadabccdacbccbbcccaaacadbcdbbcccabdaccaaabbcaabcccabbcccbbdcbcddacaddacdadabdcaccacdcccdbdbdccdbcdaacaaabababdbaacababadbdacacddbdcbbdddbbbdddabdacabaabbaadbcabbcccccbdcaacabbacdabbcadcbcdbacaadabacbcbdcbdabcdddcabaccdadccabcccabcbbbbcacdbcdcbbbbdbbabaaccadaabdbdbadccbbbccbdbbcacdbcdcccdaaadaccbbaaddbcbadcdcaadcbcbdaabddacbbcdbcddcdccdbbaadcdadcbaaaadadbadccdbbbbddcadadbcbdbacdabdcbadbbabcdacaabaccdbbcddadbbbddbcbacbdcabcbcabcabbcaadccdcbcdbacababbcbccacacdcbdaaccaddbddbccccadcadcacbcdcbaaabbcdcaabbdcaaadddabbdbddaadbddcbacdccbbadbaacccacdddbacddbaaddbdacbbbacdaaaccccaabddcdddbbcabccbbdcbdbdcadabdabcdbbdbabacabcdbddabaddccbacaccdcdbcbbacdaddcbdacabddcbdbcbddcaacdbbcbaababbbddababbddbbccbadbbbccbdacdcdddcbbcaabcddddccadbdbccaacacabdcabcbbcbbcacbbabccdaabdbadbdccaadcccadddaabcbdcaccdcbdbcccdcabbdbbcbcdbadddbabbbbcccbabaacbbccaccbadadaabadcbdbaaaabbccaadbcddbdaccdddaacdcdadacadadbbbbacaabdcbaabcdaadbdcbbaaaadacbdcadaddbcdbadbadabcaccdababcccbcacbbdccadcadcadcbbbdccbdcdaacbbdbdbcaddddccadaacacccaaccaabdddbddabacbcbacaaabcccbbdbdbdbbbadbbdcaabbadcaabdbcdbbdcabccbcadaddccadcdcbdacbcdccdacabadbadddcdbccdcbdccddaadbacbbbabbacbaadcacbbbadccaabbaccabccaccddacadcbccddbadcccdabdbcabddbcdaccadddddbaddcddcdbaaaddbcdbbbdaadcdcdcabacbbbdccddbdddacccaaccdcadacacccadcbbcbdddadbcccbcddbcbccaaacbacacbcdbbacbdcacbbbcdddccdcbddabaabadcadcabccbaddacabbadbbccdddcccaacacabcabcbdcddccbabaccbdcacdbcddbadbdbbacabdacdddbbbdcbcbddbaacddbbcbdabaadbabbcabbacdacbbadaabcdbdacddcccdbcbdcbcacabacabadabcbaaaaccabdbaaaabdcaabbbbbddccbbdbacddabcddbbaacbcbbabdbbabcdacdaadcabdbabadbddabbbbaacbabacabaaaddddbbacabddaaccbdccbcabcbdbaadbabadcaccabccabcaadabcbbbdbcdadadaddacbccbcbacbdbbdcaacbaadcbbdcbbddbbdbdadbccabcadcbdccdadadcbcccdabdaaacddccdcddacbdcbccabaadbbdbbbccadbbcbdaddacdbcbdccadcdccdddbdcbccdcdbdcacdbaabcaaddccddbacdacdbdbcbbdaccdbdbbcbdddbbdbdacadcaaabcdadaadbbbccdaaccdabcabbadadbacdbcbacbddcdadcadacbdcdcaadacbaaadbbadcbbbaaaabaccbbccdaaddbbcadacdadddabdbaadbbacbcbddbaadcdadaacdcbbcdadbbbdbaacccdbaaaacbbdacacbdcbdacbbaadaadcddccabbaccddbbdbdbcabdcbacbdabaacadcacbcabaabaaaabbdaaaaddccdbabdaacaacccaddbbcdbadcdabbccbcdaadbddcbdcdabadbaadccabadccaccdaaaacdbbaabcdddcbbcdacbbcbcdccacdabbaacbcdcadaaacaaccccabbcaccaaabcdbaabcdcbbaddddabadcaabcbabababcbccbaadcaddacdacdbdcdadaccbadcbcabcacccdbdbcaccdbdacacadbaacdcdcdcaabdadcbbcbabaadadcdccaadbbdbbddacbadaaaaaccadabaccabccbabadbcdcbdddddbdccdbbabcddccaadaaccbdbccccaaadbccadaaacbbbbbaddadcdbbdbcbbacbdcbcadccbdaddadabaaddcddadbabdddacacabcdbdbacaddcdabcabcdcaccbdbabdcdddacdccbccabbbadcacaabcdadabddacdadbdbcbcdbbcccaddadddccadabbcaccdcbcbdacbaccbabcbbdbbdadccabbcaacdbdadaacaddabccbadacdccbcbbcdabbcdbabbabdaacbbcaadcbdabadaadaadbcabdaacbccddcdcbccaadcbccdadadaacdababadbbcdadbdaaaabdabbadaabdddaddbabcdbdadadaaaaddcdaccdcddddabaaccbaccdbdadbccadaddbadbbabdbbcdacddaabcbdbbdadabdadcadbdbdabcccdadcaabddabaaacdbadbddbaabadbcbdddacbcaaacccccbadcacbbcdbbabdbccdcdddaabddbabbaacbbbbbadccbaaadaccccccddcacdbaababaddaccddddcdbcdcbccabadbcbaccdaaddddbadbdbbddbbcbdbacdaacbccccabddbbaddcbbdbbaaacdcdaccddacdcdccbacdddacadbbadbbbccadbcdcadbaabbbabddbcdbdabcacacdbdddccabacbabdddddcddbbbdbddaacbcdaccddcbbdccbcbddccbcbddacdcadabbaadbbaacaddbbbabbabbdaabbdbbcbbdacccddcaddacdddbdbbaacdbbbdabbbdcbbbaccccbbccaadddaccaddcbcdcadbabaacdbacccddcabccacadbdddaccacaccadcabdbaaddadccccbccccababcdcbbdcdcdbbcbbcaaccbdadacbdbcdaabdacaaaadacdcacbaabaccacdccbdbcdcbccbaabbccdbabcdddacbccccadbbadbbcbcabbcbccaaabccddddabadcddacbccccadbacbdaabccaccccaacaacdcdddacaabbabdabdadabbbbabacdccaaabbcabaaddcccacddcbdbcddbaabdabaddbadccdcbdaddadadaccddbabadbddbacdacddbbbabcbacccaaabaabbddaddddaddadccdacddadacbbacbcbadbdcaccdcaaccacbbadddcdabaacaddadddacacadcccdbcabadbbbaccbdddaaaabdddcadcadbacbacbcdcdbcdbcadaacaaaaccbcccbbadbaccbdcadaadbadccbcbcdaacacabccdabdaadbcabcbdadacaabccaaabdbcdaaadaaccbdbadbbacddabcadbddabaaaabababaddbbcaddcbdbbbbdbbbacdcccbdbbddddcabcccacacbcbdaabbadaccaacbbdcbbbcdbdadccbbadbcadbbabbdaaabcdbcdbdccdabdaccdadbacdbdbcbadcbdccdabbcabcdadccdcbbdbdadacdacbdacbadbdcdddadcaaaddccacbcccabdbcbabdcdcadaadaabbdbaabbbabdadcdbadbdabcdbdbbdacdaccbbbcadbbadabdbacaabbccddacdcdcaccdbbdcddbbcbbdbdcadbcdbcdcdacadbcdcdbcdbddadbaaadddaadcdcdddaadbdcabccbdcddcacdcdaabaaadbbcadacdcddddcdbdccdcaaaddaddddcbcaabcdabcbddbaabcacbcbdaacbdabdbabcdcbaabacaacdcccccaddccdacbcbdacdbddacdbccdbabbcacbbdbcbdccbbcaadcccddbcabbbdbadabcadadddbcbccddacbbdbacbbcaacccbacacabacbaabdbcbbaadbccaccdbcdadabbadcbcabbdbaddadbadabbbbabbdacdbcbcaddababacbcccccacddacacbbaadccabdbbcaacdacdadaccbacbcdaadbbaddabbbddabbcabacbbcdbddadaaadbbcaaadcabbdcccbbddccdcaaaaaccbdbbbcacbabbacdacddaccdaadcaddddacbdbbdbdbbacaacbdcbddbabbdabdbddacabdddbbccbabcbdbacacddbadadbabadcccbddcabadbdcaddddbacdcbdacabbbdabbaabddbddbaaccacdcbbaaacdccbbcdbcdabccdcadbbacbdaaaaabcababddbacdaabdacadadddbadcdcbcdacacddacccdadcababccbbacbbdbdaadbbccdccbadacaddbcbdaaccacdcdcbdbdddcbbcbdccccbdccaccaccdccbdbddbaacbdcdddbacbdababdbccbabccbabdcbcacdcdcbddccacddacaddddbcbdcddbbbaaaaacdddabcbddbcdcbdabaddacabaccaddaaaaaaadaddbdddccbddaacddbbdadddcbbaaadcbddaaaaaabddccbdbcccddcdcdaabcabdbbaaabbcdbacbdacdbabcabbbcacbababbbcbdbdbacdddbcbadccaadcdcbbcdcaddcabcdcbbaacababdacaadcccdccdbbcbdbccbcddaccacbcbbbbcdaaaddddabbababaaaacaaaadcaddbdbddcddbadbcacdabdbbcbcabcbbbbcdbaddabccdcbdbadaacdacaadbccbcdabcdbcdbddbddbdcdddadbdaadcddccacaacdaadacdcdcbbcdbcabadbdadaddcdbbcdbbacddbdadcbabbcdaadcbdabbadcbdaacbdcdccddbdddbaddbcaccaadaccaacacbabddaaacdadbdcbcaddbbccdccbbcbdadcaddbbccdabdbccbbcdaabdbcbdbbdccdbaaddccadbdbdcaabadccbddbccdcbcddcabbcacbddacdacddcbdaaadabaccbdbdbdabaacdacaabcddabbcadcacbcdacacccccbadcacbabbdbbcbbcccadbdbbdbdabbacdcdbacbdacbaaaccadddaababdcbabbdbccdadbacddbcdcadccbabbcaadcabcdbbaddcabadadbddcbccdabbacaaacbabdcbdaacbcaaaddcdacabacdccadabacabcaacbddacabcbcdabdcbbcdcddcaacbbcdcaddaacdacdccbaccbccadcddbaddcccbcddabcbbdbabbbcddcbadadabcdaadcacdcdbbabdddabadccdbddaaddddcdddcadcbbcdcccddbadddadbdbbbdddcbdbbddcababacdbccbdacbbacaacbabcabccaaadcdccbadbbbbaaaccacabacbacbbbcdcadbbcdabdcbbccabaaacbacdbdbbaaababbcdcddcbccabdcdacadcdacbdcaacabbaabddaabcaadccadadbccbcabadddabcbdcaabcdaadaadaaaccaaaddddbdaacbbdaddaaccadabcbacabaddcaaabaaacdbdbbaccbbddcacbbdaccdabdcbbbddabdbbbacdcabdcbaadddcbcbcdbadbcdadbdbbbadbddabadbacbbcbcbddbbbccbababbccdccbcacbcdbddcacaddccccabcbbdcabcdbbdcbccbbbdddbabcaddacdacabbaaabaadbccbabbcabcdcddbbcdadbbddcdbaddabdcdcdbbabacacbcdddbacddacccdabccddacaabacdbbabbcdddbdbcdbabdaaabddabacbdbccababadcacdacacbcbbbdbcdcbbdcdaaacdacadcdccbdbbccaddabaacdccddbbabdadccbbbcdacdcaadccadcccddacbddcbdaaadbdbbbcbcddcaaddbcddadcaabdddcdcdaaccabbcbcbacdcdcccaadcacdcaadabcbbbbbcaabdcacbabcadadbdbaabadaadcbdbadbacdcadaddbdbbddadbaadddcccdaaacddadcccdadbdadbcdccddcaccaaaccabacdccdaacaccadcaccbdbcabddadcabdadabdcabdcbcbcbbaddbbabacbabccbbdcbcdcbcbbadbcddcbbddddbdacccacbbcdcaddadbcabcddacccbcabacabcbdbdcddcacbacdcbcbcbbabaaaabaadbcbdcbbbddbdccdbbabdbbabddcaaacbbbabcdbacccacbbbdccccacccabcbddbccddabaabdbbdcbdddadababadadcccccdcacccbdabbabddbcbccdcdabdbdadcdacabddcddbacdddbcbcadcbcbcccdabddbabaadddadbbdcabbdaccccdddbaccaabaadbadbdcddccbadabbdcccdcadcacbdbccabbbbccdbacbdbabbbcbccbaddbccaacdcabdbabddcddaaadbcbcbbbdbabdbbddddcbbdaaddcccddcdcbbdbbdacbbcbcdaacbaddddccadaddcdcdbdbbdadcaccbbddbccddcbdcbdcbddbbacddcdbbaddcddbbbcdacbacbbbacabadaacbcacbddcbccdacacbbcbbbbdbabdcbbdccdcdadbdbbdbbabaccaccdbdadcdbbcaabbbacabadbdbdcbdbcadadcdddcbcbabbadbadbaadddaadaabbbcbcbcadbabbcbaaccacaadadaabacbbcbcbcdbddddbdadddccccadbbddbabddddcdcaacbacdddcdccdbadbaddaadabaabcdabaaabbbbcbdcaccbcaadbcdcaacacdbcbacaacbddbaacccddbcacabbbababddcabaacaddaaabcbaccdbdddbcccdacdbddbdaaacadcbcdccdbdacbbddbdabddccbdccddabaababcbacbcbccdbabbcabcadaabddcbaaccabdccdbbdadbbdabaacbabbcacadbdbcbcdadcddbbadcabadabadaabdbabbbccccdabbcdacdbdcbdbbcccabddcbcdbbdbbdbddddddaababadbabdaaaaddbdaabddadacccababacdccbccddccdbccadbbbcbdabddababbdccdcbdbccaaccdbbbbaabcadacadabdcdbadcadbaccbdddbcdcbddddcbbadcdcbccaabdbababcadabacaddadbcbbcdcccaabadabcbdbcdcddcababdabbbbccacbbdaddbccadbddcccccadcbacddabcaccdddadaccdacaabcbccccacadabdbbbbbaccbbbcbaadadbcbbdabacababdddbdcbbaacdacdcaabcbabaadacdacdaaddadcdadccabbdcbbcdcdcdbacdcdacaacdcacacabdaaaddcbdadadababccaacaddbcdddbdaabcbcaaaabcabdbbaabbcadccbdadbdcbaadbbbaabdbbadddcabacbbbcbbcadbdcdbbcdbdbdaaccbbbdbbcbdcdabddcbdddbdaadbacddcbbbacbacabbbbdccaaabddbcbacbbaaacacbdaccbcbddcadacbcaacbadacaddbdcbcaacdacdbbbbcbcdbbbddccacacccccdbcddbadabcccbccadbabcbddbadbbaddaabcdadccdbcaaaadcabacdcabbddadccbacdcbaaccbadcbadcccdaddcacaabadccabdaddbcaccbacdacbcaabaaaaccacdbcacadbcddbaacdbdabacdadadcabccaccbcabbcabbdadbbbcdbcbcabaddabdbaacadcadcbaacdbcdbccabbaabdbbdbcdbddbcbddbccbadcdbadadcbdaadbddcbdcbdbcabddccbbbabcbbacbdbdbdddaaabcbddacdbaaccadacaadbaadccaaabaabdcbaabcbdccbbdccabcacacbadbbccadaabbbacdccbbcbdbcadcabbcbdbcacacdbdbabdabaaabdbbcddbbadcacbdcdacdaaacdbdaddcaadaacbbdabbbbbbcbacacbcbaacbdaadbdcadaadcdddcbcbaaccbcccacdabbcbdcdccdcbbdabacdabddcdaadccdaadacbdbdcacdccdbbbadccdacbdbdcbbdcdbbcbddbcdcadbbacdddcccbdcbbabcaacddadcadddabbbbbacabdcdddcabdbabcaabcccbaabadadabaadcacbadbdcccaccbcabdabcbccdbadaadcdbdcbbbcbddbdabccaabbdbcaabaacacbabbccaabdbbbbbccdaacbacbddbbdaababaddbaadbdababacdcccacccbdaddbbbcbdbcdbbdaddbdacbbbbbdaacadaacaaaaddcbcdabdbcaaabbcaccdbccbadcabdccbdbcdddbcabacbdaaaaaaadcbdbcbdcdbbbcaccbccccadbdbcabbddaadadcbddbabaadddabbacaaadbddaccabdadbacbbbddbccbcaacacbccabdadccacbacabbbaaccdbcaadddbddbccddbbaccaadbccddbcbaaccadaadacbbbbccdddcbabaaadbbacdbbdccaacabaabdcacacbbcdbdcdbabcbccabcdbabcbaaabcbacbdddddcbcdcbaaddbabbcbdabcaaacbadbdccaaaaababadcabaddbddabaddccbbcaaadcdddcaccabbdbbababadbbacdbdcbabadaabbbdcbdaacdcaaaaadcbbbdddcdcaddbbccdbccaababcbcbddcaccddabdccdcadabbabdcdcdbbcacbddabbbbbdddbadcbaddcdcbdcdbaaababacbddbabdbbccaccacaadccaaabccbbaaccdbccbdcababcbbbbccacccccacdababcbccbcdaccdacdddadcacaadaabbcdbcaddcadddabadcbcbccdaadcacdbbaaaabcdcbabccddcbaddccaaddbbdaddbdcddaacdadcbbccdcbbbbcbacaabbcabcdaabbcbccababadbddaaaadadccdaaacacbddabdbbcbdbabccddccaddcbcbcbdbbcadcccdbdcbbdccbcdacddbaabbaddbaaadaccccabdddddcbbcbdaabadbcadadbdadddcccbcaabddcbbbcaadccbabaabccbcbaadaaabdbccdadccbbbadbcbcbbcbcbabcddbbadcdcadbbbddcdcbadcbabbaadbdbadaaacccddbdbbcabdbabaaaadadbcbcaddbbbbbddcacbccaaccbaabacdccbbbadadbdadcaccaaaadcdcaadddcbbaaabbabbcadbaabacadaaabbcaddbdbacccabdbcaddbddcccdcadababcaaaaaaaccbaacdbcddacccdabaacaddcbdcaadaaabdbddcbddabccdbdbcccddabcbcadacadbbbcadbabddcacccdaabbcdbdcccbabbcbabbcaaabcdddbbdcadaccadccdbaccdacbcbaababdbbddbdadadbaddabcbdbaccacaadcdcbaadbcbabbdbdbdbaacdcabaadbdabcbbbaabcaccbcbcbaadcbdbdbdcadbdbcadcdcacdbabdacacaaddabbacdbdbbdbdbbdbbabaadccccdcabbbaaacdaadabbaaaaddbacdcadcccdcbaccdcddababbcddcaddbcdabdacdcabaaddcbcbbdcddccbabadccdcbcdacccccdbcccdacadddddccabbbabaaddaddabcaccadaacddadbbaabdabbcbbdddaccbaccbcdbbbdcdcadcbbabdcbcddbbdbddadbbdddbaddcadbbcaacccaddccacaaddaacbaabaddcdcbdcdbdcbdbddcdbaddcbabaaccdbcdccddcccbdbabcabbacdcabbddadaaabcacbbadbbbccdcacaccdadddbbbbacbbcbcaaccacadbbcdabcdbbccdcbbcdbbbaabbbacbcababbcaddbddccdbdbdbabaccbccbaaaacaacadadcdacbbbcbccacbaccdaccddcdbdccdaaadddcbdbabbdbbcdbcddcdcbccdbacacacbdbbacddccbcadccdabdaacbdcddadddcccccbbcdcdabdbcdcacbdccddccbdcaacbcadacbdadcdcdcbacddbdbbbdcdcaccacacdddaabacdcaabdaacaadaadccdababbdaaaadcbcbbbccadccbaccccdadbdddcdcabcbcadddcdadcacbbaadaccbadbcdacbbadbdbddacacddabbbbbbbdadcacdccadddaadcddccbaacabcbdddcaadaccbbacadbbaacbdacdbacccdabdcbacbdacddccdddaccabbdddacbcdbbcacbacdddbcbbbcbdbcbbdcbbabdbadbdbcabccccabbabcbbaadbaddbccccabcabcdcbbbacbbdccdabaabacbdddcdabbcbccdcdbaddabdddcaabbcbbdadcadadcacaabbbbdadaacccacaacbdbbcaccbbdbbcacbdccdbadbcbdcccacdcdabbbbaacddacddccdbdbdddbddcaaaaaaabcbbddaddddcbdcbcaccbcdcdacbdcdbdbbabdaababdbaababdccddbabacddddbdbcbbcddbccbacabaabadbbbddddddcbadacbabaddbbbddabbcddacadabddcdcdcabbbbbcbccadcabadbcbadbddcdbbdbaadaababcbccbaabdddaadcccdcddbdbaaacbbabbcdadccccdacbbdabbbacbabdcdcadbbdcdacaabdcabbdbabadbdbcbadcaacaaabaadcbdcaaabadddbdbccaaabdbbadaadcdcaacbdcdbabddbcccdaddadddcccddaaaadabcaaccbbbddccddadacadbbbbcabccbdcddacdacdbdcaaddbdccbbbdcdaadddddbcccbaaccbabbaaccbcaacaccaacbbddaaccddccdbccbccaaacdaacacbdcacbcccbdbbabbaabbaabcccaabdbcabcdbabcdacbaddacadcacbccadcdbdbdbdaacdbddbcdbbbacccadbbcddadbccbcaccacabadbadcadbdaddacdcacaaabaacabbacdcacaddcacbbbadbbbbbcabbbddadccbdacdaccddddbbbdccdaacddadbabaaabbbbbbaddabcbbaddbbdcddbdcdbaddbcaadbcbdcabcadbaaaaadbdabcddddbdadccaacadcbbadadabbdbdbcbbcacbacbdbddbaaaaaddbbbccacaabccdccccccdacaadbadbccabcacdbbabbdbabddddddcdcddbaadbcdbccdabdbbacbaaccbbdcdcddbdbacbadcbcaacadcccadccdcbaccadcdddcaabadbbabacbaacbdddabcaddcddbddddbaabcaaccababdcddaccdcdbdbbdcabcdcbaccbdbdccbccbcddccdabbacaabcddcbcbddabcdabcbdadbdacccdacadcdbacddccdbbcaabaccdcbdbbbabdddcabdacccdadacdabdbabccddbccbacbcccadbdccdcdcbadddcbbdbdcdbabbadccabddbaddcdbdcbdaccdbabbddbbababddddccbbcbbbcadcbbaacaccddbcdadcadccabcabcaacccaabcbabaaabbdbdacacabcbddccdbdcccddccbbdadccadaccabccbbdacadaddcccabaadaadccccdbdaababcabdcacaccacdbccaaaabbacccddbbacbbccbdcdadacacbccacbbbdbcbdadcbbdcaababbadacdccccadccbddaddcacacccbbcccacaadcbabcabbacbdccbdddddbbbddaaddadcacaabadddcdadabcbcabaaabaabcddadddaabadacbdbdbcabbdacdabbcbadbdcbbaaabcdbdababdcbdcbbbccaadccdcadadbbbddcdbdabbddbcdbcbcddcbdddaddadcdcaccaacbaabcddabdbbcbdcaacddbabddbcbbbdabdaaccbacdddaacbacbbbadbabbabdbabbaddbbaabaaabcdccacbbcccbabcbddababacbdabbbbcbcbaacdddbcabacadbaacadabcbacdabaaabadacbcaaaadbacaaabdcabcbabacbbadabccbbcbdbcbccabdbdccdcccabbbcbdcbbdbcdddacbbcbcdcdacaacaabcbddccdbcbcaacacdcccabcbdacddbadadbbaabbacccdbaadbaabdaabbbdbcdbdbccdaaabcdaadbadacaabdaacbdcdabdbbacadddcbcdbbcdbdcbbcbaabccdcddadadbbbdccacddbcbbcccbbcbcbaccdabdadbdbdcdcdabacadbcdddbccbcdbddcacaccbdaacbdbbadadabdaddddcabaaabbbbcabdccadcdddaadaddbcbddacabbcccbadccbabcabcddaacabcaccdcaacacccbaabdadcaadddcdbddaaadacbbdabbdbbabadadcaddadbcaadccbaaacdbcccdccdbaccacbbbabcbbccadcddcacdabddccaacdcdacdabdadccdddccbccccbcdcababcbdcdddcaadaadbcababbcaccacaadbadbcbdacadcddcdabddcccabbbccdaaacddcdbaaddcbccaaccbcdcddbadcbacabbcaabaabadbccbbcabcbcccacbabdcdbacdbdcbcbdabdccbcbcaaaaddaadcdbdcdbacbdcaaacddaccbbcbbbdcdbabacbcdcbabdacabbdaacbbbaccdccbdcbbdaacddcbdbdcdadaaccdaccbaacdacbadacbdbdcaaabddaacbcbbcaadadddabcbdadabbbaccabdddaadbbbcbdbcbbabaacdabbadddcbbcadcdcabcabccbabccbcdcbcabaaaaaacbaaacdcbbcadcdcbcbccdacbccddcdacbbababdcadcbbdcacabdbcbbcacbdcddddbbdcbbcabadddbbacbcbbaaaadadbddccdacaabbacccbdbbabcbabbccaabaadcdadcbacabcbcdadddccaacbbbcbadcddbbdcddbcadbdaadbdadadaddbcdadabdabadcbbdbcbadbacdbaddaaaacabbbdcaccddcbbbddcbbdbadccdadbdccaadddccccbaaccccbdcdccbbdacdccbdaabacddaaaabbbddcdcabacaaaaddaabcadcdbdcbcbcbddccbacaabbbbbabddacbaccabbdbbacdbdbaacaadddacccacbbaacacdadcdbadcadcaaaadbbdacaddcdddcdccbbcddacdababdaccdbbbdbbdcaadbabddaaaccccbdaaaacaaacacacdacaabacbccbbbbdddcaacdcacdabdcacbdcdabbcbcbcabbccdbadacccbcbbbccbdddacaaaabccacddaaabddbcbddbddcdaaabbbcdbdbacccabbdbbccbbbababbadbcabddcbacccdcbdcdbacaadadcdbcbbacabdbaaacbbbabbbbbaacaacdbabbcabbdcdabaacddabdcdbbbaaabddbdddbaddcabbdabcbaaadcbcaddabbbcddbdaacabbbbcbbddcabdadcacabcdcbabacacbcbccbdcddbabbcabbbbacccbacaccabbbabaddaaccbbdadccccbbcacaddacdaddaabddddacaaccbdaabdbbcdddcacdacaaadddbacbaddacbbdcdbadccdbbabcddddacaaddccdbaccbbbccaddccbcdabcaabddbddaccacdccdaaaaadadbdabaccaacdbdaddabdbcbcbcaadcacadccbdbbdcdcadbbbddaabaaccadddcaadccbabcacacccccddcdababcddadbdccccdbccbccbdddadccaacdbaccacabdcddcbcaaccddcbacdcbbcdcaaaadadccaacacacbcbabdbabdcabcadbabcbbcabdbabdabaddbbabbabcdaddbaddbccddcddcdabdddbaadccdcdaacdacddabbbabbcaabbcccbacadadaacbccddabacdbccbaadcacabdcbadbdabcabaacddbadcacbcbabadbcaacaabdabaaabcdbcbbcddabdbcbababbaccacdddabbccaddaadababbacdbcaccbdcbaabdcbcadbddcbbccadddbbadbaabacdcbbccacbbcadaaccbbbcbdabcdbdabdacdabccbcdddbddabbadcbcaacbdccbabbaddccbabcadabbbdbbcbacccccdaddaadddbbbbdbcdddaacadcdcabbdbbadabdccdcaaaccdcdcabbbcadccbdddcbbaaacbbbacccddabaccdbaabbdccbbacdcdbcdaadbabdbcdccbcaacdbadcccddbbdcdcddcbacaaddbabcbdcadaccbdadbbabdbccaddacddbbabcadabcdadaaabddcccddcdbbbaddaddcbdbadacdaaabadcbdcbcdbdcdaabdaacaaacacaddbbcbdcbdbababdcdcdbbdbbaacbcbabbdabacdabbacabbddaaadccbcbccccdaaabbaccbabdcbaddcacaccacccbdddbccbdbdbbddabcbbaadabcbddaaddcaccdbacabcabbcdcabdbdbabcaadbcbcdacdddbcacbacccbbacdbcbbbdaabcbdddabaaabbbdcdbdbabdddcaddaacaccadabbcadddabdadcbdbddcddddddbbbdbdbdcdcbcccdcdaccbddbabcdbbbdddbccacadcbbcaadbdcbaabcbbcbacbcabadbbacbdcbacbcabccbaddcbdbcddbaccbddbddcccdcccbbcbdadcbacdbaaabcaabcabcacaacaabddadaabbcdacacdddbcbccabcbbcbaccbdaccdcaadddbdcdaacbcabbdadccbbbacdaacbbdcddcacadcdccaabdcccbcadbaabaddccbdcaadcbacbddbbddbdadbdbdaaabaddcaaccacbbccbdcbbcadaadddccabcbcdbccbaaaccbadbbccdaddbabdbaaaabdabadbddaadabdcbdbdddbbccddabbdbcadcdcbdaadcdcbccbacbacaddadcaaabadabbcddcddaccbdadcbbbbabcdcadcacaacddccbaabbdcdccbdabbddaddbbdbdacdbcadddddacdcdddacdbdddadbdbdbbabaaccadcdccabdcdaacaccdcbbcdcdbdcaacdcbbbbbadbbcacbabbacccacbabcacacbacbcbdbcdbccbcdbbaddbdacbcdcabbdaabbbabaccdcacddabbdbccabdcbdbddbcaabddbaddcabbccadaadcbbcdcacaaaaddaababcbcbcbbcbcdabcbaccadcbddbccacadabbbccccdaadadcaadacacbbbcdcdcdadcbbadaacadcdcaabdbdbbdacddbabcdcadadbcaaabccdbcbcacababaccddcdcbdbbdaaddcdddbbdccccadbaccbaaabdadababddddaacccddbccaaabacdbadbcacabbacbcabcaacaadbcadaddadcbdbbbaacadddbacabbdcbcdabaabadbadcbabbacbcdaaccbbdbcacaaaabacdaadcbbdacdacaaccdbbbbbbaccdcadbcccaacbbaabbcacdcbbacbbcbdbbccbcbcbbdbdbcabddcccbcbbcccdbdabccabcbcacbbcdbbaddadbcaababbccdaddabcaadbdadbaddccacaacdddbcababbcdbbcdccdcdccaddadadabccdddbbdbbaaadcadabdbabbcaabbbbbabcbdbbbbcdddddaaabccbdabbbadcaacccdbdcdbbcdcabccccbbbadbbbdccbabdddcdadccddcdaabcbaddbacbadcbdabcbaaadabdabdcddacbbbabcbdccdddadaaccadcbbcdadbdaaadbcacdcbddbcdabbdbbbbacbadbaaaccdbcddbbacbccacadcbbdcccdadcbaddadddaccadadcaccdbabdbddbcbcdddbdacacadccddcbbaabcddbbccadbbaacadccabcbddcdcadddbbbbaaacaaaddccccbddaaabcdaddbcadcbacacbbbacaaadcabadacbcaccbcabdcbabbbadaaccddaadbbdacccdaababbbaacaaaabcdacacbcdaabcaaadddbbbcddbcccdbbdbbbbbddabcdacdcdadddabdcdcdbcdcdacbbbbbddaacaabccbcbdbcdcccbccbdaacaadcdaadbcabbbacdcdccccaddaaaccbadbcabaacbddbcacdacddacacabcbababdbbdddcddabbbaacabcdbbcccbadadadaaacbaacdcdbadcccddaddccbdddcbdcbbdbcbbccbdbaaaadaaccaaadccccddcbbddcdacccadaaabacdaacccbcdddbdbbbccacdccbabaadbcddaaacbcbbaaabdcddddcaaddbbdcbdbbdcacabacacdabbdcdccdcaacdacbbcadaaacdcbbbbdbdddcbadaaaccabdbbdacdacdabdacdadaaccabbbababbbcbccbdaddabdccbabbacabbbcdbababcbacaccadbcaaadaddababaddacddddadbbbbdcabdddbdbdabdbacaacddbbabadddddbbddbabcabbbbbbbbdbaccacbcdbddabbacbbbbbcddadacdacacbabbabacbaacdcacbacdccccaddabdbdbdcccbaaaadbadacacacdacdbcbdcaddbccabccaaddbdabcbbadadadcdadabcbacdacabccadacbdcdaccdbdcdadadcddcabcbbdadaacdcdbddddcadcdbaaabadacacbabdccdadbbababdadbccdaacdbacacbbabcbdaddbcbbdbbbcbbabcccacbcbabbcdddccdbcbbcdbcbadbdabcccbdadcdadabdacdabcdbadbbbacbaddbcbacbaccccbbbcddcdadaadaaddbcacbaabdbcdbabcdbdbdaabdccbdadbbccbdbbbdccbbcdddacacbbbdcccacbadcbdbdccadbbdccdccabaccdcddbbdbcddccdcdabcacbdcbdcdadbbdacdbcbacdbbadbdcddcdabbbaabbbabcacbbbdaacccacbadaaccbdaabaccdbbabcbcdbaaaddaddaabcbbcacbdaddbbbdbcadbdcbbacbcdaabdcaabadabcabcaacbacacaccbbbadcddacccddccbcbdbdcacaccacacaddbabbdbacdbdabdcbaaabddcbbbbddcdcaabbddcdccdadbbbbbadbbaccdbbcbabdaaacbdadbbbbbdadaadbbddbbcdaaabbcadbbdbacdccacddbbbcabccbddcaacdcdcbcdbadcbdbbccdcbbdbcdacabdbabbdcbcaddbcabcddccdbacabbcdabcddbccacbbbbbdbabdabcbccdaacbadabbbabbbddddccbaaaabbaaadcdbbacdacdacdcbadaccbbacbabaacdadbdcbddbdbdaaabaabbdbadcacadcbdccdbcdcdcdacbccaaaaddbddbaccdadacbbccaadcbbcdbcadddacbdcddcaaabbdabcdcddcdcadddddaabbbdddacaabccaacaacbaabaadbbbcadbacccadbdbcdabdabcabdbdcbcddaacacbadacacaacaddacacadcdddcaabadcddaacbccbcdbdbabacaaaddbdbdbccacaaabaddaacdabdcabccaaacabadabaabbaccbdaccacdaabbaabaccabacdbbbccdcbdbbccdcdbdcbabbbcbbdbccacdbbcdbdbdbccbddaccabccdbdadbdaccdacdaacacaddacaaadbcacdbadabbbbddbabbadaccacacbcabccbacdcddbdcbdaddaadddcdbdcbcabaadcabdddaadacdccdcbadacbdccabdaccbcbacbccacdccccdaabbbddbbabddbcccaccdbbbbacabcccdcbbaacddddbadbcabbcccbcbdcbbbbdbcdaaacccdaacabbdaadccccdcadabbadababddccbacdbccdcbbcbaddacabcddcacbccdbdbbaabdcdaddcbbdcbaabcddbadbbcbcdcdbbcaaadcbdbabaacddbddacbccbbaddbaacccacaacabddabcbcbbaadcacbcadcbaacaababccbdaabcbcaddddbdaaabdcdbddaabcadbdacddcdccacccacacadcbabbadbcbbdabcbcdcbdddcdcbadacabbbbabcbbddddccbccaabcbdacbdbaddabbdbbaddcddcaccddbcbabbccabacdcbaddddaccbcddbbddddbdadbaccaaadbacadbabcdcccbadcdcdbdacdabbabdbcccdbbdadbdbdadcbacbccdcbabdabbbcabdbcbcdabdcacccdcacabacdbbbdacdddabdacaccbbdbdcbcadcdbdbdbccccadcdadbddccdbccdcaabccaabccbadcbdabbdacdababdacdcaacaddaaccbacbdccbbacbbcabaabcdbbcbaadbbbaababcdcdcdaddbdbddcaccacccdabdcddabbacbcbbabbbaaaabcccbadcadccdccbacbcddbcdbbbbbcbbbdddcacccbccccaddbdcabccacdaadcdadbabdbcdcdaacabbdadadcdddcaaacbdabdcbcdbcbbacaaadaccaababcacaddbbbdabcadbccabccddaababacbcbcdbdaccdaaccaaaadbccdcaabdcacaaaddcaadbdddbbbdbcbccccddbacacaabdbbdabbccbadaabcabaabcdcdaadabcacbcccbbaadddcabdaadcbcdbaadccadcabadacbbcbdcccdbbaacacbdcbbacdcbcaabbcacdaabaccddcccccbccccdcaccabdcccdcacbcdddbcaaadadcadccaadbadcdcbaacbacbdcbbcccacccddddadadbacdccaabcbbabbccdbdabdbdbddbbddccacaabaabddddbaaabddbdadcdbdcbbaccabbbbdbcbcadbbaabbaddacdddabdaabcadcdbdadccccbdbccaacddcbbbabbdcdababbbdbdbddcaacabaccccbbbadcbdbdcddaaadabcdcddcbcddabbadcddcaadcdbaacbdddbdbbccadbcdabaddadbaadddbbacabcacacabcddbdacbabbdbbacbccbbdacabdabcdcbcdcbdcddddcbabdddadbabcaabbbacabdacccbaaacdbabcccdaaabaddbbbdcbcbabbdbcbbbcbcbcbcaccdbbadddbabddcbcadaacdabdbaccaacbbdadababdbbcdbadbdaaacadaaabddbbbaccdbaccbdaabccdcaadcaadbaabdbacadcdcbbdbdbdcdcddbccaabadadabdacbdaacdbacbaadccbddcadadadddcbaaddaadbaddbbbccdaddccdbdbdcbbcdadadbbadabbccaacaabaaacacaaaccadbdcdbacccdbaddbbacadaaadbadcbdaccbdbbabdcdccccadbccdacbdccdddaadbbdcbacdcbbdcccbcbacabbadcbbadcabdccbbaadbaadccdcbdbddccdcadbdbababacaacbbbccdcbbaddbdbcbdcdcbcacbdadcccbbbddcabaabcccdcdbaccbaaaccadcabbccdbaccbbbadcbadbdadabbdaacbcddacbdbcaabbacbcbddaabaacaabaadcbccaccdcaacaadadbacddbbbaacbbdddcaadbdbcbbbbdbadacaddcdaaccacabbccbbcdccadddccacccbdbadbbbddacdddbacbcacbcbbdddbaccbccadaaadbcbdcdaabbbddcacbcaaacdcbcdaadcbdbdbadadcaccddcacadaabdcbcaacbaacdcabacdaddbcdcdcdcadbcccaaabbbdadcddddccabcddacdabddcdbdacacbbbddccbccbdccbbccdcdabdbcddadcbccabadaadbcaccacadcccbddcbbbabbddcacbbddbabcaddaaabcbcdbdabbcccdaadacaccaaacaabaabddabcddcaaaacddcdabbaacbdacdaaabdbbabbcabccdbabbdbaabacdaadbbddbbcdcdadabacdddcabacbaaabcacbddacbcdcdaacbcaabdbbdabbcbbddbcadacdcddabaababaddcbbaaabddabdacddacbcdddbdbdcccddabadadcccbbcadaddbcdbdbbacbcddccbccdcaaacccdaddadbdadbcddcaacddbccababcaccadbcdbcbaabcccacbabcbadccbabcbaabcdccdabacaacbadcbdcddabcddcbccadadaccdcdbbdddacabcdaaaddccdbcaadcbbadbbcadcdbcdabaaabdbbbdbccaabcabacddcaabcdaddbadbbcccbbabdcadbdadbdcaddbcdcbccdbabcadabddcdaccdbddcbccaadaccbaccbbbcbcbbbbaacabbbaaabccabbdcbbddcccbcadcbacccdcaacdcbbdbacdaddcbcacabccacbadcbadaacbbbaddbabbabaabdbdbacbbbddabcadaadadbaaabcbbddbdbaddadabcccabdabdbbcabaddcbdcdcabbaddcccdcbcccaaaaadabdcbadbcbabbadbdbbdcbcbadbccbdacbaadaddababbbcaadbadbcbaacabaaabddadabcbcbbdccbabdbacacdcccbcbcbaddcbccbbabdacaaacaacbddabbcdbbbcabbbabbaadbbaaacadbbacbbccacbbaaaaaababdccbbbabaadccabbabadabababcbccacdccdaacddcadbacabacbddbbacccdabddbcdacadcccbccabbbbaccdcdaddbdcddccadcadaaadbbcdbcaaaddadabcbdcbbbcdbadabadcabbcccaccbdadadacacdadacddbbdddaaccbacabacbacdbcddbbaadacddbbadbbaccdcccdcaabbadddddababdcdaaadbdadbbaabbdbaadabddaddccacdacdaaabbdbacbdcbcacadcacbcdacddacbbdcabadbbaadcbdabcccaaddcccddaabbdadcaadcbadddddddaadadcccbbbaacddacddcaabacbbadbadcaaabdbcbbcbbbacadccbccaaadbbbcabbcbabcccdabadcccadddddaadccaaacddadadadcaabdbaadcccacbcdbcbcaabbddbcbdabdcdcbcdcaccbcccaacbcbcdddbcaaaccdaddbbbadcbabbbbddbdacdbadbaccbdbcddadacccccdcbaaddccddaabaccdababbbbdbdbadbabbddcbbbcbbccdacdadbcacaadaddbbdacdbcaddbbbdddbaddaabdadabaaaaaacddacadcaabbbbcddbddbdbacdabcdcacaccdaccadcdddcabaaababcbdbccabbdadbdaccaccdcccbaacaacadcaccacdabaacbaacddcaccbddbbbbddcacccccdcaccbcbcdcdabaacababbacbcabddcbabcbaddddddbccdaccbcdaacbdccadcbbbdcacdbcbcbdcaadbadbddacdabbbddacdbadbabbbbdacdacabdadcdccacdaaacbdbddbdaccdaabadcbbbdbacaccbcdbbcbdcdabbcbcaaadaadbcadddcdbdbdcaabdabbddbdbbbcbbacdbabbaccbdbddababdabbddbcbcaabbdabbcbcccdbbaadaaacaaddaddbaacbbddabacaabbdcabadbddbcbcadaaddbddbadbbddaddbdbbbbcadbdabaaccabaccadcbcdadaaadabddccdcbdbdbccaaacbacacdbaacaaccdaadbabbbdcacbdcabaddaadcbacccabbdadbcdacabbbaabddaaddacacacabcccbaadbdabdcdbcbbbbaabdaabcacdcabddbdbadaadacaadccacadacaabaaddbcbaccbcdcdbacbcbbcaabdabcdabadbcddacbbaddacaabdbdbbdcdbbaacbabacbbbbbcdababadbaddccaabccadcacaabdcacaacddddcbbbdaaacbabbabcdcaccdbbadabbdbacaaacbcbbdaacadcbdbadcaaaddcacaacacbdcdcdcccabaabcdbaaaadddbbbbbbbadcbdacbdbcddbddbacbcdbdabcaaadbcaacdcaabadcacbdbadaaaababbbcdbbaaaddbabbddaabbdacabbabcaaacdbabdcbddaddcbaaddbbbcbcbacbdacccddaccacacaaacbacabdbbcaccabaaabcbabbbbcaddddbcbacbddadadcbaabbaccbddbcccacbcdcbdcccdaaacdcdadcdbcaacbdbddaacddabcdcacadcaaddacbacbddadbbcbabadddaaabbabdbbcdcccbcdacdcbbbccddbaddabdabacbbcdbdadbbbacdabacbbaacbacdadbdcbadabbadbadbadcabaaaacbdcddbaadddbdddccbddcbdabdccddacadbaaacdabbbbaadcbbbdbaabdcaccabaddababbbabacdbdbbaadadadccaabadcacbcbbcccbadccaaacbacabdccbbaccdcbddbbbcddbbacbbbccbabddbdacbdccbabcbdcadbdbcbaaadbbabcabadbbbbbdbbccddaadacddacccbbbaccaacbbbbbbddccbddbacdddcaacdbdaadccabccdaadbcccdccdbadccaaccdcabcbcccbbbccbaadbdadccacacccaacbdabcdbdddcadadcbcdaadbdaacdbdcccdacbaccdaddbaaaabdadddbcdbbcadddbdacbadcbddcbddbcacbbdcacadccddabccacdcddcbcdaadbcbdcbbdddbbccaadacaababdcdadbbadacaccbaccccacaccbdcabdbdddcbadabdaabccbbdddbacbbdccacdddcdabdcccddbaadaddaddbbbdcabaddcdadcddbaddabaccdbbbacdccaaaadccdcaacadddaadddddcdddccdacbcbcbdcabcdabacbccadcdcddaadcdcddabcaacabbccccabcadccbcaadcdddbabacdaaacbcadcbcadbcaddaadddbbdaddcdccabccadbdbcdbdbdacbcdadbdbcaaacbcbddccacccbbcadacddbbbcdbaaacccaacdddabdddaccccbddcacccadbaadbbdaaabdddbcccdddcaccbccbadccbddbbcccbabcdaadaabaabbbdacccccccaaccddbccccdcabbacdbdbbcdcbcabbacccbcddcaaacaabdbacaaddcccadcccdbdaccdcdaacbbccacaadddcccdbbbcbdcdbbbcdbdabaccaaaabcbaccacbddbbacbadddccadaaacdcbaccdddabcccadbaabcbdaaacaddbbbddbbabdcbacaccdcdbadbaabdacbccccdccaadbdabcacdbadcaacacdbccbcabdbdbbcabdabcaacaaddadbccaaabcdcacbcbdaacbaacababdbcbdbcbbbdcdabaddcbcbdbdaddbbaabaddcbadabbcacacbcadabbcadbdbadacdccbdabcadbdbddadaabacdcdcbcddadabcccaadcdababcdbbbacccacdcccbcadbdaaabbcdcdbbcabbabacbdaaaacaacabdccdbbdacbdcccadacccabacabbacaabdabdacdaddacdbbdaaccddbdbcdbcabcbdbbaddbabcacbadacbbbcadababccbacadabacbcdbdbcbccadcdbbcddbdcdbdabdbacdaaabdbabaadcdbbaddcdbcddadaddbaabbdcdaabcbbabcaacbaaccaccaacdcacddccaddbacbacabddddcccbdcbcbccbccbbbabaabbacdcdadbcdbddcdbcadbcbccacdddbbbdbcdabbadabacbabaddbacdcaadcaadbbabadbcaddbadaaadbadccdddadcbcdbdbbbddabdbadcdaacaacccbabdccbbbbccadadacdadabccbacdbbcddcaaaabccdccdadbaddccdbabdcccdbcddcaccdddacaccabcccadcacdcdcadbbbdaaabbdcaaacbcadaaabbaaddbdcbdbdcadddbbcbdaaabdddcccadbdbaddacbabababacacadadbdcbabcdbadbacdbbcadcdccaabdadcbccadabdcdacadbdbaddaabbbcaaabbcdaacccbabdbdddaabbdcccdbdccddbbcddbabadadbcaddabaccdddbbadddabaaabdbcadbccbcaacdccccabbcabbcdddabdcdaaacabcddbcadcadaaadcddcabdddaadcdcaabcaabcbbbbdbdccbcbadbcbdccadcbccdcbcaddabcbbbbacdbcdaccddccdaaadbcabcbcbcdcbdddabadbbabdcdcbbdcdbbaacbacbdabbbcdcbccbccdaacdcbdacaccdbaaddbbaacdcccbcbcacdaacbacdacdccdabaaaacbdbcbcaccbcdcbaacdbccabdbcbdcdcccdcdbcdadabadadcbabcbaccdbacdcabddccddacbabdbbbcbacabacbacbbdcabcabbcbaacacccbacaddadbbccaacccabcdabadcbdddabddacbbccbbcbabcacadadddacbbbbbcadababbaccdddddccdbacbacdacaacdabacabaddddbdaccadccbaabadcbbdcdcbbdbacccdccbaaaaabbcbbbbdbddcdcaddbcbbcdbbbaadbadaabacabbaddcaccdbbddbdddbacaadadaacdabbdabbbcaacaabbadcccabddccadaaccbdddacbadbcdcabaddccdabacaddcccccbaddddadcdddbcadbaacadadabaacdabccbcdbaaacddacccdccdccacaabdcbdccbcabbcdcacabdddaccaccdcbcbdddbbccaaccccaabbbdbcaaaacadacacacabacbdcccdcbacadccccaadbcbccbadacaccaadaddabdabdcddbdabcdbccabbabbbbcadcbccbbccacadaaadcbcddaacabcbccabbadabcdbabcbbabdbcbdbcadccaaadadddabbdacdbdcbcbcbdacbcbcaaadbdadaaaaddcacadcdcadaddacbcbbadbccadaacabdcdabcbcdbcbaaaddccbacbaadaccdbbacbdacddcbaadbcbbdabcdbbaadcadccaddbdcbbccdbcdcbacdbdccbabccbacbaaabbdacbacbabdcdddacdbcbbbaacabdaabababadadaccccbdbdcaddbcdbcddaddabaaddaccaddbdcbbcccababbbcabdbabcbccacaddcacaadcbbaacabddcadccacdccacbccaacbbacaddcaabaddbbacdccbcdcbcdcaabbddaadadaccdbdbabbbddacccccaccbcdcaaaddbddcdcbbccdacddcbcdbcdddcbddaaddbcdddaaabacabdbadddbcbcbabcadadcddaabdddbabadaaddbbcaccdbcccdcbabcaacdadcdacbcbcaddaddacdcbdcaabcbaddbbdaccaaaadabcadbaabacdbbccdbddbdaacaabbbbdaaaaccabccbcdbbaddabadabadabdcbdbcddaaccbddacbdaadcdbabbbbbbbbdbddadcddddabdcbacbbdbacccaacadcdaddbbcacbacbaddaacdcdadaadbbabcbddbaccacbabbccdbdbcdccacbbbaddddbabddccaadcdacaacabccbcbcaaadccdbacaccdbcaccdadbbcaccddbbbabbbdbcacccdacdcbddddcbbaacdacddacbbaaabcabdabcadcaadacacbbcbadbaadabaabcbdaaaaadcccacdccdccadddccbdcccaabbdbcccadadccaaacbbbbbadccbddcbdbdccccaaacacbcbabdcdcadddcccccabdbbaadcdcabcdbacacaacacdcccbaccccdacacadcdcddbdbadbcbdcbccccdbbaddddcdbabdccabddbbcdcabdaacacbcaadbccadabbacccbcaacccdbacdccbadbbcbbcaadcacbccbdaaddcbbcdcabdcbabcbdabcdaaadcbddcdbcaaaacaabcdccdabdbbcddbbddddbadadbccdaadacaaccbccbaacbaddbabbddadbdadcabdacbdbdcacccdcaaadbacddbdbacbadccaadddcddbbcddbadcdbcddbccccbcddbbcabcdabbdaadcadaabbababcbacddcacaddcaabbadccccbaabcbcaddddcaddbcddacabbadaaacadcbbdaacdcdaddbacacbcaccccdbcadbccddbaaabbbaddadabbbadbaacabdaadbacbabddaabbbbbbddcccbcdccddaacbdbcdbddadaabcdbccdacbbbddcabbccddcddcdadbbbccdcbaacacdbcacacbdaaddddcabdcbbcacaaaabbddacbadcbacabbadacaacccaadbaccbcdbbadcccaabdbcbdacccaaacababdbabaabadabcddaabdddccccbcddbbcdcacadcabaddcaddabddbbabadddccbaabaaddbabcbccacacdabcbacabcbaaaabbbbbbdcacdddbdccacbbcddcdbcabaaadaacacbdccbcddadcdcbcbcbbcdbbacdbbbacadadabcdaacadddcccacbdacbabccbaabbdaabcacaccbbcbbcaddaccdbacdcbabdddbbbaaddacdccabccabbacadccabcbcbdbbbccacccaaaddbbcbabacddacbdabbbddbaddcdbaddabcddbcdbcbccbbcbdbccabbcbddcbcabddcdbbbaddbabdcdbabdbdddbbdcdbaabbdacdaacbabcbaabbacaacdbcadacbdadcadadadcccdaadbdacddcadcbcdacaadabccaacdacdcccdcddbcacddbcadadcdcbcbcadccbaaabddbdbdbbabbbbddcbacddcdaddbadcbbccadcdddacddbdcdaacacccdcbdaaabdadacbcddbadaccacbcdcaaabaaacdccbbaababbdacbcbcbaabddaccbdaabaaaacabaacbdcdaadbcdadaddadacdddbdacccacaccddcbbacbccdbabbdbbbdaaaadbcddbdbbbcbbbcddaccadabbdcaacbbbbadccddccabcdcddadcabccbbdbdbdbcbbdcababcccaddbaadbcbdaababbdaadbacccdddbabbadbddcaadbdbcabdbdcbcaaaacadddadadacddadacbdbddbabddacdbbccdbbccbadbcdbccabdcacddbcccbcabbccababbaacccdbbbdbacadacaabcbbcadddadbbbccbccbdabdbdbddbddaabacdccccbcddccababcbcaaacccabdcccacadccdadddbbbddacbaabcabcbdbddcbbdbccabbadaaccbaabcccaacbdadadabbbdaabcaadabacdbacabadccabbbbcaabddcbacdccddaccdaabdcadabbacbdbaabdbbddddbbbbacadcadbcacdababbcdcadaaaaabacddacaabadddbbcccacddaababbabaacdbbcbdbdacbccbaadcbcbdbcbbabdccabcacabcabdbbcdbbdddccdbdabacabadbcdccbbbdccbabbbacddccbbbdbbdbacdbbbbcdaaddbccacddbdadcdbcacadabbdbccabddabccbdddadacbacdcbbabddbaddaddadacabaddacbbcbccbccadbbbcbddbccdabdccccdbabbacabcbbabacadabbdcaacabddcbbabacdcbdbacdaddcbcbbabdadabddbabcbccacacddbcbbbdcbbadddcadbcbbbddcddbdcbdbbcbcccbdaddaccbdaccacbcdbcbdbdcdabadcdbcbdcadcaaabddcddcddbbaaccabaadcbbdabbdabbcbacaaccdbcdaabddcbabcbabccabdbdaacdadaccacdbdcbaaadddbbbbcbbdcbadbcaddcccdcbcbcddabcadccaaadccbcccdabdddadcaccadabbcadccdbbcdacccbcdacadccdabadbaaccbccacabaaabbbbcabcbbaaccbabadabbccacabccaaabdaddcacccaddacdcccbdcaccdbacdbbccabddbbbacbdbadccccdabcdbddadcbccbcadbaddabdbccccdadadbaabbdaacbcaddadbdbbdcaacadddbaabccddcaabacccddcbcdadabdaabdcbccbdbbdbdbbacbdaaabaccadcabdccbbcbdbbbcabbbbbaddacdbacbddbddccadbdbdbbdaccacbbdbacbcaaacdccdbbdbdcddddacbbbbabdbcbcaadddbdbbaaddaaccabdbbbcaadcadbaddbcacccdbbabdadccbbdccaabbbddcbcaddbaaacbaacbdcbaadccadadabcacbdcaacacabaddababdbbccaabbbaacbacacacbdbaadadacccabbbdbaccdcbccabadddcdbaacdadbddaacdcadbcbbcbdbcadbacdcacdacdbbdcbbdcabddcbaccaddbdcbbaadddccccdadccaadaaaacbbacbbdbaaadbdcdccabdbddbcabdbdbdbbcdbddcaaacbdbaabdcdbddadbadaadaadbcbadcaadbadccccccaacdcbdcddadacbdcccbdbabcbdababdcbdbabbbccbcbaaaabbbdcdadbcadaabbadcbabcbcbacdaadacaddcbcccbacabdbbbdcacbbbacbdbabacdadcbccbcbcdcbabcaacabbbacadaabdcdbbbdaadcdcbddaaaacbdbdadbcabdcaaaddbdcabcaabcbddaabbabaccddcddddbdcadadadbccdabadaadcbddbadcccbaddacccdbdcbaccbcbaabbbbcaaaccaacdbdbadaadcccdccadaacbaddccbdadbbbdbcabddccdcdabdbacbdaddaaccdddacaabdcabcadcccbaccabaaacabaddccbcadcabcadaccbaadaadcddcaacdbaacdbacadadcccdbbcdbbcbbbdacabbbdabdbccbcabbaccddabbdabbdadcdcaabaaadcabdbcabbbdbaaacbcdbbaaaabdabbadbadcaaddbdbaccdcacbdabccabcaaddaacaabccdbdcddbdaadaaddaacbcabdacccaadaaacbbcdcbaddabdcbdcccbccdbbdcccdcaadbdbabdcbcbddaccacabadbbddcbaaaabacbadbbbacabccbddacbabbaabddbacabacdcaaabccdcccddcccbacabcbbaaccdaaabccdddccbccdabcdccacdbbaadcaccccccacbaaaadcdacabbadbbcacbddcabcabaaccddabbddddccbbbaddaddddacbccdbabcadbdcdbbdacddbbdccdaaaadaacbdddacacdadbabcdabacaadddcdabcdcdbccdbbccbddcaccbcdcbbcabacacddcadaaaccbcacbdbadccdbbddabbdccbadabdbbacbbcbbbdbcdccbdaabddccdbcbabbbcddbccabdaabddcddcdacccaabbaaadbbadcddbabdccacbadaddbaadabcddcdbdccdaacbabcbabbccccbdbbcadbcdbadacacccadbbbbadbbcccbbbbdbbdbbcbcdcdcbadbbdabadabaccacdbaabdcdddddddadbdcbddbbcbcaacacccdcaaaaaabdcdacdcbbcbaccddccbddabddbdbdaaddbabcabacdddbaadddaaacbddddbbdccbcbcddcdcccbcbbdabbbdbbcbbaabcbaccbabcdaacbabadcbcaacdcacaadcccacbbaaadcdbacbddcabbccbbcabbcbcdbbaadabcbaabddbadbdbcbcadcddcbabcdccbcbadddbbbbddcdbabcdaaaddcddcbbccbcbaacddcaadacdababcaacdbcbccdadddadbbccbbcaacadbacabbcbddbcacdbacabadbbbbbbacccbdbcbadbbbbdacdcadbdcbabcadacbacddccdbccdacddbaadbdbcddcabaadacbcadbaccbaccacbdabdacbbbbbcaacbddbacdbacdddcabbddbcadccaacdaadcacaacbadabcabadcdabcdaacdacdaadacdadbaacbacacabccbdddabdaddbdcabbcdbabdbacbabcbbdbacbaabccccaddbdbccabdcbacbbdbcacbaccdddbbcdaacbdcbbbabdccbccbcdcbacbbcdaacdccadcdccacddbbbbcabacccbcbbaabadcdccdbbaaacabacbddddccbbddcababcaaddabdccbddcacabacbbbcdbadccddbdcbdaabcaaabcadcbdaacaabcbcbddcdadaacccabcdccdddaabbabcbacabcadabbdcbabbbacbccabddbbdadbdbabbcacbdbdcdabcbddbdccdddaaaacddbcabbdadaacdbadcbcabccadbcbcabadadcbaabdcdaddcbbcbaddbaddadadbdcbccbddcacccddacdacbbdcaabdbabcaccdccadbddbadcbcddcacadddcadcbcaccdadcbabdbababddbcddbabdaccacbbcbddadccbbccaccacbbddcddbcbbdadbbadbcbdddabacdbcabbaaadbbddbcbdbdddcacddcabbddabaccaabaacacdaadbddcbbdabccddabcbddabcbbdcdaddbdcdabcbddacacbaccabcdacbccccbaccdbdaccddcadbdacdbcdacdbbbdaadcccaaccddddbbdcbcbdccabbbdbbcacacccbddaaabccacbacacaccaabaddadbbdcbcdcacccdaddaccddbaadabacacddbbdacccddcddbaadadacbccbccdbcbbabbdccddccdabbbbdacadbdaadddacdcadbbddccdddbcddbaacaaabbddddabbdabdcabbbaddddddcdabacccbbcdbdcbdbbbccbcdcddcadddbbaaaabccaccbbadacadaddbdaacadbdcdacccaaccbccccabaabccabadbabcabbcbdaccbbcbbbcadbbcdcabcbacddbbccdbaddccdbaabddbddbaaacacbccadbcabcabadacaaaddaacbbcabdacdbbcbaabcaacbdbdbaacbcbccbccaabbdbccaadacbbcdabdcacadccaaccdcbbdadccbdddaacddabababbabacbddcacbbbdccadcacbbadbadbbcacadcaccdabcdadaabddadbbbaaaacdbbdcddbbcbbcaabdbcbcadbacdabddbcbdcccccbcabcdcadcdabccccddabcadcacbbbaddaacdcbdbdbcabcabdbddadaaaabbabbadbacabadbdabcacadaadcbadcacabacacdccbcaabccdbdbcabcdccccdbcaabdddbbddbdaabcbbabdacbccbaacdcdcbbbbcadcddccaabcccbaadacbcadccabcbbbaadcdbbcadbbcbbdcadcccbdccadababddcadbbdacbaadccdbdbbcbcaabadcccbccdcdbbdcbdbcaddccddccbbcdabbdabbbcaabcbbcddaccacbbcdaaabcaccccdcabbccababbcadbbdbdcdabbbbbbbbbcadccbbdbbabbdcadbccadbbadcddbacbbddbbbbcbbbbddadbcaaabaabaabbdbbacdbdcbccbacbbdacddccbaaccbdbbaaacbccabdcdbcaddbbcdcbabcabaaddcbacaccbbbaacbdcbccaaddcbdccbcccbdccbdabdcbacbabbccaacbababcdcbcbcdcddabcbcddccabbddddbcabddddadcdabacbbdbdccdaabbcbcadddabdccddbcadccbcadaabbdcbccdaaaccbcccdaddccbcacddccacbdbcaccbbbddccaddbbaabadbaccbdbbcaacddbbaacbcbacaabaddadbdbdcdcbcccbabbababddddadacdabbbcbbadcddbadcadbcaacbdbadccaaadddaaddaaadcdcabdbdaabcccbccbabbabaacbbcbabdbbdbadbcccbccbcadccccdccdadabddccdaacabbabaccbccddacdcaaadbaadcabbdcbddbcaadbbbbbdbcccbcddaddbbdaaadadbaaacabdbcadbccabaaccdacdbccdacdcdcdcadadcccdcdbdadabdabcddbacdddaaacbddbaccbbdcdabbaabbbababddccdbddcdcdcddcaddbbacabbdabbdaabbacbaccadcdbddbadddacabddccaacbcadbcddbaddaacdaadbdddbabccbdbbadcccbbadcaacbbbcddaddbaccdaadbbddacdabcddccaacdaacacbabdcacddccdaaaddbdaadcbacacaaccabdabcdcaaddadaccbccdbdbbcdcbddcdbbbbbccdbbaabcddbdbbcdbabcdabadbccbaabdcacdbdbcaadbbacdaaadbcddcacddadccadddbbadabdcccbcdbbacabcabbcccdbabaccdcaddcddaaddcadcbaacbadddbdaddcacacbddcddcadabcabcaddbddbaacdabccdaacaacaaabbcaadbbcdcdbaabbaaaabbcdabaadbdbbabdcdbcabddbcddbcaaccabdbadabacdbaabadacbbcccbabadbccbdcdbcadabaddcccbcddcbbdbddbadbdbdbcabdbbdadadcbbcaabccdddcadccdcabcdbcaacabdcbadddcbabbabababdcccbdbcaabbbcadcccdbcbbacaddbabbacabcddbabbdacbdbdbdaabbddcabadbcbcaacacccbbabcaadcbbbbaddabbccdaaddcdaaddbbddacdcddcddcdbabcbadcbbdadbcbccabddbbbabdbdabbaabbcbaaddadccbcdacbcadaaddacaaabaabadbdacaabccbbbdcdccbcdcdaccbcddcbdaddbadcadddcaaabacdcdadbabcdabbacccabcbaddcabcbbcacdcbbdadcaacacadcbbadcaabdaabdcbdbbadacaaabdadcdcdbacadccbcbadabcbbbbcadbabbcddcbaaacadddacbdcdcbadaccabdabbccacdddcbcdbdbccabaabcabadbddcacbaccdddbbccdccadbbabdccddcabdccaacbadcccbcadacdccbcabdaddabbbcdbddccccdcadcaabdbbbaabcaccbbcdaacccacccbdcbdacdadacabcacdcacbdadbacbdcaccbadbbddbbdbdababacdbbaddbbacacdbdadadbdaacaaadcbbdddacaaadbdcddbcbababbadabccdbacddaababbdaacdddbcdaaaabaaadcdaabbbdbcaaadbccabcdababbcaccdcdcbcdacabdadaadbcbabaacdabdbdbaaddccbabdaddbccbbbbbdddbdcbcdcaacbcaaaadddbcaccbdacdaabdaaabaccccadcaccbabddbdaddaaacdabaabbddbabdaccdbbdcdcaddabdabdcbbcbabbcadcbcaaccbbdddbdabbdbcdabadcdaaaacaacbdbacbcbbcacbdccacaccadddcdabcdccdccaaadadbcbadacddacccaccadcacbcccaabdccddbabaacddabcbdcddddbdadbdbcbdadadacadcbacddacaacacadadbcaabadaaabdacabaabdcdaadddddbbbcbbccbcbabdbdcbdadaccccdbcdaadbbabadcadbbccacabcbccdddcbdadbadcccababadcddcbbabccdbadbbabdcbbaccadbacabdcbaabbbccadbbdbcbacbaddaaccdabdddcdcdacbccbbccacbbaccadacbbacbbccadddacabdcaaaaddabcbdaddcdcdabbdbbbaddcbcaaacccadbddcbcaacacabcdcabacbdbcbadabddcdacacabcdcabbcaacaacbddbbcdddbbabcbacbbadccddcadbabbaaaccdccddcacbbaabddbcbbdadbcabcbbbcbacbcabdcaaaababddaccbbcbdadaabdadcddacaabbaaccdcadcaadbdbbcdbcbbddcdccbccbbabdbadacaadbabcdaddbaaaccbddcacccbbdcddccbcbcbbbcaabaadaaccbabcccbddaddacbbcabdabdabdbbcaadcbcadaaaccccccdbdcadbadadbabbbdaacacdacbbabdaaaacbdaaccdbccaacccbcddadcaabccccadccbccddccbdabaadcacaccadcadddaadcabababdddccdbadcabccdddcbbadcbddabdcddbccddcaaddadccbcdcadadcdadbcbabdadcdacdabaaaaaacacbdbcdbdcccabdadaaaaadcdbddbccbddcbdbbbdbbacdaaacadcacdbbbaccacbdbbadbcbdcaadcbacbbccbaabcabcaabbccaccddbbcdabcaadccdadcbdddbdddbdbdaaaddadbcaacdbbcbacbcbabdabbddacbcaaadbdcdadbdbbadaadaacacaccbdbadbddbcaddbccdcbbaddcbacacccacdcadbbdcbaddaacaaabbcbdddcbcddaacbbacadacadcbddbaabcbcadbcbababcabbbaccdcdacabbdadadaababadccddbbdbacbcbccdadcaacaccdcdbabbaddbabbbdacdabdccbaddbddacbbddbaadbbdaacbdcccccccdadbdaccdddbcdbabadbddabbccaddabcabadbbbbdadadcdbbccbccdabbcbbcccbbabccaacccbbababbbabbdbbbaadccdadbcacdbbbacdcabdacadddddbcdcccbdadcbacbcdadadbcabccdacdcdaacacdddddcabbaaadddbbddcabbdbdcabcbbdcbabdadcdabababbcdbdcacaadddabdccdbbbcaadabababcbccccbbcbbcaaddbacdbcbcbcdbadbaddccacaabacdadacadcbaddacbcabdaabacccdcccdbcdcaddacddbaccbcadcddbcbabbcdbbbdbdabbcccbbbccbacdcccccdbaabddbacbbcddbdacabadbddbadadddddcbdcdaaddaababcaabbddccbdbcbacdbadbcddcbddbabacccccbabaaccdadbcabbdbcbcaadbdbcdbdcbadbbcbcbbccbadbcdacaabccaadbcdabcdccdcadbbdccccbbaddaaddabcabcaaddbbbbdaddaccabbdcdbaaaabdccaacacbbdcaadccabacbccaddbcbcbacbabbcabacdddbbcdacbcabdbabadddbcbdcdcddcaacddbdacabdccddababbbadabaaabadccaddaddbbdbcdcbacccddbdabdaaabacccadccadbadbcaadbacdcababcdbbcddbbdaacccbcbadaaabccbabccbacbacccdcbccdaacabcdbacdcdbcaabacaccdbadaaabcddbbcdbacdcbaaabdbbacacbddacdadbdabdbabcbdacdabdaaadbabadbcaacbbdbcbbadbcbddbaddacbdaddbcbaddcaacccdcddccdbbdbcaaaadacdbddbdcbddcaddbabccddaabdaaababcbdbbccadabcbcdcaaccdaddbcaadbbbadacbddbaddddcdcdadcdabbadadbaababdbdcbccbaddbadcdccdbbbaabbcbaaccaabbddbddaacacaccdaadbaccdbbabdcbdcdccbcaabadadcacdbbaccdbbccbccbdadadccabdabcbacadacccaabaaadbbbadbcababbbcaabccdccccddcbacaaacbcdddbbdaddbaaaababdabbaccabdbaabddabbabaaddadcdacabbcdabdcddababcbccdaaadbbdcbaaddcabddabccccdbcbacdcabddcaaabcabccdbbcbdddbadccdbdcbbacbcccbaadbddaabdadcaabdccbabdacccdbdadccdbbcdcddabbbdbaaaacaccddddcaababbdadaccaacaacdcbaaddadbaddbbaccaacaaadcaabdcaccbbccdadaccabadddaabdcccddcccabaccbcdbbdcaccbdcacdccbbcbddcbbcbbacabcaacbdccdcdbcbdacadbcddbcabcadaddcbbdbdbcdaabccadacadccddbacdccccbabddbbabcbdcabcdcbcadcdcdadaacdabddaabbadbdbdacaacbcbdaabdcdbcacdbbbacdbabaabcacabccdbbbcacccabdddcbadabbadaadcbddbbcadcacadbbacdcaddadddadcbdccbbcccddcadbaccccdbaaddaadabdaadadccaddacbaaddbdadbdaccdbadbbbaddbcdbabcababadaccadbaadacbddaadbbddcaddcdbbcbabcbaaccdbdbabaccbadbcdcbbacbbdaccbccdacdbcdddcbdcddcddbcbbaccddcaacbbcaabddaabaddadadbcadaaadccbaddadcbcaadbccaabacdabdcccbdaddabbbadbcdcbcdbbadbcbcacdaddbdacadbbcbabaaabdcddccdabaabdacdccaaaabbdbdbcdadcccccbbcbacadddcccaddcdbccaccdbabbbadbaddaccdcbcbbdacbdbcccccccbabadcaabcbdcdccdaddcccadaaddbacacaabbdbdbddadacbbdcdaaabadababcbdbdacdacabadcdbdbccacaacccbbbadcabdaaaaddccaaabdbcacbcaaccacbcbbaaadbcbcaadcacdbdaddcccadaddaabcabaddacbcdcdbaddcbbcbddcddbbbdcdcccacdbcbcadccdbccadcaccdabcdaddadbddbabadadabdcababaddbadbaabbdcdaabccbabbdacdbdbdcbddbddddacabbbabcdbacabcbbdbccbababcbbadcdddbacbbccdbcccbdbddbccbccbcbdacbbbdbcbbcadcccaaaacbbdabdcdbacdabaccacabaddcaabdcbccadbbacaacdcdabcccccbcababbdbaadbcaacdcdbcdbbdaacddcdadbdbbbacbadaccdabadddcadcdbcdddcdccadabacdaababbbdbdcacdddbcbadaabadbdcbbbcdacbabacdbdbcbcacddbcddddbabdcacbadbabbbcccdbbdcdccbabaacacdcacbcbdadbaaacbabaadaaacbacccacbbcbbdbaccacdbbadddbdadddcaacabdbdbacbdddcbabccddcababdcbdacbccabbbdacbdcddbdccbdbabddccdbccbaabbcbbcbccbbabcacbdbbadbccadcaacabccdcdadaadabbcccbcaadbccabbdbbbadccbbcddccbbcaaaadbcbdbdaaaaddddcadbdccdbbcdbbadaddacaabaaadcdaddcacdcbdadbaddbacababddbdbdbbcabcbacbcdababdaaacaccccaaaccbcabacabdbaccaaacadadcccabcddbcacbaadacadabcacddcbabacbcdaacbbdddabdacccbcadbdbbbcbcabbaddcbaadcbadcadbdaccdcdbdcbbdccaabbcaabdbccdbcbbbcadabccbcadbbbabcbccdcdabdbcbdcadabdcdbbccaacadddddcbabbdcadbdbcbccbbdcbbdccabacdcbcbdccccbabdddccbdccacdbbccbdddbabdadabdadbdaccccdaacaabacaaadaaacdcdadbacbbcacabdabdaadabbccbddbcadcaabccccabccaadbbaaaddccdadcccdbcababddabacbdcccadabccaddbacdacbbbccdcabbcacbbdbacbaabbcabbacaacddcaacbccdaddaadddbbdadbbaadddaadaccadbacbbdcabdbaadaabdcddbddabbcaccbaacaadcbbdbdaccddbacbdadaadcbabdabcddccdacbdcacbabacabbaddcbcdcbaddcdccccbcdddaabcabbccdccacaadcacdbbaaabacdcbacccdbccabaabaccbaaaccbbbcbbaaccbbcdacbcdcadbcdaddbcccabcdacdbccaccaadbacddaccabbaaddbadadcddcbbccccacbccdaacbadbadbcbadcdcbacaaaccbcacdbadaaacddabbddadabcadacdaadcadbbdcddcaacacaadadbaddaccbacdbdbadbabcddddacaccccabcaacdbbdbdcbaccbadabbbadadbbdbbcabdddbcabacaaddabdccddbdcdcbabbadbbaadcddaadaacaaabaccabcbdbddadcbcbadbbdbdcbbcdabbaacaabacdcaacccabacdaddbbcdcdddaabdbcacdaddcbbcacbabadabbccaabbdcbbddbdcbcddacbabbbaaccdddabcbccaabdccbcdabddbbaabcdaccbdaababdaabbcbdcbbdcdbdcabadbaddcbadbdabdaaddbccddbbabbdcbdcabbdddddddaaabccadcadcabddccdcddcdcbaaaabdaccabbcdbddbacacabdcdcdccababcabcdbbdcbcaaaccbcddbbdbbbdbbacbcbcabcacdbdabdadabacbcadbddaaacbdcccaadbbabcaadbacbcdbccdcccbbaccabacaaddcabcbbbdcbbabdbcbddccddbbbdccaccddadddcadccdcacbdccabcdcdbdcdbaaadcbbabbcdbaaccccacdbbacadaaacccaaabdabababaababacddcaadcbcbdcbabbdaadadcabacddcbcddddabbdbbdccaaadaaaccdbdaaacbbcbdcdcbbccccacccddcdcddacbddabcbaaddbdabaadacaaccabadaaacdddccbadcadcbccbcccccdacdabbaddbbddbcbcdbcaccadabbddddadbaadcbbbddbbdbacaababbdbaaaadccdccdbaabdbdcabdcabbbaaacabcbdbdbdaabbbcccdcddcadbdabcddbcccbabcddbaabdcdaddaacbbacaccdbdbcbccbbabddbdcbccbbbadbdaccacdbddcddaadaccddabbdcdbccaaaadabddcdcdadcaccbccddadddbbadadcadbadbdadabcbaddbdacaadddaccaacdcbdcddcddbbcdbdbadbbbdbcadadbbdcbcccdcaadacccabacdcadacacbdacdccbdbacadaddccacadbdddcccddbdbbbcdbabbbaaabbbdabbdacbcdabdcbabaccdaaaabcaccbcbacbdabbbabbccbdbcdbaaacaabcbadcccbdabbcdbdbaaadddccaccdacddbcccccabdbddcdddcbabdcbbabdbcccdbcaddcdcbabdcadbaddaacbaadbdadbcaddabcacbccbcdacadabdbdadccaddccbcdddcdddacdaaadbdccbbbacbdbdddcadababcacaaddcdacbaacdaaabdbbbbccdddbcddaadbcddbacdbaaadaddccdbabbccbcabdadbddbbdaccbbbdbdbbaccbacdabbdbabdcbbacbcdabaddcdbabaccadabccbcbccdbacdcacbacccabdbddbcbbdadbddcdccddbdcddbdadbcbcdddbcbbabcaacccadbaaaababbadbbbdbbdabbbddccbcddcbabbdcbbadcddacbbcbcbbabcbacbcddcdddcbcdbacdcacbcdbbaacccccdbbbdbabccdddbddbaccdadbcadbdacccdabccaaccadcbbdcbdddbaccccabddbadbdccabdcbaabbaaccabccbbcdcbbdcaccbcdbdcbbaacbbbddabbacbadcdbbcbbacacdaabcaddaaabbabbdbabbadcbbabbdacbddabcaccacdcabdadcadcbadadacadccacbcddccddaddbcccaddddbdcacdacdcabcbcbdddddccdcaddccadaacddcdbaaadabcadbbdaddbabacbcabbdcbacacbddbbccaaacabacdbbacabdbbccccaadddddaababbccbcabbbccbddadcabcabbddbaaadbdcdacddaccddaddcdcbbbbbcbdbdabacdddbddbadddbbdaadababdbabccbcddbbdcadcdaacabdabdabcabbaaacbcbcacbbdaddaadadddbbcaabcdddaaadbdcbacbdcdabccccaaacadbaadcccabccaddbadbcbdabbcbdacdbdacbcbcdcacdbcadbaabdbadbdbbcbbabadbdabccbddcabbcacdbcbbbbacddcbcccaddbdadaabcadbccbbacbaccabcbdcacbdcbaaabbdabbdadbdabbccaadddddbbadbdaadcbbcbbbdacbddcaadcbadabddbaabdccdddcaabbbbdaddacbcdbddadbccdcdbbdccddabbaabcadcbdadaaaaabcddbcadcabccdcbcbdcbdaabdcbdacdccdbaaadbbadcadbabaaadbddcbdddbabbcdbaabacddaabadcdddbcbaaccacabcdbadddccbcbbcbadcdcdadbccbacdbdbbdcbaadcbddcdddabcddaabdcaabbdcabcbddbdacdadbbdcbddadbaccaabcdbddacaadaadcacaabdccbddaccbcddbccadbaccbadacdcdaccbbbddaaabaaccccaccabcddaaacdacaaadbaaabcdcacccacbaacbbdbcdcdcaacdbadbbdcbaadbbbbabaaabbadaccacbdcaabbaadccccdaccdaccbcbdcdcabbdddacadcabddaaadccbcbbccadabccbababdcaddcdacdacdacacbbaabcabccbcdaddcaccbdbdddadcbadadccbbbcbcbdacdbabdbdbdddabbdabbccaddbcbacacdbbcbaacadbcbbaaddcddbbcdabdcbabddcdcccddbddadbcbabbdaddaadcaadccdbbabaaaaaabbdcdaadabaacaabccccaabbbcdacbbdcddababadcdbdcdbbccdcacbdaacbadbcbcbabadbbcaaaabacabaccdddbbbadaccabaaaadacadbacdddcbdacbbcbcbacbaadabacabcbbdcbdbbdddabdaddcccadcaaaddcdddddacddbcacbbbbcadcabbccadcbdaacaaabaadbdcdbcdccaadadbbbcdcdcdaccdbaabbbbabddbcdbcbbddbcbacadbdddcbdbcdcabbccddccdccdcacddccaddcbadcbddcabbaabcacbdbabccdadbbacaaacabddcbdbdcccbaaabbcbcaacbabacdccbdaabdccdddcacbadbcabdccacbdaaddbdcbcdabbabbcaaddbbdddadccaddccaacabcccacdcbcadadbbddcbdbcaddaabdcdbcddccdcabaaacbcbbccacaacbdbaabdadabcacbaaaadbcccdccbddacbcacbabccbcbacdbbaddccddbbacadddaccdcbabbacdbdaacdccadbcccacdbdccbababbdbdbdaaccadabdddcaccddcabaccbcabcbacdcdbdacacbdbddcccbdabddcbcccbbbabaabbdcdbddcdccbcccbadabbddcabdbdacbcdbcbadadddcbbbdcccabdccdacddcacdbbcdabacdadddaccdddbddbbadbadbababcbcadabdcadbabddacaaddddaccbdaaacadabddddadcaadacdbcabdddbdadbdacbcadcadbdbdbddbacadacdcbcdbdbdccdcdbcbddadbdcaacdbaacccbccddcbaccacdadbcccdaabccdcdcbcaadacadbabdbacdabddbadcacbbcaccdacbbdbcadabccccdcddbddcacacdcdcdadabdbaabdbdaadccacacdccbcacbabcacadbcbddbadabadacaadbccbcbcaadbabcbcacbacbcbadcdcbbbaaadaabbbbcddcbdddaaddccbcccdbcccdbabacbdaddcccadaadcbccbbcbaacccbdaabcddadbbcaabbbbdacbbabccacdabcbcdababaabbdadcbdbbadaacbbabbcaadadcccbddaaadabbcddbadaacdabaccaacbdcccccadaadaddaadacacddcdadaccccbadabadddbbcccbcbcaadbbcddbadbcbcaadcabbbcccadaddabcbaabadbbddcaddbabbcdadbdbcacadaddbdabcddcaaddcbaddccdbbddcdcdaccabcbdbbdbbdccdaccadabaacaddccdbdbdadadccbdacbdadaddddddcbbabbcabbbabdaaacdbccaabbcdddbddacaddbabddcbdbadccabadbdbbcdaaabacddaaadbcacadcbcdbdcaadddcdbccaddabadacbabcbaadbcdbdcbddcadcbacacababbabcadaaccdcddaadbbcabbbbdabadcdcacabccbbdccaaddcaabcdacddbcaacddbcaaddcbcaabcaddcadcccdcbdcdccacabbdddbdadacbabaccadcaabcdbbbbadacaabbcdbbcadcababdcbcaacccdbaaaaacdaccdbbabcbcbbdaacbdbabcdcdbdcacccbcdbdcaaaaacdcddbddbcaabdaadcabadabbcadbcddbacbbaccbbaadcdcbdadbdaccacaccacaaddcccbcdcdbbccdbdccdbbbababadaaddacdbbcdaadaccbddadcccbdbbbaacabcdcdbcccbbacabbdbbbcaadaaccddbccacaadcddccaddcaddabcdbcbdbddcacddbadacaddadddaccdbbcdbcaacbbbadbdbadbcabdbdcccaabbdaaddcabbbccbbbcadcdbcbdcdcbacdbaacabdadcdabbadacddcabadacdcdaadadabbbbcaabcdacbcbdbcbbcbadbbdaccdaadccbcacdbcadbaabcabdcbbaccabccbbacaaaaaacddddbbacdbdccdaddccaaccadadbabbabbadbbbdddbdddcabccaddccaacacdcabaacacdadcaaaacabbaabbcabadccadbbdcdcaddddabdaddcddabdaaaacdcbbdddbaaddabdcbdadcccbdbabcccabaaacbacdbcaccdcbcbbddbbdcaaabcdddcdcdbbaaacacdbacabcbdcbacabacadccaabaaadbcbbbdadcbaddadaccdbdabadaadadadcdcdcbdbadbbbabdadcabdbbbbadacbcbaaaaddbaabaaaadcccaaddcbababdbbbbdaabaababccbbadbadddabcabbdcbbacdbababcdacdbadadbbddabdddbacdaadadaadabcadbacabdbcdbddbaadbddcbdcacbcbcabcaadcdadbcdcbaadabcaacddcbdacbbdbabcabdcdddacdcdccdabdddcddcdadcdaabbddbabcdcddbddbcbbdaaabcbcbbacdabcdbcbdbdabccdcbcbddbcddccdcadabbcbadadcdcbccdababdcbadcacaccdbcbdadbacaabcabbadabbaadadabacddbbdcddddbcaabdddbbcabdaaaadcdaaaadcbddccdcbbaddbccccacdbaacaabaadccacddbbaccddbbacbbaabcddabbccbcacbcbbbdaadababaccdcdaaabbacdadcaaaddbbbdadddaabaddcccbdbdabcadacabcabbaddbbbdcdbdadbbbdbbdaddcddacccadbbcabdaccbdaccdadbbccacbddbddaadadabdbdadccaaccadbabdddccbcacdacadacbabaabbcacbbbbbacbbdcbdaabbcaadacbacacacacbcaaabcdaabdaddbdabdabcdabcddbbbbaddbdcbbddacdbcbbdbacaabdcbbabdbcdaaddbbcbdacdacddbacbadaacccadcabbcbabbcacbbddbcbcdacabdaacdddbdbcdacdaadaddddacdbcabbccdddbcbdcddabbcdacdbbdbbabaacadddaacadaabbcadcddbdbdddbddccabbcadcaddbacabbaabdbdddbbadcbdabbabdddaccbbcbcbdabdddabddabcacbcccbadcacacbacddcaacbdcbacddaadabdbddcbcccbaddacbdbdcbbbdddbcabbcabbdaccbabcaaacacbddaaaaabcbddaddaadbacccbbddadacdddddabcaadddcbabbdadcaaddbcddacadbcdcdbacbcdcadcbcddadabcdacaccaccddcaaddcaddcccbcdcabacbbadadcbbbcccddbbaadbaadddbdaacddccaacccbbbaddabaaaaccadcbacaddacaadabcbabbabdddaaacdbdaadbdddacdabcbccacdbabbdcabccddcddcaaaacdccbdbacadbbdbcbdbdddacbadcabcdbdbacbcadabacdccacdcbcadcdcdccbabbaabdbbccacbddbdbbbdcbdbdccbdcacdacbdacbcbddddcaccbddbacaccdcbbcbaddbcadabdcddaabacdbbdccaaacccadccacaaadaddadcbbcaddcaadbccbaacdcdccbcccaacccabbdcaabacdbaadbdbbbabdcdbbbadbcdabcbbbdadcccddaddaccacabbddbacbccadacbadcaddccbdaccacabbbbcabaaadccacbcabdabcbcdddbaaccbadacabccdbabbcdaacccdabcaabbdbbcbaddbbcbabdbbbaccbbcadbbbbddacdcabbcdacbdbdcbbbadbddcbddababbbdabccabdaddbdccddcdcacaaaccbcbabdaabaaccbcabbdadbbddbbadadbcdcbcaacabdcccaccdaadcdcdbbcaddccaacaabaadbaaadccddbcccaaccbacdaabacaccdacabbbaaaccbabdcbcdcaacabbababccacaabcaacbcccacdacdbbcdcbadacacbdddbdbadbcdabaaacacaddcccbbbdbbdcadbddbdacdbcbcddbacadabbccbbcccbabccabccadbddaacddacabadacbcddddcabacaddcbaacdcccacdabbcdadbaccbacadaabcdacbdccdadcabcbccdbabcbadddbddcdcccdabbaddbcdbaaaabccdccddcdcbbcbbcabbbccdabcbbbaddabbbacdccbadbadadadbdbdcdccbbdaabdcccacdccccaacaabbdcacacdcdddbcbcbaabbcbddacddcabbdbbcbbdbbaadddbccbcabbbbbaccbccdcaaaccdaccacababacddbcacdabbcabdcacdccdccdcbbcbadbdbdadddbcdcbdbcbbbaabdbbcdacbbadbaacdddddccdcbcdaadbdccaddbccbcabdacadbabbbabadbabacddcabcdcacdaddddbcccdbdcaccabaccdcdadaccbbbbdcbadcbaacddaddccbaabdcccdddbbbdbcdbcbacdadcccbaacaadcbbadddddcdabaccdccbacddacadcbabbdddbddaddcaacbcbcbdcacbdccaacacacbcbacdbacabdaaadacadbdcdacbbbddcaadacabcbbcbdaadabdbbcbadadcbadbaddcaddcbaccddababcaacbbbdabaadbdddccccbcbdcbdcbdbddbcbdaabcdbccbcbcacbaacaddabbddbbbcbbcacbdabbddcabbcabdcbdadbdbdaddcdbdaacbbddccbcdadccdbdddaadbdbaadaccdadadaaaacbdcbcdddcdabaddbcbdaabdacaddddaadcdcddcdabacacacccabccacbacdabbadcdaacccddbdbbcdbaccabccacdaabaddadbacadbdcaaaabccdbdaddcbdddbcbbbbbabcaacabcdbbbdadbdbcccadddbcddabaadabdabdaacbaccbbaacdaacadddbdabcadacccacadbdcdaaadcdbacbcdcdddbbcbacaaccadcbbcccaddbabccacdbdbabaaadcabadbcdaddbddbbbdbcbdbcdabdcaabccbdcaadadbdccdaabdaabdbaaababdccacaabddcbbaacbdacdcbbcdbaaabbccdcdaddabaacdbddbaadddcbddbccccbcbbadabdddbcbcbbbaababcbaadadcbddccdacdacdcacbccbdabadbcbacacdabbbddadbbdddadcabcddbdaabaadddabcabbaacdddccdadcbbddbdcccacabaadadaaadbccabdddccccccccababaacbcbcdacccbadacdbcdadcbcbbccdaddcdccccbabbacabbacabcdadcdaaccaacddccabbacddbbbbbcadbdddbacbbdcadadbbadabdccacacccaccadbabcbaaddbacccadabddbbbbddcbbbddcabbdbbbddbcabdcddcbdabdcaccdcdaaaaadbcaaacdcaabbadaddbdbdbbdcddddabbdcdbbdcadcccadbbdcadcadbcdcdabaabaaabadcccbbbdcbabcdabdcbdaadcaaddbbcadbccbddadbccbabaadbcccacccaaaccacaadddcbabdaacaddacdcdbaddcacaccdcbaddacabbdaacccacdccdbbbabddcdcababbcacbcddbadcaacdaabaaadcccbbcabccddcbdacacdbadacbbccbcadcabccacaaaabcaabcbbdbbacbaaacadddbdcbacaddbcbadbdcaabbddbbadcbbbaadabbaddcbccacbadbdacacbdddcddddcccbdcdaacdbbbdcdcabdbaaadabaaaccbabddabadcaaabbabbaacdaabcdccdbcacdccbdddaacddadabdbdcbdddcbdbdbdaccaccbabccacdaccacbccbacaabadcbbaddaacaccbdabdbacddcabccccbdcdbdaadbcbcbdaacbcdbbdaabbcbdadbccdcdbbddbbbcaadcccbdadddbbcdabaaaacbacbddbdcccdcdbadadcacccbaaabdabcbacaabbadbdbcaadabababdbddbaddcabddbdabdccdacbcaaaabdddccbdbcbbdbcbdcbdbadbbdcacbcbcabbdbbddccaccacabdcdadccbaadbaccdcadbadbbbccccdbdadabbdbdabdccadbbdacaacdcadccbccccbaacdccacbdbaaabadacabaadccddaddbccdaadbbaadbbbbaababbcdbabbadbddabadabaccacbbccbcabacadbdaabbdbacdbdccddcdccbadbdbbabdbdbaaaddcabaacdcccccbdbcabbacdabcababdabbaaaddccdadadbadccbddcdbdcdabcadcdbdbacbdbabdcacbbacdbddbdddddcdaadbababaaccddcdabbbaacdabadacdabbbaaddcbcaaacabdbbdbddbacbaabbdcbdabdbbcbbbbbcbbbdbccbaaccbcbdabdcaddaabaacdacbcadccdaaacdcdcdabbbaacabbdcdbdaacdaaacdcbccddadaaaccbbbaacaddbaddccdcacdadadbdbcabddcdadbcbcdddaabdbbdadabdcbbcbabbbdadcbcbcdbbcbadcacbccacbacbabacccbdddcabaddbcdabddbdcbdccbbddbcabddadacbbbbacbbdaacbdccdacbabcbdddbbdbdaadaaccacddbcbcacbbcccdbbbbcdbbbccdbcdababdbbbaabdccbcadcbbdaddbdbbcdbabbbabbaaabadcaacdbcdbcadccbaccbaaaacbadbbbcabaaccadbddaacbcdcddaacdadccbdcadddcccadbddacbabaabbbcbbdbaddbcacaccbaacdacccddbccddddbababcddbaccabacaccbacdaadadbaababddaaadaabcacbbcdccacddabcbccbaabbdddacaddccdcbcadbcdacabdbccaadadcdcdadabdbbcadbdabdddddcbdacddbaaacddccaddacbccbaaddadabacabababdaacbbddbcdbcadbaabbadcaccaadaddbcaaaacabacbaaddcacaddcdadbdbbdbaccbcbabbacadbdcbdbadcddcadacbcbdccbddbbbaaaaddabbaacbdbbccdadbcccbcacaabcacbbabbcbccdaccbdbabccacaaaaccccbabdabdbbbaadbaddaaadbadbdacaaaccacaaddccccbacbbbaccdcacdbbabcaaabbaaadacbaadabdcbcdacadacbbdbacabdadcbbbabbbdadccadcdbddabdaaababcaddbaccbdbaddcaabbcddaddbbdddadbabbccadacbadaaabbcddbbbcddacdaaddbbcbcababcaadaabcdacdcdbdccbdacdabcaabcddabacbbabadbddcdbcbdcccdabddadaacdacacaaaaddccdbaaaacacaacaadaddbdbbbddaadadcddadbdddbcdccabbdcaadaccdbaccdbcadddabbabbacdaabdacbadbdaababdcbdaabcabddddcacabbaadbaccdcdbacabbbbdbcbabdcbacdcaadddacccccdddacaddcaabcdaacabaadbbbdccbdbcccdabcdacadaabbbdbadacbabdddbcbbddbdcbbbbcdcbbabcdccbbcadbaddbcbdbdcdcbadadbabdbcdccbbabbbddacaaddccdbcaaaaddcabdabbaabbdacabbcbdcacaabbbdcbdaaddccacbbcaadbcccabccddababddbdbdcbbdbacaabcdaabdaddadbcbbdbacbdbdabbbbbbbbcdabdabccabaccabbddcbbaddbbcbacacdcaabbcddcacbbacbbadcbaabdaaabbdcbddbbdccbddadbabdcccadcccabdbaabcdadbadddcddcabcccdbaadbcaddbaabbcaddbddcdbacacadaddabccaabbdacdcbccbcbabaccdbddccadabacaacabdddabcbcabbabdddbdbbabbdcbadaabdbdadbccdbcbddddcdabdcdbdbdbbccbcabbadcdccaabcdbcdaaabbdccacbbccdacbccbbdddabccccdadccabaaaaacbcdaddbbccdddbdbdcdcddabbddccdcdddbcacddbbdbddcbabbdabcccaabccaccbbdcabdcdabcabadadbbddbcbddbacccbcccbbcccccbbabdcabdadbdbaadcdcbacbcdcbdccdbdbacdcaccbbcdabbcabbcacddcabadcdbbbddaabbcddadacaacaabbcdbdacbcaadcbbaaaacbaacdcbaadabdabddadababdbdbadaddbdcaababbaacccbbddddbdbbbaaabcaddbababaabcccddaccbbdbdaadadbdacabdcccdaadcdcacbbdabbdacccadcdccacadbcbcddaacabcdccccaaccadabdbaddccaabbabdbbddccbbadcbcccadbbccacddadbddacbdaaacdcdabddcdadacbcacadadbabbbbcaacccadbadccbcbaddabccadbdbccaaabddadaabaadccbcbabbbdcaddabbaaabcddbbaadacabcddddddacaaaaabccababbcbabcadadccaababcbadcbabcdabccdcdabacccbcbdddbddddbccadcccbdaddbaadadcacbcdbdabbddaccaadbdacbacccacbadbcddacddccbddcddcadabccdcacccbcacdbdccdbccdbdacbabaaabacaadaddbbbdcabbccccacdadbdbbacaaaccdbcaaacdbdcbccacaacdaabcddaabaadbaabdcdabdcccccadbcdcbdaacdadbdbbbcadbdcdccadcaccabbcbabadbaaddbbccabdddddadbbccacdccdadccaadcaacccdbcdbbadbaabacddbbaddccbdcbddabbbccdbcadadcbaaddbbcbbacdbaddbcadcddccaacacadaddacaabcbcdddadbaacbdcacdbdabbcdddabcdaccddddbbbaaccddddacdbcbaabaabcddadacdbacccadbcaddbdbcdcdbcbaaaaccccdadcbdaacbcdbdbdccbcdcabcdabacccccabccacadadadcadcaadaddcaaaadabdbadbbabaadabbdaddbbdbccabdcabcacddcbaaccdbddacacbbbbcadcacdbabbccaddcadacbddbcacdabbdbbccdbadcaaacbdbdddaaacadaaaacbcddaabdccdbcbdcbbddcbcacbabccbabacbcddcbadabdcbbdacdaccbabbbdddbddaaacaccccabbcbccdbccbdddaaacbcddcaabcacaacabbadaccddbbbccacdaabadbabcacbdbadbddaccbddbddcadadbcacaacdacbadbbadbddbcbdcbdacbddacdaadddccbdacbdcdaddcccbadbdcdbabacbbacdcddbdbcaaccdaadacdbbaaaadbadbccadaabaadbadaacccdcacaabcaabbdcbdbaaaaccdcacaddcadacdaabcccbadbdbabbcdcaddbbccdaccdcacbaccaccdadccdccbbbccccbcdddddcdcabdacdbadbabcdccaadbcdcccdddddcccaabbcbabbacabaddaaadcdccdcdbbbcaacbbcbcabadaccbdbaaababcdadccdbadcdbcbdccdabcccbdaccaaaadabbbdddcbadacadbbcdadccabcdddaaccabddaaddcbcacaddadbaaadbbddacaaaadbaccabdaadcbcabbcdaadbdcabbccacbaacadabdcbabaccbcbaddddccabccddcdccabcbaaaaaaadddccbcaddababbdbdddabdbddcdadadaddbdbdcbdbcabcdcddaabcacdbacbbbdababaddbacbdadddbacaadccdccabccbacbacaccaaacdcadbcddaadbacdcbdaacacbaacaaddbaccbbdbdbbcbbbacccaaddcccdaaabbbcdaaaaaccbaccacccbabbabdacacdabbcbbdbbccadcbbbdcbacbbacbccddbdacbcddabccacbddbddabaddacccbdbbbbcbadcbdbaaddabbaacdadcaaddcdcacdbdacaddaaccccaddbbadddbcbbabcbacbacbdcbddcdcabadcbdccabbccdcdcddbbaabaacbbbbbabccbacabbbdbcbddaacdddccaaccaaabbaabcbaacbcdbacbbabdabcbaadcdacbaaccaddabbbcdbbadcdcabbcdaabdacbbbdcbccddbaabbcbcdaaaabbbdbbddbacdaccdcccdccbacbbbbaadbacddbccdbdccaaaaccbabaccddaabadbbbcbcbcbdaddadabcbdddcbacbabadccdcaddabcdbcaaddccaabdcdbbcbabdacadbddccaaadbbcdcdbadbccdadccabccadcbbaacbdddaaadbcdacbabdbccdadbdabadddaacbacbbbacdaccbadcdcbbbbcbcbdbadabacdadddbbbccdcbdabdbbabbaabddcaacbddacacdabbccacaaaddbddbacccbdabcbabbbdbddabbdcbccdacadaabaccabaccdbbacabaabaaabbdbbbdadabccdbbccdcbcbbaadadcadddaddaacadaacbadcbddcddddcdacdbabdabdbcdcabaacdbdaaccdcaababdddbdbabcbbccabcbcdcadbdaabacaacabddabbacdddbdbbbacccdbabbbbbcacbcbabccdcdbcccccbcabcadabbdbcaaabdcaacbbabbdcbdadcaacaacdbdbdadbabcccacdaabbdacbbadbcbccaadacadadbcaabdbaaabadadabaadcdbbcbacaadcbaadbdcbcbccbbbbccbdbcacdbadaaabcbcbdcbbbadddcbdbdbddccabaaabcbbddaabccccacdabacadcbdadbbddcbbdbddcacbbaccadbdbacadbbdccaaabababaadbbcccdaabbadabcabdbddbbadbcbaddbcabdbdddabacacbcdcbbaddcaadbcadadacaaddcdbcdcbbbbbcbbddbbaabdccbcdaacddcacdadacdcbcdadcadabcbbddccbabcbcabadaddaacccbcdacbadcbbbadbbdbbcdbabdaadacdbddcbdddcacbcdacadcbaaaabbdbaccdadccacbadcddcdbdaacaadcaddccddbcccbbdacbbcaabbddddababdaddddaababbbbdbdddbadcdcacdcddcabdbbdcaccdcbaaacaaaacbdbccdabbbccbcbadbdaadabbbabdbcdcbcdadcbccccdcbdcbcabdbccbbadbaacabbbadabcccacdcddddbcdcbacbaacaadbbccbdaccaddbdaabbcddcdcddacaaacdbbabddccbabbcbaabbcbbacdabdbdbccacbbdbdacdbdcaaddddbacaabcadbbadcbaaccbdccbdabbbcdbcccdbaacadaadbaddacaccacccbcdbbbcbdbdbbbcddabadddcadcbdcbabdcaacbacdadaccacacdbbacdccadbaccbcdaabbabddcccdabdaccabccacdbcdacacbddaccabccbdadcaddbabaabdadcddddabaaaadcdbabadacdaaccaaccbadbddcbbcddddddbccdabcdcbaddbdbcbcdbbcadadbdabadccadbdabcdbbbcdbacacdbdbacdacbdcccbdbbccbcbbcdbababdcbbcadacbcdcdbacdbbbacaadbdddaacccaccccdcbcbbcccbcaaadcccacccabccacdacdbddadbdbcadbdddddabcabbccacbaadbcaadabbdbaaccaadbdaaabacdbbbcddadabaddbaadbababdcacbcdbcaabcbaccbaadbcbddaabcdababbbccdbcbbbbaadddadabaaadaaacabbabbdadaccdcbabdabaacddbcaacbabcadabdccddabaaddbcacbbaccacdddcccbcbdacbdddcbacbbaabccbacbaaacccbbbbdddcbdbcccabdccbabbcbacbdccbacccdcdccdddddddbdbbbdcaccdbaabacdccbdacdcacbacbbcbbacccbacddbaadbcbcadabdcddcdddbdbdbacdadddacdccbaaabdabdbcdabbdcabdacbadadaaaaabbbaddadaacbdabaddddcdbdccabbbabccacddbbabacdbbddacbadacadcdaddacadbaddbcbbdcbdddabadbddbaaadaddddbcacccabdbcbdadddbbadaddbbdaadcaababadbcdbacdbdbccdcaadabacbaccbdacccccaabccbcaacdccacccaaaabdbbdccbadbcbcbddcbabbabbdaaddabdcacddbbddddacbaacbddbbddccdddcddcbccaaadddccbcddbabddbdacbcaadbccddcdabacadbbbcdccdddccbcddbdaabdbaccaadccbcbabdbddbdbcbdacadbcdcddcdbbdacabcbdcaccababdccbbabbaadbccbcdbaccbdbaadadcadddbbdccdbaaabcaacdcbbbdbbccbdbbbbdaadddcabbcbcacccabaadcbacbbcaadbaacdcdbbcdbcbbacdcdbbacccbabbacdcbcacbcdbcdbaaaccccccdbddcaccdcbbaacbaddabcdacbcaaabccdacacccbaccccbabcacbcabaaaaaccacaaadacbadadbbcaacbdbdcbccddbabbccaabcbbcacdcacbdccadcdbcadbdacaddbdcbdcdbbccaddadccaacaadabcaddcaaabbaabbbbabdbadbcdcabdaadabaabacabbcacabcbbbdbbabdcaacaccbdbbdadccbdbbadbdccdcbdbccaaabdbcbbaabbbcccacacddcacdbbbabcbbdabddcddddbbdddaabcbabbbdddaaccbdddabcbcaaadbcbaababcbbbcdcabddabadbcbbdddbcbdabddccadbbcadbbacdcaaccddccbdcdadcadadabdacbabbdaddddcdcacdbabcddacadcbcaadaccddbacdcbacbadcdcadbdcabaabcbbbbbbbdbdccbdcbadabaadddcbacbdbcdcdabdbbdaacadcdacbadcdbcbcbaadbaaacbbacdccaaabdadadaaddcdcdcbcccdbbbcbdbbaacbdcbadbcabaabbcadaaaacdcadbabdaadddbcbbaaacdbdadccadcccbdbdbcbacccccbdadadccccaddbbaadcbbbdcbcbddbccacbbbcaacabbcadadadcaaadbbccbcdadacabcdcacbcaacbadacabddbdbbdbbdccacddcbbcbccaaccdbcdaccabbbddacaccabbabbbccbdacdcdbcbbcbbddccacbabddcaddaadcabdbbbcaddababdcdcddaacbaabdccbddcddabbcbcbbcbbaaadacacdbdbaddacaaaabdbaaccdbcdcdcabdbccdccdaadbbdababbdcdcbcddbcbcdacdcbaabdcdacaccadacdabaddbaccaaabccbacbaccaadaaddadcbbdccdbcaabacdbdadababcbcdcbcacdaacdbdcabccccdabbbdcdcbdadbdbcdccdccdccccbdcdcbabdcbadbbdcbbccadbdbbcccbbbdbabcaaddcbccdabcaddbabaddbbabccbbacbcbcdaaccacadbbcbcdbdbdcabddddaacbbaaaadacccbadcaaccdcdcdcbbacbbaadabcdcdaaddadbbbccbabdccbcaacaacbcaaaddbaabbbadcaddbddadadbbbbadbbbaaadacbdcbbacdbaddabacaabdbbdadcbabdcaadcdcadabdcdcdbccdbcbdabdbccdcbdbddbddbbdbccacbabbdbbabbaaadbadccabcbadabdabdbddccdcbdcacbbcadabccbbaddcdabcdaaacdccaadccdbdcdabaadbbbcccabccbcddcacaaaddcbdabdaaccdbcaaabacdadcddcbaccabaacadcacbadcbbcadcbbbbaadabbbcabcbaadccbbcdacdcdcbbccdbaadccaadccbdddaacbaccbcdddabcdcacabaddcdcdbddbbccddbbbbcadcccdbcccbcaccabdaaabbbbbdcddcacccdbbbcacccabcadbcdcbcdabaadcacdacacaccbdbbacbadbbdcdacabbbcbaaccdcdaabccacaaadadcabbdccdddabaacdacdcdaaddadcdcbcbbdcbdabaaaddabddadcdcacdcbadaabdacbbabdbabadbacadaadadbbbbbbbdacacbcdabaadaabdacbaabbdadacbdaddbddccaccdccabdbcdbbacadacdacacaaadcbcadabbbadddbbacdacaabcccaccbdddadcbabababdcadcbdbcbacacdddbdacadacacbdbbbdcbbabbdcdaaaaaadacdabaadbddbbcbabccadcacdbbabcdcdcdbbbabaababccdabadacdddccbdcdacdaddacabbdbbbcacbacddccdbdbacbadcdbacaacbddaadcbbbdadabcdbbccbabdcadccaddcbcdccabccacdbcddbcabbcacaacadaccbbdbcbaadcadcccbbdbbcddbbdabcbaaaaaaacaabdccbdacdabbbbbbddabaaaaddacdbaadcacadddbbaccbccdadccabddacabbbbadacccababacadaaabbddbaccabbcdbcacabccccddccdababdddcddabcddcabaaccadaaddbacadcdabccddcabacdadcbdbdacbcabaaddadaaccaddacaacbdadccdaabdcbcddbcdcccbcabbacbbbababcaccbabdcccbcbbaccddaaaabbcdabadcdbcbbaddadbbacbabdcbddcdcacbcbccdbddcdccdbbbdccbddbddbbbccbdaaadaabdbabdbdbdcddaabdddccabdddbdbcbbadbdabcbaaabbdcaddcddbbcbbabcbaaadcccbbacabadbcbcacadadcaaddbdadccdcaadbccabdaaabaaccbdadabcdbaccbcaccababcddbabcbbcadbdadbcbadaccabdddddccabcdbcccccbbdabaabadccccbaababdcbdbaddbadabbadabcabbbaddabcdaacdbdcabcadcdcacbddbbacadcbbadbdbdccbcadbadcdccbcdabaddccccaabddddabdaddbbbaccdddabbdbdbcabadcbaadcaddcbacdbbcdbaccabadddbdbbbcacababaacbccddbbbcdcdbacbcacbbcccdcdbbaacacabccdbaaacababbabbaaccdbcddbcabccbadcbcabccdcdddcabbddadbbaadbddadbccbdacbabdbdbabcbaccacdbaabbadaaacddddccccdccadcbbdacdccbdbadbaddcdccaaccdddbabcdbbcccbbaadaacbbacacdccdddabacddbdbaccaddcdabccbbbdbaacbbdcabcbacbacdabbcbccbbcabcaddbcddadcbcacbbaaacdbbcbcdcbccccdabcaaadcbabbcddacdadddabbbacabadbcdcdadcccbabcdcabadcbdacdcabacdadcabdbdcdaddcacaccdadacbadbaaccadaccbdbadbaaddadbbabdaacaadcabcacaabcdbdbcbabdcbccdbbcbbdbdcbbccddabcddddcbadaccdbadacaccbadcadbdcbcaaabadcbbdbcaccbacaccdbddccabdcadcaaccdbccdbdaadccdbbbdcbccbbdcbabdbcadcadacccdcbbaccdaaabccaaddddccaadababcbdbbcacaccadcbbcddbdbccbdbabdacbaacdaabcadadddbaddcccabdcdbacadadaacabbadacddcdbaacbdacdbbddcdaacdbbbacbcdddcddbacccadccaaddacdabbdcaaadddcbbbbcbdbabdcbdccacaabbcaacbbdbccdaadcbabaabcddccdbabbdccdabdddcbbcbcadbaabddadcddbabbcbbdbcdbbcbbaacccbacaaaaaaaacabcdcacbdacccdadcaddadaabadacaabadccaddadbacacddcdccadcacacbddbdabdcbdbacdcbddadcdbabbaccdcbbaabaadbbccaaccbbbbbddcbcbbcbcddcbdbdcbaaddadddaadbadbddaddcdacacdcdddaabdadcbddbcaddaabdcccbbbdcaacdacaaaddccabbdbbbbacaacabbbbaddabbbcbbdabbaacddbccadabdcbddcddacbdbcbacdbccbbadaaccaaadbabdbbdbbbaddcdadcacddaacbabdbbbcacbbcaddbdbbadddacddbaadcccddbbbdacbadcacbbaddacbabadcddacccddaaadacdbcbddbadaabdbbacdbadccccdaaabcaaadcacdddcadcaabcbbbbaccdcaabbaddccadbcacddacddadacbccaabdaddabcbbdbadaccbaccdbbaaadacdadbccacdddaaccbdbdabbaabacabadccbdbabaadcacabdbcadcdcbcdccbbcdcccccdacdcabbabcdadbcbbddbccabaabdbdbccddbdbbdddaacacbccdccdabdcbcdababccbcddbdababbcaddcccbbbacdcdcddbbaacbbcbcccdacacbaaaaabcbaabaccdcbbdcbabdaddaacbdcccadacabcbbaabbbcababcbadddadcdcadaacccbdccbabbaaacdaddbdcacabbccccdddbcadddbabacbbadaabacaccdbcacdabbadcddcdcdbdaacdcabddccacbabbabbbaadaaabaacdabbaaacbbdacdbccddcdbaaabccabdaadcccaccbababcdbcccacbcdcacabbbdacddbbdbdbbadaabcbddcbcacababcbbbddbbdcadbaabbbadcbaaacaddacdcdddbaaaaabcdbddddbadddbbcacdccaaadddadbdacbbabbbdaabacbcccabbbcbaddcccddddddadcbdaccadcbdcbccaaddccbdbbaacbacccbbdaddadcaccccdabbcabbbcbcbcabbabaadbbbadddcaaabaddddadaabdadddababbcaabddcbabdacaadcccdbdabdababbabaaddddcabcaaabbdcaabdbcbdcbdacdadadbdcabbabcbccbdcbaacbcbacccbbddbcbbbcdcddbabcabaddabdddabcaabacaabaaddddcaaaadbbadabdaddcbbdccccbbacaacccbcadbabbdbabdbdcbadbcaaabacaacacbbbccbabdcbcdcccccbccacbbdcacbbddcbadcddbcaccdcdbbcaccbdddbdbccdaabdacbbadccabbaddaadbcbcdababdabbbabbbbcdcbaaaddddcacbddbadccddadaadaccbcbcabaccdabdabccccacbbaaabbbaaaccddbdbaccabbbbcbddcabaacccccabadddddcaadbdcbdcdbacddaaadaadcaaccabbbacbbaadcbbaadbabbcbabaabcabccdcdaababbabccbaaccdddbbdbbacdcbabacbddbacbbbbbcddccbadcdadacadbabbcdbbaabbacdbdabaccbcccddaadbbbbcddacabdcdccdbdcbabdcbadabaadbddbdcaaacbbabadaddaadaabcaadccddbbbdddcbacdaaaddbcdadcacaabacccaacbbdabcdbdbbdacaaaccdbdaacbcaccddadaccccbdadbdaabaddbddbbdabbdacadcaadcbdaddacbccddacdcbcaccaacbaadddabcbdbcdabbabacaadaaabdaadabcdbbdbbcaacdbaaaadbdcdcaaddcaacdbcabbcadaccbdccbdbaaadaabdcbabbcddaaadabaabcbcdddaacacaacadbdaaaddbbddcadabbdcdcbddbbdbbdcaabbccccbbbbbcdaddacbcadccccdaccddbccbbdaccacbbacaccbcaabaaabbbccbdbaabbdccbcabbabcadadbdccbcbbaadababacccaccbabacabccacaacbbdcbbcaadcbbcdbbdcdcbbcadbbaccabbcaddbdddbbddabdbccacdaccbdcbbdacaccbdcdcddbbbddbddcadbcadacacbbadadbcdabbadbcdabbaabcdaccdddadcbccdadbbddcccacaddbbdabaddbddcabcbbcbadddaccbbadcbadcabcbdcacaccadddbbcadbdcdaadccccabcdddaaabbdbbbdacbbcdddabcbdddabdaccabddccdbdddaacdcadaabadabacccdccbdbadacacbbdbacccccaddddbcdcbcaacdbdabdbccbccabdacadcadaabdbbbdcabbbdcaacdabdcddabddaaabbcaddbbaaabcabdbbddcabaccddbaadcbaaabdddbdcadbdbaccdabbccdabcbdbbcaacacbddccdabcabcbadcccbaacacaadddbacbcccdaccbdddadbdbdacdccbaadcaaadbabdadccddbcdbcadadadbcdbbbccdcbcdcabdcdbbdcadbddbacabadbacaaccabacababbbccaaddddddcccddbdaccaccbdbaacacdbcbdacadaaccbdacaacbddcdccdbdddbbcdacdaccbbaadbbadaccdadcaddbbccaddbdcaacacddbcbabbdbadddcbcccbaabdcddaaaaddcbaacbbadddbddacadbacbdcbcaadbadaabbbddddabcbbbdcbabddbdaaaacdbcccaabadacbcdacbdacaddbdddadabdaaabcbdcbdbbacbdbccccbdddacbacadaabbccbbacabbbcabccdcbcaacdaaacdbbbdccddcbddbabccadbbabbbcaaaabdbbbcaabbddbaadacddaccddcbcddbddadcbaccdaaadcdcbabcbbdadbccadbdcddcbaababccccbaaabdcddbdabdcdabdbcbdabadcabddaaadcbaadbcadaacaaabdcddaddcdadbcddcbbbdabadaabbcdcbbdbaabbabbbabbccbbabcadacaddbaabdbcdaaddaaaabbcbcbbbdadbdbcdbaaadcbbbcdaabaddddcbaaabdabcbbbcbbaccddccddcdcbccacaabbbcddacbdbcbbadbcadcdcabaabdbcdccdbbbbbdaccbadcddaddcbadcacbbaaabbaabcadcbbaddacaddddddbbdbdadddcbdbcbadbaadbdabcaadbbdabbcbabcdbcacdbdddaddcbadccbacdbcdcddcbacacbbdcbcccbacbcbcbbddbabcddcaaaddbaaababddbadadbdbcddbccadcdccaaccbbdaababcadabbbbcccbdbabbbbdacaaccabcaacbdbccdcacbdbdabbccacbbcaccaddcabbbacccdaabccdcadbdaddccaabdcdccaddbbcbaccbddcabddbcddabcdaababbdabbbbddcdaabdbacabbdaccdadcdccdcbbdddabccbadabccdbacabaacaddcacdbbaababddadabcdcaaccbcababdadacabbbabddbbddcdddcccacdcadbdbcaaabccdbdbcccdaaadcdddcdcbbbdaccacaabcbcddcacddabacbbcccadbadcddabcdaaaccbacaccdbcabddddacabbbcbcadcadbcaadbbcbbcddcadbcccdabcdacabbbabbcccccbcbdbdcbdabbcccdcabbbccddbacddcddbdacdcbdbdbbbcbadccdaccadbabdcdcbabbbbabbbcdddaabbaacdbabcaacbbaddabadcbcaddbdabcacdbbdcddcccbcccbaadcdabcbbacdbbbdbbaadbaaddbcaacadbabcbcbabbaacbdbdbbbaadcbbdbcaaacdadbdacdddabccbcacddcadabdacddbabbacbadbaaabbabcabdddccbabacaaaabcbdbadbbabbcadabdbbbcdbcdbcdcabcbaddacccacddbcdbcacdcacbaadbabadbbdbcadacddacbdcabbcaaddbcbccabcadbdcabbccdacbbabdbbabbabdcbbadbbadbccccbcaabbaabaadaadbbbadcdbddbbccbbacbcaaadcadbddbcdabdbadaabaaddcdabacdabcddbbabdcbabdbbaadbacccddcddadcbcccabbdcbbbcbdbcbdaadaadacbdbaaccaaadddccdbababcadadaadbcbabbbacdacacbccaacaabbbcccdcaccddaadabaddacdbccaabbbcccaaadbdaddbdddbcddccdbbbacbddbcddbaccdbdddaaadaabbbdbabcdaaddcacdbadddbbcccbaaddccccbccabccabdbbdcccadbbdddbbbaabbbabdcbdbdbdbdacdabbadabbbcdcdbbbabaadddaaadbbdbddaadadddbcbadbbcddcbabccaadbadabadcadbccddadaddcbaaddddaabcdcbcbcbbbdacdbcdbcaacabbcdaccdddbacaabdcabdcdcdaaaabbdcbbddbdcdcdaccdbaaddcadacdcdbcaccdbdcbdcbabaaddcdbbbcdcddbaaabadbbbaddbbbadcddccbcccababcdcacdacbdccbacaabacaadababaccaccdbbdabcaaddcbadaaacabbbbaddbccbababdbdaddcaaababbabcbadccbaddbcdcddbdcadaabbaabdacacccdcccdddadbbaaaabaacccdbabbcdbddbbcdabdbaabdcbccaabcdcbdcdbcdbabbbbdbbdbcaadcdcbababdbddabbbcaacbbdacaacadcaddcbabccbbbdbbbdaacbabbaddabadbcdaccddabaaaccadadbaaadcacdaabcbbccbdaaaaaddaccbaccccaadbccccbadbadbaadadacdddabddccbbbbadcdabcccabaaadadbbcddcdccdbabbdcbdabdcbdadbabdbaddbacdcccaaadcadbbbdacbcdcdccbaddacdcdabcababbccbcabcccdbaacdbbadadbbdcbaadcaadadbdcabdcabdcbdcabcabaabadadcbbddccaaabacacdbdbadacddcbadabaabaaabdddcbbddacdcabaccaaaadcbbcddaabbdabbdaccaaccaacabbdcddddbcabdcdcadadcdadccdbabbabbbbacdaddccabbacdbcacdbbddbbbbdcabbcbbadccadbbaaccdabcbabbcddcabacbacbdddcbbcdcdabddbaadbabbdbacccbacabdabbdadcbccadbacbccaadccbbaadacdbdcdbbadcdcbacbccabdcadbdadabdbaadccbcbaadaddabadbacabddcadaadababbdbcbdabadaddaadcacabcdcdadbdbdaddbcacdbaadbbaabdbcdacacbaccabaadcdbcaabcdaccbdbdccbdaaacbabaaaacbbaddaacacaddcbbdbcadbdadcdbacdcdabbabddbcbbdabaadcaddccadccaccadbcddcddacddacbdddabdadbbaacdccadbcbabddabcbcdddabbabbddccaaaccaabbacadacbbaabadcaccadcdcdcdacbdbadbaabbddcdadaccbccdbabbcdbabdcccddadadbbdbdccacaaaaadbbaaddbadcbdccdcdaaccbabddbbacbadaacdccbaadcacaabdacaddaddbccabbdcdaaddbcbacbcacddcdddccaaaddccbcbcdadbaaccdcbacadcdaacadbbacdccbcccbccabdacdddccacbbbccbcccaaddcacdaddaccdbbdddcbdcdbacbadbadaccbacbbcccaccacadbbccdbbdbdaaadcdddbabbabdabdaacdbdaccabaddccaabdacccddbabcabacadbcaddcadbddbadacdcabbcddbcddabcadcbbaddbabadcdbdcbcbbbdaacddabbbdacbaadaaacdccbcdbcabcadacdacaabadbddddbccdbbddcaaaaaadacbcdaaacbdddbddccdaddbcabbbaabcaadabdcbddcdddadccbbccbdbbbadbabcbaaabdaaadcabadbdadbbcbbabbabccdbaaadacccbccdaddbcadbaabcdddadaadabacaddcabaadacabadaadddcaababbabcbdcbcdddddadddbdcbaddbacbabcaddbabccdcbdbdaaadabdaaadbbbbddaaabdcccccddddadcabaaddbbccdaaabdbaacbaadcaadbcccabdddacadcbbdacddcccbbdacdbcacdcdaaadbbabcdccbdcbdbccdddbacddbdbcdabccbdaadccccdbbdbdabcadaadadcaccacbcabdcdbdbbbddbbcbdaabdabbbcacaddaddcbaacddacaaddcacbcdaaaccbcacddababacddbabadbcdabaddccbbcbaaabbbacabbcdcbcbadabcdbccddcdbacbdbbdbdcbddddaccbdcabccabbadadcbadacabaccbaccccdcddcacadddbdcbcbabbbcbdaaaccdcacdabcadcaadcbbdbcbdccaccbbdbbacbcccaabbbddbbbbabcbccccdabdaaacbadbddbadbbccddcbbcdaabacabacbccbcabdcdddcdcddbdcccbcbbaccdaacbcbcaadacabdddddadbcacaccbaabaadddaaddccdaddbabdbcdcdaadbadaaacaaaabcdbcacbcbaddaabdbacadccbabbdcbcddccbaabbdddaaccaaccbabaadddbddbcccdabbcbddabdacdaadcdccabbddadddaabcabbbdbdbbbbccaabaacdccdbcbcbbcadabdcddacbbcdadccbbadabdbdabbbbcbbbcbbdabacbbdddcbadbcbbbdcdbbbbadbbabcdabdacdbcbababcacbdbcabdbddddacbbaabcabcaabaabdaccadccdbbbdbbdabdccacdbaddcbbddacbabadbbddbacadcdbcdcdcddccddabbddddcbdddadbbbcdaddabdbaaabaccbbdbdaaadacaadbbbbcccacaababbaacacbacabdacbbcaacbdbcaaddaaacadbbcddaacacadddbcaabcbbbccadbcccbcaacadddabaddcaacbbcdbdcacabdcacacdcdcaacadabbccdadababbadadacdbcadbbccdbdabcbbdbbbbbccbacadddcbcdbadbcbddccccbbadacbacddbacbccdbbbcacbddddbcccddbacdcbaabdcabddbdabadccdcaccdccaccbbddcbdddaaacabbbccbadcaacacdadabbdabcdbbabadacacbdbdcacbcbabcadcadacdacddcdabddadbdccddddcdbadbdccbbcabddccabbddbcabcbadbaaccbdcdbbdddabbbbbaddcbaabdbccbccdbbbbcccaacdbdcacbaabaaddcacdacaadbdddadddccddabcbddbcdbacacaddbddcdabaccddbacbcbacbccbcbcbbaadcbbbabbabbbdabcbbdcdbdbbdcadaacabaaadbccbcdbabadaaccdacdadcdddabbbdbdcabbacaadabcacbdcdcabbdbddadabaabbcaacbadbcaadcaabaddbbacaddaadddadddcddcbcbbddcdbacdadcccbdbabccaaadcadddabbaaaacdccccddbbabccccdababadcdcbbcadabcddccbaddbaccddccaabbcdcacddbabdbdacbbdaadddaadabcbccbccbabddcbaaacaccbdadaaaddbbcddcdcddadbbdcadabbbcacdcbddbadddbbccadabbbccbbcdddcbbacddbbccacbacbdaaccbdccbcddaaabaabddbdaaabcddcccbbacbbdbbbacbdadaacabbaccbcdabcadccccdbcabaaddbccdccbbdaadcaabccdbcabcacbdbdbbdabddccbdbddaabaabcccdcbbadbcdadddabccacdbdddcabdbaadabbcdcccdbdabcadcdbdcaacaaddbbdcdadccbcccdcadabddaccacdbabaaacabcaccdcacacdddcccdbbbcbbdbaddcbcbcdccddbdcbdabdaacdcaabccbbcdbbdaccbadcdbcacddacbccbccbddbbacddaddcbbacdcdbddbdbaccbaaacbcdddcacabdaccbcbbcacadadadadacdbaaaabdaabadabdcbbadabcccaccbbbdabdcabaadddccaadadcdcddbcadccdbccbbbdabbacdadabbaabdacdbacaaccbccaaabcddacdcaddbcaacacacddccbacbacbdbbacbaddccbdccccccdacdcbacadbcdbaddcbbacbaadbaaaabaacbbdcdddbdaaddcccaabdbdbacdbcddcacdbbbdabcddacdbddcbbbaccaabcdcabaadadddacaadbbabbdbcbabdddbbccaadcadbacbadcbcdcaacdadaadcdbbbaccddabdcaddbbbadaabcccccdacdacbbbababdccdbabbcbdcdbdbbbaddbccddbbddabcccbcdcdaddbaccacdbaacdbbdabdacddbdddcadddbaddcbcddddaabdbcddaaadbdcbdcacddbcacccbbbbcbdaddccbcbdcdadadbbdcdbdbabbaabcbabacbddbbbaccccacdbdabaaaccdbaabcdddcddbcdaccabacaacdcdaddcddabdbacaddcabccabbcbaaaaddbdbbacddaacbbccbbdacbcaccdadbaacbdcbbddabcdcdddaccddadacddadacaddccdbcddcbbcababdbdaaddddccbaaacbbaacddacbabddccabdbccabadbbbcccdcaadabbbcbaddbcbbbddbbcbcbdacccbbccabcddbdccadcdcbaddcdadadddcddddaddbbacddabacacaadabaccbccbbbdadccbcaddccabacaddbbddbddbcdcdddccbcddbccdbbdadcddabbbbdbdbcbdbbbbadddccdbbbacbcdabcaaabbbadcbcbcaacabcaaaabbddbbbbccdccbccccbccbaaaacabadaabdcdcdaddcaddbaacdccbcbdadabccadddbaadbcadacccdcaccbbcbbdbacdcaabbcbbabcbaabcacbdadddaaabbcacbbbaabcabbcabcddadccbaadbcadaacbcdaccbcbacbbabdbaddbaaddacbcdccdadbbbacbcbbcaacadcbcccbacabacbcdcdbdddabacacdddcbbdbccababcdabaccddababadabadddbcdcdddcadcbcbcbabddccdabadcdbcbaabdaadbdcaadbaddbabbdaacaaacccabcdcbcccbabcacbadcadbcdbccaaacbaaadaaddabbabdaacadcabcddaddabcaaaacacaccdddcdbdcdacbdabbbdbabcdacadccaaddaabdbdabacdcdddcdbccdbcbcabdbcbbbbccacdaacddbcbdabcaddddcdabbaadbcaabbdaaadcccdadaddcdbcdcbadcbcbdbabdcddbcabbbadcaacdcbdcbcaadbddaabbdbadaadccbbaaabdacdbacccacaabdbdccdadbacadddccdbbcccbdcaadabbdcdbaadbdbcbaaacbadcaadbdbbabcbddcababbabdcbadbdbbaaabccddacdbdbcaacbbbcbaabcdbbdaaaccdabdadbcaaddcdbcddcbbabcabadbdbadcbbabbbcccbdddaacbbcdccbcbdcdbbcaaacbdcdbabbadcdabaaaaccaabdccbcdccbccaabcdcbdabaacbaccdcbdabbacdacdccbadaccbcccbabacbbbddcccaddbdddbdabdbcbddacacccaadaadadbcbaddbabbdbbcbbaddcaaabbabacbddadbddaccdbbcbbccbbcddabbcadacbaaabbbadbdcbbccabbdbdbcadbacabdbccccdbdddcccbbcbcddcabdabbabccbcdbaabbdbbcaccbdadadadadbbaaaccbdcdbbcbbbcbababdaaabdbdcbbbdcaaababaddccdddbbabadbccdcbdaaddccdcbaaabcdbcbcaabccaabbccdcdacaaabbdcbbacbabaacdbbaddabdcdddbbdaaccbaabaabcdbdcccdadbadcabadccbddacbcccdbbcbcacbdcbccaaacaabbcdbadcddaaadbbbcacbabbccaccccdddbdbadcaaacaabddbcdabbadaccbdcdccabbaadccbaddaacdacacabdacbbcbacbcbacbdabbcbabaabbccbbbabdbacbcbdcdcabbacdcbcbabaacdbaddabcbccdbacdccdcbcbcacdbabbbbbabbcdbacbcadbdcbcbacbcddacaaddcccdcddadbcdcbadababbabaacddcbcacbbabbddaaadcddadddcdaacacbbccacdaabcaccaaddbbcdacdbccdcabbdbbdbadaacbdccdbcdcbddabdabbabcbcbddbbabaaccacdbdaacddbbcaddcbcbbcacddbbabcddaaadcaccaccaacccbcaddcdabbbadcbbdbbadbadcccababdddcacdcbadadbabbbbdcacbcaabccccbbdabbcacdcdabaaadbdbbbcaddaaaacbaaabdbbbdadaababbcacacbbcdcadbdcdaacdccdcaabbbbbcadbcacdcbbdccacdbccdbcabbbbbadbadabdccbbdaaccaccdbadacadbbbdbbdaacbbccbacadabadbbadbdcaacadbbddbbbbaaaacaadbbcbaddcaaaccacbbdcbdbcbcdbbabbacabaacdbddcbdcadcbbaacbbccbdcbcdbdbcdbbbbbabcaabbdbbabacdbcddbcaaabaaacacabbaadcbdaccdbccbadbcdaabdddabbccaccdaccbbaaaaacdaccbcbdacbbcccabbaddadbdcdacddbddddabbcccaabcaacdbabcbbddddcdcdaaadccbaadaabccbaaccbddadadabccdadcbcccddacacdcbcadaddbdbdcababcbddaaabcbdabadacbadacdcaaaccdcbdbddccdccccbabcacbabcbbadaacadacdcdddbacbddddbdbcbcaccbdaadcbcdbadcddccddbadbbddcddcdcbcdabcdaaacbccbacaadbaacbbbadacbbcccadbdbcbbadcdadbcbdcadcadccccbbcbcabcdcdbcbcbdadcacbbbacbbaadcdbaaccacabbddcabcdbdacaaadaabbbbdbbbadcaadcddcbbdcaadcdbbcacdddbdaddbabbacadccabdbdccadacdcdacccaabaacacaccbabaadbadbcbcddabddccdccabbcbbcabbcabdcbbdccaddcbaaddbbcbcadcdadbaddbdccaaabcaddabbcdccaabdbbbbdacaacbdbccdcbbccbbabcaddcccaabccdbcacdbaddcbbccaddbcaadcdccccaadccbadddcacbadcacbcdcdbbccbbbddabbdbddaddbaaabcbdcabccddaddddcbcbddccdadacabdaddbdcdadddccadadbbacddcdadaaabaabccccdbcdaadbcdacdcadbbcddddbaabcdaccccbdbbdcbcaaaddadcdabcbaaaccddbabdbcabbbabdaccbaadcadccbcbdadababadaabaabaabaddcdaababcabbdbbdabbacadadaabcddcaccacbcbcdbbdcddcbadddaacbadbccadcadddcabddaabccabdcabccddabbababbdadddabbbcbbacacccaccbaacbcacbbcdaaaaacbbaccdcbdcacaaaccddabdaaaddcbcbcccabcdbdbdbdcbdadbbcbbcbcbdbbbacbacddccdccaacbcbcccbcabcdbbaabdadcdadbbbddbcdcbddababbadbdcbaccbabdbadacaadbbbbbdcbbcbabdabddcadcddddbaadbbbbcccabcaadbaaccabcbadadcadaddcabadddbcbbacbcbcaabbdadbcbcacdbcbdddbdacddabcaccdddbaccdabccbbbcacddbcbbbacbccdcdcdabdabaccdaabdbabdcabbbddccacbcbbaaccbddacadabbcdbcbaaabdbaacdbdddacdababaabdcddabccacaddcdcdbcdaddaaaacbdbcbadaaccdbbddaaddadddcbadcbbccacdacccabcaadcabcacaaacbbacabadadddbddababdcadaaabcaadbcdcbbdbbbabcabcccabdabbdddabababcbcdbcdacccabcadcccdaadccadbcaaadadaabdcdcbcbbddabdcdcbbaadbcbdaacdadbaacabcacabcbccbbaadadacdcabcababdbbcccbdcaddacddbcddabbaccbcacbccaacccbddacdadcdadbaddcbcaaabddacbadabbbcddbccacdaabccbcdabbccccdbcdbbddaacbbdddbabaabcaadbbbcbbbabddccabbbcbabbbacddaddcdccaaccabbcdcbcccadabddcacdcdabccdcacbddacbdbbdbbdcadaaddccddadbccbdcbcbbabdadbdccdccbdbdadadcdccbcbdabaaadbcbadbaadabcdcacbcadacabbccabddcbadbcbdcaaddbcbbccdbcdcadbccdddcabacccbbcdddddabcaaabdcadbcdacdbaadacdccbadaddbccdaccbcbddadcccdcabbabdaaadaccaabadddbabdcdbdbbaddcdcadccbcadbcaabddabbcabccabbaccddadbccbbacaababacbcddaaadadcabbddbdbbdadcadacdcbbadccbccbddaadbcacabbcadccbabbcabcdbadcdcabbabbcbdbbbbabcbdbacbcadccdaabdacbcabdaabdddcaaadadabacbcbccdbdacbcccbddcaaaacaadddbbbdabdacddccddadccadadbabddbbcbacbadacbbbddbddcaaacbacccdbabacacdbcacdcbcadcdaabbdcdabcacadcaccacddaabbccadbbaacabaddddbadabcabdccaabaddaddabcdcddaaaddddbddcbcacbccddcaddcacdbbcddccccbabdddadddcbcdbcbdcacaaaacdbcdbddbcabdbdbcadaccccbabdacbcdabdbcbbbccddcdddbccacbddaaacbabbdaabadbadadabcbcaaabaaddbccaabdadbacdcadcadbbdacbbcbcbaaabccabdbdbcabbaacacdcabddcacacaccaabbabadbcbbdaabdbcbcbaddbabcbbdabbddcbbdadaacabbcabddaccaabbcdbccbdcbcbbbdcdaddcaccdbdddcabdbdbcdcdddacbbdadccdacbdaacddadadcabaababbcaccbddacbbcdacbbbcbaacababdddbdbdddbbbdbcaaacdcaaadddcbaadaaaccdbcbdcbddccacacaabdddbacdbbdcdbaaabcaabbdbcddcaabdbcaaabcbcddccacaddbaababaabbccaaadaabbabdacbcdabbdcbbdbcaacccdbacbbcbdadaacccddabadbbdabaabacbadcccbddddbcdcbabcdbcabbadabcdddcacccbbaaadaaddcaabdabdbabbdaabdbdcbcaaddbcbcadadbddccbacadaaaccdbcbdcadaaaaaacadcddbacaaccddabcaabdababbbdcdddaacbdcabdaabaabcdaaddcbbcabddbdcabdcddbacdacaadcddaaabaccabbbddbdbcbccdddddabdbdbcdbbadcacdbcacbacaddccacccbbcabbaaabbccaaddaccadabbbbbdccdccabaaddbadbdbbcadcdcdccbcdbaacdcadcaaddbdbbbacdbbabacdcbcbbacabadbdbcdabadbcbadcbbbbaabddbdaaccddcbbdddcabddaabdaccaabddbcbadbbdccdabadcaddbdadbdbbbbadabaaaabbbcbbcdcbacabbdcccccabdcdbdddccddaabcdaaddcbadbdadbbbaccabdbcdaccdaddabbaaaaddbababcabbacbbcbbbabdadccdcbcbcbdcccbbaabbdccadccbbdbcdadbbcdcbabaaccaaddcdddcdcbbacdcdbbaacabcbbcdcdacadbbcccadddcccdaacbadaccaddbabbbdabadcdabbdcabdbbcadaaaaddbdabcaabadddbcadbcbbadaadaadabacbaccbbbbddccbdbdbaaabbbabdabdacdccdcacbbdaacbbdacccdbaaabdaaadcbddcdcaacddbdaacadbabdcadaaccacddaddbbcacbcdabbbcbbddaadaddbbcabbbabccaddbbdaacdbdbaaaacdccaacacbbddcadbdcdcdddcdcdbbadddabbccddbdacdaabccdcbdbcbaadcbbabbbdabaacabdcadbbaddbaabacacccccbbcbcacbdadadddaabcdccdbdbddcbbcbaacbadcbabdaaadadaddabddcabbadababccbddcbdcaaccdddaabbcbaacaacabbadbccabbbbbbadacdddcabadabadcccbcddddddadaadcbbbbaddabadcbadbabddcdbdbbbacadcdaacbbddbadacadacaaddcdcdbadbcadbaaabacdbaaabadbbddbdbcaabbadbbbbbabbaaabddaccccdbdddccdadcdcadccbabaaabcdacdadacbaabdcdcadcdbdacadadaadbacacacdbcaabcbbdaaaababaccbcbbbaaadcabdcbadbadccadcbcbbaabbddcbbdbdbadaabaaaababdbcdabbccbdaabdabbdaddbdbcddcabbaccddcbcbdaaddcaabcaccccbbabbbbacddcddccddbabbabdcbdbcdbdbadcadbbbbabdcdacbdaabadbddcdacabdadadbddabaccbccccadbbaddbbcdcddbcabcabadaadcadddcdbccbddcabbdabdadacdadabcabaadabbaccdddbbddbbabbddcdcbcabdaabccbdabbabadacddadcbbadabdabacbcaaddcbddbbcbcdbdbcbddccbcbccdcbbcbbabccdbbbcbddccbddbbaccbddbcdadbcaabdccbaacababbbdddbcdddbabcbacbdcaacabbcababcdaccabbcacccbbcdcbbaadbaddccbbdccbbabdbaddbccacaccbaadbaddaddaabdbbcaabcbbddaadaabbbcaccddabdbaddadccadbdcdbdabcccaaaabdbbaadabdcadabcdcbdaaacccababccdbcddadbabcdbabdcbbbabbcabcbadcbcdcdbdccbcabbbdccdacdbcbdddcccacdbddacdbdcabdbdbbdcbcaaacaacdcacccbbccdbabadcddbcdccdbddbcccacbbaacbadaadaadaaaddbcdbbdaacdbcacadbdabadcddadcabacdbdcbbcbbaddcbccabaabbdddcdbbbddbcdcdabaacbdddcabdadcbbbdbbaccbbacaccbdbaaadccaadbbdcaccdbcdcdddbbaccbaccacaaddaaaacbbbbbdabdcaaaaabddcaabcdcbdbcddddbcbdcccbdbcdaabbcccdcadcbacbbabcdbddbccacaacdcbdcbcaddaabaaddacbbadbbabbacabaccbccccbabdcbbbacbdbcdddaadbccbdabbbdddddaccddccaabbbacacadbdabdccbbcbbcadacdcbddcabbabbcdcdaddcccacabcbcbddddacacdccbcababcdccddddaacabdcadbdbbdcbcaaabdbcaaaabaccabdcccacddddadbaaacaacaaacaaabaaddccddbcbbcdabccbadbccbdaccdbaacabbddbcadabcacbcaaaacbccddcbcacccacddaaddbdbabaabbadbccabacadacbcdbdddadbbaaabbbacccacdcddcabcdbaababdbaccaabdbcbdadbabbabbbcabdbbacadaddabdaccaacddaabddabbcbddddddbcaadcdcadcccddaabbaddbddcdacacaccaacaccbdbabbbcdbccabbdddccbdacbcdcdadbaadbbbbabdcbdbbcadbdcaccabacdbbcdbacdddcdbaacaddddccdcddcbddaccaababaabcbddbaaacadbdacddbcaddbbddccccabadcdcadcbabbdbadcdabaaabcbaacdcbaacbadaddaaadbdbbdcbcbbbcbbccccacdcbdcbdaadcdbdbabacadccbbdccbdcadcdbcdbacacdbbbabadbbdadacddbbcacbacccdcdbcdaacdccdaccbcaaadccacdabbbbdcacabcddcccccaaadcbcbcacadccbcaccaadbacadabcdbcdcbdcbabcbdbaacaadadcacbbbadaccadadadcabadccaabccdddcdbabcaccbabdaacddcccaadabaaadbadabdcbdcdaccdcbabdacdcbabcadabbbacdddcdadcabcbdcdcdbdbdbbbbbdbadbbcddcaaabadcdbaabcdabdbadbacabbbcddbdcbdcbcbbadddadccaacbdcbcabdaaabadadcdbdccacdcdbbdddbbcddbabdbacdadbdabbbbadcddaadadbccabbbbcddbdbaaaddabadabcadadbdcacbaaacbccccaddbcdbbdcadbccddaacaabaccaacdaccdaaadcbbbdbcdbbdbacbacdcaaaabbaadbadddbbadbdaaaabaabccddbddbcaabacddaaadccbaadabdadacacddacddbabadacdcabdcdabdbbdcbdcadcbadcddabccacaddcacbacddadccbbbcddadbadcbcabccbabbcbdcddddbabadddbbbacbbacbcadaddcabddcddbbbbaccdddaaadbabbacccaddbacbaddcccbabacdbbaacccddadbbcacbaddbababcdacaacddbdabdccbbdddaddaacddabbaccbaadacbccbcdbbdbbdaddccbcdbcacccbbdadcbaadaadccdabaddddcdcddbacaddcaacccbadadbbcccccccbbcbdddaadddddcdabbbdabbcabdcbdcbcbccccaccbbacaacdddabccaaabcbbcccdcdbccdcbdcadabddaabdbbdcadababdacdaacacdcdbcabcddcabbdacbacbdddddcbdaaadcbabbbcdbcbaabdbadbacdcacddddacccbaabdacbccdccaacdcbdacdbdbdccdabbcaaacdaacabdadacadbcdadbdcddbacbaaababcbdddabccccacbaccaaccdccadcdcddadabcdddddbdaacadbdabacbcaadcbbccacaaacadcdcdddbaadbbcabaaddcbcbcddcbbbacacdddcbbaaabbdbadcaaddbabadcdbaccabcddacbacacdbabcabcbabccacccadabbcdaddbccdbbcdcdcdddabddbabbacaabbadbbdcadbdbdbbdbdbaabdcddbbddbcdbbaaacddbacccabccaccbdcadcbadcbccdddccbccabbbbdbbacdaadcdcbbcdabdcddbddbbacacddccbddbdbddcccdbcbbbbccacaddbdadcbbdcbddcadbcbdcdcaabcadccdbccacdbaddbcabdbcabacdcacdbaabadbadbaaaacacbcbaabaaaadcbccdddcbbaabddbaabbbccadccdabcbadcdcbbcacaacbaaddacbddbbcccbabdaaddccdbcababdcdcdcacdcabadbcbaaacdbaabcabdbbaadcbcaddaadadacaaabcbddabbdbbcaabadcabccabcaaadddbcadabcaabcdcadaaaccbbdabcaaadadbbbdcdcadbccdacddbdacdbabcbdbccbdaddbdcbddcadabddcacabbacbccdcdccbbbbcaabdbaabdcaacdcccbadbbcdcadbbcacaadbbcbdcbdaaddabbadcddaaadddadadbddddccdaddbbbcdcdaacabbadbdddaccadcbcadacbcadcbbbbcbbcabbdcacbddbcbabddabcacccaadccacbdaadbaddcdabcbdddabdacacbcabdabcbbbacdadbccddbdddabddbcaaadabdadcaddddbbcbacbdbcdcbcdabbbbbadcaccdabacdadbcbaccbcbcddcddababbbcdadadccadbcdacaddccbbabacacbcdcccdbdcddccdadcbbdcddcaacdcdcdbaabacdbccbadcccadbaddbcbcbddcdadcabadbdcaccdcddbabddccadacccadcabaacbddbbbdaadddaddaadaaccadbdcdbdadbdddaaabdbbbadccbacdbaccdaabdcabdbbbbaccbdbdbcaaddbbbbbcadbadcdccbaadcbcbbbccdbdacabbdacdcdbdbcbadabccdcddbccdabcacaabcdbdbcbbdabdbdcddbabcbdcdabaabdbaaadddbbaadcaadcdadbbbcaadadbadaabcdaaabadbadddbccbcacdbccabacadccbadbcbddbaccddccabdbccbbdcbdcadcbcdcbdaddabbbbbaabdbadbcbcbdacbadcabdcdaccbbdbdabdbabaaaabcabbadbbddadaaaadabcaacdbccbdadaccbccabbbaaaabbaddaaccbbdaabaaddbabdaaddbcaaccbdacdbdcababccbabdabdccdcdabddbacabddcdcbcdbdbcbdccaccabddbabbacaacdcbdddcdadaaadcabdabdbdddbaaddbbcdaacabbbcbcacbbdbcadacaddbcbdaddddacbaacdbaabdddaddcddcbcdbcdbdbdabdccbccdbbdddcaadbbccadbbdbabadadabacadbbbaaabcacdabddabdbcdccdabaabacccaddabcbdaaccacbcdbddabadbcccbaccadadcdaaabcbbabbdaacdcbbdaccabaadadabbacdacdcdcbaadcdcabddcddacdaadaabacacbbbacacbadbcdcbddcbcadbccacadbccddcccddcddccdbaabbaacdacadbbdcbbbdcdcbdacaababadcdbdadacddbbcdabbbbcabcbdbadbabdbaabcbcbbadacaaaccaacbdaabaccadcdccadbbaabdcbcdddcbdaaaaddaacdaacacacacabcdabbcbbabaaabcbdcbcdbddadbdabcbadbcbbccaaddbbccdaabcdcabaababcabaabdcabcadbbabbbcdcaddbabcddbbabdcdaaadcaaababcbbadbabacadbabaddddaacddcacdddbdbaacdbcaacabbdccbbacaaddabbcdbccaaabaddbddcabbcccdbcadaacadaadbdcbdbbdadaadabbaaaadabddccbadbdcacdacdbcdadbacacaaccdbadacccdcdacadcadccdbaaadabcccadcbcdbcababccaababdbadccdcccccbdbabbaadacbbabaddabdabaabcdddbbacadacdbcbadcdacdbcbcddddbccbcaadbbcbbcaababcbdcaddcaaddbabdcdccbdcdddcdbdcabbaaadadcdbaabdbbaababbacbdbbdaabdccdbababbbcdbbbacaaaacaddacbcbbcdbbdbaccbddaadcbdacccabbdbabbbbbbbdadbbccabadbaabcadadbcccccadaabdcccbbbbcadabaaacbabdcaadbaaacaabbdbaacbbccdbbbdcdddbababaaddbbacbcbdcbaccbbbcaabccbcabcaccdbacdcbaadacdbbdcbabdcddcdccccbddccccbbdcdcbbabbdabbacbcdbcabcbdccaaddddbdbadbcadacdaadcbdcacbbdaacabcabddacabaaddabcbccbdbcaddbcbaccbadddadababacbccdddcadbabbdcdbadbadcdacdacaadababbbabcccbddabdcbcdcccdccddbdcaaaddbbbadacadcaccccdcadcbaaccacccbbacdbcccbaaabbbbabbcccbdbcdaccacaacbabcccadcbcdddccaddcdcdabdddcdcacddabadbcaaabccdacacdabbccdcbacbadccbdcadcbcbcaccddabccccbadbbbcccbacbabbacdbccbcccccadbcbcddcddbcbccadbacddadacccadadabaaaccddaabdbdcccbdbbdacadccaaaaabbdcaaabdaadbccadcbadbddcbaddcbabdadaccdccdccdcaadcbddaabddbcbaccbcbbacdcaaddcbddbacaabacaddbdacbaadaacddcddcbbdcbbcbbbaadbaaabaddddccadbbddcbaccabccccaccddabadacbbcaadbabdababdadacaabababcdbdbdbcaddbccbcabdacbccacdddbacbabcbdcbcbbbcddbbdadbdbccdbdddcdccbabbbbacbcbbaabacacbbdaaabccdcccbcbdbbcaaacbdadcacccdadbabacbbbdcccacbcccabcdbdcdbdddddcdaccdcbdccadaccbadcaaadbcbdadbaaadadaaaaabbaaddbcabdddabcaaabcddddbcddcdcbacbadaadaddacaaaadadcdcabddddacdaabdabbbacbaabadbdacdcbacaacaaadbbcdadddbccbbdbdaaddccaabdadccccadbabbaabacbdcddabddaccbbacbdccacdcbaabacdccdddacaabbcadbdbbcbabdcaaabdbcadadbaaddcbddaabbcbacbcbcbbdcabbcbbdcdccbcaaccabdcdccbcccbaaadbdbacbaaccdabbcbbaabaccadcaadacccaaacbdcdabddbccccadcbcabaabbacbbccbacdbbdcbccadcabcccbaadabdacccddccccdcabcbbbaaaddcddbdaabaaacadcabdbadacbadadadccacacdabdcadbdaabcabdaddaaccbbabaacbddbbaddacdbcdcdcaaccdbdacbccddddbbbadadbbccddaaccbadddbbcbcdacacadcbdaccabaacaabddccdbcdbbdadcddacbcbdaddadcaadacadbdcdcbbdcabcbccbaccbbdccdcdaadaddaccbcdcbaabbabbccaadabbddaddccbccdbdadcadaacacdcdbdbcdbddccddbbbaccabbaabdddbdbaccdbbaabacccddadbbcddcadcdbdabcadadcdccddabbddcbaaacdddacaccacbabaaccababaacddabcadcbadcbbdcadbddccbccdcacadbcdcddacabaacbdbdbbbacacaddcacccdcbbdbcbaacdbccacbadcbbabbadcacbcdababdcabacbaccaccadbbaaaadddddcacdbcdacccadaaabaaabbbcbadcbcdcddbbacdbddacadaccaccbddddcccdbdaaaddcdacadbbbdcdbdcbbbabaacdcddbabadadcabbdcacabdaabcdbddbbabbdbadccabbdcbbabddcabbbadbdcddcababaadddabcbbbddaacbdaacaadddddacdbcbbcdacaddabadacadbdbccdcacadbbddcaddcccdcacbdbbdababcddbcddadabaddaaababbbbbcabdcbabdaaadddcdddbbabdbacdaacacaccaaadbaabdacdadbdccccccabaddbbddabccbbddcdcddddcbcdbbcccbbdcdcbbccdaccbcdbbbabbbddcbbaacbbdadadccbabaaaadccaaabadccacccbddcdbdccbbdbccaddadbddaaaddcaccddaddbcddaccbcdaddbbadcadddcaaabaacbccdadcbbdacdacbcaadbbbdccccbaadabbddadbcacbcaddcbbcacadbcbcbddcbdbbccdadcddbbaccccbdbcccddbbbbaababcdddaadbcccddaabcabadbbbaccabcbaadbaddaacadabcbaacbdbbbdbbcabbdcbccbabccdbaaabcabdcdcccbadbdacbdabdbcbbacbdaccbdbacaabbabbcddabadbbcbcdbcdaaccabbbdaadcddabcdbbddcdcbbabbbccadabdbbbcbdcdcbbbcdcbadabcaddcbbdacbcbbbdddccbbdabbaadbabbbddccbddcbacdacbcbadbbcacdbcaaacabacabcbbbbbcbbdbaaabaccbbaabcdabcddbbabcddbdbbadbcdbaaaccdbcabdbabbdadaacdbaacaddcbdbdcdccacddabcccbdabacaabdcbdcdabaaabbcdaadbcbdccdaadbdabdbabbdcdaaaaabdcadbccbcbaadbdbdadaadbbdababacdaaddbcaddabacbddddbacdbaddcaabddabacbaaddbbcaadacaadbbacbacdbbacaababbaaaccadbdddcabcabbcbaaaaddabaabcbccdccdcccdcacacbbccbbbadcabadcabdabcbdddcdaadbdacddaadabcbcdbcaacaaaadadcccbbabacdaaccdaacadaadadcbcbdbacddbaccbababddbdcacdbabddbdcbbdccdbcabbcabcdadabddbdddcdbcaacacadbdacccdcdabaaaadbabdabadaccdbadabbccbbacaadaddacdcddbadadbadcdaccbaadcbabaadbdadbaadbdddbdacddcdcbaabcbbdcbabcbaadcdcbdbdacbbcdbbaddbccddccbadbaadcbdccbccbcccbadcccdadbcaacbdcddabdbdbddaacacddcdddaddaaaddbbabaacbbdcdbdadcdacabadaccabbdcddaccdbdbaaaddabccadcbaacbdccaccabcacabbcadaadabaacddddbaabdaddbccdccaaaccabccbbbcabccdcdbadbbdbddadbdbcbbdcaababccadcbcdabdcdccdadbaccdabcddbcdcbbaddbccacbbccdaadbbcdddbacbdaacccdaababdbabbbdbddaacadbacacaacadabacbdbdcdcbbcdbddcdaabdccbbcbbacbdaabcababcccdaababcddcbaaccdbdabbcdabcddddabaccbcdacdacacbbcdbbcbabbccddbaddbcaddccdbdabcbcddcacbbcabdaaddbbcbcaddddbcbcaadbcadbddadcdbdccbcadbaacbdbdabacbcdaaaaabdbbabadacbccccddaabdddabbdccabdabccabaddaacbdbdccacdbdbcacbcbccccccdbbdabcabcdacaacadcbacaadcbbddabbdaabaadbcabdbcdacbcbdcbaaacbadbbcbdbcddaaacddbcdddbdacbbdadcdacadddbdccabcbcbdccaaaddabdbdcaabbbddbabccccaddadcadbcbdabccbdbcbabcaacbaddabbdadabdcacbabccdaacdcaaadaccdabcadaacbdbcbcaccacbdabccdadaabbdccacbdbddcdcddaaddcbcdcdcddbdacaddddbdcabcadddbbccaddbabcddbbcdabcdadcbdbccbcdaadaadaddcadcacbcacbccaccddacddcbcdccddcdcccbcdcccaaabdaccccddbcbcbccdadccaadacbcdabbddabbdbddbcbaadabacbaabacaadcbccdddcbbacdddcccbbaddccacdcaaaacbdcadbddadcddcccddcadaccabcdcddbadddddacaaaccdccdcbdbdbdbadadcdcbbbadabdcdaaabccbbcaccadddcbdabdabbcacaabddadaccdccdacbcababcccacbcdacadacabdadcaadccbdbbcbacdcdbdbdbdbcaccbdbccacaaddddcddbacddcbdbbacbcbcccdcddccccacdccadcbacaadcadbbcccbddbacaacdbccbdcdacabaadcbddbcacccbdaccdacbccdbdadacaaadcbdabcbadacdbbdcbbcccadbddbdcabbaccbacddcacacabcdbadddbdaaccabcbcacbdaadbdcaacddaaacaccabcabacaadaabbbcbcdddccabdbabdaddccbabbdacbddbccbdacaaacccababaabcabbcdbdcbbbbdbadbcdccacbacdaadbadbbbcbbadababbabbbcdccdcbdacdabddaadaaadacadcbbacacbbcbaddcbdddbabcbbdddabacdaadacabdcbcaadabacdaddbdacddbbadbaadcbadabacccdbbddaacdbdcbcbaddbaddccbdbabbababcabacbccbbabbbbdadddbcdbacccaccccccbaadaccacabcacabdcbbaccccbccdabadbccaccdaaccbdccabdcdbcbaccadcbddaddbccdddadcddbabcbdcddbdcddaccbbdddddbdbcdccbcabddbcdacbdbbcbcabdbcadaabbbcdcbcbbacbcacccdbabdbaddbaddcdcbbdadcaaadddcbabdbbdccbcdbbbabadaccbdcbdbbacaacacddbcdcbacbabbdbccabbbdbdbbdacbbbbadbdadaddddaccacddaddabadddadcabaacbcbbdcdaadcdcdccdaddcdbcccdbdcacabaabdcbdacaadbaccbdcdbbabbcdcdcabacaaabaddabcdcbaabacbdbcaabbccadccacccdcadcbcbadcbaaddbbdaacdbdabdadccdbcdddbccdbdddccdbcbbaabcccbbdbacadadcdcabcdaaaaaabbdcabdddcbcbdadbbcbddaacddaacbdacaddabddcbabcdadcbabbcddcbccaccccccddbabadcacacbddadbaadcbcddcabbdccddddbcabbacadbbbacddadcbbbbdabbdbabdcbadabaabcbabaacabbdaddbcbadbacadcaabbdabbadadbddcbccabdbdbcbbcdbdbcbcbcccaadcacdaabddbdbbbdccbdacaaddaabaddccbddacbacdcdbabdaadadbbbcbcbbddcacbbbccdaaaabcacccdcbbaacdcbdbaccacbcaaaccadaaccaaabbbccdcdbdccdaabcbcbdcdabdabaabcbcdbdcaaacacdbdbbcaadadabbbcabbbaadbaaaabacdcbadddcbaacdadbdbdadaddbaccdbdbbbdcbcdadacdabcbcbbcdadabaadccccdbbcdbccbcabacdbabccccacbcacacbaaadadbbacaaacaddbcdccabbbccccbaaddabbbcbbcdbdbcacdcaddbdaddcabaabbbbcabaccaabdccaadcbcabcdbbaabdbcdabadabcdbbbcdabcadddcbabadbcbdcddcdccbdbdbbcadcdccaaadbcdaddcbaabaaccbbbddaadccaacbbabbdadaadbbcbbbdcdcaacccdcddaaaacbddabdbbaccabacccabccababdcbcdccdaddccbdbcbbabdccabdaaccddcabbdccbdabdaaaaaddbbbabdbcabcbadbcbdbacccbdcccacabbdcacbdbdccdacaddbddccdcbbcbaabbcbabacdcbbaddaddbaadcbaadadbdbdacdbadcaabbdbbdbabbddacdccbaccbdadcbaabbcaaddccaddbadaccdcbddabdbdddacadcadcddabaddbadbaadcabbbdbddcddcddbabaaaccbdbbaacdaaabbbabbdbdbddaccbdddadbcdcaccbcbadcbdabaabbcbcbabdabdaacbaacddddbbbcbacdadbbcdddaaadcbddcddbbdbacdabbdbabbbbbccbaaadbddcccabdaabdbbcadabdadaacabbbbdbcadcadbcacdadddacdddbcacbdddbbacabbdacabcbcbabadddabcdbbadaacabddbbbaabacadbccaddbbcabdcdadaddbdbdbdbdbcaddaacddacaadaadbbbacccbcccacbadbccccdaadbdcdcddbddcdbabdacbcdcbccaddcddbccdcddbadaaaadbadccbabcaabbcbbdccbddababadcbabdcccdbbbabcccacddddcbacddbbbdcdcadaabadbddbdcacbccabdccdcbaacaaccacddcbbcaccaadaabcddbdcacdabdcddaaabaaadddbdacbcdcacabadbbccdbdcdcccacaaacbcdaacbbccadccdadbdacaadcabacbaabbbadbdbdbcabcccaaddaadaaadcddbacbccdaadbbbbaacbdcdddcdccacddbdadbdbdbdccbaadacdbcadbabbbdcadbdcaadaccccbaabdcbbccddacdcdddaacabcadcadcacdaabccbbbdccbadcdabaccadcbccbddbddcdcaadaacabaabddaabcdcbdcccbcdbddaacaacdbabdacccbbabadabdbcbcdbdccaaadbcdcccabadbbbcbdcdacacacddcaaaccbaabcbbcdbbccccaabdaadcababcbcdaccdbccdabcadcbdbcccaacbbdadcbbbadbccacadcdaadabdacaccbaccddbadadaaabcaadbbdabddbcdaaabcbcdcbdaddccabacbdcbcdbdcddabdcdcdabdcddccaddbbddcaddcbabdccaccdcdaccaddaccdaacacdacabdbbbdcbcadbbaacbababacccbdcbccaaddaaabaccbddbdcabdabaacbabadacbbaacbbdcdddccbbdcaccaaacdabccabbbdcacaacaabdbbddbcbacabacbabcaacdbacabbbcadacbccaaadbccddaabaaccbbcaaaadabbccadaccccdadccdbbbccacccadccddaaabacadbaddcacacaccadcbdccbdbdbbbcdbccbdacabbccdbccdabbccdbdbcabdcbbabdcddadcccaadadcabacacdacdaabbadbdbdbcaaccbcbcacdcbbbaacadcaabbabcddacdbddbdcddbcadaaccccddaaacadbacacdddbabbcbddbbaadcbcaaaaccccddabbdcadadabccbbcadbdbaccdabcabbdbcdadabadddbaacbcbcacacccddaabcacaaddacbccbabdbbcdaaaaadcbccacbdcaaabaadcbcacdccbbacabaacdcacdbbbcacdaaddaccdabbbbbcddaccaadbacbbbdcdacaadcdaabadabdccddacdcbadabdadaddbdcbadbabcacaddbbacadabcdcdbbcaabccdccabcbdacaccbabdcaccdbabaaacacbcbaadddccbdadaddddacbddddcbabdcacbbabcdacddbbbcccaddaaccddcdbddadabacdcacbdabcabdbbcddcabbacbbdcdcbcbcbaddabbcbcbadaabcaadacbabcbaaaaacadcacbcbddcadabcabdbabdccddaaacbdccdccbcabdcaaccbccbdbcddaacdbadcbbbacdbbdbacbacbbdddcdcbbababcaccdcaddccbdcbbcabbaacbbaaccdcdcaacbaccccbccaaaacadcaacddaabbcdcadbbababcabdbaabbbdbcbaadddcddbccaaabccdbcddadaabacddacbbddbacbacbdabbcccabcabdbaddbbaaaddccbbabbdcccacabbabdcbbcbbdbacaadbcaadbdbccbabdadabddadbbddadcdaddacbcbcadcddcadcdcabcbabccdcbbcdbcdbdbcacbcadcdccabadbbbdbdccdcaabbbacabadcbcaddaaadbcdaacabbdbdbdcbdcbabcdbcadcccddbcadcadbcaacaddddbaadbbcbbcdaddcbdadbbccdcbbaddddbabaaacdbddadbcdabacbaddbbdbccadaabbdadcbbadcbbbdadddcacbbcdcbcdabadacbdbbccdbabddcadcdabdcdccaccacccbdabbdcadadacbdbccbabbbbabdadcabcbdccbdaccdacdddcaacdbccdcadabdbcacaccdccabcbcbdcbbbcbbabdcbbcdadbadbbddcabccbcbaacccdacddcbabdbbdabaacabbaaaabdaabbdcacadbdbbbdccbacbabacababcbadbacccdbaadbcbbccbbdbaddacccadcbcdcbcaabbbbcdaddbbccbbddccdabaddbadddccddbadbcccdaaacaddbaacddccdcbccbddccbdbbcdddcdadbdcacabdaaaaacabdbdacadacdaaacdcbdacdcabcdadacdbbcdcacdbbbaacdadbcdbcbbbdcdbbdadbadcbdaaacabbcddadbbcbddaddbcadbcaaadcbbcdbbbcdaabbbaaacbbcabcaccadcddbbdbdadcbcccdddcabccdcccadddcadbbbcbaadccdbdbcbcbaddaaadadbabcadbaaaadccaddcaabaacaabcacccdcdbbbacbaaccaacacadbdacdccdaabdabccabdbaadadabbbadbabccbcbdbdabbadcacccccbccbcdaadcadcaadadbbadbcdcaadbbabcbcabcbbcadacbaacddcaabaacbdabdaddcdbbbdcaadabbcdacbcbbadcbabbddabbbabdadbbabdbadbabdddcbbcacddbbcaababddcadabdabdbcdbbabdddbacdaccbcdabcddccbbcccdaacdaabcbbdabacabbcabdaaadbcadcbdbadccbcdbadccacaaaddccbbadacddcabbdacabbcccdbabaccbbacccaddbcbbaacdddcbccdbcadbcabdbcbcdacaabcbcabdcacddcbdcddaaddacacdcbabdbaabbcadaaccabdddaccccbbbdbcddccddbcbddabaccbcbdccbdbaabbdabddbbaaccacaccbccdaabccaaadabbbdacbdcdaadababdbbbacdacabdbacbbbaabdaabacdbddcccacadaddabdcdbbbadbddcbddbcddbcbabdcdcdbabbbcbcccabcdccdcabcbddaacdaaaccdddbbaddacbadccadcaccacbcddadaadddcbccaaddddaacbadccaccdcdbbabadcccccbabbabcabbccbdabaacadabbdbddacadadadccaddcbaccabacdbcacccccabcddaaabadbddcddcaccbaabbacdbbcbdddbddcbcacadbcabdbbbcdababdbacadbcabbadddacbbbbcccabdcddcaaccbadbbdddccbddcdbdadddbbdaadaabbbaacadcabaabdcaadddbdddddaaacdaaaddbcbcabccacaadbadaadaadaccaadcbbcdcbbdcddaaddaaabdbacdddadbdccdbccbbadaababdbddccaabaadaabcccbadbaccaadcaadadcbaacbbabcdbbcaabbdcdbcbdbbccdbcdddacbaaccccbdcacdbbcdacccadddaaacdcbdcdbcbdcbbdbacacdbddddcbaccdbcaababbabbcacbadaabdcccbbdcaabbbcacdcccaccbadbdbcdddabccdcaabacaccaacbdcccbbdbdacbdadbbccacadcdcdacbadbadcbccddbdaddadcaabdacbcadaabdabcaabadabcbdcdcdccabcdccacbbbcaaabaddcadbdaddcadbcaddccbccacaacacbccdbcccdabbbaacaaacbbbdbcaaadcbdacaddcadcabcaddddcbbabdbbcadaccacbaacdcdbddcddcccbaddbacbddcaadabaacacacddcabbdadcaccaccbaadcadbcaccbbbaacddddcdaaaaacdaacaccdbdcdcaadcbbbadccddcbadccacddbaaabcbbaddbdadacaddbaacbbbddbccabaccdbbbababaacaaaccdbaacdccdabdbccddccadcacacdddacdcbbccaadddabbacdcddbcdbbadababaccccbdbdaadadbddcabbcccccccadbccbbbcbddbcddccdccccdccbadbabbacaddcabdcbdccabdaaaacbdcbcbaaddccdaaadadcbbbabddadcdbaabbdcdccadcbaddbababcabadcdcbacdcbaabacbbabddadbadbdcccccccacaaccbcaadadaadbababbbdbbabdbdcdbabaabdcacbabacabadadbacadccbcdadcaacacdcaccbaadacadddbcbdcadcbbdacbcbdcbbbdacadbadbbaadccadabacdbdaadcbacdaddbaacabcbdbbdccbabbcbabadbbdccbbbabbcaabcbcbdcababbadadbdaabdbbdcdbdbbbcdddbddbdbbcbcdcaadaaccdccabdbbcccdcababdcacbdccbdcccdbbbccdaadbacdbbddaacdabbbcbadbbadbcdcadbdbaddabaaddddabaccddcbccdddcccdddbcdacabcadadcacbcadcbbbcdcaaadcddcacbcbbbcddbcbbacbabcdddcdbdbcddddadacdccacaaacbaabcababcadddbbddddddaaddcdaaddddbacbbddaaacbcbcddddcdbadcdcbbbdcabbccdaadacaadbcadcadbddcddbdbdacdaddbdacbaccadcbadcccbabcbccadacbbadbdddbbbdbbadbabbcacbcccddbabbcdbabbaabdadccabddadcdacdabcacbdcacccdcdaddcdbdadbabcbabaccabcbbbcbcbdbdcaddbaacdbddabdadbdbbcacdcdaadbbccbbccdaacbbbcacaccdacdbcacddcbddababccdcbadccccbacabdccacddccaaddcaacccbdddcdcabcbcbbdcdbdadbbdccaaccdabaddbcadbbdcbbbaababacadbddaaacbaaabbbccadbbadadddcabddbadbccbdabcdbdcaaddaadbaacdcdacbcabdadaccdbcdbbccbddcbabadacdccbbcdaccbccbdcbbabdaacaadabaaadabccbdaadbdcaadbccabcaaaccbadadcbadabcdccacbcccbbbcdbbaadcddabbadcabdddcbabbcdccadabacaacbacdbccccddbcacabbcadddadddbccabacdcccaddabdaacaccabcbdcbacdadadbaacaabcbdbbddbdcdddacbdddcddabdbbbccaadcdccbcbbbaaaddbccdddadbbcdacaddbdddaacdaccbaabbbdbbdaccbbcbabddcaabcdabacacdbaacadbdacdaddbbaababaccabbbdccbbdcdcaabdddadbccccadcbaccabbdcacabaccdcddacddabbdcdddcbacaddcaacbacadbbdbadbbcbacdbacbcbdddbdddcbdbaddbabadddccdadddddcbdadadabbaabccbccbbadadddcbcacbaaaddbbccbbdcbcdcabcbabbacdbdcabbbacbdbcabbaabcadadbddacbbaadbcbdcdaccabadcacdbbdcaddabccdcddcabaaacdbcaccaabbccbbabdcbcdbacddcbdaadbcaaccaadacbdbccbcdadccdcdaccbbabadcddbbbbcddabdadacccdacdbccacdbddcacabaabdbcadddbdccdbbdbdbaaacccabdcdcaccbaccbbbbacbdbdddbacddccdbdbbddcdadbbdbbbbaaaabbbadcabcbacbadaccaacdcccbbdbccbbabacadabdbacdcabbccabddbadddadbddcaddbcaabcacdcbabdcabdcadaddbcabcdbbbbaaadcddcdbbdacbcacdbcddbcddcdacdcaadddaddcaaaaadabccdadbdbacddbccadbcacabcacdadabdcbadcbaaaaddacddcbdcddbadbcdaacbaaaacadbbcdcaadaacbbccadccbacbaadccbcddadababdbcdcccbadabaccbdcddadddbcddadcddcbcacbbcadabdcdcadcaccaacddcccdcaacdabbbddabccaabdddbdbbabbddbdbbaacddacbbadabdbcbdbababadacddabddacadcacbbcbbdaddbdcadadaddaccbdcbaabbdddcadadbcdbbbdbbacbbbcdaabacabbdbcddcbbdddbaaccabbcabcbbccacbabcbbabcabacabcdbabdadbbbadadccbaaaaabbacdbdababddbbbaccbcdccabccccddbaaddcaaacbddcbdcbbddabbbadaadacaadcdbdadddbacddacbbdbbbccdccabbddcdcabccbaabccbdbacddbbdcbdbcabdbcabaaccdababbdcccbcdbbbaddadcacccadadaddbddddcbdadacbbcabbadddbddcbccddbccabacacadabadabbbbdcbacddabcaccdababcccacadaacbaddcdbbccbbcabdacccaacbdbdcbdadcbcdbbcccacdbdcdacbddacaddacddbbbacacadbccbdadccacddbcacbcabbaabcdbbadaadabcdcbdbcbadddaabdcbbbdaabddbdcdbdaabbccaccddaabaabcbcdbbcabdbdbddccddcbbabbddcbcadaaddbdaccacbddccabbddddacdcabbcbbcdabcabbaaabaabbabaaccdcdbcdcdccbccdddccbdcbbaaacbcbcdcddbbdddaaddacbdabdacbacbcddccbdbabcbcddcdbabdacbcacbcabdbbcdaaddcbcbdaadcbbddbabdccabdccbccaaaddcbdbbcbccdaddccdbdcbbcbaaddacacaccdbbdadbdcababcccacaaadbacbbddbbbdabdddaddadddcaabcdccbaddddbbcdcdabdaabcaaaadbcacaadddaddcadcbccdaadaaadcbcdabcdaabbccdabadccbcdbbbabaabdacbcddbddcbddcdabdaaccddcabccdbbaacaacdbdadddadddcdcabdcdaaaabbcacbdadacddcbddddbccddbddaddddbddcbabbdddaccbdaddcddcbdaaacadcaacdddadddbbbdccdcadcbdccdbcdcddaaccccbabbbbaaccbcccaacbcbbbadcbabccaabaabbbdbbcbabadcdcccaaddabcbdabbcdcbbddcccaadcbbadcbcddddadbcddacadbabaaadabccdaaaaddccbdddbbbcbbbbbcdcccdbddbbbcdcbbcdacaccaaacbcddccddcddddaadabadadbbddccaadbadddccacbcbadadadabadcbacbacabacccaaabdabdcddbdcccdccbdbdaaaabcdcbdbbacaddabbcdccddabdcaaddccdabcdaddbbbaabdddbbcdcbddacdbbdbacddcbbabbcdadadbcabaccabcacbccbbaccdbccdbacacbdddaacbdbadacccaadcbdbbadacddbbadbbcdbbdcbbccaacacaacabdddcdbdcbbdcbdcddaacbddccdadabcacaabbbbabadbacccbcaddcdcdcdcacbbaaaccdaddbcbaddaddbaaabdcbcaaaadcdabdbbaccccbbccacbbbdbdaccbbcdcbcdbdcdcdadcadbcbabdabcbcccbbcdddccddcbbdbbdcbddaadcaaaddbaabdcbbbcabdbdcdddaddaabdbcdbadcaccaababddaddbddbdbaabacbbdcaaadcdaabbdacdddabaddddcacdabdcadcaabcabcddbbacccdcdbccdcbcbddacbddbbcdcdacdccbcccbddcdcccacccccddcbdcbcbbcadccdcdcbabbbabdcddbbabdcacdacccccdbabccbbadabaaddaaabdcbbbdddbddabdabaddcbabccdcabdddcbbabcdcaaabbabadccccdaccadcdbabbabcaabbdcbbdcabccbdddaacdcaacbcaacbabdacdbcbdbadadaabadbdcadcabcadcddddaaacdcbbaaaabadcaccadbdbabbcabdbddcadbbdbdcbdacbbcbcddddccdaddddaadcaacaacbbccccaccbbbabbcacbbbdbbabcbdcadbbbdbbcbdcbdcdbdcbbbacbbdbdcabcabccdcdbccbcacaddcdbcaacbcddbadcacbddbabbbcbdbacddacdaabacabbdbadcabccdbcbcbdacbcbdbacdcbadcadbcaaccacdcdabddcbacbdadbadbaddaabdabdccdccaaacdadddadbbdbddcbcddccbbbaccaaddcabbdcbcbdddbaccbcccababddacbbaaaabdbcbaacbaddbabccccadbdcdccaddacbdabdaacdbacbabcadbacacaaacdcabdbabbdaaaddbabddaabaddbaacbacbcdaadcdbaccddadaaaaccbadcaabcdacadbcaaabdccdcdcbcbccddcccadcdcbcabcdaddaabbcbcbacabcacbdddbccbdcdacddcdcddcbcdcbbaacbcdbbbbabddadccddcdaaaadddddccbbdddcabbbadccacbaabcbdbcbdbabccbbbadbdddbbbcccdacabdabbdcdcddbcdacabbacbdbacadcdaaccabacccccccdbacddbdcbbbccbcabdcdbdcacadbcbadbdddccccadccdccdaabbaacbccbccabbbcdaabacbaacbddcbbbddddcddccbbcaacccaaaacacadbdaacbcadaabddbcadccabcbdbcadbaabcdbdddbddadddabcadccbbaccbdaadccaabcabdddadcdcbdbcdcccdddcaccacbcbbcbaaaaacdaddaadcbaaddcacdccbabbcdcdcbdadbdbccaaacdacbadcbabaacbbcaaddbabacddcaaaabdddadcaddcdaabdaddcddbabccaddbabcbcbabbccbcbacadccdbadbcbbcbbcccbadbcdccabccaddbbadcbddbabdbcbabccbabaccaabbcbddbbbbbacbbacbcabddbacdcdcdaaaacadbcdbcbaabaaddcbddcadbbcdbbcddbcabcdcbbabaabdacccabddcdbabaaaabcaaccddcabbadcaaddcadccacaaccabdbbcdbbbdadcaabbaaabdcbadddababacbcdadadcadbacbacdaabbcbdcaaadddcccabbabcdbbcabddbccdadbcabaccdccbcddabcbabcdacbdabaddaababcadbdaabbababacccbbcaacabcdaaacabddbbcbbbbcdbdbcabbdacdcbddbacdccddccdaabdbacdcbaaccaadcaccbcdabcddaabadbcbbcadabcccababdbaddbddcdadbbddaaacabadbbcdcbcbbabdaaadbbaccdbdaacdaaabbdacccacbbbcabbbadcdbacaaacdcccbbcbacaabddaddbabbadcddbabcccadabcaabcbcdcdaaaaabccdccccabcbadaaccbdbbcacbbaaddbaddabbabaaacbdbbbdbcbacdcddccddcbcbbdcabbbcaabdaaadabdaaddaddcbcdabaddcaaddbdacaacbccababababddcacccbaadcdcbdbdbbccbcabdddccbddddbdcdadbcddacbacdcabccbcdddccacababddabbdcbddcabdbadadbcbacbdacbbbccddccdccadadacbcdddcdcbdcbaaadadabdbcadcddcaccdcaacabbdacbcbadcbadddababdbcdacbcbcaadbddcadbddaaabdbdccdbddcdaaaaaddbbaacdbbcdabacbcbcacbbcddcdccbcccacbcbbcacadcccadddaccaccbddcabbacabccdccbcaccbacbacdcaadbbcadadddaabacacabcbddadadbadabcbcdcabcddbaddacccbabbbbcdaccbaacbbbacddbaddbcbddcaacbdcbdaccadcbcacbddddaccbaadbbcbdbcaacbbcccbccadddcbbdcdacbcbbcbdaadbcadbcaabbcccaaabbadaacbbcdadcdaaccbddbcabdaacccaccbcbddadcdcadcbacccabbdbabbaddaabccaabdacbcdacdbadaadaaadcbabcbbdcdbaabccadcbcaccabacadcccdabbbcaacdcaaaadbcdcabbbbdcaaaadadaabdacababbabbaadabddccdbaacaacdaabbbacdcacbaaadbbaccccacbcbdaccbaddddbdcbccdbbaacdddbadcbccaadccbaaaadacdcccabbbdcabdddbbbaccdcacdababddbdabdcccbadddbbbadadbbdddbbbdbccbbddabdaacdcdbadaaabcabadcbbcccadabdacbabbabcdddcdbabaddbddabdaaaaaababdabcccbbadcbbacccdcaddaacccbadcadcaaaadbbacbcabdcbbbdddabcbdcccdccaaaaaccaaccccabadaabccbbbbbdacaaababdbcadadbaadcddccadcdabadbdbbdbaaccaadbbaaccccbdbdcbabacaacbaddbaaacaabbabaddaadaaadbbbdabcbbacaddbddacdccdcdcaacdcdbdbcaabcccccdacbcacacabcdcdaabcddbacbbccbbbccaaadabddabbabbbdadcadcddbdadddadadbdaddacbcdccabaabbaabbdbbcbdcbacacaabcbbdccdadacacbbbcababdbcdabbcabccadabcdcaadadadaacbaccabbccdaddcbccccddaaaccbabbcbabcaabbcccbbdbacbdddddbdcadcaadbbbdccadabcbadadddbadaabaaabdddbbaccabcbadcccaddaaabdbccccdbaaccbdcdaabcccaddcbbcccbaaabcbdccbbabbcccaaababcddbaaabbaaaaabddabdcbadaacdabdbdadbaaaabadbddbdbbabaabaddcdadddabaddacaacadddbadbacacbacdcdcdbacbcdddcabdcabdbdadbcdcadcaacdbacbdccaadaaaccabcccdcababcdabdbaccdadcbddbdaccbdacbacbdcbddcdcdbbdabbcbccdcadccddbbaabddbdcddaddcacbadcacbadcadddbbbcdbddccdabbaaaccbaaacccdaaacbdccabacbdabcdbabacbacaddcdbaaabccabcdcabdadbbaacdadddbccaddaabacdcddaddabbbbddbbcdbbbccbbabcbcaacdccdbbbbbaadabdcadaccdbdbbbbdbbcaacbacabdacacaddbaccabccdbdcaccbdccdbbaccacaaacaabdcaccbccbadbccacadabdacdbbcdcbccdddcbbccaadccbcabaaaaaacabbacddcdadcbcbdabcddddbabdadbdccdcdbbcdbabdcaaabbbdadaacdbdaacbcbbaabbabdddbcdbdbbddbccdaabccacdbcabadcccddbcabbaccadddcddcaacacbcbadbbbdabbbbaacbddcdaddcaacdbbbbdbddaacdcadbdcddddacdbdaaccbdcdbbccdaabaddddcbbdacdcabbcaacdddbadaacccdcddcccbbccbaacddaabaabadddbdadacaadcbbdadabadccbaccdbaadbddabcaadddddccbdabacdccbcdacdabaacaaaabddbadccdcbdcbccbadacacdcbaaaabdcdcbbcddbccaccdcdddaabddccadbcdbaabaaacdccabbcbdcabbbbbdbbbcdaddadbdaabdadabdcdbdacacdddadcbdbbdbaccbddaacbbaacdbcabbdbdaacadbadddcddcdacacddbcbcbcbdabbcacaaacbcdadbddbdcadacbcdbadbaaacaacdbcddbdccdccacaadddccbbbddbddaccccbbdbcaccaccaacaadaddbbdccccabaddcbcbaaadcddcdabbadabcccdacaadcbbdbaadcbdaddbacddbbcadadbddbdddcdbacdabddbbddcbacdaaaaadabbaadacbadcdccaaabbbcabdcdbccadaaacbddcdadcabbbdcaccaddbdbccaccbcadccdbbddbaccdabdbbaadbddccbdbbbdadbbcbaaccbcbaddcaacdbaccabdbbcacdbbbcbccaccabccabdbaabdbadcaccbbadadadcadacaddbbdddccabdbbabdddbbddddbdbcdacddbabdaddddabcbbaabbbadcacdddabdddacaadcddbcdcbadcdcacdcdcbaacdbccacaaacacbcdadaacbabaccbbaaadbadbacadbdccaccdbcaaabcbadaccccbcbdbbcbcbbdccbcccdacbdaacdbdadddccaabdacddcddcaabaabdcdcdbbdcadcddacbbcaabbdcaccddddadbdaabbccdbcdbadbbaccabdcaddcbcacddbcdcbaabadcbddabbacdbaadacabddadaaaddcbcccaaabbcddcddcccbcbabcaacddcdaacadbbbcbcbcadddaaaacbcaabbcddbaddcabbacaadbbddaccbcbdbddabcdbabdacdbcccdaacbacddaddbcddbadbddabbaabadabacbcbcbacbddbdaddacbacdacdcddabbddbdcdaaccdacdcccdabccbcaaabdabbcbddcacbbcbcbaacaacbbdacbacaabaacadacbdadacbbabbcccabbcababbdbddddbccabbbacccaacdacbdababdcddddaddcbdbaacadadccaabaccdabcaddadcbcbaaadbbcabbbdabaaddaacaccbdadccabcddacdcddcccbcbaddbaacaacdcdbcaddadbddbcccccbbabdaccbdaabcdcbcdacccdcbcbcacaaacddadcbbabbcddbcbbdabddaabdaccbbadbbcbbbadaadaddcddaaccadaaccdcccacbadcaacbdbcabacccccbacdaaabcdacbbddbdbdbcdacdabdbcbabcaccccdddadaacdccbaaaadbbcdbcdbbabacadcdbdbdbadddccdaccbaabbcdacaddabdadcdccbccccaaadcdcaddacbdadaaabbabbdbcccccdbcbdcccdcdccdbbaccdbadccccdacddccdaabcaaaacdabacbdacadadcacacccaaddacaccaccccbcbdbacacabbcadacdcddccbbbbbdacacaccbbddcbacdbadbcbccbbaabddbdbadabdacccbaadbbdcacacdccbabbabadcbcdcdabdaaacadddbadbabbccaaabbadbcbaddccdaabdcdcdadcbbadbaddccdacdbaccbcddcbbddaabdbcaadbdcbccdcbcdcaddcddaaaaacaadbcdcdbbccaddddacccdacacbcaddcadcaacddddcdcdadabcbbdbcdccaccbbabbbaaadcabdbbdcdaccabdbbbaccaddcdcbaaacccbaacabddddcddabdbaaabacbabbbdaddabddcdbbcaaddcabadbacbdccaadacabacbcbddacdacdbaadabccdcdcabbdaacdbbcaaaacacddbcdaabbbbabccaaadcdbccaaccbdcbbaccdccadaaaaabbbabacdacddacdadaaadcaabbaabacdddbbcccbdacbadddcddbdcbacdcccdccdcddcdaccbadadcdddddcbabbdcdbbcdcabaddcccdbbdaadbadacdacbdbdbadcccbcabdbacddbdccbaacbbcabbddcdacabdacbaadcdcabbddbbaacdccbcccccbbaabddcacbdddbaaabdaadbadccdacaabdbbdbdcccbabcbdbbcdbaacdddabbdcdcdabcadbdcccadbaaddbcacdcddcbdaddbadbcbddabbbcaaaddcabbaababaccbcabccabdbccadcbbbabbacadabdcaddabdaadbbadbddccacbadacccabaaddcbacacccbbdabcadcccdddadcbdbabbbaaccbacdbaddbaccbdaadacaaddaacaadcdbccddabccaccdbdcdaaabbbbcdaaabbbbbabcdbdacdbaaaabbbaccdabccdddabcacbbdcdbcdacaaabdbbbbbddcbbadcbdadacbbbdababcddabcdabaacaccbdcabadbcdddccaaacaacbbcccdaccdddaadbcbdabbadaccbcacbcaddcdbaadabdabcdabcccccadbacaadcdddbdccacbabdddacbdaacdadddcdcaaccccdcdbcbcaddbbbcbccdcaccacaddbbbbcdcaaaaabbccadcbabdabacadadcaddcddababccaccacbacccdddcacbcaadbcadbcaadbccbdacadccacadbcbdcaacbdaabddaadbddddbacbddbcaabddcaacdadcdbdccdbdcaadbbbdbbbcacbbddbbacbabcccdaacdadcbbdccacaaccacdadbcdacaabbbbddbcbddcadcdcdbdcdbdccdaaccbdbddddabbbcadacababdccbcacacdcbaadadcccabbcccaddcaddcabbdabacabdccbabddadbcccabbaadbbddcddbbdcaddacbbadaccbbbcdcaadbabbcaccbbcdcbdddbaabcbcbdabcdcbdcbccbbdbdacbddbccdabdddcbbadcdcaacadbbdcbbddaaaacdbcbddddadcbdcccdddacdddabdccdbadbabdbbbadcbbcdcbbccaabbccaaddddabbcdcccbdaddcbbcabdbbbbbddcbbacdababbbbabaacbbadccbbadcdbdacdaddcdccdacccaabbadbbcdbbdccdbababcabbcbbdcabcdbaaacbaaccaaddbbacadcbccbdbdbbddcacbcbcadcadbcabbbadddcccbbdbadaddadbbadcaccdacadbbddbcbaaaaadbbbbbbdddabcdbdddddbcccaaadbadcbbbbabbcdaacaaddbdadcbbaacdabadddbcbdcdbbcabdabacdadcbdadabdbdccccccacdcbadcdddddbddaacdadbddbbadccbbaadcabbadbdadcadbcadbcabbdabbbcdbbbcbbdabbccaddabdcbdcdadbbccdaacbdbcbdcbcdaccddbccaabdacacababccdabdcbacdccbdccdbaadaacabcadbddadccabbdbcdcddcbcddcddabbcaacaabcabacbbbaaadcbaadaadccbbdccccbbaadbabdcacbabbbdccadcbbddacdacddaccdbcadbdacacdbdaddabbbabbdccddacdaddccadcaacdbcbdadcbbacddcaaccccdbcbaccacdcaadcbdcdbddcdcacaccbabcabddadacddddabacacdbdacccaddaccbadbbabcaaccbaaacbddbbdccadabbcbdabcbcdddcbbcadddbbdcadaaadcaddbcbacccadabbabbcddaacbcbabddcddddbadccacdbccacabadaccbdbccdbabdabaccdadadcadddaccdddcbcbabacdcccdbacababbbabcdbbcacbadaddadcccbcabddbcddbbbcdbbccbddbcdcbabdcbacaadaadabbcddabaaaabdbcbdadabbbcbbaadbbccdbcbdbcdcabbbacddaababcaabbccbbbcadcdcaccbaaabcacbcbbbddbccaabbabbdbddcabababbddbcaaccdddddccbaddbaacbdabcaadabbdbabaacabacbcdabaabbcbddbbbddacdaccbcacababacdcdabcbadccdaabaadcdadadabadacdcdbbccbbbaadbababbdaaddbdaabdadcddaacdbacbccdcddddbaccbadbaababacadabcacdaaaacdcbaddbacabdadbacbddbcacaabbbcbbbccabadcbabdbbccaaddcaaabbacbadbdcbddacabbbcbccbacadddcbaddcabcdbdbdcbdabcdbaacbaaabdaaabcdddbadcdbcabdcdcacadcbbbdaddabbcdbacdccadabcdccbdbccccddadcbcabdcaddbbacdaabcaaaabaddaccdbdddabccbdaacdbdaadabbdcbacdcdcabbadddaadacaabbabdabdabadacdabbdbbdaaacadcbccbcdaaabdbbddcdddbacddabcaabbacdcbcdcaadcbbdccdccddccadadccabbcddbacbadaabadaabaddcacbdbadabcadccbbcdbcabcbacdbdcabacbadbcabbbcccbbaacdcdcbbbbdaababcdcbbabbbababccbbaaadbbcaccdddaaabdaddbdbaabaddadabdccbcddacaddaddaaccbcddaccadddbbbaaddcdaababcacbbdaacddddbbcdbdbdddbabcbdabcdaabaabdbcdccdcbdbddadcbcadaadaddadcbcddbbbccdabababbddbdcbddcdabbdaabddcdcacacabdcbdccbddcdbddbccccdadcbdccbbbcdaacddbdcbcaaadbaccbcadabaadbcddbddabadcdadcddabcacdccbaddccbbdabbccddddcacadabccccccaadbbbaccbacabadabddaccbaabbadccbadaadadbdbadddacbcacbbbdddbdbaddcbaaaccacdcbbcdbbdccbdcbbbdcbaaabbbbdbbcaadbacdbaccdababdcacacbcdccbccdaaccbcdbddddbcbdaccbbabcbbadccacbbdcdbccddbcdacddcacddabbdadbcdadaddabcaccddcaadcccabdbaaabbbcdcdabddbabcabadbbbacacabaaddaabaabdabcbabccdddbadadacacaccbbcdddbcbdccbdacbbdcdaaccdaddacbcdadacbbdcbcabbdbbdbddbccacdadaddcdccdbddccacaccdcdbdaccdaadcacadaacdaabdcdddbbdabcccdcaaccbcabbccddbcbaacbbcdcbddcbbdabccacacacbdbbbbddbbbadabacccccacaaccbddcddcbccbcdcdabaabbabaaaaaddcbadcaddbaaadcbbaccacdcdccbaddabbdcadcdbacddaacbacbbbcbbbcdccbbbadaccabddacdbbbbbbaabcbcbdacbdccaabaaacbadcabbbadabcaadbbcbbcccdbbbcccabcaabddcddbdccacdcaadaabccbbbacdccdcdbaddbaaadbddcccdccddbbaaadbdaccbbdabdbbacdadabaacbbacdcbadadcbcddccabcdaabdbdbbbddccdddbbbacbcdbbbacbddacbcccdbbddccacaadcdcbbcdcacacdbcaadddbcdabcbcdbcaccadcbbbdcbbdcdadcbacaabcbdbaababbcacadbbacabdabacbbabccbcdddacccbbbbdbbbdadcbcbccadddccdbadddbccaaddabbbdabdabcadccdcdbadbdccabbbbaaaadbacdbcaaccadcbaaacdaccdcadbaabacccacdadbcbacbdcbaaacbbbdcadcaaddcccaccbaaadbbaaddccbcadbcdddcabbccccaaddabacacddcdbabbbdbabaddcbbccabaaddadacbbbbadddadccccabccbbdaadaadcbadcddaddcbacbcbccccddaabcdcdbaccccdcdbadcadaadababadbdaadacbbccdbaaabbabdaabcaddaadbcabaaabadccddcdcccccbacbabccbcdbcbddbccddcbdcadbdcdccaaccbbacaacddaaccbadbadacaacaadbccdbbacaacdbdcdbabacddcddbcadabaacacdabdaddaccbbabbdcccdcdbccdcbacbdaacccbcbdbaaadcbbcadabcdbddddcbadabddaaacdacababbcdddbbcdaabbbbccaccdaddcaaaabccadadaabbbcaddcbcdadcabaccdccaddcdaaccdccadbdbbdbbbbccddcdacbaadcccaabcbcdcadcaaaccbddddbacdccaabbbbccdbbaadbbaacacbaacdccaccdaabdccaabcbbbdabdacccddabdadacbacaccbbbdacbdbcbdabbbbbccabaacdaaadaaaccbaacacaabbcbcbcbccbccaacccbbdddcdccaabcbdbbdaacccbdcdcdbcacaddbbaabdcadbadcbddadcacccdcaaccbbbdcdbddabdadabacdacacaddcbcdbcbccddcdacbbbcbcbbdcbbddabadcabbababdaaadcbaadcdcdbccdbcbcbddbbbbccdaabcacbddcaacdaacccccadddcdbadaabcddbbaddaaadaadbabbadbbbcdcbdcdbaabadaaacdaddacdadcbbcabdbbacacbccddcabbdadaaacdbdcaaabbaaabacdbadadbbcdbbcbccbbadcadddbaaadcccacdabdccbabdddbbdddadaaacdccbabaadaabbdccddbaaadbbcabdabdacababdcccdcadbaadcddbbcdccdcddbcaacacadbdbdbcaaacdcacdbbacdbacbcaccdadcaddcbdbacbccbcbdbccdaddcbddcdbcdbdcdaaabbaddcadbaadaacaadababccbdcdabdcbbadbadddddbdddccaddcbcabbbbcbcacbdabdaaabdbbbabdabdaabadbbbbdddbbaabccaccdcdbbbccacbbccccaabdcddbdddcaaccdbddcbdbcbddccaccdbdcbcbcbcadbbcddbdaadbdcccaccbbcdddababbbbdcdabdabcdbacdccdcdccdbdddcbdcaaaddcbcdbbcbccdcadbbdacddcbbbabaccddbdcddcdbacbaabadcaabbdadacddcaacabbadabaabaaddaddbacccadbdaababdcbbcabdddcdbaadbdddacccabdddccdabaddcddcdddaacbaaddddddacbcbcdbabcbaadcabcdcbdccabadcccacabbabccbccdbdbbbdbcabbdbbacbdaabdbacbaccdbbadddadbbbddaddddcbcdacbbdcbbabdacbdabbdaddabbdacddbbccbcbcbdaaccadaddbccadcbbbdacdbbaabcaaaabbcdcadbccdcaacbbbdcbbabbdcbabaddbbcbaabccabbdadacccdababdbcacdcadadbbacaaccacdbbcbaaacdacccdcadbacabbcddbacdccacdbddaabacbdbbdbdcabcdbdccaaabbbbadccdcccbdccbaddadbbadbdbddbabcabcbdddcdaccadacadbcabaddcdaddaacdbccdddacbbaaddbcabcccbdbcbdddcddccdabbcbcbacbdbcbbddabccbcaaccbaadddcabaccadcdaddccaccddcccacbbdcdbccbbbbacadabcdbdcbaadadddcaccaccaacabcbcdbbacbcbcdaaacdcbcbaabaaadacccaadbabcdababbddbbbcacbdacdabacdcdaddcdbcbcbbbddddddabcabadacdcabbaabcadadddadddcaddcaccccacdbbdabbcadbddaddcaadabcdcdcabacadaadbacadddabdbbcddddcadabacdbbccbaaddcacdbdacdddacddabacccadadcddddbbbdcdcaacbbcadababbdaadbabdcdbcddadbbcdbabaaddbbbdcccdddbcaacacbcadcadbbabacdbcbbbcdcaaacdbbbcbbbadbbddcacaddddadbdadbacacdbbbaccababbabdbddcadddcbdccdbcdcbbacbaccdaccacddbcaacccbcdbdddaaadbabcadaacaaaadcbaaabbcaccdcaabbbadacaaaccadadbabcbbcccddccbccaacdddcaccabccacaddcadddcdbcccbbdcbdbbbacdadcbccbbdaacbabcbcbccbcdadabdccccdcbbbcaaadbbdbcabdbaacccdaaacddbcdcdcbcbdcaaadbccdcaadcbaabbbccbaabacabbcdbcdcddbcbaaacbcbbbccdcaddaaccdbcadcdbbccbcabadaacababdaabcddaccbcbacbdccaccbcdadcbdaaaacaacbbbdbacacdcdaacbaddcddbadccaacbdbcbbabccccbddbdabcabbcdbcabadbaadbdbcbcaacabccacdbadbabadbcdccdadbaaaaabddccdbbabaadaabdbdcccdcddadcddacadadbadbadaacbdcbbaadbdacaaccadccaabcacbbabdbaadbdabadaccbcddcdaacdabdddcccbbdabbbcadcacddbcdbdacdabdaacddddcbdbbabdadbdbaddaaabdaababdbdbbdcddbbccbdaadbcdbcdbacdcbadcaddbdadabcdacbccbdacabbcbbbbddccccccdbbcdacddcbadbdbacaaaacdbaaacccbcdbacccdbdcadadddccbcccddcabbddaabacbccadbcdaccbdcbdbdaaacaaadbaaccdccadbdbccdadbdabcddbccccdcdddabacabcabdadbbaaabcabccdacccdcdbcacbbcadcaadacbaadddadabbacaaddaacadddcadabdbcccadadabdcabacaacbacaadcbddddaaacbdcabaddbbcbbdadcbdbdccdcdcddbcbbaabddbaacdcbdcaaccbbaaababdcbcbcacbbbaadbacbdcdabccccacabbdcbdabdcddabdbcbcbcdadccddaddcaadbbdcdcccccddbcdcdddcbdcbcacaddababacacacdcabdbdcdccbbaddcccbbcbbdbbaccccaccadcacadcbbdcdbbadcbababbdccccbdbaccbbdbdaccaccbbcaaaaddbcdabdcdabdbddabdbdabdacbbccbddbaaabacdacdcdbdccbbbccbabdddcadbddaabcbbdaabadbbbddabadbdbddadacdcacaaaadcdcdbcbababbbddabdbcddddbbcabddbdaaacbdbbabacbddaadaadcdcdccbccbdbbdbbddbccadcbbccbaadbdabaacabaaadccbbcccaadbadbbabdbddcccdbcbaacdcdaadbddaadcccacacaacdaabbdabbcbaacddcaaccdcdaaaccdbadadddcdcdbbcbcdbaaabbddbbabcabadbbbabcadbacadadbadaabbccdbacdadabcbcdcdddddcbbacacdcdbdcaacbcdbaabdadacdabdccacddcddbcbcaacaddcaddbdcccbddcaddaabcaddccccadbdcabadddddaacbdcbabbbccdacbdbaacadabacddcacdcdcbbaccbcaadcdccabaccdbadbadbdbbdbbbcbddbcbbccbcdbcdbbcdbdbdcdacdcaadcdaadbcdcdaaaddddcddaabbbddaacbbbddacdaabadcccbbbdccacdaaaadddcdadabacaddacbdcbaadcacabbddcadadbabbdcdbbcbddaacbdccddbdcccdcccabddccacbbbadacaaabbbbddaaadbcccadbadbddbbdbccdacdbaacdddbddccbdabaccdadccdcbbddaaddddbdbaadbbbaacdbcaabbbbbcbdcbaddccdddcccddaddbdbbcadacbcccbbabdadcacdddbddcdadbbbcbcbbbbcbdcbdbccaddaaabddbbcabdcadcbaddcaddbbdbdbcadbcdaaddadaccacbdcdabddddbaacdbabaabdccaadddcaaddbcabbaabcadccacaabcbcbdcbbacdddacbcbdcbdcdccbbaaabdacdbbaabddcdacdbbbcabbbaaaabcdbbccbdcaabdcdcbbabaabcbdacadaaddacbcbccbdcacbacabddabaaacbacbdabdbbaadbcbbaaacdbdbbababdaccdbcaabbadcabbdabccbcdabbbacdcbadcbcccacdcabdcbadbcaaacbcdcbabdacadcacdaccaaccabcadcbdddaadcdabccaaaaaaaddbbbaabdacbadcdcccccadacccbbddcacddbdbcaadbcccddcbabaccadacdcaabcdadddadaabbbdbdbbbcccdcaacaabbacdbbcccbcabcdabadbbadcdadbcccddbababbdbcacdcdaaccbadacadddcadbcbcabbabddddbbaccddcbbaadccaacdbaabcacbcacabddccdbdbcbaabbdcabadbdbadababddabbadbdbacbcbcacccddddcdbbdbdacbdbcdccbdbaaccaacaaaadbcdadbbcdccbaccabacaaaadbcdbdbcbcabbacbacdbacdadacbabaacccbacccaacaacdbacabaccdbacbbcdccddaacbadbcdacdbaccbdcccabcacddaadbaacbddddadaacdccbdbbcbbdbabcacdddadbdabbdbbdaadbcdcdbdabdadbaadcbdacbbdcaaaadbaddabdcbbcdcbbdcdbbadbaccabccdbbacdaabbdadadbabaacbcdbaabacbacddcabccbbcbbadabbccddacbbbbcaccbdadbacdcacdcaaaadbbbbdbbbadbccccabcddaabaaababbcbadbddccadcacaabacbdabaabdacbbcbccccabcbadcbdabadabcbaccccdcdcabaddaccbcbbbbbacbdbacbabbcdbcbcbacbbcdaaaaaccddcbcdacdbbaccbdbdbbdcbbcacaacbccbcbaabdbbaacbadaaaabcccbacccbbadddbbcdcacadaadbdbdbcdccdbcadcaacbacaddabdbcdcccacaabdabdabcdaacdaadbccbdccbaaabbaacaddbacbdddaddcacddadddbbadbdacdabadacbaabdacbbadabccacaabcccddddaccaabccbdabddcdddbdbaadbbdcddadbabcbaaaddabdacccabddbaacdadbcbbaababaabbddcddbdabdcddbddbbbcdbabcdcbaaacbbccacdbbacabdccbdacdbdccbbddabaccccbaaaddddbcbbcdbcadddacbcbdadcdcddabaddacbacddacbbdacdbbaaaddcabacbbddadaabacadbbbacddbbabccbdccccaacddaabaddbabcbdabaabddcbabbdcccaacabbaccaaddccababaaaccddbcbaddacadbccabcdacccabbcbababbcdbccccbbaddcdcadcaadcdabbaddddccabdaacadcdabccccbddcbdcadccdbaaadbbbbddbdbacaccdddbccddccadbcccdbddcbcabccbbdacbaaadcadbccadcccccbdabddcccdddddabaccbabacabdadadcbdbbdbdcddcbaabbccccdbabbdccacabbdbbabdadcaaabcabbaccddcdacbcaacdbabdbdccdddbcabcbadbdbacdbcccaabaadbcbbdccadcadacbccaadcddcdacccddbdccadcccbacbddaddcccadbdbcacdbdadcbccaaacbabaaadcaacaccdcbdabdaccccccbbdcccbdcbdcaaddcacbdacacccdbdbcddaacadbaddcbdcaacdacaabaaacdbdabaadaabadcdddbcbcacccdacbdcabcdacbccbadddabdbadccdcccdbcbdccaaababccacdcabacdddabcccccbaddbdcaacaabdabdabacccbcccaaccbbaacbcbcddbbcabadbbcbbaddcacccacbcccaabbcbbadcdaddccdbddbddbdcbadcbbbcdabdaacacbadcbdcbbbddbbaadcacaadddbaddaddaaadcaaddbbadbccdabdbddaabcccaadcbdaadaacbaaabcbdbacacccbccbbdcbcdbdcdcdbdbddcbccdcacdaacabdbaaacdadaaaadcbadbdcddaddbaacbbdcdaacabcccdbbabbdccabdbbabcdabaacdcabdbbdbcadbcaddccdccadadacbdddccbdaccabaaccbbcbccdcbcdadbbbddddadbbbcaacccadbdcbdcddcdacaddbaddddbaddddbbbdbbacddddadccdbcacbbacbacbbcbccacbadddbcbbabacabdaadcaaadcbddcddbcdacdcbddbddabaacabcabcdbcdabbdccabadaddddbaabcdabcbcbbddbaccacadcbbccbacaddbcddbdcdbbcacaabcdcccbcdbcccdbdbcbdabcbaddadccdcbcaacacaabdaadbbbbcccdacbbcaccdabacabadbbadacccbbbbdbdccbccccbcdccabdaacbdccaddacdcddadadbcdcdaddbdacababacaccbbbbdacacbdbabdbadddbbcadaadbdcaadbcbaabcacbabcdbdacaacddbbddcddbadbdddcaaddcdcacbbacbccbdaaacabcbbadacdcdacacbbbdbbbcdddaacdcbbaabaabaaccdccabababadaddaddcbbdaadcbaaacdaabcaaabbcddabcadbcdcddcdbbcbbbbdbdbcbcbddbcdbdddbaacacbbbdcdcaddcadadbbacabdacadbbddbddccacabacdbdcdccabacbcabbcdcdaabcadcbbbcaadaacdcbcabadaabbacacbadddabaacbcddbacdcaacacdddbdacabddddadbcbbbdccbacdbddcbdbbbcaccaddbaacaabbaadacdadcaccddcdbdbcccbccdccddaadcbdcbacdbadbaddbcbacdabaabdabdacbaaacbcbacbdcbddcadcddbbccccacaabcbddbaababaabcbbabcddbcdaaadbcbaddccddddccbabadacddaabbabbdddabdcaddcbdcadcbaaacbcdacbcbcdcaadacabbbbccdcbbabbaadcccaddccbabacabdddddcdbdbacaccadcdbbbbacdacbbcabdaccacbabdcdadcdababacddddacdcabbbcdcacbcdccccdcddcdbbccddcbacabcabbcddbcacdcdddacaaddbbbbbbacaacabdcddabbadddddabdbccbcabcccaacadcddcddddababbcabbbbcdccdabbdabccbbdbdbbbadddddabdaacbcdbbcbbcccbacadaaddbcadbdbbadddcbbaacddcacdbdbcccdaaaccccacaaadacdcbccdacbabdbacddcdcabdcabdadbcddaccaadacbcdaacccaabbbbbdcdabccdcbbaadbadaddadbdabcaddbabadabcadacbcdcdbabbdcabcdccccdbbcbbdccdcabbbdccbccadbacdabacdadbdbdbbcabcaacbcadabbdccdadddbcbbdbdcabbbcdacacabdabaabdacddaacaabdacabadaccbcdabcadadaddcdcddddaacddcdcdbdcaacdacacbddcdacaccdacccbbaabcadacbdbddbcbbccabdbdadcbbdacadacddcbbbcbdcbbbbaddaadbdbdccdcbacbcaaabdbbddbadccacabdccacdaabacccbadcddcaaccdacacaacabcdddcbcbacddbdcbaddcaacadddbcdaddbbaccdaadcaabbdcbdaaacdbbccbccdaadcccadcacbaacdbcdbbbacbcadbdddddbabdbccbbbcbcdaddbbdddcbbcbddbadcabdadacbcbcbabcccbcaadadbadbcadabdcccdbcadcbcadbbbbdcbbdcbbdaacacabbdccabaacdbcbbdbddadcbcbcbcdbdbbdcbcbcdacbabcbabcccdabacbcbbdcddbadaddbcddbabbcccaccddbbbbccdddbbaccabbbcbadcdbacddcdbabaaaccacbadbcdabbbdbbcbbdccbbabccdcdaddadbcdcdcdccbabccbdbdcddcbcaccdbcaadccdcbddaccdcacdacbdaaddabddbaaccaadcddbaadbaadcdaaaababdcbabababccddbabdaaadbcdcadddacddacaccdbddccbbcadcdbabcbaddcccabcacdaacabddbaccacbacdbaaadcbbcbaaacdccadabaaccadcaaadbacbdcabdcbcacaccdaddcdaaccbcddadaabdcbdaaaddcbdaddaaaccbccccbaabdcdbcccbcbabdcccadcadacdccbdcbbbacacacacaabcbbabcbabdbbacacaadabcbccacaabbbaacaabbbcdccaabbbbdadbdbacbbcaccabdccbcaddbbaadcbabdbbdadaddaaddcdbbbbbdcdbbdbdaabaccdadcbbcdcabaabcdaacdcccacccdaadadcbbcccdddddbacbcabddbbcabdaddabbadacaabddbdacbddcaaadbababbbcaaaabbcccbcccdaaacbbcadaddaddbbddbcaabddcbacdddbbddbadbcbacacdcacbccdccdbccbdabddacbabaccacbcaaabadcddcbbcbbdadabbadcddaaccdbdcadcdbdcbcababbadaaccbaaacdcbdabcdbccbabcbbabbbdbcbbdbcdadccadcdcbadddabbcdbdbacbabddccbcaaacabbccddaacababbdcdddbcbcddbbbadbbaccabdbdbcaadacdcddbaddccdcdbcbdbdccaacccabcdbbadaabddcbcacbabdbdcbabdbaaacadbbddadadddbaccaadbdcccbbbdbdabcddacaadacababbacbaacadbabcccbbabbbcccdaaabddcaabcabcdbaadbdddcccdcbbdacdcacbdabaaadcbabdddbaccbccdabaaaabdbbdaaaabbadaaccccdaacccaabddabacacbccdaadbbdbadcbbbdaabcbcbbbcbbbdccbaccbadccdbbddbcdadcaaccdcbcadcadccdbdddbbbcbcbbbcbabbcbbdbaccabdabdaaccdcaccadcbadaabcbbbbdbacaddbddacadabadbcdcdbbcadcbddddbdbabaaaacadddabbaabadcaacbddbdcdaaddcdbabdacbcbbdcadddadbdbdcaccccccdcacdcbbdabbccadcdbccabcacbdcabaccdcadcddadcdbaddddcadccbdbcccdddbbdbcdadaddbabdbcdbbadcccaabcbdbccbddcdbaaaddccbcadbbcccabaddaadbabbbacdadcbbdaacbcbbddbbcdbbcdacbacaacdcbccacdcbbcacbcbcbdadadcdccdcdbbbabbdddbddbabaacddbaadbbcbacaabdaaacbccdabbadbabacbbcabddabccbbadacdbdacbadcdabaadbaadbbabddbaacaaddcaaaadbaababaabcabdbddacbbabbdccbcccdbddaaccbdcadcddbbadaadcacacbbadadbbbcdaaccdccdbcdcaabbbccbcdccbbaadcadacdadaddccdcccdbaaaadbccbddbdabaddcadabadabaccdabcdaabaccdbdbadcccaddaadbbbaccaccaccdbdccddddacacbbbcbcdbdaaccbdcadbbcdacbcabbaacacbaadaacdabaacbaaabdddacaadddcacaadababbacdbcdaccddddadcabadbbbcabcccadabbcacbbddcccbbadcadadaadbcaabcacadcddbcbdadcddbaacbbccaddcaaacbcabdcdbccbdccdccbaabaaccbabbbccdbcbdbacbcbddbcbadcbdaadccccacdcdabaadcbbbccbaaadccbbbdadcabbddaadbabdbcbcbaababdbbaddbcadcacdccdcabbddcacaaababdbccaadbadcbbcbacddacddcdbbcdccbdacbddbdacbdbaacdbadbbacdcdddcddadacadaccbcccbbbabdcdabdacabbdbdcdaababacbccddbbadccccdbdbaacdbdddadbdcbacaaccbbacccadcadaaadbbbcdbccbccbacccbbcbccccabaaabbabbbadbbbdadacddcbbdaadadcaabccddcbcacadaabdbbcabcddbbddcbccaadcabcbdbbcbdbaabcaacabdadadbaaaabdbcdcdabacadaababbcadaaabbcbcadaadabcadccdabcbadcdbdbcbbdcddadbbabdcdcdabccddcdddbcccdccacbaaacbcdabaadccdabccdcbccdcaddcaabdbcdbccaaabbbbbbcadbdddcbdbcddaabbbcbbbaccdbabdadbacadaaaabcbabdaacdaadcccbcbcccdacacbcbaabddddadbaaabddcdccbcaaadcbbccdcbaddddbccddaaacdcaabdaabbcbdddcaacadadcbabadabcbcdacbccddcbcccbdaadbbcaabcabdbcababadbdacabbabdbadbbdddbccabbcaaadcabadabdbdbcccaccacaaacaaaaabddbbabbaccdcbabadcbaccbdddbacbacddaccdbbccbbadccbbbdbdbbaacdaccacdbacbcbcaabacbcacccccdacbbbbadbabdbcbbcababdbcabacabbddccdaccaadccbadcbdcdacabccbcadbccddacacdbaadacddbcbacbbcaaddbddccbcaaabbcaabaccccdbabccacbcaadcdcbcddcaaccbbcdbccabacddcccdbcccdddaddcaacabaacddddcdcadacabccadabbdadacbbddbbcbdccdadbdbbadadabcbdabdaababdbbcbbdadaacaccacbabaadcdaddcbcccdcbcadcdbbabccbdabdbcbbaacaacbcadbdcacaccbbacaacbcaaaacbbdbddddbdaaccaaacbcddaabbdacbcbcbdaacddbcdbbabcdcddaaddcdddbdcbccbbcdbacbddaddabdcbbaacbaaadacadddbdbadbbbddaaddbbdaddbabcbacddabcdcccaaacdcdaababaabadcbbdcacbbaadacbcbddbdaddadababaabcdddbddabdbcbdccddcabcbdbdacaaacbdccbadcaacddbdccccadcaadbcdcddabbaddcdcbaccaccaadbcbbcdccadadcadadddcbdacdcdcacdcbbdcacbbcaaaddabbdbabccddbbabbacbcadbccdcdccdbddbbbabdcaacdbcbdddaacddbacabaaddcdbbbcdcdcdbaacaacccbacbabbabaabbcacabcdbaabbdbcadcdbbbbdadcddbadcabcbccdbcdadddaadcaccdcddbccccbdaddbdbacbabbacdbdccbbbcacaacbadbbabaddaccbcabacddddaccbddbdbdabbbcbbcbbcdadcdbdcaaccccabddddcdbdcccaddcdcaacaaabbddabdcbbdacdbdbccdccbcbdbcacbaabddbddbadcaccbaacdbaddcdcbbdcaadcadadbcdacabdbcdacbbabaacbdcbacabdbacdabcbdbabbdcdadaddcdddababccacddbddbabccdbcaabaddcbacccadddabcdbabbbccddcdcddcacccccaadddaaaabcacdcaaddacaabcbbacddbacccdacaaacdcddddacacaadccbabcbbbdbdccbbabcbbaabcaaadabaadacddbcbcadcdbbadbbdcdbbcdbdccacbcacbbddadcbaaabdbbdcdadbabcabcddaacdaaacccaabcaababbcdacacbcdddacaccaadbbbcccbadbadbbdcacddabadccbabbadbcbaccaddbadcddabaabccdddbaabbcbbdbabaddabadcaabaabcdccbbcaabcbccaaacadaccaaaadaccaadaccbdacabddcaabdcbcaaabbabbdaadcbadbdbdacdbacdcdbbbccdabcdcacbdbcdaabaddacabaadccdcdbcddddccaacadabbccddbccbaddcbcbdcbccadbcacdbdcbcdddaaccdddcbabccadcccddbbaccdbaabbaadddacadcacbcbbcbbabaaadcdabaacdbbdcdbadabdcaabcdabbbbdacabaabdacaccdaccaaabdcdcaddcbbadbddadbdccbccddcaaabbadcdabaddabcbcadbbbdcaabdcabaadccbddaacaacdbddbbcdcccddabcddbdcddacccdacadbdcacaacacbcdacdbcdaddadabdbcaadacccdacbcddadbdccbcddbacadbbcdaaddcbccbabbcadacabcbbabdaaaaadadbdbbbddcddbaaaadcdadccbadbabdcbbddcdbdcbbdcacacbbddbabadbadbadcdcacdbabadaccbbdadbadddadbdcdbbcccbbaadbdabaddcddcdbdbdbbcaaaddacdaabccdddabddaccddaaaaddcddbccdddddbacbcbdacbdbcabdcbccbacccddcbddbabbccdaadcacbcababbcbddadbabccddcdbacdbbbbccddbbbdbbdcbddaacaadaccdddbbddbbbbbccccbddbdcabbacbabdbadadabadababccdcaadadbabcacabbccdabbdcdbdacbaacacbbdbcccaabdccadbcdcaaddcddcaadcddacacddbaccaacbcbcaccdaaddadcbcddcaddacabbdbdcaabbbcbddababdabcabaabbbdacddaaaaaadabddbbbcabdbabbabbdadccbbcdcbdcbcddadcabbcdcdbbbabaacbcdabcddaacaacdaccaacacadadcbcadbdddccdbaccbddcdaacdcddadccbaabcaddcaaadcabcacadbbcdadbabcbcccadabccdcbcdacadbabbcdbdabdcdaaacbbbcdabdbcdcaaccdaacbaddadbacaccddbaacdabbbcadbddbdcdbdcbbbaaddaaccadcbdccccdadbcbbbadbcbacbadccbacdadcbbcdcdbccccacbbabdaddbbbcdcaaabddaacbcdadabbcdcddacbbdccbaabbdbaadbbdcdbabcdbcabdabbcddacdccabbddbdaadbcbadaccbcadcbcdadbbabaaabdbdbccdccbcdbadddbcbaaddddbabcdaddcacddbdbdcdadbbaadaabcddbddaacaccdacddbdbbbbacbbaacaadbbbcacbacbcddcaacdbdababdcbcabaabbacbcadccccdcabdccaabccabcddcddcddbbaacbadbcbaabdcdbdcdbdbdaadacddccadbcbcbdadcacacaccdabccbcacdaabccadacbadbdccdcdcdabdbbabbdbadcabbbcdaadccbaabcdabbcbaadbcaddaccbdbabbacadbabaabcadccadddbdababbccddcdccacacabadabcdcbaadbdadbdababbcaccccbddaadbabcaaacaadcbaadbbcdaabccaaabcdaddbbcaddcaaddacdcccbccabbcbbcdbabdbdbaddddcbacddadcbcdbbaddbddccbcaccacababbbbcdbcbabdabcaaddcddcdccdccbcddbbabadcdacdcacabbbabdccddaaabdbdacaacbbaacdbbcadcbcdadddbbcdcdbbabbdadbcbddcccbbddbbcbddbdadabbaadcbaccacbbadbcbbcdcbacaadbbdbadbcabbabccccbcddcaccabacdabbcdbaadcbaddbdbbdaaaccaacdcdbdcbcddbdabaccddcbacadacdaacbbdaccacbdbcdabaccdaaccccabdbaddcdcdadcbdadabacadddaccccbdadddbdbdbdabbcdaccdbaccdacabcbbacbadbbcddbacdaadcabdcadccbbbdaccdaccbbbbdbbcabadbdaacdcbbabbcbaaaaacbadacaccbcdbbdbadbbcddbaaadbdbdaccdacdddcaaadbdcabbddacababddadabaaacddddbcbadcccaddcdadbcdbddbaadbaaaccacabaaccabcacddaadcdacacacccacadaaaaccacdbdbddbbcdadddcaadaabaabbbbbbcddadadddbdbaddaddbabbaaddccaadcaddbdadacbadcbcbcaccadccabcbadccddcbcccbdddcccaadcdbdadadcbdddccbcbdbbbbadabacaccbbbaccadddaadabdcdccacbbcdadabbdbbcbadbadbcbabcbadadddcdacbdbdbcdcabcbdbbacaddcdcbcacdbacbcdcccaaaccbadaaccadbcdddacaccbdbaabdcdbbcadadbcbcabdabbcbdbacabaadccbcbbbcbacdbbdabbadddaadcbbbdaacdbbdadbaadaaacabdbdcaaacbbddcbcabaccaaacbbacddabcacaaacaababbdccddbbbadcaadccacddddcddbbdabbcdabbdbbcbacbcdaadbcbcaadbaddbccacdbaccbbbadcadcacdbcabaaadbaacdcacaabccddccbabcbdcabbbcadcbdbdabaddcbcbadbccbabdcaaacabddcbacaadccabadabbcbbbbccddcadbcbdccccccccdbdaccadbdcddbbdacadadaddacadbabdadacdacdbcdabdaaababadcddbaaabcabbdadcbbbdbcbbdcbdcdbaabdcabbacdbcdcbadbbbabacdbaddccdacdaabcbacdccaadbbdabbcbbbdddddbdbbdcddbcdbcddbabdcabcdcacbbdbbdbdcacacccbcbdaacbbdbdcdcbaccddaaccacabbcbaddaddaddaadbbbbbababdcccacbcabaabcbdcccccaabdbabdbaddbadcabccadbdcdabbbabaaaabbccdccbbddaabddadccabccdbbddbbcbbdababcdbadcaccddaddabaccdaabacccbddaacdbdcadcacaaaaacbaccadcddbbcdccdacccbcbbbaadbcaacbaaacbbdaccbbacdadacccdddcdadbabaaaccabdaabcbabdbcaacdadbcaacadaddccaaacddbccbadcaabaabcdbacbaabbcdddabcdbdbdbdbaacaabadadbbdacdccbacaddbbaadcbbbcccaddabbdcacdbaabddcbcbbcbaacdbbccdbcabbccccdabaaabcbcdbdcaccaadddbdcdddbaddaabbccaddbdbaacaccabdbcaabadabddacbbadbccbcdbcdabdddbbbbcbdaddcacbdbcdaacdbaaddcbdbacddacadddbcbdcadcdabcccaadcaacddbaaadbcdaadadaddacdbdbdbccbbcdddbdaacbbdccdaababacaddadaaddadddddcacbabbbbaacbbccddcbacdbaadbdcbcbacacbbaacabdbcdaccadaddacacbbcaadbdacdcccbababdbcdbcabbbdcccccdbbccccaaabaabbadcbcbcaccacbcdaadddaadbcabbccbddbacdaabcbcbcdbcabaabdddcdadaacccdbddadbccbdaadbdadbdadbbabdbcabdccabacacccbcddbbabaccbcadaadcbddbabcbcaabdbddbcbcadcdcacacbbadcdddabdccdabacadadcaccccccaccabaaccabbabbddcbddaacdcddcbcbbcacdbddbbbbbaccadcccabccbdcccbcbdababdabaaacbcaabbbbadbcdbbbbbccdbbbcaddaccbacdbbcdacbcbacbcabbcdabcbcbcbdadbbabccaadcbdadcaabbcbdabbcbbadbbbddbcdabdccdbddcabbdcabdcddabbadcbbcbbacbbdacaaacdcddcadadbdbdabdabbbdcaabbdcdbbcadbcbbccbdbdaacadccccacbdbbabcbddcdaccccbcbdcbdbdcdcaddadcacddabbddcbdcccacccacbdadacabcccdbcccadddcdbdbaaacdcbdcddddbaaabcccbadadabbccbdcdadadcbaacdbbdadaccadbbcabccaacabbcbbccbdcbabacacccbaaacbaabbcbdcbabaccdacdbdccdabbdcacbdbbdcddccbcccbbacdddccdccaaabbdcaddddddcbbcbddcdabbbcaadaabbbaccaacaabaaacbaadcdbcbddbabdaaabccccaacbbcccabcadaacddacacaaadbbbdacddcbcddabbcabbaddadabddbacbcccdaddacadcbdbdabadbaaabddacbaacbdabddcddbbcbbabbbdaccaabdccdbaaadbcbcccabbbdaaddaadbacbdbdbcdddbbdbaabddabacdbacaaccacdbdadadbabddadcbdddcaadcabbdbabddbadcbdaccabdbbdbaccaddbbdabbadabcacaddcdcccadacdcddabbdcbcdabdcabbdbcabbcdbcaacccbbdcdcccababcccabbcaaccdaaabcdaacdbbcbcdbadcaadbcbadcdbabaaccaabcdccccbadaacccabdbdacaacaaacccbbdbcadaacdcaccacaccdacdbbccdbccbcaadabbababcbddbddbbacbdadbabcabdbadabbbaaabaabdabbabdcdcccdddacbbcacabcabadbabaabbadadaccccdbacaccbdcdbbddacadccadddbcbdccaccbabcbadbdaabccabdabcacddacaccccaacbacbdcbbdddcabaccdcdaaaddbadcbaaacdcaacbccabbcdccbacddabcbdbdbbbbcbbaaaadcdacadcaddbbcbdbdacbcacbddcddabadbaabaaadcbaabababaacadbbbcbbdccaababcdbdadcbcadbbacacacbccdaddaaabcddabbaacaabacbcdbcabddcdcdaddcadaddabbcaabcccabdadbbcccabbababbbdaccbadcdbddabcaaaaacaaabdacbbacabdabbadaaacacaaddcddacadabdbabbacadacbadaddddacbddadabbbdabcccdadbbcbccadcbddcbddcdcacaddadaaddadabddacadcabdcccdbbcbdcdbbdabaddddbdcadacdabbcaadaccddaacbdbaaacdccaadaddbccdcbadbbbcdcddadbbccbdcadaddbaacbadaccddacdcddbdbdbddddadccabccbcabccdbdcdadadaccdbbdcabbaccdccaacdabccdcdbdabbacbdbbadbdbdadcdbaaadabbcbacbdbbdacdbacbbbbbbcccaccddcaabddacabbaabdcbcbbcbabacbdadbcbdbdbddcaabcbdadaabcdbcbcdcddcbbbdccbcadcacdcbdabdbaaaacccacbddbcadabaabdddbdaabddbbdbcadcbdcbacbbbcababcccabbbcaacacbbcbccdadddbbcbaaaaaaccdcaabdbdcddadbaadccaacbcbbcdabdbadccdbbaaddcbcbdbabdbccccbbcccccdabbdbdbcbbdcbdbcdacbdbbadbcacaddbaacbbabccccabcbbbbcdaccbdacdadbccabcabaacaadcdadbaacaaaddabbdddcbbcabbcdaddbdbacdcabaacabcacdbcaccdcadacadacccbcabbcdaabdddacabcccdbbabbadbcdabadbdddcbdcbbccbddaaababddbdadddbabbbdbccccdbadcdccbccbdadabcbbdbcdaaadbbbabdddbcbdabdbdadadcdcbbcbadddcccacbadbcdbdbbcabbaadcbcbcacddbcdcbcdbdcdadadaabcbaacbcadcdbbddaacaadddbbacadcbdcadbdcbbccaabdcaaaaaadcacabdcabaccbddabbdcaaaddddcacdddbcdcdbbabcbcaaccacbbbcabcabacabdabbbbcaacbdaddcbcddccccddacadbdbbdcadababddcbaadbdbadbdcbddbcbadabccdbbaaabdbaddcbbbdadcdcdcacccdacbadcaaccdcbacbddddbcdcbdacbddbadcabbaadcaacdcbabdaacccdacdbdaabccbbbccbddabadacbabbdbacabaacbcabdbcabacbbbcdabcabcaccbdbcddcaabacadaaaadadddbdcdbbaacdacbcaacbacbadaadcabcbaccdcacaddccabccaacbbdaccccbcbdbbcbaddbdbbcbccccbddaddacabbcadaabbbaaaabbbcabdcdcdbccccbbccaccacacddbcadddbbbacddbcdaabbbcadbbadcbaabaadbaaaadbaddacabaddabcacdabbddbdaacacaacaaaaddbcdbabdbdaccbdcbaddcbcbcdabccbabddbdbabbabdccbaddaabbbbababadbccacbbcadcbbcccbcabcbcdbabacadcbdcbbbcddaacbbbaabaaaadcbccadacbabccdadcdbacdcacbaadcdbbbdccdbbabddaaccbbbbdbbbddddbabacbdcdaacacccdbaccbbaccacdadaaaadcabbdabbdaacbcddaacacabacabcadadcababdccbaabbdaccbddababbbaccdcadbaddddcbaacddaadacccccbbcaadbdcbddbbcddcbbbbcadaccdcaadcdbaadccabdbaaadacdaadcadbcdbabcbaadbaabaddcadbdaababdbbaabcaacacbadcbbacaddccdacadccaccdcaaabbddccadaabdcbbbcacbabdabababddbcacacadddbddccccddaaaacadaacacdbdcabdcbcdddddccdcdbacaabbabdbaababcadababcbabbabaccdcbadadbddbcabdbcdaccbacbcddadbabcdaccbaabdbbdacdccacacabdcacbcacbbbcdbcaddbccacabdacbaaccdabdcadcabddaddbcacdcabdadadabddaaccdcddacbbadcbbdbabcbddacaadbbbaddcacaacbabccaabcdcbdbaaacabaddbcbaaadaaaabbcacbaacbccdddcbbbddadbbdcbccddacaccbdccbdcdadcbaacdaacdbadddcadbabbbdabbcbcabbacabbbaabbaccadbdadaabdacbaacadabcdaacbbdaaccddbacbdbcbdcadaadbadddaaaacdadabcdccaabdcddbdaadaddddccbcdacaadbccbcaaddbccaacccbabcbadbdadcbcddbaddbacbcabaddabbacddcaabbaddbdddcabcbcccdcbcccbaddbcaabdbbdaddaadcbddcbacadaccbbacbdcbcdbabdddbdbdbdacdaaacbccccabadbdbaaaccdbbbdbaabbcaaddcacbcbabbaacbabbdbddbdddbadbdabdaddcbdabbadcacbdddadcdacbcbddbaddccdcbcabcbdbcdcbbcdcccbbdadbcdbdacdccbbdbdcbbdcbdbadabccdbdaacdbbccbccdbdaddabacdcccbbbdcadbdcabbdbabbdaacddcddaabaaccdccbdcdacdbccdbcdddcbadbdccbacacdcaaabccbbbacbdbcabccbcdababadaadcdddacaccddbbbcabaacacbabbcdcdbcddccbaaadbbadddddcadbbbcadbaabbbbbaadadabdcdacbcccdccdcbdabccbabdbbbacccbacddbabdabaabcddacdbabbddcdadaaadcaaabbabbcccadcbaddcddaadcaaddcabcdbabdadddaabbbddbbcdbbbbdabdddbdddacccbaadaaabbdbcacdaccbdbddbdcbaaabdbccdddcdacbbdbcaddcabcbbddcdcbacbdccbdccdadcaaaabcdabaaddcaaaaabaabbabaddacaccdaabdccadabaaacbcbccddddcbbcabcdabdadaccccabdcbbacbcbcabdadacbccddcddaddaccccddbccbcdaabbbdacdcaadccdbcbdabdcabdbadaaddbcabcbadddbdabddbccacccaacababacabaabbccccabbabcbcbcbbcbaaaadbabdacabacacbbdcabaaadcccaaaadcabddcaccbdbbbcadcdadacbbdcbbbcbaccaaaaddcbaaaaccdcdbabccdacacdaacaadbcdcabcabddbdddaddadccbdcbaadcadaccddbbbbcbaccdcbdadbdabdadbaadaddbbcddbddbcbabcdbcdbdddaacdccbcacddcbaddcbddcdacacbdddcaabccddbdbdbbcacaaddbacbcdddcdabcdabdcbcbcdddbccacbbbadddacddbccbbcbbcabacabdbcbdcdcacbbcadaacdaabdcddabbacbacbaacccaaccdcabddcdccbcbddcabaacddcddbabbacbdbbcbacaaaaabaadbacabccabbcaabdaccdccbbaadbcbdbcadcabcdabcaddaabdccaacdddcbabcbcbabaccbbcabcabdabbaababbdbdbabaccbcacdddcccaacbbdbbaacbdcddcadbcbdacdbdbbaccbddbdbbcadcadcbcacabdacbbbdabcacabcbdadacdcaacddccbaababddabdacbdbbaddcdccabaabcababccddddacbdadbcadccddadcdbacbbdabacbabbcdbbccccbaadbdaadabcbacbcdbaccbbbaadaabccbdaccbcaaccbaccaccbbacacbbbbcdcdcaadddcbbcbcbbcbcabdbbacbccdacaaddcabdbacadcdbdbdcabaacabaddbabadbbbcadcaddbaababdcbbbbdadbddddadcadcdbbaccdbabdbdbcbaabcccadcbadbbddbabdbcabacdcaaacccaabcccdcbabbacdaaabaadbacdcddbcbbdbdbdcbadbddbcbbacbcdabbdadadcaaacccccddbcccacabbacdcbcbbcdbcccadcabcddaccbbabbccbcccccdcbccaadccbacdddcbcaaababbaccbdbdcacabdddbdbaadaddcabdbbababcabdaacdbdccdcaaabccdadbddcacdbdadcdccadccaadacaadccbddbadcdccdbccbcddbbabbcbddcddccdacbdbcbaaacabdadabdbabacbcaaabadcaaddabdcddbadccbbbcabaabcacdcbbddcabddcadbcddcadaaccadccddbcdddbabbcdbccbdbaabdaddccbabdabccdcdcbadcbdadcabcabacadbacaaaacacaccbdababcbdcaaccacdaddaddaccbcdccbaadbbacbcddbbcccdcbddabdadcadbddcbddaacaaacdcbbcddabadabacbbdbaddbadbbaaacdadcddcbdbbcdadacdaabcaccdbdccadacadacdbacdddaadabadadbadbabbbdcbdddcbcbabccdbddacbabddbabbcaacaccbbcdccbccbcacdaddabdababaadaaaabccccddabadbdcccadbdcdbbadbcdcdbdadbbdcdcdbbacbbabccccdcbbccbdcdcdcbbdcdabbaabcdbcabdbaaaabaadbcbcbdabcddadddbdacddbacdcccdccaccadbaabaacddbabddcaccbaaaadadaaaacbbaadaacdbacabbbcbadcdcbadadccacaccadcbbabdbaddcdccaadacbdddaaabbccbcdcaaddaccddadcbaabdabaccacbddddbccbaddbbacaddbadbccbbaaaddcddbcbbdabddaaccacdbdcbddcabaabbccdbcdcdcacadcdbddacaadbcbbbdacdabadbaadaccbabddbdbcbacadacadaaadbbccacdbdcdaddddddcabddaadbacbdacbaadacdccdabacdbadcdcbcdbbbbcbacdbadbacadcddaabdbadbcbddbddccbdcdcdadcdaacabacbbcdbcadaccbadacccdbddbabbccdadddccbdcacabdddbdbaccbdbdaabbcbdcacddccacababdccdadaadbadbacdbcacaabacdbaacbaacacaacadcdbdcbacbbdaccdbaaacaadccccdadccdbccacdddaaacdccaadcccabbadbcacadcbabbcdcabbabbbddbaababdccddcbadabcdccaabcacadcaabaaddabdadbbacacdacdbbadddadbddbbdbbabbcdbababbbddcbcaabccdddbbbbbcababcdbcdaaadcabaccbbbdaacbadbcdacbbcdaaddccdabdabcbabcdaaadadaacdaaadddbadcccccabbdcacbcaccbddbacdcababcaabddaabbdaacaaddadaaddbbabdccabbdacdddbdbaaadcdbcbbcbddacccdbabccccbdbdbabcabddabacccbdbcbabadccdccbbaabdbacaddbacbcbccbabbccacbaccbbcdadabbabdbabbdacaadbacbbacdbaaabaadabdcacaccacdbbadcbddcaccabbbdcbcadcbdaddababbbdacbcdabbacbbbcdacdbabdbadcbdbaccdadaadadbadacddabcaabbccdbccdccdabaddccbddccdddadabdbbaabdbdbcdbcacbaadcccbabbbdadabbaacdbcdcdbcbcccddababdcadadabaaadcaacdcbdbdaabbddccaadcdbdccacccdadbcbdadacbadcccbbcdbbbabddddcddccbcdadbbcccdcbbacaabdbbadcabdbcbabbaddaaababaaccbadcdbdabcdaccdabaaccacbbadbbbdbbabccacdbcbdcddcddddaaaddccbabdacdddddbccdbbcddbddabbcddabbadcbdadbcddbdbccdabcdcdddbdccccdbdccaadaababcdccbdcbacabcbdbadcaacaabbdbbdcdddbdaadabdbdbaccacdbbdaabbbbcbcdcaccddbacccaccacbddabbcacabcaddabbdcdddddaccbbcbbcbdccbbdacaaddabbabcdbcdbdacaadabdadabcddbbaacdccacadcbabdabcbdbbcdacbccdadbbddcbbcdaaaadaacdabbadacadcbaadccabbdcabddbbddacaabccabccadcabddbaaacacaacdbdcbdcbbddaccbbbadddcbdbbcaacbbacaabbbdbaacdabcbbcaddddadbccdcdcadcabdcccbccaadddabbdcdadcdbaadbabacccbbbdaadcaabacdcacabaaaadbbdbadbdabcdbddcbcdbbdabbbccbccbaddbdcdaacbabcabaadbdbbadadbaabacacbcaccddaddddabcbdadddadadbcabbcabbbddabcaccbdccaaaacaccdddbabdddaddaacbacbacbdcddbabdbbadcbbddddbdacccdbdcadabdabdaadbaccaaacacadaddddccdbacdccadbdaccdaccdbcbcbcbaabddaddabdbdbccaddaddcadccaaaaaababdadccdbddacbaaddabcdaadbbdacdbcbadaadadcbbbbabadbabaadbaccccdddbbbdccabdddbaaaadacbabbdacdacdcabdbaacddabcccccaacdcdbddccdbacdcbcbaccdbdaccbccbbabaabcddaabdadccbadadddcdddcadacbbabadbdbadbbacabcccbbabdabddccdacddcaddbddbcdcbdabbccdadcdbddacaccdbbcaaaabaacdbacbbbddcdbadaabdaabbbbbcadddcdcbdddcdaadcbbbbdbadbcacdadbbacdddadbdbbdbaddabadacdbdccbbdbccdacabaddaaddacaacbdbddbdcdcbaabbaadcadacabdbbcadcabddbccdabdcdadddbbcbabaaddccbadcbacbbdaacdcdacadabcaddabbaccddabbdccadcabacbcabccadbcdcaadbddaddbdbbddcbacbccacccbcbdaddaaababbbcdcbcadddbbddacdddbbcbcdbddbaaaacddddaacccaacbacdabadaccdacddbbdacbabacccdbacdadcacdbdaccdbbdbccbabbbbdabbbdddabddcdcabddadcdbdbcdddbaaaacbcadacbdbcbbddbdbabcdddcbcacbdcaaabbdbdbbcbbbddabbbdabbadcdacbdabaddaabbbacbbcdbcaaddbbbdcadbbbbaccabcbbbabccbcaadddaddcddadbbcbacdcbbcdccbbaddaddccbccadddccdcdcabddcdbcbcdaccdbcadbddbbadddaadbcaaaabcacabbdccccddddadacaccabbdacccdcdacbacccccddbdaacdccacacdadcacbdcbbbdcbccacdbacdccbcddbcccdbdaacaabdacdaabdcddbdaacadbbcdbdacdddbaaccadbbbbcacbdccbbaacbbababaaccbbcdbdddbbdacbabcdcccbacddcadbdaacbdcccccacbbddcbdbbccdcbbabbbbcdcabcaadcbbabdaddcadacbcaacbbbacccbcacbccbddcadadcddbcabbbdbdbbdbadbcabacbcbdabbdbadadccdabdbbbacabccdcccaaaabccdcdabbdcdaacdcadcacbacabbbcbbabacabcadbdbaadbdaaadbdcdcdcddddbdddaaabdcbcdcdddbdbcbabcaaccbcdbddcadacbaccdacabaaaacbadbaacccbababacbbaabcbcdbcbcbcbdbaadabbcabaabbbdbbbadcccbacabadacacabddcacdcbcddbcdbdcccddcbbcababdccaaabaabddbdadcacdcadbccabdbdadbccddabdacbdddcdacdcdcabcaadaadbbdaccbcdbdcdadbdcbbabbcbcdabcbbdccadbdaaadababaacbcbacdbaadcdaccdaadcdabcacdaacdaabbaacdbadddbdabbccdbdaddbabdbbbcbaadddacccbddbcbdaacdaddcdcddddaccdbabacbadbbadbdbbcbdadadcaababbcabdabdaabccdbdcacbdbdbcdbcbdabcaddcddcbdccdbcabbdacbbadaaaddcdbdbcaaccddbabdcddabbdcdcdbbddcacbdcbbdbddcadbcabacbbacacaaabadaccabbdadcbabdcbdccdcdadacddaabccacbcadaadbcddbbdacbcbccbbabbcddddabdaacbadcbcacadccccdcddcaadcbbcacccbbdbcdbdcacdddaccdddbdbbbbbacaaadabcacdccbbaadbacadababbbdccdbadcdaddaabbababbacdadccbbabbdacaadbcbdbddadaddbbcdcdccbbbdacadacbabcbcdaacbbadbadbdaccdbbbcbbcddcbdabcdcaaabadbcbcdaddaacabcaaaabdbacabbdddbdaaccbcbbdabddaddcbccbdccdbcccbabcacdccccacacdaaaaabbbbacdbcccbdadcdccdddcccacacbaaabdabddaabdadbbdabdabbbdbaddacdaaaabadbdadcaabcdbbddccbaccabcaddaddadacdbbabcbdbbbbaacbabdaadccdbcdbdcdbabbdabdcadbbaadcacaabdcacbccdcccaacbcbabdadbccbbaccdcdadacaccbacbcacdcbbcabcddabdabdcbbaddbdcbcdcbbcddcbcbcdacaccddaaadaccbcbabdadddcbbadacdadddbabcdcbaadaccccdadddabdbbccbbabddcbdbbbaacabdbaaddacdbccacccccbbddbbbdbcaccccdddaaabacbabdaddbddcadddbdccadbcdddccbacddddcbcadadaddcdcaabbbabbbcddadcbcbadcccaaccbcbacddcbbadabcccdbbbbbddcddbbabbccbcbaacbbbaccdbcdcdcbabdcabbbdcadacdcbaaccddcdbcbbdcadcaaccbbdbbdbccbdaddababddccbdabbbcdbbbacbcacdbadadddacbddabdccaabdbaacbdacdddaabcbadaacbbaaabcbdccaddabadaaacdddaadcaababcdbbaaadbccdbbdacccabbdcabdcabddaababcbbaacaacabbadaddcbcabddbbbdccddabcbdabbcddcbcdacbdabcbcdbdbbaddbacabccdbbacbdbaababbacbcdcacbacdacbaccaadaacddaddbacbabdadddcdaadacdaddabddcaadabccacbdbcdccbdbbbaabbbcbaddcbccdcaadaababddaacaabdcaabddcddbbaaaccdadcabdbaacdbbcaadacdbcabadacaaaadcaabcbbbcdcdadcbbcdcdbacbdabdbdadbccdccaaacbbaacdbdbdbadbbddadaddadcbacccddadadbdbbdcdbdbadcdddbaadddcdacddaacdbdaccadabcccaccbdbaaadcbcacacadacddcccaabccacacbbbdbaadbaaccdabaccadbadcabbbcbdbabcbbcbcdcdbccdaaddcddcdadbcaaddaadcddbdcdabcacbbbcdaccacabbdbcdaacacbaaabbcdbdcdabacccadcdccbdbcbdbdcdddcabbbadbcdbbcddbcdbbbcddacbdcdddcaddbaccdbadccbdbbdaccdbdacbbcacabdbcabbccbcacdcccabbbbaabdabbbbadaacaccbacbbababbaccdabaddabddbcadcabcbcbbacddbbbbaccbbbccbabcbccabaabcdaaddddaccbcacbbccccbcaadcbdbbbcbbadadbdaaabbdbacbdbccccdbdcabbabddcdacdacdddaaddcdacabadaccdbdabcaaccabbdacbbbacbdbdbdbaaddcccadbcddbcacaabcbbbabaddcadabbbaaaccadcbbacbaaaaabdbccdbaaccbdacbabdacbdccdababbaccdcdaddccdcaabbcabbccbaaabcdcdaaaccdaaacdbcddbacdddcdbadcbdcbccdccacbdaddcdbbdcddddcddbabbddbcabbdddaddcdbbbdcdacdaabbbabcaacbbcdbdbbbbcccbaddbaacdcadcdcaaaacbcadbaacaabcdccadcdcabddbcadbccadbbabccdcdcacbcdacbbcdcbbbacacacdbbababadcadcdbcaaadbabcaddbbccbdbcbdaccaadccdbcbbaaadcccbcbabdbbdbbccbaddccbbdccdcaaadbbabbbdbcdadcbabbaddcabcccacaaaaacdbcdcdcadabdcdcabdcdabadbcdbcaddabadcccdbaccaccbbaddaccbbbcbcccdbbacacdabddbdadbbbddccbcdcacdaabcbdbdadadbabcacaddcabadaabadcaaadadccacbdaadbdbddbccacbccddddcaabbbabacdabcdadbbbbaccdbaaadbbccddbcbbbcadbadaadacaccaddbbbbcdcbdddcbacbcabbaabbaadaacbbcdcbbcdabadbdbaaaccddcbbabbbcdcaacbbddacabbdacbadabaaddddcdcbbbabbcbcabbddabbbdacdcacccadacdbdacdadccdabcddaacbcaaaaaacaaaccababcaabaddabdabdcabbbbdacdddbdbcbddadcacaaacbdcbadbaabdbdabccdabcccbdcbdacaddccccadbdcaabbddcbcbadbacdabbcbcadbcdcbbbaabadbcacdabbcdacbaacabcbdadbcadddadbcbabbaabbababccddabadcbddacaabaccbbaabdbacbcdcccadcacabccbbdccbccddababbacccbccdcaabadbbbbadacbbdccabaadabbccabbdccaabccdbbaddaccddcacbaddccacdaadbdaccdaabddbdbbbaaccabdbdbbbddabacaadadaadcbabbcdaadaddccbadacbdbaaacabcbdbcbdbccddabbaacaacbbbccbdadaabaccbcdbacccabcdaddadcccbbadadcbddaaaadcbddcdadcbbbdacbcddddbdcacbabdcbbcdbdddcdacdbcabcbcbbdadcadadcccbbbbddcbaabbdcbacbbdccacbcdbbadbcbdacbdbcbdcaadccbdbccaaccdddcbdccaacbddaababaadbddbbbbabadbcaacdcdbadaaddbbcbccbddbaaddccaabadcdcdadbddbaddaddbcdaadcbadcbaabcdaddbabcbcdccccaaddcbbddbdccdbbabdbbbbabccaccdcacabddcbacaacdaaccddcddbacdabbbccddccdadccacccccabbcdcaaadbdcaaccbccaaadccacbbcccccdccdacdadbcadccbdcbccbddbdcabcbabacacdbdacbadddcbbadbacbdabdcbbcabbdacbaaabbcabbdbcabbaaddcbbbcbdaccbbdbabcdccbdbdcddbbaadccccacaacadcadccccdbbdaacadaddcdcacddcdbbcccaddbcbabbbcccaacaaddbdabdbcbdddadcddaddcccaaddbdacdddccaaaddcacaccbbadbbdcaaddccadcdabcbcbdbcdddbcaaababcbbdababacaadaaadcaabbcdddcadcddacdaabbacdadaaccbcdddbadbabdcdaadcbddacdddacbcadcbcdaccbcbadcaaabccdcddccbcabbdbbbcdbdabcbbadcaccdddaabbdabbbbccdbcabcacddbaaacdbabbcbcdcaddbacaacadcbabadbbccdcbbabdcaabcddcccadcbcdcdcabdbcccabcacbcdcdbbcddacbbbbbdbdacbdacddcbacbacbbccbababdaabddbbbddcbadaacadbacbdabcdddabdccdabaacccbaddbbbdbdcbbbcbbcdbbbadcbacbacccabcdbbabcbcccdcaacabdcdccbaadababaaacdccabdcdadddbcbaadcaaadbdbaadababbacdbccccabccdcbddabcacbdadabdbbabcacddadaacbbbaaacdcaccaaadbaddbabbbdadccccdbadcabaccaddaccbccdbddcdccaccccbabcdaadcacaabcaaaaadbcaadbbdabdacbbaddcdaadddccdcabadcadabaadadbdaddcbaddabccccdcbdddacbbaddaadcccbcabdbdbadcbcbcbcacccbbdcacdbbbadbcaadbcdacbaaaccdcbbbadbadacbcdddbdbddcadbadbdadaddccbdbbdabdaaddcaaabdaddddcdcbadadbaccdaddcbdadddcdcadcaadbbcacbcccbcdabaaaadcdaaacbadabbadacbabbcbadadadbdabddbcadcbdacbaccccbadbcbbacdcadabaddbbcaabbdbbbacbcbacbbcbbdbbacbadcbdddcaadaddcabdbdabdacaadadbbccadbdbdddaaadacccabdbaabcbabddcbbbdbbabbaddcbbaaacbbdabadbccbddcddabcaccaddaaddacaaaabaddcdcaacbcdaadbacbddbaaddddadcbbdbbbdaddadcbcbadbcdccacaadcaaabccdbadabdddcacabbaddcbaccabbcbcbcdccdbbbcabccdacbdaaacabcadaaddbcaacaddabbacaadddddaacbaadcacabadadbdbdcdccdcabadcbdcbadabddcbdbbbccdaadadcccacaadbbabcccbbcbaaacaadcbadadbcaaaaaccbbbabbbcbadcabacbbddbacdccbabbbdccbdabdddbdaacbcdcdbabcdcbacccccbbbacabdcaddcdcaaccbaaadbdbcacaccbacacddcddaaaccbdbdabccadbddadcddbbddccdaddcadcbaaaccbaabbadcdaaddacbdabbcbbadabdaccddcabcabadbacacacdabdaccdbdcdacccbcaabcaaddbbdbcacdbabcaccbbbaccddabccdadcbaadbdccbbdccadcdddabbdcadadbdbdaadcaabaddaddadabddabbacbdbaaacdbaabaddbcbdbcddbdaddbaadcadbcbdccdbdbacadacacdddcccabababcbbadabdcacadccddcddcbdcbbcdcacdbbcaddacddddadcdacddbaabccbaccaabcdaaabaacacacbacbcdbaabddcbcaaabbbddccbadbcccbdabccdcdaacbbbccdaccabdbbbbcdaaaaabaabbdbccaadcbacdbaddaddbdcadadbccbbccdddddcdaddbcbdbadcbdcabdcacbaabadadabcdabdbdababdbdabccdbcccbcadadaaacbcdccaacddbabbdabbbddcabacbddabcacdddaadcddbcddddbccbaadabdaaacabcbbbbadaddbcdbcabbcaddbadcbdbdbaccadccbcbabdbadabbbaaccbbabadbcbbabccdbccdabcadcbbccaccdcbaadcacabdadcdccbddcdaddacacddcaaaddaabbbaabbacdadcabaddbaaccdacbddcbacbacacadcdbbaacdbaccaadbcbbdacaadcadccdbccdbcccaaacabbcbbbbbdbcbbcaaacbabdccdbcadbcbacbcbdcccbdadaabccabcdbccccbdabcbddadcdbdbbbaddcddbbbcabbbbaadbbadcacdabcddbcbadbaadddddccbcdbacbbbadcdbcbaabddcaccabbcddbccdabdadcdbacabcacddbbbdaabdbaaacdbbcbcabdbaadadacbaacacacccbabbcdcbaccadbdddbdcbbddbcbdacdaadbcbabdbcbbadbdadaaaddbaabaabccbbabbbbbbcdcccccbcaadcdcabdaadcbddcbdbcabbccbdaaacdbaadbdddcddacadcbcbaabbbbdbbbdabcdcdddcbcabbcccbbcccdbdcbabcaabcbbcbdbbcddadacbccccbcabdcddddbdaaccdbbcddcaccddbdadabbdccbcdbaadcbcbaadabaaaaabdbdddbadcdacbdbacddbbcbdabdcdcbbccdbacaddbcdbdaaaacbadcbabbccbbbbbaabdcdbbbdacaabddccbabcdcdabcbdabaadcbccdddbcadabbaacddabcabcabdbccdcacabbdbadcdcdcaaaabaccdbccabcbcddbacbbaadccaabdbacabddcdabcadcbdddaddacbcccacabadaddaacadbdaacbadbbcdbcccbaaaadadaaaacabccbccddabccaadddddadccaacbabdddaaddaddbacabbdabaabbdccbcbdbaababdbabdbcaabcaadccbcdbbddbbbadbbccbcbdaddbcbdbbdbabadcbcacdddbbbaadbdbbcbaddadddcccadcccbdcbdbcaabaabcdadcadcbcbbddabdacaabaabcaacbbccaabaadcdcddccdadcdaddddbcadbbaaddabaadbcbdbabaaabacbbdbdbdbdadadadddabdddddaababadcddabdcddccdcbbaabdcccdcaaadcaccabcadbccbaabccacacbdbbbdbbcbbaaaaaacbcbbadcbbccbbbccabcbcdbbacbdadcbdaabcdddaddacabcacadbccbbddcccdaccdccaadbbbbcdacababcdabbacdbdbcbbdacbdbcbbbbcdbbccddbaccdbbbaddbbaccbcdbadcaaddbcdbbaaabaaabccbbcabbbdddbbcbacadadacabadbddcbabcaababdbcbcacaadaddcbbcccadcdaabdbdbcddcbbbbcdbbbabbcdcbbcdacacaabaaacaccddaadbcbdabdabcbdadaaabbddddbdbbdddaaadabadbacabdbbbbbccdbcccdbaaadcdbddddcbabdbbddacccccacdcdbadbadacdddaccdcbcbccbcdddadbabaddaacdccbdbdadcccdadcbbabcabaabdbcaadadcccdcabdaadbcdabababadcacadcaccddaadacabaddcbdbcdaacbcacdbadacacbcaadcbabdabcabddbabbbbadbbddbdbdaccbbcddbbccdddbbdbbbdbcaabaadcdcccbdbbbabdacaacaabbcccddbcbbdbacaddddabadabccacdadbbbdcbaddcdddbdadcaabdabbbcdaddcadbcaabcddbbcadcdbbbbbaaadbbdcbdbacaccccbcadcaddbaacdadabdabddddccaccddbbcdbdccbbdadcbbadabbddacdbdccdddbddbcddddccbbcabaadabbdaabdbddcdddbaaacabacbaacbdcdaabdcddabaaadcdababcbbcacddbacccadbdbcdbcbdcbaaadbcaaacacaacacddbadbbadddacbbddbdcbcbdddbdabcbcbabccaabbcadccadabdccacaadabdddcbdcbbbbcbbabbabbbcbddadbbaadadabcbccbcbddaaaabdcbccbbdcdbcdababdcccbccbabcbcabcbcccdcddbbacabdbcaccbbcacccccbcbdadcbbcaddcdbddbacbcdaccdcadcbadcadacdbaddaabddcbabaadcdbdbabdacdbdbadadccdcbdbdbccddaaadcadbaabcdbdbcdccdbadccddbabdbcdbbdabcdccdccaccabbadbbcacdbaaddcabaaaadbabadcdcddadbaaddbccaabcdbabbcaacbabcdccdacdbdccbbbcbdbcdbccbbaacbbbbdcadabbbbcbaaddccbdbcdcccdacccdbddacbdabbcadaadcdbcacdcdbacddcbbbaccdacacbcaaddbbbdbadcdcbccbbccbaccdcbcadcccabcacdbdddabaccaaabbcdaddbdbaddcaccccbdaccaaadbabadabcddbbbabdaadaadccbcbabbbcdcbbbcccaacdbcacdddbbbcbcdbacbcbbaccbcdddabbabdaaabcdbaadaababccbdaabaacbaacdbbadaddcaacddaaddccbaadacddbcdaccabcabcccaadbcbbbacccaccdadaaabdacdabddccdcbabbcbbbddbbabdbbabddcaacabbcbdbcbbdaacdabcddbcddddbababcddacabbcbbddcdbacdbdcaaadbaddbadccacbabbddddacdddcaadddbbbbcddcdadcabaddaaaaadddabaaadabaaaccccbaaadaabbdbbbbaddcbdbcaacccacbaacbabcbbbdbbbcdbdacdaaacaabaaccaaacdbdcdcdaaaadbdcbdaabcacbbdcbbaabbbddbcccbdbaccacaabcddbacabadbaaacdabadacdadddcccbabddbdbbbddacacbdccdbadcaacbaddcbdacdcaacdaadaadcddaabdcddbdbccbabcdadadbccbddabcadcaccdaddbddcccaacbabcacdcccabdbcacbcdccdcbdbaaddbacbbdccacaacddbdccdabadbdcbdbcbdadbdcdaaddcdddbadcddaddadaabbdbcbddddcdbdbdaddbdbbdbcbdadddbdaacbdcdcbbcdacdcdbcddccadbdbcaabbdcdcbacbdbbcbcdbaddcdcabbdcddbddbabadcdabdaddcadcdadbbccdbddcdaaacadcdbdcaccaacdaadbabcdcdcbdabdbbbcdccdcccacdacbacbabbdbbaacdbabaacacaccadaabacabdabdabacbdabadcabbabbadbccdcacdcbcdcdacababbbdbccbacbcccabbcdacabddbdcabaccbdadbbdbcbbcddcadcddcddbadadbdddcdabcdaccaccbbdddcbdbbaddacbdbacdcbcdbdbddaddddbbbcbcbcccddcbcdcbdbabdbadbbbdcbbdbcacbcabadbbbbddadbdbdcbbacacddacbaadabdbabccdabcacabdcadccacdbcaababacadadcdacdcbcbcbcaadaccbbcbaacabaacddbaabdbcccabcdcbdaadbbacdcdcbcbdabacabbcdbaacbcacadaddadcbbbabbaabbacbacbdabbaacdabaaccbdbdcaacbacccacdbbbdadabbdabacdbccacbdccababcbbdbdaaddabbbaaddddbadbddaabacbbcbadbaaabcadddddbbbdbadbabccccbdccdabdbbbdbcaaacbababdaaabacccadaccbcaabddaccccdddcdcaaddcaccbbcbcdadbbccdcddcbccbbcbcaadaddbbcdccabdacbdccbacaadcdabbdadaaacdcdbbaddccaabdbdaaaddabbbbbbdccbabbcdbdbbacabdacdaabacbaabbbbcbddcdcbcaabbcabadabadaddbdbbdcacddabccccddababccabdcbddddbbdbcdccddaaacadbcbbcbdaccdbbcdacddbcaabaadaddbcadbdbadcaaccbbddccbdcdbdbdbcddcbcdbabadccbcdcabacdbdbddabdaddcccdabdddccadcdaaaabadbccbaadaadbaddbddbccdbdaccddbaabdbdaccadcdbbbccbdcbdbcbbdcccadcbaacdbdacdacabcddbddddacabbcaabddabdbaddabbddcdacbcaccddadcadacdadadaddaddbdcaadadabbdabccbdccadccddbadacbbbabacabbbaddcbcdcdcddcbbbddbbbdbdabbadcbbabcbdddabcccadbccabacabbdacccbddbcbddbccdaddaaacbdddcdabddaabcbbcbddbcaacbbbdbbaddcdabcabbcddbdadbdcbdbcbdbddadbcbadabcbbadcacddbcacacbbbdbddbadcddaabbcaabbacddcdbbbdddcddcccbbbdcabdcbbaadbbacacbdadcccdcdbbcacdaabcdaddbaaabadbaabcaddcaaccdbdcbacbbaabadbbadccaddcbcbbcadbbabacacdccbdabbbdbacbdaacacbabbdabcbcadcaabbdbacccbcbacabbbdabcbddccddadbbbddaabadabcdaddabddcbbcbaadbcbbcdbddacbaacccdcdccddcbabbdabcccbddadddcadccabdccdddccbadadcdaaaabddcabcbaabacbdcabacaabadcdbabbbcbdcccbaddabdacddbbcdbcddcdbbcbdbbcabcdcaabdadbccdbccadbcadabdaaacadadadbdacdcacaacbdddacdaddbcdbbdabcaaacbdbdaadccbbadcacbbbddbcabddacadcbdbacbbddacdccccadcdbbcbacbdddddbabdadabbddacacbdbcdbbbadbbbbdcacacdabadacddbbbcdabadaadddacacacbcbabcaccacddcaaadddbacadccdacddcdddaadbcbaacdbbdacbddcadadcbdccbbaccaddbcadcadabdbabbabdaaccbcdbaddabcbccdcabbbaacababadacabcababcbadabdaddbcabaaabdcbbddcdbabaabaabccbcddaabaccbddddabdcbdaacbadbbaddcdbcaacbabbcaadcdccdddcccbbbcaccbbaccdbacdabbdcadbbaddcaddddcaccccccdbcbbbbcddbabcadaaadcaddbdccabbcbadccbbbacababbbbdaddadbccabdccccdcbcdbabbbbccbadacccbbaaaadabdadbcddbbccbbacbaabdadaaccadddcdbbdcbbdcaacbbbcbdacaacccdbbdaacdacabbadcacdcacabdbaccacdcbcbcabddcaadbacdccdaaaaccbbddbdadacddbdaabcaaccbbbaddccaaaddacabaccddcbdddbbacbaabadabbadbadbdbdbcdcaabbaccbababdbccdbadacaabbbbcabaaccaaccaadcaccaccadbccbabbcbdbbababcacabacaabcdaadbdbbdbacbbbaacbcbabaabbadacbcdbaadadbdbcdbdddbdcbddbdbbdcbcacdbccbbccbbcabbdbaadbbddddaaabddacaacadbdbdcbacdddcdcdbdcddddbdbbcddcbcadbcccddbacdabbcbbdbadcbbbccdcdbdbdaadbcccbbbadbaabbaadbccacadcbaddaadcaadcabbddcaacbdcdaaddccabdaddcdbdbbbbdaaddcaadcadddcbbaacbabbccccabaccadaccbdcccaaddbccccdcbbbbddbadadbddcccaddaddbdbaddabbbbdabddcbbcbaabcbcaddacbcbbbdabaccdacbadcccbcdabcddbdaccccadbdabdcbcacababdadbaddccddabaaabbabcaccabdddbdddabcbccdcababaaaacbcbbbdabbabbacaddddbdccbadbabbbdbdabdccabbbcbaccaabbdaadddaaabcbdcdbccdccbddcbaacbdabdcccccaaaaccdcbcdcbabcbccddbacdbdcacbdbbbdbccacbdbabdadcaccbabcbccbbdcbabadbdbacbadbdccdaadbaaddbcbaccdcbccbcbaabccdbdcabbdabbaacddcadabadadcbabccdacbddadcdbccdaabcadbacbbdcbadcaadadbacdaccbabbcabbaaacdbcbacaacaadacacdbbbddacbdbdabaaaddbbdcbbbdbccdbdbaacdcadcacdbabbaddddbddbccccbbbcbccadbbcccdcccddcdbacddaabaccdacbacadacdcddcbbaabdaabbaabbaadbacdcdaaadddababcdccabbdadacddcaadddddbddabddbaababcbcdbdbbcbcadadbddcbdabbbdcdbcdbcdcacdcbdcccccccaddbccbcabcadbcadbbbadcdbdddbdbdbcbddddaddbbadcbbbadadbbdbdcadaadbcbdcdacacdaadbdabdcdadbaaaccaaaaccdaaadcbbddbdcbabbbbadcccbdddaacacbccbbdcadbdaacdacbddbdccdcdbcbdbcdcdbaabbddababaccbddaaadbadcbabadabbbacabdcaadacdbdbcbcccbbdbdaaccaabccadabddaaccbbdbcdbddddccdbacabbbcbcaaddcadbddbdadbacbdcbaabcadbacbbcadbbdbdcbacabcabcaacacadbdcadcdbbddcbccccdcabbcddbaaaaabadabcbabcaddbcdbdbcabcacabcbdadddadcaadbdabbccbbaacacdbcaadcbddbbabcddcdabbdddcaccccbdaacddccccaccaadaadaacbabaacbcadbdbcacdddccdcdadadddbdcccdbbbdabdcdbbdcacbcbdcdacbdcabbccddcdcbcbdbcadcdbaacbabcacbbbcddadbccbbdbddaddbaaaabcbbabdaccaaabcdccbcaccdaaddcacbdddcaccbbdcaccdbaaacbcbaacdbbddadadccadbcdaabccdabcaccdbabcbacddabbdccbddbbdabccccdaadacdaacbbddbdbcdbbdbcaacdbbacaabbabcaccccccbabdbdcdbaadacbdabacacbadacbbdbccbabccdbaddabaaadadabbccdcdccbdaadbbacbcaaddcaccbcbaaccdaccbaadcbdddabcaddcbcabdacdacccbbaabaadadabbcdddccdcbbcadbcdbdcbadbdcdbddbdcacbddcaddccdcbcadabbabcbdabaddbbcccadbbbbaaadadcabbbadaddcacbbaaaaccbbddddadcbccacabcdbdbdbbabcaabbcbacbdaadcabdadcccaddaadccdccdaabbdabcdaaddddbdcddadaccdaaaabbbdcdabccabbadabbadaadcdccabacdbcbaddbccdcdaadadccaadccdaababbdccbacbdcbbccacdababdcdcbcbabaadaabccbbdcdbadadbacdadbcaccabadbccdcddbaddbabbbbdddbbcccadacacbdcababccbdbaabbbbaccdaddbbcbdddbcdcbacababbabbdbcdcabcccccdccdabbadbdadbdadcaaddccbaddddbdaccabcacccddbabdcbbabadabddcbdaacbacbbaddcddcbacabcddcaaacbacacabcbdbdcddbccaacaddacbadbcabbacbcabcddcbaddcabbbacccabdacbcdcdaacdabdcbaddabcbaddcaaadbbacddddabcabddcccbdacaaccccbddcdccbbbbacaaccdaabdbbdbcadaaddcaccabbccacabacacdbdbacbbddccdcbaaccdbbaacbbdabbaabaaadbcbbddbdaabcdbcdaaacabacddcbaaabdaaabbbbbcbacaccacddbccddccccadcdadbabccbcbccbabddcacdadacddcdcadbcbbbcbdcacbdbcdabbbcdabccccdcadacabacacddbaddbcdabbacaacababcccabbaaadbabccacaadddbbbbcaabcddaddbccbaaaadabcbddcbdcdbdccddcdadbdcabbacadccdcbcddabdbaaacdbcbdabbdbdcbccadaacdabbdaccaadbddbccdccddccbbcadccbaccadcdccabbacbcbdcddbdbddbddbcdbbcacabbbabaaaaddaabacbdbbcccbaaccdbacabbcbaadbadcbacbbadcbdababddcccbddabacacdbdabbbdacaaaaaacbcbaccdaaabaabaabacdbdddccddaccbdacbcabbbcdbaaddbbacdbcbacbdabcaccdcaadcadcbaddbdcadcbddacadccaaabcabcdaccbcababbccdcddbabcdaacbbbcbbadccbbbaacbbbcbacdcbccdacbdaddbdbdabdaadcdbcbbbdbcbbcdbdbcbcadddcababbdbbbbacabadbbadbcacbdddccacbdacacbbcbcbcabddcccdcdbcddbabdadbbcdbbadacababbacaacacbcddcacdabddabbaadbabdacbccbbbcbbaaddbcbcadcbcbddaaacbbbaabcaccdbccbddddcbbabcbabccaddbbbdaddddbbbdbcabdbacbabdcadddbaacadbcbdaddadcaacbddccdabadcabcacbdbaccacadadbadbddadddcadacadddacbadadcbadbcadaababaadadadabbdcacbcabbadbacdbbcbadccaacbdccbacadbabdaacacdadbaaaaacabcdcbcaacccdaddcdbdccbdbddbbcbdabcddddaddcbcdccacdcbcabacaabddbbdbcdbabddcaaadbdddbadaabcddcdaabdccdcbaddcdccadcabacdadbdcacaccaddcdbadcaabcbdcbadbacbdcbacccbacdbaadcabbbbaaccdabdddacaadbccdbbddccdddbbbccddccdadacaacbaccadacbdccdbabbcdbdcaddadadadacacbbcdbdbbcbddabdccdcddbbddbdacbbcbabaaddbabbdaabbdcacabcabcdadbdcbacabbcacabcbdabaaacdacdccaddcaabcdbdabaadcccbdbdcabbdbacdacdaacababbcbdabdcbcddcbadacbcaccdbabaccdacdacddaadcccaddcadcadacdcbbcdbacbddabcdadacbabadcbbcdaacddccdbbcbdcacccdccbdccbaccddababdadddacadbabbaaaccabdbbadbcabcccccaaddbbdacdddaadaacaaabbaadccccdbdadbccaadbcbcadbbbcaccaccadcabaadadbcacdaaabbdcbacbaaadbddccabdaadcaadcdaccdabcaddaabaddcabcabdbcaacaaacccccbccccccacbbccacabbdbcaaabcdccdbacdadabbbbcdacbbbddddcadcccbbdabcdbbabdacccdcadcbdcaddccabbbaadbbcadcabbdadadacaabdbdabbadbdcdcacdddcddbcaaacbbdcbacabbbbcadccbabbdbcadddcccaccccbdacdadcccbabbbccaccaabcaaaddaaadbdcadacbcbcbdbdacacdbcadbaabdbdccaacbbcaadbbbababcdaabcaaaaabcdcaacccaacbdbdccacbcadcbcaacababaacdcbccbaaaacaadcbcdbcdcacabccadcbdbcddcabdccccdaccaaacddcdbdacdbdaadccdbbadbdbbccccababddbaccabbaaabbbbcbbddbaacaadcdcaababddabaadcadcdcbcbbcabddddbadcccbcbdddccccddbdaadadabdddbddbdbbacdbdacbcdcbacdbdcddacbdacbbdacbacbbcbdcbaccdaabddcaabcacaddbdadaacbdddcacbbdababbdccbcdabbbcccbabbccaddaadcbbddbcbabcbacacddcbcdabbdbcdbcacdddbbddddbddcdbdacadcaaadaddcbabcccdbbabddbbdcccacdbaabbbcabaaddbcaaddbaaccccacdcdbddaadaabdcdaaaadbaabaddbdbcbdcdabaabaadccadcabbdbacbacacbcbdadbadbddcdbcdbcbddabbddcacdcdadbdccacbacdacdcdcbddacdbbcbbababacdacbadddabdbcadacdcddabbadbdbacbdadcdddcbbcbdbdcabcacaaaacadbbbbbabbadcadacdcdbacbcabcaaddccccbcabbccbadcaaaddaadbdbbabdbacdadbdabbbcbdbadaddacbaadbddbabddaadbcaacdacdcaddbbcdadcccbcdcadbbabdbbabdbabccddcdcccbbaddbabbcbbdcbdcddcaaabadabcabbacadcdacddacbcdcbacadbabaaabcbaacdcbccdacacabdaccbbdadabbbcdccccdbdccdabbdbdacddbcaacaadccddcbcdacabccbaccddccabdbbbbdcaabddaacbdbababdbdddbddcbcccbddbacdadcdddabaadadcdcdadaabccdbbdccdbadbbacaabadabbaddcabccbcdbcaacbbaddcaccbcbdcdbabdadacabdbaaddbabbdbccdbbdbcdddcabcdcabdaccdcbbaaacbbcbbbdcabcaccbbccbcaacdcadddccdbaabaaaaadbccddccadbbbaddabddbcaabbbacdcbcaadcadacacbacccbaaccbbabdabdbddabadcbdcbbcbcbbadbcaabbcddccabdcdcccbadcdacbbdababbacdadbcbccaaadbcdcbabcdddabbbbaacdcbbccbabcbcbcdcdaadccdadddadadcddbdcaadbbbdcccccbcdaabcccbbdabbcacabdbcadaadbcbacdbdbccbbcccaacabaaccdadaabdccaaaabbddbdabacbbabbbccabadcdbaddabbddaadaabacacdccdcbcccdcaabaddabcbdbdabbaddcdcdcdcbaabbdabcddabbbbacbcdddbdcaddacacbdbdacbdbcaccbcbbbbbbccbcbdcbdcbdaadcdbbccbbbbcbaacbbaddbdbddbdabbcbadaadbcbcdbdcbbdbabcbdcaddbadabcdcbbcbcadaddbbcddbadbaacbdababbcdacbddabbabaacdadcbbdcdbbcdcbdddaccbdcbadcbdbcaacdddddbcddccacdbabbcbdccbaacacabddddbcdcddbddcbaccacacccdbbcacccadddabdccacadbacbadabbaadbadaabdabccdcbdbababaaccdcbdbcdaabddcacbcdbdabddbdcbdacbadbdddccdddcbadaabcdadaadadbdbacbbcdbabcddacbbbcbddadcabccaadcdaabbaacaccadabacdddbcadabbbccbadaacdddddbccddccbccaabcdcbdbbacccccdabcccddbbadbdaddbadadcadadcbbadcbadddaddccbaabdacadaaaadaddccdccbaccddbddcbcdcbdadaccacaaccbbdaadaacabcbaadbdccadaccccccaabbdbadbaaddaccdbcddcadcadcdabcadaddabcddabcddbaccdacddacabacdbdbadddbcdcaabcadbdddddaacccacaacdcadcabdaacbdbadaacaadbabcccbabcccddacbbcbdabacdbcbdddabacdcabcbddbcbaabdbbaaddaaababaadaadbcccabbcabdcdacbdddaddbddaddcbbcdbbbdcacadbdaaadcbdbacdaabbadaadaadcbbbcadbdbddddcdcdabacccdccbdbcdcdbccdaadbdbacaaabdbcbcaddbdaaaccdddacabcaacbbbaababaadabacdbdcdbcdadcdbdddadddadbaadacbbcadcbabbddadadcabadddccdcdadbbdcabddcdcabbcbacdcaacadccddddabdbbbabcaddccbcdcdbabdddbccabbcbaddaccaaaadaabbcdacaccbbaaaacaacdabadbaddabbcaacdccaadbdbcaccbdabcbbcbddddadabcaabaaabcadddcaddbdcdbcadcacaddadcabaaabababcdbddcaabcbcbdbcaabdabcdcdcdacacbcccccccabccadddadadbdcdccdbbcbabbcdddbbccabacbaacabdabbaccaaabaadcdcdcddadcbbbabadaababbadaabaddcdcdcbcddbabddcabbcbbbdabcabddcaddaacbdcbdaddbdcadcabddccdaaddacabdabdacbbabcbdcabacadcabbadccdbcbbaccdadcdddcbdadbaddcdaccacbccbbbadbdcaaabbdabaadbbcdadddcbddbcacdacaaccccbbddbcaadcbcccabdaaacaadaabbbaaaadabdccbcaadcbcdbbcbabcaabdcababcaadacbccdabaddacdcbbcabdaaddcddbacdbbbddacadbabdddabdcadbcacbbdaaaadbcdbbcbdaaddbabaabdaddcddaaabddddcbabbcddbaabcadccddcabdaabdaabbdbcaaccaacadaadcccbcbbdbdcbdacbdbdaabdddbccbbdbbccadbdbbaabddcbdbaaababdbababbcccabcacbbdbbabcccdbabacabdcdbaccccbcadbaaaddbcacacbdcbcacaddccdcccccdcaacddbddddacadcdddcaccdddcddcaabcbcbdabaacccbcbddccbbbddacadbdbdbbabbbaddddbbcaaadccdabaaccdabcdcabadddddabaacaaabddcacaccccdaabdbadcbcdbcaddcbddbbcdccbaadbbddbbcadbdcdbbabcacbbbddbaabdcaacdcaabdcbdbaabcdccadddddddbaddbddbdcdbabacdadaabadbbcabbbccbbbbdccdcbcdaacadbaadddbbdadaddbcbadabadccacdcdbccdcaadbaccbcdbaadbabcdccdbcbbbdbddbcbcbddcbbaabcbdcabcbaabcbdcdbaacbbbddbacccdbcdbccccdcdcabcbcdccaabdcaabbabdbcbbadabddbdcbdcbbabdbdadaadbccdadbbdabaabadddbabbddcacbadbabcdbabdbbbcacccaadddababdcbadbccbdbdaabbbbdcacababacdbcbcbaccaccbbbbdbbbddcdccddbacabcbdbabbcdcbbdcdabdabcdababcdaacaccaaadaadddbdacacddcabadcdccbbdcabccdbdcaccdcaaaaabbdadbcbbdcadccacabcadcbcddcadbbbadbaaacbcacabadcbacbadbbaccadbadbdaaaaccbddaabccaacdbaabccdccababccdcbcadaadadddcdacccbadbbddacdacbcbbbdcdaadddbaacdccbbccddccacbcdcbabdcabddcbccaccbbdcacccbadbdbcdcbbcaccdbcddadcbbbdddccaabbbbbbacbbabbadabdacdbaaccdccadacbaaaabbcddbcbabccbdbaddabdbdcbdcabbaaddddcdaaadaabbbbcbbbaaddababcdcbccbdbadbdcaaabcbccaddacbcaddaabacabbdabbbabbcadbcacccacbaccccbcddadbbcdcbcbcdbcdabaadacddabacdabcdcccaaaaadacdcdcaaacdbacddcbcbaddaadabbcdbdabaddccacdabbbbcaaccddbdbddabddadbcddbbabbbbdacbccbccaccbbaaababcbbbddabcbddcdaabacbbddcccacccacdadcaadcdcbcbabbbaacdcacbadcbddbbcdaabcabbdbbcadbabcbbcabbdaaadbbcddadddcacdadddcbcbdabccadcdcdbcbcbbdddccabcdabcadabacdccadccdcabbabaadbacccbbaddcbbdaaccacacacbdabcacabddbdbbbddcacddacccadcbabdaaaabbbdadbccacbbcacaadacdbcdbbacdadaadcddadddaaccbbdbcadcccbaadccbcddbdbbdcdacbaccccdcbdaaaccbbabddadaacbbcaaabbaddcbbaaaddbdcadadbdbdadadacadcdbadaccbbbaccdbccbacbabbdacbadddaadbdacadbaadaabdcdbcddaaccdbbcabacabdacadaadddcbbbaabcdacbdcabdabbacacbbcdbabdccdacbbbaccadcddaaaaacdbaadcccbbbbbbadacbaacbaaacbaaccbbcddbcbbcbbabdddbdbcadbddcbdbdddcddbbddddcccadbccdadcbacbacddaaabdbdbdadcabbdbddabbdbadccccddacdddddbdcddacabbcdbbccbcacbaadaccdcacadcabcbdbaaacbaccddcbdbbccbddaacaaadbcbaacdddcddabddcddccbddbabcddacccdccbdadbabdadaddbdbcddcbdacbdadacaaddabcdcadbdcbccdabbbbcbaddbabddaacbcbbacddbdabccabdcdcbddbdbbadcabdbaadaacaadabcadcdadaacddabbcacaacbdbcbccdcddddcbdddcaaabbddbbbcbcdcdbbbadbdbcdbaacbddcdadddacccaccdbaccdadbbcddddbbbdcbaacdbbdcaadcbadbacbddcaabadcbddcacacadbbbcdadaabaccbbcdbddbddadbbadbcbdcdbdcbacdbaacccaababcddacbdadaabbdcdcddabaccacdaaaddbdaaadcabcccddbacdcdbabcadcaaabcabaabdbbabaacdcbacdbdadacdbdccdcdcaabbaabcbddbddcddadbbbbcadcdccccbbbddcabaacbcbddcdacdacdabacaacdbdcbcbdcbcaacadcbadccbdbcdabcbdbbacabcccdabaccbaaaabbbabdaddcadacabddccbbcdaadcbbaacdadcdbcbdbdcaaabcacdbacdbaacbbcdcacabadaaabddcacaadbcbddccadababaadbddbdadcabcbbccaccaccbcabdaacdcbdbdbbacaacacacdaacccaddcadadacbacbaaacabbdbbacdaabcbbbcabbcbabacbdccaadbbbbbbacacadcacdcddbbdbcbcbdaddccacdcaadcdadcbbbdaccabbabaabbabdaadaabacadcabcbbcccdbaaccaccbdcdadbdcdcacdddddaacddbdbbbbaddbdbdcbdbbcbdbdacddaddbcdabccabcbadbdddabadbcaadaacccdbcdccabaddbacccacccacababdbcdcbdcdadbbbabbdcaccdcbbaccadcdbdcadcbdabcaccdddadbddddadadaabbdbdbadaddddddaaacbbadbcddabadcbddddcadcaacccadbddcdccddaacbdbbbbbacadacbadbabdaccbbdbacbdbddcacabbcaaaaabdbcaacadcbccdbcbbadcaaccdbcacabbaabcbbbaaadacadbaacbdcbbdababccdadaabdcccbaabdcbcddaadaddddbddbdabccddbcccdbdbabdddaadbacdcdbdcbaddcabdabcbdcbccddcddcbcccadccbcdbabbdadaaddcbbabdbadcabccbbbdbdadacdcbcdddddbcdccadbccdcccddcdcdcabadcbcacccdbbbddabbbcacdbababaddadacbcdcbcaadaaaaaacaadadadbdbbbcdcbbdcbbcccdaadabbadaabbadacdadcdcadccaccccadadddcccbcbbdabcbccadcccccccdaacadaadaacdbbbbbbbacadcdcbcbcdbbbacbbcddbdbbaadcdaccdcacadccdbdccdbdcbdcddaacabacdcdccddddcbaccaaacabdadbaaaaccbbaccacbbdbbcbbbababaacbccbbdbbddddcdacdabaaccaaabacbddcdbcdcbbbcdbdbcdccaaabddcdabaacaddbdddddabbddbdcbcabbcbcccbcacbdccadcabaabbadabddccbabcbaacbdbaaadbaadbcaababdccbdbcbbbaddbccbcaabadbcaadcdcbccbadcaaaddbdbcbabbacaccaccddddaaaadbadcacdacbcbdbabdbbdbcbbcbccaabaccaabbaaabdadbacddccaabcbdcbdddadaadbadcdcaaacbdddcddcccccaddcaaacadcbdddcbaddcaaaaaccdbacdcbcdccccbbbbcadaacacdadbccbcccaabcbdaccbccbdbbdbadacdcdddacbbbdbbaddbaaaadcdbabcbbcaccddbcabddddcdcbbddcadbccbabcbbbbcdbaaaabbcbccbcddddababccacdbcddcddcdaaabadabdddbbdabcdbabccccaccbccacdacbcadccbdccacdcabdacacadcbbbddcdbcdbcabbaacdbbddccbdcbabccacbcbbcadbbdbbabcbdbcaacbddccbcbabbbbaccdcdbdbbdcbdabbddcbcaddbbcdabbabdaaddbdcabdbaaadacbdccdccbddcdaadbabdddbdccacacdddccddddcabacdccacddccdccacdbcdbcbdacadddbddddccaddbcdcccddbaaacdcabdaabcbacdccabbaacacbbdcdccdbdddbccddbacccaacbbdacdcccaccddaccbdddacdbabaabbbbdddcbabadaaddbacdcbabcabbcddbcbcacdbadbcccaababcccbaccbcacabbbbcdacccabaaccbdcdcdabbbcaadccaaccccdbddadabaaccdbcbbbdcacabdcdccacdacabababdbddbaccddccddbbabbcacadbbbbbcabdaacbbdbdabaaddbbaaabbacbbaccdccbacdacddddacdadcdbaddcdbddacdbbbdbaccbcbbacbdddcbdddaadcbacbabccbddcabdcccadcdadacccabbbcbcbbcbdddbdbcdaccbccadbcddacbdccdbabbdddddbadaababcddbdddcbbdadbcdbdabbbabdccbcdcdaccbdcdbdbddadddadabddcbbacbabbdbaabababcbabddcdbadabadbcccdbcdaaadddaddbcbddbcaaccdcdcdacaddbcacaababdaddaabbbadadcbabdbacdaabbcdcdaadcdaddccdddcbdccaaabccbcabdbaddccaacdcacaddaaccabbddacbabbbbddadbbccabddbddadaadccdcbbbacadbcbdaadcbddcaababacccdaacabbddcaadbdbbdcadadcdcddddbdcdcdcbcbabcdabdcdbbcabccaadbdccaabbaccccdcdcbddcdacdcaabdbacacbaabdddbcacdbccbdaacacadbccdabccabdaabadaaccacddbccadcacccdaacccacbcbcacbccccdcddadbcabaabdddcddcdcccdbbbbbacccabbadadcbbdbcddbcbacdcaddbcbbadaddabaddccdbdcacddacbdbcbbddaacccccacdcbcdbbbabdbddbcbbbdaccbbdddadbcccbbbacacadcdabbccdcdcbbbbbdbccbcdbbabcbacbcbccbacdccdabbbcbabdbaaccccacdbaadccddddabdaaabccdbadadbcccdcdaddddababcbcbccccbbaabaddabcddcbbcaadbdcdbacdacadddbacbbbaabdbdbdbcbbdcaddcabbcdbadaadcbabbdcaadccbbcbaccbdacdcbaddbdcaccbaddbadbdcacabbcbaabbaabdabdbbcccabcabbabdaadcbaabdaadbdacccdbadddcbadaccdbbbcbabbbccbbbbacdabdbbbdacbaacdcacbccdaaacbdbdcabcaaaabccdccdbddbbabbbbbacbcdbadcbbacdacacdacbacadadaaccbccdccacabccacbddcdccdbcdccaadaabbbabdadbccbadcabcbbaaccdbacbdabbaacccdaddddddcbaabdadaaddcddddcdbdadbcbaaccabdbabcddbdcddaaacdabcacdaaadddacadcdacdbacdcabbccbaaacdaddcbcbbdaacdbdacdddccddcbbabaaddcabdcbbacdcadaadcbdcdaadcdbbcbcccbbabdcabcbcabacaacbddaddbbacbabdccdadacadbcdccdcbcdcdadaddcdcbdbaabaabcaacadbbbddcbcbddaccaccccdaaacdbdaadbcacbbacdbbcacacadcbabadadcbcadcdaabddddbacacabbdcabaabcbcdccbbacbcdbbbaaacdacacbbcacdbaccaabaabdddabccbacadcbdadcacdccdbcbcbaccbcbabaaadddbdacbdaadccbddcacabadbabadaabdddbdbbaadaadbdbabcbdcbdbbcbaaadddadbbbabcbbdcdbdbbdcadadcacabdddbbcbcbabbacdbabcaccdadbdbcccaacdcaaabcdbbcdccccdacbbcbdaddaadbbadbddbacddcdddbbbacbddcbdaaabdcadbbaabbcccaacdcdabadcccdbbccbccacdcdccbcbacababbbbbacbbccadabdadadbadcdcdbdbddbcacbbcdaabdccbbaadcbdcdaaccadabacdbddcabccbbbabcbbdabdcbdddabacabdddddaddacdcbadbdaaadcbdbcaaadbcacccdddadaabccddccbbccccdddcdacdbabdabcaccbcdbcbcdcbacacdcdcddaacccdabcabcbcdcbcdccdcddaaadcdcbadddcbbacdddcbcbcdbabdcdcdbcabccdabaccdaddccbbaccbadcbaccccdddabcbbbbbdbdadaddcdcbadadbadcdcacddcbccabbbccabddcadbcddbdbddddbcdcddddccacabaabbdcdadaaccdacadbcaadbabbbbabbbcbacacdacdbbacadcbccacacdcccbaacdcbbabcbabacbdcbdcddcacacbddbdcbcddcbabbabadbabaaadcacbabcbacaacdbbcdaddbccccccbdcbdbccaddcbdccccbcbbcddddccbdabadbaaadcbdbaabddbbbadddcabaccdbccdcaccbdbdbaccddcadacccaababaccbbbcbdcacbdbddbbddadadcacdbabaaaaaccadaabaaaccbbcbacdcdaaaacbadbccbbbcdcbdabdbaadadbbdabcdbaabdbbabaabbaadbcdcbcacbddbbccdadcccaaaccbdadadcddabcbdbcadbdbaddaaacbdcbcadcdcdaabdaacccbadaadbaccbccaddaadbacbabbdccadaacaddcadabbdbbaadbccbbaaadacbcadaccaaadbadbbbbdbcdcccadcabdbccabbbdcabbdabdddddbcadabdccabacbbcabbcaaaaaccaabaddadaddacbcaadaccadacdcbdbadaaadcbadccbaabcabbbcbcabbadbbabbbbcadcabbdaccabbdaadddddbcbaaabacdbddccaddbcbdbcadbaacabaaadaaaccbcaaccbbdcbdcbdbaaaacdaddabaadcbaddbcddbcdabbbabbababddaabbcbbccdcdbccdabdbdbdcbbadbdbaacadbddbddbbcdbabcddbbbdbbccbadbdcccbcccbdbbdcbddacccaaabbdaaadcaacbbddacbdccabbbddddacdaacbacbdcabbdbabbbaaaabacaaaabdaacddacdaaddbddccaadadccaacdccdccdcaabbaaddcbddadbddadaddcbbcbaaddcbdccccaddabddaacbcdcaccdddbadbbaccdccdbcbaaadcababbbdbcdccbbdccdcabdacaabbdbdddbdadbbbadabacbdddcbbdcbbdcaaaaabdcdccccccbabacdcabdacddaabcbaadcbdbdbacaadcadcaabbaacadcbbcdaddbacbadaacbbddcbdaabddddccacbcbbbcdbdbccaabdbdbcbadcaddbdcaddbbcdccabdabaadadabbabcabbbdadccdcbdbababccbcbbaabadabaabadccdcbcacadacadabbcadbdcbdbabdcdaddacddbdbbbccbacabccbddddacadbcabbadcdacbbdabdbadcaabdacbaabdbdabaadabddcdbadbcdcdcdadaabaadabbcdbbbdaacaccbddcadbacbddcbdbbbcbddbbcbabcdcdcbbcbdbadaaacbbaacdcbdccccddabbdacbdbdacaaaddddacacdcbadacbcccbdabacdbadabdadcccadaadadbadcacacdccacbdbcabcbbbdabccccbaababcacaacddcdbbdbdadbbbddbccaacaabcaabdddbaddccdbbdabbddcaaababddbcdbbcbbbaacaacccbbaddcddacdccbdaccbddbbcacaaddcbabcbcabbbbdcdbcbdddddadbacacbdacacccaacbcdaabbdcabbbdcaaaadacadcbdaddbacdccbdcaccbaacdcdacbddccaabdacdadbcdcaadcaaabdbddcdcaaaccbbddabacacdbcacaccbddcdabbbdaaaabcbacdadacaccdbadbdcabdbadcdbdcadbbacaabadcdacdaabdbbadadcdcbaabaddcdaccbdbaabbcacadaadadabcbcadcbadddaddbdbbcbaadcdddacdcdbbadbdaddccccbbcdcdcadcdbbbdcadadacbbbaddabadddbbcddccddcdaacacccaddabcccdbdbaddbddaccaccdbdcbcaddabbccddbbadcbadabdbcaadabbcbdaaadcabaccbcbadbdaadcaaacaabbdbcacbcbacabbcadcadccaddaccdddcddcbbdbdacccdddacdcccaaacacdcadcbdacaabadbbacdadbddbcabdbbbadcacbbddaabaccbbdbbabbacaddddbcaccabbdacdbacbbcaaaaccbbbdbbbccacabcbdcdaddaacdcdcbbbaddadacadcbbacadcaadacaaadacdcbdccadcdccbbaaddcbcccaacdaaabccadbdcabdcdbacbbcccadccbababcbdaabaacdcdcadcaccacdbdadcbdaacddbcacacbaddaaadbdababcbcacbccaaaadcdacbcbbbabadbccdcccbdaacdcdcbbdcbddbabaadcaccbdacdbbdcdbabcacabccadaabacdbdccadaaddbdabbddddbcbbdccbaaadbbacadadaddbaabbbacacadbadddcdbdadddccbacadcbdbdcbbccacdcacbaccbadbbaacbbbbabacbbbbdbbbcdbbabaacaccadbbdbdadbbacacddbabdcbdcacddabdaadcbcbbcbdabcbdccbbdbacbbdaabbabdaddabcddabbadbcdbcbcbbcdbcdcacaaabbdcbacddaadabcaacccadaabdccddbadbcabdbccbabbdbcabdcaadaaccbcdbdaacddbcacccacdacdabddddcbdbddbccadbdababccdccddbdaaabdbbbdbdcbadcaccbbcbbaaadbcaccdcbbadcddbcddbcaccaabccddbbddbadaadadadadabddbcdcabccdcdbabaaddacdbcaccddaaabacbdabdccbcbaddbdaacccaadabaaabdaccbcddcbdaacdabadbdacadcbcabccadbbdbdccacdaacacadacbccddaaacdddcabdbdddabaaacaacbbcdadccaabdbdcbacdacabdabadbcbadabcbbabdcaaacdddabbabadcbbababdbbccdabaababaddabcadbaccdbbdaccabbdcacccadbdabcadcdaadabdbcbdbacbaabcadcbcbbdbddcdcadbdbabdcccacaccdcbacccaccbaadddbddaadaddccdadacabddbdababbbacdaaaadbbbbbcbccacddbbbddadaaabdcbcddaabcddbacacbbabcbabdbcddbdbbcadaabbbbddaacbbcbadcaccadaadcbadcdcbbbcddddddbcabdcababaadaabccbbddbbddcccdddbdacaaccbcbadaddacdcdccacaabbabbdcbdbbcbcbdbacdcaaccccacddbbddbddbdbcccbacdddabbbbcccdadaddbdcabcaabababdaadaccadcabdddbacbccaabdbcaadaddddbdcbabccdddbbacbdddcacaddadbcaacaadbdadcbcaaacdacbabaabbabbdabcccdbcdabdadbcdbddcddcccbbbacbdbacdcbdbabdacccbbddadaddbdcddcdadccaaddbcbcbaaccccaadcbadbcadaacbacaaacdbacdabadadadcddacdbbccdbccdadacbdbcadcbadcbaccdacaaccddadccdccabaabdccabddbccbbcabdabccdbdbbacbabbbcaccbbcabccaabadbcbcacddcdbbbdcccddddcdcbbdbbabacdbdcbabdbbdcbcbaabcbbdaaabcbbacaddcaacddadbdcdddbddabbdbcccaccdcadbaccccbbbcbacbbaacbdbaacdcbbcaddcbccbdaaddcaacabaadaddbbabcbddbcaabcadcababcddbcdcbdabacdcdabdbdabddadddaabdcccbaabaaccdbdcdcacadccdaabbcdcaccdcaabdcacdabbaadcacddbddbcddddbbcacdcbbadcacbdababaacbdbacdcdbbabacabcadddaabdddadabdbccabbaacdaabcbddcddbccbabddddaaccbccaaddcbadadaddbbdddcbcdcdccdaaaddadaabdacbcdcddcdabbbbdbadcbccddbdaadcbcccbbcdbacadcccdcabcbddccbcdbdbababcbdcabacbccbbaaabbcccbcabdcacabddcbabcabadacbddbcdbdacabddaddacbbddbadddccdabababadccbbadbbcbbbbddacddcdcddbcadacbbaddaabbadddcbabdcdbcacaaacbcdbccaaadddcccdddbdbdccdccdbbdbcaccdbddbdbbccbcddbccdbbdabcabcbcaddbbabacbbdacacadbbbdbababbcabdbdcaabbcdadbbcabcacacbdbcdbabadccacbaadcbdbdbcbadaacccdaaabbdadbddccaaccbbdbabddaddccaadddcadcadbadaaccddbabcadaaccbdcccddbaccbdddacdcbdcdccbbdcccdbabbccaabdaaddcacddbcddabdbcaaabbccbdcbacccddcdbdcdbbcabacbcbccbddcdaaddacdcbacbbbdbbdcbccaaaaddcccbcdbcdbccbababddbbddbddcabdaaacbadbdaacbabadcdaaaccbbadcbabcdbcddbbcbbcbcdaadccaccbbbbdcdabddbadcccabaaaccbbaddbdcacacbbdcadbcbbaaddbbaaabdbabdabccabacccdbadcdcccbcadacbcacddcacadcdbabdaddaccabdbaacbadddaadbaabddccadbcacbbdbaaadbcbbdcdaaaadbccbbdcccbadaddbabbcbdddbadddaaaacdadbacbbbdcadabaaadacddccbccddcbadbccccdbcabcdccaccbacdaadcddbcaccdbcaabdbcbdccbbadacabaacaabddbabbdaccbbadcddcbbaaabdcabbcbdcbccacbadccbdcdcbacbcadadcaabdbdbbcbcddbddcbbccbddccabdddabbcdaccdaadbcbdcbccadbaaaadaabccaddccbccbbbdbabbccdacdacbcbaaaabbbbcadcabcbcdcacddabcaacbbadbcbdcddbcbadabbbadbadbcdabbdbdbbbdbcddaccdaaadadcddadcbadbaaabcbadadcdcdbdbaadbdaabbcccadcaaacdadabbdbcbccacbcbaddcccdcdccadbaaddaddbbccddccbddcdcbdaaadbaacbdccccdaaacabbacbdaddacacdadcbccdbabdcaccadabcbdcaccccdacbcdaccddbdbdacadbdddbccaddddbadcacbdbabdaacaaaacbaddbbdadddbcdabcbdbdddcaacdcabddadbdbbdccdabcaddcdcccccdbbbbdbcdcaccdcadcaccaadccdadaacdacaccdcaadcdcddadabacbbbadcdaacabccccdbddaacccaadacabdddaadcddccabbbdddaacddbcabbdbdacccbbdbadaababbdcacadadaadcddadabacacdbacaccddacacbccbacbcbdbdcaacddbccaaaaacabadbbbbbcaaadaccdbacccbddcbbbbdbcdddbbcdbdaabbdcaddbbadbabbcdccbdacbacbbdcdabccccacadaadbbcdddcdbbcddabcbbbacddccdddbadccdbcdcaaddbcabaaaabaccbaccdcbbdccbcddbadaaacabdddcbbbcbadcabaaddcbaadbbbdddaacdbcabcacddcbddaccddabcddcdcbccaaaccbbdbabababbdabbacdbadcddabbdbaadaaabbcddaaacdbcacddadddacddbaaacdcaddadcbbdbcacdbdbadadbddbcdaaabdbbbcdbbabdacbcbacddcdbbbabcdbcccabdbdcaabcbacaddbabaaddddcabdddabdbcccbadbddbdcaabaabddddaccddcccbcbdcbddabdadabcccadacdadcdcbbddabdddccaabbcababcacddbdaccbabccccaadccadabcdbddbaabacdabaadccdcbabcbbdcbabccdbcabacaacabdddbacbabdbacdbabbbccbbbadaacdddbcabdbbddcbbccadadbbccbcaadacaccdcbacbbdbcccacbcaaddbddcbcbaccdbcdbbbbabdcbabbcdbbaaacbadbcacbdddbbcbbabbadcdcdcdddbdcdbdacbaacddabcddbcbaacbaddbbaddadcabbabbbdcabbdccbdcddccdccbbccaddaddcddadaabdababcdadadcbbcdaadacbbdcccacdaddacaadcbaaddcbcaacaacabbbacabccdbdabdbccbaadacabdcaacbbbaabaaaccabbcbcaabbaccddddcbbcddccaaddbdacabcaaddabbaaaadadacbdacabbbdabdcdbcbbbdbbbbdbacdbcbacdbccdbabcbbcbbadbcacdcabbaaabbaccdcaaddbcaaacbcdcbbdcaccbaaabcaabddbabcbbcaaccbcaccacbbdccaabccacdcdbbabbaaacdccccaddbdbcaddabdccbddaadabbacbbadadbabbcbaabcaaaccbdbdbdaddcbccadcacccdcbdaaaccacadabcaabdabadacbbbcabaddcdababbbadcacddabddcccbdcdaabccbcbdcdccabbdbdcbacdbaaaabaabacbcdcbaadcdccbacabdbdcbaddabacbdbbdabdddcddbdcdbdbbbadabbcacdbaccabbbcbccaadaabacaabccaaabcdabbcaddcabadcacdbdaccccbabdbabbcdabcadddbdabcbababdbaaadcdddcdabbacdaadbcbcddcaddadbbabcacdcacccacabcbbccbbddcdaacaabcacccbddbacabcdadccaaaccdcbccabbdcccaabcaacdccdaaccdacdcdacbabcbaabbabbaadbcbdcbacadbaaccabdcdadddaabadbabcddbbaddadcccaddbbbbccabcdadddaccaddadcacbbcbabcadbabcaacadbbdabdaddbadcacaddbaaabbccaddbbbdddbdcadaaabbdabccccadbabdccdbaabbbabcbcddacabcccabddcbdbacdababbbdababaadbbbcbddaddabcbaabcddbdabdddbddaccaddcaaabacddccdbcbbcacbaabcddcccbadbcacaacacacbbbbbddaddcadadacdabadabbbbdaaacdbcbdadcdbcdddadbdcdcaadacdbbbddcdbdcbcdabcdbaccbdbdbcaccadabaacaddcbbcbdacbbaacddbbbbbddacdccaabdccaddbaaccdbcadcdddbdaabdbbdaddbccdadaddabdaddbccbcaabdcdbbbccdadbcdaacbbcbbddbbcabccbddcddaaacbbbcbdcaaaabdbdbcdccabbdcadbcacdbdabbdcbdabdaadbabdcaddabbdbccdbaadbacdabbbdccdccabcaacabdbabbabacbbcbcdabbccbdcdadbacadadadbadcaaaacdbdbcaaccbccbbabacadcdacdadacaacacaadcbcaabcbdddbbdadcdcdadccbaaddbadbacaaabcababbaaccbabaabdbbadcccdabbdadabdaadcaaacbbbbcabbbaabdaaccbdbccbcbaacdadbbbcccbcacaccdaccdddbcabaabcbdabcddabbcdaacbbbcacdbcdabbcaccbcddcaaadabbddcbddddbccacadcbbabcdbadcadccaabdadcdbbadbdcaccdccabcaaabdbacdcbcbbdbcbdacbbddddcdbadadadcabbbddadabdacdcdaababdcacbaabbcdadcabdabccddcbcdaacabaccbbcdaccdbabcbcaabbdddbdbdcabcacbbbadccdadcdcbbddadcadbdabacbaddaadbdccdcbbddccbbbcacaabbcaabbdadbdbabcaacbbaabcddcabbbbadbccbdbcaacbabdcbacddcaaabbdcdcaabdaabcbcaaabaaabaccdbbbaddcdabdabddaaddbbabbacbcdcccadbadccacddddaddcdbdacabddcadddcacacadcdbdcbdcddaccbccddbdcdccabbbddadabcacdbadadcdbccabbbbcaccdbadaccbbcbacbbccdaabdbccddadbcbadbdaddbabdcbabcabaddbcbcdbbcbcaadbcbddbaaddadbdbdcdccbadbdddcabdcbbbcacadabdddccdadacbcabcdcbdcdbabadaacabbbdcaabcccabadaddacbdadbdadcbbacddadbdddbbdddbacbdadacacdacdcccdccddddbbdabdabcbdcccbddbbcbacdadcbdabadabcbcadbcdcacdabdddacbbbdcbcacabbbbdbbadcacddcdbdabbdddcaddbbdbdbdddaacbcdbdbdcacacbaccbddddcdbdbcbabbbdcaddccbacddacaaccbabaacadbddabcbcbacbbcdacaaccdcddaaacdbabdcaacbdadacabbacaaadacabdbaabaabbbbccabadadabdbbbbbdbbdaadcbcbdadbbbcdacccbaadccaacbccdbddaabdbadbcaddacbbcccdbaadbaddddadcdbddcbbcbaacdcdadacbbadbbcbcbdbaddadddbcabcbbddcdacdcabcbaacaddcdcbaddadcdadcdaccadcabddcdbbcdbbccdcdddcacdaaabacacacdbbbcbdcaacadacbabccbbdcdbdbabddadcaaaccdbbdbbacccdcacdbcabdcbabdabbcdaadcbdbabcaaacbdcaddbdaccaccdddaccbcadcaadccaacaadcbbbccbccbaddcdcdbdababdcaccbccbdcacacbddcdbbbabdbadddbcaabdcadcbbbdcbbbbabdadabbcbbbbddbcabbbbbdcadaadaccaccbcbbcddddbbadadbccbbdabbabddaabcdbcdadaabccccddcddddabddacbdabadbdbbddbcbdddbdcabddabcdcdaccdcddccdbbaaadbcabdabbdadbdabbabddaddddadcbdadbdccccddbbcdbbdaabdcbbaaadbcaccccdcccdcacacbcdabdaaccdaccddbdacbcacbaaabdcaccdddbaabdbbbdbdddbcddcacdcbbdbbcccbaccdaaaccbbdbbbddddaddcadcdadcaaaabbdbacbbadaddcaacbdaaabdacadbdcdccddbadcddbdbbacbabbddbcdcaddbaabcdcddddbcbdacaccaaccdbabcbbbcddcdabdbaddbacbaccdccdaacabacaccccbcbdcdbcaadacbcaccdddddcbbacbcddbcdadccbbaabacbbabaacbbadadacabddcaccddbbbbcddbbdbbbbcdbccddabdbbacbbdccdddbcacdabaabbdbddcaddcabacbccabaaadbbcdadcbbcdaaadabaaabcbacabbdcdbadbddddddbaaadaacadccdbabbddbaadabbbdddcbbcbabcdaabcdcdbccacbbbccdaaddbcbaabbdbdcccdbacaaaadaacdddabbbddbddcdcdcbbbdaaaadccbdbdbacaccaadbdcccabbdccabdabcddbbdcccbcaaabababdbbbdbddadaadabbdacaddcdbcdaacabccbdbddbcbddbcbdbacdccdaacdbdcdabdaaaccdbcdadaabddaaaaabcccdcddbdbacbbcccabcaccbcacacbccbdbbadcbacbcbddbacaacdbbbdabdabdaaaaaabdabbaabdbdbaaadcbdbdddbaacdbcbdbaacbacccaccddcddaabadabdcabdddadabccbbdcabcdcaadddccdbbadacbbdbadcacddcbccabbabababacccccadcbdbddbdcccadddbcbacbadddcdcdbbabccbddbbccbcbabdabccababdcccdacbbcaaddaadbdbcaaccdddcacdcbabcddcbcddaacddbbaddbcaaacddcbdbddcaabbdcadbccabdbdbddddcadbddbddbbcadaadaccbdaabbdabccbcdacabbabbbcbabcccdccaacddacdcbbddcdbbabbbbbbcabdcdbaaacdabaadbbdccddbbcbcadcddaddbdbccddacadbabacadaadaaccdbcddccdcbaadcbddbabcddcdbcdabdbabdddbaddccacacccbdcbadaadabbaccdcbabdaacbbdddacdabaacdccbadabadccbcccacabbbcbcabdcbbacdaddbabbbdbbbabdcccbccaadbdccaddabcddbddaacadacbbacbbcbcdddbccdcadbaaacccaabcdbdaadcadbcdabcbdbccaccbbdadbaadaccdccdacacdbacbbdbabadccbdadabbdcbddbabbdaccddacccdadcbcabdbdabdabbbcdbadcbccbddbdbddbbdbabcabacbcdadadcbbbdcbbaacaaddbabdacccaaddbdaabaaddbaaaababcaabdadbcdbaabcbbbacadaadadaddbcacacbcaabdbadcaddbddbadccdabddcbaabbccbcccabdccadbacccbbacbddcdcdadbddaddcbcdadadbcadbdddbacddadaacbbbbbbaaabdabbdcccdbcccaadcccdbcddbacabdbbcdbacbadbdbbdacdcbbdbacbdddbaabcadccbabccacbbaddaabaccbbbbaaadabdabdaacabadadbcadadaabddbdccabcccaaacbdcbdcddbbbbacacabcacaccccabcbacaaddccaabbdbdbddabacbddcdabaacaabaacaddadbccdbdcbbbcbddccbcacdccacdadaaacbaacdbddbdaabdddbdaaadababdcccdacddcddcbabacccdaadaddadcddddaddadddbbbcdcadbacbcabddbbaaabaadbbabaccddabdadcdbcbdbdcbdcabbaaacccabccbbccdddbccabbacdddcbcabcbaabaddcadacaddcacbccbccbcaadcdcbaacddbcbbcdbbddccbddbdadababddbadabadbbbaadaadcdabcabaccdabaaadccdcdcbdbcdccbddcacbaadbdadcdddacbbddcabddaabaacddbbdaddaacdbcdaaaadbccdabccbdcccacabcbdadcbabcbdabcdbbbdcaaadcaaacdadcccbbbdddbabacdbdcbddaaabdadbbbdcbbadddcadccccaddaaddccbdddabaacddcccdbaabaccaaadcbbbdcddbaabacbaadddbddbcacaadcbcdddbccacabcacaadbddbcdacabbcddddddcadcacbdccdbacdacbbcdccccdbdbbdacdcbaaadcadddbbddcabaaaadbcbddcdbdbdabddcdbabcdaddcacabcbcabcbcdcbbdbcbacbbccaaacccbabccbccbddddaabaccdbdccddbccbadcbbdcaaddddccbdcaaacaaddccacbbcadabdcbbadacacccdccccccddacdbdbdadbdcaaaadcaabbcbccbdbbdabbdacdcdccbbcbdadccaccdaacadadadcddbcbbdbbddcdabadabcadcacdcbbadaaaaaddcbadbdbcacabbcccacccdacbabdcbcbcdbccbbbdccdaaadbcdaccadcdbadcbdcdbbbdcaaacabaadcdbacbcbbdbaabdbddbbadadcbabdcabbadaadcdbdaddcabdcadbdadbdbbaaadaddabbcbcbbaaacabaccbdbbccdbccaaabbbcddadcaddcbbcaddaaaabaadcaadadbdabbddcdbaacadacabacbadaadcdacbdadabaaddbacaacdcdccbbbadacccbaadbdbaacdcbcdcabcaaabdbcbcacbdabbaaaaaadaaabcbbbabadbcbbaccadacbccdbaadccdacddadbbadddbbddddbcbdabadbacaaadddadcacdbbcaaadacadbdccababcdaaccdbccabdddbdcccbccbaacdcbdabcaddabdcdbacabcccbdbcaacaaadaccbddccbdccaaccbdacbcdabbdccbccdcdbacdcbcbdaabaabbccacdbaaabacbbdaaccdbbbdbbcadcdddababadbadccbcbbadbaacbdabdcccccddadbcdacabadddddaccbddacdbdabcbbcadacdbcbddaaadaddbbbacabdcaacdbbbccccaddaadbabdcabdcadbbabddcdcdabbbcdddbbdaabaaaabacccdccdcbacdbcbccdbdabddbadaaaaadddccaadbccabacddcbddaaabcacabbdccbabcdbdbcdbdccddacbabcbccddbccacbbdbabbacabcbcdcdcdbcacbcacadcbbdaabbabacdadbcbacbaaabdcdccddcbacbbaacaabbdaacdcbcccaaabbddbdccaabcadccdacabcccdabadbcaaabddcabacabaccdadddbddbcaaaaaaddabaccaabdcdcaacccddddacccddbdaddbbdbbcadacacbdbaabdcbcbcaacadcbdcbacdcdbdacddbbbadcabcacbcccdbbccbbbccccbacdcaacdcaaacbcdddabcbcadadddcbdbcbabdaacccdacdbacaabbaaaabddabdbdcbccdadbbaabaccabcdcbdbdbbbbbacdcbdabddbabbcdacabacbddacaddbdacbbcbdcabacdadcccdcbbcdbcabcbdbddabbbcaccdacbdbadcbaabbddcbdadacddaacddabcaabdaadbabdcccdbbcaacbcdabbabccdbdcdbccdccacdbbddaacdbcddacaccddcbddddacbabccabdbcadababdababdbdabacddbaadadbbaccccccaabddadcccbaaddbadadbbdbadbcacdcdbaccbcadcacabcabaaccababbcacbbdddbaaccbdbcdddbdadcdcdabbbbbbcbbcdddbbbccdadbdaabbccbbdbbbcbcbaaaddadaabbbdbccadcdcaadacabaaacaccacbcdddcbdcdbdbcbabdcdcacddbdadcbadcabbcbaddacabcabdacbcbbbdcacbccdcdbadbcacbacdbcccbbcadbdccdcdbcbcaabcaccdbdbcbddabaaccccabbbdcddccbbbacbaaacbcbcbdcdbadddbcacbadbdadbbbdbacacdcdabdbbccdbcacbdacaabababddbcbdabacaccabbbadaccaccddaababccdacadcdaadcbbdbdddbcbaacbcabadccacacddbbdcabacdcdaccaabaadbacddbdbdacbbbdabaadcabcbcdccaacdbacacbbbcdddbabcbccdcacdadcbabacbcbddcbdbcbbbdaadcabbbbacacbaabaccdbcaccddcdddcaacdacbaaddabcdacacbabcbacadbcbcaabaadbccacdcbcdccabaadbcbcdbacdbbbdaacddadaccbbadabcbddbdccbabcddabcbacdaadacbccdbdadbdacabcacdabbbcddbcbdbbdbcbdabcabbcdbcabdabddaccacabbabccdbdbcbccdaddbcbadaabcdcbbcabdcbbdccdabdccbcbbcbdcdbcbaddbadcbadadcdccdbdbddbdaacaaaaccababbbbbbcbdbcaacadcabccbcacdacbadabbdaaaadcbadacbbaacddacddddadabacdadccddbddaabddcbccbbdbaabdcaaccaddcadaaacbcacdabdbbdddbbaadacdadbcccaabbcdcaaddacaabcacdcbadbbaddabcdadbabbabcdcbdacacabdcdddddacabbadabcacddbcabdadacdccacabbdacaababcbbdadccbccdcbdadcdbdccdcbbcdadbdbabdabdddcdabadbacdbdddcacbcabcbcbddbddcddcdacadccbdadbaccabdaabdcacadbbdabdcabddadbaccbcabcbbdcddbcdbcdabdbdadcbdccaaddcaaccdbdbaaccbddbccacbacbcddbaaabbabcadbbdbcdbbccadabbbccbdccaabacabbbdcacdbdcdaaabbcacbbcabdbbaabdbaabcacadcdcabdbabcbaddcbbadbaabbdbbbcaadacbadbaacccabcddaccccaccaabcdbcddadddbadcadabaabaabcacdcadacdbbbcaaaccccccdbbccdcdbadabadddbcadcbddbdddabbdcbaaccbabbdbabccdcccbdababbbaddccdaacbacbdadbcaaaaacbbcbcaddbabddacbbbbddababaabcaaccbaaddabadcdddabbcdddbbbacdcaaabbabcaadacaadcccabbbcbbdbaabdcddadcdcaccacddddbacbbdacddcbbdaaccacbdddadaadacbdcadcbdcdbcbcaadccabcaabbdbbcbbaadcbabdabddbacdbbacddbaacdbaaaaaddbdbddddbacdddcddbdbbacbdaccdbbccaddbdbaaabbcbcadccdbbdcddaadbcddbaaacadcdbdccbaabcbbcadbacbddbbbdcdadccbcccaccddaaacdcbcaadacdcdbbcaabcbcdcbdbddbcdcaabdabcdabcacdbbcdacdaccacdbbdabdcabbcccadddbaacadcbdcaaadbbcdacdbdbcdaadabcacbdcadbcddbcccdcbabdaabcdbbacacbcdbcdacaacaabdbbabcacdaabbcdaddbcbdcabaabdbaabadbddaadcccabccccadcaccdbbccdcbdddbbadbddadccbccbdbcdaadcccdcadaacdcbcddbbdccddbcabdcdccaacaaaacbadacdaacaacbaaccadbddcacacdccdbabbccabbdabcbcdacaaadbabcdaddbdddacddcbdacccadcccaaacbbbddbdccaccbddbbbdaccabbababdbcabbabddbcbadbacbdcdbdcbdacbcbadddbabdaacdcbcdabacabdaaabbccadbabdadaadcdcacdbdcdbbccaabcdcaaacaccbdcacdbdbbaadadbbcbbdcdccadcbdcdddbddcbdabccbadacdcddbadccdcbcacadbcabbbbdccddcddddcaaaadbdaabbdbabbaabcaabbdcaddcbdcaccbcabdacccbddadcdabcbcccabbadbccabaacaaddbdcacbdcccbccacdbdbccaddbdaabadacdccdddcbdbdbcacacddacabdacadbaddbdcdcbbbdadbccdabacdbdcdbbcbbacabadbdbcacdcbabdccbbaacbcbcaddbcdabdbbbbcdbcbbaacadabababcadadbdaadbcdbadaccaccccaddcccaddcdbbdbdcbaabcdbcdacdbabbbacbaaaaddbabcbadacccdddcacbbdbdabbdcdcbddbdcdbadcddcabccaadaaaaaccacbaadadbdcdccaccdabbdcacbbcdadbbcbdcadcbbaacdaaccbaddddaaadcbdbdbddcbbaadbaaacabcbaabcadddccbbbddabacaccaacdaabdccbbbaddadccbbdacddaccdaabddacbdcbababcbcdcbdbcdaadabccacdbbdcbddcdabadbbdcabccbadccbadadbaaaaaddbaddabdabbdbaddabddcdcabdbdcdccaabadccdcacbdbaddbdccccbbdbcdbbabdccadadccadabcbdcabbcbcdacddadaaccbabcaabdaabbcbcbddabbdaddbdbdabbbccbdbabcbaaababbbccbdcacdbcdadbbcbbbdcbdcbdaaaabcacbdabbbbbadadababadacdbbaabbccaddabbacccaadbdcacbddbadcacaacacabcbabadbdaaaaccbdcbcbdadcddcdbbddabccaccdaadcaccdccbdaadbcabbaddddcbaaaccdcaadbdbdaaddacadacdbacabcbcbdacaaabaabaaaacadcadaabdadbabdccccbdbddbadcdcacbbacdddacadcdbcacacdccadbacddcaccbcadadcacaabcdbabacdccbcdacccbadababcabdbabbdcdaddadcbacacddabbcbdcaacdcbbcadddadabaddcaadbcdadadadabcccccadcaddaaabccadddbdcbbdbcbdcababcadbaccbccaaccddddbddadbddbcbcbbcabdcbcdcdcbbbcbbbacbdbccadacdcacadaacbacdcadbbbacddabcabadcdbcadbdcdcddbddbcbbdbaabcdddacbbaacbdabcbacbdbbacadbcbddcccbccaabaacbddbaadacacdaddcccccddccdaadabaddcaccbdbaabdcbdbccdacbbcbbdacacbcbdccdcccacaacdbdcbbaabcaccdbdbcdaacddadadbbbdbcaccdacddadbbbbaccbddadbbcadbccdabdbbcadaddaddcdcdcdcddbdabdadbbaadcccadbdbcaacabbdddabcaccacdccbacdcacbcdbcdcdcdccadbcaccdcadacdaadcaccdccddcbdcaddcdbcdbbdcbddccbcabaddddcddaccabcccbbbbbacacaddddcccdcdcaaaadcbbbabcccdcabbaabbcdbadcbbcbbcaadbbbcabadcdbbcdbadcacbbbdaadbdcdbacdbdccddbbdddcdacdddcbdccacbddcaadaaadcbdbdbadabbccdbbddbcabaddbacadbaddbbabdabbcadbbbbdabacabbbcdabdbcbdbdcaabbbbacbdcabcdbacdcaaacdacabbcaacdbccacdabbacabdbbacabaaddcacaacabbaacdbbdddbaacaacbddaccdbcbdcabdddcbddabdbcbdbacaaddbbbdcccddbbcdcbdcdbaddaccacbabccabdabdbaaadccddabbdcbbbbbaabcddadddcabbababbbadbddcdabbcddacccdababbbaadbccdddbdbcbacbbabcacdcbabddbababbacdcdbacabbcbcdcbaadacdabcaadcadaadbdbcbaabccaddacbdbdbcbbddbabbadbcbccadcabccadadbacdbabcdddabdbdabbacabddddcbcddcaccacadbcabdddbabcbcbdcbbabdaabdbacbcabaabddabddcbdbcbddaadcddabdbcbdccbcdcabdaadcbaadacbabdcadbbcccddaacbacdbdaddacbbcabcbbdccacdaacadcdabbddcdddddbbbccbdadabbdcdaabbacacdbcacdcdadcdbabdbcbacbbaadbcaadccdaadcdabcdbbaddaaaccaddaacbbcbbdaaacbaadcbcdcbddcddbdadbacdcbcaadbdbadccbbdccdcccddccddaabcabaddccacaadbbdabbbcabdbdbabbcdcacaabcdadcbdcacbddbbbccbddadadaccaccdbcbcadadcababcdaacacdaababdbcbddbbdadcdabbbaacadaacbcbbaadcddaaadcacdabddbddbdccddccadaccabbbdbbddbddbcadbdbdacaaacdddddccdbccacccdcdcacbdbdabdaadbddbddbbbbbcddddcdccccdcddddbcdccbccccbabaaabacbcdcbaacadacdacacddccbdddadddabddbaabcdacaacaddabcbdcdbbccdadbcbcbbadcbadcddaacdcdbbadbcbbaaacdcdaddcabaadbdcdaabbabbbcbdaccadbcbcbadcbbddbcbddbdabdddccbcdbdddcadcaaacdaaadbddbcdbbdcaabbdadbdbaaadaacbcbaddbbcabcdbcadcaccadbdbcbadbababcbddccbaaccbaacbacadddbacdddaacbabcdadabaaddcbbaacaacbacadadccabacaacabacbacdacccacccdacacbadbcdcadbbbcddbdbbcdadaacbccdaddcbbbbbaccddbaaabbbaaadddabdcdbcbbaababadcccadbbbccabababdcdabdddabaacbcdbaddbcbbdddadccacbdbdcaacdcddddbcdbdadcabbcdaadddbbaccdcddadcabdaabadadbdcbcbadbdbadcadcbccbdacbbcaadbbaaaddaabcdcddcadacddccabbccbcbbcddcddcbccdbacdacdaacadacacbabbaabbbbdabbdabaaccdcaddcbacabbcdacdbacaaadaaacdbcbbcaabccbdbaddcbbbacbcacbbbdbcadddacadaadbaddbcbacdaaabbabccdddcadacdcaacccabaaaababbadcacdccacbbdaacabbabcdbabaabbbabaaaabcacadcaabbabacdaddccacbbadacccaddabdacbbbababcdaddcabbdacbddaddcaccacddbacddacaddcabcabddadaadcaaabdabbcdabbccdaaabacbdaacdbaabdbbcbdaabdcbcbcdbbaacdccbbcdacabbabadbdbadcbccbaadcddcddabbbbbdcbcbcdaabacaccadabdcbcdbaaacbabdcdbbdbbbcbbccddbdcabbacbddcaabddabcbbdadddabcdbcddcbaddacccbccbdbaadacdbcbbbbdaddcbcccdccbdabdbacddddaccbcdaaadbcbbbdccccaccadacbaabacaaabacaaddbacbaaaabcdbdcddcaaabaacbcdadbdbaddaadddabddacacaddadbabcacdbbadadcbcdacbccbabadbbcbdaaacbacadbacbaaddcabccaabdcdccaaaabdbccdbaddcbbacbaadcacbbddbaddaaaadccdcaabddbaccadccddacdbdbcbaaadabccdcaabdddbaacdcdddbbabcdacddacddacabaadaaaadbbcddbddaccdcddaadadddcdcaabcaaaaaccbcdbddbdadacdbaaddbcbcaccdabcdcdcabccdadcdccacbbddcaaccbccdcdbcdcbdbdbdbccdacccbbaccaadcbbabcccdbdacdbcdabdadcbdbcbbbcbacccacdddbcdbaaacabdcaabdcaadcbdacadadccdadccddddabadbccadabcaaaadbaccbbadcbacccaacacdcacdaddacbaddacddcdbadabcccdbacbcbdbcddbdddbbcadccdabdbadddbdbcdddcddadbdbcdcbccdcbbacacbcaaabbdadbbaadbddadcaaabbaadbccaabdbbbadbbdaabacbcadbaddddbaacddacabadcddddadcbcacbdccbddcdbdacabbacdbadbdacbcbabdacdcddadacbbbabcacacdaadbdbcdbbcccdcccbbbacdcacbbdccbcacacdcdbcbabddaaacdaabbddcababcbddaccacbdccaacdbbbadbcabbddaaaabbaddccabcbbcccaaddcdccabcadbddabbbdccbccbbdbadbcbaabbadaacbcddbbbcbabaccccbcaacadbcbbcccbbcadacdcaadcaddcaaccdcbaccdaddcbbcadacbbdacaccddcbbbcdcabcacaccbbbcadbdccaadaacabdaaacabbcacaabdbabaaabaccdcacbcdacddbcaaddacbdcdcbbbaaaaacdbbdbccbabddccccddcbabbcbdacccdbccdadbccddbdacbacadbcbacccaacadbbcaaacdacbbdddadabacabacaabbdbbdbccdccbcadcadbabdacdcbddadcbbcbaabbbddabcaabdcbbdcabdcbccbaadabbcadbbbdbacaaacdacbabbbbdbaaccacaacabdbbacaabcbacacaddcbdabbdaabbbdbdabcbdcaaaadcadcbddbdaccdcbcbbcdcdabdbdacdbbbdbbadadbbabadcabbddaccddcacacbdbbacddbbadbbcadcbbabacbdbaddcdcadacaccaaabdaadcdcbaccadacaacdadadddbaabccabcbbaaabdddbbbcbbdcbbbcacbadadddaaacbcddccaaadcdbacdacdbdadbaacbbddcccaaddadaacdcaabaacabdbcabbcbbdcdccacbbbadcbbabcdbbcdadadddcacdcbaaabcddbabcaabddbcbaccddddaadcbcadcdccdaacbdabdbaacaaccdbcbdacabbbaabcabccbbbadbbcdaaabbbdccdddaaddbabcaadddccaaacabbccdbaddbcdbccbdbcaddbbcabdcdcbccbbcaacadbccdabcdbbdcddcbaabcdadddbaccdacabbcbacaddcacdbbbcdddabaddcdcdbbcbcabbacdcabbabacdbcddacdccbddddbaaacddcadcabddccadccccccacbbdabcabbdbcdabccccbdcbddccdadaddbbabbbdbbddcadabdccdccabdbccdcdbdbcbadbdaabacaadddacdbdacbdccaccdcdcbaccdccdaccdbdcaddbaacadabaccabdcadcdadacbbadbdcdbcbaabacbdaabbddbdadbadacddbdcddbbacbdbbaacbacbcdddaaaaaddcbbbdcbbbbabbbddbccbcadccabbcdcccbdddabbcbdbbbcacadaacdacbdcbabbacaadcadbdccccbdcdabcddadccacddccdadacbdaabddbcadabadabadbdbbbcbddbcdcddddcabcdcaaccacaccaabdbababbbbcaabcccadcdabadbbcdaaaabcaaacaabcddbcaadaccccaccdcaddadbbcbadabddcdadcadadacdcccdacdbabbcdbcaadbbcdacacbacdabcacbacddcccbaabcbdcbbcbabaaaaabbdacdadaccdaabaaabdcabcabcbcbbbaadadcddcadacbcabbacddaabcdcdcabdbcbabbabcbbbdcddcbcccadadccdacdaddacbbdcabadadcbbdcbbdcdcdbcaccaabbdcbdbddcdbdccbddbdddacdbadcbbcababbcdbcbbcaabcacbddcdcbccabbbdcaadbbbddbaacbccbbdaaadccbcbccadaccdacbabdbdbdddadcbabcaabaaccbacbccbcdabdadddbbcdcacabcadbaabcbddabdbaacddcacbbcaacadcccbbaaccaacdbabbdabcadcdbddacbacaacdcaabbcaaccdbbabcaccbcddcbabadbbbcdabcabdbcbbbcdddadcaddacccdaddcacddddcbacacaddacbbaccccbabdbbcddddbdacadddcaacadaaccaccbacbcccdcbcababbbaaddcbdbabacddabcbdcdcaccbdddadcddddaaaccbccddcbbaabcdccdcabcadbcadaaadacaadadaaacbdbdacabccbcbcaaccaaaddccbdabcacdaccccaadbddacbdabbdaaccadacbcacabdbcabcacaccccbbdccddbbbcbbadbcdacdccdcbbcabadcbabcaccbdbbbccddcbbdcddbacabbadbcbcbabaddbcadcddaabccabcadcacdcbcdccdacddacaccadcdddbbaddbbaacabdabacccbccddddcbddabbdcbacbabddadcaddcdbbddcabdbdabcdcbcdbdadcbcabdcaaccdbddaacdacbcaabccadcdaabbbbdbaaccccadbacdbccdccadbabababddcdcddadccbbdaccdbbdaacccbaacadaddcdbcbbdbbcadcaadbaabdbdcdbbadbdbcacdbcaaaabbadbbadbdbbccbcbbdaadbadddacdbdbbbbbdaddbaaaccdddccccabbabacdadacbacabcdbdcadbaacdcabbcaccccbadadbcddabdababcbcaabccccddcabadadbdabaabbcacabbbabacacabcadcccadaadbdbddaaacdabaddbcdbccdddababaabcacacbdaabcbacccddbdcbacdcabdaacdbcbbbbdbccddbbbdabdbbbabbdcbdaaadccacacadcbdccbcdaacacccaabcbbabbdbdbdcddddbbbaaddbcaacbbdddcddaaddabcabbbddcddcaccccdacbdbadbcccabbcdaddcdbcbdcdcbaccdcbcdcbcbcacddbdcdacccdbbcabddbccbbbdaabddcdccabdbcdaddaaadadaccabaacdbbaadcbdcabcbbbcddcacbbadbddddccbbddcdaabccdddbdbcdbcadaccaccddcddcbbcccbdbddbbddbaccacdbddcadaacdaaadccdbaacabcbdcbddbcadaadabbaacbbbadccdaacaabacdddaacdccaddaabbbddcababddbcabdddaaadbcdcddddcbdbacadadcaaabbcabdddddabdbcbbdbcadbcbbaccbabadbbaaaaadcabbbadaabbdbcdabdacbabbaaabbbbbbccdacaaabdddbccddbbbdcccdbbbbbddbacaacccddadbbbdaccccbcdbccbbcacadaddbcdacacddcabbadbacccdddcacadaddadaabbabacadbccbbbbbbabddbbbbbccdcbaadcbdbbddacddddaabddbabaacaacaacbcaddadaccbcabcbbbdbbaaccaadcbaabddcbdddacaacacadbbccccdbccdbcadddddadcbaccaaccbbaaaccdaabdcbbdaddcbdcbddabbbbdcaddbcadacdaacccbaaaddbcabddacabbbacccabccddbbcddbdbaacbccdaabacdcdbccabcdccdcbcddaaaddcaacdbaaadabdbccabbdddbdbddbabcbccbdcbaabbacbacdabbacbaabaaddcbacabdbcbacacaccbcdcbdbcbcdcbdadddcbbaddcadacacbaccdddabcbbaaddbcddbdcbcdcdadcbdbabbcdcadbcaaabcaaddcacabbdbadbdccabdadbacabacbbbcbccbcbdbcddcdcaccadadbcbbddccabcddaddbccccdabcabdbaababccdddddbcbbaadcdabbdcdbbaaaadccbdbbdbcdcdacbacaadbacbddabcabbdcdbcbabddbaadcdbdcddbadddacdadbacabbadccdccddbbbcdcddbaabddaaddbadcaadbbbacadcbbddbccbdbbacdcabacddddabbaadacaddabaddddabbbabbabacdaacbdbacbcadabacbbaaabaabaccdabdaccbadadbabcdbaadddccdaaabacbbdbbaadbcbbcbaacacabacbbbabdbcdadcdbdddbbdabddbbdbabacccbbccdaadbbaddbddadacdbbdbbaaddbdbacdccaaacadaccdcaddbdbabcccadadaaddbcdbacdbbacbabcbaaadbccadcccdcbcbdbdabaacbbcadbcacacdbdbcabbcddccabdcdccbadaabddbbcdbdbadadabaaababccdbdaaccacacdbbbddcccadaabbddbadbddbabcaabdcbadddabcdcdabccdbcddbbbcbbdbddabbbbaccbcccadbcdcadacbabdaaddadcbbbccaddabcabacdaccacbcdcdabbbbcbaaabcdaccdbbadcdcdabcaacccabcabaccaaaaaddabcadbcdddcdabdbdcdbdbadddcaabdacacbdcbbbbaccddaccdcacbabadcbaadabbabbabdcbabaddddbbccabbadbddcdbbabdaacddcddbaadbcccddcdabcaccacabbbbaadddacbbbdbdacaacddbacbbdcbacdcabcbaaabcddcbddacbccabbbabdcbaccadcccbadbaddcbbadacccaabadacbbcacdbcaddacadccddacbaaadddbbbcaabcbabcdadbdccabbadbcadbddbdccbadbcdbaaabbbddcdcddbdccdbadbcccacdddbaaacabdddacbbccdcacccaabddbacbcbdaacaaacdbbddabcbbadbdcbcbaaccdacbcaacdbcccdabdabaaacbabdadbdacaccdbbcccbccdbabbdcbabdbabdbcadddddbacbdcddbdbcdbbcabbcaaabbacdcdbbabbbdabcadacaadcddbcbadaccacaaadabdbadcdbadcadcdbdbaccccddaadcacdbacbadcbdbacbdbabbadbababcdbadaaddbbbcddddbbadacabbadbddcbcbddcaabcdcddcaadbdadcbbcccadddccadcddbdccccaaaddacbbcddcacabbbbcbdccbdbdadbbadbcdabdacdcdabcccbcdddbcacbdacccacababcddabcabadddabacaddbadacdbcbcaddbbacadbdccdcbaaaabccacadbccadbcccaccdaccdadaccbabdabcabdabcdbbccdabdcdcabbbdbdadcbbcbcbadcdbbddbacdcdbdbcadbccacbbbcbaabbbbcbdcabbcadaaccccaccbccadcaababddcdcbbbccaacaaaabdddabcbcbbabdbacbaadaaaabbdbbbdadcbdbabcadbaabcccabacddacdcadbaabbababaaddcdcdadaaccbaabdbdcccddcadcadadcbbcacbdcbbcbbaacdaacbcbccdbddddbcbdbdddbcbccaddabccbddbdbdccdabdaaadcbdaacbbccabccbbcaddcacabbbabcbcdacbaadcdabacdadbcdccbadcdbabdacdbacdbcbaacbccbaadbdadccaadcccccddcbabccbddbdabdddcddcdccacbbadabdcaacddacbdcbaabbccabcbcacccdaaaccadaccdddabacaaddbbaccadaddcccddbabcbdbabccabcabaaadcdccbdbcacbbddcdbddcacbdabadababbcaacbccaadcaacaaabddaaaaacdacccaaddddccddaabadcbcbaabaadcddacdbaadacccadadadbaadaabaddadbcdacbddbcbdbbdbcaddccdacbadbaccdbcbcddbaaacbbbaabbcdcbddadcdcdbbbddbcbcdcbdbdcdaaddcddaabdbacbbdaabdcaabdacbbcdabaabcdcddbdadcddccdbddadcadbcbbbaacbbbcbaddadbdabccdbcccbcccacdaddbaabbcaaacddaddddcbcdadbaaccacccadaaadcaacdabaababaacdcbabddadadabacdddaacacdbdcbcabdbaacdabacbdbcbcccbadbaaabaadbcbbcbadaaddabdadbacaabaccbdccbaddcdabbacaadabbaaccbbacacdabadbdbcbccddddddcaadddabbbccbcddccabddabcdbacaccddadccbbdcccdccaaadbadbadabcaadadabcdcdcddcdabdaddccdcccccbcabbcbbbdddcdcccdcddacddaddabdcbdcaadbdddcaddaddbdbbccbdbacbabcbabcdcbdcdbbdccbccbbddccdacccadbcabbdacdaddbcbaacbacdcdcddbdadabccbbdcbbccddcdabcbddcdcdabcabcdacabbddcdcacadbcabcdbbbccdbcbabdbbababcbbbdacabaaabddcacabdababcdaccdacdadaccdabdabbbabacdaddcaacdbdcdacbcbbdcdbcdbccddaadaddbdacabcbadcacccacacdaddbdccbbdcabddacbbbbcbaddddbdcdcdddcbcddcddadcddcddabacaaccbbbbcaadccacbcbcdcbcadcdbcbdbbdaacdcdcdaccdcabaaababbadabdbccdcbbaaabdbbddbbbbcabccdddadbbdbddbdbcacddcbabcdabbcdbddabbadddccddcbaacacdbadcdddbcdabaacbddddcccdbbcadcadbaccccacbaabcbcdccbaddcbcdcdaccabcdcaaadbcbbabcddbcdaabdadadccbbabbbbabbabaccbbabadbbdddcdbbadddbcdbcddbcbddcadccacdadacdddcbaadcabcbacbbabdabacbcccdadacacaabdbcabbcbbaccdccdadbdbcccddcadcdcacabaadaacabcdcaccbaccabcdccddbbdcddabddaacacadccbadccabcdbcabccdacdcbbccddcdddcccddaacdaddbcdcdcaabbaccbbbcdacbbcabcadbaddccddbccacdddddabbbbddbbbcdabbdaaadabcbbdacbddcbdaaccbacabaccabdccddacbbdddcacbdcabaabbcbbbbabbabdbcccccbcddadacabcaadbcbacdbcaabcbadbbbcdcdccbddcbcdcaddddbcdbacccddaacdbcadbccaccbcdcccdbacbcdacdcdbdcbadddbddcdbbddacbddddcccbdbadbcdcadccdbbccaadcbbacdabacbcbdadbacdbddcabacacbacddbdaacbddbcabddcdabbccdadbbadccdadbcdcbacaabdaaabaaaddcacdbccdcdaacbaadbdcaddbabcbccaaaadbccccbbddbadacabdabacdcccbaaaacaddccdcacaccbaaabdaacdadaaaaabcaabcadadaddddccdccbbdcbbbccbddacabacbddccbababddcabcaacbddadbaddaaacaaadcbbbbdbdddcdcacbaabdadcbdcccbabacbcddcccbcbdbccdadccddddccadcdaadccadccbbcdddcbcabacababcdbacacdacddcabadaaabadaabdbabbdaaddbcbbcdaccadbbacaddaaaccbadcbadcbbbbdabbbdacdacdacddaddacddacabccbccaadbacabdbaacbaccccacbddaddddddcabcbacbcaaaddddcaaaddbdbbbdaddcdaaaabdbddcdaadadbacacbbdacbadbbcdbaabddacdacdabcccaabaaddcaccaccddbbcaabbdcdaadbaadcadadacabdccdbcddcbaaaadcdacadbbddadcadccaacaabccdbacccbbaabaaacddaabcacadbbbadcabcbaabbdcaaadadacbbddaccdaccdacddccadacaabdababdadcccccbdbcddadcaacbdcdaaccdbdabdadbdbcacbdcddcdaddabaadacdddcadbccbcadcbabddccdbbccadacddbabbddbcdcbcabacbabbbcdcdcddccabbbcacbccadbdbadbabbcbaadcbcdcbdbdcaabbbbdccaddacbbccacddddbbdaabdbcbdcdbbcdddbddcbcaccdbcccaaaadcccbabaabddaaaabbdcbbccabdbcbadddbdccdbbdbcccbbbabdcbbbcbadacaabbbbcbdbdcbabddbdcbcbbabcdcdddcbcaccbdcdaaababaadbddbcdcabcaaddbadbabdbcabdaaacccaabdddbbabacdaadbbbacaddcccaaacbbcbabdadbaccccdccbdaadbddcbdadbdbddcccccacbdbabadabaddccbcaddbbaadcbbcbabdabacacbaadbdadaadadaaccababcccbddacacdcdddbdbcddcbdbdaddadadcbbcdbdbddadaaabbcdbdcaacabccbacccdbbabdbbabacbdcdabbdcadacadcdccacadcadbccbcdbcccddbcbccabcbbacdbcbcddabcadbbaddbcbaacbbbdbddadabdadabbbdbcaacadccdbacabbabacbdadacacbbaaaabddbcbbabccacbcbbbadbbcccccdadddbdcccdbbdbddaaabccabacbacbbcaddddcbadcbddccaccbdccdcdbcdddcaabaabaacdccabdaacdbbbdbbaadcadcaaaccdacdbaabacbcdadacbaacdabcadddcdbadcdbcccdddddccbbbccabacccddabcddaddcccaabaaaccacddbabbbccacdcabcccabcbacbddacccadaadbacdcbbaacddcbadcdadcacbdacadacbadabaadcdaccaaabbabcddbbccabdcdacbccbbbbccddcdadbdccababddacdaaccdcbaadacbbaaacabadbdccdbdbbbbddbadacbbdcbdbdbabacabaacaaddcaadcaaabaaacdddcaabadbbbaaddbbbabdadccddadccaaddcdbbaccdadbadaaacabddbcbcaadcdabcbccbcabbcbcbcabcadaccbccbaaccadddbcbbabcbccbbbabdcdaccabaccbbdbabdaccbcccdddcbcbaaabdbacabbbdabcaabacbbcacddddcbaabaaabaabadacbbdcabcdcbbaacbabbbbaacbadcccdaaaccbcbcddacadbddddaacadcdacabbcbcaccadadbcccccaadccdcdaccbdaccdcdadcabbadccbccadaaacbaaabbbaacabcbdccdccbdbcacabbdbcabdcabdcbabcdcabbdcabccbcababddaadddacabbcbddbbbcccacabbaddbaacbcbddbaaacbcbacbbddacbcababcbbabddaadccdbcaccaabdbaddacdcabdccbdbbdccbadbbadbbbcabaaacbaaababdadcabdaaadccddbcaadddcaaabaccaaadacddaadcadbdcbcdddcadccdcabccaaabaabbbbacabbdccbcbbcbcdabadbdbdbacabccbbcdbdccabcaacbcdbcbbdbaabacabaadcbbccacccadacdaabbcdbadccdcdbccdabbcbdbddcabcabadbbdcdcacccccaadddbdccbbcdabdcbdcabdaaccbcacbdcbaaccbacdcadbaacadbbcabaaddcbaacabddbdadadddabdaacbbbcbcccbabaddcccdabbacbabcdbbcadcabcaabaadababaaabcaddbdbccdbbbbcbaadddccbbbbacadbaddaadbadddaabcabddbdacdbdcbaaccdccdddcbcaacbaadccdbbcabddbbcccdccbcacbcdbdcdadbcdaacdabdabacdddaadaccbbbacadcccdaabccdaadbbabcddabcdadccbacdbdcdbdbbdacbbbdbbdbccdbdabcbcdbddcacacbcacbabcbacddddadcacabbbaccddbdcababdabccaccddbddacabacdcaccbcaaccbcbbdadbdababadbddbcaabaccbacdbbdcbddbaddabbacddcdacdacbbacacacdcaccdcdcccaaaccaadddbadddcabccccdcbdbcadadcbacbcaaddbbdcdddccbbcababbbccaadccdaabcaaaabbcdaaabbdcbcabacdcadaaddacbbdadddbcdbddcadcccbbbbcabcaaaadadccabccdabcdcbdddaabdcdcabdccacbdbddbcaaaaccbccddabcbbddabbdcbabcabbcbdbacacdbaddbddaabdbabbbdddccadbdcadcccbccbbddabaadabbcadddadcbbbdcabddccadbbbadbbdddcaadbdbabbcdcaaaacdcbbdababcacddcdbdddcabbcbabacbcdadbbbdbbcbbcbcdbcdbdcacddaacdddcccdbbbabcdbadccbcaadbbcccacadadacbbacdddcbdddbaadccdacbacabbacdadabbbccadbadcbaabcccbbcacdcaddbcbaacbdddcddaaabdcbbabddbddbacbababbabcbbbcdabcbbacbdbddbadbcadcddaccbddccdacdbaabddbcbaccdaccbdaaabdbaaadabaaddcdcbccbdbaccbbadbaaadbdbcdcdadbabaacdcddcbdbbbcadcacbdacaddcbddddacbbaadbcddbdbcdddabdbccbbacdbbbdbadccbbaacdddcbdaabccbbdccadbbabbacbbbbabacadcbcdbaacadcbabcbacdabccadbcbaabcbbbbabbdacacdadacadcdbcbbdcbccabbaaacddaabacdddbcbcadcdbcacbbcccbbbbcdbbccabccadaacbccccbcaaabddabcdaaacacbababbcdbddabcadccdacccadccbbddbbcbbbbacddbcccbdbcbbabbbcaccbbbadbccddbbcbbddaadaabcababbdbcdccbddbddbddcabdacbbacadcbaabadadadaccaabdbbaaccaccbcdbbcccbccaaddbddccbbdbcbbddaaacdcdbccbcacbccaaabdbaabaddccccbbbaddbccaccbdcccbdcaacacdbcaaccaccbabadacdaabbabaadbbacabaacdbbacccabdacbcdaccbaccacbbccddbdabdacbaaaabdcddbbccbacccababdcccdabdabddccbacadadaaaaacddacaddddabcbbacdbbbccbcbddddbdbadcabdacbbbbacdddbdbdadbccaaadcddadbdaadbacddcbcddcbddbbcacdacccaddbbaccacaccdccccddbaacabcbdcabcabcddccddacaddbcdbdddbabdbbddbaadcbbdbcdbdbcdaaaaddabcaccdcaddccdcabcabcbbaacbbacbdcdadccdaadbacdadccbadbaadcbddbabacaabbabaababdbcabadbbabcdbbaaccdddacddaadbbbdcdccdadcdddabccdabacbdadbbddacaadacbaccbacdcdbbadcddacddbacdcadcdbccdbdccaaadaddcbcacaccdbccbbbcdaaaacbbdabbcdbabddcccdabdadbbbaabbddbadacbbccdbbccdadddaddccddbcdbdbaddabbcbbdbcdcaabcbacdbcaadcdddcbaddbbbdadcabbdcccbdbdbddccaacaaaaddcbdcadddadcddacbcbcdbdbccbabdabdcbadcabdcdbbccddabcadabbdbbbddcdddabbcabdaacdaaadabacbbdbbaacbbacabaddccdadadcaddcbccaaccbaacacccbbdabbdbaadabdcccaabcddcdcdbcdcadcacdddbddbcaaabccacdcbdcbdabcbdbccdddacbadcddcdccbbddcbbbbaacbabbdcbdbbcaacdbddcdbbcbadacdabcbbcdabcbcddbdcacccdcbdbdaacabadcbdbabbaaccddbadbcdbdabdabddacabababcbdadddacacbaabdccbbdacdbbbdbbadbabacddcaadacaddcaaacdbcacdbbcdbcbcbbaadadbdadbbacaccadaaababbdbacdadbbaadbcdcdbabcabcdddcadadacbcdaabbdbbbbbcdcdaddcbbbdabcddddadbbddaddcdbccadabbbdccbbdaddadccdababdcbbadcacdbbddbdbdaacccbccbbdabbcbcdcbcdddaaabcdadadacbdbbbcadabbdccabbbcbcbccadcdabbdacdbddacbcbaabbbddddadabdbbadddadadcbabadddbaccaddcadcdccdcaaaaccaccddabcdccbbbbcabdcacddbbdbbdaddbdbbddaabbdacdbdddbccbcabcbabdaccbdbaccabbaccbaaccaaddcbbdcdcdaabdbabddbaacbbaaaccbbaadabccdabccbdcccaadccccbaccdcbdbccdcdaaccbaddbadbddbddcadacbcdcdbabdcdbcabcacbcaadcbbadcdcbbaaacdbbadddcbcbacbcdbacdbaacddadccddadddbbaccddcaadcadabbbccdcbaabddddbbcacddcaacdbbbbcbcdcddadcbacacdcadbccddadaacdcacaabcabdbdacbacaaabaaababdbbcbcbbdbdabadbcabbcadbccbbcdcdbcacbabbccaaccdacdcbbababcbcdccbbdcdcaccccbcadbdbdabbbcacbcdadcbddbcacadbcadcbdabbabcdaadbcaaadcadcadbdbddbddcdddadacadcbdbadacdbdcacbabcdbbbcdabdbabacaddbbdbcccbbbdbcdbdbacdbcaadddadddbacdcccaacadccdbcbbaabbdacabbaacaddcdbbddccdabaaddcdabdaadadbacbcdcabbbcbaaadcdabdaabbaacbbabdbbdcbadbadccaaadabdbdbdacbbbaabadbcdaacdcdcddbadddbccaccacbbacbdbcbdcadadcccddcabcddddacadcdadccccbccbcabaadcdbbaadcbdaabdddccddadadabbcbddccbaacddadcaddabdddacbacbcbabdadccbccdadabbbcdbdbcabdabbaaabccbadbcbdaacaabbdcbbdadadbcbabccbacccadbabbabcbcccacbadabbaabbdadacdbacbbddbbdaddbcbcbcbaaaccbcdbcddbddddddacbdcabbbccbcbbccddbabcbcdcaabaaccbabaadddadccdcbdbcbadbdccbdcbddadaaaddaadacbacabbcccbaaaddddddbddabcadbcaacacabacdacbaaadccdbdccdbacaabccdabccdbbcbadbbcbbbbbcbacddbabaaadabacddcdcadbdbdbcddaddaaadcacbdbabddcaabaacbaaacbcacabddbbccddbdbbcbcdaaadadbcabdddddaacdadcbdbadacdaddbdabdcbcddbccdacdbdadcbddbadcdacdaacbabcadbdbaabcdbdabaababaddcacdbabdbdadbccaacadbabdababbdaaabddbbaacdadcacdcacbbaccdbbbadadabdcaddddabacbcabdacdbaccaabdccacabccdbcdcdbacccabaadbbbddaadcabcadaabaaadaadabcdbcdaacbabddadbccabbaaddcdaacbccbadababccccbcaccabdaabaaadbcddccdaabadaadbccdddaaddacdcacdcaccdacadbabdbbdcddcbcabdabcccabbabaadadaadbadaacbcbaaaabbcbabcccbaadabcdabdcdbcacbacaddacbadddcbcbabdacbcdadbbdccddbaacaabcdcaccccccadccadabbddcaabccacaaacbacaadddcbbdbcbdbdcabccbcbdacadddbcccabdaaaaacdddcadcaccdbaddabbbabdcdddcdddbbcdaabcabcdacbdccaddbdbcbddbcdcdaacacbddaabbbdbabdcccbbcadacaaccccdaacbadadabbdcbabbdcbadcabcbbbcaacdddbbbaaacacadcccdcdaadabaabbbbadbacaacdaabacccbcadbdadbdabdadcddbdbacadbdacaabaadbbacdddcbcbbbaacccadbaaacbdacbdaaaccbdacccdbcbccaddcabcbccddccbbbbbdbdabcadbcbcaaddcdbcbdacaacdbccaacddacbcbcbbadcccbddabbcaaddacddabdcaacdbdabbaadaddbddadabadadaadacbbddabdcadcaacacdbbaacdaadabccaccacadacbcabdcdadbbdbdccabccbbccdbabaddbdcddbccdcaddacadadaaabdbaacacddcbbbabadcbaacdbaadcdbdbbbddcccbbcbacdcbdabdccdbbadcddccddabaacdbcadaccacbdcabcdbadbadabcddddadcdaddbabaaaaccbcbcbbabcdbcadcdaaadcacbdbadabdcacbaabbbdbaaaaccdadaabddabdccbacadbadcdadbbadaabaddbdabbabddaadccbcacabaabdcbabbbacabccbbdcaaadbbbabbbbcdacddcdcaddaabdcabaadbadaaaacccbcaadccdbdcbddddbdcadaabacbbddacabaaaaaabaaadabdcdcdbdbdbcdacaacbdccacacaadbabacacdcbdcbcccbdccdbdcadabbadbddabaddbdcadddabadbddccaaaddbccdcaaabbccbdccdcabadacbacddbdadaddabbbacadbbbcbccaaaddabdaabddcbacabbdcbaaadaddbcdaaaaadbbdcacdaccdbdaddabdcbacabbadbdddbdaddccccdbdcdbabaaacaabdcddddddcacabcdbdddadbcacabababadbcbccbdcaadaadbbbddbddabcbadbddddbadaabdbdccdbadacabbdaaddbcbaaacccccaddbbccabcdabbdaddbdddbcddbadcbaccdaddccbdbbdbbdcaadacdaabcacaccdcddcaddacbaaabdaccddccbbcacacdcdbcccdddcaddbacccaadbcbccacccdcadccbacddbaddcccabaabbcabcccaccaabbddadbccbbacdacbbdbdbdcbcadbdccbdadacccadadbbabacbabcabbdbdabbcdddbbabcbbbcbdcbbdcdbbadcbddbdbccbcabbccdcabdcadcdbddbdcabddcabddbcdaadaccbbacbbbcadddaaacbacbdbdccacaaadcbcbbaddddcbdadbbbbdcaabdcdcadacaddaadddaccadbccdadadbbdabaadcadcacabcdabcbaabcbcaadacdbabcbdcaddbadaccbbcbaaddcdabadbcbbbbbabdcbcbbbdbcaacbbabadbcacadaccabbdcddbcddbddbcbaabbbacaabddbaaaaddbaabcaacbdbbcbbcacddabddccbabdcdbaccbcdbdccdababcacdcdcaadadccdacddddcdcdcacadcbccbacbaacacbacababcbbcdcdabcbbbacaccacdddcbdbcccacbadcaaadcccccaccddddaddadbcbccbcdcdacacacbdababddacabbddbcbcabbdadcbababdccdadbbdcbabaacdaabaabdcdcccdaddcbcddacdccdddddcaaabcbddddcbadccbaccdaccabbacbcabcbcaabaadacbbdbbbddddcdbabdaaadbadbdddbbddcbdacdacbdbcdcbcdadaccdaacabdbdcababadccbcccadcdcbaabbbdbcbbdbaccacacdbcaaacbacacbdbacccccbbaadbdadcadabcacabaabaacacaadaaabdaddcdbcbcaabbddcacccdbdaddbccabdcdccaadbabbdbbcddbbbaccaddbdbcdbbaaabbdacbcbbbadadbabcbddbcdaaacbdcbdddabdcaacacccbdbdcbddacacaabbbccccccccdbcacbddadacbadaccddcbadccbacaadbdadcadaabdaccbbbddaadbdbbdaabbcccaacccdddbbabddaabbddbdcbdacdabdcacdaabcdbacdacbcdbdaaddcaacacccccbbbcdbacaddaadbadbbaabbcdacdcacdbcdcbbcccadcbcababcacdccbccadabccbbacccabacadccccaddbadbbaabbabddcabadddbdadbbddacbdcabbbbabbcdaadacabcdaaddcddcdbdbaadbccbcbdcbacadccacaaaacbdbdbddbabdddacaacdbbcbdcdcbdadbdbbcbdcddbbaddbcbabbcadcacabcdabccbbacbcdbddcabdddcbbdcbdccacdaddbcdaddcbabcbadbdabaddbcaacbbacbcdbaccdddddccbcaddbaabbabdbdcbbdcbbcbabcacbdbcbdcbcbaaaadbdcbdccddbaabdcdbbbcdabcacacaacbbccdcddabaababaadabccbabdbabadddabcddcabbabdadbcbcbaaaadcaacbddaadbdcdbcabcccbbadabdccccdabdcddccadbbdadcccacbaadbdacbdcacbcaaccdcbdbadabbabaccabbbadaabccaddaaadccddbacaccbbdaacdcdacdbcbbbbdaacabdbccbbddbcabcdbcbbadbdbccdadbaadabaadbdcdacddcbccbdcadcacbdddacbdbdbbdaccdcabdaacaaddadbcdabdddacbccbdacababdabbbadadadbabddaaddcbaabdaddbbccdcddddcccadbcccabbdbbdcdbbbdaabcccccdadacbabaacdddcaaddacaaddabcbdacabbdbacdcaaaccdbacddaddcdcccaabdddadccdbccabadcccdabdadbabbdddabddaacdcbbccddbababdababcabacdddbbccaacadcadccabaadabacddacbbacacdaacaddacbbccdddbcaccbaccdabbbdbaacaccdddbaaadcccadbbacbcbddacadbcdcaacbcbddadbaabdddcccacbcaaacbaaccbcdadaabbaccdaaadcbdadbaadabcdbccadabdadbcadacadacdccbbabadbdbacbbaadaaacbcdaaabadcccbbbcdbbcbcbbacaacdccbaabccabacbbcabdbbdabdabbaabdbdcacdddbacdcadcbbcadbcdbabdbbcbbcbabaaadaadadacccabdbcdbbdabcdcdbabbbcdcaabdcaccccadabbacbddabcbacabdccbccadabbcbbccadadadbcdabaddbcddbdadbccadbbdacdbbadbdcdabaacbdbbaaccccbcdbdcacdcdcaacdcbdadbadadcabddabcddbadcddddbdbcbacccdcdcdacaabbddbbdccdbdaacddddbcbcbdddcdbbabcdbccadabaacbddcaccaacdcdccaaccbccbdbabcbcbbaddaaabcdabdacbadbdbadbbbdcbbdaabbaabcdddcdcdbbccdbcdcdcbdcaacadbadabdabbabbacdaacbbdbccacaabcbbbbadcdacbbbacdcdcabdbabcacbbdbddbdaadbdabdbcabbddccdcddaddbcdabcddbdcdddbcbdbaddbdddcbaaabadbadabacddadcddbaccbabdbcbdbcadabadbcdccbdcabacadbdbdacbbaaaddbbbdcbcabdadddadbdbbacadbdccbbccacdbddcabbcbdbbcdddcbdbbaadccbbbdccdadddddabcdabdddccaaadbdabdabcdbdbadddbdacadbccbcdbababdcbadcccddcabcbdabbcaababcbdbbdcbdcaddccabbdcddacdccaadbcddacbdaccacabaacdaaacdcbacbbacabcccdacaadbcbbabcbadcbacdabbccbcdddcbaccdcadbadcadabcdadaaaadadadcabaccabdbacdcaacddbdccacdbcdccacdacbbcaaaddacbbbcbacccbbbccbaacacadbbcbcccdaabdabdacbbadbddacadaaacdadaacbcbcaadccaccddcdbcdcdbcabacccbaaacacbccddccbabbcdaaaabdbaaddbdacbbcdaadacbdddabaddcbdccbbdddadabddcacdbdacadccdccabbadaabdccdbabdbcccbaacdbdbcdaadbcdabcacbaddaabcddcadccdcbaccadcdaadacbccabbacadadbbdabdbdddcbcdccbbacaddabbdadaadbbacadacabbcddbbbbcdcbcbccdcadcacbbcaacccaccbcaadcbacdaaaacddbaccddbddbdddabbbdbbbdcadbdcaddcddacdddbcbaadadcccbbbbcbdcdcabcbbdbacaccaadbadcbbbacdcdbaaabbbdccdbadbdbdacabdcdbdccbbcbddddabadbdbddadaaadacacbddcdcabbbddddcababdacaabdcdcdcccbccbcbaddbdddabdadddcccaadccacdadabcbbdabbabacadabcdcaccbbcaddaccbdbdabacddcadcbcbadbbadbccadabacddacdacbdaaabacddccadbadbacdbcccdbbadbadadcabcdbabdbaddaaacacadddbaadcadcaddbbcadabcdaacadbdccacbcccacbcdbcadcdbdacddccbddcaaaddacbddaddaccacdadcabaddccdbbddaadcbcbaddbccbcdbaadacbbbcdbcbcccbbbbacabbabbbcccbbababcaddbdccbbaabbcaabdbdbbdbcdcddabbbbbabbbcccdaabaaaaabdcbdcbcabacadbdcbdccbdddaabbbdabdcaacadacbccdddbadbadcabbccabdcdccbcabbbcddbbaadbbccdbccdabdbdaabbabadbabcacdbadabcbbdacbccdcdacadabbbddaddbbdcabaddcacdcbcbcbddcabddccdbaabcadbbbaddcdbdccabacbddcbadbdccdbcaccdaaaddacdcbdcbcaddccacbaabdcccbddaabdbccadbadbbcbbddcdcdcbbddbbbbcadcdadabacdbbbdcadccbcddcbaaaabbbaabddbdacdcdcbbdaaccaacaaabdcbabbccddcbbabcdcdcccbdcacaacacbccaccdcdbacddadacbbbadbbcbbbccbddacadadaddccddbadacaccaaddbaccdccbcaddccaddccbbabaaccabadacddaaaadabccdaacaaddaabdaddbaaacbcbcbbcabdddbddbdaadccaaadccdcbadbadadcdabadbddddccddabdcabcbcbcaaacdaddbcbbaddbabdcbacdacbcaabacacbacaaadadbadbdbdbccccaccacbcbcbcbdbdbcabacadbbbddcddbbbcbadabaacacaacbabddbcdabdbbabbcadcbcccaabdddbacbdbaaaaaabbadcacacddaaddaacdcbacbdadaaaaabbbaacdadcddbdcdccbddadcabbbcacbdbaabcdbbbdbdadbcdadcdcbacaabbdababacbadbacabacccabbbacaadbbbaacdaadacbdbbbabdaaadbbdbbbbcbbbbabcbbddabccbdabdbcccaaabadadcabcbabbbbabccaccdabdccdabaabbdbadcbaaacdbabbcdcbaabbbdbbbabcddaddababdbdddbbcbbadbdcbdaadabbdbbacccadaaacbbabccddccbddbabbabacbbbbcaaddaddddcdbdcbcdbdbdbcccadbccacabcbcadcadcdbcaccaddccdbacdcbabbddacddccadaaddcdbdcddddddddbdaccdbbaddddbbccdcdabbbdbbcaabaddbccdbddbddadddbdaaccdcddbbcabcbbacdbcabdcdbaadcabbaabdcdadabacccbcbdaacbbdacdabdbccaadcbacdaccdcabdaabbbdadcdbacacdddccbbcbacbcdaddbcacbcacbcdbacbdcdccbbcdabcdbacaabcdaacbbbdbccacdddddbbbcccddabacbcbbbbdccaaacbabcaccabdcdbbbbaaadcddbbcabcadabacbabcacabcdddacbbaabcabbbaddbcdbbbacdcaaddbadbcabbaabddbddbabababcbdcacddbbcccacdcddabaabadabbabdabaddadadcdddbcdcccbbbbbaaddbdbaccbbadbdcdbdcdcdbdcdcddbdaaabdcdcccbdabbcdaadbadabcddabaacbcacbdbbdbacdbacabdaaaaacaaaaddcdbabdcbbcdadaabbbacccbabdacaddaccabccccbdaaddcdadbdbbbaccbdaaddbcbdddabbdadaddccdbbaaccadbddbbcbaadabdcbacaacddabbbdaacdcddddadcddacccaabacbabdbadcbdadbdddcbddaaabbbadbbbddaabdbbaadbadddbccadcdbbaaaacbacbbcdddbcddcabbcdddbbaadabacbdcbabbabcdbacbacacabdabbbadaabcaacbabaabadbddccbabaddcadcbbbbdcdaddcccbaccaadbadacdcdcdddacadcdbbccaaccbaadcbbcadcccbadacbacabbcabdaccccabcadadcdaccaddadadbcbacccccccddddcdbabbaccdcaabdbddbccdcbaccbccaabadcadbcdbdddddadadabcbcdcbbcabcabdabaaccadddccbccbccaccaddcbabdbcdcbdbaacacaacdbccaddacccbacdbbdcaadbcdcbabddababaaabaccdbcaacbadbdbaaddbaabbacccaabbbabbbdddabcdbabcbcccbbddbcbccadcacbddbcdbcddbbccdaadabdcaaaacbcbcdbabaabbadccaabbcadabdcaccadcabaabdcaaddbdbabdcacacaadaaabdcaddccbbbbabcdbbccbcddaabbbaaadaacbadaccbccdcaacaccbbdaabbbbcbacbdcdaccdadbccdbaccccccaaaacdaadaaabbabbbabcaadbacaadcbcdbdbadadcbcababacadcdaccbdbcbdcdddcbadabdddabacdbabdcabbacbbcbbacadcacddadadbadadaabbabbcbbacbaababbbbccbcadcadcddccdcacdabbccccaabbaadcaddcaadaccabacddccddddddcdcbdabdabdacdcdbbbbcbdadcbadabbabacbdddaddbbbaabdcacdbabababadaccccbbaaabcbcdbcaabdcdadaadbadabaacccdcadbcbacbdabdcdcaadaccdcbbbdbaadccacadddcbcacdaccbbcbcdcbbbddadbdbaddaaadccdbcbccdddbbaddadabacbdbbbabadacacdddccbadbcddbaccacadabdcaaccaaacdccdaacdbaacabdbcaddcdbcccaabbbcbbcddcdcdbdabccaaaacddbbbbcdcbccbbdccaddbdddbabcddbbbcdaaabdcdbdcbbbadabbbbbbbccadaabbbabbaabdddaacabddcdbcbbbcaccadbcccddbdacddaadcccbcdaaaaccbdaacbbbcbadccbddbbbdaacdccdadadcdcdcabdcbcadbbbdbbdccccbcdaccbbbbcbdaadbbadaaabddaabcadccacbbbacbcdbccbbcdbccbbbbabadbbbbcacaaacccdababdacadaadddabbccaccddadbdcdcbbdcaccdacabcaaaacabddacadcbcacdbdbbcbaabaccabcabbbcdbacbcbdaaccaccdaaabcdacaddcbbcacadccdbbbcbdbdbcacdacbcaabbcadcbcccbacabcbbadcdadacdcabdbcbddadbdbabaddccbbacaaacddbabcdaddcdadcddcadadabdabccbcdcbbbaccdcaabbdbbabbbcabcbdcbcbcadcbdbaacaaccccabdcbdcaabaabbacacbccbddadaccddbbdbbddcabbccccdaacabdabbbacbddabcbadcbbacadcacbbddaccaddcdbadaacddcccdbdcdbbdacdddcdccbbdbdabdbdcccbbaacdaadcadbabccaaadbdaccadcbbddddddbcbcbccaddcbbbccacaabbdcbaacdbdcbcbaacbadabddbdbdabbcbcababcaccbcccbbbadbaacdcdbdcdaacaadddcbccbdbcddabbabbccbdbbadabcbaaadddaccdcbbdcabdacdcdadaadaacaacaccbdaadcdbddcbabcbdccaddddccbbdccacacacbbcacbcadaddbdbdcdcbcdbccbbdadacbdabdcccbbddcdbbacacdbacbbaaadbacdbdcccbbadbcbddcdcccddaccbdadbaaaaabadbaccbddcbcdbacdcddddadddabcbabddabdcaababbadddddacaacbadcbdbccabdaaddcbbcaaaaacabcaacabcdcdacabcdabdaabdcadaddadadccadaaabdacbdbbdaaacbaaacbaccddbbcdccbdababdcaacacddbdcbbcbaddbcbcdccadbbbaabcacbbdcbccbdbaddbaddabbdbbaaadbcbaadbabaabbbaaaadcddbbbdacacabbbcbcbbaadcdacccdbacbddabdbcddcdaccccbdaabbabcbcddbabdabcacdcaabcabccbaadcbbccabdadccaccbbdacbdddccdbabcddbbcbbababbdbdadcbadbbbabdaacaadbcbdcdcbaaabcbaccdbddacababcccbabccccdbddbacbadcdcabbbbcccddbbccaaacdabadbccdcaacddccdcddbdbddbcabcaaaaaabadccddbbbabbbabccdbddadcdaaabacababbabcaacccabadabadbdcbddcbdccbccadabcdbccccccdacccacccbbaacbadcdcddbbcbddacdbbddbdcbdabdbdbcbddccddacaadcbccdbcadbcbbaaadbbcbbcabcbabddadaaacbabbaddddbaaadbbddadcaabdacdaccdcddabbbbbbcaccacdbcdcbcbdbcbbacbabdcddcbdbbcdacbababcacbcadacaaccbbbcacbbbdccddbbbadacadbdccbaacdcdccbdaabbccccdcacbbbcbbbbabcdcaacabcbcbccbbadcacadacbacaccbdacdabcacdcadbcadaacdcbdddadbbcdadcabadacbcbcbddcaddbbcccabadccdddbbdadddbcabcabacbaccbacddccaccccdaaaabdabddcbbddacdccacabbcacbaaccadcdbbdcdcabccdabcdcbcbababddbdaccdaabbadbdacbbabdabddabbcbadccbcccadadaabdabcbcddbabdddddaacbddabcaacbcadbcbcbbbabbcdbadadcaacaaadacacccdddacdbaabbaacccdbacbadacbacbbadaccdcbcdadbcbdbbdbdcacadbdabcabdcdadacbdadbbbccbbcddaabddbdadaacdabccbdcdcdccccbabcdcacabbbabbccdbbdbdcaddbbacbdcadbabcbdbcddabdbacbbdddcdcbdcccbbacabdacdadbdabadcbbdcaadacdacadbdaddbadaaddcabdadadacbbacdadabbdabcababdbadbacddcabcdbbabddcdcaddccbbbdccbaccdcacdcadbcddaddddacbacddbdabdccdabdadabadbabbcbcabbddbacabbbcacababbabdddabcbbaccbcbdcdbdccbccdbcdbbcccddbdcbdbbdabdbcbdcddbaddcacbbcbccddadccbbabcdadddcaacbcabadababdccbbbcaddabcddaadbabdbcdbabddcabcddbbaacbbbdbaccddaacdbcbbdadadadbcbcdcdcaccbcccadbbacdacbabbdadbccacbacccabdbcaaccaddbabbcbabbcddacacdabdcbcadabadddcadbddbdcdbdcabcbabbcabcdbdbaadbcadddcbdbbcddacbacdccdbdaadcbcaabcbaadccdacaddbddadcddacbabccacdcbddcdbcbdcabdcabcdcbbbddcaaccaabbbdbacdababbcccdcbdadddcdccbacbaaadddabdadcddcaabccadbadbadbcbddbccbadccdcbbcbddbaabaabdcbcbbbcdddacadbddbbcddabbccbcacaaabccddccadcabbdabddddbcddccbdbdcdcaaabaabcaadccadabbdbaaccacaddadbbbacaadabaccbadabbdcdadcacddcbabacbcddcbdadbbbaaacaddbaddcbccbddabbcbdddacbcddacdbaadccabddbbdcbcdccacadbaccadcbdacaadddddbaacdcacbcbdbddabcadaadaaacbcbdbabbbbaccbdbbdbbdcdacacbadbdccccddbdcdabdcdaaabdcbaadbaacacbcddcbaaaababcccaabddcbdcddadabdabbadacbbbcdcdacabdabbcdcacabdccabddbaadbccbaaacabadbbbbdcbbcbddadadcdcddacaaaadadddddcbbbdaaccabdacdcdcadbaccbdcbbdadbadbbaadbbcbbbdcdbccadbcadadadbbaaddcdddaddabcdbdaabdbddabdcabdcddbccdcaddcdcdcdbdaabdadccdadacccacddbccbccabdbacbabbdadbbabbbdbdbbddcdbddbbddbcaccccbddcdccaccccdabcbddacabbbacbddacbadcdcbdcadbbadccbdbdaabdabcbdcdccdbaacbbbbbcdbdcaddbabbbdbababacdcdcdabcabdaddddadacaaabcdbabaacabaadbcddadadcbcadadcdbcbaaadcbcabcbcdcccddccbbaacdadcdadbccbccadabbadddabdbdbaccadaddbaccabdbcdabcbadccbbbdbdbaacddacacbbbcbdddcbdcaddadccadcacdaacbbbdbbaddbdaddbaadcaadbbdbbacdbbbcccbdccdcbddbadcadadaddbbabbcdcbdacbdaccbbacbbabbaadabbcaddbaddbbcabadbcdacddbabdbbdbbbcbcbabaccbdcddcdbdbcaaaadccbdbacbcabbcddbbdddabbcbdcddbdcccdabccdccacaacadbadccdbcccabaabdaabbdcdbddbddbacbcbccabcbadcccdadbccabdaddcddbcdcbdcbbcdbbacaccdbbcdbacadaacccbbabbdcacddaddadccdcbbcbcbdbcbcbcddadbdadacaaddccbbddbddbacadcdddabcccadccccbacbdadabdcacdaaddbdbdbcdcabdacddabcaaadabdcccdcdacdadcdacaddbdcaddddacdcabdacadaaabdbcadaabdbadccacbdbdcbccadcbccbbadddddbabbbaccadbbbbcdcbbdabdcadddbbcccdbbcbbaccbabcbdcdccaccdbcbdccdbcddadaaaabaabbcddadbadababbccdcbacacbdaccdaabacddddbbbbbadbdacababdbaadbaacdbcbaabdacaacdcbbabbdbcacbdcacdaadbcdabcacdaddabbbcdaaccadddaacbcdbaacccccacbbcdabdcdaacdabcbbcabbaccdbbdbbdbaadabdbadddcbcabbbdacbabaacdccbbcbccddadadcbaccbabbaabbcadaccddacdadbbcbdddcdcbabdcbabcbbbbbdbbdcddbabbdaccdccadbbbcdabcddaaddbdaddabbcaaacdaacddddacbcdcbbdadadbdcaaccbdbaaaaccdaccbaabdcccdcbdbbbababccabdaacadaccaadddbdabcbdbccdbdbacbbdbbbccdcacccacccabddbdacbbabbabdbbddbdabdcdbaaabaabadbdbabdcacacaddcaaddacbccddbdabcbabbbdabccdbdaaabbbcbaabdbbabaaaddadcbabcdbbdaacaaaacacdcaaddbddabaddbaabcabbdacdabcccabcdcacacbbdbadadbddcddcccaaabdacdcdabbacadbbcdaabdbbbdcaacbabbadbdcdbcdbddbbdabdcbcdddbcacddbdcacdadbcbabaaaaadaccdcabccdbdbacdbabdcbdbdabdbaaddabdadcabbcadbcabbabcbdbcbccdacdcaacbbccccdcddcaacabbbaaddddaabdadcaccdabcaacdccdbbabbbddbcccdccdbcdaaddcdbdccbccadcabcbbbddcaacbcadabacacaabcbdacddcacbadbaacbccadabdcdaaacaabcdbcadadddddcdbddabbccbdabbbbcabbdadcabacbcabbcdabcbcbabccbdadbbadbbbcddbcaabbcbccaaddccbdaddbaabadcbccbbddbadbbdaacdcccadcaaabcbcaddadacdabcabdbbdbbdabacdbcaabbabbabbacaabbacabddcbddcdbddcbddcccbaccccbaacdadaadcbabaaaadaddcadacacdbbbadaabdaddcbdcdbacddcbbbabcbaadbdcbbacddbbdacbcadcbccdaadcaadbbddbbaccddcdbacbbaccacbabddaadbbdbabbcdcabcbaaacdbcccaacbabacabbdcabbcbbccabdbcbbdbccdbcbcbcadbcbdddabacccbdacdcbaaabbcbdbdcccbbcdbcdbcaccdcbbbcdbbacacbbcbbccbadbdabbccdcacdbdbabdbdbcbdaaccddbaadcdccaacdbacdcbbdcbabddcabdbdcbdbcbcbaacccbacdcabbcbdbddaacdbbcacbdabcdbaccacbcadaddacdbbbdccddacaacbbaadbbaabcbacaddbababacadddadddabaabdcccacbcaaccdbddabbabacdbcbcaabcbdbadccdddccbdbaabaadcdaadaacdabbcabbabdadacbdcbacccadaacbdabbadcbbbcdacbddbdddbcacbcccccbbdddcabcdbbcaabadbcddbdabcdacbbdbdcbabddbdcaccaddbaabdbddccdabccadaaacdcbaabccdcccdabccdcabcbdddbccbadcaddddabcbadcbdcbaccbaccacdcdddabccadaacdbbdadddbcdcabcbdccaaacdcbdbcccaddbdddbcccbaadbddcbbcacaabdcacbacccbaadbdbdccbbdccabacbcbbbdbabacabcbbdcadbacadadbcabbdadcbbddacacdccabdbcccbadbdbbaadcccacabbaacbcdbdbdbcdbadddbddbadaaaababddccdbcbcdcccbadacabdcdccbdacbcacdabaacacdcababbddcabddadaddabbdadbbdacabbbdccabddaaaababcdbdabaacddaaccabaaabdaabbdbdadddaddcaaacbcccaaabbbabbabdaaabdccbcddaccbadbadccddacaaacaaabdcabdbbbbbcadbdcbbcacccdbbbacacadcaabcaddaccbbdccabdcabbabdabbbccaddbddaccbdbaacbbadccdbbbdcbcabccbcbaadaacccabcadaccadccbbcbdacddbcbbddbbaacdcaccaaaacccbacdabdbdadddcdabdacadacbdcccdbcbabdacbdcdbdcabcdaabacabbcccbbdacbbdacbccddaacccbabdddbbbabaacaacdccbabcddbbbadddabccacccacbdacadbbbaadadaaddaaacbabadcabdbdaaabdacbddacccadcbbdaadacdbbbbbabbcacddddbdaaddacdbcdbbcbaabccabdadacccadbbcddbacccabdadaabcacdacabbadaddacccbccaccadadccbadaabdaacbddcdcdadbbbcbbbbbcbbdbbbcdabcbbabdcccbcaaabbbacdacdccbdcadaacddcacbbaccccbdcabcbbdaddacaccdaabbccbdddabaddcccdddadbddabaadbbaababbbdccacdcbcacacbadcbbabbcbdddcbdcbabbbadddcdcccabacaacdaaabbaacaadbbbbadabadacdabcabbadcccaccdbcbadaddcaaaabbbbacbaccacbcbcbcacdabbdcbddbdccccbcdcdbbbbdcabacabcbbacaccdacccaaccadaabdccdbcdabbcbbddbdaadcdadcdcacbcccbcdddcbbcbbbabcaccbbadadbdaadcccddbabdcacdccdbbccaabdcdbcabddacbbaabccddcdcddddddaccbddbbbdddccaccdabacadbbcccbdbabcbadabbbdcddbabbbbdacbccabcadddababddabdababddbbdbbbbaadaccbcacabdddaddbbcbacbacbcbdabacdbdbdbabaddcbdbacadbdbdabadacacbbbcaaadccbcccacbacddacddacabbdcbbadbdaadbaadadbadddbcaaddabdbbddcbacadacbdcaacdbbcdcaaddbbbdddbcdcabdbcbbadbbbdcbaabbdacadaaacdcaccaabdbdcaaccbcdddaabdcaaadcddadcbaddbbdbabcdabcbdcadbddabbacadacdcbbacdbdaddcbccaaccbdcdadcacbcbcaaaabddacbdddacbbcccdbbbabddbbdacbcacdddcbdbadbddbdaccadccacaaccbacbcdbcabdbbaddabccdabdcaabbabcbccbdcbcbaacddaadbcddddbccadddccabccbbcdbbcdcdcadaabcaacbdadcbdcccbbcaabbbababccbdcbdbadcdcabdccbcbaaabddddddccdbdccccdaadcaaddddadbaaabdbbabcdbbaabcabdabcdbadddbddbbacdcbcddcdcabbcaabcbdaadbbaaabcaabcdacbadcbccadccddbaadadaddbdbacbdbcbccdaddcdababacccccabbabaabaaacdbddbbdccbcdccadccddcbacdcbcbbcbcbcccaccbcacbaaadbaaddcaacbaddcdcbcdacdaacdabdabbbcdadadadaabacbdadbcbdcbddadcabbbbbdacdacaacbccccbbabacdadbabcabdbcdabdbdcdcdccaabacbbdaaababcadbcbccacadacdddbabddccdcbcbcdabadbdabdadaddbcdccaabdbbbabbddadaabbdbccaccdacaddabbdccabacaaccdadabbabbcdddcbcadaaccccccaccdbcabbbdbabaddaddbbdcadadbcbbbdaaadcbdbabcdbbabcddaacaccaadcabdbcbcaadabccbdaabcacdadadcbadbbbbcbbbadaaddbbbccddccaabccdbaadcdccbbbcddbccdacddcdbccdbadbbcbdabdbdcddcbadcdaccbbcddaacbdabdadadcbcdaccdcbacbabddbcdccbaacdbccdbaacadccabdbcdbacbaccdaacccdabddcdcaaadbccbacbbcbcbdcccddaccbdcbcbdaabcadcdbdadbbbdddddadaaaadacdaacddaaadbacabdabababcdcdbbbddcbaaabaddccacadbcacbdbaddbbdcbacacdaccdcccadcadbacacbdbaccbacdddaabcabdaabcdbccddbbccacaabdadbdadbdcdbaaabacadcddaaadbbabacdadabbdcbdbacddbbacaddcccdababdcabbbcdbcddcbcbdaacadcabbadbabbccadddbdcabcbbacdcbdcadaddcdccccabcbddcaddbabccbacaacabbbbdbacbbdccadacbdaababacbaaadbaabacadcadaaacdadaaddbddbbacdbaabababdacbbcabbaacabacbbbbaddcabbcadbbcacdaacbadaccbdcbacbaacbccadbbbabaccbdbbbcacbbdbbcbcabccdcaadcaacdacdbdbccbdbdbbbdacabdcbddbcdcadaabbbadabcadaacbbbadcaddbdabdddbdccbdcbadcccdbbdabbdbbbcdacacbbbccadaacabdcabbbccbacddcbbddccacbadddacabcbbdbaacaaadacbbbcbdcdbbccbabbccdbdabbdcadbbcbbdcdbaddcababbdccccabadbacddddcbdaacbdcbbdbcbdddcbdabaadddaaacabcdccaacaccaacddbaabadbadcdabbccacbacabccabacabacbbccbcccdacbccbbbdabdbcabdbaccaaccdbbcbdcbcbbbbdacaaccdccdcbbdcbcaaacbccabbdbbacbcdacbddcabbcdbdaaddcccbcdbdcadcbcacadaacaaccbbbdacbabaccdbabadddabbbccdcadbbbaaaadbaaaaccbdadbcaaccaccddcacbddcbaaccddcbadcaabddaadaadbbdbdddcabddddcbcbbddacdbdabcbabaccdbbcdcbbabdcddbbcbbcbbabadcddadbabcdacaccacccbddbbbbcbaacabddaabdccbdcbdbbbacdcdadbcaaabbbadccddcdccccdbabadaacdbcdcbdabcccabadabacbdcadcbccdbcccacddbdacbcabbcbdabdcdabababbbbadbdddccadabdcababbacabcabdcdbdcbcaccbcbcbbbbaddbdbbaabcaaacbcadaccbdbbadbdddbcbbdababbcaaddadbcaaddbbddcbdadbbadcdaacaddcddbaacccddbacabcbdaddbbddbdbdddcaadddbdcbcbbadabbbdddaabadcdbaaccbdcdbdadacaccadcbaaadadaacacacdccbddbbacbacaacbdcbbdaaccadddcdcccacccdcdabbbaccacaadccbdbcbbbbccaaccaaacdbacddbacdbbcadaaaaaaddcaabdaabdcacccbdcaacbdbddbccdbcdcdadbbcbdbbbbcbdcbbbcddccbdddadacdadcbbadbddcdabcddbdabaaacddadacbddcccccdaccbcdcbdadcacacabbaadbadababdbbddababadddbdbccdbabdbaacbbddaaadcdcbaacbddaadbcbdabdddddabbcbdbdcaaadcdbcbdbadabddacdcaadabaccbbbdadacacabbbbcaaaccbacdcbdacbddbbccbcaadcbccaaadbbadacacadadacbdaadcbbbbbadbbdcccddbcdddbdbbcacaacccdcacbcaacbbbabcdbbcbbccdaacabaadcbdccbcaabbcdbbbacddcbdddadabddaabcadbaccdcccbdbcccdcacdccddbbbccdbbbbbbabcdacbdddabdcbacdaccdbabbabdcddadaccbaddbabdcccccabbdcadcaaabaddddcacaccabacccdbabcaabbbdddbccabcccaaccbbbcbdbbaaabdabdbacabbdcccabcadddbcbdcabcbccdddbadccbccbbcdcadcabbbdbdabdddababdbdbbbadabdbababbcacdbcdadccbcbcaabcdcabdbcdcdbdbbcdaaadbdbadcddcbcccbbadbaddbcbdcccddabccbcbddcbacaabcaadddaabdadbaddccbcdaddbdbbadbdbdabdabcdaddbbcddbccbdcbcdcdacddadcbaccabaacbcaabcdbaaccabddddaaabaadbbdbadaccbccbcabacbadacaabbcbbbcaaaabbbbdacbaabcdddbbaaccdaadbdcacdacdbaccbbacbdaadadcbdcdcadbbdcdbdbcadccdaacddbbadaaadacbcdacabcdbbcacbcddadbadcbaabdaddbddddcdaacddbbccadcbbbccaadcbacadbbbaabacacbcbdbbdbcaacbdbbbdaccccaaacdbaabdbcabadccdbbbaddccaacbddcadadbbdabbbdaddbbaabdaabbbcdacbaadabcadddbbbcdcaaddbbbcabdacdbccdcbadcabccccaabadbdccdaddcddaddaabccbcddccccdbbabdadcbbbddabcbdbdbaddaaaddddcbbccbbdacbdbddbcadccacaaddcdcbbdaaccaaddcabbbabaacdacbdbbaaddccdbadacccaababdbcaadadabacaaacdbccabbbcbaccdbabadbaabaacadacaaccaddccadbccaabcabbaaaaabdcdacdbaddbcbcaddabcbcadadaadbbacaaaacbcdbdaadacdabadddacabaacababccdccbddbacdccacaaaaddcccaccccacbccdbaacabddaddcdcddddcaccdbcdcccadcbadbbbdcababddaaadbcacaaaaddaacaaaadddadcacacabcbacddcdadbacabccbcaadbbaabcccbbdaacbacdccdbaacabadbaddcdcbcbabaadbcbdaccbbbccdddaccadabacaddcbdbbbadabddcbadcbaaaaabaccbcaaddcdccbaabadcdcabadccbcccadcaccaabccbbdabaaccbbcdccbbdddaddccccdacabdccbdadbaaadcabdcddbcaacbcbdbdbadaabaabdbaabaaccdbacdbcdcaaaccdcdadbdbadbdbdacdaabbaadcbdcadaddcbcdbddbddbabcbaaabbccccbdaabddbaabaacdcddddccadccaadcaabdbabbaaaabcbaccdcdabcbccbcbddcadbbbabbccdbbddbacdbdaaddccdddacacbbbbcccbacacbdacdcdcdccaadbaabbbccdacbcabcccacccaddcadacdbcddbadcbbccacbdbbddbadbabbcdadbcbbcddbdaaabcaddcbcdbddbdbccbbcbbacbcdccadcacacdddaaacdabdacdbbacdddcaabadadaacbbcdacdddbbdcabaacdccdaccbbaabbbbabddacdccbdacdddcdadabbdbadabadcbcbddbcabbcbbbdbacadbadabddcbacaccacbcdbdcadaabbcacacaabbdccdbddbddbbabdbaabacbdbaaacddbabbdddbdbdcbdaabadbbddabcacccdddadaabcbbcdbdaabaccdcdbdbbdbcaadccbdaaacccbcaaacddddaacbabcbbaddabaadcccddbbcbcaaaabcbbacccdcddcabbdaadcdbbdcddacbbdccbacacacabaaaabcdabcdcdabcadcacdabdddaccaabacdcabccdadabbdabbcccdddcbbabcaabbdcbbabdabaaacacdbaccabcaaccaacbcbbcdacdbbaaadabdbadaababacbbcdaabbdddbdaaabdaababcdcadabbdcdbcbdbabbaaccdabdbaaccacaababccdbaaaaaaadbbdccbadbadcbbacbcccccbadbbabcbcbbacbbbacbbdbbbbabcbcaadcdcdddadbabaaaccaaabcbdcdbaaaccabadadabbbdbccddccaadbcdcabbaccacccdccbccbaadcbbaccdbbcdcdcadbbddbdbcabdbacdbdbacbdbccabadbbadbdcbbcbdbdccaabbaddbbddadabacbdbaaaaadcbbdadabaabbbbccbdaddbabdabbcddaccbacadbaddadbbbdcccbccdabcccddcacccadabcdcbbcacbddabaadaabcdbbcdddcabacabdbcabaaabcdcadaaabbdbadacadbcabaabcbbabbbadccdddddcdddcbbcbdcadbcdbbcadcacdbdbdcacaddddcdbcaabccbaccdcddbaadadcaccddbdbdbaacbaadabbbcaabaabacabacadcbdbdcadacbdabbbcabcaadacbddcaadaddddcacdccdcbbaaaabddbdcbbabccdabbbbcaadabaabaadadddcbdaaccccadbbdabdcdbacbddbcdbaacdbbdaadddddcdbcaddbddbbbbbdacccddadbbaaabbdbcacbddbacdbdcdbddbbbcacdbdbdbaccddbadaccacadcdabacbadbaabbccdbbabcadbacdbbdcdaddabcddddddadccdbcbbcaaccbccbbdddddaaadcadbcdbbaadacbacddcccacadcabbadbbabcacbdaadcdbaccdbcaaccbadaabdbcacdbddacaaadbdaccbbbdabccccbbbdacdaabdbaacacacabbdacbabbcbdabacdcbadcacccdcbbdccaabaaddbbcdcccabbcbbbcadccbddadacbccdbdcdbaaccbbccdadcddcbcaddcaddbcabdbbbccbdacabacadcadcbcdbbcdadcbadbaabdddbababacdcdccbdbcadbdaaadadbabdbaadbdbabcbbabbcdbcaaababaacbbbbcaccaddaadcdadcbcacbbaddbcbabccaaababdcbacbadcbccbcaadadcbcaccaabcbacadbbaacdcbcddaaadcdbdacdbbddbdadcdbdbdbcabccbaabcabdadaccccbbbaacbaabdaacadccbdabbcacdcbaabbaaacacccabcbbccaaadabdabcdbdbbbaacccaabadabaabbaadbdaccadadaaccdaabacbdaaabaabbcabddddcabdddbbaacdabdbdddbdabdcddcbcddadcdaadcbbccbbdbbdadcbacbcbabccacaddcdbacbbdcaaaccadacabddabdbbbcddbaaddabdacbaacbaddbdcddbbabccbcbbccaccacccbcaddaccbabaddbaccdacdcdaadbadbbbddccbcadcbbdaaadaadaabcbbdcaabbaddcadcdabccbdaababdbccdcdbddaabbdcbadcdaacdabcaaacacdcdccbdddccdbccdabcadcdacaabcdbabbaadcacabaabbddbbcbadabdcabadcbccacacbaadacbdbcadadabdbbcbaabaccabaacbacddcacaccaabcaacacccddcaaddcaabdbdbdadcdbccbbcdaabbadcabcdbddcbaddbdddbdcdbbaabcdbbdbcaacacaaadddddbaccacbddcbccccbaaaababcdcbdbcbbdcddbbbdddbddabddcbadbcbbcddddccddaadbaabbabbccaabdbcaaacbccccabacdbadabadadbaacabcbcaacacdddaacadbcbbbaabbdbcbddcddcabacccccadbcadcbccabdbbdcadcbddbbdaadbcacdbdddbcaacaccacaccbcccabadbdacdadcbaabacacdbcbbdbdaabdccbacadddcbdaccbcdbbdcdbabdcdbbabdccdbadcaaccaadadbcaaadbddcadacbbadbdbaacabbdccdabddcbadabaaabbdddaabcdaccdccbccbdbdacacdbbaadcaaccbccabdcddcdbcabdabdbdcbcbccaacbabccbbcacbddacabcdcadabacdbcabcaabaddbaccdadadbddbacbbbdacdddabddcddcaccbbbacbdabddacdaddcdaaabbbadcaacdcbdabadbadbababcadddacbbdaadcdbdbdbadbbdcaabccbbdaddbccbbddbcacabaccdaabdccbbabcabbddbbcbdbccbccdabbabbbccaaddaaccabadccdcbbddccaabdbadbbdbdbdaaadaabaccbaaacbcdcdcacbdcccaadaacdcdacbbacbabbbbdcacabbccdcabbdadbdcdaacbbccaabbaaaaaccdcdabdccdccbacccdccdadcaddbaacdbbcadbdacabcaabcacbaccaddacaabbdbcaabbccccdaccaadddbcadbbcdddbccbacadacbcdaadccdddddccaccddbbddcabdccdabdccccadcbabdddcdbacddacbcccdbbacbadccdbaaaacdcaabadcdcbddcdddbbdcdacdabbdbbcacddaaabbcbccadbdbbcbcbdcbdcdaadbbbbcbccdbbddaadabddacdbbacbcdaaaaacbbccdabccddcbdabdcdacadbadbbbcbcaadddaaadbbcadbcbaabbadcaaaabaddbcabdadcbaaacabdbbbaccabbcbacdbcbcbccbcdcbbdadcaccccdaadcbbaaababddbcabccabdbbdbacbcbaaaaaddcdacbbcdbabddccabcabacacddccdbbaacdacabbaccbdbdaaabacaadacadddbadcddcabcddaddddaabdcbcbadbdcbcdbccadbcabbadccddaaddbacddbbcdabdabcdbdaadabcbaccbbdaadbbdccddacddaaacabcdaacdddaabbbdddacbbbdcabbdbcbccdcaabdccaddbdbbcdcbabcaaddbaacdcacdcabadcbbbdccdabdaabdcaadddbcdddcdbcbabcddccdccddbdddcccdcaccadbacdabbbbbcaadbdaacbadbddacabdaccbacccdbaaddcccccbccadbabbaacadaabcbacddabdaaddcccddbdccdcabcbdaaccccaddcbddbabcbaccacbaaabbbddccbaadcbcbdaccaaadbbdcadadabbcacdbadddcacbdccdcdcbacdbdadaabcacdadbadddaacaabdddbddcacabcaaabaaabaabdddacdccddbbaadcadcbdabcdddbaddbcaabbbcdddcbdcacbadbbccaadacdadacadaabacccdccabccbaadacbdcbabbcbdabcddddccaaaacdbdcdbbbaabbbbccbdabbadccdcdbaadbcbbcdabaababcabbadadaabbdccabdabbadacdccdcacabcadaacdbaddbbbdbababdbbbdaacbabccdabbcdccdcabadcdacdbdacbabcccbbabddacbbacbccbdcdbddacacabbdcbaccdccaaaabbdcaacaaabcbcdbdaccdddccdccdbaddcabcbbabcaacdccdacdbadccccdccdcbbdcadbddcbbbbdccabcabcacddbbcbccdbbbddcaabddbdbbcddddbaccacdccdbddabdbcaabcabaaabcdcdbcabdacbdcdbdaacbcbbcddcabcaabbcdbbbcabbaadbadacabdcbaaadabbcbadaaabcdacaccbcddacabaadbabdcbbcccbdddcbbcacbbdcaabddaaaaacbaadbbaabcccddabcdabbababcddbdadbbbcbbcbccccddaacbcdcadcbacdbcadadcaaacaacbbdbaccddaddccddbaaacddcaadbbabdaaddcbbabbbcdbbbdbcaaddacbcdcdbccbadaacdadabddcaccabcbcccaadcdaacaacbdadbcdaccbcdcbaaccaaaadbbadadaabddacdabaacdbdddbaaaadbccbadbaddbcacbcdaababacbaaabdccdbbddccbaadcbadcdaddaccddbcadbcabbcbadacdbbcdcadaadddbaccdcdbadbabdbabdbcaababdcddddadababdcacccabbcdccbdcbbddcdbcadbbdbdbcbddcddbddadacdaacbbddcabcbabadacbdbbaddabadadddbbabaaaadcabcdbabbddddcbdcbdaaaaacadbabcdcbbcadbdacdbbcabbaddcdbcaddddcdbcbcabbcbdcadacabdbddbddbdcbcabdcbabdaabbbabcbddcaccccabadddabbbadcdbdcabddabcbdcdabccccdcdadbcbcabdcadaccbbcccacdddbbcacabdcdddbdbcdbabcbbccdbdbbcdbacacacabadabaadcdabbbdacdbcbbcdcbaacdbadadbaacbababcdaddbaaacdbcdcbcccbaaacaacdbaaaaadcbbddbdbcaababaccdacbabccbadbadaaddbbdcbdacbcccababddddbabbcadbbdacbccacabbbbcbbdaccdabdbbcbbadacaacaccccbbbdaaccbdbddadabcaddacdcdcddbdccdddbbbdaabbbcbdaababbddccbdbbbdaadbabcdbdacdbacdcadcdcdcbdaaddadcbaabdaaaaabbbbdacaddadbbbacbaaabadbdddadaacadbcbcabbbbadcdaaacdacdbbcaddbcadcabbcdaddbdaabaabdbdbdbaddcccccdadadbdbbdadccbbbbaadabbcbddbdaacaacdcaddadadcacdbcccbadaaadadadddddbdcacbaddbadcaabaccadabbbccbaabbbbcacadbbbbccbdcddcbbcacddabaaaadabdbdddbcaadddbbccabcbdddbcadacaabacbddcbbdddcdddbddbcdabdbbcbbdbaaccacabbaabadaddbbbabaaaaadacccdabdaadcccaadcddddbbccaababcbdcbabaddaccacdadccbdbcabcacdccababcdcdcadcadccbcdccabacadabaaccbcccacbacacdaccbddbbcacddbdcccdaaaabdaccabdccddadacdbccbdaaacdabaaaabcdbadbddcdbbddcbcddccaabdbbdacbdcddddaaaaacdddabcbccbcadbbdcccabbacacbbdbabcccbccdbadbcadacabdbacacccbbbabddbaaaaacdbaddadbcbadcabacdababcccacacddccaaadabacbabdbacdabcddbdbdbcddcbbacbbcacaadaacacabbabadcccccbadbaabcaccacddbabdacccadaadcddcaabcaaccabcbabbbbacdbcaaaaadcbcbccdaaddbbabcaacbabacdadabdcabaaabacddacddacacabbacdccabcdacdcacdbabcdbcbcaaaabbbacbbbccbbabdadbbcdbbdddddddbdadcdbcabaccbcadcbacbadbcdacbdbdcbcddbcdbdcacbdadccbaccbacbbdbdaabcabddbbbdbadacacbacdabdabccbcccaadabaacbbcdcccdbadbadccdcdccbcadbbdaaddcdabcbabdbdbccbbabbdbdddbdabbaacbcdabbadccdaacccaaaabbbbddabbddbcbcdccacacdbbbdcaacaaccadadaaaabddddbacbccbdabcbdacccbabadbdaabababacbbbcacdaddbbbbbcbcabaccaaacbddbddaaddbaaadbacacbbbcddcaabaaacaacbbbccdddbbaadaacdcacdcadcdccdacdddbabaddaacdbdabcaaaaccbcadcccdcbdbccdbbbabcabacbdcaaaaddccdaacdcdbacccdcaddacdcbcdadddddbababddabcaabadccaabdbdabacaadacbcdaabddddbddcaaccaabbbabcbabcacbbcdccbbbdddcddbdaacbcbcbdddbddabddddbaabaabbbadcccddaaadcabdbbaaaccdccbddcbcabdddcabcdbbddcbdabcdacaacacbdbdadbabcacbbbcbcdaacdbbdcccbdbcdcbcaaddcccbddbadcbabadbbbcabbbaccdadbccabadadccdbcbbcdccddcddacbccbacaccdbddcacaccdabccbbabbadabbabdcdadbaaaaccdcabbbaddddccdbacacdaadaaaabcbbbcddddadccaccbcbcbaabbdaaccbdcbbdbdaaddbaddcacabdabaccacddacacdabbdccbccdcabdaadaacbccacaabcadbcacaabbacdcaabccdacbbbabccbccddbddbdbbdbdadbbbbddbabddbabddbddcbaadaadbabcabbbababbbbacdabadcddbabcddbdabccbbcaccaacccadacbacababbdbccaccbadabddabbabababbdbcacdbdabdcdacaddbbcddacbaadabdabbbcbcbdbbcacdacdccaadacbcdcaadbddbddbcacbdbdbaccccadcbdbcbbbbcddabacbdcadbcadbacaadbbaaacbcababcbdaaaccdabaacadbdbdacbacccbbddaaddbcdcdddcdcabbdacaaabbacdbbcbaaacccbdcbbdabdbaabbaaaaabccbcddbaaabacdaaadbdaacccababdddacbdbbbabbbcadadccddcadbdcddbbbcbbcbdcabbcbbcbadabbbdabbbbdaaadcddbabcacbbacacdbabcbdddbdcddbbaacccdbabcbabddcbadbabbcdbdabaadbabccbccdcacbbbaadbbdcbbccbdbaacbbaacddaccbdcbdbdccbbbcadaabdcccbdabbaabdaacdabcbcaccadcbcdadaadaaabbcbaaaadabbacdbdabadaccddddcbcacaabaababbbcdbbcccabbdabbcdacdbcbbcaaccaacdcbcddbcdbaddbbdbabababbcaadbdaacaabccdcdcbadcabadbbcaccbbcadadaddcaabbadddcadacdccbaccdddddbabcabacbabddcbcbdbbababcccbdbcacdaababbbcbaddaacbccdadadabcbbbbdbabaadcbddaaabbadabdaabdadccdcbccbcddabbadaddbcccbaaadcdabaddadcabbadacdabcdadbbdcdbddcdacabddacaabaadbdcbdaacadadcbacaadbbcaadcaddbaccabaaddacccbcaabcdbdaaccbcbdaacabadcdbbbcdacdddcabaabcabbdabbbbdacddbabaababccbbbdddbaaaacbdcdbaddcacbadbbdbbcbbbcadcdcabacdcbbadbdbbbaabddbabbdabacaccbcdbddbdbdaddacccdcaaaadddcbacaaabccdbcaccddddbbdacaacaabaabdabadcddcbabdaddccbaacdcdadbaccbdadccbabdaabcadaddaabbbacaaabdaddccdbcadabdabdbbbdcdacdaabcbbdaadadbbcdccabbcadabadbddbabadabcaabdcadcdadcbacbabcdcbdbababcbabbccbcaadaadbddcacddcdcdbbbdadcbcddbbbbcacbdccabadbbbadabbcdbcbacbcbddbaaaccbbdccacdaccbacaacccbdaacdadcdddbabacaacabadacdbaadddbdcacbadcdccbccaccacddaaabbdbcadaabcbcdbadaddabdadacbcccbacbaccddcadbbdbbdcbcdbcdccacabdcbadaacbbbbcacabaabcbcccabddbbabacaccaaccdbddbddadaabddbcdbadbdcacbacbacaaccbbcadbcdaccaccdcdbbbbadcacdcbcaccabbcddcaddbbaabbaadacbcbdcbdadbcbbddcdbbdaacdadaaddbdbbccbcdadaadacdddacddacaccaabcbdbdbbbacdccdddaabccaddcbcaabaabdaabadddbcabcddbadcbcbbdcaddadbbbdbdccddccbdcbbbdabbbdbddcbdbdbcccadcccbdaababdbcddcaabbddcaddaccbbabbbdcccacabddcbcbbcdadbacbcadcbbdcdbbadccbcdaadbbaadddabaccddcccbadbbacdabcbbbcbcbcadcddbbdacbccbdcdcacadbbbcddcdcbbbbbdbadbddcabddbccbcdcdcaaaaddaacaabcabacdbcabcddbacccadddcacddcdaabacdddcbcacbabbccbddbaabaadddcddadbacbbddccacbaaabcccadacdabcbcddbcdddbcadbccccdccacddabbcadacdbabbdabcbcbbadcdacdbdcdcbbaadcbadacaadaacbcdccccdddccbaccbabcbbddccdaaaadbcccdcdbdcaabbdcbbcbcddccadaacacddbdcbcbcbccacbdbbcbcbcdbbaccbdcaacdadddcacccdcadcbbbbcacdbbadabbdbabcddcbcddaddadcadddbaadbcdbbaadddcacdbbccdcababccbcadbabaaacbcddcbaabdabcbbccdaabbdbccdcdccaabdbcbaaccbcddcbccdddbadabbaddcbbcaadbacabdaadacbdacdddbbdabcdbccddaacadadaddabdbbdcbaabdddbdadbddcbcdaacbbddcdbddacdaccdddacbbccddaadadbbaabdbacbcacbdacacbabaabbcadbbbddabbcccbddaabdcadbdcbcbcbcdbadabdccabddcddbbbabaacbcadddcadbccacacaddcaccaaddcbbdcaddcdbbbaccdaaadbbbcdacdbbbacdcccbbcadadcddbcbccbccdaadabdadbbbcdcccdbddaccbccaabaddccadcaccbbbcababcdbabacadbdbbcbabbbabacdabbdbabdbbabdbddaacabcbbbadcdddbddbaaccdcaccaaadabbbbddcbababbbadbbadbdcbbadcccdbadccdddaddacddcdbcbccccaaaaaaccbbdccbcbdcbdcdcbdcaaccdbdaccdccaddcaccddcaddbbadcdccaaadacddbdaacccdacadcdcaaaaccacadacbabdadcbcbccbbdccddbbbacbacabccbdbccadddbbacbbadaabcaabababcbbcacaabcdadddcaccbaadaddbaccdbbcdadddaacdbcabadcdcbadbdbaabaaddbdabadaadabadbbcbdcdcdbaacdadbccacaadddccdacbbaaccabddcccbdadcacbbdabbddabacadacabadbbbddadbdcdbadcbddccadadcdddadadaacaccdcbbbaaacababaaddaadcacdbbbdadadabdccaddbcacdadadacccaddbcdacdccabcddcbcabdadaaddaadcacaadbdbabddbbacdabcabcbdcbcacbadacdccaaddacabcbcdbcbdcacabaabbbbbadcbcdcaacdadadbccbcbcadbbdddaaddcbdabcaaabbdbbacaadaadccdddcdcbaabadcbaccacbaccbcaaaccbccbbbdaccdcdddbdacdbbdcabddbbaaacbcbccbcdaddacaabbaccddbabdbcaabadbbcbaabbabcccbbdbddbdbbcddacdaccbbddaabcbacdccdddbcddabcacabbaddabadaaacacbcabbbcacbcbccdcbaabdddbbcccabbaccbdaaddcccddbccbabaabaabbdaddbccbcdadaddccdcdaddadacacabccdabaccadbdcddabbabccacaccdccdbdadacadbbccddbddbabadadcdbdabbcbdabbbdddbbcddbcadcbadbccdbddbccaaacccadddbcadddbaccbaacccabcdacabbaddccbdcadcdcdcbadacabdabbddbbaddbbcabbabddcdddbdcaacdabbadccdbddabaccddacbdccbacccaabbbccdaacdbbddcdabaddcaaadcdcbbacbbcddaadabaccddbcbdaacbddaadbdcacbadcbdbcaacacddcccdacaabadacaaacdcbbcaaddccbacaabddacddaddbddabcabcccdbabacbabcabdcbbdbcacabcdddaabbbcbacdabdcdaddcdbcdbbabbbdccdcaabbbccadcacadacdabaaadacbabaacdbcdcdaadccdddcdbcbcdabbaabddaacbaddbdcbbbbbacdabcbdbdaaacccaadcbbbabbabacabdbbacacbabbcccdccdaadcbbabbdbbcbcbabdccbadaadaacdaddccacccbaadaacccacaddbbabacacbcadbacabbcbbadcbdcbadcccaabacbdbacddbbacdbbadcadadbbcabdccacbccbdbbcbacaababbdbdbdabbaabadbcbbaacadbbcabbacbdabddabcbabbbdbbbbaadadbcbcbdcadcdcaaabababddadcbaadaddcdbdcdbdbbdddddcdbddadbccccdbcaaabaaaadbbaaacdbccbbccabdcbadaccbdcababdddbcdcaaddddcaabbaabdbbaadbbbdbdaddbcdbbcdcbbbbddbcdcabcbdbadbbabbdaaaddabbccddbdbcadccdaadddcdbacddacdbcdabcacbdacbcadcbddcbdbcacbadacbdcdbabaabddadccbcdbbbaccbbbbabbbccadbdccdaabbcbaabdbdbbacdbaabaddabbabdbaacccacadbacccbcbbcdacbbdaadadccddacbbcabdbdcdbcbcbaccacdcbaaccdcccccdcbbbddadbbbdbdbccdbdcbcbbbddcdccdcccacacaacddbbcdacbcbadbcdaabdaabdaccadabbdcddcdbddacadbbbdbdaaddbdccaadbcdacdaddccabaacaaadcabaabbdcbcdabbdcbbabcdadcbdacbadccbddbccaacccbadaacccbbddbdaddbbbbdabdcbcbdcaaccbabacdbbbbabcdaabbcbcbdadadbdbcccdcadaccaacaccddacadcccdbadccdbaccccdbbadadbaadcddbcabcbbdccaabacacbbaacabdbaddacbdbdacbdcbbdbbcddacdbdcdbabdabbbcadbcadadbdbbcacbcdaacaddcccdddacabcbbdccbbbbaddcbdcbdbabaccbbcadbbcacadabddacdacbccccdacabcdcdccabacbcaaaabdcaaaddacbcbdabccaaaaacddddbcacbcbbcdccbbdabaaabbcbcccdccbcadacdccccdbbbacdbddcccaadabacbdaaaabcdabadbddaddbbadbacbcbadabaadbcbbaadbadcbdcaaabbddabcbacaacbdcacdcccccbaabddccabbcbabbbccbdcddcbdbaaacdacabcaadcddddbbbcbcbdadbacccabddcabccadadaaaccdbdbaadaaccacbcdcbbaadcbccbdbccabbbdaaabbbacacacbacdcbbdbcaaaccdbdbdacdadadaaabddcabdbcbccadbacbdbdccbdcadaaabccddbadbdacabcabbdccdaadcabdbbcbacabccccccaacdaacaabbbadbcaadbacacbdabdbbccbccdbcdaaccbdcbcbacdcddbcabadcabaaacbcaadcaaddbbababaaddddccaadccdddacbcbdcddaaacacdbacabcdbaaaaabccdbbaabbddccabaaddadbbbcbacacdddacddbdddaddcdabdbdbacbaaaacacdcadaabdbcdcccaadcacabbbcbcbaabcdbdddabdcacbdbacacdcacaaadabdcbcccdabcbbccbcaaadadaadcccccbcdcdbaaaddbcabaadacbcabaccacdaaaadddcacbbabddcbaccabcccccddaacbddbcacacacccddbcdddacdbbacccabddccacddabdadabdaccddaddbcadddcbddaadadbccaadcdcabdbdabacbbccdabccddcbbcbdbaaabdbabddcbcddbccdcbdacacacdbacbadabdbaadcabadbadbabddaabacacadaacbcacdccbdadbcccbddaaaaddbdcbdbbcadcabdbdaabcbcdcbbbaadcdaababdabbcdccccdbcbdadaccdbdcbdaadbdbcaccccadbbbddcbabbdcbddcacbdacdcbacdadaaacacabaaadcbdbcaabaacabdacdbdaabbcabdcdacdbabbddbdcadccadcccdacabbbaaabacaddcdbadcdcbbadcdbacdcbadccaaccdbdddcddaabcacdaadbdacaacaadabdcddadddbdaaccdbaabcbbaabaadcbbbcdbcbdacdcdcacaabaccdcbcaaadbbbacabdcaaaadbcbabcbdbaabadabaadbbaabddadaccbadcdadcbdcaabbcddbbddacdbacdbadcdaababcbbbadcbcdcddadccdaacaaddabdbaccbdaaddbaddaadbdbaacccdcbadaabddaaacbabdcdbbcbccdacddcabbcbabdbdbcabbacdadbaadadcdbaadadadddcbdcdcaadaadcacabdddaabddbccbbaadcadddbbcdbccadaadbacdbdacdcccdbdbcaaccaddcbdbdbbbbbbabaadcdddbddbddbadbabdacacdcabccaabcaadabbabddbadcddccadcadadddddadcababadaadbbbaadcabcdcdddbabaabdbdcdcabadcccbccdccbadbabdddddbcbddcdcaccdcdbdcbdadbbcddbabddddbbbadbbbcdbcbbacbbcabbcddcaabadaddcaadcadbcaaaaabadcbdcbcbcbabacabbbdbcbbdabadabdbdaaabdcbcbbddacbddacdbbbabcdabbccbbbcdaacccbdccaadbdbcaabbadcacdaccbbddacacabbccdccdcddcabacbadadabbbaabadcddcccdcdaaddbddbcdcdaddbadaddcdbbdcabdbacaabaccdbcabcddddadcccdddaabddaaddcacddadcadcabbcccddcaabacbbacadacddadadbddbbdadcacacaddbdddcacaddcadaaaddabbcacadbdbdbbcdbbdbadccabadaadcccacbddcdcadbdcdcabdacbbcabaabdcdcccaaccccddaadbccdddcacaaabccbdcbaccdbdbbbdadcdbdbacccabdabbcbbdcdcaacdcaacddddcdadcddabdadaadcdadcabcccccaacadbbcccacdbdccccbadbcaadcdacbaacbbdcbcbbcdbdbbbabdccddaaccabbbabdcbacdcaccaaaaadadaddccdcbbcdacbbbabcdccddbdacdbbcbaaaaacbdcbbbccaadbddcdadbabbcdcabbcaacbbadbcaccbaaccdbcadabdbdcbccabbbdcabdadcdaaaacbbaabcddaaaacccaabacbadbdaabbdbaabdacbdcdbaaaabccbddbdacbdcdcbcaccabdbaaabacaacaadbabbdccccbcccadcaadbbbaddacdcadcbdccbcdcabbbdcdcaaddabdaadcdcaacdcabcbbcdadddcbacabadcacddacdacbddbbbcdddadadbccbcbaaaccdbbdcbcadaacddcddaaaadabaacacaaabaddbacabacdbdcdbdaaabdcdaabcabbabccdbbadcbbabdbbdbcacccccbddcabdbabacbcdbbadabcdcdddcacccbdbdbacaabbdddbddaacaaddbaaacbbabadddbbadccbdaabbbadacbbadabaccbaaddbccabcbdcadcbdadacbbbdaccdbccbccadbccacacdbbdcdcdadcdbbdcccbaddcdbabbcbdbbaabbadddbbaacaacabacabdcacacbcccbdcaadcaddccdabcaddadcabbccccbadccddacacdcccdccaddbadabdbbaaabcdbcabcbdadbddabbbaabcbcabbcaadabddccdcadaadbcccadbbdabcbcbcabcabacdbcdadaadaaabdbbcbcdbcbdacaacdbbaaacacdbaccdcdbccbbaaadcddccaacdbabdbadcacbacbacbddccccbabcadcbcdadbbaadcbabbaccbbaaacabcaaabdaddbdacccacddbbadaccbdbadcbbabaaacbaaabdbcadcaaddcddcbabdadbaadbaabcbadbdccbcabdaaabbdcaaabcdcabbaaabbcbbbccdbcdaccbdcdbcbbbaaabdacdbabcbaddbccbcbbccbcdabcacdbdaacbbdaacdcbccbbddcdbadccbaaabcdaaccbacabcadbabcacbdcdcabdaaddadadbbbbabdabaacaabbbddbdddaabbabadacbddccdcdccdbccabbdbbabdbdccadabbcaaacdccabcaabddabbbababcaabdcdccacdccacabcdccdddcabbdadcddbbdbadbdacdbcbdddbacdaadacbbadbacbbadabddaadadddacacbcbbdaccadacdadcdcdaaadbaadbbadddabbadbdccbcacacbbabcaabdcbadacddadadacaccdccdcaabdcdadbaacbbcddcacbbabaddcdbdacacaabdcbcccdaabccbbadcacaabbbadacaaacdabaccdabddbcabccdaaadbbbcddbcbbcbaccddcdadcacabdabbbbcdabdacbdbaacbcaacbcdaadacdcbcdcadddbcbdcddbdcdcbcdddcccdddddbabaddcadbbcdccdcbcaddbdbbaccabcbaacdbbabbaabddddbdbddcabbddaadcbbabadacdacccbcacdbacdadbcacdbbbacbdccddaaccccbdbccbdbadcdbcbadbcbddcaccadbccdacdbacababddabcaadadccabaddaddcccbbdaabdcdacdaadddbcbcbaaccbbadcdbbccacccbacdaacccccaadcbacabbabbbcbcbbaabadcbcbddabbdbddabaacdaacbbcbadccabcdccdccaccdadddcadbdabbdbcdddcbddcddaaccbbaabadcdaddbcadbbaccddaadacdabbdbdaddbdbdaabcadbcdaabdcaddacbbcdbbcccbdbaaaccccacbddabbbbbabbbcdaadaaaaadadcacbabddcddabaddbbcacdcbbacdbbcabdbaabababcdbcabaacbbabcaadaaaacbcadaabbbdabccacdcabbaacababcacabcadabacdbdbaaacbbbaccbcbcdbadbdcabaacddcbbcabcdaccacbbbcadaabccbddadbadacadcaccbbccdadbbaaccaaadbaddadcdadcdaababccabccbcacdabddabbadbbaaccdadcbaadcbccdbcbcdadbabdcbbdcddbacbdabbbcacbacabddcbbabdbaccbabcbaaadcbdadadadcbbcddadcadacbabcccbdcadbacbbbbdabdddbddbcabdcabdacacabccbcababcbbcacbbccbaddadbbcbbdbbdbdddaaaddabddcaadbdddbbccdbaaaaababbcdcbbacbdadcbaccddbbddbaaabcadbabacbbaddaccaacabdacacdaacacdcbddadabdccccdadcbabbadbbbddaacbbabbbdbdcdadcabbaddbacdcdcbbadcbcbccdadacabdcbacccacabbdabccbdbaacaadddbadcbdaaacbadaccdadddabdbddcbdbcabdbcbbbcbddacaaadadbdddbcddbddbacccddddabcbacabaaacbdbcdbddbcaabdbcadabdabbbdabdbdcacbcdabcddbcdaccbbbbaaabcbcaadbacddcdcdccaacaacacadbbbbbdbcabdbcbcdddbccbbcabacdccacbcbddabcdaabcadbbdacbbcdcaacdbcbadcccabccbdabbcabddbcddcbcaaccddcdbcddcddcbcdcdadbacbadacdabaadcadbbdadddaaabadbddadddbddbadabbcdbabbbdcadbcabbdddbdbbbbbddcdbdbadabcccaabaddcabacbdcbadbccadbaaaaaacdcdaabbabcabbdaaaabbcbcbdccaccacbbcbdadadddddbcabaacdaccaabddadcdacbccdabbbcbdccbdcabadcddcdbaddbcdccdcbcbcaacdddcdbddcdcdbaccccccbaaaabdbcabbdbcabbcbcdccbdbaacdabadbabbadcbadbbbadcdcccbcdbcbbdbacaaaaadbcbdbcadbabdcbdaadcdbdaadbcdabcabacaabbadddccbccbbaccbacddbdccabbabcbcdddbcdccdcdabcdddbdadbcacddccddcadacadbadadcabbddbbaaaabddabbbadddbaaddabbccdabcaadcddadbbdcabbcdadabdbcbaaddddbdacbcadbccbdcdcddadbaabbccbccabdbcabbcaabccaadaddcdcdddbbcdcbcbbacbdabbaadcbbdbccccdacdcacdcbbaadaadbdbccdbcadbbdabdbbdbacbdbcbabababacbddddccbdadaadcddacdcacbacbadbbbcadcdbadbccbacbdccbdbcdaabdbcaaaacdaaaabdcbcbbcabdaddccddabadbadddccccbddccabcbababcbbccddcdaddacdddcddccabdaddcdbbccdcbaccbbccccbdccabaaaccbbdbbccdcaadccdddcaaacbbadbacccdcbbabdcdcadbdcaabcabcbcabdddddacadabdbbbddddcbbaaacbcddbddaacaababbcdbdaabdaccabaccbbdbdabdcabbadbdccddadcbdaccbbbbcbacabccdccddabaccbcddcbaadaddcbadbddbcdbdacadbbbababbdcddadbcbbdbbdaaaadacdcccaaadbbabdccaaabbcadbcdabccadabacadcabcabacacaabadcaacbabcdbdccddbcbbcbdcabccdaacbbabdbdbcbbabcbdadacaabbbacdddaccddbdcddabacbcaddcbbddbbaacccbdccdaabbcacbcdddcdcdcbbccdbdbcdcdaccabbbbcdbcdabbccbaaddbabadcbbdacdadbdbbbabaddaabbdcbcbccaaababaadacabbacbccdbabdcaabbcdcbabadbbbbddcbbbacadaccacdbcbdcbddacabcaabacddbabbcbcbabdbcbbdcbbdaadacadccdaddddccdcdbaadcadcaccaadaadacaaaddddbdacdcbacccbcdcbbccaaaaabbaadcdacdbdcbaabbacaaddacddaababbbbbcdbcabaabdddabddbbdbbbbcbbcdddddadbcadbadcbaaadcbacbbdbdbddabdadbcdbcdbadbbbdcdccccadcbabacddaddcaddcdadacddccdccaaccdcababdabadbdaccacbaddacddbacccaacadbbccbdbacbdaddcacdaddadaccaccabaadccbbabcdabcdbcadadcabccdaacadaabadbbbbbddacdbadbddabcddadacddadbadaddbbcadcdaddcbbcccddaaadcbcabbcdbdaaccdaabbcacbdcbcccdbcdbcdbbdcadaccbdacdcdcdcadccdabdbcbddddcbaacadcddbaaadccbadbdacaaaabcbadbccbddbddabbdaccbbddcacddbabaabaaccccbddcbcbcbcbbcbaccddcdaacacbcabadbacbcdcbcbabdcdabcbbdacdccccbdbbadbcdbccdabbabaaddccbcbabbabbbdddbabaabdacdadaadbcadcadcbbbbbbdddcacbdaacdabccadbcdcddbadaaaacdcbabdcbbddcaaacccababcacdcbbbbcbdcdcbbbdabcacddadadadacbadddbbacdbcbcadccdbaacbccdcbaabcaacbcbcdcdcdccdacacbbbbccdcbbbcadbabcababccdacbcaaaaddbcaabcbbaacdccdcbbaaabdacacdadaccbbbadddbdaadcbadacacbbdbcbdaddcbcddadbcacbcbbbabbdcbabcbdacaacbadcbdcdbbadcabacdcdccddaaccdabbbccbbdcabcddbcbbcccccbabdcbbdbcdadcdbaccddbdacdcacddaacabbdbccbaabbbbabdccaabcdadccbcbccdadbacabcbcabddadadcdccacaddcbbcabcaacbcbbbdcccabbdaadaaddcadbddbddbdbbccbdcdbdabbbdbcdbcabdcbbaccdccacdbadcbacabdaccbacdbaadababbabcacbcaccddccbcadbdacaabbbbbdcacbabcbccabdabdacddbcdabbcdcadddbbdacacacbddbbbbabbcbadbbcdbdaabdaadaccbcbadbdaaabcdcbbbddaabdcdbabdbcabdccacccabdddbccbdacadaacdbddcdbdaaccdacbdbcdadadbddcacddadbcdbccdcccbccadbccdbbcabdcabccdbdbcbacdaababbcddcaabdbdbcccaadbbbbaaabccccacbbacccbbdaadbcccadbbbabbbddaccbbdaadbdbbcaaadccabdabaddacbbdccccdddbdbcacdbdddbcabdadbabaddaaabdaddcddacdbcdbbabcaabdacdaddcbddaaccdabcabbbdcabcacdcacdccacbddcdaaaccbbcdbcbaaacdbdabddbcdbdddacccbbbcdabbadadabaaabdcdaadccdcadbbbdbcccaccbbbadadcccabaadacdbaabababcbaabadadaaddddcbbdcadbdddbddcbbbbdababaddababadcccabcbaacbdcbcbcccbdbcdbaccabbbacabbbabdadabcabaccbdacbaccddbaababcbbbcacccaaaadaadbdaacccdcbadcdbdaabccccccdcacabdccaddaaacaccbcbbbcacbaadcbbcdcbabbccbdbbdcbccabbbadcbdbbcacabbddbabacccacccbacabcaaadcdacbaaccadaaccbcdbbbbabcdbcbaabcaddcacbcaacadcdaddccdaacbaabbcdcaccdbaaadbcbdcadcacbbabadddbdcdbbacbbdaaabcadcaadbccadddccadddbacbdcdbabaddbcaacabbcbdacddbccabbadbbadbaccbbabcaddbdaddccaaccccdcbacdccbddcdadaaacdbaadcacbaccbadacbadbbcadadabcdcdaadbcdbdbbabacbcacbdcdbbcdcabdccdaaaabcadcbbbdacddbdaccabdcbdbdadddccdcdcaabdbcbacacaabdbabbdcbdbcdddadddbaddaabdbaccadbbcbddddcccdabcddadaaaacabcabbbddcdbbcbadacbdabdabbdcaaadbdcdccbabdabcccbaddcccdacccbbbbacdbdadcbbaacdcaddcabbbaccaaaaaadbbdcbadcaacaccccaccacadacaabcadaacaccdccbbacdccbadbdcabaadadccadbcabccacbdbbacbcaccbabbcaabdacbbbcacbbdcddabbcabdbdacbbdbdcdbaccdcdaabcaaaacdccddbddbcbdbccbbbadadbadbddcacbccaaddbdbacdbdacbabdbabbaadbdcbdacdcbaaacdacdcbaabdcdaaadbaddcdddcbbbcabbdcddcadbcddaaacdcdabadbcccbdbabbdadccabdddddaadaaadbbaabcddbddabddbaaabacbdcbbcbdccdcddddbdddccbdbbbdbcbcaccccaddcccbbbbbacdbacbbbddbbbcdbcdcdcdadbdacbdcadaccbdddcadadcccdcddbccaabccadcdccdddaababbbbcbddabbacacccccccddacabadcabadbbbcadcdbbbdabcbaaaabaabdbcdbcbcdddcbbaddbbdaaacbbdbbacabccbbabcaabbcabcbaadabdaacddacaacbddcbdddcbdcccccbdbcdbdaabadddcdbcbabccbbbaacbdcbdbcdacbaaddccddccabcabddbbbcadbabadccaaacababbcaabbbdbbabbbdccccabadbdbbacbbcbbcbaacaadcbcdabbdbccdccddbdcabdbaaaddbbcdaccddabcdbbabcbcbdacbbdbacdcacbabaddbbabbacdddcbabbbdcdcddacdccccabbbcabadcbcbadbdaacbdadaacaacbbbdadbcadaabdbaabdbcdcacbaaddcdbacbdabadcbaadaadacaacdbcbbadcbabcbabacabcbadbdaccabcdbabdbddcbbbbdbcaccaabcadccaccbbaabbcbbabdbbdcacdddcaacadcdcbbdcddcbbdacaaccaddaddbbbbcacbacbccaacbadabaccaabbbdcbaccdaaddcadbaddbdbbadabdadbdbcddadbcdbdcadcaacbdbacbacbaababbdabcbbcbdbadbadbccabdbbbcdaaadbabbbdbbdcccdabbddabbdbaabdcacdcbadbacccabddaaabaddcccacdaacdcbbaddacdabaabdaaadbcbcbbcdacccddcdcacabaabbadbbcabaaabdcccbadcaacbdaaababccccddacbadacdcabcadccdcabaabbbbaccadddacbcdcabdaddadbbdbcbddbbabcccdccdcbdbbcdbaaccbddddaccdcbdacabccccdabddcbdcbcbcdacbdacdaddaaaddbacccbbddacccabbcdcbbcdcadabddaabdbcdbcddcbdcaacbcbacdaaddbbabacdadcddccddccddacdccbbbbcadacbddadabbdbaacccbbcbadacbccbabaddddcccaacaaacadaccdccccdbbbdacbabbdbcbcdbabcbdcbcccbdbcdddcbccdccbdadddadadcccddabdadcadbaacccccbdcdbaccabaccabcaaccaabdbbbbdbdcabdcadcabddaccddadddbacbacdabbdacbacddbdadddbdbbbcacdcbacdabbcadcacaabaacaabcdbbaaacbbdddcdddbddcdbacbccdcdadacacbcdababddacccaabdbddacddcdcdacbabdacbabcbcadcbbbdcabbcbadbdddddbdbcbbadabacadacaccdcacacaccaacdabcdaadaaccdabaaddccaddcaacdddbcdbacabdbabacbaccbaaddccccacddbbbdadaddaacdbcbacbdacaadaadabccdddbadddacbdabaccabbdaccdbdacbdbbcadbcadbabbaccbbdadadadbbdbababaccdddbbbcbaabcdcbbbbaabbacbabbcbbaddddccaaabbbdadcdacbcdcbbdcadbdbccacaaacbacabcdccabcddaabccdbddcdcdabbbccacdbcbdddbadaaacbbbcddacdabcbadddabcccbcdbdbacbcbcddcddccabbdbadaabbdbbcddaaaaccbcbbdcdcdcdcbabbbccacbbbddcbcabbccbbcaccaacdacccaabdcdccbcddacbababcbbbacbbbaabcddcddacccabaaddcdcaaddbcdcdaaaccaddadaddddcbaddccabcddddccbaccddbcbddddacbdccdbcbbbccdbbadccaadcbddcaddcdacbacdabcbacdaabbdcccbcaaaadbbbddabcbacdbcaaaacaccbbbacbacacdbbcaacaccbadbddaacdcadaabccabddcbcccdcdbddbbacdabcbcdddccaabadbbcccbadabccacbbbdcbadcbacdacaaacccbacdcccacbcdddcadabdadbccdddbaaddadddbcabdccdcababdaccdcccdbdcadadbbbaaaaabbdadbdabbdbcbabaadaabcddaddbdcddcdadcaadabdbbadbaccdbdbadcadacdcddbdaadadbbddddcacbcdbbdbbcdbccbcdccadabbbdbcdccbcdbcabbdcaacadbacdbbcbbdccdcdbacbdddccbabccbdccbddccdbcbddaabddcabcdcbbcaaccabcacbcadacbcacaccadbddccccccdcadbbbabcdcadcbaaaaacdbacbbccaddbdccbaacddabadccdbbdbbcbbcabaabdbccbadaddccccdbcbdcacddbbcacadaadbbdaadbbbbabbdcdcacacbbdccdddaddbdcddccabbadccabcbbbdcbcaadabbdcbcccdababdabbbddbcacdaacbcdbadacdccbdcdcdbdbdbccdbdadbaacaddababdbcbccdabacadbcdadbbacadbaabbbcdddbabcdbabbddbccabdcbacccbdaccabdbbadadccacddbdabbdcdddbabaccbcbccdcdaacdccaacccbbbadbacbccbdabbdaadbcaccaacbbaaccbbabdaaabbabcdddacdcccadbcdabadbbccadaabcaaaddbcbacdcbbdddbdacbdbacbdcdacdbccdabcbdcccbbcbbbdccdbaaacbbdabccdbddcdaddcdbcdadbbdaabbddadbcbbbdbccdddaccdadbaaadacdaacbcddabcbdcdbddbdcbbdddabdacdbbaccadcdcbbbbcaabdbddabbccddcbbcbacccbbbbbddcdabcadbdabbadadbccdaacddcdadccadbdbbddbbdbcbcacccacccddbabcddbbcbacbbcaaadbccaddccbcdacdcddaddccbadcccbadcacdadaaddcbcbacdababadadbdcabadddadbdcbdaccdddcaaabbaaddbdbcadbbcaddccaccccccdadbadddbadacacaaabddadcdcdadadcacadbabdababdabcbabbcbabbdddcdbbcadaacbcdadbdbaaaaddcdcddbccadddaccbdbccaccabbbaabcbbbbdbcddddcaabbaaaaaaaddbbbadbdccaabccabbabaabcbbddaccbadaaccaaadcadbdddbaaaddcccbcbdcccdaddcbbbbabbcbadccddcccbaccbacbdddbaacccabbdddcadcbbbcbbbdbcdccbdaadbccacabcbdddacbaccdcdcdabdacbddbccccbdaccdcacbababcabdabaacbbcaabcdbbdccdacabcdcabbbbcacbbcaccdabdbbcdabbcdbbabcbbcaadaacdaaccdcaabadbdabbddccacabaaaabcbbdacacbaadacaddcbabaccdbbddbadcdadacabcadbcacdcbbbdcbcabcdbaaadddcccbadbadcdabbabdaddabdadbccabcdcbdccaacccadcaddcbbdccadbdccbcbbccbbadcdabbdcddcaccbcacbbdacbaccbcdaaabcbbdbaaddbcbccdccdbcddbdbaddddbbcccaacbabbdbcaaabaccaabcbababaadcddaadbdddbbbccdbbdccdbbabccabbbdcadbbadddcaacdaabadccadcadcbccdababcdbdaadbdcadaacbdccddacabcdccadbcdcbbbdddabbbccadacdcbcabcbccdccdbadbddbdaddaccdbbddbdbbababbdcddcdadbcbdcaaadccbdacbbdaddcadadbaaabbdadabbabadcabbdadaccddcbaddaadddbacbacdaccbbaaaadadbdcdbbacbbbbbbdaddcddddbbbabbaacbcbabdadcdcabcddbaacdbccbcaabaaaddcaccbcacbddacdadcabcbbbbacdabbaaaacabbbcbcaccdcbadacbbdabddcbdcbcbbcdaaabbddcccacacddabddaaaaddbbbaabaaabdbaddbbcddcddcbcbabababbcbbccbdccbdcccadabadcbdadabbcabaacdbbdccdaaacdadcdcdbcddbabadccabcadaddadbcabbadabaacdaccbcbbcbdbcbbbcabaaaacdccadccbdabdacddabccddbbaacabddcbccadcccbadabaababbdadaadcccbdbdadddbbbdaacbaaabdbbdcacdaadbbbbbbbddbddacccbdaddcdccbbdbbdbaabdbdbbcaaaacbbaabbadcbcbbcdbbacbbaabdbddcbbacdbccaddbabaadbbbbcdbcaddcdcadccabbacaadabaddddbcdcaabaabdbdcbbdccadadadadbdabadccadbbacddbdbbbdcbbaabaacbbbcaddcdabcabaddbcccadccbcababddcabcabccbdddbaaadcaacacaccdbdcbcabacacaaccabcccbcaaddadaacbbacccccdbacdcddacabddbacdcaadbacbcbcbbcdaddadcaddacddacabbcabdcbacabbcaaddccaacccdbccbdddadbaaccdcabcadcbcabcdcadcbadcdcababacbacadddbacdbdcbdddbaadddacbabcadcbdbbbdcdaabcddbbbacabdcacbbbdcdaaaaabdcdbaabdbdacdabccbacabababcaaabacaabdcabbacccccdddbabdbabddaadaaadacdcdbabbcbbccadabbacbcddadbaabcbbbcbbcdbbdacaccacaddbaccacdadbcacddcaccccbacacbcddcddbdadcadacdcdaddcabbdaddbdcdccbbadaaacbcacaabbaccbddccbbbccbbccccabdacaadcabdcccbbaccdaabcddbcdccabbccbdcaaacacbaababcbbaaacabcdbdcadddaacadcadbbcddddcabddbdacdaadadadbcaadaccaaddaaabcbbcdbacaacdabbbabddabdcbabddabbcdbcadcdacaaaddccbdacbdababbbdaabdabdcdcbbabcbbcdcdbbbcdabaabbbdadadaccdabacddbbcbccdbbccacbdacccdacddbacacccdbddcdbacbdddcbcbddacaccaaccbbccacdacccbbbabbbdacbadaddcacbcccdabaddcbaababaabdbadabbadcbbbccaabcdddaddccdbaddcaacdbbdbbbaadbaadbccbdccbbdcddcddaabbbbcbcccbcdcaadacbdcdccacbdaddcccddbcacbbcabcadbcdabcdbddccccbbcbbdbbcacdcacacdbabadabcbccdacdcadddbaabbaacdbbacbabadaccbacbdbbcccdacadcbbaacbdcdbaacbdcabaccbbcabdbcccadadcddbcccdabcddbdbddacbcddaabcabaccbbaddbdbccccdabbdcabdabddbaacdcdaadbcabbbbbadcbbcadddaaabbbdcabbccacccdbdcacdabbddcdacaccdcbcbabcbddcdacacaadddcaaacaabdabbabcaacabcbbcddbbbbbbbaacadbbadabddcdaddcaadaacdadaacaccccabdbbdadacabcbdcbbbbdbcdaabcccccdcabdccabdcabbdcaadbbddacaddaccdbcbbdacbbadccabaddcdadbdcbbadccdcddddaabbbabaccaabaabccdbcdbdbcdccddcdcccccbdbdbdcadacacaddddbccbcbddbdcadabadbbbaabcdddcbacdcdbcddaacccddddbdacbcdcacdbdddbaabcdbdcddcbcdcadaabbdcacaaaaccbbbddabbbdadbaadbbcabcacadababaaaaaaddbcdccdbbbabcbbcbdddccbcbdaacaccaaccadacdcbdaaadbddacabdcccddbddaadbacaadcaccbdacacbcaabaadcdbdbddcdcaacccadaadcdababcbbcacbcbcdaadadccdbdbbccbdcadbdadacadddcccdaddcadbcbdccbabadbbbbaadcccbabddabdbdadcdadacdabaaccbbaadcdaccbddcddbdaddcdbbdbdccdbdbaacbdbcbbacdcaddaddbccdcdccbacbcbadaacbbcbadbccbccdcdaadbbadadacbddbcababdddbacadcacaaacadbabccdbbadccadcbdadbcdbabbcdaabbddcacbcaabbaaccacdaccdbaaddcbddcabacdcdadadbadcadaabcdbbabdcddcdcacdadcbabcccaddbccaacdddbbdccdcaacaaabcabaccccacdccadbbbddcdcbbdaccbacbcdbccbdddcddddacccadbbdbbcbbccccbdabaaacbdabcddabbadbbbaccdbbdbbbddbabbddabadadaaddbbaacddcccdabadaccaacbabcacbadabbdcdacababddbbdabcaddaacaaadaddbcdcabacdaadabdaddbccabaddbbbcdaadcbacaabbabdaccadcbccbbbcbcbcbdbcaddddacabcbcbaccadddacdbdbcbccbbbaacabadbdcdbdabdacdcccabaaacbcbacdddcdacbdcccbdaabddabaacdbdcdbccbdaadcbbbcaadcadbabaabbdccdbaacaadcccdcccbaabdcbbababdadcbddaadaaddcadacdaddcbbcdcddccbccaacbccacdabadacaababcccabcdabbbbccbbdcddcadbcaaacddbccdaabadabccddaabaddcdcaaddababdacbabcbacaccbadccbbbbcdcacbcacdabbacdddbacbcccbbcbcdccdbbbccdcbbacdabbaaaccbaadccdaacacddbddbbdabcaabdcddccdccccccccaaccacbdaadacdcdaabcbbcacddbcbcbddbbcaaabcbaabaccbcdbcddbdccacdbcbccabbaddbadcacabacbcadbabddaaacacdbdaadbdbdcccdccacdababadbdcccdcaaadddbdbbbcadbcabaacaaaadaadbcbddccccbccbcbcbdaadadbccbcdcbcbbcdccbacdbbbbdccacbbdccadbbdbadabdadabacdcdcadaaabddacdaccbdbbdbbacdccadbacaaadbdacddbccbbdbbbbcdbadabccdbaacaaabdddbcbbbcccccbcbdcdabdabcabbbadbdacdbdcddabaaabaaddabadbabdddcdbaaabbdbbddcdbcaabcbdabbcbbdbaccabbcccacabbddadcccccdddbabddcccccadbaccabbabaaddbcaadddbdbbcbdbabdabcbbbdddaadcbaabbadcbcbcbcbbacacccbbcdacdaaadaadbbaccacabbdccdacdccdbddbaccaacbbcbcdccbcbddcadbdddbbcbacaddabbacdaddddcccccaaabddbcaccbcdbaaaabbdbcdccdddbddaccdcbcaccbabcabacabadcbddbbacdbaabadbaaddcccabbcddababdbdabaddcbaaddcdabbbdbdbbdacbcbaddcdacddbcdcbdbccaaaccddaacbdbcbbbaccdbaadbaaacbbbcacdaadaccbaaabcaacaddcabbcbacbbcaadbdcdccacbaacbbccbbbbaabdaaaadbdbbcdabdbbddaacbbadadcdcaabddabcbdadcabadabaabcaccbccdabdabcbadcbcbabdcdcdcbcbaacdadddacbccacaccdaacbcbdaddbacdababbdacbaacdaaccddcdadcccddabdabbaadcbcdccaacababdaabbcdaccddbabbbbddbacaadddcccbdcdbccdddbabcacbbbbbbaacadcddcbbdaddbabbaadaaaddacddbdacbbdbdcdabdaadcaacbcbabcbbcbabcbbabbaaaddcbbacccbaaabacadbddcbccdccddacdcdacbdcacbbbdabcbcbdccccddcabdcbccbccdbcaaaaacdcddbdbacabbcdbadabdadbdbadbbaabbacccddbcddadbdcabaaadcaaababbdbacbddadbdbcaabcbddddbbbcccdbbaabcccaddcbcabbcdcababdbdbbabbbcbdcbadccbbbadabaabccabdacadacadbadbcbcabadddddacabbbdcbbccacbcabcbabbaddaabdcadccdbaaccdccbdcadbbbabbadccdacdacaccbbbccaddbdccabdabcaaacbbcbccddabbcabbdcadacbcdcdabcdbccaaaccdaddbdbbdbbccaddbcdbaccbbbcccdacbdbdaacdcddccaabcdcdaacdbaabcdabcbdbcbbcbdacaadacacaddcbaddbacddacbbbaddbdbccbdcaacbccccbbddadadbccddddbadbbcdacbdbaadaaaadcccbddbddbdbbaacaadcabcbcbabbccdabaabdccbcbdddccbacbcdbbbadcaddaaacacabdacdadbddacbbacdbcbcaabbcdabcdbcdbdcacccdbaccbcbaccadbcaacaabcbbbcccabdbddaaddacbddaadddbcddcdcbcdbaddbaddaddaaddbadbbccbbcbdbcbddbbcdaacacaaabbacaacdbbcdbbdbcbbbbdbcbdaaadbdccbbbaccdbdabcdaabbcaabacddbdbaadcbcadabdaadababbadbcbddcadddbcdcdbcbacadbcbbabbbcdabdcbbcabcaccccababcaaccccdacbadcbbbabaddbbaabbccdacabddcddaadabadaccddbcdbacdcbbaadcccacccbccdacaaaabacaabdbaacaddaabddcbdddddcbcbccdddbdbcacaaddacababaacabbcadbcdadabbdbbbcaddadbccaccdabbacbcbacacccacddaabaadadddacacdbccdabdcccdbddbcdaacabcdcccdccbacbdabdacaccdbcdccadaadddbccdcddcbdcacbabcbadaadbddbadcadbabcadddcaaacbabddabccdcdaccddcbadcdbaddccabcddacbcaaabcadacbabbcaaadbabacbcbbdddbdbdcadcaacaddaaacdcbdacdbbadacbcbacbabddbdddaddabddbcaaaddbbdbcdccbaaaabbcaddbccbbcccccdaccababcabdccbcacaacadacbddbdabacbaacbbccdabbbcacaadbdaacddbbaadaadcbdadadabaaacacccbbbbddddcadcbaacdcbcbadaddbdddcabaabacdaddccaabacccabadccaacacabaaadcaaabcdccdcbddbccbdaadaaaaababbddaddddddabcddbabaccbbcbbcbbbcabbbacbbacbbaacadcbccddbbaabcaabddacdcddccbabadbbaaaadcabacccbabbcdadcabbcdacdabaaadddbccbccdbdbbccbcabadddabcadcabaabcddaaaccbdbdaccdadbdbddcbdabbaacbcbcbccaacadadbcccadcbacbadcbcbbcaadabdbabdabdddccddcbadcaddccdadbdbaadcddbabccdcaadacaaccdbaacdababbbdaaccadbbdbabbabddabcddbbdaccbdbacbdbbbcdcdbdcadabcdbbdcddbdbdbaddcacbcdacabdddcdbaabbaccccbcdababcbbabaabaabdbdadaaccaacbbcacddadcdbbaddcbccadcacbdcdabccbdabddabbcddcdbadadddbcdaacdcabcddcddbbaadadacbabaacbcabadbbdddddcabaabbdaccdddcccaccdcbabbccbbbdadccadbdcadbbacddcbdbaaddcdcdbcbbbdcabaabdcdbabaaadccccbabbccaccccacacddbaabbcbdadbccccbdaadbdacbccdaaddcccabadaccdacbbbbcdadbdbdcdaddcbaccbbaacbdcbbcadcdbcdaaaacacbcdadcdaccdcdcccdaddbacddbbaacbbcacbbacbaaaccbcabbcabdcacbbbdadcbcabdddddbddcbaccbbdccccabbcddadabdcabdaddabaadaabcbcabbadbdbaaadabddcdcdaabccddaddcddbdbaadbcdcdcbaadaadbbcdcacbbabaacddabcddcadadaaddadbbcdbbaccaaadccaccbddacbcbaccacdcbaddbddbcdbacccdccdbcbdcdabdadabacdddabaababddadcdcdbcddbbadabaabacacaabbdbaaacababdcabcabadabdabbdddaccccaabdacacdaacaccdabbbbabbabdccdcdaabdbbcabbcadabcadadacdddadcbcadaadbabbdcdcbbcdcaabcabccddddadcadcddcbcbcdaabbccaadbadcdbbcbbcbadcaaacdcccbcbbbdccdadaacabbaacadbbdcabbccdcdabbcdcddadcccbdccdadbddbdbbcdbcccdaddcababdaaabbcdbcbccabaabcbbcbdbbcbdccdadbabdbdbbbaaaaddbadddaadbcdcbdcaacacccdcabbdccbbcdbdcaddbdcddcbdbaabddcbdbbddcdbacdcbacdacbccababbbbdbadaddbcadaaaccaadbcadbccbcbacbcbcdbdbbdbcaadbbabaddccaaccdbdbddabbcbbdababdadcddddccbbbbbbcdcddccddddadcdadadddcddbcdbabbdcbdbcacdcbcbddabcbacccddccdaabdcbbcaabaabcccdccdaacacddcbccddaabaacbbbabbbdccbbbbcdaaacbcdabbbabaaaaabaadbdbbadadcdcabcabbbccbbbbaddaacbbdddcbbbaaaaaddcdcbacddadbcbbcdbbbbbddaaaadabdccdbadbaccbdaadbbbabcdabcdbacacbacdaaddadcacdccdcbccadbcbcdaaadcadbaabdccadcdbacbadcddacdcbddabccbbccdbdacbccabccacdccdbaccaadaabdcabdacaccaabdadbcacdaaadcabdadbbadcadadcacbaacbccdcccddbcaccdbdaababdbacacbcbaacbcbbdbababadbbadbcabdcacbbdadaacdbddabadbaaaaadaccaacdacdadccdcacadcbccdcccdaddaaabddbdcadccbdcbacbdcccbbbbdddabdbbbdbccabcbdaaacccaaaddbddbcbbbddcbbcdadabaacdcdcadcdbbdbcdddcbcdcdbbaadbcadcaddaabcdabddcdcccdabbacadcaddbcdddbdcbddaacdcadbcadcabaacbadbbcdcbddcbacdbddcabacbabbcbbadddccdabaacaccdccabdcbbbcddadabadddabaabaacdddcbdadadabaababdbadbddbbbdabdcdbbadcaabbdaccddbbabbccabbbdadcdaccabccbcdddadbccbdddbddabbabadbccbbcdaccccdbadcbbabdcddaadddacbbaadbcdaccccbabcbaabdbcdbbabbdadbbbcaccddcddbbabaaccacaaadbaddadabacaacdbdacdcbdddbdbcbbbcabbdddaaaabdcddbdacbcdaabbaaacbcacbbcacbadbbcddaacdbbaccdaadcccbbbcddabbccbbbbbaacabddbaabcddacccbaaddbddadbcbcbdaadcabdbddbddbcadbcbbbddadacbbadaacbaaaacadadbcbbdaaaabbbabbbcbaccbaaddaababdababbcccbaacdaaacddcaabbddccabcdbadaccbbccbbcdcaabcbbddbcbaccabacbbaaaadbcbcaaadcdadddcdaadabbbadcacacbbacbcbdadaaadcabcaabdacdcaadcbbbadccdcbdddcdcbbbadbbcdbbcaaddbbdcadbbdccbccbddcbbacbdaabbccdccacdbbabbacacadcdbdacbbccaabaccaccdadcabdacabcdbcaaadbbbcbdbbcdbcbdaaccbcdbccddacdacadaaddabcbcccbadcdddddbddbabbbacdacdbdbcbcacadcdbccabdcbdcbaddbcccbcdcbdbbcbbcccdbadcbdcdbbcdcdaaabbcbabcbddadbdddbcababbabaadaddbccdccabdaddaacacbcdadcadddaccabdadccadabdcaabaddcdbbdbdcbcadcbbdddbdcbbbcbcbbcbbddcbbdcbaadccbcaddcdbbdbbacbcaaaacaacdbbccbabaccbaadabaccbdcacccdcddaccdacccaddaabcdbabbabadabddcbdcaddbccdbabcdcadaddbdcbbaaabbccadbcadacdcddcddbbcdbcbddccbdcbcdacbdacdbdcdcdbcccdbadaddadcabaabbdabcbadcbdbcbabcbacbbdcabddbacdbcbddbccddccbbbdabdbcaccbdcdcccaacdbdbdcdacbcdcdaadcadacddabdccababcadbcabacddacbabacbbdadabdcddbddbaadabbbbcbabbcbbbcbcccbcaacacdbbddccadcbbbdddcababbbcdbadcbaaccaabddbdcbdccddcbcaabbcbdaddaadadccabbbcccccccbbbababbcadbbabbbdbcaddcdcabdbbcadbbabbbacaaadacadaaaddbbbbdaaccbcbbabcadcbbdadaacdcbbcabcacbabcbdcddbbdcddddcbbdacadcaddccacdaaadcdaacbcbaccbabcadadcbddadaadbdabcbbaddabbbdddcabbccaacabdaabcaacbbdacccbccbaddaabcbcbaadacbaacbcaadbcbacacadcbaccadaaddaabbaadcaddddbcabbdabbaadcbacccabdbbbccacdabdaccdbadddbcdccdbaddaccbbccabcbcabacaddddbacaddbbadbcbdcaacddbbdbcacddbdddcbcacaddbbbadbdcaddccadbadbbbcbbdddbdaccbcddccaabdadcdcacadbabaadccdaabbdcbcdacccaabcddbdaaadabdbdbaabdbcddccbcbdcbcacdbdcddbbddabbbbdcdacddbdaaaacdbccdccbbabbaadbccbdcbbbaccccbbdaaacbaabcbdadabcdccdbbbabcbbbcbbccbaccdcbccdcabadccabadaadccdbaaacdbddbabdbddbbbdcabccdcacaadccdabacdbdaabccbddbcacbbababbbbbdbcdbadbadbbcbccbdacbcbcddaaddadbbabcdcdcdddbaaadbbcaaaacdaaaddccacbccdababbacaacababdabcbabdddacabbdbacbadbbdacdbdbacaddbbccbdabdabdbdacdbaddbbdbbdcbacddcaccdbaaadaaddddbddcbccdcaabcddabccbdbdabcdbabbddabcaddbcabcdcdddcccccaddbddbcddcadabbbbabccaacaacabcbcdacabbacbadaaabcaaadbcdbbdbaadbccabdaaabcbabaacbadadacddacdbdcbdaddbbbcaaddabdbdbbcbaadcbaabdbacbaccabaadadcddaaaccbbccdcadbbacbcdacadacaabdcddaddbdcbadbabcbbcbabbbabccaaacdcddadaacdbdccdbbcaaabcdadadadaadbdddcccabcccbadbbbaaccbcbcaaddbdcdaacbbbaabbbacbaacdccdbaabcabccddcdcbabdadadabadaddacbdbbcdabccbacacbabcbbacbbbddcbcddbaabdccbbcbabaabcbabbdbbcaccadcabdaddcbdbbaaddbbdcacabcaddadabaabdabcdcbaaabdcbbbbdaadbbaccdacdacdbbbccbdaabcabbccbadabcadabcbdbbaacadcbacadcabdcdcdbabddadcabadcacdbbdbaacbbadbcdaaadadbcdbcddcadbbaacadaddcdbcaabdcabdbbabacdadabdbddbddcdcabaddadbbcaacbadcabacdabbaccbbbcdcbacbdbbcbaccdbdbdadcadabbdcacccababbcaaaadddbddcbbdadacdacdcbddaaaadbacacdccacdaaddadbadbcdccaabcdcaaababdbcbabbcdbdddabaaaaaabacddbaacdabccbcbaccbbcadbcdabbacbccbdcaacadaddadaabcadddacacbdbbaccdadcdbcdcbddddbaddcadcabdbcdcccbdbccbdbcdbcdbdbdadacbdacbcdbbbdbccccadcdbdcbaabadbdcadccaaabbadadcdaddbcbdaaccccbddbdbcbabaacaaccbbcaacccabbbabbccbdcccbabbaabcccbddacdabacdcccabbaddbabadccbdacbbdcbbbdaacbccabadcbbdcdbabcdabdbacdbcbcdddccccadbacdaacbbdbadbcdbddccdadcddaaadcadbdaaadaaaaadccacbcbbbabaccaaabcaacccbbdcacbbbdcbcbdbbacdadddbdaccbbbdcbadcbdbcdbacdddbdadbcdcddbbbbdbbaccdbddccbbcdabddcaaadbddddbdabcaacadbcabcccccdabaabaadaacadbcbbacadccabbbdccbbbdabadbdcbbbdacaacccbaabcbcddadbabdbccddabdabccbcdbcaabccbbdcdbaabaaacacccdcdbcdacbabcddaabcbbabadabbddbdbaccabdcdbccabcbcbbdcdadabcacdabdbacaacdaaccabaddadccdbadabccadcadacaddbcadabbacddadaaccbcbbbcaadacbadcacaadbccabbabbbdaaaaccdabbadcabadddbabdddcbbddccabcaabcdbddccbadbbbadaacdbcacabaacddbbacabbdaaacaccbdcbaabccdaabddacbaaadadcbaabccbdcaddbdddadbacaaabcdbbdcabcabccccbccbcdbabadcddddbccccdbbccdadbabcbbadaccbddbdacaabcbddbcacacacdddabcbaccdcbddbbabbacddcbdbabbbaadcccacacadcdcddaaacaddbaacccbaddcdbaddbbdbbccbdaddccdbbaccbdbdabbdbcccccacbbbabaabddbacbdaaacbdcdacbcbabdbbbccbccdcbcdddabdccddccccababbbabbdbdcadabdbccdabcdcccdaabbacccbccacbabbddddbdcccddbadacbddabbabdddbbcbadcddccddbcdcbdcbcbbccbcdcaadadcccdacdcaccbdcddcadacbababccbdcabbcccbddacbbdaabababccbddbcacdaacdccdcbabdacbcbcdabaccbbdbacbadcbdbacdddbbccbbbaddaaadcabbdaaddbbbccadabaacbdcbcbddaccaccbadddcdcacdbbbcbbbccdabdddddbbccbcddcccbaaabdbacdcadcdaaddbbababacbbdaaccbbabdbdaadcacccbdaabcdadccbddbdbcdcdddaadddbbdcadaaadadccccdbbdcacbcbccccaacdbddcadacdcbbccbabacdccaacabcabdbadbbaaabbdbbdbbabaaabdbbaacbdaadbbcdabdddcbadbaaacbcacdddbdbdacdcdbadcdbdcaadadcacbbaccdaaabdcdbdccaccbccacbccdbcccbcbcccbdbdaabcccabbabbddbdaadcbdadbdbabadbccddaddadbaaadadbdabdcadcdbdbbcdbacaaabdcdbbcdaaaaaddcbbddabadbbabbccbddddccdabbdbdaadacacbccbdabcccaadbcaacdbbdcbbabaaabbdcddbdbdaadabddacdaacbbcbaaabdacdbcabbccdadcadbaaddccbddcacbbdbaacadcaadcdacbdabbbacdbddbdcdacdacddadbdaacabcbcdddcdbaccabccadbabdbddbbbbbdaacadcaaddcbacbcacbaddddabbbabcabbcbcbaaadaabbcdcaadcccbacbcdcccbddbbbbdcbccacacdddccacaabacdaababddcdacdbbcbbacbaddbacabcccadcbccdbddbdccdcdaccbacaddcaabaaccbadbcaabddbcaabddbcbdaaccabdcbccbdaabccbacbddbcdcdcdcdbdbcabbbacdcabbcabaccabcbcabdbbabcdbbaadabaaadcccdbcabdabdcaaabccacbbcdcccdbccbddbaddddadcccdadcacdcdaabccddacaacbdabccabccadacbbccdcbdccdabbacdcbacadbcaccadcaaabaacaaadbbaadbbdcbbbcdaacabdabaadbabbcbdbacabbaccccdddbbadcaabadbabdacdcbdbdbcdcacbbbccadacbcdcadcbcccacbaddcccdadbaccdabcbdccbccccadadbdadacaaaacbdddcdbdbcaabacdcbcacacbaaabaddcdddccacbdbdbabadaaddbbdddbdbbddcabcbbbcacdcddcdacadbadcdbadcbddcccabcddababcbcaabdbabbabaddaccccbdcbdcdacbadabdbbdbccbcbaddbdacbbbdcaacbbbbbabacbcabcdabddbddbbdbdbcadcbcabbcaddccaaacdbcaccabdbcbccdccccdbccbdacccbbdbaacdcacbaaccbcddabdcbacaaaccdcbacaabaaabcaadcabdbcddbacdaccbaadbdadccbcacdbbcaccdddabcbdcaddbdccacdbbcddaacdcaddbacccabcdddcbcababdbcabacbdbdaacdabbbdaabadbaacbbdbcaaaabdaabbbcadcbcdacddbdabbdbccdcbdbdbcaadacadbacaaacbbdacdaabdacaddbaaddacbcbadbaccbdadbadbdbbbbcacbbcaacaccbcdddddaaabbddabcbcbccddabbbdaacadcdacdcbbabbaaabcacdcabadcaddbbbcbddbbacacbaadbdacabcccdbbabadddaacbccdcacccbccccdbbabddbacbcbcddbcadadbccbccdbbaadaabcadcddcdcadbdbbbaddbcdccbaccdadacddcaaccbbccbbaacbcbdacbcbdcbcabddacdadcaccaadcdadbccaccbddccbcadbbdbdddaadbacbcdadbbbbcccddbbbccbddbbadcaabcdbdcdaabcadbdddbbbbadaabdddddbbdbcddbcadabcbbbbacbdbcaacabcdcbcbdbcdcdadcdddadcbaccbaababcbbdcbccacbadaabaaabaaabcadaaaaacabdbcbaccbbaacacbddccddbbdbbcbbcdadddcabbabdbcdcbabccabacababdbadccdbdcddcbbbcbcabdaaadbdacdccbabadcdcddbddabccdabdcbaabaaabacbdcbaabdbdbcddcdaccabcccaccdabdabacdcddbbdadaacaacdbaacabbbdacacbdaddbcbcacabbcccbcdabbcadacbbdadbdbcdddbbbaaaabcbbadadddccdabccdaccaddadcabaacbdcadbccdbccacabccdabadcbbabbdcddaacaacddcadccbdcbcdbababbacbbcbabaaabbabdccccddabdabbccbcdddcdcbdcacbbbddbdbdbbddccadaddaaccbcdbcbcdacccabcbbbcbbdbcbdacbdbdaaacdadacbcbbaccbcbbcbababbdcdbcdaaabdaadccdadadcddbcbcbbbcbabadcbcdabddacadababadcadbbbdadabaadbadcbaccdbccbcccadbaabbbdbbacbccbbbccccdccdccaacdabcabdbdbbdccccdbdaacbcbadccbbcbdbddbbcccbbbaaadbaadadabbbcabbccbbbcccabadacbbaaacdbcddacbbbdccaccbcabccdbdabbcbabaaabaaabdccadccddccbdccdbbdcccbcbabdadbcaadbadacddacbaccbdabacbdcbccbbadcadadcbddaccbcddbadacbaaddcbcddaaabcaadabdbadcadbddabdacbdcaaddbbdbaddaacbdbadcccdaccaacdcddddbbbdcacbbbcababbdcabdddcccbbdabdcbcccabddbdabddacaacccbbbdbcacddbbcbbbbcadacdcdcaaddddaabacbddcbdbbbacbaabbcaadbacdcbcaccaaaccbddbddddbbdddcabbcdcdaacadbcacabaadcdbaadbcbcbacdcdadbcbdddbcdadcaacbbdbddbdbdcdcacbcaacdbcccbdcddbddbcadcacabccbaaabaccdbdbbcbaddabadbabcabbacdcaaadcaccddcddcdacddbadcaabcccccadaadbbadbdcddcbdabadbadbcabbcbdcbabddadcaccbbdaabbcaadaacdcdacccabbabbddaadbcdcdaadadbddcbccddcaddbbacdbbacbdbbaadccbdcbdcbcdababcabcabaaabaadcddbabcccbbbadcbabbabbaccbadabdacdbdcbcbcbbbdccdacbabaadabdbbadcbcdadaaadcccbaaccdaabcbdbcbdcdddcddcbadbbcaadbcdcccadbbdddadbabbcbbdbdcabbdcdadbdbcddbbdbbcdddadcdcadabddbbcbbcdaccbdbabaadbdbccadcaadaadcdaaadcaabcddbcacaacdbcbcdcddbbdcdcbdccaddbbadcbadbccbaadbcddcddaaabadabccbdcdbdcdddacdbcdcaadcacacacababcadcbaababcadacdaaccddcccbacbcbaddcdddbbddbcbddbcdddddddbcabddcaadcdbcbadacbacadacddabdbdaacdacdbabbbcabdabdacbddaccacccaccabacabcbaddaccaddbbaaabdbacdcbcbcaaaabcbdcbbddbbdcbacadcbcbabdaabddaadbcdcbacbdbaadbacbbbdbabdccacbdbcbdadcdddddcacccdbcacacaaddbdadbcdbcccaadccbcacdccbcabbcbdddcabbadcbdcaacbcadddccbbdcadaddcbdabdcadbcbbabdbadacddbcabcabddbaabaaaadadccbddcdcbdbddbaddaabacbbcbdabacddadddbbaabdcbccaddbdcdbccbcacdcacdbcbbcdbcaddadbaddadaddcdbaababccbbcabdacdaddcccbcdcaddcccdbbdacadbcaccabcbdccccbccbdcddbdcbdbdbbdcbabccddcaaaddaabbcaccddbccbcddadadbbaacbacdaacddcbdcaccaccdbdbcbdbcccbbadaddcbbcbdcdbdbccdbaddbcdabbbccbaadbcabcaadccbccbcddadcdccbcccabdcdddccbbdcadcacbaadccadcaadbcdcaacbaaabbbcccbdabbbacbcdbcdaddcccccbbaccccccabddcdcbdcbcddbabcdccbbdadccacadadcccdbdbdbccdddccbabcbcbbcbdababbbcbbbbdbbbbabbdadaadbbbbbccadbbbbbadbadbcbddddaaaabaaddcaadaddabaabaabcccbccbadccdcdbbabacaaddcdcdcbcbdcccbcdbddcbacdbccbabcbadaaddddbacdbbaddbaccbccacdbbaabcababddcbcccabdcbcbdcdabcdcdccbdacbaddcbabbdddaadbcddadaadcbcdcccdbbbcaccdaccadaabcabddadcdcadabdddaaddcbabdbbaccbdadabadcbcdccaacacadabbdcaabdadbbacdbdaddabcdbdddbcadbbdcdcdaaaddccdddabccaccccccaadacabaaccabddcabcdddaddbddbdadbacbbaaaacddcddabdbbdbdcbbbcccdacddbbccaaddbbadbaaadacacdcabdaaadcccdbddcbddaababcdaddaaaadabbcccddbdbcabdbddaadcdcdcbccbbdbcbbabdccbdccbccabccadcbbaaaccbdadcacbccabdbbcbcadddcbaccccdcddcbdaacbbaaaaaddaccacadcdbbaadbcdccccdadaabbaaadadbccabdcbbcabbdcdabbbbacabcccbbcbddbdabbaadcbcbdddabbaaacddddadbccdacadabbacbbcccabaaddcaacccccbbddbcabdaabdaacdaadadcdcbddcabcbcdcbbcacababcabbadbcbacdadacdaaccddddcaaccddbbcababcaabbbddcacaccbbbaccacdbcbcabbcdacdbccdddccaaddacbcbbbbcccaddabccbdcbacbdbdcbddbddcadcddcdcadacbcbcaabbcbacddccacabbdcbdcadcdcbabbbcdbcdabddabbcabbbaddbbcbcdbcadcdabcdbcbcaacccacddcdabaddadbdacbaaddbbcabdcdcaccbabbbdbacdbbbbbbbcdbbdcbdddddbacbdbddcabcadcdcdbccadbcadacbadccbcbdcdacabdccaacaccadcbaabbdccabcbdaacaccaaadddbdaccaaddaadcdbcabcdbdccaaaacaabddacdddabddcadbcadcacccabbbacddbcccbbccadccdddacbdbccadadbadadaaacbdababdcaddccbbbbacdcabbcdacdcddbdadbdcbbbbbbaaddbadddababcaacbcaddcddbdacbdabcbcabbcbdbbadaabcdccbccdccababbdbccaadcdcdcdabdccadcabcbababddcadcbcaaabaacdbaacbcdcbdaccdacaaccbaacddcbabcdcdbbabcccccaddcabddacbbccacddcbadbcadcbcadaaadbbdaccbbbacacdbcabbdacddacdadbbccbccbdcbcbccbacbbbdadbbbbbaccaccaddbccdacccdddcbbcdbddadabbccacacabbabbcbbddadbbdbcaddabcccdbbccabbbdbbbadcacbcaccadadabadaabbbdadcaaaccadbadacaadbacbabbbcbbdcaddabbacaccccccaacdacbcbbadcddbcccadabbcadaddbdbccdacdaccdcadcadbdbbcbdccbccdacbacbacdabaccbacaccdadcdccaacadcdcaacdccababcdddaabbccdaddddcccbdcbcaccbabcbdbdbbcaabddaacaabdddaaabdaadabbddcbcadadccadbddabddadbdacdcacdccacdcccbacdcdabdbdaacabbaacaadcdababacdcbccddcacdccabbdcbaccbbddcdbaabacdcdddbbcdbdcbaacccaaaacdccccdabdbcdcbbdadbabcbddcadaabcbcccaabaabbacbbacadacdcbbddbadcaaccbacddddaaddadaacddbbcabcaaddcdcbabacabcbccccbdaddcbcbcdccdbaccadccbcbacbaaaccdabaabcccddcdbaabbaadabcbdadbdbbdacdcdbbccdddbdadddabcbcadaddcccabacdcaaccaddcaabbcadccadaccadbadadccacabacdbbcbaaaaccddcaccacbbdaaababbdbbbdcabbabcdacdbdbadbcbcbbbbabcbcbbbcaaababccdabbdccadcdccbbccbacacbabbdccaccabcbdccdbcadbababdcbdaaccabdabccdddadddbdadddaaaccddadbcbabbdbbccbbacbcdadcbdabddabbbbaddbbdabbdbdcacbaaddaaadbdbcccbaaaddcddbddcdadccbdaadacadccdacabbadcddabdcadbbbabbacabdcdacdcbddcbdcadbdcdbcbbddbacaadabbacccaaccadcbddcaabbcbbaaaddabbacabccbcaaabcdddcdcbbadabcdcbccbcadcdabbabbbbaaddbbdcbbbcaacbdbccddcbbbcbbcabdaddacbcbddbcbabbbdbabccacaaacaccbddadaabcdbcaabdbcccccdbabaccddbbbcaaabbadcabdcdddadabaadbaabcabccadaddbcaaabcbcbddcbabdaadcdcdddbccdcbbbccddcdacdacdabcbbadcbbbcadadaddacdccadccddabdcbdcacccbacddbdbaaabccacbcacaaddbabbddcbdbbcdcdbddbbdcdacdcacdbcbaabbdabdaddddaadcdaccccddbcbbbdbdbcbcacabadcaddbbcbdccbcaddcdacaabaaccddddcdcacacdcadbbbdcbbdaccacccabadbcbcacdbabddbccbadbdcdcabaddbdcbaabbacdaacbbaaddbbcbbaadcacccaaaddbcabccbaacbcaabbcabccccadaadaabbcaacabbdbadaabdccbccabacdbddabccbadbdcdbccaaadbbbabcbddacbcbdcacacbcdaaaacacaddcbaccbacadccdcaddaccacabdabbcbbabbbbbacbcabadacbcbcdcdbcbcadababcdcadbbabadbdaccdddcdcdccadbcaacdcbabbaaccbdcdacdbcacdbcbbcadcdddabdbbccdadaadbadadddbbcbaaabaaddacbababddacddcdbcdcdbbbbdccabacdadbaaacbddcddbdcaacbdbaccdcdaaacdcbbddbcbcccadcaddcccabdbccabcdcbcdbabcdddbdccbbcacadcdacabdcbcddcccadbabbbbbdcabadabcdbbccdbdbacbdcacdddcbacbdcbaabbbababcbacbdacacdddcccbbdbccacacaaddbdaccbbbddacbbdbadadacddadacdbbdbabdcaacdddaadbcbcbcdcabdadcdcadcdbadbbadbcaccbbcbacdbadadaaadcbcdcaaacdcdccbbcabbabddacaccaacccdbdbadbaabcaaddcccccccbcbaccbbaabcdddbcacdbbcaababcabaacdbdcdbcacabbcdccaddabcabbaccdaaaacbcddbbcddbddadabbcdbdbabbbabccdbcdcadbcaaadbbaacbccbacddabaddacaddbbcbacbdcdaaadabacbcbaaddcaabcaacbbcaaabbabbaadabbbbabaccdcbadbdddacbabcaacdadadcdbcaabbdcbbcdabbdcadbbacbcccacbbbddadabacadcabadcdcababbccddcbbaabdcdbdbbaddcacdacccccbdddcdbbbcadacbaabcadbbdadbbbabacddcacabdadadabaaaccaacacaacbacccbabcbdcddbcacbaddaaddcddbdccadbdadddaacdadadbaabacbbbcdbcbcdaabbabdbacabddbaddbabddadbaacaadbaababcabbbaaddabdabbbdcbbbbcabccdddbccddaccdbcdcbbabdadcdbcabcdaaabbdbccadacacacadabcccccabdcdabddbcacadaadbcabacbdbdddccbdbdaacdcabbabbdcddaaadacaadaaacccabbccddcbabbbbcdddcdaabbcdcdcacadbccddbdabbcccacccacbbcadabbbdabaadbabacacabaacadcccbcacabbbdbcddaadabaddccbbdcacdbcabbcbdbabbaadbdcbdcbbbbbbddbadadcddbacbbdbdadadddadbaabdacbaaddcbccdadddaacbbdbadccacbbcdadccadcdbaccbbacabcdcbbdddbababdaddcaacaccabbbccabacddcbabbaabcbadddbdccdaadbaaddbadbbbdbbbbabcdacccbdaabdbabbdadcdcdbdcabdddcdaccdccdabadbcbcdaabbadcddacbbabcbcdbaadbcdccbbdbbbdbcbbbababcbbccddbccdcbbbdadbadbabdcdbbaddbdaddcbdcddcbabddaacbdaaaacbdbbcbdbcccbaababcccbdccbccaccadaadaccdcbcbcbdddbabacbaadabadcdccabbdcdabdadcdcbbacacccabbaddccdcbcbcdcbdbbcabaabcbabbbddbabdcabcdaabdcadaddbacbcdabbaddddbddbbbdbdacbdbdddcdadbdcbcabdbbadabcacaccdbbcccacbabbaacabddaacbddcbdddbcacdddddaddabcabdddcbbbabccbbbaaacbadbddccaabcdaaaacbaaccbdccbaccbcbccadbabdabccbabbbccdcccddccbdbddacbadccabbaccaadadcbccdccbddbabdccddbadcbbadbcacbcdcacbbadbcbdaccadbcbcacbcdacacbbabdbdddcacaddcadabdaccaddacbbdadcbccbbaccdabccdcaadbadadcaacdbdbaadbbcbaaccbaddbadbdddcbdbbaabbdbddcbdbdbbddaadcadcbccaaadacbabddaacdbcacccdcadbcdddacdaadccbbbbddaabaacccbcadcadcdaabacbbbdaadabcacbdcacaacddddadadbbbccdddacbaaaaadabbaccbddccadadcddbbacabbdadaccdadaddaacbabaadadcdbcdccccabcbacabdbbdcbaaaaacbcadccbcdbbaaccaaabcdddddabacccbcbadccadbcccbababbaccdbacabaacacbacbacacdcaabcdcbbdbacbbbcdcdcabddbdbdaacdbdbaaaacddcbcadcddbacddddcbbcdddaccddcdcbbdbcdcadbdbcddcabdcbddacdcabbabdbbccbbbdadacdddabbbbacccabcccbaabbabdacbcbcbdddbaddbcbbacdccbcabbaccdbdbbadbbbdabacddbadacacbaabdcdabadbacacdbbcbcacdbdbacbadcbbbdcabcacddacadbdabacddaaadacdcdccdcbbabbaacaddcdabbbaacbccdcbdabbbcdaaadacadcbabaadadaadcdbbbababdacacdacdbcadccabcbbcbddadabbddbcbbbabbbabbdbbcdbacdcbbdccbdcacaabdabacadacccbddccdbabaabadbcabbadadaccdbdddadcdbcadabbbababcbbbcadadcccdccbbcdddbdbdadccdcbadbbabccbccbcbcddddbbddccbadcbaddacbbdcaacbacabbddcccdbbdccddccabcdabccdabbdbddcbddabddbddaddcadacabcaabbccddcaccbacabacabadbdaadccccbbaacddccdccbcbaadadaaacacaddbadbbabcaadccbdabcaddadbbacacaaabcbbaadcadabaddddcbadbddccbbabbdbcaddadbdbacbcabbdcaaddacbaabdabbdbcdabcacbbcabbcdcaccbccbdbddcbddbccbcadbbbbbdabadaaaaaacdbccbcbbdabaaddcbdbaabcbbccdadcccdbccdbdabcbbaddacbadddcadacddbadadbcabdbaabccbdbadbbdddcdcbadbcbdbdaddcdbbdcbcdcacddcbaaadacdadaaababdcbdbcccbdbaacababcdabacdaccabbbaddcdcbccbbdaddcdbbcbccdcbbccaacacbdccbdacbccbcddbbdcbacbdcccabcdaaacdcaabbaabdcdccaddabbdbbddbbadcbcdacaabcbccaccdccababcdaabcdadabdddadaddacdcacdcdddacdbdbcaabbdcdcbcaacdbadbcadbacacabcdcabadacaacbbcbdaabbccdbaaabbdbbbdadcccddcbccadcbcdbaaddbadcbcbacaadbbaddbddcacbddbdbbbbdcbdbcddbcaaccacbadccbadcaaabbaaabbcbbbcaaacdadbcbcdccaacbaadacdbacaabadcdcbcbbddadacdcdabdbacbcabdddaccacdbcbadbdcdadbaddddbacbccddbbccdcbddabdbcdcacaccbdcdaccbadbccaabbaccdccbdababbbbbddccdddcdbadacacaaacbbacaabdaddbadccbaabcbbbdccacabcabdbcdcddaddbdbcbabcbddbddbdadaadadacbdbdbbaababcccaaaadcdddcdaddacaabcaabacbcdcbadabdbabcbccdbcbaacdbcdddadcdbcddbcdddcbddccdbbcbaddabdbdbbcddbcdadbbdccaacbccdddbdacabaacadbcdbdbabadbaaddabcbadaadcbbdabcccacabbcbccdbcabbacabaddcdcccbbabdadaddbcbbbaabbabbddbcdacbbbccbbbcaccbccddbadcaddacbdabcbdbdaddbabcbdcaccbddaadccbcacacbcbcaddcaabbcdbaccaccbccaaadcaadcdbaccacddcabbdaccaddbcaacbdcbdddadccdadabddcacdadbadaabadabccadbbbbccacabdcbcdaddcbcccccbbbcadaccdcdbabbcacbabcdccdaaacbacacadabcddcbbacadbdaadabdccbbcdbbdbacaaddbbaabaabddbcdcadccacdaadacdddcaacbdacdcbadcbccccbcbcccbdabccaccbbbbadaacbdacaababddaccbadcaddcacbdbacacdbddabddbaccddbdcddccbccbaadbdddddaddcdaccaacabadbbdaccdaadddaadcdbbbddccbaccddabbacccaabbbcccdbadbadcaabdaacabdccccbddbdacbaaccabdaaccbdccacbbcacdccbcddcaaacdbcacdbdabadaccccaccbaacccabbcddbdbacbadbccaacbdbacdadadbaddbcdbabababcacaabbadaadcaacddddccbadbbbccdddcacbcccabddbababbacaabdbcbbdaabadaccdadccccdddbacccabddbbdbdcaddbbaabdcdcdddbdddddbdbaaabbcdcdabaacdbcbadcacdbdcbdacbadacccdaadcabacadacdacddbbbddacbcaccbadadadddcccbdcdbccaddadbabdddadcabcaabbdcbacdcddcacacbdadbaddaabdcacadacbabbbaddccbaddbcadbbdaaccbccaaababadaabcbbdbbadcacdcbdcbdcdcdcdababbddadddbadabcaacabcbdadccabdddbcbccddcdacabcabdbbbcabdbacdddcbdabcdbbdddbcaaadcaacadddccadcabaabdddcdbbbacadabaabbaccdacccabadadcccdbcdbcbabddbbcdaacaddadccdaaadccddcbbdcbaacccdaddcacccbcdbabbdaddbcadbbdcadcbabcaacdcccbdbbbdbccdddbbcadaabccbdacdabadabcbaddcaaaacbadddcbadcadcacbbbdcbbbbabdaddaabdcbbbcbdccaacbccbbaaabbacccbdbacdccddbdacacbbabdcdbabbacbcacddcbcbcdcddaddbdcabcbddbcccdadabacdbcabaccadddbabddabbcaadabdcdbdbcbdcabaccbabdadaaaacdbddcbaacaaadcadcaabccdaccdbddcccbaadbacbbddadaacbcbabaabadcbbcdcbabbaaabbcbdbddccdcdccddabadaccacdadcbddbabcdbcdcdcdbccdadddddbddaabdaabdbcadccbcddaabaddabcbacdddcdcdbcddaabbcababcdbbbdddddaaabccacdbcdbdccaacdabdbbccabaccdcdaddadbcacbabcbbbbbbaacabdcbaddacbbaccdddccbdabdbaddabbcbaccaccaacccabacacbbcddbcddbdcaadaddadabcbdabddcbdcaccbbaccdcbbaabdacdbadaccdbcbdbcadddaabbcccbdbbdbbdababaadadbdadbcdbabdbbabbcccabbaddabaabaabcbcdcabccdcdadddbbcbaaacacaabdacdbcdbdcdddddbadabaaabaddcbbaacdcaabcabdcddabdcabbadacdaaabbcbddcdcabadaccadcddaaddbbdabcbabddaaaadddcdccccadbdbcaabaadccddcaababaaadbabcbaaacdabccaadabdbacabaddabdbdbdbbbcdacabbcddbddbaddadacbbcacccabbcccddaabdbabcbbbdcabbcdcbacddcabacdaacbcabaacaabdddaacbdbadcbaacdadadbcbdbcdcdacddbcaacababcbcaabacaddacacdcdbdcaaddabbabaabbccbccababdbdabdaddcdbaadcbaddacdcdbcabacdbadacacbddabbabccdccdbbcaabbaacadccbcccadbacaabdaadcdbcadaddcbacddbdbbbaabbccdddbbdbdaaacdbcacbaddccdcccdcddaccdbdbacdcbbacbbcdabdbbbadbdabbdcdababddacdbcbbdbacadbcabccaccdccbddccbdcabdccaadbdacabcaabbdbddbaccacdacbcbddbccdbbcdbadbddabcbdaadcaaabdcdcabbbdcbbcbdcaacdacccbbcabccdcdbdbdaaccabaabdadbcdaabaabbccabbacbbaabbddbdbadaccbbccbdcdacdcbaaaccddbbbbbdadcdbcbbcdcbdddabbbdaddbacdcdaaadbddbddadaadccacabdaabaacbbcadcccbccaaacbdabcbbbabcaddadcbbcdaddbbccdbddbadadbbbbbcacabccaaccaddbcbdccdbdababcbabdbccabbaaababcbcbcadbdccaddcbbaadbdcbddabbcddaabcdbbcdcbcbddadcbdabdcdbbcbababcbcadbcdcbbbadcdddbbccdbdcdcaacabbbaacbdccaddccacdbdcdaadaabdbdcaadcdcacdabdadbdadbaccbaadbcbaadbddacadcbcbadbcdabaddacbadacbadbdbdacabdcbddcdabacdadccabbddcdbacbaccbbcadddbacabccdcbdadccacadbcccadbbcccdddacdadccaabcbdbaccacdbcccabdcbacdbcdbbbbcdabcaacbdcacdccadcdcadbddbabcbacbdccdaacddbdacdbaaddbcbcdaacdbcabacdbdbbadcccbdbdbcabdaaacabdcdacadddaabddadacdabddcbbcdccbdabccddbbdbacbcabdcabdddaddbbbadaacdbbdbcdcddcdcabdcdcbcacbbcbdbddaaabbbcddaddbaccdbabcabddddcbbbdbaccaabcccaadcaccbbacbabcdddcdadcbdddbabadcdaababdaaadcbcbacabbdacabdadaadcbdadbaaaabdabdbdbdcabdabdbacccdbdddbdbdaabbddbbaadabcccbaaaddcbdccdabcdbbadbaadadabdbdabbaaaaacccbbcbbaccdaadbcacbdbaddaadadcccbcbdccdddabacadbcccaddbcacddbdcdbabdabcaacaddbcbadbdbbbdbcbbdbabbcbcbcccddcdcacbbcbdabbdacbbccaddbcbcbdaadcbcaccbadcbcbacacdcabbbdcaaccbadddacccadabdcdcdbbaaccbcdccbccabaaabadbddadbdddbdddbacdcdbbccdaadcbbaabccaaacbddaababcbcbbbbddaddcdadbacbadacdadbdcabadcbacaccabdbcdadaaacacbcbdbabcadaadbbdadddddbbadcdcdccadddccbadacbaccbddadcbbbddbabbbbacddbccadbcacbdddccadcaacbbdbabccbbdcacacbdccdcbadbddcbcbccbbcadbaabdcbabcacaadaacbcbbbdddbddbcaaacbabbddccabacbdaacbacaabcccccdccaaacbcbbdcddbbcbdcdcbddbcbccdddccbbdccacbadaccdadadbdbcdccbabdbcabbbacbdabaaddaabcdcbbbbabcdadcdbbccabccddbdcbbcabbccdaababcdcabacbbcccbcbabbacccabdbaabcdcadbacbccacaaacdcbcaaabcbddadabbaccbbdacadbbbdcdcaaaccabbdbdbbacccccdcaaccacccddbccdabccdaccdaccdbccdbadbbcacdbcddcbabcabddbaaccaabaadbadadcbcbbcdcdacaccbccaaccdddbcdababcabcdccdcadaadccddbdadcbaccddbacbcbdbaadcacaacbbaadbddbbacbaacabddcabddabbaabbbdaaddbddccaabbcbcdcaaaabcbdaacdcadcdbadadcaddaaacdbacbcdbccccdadcdbdabdccdaabddcccddabddbbbbccbaacabccadcdcbddcdaabbbabdbadbbbcdaddaabdcccbbbdccbbbdddcbbbdddcaadbbcdcdacdddadadbdbbadcbcaabbcccdcbdaadccdbdbdaaacabbdcaccbcccdccadaadcabbabdccbbddbabbccbddcadcbbbcadaacaabacddacdaaccddaadcabcdcbbcabaadbcbbdbbccbdcaadacababcdacdddcbbbdaccaaddaaacbcdddccababadacabdbbaababdccabbacbaaaccbdbbdcbbbcbcbcddbbdccaaabcdbaccbbcaaaddbbbaadcabbdcacadaacbcdbcbaabbcdaadadbcbdbacadccbbddcbddcdcbbdccabdccdcdbabaddacbddcabddbcadddacadddcacbccdcbbdddadcbbbbdbdddbcbaadcbacabbcacbbddabbddccbbcdddbcaadbccdabcccddcdcccabbaababaddcdbdacbcabcbddbdbbcadddcaddaaddcaddaacdbabbaddadbdcbaabdcdaddadcdacaaabdbdaddabcbabbbcdbabbdadcadaacbcdabbadaadcabcbabcadcdabdbacdcccdaccccbdbabbacabcbacbabcdcacbbadcdabaacacacbdbdaaacbcbbbbddaccdcbdcdbbddabbccdbcaddcdbcddbabcddbcbcbbbadbdbdacbbdadabdcbdadcdcdbcbbdccbbdbaacaabbdddddcdbbcacbdcaaabdcacadacacadaadcadacbacbdbaddacccdbdddacdabcbaabadabadbdbbbbdccbcdcccabdacadbdbcbbdbdaaaadacbcbdbacbabdacacacadabdbacdbdadcccdbadbcaaabaacacaccbbbcbaadbbdbdcaacddcccaacbdddbaabcacddccadaddccadabbdccccaaadbddacdadccabaccbdbdbdacccbdcdbddbdcdcdccaabdddddcdccaaacbddabbccccdcabdacbdaccbcadaaacadbcbbabbbacaccdccdcdadbbccbcdaabdcdddddcdabacbacbdbbbbadaaacbaacaadaabdacacccaaabdcadbbdbadcddcadbdaccbaddccbddadadaccbcbbcbacdccddbbadccbabbcadaacaabcddaddaccdabbdbcccddccbacaaacacaabcacdcbcdddaabaccdcadddddcccbdcaabaaabbaacccbabbcbdcdcdbbcdaddabddddbaabdbacacabbdcbabdcbcbbdaaaadaadbdacbacbdadbdaaaabcadbbacbdaadcbcababadbabddbddadabadddbabdccadacdbbdadcccbddcbdadbdccdbacddbdcccaacbcbaadddbcdbaaddcabbcbbaaaaacccbbdcdcbdaaabaaccdcbabccbcdbbbddaacddaabddbaabccbdbbbabbdcbbdddcadacadbccbdcccddbccbdacacdacabcbbbbcabaccacdaabdcdcbaabcbbdadaabacbbbcbdadadcdabcbccccaadabdaabdaadaadadacacbdaabcbccbcaabadaaabadabdcbbddaaacbaacbbaccacdddbddcadbbaacdaadadcdbcabacdbcabaaabbdabcccabacbcdadbbcaacaabbddcbbcddcacdcccadbacdbbcbbdbdabbcdabdaadcabbabbdaddbbddabdcaabadbdaaacbabaacbdaddcabdbcacabcdbbbcbcdbbcbcadcbadcbbbcdbdbaccbdccabcabbaaabbbcadcdddbadbcccddbadddacdcacbadcdadbdbcccaadcddacdddbccddcbcacdadbccbdbabaabadcabacbaddcbbcccddcbcadabddbcdbbbddacadcccbcdcddaacdadacacdcacbddcbcdbadabcaccdcbbadccbcbdcbdddcaccaddcaddadcccadcdabcadaadbddadaaabcdabcdbaabcabccbaabcbcdacbaaabaabcacbdccbdacdcbbcbabcdddcbddbdadbcbbcacabaddadcabdbaabcdcdccdcacbdcbbdcbbdcaadcaacdbaacdadbcbdacbcbccccbadcbcacbcdacaaccbabcddcadabcadaadbcddcdacbacddccddbbcbdbacaabcbcdcdbbcadbbdddaadcbaaccbbbabbbbbdbadcacddaabddbdaccbccdccbbccbbdadaacabdccacadabadcbcaddbbbbdbbbcbbabbdbaaccadcdabdcacdcdbddcbdacaccdcacbbbdababddccbcdbbbacaacddbbbbdacbddadccbcaabdbdcbacaabababbccdbabcbbbbabcdbcccdcbddcddbaabaaaccaaabccbbcdcdddcdbadabccbdbbaaadcbabbaaaacccbdadbcbcbdaadbbbbcabcbddbcccaaacdcbdddbbcdcbdccdddaabadbddcababcddddaccdacdcacbadcabaaabccbacbccadbbbbcbddabdbcadadddaadbacabbdcbcbbabbddabaadaaaaacdbcbcbadbddaccbdcdaddbccadcaaaabdbdcdcaadaabdabbcadcbbccbdbdddccdddcacabacdadcabaabbdcddccbbcdbdcaabaadbaacdaddacaddbdcdcbddcbbcaccbdcbbabbddbbbaadbccaabcabbcabdcdcbabccbbdaabcaddabbbddbacababaacddccacdcbdcdddcdcaccadacdaadbdcadbdadccbcbaaacacbcadbbcddabacdccbdbcaacdadbcabadadbaaccdcbacdccccdbcacddabacbccccabbbdadbbcbaccddabdcbabcadadccbdbaacdbdbbdabccbdbdbbbddadbabddbdababddbadaaaadaacacdacbacbbdcabddbaaabbdacdbbdddacbaabcbadadbccabbcdaadddccbacabbaaadacddacaacdcbdcdbbbaaacbbcdcaccbcddccdadbcacdccbaadacacbcdadaabbdabdcaabdaaadbaaababcbbbccabacbbabdabdcbabbadbdbacdcddaddbbdcacbacbcadbabaacddbbbadbcbadbbbadccccddbacdcacbcbcbadbbcacabcadccdcddacbabacaacdbcbacbcdcadbccacccaddcdddacabadbcddbdbbcddbaacdcdddbacbcabddbcaddaacadbdcdddbcaccaacbabbcbadadcababdbabbbabbdcdccadbaccbcdbdbbdddadadcdddccdcdabcdbdcdbacbbcdddbcddabaddabaacbbdbdbbbaaacaabccbcadacbdaabcadcadabdbaacabbcbdadcccadbbabcccdcbabddcdbbcaccdccacdbdcbadaddbcaabadcbdbdcccbcccbcbaababcabdbbaadccbddbcabdacddcabadddcdccaadabcdaddcbababcdbcadadadaaababbddbbcabccacbaccccbbcbddbcbddccbdbbcaabcbaddaadbccbdabaaacbcaaabaabbabbddaccccdcdcddbbdaadbcdcbdacbacbdacbcaabcbbdcbcddabaadacdabcbbdcdddacacadadcaacabcdccdcacacdbaaadabcccdbcaacccadcbcdbbaaabcdbcbadcdddacbcdabdaaddcaabbaabcacbbcadbabbcddccbaabaacbaaadbbcdcdbdbdbcbdbbdcabaacbcaddcaadcccccabbbddbaddbacbbdccdcdbbcaaadbcdcbdabaadabcaccdadbdbcbabaacbaadabacdaadaaabbdadbabdaadadabdbdccdddcdbbadabadabdcbdaadadbddbbcdbbbdbbbcdbdcccbaaccaacdcccacbbddadacbaaddcbdddbcadbdadddbbccdbdadcdcdbdddcabbaabacccbbabdccbcbccabacdbcaddcaacbbbbdcdabccddbbdaadaacabaaacdccddcdcacbdcdcaadcbbbdcdcdadcbcddbdccdcdbaacccbbbcdadddbabaaacbbddaddcacabcdccddadccbcdcddacddabdcbddabaaccadddcadbbddbcaadbabcbdbdcbaddcbddddcadcddccdbbdbccdabcdcdadbbaabdadacdcccdddddccdbaccbbdcdcdaddacccdccacdccdaabadbbbacabaadbadaabbbdaaccdbdbabaacbcbddadcadccddccadcccccaddccccbbcdabbdaacbabccbcbbabdabaabaacabaddadbacbddccdcdbbbcacacbdbcbdadcdcbcadacbddadcbaadabdcaaccabddcbdcaabdcddcdcdbbaddcacdbbadaadadbbabadbcdcddccabbbdadaaccdbbbccdddacbacccdabbdddbcaacbabdccaaacbbcdcdbbadbdbbbbcadbbccbdadaadcbcaabcacabdbacddcbdbdcacbcccaadcccaaaaacccaccddddcbdbaabcabddcccdbaddbdbadccbbaaaacdddbcacddcdabaadacacbbadccacadadcbcabdaccaabdacbdadaaccdcdcbadaabcdbacdccaadddbdbadcdbcdbcbacacbddbbdbdaaddcdadcaddddaabbdbdadbaadcbccdcddadadbadddcacbdaacbaabccdcbbdbcdbbccacbcbadcbacbcbdadaabaabdddccacaadbcdbbdcdadbadbbccbbabccaabddccbccdcbdcabddacaddcccbbbdcdbcaccbcaccdccbdbbadcbbbbcdbabbdbabacaadddcbcaaccbabcabcbadadabbaacdadaaddbcdbcbcbcadbddbcbcbdbbcbabccaadccdabaddcdbbcbbaababbddbcdbbadbbabddacbbbddcddbadcbbcabdaabcbbcacccdaddcbcacdaababccddcbdadbacbbcbcbcbadadbdbadccadbdcadcccbadcdccdbcaddbcbabadcbcbccdadbdbbcabcacabccdaadbabacdbcaaaabddabdcaccddaaabbcacdcbdaddaadacbbbdcdcaadababcaaabaccdcaadcbabcddacabbbcdbbdaabbccbdabacddbbbdbbabbaacdbcdaabbdbdcdabbadacaaddbdcccbcbcdbdbacacacbbcaaabcbcdbdaccbccacaddcdcaacccdcdddbdbaacbadaddbddbaabbaccdbcabddbcadbadcbaabadaccabccdcaaaaacbccbbacbacaaacccbaaaabbcbdddcccaddcbbcdabbbdaacadadbcdacdcbcdacabcbcbabdababdbadbcdccbbabaaacbdbdabcadbcbadadaacdaddccbadcbcbbdaaccacbccbcbaddddbadacbabbbadaddadcdbbcdbacdacadcbbdcccabcbaadabcadcabdcdaadccabcbbdbcbbdccacbabddadcbaaddcadbaddbabbddbdadbdbbadcddbabaccacccabacacddaacbacbdccabcbacbabcaacdccbdddcbaccbcddaaddadbacaaacacaacdbccdddcdcadadbcdaddcdacdadcccdcccbccbdddcbccbdcdadbcccdcbcbddacacdadbcaccaababbddcacddaddcdabdaaaadacdccbbbccddacadddcdbdbbadbbbbaadbbcccaccdddcbddbadacdbbaadbaddaddcbcbbcdccdbabcccaddacdaaabaddadbcdbcaccdaaabdaddcbbacbbbcbbdadbbdbdbbcbbdcdaccddbbcadddaadccbcdacdcddbcbcbdcacbcaccaabadbbdbccdabdbabcbddcdbcdaaadbabdabbbbddbcbbdcbcbabdcdcddabdabaadbcbcccacdbbcdcaddbdcdcdcbabcbbaddbabcdccbdacccbbbbaaadbcdcadcccbcacbddadcabcdbdbbcbbbbadbbbcdabcdacbcbdadcccaaabbdaaadcaaaadadaaadcadcddaaccbdcaabbdcddcacbbdabbdcdbabdabcdabbcddcbabdaaddabbdcaaabaabaddaadccccbbabcbddbdacdaddcbcccadbcbcaaaacbadbacdabddddaccbbbbcdacdbadccacdcccdccdababacddccdabddaaabcccdbcbbcbdcabdbcbadadbcdcdbcdcadcaacdbabbbaacddacdcaabadbdcadbcccbbcdaabcbdcbdddcbcbcbddadbddabcbaabacadcddccaabbbbcbdadcaaacaddccadddcdbbacbaddaaddbcadcabdcaddaccbadaadcaccccaaaacdbbcbabacddcbddababaccdacccbadbccaadcaccbadbccbddbbbdadcbadabcbabcaddabacaccbcbbccdabdbabdacacbdccabbabccccbcaacdaabdbabbbaaabcdcacaaadbabacdbdacdcabacbdcabbbaabacdcadaddcdbccdbabbcbdbacbcaabadaacdccdcaacdaddcbcbcbcbaccddbdaacbcddbccdcddddabdcdccdcdcbddadcaaccccadacdaaacdbbcdcaacbaadaaccbabcadbbcdcdaaabddacadcbcbcdaacbbdbdddccadbaacdcaccadcbdbdcdbbabaaabaacdacdbddbdccbabdacacdabaddcadcccdbacdcdddbbabcbaabcddaaadcadbbacaddadcaabccdccaccbccabcbccaabbcabbaccdccbbccdadbbdbadccbccbdcbdbbdbcdbbdbdaabbdbadbacdacaaddbcbcccdcbcdadbbabdabddbddbdbbcaddbabccbabbcbaacdadcbbaadadabbbcabbbbdddabcabcaadccbcdcbccaddcbbdcacbdbbdacacdccdbbbaabbbbdcdddcdabaadaccccaccbbdaabdbbacbabaaaddcccabadabcbcaabbcadaaaadbbdbbbddbacaacaabcaadacdddddccbdbcbccacbccdbacdcadcccdcdadbbbbdddaaacbdcbccaaddbbdbbbaddbdbccadcdbcdddbcbabdccdcdccaabbdbddbbbaadacdbcddcddccbaadbcddbddabcbdbababbdadcabdcabdddbcadcdadaacbcdccdabbcbbacddddbbababbbdaabacabadacbbabdabccddcbddabccbbdbdbbbddbbdcdccbaabcddabbacbddcabdcdbabdbdbddaccbaabcdaadcaacdaadcdddbcdcbbbbacaaacdbddacadcaddbbbdddccaabbdadaadadcbbbbbccdbcbaaacddccaddcaacbcacbdbacbbbcbaaaaabddbbbbbbdaabacdabdbdbdcadcbaadabdddbdcaccabbabcddcabacbabaabaacbdcbbbdccbbadcaccacaacbabbbadcdaabcbaacdaacadcabdcabcdbacacacabbacdddbadaccdcaacbdcbabacaaddcaaabcbcdbcaadbddbcccccbadbaabcaaccdbdadadaaabaaaaddbbbbbdbdabbabaddbadbbdcddbacddaaadccaddbbaddaccbccabaccbdbdacaddabbbadcccbddbdcdcddbbbcaaaacacdacabbdadbcbbccdcbcddbabbbabdbcccccbcbabaaccddbcdbcabcdaadaacacddbcddadccccbcbbadabcccdabbabcdbdcaacadcdcccdddcdcdacaddcddccccdadaddadbbadabbdcbcbdaddcdcdccbaacbbabbcaccaddabaccbbddbccdcbacbcadcacbbddacccaaccdadbdccdadcacbcbcaccaaadacdcaacbbcddddcddaddcacabdcddadacdbadcccadadcabbdaabaccacbbaabbccccbcddadbbdaababbcacaccdbaccdadaabdbdaaaccadbcabbabdaaaaaaacbbabcdbdaabcaddcabaadbdbbadbcbdacdbcdabdddcadcdcbbadbdcddcbddabdddbdddbadacbdcababdcbabcacabdbcbdbaaaaccaadddadccacdadcabdaababbacbddaaaadadacadacaadbddbadaaccbdccbcbcdabbaaadaabbcbacdbccdcbdababccdbbacadcdaccaadcbdcdaccbadcbadaacaddbccbcadaccbacbbdadaabdaacccaaacbaacbacbdbdbbcacbbaaabaabbbabaaadccbaddadbcadcbdaabcbaddbbddaaadbbababbbcacddbbdaadcbbcaddddcccbabacdbddbadbbbbdbaadabcbcabbbbaaacdbabaddccdcdbadccbadabbbbabdbcaaadccbacbbbbdadcccadccbdabaabbdbddddadccdabddcdaaaabccbccaababddaadcbdbaabbadbcbcbcbbddbbaabaabddcddbbaacdddaacdddddbdddbdddaadcbbbadccabaaddcacbacdaaabbbdcdcabccbddbabdccaadbbdddddddadddbaddadaadacddadcaabbbcadddcabacdccdaaabdbbcccccaaaabcdccdcdcabddaaaabddcadbbbdababdbdccbbdaacacdbbacdddbdadcdcddacdcacabddadddbccbcaadabbadbddbcdbacbddcaddbdddbcaabdbabddbccbaaccadcccadcddbdbbcacdbddacacccaacadccacbcacbadbabacabdcccddbadadaadcaabbdaabadbbabdadcccaabccaddaccbcbabccacbabbbacacddcbaadaaaacddbcdbdabbcabdcdbdbbbcbddaaaabdcbbadccccdcabdabddaacaddbdcccddaddcdccccbbcadbbabaccbcbbbdbdcddbcbaaabacabbcbaacacdcddbbccccbadaaaaacbbcbadddadcdabadadcacbbadcdcddbddbaabcdcccacdbaadbddcdcccbcaacbaaadcabbcdcbccbccccdbccdcccbbccdaaacbcccacaadcdcdbcadbbccdadaccadccdddddcdbcacbccadabdaddcdcaadbcdbdacbcccbbcddbbbbccdddddbcdbbacabbccbbaabccadbccdaadbcbdbdadcddcbcdbabbdabaddccbdddbaabdcdccbccadcbacadccbbaccacdbbbdaadcbdbcddbaccbdccadcbbbadcdcabddaacbadbdcdaabbccbcabbbacacddaacadadbdbdbaadadbadbacdcababaccccadadaadbcbdbbabbbcbcdadcadbccdabdaaaccbbadbcbadbabadcddccabcdccbacdaabaaaadccdcdbabccccbcdadaabdadddcccabdcbbccbdaacacdcabbbbcabdbbbccddbdddcdddddcddcabddcbacdbcbbcadcabbbcabcbdbdbbaddccabbbacbbbcccbdcddaadaccdabadababbbcaaddadbbbcaadcdccbdcbacdbdccdacabdbddcbbabbddadcbabbbcbbbbcdcdcaddbdbcaccdddadabbaabdbadbcbaadddabaaaacabbcabbcadbbdbcbaacdbbddcbbdaadddaddadbdcaaccadaaddcbdadcbdcacbdabdcbabdccbddbbbcadadacbcbaaaadbdabacaabcccddbcaaabbbacbdbdbadaaabbbaacccbbcdcbdbcaaddcbdabacabbddacbbbacaacbccccbdbadbbacdcdacadadcadaabbacaacaddaacbdacdcbcacbabbaabacacaaababdbcbababcbdbdbbcbdbdaddcadcdbaddcdcbbcbbbbbcabdacadccbaacdcdaacbbcbbdcccdaacacbacabbabdddbbcdabcacddadbadbcccaaddacdbdabdcbdddccbaccbbadbccdbbbbdccbddadbbbcaabccbdbccbbabbbcdaacabdabadcacdabcddcdbcbddbadaacdccdaccccdcccacaccbccdbacaabcbacdddcddcbdbadadcbcacbdcdbcddbdbaabbbbabcbabddbddcbbdaccccabacdbaacabbaaaddcaacabaabaadacaaabccabbbdcccbbcaadacddadabddaaaadcbbcdabdcccadadcbadccdacbccaabcbbbcdaaccadabadacabadacabacdbabccbccadbcbcadbacdccbadcdcdaddddaabacbcacabcbcbbdaabacdbbdbcadbaabbdbdcacacabbabbaaabbdcaacbcacbcabdddabdaadbacaabacbacabcdcddcddadcdadbbddccacacadcaabaccbbadbabcacbabcdcdcbbddcaccdbdcdbaaccdacccbccddabdcdbaacbcbcdaccdbdbacdbbadcbddcbddababcabacbadbdcadcbabcbabddaaadbddcbadddcabcbcadbccdabbbbcdbccdbbbaacbbddcdcabbddabcacbaababddbbccdcbcccdaddaabdcbbaadacdcadbcdacdacaddbddaddaabdbbcbbbbbcdaabcdabbdccaabddccaabbcdbdbbcabbbccacddbaccabacbbaadadbacbdbbdcdaadbcbcdadcbacbdaddcccdcccabdbcbccdcaccbababbcabacadcbbdabddcadcdccadbcaadacbbbccaddacaabacccdcccdadabcddabbdabdabbadddaaddcaaadabbccadbbcccdbaddddadadcbdbabbbcadccadbabddcaabbcadcadbddccaddbdcddaccabaddbbdddcbbabadccbbcabccbabdcdcbbdacdcdcaddccabddbabbbccadbbabcadadbdcccacddaabdcdccbbabdaccaabacdadcbcbabdabdddbdaacacbacaadabaadcdacdaddbcdbacbabacddbccddbddddddacbaccbadbcacabcadbdccbcbbacdaaddbdacdbcbacaacbdacdadbcddadaaaaabcabbdacacabddcdacdccaccbcbacdcdcbcbadcaacadcacddcccdbdcdabcdbadbadaddacbacadbddbcadbdbccdaacdbbadccaccbbaabcddcddbabdbccadcbddcddaddbdcabbddbaaadabbdbbcabbccbadcaaaadbdbdcddbdaaadadacadadbdcdaabcbadcdbaabdcbdcbbaabadccccdaaacddbbbdaddacdccdbbbcadcadbacabbdaacdbcdddaacabdcaaaadddddaabdcabddacbddaccbacbbbacbbcaaaadcbddaccabababbabcacabbcdbdbaccdbcccadcabbaabcdacbcdcddcdbdcbdacccdacdcdbacdabbdbbbadbcacdcdbddcddcccababbcddcbbcddbcdbacacbadabcbdadadaddabddcbbbccccdcbbdcdcddcdddadbdbababddaacadacabbbbcbdbbddadbcdadadabbaadcdccbaccccbbdcbcdaaaccadddcaaadacabbabaabcccdcbcbccbaadadcdbbdbdadbabbaaaddbacababaddbcbaadabbbbbbccbadddabdbadbcbbaadcdbccadaddbdaacadddadcbabdbdabadaabbbbdabdacccbabcaccabbbbbbccdddadadbdcadbabdcdddccddbabcbbcbbbcddaabbbaccddbabcbdaaadabddbbccbddaaccbcadaaaadaadbddaabbabcccdbabbccadaddabdadaddcdcbbacdbddbbabacbbcaaabdaadcbacdacaccddddaccccbdaacdadcddcdbddaadacadbdbccdbaaabbccaacdacadbccbadcacdbadcddbbbccddcbacbccbbbdaccbabcbaacbccacdccdcddddaabcbcbaccbaabadccadaabaccbdbcbcbcbcbcddaadbcdbbbdadccababdabaaddcdaabddbcddbaddcbccacadddaacbbddabbbbbaccdaabdbabaacdbcdbcbbbcadccdaadaddccacbdaddcbddcdabacdaaabbbacacbdcdcdddcacacbbdbcdbdbddabdbaaadbddcdcacbbabdabacdadcaaaabcabbdddddbbcccbdababbcaabccbdcbdbdbdbbbbadcdcaaacbcacbcbdddccddcbcbbbcbdddccbdbcddacbbdddadacbcdbcadbaadbddcacdcabdcbbcbbdaaabadacbcdcbbdbbccccbabacabcbbcdacaddabbcabbaaaadccbdbddbbabdcdcddaaabcdbdcadbcdcaacbacddaabbdbddabbdbdcbdcdadbccadabaaaccbcdcbbcbbaadbcabaacdcddaabdbbcacbcbbdabddbdaccacddacbddadccbcadbacbccdbdaadaddabcbbccbddacbbbccddccdabbbddbcbbbbcddadbbaaacdbccbdbdbbabacdbdddbcaddcdddbbadbdcbdcabcaaaadbbadadbccacddaacaaadadbdadcadddcaaadabbcdbabbcaaabcbbcdcdacbaadbbbbdddbaaccdbccdccddbabdacaadcbccdccdbdaababacabdbdbcaccaaaadadbcabacdaacaabbcdddbccdcccdbdaddacbabadcdbacdaabddbadbcadbadbcabbaaacaccdabccaaabdbbddacaabcbcbdadabcadbccdbdadabcacabaccddbddbdadcbbcbadadccdbbdccbcabbdbddbcbbcbcadbccbabdacccabdcbddddcaccbabcadadacdbdccbacbccdadccbcbbdcadcaccbbdcaaacabdadccabdaaabcbddaadddcacabcdcabbacbbbbccbbcaabddbacbabbdaabdabcbbcdbccbbbbabbbcabddaadcadddbdcddacccbbadcbabddbddddabacdaabcdbbbbddddbababbcabbaabbbbcbddccddaaadaaadccadcadadaadaddbbaddddcbabbdcbaaacccbcdaddabdcdcdbacbacdccaaabdcaccaabdddcaaabcccdcaaddcabbddcadabdbcdbbacabadbbbdaaccacbcbadbbdadacaaadcaacbadbdcaddcaaabdbcabcdbccaddadaabbcaadbdbccaadbcdabcdcaccdbadbdcdbdcaabbaaddcabadcbcddadbcccacdcbdbccacbdaddbbabddcdacabacddcdcbdbccbccbaaaaabbcdbcdcadaaaaaddcbdcccacdbcddadcddadbbbdcbdbcadcbadcddbadaaccddbdaacdbdaabccbdbbccbddcabdbdbdaacdcbbccbbdccddbccadddcdabbdaaddccbadddbacbdbdcadbadcdddbaddcadbbdaabbbbababddbaacbcbdabdbbaadcadaaaaddcccacabcbdadacaadadacaadcbadbaacbdbdbbcbcaabaabbbdbaabcbbabbcdacbacabdccadcddcdbdcbdbbdbbdbaaaaabdaaadacacabbcbcdcdddcccacdaaddcbcdcabbbcdbabcdcccccadbdcaddcabdcdddbcbbbbdbdbacacbdcbcdadcdbdddcdddddbbbcadbddbdbbbccddbdaccbaadbcbcaccacabbdcbbbbaaccbbbccacbabbdbacacababcddbbbcddbddaccdaaadbbcddcbaccbddcccbbdccbdbcabcacccdbcdadaaabbbdcbbadabddbbdbcacaacbbadacbddacabdbaadccbbbabbbabcacbddbbadcddcacacdcccaabcabbaaabbacacdaddcabaadabbbaaababbdbaaddbabadbadbcbcabbadcccbcdcaabcccacdccbbbacdbcbcbddaadbbddaccddbdddddaadacdccabcbdabcdbbcadbbccbdcadacadddcdddadaaaadbbdcabbabcdcdddacccbabcacbbbaaadbcaaabcbaaddaadddbdbccdccccccadacaacbadcbaaabbdbbacdcabdcadadcdbabaddadabbbadaccabbdcbbccdccbbacabadcdcbaabdabdacbcbdaaadcbabdaacccabcabdbaaaaaadabbddcbabbaaadcdaabacbbddaacbbdabdaaacaccddacaabaddcabbcbdcacddcadaaacccabccbbccaddcbdccbcacbcdadcaddacdaaaabdbbdbcdacbcddadbbcbdbdcdbcababacbcbdabcbadcacbabadadcadaabdcbbabacddcdadbdbdbadbdababdbacdcdadddccbabcbdabadcacbbdaadddabcbacbdbdadbaccaabdbbdddbbdacaadbdcdcabcbcbadaadbaabaabadacccdacdcaddbcaaddbbddaadbdacccbdbbadbcabbabdaacaaabcddaabacbbddaadbbdacacdcccabccacbdadbddbcccdcdbdddccadaaaacadcdbdbbbcbbdccbadbaddbbacaadcabbdabbcbbbcbbadcccddccabdbccaccbaacbccbcbddbbddabdcccbccdccccdcbbadcabbccccadaabadbcddddcddcaacddcdbdbbdbbcadbaadadcdbbadbddbbaccbdbbacadcaabcbccccaaacbbbcbcadcdcccdddbdbddcaadaddbdcdcadcbbbacbbbdbbbcbdbccdaabdaaababbacdacacddbbdbaaccaadbdabcabcadcbcdccbddbbbbddbdcdadbbcdabddbaddbbcdbccccdbbbddcadadbabbccbaacbaadcbaaddcbddaababcadacbadabdbaacaddbbdccababacaabacddccaddaaabaabbacbcacaddbccbcacdcbadbcdaabdddccbcaabccdcacbcbbacaadddcbaccaccddbaaaccdcbcabdaabadcdbadadbdbabcccdbbbaacbabcdcbddbbacbdaccbaddbcabbddbbddbaacbbdcbadaaddcccdbacaddbcacbdaddbbbbdbdabccbcdaabcaddcdbbdcabcaacacbbbcbbbbcaadbdcbbadacabdadbccccdbbbbdccdbacaabacdccabbcbaaccccbddbabccabcdcdcadddcbdacccbbdbcddddcbbbbdacaabdcaabaaacabababbbdddaabbdabdcdbadaaacacdbddaddbababbcdadccbaababbdaccaabaddbcbabaaaabdacdaccaabbacabbdbabdddacbabdbabbbacabdcccbdabbbcaadbbaccbbcdcbbabcdbbacadddcbabbbddacbdacdacccdaabacbdabacbadabaaaacaccbbacbadabdaddcbbdadcdcaaadcbabbddaadadbccabacabdbbcbcbcbdaacaddddaababdaccbbcbcdcaaccddadadaabbaaccdbbcbaccaadaddcbadcdadbacbbcbcabbadddaddbcbbbbcddadabddbabadaacaddcdadddbabbbbdaccdcadccdacdcaabccaaaaaacbcababcbcddabaabcbbbcabbaadbcdaacadbccdbcabbdbccbdbabcbaaaaaccadcdacdbbbdcbabcdbbcaacccccbdcccaabccccaaadddadaacbdbcacdadccdcaaadccbdadaaabbcadabdddbadadaacabdbcddbdbcabcabdbbbcabcbadddabbbdbbcbcabaaabdacddbbcdabddcdcbcccdabcdaabadabbdbabddccbacdcbbdcdcdaacdcdcaddccacacdcbabccbcdadaababdbbaaccdccdabdaadaddbcddcbacccccacdbdbdadbbbccbbdddcbbbdcddaababcaaccddabcdbacdaabbaddbcabcbcbbabcccccadbcaabcdddadbbbbbcdddacdcababcccdcdacadaaadcdbdabcbcdcbcbddadddbddbadabaadadbdbcadcbddbdabadbbabbbbbacacacadadcbbdcabcdddabbaaadcacabadabdadcacacbdccabddccbbcadccbbaacdccabccacbdbcbcadcacbacccacaddcbdccdabdccadbacacdaccbdbdddbbcdcdbcdacacdabbbaddaddbdbddbddccabacaabcdbdadadabadaaacabcbccdbddcaacaddaddbdacadcbdcbbccadbbbbbdabbbaabbbcadbdccdadbdacccacacbbbddaadaadcbaacacdbdabbbadcdccdaacbdcdcbbaaccadaadcbabbcccacbacacaccdcacbdabaccabcbadacaabadccaadaccbbaadbcbcadbbbbbadabdbabdcabbacacaaabdbbcacdaddbccdccdbbddadadaababbdacaabadbdbaddccbdbcabdddcacbcbdaddaacddadcbadbadcbbabbcadcdacbbddbcabcbbdababcacdcbadccababacdcacbcadaaaadbdadbdabcbcccaddaaabdbbaccbdcadbdbaddbadccdabccbddbccdcacbbcaadadbcabbcdbadaadccbcabababbdcddddcddaaaaddadcddbadbdcadaddaccdacbbbdbbcbbdbaccddccdddadcabaddbacbddaacdbdcdabcacbabdbcccdabdcadadabcbdccdddbcbacdcbacbcdddcddbcabcabddcacdabbdccacaaaaaaddcbdabcabdbbddcacaccdbabcddacabaacbbdbdcbbbbbcbbccaaccacbccabacabcbddcbbbaddcbbccbcccbabbddbacdaadbddbcbcccbbbccdddbddbabbddbcdaadabcdbdbbbccdadddcbbdcddbdcdcaccacaabdabaacaabaaabbbccccddbcbbacddddbadaabaabdbaacaadbbcbadccbdbdbdcdbbadbaabbabbdbddabbbbaadabcabdbabdaddacdbcabdbcdaddcbbcaddacbbdddbaccacbcbbdcdcadddabbacccddddacbdacdcaaddaabaaddacccbacdbcbcddbcbabccccbcadcaaadcccadbaccddacdadaddbdaabaddcbbdcccccababcdcacdbbaccbcdcccadaabadcdcdcacdabbcddbdcabacbbccbdadcbdcccaabcbddddddabddbcadbaacbadabaccadbabdbcdbdbcdccacbbacbaacbccbcbbadddbabaaaabcbaacadddabcccacdaadddcbacacaacaadcaabbbadbcdccbddcbaccacddcaaaacddaddabacbaaccbccbaadabbbdbcadddbcbccdbbbccbddbbdaabaabcbaabdabbcabdaacaadbbcbacbaaadcacddddabcabdddabddcbdadddcbacadabacddbcdcadbcbaacadbacbcdddbdccbbcaaacdacaacbdbcccdbabcbabcdcacbccccccbdccdddacadddabcbabacdbbabdacbaabdcaadcdaccadacdbabbbdcaaaddabaacbcaccbcdbddcbcbcabccdaaddcdacbddcaadbddccacbcacdaaaddcdcabccdaadbabacddbdcaddbcacbdbbcbccccaacdadbcdadcdcdacabdcadddbdbbbcbcaabbbaabddcccbcdbaccddacbaddadccbdabdbbcadabbbbcddbcdbaadbccdcadcabcdacbcacccdccaadcaacdabdcbcdccbcccadabdbddbbaacdbbbbaabbcabcaaabcddbbdadbbaadabbccadcababdaddddcbadbdbbaddbdaadccbaaacadacccdcdbdadabcbdacbbdcddccdbdddaddcdacdaabbdadddcdcddcacddaddddbbddaccbbbdccdcabcbbcbcddabcaaaabccdadbabbddbcdbdaaccbaabadccccdaddaddcbcbccdcadbadaaddddbbadcdcbaccddabdadaddbbbdbddcabdacbabcabdcbdcdacabbabadbdadcbaadabbbbadddbacddaabdcccdcdcbbbdbddbccddadcddcabccdaaddabdaccdbabccbdadcacddccdddcbdcbbaccabdddcdabcabccaddaacddccbbdbbdbbcccaccbcaacbacadccaddcdaddbabcbccdbacacdbbabbbccdbcabadcddcccdbcbbbbdbbcbbdaaccdaaabbaddbabdbdddabcdcddbccddabdbdccbabdadabbcabbabaabdcdcccacbccaaddbacdbbadaccbccaddaccacbaaabcdbbbaddbacdcbaaacbcbcdcdcaadbaaccbccbccbaadabacadbbdaaddcdbcbadccbcbdcbbcdbbbbddbdcbbaccadacbaacacbdccacabdcdbbddcdbddcadcdadbdccdcdbbabbdadaacaadbacabbadacbabaabaacdabdcbaddddddcabbaabbbaacdcaacbdcdbaadbbadcbcdccbccadcddccdcdbbbcdbbcadcaacdddabcacbdbbccdbdacbbbdcaccabdacadadababddacdbdbcadcbdcbddadabcbcbaacbacaacaaccbbdcbbaacccbadbcacacabdcdcbbbcaadbcabdbdacbcdcbbbcabaadcbbcdcbcacaacacdcbacbabccbdbbbaadbacdabcdbcccddddccbdbdcdacdacdddbadbcbdccabbdacabddabdaaadadbdcdbbacbbddccbbbccbccaabbabaababbbadbddcacdbaaadabbbaabcdacabcaddcbccdadbdabcbabcdabbbcaadcbcdabdadbcddbbcbdcbddbcdbcdacabcccacdccaadcbccdbcdbbbaaaccabcadbbcccddabbcbbcabdbbabbbcbaddadcbaacddccddcdabacdcddbadbbcdadaaccdabdcbabbaaaaaabcbaadacccddabacdccacbbabadacaaaacabbbadcabcbdbcadcacdacadbcbadaaacaacdbacacbbcbbdbacbcccabcbddbccadaadcadcdbdabacbaccaacaabacbbadbbdbdacadcaccdbbdbacbdaccadaaaadcdcdcdacddaaccaaccdbacccdbabccccaacddccdbabbcddcbdbacddbcbdcbbcccdddcccbdddccccdcaaabdbbbbdcadbacacadcdabdaddccbcddcaaddbdccbdadbadcdbbbbdcabaccbbdcdabccdcbacabcbddbcbabbadbacdbddbdaacdbaadcaaaacacdabdcaaccabaacabbcbaaabbcbbdbbcbdcadacbcabbbababddbaaacdadbcabaddcaabddccdaccacabdbaaddabcbaababbbaddbbbdcddacbbcabccbbadbabddadabccddcddadabcdcdcdcaadbcbdddcdcabdabdbabbccbcbdcbbbaacbcacaaaaddbbcdabbacdbbbdaddaaccbabadbddaabdccdabdcbcbbbcdbbdcbdbacabbcdabadaababddbaabcddbdcadaacdcdaccbdcccbbdcddcbacbdacdaccbadbbddbaccddaaadbbdbbabdbddbdaadbdaaabcddabadcababcadccdbcabcaacabbbacdacbbccddabcccbcbadbcbcdbadaabdcddaccaddbdbcbcabccdabcccdadbbbcdddcaacdacdcbadbdcccbbcdbbbaddcabcbddbccdbacbacbbbbcdbdccaccccacccbbdbbbaaaacdcaadccacaacbcdcdcbcbdabaccdbbbbbdcbbbddcaadcdcbbcccccbdcbacddcddbccadabbabbddaacadcabdbdacdbbdcaaacacdacbabccadbcdcdddcddacbbaddadbbbdbcddcabacacbcbbdbbaabbcbbddadbababcdccdbcacdacdddbdcabbbccdcbdddacacbbbdbbcaadbaddbddbcccddcdacdaddadadddcadccaaabdacbbbbdccccbddadcabbdabddbcbbcaacaabaaaabcabacddaadcdbdabbdbbacbcddcadccaabbdaccdddcaaabdaaacdadbbddbacadcbcaabbdcabdabcddaddbaccbcbdadadabcdcbbdaaaaaabbdadddaadcbccbccdcbdabcacababccccdbcbdbccabbbbcccdbccaaccdddaaddccdbcbbddbddccdcdaadaadcbcbbcbdddbdbbccadcdabcbadbdadbbccbdabdabaacbaccbbbdbddcdaaabcdadaadddbbcadddbbcbdaccbddccdacdcbdabdabaabdbbacacaddabaaccbbbacacabcdbdbdadbcbbdbbbccbbaabcdbdbaadacababdcddcbbcdbbdbadcdabaadacdbcaacbcbcbbcbdaddacabbddaabbddabccdbccdcacabdcadbaddbcdbdacdccadcadcaddcdadabcabcdacbbadcacccadaacabbcbcdccababddddbcabaccdcdcbbbbaaadadcaaacbaaabcddabdbcdbddcbcccdababccbbccbcdaccdacbbaaaabdabacbcdbaacdbdcacbdbbcaabdcbdaadaaaddddadddcdcdacbbaadbdddacbaaaacdacacccddbaadcccabbbdccacccdbbdcabdddbabcacbcbbcddadbadbabacacccdbdaadacbddbadacdddcccdbbbdcbabccdacbbbaadddaadcaadbbbacddcdcbddcbdcababbbddccacbcabcbdacadddbdcaaabbaaddddcddabccaabcdddbdccbdbdbbbbdbacdcadccbcacbadbdbacdddcbaabbbaadbdaadbdadbacccccbdaaccbbdaddacdccbccbdccdaabdccbdcddbdaddabdcbacdbbacaccdabdadcccacaddcacaaccdccdcacbcbaacabdcaccdcbabbddadbdbbcaadddcacbdbcbcbbbbcacbccbbdccddbdbabccdabddacccdaadaabdcbdcadbdcdbbbacbdbddcacbcbbcabaddaaadbcbaadbbaababdcddabdbbbabaacbbcbabcdbadbaadaddabbdddaaabcabdcdaabacaabcdcbdddbddccbccddaccdcbdbcaddddaaaacdabdddadaabcadbadacdabbdcbdbcdbdcccabaabcbdcdaadaacbbdcaaddcbbaabdbcccbabddaccddacdbbadcbbdaaadbaababbdccccddacdcaadaaaadbacdccaaadadbdbdaccccddbdccddbabadccbcabdbbcdaaacdcdcacbbacdcbbbdbbbcdbdbdbcccacaddbbdcddbbdcbcadcabcadabdcddcdbdaaabacadcbacccdbaaddaddbccbbbcbcdbacccbddbaaacdcabdadbbaabbbccdccdadadcddaadcdbbdaaddbbdcaadbdabdbdcdddabdcbabddcddcddacdcdcbadbbddabcddabddbddddcabbabacabddcaccccdccdbcdacbdccdcdaadccdcbdcbadacdcdbcbacabddbdacbdcbacbacbcbdcddccccbcbcccbdddcadcadbacdcdbaddcbdbdabbdacaabcaddcbbacdbdcabdcddcbdaccdabbaccdcabccdacaccdaabdcaddbadbbcadbbbbaabbbdbdaacbbbabdddcbbadacaadabbddbdbdbdcadcdbcdabcacabcbbccdcccdaabacaddadccaaddaccaaabbdbdcddccabdbabbaabaacdbbadaddcdddbbbadbdacbbdbadcbaddcbcdccaadccacabdbddcaadbacadbddacaddddadcdddabddaabacdddabccdddccdaccbdcadbdcbabaaccabccabaacbbdccadcaddcadaadbaaaababbaccbbbacbbbcadcaaaabbaddbbabccababddbadbdcdaabdaaddbdbbbccadacddaacaaadbaddcbbcdaaddbccbdadaabadcacbacadbbacdbcdbcdbaaccbababddccabdbcddacbabacdbacbbcbaabbbabadbcaaabcaabbacadacbbdbdaaacccaddbacbdaadaacdcbadbdbccbcdadbbdbacbacdaddcdaadcbddbcabdbacdcccacdacddaaadbbbddbbbacbbdbddcabacabdbcaabbdbdcccdbccdddabbbaaaaaadabbaacadbdbdcbddcabbdacaaababcbdbabcccacbbbbdabdcdcaaadddabdccaccbabbbadbabdcaabaabababcadccdccabbbadacbcdbbdcdacadaabbadaaacbbdaabdabcaacadbcdbddbcadcbabacaabcbbbdcabdadbbabcdabbabdbbbdaadaaddbdadcacddcdadbcbbcdaabcbbacbcdbccdcdcbcadcbdbdccdbabcaacbddadabbabdcccbacbbbbbcbbdaccddddbbabbcbcbddadabbddcacbcbdadddbbadadbabdaccddbcdbabdbabbdbdcdacadcbdccbacdcaccbdbadcdbccddccbaccbbaacbdbacddcddcbbcacababdababcdbcadacbcdbcccbbddbbbdddccbacaddbacaacbcddbadcdabbddddadcadcadaabccbaabccbaaddcdbcbddbdcdbcabbacdabcbadbcdacdabaddabbdaacabbcaaaaaccacbbccbaaaccdddabcccadacadcbccbddbacabdcdcaccccabddbdaccadbcacadcaadcabdcbcaaadddccacacacabddbcbacbcccabcdddadbccababbdbadaabadcccaccccaabcdbaabcacddcddcdabbbaacdababadcbacdbbdcbdabaacabbdbcbaabcdbacdcdddcaccacbbacbadaddaabaabdadddaacacddacccdcadbbcdcdaacdadaadacbdabbaadccdbbbaabbdaaddadcbacacddbacacccadddcdbbadbddadbabacbcccdadcddaadbdbbdccaccdbabdaabcccadcbcbdcdaacddccaabdcbdbdbacaadcddcabdcacbabbcadcacbbaadbccabdcbadcdbbabcbacabdbcdadacabaaccccbdababcccbcbdabccbccdcaadbacddbadacbcbcbacdcbbdbaacabdabdaccaccddcabbbcdbbabbdbddcbaacacccacdadbbcdccdcbbbaaaabdbabdccdbbdbbbabbcaacdacbdcdcddcadcddbbbdadaccacbddbadbddbdbaabdadcdcaabcbbdbcdaccdddadddacabadaabbdbccaaaabaaccdddaaadadaaccdaddbdbaacbdcdcdbdcdbccccaddabdadaadcbabbdbccccabbacbbddcabbbcacdcadbbcaabcdadcccadbcaaadbbabdcddccccdacbcbcdbdddcdbcbbbcdcbdcbbcdcaabdcdacdcddcaddabddabadcbacaaabaaaacccdadbbbdbaacdabcbaccabbdaddaccbccbdabbdbabbaaccbcdcabbadbbbadcbdacbbcdcccbbbaadbacdbbccadcaadbdddcdaaadbdacdcccdcacabcccbcabadabbbbddbdaadbdbccacdbdabadbcaddbcadbbaacacaaaadcbdbbbbddacbcddbddddcbddbdabcbaabdbdbbcaaacdbabdcddbdddccdbcddbdcdcdbbcadcbaccacacbdabadbbdbadaacdddababcacdbccdacaabbabdbcbcadaaacdbddbddbbdccddcacabaccdcccbcacddbdbadbbbbdacacdccdcaccabcdaccacaccabbdadaadcbbdbbdcadadbddadadacbbdbaccaabdaadbddccbbdbcdcaaabdbcababbabbdadbcacdbcadaaaccbbcbbabdbdabcdbddbbcadcccabcadaddbbcbacbcdaaaacbdcdbdcaacbcddacccdccbcdbdcbcacbdccdbcabbdcbdaaaaccccdbbdbbcbcbbcaadcabbaacacccacaadbbaadcabcacbbadbcacabddcdccbadcabdbaccbbcadcbbcbcbadcabbadbcaddbdcdbaaaaaababbddbadcdbddcdaadaddcbcdcaaaccdbbadadcacacbbaadaacdaddcabdddaccabddabbacbbdadcbcbbccdccaaddaaaaabdbdbbdbcccaadaaabaabbddccadabccbadbbcbadbacdaacaabdcbcbbdbbdbcdacdbadccdccabaddabdbbbbddcbaabdcaaacdaccdbddbaabbdcacddcdcdbcababcadccdabccdbbcbbdcddaaabcaacacdcaacbdbbcdbbdbdaddddbccdcccbccddabbbadbcbbcdccabcdccabddadccbddcbadbbbbdaaccdbbcbdacbaacccadaabbbacbdabbaabcabbddcbcbddaddcccbcddbbaadbddabdcaabdcdacbbabbbdcbdbcddcccbbbdcdaabdaacababbaacadccbbbcbdaddabdccaabdbdbdddcaadaadddaadabcccabbadbabacdbcdbcbbdcacabbacbccbdccbdbbcdbaddcabbcbabddaadbbdbcbdaddddbabcbbaaabbddccbdcbdadcbbaccacccdabdabdddabbaddddababddacccacbbcbdbcaaabcbbbaacbdbcbcdcbaaaddbbbadbcababaadbcbdbccddddbcddbcdacadaccdbacdacdcabccbdbbdbddadacaaccccdddacccacddcdbbbcbaddcdddabacaccaaabbbcbcabccbaaddbbdcdcddcdadaddaccddccadbdbacabddbcbcdbcaadddbbdabacbbdbbdaccabbbaddbcccdcbcadcddadbcabcaadcbdcacdccdbdaacdddccbdccdacddddadcccbbbcabbccaddcdacaacbcdbbbcacaaddddabababbacdccadbcadbaaacdcdcacbcdbadaabdcadacdbacdcacaddddcccabccbadbadbadbcaadbabbbbacbbcaaadcaddbcaadbcbabdccccabbcabadabaaaccbdaadbccdddcadcbadaddbaaaadadcaacdaccccbdcacbdaddabdbbcbdbacbdcbccbddaaccaddcaabcaabbcbcdadadaacaaadbbbdbbdbabdcacddabcdbcacadccadbcccdcbbcdbbcadaddaadbcdbdcbabcbbbddaabcaacdbcaaabdaaadccaaabdcaacaddbacadcbaddbcdcbbacabcadbcdabbbadaccbbdcddacabdabcbcaacbcadabacbdcbbaaacccababcdabccdbabdcaaccdcbabdaccdbdcbabdacccdabccccdadcacacbbcaaccabdcdcadbdcdaccbdbddcacbadcabababddabdbddcbbdaadbbcccacddadaadaddbcbccaccdcaacdcadcdcdbdaaddadadddcddacccababccaddccbaadbadbdaddcdbdcacbaabcbaaccabaaabacbdadddbbbcaacdcaadbadaddaacdacabadbacccccadabacaadbaccbdddabdcdddcddbadbbdbadddbdcdadcdcacadbbdbabadadacbbcdbccbddacdadabcccbddbadaabbdcaddbdbbdabadbadbddbccdabddcccaadddadcbccacabbdddddaaddcbccadacaadcabdddcbbadbacadaabdcbbaddaabdcdccdbbabaabdabbcdccccdadccabacbcacacbdbbbccddccadaabdbdbacdaaadbabacbdaadcdbbbdaddbdbbddadccababcaaabcccddddacddaacddaacdbdaabdaccccdbddbadaabacbdbdcabddbbbadbacdacdccabccdacadaaaddddddbcababbbdccacadcdacdaabaddcdbcbabbccaaccacabacdabaabbddbdbaddddadabbbccdccdddcbdbababbbacddbbdbbdadaaacbacccacdbbbcbddadddcbadcccacadadbcdcccbabcdcbacabddbbadbdabcbddcbdbaaadbddacbdadabdbdbbcbbdadbddddcdadcccabcabbbacccdcddcddbbcbadbcddcbbdcdacddbabddaacabdcdcbabcaaabdbdadadaabcccadbaacdbccbbabcbcbdcbdbddccdbabcabcdcdcdbaadabbadddacadacbbdcbcabcbadbadccabadaddcccabaabaccabdddadacbcabcabbdaccbacadbaddcdadacabdacbaaddacccbcbcbabbaabbbcbbddcbbbcdadcdddcbdbaacaaccdcaddbbdabbadcacadaadabbacbbcbabcbaaabcacbbaababdddacbdabadbbcaadbddcbbcdaabadadaacaccddbadbdbdcacdbdbbddbaabcbcdcdcdaccbdccbddbcbabcbadaadacaccddbccdadacdbcbadacccacbabdccbcaaaabaaacbdddabaadabbabcccadbdbaccccdcaaacacaaaccbabbabcddbcacdccacddbdbbabaadbbbdccbcbaddbacddadaadbcaaadcbbcbadbadcddcccbdabdbcaaddbcddadacabbaacbbccbcdaabddacbcadcbddbdbaabaacbacabacdcddbccbdabcdddbaaddbccbbdadcdbaaacbccbdbcbdadabddbacdbccadcaadbcdadddabddcadbbabbbbddcdbcdabdcaacdbddabbacddcbddcbcdcbcaacabaaaaaaadcaccacdcaaabbdbcdcbbcaaddacdbbdabcbdacdccbdbddddcbaadbcbcaabaaabcacdabaaababdababbcdcaaaaacdcbacabdccdbbbdcbacbbcddbbbabacdcaabaaabaddaaccacdcadcbacbdbdaadcbbbccaccddbbadcaacacdbbcbabdcbcccdcddcbaabcccbcbbdddcdbbdadddcdbaaddbddcccbcaacbbabddbdbabdababbabddccbcaacccbdadbbbccacbcaacdaddcdcaabacbbbcbbdbdcaacbcadbdaaacacabadacbdcdcdaadcabcbdabbbacdbabccaddcbccacacccbcdccbcdaddabdddbcdaababdcbcacabcbcccdadbacddccabaaccaccddadccbacbcadcdabbcbdadacabdcabdabaabbaaccdbccccbdbcbaabbdabdbabadaadbadbaccdbccdbcbccadaabdacbdbccbadcdadbcbddbdcbcacbcbbbdaddbcccbbbacbbdddaadcaadddbadcabbccacbbccbcacddccabbacbbbaaabbccbaaddcbadbbbbddddabbccaddbdccacbbacabbdbbcbccabacdaacdbbadcdcacbdcdcaccddbaacbaabcacaaccbaacadacabddcbacccbbccbadaaabacccabbbcdbacbdbbbdddcdcaadaaaddcbcdbddbacdddbaaddaacadbbacdacacbabccbdbacacabacdcbacabddddcadabadccdabdacbddcdbdabccbadaadbbcdcdcbbdcbababcbbbccacdcbbdddcbdbddcdcccbdcbadccccacbddddabddbabdcbacdaadbbbdaccabbbabbdddadccbcabacbabdcbcaccbdbddcbccabcdbbbdaadbbcdcbcdbcdabaacdcdcaadaaaddbcacaacdcdacaccdddabbdddcdcbcadcbcbdabadbcbbacadaadcabbdaccddcadabcadaccdcadbaabcdcbabbbaddaacbddbcddcaccbbdbcadbbccbbbcaaccccababadadabcbadbaddcaaadddaadacaaaccabdddcddaccdccaddbdbcdbbcbcabbdabacdcdabbdbdddcadbababbbccbdcaabbbbdadbaabaccacbcbbdadadcacabacdbadbdddcbcccbabcacbddababcddbbccdbdbbccdcdcadccbcacaabbaddadbcbbbbcadabcdaccdbbddcdccaaddbadbdddccdaadddbbacdcbcaacdabaadcbddababbadcadacbbccabacabdbbcccdababacddacddcbadaddbbbcdcdbabbabcdadaccccacadbaacbddadbcaccdcadabccadbcdaababacccccdbacbbdcdbbdcbcbbbdcbdaaacbadacccdcbbbaadcabbaaddccbccdbdabbcadddabdaaddadcabaabccdbdccbbdaccaaacbddccaadcadcdccaaaccadccbbcacbbbddddaaddcdddcdbaddaaddcbbdacbabcabbccaadbcbaadccdbadcaaaaacbbcbcadccabddacbdadbdadbcabbbcadccacdcdaabadaccdbdcbbcbccdddcbacbbdbbadbdabddabbcabcabdccdbbdccadbddaddbcbbddcdccbdcbaacbcbaaaababaaabbbcbabbadcaccdddbddaadcbbadcbdddccccdabaaccbaadadaccbbdbabbaddbcbddbbaacacbabdacadbababcbcddacdbaaddcbcdbabbacabbadaabcccdbacccddcadadddabaadddacaacbcaaaacaddadcdcdcccddabcadaabbccdabdbddcccdcddccbaccdbadcbbbadcddabcbcabaaaadbdadcadbbddccccbaabdabcaddbaadbaaccbbacccdbcaccddbdbcdbbcdadabacdbcbadbbdbcbdcbacabbbaccccaabbbbbdcbbacbdcbcbdaddbdbcbccbdccabbacddacdacbccccadddddccabacadacbaabcbdbcacbcbaddaddcccddbcbabccbabccddbccccaccaccdbdcccbdadcccccbaccbccdcaadddbdddbcdadcbbbcdadbcccabcddbccdadccdccddaabdaabbbabbccadddbdbbbbdccadbdbdccdccadadcdddcdcbdbbbccdbbddadbaddbcaabababdcadacabcabcbadbcbcdbaacaccbbaabacaaddbbbddcdcccdaababcbabaabbdcbbddcaccdcdccbdcaadcbaabdcacdbbbddcdbdbbccbabaccabcdaabcabdaadaaddbbdcddbddbdabdaacadbbbdacabddddcadaddbbcaddbddacbbbdbbaacabacdcbcbcbbbacccdcacacabbacdbccaaaacaadcabbcbcacbcbbcddabdacdacdddadbcdabaccabbaababcccaaaadaccadddbdbcaddccabaabadacdcacacbbcacdacacdbdcbcaaddcccbdacddaabcacdbcaaccadbbdbadaddbccdbdabdabaccddcccbacadccdcdadcbbdbbbbddcddabddadddbddcdccdcbcdaabdabbdaaadbbcbbababacbbdbacdbcddadabdcadcccaccaadaacbcddaadbcdcbcbcabdbaaabdbddcadcaddcacbbcddccdbddabacacaabcddbdcaaabbddadccddbdcabbbaaaabdccacdcababdcadaabbabdbabbdbbaccdbdcadbabbdbacddbacaaacadaadccbabadcabaddacaaddccdccbbabbcbbdaadccdcdcaadbacddccbaaccaabbccbacbbdbbbcbdaabadccbdccbbdbddbabbadcacbdbdaadaaddaadcbacabcccaccdbbccdbacadcddaddbdcdacbcdcccbdcbdcbcbdbabdacacbacccdcdaabbaccbddcabbbcccdbccaddcbccbaacbcacabaacdbacbcbdddbadbbabccbcaababdaaaacbbccdbddaaaddddacdacdbdaddadadadabcbbaddcbdbccaddaccbbacacaaadbbbaabadbcddbddbdcacbacaabaabdcdcabcdaccaacdbdddccbabddbbaddadcabcababdcbacadbddcbbccadadddbdbdcdcabcdabbbddbdccdabdccabcaaadbcbcdacdbbababddabcabcdacaaacdbcaccdaabcadddbbbdcbcddcacabbabdbabbbccabbaaccbaacdadcdaacaabdcbbdbdbdadcacdaaccaaaacbdaaadccadbdcdddcaaacbcccbacaddbbbbdacbbaddacdcaccbaabccaaabbacbbdacccbcdcbcacbddaabaccdccacaaccddbbbcdbcdaddcbdcabbaccddbdbbcaaabbbadbbdcaaaabdcccdcdcabddbccbabcabcbcbaccaabaabccaaccdbcaabdbacdbdcbbcabacccbaccdbaabccddbccaabdcdbddabddbdccacccbbbadbdaddabdbabcddbdbcdbddcccbccdcdbacbcdbbbbbadbddddcdccbddaaddcbbbbcdbdabbdbaabbcaaadcbbdcaacbadcddccddbddbbacadbbbdcbcddbbdbcbcdaacdacadbaabbbabbdbaacdccccdcbdddbbccabbbcbbcaddddbcacdabcaadabcdbccddaccaabaaacbbadbddcdbdabbcacdacbdbccddcdcdadadcdbbabcbdbbdbdbaabbacbcabaadaaadbbcbabdddacacbbcaddccaaccdaccacadadbbdbbaaabacbdadaccdcbadbbdbbcbabbddcccaacabbdccabadbcbdbcccbacaabccbddabddaaadbdaaabccabbbddbabdcbbddccddadacdbdbddcbdbccaabcaaabdcaabccdabcabdcacbbbddddaaacdadbbcadaccdbccdddcccbaaadadadcbddbabbddababcbbdabcbcaccabcbbddcccdbbaaaaddcabddddabdbdcbbbbacbbbadccabacbcdadbadabdcbbcabbbabcadbdaadbacadbaaaadcdddaccbacaddcbcaaadacdaaadcbaacbaddadbdbbbaadcabaddaabbaccadbbaccbdbaadbaadcdcddcbdcdbdcabbdcdabababacbdcbcbdcabcbcadbbdadcaadbadacbcaaccabcbdcdbababadddbccdcddcbdbacadbaaabdabaccaabcdbcccdaaacdddadcbbbdbbccdbaacccbdcddccccccdcbbccacdcaabaaadcbddbbdccdbabcccbabaaadaacdcbdabccbbcccbbaaadccaabcdbadbbbbbdddccbcddbbdcdcccadaacadcacadaaadbaddcbbbdaccdddcddcadddbcdaabccdcabdbaaacacccaccababaabacbdaccaccbbccabcddbacbbdddaaddaaabdaaaacddaadcbcddabcccdbddddadbaaadcdccdcccbbddbadaadccbaaadaccbccbacadcabcddabccdcaaaddbcbccabbbaacccdbccaadcacaaccdddbdcbcbcbaababdbadbdcddaadcdaacddbdcdbadbdabcacdcaddcdbacdbbbbabcbdbacdacddbabdcddbabcccbbdccdbacdcdcacaaacdcabdbbbcbbdabadbdddabccbdbbbdbdcadccdcbcdbccbdddddbdccbadacabcccabdbccbbcabccbcdbcadacdddbccdcbdaddcbaccaaacdcabdadacabbccacaadabcdacdcacadaabddadbccdabddccadbbbcdcacdcdacdbcbbcdacabbddddcccdcbbdacbbdbdabbcbddbbcbcadacaacccdcabbdbbbbaccbdaaaacbcbbcabcdaccbcaaabcdcabbdbabdcdabbbaaddcbbcbdccccdabbaadacabacdabbcaaddcadabdbbacaabbcacbbdaddbdcaaaaddbccdbccabcdbbcccbcdcabcbadacbaacdbdbddbaadbbdcbdbdddcbbddddabbcdbadacaddabbadccbdbadabbcabdbababcbabbccaaacccbcbabddbabdbbacaddaddaacddcdcbbbbccbbcdaccccbcbbcddabcaaadbdcbccdcccdacabccbdcabacbbaaccabbdcccacaabccccdabdcabbcbbadbacdbcaacacbdbdaadcdbcabaccaabbbcdaddcadddadadbddadcddcabccdaaaabcbcaaddacadccdbbadddaddbbabbdadcabdddcbcaabadcbaccbadcdcdbdddcbcddacbdcccaabbdaadcacaabdacbddacaacdccddaccddcbcaccddbaadcbbdcbddbcbcbcabbbbdcbcbabbbbaadcbaacaaddbcdddabbddcbbacacccacbdcdcbcbdaacbbadbcababacaabbacadaaaabbcdcdaaaaadbcbdbcdabcaddcdabdbababbcbdbdacaddbbbabbbbbbbdcbabaccbccbbbbbcadbbbcabaabbaabbabbddbadadcabbdadcbddadbcaddcbbcabccdbcccaddcdbcbbddabdabacbccdcdddcccbadacdddbbdcaddaabaabdbdaadddcacdabbdbcddbbbcabdadbdabdddbbcdadbaacaddbadabbbbbccaddaacddbbcbdccaccddcaabbccccbaddcaacbdcddabdbbdcdcddadbbddabddcdcbadaabbccdcbacddbddabbbdacbacbddcadcbabbbbabcbbdbdcacdbbacccdabaddbbcddbccbbbcabbaaddaaaabdddaacacabbbddabaadcbaadbaaddbdcdaadbadababacdbdcaaddddaadaaccadbddadccabcddbabdaacaacdadaaccaaacaacabddddcdadcbcababcdbcabcbcbabcbbcbcbcdcaabbadbcacabbbcacaabddabdadddcbcabddcccbbbaacdacbcbacabbbbacdabdbbbdaaadcddadcbbdaadaabdcacdcadbcddadcddccdbddbaacdcbcadbababccdcaddadacabbcadacbadbcaccdcddaacdadacdadbccbcabbacbdbdbdaaccccaaccaaaacaacddbccabccacbbaadbcdbbbcbcbddbdacccccbadddbdcdbdccdabdcbdadccccbbddddabadabacbccbbcbccbcccadacdcabdbccccadcacabcdacbbbcaabcdbbacaaaabcdcabbcabcbdbabbddcbaaaadddccccdcbaabcbadcaddaccacbabacbcbacbaadbdcaaabdaddbbdbcaacadcddbbabcbaabadccdcaacdaccdacdacaaccadabbaddcdcbadbbccabdbadbbddaacccdcccdacdababacccdbbbabdbacdcadadcdcdcdbabcbacddcbddacabcabababbdaaccbacbccaaabcddcadcbdcabababababcaaaabccaccdbbbdcadabaaabdbbbcdcbacbbaabcdccabcbbbbabcdbdddbbcbbdbabbbbbcbaabddacadcabccbdddcbddbbccdaaccbbadaaabccdaadcbdbddacacaabcdabcdbbcccdaacdcdcbccdcadcdaddcdacaaabcdbaaaabadaccbdbadadaadbccdaabcbaacbadcaccbdabadbbadcdbbdabdcdaaacdbcdcacdaadaadcadcaddbddaccadbcdacbbbdccabcccbbcacbbadaaabbaaadabbbacadccbddcdaacdcccdbddbbddbcdbbabacdcbcddccaddacababdbbdbaabdaaccacddacbbcbbdcccdabdbbdadddbbadbdbccbdadbccccacccbadddadcbdaaabdccdbdcdabbadadcabbdcccdccdccdbacdcaadbbcccbcdbcddbdcddaccabcccbadcdcddbbaaccdcacbadbdacacddcbabbaaccbccaaddcabbcadbcaaadaabcdddbabdcadcdbccdabbdbdccdcdccdccbbdbcaadbbacddcadcaccbbaccdadcadddbcadbbdbdbbbddcbabcdaccddbcbdddaaabcdbbdacbcaabbcacaddbbaccbdabccacadcaaabaccbddabbcbcadbaccdcadcbaabdcbacabbababddcdcbbbabccacbacbbdbbdaaddbddbadbdbbacbcaacacbabacaadcbdbdabcdccbaaabcbdcababdacddabcddccbabcdbbdddbcaddbbbaccaaddbdbcbaccdabbaaaccdbccbdadbbdaaccbadbadaccbbacbaaacaaaabadccacbbcdcadcbbcadddcacbcadbabdddbbadaadbcddbbcaadcdbddabccdbcbaaaccbbdaabbaabaabbbccdaadbdbccccdcdccbcdadadbbddaccdbaddbbbaccdddbdbdcbdcbbbaadaaaabcdcaddadacccdacabdcdbbbddbdaabcbaddccddbbdbbbbdcddbbdaddababbbccdccacbdaadbbdabdbbbcddcdadabadaaadcaabbcddbbdcdcadacbabccdadbdccaacbdbdbdbcabbaacaaacadbcaaaabddccbabbcaddcbbbdcadbbbbabdbabaccabccdbaadacaccbaacccacaabacbcdabbbabadbbbdbcadddcbaddcccaababccacdcbaacdcdddabbddddbbbdcacbbbdbdadcbbcabbbdaacbddbaddbaccbbddaaabdddbbadbddcdbccbcdcdbdabcbcacdbcacdccbbbcdcacacbaadcddbdacdadaccbdaabaccacacddbaabddabddaaaaaccdcadabbccdcdacaadbcbdbaadcabcddbdddbcdbacabcbbadabbcccbdbaabdcabacbcdbdadcdacaadbcaccaaaadacaacdcbadcaadbabacadadaabdacababaccdabcdccacdbcbaabcccabcbbccbcbaddbabcdabcdabcadcbccddacbaacadddadcdddaccabaacacbddcaabbbdbadabdabbdbabaaddadddcdddacdabdadaddaccaddbbbdddbbaccbbbadccddcabbcbabcbdddcbbddcdadbcdaddbdadabbbabadcbdaacaaacbdadbbccadbacdcdccddbbcbcccdacbcaccccbccddadaadacddbaabbdbbacdddaddcbadccdddacdbddbcaacdbdadbddcadcababadddaacdbdccabbbdcababcdbdbbbadacaacdddacbdabdaaccbdadaabacdaddbcddbabddcbbbadbcbcbccabaaccbacdcbaaaaccbacdacaadbdcdacddacbadabaaabdaacaaaaddbdbdcddcacdaaacdabcdbbbdddcaccddaadbdbbbcdcacbcdccacdbdaabcbcbdcbbdbbdcdcaaaacabdbadcbbaddbdcbdbaccccbbdbbabcadbcbabbaadcdcaabbddaabaddddddddcbcccacabaddaacccdacdbacaccdbdbaadabadbddbccaddccabbcbdcaaaabbdddadcbdadaccbaccbdbdbcdbdbcccdcccdddacadaadcacdaaacaadbadbdddacacccbabbdbabccbbacacddacbbcacccbccccaacacddcabdbbddbbabddccdcadcabccbbcabbbabdcbdcabdbbdaababdbddddcdcacbbcbaccadbcddbdddddabbcbdccacdddbcdacdacaadbdccdabdbcbdbbadaacdcabaddcccabcabaabdbbcabbadabbcdccabbacdbacbcdcadbbdcacdcdcbddadbbaabcbcdabbaadccbbbcdbdadcabccbcbbbcdbcabbcbcdacacddbdbdbcaaabcbbccdcddaaddddaacbddbadcdcddddadaadcbbcbddcbadbcbdccdbbdbbccbdcadaccddacadddadbdbccbbcddbcabbccbdaaadacccbcccaacddbbabcbbdadbaadbabbcbbbdbcbcabdacbaababacaaddbdcccaccdacdadaadabddccbcdadbbbdbbcaaaadcdcbccbdaccddcdbaddbbccccbcbddccbaabcdbbbadabdcacdddcaaaaacdabbacadccbcacccbcaddbbdacaabbbdbdcabadccddbddcdcbbbabbdaddbcddbbdccdbdaacdadaaaccaabdaacdbcccababddcbdaadcaabacbcdabacaabcaaabbcbabcacbdaaddddbadbdadbbcacdabbcbdbbddacaaadcccacaaaaaacddbaaabccacbcbbcabbaabbcacdaaacaddcbdcdabaaaadbabbbcdbabaacbdccdccadcacaabccdcdadddccddcababdacdbcbcaababbbbcabcbaccbabddbbbcccababddabcdddcdcdacdadbcdaabdbcbbaacbbdccaccbccbbdbabcdaacbccdaabdccdbcddddadcddadcaababdbddbbabdcdcccadcdcbddabccdcdcabbccbcbbadbddbdbbbdbcbbbbabddcadbcabbbcccaacdbdcccbdccdabadcccababbdcdbdbbdaccacdaadbaadcbdddcdcbabacdcaabcdacccbacabbbbadabddbbacdcaddacddcccbddadcbabccadbabbbadadcccccbbcddcabcbcadcacbdccbccaabdddbaaabdcadaaaabacbccaacccdbdbcaadbadccaccddadbbbacdbcbacbdacdbbaabaaabdddbabdaddaadbdcccabacabbdbbdadbdcabbbdcbdaaaccaacaabbaaabdbbbdabbbdcbbdbadbbcccbdbabcbdbadaaadcccdcdadaaddcccdbbbdbcacbcdbaaddbdbdadacddddbccbdcdcadabbccabcaadddbacbbabbcbbcdaabaddacddababcbabcdaadbcacbbdbacdcbcbdabacadbaddabbccdbcaddcdddaccababbcddabcdaccbaddcdaabccbcaaacbbacbbadccacccddbbabdacbbcdbbacbcabddaddbbaccccddbcbbdcbdbbaadddddbdcdcadbccbccddcdbbdcddcbbbbdabadddbcacaabaacaaabbddaaabdbcddcccbacdbcdabacacbcdadbcbaacbdcabdcdcbbcbdccabdddcccccdbaacdbccbaaadddbccdaaadacdddaaccadcabcddbbdccbddaccaababbcdaccdbbcdccbcaabcdacabbdaaddddbbbbbccbabaddbbaacabdcdccddcbccbaaaccdbacdaabbddcaabadababdbdadaacbddaaaacccdbabbddadbaaaacadcbbbbbdcadcbbabcabdbdddbcdacdcdabbdbacaaadcdcbadcdccaabadabdbdadcbabdbdadbdaaadadbbaaaacbbdadbdbaccadcacbdacccdddaaaacacaddabbadcbdbdabdbdacbaaabcadacdacdaddcbdadccbdbcccaddddbcbddbdbabbdcdddbcdcbcdbbccdbdaadcdddccadbdacaaccbbbadbcdcdcdabcdbcccacbbddcabcdabaadccdccbdcddbdddcddbaccbbccbdcdccabdabdccbbabcdaaadcbabddbddbaacbdabacaaabacabccdbbdbcdadadbbbdabadbbdbacddacbdadbbcaaddbaccdacadacacdabbaccbaccbbbddcbbabccdaaaaaccdddaadabbdcdcadcdaccdacdbabbdadbabdbdaddcbaabddcbdadaadcabdbbdbcdabacbbbdcaddbcbcbadbddcbcbcabbcdddcabbbbbaacaddadcacdbabaccdbccdccdcacdcddbcacbbadcadcbcbaaadbcdbcddbbaacbbcccdcbccdccbaabbcccbcacadbdbcabbabddbbdcbabbbbbcacdadadaacdcdcdcbbccdbccbaabdcddacccbbdaadddcdabbcccdbdbbccbbaaaadcdddcacbdcbdaadacccaccdcbabccacdadbaadacddddaabbcaadabcdcaccddcaadababdbbabbbccbbacacacdbbcddaaddbdcccacbabbacbddbbcddcdbaadbdadbbccabcdbbdddacdbcadddcacacbaccaacaacdddcdbbbcacaccdaddabcdacbccadaabbaacbcadddcdbdbaddccbbcdaddabbbdabacbadcbabcccaacbadbbabdabbabcdadcbcabbcabbdabcdaccbcbbcabdbaddbdabccacdbbbbdadbcaaaddbdcbbddbdddcbacacbdcabaacabccdddbcdbacdbaadaabacbbbcaddabbddcadbcdabaaccdacdccbcdadddcdcdccdbacadcabdbcbccacadaccacbccbcdbcdbaaaacbbbdccdbbcacadbccabdbddbdbabccbadbdccdcdcaddabadcdacdaadaccbabbcdbbbcbaacdbaddcccddbbcddaabbddacddddcdaaabdcaaccdcbadabbaddcbdbcadaccadddabdacbaaaababdabdacbaacdcddddadabcabcccccdadadacbabaddbccbdcbccaccbdacdcdbdabdcaccdadbaacacddabbbdccadcaaabbcdcdbdaccbaaddbaaaadacdddddcadbdaddbaaacdcbcdbccbdbccddacdbabadacddbbbbadababbdadcddcaddbddbacabcbcadcdcacabddccdaddcabaddbdbcbabccbadacdcaccccbaacbbdcdccbcdccbaadbcbbbacadaacddabcbbbababacabcabdbbbaddbdaadcababbdddcbcbadcaadadcaccdadddcdbcaaadbbcbcbcdadcdacbccabcaabcadacabbbaadcabcccddbdabdbaacbbcdabbbcccaaababbbcddbccdbabbdcabcccabbcdadcdbcabbaccadcaddcbddaaacaabadddbcacacaccaadaddbababdcdbaacacacdcbbbaaccdbbadbddbdbcdcccabccbdcadbbdcadccdaaacaccdcbcaadaadbaacaadadcbdbbccdbbdabaabdadabbbddabccbaaadcbcaddbcadbcaaadaacbbbacddaacacaadcacdabcdcbcdcbcacddabbdaaacdcbdbdbcccccaddaabbaccdadbbbadacccbcbaccadbcbacadbcdabbcbdbcbbcddbdbcacccaaaddacbbacbdcbddbdbbbabccdbbdddacdbabbacddcbdadbcbccaaccaaaababdbccccadaccaadbdbbaadabadbbdbcbccdadccddcbccdaddcaabacdbbacccccacbddacbbbbdbaaadaadaacaadbdadccabaabacbcadaabcacacccbababadcbacbcdbdbcadaaddcacacdbdcdcbdacdbacbacdcbaccacdcdcdbadacbbbaacaacccbadaaadcaccacabdbdccbaccabbbabcadaadabcdbcabcdccbdacbadbdddacbbcdadcdcbdbcbccbadabddbccadccddbbbccbcaaadabcbccbcbacccccddadcdccdabcbaddcdcacbbdbadbcaaaadacdacaaacdbaabaccdcdcbcadbdbcdadabbdabdbbabccdcaabbababbadabacbbccbcbdaaabdacbdcbcdddbcbadcdbabacacaabbbacbbbcccbdcddacdbacabcbbdcdcdacadbcbcacbdbbbabdacbadbcbacbdbbaacdcdbcaddaccdcaacbaabaabdbccdcdbacccbcdbabaaacbcadcbcccaccdddacdcdddaacbbabbcbbdbdbcbaccacacaabcccdbaddbcdbbcdccacccabdccdbcccbdbacbbbbbcbcdaccdcbcdccdddcbdbcbdbbddadbaacacabadbbbabdabddbbbabdcddbccccabbaabaacccabadddaddacdacadddadbbbadbcddbdaadbaadbdaaabdaddcadbbaacdabdaadcccbbacbdbdbabaaddbadbabdbacbcbbaccabaaacddbcbacdcbaacbcccacdabcacbdbdcacdbbacbaccadabbbbabababcdcaddcdaccababdacbdccaddbabbdaaabcdcdcbaacadaaddabdabbbcbccddcccaaabcadbcadbbbcccabbdcdaaaadacbccddcdbcabdcbcbcccabbdacbbacdcdacdadacaacbaadbdbbabddadadcabaaacbccccabcdabdddadadbadabcbccddbbabbccddcbbacbcaaacdaaccadbaadbdbcbabdacbcadcbbabcdbacbadabdccdbacdabadbcbbcbdbcbaaaabbcdbcaacaacdcbdbcbdbbdbdbccdcdbacaccccbdbcddabbbdbdbadcdbdadccdbdabccacabccadabadcbbdbadcabbbdccaaddcabcddabdadbadadabaabddcadbcbbacbadaaabbbadbcabacbacbaacdababcccbbccdbcbccdbcadaacbddbccdddbbabbbaacccadbabdcdaccaacbcdbbdcadbaadbbaaddadacdbcadbddaababbcacbcbacbcccabdbacdcdcbabbdaaddcbddacdcaacccdbacadabbccdcdbaaaccdcacbacaadaacbbdabcdabdbdbdbaccbcddacccbaccacbccabbcbddbbdaacabaddbdadadacbbcdacccbcdddcbbddadcacbbadbaabacbacbacbbbbbbdbcbcbcdacaddacdabcdcbdadacabdcdcacbbdbbbcddbdbddddcdbdddabcaacbbaaababcbabbcbccdbbcbabcabcdcbdcdaadcaddabdadddcbccbacdbbbccdcddccdbaaccbccadddccbcdadbccdddcadcaabbdbdccbbbdabcdcdadccbacddbdcaacccbbccddbacbcbbccadabaadbddcbdcbabccdbcdabaabaddbaaddaacaacacdddabadbdacbcbdacdbcaabccbbcdbcacdadcdaaaccccaddabacdcdddcddadcacadddcdadccacbbdcdbbccdcdcdadaccdbcbccbbccdbddbcadadbbbddbcdbdbacccdacadbadabdbbbacdbabaccbcbadcadcabccbdabddabcabddabadacbdbdcaccccdbdcbbaadcbabbcbadddbbcaadccaabcdbaadbdacaccbaabacaabdaabbbccdcbbbaacabacdbdbccbdabcdddccaabcaaaabdbacbddaccabddcbbbcdaccbdddbbdabcaaccccadacdcaabcacdcbcdacdaabacdaddbaddbcbadacdddaacbaaabbbabdbccbadabacdacdcabdcabcdcbbcccacdbdccadcbcbadcdbdacaadcdbdccabbddaaaddacdcccbdaaabaabdacdadbcbddaaabcacacaccdccacbbcdbbbdacaccacbdbbbdaaabbbdbdbaddabaccdcabbbcadbccdbcbdbbaccdabccbcddaabdccbbacdacdabdabdabadbacbdbbdddcdbaddddddbbdddaddddbdcbbbdbddaccdbadccbbbcdbdaadadaacdcddcdbbdbdabcddaccbbcacaadaabdcaddacbacbcabbbcacddccddbabbacccdaabbbccdbdbcdbdaadaddadcbcbdcacccababbcbbcdcbadaaaadbccdcbddcaabaddaadcbcacddbcaaacbdcbccdadaadbcdadcddabbabccacdaacaccabbaacaacdddddcbbadbcbbabcbccacabdbdabdcabaacbcddabbaddcaccabbbaccadaaabdadbaacacdbbdddcdacdaaabdcacccbdbccbacccbbcbacaacccbcaadccddbcabbddbbcddbccadacddcdcadabcbcdaccccacbdcdaabcacabddbddbaaaabadccbcadcdadcaadbdbdbdccbcbdddcbcddadccdddcadacaaccacdaaaaadadbabbaccdcadababbbabcadcbccddbacddaaccbccbaccccaacbbbaccabbacabababadbbdabdbdbdbaadcbdcabacbcaabdcabaadcbacdbbaddaabdaaaabcbcddbbbcaabbdbccbddbcbcabdddbddcdbababbcbaacddcabdaccabbaadcdacdccbacacabcaadabbacdabcacaacdabbcaddcdbccdacbbcabdbbcdabbcbcccddabaadbbcdbcdcbaddcaabbddaaacacbbdddacbcccbcdcbddbacbadccbacbddadccaccddddaabddbcbcabcbbcbdbbbbcdccdcddbabddabdbcadbcccdbaaaabcacdcabccddacbcbbbbabaccdccdbdbdadbdababacacbbbcbcbbadbbdaacbaabaadcacdabcabaadbbbabccaccbbccdbbccccbbbacbbaadbdbcbdbbbcadacbdaabacbcaabbacdbaccdacdadbbbddacdbcbdbbbdadadbdcaccbbcaddddbbddaddcdacacbbadbcbaacdcdbbbbbcdccccbdcdbabccbbaadbcbaaddbbabadbdaadbbcbdbcaddcccaabacadababdcabbcacdacbbdcdcbbbacdaacacdaaccaadcdbbcbadacbdbcccaddcaddbaacbdbbbcabbdaddddbdddababbaaccdabbbacddcbddaabababcbdccdbdcacbaccbdbabddaccabaabaaccaccbdbcbdcbadbcbbcadbabcddbdaaaabacccaccbaccacdabcadbcdbadabacabcaaacbacccbbbcabbadbabdcbcddccdbcbdbcbadaaadcaccbcdbdddcbaabccddacacbbdbcdbdbaabbdcacaaacaadbaccbcbdccabddbdadbcaacbddaddddcddcaacacdddcbaccdbbbacbdaaacddbbadacbcbaabbdbdaabcbacaaacadccbabaacbddaadcdaadbacbccbdbddbcdbcdddbddbccbbccadbbccdbbcdacabaaabbbbdadbabbabcbdcdcdccbbcaddcbdbacccccdddadcbdcdcbbbabccdadcabbaddaaadccccbcbaadcdddbaaacbccaacdacdadcbcbdcddabadbdbdccdcbcdcdddacdbbbababcacddacadadccadbcadbcbcbbbbaaaabbcaacabcbdbaadddaacbacaabcbccbbbddcdbabcdcddaaadcbbacdabacbaaaaabcaaadaadcdbaabbcaadcdaddbdddbccbcacaabbccddbcdbaddacbbdcddacbbcbdcdddaaacbcbbddaadabadbbdbcbbbabddbabbaadbacaadbbabdbdbcddddababcdaacdbcdcdbadbbcadccaabbacaadacbccacacbbbaaddadbadcccabbbcdcaaaabcaabbdcaaaabaddcbbadacccbcabcbadbbcacbbcadacbddacddbddccadcadddddbdbdbcddadacdbbdcbbdbcbadaadacbbbddaaddbaadbacabbcccddbbaddcdcaaaddbbadbcdadddbcbddbcdcdccbabcbbaadaacacccbaddbadbdccdbaabbcbcdccbcdccaddbdbdadacddddbbbdbabdbacdddddabbadbbdbbcbbbaabdaaabbcbbadacbbcadbbbbdadccbdcbcabcdcbbcaccdddcacbbdcbcbaacbbaaddcbcbacabbcbbdcdddbabdcdddbddcaaccdbacacbdbaabcbddbdbddbaddabbdcaacbadcdadabcadabcbdccbcbcacccaddbbbbdbbcbbaccaaadbdddadacdddcbabddbcbbddddcdadcbbdbbbdaaadacadcadbdadcbcbbdabaccbdcaacaccbdbccdbbbbddcaaadaccacddcbdbacaabaabdbcdcbcbbdccdcdabacacbbacabbdcbdbccccbccdbabbaccbccadacadbabbcdaaccbbbbacddbcabadcdccbcbbabaaadcdcadbddcddcbdbcbbddcdcaddddbbbadcaacbabcaccdbdabccdacacddccabcabadaddabcccccbdbcbaddcdcbdbacadbdccabbdcdbaddaadaccaabbdcbdbacbdacdcbabcbacbccdcdcbadbccdbdcaacabacbdbcaccaacbbbadcbaddbcbcdadbaccacbcabdccbbbbbcccbabdddaaccbaaabacadcbccccddccabdccaccbcdbbcccbacaddadacadabcabccabddbcbcaadcacdbcabdbcbbcdbddcbacbcdadcdcacabaacdcadccacdadacaccbbcbcddaacbbbbdbdccbadcadcbbabbabcdbcaadabaacacabcabddbaacddaacaccbadacbbacddddabcaccbcabbabcdbdbcdbbdbccdbcacbbcacadacabcaddbdbdaaacadadabaadbacccbdabdabbdcbacbaabbcbcddcdbcabacdacacbcbccdbdbccddbddadcabdbdbcccaccaccabcdbbdbdbcbaddaddbbbdcbbabdadadbdadcbbccacadbbacbdcbcbdccccabdcdbdbccbacdcbbbaabcabdcddbbdbcccabdaadbdcdbcdbbdacbbcaaabdacbdbdbddcabdaccbdcaabcaabddcaddbdaadccaaabadccbccbabbadccaaabdaaddbbadcadadcbaaacbbaacbdbcaccbcdabbcaadbccddcbabbdbdbdacccccbadcabadbabaabadaaadbbdacdabdaddcaddcddbbcdbccdcbbcdaacbbcddbacbcdabacdaaddccaaddabcabcbbbbcacabddbbcbbcaacccbadbbcdddabddbbacaaabbbddccbcccbccaccacaaabcddacaabaddbacdbaacbdbadcbcdacaccaabcdadddccbacbdabdabdbaabacbcabbdccccabadbddcaddcbcdcbaacadbdccddaabbbadbaadddcabcacbbbadbccddccbababacbbcdccddccdbdcccdbcdbcacccdcdbaacccacccdbdddcbaccaaddcbcaaacbdbbaddbccdcbdabccbacacccdaadccddbaadbccdbdadbacacbddbbbacaccaabdbccbadbbdbbabcbcdcdbdaddaadcbcdbdbbdacdcadddbaccbdacacaacaaaadcaaaabcabaaadccabccddbbccbcdccddccadcadbcbcaddbbcccdbbaabbdccccbbdccdcabddabdcabbaadadacaaacbdcacbaaddabcdbadbdaabcacaacacadddcdccaacdbaaaadabbddadcadddaddcccdcabaababcddddcbdacdddcddcbdabbbadadbcbacdbdadacbcdddbdbdcbbabbdbcccbcadcdaaacbaaaddbccbbbcaaddddabababcdababbbddbbbabadddcccaddddcbbbdbaddddadaddcbcdcabccbdcacccddbdccbbaacdaaabdbabbcdcbacaaabbabcdbddbbcdbdbabdcaccdcadbddcbadcadabaaccbcabbdbddbbbdbddddcadbcadcacdcbdbadddbddbcacbdcbabdbbbdbddcaaddcbbccdadaddbcbbacdaadccacadbdcdcbbbcbdadadaaadbddacccbdcdddcccbaaaccbbddcdccdcbbdbdbbcacccbbdcbbbbddbaaaaabddbaadbbabddbbdcadbcddaddddccacdbcccddbcacaabdcabdbcaacdcbccbacaadbbcccdcdabdcbbaddbcacdaadbaacabdaabcccaacaabdccadcdbdcccbcabacdbabdccdddabadcabacbacdbadccbaabdaaccccabcccaccccdbadaadadcccbcdbdaadcadcdacabcccdbacbaadddbcccdabdbbbdcbcdddcbddbbacadbacaacdcbcaadabdccadcbbcdcabcaacacdabadbbadabcaadaccbaacddcdddbbcbcddddaaddadbcaabbbdadbcaddcabbccbccccaabaabbbbdbbdcaacababcdcdcadbbcbbadaadccbbcbabcdbcccccaddbacacdbdaaaadcaccdacadccadaaacdcdcbdcacacdbabdabcbbcbbcbcccdadbacdcbddcdbdbdbdacbbcbcabbdccbbdcabdbbbbbabbbcbbdaacdcadacdccbcdbabccbbbddcbbcabaabccddadaddaadaccdcaaccdbcdbddbdacddcdbddacbaabbddadbcddabdadcddbbbacbacabcbbadadbbcdbcadacddacdcacaaacbabdcdbadbdbbaddbccddbacddadabdbcbccbaddcdbacbbaaacacbbcddaadcccbcbabbcabbacaddbdadadadbcdcdcabcaaccbcadadaaababcabbdbcdddcbbcaddcbbbabdbbcaababcbaddaaddbcccaccabbaddcaaaabbdcbaadbadadddbbdcabddcacdaddbcccbdadccdbdbacddcbddabcaabbcdbadccdcbabdaccdabdaaddbdbcbbabdccbddcacdbbddcdcbdbbcbbdccdbcabbabbbadccbddcbbbdddacbbbbbbacaccdcdbddcbaccdbcbdacdbcacbdbccbdacbacbddacbbaaaabcbbbdacdadcdadaddadadaabcdaaabcdabbaababbdbcbdcabccabddbbbabccabbaabdddbdbbcabbbdbcabcbaabbcbcacdbabbaaacbcadacdcacbccbcdccbccadacbccdcaacdaabdccbcbcaaacdbddadaadcbdabcbdabddbcccccaaaabbcbadababadadcabbaddacbcabbbccdbbdccaaaabbdaccacbdccaccdbccabccadcdbcdcdbddbcddccdcbbabbdcdbddbcbaaddccaaccbdacbdbadcaaaddadbbdccddbdcabdbcccbcbbcddbacbddbbccccccbdcacddabcbcacddcbddadcccdbaabcddbcdcbbcaadcbdbbdbdadacdbccdabddccaccdadcaabdccbccbcbddccdcdddccbbacddddcabcbddbbbcbadccdbbdcacdabbabccadbacbddccccbcbcbbcdacbcabacdacdcdcdcddbccdcabacacccacaccacbdcbcdababaabdbdcddbdccbababbacbabdddacdaccaadaccbbbdbbdcbdbdcbabccabcbaccadaacabdcbdbcbbbacdccdbcdcbcdbbacdcabcdaacbaadabbdbdacbcbadcbdddadcaabbaacbabccadacddabbddaddabbbddacbdccdcbadddbcbbbacacbabbbbdacdccacdacccbacabaddadaddddaaadaddbbdacadacbdcdacdbacbdbcdccdddccabcaddacccacaacdabcddcaaddadbcdddcddcabbccbdbadcbcbcadaaabbabcbcddabcddaaccbabcbabaacadcbbdaabbadbcabcaddddbbbaacdabddadabababcbdbbcdbbcaabcdccabbbcdaddacbcdaadddccdcbadcbbcbcdaaacbcdadaadbdabbcddbcaaacbdcbbbaadddcdddababbdbcdbdccbbcaacbacdbbccaadadcdaddcdabcadcccdbadbdaddcdbdadabbbbbccdadbbcccaaabcaccababadbccabaddacacdaadcbdddabacaabdcbcaababaaacaccccbcbcddbdddabbcbabcaccbaabccbadbbdbbcacccbdcababcacdbbcdbbdbbcbcdabbdbbaaddaababdbcbbdcbcabbdaabacadbcaacdcaaadbacdbddcbaacdcbdcbbacdbaccaacddacabcbccacbbcccdcadcbbcadadcbcddaaccaadbabcacbdbcbcbdbaccbcaaacbcbcdbaadbaacacbaccbcdbacababdddbdadbddacbabaaabaccabdbdbcaaabbdaadcabbaddaacadabdcbccdaacbabcbbcdbccbdaddcdbaaaabbcaddddbacaaababadbbbcddddcbbaababcbdcdcaabdbacbaddcbbcdbcdadcbbabcdacccdabdbdbcdcdcacbabaddcdbccaaddcabadadbdaadbaadabcadbcbddcbdddbdcbacdbbdccbdcaddacbabadbbcbaaaabaaacabccacdccdaabadcabdbcccbaaadaacdabbbadbbddbdbcdcbdbbcbbbcdbcbbccaddcbabcddcbcaabcddcdcacdccdcdcbabbaaaaccdddcddadaadcbcbcbbbabbcbbcababbcacaacaaccdcbbbaccaaaccacbadcbbcdacdcabdcdaaabdadbabbacddccdbcddccbcbcdbdadadccaaadbcadbbcadbbdbdcadbcccbacdddbadccdcbdcccbaacddcaddbccadabaccbdcdaaadaacdbcdbcbbbaaaababbbbbaabdacacabdabcdadaacbcadadcadbddddabaadabcbcabcdacdccbdbcbbcbdccaacddbbdcdcdaaaddbacdddbacabadcadcadabddacaabbcbddbdaddccdbacbbababcadaaaacacaddbcbdaaacbacababccdacdcdbabaaadddcbaabbddbcbbaabbcbcadcabdbacbbddacbddcbdcaddbadcdaadadaabcdbcadbbdaaccacdcbbbcdbdbccbbadcbdadadadbdbcabcccacacdbcdabaadaddaadaaddbdbaaacdcddbadcdcdbacaaddcabcadcddcdbdcbbcdcdccdaddbbabbdaaadbccdbadacaabbcabaadbaccbdbddcbdaddabccadacddbabddacccdcacdddccaaddaaabcabaccbcbcccaadaddbdbacddcccacbbdadcdacbcdacadacdcbdadddabaabadabbccbaaccccaacadcbcddbccacbaddcbbbbaddbabbbadaaddabcaccaadabdcdbaddcbdcbcdccdccacbcdccccddbcacddccdccabcdbacdbcbadadcbbdabdbabdcdaacbaaaacacbaddccdcbdcabbbbcbcdcbaabcbcaabadadbabaccabdaabbabcddaacdcabdbccacabdcddaddcdcdabaacdcdbbbccacdacacbcbcdddcadbbabdacbdaacdbbbbdcababcdcbaadcaacacaccccbcbadccbbbabdbdcadacccdbadddaadbdabddaabdcbabdabadabddcbadcdaddbcdacadbbcdaabbdbccabdadabadcdddaadbadddbbbabadabcaccbbacaadcbbacadccbcababcdacacdddcbdbddbccacaaabaccccddbbbdabdcdacaabbbabbcbcabcadadabaddbdcdadcdcdbdcbbaaaacaadcddadbbbcddaddcaccbacbcbdcddaacacdddbdcccbbdbadccccccbcaaabcacdcccbaccbcadaccacddbcabddaddbbabcdaaccaccdcbdaababbbccabddbccddbddcccccbbdacababdddbbacaaabbcaaccccccccbddbbcdbdcdddaacdcbbbdccbcaccadddaacdcbbaabaaacbdbbaadcddddacaadbcadaaaccbdadbbaabdcaaacccccdbcbbbbdbdcabbcaccababdddcbcabadbcbcadbddbcaacdbccddcabbaadacadddbbabddcbaadbddbbcbcbcdbcdccbacacacdacbacddbbbcdcddbbadcaaaadbcbaaacbdbbbadcbcbbdbadadbbdbbdaacabdddbdbacaacbccadcaddbdccdcdbccdabbdbcbbdbcdcccaaacbccdbdadaacbbbdaaaaadcdacdbdacbddbdbcabdabababaabcccdcabbcccaccaabbdabcabacdcaadccabcbbccdcddcdabdbdbbcccdddbbcbcccbdcbadcdaadbadacdadbdabcbbcadabbbcacbdcdbcbddcababbadaaabdcbcadaacbbdbccbdcadababcbdcaabacbbabbddbddbdacccdbddbbcadadbaabdcddbbabcdcabccaabcdbbbadabcdcacbaadadddbdbbccdaacbadbcbbbcbaaabbaabdbccdaaacccbbbdaabdbbbcacacbacadacdabdbbaadacaddabccdcddabccbdbddcababbcdcbdacacdcaaadccdabcbdcdddccbadabdadcabadcdbacabbdacdaccbcdbaccadacacabdabbbcaddaacdbbdddbcbbbbcbaacdcabddbcdabdccadbdbdddcbdabcbdbdcccbcbaaacaacabaabbdbddadbddacdddcddbabadaacbcdacdcddcbdbbbdabbcacddaacddddbcbbddbcdccabdcdbcbccaddbabdbadaccbbccdbadadaababbacbbcadbcadcddcdcdccadaaabaacbaadbbdbaaacaadacdadccdaacdabccbabbacaacadbaabcccbbaaadddcdcbbbbaadcababbccdabccacdbbbdbbabccbbddcdaabbcdbaabaadbdbbacbbcaacbcdacddaacbabbcddbbbdcdbccaabccbdbdbcdcbbcaacbbccbbcddabddddaddbdcaacdcbadbadabccddbbcaaacaabbcacdcbbddabbadbccddbbdbbcbbbdbdbcddaabbabacadddbacabbbabdcaabcbcbbbaaacdbdccbbbabdcabacbbdbdadcdbbbabcadacdbbcaddbbdcbdacdaaaaaddadcaacaddabcbddabadbbbacbcdaabbbdabbcbcdbdbdcaabcddcdcdcbcadacccbaddbddbddccbddbdcaccbcdcccdddddcddcdcdacaabbbccdddcdbaabddbddabdaacdaccaadaacddacbcaacabaadddbdaccbcbdbbcccdcabcbbbddadcbadbcdccaddcaaadcccddcacdbdbbabddcbbbdddbdddbcaaaabdabaacbcbadcbbccccbccbadcaabbadadbdbcadddbbbcbcddcdccababcaaaaaacdabbdaabcbdcbccabbddcadbdcbdacbabcacdaaacbddbdbdadcbaaabaadddbaabcbcdbdacbbcccabdbacbcdcbdcaddcbaadbdabcdadaabcdcccbdcdcdaacbcacabdbcbcddddadbcbadbdaababaccbdcbaccdacbacdadacbcdbbbbbabbbdadaaccabbcacdbddadbadbcddbbdacbdabdcbabadaccadbdbbcbcadccaabaccadadbcbabbcbdaccaaddabccdbcbcdabcbbcabcaddabcacdaaadccbbcbccbbdabcacdcbaadadbcccadacddccbabababcaccbbcacdacddccdcadaacbcdbbaacbabbdcaddcbaacbcaadddcbbdbbadaaabbdcdcccdaddcbcabaabadbabddaddbaaaabdadadbbbbaadbcbbdbdbcadbbabcbccbddcaddcacdcacccccbdadcbabcbbaccadacddcdbbcbddbabcbacdcdbbddaddaccbaaaaabaaabadbbcacacdacbdcaacdbaccbcabbcabbadbcbcadabcabbcdabacacdabadaddbaabccaadaddddbcdbbcbcaabcadbcbddcadbabdaacbddddabbdcddccdbdcdcdcbcbcddabccbccbaaccddddaccdaacddcacdbcbdddcdccccaababacacbdccbadcaccdcbcbdddaabcdbbcbcdbacabacacbbadabdcacdbccdbaaaaddbddcccdbcacdcabcacadbacccabcbdccccaabdabbabbcdcadabaadbacbcbadcbbddadbbbbabcddabbcbaabbdbabbddbadcdbbdcccbbbcdabcbdccbcdcdcbddaadbdcbabcabbabadbbccbaadbdabdbabdbcaabaaabbcacdbcdbcddadcbcdbcbaadbdcdbcabdcddcdcbbaddabbdacddbbaaadbccccaaccddcabdcdadbdacaadbcdabbddcbdcdcadbdabdcbaacacbacdddbaacddbababbadcbcdcacbbdcabdcdcbbbaaacdcbadbbacbcccaaaccaadbdcabdddcbabbaabdbbaacccadaabbdccaabbcdadccbbccccbbdacddacbabdbcdbbbdbaaadbbbcaabddcdccbccdcdabbcbbddcadccbbdabbccddcbacacacabdbdcddacacacadcaabdcaababbdcabacbdcdadbbcddbcddddddadaccdcadddadddccbbdabcbaadabaadcddccdabbbbcdbbdbaacccdabdacbaaddacadddddacbcdccadcccadcadacbddaabdadadbcbdbdadddbbdcaacacbbbcabaaddacbbccdddabbacccbccbcbaddabbbaabbccbcccababbdabbabcdddcbabddbdbabcbdccabbbbccbddddbaacaaadcbcbbbacabcbadacbdcbadaabbbdcbabcdbcacccaccbabccaacabdddcbadbcdbabdaddababcdbccccbddcdbdbacddacbcdacbacacadcabacabbbddcacbcddabddbaaaddaaaddaabbbbbadaadabdacddcdbabdbcdbbabbbddaabaabacbbadddadbbdbbdccdcdccbababdaadabddcbadcbabcddbbadcacadccacbbbababddbbdcdadacadbbdcdabcccadaccbdbdcbbadbccbbccdccadbbbabcdaaadbdabdbdcadaaaddaabaacaadccbbcbbaabcbbcbbcacadbcbbddadcbccdbabdadcddbccbbbccddddbbdddbabbdbbadabcbdaccbcccbbbbbaacacbdbdbadacbcabaadccdaacadabccddadabacadbddcdaabacbbdaacdccaacddacbbddcabbaddabdbbcbcddabddbaacacbdbdccadccabbddcdcadccaacacdabbccdbadaaadcdaccabddcdbcbcacbcacdcaabaabbbcaaacbdcddabcbabdccdacddacdcacbbddadbbacbdaddcdddcbabacdabcccbadcacaaadabbdbbabdbbbbdddcbddbddaadaabdbddadccbacddcaadcccbdbccaccabbbabbddccacdcabbccbbccbcbdadbabaacadddccabdadbbbcdaaabdacbccccbbcdbddcbcdbbcccabcaadadcdbcbdbcadbacbbcdcaccababbddcaaadcbaadcdcddcaacdbacbadcddadcabbddcbaccdadaababbadadbcbdbdbcacabdbdbaadddcbacbcbadccdadabacdaccdacaadbbababbbbbbdcbcaacdbdbabddbaabaddbdcbbdaabdadabcdabadacdddaabbdbdbcdcdbbababdabacbaababbccbacacdcadcaaaacddaabcabdbbbaccaccbcabadcdababdaddaacddacaccdcddcbddcccbadabbdabddccabcabcbddbdabadbbcadaadbcdaadcddcbbcdddacaaaacdacbcadbaaaaacaddaaccadcaabdbaddccaadbcdaacbbddbbbdaddcaadbbacdbacbbbbdcbccddbdacacaaabdbccbcbdcdcadcadaadabdbdbcbccbaddaadcdcaccacbccbddcbabcdabdddbcbddcaacbdabdddcddaacbbabadabaacbdccaaabbccaaabbbcadacbddbacadccdadadacbbbcdabadabaddacbbacadbddbdcadacdcbaccaccadcbaadacabbccdbbcbdcaabcadabdbbcaadbcdccddddbcabdcbaabcdddbdbdaadadbdaddccbbdbcdcbdbabdbbcabdbacaaabcbaabbbadaaaacddcadcaabbdbcdddaacdbadcddbdbddabbccdccbbadccbaadabbaddacbdaddcaaddbdbcddcabababaabdbacadccddacccdbcdbbaadaccccbabdbaacadddaacbdbcbacabdbdbbdccabbaccbccbcaacdcbdbdbccaaaaadabacbdbabbdbbbbccddcdabacabcbaddaabcdcbcbcbdabdadcccacccddadaaabccadabbbccadcaacdaababdcdbbacdcbcccabcbbbbbcacbcaabdabdbadddcabcdddaabcbbdaccabbbbacbbccdacbdddabccaddabacdadabaacaabddddaacbcdbadbcdadaddcacbdbdbdbddadcaabbbbcbdccddbcbcbdbdccacccbcccdcaadcbddaadbbcbdbabdacdbddbdbdcaacabbcabdbaadcccacacbadccbacdccbccbaacdcbdacabcbbccdcccabbdbbbcabbdaddaaccdababadbdaaabbacadbaadaddaaacccdaaabaabbccbbadcddcbacdadabcccbdccdcdcbabacccddacbdbaddcbcdcdabbccbccbcbcacbaadbaddacdddcaaacaabdcddacadabdccabbaadccbccdcbdbccdabacdcbccddbdaaaadbbbacccddbcddacaaccaaabbccbcdbaaacabcaababacdccdadddadaccbbacbcbbdcaaddcbdcdbabacdbcbdccbaacbdcacdaabcdaadccddbadadbbdcbcaddacaabbcddbdccacaadcabbacbadacdbccacddaacacbdcbdddacbddacccdbddbacdaaacadcbaacbcdadbccadbdacdaaadbcdbcdddbdacadbbacdabadbaabdbaacacbddcbbadbaadbbadcbdbdcccacddacbaaaabbbdcbcccdacadbdbbabdbaaaacddccbcbaadbdcbaadbbcacaadabcaccccbdddacbbadcadcabaaacddcbbaabcadacddcdcaddbcaaabbaadbaddcdabbccaacbcbcbabdbbbdcdadbddcddabaccdacdbdcbccdabadcddbcbdbbdbbdadabadbbdcaacbcbbaadbbbccbadccdcbdbcdddcdcacbadbcccdaadbadbbbbbbbbbdddbcdbabcbcdbacaaccaabddaaabdbaaababbccabaabbcbacdddbabaaaaaaacaadbaddcbdbcdcbccbdaccbadcdbdcbadbbaaacaaddabbccaaccacbcbabdacbdabdbaabcaabdcbccacaabbbaccddabddddcdcacbbcbdcccdbcabbbdaabddcbcaddadcdddabdcbcdbcbcccdbadacbdcdcdbadcabddddbcadabccacdddbabbbccabdbccacccddcbbacacdcbddcaaabbbcbcaaacbacbaadcacadcacbbdcbdaabaaccbaaadbbaddcadcbcaabcabacccccdbbadaacabcabdaadabcacaddbbcccccddcaabaabdcbbccccaadabdcbacddbbbcbccdaacdcbadbbcdbabadbbcdaabdbbababbbadaddaddccdcdabbdaccadddccdcccdacaabbacccccabbbaadbabaabdddabdaabaaabdadacabcccbadbcbcdddbaadabbccccbabdaabcddbadabbdbadcacdabcccccacdccbbbbcbcbcdabcacddcaddbaaabcabbadcbbbbbadbbbccddbcbadabadcdabcbbcbdbaabdabbddcbdbbdcdadabaabdbdbbcbddbbbbacabdbddbdcdbddbccbaadabddadcbbcddbdbadabadaaacacacbacadbdbadcadccbbdcbdbdddbcbaccaaaacdddbdbddbabbccdabadaaadcccacdbbaacdaabccdbcdaaacacbbccbbdcaaaabaddccadbccbcaabbdbbdbabcddcccacaddbbbbcddacbdcccbbbaabccbbacacaddaabbdbbdbbcdadabadabcbcaadbbadacaddcadcabbbadaaadadcdbcdaacabccbdcdbcdddcacadcdcaadcbdcbadabddbbaacacdadbcddcbababcdddccbabbadacbaddccbbdbbcbcbadcdaaaabccdbdcadaacaacdddbdcbccbacdddabdaadbcbabddacdadacbbacccbbaacbbaabdcdddbdccdbbadbdbdbcdbdbabdbbdcabbadabcabcdbcddcdbdbbbacbcdddccabbcbcacbbaccdbbdcdccdaacaabcdcdacccdacccabbcacddabacbddadcdccacadbaacdbadbbadacbacbcdddddccdaabadaababaabaadcbcabababadacaabcaadbddabdbdcabddbaaacabcaccccbccbdccacbadacddcabaabbbcddbcacdacccbacdcdcabbbdadbcbababacbcddddaccbdddabdbdcddccdbccbdcddabdccccbcdaacddbaddbddbabccbcbaccaacdbbdddadadcacabdcdcaabbbdadbcccdccabdbaaddbccdddcbcacccbadbcbcbccaccdacbbaccbabdbdabadaaabcdbbdaccbcdccaddbbcddbabadaabbdbcaadddccccbcddaacbadbacbddbcadbaccadbaacddddcddacaddcdacdacddbadbdbccbddddabcbacbddccabcabccaccacbdcabaadcbcabcacacccdacdbaccdadccbbaddbacaaaaabdacaadadcaaaaccbdbaacdcbcacabcbacdbcbacbaabccbdcbbdbadcaabdcbdddbbcaaddadbbadcbbcbbcbadbdccdbddabbacdddcdadcabbbddbbdbbddacacbcddcabacaabbdddbcaccadbadcacacdabdaaccbdbcacaabdddadccbbcacbdbdabdaabadcbbaccaacbbdacaadcdabdabdcbadbaabaadddbdaabcbbbcdcadaabbadcacabbadddaadcdbcddcbccabacbaadcdcacccacacdbcbccabdddbcddacacbabacbcacbbcddcdddaddcbcdccbcdbacbbcdcbcbcddcdaacaabcaaaaabdccdaccbcadbccbadcadcdcabcaacbcdbbcddacaabadbadadbacacdacbdadccddadbaddadcacaaababacdbadccabcdaababaabcbddcdadcdadcbcabbcacdbbabdcbcbabacabadadbbbbbcabcdbabbdcdaddabbabdbcadadbccbccccacdbdacbadbcdbbbcabbacbdbdaddabcdbbbcdbcddcddabcbdddadabcdbcadbbbdabcdcacaddaacabbcadabbdccdbabacdbbacbbbcbaccbbacdcbadcdaacdbccdcccbbabaaacdccbcdbcbaddacbccdacbabcbaabcccaccabbbacbbadbcdbddbcabdbcadacacadaddbadbdcabddacbdaabaaacbdcdcaccdbccdcbcdbdaaaaadaaccdccbdcbbaaacaaabacaddbddbccbcadcabbdaccaabadadcddaddcdbcddabbadbbdaaacdcbacacabdcbccbdcbdbcbbdaacbbaaacdcdcbbbddcaadbccbdccaddadcbabbbadccbacbcabbbbdddbcbaaabaabadcaccadcddbacbcadadabadaaaacaadaaaddbbabdbcccdcdcaaadbdcaaadbbcbdcbacaadaaadcbbbadccdbbcacadcbbacccabcbdcdabcaacddddadbadbabbbacbcbbabdabacddbcdcbabadacbcdabbbbccdaacbdcbdadabbbdcbcdcbdbdddcbbdacbcadaabdadabcdbaaccddddcabbdcddcbacbcbccbabcaccabccdbbbaabaaccdbbbbdcccbddbcccdbdabcbbcdddcbcdbdddbdbcabcccdccbcbbdbcbabbdbbddadbbbdbcdadabcbbdbadadabdadaaccaaacbbaaadabadcabcabbbadbbdbbdacdacabacdaabaaabbcbbababaabdacbbccbccaccaadcacbcbacabcbacdadcccddacbaacdbdddbbdbcccdbbdcaccadaabadbbadadbcccdddddbdaddbadccdbbaadaaaccbddbbdddacabcccbbcdaccdaddccadacbdcddbbcacbdaadcccaababababbdcbbaadcdcbdcccabaabadcbaddaccbddbcaadbdbddadddcddcabacacccbbddcbbabcbbddbbdbcdcadcabaccbcccdacaaacadbdbacddcdbacaadbcdbbdbacbdcccccbaddabdacbbcabddcddcdcaddaccddaadcddccbccbadbcbbabddbbbadccdbbaaccdcacaaaddbbddbddabdabcbbccdcbbbacbcacdbccadccccbddcdccbbdbacddccbabacbdddcdcdbbacaccdcbdabadccbdcbcccbdcdbdbadbccddbcabdbcacdbbcacdbabddcdccacaddddacabbbdabdaacabddcbbbabddacaddddcabcacaabcbbccaadaabcabcbbdbbbdadbccacbbcdbadcbcddcbdacdcbccbddbbbabcaabdccaccbddbddbadcdbccdbdcdcacddccbddbdbcbcccacbacbacddbdbbaadaadaacbaacccddbabbddcdbadcadcbadacbbbacbddcdcbabdababccbaaaabbbaacadabdacacddaabccbadccccaacddadcbcbbcddddadabcaddcacccdcdaadbbaccdaaccbdccdbccbdcdcccacababcaaabcaccbbdcddbbacdcdddadaccbcdabdbdcaadcdadbdaadbbcbbdccbcadadabacdccdcdbdcddbbdbadbcddccbadcdbbbbbdabbaaadcbbadabddbcdbdabbddaabacbabbddbcaabbacdabacadacababacadbbcdcabdbdcadbbcabcdbddbccadddacddbcbcddcdcbbaccdbcddbadacbacdcbaddaaddbdcbaaacdbbaaaaddbcdabbbdcdbadaaabcdadbcdcaaccbadbdadacdadadccccbbabbaadddabdcdbdbdbccdbddbacabcdcacbaadabadadcbcaabbcabadcaadadbabdbaddbdcddcbacbabbdddbaaaababbcddadabdadccdcbbbbddacbaabbaababbaacbbdcccadddcbdadbcaadcbdcdbdbacbbcdcdbbddccbdcbabbcabbadbcabdaddcbaabddacdcdbacdcbadacbbbbabddadaaadbbbbcadddacccbaaadaaddbabbdccccbbcabdabddacdbbbccbdccdbaddaccadaddbdabbcdcadbdccbcbcccbababccadabbcdcdddacbaaabbdcaabbcbccbcabdbbabcaddadacbcdcbbdadadbaacbbdbbcabcbcbaddccadbabbaccbbdcdcdcaabcbabadddcacaaddbbadadbacadccdbbcdcacbbbaccaaccaabacbabbbccbbccccccaadbccdadacdbcacaaccacdccdcaabcbcaabaabbddccacbdcacaccadcbccbdbcdbbdbbadddabdbdcccadddaabbcadbcdbdbaabaadbccdacacccdabaabbbbdacbbcaabaadaabcbdacbaacddaababbcbddabdcacacbbcdccdbcbdaacaddcdcdabdbdcbadadcbbadbddaaccbaabbdbdaddbaccadcbadcbadbaacbaddaabdadccbcdaacdabdcdddacdcadacbcbcddbdaacccbcccccdbadcaadbbddacbbaaaaaddabcaabacaaaadbdddbddbddaabddccbbdaacdbcbbbacadbdcccdcabbdbaabcbcbbabbbaaacccaacbbabdbadabadccbbbdadcbbaabaacacdcccaddcccdbddabacbccdbdbbbbddaabbbccdaacdcabbdcbdccbdaccdddaccccadcacbdabdcadbcbcbccadbadbcccbcdbbaadbbadcbacdcdddaabadbdadbbabbbdcabbacbacdabcbdcaadbadbbcbbbddbadacbadbbcacbabababdbbbbcadbcccdadccdadbbcabaccacdbcacccacdaadcbadbbccacabdbbdbccaabccddadddbdcdbcdcbaccbcbaccdccdcdbdacbcdddadcbcbbccbbdaabdccddabdbcdccbaacbbddccabccdcaabdadddccbbcdbaaccdcccadbaaddbccacccdbbbdacdadcbccaabcbcabcdbccdacaacbdcbcbdbadabdabaddcaacbbccadabdbdcbcbbdcadcbdaabddbadddadbbbadcacadadcacacaabddacbdbcbaaadacdbabdcdcdabdbbbabdadddadddadaccbbbddddcacbbbdcdcccdddbbccddbbdaaccbcbadcbcdbabaacbbbdaddddbbdcaaacadbcadbccdcbaadadddcdbbdadddacbcccadaaaaacabcabaabcbbcbabaccccdaccbdbbcdbbcdcadabbddcdccdcbbaacbaddcccbcdadbabcadbddbacacacbdccbcabaaabaaaaddbcbccaadaddacbaaddbbbaabdccbdcdaadcabaababcdcdcbcdcdcdcdadbbcbdbcadccddcdadacacdcaddabbabbaaaadbddadbbabacdcddcabdbbbdcadbccababbaadbdaddbbadcbdbdcbdbaaaababbacaabcbbbcabddccdcaaddddaabadcbbaccbbdaddbcccacbaddbdacbbbadddbdabbaaadcbacaaddcbbacaaccdddacccabaddaaccabbbcdabaabaddcbcaadbdccbbccbababdccdadcdbdbcaabcdccddddbcaddcbdddadacdaabdcacbccbbbccdcbbdaaabcabdcbbccbacadbdddddddaddbcdcadbdbdcccbdcccdbdabdcacabaaccbabcbbbababbdbcdcaccdadbaccdabbddacdbbccbdadabcadaddaabcbcdaaccaaabbbaaccacdbcabacccbbbbcaacbacacaacdbbbcaddcacadabdcabadcbdbdbadccbdcadbdbaddcbbaacbdbdcabdadadbdaddbbddddabacdbbbaaccbbbdbdbddcdbcbabbbcaadbdcacdacababcbcdbbcdcbccdbbcdbbddacaabbcdccdcbadcdcccacdadadddcbadadacadcdddddadbcdcdadbabadcdaccbbdcddcbcdbbdadadabcbbcddadbaabbabbbacacaddaccaacacbacdadbbadabdaaaaacbcbbaadacddddddcbbabcabdbbabbbbdcbbaacdbdbacbabbdaaadaddbbbbdbcdababcdbccabaababaaaddabddcdcbbcdadcdbcbcbcacabddcacdddcdbaadddcaaaacacaccbbdbaccbdccccdaabdcdabcdbdcadadacacadbaacabcccbaaabbbcabdbbdaddcdcabcbdbdabdbdaabbdddbaccccababddabdccddbbababadabdcbaaaaaaaacadddbbdcbdaadcbdccbddcdccbaaccacddbbdbbcaadadabaaddabcadddabcabcdacadabdbcaacccdcddcbcaadbbbdcadadbbbccaccbdbbdadbcacabbbabcdbbadbdbaaacabcdaddccabcbbbbabdcadcbbaacdcdaaddbaacdbdbabdadacbbcbddbdccdbacdadbccddccaaabacbcadccaacadabbccdbdbbabbbaccdabccabbcaadcabadccbcdabccbbcdccdcababbcdabcabbaabaacbdaadbadbcdcddbbdbacbbabbadbcacdbcbbbdbcadacdcdadbcbbddbcccaccbbbcdadddcddcaccaaadbdadcdcdcbdcaacddbddabdabadabcdbbbdcbbbdccaaccdaabcbccabbbddbcadaddbbddadbcabcaacccbdccadacbccbbbbdaddcddabaabcbabcaddccbbabaadbbdaacdbbcacdcaddadcadaaaccdbdddcaddabbacdbbdaadacaccacbdbcddabcbaabbdcbaaccdaacdaacbbcddcaacaadcbdbdbdddbcacdadcbaaddcbbdbaccbcddabcbacdddbbdbbbcccdcddbcccdbacddccdbbabdabccacbaabcabcbcbacaccdddacbacbbadbccbdbabcddcbdcdbaddcabbcadcacdabaacbacbbdbcdbdacdbaaddcdacbaacbacbccaadbadacdaaadadaddbdcdaacbabcddbccdddcacbbaadaaddacdaadadccbbbdccbaabaacdabdacaacbabbcdcbbcbdacabcadbdcdadaacacbcadabdddcbddccadcdadcdddbadcbbbbcbdadccddcccaddcccabcbbdbbccbbcdbbccaadcdbaacabbaaaaadaaaabdbccddcabccccacdbbdcdcacbdccadaacacababccbaacadacbbdadacabdddcdabddcaccadddbdabbddabbddadbcbcddbbbaadcbacbcaadcbddcbbcdbdabadcdcaccdabaddcdbcbdcddaacabcddddccabdbaaadaabacdcccbbcccccdddbddbbccadcbbadbaccaabcddbbcdcacddbdddbbabcbbdabdacdaccdddbbcbacacacbddaddbdbccadbcdaaaccbdbbdbcdacbdbddcaaaadbccbbdccacccaabdacadcddbcdbacdbadcdaddcbbdbcbbaabcadabbbddaddddadaadddbacbaaacdbcdbbbabcbcddababdaabcacbdccaccdbcaddbadaababdbacddbccaaacaacaaddbcdabcddccabbddacdccabcdaaaaaccbbcdadaaaaabddcdcccadaccabbdaddcdcdaccdbbdbdcdcddccddbbcddcddcacccdaacdcbabbcdbadcbbbaacbdccaaadcaaaaddbcccababdddaddcacbbcaaddddacccbccdacbbaacbcbbadadbbdaacacbdbabbdabdcaaadcbadbabcacdbdccaacaaaacdbdcbdccddbdbcdcdcaacdabcdbdadaaddbcbcbbddcbddbbcdaadabcdabbcbaccaaabbadabcbaacabbdcbcbcdacbdabdbbadacbaadccaddaadcbdbaccbadabcdaaacadcdbabddddccaabaccbdbbadbccbdbcaddbdcbccaabbabbccabddccdbccdbcbbcacbbbcdbcdcaacadbbccbcbdcddbdcddcdaacdacadbddcaaacbddcccbdbdbaadbadbddcabcadbbdaacbbdcdcbaadbddbbcbdaddaddbbdadcdbdbcaccbcbadcdaacdaadbaacacadcaabddccabcacaadcaaacadadabaddccdcacaabbbaabdadbbbdbacdcbabcddadbcbbdbcbddaddacccdbaddbbcadcdbabdbcaaaddacdddbadabacddacaadbbdbcaaabbadacddbabbbcaadacbbaabccbadddcaddbdcbcabaacbdabbbacbccacdbadccabcbbaacccbcabbccaddbabbacddcdbccacabbaadaccddcbdcccabbcabccdaadadabcbdaadbabcbabaccadccdcddbcacdddabbbccdaacaaadacdbcbabddaccdbddaaabaddcbaacabcccabbadaabdcbbbbcbdbcccdaccabdbdaccbabdbbdcbaaddcabdcbbcaadcadcacbcadcacdbbdbcdcadaaadbaabaadcddadcdabdcaddccdccadacadbcadcddaadbacdbcadbdbcdbcdbbdabaccaadbbcacbacbbbaccccaaaabaaddadbcacdadbdbdbdaaaaadddcbaaadcbaddbbbdadaccdbadccdabbaacbdccbbadcbacdaabaacbcbadadbdcdddbcbaccaccaaaabadcadabdabcddaddabbddcdbcbbbdbadcacdcadbcaddbcdbaadacbcabbbcdbccbbbdbbdaddbaacaabdddcbaacbacabcbabdbbbcdabdcddbaddadbcaaaddaaadababbddddbadacadadbbdbbdbabccbccddbdcdaababdbdcadcddadcdacbabdbccbbcdcdcbbbdbcdcadcdcacddbbbccbdabcadacbcccbcdbcbcdaacbbbdadbcbdcabddbaaabaccdbaabaacbbdadbbdbdccaabbcdaacbadadbbcacddbdcbddccdaadcadddcacadacbbbbbcbcabacbccdabccdaabacdbcbdcababbacaddcdcacccabbddcbaddbadabbcbaadaaaaaaadadabbaabcbcddabaaaaaabcdcbbccaabcbdbbaacdcabbacabbbacbaccbcccadddcdaaaddabdbcaaacbcdbcbdadbdbcbacaddcbccacbddacddccbdddcbddadaaaaabbbbadbcdcbbaacdccabbccdcacaadcdcacdbdcdcccbcdbccbdacdcadcddcadaccdabaaaaddaadcbbdcbababbdadbddccddaaacdcbcaabaddbadcacadcdaccacacbcacadddadbcaccdcbcdddacbaaddacbabdcbaabdacabaaddadccccadddaadcabacbbbadcacbddcccbcbaabcaadbaadabdacccccddaddabbbbbbabacaacaaaacbbaaacddcbdcbbbaabbbcaaddddabcdadacacbaccbdcbcccbccbcaddcdabcdcddabbbabaccacdbbbcabacbbdbdcbdcbcacbdbdacbacbdbddaddacdddaabdccddbbbcbadbbacdabccdddcdbadbdcadbcadacdccdbcbbbcbddbbcbdbaadcbcbcbbaabcbaadbbcdcaacdbbbcbabdbbddddaccbbccbabbbcccabcabcadbccdbccbcadbbbdaaacaaadaabaadbbcbccbadcaadacacddacacdcdaaccacaacdbcdbacbcdbcbbbbbcdadaabcdabdcabccdcbbccccbaddddbdccbcbddaadabadbaddcdbbdcabdaaccccaaaaddbdacacbabacbdddddbabaadddaadbabaacdbabadaadddcdaacacbacdbbaddcdbbbbdcdccbdcbbacdaccaaddadcbcdddadcbabacaccacbddddabcdacddadcdddbccbaadddbcddbbacbcacdaddcccccbbdccabddccdadadcccbcbdcdddcdccbccbacbbabadbacadcbccabbddccbdcaccaaddcbadbbaaaaabbdbbbcdddbbbabccaddaccdbaddddcbbbdabcddcddccbbadbcababbcddabcbdccdccaaababdcabbbddadacdcdcadacdcdaacbcdcbdcdbbddddaccdcabbbbbdabbbdabacbbdaaadddadddddbbbcdccabbbbbadcdbddbcdbaadbbdcaccbbdcbbccbabaacaddcbbadbccabbcdbdbcccccbbbbccabadcddbcacdbbaabcbcccbdaddbdcbaaadaddaacbccbcaabbcacbccdadaaacccccbabbcbdccddbcddacdcbcacacddbabdcabaaddabdabbbdbabcadbbcbaabdadbdcdcdbbbabdddddbbdbdddcdabaddacccdbadababacdadddadcacbdabadababbbbbbcdddadbddacbbdbcbbbbcdcbcbddaacabadddcdbdbbcaccccdcbbddadadbdddccdcbbadaddbcadabcbbbdcbbbbadbbddaacabacdaadbbaababdddbdadadbcdcddacdbaadaccdbaccccbacabdadddbdbbccaabbbbacdabdacacaabbacbaccaadcdbacbabaaaddbaaccbcbbdcbdbddadcbdbcdacbcacbcaabaabaddadddbbbbcadaacdcdbbabdccbcdbcdbbbcaadbabbabcdccaabacabacdcddaaacdcdaaacbababacccdaabcbbbbbdbcdccbbcacbbdddddbcdaccbbbcdcddbddcdbbcaddbbbddccacaaadbbabbcadbdddccbcdcbbdbbdabcccdbbdccddbaacdcadccacccbbacccbbcadcacbacbdaacccdadbacccbdcabdaacddcabdacaacdbadbacdbbdcadacbbacaabdcababaacddaadcdbddbdbbdabdcbabcbcbbbdcadddadcdcdccbdaaacdbcdbcbacccabaccbacdabbcabcacacdcacaaddcabcabccdbccaadcccaaaaacbabaabdbbcbdabbcbddccbbbbbabdbabbaaacdaddbdccbaccdcadadbdadbabbddbcdbcdbdcddbbdcdccacbbdcccaadbdbbcaaccaaddabccabcaaadbcbcababadcbddbdcdcbbcddddbddcbccccaaacabddbbdaabbaacadcdcccbcabadccbadbbacbdaadabcdaaadabcbbcdcbabccaddddbabacbbaccdbaababdcccccdabbabdcbccbbcabaadacabbdadddddcacaacbdbdbdbcbdacdcdcdbaadbbcacddcdacbbbddcbcadddbacbaddabcbacbcabbddddcbbaadacdcdaababacdccbcbccabbbcacdcdbbbddabaccbaabddcbcdabccdaabdbdbbaadddabdbdbcacccbdbcdddbdabdabbbadbbdbbcbbcdcbcabddbaabaacdaadabacdcdaddcbbdcddddddcacbdcbbbdddcbdbdbccdccaaddbcbdbccdabcabccaccdacaabcbaddcacccaccaaaacdaaaaacaaabaacdddddcccbaddaccbcdadabbdddcbdadadacddbccdbbacdadbbadbcadabbbbbdccbbcaacabacbbdbdaadcbccdabbadacbdbdbcbddbbdccbadbadddcaabdbbabaaddddcaaaaccadaddaccbbabbdbaaadaadddabdabaabdadcdcddabddcdcaadcbbdcdacbdbddcddbcacacccdacbdcddcbcdacddbdddcbbaaccdbabacbaaacdbadcaaaadccdaccabdbdbcdddccaccbddbbbcaabcdacadacbcddbacbaaccadabdabbbabdaddbddcbbdbbcbacdcdacbccdcaaaccbbcdcacbcdaacbbdbddccbdcdcacabccadabcdacbddbbbbcbcaaaabcbbbcaadacbcddcaabbaccbccacaaadaddabcacdcbbcdbcbacabcadabdbdabccadbabbdcabccbcbbdbcbacdbdbabbacadddbaaccaacccbcacabcdbcbccbaaaaadbbacdaadabbcbcacacdcdcaaadabdbcabcaacdbdcadabbddaadcababcaaacbaacddcdcabdddbdacbdbbdcddacbadadcbdbaddbacccdcddcbbbddbdbdbccdacbcabdcbbccdbbbbdddbacddbadcadacacdaaddbbddbdbbacaddcbbdbbbdcddbacabbbccdcadbadcdbbcddabcbcdbdbcbabbcadcbccaadaadbcdbdbbbabacbadccbcccbcbbddadbcccaabdcbabbadabdbabbadbdcaddcdaaaddbcabbcdaacaaccbbcbaddaadbdcadbaaccaacbbbbdcbbaadbdcdcddbabdbdaaabccbaadacbdaccabbbcaacacacbdddbacaacbccbbdccbcddcbdaccccbbaadbaddcbcdcccdcbacbcccbdbaddabdaaadbbcccbdcabcbbbaabadcacbddcacdadcbadbccccaabababdbcaaaababdacbbdadadaacbcbaacabadcadcadbacbadadbdcbdbababbdaccacabbcdbddbaaaacabdcdcdcddbaabcdddcbadaaddabdadacabdccaddcaacbbdcddcacbdddbdcccdcbcabaabbdcdabbcdadbacdcccbadaacadbccaccbccdcbadbabcbcaaacbabdaabcdbbdcabaddcdabdaacdccababbdccbacabbdaddbddcbdabcaadaacdcdcbbaabbbdbdadbdabdddbbacccabababcdcdcdbaaabdbcdbbbbbbaaacbcabcbdbbcacdcdccdbcaadcdaaabaabbdbbdadaacadadbddbaacbcbaaddbdbccdcbdabadbdabdadbabcdaacddbaabbdbccacbbdadddbbcccbccaddcbcbabcdcbabdccbcbaddaaaaadadbbaccbdacbdbbdbdbcbbddbbccbacbbcbbdcbcbcadbaabddacbccaaadccdcdbdccadcdbddbddabacaddccdcdabadddbadabdccbbadabbbcadcbabbcbbacccaadadddadcaabdbccdadddbcacbdbcadcdabcdcadbdcdaddcbadcbdaadbaaaaaadcbcbccccccdabdacdbdaacdcabcdddbcbdbccbacddcccdacccdcbbadcbccbabcccbdcabdaaccadaddacbbbccbcbaacaddbaaacdcabaacdaabcdccaadbcddadaabcbcaadccdaabbbdbcbadbadaadddbdbbbcabbbcabcabdabbdddadcabacadccaaaddadcdcaadadacccbdabdcbbbabdddcbdccaadabccdbbacbacacbccabaaadcbbdadddbacbddcdcdabaadcdbddaddbadacdaaadbdcbacccabcbddcdbcaaacccadcdbbbdbcadcaabdbbdacbcacbcbacbdaaabcbccbbddcbbccdabbbdacbdcbbcbbcadbdbcdacaabccaabcbaabdacbbbabacddbbdccdcaaacccabbbaaadbcbacccdbcaacbdcabbbcaaaabdbabbcadbcaadbbbbcadcdbcdaabcaadddddcdabcccbcbbacdcbdadbdddcdbbaccdbaadddcbabddbbcbaacccabccbbaaababbcadcaddccacbdcdcabacaccdcccacabddabbbddbacbcaddcaabacacbddbccbdabdbcccdaabdddbbdabcbadddcccccddbcdbbbccaaccdbcdcaaacbddcacbcbbcdbbbadadadbbbadbbbcdccadadccadbacaccccbcbaadddaabdcccbaaccaadccadccbbababbdcaccaabacbbdcccaddcbabcabccaabdbacadacbbabbdaacddcdcabccaddbacddcddabcccddcbdacbbcabadcadcdcbcadadcbdacbdaabaabbaadabbaaabdbaacdbcbddbacddcaacdabaccbbaabcdcbddddabddccaaabaacaddacacccddbaaaabacbbacbbddbadbabdcbddaabbcaababbbaabcbbcdadaddadabacabcbbacbdcabbdcbcaadacaadbccaabddcbddbcbdcaadcdcbcbaaaccdcacbddcdbdcbdaaadbacabcbdbcdcabdbbbabcdabcbaaababcbabbccccdadaadddbddddacacdcdccdbbdadaaddddddbdbddbbcbbcacbbccdcbbcaddaabdaaccacadbdcdaaaabddcacdaaddddccacbadaaccbddcccbdaabdcbbaadddcdbabccabaddacacccadcbadadcbacbababcbabaadabbbcdabdbdcddabcbbababcdacddbacbabcddaddcdacdadcabccddaddcaddddadadddccbcddbbcabbbdcbcdddbabaacadcdcbccbddbaccddadbbcdacdddbadccdbdcbbadaabccbaaccabadcbdabdaadcaccbbcacccadabdcdbbdaabbdddcbcdcbbadcbcbaacbbccbccabbaddcdcadbaddbbabbaabbbbcadabbcdcbdaaadbcaadadcdcbcbabccddbacdcadccabcbaddcaabbabbdacabbccdbcbccabadbbcdabbbaddcdbaaddbcbdbbaaadcbdacbcaaccbdcddcaacdbccaabaddddbcbdbbdbadbdbbadaadbdacacbacabdcdcabddccacaaaddcaddacdaacbbdaddbcaaaddddadadcdaddbcbcbdbbcbdddabbddabaadccabcabaccdddaabdddddcddbddabcdcdcaadccabcccbcabbcbdddcbaadadcbaaabdcbbadadabddcbdcdacbcdbaadbacaadccadcdccddccbacaddacbbcadadacdcbbbdddbbcdddabbbbccbadadbdadabdcbdbabbcbadbbbbdbacddbbcdabbcadacdddbacdcdbdbabaacbcdbddbdabadbbdaadcbbddcdbadbacdbccaaddbbaacbadabcbdaabcbccbcdbdacbbbdbdbcccbcacadabbbaddbbddbddacbccdbbbddbacddabbcaacbcabdbcdccbabacdcddcbcaacbbaddadccacabccabbdbbcddadabaaacbbabbbaddbbadcadacababcadbabbddacabadbcaaaddccdaacbddcacdbdaabcccacbaadddcbdcbadacabccdcdcabbdccdccaabcbddbdabcdcbadddadbdcbdbbcadacdcdcdbbacbdadcbcbbbdcdcbdcdbadcbcbcddbcabadabcdbdcbdacaacdddbbcbdadaaaddcbdbacabddcbbbbbdcaabcbcbdcbaaadacdaccbababbcdcaadbabbbddbbbbdbbcbacdccaddbdcacdadbaaaabccbdacbcdbdbcbabcdcbbccabcaacbbaacadcdcbbdcdbcdacddddaaaddbcdbddbaccbadccddbbbcccdaccbdababacabcbcdbabcbbaccddaddbbdabbcaaddcabddbabcbdcadcbcbbbbccddbddacccbbcccdabbddadbbccbcaaccadabcabaccbddadbcadbaacdcbbacdbcbdabcaddadddabddabbdacdcccbcadaaacccbbdaacacdbcabacdadcdbbcdaddcacadbcbcbbccdbccbaacdccbcbccabcaacbaccccdadacbdacababbbccabddbcacccbbcbcdbcdccadbadcdcbddcbaabbccacadaabdcaabbbacbaaddcacccddadccadadabcdcbcdcacadacdabdbddabdacdddddbaaddbdddcacaadcdbcbbbbcaacaacbacbabdbbbdcbbccadbadcbbcdbddcadcbcbdddccaaddcbcdcbadccabbaddddbddadccbacddbcddcccbccacbbcbacbadcccbdaacbddabbbdaadcbabcbaddadccbddbacbacaacbbbaadbddaaccdacdbcacdbcdcbddcacccacacdddbdbbdccaabccdcbcaaccaadbbbcdbcdabdaabbbccccabcbcbccadaccaccacaaabbcacbbbacaacababbdcbabadbddaadabdbdcdddcdbadddaaccacaccabdbaddccccbcbddbbbbbddaaadbdaaccdaabbdbbadbcddadbdcacdabdcaaabaababcaaadbabbcccbbcbdcdddadcbcdbcddcbacbbbadcadbbacccdaddbadcdcdcacbdbbdbdadccaccaadcbbacabbbccabcabbbdcdcbdbdaaaaacccdddacdcccbdbccaaddbddacdabaabbcdaddcaccdaabcaacadcccabccbdbcabbaabacaaacddabaddcdaaacbbcadbbaccaccabbddacadadcdbaacccdabcdddaadaaabcaddabbaddbbdbaddaadbcbbcaabdccaaabaabbbcadabbbcbbcdadcdcccbaccdccaaabbbdcdccdabadcbdbddccccccabbbaacacbabcdadaacababbdcbdcbabcbbabbadaabbdcbdbcabaabadbccccbaadcbcdabddcdcacaacdbbdadccaacbaccbaabadbaacaddacdcadcdcacbdcdabaacbddacbbabbdccbccbddcdabdcdbbddccdcbabbdddccccacacadabadccdccbbbdacabbcadddccacbbdcbbbcbcbdacadadcaddbbabdbcbcdababcdabdcacaddcddbabbcccaddbbdbbddaaadcdcccdbadcbaaacdbdcddacbddcddcabcddababbadccbbdaacaddaacadcdabcccdacbccbbdcddaabddbbabaddacdcbaabdbbcdcbcccabbbcbcabbabcccdcbbdacdccdadddacddaccbabadcbcaacbddbacbddaddddbdbdddcaaaadcccbdabdbcbabbcaaccabcbbabccbdabbadacbcadbaaaacbdbcddaaadcdbcaacdbaadabbadbacacbcbacbdcbbaadbbdcbaabbbbdbadbbddbccadcddaaabdbdcaaabdacbadbaccccbbacadccbbdbddbbcdcdcbbadbcccbdbacacbddcdcccbdcaadccdaaddbdccdddcbdabcdccdcdcbaadcbaacaacadbcbdccabbcabacbbddabbabcddbcabdaadddadacccbcabbacdadaaadbdaabddbdddaaacddddadabacbcbdbccdbacadadbdadccabcbbadcabbbacbcbbadacbcababcaabbaccbcabbadadcdbbcaddadbbbaadadaabbddccacbddcabaacdcbdaabdccadacddadbabbabadcadaccbcccdabaacadcbdbabcccadbbadcaadaddcddccbddacdcccbabacdcbbaadadcdcbdbabdbcdcadccbadabcbacdcdcdbcdccadccaaacacacbdacadddbcdacdbabcbcacdaabdbbaaaacbccbdaabdbdcbbbbcaaddddddcadacddcccbdccdaccacadcadcaccaaaabdbabdacccbabababbbaadcdcabdbcabccbcbbccccbaabadcbcdccdaadabccbdccdbcccdcdbaaaddaaaadcbbbddddcacbddbbbaabacbdbabaccaaadcadabcacbdcccbacadcadddcaddcbdacacbdbcadaacddadbccddcdddbcddddcaacdcaabbdddadaaacadcddbacdbbbabcddabcadbbcddbaddbccdcdbbbadbcbbbaaaaaadabccdbbbbdcbcdcddbddcdaaaacacbdadcccbaabbadababddbdbcddccacacbbccaaddadcddbcdcaaaabddcccdbadacbaacadcbbdcbbcddadacdccdaacbbbddcbbaddacabddcadaddcababbcacdccdbccadccabdddbbcacbcdbdbbdddbcaacdaabcbddbacaaabbabbbbaababcdadcdbdbddcdabacaaccdcddcddbadbccbbbabcbadaddcddbbadaddbcbdddcbabccdbacbaacccbdcaadccddacdbbabadcabbcdbacdaddddaddaacbcabbacdbabcabbdacbaccdbcdcaddbdcddbadbaaacabbcdccdbaccdcbabcdacdbaabacacbadcbcccaabccadcdaddbbdcdbcacbaabababbbbcacbacbabbdadbbbdbbbabcdacbabddcadbcccbcbdbacbaddcabaadaddbacaddcdbcdbccbdbaadbbdadcbbbacadbaddcacaabccbaadaccdbcbccdcbdbacbbbcaaabdcdbaacbcdbabcdbadbadbcadddaaccdccacdbbcbcadddcaddbbadcaccccbcdbcbcadacadcdcbbddaaccaccabacdccacabbaabdabbcddcdacdcabbaacdcccadcacbaccbdabccbcaabadbdddacacdcabddbdadbbadcddacbdbaccdacbcabbdbaccadddcbacaddcbbccdabacaabaaddccbddaacbddabccdbaccccaddadaaabdadcabddaaaccbadaddaccbcdcccbdcbdbbcbbbabcddacbdcabccbcacbcaabaaaccdaababcabaacaadbdbcabcbadabbcadcadcbcaacbbbdbbcdccdcbbccbddaabdabddcccdabcadadaaaadcacdcadbdadcbadcbccdcbbbabaadadbbdacccdacccdcbbcacbaddcbbdcabccccbdcaddbdaacabcbccabdbbdcdcadccbaaddddbabbbcdccacadaadadbadddabdbacadaddbdcbbdbbbcbacabbbbaacbdcabddcdaccddadbaadabcbcbaddbaabacdccdbacadbaabddacbcddddacbcdddddcbddbcadadddccdabdabbaaacdacacdcbaccaacadbbbbbbbcbaacacabbabddbaddccbaccdcdccbcdbaacbacacbddaabdacbaadbdcbabcdcbdbbddcbccbdabdccaaddcaacabcacbaababbbcccbadaacadbaacbbdbadadaadcdbbacdacbcdddbabcaaccdbacadbbcdbbcddaabdbcacbdbbbddbabcadcbcadabadcdadababbcaccdcacbaccadcaccddaacddadbcadbcbbabdbdcdcacaccabbdabaaccaccabcacdbbbaababddabdbddddcbcdaacbcdcbacddaaabbdbdcdccddadddddcdaddaabddadadccaacccbcadcdbcdbabddcbccdccbbaacbcacbadadddbbdddddbbdddcdccdbacabacdcbccbddbbdadbacbbabddadcddbdbdaaabcaaaacacbcabbbbacaddcdbcacbacbbcddccbbcabdbcbcbcdcabbdbaaccdcbbdcaaaccbcbadacadcccbdcdcdccabbdcbcbaccdbddbdcbddadacdbcbdbadbcddaabdcabcbabccbddddbddacdabbdcbdcdaacaabcdcabaadcbcbacccadddccbabaacccabbbabcaaacbcdbabaaaccdcdddabcacdcbbcdabccaadcddacccdbdcadaadcacaacadccbccdcacbcbcbcacbaacbcacabacddbbdcbcabbadddacbcdcbdaabbbdbbabaddcbcdadddbcdbdbccbdaabaddabbcaaaacaaacdaacaaadcdcbdadcaccbaccadcddadacbbcabcccabdcabbcaaaaaccdcddddcbbcdccbbbbadbacdbdcdaddbdabcbcbcbcabdaaaadbcbaabcacbbaadadaaccbbcadbcddbcdacdbccaadadcccbccddddcbbbcaaddcddcbdbcbddcadaacabdcbadbbbddcaaaccbdabbaddbdbdacabaadaccaabdcabbcddcadbdccbdbbbdbaccdbabaacdaaaaababcabddabdccdbdaabcaaaaabddbccabbcdccbdabdcddaacaabccccddbbddcaddbdaccaddccaddcacadddcbaddaaadbdbddabdddbddcccbddddabdadbbddbdcddbccdddadcdabbaccaabdbdccbbcdbadcacdccbbabaaaddddaacdacddcdcdcaacbcbbdaadaadccbadccacccbaadddbbbdacdaaaddacbaacbdbaabbbcccddbdbbaadcacaccacacadbaacabacbcdcbaacddacbababababccbadabddbadbdddcaacbdbcccaabacbbcccaaaaadaabadbbdccccdbaddabbbbdbacaabaaabdadcdccbabddccdbdcabcbabbaddadbcbccbbbadccabcaadaaacaadcaccabccbdabdddbcacbcccbcdadabcbbddbcabcbcddddabaadddaabcddcbbdbcbdccbddacadcddcaadbbbdacbbdaacadddbddbdcdacacaadabbbcccababcbddcddbbcbadadccaddbbccdbbccabbdbabddbacccbbcddcbbaadbabdabcdabbcddccbabdcadbacaccbbbdabdccabbabdcadcdcdbbbbdbcacbbcccbdabbdbbcdacccaabdbcabcbcccbdacbbccbbdbdddbccdcdaccadcacbdadcddccdcbcbcdccbbbbbaaabcdcdaccccddadadcdabdabbcabddccbdbcbcadbdacaaadccacddcadbcdbaadbdaacaaaadcdabbdaacbabdbcddbdaacacbddbbbbdddcbcabbdabbdcaacccadbadaaddaabbdcaabadbaababbbcaddbaaddccdbdddcdabaacabcabcbdaaacdbdbcbaacccadddcddddbdaacacadabcbabacdadbdcabbbddbaaacbbdabbdcddcabbbccdbcbabccdddddcadbabcccbcdadcdbdbadbabddbccaddcbdbcbcacdbccbdbbadaddabbddbddcadaddbcbcbabcacacbaacbabbcadddcadacbcaacdcbadcbbbdccdacaacdbacdacdbbdaacbdbadbaacdcdaaaacddcadaabadcaddaccbdabacddcaccccccbcbdacdddbdcccbcacabaabddacaccdbcbdbcbddcadaddddbcbaacbbdbaccdadacacaadcabddccdbacbaddcdbbddacbbcadddbccccbdbbbbcbbbcaccbcabbaaaddaabaccbbdabacdbdabacaabccddaddcdbdcacdcbdddbccdbacddddabbcabdcaaccabdbacbcccdcacbcbcbcddaddbaaccbadadbcaddcbbdadbaaaddbdddbadbaacabdaccaacabcadbabbacaacdbddabccdddaabdddcdbacdddcbcacdabaddbaddcbdabcbabadbaadacaddbcbbabdaacdbdbdbcbcdaabdabadbcdddcdaaccacbbbadabcbcddddaaabcbabadabdcbddbbadbdddbcaabdbbacababbdbdcbaaacbddabdbcdcbcbababdccabbbbcacccdcdcbbadabbdbcdddabbdddbcdbbadcabdbbbdcadddbadadcadcccbcbacababcaaabcdbddabddbbccdaddbaccabcdacbdacbcbacbcbdaadadacacbdacdbcabcbbaadcbadbadacabbbcbaadccbddcaabadddabcaaaccbccccbddabccbcaaaabcaacabddcacadadccadbbaacbbccabccbdbbbbdbcabbabdbbbaacddbbcdddcbddcdbbccacbaaaaddbadaccdbbdbbadacbdbdbdaacdcbabbbcdaddadcbbdcaadccdadacbcaddcabbbbbdbcabdbabbddcddbcdcdaccabcaaaacbbdabaaaccbdabcaacabdbbddabbcdccaabbabbbdabaabcbdccdabadcdbbadcbbccacacdccadabccaacadbaddbdacabcdcabbcbbdcddbdaadccbaaccbbbcdddbbaddaccdaacdbcdbaaacadbbdcbdaaddbdbcdccaacdabddbdccbbabbbdcabdbbaddaacabdbbacddbcaaadbadabdaadcbdccacbdacadadcbbdbabbcbdbbcbababaacbabdbcaaccbbcdadddbcaacbdaadbdbcabaaacddcccaccbbacdbbabddbdccbdcbddbdaaaabcdcabcabbdbccdbdcabccdcaabbaaabddcbcdaccddcadccacbdaadbbdaccbadcddccadbdbdcacabbaddcdbadcaddabdbaadadccdbaadbdaadbdcdaacbbcbccadcadcdcddadcbbdccacadcadbdbdbcccddadabbcacdabaabdcdbcaadcadcbccadbbaabaaacacabbaddcccaacaaacacbddabcdcababbabbadbcbdaaccbbbababdbddbdaaabababbcadaabddcacbbbddccbbacdccbdadddcbbaadcaadcdcadaaadbabaccdddcbbabdaaccdbdadddbbbcdbdbcaaaacadcdadaccadcaabddcccadbbacdbcaabdaddbbbaccccbdacddaddccbcbddbdbaadbdbcdddbcaddbdcadcbdbcdcdabddddcdbbdbbcabdcaabccaccdbacabaaacbcdccabcbbdbbdbdcccdaddccacbbadaadbcbcccbbbcbaaaabacabdbbddaaddddcadddbdbbdaaccbbdacacdadbcdbbbbbcbcbcbdaadcbcbaaccccccacdabddbcddacbbbbaaccaadcdbcbddbacaaddabdabbaddcbaaddaccdadccaabddddcddabacdabbcbcbdcbcacabadadaddbdbaccccaccacadaaabdadcbdcabdcddddabaccbbabdcbabbaaadbbbbbddbccbcbbdbbbbbddddbcdcbbdbababbddbdacbcabcabbddbbcabbdcdddccdcdabdbbaadbcbdbabbdcbaaddcdddccaccbacaabdabcbdaaacdabacacaccdbabbcadcccbdadcabaabcaadbacbbbbbccdddadabbaddcaacddcbaaacdbabdbbbdbccbbdcccacaadcbcacbdbcdacdbbbbabadaabadddbcdddbaccdadaadabcbdabcdccaaabbaadcbdddcbaaacacadcbccddddbdbdbaabadcbdcdcdbcbccbcdcdccddcaccadaadadadbccdadbabddababdbddbabadcddccbbdadaddbccbdbbdbcddcdccbdbacccbbdaccbdcdbbddbcaddacaabbadabbccadacdaddabcddbdaadbabcbbcdcbdcddacbdbcccbdcdcdacdadaccdcaddabddabbabddabdcbdbbbbdcdcddccaddddccccbcbdbabccadbddddcccbaabbcadabcbdccdcbbdacdcdbdbbbdbaadaccbcbdacdccdcacbccccabacbdcabdbcdbaacaddadcccdddadabddabdcaddbdcaabaaaabddccdabbbcddcbabccbdbcbcbbbbcacdddddcaabdacaccddbdcbbcccdbbbcbacbdbdbbabdadadcdbacaaabdcaabbbabbbccabdbddcddbcbacacbacbbaaaadadabdbbcbdcdaccbcddabadcadbcdbaaacaadabbddaabbcaaaaaacbcccdccdabdbbdbbbcdacbbcccbcdddacbcddbdbccbbcaacbadbbdaabccaddcacdaadbcccbbadcdddcddcbcdcbacbbcdabbacbbaccadbbbaccddbaadbaabddcdbbcaabbbddbdabacbcaaccbcdbbbbbdccddaddbdbccbcbdadcdcaddbbddaaadcbaccaccddadadacaaddddadacdbbabdabadddabbcbdbabdbccbabdbababbacadbdaacbcbcbbbbcabbacdbdbdabcbaccabadddbacbbbadcddbabbacaaacaddcddcbdbcddcabbccabcaacadcbaadadbbadddddbccababcacbacbadbcbdbbdbbdbabcbbddbbacdacacdbccabdbadbdbccdabaacdabaacdccdddcbabddcadcccdbddaddbdcdadddaadbbdaccadcdccdbdcbacbbabccbdbbbcdbdcacdddcbdbdaaadacbcadacccdcacdddbadaccbbbabadabaddddadcccdbcdcdcadabaadcccdabcdcbaababcaccabdbaadaaacaccadbaabacdcbcbcccbdddadbccbccdbcacdbccddbaacccacabbaaaadbdcacbddbdbaaaaabbbbdcdbcddacaacbdddacccabdcbaabacbbaddbcadbccbcccaddbaabdbcadabdcacabcbababbdaaccbccacdbddbddaaababaaaabcbbccddccdadbdcabcccdccdbabaadbccbdacdbabddbcdbbacaaaddbadcabbbcaccdacdbddbaadcaccbdacadacabcddadbaacbbaaddcaaabdacdcbacccbacbdbadacdcabbacdaabbbdcacacdbbabadaabaadaccadaabbdadcdcaccadaddcdabcbcdbcbcbdbccdcbcadbadbcaddcdbbbbbaabbdcaccddadccaacbaacddcabdabdadaaaaadbacaaddadccaccbbdddcbabcadcdbccaccabbabddacaaddaccdccdcddbbabaadadccbcabcccbbbcaadaabdcccdcabcdacbbbcacdaacaabdddcdbadaaabbcdaabcbadbcbccddbdbabbdaddddddbbbdaabdcccbdbbacaaacdcabccabbdccbbdadaaadcbbaadaccacdcaccbbacadabddbcaddcdbbdabaddbdadacdaaaccbcabacdbdaacabacdcabaabbdcdbbbbaccbcabbbdacadacabbcabcddcbadbcbadbacdcaabbabaacaaccaaccccbabddcdbabccdcccbadbbbacdaaacabbcbbaaccaccddcdabdcadabccabadcabacabbbbadacbbabaadcbacbdccdbaabbdbddccddddaacbabbadacdbbbcbdcccacadccddbcacadadcdcbdaaabcbadadcdbacaaddbdcacadbcadaabcbdaccccacccaacccdbcabcbcdbadaccbcadddbabbbbabcacbabddcbccccccbbdbbdbdadccacacbcaddccbabbadacccdbbbbcbbdcdbdccaabbcdbddbcadabadbbcccdbdcadaaacadbcababccdbcaccbadbcdccbaabbbcacadddbacbadadbbdaaadbadddcdcddbdbacdbdbdacdaaaaacddcacaccbbbbbddbbdacacdbbdbbaddbccabcccccbababaadbabdacaabaaadbdaaacbcdaabcdadbcccdcdacbbdcddbadabdccbbaabbaccdaaccdadbbaddcdcbcdcbbbadbbccaadaacbcdaccdbaadccbcbbdaaadcdbdbcaaacddbcbacdacddababccbaaaddcabbdabbbcddabaacbaabbabcbdbaabcbbacadbbdcabdcbcbdbdbdccbcddcbabdadaacabbaacbacdbbdabcacdabababaccbcdcdccdccdcaddbaadcdddccbdccbdddcdadadcabaacacababdbbdaadbdcbaabcccdbbcaaacadadcacdadddcabbbbdadcadbabcabaabcbbbbdbcdabbacddacdacdadbddbcadbbababadcdbdcdbdbccbddadbbdbdcbcbcbbdbcbcdbcbacbcbcabddcccbddcdbacabbccabccbccaabcdaacadabdbcacadbcdbaddadbbcdbcdacbdcdbacaacddccbbcabdbbcdcbaccdadbabacbcbcbcbdadababdbbdbbbdbabbccbcabdcadcdccbbdbbabcddbabcdbaccbaadabbcdadbcdcbcdcdcababcaaaccbcaabdcadbbaddcbadabacdbacdddacbdcacccadacdbcdccbbdccaabbdbddaadcddbdacdbacdddcaaaaadaabdbdaccbaccdbbabaacaddbadbcbcdcaadddadadbdcccbddddddcbdbbccabbcdddcdcacaccababcaabcbbadbbccaaddbcacbdcbbaccdcbbcddbabcbaaaacacbbbbaacdbabbcacabbbbbbbaccdaaccbadccacadbbdcaddaaaabdcbbdddabbdbccdacdcaacbbcdcbcaaadadbadacbbcdcbbaaacdbbddbdcdacbaddaccadccbabacadccdcdadaddcdabdcadbccbcddadddbbdcabbcaacadacaacdadccdabcdabbbddadadaababaadcccddadabdbbbcccddabbbdabcbcbcbbdddddcdcacaaadcddcbaddcbadabcdbcbcbdbcbcdcaadbbdcbcadddcaaaacbabdbdcdabaaaddcabdccbacdbcadccdaaccdaaacaabcbbcbddcbcbdbbdcdadcdabbcbcdbbabccacdacbcabcbcccacbaddcbdcabadbadddbcdcabdaccdabccbacbbcbadaddcbbdbaaaaacabbdabdbdadcadcaadbaaacabdcbcaababbcaccdbaaaaddcaabbbabadcccbbabbadbdabbdccdcbaaaaddcddbacbbbccadccbabaaddcdddadbbbdbabdabdcbbabdacbdcdaacdccacadcabdaaadbcdadcdbdaacdcbadcbacaabbadddaabdccaabbbbbcaddcacdcdccdbcacabdacbaaccabbdcdbbcdcaaaabccbabddcbbacdabcddadbbdddcaacbbbbcddcdaaadccddddcacbccdadacaabcdabdbdcbcabaacadacdcdcdcaadbcdadbbdaaddccbcbccddcbbbdbbcdcbaddcbccbcbbabaddaaabbbdbadcbbadcddaacbcadcdcccbabdadcbabddbcbabacadadbbdaacabccdccdbbbcbaddacabdccdccdabcabadddbaccababacbdabbcbbbabbdbcacacbdaddcaddcacbcbaddccaaacdadcbdacadaababaddacbbdbacdabbdabbbcaaacddcadbcbacbdaccccbcbbdbbbabbbdcabdcdbbbcbdcbdabadddbbbacabbabccdcabbccbcdaaddbacdcdcbbbaccbaadcdabbcbacadaabdddacabadcaadbcddabadddbdacbcbdbdbacdbaaacabaddddabcbacbaccaaccddaaabbcdbddabaabdccacaabadbbdacbdaddaaadcccccacdbccdbbadbbaabbcbccbcddaaccdadddacdbbbccacdbabdadaaacbabaababbdabdbcbdcbbbbabdbdddbdabbdbcdababcacccaacbbdbaacddaadabaccbdaaacdbcadcacabbddacadaabcaaccbacbcabdbcaccbccadbdbccdadccbcbcbabcacddaddbbbbddacaabbdaccdcdababbdbaacdbcaaabbbaabbbdcaaccddaacbabcbbadacaaaddbdbdbaadaababcaaccbaaaaccbaaabbabdcbabbadccacdacbcaacbdadaccbdcbacaaddaddcdddacaaaadcaacdddcbdaccdcbdbddacdbdbdbbcbbaaadddbcabcdcdcaaacbadaaacbdaccdcccbbdbcdacccbabbddcccbaadcbdbcbcdacdddbdacddacdadcccddcbacccaacbcddacccabbcddaaabdcbdcdbadacaccddcbacbadbcdaaaadababaccaabadccbbbddcdadadcacccacaccddbccadbbccccddaacccdcdcbcdbdbcdadbdbbbdbadddcdbaccccdbbdccdbcbddcadcbbbdddbcadcadabadbcbdbaadccaaadbabbcbacddbcbacaadddaddacdabdbdccbddddcaddddddacdcbadbbbbdaadbddbccbcccbacccacbcbbadbacddacccadbbabbaddcddbbacbbbcacccabcaaaccabbacbbcacabcbbcdbbddcbbabaccaacacacdcbdddbacbadddccdbbdddaaadadaabbcbbbcaabadbabddbabdacbaabcacacbccdadbbcdbcabdabcdbdcbacaaddccbaaccdcacaaaaadacaabddaadbcdaacdbacbaccdbddbbaaabccbaabdcbabbbddaaacacdbacbacdacdbcaadadbacbbadaadaabbdacddacccbdbcabaaddaaaaadbacccabbacabdcccabddcbdccccdcadddbaadccaddadcaacabddacbdaacbadcddacdcdacbbababcbbbbcdcdcaccbcdbdaacabacdbcbaabbddadccaaabbbaccbdadabadddbbbccdabbccbbdabcabcdaddccccaacbccbbbdcdcddcabbbbccadbdbcaddbbddaaccbcccbadacaaaaccaadadcbbbccbadcacbaadddcbdcbbdcabacdaabcbddbcdddbbcacbbbadaacbbcabdabacacdccadadababdbcddcddcababdddcccabcbadbaaddcdabbabbddddabdbdaccbdadcccbcbacccdddcbbdbbaadcccbacbbaadbaacacbdbcdbdcdacdbbdbbdcccaccdddddcaadddabccadcbddacacdadbdabbbbacdbcbcbacccbcabccdccbcdbdbddababacdcccdbabbcdcdcaadccbdcddcddbbcdacabcaacbdbcdbaaccbccdcdbadacdababdaabbdaabdcbbadbdcbbccaaddbaadaaaaadbdbbaacccbcdcddccccacdadadcadddbdcbcaccaabbdbadbdbcddddacaababddadabdcaddacacacbdbdcaacdbbbcbdcbadbacacaabbdadcacacdabaddbcdddaddddaccaabcddbbcbbaadcbbcabcbbdbbddcbababcdbbabdabcbadabddcbddcacaddaddccccdcaaabdccdcbdacddabbcdbdabdcbbbccaddccaacdabcbcacbdcccbcdbcaaccdbbcbcdbaacabaddaaabacdccdacdcccdcdddbdadcadcdcababbcaddaaabccbabdbabbadddcadccbadbcccdbcbddddaadacdbdabbddaddbdccdbcaababdabddadbcbcbacaddccaaabdddcacadadcbaadbddbcacbaadbaadcdcbddbabddbddcccbaabaabddbbdbddddcddccbccabbbaddbdcbdacaaabbcabbacadbccbdbddbbcadcdbbdacdddabacaacbbcddcabbaddadbcaabddadcacbcabdbbadbaabcccccdbadcccdbbddbadaaddabcbccacaadccccaccccbdcaddcaacdaaacabdddbabdacccbbbacbdbccbdacacdbddddcdddbdbdaadadbdbaccaddcaabdbcdbbbadadbcbbabaaddbadcdccbaabccbcadbdbbcabcdcbdbdabbbcdadbacccbbdaadbbcdadbcdadbbccadcbdadbabcbbbdbdcdcdcccaacbcbbbababbdcdadbbaaadcbdbadbcadbcbacabdbbacaaacdccabacabddadaabacdcdbabcccadccdcbcacadbbdbdcbdddabccbdbabbccacdadddabbdcbbaacbbaabbcbbdcbcbbbdacccbaccdacbadacadacabbbbaaaccddabcddccbdccdccabbcbdcbccddbcaccadaadbbccaabdacbdddacabadacbaccbbacabdccadcdcdbabbcdbaaddbcdcbcbaaccbacacddbbdaadbdacbdbddcbcaaccbabbccdaacdcbcacbcaccccababcbaacdddacccacbaabdddcadaddccddbabbdccbbaaccbcdbccbcacabbabcdddddabdabcacdbddabadbccdbdddbbcdbbbbbbadcacbdabcadaddcbcacdbdbcacdcadccaacacaabccddabccaadadbcaabbaaddcbcbdbddadbabdbddacdcadbcaabbbacaccdddabcccdaacbdbdcbadabcdddadbbbddacbdaabbadcbbcbddacabaddaccbbbbdcdddacdbabababdcbdacdcbdccbcddbaaabdbcdddadcbabbabccdccdadacdabcdbdbdbbddbacaacdcbdaaaacccabbdbbadaabcababcbcbdbdabdbccbccdcbddcadbcbcdbdbaabdaacbdcccabdbacdabdccbadaadacddcabadbdbabdadccbbbababdadacdcbddddcaaaacddbbdcbaccacccbbcbadcdbbcbddccdcaacddacbadcbbcaadbadadadadbcddccdadaccbababbdcccccccacbdaabbbcbccdabadbdbdacabbbbcabbaabaddccacbbcabcccacbadbadaddddbdbdcaaccdddbdcbabaaddcaabcbadababbacabdcaaddbdaddccccbaacaccdcdbacdbbbdcdabacdbacbbbddbaccadccabbcacaaddcddabacdacaaabadaaaaaabdbcdcaaddcaddccdbcacbcccbbcbccadbababbccccddddcbbdaddcdcdcbadccdbaccddabaacaaadbcccbcccdcadbbbacdacbacdbaccbcacadcadbbdbadbdcdbbbabaadbabbcbdddcbcacdcbadcbcbcacaaabbacdbdadabdabaacabaacbaaacddaacbdbadddadacdaccdadcdacdccbcababcbddcccdcadccbbdcabddabdcdccbdadaaacdccbbbcbacccdacdaaabcbcdddbbcadbaddccdcbdbbccacbdddddccdccbcccddbcdccddcddaccabadccabadaccabdacccccacddbdadabdbccdbaadbdcbdbcbbcbdcbcdacbdabdcbbbacabcccdbbdbbdadcdadddadddccdbcabaccbdacaaadcbacbddcbabdbdbccacbcdbaaaacdabdacaaabdcaacbbbcdabaacddaaccdbddddbcdcbdbbaabdbadbccbacdbdabccbbcbbaacbdbbcbabcccadbbadddbaabdbbcabbddddacdabbdcabdcacccddcdbdadcbccbaacbbbdccbdacbacaadbabbababbccbadabcbdbcadccdabdddacadaddaabbadadbbddabacdabddacbaacbccacdbddddcdcdacacacdcddcacdccdbcbdcbccddcadbbdcbbacbccbaccccccabaabadbddbadaadbbdccdcbcadcbbdbdabccabdbcacabbbadbadcbadcdaadcdccbaaabcabdacccbdbdabbadadcacbcdbbbbcbcddcaabbcdbdbdcaacaacccdaddaadabccbbbabbacdadbaacabbbdccbaadddcbbddccbadcddccadcacabbaacaddbbdaddbbdcddddddcccbbcdacbacbbcacdaddaaccacdcdcdadabdcacdcdbdcdabbbdbbadccaadccbacaaacacadbaabcddcdabddbdabcbbbaacbaccbaaccdbcadacddaabbbdbdadcbddababddcddbccbaaabdadbacabaacabddababbdddccaacccdadacdabbbbbaaabaadcbccddbdddcaacddbbacbbbbacbcbbabadbabdabcccdddaadbdddccdcbcaaacbdbabdacdacacdaaccaddabacaaabdccdbcacdbcacbddcccbaadbccabdaaddbbaccaaababbbddbdbbacbbaacaaadcbccbcabdcabbaaadbcbacbddbabddacacaccaaccbcadddbabdbcdccbdccbcccbbabddcadabcbaaabaaaddcbcabccabbdddaddddccadddbaccdcdaabaacbadbbcdcbaabcaaacdcabdaccacabbabdbcabbdadacdbcadbddaacbbacaaaddccdabdabdccbcbabddccabacadaabcdddbdccaaadbdccbcbaaaadadcddcddcacbddadbcdbdcccaddbbdaabbbccadaddacbdbcdbdcbbdbabbcdcaabaaccddcbdbbcaabaaaacababbadbabdabddcbcadbdadaddcdadacbcdccbdaccbdbaadddaadaccdcaaacbdbbdabbdcabacacadcdabaaddacaccbdcccccabaaadbaccbbadababcbccbaaabdcdabcbdbadbbddaacddbdbbccbaddddcabdcbbbaadbcdbacabbbdabbdadccbcdcabdbaabaadcbdddbcbbdcbcdbcaaadccccdaabbaccbccadcbdbcdabcabacdcbdbbbbbababaabdcdcbadddabacccbcccabbdadbcbcdcbcadbacaaccbddcbccadabdbaccbbadbdbbbdacdacaadacbadacacadbcbdcacdbabcdcbadccddabccadcdcbadbadcaccbdccdacddadbccdccdbbbdbbbbcaddcbbbcdacaacbbadaaabccaaccccdcbbbbbbdddaaaccaacaaddbaabccbdadacdadadcabccddbddcbbccabdacdaccdbdcbbacadaaaaabaddbbacaaccddccdbdacbabccbdcbcdbccabcdaddbcccddbcdbdbacccaacddabcdaadaadbcbddbccbbdcbcadbccbacbcccdbbcbdacdabadabbcbccaddaabddabadabbabdbdcabacaddcbbbbabbacaccdbacaabaccbcbcbdadcacaccbbbabbbdcccaaccdabdccbbdaaadbdccabbaabbddaabcabddcdbbcdcaaacdaabcddaaaadccdabcdbdbbbcddadcdbacdcaaddacbbddabddacadbbdabbdcbdddbcccadbdbdddcdcbdaacbcbbbdcbdadcdbbadbdaacaacdacdababcdcabcabcadbcacdadcbdcacccdbbabadaacaaadcacccaaadbcddacabdaadaaabbbbccbdbcbcbdbbbbcacaaacddacdbbcbbdbadddbbcbcbbddcbbcbcbbabbdbaacccdbbdabcaccbbbbacddaddabaadddbdaacdbbccdcadcbdaadcdabbccbbabacaddbdabdbbcacabadccbaccbaaddddacccabbcadcbcccdcddacbddadbcdadadcbacdabcbdccaadccabcacddccdbaacccaaabbacbaabcaadcbdbbcccbddcbcdaddddbaccbdbbcabbcdbcdddcacdadcbaacbcdbdaabcaddaaacccccbcdaadbbcbcdabacccbadbbdcdaaccabdddbdbddbccbcccaadaadcdcadacccbdcdadcbbdcbdcbbbdaaacdbbcbacbccdbcadbccabddaddcbbabdbaccbbbcaacbbbbcdcbbcdbbbaddaadbcdaccbdcabdadcdbcbadcbbcbcadadbacaacbddbbdacbbcdcbbbacabccdccabbabacbdaccacadadaccbbdabdbadbabdbbbaccbacbddabbdddabdababacddaadcccdcdcdadcaddbcbdcbcdacadddbdccccababcdaddddbcdbcddcaabbdbddaccdddbcadccabaacbdcddbdababaaccacadcdddccbabcaaaccbacbddaacaadacadccdcdcbbacdadccdadbcacadbcadadccbccbddccadccaabaddbabaddbdcdccbdcdabcdcdbccadbddcdbcadaadbcadcabdcbddbaddaadaddddddbadadccaabadcbaabcacbccddbabbbbdbccbdbddbaddabbbbacbccacdabaadcdcaddadaacbdadddcddbcbcbcdaabccbbcddbcbcacbdaabbaacacccabcbcdbcbdccddbddddcacdbcdbabbccccdbaccbbbbbaabcbabbcdaccddadabdbcdccabbabbcddaadaaadbddadbaababbabcddaccacabadbdcdcdadadaaccbacbbcadbbdbadcbddbacaacdaadbabbccdadadbdcaaacdadddccacbabcdbbccacacbccdcdabcaccadacdaadabaabadadacdbdbacddcbddadacbadadaaabadbdacabbdccbbbadacbacdcbddcbaaadacbdccdddaadadbbaccacdbdbbbcbbbcddbccddddabaababaabadbcbabcaabbabdddddbbadcbdccbbbacadcbcbadcdaabdacbbdbbccdbddaaabadacbbbaadaaccadbbddbbbdcbdccadcdbdbdbcacbdbdaadadddaddcadbadbaccabdcddcccbcbacadcccaabcadbbdbbcbbdadcdcdacbccdaacddaabbccaacbdbadcbbbbbcddaabcdabbaacdbadcabdbddcbacdcbaadcbcdccabaddcbaaaaabdbcacbccbaabbdcdbbaaddadacccbcbabbcadddabcdbbaddbbcacbddccbaaccbcaacbcdaccddacbaccbddcabadbadcabccdaacadaccdaddacbcbccdcddbdacabccbccdadcbaddbccddbbadbccbbbbbbcacaddaaaaaacacdabdcccbddcdadbcccabbbbdcdcbddcdcadddabcdbccbdccbbdccabcaddcdcbbaabacdccdcbcaaacdddaadddaacbabbdbcbdcaccbaaccbbdcaacbcadccadbcacdddcabbcacdbaadddabddcbbccdcdcdbdcaddcdabddccbccbcabadcaccbcdbdbcbcbccaabdcddadabbaddcdbcabcdcbdaaadbadddabbcbabbcaabcddddcaccaabdcacdcbddaccbbccaacdabbbddacdcbddacdaadaaddbccabaddbbabddbcaacbbdaadbcbadbcacdcdaaaaacdbcbacbdcbabddccbcccbcdaadcdbacbdcccbdabccdbdcbbadcadacbacdcaccacdcbbdbcbadccbdcbbabdbbbbaabcdbdcacddbaabdaadddccbbdcdaacdcbbadddaaddabcbabdbdcbbbbbaaacccdbcaacbddabcdcbddaabbbaddadcaabaccbadbdcdbcdbdbbdcdadcbdcdaaabccabbbbabbdababbaadcabcdcbbcbcbccdcdbcddccdbdcbdbaabbcdabdbcccadcacbdcdcbdaaaccadaaabdcdbbddaacbdbaacdacdbcddbbdbadcaadaccdbcabcabaccadcdabadaabbcbbabcaacdbbbbbaccdbdacadcdcacbbadacdadabdddbabccccdcbcbbadbbbacdbcdcbbaabadcdcdcabdaddbddabaadabdcbcdbaacabbaccacdcccddbadabdcbdcdcccaabcddacbacbdbbbaacbbbcdddadacdcddabadaadaaadbbcdbadcbccacacbbaaccccbbcdbaabbadcdcabaadbdacadcacbacabbcbbddbbaababccbdabbcccdbacaacdabbaabcdcdbcddcbcdbbbcacddddcadbacdabcbcdbabcdbcbcdbccadccacdaccbdcdccbbcdabcdacccbbbdbcbbbcaacacbaacaccaddcbabdcbcbabdcdcbcbddaabaababccacaccccaacdccaccdbabbdabadbdcbbadabcccddcdabacadbabbcddcbbdbacdaaacadccdaacccadcbaaacdbacaadcbabacbbbaacdbbabdadcbbdacaabcbddabaabaabbbbdbdcdcadacdbbcbbbcdcabcbcbcdadcbaaccdaaadcbbdbcbcabacabbacaaacacdcacaabbdcdbabacaaadbaadddbddabacadcbdbbcaccbbbaabbbccbdacdddadadaadbdcadbbcadbdcbcbacddbcbcbabbdcabbadcdcabbbbdbadbdbbcdaaacdacbbcdbaccbcddacadaabcadaccdbccbacaabadbddabaaaabcbbadbacbcdabccdaacacaddaadcbccdcdcccbcddcdaaddcccbdcdbbaddbbadadabbcdcbadabaacbbbacbdbccdbdbcbddddbaddabdaadbdacdadbbbcccbdcdaccdaaaadabcbdbdbabaabccaccdcbcdadbcddbbbacdaccabcaabdcccaaadbdbabbbaadadcdaccacdddddbcacccabacaccabadcabacdddddaadbdccbaabcdddbaaabbbcbdacadaddbbbbbcdcacbdbaacbbadccbbddbbbccddabadcdbbabababcabdcdadcbcabacccdabdcddacaadcabbdaabbddddbbbdadabccbcaaadacdccacddcbddaadddddcdbddbcadcbdabccdcabdbccabdabcbccbaccadabdcdbacbddccadbbdaccddbabccadccaaacbbadcdccdcdccbaadabddcbcbbdbacbbbdbcdacacdcadcabacbccddbbdcdcdccadabbbcbcadbdcaaccadcaddbcbbbaacadaadcdcaaaaccacddabccbcacdbccbadcbadbcddcbbaaabacdabdabacbcaaabbbcbccabbbaacaaabdbaacabadcdddddbccdccacdccadcbcddbcadcccbcbddabdccbddcbbbddbaabdbadcbdcababbdbdccdcacbacbdcaccabaabddcdbacbcccbbaddbbacacadabcdbabdbaadddddddcadccabbdbdccadaabaadcaabbacdaaddddbcbdbbbddbcbabcdddcaccdacbdbcdcaaaaacbdbbbdcabbcaacbabdbcbbdbcdccccccdbcdbcaddabbcbcdcdbdbacaacbccccaaaacbabcbcbbddddbdbcaadcbadcdbabcbdbdacdcacccbccdbdddbcaacdcabdbaadacbccdaddbbccccdcdcacbcdcdabdaaaccbacdcabbddddccddbdcdcdbacaddcacddccdbabdcacaccdbacdbbabccaddbccabdabdabcdddbccddaabcccbbaadabddaaccbcdddabcbcabbadbbbdbaababcbacccabbcabcadbabbcbdbcddacbdabddcbdcbdbcbaddbdddccccdaccbdbbacdabbdacbabaacbabdddbcdccbcdacdaccacdbbadccbbcbacaabcbbdccbacdadcabdccadabadaabaccdabccabdbbadbacabadadcdbaacabdbdcbbcdcadabbbdabccabbaacaddccccaaddaabcaccccdccddbbbbadddadaadcaaccaadddbbdadabdbbccacadabbccccccdcdbbcdadaababbccccccaccaabadbddcdaddcddbabdbcbdabdbbbccbdbbbcacaaccabbbdaaddadabcabddbccabbccaabddcbcdbccbdbccdbbabacbddccccaddadcdcbdaaddbadaddccaadcdcccadccccdaddbdccdcacbadaadbdabbcbaabadcdbccdcbacbdbdbcbadcbddaadcbaccdddbdccdccbcdcdbddcbdcabbdcabdccddddbcaacaabddacdcaadcdcadbbdddbcbbcdaabcbcbdadbadbdacaaaaabacddcdaccbdacbcbdbaadbddbdddddcaabbbaccbdabdbdcdccacbbbbbbbbacacdccabbbdddcaaddcbbadcdadbdcadbbdacadacaacdcbccddbbbccacaddbccccbcdccdbcaaaddacdcbccccbbaaddadbdccaaddcccbbdcdccaaccdacdcadbbddbabdddacbdbcbdabadccdcbaaacacadddccccdbdcbdacdbddbdccadbaaacdcabbbbabccdbaabbbacacdbdcbbcddabdbdcbcbadbbbdcdbdbcbcdaaababdaaacbaadcbbdacacdbbbdaccddbaaacbbddadacdaddcacdbdcdcdacbbbababacdaddaabcadbcdddcbadcbcdbcdcdccdddaccacadbaadcbacbcddccacbbdbbcdcaaaaacbdccabaaadcadddbadaddacaaacbbabacbcdddcbdccdaabcbacbcccddbddbaababacddcacabddcadbdcdaddabcabbbccdabacbccdcacadabadcbbbbcbabcabcbaaadabddadaddaccbcbaccbdccaabddbcadbbbdacbddacaabaaddbacabcdcbcdababacccddcdadcdbaaddaccdcdbdadabaccdcacbcdadbbdadcaaabbddccbbdadbccbbacbaddaaacaacabcdddcabbbadcabdbbacdadabcaaaabcdabaaccaacaacccddacacbccaacbbccbbccbbcbbbcccddabcaddaaabdcdbbdabacadadddbbdabcbaccdabdacbdcdaaccdcbccacdaddaacdbbadddddbcbbaccadaadcaacdacabcbdccaddaadaddcabacbabddddcddddadadbadaacbbaabcddbccdbcbdaabbadaaddcddabddbaccaadbcabcaacacdccaadabbcdabcdacaaabaadcacbaadbbcbdbbaadbacbdcadccbcccdcdaddabdcacabdbccabbccccddaacdbbbdaacabaacaabdcdadbcbbcdbdadcbaaabddcdabdbdbccdccbadadbcaaaacadaccccaccbaaaccccabccdadcbdccbadddadaadbacdcdcbaabaadbaabbddbcabcdabbaadbcddbdbcaaadaccadbcbadbabacdbbdaccaccccdbdbabccccdacabbababaddbdcaddaadbddbadcdcbccbacdcbdaccadbdbacbabbddaaabbbbddadbacccabcbddddcbadccbbdcddabddbbbbabdacaccacdadadcbcdccaddadbbaaccddacdcaccaddabbaccabaabddccaaaadccbbbcadcccadaccaacacabccddcbbcaddcbadabdbcbabaccabcaacabcaaaddaddccbaadcdddbbaadaaadbbadcaaaadbccbabcdbacbdbcbbbcbdcbcaccdbaccabbdddcacaccabdbdbadbdbbdccaacbcddcbbcaccabcbadbbbadcddddaabccbcbcdcbcaddaacabcbccbbbadddbcccbdddbdbabaacbccbaddbbbcaaabdbccddccbcaadddbdcabcbdbaabdcbaabcbbddabdcddadabbacbbccbbcaabddddddcdbaacbbaddacadaabdadcccbcddbacdadbbabbadadaddcaabaabaddabcdbadabaadabaabaacdcadaaabccbbbbcabccbccbdcbddcdccbdadbaddbcdbddbabcbbadacbaacbcadccabcdbcabddccbdacdabbbbbadbabacbabbcbdcdabbbcabadddabcbdababdcbddbddbbacaddbaddddcaccaabdcbccbbcbbabdabbbaadcddbcbbdcbbbdbdbabbadbbcbbcbaccdddcbaadccddbdaadbbbdbdbbdbbbcddcaacddacddadcddbbabddbaaaabbdbcbbbdcadadaaddbabcdddcadbbadadacdbcdcbbdddccaaddddbdcccdcabbbdacbcddabcdaadbabcabdcabdcbaccbcdbcdcabadbdccdbdddddddbdccdcabbdbcabadcbdbcdcdccdabbaddaaaacabacccbddddaccbdcadcaccccbcddabcabadddcdbdaabbcdddcacadacaaccadabbaccccaacbbdcddbdcabadddcbcbbdaacdcaccbbcbccaaccadacdacccdcdcadcdbadcabddbadaacacdddadbaadabbbbadbbabaacbaaaaaddaabcdcbcbcbbcbabdcdaabcaddddccbaaaddcbdabccbbabacdaccbdbcabadbcdddacdaadccccbbabdcadbcbacababaabccadbbbacbddbdaaddbbccacbbabdddaccbabdabbdbbcaabcdbbaaacabdacdbdcbbddcdddaabbddbdcdbbdbdbbaccaabaaabdabadcabdcdcbbcbbdbdacbacaabcddbaaabdbacaacccadcacaaacaddaadbaccaacbdccaddbdbcbcdaabcacdcaccacbdbabadcbadcadddabdcdadbccbcbdbbcccdaadbcbbccddccbcbabbdddadbbdbaacdabcdcaccabadddcdadcbabbccdaabbacabbccbdadbddaccbaccddbaaaccddbaabbbdbbabacacbcddccdacaacdadbbdcdcabbabcaabaccdadaccdcdddcccadcdaaadcbcccddcbadcccbaaacadbadbcdcbadbcdabbbdabbabddddbabbbdabdccdcbbabcacdbddaaccbdadcaaadcacabddaacbbacdcdabcdbddcbbcaabccdcbbcbbdbddaaabbdacdadcaadaccbcbbcaaaaaabddbadbddccbcdcbcaaacdacbacbaaacdddadbacccabbbbcacccbbccdbccdcddcdbaadabaabcdaabdddcdbdaccacbdadbadacbccabdcbadabbdddbabcababddcdccddabbaddadbcacccdbbabcdbddcadacdcabddcddbbaacaaacacbbbaaccbccadaaaabdcddcabcacdaacdbdccacabcbabaaccdacabdabbddddcacdadbcaaddadababadbddbbcaaababaaacdbaabcdcacadbabacbdacbabdddcbbdcacbcbbbbdbaaacaccadccdbbdccabcddbbcacabbacddcbaaabbdbbcbbcbadadbacabdbcdddabadcbcabddbdcaaacaaacabdaabcaabdccbddddbdbbcbbcabbacadcbccaadbbcddcdbcaddbcdabbbcbabcbbcdaaacdcaacabcbadcdacabccdcaaacbdccbcacbdbabddbdccaadababdccdcadaadbccaabbdabaccccccddadaacacbcbacdaadbcdaacaaacbbddaaacdbbdddccadccabcbbdccacdbdbbbcabdacccacdddcaaacbdcbccbadcddaaccdbcabacacbcaabbbbdccdbbbabaacccdaddddaccabddddaaaacabdacdbccdddcbbddddaaaaadcacdbddbabacaddabaabbdbcddddaaaabbcddcacdbaaaacddaaaadcbdcbdccdccccddcccacbdacdcaabcbbdaaaabcadcabcddadcbdabddbbacbaabccdcbcdcdcabcaddbaadcbabdcabbdcadaacaacdaaddbdababccdcdbbdccaacdddacacddddaabddbbbdbbdbcbaadabcbdaadbdddbbdbdcbcdcbacdabdddcacdacdacabddccbaaccbddabcacdadccaaccdaabdbabbdbdbccdaccaaadcdaacccbcaacbbcbaacbbbcbbcbdbcdaaadbbddccccdcacaadcadbdcaadaaabbaccabcbdcbcbbacbcdcbbdacbddbbcccccbbabddcbcdbdcccabbadbcbccadbdbcaccdcbdadbcadcadabdbcdddccdadccbbcbaaddbddcbaacdcbcbcadacccbabbaccbdacdcdadbddacabdbdcddabbdabbddcbcadabacdcbdcbbadddbcbbccdbcdbcbbcaacbcdcdbcbcaddcdbabcbdabdbabbbddbbaacadabdcdbccbcdddcdcabdbabbabbdbddcbdbcdabbaadacdbabadababbcccdcabcdabcddcacbdbcbdddabccaaadcddcacacdbcdbcbcdbdaaadbbbcdacdcadcdaaaccaadccdaabdddddcaadcaaadcdaacabdadabcccccbbacadccaccdbaccddcdacccbbbaabcdbcbccbabbbcdadddaccdcbabbabacdabdbcaddbbcddccabcccacdcabbdcaccdacababdadcbabaccddcdacbaddbbdabdcbdbdcbcdacdbddbcaacaccdcbcccdcdbacbaabdcccdbcaadbdadaaabaaaacdbadddbdcdbcacddbcadacbbddacddbbbdbdabdcdcddddabdccabbdccbbcbdbabcdacacbbdabdddabcabdcdbccccbdcbbbccbcbaabdddcdaddcdcbddadacbbddbdadddbdcbcbdbcdcabdbcabbccbaacbadddbabdbaaabccaddcaccddbadabaacacabbcbbabaccabbacdacabcacaacddbaccacaccbdcddbdaabdcbcbcabddddabaaaacbcadcbaacbaabbadabbaaaccdcadcababdcbbccbaadbcaddcbaccbadcdaacdccabcbadabddabaadcabddddccadabdcdadaadcadcbccdaabdaabccdaddacdacdcbbadabcccbdcddcccadbbcaccdbdcdbaaaadcbbbabdaaabdddcbcccaaccaaadcdbccaccabdcacacaabdacdbaadacabbddbabaadbaacadcdabbaadcccdccabaacabbdcdbdbccabdccdbaabccdcbacbcbbadbdadaaccbcacaaabcacabccacbbabbcbdcdaadbcbdcabaaaaaccbbdcacbaabdbbcadacacddcaddbadbbcbcddccaddcdbcaaaabacbadcdddbabdddadaadaaadcddacccacbbdcacbdbaccdddccabdcbcccadacdddaadaddbabddddccdbbcbbddbadcbdbbbcbaaacdaabbadcbdbcaacdcbcabaddddacbccddabcdaccbbccadcadbbcbdccaabcacaaaaccdbaadababdabbcadbcccbbcdbdddaabbbacbcaacbdcaacacdaaadccbcaddcdcbadbabcabcadacbacaaccbacaadbadcccbcbabdabcabadcdcacbdcaadddadadaadcaacdabdcccaaacbacaacacdbbadacbaddaababacbabcadbaddcbbcbcbbdaacbbcccadbccaccaaadbdaabbdabccdbdacbddadcacababcdacbcbcbbbddbababbabbbabaccbbbcabdababaacaccadcccdaadaccbbaacabdbdccddadddbcddbaadbaaaddacabaacbccacbbcabddccdaadddddcaaaccccbdadacacdaacccaabdabacbcbcbacccbcacbcadbccbbcbbbaaadcbbdbddbddcdadcbcdbabdcbaabadbddbddaacbddbaddcdbaaacaacbcdaaacadaabddcaaaddabddcddccbadcacddacabaacbabadbbbcacaaddbcabbadccacbbcddcccbcadacdbdabbdcabcccaddaacbbddddbacdaaacabcdbdbabbdaddaccdababdcdbcaacacaadbbaaaabbacaacddbbdcabbbababbaccbddccbcaaacbddbcdbddaddabaaddabcdddccbadbbcacbcdaaaadbabcbaabacccadacadbadbccbcaacdaccacddadcbcdaababcabacabbcadddccabadbacdaacdccacbbbadaacdddcabbcbbcbbdadcbabbdbbaacbcbabdaacbddbadacabacbddcbcbbdabadadddccabcbbdbaabccbaddccdbdddbcaddbcdacdaaaadcdabadcacabcdcbbdcbadbdabbcbccbabccbadddcdcddaaacabdacdbbabbaccccadabbcbababbcccdaaaabcbcbabadbadabcaabcabbbcdaacdacbccaccadaddbadcbddddcaacdbbcabdbccdddbdaacbdadcdcdaabcbddcdacaaccccbbcbaccadbccdcdcdcccddaabcbdbacccadbdddcdbcbbdacdbbadbddcddadaadbdcdcadaadcaaccacbccdbaccabccdccacbccdddbcadcdadcadbbacdbbbddcbbbcccbbcadddbcddccbbabcbcadcdcdbbadcbaaccdbbdccaaaacccacbacdaccbddcddbbccbccdbbbddcdbddcdcaadbddbbbbccdcdbbbdddbcacaacbbbdaddcccaccbbcadabacdabaaadbdbadacacdcabbdcaccbabadbbadbbdcacacadbbadcdbabadaccbcbddacadccacdbaaccbaccccdccdbdccaaabbadbcdadacccdcdabcdadcababbbabdcdbdaccbacccdacdadbbdabdbdadabaccdbdacbbcaabccabdcaaaabcaadbabbcdbcbdccbccdbbcaaadcdccdbbcbadcdccdbdcacabddbbdcaddbccbdadadacbabaabbbbcdccadcbccbdbacaadabcbcbacbbdcdcaadcbbbbcccdbbddbacbbdcbbcbcccbcdbabcabbdadcbdacaddbcbcabacaaddbdddaccbdbdcdddbaabcbaadacbbccdacabbbccdcaacbbcdddbdbddbcddaaaadacaabbbdabbbcccaaddadcabcddcbdbccacaabcdabaabbcbdcbdccbaddbbdbbbdacbddbbbcddaccbadcbaaddddddacdbccaaddadccbccaaadadcddbcbcdbaadbddadddbddbaccccaaccdbaabdabddddcbcdddacdbadadddbaadddbbdbcaaacbadadaaabdbccbacbdcabcbaadadbddcdcccdbddbccaaacbdddcbbaaaddcababbccaaaabcaccddadddcccccdccbdcccbbdbbcdccddacdaddcccbabbdbcdacbbdaacbdaacabbacdbacbaaabababbdaaacdadcaabcaadabbbdabbbdbccbadcadddabbaaddabcabdcbcddadacdadbcbbaabbdccbbaccccacbbcbdbbdbbaaacbacbbddcbbdccacdbaccbadbbcbdbccddbbdbcadadccbbcabcdbbbdddcdbccdddadabdabbdbbaaabcdbccaaadcdbabbddaababcdbdacbccaccdcdddddcdabbaddbbcaacccdadacccccadbacbbbcabcdcbcbbbacbccbacbcddbdabdadccbdbdcaacadcbacdcdbdbbdbddcbdcddacdcbbbacdbaddbdcdacccdbcacbabbacddcdbdbacadacbbbbdcaabbbacdbcdbcbddcbadbdacbcdbaaaccbdabcaabbdbacaacdbbbcbcacdbcdcaaacbbacccabcaddbaadaaccbbcadbdbdaacbbacabcccadcddbcbbdaccdbaadadcdccabbbdbbcdbaccadbacdaccacabbbccdcdabcadccacaadbabdcaacccdddcdaccababaacdbcdbabddccbbbdcdbddbdabbdbaddcadcabdbccdbdadcddcbbddcdbabcdabcdaddabcbdbdcbbcdabbaddbcdbacbcdbcadbbdaccccbcaadbcabbbbabdccadadabbddddbdcdbcaabcdcccbcdbadadddbaccdacdcaddccbddaccbcaccdccbddbdbccabdbcdcaadcaccbcaadcdbaadadabaacaaabaacdccdbdbcaacbddcdcadccbdbcbbdbbacbcddbbadbccbdcdbdadccdcdabcdccbacaacadbbdbcbdbabbbcdacacbcabcbbdbdbaccbbbacccabbcccdababddbcacddbbddddbadccbdbcaabcacdddccbdcdabbacbbddddacbcbdbdabadacbcadadbaacadbdbacdcddbcdacbabcbbcbbdcbccabbdadabcbbcbacdaacabaaccbaaadaaaacbbcdddbdabccdaacbcbddcacddbcacdaacacacdabcabcbdcdccacbbcdbbcbaadcbabcccacccbddcccbabadddbadbcdccdcbdaccdddbacccdbdbccddbcbcaadcdbdccdacbcbbdaaacbcdbdcaacadccbbcdabcddcbcabacbbcabcbcbbbbbcdabaadccdaccdccdddbacbbdadacdbcbaadbddcbdddddabbabdaabaadaaabcdcacbbabaccbbbadaccdcabdddadbbadabdadadcdbcadaccaaddcadcaccadbdcaaaaccdaccabacdcaaacdcbadabcadcdbacddcbaccddbddccdddbbabcdcdacadbbdbccacccadaccbbccdbbbacdcaddcddcccccbdaaabbbbccbddbcdbcbaaddccbabdaaaabdcbcbddbabbdbbdddcbabdcdbaddaadcdbdcaaaabcdcdcdbdbcbddacdbacbcbcacccbdbcadbcccdabaaaaacaadbcccaddcdcddadcdbcbcaadcbdacdcbcacdbddddcbbcccaacacccbdbdcccdacaadcdbcddbbcabaccccccccadcdbbbcbbabdbdbdcaccabbcabddbadbcdcccaabdcddcccbbbacbcbbcabdcabcbbaabcbacbabdbbdacbdabdccaddcddabaabacbaddbdcbacbacabcabbcbcdbcadbbdbacdadcadbcbcddababdcbdcbccabbaaddbbcabcdbdbdbbacdcbadcdabaccdabbacabbaaacbcdabaaaabcacccbbdcbcaabbaddbbdcccadadadbddbbdadbdaadbdadabbaddbaaadddccdaaaccdbdabddabcdbbaddcbddcbaadadcbbaddbbbdbccaabbdccdacbabadaccbaacbddabcdcddccdcbcbcbbacccadadbcdbbbdcacdaddadccbabdcaababbdaccdbacbbbcbaaabdacdabddcdcddcaaaadacdabddacdddcabbbadcdaddcdcdcaabcaaaadcdbdaddddcbbddbbaadcbbbdbdddcbdcdacaacdddacdbbddacbbaddbabcbcddcabbbbaabaadbccddcabcacdabdbabbaaacdaabcbdcdbccdbbccadcbacccaccbcccdbddbcdbbcbaccaabcbbaaabaabdabbabadbbbabccabdddbbdababbdabbabddcabdbdbadccbcdacbcacbabddbcaaaaacbbdbbbddbbdbdbadcbaaadbcccdcccccdabcddbbdccabdbddabcbbabdbcddcccbddbcdcaacaacbacdbacbabbbdbccabadaabaccdbccccacbabaddacccccabaacbbccabbacbcacbdcbcababadcdbcbdadabdcddaadbcdacaaddabcccccaabdbccdacdabdcbbbccdcadbbbdcbaadabccdcbdaacbbdddbdcdaaadccddbdddaddbbabbaaddcadcddbddbdbaaaadcccbbabcaccdbdbbbbcadddadacbdccbbcbcdadcaccbbccdccabacdcdbbbbcbdccababcdadbbaaabcdbdccabacbccbdbddcdaacdccdadcbbacacadbbbbaadbadbabacbdddababbbabbbcdbcacadaaddddcadcaabdbbcbbaaccbadacdbabdbddadababbbbdbadbdbbaadcaadbbbbcbdcdbabbdacabdbcdacddbdbaddcaacacadcadbdcdabddbccdddcdacdbbddcbacbbddcadacbaccbbaaddaaabbdbcadddadbaccaaddddbdadaabaddabcbbbdbdcdcbbbdadcbcadcbddbadccabdcccababbbccabacdababdbdcddaccadabbdcadcdcabdccddbaabdbdddaababdcbccccccdcdbdaaadccacdbdadbdcbbcdbbcbcdabdcabdcbacbddcddbcacccdaabcddadabcacdbabbdcccaacdaaccbbbddabcccacaacbdadcbcbcdddcabacbbacbacbcbbcddabbcdcdcdaabcabcdcacccbdbcdcdbacdbdccabbbabbacdabbbdbddabbbaaabacbabbacbaaadbdddccbbacdccbcacbaaadcccaccbcbabdddbdcdbdcacbaacdcabaabacacdbdaddadaabcbbccddababbcbbcabbbdbababbcabcbdccdbadcccdabddaddccabadbdadcccadbcbcadbcbbbcddaabbbdaacbadadccadccaadcdcccdcadadbcdbcbdbaaabbcbdddacbbcddaddcabacaddbcccbdcbdaaaabdcdcdcddacdbaabbdbddcadbabbdaccbcdbcdddddddadbbaaddbcdcbbccddaddadbcbabccdadbbaaabcccababacdaccaccbdcadadbbcaacdddcbacdadcabaccdadcdadabddbbdddbcdabccdccbaaaacdbacdacbcccdbcbccdccccaddcaccbcbcbddacabacadbcaadcbcabbbadabbdaddbdaadadcdbdcadaddaacaabbddbadcbababddccdbabbadbabcdddaacbacdbccacdadbbbcadbacdbcbabcbddcbacabaadcdabdbdabacbadbccddbcccddaadcdabcbdbabababbacbacdacccdbbddaadcaadcbddbdaddcacbdaaccadabdddcddadbdaacadacbcbadcdddabddabddcdabdbdcadbdaadbaacdacbadccbbddacdcdcbdbbdbbbacdbaaabdaacbabcaadaabadbababcdddbbbcabdadbbadadddddadaccbabaadaacdccdadcbadbdcccccbddcbaabdcdacadacabaaabaacadadbcbacdcacaddadbabcdbaabdddaaacdadcbdcaacbdcdcbcdcacbccabdaaddcddcaadacacacbabadbcacbaddadbdccbdddabbcccbbbbddcababbbdacadddaaabddcbdccdddcdbccdccccbacaddddcccdccbdabcdbdbdabbabcbdcacaacaaccabdbcaaaddcaccadddbcbaddbaaccbbcccaacdabbccbaabacddcacdddaacddadcacaccdabaddddaddcddccccdabbcdadcbbdcbdcaddabbcaddddcdcdccbaaccdcbcbcccdcdbbbadccbbbcbcbdbddbbadabadabbbcaaaabcaaddcbbcccbccdbbacbdcabadcdccadaadaacbaddabdbbbabcabdddbdbbbdbcabacabbaabcddabbaddaaabadacbabadaddadcaddcaadcdbcabcdcbcacdcaabcccacaacbddcaccacaadabdadadacdbbcacabccacdaaadcbbaadbccdbbdaccbccccdcdaacaaddcdabbbccaccbddbccaaabcaaacbacbadccaccbbddcabbcbdcbdbcdccaaccccdcadadcaaacbcbcdadbaacddbbcddccaabcccdabcaacdacbcdabcadbdcabbcdbbbcdabcacddcbbacaadcddbbdcdcddccdbabdacccdcccddbabbcdbbadabaadccbcabbbdbbbaaddddcadacbbadbcbcdcabbbadbbdddadddabccccbdcddaddacacdaabacabbcddabddbddaacbabcdaadbbbdadaabddacbddacaacadccdaccbcbcccddccccddcaabdcacdabddbddadcacaddcbdaadaddacddbbdaabbcbcbbbbdbbcadaabccdcbbbaacbbbccbabbadccccaddccccacdccdbccbdacaaaacabdcdcdbbccdaacacbcddccdaabbadcabaccbbdadcacbbabcbadcccaadcbbcdabdacaccbacadcdadabadabcacddaadbcdadddaacccdaacbcbdbcbaddabcadadbadbaadacabccddcaacacbbcbddddcdcabcaacdbbcdbddacbccccaabdccdccabadabbbdbbbabdabdcbcaccbacbdbacbbabbdacddabbaccbcadabdaddccdacacdddbacbcabbdadcacbcbadbacccdabaccccbcdcacbbdbaabcaadcddccbcadacbbddcabddaacdababadbcacabbdcdbddbcadbcabbbadbacaaacaccdaaabddcbddacaccdaadacdbcabacbcacdcccbbccdbacadbddbabbbcbaacbdbbddadbacbabbdcaabcdcbccdaddadacbabaacbcbdbcbbbaaadccaabccbbcaaddddadcdbcadcadccdbacccdccacacbbdcbcbacabadbacdbdaaadbbdaaabdcabdabaccbcdacabddcbbdababdbbddacdbcbbabbabbabaadbaadbdaadcabcaaddcccacabaacadddaddcccacacabadacbcbddcbbabdabadacaddabccacccaaacaddabbdbcacbcbbbbdcdacdcbccbcabaaaabdcbcddcdcabccdacabdbbcdadcbdbbdbdcabdbcbdcdbccbbbdddddcadcadadbcaacabbbcadcddadabbbddbbaddcbbaccacbbbcadaadccadadcbdcdaccddbdbdadabdcdaababadaddacdcdbdaadccaadddadacddcaabbcabccdcdbdcdbadbbbcccdcbbdcdbacdddabdcacaaaaadddcacbaabbdbbcbabbadcccbbdcbbdbaabccabbdabcddabbcdbdcdcbabdabdcaddbbbbcbcdaacdcccbadcbaabdcddbbcacccdaddccabdabccabcbaddbbabadabbaababbbacdbadcdbbdddcbbcbbcdbdacddbddcccadbccdcbccbccbcdcdccaaddbacdacbdcdbdbcdcabdcaabbacbdccccacbadbadbcabbaacbbcddbbbabdcbaadcbabddabbcdbacadbdcbcbdddddcdccdcacbaacdaadccbcabacacbbdddabacdbbdbbcdcdcabacbadddddadbbacbaadbbbadadadccadcadbaaadbcccdddbaccbbccadcadacacbccbccdbcacacbddcbabcbabdcbacaccdbadccbdbcdcdaccacbbbbaccbdddcbbaacdbcccdadcadbbbcacaddddcbaabacbbdbabdbcbcbcdcacaddaaacadbadbbaaadaaabbadaddbcacaaabccaccdcaacadccddccbadcbbbabddcdbbbcddacaababdabdcdddbdcddddcbdbdccadbabcaadcdccccdccaabcbaabadbddacbbcdadbccbbcaaccdcccdbddadbdabbdcabcaabdcaaabbdbaabbdcadcadadbdbbdcabbacaabcaccaccccdddaaabaaabadadddabacbbdddbccdccacbbccdaaabbdccaddccaaabcdbdccbbbbdccbccabdacdcbbcbddbdababaddcbbddcddaccdddbbcacbdaaadbaddbdaabaabcbbcbbcddaacbabccabbacacdbccdcbddcddbdaacbbbaadabdabbdddbbbccdccacbdacaaacdaaacbddbacbddbbabadcabaaadddddbadccaccaddcadcbadaacdabbacadcdcdccbdbbacdcabdccbdbbbaadaaadcabbdabbdaabdbdcaaaaaabccadcdabbddcacacbbadcabddbdbaddccdddcadbdddabdadaabddacdccdccdcabcbbddacddddcbbbaadaddcdcbcacaadaadcabbaabaadbadddcdcddabadddbacddcccadbddcdcacaddccadcbdbdbcbabccaddcabdcbbcdbcbabbdaaaabaacbaaaadacdaacdcaabbccbbabcccdbcadbddccacabdbcbbdabdcacdbbbaddbbcacbcacdadcbaaababdcdbdadcadadddabccacdbdaabababaacbadabbcdcbdaababadacaacdadcbabcaddcaaabbdadcccbacbccaadabcaacbadacdbbccdaccaccbcbbacbcadbccbabdadbccabccdacabcdacdacbacbbcbaddcabdddcdbacddcdbcbbcababddddcadaacdbdcdadddaaaddbdaabaccbbdcabcbbbbdbbccdcadabcabacdacbcacdaaddbdbdabbadddbdcddaaabbbabdbabddccdabccccababbdcadaacaaaddabadaaabbccbcddcdbddccbbddddbcadbddbcadadbadcdaabababdbbddcbcaaaccccaadcadbbddbbdbbbbbdcddaaccbbbcacbddaddddbbdcabcbdcbbbdababaaaacbbbcbbbbdcaabbacdcaaadbdcaaabddbababcadccdcabacccdbdddadadccbbaacbdaabbacdcacacbdbbacbdbcaaddcbbbddcbdbaccbbbbbbddcccdbccaccccddcdccacddaabcbbcddbdcdababcbaabdaabcddcbdbbacbabbdaccbcdcadddcbdbbaddcdbdddbbbcdcabbbdacdbcaacadcdccabdbbbbdabdcdaabcbadbcaccaadabaaccdcacaccdaaddcbdbabcabddbdbdbdbbadddddabacbdbadcdacbcddddadadacacaacacadbadaacdacddbcdcadddddbbaababaccacbdcaccbbddcdbbcbaadddbacacdabccdccccdcaddcdddbdbdaadddbdccadabcacdaccabdadccbdadbabcbcacdcddbddbbdccdcbabbcbabbbdacadddbdcbddadbabbcaccacccccbaaadaadbacdccdaccdccdaabbabbccccbcddabcabccadddccdabddadaddcbbabbdbaddadcdacacaadbdbdbdbbbaabaddacacabdcdcddcdcccdcccdbcaacbdbadddbcdddcddddcabdbacdccdccbccabaadacddabacddbabdbabbabdbbadbbbddcacabddbaaaaaaaabbadddaaccbdcacabaadcdddabaadbddabdcdabdabdabdbabdbaababddbdcbdadcabdcccbdbcdbbccbacdcbdccbddaacaabcdcccabcaddaddddaacbbadccbadddcbcbbabcbaabdbbbdbaccaddbabbdadbbdddcddbbbcbddcaabcdcccdbaacddaddacbcababacdbdbddbaabdaaccaadaccbccbbdcbcdcddcbadbacbacacdbdadbbcbaabcbbabbdbbadcacbaddcbbacdcbbcaaabbbbdadacaddbbbdbcdacbdcbbaadaadcacdcbbbbddaaabacbdababdcbaabaadadccbbbcabacdbacabadcdcbddbddbddcbbacddcabaabdabdaabadaabddcaacaaabcbabcddaabcdbdaadcdcabcbadabacdabcddaccdcadbaaddddaaccadacabacbcadaaccbddcdbbbabdddcdbaabbcbbccdbcaadbdcbbadaabaaadaaacaabcbcdbcabdaddbcabbddbbacdbbdcadbabcbddbcbaccdaabaabdccbcabdcdabdbcbccadadabcbccbbcccbcadaabddddcbcabaccadcbabbcccdcbbbdcdbaaacbbbacccbbbbccdbdcddacbbcadcadddaabbaddadccdbccdbaadbadcaacbdabcddddaccdcddcdadaddaadcdcdbcaaadabddadaacccbbcaddaddccacdaadcddcdabddcccbcaaaabcdccbbbadaadccadcdbccaabbddddbabbbdaacbdbdaadaacbdbcbabaddcdbcccdbcaccbbcbbbdcccddcbcdcbbbdbbbcadadcacddaadccdbdbaaccbacdcbadacaadadaabbbacbcbcdcdcdbbbdcccbbbdadcabdcbddadccccbabcbdcdcadacdacbaddaaddcddcbcdbdddcbdcaabdacbbcdbbcddbcbcacbddddcbcbcadbdcbacbacabcdabbcbabdcdbbbdcacacddccdddbccacbaadbbaddcbdacbcdcbabcddabcccccaabbddccdcdbcbbadacbcddabadacbcaaadccbbddbacdcddbdcdcabdbdddddcadabcbcdcddbdadcadbabbacddacdbdcdbddbabbcaabddabcccaddabdabdacdcadacbaacbaabccaabbbbaaaacbcabcbadbcbadaadbccdbabaccddcdbcacdbcbdaaabaccaddacdcdbccacdabaddcdbaccbcbcccdcddadbbdddbacbcabcababdbbdabcbdabcaccdddaaacaccbaadadaaaacccddcbbdadbccdbbddcaadcbdbbaaabdadcbadaacbdddcadacddbccababdccbadbdaddcaaadddbbdaaabddacbaccbabbbcaccdbbcaabcdcdbbababbacabbdbaadccbbcadcdccaaababdabdaabadcaadcddddbcaccbabcdddadccddabcddccaadbcdabdadddbbcdaadaabbddddbabcbbbcbbabcbccadaadcbcdccccbaadbbabcbababdddaaddbaaacaadddacdbcbaabbcdaccbabdabdcabccddaaddaaaabcbcbbcaabadaabdbbdddacbbcacbabdddcadabdabdcadaabdaddcaadabacccbaccdbabccabccbdacbddabccadcabbddaaacccacadccbcdcdbbacbdccbaddddbbbdcdabbccdbaaacacaccacbdbdbdcbbcabbaadacabdcbcbcaacadcdbcccdbdccccbadcadcdddacdaabdccdddcbbabccbccabdcbdaabaddddbbdaababccaaccabcaadabcadcccdcbdddbacddaaaacbcbadddbcadbcabaabbabacbdcdadbdbbcdbccaaadccdbabaacbbadcaabaaaddabadddbcddcdbccaabaadaddcbadbdcdacbdccbbbbdbacdaabccabcbabdaaaabbcddddaacaacdcabdaaabaccbaaccbacdcbdabbbccacaccdaabaabbaacdaaccabbcbccddaadddbdaadaddacbcadadabcadadaadcdabcbdbadcacdbccaaadbddbbcbdcdccbdddbcacabbcbdbacdaaaacbbddadabcbdccddcadbbaccbbbcabbddaacbdddabbcbdcaabccaaddabbbbabbaadddcbdcbbabccdcdbdaccbbdcdcadcbabcbcdbbdcbcdbbcadadcaccacacbbcbbbacbdadbdcdbcbaabcbcdddbabdbadadbcbdaddbddabccdaabaaddddbcaabdaddbbcdaccabcddcbabacbabbdcdcbdbadabdddcdadadadabadaadcdcabbbcdddcbaddbbaadcddaadbacbddddddcdddaabacccdaaabcbadaaadbbdbcbdabdacdcdabdbdbcdddbaacabddaadaacccdbdabaacbadbccdbabbbcbdbdaaacdbdbaabcacacbbbbdaccddddbaddabababdddbaccbacaabddbcdcdddbdddacddbddbdacabcbbdadcdcaddcbdcabdbddcbaaccbabcaacbcaddbbcbdbaabcbcabdbbdaacbbdbcadcbaaadabbdcbdbdacdaaadcdddbcbccbbbdcdcaabdcababccabccdbcadccbadcdadcadbdddbbacbcccbccbaaaadaddabaabbaadcddbdcdaacacaabbccaadabbabadadadddbdaabacddccbabdbbddaadbacdabcdbdbaddcaddbababaadccaaabbdccaaadbaacdccdcaacbdabacabdabbbccababbcacdbbadcabadbbbbacdccdcccbdabccccdabbaddaaadabcabcbdcccabccbdddabcbbddbccaaacddbbbcdadbcaaccdadacdcacddadaccdacccbbdbcabbbacccaacabcdacdaaaddacababbabadddabccbbcbabbabddcaadaacdddcbddbcbdaccdbbcadbdaccdbdabcbcaadcacdaabbdadbabdabcdadbdcdcbdbbdddbcbaacbaddabdacadacacdbddcbcacbdcacaaabdddbbbabbdbcccdccbdcdcbabadccbddaadddbadcaccdcbcdcabacdbcdacabacdadadbcbddadcababcccaabbdcbcacaabcabbaaabacbbabdbaccccddabdccaacccbdadaadabddacacadbcdbbcdbaccccacdcaabddcbbdcdacabacccbdcdadcbccbdaddcacbbdddcdababdabdaacabcacaaddacddacabdacdaddbadddcacabaaddabdbacddccdccadacbcbdacbdbbbddabbccddaddabdaddabccbdddddcdddadaabdcacbbabdaabcbdaababdbabbccabdbdccbcccdaaacddaabbbaaaddbadbcdadbaccbbbaddcdcbacbadbbccbdcddacccddcacbbcdcdaccbabccbbbdccbbbdcbadbdcaaaddcaaddaaacacbccbcabacbcaddcbdabbbcddbcbddddbdaddadcbccbabdcdadacbbbddadcaabaacbddaaacbbaccacaaaadcbcaabcdbcbaadbdddddbcbbbbabcbdbbcbbcddaaccdabdccccdaabdcbccbcbcdaccaabcaadcddbabdcdbacbcdacbbccdbdbbbccaabcccabdadcadbcddbccbddaaaccbbdcbcbccacbabddaaabcaaccadcddcccdcabdcdcaddacddddcaaccbacbccabbbbcddcaddbbadadadbbabdddbbababbacaccbbcadadbdbdddaccaccbacccbaadacdbbdabaddbabacbbcdacdcdbdadacacdabbbaaadcdbbddddbcaabbdbcbabccdbdccaaaadacdbbdcdcaaadaaaaadddabdbadcdbbccaabaaabaaddadcbcacbdbbaabbbcddccadbccbabdacddddccbaabaacdbbabdcdddddacdbcaccbdadddbbcbaaccddcbdcccbcdccdcbacbddbdcbbdcdcbdddacbadcccaacbdbbbdcdcadaccbaabddabacaacadcbccccaccccbbdbccacbbbcdabacdcadbaaadbabddbdbdcddbabbdbbbbdbddbcbccbcccadaabaddcaacddcbcbbcbbcdcbcdddacabddcdcbadcadaacdcdbbacabaccaccbcdcbcadcabcaacbbccbbcddaccacabdbbbdcdbdcbcbcbcbcabcabddababddcdcabcbdcddcaadddaaddbaccabddcdcbbcccacabdccabcccdadcddabbdbbbbdccdddccbdbdccaddddabdbcddaddbabcabbccbccdadabccbbbccabbbdaddbabdbadbdbdcdbabaddbdbdcadbaccdcbdcdcddaadcbdbcdadabcacdbacddacdaadcdaabdbddbacbbdabcaacccdcdabbadbabcbdddbcacdddbdabdbdbdaacadadcbaacbdcdbddcccabdabbccacaadabdbcabbbcacdcbdbcdbdbbacdcbabccbdddcbcdddcdacabbbabadcbcaabdddcdaacddcbdabaacaadadbdddacabbbdcaccadcddadccdbcadadabdccdbdcaadbdddacdbdbbadddaccdacaaaaacaddcbabadabbcdadaaaacbddbccdacaccddcdacddbdbdbdbbbbbbcdcdaccdccdacaacdaaaaddcadbdaddccdbadddaddcbaabcddcadbcadabaadcdcdddcbdcaccadbccbdbbbdcbbbbbbbbdcddabbdadbadacaabacaadddbbcbadbbdbdbbbdbddcdbdcaadddddadcabddcbacadcadbdddbbbccaddbbcdadacddbbdbcabbdcdccadbadabdbbcbdbbbdcadddaacdadcbcbdbacdaddbabcddbdaccddcdbbdcbadaaddbbddaacbbcdacbbcdaaacccbdadaaacbbaacbddaccddaabbacddabbbadbdcbbbdbddabcbdcbcccadbdddbbdabddcdbaccadadaddacacaabdacdbbdacaddadccbacabadacddabbbacccdbdbdbbddcadcbbcdacdcccddbbbabcdcdaccccdddccbcccdbccacaacccccddacccabdaadbbaddbababcbdbcbbddbaaaaababcaaddadbdccbbdccaacbbaacaabcdbbcabcddcdcadacbbccbcdbcacabbacabdacdcabcdbbcdbccaaacdddddacccbcddadaabbdaadcccabadaabdaadcbbbddaddcacaadaabcdccbdacccdcadcbabdccdadcbaadcbcccdbbadbaadcdaaccddddbcabdabdbcacbdbbcdddcadadadcdccaadbbbddabccdadacbbddabdcabcbdadddcbbbdcacdbbcadcccbadcadbccdbbcdadccddacaaaadcdbbadddabbcdccbababbbdbaabcaabcbdbcddcbadaaabccccbbdacdbbdadcbacdcdbdccdabcdbababcddcccaddbcdbaccacabbacbacdaacacadbddbbbdababdbcccbbdcddcdcacdbdcccdbdddcdadccdbcbbcdbddaacaccacccadcbcbdacdbbadbdabcbdcdabcbaacdcdcacbbbbdadcddcddabbdacbbacabdbbdccbdbbdaaddcbaddaacbadbdccdbaaccaddbbdacbcbcdbdddcaacdcdcddddbbdbadaccbbaacdcdcdcdccbdcbaacbccbaadcbbccaaddcadcbdbaacdddadacdcadbcdcddbadcddcacaabbcadacdbbcaaaaaddcabdaccbbdbbabaddddadcbcdaaadbbdcaadbacdbcaadabccdbaabbcddcccdabbaacaabaabaddcdbbbcdabbcddaaadbbbcccbaaabbccacadcccbadaadaabdbacbadaadaacccdddccbcdbcccddadababbdddadcdcdadadbabdccabcbdbbabbddbdbbdabdaabcacacccdaacbbbacabcdcbdaacaadabbddbbbbaacbddcabbdcaccaadaaacccaabcdbabdacdbbcccdddcabcdaccdbcbadcbabadbdcbadcbabaccbbcbabbcaaddbcdcababdbbbcdcbabdcbbdabdcadaacdbbdadbbadbbbdbbaaabcdaccaaacaaddaaaadaabdcadacbcbdddbdabbcadccdadddbdcbcccdbabcddcdbdaaaacabacacadcbbbcbdaddccddcccdaadabbcbabddddabddcdaddbacccccbdbbcbdbddbdaddddcdcddadabddbcabcaabbdbcccddbbaababbdcabcaaabcadbcadaadabbaaaddacdcabccbcadbdabaddbcadbcadbddadbccccacaddaddbadbddbdbcbccabdbdbbdbdbcaaaddddcadacbddddcbdcadcaacdcacbbbdadcbdbadabdaaccdcbabcdcbbdabbadadaabaadcdbaadaadbccccdbacbaabcbbcdcddccadacdbacbaadaaacadabbcaccddcacbdbaaadccbcbbbadddcaccbaaccbacaacdccabbcadaacbaacabbbaadbcdacadcccbdbcdcbdcbaaddbccbabdaabaaccdbcbbcdcdcbdbbdddbcccdddadadcaaacdcccccbbbbdacdcccdbacdccbdbcbbaccaaccdcbadbbdaccdcddaabadaddbcacdbcdccadcdbccacdccddccccaacbcdabacacdbbabbdcacabdcbddbbbddcdcdbdaabcabdbacdbaadcacbcaccbbdcadabcbdbdccabaacdabbbdbccdbdcbcbaadddddbbabbddddaaabaabdcabdcbddcbdcdaddcdbaaacbbacadcabaabdccdcaabaadcadccabbaabbcbcbdbbdbaaaccabcbdbadacbcacbdcacbdadbddccbddbdccacdcccabbcccddacadbbadbacacdcaaaadcaacdbccbaddcbccacdbdabbdcccadccbccabccddcbbcdbbacdbacddbdcdbbccdccacdbcbdddcaadcdbaccaaaadbdddadbabbadaacccbbbbbcdbcaadbcdcabdadddcaddcbacdabcddbcbcacbbccbccbacbaacadbbdbaaddccdabacbccabadcdadbcbcdacbcacbdcdaacccbdcdaddbdadbcbadaabaaabbdbaaddaddaaddbdbcbaccbdabaaabaabadbacbdadcabcdbcabadbbbcaabcabacbbdadcccbbbaaddddacbdadbbabacaabbdbdcacaaaababbcdccbcccacbcdacdbabdbabbadaddbadadcaabbbbbdaaaddbaadacdcccbdcbabbaddacdabdaddcdddcdcdddccbcaadbdbcacbdaaaddadbbcbaaddccdbbdbacdcddcdadbcbdabccbcaabacdaabdbcbbabaabbadabdcbacddaccccbddddbbdabbbbacccacdbdcabacccacbdabcdadddcacdddabababbbdbadbccdadabbbbaccbdcbbbacaadddadbaccababcadccdcbabbbdaabddbcaadccabaadcccccabaaaadaabbdddbddaddbdbabadbdabaacaccbdacbbabbaabdbbbbabcacabbdbbcbabbcdcbddcabbbbbccacdbbaabdcccbbccbcabdcbaabdddcadacaacdbacbcdacabcadcbbcadaacccaccacddabbcababcbcccdbbcbacbcddabbadaacbcbdcdaabccdabbcccdcdacacdadbcacdabdadbddacdbdddbaaadcabbccbdbbddcdbabcaddaddaacadbbaacadabbbcdcccbaacdbbccdabcbcddddcaddaadbbdbadabcdbcdbcbdaabdbdcbbcacbdbcbaaacccbbdcbdadacdbaadbbdcabddcabbcdcaddddaaabccdabbbcbcdacccdaccdaccdbdbbdccbbbadababdaabcdbbcdbdcdaabbcaaaadddcdadbbabddcdcaddaacbccbaaacdbabacadcaacdbadddaabdccaabbccdbdcdbaabbcabdabdbdbdbccbacdcbababbbcdadadadbbbccaabdcadbdbdccacccbcdabcccbdaddbcdcddcadddbdcbacaccdcccbbaadbbbbbddddcaaaadadcbccbbcdcdcbbbabcdaacacdcdcaccdcccccbbdcbdcddaadacacabbadddbabdbcaadaddcdbbcaaddbcbaddbdbcacddcabdababdadddcbadbcabdddadcababddbaaabddbcaaaabcddbbbbccbdcdbbcaacddacbaddcadcdccaabbbccdbdbcabcddaacacdbbdaaabddbdbbccddcbaaadbbadccbacdbbabbaddacadbabacbccaaabdbccbcbcaddabbdacbcdbcbcaadcbcdadadbabbdaccaddcabddbcdabbccdbabbcaadbbabddaaaddacdcdcaabbbdbabcacccacbadbccdbcaabdcdcbabccaacaddbaddcdcbbdbccbabaacccacccaddcacdaaaccdbdccccadbaaaabddbbcdcdcdcabaccbdbacdaacbccdbdcdcdaddbcbdccddbbcbcccaadccacaaccbccbbcdabbbcdababacaadaaabddcbdbaacdbbdddaccadadacbcdcaaabaadadacdabbcbaabccaccadcacaabbaacbcbcabcdbcbcabccbccbcdcccdbbaabdccdcdcaccacdccdcddbaacdcacdaaaccacbcbbbabddcaadcaddbaadbccabdbbccbbbbccaddbbadbacadcbadbcdacdddddcacdccccdcbcccaacdaacbcddaccdbbaabbcabbbbdccbdacdbddbcbdaddbbcabddadcdadbabaabcddcbcbaabcdbddabdabbabcdaaacdbabcdbdabcdcacbcdddcaadaccaaaacacdcccadccdabddbcbdcbddbcccaabcdbdbcdaaabcdcccdbbadbdbbabcadbbdcdddddbcbcabcdbcadacccacbaacabadbabdcbadbadcdcbcddcadacbcbbdbddcbdcdcbacabadbbdcbbacacbcbdabacbbcaacdabbadbbdbbbaadccabbaddcdcbbabcacbabdbbbaaabaddacddadddddccabcaadcacdadcdddadccbcccabbcacadbacadcbabccaabbbdbccdcdbabbcaddbcadcbcaacdbbacdacacaabaccbcdadcddbcdacccbcaaddcdcbdbadbaaabadaadbaaccacbdcbccaadacdaadccaddbccabadcbdcbadaabcacaabddaddddbbbdaadaddbadcadcabcbadaaadcbbcbdbdddccccccdcadaabdddbddbbaabdbadaccbcaaddbcbbcaddbaccdbcbaaccaddacbdaababaadadcbccbddcaabdcbcacbbadbbacaadaabdbdcdacdddbcbababdcacbbcbbacaaacadaadcccddadcbacccbdacbcbabdcbdcccadbcbddbcccbacacbbacaaacdbdcaccaddaddbcbaadcacaccbdcccabadbadcdbadcdcaacbccbabdbdbbbcadcbddaabaabbdbacbdabcaddadaaabddbdcbadddaadbbaccaccabdbaaabababddacaabbbbacddddddabacbddadbdabbbddccccdbdbdbbcdabaadbbdbabbaaabdccbdddcabdaaaadbdaacbcbcdcbcbcbdcbaddbcaddddddcadaacbbbaaabbdbbadacbadbbdaddbbdbbadbabacabdacdcdabbddabaaacddbcadaddaddcccbbdacaddaacbcdbddabccbdabaaacbcdadddcccccacbdabcbaaaddaaacddbbbbabbbcdacbbbccbbdadaacaacdcaabbdabcbdacaabaabdddaddddbcaddbadacaaababcabdbabadcadaacaabadddccbddbbcdaddcbadcddbbbdabcbdccddcdddbbccbdabbaccaabdbbbbbbadbabddbdddbcbadbddbcddddaddddcacadcbcaaacccdcdcabaabcccccddbbcdbabadbbbcccadbbcdcacccbabdbccdbbdacbddbbcbcaabcbcabacdcddcdbadcaaaccbddacbdbadbcdbccacbaccdabaccdddacbcdbbdaacdcbacdaacaaddabbaaabcbadccdadbdbcbcabdabcabaacabbbbbcbabbdabdbccbdcabdddbbddcdacdabacdbdbdbaccdaabbccbbadbdadbbdbcacccbbadbdbabcbbdbbadbdbbbabdccbbdaacddbdacacaaabddbaaacbbddccdaabcacbaddcaaacdbbbacadccdabcdabadbccddcbaccbacbaddbaaacbdcabcaabcaaaababcbcbbccbaadcbcdddbbbdaabadadacbcacdaaccccbbacddddadbabbcadaccabdcdbcbacccaadcaccccbdbdcdccadbacbccabcddcbdacabdbabccacdcaabdaadcddcccbbbcdddbaddcccbbcbddccbbbbcdbbdaaddaccddadcaaabbcbddccccabbdadadbabaddcddcacccaddbadbdcddcdaadabadabcacbdbadbaddaaabadacabbbcbbddccaabddbbbdbbdbcaabacadcddcaabadbdacadbcbdabcacaabcdaaadadbadcccabcccbabdccddddbaacdcacbddcbdcacabdcdcadbddcdbdcbbbaabcddbcabacaacadabaaabcccbacabcbccbbbbcabcbbbdbcbdaddbbcaabcabbcdccbabdbbbbccaacdaadbdaccdaaadbcdaccdaaabaaacbbbcdbbbbadddbcadbdbdacbcaccaaaaabdbaabbaddbbdacddcbcadbbdccdcdabcbcabcacbbbabcdaaabcddacbbdacdbbadccacbabdacaddccccbaaddbcadbcdadcdbccabbccbaddaaaccbdddddbcdbacbabaacddbddadcdacdbadcabbabccbccbaabadacbbabbadbccbaaadbaaccbbccabcdcadcbdbccdcbabcbdaacbabbcdadcdcdaabbbbdcbdcdddbbcdbaadbabdbddbadbbdabdddaaccaaccdcbaabbddbdaabacbabdbbcbcddacabddbbcbadccdadbbddbdccbbbdcdbabcbdadbdbaabbaddbccdbbaddcadcbcdbcaaabaadbababddabdcbdbbccbbdddddccaaccdcdbababcaddcbaadcaadddcadacbbdcbccacddadbccdddaabbdccdcdbdbbddccacdbbaaadabbbbbbababcdccacdadddaabaabcccbaaaadaccdadbabbaacacdbdacaaabbbdcaacadbcbcbdaaaacdbaadbaccacbcdcdddbbbdcdddadcacbbccbdbacaaddbccccdcdacadbdcdcbcacbddbbabbbbabbcdbdbcadddaabdacdcdabddcdbbacadcacaabbccdbdcccbcdbdbccccadacaadadcababcaaabadaddbbddbcaaabbdbcdacdabbaccdbdbdbaadbccdaccaaaacdcacadbbccbcbbbadadbccbcbcdcccaaabcaaddaabbdbabcdddbacdbccacbadadcdcdcdacbaadadcbbccbadccbcdbcadacdaacbababbacbbcbbdbcabcdabbcddcbcdbadaacdaccdaabbbdadbcddcbcbdcbbccccbcbabdbbadbaccdabdaccdcdacdbadabbcdabccbabbcbbcabacabbcbcbabdddbaddbddacadabaccadcbcdabdbbbabacaabdabdcbbcbabbbccbcdabcacababdadacaccacaacbabbaddcdbdaababccbdacbdddcadabdcdaacbdddabddbbaccbcddbbaadadccdabdabaddadcbbbaacabbbbadbcdaacdabacdccadacccdbabaaadcdacabaadcbbddddbaaccdaddaaabadbccddacdcbacbbabcababaacaddbccbddacbacddadbabadadbcbabbcdabccdbaabccabddcbbdabbcdaadcddcdaccddbcbacddcdddcddadbbcdabdbbaadcadcdadbbccdcabbacbdcbbdadcabbdbbacbdccdddbdcdbabddbcaddbdabbbadbacbcbcaabadddaacddddccdaccbddbdacabbaadcbbaccbaabcbdbbbbccacddbadcadacdadcdcacadaccacadabdabdbcaaacdbdbbccbbbbbadddcabbbdacbcbadbcdbcdcbddddbccccbbacccbadbbaccdcdbdcadddcddcdaaadaccddcabbabdaabccccbbaacabdccddcddcbbadbbacbbdcbdaabdcbbbbddcabdabadadabdbbabcbdcaddbdcabdbcdbdbdcdcdbcdabacbbbcbdacdccbdaddaadabbdbdcaddcbdbcbccbddbbababbcdadcdadaababdaadaaaaddbbdcbbdcabacbddacbdbdabccadbbdbcadcbbbbadababdbdbdcaabccbacccadcdacdbbcabbdbadbdabadadadcbcbddcaacddcaddbccaacdbdcbaccdcbccdaddcabaccabcdccbbbcddbadddbcdcddddaacdadababdbabddaaaaddcbadbcaccbdccdcaaadbaccacccaabbbcbaadcbaadbcabbbcdbcbaacdccadaaaaabcdcacccadcdbbdcccbdddadbcbbddbdadaddabcbdcdaadaddcbdaacdacdbcdabcabdbadcbdddbdbddbacbccdcbccdababdaabddadaabbcbbdddddabcaccaddbcbcddbbbccbaabadbcdacabbbbdacadcbcabdbbdcaaacadcdcccaaaaaadddbadaaaadddcaaacabdcaccabacccababbddbbcbabbcdbcccacbcdabadccdaccbddcbbbdcabdcbcdacccaaccccbccdababacacbcdababacacbccbcccdbcbcdcadbdacdbdacadbbdcacbbccdbccdcdabbaaaacbcbccbabdbbdcaddaaaddaabcddadcdadacdddddcbcbaddbabcacaacdbdabacdadccdcbbbacddbabadcaadacbbaaacdcacaddadbbacbddaddbacdadadbbbcadbdabccbdcdbdacccbcaabadcdaadbadcbdcacdadbdbdbaddaadcbdbbcddbccdcdcdadcabdcaabacadccbbdcacbbbdadabdcbbcbcacbbcccacbbbdbcccaaabcbacddcadbcdcdabcaaadcacbdbabaadcbdaaddddbcadacbaabaaacddbdaddbdbcbadbdcaaacdbcbbbcdaaadacbccabcabddbdacaddcccdbccbabdbadcdddcddcbbaababacbaddbcddadcbbcdcdccaddbdbbadaaaccacddacdabaadcadcadcbdbaaaddddbacbdbbddabdccdcabbdcbaabddcdbdadaddbabaacacddabbddaacbdcabcbcbaacddbccccadabaaaadcbacccdacdabcdaabdacbdcdadcbbbbbdcadccbccdbcdcbdabddbaacbccdbacdbbbcdcdbacadddbacbabaddcbbcdddaacaabdcadabdcbbabcdbdadaccbbcbabdbddccccbadbdbaaadbcddacbbddbcbdccccabcbdccddaabdaaadbcdddbdaabcbbbaccbbbccdaacbdbadbcbbbbccdddaddadbaddcadacdadacbaadbcdddccbcadcbcdadbdcbdcbbdbbbccdacbbbdabacbdcbdbcbadcadaaacadcadbadcaabbcdaaadbdcddadcabaaddddababdcbacaddabdddcaccbbcdbbcbccabccaaaadbadaddcaaadcacddacbacbcddbbcbccdbcbaddbbadabacdbdacdabbdccdbcaabacbdbcadcdcbacbadbcdabdbcdadabccbadbaaacccccccdcccababacbcbddcdbdbbaaacbccbacaaaccbbadbddcadabddbbbcbdadacccaacbbaacdbdcbddacbcdccbcdcddacdbcdbcbacbaaddcdcaddcdbcdbadbbcccdbccdccbbcbdaddbddbdcdcdbacacbdadbbabdacccbcbbdabdbdabbbbcabcdcbdcddccdddbbdadabbaaaccdbbcabbbcdbcbababdbcdccbacbaadaacacdadddcdaabdcbaadaaaaabddabbabbbdbcccdabacbabcaddbbadbacaacbbabcdccabcaaadcdccbddcddddccdcaabdddbddcccabbbbcaaddbcacdadacdadbbddbdbababddbacddacaababcaabaccccbbbaaadccabbabdbbddbcacadcadaadaaaabababbcaadcdadcddbbdaaccbbbacbdcdccbdbacbabccddbdbaabbdbaccdcbcaccbbdcbabdaadaddcdbabbbcbdadbaccdabdcdaaccbadbbdbdbbcabdccbcccbabcaadcccabdadbbcacbadaabcadbcbbacccadadcbcdddbcbbbdcdbaccdadabbabccbbcdccdbcaadabcacddccccdabccddddbbaaabdbdbdadbacdbdcacbddaacaccdbacbadbbdadddcbabccddcaabadcdbddccdccbdacddcbbcddccaaccbabbdcccbaddccbaadcdcbbbaaadcadcbcbbcdcabcdbcabdadaabccccababbaacacdadacaacccacbddbbbbbcaaaddbbcddcdaaadabbbadcbccbdccdbddaaacccaccbacabacaddcacbdadddbdadcdbccddbbadcddacdabdbdaddccccbadcdbbcccbbdadaadcbccdbbcabbddcddbddbbcbdacddcccdbdcbbabdcadcbcbacdccaccbababacddbadcbccbbdbcadacbdacbdddbbbabcdbcbbbacacacddddbcdaddbbccbdabdbbbcddacbacabbddcbbbcaccdcacdbdbbbaccacddacbacbddbcddabdaabcaccbdcabadaabdbaccbcbbbaadbabcbcdbddbdbaaccdababbabdccdbbcdbdbdcaabddabcabbcbdbaddaabdcbddbddddadcdcddabcdbbaccabbadabaccbbbdaaacdbbcdadbbcdbadadacadaacaabbbcdbdabdabbdddcccbcaacabaabcbabbbbddacdabaabccdbccdbadbdaccbcaaabacbdaadcbdbadabdcbddabccadabbbcdacbbcbcacdcdddbcabacdcbcdbaaadccaaababcbdbccddaccbadcabccacabdddadbcddbcacdcbbbdcdbaaaddbddbddadccddddadbcaddccaadcdbbcdbdbbacaddcdbaaaddaaddaabaabbcddadbacbcacabcadadadccdbacabcbacdaaaabdbcaaabdcaaddddbdcbdaaacdcbccbacaaaacadbbdaababaadcbaadabadccbbdccdaabddbaaabccdddcbadabbabcdabaacbbbabcabdccccbbdccdccbdddcabdaaccadadcddbddcadacbaddaaacdcabbbdcaccdcbbccdabbaadabaabcdaabbadddbabddaaabbcacaaabbacdabdabdadaddbbcaaadaadcdcbcabbabcaabbcbdbacbbccbbbabcbdbdbadacbadccdabbaddadacdbcdbdbddddaadccccddaaaddddcdbcccbddaadbacbcaadacbacccccbbdacccdabbddbbdbdcdcddaacaddbaaaacdcaacddddddbbdaacdadcaaadcbdcaacdadbcddadddbdbbcbddbcdabddbdbaacdabaabbbbddaddcbabcadacdaadaaaaaaddcdaccbcacddbccdcaccddcbcdbdadcbdacccbccdbdcbcdbcdaddaacdaddbdcdaddbbcbbaddddddbdbbbcadcacaaababababcbccdbbcbdbbbaacbabaccaddaadcdacacacacccdcbacdadadacccadbcdbdbabcbcadaababdbacdbaccacabbbdabdadbacddcaccaacabdbcbaadbaacbddadcccdaacaaaabbccdadaadacdbdcdabdaaabdacaaddacaccabaabcbbccbbacbcacaabbdabbbdbdacdbdbcddcaccdcccdaccddbccaaccabbdbdbdccccdabddabccdbabacdcaabddaacbdbaaacccddaaaacbdcbcdddddabcdabbacbaaabcdcdcababacbbcbadbadcabadabbbcadbdadadaaaaacdccdcdabadcdaadaabaabaccdddcdddacbcddadcdacaaabacbccdcdbdcaddcadcadcccbbadcabcccbadbabdaddbdbaccdcccbbcbaabdbdccdbcbbbaccbddcbbbbddddadbbdcacbbdabacdadcbdbddddacbbccabadadbadcdbdadddbacddadaccccdadaccabbdcbadcbcadaccdbadbcddbccbcabddbdcbaababaddbdbacddadddcdbaacbabdbaadaacdcadbaabbcbadadbabaaaadddcbccabbdaadabcaddbcbcdabbcabaacddacbbdbbbbadcbdcbabbdcaadabcbcadbcbacbcbbcbdbdbaaabbbdbcabdaabcaabddcddcacaacddadcdabcdbacbbcccbddacccaacdcddbcccbdcbbabddbcabbadddcccdbbcdcdcbabaabcccbcddacddbadbbccbbbcabbdbbaadacbaacbcbddbbdcbdbabdccdacccdadabdbbcadbaccccaddabdadbcbcbddcddbbbcdacdacbdbacacbccabdcddcbbdcbbacacbdcbdacdcbbccccbdaddcadcdddbcbdbbcddbacdcbadadacdcddcdbbacdbcdbbadcccaddacbdacaadacadbcdcabbcbbccdccacaacdcbdaddcaabcaaaddaccbcabddacccaabcdbdddbabbaabccbabaabdaadabbcdcbccdddcabcbabdaabcaaaccbabcaadbddbddaacddbadabaabadccbcbcbdaddabcdacacadccaabbbaacbbbacddcdcabdbccabcabdbacbdbbbbccaacdbdadbddabbcddcbdcbbabbbccaabaccadcbaaabaaadbacbdcabccbbcdbdacddcdbdddbdbcadbccabdcccbbadbddadbddaabdbbcbdccbccacbbdadbacccabbbcaaaabbbdbdaadadbbcbcbdbcbbbaabcbadbcabbccbbdcddcbdcaaadaaabdacaccabbbdabcdbddabbcadbcabbcdacbdcdddbacddbcbcccdaabbbcbabdbdaacbadcabccdbbccbbaabdaadbdddcbdccdcaddabcaaabcddbacadccbdddbaabacbcddbdcbcbaaccdccadbccadaadbcbbacdbabdbabacdccbbdabcdadccbdcbcabcaddadaaacadcaacdccccbcbacacadcbaccdcdcdddaddcdbbbabcbccabcacadbaaabaabadacdccaccbbbabdaaabbbdccbddabcabbbabbdcbddbcccdbaabddccddcddccaabadadbcbbbbbadbacaddacbbbaadcdacacabdadaddbcdaddabbabaddabdacbcacadbaaaddbabddbcbdaddabbddcabaacabacbccbacddacbcddbbbabddcdaddccdcdbddcdcbcabaaaaadacbbbdccacaaabbbbdcbbbbaadbdbdacbcaabbcdadbbbaaacbadbbdbcdbaaabadcdabaddcbdbdaacacadaccbddcacabddcbadcbaaacdaaacbcaccacccabddbdbdcdaabbcccccbcabdabbbadcbcdccbadcaddddbdabadadbbbacbabdbabbaacaccddbddcdddbbaacdbcaacdabbdaaccddcbbbdaacbadbabaabadbdaddbbccbcccadbabdcbddabccbbbdbbdccadaaccbcbaccdcacccaadacddcbaabcabbbcadabbcddaadddbabbdcbcbdbdadabddaddacdbdcadbcabcacbcdabbccaabadbbadcaddaabaadadaddcbadcabcbadaddddccacdcaddaccbbbbacacabbbcaccbbaaddbdaadddbacbbadcccdcdadbccadddddacbacbaddbbbcadadcbbaddabcccdbdadbbaacaaccbbbbdbaaccdcdbcbdcdddacaaaddcbdaddacbaaccabacdcacdcabbacbabaddbabbcadaabdbdbaadbadbbbbabccadcdbabadbdabacdadbacdbcdbdaaacccbacdbdacbadcbcbabdadbacbdcadbcacbbcbddabadbcabdcadccdccdadddbdbbaabbdacccaccdacacdaccdcbccbbcdadbdbbbbaaaabdbaaacabcbdaabcdadbcdabddbaccdcbbbccacbdabddbabbaddddcbccccdaabbdbdcbdbcccdbccddcdbabacadddcbbbdaacbabcbaabcacccbbcbccbccccdbadcaacccdccdbaccabdbdcdabbadcabadcbcdbaabcdacddbcccbcbdcccbbdaadbadbdbddddabbcadbcdabbdbacadabcbddabdbdacddccadabbccacdabcbbaabbccccdcbdacdddadacacaaadadacdcbdabccbcbccbbccacaccccdacdaadbdcabacbacadacdaacdcbbbbbbcddacbcbabbdadcbacadabdcbdcccaabaacddbdcdadcdbaacbcacdcbddbcaabbcdbcbaccddabddcdaadccaacddbdbbcddcbdabdddaddddadacaccbccdbdbacbdaccadaaadbbadabbdccbbdccbacadacdacdaadaccabbccaacacbabdaaddcdbcddcadcabccbbaccdacbbbadbbdaabaacddccaddccddbaaacbcabbdccdadbcdbcabdcacadaabcadbcdaddadbadcaabdcaabdbdaccaabcaacadbacacaabbccbbdccddbbabbbcacbbacccdcababaddaacdbabadcacbadadcadddbcbdcdddcaaddcbadbdbbbccdcdccbacabbbbdbcbcccdbabcbacbccdaaacababccbdaadacdccbdcaabaddddbbcbdacaacbddacbbcacaaccaaabcccbcdacababcbaddbcaaaadacbbbbcbccbbbbcbabadbbdaccdcdbcbbacacdddcddadaaaddabbcbabacccaddcddbccabadbbddbdacacddadcdabbcdddcdbccacbdcbdcdbcacdbcacdbddddaaacacaddabddcacbadbdabccbacdadacbadacdadadbdcdcdbbbccccaaabcddddbbaabcdbadacdccdccccbddcdcbcdcddacbdcbdbbdacdbdbcadadaadbdbcadddcdbdbdcbadaadcdabaadbacdadacddbccdcbbcbabccdbbbdadacadccbdcccdcdaaabcbdbddbbadaaacadabdbbcbdbbcdbccdccdababbaadacbdccacaaddbabacbdbdbbdccbbcbcaccabadcadcbccbdbbbccdcddacbddaabbabcadbdccadbbbabbcbcabbbbaadbcadcadcdddacdacbaabacbbbaacbacdbdbaabcaccdbaaabcbdabcadaabcccbadababddabcbddabcbacddacbdadbccbbbaaccabbbabbdcbdbcbaccbababbcbcbaccccdaabdcddddaabacacbbadddabbbcaaabacccbdbbcacadabadabdcacaaccbbbdbaaabcaabaabbbcbdadacaaaccbabcdabdcbabddccadbdbabccaddaaadbdcabdcdddcdabcbbbbbccccdbdbbccdccdcaccaccddbbccaddbbadccdabdbccabcabdbdabcbabddcdcddabbdccbcbcdacbcdccabacbcccbcdddabcacdcacaabdaddccddbacdcdbdabaadcabdaccbcbcbdaddadccadbcbbbbbddccbbbbaaabdacaacdcbdcbbcbdcdadaabccccabaadabdcbdbdcabbcddadbdcccacdcdccdcbbcbdbcbddaaccdabcbacddbbbcbaaacadddadaccdcaadbddddcbaaadcdcdcbabcadbabcbdcdcdabbccdbdacdaccaddcbccabdbadcabcccbbadbaccdbadcdacbdddacacbcabcaabaddbdadccbacdacaccbacabacbaddcbccaddbbcadaccdadbddcbbdbdcaadcdacaaadaacacdabdadabbdcabbaccdacaaacabbdbabdbcbbcbadadacdabadcdaabaadccbcaaaaaabddcdccbbbaddaabccacaccbaaaabaacabaabbadcdbaadadbdbcadaabadcdaccacaabaacaccaddacbbddadadcbddcdbacccabddbadcadcbacababccbbacacdabcabcbbccaccdccacbadcbaccdadababacbdaccbacabdccbbdacacbdbadccdaccaccadbadbcdbdbabcaccbcaaacbcbddccabcbbaaacbdcabdacddbddaaadddacbcbbdcabdbbbccaacababcccbbbdbdacadcacbbbadaccacddcabaababcbcaabcadbcbbdabbabdcbabadbbdbaccdcddcbcbccbabcacabccddadabcabdaaddddabcddbdbabdcacdaddcbbcabcaaacadcdbddccdbbaacadadcccabdcbbdbdcdcabbbbbccbcccaadbddcdbcbcbbdabbdcaaabdcadcaddbddaadccadbcacdccbdbbcabaacabcdbcdbdbaabbcdabddaaaddbabcadbddbdcccaddbdcbbdccbdccbacbbbbabadadbdabbaacaacbdcadccbbcaddabccccdaadccadbcddbccdaadadacbbcdbcdadbdacbcddaaddacdadbadcacdadaddbdaaaadaabcdbdcbbbdbcbbcdcbdadcdcaaadbbbccccbbdbcbcdccdadbdadcdbbaddabaddacaaddabccdabbabaabbacdbdccbdbcdacabaccdbacccbcdbacbcbbcabcbcbcdabbdbddaacdbcbdaadbbcaabddbaadaaabbadbadbcbbbabbdbaabcbaccddadbbbabcbddcdbabbbabccaddbbaacddbdaadcbccbcbcbdcbdddccddcddcbadabdacaacdbccabbadbdbbadccbabccadccaadcddddcadcacabaacddbddadbbdabaadddbaaaadccdbbdbbcbcbabbbaddcabbdadbbdccbbaadcacaddbbdcbddbdcbaacaaacaaaaaaabcaaacbabbccabccadbcbaddbacbaabacdbccdcbdcdcbcacabcacabdddccbbbadcbaaaddcbcbcacbacdbccabdcbaacddbadcabbaadcbdbcdddabcadbbbaaabcdbbbdacbdcabdbbcaacaddddddbaaacdbccdbdaadbdcaccdcdabcbaaadbcbabbdbcddbdbbcaacacdadadcadcadbbcaaccbccbdbababccdddbcaaabdcddbacdabcdaaddcaaaccabdbabdcbccbddcdcaddcddadbcabcdbcadddaaccdcdbbdbdddaadcdadaaaccccdaacccadadddbacdcabbbaccccdbdbdbabbaacdccdddadbcccacbacbddaccacabbdcbacbcbbdcbcdbaabcdbadabddaccdabbbabbacbcabbccdbadaaacbcaccdacaabbcbcaccaddbdddaddccadbbbdbcdcabacdbcaddbcddcdcccaaabadcaadaddbccccdccddbabddddddabcccddcbbabdbbcdbcbabcccadcbccddbbdcaabdacdadcabcacddabbabcdbbbcaddabcadabbdcdcdbdccdacaabbdddcbcaccaaccacbdaacbacadccbccaaaddccdddbccbacccbadcbadcabdcbdcddcbccbcbbbcdcacacbbadcdcccbccddbbaadbbcdbaaddbbabbcadabaadabbdbccdcccababcbadccbcbcbbbdacdbccbdbbacdbcbcbabbbcddbbcabadbacabbdbbaacaaddbabcbcdcadcacbdbbaddaccacbcabdbddccadbcbbbdbcdcaadaccddbababcdacdabcbbbacbdcdabaaaacacbacaaabadbaabcbddaaccbdddabcbdbcaabbadcbbddbbacabcabccdbdcadaaacdaccaaddacadbcdbdcbbbaaadcbabdbbbbbcbbcabcbccdbacabdbcbcacbbbdaaabdcbbaaacccbddddbcabbcabacbbadcdbdcacabcdacbcbdcabadabaddcdcabcddcbdabcdbcddaccacabadcacaacbbcabcacddaabddabacadabcbbaaaacbbbccdddbccdacdbcdacabbabbdccacdbddabbdccabcacdbdbcadaadbdaddcdbaaccdaabaddcddbbabbadddbdbadddaddabaccadbbdbcbbcaadcbbadadcccbbbdacbdcaaacbbdccbacdcaaabdccbdacbdbdccbcaacccdcadbddbdaddcbbacadadcabdacbabcdbbaadabacbbdaabbbbdbdcaabddbbcdaadccccaabbadccbbccdcbadacccabbccdccdcdababbccbdcdcbbddcccadbddbabdaacabaacbccabaabbbccddcabddbabacaabbbbdbddaccaacacbbbaabaabcbcbdbacbabdddbbcdcbadbbababcdaccbacbbaddccaabccababdaabdccaabcaaacbcdbabdcbbccbabdacddddadaaaccaaacbdabcbbdbaaabcaadbbbadadaabbbbccbcbbbaddcdadacabdcdcdccbbabbbbdaaadccbdbbdcccbadccddcbddbcccdbcdcdddbaacccbbccccacbdcaccdaadbbccbacaccddcabbcadacabaddcaadbdddccccdbcdbcdbbabccdcdcdbbccbaabbbcbaadabccaccdbaddcabaaadcdbabddbdcbcdddcabcddbdbcbdcacadabbadccabbabcbcbdbdadbcabbbddbabbddbdbababbcccabdddcdabddbaddbcccdddbccadadabaabcccbcbabccaabacbcdcdbbacbaaabccdcbdcbacdaaaddadbdbcdcabcddcdcabcbabbcadadcaddabcbbddcabdbdbbdaabdcdddbddacdbcadcbddcbaaacbbddcbddcdabdcbabbbcdbbbbbaccadddbbcdcadddbadbacaccaaacbacabdbabbbbcadaaaacdaaddccabcddccdbcdbddaaabdbadadcdbbadcacdbbcbadadcdddabbcdaaddccdbabdacccdccaadcbdddbbcabdbbbaaaacabdbdacddaaaaddcbabaaabdbadbaadddaadbbbadbcccdbbdabacbbaccbababddbadcabbcdbabccbcbabadabcccaaadacddbbbcccbdcabbaddbbaddaccaddaabdddcbccadcabbbacddaabcabdadbaccdacbbbbbbdbbdcbcdadcbccbdcacbadbbbdaaccdccdacddcbdcdabdbacdaaaabbcddcbbbabbdabaaabbdcdbdcdddcdcdadcadbaddacbdcdddbbadbbacbccddabcdcbaadacbdabcbdddbcbddddcddbbcaabdcabcbbbaacdbaacadbacdaddbbcddbbdbccdbddbcdbaabcbadacdbbcadaccbbbcbcccadddccdbaabddadbcdadabbdbadcbddaccaacdacbabcabdcbbdcbabcabbdabdacbadaabdaabcddaacacaabbbacbcacdbbccdbdcacbaddddadabcbddcdbdcacbabcbabcdabbaacdbaaadbdcabcabbdbaaccbdcdccdbbdcdbdddcababaadacdadbcdbbbccddccbbdacccbdccaccacaabdacdbcdaabdbdcbbbddddcaabbdcacdccdbadbdcabddcadbcbabbcdbbabcccbdaabddccaacabcaccbcdbdbdabdccacdacbbccacabcdbccbbdababcbdcddbdbaacbbccbacadbbdccbbccdbaabdacabaccdcbddcdcbcabacdcddcdbbbccacbbdadbbdbcaadddbdbbddbccdccccbccdbddbcbaabcdddbbadcabdcddccaccbbcddabcaabbbdbdbadadbcbaabcababddddacbcaababdadcaaacdccbccbcaacabadcbabcaadccdcabcbcaadddabbacabccbcccddcbccbcababcabbbcbdacdabbaadabbbabcaddbcdcbbbdbdcbbaccdcadcabdadbcbbbaabbdcccdcdbcccdbabadbccadbbddcddbcabdaaaadddbcdcddcbdcaddaadbcaadcadacaadbdbdadccadcddcbdbbabaadbadaadbbabbbbdccbadbadbaaaacaadbcbadcaacddccbcddbdcbbddddbcdacddaaabcaccaccacbbdddcdacdcbdbdbdacddccbddaddcbacadcbaadadcaadbdaddbccddcadccdaabbbaabbcbcdcbbaccbbcacbaccdddccabcbacbbadabbddddcaddaabccbddcbbbdddbcbdbbdcccccbbdadcbaddabcddaadbacbbadaabdbdacdaacabbcabaaddbdbcbccdcaabadbbcdadcdddaadbdcdcccdddcbbcadabdcbcaacbbdbdbccbadbdabbaacbadaabcbbadaadcaadbcbabcacbdcacaadcccbaacdcccacacdbbadbbacacdcbcdbdbcaccdbbaaaaabaccacbbdadaaacbcbabcdcabcbcbbacaaddcbdbbcbcbaadbccbbdadcccbccbdccdcaaddbadcbdddddaacbabcbdcdcdcdabcbdccdbbbadddaadaacaddabbbbacdcadadabcbbadabbacccdaaccdcbddabbcbbbccabdbdabcdbdbdddccdaaaaaccbdcbaddadbcabdcdadbdccbcadcbcdcdbcacccbabdbcaabcdcacabadbbcbcbacbbbcacaabaacabdcadcabdcbadcacdccbcbcaadbddbcdbabbddcadbdbcdadbccbdcabcbaabcbadaddbdbbbcbacccdaabbdbacacdaaccbabcbabacadbdccbadaabadabadcbacbbadbacdbadcacaacdadcbcaaaaaadccbdadbadbcdbbaccacdbbccdccaabbbddcbbaaddbbbcdccbdbcddccbacbdadaacbdadabddaacbadbcdaacaddcdbaaaacaaabccccaccabddcdbbbbccddccacddccdacdaddcccdbbabadaccbcadadbbbcbdbaaadccdacbccbadababdcacdadacaaadbaabdabbcabbbaaddcddcbbcdbbaccacadacadddcbbbcbbddddbccdabaabaabaadaabaddccdaddcabdbacabbbdabbcaccdccdccdadabdcdcbbbddddccdbbbbacbcdccdbcaddddbadcabdaaabccaabcabbacdcacbadcccccccccbcbbbbdbbbddabaaddaabbbadabacdaacaabbdcaabcabbccacbdabaadcadadbaaaacbaaacbddddcdbdaadccccaddbadbccabacbccbcbbcaacbcbcadcccbdbdcbadccdcbdbdcbdcbddbcaacaddadddccddcadcacdbdcbbbadddcbcabdcaabdadbbbdbccbbbcbbcbcbadcaabdacbbcddbbbdaaabcacaadbbddacbdaddcbdadcbdddbcddaabcaabbbbbadbadcccaaacbacbbdbcdbacabadbabdcbcabcaacacadcaadbaaaddddbbbcbcdbcacbacadddccacbbbbbbcccbdcdddadcadddcccadddadddcdcdcdcdcdcddbcababdbdddabcdabacccbccdabbacbdbababaacccbdaccccbaaaabdbaacbccacbddbcbdcdbaaaadcddcdddcacacbbdcccbbdbdbdccbcaacbdbbcacdddccbddaddbdcdabdbddacabccabbbdbabadbdbccaaaabaaabcbdbcaabadaccabcabaabacadcddabadadbacaddbaccbbaaabaadcdcdbddbaadccacdabbdcbabacbcdbadaddbbaabccbabbdccbcbbaccbcabdccbdbcccbccababbaadbcbbaccaccaacacccbdbababcbddabbcbbabadbdcaddbcbcdbbbcbdbabddbcbabbdbccaadaacbaccccdcaccdabcdbabdaadbcbcdbdccaadadcadccdcacaadaacccaaddccaadbdcbdacacdabcaddddadbbbcdbabddabaddcabbcdaaacdacbaddaccacbdabbabbabbbccdacabdbabaadbaabddbadaacadacbaaabadaccdacbadbdbadbbbcdbdadcaabcddbacccccccdbdcccadbabddbbbdaacdbdaacacaadaabacacbacdbaabaacccbbbaddbacbcaadbbbadadcddcadbdcddbcdadbcacbacababccadcbbdbcaccabbdbbcabacbaacbdbcdbcccccbaacbacccdccdbdcdbcacaadaccccccadcbcbddccccbcdbccbbdacabacdcdacddabcbcaddcbbabdccbdcabbaabcddbabdaddcdabaaaabcabcdadabcccdccaaacdaccadadbcbddabaacccabcacbbaadbabcdcadaccbaddcaadddcbbcdbddccdbbcdcddbaaabccbaadbbddbacaddbdbbdcbdacddccddbbccdddbbccddbcdccbdacbbddaaacbddcdcddcbbacbcbdccabbcbbbcbbbccadccbabbaddbcdbaadcabdacdaabdbdcaaacaaaacdccbbdbdcddbccdbaabadabdbcaacddbacdacccababcdaddaacdababbdcdaaadcdbbbcdcdddaabaaccdddbaddcdacdabbabcdbbddcddcbcbcdcbaaabdcdaacbcdbacbdbbabccbcccbccbdcbccbdadacccddbdcccbcdddcabadaccccdcbbccddbbabbbcbacdbcabaabcabdbcacbdbacdbacbbdddabdbbcadaddcaabdcccdcdddbccddaccbbbbbdcccdddcdbbabbabcadbaaadcddbabaabbbdbbbdbbcbacbbdbdbcacacaccbdcbcaddddbdacaadccbdaabbbbdadccacdadccdcbbddacbaabdcaaccdcacbabbbbdacaaadabcddcaaaccdccdaacdacccdbbabbdccdaaccccabcddbacaabaaaacccbccacbdccaddcaddcaacdadbaaacddbcddbaaacadbbabdcacdddacaccdabccbcddbcdadcbdbdccaabdbacbabcdddcadabbdbcbbccacbacaddcacaadacbacccdbbdbdcadcddacadcabbaabddacdabddccccacdacdddaddadddbbcbbbddadccacbdcadcddcdbdbcaccdccdccbadbabcbadacadbabddcdccaabcbaddddcabddabdadcabddbcbbcabddbccbddcbbdccdbcccbbdddbcdcdcabbccadbbcbbaacdadaabacbdcdbddddacbcabaddbbdabcaababaacadbabdbccdbadbdadccbcaabdaccdcddbcadbcbaaaacddadadaaddbbcbcddaaccdbccddbdcddbccddbadbccaadcaaaddcbdddcabadccbbdcdbdacbcbbaadbcddbababddcbadbbdcacccccbabbadaccaaccddcccccabbbdddacbbaaddaabcabbcbdbbdbcdbabaddbbadaaadabcddccbcbbdbacbbdcadcbbdcaccbdcaadabccdccbcdbdccdbacaabadbadaaddcaaaaccabaacbdcbaacbbcbbdaadabaacbdadccbbddaccbcbcabcacdcabaaccdaabbdcadaaaacdbaaacabbdaacdbdadabcdbbadaaadbbadbbdcbbbbcacbcdabcdacdacbccdadacbcacadabdbccaddaccaadccabaccbcacacacdbcbdcdbabbcddabcbcacadccdbaccabccbccdadcadbdacbbbbdcccdacaabdadcbcbbcbbaadbadcbcabbcdadbdbccaadabbbccdcadbabdacabacbadacbdbabdadddccadbacaabacdcadcdbcddabbbddcababcbcaaddbdbcdcdaadbdbdbdaacdbccacdbbadccddbbcdbccbdacddbbdcbbcdccbbbddbdccaadcbbbaacadcaadaaaabdccadabbbbdccbbcddaddbbdddbdccbbbbacbbcabdcbbaadbdabdcabdbabadbaadabdbabdcbdadbdcbcabbaabcdcbcdddcbcaaabcaacbdbcadbcaddbadcbcccbbbcaacabccddcddbcabcabbbcadcddcacbccccbbbcabadaaadddcdabbdcdbbabacaddaabcadcccdbbaaadddacdcbbacccbbdaddcddaacdcddbdcdccbcbdcdacdbcacbcdcabcabbabcddaacdbbbddcddbcdadababdbbdacabbcddacbabbcdcbbddbcbbdcdcddcdbddbcddbbcbcdccddacbbacccbbbacdaabdbcdbccdaddadabacbcaddbbbaabcaacacddbdccadccadaababbbdbbacdbddbcbddbddcbccdccbaadcdaadacaaabdababdbcacadabcbccaddbaccacdabbcdbdabadacdaacadbaddcccdcbccdaddccccbcdcbcbacabdcbcadbacdabdcbcacacdcbcacaabdcbaabcadddadcbcccbccdbbabcccaacabcaadadcabacdbcdcbcaddcbbabbcbcbcbdbcbdcdbcacadabbbdabdbddabbdbcbcbabdbbdddcdcadabccdcbbbddcacddbbddbacbbbcdbcbacdbdddbcaaaccccaabacbccccccdbdadbaabdbcaaddbabccabaddabdcddcbddddcdcbdcbbdbbccadaadcbcdabdaacabbbabbacdbacbdcdccbbdccbbdacbdaddcdbccabddaddbdcdddacbbdbaccbdcabddbbdccaacbbddbcbdaccacaccddccadcbbcbccbbccbcbddccdcdbdcbbaaaaddbdbadaabdddadccdbbddbccbccacbacbababacbbabcbddabadaddbdbaccadccccacbbdbcabdcccabbddcdcacaadbccbcdaaacdddbbcbdbacdcabcbcdacadccdcabcbcccaadccdacabaaabcdabdadcbbdcdacdcbbaddccdabcadbcadacddbaaccbdacacdccdbcddadadddcdbdbbdbbdacccdcdabbbcdcdabcabccdacbccdccdbbadcbbbaabdcdabcccbbababccbdbacabbdcccbbadaacbbabddccbabccdadcaaaadabbadaccbbdbddbadbccbbbdcdbacdcbcaabbbabccdacccbdcacadcabdaccdcdcdcaadcadbbbaaddbdcbadcdbcbdbacacaabcdadcbcaddcabddbabadddabbcdbbbbaabbdbcbdaacdaadbdbadaddaaaabddbcdcadcbadbddcdcbdddabddccdbcaaaabcbadddccccdbbcdddcdbcbbaacdcacbaababbcccbacdcddbcacbababcbbbbdbbabadddbaccccbbaddcabbbcbdbdabbdddadacccbbadccbacaabbddccaadddaccabcbdabbccbcacdcacbabddaabccbbbadacbacccabbbcabbdccbdacbddcacbcabaadddabdccabacaabacbbaaabbcdbdadbcbcddadabbddaadbbabadcdbadabbdadbccaabadbdadcaaabbbcdcabbbacbcacabacdbaddcabbacddbcddbbbbddbcbbbddacccbbbcacabbbbcbcccaadcdccccddbabbdbcabccddccacbadadababbadbaadbbbaaccbcdcacbbaacbaabcbabbbcdadcdbdbdcdaaadccdcdaadddbcadabbabdabbcaacbccbaaaaccabcccaacdababddbcaabcacaadbdacdbddbdaadabacddbdbcbbbddbcacabbcadaddcccccccdacbbbdddcdcbdaadadbcdbcadbaaadcddaabbacabdaccacbcdaabadcdadbbacbacccbcacabbacdcccdabdbbaccbcdccadbddbcadcccdbcbbcbabcbaaabcbbdcdbbbaaabbdbaabacddbadadcdaadaabadbaddaadcbbbaccbababbcdacdadabcccbabccbcbcadcdadbcbccdcbdabbaabcccbbacacdbddcdcbdaccbacdadacbcddddccbcaabcdacacdccbacacdbadbccaccbbddddddacaadbbaadadabddcaaadacbddbbcaccdcdcdbcdbddaadbaaabbaabcbbdacbcacdaacddacbdabadbcadbabccabbaaadcdcdddbbbddacabcddaaccbccbcbddddabccadcbcbdcbcbdbddccdbdcbacbbacabcbcbddbcddadddbcdccbcbadbdbabbbabaccbcbdacdbaaccbcdcddccacacbccbabacabcdacbccabadcdccbbdcbcbcabaccbdbaccaabcdbcbbbcdaaacdbacabccbddadaccccbdcbcbdadbaddbbbbbdcaadbcdadddaabadacabaadcdbcddaabbcbccbcaddabcacccbccaadbbccdcdadcbbddcdcdbbabdcacdbcacdadadbddacdcaaadddbbbbbdbcadabaacdbcdadaddbcbbccadbacbbdcbcdcabccbbbaabbbdbdbadaccaddaaddadcacbccccdccbbaabaccbdbcdbbcbbccadabbacbdbbacadcbbdbacccbdddbaabaabdbbabbdabddcaaddccdcbacacccabdacbbabdbddababbdbddcdcacadcaadcdaadbbbccccbaacdbaaddbdbccdcaadddcaccabdbbaacdbddccdaabdadccdaaabbbddddddadabacbdcbcbabaccddaaddbbabdccbaaabbdcbdadcababbdcdbbcddadbccbcbabdacddadcaadcdbddbddcddabadcabbdbcdabbbbaaacabddaadacdccbccacadbdcbbbabcdbbbaaabcabdcaaadcadbdbbadabdacdcdacabddcabddbbcdbcacbbabcdcbdbcbabdcbacdcaccabddaaacaacbaaabadcdabdcbccddacacddbcaadccdbdacbcccdcadddbbaacbaacbcdbdaadcddbcaaacbabbaadbdccbabadbdabbadccbcbdadbdacbbabdccdbddacbcabbbaacbbbdddbbadcddaddadcdbddcdaccadcdbabcaadabdbcdbddacaaddcbbcddcdddddccacdcadbacddcbdabdbbadbbcadcccdadcdccadacdbdbacabadbbaccadbcdddbddcdccabbdcacacabdcbcbbddaabdacacdbccccdbccccbabaaaabaaccbddddacabdcacadaabbddbacbcbdcddcccdabbcdcdbcdcddabdccdaccaaaaaaddbcbadacdbbdaaccbdcaccbccccbadaabcccaacccbaccaddaadababdabbababdcbbbcabaaacdbbacdccbcdaacbcdadaacabbcdabaadcbadbaccbadabcdbccacaabbbbcdaaaadacacabcbaaaccddbdcabddcdaaacddadbddcbacaddabbbbdbcdabadcabcdabccacdbbbbaaaacdbccdadaaaacadabcbbdbcdadadcbdbaabdddacadcbabadbccdbccabdcaaddcdacaadabaaddacdcaacaabaaaaddadbaaadbcbabddbcdabcdcdbbbdacaccacbcdbaccaccacdacaaabddcddbcbabcabbdaaccddbcadabbcbacaaabddddcbbdcabcbddbbbacbcdbbccaaabdaccdbccabaddaddbdaacddbaacbaddbbbcabbdbadadbdabbcbbdabdcacbccababccdcbcadddcbbacccabaddabcaddcdabaabbcabacaadccabcbaadcddbbacbaabadcdbcacbdbddccdbcddcddbcabddbadccaabcccaaccdcddadbcadaaacbccbddbccaddbcccbdcadabcadbaaabacaabdaabdbcdcaabdaaadaadcddacadaaaadddbabccadbbbbdcdddadcabbadccaddcdacddbdbcdacabcbdcbbbdadbcadcbaaadcccbacdadcacddbcccabdcdbbdcbdabdbcadbcdccabcccbccadbbdcbaabbaabbbcdbdbacaadcbdcacbabcccbabdbcabdbadbbbbdddcbbbbbccbdcdccaddcacbadcaccabbbdacdaabaadcbbbcddbddbaadcacccacbbabbbccadcdaccaabcbdcdcccbacbdabcbacbdbbbabdacdcccacadcdbcbddbacdbbdcbbaabdddbadaaddaabdabcdaaaccaaabdbdbadadadcdbcabbaadcaacdcbbbacbaaddabdbcdbcacacaacbbabcbdbccadbccdbadddcacdabcddddbcddccadaaddadaaabddacdadcacbdbdabaadaddabddbaaacdadbdcccddaddcabddadcccdcabdaaacdadcddadbacccdaaabdcdbbcddccccacabcbdbaaabbcadbddcdbcadccdbcaaabccdbcaadddadadbabadaabbdacadcaadbdadadcbbdbddadccbabdaddadbcdbcbacabbbacdbaccaacbcdbcbdbcbbcccbaddbcdcdcbbacdadcdccbcbcacaacdabcdbababacdaacdcccaabbaabbdcbaaccaddbabbabddadcdbabbdcccddcdacddaccadbaddadbccbaacbcaddcadcbcacbcdbaacdddabcabaadcddacbddcbabbbcccaccaaaababbdabccdbdaddcaddaaccaacbdcbbdacabdcbcaacdaadbabccbccbdbbdbbdaacdcbacbdbccabbbbcdcdcacdaabdbadcbddccbaddbbcdbacdadccbccbacdbbcbcbdbcbacabbaddccbabaabdabcdaddbbbadacadacbcccbdbcacacabacddacbbcbddacbabcaadccdcabbbabbbccdcbccbbcbbbacacdbbddbddaacbdbaaacdacdabbdccaaacacdaccacbdcddcbcbdbbadbaabccbdadccadbcdcadaaccdbaabccbbacbbcdccabaabbdbbbdbcdcbcdabbbdbddbddbcadabdacdcccdcbaacbddddbbcbacabcbcbdbcbabbcbddbcbdbdacbcaaacdaccaddbccdcadaabcbbabccdaadaddbadcaddbaccdcdadbcaabababdccddacddbcbabcaaaadaaccbbccccbdbbdaabbaddbbcbbadbacbcaaaaadddaaccadbaccdbbdbcddadcaadcbaabacdbcdadadacbbcdbaddbcbbacdacdbdabadbddbdcdbaabdbddcbdadbdcddcbddbbbcadbbbdbccbcaabadccabdbdabbdadbbcbdcbbabbbcdabdbcbdcbdcdddaabccabaccdabcccaabdcbbcbdbaacbcbbddcadccbbddacdcacdccddcbdddabbadcdbcbdcacaaaadbdddadbaacadacacadccdaabcdacaacabcbccbaacdaddcdabddbcdbadadbcdabdbdcccccbcbdacbbddacbbdbccabcccbcdcdaadacddcddaadcdaabaacccbcdcbddababddcdcdddbcdccbdcddaddabacdabcaaaabcacbaaaacdacbcbababdacaacbddcaabdcddbbddacbcadddbbbabdabdabbcbbddabdbbdcddcabaadbaabdbcbadcadaaaabadcadbbdcdcacbaaacbcddbcbbbbcbadcdcbbbcabaddbabdccdacacababacabacccddadbdacabcadaabcbbadaabbacacccdcaabcdadcbabcbcddccdddddbcbbcdbbacbcababccdcacdcaaacaabcadbdbdbddbbcdaadcaadcbdacddbcbadaccdaacbcccacadbdbddbccbabababacaabdbbabdcababbbabdcabbbbaadcaadcbcdbdbdbacdbccbdbcbcbbbabaccaaadaacaadabbabdabcbccacbcaadcbdacadcaabbaccccacbbabacbcadabbadcdaadcddbbccaaabcadbdcbdcaaadcdbaddbabbbbbabddaaaaccbbbabababdbdbcdccdcdcabcdabadcadddccadccaaabbbbbdcdcadabcadbaccacabdccadabbcccbdcbcdaacbddbcbacaacddbdbbdcdaabcaabdaacdaabbcaccdcbccdbcddcdababbdcdbddbadacccdbbdbcbbadbbacddcccbcdcabbacdbcacdabbadbdcccccdaccabcdbacccbdbadbbddddaadcadaddbaabaaacbcbaadabbbaaacaaaaddbbbacbddbbcbbbddcdabbccbdababacdaaadbadacaabadbdddddabcccadabdbaddbccdbddbcacbcbcabcabccdccbbcacbdaccbcbacadabbacbaaccbaaaccddabbbbcaabaccdbdcdcacdacacddcbbaddabdbcbbcbbdcddbddbdbacdacccadcabacacbaacbadabbaacbabaddbddaaadbbddccbbdacababdbadcaabdcccadaabadabadacdddcdccabbacddcacaccbaacdacaadccdcbcbdcdbaadbbadddbbacdddabcacdbcdaaadcbbaacbddcadbbdcaaacccbbacbbcabacaaacbdbcdcbaaccbaccaadbaccadbcacacabaaacaddadbdccbbcaacccabadbbbbbcbcbcbdbdacacbbaaaaadadabbaaaaabbaaccadbbabcdadcbdcdabbdcbababdbddcadcdcdcaabddbacabacdaddadddbdcabaddabdbbbdccaacbdcddbbcdacdbcccaadbacaaddcdacddadabddcbadbbdacccbaccbddddbaacaaacdaabdccdacbbdcbabdcacadcbcdbdbdbdbdaabdcdabaacbddbcccccbaddbabdbbabccdcbcaccccacccbaacadbacbbcdacdbdacbbabbacacadcbdbddadbabdabcbdbddcbdaddacddcadbabababdbababcdabaaacddbbabbbacadaddbaaddaacadccdadbcbdddbbabcbbadadcbdcdacbddacaabdacccbdbbbaabcdbaccdbcdcddadbdbaccbdbcaccbdaccabbbbbcdbdddacadcacbaabadcbaddbdaacadadbabcaaadbccabaaacadccadaabddbdcddcccddaddaddbbacddbcacdababcddabcbaadcdbcdbbbbbadcadaadabaaacbaaddbbababccdccbdacccbddbabbababadbdacbdcaaabdddbcababdcdbaacabbbbcdcadbdcbdaacaddaabbbddbbcaddbddbbadcadcbdbcbacbcaaadbdbcdbacbbcabcbdabdbcbaaaccdabdccdddadbcadaaddccdbddcabbddccacdccdbbbbdcccbbabacdaadbccadbabadaabcaabbcbdadbbcaacbcacacbdbcdbbddbdbcbdcccddbabadbcbbbdcddcdbcccbcdcbaadccdabbbbcdbbdcabadcdbdabbbcdbabbbdcbabbbdbbccbbdbbadbcabcddbbddccbbbdcdcbcbbdaacacbcababcbbcaabbacbcccbdcdddddccacbdbbbaaabbcbcacbabcbcaccdddbbadadbbabbacddddbcdbbdcbaaccdabbdcbddbdccddccddbadaacdcbcddacadccbbbadbbdcadddadbccaaacdaccbbccdaabddaaacadcdadbaabdccdbccaababbcccabaddccabdbbacdaaaddcbdcabbadadccadccbcaaddcabcbdbcddcdccdcdabbabcbcdacbccdbbcacbdbcbbabaccdcdcacddadacbddabbbabadadbabacaaabdcbdabacbbabcadcaacaaaddbccdaaaccdabadbcdaddddcbdbaddbbbdaadbdccaddddacadadadcabcbdcbabbcdacdcaacadcdbcbcacadbcdaadaabdbcaadcccbbabdbcbcaaccbbbcbddadadcddaddddabacddcabadaddddbaadaccbacdccacbadaabcacdcbadabcddccadabcaabcbdcaccbdacccddcacbabdababbdadaacdabccbdaadaacdddaacbcccbcdddbcabcadbbcdcadbaddcabaaacccaccbadbdbbddaaaadaabcdadcdbbbbdcdcdcbcadbdbdaadbdbadcdccddbbaadbdabdccccbabdabdbdbdaccdbadbbddbbddccdabdaaddcbadddddaabcadacbcbdaccbbcdbaadacdadbadacadbadcbbbbabbbcdccaaadbaabbacdabdbdcddabaacbbddbbdbabdcdcccaabcabddcbcbbaadbaadcadddbabdbacaaaddadadbabadababcdbccddbacccacaaabbabaaababddcdaaabdabaaddaccddbdbaaacabbddbbaababddcbbbabdbccacddbdcaaabbdacdbcccadcacbcbccadcbbcbaccdbdbaadadaabaaddbddcabaccabacbbcbacbbbabbdbcddcdbdadacaddddbaadacbadcbdcbadbacccabccaccdabcbaabbababddbcccdcbabddcadbcacdaaabdaabbccbacddbbcbccccabbcabbdbdddabbbcdccbcaaaddcbadbaccbaaddacbbccdddbcacaacccbbbddcacaaaaaddbdadabdcacbabdddbddbbbbacdadbadcdaaabbabaddcdcdddddbdbdabaadbadadcdcdbbdacbcbbcdacccbdcbbcbbaabadbcbbccbabcabcbbacbdcbdacdbdcbadabacbcdccdbbbdcaacbbbcccdbbcdddadcbdbddcddcbbbcdbbbaddcaacadcdaabcbbdbddbdcccbadbcaaaaadcbdbcbbcddbcddacddbabcddaadccdabaccbbbcbbdcdbadccbdbdadabdabcdcaddddacccdcbbcacccaacbaaabaccbdcccbbcbacabbccabdddacccdbaaacdadbccdddaaddacdbaddbdbddabcbbbbdcbcdbabdbacbdcacddbbacaccbdcabbaaddbdddaabddbacabdacddabbcbdcabaddabaddbbdbbcddbbdaadbddcbbdbcbcaabdcabcdbacacdcadacbcdcdacbcacbccbdcccdddaacccccadccbbdccdaadacacbaabadcdcbdcbbcdacbcbbaacabadcbacddbcdcccbddccdcacddcccccdbabdbcdbbcaababbbaddabdcbcaaacddccdbcccdaadadcbabbdcbbcbcbbacddbcdadbcdbcbbcbbdbaabcddbcbdbcbcbccbdaabadadaabadbacaadbcaddcaabbccaccadcaabdcbdccbbcddabaadbbccadacaaaaadabaccaddbdcadbcbbcdaacdbcaaaccaacacbcddabacccaddbcaacaababaaacabdadccacadbacabbdabcadcbbacbcdbccbadcdccacbaaacdadadbdcdcacbcbcbdcccdbcbbbabcdccddaabdaabaabbbccddababcbaaddbdaccbcabcbbbccdcbbcbcdaccaaaccddcaadaccdccabdcdbadddbcddbaccdcabdddcdcbccabaabaaadacaadccbdaaaacdbabbcdcbccbbcbadbcacbbdbbaaaacacccaddacdccbbadbcdacabaadcabcbbaabacadacadcddcbbcdcacadcbbccdccbacdcdcdcddcabadcdaaacdbcababbdaaaccaddabddcbacaaccdbbdbcbbaccdaacddacabcccabdaaadabbaccdadadcccbbcacdabcdbcbaccabadcbbddacaadaccadbcdbadccbcaabbcddacbdccbdddacccbccdbdabdcacacadcbabadcbdacbcacbbadcadbcdbbbadbcccabcabccdcabdacaacaabccdcdcbbacadcaaadbadddcbbbddbacaabbccbcacaaabdddadadcdadccdcadccabbacccadcacbbcbcbaadbacbdbddbddbabcdbbbbdbccdadbcaabcbdcadbabadbbddcdddbdcdddcabddcabaaabccdadbabbdaacabababdababbccddddddcdabddaabdaaabdccbbbcbdcccbddcbacbcacaaacccccdcdddcbdbdbbcdbcdddcabababaddabbcdaadcbaabbbcabacdbcdcaabbbcbbbdabdbaaaabacbabbdcadcdabdaaaabbdbddcacdcaacacdabccbadccabbaddbcbbbbbadddcabbdcccbddcbcbbacdaddacabdbcacccabaaacdbbcbbbadbccbcdcaababbccacbbbaaddacaaaccdbccdbdbcabccaddaadbdccadabddcdbcbdbdbcdcbbadaaaabdaabbccdaccabddacabddcbaccdcbddadcbcbabcbbbbdaaadaddddcbbcbadcaabddcadcdaabbcadacbbcddabbbccadcabccabbbdcccccbdadcdcdcdcccccbcabbbdacbacdbbabbabacbadadddadcdcbaabaacbbbcbbdcbcccdcbaacdbbdbcbcbcbbcdcddaacaddbbacbcaccadcbabbbdbbcabbbadbdabbcacddbababcbbbdbcbcdcdadcdbbbdddadbbadcabdaaaabcbdacbadbadabbadcacbacddabaabacabdbdcdcdbbabdccddccbbdcabdddcadcbadbcbbcccdcdbbbdaabbddabbcddaaccaccaadcbbbdbbbdcccbbcdccccdcacadcaadbadbbdcbbaabccaaccacbdcdddcbcdbdccadabddccbcbcdcbdbbdcbdadbbcbaaccdcdbdccdddacabdbccddbaacacbbcabacadcbcdccbcbbdbabdcbdcddccacbabadcadaababddabcabbbccacbabbcddbacaccabacdacccdbdcdbdbcbcaaaddddabdadbcbaacaccaacbdabddabbdddcddbbdadabcacbabdcabcddbcacdcddabdcccddbbabbbbaccacbbbddbdbcbddcbacbbdbbbdddbbababcdaadbcdbcacbbbdccdccdbaddaadcaabadbababbdadabadbbccbccbdbddcbccbaabadabbadbdbcccbabcbbccbdbdacadbdacccbcbbbddbaaabdddcccdbcacabbcbdaccddbaccdabccdcdacbabacbcbccacbacdaabacabdcaadacbadccdcdabcdbdcaaababaaacbccaabdabadababcbadcadadaccdcdbaaaaaabaddabadcdccddbdcabdbdcaabdccdbaacbbaadcbaaaaacbcabcddbbdadbaabbaadcacdadbdcccabacdbbcdadabbccbddcadccdcbbcbbcbccabacccbdcaaaacbaacccdadadbcabbbcbddbbddcdcbbdacaccbadabdabadcbbcdbcbbabbadaadccabdbddbabddddccaabcaccacbdbbbbbddbcacadcdccabbdcbcadcbbbdacbbccadcbabbccccbacdacabcdccdccabcddbbcdbcbbabdbcddbbbddbbdbbbddaabacccbabbccbadbbdddabbbdcdcdcbadcabcdabccabcbcaddaadabcccbbcdabbcabcacabbbdbdbcbbaccddcabdccabdbccbdacddadcadcdccbbdccbbbcbaaaccacaadbbadcbccadbbdbdaccbdaacaccbbbcbdbdbddcccaddbbddccbcaaadccbbcdbdbcacdacacbbaaacaadcdcbdccaabbcdbbcacbbaccbdccadcdcabaacbbabbaccbdcabadcadbaaaccacadbdbbcadccbbaaacabbdbdabbdacaddbddabccadccbacbcccbbbbccdcabdcacabbbdddbbabcdbabdbaadddbadcdbbadaaddcacdbcacbabdccccdacdaabccddadbdccdcbbbcdcbcabbbbdbabacbabcdddbdcdbdbdddacbcbacdadddccddacabdbacaccbacdbcaabdacccbccbacdacacddacdbbdbacacbbdbcdcbdacaacdbdacdbadaaabaddbcdcdcaabccbccdccbbadcbbbcccddbdccccaddababcacbdabbabdabdbcbbddbabbcabbbddcccdcabcadabddacddcdbdaadcacbaaadababacbadcbccbcddaabddcadcabadabbaadccbcccdbcdccbccdbcddcadbabadcbaaddaaccccdbcbccddcddabbbbcadbdadbcdacbcddcdcbccccdcdcadbcddbadddbdbdaaccbdddcadabaabaccadaaaacdbdabcdbdbaabdadbdcdaabcccdbcddaadacbbcdaabacbddcdbdcacbdbddbbdcabdacdaabbdcadbbdddabcdbcddbbbbdbaadabbadacbbbacbcabadadbdadbdabcbccaadbcdcbbcdbdcccdcacdcddcdabaadcbacaccbdbacacddaabadbcbcabcdbbccbdadaddcacccccadcbbacabcadbabddaaddbccdccbbaacaddcbadaddcbbdbbcdbdabdbcabdaacbbdbabbaadcdcbbdabacdcccaabbdbabcaadbddcdccaabbabddaaccddaadadabbbddbdddaaadaddbadbcbaabddadbbbbdbdccbcbadbcddbdbbbdccdadbcdddccdcdaaabccdcdddbccbddcbaabbddbdbbaccdbaacadbdabadcdadabccacccdcddbbaadbcbabbbcdaddbabdbbbccddbbabbaccaadccbbaaccacbddacbaacbbcbbbbbddabadcdabbdcaccbdccdbdbdaadcdbbdbccdcdbbcaaadaabbdaccdabadbacdccacbaacccddddbdcaaacddcbaddabcccbddcacddcbddbbbcbbadaccaaadccadbcdccdddaaadbcdcdaabdbbaaadaacbcaadaddaadddadbaabcccdaabbbaacbbdacdbbaabbbacbaabbcbbccbccdababbcdbdbadaacaaccdcdbacaccbabcddaccbdcccdaddbddaacdaccdbadddacdbccbacbcccabdaccbcaacdcdcadaadbbaadbdddbbccdcaabddddaaadcbaadaddbabdddabccccdaadbbbccbbcccbccbbcbabacbcadddddccbacaadbdcbcacddbbcaacbcdcbbcdabadabccdddadcabdccccaabdcdabcbccadbddcacaccadacadabbccbcabaaaabdcaabccadddaabdcdcdadcbaaccccaddcacbcbdadcdbdcbadaaacdcaabadacbdccccdbaabcbadaccdcaddccdacdbacbcdbaaccdcaadbcbbcbbaddcbdaccadaaccbaacacbcbabacaccbcbcdadbcacabdcddbbbcbcdccdccddcacabaaaaccdbcaabbababdddcddabdbdbcdcadcdcdbaadadbccabdcdbcbbcacbddaacabcbcbadcbaddbacdbbdcacacdbadaadadaadccacbbcdabadbdadcdcdbcdddabcbdbdacbdacbcccbaadcaadccdaadadaccdbdacadddccdcbcccabdcbadddaaccbadccdaadbbaadbdbddcccddacabdbcccacbbcdbbbabbcbdcccbbbdabdcbdbdcbccbadabadcacdaadcdabaccdabaabddbbdacaabcbaacabdabaaadcbddcccadbaccadababababcccbbcccbdcbcacbccbacaabcbadbcdaddbbbcbcbadddbdbacaacdaadabddcdabbadababcaacdccacbbcdcaabadbccacbbadadcbabbbbabcccbadcccdddbdcbddbbaccaccaacbbadcdbdacdaadaddcaccbdaaabccbbabadbdccaaabdcacbdbbaccbcdcbbadbaaaccbadbaccbdbadbbcabbdbdcabccabcaacbccaaabdccbbcacddcadacdcdaacaaddbcaabaadcbbbcbddcbcdcacbbadacdbbdadbbbabdaaaadcbdabbcbddbdaabdaccadddbccbdabbcdabcbadaaddbdccbccbcbbdabdcbdabbacdbbadbabcddbbadacbdcccabbdadacaaacdaadcccbbdddcadbbdbcbcddadcaddcccdcaadacabadbbbabdcaacbaaabaaddccdcababdbbbbbdababdacaabccdabcbccbcdacdaddadbdbbcacbddbddcdacbdccacdcbadbacbbcaaadcacbdbccabaabdaacccaccbabddaabadacaddadadaacadcdcbdddbcbbbccdccaccdcdcdbaabacbdcacaabdddadbdcdabcbbdbacbaabdddbbabdbccadadddabccbbdcbcaddbbdaacaaababbdabaadaccaaaaddbcbcdbddddcbbcdccddbcbcbbbbacdcbddbaacbdbddcabcadbddcbadbdaabcbdaabdaaabcbdddabbcddaaddccbaaacabdccadccdcddcbccccaaccccdcbdacbadcdaddbcaaddbabcabdcacacaaadbccddadddbccddcaccbbbadbccaadcacaccbcddcccdccccbaacaaacbcbacdadadaacacccdadccaacdabadccbacddabcbcbbaaadadcbaadaaabcdbcddbcbbbbcacbcacddccaabccdddcbbcacbccacbbbacaaddacbabadbaccbbdbdabcbbcbcdbdaadabcbbbaabacdcdbdbaaacacbcadbaaaccbabdbdbaacccbadbbadbdcacaacdccccaacdcdcaddcbcacbccbbccbddbabdbbbdcbacadccdacccbccdaddabcdacbbbcbcaaccdbbbcdccadbbbbddbdadccaaadbbaaaccdaccbdacdddcabaadddacbddddcddbcbbcdcaaccabccacbaaabcddcdbacdbabbbbbdcdccccdcbdabdabdcbacaadddbcdcbbcababbdddcdcddddbabbdbdccadbcbbdcbcdcddcaadadbacdcabdcdbbdcacabdabadaabbbbcabccaadacccdacdabbbdbaccdadbadcaaaabcdccccadbdddabddcccbaddadcdcdbcdadadcdcdbbcccbabbdbbadbbcdacaacaccdbccabcbaaadbbdcababcddbbbdbcbcdabcdadadddcadbbdbbcbdddaaadadbadcbcbdbddbdbcaddbcccbadababdacabbacacaaadbdcbdcdadcdcddcabdcbcddbacdccdabaaddcccbaabbdcdadaabcadbbbbbbbadcadadcdbabbadabccbabbdcaddcdcaabbbcdabdabddaacadbbaccdddaacbdbcbdccbadccdadcdcbdcddcdccbcbadddcabddaadbbaccbdbadcadcbcbabbcdbdaacdbbbcccdbaabbadadacdaaccbddcdcbcaccdaaddaccdcbccdabcbdaccbbbdacbaddcdbccbdbcccccacdcddcaadcabccadcbbbaabdaadddbcadddcdabbdbbbadaaabadacdccddadabaddaacbbcdbaddaabbbbccbbdabbbdbdcadabcabbdbdcbadbbbdbbbbbccddbcccddbdddbcbdabbbadbdabbdbdaadaaaacaacdcabcccaaabaccbcababaddadcbbcdcbccdacaaccbaddaddbdbcdadaaadddcbcacccbcadddcbbcdabcbbbccabacbcbdcacbcddbaacabcddbbcdbcadddbcccacabbcdccdabdbabaaaabcbcbbdadabcccbbbbdbbcabbdcdcadaacadcdacddbccbcbcacbdabadabbdbbcacccdddabcbcabbcadcdaccddbbacbdbaacabddabcdbcabdcdaaadbdbbcddaccdccabbbddbcadccdbdcdaabcdcdadbcacaadddbbabddabccadaacbaabbcdadabaababbbbbacbdaacbddadabaabadadadabdbdabccddbddaadbbcdbbdbcaacdbbdddddcccaccddcccbddcdaaddcacaccbcbbdbdcaaccbaddcadaaadaadabdbabbcdbbcbbcbaaacabdcbcaaaacddbbdbbccdcbcbacabdbababdbcbdddbdbaabacbdccbacbddadbcacdadaaabbcaadacacbdccdacbacddcbcacdabcdbbacbddbbdbabccbacbbbdbbddababbdaadcadbabdbbbdcccbbacabcbcbdcbadbdbdbdbadaccbcbdacdcdbdbcdbcaadcbadddadcdbadbccbbbcbababacddbaacbcdacdccdcbaadcbbdcbadccdcaacbacabcabdbbdcdbdbbccdacccadaadbbacddbbbdaabccabbbbadaabbabdaabdadbbdaabcaabaadcadccadddaaabaaabbcaddbdbadadbacdcdcaaadcadcdccaabababbbbbaccadcbdbbabbacddacadbaacddbdbbbaccdaabcdbcabbcaacccadbababbcdcddbccadcaaacaadacbacdcddabccbacbaadccdcacabcdbaacccaccaacddddbbaacdcacbadaadcabdcdbacdbcacdadddcaaaddbbabadbabacaabdcabbdabadccdddcacdcbdbabcbabcbdccdcdacbdadcdacdddbcdcdaaacaacdaaadbcaccbaaadaadbdadcddccadaaccdddabbcbbddabcddaadadcaddaacabaadcbaabaaaaaccbadabdcbbbdbbcbbdbacdacdcddadcdaaacdadbabbcbdcacaadacbacdddcacdbddabdcdbabccabbcbcbcdcdbaabbddbcdadbabdbbcbddddbbbadcabcbcadddcddbcbcbadaabddaacdabdcaaabccaacadacdabcdcbcbdbcdacdbaadbccbdaacdadbcddcacccdabcabbbbbaaccddbaaccdaaadbaccdaaaadbccdcabdacdddbbddbacaabdadababcadbdaccbaabaadbbdbddcabbddacdacaaccdacacabcdcadcaccbbcddabadcaadbbbaaabbbcbbabdacaddcddbabbddbacdacbbdbbcacccabdabbdacbbbdbaabbbdaabbbbaadbccdbdcabcadcbbcbaabcbbbddbddcbbbcaccbcdadbbbcaabcdacacababcbdbccddcdacddbdcbacacdaddbdddbdcaddcadcabdbddaccbacbdbdaccbccbcbcdaabddcabacbcbaabdbbcdbacddbddbbdadadbbdacdddbddcbdbbdaddccddbcdbcddccdaabdccbdbddbcdccbbcadccbdcddaabbcadbaaaacabbcabababaaddbbbdcddaccbccacacddbaccbabbbdaddcdacacdbaabdcbddccaaabbbbdbaadbbabbcdcdadbbdbccabdbdbbdbbcaccbddcbacdbbabcaabbaababdabdbdbbdccacdccdbdcddcacbadddcbdaddbbdccddcbcbdbccadcbabbdbabdabbdcddbabcddcddabccacbcccbcccbdcbbacadaaccbdacabaaadccadccdccdaacbcadbbbbaacacccbcddcdddcbaaacdddababcdcdbacdcddbabaddccadbdbabbabcaddacbabcadcbdbbcbcdddaddbdbccbbbdcadacbbbdbbaddcddacbdaadbcaaccdabdcaadcdaabcdadcbadaccadcccddcdcbcdbabccbdbddbcaaaabdbbdcacabbbcddacaaacdabbaccbcdcddddabaabbbbabddbdddabbcbbbdbcdaacbdadbdaddcabbbcbabcbddabdbccbcccddabdbaabbbccbdcaacbddccdacbcdbaaabcbbabcdddcaccdcbabbdbccdcddbcdcdadaaacdcadacbbbbabaacdaddccdbcdbcdaccbcadabdbaddbddabbbdaddcdababdaddadbbaddcabcbcccabdbcabaadbaaabdaabdddcaddbadbcacbbddbdccbacbbdddadaabcaaaabddabaacaccbdaaabadbbcdbcadacccbaadacbccbacddaacaadabdbbbbbacbadadbadbaccadbbdaabbcacddcadcdddacddbbdcdbdcacacaddbdabaddabdaaadaacabcacacccadaaabcdbaaccddddbababdabcdbadcccccbbbacaaabcdabbdcdbcdaadbdacabbcaacdcdcadabbbcbbcdaaabcbbdbbbdddaaacdcdcbbabcbcbdbbbaccababcdccbdcdbabcddaaabbadcbcdcbaaccbdcdbdcbccdadbcbaabbabccabbacccdbddaddbcaacdacbddbabacddacbbccdbbccbbcacabcacdbabacaadacddddbbdbdbabcabaabaaaddbdccbbbbdaccaccaabbccaabdcbcdabcbbcdacdaadcaabcbaddadaccaaaaccdbdbddbacadaadabdddaadccddbdaaadcabacbdaadadadcabbbadbacbccbbaacdaacdaddcddacdaadadbaaadacaabdcdadddbdcdcabbddcdadbbbcdccdacbcddbcdcbbabcccbdbacbcdcbdbccdbdcaccdadbadaabbdaccabaaccbacacbbcabacdadabddcabbbbaadcbddbdcddaadcaabcdadccaabdabbdaabacccdaacabddbaaccaadcbdcbdaadacacbdcdcbabbbddddacbbadaacdbbcddbcddcdbaddcaabdbddaaccbdcbdddcccacbbcaddcbdbcddbccccdbacabdddaaddacacabbaacaddbcdbcbbbcaadabcaccaadbccacbcdbacaabddbdaabcabddbcabbdaacdabbacbdaadaddcdcddacddbcdaabdaddabdcadacaacbbddbcabbcbbcaadbccaaaddaabddbdbddadbdcbaaddcdcdcaabcbbadadadcccdbbdaacdbcdcbadbddacabacdccdcadcdaddcbcdcccdcabdcdadaabdabbaacabbdccbccbdbdbdaaacbdcbadacbbccacabbabaabcccbddbddbadadaaabcdbbaacaaaadbaddbababdadadcadaacabaabaaaacbdcbcddcdaacaabdacbaabddaadcdbabbacdbcabcddbbbcbabdbacddbaaacbaaddccbccddaacaacdcabbcabddbcbdabddaddabbbcccbdadababbbadadbbdddcdcbacbacdcadabbcadadbdabdddaacdabcaddcdaaabdbdababbbccbaabcadbcccadcddababacbdbacddabadabdabacacbcadcadaababddaabacaddcccbacccbcddbcaddbcbdccadacdddcabcacbccadabbccaacdbdacabccabddbdaddddcbcbaccabaccbcabcddccbdbccbbcaaacccdcddbdcbdaaddaabdbacadaacccbcadaccaababbcadaaadcbdaabdbaadcbcdddaabbbaacbacabbdbabdbcbadcaaccdcbbcbcbbdbdcabbadcdcdbbbabcdbcdcdbcaabccacabadbbacdacbbdbddbabcaddcdacdcbacaadbaabbbcbdcbabbcaaccbaccaddcbdbacacdccbbccdaddcddcbbaaccbdadcddbbabcdbbdaaacddbcadbacadadcccbbbbddabaacdadbccddcdbaaddacabddabccddcdbcdccaadcdbcaadbaacdaccdcccccdbabdcdabbbdaaddbbdbbcbcbacdccdbcddaabbacadbadcadabbdbddbdcdbdaababdcadcadcbcaaccbaacbcbcdcbdcbbccccacadddbbadacdacbbdcacbdbcddaadaadaaabccddbbbbaacdadbbabbbdbbcccbadabdbacccdbbbaaabaabadcabcbcbdabdcdbcccbdadbbdcdabacbadbacbaddaadddbddcdcdcbadbadcdccddbaccbcabbddabdcbdbabcbbaccabcaadcdcbbabaabdcbaabdddddbdacbddcaabbaadabacbcbbdbdccbdcccbdadbabdbccdaadbcbaaabbcbadcabcdccabcccabcbddcaccacaccabcddacdccabcddcbaabacdaadbaddbadddbcbdcbbacacdbadddabbbcdacdccdcbbbcdaadccabacbcdcaabccbcbbcacaadddbdaccbacbdabdbccabddcadbbcccaabdcdcbadacadaddbdccccabaccbbbbdaacdbdcaaababbdcaabbbcbcbbccbcacbbcdacbbaddddddddbcacaabbbdbacbbcabddbbddaaaacddcacbbcdbddbaddaaaddadbaaadacccbcdaadcdddacaddbadbbddbdabdabcdddbcbdacdcadacdccbcabcdabacadbadcbbcbdcbaabbabdcccccccadbbdaacabdcaabadbabacbdabbcbadacbbbbbcadadccaaacdbabcdcddacaabbacbcbaaccddbcbcaccdbbacaacbaacdcaaddbdcbccccbdcbddaabccbbcbacbbaddbdcbddddadbabaabbacccbdcaaaabadccdbadbadbababbabcadaccbddabadaccdcdbcabadcdbaddacdddacdcdcbcbabbddcbdcdddbdcdaddddadcbbbbcdcadddcbbdaccccdcaadaccabadabbbabacddcadaabcbdcbdcaadbdaabadadacccdcddbcabbcabcaddcbdbbdcbaccbbbcbdcbddcbaccdbcabdacbabdabacbdcbacccbbdabbbddcdccabcbbaabbadddcddadbaabddabdadddadcaacbcdcabbacbbcdaabbdbbccbbcbbcabcdbbabaddcaacdddbaaccdabcaacadcaaaadabddabcaabddccddbccadacacccaabdabdabcacbddcdbdcddcbacbdcbbbbdcbcaabdddacdbacbdccccdaabbabddbcbabaadcbcbabcbacbbdcdacddacacaabbbdaabddccaacbdccaabcabdcacbadddbddcccbadadcbadaccbcddcdabbbbabbcbbadcddccccdddbddbdbbbabdbbccbdbccccbbaacccddcacddabbacadcdcaadddbddacbbaacbaacdabbdccdddcbdbcbaacdbbbbaddbddbaabaddaaccaddacbccabcddaaabcaaaaabdccadbdbdacccacbddbdcabdacbbbadadbbbbccbdadccccacabbabbdcadadbaacbabbacdacbbbdcbcacabbdbaabbdcbcbdabdaabacdacdbabbccacddcacdacccbcadaaabddcbcaabbbcbacbaabbadbcadcacaabdbddcbdaddbdbccadcbcacdcadabaabacaadcdddccdccbaaadcdbbcadbabcbcbacbaacddbdadadcabbbdacbcadcdadbaabbcbddaddcdbadbadcbbcdaadabbdcaaadacaccbbcbacaaddabddbcdbbddbcbcaddcaaabdaaccaabdbdddcdcdbdccabdabcdaadcbcacdbcdccddbdbacbcbbdaccccbcabcccaacaacbdbcaaadcbdddbacdccbaaacdcddbdbcbdcccbabbcaabdbaccbdabdcdaaccabbbdcabdadbdbcbbbcbcacadbbbdbcbbcdbadabbcdbacacddbcaabbdcdbbcbbdddccadcdccdcadbbdcdabcacdadacaaaacbbddabaaabcdcccdabadcbcccdbdacdcbccdbabadabccbbaadbdcbccaabcaddcbbdbacddccaabdacbbabadcaaccccccacddcabbccaaddccbaadbacaabbcabdcacccadbacbcacdccbbbdacddbcbdacddcaabcabbaabbdaaaccbcbcdbaacccadacacbcbddbdbabdddbdccccdcbcbccddcccbadabcacddabcaaacabacdabdaadddcacabbadacdaacaacccadadbdadbdbaadacbdccccdaadabadaaabcbdbbbdbacbcabdcaaaaddabdcdddaccbabddccacccacbbbcbcbaaabaccbbaadcdcdaabdbbadcdbcbaabbbcddaabcbcaccadabcadccbcccdaaadabbcaddabcdbcddacdaccbbacdbbbabbddcdbdbacaababbcbbacdadcdbdcaddbabccbbdacbddddcdadcbbdbabcdabbdbabdbaadcbddddcbccbbdacaacaacdcbdcbaaaadaadabbcddccdbccccbbdcaaadbddaadddbbdbaaacacccddcaacbcdccaacddaddbcbcaddaccacdcbcbacbbabbcccbbbbbaaddcdcccdccbcabbdddbccdbbcacadacbabcbccacdcadcabdccdaaccabdccdcbabaddddbacabdabcaadcdaacdaccdbcdbcbddbbddacdabbadaddcdcbbbcacbcbcacaccbabbacbdcacdcccbbdcbadcbccacbdcdcdbdbcdcbbaaaaadaabcadbabadcddbccddbadcbbadbbbbcbdaadaabacaacadcdddcbaabcbdcbbabddddccaacacdcaccdccdcabcbacbcdbacacbdddabbbcadacacccbdbbdbdaaaabaacdcbddbdabbacacaadddcaddbcaddaabbaadbbacbccdaabbabdbcabdbbcbdbdbabddaddddcbabbaddaaccdacbbdacddabacdaabdbbcadaddbdbbaabadddadabccadbbcbacbaaabbddcbbbbcbabdbbacabdcdbdaaacddaadddbacaddadacbbbbcddccbcccbcdbdacdbbdcbbadbddbbcacddabcddaaccaadaacbcbadcdcadcbccacddcabacbcaacbcbbdbddddbbabaddcabdbbaaccacaacdaabdcbcdaaabdbcabddbacbbaaaaddcbbabdcacdbcbdbcbccdabbdabbaadcadbbcaacadcaabdadbbababacdabcddcaccdacdadaddabaababcdccbdcdabdadaabcabdbdddcdcccdcabdacbacdcdccddabdcaaccabddbadccdbbabbabaabdddcaacacabdaaaccbadacdbccbbbabdddcbbbaccdbaabbbbbbabdddcbbcbddcbcaadaccadddcdbacacaadcdcdcbbbcdbdcddabacbcabbadaaaaddbbabbcbbabaaaaccdccbdcbdbcbaadbcddbacaaaaaabdcbdcbbddccdabccbbbbdbcddaaadcacadbbcbcabacbaaadbabdcdabadaabacacaddcddbacaaddcaabcaabbcdbddddcadbbcaaddabcaccbacdacbadbacbdbaddccdcdbbbcaaabcbadcaabaddcccadbaddcdcbbadbabdcccbccbbcaaacbacbbbacadcbbdabdacdadcdcadddababbbaccddcdcdbcdbdadcddaaaaccccdcdacabbaacaadbdbddabaabbdcdbcccaadacccbadcbcdbccbcbbaccabdddacacaccbcbadcddcbbcadcaaacaccadacbdcbbaadabcacdaaadbcbcbccabcaabcaadacdbaccdaccbaadacbcbacbadcccdbacdadbbbbdcdacbcddadbaadabcbdcacadcdcadabdcabdadaacbbadcddcadacabaddbcadbcdccabbaccdcadaacbbdbcdcabbacddbbbaddaabdacdaaabddbbaacabdaddbddbdacaaccadcddbcacbcdcdabbaccabccaddadcacbcdaadcbbdaccbbbcacadddadacdcdacbbaabadcbdbcbdabacbacbbdccbcabccdbbcbacddcaddbdbdcabdddcbabbbbccaaaabacadbdbdadacddaddbdcaaaadcabdcdacdcadcacddddabdabdacbbaaacbcdcabcccaaaaabaadcbdcbdaaccaadcaddbcacbabdccabddbbdacabdabbaacdccabccbcdadbadacacadbcbdcbccadaccdabdaacbadbbabaacaaaadbdbcabaadbaadacaadacbdaadbddadbadaddbcadbaaabddcacaacadbbbadaddcababadcbaccdaabdabacbcbbbddbdcacdaddbccadbadaddbacbadaccdccbadbbbdbabdbadbcdddbdcaaadaaaccabbbccbcbbaacbdbcbccccacdbadcdcbbcdcdacddcdbcaddccacdcbbbbcadaadbbcddcdddbbccaabbbcdcadbdcbcaddabcdaccdadbccaccbbcbbabcddccdadacdbdccdddccdcbccccdcdbdaababadddbbcbcbabaddcbccacddbbbdbdaacbbbaacabbdbacaabdacccccabddbacadaadcaddbbbdbdcdaccbadcccdbdbdcdbdbbdacadbddcbcbccaadacddadbcccbbcbbadaacabbbbcbbbdcadadaabcbddccaadbacacbcbbacaccabdbcbbbcccaaaabdbddbcbdddccbccabbbcaabdcccacacabbaddbdbdabcdbdcbbbbadcccbababbddcaaabdccdbadbcbbbbacccaadbdacbdbcdabccdddbbaaaccbcbcbcaacabacdabbcbdbcaddcbbdadcaccccdbcbccdbaadacdaccccaccaadcbbcadbdddadaaddbcddcbbcadcadbbcbcabddcdccbcacdbcbbbbdbcababdddbcadbdabdacddacddddabdcbadacadabcddacbddbbcacacdcddcabacbcaaacdacccaacdacdccbcaddaadcccaaadaccbdcaacabcacbdadabaaabcdbcabbbcabdcaaacdccabdbbcdcbaadbdaadbbaddcbcbccbacadcccbadabccddbaadbddbacdddcaaabaaabddcddbbcaadcccbacdbdaacdcbbbbbaabadbbbbabbdcccdaccacdcdbcccabbaaacadacbaadccbcbcdcdbdbbbadbddabdadcdadbddbbcdbabcdaccbbbdcbdcdbdcdabbccdbbbabddabdadbabdbdacdddaddcabbaabccaacdbdcdacdbdccbaddcbdbcdabcaacdbaaacadddcaaddccbaadbaadbaadabcdabddabcdcbdbdcddbbacddccbdcccbdcdcbbcbdcdadcccdcaabdacdccaaabbbccbadcdcaaddcdbadcdccabbacdcabdcdaabddaaaabbacbacbddaabcdcacbadbccaadccdaadcdcdaaddbacbdacaddcdbcaaccdbbbdcdadaadbddababacdcadaaabdabbbcabadbbdccadddacbdbbbdadddddbdacdcdbbabcdabbbaabacacbaaddacbbbbdbacbbccbdcbbbddbccddcbdcddacadbdbbbcbdaacdcbcdadbbdabdbabdbadccdcdbcabdabdcdbdacadcaccadccdcddaccdadbbccbcdcbaccbbbacabddaaacccbdbccbbddbadccbdccacbaddadacdddcbaacddcacadbcdcdbcbdddcbbbdadbcddbdddccaabcdaddbaababcdabbcbabcbacdcbbacdbcbaccdbcdabdcdccddcabcacbbaaacbdbcbbcadaacdabdbaccddcabaadbbcdbdaabddacdcdaabcabbdbabbacbddadbbaaadabcacabbbcacdcbacbbdbdcbcddabbbddcddbbcbcdadcdadcdcdbadbdbdbdcaadcacabbcbabddccdcbddaadcbddcdcdacdcbcabddbcbbcaadcabbabcdcadabaacbbdabbdbdcdcddacdcaddcccbabaadbcbcbdadadcbdaadbadbbccacdadacacacbabadcdabdcbadbbccabcddbaadbcddcbcbacdcddbdcdbbcdcddabbccaacddacbadabcaacaabdccbbabdbdcadaaccdaacadabcddaccacdbbcbdcacccddbdcbddcaaadbbbdbdacddaacdddacccaabbbbccadadbdaacaddccbadaccbbabaaacacaaaadbbddcbabbdcabbbcaddccdbbccdcbaccdaadcbaaaabaababdbcbabbdbdcaccbaccadabacaaadcadadcaabccdddbccdcbdddddacaaccdcdcbdadcdccbbdcaacdabccdaacbbddcdcccadcabcccbaddbadddbccbbcbbbcdbcbcbbcbdcbdbdbaabddaabccbdbaddccabdbbcabbcdacdaddabcbcbacbbaadbdccbbcabbadaaccbacccbbaddaaabccbcdbadcdddcccadddbbdbbdcddabbacddbbaccbbaccccccdbcdcbddcbccdddddadacdabcdbddccdbbcadccabbdbbabaaabacbdbbccbaabbadddaaabcccdbabcaabdcbcdacacdccdaaccdacaaaccababcaacdacacccaddbbdcdaaddacacbaddccaabbbdbaddbacbbabcacbbccababccaabcdaaaccaacaddbbccbdaaaacccdbcdbbdbdbabcdaabdcddacadabbbbdbccdcdcdcbdcaacbcbddbbbcadacacaccadcaddbaabbdcabacdccbdcabdacbbbcacddddddacdbcaaabccccdbbaccbdbbdadadbddccbacdcbbbcbacadbccabdddbcccbadabbacacbdacdbcdbddaabbaadbadabbbbddbddaabbbbadcaccddabaaaabbaaacdcbcddbaddaaabcbadbabdbbbccaccabbabbdbabcbbdcbcbcddcdcdbcbabcbdadbdadaddbdaacbaaddacbadccabdbbdbbabcaaccbdcacadcccaacaccccdbcdcacabdbcabdaadbbcabcacbdaddbccdaccbdcdcabccaabddbbaaadcaabdddddacadbccdabddcddaadcacdadcbbbcabbdaccadacaddcacdaaddabdaadccbaddbccadcbdbdaaaddadbccdbdbdcabcaaddcdaddcdbacadbddbbdcdbadaaddbdbbdaadddaadddadacccbcbbddaccacaaccdbbccadcbbbdbcacbddbbcadaccdbdbacaabdbaaacaccdbacbdcbdabcdbbcdbdbbbaddbbbaaaaacbbdcacabdaddaaddcabbbbaccbdddbdabadabcacccccadcaabbdcaaabdcdabacbddbbdabaddadcadcacdcaddcbbaadcacaddaacbcbbdcdaddbcdcadddcdcdbacbcbcaabbabbcdcaaadaccbbacbabadaddcddcdbaadcccabcdcbadcbaabbbcdacdcbacdbbbddaddadbdddbaaaacccaccaadcdbaaccdcbacccadcdadadbcdaabddccbadddaadacaabaccacddcbcbdcbadbcabccacbacacabaacdbdcddcbcbbaccddcbcdbdbabadbcbbaccdbcadbdabbbccdddbbbbdbdccbbabbdaccadbaabbadacadbddaaaaadbcacbddcaadccdababddbcdaddbbaaadbdccababaabadbdbdaddadcccdabacadcaacabbadbdcabdbdadddacacabccacadbadddccadbdaccbbadadaadbbbbbacacbadcbcabcadbabdbbcdbaddabcbbccbcdbcaccbcacbbdcdddddddbbdddabdbbaaddbdababbdccddbdcdbacbcdbddcddccabdcbbddbddbabccaddbcabcbdccdadaaaacdacdbaaccaddbaadcbabcbcccaddadcddabdababdacdacbdcccabadbcdcccddcbdcacbcddbabcdcddbdaccddccbbccacccddcbcdddbcbcadbadcabcaacdcccaabcbdcdadbdcadaddabccbbdcbbbabdcbddbdcbdcbadaddbcacaabaddbaadccadcbdbbdddadcbacbbaabcdaadbacdaabaacbddddbcbbbaacbbadcdbbdaaababdaccdaaccddbccbcaabaabbdcacbdbbcdddcdbaacacccbaaccabbbbadcbcaccbddaddacdccbdbcdbcbddbdbaccbdbdabcdaacddcbbaacdaadadbcbbbccdccadccdabbcadbdcdbdbcccbabcdabbcabcbbabddcabdbbbaccddbccccdadcdacbdcdaadbbacdbcbdbcbbbdcbbabddacbabcbacbaddaccaabbbacbddaacabacccacacaaabbcadaaabdaddbbaddaabbcddcacbcaddcacbbacdbdbaadcdbdbdcbdadabbabaddbbdcbadddaaddccbcccbbacdaabbccdbcbcccbacdccbbdbbdbaccbabaadbcccccbdcdadcadaaacacbabcadddaaadcddbbcdcabcabcbdabadacabccdbdbdbbcdaadbaacabaadbbcccbcababddbcacabcbddbaccbdacdcbcacacaddaadaccdcaacbbaccdbabbcbdbdbaaccbbabdcbacddbacbbaaccdbdacabbbdadbcdcbcabdcbcaccbbcddadddaacccdacacdabaaddbbbcaabbbbadccdcdddabccdddcadcbbdcdbdaaccdcaabaadbbcaddbddddbabdabcdccccddbbdbacccccdabdccccbcaacadabcbcdcbadbcaccaaadcabddcdcdbccdccaaccdadaaccadcbdaacdacbbaabdaabdbcbddcbbabacdcadbbccdddbaccdcdccabbcbaadbbacbbabdddadcbcdccdbabccaacaaaacbabbbdadcccbddacdcacbcaabbbdcbbbbbcdccddccbabbabadbacbbcbaabcccacddcccacbdcadbabcdccdddbcdabbcbbcbbbabcacbcbabaaccbabdcabcaabacddcdbbbabacbadaacbbcbdacccdccccacdcdacdcabdadaddbccbbbddaabaddbcbdbcbaddaaccdbbbddacbccdcabaaccdadbdcadacadcacabdccbbbadbdabccbbdcbdbcbcdbdcbacaaaaacbcaaddabdbcbbaabaddcdddaddbdacccbdadacaacdcaabaadddddcdddcbcabccaddadabadadcabbcbadbdcadcbbbaccacddbddcbbbcbbcaaabbacadaadccdbdcdabdadcbcbadcbbddbacadbdbacbacccabcaddcdddaacadcbaadcbcbbdababccdacadcccbdbaaacddcdbcdcabcddbbcdddbccbdcabbaaaccbabbbaabdaacadabbadcaabdbaadacccddccabcbcdabbabddbdbcbdccbaababcdddbdbdacbcacbdacbcbacccacbcccdaadadbacadccbcdabbadaabaabdbcaacbbccaddbbaadccadcdaacdcabcbddcbbbdbabdccbbadccbccababacdcdddbccdccbcabbabaabdbaabcaacdbcdbcadcacdadcbccaadbadcdddcbcbcabdbbaabbdaadcabbaccabddcdddacaadbbdbaccdcabbbbbcdcdcaaaabdbdbcbaadacabcdcdadbdcbaddbdddbdbaabbaaaacdbbadbcbdbcbbdadbaabdccabccccadaaaadadabbcaccdcbdcadbbaadbcbdbddcbcdddccacaadcbdbaaaccbbaddcccdbcaddbddcdcabaddbdaabddaadbcbddcadbaccabadcaacdcadaadddabbadddacdabbdbbbadacacbcaddadbbcaddbabadacddcdcbdcccdadacccacbddbbdadcadcaadbabdccabccdaccbaabbabccddcbddacaaaaabacaaddcbdacaabbdccbcdccdcdabaadaaaccadacdddabcccdcdbadabbaacabdbdcbdacdcbbabcddadbcdbdccbcbaadccddcadacabaccdbcbbdbbaadccbdaddddcaaaddcbacbaacabbcbdcacaccdcabddadcacdcbabcccdabbdbacddacbcccdbacbcbaadaddcbdcbbdbdadcbddbdadcadbabcddcadcdbacdcbbddbcabadcabbccbacddbbdabbbbdbcabcddabddcacbdababadabcbdddcadddcbcdcacbaacdcabddaacdbacbaaadbbbbcbacdaaabbcacccbbdabdcdabcabcaaaaddbbbacbcdaacdbaabbbadaddbdadaabbaaddbccbbabdcaacbcdabcbaddbaacaaabaccbdbdddccdabadbdbbccdcabadabcbdcacccbbcbadcadacbbcacdccbdcdccacdbabbbaacdbbadaabacacbbdccdcddaadabbacacabadbdcaababcbabcbbdcdbdcdabdcdbbdabbccadcacbaabcacadacbbccadbbaaddabdbcddabbabbcaadabcdadadaddbdcbaddcdbcbabacacbbcccadaccccacacddaadacbdacdacdcdacbadbbabccbcaaddcdacdbbdbadabcdcaacabbabdadbdcdbbdabcabbdacacdcdccdcbdccdacbcdcdbacddcbcabaddbdabcabddccadaddaadcacbcccbdddbddcbaaaccaacdaadbaddddcbbaabbbcbaaccbbddccbbcdbdacbcccdcdddbabdcdcaacbbbacbacdabdccbabcdddcddcccbdcaaccdabdcddabadbcabadcdbbbcbdcbcdccccccccaacaddddbacdbacdddbaadcdabbcbddcbcadcdacaddccbadbcdadadadaddcadbabbcbbdaabdbaaaabcbcdbcddacdddabdddabbccabaabbcddbcccdcadbbdccbacbddcccdabddabddabaccdbadbdacbddacabdbadaaaccacddcccdaccdcccadccdbadddccdbbaccabcadbbcacbbabdcacabdbadddaddbddbacaddddcbaababbdccabbacbcadcadcccabbbbacbbcacabddadccacbcdaaabaddcaabdcababdbbbadbadcdbdbbcdbabcdacddaabaacaccddbbdbaabdaabdbadabbbbddcdbbbcbaaaaabcabccbcbbddadcbdddccdaacbbbcbaadabcbaaacabdacbbbbdadcbbdbccbcdcdcbbbacdddbbcbcbcdcdcaaccbabadcbaacbacdddadadbadbddabdaccbccbcaccdccadabbadbcddcbcdadddacaabaccbadabdaddbaabbbddcdadadbddadbaaccbddbdcaccddddcdddccbcdbccbbbdddadcdcdabadcddcaabcdadaadaadaccadbcbdacacbbddadddacccdacccdbcdabdcdabcddbdadcdccddcddcbbcdcdbdcbcacbacadbdacbdcddcdbabcdcccacccbcabdcadbabaacbabcdccbdddaadcdccbabcbadbbabcccbbddddbcaddcbabdadcbabadcdcabcccbcadaaaccdaddcadccdaabbaadbcccdddddaaabbbacdabcbdacdcbcaabcbcdbcbbabadddacdabbdcdbabddbbdbbbaccdabaaadbcadcdaccdcdaadabcbccacadbadbdbcaddabccbccbaabbacdcdbcadcdaabbadcacdaacaadcdbddcccddbdbaadbadbdbabdcbcacadacaadcdabbacdbdbdabdcdaddbddccabbaaacdadbcabdddcddcadaaabdbbcdabcdbdabdcbcdcdbaabccbdbdbbcbdaaadccaacbdcbbcbdcccbdcbdccbabadcbcaabdaddcdcddbbababdcbdacdbcccbacdddadadddabaaaccbccbbbdcaabbbaadbcbdbcaaddccccbaaadcdbaabdcdbaaaadabdbcdccadabdcbabcbddbbaacabdcbdcdabcbbdbbbabaacaabcccaacabccadbacbdabadadcdbcdcdbdbdaacbcbbadabaddaccbdbbddaadbaacbbcabcccabdabcabbaddadcccdabaddbaccddaabaabbbdbaabaacccdcaacacdbaaccccadccbacacadbbdbabadacaadabdcadbccabdabdcdadcbdcdbcaaaaacdbdaddaaadcbbbcbadcbcbbcbabacbabacdbdccadadcdccaaaadadadbcacbbbaaacddbacddaaabdaacbbabbacbbdcdadbdccdcccbadddccdbbddbdcbbaadacbcdbbbbdbdbdcdccaaadbccbaabbcbabddbadaacdabcdbccbabbacacbcbddadcdbccdcacaadcdcabbdbaabaccbdcdccbbbbcadcbdacccbbadbaccdbdcabadbcbabdcadcdbddabbcdbaadddacdbdcdcdaadccbbddcbbbcaabbadcddcbbdcacdddbcdcdbddcdcbacdbbacadbcbaadadaaaccabbddaaaaccdbdacbbbdabdbbbacaabbdbbbcbcdaaadddcbbddbdacdaadbcdcbacaccbcdcbbdbddcbadcbacbdcbddbccdacaaadcdbabdaaabaabbbbcbdccacccacdcaacccacbaabbabaadabaabbbccdabdaabbccabbbccccadcadbcbdbbccdccaccbacabcdadcadcbbbccccadbaccabaadbcddaddbddbbbdbaaabcccdbdbddbdadcdaadababbccaadcddcdacddcbbaadcdcbccaaabadcaaaaccbacaadcddbacdacbcbbbacdabadbbdcccbabacbdcccaaadcbacddadcadbcbbcddabbdcabbaddcbbaddbbbbbacbcbdccabbdcbbabcdbddbddbbcaccaaddabcbbbbcdccdadccbbdbbabbbabcbadbdcdcdccccaabccaaccdbddbcbdcabbbdccdcabccbdccacbddcccbbabbadcbbccdcaaadcadbdabcbdddbddccdcdaacacbcbbaaabbaccdddddbcdbcaacbdbbacadbdabdbdacddcbccacddacbdacbdabbcddcdddccdcdcbcccbdcaccdbcbdddcbacccccdbbabdcbcbabccbcbcdaacddaacbbbcdaddacacadacacbbccdabdddcddadbbacdaadccbcbbacabbcaadbbbcbbbcadacabdaacaccddddcccddadcdabcddcadddbadcbdcacdccdbcbcababdbbdbcaddaaaddaaaddbdbddaabddaadacaccbbaccacaccdadbbdbaacddaacdacddbbdaababcdccbcccaadbabcbbcbdbdbdabaacdbdbaddbdadadbadcbcbacdacadcdcaabcccddddcadacbcbadaadcadccbcdbdaacbbaabbcadddaabbbcadccacbccbcabbbdcccabcbcbbdcadbcddddaadbaadcadacdcbabdddcbbcacdcadbdadabcdbdddacbdcdbccaccaabcbdbcdddcbaaddcbcddcbbcbbcacbacdabbcbcacdabdadadcadcbcbcdcdadddbdaddcdabdaddadccddaaabdadbbccdaabcbcadbccadcacbdbbbbdbcdaacdabcdbaacdccdcdaddabadaddaabaabcdddcccadabadcbcdcdcadbbaacbccdcaacbbbdcbbcdbcbbaacdcddacdcacbddcabbcdbcbdaababdcaddcddadadbbdabbadacbdbcddbadbddddabbbbbabacadbcadaddbdddcacbbccddcdbbcccaaddcacacacdbaaaacadadcbbdaaacdccaaadbdbddacbbbcabbbdabcbacccabbcdbaaadbbaaadccaadbacdacbccbbcaabbbbdaadbbdbcbbbbcddccacabdaacaddbccadcacbcbdadbcdcbcccabaccccdbcbaaabcbbcdbcbdbaaabccbdccabaabbcbaacadadcabcbdcdbdbddbbbacbcccdbdbcddbdbbbcbabbacadbddbdcaacabcbcddbcddaaacadbdcbbbbcbbcbacbadccbdcbacdacddadabbcbbdbbdbdcacdcabcddbcacabbaacdcbdadbbddddabaddcdccccabcbdddbdbddddcccbacbdbbacbdccdddaadbdaaadbaddddcccccbbbadaaabdccdbcbbacacaaccbdbdaacbcddbadbbbdabcabddcabbabdbbdbdacbdcccbbbcccdacdcadcbdacaccabdbdbdaaccddbcaadabbadaccdbbccbcbacdacabacbbbcddabcbcbcbcaccdccadbbdcaccadbcbcabaddddccacabbcbbdbcabbbcabddcbccbbdddddcaaddcdcbdabbdaddbbcdcccacbcacbbcbddbccdbbdabcadaddcabdbbbdadbbbaccdcaaaaadbdbcaaccdbadaccbcccdddbbbaabacacddabaddabaccdbabbbbadbbaaacbddddbbccddbacddabcccccdaaddbddcdcbcbdacbbdccaddddbdccbbddbcaabbbaccddbadaadadbbabacdadccddcbabadcabdbabbaabacabbaabbcdadabcccbbcbbdbbdababbccadbdadcdcddcdbabadddacdabcbdaccdcddcbccbcbbadbaccdbdbcbaddaaabadbaaaabcacbadadbaabaccacccbbbbaccaabddddcddbcccabccddbacaabdccacabacdccbbdcddbdbaadababcddacbddbbcbccdccabdbabcaacbddddadaacdcdcbcdabacadabacbbccbcbcdadacbbbabdbcaabddbcdabaaadaccaabcadaababdcbddbbbacbabaccdbadadadbcddcdbbccdadbadabbddcadbadbccbaaaaaaaccdaaaddadbdabdbbdaacbcabcdbbdccbacbaddcaabcbccdadcbdbccddcdddcbbcdabdcddcccddaababdcaaccadbccbdbccbdaadbadccabbbdccbddacdabaccbbabdcddaabcbdbdcdadcddbbaddbaaaddbabaacccddbdddcdadbccadbcabdbddbbacabbaacbdababacabdbccaacadddddbcbabbadcdabbadaccadacdbbccaddadcbbaabcaadbadcacadaaaddccbdadbcdabcdbcdadbdbaaabdcdcbccdccbdacabacbdbababdcbcbabdaabcacacdadbadccacaaacbaacbabdcccabdcdcbaabcdaaabbdbbadcbcddbaaacddbcaacadabacdccabbcbddbacbbabdadbdadadddccdddddbabbdbabadcdbdacacbcbdadcddaacadcbdcddacbbcadcdccddcccbacccaabdccdaaadacbbadbbbbabcdadadabccbdbabaaabddbbcdbadcaadddbbbbbaaacdcdbdccbaacbadccbccadddaadadbbbbaacdcdbaacabcbacbbabdaadaacabcabdbbbdbdadcabcccdcbdbadbaadbcbaacccaabbbbaabcdcdbbbdabdadbbcbbacdcacadcccbbcbdbaacbbaaccababccbaabddbbcdaabcdcdabdbbcbbabddbabdcabcddaadcbcadcacabbaddbcdacdabdabdadcabccccdcabadddbccbbdaaddccccccabaccdbbabdbcdacccdbdadbddbbdadabbcbbadbacacbacbdabbcbbbacbbbbcdcabacbaaaaddddcdbadaccdbddbdddaabbccacacddbdddcdbdbddbacccaabadadbcbdadaddddbcaddadcabaadadcddbdbcbaadcbacabbccadccbbddbcaabcdbcacbcdadabaccbabbccabbdacbddddddcdccddadabbbcaacbadbcaabcbadcaacccbbdabcbbbaacabbbddccdcbacacbddaadbcbdbacdcadaabcaddbcaabdccadbacbbabadbaccdddbbadcdaccbbbdcaacabacdaccbacdbaccaacdbddddcabcacdcbbbbcaddbdabcbababbddaccdddccacaddbbbbbddddccbabdabbcabddbdaacadcaabdadcaabccbabcbdbddcddbcacbacabdccdaccabbcaacdaacbbdbbcccccdccccbdcbdcaaddbabacccddacbadbbadcddddddcaddadbacccbcababddcbdcccdadbcadcbdbbcdccaadadbbbabbcacccdddadaadddcdcdbcdccbacbaaabdcdbddcbcdcdbdcdbcdcccccbcabdbdadaadbaabadbdaabccacdabdabccbcbbbbbaddbaabcbbccbaccdabadacbbccbadccaccabaddbabdbbcbbdddcadacdbbccbabdacdccaaaaaaabbbcbdbaabdccbdbbbcbadcacabcacdcdaabdcdbdbcacaadbbbbbbbddbdcbabbaaadbbcacbcbadddbcdcadcaacddddabaabdcaaacbddbcaaabccccbbbabbcdacddbbdddbacadcbcccbbcdaddcacdbbcacacbbcdcabacdbcbdcdabadacdabdbddaabcdcdccadbdddaaccddbdddcdacdabdccccdadddbadbbdacbcbcacacababbdacbcacdbcbacbbddaabaccaacacbcdaabcbbaaacbddaacbbbadcddbdcdbdddbabddaddcaacabadabaabbadbacaacbdccdbadacbcbaaabdcdcbacabacbabdaabaccdabacadddddbddcbbadbcadabbadaadbbdbabccbddbaccbaaaccaacdaadabdbaacdbadbbddadabadcbddcaaacdcabbadddcddbcbdcacaddaadadbaacdcdbdaaacdabbdcdddadcadcdbddbbbddbdbbdcabcddcddabdbcdacadbdccbbdbbdbbadbaabccccaadbbacdabcabdbaddabdaadbabcccaaabbdabbccdcdaccbdddbdabaaabbbdaccaddcacabacbccbbcabdcddadccbbbcacddaaabdcacaccacabbacdbaccaadaabacbcaadbadddcbddbacdabbcbdbaaacacabbadabcbababbaccabbdbcbbbacbbbcbccdccdcdabbcadaadbbccbdbdddcabdcbcbdbacbbaadddcbbdcdadabcbdabbcbcaccaabaabdcdcddaccbacbabbaaabbccdccbcbcacabbddbaddccbcaadabdbcbabbddccbddbdcccbadddaaccccaaddcccddcbcddabbdbbacdcacaaaabcddbbacabbcdbacdbccadcbbaacdaadccddadcabadddadabcbbbcaccbdadacabaccabbbbbbaabcccbaaabbbdbadddccdaabcdacddbabdbbaabcaaacadbcaddbbcabdbbdabcabdaaabbcadabadcccaccacdcdcbadbbabccbaccdbbdccdcaddbaabbbabaabcbcbbcdababbcbbdabdadcacccabbcccdcacaadcabcabbbababaccccdadadcdbaaadcbcbcdbdacabaacddcaaaddabdbadbacbccaccadccacbcddcbabcacadbbdcacdcbccccabbcaadbbddadacabdbdbdadcbaabccdddaaaabbabaabadbdabdcbbdbdbbddcabdabaccdcdacccdddbcbbcbacacbadabacabaabdbdabbcddcbbadbaccdbacdcaadabbcabbbbdbcdcdabcabcddaacdbcabbcdcaddbbdcbccbcbbccbdbbadbccbbcbdbbcdcccbdaabaddbabbdbacdaaccbdcdddcabaddddabbcabcbccdccaacaddcaabbdcaaadcaadaaaadccdaabbadbccdddbddccacbcbccbcbacbdddaabccbcdccdbcadbadccadbaaacddddbaabbcddbaabbaacbcadbbabbaadcdcabdcdbbcbbabcabddcccccdcbcdccdbadabcdbdcacdcccddbcbdcdbdaadddbadcbbbbbbbcbcdbcdbabaddaabdabaccaadddcbbcddbbcadabdccbadcabbaacddcdabdaaaaccbddddddcbcbaccdabcbadbacabbadadbdabacbbabccaaabaaabdbdabbcaaadbbbaddaddacdabbddaadbdadbcdbabdaccddccdababddcddbacacacdcdcbbbbdcbdcabdbadbddbbbdccacaabcaabbbdbccbcbadcccddadbbacdacbaacddcccabbadcbcadacaccaddaabaccdbcabcbadacabbabdbbacddbddbbaacdbdbdadbacaccdaccdbbcabbacbaddacdbbcbddbbabccacccdbcdcddcabaabdacdaddcdddbacccaddadabdabbddbadbacababaacddcbabaccabdadddcbcbdbbdacdabddacbbdacdabddbbccccdadbcdbaabbbabcdabcbadcdbdacabddaadbaacccddcaabbabbbbdcbcdaacbdacabacccccccdaabacbaccabadccacdcbbcdcbcbbcdaacaddccaacadaccdadbdccdccbbdcabbbaacdadadcbcadcbaadccdcaadacbbaabcccacdcdacbacacbaaaaabbaccdadabaccccabdcdbbcadbddbbddccddacaddaadddaccdabdaadacbabbcdbdaacbdddcccdccaddddbccddcbbacdbabdbbdcbcbdbacbbacbdccaaabdacccabbdcbcadcccbcbdbbbbaaaaccccdccbbcabaabaaabbaccaddbcdddbababcdbacadbbaaadadadbbdcdbcdddbaccabbccaabbbddcccdccadacbdaadaacddbcabcccacddacdcdcdcacadcccacdbabbdababdbabdabacaaadcccddaaacbccbcccdbdbaccdabcbddadccaddabcacdddbbdbaabaccdcaabcabadcabbcbdacdbaadbccbaadbcacdaababcddbaacacddcaadadbbacabadbbcdddddacbcabadbcacbacccdccaaaacdbbaddaccccbadcaabaacaabbacdbcddbbbcbddaaddcddddbacbaacbabcaacaacbbcbadcddbdcdcdaacdbdabbdbcaccaaddccdcacabbacdbdcabdabacbdaddbddbdcadbdcbacacadadcaaadcabbdbccaabcdaaaadabcbbccdcccccadcddbcabcdccdcbadbadadabcdcbccdcbbbcddbaccdcacdaaddccabacbbcbbbadbbdadccaccbbbcbddbbdcabcadcabdcadaaabdaaacdabddcdcdddbdacaacdcacddcacaadbdaabbddbcdddbacababdbccabbbaccaaadbaabdcdddaadccaddaddcdbaabdcbccbadccdadaadcccddcacdbbdaabcdadabbcacacccabbdbcaadcdccdadbbdbcbbcccacadacbbaaccbdcadbaacaaaccdddaadadbdcbbbdaccbddcbbcdbcabcccddadbcacbcadbcbdcccdbdbdddcacddcbbcddcbbbbddaabcbcbbadacccdcbbddcdcddbabaadbbbcbdaccbddbbbabcddccbccbbcadcddccbbddbcbaddbcaaacbcabdaddbdbbbbacccdcacbdccbcabddbaabcbbaddcccadbcdcdddbcdbdcbdddaabaacbbadaccdacbdaaacdbbccaabcacacaadbddbbdcaaddbbdacaadcdcbabbaacdcdadbaaddacdbcdbbdadbbadbbdddaddcdcbdadbbacddbbbbdcabacdacbadcddbbdadbbadbbcdbcabbdadcbacaabdddabddacbdcacdabcbddacdbadcbacaacaccdddbbdcacddaaccacccacdadbadcaaddaadadcbbdccabdccdbababcddbdbbaccbdddacddabdbbbbdbbcaaadabbdbadbccdccdcbbbdccbdbcdcabaaacbcbdccdacdccdaccbaddadcbacadbadccaddddcdaadbdbacabddaccbcdabbdbacbbadcdcbacbbdcbbdaabdadddbdcdbccdcbcccbacbcccaabdcbbcaaccdccbcaabaabbaacbcdadbbccdaaaccbcaccbabcaabbabbacdddddddaaddaacbbbbabdcccdcbcddbcbcdddcbbcccbbcabcacdcdbbcbdabcadccbacddbbdcadbcaacbcadacbddbaccddcbbaddcbbcbadbdcacaddaababdaacbdcbaabddbccabdadcccccbbdcbbbaccbcbdbdbbdcdacacbaabbabcdcadcbaacbccdaddcccbabbbaddbcccabbaddbcddcdbdbcababbcabcaccddbcacbadbddbbddcbdbdacdcbabbdccdccccdabccadacdcdcbabaadbaacdaacccabcadcadbbccbdbcddcbabaaccbbcbbbbacaadadddbcacdabbcbcbdcdcdabaaabdabcdbdaababbadcbacccacbbccdabadbdabcdbabdcadaccddddabddcbcacccacacdacabadacbacbaaddaabdabddbbcdbbbcaddddcadadacdcdaacccbdcbbaabbabcbccbcdabccacabcdcddccccbcdbbcdccdabaccccbacacdacdccdbbbbcdbcdabdbcbadbddabbddaccaccbcdacaccbdbcbbcccaabddaccbabdbaaaddaadddcabbcdcddabccbddcbbcaaddabcdabdaaacbaaacacdaabcdaccdbaacbdbbaccbdcdcabcaccbaddaadccbbbadaddbabbbccbbaaccbccbbbdccdbbbbcdbcadddddccacdcdbaadddbcdadddbccbdcbaaddcbbabaadaaaaabadcbbcbddaabbaccddacbbaaabccdcccbcbbcdbaaacdbaddaaddbacddbddaaaadaddaddcbdbcbddcdccadaadcbbcacaaadbdcbcbccdcdcdddaabbdabacdadabadbdabbdccdaadbbaaaabbcbaddcdadccbdbbaadcabbadddbbabcdbbbdccbbabdaccbcacbcdbdbbbcdabbddbdaacdccabaabcbbdddcabbadadbdcababadaabcacaadabdccbaababccdadcaabcbdcacdabdbcddaadaadcacdadcddbcbdddbdcbaddbddcadcdacabacdaabccbdbdbcdddbbcccaaadccddaaaaaababcdccababdbcbbcbcbcbbccddcdcadacaccadadabdbcddadddaabdbcccaadbacabcbbcacbccbbacadaaddcadacddaadadccaaabcbabbbbbddcdccbbdcddadadcdddbabdcdccaacadccdaddbcbcdbdcbcacbcbbaaacdccaaaaaabbbdddbdbdadcbaccadabaabccaaadbbcdbbcdbadcacccbbddccdbacabcbddbbaacdbadccaaabaacacaaaacbaabbcaabbaddccbccbdcbcaadbadcbcaacddacbaabcaabaabcdbccdadcccccccabbbaddaabbabcdccdbcdabcdaaababdaabcdabcdabcdddbcccdaabbcdaadbddbadcdcadbcdbddacadaddcbadcdacdcbadbacbdcdbbdcbaadababcddbbddbcbbdbdccccdbbcaacdbcdadaadcccbbdabdacadbcbaccadbcbbcccccbacdcbacdccabcaabccabbbadcdaabdcdaccbcdbccdadcbbbaddaacbdadcadcbdbaabdbccbababbcbadbdaabacdadcabaccbbdabddcbaacdccabbcbbbdcacddccdcaadaabbadcbabbabcdaabaccadadbcddaccdaabdabbdaddbdcadadbbaaccabacaddcdaabbbccbdcbacadabadddabdbcbbccdddadbcaaabdbcbbdcdadbdbdddcaabccdccddacbaacbaacbdbbadcbaddacbcdbcbdccbbaadabbdbbaacbcbaadabbcdbdbcdcdadbdcdbaccaaaaadcacdbdbabbddbbbdabcdcccddaadbabbabdaadbacaacdcdbcaaaadbdaccaaccabacbdadacbcdccbbbdcaaaddbbddddcccaddcbadbbdbcdbbbcacddadacbadbcaadbdaccbccdaadadbbacbdcdadddbadbbbbddbddcaddabcccccadadbaaaccdcbdccbdbadabbcaadacbbbcaaaccabbaacadbcabaabbbacbadbccdacacddcdccbddbdbcaccdacdacacbcaddbbcdbbdbbaaabacbaabcbabdbccbbbaaaadbcdddcabdbadcbddccabdadcbabccaadabcabccbdadccdbacdddcdbddaacbdbcacdbcbddbdbbbbadbbdbcacdcbbadcbabbdbcbcadcaddaacdaddbccdadacabbbbcdcbabdddababcccdbcddbdcdbccbbcbdbacdbdaaadbacdcacddabdabadcadaaccdccadbdcdacdadcddbabadbcbcaacbaacbaaaddbcdaabbcbbcbcdaabaaccbadbddadcbbaabcdbdbacbacbcadabbabcbcabbcbdbdaacbbcacccbbcadacbdadadcbcbcdcabdbcdcaacabaadcdabcccbbdbdaccbbdbbadbadacddabdaaaccbbadabbbbcccabcccbdbbdbaadcddbbcddbbbbcccaddadbcdbbddadaacddacbdcadabcddbbbddadbbcbacdacddaddbcadadccdcdbbcbbdbaddaabacbcabcdddacdccaadbcabccabbbabbacaaddbacdadabdbdbdacdcadcbcbccdddbbbbabbddccdabadaaaabacdadbcdbddaccdadbadddbbadcbdccbcbcaadcbcabcabdbbbabdcdaccaabcccadadaacadccdacabacabcabbaccbaadbbcaadacbbdbbdbbbabcabbabdddddacbcbccaabbbcabacdababbdbcddaccbccdacbbaadaccdabdbbdcacbaaaddcccbddbcabcdabdbddbcdbcdbacdcaaabcccbbdcdcdcadaabddadddcdddcaccbcdbccabaccdbbadbaacbcdcdabcaaadbdddbcdcaddccbaadddddcadbadaadcbdcddcdbbcacacdaacadbbaabcabdaacddaaccbdaadcaaddccdbbcaadbcbaaddbbacddaaddaadaabbccdbbdabbbacbdcacdbabddcdbcbbdaaacabbabdaadcddddbdaabadcbacbacdacaddcaacccdbcaacdacaacacbbcbcabcbbdcacbcdcabccdadaacddddbbbbaabdcbccdbbaccbbbcbbacbabbaddcdddcdbcacacdbcdabdcacadabdcaabcadbcbcddacdbcbddcdbbacaddcddbdcbbdaccbcccbacbcdaaddbabadcbddadabbdcabadbbcbabacbbbcddbdabbdbcbacbadbcdcdbcadabddcdcbadcdaadcdbcabdcbdacbdabadcdcacacdcdcaccdcbdcbbcdbdbcabcbddaacbadbdcabdabddbabadabacaccccbaaadcdbddabcacdcdadacdbddbabdbadddacadbaccbbcccabcbabdbbadacabddabbcddaacbbadbdcabcdbbdcaadacddacacbddadacabaabacddddacbdddabbdcadbbbacdadcaacddbbbbbbdcbcaadccdabdcdbaaacdabdccbdbdbaadcbaaacaadadaccacccabddabcbdaaaababcbabcaccddbdbdccdbcbdbacdbbabdddbbcdbabbcccbacccadbdbdcbccacacaabcaaacaaddabbccbabccdbdbcccadadabddbccbdddbcbdabcbbbdcbacbbbcdabddadbaaacbaccdbbbbbaadcdddcddacaddabcdabcbcaaaacddaadcdcabbaddcdaaaccaccabddbdcdbdcbccacdcdaddbdbbcdadbbabbcdccccdccabdbccbaaacdddbdcbbddcbbdbdddaabbcddaadabaababacbaadbacaaadcdbbcacbbbbaccbacddcddabcccdacdcbdbabacbcbccdcbadabbacbddcbbcacaadabcabaccadbcddbaacabdbcdbdccaddcbacdcdcdddbbccbcdadacabbacadcacdbadbbbdcdbacccbcddcccadccaddaadaaacadbbacbabcbadbbbdacbdbcddbccadcccabdcacdacdcbadbadababddbdbbdcbcabaabbbdabdacbabcbcbaaacacdcdbabacacacccadacbbabcbbdaadaaadabbccbcbcbbacabcbaabdbbbcadaababcdacadacdbdcaadbcbcdcdcaacbdabaaacaddaccbddcacbbdbbabbcacccccdbddadbcadbacdccbabadbbdbbbdaccbdbbababacccccbccaacdaaaaabaccdbcddbdcaccbcbbabbcbabcdcaacdbaaadbcadaaccdbcacaabccadddbcaabccdaccbabdbbccddccabacbdcabdcbabccbbbbaddbadaccccdbbadabccbbdbdaaaaacabbdbbddbcccadbcdbaccdacaabcaacccccacdcccadbcbdaacddcbbbadabcadcbdadbddabdcdacbaabdbbbdccadadaccbcbcbdddbcacdcbcadbbdbabaabdabcddaadcdaccdaaaababcbdacabbcabbacdacacbadbbccbdadacadcacbdbacbadaababaabcddbbadbdabddaabdacccdbdcdbcdabdacadadbbaabdbccabacbdcddddacadddadbcdddbabadcbcdabbbcdbdadacaacacaadbdbbcccdbacdcbaacacbccdcbbcacdaabacaadcbcaaccdcbcdabcbcdacabcdbadccccbbbabddcbcbdcdbaccbdaabcbccbacdbccadbdbadcadbadbbabadbdcadddaccacaadbbbccdcadbcdabbcadadddcdadacacccacbbaccaabdabaadadddabddbadcbadacdacaccaccdcbadcbcdbaaababdbddddbabccdadabbacbdbabdaabcdbdcdadadbabbdcbaddbdddaccdddbbaadbcaadbadbabdabdbbccbcaabccccbcabadcaaacbdbdbabcacdddccbcbddcaadbddadabadabdcaacaadaadbdaacbcaaadaadacbdccdcbbddbaadbaadaddcbcbbbacbcccbdabdbacaadacbddbcddbdacabacdcacacdabcaabbbacbcbdcbcdcadbabbadcabcbbdacaaccbdbdcaacabdacbdbbcbbcaaabccdcdcaccacbbcbaadccdbaccbccbbbbdccbbdcdbdcacdcabddbdcccddbbadcadcbbbababcdccdbbcacbdccacdaacdacbbbacdbdcccdadcabdcccabdbaacccccddcdaabddcaddccbaccbaabacaaccaaabdbdcdaccbabbbaaadacadcdbcaabdccddbbadccddabcaaacccdaadcdccdbaddabbcabbabdaddbbcacccdbdcdaddaacbadaaccbcbbbbaaaddbabadbbaddacabbdaacbaccbaaaddadaabcbadcddbcaacccddbccbbcdcdadaccdbaaddcddbbbddcbadbcdddbcadcdbcbdaacaaabbacbaaacddcbdbcdcabdcddcdddadcaccbbdcdccbbacdcbaabadcadbacabacdacbbbccdccdabcdbababcbabdadaabdbdacbdacbcaadaaccbbcaaccdaddddcadbcabaabcbbabbbcbadcaacbdaaccccabadbdbdcbbcaccadccdadbdcabadcdbbcadabbbbbabaccaacadcccbbbadabcbbdaaaacccbbadadcbacbaddcddcbaccacadbdcaadcdbdccdbddcbacdbdbccdddcadacabdbcaaabcbacbdbbacdaacbbaadabbcdbddbccbadacdbdadaaadcacbbdbdadbbaabdacaaadccccbcdbcbbcdcdaadaacaddaaadabcbcabbaaddbdcabcaadacdddbabaacbdbadbddbaabdbabbaaccccbcacababbcadcbbadcaddcdcdbaaaaacdabcadcddabbcdbcbdccaacddcacaabacccbdabcabcadcaddaaababdbaacbccadadbadadbbcaadbddbcddcacacaaccdbdcddbdadcacdbadbccbcdbdcaacbbaabcdcacddbacddccbdcccbbadcbcdbdabcdcbccabdaccbcddbcdbabdbdbaacbbcadcaddcaccbccdbbbbbabcaacdcccddccadabadcacdcdddaadbddcbacbddcabcdcccbabbaddbaddaaacacbaaacbbbadcabdbbbdcacbddcddabacbcccdcccbcdaadccabaaadcdaddbbaccbbcdddbabbadccacddabcaaacbbbcdbcddbdadcabbabcdcaaaadcbcacdcacdacadaaabbcabbacddbadbcbbcdabcdadadccabaacbdabbbddddbdddbabbcbbabcbcaadcbaaddddcdaccabaabcdcbcacabddcbcabcbcbabddaaadadddcbabbdacdcdcdbaacccdacdcaadacbdcdaccbdbcdaddbdaccbadabdaccbaaccbddcaaabbbcdcbcdbddddbdacbbcdaddcabcbcbcabdacbdaabcabdbbdccacdddcdcbdcbaadcbadadbdbbdccddcaadbaacabbacacdcbbcddbcbbbdcdddadbdbbaacddaddddadcbadccddcaacddbadcabcaaabdbaacdaddccaacbdbabdcddbbccdbcddcbccaabbcacdbcbccbbbadbbcadaabcdabaddaabbbbacaaacbdbbbcccacabcadaccdababdcdbcbbbdabbbbbddcaaccbadabcddccdccdddadcdcdcdaccbbbdddccdadcdcbccdbcbababccdcabacaaaacbbcbdbaddaddcddcabbdccbcbbbbdadcaddbdcdadcbabdcdbacdbdaaaadbdbddcdbcdccccdbbacabcabaabbbcbddcccbcbababbaaadbcacbccaadaacaabcbabccaadabddbccbadaacddbbbbadabacbaaccadaadcdacdbadccdacbbbdabbaabbbccdbdbcccbcbddaaaabbdcccdcaddbbddbcaaddbbddbcababadaabbcaddccddcaacdaaaabbabacaaaadaccdddaabddbcccbcddabdddcbacdaabddbbbbbdbbacdaaccaadcbcaaddbacabcccadbcdbccbdaacdccbaabcdbdadaccbccaaaacdcabcbbdddddddddccdbcccbdabdbdccadbaaabddbcbccaabdabbcabacbacaccbddbacabcaacbadbdcdbcacdccccadaddbccacbacbaccabddcabbbcbcccbddaadcbddcacacdadcbcacdacabcbabbcadcdbacdacdcbdaabaacdddcbccacdbaadcacdbacdaadaabdcddcddcadabadbadddadcbccddaccdbdaddddaddcbdbdcbdaccabbdbbaadadadadccbccbddbabaddbababddacdddcaaaaddacdaadccdccbbcabbaaccdbabdadcababaabbbacacbdcbcacccababcbdabcdadaabccdddcdaccddabcadcdadbbaacbcbabcadbdabaaddbdacdadbddadbdcbcabbdbdadccacbaaccacacddabcbbcabaabbaabdbcbddabbbdddadddcbcadadbdbcbbcbabcbcccacdbccadddcaccbdccbbbcbaabacacaaccaccdbddcbcddcbcaacabbadcdaddabaddcbcbadbababdbaccccdcdcdabbdbaacdcccbaabcbaddbdddabbabbaacdbcbbcdacaaccaccaddadacdbadabacdbbddbcdbbabcddadabcdbbddcbdcdababccbbdbbdbdcaaadccaabccccadcbabdabdaaccbbbabdcddbddababbabaabddcbbbbabbcaadcacdddabaadcdbacaabaddaccabbcbdbadcbbdabdbacabbcdccccaddcdaaccacabcdcaabcaacdddbdaacccbaddbacacbdbbaabdcdacacdbcaabadbdbaaddadbaaddcabdabcacaaaddbcbbaddbccdadcccdccdbcddcddddacadcaadbdddaaadcaabcdccdabcbbadcacabdcbcbbadccbbcacdccaacaaacdbabbcdbdcddacaababbcccbdaccaadabcacaaadcccadbdcbddadcabbccbaacaabacbaaadbccdcccbcdcdbbadbddbcccdaaabdacccadcbaacbbaacddabddbbbcccbdcbcbabbbbcbcdcbbcbabccabddccaadbccadccdddcbdcbccddaabbbcbccadbdcddbccdadababcbdccccabcbddcabcdaacbcbdccacaabddbabdcabccccdcddabcbacbadaabccabdcbccbacaabacdbcdccbcbcccbcbcbcaaabdbccccaddcabbbcbdbcadddbacccacbbccccddcaddddbcabcbdbbcbddaccdaaddbacbacaccaacdabbbdaccadddacbbdaccdbdccbaadadbabcbcbccbdcbcacdaacaaaadbbdbaaadbdabacabaabacdbbbccacdddabdbdaacbabadbbbbababbbcadababcccdbaabadbcbdbadbbcdcccbaacbdbadacbacbdcbbabbbdbacbbdddcbaddaabddddbadabaabdacabcbcabbbacbbbcaadacbaabddacaadcbbccbbbcbaaacccbcbdcdacaadacbaabddccbadbaddbdcdacaaabbbabdcbcbbdabacddbbcaacdccbaacacddaacccdadabbaaaccadabdbadbadbdcdcbadabcdaaddacbccacbbcbbaaccdabcdbccacbbcbaabbcbcbbccabadcabccdbbdbabddcddddacdbddcbabbbbdbabcbcdcaabbbcbdbccddcbbacaaadbaacbbcadadbdbdbdcdcacaccdabbdbdadabaacbcbadaadddbbbcbbcbcaaccbaccbadccccacbbcddbccaabdbdbddcdadcbabddaccccaddbbccddccdbadcabcabbdbcbbadabccabdbddddbdcdbadcccbddbccdcabcdcdbbcbcbbdbbabaacbdbbbdadcabdddacdaacacdbdabdaaddbbddbddabbbdcbcbaddddaabcbaaadddacbcdbdbbbbbddbccbacddcaccbacbbbbcbcbabbddbcaaccbbadacdcadacbbabdddddbdbadcbdcabbbdabadbabcaabbbadbbaaadcdbdbccabbdbaddcdcbaaaadbcbcddbbcaaaaabaaddbbddaaccbacccacbadcdacdacbbbcacbbcaccadcabcabdbaacdcbaadbcbcdabaadcacccbcbddbacbdbdbbbbacdbbaacacbaaccbdadddcabadccadadbcadcccabccccddcbdcaadabccbbccdcbdcbbbdcbbaadbbaccdbcacdaaccabababcabbdabcacbacdbbbbdbcbdbabacaabdabacccddabcbcacbdcdaaadaaccdccacaadcbccccbbbbacaadacacbcdaaadddaaabaacdcabcddcdcaaadbbcaacbddbdbbbddbbbcaabdcacbaccdcabcaccaccabbaadcddcdcdbacadbbadccadbcabbcaddcbdacaadddbccdababbbcbdadbccacbadadbacaaccadaadcdcabaacbbdbcdcbddaabcbdaadcbbcbdacababddacbaacddccadcaccabdbbaadbbccadcaaaaaadbaacddbbabdcadccbaaacbacddaabdddabdcbbbbabddccdbacdaababddccbdbacaccaadbbcddbdccdcbbadbdaaaadabcdcaaadccacdcddbddaabccdaadcdababbaabdccabbcbbabcbaabaacabccbabcbbcdcbddcacdadbdbbbcbdcabacdadbbadbddbcabbcccbcabdcbccaddcbbbddabbdbdadbcdaddbdcbaacdbdbbdaddadbbbbcbdacbdcabaddbdbabbbbadbdbadbddbddabaabbadddcddbabbdbbcaaabaadaabadcbcacdaadacabdaaddbbddddcacbccaaccacddbabcabcdadabdbadbbbbcaabbcadddbbcbaddcbbaddaaacdaaababcdacdaadcbcdcbbadcccccbdcbcdadabccaaadaaaaccbadddbbbbbccbcdddcacabcbbabcdacacbbcabbaaaaddaaaddcadddbabbdadddacadccaabcbdadaaccdbbcdcbadadddccbbbbcacdcacbcbbcacaccbbcdcbacbadacbdbbacbcdcbabdbdcaadbbaddaadbdabdcdacdaacadcddbbbdacaabdbbadacabcdcacdadbdcaadbcbabdbbdbaadbccbdaccdaadcdaddbdbcddabaccdadccdabaacbdabcaacdaddadcdabaddadbdcbabbbdcbadcdbdadcbbdadbacbaaaabbddcadccadcbaacaccbbabccadbcdaaacaaacdddbcbccccbdadbadacccdbcdbabdabdbdbcdcdcabaddacdcaaadbcadbacdaccdbdcbacccdaccddccbcccbbbabbcbdcccaadabbadccaabcbaddcddbdbcaadbcabacadbccbbabcccbdbbacbaabcdaddaabacadcdccbbaaabbdcbbbcdcaccabdcdcccccbadababcdbcdddbacbbbdcccaccbcdbdcdcacdddccaabcddbaabddccddddbcdcbabcbadcdbdcbbcdbdbdbadacdaaaacbaabaaacccadbddabcacaabcaddcacbbcbabbcccdbcdcdcdbbbabbaaaacdcaadddcddbcaccbccdbdcbdbaacbacadcddaadacbaacbacbbbdbdbacaacbdbacddcbdbaacbabaaaabcadbacbbccabdcbdbdbbccdacdbbcbcbbabbabaaabbaacbdbaabcdacadcaabdbbdbaacaacaaaabcdccadbdbbbbcadbbcdccbdcddabadbddabacbcabadbcbcbdddcbacaadbaadcacbbbadadbabadbbbbddadabdacbacdcbcdbbaccadbcabdcabccaaccbbcacacbcbcbbbdcdddcdbaddcacbcbcbcccccddcabdccaddadbddadbbbbccccadccbbbacdccbbaddaddaccdadbbbbddacbaadbcaaabaaddccadacaaacadaaacbddaddbadbacabacbbdbaababdbdbbbaddbddcdbacbbbcbcacdabccddcbabdccabdacbabcddaabcbbddadbdaabcbacaaddbdcbdbddbbddbddccdddaacabbdcdbacddbbbbdcabcbddcadbbacbbdccaddbddabdabdbaaddadbbadbcacccacadcbaaddadacaacdbcbcddcabdccbddbcdabadccabdbdcadabacdbcbabdbcababccdabdcbaadcdcbcbdbdcabaccdaaddbaddbcbaaaccbdbcdacccbcddcacababbcacdbcddbccbbadbadabdbbdcbcddcdccaaabbbccbcabcbbbbadcabddbbbcdcaaccdacdddbaaababdcaabacbbbbddadbbcbabcdbbdcaabcdabcbdbacdbdcadccccddaaabcdabadccabaadaaaacbbcadbdbddacaddacacbcdabacaabdcdbcddcdbbdcabadcdbbdcccbaaabacdbdbcddddbccddadbacccbacbacbdaaaadcacacbcdcadddacccaccdcbaaaaacdbdbcabbdaadacddaddccdabccadbcbcbbaccbcbdabcdbdbccbbcbbbdccabadbdbdddcdabdabdbdcbcbadbadcbbbbbddadcbabccbdcbdadbcbacdbaaadcbcbcbbddbacabbbdbadddccacacaaadabbdbccdcdabcbabaaccdbacdcbdbcadccabcbabbccbabbccabdbbabddccbbbacacccbbcabcaaababdadcdddccacddcbacabddacbbcaaadcadcadadaadaaabacccbbcbaaaadcaadbcabbbbdaaaccdbbdcdbabdbaabdabdaaadbddbbacabdacabbddddcccaacabddbcdaabcdbadbcdabdbdcacbcdaaddaabdddbdaaaaabbbcababcccabdabdcaabaacabaacccdbdbaacdadaddbabbdcabbadcadddcdabacabcdcadbccbcccaabbacbdcbcacabbbbcaadcadabbaccaccdcdadbdccddcbbdbacacbbadbaddccdaccbbccbacadbdbbaaabccacaacddbbabdabccdbbaddcbabaabacababaabddadcbbadcdcbccdbcbdaababbcaaddcccbaccbbadaddddabbadcccababddbdccbaccabcabdacbaaddcccdcdddddadcadbacbbabdacbbbccbccbbdbcbdacbcdcaadbcadadacdcbdaacbadddbcdddcaabcdaaadbcccabcdabdacdabadabdabddbddcdbaccdbacaadbbaccbbbcbcdabdcdcdcbbbddccbabbcdcbdccddcadcddbcbacbbdacbabdadbdadcdcbdbcbcaaacbbcaabbabbcdbdaaabdadbaadbacccadcbdbcbddbacdbccaaaaaaddcabaccbcbacbbbaacddcdbadccbaacdacabdbccdddbaddabbbabadabacccbaddccacdddabaccbadbddcbaddbdaacadbcadaddbadadcbabcacadbcbbcddbaabcadaacadaadadbbdddcadcacbadcabadbabccbaabaadcbbdaabdddabcbaaddbcbbacbdcaadcccaabdbcacbacbdbaadabdacbadcbabddbddbcabbbcbdadcadcadddbbacdabccaabacadadbbcbababaaadcabacddbcbbcadcbdccabcaaadcdbcbcdaaaddcbddbacdbdbadbdcddcaaadaadbaaabadacbcbbbcaaacbadddbdabdbacaabacccbabbccbbddabbacabbaacbaadcccacbcddddbbaacccaacbacddbacdcbabddbaddbbdbaccbacdccaccbbddadaabadcaddddddcccbaccdcbadbaabcbdadabcddbdbbbbddbccbdbccdacbaababbbccadbbadbaadacdcdcccccdddcbdbadabaaacdabdadbadbcaadcbbccdbcabcdbcbcababbdbbcaacdbcbcaabbadddadcbcbaacaadbdabbdddcdccddcdcacadbbbbabaccddabbbabbcbbdadbbccdbdaacbdaaddbadddaddadadcacdbabaddacddcbdbccdcccdbbacaadcbbbadcadcdacdbcbbccddddbdabddddcaacbaabdabcabcadabcdaaadacbcbccaabacadbaaddabadaaccaaabdbbdbdabcaccabdcdcdacdbabdcdccabdbabadcabaccddcbdbcdccccaccccacdbcdacadbdabdaddbacbdddaaaacbdbcdbcabdcabcbabdacddcbaacdbcbbdcddaaddccccccadbcddababccccbcacadcbbaaaaddbbcadcdaddcaadddadbbcbbccdabdbcddcabacabacabbddbadbabdaaadaabacacbbdadcbdcdbaacbddbacdacbccbbcccaacbbdcaaddcdadbdacbccaddcdcbcdaaacadcddbcbccabdbdbaaabddadccababbccdbbcadcdbdddadabadddbaaadcdbcccadddccabcabaabbbdbaccdcbddbabdbbacbddcddacaacbbbadbabdabccdaccdccbabbcbccacadbbbcbcaabbacadcddcdbabcabcdaccdcdacccbadaabdacdbccdddbdadbdcabcabcadcaacabdcdbaabdbbadcbaacaadabbdcccbacbbbdbbcbbbbadacddabbddadaddabdcadbbccdcaadbbbbdaacdcbcaadabcaaadbbdbdbaacbdacaaaacabdddacbaccbbadacabdaacbbaaadbadbcadbabcdabccbdacbccccbcacabdcdabaddbabdcaddcbaadaccaaabadbbadbdcaacdbacadddacbaccddcccbcacdcbdccaaccaddccadcdacaabddcbdcabcacadacacaadcbabcaccbacdaabcccbdddcbcbdcccaddbcacacacaabbbbcccdddaabcddbdacaaccbcbaccdddbddbdcaaadaaaadbaddaddbdbdbacdaacccbabbdbadccaabbbbbcaddccadbbbddaaadbacbcbaaddadccccbbbdcdaddadbadcdddabcaaadcddaaacaaacacacadabcdcababbaacdbcdabcbcdccbccbdacbacbbacbaaccdbbadbdccbbacdbbcaaddbddcbbbccadadaccadbbbaadddcddaaabdcadabcbbdcacbcbcacdbadabbbbdddadabdcbaaddccadacbbadbcdddccbabcabdbbadbcdcbdbbbbddcaddbabbcacaabbcccaadcdbaccaadddcbdaadbccbddbcdadbacddbcdcaccbbdabdcbbcbbacaccddcddccbbccadbabccbcdbadccdbacabadcbbbacbdccccddcabcdabccdddababadcdadadacabdddcdddbacadbbccbaabbcdcabbbddddabddaacdbbaacabbddcadbadabddccabccabddccacdacccadbcaacbcbdabbcaabcdacbbdbdcbadbccbccdadbacdabaadbcaabcadbbcadbcbddbbaaaababadbdadcadbdcabddcdaabacdadddacbbcddbcbaaabadbcdabdabacaaccddaccbcabcdbabbbabbcdccddaadcdabadbccadccadcadcacbddbbdcbcdcaacbbbbdcbcbcdbbaaadbcabbcdcaddcacaaaadaccbbdcaadacabdccbadcdbdbdbcbabcdbaaabddcdbbabccbddabcbcadabbbbcadadccabbcddaccdbabcbbdccdddcaaaddbacaccbcbccccccadbdadcdbbaddbddbbacccbababdaaaaaaacaabcabaaacbbbaccbddbabdbdbdcdadaccabccacdacdabadcababaccbdcbbadccadbbddacdbcbbdddacbdcadbddccbabcdabccddccbccbacadacbccccbcbccacbabcdbbbcacaacbababcbbcbcdcdcbbcdbcdcbacbcabacbdbaacdaadcddbbcbacdddaadccabcacdaddaababddcacabaadabccbabbcadbdbabdcbcbcabbdccadcbdbcdbdabdadaaccbaaddacaabcdabccadbbbabbdadbbdbcaccbbdbcaccbbbdbccaabcacbcbaacbddbcadcbbaabcdbbabcdacaacdbdcaadcbbcdbcdbcccbdcbbdaaddababdbaadaccadbbbaccacbabbadbaabccdbdbabdbcdbcacbaaabdadbdaabaccaaddcddadcadccbbcadacbdcadaaaacdbcadbdbcabdcbbbbcdcdcbcabdddcacacabaddcddcbbcaccaacacdbddbabcdbdcbabbbdcbcabbcbcbbbcaacabdaadcabbbbccaccbadbbddbddbbddbadbccdcadadbacbccadcbcbaadccdccacbcdadbacccaaccbddbadbdbbadaaaadbdcbdadaabcabdabbbbabcbbabdacdcbabcaabbcddbdbdbbbcbdbacbdbdbddcdddcbdadaadcccdbcbaacaadcbdccdbabbabccdacbcbdacaaaaaacabddcacaccdadcabbbdbababbdadcbddabdcddbcadaaadabbddadbccbbdcbbbccdacabbadbaadbbbaaacacddbccacabdbccbadcaccaabcbbbdcdbbdacacadddbbabdcbdcbdddbcbacbadacccdbdbcdaaddbaadaabacdaacabaadadbbdccacbbbbabccbbdddcbacdbcabbbdddbcdbccadcbbdccadaabdcaadcaaacaccdcdcadccacdaabccbaaddabdbadbbbcdbdbabdddacaacabdbcadbbadbacddcdccadcdddbbcdcbadabadaaabadababbcacbcdcdbdddbaddbaabbbdbccbbcababbaabddcdcaddccddbddcbdcddbacbccbdbcbdacdcbcbcbccbdcaddcbbcdacabbbbcdbcdddccbcbddddcddbcdccddcaaabdcbdadbdcbcdabcdcdbdaadabacbdcdcbddbddacdbcbdbcaddcbdddbbcccdadcbacbbbcabdddaacddaccbdcdbdcccadcadbbbdbbbadccddbdadabbcddbdbdabbdccdcdbaacdbbacaacdbdccdbacadaabadbddbadbbbbcadbadbddddbdaaaadcddbcccacbbbdabbbaabbaaabddaccccbddccadaddbaddcacbbadacbaccbbdccdaabdaabaacdddcdcacadccadaaacdcbcaabdbbcbcdbdcacccccccbbddbbddabdccbdbcaccaadbbbcdbabcdccbbbadcbadbdadacbacabcaddcbbacbdbcdacabadcaacccdadadbdddadcbddbcacccdbdcaadbddbcaddaabccaaabddacabcbbbbdababdabddddbadbaddbabbbabccadbbcdcaabbdddaacbcabababbdccadbcadbddcbacdddcdbcdbbcaaddbdcbacaaddacdabbcbaadcbadbcdbdbacccacdddcbcbcbbcbddddacadaaabbacdcabcdcacbbbddbcbdaddcddbbccbbaccdcaabdabbdcbacaccacabaccbadabaacbdddbbabaccaaabbadbabcdbbbcabaddccacbbccbcdbdaaabaacdcababcbcabddcdcdabdbcbacdbcdbccdddddbbbdbbcbbcadcbadbbcbbddcabbcbcbbddacbcdbcccbdacccbdbdbbacbbbabcabbcdabdcacbccddcaabbdbbdaabddbacbbdbcabdcacaccbbdcbccacdaadbadadcbdcdcaaddddacaaaddccbcbcbdcbccabddaccacbdaabcddabcdcbbcccdcbcbccddaccbdaacdabddcccbabbaaccdbccccbcbcdaddabcbbcddbbdcadccaababcddaaabdbbaabddddacdbdbdcbdcbbbacbabaddbcdaabddbddaaadcddacadcabaaddcdcdcaccaaaaaddcccadbcddbbdddcadddaabaddcaccdbadbdaaaabcddaccabdacbaddcacdaaddbcdadacdddcccbbbadbdcbddaabaadabbbbdbcaadacbdabbdcddbcaddadacaadddcbdbcdcdbcbadbddccaaaaaaaacbdabbabccaabbcdddbbbdbaddccacbadaacddcdbadabaacddaadbacbadadcabacabdacaabbdbbbcdabcbcbcdaabcdccddacbbcdcdccabcccaddadccbbaababcacdacdaacccabadaaaddcbacadbbacaaacabdcbbcdbcbdaddabcbcbbcdcdcdadddaddaaddcddcdabacbaadabdcabdbbbacbccbacbaadcdaddadbbabadddcbdbcdccdaabcdaabdbcbdadbdddcbacbacdadabdabbdaccadbaacbcaddbdacabdcdbabcdbaacbcdddcbccbccacdabaacbacccdbacccbbbddabcdbcacacaacdaccadacdcabdadcbaaddccccddabdccddbadccbbddddadaccacbbcbcdddbdbcdacadbddabbabaabaadbccccbcdcabcdbcacccadacaddcccbbbbccacbbcbcdccdacacbbaccbabbddbadadadcdccabddababccbbcbcdcdaccaccddadcbaaaacdacacdcaccaaccacdcbbdbdccaaccabdbdccdcbbdacabdcadaccdabdcbbdaaddddabdcbdcaadabcddadccbabbbbdbadcacaccbdbdcddccccbadbbdcbaccabbbaaaadcdcbbdcabbcccbcdaaadaadccdcccaabbabbabbdbcdcabcccdbdbabdcdadaaabcccbabadddaccbdbadacaacbcdcbcdddadaaddddddbcbbccddaabccadbacaaaccbcdddaccdadcadcdbacabdacbabcabcdaaaacdbbdadcbbabcbdbcbcbbdabcaadbacddddadadbbdaabbdabccacacdaadcbbaacddcbdcccaabcbbdccaaccddbdaadcdcaaacaadacccbaccccacbbcbddcbcddcccddabbacadacadddbccbdbbacbcacdbbbbcaddaabbadcddbaccabcdbbaccbacdacddabaaddbcccacbaacccbdbcbdaacdabbaaaabdcbbdbdbaccbacddcacbcbbcdcabdbdabdadcbaccdccaabbbcbbccaccddbbdaabcdbadcbccbaddbcabadaacdabcdbdbcddccdacdbbcdacacdccbadcacacbdadccbbaaaacdbcaccadddabdccacaacdddcbcdcacdbaadbccdbbdbccdaadbadccabccaadaabdbdddaabddadbcaccabddbbbcdcbaddbadccdbcbcacbcaacdcdabcdabccacaaccbbaabcbddbbcacabbbaabadbdabbaabcdbbdacadbacdaaacbdcaccabddddbcdbaabbcdbabdabdacadbbdbcdacbdcccdbcccccaaadcdabbcaacabcabdbcdaacadcabccbddadaacaabcdddcbcbbdddbaacddbaacaccabcdbddcadbcbadccdcdaaddbbbacbaccddbabadddbcdbabadbabbdcdcdbcaaddadaccdbaaaaacacadabdbcdddbddbbadcbacbdcababbbbddbcbcbacddacbadabacabcacdadcbcdcbadacdcbdadadacdbddbabcbcbadadaabbaacadcabdccccbcadbbdacadadbadaaddcacccabaaccdacdaacbaadcccbdddcccbcbbbdbddbdccdcadadabbdcabbdbbbacdddbbbcbcabdbadbbcdddcddcccbbaccccabcdcbddddcbadbccdccdcbaddddcabcbabdbabcaccdadccbdcdddacdbbaacbcacdbabbadcbcbbcdbccbaddcacdddccdddbcdbcacccdcdabcdacabbdcbcddacdbbadaaccabdccdccbbbcccbbadbdababdbcdacdadbcbdaadabcbdcbaaaacdadabcccadacacdcdbccabbcaabcabaaccabadbbdadbcabcccccabccababdddddbdbcbddccacbdbaadaabdaddbdcabddacadbbbbdcdaaaaabbcbababcaadbbcdbbcbbcdaabadcadbdcadadacdcdabbacbcdabdaacbaabacadbcaacddbdbaacbbbbdbcdbacbcaadddcbbabdbbbddaadbbbbacccabaccbccabdbacbdabcbcbbcaccccadacdcaadaccabcbdcdcccacbaddcdbaddbbdddcdbdbbcdbaadbbbcbdcadddabdcddddcdddbbdacdbdbbcdddabdcacbdcaaddbaccaaabbdbdddddacbaaaabdadabcacaaddbdbaaadadacdbbabbdccddadbdacdbdcdbaaabadcbbabddcbbcbdcbddadaaaaccacbcdbacccbdadbddcdddcaaacdaadbbdcdbaaaccaabbdcabaabdaddcbdbbabcbdabcbbacabccdcbacadcccbcadbdabdcbdababdbacadbbdcccbadcbdcacddbbcccaabacabdcbdbabbbaabadbacddbcabbacacbcbbaadaaadacadccdcbaadcbbabaabbbdbddbaababdbdcacbaddcdddccbcbacddccbcadbcbcdbdaaddcdadaaddabdbbabbccbbddddccabbabbbccbbccbdcdaadacbbadbaddccabbddddbcbadcbbaadbcccbdacabacbcdbcdabbcadccbacbbcbaccabcbddddcacccbdbcaacababcbbadbbaacddaddacdbdccdbcdccadabdaabdcacdccbcadacbdadcdabddacadaaaaacbbabcabcabcbcbdcbbdbbdbbbadadcdcccdcddaddddcbcbbdaacbdcbaacddbbcabdadadcacaccaabdbabdabdadbacbaadcbcbacbaccabbdbaabccbaddacddcdccdabdacabbdaccacbcbdbbbbccabdbccbcaccacaaaaabadcccaaaaaaaabbdbcbccdaaccddbcdddaaccbcccadbdadbdcababacaaccdcabdcbacaadabdccabaaddacccdbbbbddbccabaddbaaabccabbddbcdbdcdbcbdbcddbdcdcdddbddbbdbaccdbaacdcbbacbdaddbcacddccccdabcdaccacbccbbdcababaccccccbbbabaddddcbcdbdcddddacaadadcacdddcddacaddabccbbabacdcccaddcbcaabddacccbacdadcabbaadaaaabadbcbcdbadbcbbbabbbbaadbdadccddadbdcbcadbbbcbcdbcacccabcaadadabcddcdccacaaacaaddcbaabcccccaaddccaaddcdccdbcbdccdbadacdbdcdbbbacbdadcdcbabbacbaccbcbdababadcbabcdccdbddbcabbaccabbcbaaabcbcdcadccbddbaabbaacadcccaccaccadaacaddbdcbcbdbabbcbaddaabaddbcdcccdacababdabbcddaaabbdadbbbaccaababbcaabbdbaabbddddcbbcbaddcbcbdbbbddabcdbdbcaccadbcabbbadccbdcdacddadaabdcbcbabcddbadcaacaabdacbdcbaddbddcaabccccadcdcabaabaddcaddaacdaddbdaabaaaabccbabadacddcbabdbacdabdcbdbabaacddcbcbabaaccdcbacbdddbbbdcdaacdbaaadabdbdabdbacaccabacbdddbcddacabbcdadbdcdacbaacbbdaabdbaabadddbcabbabbdcbdbbaccbcbcabcacbcbdabbaddbadcabbddccbbadacbabccddbaadcbcaacbcacdcddccdbbdaccbbcbdddcbbbdbaccaacdccbadaddaaabccccbdbdbbccddbdcaccaccbaaccabdccaccadbcbdbdbabcdaaaccdccabbbacaaccbdacdcdcbcddacdcbadcbdbbddadbcdaadccaacaaacacbacccbabcadabbacbabaadccdbbcaabbbacaaabcbabaccdcbdcdbadaccadbbcdadbacadbabadbbaabbcddbdcdaadaacdbaccbdabacccbadaccddbcbadccbabdaacbacaadadcabddaabadaaccbbcdcaabadbdbacbcbadddbaabdaadacbbcdadaadaddcddbdabcdbdadcabaacbccabccbcbbccdccccdbbaaaccddabdcacdccccbbddddabdcacbaadaccaadcaaacccaadabdcddabacadbadaabbbcacdcadacabddabcabaabdddabcdccbabcdbcbcccdacbadbdaabdbabaccccdbddabaccadddadbdbdbaabaaabdacaababddbdaacdbabaaabdaacccdbddaddbabdcdacdddcbaaadabbdbbadccaddbaacdcddbddcadccdbdbdbbccdabcbccaadabacddaacabddddabcadcccbbddbcababcaaacacccbccdbcdcdabbbabdbcdacbcaaccdbdccaabbdbbabbcdadbccddbbabbdcaabddcdddacdadbdbaddcadacdddaaacaccdabcbddbaddaadaacdadaddbcccdcdaacbcbaacdddacccdacdbcacdbbdacacdcaaccaacdaaaaccbdadacdaccabcdadcbabddabaccdadaadabaaabbcbcccdccddaccdaadadcbaabcdddaddbbacbacbdccdcdbcdabaaabdaaadbdcaadcbbbbbccdbacdaaaacaccaacacbdbdbdaaabbabdaaaccbddaabcbccbbdbcadadcadaacababbccacdbacddddddcdabaacabaadcbdbcbcbcbbbdbdbbbdbdadbaaaaaabdacaadaabadddaccaadbbcdaccddbdccdcaabbdcaaaddbcbdddcaacbdcacdbbdacddabdadbddbdaacabbacbcddbcbaadaddaadabbcababcadabbcdaacdcbcacaabadaacacbadadcdbbdaaabbbccbdacdaabddbdbdcdbbbbbbdcbdccddacdcbccdcdcbcdaacccaabbdabcdbbcbcadaaadacdadaaccabcbbcadcaacddddacdabaacabbadaabbabbdbacbbcccaacbcddbccabdbbacadadbbdbcdbdcacccbaacacacacbadddaaadddaacbdcbdccbabaddddcdcaaddcccccbcdcaddadbcbacdbbcddddadbdadabacbcbacaddbdbbcaaadbddadcadabaaadddbddbbcbadacdcdbadccacdcbddcbbcbdcaabbcbadaddcbacaabbcdadbacbbcbbdacddabdcbbddcdddbcbdaccbdbbbcbaaaadbcdbadabcadbacadcddcdcaadbcddddbbbacbccacabddcbccccdcbbbcdddcabdadaddadacddcbcbcdbbbadabdabbaadaccabbcaaacbbaaddadaabbbbdddcadabcdbdbcacccbbcbaaabccbddddccaadadcadcacbdaabcdcaaadcdcaccdacdbcaabacacbcbbdbacbaacdccaadbdbdcbaacabbcdbbacbabdbcacadbcdccaddcbbacadcaabaddbbbcaadabcadbaacbbadbcabccdddabdabbabacabbaaccbaaaddddadacdbdaaacaaaaccbbdabdbdcbbcddbabacaacabbbcbddaddabcddaaaaadcbdabbcbbbccbabddddaadaadbcccaccababbdadaddcdcaddadaaabbcadcccabdddcadbcccbacccadababdccdadaaaabccbddccbcabbcacaaacdadaaaababcabddaddacdbaadcbcabadbadbcccbdbadaadcdcbaccbbccadadcabbbcabdbcdbbbdcccccbbcbbdaddcabdababdadacbbdaccbbabdacccddbcacadacabcccdcacaadccacdbbbcacaadadcabdccdaabdcccccbadbccbccadddadbdbdacbcccbcdcdcccbbbcbbbcabddcdddcaaddbcdbddbccbdbbaaddcdbddaaabaaabbdcbadcabadaccccabcddaccbddcddabcdccddcacddcddadddbbaadbadcbbdadaaadadbcadddcabdaacbcdbadddaaadcadbdcbbbbbacbcdddcbccbbbbdcdccabdddcbcbadbabbbabdaccbcccbdbdbaabbbaacccddcdbddbdabcccccbcdaadbadbcdaaddcbdccbdaacbbdccaaababcdcbadbacddbadcaadbdbdddbbddcbdbbdadabcdbaabdcbdcaacdabdbabddcbdbabbadccccbcddccbccccbbdcacadbbdccaabaadacdbdddaccdaacdaccbdcacbdccbbbaacabbbbcbbcbccdbcddabacdbcabbdbaccabcbcdcbbddacdacbbcdccddbdcdcddbdcdadbddcbccbddaadbbccaccbdbbdcadcddacbabcdababbcbbabcacdabdaddccabcaccdccdacddbddddcacbdaaaadbbbcdbcdccacaadcdcdcadacabbbdcaaaacaabcddddcbddcabdbcdddbccabccdacdbbacdadbcadacdbdcbbbbddccabcbcbcbddccddacdadacdbadabaababbacaabdadbcbbdaaccdddcaccccbcbcaabbcdddcccdbdabacdbbccaaaabbcdbbbdcbababbbbccaaacaabddbcdabdabdbdacbcbadaacbcddcababdaddacdddacdbbadcadaaacbabababbddcbdadabbaaadcbadbcccdaddbcacadddabcdcbdbccbcddacdacbacbccbbccbbdcdbdcbddabdbdbabcdabbbbaccbbaccdabccddcccbbaabacdaaddbadbdcdaaabaacbcbccadcabcaccadbdcbbcabcaaababdabcaadbbdcdadabaaddbbabbdacaccccbdbacdbbcbccbaaaaacdadcaccbabcddbadbdcddbacadbbddacaaaaadaaacdbcbdabadabcadcaabddbbabacadddccdbbdaadcbbcddcddbbdbdbadbaabaddcdacaacbbdbdaaccddcaadabbdabaddacdddddadccbcbdddcbacadcaccacdcdccccdbcdbadcdbbaaabbdbacabbbddbbbaddbcabdcaaccdacdcdcdaabdbabaccdbaacdacbcaaabaadcbccbbaabcbaddacaadbabdcdccabaccccdaabbbcddddccadadbccacdcdcbadabddacabbabdcddcdddbcabddbddbbcadbcdbbbdadaaadbacdbddcbdadadcddcdaabcdbcccabbddcdadccbccaddcddccbccadcdcbadcaabdabaccdddabccabaabcbcdccbcacddbabddccdcbcbdbaaacbdcdaccccdcdcdaccabdcbbcccdcbabddbdbcdbdbdccbaddddaddadbbbbacbdabddaaccdaabcacccccdcbdbabdddcdbcabbcacaadbadadabbcdaddcbcccacccdababacbdcbcaddcbadcbccababaadadabaabdcdbabacadddadcbdadcddbddabaabdcbaadcbdbadcaccaccadabacacaabddcdcdbabdacadacccbcabdbcaacbacbbcdabcddcabdbbcddbdcbadcabbcbddaaadacabdbcbcddabaddabdaddadbdaaaadabddbbabadcacabcadadbabcbddcbdbddbdddaacdabcaabbbdbabbcdbbddaacdabbabbdcbbadbdcccbbabbbdbcbddcdabbbdddddadadccaddcbbbabbbcbaabbdbcdbacbcdbddabcaddbcddcacdaaabddbcddbaadabdbbabababccdcbdbdaacdbddccaabbadddcccbbadddcddbbaabddbcabaabcadabacccadccdadddadddabcdcbbdbadaccbccdbdcdabbbdacabbacbabaccadababaacccdbddcdbdbadbbabddadbabadadbdccacddddaccadcbbadcaababbbcddccdabaddbcddbcccccdbcadddacdcbcacdcdbbadddbcdbbbcdcadaccaddbacbbcbdbcaacaaccdcbcabaddcabddbcbdbabcdbdabcaaaabbaadbdaccccbbddcbcdccacbbaadacdadaacdbddbccdaaaaaccadaabbbabaccaacbccbccbdcbddabddaccbabddbdbbbccabdacaadbcdacddacdcdcbaddbadcdbdacbdaaddadbadcdbbcaadadadabdcbababcbbddcddbcabbcbdbbccbdccaaabacbabdcccdbddaacbddcaaacdaabcccaaadcbcbaccddbbbcccabbcabaacccccabbdadabdaddbabaaaacbccdbbaddcaaadbdbdddccbbacbbccbcdccacbacaadacabdddcbbbdadbddbcbdbcdbaaadadbcadbbdcaabbbbaadadbbdaaddccbbcddbabbccdcabbbdcdbbacbdaadaadbaadabdbbacdadddcdabaddcabddacbdacdcddbcbbcccdbdbaadcdcacbccdcbbaaacababcccaabccbdbadbadaadbcbbdaacbbddbdcbbbaabdaaaccdcddcdabaadbbabcbbcccbdbcdccdcdbabcdaaccbcdcdcadcbabcdcdddabcbdabcabdbdaaaaaaddaadbabdbdadadbddbbcabaadacdaccababdcbbaddacadaaaadcbddbcdcbdbbacabdbdcdbddbabadaaadcabadcdaabaadbacbadcdcabaaacdbcadbaccbbbaaccadcbbcdccddbdbadaadabbcbdcadbbdbadcacaacabaacaaabacadccbbcbdcbbddcddacbcaddbdcdabbcdaddadbaabbddadcdbbbcbaaadddacbdcdaddcdadaddadccbdcbcabababbdadbdbaacdabdbdabdaddcdbcbaaaccddaaddbcbdcdbddbadacbbbbaaaadccdddcbccbcccbcdbaccacdbdbdaddbacbdbcaccabcacbababcabbbbccbcadccaccbddbabbbdcbaacbddcbcddddaadddcdcdccabdcddabcbccddabaabbdbcaddcddcdcbdbadccabccccbdcabdaaadbdcdaccaacabbdaddcbadccbbbdccabbdaadddbdbdbbcbcdbcabccbdacdcdbbaaadabaacbcdbbbdcbbbdbabacbbdbccabcbbacdddaaabbaabaacaabcabbcbddddcacddbcbaaccbaabbaacaccaacacadabdadbbdbddbdbcbdccbcdbdaccaadaabddadbdbcaacddbdcbdbacccbabdcccdbbaabcbcdbccaaaacbcabdaacdbaadcadddbdbadadccddacdcadaadcbaaaacdabacdbacacabdadcccacdbdcdcaadaddccdbdaaadcddadabcbdbdbcadddcccabdabbacdcaabbdddcdbdbdcccaacdbbdaadaaaaacdacccdbcdddcccccccdadcdaabbcabbbdbbcdacbccdadbbbabccccdbbdbaaabcadcccbdcbbaaacbaddaabbaaccdcacadbadaadbccdbccccdbbdbddacbcabdbacbbdcbcaacbddddadaadaadabadadddccbddbadabdbbacdddadbcbdddadcbdaddabdbaddaddbddccdbaccbdabbbdddabddadaadcbcbcbccddbcadaddabaccabdbabdbaddabdcadabcdababbdabababbabdddbdcbaadaacadbacbddabbbcbcacbcbcbadbcccacabcdaadbbacdcabbbddbabdacaabdaadaabdbdcbddcbacdabbccbdbcacbaccdbadbadacbbcbcddcbbbbbdcdbbddcddadaadcdbdcddbdcadaaadbbdaaccdacbdabbdddbbbdccbcddcaabaaaadcbccdbdcbdbccdcbddcbbacbabddcbdabcddbcddaabddbabaccabdcadadcccaaabbabcbaaddbacdbbbdddaaddaccddabbcacaddaabbcacadddcbaadaddcaaacdabdbcdcbcddcaacddcbbbcddcbacdbddddcbabcbbdccaacdaaaacddadccdcbccabaaadcacadcdcdabdccaccddcaaabbccadbdbbdddcbdccbccdbcababcadaacdcacaddbdabadaaddadccbddddaaccdbcdbbbbbaaccbcacdcbabaaaddcdcdcdbabdcabdcaccabcccdacdbcdbbddbbbacdcbbaaabbbcacddadaabbdacdabdbadabaccbbbcbbcccdbcbaddddacdaabcbdbcaacdbbcdbbccbdcaddbcbaaabbdacdaabdaabadcbcbdccababcbaadcbdaacacbabcdddddbdbdcccadcccddddabcbccadbcaabcdacaadadbcdaddbcddabddabcbcaadaddddadcadaddcccbabdbcddddbdcbdabbdbcabbbbcbdacbddcbbccdddacacaaacbbbbdaadaaccdddbccacccbadbdadaadbaadbbdabdddbbbaabbbbcbcccaacadcddacdbccdbdadbccccadcdabbaddadaabdaddcbdacddbcccbaacdaccccbdbbcacaccaaabcdcccbddbdcdccababacacadccadcdbcbcabcbdbaacadbdbbdddcbacabccdcbabdccdbadbbddcbabdacddcabadbcbbbcdaaccdddacbacabaccabcababaaadddcdcbcaccdcdcacadcdadacddaadcaabcdadbabcadcccdccacdbccaaadabaddcaadcaaacaccbacdddcdaababcbdcbcccdbcaaaddababbcdbaccbbddbaabbbddcbbadcbccadacaadcabbacccbcdabaaaabccabdabbbccbcabaacbdcdbcbacaccaadaadcccadddbccaadcbaddcadcccaccdcaddddaccddacbbdcdbbdadcddacccacaaacbbacccbbacdcbcbbaababddbbdadbbbdbadccacdbcccbdcabcabccdbcddacabdacaaaadadaacacabccacabdddcdcdcbcbcdccabcacddcbbbbaabdbbadbcaddcdcbcdababacbadaaabccbcdccbccabdcacacbabaddaaaccadcbcabaadddcabbabbddbbbcacdddcccbacdabdddbabcbbbadcdcddbadcdaccaaabdcdcaadddbdddddcbbddcbcdaaabbbbccabbdbccbabbcdaabccdccdcadadcdbcbbdadaacacbdaddcacacbdbaabacccaacccadadcccbaaccdbabbbdcaacddddccbdbabdbbdbbdabbdccdcdacbdaacbdcaddbcaaccadbdacbbadadbddddcbccaadabdcdaddaadcacaaccdddabbaabddbcabcaabaabcabbccbbbbbadabbbbcbacaabdabacbddbcddcadbdaabdcbccdaabbdaaadaadccccadbaabaccdbcbdbddaacdaccabaaddcaddabccbcabaabdcdaccbacddcdacbaddcbcdbaaccabcdcdacbbcbaabccbabcbbcacacccaccbcddbdbbcdcddaaabcbcaadcbdbbadcbbccaddaabbcaadbbbabbdbbbccbbbbcdcdcaacacccabbcadbabccacabcdbbacdcdadaccddbbaccdadbdabbacdccdcabdbbdadaccdbdcbabccbdabbccdbcdabcbcddbdaaadbaacbabcbbcbcbbdcdaaababacdbdbbadbbcccbdcabdbabbdacacaaaddaddbabbbdccadddbcbbcdbabaccaccddbaccdabacccdadccdcaddcaadbabdcbabcdbacbdcacdcbbadababcaabadcbcbabcccccbbbbdbdcdaababcdcdcabcdddbbcdacdcdabdbdacbbbdababddcbadcdbadcdcaabbabbdabbbabcbddbdccbcdacaaddbdabaadcaaaddaaaaccbccddacbbacadbccabddcbdaaabbbcbcaabbacbcdddcccadbacacabbcbbcabcccdddddbdaacababcbddacbbdcbcbcdcaaacdbbababadddbdcdadacdbbcbaacbddadcbdacbabcabcdcdaddcccbdabadbadbbbbcddacdcbaacbadaaaaccdbdbbccdcabbcbdbdaaabacccaaaaddabdddaccbabbccaccddcccacddaddabbdbadbabcddadbdddccbbbbbcacdaccbdaddcabaabbadaacdcbbaabbadbbdbaadcbaacaadbdbbbdbccdcaddacadbbaccabdbaabddcbadbccbcadaacbacabdacdddadacccbbddccacdbaaddabcbababdbbccdcaddbaadbbdbcdadcbbbbdaadabbbabcccdbdacbbddcccbcdccaacddbbdddadbbdadaabbabcabddaacbccddccbbabbccaadaddddccbbcdbbaadabbcbcabbdabcbcbbdadadbaadaaddccdbbccaacccbdbdacbbdcdaacdadcaaacccadccbcbcdddcbdbcdaaabcbcdcbacacdcbbbddabdaadbcbdccbbbbaabcdcdbdadacababdddbbdbcaabdbadbddcabaabaaacbbccdabbccdccbbdbbaaaabddabdacddaabdabcdacadabbcadaabbddbdacbadbdadcdccdacbddcdcaddccaccbbbccaadbbdbcbcadaccdddccaaaadbcdabbcaadadabdddcdbbabdddbbdacbbcbadbaacacdbddcccababaaaabaadacbbabddadbdcabcbcbcbdccbcadadabbaddadddabcdbccaabcdaadccadaddacacacbdaabbbcdbaddcabdccabcbbbdcdbccbbacccbcadccaccbcbcbbcdaabcbbccddccbabdbbccdaabcaaccbccaadbccaacccddbdacccaaddacdcdbbdbbbbdcbcabcdbbcbbadcaacbadbdcbdcdcdcaddababcadbacadacbbacdbccabdababaccdbcacabccdabcacaacabaaaadddcdcbacdccbdacabbdaddbbdabacabddbdaddaccbdbcdbaaabcbbaaacdddccaddadaaddbbddbbbcddbdbbccbacaaacbdbcaadcbbbcccacdbbddbcbccaadbaaaadaabdadcadcdcbcacbdaabdabdbddbbaaabadacdcbdadbcdacacdabaccbbdcacbddccdcdbddababacbcabbaddcbccdaaadcdccddcbaaddbbaddbdcaccadaaaaccdbbbabcdaccdaadbaabccdcbbbacaaabdbcdbbdabdadbbdbcabcbbdbdadcbcbbcbccadaabcabacabdddcaabbdbdcccccdbbaccdcacacbadcaacdacacbdbdadcdcdcdcddbcbadadccdbaddcaddaccaaddbabddaddbccaaaadcdbccaacababbadbdacbacddccbbbdccbbcdbcbdadbdbadadaacccbcaabcbbdbaadbabacbcdaacdccdabbdbbacdacabdabbbabdcbbbdacdbbbbbbccdabddababcacbbcbcbabbaabdbdbcdddbddacbbddabbddbdbcbacbbacccabdaacadaaccbbbcccbddabbaabacdddacccbacdbdccbadbdaadaddcaddcbbbdcbaaaddbbdadbbbcdabbcddbabaacaadbaaaadbcdbabacdcddddcdddadbbdcdaadcbccdaabbabdbbcccddccddbddcdbcadaacacdbabcaddcdcdbcbdddbbcdaaccccdbcdcdadbbbabcadcddacbccbcccccbdadcbadccdadacadaaaacaaaadbaaaddccddaacbaabbcbbcdaccacdadccadccbacdbaaadbbbacabcbbbabcdaadaaacdcdbaabcadabbbcbbaccdacaadacbdcbddcdcbdcbdbabdabcbdbacdcadcbddabdbccaacdcaaadabcbbcacaccbdadbadbbadbcbdaadccbaccbdddcddcdabaabacddbdacbcabaabdbaccdbbdcadaaabbccadcdcdbcbbabbcccbbcababdcdaacbababaaadbdbbccbddbbddddcaaabbdccdbbcbabddcccacccddacbccababaacacdacdaacdcdbaaccccadbdaacabadbbaddabbccaadaacdbbaddbcdcdbacccaaacacadddaddbddadcbdbadabcbaabcbcccdabbacddabdbbbbdcccdbacbdcdbcdcbaaaaddccbabcacabcccabbadabdbabddcaaddbddbbccbcccacccaccddbcacdacccddcbcbbbacbbbbaabdbaabdaaacbbcacccdadabaddbbccabbbaddcddacaadadbcdaccadabbbababdadbbdacacbbbbdbbbbbacddcbabbcabadabddabbdbccaabdddacbaccaaccadbbbddacbadbdaabdddacbddbbdadcbbdbabcccccbadbdabdabdcaadbbccbbcdcacdcbbdadcdccbbcbdcbabcabbdabacdabadbcacdcacbcdacdadbcddcaacdbbbbccddbdbdccdddddcacbbabadbaccbccbabdaccccadbbbbdaddcbdbbcaddccabbbcdbccadaabbbadabaaaaaccbaadadcabbbdbdabbddaaabcbaaadbdbddabbbddcbbdadadbbbcdabccdddaacadaabaabdcabcdcdccdabacaaddccdcaabaacbaabbdbdccddbccbacbadaabbbcaaadbaaddcdbcbcaddcddddddddbbddaddcdbadddddbdabaabcbdbdccdbadadbbbcbcddabcacaadbcdacdbbabadaacbabdbaabcacbcdbcacbadbaacbdcbbcccbcddbacabcdaadaadbacadccbdcdcaddccdacccdabdaabddcabbabbaadbbaabccaacdaaaacadaabddcdabcaadabccbcdccdbacdbbacbbbccdcdcdbdbabbaddbdccaabcbdacbdbacbacdbdbcdbbbccbbbbdcbaaadcdbbbdadddddbdbbbdaabbadbbcaaaabdcacbbcaccdacbdbdcaaadabbdcbdabcaccacaacaadccbcbabbbacccbddaabbaacdcdddccdcbaacdbbdadddadcdbbbcbccbaadbbbcabcaaccbaabdcbcaddcbacbbbbbdccccccdaabdbbbadabdbbdbcbdadcaaabbcacdadabbbaabbbacaaaddcaacacadcddcaddbcbcbddccabcddaabcbaabccadbbaadbddccddbbdcaaacddbacaabbabbdcddbcccdacaabadbaabcaaabccdadaadbdcaaadbcabaacaaacbccabdddadbbbddcbdbaadcdbdabdcdcbbbccbcbabdbcadcaaaacddbccbacccdbcbddbbcddcabababcdadddadbdbbccccdbbdaccdccadccccbbabbbdaacccbbabaabcbaaababcacddaabbadbcddacccaddaddcddcaacbbbcdaabdcacaaadaaacbaddcacdcbdabccadcaaaadbabadaadbcdabdacddadaccdaaacdcdadaccdcdaabadbccabddbddbcdddcbcddaabdcadababbdcabaaddaacaddaababcbabdbadcdcacdbcabbbdcbcaddcdaadcccdbbcbcbcacccbbddacdbbacddbadddbbcdabbdccdcbacabcbccdbdbcdbaabdbadadaadadabbcabddccaacacabbcbddacdcaacccdbdccdbadcacccaddaadbadddbbaabdacacdabaddcccbddcbaaabdcdccdcbdacdbaadcccabcdbdbbbabbcadbabdacadddbaaacacccddabbacbddabadcacacdcadcacbbcbabcbadbcbbdbcdacaccbbccadccbdddcdcddddccadbbdabcdcababcbcdadcaabdbdbdadacdccacdbabbbbdbabbabdacbadbdccaaabbbabcacccbdbabbacadbcbaddbcdcacccbdaddcbccdaaabddbdaaddabdabcccbdaacdbcadcdadbabddbcabbcccbccbacbdadcbbaadccadcaccdcaddaaccbbdcaaabbdcbabdcadccaacdddaabcabbaabdbcaaaaccbdaccacbbbcbbbabbbbaaccabbacbcbaacadbaccbdadbdbbdbbccdbcccbdcdabccbccbadddcccaaabbaadadccacacccbcccdbaaaddcbdbdabcdddbdbaaabadbaccbbdcbdbbdabbdcbbcccaabaadcddcbcbddbdabccaabbacdaaccbbaddcdddddbcaaabcddcadccaddbbadaaddaaabdadddccacbddccbabaddbbbbbcbdadbcadcdaacdacabcbacbaaaabbcaaaaddbddaacdbdcbcbdbadddcbdccdddadbbdccbcbacadadbbddaddbaccdbacccaccacdbacabcbdcaaccaabbdccadaadccadcaababbcdbcdaaabdacabcddbaaccacbaccacadaccdcdcabdadaaaaacbadacadccaabacaaccacbadaccccbcacbdcbcacbbbccabbbccddadbdaaccbddbabcdcdacbcdccaadbbadbddaadddacbbdbcbbbdccbbaabbcacabbadbddcbdadadddbcbdababaddbbddadcdcbdcccbddaabdcbabadabaaabccabbabbbdbcbbdbbcccabacbdaacdaaadabdbbcbcadcdabcdbcabacbcabdbcaadbadddaddbdbaddcdcacacbcbdcababcccadbbbbdabdcdabbcacccdcbaabddbbddddaacbabdbcabbbcdabaccbdddacbcbdddacdbddabcaccbdaabbbbccbddbddbcdcbacdaddbdcdddddcdadddabbdbdabbccccbddadacdcddddababdbacbbabdccaaadabdbcdbdcabcbabbadddabadcbcacdcbbadacaaaccdddcbbdaaccaaccbbccacaababdabbacbdccbdbbccadbbccdbcdddcddbaccdcdccccaacaccabcdccbdabdbcadaadbdbccbccdcdadacdbbabdacdbbbccddcabbadddddbcbbcccbdaddcdbbacbccbbbcdaccccacdbadcdbcdbadabacdddcadacacaababdbadddadbaddccddddcdddacccdaaccabdadbdbcbcaccaacacdbccadcccdaddccadcdabddabccdcdcbbaccbcadcacdababbababcbbbaaacbdcdadadaaabbacbcdabdaadabaaddacddacbbdcbddddbcbaaaabbdaaddddbbbcccdcdbdbaadaccccccdcdddbddcdcdacdadbcabddbbaccdccadacccacabdddbdbdcbbabbdbaaabdddcbdbddacbadaaddaddcabbadadcbdddadcbbaaddbabdacbcdbcbdddcccdabbdbadcaccdaacaadbccdbbcbbadbdcbdbcaabcabbdbcaccdcdccdcabcbbcbbddddaddcddcaaadcaaccdaabcbbcacbcccaddbdadcaacbaacbcdddcdbbbaacddcbcbdddacdbaccdacadcdaacddbbdacbcdddbdadacdcbccdcbcdcbcbdbaacbacbcdcaabdbabbaababdccacaddbcadaadbadccadcaadbccabbdccdcdcbdcadabaabcaccdacacdabccacddbbbcbbcdbbcccbddbcdbccadbababbbdabbcddadbbdbdadadbdaadbcadadbcdcbdaacabcbbaaacccdabdbcadcdccadbbaacbdbaacacaacccdbbdabcacccacaabcbdbccabcbdcdccadacbbddadddbbddabdcbaccdccdcbbccccdbabbbccbacbdacacddaaabdcdbbacddcacbbaabdaddacacccbacbadccdacdccddbddabbbbaaddbbababbbacabacadabcbbacdacbbbaaccddbadadbbdbcaaaacdbccdddcddbcadabbcccdadbdbdbabdbdabdabcbddacbcbbbcccbabbadbaddbdcbcdbabbaaddddabaacbdacddabaaaddbdacadddabababbbaadddabcdadbcdbbddcdbacbbcbcdccdccdcaddadbccbcaabcadbcbabbadadaccccbdcbcccdbdbcccbbdcbaaaddbaacaabdabccbdacddadbacdbbadabbddcbbdadccbacbdddcdcbddbbcbcbbbddcdbbaababadacbadccaaadcdccdcbddcccdbdddbcadcacadacdadbdacbabbddbbbccabdaabaccdbdcdbbaccadbcbacaaabdbbccdbdcbbddcbaaacbaabacbbdcaccddabcaadacdbcddcdbdbadaccacacbcdbacbaddbdbbbbabcbbdddbdcdccdcdadabacddaacabdacacbaadddcdbcacdcbabcaaabcbcdabbccdadadbdcaaaabcdbbabbcbbccdcbdbabaaabbbbcdbdcadbbcdddbbaadccbbcdcabdacabcbdbabbdbbaadcabadccdbdcdbaaaaaacacabdabbaaadacbdcbcaadcbadadcdcdacacdbbcabcddbdbdcddbcddbccdadabddcccdccbcacabdcadadbcabdcabdbaabdddcabdadbbddccbccbddacacbaaadcbdaaaabdbaacdcbbdbdddbbcaaabdabaacccacdaddabbbadadcabbbdaaddaabdbcdabdcbbbccdacacadbccdbcbcdcccccdbcacbccbcdadacbcadddabdcdbdcbbacccaddbacbddbacabbccdcdadabdddacdcdabcdbabccabdcccdbdbdddadabcaacbdbdbccdbadcdcbbbbacbdccdcabcbddaacaabadbbacacaadbdabcabddbbcdcdadbacbbabbdbdaaadabbaccccdbdacaadadabbdacbcbbddabaaabcdbaddcaacbbdbbabdacbbdadbddaacdcbccacdabddbcdaddbdaadaadbaabbdabcbdacbacaaaddccbdbbbbddcdadddcbcacccdbaccadcbcadbdbcddccbddbdadbacacabbabaadbacbdbcdccbcacacacaccdaccddadaadcdadbbcacddcaddcacabdbadddccadadcacbaacbcbdacdbbcadccaaaacaaaddbacbcbacccadbbdbdaabbdbcabbababacdbbbcaacaaacabddddccdabcabacdccbdbdbaabbbabcdcddbcabddbbcbdbdbadadcdcbdabbcdbacdaacbcbcbccabdccccabadaacadcddddbabccddcdbbdccaaccccdcbdccacbdcaacbcccdacacaccadbdbaccbabddbccadcbcadaadddacbbaadabacbdacabccddddbadcaadbaddcdacdaabbddddbacccacbccadcdddbbdcbddcbbaccbcdddabcabaadddcbdaadddddbccbbdccaacbadddcadddbccdabdabbadcbddddccdcbaadaadbccbbdbbddccabdbaddcaaaadaadccbabccabdadbcdcdbcddaaadcdbbdcacbdaabdddaacdacbccaacccdcaddbbdcbbcdcbbaccdbbacabcbdbddcccddcdaadabddbcaaabadacdcaaaddcacadddddbbabccdaddacbcadbcddbbdbccccadaabcabbdddbaaccbcccddbbcdabaacacddcbbdbbcdbadddcaaabbcbcacccbdddabbbaacbbaaaaadcabccbadcacdbbcacdacacbddaaccabacbadbcacdcccacbccddddccdddbaacccdabdbabaaacdbbddccbacabcabdccdcdaabacdcbabaaabacdabddaaabdbabaddbcdaccdccaacdcbbddaacaabcdcccabcbcaccdacaadccccdbccbcdccccdadadcbdcdadadccbdcacabdcbdacdbbaacdbbcadcdadacbbdccadcbcaadadbcacaadcddadccddbaccacabdcdbdbacbcbddbcadcaccdacbddcddadcbaadbbbcdcabdbbcabbdabdcbaaabcaaacddddacbadcbadddbbccbbccacdddaddcbddaabccdbaccbdcdccdcababdbcbcdbacaabacacddbacadcbbbaaaaadddbcbbdddabcdbadcaacdadaccddbccbdccababcbddbaccccdddbbddcadbdbbaadaadacadaccbabdbccaabaabacdbcbbaddcbbdcdaddcadbbaabdbbcbdaddadbabdabccdabacdabddcadbdcddabadcabababdaabbcadaaccdbbbbdbcbbbdadccbadabdadabccbadbaadcdcccbcaaaddcdbbdcbdccacacbbbacbadbbaaccbccccadbbabadabccdbcdcddcbdbbabbdabbbdcbdbbdcdcbaccbadacddddcdbdbcbdbcccaabbbdcacbddbbbadddcbbabddcccaddbdabacbaccdaabbdbbbacaaabdbbaaabdadcdbddbcadccbbbcccbccccbcacabcdbacacdbcbaacdabdacbccdbdadbdbdabcdcdababacbcdbaabbaacbabacdaabbabacbcaadbbdddadaddacacdbcacddcdccbcddbbddddbdaddaacdcaccbcdcdacccbcbcadcacbdcbbacdbbbcbcdbcdbdcbbacdbcaadcaadcbabdbcacabccbccadddacdaaddbabadaddcabccdbbcadcdadddbbcddddacabccacdabdcdbbdbcccadaacadcadcdbdacddbbaccbddaadcaccacdcbddaabbaacdbcbbbcbdcacdcbabdcaacbdbccbbcacdcccddbcdcabbbcaadcbdcbbacbbbcadabdbacadddbbcbdddaadcacabdbddbdcbdcacbacddccccaddcaacaacbaaacacdbcddacbdadcdcdaccaabdbadcdbddcabcbdcdcdbbadbcbacbaacdcdacddbdcddbdadabbdcadbdbaaacabcaababcbcabcbdccdcbcbcbdadcccdabccddddaaacccadbdbadccbccdbadbbdadcbbadcccccccdccacbcacdcdbdbccbbddaaabdcabdcbbcbcadbababadbabbcaaadcddbcdaabcccabbbdcbbcbbacdaaabdbddccdbdabaacddccbdacdccadbcbcbabbbddabddaacbbabcabcccbcbbbdadbcacddaadabdcabdddbbdbdddbaaacbbadcddacaacccaaacccabcccbacdbbdaddcbccaabaaccacbbdbadabbaaccbdbbadacdcbbdabacdadbadabdbadbcccadaabcdccaccdddbaabbccabbcadcdcccacddddbdbcdaaaabaddbdcccccacccbbdbddddbbdadadaddbdbcdadcbaccbdacbdbbcaacaacbbdacdadacbcacadbbbbcbdcaacdbccbccbadacabddbcbadccaaadcacbabadaadbcaacdabcbcbbbabdbdcbabcdccacaaaddbcbdcaabcadccbbbdcddcacddcadcdbbdbdacadadbacacaabbbccdcdaacccbdbbcaccbbdbcbcbbaaabddbbdddcdbcadcdbdcdcbdabbbbaabcbcabaacbbbccacccbcdadcbdababcccbadbdaccdcaacdabdabdbaaacbdbdbdcdbdaababbcdcdcacaacddcdaacabbcbcbbdcccdabddbcbcdbccaadabcbdbdbdadbdbaacbbaabcacaddcbbdbcbdcccabcbaabcbddcbcdbdcdbabddcdbdbbbabbabcabcaddbbbadcbcacaaacadbdacdadaadaaacaccdadcacdcaaaadddaccdbbbcabaabbbadddabdadcadacdcbaaddbdcbadcccdcbaacdddaacdadccdcddcbaabccbcdbcbadacaacadabcbaacbbdcdddccbccabbcdcdccdbddadcdddabdadbdbcaabddcdbbaadcaccdbdbaadddbbbabbbcadbaaacdbbdcbabcdbadcbcbbbbccbdccbdcadabccbbbabcaccdbbbdbbdacccaabacacadcabdccdaaacadabbaaabadacdccdbacddacbdcadcdbbcbabbbcbbbdacbdbadbcabcccddaaccaaccabbbcdadbdbcddbbcabdddbabddbddbdbccddadbdbadcacddacaaadbcbadcbcacbaaccadbadadbdcaadbdcaabbdaadabddbbabdbcadaaadcaadbaabaaccbaaddcccaddcdacbbcbcbdcdcacdccabacbbdbddddcbbddddcbbacddbdbcdbcbddbbdbacdacadcbcabdbbaaadcdcddcdcabddaddddabaabbcbaaccdcccbcccabddabbccdbaabcabcacbbdbaacadaccaaabcbdbcddccdcbbccdacbccbcbccbacdcccccdaadcdadcbcdbacccbddaabbaccccaaabacaabaaadbbabdbdacaabddaccbabbabdaabdbcacccbdbbaabccadcbbdacaaccdcacbaddddbcbacdbdbcbbbabddbccdcccaaddcbccddabadabdabdbdddadabddacdddabbacacbaccdadbbadcbccddcaddcacbdddbcadabbdabaaddacadbbcdcbbbcdbcaadbbaadccdaadcadddcaacdbabbacbddbcddbddbdabcdaacaabaaccddbbccbaabccbbbadbbdcbbdbacbbbbbaccaddcbbadcbaaaacaadccbbbaadbddbabdbdcaccbadbabdcdbbdcdacdbddbcbadcacbddccbadcaccacddbcbcadbdbaccacaadccdccbdcbcccadadcdddcdbccdadababcbdbaadbdacabbbdccabddbcdccabbddcdcacbadbccbdccccaaacadacddacbabbbccdadbbabdbabbdcdcdaadccbadaaabacdbcdacbccbacdacacbaacccbdbccbbabbcdabaacdcababccbbcbcddbbdabcabadbcdadaddddbdcccaadcacdccdbbcbddbaddbcdbbaacdcacaabdadbbcccdbadccaccacacdbcbcbdccbacdcccbbbaacbcdbaadcddcbcacdaadbcdbabcaccbaccdaadbdbbaaacdcbdcaababadbbcbadcbcdacbdcdababbbbdcbdadaaccdadccaddadcccaabbabbbcbcadabadcdddacadaacbacdaaabbacdaadbdccadabdaddcbbbabaaabaaacdcabddadadcdbcccbddddadbccdabccdcbddadbaccbcaadacaabadbaabdacdddabcdccdbdcdaccacaacbadcdbdbaabbbddacbddcbabdbdaaddadadbabcbabacdcccbaccbbcdcaaadccabcdadaaabadadbbcbbccbdbdcdadbaaccdbcbccbbdbdadcadaabcbbdbddcdaadbbdddaabdaaabaddcddbcbddacccadbdcdcdacdbbbdbabbcbacaacdabacdcccacbbdabbadbcbccbbcdcdccbdcbdacacbcaabbddadacaacddddaddbdacbdcadccbcaacbacbcaaccbcdcdabdbcddabaaabadcaddcabcddbdcbaabddacacbaaaaddcdbaaddcdabbabbbcbccdbabbcadabbbcbdacaddcadaacccbcbcaccbbadabadcdcdcdbabbaaabddacbbcabbccbaaabadbbcddacacaddcbdbdacabdbbbddabdadadcabbababdbcaadbbdbbbbcdcabccbcddacdacbdbbbdccdcbdadccaabcaaadababddcccadaddbdacccbaaaccdcccbccadaddcbbcccdbcdbacdbaacabbbdaddddabdbaddbabcbbdbddbaddabbbbbcabdcdcdcbadbacdadaadbbdccaaaaadababddddbcacbbdbabaadadabbcddaaaccbbcaaaadddaddcdbdcaccccadbadccabdbbbddcdcdbaadcaaacdcaabdaddbadacacdabacccbdbacdadbaaaabccbadabaaddcbccbbaddadcbcbabcccadbabcdababbabdaabcaadaddcbdaccbbcbbddadacddaaddadcbcbbdbacabbcbdbaacabcabdccaaaadcbbaddaacdccbcdcddadccdddcdabbccaaddadadabcaadbabcdccabacadacadcaadcabdccadabbcbcbcabdbdbdbaacbdbadabbaabcbabbdbccbbbacbabbcaaabbacaadcdddcdabaccabdbacdbaadbbdacbacbdbdadccaacbcacaacdabdbaaadcdbabdaababaabdcbadddbcbbacacdaaaababaadddadddcbabbabbddbdabbcdaacaccbcadacdbdbcdbcaacdadbdcabadbccaaadaabdbcabcdbcadbdabdcaaacbdbcdaaacbaadbbbbcaaacaabddadabccbadaddcabcaabcbadddadbdbccccbadddbdacddcbadadbcbccdadcadcdacaccbbdbcacabbdacaccbddccbadbacacdbcddbccbaccdcdadadcbacddccbdbddbcdbdadbbbddaaccdcbacddbaaaadbdadbbaacaccbcbaaabaccdcbbbdcdacadabacddccbcddaadbddacdcbcaacbbdaddcccdcccadcbcdaacaaacaaaabbcdcbbacbbaaaadbaabdaaddbabcacddbcccbaabddaddcdbdccbdbdbcdbddacbacacadddcadcdccddbbcacdbcabcaccbddbaccbbbaadbbacbddcbadadbdccacbdccdbccdaccdbdccaacddbbabdddabadaccaccdccbbbcdcbcccdbbbbadadacdcbcccabcdddcdddadccbabdbacbcabcbbabcadaabcbcbdcbcbdbacbdabcabcddbbabbbdcbcadbcccabdaadadbbbcccdccdaccdcaaacadcccbddbcdbaacabcbacaaddcabccbacdcccdaddcbcaadbbccddabacbcacccaacaccaaaabdbdcbcbbcbcbdacdbdbbdbaadbcaccbbbadaadacabccdbddbbbccdddaabdcabccbbbcccdbdcdadccdbcdbcdbdbbcdaabcdddcddbdcddabbbddccbbdcbcbddbccaacbdcbbcddcdbadacdaacadcabadaaaabccbbcbccadcabdbaaccbdadbddbdbdbabbbaacbaacadbdcadaccacbdbcbbdddbdadbbddbddacbdbddccccddbadcadcdbbaacddcdcbbccaccbacadbacbccbbbbbadcdcbcddaadaadbccabbcbdcadaaadbaaabdccdcccddbaadcddddacbcddbbddacacadbdaabcabbbcccccccbacbcadcdbaddaadddbbcdcccbcbcbaddacbabbddbbbcccdcaaaacdbbdcbbaccacdddacbcdbabacdbccbaacaabccbcdadbbbcbbbddcdbdcaddbdadccccacbddacabadbbcaaadbddacbacadccdcabaddcacdbbddcabcaaacbcdcabbacbdcbdcaccacddbccdcabddcdabbcaadacabddbaadbcdbaabdcdbbddccdddbcdccbdbadbbdbbdadaadcacdacbcaaabacdcabbdbbdcdcacbcbbcbdacbdbdcddbbdddaaaaadbaaccdcabcdbcdbabdcdcdddabcbbabdcaaaddbcaaadbbcbccccccbcbdbcbdbaabdadaddddbaaabdadbcdcaacbadabbdbdbabaddddbcabadcccacbbbcaddabbbbccdbaaaaabdbabddbabaddbbbadbbdcddcdaacdbbadbdbccdadccddadbcabdddcdbadddccdcbbdaacccabbbcdcdcdacadcddaccdaabcbbcacbababdabaaddbadddcbcbbcbbacbbccdaddbadacdaddbcdbddccadccabdbcdddbcabccabbbdcbdaddabcadbccaadabcccbbabcdcddcdadbacbcadddadbbadbbdcddacdcbdcbddcdccdcbdcdbdcadcbdcdccacdbdabccdacaddadbcdabbadcccaabddbbcdabbacdcdbcdbccddcabbbbccaabccabcbabbdaccdbbbcdcaabbcadabaaabddbcabcbdbbadbcbcbdbaaaadacbdaccbddaaadcabcabdbdbbbcbdbabdabaacaddacbdbbcacbddabcbdabbddcadacaccbaacadccddbdbccbdbaaadddadbdaddabdcbaadccbbbacbabbaababcbadaabdcccdbaaddcabcacddadaaccdcdcabaabdbabddbdcbdabaababdcdaddcaadadaaaaadcaddadbdcbbacaaadbdddcacaccadababbbcacabcbddbdcbabadaddaabdbccdbcdaacccbdaabcbaaddabcdddbbddbacdddcdbcacabaadaccdaaacadbadbdccbcddacbaacdbcbaaaccccccddcddddbccadbbcbaacbaabcbcacbdaaaabdcdaccbcdbccadaadcaacddccdddabbcbccbccdbbddddcdacadcbbaddddbdbdbabadccabacadccbaaccbddabcdbdcbdbbdbbabdccabddaccdaccccdbdaabbccdbaabbaaabadcdacabccadabddcccabbdccdabababbdbdaacacccbdaabbdaacbdaaadcacddcdbabccbadaaacdbaddadcdcbdbacabcadacabddcddcdcbcdbaaadacdcabbdaaabdabadcdcdbcababaacddaddabddcaabdabcdabcbcbcbadbdcdcdddbbcbbddccaabcdcdcaddabdcccbdbbadadcbabbbacbbcbdcbacdadbdcaddabcadbbcaddcbbcddcbcbaabadcdaddddadbbdcdabcaddddabaadbbccabdbbabbbbdcbbbbdcbaddaacabdddcbbdadccbddacaaadcbbccadbbabbddcabbcbbbacabbbcbcddbdbabbddbcbdabadcadbabdbbdcbcdbacbaaddacdddcdbaaabcadbdaccacaadcadcbaddadadaddcdbcddbcabdddbcaadbacdcaacccabaabcbbdcbcdccadaabcabcdaacdcadbaacadcaacbbddaacaabdabccbbddcdadbdcdcacabddcaaddcaaadaacdbacbcbbcaabdabccdcdbdbdcbaccbaaadcbbdbadabbacaabdcabacbcdddcabacdcdacacdbabacccbdadabccbaaaccaccaabbaddaddcbdabaadabbbcccbcbbcbbddaadddbcbacdcbdbbdcaaacaabbabaaacacabadabdaaaadcaacddbbacdbdadcdabdaddcbddcbbbdcbabddadacddaaddbbcadcbacbcacbadabaabadcbbbbbcccddcdabcaaaaacccccddadcbcadcbdaadbbdacaabdccaacabacbabbcccdcccddbcaddbbacacacbacabbbbdbcdaaabadccbabddabaaadcbcbacabcbbbdaacddaccbdabaabccdbadcbbadcacbdcbbdaccccccddbdaaaaccacbdbdddbadcbddbaccbacdbcdccabadbcaacbbddbdbabbbbdbcacbdaacbbacdacbcabdaaccbdbcbdbcdadcbbbbdcbddcaaaacbdbccdcbbcdbdddcacadbbcdbabdbcaadbaacddcdbacadddbcabcddccabbdbdcbaddcabccdaccddbddcdcbbbdbdbadabbbcbbbdbcbbbadddcdcbcbacabdcdabcccacccbbccbcdaddbcbcdaaaacaacabcdbbbcbabdbbbdccaabddbacbadbdacaddaabcaadadbcbbcbdcdacccddadcdaccdcaabddbcacbbddadcdbcbcabbaacabcddcbabdabcbabcbbbbbabbcccaadaabbcdbddaaaacccabababdcacbaabcbddcadcccadababbddbdcbbccdddcdcbdaccdbaabcadccddbbbbcaadcacdaabccabdadcabbddcaaadaddbbdbdbabbacaacaaaccdccbdbbbbdaaadddaaddbbccdccbbccccadbbdbddcabaddcbabbcdcaabadabbdabababaadbbadacaccbdaddbcdabcccadabdccbadddbbacdcacaddadbacdbacddbcbcddccdbaacaaccaadabdccbacdccdbaccbbdadadcdbacbdbbacabadbbcabbdddadaaaccdbaddcaddddcbaabcdddcbdaaadccdbaaaacacadbdddaadbabbbdddadcbcddadcbcabddcbbbdabacddbcdabcdadbcdcbabbacaddadadcdcacadcdbbbdcbdbabcdbdcbbaabaabbbdbcccdacdcabadbbadbaacbbcdbccabcbaacbabacaddcbaadbdadcdabaaabdbaadabbadbccdbbadbbadbaacabccbcccbbaddccaadcadbbaababcaddddabbdbdbbdbdbaddbcbacdcadddbabacbadcddddcacccbdbddbdcaacbdacacadaabadaaccaabbcdaacbcdddcbdbcaabcddcccbdaaacacccabacaadaddcacacdadaccbabbdcacacddbcbcdaaaabcbcdbcbaaccadbdccdcbdadbadbbddbaadaadabadcabaddacdcdcbcbcccbcaaadbddababcbaccdbbdbcbcdbcadcbaccaddcbcbcbbadcacaadcdbadaddbdacbbdacddbacbbadcabdaaccadaaadbcdcdbadbdabdcadbcbdbdbbababcbbccbaccccbbbabddddcbcaadbaddaaaaabbaddbbcadaabcdcdddaaaacbaddcbabcabcdadcdbbbbadbbabdcdabcbcabdcbabdadabaaabbcdaadcdbbabcbadacdddcbacaaaddbabbaabaadcbadabcbdbbacccbaccddacadcabbaabbcbcdcaacbabbbacbaddabccabbbbbcbdacacbbcddddacacabbdbccacddddaaddabbadcaddcdabbddccabacbcaadcccddbdabdaddaaadbdaddaaccaacdaaacbdadcdcbadbaadabdaabbddcaabacaddbdbccbdddcbacbcbcacbddabdcaaaccaaacbbbcdcdbcccabbaadcacddcdbbbdbaadbbcacdbccccbbcabccdbbabdcbbaddcddaccdbaadcadaddccccadaadabaaccaabdddbdabaccbbbcadcacbaabaabbaabcddbccdbcccdbddddbddbaabdacddaadddddbbcaddcabbdbacbddaaadaddadaaccdccabcddaccbdccbbbacdcbbcddacbbabcabbcbbcaababdbccddacbdbcdabaababbddaaabddcbdaccccbcdccadccddbdaadabdacdacdbacbdcaccdcbbaddcdcbababcdcddcccdccdadbcacdcabbdaccabdcadadcabdadbccadadacccccabbaabdacaccbdcdcbdddaadbdbadcddabcbaadddcdddbadccdbbdbbadccbaacaddbcaccadbbcdbaadbccccadbbccacabbbabcdcbbbbcbdccccabdcabacacbbdbdbbcbaacbcabaccbbcdbaddaabdcdbbbbdcddbcadccadaaddbadddcacaacbaadaacabdddbcbbcdddbcdadcabdbbdbcbcdddaacbbababcdabbaddadccbadddbbcbbbdbdcbbabcddcbbbcdadaaabdbcdcdbbacbdabdcaaccccbdbdabdbbcbabcdcaabadaddccccaababcbdcacccccbbdbabbdbadbdbccdcdcadaacbccdacbddaabadccadaabbaaadbaddacdccbbcbddcbabaabbbdbbdacaaddbabcdcbaabbcdadcacdcdbaccdaccbbaacaccddbadaddadadcbdacbddaacddbacadadabcdbcbcbbccadcbabdabbdbcdbcdbdcdabccadaaadbcadcacddcabadcababbcabbcbadadabaccabbbdabacadbbacccccbbadabcbbaacacddcbaccaabbbdbaccbcababaaabddbdcccdaacaddcbadbccdccdacdbdbabdbabdacacaddbdccaadbaccdbcbbdbaabaccbbcddddbadbdcaddcadccaacaaaaaadcabbbccacbbcddbdcddacbdcdbbbabdccddadccadcbcbadbcadacbcbabddbdadcdbdcacaddcacababdbbcbacdadcbacaadddacbacdabadcacbddaadaabcabbdcbdbdbacbbbbbdaccbdaccbcabccaccdddccbabcaabdccdadadcccbbdbcbbbbcdddbddcbccbcddbbcdabbbbcbdababaccbbaccdbdcabcbbcaacddaaadadbadcbabaccbbabbbbbacacddddbcdcdabbaccddadadcabbbbbcabcbcdcddacdddadcabacdabcaccccaabcddacccbbabbcbbabccbccddaabadcaaddcdcdbadaacbbcaccacdbddbdadadcabbbdaadaadaaacaddaddcdbdccbbacaabadabdbddaacaadbaddacaabbdbadbcadababcbacaaaccdabcadbdadcbcacbbcacbbacddcdcaabbbbabdbdabbbdccccaacdccbcccddbacccdbabcbbbcdccdabcddacadaccbcaccccacabacddabddaaccadabdddaaacaadbcbbabacabdabaacbcddddabdcbcbadadabcbbdabaadacadacbbdbababcadaaabcabcadbcdcddbaacddbbbacdbbbaadddcbdddccabdaaddcbccabcbbbddacadcbdccbdbddcccabcccccacaaacabadcbcbcaddddccddcbaaacbcbadaaddcacbdbccbccddabbabbccbacccaabcabcbdaaaaadbaddbdadccccadcbadcabddddccaabcbbbbcbccdcaadbaacaadcbbbadccdccbabdadbddcdbcddaacbcbddaaacbccacccadbddcacacdaccddcdaddddbcddddbadcaacdbaacbdbdabcbbcdabaacadaadaddddabcdcbdbaaacbbbacabbbdaaacbbdcdcbdbcadaadcaabadadabadaddccddaacabdbbbaabddbdcacacdadbbdcadbcdcdabaacbabbccdcbcccbcbbcbdcccaacadcbcdaaccabbaaacddbaaccddbdbdcbcdaabcacccaaddcdabdabdcdcdcdabcacadabccabdddcbbaddabadbaacbdcbbaabbcaadcdbabacabaaabbcccccbadddcadcdcbccbbcdaaabbabaccbbccbacdbbdcdbadaabcaadccdacbdbcbcaabdcbddcaabcbdbdcdccbcbcbbcddbcadcbdccdacbcccddcdccdaaddbdadcaacabadbbdabccbacbdddbdacdbaccadcbccaabcdacadbdaaacaabacabdbaccadbbbababdaacacddbdadbbabbcddbbaacbccbcbccaddabbbdddccdbcbdcbcabbbaacbaadaaabbccabaaacadcdcdbdacbbdccdddcaaabcbbaabbbaaaccaccacaddaaacbadacaddcddcddcddcbbcacdccaaddcccdcdacabbbdddadadababdccbcbcbdcbbccbaddbadaaaacacbcacdddddcbcaacbdbaacbcbbcaaadbaaaadaadccdbcdcaabaaaccccddcadbabdbbbabbbcbacbdcdccddbcccbadcdcdbdddabacaabadbabbcbaacabcccddbdbbabbcacdacacccccacabaaaddadddcdaaddcddcbacabbbbadbacbccadbcabadbdaaabccbcdabdcbcbcbdcdaabdbdbababbddadaacaaaccdbbcbadabcdbdadababcdacdbddbdabdabacdacbaddababbbcacdcaaacacdaddbdccdbcccdcdacaaadcdbcbadadbaacbaddaababcdaababdbcdbabdbbdcabaababbccdbadabccdcddddbcddbcbadbacbbaabaddaaacaddcddbcdabbbaabadcdaaadcbbbbacacddccabbdbddacababaaddcbbabadbddbaacacddbaabadccbaabbbbadbbcbcddcbcaaddbaadabcbdddabbbdcdcabadaaaacdabdbdcddbccaaccdbbcbddcbdcccbddddddaadbdbdbaddbddcacdcddaddddcdbbbacdbaddaacaabdbcadcaddbbaaacabaabacccadcdbdaddcaadacbaccabcbbbcabddbabadadadbbdbdacbbbdbcbbababdcbabdddacbdabddcacadaaacbaddbdbdcdbaaacbccabcdaacddbbccbaccbdbcdbadaccaacdacbcbaadbcbbabdbddcdcabaccdbabcbbaacbadbacadcdcbbbcdabacbaaadadccdbabcdabcbcabbbcdacdadaaadbcddddcdaacbdbbacdcdcdcacbbdccdbccaabacbddbaadcdcdbdcdbbdadaaabddacaaaabddddacbdadbdbdcbaacccabcdbadcdbbcadddbaddadcbdabcbaadabddcbaaaccbabdcdbcccacaacbabbbdabaccabbdacdccccbbabaadbcadadaadbcabdbddbdddcbabaadacadcdcaabdcabacacaacdaaadcaaacadaadcdaadcdbcaabcbadccccddaaabcadddbadaccdcaadacddadcaaabdbabcacdcdbdbacabadbabddbcbcbccdbacdbcccdbacacddbcaaddabacbdbccdacbdadbcabdcbabdbddabcaaacddaccbdaacbacbcadbbdbddcdbbdddabccddcdabaabaabaabdbacbdddbcddaaabcdbbaadbcbcddabcbbcdacaabacbbabcbbbadcdbdbaaababddaadbcbdcadbddcdbaadbacdccacbddddbbaccdbbddcdcdbcdbbaaadbbbbdbbabccdabbcdcdcbccaccdbdabdacabbbbdacbcbdabbcacbcaccacddacabdbbbbbddaacdbcbadabbcabcbcdcbaccddcabadcaacddbdbadbdacdcbbabcbdaaddddaabdddbdaabbbadadddbabaabadbbcacabbadbaccbabcdbcababccbcbaddabcaaacddcccdaddcddaccabcddccdaabbaacdadcdaccdaddcccdccccbddadcabadddcdccdcbccdcbbcadaccabccaddcacdcacaaadacdddccabaabcdcdbbabaabcbdbdcabbadcaaacbcbbcddcbccccabdaacdadacbaabbdcacadcbbadacbacbcbaaabdddcbdcabdccddbacbccaadbccaabcdcddacdacadbddaadbbdccdabaccdadcdcbdccbdadcaaadbdbcaacacacdacacbbddcaccdcacacbbcdbbadabbabaaddcccbdaadcddadbbadbabddabaccdbbcadcacdcbacbdcdcbcddccabddbdaadabdbbabbcddaabbabbdbcdacccdacaccdacccbadabdcdacaccaaacbbbadddadbdccbdcbbadaaccbabdbbcdcabbdccacbbccbcccadabaaaabbadbadddbbbbcabcbabccbcabaacbddcdadbcaabadbacadaabcbacaccccddbcadaadaadaaadcbdcbcabacdccadbabcbadbbabbcabbaacbacababdbbdbabbabdcdadccbcbbdbcbdacbbcbaacccbbbdadadcacdccabcbadbadcabcdadcbadbdacadccccdcadcdaabddadcaacdacbadbaccbdddaabaabcdcacadcaaccbaadbdbdbacbdcabddbdbbabbabaddcaadbddcaaddbcdcdaabbcccdbdcaaadabdaccbbbdaccdcdbbcdbaaabbcaccacdbcbbccabdcdbcddccacddbbddbcddbdcdcdbbcabdbdcbcaaacbbcdadbacaacdadcadbccbbcabcccbbccbdbaaaaacacbabcddcacbdacadcaacbcdbcaacbcbadbdcdcdddddddbcbbccdcabbbbadddcadabcbdccdbaabbcdbacbadbbcacbaabbcccbdbdcccbddcdbdbadcabcbdcacadccbdbbabcdcbcddcadbbbcbadddcaddacabcadcabdcbcaacdaadcbcbcccdbcdbadabacdacbaccbbdabbdcaaaddcaabbbbccdcbcddabcacaadababcbabdcbcbadcabbddccacaaabbadbaccddcbdcdccabbdddbcabcadbdcadaaccdbddbdbcddbadccbcacbacbbbcdcbbbbcbaabacbdbbddddadbbdacaaddbbdcddccbdddddacddacbccdaabdcaaabbcacbdbcbbbcddcdabbbadcadcbcdbaddbdddddcadbacbcbadaababdadddaccdbbaaacdbabdcdbdcdabcddddaacdbdbaacaaabacabcabbccabadccaacdcaacbddbabccaadcbcbbacccbbcabbbdcccaddbcdccddbdbccbccbbacaacddddaaccbcacaabacbbdbcadbdbabcdcccaadbbabbdbbccbbdbaaabbdabbacdaadaadbbdddcccccbcdbbdbcbaaaabbacacbdbcdddccbaccdbaaabdbbcdaadaaabccaacdcbccadcbcbdcaccaadbadbdbadccbacbcbbcaacccbabcabbadbbdccbdddcdcdadcdddcbdcacadddaacaabbbdcadcabdbdcbbdbcbcbcacdccdcdacdcdddaacbdccaccaadabadbbbadddacbbbdbbdcbbabdaacdabaadddcccbbbdbbadccdcbdabbadbbddccabaadbbaddcdbabbaadbaddcdcdbdddcacacbacbbaccbabdccabdbbabccadabadbcabdcdaddbdddbcdaabcbadadabcdcbcddccdacbdbcdbaabdbcbdbccacccbacbcaccacdccbcdddcaabcbcabaaccdabbccdcdadbbdbbccbabadbbcbddacbdacabdbcccdbbabacbbacdaaacddbacbadacbdbbccaacdddcabcaadcbdbbcbaaccdbcdaacaabcddbddcdddccbbcccbddccbdcdaccbddcbcabbbcccbcabacdaabababbbbbcdadaadcddacbbaccbbaddcadddaabdaddbabdbbdaaccabdbcbccacbdbbbbcadcdcaacddaccaaccaacabacbcdaccabdcbacbaccdacadcacbcadcddbcdccddbbacbbccbbcbbbbadbadbcabccbbabbdccbbbdcbccdbdcdbbadccddacbdaadbdbbadcbcadbcadccdaacbdabaccdcdaabdccabbbbcdadcbdbabdddbcbcdbbbcdcbaddccabcccadaacbdbbbddabbbcdaacaaabcbdbdcbbccccbadcaddabaacbdabcabcbccdccdccdccbbcbcbbcadcbcbdcdcdacbdbdabaaacdadbbdaacdcacddabdbbcbabbbbababdcbabdddcccacacdcacdbbaaaddacbbacaadacadcdbddacbdbccabbbbdbbbabbaddccdcaaccabcaddbcdbabdcdccdcccdbbacdbccbdbdaacccdacabbabbabddbdcbbcaddacadadbcadabbbcddbbabcacdddbbbabddabdaadccccddccacaaabadbbabadccadccaaacabccadddbdbbcacacaaaabcbcbdadaabbcccdbaacdbccccabcccdabcbccadacdcbdcaabdacdabcdcddcaaabdddbaabadabacccacddabbcaddbccaccddcabbcbbbdacdacaabbbdaadbcabacaddacbabadaabdccddabcadbbcacababbccaadabcccbddcbcbddaaabbcdbbabcacbcabcdbacddbcdcbcadcaaddcaacbadbccbddbbacbabadaaabccddcbcacdbacdaaccbdacdaacccddbcadcbdbccababaabccbdbddaadcbcbabbddbbcbaaaaaadcabbdcbdcbcaaccabcbdaaabddbbdbdbabaddabcdacbdcbbabccababbdabaabacbdbbaabcbcbccaaadccbbbadddbdcbcaacbccbcadccdadbdcdcbdccdacabbcbbdbaaaadcaabadbbacdacaacdbccdddcdbdbcddbdbcdbbbaadaaaccbabbcdcbaccccaccddcdbabcbadadaaacdbaccaabbcaaacdbbcdbadcaaccbbccdcbdbabcbddbbbaccdbbaaaddabbddadcdbbcbcbabcdbadbdbcbacccbcdbdbabdcaddddddbccacadcbbadadcaacbcbaccbccbacdbdbbcaabbcbdcababbacadddbdddbabdcacdcbcbacabbadbddbaacbcaddcdaaacabdcbccbccadccacdaccabcdaddcaabaabbdcbbbbcbabbdbbadddbbbcdcddddaadbdbadcaaacbbdcabdabccabbaadaccdcacbbdaaaccbbdcbadcdadcbcadbbaaabbbccbdbcbcbdbbdbddcabbcbcabaadcaaabcdabadadcadcbddbbccacddccdcbdbaacadabadbbdcbbdbbcdabbbbacbddcdbbdcabdcddbccaddbdbbaabddacaabddcabdaccdaacadbbacbcaacaacacaabddbacbdccadaabbdcddcabdadaaaaaccabbdbcdbabaadcbdbdddabbdadadbdbbcdbadbcbcddcbabcbccccadaccbabdddadbcadcccddbabadbaabacdbbbbaddcbbabbaacbdddabaaacbcbcdcddcdbdabcccdbdaaacadaacbbdbbabcadddbabaccbbaadaccbdbddbbabdbbbddaacdacbbddcaabdccccdbdaababaaaaadacbacaccbdaadaddbcdddbcaaadaddbdabdbcbadcdadbacaaaccccacaadddcdccadcbcaabaadcacabbdccacddcaadacbcbddcdcdbaadddaababccbacbbcdcbddcdcbbbababcdbadddcaccacbdcdcaadbbccccabbadddaaadbbcbdbbbbbadbaddbdddcbdabbcdbcadcccbcbdddbbbccbbccbbabccbbbcdadbdaacbcbaddcbbbcaccacbcacccdcbbacadaddcaddcdcddccaddcddaddbdcaaaacddadaaccadbddadabdbbadbdaabdcbbdadadbccbbdaaaddbcbabcddadcbadaccacdcdbadcabbdadaabbbbddcbdcacaddcabaadacbadadabcbcddbdadbabbaadcaabcbbdcacaabddadaabbbbaaabcbbdcbaabccabdddaabddaccdabbcbcadbacddabbacbddbbabcacddcaccccdcdabbacaadbdcabbdcbdcbadcdbdccdbacdadadcaaddabacadbaddadbbacbdaacdbaadddbabbacddcccccddcabbdbbdacbacadbadccdccdbbadcabbbbaaddadddbacdcdcbdcacbbdbccbccaacbdabdadbcdcaaadbcdcbdacdcaddccbacbabccdaddbaaacacdabbbcdddaccbabccacbbddbaadaccacaaddccbaaadbbbcdbccbdbcbddcdcdcbdccbbbadaaddcccaaccbaababddbacccdbdabccadaccdcdabdabccacdabaacbbaaaaccddbccdcccaacccabacbdacabdaccbbccccbcdaacbaaaabbdadcacbaacccdcccaacbcacdaabcdaacdccaacddadddcdcaaddcdbaccbbdcbaaddbdbddcccccddcaccaabbdbcdcdcbbbccaacbacdacaabcbdbdcadbdcbdccabccbdbbdacdbbaadbbcbcbdcaabdbabcbcaaadcccacacbcbbbaadddcccbaadcbbbbdbdacbccabddabccbcdcbccabdaacaababcccdbaccdccddddcbaaccdababbadcacbdccdbbcacacbbacdaabdadcdcacbccdbbbabdacbaacabaddabcbdbbabcbdbdacdaabbaaabadcdcdddbdddbadaddabadacabddacccaacddaabccadddbcabddaabddccbcdddadcbdacbaabadddadaccdbcbadaabacdacddaaadbaacbbccddbdaaaccbbabbbbaaddddbbbccaabcbddbddccddbacccabddbbdacdccbabbcdcbdaabaacaddabdbccbabaaccbcddbcdababcdccdddadadaccbdadacabcbacbcadddaaddddbbbcdaadccddcccadbbddbcaddbbbddbdcacdbbacbccadddabcdcdbbcdbabacbdabaddcccdbbdcadddcdcbbcdbabaddbcddadadbacdbabdadddbcbcdacadcabddabacaadcbddacbdcdacbcdbaacdacbdddbdaccdbabdccdccdacabadaadbdacbcdcacbbdaabbadbadccaaadccdabcdcbcddcbbbbcbddbbdcdbdbacaddbcaddadbdadadadcdcccabdabdabaddcbbbcbdadccabbcbcaabcbdbcbddacabcbcbadcdccbbaddadbccbdbbaacbabcabaacbbcbdabdbcddaccddbcbcaccbdbabddbbaccbddbcaabbacdcbccbdcbcdcacbcbbaaaccccaccbcaadacbcdccbcbdbadacccaaaddadbcabbbacbabddbbdcbdbdbdabcddbbabdbcdccbcbcccbcddacacdccbbcaacdbadbaadccaddcdbadacacdaabbddbbadbdaaabcbbbacbcadbddcbcdaaacaadaccbcbaaadcbaaadbadaabccaccabaccddabddbbcdbbabaaaadadadabdabbdadcadaccbcaadaadaccaaababcaaabbbbbdadbdcddcacbcdabcbcbbdacdbdcdddabcdbcaadbababdddbccbbbadddbbabcccbbcccabbadabbacacddcaaacccbccacdaaacabaacdbbcbdcccabadbbddadddbdbacacddbddccdddbbddbdabbabbadbdcccaccbddcdaadbbacbaabacbcdbbcacbacbbdadcbcbdcbabbdbcaadacdcabaaacbacbaaaacadbddacabacabccadbcabaaacbaccdbaaaacaacbaacdcbacabadcddaacbbbcbcbccaccbadcbddcbbcadbadacbbcccdbbcadabadbbacabcbccbdddaaddbdabbadaacdaadddacccdccdcbdcbbdccbdbabbacbcbababcacbccbcbadaaaabccddcbdcbaabbcabacadddddacabdacbbacaacaabbacdacdbdccbcdabcdcdbcadbadaaddcdbacdccccbaddddaccccddbbcbcddaaabccaaccccdbabddcddbaaddcadaddcdccbbdbcbaddddaacdcbcdadcacbaddbadbddccaabdbcaaaccaaddadbaaaddabccdabaccacabbbdbbaddcabbaadccadbdaaaaccdbcddcdabaabdbdbdcbdbacabcacacbcdacddddbabdabdbccdbaacacbbbcbddbcbaaacadcbdbdbbccbadbbbcbbbbacdacbaddbdaabdccbdbddcbbcdcbccdbdcabaacbddcbccbccccccbacbdcdccdadbadcbcaaadcbdbcbbcbbbadadcccbccbddbcbdddadcdadbababcdacdaadcbbaaaabcbabaccadaccacadbacdacbdcdaabbbdddabbadbcbacaaddadadbcdcabdccabcddaccbabcdddcdacdbcbdbbdcddccadbaaabcadbbcccccbdbbbbbccadbababddcbbddbbbcbacadadcbbacdccccadaccbcadddddabbbddbbccccdbabddbbbbbcaadcbbaaabdabcbcddadcdcbddbadacabbdcaaaacbabacaabddadadbabdaaaabcabccbbcccadcababdacbccdbadbdbbdbddabbbcccadbabacbaabbbabcaccbdcdbbdcbabbbaabcaacbbddcdacbddabdcbabdbacccaaccaddccbabbdccbbddbaadddcbdaadddbcdbaabccddcdbcacbbccadbddaadddabbbdadabdcacacdcccbadacbcdaccdadbbaabcbcabcacdddcdacaacbbbacddcbcdcdbcccaabcaadacdcddaaddcdbabacdabdadddacdaadddabdabaacbacdbcaccaccdbdbbbbdcbccacbccdbccbccadadbdbdbcbababcbdaaddadbbbcccdbcbcdbcaacaaaccbdbacdbdbaabbcbdddabbaacadbabdbadbaaaaacdaddbdcbdaacaaacbbbdbabdcbacaabdddaadbabdaabbadacadcdcdcbcccdacdddbbadddcadddcbbacbbcadbadcbcdabcbdababaadbaaddcdddbaababdcdbcbdddabbcbdcaacaabdccaacdabdadadcddbbdabaadddadacbdabaddccacdaabcaccbcadcccacddbbaadbcdbacdbabddaccaccabadcccabdcacbadcacdbaacaacccbdcbddbadabaaabbadcdbcabcbcaabacacabaaaaacdcacdcdabacabcbaaaabbcaaccadadbabadacacbabccdaadacbcbaabbabadcaabcbacaabacbaadcccbcbcacbcbbcbdcdaabdbadbbddbaabddbccadbbddbdcdcccdccabccadacbcbdbbcacccabcadbbacaabbdbbbbabacabbcacadbacbcbddcbddadcadcabcadabbaccdacbbbbbaacbbaaccdbccdaacacabaaadcadadabbdddbddcdaaacacccccbccdbcdcbcaabcdcadccdbddadabdbbacbcbbbacdbcacdbbaabbaaccaccbbcbcbdbacaccaabdbdcaacbcddabacbaadbbbaabdcaacbacaddddaccdcdddbabcddbabdbcddcabbbaacdacbabdaaaaaadcdbbadbaadbdccdacdabbdaabcddcdccdaabddcccbbcbbbdcbcccdbccdcdbacbbcdddbbcadacccbdadbcadddddabaaabccaaadbcdddcbdabcbcabccaadcaddadcdadccbccdbcdbccbababccbbaabdbadcdccbddcbdcccccbdbbabdccacabcdbddacddbdbabcdbadaabbacccbdccacacccaabacbabccacbcadabcabaadcabdacdbbdaadbbdddabbbcdcbddbcccbbdbbbaaacadcdcaabbcddacbdbdbdcaadcabdbcdddabbadcdddccdbcaddadbabbbbddabcacbdbacdddddabbbdabbdaaacccbcdadcdbdacacdaddbabbacbbddcbaaccdabccbcbaabdacccbaaabadcccddbaccdaacdaadddacbdcbdabddcadbdccadcabbcccccabcbddddbbacbbcbbbdcddadabaadcabadbbaacaababbabaaabcbacbacdbcbcadccddaacdcdadcabbadbdbbcdbcdabcabcccacdbccaaccdbccaddcbaaaccbddddbbcbbaaacacbbaaadcdccbbbbcaaacbdadccdcacbabbdbbbdcbabdcbcccaaddcdbbbcdccdbdbaaaccccdacdccbdaaaddacabdbcdadddcadaddbbbbbccbcdadcbaddacaaadcbccccbccbdbbcbbcbccaccdcbcddacabacbaccabdacbacadcacadcabdacaaaddcbaaddbbbbdbaadbdbcccaacbaabadcddbcdcaacbdccabdcaabbdbddcacbbadcadbdbcabccaacacdabcdccdbcaabccabcaaacaadbbabdcbddbdcccaccbcddaaadbbbcbdbbacccdccbbddccbcacaadbbbdbbabdbcccdcadacbababdbdaadcabcbcdbdcdaddbcaddaabdddcadaabadabddcbbdddccdbbcaabcadabadddbaccacdcaaaabbccccaddddcabddccdbabdaabbbdabcaaadacabcdabcbacacdbbadadaadbaabcdccbcddbcbbaaccccbdaabdbdadcddddbbaccccccddcacccdbcadcdddcdbcabdadacbdbdabbadcbccdbbbdbabdbbdaccaaddbcabbabbdcbcddbabbbbadbadccbbbdbacdcbaabdbdcababcbddcbcbabbbdcdaacadaaddbcaccabdbbcaacddbbcdbaadbbdaaaadacdbdddaaddbaabdabdaddbdbdbdccbbacacdacdddccddbdcbbccbdddbdadbaaacdbbabbadbbabbbdbddbddbabdbadbcabcaaaddcdbcabdbbacdbaaaabcaaabacbdcbabcbccdbdbcbabcdbbccddadbcacccacadaaacabcaadabdddadcdaadddcdaaddddccaacaacbadccdcbccbbadcdbdcdbcbbbdcbdabbcbddddbcbdcabdbcbcacadbccabcabcdcccaddcbccaaabacadcbadaabccbaacdadddacabaaccdddbcaccaddcbcabbdabaccbacdbcccbbacddaddbcacdbbbdaaabddabcdabbdcbabcdccabdbccaaacaaccbbaaaadcaadbbcdccadccbcbddaccbbbaacdacdcdddbadacacbadddcbcaaadbacdbbcdcaabdabdcccaadccdbdcbcdbcadbacaadddabababcaccaaaaccdaccccddadbbbcbadadbdcbbbccbdbbdcdadbdbbaabbaabcddcbbacbdaccababbddcddcbdadddbadcbccbdcaabbbdaaadcdcbdbdadcdbadacdddcdaacbaadbdaddbdbaddcababcacbccdabccbababcadcabddaddddbdccadbbdabbcbcabcadaadaddddacaacbdadcaaddbadaaddcdabadccdbcddbaabdbbbccbcbddacbdccccdcbaabaccadcbccddacccddbcbcdcdaadcdccadcdadcddabbcadbaacaaadaadccbacaadabaadcddaabcbddbaaaccdbbbadadcdcacaddcccdacccadbcbddbcdcadabbadccddbcbbbbaacbbbaccaabaccccacaabdacdbdadacddcaddbbaabcaaadaccbbbdbbadbddacdaadddadbbcabbccbbbaccbabdaabadcdddabbcbbcccbbcdbbccddcbaacadabdbcacaddadabababdccaabdbdcddbdbdbadadcdaabddadcdaacbaccbabbaabbdaaacdbddbbbbbbccdcadaccaadbadcddbdbdabcaadcbbcbcaababbacacdcbababbadbdabbbddbdccdcadddbbddadccaaacdbdbcddcbabacbbdccaadbcdbbdcbbadadbddaacadadaadababadbccabbbdddcdbdcbdcdcbcabdcbbddbccbbccadcabcdabdaabcbcacdcbaadbdbaaaabbccaacdabcadcccadabccbddcababcbbdaddbacacabdddaacbabacaccdcabcbcaacaaacadddacbcabbdcbaaaaabbbacdcaccddaadcdbabcbaccbaccdaabdaadcdddbaccbdcaacbdbcdcbabaddbccadaadddcaccbacbddcbacccccbaaddbcdccdbaaadddcbabddbcacdcbddabdccddbccbbbcdbbbbbaabdadcadbdcdbdcdbaadcdadaadbbdadacaddcbcbaadddddaccddcbabadaacaaaacbaadacaabdbcadaaaaccdbdbdaddcaddccadcdccbccdcbdbdccbbdccddcccdbdbadccadcbbadbcccccdbcabbbcdbacddbaacbdbcdabcaabcbbdbdadbdcbbdcacdddccdbdabacccacbddbcbbaddddcbdbabdcdaadccbcaaadccbbababbbdbdcccbaadacbbcabbcbcbcabdddbdcacbbddcccbaaddbbccbbcaabcbcccdccacdadadaabddbddcdbadaaadbaaaaacbcdbdbbdbcbbccbcaddaaaadadadadbabdbdbccdbabdddbdbbcadddbdcbaccaadacacdbbcadbbabacdcddbbaabbcadabbdcadccabbacacbaadadaccbdccbbabcddabbcbbcddbdcaccdccbbcbdadbcbaccadcbaaaadcbccdcdaadcabdbacabcbddadabbbbcacbcacdcbcabcdaacbbdcbaacdacdaacdcdbdddcabacacaccabcbacbbdbcaddcbbdaddadabaababdbcababbdbaabccabbdddcdadbcccdbabbbddbaabcbdabcaaccbbabcadccaadbcaaacbbbbbddacbbdabcbcbcacbbdcbcbdaaaabbddbdccaccdbdaaccccdbaccdcdaabdacddbbdcaccdccabddbcdacdbcdcbacdddbacccaabbadcddaadadbddbdbdddddccaabbacddddbabdddddcdabdbacabbccbddaabdcaadabdbbbcdbcdcdbabbcbbcbdadccabbadaadbbacadbbdcabcbddcacadbaddbadcabdacbbddccccdbbcbbaddbaaabdbadadbdadbcbbbdcdbadbacdbdacccddaadcdcccbcaddaccabcbbcabdadbbbcdccddbaadcaabcccbbbdcabbdadadccccbcdbabcbddbccacbdcdabccbcccaaaaabaabbbabcdbadaaccbabcbcbdabdcadbbacbccaddbacbbbadabbccdccaccccaaacabbbbddadbcabccbbddabbbbaacabcaabadabdacabadddcddcdbdabbdacbcbddddbadabcabdbadcdbcdaacaccbdcdcacadaadbcaadbccadabdbaadbdbdbbcbbbbacaaadcbcbaaabbbddcbbacbbaaacbdccaddcbaddccdabaaabadbbadccbddaabaaabdbcdbccaddabdbcdcbabbbcbaabdbcdadcaadcbaabbcaccdccbcbcddbccccbcdcdaababbdbccaabcaddbcbddddcdaabacbdbbdcaddccbccccdadbbcbbbdcccabddcccdadbdbcaccadaaadbaaccbbddadabbdcdcaadcccabddabbddacadcbccadbaddadaddcdbaacbccbcccdcbbcccdbbcdabcaccccbcdbbbbacdaccbacaaaddddcbacabdddabbbacacccbdbccaccbbaaababbdccacdbcdccadcdbdabbcbcdbccdadaaabccadcdcabcaaaacabbcacabddacaaabcdbadbdbadcabadbcbcddbdaacbacbccbddaacdccaabbbddcbcaabdacadddbbbccbddcbbdbdcdbccdbddcdcbddaaccbbbddddabbabcaccbdbdcccbdcdbcbacabcdddaadbdadbbddccaaaadbabcacabbddbbbbdcbcbcdcdadabddbdacbddbbcccddcaaaaabdbccdbdcbcdccdddbdaadbddcdbbddacadccddcccccdbadabadcabaaadcddcacbcddcaaaadcccdbdacdcdacdbdacaaccadadcdbdbacddcdaaddabcabccadacacbaddddbdcccddddddccbacbddcdadadccbacacbaabccdbcaccdbacdbabdbbdadaadcbddccbbccbcdcbbabaabcaaadadcccdcdbdabaabbbaddcbacbddbadbbbadcdbabaacbdacaaaccaaabcbabbcabadabccddbcdcdbcccadccccdcdcadcbdddcadbdadbddbdbcaadddccaacacacbbdcbaccabadbbadbcbcbbcaacdabacbdbdcabddabccaadcdddbbadbdbcaacaaaabcacadbddcabbcdaaacdbadbcbddbcacbcaabbbcdcabdbacacdbbbdcccdbccbcadabdabcacdcabccdacaacbabcdcbbdddccadcdbdcbdbdccbacdcdacadccaddadbacadcbbdaabcaaaddabaadbadabdcbabcbdaaadbdadcbdbabdcbbbdaddbccacdddcaddbdbbacbccacccbccddacdcabbdcacdddbbbbbdbadbdbdcdcaccaaaddbddbdadddbabcaabdccaacdccdccbacbdaabccdccaaacdccdaccaadcaaddaaaabbbdabcccdcacdcdcdabbcbdcddabadbaccadcdacdaadcdbbdabadbacdddcabcabdaadbbadbccbdacabdcacbbcdabcaacbbbbdadbddbbbbbacddbbadcddacdccbddbdcccddcbdabdadddbdbcabbbdaabcaacbacaaadddabdccdbaabadbcdcdbbbaaaabbbddbdbabacdbadabacdabdbcbdaabdcbaacccaabccdabaadccdacbacbdbabcbcabbcdccbbaaaadaccbbccaaddbdccdccbdcbccbcbaacbddddaadadbccdbabbabbacacdaaadabcabcddabcacabadbcccaabaacbdcabcdbadacdadbadcaacbaacbbaabaacadacbdcabaddbabbdadcaadcaddbbbbaabcadaaacbcdbbcccccacaabbdbbacacbabbbbdaacbacdcdabaddbbbacaaaacabccdadabbabcbdbdcbcdadddccdcccdbbcdbbdddcadbdacacadcadacbaadabcdccaccbdbdbabcdcbbcdcccadababaadaddddaacacbcccabddddcdccddbbadbbcacdbdabbccdbbccbcbccaadbdabadabbddcbcccdbbddcdbcdadcbcdabcbacdccbccadbccdbbddbbaacbdcababadacbcbbdbbcadbabdaadbcdccdddbbcccbcbbbcbbdcdacbbaddccddcbdababdcadadcaaccbccbcbdddcbbdcbbbdacbccdccabaddcacbddabdbadcbcbddadcaadaadadbbabcdbcbcbbabdabdbadddbccaadadbabdbbbabdccddcccaacddcdadbbacdaadbacadacaabbdcbaacbdacbabdbabbbdadbdbadcaaccddbaddacacbdbccdbcdadadabdacdbddddaddacdbbdaaadbbdaadcbaacdcaddbcccacabbcdbdcacacaddabdccdababccdbbbaacbbcadcdabaabcbbdcdbbbdcdbcbbacaadccddbbbbcbcddadabadaccacbbaccbbcbddbdacddbaadcbacccaacddbcdcadcdacbabcbccbbaabbbdabacbccabcdabdcccdabaaadaabbbdcaadbbbadaaaccacbbaaaabdacbdbacacbdbaabbdabdddbdcdaadaacaddddbadddcdabbabacbcbbbdbbbddcbdcbbccdcdcccbcaadcdbcdbcabcaddbaaaaaaaaddbabdacdbdcbbacbbcadaabdcbdccaaaccadaadddcbbaaaadabadabcacbabdaaaddccaadbccbbacdcbcbcccdbabddbcbbdbbabbdbabbbbabdcbadddbddacabccbccdcaabdabddbcacdacdbaccbbaaabddbbdbcbbbbcdabdcdbdddcdadcdaccaaccabdbccddccddaabbddbddaccccaaccaccabaabbadadbacaacdcaddaaaadcaadccdadcbbabadcbbdcadadddcbddddadadcaaacdabacadabdaacddbabddcabcbbccbabdabdcddacdbddccdabdbcbdbacbbcacaccbadcbcdbbccdddbccddabccacadddcacadbaadaaaddcbdcdcbdcaaddcccdcadbdaabdaddccbdbbbaccdacbaddddcbcacadcbcddbaadcdbacbddcaaccbdabdaccdbbbbaaadaabbbaddbddaddaadaaaabcaccdddadaccddcbddbaaabccdacacdbacdbbdadabcbdbabbbbcbdbbabcdcbaccccdacbabdaababdabbdcbacacaabdacadabbcdccacdcbccacabaccdddbbabcaaadacbadcdbadbacccccaacddadbcaacdadbcadbabcccdaacabbcacdcbdabaaccdcbabdabdadaaacdbcabccbadccbcdcbacaccbdbcddcbdbcbbbcaacbacdbcbdabbcbcadabbbaaabbcdbbcdcabbdbcbbcdcbcbabdacbbbaacdaddabdaaadacabbdadcdcdcabbccbddcdbdbcacbabccccccbcacbaddbacdadcdbcbaabbcbbdbddbbdadbdddabccbcacaadcbcbbcdbbbcbbccabcbcdbadcbcadddadbdacaacdaacdadddddcaaddaabadcdddccbbdddbabdbddbddabddbbcddacaacadddbcdbaddaaabdacdacdccbbadbacdacbcbabcbaacbbbcabcbdbdaacddbdabddccaabbcddcdaaddcddddcdabbdaddccbcaccbadaabdcbcbbacbbaabbbbcbabbacdcddccddcbaabcbdddcbbacabdbcbcbccacbacbdacabaabadcdadbdcddddabcabaacdbaccdaabbbbcabbaaaabadbbabbbbcabadaaccdcacddabcbacbcdccadbddadcbacbdbcdcccacdbbcabdddcabcbcadcbbadddddaacbacbcdaacdaacabadcdbbcbcccdccbdcbbddbadcbccadaacacaabcbbdbbbcbbacabbcabddaddcdadaddbddcadcdaabbabcdccbdcbcdcbcacdcdcdaacccddadcaadbcdbacacbaccbdacdcdcddcbbabbacaadbacacdabbadbbdaaabbbcbbcaabaaccacacccbccabcddcabbdaacdadddcbcaadcccdbbbbcbbbaababbcaddbacddbacbabbabdcbdbcbdbdcacccadccdbcdcbadabdcaaadbbcadbacdacbdbdcbcbabbddaadbadcccdcbcbbbabdddbbadcaacbdadbcdbaabcbdcdabcdddabaaccadbddbdaddadacbbdcdaddabdbaaabacddadabcabbdabcacbaadabaadbcbbbcbaddcdadbcbcbcbaaabbccccdcbddbccddddcaadcdcaccacaaabaaccdaddcdcdbdadabcccbbbbaacacabdccbbadbaccddcdaabdadcbbccbaadadbdcdbaccdbcddbdbdcbcddabdaccadbcccbaddaadbbdbdcabbbababccaccbbbadadbcdadcababcccccbdbaccbbccdbadabccbbadcbccdcdabbbacaccbaacbabbbcbddcabadcbdcddcabcdbaadcbcdacabaacddbaadbbdbdaaddddabadcabdaccdabddccacdbbcddaabccbbcccdbcdcbcbdcaaabbcccbdacbbccddcdcbbdbadcaadddccabbbcaaaaddacddddbabcdbcadbaabbabcbadadabbaccacdabcaabbabcdaabbacbbbdddaccbcbbbbddccadbadaddabcdcaacdddabdcbdabacbccccbbbccbadddcaacbdbdcadcbdbcadbdbacadabdabcaccbabbbbcbcccdbbdadadccbcbdcacbcabcacbdbcbdbacdddacddaaacbdbabbadbaddbcbabdacdbdbdbcdadcadbddadcaabcaaddccddadbbabcbabcbcbbcacbbaabadcaacbddbbaaaaccadbaabcccccaaabdaadaccaadddcabacbbddddacccbabcdcbbbbbddacabaadbcdacaabbbddadabdccdbbccbccaacbabdddccaabbbadcbbddcbbdbcdbbcbddddccaabdbaccdddadbcbabacbabbcaaacacbbccbdcbacddcdaddbadddcccbbbdbaccbccadcabbdacdcccbcdaacbacddabaccbaccbccbcbbdaaaaccbaadddddabaaaddbbbadcacadddbdbdacadcbcdbbaaadcdbcddbbcbcaccaadaabcccddccbdcccaadcadbbbdadaacabbacaabcaddcdccadacdbaabaabcbaadbacdddacdbccbcbdaabbaccbdbdabccddcccdaacccbddabdbddaadcdcacbcbdabacdcbdacadbacbabacacddbdcdaccbacabdacbabaabcbacdadaadcabbbcdacbaccadbbddbaadbaabccdcdccdccdcdccbdadbadadaabcbaaccaaddabcbadbdbbcaddbbdabdacbabccdaaddcdabbddadbdbdcadbaacccccaddddbbdddbbbacaaacdadccdbdacdcbdacabbbdcacbbbbbaddccdcabcccadbadcbcababaacdcbbbbacadbcabbbdbdadcbcbcdcbdabdbdcacbcdcacdcddcaabcbbcdbaccccacdabcdcdbbacdadddacbbbcdcdadcdccaaddadbbbcaabdcbbcdcdacacccadcacdadacddccdadbbacaacbddaabdbcbbbadcacbcbcbbddbaddacdbddabaaccadabdbcaadcabadababdaacabcbbbacabaaaadabccbcacbdcccddbcbbacdddbbabdddbadbccbaadbaadacbdcdabccccccbaacacbbcbacabbdaaacdbacbdbbbcdaaaccbacccabccbcadbdbbdbdaddcbabcdcbbdbbbbccabcacdacccddaccdadaacbbddbcbcadccacbdabbabaccbdabdbaadbacdaaabcaaabbdbcdcbcdadcdbaabacbababbbcbdcbdacbdddbadcdcacbcccbcccdcdbbdbbbadccbddcccbbdbbcdbccacdadbacdccadcaaabbcbcdddabdbdaabdaaadabdcaabbcabcdadaaababbddbdabdbbbdbbdadadbdaadbbbacdadbabaadaabaddcaaababbabaadadccdbbcaabbbdbbdacdbdabaaaadabcbabdacdccbdadbdbabccaacbcbccddbcacccacdaaccdacdbacdbbbcccddcabcbadabddcdbbaacabbbabdccdaaccbadadccdbbbccaadcbacddaccddabbbaaabdbbcccddbaadaacbddbccbbccccabdcbcccabaadccbcddaadbbbadbcaddaaabaaacacbdaabaccbadaadabcdadccbbbacbadcdccacdcbabbddacadcdbdcccadcdbcdaadbacadcbccdcacbabbdccbbccadcaddbbcabdddcccbcadbaacadbababbcbdbbcccacaccacdddacccaaddcabdbdbbbddcdddbadcabcbcccddbdaadccbdbdbcabcdacdbcadbaacbccbcaabcdcabccbdcdcddbcbdcddbcbddbbbdddacbccaacddbccdccbaccdcdadbdbabdadcacdaabadcbacaaaccbadaccbccbbabdbadccaadcdcdbaacaddddacdcbabadcabdddabdbdbabbdaddcbabcbbcdaddaaaacccccaddcccacddddaaaccbccdbbacddcadcdbdabcbbcdbaabdadcdbcdacccdacdccdcababcabbcacaccbcaaaadbbbabbdcadddbadacabbdaaadbbabbbdcbcccbdddcbdcdcbddbabdbbacbabdcdbccadacccdcbacaadcbbcadbddabccddcbccadcddddbcbddbddcdbcadadadadaadcaaddddbaadbcaaaadccbbbcdcddaadbcacbbdaccbbbadbacbabbbdccadbdddcbbadcbbcdcddbdcbaabdabaaddaacbbddcbdadaddbbaccdcbadacdbbcadbaddcccacccaababacbdbcbdcdccdcbdcbabdabaadddaacbbbbdbcbddaaacbbacadbbccaabbabdcbccddccbbdbcaadbbddbadadbdddcacdcddacdcdaaaacaaaababbdcccbadbadcbdddcbcddddbcbdddabbbcabacdddbacaacbdbccabcabcdaccbadbadbcdaabcacbdaaacdbbccabccabdbbcbbbcaaddbdddacbaccbdacabdabbcbcadcaadacbcbababbbadbdbdbdbbbaacadcbbcabdcdcdcbddbaaaabdbacbbcdbaadbadcbbddbbdabdaddcdbdadcccbddadcacadbdbacdacaaaacacaaaadcdcbcabcababacdbcaabcacbcaadadddcdabdcacbdddaabbadadcabbadccddabccdddddacacdcacbcaabdbdddacacbbcddabccaacddabcdbacacadadcdccddbdcdabbadcdcbadabaabdbcabaccdadcabbccdcdcbdcaadbacadbddacdddbbcbbcbbcbdadbbdccbbdaabbbabadabcabacdacbcaadaaccbcaaacdcabcdddbcdbadacaaabaacbacddbacbaaaccaaadbbacaddbdbbdbcddcabbcddcbcbbbdcacccccacbacacbbaadabaddbcdbcacdadddaadccddaaddaccdbbcbcacdadacacaccdaadbadbdbbdacacbccbdaacddabdbcdbbcbdcabcbbbacadbacdcbaadaadcbddabddbcbbcacdadacacdccbabdaadaadddbadbabbbccdcbddbdbcbccbbbbabbcdcbbcdadcbdaddbdaadabaabbcdbdbadcdaddbdabacdaadababcbcdaadcccdcbbccdaacbacbbdbbadbbbaacdccadbdbdacdabbbbdcacdaaabcbabdbccbdbdbbccadcccbbcddbcbbabddbdaddacaaabdccbaacbddccbabddaadadbbaddaacddbabbbbcbaaddddababbacccdcccbbcdddacdbabdadbcadddddaadacbbcccbbbdbabcdddbacacddadcbadbddcabacdcbcadbddadabccacccccadcdcbaaaacdaddabaccbadacccdaadbcbbadbccacbcacbabbbbccadcabdcbddcbcacdddcacacbacbdadacbbabddaacdcbbdaddccaddccaddaddbcbdcddbcccbdcddbaadadccdccdaadabbabbbdbdcbdaccccbcbbabdabaacaabbccabcbabaccabccdbbbcdccbadacbdccdadadbbcabbdacdbcacbbdacddacdddacddadddaabcbcdacccabdbccdbcabbccccbcabccaabbbcacbaccabacccaaddbacbbaababdadaacbdbcccccbcbcbcbabdbcbbbaadbbcabbadccbbabbdacbcdabcacdbaacaddcabcaadadccadbcdbbcbadadcdcabcbbcacdabdbdbacadcabdcbcbacadbcbadcabdcbcdbcabcccdbddbcbdbbbbdacabcdcbcddbbddacbdbccbdbdacaccdddcbccaabacbadcabdcccccbababacbcdbbcbdcaccaabcadddabddccdcaabdbcabdabcabdbcddccbdcaabbccbcaddcaacabdccadaabddddbaaddaddbacbdcbaddadddcdadccccbaacaccabdbdcaaadbdbcbadbccbddabbdbabaccbbdbbacdaacabdbacadadcddaaaddbcbadccacdacacaacddabccddbdccdddcbbbacaddddcaccaaccbcacdcdbabccccbcddacdcabcbbccadddbaddccbabcdbaaabcdcacaaadddaccdccadbcbdadbccdbdaaadacbcbcbacdbacddcbbbdddabcdddbddacbdbaabdcddcdbcbbdabdacaccabcbdddcdcbacacbaaababbdcccadcccccaaaadbbbbccbabadcbdcdcddbbddacdbaadbbbdcccddabbdabcbaaaaadabcbcbbadddbaabcdbcdbbabddaddccaacddbbadcdbabdddcddcccbdbbcbbbababddcdccbaaaaaddccdccbbdccbaddbbbdbdbcabbdddaccacdccbaabdcaaccdcbdcaddcdbbbbdaaaadcaacabaaaabdcdcacdacbabcbcbaabbcdaabacabddcbdcaacbbabaaddbaadcaadcbdbddbcbadcdadaabcbaaaabaccccddddcbbbcddddadbacccdaccbbabbdcabbcadaacbbabdbcddaadacaacadbdbddddaddcddacdbdbcdccdaddcdabbacdcacabbdaadacbbbacadaaadacdacbabadacaddcdadcabbbadcaaadcdcbcacdaccdcdcccddbabbbccdcbdabcbabdccccbccbacbbdbdbdbcddaddbbaddcaabdcccbcdadbbcaccbbdaccbabdabbdbdacbdabcdbbdcaacaabdcccaaaadcadcbabddbaddbbbabacbadcdabbcbbbabdcdddbddcabbcbbdacccaadccdbdcbbbbacccbccadbaddabcdcdcbbbcdacdcdcadcbbadcdacbdbbcbdbdccdbbccddcacddccdaddbbabcdacaddadddddacccbbdbdbcbbcccddcbdbddaccdbdbddcbcbdcacbacccdbadbbdacddacaaddbbadddaadccccbaacddcdaaccacbaaaabcacadbacaacbccddadbbbcdacdddababcdcdbcbbbbdcbdcadcdbaccaacaabccbdadccdaabdddbcdadcdccadbdbcacbbccbacbbdbddddbdbccbcbdcbdaaabadaacbaaadcdddcadccaaaaaddcacbdbccbbdadaddacadddcbcbbabcccbbaadcdcbabadbbcaaadbcdcabdbabdccaaadbaacaacbdbbcbadddddacccadbcccddbdaaacacdaccbddaaababbcaadbbdbcaadccaaaadbaacbdbbbabacddcdacaaccaabbaabcbcbbddbabaaabcbbaabcdcacddaabbcaabbbddbaadaabaccbdabbaabdaacaacabbdcabbaacdcdbccddccacadcadcdaaadcbabcabdcaaadddcbcdacaccbbcbacabdaadbabcbdacbccdbdcbabbdccabaaadadcbcbbbdacbadbcbccbcdadaccbbacaccaabadacbaabdaabdaaaadadcccbddacbbacdbccbbbdbaabccaabbccbbabcdbcdcdaddacdabcbcbbcbabaddacddbacddacbbbacabbcaaaccacddaacbbdaadbdcdbbbddbdcbdacadbcbcdccdddccabccbadabdadacbbbbbabdacabdddcaaadbdabdcbcbaadddbbcaadcbaabbccdcaadcaccdacaaadcdcccdccddadbcacbccdcbddabbdcacdacdadaabcbbaacabcabbbcbabbdcaccbacbcaabdbaacadbbbbdbaabdbadabbaccaaadbbdadacddabaccdbbabdbbabadbadaacaccdcdbdbbabcbddddccbddccddbdbdbdbcbaacbbcbddccdcabaadddbbabcbdbadadcbdaabaaabbcaddcdaacbadcdacaaabccccbbadddbbbabbaadbadabddcbbbacdcccadaabdddbbdcaabbbdbccdaacdccaaddbbabddadcdcadcbbbcbddbaacbdddacddcbbaabdbbbcadacaaaaaabacbabdadddaaddccddcbcdacacddaacaadcdccdcbddacbdcdbccadbddaddddacbacddbdcdcdbbccbcaadabbdbbccabcbcdabcdcadabddacbdcabbabdddccacadccaaccaaaaddabccbdcaadbcacccbccbaccdddcdbbcbdbadacdbbaddccbccacbaadcccdaccbcaddccaddcbacaaacdccdbddccbacbacacabdcbbcbdaabdabbbccdcdbabcaddadbddcbabdaccdddbcbacdbbaadbcadbddabaababbdabcbcabdccacbdccbbcbaddacbbbabadbaccbbbbbddbacaccddccbabbcbaddadcdbadadddcabcddbbdcbbdcacbdcbabdabccdcbbaadacacabaaabcdcacdaaaacdbbdbabdbaaccdacbbbcacbbbacddbacaccddabbcbdbdadacdbdcdbbabdcbbacbaaccddaabccbaaadbdbbcabdbadcabbcabdbaddbccdbabdababadddbbadbcbbccadaddbadabbddccbcaabababcccbdbabbdcadbbcbabdaabdacdccddaabdacaabbabcbbdcaccccaccccbccbdbaccccddcabacdbbcaacaccdcbcddcdabcccacaccaddabaddacbabcbaacadbbabbacdccacbcdcacbbacddbcacdccdbbdbbbaddbdaaacadacaaccdbacaadadacbabddacdbbbdaaaddcaaccbbcbaddccaadacdcbbccdcbcbabcddddccbbaccaaaabdcdccbbddbccdcacbaabcdcbbcdbaaadabdaaadcacaccbaabaacacbdadbabbbdcbbcdcbaddaabbcaabdbdaadaddaaadddcadaacabcdadadbbccbaddaacbcddbabbdbcabbcaacdcbcccacdabddabccdddacaacdcbcdcbaadbccddbccaddabbddbbdcdaadbbcbabbdccbacdcdaccabbacacacdadabbbcbaaccdbddadaabccbcadcbbdbbbabaccbcaadcdcadabcbcbddddacdabaabaacbaabddbbcabadcaccdbcdababbbdccabcadbaccddddacadadabdbdccbacbcbdbacbaadbcdcccbcaccaddcddcdddbabbddabdaaadcdcbacbdcdbcaabdcadaddbccaabbdbaaccaadabdcbccaabdcdabdbdbdbdaabdaaabcbbbdcdbcbdabccbcabcbbdcbdbdbbcadadaddabbdacabdccbccccadacbdcaadadcdbcabcdaaccbacccdacbabddcbadabbddccbdbbcddaccaaabbbcacdcadcddbbdbaabbbacaaadacbcdaaddbcaadcddcdcabbdbdbdddadccaabbaadccbcbadbcaadccdabbdbbccabcdbdcbcbcaabdbaadcccacccbbbadacadccdccccbddbdaadcbdabcbbbbcabcaaabcaaabcbacdadbabababcaccaccaaddcdabcdbbddcddddcbbdabcccccabcabdcbcdddaabacccadadcbcccbbacccccabcabbccadddabccddddaacdbdccaacdbcdbdaabcbdcabadbbbcacbacbdcabcbdcdabbbccbbddcbdaadacabbabdbdabcdabadacccbdcdcbaddacabcddbaacdcabcdadaacccbabaaccbdcddddadabaaacbcabcbdaaaaaabccaadccabccddaacdaacabdcaccacadcbbcabbbdabdcaacdcadcccbccdddcbcdbcccaaddccacadcbcadbadbadcdacbcacbbdabcddddddcacbcdbaccbccbdbabdcdddcdaadcdbdcccadccbccacacbcacddadcbcddddaabbdbcaacdacddaabcabbdbdcbdccccdbbccacdaacbccbdbbdccdbdcaaccbcbcbabdddadaaabdccbcdccaadaccaacbabaccacdaddbaabaaacacabcdbbdcdaddcabbbbdddbdbdcbadcbcaaaabbbacbdadbbccbbaacbbcbdddbdccbadabbaddacbbaacadcbdaabacabbdacbdbcbbaadacadacdabacacbdbddbdbdcccabadcbcbdddcdccdadbbdaadddcadbdbabcbdcaabcdcbcddccaaabaadabccbccbcaacdabcaddbbddbbbcbbccbacdcbdabdaacadbaaabaccbdbcccacddbabadcdacbdacdcabbadcaccddbddabdcccacbadadaabdacadbbdcbaaccacdbdbacdbdbcbabaadaddcabbadaccadcbdaaadcaadbcddbbabbccadbacbabbaddbacdcdabdaccabdbcccdccadddbaacdaaaabdadaccadbddadaaabdcbbabbacbcbbddbacbadddabcbcbbbdacdbbdabbccdcccddbacbbaaaccacdacaabbbdccdcdbcdbcbccdcababaaacbaacabadcbbddaacaacccdcadbdaaccabcababacadbbdbcbcddddabcaaaaaabadccacbbbabccbdcadaacbcbaddbbadcdadccccdaaddadbdacbdcccbaadacbdddbccaacbbccaabadabdcdcdbdbbbbdcdbdbaccccaadbbcdabbbcbaabdbddddcddddccccccbbcaabcdadadccdcdccddbcbaaaadccacdcdbbbdbabbdcacabadbdacbcddacabcaaacddcadadbacbabdabbcadbcddcdacadcaadadbcbccccdddccbccacbadabcabcdadbabacdcbcdbbcbdbbdabdddaaaabbcbdbbddcccdbacbabdcabaadbaccdacbbdcabcddaadaadbcabcdaabaadcccbcddcbaccbcbbcaddccdaabddbadddccbdccdaddbcacdcaabcbbacbbdbccdcbcdccaccdaccdddacacbdbabbdabaccaacbbaadacbccbaccdddadddddaaccbcaabbbcdbbcdddabadabbdbaabdddaacdaacbdccaacbbadabcbddcbcadddbbdacdbaaaacbabcbbcddcdcbdbabbbcaabadddaddbcbbcbcabdabaacadaccabbdcdbbaadadbabdccbbdcadaccadcdbccdcbaaccddbbabcabcbaaacacbdaadaaabcbaadbadbbbdcbcabbbdbadaadaaabacabccccacaaacabbbdcccdcbcacddadbdbbacccbcbbabadabaccaddacdccbdcabaddcaacdbbccaabbacbdbbabdcbcacbcddabcdcddacdddbadbadcbcdabdbcdcdaaaaaacbadadabbccabcbdcabaddbacdaaaadabadccdbaddbaaacbbacddcdbdddbcaddbcdaaadcdccaadcbcacbdcdacabaadacdbbaadcdadacababbacddccccacacdabdbacdbababbccddadbdbdbaaaacacbbccbbbcdacdccbacaccdcdabcbdddabadbbbccdadbdaadccadcdbcdcdbbcdbbdcaadbacadabcddcbaaadaddabbbcdbbdabbddbbaaddadabbbbacbdacccddddaabacddacabcdbcaacbcdadaaddcddbbdacbbacabdcacdadacabccacccdaaaddadbdcaabbcdbdcacbdacdbbdadcccbcabaaacbddbbbddcadaacdcaabadbdddbadadbacaaaaadcbbdcbbbabddabadaabaacabbabbcbddcbbdbddbdbdccdbbabbabccbbdbddacacabcdcbcddaabcbddbbadcdacbcbaacabadccadaaaacadccbbcdaabacabdaaaddcdbadabbbdcccadbcdacccadccbadbbbcbdbcbcdcbcccddabaaacddcbaadcdbadbabcdbaddbbdcccabdabacdaaabbdbcabddaccccbbdadcabcbbabbbadbaadcdaccbcbdaaaccaaaadbbbbabcaaaddcadcbccdccaccbccdaaadaccbadaccdcdccaabcbadaabbccccbcabbbcaaaacccdcccdddacaacbabbcbbbddacdaccdbbbcdaacbaaaccabbcaddbbbcdbcabbbaadccdcdcddccabadaacabbccbabddddbdcbacbbccaadddcdbbabbcbadcddaaaddbcddddcbbcddadaacbccdcaabcacabcdcbcdacbcbababacaddabccadadbdadcbccdbbababacbacbddcadbbdcddccdbabaabccdbacabcbaabccabdcccbccbbaaaacbbaddccbdcccdabdbbabccacbccccbbcdbaaadaccdaaccbcbabbbddcacddbbbaacaaaacdcccaadacbbddddacabcbddbbcaddbddbddcaaccabdadbbbbadbacbdbccddaadbdddcaadcaccbcabaadbbadbdcdcbcadbaacaabdaadacdccdcacbdbdcdbdabbccddacdbabdbddcbddbcbdaaabbdbaabadcddabadccabdbdbbcddcdaddbcbdbdaacccdabaaaddccbadddaacbbbdbdbcaacdddabddbabcdddaaaaaacaccbdcbabcdcaabaabcbcaaabdbcddbcddcbddacdbcccbddbdbcdaaacaadcbcabbaadbabbdacbaacacacbdaabacdbabccbbabdbccdacbadbbbbcdcacdcbddaccbccddddbddbaaadbdbcabcdcdabdbdaddcdbbbcaacdaabdabcbadadcaabbacadccbadacddabdbabcabaabaabdbbdcbcacbdabccbdbdccbcbddabbccddabcdcaabcbdbadddcdbdcabcdaccabddbcaaadcbcbaaadacaabcccdddccaccbacaaacacbabbaacddacddbbcacbdaddcabaacdddcbabbddabdbbcabccadcdcbbdbbdcddbdbdbbbbdbbbdbcabdacdabccaddbcabadbbbabccbbcacdcbdddbbcbaddaaaacadcdbccdddcdcababcaaabbbccdccadbcabadbbccdcbccabcabcbcccadbbcbdbadcddbdcacacbabdbbabdbdcdddbaabacbdcbacddbaaadbbcadaaaacdccbaadddcbacabacbcdaaadcbbaddaacbdacaadbcdcaaccaddddaadacdbdbdbdaaccaacabbdabdacdcdaabbbcbdcdaabbacdbdbadcaaaaaaaccabbadbddcdbbddacdbadcacaacdbbcadacaabcbbbdbcbccadadbcbdadbcdabccdbaabbcbbddbcdbbcdaaddbabbbacddbddcccbbaccddcbcbcccadacaaaccdaaaaabbcbbdcdcbbbdddaabbbaccddcbbdddaacdddcdaadbbacbacbdcdbbbacddcdadadaddccaabadcbbdadaacbabcdbdbabdaaacaddaccccdddbddbdbbdaddabacdadadbbdacabcbdaacdabacccbddcdbabcabbbdbccaacaadddcddbaabcbbbddccccdcbcbaccddabacdcccddddbaccaaadbccabcbaabcbbaaadcddbabbcbbaadaaabdcbddcbcddcabdcdacdbddccdbdabbbbdcdbdaadadababdaadadbdacacdbcbbbbcccadcbcdccdbcccadaddcdaaadbddcabdadcabacaadacbdcbdacdadaacdcbddddccaaacbaadbaabddbccddbddaaaddabdccadbbcbcdadccadbbacbbbdcacaadcdabacadaddcbacdaababccabbbbbaacbbaddaaddcdddbdabbbccaccacdadcabaacabaabacccababbdaadddcabdbdbdbcdbdbbaadccccbabdbdacbbaaadcbbbdccadadcdcbdcacdaacddaaccdacbcacbacdaaddbacadcbacccbdcaabbadddcaadcccaacbbcbdbbbdbabbadaddbcdbadabbacccaccdacddddbaddaddddacacacccdaaacdccdcacdaddacdabbcaaabaccbbcacbbbcddacaddcddadcbbaaadbddadccaabbbbacdaababccbcbdadbbaaadbaabbbbdaadaddccddabdcccdaccddcadcddabacaadaddbacbbacbdccccbcbadcdbcdddaabccbcdbbdbcbaddcbacdbadadbccacabccbdabbcdadcdccdbcbbbdabbccdbddcaaaadbaadabacbdbababadcdabddaacddbdadcbaaaaadddadabcaadbdcaabcbbcbdabdacdadabbbcaaabbdbcabadabddadccbaaddbbacdabaadaccabdabdaccabbbcacbccdbdddddbdcaaadbbcdabdbacbdabcccadbddbbaaabbacdacbadbcbcdbcaabcbccaadbccccdbcdcddacabcbbcbdaadbbdabdcbdcadbdbaadaaadbdcbcbbcdcacccbdabcbabbccccaabcdaaaccddacabdadbcbbdcadccabbcddbcbcdbaaddcddddcbaadadccbbcddbabbdcbbbbdabbbbabcaddacbcbbaaddbabdddbccbcddbaacbccadacbdaaadabccdbbccabadaacababaabaabbddbacdddcdbaccacddcacdabbaadabddcabbdccccccbbadccabddaccadccdbbabcdcacdbdcdbbddcbadcccacacaadcbdabdcaaabadddabccabccbbccdacccddcdbaaaddaddccadbaacddadcabcddaabdcdbccbcbabbbadbbdcddbddbdacbbdcdcdcddcdadabaababbaabacdbaccaccbdbddcbaddbbcdcdccdcabaadabcbdaababdacdaccbcabdaccdbdadcbddccccacbbdbacbddbaddccdbcccaacbbcadadcdbdbcadabccabbbcabbbbcdbbabaabbbccccaaddbcdbbaccbbcdcccbcbabbadcaaccccdcabbdddcbbbcbbcbbdbdbbbabdabccabccccabdcbabbddabbacaacbaacdcccbaabcbdcbacbabdccacabdacbcdcccadbbdccbaabbdbbabacbcbddacabdacdbbcaddbbadbcbcaaddbbccaddcacbabaacadbccccbddbbbbccbacbacddbcadbacaccddddcacbbaacacccbacdbadaacbcabcaaaddcdcabbadcdaacaddadabbbacddddadccdaaccaabcadaaaccbbabadacabdabcacbdbabccbcbdbabdccddaadbcbbcabdbcccabadabcbbdbacddaababbddccdabbbcdcbacabaaaadcacbbddcddcbdaaaabbdccccbdbbaacbbdacbccbccbcccabbabcbccdbacaccabaaccbcccdbacbaddbadbdcadaabccabcddcacdaddbcccbacabbdacccdbcaaadcbabddcdbbcaaacbadddaddcbacadddcaadbbaaaabcbdbabdadcaaddbccccacaccaccacbbabccbdbccdbdcdccbcdababbdbccbaddabacaddaadcacdbacaadabbbadacbdcbbaadcbbdcdabdbbcdccacbbdaababccdbdbcdbbbaaaaddddcbcdaccbbdcdccaaaacbbabcabadaccadbdabbdbcadabbcdbbabddbcbabdbabccaccabdacbbaddcaadcacaabadcdbcdaacadccacaccacababddcccdddbabcbcdabbcbabaacbdadbcbddadbacbbccaabbdbccbdcdbcbbcbbabbbbcbcababadacbddbaaacdaadcbbdaadccdcdacadcbbaaadccadcdcbbbbaacddcaabadadbdaaddcbbaacdcccbcccccacccbcbcccacbdcbadcabbbbaabdbdbacbadabbdbadcaaccadcdbdddbbcdbcabcabcbadcdabdccdbcbbcdcddaddbbabbbaaddddadcaddccababcabdccaabdacabaacbbdcdbaccddcbadbddbdbcacacbbccaabcbdbbdbdabadcacbcbdaccaccaddcdcbabcdbcbbdaabddbcdaacdadccacddabbacaabaaabbcdbbaacabcdbaacaaddacdadadadbabcdaabccbcbdcabbcbababcdbbcacacbdcadbacccdbcdacacddbacddbddcdcdbdcdbaacddabadabdabbddddbaaddcacbbaadbaddabbacbaddcabbbddcbbcbccaaaaaddadcbbbdddadccbcbbaabbabaadacdaccbccdccddadbdbaacdbbbcdcadacacdbcadcaabbaaccadabccbdcdbabbacacdbcabcaccacdddcadddaccbdddcbdcccababdbaccabcddaacbbddcabbbabcbaddbbddaccdddbccbcdccdcaddcbcbbacbadccacabdbdddddacbddcabccddbccbccaadadbcaaddaaacbdbcacdcaacaacddbdbadcadadddadaaabdccbcbcbbacadbdcabccdaaaadbacbdbaddaacadbddaadbbbdbbbbbbadaaaaaaadaadcccbdcddbdcbacbccaabddcabddabbbaccdccdcbbabbcbaaccaabcddbbaddaaacdcbbbcccaddbabbdacdbabbbdcadcdabcabcbaccbbbacaabbabcbcdbcdacadabcadbddabcbaaddcccbbbcbabbcdaabacbcabaddccbccddbccccbdcdabcaabccdbacddccaacaaddcabbabaadcbddccacaabacdcdddcbcabdcbdcadcdbdcdccccbdcdaaacbdbcbcbcdadbdbbabcdcdcabccadacdbacbccbbcadccdcbacccddbacaddabccddbabcbcadbccdabdaccdbaacadadcbaabbbbdcaddbbbdbbacaccbaaacaddbddadddcbcaddddadcabaaaddcbadbbadddadcdababcccddccbadacaadaaaadabbccccbaabcabaadccadddaddbcaacdbccabddcbdddccddadaacbcaaadadbcdacbcabdbaadcbbabcbdadccadcbdddaccbaabbccbddddadadadbddaabaabacabbbcddccbaadbadbbdbbdbaccacadabdbaabaacccdcbbcbaacacddcbaaaccbdbbcaabdddbbaddaadacbcdbbbbacdcadacccdbdabbbdddabbacacdcdaddbcaadcdadbbaabacccbddddcdbcdcbcbbacdcbccccaccccddcadbccbbcbaabdbdaccbcbbbaabacbcdadcdbaddcabdcadaddadcbbdbcbcbbacdababdbaababbdcacadbcabbabadddacccbadcacdcadcaaddbbcaaccdaddbadacaadbbbddbbcdbabddddabdadbaabadabccddaabcddcbbcddddccdaabcaddccbbbdaabccbbacdaccbacadbadbdbbdcacbdbabbadacccbdccccccbcaabbaabadbdddcbdadcaaccdcdacaacddbbaabcddddaccdadcaacccdacabbbdcddddadbbcadcbabbccbabccbdcbccccbbbbabcccabaaadbcadbdabbcdadabbacdddbbbddababaaaadacdbacadaabadcdadcaadbaacbcaccbcdabbccbbcddddcbdadbdabaaccdbcdbccacadcbacbacadaacdaadbcaccdcacabacddddcdccbbbadbbcbbccbddcbcbbabbcdddaacdcbccbcbaaacdccbbbcaadaccbddbdadbcbacbabbaccadbbdaaddadaaccbbaabcdaabacccccbbcddbdadcdbdacbaacbdaacadcbabbbabcbacdcddddccddbdccdbdbccdddcbcdaddcdcbacadbcbdccdababaaabdaaaccbacdcdbcadaaabbdbbcaabbdbcadbdbcddcbbadbbddcdbadcddcccbacabcdaaadcbbdcaababcccbdbbabdbbbddbbdcdcadcdbadabdaadadbcdacbdbddbabaabadaacdbbdcbaadbcbacabcccbabbcabcaacbccaaabdabddaadbbadddccadbdbcdaacaacbcdadcdaacaabccccddddbcacdcbdddbdcdacdcacaccbababacbaddcdaaadccacbbbdaddbddcdddddbbbccdcbbadacdbaacccddacacbadbdaacddaabbcaacdabcadabbdbbabcacadcaaaddbabcdbaddbdacaccadcccbacddcbcccaabcadabaccaacdcaadddacdaaacbcacdcbbacddbadddcddbbbdddbbaabddaabbcabcdbdabdaacccbacdbbccbadccbddabbbbcbaaddaaabaddacdabadadccababbcacacbadcdaaaabdccccbbcddbbbddbcbbacacbdcddcabbaacdbddcbdbaccbacaaaaddccacacdbaaaacbcdbbbdcbcaaccbadaaaadddbbddbbbcccdbddccaddadbcdcacaabbacbdbadbdbcbabddcbbbcddaddaccacbdadbaaabcaddcdbaabbdbddcbcaaabaaabbaabcbbbbbbbbdaabdbbddcddcddabbcdbddcbccbaddbbaacbbbaacbacaabbdbdcbcaadddbadbbacbbcbababadaababbabacbbddaaaccbadbbcaabacaadacddadbbdacddacbcccbaddadbbdbbdbbdabaabbcdaccaadbaacabacdcaadcaaacbdbcccddddacdcabdccdbabaadbdccaaccaaddaabcadcbaccadbcbabadbcabbcdccdbcbbacaadbcdcadbadabacabaddcbbcbaaccacacdcbdcbacdddcaabaaccbadcdbbcddabadcbbdcccdaadbadcacbddacbadcddaaccaacccbdaccabacbcadcbcacabbddbbdacdadcaccbdbbbabcabddadacbbbcbacbcccdbbccbaaaacdadaddddcaababcbccbcbcdcdddaabaacabdcbbdbbbabacdacabcaabcbbbbcbddcdbddbabbdbacbdbadcdcdbcbcacabdcabacccadacbddcddbddcddbccadbdbbbcbcabbaaacbcacaaaacaddcadbdacbdaacdacbbabbccbdccddababdbdabcdddcccaaadbaddcddbcccdcacaaaabbcdbcaaadabccacababaabcdbbaadbddddbdbabaddcbbbdccadcdbcdddbbbabcdbacdcbbaacdaaadddaaccbddcccaddcadcacdcbabdadbaacadacdcadddbaabcaacddbbaccdcbbabacccadbcbadcacdddbcaadccddaccadcddddaddbbbacaababbacabbaaabdbcadcddcaccbccbbdbabdcdadcadbbabcadaabddcabcabaddadcadcdcbbcdaaadcadababbcdbabbaacacdcbacbdccaacaacbcbdcdcacddcacccbcaacccdabadadddbbdbcdbacbdacdabcddcdabcbbdcdaaacbaaabdaacbaabababdacdddabacdbabbdcaaccbdcaabdcccabcdcdbabcbadbccccaddaadcdadcbddaaaadabdcbbabbddbacbbccdcbdbababbcbabbabbbaaccbbacdcacabadddbdbbadaacabdaaadcbdcdadccdabbabbbbbadaaccbadbaaacbbabbcbcdcccaaaccdccddbbdbacbbccddacaaacaaccacdcadccbcbaccacbabddbdbaddcbbcbdbadddbadaaaddabcccccaaddacddbaabdaacbaadbbbcadddcacccbaaadbabdacbbacaddbdabbdaddbdbbbcbbcaccbccadadadbdcbcccdbcaacccadcddddccabaabbdbadddbccbbaacbbccbddaadddbaddbccccaadacddddcabbbdcaabcacddccddcdbcdababcddccbbccbbadacddbacabbccddbbadbcddcdcbcbccddbccacbdabbdadaccbcdabbbcdddcadcdcbbdbbdcdbcacbddaddcbcddcdccacbcccabdbdcbabadacbccbcaaabdbcaaacacabadbbabaccbbaabdacbaddbaaccdbadcccaddcaaabcbccdaabcdbcabbddcdacccdaadbbbdacdbcabdbbbadacaadcdadbabaaaccaacbcddcccbcdbcddcadbdcbcacbadbcabbbadcaabaccdbaddcbcbddbdbadddbbcbddddaacdaacccddccbcacccdcabddadbababacdadddadbdcadadadcabdbabbabaaabdababdcbaaabcdcdbbcbcddbbaddcbdbdcdbbadaadbbcbccdccbbacabcbdbccdaaacadcdbcbcbaddcdcaabdcbcdddaacdbdccacccbabcbcaaaacdcaaddcabdadbcddbabcdcadccbbcaccaaaababcdbdcbccbaadcaccbccccccacaabbcbaadbcbbabaddddbcbcdbcbcbadbddaaacddcaaaabacaabaddaacbdcdbabcbaddbaadbdcaccbdbbbccccabcbdabdcddaadadcdacaddcccbcbaacbbbdcbdbadadacdcadccadaaaccbbadacdacacaccdcbabccacdadccdacdbdabaabaaacadaacbdbcdbaaadaddcacadacbbcdbcdbbadbabcdadadaaacdbaabccbbcddccacbdadabadadcaaaccdadadcbccdacacbaabbcaabdddaccdddadcddbbdcccdbabbdcdcdbcacccbcabbabbbacbcbdbdacdcccabcddcccdbaabbacddaacddaaccadaaabcddabbdbdbbccbcddcbddbdadbbdbddbbdbcabbccabddcdaccaacdabdcaacaaccacadbaabdbcdbadadcadaaabdaddbadcdbcbdcaaacbccccdaaaabadbaacdcaccddcacccccccbbbccdaadbdadacadbddddbaaccccbbcbcacdcbccbbcbbcdbacbbabdbbacddadaddabbccabbcadddadcaaddacdcbcddacbcadbbddcbcaddabbbacbcadaddadbdcadcbbcbbcaaaabdcaaabcabcdadcbcdbbdbbdabbddbacabddcaacccdcadcdbcdbccdbaadbcbadabbbdabbacadadcddaccddbadbbdaddaadbbcdababbccccdccaaccccdbcdbaabbcddabbbaabdadcacbbcabbbdcdadcdcabcadbbdcdddaacaaacbbdaababbacbbccbbbdbbdcaadcbacaababbccdcbdabaacaabaabdbbbaabaaddbbcaddcabcdabcccadabadcaacaabccdcbbaddadddddaaadbccbbdabbcaddabdadacdbbbcaaddbaacbcabbbbabddcabddcddcbacbddaadbcadcdbaabcabdbccaadcabccababbacbbbdaabaddcbabcbdbcaaccdcadcacdbdcbdadcbbbdcbaccadabadcdbbadcbccbdaccabdbcdabcdaacdaadddbdbccdbdbbbddbaddcdbdacbbadaacaabcbbbbbdccbcdaaadcbddaddbdcdadbbbbdbbabaaddccaccbcbbadadcdbdadbdcacdcbdcbdcdadaabccaaccaccdcdcdddaddccabcbbbabcacbbcbddcbbdbdbbcaddbcdaaabcdabbdbdcbcbadcdcdbadddcbddbbadcdbbcdaddbcabdcaaabdccaacacdacccbdccbcaacacbbbaccdaaddaaacacacddabbacabdbabaaabdbddddcddabdaccdadbdacaaccabacbcbaabbdabcaaddcbbcdcdbaccbbdbddccadbcabbcccbccdcabbddadbdddacdbcadbcdbdbacbbcbcabcddcaabaddbcddcbbcdabcccacbbbcbdadddddbbcdcbdddbaccbbcddbacdabaadadadcbcaaccabdababcacbaaabdcabacddaccbdabacccacadbaaadcacccabbbdbdcbdbaacbaabacbcdddccaaaaabbabcacdabaddddcbcbbdcbbabaddbcdccdccccbdcccdcddacacdcbcacbbababaddaacaacbbbaabbddcddcabbdacbaacbaddadbabcbdacaaadcdadbcccbabdbbcbbbcaaddadaabbabccbbbdbdbccaddccdbcdbcdcaddacabbcbdcbdcaaaacdbdcdddcbaacccbababdbcbdadadabcaaaacbabbbdbabccaaccdbcdcddcdaaddbdddbcdacbddccdabbcddbbaaccdcbaddcddbdccccddcdccadcdbbadbaccbadabcbcaddcdacdbdbccccbabdaaabbccbccbdbbccadcccbabbbdcbdaddabaccabdcdbbdbdcccbcdbaccbbbabcbdcbbddadaacaaaccccdcacbdcbdbacccdaddcbdcaacbdbbadcdcdddbcadbacaabbcdacdcaabaddadddcdbdacdacdcdbdddcaaacbdcbdabdcaabdadaadbbbdacdaaddcdbaabbdbbadcacbdbbccaabbbbccbcacdddcdabbcbcdbbbacdbaacbadcddbbcbcdabadaabaddaaadbabcbacaddcccccdbaabdbaddbbaabbdbbcabdcacadcdaacdcddbcbdaaadcbcddbdcdaadadabaddcbbadcadabdccccdbabcdabacbabcbaacbdadaccdcbbbdddcdabdcdaccaadcabdabadbcaacacabcbbbddaaacbcdbdcaacccbddacadddccacbaabdbaddbaacbddcdbdcddadbadbbabaddaacbdabdbcaadadbaadcdcbbccbabaccbdaccdbbbbaaadabdddbdcdbbacdcadbacddddbdbdabbddbdcddbdcaacabbacbabccbbbaaabbbcbddacabbaaddbcbcacdcdbcbacbabaccdcacbcbcabaccbcadbdbcacbbabbdaddbdadabdcbdbcadacaaaddcacdadddacbacaaacbdcabbcacddabbabaccdbcbbdcdacacdaacdacbacbbcbdddbbddacddcabccbdddacaabdccabaaccdccbaaaaabcaaaabcababdccbcdcdddadaadbbaadcbbddbcbbdbdacacdbbcbaadcddddbbacbaccaaabdcdcbbbacabbbbabaaadcbdbdbdbcadaabbbdcdadcdbaacccaddbbaacbcddaddcbaacdbbcbbdaaaaadaccbbcbbbdcddbcdcbbcabacdaccdbbadbadcdadadabacdabdccdacccaabcaadcccbdcbcaadababcdadacabdacbdcdcaddddaddddccbbbcabacdaddcabcddabdaacacabacbdcccacccdadaacbccbadbbdaaabacccbabbbbbabddaabdcdccaccadbcbaccbcbcadadcacdcdcbaddcaabdccbbddbabbdacbdaacbabacdbcdbaabbccdacdbdbddabbcabaaaddcddbbccbcabbcdbccbaababcadaacaddabcadbbcacaaccabdbcddbbaccddabbcdaacbcabbdacacdbabbacaccaabcdcbdbdbcbadcbadddbaddaacaabcbdbcbaccbdaacbacbacbcdbddcbcbbbaacadbdabcabdddbddbbbdcbaaaaccadddcababcaabbdaddbbdaaadccbdccdddaddabccbbabaadbaccbdcbaabddcaadcdcaadacadacdaabcbdbddcccabbadabdadadabcdaaddbcdbcccbcbaccbaacbacacdbddcbdcaadbbcddabdaddbbdabddddabddbacddbcdbaaadbcadcaacbacdcbccacdbbcabcdcbacbccacbbaaabcddbabbbbaccddcadbbcbbabcadbbbccdbdbdddaaabbaaddccccbccdbdbbcabcbabcdddddabdcaaddcabcacdcdcbdaadacacbddcbbcbcdcbadbacabdbaadaccbbddcdccabbcbaabcbdcbcaddcdbbbdbddbbcbccbdbdccbcddcdccaddcbadadabcccabaabdabddcbcacddcbcccabacacaaadccddbbaaccadbadaccdbddcbaadccdababcdbdaddbcdbcdababcbddbbdbddbadddcacdcdcddcdaaaadbccbacacaadabadddcbacdccbdccdabccaadbdcbaaaaacabbcdcddaababaddccdcbcdccddddbbddbaabdbcccdbcdbddabbcaaaddcabbacdcacadadcaccbbdcbabaadadcbbcbadbabcbdbcddcaaccddccadccadacadbcabbbbdbddcaaccddbcabcadbacbbbacaabacdcaaaaadddcccccbbbbccdbabadcdbbacababbaaacccbbbdbbcddbabcadcdadacabadcadbcddaccacababbabcbcdaddddbdddbbcdcaabbabcbbbccadcbacbacccaccddbdddbdcdaaacdddacbccaadbadabaaaaddaabcbccabaaabcdadcdcccdbbabddddcacbabccccccdbaaccaddaadddbdcbbdccccadaccadcabbadbbddaadbaacaccacddcbbbdbaddacdaabbaadacacbdbadcbccbacccadcddbcdacaaaaacaacddcacadaacbdabbdbcacbcbbbcdcdbacaacbdbcdcabdabddbdcacdcccddaddcadcacbbbacbabdbdcdbabddcdcccdaaadaaabcbdcababbcbcaccdccdaacccaaaaabacdcdabcbcaabdcbdbabdacaabaabccbcdccdccbdaddccdbdbdbdcdbaabcdcdcaaacbdcabcbadcaaadcbdbdbcabddbbcccaadbadcdadcbbcbbddcaacdbaabaabdcaccccaacbddaaaccbbdbdcbcbbdadcadaaadcdcacbdbabddbaddddadbadddbbbacaadcbacccacbbcbacbdbdcbbbbbaabcaaaddbdbcdbbcdcadaadcaacacccbcddabcdddddbbdadacacbbdddbbcabcbcbabadcdddbadccdbadbaaaabaddabbdbabcbcbcdbcaaacbabdbdccbacacacbaddccdddaadbadcbcbadbdddcddddbddbbbaccdcbcbbaaabccadadbcbbddabcdabcabdbbbdbdcbbdccdadaaadacccbcacdcaacdbcddaacbcbabdddbccbababbbbbdbbddddaabbacadaacacbbabbdacaadbddbacabaddbccacdbaadacdbadbcbadabdcadcabcbadccdbabadddbcabdacdcddbdabbacabbadbcabdccbddbcdbccaddcdcdccbcbdaddacdacbcadcdacddacaacabbdabdbbabbdbbddcadbddbbaaacbcaadddccbbaaaabaacddcbbdbabbdaaaaaaccbcdcacacbcadaaacadcbacddbcddadbbdbbcbcaacdbadcacbbdcdadbaadaccdcdcdddbdaaaaabacdacdcbbbbbbdcaccccaadbbadcbabbdcacbdcbcbacbbcdadddddaabaadabdccbabbcdaaddbdbbaadcdccdcacdbaabbddabaaacbbadcbdbdbbcdbacdbcbabbccabbcbbaadbacbbabdcdaadadbacbcbcbcdbdabdabdcaadbdcdadcdabdbcbadbacdacbccdaaabcbbbcbcaaacdacccdbbcdaaaabaacaabcbbabdcdcaddabbacbaccabcbdabdccddaccabbdaabacdabaabbdddacccdaadcabdcdadacbccccddbaacbcabababdaadccbacddcbcacadcdcadbdcbbbaabdbdacadacdaaddccacadcbaadbbbabbdabddaababccadcdcdccacacadbdcbcbabccddaacdbcbbbacbcaaccaaacdcdcdadbbabacdabbbdcbaccdabdbbcacbbacdbbbacaddbbaabaabadcccdbaaaadcbaccdacdddaddabaabdcccdddcbbbabcbabdbbdcbccccabacdaadcbadbaacbaddcbcdcdabdbcbacbbadbabcabaadddcccbbbdddacdbacbdbddaddcccddcabcddaabcccdddbccbbdcbdbacbacbddcaabbacccddbcabdcbabdbbaabdddbbabdbadcccacccaacadbccbdaadcdddbadbbccbcacabcbcbccbcadbacbbbdaaabbcabdcddcdcddbccabddbcdbbadadbadacdadbabcaabdcbacccadacaabbaaddbdbdcbbbbbdcdbabbddbcddbbacdcdcadcccaacaadacbabddadcddacbddcadbbdbabadddabcddcdccddadcdbcbddddbccccbabdabddaabdcdcccdddbbbbacdadbaabcdccbbacadabacdbdbcbaabcbdbabbcdbdddbcaddaadbddacabdcadbbadaddadadbcccddbdcccbbcbbadadacadbbdcbccdcdcddbdcdadabcbdbcdbadbddddcbacabbdaabdbabbaadddcdadbdbbcadabcbababcccccddabdabcabccddbdacacadabcbdacbaaadcbbacabddacbcbcbcabbadcdaddccdaaaddcaadbdcdbacdcbcacacbdaacdcccbbbaaddcbbbadbddababadbacbdbcbccddbbcdccdddccdccbbbaacbdcbaabaddddbcccacbbdbcabbcdcdbdacdaddbbcacbbbbdaacbadabdcdbbdbabccddddcacdcdbcbdccccdaadccbdbcbcbdadbaabbaadcccdabacbbcadbddbcadabcdbdaacaacbdddcccdcdbccbbdbddcddaddaccaddccacdbdbbcaabdbcdbcccccbabcdccddabaaaadacabcaddcacdccbbbddaaaacdccbadacccbbaccbbadbbccbdcaacacdcddbdccacadadbbbddaaabddddddbbbababcbccaccadcbcdccdaacbcdbdbadcdadacaabbcbbbaddbacdbcccabbdbabadbaaaddcdcbdaadcacdcbbdabdbabbddbaabacdbddaccbddbaddbbbbabddcbababdbabcdbdccbdcbabdabdccdacbaddcacdccdbbddacccccbccdabddacbbbaadcddabbacdcdadbaabcdcbbacccacddcdcabadbdcdabdcbdbdcdcabaadbbdcbabdbbacbbbddcadcbcaabcacdaaccddcbaaabbabcdcbbccdacdbdbbbcddacddddcaaabaccaacdcdaaaadcaacbbcdbbacabbaabaadbddabadbdaaadbacbbabddabcbddbdaabcacadcdaacdcdbcacacddadcadcccbabccddcaaacdaabddbcdaccbbcadadbcdcabdcdbbbccddadacbbddbaccdaacccbaccadddaabdbbbcbaadcaddbacdcaaabadddcacbbdcbcaadbcddbbacbacbdbcddaaddabbddbbccadaacbdccbbabacccdccdcbdcddaaddccabdbccadaaabbddcaadcbdddabbcbbcbcbdccbdaccdabdcdcabddbadbcadacbccdadabbbcdcabcbcacdaaaddbcbbbddbdbccaacaabddaaabddabdcddaddabcacbbcbacacadbdddadbdbabbabcdbddbdaaacaaacdaddbacbaadacdbbaacdabcbcddbdbbcbcabdabaddcabacdbabbdcdbcbacdcbbbddcbabdaccbcdbdbadacbabdadacacdabdbbbdbbccdaaaabcbaacbbbdbcdacbcdccbabbbacccbcdaccccdbcdabdacadddbdbaacbaaddbbcaccaacbbbcdbbcbcdadbddbccdbdbdadabccbdbccdaccaacdbbdabbcdcadccdabcbaabbbbbddbccacadadcdbdbbcbaabaddbdcbbaabadacdcdbbbaabddbacbbdaddbdbcbacbccddbcabdadacacacbdbbdccadaddbaaaadabcaaccdddcddccabcaaacaddaaacdabdcbcbabdcdccdaacdabbdacdcaaaadbadbabddccbaabbdaaabcbbbacbabbbbabbbcbdbdcbbcdbadadcdddbadbaddcaacdbdccbcbbddbadbddbbddcabacdccdcaadbdbbaaddcbacddbbdcbcddaabadbbdabadbcccdbccdcbbacbcdcbbbcddbddbadccbdcaaaadddadaadbacbbdbacabdddbbadaacbbbcaadababdddbcbdaacdbcddadabdbabbcbdddaccdababbccaadddbccddddaabdabcbabbcaddcaadabacddaacbbbbbccdbddcccdaacbdcbddbcbadaaccbdabccabcbddbcaabbdbcdaacbacddbdbcbdaddbdacabadbbbcbddadbbbabacbccccbdddcddcdbbacbdddaccbccddacaaacdbadbaddccccdbbcdbbcdacddacdbadbccbaddcadbcbdadadccbabccbdadbcbaaabcddcdcbcdbaacdadddcaaaddacbddbcddacaacadaaddadaacbdaccddabaabaadadbaadbddbcbabccadccbaaaddbbdbacbbbddacdcaddbababaadcbcbddaccaddbaaccbbacbdcbacbdbaadcddcdccbbdddcbbcadaacbbdbbccaccdacaaaddbabaaccbcadcaaddcbcddcdaccbcacbdaccabddbaddcdabaacddacadadcddbccacccbcccccacdcabdcddbadbbaaacaaaaccdaaccbabcbaaadcacdbdcaadacbcaabdbacbdcdddadaadccdaadbcdcbacdcaabbbcbbadcabcdccacdbcaddccbcdaadcdcbbdddcbabcdbccbbaddabdccdaccbdcaaacdadcddcbcbbbddbcbbbaaaaddaabcdbacaacadcbbdcaaaddddaaccaccbadaaadaddadcccadddbcdcadccdddbaaabcbddbadaabcbcaccabadbdcccddadbccacabbbdbcccdabbdbabdacdabbdbabdaaccbadadadabdbbbadcbadaaabbbaabbaccacacbcdaabcdbcdcbccabaccbdbcaabaaacaccbbdccabdcbdbcccbcdcabdcaabbcbbcadddcbabcdaccdddccabdbddddaaaabdbbdcadbcdcacbcbbbcdabbdcdaddbdcccabaddaaaadaacccabaacdacababdcdbcbcaabddbcbcaababcdaaccdbdcbcbcddddcdccaddbbadcbadcadddbcddaabbdadcddcbbbabcbbacbbbbcddabcadadacbcbcaabdaacabbdcdbdacdbcaaadcdbccabacdbcabadcadbbbbbbcbabdadbaaddcbbcddbcaaaadacbaacadadabbcdaccaaacaaddcbddcdbdbaadddabdbdbadaacadacdbcbbbbabdbcdaddaabccdacdcccbabdbdbdccbabdacbacadcaaacacdbaacacacddccbacdbbaaacbbbdaaabaabccdaaadcabacbacdbbcbdcabcccaaccaaaabbbaadbcdcccddcadbacadcdbdddbaabadaadcdcadadbdaccbabaaddaccaabdbcdbaaaabcbdbadddabacccbacbdcddabbdbabadabaddbaacdbadbbcdcabbdccbdcdcacccaaadadadadaacdaddbbdacbabbacbccbcddddbcaccdccbabccdddcdcdcabbcbcadcabbcccbccbcadcbcbabaadbdccbbbdccdabacacbdcdcacbdacbadadbcdacacbdaabcaccacadbcdabcdcdbacaccaddaaacdcbadddaacbdbbccdacadacdccdbcacdcbccdcbcbbdbbaaccdabadbdcbcccdcacdcbbacadddcacbcaaccddcdcdacdacadbcdadcdbbacddadbabdddbcdbacbdbcbddbbacaddccaacdccdacaccbbdadbacbcbdadddadcdbadcabcbbbcddadaaadcaadccaaccdabaabdbaddcbabccdadaaadacddcabcddccbcbddbccbbbacccabdcbdbacaaadbbccbbabbabaabcdaaacabacdabbcbacbcbddbdcddccbcdbababaabbbbbadbdbddcacacddabadcaabbcadbdcbabccacbcbaabdbcddadbccadcaaccababaaabcbabcdcdbacddacbdbbdbcacddcaddcbaaccdcbbabaadcbcbcabacdbdbcdbddcdbdcaacddbabbdaadcbadbccccdaaaacbdcbcbdbcbcdddcabbdbcbadbaacaadbbbdcbbdabaaaddaddddbdbcdadadabdcbabaacdbbdbcdabacbdacadbdcdbaaadadcdbbbdaddadbacbcabccbcabddadcbbabaabbdcdcaccbabcbcccbacbdcaacabdcdaddddbbaaaacbcacadaaabaddadbadabccdcbddbcccdababaacabdbacbdbacddbccadddccbabacdbbccccddbbabbaddbddaadbcabccccdddcaacadbcaddbadcabcdcbacacbdcbabadbdcdaacccbbbcddbbddbdbcabbcbdbdddbdbdbadcaaacaccbcbaacbdbccbbcabcacbcadcaccdcbabcbbdcdcadbdcacaabcdbbcccbcabbcabadabbcdcbcaacbabdaadbbccdbdbaccabcdaaacddcddadcdcacbcdbddaaadddcbdacbccbaddcaccbaabdbbcbddbadadbaddabacabacacacaabacbbaabbdbbccabbcaaadbaadddbbbcbbbacbcccccadcaaccbddcabaadbdaddbdacdbcacddabbadaddbacdabcbabcdcbdadabbcdacdbaaadaadacaadccaaaabdcbddabbcdbbbccadbdcdccabbadbcacdbdbdcabbbaaadaaabdbcbdabbcbacbccbaaaddbddcbbddabdcbdbdbdbcacbddaccbcdccdcaccdbdaacbccbabbdbcccaacbdbdabaadacacdbcabccbabbcbcadbacacaddcbabbcbbdabbbdbbcbbacabccdbccdaacdaadcdbdcadaccdabbcacbcbbdbbacadbabacbadadacbabdcccadadbacbcbccaabbdaaadaadbbcaccddccacabccaacccadcacccbcdcccaddabbdbbadadaabcabadcacdbacccdddaaabacdbbbaabcdddcdcddbdccbddcbdccacbbbbdcdccababaaabdcdcbcccbadadbbacbdbaddaacbbbbadacabccdadbdaacaddaadbadbabcdddcacbbacddbaaacbbdcbdddbcaadabadbbbbdcabdbacbacbbabccadadacadaddabccdbdcdacdccabcdccbcbbbaddcbdaabcaaaddabadcadcbdddbcbcccddcdbadacaccaabacacdcbaddcdbcbcdacbbbacbabcbdcbcaabdddbcdacabdaccccbacdbdbdccbdcbdddadbdacccddddbdacddbdadcbbdcbcabbaaacbbcacbcacdccbababbdcacbcaccacabbdbaabadbcbabcbdbbddbcdcdbcbccbddcdbaaaddcaabacccaaababbcbbbbaacdabbcacbaddaaabdaaadbadccbdbdabaaccdddcdbabbaddcabdabaadbbacbddbddbcbbbabcddcccbcdbdbaacabbccabcdbccaddbcdcdcbcdacdaadbccdbaccbbcdaabbbdaaabdcdacabbccabbcadcadcdbcbcbadbccadcbabbccddbdccddbcbadaaacbdbdcacababcbccbbdbdcdbababbbacdaaaaaccadddaacabdccdaabccdcddaddddccddcacabdbaabaccadcdbddcddddbcddcdabaacbdbcbdbcdcaddabcddccdacabaabccaaddadacbdaabbdbddbaccdcaddccaddcababdacacbaacabcbdbdaaaddcdcacdcbabbbaddadadddcbaddbbcdcbcabcbacaababdbbacccaadabdaabdbaaadadddabdabbaabdcdbbddcbadaaababadacaaaddddbbadcabcbbdadccdcaddaabdcaacacccaadbaabdcaadcdcdbcdaccbaadccccbbdacbcbbaaaabbdaaabdadbccccddadcacdadbcdcdcdbbcdabcdbabcbcacbbadacccbaabbaacbccbdaaabddacaabdcbabadbcdddaacbdcccacabacddcccabbddaccbbdbddcadbcdbcdbcdacaccdbbbbcadbcccabacabcdbadccabddaaaccadaababacddcbbdababacbaccbbadaacdaaacaadddbaadaabbcbabaaccccadabdcabdaadcaccbbdabdcbaadbddddcbcbddbdccddbacbdddababbbabdadadadbbcdcbdbbaaaacdcdbbaddbbdcccadbaaacdcabacaddabcbcbabbaaadabddbcaccbcaaccdcdcbbbbccacdbbddabdcdbabcaadcaadbbcccabdadbccdacadcbacdcccacbcabdcddbaabbbabaadcaabdabcadbcabbdcbccadcbcadcdabccdbbddbccdababbccbcbdabcbbababbcabaabadabadbabccbdbcdbadccbcdbdcaccbcdacdcdbdcdbbbacbcbcaabadaddabcddddacacabcddbdcbaaaccacdbdcdcdacacdccaacacccaaadbdacddddabdaaadbdacabaacbabdadbdddacbacbccabbcbbbaccaddbadabcaadadcdbbdadddadbdbcbaacadbcddcbacdabbdabdaacabbdaadbcaadcacdabcaddccbabadbcddcdbbdadcbacccaddaacbbcbddaaddcdbbadbaacacdccdadbdbdcccddbccdbabdcbbbcbbbaddadaddcbadbdcadaaaccccccbbaddacacbabbadadcbaababbcadbccdacccdcddacbcbbbbbddbbacbdcccabcbbdacadbbacbacddbbddbdadabcccaaadbadcacbbdabacaabaaadcdbbaacdcddddddcadcbdadabbbbdbbadadcabadaccaddaaddbdabcadcbbcbcddaaaabaabbabbaaccabdcbccbccbbbbbddccddaddcadacdcaddcaaadcdcdbdaabacaadcddadbbaacaaadcbbcbcccbcbccbcdcbcbdbbcbdcdbdddbcbdaaddbcccdcdbcbdccaaadbaddddacbbaddcccbddbbaaddcbddbdaabcbdcabbbcccaabbbcddcbdcbaccadbbdbdbacdcdcddbdcdadadbdabbcdaccbdbcdcaabadaacbccdacbbdbbcaacdbadcbabccdccccddacddbacadacdacdcdcccbcbdbbccaadacaabbccabdacccbdadbcdcacadaabdcbaadbcbdbbcabdccbdaadcdadcacccaadbddadddcbacadaabaccabbadbabcccaadcccdadcbaadcadbadcabababbdbbdbbcbbcbcbbaadadbadadddbddddacbcddbdcaaaacddaacadddcaddcdaadaccdabbcdddcbbbbbbbcccabcaaadbddcdcccacddccaaadabbbacaaacdbacaaadccdcdcbbcbcdbaabcdcbdbcdbdbdaacbcbbdbbbcdcadbbccadbacbdadddcacdccdcacbcacaabcbbcdcbccccacdbbcbdbcdaaddbccaabaabdcaacaadddcbacadccbdddaacccbccbbcaaadaadbcdcbdcdadcbcdaacdcaabddccdbdddbdbdbadaddadccddcbcbbbabacbccdbdbdbcbabdbbbbdbcbacbdbadadcbacdabbdbccdcbcdcdbcddaccbcdbadcbdaaabbdadbbbbdcacbbccaabbcccacbdccccbcdaaaabcddbaabacbbcababbddddbbaaacaabbccccacdcaddbbcbdcdaaadcdcabbcaadabcaccbabdcbbadadbdccdcbbcadaacaddaddbcdbcdcdacccbbababbbabbddccbaabadbcbbbbbabbcbdbdbaabacaccdcaaaaabdddddabbbaccbddcdbacadccbdcadacdbbdcadcaadddacdbacbcaddcccbcccaabdbcddadcaacdcdbbdbcbcddbdddadbacaaacdaadcccacbbdccdcbaabcdccdaddaddaabdcbcddadbcacadddadcbbcbcbbdcadccabdcbacaabcbccadadcdacababdcbdbdbbcdbbddbbaaccdaacbbcadabbbbdabadcdccabaaadadbcadddbdcdcbddaaacaaddadddabdcccccdabcccdbbcadadaadbcbdddcdddcbdbadbacbcddcdbbbccacbbbbddbcccbdaaddbacbccabdcdbdbadbacdbbaadaadaaadabdbcbddccadddbbcdbacdabdbddadabaacbdcaacaccbddabcaacdadcccabdbcbbccaddbdabccbcbadbcbacacacadabccbaddaaddcabdcdcadaaccaccdbcaaddaaccdbacadadcddddaabcaabbadbacddbaabaaddcbaabaabcdbdbacadcacdcdcddcdbdbbacdccdcdacccacabdbadbddbabacaaadcbcbaccaabbabcdabcdaddcbcabccadbbaccbaddddadadaabbaacacadabbbddaacdccdbccdaadbaaadccbadcacbbbadddbbbdbbbdaccdcbbadddccbaccadbbabcaaddccbdbbbcdcaccdcbdcdbbdabacddcabdcdcaaddccaaaacdadcccdcbdbdacaaddabbcbcdacdaadbbaaadcbdccbbdcabcabadcadccdcdcbbdbaadcddccabccacdbcbbaccaacbcaacdadcdaccbbdbcdacadcdadccdcdbddddcabdabcbccbbdbddcdcaddcccbabdcdbccacccaaaddadbaaccdadadccacddbdbdabbdcdcaabcadacddddbcbbccdabccbacaddaadadbdaccbdbcaacbdbbdcbadcdcacbddbdbcbdbdddcdbccdbcadbbcaccbdaabbbdbaaccbaadabbbcbddcbabddddbacbcacccbbababaabccccaacbccadacbbbbbbbdcacadbcaabaaacaaabaadbcbbabbcbbaabaccacbbaacaaacdbaacabbaccdcbdacaddcaadbdadcdddcbbadccddcadcbcdabacbddaacabadadcddbdabdabddcbbdadbbdcdbdcdadbadcdaadbbdbaacccbadaaabcddacbacddcacccbcddbcbbaaaccdabddbdcdabddbdbdbcadcccdbcbccdcdaadbbcdbcdcdadbaaadaabbcbaaccaccbcabdbbaddcbabbdcdccdddaaaddadcaacbcabccbddbbcabdcadaddcbcadcaacbdcbdbbcdcbccabbcdadbbdaaadacdcabadabcdddcabacdbbcbddadbccddcdbbadcccabdaacacbdacabdacbabadbccddbcacdcdaabbdccbbaadaadabdbcabbbcdadcabdccaabcbacdbcbbcbacccbcdcaaacabbaacdacdacbcadacccbbadcbcccadccbacdcdccbdadabbdacdccccbdaddbdbabbccdcdccadbcbbbaadbbcaddaaddaaaadbdbcadbdcdabdbcdabcbcbaccbaccacddbcbbdcbdcbddbacabdbccdccabbdcbacbbadcdadbdbdcbccddbdabacdbacaddaddaacbdacaabcbabcddbcaadaccbdbdbdddcbdddaaacdbdcdbadcabcdccabdacadaadcabbaccddbdbbbdaaddddbddbbbacbbcdbcdacbcbaaadcaabdbbccacdaadccaabcccbadbdabdaabcacbcaaacdcbdcbccbcdabdaccbdacbcaadccdaabacdbcbddccbddacccaadbbcaaadcacaccbcdabadacdcaddaddbbaaaacdbbcaabddbcaddccddddcabbbadccddddadddadabddabacaddcdcababdbcbabddacdbbdaaadacbdbccacbbbcbabdcbcbdcdaacadcddbabbdcadddbdccdbcbaaaaaacabdccabdbabbaaccbbbaabcaddbbbbbdcdccbbbadacabacccbdcabadcaaabddcadcdcddbccdcababadbcbdadadacdcccdcdcabaaadbaaabcabddccaddddcbacacdacdadadaacdcbbabdbaaccadbbbcbdccbcbdbbaadadbbdadbccaddabdbacdaaccbabdaccdabdcbadaaddcbbbabdddbddccbdcdbadcddabbbddacbaaddbccdaddcbcdbbcbbccabcbcdabdabbacabdddbcdccccdabdbcaacbcadabbababccddadacdabddccbacdbddbbdbdbdbbbadcccbbabbadccdadacacccccbcddbcbdaadddbbdcbbaabddddbccbcdcabcbcacbbcdbdacdaddaaacdadcbdddbaabcaadabcaccbcadbacbbabcbbdbaadbdadabbdbcadcacbaddbdddcbddcbabcbddbbbdaadadbabbbcdbdcbbcacdbbbacdccdbabbbcacbbcbcbcabbbcbbbbddcaaabdcacbcccabaadcdadbbbaaadbcddaaaadcbcdbadcbacadbdacddacbdabccdccccccdbcaacacddcbacbbbacbdadbcbdcaddbcacadbdcadcbbacccdaaddaacaaacaabccdbdcababbcbbbcccaadbabcbdaabdbcbcdddbdadcacbacbaaabcaddacaaaabccabadbbcaababacaadacbacacbdcddacdbbcbacccabdcaccdbdbbaadadadddaadcbccdbcbcbbbadddbdaabcbbbdbbaacdcbdabacbbcbacbcacbaccdcbdacdcababcabccdcaccdbbdcddccdbdbcccabbcdddacbcdcdbdbcadbdbddabdcabdddabaaabadabcabbbaccdaaaabdddabaacdbbcbacbccacdcabcaddaccbbabcadccdbabdacdcacabcaaaccccadbcdcddcddbabdbcabdbbbbdcaadbabcbacacbdcadaaabbbccdddacccdbdbbbbbcddcdaaacbcabcabdacbaadcadcccbaaaadddddcabcddbbdddbddcbddadbcbcdbbadddabcacccaabbdacacdbbadbabbbccbacdccadbaabacdbbcddabccaaadbcbaaaabddcabbdcbbabbbdcdbddbacbbabbabcbccdadaadcaccbaacbaabbdcacadbaabcddaddaacaadbadbadcccabbdcdcbdbbaadabccaccbccdcaabddbaaaaccbccaadaaccdbadabaaddcdcaabadcccabcaddcdbdcdbdcbddccccacdbabdccbbcabddcddccdbcbaacaabbcbcdbaccbaaaaccabaacdaabddabbaaaacdbadcacbbdddccccbdbcdbbbbabccbbabdaacccaacddcadaabdbaabbcbcdbcddbcbbdccaadabadddacadaccacbbbbbcabadcbaabdccccbddbcadaaacaaabbdbccaacddcbcdccabddabaccaabccadbbdbbcbddacdbaccbdbcbcaaccbabbbcdcaadacdadbbadaddbcbcdaddccaabcbbcbdbdaaadddcacbcbcacabddcddabcbbdaddcadbccbbdabbdaaacbdaccaaadcdccddadcbcbddabbacdabbdbcdcccaaadcccaacbddbaaaadddaccbdddbdbadbccccdbcdccdcccbdddbadbaccdbabbadacbdccdaaadccaccdcaccdcbababcdcdcdabcacdcacdbccbdaadacabddcbdbcdcbaabdadbddbaccbbbcdaadacdbbabbdbadadadbadbaccddabddbcbadaabcacdaccdcdbcbbbdacacbacdcbdcbadccdacbaadbaacbadbacadbbdbcbdccbcbaababcabdcddacdccdbcdaaddddddacbcadddbbcbcbaaaacdbddcbcbaddbbababdcdadadcbaabaddbbdcadbacdcdabdaacdcaccabbdcdbbadadcbbbbacadcbadbddcccbabadcaaabcdadabbbcbbdacbadabddcdcbddacaccacccdbaadccacabacdccadaabbcabbabdcbdcbdbabdcbddbddabcddbdcbaabccdabadbabadcadcaddbcbccaddcdabbdcbbbbcdadaddacbbcddbcccbdbcbdbbdcabdbdcaaabacbbcbacdbbcacdccacdcabcabdacdbbbcabdcccbababbadcaacacccdbccddbddbbdbcdcdddbbdbacddbccabacadabaccdcdcabccaaaddacaabadcccdbcaadbcdaacadbbdabacbaccbbabcbbdccbccabaaccdadacdbbbbbbbcaabdddbddbaddbadaacaddcaaaacbbcddabbacddddbdcdbbcadbddbabddcddbacccdbddcccabbcabddabcddbdabbdaacadcbcdadbddbbdbababdbacdbcdcbbcdabbaddcbbbbcdabcccabacadabbcaddaadcbbddbcaccbabcdcaababddbacbbdaddbcbcbbbcdbdcdcbadcdacdbcacdcbacacccbcadadddbacdbaaadbacbccbbdbbbbbccccdddabddccdaccbcccaabcdbcabdbbbdbddbabaabcaadaadbccabbbbdbdbccacddabcbaccccadbabacdaaddadbaacacccbddabaadaadbdabcbadabadabbccadcbdaadaaababcdbddcacabdabcbdadaaccabcaccbbbcbbbdbbbaddbccaacdcdacbccbadbccdaabcbcbccdacddbbcdddccadcdbcdbcddddbddaabddbdcbbdadbaccdaaccabadbcbacbbabbacacaaccbdaabccaaacababdaacbbadddacdabcbaadcbbccacbccaaddaabacddccbaacaadaacaadcbdcdaaaacbacbcddbcaacbaadaaacbbbbaaaccbcdcccbbacdacadaaadcbddddbbcabababcdaddacacabaacadcbddbbdbcbdbccbacdaddcccdccaccadaadcdbcacabdcdbcddaacdbcbacdabcdadabdacbcdadaabddbdddbbddcdcadbbcdddaccadcddbcccdcbaddabcbbdabddbdbabaaadabbacaabaabbbdacbdabcbbbcbcbcaaaccdcdbbdbacbabbbdccbadabbdcadacdbacbbcabbddaadaacbcabcadbccabccadabbccaaacabccaabbbbaccdbadacdbadabaabccadcabbbdabaadddcadddbaacddbcdcaabbdccdbdcaaabbdbabdcbbccbddbdcbaccadddaddbdbbadddbcdcdbaabddbcbbcbacbadbbababaacbadbaaddbacccacaccbcccddbbdadcddbdbbadcbbbdcacdccbdcddcdddbcdcddcbbbbbddbcdcccdacdabcabbbddcdbaadbcccbcdabcadcdccbcddccdaddaacbdadbdcabbbacbdbdbcdbabcdbcbcbcccbcbcabbbaccddaabcbaadacacbbcabddbbdcbacccbbacabccdcdcbbabcdaaadcaadcbaadbaabcdbdbbbcdbacbddabbcacdadbaacdbdccaabbbbdddbddddacccbbdaccdacbdbaadaddbdaabbcbcccaccbbdabbcbacbbbacddaaccbcbababcdcccaaaaacdaacdbdbbaaddacbdcdbbddababcabcacdbbbdaaccccbccccbbcccaadccdddbadbdddddaabbaabcbaababaacacadcbbdbcdcbdbbbbdcabcaccddccabccbbdabcddaddacbadabcbaabcdcdabacadbdacbacadddccaaacaddcaabacddccdbaacbadbbacddaacacabdabadaaacadbcacaacbdcbbdbcbadcdcbbacdacbbbdabbdbbaaabccbcdbdacccbcdccbdddcddaabccabcbbbcdbdacdbabcacbbacababcaabcdcaacabdbccaccbbbaacdbdccadcadcddbbaaabbbcccabcccbacadddcbadaaddabaacadbcdacdacaacabddcaaadbdabdbcbaccacadddbcbdcbdcdbaabbcadcddcaabdbddcabcaaaabadadddccadbbacdacbdabadccbbabbccacbbacadaadcbbdddcddaccadbaaabcbcdddbcacacaaacdaaddccacdbccdaaabacbcadcbadaabbddbababcbbcbadaababbdabdcabddbbdadadcaddcbbabaacabdccbcdbccddcbadcdccabdababbccadabaacddabcaaacbddbadbacdbacccddddcacdacbdcbccccccbddbbdcadcbabacaacbbcdbcacdcadbdcdcaaaaabbbaccabdcabaabbdaccccaccacaaddcdbadaadaacbadcddacabdcddbccccdcacaaaabbbbdbcadcaaddcabcacacbcdcbbcddddbaccacbbcdaabccdbbbcdbbdaddbaacbdabbcabdcdadaddacadddcbadacadcaddcdadbabbcdbacbcaadadaccbcacdccbdcaabbcdccadadcdaaaabddaddccdddddcacadadadccadcbcbabbbaadddbddabcbdaadabccbcdcddabcdcdccabdadccbaddbdacaaddcacbbcbbadcadbccadddabbadbacabcbadbbbbcacacadabdbbcacdbabbcbadcbbbacbabcccbcdacbcadbddcabadcdadadaadacdcaabdacaabcbcaadcacaccdadcabcaccbcbdbadaadadcaacbcddcbddbcdbcaabcbbbcaadbddbdadbcaaadddaacbacdcbabbaaccbdaaccdbdbacabbbaadbcadcdcddbbccdabdccdccbbdcbabcdcacbdadcbcbaacadbbcbddbabbacdbcabcaccaaabdcddcddbadcaddbdcccdcadcacbdcbacdbabbcdddcdadbbdbbcdccacddaacbbbcdbbcaaababddbdbdbdcdabccbddccbcdcaacbbaacaccbadccacadbaacaadbdcbbbadcbcdbbbadcdddacadadbccbcababbadcaababcbcbccabbbdabdccdcabcddbbddabcabacbbbbbbdddaaccbdbdcddbcacdddbbdcaabdbdaddcaabaaacabccdabbaacacabcacdbdbbddabbcbaadabadbbbaddbaabbccbdbaccbdaacdbabdbcbabacdbdbdddcaadbcbbacbcaacacacacddabbdacdccaaaccbbcbdaddcaaaccaddddababadbdaadcabcbbdacddbcdcddbcdabbddadccbbacbabdbcadccbdbcabbdadcabbddacdbdcdbbbdabcadabcdccdcdcdaaaccadadcbbdadabccbdbdcbbdcadcdcdbacccbddaabcbbbbcbacdadddcdcaaadabbbbddbdcbcacccbbddbbbddabbdcdbdcbbdcdcbcaabdcaddacaaccddbdadcbdccbbddbcabcbcbddaabdadccddbcbcaabbdbccadacabcacbccababbcabcdabddadabacccbadabbbcabacacbdaddaadccdabaadcaacbcdacbacdabbacbcaacaadbbbbaabcbabbbcddbddcaaaaabcbcdbaddadbaccbabcbadadbdcddadacbabacddcaacabadbddcbddcbdcbbcbcbdcacdcbccbabbcdacababaddbddacdcbdbbccdccccaddbcdababbcaadccacabdbcbdaaabdcacbdbdbcbcdbbabbaccadbcdaadcbddacddaacddcdabcbcbbbbbbaabbdcbbacbbcbabddbbdddabdbbbaacdcdbdaadddbbcccaabdacbbcacdbdadcdcdaabbaaacbaabcadccbdbdbadadddbcaabbacaaacdcbacabbbcbabdcccdbacdcacbaccbdcbcbacbcaacababbbbcbcbacabbdbdaabcabcbcacdadaaaddaacbbbadddabbabddddabdcdddbadbcbbdadbaacbdaaaaacbdccbaddbdbdbadbabccbcbcaccadbadaaccccacaccdddddcaaddacbbabdcdaabaccdadacdbbdbbdddddbaadcdbabbbdcbaccaacadcaccabbcdacbbadccdbacbdcbbbdadcbcadcbccabddbacdaabadaacbaadbcabdacaadbbbdbabcaccbabbdccbacbacdaabbddacabbbbacddaddacbacaccabcdbcdcccdcdabcbddbcaccadabbbbbbdbddadcdbcbbbdabcbaaabccdbacdcbdbadccaaaccaddcbcdaaaaaaacbbcabbcacadcbcadddacdbcacabccadcadadbbdaadbcccdabbabadcabddbaaacacdacbddbcccbaadaaadbbdddbaacddacdbdcbcbbccaacaabcbdbdcacaadccdacbbacbddbdabcccdadbbaddbadbccdccbdbbdadbadcbdbabbadcaaccddcacdcdcabddbbacbccacbaacbdadbdccbdbaaacaacbddbddcaababbadaccddcbbbbcccccbdcadddabddbccabdacabdbbbcbdbddcdccaaddaacddadbbcdcadabcadccddddbdbabbbcccacddcaadcdabbbcdccbbdacddabcddbbcbaaccbcccdbbddddbdcdbcabbaadbdcabcadbdccddbdbbbacdddbaccaccddacabdcccdddcaddddbddbbddadcddaadacaccdcabddacabacbdccbbddbbdaacdcbddacccdabcdcccaaacdcaacdabcdaddbacccaacbdbdcdbadaaabadbddcbcbcabddcdbaaabaabbccabaccddabaadabaddbacccccbadabcdaabaaaabbbadaadabbdbaccabdbdbcdbdbbdacbdaddccdbacdcbabcccdbaacddbbcaadadbcaccaccbcbccddbabdacdadbcabcacbadbbdcdbdadadaacaadbbdaccbbaccadbbcbacadcbdbabdcbacaccacdacccdccbadddcbbdbabaaddcbcbcddddccbadacaccdcaccdabbabdadadcbdbcbabdbbaaabadabbaacacabcadccccddddcccdcdacddcabadaadacbaabcabbccdcacccadadcaaddcaacabccbacabdaabaccbbbacbbddaabaccbcbdbddddddccabbabbbdcccbcbdbcdcdbcccdccdbbbccddaadbccbbabbdbadadcbcdaaddacdacccdadadbaccdaadbddaaadcbdbcddbbdabbccbcaacacbcdcaabaddcaacdcadddacddbcddcddadbdccbaddbaccadbcadccbbcdcabdccabacdbbbbbbabbccccdadddbcdbbbccabccacadbaababaddddbccbaadcaddbabddddadccddaacddbcaddbadbdaabcabcdcbaabcdcadbbcdbdbcababccabbccbbaadabbbcddbbccacddadcdcccbdcdbadddcdccbcdcdcbdcdbcccbcdaccadcadbbbbbcdbbdbbdcdbcbadacdaccdcddaababacaacaabcaccbdcdaccccddbbbdcbdcdbbccccbbdcdacadcbddcacccbabcdcccddbdccccbbcdbdbaaaaadccdbdcccdbaddbbdbdaacabccdadddbabbadcbdcadbbdacacbcbdadacbdaabcbdaccbabbadcbdcaabccbadacdaddcabbbaabddcdbaadcbbccdcdcaabcdbddcbbaaaaabdcdddaabbcdcaacdcbdadacbadccaadcddbcaccbbabbacccadacacabddbcdbacbcaadabbdbdcbdccbbcacabbbcbdbaccbacdadddcbdabcabcccdbbcccbcddaabacaaddbbbaadcabcdcdbbadabcdadbbccabacbacabdbbbbbcabcbbaacdabbbbbbadadbdbccbdadcdbccadbaabcdbbcbbdaadbcdbdddadbccdaaaadcbbaccccbdaccaabcbabdabccdacbbcccddbacacbacbaaddddcdbaacabbdcaaddacbdadddababaabcadcdccaddbcdbaaababddddacaadddbcbcddcdddcaaacdaacbcbadaababbaabddcdcaacabcabbadaabacbdacbbcbddadbdbdcdbaccccccaaccacccdaabadbddaddbacabbbdcacbbaddbadacabbdaaadbbbbddbbcaaacdccabccabccbcabcbcdcadaabadadbdacadbccbdddbccdccbdbabadddbabbcdabbddabddacaacacddcacddbddaccabbbbdcbadbbddccaccbdabaabacbacbcdcaddccaaadbdcdbcdcddaabbabadacbdaacdbaadcdacaabadbcdccdcdddcdabdaccbbacbabbacdbdcdaccccbadccdbdaccccbbbdbcbbcdadbddbbcabdcbabddccbcaaddcbadadaaccbaaadadcbbcaccdddcabbdcbbaaaaadaaabdaaaaabcdbcbbbdbabdcabadbccabcdcadacddbdaabaadbabbbdbdacdcdcdbddbaaddbdbbbdbddccddcbadaaacccbdabbbdcdabcdbadadddccdbcbdaaadabccabadbcaabdaaabbccbacbbaabbbcbcbdbbbdacbdaddbccdbdabddbbdddacacababbdbdcaababbaccabddabaacaabcdacbacbbdacbdbbccdcbaabaddabcaaabdcacbdbaccbacbabacdbddabdadaccdcbcabbcdaadadaccbcaccbaacadacbabbaccbdaacbbccdddbbdcccbddacabbdddaaaadacccacabadabaadabbbbaaacabbdcdbddccdbdaaddbaaaabcddbaacabccbaaccdddbabddaadcbadcdbdbbdcccdbacbbaacaddbcdbbbbbbacaacbbdddabacdbadcaccdaddcabaccdcdcacacabaddacccabbdabccccbcdcbcbddabbacadadcadadaacbdcdddcbccccabccacbbccccdbcacbcdabdadbabccabaddadcbccaaccbccacddcabccdaabccabaacabdccdcdbcbabcddccadbbbabbadcdbcccddcaacdbdacabdbabbcadbbbdaaaaddddcbdabcbbbbddabaccddabaaaddcbbddddbcadcdcabcddcbbbaadccabbdddbaaabdbaaabddbbaaaabaacbabaabdddbcdbcbabbdcbdbcddbadcbbdbccacbcadadcadbdbacacaaadaccbbaccbaaaccbbcdcadcadcacdcabaddcdacbddbacbbacbaabcbcaacbbbcababcaadcccbaabacbcacdcaddbdaabdbbdacbdaddbddacbdbcdcdbbcbdabddbacbabdbaccdbbcbbdabbcbcbcbbccbbbbccabdbabdbaabaadddcadccbbbdcdaccbadaaacbaacdbcaababdadbdcbddbdabcabcabcaddadbadccbaccdddaddbcbdbbdadcaabbbaccaaddddaaacdbbbaadadbadbdcdbaabbbadcdbccdabbadabddbbccdddcaadadbbdadaddbccbaccddcbbdccacabacbddcaddccaccbabaabdcbadbdbacccbcbcbdbbcdcbcccacadccaabdbccbdabdbdbdcddabcaccbdbaaddbaadababccccbabbdabcdbbbbbddbbabddcdcdbdbdacbbbbcbcdcaadbadddbadcbbcdabcdcaaacdaddbabdbbbbdabcabadaaaadcadadcaadadcacacbaacdadabdcabdaacbbbdcbacccbadcdddaaddbdcdaabaacdadabdcddcbadcadccbbdabcaaaadccbadddddcbccabdcbccbbbdcddcbcccabadbdcdcadcdcbdabddbaccabdcacacabccacaadbcdcbddacaabcabcddabaacacbcbbdadcaccbcbbcbcbbbbacabddcbacbacdcbbbcbbbbabbbbddbbccaccbacaccdbbcbcccdbccccbdbcdbaddadbbcbbdbddaccaccbbbcbacbbaadaccbabbdcbcdbcdbcabdaaadbbdccabaddccddbaaaaacbdabdcdacdcdcaabaaaddddaddcdbbcddbccdaaacddccbbadbdcbbdccccbaabdaacacacaaccdcddacdadadaabadbbddbabadaaccdadbbacaccbacbdddbddabdbcdabcdbcdabdcdbbdcbabcbaadadbdacbcdaabddcaadbcbccaacbcdabccacadbdbccacbcaabccbcddbcacdbbcdadaccbdaadccbbcadccadbaaabcbacaddbdbddadbacabccdbbdddddacbbccabdadababddcdccabdcdabbcabcbccdabddbccabacabacbcbcdadbabbcbcdcabababaacbbbdbacccdccbaddbacbbcacabbbcbccaadbccbcdcbabdccdbdcddcbdacdbccdadabadaccbaadcdcdbacbacadccadcdacdbddbbabbbcddbdbbaababbbabdabccbbbbbadacddbdaabdddcddbcdcdaacdbdccccbdcaaadbbcacddbdacbbadbdbccacdcddbacbddbaddccdbdcdadddddadccbcadacdccccdbcadcabccdaabbbbacdcdcbddcaccbdbddcacaacdacadbaabdadbacacacaadbaaabcadbbabcabcdcdbdbdacabdbadbccbaacbcabacdbbbcacbaabbabbdbdccbddcacbcadddacadcabdbdddcbcdcbbbdddaaaabcddcbadcbdccbbaadcadccabcabddbdcadababccdbabadbddabbdcccbbbbcabcabadcdbcbbbccdaadadabbcbdbdacdbcccdbdadcdcbbcdbdadddbcbcdcddbbacdabcddbccababbddcbcacaacbaaaacddaaaaadacbcadcadadbabacbbbbdadabacbacaacbcaccadddbbbbcababcaabadccbdddddbbbdbccaabcbbaccaaaadbaaabdbcacdbcbbdbbadccbabcbadbadddcaddcdacbdbaddacbccacacdaacdbbbcddcbbdacaadcacaaddbbbcdbdbaccbabcbdddbbbddaddccbcaccaadbcbababbacadddddcddddcabdaabcdadddadadaddcbdaccadccadabbccbbacbbaaaacbacbcabbaabacacabcdcabbaccaddcabcbbacadbbaaccacbaadaccbcbaadccdadcddabddbadbdaaaccabdbaaacbadbbdccbacdccdccdcbabbdaabcadadcbacbcbcaaaaccbccadbcdabdabdcdbbababacdbddadaabdabdccdbacbbdaaaabdccacdbbcccbabbcabcddbcaacaaadaaacbdbddadacaddbaaabcccabcddbcbcadcdbcbdbacdbbbcaccaabdacbacaadbcccdbdcaadccbaddbdcdaabcbbbaabdadbcbbdcacbbdbdbbcccbbcbcabbaacabbdbbaddadcdbbbdadbcbdacdadcadccaddbbdabcdcbadcbbcbbcdbddbbabdadbbaacadcaabdbadacbddbbbdccdcbbcbabbdcdddccdcacaccbaadaadadaddcacbcacddcccaabacdbbacbbbadbcdddccddbdccbdacbdaaccbddcbbbddbabaaadcaacbddccbcbcaddcbababacbabccddbcccbaacdccdcaabccbadbbcbdacacbbabbbbaaacccccadabcdcdcdcbdbdabdacbdadaacdcadddacbaadccdbcbadbbbcacdaaadabdaddcaccbaaaaddaabdbcbaaaabcdbdacdbddcadbcaabdddccbdadacdaaacdacbccaaaabbdbbacacadbdddcdbdbcadddacaabdcaccdacbcbbabbbcdbdcdccbcbdaddcabcdadbbabaacbadcbacdabacddbabcdccccddadcaccdaabcdbcdcccbdbababbdabcadbbabcdcdaddbcbdbcdcbcacaaabbcaaddcdabbbadccddcddbcbccaaaccdcdddccddacbaababadddccaaddaacdddacbbcdadbbabbcbabccbabdccaabadacababbccbadadabdabddbbbcdcabaabcccbcbacabbdbdbbaacaccbdcbacadabdbcbcdddddbdbbdbadaaadbdccabcbdcadaaacadadacdbbacbaadbcabacacacbbabaacdccdcaccadaccbcbdcdcbaabcacdcbdabcaadbadcdaaddcabbdcdbdccabbaabbddcbbacbbcdadabbabcbccbdaaaccadbacccdababcbdcbdbaaaaabbccbcaccdcdbbacbbddcdcdcddddcddccccccccbddacddccccbadcbccdcbbbdacaadcadcacbacbbdbadcdabbbbbbcccdcdaddddbdcaacacdbdcdbcbaadcddadddccabbdabcabdbccbddaabcadbacdcdaddcadabccbcdbdbbdccaddcdabdcabbbdccdddcacaddcacbbdcbddbdbbcccabcabcddaaaaadaabccddadaddbcbdabacccabbaccacadbdaaadabcabbcacbabacccbaccbcbbcbacbbbbcccbdaabddbcaaacdadabdddcdbbaccbbabddabacbbddabccdbdcdcacbcdcbbdcadcdbcdcbcdbdaabcccdbbdbbddbbcdcbabdcdbdadbdddacdbcbabcdaacadbdbccadddcdacdbbdcacaddabbadaaacaddbcbcbbaaaddcdabbaddcbccdccadddaadcdbcabdabaadadccbcadbaadadccbcddddcbabbacbbbccaacbaabddcdbadaddbbcdabbadbcbbcddabdaddddcbbbdcbcadcdbadbdbddbbcaabbdbdcaacdabbcbbadaccbddccdddacbabbaddcbddcdcbdbccbbcccbbcbbddacddcbccdadabadaadccbcbbddbdbbabdcacccdbadbdbbcaaadaaccdddaccababcbbbbddccbbccddcbccdaacbcbbdaddbddbbbbadbabdddaabcbadabccababcbcbcababcadbbadacadcacaadaccaacbcbdacdcbccabdacccaabbdacbbbbbdadadabbbadcdddbbababcbbddbbdddbabdbaaaaacdbadbbcaacdcbdcaccbaaaaccabacbcbddacdadcaacbbaaacbdcabdddbbaaacdcaddccbaabbabbaadcbbccacacbcababcbdccabadcdbacbbaddabcabccaacbbdacabaaadbddbbbbacccaddbbddbdccbaaaaadbdbdcbaaddbddcbabadccaacbadcbdaabbcccadcaabccabdddbdaacacabdaaccbddbdabdbcadabdbabcabcdacccadadabbdcddbccadaccbbdbabccdccaacaabdcdcabddcdbcdadccadbdcaaacdcdcabcbddadcdccddbdacacddcbcdccbcbcbbdaadcaacdcbccddbbbcbccadbcdccaccabcaabbadbabdbaccadbaadbdaaddcaadbcdccbadbdbaabcbbaacbbcdcbdacbababcdaacbbbbbabbadcbcbcadbbcbbcabdacadcacbbcacccdccabbdabdcbdbcaddddcaddbbdaadaccabcdbbcadccdbdabadcaabdcbdcccccaabcdccaccdbcdabcacadcdbddbcabacbcbdccbddabbaabdabacbbdddccccbdbcbdbcdcdaddaabacbabbddbbbbcadbaccccbbcbdcbcbbcddaaccdbbabaadacddccdccacabbcacabdacbaaaacccbbcbdbabcbadacabcbdcdcdaabdaadaccabccbacaddddabdacaaaadccadbadbbabbcbcaddbdcddbadcadcddcbabdcbdaadcbaddcdcbbcbbadaacdcaccadcdbadbcbacdccbbccddaaacadbacdddccdcaaabaacccdcbbbabbbcabbccddcccbbaddaccacaacaabbadadbdbddbdddbbcbabbbabddadddacdbbddbcdabdddbdabbbabdcabbbdbadaaadcadacaaabaabbbddccadccbbcabaabbadccbdcadcbacacacdadbcbdbcdadaddaacbacabdaacdcdaaaabaddddbdacccddcadbddbcbdccbcabacdcacaccabdbdddbadcbdaaacdcaaadbbcbbcabdccbddbccbabdcdcbbbadbdaadaabababcdbadacbddccbddcabcdcaaabbabcdaaaccdaabadbbcbbbaccdaabdbccdcccccabcbbdcbdcdbbabbdbcabcdccdbabccbbdaabddcbaccdaccddacbadcabcabccadbcccbcbacaaaddacdcaccacadabacccbaadddccaacacbcbbabacdbdbaccdbaabbdaacdbcdadacbddbabcbcdaaadbcdaabbdbdbdbaaccabbcdabbacbbccbbbcaadabdddddabddabbbaaccadbbabaaccabccbadbabdcabdbbcdaacbcabcbbabaababacbbcddbacdcddcbddbccabbccaaabdadbabadbabcbcadadccacdcbabcbbdcdddddbabdbcbdddbdcabacdabbcbaddacaacdbdaddbdbacbbabcbbdabddcacbbcdbbbbacadaacddbbcdbabccbdccacdbbbcbbaaddcbcdbacdcbdacccacabcdddcaadbbaaddaacabaaadccabaddbddccadcaaaabdacaccdbbdcdbabbdcadaaaadbdcbbbabcadadbacadcbccddbbacccdccbcccbdaddcaabdabccbcabccbcdbdaccbcdccaaccdbabcbbdbdacdadcdbddbccdacbcdcdcdcdbbdccbaadddcddccddadbaccdccbcbccdcdcadcabccdbaacdccdcccddaaaaacaaabababbdccaabbcdbdadabcacbabccdbcddaaacbbacdbbcbaabaacabddbdbdaabadadabaacacddcaacdaccdbbbacbbabbbcbdccddbcaddbbacadcacaacadcbbbccccddcdccacabbccbdbcabbccbdcaabdadabaadcadbaadcabbbabccbaaacdabddbddbcbabbccbdbcbdcccdcabbcacccdbddccaacdaacdcbcdbcccadaccbdbbacbdbcdbcbccbdccabacbcaaabadcbaabbbbbbabdaabbbbcbbccaadcaccabbdacabcacbbbacdadaaabadbdccdbaccaabbdccbdcadbcccabcdacabbaacaddaacbcbbdbabcadbacbccabbaadbcaaadddacbdbbbabbcbcacddcdccdacbaadcbddcdbacadbbbcabbbdbbadacbbbdcaaabdbbcdcddcbcdbbdacaccccdbacdcdcccacaaccdabaddacddccbcbdcdabcabbacccddbcdaabdcdcacacdcdbcbbccbaacadddaaaadcacaddccbcddbdadbdabdbaabbaddcdcdbacbbbacdbbaaadcbcdcbddbdcadabdaaaddbcccbccaccbdbdbbbbddaaccaaaabddbadcbbdabcbbddddbdacabcbcbadabacbcdcbcabdccdaadddddddddbdabbadadaacadddccadcdbabdbbacbbabdaadbddaaaaddddcdbcacbabcaaaddcbbdddadcaccddaccabbbabbaaacabdabcdbcccadaaddcadcccadadcdcaccbbcadabcaabcadacbcbdadcccbcbaaccbcdbabcadbddbabdbdddcbcaabbbddadddaaabdabbbcbdbcaaaacbacbaaadbddaacdacbccddccddadcdacdccccdabdbbbbbabcaabdbbdbbaccbdaadbcbdbcadaccaaaadccaaddabbabaddcdbdaabccaaabdbaaadddaaabdbcadcabdaadbdacadccbccdbacdcdacaadbadcbbdadbadbcadddacddadcbcccaaacdadcaccdababadcbcabbabddacadbacadcddcbdcbbbcadbadbbbbbccbacdbbdcbaddccdbabaaccbddcaaacadbbadcdcabbaaccdabbaccdabacaddaadddbaaabdabbdcbbbcbcccdabbcdbbadacdbddbdbcadcdabbdbdabadccaaaabcdbbdacbbbabbaadcabbccdcddbcdaccbccadddadbabdabbdbccbaccddabadcbbaabbdcabdbcbdbbbadabdddddabbcacaaadcccccdccbcccbacdbcbcdbbcbcdabbdacdbddddadaaddacaccaacbcacbcbddbdcbbdbbdddbddcbdadcadbcbabddbcaaacccadabbddadaadbddbaabddabbdcdaddaadbacaaabdcadaacbcdbdddbcbddcccbcdcccccdabccadaaacbddcbacdbccbbbaaaccadcdbcaabbcacaddaadcdbcbccaabdaacbcdbaddaabcabbdbaaccbaadaccdccadddcaaadbcadcdcdddcbdcdbacbbbddacdbbcbbadaaaabdadbccacdaccddddbadaaabdbcabbcaaacbdbddcdadcdaddbbcbbbaadabadbadabdddaabbbcdbcacaadbbdcccbaaacddbacacaabbccddaddbcadaaaacadacbacaadbdcddccdcaccddcbbdcccacddadabaaaaabdbdabddcdadcabaaddcddcdbddbdadadacdbdbbacdaacdaabbaacadbcabdddcdddbdcddddadbaaaccccdbcbbabccbadbdbadaccbaabcdbdbaadcdccccaabcdaadbddbadcdaddaddcbaccaaabdbdcaddcadaaddcbaadcbdcbbbdbcbbdcdcbddabbadabcbdadccaaddbbacdbbaaabdbaaaaabccdbddaacbcadddbbbddbabdbbccdcddcacbcbbccdadabcabaddabdbbbddaacadccddabadaccdbcbbcbcccaadcdcbbbbcdcdcadaccdaadccbbbbdbcbcdcaacadbabacaccbdbdcbcbdcbbccdcaacdbddcbaadcdccbbbabdbdaadacbbbccbacccdbcababbddaccdabaddccddaaaadcabbabbdaabdabdabaccaddccadcbdadbbcdaacacdbbdaddddbdbcdcaaababaddaabbccbdcbbabadbabbbabaccdabcbbccaaadbcabcdddbddbbdcaccaccccdcbcbdcbbcbdbdcbacacbbbddcbcbcbdddcbcdcbccbddddbcdbbabcbdadaababbbdbabbaabaabbaccdccdbbadcddddbdcbcacbbaacbcaddbcadabcdddcbdcbcdbdaadbdcbabadbcbbbabdcadbbbbddabadccabdadddabcacccadacdbdbcccbaaddaaabdcbdacbcacbaddbcacccbacbadccddccdbbaabdbdaadbdccdbbcbabdcddbbdbcdbbdababaddcbabacdadbbcabaabdcdaccbabcbcabbccaadddbddcacacccaddacdacdcbcccdbdcdbbababcacdbababdadbbcdcdaacdbbcdacddabcbbcdbbbdabccdaadcaaacabcbccababbbcbdcbbaabbbbadbcbddadadaabcaabdababcddcaddabdaadbacdaddcbcabdbaddaabdadddacadaaababaddaaadcaaacdacaadbcabbbccadcaaaccacbbcdcaddccdbadbabcccdabcdbbcadbdcadbbccbbbacdcadadaddcbadbbddcabadccdabbbacbcdbddaaacabcaaacbdcdbddabbcdbccadcdacbdaacaddbaddbccaabdacccdcdbcbbbccbbaaccbadacbababcdcdaabdccaaadccbbbaacabaadbcbbabcadadaaddbbdccadccbbacdacdaccbdccbacbadbabdaddcaababcccccaabacdddcdbabadcdcddcbaaabdcacdabaaadcdcacaddbadbddbcbaccbbcadbcdcbcccbbadbcdcbdcbbdddcbdaadbbcadccacbbabdacddabddcbccddcdcaaabbbddbacadbabadbbaabadcdbabdabcadcbcaacbdbabcadbcdbadcbbabddaccaddcccaddabadcbddbddaadbaddbddaaadacdcdbbbdddbacbaccbbbadbdadabbcbacabdacabaaaacaaddaddbaadcaadbbcaabdcbaacdccdbdbcaababdacaabdbdbdddbbabacacbbabadabcbddddbabdbacddabcbddbcaacacdbabadbacddbabaabdbbbabdabcbcddbadcccddcbacaddaccdadbcbabdabdcbaccacdaccadbdcaaabdbbddcdccdcbcbbcccacbbcbdaabacdbbdbddcbcabbcbcdcaaddcddcddbdddacccdaabadaaaaaabccdbdbcaaaddaadadbbbcadbaccdbbcbcbdddcddddccbdcbaadabdcaddcbaacccccddcbcbacacacdbadcbccabccdccdcdabbddcbaaaaabaddbaddcbaadcdccbbacadbcadbcabacaddbaccbaadacacdaabdbaccdadbaccdcaccaababcabaadabadcaaaabddcbddacbbdcaddacabcacabdddaaccaadacddacccbacdaccbdabacacccadccbbdbacdaadbdbcbdadbdbcdadcadcabcbdbbdcacbbccdbdbbbdbcbddaacbabbcbdbadbbcadcadddcdbbddcabbbaccabcacdcddabbdcbcbdbdabbbbcacabcacdbdabcabcbaabadcdbabbdbaacaaccccbbcabaddbccddccbababccbdcbdbdbcabbbaaabcaabaabcabcbdddaaadbdaaacaccdbbccbdcbbbacabadacdcdababbcbcaabdbcdcbccabddaddacdacbcbbdabbadddbccabbabdbaadabcbbadabaabccbccdcdcaabcbccccddddbdcdbdaddddbbbddbcbbdddddbbabccaaaabaadcbabbabadaccacbbdcddcadbcababdbbddccddcbbabbdadddabbbbcaabadbcaddbcdacdadcdabcdacdbdcdcabdcbdcbabcabbbccdaccaddddbaccccbaccdbdaddccddcccadbabbbdbcddbcaababadbdcdbdcccdaaaadaadddcccbaddbaabdcabdddadcabadcdbcaddbcbdbcdcdaccacadadbcbaccbbbcabdddaccbacadbbdddaccbaaddbbbcaaddcacacabbdbadbacbbbdbdccbcbcdaadcbacacaaacdcbdbaaddbbbddddabbaaabdccbbddbdcabbaababdbddaabcadadbdccbacabdabccadbccdbdcbddbbdbaaacccddbcbaabbdddbdabacbcababbdabbcccbacdcddbabdabdbdcddadbabccadababacbccccacdbaccdabccbcdaadabdbacadbdacddbcacaabbbbcbadbccadccaacbbadaabbadcdddbaccbdabcbddcdabbbdacadcdcccbabdcbabdddbbddacaadababaabcbacabacccccbbccaacbbbcabaadbbbbdaadbcdbbbaabcccdcdcbbcbadbdbdadbbcbbaabbbaaabbbabaacaabbaaacbbaaababacbdccccddcbababddbcdcdddbdadcddcdcbcadaadaccabbcabddbccccabbddacaddcadbbbbdcabcbbdcdababbacdadaacdbabcdaaccbbdddabbaccbbabbdbcabbaccabacaabacdbbdbaccabcddadcacdbdabdbabbdbaddcadadbaddaadbabbddbacacbcbccdcabbadcdbcbaaccdbbdaaadbdacdbcaddabdacbdbaddbdcdaabccbddcdddcdbcbdcbbaaacdaadcabacbacbbdadcbcddacaaddcbdbddbdaacaddbdcdaababacbdcdaadaabddcddcdbdcddbbccaabbbbdbcdccdcddaacaacbabcacacabcaddacaaadaacadddbacababdabdabcacddbbadcadbcdddccddcbbcbadddccadbcaaabcbdacacbcbcbdbdcbccacdaddbdbddcbcdcabacbdbabccbdcbdabadabaabaabbbdadcbbdcbcdcdcdbcabadadbcdddaddcccddbcccdddbddcabcdacdddbdbcbcdadacabcaadaaccbbbdabdbbcccbacabdadabdcbcdacbadcadcdcccbadcabdbacbaaaaddbdabadbbbddbccbddbbbdcdccddcddcddddaadbbaaaaddcadaabdcdcdbcdabcacbccabcbdaaaddcdccbbadccdcbddadaacdcdacbccaaddacbbcbcddabbacdbdbdaaabdccadacdcdbaccddbcbdacccadacdcdadcbddadbcacadadbabdabaabcabaacbadccbaaadcdccbdcdccbdbccadccbdbdacbdbdbabbbdcdccbdcbcadbabcdabdacabbbccbaaacbbdbdccabcacabadabaaccccdcdbdbbdddbadadcdadbccdddadbbbabbabddccaddadacbcaaaaddbbbbcbaaacdacacbacadcaacabcdaccabbadccaddbacbadddbccaabcacaadabdcadaccdcaadbcabadcdcaadadddabddabaddcaacacbbbcacbddcaccbccdddddccaabdbbacaaacdddcccdabaababcbccccabdddaaaaacacdabdababbcdbbbddbcbcdcbadacddcacabcdcdaddbcccddaddbadbbddbabdbcdcbabdcaadaadcadaddbadbcdbadadbddadabbcaaddcadbbbbbaddddcaaaacbbddbbbbbcaadaabaddbbacbccbacbddaadddcaacbdccdbacdddcbcdbabdbbcaacdbadbdabdbcdbdccbadababbadbddbabdadcccbbcddbcabdaddddcbbcbbbdbbabaacabdaccbdddcdbbbccccbdddddacdadccbacddcbadacddcddabddccacbbabbcdcdaacabcdbcbaccabaabbdadbdcdcbbccabdbdcddbaacbabcbacbccaabccdcddcacbdcabdbbbcdddccabacbddabacaaaaabccbcbdcdbdadddcdbdcdaddbbbacbccbcbcbabddacdbcbbdbcdabbabbacaabacaaabdddadcdacaaabcdaddbddadadcabcdacddaaadcbcbccdddcbabcdccbcdbcbdbddbabdcdadaadcbbaddccaddacbbbdcacdccccbbbdcacdadddcbaabdabadcbbcdcbdbbcdbbaaaacbccccabcabbbaccbdaaabcaccadaddbdcbbbbaddbcbcccaddadddadbccdadaacdbadabccccddaaaccdbdbcdddacabdbbdbbcddccaaadabbdbddaadcbcdbbcbbccdadbddcacdbbbacbaabacaccdcbaababcbaddcdcbcdadadcccbcbbcaccdbabbaddcbacdbdcacddabbbbcdbdbbacbbbbbbadcdddbbccadcaacdcccacacdcdadabacabdbddcadcddadcdccdadbcabcdbbbdcdaccaadcccabdddbcdddcdbcdbaaddddddbabadddbbbbdcacbcdcabbddccaaaccdccadbdbdcaabddacacabbcdcbbcccababccbaaaabdcaaaccaaddadaabddcabadaddacbbbbdbdcccbcdddccccbcdbcccdbcacdaccdaccbbcbbbdcadcbbdbccbdacbaacaadcddaaadabacdabbdabadbadabcbaadbaddbabdaaacaabccdbcaacbaabddaaacabbbaacbbcddbcddcacdbcddcaadbaddaaddddcddacdcbbbaccaaddcdddcdbdcbcdaddcddababdaddbdbbdcccdaaccbcbddbddcbdaddbcacacabcccacdabdacaadaaccddcbdbbdcbdbdccaaaadabdbabcaacaaadcadabdaadcacdaddccaadcbcabaccdbadbbaabaabcbbbadcabddacabbbbabcdbddbbaabaddccdabdbaddabdcbbcaadaccaaccccdccbbdbcbbdddbdabbccccbadcdbadbbdbaacadaaabcbacdadccaacbbbdccccdbadcadcddacdbbdcbadbbccddabdacdbbabdbacabcbdabaadbbbaccdbdacccdccdaaabbacaaaadacaacdacbcbadcddbaccacdbbbadbbbbadbdccabddddccaccbcadaacbbaabdcdaccbcdbabbdcabbccacdcdcaaaadbbbaaabadcdbadabdbdaaacdabcaadcbadccbdbacadabccdacbdbbadcddacdaccabcddbccacdccabcbabcbaabdbacaaacabbaaaaaccacaccadbadaadddbdbddcdddadcacadddaaaaadadadbbabdbacccdbbbbbdbaacccbbbdbbbcaddbdcddcbcaccbdcbbdbbdddddbdaaabbdadacabbbdcbbcbbaadbbadbaadcdbbdbcbbabcadbacadacdcbadbbddccdddbbdcddacbaadaabcccdddaddcadbabbdbbacaccacbdaddacabbacdddbbdcadbccdadcddaddbbababcbcdbdbdcdddcccccabcccccabadadabcadabbbdbdbcbccbabacbaaccbdbdabdccdcbbacabbddbcadcbadbbbddcaaadaabbbdbbcbcadcbbbbbdacbbcadcbdcacaddbbbdcdbdbbdddaadaabbadddbaadcbbadddccabbbddddcadbbccbddcacbaadcabccbdbabcccdbcdbcdbbbdbccbdbcddaaaddbdaddcaabcbbaadacdadcdddddcabddbccbccbccabbcccdbddddcccacccaddbbaacadbbddbcbaabdabccaddcdcacbcaaddccddcaabacbaabddcddcdccdbdbbabccaddcddccaccaabaadbadaaaddcdcdcbbdadaccbaabacbccdaadacbbcbcdddacaddbaadabdadaacbdcadacdaadcbcadbbdddcdcdcbddcaacdcaabcccbacadbbbccdbbabcabccbdacabbcdadcabccbbaccbbbacdaadbcccaaadbdcabcbbcdddaabadccbbdaccdadccaaacbddbadbbadaaabadcdbdccabdcdbcccbbdbcdaccaddbaccaadccacdabaababacbcbbbcbabccdccddbcccbbcdbcbccddbacacbbccbcaaabacbacdadcadacddbbadccdbbacaccaddccccdcdbabbbccddcdccaaacdccbcbddcaacccdddccdabbaabcdabcccacdaabccadbbaadabadbcdabbabcdcaacaabbcacbadacaadadacbacbbcbabacaacdaaccddddbcadccbbdaaccabcdacaaacddcaabccbdadcadcbcbdcacadcadbcdbbccdabdadcbacdcddabcadacbdbddabcbcccabacbbdddacbcdaaadccaabacaccacbdadaabcdcddbbaacacbdadddaaadadcacdabbdacddacdacbcbbaaadaacabcdaaacdddadaddaabccdaddabadccdaddccbdcbdbdddbbbddcdaadcdbcdddbcdaccbadbcabbbaabbabcadddadbccaacadbdbdccbadaadaabacaabcbabcbccdabcacabaabddcbadbcabbadacbcdbbbbdddabaaccbddbaadcadacbdcbdddbcaadbbbccbaddcaaaccadbdcbcbcadcaccbcbdacddcdabbaacbacddadbcbccbdabdbaddcddcabbabccbadaabbadbacddbbccadadbacacabbddacbcdbdabaaaccadabbcadbccdbccabbaabbabaacbddbaaadabcaddabdaadcdbcdddcaaaaabcccdddcbcabadbadcdccbdccaabcbbbabbbabdbabddabddccadbbbccacdcbcacadacadaabaccbccbbbcaccddbdccadababddbacacdcccbcddacdbaaadccdccbacaabaadcbbcdbaccbcbcacdcadabcabcbaabdaadcddadadcbbabcacdcccacdccadbddcacdbbdcdcacbadaccabcdabddbdcbcbdabccaabdbbaadbaadbcdaccabbbdbadbaccbbbdbdcdaabdbbabccbaacbbdacddabacaddaaccadcccdcdaaadbadabdcddabccdaaaccdcbadacaaddcccdbaabdbdacbcdbaadaddbaadadbbbdbcbddaaacbadddbcdcbdaabacbcdadcdbdbccdabacaaabcdbbadbdbccbabdadcaccabbbaacaadabdacbacaabadbcdbbadcbcacaabdacdcaabcacdaadcbaadaacdadadaaadbbbbdcabdcbbcadccdaadcccacbbadbabdcccaccbaccdabbdccbcbcbbbdddacacbbbcdaabdbbbdaddbaaabcadccccdcdccdacdabcdcbdbdbdcadbcddadbadbaacdccbaababbddcbbbbdbaccadcccabbcdaccbddcbadacaadaccbacbbcdbbddbdccdcdbbdbdacbbcbdaddcbcddaddcdabcacacbdacaacddbdbccabbadabadabbacdbcacdbcdbcdccacdbbbcacddbaadadcbbbddaabadacccadccabcaccbcbccbdababadaaccdcbacaaaaabdaabbdbabcccaabbcabbddbdddbdddacacdaabbabccbdcbcbbcdabacabbaddcadccccbdbdbbdaaacdbabdddcaaddbdddccbcadcdccabcdbabacdbccaaaadbbadcddccddadbddcdbbbaabacaddbcdbcaabaddcdabaccbcadcacababdddcabcaddcadbbcdaabbadbdacaadddacdddcadadcbcbcaabcbdbdbaadadcadacabdadccbbadadbcbacbdabacdadbbdccadabdcdccccbdbbbcdaadaddbddaabbdddcadbbbdacdccbaaacadbabcccddacdbddcddacadcddacccdbacdaabcbcbccddbdabcdcbccadabadbcbbaccdcdaaddcbaccdacdaddaacbdaaabadccccabbbabacacdcabacdccbbbbdaccbadaaddacdacbbdccbabcadabdcdaaacdddaccaaccdacdbacdcbbccdbaabcbccddbbcadacbcbbcdbcbabdcbabdabdcaddcbcdacdddbcdacdcccbacddabaabbcbadbdddacabbaababbbadadddbccbaddacbbbbccbdbddaaddddbcdcddacbcbbadbdbaccbabcddbabdadabcbadcabcaaabcdbbbccaacbcaddbbdbdbbbcccbdaccacdaaddbccdbcbaddbbcacabdbacdcabaaaaadccbcdadbcdbcdcabcababbabddbbabaabbcdcccadcbbdccbdbacbadaaacadadadccacaabdcbcbccaacdccabcaadbaacaadbcbadbdcdaababbbdcacbddacacbdddacdcadbccdcbddbacbbcaadcbdacccbaadccccacddbbaadccabbabcdaaaccdbbccdbccdaadadbbacdcabdbbcbacabadaabbacccbabaccbcdccbccabbccddabcaadddaabbbbbbcdaadbabccddadbacdabbcdacaabaaaabcacbacbbdccdcdaddbaaaadcdcdbcaccbdddaddbcbcbaddcccbdbbcddadcbbbcacaddabbcdbdbbcdcdddaabcdccabadbaaacbccdacdcdcccadacbddbccababcdbdddbbccaccaddccdcadaaddcacdadcbbbadddbadbadcaacdaaccdcdbadbbbdbdabddcbbdcbbcadcbabadbbbaddcdbccabdaaaaaddcdadccdbbddbdadbcadddccbbccbaabdbaabccadcabcabbbaddcacaddcaadbdaabaddabcdccddabdbcdbbdadacdcaddbbddabbabddbbcabccbddddaddbabcbbacbdcacbdbdcddcbcacbccccbccacdabbcccdadcbbadccbbcaddaaacdcbaadbbdabcadacbbbdbcdcdabbbbdcdcbbaadcdbcbdbdabccdbaacddbaddbbddccbcadaccaadcddadbdbabbcacaadcbdcdcbddbddbdcccccccbdadaddcdabbcacbabcacabbacbadbdbbbbabcaddadbbadadcdcddcbbcbdaaddcdacbbdbcbbdcdacbdcacadcdbbadbcddabcccbaddbdccbbcdcbbadaadddbbacdcaddcbbabdabcbdcddddcacdaaddcccdbbcbcdddaaccdcdcdcdcdcbcbcbcbddadbbccbbabdadccdbcdabbbdacaabddcacaadbaccdcabddcaabdcdacbaddbcddbabdbacababcdcccdacadcbaaccccacbbaadcbcdadacaaabdaabccdbdbcbcadcdcbdadabbbcbdbaabdbddacddcbdaaccbcdacbacaccabdbdbaacbcbaaaddddddcaabdaadbcdaaacdadbacaccdcbccbaaadacdaccbdbabacbacadabacdadadbdacbddbdabdccdbdccdddaacbcddcaadbcbbbbbdcbbdbacdcbdbacabcabdbdcacaaacccdacaaacabaacbdadcbadddadabbdacdddaddacdcddbbbdbbbabdbbdbccdacaacbddcbcccdadadcbabaacacdadbbcdbaabcbbddabbcbadadcdaddcddabcbcacdbddcbddabccadadcabbacbaddccdadccbaddaabbdaccddbbbcbaabacaabccdddcdcadcdcacbadcdabaacbbbccdadbdcddadbbadbdacbcbacdcbccbaabdcddcbbbcccbabaadcddcbbcddabcbadbdbdbaddbaaddcaccbcadadcbbdadbaadbcabddbcdcdabdcdbcdcccaabcbcbabadaacacdbbbcdbcbdcdbadacadaabdacccbcddbcadaddcccadccddccdbbabdaaabcccaaabaaacabaababbbacadddcbabdacacabcaadcdbcbaddbabadbcdbddbcbcbdccccbacbabcbaaddcbdaaddaddaabdbabbbddccaccbacaabcacbbaababddbdddbddadcabacbaaccccbadccbdcccbddcdaaadaaadaaddcbabcbdacbccdcacaaabbadddbbddadcaddcccbcacaacbadadcbccbaabcbacbddbadabcaaacbbcacddddcbacbaccabdcbbbccccbbbcabdddcdccccacdadcbabddbcadddbcdbdaddcccacacacadabbababacacbdcddaccddbbcabbabacaaadbbcbbbadabcaacacacbdbcdadcabddbdacdacaccbcdaccbbdbddaaabdbbcccadabcdacdaccdcaccdaaabacbddbbdbdbcbbdbcdacdadadbcadcbdacbcbcacdadcadbdccbacbbacdabacbdaababccdbbcacccdbdcdbbddbdbccbdadaddbaabaaacdccbdbabbabbdacbcdbadacbabdaabbacdbcabcaddaaddbcdaddcabdccabaadbcbcaaabaaabacbbabdbbabdaacccadabacaccbcadaccaccabaadadcddaddccdcbbaaadadbdbbabdadcddbcdcacdcdadcbbdbddacabcbdcabcdcacabdbcccdaabbdbbcddbadbdcdcaabcbbccdbadcabcabcddcadcccacbdbdabcdcaacdbbcacacdadcdcdabacacbabddcdbddcbbdacdbccbadcdaabadcaaddbbaddadbababccdbdadcaccddadccdbbdaddadcddbbdacaabbbcddbccabbcdaccdcabbbcabcbdadbcddcdccdcbdcadcacbcaddcdabbadcadacdaabbcbbbbccbbacccbaccbbbabcbdacbbaccdcbddadddacbdaadacdaacabdaddcadacaabbcadaabccddcabddccbccbbddadcbdcbbcacabbadbbbadacbbaadaacdabbabaadbaabacbaabacdcbacadaddaadccbaacaababcaabbaacbbddbadbbddaaadddadbbbaddcdaacaddcbddaabddbaaccbbbacaabbdbbbcbdadccccdccbbacbbbddddcccddcdbcdcdcccaddcddbbcdcbdccbcdbadcacabbbdbacaccdbccccbdaaddcaadbddacacdbaadcdbbbacacacbdaadcbbdddaadcabddccabdaadaccdcacdcbbddabcdcabbadacddbcabcabccaababdadcbbaacacaccbbadadcdbcdaadcbbdadbbbbccaccdacdbbadbcbcbacaadadbbdbcdddbadbcabbcabadadcdccccbdddcbadbbaabbbdaccdccccdadddaabacbdbbadcbaadacabacbacddccbdbbaacaadacdccbdadababcbdacccdcdaaaadccabdacbdbcbdaabdbdbaacabdaadaccadadcaddaadbbcaddbabcaaacbbbcadaadddbcbbbbdcaadccaabdaccbddcbdbabadddccbaacaaaddcdadbadcdacbccabddabdacddcaacbbbbacbcacaabbdcbadabbccaccdddcbdadbdbacccabccdbbdaadbdcdadabcdddbcddcadbbbabccdbacacadacccadccbdddccbbbdacacdcdaabbacbbaabbbbddadaaccbbddbdbddbbaabdcdbbcdcbddcabadccbdadbcccbadabddbbddbdabcabdbbcddabacbbcacbbddbabddaaccacadcccbcaabdcacbdccacaababddabbbcdbabcbabcacdadcddabaabdccddaaddcdddccbcddccbbdcdcbbdcbcaaccacadbbcbacbcbcbcaabadcbbbdbaabdcbddccccadabcddaccbdaaacdbaddaadcabaadcdcbbcbaaacadbdbdacccdcbdacbbbbcdccaabbcaaddaadbdadbcbaaddbcdcbcbbcdbddbacccbbdddbacbabadabbcbaadadbccbdbcccdadbddaadadddcdabaccadcdbdcaadcacdccbdddbcdcccaddadccdcbcacbddaabccbbbdcdaccaccadbcdbcbccbbbddddbcbccdbddcdbdcddcdddcdacbaabbbabbaacbcbaadbcdaddcabacdaaabbbaabdcccdbaacccbaacddbccbdcdcdaddbabcabcadaadabaababdccacbcaaaacababaaadbdddbcadddccdbdddbccdacbccbdbbbdcdcdccbdaaccbdcbcbdaadbcbadadcdaddbcccaaadaadaccbdcadbacdcddccbcdacbcaadcadbaabcccbcaccacaadaddbdddbcbbcbaaccdcddcdacadcbbbaacddacadcccbbcbccacbdabdabdcddcdcaaddaabbcddcdaaccddcbcadadaddcbddbccdaabbcdccbbabaadddadaddaddcdbadabacdcdddaccaadcdbcdacbdacdadcbdcbddbcddccaaaddccabaadaaddadabddbaaaaaaabbaacddaddbcddcccbaaaadbcbadaaadbadddcacacbbcbbadcbdbabdddccddbdbddaacadbccdadcadbccdaabcccabccaabcbadcacbbdabbcaaabbaaacbccaabcccadbababadcdcabaaaabddcccbcddccbcbaacbbcbccadddabcdcdcbabdacbadcacadbddcdcccdabdbaabbacabcbcbcdddcddddcaaabccdcbcbcccbbcdccbbbacdacaacbdbbbdaccbdcacbbcddcddacabdcbabdcadbddddcbdcdacaccaddadaacabbaccbcaabacaacdcddbababdcccdbdbaadbcacbdacccbcabdcbdcbdadbabccbddbdccddaabaadaacbbbdbcdaaddbcdccababdcdbbdbadcbdabdaacbbdaaadcacbaddbcbcaaaddaaababdaacccaaabbcbabbabcbcaabbdbddadbbdbdaddbaccddadcaacaabcdbddbccacdcabddbcbacacaaabdaaaabcddabbdbccbcbddbacaccbcaadacbbcaadbcdadccbbbbbacdbddacbcbdcbccbadbadaddaadcccbbcdbbddababdcadcccbacbbdbacdccdabdbcabcddbbbbcacddbcabccbccccacbabaadcbcdccaacccacadcbdcccddbcdcdaababddddbccacabcbccbaabaacbdbddadadaddacacdbddddcacdddabbbcaddbcccddcbbacbaadcdcbacadbadabcbbbddcbbdccaddabadcacadccbdbdcdacdaabbcbccbdaadbbadbdbcdcdcadaacababbaaaaddacaacddbddadcccaaabaabbbccacdbaacaacaddbadbccaccddacaabcadabcabcddddbbdddcdcaaacbaaccccbbbaccaacbacacdccdcdddacbacadadcacbddbbddccaddadddbcaacaddaabccacbbdcabccbaacbacbcddcabcacdbdabdabaadababadcddadbaccaddadcdbbbcadaadbddcdaaddacddcbbadabbacddaddbabcabbabcccadbdbcaddacbadcbdddaabccadbdcdccdbaccdddddaccbccdbbdddabdacbdcbcbbabcbccadaacddadaccbaacbcacbdccabbdbdcbccadddaccaaabbbdddabbaacbcdbbcdcbbbddbdbacabbaabcdcaadcbbdadaacdcbcdaaadbcccdccabadbcdcccdacbcaaacabaaadbcbccdaaabdaccbbccbccacbbadbcbcbdbdcdacdbadbabcbbbcbacbcbaccaadddbcbdbcbbbcbbcccddabcadbdddcdbbdcddcabdcbbaaabdcaabcbbcbacbaccacadbccaaaaccbcaccbcbbadddbcdababddaadbdcdbcdbacbddbabacdbadccdaddbbbcaaccadacbaaaacbdcccacabadcddbabaaabbdaddacbbbaccabadbccabdbdcadbdadbcccdbcdcaadabcabcbaabddddcdbbdaaaddaaadabadbccdbaabaaabbaaaaaccabdbcaaaaaaaddadbccacaccbcadabdcadacadaaddaccabbbadaaadbbcbaccaddbabbbdbdcbdcbdcacbcadcadcbaaddcbcddcaccadbacbababbbbcaacbdacdcbcdbaaaabbdbaadbabdbdbaacabbadbcabcdbaacbabbdddcadbbbbccdbdbddcaacadccdbadaababddcaacabcbabcdabcaacacdccbccbabdcacbdcccbdcdaadddaacdddbadaabcccdcdbdbdcbbdccccddcbddcccdbccbccbcdaddacabbacbcddadabbcbacbabcbabadabcaacdddabacdcacdbccbccbaacaadbdacdbbbccdcbdcacddaabdcbcccbaadddbabccdcbdadabcddcaaaddababcbddcdcadbccddadccdacdcddacdacabcbbaaccaddbaabcacadcadcacbaaddddcbcbdccbaddcbabdccdddabdcbdcbabdcdabacbbddbbcdcabadaccbcacaabbcabadcdbccbdbbdaaddabccbdbbcddddababcaadbaaccdcdbddbbccbaaaadcdaccaccbaacdaccdabcdcaccbbcbcccbbacbdbabdbdbcdacacadaacbcaacbcbaaccabdcbbaccdadabddaccbabccbbdccbabccbddcbcadadbbcbdcadbcaadbcccbdbccbbbbdbbcdbbdbccbacdcbdcdcbabdaadaadbdcaccaacbcdbadcaacaccaccacaacccacabcdcadcbccaccdbabdbddaaadbdcdccaccdccabcabaacdcddacdabacdacbdadbcabdccaacdacacdaaddcadbcdddcbbcccadcdbdcacbddcbbaddcabcabdadcaacacdcddccadbbaadcccaaacadcaadbbcaccabbcacbbcdbabadbbbbbbabdabbcbbabbacaccddccaabcbdaabacbdbbbcbddcaaaabdbccaaaabddadcdbabcadcbbddbbacaacbddabbaacbacaaadddbbcdbdddabbbaddcbcdadcbbddbaaccbbddbaaadabbdabddccbcbcbaadcdccdbbbcaccaaddccdbcdbcaccdbbccbccaddcadbcabcdaabddaaabbabcccdbdaaaadcdbbadbacbdcdbabbabdadaaaabcccbabbccbbadacbaaaaabaaaabcbdcbadadbacacabaaabbaddcbdadcdbcbbdabdccdcbcbacadcaacaabacdccbcbbabdbacbddccbdacbbadaabbcdacbbaddacdcbcdadcadadccaadcccbdabacbaccdddbddadbccccbddccadcdbabacbccbadaaabaabbdaccdbbbdbbbcdbabddbabadcdaabccdddaaaadcbcabccdcabaccccadabaaaabbaaaadccbaabaacbdcacdababcbddaddccdabaacccabdcdaabadbcccaaabdaaaadcaadbcccacabccdacdaddaccbccaddbbdcddcdcddaaddbbcdacabaaabcacccdcddbccadcadcabbccddadccdacaaacccbbdabaadbddccbcdaacadcbcbabbdacbacbaacdbbccbddbbacababbccdbaddcbbcdcacabbabbacaabdadacbaccbacabccdaabdddbcdddabbdbccbababcaaaabbbadbadaabdadbdccbbbdccbdacbabddbacbacbdbbaadcabacacacdbdbccabdacbacbdbcadcdccadddbabaadacdcabddbcaadbddbaadbabdcadacdcaddcaadbcbadaccbabbdcacdaddabdbaccaaccdcaacdacccbabacacdcabadacbacddabdcbaabadabdabcdbdbaddaaabddaccdcbabbacbbdcadcbbdbbcacbdbcaacdaddbbdaaddddccccddbadaaddbdcdbbcdabdcdabbdbdabddacdcdcbcdbbcabcdcddccaaaabcbacbdccaddabccddbacbabbcbbddcbdaacbacdbbdbddaababdcbdcbabcbabadabacdbaabccddacbdddbccadbbdacabddbcddbcaabdcbbaacbdaccddcbccdcddbbcbdddabdcbcadacdacbabcaaadcdcddacaddcccbcbbbddadabacababbdabaaaadbacbbbdcdcdbadababdacacadbabcdabcbdbbbabbbddacdcadbbbdccadbabddaccbdddacbbbcbdddacbbcbadaabcbdbaaaaaabdcabcbddbdbddbcadccbadbaaabddababdadacdaccddddbdbadacddbdbadacabacccbbdcbaaadaccddbbdbcbdcdaacacdadcdadcbcdcabdaabbaadacddcabdcccabacdcacbabadadaabbcdcddbcadcccbcbcdacccbbaccbcccdbcbdcacabaabdcabdbababbcacbaaaacaaaaddbdbbbbbaadcccbdacddcbdacdbdcddaacddabcacdddbacaddddbddcccbdacbdbddacaacacbaaadcdcbadbaadcaddabdcddbdadcdccacbcbacabaaabcabcaacddaacbcbbbadbcdacdbbacbaaddcabdaddbdccaabbbdddaabaccabcccadbbabdcccabddaacbddaadbbdbbadddbacddbdbadaabcdaddbccdabcabcacaddddbbbbccdbbcdacccdbcabdaadddadccccabbcacacdabdccbdbadaadbccbabbbdbbcaadcbcdabcbabdbbacdbbdcadaacbadcbadcadaccbaabdcbbcbccccdcdacbdacbdabdcdbaddbdbcdcaaddbdbdadddaacbaaaaabacccdbaabccdccccadbbcbaabaadbccabaabaacaaaadadbcdadabaadddbcbacbcacdadbcdadcacbcdcbbcaaaaccbdabcccacddccabcdbddbbbbadcbbddccadcaccdccaaaacdaaaccacbddcddcdccbaadaccdcbbbbccbaadacdbcbcdabbabbbdbaacadbbababdcadaccbdcacabdcbacaccacccbddccdbdcdbbdcbcdabdcabadaadababcbacacacddacdcdcddbddabacddadbabdaaabbabdbdcaabdcdabcbddabbbadacabbadcaaadbdccddbbdabaacdbadababddcaadabadbadcbacbcdcadcdbdcabccdbdcccbacabbadbbbabbbabccbddaadacdcacbaadbdcbabdacbbdaabcabaccddbabaabdadcccccbdaaccdadbdadaaccabbbddcbbbdacdddbdbccadacbbadaacaabcbbaaacbbbababbadbdaccaaabadccaabadbdbadbaabdddaadbdcbcaadcacaacdaccacaabbdbcacbbcddacaadaabbaddbadbbcdaccccdaccbdbaacddcaadcacbbccdbdacdbdaaddaacbbcbcdcccbdcabdbcbccbbbcdbaddddaccadcaabcbcdbdaccbbbcadcdaccabdbabbcdcadcdaaccdbadcddcdadcbacccbbbccbddadadcccdbcabddcabdbbbdbdddaabcdddbdcbcbcccddcacacbbacadcbbacbbcadccbccdadcbacdadaababadaccacadadddbbadabcbccdbabdadcbacaccacbcdaaabcaaacacdcaacdabcbcadbacbaacababaccadbaccbccadbcccbacdcdabcbbbddddcdaadaaddaacbacaaccdadbbbccdbbabdbddcdcaabcacaaabbbcdcdacbaddacadaddacbadbadbdcabacabaccdcadacacdaabbcadcaacdcbcbbcdbddacaaadddbdbacbdddbbdbbbcaabccacccdbcadaabdaacaddbdbccbacbbaccbbdbadbdaaabcbcdaccadcaaacababcdbacbccbdddddcbcdbbcbabbdcdccadcbadbdbadabcdaccdbdccdcddacabbcadddccabcbdbdbcacbdabbccacdcacdbdbbbcaddbccadbbabbacababcadcdccdacabbdcdababdddabdcadbbcdaaacccabbcaaccaabcbaddcdabdcbadcaabcadbacdddbcbaaabcaaabaddccbadbbdcacdaabcccacadcdcaaaabbcbccbaacabacaccccbcabaccdddcadbccaacacbabaaadbbbbdcacabccabbddcddcdcaadcccbbdbdbbbbbabcbacdacdacccdaacbcdadccdcaabbabbaabdddacddbaccdcbaabbdaaccbcadabacdacaddddcdacbbbbbdaacadcbacacbadacaddbbbbcbcbdcbbbdccbdccabcaadbdcabcccaacdbcaabdcacdcdaacadcdcbdcbacaacadacabcdacaabadbdbddbcdaadcdccddbcaabbddbdadacdcccabcacacaddcaaddcbabbcaabbbcbadcdddcdcdccdcbacbaccadbadbabacdbcdabcbcbdcccddabdcdaccaccdacbbcdacccaabcccbcabddcacbcbcaacbbddcbcadaacbcddbcbaaddbbaddcdcbadbacccbaadcdcbdbdcbbcddcaccdbacbaabcaabcddbdddddbbcbadcbddbcddcbaaccbcbbbcbabcdcdcbaaccadbdcabaccddadacbbccaabbdbddbadabdcabcbabaddbabcdcbcccbbddaadcccbcadaabdabcadbadbdbbaaaabcadccadcbacbbccaccbdacccbbabdbddbddccaadcaacdacabcabcddccddbdcaaddcbabdcaddbcddabdcddbbaddbacdbcaddcadccadbbdadbcdddbddddbdacdaaacbbaacdcacbabbdcdbbabaacbbdabcccdcdbcadaaabbbcddbbcbabcabdabcdcdccddbbdbddbaaddbaadddcbbdddaddabdbdadabdccdddccdaadadcbabddaacdddcbdddaaddcbbcabbacbbddadaacddbbcdadcaaacdbdbcdaababacccbbbbaaadbdacabcacdcaaaabcdbdbcacbaabcdcbcbaaddadacbbcadababdcdddabacaccddbdbabbbabacbbbdabbabbdbdcdcdbaaadcdbbbccbaddcbaabadcbbbccbddaacbcddddbdcbaacddabdcaacabdcacbdbdbcccabdddadcabcccdbaccacdcbaabddbabcaaacbddaabccabccacbccbbbadcabdabbcaaaccaaaaabcbaddbdbcaccacaaaccacdabcbdaabcbccdddaacccacbcabdacdaadadaaddaccddcdcbbddababcdcbbdcddccbdcbccadccbadaabaddcbcabbdbddcdcdbadbbabdddbbacbccadaadddacaabcdcaacbaabcadababccacbacbadacdcbcbbcdbdbbdadacbabddbacabbcdbbccbbadabacacbbccacaadaadddbdaaddcadacddabdcbcadadadddddbabacacbdbdcbaddcddddacdcdadcccadaaacdbcbdaabdbcaccbbcccacbddacbaaadbbbabbdcacaaacbdcccbbdbbbccdbcadcbdcaddcbbcbcdddaaabbbdcdabcacacccccaaaabdbcbdccbaaccabbddaddccbaacacacbccdccdaadabaacdcbddadbdcbbccbbcabadccadbaddbbdddbbabdbddabdadaccddbabababbcabdadbbbbbbbccabadbdccbccbadabaaacbdbadaadbdcddccccdcacbccabcdbbaddddabdaacbdcccbcbdbbbaadcaccbbdcdddddabddcdadcdcaacbaddbbaccbaddababbcadbdacbbddbbddbbdcccacacccbcdcdabacadcdbcadccbdbbbacbbbbcabbbbddadcdccdaddbcbbdbcccdbdacbcddcacabadddbcaacaccbadbdbbbdabababbcbcbbcdabcadadbbccdddcadacbcbadbccbabccdabaabdacccbcdcddcbdddbbcaadadcababbcbdddbbacbbcaadcdcaccacbdabcacadbcabacdbbbcadcaddcaabdbddbbdaabdcaabbbdbddbaddaccabcccbbddbdabccdadcbabbbbdcbadbacbcadadbdcadabbbcaccbcaaccbdabaabadadccddaacbddbcbdbcbddaabadbcbddbddadadcdbdcdabbbbdbacaacdcbcabcbdddddcbbbdabddcbabcccdbdcddaabadbbaacddacbbaadadaacbdabccccdbbbddbddcaababdcbadcacdbcabbcacbccdddadddabacbdcacdabcbcbbbaddbccccccbccccbaadbcbcdbcadddaaaaccbaadccaaadadcdbcbdaaaaacbadcdddddcbacccaadddaaabdccbadcddbdcbbbbaababcacadcabdbbcacdbadaababbdbcbbbaacdccadbdbacabcdacbdcbbcbabaaabcacbddcdaabbaaaabcbdbcdcaccccdabccdcacccdbdcaaaaabbbdacbcdcacabaacbcabdabbabbcdbbdcccdbbbaaaadddabadbcabcaccddbddabdabdbcddaaabdbcbdababcbbcbdbbabaaadcdbdddcbcabcabdddaaabddaabbaabcbddbccababcbacccbbccabadacdabbdbacdbacdbbaabdaabbbbddcbbbabddacbdbcbcbbcdccbaddbdbdccddbdcddcddbdbccaaabaccaabbadccbddcbcbbdacabbdadaddaaabaadabbaadcbababbbbcabbcdddbaabcadddaaccdbbbbcdbbaaddcdadcacdbbabbabddabacddcbaddcadacdabccdbcbddcbcadbcadadacacabbaccbaadbaabdccabddbbcdbbcadaacdbdcdccddabcbcacbacaaddcaaacbcbacdbcaadbbdcaabadcbcbcadacbdabbabadddabbdbddcabddbacbcddcbdaaccbaacbcbdcadddbaddbdccdbbbadbcddaabaacbbacbbdcadabddbcdcbbcbbbdadabaaacacdacdabcaddbcabdaadcaadbaadabddbcbcbdacccdbadcaabacbbcccaacdadbabdcbaccabaccaabaacdcdabacabaccdbddbbabccbccbdaadccdcccdaaabcdddcbddbdacabacaccbaaaaaaddbabdbbcdaddcbbddcabbbaccbacaabbadbdbdbdcbbdadbabddaddbcbbacdabacbdaadbdcdddbaccbbabaadbbacabdcdccaadccabadbbdabcbbadbadaccccdbdbcacddbbbaddbbcabcbdbbbdccccbcabcddbcdaabaacddccabdacabaaadaabacaabbdaacdaaacdbaaaddabdbbdccbcbabacaadbabdcccaddacbcacadacdadcccbcdaadadaaccaabcacbddbcdaddbcccdacbadcaadbbaccbbaaabaacbcbbdbcaadacadbdabcdcaccbaaabbbbbaccddbcdccdaacbdbbdabcadddacadaaadbabccaccaacdbbbadcbcddadccabcbcacdbbbcdbacdddddcddcacacadbccdaaacdccaddccacbdddacbaaaacddabcaacccacadacaabddaccdbadabddadaabddbdadacadbcdccdacdbaabaadcbbbbadaabdaccccbdcadbabdcbdcdcabcbdcddcddddccbaaddcdaabacbbbcddbcbcbadbadacccadcdbabacaaccacdcbaddadbaaaadbbdacccdabbccaadadbadcaadbaadbdcbcbcbdabcddcddddbbdabcabddadbcccbadbdaddbdbcbbaddabbbbababccbcdcccacccbdddcbdddcabdababadcaddbbdcabbcddabbbaabbccaccabdcbdbbbdbcccaaaabcaaaaabcbbbddaadabcdbbcdabbaadcdbaacdaaabbdbacacbdbabcbdbddddadbadaacaccabbccbddacbaddadaccccddaadacbadaddbacdbcdadccbcabdbbbaaabdbaadbccbbccacacbaddcdaccddccaabdbbdadcbadccacddbabdccdaddaaabbbcacbbadadddddabddcabcadcacbbdbdbbadaabaabddaabcbacbdcaccdcccbbaadbcbbcdbccccaadadccbbccabadcbccdddbcddccadcbacabaabcbddaddacbccddbcdacabbbbdbcadbdbbaabdabdbbccbcbcbbabcddaaabddbccaababcdaaddaacbadbcbadbdcdabdbabcbaccaacbacccdccbcddcadbbddabdbbcabaadbbdbcccaccbaaadccbacdbaaabdcacbcbacacbcccaacbaabdccadaddcdaabbaddbcdcbdbabaddabdadbacbbaabbaaadaddbbcbdccdcbdcdabbbbdbcdbdbdacdaabddbbdaccdbabdcabbaddbcbdaacdabcbcdacbbaaabbbdcddcbbccabddbadbacbdaccbddadddccaacbcbdccbdcbacacccdaabacaaacaccccaddbdaddcaadacacdcdccbacbddcdbccbbbdadaaadabbcdbdddbacaaddbcbaccccadcabacacaaddabdbdbdbacabdabddbccbdaaacbacabdbddacbccbdabdddbbbaaddaddaadadabcbdaaadcadbaaaccdcdbcdcbbbaccddddcacdcabbddbbdbacbdddddbdddcbababdddcbcdcacbbbcbdaaabbddddaddbdccadcbadcccadadbadddaacdcbbdadabdcddcccbdaccddcbbaacccdddcabbaacdadbababcbadcccbdbcaddcbdcbbdccadbdcbccaddccbaccdabccdcadacbadcaccddcabaabdaddacadbbccccdacbacabdabddcdaaadbabababcdbacabbdaacdbbbabacbbabbbacddbbdcdbbbdbbcdcddabadabcdcdcdacdbcadbccdadadbddcbcbbbacbcdbccdbabbddaabadcaacddbabcccdadabbabcbdcccbadabbabbababdabccddacbcacbbaddbabbabaabbdbbbdbcadaadddcccdacadbccaccbcaaadbababdbabcddbbdabadccbdcbbaddaaaddabaaaddcdcbccdacbddbcbddcdcdbddcbbcccdaddcbdbacbacabbcbaddbdabcacbdcbbbdadabddacabaaacdcbaaccdcdbdaacddcbdddcdbabacddbdadcdbbabcddbbbccabcbcbaddacadcdddcaaccdddabddadacccdccabaabcbdcddbcdaaadcbddbcddbdaaddbcacdccdcdbadbbbcadbbbbdbbbadddbcccbadbddadcbbdabbbaaccdacccbadddabbbcbbadddbacbacccdbdbbcdbccaacbbcdccdaaccaddacdadbdabdbbdadbaaabdccbbcabddbaadccbaacdcbcbbddacbbbacbabaddaddcdbaadaadcdbbdadcaadbdabdbdcddbabaaaabbddbaabcacdbcbcaacabcbdbcbacdadcaaccbaaabbbccdabacabadbbbbcbadbdddaccacdbcaacccadcbccdabcbdbcbdbabdabddbabaacaddbcdadcbaaddcabccdaccbaddccadababdccbadbaaccdcacaccdbcbabdcccbcbddcabcbcdbaacabcbdbcdbcaaacadaacaadacdcaadbdbcbbcccccaadcbbdabdacdcadcdcacaddacbbbcbaacdaddbadbabbddbcddacdbdccaabdbbbbadcbbdbabbcdbacaddddcabbcbadacdbbcdadccdabbcbdccdbcaaccbccbcbbcadbdbccccacbdacdbdaacddabaddbdabcdcacdbcddcabccdbdcbaccabddadadcbcbcccbdccadaabbabcdbbddbababdcccddaadbbbbcbbcdccbcadacdbaaabcbcadbabddccdcbdcbbabaabcbcacdbdcbcbcdcbbdcccdcabacdabccdcccbdddcbbbdcdcdbddddddbbaacddabaaabbcdadcacaabbbdbddcbcbbbccdbabcacdabcadcdbdcbccbbcbccacbbbaabaaddacddaabacddcbabacacdddbbcdcaccbcdcbcbbbbbadacdbbbdccdbbccbabaddaabddabcbcaadcbbdccbbcadbabcddbbcaaddadaadaaaaddaaddcbcbdacadaaddbacddbcababcaccbbadbabaacbcdbbbadaadcddacbdadccbacaccdacbddadbadbdadabccddccaabcccadacbaadabcacdcabcccddcbcbdcccbbccdbbddbbbcdaaddbbacbabccabdaaddbabaddbbcababbadacdccdbbccddaaabbcdbaabaabbddbadbcdbabbcaddcdccdaaabbacdcacbdbadccbaabadaabdcbbbdcbbcdadbbccbacacddcdaccbccaddbbcbddcbddddbdaaddbdaacddadcacbbdbbbbabbccdaccbddcaddcacadccaaadbbadacacacaaaabacdbaddcaadccccbaabbabdcccbacccbcdcdbdabbcbddcddbacbdaccaaaabadadacacdbcddbbdaccaddbabbbbbdaddbdcabdcaadabdccabacbbdcdccbdabdbcdbcdadcbccdbcbabaababbcacddabccdcacadbbcdbabbdddabcdbbbbddcbcbdcababcbcbadaacdaabccdddadbccdadaacabadcbdabaddbacbbcbcaadbbcadbbbbbbaccbadacbcbdaacbbdbbbcaacdacbcdabacadbcddadccdddbcbaadcbbaaadbbabddadcabcdbdcaccabcbdccdcbbcdcabbccdbadbbaabadccbcaadbbaddbaaddacddaacccbcbadbcdbabdcaccdaaaabadaacddadababcdcbbcdccdadbcabdbbddccabcbbdbdddbccacccbabbcbdcbdabbdabccbdabddcdbcadbdcaddaadcbbbddbbbadabddadbbddaddbcdaaccdbbadbaaadacabddbdabbdacadacadaaabadbddbdbcbabcdcabcadbadaacdabadbdaacbcdcdcadadbddacbdcddbaadddcccdacbcabcddcdababdaabaaacaabcacdbbacdaabadbbdaacacbabaacbdcaabbbdbacaadbddbcddcbbcacdcdddcddabdabbcdbdbdadccbdaccadbabbcaacddbaacadbabccccdcbaabdcccadbabccbabaadcbcbdbbbbbaddcbddbdacccacddbbbaddbbcbccbdaabdbdcdcbcaddddcbcbccbbaacbccddccaabdadadbccbdbcbaccbdacddaaadcdabacdadbacabcdaabcccddacdcbcdbcbbacabcbdcddcaabadbaaaadacbacccbbccdcabdadcdcbabdcaabddbdddbbaabdcacdabdadccbbbadcdddabbaaaaccaadbdaacbdcbbbadaccbdbdccddbcbbbcabcddaddcdbbbacacabbacbddcddaadbacaaababaabbcdccabacbbbbddccdaaddcdbbbbddadccabaabcddadbbabbababbcadccdaccdaacadddcaaabdcbadccdacdddccdbbbaadcbbacdacdbacbdbcacddbabcccbabdbbbabddddacaaddcdaabddcbabcbadcdbabadcdabbcdadbcddaddadacadbddaddbaaabccaaccdddbcdcacbcbbbbcaaadddadbabadcbcababbadccbbcaadcddabdbcbdabdcaaacaabdabbadcdccdcaadadabacccddcaddadbdcdccaabdadaddcbbaabbddabbadadddcdbaabdaccacbdabdcdddaaacaabdbbcdacadcddccdbddbbccdbcdbbcdaacabcaaabdacbbdabadbbbcadadcbdbaccdababababccccdaddbbbcadbbcdbcaaaddabbbcbbacdcbcdadadbdcdabcabcacccbcbcbccdcaabbddacacabbbbcaacbbcbdcabaabdaabbaababdaacacaaabcaddabddbbabddddbadcbccdcacddcdbddabdbabbacddaadcdaabcbaadcdcbaadcddbccadabbccddbacaaacabacdaddaabdcccbddbbabdadadcdcddacacccdaabcccccbbdacabcbacccbdaacccbccdabaaacddcbdabaaccababcabbddacbddccbccdccababccadcbcadacbabdbbaaaadcddacbaaccbdccbbaccaaddadaadddbaadbacbadbacadacaadcadacabbbddcddcbbcbdbaababdbbaacadbdabddbbbccccabbcddbcdcddbddbdaacabdcaccabbacdbabaaaddadacdabcddaabdcddbddbbbbbaababcccbdbcccbbdbddadbacddcbdcbaadbccbaddbbbacadaabdbddbbcbcccbccbccdcdbbdddcacacabcabbbdadbccbcdaacaadaadadabbdacbdcadbcaddabbcbbcdddbbdbacaacdbcabccdcbcaaaacbcbaccabdbacdbcbdcbcbdbdabadaacbdcdcdbccaacddabadadbbdddadabdcbdddcbabcacbbdbadadcbcccabcaacaacbbabacbacbaaddbbdcdcbbcdccdcabbccaadbbcabdabbdcdaadaccbcdcdbbaacdadacbaaccacdbddcbabcdbcadaaadbcbabcacbabacbcddcdcbdadaaaaacbadaadbcabadaddcdcaaadddcbcacdaadcddbccdbdabcbcaccdcbcadaddacdbbaddbdbcabccbaddbdcaacababbccaacdbabcaccdacbbaccdddcddcbacdbcbcdadbcdabcacbacddaaaaaabcabcccdddaacdadacbbdcdccbbbccabcbbdabcdadaddbbbcbcbbbcdaddadcacdcababaaddbdbacaacdcbdbaacabcaccdbbacbacdacdbbadbbbcbaababacbcbddaaaacaabbaaccacdaacabcddaabcbcdacbaadccabdcbadbadbcaaadbbbbcdddaacadaccabbbdadabdacacbbcbdcbabbaccdbbabdcacacbdacbbacadbbdbabddabbbbbdabcbccacdbcddbaabaccabaacabdbdbacbbccaabbcababaddaabbcacabbacbacbcacdddcacadbadddacdaabdadaddcbbadcdaccbbcdaadacaccbdacbaaacacacabdbabcbacbbaddadbddaaddcabbdabdbdcbdcabbdaaddddcbbdbbcbacccbcddabdbbdacbcbcddcbbdaddcaddddbbdcbbcddbcabbdcccaddaccbccddaaaaaaddddbddaacdbaadcdbbcccdacdccbaabbdaddaaaddaadbbaddabdcbbcdbababdcaacdbbadadaadacbcddcdcdcdbcdcaacaadccaddbbdabcbdcdbdacddabbcabdaabddddccddcddaccbbcadddabbdcdbdadcdbbdbbbbbbcadccdbdcdbbccaaadcbdbddaccbabdddbbaaaabcbbaddbaadacbdbccaabacccbdabcdddbbddcacadcbcbbdbdaabbcbaabcbcadadcaabacbbaaccadaadccadcabbbcbcddccdadacaccbcaabaaddbbbbcdabcdccdaaccdbabaadbbcdcaadccdbcdcdbddbdadadabaaadcbcbcdbbdbbdbdbddadaaacaddabdddabdccbdbabccbdcdacdacadcaababddadbabdbadbabadbadcdbbaaabbdcdccdbccbbcdbcabdbbbdcccadbcbcabccbdadcdabdddddcadbdbcbcdcccddcabccbcbdbcbdcaddcadddaccbcbabbbddabcdddbcadcbbcabcaccdcdacccdbbccbdbbacdbbccbdaaaddbdcabaddcddbabbaacadadbdbbaabbbbadadcbdcbcdadcbdaaaaccdcdbccbdcdccacaabdbdcddcacaaadddbcdabaadbaadcacbaacbdbbdbbcacaabbccaaadadaacdbdcbcabcdbdabdbcabbadaaaadbbdbcddccaccbadbbbdaabbddddbcabbbcadabbbbdadaddaaababcbddabdcaaabbbaacccdbcccddcdcadbabcaccbcaabcddaacaccdcbdadcdcbbadddacdccabcbdabaadbdbdbbdddaaaddcdcbaccdaabadaabdbcdabdccdcababddbdcdcaddcdabbabcadccbcdadaaddaacabbacaabcacabbbdbaaccbcaabbabbcccbdacadbcacabaddccddcddaacdbabcacadbcbbbccabaccadcacabbaacddbabadcbbcbacabcbbccbadbdacdcaadbbaaddbabbcdbddabccccddcbddcaacbabdaaacdccdbbddbccbdccbdbbcaccbbabcdadbaaaccaaaadbadcacbaccbabcdaddbcddaddddcbccdcabdabddbbaacbbcbbcadbbcadcbbbbaaddddbcdaacbbbaccadbabcbbdaaacadccacdabdacbadababdbdadcccacccadbdcacabccaccabadcabdaabcbcbbcaacbcdbccbcbcdbccdddcbdcccdbdcdbbaccbdaabcabddcdaaadaaacccacdbdcdadcdbbbadaccbbbbddbbbbdcbabdbbdcbcaadaabbbcbaccdabaacbcdccdbccadcdbccbbccacaadaaddccdacabbcccadcdadbaacbccbcbcabbbbcabbbacaddbcdbcabbcaddabbbdbbcbccaaacaddccbcdddccdcdddbbcbdadcdcbbddbbddabddccadabadcccaccabccbdabcdaaccccacddccabddabacdbadbdccdcccbdcadbabdbbbbdbbbbbdcccabacbbbcbdcbadcadbdccadcccdbdbbcaaadcdbcbbbdbadadbdddabcbccbbcbacdbbdcdacccadbadbacdbabdbdbddccabccabaabadbdacbddcccdcadbadacabdddbddcabddabaaadbacdabacdcadcbabcbcadbacabaaabcdbcbadcbabcbdbaabdcaadcdccbbcabdddcbbbccabdddbddacbdadbbbcddbbbabdcbaddadaddaacbbbacdbabaabcccdcbbadbaacdbdaadacdbdbdbbbabcdaccdccddddcdcdcabdaacbbaadbaabbaddabdcbdddcaccdddcccdbaccbdcddbdddccccabacdddbbadacababbdbccbdadbbcccbbcdacdacacbdacbccdabdadbddcdddcbdbbcdababaabdcdabbddbadcccadbaccdbbacbdcdadcbcdcbaacbabacabcadabdcbbabdcbaabbadcbbcdbcbadbdbdacbbaccaaaddaccddabcdbbddcaccabbbcbbbaaacabaabddacddddadbcbcabbbccaadbdacaaabaaddbaadcbdcccdcadaddabbdddbabaaacaaabcddccccbbdbdaaadcccccddcabcdccbdcaacddcbcbcddbbbcaabbcbccbabdcaccaaabbdaccacabcaccbdacabccdaccdbacbcaacccdcaadcbbbadbbbababbcaadbacaddbabbdbcaddbcabbcaabacaddcacdddccacdbddbcdbdbbcbcaddbacdcddccaabcaaccaabccccccabbadbbccbabaacacbddcadaddabbbbbbacbadbbcacbccccdcbddcbdbcadadabdcababbacbbaadccbaaabddddacaadadbacbbaddcdbabacdccabcddbbbdddcbcacadaabbdacddbacacbcbdcbcabcdaabbcaaacaccacdcdccaabdacaaaaadcbadacccbddbabbbdabdcbddbcabadbbaccbbaabcadbacbabcbbdabbcadadadbaaabcbacadcdddbacccbbcdcbddaadbcaabdbacdcabddcbbdadddccaabbcbaabccaabccbdacbcbbcbdaaadcbaddbdddacdcdcdbadcabaadbaaaccacaaabaaadaddddbaaddddcddbdacbaacaadadcbbbbadcdaaacdbadcacbabcadbabbdbbbadbacbacadbdccccbaaddabcacababadbacccaddabcbacddcbaaccbacaaddbdcdacdbcddddaaaababddcdbcdabdbabacdbcaadbaccbbadaabdbabaadbbddaabcdbcabbcacaabbcdbbbcdabacbdbbbaababbaacdcddabdadbcdcdabbcbbcbbbccacaabcbdbbbbbadacacbcdabacddabcccccbbadcdcacbcbbcbbccccbadddcdcbdbcbadddababccaaddaabcdabaddadddcdddadbbaaadccbcdaccadaaaddabdccbdabdbbacbdbccdbcacddcdabbcdccbbaccabbaaccdbbdbbdcbddcabddbacabbdcadcdabcaaadcdddccabadcdcdccdddbbdabcdaadccdbadcdcacccaddbabccbadbacacdddbadcdbbdcdacccbccaaaadddbabbcdcdbbababacababaddddcdbadbadcbaaccaddbaadacbcadcccdabaaacdadbdcddcaaddbdbdaabaddbbccaaabbabdddbaccdabcdcbbcdccadcbbdaadacbdaacdacbcaadcdaaddcaabaccaacddcdabdadbddacdaddcdcbcadbabbbdbdddcacabcddacaaccaddbdcdbbdaadcbadddcccddabcdcdcdbcacbcbbaadddcbcddcddaacabdcbdcacddcabbaadbccccaddcabadacdccaacbaaacbaaaacadabdacdbccccdbabccbcdacdcdbacbddcbacaccacbdcbdadbabcacdccbabbdcaddccdadabbcabaadcdcdacaadcaacaabccbcddacddadccdbabbddabcccdaccabbaccaaaadddabcddbcdbccaccdddaaababdabdabbccadbbdacbaccbccaddbbaabddcdbddaabaddcddccdacbbabdcababcacdacbdbdcccbdcbcdacdacdbcbbdcaadbbbbbcaaddbdbababcbcadbcbcdbadddcbbdaabadddbabcccadaccbaabdbdccccddbaaadbbbdbdcbdacbdcaaadcbbcddbdadddddccadbbbccacabbcbbdbdabacaacbddddccaccbbdcdacbccddacdabcdddddaaccbaccbadbcccdcccdccaabcbaacabaabdaddccabbbbddacdcdcaddabdabdadabcbbbbbdbbbbcbdbbddabcdadcbabdccbdabbddbccaaddbaddbbccbadbdaccbdbababdbbbadadbacacbacbcbcacbcbbcbdabcabcaaaabbabbbcdcaccaabaabdbacbdbababbaadadcdbbcddaadcabccaacdddaadbcdbadcbcbbddddccdbbcaadacbdbdbadcbcddbdbacaccdbbcdccccdcbbddbbbcdcdcddacbadddcbddabcbacdaacacbcdabcbdacbcadccacccabdcacbddabdccbbbbbdbdbcbcdbdcbddbbbabcbbbdaddbcbcbacbccdcbbcbbcdaacdabbcdcabdacccaaccbdccbcbbdbcacaddbcbbbdbbbadabbacbbcaccbcbccdaabacdcacccddcbacaccddcadacdadcadacbacabcaabdaccdccbddcbccbdacabddcbbbadcbcbbdbbbcbbadbcacdabdddcabdbdcdbdcccdbaccbbbcadccababbbbdbbddaaccdbacabdbdabcbabcdcdcdadbcaacbccbbccacdbcbbacbabbacbcbcababcdaddcccccaccabdacbbcababcadddccbcbcbddcacacadcbdaddbbbcabacdadcdcbcbccbccacccbcaacaadabcabdadcdacddccaabadaaddbccacdcdbcabddacadadbcbabaaccdbaabbbbdcccdbddddddaaaacdbddcabbcdcbdacbadbbbcbcacabbdddbcccacdbdbdaddadacaacaaccdbbccabdadbdaabddbaaddcbdcbddcaaddabdabacdabcdcbccddaccdbacbbaadadabcaddcccabcacdccdcbaccacaacccaaddddbbccdccccbdcccadbdcdbddcddaaaccbddcdcabacaabaddcbbddaaadcabdbcadabcddaaaadbdcdabcbcadadcaaaaccbbdbcdaaaaadacdddcadbdcbbcacbdcacaabdddccaabcabbcaaacddcccdbbcdbbdcdbcacdbacbbccaddcbcbbbcdabccbbdbbccccdcdbabdcdbdcdadabcbcacadbbabcdbbbbbdabccdadcbbdabcddbdddabdbacddbadadabdababacccddbbdcddaccbcccdacccadbccabcdcaacccdddcdddabbdaabbabcbcddabacaabacababcaacdcacdadaadacaacdacddcdccdadaadaadddcdbacaacaccdbcdabbaacadcabdcbbcbbbacbadadadbaddcabbcabacdbbcaacddaabaaadbcadbdaabbdcaaadbdcdddcadabdaabacacdcacdabdcbbcadccdcdacadacccdbdddacbbccbcdabccaabaacabdabacbbbbbbcdbcddacabcdbcddaacbaabaccaacbbacbbbcdbdcaccdddadaddcbabcbaabbdadddcaadbcbddabdcbbacaabbbbdbcacddcaacdcabbbbccdddacbcdcbcddcbaddddbacacccdabdadbbdacdadacbcdcacddbaabdbabaadcdabccbccacbaaadaccccdbcbcdbbbcdacccbbadcddbbcadbddbbdcccbddddcddcadddacacccabcaaaacccadbaaddadbccdaccbdbbbdbcddabadcacdbacbcdcccbbbdcbcbdacbdcbbabdccbaabdcdbcbddbdbcaccdccccbadabcabbdcadaabbddbbcbdcabaddbbaddbdcdbdccbbdcdcbdbcdcbbccaccdbcadbcdbdcccaccddaabbadccacdbcbbdcccdccbcbcabbaabbccbcaccddcaadbbddcaddddddbaabdbbaababbacdbdccadbbbaaacadabcbbbaadbcbaadaaccddccdcdacbdabbbaaacdcccbbabaadadccadcbaabbababcaccadcddaaabaaadcddcbbdabddaadbddaaabbaacdadcbddbbaabbbbacccaaaddbbcccdccbddabadddbadbcccbacbbbcbacddcadcabdbbddcdbdbbddaddcbdbadbcdbdababcabbcbacdacddcbadbcdabdaabacdacabdabacdadaacccdccabacdacacbcadccdcdaccddbdabdcccdccbcdcbdaacacbddabbcadcbacaccadbcdbcdaccabaababccacbdccacbdadaacaadbabdbadbcccbdcadccaddcadbcbaabdbaabbbdcaccbcdbaadbbbbcbbabadddbaaadaaaacbcacbcccbbccbbabbdccdbaddccabcccdaabaddbdcccbcbddbdbadddadaacaaaadabbcbcbdaccdabaddbbaddaddabddccddcbbddbddacdcbabcabdacbbaddabdbccdcbcdcbaacdabcbadddcdbdbdbcadcbdddadcbbcbbabacbacdbadacddaaddcdabbdcacddaacddcdccdadcdadbabccbbaadbabcacadcadcdcdcccaabbbadddbdddcbaaaddaccadbccbdbbbabdbddadbdaccccdabccadbaddacdaaddacdacaccddccbbbcbdbbddbcbdcdddbdcbdaadabdadcdcadcaaccddadcbacdcdbdccaaabadaaadacbdababcbaadcadbdccddabbadcaacadbdbdabddbcabcbdadaabacbdbadadcbbadbdbbccbdabababdaddddaaaadabbbccdbccbdbcbdbadddbcaaadacdbcdaacdaacbdcbbdbabcbccacabadbabbcbdccccaabaabdadcaabaaaabbcdcccdbcacbcbdcdbcabaaccbbaadcdbacacccbaaadccababcdccbbbcabdbbcbacabcacbadbcbabddcadaacdabccccdcdbdaabcabbcbadcbcaacacdaaccadbacddcaadbbcadcaaddddbabdaccadabaadadcbccccbcbddaacabdbbbbabaacdbddcaccddcbccdadccccdcddcdbcdbcbddbbabacabdddccbadcdbbaabbbaaaaabddcbdcbdadcdbcdccbcbbaccdbaacaccddaacacddddbbcabaddbcacddacbbdbdabdbcbdcbbdbcaccaaacbacdadbddbcbaddbaaabcbbcbbdcdcdaacbbbbcddadadaaabcaaccadbbacacadbccdabdbdaddaabacbbcadbdadbacbadabacabbcddccbaadaddcbacbcdaacbccbdddcbadbdcaadbdabdddaacacccbbdadbccadaabcbcddaabcbbadbdcbcaacbbabcaacbddcdabaabbddddbaddccbaccaacbcbaadbaddaacdcbdbcabcbbaaccbbccbccaacbddddaddbdbabdddbdddbbbcabbabccbcbdbbaacdcaadaaaadbbcccadbcacbcdccdadadadbcbbaaacaabdbbaccabdcddbccadabccbddbacabcddbbbabddcacdaabdcdabbbcddbaaadaadbbbcdbdacbdbaddabdbbaacccdcadbcacbdcddacdcdcacbcaaaadddbaaadbcadccbdcaadcddcadcdaadcddcdaddaabbdabbdabcdacbabbccadccbdccabaaadcaaacddbbdcddbadadbdbadabccacbbddcabbbddabddcacaadabaaddddadacdbcbcbbdcbaaacadadbdabbaddaaadcabcbcccadacbdcccddcaaacbabbcccdcaabbbccdbadbbbcbacdcccadccabaadadabbcbbbcbddccbccbbaddabbdbddcdcccbbabddcdadcbaabdabbdbaddbcdccacdcadbdddacdacacdaacaddddbaaacbaabaccbbddccacbbbccadcabaabdcddabbdbdccccbabdbbcbdcdbbbcdadddcabdbbcbbddbccccaddabbdbabaddbaacadbdccaacacccadcccaaadcdbcbaaabaabbcdcadadadaadbabcbcdbbcabaacbbccacdddccbcaddbbbaabcdacacabaadaaabacbdbdcbcbccaababadaadababbbbcbbcdadaabcabaabaccbbcdcdcbcbaddcdadacbabdbbcddbccdddddaacddbacaaaddbacacddcccabbadbabbbcaddcaaaccdbaabccbdcdcdbaadaaacbbbbaacdbacbcbaadddbdadcdaaddabacddcbadccdadcdddcccadadbadaabacdbacbcabadbdacbacadccaddcccadcacbdcbacadaccdacbccdcbbbaaddacbadabbaddbcccdbdabbadcdaaaacccbcdaacbadabddacbabdabaddadcabdbbcdacadbcddddcacdbcacdddbdcbcbccadcdcdbdaaabcdbbabbcbcabbccddbaaabbccadbcaacccdcabaaababcbdcbcdcaccbbcabacaccdcdabdadbacaccbcbcbdaccadacbcbbabdcacbdccbcadbdcacdcadbacdcbadcaabbcdabbdadcaabbdabbbabcccddccccbccacacacbbddabccaccbbcccdbacdccacacacdcdaaccbdaadbaaacadbdccdadbcaaccdbcdbacbbbaabbacccccdbcdbaccdbbdbcbbadddbcaccccaabaddddcabbbbbbbaaccdccbcdaaccabacadccaccdbbcdacaddcdcccdadaadbaadcababccdbddabdbaadccddbbbdcaddddcacdbadcabcdccdcaabccacbacbbbbabccadaadbcdbcccaabacbbdbacdddbaabbcdabdbbbccdccabcdbaccddbbcbcadcabbccbcbabbbdbaacadacccdcdbadbdaddccddcbcbcccaadaddcdbdaadcbcacdbddbbacdcbcdaacbaaacdabcdccbdbddacaccbbbcbcdacbbcaccbbcdccacbbbdccddbcdaabbcdacaadbaccbccbddaaacbcdccdcaaddcddcdcababddbddbcbacdccddaaacdcbcbbdaacacdadbccaadbccaaabccbaaaabacaabaadcababbbccddbcadcabcbbddcbaacddacddcbbbaaccbdbbcaadbabacbbadcdddbbbabddccbaaabcdadcaaabcbababbcadacdaddcdbddbbcabdaccccacdbbadbacdbbbabdbcdbbdbcbdcdacdbdcabdbdccadcbbdaaddadabbadadaaababaaadcddaacbbacbccddbccdccbcccddcbbacbbabcababbabbcdabdcbddcbadacdadadabdbbcaadacbabccccbbcadadbbcdcbccccabacdbcdbcccadcdcbccabdaaacdbbddddbbdabdcabdcadaddccbccbdbbbaabcdcdcbbbacddaadabbaaddbabddcdadcddbddabaccadacdcbaaadcddcbadcaadbcbabbbadcabcaabbadacccadbbbddabbdddcbdcbaccbddadcadadcbdbaacdbacacabccbddcbccabccacdbabaacadacadcacccdcdabbdabdabddbccdaabbcaaacdbdbaccdadcdbcdaccbdaaaabdbcddbdcccaaaaadadadccbacdaccacbaaaabacdcdbbdcdababddabcaccbbdbbddadbdbddacddccccbbbbcbdcccbcbbdacdaaccdaaacbcddaccdadbabddbdccbbddbdbbdacccbbbdaaaaacbacbccbbbaccbcbcdabbdcbabcdccbcddccaacbddccdddabcaabddcacbcbbdbaaadcdacabcdaccabcbccbaabccabbadabcddbacabaaabcbacbdcdddcaaabbcaddddacccdccacacbddcbbdcacdcabbbabbcddcadadaadcdbbbaadbbddadabdbadadcabcbcadddbbbccaadbacdadccdbaaabbbbbdcbccdcbdbabadadccbcdccadbbccbacdaddccbaaaacbbdcadddcbbbaacccbcadadaddbaacbbbbcdcabdabdbacbdddcaaabababbbacccdacadcbcccbacdccacddabdbcccacbddbdabaaabcddadbcccdadabdbbbcaaccbacddbbacbdcbdababaaadacaccdbbcdaacacdacadcdcdcdabbbbdaacabccaaabaabadaccdbdabcbdddabdacdadadababccbaadcbccdcdacbaaccdcbcbaacdadddbacdacbbabdaaccbddbbcbdccdcbbcddcdbcaabbbadbcdbabdbbcdcdaabcdbdcbadbcdbdcbacbcbabbccadbabbaadbcbdabababdbcaacbbcddacccadcdcdcdbabccabdcaddddddadbcbacddadbcdabbcbabdabbbdabcddbbdbbdacbcbdddbaccbddaabdccacbcdcadbadddadccdbbbcdadadddadcaccbbdbdbdbcddaacacabcbcacacadadacdbbdbccadbcdccadbbabdbdadaccbcccbdcdaccbacbabcddaddadbaaabdadadabbcdbadcadbacaaabaaaacddcbcbcdbbaabcadbddccaddbddadaaddadacaddadbbacbadcadacdbbacdccdaaacdbcbababcaccaaababbddbbccdccdaccaabaaaaacccdcccddddbcabdcbbdcddcbabbdcbdbacdaacacbcdbdbcbabdaaaabdbdbbccdcbbcaacacbaaacabcbdbdadcdacababcaaabccbcddddadcddbadbbbbdadccccaabbbdbbbcbbbcbbaddddbdccbbcdacbacbbccdbccbdbbacdadbdbcbbabbacbdbcadaddcbadcbdccbcaccaacddbbbbcbadddabacadaccbcaaacdbcddaadccbacccdbcdbcdbbcdacdbbcaacddccdadbddbcdccdcdbdcdcccaacaaacbbabcbbccbbccbccaacbbbcadaacbbdabbdcaddcccdcbcabdcddcbbaadacdacadbbdbbbcccbddacbdcdddacababadddaadcaabbdacddddcdcaccaaababcadcbcacbdbdddadabadaddacaccbdcccbdddacdbcbbdccdbddccacbabdddcdbdddcddbbdbdbcdaacddaddbabcbdcdccdcbdbcccacdcabdcccccbccaabdddadaaacdcadcbdaddacbbabcdaabccdcccaadcdcddccdbcccccabadacaaabaddcadbdbccddcbadcdaabbcabcbbcaadabdbcdbbccdddddabdccdadbadccbdbabbbbdcdcdbddddadaddcdcaaacacaaccbabcddbdcbadccadabccbaabaccbbaccdcadbdbdbcbbbdbaabaccccdacabccbccdabddaaccdbdbadabccaddaaaaaacdaadabcddaaaaddadbcbcbdcbcacbddadaacbccbdbcaaabdcdcccaaaaabadcbabacdaadcdbbdcbaacdbbaccdaddacadaadbbacbccbdcabbcbaacacbcbddddcadddaacccaccbdcaadcdddcbbabbccaaabcdbcdaddccdbbadbaaccdcadcbbadbcbacdcccacdccbcacbababcbbbdcbbcadddccdcbabbdbbbcacacccddbaccdddccbccaacbcddabaacabcdaacdccaabcacdccbbbccbcabcbddaadcbdaaaadcdaaadaabcacbccbdccbbdbaacadadbcdabddddbbbabddadaddcbccdbcbbbdcaaadcaaaccbbaddacbadccdccddadacdcddccbadccccbbdbcbbabcaadabbccbdcbcdbdbbadcbcdcadaddbcdadddabcbadacabcdcabcdcdaadccaabaadabdddcaababcccadadcddaaabdcdaaccaacdbcadddbbadcbdbaaccdabbddbcbadcbadadbcadcbccdbcbbbcdaacabbacccdadadabdcaabaddbacdcddadaadcdcabddbdbabaccdabbaacdadccdadcdddcdcbaacacdaabcabdaaaabdcabddccbbdcacaaabbcaacdccbcdadbccdddaddbadaaabacabbccadcaabccdadaacbabcdaabddbdbcbbcbbddabaddcabaddccdadababbdcddaadbabbbacabdadabcacbaadaddcdbdabbbaacbddabaccabbbbbbbbccdbbbbccbbaaacaddccbaadcadacadbcbbaccdcdabdaabacacdbcdbaabbacbaadbcbdadaadacbbbdccbdbadabdaccdcdaddbaddacdbcacccaacbbcddbddcdaabccdccaadbadcbddacbacadcadbaabbbcbcbdbccccaccaccddbbddabdaccdbbbacdbdbccaccaabdddbbcabbcbbdcbadcaccbdcdaadaabaadccbdbdcdaaccabbcdabacccdcbcbbdcabbadbacbcababaaddccbccbdccdaadccaacbcdcbcacadcaccabbaaddabccbcdaabacbdabdacbbaaddcbacdbdbababdcadcacdacaababcdbaddbcaddaccdcbbaacbabccdaddcbdbdcbccaaabaccdacacdbcabaaacccbddbaacadddcaaabcbaadcadcacdccadacbcccacbcacccddbaaaadbabcdabdddadbcbdcaaaacbddcaacacabdaabddbbbdcacaddaabbdbacdadddbcacaadabcabacaacbccddaadcdccbcccaaddbacadbbcbaacdbbaadbbcabbbdcdcaccabbadbcdaaccaaaddbcacdacdddbcacdbabcddccbdaccbbbccdbadaddbadabbadbbacdabbadcbdcabcbccabcdadcbbbcaababcbbcaaaddbbbbcdbbdcbcbdbbaccdddcdcbbdcabddcdadaccbbcbbabbbcdabacdcdcbbddaacdabcdccabbbabdcdcaabcbdcdbabdbbccddaacdabbbbdddcadccabccdacccbbccbbdcbababaaacdddbbadacdccdbacdcbbcbabddabcbdadbddcbadabacbdcccccdccbbcaabaaaacadbacacdbbcbddccbdcdcddddabcddaadaddadbbddbbdddcddbbbcaddacccdadacacacadabddccbdbabaacabdaaabbcbbaddbbbabdaaaaacababdcdbacacddddaccadadccaddacddbdcdbcbbdbbdabaadcccbabddbddcddbdddddbcdbacdaadaababdaabadbcccadbaadbddadddddcadaaabdccccdbcabaacbbacddcbccabccbbcaababcccacbbcccddacaabdcabbadcdbacabbdcbddaaacdbacabdbdcadbbcbdcababaabbacddcaccadccbcdcccbdccccbdabadcaabdadcbadaddacbcdcccacadbbaccabdbdacbbbcdaacccbaabaaadbbdccbadacdcaacccccabdacbbbcdacadabdcccdbabaddabdcdbbabcddbaddbbcddbbdbdbacaacacbaaccdaacabadddbcdaccbbccbccabdccdcadaacbbacaabdbcadabdbcdbdcbbadacabddbdcababbdbbddcbbbcabbacbdbadbbdaacbacbcbbbcabdbcdcacbbacdbdbdddadcacdbbbcbbdcddbcbbaddbbccaaadbbdacbbadabcadccbcbdddbdcdbaabcaacaacdbcaacbbbdcdcdabcababbbaddcbdaadaccbabdbbcccccaaacbaadddaacaadbbbddaabddcacbdccaadbcdcbcabcaabbbaaabbdbabacbcbaccadbdacaaaabcddbcacdbcbacadbbbcdccacbdbbddaacdcbccbaaadbbdbbbdbbcddaddaddadbabdbdaabaacacaabddbadcbcdbcacbddcdcddcadacdcccbcdddddbabbbbccddbaddcadcadaadacbbabcadaabddcccbbbdbdbdacabbdcdaadcbccdcbacaabccdcdababccdabdbaacccbababdddccbcabadcbbdbbdacdababaabaacbacbdcdcadcddcddbadcbdbcadcbacadcabcacdcccdcbcacadcaabbdbaacbcccbccacdaacdaddcdacbacdbaadccbddcddaadcdbbcdbbddaabbcbcdabdacabbbabdbbabaadbcacbdaccbabdbdbaddcdddbcadbcccaabbcbcccabaddacdabdabadaabaabdcbbbcaddcaccdddabbdcbbcbbadcbcdcadbaccbbdcdcccacccbbbdcdbcdcdbbabaacccdcbacdbbdcbaabdbcbbdadbdbadddcaabbacadadcbdabadddccaabcdbdcdcdcabcabbaaadcabbdccacdbaacbadcbdbcdacbdaddbaccbadcabcdbddadbdbccdacbcdabdbabbbddbbbdcacadcbdadbaccdcdcbcdbcacacdbcddddbcadaaacddddcbdabaccdadaaabacbacdbbadabbcddbcabcccccbdcdcbdaacccccbacddbccdccccdcabaccacdcbcbababaacdaddbdbaadaaaaababbbabbdadbbdddacddcaaccccbdcbdbdbabdbccabacddcaadcdbddbaaddbcaadcbacccacadddbaaabdbbcbbbcadcbbccacdbdabdcdaccacbbdaaddaddbcdcadbaabccaadbaacbbabddaacddbabbdaaabbaaccbbcdababdccdadcbcaabbcbbdccbcbcabbcbaccbacadbccdbbaabcadbbacdcccadadadacdaaccabbbdbbdadbbbdcbcdbbcdccdddbabbddadbadaaadabdcabadacccabaabccabadccdbbbbabbacbacabacbbddacdbdaccdcbbcaddddbadbddcbadaccbaaddbdbabdcabccbcddcbdbaccaaddcddbbbdacdccdbdccbddbabbdbabdabbbadacadacaacbbdcbcaacaccbdabdacdddbdabbadbccaabdbcbcdaaabbddbdcbcacdbccdaacdaaddcdbbbacdcbdbdbacadbccbddaaccddbcbddcdccbcdacdcaccdddacdccbcbbdbadbacdccbbaddbaaacabdcbdcbbadcdcbdbdabcaddcbbdbdcbbdadbcababcdaacabbcbccbcddcbbccbdacadcdccbbacccdcadacddcdbabdaaaaacbcdaaadabbbdcbaadbadbcdcddaabdbcbccaaddbddbdccdbbacdbacabcdbbccdbdbcdcccabdacdddbaacacbadcbccabdcbddcabcddaacddcaddaddddbcaddbbabacdacddaccdbbcabcddbccbbaccddcdacccacabbbdddcaabaadaddbadbacccbccaadcdcaabadddaddbacabdddcddcdcdddabaddaacbdbbddaddadbbacbbdddacdcaabbcacaacdddabdcbcdbbcdbacbdcdccbbbbaaccbbdbddcbbcddadbdaabbccdabbbaabdbbdbbdacdcaadcbdccabccccaacdcdbbadabddaabdabcaaacdbababcbabcababaddddcbcadccccbdcccbacabadadcdbdaadcabbaddabadcdadbdbcacbcdbcccddccaddaccdaadcdcbdbcaadaaaacbdabcbcdadddbbbaaddaadcccccaccacdcaadadbdcddcdddcbdccabacabdaababdcbdbccdbdacabccdcdddcbaadbdcbabbabccaaabbcaddaddbaccbababcddddcdabddddbcacdcbadaadacbbcdbcccbcadcadbcdbcbdcacdaaccdbbcadccdddbacadbacdabcacdbadabcdcaaddbbadbddcaacdcacbaccbcccdbcabaabbcccbdacbbcacdaaddcbacbbbaacdaacdabbdadcacdaabccdbcdbcdbacbaddbacbdddaadbdddcccddbdccddacaacaacaacbacaabaababacbacbdbccaaaadddadcdcdaaddcdddabdadabcbddcaacddddcaadaaabcacddadadacbbdbcaacdcbbcdbcddbbbcddadcbdabdadadcddcdacbbabdddbddbccbdbcacbcbdcdaadacddbccaaccdbbccddbacbcbaadcbbbdbcddababcbbaccddcacbdcdadbcbbdddaadcaddaaaacacbbabdaaaaabadccacdadbdbbdbcdcddbddccabddcddaaabadccccacabcddabddcadadcddcaaaadabdaabbbacbbbdcdccdcadadddabadccdacdbbbddbddcdcccddaaddacdbddbabdbaccadabdbacaacacadadbdddaadaadabcccaadcbddaccccdbbcbaddabacaccbbddbbbdcdbddcdbcbbbddaabaacbdabcaadabddbadbbdcacdacbdcddcacaacddbacbbaddbbcadacdabdbdcbddcdbacdcacdabcabdadbccadbbcbdcaaabdcdaadccbccacdcaabaabbcbccaaaaaacabbaccbaabdbbcabaaaaaddadbbadbcddbabcaabcaacadcadbdcabcddccabdccdabbcccddcabcbbaadbadaabbacabacacacacbcbbacdcabdddabbbbcdcdbbbbdcadcbabaabadbacddbcccdbbbcccdcabacdbcbcccbadccababcdddacbdbacbddcbcdcbbcddaaadbcdabbbbbcbdccddddaadaabbaddbcdcaadbdbaadbcbcabcaadddddcbbbabdcbdbabbdccdddbdabdaaaacbddabbbdcddcdcccabaaadbddacabadabddabadcdccabbbcdbaccaacdababbacdcbacddaacacbbcbcaaaddadbdccaaabcbadbdadbcbcaabdbbbcaabacadcbdbdaadccdabcaccbbccdacbcddcdaaacaccabbcccabdacdaccbbbacaabdbabdbdccacddadadaddbcdcbdbbbbddacbbacdddbdcacccaddcbdacdbaacadaadcbcacdcadadcdcbabbddaccaddcbdacabcadbccabccbdbacaccddccbaabbcbbcabaabbcbdacdbabbccdbacddabaabccccbcbbcbdbacddcadacadadcbddcdcddabdbbbcdacbcddadcccadbdabbabacabcddabbbaadacaccdcadbccadabbccdbdaaaddbcadddcdabbaabacdabbdbacddbbdbbabbbcbcaadbdbbabdbcbdcabaadcbddcbbbcdaddcbacdbcbcadcdddaaabdbdbdcbdcabaccbccdadcaccaadbbcddbaabaacbacabaaacdaaabdcdabddaaadccccbdddcbacaaccccaddcbbbdbcdbacadbcbaaadbacdbbccbddccccdbbbaaaabbdaddccbddbdacbcaccaadbaaacccdbdacbacdcaacbdbabbbddadbdbdadcdbbddbaacdaaddcaabcddaabcdccacccabacdacabddaabbdccabcabbadadadadbdbbabacbccddabdbbbcdccadccdbccdbddcdcdbbbdcbadaacabcaadcdcacacbaaabaaddddcdaaaaabddbaabcbadabbccaaaacdcbdaddbcbabbabcabaccbbdccadcabaaadadbdadaddcbbcdcdccacababdddbaacaccbdadadbdacabdaacabacbbaccdcddcccbccccbbbbcaccbcbbddddabdbbdddbadcdadbcbbbaacbdcbacdaaabdcaccdcabdbdcccbdcaacccaaadbbcdbbbcccbdadbbaddddbcbcbcbccaabcbdbdcdbaddadcddbcbdbaccacadcbdaccabccdabbbbabcdbbccbbcbdcddcadaaaaddddaccbdddbdaddcdddccbacdaaccabbcacbaddbbbdbaadadcbcbcbcbbacdbddacdabbccbdaccbaadbbaabdbcddbcbcbccbacaddabcaddabbdbdacacddcccdccaacdbadcaccccbdadadccbbcdbbacddccdbaaabacdcbaaadcbcddcdbdadcabbacbdabdadbbdacacdaabcacdcbddbbcbaddadccddbbcabcccbbcccbabdbcdbadcdddbcacbddddccaccdddacbcbdcacddddcaaadbdaabddbcabcaddaadbbdbbddbcdddcdbbcaaccaddbcbaddcbadbadabbbabcabacaaabbbdcacbacadaabaacbcccbbbabbcdbdcdcbbddcaabcbcbcccbcacaccdbaadaacaccaddbcdaaaacddabbbadaadcdbbbcddcaaccbadacbccaaccdbcbbaabacddbadbcbdabbccbcaabdadacacdddcbcdadbbbaaabadbaaaacccadbbdbddcccabaaabacdacdbabdcddacdacbabccacdddcccdcbbcaaccdbcccddbbbcabbacccbabdbbdabdabdabadcbadaabcacaabbcabdcaacdbacdcdacaaddddbdadcbaaadadadccabddcaccaaaadcdaadcabcddabcbabdcabcbbdbbcddcdbadcbbdbbbbcccccdbcaddaccbbbddaabdadacbccabbaacbacbbcbcacacacbdabcccaddddccacbcbacbabcdbacbaadbcdcabaaabddddbabccdbaacadcadabaaadacbbacdbbcbcdadcddbddadddacccdadbdabdccbdddcdbabbabdcdbddbcadabbadabdacbdccdacaabadaadbdcdcbbaababbddcabdbbaadbcdbcbbbdcbbbccdddadcabbbbcbccccbdaccddacdbabccaacccbbbabdcacdaaaacadddddbdbcabcbddababdcadadadcbbabbccbbccbccdaabaacdccbaabdbcababdbaaaadaccaaabdadaadaacaaddacddaaabaacadbccdcdacdcabbbaccadacaddbbdaddcaadbacccbcdccacbdbbddbaddaddbcddaacdacbcdddccabaaabddacccaabbddadaaabcbabaabbababcbddbbbdadddcaccaddbacaccdcdaadabacaaabdabcddacddddabaabcbdbccadacccddbaabcdcdbccdaccdccdaabaaaacddcdadaddcdabbadabdacdacdccaabaabcabcdabddacbaccbaccbcbacaddcdbcabbacbbcbdcdbbabdccdbbabcdacdcbaddddadcdcbbbadcabadcdacdddbacabddbdbddbbcbaacabaccbccbbabdddbdaacdcaccabbabbcaddabdbaaccccbdaccbccabdbbbbdbcaccccacdacbadbadabaaabcabbbabcbbdbabcbbbcdbbadcaabdcdbaccacdcbbbbaaddcbabbadaabbbbabbacdbbbdbdcaddcabbbccdaddabcbbdaaddcaccbdcacaaccbdcdadcdbccaaaadaacddcaabadcdcdbbdddadbddbcbdaacbcdccdccdbbbdbbcbcaaaaacbdbaabaacdcdcaddaaacabacdbbddbaaaccdacccabdcddadcabababbcbcdabbbcbabbcbabdbaadcaaccbaddbcabbcadadacdadccddadbcbcccccdacdbcacbbadadacdccdbdaabdabcbbdbdbcacdbbbcccaccdbbabccdcdadbcbcbcbadcadcbdadccbdbdacdabbbabbbccbdbcaccddcbdcadcabbcaccabbccbcbdbabcccbdaaddcdccacddbcbcababcdcdcbacdbbbdbcbccdcccccbbacdaaabbdabcbaaaacddbbacdadcdbcdcababdbadaddbdccbcacabbcccddadcccacaccdccabcdbbbbabaacacaddababbabbaabbbbcdcaaaabddcdabcbbdcaaccadbbdccbcdcabdaabbbabcccadcdadbadbdacbbbccaddddcdaddacabccbcbcaccdbdaccabcaadadbbacdbaacadbaabcdcbabbdacbcbcdadaaaadacbbbbaabcabbaaddbddddaaabccdbabdaacadcbddaacdabbbbbbbbccddccaaababbdacbdabdbacdcbbadbabcdbdacaadadcbbbdbbdbcddbadcadacbdcccacaaaabdcabddaacddcbbbbcdabdaadcddcacdcbdddadabcabadaccbbbadbddadaadabcddabdccccadadcdaabbcbcacacbcbbabadcabbbadcdbabccddccbdcbdbaaddbaddcdcbbbdadcadddbadbdabcbabccabcaaddbbbbaaacbbcdcccdcaadadacbadbbacbbcacbdcbbbaddbbddbdcdccdcdbadcabadadbaddabddacbaccccadcaddbcadccdcdbaddbdcabacdbcacbbbdcdbabccadadbcccabdbbcdbaacbbbcabbbacbcbbdaaadccbcbbabbcbbcadccbbadbddcdcaacbaabccaaddadbaababdaacdbaddabaccddcadacbbdadbdcdbacabdacbbdadcaabdddcbcacaccbbdbcdbcdacccadbaadbccbadcdccdcbcbccccabaadbcddcaacbcdccccdcbdbabcbaddcdcababbcdaacabcbaaccdbbdadbccaacbccacccaaaadaddccbcaaadacbcdccdaacbbccdbdaccccacadcccaccdbaadbacbdddbabcabcbdcdbbcaadcaaacdaccabdbcbcbcabddcdbabdcbbcaacbdbdaddbcdbbbbddddbcdddcadaccbaadbbddcddccaaacdacbcccbcdbdbcdcbaabccdacbabcdaddcaddbdabdcbdcaaaaabbddacadcccaaaadabccdaaccadcdbbbbaccdbcababadcbcddddcbcbacdcdaaccbbdcdcdbdaddaadaacbdacdcaddccdddbdddcbcadddddadaddaaaddaabbddbdcdcaaaacccdcbdddadbbcdabbacaacbbdccacbddbabaddaaacdabdcdbccbbbbdaaadccdccdddccbcbdaccaacddcbddbdcbcacdcabdbddbadbbcaccbbdccabbacabbaabaccccbcccacaddcbbbcbdbbbdcbdcdcccbbdabdadacbccbbbbcdbdbadcdacdddcbaacccbccaabbdaacbdcaccdccbaacccaacccbddbdbdabaadcdbcacddcbbbbcbddbccdcdacddaccadabadcaabcabaaaddbaacbabaccaacaaabadaabdacddabcddcacdcaaabaccabcccdcadcbcbcacaddbbbccdadaddbacdbbacccaacaababcdadabadddadddabdccaaabdadccccdbddcacbccbaaddbbaacbdadbbbbdaabbdcaaaddcadcdbcbcbbcaadbaacabdabbdbadccdbcbdddccbbadcabddddcbcabbcabcdddababbaaaababcbaadadcbcbcbcddcaaacdbcddcacaacaccadccabcccdbdcdbbdccddbcbbbaabcccccdaaddbcadcbbaadabcccdbcddbdacaaabbbbabdcabdabccddadbcabaddaabcdaddccdccaabdddcaddadacaaccbcdadbdaddacdbdbabddcbdbdbdbbaddbbdabaadcddacbaddadbaaadabdacbcbdcdcdccbabdaadccbacccaddadaaadccbcaababadcadacaddaccadbaaccaccccbabbbacbdccbaadabaacacddbabadaddbdccadadaaacbcdcddabbbcdbdbbdabccababbcdacdcddbddbbcabbcccdcdbbbbabbadacaaabbdbbdbccaccaacaabdddaaccbcccbdbdaddadbbddbdcabcdbbbdcddcacbdddacadbbcbdbccdbbbddddddabbccbcaddaaacbababcbdcaaacaacdbacbcdcadbcaddaacdccbabadddaccddbcddddcbbdccdcaacbcccdabaaababdacbacadbdabcaddbcdbcadaddaddbbdcbbacdadbbacbcdadbdaddacacacbdccaabacadbbcbabddccdcccbbdbcdbddddcdcbdbccddaddddbddaccdabcccdadcaaaddccccbacbbdcdabbdabccbaadabacbdbcdcdbcdbabcdadaddaddadcbdbcacaabcabadbbcdddabbbaaaadcaacacddcbccadaccabccaababbdaddbdbadddaabcbbbcaabaabbabaabaaddbdbdddcdabcbdbbddabbbbcddbdddbbdcdaadabadcbadbacbdcadcaacbdcbacaaaddcbbcbbabbcbaddacabadcaaddaabcdcdccdcaabbadababbdbcbdbdbdcbbdddaaacaacacbdbdaadbaacdaaadbaaababacbcdcdbcddbddddabddcbbcbcbdabcccccdbdcbdadaadabbccdadcaddcadcabcccdccaadcbbbbcadbbbacacddbbdbddaacacbaccdcdccbdbbcadacccccdadadabdcdaaacaccaaadcdacddcdcbacbccabbdcddadabdbbcabdcddccdddbbbadababdbdcdabdaccddddcbcdcabccbadabacdadabacacdbbaccdcacbabcaccbabadbacdaaabbdbbabbcbbdddccbcbbcacadabbbbccadaaadccaccbadaddbbbdcbddaccddabcbddaacaabbacdabcabaadbadcdadadcdcbdacabdababbbddcbdcdbddbddbcacccdcaadabdcbcbbbccadddbbbddaabdadddaccdcacdcbadcdacaadcbbdabaaaabbcdbdcdcdddbccdadcddbaaaabbddbabbacbdabdbcdbadbbbbdacacdabbdddcbccddccccbdcddccdcacabbbbcbbccbdcccdcdbabaaaaddabcdbccacabcdbddbddacccbddbdabbdcbcacaccaaadcabdabccaaadcdbdcbbbbbdbcaddcdbcbbaadaababbccadcdcdaaadcbdabccdccacadbadaaddccbdacbbdbadcdabdbaabbcaabdaddadccadadaccbcccacaddcbbdbbdbbacaddadbacdccbbdbbddcaadbdbdbdbbddbdbbbbcdddbbaabddddddaccccaacabcbacabcdcccccddbbdaddcddabaacbdbdcdcaccadadbdbbdabdddbddbbbabdacdbbcbdbbadbcccbddacdbbacdbccaaaccdabcbbcccaababdcdacbcadabadbbdbbbadbaddbabcbcdbabdcdcdadcaaaaaaadcacadbdbcabadbabcdbbcdcdaccdbccbacadacddcbaaabaabaaabddaaabcccbdbcdddadaabdabcacabacbcddaaabaaacbacaddacbdbbbadcbacbacdbbcddacccbcbdcdcccaccbdaaadacdaaccccdbccbbdadadbaadabacddaddbabdaabcabdbccdacbcacaccbadbbbadcacadcccccdccbcbddbbaacdbdbddabdadadcbaccddcccbcdbdcdbbadcbacccaddaaaadaddacddcbadbcdcbbacaddbddacdcbcddacaaadabbcdbcbcdbddbacadbcbccaacdcabddbdaacaaacdcbaaadaaddccdbabcaccccaabaacdcbcdcbdbbbacdbdcaaadbaacbbddbadcdcdacccbaacbabcbdddaacbbabdcbcbadcadcabadcbdadddddbaababbacbbdbdbcccadbadabcccbcddddcdbbacbdbcabdccabddccdcadbaababbddcddabacbbaacaaddbcddadbcdcacdadcdddcaadbdbbdcaccbdadbadcbdabadbdcbabdcddaddacdcbaadcbcbbbcaacbacbbbdcadcabaddcbccadcccaccaccaacdacdddbdacbdbbadbbdbaaddbacabdbabdcbaccdccabcbbddbdbadacdabadccbbccdcdcadbcadcdcabdbaddababbdaadccbbbcdadadccaadcddabcbadcabacdaaacdbabbdddddddaddabddcdccdccbacaadaadcadacddbcabcdabcdabddbdddaccaaacbaccdadddbdcbbbacacdcccbbbcdaccdadccbacdabcadbbbcbcdcdbbccdcdbcaabcaadcdcdccbbadaadadbdcbbcdbabcbbbacddbdddbdbcacddbcccbddaabaadcbcdacdddccdbbbccbbcbabcccabcdadaabcacddaaadbbacacaddcbddabcaaddaacabddaadaccdacabbdcdadcaacadcbbcadadbddaaabbcabacbacdacaacdacdacdaccbbdbacbadaacbddddbdadcdabbbadbaadcbdaaaddabacbbadaccccbaaaacdacddccbdbccbdcbaabdcdbadacadddcbaaababbbcabddabddcbcaccabcbdaaabdaaadcabaabdabbddaabddddccbbaabddcabbadabcbbbcbddabccdcdbcdcabcdbdcdcdacbdbaddcbacccababdbdaadcadaabdadcabaaaadacaabcadcabadabcadcabdbaddbabaacccbddccbddcbbdcaacaabaaabbcbccbdaccbcddbdcdaadbdbdddabcaacadccaabdaaaccacdbabacbdbdbcbacdddcabadacbbdbaaabbccbdcdccbabccdcdcccbabcadbbcdbaddabaccbbcdadabacabbacdacaddaddddbcddbabaddbaaabcccabcdabddbcdbcdaaaaddcbbababdddabccbcdabcbccbcccabdaadaaadddadbcaccabbacbdabbbdbccddcadacbbadcabccdcbaaadabcdabaaadbdbaacbbadabbcddbbbcbaacdccababadaabddccaccdbaadbddccddabcccbdaadbadadadbadbcbabbbcdaaaacccbdbacccddcaddcbbbacbbbcccbcbcdccdabccaaccdbdbcbcaaddabdbaccacbcdbaadaddaabcbdcabdcdbdddcbabacbdabcdcdcabdbbaaddbbcddbdadaaccdbbbbaaadcadcbdcdcccdbcaddaacacadddabdabcdaadbbdbbbcbbaadccbabaaaabbababaacbcccccbdbbaabcbcbddddadccaddddcaacadbcabdadaddcbdbcaccccdbdbdabdabdadbcddbbddacbadbbcbabbaabdbcbcabaacdcdcaacaddabaadbdadacacddcbaabbbbcbbcdaabadcaccabaccbcacdbbcbbdcbcadbcbdcaadbdbccabcdbbdbdaaadaccccdbcaacdbaacaccbcbbdbccdbddabbadbaddacdadbbadadabaabcaccbdbbcaababdcddadbdbcbdcddddcaabdaacaacdcdacacdbadacbbcadbccababcbcbcacbcdcbccdbbaaadbdadacbbcbbcabaadcbadaddadacadacbabbbcdbbaabaabccabaccbdddbbdbadaabbbdaacdbaccdcaabbccacdaabaadddcbaaacabaabcdcacdbccbbaabbabddddbccbabcdccadcaadbbdbccdcadcdaddbabbcbaacbbcabddbadcadddbcdcbdbbaacbdddddcddddcbabbaacbdaddadcaddabbbcbcaadcacacddabcccadcddbaacaccccabacabadbbdcbcbadcbbcadccdccccbcdbbcbbbcbabaadcddaaddaccdbdaacbacbbdadbdddbbdbbcbddcbcbbccddbbbdadacccacbadbbbddbaaaaacbbcdbabbdcaccdddcdcabdaadbdacabcadadbacdbaccadadaabaadbcbaddcddcbdbadcbbcddabdacbdddadcbcdcabaacbaaabcdbaddbbccadbaddbdbacaabaaccbabbaabababdadddaccacbbbdadbbcdbcbcddcdcacadaabdccbdbdbbbaccdccababcaabaabcaadbdabacbdbbdacadbaaddccdbddadbbcaaccaabdababcbcccddcbabdcddacdbaacdaddcdcccdbadbbccadccbcaaadcddddcadcbbabacdadbabdbdccacadbbbdadcbaabcccaabccbddbdcacbbdaacbbdcdcddcabcbdacdcacccdabaaaadcdbcaacbadcccddbdacbabcbcdaaacccabadacddaadbdcbccabbaabdddadbabcdddbbdbacbbacacabdcabbdddabababbaabcdcbacbdbdaddacccbbcdbddcdcadddacdcdabdbaaccbcbabacccdbdbdddbddaaccaadcdacbcacdbbcacbaacddabaaddabdcbccbaadcbbacdbcbbcccbabcaccbbcabddaacaabdbabbdaacbabdcddababbbbcacdbdcbcccadbdaacbdbbbcaacacadababccbbdcddadcacacdadaddadddddbcbcdcdbcacaadcabbbabdaacdbadcbacbbacdcdbbbabdddabdcdacbddcbbadcabaadbddbbdccddaddaabadaaacdbdcbdcbdcddabdaabdcddcbccddbbdabdddaacaddaadddbdaabcccdbddabbdbcacbbdcbbbacbaabdacacbdddccabdaadddcbacbddadaababdabdbccbdaadabadbbdcddcaacdababdbabdaddadbaabcdcdbcdaadaadcbcaddbccabcdabddaababbcbccccaacddbdabacaaabcbdadcbaccadabdbaddbccdcbbdacaadcbaabcddcccbbccaabadccaccbaddbbabaaacaabaabcdabcbadcacabcddabacaadadbcbdadbbbcbbcbdcdbcdcbdbdbbdcaccccadbadcdcaaabdcddbccdcdacadbcbdcdcaadccdaddadcdbdaddbbbccdbcddaacdcccaadbacddacbaadacbccdddcacaabbaabccdabbbaccbadbaccdaadddaabbccdacdccbbadbbadaaaadabacdcadabdcbcbbabcdcacddcdbddbdbdaadcadacdcccbcabccadccccbcdbabcdadcbcdccdcdcbabdbdaaaaddacddaccaacddbdaadbdacaadadacccbcabbbbbccdadbcaccbbdacabbcacaabbdacddcbbdacdcccbbdddcbdcaacdccccbcadacacccacaacbcbccacbcaacaccdccdabccdbcdcaadddbbbbbacabbcabddaddccccddbcaaaabddcdaabacdccdcabbcdbbdadcaddcdbbaadbbcddbaccbcbddabcdadcccbdbadcdbcaddbcbabbbcaacaabddaaabdccdaacdbaadcdbdbdbcaadaaabcddcbbdbdbddaddbdabbbbacbbddccbbdccbaacacabdaabaddadaaaabcbdabbbcbddacbcabdaadaaacbabdadbbbabbaacbaaabadcacdabcaaaaddcacdabadacbbacabaacbbcbbacbcccaaadcbcdadacddaaabacaccacbbcddaacbcdbcbbbdaddabdbbaadaadcdcdcaacbabaabaacaaacdbccbbaaaaaadddccbcbcbbbbddacaabbbcacababacdddbdcbacddcabccbdbababbddcbccbcbaaccddadadaaddabcccadddacdbcbbbcbacccabcdaddbbbdacdcbbcdbdadbcadabdddabdababdccdccbabcbbbddccbabddcddaabcaadbaabcdbdcdaccaadbbacadacaaaaccbbbcacbabaabbbcabdcbcdabadadccaabdcabdaccaadbdcabdbcbbbdcbdcccddadbbbcdacbdddcacddccbadbccacaacddbaaabcadddccccdacccbcdaaaabbacdbdbddadbdcdccdcbdacacabcdaaaabbabdcadadbdadccbacbdbcbccbcbbdcdccddadcdadbcacababdbbdaacbabadcccdbcabcdbcbdbcdaddaaabccdabcbadbccdcbcdddbdaddabcdddbcccdbcbdddacbbcacdaccbccbdcaadcaaacadacabdcdaccdacadabbdadaacbacacacbdbdcaacccbcabacdcbbdbacbdbdadbbccdcdaacddababdabaddbdbdcdabbdaabddbcbdcacbacbadacdbbaaacbadacbbbcaadbddacbcacadddcdcdbbddaadaaccacbbbabccddadbdbbadbdcabbbbdcabdadababcdacdcdbddadccdcaabaaddbbbaadabcdcbbbdbdabbabddbcaabadcbbaccabcabdbdcbdacdcacdccdbaacdbdbcdbabbdaadabbbcbacddadddbbadddcddacbbbcddddbbdbcddcccdadbbbadbbaddccdbccadaddcddaddcbccddbbcbbbdadbcdacaabcccdccdaaaadbbabaaadbccdbbccccaadaddbcbcadabdbbcaabccbaabaabbadbdcabbbcacabaacabdabcdacacacbcbcbbbbbaccaaddcbdccbacccabbcccbdccbbcabdbcacddabcaaccbadbdbadacbcbddadbcdcccdcdbadccabdcbcadddbdaccaabadbcdbaaacbbcdaddbabcbadccabbdbddacddcbdcadcbabcdadadabdbcaacbadcbabdddbbabdbdddabcbbabbcdacbcaccadcdccccbadddbcbbbbbddddccbbabdbacdbbbbabdcaccaacaabaddcdcaabbbbcaaddaaabdbcacbdbacbaacdbaacbccbcbdacadacdddabcbbababacbabbaadaaabacddcbdbacddcbbcacdcbbccaccacbcadacdcaacbbadabdbbbdaccdabaccacaadbcbbcabcbbbccdbbdcbdddaddbadddcdadccadbddbadaadcaacddddbbcabcbcdbcdbacdabbabdaadcabddbcadadaddacdaabbccbadadadaabccdbbdaddcbcaacdbcaaadacbdcdaaccbddccbcddadbcbdabdacabbbabcabbcbaacccbbadccaddcadcbbdaccaacabbdadaaaabaddcbaddcdcadcddcddcdcbccbdbacadcccaaccaaaabdccbddcbdabbcaddbcaccdbcaddbbcddbcadcbabbdccabbbabbdbdddbdacdbbdadaaddacacbdbcccabadbcccdaccadbbbaaacaabbbddababcadabcccdaaadbbcdccddbcaddacadbddbacdbdbdcadabcbbaadcbddaddaddcaadacbbbaccaabaaaabaaacdbcccbdcbbdcdbbcccabbbaddacbabbacdcacbbaadaaaaabbdcccadbcacddcdbdddcaccacddbddbabbcadcdaaaccdcacaddaabdccadcdaabdbbcdbaddbcbdbaddaadabccddbddcadadcbcaadaacdbcccbcccbccacacbbddaaaaabcadaadadbcdbacdbdaddadbadadddcacccdbaaabdaddbdabdbbbacbcadabbbdbcadcdbbbddbdcaacdbccdadacbacabadcadaaacabbdccaaaaaaaabcccacbcdbbaccbddcaaabbbdbbadbbddaacabdbccdadaabbaabbcdabacaaccccdbdcccadcdbccadddbcaadacdddccaddbbcaabdbbccaaccbacaaaadaacbccbccdccddcbccbbabbcadddabadbdcadcbddbddadaaabaaccdddacadbaddacaabaababddbccadaccabcdabbccadbabddadccbabaabdaacccbadaaaaddababbabdbaadccabaccabbcaddbaabcdccdddcdbddbdcbbbbdadadbccabbdbccbcdaabbddabacaaadddbaaccabcadaddddcaacccabdbbbadcaddacabaadcaabbbcabbacaccbdabacaccbbaaadabdbdabdcaadbaccbbbdbaadabddccccdacbaaddaccbdcacbdcaadcbbbbdbbdaadcacabacdcbbddcabcdccbbbabdcbbbbabdcbbddadabbcdabcdddbdcaabaadabcbadababdbdbbdabbacccdccdcdbcaadcabbabbcbcbaababcdbccacdadbabaccdbbcbcccbdcaccbbcccccdbabdddbbcdadccccbaccccdaacddacdcbccdbacbababadbdbcccccdbbadadbacbdaccbdcdabcabdddbcdddbcbaadcbbdbbcaaadbccdcacdddcbddadccccdcabcbbcdbbcacdbdddccbdbbacbcadbacbcaddabcadbdaddbbcadbbbcbbccabddaccaadcdbcaaacabdcdbadbdcaadadaccaccaddaadbcdabcadbdcdaadacbcabdbbcccdadbbddacdacdacaccbaccbbabcaccaddaaaaaddcbbcccdadabaccdacccdacdaadcbccacabbabcabcbcacbbcbccaacdacdcddabdbcacdabdbccaadbaddccaadbbdcccaabadcdcabadadbcabbbaadacdcaccadabcbcaccdaaaddcdccccbdbaadcadacaaaacdccaccaddababaabccbacadabbcaddbbcaadaaddccacccccdabccbdcaabbdadcbbdadbcdbcccccddcaadbabaddddcdcbabbbbcbabdbcdcbbacdabddaacbddbcabbdbdcabcbbdddddacbadcdacdabdabcabddaaddacbadbbddaaadccbbdcaccbabddddbdbacaaddddacacabbbdcbccbadabdcdbbcbcabdcaccaacbccbdbdbbabdcaaaadddbadbcddccabcdbacbdbbbbbbcadddbbbcdbacabccadcddacbbcacbbbadacabbddcbddbbdcdbbabadbcbadccddbdcbccadcabcccabbdadbabdccddadcacdbaaabaccbacbddbbcddabbcbdacadabacacdabbaadbcdaaddadddbbbbcbabccccbbaacaabaddbaacccbbdcbbacadabbcacbdbdcbdbbdcbdbcbccccbdbcdbdbdbbbbcbcbdadbaaacddbdccccbbccbcdcccaccddbbadccccacabcdbcadccbadcaadaabcacddadcbddccdccacaadbaaddcbcdbabdbcacbdaaccbbacdbcbadcccbcddbbcbaabdacbbadcdbacbddbbbdbacadbdbdaabbadbaddaacaadbbbdddbaddcddcbbdccbacabcdcbadcddadabdddacbbdbbabcbbdbbaaabcacbacbabaadbbacdacccbdccbdbbadcbadcacabcacbcadabcbabaabcaddcddbdbccdadcbacaaccdbaaababddbabcccadccccbaaaacabcbcbbddccdbabcdddaddccababbaddcbcccacddabccccccdcbbaacadbadbccdacaabdcadbabaaaadababbccdbbdaddcbadcbdacbabdccabcdcbdbadacdcbbdaddaddbdbcddddddadddddbdabbbdbbcbbcaaaccdbdaadcdcabcdcddbdbdddbdcabacddacdbbcbdcadacaaabdccaaaddaadaddabbcddabbabdcbcbdadbdbcdccadaaaccccaabddcdbddcbcdcddcdcdccdbabdacdbcbbacbbcbbddadbdaddbcacabadadbbcdabddcdbbddadccbcbacdacdbbddcbbccccccdcabbdacbbbbadaaacdbdcaadcaacacdbadccbbdadbcbbccaddaacbabcddabdabbadcacacbcabbddcbdbcadcddababddcacddcdaacbcbabaabbbbdbbbbbbbbdabbcaccacacdaccdacaddddddbaadccacabadcccbacbaadbdbbbdccadcabcdbdabbadbcaaacdbcbddbdbcbbacacbcdcabacdbcdbbbdadbacccbabddaaadbdbcbadbbadccadaadbadcabcbaaddcdbddabbcbbdacccbdaccbbbbdacddbccdaddddacacccdbaddbcacadacbbcbdabacdacdddcbadddcadbcacbdbdacbababdabcdbddcadbbadaccdadaccccadcbcbbbacbcaccadcdcdcadbaaacadbcbadccaaacbadadcbbdbcbadbddbbdddbbcdaaaccbdcabddacccbbaabbabcbdddabacbddaadccdadbbccbabbdccbcadcbabbcdaaaaadadaaacababbbdacbacabaddcccbcccccaabdabbbdbddaadcbaddadbdddadccbadcbbacbbadbdcdbaaaaabacbbabbcadcddabcdccdccaacbcbcacbaccbbacbcbdaddadabdaabbcaddcbbcbadadbcbaddbdcbbcaadccbdadadbadbdadcabdbabbacdbbcdcbabbbabbbbaabbbcaabbbcbcbdaaabcccbaabddbdcbbdccadacaaabbdbdcbbbadbbccddddadadaaccddcccaaacbacadabaddcdcdcaaabbbcacdcdbbbaddacbdcddbbcbbdbbbaabacaadacdccdacbbddccabccccadcadbadbabcbdaaacdacbcabccdadbbdbbccbddbcdcdbcbdcdaacddabcbbdbbdbcbbabddbdddbcdbbbdcbdbbdbaaccccccdaacccbaadbaaaccaddcdabdddabcaddddadbbddcaccbdcdadacdabddaacabdcbaaddbddcbcccdcaaacbcbbcbabaaaaccccacddcddacbaddacbbcdbdbbdbbbdbdaacacacbddcbcddbcdbddaacddbccdccddbacccddaaaadaaaabcbddabbacbadddccabaaaabdcbddaabbadcccbacbacdbbacdbcbbdbadabadacdacdacadbddcaddbdcadcadcbadbcaccbdabddadbabbbcadbaaaacdcccbbabbbbbdcdbcaadadcabcadabcaacdaabbccdbbbdbdacbcaddbdcdbccbaccaccbbcaacdabbacbbaaaddadbabbadddbaddaabcbddcbcbdadcaaccbcbadcabdbbbccacdaacbccccbdadcbaddaddbbbdaadbcbccdbddbaaddddbdcaacdddaabcccdcbcdcbcadaaacadbdbbabddbbbaddbdddccaaabccaccadbbbdccaadbdadcbbcdcaaddbccbcbbdadababbaaacddabdabbaabadbbcaaaababcdcaacababaaabdaadadaddbacbdcdcaabccacdabccbcbcadccdbbadbadcacacaccacbbbbddbdddbadbbddbbcbddcadbadcabbbddaacdbdaaccccbabccadabcdacabbccaacdcdaddcdcbddddbcbcaacbdccbbaadbdaaddbcacdbdbcbdaccdacbddabcacbaacbbbcbdcddbdbcacdddddddcadddabdabcbbdacaacacacbdbcacbabadaacbdcbdbadaccbbddadccaaacabbabddcbcbbcbddbabacdbadbbcdadccbabadaadcaccbdabcdadacdcbdbdcbaccbbaabaccddaddcccadccbddcccbcbbcbacabdadbbcddaabdaddcddccaabcdaabacbccabdaacdaabbcbbdadcabccddababdcadbdbdaaadbbbddaaddaddadabccabccabbbcccbbabcdcadacadcbddccdbdcaddbccddcabccdaabdcccadcdbcabbadbdabcaccbcadccccbdbdbaddadccbccabbaccbaacccaaaadaacdcaaccbbbdbddaddaadcdddaabcabaddaaacabdacaacdcdddbccbbcddadbbcadbcababdbdbdbbdcadbadbdccdbdbadccccdbadabcabbcbdccacbccddcaccddabbcadbacbcdccccaaabbadadbdcbbcdbbacdaacbdbaaadacaadddccdbcdabdbcaccacadaaabcddadddbcbbbdaddbabadcdbadadcbcdaccaaadbccdadcccacbabbacadcadcbacbccddcdabdadcdabbcdbcdcacacacadbcadaaacadbcdcdbbaccbcdcddbccdcababaadccaaacbdbccdaccaabdabccdcadaaadaacdabdaaaccdababadbcaadaadacdcbcaababadcbcbbdcbbdbddcbddabbbdaccdcbbabcacaaacbadcaaaddaddbaacabdbbddbaddbccaadbbcadccbcdbdababbdbcacdabbdbadbcbcdbbcbbacdbadaccdddbbacddabcabaabcacbabacdddabbabdbaddacbbdabcbbbdaddbcdddcdabadccbadcadccabcdcacacbadddbbacbbdaaacbabbaaaadaddcdbcadadcdbaddabbbbdbcbcaadbdcbdacbabdbdaaccbabbbaabdadabcabaadccbcddbbbbbabbcdbcbcaadacacccbdcdbcdaaaddcdcbddccaadbaabcbdbacaaaacdacdddbbccbdaccdddadcaccbdaabcabaacabdababcdbcdddbddbcaaccbaddcccddaadbbacdcabbaadaddbcbabcbdccbcbcbaadbdaddbdaabbcbcdadcbbddccbbbbbbccadbbdaaaaccaaadcaaccaddaadbccdddacabcdccddcdcccbcccabbabbbaabdaccaccaccabccbdddacabddbacdaaaaaaadcdbbacdddaaaaadccbccbbbbbcbbddcbdabcccabdaabddbbcdcbbabbccbbccbbaadaadbdccbbcddcdccbacbdababcadadcbdcaacbbbaacddbdbccbadbacaddadaadbbddaaaccbaccbdccadacdcaccacaabacdacabdcdaaadaadaacbddabbcabcacaddaccaacbcbdabccadbcccaacbaddbabbadbddcacacbcacaaddcbacdddccbcbcabcdcccbddcdddbdbdbcbacbdcbccadacddbcbdccdcbabcbdaaccdaccddbddbabaaabaccdddcacdbbbcadccbaddbabbacbaccdbaadcadbddaacabadacdaadcbcdadbbcbabccbdbdaccacbaccbbcdbcccaabdadabccdadcdbbbcccbddbbbdaddadcbcdabcbcaadcbaadbababdcddacaddddbdadccaadbbcaabcadddccaadbdbcccddbaacdcccdacdbdcbbbdccacbdcdcaaaddcdcbcccbbdccacddadbbcbddcdaccbcbdadbcbacbabcbdbdadadcababbccbdbcbcdcabbacccbcbdbdacbcbadaaacccacabbabccccaddbbabcbccacadbdddcdbcdacbadcaacddbcbabdcbaabcbcadcaadbddbdadbdbbbbcbadcabbddddaabbcbbbadcbcaacbcbacbbaddacccdccddcdcdbcacdadabcdcbaabadcbcabddaaabddacddbacaccddcabbdbabaccdabccbdbdaddbdbaabccdadadabbdacabbabdccdbddbcaccababacdbbdcdaabbdcbaadadbadadddbbbaddacdbcaadbbadcbddacbddacaababaadaaaadaaabdcbbbcdaddddacbcdbdbcbbdccabacbcadddaddccdbdbcbaaddcbccdaccccccacdddcadbbdabdadbadbbdadcaadccaaccdbddccdbccdddbabdccacacdbcbbccccdabbdccbbabdddbaacbdabbcdacdddbbbddccadbcbbbbccdcbdbcddbbdbadddccbaddbdbbbbaadaccaadbbdddcbabdaadbbbdbbabaaaaabcdddcdadbdacadddadbbbcbdacadbbdacbababddcacaabdcddbcbbbddbabadbaabacdbcbdddabbbcabcbbadadbbabacaccaababbaadabbbabcccbabdbaaabdadccacbdadddaaabcababdbcadbbcdbaaacbbcbcdbaabcadcddbcbacadbdcbdabbcaddccccbdabccabacbacbdcababbbcbdbcdadcdadcbbdbababcbbadbadaabdacdbbaccdddababaadddbbabdabcbbbdbabaabbbaacdbacbaacdddcabadaccaadccbdbbdbabdccabccabdadabbbaadbccaadcdbcbdaadaabdcddddaacadacdcbdcbcbccaccdccdbaabbbbcbbccadcaaabdaacdccbdaaacccbcbdaacdabccbbdacadcdccbdcdccadbbcdcabdcdcabddddbdcacacadbbaaaabdccbacccbbdddbbcdaadddaadddcadabaaaadcaccbbbaddbbabcdcbdadaddbcbaddcacbbbbdcbaaddaaabadbdbcccbcdccadbcdddabcbcdcadbddaddadcbdbaccbcbacdcacaacbcbddbcdadcadcaacbdccdacaadcdabcbcdcaacdadabaadabaadcddcabcdccbbddbaacdbabdcaaccdaacbbcbcdadbbcbbaadcabbbbabcddcbcddbbbddaaadcbbacadadcaaaacbdacdcdddbbccdddbabbdcdbccadbaadabbadacbbadcaacacdaaacabbbadcacdababaaabcaddcbcbdcbccadabddbbccbadccbaaaacbbcdbccdbbdcdcdcbdccacaaaadcbdcddadcdabbcbaabcdbbdaacdcabbdbbbcabcdccbbcbcdbddccddccddbbcbcacaabbaabadbbbbdbcbcadcbcabcadabccdccaaccbbbbcdadddcdaacadacdacbdadbdcacbbdbaabdaababcddbcaddddbbadadcddccaddbaadcddcdabdbbaaadadddadacccabdbaddbdadbbddbdcabbaababcabccabbcccdababdacaccbbddcbcadacbcddadcdabbcccbcaccbddacbbcabbaacdbadcbbddcbcbcacbdbbabadbaaabcddcacabdbcabcccababbbbbdaccdabbcacbaddbdcbbbdcccaccbaccabbacbcbcccaadacacadcdcadacccbbdcccccddadbdcbcbbcdcacaaaddddcdaabadcbaabbadadccaaccbcbabbadadcdbddbbadaaddbcbcdddbbbbabadcbdbbdccbbbccccccdcbacabbbacbabaddcdbbaaccbdbdaccadccadaccaacabaadcbdddacdddbbabadacdaccabadbdddbbcaaaddccddbaaadabadbaccaabcbccabadccbbbdcccbacccdabadcabbacacdcaccccbacdadacdbdcdbddcdaabdabbaddcbcdacdacbcaddacbbcacaccccccbddbaadaddcdcddcadddaacdaabccbbbdbacdaabbbcbbabbcdcddacacbcaabbbbcbdcdcaacacdbacddbdcddccabbdbdabbbccdaddbdccbdacaabddcdcdbccbdbcddabcbdbccaccdbcccdbbbddbddaaccdbbacdccccdadbbddabdbcbdcabdbbbaaababadaaacbabbacbcbabbdbddbcabaddadaabbbbdbcdacbabdbacdbccddacabbacabbcdabbabddcaadbbdccaaacdabaacccbcbddaadbacbbbcaccdccadcbaaabcbdbdccbdabbbcbadbcadddabacddadcacabddabccccbdcaccabbbdacdbacbddddcaacdcacdcddbbccaabccbcadaaccbbbdcadbcbdbaabbadbabcbaacaabbbaacdccbccacdbdbabcaddbcbdbddddadadddbbadaaddbbbadadabcbaacbdbccddbbbbdcbbcacacbbadaccbdbdbaaadddaccbbbdbbabdacbddabcabbdadaaddcaacadbbdcccbcdaadaaaccbdbdddbbaabacbdbbddcadcbccacdbacddabccccacabaddcaaccabcbaccbdbcddaacbaacdaaabadcaccbaaddbcdbbcaccddbdccdaadbdbbcbbacbacdccddbbcccacdcdbdbbdacccbbddaddabaddcbbadbbcbbcdaaccaabcabccbddadbaacbcbaacbacbcdabbcabcbbabddccdabcbdaacaadcccaccbabaabdcbdabbabbdacaadadbcdbcdacdaddccbaccdabbcbabbdcdcbbcdaddcbaabdcdbaadddbbdcacbbaabbbcddccbaabdabcdaaaacadcababaccddbbdcdbddcbbbabcbacbbdaaadacbcbbacdbabadbaaabcaabccacadaccabcddccacacccabcabaabdabaccbcdacacdbbcddcbaaabadbdabddabdaccdcaddaccacddccadddbaacaabacdadcccbaaaaabbdacdbcbdadcaabbbdcabccabdbbcbaaaccdcbaadbdcbcbadacbabcccddbdacadaccdcadcabcbcdabccaacbcbdcdcccbdaadcccaadbdbdababddadabcadabdaccabaacadbbdddbdabbbaddccdbbdcabdaaabcddcbbccaacaaaccccbaabbabbaacadbcbcdcabbbadccacabdacdbaabdabbbbdddaadddacdabdbadbcdbccbadcbbbdbbabacbbdaccadcaabbdbdbccdaadcabdcbcdacbaacdcdadacbdcdcacaadadbdcdabbcbbbbdcdbcdacdaacdacccdacdccdcbadcdaadcdcbbaaddbadacbcccabbcdaabddcdabacbcdcdddbbcbbbccdbbdacdaacdccaccbaddaddadaabcbdbbdacaacbddddcbaadabddbcbdaabdddbadaaadcdbcbbdaabadcbcadccabcbcbadcadadcddbabdbacbbcbcdccdbdccbcadbddaccbdbcaddadbcdaddbaabdabdbbdcbddbbbcdbbcabccbabbddddaaaccaccbddacaccbdaabbddabbdacbacaaacdddccaddccdabbbacdadadaacdbcdbcaaaadddbadbcdddccdcbcdaccbcdcaddbcbbbadbbdaabddadcbdacbabdcbaaadcdacdcdccbdabcaaabaacdbdacbcacaddddadcaaabccacacdcaadbccbdbdcaccbbdccdaadbbbccddaaacbbacbaadadaabdccdbcadcdaaacccbdbbabdaaaddbabddbcdbddbaacbbdbdacdbadbbaddbcbaddbbabdbcdaacbbadadbdacbdccbbbaddccbbdaddcccbdddccdadaddacccabcbcadbbbcaccabcbdaabcadbccbaacdabbdcbcdbcbabbdaddccdbbcdbbdaabcabdaaabcacbbcbdbccaccbdbbacbacdccbddbdbcccbacdccacccbdadbbcdacddbcccddbcccdbbaabdcababdcbbcbdabaabdbcccdbbacdabdccadcbccbadddabaccbbaaabcbcbcbbddcabbaabbbbcaacaadcccaabddcadcddadacbcacacbcacdabbdabcbdaccdbaacdcbacdcadbabcddcdacdcbacabacdabdbabbbdaadcdbadbbbcaaccbadcdcbdabbcbbbaccbddddcbcccbcdccdcbdbbccacbcabacdbbcccbabacaaccccdacdcadcddacbcbdaccdbccdcabaaaddbdbdbdaabbbcbacdbcddacccdcbdabadccdbcaacbcaccddacdbccaadbdadbddbbcaacbdcbbaddabacbcadacbbaaaabbcbabaccbbdadcbaadbbdadddadcbbbddabaccaadccbcadcddcacdbcaacdbcabcbabdcbcdcbcbbaababacddbcadcaacabbcbadabadccbdaaccabaaaadbcbcccdccabdddacacdbccdddabdcddabbabdcdaabcbbaaacabbdbcaccbadbbcdcddcbdabddbadcabccdaccbddadbdcdcdaaadccbcbaccbcabbbccdbcaddcbcbdacabcbddbccabbdccddccbabccdbaccbdbddaaaddbbbdcdbbddbaaadacbcdddaddabcbbaababccddddbadcdcaccaaabcabbdddbcaadcbcbddacdaaadcabbbbcdcbadbcdcdbcaadbdcabbadddadbdaddbdbcabbddddaccbdacccaaaddadacabbdcddbdbcadcbccccbcabbbacbaabcddcbcddccdbaacbddccdcdbccbccaddccaddbcdaabccaaacbccadbbbbccbbbcccadabddabacaaacbccdbacaacbddaabadbcaaccbdaaccdabacacabccacbccdaaaacccbabbdaacbbdacadabadcdccabccbdaaaaabcbdbadaacaddcbddabbabaaabdddaababddacadbdbbcaabcdacaaadbdacdcbdaacadbdabdbbdbddddccdcadbcadbdcbdddcddccababacadbaacdcabdbdbbbcaadacdadcadccbcdabbbbabbbddbacaadbacdbccbcacaabcdcdbbcbdacccddddcbcbcbbddaaddddaabdbdcbbcabcabbccbcdcbbdbbaacaacdbccbdbadbbadcdcdcbbbacacbdcccaadbdccabadaddaaacacdacdabbaadccbcdabbdcdbaacdcdcddcbdabddabdadbcdabdccabaadbadcaaadcddbbccdbcdbadcdbbbdabadbcdadadbaddbbbdcaccddcdaabbaccdacdccabbdccaadcdabbddcbddbccdadbcddadccaaacacbbcccacbaacddccaddbcadddcccaddddbbadccadcdbacadbadadbdccdadddddbcdcbdbcbbcdacddbddccabdddbabdbacbadcbadddbbcabbbbbdbccaddcdbcbccacdbccdacabbabbabbdaabbbdcbddaccababcabcaccaaddcbaccbdacbbbbbbadccdcadabdcdbbdabcbdcbcdacaacbcabaccbcbbacadaaacbacaacabddbbacbbcbabbccbaddbbaabbdbccbacaccabbdbbadaacbbbddbdaddabcdbabccbddbdaabbbbadabcdddacdcdbbbacbcaaccccadcbaaacbaaccaaccbacddbbcbadaadbbdbcbbbdcbbdddcddddbaabdaabcdabcaacaaccaaabadcabbabdaacaabcaabcddaadcadcbcbcaabacabbcacdbddcdcccaadacadbdacbbbddcdbdbbbccdadbbdadaadddbcddbcddbdaaadcabccccdbdddbacacbdcdaddbcdbdaddaddcccdabbaabddcdbcdbccccabdbddbddcbdbddcacdadccbdddacbdcbddcacacbbbdabdacaabaddbcbacccdbbbcbacdabdacdddcacdbdacbbaacbdabbaacaabcddaccbbdddcbbadcbbcdccaabcbaadcdbaabaadacacbbdccaadbcdadababcddacbcdbdbdbbdadabadbcbbcddddacbbbaaabdaaddbcbacaaadddbbdabaccbbbadbdcddcacabbcbcbabcacdddddcdadcdcaacbdabdbcbbddacdcaaabbdddddbbcdddaadaddccdaaabdbbdbcabcbcddcacadaaddddaadbabcccaaacabbcdddbadcbdacbdbdaabddbddbabdabcbcbaabbbbaadddcaabdaadcacadcaaaddabcdbadaaaacabdaabdaacdbdaddcbbaadaaccabbcaababdbcdaddcaccdabcabaacdadcccdbadacabbcddacddadacabbaabbacabaccbdbcbcbddbaddcddbcbbbdbdbdccaadaddbadcabaddccdbadccaadddbabbbaccdbaaabcbaabacaacadddaddcbcbabdbbaccbcdbdcbdcbbbbcaadbababcdcbdabbdbabddaacaabaabbaddaabbacdcacdaacbdcacbcacdddcbadcddccdcbacbdbacdcbdacababddbabacabdaacdadacdadddbccddddcbdbddbbaaddcdbdbbcbbababaadbdcbcaabcacbadbccddbaabaaabcdabbcbcbbcaddccbdbacbbbdbbacdcdcbabdaacdcbcbbbbadacccaddddcbdbdcccdcbbcdacbdbaccabccaaabdbddacdcadbcacbadcabcadaacaabdaabdaddadcaabddaadaadadcabbbaacdaadcdcddadcccccddbccdadaacbdbccaadcddbbdacabdcdcaaccdcdacbbbabdbaaccccacbcbadbcadcacccaabcccddaccdddcaccaabdacaabcdbaccaaddacacdbccccddcbcdaddbcacbdadaaadddadcbbbabaabdbdbdbddcabaddcdddcdcbdaabcacdbadaaaccdddcacdccbbbcddccbcdcbcddbaaadabbdaccadbaacccbccbcddbdaddbbbcdadddbcacbaacacaabddbcadbbaadcdbadaddbdabccdcabdcccdbbacccbbadbdbaaabbbdadddcabddcbcbbbbaaccabcadbcbbdcbdbcbcaabadacdcdccbcaadccabdabdadaccdccaccdddacbbddbccaabdaabdcacccaabbbcbbdcbcabdcaaadbcdaddcbabdccdbbcabcbbdcaccddabccbbbccbacacdaddccadbdacadddbccdcccdabdcdbdbbaddcdacddaacdcadaacaddadbdbdadddccccccadbbbcbabcbcacbcbccaadbadcbaabbabddacabbacbbaadacadcdcdcaadaacddcddcacddbccbddabcabdcbaddacacbbacabbdabbcbdbddbccdddaddcbbdbdccbadaaadcbddddccacadbbcddbbadcbdcbbdcbcadabdabacabcbbbbbdacdcdbbcdccacbbdabcccdbbdbddaaaaaadbddacbadcadccdaaddddaacbbcabbcadcddbbcacdaadbddaccbaccccbcdcdacabaacbcdbbbadbdcccadcdbaaabcbbdcdbadaabccdaaaaadbcdacbaacadcccbdddcbdcadaaaaccadccddccabcdcccdbddbdbddcbdbabdbbddbcccccdbddbcddccbadbbacbdddbbcbcbdbbaacccddbbcadcaabbabcadcbbdaadcadaabdcbacccaadbbccdbcbcddddcaababbddccbccdbbcddaaadcdbddaddbbdbccacbdabaaddccdcdcdadbdbabbcbbcbbcabcdcddcdcdcbaddbcdbccbcacadaccbbdbbaadadaadacadbbcdbddbccccadacdbaccadacdaadbddabbccddbdbcdcaaaccbdcddbdcacccdaccdadccbcbbcdbddacaccaababcdbdcccbabdbadcbddbdaccabaaaccdaadbccdbdbbdbbdabcdbabaddccbacbdbcddcbddaadbbabbbbdaaaadddbdbababddcaaddbdadbaabcdddabccdbdbdcbcabdbabacaacabdcaccabacadbdadacdaabcdbbcbdccabbcccccbbaddbcaaadcdcacdcccbcacdbadababaccdcbbcddbaaaccddaaadcdddccbaababacdabbdbdaadcbdabbbaddccdccbabddacabdbbbbcaaccddbdbdbdbadbabbbabcbdddadaabbcdaddaddcabdaccdacddcbdacacacddcddabdcbbbcaacbadaccbadabbacbdbadbbddbadbbddcccaacccabcccadccddbadabcdccadbaddcbbacadcccccaaadcaabbacacadcdbcdccababdbaaabdbbbcadbbadbbcddcdabadddabacddddcdaadabdbdaacacbbddcdaddddddacbdabdbbacaaddcccbacccdacaadcaabbacdcdbdcbdbbabcbccddcbdbbcaaadcadabdcdbbabcaddbcbcaaddbdbdabcbcdbbadcccaccccccacaccbbbbaaadabadaaabccddbbccddacabccdcdabcdcaddacccbcddbcbddbadabcdbbbbdcdbbdbdcddacdacaacaadadbbcadbdcdccadbdcabbadbbacdbaaabdadaacdaadddbaabdabcbcacdcbbccabbdcadccdcbbcadbbabccadcbccadababbadaacdcbaddbcacbaaddbdadcacbccbaaccbacacddbbdcaabbddcbaaababdddcdabddcabadbddcbaacbbcadcbadadbbccccbcccaaacababcbacbaccacdacdbdadabcbdccdcbcabbccbccbcddddcddcabdaacadcbbdabaccbdadbbcbababacddcdcbdbccabdadacaacbcdacabdaaaacbcdadddbcccdabbccbbabbdcdbaabdbcaabacabdddaadadaadaadbccccabadabaddabbdbcbadaacbabdabaaddbcdbccbdaddbadcdccacddbcaccbbdbcacaaaddadcadacccbdbdbcadbdadcacabdccabddcacdbacabdaabbbaaddacbbaacabbdacbbccadbaddccbcccdacaccbdbcdbadcabaaaadcbdbbabbbadcbdcadddaaaabbddcddacabdbddabbabbbdaddcbaadacbbcdbbbcbbbbbcbdcaadcdaaccccacbcadbcbbbbddaaadcdccaabbaadaddbdbacbdbbabccacddccacbcbabbddcccbbdbdcbdcdaddcccaaacbdcdcaacabacbbcddaabdaaadddddadabcccddbbbdbadcccdaababacabadcadabcdcaccdccdadbaaadbdcbcbbcbabdacabdccddbbaccbbddcdcdcccbdbcdbcbbcadbdabacddbbabacccaadcbbdcddbdaacdcccadccbdaabbccbdcdbdddcadacbccbdabdaaddbbdaccabaabcaacbaacdcdcaddbacdaabbbbdbaddcaadaacadabacabdadbaaddadcaaaaaddaacadbacacbbdcdbcdbbdccabbcdbbdaccdcdbbdcdbcaddabcbccbabaddaaacdccbbbddaacabcdadbadccadcadcccbdbcdbdcadcbccbdbbadadccaaccabbbcbdacbbdcdcbbbadddddcbadbdbdabcadabddcaaaabcddbddbccabcbccbbbbcbddbddbdbabdccbdcddccacccdcbbbbcdaaacadcbadbaaacaddcddcdabcabbbdbccccdbcadadcccaacabbbababdacbbbccdaddabcbcaaabddaaddccabbddacbbabbdbdacddadcddcaacbdcbcdcbbabdacaacacdaabacaabbcdbdbadbabaacaccdcadcaddaabbdacdabdbacbdacddbdaabbbabcddcbcabdcaaaccbcbdccaabdddabdacaadadccdaddcbacabbbaddbbacaaadbdccacbbcbcaaacdbcdbbddcabcbaadcdacbaabcbcddcbbdcdbbbdcbdcdbccaadbddcdcabdbacadbaabdccbccdbcddcdabbbddcddaabcaaadccdaadcbacdcabcdbabdacaccadbcbbbbcabadccdbbbbcadbdccccadbbabbccdcacadbddcaadaabcbbadbddcabcadcdccabadcdccacbacccaabbbcdabacabbabdccbaccabbbbcddbadbbbddbcdcdbdbcacadaacbbaaddcddcbdabcbbaadbdddaaaabacabddbcabbcbcdcdacbccbcbaccccccbabaadcdbbdcbcbbbbdbddbaadaccbbdcbdabbbcbabdadaacaddccabcacddadcadcbaababbdcdbdabdbdccaccdcccccbddbdaabccdacdaddcdcdcdacbbbbaadcccdbcdcbddbdbbcaddacccddcabbbdbaccabacccaaccaacabdcaabaccdacbadbbddbccbadadccbdadcbdbddcbadddbaacaaacacbbbabcdaabbbcbbadadbadbbaddddbbdddcccadcbbaacbaacbcdabcbccddcddacddbdbbbbaddcbdabaaaabccdccaabbcacdcbbacbaddbcbcdbcbabddbbbcaaccddbcabdaadcddddcaddaacbbddbcccababbcdbbddaacbdbabadabaabddadbdbbbbbbccccdddcdaccbddabaccaaadacbcaddccddcabadbadcbbadbbdbddcbcdcdbbcbdbbdabdbcddcaacbabbbcbcababbcbacabdcadcbcdcccddadacdcbcddcaaddccccdcaccbdacbccdbaccaadabbccaccbbacdadbbcacbdcdacadcadddbddbdbcaccadcdbaadacdccaaccdcaadbdccdbacacddcccccbcccacadbcbbbcadcbcbacacbdcadcbccacbcccdacdaacbcbacbbabcabaccabddbadcdadcacaccbaaacabacbcabbccaccabaabcabcbbcacdddcbbddcdbcabbabcbbcddbbdbccdbcabcbbdcccaaddcabcccaddaddbcadbcccacdbdbbacaaccbccbacbcdddababbdcdccacbbaabbdbcdbbcccdaaabcaabccacdccdbddccdaabbaaaccadbcbddcabababcbcccccbcdbcdabaccddbbddcbaccdcddbbbbbdbadccbcdbcdccdadbbdbbabcacabbabbccdbcacadcdbccdcbaddcdccacbbdaaaaacababadccccbdccabdadddcaccacddbdbcbdbaadcccadcccdbddbabaacabcaabddcaadadbacbdcdbccbbaaabdcadbcdbacdaccdabadacbacdccbbadddabdccddabaababddadbccbcdccbcaaaacbbddddacacddbccdcdabaadcaaccbabdddadaaaacdcaccabcaddacadbadabbbbccbdaababccbacbcaadbbabaacdabddabbababccbbcadbaaaacacbaddcaabdaccbcabdcabacdbdbbbbadaaddccddadccabdcadccddcbbddcdbdbbcabbbacdbbbadbddbabccbacdbbabdbdabdacabdcbaadcbbbdaddcbbaabdaadacabdddbdcdbdccddbabbdbcddcabdabacdbdcdcccaaadbabbdbbacbccbbbddaabaadadabadaaddaddacccababcbdbaddacaaaadbcadcdcadcddbbbbababababadccdbdcccdbaaacacdabccabccbbbcdcbcaabbabcababcaccdabbcdcbdbcdddcadccddbbadaabbdcccacaaccccbddacddddddcabbcbaccccaabdcccbdabbdbacdbbabdcccddcdddddddcaccdacbababdabdcdddcbccbadacbcbcbabaabcdbdccaaddbdabbadbbacaacbdabaddbacacdadabcccccbacadccadaacddbabbccbdcdbcbdcdbddaaaaddcaadccbcbadacdcbbabbcccaacabccdacbbadddcbabcdcadaccccdbbbcbbabcbbadbddbdacacabcacbbddbabdadcdddcaacdadabbdbdccaccdccacdddadbbccbcbbcabccdadcabddcdbcdaadcbddacadcdcdbcacdaaaccadcdcacbddcccccdddbaddddadbadcabbaddcbadccdddcadacbacbcacccbabcdabcbcbbcaccccadcacbbbdbbcacdbdcbbcadabbaadacaddbccbbcdbcddadcdbcacccbccdadddccacbbdddaccccdaaabcadbdcbbdabcbddcbaaadaaacddbbcbcaabcabacbbcbcacbcdcaaddcadacabccdacbbadcccdccdbdbaaddacdcbcadabadccddddcaadcbdbddbddbadbabbdaddbabdcdaacdaccbbbdcbaaaaddbadcbacabbdabaaacbbacacadbccabcbadddbcbdadddacdadacbcdcdbaabbadbcaadacbdabacdcdabbdcccabbbaccbdaadbadbcddacadbaacdcdadcccbbaabbdcacbacaaccdbdadccbcbdaabcdbaccbadcbacbbdcdbcadcdddadadaccdbabbaccaacbbbcdbdbdddcadacadccccadccbbbaddbcbcbbdcdbaddadaacadcbdbacdbbcddbbcddbdcadcdacdacddddbdbbaacacbdbdabaadccdaabdbcccddcbddacaddddbcacacdccbcbabcbabddbaaabaadabdabddccdabccabddacdaccdbbaabbbcabdadaaccbddabbbaccdbbbdaabcdadababddcababbdccaacabccaccabdcadccabbdacccaccbcbdbccacbbcdbabacacddabbcbdbdcccdbddbacaaacacdbdaacabdcbcadaabdbccdbabcccccbccadddbccacbccaabaccddbcddbdcdbacdcabcdabcadcacdcadbddadbcbcbbadbdaddabcbcbbdbccdcdcbccbcabdcddccadbaacbcbcdbbaaaabbdabdaaaccaaaacdabaccbbcccacbcabdbcbdbccbabaccbabddaadcabcddccdacabdddabddacbbaacbcaadabbbddbbabccdbbcaccddcabbaadbabdddbcddacdabdcddcabdaddbcdbdbbdcbcdaaddacdcbdabcbcaacbccacdbbccbbdbacdaccbdcbdaabdccbdacaaabcbbddbcbcaaacabccdaabacbccccaadbbdbcdbacadccdcbdadbababdddbacaacccbaacbabababcbdddbdcdcdabdcbdaccbdaadaaacdbddabddcdcaacabcdbbbaacbaacddaaadbdccabdbcccbcdadcccabdadadbddcdccbccaadaddbdbcbbcdcdbbabcdcccddddcbddadacadbccdacaddbacdcddcbcccbaaccdccbbcacbbcccabbdbdbbacddaacbddcdaabbaccaacccbddbbcdccbadabdbbddadbcccacbdccdcaaacdbdcdbaaadaaabcbcbcccadccdcaabcabddaacbabdbadabcbbddbbdbadbcddcacabbaacbcbdccaabbacaadbabdddcdbccaaaccdbddadaaacdbadcccadabddccbcddbbdbbdbbaabdddcccdbbcdcdacdccbcadacbcaaabdbcdadadadcdccccddddcdbbdbcdbddcddcbdabaacdccdbbbaddaccbdcdbdabdacbdacadabccbcdacdcdddadcacbbcacdccacdcdcccddabbbcccaddddabbcbdadabdccbbdbabadccddcdcadaccacadcacddaabbdbcacbcbadacdbdcdcbaadaabdadbbbacbcdcabddbbdcaabdddddbdbacbdddadcbcdabcbbccadcbcadcabdbaacdcbcddbcdddccdbacaaabdabddadcbcadccdbccccaacbdaacabcbcbadaacccabaddcddabaadccabdddddcacbabaaddabadbcbcbcbdcbbdabaabacaddcacadaadcccdbdccadbcbaacdbabdbddbcadddddbcbcadddbcbbddabbdabbdcacaddcdaababdbbacccccabbdababdccbdadcaddaacbaccbadddabbbccdacadabbaddacaabcdcadcaabccbbbbaadbacadcbbbcaccbabbcabbccaaccbdddcdbcacdaaadabadcbbaacaaddabbbbccabadccbaaabacbdcbdccccaccbcddbdcdadbabbdaccbaadbabaccdaadaaacdbabddcdcaadaddaacdabaaabbcdcbabcbbccbccabadcacdcdbcccbccacabcbcaabadbcccddccaadccbcdadaadbcdcaaccdbbbcaddbdcdbdbbabaaacaadcbbacaadcacaaabadacabbacbbcbbabcdadddbbabcddcdcaaadbacbbadabccdabcbdaaacbcdbaabdcdbcbcaccccddabdaaadbabadccbadcbaacdbbaabdbadcbbaccbdcacbbbbaddcadbacabcddcabdbdabddccadcdcbbccbdacbaaabddabdbcbabcddddcbcabccadddcdadcdaabcbadadcadbcccbccacbadaaadbdddbaaacbaadcaacadababcbbaaaadbabccbacdacccbdcbbcdbadcbddadbbccacdbccbbbdadacdbbacabddcabbaadadcccdcaabcabadcddccdddadbaaccaccabcbadccdcdccabcbabbbcdbccddbcaacaddcbcdaabadaacbbccdbdbabcadcbbcaaaccadcdadcddacaddacdbcdcccaaddbbaccbdcccbbbaadbcaaddbcbaabaaadcaadcbcabacaabbabdaadbdcbddbcaaddadaaadadbcbcbadbbbaaabaadcabcabbdcadabbdbccbcbbadddbbdadbcacbabbbbbacdabccacbcbbaabbdbcabbdcabcbdbadcdccddababdabbacbbccabbbaacddcbcacdabdcadddbbddbaacdcadacaabcadcdbabccabcbaaacbabdbdbccddcacaabaabbaaadcabddbacdbabdacdcbdddbcccdbbddcddbcbabbcbabdcbbdadccddadabbaaccadaadbcbaacbbbdbbcadadcdaabccadaadcddcbaadabaaaadbbddaccbacacdadbcacbbbadaaaddcaaabaabdacdbbcadddbddbdadccaaddadbcbabbacacabdaadadbdcbdbadcccaaabbdbcdbabcabcadbcaabbabbababcabbaabadbaddbaaccbabcbddccdaaabbccabbbdcdccadacacbbdcabaabbaaadbbbbdbdccddcbdaddddcabbdacbbcbbcaabbdbbdcabaadabcddaaacdadbacacbbabdcdbbbbbdadadaaddbdbaaccbcdddccbdbbbccacbccaaacbcdccdccbabdacbcbdacbcbdbabdacdaabcaadaacbdadddddbddacbbbabadbcadcdbdabcaadbdbcddabadbbadbabdcabdcdcdbabaabcdccdbbcadcbbccabbdacdbbbdbbaabdcdaddbbcabdcbdadbdcadacdbadbbccddbcabbcacdcaccabaadbccbbaddcbadbaccaaddaddddaddbcdbcabdadcbcbbbddbbccaabddbcadddacabadbbbcbadabacdbcdbaadbdbdacdaacddccabccbbcadaaaccacbccadbcbbadcacdaddbdbadbaccaaaddbccddabadcadbcbdccbadbabbddbaabbbaababcaaacdbccccaabdacaadadcbbcdadbbaadadcccdadbadacabbdccabcacccdbdcdbdbabbdbcbbadabdbdbbaacacabbcbcccbdcccbbbbaccddadbdcbabbdddddcdabddaaabbaaddcdbaddacdbbbcdaddddcbdcdcccaddadccbddbddcddcbbdabcbbbaddabcabbdcdbacacadcccdbdabbaaaacabccabddddbdcdcdabacdcacdacbcaaddcaabbacbbaaaccbdacdcdbcddcccdcbdbbdbdccaaccacdbccdabcbabbbdbbdabbaacaddcddddccdadcddbbabcbcbdaddbcccdcddcbacabdcaddacdbdbcabcabdbcbdbaaaddcdcaacabbbbaacbdcbacbcdabbbddbcaaaabddbbcdbcbddbbbcabbbcbcbacabbdbbadcaacbdddbbdbdadaddbdbdccdccadabbbbdabbcbaabcdadbadbdbdbdcbbdbbdabbdcdadacbbcdccdbdddcadccdcbacdbcbdabcbcaabadcaccddddbbbcbacadccbdbccbadbdcbdbccbbadaacbacbbcdddabadabddddbcdbdcaccdabdaabbdcbadadaabdbaadcccdabdbcaadcdbadccbdccdaaacdcddaadccbacdbaacaddaaaccdabdaadddababcbddadbabcaaaacbbbbdaaadcdadcacbbbacadbdcadadacabacacadabbdbbdbcbcbbaadddccdddacdbadcdbccabddbbcdcaabccbbaadaaadbbccdcddccdacdacaadcaaaadbacadcabdacaaddddddaacabaaddccbccddcccdcdbaccdbbbacdccbaddcbdcbbdcdabbbbcbdbabbbadadacadbabadadbbcdbbbbbaabdbadcaddadccddaaaadabbbacdaaadcadddbccdcbbbbbacaaacbdcbccacaacbdbadcabdbbddacccdccbddaaccaadbdadcdbdbabdadcdadcbbbddbccabcdabdcbabcaaabdccbbdaddbadcbbadacbaddabcbcadbbbacacabbcaabcbdcacbdbccbcdbdabbadbccccbddadddddccadabdddadcccdbaadccaabccdaddbaadbadcadddbbdcdbbabccbbcadddbdababaadabccadbacddcbccccbdaddaccbcbcddbbadcdbcbbacdacbdcdaabaddbbdcabdbbabbdddcdddadbccbabbaddbbcadaaaddcbcbcdddcbbbbbcadccaccbbabaddccdcbdacdadccbacccbbccabbbcaacaadccdddbacaadaccddcdadbabbaacadbadccaccddbdddcbdacbbabcdccbcbbcabbdaccdbddcabdcccabadbaaacbadcbcdabaadababcdcadacaccdacbdbccadbcadbcacadbacdcbcaadcaabcbbaddbbbabdbdbbadbddcdbdccbdbdbcddacbdaaadaddabdadbbbddddabcababadccaaabbabcdbdbcabbcdbaddacdacacdbcdccccaaacdcabbbadadabcbabacdabadbddaabcaadcadabdcdbdaddbdcbccaacbdddddadacabacbddccbcdbacbbbddcaaccddbcacccbbbdabacbddadaddbacbddbacbbccaddacdcbdaaaacccddaddbcbbaabcdaaabdbcbcbaabdbadccbaddabaabcdabacaaacbacbaaacbcabacbbaaddaacbcacdbdadcbaabddabaabddcbacabbcbddacdbcbabcdbadbdcdaaddbababbbcccdbaddacbcccbaccccccbadcbbdbcdcbabbbbdbdcbbacbaadbccabbddbdcbdacdccddaccdadccddacccccdbbdbbabacbcdaacaacaccbdcdcdcccadacbdcccacadabdaccbcaaddbccadadbaaadddcabccdddaccdcbabdbcacbdbbbdaaadbaadddaddbcaaccdcdbdcaaadcdcbaadbbaabbbbdcabaaaccaabdcdabdbcddbaadcccccbbacbbccddaccccbbacdbadddbbbcdbdacbcbdcbbbcbaccbddbadcacdbdcccaadcdbdccddbaabacccdbbddcdbabacdaccabbddcdccddbacddabdaabadcccbcdaacbaddadbdbbdbcaadacacadcddabacccaaababcadbdaddccaaddbcaddbadaddadbccccaaaddacbcbcaaddbabaadabccacbaabaacdbdacdaaabacbcdabaccbccaadadcacdcaabbdbbcbdbdcbbdcddbcdbddbcbdcaacadbbbaababadddcadcdbdabadddbbdbacbdddbcdbadccbbbddacccccbbaacccbcadaaabdacdddccdabbdbcbdacddbbbaabcadabdaaaabcaabccacbbabbcadbcacccdddcacaadbacbdbccbacbaadbcddbdbbccaaabbcdbacabbaaccbdadaaabcaabddcaaddabbbacdbcabcaddcccadccbdcaccaaaaccaccaaccaddaddcbbccadcaacadbbabcdcdbadcccdcadacadbbcdbcaaaadbdcdbbbcacabacbccdabccabaccacbbccdcabcadaccbcadabacaabbcbabbdacbbaabdacbaddccbccacacadcbbcbacadbcaabdbdcbacabaadbdbdaacbaabcccacbcaccadccdadbaadbabbadbbbdcccbcabbccbacbdcddadaaddbbcadcddbdabdbcdbcaccacbcaabdcabbccdddaabacbccdabbbbbdadccaaabacdccdddaddaaacaaadcdcabcaaaccaabdacdadcabdacbbbbaabdaabdaccbaaacdcabddbbacacbdcadcbcbabdabbadbadadbbacdbadbcdadddbcbbdddbdbbbbadcbcdcdacbdacabbbbdaacddaaddadcacbbbddadacaabbbabcaaabaaadcbabdcacdcbacdbdbbbadbabcbbdcacadddddacbbaaddadddcbbbccbbcadadbdddbbadabddcbacbacadabadbdaabddabbacbbdddbacabbcddaacacbdabbdcbcddcaabddacadbcbcaaadababcccaacbdcdcdcabdccddaacdcacbcadbaadbbdcdadbddbcbadadabdbabacdacddbddacbacbacadadbbcdabdddcbcccddbbabccdcbdcdddcbaadadcddbbdcccbbadbdbaadddcbccbbbcdcbbaababcccaabaccdacadbbabdcbcaddbabddcbccddadabdaaabddbdadcddbdcbaadddccccadddddcddbbccacabcdbaddbdcacbdbdadbcacdcabaadbcadbdabbbbbdadbddaccabdbcbadcdabbcaacbdadcbdacaacccabbdccadcbbcdbdaddbacaddcaaacbddcaadddcdbbcbdccabcddcaadaabacaddbabcacdcccacccdadacadadbbaabdddacddbccbbcabdcabbcddcbdabbddccaabcdccacdcdacddbdbbabbdcccbdacbcddacbddacbccbaaccdadabcacdadaadcddcdbbaddbbdadaaacadcbadbbcaaaacdbcbbcbbdadbdcbdaddbcbbbdacdcaacacadbdcaaabadbbbcdcabdccdcdbddcdadacdccdbdabdbccababcdcddbaabdbbcacddbcdadcaadaddcdacccdaddcbcccdcccbbbddabbdccabadccddaddcddaacabdbaccabccdcbbdcaddcddddacdabccaddccbbcbadabbacbcabadaaababbabbadccdaabdbcdacbcdadbdbbbacacbbaadcdcccbdabcbdbdbaaaccbdbdbbccabbbaacacbaaaabccabadabbacbdbbbbdbbcdbdcbcadaaacddcacacdacaddbacbdcbdacccbacdccdddbbbcbaccccaccabacddbacabddbaacdcbcabaddbbccddddadacabcccddaddaddbdbcdbdacbbccbcaabbdcaaacbbcabbcbdcbbcbccccadacdbcccaddaddbbcbdacacabacbaddaacbbcbdaaccdabccadaacbbbacccdbbabcacbaaabcbbddbabddbbabbbbddabbacddcabadcdcddccacbbbdccbdaadadcdcacbacdabbdbacaaddbcbcaadcadbcccbdbccabadbabadbbdddcbadbcddacbccacacadbbcdcaaccabcadcbdcddacbdcbdcaabccadcbddcadbcdbcbccaaadcdacbcbcaaacaaaddcbaccabbbaaaabddacadcbaaacdbacbcdbaadddccbbaddbbdcaccddbdcdddddbdddcccbbbcccbdcdbabcccdaddababdccacbabddbbdddddabcbddcbabcdbadabccadbdcdabbdcabaacabadddddcaddbbdaabbbadacdbadbabbcabdbcabaaacbddacdccbdadddddcdadbbbcdadcdcadbadddbcdbbdbabddaabacbdbcdaabaabacddcbababcbcbccdaabdadaadddacbbbaaabbcbadbbbcddaaabadddbcadacddbbcdddddbabacbadcacbccaddbbdcbcccaddbbdacccdbbbbccbdaaaabcbcbbabbbcbbdbbaadacdbdcdbbcdcadbbdadabdababbcdadbabbcdadcbabcdcacbdbcbdbcaadaaabacacdbbccdabbcbacddbaddcdacdabdcbdaddaaddaacdacbbacaddcdbdacbdacaccabbdcacbbdbdcddbcacdaababbdbdabddbbaacaccbbbddccbbaccccdcbbacbdbbdbbadcababdcaadbaddadbddadcbbdcadabdaadabcdadcbcddcbddcbccbacbcdbabcbbbaccadbdadadabddccaccadcbddccdcbdbcbabbbacaadaadbbccdbcdcaadcabdbcaacbccaadaddaabaadcacbacccdccadabdcabcccccbdadcabcccdddcddadaaaaccacbcbcabccbcdbbacccaccbbaacdccadaaabcacdbacdbcdbcadddaaabcdaccbcbabcccbbacabbadccdaccabcbcadccadcbacbababaaaabbbabacabdbaccadcacaddcadcaacdcbcaadbdbddcbdbbbcddbdbddaaccbacdaaabcbaadbaddcbcbbbdddacbcdadbdaaabdcbaadcbddbdaadadcccaaccabddcadadaabadbcbacbbbadccccabdaacbbcdaaacbacaccddbccbdacbababcdaddbdacdabbadcdadcdabccdccaacddddbddbcdbdddaaadbcdcddccadddabacbaacacbdbbbcdacbcdddcdddcccaaaccdddbbcabbdaaacbbddbdaabdaabcccdcbadbdddacccbcacbcacccadbcdacabadbdaadcddbdaaadaadcaddcbacdbdcdcdddcaacdddcbaaaccdddcbbaddddbacbbcbbcddadbccdabaccbdabdabdcbbccbdcbadacbabadacdcaccbcccbababbdcccdbcbcbdccdddbcdcbdbdcadcdabdaaabaaacdbcbacbbbcbaacadddaadadcddcbbcaacabcbbbadcdbcccaabaacbdacbbaacddcdccddadbadadadababcccddaabddbbaabdccacdbcddaddabccadbbbdabbaddccbabddbbadadaacdaabaadaaabcbbadcddcbbcdababcdbdabbccddbaccbadcdbaadcabcdbcdadddcbadcdaabbddbbbddbaaccabadcbdaadbabbadacbbdacabacabdcdaabbcbdbcacdcdbacddadbabcccccbdbdaabcbaccabbacddccccaabacbdbadcadacabbaaaacddaacccbbbbbdbbbabcdabdabcbdddbcadabbadbddacbdcddccdaababdbbdacccdacdabdcbabacdbcabaaddbbbdadddbaacdaaaddbadccddbdaabbdbbcadcbbddccbcbaaaaddabdbcbaadbdbadcccdcadcccdbaaaccdddabcbdacccbbcdcbdabadbcdddacccbbabbcadbacbaaabacbdcadacadcbcacdcddadcbbddcabaabbbdaaabbaadbcddadcabdddcbdabbabdbdbbbcccdacacbaaccdddabcbdacbacccdcbabdadccacbcdccadbcabcabaaddaabccccdacaaadccacbabbddbbdaadcbdbcbaddbabcaadbdadacadbcdadacbababcbbbcdabbdcabcbacbabdcbcdbcbdadbbadcccbabbdbdbbaaacddbabbbaacdddbdccaadbcdacdcccabdacacaacccddccbddcadaacdacdaabcbccbaabccacdcccabaaaabbbbabaaaacddaacbaccacbdbaacdcdbbbcbabadcabdbcdbbddaadadbccabddbdbcccddcaddaacccdacabbcbcadbdaabacdcbddcacaccbadcbadacdbadadbddcaadaabddabbcdacacaccabaadcaccdbcccdcabbcccbdddcdbacdbcabdcbbcaadcdcacbbdbcbbddccadabbcadadbdabadbccacdaccbadbcdbbdbcbdabcbcccdadcddbddbadcddaccacadbcbccddbdccacacdbcbdddabdacccdcbbcbddddddbbaaaacbaadcaabdabbcddcdbdaadacddaadbaabbddaabdadcddddbdbabbcbdcbadccddbcacabdddbbacacabadcdccdadcaacadddaaadbdddbbcadbcbdbbbaaccdcbbbcddaddcabdacadddadbccdcbdcdddbacdcbadcabcbccacadbdabacadaaabdcbccbcdbbbdddbbbdbbaddbccbaccbaacbccdabbdaadbacbdbbacbbacbcddabcbdbcddcbbbaabbbbccdbbbddabdcadaddccddbabbadcccddddbacdcddcccddbacadccaaabccbdbbdcddccdbbdcaccbacdacdcbdcbacbcdabdcddaaaadbdcdacccdacdbdbdcaaaacacddadbadacaadadaaabdbaacdaaaddcabbccbadddddcdcccaacdcdcbdacbadccbccbcabbccdaccdccacdacacaccbcaaadcddbbcccaaadbbdaaacbacbadcdddcbddcaacddcacadbcdcbcaccabddbdaacdcadbabbaacacdbbdaaaacccdddccbdbdaddcbbbccbbcccccabdcaacbdddbaadabadbcccdccaaccccdcbbdcdabacaaadcacdbbdcdcccaaadadaccdbbdcdadddcbbbbdacadbbaaaabbdaacccccdbdadccabdbbaaabccbddbbdcbaccbdccadacabbccabdcddbdabcdbdabcbdcaaddccdbccabcccccbaacabddaaabbdacdabdbaddabcabbbbddadbbcdbcccdbadcbccaabadbdccaaaadadccdaacababbcaabdcaadcbdccbaabdbdbbbdabbdabdddbcabdaaacdcacdadcdcbbbaabdabcadcbabaabbdcccccdadddbbdbdacabaccbdbcdcdcdcccbdbcabacacbabcdcdaccdaadccbcbbcdbdcbdcaacbcadcbbdadacdabacbbadcbbdbdcdddaadddcbcaddddbaabaacbcccaccccadcbbdadcdacbadcbcbaabaabccdcbcbaacdbbaaaadddaabdbdbadbdccaaadbbcddcabbccdacaadcababccdbadabdacbadadddbbdbddadcdcabaddbddcbcdcddcdcaccbcdacdbaaaccbbbcaaccadadacacbcdcdccadcabdcbccdbcdccabcabbddbadcacdadddcccaabcbcccddcdaaacccbbdbaacbbcdbaddacadbbccdcacdbaaaaacdcdacabccdacdddbbdadbcbbbddbaddacdbccbadcdabdaaabaaccabcbabcccacacdbadccddcaacdbcaabdacdabbaccdacbacdaaaabccddadcdbadadcbdcadadcbcaacbcabdbbdabbbdabcdacaaadbcadacabddccdcdcdadbaadbdaddaadaaababdbabbbcdcbababacccdbcdccbcdcacccccbccddbddbbdbadccadddbadbbabbddccddaadacddcbdddabcccaabcbcacaabcbbdaadbdccdbbcddbcdacccacbcbdbcdcbaabbcbbddbddbdddcaacabbacaaddbddacadaabbcbacbcdcccacbbabadbcccaaadadaddcbbabcdacdbabbcdbcbcdbdccaccadcadbcccbdbbcdcdaaccdccadaaaadcacdddbadcbbcadbccbbbacacbaaacbddcdcbadccbcbabbacdacdbdcddabbabccbcddcacdadcadcabdadadbabddddcbbcdacbdbcdaabdcdbdabdccbbbcdccdcaabdacbbbaabccbbbbdadaaccaddcabddcbdabdaabadddacacabbbaccdcccabaaddabcacdcadbbadcaacdcccccabbdbdbacdacaccaabbabaadadbddddcadcaddbacccbdbbdcbddddabacaadabdbaccdccccccbbcbbabdadbcaadccacbcaccabcabbbbbbcadcabcacabccdcdacadccdacabcaadbdcabddadaadadcccddbadabaccabbbacbcbdabbdbadacdaabbdaabdccacccbbcacaccdbbddddacabbdcbacdaaccaabbddddccccccabaaccdcacbcbabacdcbcbcdadadccbabdbdbbccdcdddbcaacaaadbcbbacacbababacaccdabbbcddaaacccdbccbcbbabdccaaaabadadbcacdaaccaddabadcbbbcdcbbdaaadcdbdbbbbcaddadacbcdbbacaaaaccbbdbcaaabdadddbdccdcdbcbcadbacaaabcacabbbababaabcbddddbdaabbaddbbddbadadbddbcabdbcdccaacaacaabbabbadbaaaabaaddbbadabaabdccbdabadcaadbbbbadbcbdabdaaadccacbcbcbbbccdacdbdacbabbaddccaabcbccbdabcbaabdacaccacabbbcaabddaaadaaabacdadcbabbcabbcacbdddcbdddabbcbdcbcdcbddcbdbddcddbacbcbacbbbcbdbaabcacaadcdabdcacddadbbddaccbcccbacbbdadccdbcdcabbabcadabbcacddbabacddcdbddbacabbdcabcaccddacdccadcbadaadcdbdbdbdcaaabcdbbbaddddaddbccaabccdcbabbccadabbbbaadbcacdcbddcadcdddbbacdcbdbadccadbdbabbaabbbabaabaaddcdadbccdcbacdcddcbcddcbdbdddbabbdbcbbcbaabbcdbabcdabbccbdbacddabacbbdcbddabbacdbcccbaaadadaddbbcbcbabbacbbbbdbccbcbbbbdcbcadaadddbbcdbbdcaccdbbcdcdcadadacdabaadbbbbaadadadacbabacbabbccccdabbbabbbcbbcccdcadbabbdbdcdbabcddcbaacbdcbaaabadaaaadccacdbcabbdaccddcbcddabbcccdcddbdaaadbdbddadacabadbbabdbadddcdbdaadccaadcbcbcbbcbddabcdbcddcacdbcbdaabacabbcbdddacacbdcabbdaddabddddddddbbcaabcadcacbddabadccddcaddabacdacabcbbcbcbcdaddbbacbadabbaadcaadccddbdccaacccddbdcdaddadaaadabcbbbbcdbccaabdbbdcbdbadcabdcbcdaadbcbccbcbaddabaaddcaabbabdacaabbdbacccbccccdbbccaabdcacddbccaacdbabddacdbbcaccabbcbabdbcabbbdbabbdbbbaddbbccbdaccadcbaaddabccbdcddbdbccccbdcbdcddcdabbdaaccbaabdacbccdddadaccccbdcddccacaadbbdccabcbdbcbdbdbbaccddcadacacbaadacacaccdaacbabbbccaabcbbdcadaadbabbcaabaaaaabbccdccacabaccacddadcddccdcdbbdbaadccccaadddcddbaabbbbcbbdcdcbdcacdbbaddacdaaabcaabcdacddcccdbacacbadadcbbdbcaccdcacccdbbddcdacddbcdabccdadcabdddaadaadbaadcccccddaccaddcccdacabbbaddadabcdacddcdcadabdbcdacdccddcdbcacccbbdcbadacdbbbbccadadbddcbacbdbdabcdabcbadddbbcadbaaddacccabaababaadccdbccaabacadbbbbddaadadddaacabcccbbbcadccdadddadcbdbbcbaacdcbbabddbddcacadadaaccabcbbcadddabdbaabcdacacabdcdacddbdbabccadbdaddabbcdcdaabaadabdacbabcdadcaaaccddbccaacaddbadbdbcaadaddbbdacdccdbdcaaddbdcdddcadcdbdbaabddbadadaccbaccbccaabcaacbbacdbdbcbbdccaddbabaacbdcabcacdbcbbabcdaabdbdcdadbcadbaacbbddcbbcdacddcbbdccbbaaabbadcddddbcbdadcbcabcccaaabcccbabbabddcabacdcbcbaadacbabacbacaccbdabcdcaccbbbdabccdcdbdcaadcaabcbbdcdabbdcaadbbcbdbabdacdabbbcccacdcccbaddccccaadbbcccbdbddaabcbcaacacbaabdcabddcadadcacdbbbbdcdaabbdaadccacdbcadabcbcaaacdccabcbcababcbadcbdccbbadccccaccbcacaccdcabacdbaddadaccaaccdacaaacdbaacdccbbacabbbcbcdccadccaaaacdcbaddcbbbbaadcaddcccdaaadabdbbbadabacbdddaacccaabcbcabadcaabacbacdbadcbdaddaadbbaadcbdbbbbabcbbbbbcbcadcdddbdbadabcbdadabaddcdadaddddbbacbbcdcbbcdadcabddaccaaaccdabaddabdcbcbcbaccdccdbcdccbcbcccddacbaddabacdacdcdabbdbabbccabdaabcbbddbccddacbdcbaabcccdbcadaccbbdaacdcbcaadaaccabbbcabbbdbbdcdccaaabdadaababaaadbaacdccdabcaccadcdccbcabaadcbbabdabdddabcbabbcababbbbccabdcccbaabcdbcaabaacbdaddcaaacddadbdbccbaacabcdcdddcbabaccdccaacaddcacdabccdddbbabcbccbbcabaacddaddbabadbcacaababddcacccacdccdddaddabcbccdabddaacddbcccbbbacbcbcbabbacacaadadcbbacababbddabcdccababbaddcdccbccadabacbbcbadabbabcbcaadaabcaccbcdccbbadcbdbacdaaacacddbbbdacaadbababdaacccdbaddddabbbccabcadcdcaabacccacaabcddbcdbcbcadddddccbdcabdcbacabcddacdcaaddbdbdacbdabdcdccdcaabdaccbdddddccccacbdbddcabdcdcaddbcbcddcdacbdadabaaddbdacccdcabbccacbccbdbadbaacaaddcdcaccbadbdaadbcdadcbdbcabbadabbdcbbdadacdcadbddcacccdbaacabdbddadbcbcdcadbbbdbacbabbaaddadabbdbaadacadccacccbbabddabaddaaabadbcddbaadaccaccbdbabbbdbaabdbaddadcacbcbbccaadaacadbbabccbacadacbdbaabcaaacaccbaaccddacacaacbdacdabbcacdcaabdccabdbcbaaadadbabacddccbcbdbcbacaddcaccbbbbabbcbbbdcdbacdbaccdcbdaaabdddadcbcdabdcadbbdaadbbbccccdbbcaadadbdcdcdcbdbcbbcabcbdddaacbccabcabddcbcdaabbcdadbcddddddacbcacabdddddbaddabadddcbbaadacdabaaadacacaddddabdabbacaaccdcddabdbbaddbacccadcacadbdcadacbabadddbaaadcdabdabbcdcadcddccbcabdabcaddbdbbbddbdacdcbcbcdbccbcdcaabcdcadbddacbdbbbaabdccacccbccbaacbccddbacadcaaddcccbbcdbdcbaccabcacbbacdcdaccdacddcdadbbccdbababddadcbaddaddcbcaccadabbbcdbcaddcacabdbabcbabbccdbaaddcbdbbccdbddaacaadaddabddbadacdcbbbdddcccccbbadacadbdcbabacdacbcdaadadaabaccbbcdcabaaaccccbbdbcaccdadcaabcadcbcccbbacccdaadbcbdbbccabacbaaddcbccabcbaacbacdcddcaddcabdcdccdbcbaacbcaacbacdaccbbadcccddcacdadaacaaabbddaadacdcbccdbdbdddacbdabbdbccdbaddddddcbacbdddacdacacddacadadbaccdbbdadbdaccbbbbdcbbadcccaccbdbbbddcdcacadddcdccbbdddaddaacaddddddddadbccdddabbadbbaddbdacabacadabddbdadcdbdbbccaaaadaddbadbaadaddbaddcbaacaadaddccadabbdccbddaabcaacadcaadccdaccacccacbbbdbddbabdaabbcbbabadddbabaacbabddabcbdacaccbaaccadcbcbcccdbdabacdcdcddbadccdcdabadaccccbdcabcaabaadbdaccdadccaddbaaddbaaccbacdcbccdaccddacaabdabbadddbadddaaacabcdccddccabbacaaaccacbadbabcccababbcacbcaccdbbcdcadaadababbaaccdddbcadababddbbdcddcacdacbbaacadaabcacdcdbaabdbdbabcdbcbbcabaaaddcbacaacbbbdaabdadadaadcddbddaddacbdacbbdbbbdcccccacadcdaadacbddaaccaaadcbbabbcababddccbadcbcbaccdddccbdabaacbbdadcadabbbcdbbddbabaabdbcbcccbbcbbdbdcadcaabddccdbbcbcabadcdcabacbbcbabddcbadadcabcddcbbabbabdcccabbcdddbdbddbdabbbbadacbabbcbccacbdadbddcdcaabbddcdddadbadbaccadcddbbabaadddcdbcabbcbdadbccacbbcdbabddcdbccacacbddcabcbbcabbbdacbcbababdacbdadbcabaaaaaccdbadcaaadbbdcaadcdbcacdcddcaacaccdccdcbdabddabbabdaabbcaddcadbdbabddadaccaacbdbdbbacbccbcccabdccabbbcbadccaadcddadcddacbbbccbdbdcdcdbbcdaaddabdcabdacbabadacbadaddbabadcdabdccbcdcdccdcadaaddccdbbcbdddbdcadaabcdbbadabbbddbcaabdddbbdbbbadcbcababbbcddbdacdbdadbccddaccaccbabccbbbcdccabdadcdaccbaaccbbddcbcdcdaabbacbaaaabbbbbacacccacadbcdddbcdcbdbcacbbcbcacbbcbcbdccbcbcbacbdcadcddaacaddcbcdbbacbbdbaddcaadcdcacddabcbdacaccbacbbdcdbcacddabbdaabdcbccacadbdcddabcabaabaddcddaadbbaccaabbccdcbcabdbbabccdbcabcabbbbabcbccaadbdbcacccbbadbddcaddccaaccdbcdcaacabbabcddcbccbbdbddcaaaadbdcaddadbaabcaddbdcbbdcbadbadccdacbabdbcdaababcadbbabbddcadbdabacabbcddbcabbddbabbabdddbaccbbcddbdcbbdbbdcaccacbbdaaaacbaccbdbaddacbdbbaccbbbabdbcbabcddbaabcbacabbbbbbdcbbdacdbdbcbbabaaaddbacdabcbcbddcdaadabaaabacbcaddacadccbccccccabacabacbddabdbdcdcabbbdabcadbbdddaabbbdabcbbdcdcdcdbddccbacabaccaddaccabbabcaaddcbcdcdcbdacccbcaaaabccddcccdbdcbcacbcbacccdbbdddbdadbdaddcbcdcaddcbcbcccdcbacacddcbbcdabbbddacdaaacabdddbccccbcdbccadcdadbaaabbbbddacaaaabcaccadcccdadacddbaabdbdddadbaddcbcdcddbdbbbadddbcdcaadaacbcdcadcaabbaabddaaaddccdcacbcaddbbcccbbbcddccdacacdcabbbdddbabaaacbbdcaccacbdbcaaabbcadbcdbbadcdcbdcbaadbcddacbddcdaaccdcbbacdbbbddccacbcbbbadbcbbcbabbdbcbdaabbddabbcbcbbacdbdccbcddbabaabddccacaabcadbdabaadcbdbdacbccabddbdcdaaabcddacacbcdbadbbacabbbbabcdddbdddabddbcbcaaabaabccddaadadaccdcdcaabdcddbbababdbadddaadbcddcdcabbbbaccdcbaddcddbbacbcaaadddbcbdcddbadbcbcccddaccaddaacdcabbdddaaadddbccacbddaaaaadabbcccbddcdadcddccbdbcccdaaaddbbcdadddcacbcdcbadcbdcabbdcddcbddcbdabbaccbccdbabdabdcbdacddbdcddccaccccbaaddcbdccaadbacdacddcddabdbcdbadbdcdccccbcccaccbddadacbcbabbcabcbabdcdcbdaaddcdbdbbacaaacbbccccaabbdccdadaccdbdcbcbddacabbbaabbdacccbbdbdadacdaddbacbadadbccdcddaabcaddacadbcabccccbbbaabbddaacbbbbabadacbccdaaaddadddbddabcdbabaaacabaccdcdbcdcababccbadcacaaabcdbabbddcdbcbcdcdbccdacbbcbccbbbcddbccdbbabcbdaabbababbdaaddbacdcbabaccbdaabccacacddbaabccaaddcdddcbddaabcaabbcaaddbdbdadddbbacddaacaadaddcadabbdacdaadbcdbdacdcdbddccddacadbbcaddddbdcbcbcdccbbbdaabbdbdaaadaabbdcdcdddacdccddcabbbbcdcbabcbdabcddbbaabbbbccbcacacadabacadaacaabadcdccbcabbabbabdcdaccbccbccbacbdaddddadadcdaccabbcabdbcaaddacdbbdcaaaddcbddccbcbdaccddaabaccbcdcadcdaddcdbbcacadddbbcbcbdbadbcdbcdadbaadcddacdddbdaabcbaabcbdaacdaadbbcaccbbaccdaddaaacccbabbcdddcdbabdbdbaaccaabcadcdcaadcbbbbcddbccbaadccbdcbacdaaaccabbddacabaababcacbbcaadcababcddbaabcbccabaddbdccbddaccbdddcaacccaddbaacdaabcbadcdbabdbcdacbaaabbccbbcbabbdcddcabbcbbbacbdadcbaababcbbddbdcacbbbdcbddccaccabcbcbaaadcdcbcadaaaccacdcabcdbcbcddaddabbdbbadcdadaabcbbcccdbaaabdbcdbdacbdbcacabddcbdcadcbbdaaadbdcacddaadbadbdcbbdabbaccdaccdcaccbdaacadbcddcdddcaacaacadccbbccacccbdcaadddaabddbdcbbccbccabddbacdaccbbaaccabccccdbbbcadbadabcbcaabbbccbabcdbcbccaadcbdbdccddcaaddadcbacdabacbbadadbbbdcccbbccaaccbccaadbcadcdacccdbbdadcaadbabccabdccddbadbbbacbbcadbabcddbaadabbcdccbcdcaaaccdcbdbbdbaabdadcabccccdabdacdaacbaddcaaacbcbabcbcbdcbdbaacdbaadadbcdaaabbbdbbcdacddccaccdbbdbaccdddabbddcbbacadaabccaaccdacbbacbbccbcbccccdbadcaababdbcabaaadcbdbcbacdaccdbbcdcbbcddddcadcadccccdbccdbcaabbdbcbbabbbacaadacdaabaddccbdacddacbadcaccdbacaaacbcbccacccbdaaacdcbcbbcaccacdddcbaaaadcddcbcbabcbcbddcacabacabbabcdadaddbbdcabdcdacdaadbddddcabaadbccdaadcdbdbbbcbbdbdddbcadbdadcabcdaadcdddaabbdcaddddbacbaadccddacccbbbddccbdcdabddaacbddddccdbadcbcbbcaddcddccddacddbdbdcdbbcdadcdbbcbddaccbcacdabcabbccababdbcacabddbadbacbdacacababbdddcabcaadacccbbacdaabdbbabbcddaadcbbacbccdbbaaabccbadaccbadbacbabbcbacdaccbddcccbdccdcdcdccdcaaccacddadcdcadcbbbdccccddacbcabdbbaaddcccaacbbdcdcddacaddabdcacbabbcdacbccacaaccaadaccdbcacbbbccacacabccdcbaaacacdabcbdccdacdadbcacddddbbbdbddbdcbcacbdddbacdaddbbacadcbddcddddbcdbcabcdacabdbbcbdacbbbcadabdabdcdbacabcaadddbbbaaadbbbdadcdcbcbdcbdaadcadbccaadbabccbccadbcabbbdbbbaddacdccbbcddcdbddbababadccabbcbabcbcacbbdacaacbcdcbccbdcbacccdaacadbcdbddbbbbbdabccccbccdbdacbcbdadaabcbcaddbcbdbbcadbaccadccdccdcdbbacbbbadabcadbbcaadbbccddbddbbbacdcabcbccdcbacbabbbbdbdcbbcabbcabbccabcaaddbbdadaddcdaddccaccbadaaadcaacbccbaacbbaccbddbaaddaaccbacddbaacbcdacdaadbdcbbccaabccdcdaadadbacdaacbbacbaabadabcdbcabbababacdccccbdbadcaabadabdcadabdccacbacdcacadaddddbbacdcacacdadbababcadcbdabcbabdacbbbabddbdddccabccbddbabbababdccabaddbcdcacdbddcdabdabbdbccbabdcbbbbacaacccbbdacccdcbbdadbddbddcdddbbabbacbbbbddadcbdbdcdbbacccadcadbcaddbbcbdadbdbcbddaadaaddacacbcbccccacbbaadccaaabccdacbaaddbbbabbcbbcabbbdddcacdcddbdbbcbaacbabdcaabbdcdadcbdddccbbdaabdaddddcbbdcacacdddcaddbbbdcacbcbdcdcadababbcbdbbadbddbbdbbadabadccabbbaacabcddacdabddcbcaacbdcbdaaabcccbaaaaaadcdaaccbdbbcababdacbdcaabddaacabcaadccdcbadabcbbbdcbcddddaaacaaaadcaabccabdbdcaccadddddabdbccaacbaaadcbddbdbbccddcddbaaccdbdddaaabcbdaabcdbbdbabcddabcbdbddbbccdbbacaabaccddddddcdbdbadcbbcacdccbaacbcdbcdcaabcbbdaddcbbdcdbadabcdccbdbabadbdcdbaadacbacdadacbcbabbbbcabbacdcccdcbcdbcacdbdcaacccbcdddbadbbcabbadbcbcbaccbbbacaacaddcbcdccbcbcbccdadbadadaccddbbabdcbbadbcabacdcbcbccccdbcbcacbaabdabdccacadaddccdcdccbbddaadddacaadddcbdaccbbccbacccdcbbcabdacbadcbcabacbbcaddadcdccccabdbaaaaccdbbcbdbbdbbccccdbdaababcdcdcaaccccdcdabbacabacccdbddcaddbcaabacaaccccadbacbbdcdbbbabdbccbccacdbddcaabcdbadbbcccaadabbaaaadcbcbbaabbdcdcbaaacbabbaacdaccaabccbdabaccdcbaabdbcccaccccbddccbabdabbabacdaabdddcbaadbaaddcabddcbaddbdbaabadabdabacaddacbbdbbbadcbbdaadbabaaaccdcacabaaadbdcacbabaccccacdbddbdbbaccadbdcbcbcabcdddddbbabdbbdabaaccbcbdabacdddcadcddcdaccdcbabdcbcdcdabacabccdaaadddacdbababbabdbddcbaccddaadbadbbbbcbbcadcabacaadddbcccbbabababadaccddbdbadaacbdbbabcdccaccaccbaccadbcaaadbabdaddadcddbacaaacadbcddaacaacdbcabbadabcddacbdacbbbddabbcbcaccaccbbbbaaabddddcabdddcaaadcddbbddddbcbbddbabccddccadcdbccbdcbcddbdaccbcaaacadcddaadbaddcbcdbaadaccaacbdacbdcbddaacbbabbddccdadccdaaaadbddcadaaddcdbbacccdbbcadbcbdbbcddaaaacbaccaccbdcabadddcdddbaaddccbbacccccdcddcdcdbaddcbdabcabdacbaddbcbbdbcbdccccbccabaaacababdaadcbbabbdcddcdcaccbbdcaadccacbacdcdddabadaccadcdcccdacdabbbcdcadbcdddcaacaadbbabaabadacdabdcddcbcbcaacbadbcaadbabaadbccabddbacbdcdaccbcddbcabbbcbdddcbadbcaabcbcabbddbbcdacadddccacabdbababbdcbcaaadaccbbddccdbccdadabdabaaabbbbccbaababbcacddaaadadbdddcddbdacacccdacccdaadcbdbbdbadadbcbaabbccabbabbddaddbabdbadadddacbccdbabcaddcababbbbdbcccaabdddaddaaabdaddcccdcabaccbbcbbadcaadadacbaaaabcadddbbcbdadbbaaacacbdddbbaacccbbcbccdcbdabccdbddaacaadbcdcbdcacbbcbbdbabdabdaddbabbddbbdbabababdccbabdddabcdddccccccbcdcddbaddadddcdccaacdcbabdbdacaddddcccbccddbbcbbabbbbacccaadbbadbcadbbacbcadadccdbccbbdbbbdbabadbcabbdbccabadaadbacacdacdbbddaadacdddbbcbaabcbcaadccbadbbdcacbdcddcbbdddabbcaddadbdcabccacbdaccbcadccaddddcdcbbadbcacabdaadbbdbbbacaabbcbcbdcabccbdbcadaddcabdcdcabbacadabcbaddadccdaabcccabddcaadccdccaddacadcccbabcabcdbadddcbbddddcdabaacbbbadbdbbcdadbdadbddbcddccacaabaabbbacbbabbdbdccdcdacccddbdcacacdbdcbadadcaacbabcdccbadddabaccbbbabccdbcddcabcabaaccacbbdbbabdccdbcbdaaabddbbbdabcddaabacbadaacacbccabdcadcbcdabdbacabcbcbaccddbabbccbcbbabbccbbbdaadadaacabacccccaaddadabdaaddbdbdbbbcadaaabbaaacabcbbdabbcddbbcbccabbcadaaaabdbbabbcbdccdddbdbccaabdbaccbcdcdcabbcbcdcbcabdcdbdacacbddabbdaaadadcbaabddbcabbbbbcbbbdbaaaabadbdabcccbacccbaccabbbdacbbabccbadcabcdcbbbcbccaabccbabdbbcddacbbacaacdaaacabdababbabaccbbdbbcbccdaacdaaabdbaccbcdcbdcdddabbbdbdcacacabadaaccabdcabdcbcbdbaaccbadbbdcdcbccabacbddbccabcadddbcccdacaadbcbdabadaadcdabbdcccbbccbaddadddbcadcbcddcbdbcccadbcadcacdcadadaaacbbaadbabccdbcccbcdbdcbbdaaacaabddaabdbbbcbaddcbbdaccddbcdacddcbdcbbddacdcdbdbccbdbcccbbdbdddadadaabaaddbbbcdbcaccabcbcbcbbadcaddaadbcadbcacacaaabcdcdcdddccccacacdbddadbdbbaadcbcddbaabdcdadcccbdcbcdacdddabdccadcdabababcaaaacdaaabddccbccbaddbdddbcbcddccacbdcdadaacddddbabddcbccacdbbdaccadbbdbabccdbaabbdddbdbaadcabbcdaadbdaacbaccaccbdcacbdbddbbdccdbadbadacdaadabcbddbbacaaddcbcbbbabbabacccbccdabdaddaaaccccabacaacbdbabaacabbdcccdaadccbacddabcacbcbdbbdddbcbdddcbdaddabaabcbbccbcbbbaabccbbadbcaaacbacbabddbddddcabddabbbbdabacaaabdababdcbccacbdccbbbdccaadbbacaabbabbdcadcbccddbcccbdbbadcacdbdabcdcdbcaaddabdabcdddcbdbaacccbcbcdddadadaabdaccdcbdcabddbbbddaaabbdbcaacacbdbbcaabbbdcadcaaabcbcbdbbaaccddbdbcababcacdcaaabddbcdcbacaabdddadbacbacdccacdcccdbacacdddcdddaacdbcbacbccbabaabdadaacaabbbadbcdbbcdcddccabcbddaabcaaadbcdaaaaccacabaacbbdaacadbacdabbabddcaababaddddcbbadbcabdcacbababbabbccdcacdbcaabdbdadbddcbddccbbdcdccbcabcccabcdccddcbcdbbcdacbcdbdacaabcbbddbbcddabdadacaadddbbbccdbabccdababbbdccdccacdbbdbabddccadccbabbacdbdcbddcdadbacadbbababdacbadaabbdcccbabcabdbababbdabbddaaacabdadacdadbdaccaacbbdabdbaddbbcabccdcbcaadbbabbaddbabcabddbddbaabbaddcbbbaaabcbadcddbdbbcbdcacacbdaaadaddcdccccabbdccccaabadabcddbaacccbcbdaabcdadcbdadcbddacddddccbbdccadcdabacbbcbccdabadccadacdacaadaabddddaaddccdddbdabddcbaccaabacbbbaaabdcdacccaaabbbdbabbddddccadabdaddccabbcbacacdcdaaccbacddabcbabbcdcadbbccbcbccdddbbdcaaddcabaabcbaabaabdcadadadbacbabcccbcbbccbbaabcbdcddbbbcdadcdaabdaababaadcaaabbacdcabddccdcadcbddaaabcddcaaddabaccdbcdabdadbdbcacddadbdabdaccbcdbabcdaadbbcacbbcdbcaabbbcbadcaaadcaccbabacbadbcbabcdacccacbadaabcbddbbdbaccacadacdacadabccddbbcacbdacabccaaccabaccbbbaabacbcddcacbadacaddaacccadbadbcddaaddadcdbacaddccadabcdaacdddcaadaabdbbadcabcdbbaddaaacbaacaccabdbccbabcbbbaabcdcadcccbabcdbadcbabddbabbdbcacaaddcdbccaadcddadbccadabbcdbbbdcbbacbadcbcaabadcbccbcdaabaabbbcdcbbadbbadadcdbdcadaacbcdcaadbddbddbbadbadccbdbdcccbdadcccddcbdcaddbdcbadadcbacabdbbbdacdbddadadcccaccddccacacadabdaaacdccbcdcdcacbabbabcdcbacaccdacbacbabdbabaaddbcbdbcccbaaacdaababcacacbcccbdbdacccdcadcaccaccdbdbacabacddaacabdcbbcbdbdddbddccaadcbbaadcddddcdcadaccacaadadabadadcadbcbddcdaaadbdbbddcdabbbbdbaccaadddbaccbbdadbbaadbcabadddcccbbadaccaadcbdccacadcadccccbdacbcaacddcdbbbcdcaaaccdcdcacbcaaadccaaabaacbbbaaddacacdcbdabbcbadcccabbaaabcababdaaaccbdbbaaddaabadbdbddcdacdbcccabcddcbadcdacbadcdcabccaabdcbcbaddbcdabdcccdccbbccbabdaaddadadcaddcabacabbabbcabbdacbacbaccdabcdaacdddabbbabbacccccacaacddbcdacbddcbcdbcdaaccabdabbacccdcddcacccabadcaccdcbbadadadaacabcdcdabdcabdbdabdbccacaacbcaabbddcadaaadbaadbccbbbcbdacdddccbaabcabaadcaccbddacbcacacdcadbdbcaabcaddbdadddabaabdbbcbcccbdacbaabbbabdbbddadbdccbadbbcdaadcbccbdccaadcbbdbdbbadcdcdbdcbcdacadabcaaacacacdadadddbbabbdacadacbddcabadccdacbcaabaddccdcbcabaccaccbdbcbbbbdcccbcddadadbbbcaddacdddcdbbdaadbcbdcabdddaaacbdabcdabaabbbcaacbcbacaadbdbdbdbdbbdddbbaddcaabbbcbcbddadabcbdaabdaddbcccdacdbacbbcbccbdcbcbdabcadbddabccadcdadcdacacbccabccdabcdabcabcabbadcbbcbccadadcabbccddccacbadbacaddbadbdaadadbcdbaacbcbdddccbbacaaddcabddcacacabacdcddddadbacbaccacadcbdddcbbbaabdcddcacddbbdcacbcbacdbccddabccdbabdbbacbdbdbcacdadabdacbabbdaccdbbaddbaabaacddcaccaacccdbbbacddbadcddcbdaddbbbbccddbccbaadbdacacddabdbabaabaaddbcddcddcccbbabbdcdbdcbcdbcdabcdabbcdabacaaaaddccbcdadcddccbcabcbcdadccadaadccbdddabcbabcacadcadacdddbadacbaacadcdcadcddcaacbbbdbddbcbbaaaababddcacadcadbcbacdcbbddbcdcdcaabbbdacaabacacbddddbacbacabacbdadcbdbbaadcacadbcdcddccaaacdbbbdcacddcdcaadcbdcbaabcdabbdbdcbcadbabcaddbabbaadccbbbbdccbcbacbdcbbdbabdabcbbadacbcbcddbbdaaaaddadbddaadbabbbdcbbdaddcbddbcdddcddcdaabdcabbacaddbababdbaccacccccdaddccabccabddabacdddcaabcbcacdccdbdbdcdcddaaccaaabccdbaaacbbcaabbdacbdabdcddbacbdcabdbddddbbacacdacddaaabbbbdaddccdbbadbacbaabbbddcbcbdaddbbdaacdacdccccabdadacdddaabaddcddcdaabdddbddbdaadbadddddccabdbdbbcaaddbcdbbbbbbbdcdbcadcbcbdaccbcababdcbddccddcdbbbcdcbbbddbdcccddabbbaacccaadbbbdbabcabdcdcaaccccdcdbdaddbbdddaddcbdcbcadaadbbcaaabdbabcdaadccbdaabbaccbddbdabbdacabacacdadbacaccacddbdbbababdccbbbddacddbdaaadccdadabaccbbbddacdabcbbbbbdddbcaddcadccaaaddacbbaaaacacdccdabdddadddcdaabcadacbddcbdaaccbbbcbcaaaddddcbbbbdbabbbaadaddbabdcadadbbadacdcaababdccadcddaaaaaddabcccdaaabbdadabbbdbadbbcbbddccbabdadddadcbacaaabaccdaadcbcccddcbddbabcdaaaadadaccadcacdcacaaaaddabcaadabdddaccbddbadcdccbacdaadaacbadadbbacdaddbdaaaccccaacbababdbacabdbcadbbbcdcdccccbbbabadbccaddccdcacdbbaccdabdaddaddbbdccaacbccbaaddaccdcdccabbbccdccbabcbddbdcbdaabacbbabaaccbccbadcaaccdcbbdacadddadcbcaadbadbabcbbbccaaddbccdbdbaaacaccbcaaddacaaadbcbaadadcdcbdcdaadcabbaddbdbdaadadbbbcaabbbacdcaadbbccbddaadcbaaacbbcaacbdadcdddddcbddacadccaaddbdababbccbdabadcbbdcbdbccdcccddcdabdadbaddadcdabcaaaccbdaaddbaaccbcaaddadcaadcdbdaddbccbadcacbbccabdaddcababdddbcdcdcadadcbdaccdbcaaaddcacbbacbbcddabacadbdadcbcdcbbdddaaaadcacdcbbcacccadddadaacbbcabbbdbacdbbacacbcbdbbbddcbdbabaccadbaabaddabbddbabccbddbbcbbdcaadaadabccddbcbcbcdcdbbcadccaaccaacacacabababccbcadbcaadbddcbadbacbdcbaccbcdcdaabcccabdadcabcdbaaadcbaabdadbacadbdcbddcdabcadabdbbaacdbcdbdcddaadbaabaaccddabdbbcdccdddbaaacdaaadddbaaabcadbabdcdbbdcbdadabddacdccabcadaccbbdaacbbdacddabcbacbcaadcabadcabccbaadcbcccaccbacddabccbbabcdacbcddccaabbbcadbdabbcccdbcaabcccaaabcbccbdcbacaddccabdabacbbcbcaadcccbddadcdbdadcadbbcabcdbacbaadcddbbaacadcabadbbbddcdcdcbcbcbacbcadcdbbbbacbbaccbabaadcbddddbbadcdcbddbdccababacaadccdadabddbaddaaadbdcdccacdcbabaacdcdaddbddddbccadabbccddcccbcaaddcbddacbaccbdbddcadbaabdacaabcdddacadddbaababbdcabaccabaaaacadbddacdbdcabadcbdcbcbabdccbcccccacadacdbbbcbcbacbbcdadcdadbacbaadbbbccadbadbdcaadadbaccbadaaccbdddcaddcbdcbbbbcdacdcddcbdbcddcabbcdadbabdadcaddcbaccbdcbddaddcbccdabadbbbdcdbcdbcacaadbbabdaccbcbbbbabbabaaccbcdacbdbadadbcaccbbbacbaacacdbadabbcbbdcabddbabddbddcaccdddbdbaccabcdacdaaaaaccbdbcbbdabbbaadacccdcacacbdcbdadaaccdccddcccaaacbdadbacdcccddaddbdbcbacacddbaabbbccacaabdabdddbcdbdcaadccdaccdadabdcbdbdbbaabbbccdbaccbbdddacadcccbadcbabbdccbaacbcaaabbcbcddadcbbccbbdbcdabadbdbdaaccccaadccbaaaddbbbaccbdaaddccdddacddccabacaaabdbbccccdddabcbddbccdcaabcccdcbcabdcabbccdddbddbbcdaacacdbaaadddbaadbbacadbacacabbcddadbcdaabdadbaccbdcadaddcbcdddcacbdddadbcbcbcbabddccbcdddaccadcccbcbabdbdcaabddacbcccbdccbccdacaabcdbabcadaaadbbbaaabcddadbddcbcdabccaabbbacdadbabdababdddcbcbbadcddacbdbddbbcbabbdbbbbbbaaadcccbdbcbcbdcaaadadacbabbcccdbbdcdcdbddbdbbcaaccdccacdbacddcdacdbaadbcbcbacbadcabcbdccddddbbbcccbacccbbcdcacbadcabadbadcddcdbcdacbcdddddbbcbbddaabaabaccdcdccdbcbaabcbbcdacabcbddbabdcbccdcdcabbaacccabcaccbdaddbaabddcdcbcaadbbababdabacbcdabddaddbdccccdcbacbcbadacbdbdcdadcddccdcbadaacabcacdccbaadbadbcacaaddcaccdbbdbbccababbdadbbacbdbbcacdbbdbcabbdbabbdaaacccabcaccadcbbdbcaccadacbdbbbdcbcdbbcbcbdcaaabcbbddbdaddbacccddcbadbdaabddcadbbdacbbacaadbacdcaacabbcaccccaccddddbdcabbddccdbccbbcadbdbdcdadacdbccabacdcabdaacdabbcbccbcbaacdabccdbdcccccbadddabcaddcdbbaadabaababbaadcabaabdbdbadcbbcbabcbdaaccdbaacdbcabddddbdbcdbdcbbabbabdbbdaabacabaadbbbacbbbccbccaaaacbdadaabadabaaddabddcdcbdacbaaaabbadbbbadcbbccacddadcadcdbdacdddcccbcbcbdaaccaccdcbaccdbccacdbabdbdbccbcbacadadbdbaccbdadcbbcdbadbccddabacabaabcaccacddadbdbdcddbdccadabddacbdaadbbdabddcddcbdccdcaccddadddbaccbdbccacdbbaaddabdadcccacdbadbbadbdbabdcdbbadbabcdcabbdddbccdbdcdcaacabcbabcbdcabcbdabbaabcaadaaaddacbbabdaddcdcdccadcddbcdacddcbaaabbddcacaaabdaacabadcddcccccadaabdadaddacccdccddadbccacbbababdbadcdaddcaddcbccaccddaddcdaaddabaaaacbbcbaabaddddccbccadaadccbdcadbabccdabcadcaccbccbbcbcdbcbbcdbcdcaabcacdcadcaaadaaddaacdbacadbddbbadabadbccdadaacabbbdaccdbacacbacdacdbbcdaacdaabddddcccaaddddbadddcbcabaccdbcdabaabdbdcacdccbadacaabaabadccbddabcdcacddccdcdcdcadcbdcbbbabcabcadcdbcbdaccdaccbcaddbdacdbccbcdcbcdabdabbbcccbdabbabbdbdddbbcdddbdccddcbdaccbacaaaaccaccabbcbaaddaacccdbbbdaaddddacabbbababacddbaabbaadbdcaddabcadaadcddaacbacabbdddbbacaccdbdbbcbcdcaddbdcaddbdabdabcdbcabacdbadbcccdddddcdacdacabaaccbbcbbdadadaabadccaddcaadacdcbdabcccacaaacbabddacbbbcabacaadcbabaabacadccbbaddccabacdbcdacadcccbacdaddbbbdbcddaccddaaccdabcbdbdbdadcacaacacdbddacaccbddbaaaadababaadccdbbcccdabdcacbdaabdaaabdccdaacaabbdccbcadddadadacadadccddcbcddccbdcadddddabcbdcbcbabbaccbdcaadccdcdaacbccdaadadbbadbaabaaacddcbcacdddbbdaaddccabbbadbdbacdddabbbccbdddcabcaaaddbbdbbbddddccdddcaadcaddbcaacdaccbbbddaccbaabbcdddccbdddababcadcabddddacdbadccdccbbdddbbdbcdbdcddccadddadaadbdbdabdbdbccbbabcdbabcadbbdaadddbbbbdababbabbdbbbabbaacdddadccbbdcddbbccadadddcaadcbbdabbcbdadacabccacbadbaccbcaccaacbcbadcddcaacccbabdbabcaabdacabdaacdcbbcbdacddbcbaaccadaaaacaccccbadabbcccbccccbacbcacbaaadcaddacdcadcabaadbabbabccdabbdcbbcdbadcadadcbacaaacbcacadcdadabbadadbaaadcddaaacbaadcdcabcbcadbdcabbccbabcdacdbaccbaaacdbabacdcdcaddbdcdbabdcdbabcbacbcabcdbbbaaddddbdcdbaabacdcbbbadabacbddbdbadbbabdacbabbaaadacadbdccbabbdccdbcdadbdacdaddadbbbabacccddababaddccdcaababcabaccddcbcbcdadcbcbdcbdabbabbbacacbaccccdabacadccdddacdccdcdcabaaabaddbdbadddbabbdadadddabcacccabddadabadabdbabadcddbaabaadddaabbdaacdabcaadaddadbbadabadaabdddbbdabbbdaaddabdaddddbccbddabddddbddccccaddcadadadaaaddccbabdbaacabcdacabcdcbabcccbaabbcaccacabcbacdbacadcdbbaabcddcddccabcddcdccacbdacbbddcdcbaddcbcdbaabcacdbcaabdbdaddcdadbccbdcabdbdccbcbbcacdcbddcacdacadbabcbcbacdacabdaddabdaccddccaddcaabcadbccdaddbadadacdbaccdacacbbbacccaddbdbaddbdcadbbcbcabacddaccbbcccaaabdbcbbabdadacdcabacaadcdacbdabaabdaacaacccdcbabbbaaadbcbbdbaadbddabbcadbccdbcbddbaaccadcbaccbbdccbdcabcaaadbdaadbabbabdcddadadcbbdcabddbabccbaabbcdbbbcccbdaadaaccdcbbbacbabbaabdcabaadbaddacdadccdcccaccbaadbbaddbaacbaabbaacddcccdbcabdbbccccdcdddbdaabccaaabcbadaadcabbdabbcccbcdbbaaddbaaaadabdacbacdcabadcdcaabdcbbacbabdddaabaacdbaacbdddcbacbdabdcdaabcaabdadbadadabcbdaabbabadabdcdabaccbcbdcbdbbdbabdacdacdbdadadaaddbdcaccbdcdacddaacbcdadbddadcacadacbccdbbadadbbdabaadcabcbdbddbcbccacacccddacdcadddbacabadddadcdbbbdbacdbdadadcacabbbccabbdaabdcbbadcdabdccdbdbdcdacbcacdadacdaaddccdaadbaabbbdbadcbabadddcddbaaabccdbcdbbaacadacdbbccbcddaacaccacbccbabbaacababaadddcabbabbbbbbbadcbbcaddccaabcbbbcaddacaddabbdcdcadacbbbdbbcddcdcdddacbcdabadcabbdaacbddaaacbbbbbcdbcdcabdacccbcaacbdbaadbcabdadacccaaaadccaddbdcbbdbdcbacdcbaabbccddabddcacccdddcadddbcbbcacaaccccddaddbcadcddbadbbbcbcbabcdcdaddcbcdddcdbaddaadaaadbabdaaaaddabcdcbdcacbdcacdccdbabddcbcaacacacadacbbcbbacdcacbabdcdcdcbadbdcadcccaaacacdbdacdbcddaadaacbddabbcdbbbcaabbaacccdbdddbddbccdcbdbcdcdcabdbdbcaccbccccccbadcaccbbcddcbadbbcddbbccbabcdcbbcccaaddbbcbaccbbdbbbbccacbbdccbacbaccdbddcccaddbdbcbaadadbaacccccdcabdcdddadcabbbcdbcdacdccabbcddbbaaacababcabbcbbdbddabadbdbcdbaccaadccbdcdcbaccdadbccabcdacbabcacbcbacabaabacabddacdbbadbdcbabacbbaacacadabdaadddaacbbcaddcddccbdcbddbdbaabcddadbacaabdacabccabcccbabaaaccbadcdbbcddbbbddaacbbaabaabbcbdbdacddaaddacbcbcaadaaadccddccbdbdddbcabcbacbbbcbbbadddbcabbddcdbbdabcbaadddccadaaddbccbbcccaabccbcacdbacdbbddddacbddcbbbaaadadadbcabbcbbdaaccddacbcbccaaacccdabcdcaabbbdccccabcdaabaabdcbdcaddadacabadaccbdaadcdcbdccabacdcbacabadddbaabdbabbaacccbbbbcccaabbdaddccabaabacaacbaaadccdaadbadbacaaabbcacdbddbaadcbbcbabaacccacababccabbcacaacabccddcddaccbddbadbbbddcaaaddcbcbacddbcababcabacbacdacabbaacdaddccabdaabadcacbdcbdccdacccadddadbbabcacddcbccbbccdbbcddbcbadacbcacdbcacdbbcccbaaabbcbdaddcdcbcaadbccdaaaabbbdddbbcdccdcabdbbabcbdcbdabbdadbdaaabadddcacbadcdaadbabacabdccddacabdbabcdcddbcdaabdabaacbcdaacaaaaacdababccbdabccbccbddbcabaacddccbdccbbddcbdbacdaabaddcacccaccdbcdcbcdaddabdacbdaacaacabbcabcbacdabdbcbccabccbbbcccbaabaaaaadcadabddddccabdcaadbaddddcbcbbabbdbcbaadabcbabaabccbcbdddcdbadcaabbdacccddddacbbadddccddadcadaadadcbaaaaaaadbbccccbaddbcddabaccadcbaaadbcbaabdacbdbaddbcabdadadcabdaaadbaabbcacbaaccdadbbcbcdbbabdaaddccdccbcbcdbacabdaadabdbdbbddadacddcddbbbbaddbbbccbaadaaadbacccbbacccabbcdbbcdbdbcbcbbddaccddbcdcbbadbccacaddcdadaccccdabcabddbbdbdcbddcbcbcadababacddaddcdcbddabdbdccdcbdbbdaaabbdcdcabadaadacbaaacccdbccddcaabddccbadaadddbddcadbdcddaababadbbadabccaabccbabadddcabacbbadabddbcadbacdadcdacaabdaacdaccabcbbdbbbdaddcbcdbbccaadbaaadbbacaaaddcdccbacdabbdddaddbbdccbbaabcbabbcbadccbaabadcacabdadbcddcccdcbcbabdcbaccdbbacddcdaaccdaadbaabdcadbcabcdbbbdcdddccabbcbdbdcaabaddbabacbdaacbadccbacbbacaabbccdacccddbddcdcabaccaddcbbbcadddabdaaddbccdcccbaadaadacbcaddbdcaaaddacacaacacddccacbccaaadcacbcbbadbdbcaabcaaadcaacdaadaacaccacacbacaddcaccbaccdbddcdcaaccdcbdbbaaacbbdbdbbccadadaadddcaddcababadaaacaaadbccdcaaaabbaaabbaddbccaaacadbdabdcdadacdddbdaddbcacdaccddabbdcdbabbacdcdcddcbdddcbbcadcbddbbbcdabcddcdcbbacbdaddbcddcdddabddadbdadbdbdcdacdaaccaaabdabbcdbdbcaabdabcbbacaabdbbadbccaadadbaaadcdcbbddbaddbadccccdacaccbadddddbbbcaadacbcbacdcdbcababdabcbcbbdbcbccbdaccbcdacbbddcacbabcdbabdddcaaadccbbcccbbdaddcbcbcaacbacccdbbaacaaabbdbbccdbcdacabdabccccbccbdbdbabaabcacbddbdcbccddccbdccabcadcbccdccdcbdaaacbccbbbbccbbcaabcabbcbdddddaacbdcbcbccbddcacdccdcbbaaaddcacddbdbbcbdbcbdcaaccaacbdabcadacbaacbccdabcacdbababbcadacaabddddbcdcbbadacdbaadbddcbdacbadabbabcdaacabacccbacbcddbcdcabcbadcaaccadcdadbccbdcbbddcdcbbbcdddddbacbabccadbcdccccacaaabbbbbdcadccaadcddccdcbbbdbcbbdabadcdcabdbdcadddbadcdaacccdbabccaacacbaaaaaaacabdbdabdbaddbdbdaccdccdbabdbcaabacdbccaaacadcdbdbcbaaaabacbaacbdccdccaaccddccaadcccbdcbabcbbacbabadbbdbdbacddbbabdbdaccbcaacaccacddbbbabccacdbcbdcbaddbdacccbdaadbcacbcbddcbbcaacccdacbbdbbdaabbddccbadcbcabddbddadbbbbdabbacacaabacacdbdbdaabdaadaabcdaaddacacbddaccdacbbabbdabdbadcabadddbbbabcccdbccbcaabbaacdcbbaabccdbbcbbbbcdccaaddabcadcddaaaabaadabaacdcbabadcdbdabccccbcdacdabdbcbaacacdacdbddadcaacddbabddccbccbcdbcdacaddbcdbddabdabcddccdbaddaaccadcdadcdacdbbdcbbddbbdbcbadaccbccadccdddddbabacdabccbbaabddaacacddbdaddbaacdabdddaabcadcdcacdccaadbdaacadbbcdacdbbbdbbabcdbbadaddbbadcadadadacadddbbbbaaaadaaadbcbddddcaddbdabadcbacadcbdcacadccbdabbcccbacaddbdbabcdbccacbbbabadbdbcddabcdcabcbccacdcbadacbcabbacbbbdcdbacadcacdacacbcdccdcabdbadcddacadcddbbbdbdbbbdcabbcaddaccbcaaddaacbadbaacbcaabbcbacdddaacddcacbacbaaadcbdabddddaabbcbadabadbbaddbcddcbbdcdbcbbbcaaadaadbbdccbdbdcbdcabdccbcbabcdacadcdddcdbacdcccbddacaccdaccabcbaccacbbcbcdccbadcabaadcbdccbaacbacdcabaaccadacacbcbddbabbbabbcbcbddadddddcddbbaacbaaddadbcbbcbcabcdaccddbdddbcbbcaccdbdccdcadadacacaaabaddacdaccadbccbbcabaddcdbdddddbdbcdaaccaacabdbbddaaccdcdacbccdacdcabdcdacacaadbadabacdccadcaaaaaaacaacbcddacabcbdbaccbdbbbbdcdbcaaadbabdbbbbcbcccacbbdacddcbbdbcdbbcdaddaaadccadcacccdcbbbdbaabdacdccccbabbbacacaddacbbcbcddacdabadabbbbacbbddbbccbdccdcccdddcbaddbccbcdcdddbabcbcbcabbdacaabaccaadcaaaadcaacbddcacdbaadacdcddbcbbcaddcdddbbbabbadadbdbcbadbadcbcdbaaaaacddaccbbbcadcbdadcdcaccddadbcabddcbbabbdcccbbcbddccdddadbcaddcaaabdbcccaccadcaabdbdcdbccaadaccdcacdacdacbbbdcdabbacabcaddbaaaabbabadbabdddcabbddbcbbddcddbacadbbdcbcaabdbaadbdcadabbdabacccdbbadccbacdbbdbbbabcbddbabcbcbcbdbcdbbbdcbbaddddbbbbacacccdcadadbbbdaadddbdbcccbdccaacbaabbabaaadbcdaaadadbccccdcaabdbcadaabdbaddadbccadcbcddcadcdcbaadcdbbbbddcacdcabaccbcabcdccdcacbdbcacacdcadcacaabcddadbdcbabadccbdbddddacabcaaaaacccbcacdcaacabbaabbadcdaadbcababcccbcbdbbaabbdabbadcdddacbccbabcddabacdacacbbabbcbbbccaaacddbcaaadddccbbdadcadacadababbddbbdcccbcdcaddcbccacbcacbbcbdaabbddbcacacadadabbaabaadcbddaaccabbcabbdddccabbababcdccacdcacbaaaabadddcddadcacaacbaadabadaacadbcaccbdaacbddddbaddbcdcccccbbcabacbccacdbcbdbddaabdaaaddaadbbbcbccccbccbdaacadadccbcddddadccababacdbdacbbccbbcddabdacddccdaacccdccabaddcdccbbaccbbdaacaadbaabdbbdccbdaaadadddaccddddaddadacccabaacadcdaaddadaccdaddadbabbcaacbdbbdbdcccdbabbbdbacbaddcadcccbdbcbdbbacaacbadabbaaadaddbccadadaaddcddbddaadddccbccbabcdddccbbdaadaaacccccdacbdbbcbbdddddbadbabbdcadbcdbcacacabbdddccdbbcdbbaadabbadaddbccdccdccadbcacdcbddacbdccdaddbadcdbabddcadcbcacdcbcaadaccadbcadcbbbbbcdacbcbbddcbadaaccdcabcadddccbcddbbddcddcbcccbabaddabadaddcacdabdbacdabcdcaadcbcdddbcbaccdadcacbdcccccddcddadbddaacdaccadcadbdacddcacbccdbdbbcbcadaaadcababadabbccdabdadacdaccccdcbaccbcdbbbaabbbaddcddbcabacdcdaadcbacbddbdabbadcdbbbcacbacacdabcaadbcdcbaaacdbbcbdbbbbcbaddcbbdcbddbacabcabcbddddcdddccccaacdbaaacaadcbcaaddccbddbcbaacbaabdcaaadbdaabcacabcaabbcabcbcdbdccaaddbbbadadbaccbacccaabdbadacccccabdbbbcccdaadccacabdadcacccaccdbcbabddddbcbdabccbcddcddaddbaababdcbddcbbcdbbdaaacaddacdcccadbdcadcdbdcccabdbdbcaccdddaabcccddcdabdcbdccadaaaccdbacbcaccbcabadabddbcbbcbbadacdabadcbdcbaaccddddcdddaddcdcacdcddcdadabadcbcaabccdacaccbabcdccabaacbadacadbacddddbbadaacbadbbadbadccccacbcdacaccdddcdbbccddbaddadadbaabbcbaadcbdcadcdbdbdbbdcddcbacadbdcdcdddbbabbbabcaabbdbcacbaaaddbcbddbccbcdccadaddbcbbacaddbdcdadaddcbabadcaddbacbbdbbdcdacdcddbcbadbdbddbcdaabacdcddccadabddcababcaddbbaaaadcbacaacddbacdacbcdacbbcdacaaddbcddbccbadbbadcdaadddbacaddbdabbadcdbbdaacbcabcbaddcdabacccdcdaccadcaacdabdcbdcadbacdaacbbdddbcbaccccdadcaaddbcdcdcdacadcabdbabccbdcdcddcdbbabcbbaabbbacccccadbcdabdbcbabdadcdbacbdadbbbbbcbaadddadccdccdccdaaabdaabdabbdbbcddcdbbaabdaaaddcabacbbcdcccccabdbadbbabdadcbbaadcabcacdadbbadbcaabbbadccaccbdbbadbccbbcbbdcacbcbcadadcbcbcabccacbbcdbbcabcbcbcacabdbbaddddbbaacbdcbdbcaccdbadacdbadabaabdcaadcddadacadddbaddbdccacabddabadbdacccabdcbabddcabbadcbcdbaaaadbbbcacacddcaccdcddabdbabbbccabdacbcdddbcbbadaaaacadbabbacbabdaabdddacbabdababdbdbaaadadccbbaccbadcddcbbcabbaacdbaaccbcdbaadabcaababdbdcadcdadaacdcacbabcdbadcadbabbddddcadabbbbbdbabdacdadcbbdabdcaddcbddadcbaddbbbbdabbcdddbcbbaaadacbbddcbdcbabcbcdadcdadbbaabccadaacacabbddbdcabcbdcddaadaddaabcccdcabbcacdcdcaccbccbccddcdcbdbccddbcdccdaaacbdcaddbbbdbbddcbcaaddddccacccdabcddcabccccadbccccdacdcbdcbbcdcbddbbabbcddcdbbabbdcbbcbccbbbbbccacdbcabddbcbbcbcdcdabbcbbbbcbadcadccbcbaabcdabbcababbdcdbabbadbdbcccbdbacbadbdcbbabaddabbcdaaaaabbadaaacbbacbcaacccbcacaaadcdadadbbbcacbdbccacbcddcdcccaaadaacaddbddbaaaddacdcdadbababccbabbccbbdababbbaddbdcdcaabbcddddbcbcccaacdbddacdbdbbbccacbadacaababaaaaaddddcaababbababcacdbcccadcccdcaadbcaaabdadcadddaadbdacccbcccbcbabdadcacaddcccbbadabdaabaadacbcbababadcdddbdaacabdbabcabdcaccbdabbbcdbdaacadadabbbddabaabaacdcabddaccaadacbbbccdbdbaccbbcbaccccadcabddabcdabdcdacbcaacaaccbadccdcadbbbbabdacbddabadcbcdbdbddcccdabbdbabddddabbdbdbccbadbdccbacaddaabdacbbbccbbacabaddcdacbccdbbaacdaabbadadbddbdacdcabcdbddaacbabccccddaaccbcbaadadcbdaaabdccbaddcbbbddaacdbdacbcbdbcdddbbbddbadabbcacdadbccdbbdbacdcdddcdacadccacbbbbdccbbaacdadacddbdacababadcbccccddadbcadcacbcadabbdaacbbbaabaddcacbcbbdababdabcdcdbcccbbdabddaacbbddcdabcbddddbbbcccbbcabbbbbddaaccbbacbdddabadaabcaccccadcaabdbbaccadbbbcabababcbccccabdabbdaddaaaadacbdadaacdcdcdcabaacddddbbbdbadcbabdcbcaccaadcdbdbcadacbbbdddadbbdbccacdcdbdbbcacadbccbccadbdaadacdacbbbbdccadcbdcbddacdbabcbdadbcadaaadacacdcacbbabacbadcddcccbbdaccdaccbacccaadcaddadbbaaaccbacabcbdcbcadbbadadaacdbbcbcacdcaddcabacdddadcccbbacaddadaaccadddabcaacbcaaaddcabbabadcdadbbabdcdddddbabbbcccdacadaadcdbccddccbccacbaaaacdcccbbbdbdaacbbbacaaccbaabdcaccabdbdbbdcdccabaadcdacdbaadcbbcbdcbbbdcbddaaccadcdbcabadbccdacadbcabaaabdddcbcccabbabcbacccdbabaacdadaccddbbaccbbccabbadcbcbdaddacacdaddaabbcaaccacdcdbccbcdccdbbdbcdacddadcbdcbabbbcbadaddadacdbacabcbabacaccacaccdcabbddbabcbcababbccadabbcddbbaadcadbbdcbaaabdbbbddacdadbcdacdbcccadacaadbbcbccccacdcdbdcabccacbcacdddcbdcacabbbbabbbbacddbcdbdcbdaacbbcdaaddcdadbbbdbcdcadbdcccbcdcabbcbdbcadcbcbbacabadbdbcdbcbdadccbdbddccccdbbddccabdcdbaaccdbbbbbaadaddababbabdcaacdcbaacdacdbcacbcbcbaaaacdccdaabdadcaadbdccaadbdddcabcacbccabcdbaacaccbaadbacddbcbaccacacdcabaaccbbdaadabaacddaacccdaabbbbbcdbadbdaacbbbdcbabaabccdddbcacbbcbddcbadcadabddaccacccacabcdbccabcbcaccaadcbbdddbacbbbdbabccdacbcacadccccdbbbbcaadaddcbdaaccdcabcdcdacdcddbdaccbdbabacaddbdacccbcddaccdabddcbdddadaccccbbdcacdacaddcbbcacbbbaadacacbaccabdbbdbbcdcaccbddcabacbccabcbbcabcdbaccdcbaddbaacbbdcadcdcdcabadcaacbdaaabbccbdacaaaaacbdaaccadbdcbcbaacdbccdabaabacacbabacaadccbbdbdcbbdaadccdacbabdbdadcdcdadaacacbbbdccbdbacacbdcccdcadcaddbbdcddacdbaddcbbaaaadadddadbbccddcabddadadccdaabadcdbaadcdcbbdcdcddabbbadcdacadbabbbdaddcbcdcaaabdaddccabcdcddbaabbdddbbaccacdcadddadddcbdabcaacbcbbadcaaddccabcabbcdabaacacabccacbbadaaabbacdcacbbdabdaacdbddcbaddbbcddbadabcaadadadabadacaabbbbdcbbcbbacbaaadbacdadbbbaabbbccbcdccddaacbdcbaaaaacbabdcdcddaadbcacdbdacddaaccdaccdccdcdabcdbaddadccdadaaadbccaaacaadcabbbddbbadcdaadaaddbbbaddbdcbdaadbbdcbbadabbbadbcabccadacaccbdddddddabdbdcbdddcdcccabcbbbacbbdabbbddcabcacaabcdcaabbaadcbadcccacbcbbacaaddbddadbbcaaacdbacbdcadcdabcbcabcaacabbbbccacacbbbdcbbddbddcabbcdaabbcccbccaddbbdadcabbcdbbadcbadccbbcbadbbacaabdbadaccbcbacccabcacbbcbdcbaabcabbccccbcbdcdbbdcbdcaaaabbdddacbbcaadadbdbddbdbccbbaababaddccdabccadccabcddaabbcddbaccbcacdbbccdcdacbbbdccaacdacbddbcacbdcaabdaabbbbdbbdcdcbacadccccdacbdcaadcbccbdbbdddbbddcdcaadcaddbdcdcbadaabdaaabccbddcacbcdcdbdcbbaccabadbabbdadccdbcbadbababcbabcacbbcacdaadbabadcbbbdbbddddbabdabbcdbddabdbcdcabcbddbdacbdabcbbddbddcccbbadcddadcccccabddabbcbcdbdcddadbbadaabcddbddbbabbbdcadacdcdadbdcbadadbaddccbabaadccaaacbadcacacadaadabacdbaacccbaaabbdbbdabcacadabbaaabaacddbcadbabcabcddacbbbbbccdbabaacaddaababbdcdcccacabbcacbcdacaccbaabbacbaddcdcaaabcadbbcddbdbaaabbdabdabcabcdcbbdbdabcadaaabbccbabcdcdbacbdccdaddcacdcaadcdbbbaacabdadcdaadcaadacdabccdacacbcdacdbccabcabadcabbabbababaccabdcdcaccaaacdadaaadccddccdaaabcaccadbccdbdcdaaabdacabdbadccbabcbbaabdadbdbaddbbddacababdcdcbdcdabbdcabddbbbcbddbccddacccbccdbadbabddaabccdcdadcacbccadcaddcadcacaddbbabdaddbbcbcbddbbdddbddabbacabcbdcabbdaacdddccdcddcadddcbdbadabacbcdcbdbdcdccadbccdbadbddaacbbcdaaacacbadbccbbaaaabdbadccbbdbaccbdaabccdbdddbdbdcdcdcbadddbcadaacdbaddacbcbadddbddcddaddcbddacbabcbbbbcbabdabcbbccbbdddbbbcbdcdcadcbbddbbaaccaaccbddccbcccccddadcdbcdbcbcdddccaabadabdaddacbdbdbaaaaadbacdcdaddacacbaadabdcdcbbabcaabcdbccbcddadddacbccabdbbbdcaacdcadcaddabbaccbdabadbacaabdccddbaabacabaaacbddacbcdddddccbcabcdcbcbbbcbbdabbcaadbaadcabcdbaaadbdaabddbdbbcbbcddcccacdccaaddcdcdbadaaaaadbbbdbbcabcbadcbdaccdcbabcdbadaddbddcbdbcbcaacacbcaadcdabddacccacdbbbbababbdbccacddacadcbbcaabccccbbcbaaababaaabbcdddcaaadbabccdabbbcbcacabbbddaadbabcbcdcaacbbacaccdcaaaaaaacadbdcabbadcddbcdcdadbabdadacadccaccabcaaaaaadccdabcddddcacabcbccdcabbdddbadcaadcabcbadabcbdaaddddccbadbadcabdbcbdcabdccababccbbbabbbbbccbccaababcbabcbbcbdbbdcbddacbdaddcdbcbdbdaaccbdcccccdbaaccabbdabdadccaccbabaccabbabdcbdcdbcacdcadaaadddbbabddcbdacdcdccbdcddbadbbddcdbdccbbccdcddbbadcddcabcaabacbbcdcbcaddbdabcacbdbbddcdcbbdccbccaacdcabddacdcdcddccbdbbdbcbbccbdbcacdbbcabbbadcaabbdcbacccabaaccabccaadbcdaaadcdaadcddccddbbbabbcadddbbdacddadcabbabdcbbaabdccdbbcbdcbcacbdbcddcddccbbdcbcdbbbdbdbbbdccdaacaccbcabacbddadddcdddbccaadcbdcaaddbaccbbbdcbbdbbdacadbcabdddcdacbbbcbabdcaaadacdbcaddcabcbdbbccddcbccdcddcaacbbbaacaaccbbcdcdacdcdaabbcdbdddbdccaaccadbbcacbdabcdcdccdaccaabccddcccddbabdaabcdadacdcdbdbcbcbbcdccddaddadbcdccccdcabddadacaacbccaaacadcbbcbdaaccdccabdcdacdacbdccbaacaccdcabdaaaddcdcbbbaaaacadbcaadbddcddddacbccabcdccdbacccaccdccabccbdaabcbdcbdbdbadbacabbcacbabccaadaadcccdacdadadcbabacddbbcbbcbbbabbbaaaddcddbdbabaacddbcaccaccbccccdbbccbcabdaaadacbbdbbbdadcdccddabddcddbbbcbcbcbbaadadabcbddaababbcdccbbbdcbadcbdbbdbaacbdacdcddadacbbccdddbabdcdcbaddaabbacbdbdabcddacbbaadaadcbbcdbbbadcccbcddcbacdabdcdbbdbbbcacacbcdcbcbabddddcbaadadaabcaadacaddcadcccadcccbcdcaadcdbccadcccabbcdcbbbabdbcdcbadaacddacdcaabadcbbbaabcdbdabdbccdccbaabaabbbabcbddabddbdbacdddbdbabbddaabbcdabbbbdddcadcdcacdbcbcbbbbbdabcabbcaabcdadcddbaccbcccdaaacddcbaaabbacbacdaccdcbaacaddddccddbcdadaadabddddddbaddbddbacbddbaccacaacdadbddbccddcbbaaadccaddadcdaddccadaddbcdccaabddbcaabccdbdbbbbabbbbbadabbbbaccbdbcdbdacbdbacccbdabddcbbcadbddbacccaaabdbaaacabdabcddcdbbabacadaadcadaaccbccabdbbaddbbbcacbcabcaccddbaababadaacaabcaddcddcabdbccdcddaccbddcdacdcadabddaadbccccabacbdaadddccbdbabccbacdcabdcdccaaabcddcddadcadbabcddaaaaacdccbacbbdbbbddbadaacdcdcdabbadddbabcddcbacaacabbbabcdcabcaabcdccaabacbbcdbcbababacbdaaaddcbadcabaaddabadbaccbdadadcccbbddbdbabbbdbbdadbcbaddcdcbdbbbcdaadcbacbdbdcadbaccdacaadccccdcddccabdbbcbabacbbbaaccbaaacccaacddbccdbdccbcccdbbbbbdadbccbcdaacaaaadddbaaadaadcbddbaaddbdabcbdcaacbdbddddaccdabbdbaabaacaddacdbacbadcddaadcbdcbacbabaacccdbbcccaababcaacdadcbaabdaabbdcddccccbbcdddbbcadcdadcabbadccbdccaaddabdcdcddbdddadabdbadcdaccccbadaabccbcaabbbcdadddcaccdabadcbdacbabdaccbaaaadcaadcbadbcccddacdcadadaddadbbabddbddcbdbacabbadcccaaaddbcaaacacbbcbddcdaabcadccbbdcddabadbbdbabbadaaadaddbbdbaccacbbcbcdcdbcbbdbccdcbadbbdadbccccabadbadbadbadadddbaaadaddcccddadcbdccddbdcabbdadcabadaabbddbbdabdbdabdacbbacbadabdbccbcdbaacbbbbdcdcddddabbadcbaaabbdbbababdbadaabbdcccbacdcadcbbdcbdcdbabdccddbbdbbddadcabaacdabdddaaadbdcacabdaddcbcdbcabbacddbadacbaaddbaabbbbdcabbdccdbbbbbcddccdbcddaabbadcabdcbdddbdaadbbcdbdcbcdcacdddcdbaacbdacabcdcdbaddbccbdddbdaaabddaccbcdddbccdccabdbaabdbacacadaccdbdbccacadccadbcaaabacbaadbdcadbcadcdddbddbacdadcdcacacabdcdddddaaaccdbdccadacdcacdbbaadaababcacbccbdccccacccdcacbcbdabcbdcdabcbcaadabbadbbaccadcbabcbbdabbbdabdcdacbdbcdccbbbacdccaacbcbdabdcaadbbdcacaaabdabcdaacbdacabbadadcbcbccabccbcaacacdbcccaddbcbbccbcbbddabdaccaddbaacabadabacaddadcdbdbaadacdaabdddbaadccabcbabdcaacccadddddaacadcacbbccaaacccdcddbcddaaaccabbbbccbbcdcddbddbcddbdaabbadcdcdbbdcaadcdbbcbcbaddbddcddccacaaadcbdaddbbaaaccbdadacacbdcdadacacbdbbdcbbdbbaababbccabcbbccbdaccdbcdbdbdadcabaaaaacbacaadaaabbdbbbdadcbdbccccdddbcdcaacbdaddbabdbacacbbdcabcadaabbccaacdbbbaaaaacccaaabdcacadbccabddbbabdccdaaabcaaaccaaccbacaaccdbcdbdabacdcddcdbbacacdbbccdcaacdcbcaadcadcaaddddbbabbddbbadccbdcdbcbacabdddcadcbcbdcabcbcbdaabbbdadaaabadacaccbcacccaabdddccdabbadaacbdcadbcdabbbbabbbcdcccdcacdbadbadbbbbbdbcdbadbdcbacabaaaadbaacdbbbadcccdbbcaadcdcdbbccadddabdbcbabacaaabadcddacacdcdbbdccbccadcbbdbddabdccdcbdbdbcadcabaabcddaacaddbdbdacbcabdbabaddabbcabdbdcccaaadaacbcbdbacdcdddcabcbadacddcccabbdbcaddbdbdcdababddddcbbcacaccadcdbdbcaadcbacbbaaadaaadabadaacaadacbbdacacdcbbdaccdcabbcaaccadadbbcdbccbcadadabbaacddbacccbbacdbaabacbbbdbcbdbbabbbdabdbcddccccbadbaddacbbaadbbabbadbacdbbabdcddccddcdbdbbdaacabadbdaacbddbddcccdbdcdaddbddbcabbbadbbbaabacbaaccaadcacccacbddcdbdbccabadbacbdadcdcdacdabccaccccbcacdcbddbdbdcdcdacacbacaadccbcddbdaadbadccbbccdbcddacaccbbcabcbdabbbacadcdadccadcdccdcdbddbbcbdaabbbadbdbbaacbcddabaabddbbbadaccacdbcbcdbadbbbdccbbddadddbccdcabcaaadabdcaaccddadaaccaabcacaaacdacacbcdbbcbbccdcabdaabdcadaadbdcbddbabbabaddccbacdbbcbdbbcbacabaccdcaddbcaacbbbbdaccdcddddcccbadcacaabcaacdcaccdcababbbbdcadbabcbaccdcbdbadbbdcccbdcbbcabbcdcdccdacadbabcccddbaacdacdbcaccdccbddaaccacdbabdadaacadbaddcbdaaabbaacbabcdcacbbccccdaddcdcbcbbdbaaadbabadbdcdcdcdbddcdaabaaaaccdcdaaabbaaabaacbabddbdadbacbbbccbbcdccbacacbadbddbdbddbaaddcdcbcccababcbadacdddbcaaadcaccadccddaabbddaadbddbcaadcacbcabdabdabdddbbcddbbdaaaacbccbcacadddccddcbadabbabccbaadcaaddcbaabaabbdaaabdcaccbccabddadaaacaddabcabdccbcdacccbbdbcbccacdacdbdabaadbbdbcccddbdcdaaddbbcdcccdcbbacccbaccabbcacbbdddacaccbdbcbdddccdabbabccccacbccabcbbdcddaaabcbbcdabdbccbdbbadbabadacaacbdbcdbdaddbbbddacbacdcddbccacabcacdaadcbddbbaccabbdaaddabcbaadcbcdcbdaccababddcddadaddabcbdcdadcccabcbddbcdacbdcbcbbcdbbdacbbcbcdddbabcbbbdcaccccdbbddbaaddbababaaddadaadccddaccbdcbdbaddcbacdcbbbbabbcadbdbdaacdadbdcbcdbacddddbacccaaabcccacccaabbcbbdbbdabbcacabbcdabccbacbbccbcaacbbdccaaccdcbdddabcbdacbccdbdadcbbdbbbadbbdcddaaddcdbcbddaaaccbcbbdcbdaaccbbdabaddacbdcbbccddcbcabdabdbacbdcdbcdccbacdcaabadbccdbcbbdbababccbdaadbccbbccdaadcacabadbadababdbaaccaccbbbddcdabbbabccdacadbddaaddcaaddddadbddccdbbcbbdacbbbacaaaadcbcabbdacaadddaaacabbaacbddaadaadbdcbccdcdcbcbbdacbbbcdcbbbadbcdadcdaabcabbbdbccdbaabbbbcbcdabccabcdacabaacacadccbcbabbccbcbdcaabdcdaacdbcdbddcababccdaaaacdaccbadccccddaaddccbacdbaacacbcbabddaabcaacccbbbabdabddbacadadcaaadcbcbacbcabcacdbaabadacabcdcdbccaccadbbdcaadbbbbbcdacacaabdcacdadcacacbdacbabdbdbddabdadbaaacddaadacccbbbbdcbccbdaddabcdabcbccddbdaacbcbcaddabbdcddcccaadcaabdcdbcdcccdacbcdddcdbaaaaadbbbaddcdcdcdcbccabacccadabbacdbbddadadaacccbbcbdadcdccdbdbccaacdaccaaadddbacaabdcbbabcddbcacdddaacddaababcadbcacaddcbbdcaabbbbdcdbbdcbacbaccbcdbcabddbacadcbdcbbdabcdacdabbccaabbacbcadcacccdcbacdadacbcdbcdcadadcabbbbccadaddacbbdaaadaccbcddbdcdbcacabdbabbdadcdbabbbdbababcadacbbdcacccccaadbbacccddabacdcdbcbabcadcaadbcbcdcbcacbacacdbcbcbdddabbcbadaabcaaaccbddcbaadaccaacdcaccadcccadcaddccaddddbcbcdadcbaadddbdbddccbcacbccadabcbdcacaaabacbdcaaccdbccdbdadbdabcbcacabbdaabadcabcbcddacaccaabddadcbbaaabbccdaddbcdabcbccabddcccadbdcbbdccabcabcdcbbccbacdcacddbbccbcddbcbdcbbdbdbcabcddbdcbaadcdabbcdbabdadccdcadcadabadcababccbdacbdbdacadcddcdcabacaacbbccabcccbbddcabbacbbcdcadbcccdcbbbdbdcbccdbbbddbddabdcabbadbbacbcdadbccabcacdabbdbcbddabadbbcccbbddbdbaddaaddcadbbccdbbadbdaaabadcdacddcadaadabddbdbddbcadcbdaaaabbdaaaadbccaacaaadbbbdcacaaabdcaccabdccbbcccdaabbdbdbacdccdddaaacccdcbaaaadcddcdddcddbddddbcaababcaacbdbdbdadcdbbaccadcaddbdbabcccbcdbddcdabddabcbbbddbbadaacababcbdbcabdbadcddccdcbadbcbdaccabacaaabadbdbbbdaadbccabaccaacbacdadbaacdacaabbbbadbccdccddcccbabdbcbdcdcdadadbaaccbadbdcddcacdacccbcacbabadcbbadccdaaaaaadadcadcdcbacdcbdbdacdbcbcbadabbdbadabbbaaadbcbcdbbaabadbaacdacddbdbdcbbccdccdbbbbaaddacbcbdacddbdaabaddaaabadabccbdbbcabddcadbcdabddccaaaabdabdbbbdbadadadaaacaddbbadaacddaacbcbbdbabaccbaadcadbcdcdbbbbaccbbbdddadbcbabdcdaacadddbcadabaddacbacdcbacdbdccbdccdccaabdddbcdaabccdadabcbcddababdbccbaabdabdbdbaddbcadcdacddadcadcabbaaaabccdcdabcacbabbccbcaabdcaccbcdaaabdcbacaacaacbbaddacdccdbabccbadadcabcdbcbccaacbdcaddcacbbcbccaabbddcaabbadaabdaaabbcbbcbacdbccdddddcdaabbcadbaacdacabbcbbdcdcbaddcacaabddcadbadaddcccccdbcdbdbbbabbbcabdcadbadcbbabaddcbdbccbdddcaadabcacdcdbccbddabaaacbdcdcabddaabcdbcaaccbddadddddddbbbbdbbaacbacdbabaacdadacaacdcbcabadcacadbacddaccabddabacbdbacdbacbbbbcbcadadaaaabbacbcdbbdcaadcbbbddcdbccaacdaacdcddbdcacdbdcddcacacdcaadbbbbdddaabcdbabbbcccbdadbadccaadcbabdbdddcdbddbbbccdbcccaaccdccbcdbbcbacabaacbcccabdccaaaddccdcdcccaacccccbbdabcacbadadbabdddbbabcacaaccaddaacbabdbbdacababdcdaabadaccaadcaabdccdabdcbaabbaaadccadccdabdbdaccadcabccbdacadaddddaabbbcaddbcbccdabdccbbcccdcbbdbcbbddcddadbadaaccadcbbcbcaabbbdbabbdcaaacdacbcacaddadacbabaaccabdccbcbbbabcddabbdbddcddddbbcddcbbadbacbdddcdadcccaccaaccbcaaddbaaacbbdadacabadbcacddcdbcddcabddbbcdbbbbbbdcbbbbdbccdbcadabcdcdbbdbbabcaabaccbdaabbaccdcaddaacaacbbbdddaccacbaccabdbcdbadcaaabccbbcbdbcdadcbbccdabccbcdaccaaccabacccabdbabaacdddabbccbdacaabbbcacacbcbbdcddadbddabccaaacaacbcbdaacaabbbaaadcdaaccccdaaadbbbaadbdabdadbbcdbaacbdbbbdcccbaacacabbccaddcbbbaadcdadaacbcdaddbbbbdcadbcacadcbddbbdccbdbddaabcbdddbacabdcbabbcccdbacaaaababcbbacacddcccdacbdaaddccbcaccdcadadcbdcbcdacbababcaacdbdacdadccabbdcabdcdacdcbadcaaaaaacdacabaaaddadbdddaabaacdddbcddcaddbccdaadccaaadbcacbcadddbbccadcbaaaddadaaccabacaabcdabdbaddcbbabcadbdbadcadbaacccbaabaacbabccddbacacbbdccddcbbdccdcdddaacdddcaabdcaccbbacdcbddcbaabdadcaaacdcadaaaccabdddbbadabbbdaddbbcaacdbcbdcbabdaadaabdaadadbbccabcacaaadbcbddddbbdcacbababbcaaababacaccbdadaccdacbbddacdadadccaccaddbcdbdcbdccdabdaabbacabacbcbacddddaaccaabcccaacabbccaadddacddbabbbbaacdbcadacddabdbcdbadbaabcddccabdbacbabdddbcccddabbabbdacccdabdbbaacdcbacacdaadcdbacbddbcbbbcbbabdddacacdcadcdcccadbdabacacbaaacccabcadadbcbababcbadcdadadddddaadaabcadddbaacabccabdbcbbbccbbdacdbaacbaaabddbbddcaacbabddbcabddbbcbbbcdcdcbaabadacbadbaccaabacadcbddcddcaaadabdbaadbbdbbdccadaccacccdcbcdccaddcddadbaabadddaccccbcabaacddaaadcaacbccbadcccdacdbaadcbcadacdccadccabdaccbddcbbbbabdaacadaaccbdbbccacbcbcbcabaccabdaccbcabacccddcbcdbaababbaddccacccbdcabcbbaddbbcaadcbcbccabccadcbdadadbbdadcdccdbbaacddaaaacaccabbcdbadabaadbbcabcbabababdadaaccdadccddcdabbcbaabdbbdddcaddcbdbdcdaaabccabcbccbbadbcbcdabcdbccbacccbdccdcbdadcaadcdaaadcabcdadccbacbbcbbacdcddaaddcccabdaadcabaababcaabacbcbcbadccbcbacbaddacbbbdcdadadaaaddddabcaaddddabacacdcdababaadbabdaaaacbcddadcccdadcbbabbabaaccdbdcacbbdbbdddcdccddaddabadcaacaabcabbaaadadccbdccacbabbadcbbddbdaacbcbcddacbbcbbaaacabbadadcccccbacccdcdbcbacdacdaadabbcdacccaaddcacbacbbbcbaabddaddcaccddbcdabcacdcdcdbbccbadccdabbbddddbbdadcddacaaddaddcacbdcabdcababbdccdcddbbdcddbcaabbdcbbabbddcbbbddaccccbabbbdbcdcaaaaaabbcbddaccadadcddcaddbddccaababbdadcadabbbddcccccadbdddabacdcabdcccadaddbccabdcddaadabdbdabaabcaacadcbbbcdcdcdbbabaaadbdbddbacbaddadacbdcbcaccbabccbcacaaccdbbcacadcbdcbabcabbdbadbadcacdbdbdccbabdadbdadccaddcbaacbdcbbbcadbbdaccacabadbdcdabaabadccbbcdcbbbcddbaacdadabcbadaaacacbccbdbcacdcccdaccaccdbbabaacbdbabbcdbbacbcadcacbbbacacabdaccacbabcbccbbbdbbcacaadaacdaadbccadddaabccbcaaadbbababdcbaabbbccbccccadcddaaaaddabbbadbddbddccabbddccbbcbbcbcccabbbacbccbddbdcbcccaddbddabdcaaaabcbccbbbbbdadccddacaaadbbdbacddcbdabddcadaccddcbcdaaacdccaccaaddaabbccccaabacbcaabaabddabdddbbdddbadbdddcbbabaaacdbccbdbabdcaadcbdddcccaadbdcdbbbbbacccabaabbcbcaccacdadddbbcaddbbdaaaabccaabdbdddccbbaabcdacadaacbabaadabababadbbbdbcaabdabcbcabbcbdcbaccabdadbcabcbdbcacbbdacbcdbacddcadbccadbccdcbaccadbbbbdbdcddbaadbdbcadbdcbcdacabaabddddbaaabcbacaadbbbdabbabaccdaccacdbcaccddababddadddccdbdbdabddbbacadccaabbacddccabdcdcaaaccadaddbabcbdbabdbdbcccbabddadbbccdccdbdaabcdbddddbbcbcadbbcdccacbddcaaabdbbbaacbdaacabbacdddabbaacbaaacdcbaaabdaaabdaccabadbbbcbdbacbdbbdcdaacbbdcacaabbdbaccdbcdbbcabaacaacccbababbdbadbdacbbbdbacddcbdbbaacaacbdccaaabdbbacadddcbadaaabaddbdaccccaabcbcdcdbbcddbddcccbbabadaccbddbadcdcaddcdbdbddcccdcacbcddcdccccbadbbabdddadacbbabbccaddbddbccbacdcbdbabdbbabdababdabadbdccdabddcdcaacbbddaccbacabaacdacdbaababcbacbdbbdbcdbabcccbacddcdaadcdbdbadccddbacddabbbbabdbccbabbabcddabacdaacdadddddbdaccddadddaccbbbacdddadbdcdaacacbbdadcdcabcccdccadcbbdabddadacbcbbdcdcdddcbdaacccddcbdabdcdddaacdccbcbaaabadbdcaddddaaaccbbbdccbacbccaccaddadaabaddccccadcbccacdbcbdabdabdadadddbddabdddbcdbbbbddaccbbabbcddaccacbddcbdccddaddcdbddbcaacccaacacddccaccadcabcadaacbaaacbdbcacbcacbddcaccbcaadccadabccaddbdccbbaabbdccbbbcbbadcbbcbdbabdcabdbdbdbacbcccaddbacadabdbdcdddbabdadacddcddcabbabaadbaadcdbdbaaacadcccbbacaccdcccddddabbccbdbdadbcccabddbccddcdbcdacdcccddabccabcdabccbcabddbacaabcbddaddababaacbcaabaaaccbbbabdcaaabcaaacaabaacccacccbaccdaadadcbacdddacadcadcbbbbbababbcbbaaaadaaccaabadaccdaacdcabbdcabddccbddbbababcadcbdbaabdcadaabbcadcbccdbbcccdcdcdbaccbdacccaaddbdbacbadbbddbbbcabdbcabbbcaddcbdaaacdadbaacbcddcdacbdcccdadcbccccabddadadcccacbbdbbdcbacbccbabdaadaddbbbcccaadbcddbdccbaddacaabbbccabdcbbdddddcccddddccbabdbccccbbadddbdcdbbbbcdcdabdabacdababaaccaddbbaaccbbabcaccddbacddaadabadddaaacabdbbcdbcbbaacddacdacbccccbddcbcbdccdbdbddbcaccccbadbcccbbcddadaccdcbacbbdbddbdcccdbabacdbdbcadaadbdbddbaddacdcccacdcabbddcacdddddbcaadadcbcacabdbcdbbdccdcccbbdddabcaadaacadddbddabcdbbabbdadbccbacbbbbddbccccbcccdbbadcadbbcdbdcbcccacdbadadadcaddcabcacbaacdacbacccbbddbbaccaacbddabbbccbaadcadbacccbcccbdddabddbdccadbaabadbabbddbbddccababcbbddacaadbcdabcddbaaababdcbddbddbabddbbcbdcaabbccbcbdabcdabbbbbaacdcbadcbbdaadbccbdaccbccaaababbcacdbccbdbcccdddccadbbbcbabdcbbcbdbdcdddddbbbbadbdbadbdbbdbccccbbcdbccbddcbbaaacbcccbdbabbabccbccbdaabaadcccaabadaaacdaddacbadbbcdcadbccdabdccdcbcacccdcddcdacdbacadcbaddaacdabcabdcdabcddacbbbdaadabdcdccbdbaadbacdccadbdcbbaaccbbcbddddccbcaaccbccbbccdddabcddcdacaacdcbacaaccbbcbddabdddababadcbbccdbcbaabcbbddcccbacbbdcaadaabcbbaabcddbacbaaccdadcbdcaabccbbcccabccdcdcccbcabbcbbacccabddadcdbbaaccdccbbdbbcaadcbbdaccaaaababbccabdaaaccdcbbbdcaddbbdbcbcabbcacbdcbbcbaaccaddccaccadadccdabaadcdadbabbaaabddbbdcbcdcaaacdbbbaccbdbbaccccdadcadddbbddcadcadaadaacddbabbaacdabcacbbbddccacadcabdddbcabbbdaabcdaaaaabadcbcadcbbdbcabaaddaacdacbdbbcdadccbcdbdbacbaadcbcaddacdcadbcbaddacadccdccbccbbbccabbdcdaccdabacdbdbbbdcacabcaacdaccaaaadcaccaaaabaabbacdbaadaadbbabbabacadaaacdaaabacdddaddcdbdaadbccdacbcbdadcbcacdbacacbbaabdcdbbdcddadaababdaabdbcbabbcccbccababccdbdbabbdcacabbacaadbdcdaccbaaadcdaccdbbdbbdcbbcacdcbadcbbdcdccbcaddbcbdddcaccbaaaabdcbbcdcdadcacbbdbbbccdcbdcdbdaadabbbacdcaabcdbcbabcabdbbbcbcddbcddaabcbccbdbdaddbaabcacdcdccabdddaaddcdbaaabbbdadabadbacbcacbccbdbdcadacbabcadbdbadccbcddadcaaabdadacdddadbbddaadddaabcdbdaabdbdaddbbbabbdccaaabcaddcccabccddddadcabcbdcbccabacabccbddcdbcbbadbbccdbbbacbcdcbadbadcdccdbbbcaabdcaabccdbdbdcbdcbddcadbbdacabaddbadcdddabdbddcbacacdabbcacaadcbbddaabdaaadaadbaaadabcdaabcdcacabcabbaccdbbddadaaaacbbbdcdbabcdaaacddaabcbcacdbbabcbccbadcbddbdcbccabadbbddadbcccccdbccdacabcbbbcdcabacdbccbcddacdabdcabbabdaaaaacbcadbbacbddbabbadabadddddcbabddcbbddacbbdbbacbbbbadbbddaacbbbdbcdcadaccacbcacbacbbcccbabcdcbdcdbdcbbbaaddbdbaaccbbbdbcabbbaacddbdddadcddbcbaaccbbccccdbdaabcbccdddcbbcacacdaadabdabcbaabbabbcbddadbabbcadccdcdcadabddccbbcdcaddacbdbdabdadcbadddbbcdadcaadababdbddbdabacbbaaddbbdaaabadacdbddddcbbdcbabbddaccbcbabbabadbaaccbacaacbcdadacabccaabaaadcccabdcddaabccdadbaadadaadbcddbadbdddcdbdcabdbbbccbacbbcacbddadcadcdabdacabbbccdcccaccbbacddcbdaaccbbaadcccacabdadbbdcbbcadacbdbdabddcbdbbababcbaacbddbbdbadadcbdbcbbcabababbadbaaddaaabbcdbcbaabcaabdbcaabaabcdaacdcacbaabacbdbccccddbdacbdbadabaaacbdbcdaabddacdaaaccbaabcabcbccbbacaccbcabcbbbcdcacdccacbaadbaaabaccdccddcdcbdccddddcadbbdaaccbcadcdccaaacdadadbadabbbcaaaddccbcacabaaaabcdadcbacdacacacdbabacccabbccddcdcbcdcbcbdbbdcadccaababaadbcaaabbdddbddcbcabcbbcdcbbacaccddacdacddbbbddcbaaccaacabbcdcadbcacadcbacccdaababddacadadadccacbdaacaaabdbbadcdbcddabddbddaddbbabccabbdddcbbdbbadbadaadbccbcdaaacdcdcbacbdddddcaddaccccbdabccaabbbcccdacbaaddcccaccaabcdabbaaddaddcbccddbbdabdcddddaabaaddbabacaacaadddaaabacacaadbbbdadbaaabadabcdcaacacdccacbacbcbaddccabacbcdcdababadccdadbabbbabdaacabddcbdacdbbabdcdbccdabcddaacaabaccccabdadbddadabdaadbdbccaddaccdddbadddaaaccbbccabcbdbadcbcdcabacbcbcaaaaaddacbcdcabadaabdccbdbcbbdccadaaadaaaabbbccbabcdaddbdbdacbdddccddbacacbdadaccaabdacdcccadbadbdadccccbbaadabaaaadcacbcaddadbaacadbabcaacdcbcacadbabbbcdacbcccabacaacbddcccdcbdadadddcdbaaabaacdaddabaddccaabccbaccccbdacdacabdbdadacaababbbbdcbadcadccabaaaacadaaabcddcbbdcdbccbcdbadacbabdbbabccddbdbbdcbdabbbbcabcaacdaaddbdbbabdaadbcbaadccaabcbcddacbaddaaddbccabcccbacbbacdabdabaccbcadcbcdcaacdccbaadaccddacbdcbcdcacaaabadddacaaaccbcdabddcccabccdbddddacbccabcadbadaacbaacaadbadcdcccbcbccddaaacaccddbccaddaabddddcabcacdcabbbbcbbaabddadacabbbcbbccdcbcdaadcdcbbdababacbcdacacdbdbcddcdccaaaccdbbaacacabaddabbddccadcddbddbdcacbdcdaddbbcbbccddbdabcbacaccadbbdbdcddbaabccbcccbabaacbdbadcddcddccaaaabbdbdababcddbbaaccbbaadcdaadacbacaaccdbbddccbabcbbcacbdbabccaacbaaabcdacddbbacabacabbadaadcdcbdcdddbcaccccccaacbbdcadaddbbaddadabdbdcbddbdddaaabbbccacacadbabcdaaccadadbcdcdcdccccdadcbabbabdbcabdacabbbacdaccbaadabccaacbabcddcdbdbcbabdcaaabccadacacadbbabaaabcdaaabacaaabdbbdbbcadbadddacdbbdcdabadbddaaaabadadabccdabdaabbbcadacbaddbdcadacbaaddbbcaccbaccddacbbdbdadacaaadabadabbcdcbaadbaccdaddcddbaddcaacbbdabdbaacabadbcbadbdcacaccadbcabcdccddaccbdbcccbbbdcadddcbaaaaadccdcdaabdddbabcbacbbdddddabcbcdcaacadcaccccccdddbdcddcddbadabcdbcdcaccadaadcadbbadacacddbddcdabdbaadadcdbdabcaadcdcaabbbabbdccddbdcabaacdbdbcdabdcdbbddaadcdbdbdcccadadababcdbbacaadbcdddbcacbdaddaadcabdadabdbdbaabbccddbacadaadcdcadbcadddabdcaaccadbbccbbabaacbacdbbdbcdddcadaddadbacbbdaadcaabaababcddbbccdddddaccbacdcabdbdcbbcccbccbaacdcbdacbacaddcbaddababbccdaadbbabcbdcdbcadcbdbdccadbabccacdcadababdddbcbdaabaccdbddaddabccabddacbbcabcdbcadacaaadadadcccddadbbdbdcbadccabcadbdbcadbaaddbacdbadbdaaacbabacbdbcbddcddadcdabddbcdddacdbbbaddccabdbcbcdbddabbddcccbcacabdadbbcaabdbaacdabaccddabbdacaabdcccdbabbcaabacabbbbbacbdccabccbdcbcadabbcacbbbacbbdbdaabdccccdbacdadccddcacdaadcadbccbcddcbcdbdacdcaaacccccdccbaacaababdacbcdccaadacdabcdabddcdacbbacbdbaadbbbcabddbacddddbcbbdcabaddacabdddabdaddccbadcbbbccabbcccbdcccbdddccbbadddacdadaccaacccdaabbcbbcacbbaabacbbbbdcdccbcdcbcaaddbcaccddbaabcdacabdabaabadcdcccddcccddcddbccbabbacdabadcdbacddbbbdbadabadcabcabcdbabcbcbdcacbbdadddbccadadddddccdbaaadccbcdaadcbddbabdbdddbaabaadbaabadddcdcbbcadbcdddccdaaabdbacbdacdbccdabbbbcbaabdcdbcababcddbcadbbaadacdcdddcbddaaccdbccaadbacacdbccaaddcdacdcdbdabaddbbcbdacdcaadbdabcdaccbacadbcaadbabbdaccacabcbcbcdadacdcadabadbaccdacdbddbaabbbcdbccbddcddacabaadcadbddbcbacdbacdacaaabdbddaddaadcadbdabcbabbbadabddbddadcacdabcbaacccddbbabbdadbdcbbcbaabdadaddbadccaccdddccdddbddabbabcdcdbddbdaccbdcaadaabbbddacbcdadcaabccdacdaabdcdccaaaaaadbcaacaadbdddccabaaabbabdbadaaabcacbbbadcaaabaccdccdadaaaaaaabadbccaacabbaccabbbbccabdbaaaaacbcaddcdcdadaddccabcaacdaadacabdbddbcdaabdcaabcdcdcababbdabcabacddbbdcccacbcacdbdbaddbbbdcdbddbdbcbcccbbcbdaadadddcddcdbcbbbcccdcbbddadcbddbcddcabcdccdccccbdbadabadccacddbbaccbacdbddcbcbacbbbbdaabaacbacaccddbcccccdaadddaabbcdcbdcbabbbdcadabacaccddbdcdbbcbaacdabcbadaadddadbdcadddcbbacbcdbbddaaccbcaaacaacaaaabdbddacccddbaddcdccabdbdcabbbdcdcbbccaabbdcbdccbdaaaccddcadbcaaababbcccdbaaddbdddcbbbccddcccbaabcaabacdadccccbcbddadbdaddbbdbaccbcdddbadacbcdbcaacbddbdcbaccdcccccdcdccccabcdcabbdcadacddcdbcaccbadacaddadbaddcbccdcbaccdaadacabbababadcaadbbdcbabbcdadcbddccbadccccbaacadcaaabadadbddbabcadbcacbdcdacdaccddbbdabaaccbdaabaaccaacdcddccbbdcccacbcdcdaacaddbbbdabbbadaacbdcbbacaabcbdccacbacbadbabbcabaadbdcaaabadacbcabdcabaaccdababbcabccdabbacbbaaaccdbcaabdddadbbcccbddbccaabcbabcccadaacababbadccabadbcadcadadadccbbbadcadbcdcdbacbddaacadacacddcddaaacbbabdcbabababdbbcbadcdaabbdcddcbdbacabacdacaabcabaacadbbacaabacbcccbbbdcdcdddcbbadbbababccbcbbccccdacdbaadcdaaaacadcabdacadabdabaaccdadabccccacbcadcadabacaabcbcdcabccacacacbbadaacbbcacacaabdbabaccdabbabacbbbcddaadbdbbdbbabbddcbccbbabdccdabccdacaccbaadddcbabcacacddacccdbbdbacbddabcbbdadaaccddaaaabcdbcddbbcabcbddccddbcdbaaaaaccccdacbbacbcdbdbbaaccaabaabbddccadcabdbdbbadbccdbcccbddabbbadcdbadddcdcaadacbddbcdcdddcaabddaacdadddaaaadadbdabbaaaddadcdccbadbbbbbaddbddabcdcbbcccdadacbbbadabbcbbabccabadddcabcadccbbcdbacbababccbdabaddcabcdcddaaddcddcbbdbdacdbcccdacdddbadadaddbabdcaacbaabcabadddacbcaaddbcbcdcdcadadabcacdbbabcaddcbabaabdbabbbaababacbbbcabbdbaccbdbbddaabcababcadabaabcbaababaccaadbbbbadbaccbcddaacdadadcadcbadbbcaaacdcddccdbdbbcaadaccbcaaadcbcaddcadbabdddbcaddbbbcadbcdcbdcacbbcdbbbbdcbbdabbbdbbccbcacbddcaaaddbaaaadaccccabaaacbabcaabccdadccdddcbaadcabdabbdddacaaaddbcbaadabdcacdacdaababaacaacaaccdccccdababbbacacabaaddcccbcbddbdcadbccdcacaacdbcdcbdabcaaddaddccadcddbbcbccacdcbdacbdaccbcacddcaaaccbbbacbcdacabbbaabddadbadcbbacbcdbacbcbbbdacdcccdcabcdabbdddccabccbcdaacdbdbddbcccbdcbbbbdcbcbabccbbacdadcbcaabbdaaadacabcdcbaaccbadcddacdcacdddbbddcdaacbbdccdcbdcdcbbdbadacbacbadcdbbcbcddaccaadcdbcdcdbbcbcbbadddcccbbdbadccbacaacdababcaacdabbacdccbbacddccbadabcbadabbccaaaacbddadcabcbcaabadbdaadaacdbdcadcabdaacaaddacdccccdadaaccdbddbabaacccdadbddbadbadbdbbcbbdabcdbacbbdcbaddbacddcbbbbcccabdcaddcbdccaabddcdadaccdcdbbbbdddcabaccdcaadddcbbbadcbbbcbdacaddbbdbaaaaadbabacbbbaacbbdadcaadbacadacdcbaddcaabdbacddbbbdacbaacccaccaabccaaccdbacabbaadbbadddadbbdbdbbcdbdccbccadbddddadcdadcbbdbdacaaddcdddabddabbcbcdddaccdabacdbdbabccdbddabcbcbbcdcccdacccddbcdcadbddaadaaacccabcbddacbbcbbdbdcdcacbadaacbbdbcabcdaadaccaddaadbdbabbcbbbcccadcbdaacacabcbcacacbacdbbccbbddcbaacdcdbaacadcbbddbabcdcacdcbbbcabcdadcdadcdcadcdaabaccbdbbddddcbcadbcdabcbcacacaddbcacabccbbcddadbddacbbabbdccabadbbbcddddbddadcdcaadcdababddbacdbaabbcdbdccbdcdcaaababbabaadbdabdcddbdbddaaccddbbbbadacadacbadaabbbbabacddcbcabbbbdbbabccacbcbabbcbcaacaddbbacaadddbdbaabbdaaacaacddcbddbdaacaacabaadddbccacdddcaabcabcabccdccdacacaabbdbddbabbacdddcaaabdbdccbcdccddbacdababaacddcdcacddacbdaaacccbbcacdbbabddbaccdacadcdcadccdadcdcaadcadcabddaaadbadacabdadbbacdadcdddcadbdcbcdcadbccdcaccacbbabaaccbdbbbdbaddcbcbacabaacdbdbddbddbdcacbacddcdbdcdabbbcbcaccdacdcddbcbabaccaddbadcdaddcccaaaabccddccbacbbacddaacabdcaaacaadcbdbcdbcbdaabcbccbcbaacbdcdccddbbcaadacaaccdaabaacdcdbadbdcddbcdbbacacdcbdccabcacbdcbaccbbbcdbbcbcccacadbacadbaabbdcaadcdbccbccaddadcbaaccccabbcbaaadccbacbcbdacabbbaadbabaaaacccddacbbcabbbacabcabaccbcdcadabdbdbadddcbdddabbdccdcbdddbbdacdddbbaadbddabdcbbadbabbadaabddcdbcdcddccaadbdcaacdcbcbacdcdbbcabdacdbbadcddcdacacadaadcddbdcaccbaadcdddabcabbdbcccadbbcadbcddbbaaacdccccbcdcacdadcaacbacbaaaccaaddddbbaaadadaddbcacaacccdadcacbdaababdaabdaddbcbbddabddcdccadbabcbccabccabcdddaccbccbdbddaacbccdcdbdbbcbcbbabcaacbbcbcccdddbcbacacdacbaabcddabdaadbcbadcbaacbdcbcabdcbcacdcadaaabccaaadbbbaccacbaddcccabcccadcbdcacbbcbddaacbcddbcbcdbdbccbbaacabbbacbbbdbabddbccbcbdcdacbdddacbaabbcbcbabaccaaccdbbddbccdcadbcbbbddcddbaddddbaccbaddbdcadccdcbcaacbcadabbabbdcccbdadbcdaacbbcccadcadbcabddbcbcadddcbcdbccdbdbcdcddcbbadadcdcbbdbcaabcdbcdccdcddbdabaadabcdcdaaddddacaaabbbcabdaccbccacbdaaacbdacacdbbdaaaddacbaabbbcdadadddbbddadacadbcbbccdcccbdcabaaddaaddaccaddcdacdcbdbdaccdaabdcdabbddabacccbabbaaabaabaaaccbdbbcbbdcbccaababddaddccdbdbdddcbbaabdacccbbdabbdccadbcdcabdbadddbdacdaaddccdabdddaacdaaacabdaacbdaadddddcdcbbacbaacddbacdcaacacbcbcacbdbddaacaddbcddbddbccdacdbdbdacdbadddadddcccbcbaadabacbadadabdbcbccdbdbaaccdadbcddbdcdadbdddaadacdccdbcabacaccbcaabadcdabdcccbcdadcadddbbbdaaadddacdbdccdbbdddcdacacbdcbadcabacdbddaccaddddaadcbdadccddcadadacdbaadcdbadbddabccdcaaccacccacdcadacaadacddadccdbdaabbbcababadabcacadbcadbabbbaadccacbcaadbbabbbccbcdbaabdbacddbdbaacacdddcdbbabbccadabbadbadaacdcacadcbccbbdbacaabcbabadacaaddcacbbccbbbadaacbdbcaaaaddadbdddcccbbdaddaddccacbccdadcdcbbddacabcddbdcacdbdacbbbcdddaabddbdcbadabacacdbaaaabdcddbdcabbbdcdddbbaabbcccacaabdadbbddadddbbadacddbdddababdcbdccabbbcbacadcccbabcdddcaabdbaccbcadcaadcbddcdbbddadddcbcbcaabbcbdcaacbaabdaadaabcabbaacccadcdcbacdbdcadbddbbbadbccbaadbadabbbccbaaabaaababbcaccadcdcbcadbadbadacddabbbcacccaabcbdbbaadbdcbdccabacbabcadaddbcddcacbdcbcbdbacbbabcbccdadbdcabbddbbabaabaadddcbdbcccdbaabbabdaaddbbdaaccbcddbbdadadadbbaaacadaddcadbaacdddaaddacaabbcbabbbbdcadacddcdcdbbbbcbaaaabacabccccaababdcdcccaabcbaabcdddbacdcdaaabddaccdcabaacdcbaaaaadcbcaacccccaacbdacabddabdddcbbdadcddddbccbdbabbcbcdcdbcdbdcddddcbdbdcacaaabbcdacbcbdddacadaaddbcacacddbcadbadbbbdcdcbbddbccdbacdcdddcadacaccaacddcaacababaabbaababbbbabcadbddbddbdcbdababbdcadcacdbaacdcdcdadbdddbddcbacddbbdadcacbabbaaccddadacbacbcdcacabcaaaccbbddabdababbdcdcbccbbbdcaccbccbdbdaacdbddbcdbbdcdbbdbbdddbaccaabbbaacdadbbddcbdbcbccbabcdcbbbdcadbcdcbdadcddaaaabababbbacaabadbdaddbdacbbddadbbdaadccbadddbbcdabdbacaddbdaccbabababaabdbcbcdddccbbbdbdcadcddbdbdababdddcbcadacdbbacdbddbaaadbbccacacbbbadaaadddcaaaabddddddaaacbdccdbaabcdbcacbcdacbaabdcaacbbbbcadcadccabbcadddbbddcdccbbdddacddaaccadbcbbacbccdacbcdaabbcdcadddadaabababddaddacddcdccaddaccdaccdacdcdcdccadcdcbddddcabbbbdddbcaadbbbcadaabdcbbabdcdacaddadaaabdadbdbcdbcbaadadacacddaacdbddbcabaabdbbdbbcdabaddacadbcddbbbabcbbbcaabbcbdcbcbbadddcaaddadcccdadaacbccaddbbddbadadbbdbadcabbacbabaaddbbdcadcccbdabbaaccdcdbcbcdabcdcaccadbaadccbbdadccbadcddccbcbbcadddcadccbadcbdcdcabcacbbddaaabbddaacbcaabbdbdaadbddcaccbadbbcdcaaadabbcadcddddadbbaacbdbadbdddccdbaaabccbaabbaadcccadacbcadccbcdbaadacdcccddaccbababcadccbcbbbbcbdaabadacbbcacdddcdcabbcddbcdabadcccbccabbdaccdcbacddbacaabbacccaaddbccdcdbcacdabdbbcacdaccadbdaccdbbddbdddaaddaaaddabaccbaadaccdcadabcacaabbaaaadbdaadbdcaaababbaaacadcabdadadbdcaacacacbaabdcbbadcaaadcdcdbaabbdcacdddabddbdbcbabbbccdbcacdccdabadaccdadcddcaaacdabcdcbcabcbdacdbaaccccbbcdbacbcbaddcbccdddcdacdbddacaaaccdabdbadbabdcabcbbbcabddbabacdbdbaababcdaddcdabbbabcccccbdbcaabacdbdcabaccbacacadaaacbabcbdacaaaacdcabdbcbadcbaccacdaaacdaabccbdcccaaaddccaabdaaabaacbcbbdcdddabaccdadbcabbbadadbcbdcacdabbacacadddbccaddacccdacabdcdbcbbabbddddbcddcdacaadabaabbbcbdababcddabdbdadbcdabcdcbddbbabaaaccccacbdddccdcabaddbcdabdbbccbbbbccbadaaaaaabcddacbabdddcbddbccbcdbbacaaadadacadccccbadbcdabccabdacadccbaadcbcbbcdbcdcdadbabcabcabbddbabaccccdbddaaaacddbbcbababbbdcbbcbbbcdcbcbdcbadbddabbadcacabccadbbcaabdcdcbbcadbadcccaaabbcdabbbcddccdbaaaacdcdbabdddbccdbbcddbbbcddacbbbddacadaaccbdabcddaacaacaccdcacbcabacdcdcaddcccaaabbdddaacccbdbdacaccdbbbabdabbbccbcadbbacacaabcabdbdccbdccbacbadaaccdabcaabacbcababbdbccddadbbccdcdbcacdbcdacadaddcadddbaaddccdadaacdbddcbcdbdaccdcbabdaaadbccbbbdcdbdbdaacccccbabbacaadaccbadbbdcdddacdcadabbcbaaaaabddacbcacdbdcdccddcacabbaabadcccbddbbbdbadbbadbbdbbacbaabccbbdabcdaadaaaddacabaccbccbddbcddcdaddbdbddadacbbcdacaddcdcacadcbacdcabcbcdbbbbdcaddcdcdbbbcdacbcbbbdadbbdcccacddbddacdbaadacacdadacbcdaacbccdbcadddbddaaacdbbdccbdbdcbbcbbcddcadbddbcdcccbbcadbacabddadcbbccccaaaccdcdbdcbbddaadbbabdadbcbdcbaadccbddbddcabddababbdcbbcbcbccabdccacdacdabdadcacbccaddbabbdacacccddcddabdccbbdaaaacbcbdabccdadbacabcccdcabcddcbcbaadbabcadabdbbdbcbcbbbddaddcbcacdccdbbaccbacbcccdaddadbabacaabdcbbcccbcccbacdccabbcdbbabbacadccadccaddbcdbcccaaadcbcdadcabddbbadacdacbadddcbbcaabbbbbbbaddaccbcbdabbabbabaaabbcaddbdaabbcdaadcbcacaaacbdbdbcbaabbcbcddabcdbaabacaccdcbdabcbabcccbcbdabacabaadaadcbdaacaacdaabdccdbbadcbbacbbdabadabdcbaabbcacbdbcacabdbcbcbcabbdccdaaabacbcaddaddcaacdbddcdbadcdbcbdadcbcbddabcacbabaddaaabbdcbcdcdabccdbddaaaacdbdccababcaddddcbbaabcdcdaacdbabaabadbbdadcbdbaabddaaabaabaaaabdbaddaaabacdbbbabdcaccbcccadbbadbaabdaabcbbbddaaacbcabcdcaccdcbcacacacbbaacacdbdcbdbbbcdcacdcabddbdacbadaaadadacdaadadcdccabdddbdaadccacadcacdccddbbcdcaadcbbdabcdbacbddbddabbddcdcaadadcbddcaacbdadbbbcadacdbbcbbadaabbdcdddbdddcaaacdacaccabaacbcaccbadccdcacdacccaadbaaabbcbaccbdaabdccadacdcbddcddddbaadbddbddddccdacdacbccccdbbcdbbcababcdacadcbbdcdbbdcaabcaacdabddbbaabacbbaaabcabaadcdaadcbdaabcbbdbcddddbdaacdcbbaaacbbbaacadbdaccaddacbdacdabdbbcccdaabbdddcadddbbbcbdaddcbaacaabdbabbaadbddbadcddcabdcadccbbbdaaabccdbbdbbbccbddccccdbddadcadddccabadabbbcacbabdadcdbaccababbcbdcdcdadadcabacdcabbaacabdcbdacadcddddacbadaddcdbaacadbbdaacbbcccbbadccabcbcacdddbcdccdbcabbdddddcbdbdcbbdcabcabaccaabcdbcabaaadbccddabbaaabcadcaadbbabbbcdbbabddbdacbccaaaddbbdadaacbaabaaadbbaccdcbdaddcdadcdcdcacdcccdcdccdbdcbddcccacacabbbdcacbcabbabcdcbdaccbdabcbcdcccaabbcddaaddbabccccddbcbabdccdbbdbdcdcddadabbddbcbaccacddccdacbdacdcadaaaaaaabdccbccbdddddadcbcdbbbcdacbccbcbaacabcdbcbabadbdcdaddcabaaabaddcadbbccdcdacbaabacdcdbaacaaccbbadcbaababcbcaabdbdaabadacbdcdbdddaaaccabacacdbdbdbadccbcdbbaadaabcbdddcbbcccbdaabadabcaaabdcbcbbadddbccdacabbcdcacdadaaabccddaaababbbadadcabcacbcbddcacadddaabbaacbbbadadcbbacbcbdccdabddccbdabddbcdcdadacdbdddbcadbdccbcadcaccbbdbcbabcccbcddabdbccbcdbabaddcbdbdabbbcabcacbabacbcbbaabbdddbacbcabbdacdaadcddccccccdacaddabacbcdcabccacaddcaaabdcacaccadaccdbcdcabbdcccabbcccdcbcdabbdbcaccaabccdcadddabbcbacdacbaddbabbbcaddcbddacacdcaabbdabcdcdabdcbbbdacabcbbcbccabdbdbadcbcbbbbcbdcadacacbdadcbacdccbdbabddddcccbbcacadcbbccaaabdbdabbababdcbadcccccdbbdcccdcaccacabcdcbdbdcdaacccdbdbbdbdcdadddbddadcbcaabcdbcddcddabbabbcbbdaadddadacacdbdadaacbbabbabacaabbcdbcbcbbaddaccacdccaaaddcdbbdbcbacbcdddcddddbaabbcbdbbaccbbcadacdcadcdcdbcdbabdddacbadbdacdbbacddbdadcadbdbcbacbdaaacbcabccbcdcbabbcabcacbdcaaccaaabdaddaabacbaabdabaddcccbbcdddaacbbcbaabbcdcbcccaccbbcdcabcbddddcaabbbbaadacbcdbdbcbbaddbcddccaaaaadaabbcbbbcbbdaacabaaaacaddaadbaddbaaabcbcdbbbbbdcdbadcddcdbdbcaaabdacdcbaccbcbddcaaaadcbadcbacadaaadbbbababcdaaaaccacbbadaacacacddacbddcbadbdcdadcdacbaccddbcddddaadccadabaacadabaadddcaabcacbdcdcaddcddcdbbbadbcbaddbccaccbcbccdccdbaccccaccbbbadcdcddadcdcddbccbbdbaddabbdbcaccabdbcbcdacbdbabcaddbaadadbbcbaacdddccbccbccdbbbdbdadddbbdbcdbaaaacbacbdbcadaccdabbdcacddacaadcaabbbddacdbdbddcdaaddbacbbacabbbddddbadbdbbdcdcddbbaabccbbccbabadbcbdadaaabcacdcdbbdadcccbcbccdabdabbbcbbabcbbcbbbbadbbdccbbbdcbbabcadbbcbcdbddabccbabbaccbbbddcadabbbcbdbbaaaddbacbcdadcabcadbabddddbbddbbadaacdcbabcbbdababcadcdcbddbcdcbdacddaabcbbbabdadddabdacbabcbacdcabcbadaabbddadbcaadbaccbbbbbbbddadccaabcbdbbddbcadcbabacdcbbddaddabdcddcdbdbaacbcbbbbacdbbbcabcabcdabbdcbcdaabacadccbbdbcbbadbbaabcbacdaddaadbbabcbbbdddbccaaacdcdccddcccbcbbcdcbccdbbcbccbbddcbdcbbcccdccddbdddccdcbabdbaddddbbaacdcccdccabdbdddcbdddababbacbdaddddaabcadbcddcbddcdddccbdcdcdcdabaccaabbdbcddccacaacbbbbbbbaadaaacbbcabbdadaacbacaadaccaadacbcccccddaccaccdbacacccadacccbccadcaadabadcbbbcabcdcdadbdcdbdbcbdbcbddaccadcdbcbdccdaadcdacaadacdaddbddadbcadcaacaddacbdaabadacacbbdacadbbddacdcbadcbaabdbbbaadaacacbcacacbdadcbbdaaccaabcdddacdddbcaaaaadbabcccacbaaccbdcabccacbaadcbcbcaabbbccbcaabccaabcddacbcccddaabcabdcaddbbbbdaaabddbccccdbcbadbacbbcacadcdddcddbbbadbccabddccccadbabbddccdbcaaaadbacbabcacbaacddacbadacadbdbdcddccbdddabbbcdaccaccababdbdbdbbaabcccbcabdbdbdddcccddbbdbdbadacadcdcddcccdacdddcadcdbadcdbabbbbdbadbadabccaacbaddabdddacccccbababbbaabddbcadbccaabcacccaaaddabdcbbacaadccbddcdbdbbcadccdcacbbcbccbbacdbbdcbaaabcddaabccaddaacdcdabdcbdaaaadaadbdbaaacbcabacacccdcddacdcdcdaaadcbbdcaccbdcccbbcbdadbcccacaacdabdbabbcaadcdbbaaaacbccccdbccbdbacbbadacabbdaddabbaccdacbddbbbaddbdccddaccaabbabaaadcdadccdaabdbccbbaacccbcddbbdbabdcdcaabcabdcacdaacabbdadacdcaddccbdadcccdbbbcaaaacacdbcbaacbadacbbcdadcdccdcaacaacacacccacdbcbdadcbcbabdacbadcbbbcbdbcccbdbdbaddbbdabcaabdabaabbbbddbcbdacdadddcadaaccdbbaadaabcdcaaadcdadbdacbbadcadcaddacdbccbabadbdccadacdaacddbcacaaddcbbabadbadaaaccabbdcaadcadbacbcadddaabacdadadacbabacbaccaadcccdadacdabccbcbccbdadadbcdcadaacbbdbdaccccabbdabbbadbbcdacdacdacccbcdabbdbbcadccbbbcdcdbbbcbdcdabdccaabddbcccdacdddddaaabbadabddcdaabbaadddacacccacdababddaadbacdcbcbaabbbdbddcaadabacbbbcdaddcbdbbacbddbddbabdddacbaccbacbbdabcccdaaadadcacdddabdbdacbcdbbbdcacbbbbbbaadcdbccbbabdacaddcbadcdacbcbccbcdccdddcdaccbbdccdaccbdaaaacbdcdadcdbdbcabacdbadacaacbbddaabdcaaaadababdbddccbdbbcbabbdbdbcdcbcadaabdcdddddccbadabdcadbcdacabcddabbdbcdcabcabdcacbbdbaabbbadddbcddacccbaccbdcbadcbaaadbaadabcbacccbcabdddcdcbcdadbcbdcacaddbdbbdbaadbdddcdaabdbcdbaddbacaccaacacbccbccaccdaaaabddbddadabbdddbcddcbbddbcaacddabcbdbadbdcbccdaaaaddaaaddbadbbadcadcccbaacbdbcbbadcbdaaddbccacbccdbacadbdcadcabcbbdbdcddbcbbcccdacbcacbdbbabcaccbcdaaddcbcabadaabdaaaccacccccacdcadacaabbaababdddabcdbacdbddabdcbddcbdcbaaccbbbbbbbcbcccbbbcdbaabcdbbdbcdcdcccbbddabdbbdbabbbaaddbcbbadabbdddacbcaabbaacabacabbcbcdaadbdabcbdcccdbcbaabcdccacbbdccdbbbcdadbbbabbdcaabbbcdaaabaabdbcbaabcbcacdcdcabbabcdcbbcbabddaaccbaaddbcabdcadcdcdacdcbbbdacbacccdddacadadcccdabcbccccabbdcdcccbdccbdbcdabbcbdcabbcbacbcadbbccaaabddbbabababcdcabbddbaaaacbbbdbcbbbbadadbdccbcdadbcbddcaccacadaccbaacbaccccbdacdababcdbdcbaabdbaaaacaddcdbbbbbadaaabdcdaacccaacaccbcadbcdcbbacdbcaadbcabaaaddaccdcdcaacbbbabbaaabaaacbabcbdcaaaccaadcdbbbddccabddabadabcdbdacbbabddcbccdaaaadbadadbccdbcbbbcccccadacabdacbcbcdbdaccdcbacddbbadddbddbdbdcdbcaadabaadccbdacabdbacacbdcdcbdcccbcdbaaadaabadabdddbadcabacbadcabdbcdaccdadcbdbbddbbadbdccbddbdcccdabbcccaacdaddcadadadbdcaadddcdbdcaabcdbdbcddcabbcbadacbabacccababcbbcacbababadcadddadcabdbdcdbcdacdddbbdcbdaacbbbccadcdccdbbcabdabdcdabdadccccbcbbbacbbbddaccbbdaaddbbdcaaddbcbddbccbdccddcdacddddcaddabbaacabbbbaddacdbbdadaadbdbdbababcbdbbcacbdadcbbbcccadbdbabacdcbcddccabaadbdddcddabdbccbbadbcabdddbabbbaaccccabbcdadaaabbdcbcbcdbbdcdbaaaacccbcdcdacbcdadbdcbcdaadcbbbcaaccacbadccabdadaddacdaaaaacabdbbdddcadadaaacadcabbcdcbdcccdacbaccabcadddcadcddaaaadbbdcacacdaaaadaabcbbcdbbbcdbabdbbccadddbdbcdbdcadcbccbdacacabcdbccadbbabbdadabbcbadddddcdacaccdcbadbbaacadbdadabcccaddabaadccbaacdabdbabdabcccadbbdccabbdddabadccddabababcbbccadbdbbdcdbaddbaaddaabccdaacbdcbabaacddddbbcacbacacbaabdcaabdcdcddbacccadcddbdccabdadbaccbbbadbadbcddbbcbabbdadacaaacbcbcddcdddcbbbcbacbbabbacadccbcaccdabbabbdcaadbbaccddbddbcccccddcdaaaccabcacbaabddbacdababaabdcaabacdadcdbacacccaababddbaaaadddbbacdccbcaaaaabbbdbabdaccccccdaccbdabdbbcadddccbacaaccacaadbcdddcbabbadcdadccbacaaccadadcdabcccacdbdcbdbddacdcbdaacbbccdcdbdacdadabdabbbddcdddcbcdbbcbbccaacccddcbdcdcbccdadbcbcbababdaadabbdcdccbddadbddcbabcbaacabcabcbdccbcbbbcddbadcabbbcabdbaacbabbbbcadbabacccaacbcbcadabcbbcddddbabdbacddbaddbacdbadbbddcadbccadadcccbcacdccaddccbcccabbcbcacdbbbbdbcbdbbdbcabdbccccdacacbdbaadcadadadbdbdaaaddabcccbccadbdbdbcbcdbdabbccaccdddaaacacacdaadbddcccdabbdacaacdbaaaaaccbcddbaddbdbcdabbaabdddacbccadbdaddabcccdcbbbcacabcbaacabdddcdbdcdaaacdbaaabdddaacadbcdaddaacacdacaaaaadbdbdddbddbaabdbaaabdcbdbaadbdadbacdbaabccabaabbaddaabdddbadcbadadacdaccaabcdbbacbcadbdaccbbcdabcacadbbbddababcccbdcbccaacaadaadbdabcbbabcdcbcccccadcbbbadccdcacadbdbcdddaabccdccadadcbdcabadacbcdcbdbccacddcadcbadacbacbaadbddcabdbacbadcacbacdcaadbcacacddadadacbcabacacabadcccbcbbaddbacbcabcaadbdcbdbccbbcdcdacdbcaadbbdddabacabadbabbaadbccbabbcdbdccaadacccaadccdddbacadaccdcdbcdaabdabbdcdcbaccbabbcacdcababacbcbcbccaacaaacbabcccbccdbbbabdbacdaaaddddcaabccdddbbdabddbdacdbdbcaadcadcdabaaadcbaadbbccdabccddcbcbdbabbbbdbcdaabbdacccbccacaacbcdabdbcccbabccbbaaaacdcaabaddddcaacdbcdbddacdbbdaaaadccbabcbadbdaacabcbdabadbcbabdacdbdcbabcdaadaaadcdadbcccdcbabdcaacdbbcaaaddcabbcbcdccccdcaddccadccccbbcaacdccdbdcccbcdbcabcddcbcabddabdddbbbbcadcdccbbbdccaccadcbcabdbaacddcdbcadabbddabcbbcabbbabdacabbbcbccadabaddcbbddaddbbcdcabdadddbcbcabadbabcccccbbbdbbadaadcbaaabddbbcdaacbaccbcabcbcbcbdcadabaccadccbbcaddbacabbbbcdbacaadbddbcacbaddabdbcddccdacadbdcccdcacbcbdaddccdbccdbccadcbadacccbadbadabaccdcddbcdadbcbdcccdcaabaacdcccdacdcbddcbaddbcbaaacabcbcaadabbddccdadbbdbaaabbccdcbdddbaccdbbcaacdadddbccabacdbdbbcbbcdabbaabdaccaabbabccbdadaabbbdddcbaabbcbcdaabadadbadababddcbbdbdaabddbbbacadaadadacaadccdbbdbbbadccdcaadcaaaddbadddcdbabccdbdbbcdacddabbaadbcadabdbabbcbcbcabbadbcdbdacbcaaaadbcdbaacddabadabdddabadadccdacddaddadddbadcaaacdcdccdcbcdbaaacdacbbcdbcacdddbddbdccaacdaaaaccbbdccaaddcabaccbbcccbdbbbadaaccdbdcacbaacacaacbabbbcabbccdaacbaacdbaadcaadcaaaabcbdbdacaddbcacbbbbddccadabddddacbbbccacadbccacdcbdccabadccbbacbabaadbccacaadabccaccdccdadbcdaaabcaabadadaadbcadbaacddbbadbdacbbadadcadcdcbbaddcdaacddcbacdabddbacdcaccbabbaacaaddacbaadabccacabcbaccacaaaaaadaacbbadbdadcabbbddbcabdacbdabbbccbccdcacdaabccdaaccbdadccadabbcadaabdacbccbbcddcbcbbddadddbcdbdcbddbdabbdbdcbcacadadadacabacbddbccabbcddadbcaddaaaaadabbdcdababacdbadacbcdaadddadabdcaddbddbdadadddbabdadaacdbbcdacabacaabbdcbbaccaccabbcadadcdddccacdacbdaaaddabbdcddcadaccddcbbcdcbccadabcaadabddbbdddcaddbaccbbacdddaaadaddcaabdcddcbabcdabbcdacdcabacdddbbbadccdbbadabdaaccdbabacadbadddcbcbadadaaaadbdcdddbbbbbabbbcbcaccccababcadbddaaaccaddcaadadccddbbacbdcabcdcdddbcbcdadcdbdabccbadbbdbacdcbadcaadbaacabbbaaaaadacbccdcbdcabcbbbaacdadccaabcbccbdbbabadaadabdbaadbaaaaddcdabddaabbccdbaddbaabbccbcbcadcdabbbddaabbacdbddcdccdbbdabdacbdbbdabcbabaabaaddbbacdbdaaaadcdbbcdabddadaddabbcbccbabdcaaaabdddbbdaaabbdabbcbdaaadcbdacabcdadaabdbaacaacccdacbdaaacaccbbddbbccbdabbdbdcadddabacdccbbcdcbaadabcaaccaaaaaddcaccacbdbccabadabacabbaacbdcdbdadccaaadadbdbdaddcabadcdddaacabbdbbacddbccdbbdcbaaabcbabdacddabbacccbbcabdaaaddbaddddacbcdacbcaaddcdddadcbdddbabdccbadaaabdadabcbbbdccdbabcccabdddaacaccaaadbcccbdbacbdbbdbddbabadaabcdabbabdadcabbbcdcadcddaacbacadaadaaabccaccdbadcacabdbcbaadddaadadadbdddaabcbcbbcababbbadcaabddccdbddabbacddbddcccccabaadaacbcacdcdabdbbaabbcbcdbccbdabbcacdbdbdbaaadddbbabddccccabbbabbddacbdddcaccbaabbccaddcadcaadadddccabaaccdcaacbadddbacadcdadbcbbaacccbccdadcdbdbdbdbdbcbcbbbcaabdbaacbdbddadaadacadabbbdddcddadaccababdbbcdabdccbaaabddcdbabbcddadadabdabddbbcdbacdabadbacdcabdcaacacacdabcdaccbbcdbbbdcacdbbcabadaacdaccadcdddbcadddacadbabbbcdccbdcbbdbdbdcadbabbabadcccbddcbcbbcdbbabaddbdbbdbadbcadcadacbcbdbbddcbabadbcaaccddcbdabccaabbccddadbcadbdacdbdcbdabdaaadccbdaccbdcccccdaddadddbdbbacadcdcbbbbcadbbdabbcddbbccccddcdbcabababdcdacdbddcabdadbbbdadcdabbccdcdbbabbaaabcadbdaacadbbccdcccdbbcbbaadbbbbbddabccbdbacdcbacdadbcaabdacccbabcdcbdcccdbbadadcaabbdbabdcabcddddaabbbddbddacdcccccadcadabbcdddbaadbaacdacbbaccdadccdadddadaaadcadbbabaacddcdcdccbcaabacccbbacccaaabdcbaacbdadcbcddbbdcccadbdcdcbdbdaacbadacaadbabdaaccdbbcaddbddbabdbaaadccdabcbbdcbdcdbdbcbacadcddaadadcdbacdddccbcdccddddcbddaaaacdacaadbadbabaacaccabacbbddbccbdcbccdbcabaabacddcbddcccacdddbacdbdcbcbcabccdbcddccaccdddcbcddaabcdaaddadaccaadcbccabcccccaccabdbdababdbccaaacbaacccbcbcaacdcbbbcbdcacbaacccadbdbbcadaabddccdbaaabacdaddbacdbdadcabdbccadbaabadbdbcbabdaddaddaaadccbdabdcbcaadabbccaccdccdccdcaddbdbadabdcddbcdcccdccadbbabdcabaacbdaaccaddabcaadbadcabdaacaccabbbccdbdaabaaaaacddccbcaadcbacdadbdcdddccbccadbbdaacdccaddcddbaaabccddddcabccadcbcdcbacbbbbcbacddcaabdacdacdbbabbdbbbaaadabccbcacdacadadbbbdbbbccabadabdddcbaabcdcddadcddcdacbcbdaccdddabaaabcaadddcadbcdcdabdaabaabdaaddbbbdbbbdcdbdbbdcabdaabaaadcddadbdaacaaaaacdbbacbdccaaacdcdcabdcdddaadcbbbbbbadabcadcaaabdbdddaccacbdcccccbaaaaaaadcadcaccbcbbbcddbbabacdacbbdddbadcaaaaaccbbacadacccccdadacaaccdbbdcdbddbbbbacbddbcddbcdaaccdbcddbccdadadbaaaccdbaddadcdbadadbacdacadcdaadbcbdbbcabbbbbdaaadbabbdabbbaccbcbbbbbbdccabcdaaccdbddbbcbccdbcdcadbbdacddcddbbcbcacbcabadbacabddaadbdaacdcbbdbbbbcbcabdcdddcddaacaccbccccaccaaaadcbdbbdcacbaabcbcbddaacddcccacddaadabbbccbdadacaddadabdcacbbdbacdbbcbcbcabdbaadcdcaddccacddacdbbbabaccadbcaddbcabcacdbacaabcabaccbaadbcdbdbadbbcccdcccaadbdbadadadabbdbddbcddcddadcdadbaccccbcaadabdcdddbcbcbcbbbaabadcabdbbdddabdacbbddcbcbbadcbdbbcbcdadccdcbbbbdbbdddccdbbcaabbaaaccdaadadaaaddbbdbacdcbbaadabaccdadadbcbddccdabdbabacddbabdaacbaadccdbaababddabadbabcddbbccadbcbacccdbbddcbbcddddccbdbdcaacbdcdabcccccdbccaaacdaacdbbddaaddabcdaacdbbccacabadccdcdbaadadcbabbcbcaadbabaaacbdccdbddaaaacaacccacbaabadcccaaadabaddacbdbcbdabdbbbbddcdabdaacacabaaabaadddaaddbdbabdcbabadddaacbbbbcbadcdbbaacacdbdbadabbacabbbdbbdcbaccabcccdbadcaacbaadcbcaacbddcacacccdcdbcdabaccdddbadacdbdadcababadadcbbdcbdadcdaddccbbccaaaccdaabdcdbacdddadbaaddddddcbccdabcdbbacbbbcbcbbdddbbddcadcddacdbdaccdbdcbdbdadbdcabadddacbddcdacacbdbcbcacacccaaddddbaccadbcdacaaabaadbadcabaadaddcdbaddaccdadcbdacacadcddcbddbbbbdbcbbcabdcdacbcacdbadcabbcdbabcaadaacbbdcdcbdcadbdddccacadcaaccabacbccbbddddbdcbcbacbbcdaadbdadcdcbcddcccddbabdcddcdddbcbdbbbbdaadaaddadbcbdbacccdcccacaadabdabcdaccaaccacbadbaddcbbdcbabaadadccabcbcbcaccabcabddcabccdcdbbcbdabdcddbccbdadddcabccaddcbcccabbbbacadccccccddccbddcdcddccadcababcdbdbabbdbcbadcdabdddadbaacabdcadccccadabacbcdbcdadddadcdcabacaddadbdbdabcadbcbbcbdcacbccbccddcadcccddbcadbddbadddbcacaaccdddbcddddbddabdccabccacccdddaacdaaadaacbaabadbabbdddcdbababcaacddbcdcdacbbbcbcadbbbccbcccdabcbddaddbdbbcccbcabbddbbdddadbacccdddbbdaccaaccddbdbdbbadddabbacbdbccaccabaabbccccdababcbabbadbccdcbcacbabadbaaacdadcadbdddbdbdddaaadacaaabddcbccbababacdadaabbadaaacdaddccbaacddcabbadbccbbdccaaacddbadcabcbbcdaddcabcabaddbdcdadabdcdbbbdbdbcbcbabccdadbdcdccccbcdccbbdbccacbcbdbbdbdddbaadcdabbbdccabadbbdaddabdcaacaccaccdabdacccdabbccbcdcdaaddccddcdcdbbbbbdcbdadcdbccabddbaadcbdddaacdacbdacaadccbadababdccaaadcbacadababaddbbbabadabcbdcdddcababaadddddadadbcadccdbcbabdddababcadcadadacbbccbaadbdbcaadbbcdabccccbdaddacdaaaaabccdaaaaddaabddaacbcbcbcdaadcaccbccbdabcbbbbaddbdabdddbacacbadbbacbbabcaadbabbcaccaaaabaadcaadbadccdbcddcccaaaabdccadbccdababbdadcbdcbcbadaaddbdbabcbdbcddbddcacbcdcdbabadddacacddbaadabcbbdabaacdbdabbaaaabdbaddcdcabacbadaaabddcbbbdbbddbbcdabcdcbbddabbdcacabaadaddaccddbbdccabbdadcdcbddcbcdccdbbaabacaacbbbdcbdaccbaacdbcdddddbaddcbdbbbdbdabdcccadcaabbbdbbddacadccadcdccdacbccdbdcdcccadadddabaaccbaaabbbcbcaaadadddbacdcbbcbdaacaadadbcccdabbcabcdbcddbcbacdcaddbadbbbcdbaabdbbddbbcdbcadcaccdcdaccaaadcbcaadbcaccdcaacdcccdcdaadcadccabcccacccaabaaaddadabcaaccdbcaabaacddcdadcabbcbcccaabbabdbbdaadcbdbbccacabbcacbdccddbcbdcdacdcdcaccbdbbabdccdbddddaccdcbddcbdbbbabccadbdccaabbabdbcbbadcbbdaadaabdbadbacabcddcdaaddcbbcaabbcaaababddaaaacdaaaaccddaaaadccacdbcbadbbddcaadcdcdbdadccabccbcbdbcdabbcbdaadccbcaddbbddcdbcacddbdcbcddaaaabcddbaadcdbabdaaababdaababbbbdccdbdbbbcbdbaacaadbdacbdddccaccdccdbbdbcbdcbddcababdacdcccaaaaadcbacbcdbdcbccadadddcddacaacaddbdadbaabccddbddacdbabcadaccabbbbcddcabbaccbcadaacbcbbcbccdabdcbbccadcbdbaaccadcbddcddbcadcabbcadddabdbcbaccabbcbcdbadbdadabdddccaadcdcadcbdbbacdaacddabbddbacbcadbadbadaabadbbbccdccccabcdbaddddabddacdbaccadbbcabdddacaacccabcdccacdacddcabaddbbcadbabbbcbcbcdccdacddcdabbcaacabcbbabadbadcbabbbcdadcddbccbacdbbdaadbcaddbadbbcbcbbdaacdabdbaccdcdbbcbadaabccadabdddbcbbbdacdbabbacddacdcbabdcbbaadddbbdcbcdbbacdacbdccdbbcbabaddbadcbabbbbcddddcbcaaccabbdbcdbdbcaaabdccbbbaacabbcbdbbcbdbbcbdbcaacbdcacddbcbdcacdbdaabccbbababacdccccbbbddcdbdcdbabbcbadaaddaccdcbaddbccababcccddadcdbdabcababdcbbdcbcabacbddcbbcbbcdcbbcadaacaacadbbaddbbbdbbcbadbdbabccbcdaacacddadaadbaccadbccacbdbabcdcbdbbcdabdbadcacaabaaddcabccaccbdcabaddbacabbcbcdccbddacbdadcdacdcaaddaddacbdbbacdddaddcdccacdbbcbdcbddaabdbdbddbcccbdbbbdbbdaadabcdcdbbbcabdcbcaddccadbbcaddcbcdcadccbbdacacaddddcdcadbbbbadbcddbdcbbcbccbdaacaaaadddcaccddcdadabcdcdddddcadbcabbcbababbdccdacdbacacbcddabaccadcaacadbdbaaddcdcaccccbdabbccdaccbccaaccdbdbacdbabbdbccccadbbaaddaccacbbcbabdabdaddcdabcbabccbccaadbccccabdbcacbbdbbdddaadbcbbcbdabadbbbcbdabcadcacbdccddbbbccdabddddbccaadaaacababdbaccbadaadbccbdcbddccaabbbcbbabacddacababccbbcaacccadcbdddddacaccbdcdaccaaddacdcbdcbcbddbcdcccddaabaabaacabaacabbacacbbadaacddbcadbbcaaabccaddbbcacdbaadacbabaadcdbbacaadbbbcacbbaccbdadcdcbabdbdcaabcdbdbcaacaddbbabddaabbacccbccadaccbaabbdcbacbcdcdaddcabaadadaaccdcdcccabdaabdadccbdcaaaaaccbadabbccaccbabaaaabccdababdaccdcccccbccaaadbacaabddbcccbcabdaddcdbacacaacbcdbcadadadaabbcadddbbbabcdadccbbdadbcadadaccaadddcaccaccbdbacbbcddcabcacbacbcbdccbdcbdccbbcbbacbbccaacaddbdabbbcbdbcabcdbbddaccdddbadcdbdcbddcbdddcaabcabcbcdabbbadaddbcdadbdccdadcdddcadacdaacbcaaabcbdcbdbbbcbabdbbdccbbababaadacdadaabdcbaacaaddababddcdbdbcacaabddcddbabcdadbababadcabadbcbcdacaacbccdaacddabcdacdbddbbaacadcadcaabbbdabacbacaadbccbdabcaadabdcdcabdcadbadaccbacbcbdadcdcdbbacddddcbcdcbaccbadcdddcaadbccabadabadbcacdbbddbacdcdcddbaadbdbbdbdccdcdacacbcadcccbbdbdbcbbdcbcaabbbaabacdcdccadbaacacbacbdcdcbcbbdbbcbddbbbdcdcdcbcdccbbddadaccabacdddcbdcdbbbcbdacddbacacbbddcabddbccaddabdcadddbdbabbbdcbcbbabaadddcdddcddbacaddcddacdbdaadacadabcaaadcbdaaddcccbaaadddccbdbacbabdcbbddbbdadabdacdaccdaddaccbabdacbcbaacccabdabdcdacabbdcdadacbabcaadddcccbadcbbbdbbdcdcddbccbabcaadcdcdbbabdcbbbbdbcbdbadadaccdabcbbddbabccbccacbcbbcacdbbabddcccdccacbcbdbbbbadcdaadbbdabbabaaabbbccbdbacddabadcacaabccabcabbabdcabaababdbdcaccbdbccdabadbbddcbddcdbcbbbbacabcbdcdcbaddaaddbaabdaaabdaabbbdbacddcacddacdadcacddaabccccacdaccbbbdaaabcaadbbddcacdbcdcdacccccddadbdcadacddacdcddcacddaddbaddacdccdccaaccaabdbcadaddaabcccacbcbcacbbbaabcdbcbcaadcadbbacadbbdcccabbacabcbbaabadcbddabdddcdccdacdccdbbbbaccbbcbabdbadadaadbdccdbbcaabddaadcabccbbaadddabcdccccaaabdadcaadbccbdccabcccaabdaabacddbcadaacdccbaccbddcbcbccaacabcacddddcabdddaadcbcbccacaddddcdccbcccbccbacaddcbcaaccabcbdacbaadbccbabcaabaabcdaadadbccdacdcdbbdddbccbcdcdccbabccdacabcddbcbbcdbbbdababadbaaabcacaabababcdbccacaddbcbabccdbcadabcbcadacbdcaadadbdadcbcaadcadcbadbaccaacdacadadccaadbddbddbbaddacadabcbaababdbcbbbbbbadbbaabdcbbbbbbadbdbcdcabdccbbabbabadcaabdaacbdacbcdaaddddbbaacaadbdbbaaabcabccbcaadadccabcabcbbaaccbdaddadaabbddccdcdddccbcccaccacdbbbcaaaddcdbcbbdbbbadcbaabbaacacdbadcbadbadbdcdccdacccababcdccdaaaabbdbcddddbaddadbbbbdcdcddbbbbddaaddcccbaacdadbcabaccdbcacdbaababdaaccbbdbdabdcbddaddacddaabbadbcaddbaccaccaccccccbcadbdbabbcbcabcbcdbddbcdaaddacacdbdcbbbcbbdabbcccbdbcbaacdccbaabdcbdadacabdbcdbaabacadbdbdaaaaaaccbcdbdddcdabadaabcbdadbacdbbdbcabdcccdadcdcbaaadbbadabdddcaccbbdbaccdccdcbdbbacdcdcbbaccbbccdabcbcdacabbabaaacddaccaaabdaababaadcadabddbcbcadcbcbbdaddcbaadbdaadaabdbcbcdaabaacbcdccbcddccccbdcdacdbcddaaadaabcaaabcbadddcabcddddbcabadcddbbcadbbcdababacaaaabdcdbbbbcbcddcbabaaacbcabcbcccbbbbddbcbaacaccabadcdaabbcaddddaabcaabbaddbcaacdcbaccbbdbdadcbcdcaacdaccbdccabbbdbccddbcbbdbbddcbdaaccbdcbddcddccadcacdabbaaccbcdcbbbcdcbdaadbdbadabbdcbaddbccbbddbcdddbccaabbadbaaacbbcdbabdcbdbbaacacaddbacabdddcccbbcbaacadaaddcbdcabdccdccaacaccabcbabddcddbbcdddabccccdbdbbcaaccbdbddacdcdbddaddacacaccddcaccdaccccbadcddaadcdaccdcacccacdacbabcaaddadbbababddabbbbccccdccdbdcaddcddddadccabbdcdcadbcddcbddddabdbdbbadaccccacccaacdcddcbcadbabbabbccbdcbbbbbbabdcacadcdacabacaddccdcdbbacacccadacbbcccbabddcdcdbbbadbacccdddcdcbcdabacbdaabccacbcabcbcadcbababdabbdbccdcbaadabddcddcdadacbdaacdcbbdcccadccdcdacababccabaccdadcabdcdbdaaccbadbbabdddaaacbaadcaddbbdbbbccdaadabbcbabcbcabbdbaccdbdbdddaaccbcccdbacdbabccadbcbbdbddaadbbcaacbcdaaacdcbbbddacdacdcdddcdbdabdbacdabccddaadbccddaabdcdbaddcddacdbbdcccadccbcdcbbbbcabdaadcaacbdcdbacacdaccaccddccacacdbddcdbabdbdcaaaccabaddbbbcbaccbcdddccdadcaccadcdbddbdaacddbddbdbbcbdacbdbcbaadabbbcaaaacdaadabbabbaaacbdaacabdacadbbadacbdcdcdabacbbbddabacaabccdbdcaacadaabacadacaccbacaabcdabaadacccaccdbaccdbdbbcaadbacaacbdaaababbabcbadacbbaddccdbcbbcaadbdbcdbbcbdacdbdcdddbadbcdbbadbdbaccbaccbbcbcacbcdbaadbabbdbcdcdbdcbbbadadbacdabdcaaabcbdaaacdcadcddcbabbdaabcadbcdcbbbaadbbcadcaacbbcacddaddaddcdccabdcbbcbacaadcdcbbbbaabbcddabaccbcbdbcbadacbdbaaadacacdcdbaddbadbdccbaaabccdbcbbdcacbbccddaacabbcbdbdcacdacabdbdbaacdbbaaccbbbbddaadbdacababdaddbbdaaccadbbddbbcbadccbaacbaabadbcbabbbbcaadabadcacabbaaddadcacddbccbadbcdbbdaadcdcadbdabddacbbaddcbdcacdacabbcccadaddbbdcbdabdbaaacbccbdddcdbbcbdbcdacdcbbbbadbccacaccbdccbcbcbadaacdacdbbbbcbddbbcbdbbcaabdacccdcbccccdbbadacdcbcaabcadaadcccdcacadddadabbccbdbcbabbcbadaabbcccacaabbdaaadcbdbbabcdbabbbdacbcadabcddacbbdbbacdacdbdbccdcaadcadbbdabcdbcabcbdabcccbaabdcbbadccbdbacdbdbadbabaaddccaaccdacbaadcbccadcbcdbacbbccdbabdcdabcbcbbabadccbddabbcdbaaaddccbcdaabcbbccacbcadcaadbdabdbcdbbabdbcabcabdcdbcacdcdaccaabbbcbdbbadaccaabdcdbcbbccbcdcbcbccabbabddddaddddcdcacbbdbcacddbadabaadabbbcbccbdbaabddcdadddbdaabbdccccaabaccadccccddcdcdbadaadaaaabcbaccdbcaaadcdbdbbbbaaacabcdabacdccbaacbccdcdcdcdcbdaacbbcbcccbacadcdcacbcbdcddcacdbacbadddacaccbcddccacabcbaabdaadccdcbababbbacddbcbabdbcbabcbbcbbcbcacacdbacabbdbcdbabdccbcabdaaabcaacacdbadbbdacbddabadddacbdabdaccddabbdbadbdcadbcdbdabcdbdaaaccabadccdaabdbcbbdbdcabdbcbacbbdbdcabbbbaaccbdcaaccdcbaacdccabddcadaabbbcbdbdabccdccaccabcababaaadbbadddbcdacdbddbababcdcbcaddddbadadcccaacadcbabbddbdbdcaadcbbbabaaacaaabcaadcdbcbbabbaaadcaabcdcaadccaaaabdccdccbabcccabccacbcdbcaadcbadcbbdcdcbddabbbddbbcabdacccdbbbbbbcbbbabaadabcdbcbcdcaabaccdcaccadbabdababdbcbabaadbbcbaaddbbbabbcdcaaacaacadcacabdcbcdbddabbbbdccacaacddbabbabacccabacdccacbcabadbdaaccbcbadacbbcbbddadabdbbbaaacbcadcbbadbddbbbadaddccbcdcbcddbdaaccdabdcaddddbccbbddbabdadcdcaadcacbdabddcbbccaadaacccdcabcccbaaabacaabddcbddbbaaadaadbbdbababacaddaddaacabcdbbabaacbbadabcdbacccbadccdaaddcddacbcacccdbaccacdddcaccddacabdaacdcadddcdbaddadbbcbbbccabbababdacbbcdccccaccacaadbcaddcaccadcbbcbcccabcbcbddaddddbaaabaaccbdaaccccaabbacbbabcdbbddbbcdcbbddcccbabdaddccabaabdcbcdcdbdadbacdaaadcadcbcaddcdddbaadadddaaabbcdcbbabbabacdcbdcadcacddbddcaacbbbcdcdacdddcbcbabbdddbdacaacddcadcdbaaccbacbbbcdaccddccdcbccaccddcddbccaccabbcdacbcabcddcaadbbdcacdddaccdcddccdddccdbdacabcadddbabcddaadbcbaabadccbdaaabdbbcbababacbaccacbaabdabadadcdaccbacccdaacdacbadacbaadbaddcdddacaaadcabddcdbbbcddddbabcdccbcdcaaacacdcbcbdaaddbcabdadbdccbbdbddccacbbbddadcccbdbbcbdbbdacddcdbaaadcacadccacaadbdcbdcdabcabadcbcdacbaacbabbabbcbdacccccadcacdaababdaddadaaacbadbdbdcdadbbbbabddaddbdaabdcbccbdccdcdcbadacdccacdbcdcacddcbccdccdaadbdaccabdccaadbadcdcaaabbbbbcaaddcbadadacacccdcdbbddabcccbbbcdbccccacbcdaccdcacacbbcbdddbdadddaddddbdbcabbdabbbcaadcdcaacaddcbabbbabdcadddccabbaacbdddaaccbaaccacbdcccaddabdcabbadbaaadbbcaddbbabbcadbaddabadbcdaadaadacbaacddcdbacccccdbaabddacdcbbdbddcbbbbabaabbddcbcccddcbcdcbcbadbbdbdcaaccdbaddbbaadcaadadacacbcacbccbaabaaaadcababcdacbaccdcccccbdcabadadbcaacbcdccbdacabadaccdccacbdccaacbcddbdaaacddadadadbdcdcbabdbbaaadaabcadbdbabcdbabdbabbaaddcbdbbabddabbccbbcccdaacccdbbbdbddbdbddbbcbaadcacaacbcbbdcaabacacacddcddcabcbaacbbddbaddaaacdddbcddbcabcbaacdcdbdacadbdadcbbcdacbabaddaabcbbbbbbaaacaaabdbcddcdbddbbadbddbaacadacdabbcccccbabadabadddaaaadbbccdcdaaccddbddabacaddbaababdcbbdccbabddabdcbbabdbcabccdbbadcdcdababcaaabadbbbbababdbddaadadcdbbbabddbdbabdaaababaaccccbabaaadbaabbdddddbabaaabdddcbddbbdadadbccabbcbbcdacbbdbcbcdcccaaaddcddaacdacbcbcddbabcaacaabcadbbbccdcdcdccaddbbddaccacdbadaabcaacbbbbcdadbbdabbdcbccbbcbbbcaccdacdddbbaadddbcccddddacaacbbaadababaddbccccddccaaadbcbaaadcadcddabbdabdbaacadcccabdcbdcbddbbdbadbbcaadcabbdabbcddbadccccbbadacacbcabcdbadcddcbdddbdcbcdccbdaabaaddccadcdbbabdbdbbabcabdbbbdaaacacbcdcbadbcbbbccbcdbcbcbddaccbcaaabcabbbdbdacccaadcdbabbcacdbbccccacadaacabcddbadcbadbcdaacbadbbbcdcdadcbcbaabbaacdbcddaccaabcdaccabccdbcccaccdaadbadddbbaadcdcbbadbdccbbabbaadcacbbaacddcadacbdabdbdadababdbddccdbdacbabcdcdadadcbacdbcccbdbdbcacabbabdcabacadbaaccbbbdbbcdbbdbabccdacbcccddabcaaaaaddbdabdabacadabbddbbacbdaabcacbaaddcdcdcccdcbdcdacdacbdcbabacacdcaabdacaadcbbaaddacdaccbddbdddadbddaacdbccdaabbdbdaddacaacddbcdcdacdabcaccbddcbbbacacacdbdbdadbadadcadcaaaacdbcdddddbcccccbcbcdcdccbcadccdddaddcdbcadbabbcddcccbcadacaaacccdadaccbcddbdbbdaadbaddcbbdcdcabbaddcabdcdbbacaddabcdbddadbddbabddbddddbadccbdddcacdacdaccaacdcaaabbcbbdacbaddabdacadcddddadacabdaabcddadadbdbdcabbcdbccaadbdbdcbaccbbcdbaaccaacacabcddaaabcddcaaadcabadaadaaacaaaadbcbcbbcadddcdaacdadbaaacaccabbdcdaabdcddcbccdaacaddadcbcbbadcbcddbacbcbbcddccdbacdbbacccbcddacbaacacddbabadadaddccaadacbcdaccbddaccdbcbbcaabdbbddcbadaaabcacbbbbdcbcacdcdbaadcdcdccdddbbccdcdcbaaaaaadadbddcbbadcdadbdcbaaddbadaacbcbcaacdbcbddbcbdabbbabcaaadadcdbcbaaccaaabbdadbdabaccbbabccbdaaccddccabddaacdbaaababccacdbadbcaadabbdccaccbdcaabddbbdcdcccbadbcbcabdbdacacabccbaaacbcadbdbbbcdbbdcabaacbdababddadbabadaaacaccccccbddcdcbcddbcbbcdbcbcdbdacbdadacabdbbccbbdddcdbcdbcbbdbaadcdacddcdadcdcaaaddabcbbccaddcbaabdcbcdbbcbaabcaacdddbcdadcabbadcabcabdbbadadabadcdbabcabadcadcacbbcbaaadddbdaccdbadbabdbcdddabdcbccbcbcbdbbdadbabaacbcbcdbbcccaadaaabbbdacbcbcacccdbddbdbcaaacbdcccbbbbdcccabbcabbccddcbbcdacdddaababccdaddccbbacadaadddcdddadaaccccaddcabdcbddbbcccdcacdbcadbaacabccdbddcbaacdddddbacaaaddcccddccbaacddcbcdcbacaadbcddadcdcbdcbbdcdbbcddabdabbdccacdddbdbbbdbcccbbccabbbadaccaacabdacabcccdbbdbabcdadcccbbaddaccaddbaadcabcbbcbbccbdbdadadcaabbdaabbaaccbbccccdcacddbababbaaccbdacdccbcdcbabbbcbdcbdccdbabcbbcbcbccbabddddacbaaddddbdbabacdccdbbbcbcbadbdbbacccbbabdccbbbcbaccaccbbabddaadddcdbabddacadddbbdbaabacaabbabdbadbcacacaabcabadbdbcaddcaadbbcadbbcdbbdadabdddaccacdaccddccdcaaabaabbbaccbccbbaddaabdcbdaaccabbcccbcdabccaaddcbacccbacccdbabcaacbdbcdbbccdadbbbcdbaabdbcabaccbdabbdbbaaccabbcbadacadbbcdbbbdccccacabaacbdcbddbdbacdbbaddadcbdcaabdcbcdccacacdbbdccdbccacadbcdcdcdacdabcacdddbaddcccbccaabddcdacadabdddacabacbdabbcbbdcbbbabcccdaaaddbbbbbbbadddccbbacdcaadacdcdbaacbadacdbcbadabcccacdbbbbcadaddccdbbaadddcadcccdadcdcbbcddcbbaacbdddccabddbcdcbabccccadbcdcbbabcbaddddcddbadbdcbbdbdcbabbcbbdcbaaccacddcbdbbaadbbdddcbbacddcbdaddccaacaaaabcacbcbcdacacdcabadcbadddbcbcadbcabccaddcabdaadbcabbbcadcabbabaccabbadbbcacbddbdcaddaacbcdbacabadaddacbcaaaabdccbdbadaadbddbabadbdabadbbbdcbbddcabbcdddcbbcacdcddadaccbcadabcdbbadbbabdbcbaadbbbaaabaacdbadcddacdadacdbabcdabbcdbbadccabbdbbaccabdcddcccdbaabbacbcbadbcabacdcbcdccaaddbdbcdbbddbccdaaddcbcddcbdbbbcabbdbbadcccdbbdacbbadcaabbcadbcdaabbcbadbddbbaacbdacdabddaaabcbcdbddbcbacbbbccccbbcccbbcdbccaccabcdabcbbadcbaabdbcdbcbcdcbadbacdbadbbbdbacddbacaacdccacbccbbcacdbcbbcccabbcbadcddcbcdcabddcacdbbdbdcbabddccaddadbaabccdcacdbdcababcbcabdadababcdbdbabcccbaadaadbbcbaabcddadccdaddbbccbbadcaddaadaaabbdddabcaabdbdbdcbaabdaabdadadacadaaadcababcdcaabbddabbacbccdcdbcccdcabcacaabbadcbcddbddcdcbadcdaaacdbcbcadcbcccccbaaaabababbccbcbbccbaccbddacdbbddacddaccbddddbaddbbcabcaadcdbacadcccaacbbadbdddacaaaddbdcbbbbacccbddddcabddaccdcbbbdaddbacaddacddadabdbabcbbabdbcccddccdadbdccdacbadddaacdabdbadddbbcaaadbaacaaddcdcccbbaaaaaaaabaaacaaadbdcbdbabaddbdaadacbdbddadbddcddbababbadcdddbaabcacbacbababdbadacdaddcddcadabccbddacbadaaacacdaabcadaccddcdbacadacbcbbdcccddddddbbdccaadbbcabaadaccdcbaaaabdccdbdbabccaccbaaaacadcaadcacdcddcdaaaabdbcdcabdccbadcdcabaabdacbadabccbcadacdcdaabcaddbbcdcbbaadcacddcdadaadacabbdbcbdacdcbbbbbcababdbccbbdbccaacbdddbabcdbacbadccbcccbbcadddcbbbacaabbaaaaadccdbcaadcbbcabadbbaacaacaaaabcbdcadabbcdcdbacbccccdcaddcaacacaadccbdaaacbcbbaddcbdcdbadaabdbaabadcabacabcdcaddcbacbaacbdabcccaadbcbddaaabbdcddcdacacabcababddcadbdcaadaaacaaadadccbaaabbbcddcaacddcbcdaaacdcbbbbaaacdbddcbaccaaccacdabdbdddbbddbbbadbcdaddbacddbcdcacacdbccdabccbbddccabbbbcccdbbcccdbaddaccbabbabbbcbcdddbdbbadbcbbbcbdbbabccdcaacccccaadbccccbaacaacabcaaccabddaadcdddabdadbcbaacaacbbcddbcccbcdbbdcbdabacbdcbdcbadaccaacbdbbcbdcadabaaacadababdaaccaabdccabccdbadccaabbbbaadabadcdacdabccaddbdabcdbdbbbcaadbbbcdbccbbaaaaddbcdcabaadcbaacbadacdccdcbcbbadbdaaabccddcdabbbbbbacbdccbadcbbddaccadbaabababccccaccbdbcabddbddbbdcaabcdbdcbacddabddccdabddcbaabdcaccacadccbddbaaababadbdbadabbbdcdadbcdcccdddcbdbccdccaddbbdbbcacbadcdbdaccdbabdddbbacbccaabacaccbdbdcdacbcbdadccdbacaaccabccdaabaabcabccadbcdcdddbcbcccacccbbcaddcdbcaabaacddbcddbbcabddccaccaaacbcbaacacbabcdabdadbaadcdbdbbdacdacdccdccbcbdacddcaaddcbabadadcadbddabdaacccdbdccddbddaabdbbccabdbaaadcccaaadacbbdbcabbabcadbddddabddadaadabbbbbbbdcdaadcbdbbccaabacbacbbdccbabccbabbcccdbaaabaabbccdadacdccccabbbababbdcbbddccddaabdcabbabaccdbacbdbddcdabccdbbadcadbcadddbcccbdadaaccbcabdaaacdbcdadbcabdcbacdcbcddaacbdcabdbaaaaadcdbdacccaabdbddcbdbccbdccacbdbbbdadaaacadbdbaaddbcdabcbdccbbbacacbaadddddbbdccabbccccbacddbaddbabdacbdabccdbcbdbcddbadbabddbcaacccaadadbadccbbdccabaccabcdbaccabdaddbbdcbcbbcadbadaabadbcbcabbbbccbcbaabaccbcaacdccdcbcccaddcaccbcbdbdbcadbabaababaaabbdbaccccbcabadacadacbbdbddbcdbdabdacadbdbdddbbcbccbadbaddbbbbbdbaababbdadcaaaddddccadbddcbcbcbbbacccdcbaaaaabcbacdbdcaaaacdabadddcacdcdccaccbddcdbddbaaccacacbacdcddacdccbdaacbaaabacbcacaacadabcccbcbbdadabdbccaacbacbcaddcabbcdbdaddbacddabcddbccbcdcbccadcbdadcbdadcdaaadbbaababbbacddcdacbbdccddbbabccadbdbcaddacdbacdcadbdbbccbcccbbabadbaaddcaabbacdcbddcbadcbcaabbdbdbbcbaaacadbbdacacaabdcbcaacbcdbabacaacabccacdababaabaaccdccbdcdbdbbccbdaaaadbbdbdabbcddbccacadcababbbcdbadadcbbdaabadccdbddcdaaabbadcddacacddbcbbbadbabdcddabbacbacaddadbcdbbddabaabaadaadbcadbdaadcadaccccdbcbbcabddacbbddaaccdaccdcbdbaabcdabababbdccaadcbaadddbbadddcabbbacaabcbddcaadbdacadcadbadbccdccddbaabbbcbbcdadccacabbcbcddbacaacbcddcbdaacacddaaadcdaabdbcdaababdccdbcbddaddbdbbcdbacadbbbdccbcbcbadaadccbbbbbcbbcbdcdadabdbbdcddccbcbcbcdddcbddaaadbdbabcdbdadadadbdacaabbaadcbbdacdabdcabdbdcacadabddabcabcbcbddbaccbaaaddacaaaaaabaddbbdddbcbcadacadcbbbdccdadccbcdcdaabdbbbcbcdbabdbccbcdbbdbbadabcabbdccadabddabcabaadbccdcabbaccccddbcaaccaaaabadcabdddacbaabbabacbbdabcadadadbbdaaadabbaccaadbcaddcbdabcdcdabdcdacbcaadbccadaddcbddbdaddbbbdbbcddbccabbcdaaccacccdcdacbaddbcbbbaacbbbcbcbbdbccbcdadbbcccbacadbddbdbdcababbccacdaadccdcbaabaccbadbadbdabdbbaacdaaccdbbcbcbcbbcabbbacaddcdbabcbacaabbabcadddcddbdddcdcdcaacbcbccdddadadabdbdaddcaabcdabaacbacbbdadbacdccccdbcbbbdccdadbdacdcdadcbcbacbdbddbbacdcaabdddabdaacddccbcaaaaacbacdabababadbccaaccdcbbacddaaadcddadbbbcacbabaccbddcdabbdbdbcbabddccbccbdcadddadbddabdbabaddabcbcdbabadbcdcccbabddbaccbacadbcccaacddcdbcaabdadbabbdcddabbcccdcbbddbabbcccdabcbabddccdbcccbadcaadcaabaacaddbcbdcbaaaaabacdaacabcbccaabbaaacadacabadaaadabbaadbabcbdcabcccaacdbbcaaabbcdabddddaccabdaadcdbdcdbbdaabaadbcbcbbcbbaaaadcddccacaabcaabcbaaabbdbbdbbaccabdbdabbcdccadaacbddcdbbdccbcbddacabaddccdcdbbbaddaaccdadcdcdbccdaddbdbdcaaddcdbbadccdcbabacababaaabadbbcacbccbbbaabbdabcaddbdaccacddbbdcbdcdabaddabdbdcadaacddaddbabacabbbaacdddaabadbbbdcdddaacbcdcddbaaacccabddaddbbdadacbbabdadddbcdcbaaaabddddabadabbdadacccccdaacddbbdcddbccccadcddbdcacdbcbaaccadadacaccaababadbbadbabddacabbabaccaababbcccbcabddaaababdddbdccabcdbadcadcbbddcbadbdbcbbbdcaddabbabdcbacbcbddddddbaaccdcbaddcdccddbabaaaabccccccdabababdacaabcaabdbbcbaacdbadccbaabbdaabadbdbbcaadbbdcacabbbdcbcdcaaabbcbcccccaabadabddcbdcbadddbccdbcbcaadabbcbbbacdbbcaaacbacabdbabcbbccbcaaadabdacdaaaabadbacaaadadadbdcdbccaaadcddbccddcbbadadddccbbabcdcccbbbdcdcdddadcaacadcccabdbaccccbdaabccbcddaacacdabbcaccaccccbcccbcbdddcacbdcbaaaacabaacadbdcdadddbbbabcaaccacbcddbcdaaabbadcabdbcbdccaabaadcccadbabaddcaddbbcadcdadbdddddabcdbddccbabbcdabbcddddabaccbdaadcdcabcaddabdbbaabdcadcbbcacbdccaddadcdcacbdccabaabacabccadcbcaaaaaddddcacbcbddabadcaccbdabccdbadacddabcbdaacbcbbabcdaacbcabacaacbaaadbdbcacacbdbbaddcccdbccbabddbacddcccdcacabbccbbdaaaaacdbddacccdbdaaaadcbbaccccbbaaccbaaccbabbaabdcdcbadcccddadbddacdbaabddcddcabadaabbbccacbdccccbabbdbacbaadacabbcdadbcaadaacbaaccddcccbadabdcbdaababccbbbccabdbbdacbdadbadbabcdaddcaaccdbaadacbaabbcbdbcddaabcddbcbaaadaccacacdabadddbbbdccdacbdabddabdcdacbadbccadccadadbbcbccddbdaddcccababaaadcacbdcadadaadbdacdcbbbdbdddddbdbdbacdbadbddabbabccacbbddcbbabaddcbddbbcbcbcddbbadabcdbbdadbaddcbbcbdddabaacdcbbbbccbcaddcadbdaddabcbdcacdbaacaacbabadbccccbaacabbdabcdcabdcbaabccbbcdaddbabddcdbbbaabbaaccddbaddbcdabdabacdcdcabddcdabdddcddddddabdaadaadbbdadddccdbcacddaadbbdadcccccbdadbcbbdcacbadbbbbcacbbccaadadabadbdbbdbcbccdcadbdbdcaadadbdbabaabbcdcdbcabbaacccddcdddaddcacbcbcacbcabbccdbddabaabdabdccdbdacbdaacbbabbacbddcacbcddadcadbadcdaccddaabbbbcdaabddadddccabacbccacbcaddbbbcdbbadcddbcdcacacacbacbcbabadccbbabdbdbcbcddabadddbabdbabaaccbabdabbabababbccdddaaabddcccccdbcabbcddaccbcbbbdaadcbdbaaccbbcdbaabbadcabbddddbbddbcaaabdbcacbadbdbcbaacaccabdddbdddddabdccaaddcbcccbcbcccbbadbdacabaabbcaddcbdcabbaacbacbdbbddcddcbdacbdcbbdcdbaacddddcbabcbddaccacaaaabbbabbdbdcbdcabddbbdbaadccdaabbbacdcdabbccbbccbdbabbcadccbddcabbdaadcadcababccdcbacbcaccdbababcccccacdbdcdabbddacdddabaccdaaabbbaadacdbdbaaabcaacabcadbacacdcbbdcbdaccaabcccdbdbbadbcaaabdadccadcbbabdacadacbcaddbbcccbcbccbbbcbdcddbdabcbbadccbaacdabcdbacbdcaccbadbabcaaababdcccbbcccaddbcddbbcabdabababcdadbacabdbbdcbccccaccacbaadcdccccabcdcddccdccadbcabcadabbbdbdcbbbcdbdddcddbcbbcdbbaddadaaadaadcabcbbbdcadddbddddcadcbacdbbccdccdbbbcdbbdaabcddbccdaacdddacbcbaaabcbadadcdbadcdaacabaaaaadaacbbcbaddcdccbcdabdddcdbbddddcaabccdccbdadabbdbabbacbbababddabbddcbaaacabcdddcbacaacbbdddccacbdbacdcbccaddaabcadacaabdcaddaadacddcbcbbadbbbaadcaacbbabdcdcdcbacbbadbbdcdbbbcaaccabcccbaacddcbacbdcbadbaddcbadbcbababcdbcbadaddcbccdcabdbdadbbbcacadcdabcadcadbddacacacccbbabdbbaddaadcdcbcdddbdbcadadccbacbabdcbadbadaabbcdadbbcbbcbbbcabdcaacbadddadbbbdbbdaaaccbcbccacacdddbcaddaacbbabbccaacccdaaddbdbabbccaabbcdbbdabacadbddcbbccaadcbacdccbdaadcbbacabaddcaccabbccbdccbbcabdaaaaabddbbbbaacacbabadbbdcbdcadadcdacbdcadadaacddacaccabcccaabdcadaabccdcacccdaccaccbdacbdaaadddadcadbbcdddabdddcabbdaadaabadddcbdacdbaaadacaabadccddabacacbabddaaccbddbadccabdaddbddcdadcbdcbaccadccbcdbcddbdbdaaacccabadadcbcccdadaaaaaccbcdccabcacabdddcdccacddbdbacbadabcdbdccadaabdbadbbcbdacdadddbcbbdbdcdabcbbbbabbadbdddabcadabdbdaadddbabcaccadadadcbbbaaabbbcdcbcdcdddbaabdddbcdaddcbadddaacdadcbdaccbddccacbdbdbaccbbbdccbcdacbbabadadbdcaacbbadcacdccdcdddcbcadaacdbadbbbaadabcaddbdbbdacdbbbdacdddadbccbcaaaadbcbcdbabcabccdbccddaddbadddcbdaddacdddaacdcabdddbccdcbcacaacdacbbadbcdbabbbadbadbdccddaadddadabdaccdbdcdadbdacddaacccadbddddcbcddacaddbdcddbcbbaabcddacadaaadcbacbdbccbdaccbaddaaabbccabdcbbabcdccdcbdcbaddcdbcccccddadaaddcadccacbcdddacabadccadcddcddacacdbddadcdcbcacbacdabcabcbcddcdaccaaddaadbcabbccdacaaabbdacbaacaaacbdbcaddddbdccdabdabcbcacdbcbbdcbcdbbaccacbcdcdabdacccaddbadddaaabacabadddcaabbaaaadddaaadbbcacdcdddbcdbbabcacabbcbcdcdbbbacacbcaaabbdabaaccacddbaaaccaacddddababaccdbcacccaddcdcdcbacdbaaabbabaaddccdabacccddacaadaddbcccacdaacdaddaaddaccbabbccddabadddcccdbbadbddcdcccbccdccccdbabdcddaacbccbaddbadbddcccbbbacbabbbbdaccdbbccababbdcdcaadbacacaacccddaacacccccccdddbcacbbbcaaaddabdbdaccdacaddbbddddacaaaacacabbdcbbaadbcdacdcabcbbaaddabaaddbbccbcbdcdccbccdbadbcdbbbadbccbcbcdcbabdbddbaccddbdadbbccabcddacaadaabbbcbbacbbaacccddaabbaaddccbadbacdcbcaabcdbaccccbbbcabadccabdacbcaaadbbbcaacdbadcdbcdacbdaaaacddbbdcdcdcccdcdadbbdaddaaddabcbbdcbabaadcbbdabdadcbccbcdaadbccbadbaaaddcccacccddaadcbacbaccbbcbdacbbccacddddbcdcdccacbdddaacdbcbdababcdbbdacbbadbbabadccbbacbdacaadddaadbcddcdcaddacbdcbdbddabbbdbadccaabbbdadaaccbcabccdababdccdcdddddbacbbdcabcdddddbbacccbabdbccddabddccdbbccccbaaaacdadabdaababcabcaccbdaabddbaabbcbadaacdbdaacbabbacdcabcacbccbaabddcbaaacaaccdcaaabdabdcabcbddbbbbccccdbbccaaaacbaadcbdabaaccdbcbbccacadbcbabbdbbccbcddcbdcdcbacaccbccabbbbbbddbadaddcccabcccbdcccbdabdcbdbaadadbdcaddabcaaccbcccaaddcdaabdbacccbccbbbdccbdaadcdaadacdbdcbbdbcbdccbcdcdaabcbaddcadabdabadadbcadadcbbbbbcabdbbbcbcbdaddcccadcaabaabbdbdacadaccbbbdcabccacabdcddbbdccccccdcbdddbdddbdcabccbcddcdccabdaacccbdccbadaacddcbbbbccddbcdcadbbcaccbcdcbbbaacccbcccacddadaaddccdaadcdcbbdbbbcaccbdcacaabcbcbddbdbcaaacdbbabbcbbcdcaaaaaabbbaccbbdaddcbabddaaacaaabadbccddcbdacacdadcabaacadadbdadaaccbcacbabdbabdaabdbbabbbdacbdbabadabcbbacabddaacccbdabbccdbbbcbabbbdadabdbacacbddaddaacddcdbbbcddcdaddcacbcaabdacbaaccddcbaddaaddabddaabbbbaccdbbdabbdabbcbdbbdbcdbdcaddaadaaaacdccbbdddbccdddbcbdcabbadcbbaaccdcaddcacbbccccdbcdaadadbccddbaaaabbaccacddacabbcacbaccaaabbdbddadabcadacdccbcbabcddddddadcadcbbdbabdabdcdadabdbcbdaadbcdcccccaaadccbcabbdbdbcccbacbbbcddccccdcbdccdcabcdaadbbbdbcdcadbcabbaabbdaaccacdaabddcadbdaabdbcdbdaaadbbbcdabadbabbaaadabacdabadaadddabddbaddbbbbacbabcdbbaaaacdbcbcbbbcacaddbacdcbdbbacdccdbbdadabbdcddcdbadaadaccdbcddbdcbcbcbcbaacbdcbdbdccdaddbbbbbdacbcbdddcadccbabbddcadddadaadddbddbdbdaaacdabdacaacaadcaadcddaaddabccbcadbaabbcdabbddbbddbddadbcdacddbbacdcacbadbbcaddcaadcadcaaccddccbabdbdbcbabaddcddbcdababddcbbababadcaccdcbbbacdbbbbcdbccbdbdbabbabadcbcdaddbbbbcbacbcdbdddcbbccaabccaccaddacbcccdadcacadbcccddbaacccabaccadcdcababcbaaaddccbddddcbbcaccaacbddabddbadaaddaaabdddacdcbcddbbdddaddacddaabbbaaabaababaaddaccaaaadabbdacaacdcbccababddcddacbdbbbdcbcdcbdcadccabcbacaaddbaaacbdcdbaacbacdccaacaccbdcbbbbabccaaadbcdccdccbcbabaddbddcdddbbddccdbbcacdbdbcdcbbdbadcbbcbbccabdabbccacbccdbccabcabcadcdbdabddbabcaaccccdccbcadcbabaadccccbdbaaadcadcccbaaadabdbcdbbabaccdadbcccdadbaacaddabcdcabbbcbcdccbcccadcdabccbcddcadcbacbbbbdddbdaddaadbdacaadaddcbbbdbcacbbdacdbdaabccbccbcdbcacbdddcbadadddaaddaaaacbccbaadabcbcdadcdaacccdacccbdbdaccccddcaaccdbabbccaacdcdbcccaabadaccdcdcbcacabbdbdcdbdaccddaaaaacaaabbbbccdccbbdbabadbccadacbcabbcbbbdcccddabccbdcaacabbdccbdcdbccabadbbddbcaabcdabbccdabacaddbabdcbccccbcbdaacdaddaacbacdcbbacbdbbadddcbbaacaadcbbcccadacbccabbcdbbdbbcbdabcaccdddbbbdaabccadddacdabaadaadddddadbcbbacbacacdddbdccccaddcdbbabacdcacaaddcbcddbaccadddbccbcabccdccaaccddddcdbdbbbdaccacdaddcbbbacacbaccdddcbcbaaccaaabbdcdbccdaadcbbbccddbcdcabcbcbaddcccbccbabddcbabacccacddcacbdccabbbdadcbbcbdcdabbcdbbbcbdcdddbaacbbaccbbbcbdddccbcbddddccadbccbabdbbabbddacbdabadadaabaccdadacbdadddaadbddbddabdcdabcbccacbadcdadbcdddaddadcabcbdbbddbcbbcbdbcaaabaacaadbdcacbbdcbccdbbaddbabdcccbabacabcccdcccbaccbbbbaabdabccaddaabdacadcadccbcbbbddbaadadadddbddaadbbdbbbbabdacaaabcabcacabdacddacaaacaaacdcabbbadbbaddddbcdbcbbabbaaabadcccbdcbdabadddaaddbdbadbadbccaaadadcabbcdcbcddabadcbbccbbadabddbdacbddbdcabbbadadbcdccdacbdcdccccdaaadccdbccdbbcbccaaabadcbcdccccdccbdbabcacdbabdcddcaabdcacaccabdbdbdaaacbadbccbbadacccdcdadbdbacaaacdacdbdbcacdbbbabbbacdddbbadcdabcccacdbcccddbbccccbccbabbddaadccacaccbaaadacbbdacbacdabdadabbdbccbcbcdacbcaddbddccdadcaaacadddcddabdcbbadbccdbacdbdcddacdadacdbddcaaaacacaacaaccbabdacaccbddbabdcadacadcbbcadadabadacabdaaaccdbdabdadacadbdacacacdaaaaacabbbccacbbdcbdaaabcabaacddcbdcadcadadbcbcacbcabcacaddcdcdbacaaacacacabdacdcdcacdbaabcbdcdaaabdbccbacbcbaacccbddcbaddbaccacaaabbdbbabdbbbbdbccbdadadcbabdbcdbccbaddbdbcdacddbacacacaadbacdbdcacadcabdcbaabcbdcadabcdabcbaddbadcbcbcabcabaaabcbbbbcbbaabddaadccbbbabacabcdbccaccdcbddddacadcdadddcbdacdaadabbadddabdbddbbbabbccbbdddbdbccdcacdcdaddddcdbbabdbcbbcdcbadddcdaaddcacbdbdbcbbdbabbdddaddaaadaabbbccdbabdbaaadadabbcdbbddcdcddccdcbbdabdacabdcdaadcdabdccbdbcbdccbddcbbaddacbddbacccdcddbadbaacdaccaaccaccdccdcddcbbddbdbbaaddabbbbabadccbaaddcbcdbcbadaaccadbacabdcaadabadbacdbbddbdcaddabacaaddbdacadadcbdbdaaccbddbbbcbbacdbadbcbbbabacddcdcabdcadcadbdcddcbdccbbccdccbaaacabccbdddcdbabadbaaccdcaccdcabddbcbaccdcccacbaacbbaabddaababaaacdcdabcbbbaadaddbdcddbddcbabcababcbaccbdbddaaaadcddbdcabbdacdcdbdabbaaadcbddddacaabadbbcdccdaabddddbbbaacdadcacddbaabccbacbacbdddbcacbbcbcdcacadbdbdccbcddaaacabcddcdaddadddbdaddaacbdadabaccadabaabadcccadadadacdabacccadadaccaddbcaaacbdcacacabdbbcbaaadaacccadcccbbbdcdabdbbbbdbbaacaaddaabbcbddcdcdddccbcbacaabbccabbdbadabcadadadbcaaccdcaabadbbabdcacbbccaabcdabacdbaabddcdaadbcaababacddbadcbcaacadbbcdcabdaaaccdcadbacaadbbbdcdcdcaaabaaaaadcacbbcacbdaccadcbbcdbbabdbadabacbbbbbdacbadadccbcdcaaababcdadadcddbaddaaaacacaabbdcdcbabcbcccacbadbbdcacddabacbbccacbcbcabaddbccccdadddadddbadcbbdcadcbaaacdadabbdcadbcddadacccccbcdadcadbdcacddbabaddcbccbcadbbccddcbcccdababddbacdbacbcbdacabbbacccadbdbadacdcadbbaaabcabccdcbaaaddabacbadabcbbcdccccbddabaaccddbdbbabccaabbdddacaaabcdbadbabacddcacbddbccddadbdacccaddcdacbaacaaccaabdddbbdababdcaababdcbccdbaababdababcccacaaacbccbacaabadbbcccddbcaabbabdbaccaabbcddaaacdcaddbacbccddccbbcaabbabbbbacaddbcbadcbdbdbcaaaaababbcdbdcadaabadabddcaaaacbbcabaccababaabcadadaccaacbbdbacadadcccaaadbaaccabdabbaadcacbddaaadbdcbbbdaabbcccdaaddbbbddadbcaacbbdcaacdbacccabdbaadadacaadbbcddbaadddcddcbcadbbacdbbcaaddadbbddabaadccababcbdcadbaddbcabdabbbcaaabadbcaccbccdadaaabcbacbdddbbddddcacbbcacadcccbbabdccdcccbcccdadccbbcabdbbcdcddcaabdcbdaaaaabbcacacbcacaaabacdaccccbabdccbcdccadacaaaacbdabbacdcbabaccaccbcccacabbbaadaaadabbcabacaaaabbdbbcccdbcabbcccccaabcbbadbddaadadddcbbabdaccacddacdddbccaaddddcbabacdadcdbadadacdcbddbbdacabbdadaaaaaaadacacaacdbcadcacdacddccabddacbabbaddbaabdcccdaaacdddabccadbaccbcabcdcdaddcbbbdbcbbbcbcccbcdabdaacbbabadaacdabadddccbcbcabacdababaccdcabbcbbccccccbdacaabbbabbcccbdbbdadaabdadaaddbaabcaabcadcbbdbbccacccacdbdbdabdbcbdcaaabbaacbbcbbcdcccbacdabbbbbcabccacbdabdcddddadbdadadaababdbbbbabaaaaabadcbbabdbabbabcaacdcdbbbdbcccaababbabaacbaccbccadddcbaccddbbcbcabaddcddcddaadbbbcdadbcbbbadacabdabddbcbbcaaddcabbabcabbaadcadcabaabbcdcbddcbdcaddaacadbaccabacababcddccbadbddccaabcbaccddbacccbddbdbaccabbbacaabbabdcdddcababbcdabbccaaabdccdcbbddacbcbdccadaacbccbcbbcdbaddcbacbabbadcadacccaabadadcccbdcaabaabbdaccaabdcacbaaccaabacbbbcdddddbdbbcdbbbdcbbabbdacdbabdddcaacacccdabcbbdacdccbdcabcdccdacadcbbabccbdadbddcddabbccaddaaaacdabababbdddacacddcdaddcaabbabadbbddacdbcbddbdacadacccabdccbbaacaccaabcaccacadabddbaacdbacbdadabdbbbaaacabcddaacdaddbabdcdaaadaccbccdcccaacadbbaadaabddbcccbcabbcdbbaaacaccdbcbcccbbbbdcccaadcabcbbcccdbbacdcadbdcbdbdabdabcaacbcccabacbbcaccccddaadaacbaddcdbbddcccdaddcdbbbbcdcdcadbaddcabadbcaddcccbcbdbbdadcbcccdcbcdcacadbccbccacbbbdbbddacccbbdcabdbabdadcbadaabbdcabcaaabddbcdaccabbdddccdcaaaddcddabadadaabdbdadbcabaadbdbaddadccadbcdcabacaabdbaaccbdbddbbcbbbddbaaadbcaabcddbbadcbaacadbcabaabacaadabcbbadcbacbbabacaccacadddaaccdacaddccacdddbcabbadbcdbaabdcdabcbacccadcbccaddadcbadaaacbbddbaccbcdbbcbdbaaccdaddaddbacaddbcbcbacbadabadacadabcddbbdaddaaadcbbabbcbdbdaccbdabbdcbbddacdbaccaccccaabbcbbccccaccaabaaaddcbcadccbcaccccddadbccbbbccabacddcdcbaadbcddcabcaacccbcdccdbbbbcacdbcadcadcdcccccdaababbacbddaadbcaccaacdbddcdcbcabbdbddababcdbbaabddcdbadaaaabbacddbaacdccbbdaacacbdcaaccdbcabccdbdccdccdcdbdacdccaaabdbcaacdcdcaaaddbaabdaaabbccdadbdbdbdabadddddaacdabccdaaadaaabdaccabcbbdcacdaaadbadabacdacccdaccbbacdbbbabcbbacbcdabbccbbddcbcbcbbaadabbdbabaabaadabadddbadbdaddbbbababbbbbcbaabcdaaccbcbcccccddbbcdcabcbbbdcbdbbdcccbdacdadbbaacaccdbcddcdccadccdbcdbaddbbabaacbbcaadaacdcadbddaabcbadbadcaddddabddaccddbcbaaddbabbabcddadccdbabdacdabdbadccacddcdcdcbacdcbcacabbbccdacdcdcdcaaacbcacccadaddcabcaccbaadddaabdcdbbdbabdddacdcabdcdcbacdbadbaaccbadbbbaabcdbcbdbdccabcbbbcabdddbbcccbccabbccddcadaddacbadacabbdababaabdcccdaadccddaabccacbcbdbbcacadddcbabcccaddabbdbacbddbbababdbcdcbababdbcbcdbddabdddcaabcabbaaadabbbdddcdcacabbaaddbabcbcbcadcbdbccabbdbbddcdddbbcbdabdccdbdbbdcccdcbbcdadcbabdbadaadbddadacbcdbadaadababcccbcabcdbcbcddabccacadbdbabbaadbcabdbdbdccbbdcaaacabcdcbdaaacbdcacdbdbbbaddabbaccaabdccdcddcacdacdcbdbbaacbdacdbaabacdcacadbcabdbddaacdabaadcaccbdcdabcaacbacbcdbdcdadbcdaadcbdddaacdaccbacbadbadcccadcccacdbddbccadbcbbaadbabbaccaccdccbabbacabaaacabaabbdbcaccabbadbdcacdddabcbbdcddddccbdcdcadabccbdabbdcabdddbbdacbbbdbdcdacadddadcaaaadcccabdbdbbcacddabccddaddcdbadcddbbabdccbaddabbccdcbdbdadcaaadcbdacddadcbabddcabdcddbacdbdaacdccdcccdbcddccccadbcbdaadcdcaadcbbbcabddadabbdcbddaabcbbcdccdabacadacdbabadbdadbcdacbdbbdaccaaddcbdbddddbdacccacaaadbcadadddbddbdcbdbccbaaacdbbbbdbbbbccdaadbcdabbcbccdcaccbcbbccabbccddcbbdcbbcaacdcbbdcddcbbcaddbabababcbbbccaccadbbbbdacdabaadbacbccbdbaccacacbbddbdcaaccbdbcbccdabcbadbddacbbcdcacdabadcaaabbaacabccdcbdbcacdbbabdacbbabccabbbbcbbdccbbcadbdbdcbcacbaabacdcbbbdddbbbcabadccadcbbccdccabcbcdabaacbcddaabdabccaadadddcdadbcbcddbbcabddcacdbcaccabbdcdccbcabcdbabdbdadabcaaacaabdbaddacabbaababbbccbbcdadcbbcbddcdbbdcdadaddbaddcbbcdaddccabbcabddcaaaaacccaabadbbbcbcdcaacabcdcaaccbaddacabcadcdaadcbccadbcbbcdaabccbcddabdbabbcdabaaabcbcbabbbdbddacdcbdbdcdaaccbbaccaccdbbddaadddcbccbbdcccbbbcbbbcddbbcabadaadcddaabbaccbdbdaacaabbbcbadbcbbbddacbddcdbddcabdcaaadcdaaacccdcddcadadadcabdbdcacdcddcbcdcddbbbcddbcccbccdcbbcaacaaddaacaaccbbbbbcddcdddbcbbbaccdddcdabaacddaccdcdbaacaaaadacbcaaddbaaacadcdcabbbbdbcbbabcdabcaddaabbaadccbdadadaabadcbbcaacabccdaaabbccbddacbcbaacdcdacccbccbdadcdbcdddcadaaaddbdcbbcbcdcaaddaddccccbcaaadacddaadbccbacdaaaaacddacadccdaccacdddcacdcadcdccbcadddabcdbadbcbccccbbdbbbabbdabcacadcdbacaaccaacdcbbdcdacccaadadddadaadbddbbcbabdddbccabdcbcccacabdbacccdcacdaaaadacdababaabcdbabaadabadadbbabacbbcdaacdbaabbcabcbdacabdcbcabcdcacacccccaabbdbcbbbddbdadabacbbdbcaadbaacbddabbabdcdbacdbdbabdbbcabbaaccbaadcdcadabccddbdbddabbcccabacbcbbbddcccbbaaaacdbbaadadadcddbbacabdbdcaabcadacddabdbaddcdcaaababcadbbacdacdcccbbbdabcacdcccbddccababaaccaabcbbddbdddcdabadcbbbbbdbadbacdbcbbdbaabbbcddddabccdcdaadbbbbabbaadbdbbcacbcdbdbdcacdcdbcbadbbcbcacbcbbbaacbaadababbdacddbbcaaddabdccddccdcaadcbcaaccbcbcadaccccbccdccdaacdacdbdcdbacdbdbdddccdaddaadbdcaccbccbbbdcddbbcbbadbdacbaccbbbccadbbdbbcbdcdabaaadccacaaccdabddcbdacadbabbbbbacabbbcdbbddacdbbddbdbcbcdcdccbddcbcdbacbbdbadcabbbdabbdddbdcbbadcaaacdabccadaaabbccadcbcdababacdcaddcbaadcccddccddbbaccbacabdcbcbbabccddaccaabbbbdaddaabacdabacbabbdcddddbddabcddbabbaadabdacdaacdacbcdcbcadccdccaadddcbcdadccbaacccccccdaacbdbbdccdcabdacddbcdccaccdcadaabcbbabbbaddadabacddbbbdbcbdcaddaccddbddbdbdaabaaaadbbadacddcbcdbddccbddcbdbdadcdadadabaacadcccaaddcbbadddccbbcdacbcbdddcbcabdcaadcadcdbddddadbdcadbacdcbadcdadbddaaddcbcadbddcbdacaddcdbdbaababddabaabdabbacdaddadbdcaccadaddaadbacbacbbdbddcadbbcbdcbdbbbaadcbddbbbabdcacdcbbddddbaaaaaacdbabbacababccbcbbbdababdadbcadaacaacdcdbdaabbcbccadadbabbdaaabcacbddcbcacdaccabaabbddaaacddccdbaccaddcaacbbacaddbbddcdcababdacabddbcababcddcdbbbcbdbccddbcadaddddcdcbbbacbccdccbbcacbcbdaadddaaddaccdddadcacabbacbabdbaacacbbbdccbaaaadddccbaddcadadcadbabdccccdbbcadccadadaddbabdcbbacbcbacbaddcbcdaaddbabdbbbdadbddbcabaaaaccaabcbdccdaabcdbccadccbbadaadcaaacabbdabbdadcbbdbcadbbabdbaaddbccabbcdcbaaababddbcbcbbbddcabaabaaacaacddddccdcacacdbabbdacaacdcddccdbbaacbddddcccacccadbadadacbddbccdcbabcdcadbacbdbcaccadbaadbccbaadcbbcadcaaadddaccbbcadbbcbccadddaaacdbadabdaaadcadadbabbaadabbcdbababbaadcaccddbaadcbbccdccadbdaadbaabdabccaadbabddabbaaccdacbcbaabbcdbdadbbcddacacbdbccaccabbbddbadaacbcbdaaaacbbdacbdadaabadbdcacbacaabaccbdddcbadcbbbddcccabcdbaaddcabadacababcddbdccbcbbadadbacbababdaabadbbadcdccddcaaabbddcdcccccdbccbdbcaccbaaddcdaacdcadcddbcbdcccddbdccdadbcabddbdcdcbdbacabccbcdaacdccdaaddddddadbbddbccdbcddabdccccbcacabcdddddaabbbbdcdacbdcbbccdacbdccdaaccbcbdcbdcacbcabcaddacaccdccddbbbcaaaccadaababdbcbabbbbcddbcbbddacdaccaaaacdabcaadacbbaaaddcacbadcddbadbdcddbabdacbdacbbddcabdcbaaaaabbddbddadcadcacabbdddbdbbddbabccabbadacaaaaabbabcbadacdcbdadbdbbadbccdaaaccaddcbcaccabdbccdaaadbbbdabcbbdcbadabcddcaddaaaaccbdddcbdadcddbdcadccbabcbbbdbddccbdacdbddaadabcacdbdcabdabdabdadacccacaadbabdbdadbdccaddadbcadcaddabbdddaaaaadbcdbabdccbcbddaaaddabaaaddbbcacacdbabbbdaadcabcbaccbddbaddaabadbcaaabdbbaaacbabacbcbdcccbcdcbcbadcccbdcdbbaddaabbdabcbaccccabbddadabcbcbdbacdaddcccadcadcccbcbddbdbabbbabadcbcdccbcddabbdddcbcdbbabcdccbcbdabdddaaaadabbbbaccbbdbcaacacdbdaacadcaddbdadbdabdadbadaabccbcdbacbdcdcaabaaddcbbcbcdacdcdcccaabbdcbcdbdaabcdabdbbaaaaaabdadacaabdcbbddbadadbddadabcaccabbcaacbddadcdbdcddcdaaccabdcacddadcddcaccdcdddccccbdcbacbbdcaccbdaadcacbaaddbaabcaddbbbabbcabdbbacdccbddbddddddbabddbacdddcbbbabaabacddcabbabaabbbbbcbabbdabdcdbcadaaabccbbbdcccbdccacabbdcccdcbccbdccbdcdcbbbcdaaddcabbdccaccacbacdacdcacbbabddbacdddacbddbbcabbdaaccbbbbaddacdcdcaabdadbbdaddbbaaccccddadddbbccbcacbaabbcbcccabdaabaadcbcaddaddcabdccbabdbacbcabdcacbacbcddabcaddabccaabaacaabdccbdadadbadacaadaaaadcbbddcabcdaabbdbcbabcbcdcccaccbddcdddacacadbadadaaaaabdcacabcccccdbabbbbcdaabbbbccbabbcbbaadcdcdbdcbdddcaaaabcbcadcacddbabbcbbdbabbbbaaddabbcdaccacdbbaacbdcdbcbcabdccbbdccacabbdaadabddccbbbbadcbabbbdcbbbcbaadcbcccdbdbaddaccddcbbaccaddbdcbccadbbcabacccaacdbddcccdcbdabdbbadbadcdcdbbdbdbaddabcdacbcaccabddcccaaacdaccacbacccbbadcabcdccaddbcaddacdbcdaaacbbbadacdcdaaabdaaccbdcaadbcdbabacacbdabbbdaccabdbccbabbdbbbbcddbcdddcddabbdaaadbdcdbdbcadadbbadbbcddaaabccaaadbabcadcacdbadcddcacadddabbbbdbaaacbbabbabcadbaabaaddbdacdbddcdddadaddadaaccbcabdcbabdcbababbcdcacbadcaadcbcaddcbdbdacabcbbadacadcbdcaccbadbbcccdabababccacbcccdabacdbbacbacbccabdabaaadcdbcacbdbddbcbbcbbdaacdddbacbacdaadbbcdccccbbdccacadcddaadaabcdaccaadcddbcacbbaddbaadbccbaddccbcbdcddaaabdadacbcadacacdcdcadabbcacbbdcaabacabbabbadbcbabacbdbccbdabcddacdbddaaddccdbacabdcccddbcbabbcbbdabdcacdbcbcdbdbbddacdcdcbabbddbbcddccadcbaddadaacddacabdaacadadbdbcaaababbccbabbabdbcdacddcbabcbcaabbacaaaadcacaabbdbbacbcdbabcadbcccbabadaabddabbccabcaadbddadcdbbdccaaadaadcacdbaccdbcdadabcbcbacbbccacabccbbbbacbabdbcadbdcdbddaadbddccbbcbaccacddbbddabccbcddddcbbcaacddcdcaabbbaacacdbcacbbaddccddbccaababcacddbadabbddbcadaaccbcdadbacdbaacddabaadbcbaacdaadccbbacacacacadbaabbcbcdbbdbaccbacaabbabbdbdcdaaddcacbaadbcdcdadadbbcddbdbadddddbccdbcdbadccbdbdbcacbbaaddabdbbcdcadaabbcabaccbdccdabbaaddddabdbbacadddbdbdcdbddbabbdccdacaacddaacbcdacccddbbddbdacacdbdcbbadbcccbbbaabdbddbcbbacadbccabbccbdbbaccabadcaddabdcbaacdccccbcbcccbdbdbdadbadaacacdcdcbbdbbabcddadcccdcadcdbbccbabdabbccabddccacaddddadcdacbdcdaaacaacabaccdadabcccbdccaabbbddccaccbabbcacdcddcacadbcabdaabacbcbcaacdacbbdbcbcdbddbbcbabccababacabdcbcbacbdbdcddadadaaccccacbcccddacbbbdbbadaacbdbddddddcdaaadcacdabaadaabbaaabbabbaaccbabcbaadabbadccdbabcbcdbcdcdacccabaacadcddcddaaaacaadcbadbacbbbdcadcadbacddbdcdbcbcbaccacacbcaabccadcacabbdcdbdcaccaccdcdcacdabaddacbbcddabccbcadbbaabadbbcdbacadadcddababcddabcccadddccaddbddcdabadbddabcdddddadccccbbaadadcaadcbdccbbdddbdacbbbdccbacddadcaaaccaacdbcbcbbddbaaadaaaadcbcccbacdadbccabaddccdaabddccdddabbacacdbbaabaadbabbbdadaabacddadaacaccadbbabddaabbdccddadcaadbadcacdaabdbbcadbbccadccbcdccadddbaabdbaabbdbbccdcdbaaddaacdcaddcdbadbbccacddacbadcdccaabbddaacddbddbaaadbdabcbcbcaaccdcdbbbbadabbbaaaaccabcabcdddccdaaaddccbddddbcdcbddaabcaacbabadbcbdbdcbabcaddaabdadbcdccdddcdbcdacaabbcbabacccaadacdaaabdddbcadaaacbadadacccdacdadccdbdacdbcbbdabdabdbaaabacccacbaacdcdbbcaababbadacbcbdbddcbabbbcacbbbccabaaadcccbcccdcbbbabdbabacddcadbbddacdddcdabbadbdcbacdccbddaaaccdadbdaabdddacdccddcbddcccddacbdbdabbbcdaabbcbdbacdaccdcadbcddbaddddbccbdcdaabcbbaccbcbaabcadaccdcdcabddbaddddbaddcacacadcccaaaaccaccaddcbcdbcaaabcaaccabadbbbaaaabcdbbcbadababcadccdbcabadbcdcbbabddcbbcddcbdddaddddadcbcadbdcacabadddaabcdaddabdbbabcddabcacadcaccaabbcccdbcdcddadbbbcbbbdccdbbbaaacbacdacbaaabadddabddcaabdcbccaadccbbccbcdbaaabcddddddbbaaacdadcbbccbbcdcadbbadbddabdbadcccbccbdadcbcbcabdbbcabbcbdadcdaaadddcbbccabadbdcbdaaccabdddaaaddbacddaabadcbacaaaddaadaabdcaccdbcdccaaaddddabccdcdcaacbbddbbdadbbbcbcaaccaaaaabacaacbbcabccbdababdadacbddadbcbaaadcbacccbbddccdaddcdbdcaddddcababbabcbcccaabacbabaccaaabdcbaabccbccbaccdbddbbcaddacbdbabdccdcadaaaadcacbaddcbdabbbdbddcadacdbdadcbbbdcbbbcccaacddabadaaabcbadadbdacddcbbdabbabdbbcbcdacaacaaddaddacadcbbaaabddbccaacdcacaddbccadcbbdcccdaddbbaccbaaaabcccbccbacbccadbddcaacbdabadddbacabcddabbdbbbbcadddbdcddbaaacdbbbcaadaaabadbbccdcbbcdcccbdccdcddadadcadcbbccadbacacabbcaadbdaabacbddbacbaacddaaccccaaabbaadbdccccdaddbbddacdbadcaadccdbdcbddbbdacdbccdccdddabaddbacadddcabccacddcdddbcdbcdcdcbcdcbbbbacdacbdaadbdabbadadacddcdbbbcbddccadcbdbcaaacdbcbbacbbcabbcdccbcacaaadcbdacdaabbdabdaadcdcbbdddacbbcdbdaccdcccccdddccaabcdcaaabbbcccbbbaddddcacbdcaadcaacccccdbaadcdbbbaddcabadbbbdbacdcbbabcbcaadbbddbcbcddcbbabadbaddcbdadacababcccbabddadbdccacdcbbdacdcdacadacccaabbbcabccaababbabccbbacacaaddadbddcdbdadcdacaadadbcdcbbbcacabcabdcbabacdbadcbacabdbbadcadacdddbcdbdcdcabbddacbdabdacddbaccacbddbdbbbaacbadbcbacbadbcacaddbbdcbdaaacbdbbddcbabbbbaabcccdddbbcbddccdddaccbabcadbbbdabbaadababadcbdbbbddcbcccacacccddbdbadbdbcbbcbbbdaacbbdabdbadadacbacdbbaabbbcbabbdaccaacdcdbbadadabddbabdbbaddbbcdadacadccccaabcabdcdcadcaaaaacaadadcaaccbbddcacddcdabbacdccbacacbccaabadbbdbbabcbbccbacabaddddbccbaaacadbaccbadaacbcbabdddacbaabaaaaccaabdcaccdcabbadbcaaabdcccaabdccddddccddcacbcdbccddbdaabcadbbcadcacdbdbcdaadacaadaabccbaacbaaacbcaaabcaddcaddaddccbacbcadabdbbacadcdbddbcccccbadcaccdbaadccaadabcccbbdcbadabddbddbccaddddabccccdcbacaacdbddbbbccaabcbdcbbbcbccbaacabbcccaabcaddbbccabdaaacaaccbdbabcabbcadcaccbababadddbcdacbdcdbadbdaabcacbbdccbbabacbddabdddcdacabcccddcacdcddcdabcacaabccddbbaaacbcacdaacaaadcbccabbdaddcdadbbdcadcdabcbbcdbabbabdbacddddbaaddbbbbacbcabcbcdbdbbcacbcabbdacabbcbcbdbacbcdcdabdabaabbbababbcbcbaacbcdadbbddbcacbaccccbdadbadadacdbaccdaadcccabbbdbcddbbaddcddcdacabdcbacadabaddadddbdcdcbaaabbdcadbdbbcbadbccdaaababcacaccdbbdadddbcabcdcbdcbcbbbbaadcdcadbdcccccabccacbdccdccaaacdcaabacbcabacdbcabdcadaababbaaacadddbacaddadcadadbcacdaddadbbbccdcdaaaaacdcbbabcbbdabcaacabbacbbdbcdcadbabdcbadcccddbbacbccdcbbbacddccbccdababbabbbcdacbdcdbbbbaddacacddddabacadcdccadccdadadaddcbbbcaabddccbbadcbdddddddddacaacccabacbdcddccaaccddadacbdcaaabccdbcbcbccacccbcbbacbacdacaabacacbddbdadddacdcacbacccdcbddacccbdabdbbacdccbcbaaccbbbacaddddcaacaabdbbacdbacccaaccdcaabcddbdbccddcabbaaababdbadbddbcbccabcdaccbabaccdcaddabaccbdbcadabccdababdabddacabdbdcadbcbababcbbbabddccdbcaccbadbddbdbdcacbcdccabdcdbacacaaadabbddabacdacddababdaababacbadbcdccdbcccacacdcdababddcccbddddbdaabcaacbdccaabbbaddabdbcabadbcaadabdbdbdddddbadadbdbaaddbdcdcaabcacaabdddbdcacdababbdadabcccbdddddbcbabddabddadcddcadaacbdacdcccdbcbbaaaaaaacccbaacadcacdbdbbdaaccbdddabddbcadbdacdaaddcbcbcbaabbcbdcccacddcacdcbadddadaacbcaabbcdadbbcbdbddcccccbcaabbbdcabcdcbcbdddbdaaababdadbdcbddacdbbacaaabaccbddbaddabdcabacddabcacbdaccaabbaadcdabdcbcbcacddbcaabacadcdcddbaadbbccddacbadbcaccdcaddccaabdbbbdabbbcadbaacbdadcccabdbbccabdbbcacaadbdcccbdabdcababdbdabadabbcbacababdcbdcaaddcaaddbddaabdbabbcacadabddcaabaaadaacacbbdbbcdaddaadaabddcdbbdcacbdabaabbaddbdcbccdabbabbacaabdddaabcddbcbddabcbbacbbbcabbaddaadbabbdccaaddcaddcbcdaaddcddacbccddbddbcdbabddabdbdcadcbbabdcdacacabdbdbdcccbcbdbbadcdcdbddcbabccaacdbaaabaabddccaddccdbcdadddadadbdbdaacdddcdabcddaadcdddaacccacacacdaccbdaacabacababccccbbabdadcbbcacddddcdacdcdaccbbdcbdadabaadaaddcdabcacaaacbddabacadaabacadcacbbadddbcabdcbadbddcadabccdaabcbcdabdcdbccbacddbaabdbbcadaaacbadacdaacacaaacbddcbbdacbdabacaaaacdddcaabbdcabdcdddcadbdbabdcdacbbccdddaddcadbabdcbaddaacadbbdbbbdaaadaaababddbbbadbbdbccddccadcacaadcddccdcabddcbcabbcadaccacabaddbbdbdcbabaaacdacbcbcaadcaaacdaababbdbacbabddccbcadbccaacaaccbcddbadcdbbcddbabacdbcdbdcbaabcddbbacbabddccabadbcacaabcdbabcbdbaddbbbacdcacccbcadaccdcdbdbcadbdccdcddbacbadbdcabacabbcadcdacbbabdababdcacacaddacdbabdaaacdcacdbbaddadbbcdacbdddbacabbdbdcbbdbbcadcadcbbaaabaaadcadadbdcbdbabaabdcaccddaabdacdcdddbdcdaccbacddcccaaccbcbadbacbbcadbbbcdaadbccdbbdcbdbdabaddcacbbdddcdcaacccdddbabdcbcdabcaacbbadbcaaacbcbbbdcadbcbbbcdaccadadcccacbaabaccdaccdbdbcdbbdcaddaadcccaddbdcdbcddabacdbddbddbacbdddbdbbddbabbbdbddaddaacadbdbbacabdadcccbbbcdbcdddabdcabcdbdcddaccabaddcadadabbbcbbacabacdbdabacbbdbbdbaddbcabbcbdbdcacaabaabcbdbddaaccbcbddcbcacadcdbcabbabddcdacaadbdbddacbcbdadbabbcdbbdaccabcabaaccdcaaddbaacbbbbcacbddabcccdacdbacdbaadddaadccdbaadcaadcbccdaabdcddbdcddabbaabdbadcdabbcddddbacbdaccbbddbbdbbdcdacdaadabbdabcbabbcaaabcccdbdabbdcdbbccccbdaddadbcbacdbaaddcbddabcadbcaddaacdcbdbacadaadcbbbdabddcacbaccababbacaabaacccdcbcbacbcbcdccbbcbddcbddaadbbcababaabbabbcabaabcbbabdcccccdaabbbdbbabbbdbcaccdbdddccbcddcaddacbdcbcacdcdbcbdacbcdcacaccdccdacadcabbdcbaccdddadbdbacdaacbadbbdbbcdcdbccccadddbcdadcddcaaccccacadcaabdbcddabbccccbbdcaadbabcbcddbbbccdddbdabacccacaababddabbadaadcbccdadaacddbdddacddcbbcdcaacadaacbaddcdccdbcbddcddbdbcadbdabbbbcaaaadccacadaaacbdacbcbcbaccaacbcbabbbbdbdaaaaacaddabdbcacbddddcbadcdbabdacabaacdbcddccbabcccbbacbbadcdadddccbacaddbcdbccbcadbabcabbdcacadbcbaaacdaddbadccaaddbbbcabaaadaabdddaabcdcdcddcadbddbaaadcdddcddcbdcacbabaacdcdbcdcbbcaaaddbbccbabbccadadbabbcbddcbabbdcdccddbdcacdbbbcbdabbaaabbddcdbccabbbaabccdcbdbcbbdacddabccbbbbdaabcabdaadaabccdabaccbcacacddbaaabccdaadbdbaddcccadbbcbdcddacaddbbcdcadabbccbcccbddccbacccbcbadabdddbabbcabdabacdcbccdbbbabadcdbadcdcacbaacbdacbdadabacbdccaaccdbbcadccbbdcabcddcbdcbcccdddcbcbdddbaadcadbddcdcadabbacccacaadcccdbccdcbacabaaaababddaaaadccadaacdbcadacacaaacdadbcadbbcbcdacaaaadbdbbaacaadcbcbacabddacbbdcaddbcdccaabddadcbcccbabcbddcddabdbdbdadbbcbbcbdcbbbbbbadbbccbdbdaaccbbcbdcccccbaddbcccabcbccdbaaaaccbacbdcddbaabdbbddbdacaaadcdbcccccbbbdddddacdbacbaccdccacdaababcadcddddbdddabdacdaacabbbabbdaabbdabbdbbcadaadbabcccbcbddaabbabadccccadcbaddabbdadabcdbbcaaacbccddaabdadaddbdbdccabacdadcbbddbcbacbdbcdcbaacacbadcbcddadadbdcccaabaadcdbdbcddbddcbbbbabddccddadaadcccbacbbaccaacacbcadbddaddbcbcccdccbaadccccbbababcbdcdbaabaacddccabaadaabddbadccccbaddddbbbdababbaddaacaccdbdacbbdbbbdabadbaadbacdcacccbdabbdaccbdcaadccacdabaddccbccbdacbbabaaccbacaaabcbbbbabadabdacdabababcaddacbbdcbdddbaabbddbbccacbcbacdbdcdaaddbdcdbaaabdaaaabbdbbbadbdbdaacacdcacdaddacacbbddbdbdbabdcdbbbadcabacdcbadadacbcaabaddcdaadbcdbabbaccadadbcbbcabaacdbbbcdcadaddcabdbddacaddcddaaccaabccddaabbbabbbcbdbcccadbdddcbbbcaabddcdcbabcdbabaabbadabcbddcacbbadacbdcbcaddcccdbbddacacccddcccbcbccddadddcacbadcdacbcccdbcdacaadbdbabcabcdbbaaaddbbaadbbaccdbcbdacbbcadbacbaacdcabaaddccababbadbaaaabbbdacdaabbdabcddcaabcbcdbaadcdacbaabccadbbbbcdabbdcbdacacaaccdadbccbcabcdaadccbbdbdcccbbdccadadddadbdbabcbdaccbbadaddbdaabbbcdbabccaabdacadacaaacdbcbcaabacddbbcabcdadbadbdbcabdbddbcaadccbabbbcadcdbbacababdaaaacbcdacdccabbdcbdddadcddbdaabdcdbddacdacacabdbccdccdbbdadabbdcacacdaaddcdbadddbcbbdabdddcbdbbcdddcbbbaabaaddcbabbddabcbcddbccaabddbaaacaabcdddddaadbcdcbcabadbaccbbbcdddbbaadcadabdcbbcccdcdaaadabcddbcbcccdcbcdccadbbcdddddbabbaccaaadbbdaadcdbdaccddabbdcbbdcdbbabbabbabcbdabcacdacdacbbbaccbabdbbbaacababccdabbabbdacdbbacacbccbccabcbccbdbdadadacdbdbccabcddccbaadabdadabbccaaadbccbbdcacabbcdcddbdcdbaddbdccbccccabbddcbbbcbcbdcadbcddcddcabcbbdadddbcdcbdcbcadacabbcbcddabababbdacccdbcccdabdbddcaabbcaccdadababcbbacdcdaaddcdcbbdaddddbccacaaccbaaaddabccadddcdbabacaadbacccbdbcbdbbbddbacacbaacccbbcbcaacdacccddaabdabdadbddddcbcbbdcdabbdbbdbadddaabcdadbdbdacbdcbabacdddabddccbdaacdaabbdcbccabbdbaababbaddbbcccaadbccadbabdcadadcaabbbdcdcaddcbabdacbccababaabadbaadbbacdaddbdbaddbdbbaaaddabddccbdcdbdbbcdaaccaacddbddaccabbcdaacccaabbdcbcccbbbacbdbbdadcbbbdbcdbccccacbdcbcbacbcabccaddcdbabbdcccbacbcbaadbabdadadaccbdccbbbcbbadbcbbbbbcaaaaaaddbbcacccacdccadbcbcddbaacccdabdbbbbaadccbaccbadbddbbabcbaababcbcbcbbbdcbdabbdaabbdabdbddddacbcabbaaabcccaacdcaccabcbcbbadadacdddaacddacaaacdadbbcbacabadddbcbbcbccaccccbabaccbabbbbddbdbcdcaccdcacdddbcaaccdddcdbbacdcdddcdabcccddddaabdccbbabaadbbbcdcbaaaaddcaadadbabcbcdaadddbdbdddcbcacadcccdbbcaddabadbadccababccddabbdbbaccadbcdabacadcaaadaabbbbddbcbccabbccbcbabcbbdaaaadababddcdcabbacbcaabbadadcdbddbababdacadbccabbdadbccdcbdbbdccbbabcdaacbcabbdbacdcddcbadbbbcccccdaaabddcddcbacdbacbadcbbdcbcdbcdadbcbadbdbcdcdbddccdcbbdbacdbacdcacdabcaaadcdbcacbcbabbccdcbbcddbddbaadabdadbcabacbcbcacabdacaababbcaadddcbcbdbbcdbbdbccadaccbdabbbccbdbacdcabcbabadbcbbdbabcbccaacbccbbaddbddabadaaddbcdbdadbacbccbbddbabaadcdacbcbcbbbaadcbbcadabdababcddabdcdbcadbcccbbbdbbbcacdcbaacbdcaadbadcabdddacbbabbbaaadbcbbacacdcabaddbbbadcdcdabdbabddadaacbddaccddcabdccaacddcbbdcdcbbaaaacabddcdddbddaadccbbccdaadaddcbbadcbbddbbdabaaabcbbcabdbdbccdbddaadbbdacbcbbababadcabdcdaacdabcaadbbadcabbcadccbadcbddcabbdcbbbabbabccaadadccbaaabcddbdcccabbadbbbbccddbbdcacabdbacbdadccbaadccbccacccdddcabcbaddaadadddcadddaabcbadcadacbcbbccbacabdbcacdabdcaacaaadcbdabaadaabcadacaddcddabbaccddccbdcbcdbcbdcaacbcaadcddcbddaabbdbccabdabbacbccbabdaaaadabbbacbcdababddccdacdcadddcdbabbadcacdcdaadadaacdbaadbcabcadbaddddcacdcdcabdcbcabadacbdddcaabccdbdddcbdcaabccbcbcdddadcaccdccddacccbbddccadbcbbbbdbcabdadaccabacacccbaabdcbbdcbaadbacaccdddccbddadbccadaabbdcbaabdcdbaaabddbacccccbbbdcabdcbddadadaaaccaddbbdbcbccdcaabdbdaaacbcadadbcbccacaccdadcbbcaaddbdbaadbcbaddbcbcdcacaaccdcaabcadbdacbbcaaacccaacabaacacbaabbbdbdadddddbacbdacdadabcdddbcdabbabbaacbddddcbcacccbccabacabbbcbdccadaabdbcabadbdacacbacdcccbaabbcccdcbdaaccdabbbaaaadcccaccacbdcdbcaabdbadbadcaddbdbadbbdabbdcddbacddcbcadadcacdcdacaddbaabdddbdabadbbdcabaacaadbdcbbadcddabadbdccbbbdcdcbbadacacccbcacdbdadcadbdbaccdbccdbaadbcddabbbbacbabdaabbcaabdbbccaabccddcbbacbbdacdcaddcbcacbabdbbaddacbcdabababbcddababbdbbbccbadcbccbcbadbaacddbbbdbbdbdbbbbcaadacccabdbbcdbaccadddabcbadccdbadbaadbdabaabddcdcbabadcddabbdbbaccaacdabccbaacccabaabdbbdbccbcdbbbcdcdbabbbdbcbacbbbaabdacbddbdcccbbbcbabaddcbdaddbdddbcdaacbaddacacaabcbccdacbcbaddbdcccbbbddbbdbbadddaacadbcbbddbccabacbdcaadcbbacdddcdbccddbbadbcbbbbbaddcabbaaabbbbcabadccdacdaaccaacbadccbbdcadcdcbdbbadbdaadcaacdddcdacbdcdbcbcdcdcacadcccbacbdcddabcccbcbabdcbacdcbaabcacbacaccbabdadabdbcaacdadabbdccbdcdabdbbadcdcbcdbbddbdbbdcabbcaadacdadbccbdbabcbbbdbaaaccdcaaaaabbaadcbcbdccbabcddaacdbdacbbaccabcabbacaabddbcadbbdacddacabccbdcbccbddacbbdddbbcbbdacdddbbccdcbdcbaadcaadcbbdcadcaccbddcacbdccccaaabcdaacbbdddcaccccddadbbadbbabdbdbbcaaadbcdabacbaaccaadcadbcbdaacbadaabcbdacdcadbdabcdaaddcbadaabdbbabcbdbaaaabadaabbbccdadcbbabccdbacbdbccdadadccddadcbadcdaabdacdbdddcdbdabacdccbcbaabdabbdcccbddcdabdccacadcdcdaccaaaabdacaacadccdaacdcbdbccdddbcaccddbcdcbbccbdacdcadcbaaccbdaababcaadacbbabacdddacabaabdaacccaabdddaccabcacbcdcdccbacdbaacdbdbaaccdcabacabddaadcaabdbcdbdbaadddcccacadddbbaccdcdacccdabdacbccbaadaacdcddddadaadcdababcddaacaaccbcddaacaddaaabdbadbcaadbdcbccbcaabadbbbbcacbbacbabdcddabcaabbbbaccbdbccbcacabdacaabacbcaabbdabbcaaaacbddccabdcacbbdbbacbdbddcabdbbdacaccbcdbacabbcabbbddcddbaaddbababdbddcddbabcbcbddacbdbdabcaaabbdccbbacddaaacacaaaabddbdaddbaaccbdacbdacabdabacdaacddcbdacddaadddbaddccdbbdaabcdddbbbbcbababcaccbaaabadadacdcadaabcdacccdcbdccaabaccbcaabcdcbdacdbdbbabacadcabcacdaaacdaccacadcbccdcdcaabdabbcadcaaacdbbcccbadcadabdbaabdcdabbaabcdbbbacbcccdcabcbbdccdddcccaddcbbdbcabcabcdadbbadbadbcaacbccdadbcdacadadcdccabadaacbcddacbdacccdcdaccaaacccabbdbcadccaadbdababbdabbddcdabccccbbcdcdcbddaabdaaadcbabcbababcacadbbacaccbdabadddabcdbdbdbbbcacacccabbaccdaaddcdbcbdaacbbaaadaddacdccdcadbadaabcacabdcbaadddbcacabccdbcbcddbdddbacbdaccadacaabcbccccaacbbdbabbccdcabbabbbccbdbcacaabcddbdbbaacbccbcabaacdcddbadbdaddacabbccabdbdaacbdababdadbaacbdabbcabdbbbbcbcdbdbaccadcdbadcaabcdaabbbddbdaaadaaacdacacbbabbcadbbcbbaaacdadabdcdbdcabacbddcdbdbdbcaccccaacacaadaaddacbddaacbdcacdacdccbdbcadbbccdabcbccccbcabcadadadbccdbdadcbbcadadbaacbdbdbadccdabdbcbbcdaabadabadacdcbdaaaadbbdbbbdddccadcdbddddcdcaaaddabdbbdbbabacbbdddccbabccacbdcabaaabacddacbdddbdcdbacababbdcddcdddadaacdaccaddddabcabbdccdcdabaadadadcdbcbdbbbaddaaddacbacdcdaabdcdcddacabdcdbabbcbddcbccabdccbcabcaccddbdaaddaadddcadbadbdacddbdadcaabaccccadcadadddcbdbabaadddabdacaccbbbbddadaababdaacbdcddacdaccdcadcdcdcbdcddaddccaddbbccdcadcaaadabcbabdabccadcacdadbadcbabacabaadbadcacdaacbaccbdbcbadaddcaaccbdabddcccacccbccdccabdbabdddbacbddbaccdadaaccddaccaabcaadabaadbdabdcbbdbdadcccbddcdaccabcacbdacccaddaddcbddacdcbcdabdbcadabccbbddacabbbccbcacadadbcccaddbabdbccacbdbcbbaabdccabcacabacccaadaacbccadbdbdcbdabcdbccacbadaacbbcabccbadcdddbadbcadaacdaadddbcbcddddadbdbcbdbccdcbccaadbbdabdddbdcbdaaadbccadcdbcbbabddbdbadacdcbabadbcbdadbdccaaaacdadbadabccaadddbabcccbcdccadcddbdaabcdbbbcdcaaaacdacccdbbddcabacdaddaaaababaabdcbbbdbcaaabbdddddacdbacbbbcbbcddbaaaccbcbaddddcdccabdadaadacbdaabcaddbbaabbabddddacddcacbcadbbbbabbdcbaacdddddbaaccabcdbcdaabcdadbaadaaaaccdcccccbbbdcddbacdccdadcbdbbababadcdcbbababbdcaacbcdcdcdabcdaadbbadbcdbaabdcaabbbabcbadccbbcdbcbdbcbcbdaadddccaadbababbbbccbacbdccaddccbdaadadabbccbcdbbcddbaaadaabaaabdcacdccdbcddadaaddaadacabddabaadcbabdaddadcdccacadcacbdbcbdbabcbcbcaccbcdbcaabcacadbdbcabdbcabdcacbadbcbaaccabdcbcbaaddbbdddabcddcaacccbacdabdcbacddcdbaacdacbdadadaabacbddaabdbdddaabddbdbcbdcaaadddccccaaabaaadbbbcdbabadbdbcccdcaddadbbabbbadddaaabdacddbaaddbcdaaccbbcdcaabcdddcbaabbcabbdcaaacdabaadddccaabdaabddaddcaacaddcdabdcabacdcddabccbccaddabbbbcabadccccacdccadddadbdccdcadcbababbddadcdaddbcbbcdabbdbbacccbcaddbccbbccaaabdcbbcaddbbddacddbbdbbabbaaaccacddbccaaadcbddcaabbcbdbcaccaaacdddbaddaabbcbadbabadbccbbabcaaccbdddbddcbbbccbbdcababcdcbcadacbdadacddbacacaaacacacacccbaaacbdadcdabbdaadbadaaaabbddadadcbddadcdbcbccbbacdabdbaabccdbcaabadcaaaacbcacddcaabdbdcaadbaccddbaaccbcabddcbdbccdcacbbaaabaabdbbccaaddbdabbadddaacabcbabadccbbcabdaabadccbadcbcbdaadcdbbddcbccbbcaadcaadbadbbcccdcbacdbabbbcadabbcccbbbcddbbaacadacdddbdddcabbbcabacadabdbadaaabaadddddbccacccbacccdadbddcddacaaaabdabcdcaadbdcadddcbdbcaaccadddabaaabcacdadacbdcdadbbacdabdacbbdadbbdcbbdadcbaabcddbbddcdbdddcbddbdddbddabdbdbaaaddbbabbddbcaddcccccdbcaaddabcddbbcdddcdaacbddbdcabddbacadaddadddbddcbbadacaadabcdbdaabbdacbbacdbcbccbbbabcabdcadbacdcbdccdcbababdbddccbcacacddbcacbcbdaaacbccdccaaddcbcbcdaacbbcbabbbbcdaacbcbbbbbacadcacbbccccacbcbdcabcdcaccaccaccbbbbbcdbadcbabccbdccadabaabaabaacaaddbdcdbccbcbcbaaccbbddbbddbcdacbdbccbcdcdbbcbdcbacdccbcadabbbdcaabbdbdbcbcbaadbcbbacbcddcbaddabccdbdaabccdbabcbdbaabbdaddbbaccaccaabccccbbcccaadcddacaacabcbabcadaddcadcbabbabbacadaaaabdacaaabbdcddcbabddcdcacaadabaaabdacbcdcdabccbcbbabddcadcacaddbdaccaaaacadbbbbcaaacadcbacdbdddadbbdadabbcccbbcbccadcccaabaccdaaccbcacbabddcddddccbabacbcdbacbcabdbaaaaadadcbdaadacbdacaaadcaacdabaacddbddaaaadbdcadbaaccdabddcbabacaccbcdbaabadacbaadcacbddaacbabcddcbacbbcabcbddcdbcdbcadacdaacdbdbcbbddcadababcadabaddccdabbbbddcccccdcbdcbdbdbaabcddbcbbcdcabbbbaadbdbacbacddbcabddadaacaccdabcbdacbcdcadbbacbabdcbaccbdbcbdadcbaccdbbaccaddccaccbdcbdaabadbcddacadacacaccccdcaccdacdcacacdbaadcdccadbacccbdcbaadabdcabcadbcacbbbdcaaddadbcccbabcdcaaaaabdacacbbdadcbabcdabcddaaabddaabcdcdacabcaadabaaacabbdbabbbabacdadbbbcbbdbddabdcbcaaaccdaadcccaadacccbdcdbbacbbcbdbcadabccacdccbaddbabcbacddacdabdaadaaaadcdbbbaacdbccacaddacbcbbcbacdbbcdcbdadbcadbaabdcdccaddabddacbccbdacaaaabbacbccabbddbbacddabbcbccbadbcabccbcdbddababdccaddddbbbbabcabdacacbbdbdbbccacdcdbbacaaabcabbaadddbdadbbddcaccaacddbcbcddaabbadbdabbddbdbbdbdacdbaacdabcaabbabcacabbcacbcabcbdcdacacbcbdbabbadcabdbcacccdbacdaabbdaadbcbbcdbabbdadcaddbdaaabdcbaccbabcdcadabbddadcadcbbadacdbabbddacadccaaacbcdaabdadbbdbbacacacdaaacacadabcccdbabbdbaccbdbadbbddddddddbdbacaaaaaadadccbbbcaadbbcabadcddacbcbbaaadcacabaaddbadccababcdaadbabdcbacbbbdaadcabbacbdbddddcdbdabdbcaadbacbcbbcccadccbabcadaccabcadbaddabdbaabdadbcaddacadbbdaacbddcddabcdcbccaddcbbcddbaaacdccdbdaddacdcacacaddbcabadadacabbbbdcdbbabbccdddabdbaabaaddcaabbbbacbabdadcddacadacbbcaddabccacbadccbcaacddbacdbacdcbadacddacdbbcccbccdbddbaabbdabdbbadbcbccbddccbbabcbacbaacadbacadcddcabaabcdaccccddbbcdbcaacaaacacabcddaddcadddbcbadcbadabcaacbbdaaaadaddccdbbbdbdbccbacbaabcadcbcabbcacbccbbacdddccdccddacbdcacadbbcddadcadbdcadbbdbabbdccddcdbabdbbadcbbdbdbccdbccbcbbbccdbbbdcacbcdcdccdadbcdababbdcdddaadcadbabcbcababcbbbababcdbcaccccabcbaadacdadaaaabcaccdbbbdacbbcdbdaddaaacbaaadcdddbadadaadbbadaaddacbcccccbaadddadaadddbbdcdbbcbaddbbaacbdcbaaccadddcbbacbdacaccadcbdccbaacdbdcdcbbbadcdbaccadcbabddbdbdccbcababadadabcabbcdddbdaabdbccadbcaabbaccddcdabacadbdcdbbdcbdabdabdcaaacacabcddbacdadacccaabadccadcdacdadbbbbaabbccacdbadcdbcacdcbcbbdbbabaabcbbbbdaabcdcbcacbabcdacbbaadaddbaaddcccabbaabadaacccddcabdcccccbdbaaabcadddaaadbbbabdaacdaadcbdcbbabadcccacaacbadabddadcdcddbddbbbaabcbdadabbabdbcbaaacaabbdbbcdadcbcbcddddccdcbdbcadcbcabbcdbcdabbabbdbbcdbbacbcbabddcadccddaddddbdbadaadcbddccccdacdcbacddacdaccbbddcdccdcdaabbbaccdaabddddaacdddcbcbadbdccaaacddcdcbadaacddccdcbbdacbcacbcacddacbbbaabdbdcdabacacaabbcdaabcadadacbbadcbdaabaccccbadddcabbddbdddcabdaacccbddcbdbddaadddcadbbbadadcbdbcdddcadcddcdcaadacdccdcbdacddddbbcbdbdbcbdacadbbacbbacbcdadcbcadbcccaacddcaaccacdaacbdbdabccbabbabaabdacbdabccadaacabbcbbdaccaadccacbcbddbbcddadbddbacacdcbdadbdabbaabcbbdcadabbaacdaaaaccadacaababbabbbaccadddbcbddbaabbccdddcbdaaadbdbaccacadabcddddcbbabccddacbdbbdadadacbbcddadbdabaabbacadbddaacadbbbcaaaacccabaaaccbdacbcccdddcdadbadcaaaaacccbdbbdcccdaaacdbdccdcadbcbddabadbdbccbcbdadaddcabbbcdaacbdabacccdccdbdabacccbcdccbdbcbaabdcdadacaabdbdcbbcdcdacdccbbdcaaacbbccccbdadabacbbcbdcabcdaddaacaadbbcbbaacdabdcaccaacbcbacdaddcdaabddabdbbbbdbcabbddbaddbccbcbbbabadadbbbbbcbaabadbccdddbbcabbbacbaccacdccbdababbccacbabbcbccdbbddcbcabacaabddcdabbdbbdbcbadbcabdbccbbadbbdcbdcbccbdcdabcacdaadabcaabcdccabaddddababdaabdacccbadbbdaddccccbdcadddbbbcadacbcbaabddbaddadbcdbdbcddbbddbbdddddbddccbcadbabaccddbacbcaaabcbbbccacbccbcbccdcddbabaadcbdaacdacbacbbbcaddbdbaccabbdadcacdbbcdaccbccbacadadadccacdbcdaccaacbaccacbcbbcbccbbcddbddbbcabdddaaaacbdccadcaddbcccbadbbaccadaacaaababddcaddacdadbaabbdcbdccacadccdbddaadbdcaaadcbcbccaaadacdcccdbcdbdddcddaaadccbbdcccbadcdbcacbbcacbdbacadccacadddaabdacddcbcbdbbbbcacacbaddcbacbababdddadacbbdccdbbccaadabdcbdaacccbbcadcddddabbacaaabbdcabbcbdcbdcdacbdbacaacccdcdabbcacaadbbaabbcbddbccaddbcdbbdccbacdcaabbabdababaddcddadbbdddccbadcdcacccdbcdbbaaccddcccccbdbcacdacadcdcdcbbabdcabddbddcacccbcdbacaacabdcabacabdbdcbcbadcbaacadddaddadadcdbcadbddbababcccbabcbacacacaacabbbcccadddadbdaabcbccdcdacbacabbcadcbcbdaaccbbddabdacdabdddbdadbaccacbdabccdadcacbccaccdbaaccbabbdbbbbbacadcdacdbbbdacddddbbbcbdcbcacabaddbabcdbbacbddcaccdabdcaddaadcccdacdbaccbbacabadabaddacadaadcbccbaccdbbacccabcabbcaacdbacacdccdbcccbddbbdccbdbbaabbcbcdcbdaddcbdcdbabdcbbdccdbabcbcdbacabdbcaccdadadbabcabacadcadaadcdbcabbbbddccccdbbaccdccdbbcbcbaaccccbcbdbabdcbccbaabbcaababdcaabddadbddaacbadcabbdabbaaccbabcdbbadbcddabbcbbaabdaccabbbadbadaaaddcccccccaccdaacdddcdccbcdbcbbadbbbdbddccabcaddaddbadddadcddddabddabbadcbcdaccacdcdcccbbcbbbdcabdcdacbccdccacdaadadddabcdabaabbdbbccaabadacbdcabaccaccdbddbcaccdadbaabadbdabccddadbcdadcdbdbabbdadcacddcddbdabcdabcdcbcabccdbcabbcccadcaddddddbbacccdbbcaaccdbaabdaccdadcddcdacbacbbacbbcbdabcacbaddadbbdaaaaabdbcddacddaccbbadabaabcdcacdcabbdcddcdabcadccacddcddabcbababbbcbabbdcaccdbababaaccaabcbddbaddddccbaadabdaddadadadcbcbacdacbdaadacdadadcddcadbaddbcbbcabdadbabdddbaaadaacdabcadacadccdcbbbdadddccccdddaaddacdbbdddbddbdbdbbdbdadbcabdaddbbbbcadacbccaacbccddbddabdccbdacdcaaabcbbddcdaaaccbccabbcdbbbcadbdddccdadbabbdbdadddadabdaaaabccacdcbccdbccacacbdddbabcdcbcaacbdabdbbcbdbcbbdcbdcbddbdddcddadaacbbccaddcabacdacdabcbdbbbbcbaadbccbbbadcbdcbdbcbbcdaaadcbbcdcbbcbbccddbabccdadbbbcdbdcbbaadddcdcccabbaddddbbcdcbbaabdbcbccdddcacbcbcacbdadcbdbdabbaaabccbbbcaabacdddbcbbcdaacddcbdaaaccadabcbcdabaabcdcccdbbadcacdbdbcbadbccbccbcddbbcdcadbdbcadacadcbbbdddcabccdcccadcddcacdddccbaccaabbcdcabdbdbcbdacdcacbabbbcdbaccbaadcbadcbacdccdaabbdbcbbddadaaaaadaddaadadcababaacbadacbcdabbcacadabadbadaddcaddcbaaabddbdadbcbdcaaaccdadbbddcbdbaaabcbacbbbbabacdccbabbacbacdbdacbaddcccadccabdcbabaddcadccbdbdbbbaaddcaaddbcbcbdbadbddabacadacdaadcddccadbbcbacacbdcabbbdcbbbdacdcbbaddabccdadabaacdabccaccddababddddababddddaccdcccabbddacddaabbcddbaadcaabdababdddaacaaadbcaadcccbcadbdbaabdacaddabbcbbcbcbadabcaccdddabcdccaaaadbdbaddcddccbcddcbaddcaaabcbcbaabbacdaacbdabcbbcdbdbbcadcaaaababbbcdadabdaddadccdbbddccaddddbadabaabbcdbcccadcbdcdcbccdacdacaabdbcdccbbccbbdadbaabacaaabcacadcbacaaaacdcaacddbcdbcbacaabbacccadccbbadaaadacbabcacbcdbadcdaabcdaacababbbdcaacaabcdabcbbbcaadcbbcbdacaaaadcccaabdcbbdadcbdaadaaaaacbaaabadcbccbcabdbadabcbbabccbbdcdaaaabadcddcbdcdadbbcdaacbcbbcacbdcbdddbaaddbcccccbddaaacbaddcadcdabcdacacbadbcabdacdcbcdaaddbbbbcdbcccaadaacabdcabaadcccaabbdbdaadabbcbabcccdaabaadbbbccdbdbcabadbbbcadaacadacccabadabdbbddccbcaaacbabaadbbbaacbbddbdaacbbbaddbcabddcaaaccbbbdabcbdcbcdbcbbdbadcbbadadadbdabaadadbcbcdacbcacbadcbdbccaacbbddbacddacbbcdbacddcccdaaddbcaadaacbabdabcddbaaabcdbdcadcabababbaddccdacabcbbaccdadbabcbbcbcddacbadccbabccdaadcaaaddcaaddddaaacabbcacaaaaadabcdcbcaadcabbacadbcaaaabacaaddbcdbcdbaadadccaabdcadadddbcdbbddbdaccaaacabddbddacccdadbbbacadbcadbcadaaacaacaaadccccdaabdcdadbbdacddddcbabbbcacddabdadbccbbdcbbddcdbabbacbcbacccbcbddabdadcdddcbadbabbcbdaccadcdddaddbbddcaabacacdbccccbccbdbbbdcbcbadcabbaaaccbbbccbdcaaabaccccbdcbbacabdddbcacbdddbadadccbaddcccdddaddbaaddcdcdcabdbbddcccadabdbcbcbcdbccddabdcdadbdbadbccbbcdacaddcadbcbbccdbdccdcabcccbdababadababaccabacdaabcdbdbbbcbcdadcaadbaaacddcaaddababccdcadcbccabdacbdadddddaccabbddbaccdbaabdcddddadcbcacadccdcbcdaabcdccdbdbabadddccaadbdaacdacabbabdabbcccaaddbcbabdbdabbcbbaccccaabbbbabccbcccbcbadcccaaddadcdddadbdabddaaacdaabccddcacbdaacbdcbcdacabdadaaccdddbcbdddbcaaacacabdaccdbccaadbabdbcaabbabacbdcabcdabdbcbcbaddddbcacbbdccdabdcdcbddaddcdddacbdbdbbcbbdbbbabbbbabccbdcbabadadaadcbababbbdddbccdcaccadabbcacccacaadbcccdcdabdbcccadaacabadccdccaacbbbbbabbbbcaaddcdcdabbbcdbddabcbaaddccbddacccddacbbabbaaacbbbdaacdacccbaaaadbdaabaadabbddbcbcbdbdcbbbacdacbadbadaccaabdabdbbccaacdcacdbbbaaddbdbadbcdcbdddbbdadadbdbdcdbacdcbabdacddbacaadbbbbaabccbaacaacccdcbdbcbacbdcddbcacadacbadadbbbcabaaddacacbbdccabaacbadcaadddbccdccaacabbcaabdddbddabbadbabcbaccbaccdbcabbbbddcccacdadcabddacadbacaabdcbaadbdaaccacadcdddbbcdbcbbdadbacdddcdaaddbdbadbcaddcbddcababdaaaadbacccaccadccdcbbdccdcccaccadbacadddbcdddcadcaccdadcdddcadabbccabcdbbdcbdaccaabbbbacacdcdcdccbadccbacddbbabdabdadbcaabccaaadbddcabdbadadbdabdbadccaaabdababdadbcaccacddddabcbcdbcaacbdbbcccdcacdddcaddcbadadbbacbdcaddbcbdbddacddaabddbbadbbbddbaabcabddbdbcccbcbbcddabadadbdbdbbdabdcdcaddccdbadbbbcbbbdcbdbacbccbbbccaadadcdbdbbbdaadaddddacadcccaccccaddbaabaccdcbbbacccbaadaadaddccdcbbbdadaaddcbaccdacabcbdccbdaacccabdadcadaddbcbdccbbcddacccdbcbadaaacdaabdbaaacadbbcbcdbaabdcccabccaddadbbddcbcdbcabbcdabccaacaccdacacadabdbcdaaabcddacbdcdcadbbaccbbccacababbcdadabbcdbdaccbacabddbbacbaadbccaccdbadcaaadcdbaabcaaacaacdddbbccccdabcadadcdccbccbdbddaabcbdbdadaacadbababbabbadabacbddaadbbbaccccaadccdddacaabcacbaabdccdcdacbbaccdacbcadbcadcbaacbdabaaccdbbaddcbabdbaddadbaccadacdcabaadcabaacbbbcaadabbbbbbbadccbcdbdabdddcaaabcacbcbddbbbbdcdabbaabdabcaacccbdcabddbaaaacdbcdabcbccbdcbdcadbbaddacdabcdbdcdcbcddccddddcdbcaaadcaddbbcabcddbdacbdadaddbbddabbabcddaaddcabacadadcaadbadabddccabcdcbddcadbdddabccdcbdabbddbdcaadbcbccbddbdadabddddcddbbdcbaacdddbaabcadddcaabbccdccbdcbbaaabbcbacbcadbaacabdbbcdbbbcdcdcaccdacbbdcbddaabdccdbbabbdbddcaacccbababbcdcdbbcabbbddbbacbbcabcadaadaadcddadbcaddbcddcacadcdabdbdcbbcbbbcdbaaabccdacacbbcdbabcddacadadcaaadccdaadccaddacaadabccdbcbbaadacaacddbacbaaddacdcbcddbadaabcaddcaabcababdacdbabdaaabdacabdbbcacddcbdaaadaccadcddbbacacdaaaddacdcdbcadbcdcdbaabaddcbababdcacbbcddcabdbbbbcabbcbccacbbddbbaaacbccbbbdcbaacaccccbbbcdaaddbbcdbbbadbaacaccbdbcacbdccabacabbdacacbabbbccacaabcddddbadaddbacadbaaabbbbaddcbcbdaccbccaddabcbdabcccabbdbbcdbdaabdddcabcaaadcbbaaadcdccdbabadbcbbadcabcdacdcaaacabbdadbbadaaaabbabccdbdddbbbcbbbcdaabdbdbbdabcbddbcadacbaaddadbccdadbccbdbbdbcccababbbcccbccdccaacdbccdaaaabaadddbcdbcdcdacbddabdadaaccccbddcaccbadcdbdccbbbaacdbacaabcbbaadcaccabbbcbbdadbaacdbbdbdbdacccdbbcacabbadcadccbcdcabacbcaddccaabcdbcbccadcdcdcadbacadabccacdbccbbdbcddbcbadcdaabbadddcacbacadabbbacccdcbaabaccabbcccdaabbccbdddabbdaddabcdabddbacbaadacddbaaddbdcbbcbcdbadddbdbccdabbbcaacabccbcacaadbcbccbdcadcbaddadbdddabbbdbbadcddbacabbaabbddbddbabacdbdaacacaddacbbbdaddcaabcddbbdcdbbbdcbaacaaaacdbddddcbbbcbcdaaaddbadadbccbbbcccbbbdacaabadcdabdbdacbcabcbccbadbacdaccaaadcbdddabcddbaaaadbcbbcbadbbbdacdbdccddbbcbcabcccbbabbdbadcadcacddcdbdcdbdcbccabccdcdaabdcabbadcccdadadbbddbccdbbbbcaabcaabdcddddccccdabbcdcdaadbabdbcdbdcbaccaabddbaddcbbbdddaadcadcddadcdabccbabbdbdcbccccaacbbaaadbbdbadbbcbabbddbdbcdcbcbdcdcabcaddddbabbbacdbdbbcdaacbadbdbacabbbadbcbbacdddcddcccdbdabcbbbbbdbbaacacbbccabdcadadccabdcccdadaadcabdccbbabcbccabcdbdccbdaacccdcbbaddadabccabbbacdbdcdbdbcdcbddddcccdbbddbadbbdcddbdbbaddaaaccdbdbbcababcbbdadaddbbabaaaccbbcbdddbcdaaadddacbbcdddcdbabacdaacbacddbbabbabaaaaadaacadaaaddadabddbcbccbdcabbbbddddaacccdaacdadbaabcbcaaabacaddbabacaaabdaadddddacdcbccacaacbcdacaaacadacadcdbabbbabcdcabadbaabccdbdcacdccddccdbdbcadadcdccdacacbbaabacdccddbcaaacabbdabbcbcacbabadaaccbabdbdddcaacacacbacdcdaadadbbacbcbcdaacdaadacaacabddbbdbadaddbcadcccdadcdbccadaacbbacddabcdabadcacdacbdcaccabbacbaaaddddbcbaacbaacbbdcbccaadbccbabcddbcddacddcbdbccaabbadbccdcdacdbccbdbbccddccccbcccddbdaabaacbddbdabaaacabddaaccccdcadbdbdabaccdacdaadbdbcbdcbbaaddadaacbaccbbabdcccbaabbcddbcacbdadabdaaaddbcdcdadddbbbdadcadbaacdcbbaacaddddcddcaaccdccddcbcdabcabcbbbaacabcdbdbacddcbcaacaccddabdcbdadcbbbababcabcaabbdcdacdaadbdbacacbaccabbabbabdaabadcbddabccacbdaabaaadaacaccbcaccbbbadaccbdccdccdbdcdcbcccabadacabbbaacabcdcccdadcbddadbabccbcbddcadcdacdbbbdcccccbcbbadbdcbadaacccbcbabaadaabdcbaadcaaaaadbbdcddcdbbbdacbbcbcdbcdddacccbcdcbadabcaacaababdbabaaaacbbdcddbcdbaaddaaccdabdcadccabacbbaacadbccadddacaabbaddddcbdbccbadbdccbcadccddadbcbdcdcdadbacabacbbddaacbabddcbccaabccbdcdbcbcdbbbcacccbdbadadcbbccddddaabbaddadaadabbdacbabaccabbccccaaadbcccccadacadbbdcdbadbdacaadadbccbabddacabcadbbbbdddacbbdcabdaccdcdadcdaddbaacabbcbaababdabaadcbbaacdadddabaabadcbbbbbdaccadacabdadcbcddabdccdacddddbdaadcaaadbbbdbabcacdddabaabdddaccdbcabdcddbbcddcadcdcacccadddccbcccbbbdcddabcccccbaddadcbadcbddccabacabdbdbccadcdcbadbbdbdcbadcddcbaaacabdbacbabacdaadaabbdbcadddccddbbbbcccaadcdbbaabcadbdaadaacabcbaadaabbbdaadbaaadbbadaabaccdabbcddaacbdcbaddddbaccdadcbbbabcbcccbbdcbcddadcaadaadcbcdccdbbacabdbdacababdbdcaadbaabcddccacbbacaaadbaaaaacbbddbdbdcababbcdcdabbaddacaacbbcbbbdccccddddccbababdbaabdaaaccbcbbbcdcbabbadaaddabacadddbacbadacabcddbdcabdadcaccdaacaddabcbababacdbdcbdacdcacbbaccbbdaacaccbdbabddadbcabbdaabdadaccccdadbcccadcbdbadcdbdbbaaadcdbbcacdddabcacabdcdccbdabcdcabcdcaccdbcddadaabcacaaaadbdabbcaaaddbbbbdadbbabcdcdbaacaddcbacabaacbcdaacdbdcbadbccbdcadbaaabdbadccdabababddbacbdccaacddbdacbcaabdadbdcdcbccdcabcdbbcddccdbaddcdcdcadbdadadddbcbacaadbaaddddcddadcdbbacacbdcaabcddaadabadbddccdbdccbddbdacccadcbaccbdcacdccdaddcdcaadcccdcbaacccddbabaadbbdcaadddddcbdbdbbcbdddaaababadbabccbbddccbbadbddcacdcaabdcacadaccbcdcadacbbdaccbcbbdccadbbadcccdacdddaccbbdcbbaaacbbcdaabdccccdbcababddbcdbddccaaadaaddcdbbbaacbdbccdcbcdabddaabaadadbccdbcbabbcbaddaaacbbdcaddbbdccbaccaadcbbcbbaacbbadcdddddbbdaccaaccdabbdbcbabddbbcdbcabbddbcbbaddbdabacdcbddbbadbabcadcbacbbbbcbccaccbdddccbdcbacabcddadbacbdacddababcbacadacccadaddbdaaaabbbcaadbabaaddcccdcaadcdddccaadabbdadcaccaabdcdbbddcacaddacddccaacadbdbadcdcdbcbcdabbbbbadcadbabdadacdaaacbaddbdacccacbcbbacdabcccccccddddacddacadccdccaadcadbcbbcccbaaccccbadbbbccbadbdcbdacabccbdbdbcaacdadddacbcadcdabcddabdddccbadcdcacaabcdbdbcaaadadbcdcbabccbdbaaaababaabbacabdcdadcdbdcccbddbadccdaababaabbdabbbcadcbbdcaadcbaabdadabcdaacbbbaddccdddbaabdabddaacaacddbcbbdccbdaccdaadcbcacbdddddbcaabdcbcbcdaccaacccbbcdcbcddadbdaaddacbdacbccdccaccaadacdacbabcdbcbccadabdcbcdcbdabadcabcadccbabbabcaddabbddbbcabdbdbaccadcdbcbaacaddbadbadccbbcdbdbcdbaadccbcccbccaacccddddcbbabdadaccacdabccbaabbadadbbadbbadbdcadbacbabcaddcaacaddddbdbddbdcbadcbbddcbacaaacdcbbbddbabdadbcbbcdbccabccbddddbadabdbcdddbddabdddadbdabbbcbddbccaccbbbacdcacddcaacbcadcbcacccdbcbcddcbaadcaccbacdbcbcadadcabbcdcaaaaaccbbbaccabbccddabdbaddbddcbacdbdbbabcdbddacbaddcdcdbcddaddacccaabddcdbcbcabaccacadacccbcdaabdcacdaababbcdcbccadcdcdadddcddbacddbabccccbbdccbabcacabdddcbbdbbadcdacbdbdbdabaddabdbbbddcdbdcaccdaabacdbbcddcaadcdbdbabcbaddabdcbbbbddadadbcbbadcccdddbcadccbacdcabddcddbdaabbcbdbbbacbdbdaccacccacaaadcadcddaadaadddbcacbabccccddcadcdacbbddbdbdcbadcbcaadbadaacdcbaadcdddcddbbadcbacdcaaabaabcdcdbdaaccbbccaaacabddddadaddbbabcdbbccdccccaccbbdadccbdcacdcadcaaaadcaaacdaddaaabbbdcbbbbaadddcbaddddaaacaadcbcbbddbbddbdbccbcadddacbcbcbcbbabaabddcaabccadcbbaadabbbbadbccaaabcaaccaddaccacadbcadcdcdcbacccbacabbdbaabddcbcbabccabbabdccdbbccbccbdaccbbdabbdacdaabccaadcdcaacdbccadbbdcdabdbbabddbbdbabdaaabbbddcaababbdaaaaaccacdacababbcaddaaccabbdbacacddbaaadbabdaccccaacdabccbdcaacdaadaacdccccdcaabacdacbaacdcacacaaacaccbaadcdbdbdbadacdcbdcbdbadddbcdcdddadbbbbbcdababbaacdacdcdbbaacdbbdadbadcbaccccccadadbcbadddccbbadcaddbccbdddaadcdbdbbbcbddbdbbbcaacdcdcbcbaadcdadcadcbdbbcbabbbbdddbdaddbbabcdbbcbacacbaacbdaaddaaccdadaccbbcdabbbaacbadbcbaaaadbadcbaaaabadaabbccbacdaaaabbdcbdccbdbddcddbcddcdacbabacadccbadadcaadccadddacbdbdbcacbccbbdacdacacbbabbadadcadcbaaaaccdcddadacabccbabacdcabaacbdddcdcddccacadbacdbadcbaddacdacaccddbaabcabdddcabdacdddabcbabbccddbabdbbbcabcaaadbdadddaadbdacdccacbdadcaccabbadbdabbbcdaadcdacaaccddbbbdaacababcdacbccbabadbbaddbdaaccadcdacbcbadcbcbcdcdcdcddbadbbbaaaccadbbcaadbdbddabbcdaccbdbcabdaaaddaabddbddbddddabdcaaaddaabcbdcbcbdbddadcccbacbbbbdbaacdbbcbdbbbbaaaddcbdbaaacbdccbabcddddccdddbcccbddcbbbdadabbbacdadaccbddbcbaabddcbdaadbbdaadbddbabbbbddbacbdccbcdcdabbacbdabaabddadbcdabddacabdccaabcadbdddbddcdcbacbacddabbcccbadcbcbbabaacbacdbaaddabcadbdccccabadabdabadccbcbaacbabdcdcacbadcdddcbbbacabaaaaddabcbadbdcbcddbcadbaddbbbadbdccbbdbbddaadacbacbbaddacdaddbabbcdaacaccbbabdbaabddabcdbbaddbbdddbccbccdbaacbaacbdccadaaaabbababbcaddcdcdbadabacacbdabbaadccbbbacdbdbdbbdabcabcadbcaadbbbadcaddcaabcdacbccaadcbcdaabcbabbaadbdcaddcbdadaabbbabacdddcdcaabdbbabdbbbabaacbcddddbcdabccdadcbbadcdaaaaababbacacbddabddbdbabaaaccbcbaadaaabbcdadacaccdddccadababaaaadccacccabcddddaaabacdabdaccdacbcaaddbabdcaaccdcbcbbdcaabcdcdbdaadcaabccaacbadbcbcbdcabcbdbcbcacabcddacdabbdbdbababaddbbdacadbadabbcbaadddbcdccababdadbccbddbaacddcbabbcacadbbdcddcdbdbaddcbbbddddccacccabadddcdcddaccbdbcbaaacabaabacbababcbabdbbddbccbcadcccdacbcaddacaddddcdabaacbdbddcdcdabcbacdbbdadbacbbcdbccbbdcddabbccabadccabddbcbbcadddcddcbacdacbddabcbdcaaaccabdbbbbdcbcdbdabccddbbbbadbdbbbaacabddabbbcaaddbaaddddcdadcbcdbdabddacbaccabddbccdbccbdcddddccddabbcdcbcdadacbabddaaaacddacdacccbccbbbcbacdbcdaaabddcbdaabcbddabddaaaabdbaccbbccdcdcbbacdabbcdaccadaadcdcadaccbbabbbdddbccdaadbabddcdabadbaacbbdcbcdcaccadbcccccddbdcacdbadadcbabdaccdacbaadcdadaadbdaacacabddbddcddcbbdbddcbacdbdbacadbcddbadcacccbaaacdabbacacccbaddccbaabaabacdacccabacadbaccdbaaadadccddabacddddababccaacdbccbdabcacaddcbccbdbdbdcdcbbabdabddbdccdbdcdbccbadadddcbadbbaacdacabcbbdcdbbcbababaababcacbdcacdaccadbcdacabdaacbdbcdabccadadddbbdaccdcadacadbdaabbaacdddbbccbdddbcdcddabadaccddaababbbddddacccbbbbcbddabadcaabccbabacdabbbbddccbdadbabaddabdacbcbddcbbdbdbbbdadadcdcbddadccccabadaccabdcbddadacabdcabacabdcaadbadcdcacdbbabcdaaabcacdaadcbbdbbdcccddbdcaababcadccbaacbccccaabcdababbaccddaabdadcadcccdababadbadccdbccdddbdcddbbabcbbddccadaacaaadbaadaaabdcabbbddadcddaabcdbbdddbdabaacaacaddcaadabbbbcddabdabbbdabbddddadbaaaddbadabbacbcdacadbbbacbcddbbbcdabaabdabbddddbccbbadbdaddccaaccbaccddabdcdababcbbcccbacdababaacacaaadcbbddddcaabcbddcddbcbbbbbcdddcacabdbacdbbcaabbddaccccbcbbddaabdadbbcccdaaacbbdcbbcbacdbadcbadddabaddbbbaddcbcddbaabcbbadbcbbbccbdacadbbdcddddddbbabcbcaaabbdacbddadacbcabdcdcbbdccdcddbddddbaddcbcdbcdbbdbdcaabbbcabcccccddcdcdcccdbababacbdbdcbadbcabdaaddabbbcbbbabbabdabccdaddddbbcaacddacbdcdcbbacccdcbcdcbaadcdbcbbdaadadcbcabbabbaaaccacddcdbddddbadcdcbddacbdbcbcbdabbabbacdcaaccdcbcbaadccabadbadbbbadddaccbdbabcdacdcdcabbcbbcbdaaaadbbbdabbbabaaaaaacaabaccccccbababbccddbdddbdccbccbbabacaadbbbbdacdbcccaacbbbbbabbcdcdbdcabaacccadbcbabddbaabcddddabadcdaccbdbadbaadaadcbbcabcddcddddccbddbdaddbbabccbabbcbdaccdccaacbcaccbaadbdbaccdcbdcaabbcacaaccbdcdabacdacdcdabbacbacbccdcbbddcbaacbbddaddcacabdcbaabaadbddbdcdddcdcbccdadaddccbaddadcdaccdcabadabcddadaddddbbdabbbdddcbbaabccdcccccabcacbdcdbdbdcabaddabdcdcacccacdccbccbdcadcaacdbaabacadbbcbabccaaacbaacbbddbbdabbdcccbcbabcbcadcddddbcbaaadccccbcdabdacbbccbbbcbaddaadcccbabdadcbacabaabacaddadcbadcddcccbacbcadbbaccccbcdacadcdaacdccadcababbdaddaddbbacbbdbbaddaadabdcbbaacddcdaabccbcaadccabadbdbcaddbadbdcacaacdddaddcacddbbccacccddaabbabddccddbcdaacddddcbdadacdcabdbdaaaaabaaabaaacdcaccdadaddbdcbbaacdccaaadccbddadccbdaaadccbcbddbadacabccaabccddaddbddcacaddcadcbacbcacabacadabbdcacbbdbcbcdcabccbaaadbdbaaacddbdbbbdbbbacbcaadaaababbdacbccdacadbbbcdbcacdccbacbcabbaacbcdbaaabbdbdcdbdbacdcddacbcddccacccbbabadbbccdaaddcdbdbbbabdcadbcdbadcdbbdcabddcbdbbbacdbcdddcbbbdccaccbdcbccccbaaaadbbbabccdbdbbcbdbdccdaabbcadbcdbbaaccdcbdbbdcacadddabcddbdcacabddacbacaddddcbacbbadabbbaaddaaccbdaababbddabcbbdbcdccbbddcdddbcddaabdcaccdbdbccaddaabababbcbabaabaababdbbadababdacbccddbbacbadddcbadadcddddddbbbaccbddadbaaacccbabaaccaabdadabcbcaaaddabbaddaacabbabbdaacbccabcadcdacabcddabcbcdcdcccdbccbbbcaacbaabdabddcdbdacdccababadbadadcbddacabdbcaacbdbdccacbbccccaacababbcbcabbddcccdcabcaddcbdddbbabdcdbccbbbdbaacdccbcaabacacddccccbabacbabbbaababaccccabcdcdbabbccccdbcbdaddabbcacbbccdbababadaabdddacbdadbabddadddabddddbcddcabbcbddaadcbbcbcdacdbccbdbbdcbdbddbcaddcccbbcabadcbadcdacbcbadcddbbbbbcabaacbcbcdccdabadabdccabbacbdbbddadcbdcccacabcccbdddddbabbbbabdabcdbdbcbaadaccdcbbdbbdaccbbadccbcabaddacadacaddadbcababdabbabddbcbadacddcdcabbcbbbdbcbaaabbdccabdddbbdbbdbdbcddcbcddbaabccabdcdadaadbdbcbadbadbbdcbabbbcaccbddbabcdabbbbbdbcddcbaccdcccbcccdcabdcdaaacadadccaaabdbbddbdabaddbacbdbbacadadbadbbadcdbcacbabddabbccbaacbddbabbadcbcdccccabaccbabbaabccdbcdacdcdcbdcccadbcbccbbbccabcbbcdacdaacbdbdbccacbbccadbbdddaadddbdaccccbdababdaddaacaccaadccdcccdaddccddbbdabbcbbbddabdccdddadcbbaadddabdbcdddbababcbadddabdabdadcbdbdcddaddccdaadcdcaaabbacbdccdaabcabadaddbaddaccdaddbdaccdcccaadacaabbbcdaddaadabcadcccaacccadcbbaaccdabdccdacbcacbbdcbbcbdadccacabdaaacbccbabdabaacbbcacdcdbdcbbbbdabcbdababbadcdcaadcbadcdcbdbbbdaabccacbbccdaddbcbdbcddbcbbaccadadddbdadcbbbddcaccccccacdbdcaddcdcaadabdcbbadcbcdcdabadddabbbcdbcacdaabcdcddccdabbdcdcadbbabbcabadabddcbaccdbdddbccddcdccacdabadcbabbcdccbaabccacbbbddbcaaaadbccabbabcccdbdbcdaaadaacbadacddacacbdcdacbcbddbbdcdcdaabadadabaddcbaadbbdacacccdbccdbbdbaddbccbcaaaabcabdbbbaadaadbbccddddaaaabcadcbcdadcdcdaaadcbcdcdccbcdcadddbddabbdaabbbbacddbdacdbcabbcdddcbaccccdaacbbbacbdccacdcbbadaacacaabbcabcbdcdcbaaddabdadcdadbacbbbcaaacdbaacbddcdcabbaabdcccbbdabbdacbbdaaaaacddabcddacaaccdabcccabdddacaacdcbddbadbccbdabbcdddbcccddbcaddabbbcaddcbcdaccdccbcaabcbdaddaacbccbbcbadcbaabcadbaabaacadbabddbbcabaddcdaddcbbcbdbdbbadcbabdacaabbaadadbcdcacddacddbdabaccaaaabdcbabbcaadbddacbdbdabbaaaddacdbcbcddabaabcbbcbcbddcbaddaccdbbcdbcddaadbcacaadbcaacaaaaccadaabbdcabbdaaabcccddcbbccaadacadcbcaacccdbdbacbddadbcabcacaddbbacddabbbdbcbdddaabccbccdbdcbbbbaadbbdadbdbbadbddabadccdbdacbdadcadabbabbdbcbaabcabdcabdccbcdadbdcdcbaadcaaacaadbccddddbbadbcbdcdcbcbaabbddbaccbaababdaccbcdcacaaaacacdacabadacaabcbbbbacddabcbdcabddbbcdcbbbdddabcdbadbdbbbbcadcdbdcccbdacbdbccdacaaabbcaaacaaaacdcccccdcccdcbcabdcccbccdcdbdcdacbdcacdddadcddababbadcdbbbacbaaddddcadcabddbaaddcbbdaccbccdbbccaacbdcaddabdccdcbbbbccdbcbababbbaaacdbcbaaacdbcbcaabbabacdcbdcbcaccbdbbacddbcbbacdaccdbbdbdaacdddbbbdbddcdbbdabcadaaaaadcbcbbccccdacdaacabcadbdcdcaaddbdacdbaddbbabaadadbaaddcadacbddbbbaaadcccccadadbbdcbccdbdadcbbaacadbbdadaabcbabbabcdabdacddcbccdbddcdcdccccdbcbbacbddcbbabcccdadcbbddbbdabbdacbddbcaddbbcdbabbccabaccbacdddcbcabcbcacbdbdbaacacdcaabadcabbaddadabccdadcaaaabccbcacadacadccbaacdadaccbcccbabbbcddcdccbcdbcccaaaabcabdadcbcbadbbacbdcccbdaddbbdccabcdcbdbdccaacacaacacbccabacdccaadbabdbdaabdabdcbddcbaaabdbbccadbcdbabdccbaabdabbbadabcddaddbbaaadccdcbdbdbdbbbbdcbbcadddbbbccbddddacdcddadcaaabaacabacaddcaacbdbabcbdbdabddadbdbacbddccbaaabadbddaabbabddbacbaababbbcbdcbccccccbdbadbababdaccdcabdddcbcaaacbacdabdadaadcccbbaaadbdaabbbcaddabadacabcccddcbbbdcabcdbdccaccbcadaacadccadaaddaaaaaacaccbddbbadadbddccbddcabddbbbbadadccdaddacbabbccddcbdacbdcaddaacbddcbdadddaabcbabacbbcacdabdadccaacabdabbaaccdabcbababbddaacbcacdabbabccbabbadccadcabddadcdadccaccdcdaabbadcbddbdcbadbaabbcaaabdccccdbcccdacddaddccdbccdaccabddcdbadbdddaddadddcacdddaaadbccbcacdaddbcaaacdddacccbbccbbacabdbbcddabbdbdbccbdcaadbbbdbccbdbddddacabdcaaabdcdacbbdcbbacadaacccabddabdbbdacccccaadabcdabaccbbbaacbddcccbcabddaccbcbdcbdbccbcbbadbcbddccbdacddddbdabbdbaadbbcbbbdbbbdcabcbcddcdacdcbcbabddbacccddaabbbbacdaaaadaaacaacdabacacdbbbcbbcbbbaadaabdddaabddaddddddcaabbcbbbbaadbccbbaacccacdbcdaaaacbcbabadaadddbacacdbcbdadacbbdbbcbaadddbccadbdabcdcbacbbbddaabcdccdbbaaacbccabdccaabcdcabaddbdaaddaadacccbcdbabcabdccdbdddabbbbaccbadbccabadaaccadddaadcdbdcddcaadbaadcbadbdadbddbbcdcbdccabbbcdbdcdabaaaccccbdaadcdacacaccbbbdcbababdabdbdbbaccdccdbcdcabdbbbacbdcacabadacabdccabaaddcadccbcbcbbbaacbabbcccccaacaddbdcbdbccdabbcccdacccccacadacddccaccaabddacabcddbacddbbabbdacacaccabdcbbccdcbaabddcdcbdcdccadbbaaadbcdabadacbdcdbcaabbbcdaccdabbbdbababbaccbbccbadabcccbabaaaddbbcdccbddbbbccdaccbccabdadcccbbaabaacbabbbdabdbbddbbbdcadaabbabcdcdcdbcabddabccddcddaaddacccdcbdaadacdcbbccbaabbcaacdcdccdbbaacccbcadbbdbadcbadbbcbbdbcdbbccacaddbaddcbdcbdbaabcbdaabaabbbbccbddcddabdabdddcdbdbdbbbbabcaadbabbbbccbaddbbaaccadbbadbacdccbaadacdccbcddaaacdacaccbdccddcadadddbddbaccddacbbddabddacdcbbccaccbaacdcdcadddcaaacacdaaccdddacdbaabcbbaabaabcabacabddbbccccadadaccbacbacbbcdddcdadbdabbcccdddcacdbbcbcbdcdccdcbcbaddabbacdccacccbbccddacadcbddcdaaacdaacadaacacbaaaacaaccabdcadacdbbbabbacadbcaacaaaaccdcbbdadbabcbcadcddaccbaaabddccbdccadbabdbbddbcbcaaccbcacbdaccadbcdacbaadababadbbacacdbcabaddcadddbddaaddcbcadcadaabcbdbbaabcbcdcaadadbddbbdbdcadabbbccaacadcccbbbdccbdabcbaabbbddabbabcbaddadadbaacdacbdaaababbdcbccaacbcbbbcccdbcbadabdadbddacadcabcddccdbaccbdaadbddbcdccacdcdccbccccbdccccdabadbddabbdbaaaddadcaddbabcdddbbcdcbaabbddbacabcccdbadcdaaacdbcdcdbdbbadbdbdcdbbaadcdbababddbbdcdaacaadabbaacabdbddaaaabacbadadacaaacdbbdadabdccbccadddbbcacccbaaadcbaaabccbdcacbbbcbcddcddbcbabbcdbbcccddcaacbcacdababbbbccbccaaabbaddbdbdacdbabcdbdbacccbcbbcaacaacdbdccadccadaccdabbbacdadaaaadabdbcdcadbcdcabcaacdbbadbcdaaaacdccdacaccdadbbbbcddbcbbbacabdaadabaddaddcddadbdcccbadddcddbadcabbacdccacdbbbcabcbddcbaccababbccbdcbbdaababcadcababbabccdacadcdaadcbddcbdbbdbdbddcbabccdbdccabadacbcbaddddaccbabcbabbaadccccdddbaddbbdcbcdaadcbdcabbccdacdcdaacccdcaacdbdbcdbcdadcbdabcbccadabbdcbbdcdbbcccabdabbbaaccdabdbccadaadabbdccccdbaadaaddbabbdcabcacacbdadababaacbccbdccabacaacbdbdacdacddcdaadcbdcdadadcaacaabdbcbadccabbdaccdacbdddbdbccccbdaacbacdaddacbacabcacdbaaadaaadbacacbcadcaddcacabbcababdbbdcaaabaccddadabcdcdcbdddcdddbcaabbcccadbddbcbabdcdbacdaabdcdcdbadcccaddcacbbdcbadbcbbcbcadcdbddbaabdacabacdacbaaabdaabcbacdbdcbdabacacbccabccdaabdacbabcdccbbcbbdcbdadcdcbcbadbddabacabccddabbbbaabccabcacadcbbdccddbcdadaadcdcbdcaadaaadbababdaddabaddbbacbacddcdcdabcacbdcbddacdaabbbabccddacdacdbacdabaccadcddbabcbabbabbddccbadbdbbbcbcaaadccddbddccdddbdbcdcccbbcdbdcadaaccdddbbadccdbdabaaabdbbcbbbaacddcbbdabbbcdbaadbaabbdacbaadcaacaacccabdbdddcdadbcbbdddaabbddcaaccccbabbacdbcaadcdcadbbadddbbccaaaaaddabbccdcdddacddbbbddcabbdaaaccddcbaaddcdcbccbdddcbbbbacdbbddaabbcbcddbadcbabaddddbdcdcddbabdccdaacbcccdddddacadbadbcbcaabbbaccdcdbacabccdddbddcbdaacdcbcabdbcaabbabbccbaddadbbbddacabcbadcabbabdaccadadddbcccbdccababdddbdcdcbbbcabbbbcbbbababdbdabadddbdcbccbcdaadaaccdaaacbcdaacaaaabcdbbccaacbaaccdabbccadddcaabddcadabaddddcdacaddbdcadccddbabcdccbcbcdabdbcdadbcdbadadbaababdbdcadcddabdaaadcadadbcdcbddacbbcdabadcaadbcccaddbcbddbcdaacacdaaddbcabdcbdcadaddbccdcaaabcbaaabbabccadbdbdcdbbcaaccbaacacbccdccdbbcccdddaddcccdcbbacbbcbacccddcbbbccbdbcbadbacadacaacdacddabadddcabaaabbdcdbccacdccdcaddaaaadacccdaccbbdccdacdcacacdbababadcacacdbbbadbccccdbbaacabbccbaaaaaddaddababadbbabcbcaacbcbdcadbccddbcdbcdbdcccdcccbcadcbcaddaadbdaddadabdddbddcbcaddbdddcabbcdabdcbdbddbcadcaaacbbddaccbcddcaababdbcaadadacadccbdcbcbaabdbdadacbbabdbdddadbddacccbcbcaacbaabadcbbabbabaccacdadcdcacabcdddcddbbcdcaaabdaabbadabdaaabcacccbdbddaacbdbaabcbdbdabcbdadbbdbdabadadcdbabdbcaddaabbbadaacddccdaabbcadbbbcadbbcacdbcbacdaddbabadbaadbdcadadbdcbccabbdadccdbbbddbddcaabccdaabcddbbbcdacabacdcbbdccaaacdcddbdbcddaabacdabaccadbddaaacddcbcadaaaacaadcaabadbbbacdcddbbdcdbbaaacabdadadcbbdccdbbbcaccdcabdbcaacbbdbcccbcdcabdaccbcacbcccabdccddcbcaadacbbdcbcdcbdbbbbbadcabacddcbcabacbdbabbbbcddccacbbadbcbcbbbbbdcaaabdddabcbcdabacbabccdabbacaadaddbdacadbdcdddcbbcaacbdbbaacdacacabbcaabcbccbacccacacdcdccbacdadbbcbdabcaaddcdababddbcbbabcbababbbaddddadddaadbabbcacdcadabdcdbccdbdbbdccdbbaaabbcabcdabdabcaddaabdccaabadbabbadccbaaabbbdacccbbdccdbaabcbacccaacdcccbddbbcbdabacdbacababdbdbacccbdccddabacbbddabbbcbbbdbcbdcdaabcdbcadabccbbacabadadbadaccddcdacdacadbddadaaadcdcccbcbbdacdacaacbbbaddccacdddadbcababdddbcbbadcbddacdcdcaaabcbdcbcdbdabacdbcabccddbdcbabccacdbbcdbbbcdbbabbaaabadacbdddbbcabdacdcdbadbcaadabdbdddaacdddddbacdbbccacdaabcaddaddaabbbacbdbbaaaadcdbabddbdbcabbbaccdaacdcdabbbbdbcdbdccbbddcbacaadaacaadabbacdbdcdbddbddbdacbcadacbdbbacdadbdcadddcbabbabddbcbcdbdacccdbaadbdaaaabccbadbccbdaadabddadbcbccadbbaaabaccdbcbabdcccccdadcbaaababdaacaccddbcadcaabcbabdbabaadcaabbddccdaddabdbccbcabababbacdbbdcdcbcdaaddcdacadddcbcdcbacccaaaddddcddcadbadbcdbabcddcaadadcdbaaddbaacadddbcbbaadcaadadbcabcdcbbdbabcaccdbaddadbacdddccacddbdcdddacbacdddaccdabbcdbbabdcacccbcadddbbaddabbdabbbbcddcbbdcadcbcdcdbcaddacbbabddcbdbddbacccbccbbbacdaddadcadacbacacddbbdaddcdbbbdddaccddbbdcaddaaabdccbbbccaaadbbdddddcccaaaccaccdadaadbddcacdabdbabbcccacbddccadcccbdcccbbcdccbdcbabaabdbdaadbbcadddcdabccbdbdccccdbcbacbabddddadbcabcbddbdcbaaccccacacacdbbbbadddaacbdbcbbbbbbbddccbbbbacdbabbddabcbaaccabcccbabbababdddaaaaccdacdbdbbddababdabaaadcdcddbbbbbcdbdcbccbcaacadacdcabbdcbcbddcdbccbdcacaabdbcbcabadbdccdaddddadbdbbacbbaddbccadcabaccdbcbadbbdbdbcacbadddbbabacbaacbccacccdcaabaddbbcaddadaaccacdaaddcddabccabcdadddbaabaacdcdcbdcaaccbdadccbcdbadbccbabdbbdadbdaccddaabdcbbbababbbdbcaacbaaddcdbababdbbcdcdabaaccadccaadbadcaadbddadaadcbcdddbddaaaabdabadddcadbbdadacbbdcbacbbadddcddcddabcbacdacacddbddcccdabccccdddcbbcbbaadbcbbadcbadbdadacaacdbaabbddcabccddabcacaacbadaccccddbcaadadacdcbaaacacccbdcbcaabbaddbbdaaababdbadccadabadaddddbcccbdcdaadcbddcabbacbabbaddbdbddcdaddcbbdcccccbbaaddddbbbaabcbaabcbcadcbaabbbcaccbdaadbbbabbdddbaccbbbcacaabcabcbdadcadbcbddccdbbdaccbaacdccbaccbbcdcaccdadbaabbbcbdbabbcaabbccaacddccbbcddbaaacdcbbdacacbbbbaccbcbdcdbdcdddcacbccbdcbaccdbdcdcdcabdadccddddbcbdcbdbdaddabdcdcccbdbbbdcbddbccdcbbccabbbbbbcdaaabdccaccbdaaccdbacabdabcacddbcbcbbaccbbacaadbcadaccbaaacabbaabadbabacababdaabacdcbdadddbbbcccabbddacbaadcaabcbbacbacddacddbdcbbdddbbaabadababcbbcddbbddacdbcabcaabbbbccbdccbcadccaabbaddcaaacbdcdcbacdaaaaddbaaadcbabaaddccddcadcbacbdbabbcabdadcaaaaccbddabcdabdbacbcbcbbcbddcbbadccbaccbaaccbaccddacdcabbdcabbcaccbaccdcacbbbccbbbbddddddbbcdaacabbadaacaabccbbbacccbddcdccdacabaababcccbcdaddbcabcbcbdbccbcbabdabbacccbcbbbdacdcbdabcccaadbccacdbdabccadadbabdcddccacaccdbccccbaabbaadcdccbbdbdcdbabcacaabddadaddcaaaabbacdbaabdcabcadbaabaadbcdcdaaadabcbddcabdadccaaadbaaddcccdacbacabdcbcabdaaaaddcbabadbcbbacddacccbbdbdbcbbddabdbbbddddddadcbdccbcdbbabdbaabddacbbbbbacdbdcccabdaccdbbbbdabcdaccccbcbbbcdbaacaaaabccbbaadcabddaaaccadaabcdbbcacddcbaabddbbbdddbdbaccbdcbcacbdacaaddddaabddcdcbbdcadbbdccadabbcdcadccdbbddccdcbbcabcbdbabdadaaaaaddbbbdcbacadbababbcabbcbbbbcccbcacbdaabcdcccccaabddccbbdcaccabcddaddbbcdbdcbccadbcacbccadcacdbaccaccbcdbcadabbbaabcaacadabaacccddacddbaccbbcccaacacbddaddcccdccbacadaccababcaadaadbaababcddbdbcdadacbcabddaccbabbcaaccdccddabbcdaaacbcbcbbabbdbbccbcaccbdaaccabdcbbdaabbadddaaacbdbaadacbdcbacccdbdddbdaaadbbccdccdadaadbdabbaadbdacdcbbddbccdbacbbdcbcadbbdaaaacadcaaacdddadddbdadabaacadabdcdcdaadabacccaaccdbcdacbabbcabbdbcdacadabdcbdaddccdbdcbdcaccacaddaadddbadadbaacaddcabcbddbbbbaaccdcddaaaddbbcabcdbdbbdcadcabacadccacabcababddcbbdbdabdabdabddbcbccadacabcbaacacdabcddbddbcddcbbccddbccbdacbbddccbdcbaacdccddbbbadcabbabbbccbabccabacbdabcbcbcdabdbdadcdbbccacbbdbccdbbcddcbbcbaabbcbbbcdbcdacacdadbbdabcdaccacdbbccccbcbbcddbccaaccabddcdbddcbaccabdccddbcaaadadcbdaaaadcdbdcbcdbcadbadcdcaacbbbddaabcbbbbabbcdbdbccddacccacbbbdbdaacccaabcbbbbdbaabdbbddabdacbcbbbbdaddabdcddabbdabadacaacbccabcbaadaabdbadcabcdacbdadababadccdbaacbccdadbcdaabdcdcdcababddcdccdacbadadabadbbbdccbadbdcbcaadacddddadcddccbccdccabcccdcdadaabaaadaababdcabcacddcabcccaababddcddcdaaabdbbdbdabccaccbdcdadbacbcaaabacadcbbbadbdcabddbcaabccdccaadadbbcdbbdcaddccabacdbadcaccaabddccaadaacccabdadadcbdddbcadddccdcdcabdccadaacdabbbdbdccdbbcddccabbdabaddbcacddbcacbabcaaacabadaaabccbdbcdddcadabbddbcdbbcacbbabddcacabdccccdbddaaddaacdaaddacdacbadbcbcddddabcddaacdaaccbbddcdcabaabccdccdbbdcdcdcabdadbaddaadacddaadbadadddcbacdbdaabddcbddcccdccdbbcbdaadbccbabdaacdbbbabddddbcdacaddcaccabccccaacbdcaabccccaabbacabdcbdcbdbaabaabaacbcaddcbbdacacdbddbbdaddbbcbcccdbcacabddabcdbbbcadccdcccbddcbabbcbbbacddbccdacbcddcbadcadabaacbcaacbdbcdbacacaaaccadbaabbacbabacdbcaabcdbbdcacabdcbadabbdcbacdabbdcaabbcdccbddcbcdbbbcacbabbababcbcacdadcbbbbdcabdcbdcbabcccbdbbdabaaacdbaddbbcbaacacccbaabbacdaabdbdadadbcbadaacbadcadddbabbddcacadacdacbcdaccccbabdddaddacdbadbcdabbdabcdbccbbdabacccabdcabbbcccdddbbbcacdcbabdcdcadbdbbcbadcbdbcbccadbdcbdabdadccbaddbddacddcabababbcddacadcddaccbbabacdbadbdddcdacbbdadabbababadcabdcbdabcbcbcaaddbcbbbadbbbbcdaaabadccabccbaacbddddbccdccbaacabcbbcccadddbdcdacbdbbbdbdbaccabaccaadabdbcaabdadadbcbcbaacddbaaaddbacabbbdaaacabdddcadcaaaababaadaadcbdadacaccbbdaaadcacdbdbcabcbcaacbbcbbbdccabbccbcdcbabaabbbabbcddacccabdbcbdbbbcbbaabdacbccdabababdbccdacbdaddacacddaaccbcacaabaabababbbacddcacacdbdcbdbaaaabacabccccdabadcdadbbbacaddbddcdcbbbacadbaadaddaabdadbdbbdbaabccdacabadbadabcbdabbdacdcbbcccbababacccdabbbcbaccbcbcaabddcbababdddacdadbbbacabbbbaaaaabacdbbdabcadadadbcaabacdcdccbdcaacddadcbdbaaabbcaabacddadadabcbccdcaacdadbdbacdcccbcbbddcdddcdbadadccbdaabddadbdddababcbdcadbaadaadcbcccdaaacdbdaadbabdbddcacbddcadacdcacdbbbdddaaacddbaaaadcbacdcacadabdabaadaddabbdcdddcaabdcaddbbaacdadbdbdcdbcbdbabadcdaddaadabaadbcbcabddbdbadcabcaaadbbaddadaaabdcabdbdbcdcbbbaadaaaddcccddcaaddacdbdbadaccbbcaacabbbcbbddcbcbcdddbaaadadcbcddabcbcabbbaaabccabbcdbcadbccdbbcddcbdbbbdbcaaadbbdbaddddcdbbddbcacddbddbcbcdbbacdcddcdadcaaabadaacdbdcdbabcdaddccbccabcbccaacccbbaabdaabcdbdcbaddbbdcbbbbcbacdadccaccaaabcdacdaadccdcadabdbcbadccdccabccabaddcbabbaadbdbcccdcadbacdcdbacacababcdabcccdacccdcdbdccdbbbbcbbdcdddbbcacbabccbaaabcdcdadbaacddbaddacbcbdadccbcdbadbccaccbaaccdbcbcaadbacdacbbdcbbaaaacdcdbcaaadcdcdddabdaaccccdcbaddadcabcacdddabbaadccbdcccbaadbadbdabacabbcccbadcccabcadbdcbdbdcbbadcacbababdaabcaccbcbcabdbaabbcccbcbcbcddbccaadbabbbdbaddadaaddbaabcbbcdcbbbcdcaccbaccdcdcbccdbcabcbaabbbdabacddcdcacadbcaaadcbabdaabbcddbabcaadccbccadcbacabccbcccaadcddcccabcbaaddcababcacdaadbcbbabddbdddccabaddcbdbccdaacdabbabacdcacbbbbdcdadddacdaaacbbbcccabbbadddcbabadbcbbcabdccbdbacaaccbcbdbdaccdababddbbbcadccdccadaddaacbdbaaabcaacdccddaabdacabdcdcccdbadccabadcccdabcbaabdbbddabaaabdbccaacbadcdbbbbdcdadabddbdadccbdaadcbdcadaaaddbcdadadcdaadacaccabcddddccbcbddbdabbcadcaabbcbcdcbccbcdddadbacbdacbcacbabbcdaccbcacbcbbdddcbaabdaddacdbcabccbcadadbabbbcacbddcadcbcdaabbaaddcacadbcdaabaddaadabbababdccdbdabddadcbdaccbaaaaadcdbbcbaddacdcacacacacbacacddccbcddcbbcbdadabadcbcabacabbccdbdabcddadacbdddcdabadabcabaccbbcacdbbdbbcaddcccdccaddbcccbcacbabdacdabbbadbdadccdcbabdaddccababbbabcaadadcdbcacadadbadccdcddabadbdbddbcdacddbbaccdcdabbbdcdabdcabcaccccacddadccadaaaaaddddbdbcddcacabcbdbbaadadcacabddcbbdbdbdaaddbcaabcbddcacabcbbbcdbcbdcabcbcbcbaddacdddddcbadaacdadcccadacdaadacbbdcaaaddcdabbdadcabdccdbbacbcaacbdabdcdddbcccabcbdbbacabaacdaacbdcbcbbbcdcdccabaddcbbdcddaadadccaabadbdacdccbcabbdbbcccbcaabddbbacdddaabbddddaacdcadacbdaaddadaabbadbdbdccdabccacbdacacacabddbcbbdbbcdabcbcadaaaaadadbaadaaaadcdddcdacbcaaddaadbdbbccaddbbbcdccbacabcadbacbdbcddcadaaaacbbabbaabcacbaccbdabbaabadacabbdaabbaddadccabbdcbbdcdbadacccaccbdaacdbcccbadaccddbccaacbbbbbacbbaacbcbabbacddabbccddaaccbbbbaacabcacadcacdacabbccdcadddbccdaabaadcdccadaccabaadaabdbdabcbcddbabcddaacdbabbbdabbcadbccbaabbbdbbcdacdcdbddadbaacdaacacbbdcdcaabddccbadaddadaadcbccbcbbbbcacacccdbbccccddbaabbbddaaaaabcacaacaaccbbabbbdacbbdcbdabdabbacdbdbdbdccabadbbbddacbbddcdccdbbccbbdbbdacccbddccbcdabccaccddbdacbbbdcbbbadddaabadadabbcccdcbbacbbcddccbbabadabdaabcdacbcdadcadadadcbbddcdbbbaccbadbaccbbcaacbcabadcadbbaacbaadcaababdabbbdacdbacbbaaddadbbbdbadccaadbbbbcaddbacbddccbcccbabdcadbbdccbcbddddbcbcabbcbbadcccacaacccddcdcaabddcaddacacdaaaccbdadbabbcccababaaccdcbccbdcbbaacdddbdcabdcdbacaaaaaaabcdcbdcacdcbccdaadacdcadcdbcaadadccdbddbbcacaddabdddddacbdcdbabadababacccdbddbbdbcabbccdcccddacbabaaacbbdaddcdcadaaabdabadadccdbbddddaddacaddddbbcdacccccdbadccbcbcadcdccaadbbbdabcbaaaaaacbacbcccaddababdbbcabaabcabcdacdccbbbaaabccdcbbacbaaddbdadcbcbbdbcaacdadabcaadbdadbdcbbaadaaacacbabacddaaaddbdbcdadcccaddddaadcdabbbcddaaacddababbdbdabdaaacabccdadcddbbdabccdaacdbccddabcdcbcbddaadbbadacacdaaaddbdcdadbdcddaccdcdddcaccbbaadadaabdccbdaaacdcbbdaddddbdddcaacbcbdcbdabaabcccdbdcbadbbacacdacaddabcacbcaabdddbcdbbcadcdbbcbcdbccbadcbbbabadcdadcbaabcaccbadbcdcdabbddbbcaabdbddacddbddbbdbcaabaccadbdbcbdcdbabdcddcdbbdaaabccadaaccbccacaadddbaaaabbaddaddbadcddbbadccdaaddddcbdcddadbcccaccddabdacbbabbaaadbddaddaddadabcddccaabbddbcbabbcaacabdcbcdacdbadcaddcdddadabdaadddcccddbaacdacadaddacbccaacddcdacdcaaaacbacbcddabbddbbbcadadcddddbbadddcdadadbbdddcdcdbccabddbacacaabdcdabcbbdbabdcbbdbcdccacadddbbdacdbbaabcbdbddbcbacadcdcaddaaccadbdadaccbccbadabdcddbaaaabdbddcbacdaadcdbcadadbabddddaadddadabcbaddaaaadbddcccabccbcccdacadbadbbaccdaccbcacbcdbcbabbbcbbdacabcddadbbacdddaadcbcbbdcccbbbbaaadcbcadcbacbbcbabdacddbddcadabdbdcccbddbaabccdaaadbbdababacaabaabbdbadcadcbdbcccbbddcacddacbcacdbddadabdadddaaaddaabcdcbcabdabbddbbbabddabcaabaadccbdaddabddcdbadbcdcbaccaddddabdaacbcdaabaaddadaddcbcabbacbdabbbdcdddadcccadbbadcbcdcdbdbabdbcbddccdbdcccaddabacccacdabdbdadcbddacdaddcababbbbdcbccdbabdcbdbccdcddbbbdabdadaadcbdbbdbbddcccddcbddcdacbbcabdcacdcddbabadccbabdcbdcbcccdccabdacacddbbbccddcbdcbacbaacaaacccdcadbaddacddcacdbdcdcacacbdcddbadbdcaddcdaddddbdaadccbdabdccdbacbcdcdccacbacdcaadbdaadcbcdadadadcabadcaacdabbababcdabddbbbbddbabbccbbadbbadaddbbdaadbbcbdaaccbbbbbdcaacaacbbcbabdbbbacdbacdcdddabdadccadcbaacaaabcdcccdacbcacdcbcdadbcaaaccaadacccaccabbdbcbcddbdbabbccabddccbbbbdcabccdcddaadbbbacabcabddbccdadacdcadcdcdabbbadabdacbacaabcddcabacdbdbacadbacdaccacbbadbabadacccabcdbcbbcabdacdcbdcccdaabbdcaddaabcadbcdadbaadbbbbbbbcdabbaccbcdcddcddaddbaccabbacacaacdbdccabaabaacbabcabdbcbbdcbbacacdbdaccddcabacbbbabacdddbcbbccbbcdbcadaadccbcadadcbadacabcddaaaabbaadacddcbdacadcdbdbcaddcbcadadabcccaacaacbbddaaacbcdcaacbaaaacacabbabacbddbacbdbdcbcbbadababdcbbbdbdcdccdddaddcaddbaddaccbdcdddcdaababdacbadbbacdccdcbcbdbbdbcccbaadcdbdacaaadadbbdacdbbbbccabcdbcadadbdbaccaddddcbccacdccdcdbabdbbddcabaddbdabcacaaadcaabaaaadaddbcacaaabaccdbcadaaabcabaadabdcabbabdbabbbbaadcdaccbcadcbbdcbadddacdaccdbcccadbdbdcabccbbdbdacddbbdcabbdadccdbacdbcdddbddaaddcacaaadaacbdabacbbaaacccdcadabacabdbaabdcbbcccabacbbaccaabbdabcaaccbccadddcabcabbcccddcbabbaabaccbbddbbbbcbdcacabcacbdbdacaadaacbabccccddbadcdcabdccbdacaaacacadaddadbdddbbabbbbbdabacdbabbddaccbbaaadbcdccbaaaaadabdcbcbdaadddddabadbdcacbdbaaaddaaadcababacbacdacdcdaaabbbbbcbcdacddbaaccdccbbadbababadadcbbccacccdabbdbcdccaadabdbacbcadacddccbaddcdadcadcaacacaaddabbcddcacdccaccdbaabcbcadcacabdaabaababaaccabaadcbccbabcbabccabbccaccbdacaadcdacaddabbbbbdabcbddbabdcbdccbbccdcacdcbdbcccdddadccbdbcacdbdbbcadbdbcdccaaddcadacaddacacaabbaadabdbaddadccddcbdcadbcbddddcaabbdaadbbdabddacbabddbbaacdabaaacdbbcabaacadcacdddcdbbbdcbbdcdccacbdccddbdbbcacdacabadacaabccccbdcbccabcddaccddaacaccadcdcbaacaccacbdcdccabcacccbdcdbbbdcacbdddbccdaaababadddcaaacadacacdcbbbcadbcabbcdbaccbaacabacacdddcbbaddbbbcddbcdbcccbabdcdbabcabcaddccbbcbaccdbcdcacbbcaadddcdaadaacadbbadcaaadcccaacdadaacccbcdabddcacccddbaccbcabdccabbdabbdccdbdbcccbbcbacaacdacccbdabbabacbbaddcadacbdbaadcbdccdadcdabdabdadbbccdbdddcdddcbcbcbdaabccabddaabbcabddcacdcbcbcbabdaacaaaccacbcdcdabbcacaaabbcbdcaddbccacaccccbdabbcccadbbabcabbcadbbaccddbaccbacdbaaabccbabcccbcdcabcaacdadbbabbadcbdcbcaccdcbbdaabaaabbaddaabbcacbadaadababddacddcbbbdbdadaabdbdcabcadddcbcaacccaccdaacadddbaabdbabcddacdadcdbdcdbbcbcdaadababdadccadbaacaddcabdacacadcdbbbdadaacbdccbbddbabdddccdbcbbbbbcbccbddcdddbbdcaaaccaccddcbaccbdaddbcaccbbabdcaacbabaabdbcdccacccdccacdcacbbbccaaddacacdbbbaabcbbddbacaccacbdacadddbbbaddbcabacabcccbadaaabddbcbbddbadacddbadddbddbaaabdbcddabdcccacaadbddbbdbdadaacccacbcbddbcdbaabaadadacddcccccddbdabaadbbaaaaddabcabbcaabcbcacccbdbddadbabdddacbbabcaabcddaabdddaddcadcbaabcddbaaccdbadaabdcccdbbcbcbcaddcbbcbdcdadaaaacbcababacbadbdbbbbcbcccddcadcddaddbdddbdabdcccbbccbdddbdcbccbcaaddacdbaaccdbdadbdaccddbddcadcbcacacdbbadadbccabcbddbabdbbaabddbbbbcdabbddbbdacabaccbdabcdabbcddbdabaddacaacccccaddbbbccacbcabbdadcadbadbbacacaaaabdbacaaacdbbcdccdccdbaabadcccacbcbbcacabdbacadabccaddcbdcdbcabcbacdcdbadabccabacdaadacdadcbbaadbbbcacbcdaacadbabcacdcbccbddaaadcdabadcbbacbcddbadcdcadaddcaddacbbcbbabbdabdaadccaababdcbcbcbdacadcacaccccdbcccaabaaabadcdccadacdddcdcdaccbbbddbdcabbabcaddcdacdcbdaccbaabbcdddcdaccbdabcaaccadcbcddaacabddaadcdbaadacddbaacdbbbcdbbcbbbcabaabaacadbccaaabccdbcbddadcabcddbbbbbbadacabcdcdcccdaacabdbdabbdcaaadaaadcbcabaddcacaddbbbccbccbdbaaddbcadcabcccccdbddacabadadaccdbbcccadcccaabdaccbdacdabacdabbbcaaacbabcbddddcaadccadbbbdbadacdccdabadcdacdcbbbddabbbcdbaacaaababbbadbdbcdbabbacdbcccadbbdccadabcabdbaadcbcabaaacdadcdabbbdbcbcbbdadcdbcdbdadcccbbacbcdabbbdcccdabbaacaadaaccdbccdabbccdbacacabaadacdcbcbbbacbaddadccbdacbaacdacdcbcdacdabadbbbddacadcdcdbbbbbdacbbadaddababbbadadccbdddbddbaacabcbabadbdcabcccaccdacdabccbadaccddabdbdbaccbcbdbaabadbabdbcccdaaccaddbaaacadcccccbcbcaaaddbbcaccdaaacccabdbbacacddcbbdbaccadbbadbdcadbabaddcdddcbbdacababddbbcdadcdbcaddbabcdcbbddababbdccdacbacbbbbccbacdccbdbadccbdabcdaaabdcbcdbcaaccdaadccbadcbcdbdbddcdbdddcaabbbcddbddacbcbbdccaccadcdbbcccbacbcccbcdacaccacddaaabbadbabcbdbabbbcccdcdbbaadbbcbccdadbcbbdbaabcdabccbdddacccdcbdbaccaccbcabdcababcddddbaacddccdcadccdbbbbdddcadaacbbdacaadadcadcbaaaddcddcccbdddadbbdbdbdbaddbbaadadbbadccbacccacddabbbcaacbaccdacaadcdabdccddababdccaccbabbbaaaaadcddbdbbccdbdabcdcbcaaccbbbccddcaaacdcdcadbbbccadaabddcaaaacaabcaabaaabcdcbabdbdacabdaadaacddabbdadabddacbbcbadcbdcadcbacddcacddcdddbbadbabaadcbcabaaccbccbdabadbdabdccabcbbcbdccbadbbdbbcccbdbdabaddababadbadccbaabbadddcadcaadbaaccabaddcbcbdbaddbcdddcbdbcbcadcabccbbddcccbdbdddbdadbcbdaddcacbcaccbabccaccbbcbbcbbccbaccddadcdbdbbcdcabcaddbadcacddacddabcdbcbacacacccaabccbbddccaaddaaabcaadbbacdadbaacdccdaccbacdcdabbdaabdaacacbaaaadbacadcaadbcabcaadadcdbdbcbbdbaacddaaddbcadbcaabbbdbbaabadbdcaaabbadaaaabaddcadaccdbdabccbcddcbbccbdbcddddddbcdadabaaddcacacadbccabcacaddbadcdcbcddaccabddcbabdcdabbcbcdcaacbaddabccdaacadaacdabdbcbaccbbbcccbdababdbbcdabcbdcacabcabbaddcdcadbcaacbadcbdabaaccbcdaaadaaabbcdaacbddbabcabccaabadcbbbbacadcdcbacbcbdbbcdccdacbadcaadcabccbdbddbdddbbcbaddcbadbcacbcabcddcadacbaccbadbcbdcdcbabbbabdcbdacdaddcabbcabbdbabbabdadcaaadbcbbdbadbdbddaaabbddabaccaddccabacaacbbdaccdadccadccccababccdcccbadcadbdcccdabaacadbadabadadcdabcdcdbddbaacacaccbabccbcdcccaacacbdcdaadbdcddbbdbccacacaabddcaadcabbdccdccaaababdbbbcaddbbcccbdcbcdcbcabaacddbbadcccdadbadadacbadadbacaacbadcbbaccdaaaaddaabdbcaaabdcbcbabdbbddcabdacdacbddcadacabaaabbcdadadcabcabaccdddadabdaadbbdbbabacaababbddaacbabbcbbbcbadcbdbbcdcbddbbbabdbcbccadbabacbcadbdccdbbaabdcaaadcbbccdbbbbdaaaadcdbbcaddccbbaddadadbbbbddcabadacccbbacaabaddcbdadcadcdadcbbbdddcdadacbbabcbdbcbdbaadcbadacdccacabddbdacaabdcbddccdbdbadbbdaadacdabbbabbacbcbbdcbcbcaabacaabccadddaabdcbdbcbdcdabcbcdccaccacbabccbdcdddbcbdbbcbdbbdddbdbccdbbbdbbacacabcbdbccadbdbbbadaacaaaddaacadaacbacabcbbbadcbaadcddbbbcaacdbdbdcbdccbccdaacddddccacabcaccbdbcdadddadccaabdcadbaccaaddcdcabadcddabdcccddacbcbcaddaadadbccccdcacdabbbcadacbddaddbdabcdcabbaaddaacabbdbddacbbcddcadbbbddbcdcbabadccbaaaadcabcbdcabdccacdcbaaacbabccabdbdacabacdcdaadaaacbbdcaaaccdadcbcaaddcaabddbcbdccaabaabcdccaabcaaccddcdaacacdbccaadccaaddbbcdacdddbbcadccdcacbcbccabccdddacdcdacddabcadaccbabccddbbacbcbacbccdbddbddccdcbaddcdddaabbbbcadcdcbacababdbacbcbbadddcbaaadbbddbcdaccbdbcaaddadbcacbadaaaddadabbaababcbbdcabdcbccabaccbcaddcabdcaadbabbddaabcacbbcdbdadcabcbdabbcabdcbabbadacaadaacccdabccaaacadcacdbbadbdddbdcbcdbacbcbcbaabbabbbddcdaaabbbbdcbccbaadcddddbdccdbcbcddbccdcadcbcddddbbbaabdccacdbbacaaabbddbbaaadcaddbadbdcdacbddddbdbcbbcabbaaadcadacdbcdbdccccbadabbabacdcbcabcdcdbdabbcdcdadacccbbcbaaabcccdbacccbabbcccdcadcddadcabbdddcdcdcdabdabddabadaaacdddbddbadacadcbcbbaabbcbcbabaccbccdaccbaadcbabdccababcddcdbaaacbbcabbbcdadbdaaabbccbabbcdbdcaacacccdabaaacadaadaddcababaacaaaadaccaacdaaaccccdbaacbacacbcdcaadccdbacddacacdcdccdbdcacbdbbbcaccdbcdcbbcabacdddbccbacaabddbacbdaabccbbcdaaddbacdddcabcdbaddbbdbcdababadabdcbabdcbadaabcdcbaacaabcddcadcbbbacaccabcdddbdbdadbdabbaadaccccbbcdcddadbcabaacdccdcdadabbcabdbabdcbbcabadccdbbbdadcadbadbddaadbacadccadcbccbddbbaacdbdccbcaccbcbaaddcbaaddcdcacdbbabaccbcdbbcaccbcabaccccdbaabdcdbdcdacbdbbbbdbabcdbdbbdbdcdbaccacdbbbcccddabcdadabaaaacddadddccbccbcdcabcdcbbacabdcddcdabddbaddbbcadaaaaadbdaccbaadcabcaadcdbddcdadbccddcaabdaaadadccbddbbabadaddaaabcbdbcacaaabcbcbcccbddaaaaddcbbacccdbdddadabddbcbcadbcaaddbcdddaaabdbddbcbbccabacdbaabadbbcdaddcddaabbadcbacbacdddadddabacaccabdabcbbcacabbabadbcabcdcbdaaacabaadabddaababdaaaadbaaaddbcddbdbdcbadbacaddadcbaddaacabdbcdbcbbbacaccacddcacdccbabaccabdaacabdddcdbaccccbabbbacdbdcbdddacbbacdbcbcdbbaaaccacbcaabdcbddaacdbaacbbccbabccbacccbaddcccdcadccbdcccccdbdaddaaaadccacbaddacbbacccbbdadabbaccaaddcbbddbabcbbdaaaacddcbabdddbcbaaabdadcdbabddcbcdccdddaadcbadbccaadacdadbcbabcaccbcccabcbaabcddcadaaaabcdbcbabddaddbbbdabaadccddcadabacdbdbbdddbabdddaccbdaabbdaaabdbcdcddbccabdadbdabbdbcdabdaddbddbacbabbcbaacccdaacbdaabbcddbbbdbdcaaccdbabadccdabdbbabdabddadbabbddbdbabdbbabdcdcdacddcdcdddabbdcabdcdbbbaaddacbbcacabddabcdabaddbdccabdaabacdbbdcaabdbdccdbccddaccccdcaaddcbacddcadadbccbaadbbadccabcabbacbccacacccaddacbddddacabdbbbbdcbbbcdbadbbcdccaabcdbccdbcacdbacabbcbadbdcdcbacddaacbdaabdaaacbbdbdbdddbcdcbbcaadcdababcaddddacdbbcbddbccdccbaaaaacbdaacabacdadcbaabbbcccbcaaadabbabdabadbdcababdcbcadcdbbccaabbaaaccadddbccbaaacbadabbddbabdddcccddbdcaacacccbaaddaadaddcbcabbdddaababddcdcddddcdaabdcdbcbdbcabdaddccabdbbbbcabbbcddbabaaaccddacdbadaddcdccddacdcccbdbdbdaababcbbbadcbcabccbbaccaaaccdacdcaddbacabbcabddbabcabddcaadaabdbaaacbadacaacbcdbbbbadbdacbacbdabacdddddacabacaadccaadbbcddcdccacaacbaccddcaddcadbbcdddabaabcbadabdbacadddacdabccdbcaadddccbbadbbaccddccdbdabbadabcaabdaabbbabaddddbddcbaddaddabcdddaabbccbaadadddbcaaadaadbbcadadddccdbbbbaaadadcdccaaacadccaadbcdaccbbaddbacddbbacbbdbbbababbbcbdaccbddbbbaccabbcbabddcdcabbbdddacdaabdcacdbaaabbbcbccaacaadacaaabdbaacbababaabbcdbadcdcbadddaabdcbcdbccbbbcdbddacdbabbacbbcccdaacccbcbcddacbbddbcaaacccbaaddcccabbcacaccaddbddbabdddbddbcddcbcbcaacacddccdccddacdbbbdcbaacabdbdaacdaaabbdacddacbcabaaccddddcbcbcdddbcaaaaacddaaabddbddbbcbbddabacbbbcccbdccbdbdacbdbdbbcadccdbcbccbcacbbdaabababbcbdbbbccadbbbbcdcbdcdabcadbadcababdbabdbcdbddcbabaabdcbcabcaabdbcbacdadcdcabdddaabbbcdcdcbcabbbcbcacaddbcbcadacbccbaaaddaccdaccacddbcdbdbbbbbadbbcbaaacdddbdbbabcddccbcbadccdcdabcdddcbbcdbaaccdcabaaddccabccbbdbcbaccbdbaacdbdabbdbbcbabcbbbbdcbdccbdcbbabcdaaccdbdcccacacbcaacdcaadaacddaccdcccddadbdbbcaacdcbacccddcbacbbbbaddbddabcbddcaaabccadbacccdabcabcabdbdddcabdbabcdcccddadbbbdbdaadbbbbacacbabcaadbddadbabbdcdbdabccdcddbbcbacdbbdddadcdbcbcdadccadbadadbbdcaaaabdbadbddaaccdcbbaddbabbacbdababbbacccddcddcadadbaddcbdddaabccbdadacdbcabccabaabdacddbcbcabbddaabaddcbdacacaddadcaaddaddbadcddabccbdbcabdcbaccdacbcbccdcbbacadbdcdadbcddbdccbdcccdcbcabadaaabcaabcccacddccdbaacadbabcbacdbbaaabbdbbdcbbdbcaabaabdbddccdddcbabdacdbadcadcccbcadadcccadaababbacadbcbbbabcabcbcaadabcddabcbddbdcbbbbabbabbbcabadcbddbacbaddcaadcddaabcabcccabbbabababcdbbdcbacddcbadbaaccaabdadcccdbcccbddddccacacdcbaddbadddbbbbaadcdadccaddbadbbbcbdbcdbbbcaadabdcacabadbdadadcddaddcaaaabbcabdaddcbbbbadaaabdddaddacccadccacddbdcddddbbabdbbddbdbdadadccdacddcbdcbcbaaddccabbccdddbdccdcbadbcbadbaccccbdacdcdbbdcdcdbddcddaaaaabddbbbacdaaabcbaabcbdacbccddaccdbbcddaadabcbdadbbccdcbabbddaacabddbacddacadabaadddcddbcccbcadcaabacabdacccabcdbdbbddcbddbbcbcabdcddcdcacddddcbcbaaccccdddbadabcdbaadcbdbcbccadccabcdcccdcbaccddacababcacbadbdbdbdddbaaccbcacbcacadadaccddbcdbadcdadcdbbcdcaaadbdddbdacdbbcbbdddaababcabcbbcacababcbababdadccccbdcdbdbacbabcdccdccbabdcadcbbdaaaddaadcbccbdaadacacddacccccadadaacbbbbabcdbdababcccdacbddacdaaddacccdbdaaabcdbbddacbaabdccbdacbccbacddbadbdbdaccddababdbcbcddbabbbaacabbabdbcbadbccbadcdbaadcadcbbaadcbdcbadbbbacbaabcbcbbdbcacabbbcdabccdcbcbcdbdddacdbccbbbcbcaabbadabababaacadcbccbdbccdcacddaabddcbccabcadabcdcaaddbcabddbdddcbbaddcdddbabccaabbcadabddabaaaddabcacbdddcbdcadcdddbdbdccabaabbdddbccbdbbacddbadcdbcddcbacdccdabcbabcccdddbdadcacababbbcabaababbbacdaaababdcdababbccacdaadbdbbcbcbdcadaddbdbdaccddbbbacdcbaddbbacdacabccbcdbbcbabcaddbdbddcbababbacccbcdaadacbbbcaabbcddbaaacbbbbccacaacacdcadcbaaadbdaccaaaddcbcadcddabdabddabcacdbbdbaaacdcbbdabbbbdcbddbaabccbccdcdadbcddbaddddcddbbcbaaddadabaddbacdbadbbcbaababbdaaacdaacacdbcaaabbcbbaccddabccdadbddadbdaadddbcaddddababcbcdacaadabbbdaacbbcadacdbabccdddacaabbdbdcdbbbdaadcddbbcacdcbddabcddcccdbbabccddadbbabbabacddcbbccbaddcacbdccabbabababddaacbadccbdcdddcadaacbadaabddcdcacddbbcabacdbaaadbddaabbddaaacadabbbaadaadadcbcbcbcdbcbaacdbcdcbdbabbbcabcaddddabcaddbbacadbacbbacdabddabbabddcacdaacadccbcccabddbdadbbababbaacbabcbcddbaddddcbcbaaadacbcdcabaccdbcdbcbacbcdbbbdcddacacdbdcdabcaacacabdaaaadbdcaacbbccadadbcacdaabddbcdddadbdbddacadbcabadcbdacdbbccaaaccbccabcdacbdcbbbadacbcdcdabadbaadcddcadcdccdacbbdabddcaacdcbdabcbbaccabadccddadabbbcbbddaccabacbaadabdccdbabbcbbbbcacaadcddaadaacadbcddaacbcababbddcacbcbbdaadbdcacdabddaddabbdbddacbcccbabacbdaddadaaadcaabaadcbdbbbbdcbbcbbbcdacadaddcaadacbcddaaabbdbdbbaacacccbcdbadddddbcaadbacbbbcccdadcdccbcbccbabbccdbbdaadcbbaacbdcdcadacdbabdcddbaaacadadabccadbaccbcaccaddcabaaacaadaccaaddbddcbbbbabccbbddbbbdaadadddccdbdababadbdddacabdccdcbddccbdccdcabcdccdbddaabcbbdbdacbcbabddcabcbaadaaaacbaccddccadddcdbdcdbdbccbddacadcabcddcadcbddcdadcddadcdaadadcadcbbcbbaaaabccacabccdbcdcabcacaaadbccbaddadddcadaadcadcadabbabcbadbbdbbdbbdcdaccadddbacadacbdccababcaadadbbabbdadcaadbdbabbdbcbacaabcdacbdbbaacbbcaacdaaaadcdcbccdbddbaccadaccdbadaacaacacdccdaadbdcbdaadabaadbcbdaaccbabdcbbadccbababbcdbcbbabcabbcdddccbaaadaadabbcaabdcddbbbbdbacabccbadbbcbdbdabbbbddbbcccbcbbdacbcbbaacbcbcacbddcbaddddcabdaddbaadacbbaaadbccdcddbbaddbbdaccddcdcbaccaabaaddddabdabbcdbddabbcbcabaaccbacddcbbbdacdbdacbbcdbddbadbaddbbbbdcabcddbbcbcbbadaaadabbcabbdadbcabcdbbabbabcaaadddccccbbbabccdcdcacacbcaddcaadbddacbcdacbdadbadcddcdabbdcccdacdbadbcdcaccabcdcabdcccccaccbdcacbadddcaccbdbabbdccdbdcbdaabdcddbbcabaaacabddbccdaaacbbccbbbdddbbdcdcdadccdbbcdcccbaadcddbabddccdabdaaadcdcbdbdcbddddadbbabcadcbadbababcddacbcbcddbacbdbcabcbacbdaadaadcbcbdbbccbdbbcdaaacbdcdadcabaccccadaddbcbbcadcadcbabbacaadaddacdcdcacbdcadbacbadadacbdaadddddcccacddbabddadaacbccaccaccddcbdddababbacacdcabcdcdddcbabdbbbccadddaacdadbcbddacbbcaacbdbdcbccbaddaccbdbdabbbadbdaaaacdbabacdcdaddbbdcaaacacabcdcbccdabbbaadaacbbdcaabbcabdcacdabbdadcaadbccbcacddccbdbacdccddabbbcabccabddbadbadabadbaadbbbacdabbabbcbdbbbdbdaddcababdabaaaadcddccdccdccbccdcaaaacbcdbacbbccccdadcacdbaaccbcccaddaccbbacccaccccabbcbdaddadbbcdddddabaaaadabadccbcdcbcdccaadbababaabdccbcbbdaccddbabdddbcbcbcbcdccbaccabddbbadcadaadbbbcdcdbdadccccccdbddbacbcacdbacdbcacabbdcbbcbccacacabbabcaabcbbaabbbdbacbdbabbaacacdcacccdabcdbadcabbbadabbdddbadadadbcacbddacdaaacbdbbaddddacadadcacbacbdcdabcbcbdcdaddbdbbccabdcdabdcccaccbbdbcdadcbddbdbdabaaccbcbdccbabddbdcabdcacbddacbddaccdddbcdddaaabcdbacacbcdbaadbbcabcacdcbcabbccbaaccdacdaccdcabaacdabacbaddaadaabacdbbdabdbbdbcdbbbdcdccdbdadabadcddadbdaddbdadacbbcbbacaddababababbdcdcabdbddcacbaaacbacdbbcaaabccaddaddbcbbdaacdaaacdbdaccabbcddabdcbdadbcccacccadbadacddacbddbcccbdcdbbcdacdcccbdaddcaabbaaababbdaccddbddbdcadcaacdabbdbacacdddcbaadcbbbcbabcdcaabdcadcbccdcbddbbbddbbabdababacbdbbdbcacbbccbacdbacbadbdcdbdbadaadbacaccacddadddcacbbbdbbcccbbdddabaddadacdcbacbbddabaccdbaababbdbabcbcdadbdbaddcabddaadddadbbccbddaabcbcabdcbbadbbbdbbacbcdaadcbbdbdbadaccbcbbbdacbabaddbbcbaabdddcbaaaddbccaadbabbdccabdcdbdcbadddbcbcbbbbcddbbbdbcaabdabbabbcaacacdcdaddaccccbdbcbaabdcbcdddbdcdbdcbdadadccbbcdbddbbaabdabbbdacabbcabadcdbbddaaacccbadbbccccccabaadadddacbacdbcaabdcdacabdbdbdccdadbcaaccbdccadcbaabccdaacbddaabaabbdbbddbbbabacdadaacabdcdabdcabbabaabddbddaaadcdabcacdcccaddbdaddadbdadbbbdbdaaccacccbbdcabacbabbdabdaadcbabbcbbbddcdcbbbaadcbbdabacbbbbdcdacbccaabcacbbdbcacadbddbddcdbbbcbbcbaacaaddccddaaaddbcbacdbaddcaaabccdbddadbaabbbbbdccbaadbdcdcddbdacbcaccdbadbadcbdbbacdaadbcdbcaddbbbdbccddaddcdacbadabbdabbdaadcccbcdaabbbcaabadbdbbaabccaccadacbbccabdbcdcddadddcbdcbdbbcddbcadacabbcccbbaacdddddcabbbaddaacdbabbdccaddbddaaaaddbabbabddaacccbacccadaabdaddcaccdacbbcbaaaacdcbcaddcacdcdcbccabcadcddabcacdbcacbcdcbadacaacbcacdacdcbadabcbbbcaddcccacbabababdacddbcdadcabcbbaabaddcdccbbaaacabaaababacdbcadacdcbcaccdcbddcdcdbdbababacaaddccdbdcddbacccabadcdbdcaabddbccbcbcadbcadcbacadcbddcacdbabbcadcdddacabbbadcbbbdcccdabdbadababdadbaabcbacabbdddcbbcbadbcaacbaaddccbdbbabacbcabccaddbbcdacabcdbcbbcabcccbbdabdbdcbbcdaadccadadbcacadacbcaacdaadaadbdbaddddbaadadbbadacaaddbddbdbadadcaccbdadacbccddcbcadcbdbcaadcccacddbbacbcccbdacdbabdaddcababcdbbdadcabbdbdbaaddbcbbacccbcbaabbbdadabcadabddadacaddbdaadbacaacbbbbdbacddabcdaddcadcdcacbabbbdacadccbddaaacbcbcbbacabaccaacadccdbccdbbccabdaadbaccbdcdccadadcbccddbdacaccdaadbdcabdaaaabbbddddcbacadccaabbbadbdaccbacdadcdbbabcddaacadbaadbbadcbcabbcbcaabdcaccacabddbcbdccdacaccaadbbbbabbbbdcdccbbccddcbbccaccbdbacbbadabcacccaddbdddcbadccccbcdbaabddadabaadddadbbcbdbbdbcdcbbcaddbdabcdbaaacddddccaccdbccdbcbadcbbccaabaabcddabbbdcadcdbbcabddaadbcdddadccacdddcdbccacdccbbddcdaaaabbdbbdbcdcccbadacdbadbcdadcdacdcdbdbcaaadaaddccacddbccbdabbcdadbbacbaabbaadbaccaacddcacdbccaddbacadddbacdcdcddacccabaabdcbdcddbdbdabdaabcdacaabadcaaacaddaccaadcddcccaaadcacdbababbcccadbbaddcabdacbcbbcdccbaaaadcdcbbdacadcddcadcaadabbddbcbdbadadbdccbadadcbcdaccddacdbbccacdbacdaccbaadbdabbaddadcbccbaaabddbdbdacdbdabaabcabababbbcbccadcddaddabdbccacbddcdacbdcadacbadccccbbcccdaaaaaabbbdcccdccacccbbbdaddccbdbcdddadbaddcaadbcddabcabbaccdbabbccacbccbaacccccabbccbcccbadcccbaddcbccbccccacdabcdbacbddcabcbdccddacbcbacdaddbbdbbbdbbcadacdcbabcacabbdacdabcccadcbbbdabdbccdbbdbccddbddccbbddbbaaaaddaadddcabaababaccbbaccdbcbbaddcdcbdbdaabdbaadddccbbbcbbccbbababbbaacdddcbbcbbaacaccbcacccdacaccbadbacddacdabdacbcdaababcbbbddbdcdbabbccbabbaacdaabdccbcbbdccacbbaacdaaadbbcbcabacddddbaddacbdaadbaadbadabcccaaabdadacbdbbccbbccdccdadddabccdabaccddccacdcdcaddabdaacabaccdbcaabccaababadccbadddddabdbcccaddacadadbacbcbcadbcbdaccccaabaadacabacddadbcdcbadabbccacdacacccccaccaccdddbadacbcdcacaddabcbababbdcccddcccbbcddddbcdcccbcaaaacccbdbabdcdcbdabadabbcddadadadaabddadbdddabdccacddcabaaabadaccaddcbdaaadaccdbabaaacaacaaacadacccbabcbbaacadddcababaccbdcdabccadcbaddababdccaddcabbadaddbcadbccbaabcaccaddcacdbcacdbacbdbbdddbadddbcdabcabbbcdbbbddbdcaaacabccbbcbddcbaacaccbbdddabbacbbabacdadaaadcaaababdcacabbbccdaddcacdabaadaccadcdabcabbcccddbdadbdacccdcbdbcbbccaabbacdccabdbadbdbdcbcadbaababdbdddbdbcdabdbadccccdbcaaddabbcbcbbbcbcdcdbbabcdbbdacbccbacddcddabddbdadabccaabcdcaadbdccaadbbdbcbbaccccadcdcdcdaacbcbbddcdcadcdccaddbabbdabcdacdaadcdddbdbdbccbcabadddbcbccdcbadcddccdabddaccaaadacaabcaaccacdddccdcaaacbabccaacbcdcabddbcdddcccdbdddabccacdbdbbacbdbaccbbcabaadcdcddcccbadcccabddadadaabadddaaabdacadbadcdcaacbbdbcdadbbddadbdbdadacaabbbdbaddccbaacdbbdcbaccbdbbbbbbacdadaaaaccbdbaaaabbcbbdaabbdaadaadbdbddbddddbccaabbbdbadddabacaddaccbcbcbddaccdcbbdadcccadaccbabccdcbbddbddddcbacadacbbbcbcddcbdbddadcabadbdddbabacbbbaaccccacdabaabcdbdbcadadaacdaaaccacbbbbdbcddbcbdabddacdcaadadcaddadabdaacdddccbaaddabadaaacadbddadacbbaabaddaababacddacccaddacacadcaaaddcacccaaadacbdbbbdcbbdbbcacbdbcabddbacacccbdbdbdadcabadabddbaadabdbcabdcaaaccbbddabadbaadcabdccabdbddddadcbadabbbbadbccbccdabdaddbabdcbdcbccddbaccdbcaddbccbaacdabcbdabcbcadbbddbabdaaddbbcaaaabdcadddcadcdcacbaaccababdcaddbbbbdcdcbabbbacdaaacaadccdacaaddcaadaccacaacbddddbdccbbcacacdaadacabddcabdbbddddcdddbcbcadaabcccdbabbcabbcbaacdcbadbccbdbbbdabdacbbabbacbcaadbcddbadcccaccabcaaddbcdadababdccacbcdbbbbbccaacdbbacadcdaaccbdcaacaadbabcbdcdbbbadaaacacbcabdcbcddbcdddaddacbdbaadccabcaaacabadccdbcacdcadcacabcadcdaadabdabddaabbccdcacaacababbababcddbadadcdcccababaabdcdbdadbbbbddbacaadcdcbbcddbccbacbacbdddccadbcabdbcdcaabbdbbddbbbdaccdaaccaadbbdcbdbbaccabbbcdbbbacddabaacbbdbddacbabdccaaacaaadbdbcbabdabbbccdaddddcbdbcdbbacdcddbcddbcdccadadddbcbadaaaccbacbcbbbdacabacaacdaaabdbcbdcadbbcbddaaaacacbaaabcbbbbddacaddbbabdadbbcaaddbaacbdbcdbdcacacdabbaddabdbaabacabcccdabdbcbbadbbcaccdaacabacaaaabaadbcbdabaaadcdaddabdcaccaadbdbddadcdbcbdccccdabcbcdbabccabaaddddcbbcccaacccccbdabccbccadaddccdababaabcdabcadbdbddbdcbcaabbccdddccbadccababcabccababcbbdbccadddaddaacbbbaaaaabdcadadcdbdaddcdabdacbdccdaddbbaaccbacbcddadddadbdbdddccadacdbccbdacbbbcbcdbbacbcbccbbccbcbdadabbacdcdabdbbdcbcacdaddcbbbdccdaddbacbcbabbbcdcaabaaddcaabbcbcabbdcddcccbddccbabdadbdababbbabbcccabdabaabcdbadaddabbaadcbccbbdcaacadcbbddacddbcadbcbddccbcdacdacbbdbccabdcabdbdaccdabacdadacccbbcbbbcdcacadccadbacbcbcbcdacabaabdbdaacccacbaabcdaddcdbcacbacbaacbdbcbcadcbaadccabcaacdcbccbcbaadadcabddbdccdbaddbddbcadccabdbabbaddddabadacdcbaabbdabbbacccdcbcdbcacccbbaccbbcdabdbdabdbbbabccbcccbabbccdcbabaaccbcdadaababcbbbacdaddbdbccacdbdbabaacbdccbbaadabaaccdcdbbbabadbcaadcaaccaccabdcccddbdcaacccabcbdcdcaaabdaabcddcbdbbdcbdcbdcccaadbabbbbdbabacddbbcdcaaaadababbabaadbadacadcccadcccddaacdcadacaddbcbdadddadbaccadcddadbaddabbbaddbdbdcaaacdbbabcdaaadcabcadbcabddccccaacccadcadcdacbacccccbdabdbdddcbabaaaadcbadbcccccabbcbdbabdddbddbcadbcadcccbbddcbcbccaddccdcaccccbdccadbdbcabdaabcbaddcccbaadcbabcbdbaacbadabaababadccacdccdcccbcacbcdcdbccdadddbdddddcddbbbcbdaabacdccabdadddadbcdbbbdacdbccdbbbabcabdbcdcdcaabaaaaabbbcaaabababbbbbdacccbbabcbdcdaddbcbbdbbdccabaaccdabbbbdadadcbbacaaadaacaababbababacddaaddcdddbaadaadadadcdbbcabcbcaadbcdbbcdacbccaabccdcccddcccddadaaccccadccbbcdbdccadbcdbccddbcddacaadcccbddaabbcbddaaaaddbdacacddcbcacacaacabbacaabdbdbbbdbdacbcaaddadbdabddcbdaaacbdbdacbbcdddbabdbcdbddbccdbbbcbbdbbaaddaadcbcabaabbadbcabcbbabadbdccbdddbaddbdadcadbacbdcbccaaacbcdaabaaaabddcccdacdccdccdccbddddbabdddbccbbbcabddbdbdccdcdaccbabbbccddbaddcbadabdddaabbaadddbcbbbddddcdaacacaadacdcbcbbcacdabbbaccccaccccbcbbaddbcaabbabacbddbdcddcbdbbacadaaabacdbbdddcddaccadcabccdaccbccdbadabbdddabaaabcccbacdcadccbcbddcbdbbdabcbbcbacbbbaacadaadbdacabbbbacccbdcadbddadbacdbabbadbacbdcdcabdadbbbdbddabccccdaadbcababaacacddcaacdcabdbccdbbddacdacbcdccddaadadcdcbddabaddbbaccdcddabadbabbbdaaadbbdbcccadabdbaacacaabbddacbabdaddddcadaacabdadbcbdcdddaaccacccadddacddacbcdcdadbcccbabcbbdacbbcdcbbcadbbbddbbcdabbababdbbaabaccdcacdacccbaabbadacabacadccdbbbddaadccccacaccacddbbacaabcbcccdacdabccacaadabaddbbdadbcbdabccdbaadbdcadbccadacadbdccabbdbcdbbcbbbdacbadabdbacbacbbbcaccdccdcccddaaadcdacdbdbccacadcccccdddacccacaddccdbacbdbcacbaabaabdcdcaaacdbdbbcbcabbadadadddcababbcbacaadcccbbddccbbdbddccdcccabaadabddabcdcddbcacbcdbccbccbbbaddadaadccabdbcdcbbcadbdbacddadaddabaabccdbdbccdaccbdccaadcadddbcdabccbbbcaccdababccddabbbadbaaaddadbabdabbbaccbccacccddacbbbabbbacbdaccbddbdbabcddcbddbddacdadadacccdabbabacbacdbbbbabbccdbccaccbbdacccadbabcbbadcadbccdbddddabacdccaaccaaaadbacdcdbacacaaaaabcaaccbccdccccbadbcdaddcabdbcdabaabccbcabdbcdcdadbacbabcbbccabcdcadcadaaadddbdaccabbcbadbbdddabdaaaddbbbcdcaacadbcbbbbabcaacccbdabbcabcbcccaabbddbbaddabacbadbddddbaaaacabdcbaddbdbbbadcabcbabdaadbdbbddcbdcbaadabdddbacbbbadccabdddccaddcabacaadccaaccaaaaadcdacacabcacaaacdbdaccabdbdcbcdacdaccbcaababdbdcabdbbacddabdcaabbacbacadcbddbcadabbccaaccabddadcaaaaddbbbaddcbabbcccccbadcdbadcacaccadadcabccaacdcbcadcbdcaaddccdabcdccaddcdbadbddaaccadccbabdbddbdbaacacadaacadcdcbcccbccbbccbddacacccbddbbadcbcbbbddbbbcbcacdcdbaadcdccaacbdbccdaacadadbbaabbcacbcaabbdcdbdcacbcabbadaabdacccbababacccdbaabbabdacabaccadabadcdaaddaadcdaddaccbbadbdacadbdcbabdabdbdabbddacccccddaaddadddcbcdbaccdbddcdbacbcbddbaacbbbbcdcaaabdccbcbcdacabaadbcdabcdbcabadccbcacaacdcacbaaddddcdcbaaccadadcbaccacbbacccaccbadcadccbcbdcbaadaccbcadadbccbabddaccabcdbdaccbdbadbbcdacbdbabccaccddcccdababbcdacaddcdbdddadadabbacbcadcbbaabddccccbcccbbcacddabbbddbcbbcbbdaadabbdddacbccdbdadacbdbbbcbbcbddbacccacbccdabbbacbaaacabcbddbdabbbdbdcabcdbbcccbabdcbdcdabcccdadbcbbccadbdbdcdacbdadbbbcacdabbcacbdccadabbcccdbacabbcbccbdbccdaddbdbaadbbdbadbddbbbdcdaacadacabdbcaabdbdcbdccbbcdbadcaadbaaddcddbdadcbaaacbccdbaccacbacabdccddddcbcdaccaabbdbdcdbdcbacacadbbddddaccabaadaabdccdcbcccbccccbdbaccdbaddabdbabcbaabadadccddbcbcccdcdcdbdcadcdcbcacaccadcadddccacdadbcdcdccacaaaccaacbdbdbcadcaabcaaaacdccabcccbdabcbdbbddccaccbdcdcdcadababadbbabaaaaddcdacaccdbaaacbadbacaaccaacaacdbdaabbabaaabdbabbccbacdbdadadcbaddcdddcbacaacdabacdddcdddaabaddccaabdadabddbcdbbaaaaaaaaccadbbaabbdcbdcccaccabaadcaaaabaaadacbbdaabaacabbaadadaacddcbcbcbcadddbcdcccbbbdbaabbdbdacabbcbbadabdbcbdcddaadbccdbaadcacddcddadabccddbcdcdbdcbadbddcddcadbacddbbdddbddbccdddcccadadabbcdaaccbccbacbcbdcddbcdaadcddbddadddbbaaccdcbcdadadaacadcdababbdaccbcdbdacddcaddabdabbabaaadcdacabcbcacbbbbdcdbbcabaacdbbaadacbabdbabcbcaacdbbddddaabdcdcacadbabcdbcabaddcacccadbadaaabacdbcbbdbacccaaaadbccdcdbdaadbacdabbacccdcdbbacaaddabbdacdaacdbacacbdcaacadcdaddbddaacbbbcacdbbdddbccbbdbabcaaacaacdbdacbdcccdacbabdbbcbdbcacbcbccbdaadabccbabcbbcddddaddbcdbcadacdcccdbdacacadcadabaacacaacdbbacccbccbabcdddcddbaccdaddcaacbacdcbdacacddbdbadcbbabdddcacabcaabccdaacdaaabbadaacbcaaaddbaacdbdcddcaacccadcadbdaadaccaccbabdbddbcddaaaacaabcdbddcabbbbccbcccbabacbcccdccdaaaccbcbcbbdbaaccbcddbddcdccbabbbbccbbbabaacbbacdccbcccaddabbddabbcccccddbddbbdaadbbdcdabacdabdabaaccbbddbdabbabdadbabdbcbbccbcacdbbdcdccbabcccbcddcadbbdadddbccbdcbabbcdaabcccbcbababcaddcaaddcccbcbddcdbdcbdccbdddbddbdaabdcbdcabacdbacbdcadcbccdabbdbbbcdaccbabccacddacdbddadcdcdcddbaabbbddadabacbdcddbbdbcddcdbccabdbbdcdbdacbccdbaaccadbbadbbcacdbbccaadcdccbbbbadbadccdcddcbcbcccacdbbbbcbdaadaaaadcbcacaabaacabbaacaadaacdbcdddbcabdadcaabbbaacacdabcabcdcacdacacdadbbddbcbbcacbccbdddacacccdaadccbbdaacdcdabcbccaccbacadcdcdacdccaadccbcdcbdbacdbacaaaabbdbbcaadccccabcddabbbcbbcddbaccdcbacadccaadadbabacddabdadcdaaadbabbbcdcbddcaabcbccdcadadbacbacccbdabacadaaacbbdaccbaddababbddbcdbadbdabbddcbcccbdadbaccdcaabaacdbddcdddcaabdcadccaddcacadddbdabddaccbcaacddcabccbddbcacbccddaadcdccddcbbabddaddbacbaaacabdbdadbbbacdcbccdbaacdbbccbcbcabadbdcdadadbccdacadabcdccdbbabadacaababcbddcdbbbabcdccdbacbacacdcabdbaabcdadcdadcacabccaaaddadccccadabbdacbcccdadbdbacbdcacbcbbcdcadbdacddcacbcbbbddabcacccdbbadcbcadcaaacadadcbdddbcddaabbbbdcdabdcbbdabdddddcabbacdacbaddadaaddccdbbacabdaacddcdabbcdddcdcdbacbccbcdaadacaddaadabbccdbddaacbdcabbbdcdacacabbbcbcabbbbadabccbaccccdbdcbadbccbbccaaaaacaadcdbbcabdacdbbbabaacbaadacaabbaacadbcddacccdabcbaddabbcddbccdacccaccacdbaccaacbcbaabacdcbdccbaaaccacdadaacdadcddbadcbcdbdbabbccbabcbaabbccdbacacacddcbdccadbbadbcbaddbbbbaadcdacccbdbacbdbcdbdddccdcdacacccdbcaaddadcdccbabbcbddbcdbadacddbcbcbdacbadaddbbbcdaccbcbacdaaddacbbdaddaddcccacbaadbdaaddcbaaaaccdaadadabbdbdddcaddbacbdcacdcabdaccbddabbabbaddcaadacbdbaadcdacaddcaddaacccabbbbdcccabdccccdddbabadbcacabbcacadcadbaddbcbabadaacbdcdcdccabdccdcdbddbabcadbaddcddcabbccbaaaaaabaadbbbdbdddbcccadabdbbdadbabaababcbbdaabdbaaccacacbadbbabbccbbacbdbacbbaacdbabcdcdababccccbdbcacbabddccbaaccddabdcbcdbdacadbacdcbabbbdaddaccbbddcddcaacaddaddccdaacbbbdcdabbddddcaadbdcaabbbdadbbbcaaddcdadcdcddcdbbdaaabbdddadabbdcdbddbacbbdddccccdaccbacdddbabdddadddbacdabdacaaabdcabbdbdbdddccdbaadabbcbbdadcdaccadbbddabadcddbaadadaababbabbcacacbadaabbaddabcaaaddcacaaabbbdddccdaddddcbabbacadbdbcbbbadacabcdccbadcdbdacdcdababcddababcadbdcbddccbcbccacadabddaccbbbbbbcbaabacacdccbcccaadacaadabacdbbaddcccdcccbcabbbcbdaccaccbabababccabcddccacdaacddacbdbdacddcdbacbbaaddddabaccdcacdcbccdaabbdabbdabaabdcaccdabcbbcdababbdbcdcbdcccbddaadbaccddcacccdcccadcdbaddaadbaccdaabaaacacbcccdadbdaccccbaaccbcbdbcacaddbcacacbcacbdcabccaabadaadbdddbdbcdadcccbbbacacdddbdcaacadcdabbbdabadddccadaacccbbdbaadacbcbcdaddcbcbcbdacbddadbdaaacacaacbbddbdcbbdcdbcccbcbbbdddabbdbabdbdacaaabcadababccdbcbbbcbbcbccddcbbacccbbbabbdaadaadcababcdadbdadbdcbaaddacabbddaddbcacacccababdcbddabcbaabcccdcabcdaddacbcccdbcaacccddacaaabdcaddbcdbadddcbddadbcdaabbdacbcdbbdbaadaddcdaadcabaccbdadabdccaddbbbdcbdcddaacdbbaddddbaacabdcacababdabbbdbbbadabbadcbaccdabcadcdddbdbddcdbcbbdcdcabbaadabccbaacdddaddccdbcbcacdaabcdbcdaaccacacbcacdcdcdbccbddbacccacaccbcbdacabdcaaaddaacdcdaaabccbbcacddbddaadccadbadacccadbcbcbbbbdbababdbcaddacaabcbddcbdaccbacaadbcdcaadcbcababbdadacacabbbdddcbbbcdcbdbabdaddcaadccdbadcdcdcbcdaddcdabcdbbabaaaddabdbdccdccaabacaccbbadaabddbdaddaacdbbbacdcdadadabdabdbadcdbadbadcbcaccbaadddcbaadadadabaddcccadbdacddbabcdddcabbaddcaabbabccbadbaddbadcacbddabadbbacdcdacaabadcacaacccccadbdbdacadbbdbabccbcbcbddabbdbbcadbdbbcacadccbaddaccaacacdacbbdbdcadacbadbaadbbbcdacbbdcddddaadcadbbdaacacdaaadcdcdcdacacbdbacdabdddcbbacbbacabbddbabddbacdaaacadbdbdbbbddcbddcbcbaddcadbcbdccacccaccdcbbbcdadccaaddaccaacaddabbdabbdcbacdadbdbccbdddbbababcddcddccabdbcbcacadcdbacdbddcbdcdacddacdddcaabadbbbacacabbadbbdacbbcacdaabadcabcaadbcbaaaadbacbdcaabddbccdabdaccaaabcacabcbcdadbbaaabcacdaaddbbbbdabdcbccadcbdaacddbcbbbbabcdcaabbbcbbadbcdaccaaaacacdbaacbbbaccdabbdbdcacbddbdbdbacdcbabbbddaadcbabcbbdcccaabbbcdcdaaadaadddabaddccaabccadabcbcccdcaacdcdddccadacaacabcbbcccdabacacdcbbdcbabaacaaabdbacbdbacdcbbdbbdcbbdbdabaacbabcaadcabdcdacacabdbacdbadbbddcbabaaabdacbacabdbaabbddaadaaabbbbdddcaaddddddcacaabdbaadcaadddcbcdaacbacccbccdbbababbdcaaddcccbadbaacbcdbddcdbdbbcdabbdacadabbdadccdbaddccbadaacccbdacbabbaaadabddcdaacddbdababbaaabbabcdbacbacccbaaaddbcacbacccdccbcbcabcbbacbddaaccacabbcdcbcbdaddbbacddaddbbdacbdddcbdadcbccaabcddcbbadcbcccbddcdcabbbbaadcaddddbbacbacccbaaccbbddbddbbabcaacdaaaacadcacaadcbbaadbdcdacbbabdacbcbdbbaddbccddbaadbbbcacacaabdbacbcdadccacbddccdcdacaacddaababbadccddaacbdcddcabbbadbccbabccacaaccacdbcbabbddcddabcdbabbdbbcadbcbdcdadaaaabbaacbdcabccdbaabadcbdacbacabdabbaaaadbdacadddaadbdbcccccccdacccacbbbacbbdcbbcbcbcbcaccadccdcbdacbadddaaacbccbaccaccadbbccacbbdcadacddababdcaccacccbddcddaddaabddabaaaaccaccdbbccbcdbbcbbcbcbdabbddccaadadbbaddaacbdaccababcbaadaacddaabcdaaddcccaaccaddaadbcaccccddaadabacacdadbabcdcdbbdacbbcdcdbcddccbcabbdabbccacdbcbbadabdcbcaccaabdabaabdddbccbddbadcddbaabdccbabaabdcaaaaaaadbcbcadaddcdbdaabbabddacdbcbabdbcaaabddbbbcbabccdccdabbadcdbabccbbbccdbbbbdcdbabdcdccaacbccccacbbaccbbbacccdcaccaaddcdaabdccccaadbabbddadbacbcdadbdcdbcbcadbcddabcdadaaacdcdaadbabcdddabddbddaccadcdccbbdbcdabdcbcddcbacdbddacbcddcbbbdaddbdacbbbddddbbdabbbdadaaaadcbbcabaacbadbddcbbdbadacadadcabcddcdcbcccdcaabbcddcbdbccbbadaabcdcaadcddcdbabcbbbaaaccbcdaddccadaaacbccdaccbacbdccdcbcdaabcdbddacbbbbadabcbcbcadddabdaacabdddabaabbbdcbdacaaabbbddaaacdcababdbadbbdbbdbbddbcbbabacbcddbbcbaccdabcbcbcadaaacbacaccaabcaaaccdccbdbdddddcacbacbbbbbcddcdbcbbabcaddddbdcbacaaadcbcdddbbacbabdddbdabadcccadabadaacdaaaadbdbaddaacdcbaadbdbabdadddbcdbcadabbbdacbbbdbcbcbabcbcdbaabdaccbadcacdabcaccdbacddcdcacacddddcdcbbaccacabccccadadccabacadcccdcabcaacabaddbdddccadcbdacbdccdcdddbdbabddcaaaacabcdcbdbdbadccdcccddacaabdcddbcaccbdcacabdddadabbbadcbabaacdddababbaccbacadccccbadbaaccdabcdbabcdcdcbbbdcbcbaadcbaaacddcaddaadacbcbcbbdbcddaaacdccbcabcdaaabbacdcdacddaaacdcbdabcccdabadcbdabcbabdadaadbaddccbaaddddaddbaddadcdcdbdcdcbbdbbdacadacacbacacabaccdbdadacdaddbcacdacbadbacdadbcdabcdbaacbbccbcacdabbacbaadacaaabccdccbdddbbcbcddcbccdcabacbaddcccdacccdbcdddcbccbcbacabdacadbbaaabacdacdbdddddacadcaadaaadcaaabcaacccdbabbaadadbcdbddadbbdabccdaacbbccbabddcbaacddaccccbbbacdbbdcadcbbdccadabccbabcabdcddcbaccbdaccdaaaabbcbcbacddacacccbdcbcccbcacabadbdcabbcbaadadadbababbadcdbacbdddbbadacaabddabcddbcbcbbadbdcadadbbccaaadaadbbddccdcddcbacadcddcbaaddcbbcabadddccbccbabcbcccadaacdcccdacbbccbddcbcdbaacaccaadbadbdaaabcbcbddacbcddbabcddadbcbdbccabaccacbbcbbcbdddabaacaacddddabcacbbbbddddbbcdbcddbaccabcbdacdcdbbbbadbadbaabacaabcaadccbddaccbaaccbbadccbbbaddddbcbccccbaccdcabbcaaaabbaacccdaadacdacaccdbaabbacacacbababadcaaaacccbbaabbbbcdcccaccbacbdccaadcbbbbcbbabbbccacbadbabacaaccacaabcbccdbcdddbaadbccadbcadacbbbdccacdcccabcdbcacadadcdabcaadddabccbbcdddaadcacdcbcacaaaaadbcaddacbcabcbdacadaaaaccdbacabcbabccdabdaabbcaabcddddbcbdaaaadadccddabbaabaddbbbdcaaccbbdccccbaabddadddbddbcdcbbadbddaadaabbcbaabbcaaddabaaabbaccddbabaccbaccacbacacaabcdcccbcccbddcbabcadddbbdddcdbcbcbdbcccccacabccabbbdddddcdcddcbbbdbaaadcbcddcdaabcbdadadacbdcbaadaddbcacbaccabccacdbbadaddcbbcbbcbacbbccdddacbbdbbdcaadccddcddccdccdadaadcdcbcbbcadacbdcdddaadddbadacaccabbdaabddcadbcbccdacdddbcdccbdcaaccbbbadcdbcdddddbacccddccadbbddaaabcbdcacadbccdcaddaddcabacdccbabcdbddcccdbbcadbccddbadbcbcdbbdbbddcadacbabbbdbbcccccbaaaaaccdbccbddabdbdddcabbadbdabccaaccbbbcabdbadadccacdcbbabadbbabbadcdbddacadbbcadbcaadbbdbcadbdbcdcdbbadaaaddbcbbdadadcbbbbdbacbabbbcbbaadcbaadcbdbdcbcdccdbddcccdbaaabbdbccbccaaaccbdbdaacdbacaaabaaadccadcbabdcabacddacdadddbcacabcddbcbacaabababbbcbccdcbdcddabacbdbbbadcabdbbcbaaaaabdaccdbbddcbbcdcbabaccdccbbbaaadccbadaccdbbaacbcacaabccacdaaacaccdbcbadadbaddcdcdbccadccddcadbaaacdbdbbbabbadcbdddccaacdcadcaabcacbbacddbddbbacbbdbbdbcccdcddaadaaabbbcbdbdbacbaaacbabddccaaaddddaacabcbcaadcacaabadacccabddabaccadcbabbadbaadbdcccaabacadccdabdabbaabdaadbbbbdbbabbcbdccaddbbddcaabbcaaddcdcadccacbbbaadbacbcabbbcbdbbadccacbcdbadddacdaccdccddddbcabcbadbbdcabdaddaaccadddcbdacddcdacccaaccbcdcbbbdabcdbdabcccccdabcdababdbbacdbcddbddbcbdbbdbcddabbaccbcbdccaccbaddcdbbabcaaddddcbadaacdacabdbdabcccdcdadabadaddaaccccbddbbabcdcdbcabccacbdbccadaadbcacddbcdaacabcaaadbcbababdcabcdabaadaaadbadcbcadacbaacdcacaadabccadbacdcddabacdbdcddaadcccccbcaccdbdbcabbdabcabbddcbaadccdaacdbabdbbddcbddcadcaabcacbbbbbacabdbbbbccacbccbbbacdcbddcdacbcbbcbddbbaaaccabbdcdbbacdaddaabcaccbdadaabcdcbbccdaaaaccddaddacabdacdbdbaadbcbacabcbbcadacdadabacdbcacbdadacdbabcacbbacbcbadbaaacdadddbbdbbdddbbdbddacbbbbcbbbbcbcdbaccaddbaadaababccdcaddccbacbbcbcbdbbaacacbbbbcacdbdcdbdbaaadbbbaaaaaadbcbbdcbddbdacbabdadbacbaaadacacdacaccadadcadaacdbabadddbdddccdabaacccddbddabdbbccdadbaccaccdabdbbddabaaaabacdcdcbbadddacbdbdcccacaccabcadcbaaababadabacadacaccaabdadbadabbacaaddaddabccdbcdaaaccbbabcddaabcbaccabdbcbdcdadbddcbbcdbaccdabbaadacababadacbbababcdcaccbbbdacadaadcaadbddddbcdacbcdabdaccaacbdabdaaddadbacbbacdaadcddddcbdccbccccdcbaabbaadaabacbbacbdbaacdbbbdbddddacbddabcbdaabcbabadabbccccbdcdacdabbadcccddddbdbabbdcbcdaddbbbddabcabbbddacdbddacbbbddcbcdbdaaacdaababbcbaadddccbabbabccaabbddaabcdadacbabaacbcdbdccbcbdcacaabadabcdcccdcaabddcaacccacbdcadbbcdcbbbaabbbbabcabcdaacdabdccbbddcdbcbdddaccaddcadbbdbbdcaaaabccbacdccbcdacabbdabdbaccbdabdadbdbaaaabacbaaccbbcdcbdcaaabadbacaadcaabcaaababdddbbbdbddabbbdcddbbbbabddbbadaabaaaaacdabdadbcccadbbdabaddacadadacaaccbadccaababcccbcbadcdcaaaacbaaaccddaaaadcaaacbbdaabdaaacdddadccabddbbaabcbadbdbbacccddabcadccdbacddaddbbbbbaadcddcdccbadcacddbcbcbcbddccbdddcaadbaccbcccdcddbdccccdabcdabbdbcdbcababdaacbcddcacdbdccdbbaddabbbacdddadbdbbbcdacbabcccdccaccddabbacbbdabbdbabaaddcaacddaddbdddacdadaabacccbcdaaddcdcbabaddccddacbaaadaddbbbbbcbcdaaddaacdcadcdcabccacaadacbdaddcddbdbccddacbacdacccabadcaccdadcbcbdcdcbccaaaacbcbddcdbdbcbbcdcacbcdcbcaabadaabddccbdbdbbddbadaaabccbaaabdabacbcddcccaaadccadbdbcccddbadddaadbbdcbacdadbddbdcacadcddbaccaacbadaaadcbcabbdddabbccccadbbdddaabaccadaddaccbaacdccbbccbdadbacdbbcbdbbbdadcaabbcdcbdcadcccadbdbabcdbbdddbcabccadbddcdccdcadabcabbbdbacdcabdbdadabddbcdbacaabcbbadcaaddcdacbdaaacbacdadbbdcccddcbbdaccaaacacbbbabccdbcbccdcdadabcbacbddbdccdabaaddbdcdddbbadbbdaaabbdcadaaddbcdbabbabccaddcccbdbdcadcbbbacbccddddbdccbdbdabcddbadcbdccaaaaabcacbcdaadccabbdbbbbcdbbdadddbbdaaaabaccdaccddbbccbcaddbabbaabdccbbcadcaabcddcbdadbdacdabcbdddbbbaacdbdacaabbccbdbcdcdaadbacccbbcbdbdddbadaaddaacbadcbacccaccabccdddacabcacaadbddbcdcccabbdcabaccddcdbabbbadadbaabaadabacbccbdacacdadbdcaccaccaadaabbbabadddbbabdbacbdabbcddadddbcabdccacbadbcaccccbdbcaacccbacbbcccccbbddcddbbbaddacdbdbadaabcbaaccdcacdcdbbddddacbddaccdccbbdcdddacdcdaaddbdbdbcacdadbcbbadabdbcacdcdddbbcbaccdadadcacdbdbbacaadbbcbabdcbdaadcdddacbcaccbdbacdbcbcbabddbcdbcbcddadccdacbcbbacbadbcbbdcabbacdbcacdbbacbdcbcadbdadcbdbcddadadcabbaabdddabcbadcbcbddddbadcdbbbbcacdcadcccadcbaadbabbacddaaabbacabdccbacacddccaaaacdabddabcccaaadbacddaabaabddaaaabcbacbccdbcabcbdddbcdaddbccdadaaddacbdcabaacdbcdcdcdbddabcaabbaaadbdddcddcacbccdbdbbdbbddccbcaacacdcdbbcccabaabcbaaadcdcdbcdddbccaccacbbdaddcabbbaacaddaaaabcaddbcdcdcabbbccacabbbabccbcbbacabbcdbadccdaddababddcccdbacbaddcaccdcccabcbaaccddacdcacacccacccbbcacdcbbaddacdcacdbddbdbadddccdcbbacdadadacbbababcadbabcdcdcbaddccdbdccabadbcccdbdaaacabbcdbccdbadbcbdcbcbdbdccababbcadcbdddcddbbcdbbcaddcacbdadbccdbddbcdbdddaaaacabdcdaabddabbbabaddacbbdddcdacbcbdcaaaacadcabdbbbdcadcabbdaddbdadadcdaabdcddaaccdcbbabbabbcdbacbdaaacddbbabbcbdbbadddbaaadcaaaacccddbdaacbaadabcbcccddcadabbbbddccbdbccaadaccbcbaacbddcaaaacdcaccbbbadcdccdcbcbbcddbaadcaacabbaccdabbccddadbdcdddcbcacccdbacacbcbcdaddbdddcdccaddbabdcacccaaaadbabbaccdababdadddbcadadcdbaacdbdbdccabcdcdddbabbadbcabaccdbddcdcddcdaabaacaaadadcbbaadacdbdcbdbdcaadcccadcdadbcdacaaacdadcbaddacbbbabbdddccbcbcaadbddbbccaaabbbbadbcbcdbaabccababadddbaaacddbabadcbbdbccccbcadacabaacdbcdbbcbccbdbcddaccbabdbadabcccdabaadcaddbcccbcbcdaaaddbccdcbddbbccabcccaabaadacbddbaabcabdaabdadaaabbddbcdbcbcddcccbbacdddbbabcabaaddbbdcdadaabdcabcaabcaaccbdcdaaaadbbcabaccbcdaaacaacdbcdbcabadadcadcbadbccbcdaddacaccacacdbbdabcaabbbdabccdbbdcaabbcdbabbbdabbbaabdacbdcdbabdaabccadadacddbcdcbbdaddaadacbaadaaccaadbadbdcaaddbdcaaaddbacdaaccaabaddbbbcaabbaacbbaccacbdccdbbdcdddccccbbabbcbdbbaabdadbabdadccbacbcbcaaddbdbddbadcbadabccaccbaddaabddccbdbdcacbabbdbbbadbcbcbbbcbacaccddacacbcadbdcbaccbcbaabddbbacbccbdddacaadcddddccadaacccabbabcbdadcdccccbcdcbbacdcdcccbcccbbaaacacadadaddbdadabccccbbcabdddcaaddcbccdacdbcabcdcdddbbcbddbdadbbcabdacbdcdaaddaaabbbbdcacbdcdaddaddcaddccdaccdddbdbabbdbdcdcacbbacddbdcddacaaaabcadccbdcdbcdabbccbccbbbcbbddbdcdbbdbbcdddacbacdccdbacaaacbddbadddcbacadbaabcdbadaabddadaaabbbcbccbbbdabddcadcccddbabcbccdcaabbcdbaccbccdccddacaccabcacccabbbdababddaaababdbcbadddaabdcdabdccbdbbabaaddcccdacaabdddacddcbdabacddbccbdaccdababdcaaddccddcbcabbbaabcacbdcaddadadccdddbdaadbcbdcabbadaaadbccddcbbcadbbccdbcbbaddcabcbccbacaadcddcccacdccbcdbaaaadcaaaccbadaadadddadbbdcbbdbaacbcdcabbaacbbbabcdbdaaacbbddcdbdcaabcccdddddadadbcdaddadadccddbbccbbaddaddbbaabbbbbbaadddbcddcbadaabcabaccdbbdacbaddbdbcddabccccacbaadbcaaabdddbbadabdacbccbdcddcdbcaaccbdaaaadaabdaadbdcacbadbabccbcddbcbcbddbdacdadcacddddaacaaccddcdcbbccdcddcacdaaadccdbdbcccbbcacbcbcbdbbabdbbdbbcbbdcadabbcdcadacdcadbdcacdaacbbbbdccbbdbabcaadcbbccbdcaabcabdbcccacddbbdacbbdadaaadacbddbcadcaddcbbabdaabdbcdbdccbddaaabdbadddcccaacbccddbcdbcadbbdbcabacbadadbbbaabbbadcaacdbaabbcbadddddccaadabbcddcadbdccacdabdaaabcddbabbdabbcddcadcdbdbdccbababccdadddccbddbdcabcdbbcbbcbbbbaabacbaabcbabbcadabacdbacaddccccdaabcbdcbbbdcbbadcabccaddcadaabbcbbcddbadaaadabccbbabcabbdacddbdacbacbcdbacaabacdaddcdccdcbdcabdbcdbdcdbcddcbcdccaaaadaaaddacdbbccbababddadbdacbcbdbdaaddddbcddbccadcbbcbccbbddacbbbbbbbddbdcaaabdabbcbdbadcabdaadcacaaabdbbbaadbccabcccbaddaacdddbcdbcdcacbddadadddaccdcddaccdbbacbbcaaacbabaadbccbbcaabcacbabdabbdbbddcdcdbccbcccbdcabaaddddcbdbcdbacccadccbadabccdcacdcbbdcbaddadaaaadcbbbbdbaccddabcabbbaaacdadbbbacbddabcdbcabcabbadcbbcaccddcdcaabdacaaabbadaadbcccbcbbaadbdababbddaddaaabadbddccdddaccbaadccdcabdbdacbadbdaacbadcabcddbacccacacabbccdccabadbdadbcbccddccdaaccacacbcaadcbccdbdbbdaddadbaaddacbbacbadbacdadcdabdaccdcacdabbddcacddabbcbbacbcbddcaaabacaacbadbccaddcbcdacacabbadbbcabddbbccbbcaabbbabcbadcccbdabbddabcaadcccabdaaddccdddadccadddcbabadcaaccadbddabdbdccbdbacadaaabbdbbdbddbddbbdddccbcccdcddacccdddbadaabbdbdbacabbcabaacabccddbcdadbabdddcccacddbdabdaddddcddbbdaabdacdccbcbdcaddbcccdbdcdcaadcdcdadbcdaacbbcddccaddaabbbbacbacbcbcdcbcabccabbabbcadaddddadadabccccccddccbcaaabcdcdacabadcadacccabdcdcbcddabdcacadaaccbabdccacbdacacdbaddabacaaddccabbdddcadacddbaddbcaddcdcdbacccaabbddabadddddccacccaccbbdcadcdbccacddacbdadadcbbdddcbaadcaddcccbbcbcabbbdbaadddaddcacaaadbbaabcbaabaddddcbdbbccdbccabdbbbbbddbddbddcacadcdbcacadbbcbaacccbababbbdaaacabccbccbadadddbaccaadaccdcddbcdabadcbbdbcdddbcdcbcbcccbdabbcaabbacdaaacbdbaacaacaddddabbacaaccbcdddadcbddbcdbadacbcbaabbbcadabbbccbdbaaddcadaaacbadabaccdabcacbbbacaddddbcacbacbddcdaddbbcccdcdcadbaccbcdbcdacccdaadbabcddacdccbcccdbbbbcdbcaaacbaacbccbaadbbddcbcbacbaaabdacaaacabbabaaabbdbdaaacbbaaadaddbcbcbccbaabadaadcbbbdbbaccddcdbbdddbccccabbaabcbbddbdccccddbcbacacbdbadccacabbcdabddbcdcaadddacacccaaaacaaadadadcadabccadaadbcaaccaadbaacabdcbacabbbbddddabbacbbbbbcbaaaaacbcbcdcaddaacdadcdccbcbbababbdadaadcbbacddccccdddcaaabadbabacdbbbdbabcdabadcabdcaadcaabbaadcdadcdbdddacbbdadbabaccabccbddbacbcbdcdbcbbbdddacdcbdaddacadbcabbadbcdbbccbbadddcbccddccbcadcdddaddccbacbadbaaabdcbccdacbbbaabdccccdcdddbbacadcbaccdcccbcdcbbdabaaddcdacbccccbdddcbaddcacabbbdbbcbdccacbcabaaccbdbbdbadccbdddbabcadadabcabbabaaadbcabcdaabddbddbaccccdcdcaadaaaacdaccccbadabbccbaaaacdaddaaaabaaabdabcbbddbccadbcabdcdcdcdcdbcaadccbdaccbccadaaabbdaabbbdaabbdccabdaadabbcaadacdbcaaaaaabbcaddadcdadacbaacbdcdaccdcbbddcbccbcbdbbbbcbababdadcdaadacccdccdbaddcddbbdcdbccbdbcdbdaabcaccbbbcdaabccabaccdbaacbdacaccabcbadadccacbdbaccbaabbadcaccbaccbadcccccbccabcaccadaabbdbadbcacaacadbacccdadcabcdadcdabababbdcabbaadbdadbbadcccabdbbabdcdcaacdbbacdabcaddcacccbcaaabbccbcabddbcdaddbcdbccacbcadbbdabdcabbaabacaabcaddbcbaaaadbdadcbddbdddbdbcbababbabdabddcbadbdacacdcccadbabdabcdbcacacccadcdabdcdbddaacdddabbdaaadaacddaaccdcbdbabaabcccbacbdcbdbdcddcbccacccdcbddbaadbccadcacbdcccacbbaabbadbadaddacacbcacacccbcaccdadccdcbcbabdaaacbabccddbcccbdcacadacaaaaccadcdababdbbdabaaddcacbadaabcaabdacdaadadcbbbcdabbaaacabdcaaabacddaddbbcbdbcccdbbccadcaabacbbcbdaccbdaddbacaadacbcbccaddbdbdaacddcbaaadbccacadbcdbccacdbbadadbcabdabdcdabcccbcbdccabbdaabacbadbabbbbaaddacbbcddddbabaadadccaabbbbddbabcbcbcabcacaaaaddaddddabcaaacbccddcadbdbbbbdabbcaddaacdbccbaacbabbaabcdacccaccdcbdccdccbdabbbabacbadccabaaccbacdbadbcaccbcdbccbddacdcacadaabdcbcacbcabaadbcbaacbbdbbbccbdcabacaddbcaccadbbcacadcdbdccacadbabbbdbabcaaadcaaccbdacddaabdbbadbaaaadbcaabdacbbbdaaabcddbbddcdcaaccbacacbaacaddccdccacdadcddbaddcacaacadabddcbacabaacadbcaacccbdcabcbddcccbcadbdabbcbabbbabcabcccdcdcbcccbaaabbddcaacdbacccaaacccbdadbcacadcccbcbacccbcccddacacbcccbcddbaccbdccdaaaadabdccdabddadaddaabbdababccadbcacdabaaaacdacdbaacdccdcaadddcdbcbbabaacaacddbdbbcbbdcdbadabdacccbbddccdabdbbbcddbbddbbdddadccdcdacadbcdddacccbddcaccabcccccdddbdddabacccdbdbcabadbbaabcacbadcdcddddccbabcaccddcbbaddcddacccabcddcccbcabcabcbaccbaabdcaacaaaddccbadcbcdabbaaccdcddabdcacbccbacadbdbacabbbddbaadddbacbaddbdbdccbacdaacbddbcdcccbdadcbdbabadcaccdcabcccbabcabaabcaabacbdbdabcdddcadabdbbbddbadadcddddcbddbbdbbbbbbdbbdcccbbdbcbddbbaadaddadcaccdaadbbbcccbbbabaccdacabbbddcdababcadadcaaabbabcdbaadbccdcdabbbbaacacacdcacadcdbabbccdaabdcbdacabbbcaacdabddadbbdccccdaccdcccbdddbbcbbcdcdcdbabdcadcbbbbbdcbbbbcddcabcacddcbabbabbdcdddbadccabbaadbbbbbdccbddcccdcdddcdbdaadaadcbabdcdbbbcdadbcadcbacbccbbbdcabcbacacdabcbdcbddcddcdbbbbacbaaacacdbccdddbcbcbbacbaaabaaabadcdcccbabcccbddbbbabbbaadddadadcccbcbaccadbdccbddbccddbadbbbcccdbaacbbbbcbcbdbdaddadcbddbdbcddbccaadabadbcddcabccdcddadbdbddbbbcaadddddcbddbbaabbcddbadccdbdcacddccaababadcacaaaadbacaabdcdbbdcdbbddcaddcdabcacabdcbcacbdaadaacccdbcbadadbdabbddbbdcbaacadbddddcbbdbcbccbacbddcbcacdcccdcbaadccbdbaccdcbcbaaabcdbbabcdbddcacdaddbacbbcdcbaacdcbaadadbcacdaabbdabbdddbcadbacccadadaccbddbdccdddccbacadaaadbabcccdbadbcddccddacdabacaddbadadcabdbaabcacddbaabbadcbbdcddabbbbdbcdabaacdadcddccadbbabdbaadadbccccdcdbdabdcdabbbdbbbacdccdddccaddabaaabbbcacabbacacaaaaacbcadabdbbabcaccbacbabbbbdbaaacbcddadaadbccaadacacabbadaddbdbbdccaaccacaabdbdccdcbacacbbdadddddacdadadbaaabadddbbcacddbcabacbacdaabaacddbdbddcabcdabaadabaddccdabcbddadcdbacccbbbabcadcbbbddabadbbdbcbcbbcaccbcdaddcbdbbbaacbcddbaccdabbbcccccacbbdcdbaadbccbdabdbdaacdbabcbddcdddbbddadaccddbadaadbddcaddaacdaddcccbcaddccdbcacaccaaaacbddacdbacccdcccacadccddcccdcdcacdacacbdddccbbdacdbcbacdaadbbbcbadcadababbccddcbdccdcacbbccbadcaddbbddcdcddaddccdddaabcbabbbccbabbdbacbbbbcabbbccddbcbabadbbadbacabdddabdcbbaaaacbaccacbdaabaccabacadadbcaabbcbccaddbccccddcbdacbddcdabdaccabbddccdbbaadabcbadaddbcadbaaddbbadcdddccabcabbddddabbbdccadabccbacadadddaddacdbbbabcadacdbcccdcddbdacadabcdabdbcdbadbbacddabacbbcbdbacdbcacddcbbdaddababdcdcdbaacbaccdbdabcdabdaabadaadcbdcbcbadbaaabdccaaadbbddcacbdabcddcbbddacacddcddcbacddadbaadbdaabbddaccdbcabbdbbdbdcbbdcbbccbbaaaccdcddccccdcabddcddbcadcabadacdbdddaddcdadabbdbbcbdaaacbcacdbbcdccdbabbccdcaabdaacbdbaadcbaadccacacdbbaabcacabbacdacddbddbadddbdaadcacbbabddabdccbdbdacbcbacabacaabcacccbcdddbdddacabaddbaaccaddadbcccbdaadccccccdabaccbaddacbccddbabaaccbaaababdcddbbabcdadcdacddcbbbadcbaacaabdcddbdbccaaadbdabaaaccbcbadbbbbdccabbbdadabcbdadababacbbabadbaacddcabcdadbddbcccbdbcbcbdbaccdadaabadddcddbadbbbbcaccabcadadbcbdbcabadabaddcbadadaadaabccddccadaaabcdcaddaaadadaadcaacccdcdadbcddbacabacbbdabddaaaaabdbabddadabaadacddbddcacdcaccaccdbacdcaddabdccbcaaccbacbbbdbcdbbbddcbabcbcdddacbdbcdcbbbddcbcccbbcbbdaddaabbabadcbacddaaacaabdcbdbadadbacddddcdccccadcdbdabaadcbbbdcbadbaacbccbbadcddcadcbbabadccbaddabaabacbdddddcdddbccdbbcdddbcadcdabacbdbcdacabadadaacdaccaabbdbdaccdccdcbaabcbccbbbdcdcdcdaaadacdcdbdcdcababccdbacbccbccbdabaddacabdbadddacbccbbbdbbcdaadcaaadcbcbdbdaacbadbdcaddcdaabdbdcdadbdbdbddadbaddccbbaaabdadbddabccaaabaabcbaabdcbddacdabbbcbcbdbbddcbccbcdcaadcccaabaccbdcbbdbacaddacdbbcacacbcdaddbbcdbcabacacadbcbdbcbdabadcbadaabcdcbbdaaacadabaddbbcabddadddcdbbbbabcadcdddbadcdcdbcbacbbcbabbcabddbabbbbacbbbdcdccbcdabbcccaacaadadabbdbaccaddccadbaccaddbbcabbdbccbbbddbbccadcadccddacbabaaccabbbdaddcbacbacadbbbabaccbccbbaccacdacdcdbdddaadbdbadccaaacbcddcbcbbaaddbbadcaccddabddacadabdcadcbdacabbcbaabdaabbaddacbcccbacabaccbbbcdcbababdbbaaacbdacabbcbaabadddadbdcdaacdcbdaabdcdbddbddbdbbaaaccababdacbbdddbaacaaccbadcdcababbbadaaadbdaddbbdaacdadcadbbbbdccbdbbcdbddcaabadcdccccbbcbdbabdcaddbabbbddadcdcbadbddacaccadbabbbabdadabddabbabababacadaddddddbabbacdbbdacbabdddabbbbdddcabadbcbddcccaaacdaadcdabccaadccdabcbabddadbabcdcdaddbdccbbababbcaabdaaacabbcdbcdccadcddbcbddabdbdacbbabbcabcbcacadbdddacadcbbdcaccccacbbccbdbdabbdadadabacaabacbdcacbbcabbddddccddcdbdddbccbcacdaabaaaddddcbaaaddabbbaacaacdbaccabcdbbaaacdbbbacbddcdabcccccabacbadddacbbbcabbabcabaccbbcdadacdabdacaabbccbabbbcbaaaacbdcccbbadabbcbaabcaadcbddabdddcdadbadddaaaddaddcaaaccdbadbdbaabbdddcabaccaacdbcabbbbdddabbbcadabadccbdbbacdbabcbaaadbaadabadbdcccabccaadbbacdadadbcadaacbcdcaaddcdbcaabbbbbdccdbbadccdbdcdacbabccccbdcaabcabadabbddbaccbaacbdacbacadadbcdcdbbcacbdaddabbacbbdbaabbcdcaddacbaadacdccbaccbdbadcbcddccbdadbcddacccdcacbadcaccaabcadcdbacbddbdbcccbbacdcccddddcacdbdccacdcdcdadacbcdddcdabdcbbbbaacbdcbbdcbdbaadaadddcbacbbcbddcbddadbccaadddabbcbadaccbccdddbcbdccaabcabbabadcbddaababcdcbccadacaabbcbdacdbdacdacadadcbcbaccbbddbdabdbbddbbdacbbdbbcacaabbbaccdcddabbadbbccbbaaabcddadcbdbdcadcbabbbdcdaaadabaabddabaadaabcbdacdbcbcccbbbddacccbbddbbaddabbdddbdabccdcdbaaccbaabddcaddaaacbdcbcdaaaccadbcbdaabbbabbdabbccbddadddcacacccbccacdadbbddddcbaacdaaddacbacbcdbdddacdbbbaadabbaddabdaddbdabcadbbbcdabadbdbbcbdacbacbbdcdadbcbdcdadccdbadbcdacddcbcddaabcdabbacadabbaabdddaccbcaaaddbcccbacbaabdbbabddddcccabcdacbbabacbbcaaabdddaabaadcdabbccaaacaccddbacaddcbbbcccbbbddbcddadcbdddcdcbdabaaaaacddbccdabdacddbcaccbaacbdbcbcbccdbddabbcccaaacdcccacaccdaaaddabbbccbbbacbabdbdcbaabbdcccccaccaddcbabbdcbacddccbddbdcbcbbadacbbdcddacdbccdaccbaacacdbbcaaabbddacabdcbdcadcdaacbaccbcabbbbababadcacaadcadccbccdaccbbcbdcbbaadabdbababaadcbbccccdddabacacacbaaadccdcdcdbdbbdbcdbddbadabdacccaccdabbdbbacdacadabbcdacaaddbdbbcddddbcaabdbacbdbcabddbdbabbddcbadcbdddbcddccadacdcdcacbacdaabbdcdbbcbbbbcabcadaabbcdccabcbbabdddacaddddcaddcabaaccbdcdcaddbcccdabaaabaabdcbbbddadbaacdaddaabcdbdddcdaaddccaaddaacdacdbaccdddbdaabbabacaaddbabdcddaabddadcdbadacccacbcdbbcadabdcdaddbcbbccaadcdbbacacccdadacbcccbdaccdbdaaaadcbadababcdcaabbacadbbacdacddacbdbaccdccbbdacbdcdbcccbccdbaddadbacdbdddaadccdbcbcdbbddaabbcbcdacbcdadabbbaaaaaaaccbddadacdddbdcdabbbdaabaacaaccaddccdaaccbccdddbccaacdadddcabacbcbccadaaaaaacbbcdbbddbadcccdbcbacddabacddcaabcdadccbdacdbddcbdabdacddaabaabdddbadcabbdbddddacdabdaddbbabddabadbcadaaccbcacacdbbacdcbdbabccbccbdcadabccaaacbaadcbaaadbdbaccaabacbababacccbabbbbbbacddacdaadbdbaacdddbdcccddaaadbbdbddcccadbdabdcddabbdddbbabaaabcdbaadddccdcbdabbcdbdbcdacccabcacbccabdbcccbddcabcaabccbbbdabdabdcdabbdcdbdadaddbbdddbcaddddabaaaaabcbdddbdcbdcbadcadbadcbcccbccddacabddadaabadccbbabdcababcdcbbbacbbabcaacddacaadccabdacccdcbdabcbdcbbcdacaaabcdadcdbbddbcbcacbadacdbdcbababbcacddcdadcdacaadbbcaccdadcbabcabacccdababcdbdccccaaababbadccbcbadcccacaccddbdadbcdccbdbbcbddcbcbdcaacacdbaaabcabaadcacbaabcdcadbdacaaaddadccddabadcaccbcbacbcacdaadbccdbcacdcbcccaaccbcbbcccdbbcdbadacbbcabaaabcbcabcacdaddcccacddcaacdbcdbbabddaabbcbbdcacdadcabbccccddacdcbaccdabbcacaacdbbacbdccadcbccccdabcdaddbdcdaababbcbcbccdcbaaccaddccddacaccbbaddccabccbbacbbbbccbdbaaadddacdbbdddbdaccdddbbbcbaabbbbcbccabcdcacaddbbdbddcccabdaddcbdbbdbbbcbcddccbccdacdabbcddbadbddcbaadbbcbbaadbbcabcabacbbaccaabcdcdcbbabdaaaddbabadabdcadcacdcacdbdbadccbbdacbdbcaccacbdbabdddbcadbdbdadadcdcadbbdaadbdcbbcdadccdcddbbdabcdcdccdccccbddadaabbdadbdcadcdcaddabdadbdaddbdbbcbadaccbbaaacbaddccadbaacdbbaacbbdaadcbcbabccbabdcbbcabdababbbaadbbadccabdbbcddcccaaadadadbcdddcddcdddbdddcdcdcbaababdbaababaadaadadddccbbacdbcaacbcaadccadccddddbabbbcbaababdbacadddacccdcbdaadbccaacbcdcbcdaccdbddcbccbadacbcbddbabdaddbbaaaaaccadacdadaacddaabcabccbcbabaccbbddabdbcaabbbddbddacaaddccccaddaccacaabbbddbccaccdaabbbbababddccabadacdddcdbcbcbddcdbdbdcaacddbbbbaabbcbbdcabbdccabbdbbadacadcccaccabbcaabbbdabbbacddbbbcabcddaddaabcababbcdbdaabdbbdcdccdcaadabacbddcdaccaaccaccabcdbdbcccbdbccbdccbaddabdcbbabadbaaaddbcdcbbadbccaaccdadaadcdaccaacabbcbbccbdaccbdbdccbdddbcdabbcbdbabbacdadcacbbcbcaacdbccdabddcbcdbcdbaaddaadbcdaacaabbddcbcdcbadadbabaddccadcaccbaacdcadaababcaddacaccabdcbbdbdaabbdcdbadacbcbcbdabcbbddcbdcadbcbdabcbdbbbadccaccbdacacacbdddcdabbbaadbbadcccdadadbcdbddabacbabdddcbbdadccadabbbcdbbbdbcabacacacacccacdcaccbdabaddaadacadacbdccbabcccaadcbccacdbcdabacadcdcddacacbdabcbdccbccdcadbcaaaadcbccbcdbddccdacdaaccddabcacdaadddabdcaacbacaccaccbabcaccadaaccdbdddaacbaaaaaaddbdcdaaacadcdcccdaabdcdbbbdcdddcadaadbcccbbbbbaacabadbbdcacbaabbdbcbcaabbddbaadbccaacaaadaadacbdbcdbadaaccabadbbacbbdabdaaabbbcadabbbcdacdbaaccdbcdddacaacddbbddcaddacacbdbabbcbbabbbadaabdacaaaddbabddbcdacaddcdccbbcbacdaacadddabcdadcbcaacbddbcbbaacbaacbcbadcbdbccbcbdcdabcdcacbcdddaaccacacdaaacabdadccaadacabdaadbcbcabbdcadccdbbacdcddbbdcbdbbacbaadcdacdddadcccaabcbbccabddddbdcdabacaccdbdbcaccbcdbdddacbcacabbdbaaccadabdddcbaadcdadcaaacccababadabddbbabbcadbddbcdabbdaadcccadbcaaddcaabbcdcdbcbabacaaaacababcdbbbcdadbdbddcbadcaaacdbcdbcbcacadbbcbdaaadcbabddbacadcacbadadddcabdbababccdcacbcabacbcccbaaaaaacaddbaacdccbbdbddbabacadcaaaccbcdaccaaccbdddbadcadccdabddaaccdcccbccadaabcbccbdccbadbabbcacdbdcdcbdbcdcadcaaddbbcddbcdabdadcdcbbcdbbbdccdddbcacacbaccbbbbaacbddadcdbccdcadcbdcccdabcccdbdadbbbbacccddcbaadadcddcadddadcccadacaabccaababbdababdacdccbdacddbcbadabadbbbcddbadbcacadbadbbdddabbdadbbacaddadddcadadcbbccdabadabdbcccbdacbddcddcccbacadacbacdaaacddcdbbdaacdbcdadbacdcaddadbadbdbbdcbbdaaaacaaaacbccbcaacbacbddccccbbccdbaaaaabababcaadcccbddacbccbdaaadaadaddcbbdbbbbaaabaddbabbcaddbdbdabccaabcbbdbcbdababdadcbcdbbdbbbabcaadcdaaccaddbbdcbacdbbddbaacdabdbadbbbaddaacbdbdbddaaacdddacbbdadcaaabcabcbbdababaacaaabddadaaabcaccbdaaccacdcbcdadabbbddccbaacaccbbdbabaddcadcccdabbdcbdbabdbcdbdabcbaccdbdcccbdaadacdddaccbcabadbcbddbacdbdacbcdaddcacaccdadbbaaadbadbbbdadcbabdbbaaacddbddccdaabbbcabcbdaacadcbcdaabbdabdbcdbdcbbdbcbadcacdbaabbdcdccbcaaddaabcbdcbacddadcddbacbccabadcdccbabababdbabdaabaacdabadbadaddbccacacdcaacccacabbbcbbdbabddbcbbacdbccaccdcabcccdadcccaddaaddacbbcabaadbccdcdbaaccdacadbcbdccccbcdbdbbaaabaadbdcadbcaaddbbcdaadbbcdacbbddcdbdaadcacddabbdbcdbbdbcaddcbbbdbdbbadcddcabacaaacbdbdccdacdcadcadbcdcbbbbbbcadcdbbabdbdadcacadbbcddbcaddadaadccaaabbcbddcacdbbdbbabddddcbadbdbccddcdcbbaabcbbcdddcdccaacdaacaaccacaabdcadddcabbbccadacbcdbdcabcbddddabccaccbdccdccacddadaaccdaddbadbaadcdbdccccdcbcacbbccabdaaaacbdcccaacbdbbdcabddbabcadcaaacddbacbbcacddcdacccbdccbbccaacdcdbbdddcaddbccacadabaabcdbbcdbcadbccaccbbaabdbbdddbdbccbabcacbdacbcbdddbbacabaabcadbdccabdaaadacbdccbcaddaaabaaddbabcbcadcbcbbacbccbccababccbbdbabddacaadcdadbdaadddccdcddaddaacdbcdccbcabcadcaaccadbcbcbbdaaacbbcaacddabbadddabbdbddcccabcadabcabbddcccbcacccddbbbaadccadbaccacbabdbddaccddacacabadcccacacdaaababcbbbbcddcdbabbccdcaddccbbaabbaaccbccababbcadcabdcaacbbdabbddddcadbdbcacccacdcdddacbddcaadaaddcdabbacccbacbcbacaaaccbcadbbacbcbaaacababbbdcdabbbbdcdbdacbcaddbcbbccadcabdaddaacabdaddcbcacccaabcbdacdbdadccacccbbadbbdbdaccdcaacbdbddcadacaadbcbdbcbaacdadddddcdbddbddadacaacaaddacccbabddaaaadaaaaaccbbccadccacaacddacdccbdcdbbadbcdbadbbacdbcaaacbcabcbbbacddabcdadbcddddccbcaadccabadcaccadcacdacbbcdcaaababacdddaabbdadccbabacabbcdacdcabdacdcbaabcacaadabaadbddbdadcaaaadcabbccbdbcadabdacbdbdbcabdcdadaabadcbcdadaccdbabdadcdddabdabacbbccaaaccdbdcccababbbdcbaaccaacdcddaddcaaaddcbcdcadcdababcddcabbacdbbaabbbcbdddbcbbcccaadddbbcabbbabbabbadbddacbbaabccbacbcbbabccadbcdcdcdccaabcbaadaaadbabbabbabbcbcbcdbbaabbadcadccaccbcddcddcadbbdadbbcccababbbbcdcabbcddbacbbccacbbdccdbbabcdabcdabbaadaccbcaddcdabcdcbdbacbaccddbbbccbcaacbbadcdddbdbaabaabdcabaadcdbdbadaadbddcacdddbbdcbbbacacaabcaaddbdbcdacadbabdbccdaccdbbdcdcacddadbcbaabacdabcacbdadbdbbaacadcbcbcaaabbbdacbaabacaaabbdbbdbbcdadadbdddcadbdcaaaddbccdbcbcbcdaccaadabaacbbbbdcdbcbbbdbccaddbaddabdaadadccdbbccababcdbacadddbcddcccadabccdadacdabaaacddcdcccdbbdbadcbccdbacbacbaacbcdacccbbdabbdaaaaaacccdaacdcdcacabaddabadacbddcabdcadcaaaddbddaddbdbacccabddadacbbaaaccdcbbbbddcbcbdaddcaaabadaccdcacabbbadaaabcccdbaaaaaadacddccdddddbcabaabcadcbdbababcadbcdbcdcbcacbdbdcaabbcdbccbccdbdccaaaaabccdccabcbbcbdcabbddacbcbbdcdcdaaaadcacdacbbacacddddbbbbcdacdbbbcaacabcbababbacbddacaabaaddccadbaacacbbbccdadbcacddbbccaccbcbbdbcdccbabdccababacdadcacbdddccddbccababcaddacaabbcbbbbcaacaaddaccbccccabcdbadccacabbcabadbdadcbbdcadbddccddcdccccdbcdacbaccadbaabddbdcccbacbbcbdbbccdadcacbdcccbdabbabdbcbdbcbcbbcdbaacbcbbbdaacadccbdcbcdcacbabadcacdacbccaaccddbbcdbaddbaacbcdbabcbddddbabcdbdbabbabbaaadcbbccbcadbadcabaccdddbdcdcdbcdcbdaacdadcababdaadaabdacbacccbdbccadcdaaacdabbdcdbbdcbbdbcdbdcacdbbccdcbbaacccabcdddcaabbaaaaaacadddbbbbbbdbdddabbaddbdbaccdcbcbbbbdcccdcaacdaddcacbcdbcacbddabbbaddadcbcacdcdaacaaabcdddbbdcdbacadacdbabcabcddcadbbabcdbaaacadbaabadadabddabbaaabcbcbddbddaaacccbbbbcabaabdabdcabcaadcaaaddbbbdaababdcbcccdabddacaccaaddaaaccacadbddaaaacbcdddababdaabbdcddddcdcdabddcccdccadcdcdbbaaadaabccdbdcdbbcbdcbbcdacddcddaacdbbbcbcdaccaaaaaaabcbdbddcadaadcaacaaacadaabdbabcabacddababbcbbcadcbacdbadcbddaadcbcbccdabadddddbcbadaccabcbccadccaaccbabaadddbbadadcabcccdbbdacabbabccdbaccacccbadaaccadccbaabbdcaddcacccdbaabaddcdcdadbbaacadcabbacbacdccbbbdaacbcdcabacbaaabccbccdbddbccbcdacdadbdbcdccbdddaaacbbcdbaadcbbcccbbbbcdcbacbabddcdaaabaddbcbabccadcddbabbdcadbbccccbdbcdbcbbadadbbacadbbdbaacaadbdbaccbdddcacdadadcdbcabdacccdccabdccacbddbbadbaabccadbbadbcabdbdccbcdbbadbcdbbabaadbabbcccadaaccbcdadcbdaacbbdabcacbaabdaabcdddcbabcddddbcbcddaadbddcababbbcdccdcdccdaccaacddcacddbadcdcaddadaaaabbcbddadcccaadcabcbccbdabdcdddabdddaddabdbccaaababcdcbcbaabcadadabddcacbdcdaadddcbcacadcdcdcbcbdbacbdadbdcdbaadbabaaaccdabbcbcabdbbadccddadbbbdaccbdccccdabddcdabadbaadadacbddadbaccbdcdbbbadaccbccccddbcdccbadcbaabddbdcbdcddcacddcabbbabdcddbdcdbcbdcbaabddadbadaaaacabcacdbbdadabccdadbbcdcccbdbbabdadcccdddabbdaaccccacbdacabaadaddabdaacabcdbacbdaacdcdadbcccadcccdcbdbcaccaabadaddcbacdacbdbdabaddaadadaddcbaccdbcccbcacbbbcdbcddddddbaaadcbabbccdbdcdbdcbbaddccaabacbbadccdcbbbcdcbddbddadccdacbbacdbabaaddbdccbbcdaccaaadcbddbdadddaccbcaddcdbdcccadddcdaaddacdacccabcccbddacabcddddbaccabccbacdcaccbaabbcaaadbbdabcccdacbcaddacaaaaaccddbadddabdccccbddbaadbddbbdccacaacdaacdbccbcccbabacdadbbdacdbcddbcbaabaddadbbbcccaaaaaabbddbbdddcaddbcaacabcdbbbacaddddadaddcbcdccdbbcaaadbbcdbcddbaacabccccdbababcbadbabcbcbaaacddadddaddaabadcdccacbccdcbcacddcccbbdbbcdbaaaacddddcaacdbbbcacbbddddcdabdaaadcdbbdcbcbbbadaddbddabdcadccccdbabccabdacbcddaaabbabbabbdcacbbabddddcacbbabdcdddbaddddadbcbbbcaadcbdacbddbaddcdbdbbacdccadababacdabcddccaaaccbbdcabbdcddcbcbdcabccbcdcbaccdcdbaaacabacdadbdcbaddcababcadcabbaadabcbcbacaddcbddbdacdccaacbdbccdcaacbbcadbdabaadcbcbcbadbbdaacddbbccbbdcdbcadcddccbccdcdacabccaddacaadbccbbccbccaabcaaaadbcacbabaddcdcdacacdbbacadccbbcbdbbbbaaaaadccbcbacaacdbcbbabdddcddbddbcddacbbcbbbdbdadabdabbccdbabcddaddacbdbcbaadabcddcdbbbcdcaddcadaccaddbdcdcdaddacabadcbbaadacbcdcbccdaaacdbadccdccbcdccdaaababdadaadccacdbcddbbcadbbdbbabddadabbdcbddaaaaccabcabcbaaccbbabccdadabdcbddabcdcadacacdddcadacababaadabdcdabbddabaaddabbcbcdaaddacbabbcbbdbbccbcacbdddbcabdcbddcabddadcbccddaaabdbcbcaccacddacaadbaabbdbcbaabdddaadacaadddabddacbdcbccbdbcacddaaababcbbabbcadcaccbbaacaadcccbccadacbcbcbbccbabbbadbdbaccbacbccbbabcdbbcaacbbaddddcddbcdbdbdcbcdbaabcbbcdaccdadabbcdccabdbcbbacccbaabaaaabbcbddadccdaadadccdccadbddabdbbdbcbcdaaaddbaaaccacdbdcabdccaabdcaabcccadcbcdabbdcbdabbbdbccdcadccaacabcbdadbabbcbaabddaaccabbccbcccdcccbdbcbdcccbdacdaadbbbbbacdbbaaabdcddaabbcccbdddcdddabdbabccadbbadccddadacbaaaddaadcadbcddadbcacdbbdcaccbbaacddadbbadaddccbcdaddcbbccdbacdaaaccbcacabccdaccaaadccbccdabdcccabcbcaaacdbdccccabbabadbabacbcdbdcdbbabcaaddcdadbbcacbcccccbcbabccadaabadcdadcccadabddaaddbbdbaaaccacbcdcaacabcaddbccacdbaccdacbbbddabcaddddbdbbbaaadcaadbaaadababcaaadcdbcdcddccacccdcddaabcaabbbadbbabbaddadadabaadacaadaadcbbcccddcbbccccbabadadabbacddadddabdbccdccbdaadcbcadabdacacbbacccdcdbbddcaaaaabbcacaaabcbdbabdccbbbcacdbcadbcabaadcbccabddcdbbbabdccdbdccdabcadbbdddcabacbbbaddbaabaaaacacacbabccdcbdcddaadadacdcadccaabbcbddbdacddbabddcaababcbcdabccbcdcdbcbdadcadbbcccaaabcabcdbdbbdbaaddadabaddcaaccbbdabbbadcbbbcdccabdccaadaddbbccdbcaddccbaaaaaadabacdbacdacbcddbaaabccdbcaccacabacddaacadddacadbcabbddadbbbadddbbdadcbcbddcdabbbdaccaabbaabbcdcbccdbdadadddbadcbabcbaabadcbcdaabadcccaaacddaadacaabcbabcdadaaaadbcdbbdcabdcdcbacdaaddbadadabbbbcadadcbbbbababbbcdadcaccdcdaacacaccadcbaacabdacdbbcaaabcccdddbdbbcccdcacabdadbdccacbdccbbcaddadaaddacadacbaaaccbdcbccbacddadddcbbadbbcbbdabdbdbbccaadadbdbdabacddaaacaccacdaaaaacadcababdaabaacdcbcbaadcdcabadacaabdabcccdbadbcbacbbadadacdacccbcbbaaaadbbbabadbabacbdabbabbdcaadcaaccddacabcbabaadcbaccddcdcadbcbbaccaadcaaddbbdccdcabdbbbadcaddadccbaabbcabacacbbbdaaacdadbdaabaaacaabaaaaadaadaddacddbadcddcabbddbabbdcacacacabcdcaaccdaabbcaabaaccabaddcacbabddadccddaacbcbaabcaadbbbdddbabbbbadadcdacdddddcdcccddbccaacbcdcacbcccacdbbdbdbcccadbccacbdcdabadaababbddbcaddaaaddabaabbbbccbbdcbbadaadacdccbaaabdddbcccdabbcbadabdaddcadbbdbcbcbcdcdaccadbdcadddaaacdabdcaacbbdaaddcaddcbdcdbacdddcabdadcaccbacdcabcbadaddccaabbcdbddacbbccdabdccabaabccddbbddbdccbdabbbccadbbaabddcdcbabccdccbacbabaaabbbcadcaababdbdbccddccddbccdcdcdbbbddacbaabadbacbdaaaacaacacdbacdcdcbabcacadcbddabaacdabbcadbcdbaaaababbbccdbabdcacbdadabbcadddcddbcaabbbccddbdbbadcccbbbbaddacdcdbbcccbcdcabbdbdcdccdaccbdbdbbbdadaaddbbacbdccbcdbbaaccbcdbacdbdaabbdcacabcdddddabaddbdacabbdbaabbddcbdbbbddbabadcbbaabdcdccadddaabdddccaabbaddabdcbadbbbbacdbabdbadcbacddadbbaddcbdaadadccdbbacbbdbcdccddcaaacdcdbbdbbddaaadcbabddbcbbbcacddbaacacbacbbcabaacdbcbaabacbddacbcdadaacbdbdbbabaabaddbcacddcabcbdbbbaccdadadacbcdccbbdcbdbdddccbaaddadcabdaadacdcbadcdbcbadcdaadbbacddaadabccbbdabbbadaadcbcdbccaaacdacdaadabbbacabdbcbdddcbdcacdddddbcaccbbccbbbaadbcdcdabcdcdcdaccdbdbaaadbdaddccadcdbbadcccbbddaadadbccdcbacaaabdcdcbcbdcbbcddcbaaaccdccdaddbaadbbabddddacbccaaabcbacacdadcacbabacadbdddacbdaadacadbdbbaabcacbdaccccbabbbdddcccacbacdccddaabbacbdbddcdbbcbbbcbcaababbadacdabddacdcdcbbcbcbdcddcadbddbcadcbccaaacabbdddcccababacbdbbdcbbdcdaadbcdaadcacdccacabdabadcccdcccbadbcddbacaacbdcdbbcaadabbdcbacbcabbccdaadcaabaacbcddbaccdcabcabdabadabcbdbcadccbabaaaabacbbcbbdbbdbaccbdabbbbdbabaabdcdbbddadcdcddcbabcaddcbcacdaaaacdbbcbaaccccdaabdddacdaabbdacdccbaaaadabddacadcabbbbcdcbbbadadabdbcacccbcaacaaddaaacbdbbaaaccbbdddcacccbdbcddbaacaaccbaabbaabaacbddddbcbbccdccadcbddbccddacabdcaadaadcbacbacaaabbbcccadcadbacdccdcddaaabacacbbddbacbdbdbcbbccbdaaccdcdcbccbccacbccdccadbcabacddbcdcadcbadbccbadacbbbacdcabcccdccabbcaddaddccabdbbcaddbaacaacbddabacababcdcadaddacdbcadbbdabcdbcdadcccdbdbcabcaabcacccdddaddabddcadacbcadcdccaddaacccacbcababbaadacdbbdaadabdddabbbcdbdbcbbbacabdbcabaadaabddbbdabbaadcbbbddccdddcbddbadcbacbccbccbabdddcccbdcdddaccdccbdbdddadcdadccdbacaddabbdccabdacaccacccdcdbacabacbcbdacbabadcadcdaabaadbdccbadbbaacbbddddbcbacbcbabdcccacadddacdacdacabbacccacdbadddddabcaccdaacbdaddcbbacbdbccadbdbdbbcdadbabbdcbadaababdcbadccbadbccccdbcaccccadcadacbdabadbabacbabdaacdbbdbcbabbcddbdbbcabcdddabbcbbdcbdddcdccdbdcdaaadaaaccdbccadaadccbcacccbbaaccbcdddbabaccabddacdabddccbbddcbddbddbddbbdadcbccacdabbbcdbdaccabacdcaadbdabdbabbdaccbacbcbbbadddacdcadbbababddbdbdaabcddabaccdbcbbbdbbbbbccbcdbdcccdccbadabbdabbbccaaacbcbcbdbcacaabbdabbacbaacdbdcccccbdccdbccaababcaacdbdcabcabdbaaaadacdaddbadbbdddcddcddabcbcaabaddadbabcbddbbcaccbaccaabcbabbcbcddbbcbcbcbcaadaadcdaaddadcdbddbddaddcddcacabadcacccbacbddabdabbbbcddbdaddabdccdbcdadbdcbacccbcbdacdbaddaccccabbbdcdabaabddcacadccbcbbdcabdcddaaadcdccccacddcaddaccacdbabdbcdbcdabcaccaacddbadcbdaccbcccdacccadcbccccddcabbbdbccdbbbdbccbacbddddcdbbcbdbcdbbadaacccbcbbcdcddcddaaddaadcbdbbdacccbaacbbaabacaaacbdbdbdaabacaabcdbbdaaaaaacbcaccdabcaabcbddcccababbacccabcccbadacbcacbbcbcdcdbadabcccddbccdddbdacddcdddbabaabcbbcddaabccabcabbddddbbcbcacbdadaabdadbaaddaaddcbcbbabccabccacacbbcbbdcdbdabcbbcbbdbacccdcaadbbbbdacbcdbaaacbcdcdbdcdcdcbdcdddddbcacdbcdcaddbcdbbbadabbdcddaddbbbdbcdbcbcbdcdbcacbbaaabdbcaacbadcbcdaacdbddccdbcabdabbdcabbbdbdcbbabcbdaaddbdddccbbbbabdcbadcbbadacdcacabadbdacdacbcdcaaddcbbbbacaaadddcddcadbdbbadcdcbbccabadcaccaadbbccabdbbdddbbcbdcbbcccadadcbacadaadddcadadadddbbcbbbadbdbbaaadadabccbadaadcbadbcbadaaabcbcccdacacbbbbabaddbbbcdaddabddcdabadbcaabccbdcaadbbdacbabdcbcabdbaadbacccbbcdacaaaaabbabbdbcdacccbaabaadbbcdaddaabbaadaaacbcbdbbcbcbdbbabacadddccddabdaddccadadddbcdddadcaabcdabbadadaacadcbcdacabccddcbdbdacaaddcabcadadcccdbcacbdbaccabdbaacbbddbaadbbcadaccaccdbcadabdcbcdcdbbccbdbdabbcaadcdbbbbbdddcbacabdabaacbccbdcabcccadbcdccdbbcdbbacacaababbcbabcadabacabbbdcccabdbcbbdaabaaaddaddcbbabbccbdbdaadbbdbaabdccbaaaaabdbcdcdacaabccabddbaacccbcbbccdbbccbdaaadddbcacbcdbdaacacadbabdbbadbcddddaaddaaadcbadbdccadcaabbacdaaaabccbddadbadaaaddbccbacbddacbddacadcbbadadcdaacbccabdacbdadbabbcbabbbccbbadddccacccdcdabbdacacdaaadaaabccadadabbccabddaabbaacddcccddccacaabadcaccdbaaaaabbadcddccbdcadaacdbbbcadcddaaababccdacbccdcaacddbbadcbcbbdacbabdaddbbaddabbcbbbdadddcbaaabcabadabbcccbcabbbcdbdbdbccdcaddabcabddaaddbbaccddbdbdcadbbcbdcdbbdcadbbdbcdbacbbdabadabdbddbddabcbdcccdabdbcbcadddabadbabcbcbaadaaddbdcacccacacbccbadabcbddcbadbdcbadccdbaabacdcbccbbbbbaadaccdbacadadbdbcdcdddbadccddccaaaacccaacbdcccdaacbcdaabbcbdccbccbabddabdaadbcdcbbbbccbadcdbadcadcadaaddccddccdbacaacadddbbdaddddbdadcdaabdaddcbbaddaaaabcaadcaadbcbbadcbaabbabccbcaddaabaaadbabaaadadbcbcbccabbbdbadbcabccdadbaaccaccddbbdabcadcdbbccacddccbdaccaaadccbcadcbcdbbcbdacdcaacdcbbccbaaddacacacddccbbacdcbdcbccacadbdcbdaccdaadbccdabbcabccccbdccbaaccccbabdabacdcbaddcbddadbdacaaacdbddbadacadacaaaadbcddddaaabdbddaccdcabdbaabddddcbccbdddacccabbababdadbdddcbcdddbdacaacaddbbbacaadaabbbaacddaaacaadaabadcabacdbbdddabdddcbccbabdbcabcbbccacbbbadbbcbacbbddaadddcbddcdabddbcdcbddcddbddbdccacadbcaaacbdcbdadcccdddbdccbbdcccdaddacadccaacadbacabbdcdabcbbdacbcbbccdaccaacabcbcdcbcdaabadaccdbddcacbbdcbdacadbcadcaddaadbbbcbbcdbddaabaaccbcdbbaddbbcbacccbdcabcbcbbbbbbcbccbdccacbbcbcbaadbcacbcccbdbabccacaabbdbddcadddacdcdbbcdbcdccddbcabccabddcadcbdbccbdccbdcaaabaaacccadbcccbdbdbcddcabdccddddcbbcdccddbaadbdbbdccbdcbdbcdabcbbbdaddacdbadbdabacbddababcbacbacccacbbccaddbbcaaaadacabadaddcbcdbaccdddbdddcacdacdaccdcabcdcaacadbbcdddaccbbbbbacdddadbaacadabbaadddddbabbcadaccabddcbdacadcbddbacbcdbacacbcccddadabbdcbddcbdccdacdabbbaacaccddadbbccdacadaaddcbbcadadbdccacbaccccababcddbdaaaacadaaccdcbbcbbaadbbadaaacdadddacdbcbdddcabdbadccadbaadbbbbadbbbacbdcdaabccbacdaadacbdccbcbacaccbddabbaccbbadbcccacdacbbabcbbdbabdacdcbdcaaccacdbacaabaaababddbabadaaadbcbabbdbbcabbaccdbcddadbdddaaddbdcdacbbccabadbbacbabcdadbadbbaabbdcbcbddcdcbcbabcdbdbcadcadcbcacdbddcaaddabdbdadcddabadabccbacdabbaacbbbaacbdccdcababdadbbccabbbbbaabdabaacacbcaaccaccdcbabdcacdbadabcaaabccacbcccbaadcadbaaddabacdaccbdcbdadbbdbcaadaadddaacadacdbccabcbcbadadaacabdcabbbdcbbdcbbacbabaacaccabdbdbaaabccbaacabaaccdbcdbcdaadabcbbbdbbdabdddcbbdcccdbaacbaacbbcadcdcbcdbcbcaadaacacccbacccabdcadabdcbbabbdaddbdadccbdbbacadcadbacbadadaaabdabbbcdbcacabadbacccacabbcddcbdbddccbbbdadcbacadccaddcdbccaabdcbaadbdbbbdabccabbccbcccacbcacdbbccbdacacbaacdbcdabdbcabbddaddbccbcbcbadbdcbcaadddcbdbdbbcbcddddbdabbddbacdcabcdbcbaadadcddbacacabcdcbdcbadbdbdacaacdbdaaadbddcbadacbcbbbcdabbacababbaaacdaacdcacdccbbbcacdcbbaccddccccbaaaaaaabbbdaaddaccadaacaacaaccbcdbaabadddcbdbbbaaccbaddddadaddbaabcaccbcaadaadcbdabcddcbcacabcbcdacdccdbccadadcbccbadccbbccaddababcbccbabdabcbaccacbdcbbababacacbbbbbdabbdcbcdcccbabddacdbddddccaacbabaabcdbabcaabbbdcdacaaabbbdacabbaacaabcdbdbddacccdddaacbbbbacaacacaadaaacbcdadcddaabadbacccdcbdbcbdaadbabcacccdcdbcbdcbcaabbacccbccbcadbbdbddcadbaacccddccbbcaaadcbcdddccbbacbbcbdddcadcbcbbdccabcbcaaadacccaccbbbccaddaaabcccbccabcaaddccddddbcbcbbcdaadbacdcadcbdcaadcacdbdcddabcbabdabdcbbdabbcaacaadbcdaddcbaaddadaacababdcdccdaabbdacbcdabaabcadbadbdbbbbaabaabbadabacacadaaacdcccbcbccbabbcdbacccccdadddcadbbdaadadbacdbacadcccbbbbdaccabaddcabcbdbbbddbcbcbddaabbccbbabbdabaddbaadcabadbacacadddadddbbabcdcbddddbaabcadacbbdbcbcabbdbabdbacadaaadacabdabcddaacadaaacadbbaccadabaddbcccccaddbcdbcacaabdbcbbdaadcbbcadbacabdaddbcbbcadbbbdbadaadbdcbbcddccdbcadacbddccdbbbcbcccbdbaaddadcbdbcdddacccbbaddccadbbccadddadbcddccddbbbbbaabbbaabdababaccbbadddcadcabbddbccbbbacaaabcbbcacbccbcddcbcaccbddacdbcbcbbcbdcbdbcadbdbaacdbcdbdbdbaacdddbbbdbbabbabdcdbcbcacddcabacacaadbaaabcbdadbcdababccadabacbdbcabdcbbdbadcddccbcdabcabbaabddbdcdaccddcddddbdbacacbcdbbcabcaacbcdcaabdcddddadcdcbbbcabaaadabdcabbbaaddcdaadabadabacaddaddabdbdabdaccadaadccbccdabbcdacbadccddccbaacdbccbdcdddbaadacabbbbadabcbaaabacaaddadaddbacdbccbbadccdcabcaacdbbadcbbbcbdbabadadbabbcadbdbaccdbabbdaadddacbbcaabdadaaadbdabdabacbacdbcadcbaaccddabdcccdaccdabbcbdadbbcbcdbbdcbadadcdbbbaababcadccdcccaadddbadaddcadaadbaadddbbadddcbdcdadabdcaaaddaddadbdbbbaaadabcdadbbddbaabcbdacbcdadcbdcabdbdcdcaddadbdcaabacacddcdbbcdcadacccbabcbbbdcbdbcabdababaadbddcdbdcddddcbcbccaaabbdbcbccbadbbbaaccbacdccadaaadccdddcbddcdabbbbcbabdaadacbbccdcbcdaacadbadccbdcdbddabbbababcdadbaaaccadbcdbacadccccacbadbdabaacadabdbcdbcbacaabcbaacadcbbcbddddccbdabdacbaaaddcbdcddcbccaddcccadabaaadcadacbbbabdbbdaabacaabcccccbaaabcbbbcccbdaccddbaabdabbdbadddcbbbbccbaccabdcdddabbbbacbdcdcbacddababdaacbddcabaccbadbcdbacbbdccdbdccdabbccacadabbcdcabbcbcacdcbccbdddaaccdcaadbcdcbbadaadacaaabbdcbccbaccbbcbdddaacabbbaabcaadbcccbdbcdabbbbadcdbbdbabaddbbbbcbcdbdaccccaabbdcadccadbcaadccaaaabcbbabbdbdcbbdcadbcbabbdddbdbbaabcacadccaabddbcccaacaadbcccccdacaaabbbabbbbadcbddbcacbcddabbabacdbacbaccacbabbcabcdcdbabcccadcddabcdaacacaaccdbddcbbaadbccadbcbdabccccbdcaccbaccabbabdbcabcdcbaadabccadacbdccabbdbdcacaadbcccccabcaddbadaddcacdbbabdadabddbdabcccdacdbdcccdadcadbcdcdaabbdbadbcdcababcddccabdcbbadcdbcadadaaccdbbbcbcacadcccaaaaaddccabbcbdbddadcddabcaaacabaaacdaacadadbdaccaddbabadbadbabddcbbabcadbaccacaddcbcdadbadbddadbcaddbababccccbcadcbdcbacabdadbbdcbabdaabdcdadbdccaccaccbbdbabdaccbbbaccddcddaddbcdbcccbdbabaadbddadccacdbdaaadccbdbdadcacddabddaabadcbdaabcbdddddabaccaacbcdcccdacabdbbadabcbbabdccdbbccadbbccbdaadababddabbdcdccbcdcdcbacccddbcccacababbbcdcbdcdbccbdcaccbbbcaacdcacbcbcddbabacddcdcbbdddaddddaacbcccbdbdbbadbcabbabbbbdbbbbccacadcadcddbbcccacccaccbcadcbabacbdbdcaccaccbdcdbdbdccdbbdacdddbbcbddcacbdaddcbacbcaabdddcccdbdcaacbbdcdbdaccbbdcaadbccbabdadddbbabbaabadadddbdccaaacdacacbbacaaabacbccdccdcaaddacdbabadadbadcbdbcdbcacbaaaabdaccaadbadacbddacbabaabaadddddddbdabadacdddaabbcbdacbddcbccbbcbbbdbccddbadaaddabdcccbbdbccdddbdccdbadbacdcdcdddbadcabaabdddddccdaaaccdbaddddadaadbbbddddcbcdccdacdddcdbcdbddccccadcaacddaabadbdccccdcccdabcbbadddcbcacaacabcdcdcdcbdcdccdbbaabbabdacdbbcdcadddbdacdbbbdcbbabdacdaabacacacabcabdaaadabdccababaadadbbbaaabdddddacacbcadabcaaaacacabcacbcdabaaabddaabacacdddcbadbdcaabaccdccbccdccbadbdccbbadcbadbdaddccbabaccaabbcdcbabdbccbbbdcdadbaabacdaaaadcadaaccbcdddbcbaddccccabbaabdcaabadacbdaadbcbdabdadcacbdaaacddcdadbbdbdaabaadcbbccdabcaacadababdddabbaaadccbaaccddbdbbdababcaabbbabcdaadbdbcbbbcccacdcbccbbcabbccddbaccaddddbbcacbcbadbbbbdacbdbdcdddbbcdbadcbaacccadabadaadadcacddccdccdcbcdabaccdaaabcccdbaacdbbcbadacdbdbadbbacdaddbcddbdbcbcbccdacbcdacdacbdbabacaaccbddcbcbcbcadcdbdbbccccacabaabbacbbbabcadcdacabccacbdbbabcddddbcdadadabbcdcbdaaadadaababbcdaaadbaaaadbdbbabadcbacdacadbccaacdbacccdddacbaaabdcbdcbdcbdacdccbdbcbbbaaacaabdddcacdaabdaadcabbbbbccdacbcbadcbdbaacbdcadcbbcaccabaaaddddddaccbadacbcaddacacccccccabddaddcabbaaaaabcbcadbcadcbcacaaaaabcaddbcdbadcdbabbabbcbbaacabaadadbbaabdcabdbacabcabdbcbacbbabbcdadbccdccabbdccddbdcdadccadbaaaccdbdcbdbabacdbdacaabcababdbbaaaccabccacdcbacdacdbcbbbbcbaddbaabaddbbabddbbabdcadadccdaccaaaacbdcdabadbddadbaddcbaaabcddbcbcaaccbdccbdadbbbdcdbdbdcababbabcadbadcabcbabdbbbacbbcaadabcbbdacaabbdabcddaddddcbdcddbddacbbcadbddccadddcddacbacbcbcaaadcccaacdcadcbddcdbbccdccdcacbadbcdcdaaddbddadaadddaacdcbdbbbdbcaabbcdbabdaddcacdbbabcdcdbaadddcababdadbadcdbcbdaccbaaacddcdcbbbbbdaddadcaadbaddcddcacbadcdccbabcacdbcccbdbadcaacacbbbdabcabacbaacbcacabaadccadbbdabaabcdbccadcaccaadaaabaddbabdacbbcadbbddbbbbddbabcbbbddcbbddbacbcbbcbadabbdccddcdaabdcabdcbbdddbbccbcdaaacccddbbbaccdcadccbadcdadcbbadddbabbacccbbdddddacdcccccddbcadddcadbcdccccdbdccbbadbdbaabdbbcbcbcbccaccadacbbddddadcabadcdddcdbbbbacbbcbdcbddccdcaccbcbddccddaabdbadbddbabcdcbbcabbaddbcabbbaaabdbcacdbabcbdcbcbdbdabccaadbbdadbcadaabdbdddbccbcbabadcddcddbdddcdbcbbbccdcdbbccadddabcbdacbbdbcacdbbbbcbbbdddcaacadbbbbdddcaaacbabbcdbdaabdddaadaabdcddaabacdaabcaaadbdbadcbbcacdbcdbdcacbbdaaccaaacdadbcbdaaacbabcbbbdbdccdcbbbaaabcbddabdcbabadacbdabbbadadbbbccddabbadddddbcbcabcbadadbcbcbccdbcccbcaadcccadabccdacbaadcaddbcddadabbcaadbcacadadcabaabbdcaadabbbcdadcbdbbdcacdabddcccadccccaddadaaccccabccdbccadadcccaaddcdccdacaaadcadcaaaacacdcacadaaabcaaaaccacdbcdcbdddbcacdcbccdcdcdcacbcdcbdbddabcdbbadcadccdbabcccddbdcbacabdbcdacdaccadcbaaabcaababadbadababcdbddacbccbcdccaccccdbaaaabaaddacabccbcbbddabaddbcbcddcccdbbcbcdadbacaaadddadcabdabdbbddadbbaadcdaabbdacacdcccdccababaacadcbcbaacddbaacbccadcabbdbcbaccacdccdcddadcdabdbcbbacccabdbccadaacaabdaddbddbcbbadabdadaaaabcbdbdbdddbbadbadcabbbcbddcdadbccbdbccadbdadddccbaabbabbddcccddaaaadcdaabbabdccbbcdcbccccabbdbaacbabaaddcbdcddbccccddccdcbcabbdbaddabbbbdcbacadddacbdbbcadbaabbaaddbbbcdbbdccccbcabccbabbddddabaacbdaddbaccacdaacdacabbdcbacddbdcbcadbacbdaddacbbccddcaabbcccdbabdbcbcbdcabbabccababababcbbbdbbbbdbcaccddbcacacdcbadbdcddabdbbcaaadaddadcddacbdaacccaaabdbabadccdbbcbdcababbdbdabaaadcbabacaccbadbaadccdbbdcbcbcacbadbbbdcdbacdbaaabcbaaaccccbcdcccdabbcdddadabdbcacdcbbbabaddadbabaacadbbacddddcabbdacbcddccdddbdcbadddcbbcaabccdbbcdbacbaaddcabbabadcccacddadadabcdccadcdbbabbcccbaadadacbbbdbdcdaacdddbbcabdbbbcdccbcddcbbaabdaadaddaaccbbdcdddbcbbaadbacdddccbccddddbcabdadbcddbcccbadabdaabbaacddbcdddcacddcbdacaddcaacbccbcbadccdcbcacaddbabdcbbbabcadcbbdbcbbbddbcaddcabbaddbdcccacbdabddbddcaadcbadabbacdcdcddcaccacbacadbadadadbdcbdcbdcbbcaaabbccdddadcbadccbcbcbcdaacaababaaadaadbbaaaaddbbcdddbbacabaddddbddcddcdacdacccaadadaabddcdbaddcdbddbacbacabdacddcbcababccabcdbbcdabdbbacaaadbbdcaadbabbbcacadccbddccdabcbcadadaddacdccdcdabccadbdccdbdccbbadbdcddababadabcabcaacbcbacdbdccddbcacbadacadccbabdbaabbadadaadcddbcdcadaabdbdadacbbaaadacdacbcabcbbcbcbcbcbdaacbcadcacadadbabcccadcbaabacaadbccccdaddcaabbabcbbdacaaaabbcababaccbcaabcbabcbaddababacaaabdbdbcadcaabadccbacbbbcdbbcabccbabbddacdcbcdbdcacadabdbcccbdacabcdcdabcddbaddddbdbbbadbacbaddccdaaaaccacdbddadcbbccbadcbdbbaadadccdbaadcdaacdcabbacabcacabbacdbddbddbbcbdcddaabacdabdadbcbbcccdbccccbacbdddbdcddaabcdcdadcabdbdcbccbbaccdcdaddadcbbdcdcbabaacaddcbdcbdbbcadabdddcadcaabcbcacdabcbcdddbbbaacbdccaabcdbccdcababdacbbaabaccbccccacbccbbbbddcccdddaabdbcacbdddcabdbddadcadadbdabddddcdacbbababcbcddccdadcdddcdadbdabdbabcbdbccabdcddbbbddaacbddaadcbabccdcaadadaacdcbaadacdcdcaaaaabacacddbaabddcbcaaabcddbddcbaaccadadacadcaabcbabadcddadcaaacbddababcabdbaddabddcbadcabdcaacdadcacbcdccbccbbbbcacbbcbacdcdccabbbcabbcdcbacdbacaabbbdbdaacaacccbbdadadbdadbbaccabdadcdddbccaaccadddbccabbbccddabacccadcadcbdbddabdbaddabbcbbccddabbadcddaddcbdccacccbcddcbbbaacbbdcbddaaabdbbccccbbbbdacabcadcaacddddbbddbdbdbdaccccbbbccdabbadbacadcbbcdbbcbdddccabbabcdccccdbdadcadcbdbdbabacdadddbcacadbaabddaababdaaabcbdbcdacddcbdbaaccacbadacabbbbcbbabcbbadcbcdbacabadccadbcaccabcdcacabddabddbdbabbdbcabbdccdbaccadddababccabdbccdcacbcdbcbccdccccdbccacdbacabdddccdccabbcbbcdadcdbdaacaabdaddcdcbacdaaaddcddcccaaabbbdabdbcbcbbcacccbaacbcbddbbdbcbabaabaadadddbbdabcbaaadcbbdcccbbaaabddcccbdabdbcdababdbcdbabbabccaababddddbadcbaaabbaddabaaacababbdadcccdbdbabadcdbdcbbacbaaccabaacbbdcacdbdabdabccdadcdabbcbabdababcaadbcbddbaaddbdbbbcbdaadbbcbaccbccbcdbdacabacdbbacbcaacbdcdadacbbccddbbdbcbbabdccabddaabacdccccadcbbadcbdddcdddbbdbbcbbabccdaaadccbdddcbacdacdbcbadddbcccccbcdaacacdadbabbdcbbdaacbdcdaaddbbcbdabacccbbccadccbcaaadadbbddcddcbaabdacbdcbadbbcbdabbdcaabbbbbbdbbccadbcdacaddadcddcbdbcbabccaddaccaaddbbcdbdbbacccbdccacdcdabcaddccdbbcdabdcabbddadbabcdcddadbdbbcccabadbacbaacbabbcdbcbccccbbbcaddcaacddcddccbbcbbbbabccdabdbabacbdddcabadcbaacabbdcbcabacbadcdcddbabadddcbadacacdbdbddbbcbddccdbababbcbdacdbcddcadbabcbabadbaadbbcbbadbabbadbbddbdbacabaddccbdbdabaabccbddbdbcdbbaddaccbdcabdddadaacdbddcbabbbccaadacccdcdbcbdadccccdabacabbdddcccbcacccbbadbdaabbdaabcdddccacdcdbdcdadddbabdadcbaaadcbacadadddacdcbcabbababcdbaabadaaaddbddddbbdbcdaadcbbcbdcccdaabcdbadbcaaccabbadbcddcbdabdbbbcbcadddddabacbcaddcdbbdabcdadaccaaaaccbbcbcabbdadacbdcaabdccaaadbacddccdcaccadbbbdbdbbbdaddcdacaddbbabdacdbababdcdcdcddababdbbccaaccdaddbcdadbacdbcacabdbbbcadaaaababbadccdcddbadbdcbaccabcbabaabcdcabdccbbaccdabbbadaabaabcbcaabbcbadaabbbaaccadbbaabbbdbccbbddaccadbdcdbdabcbdbabccaaabdadaddbcbadbbdddbabaddbdcacddddbaadcdbbaaadadaaddaaccbcbbbadbacbacdbcadabcdddccbbdacbddcabbacdbdaaddccccaacdcbdccccdaacbdbdadddcddbcbbbcbaacdcbddbbdcccccccbadbbbacaccdbccabbdacbcddddaccbdbcacdcdaaadcaaaacbcdababbbcddadbabcbbcacdadbddbdabbcaacdbdbaddccaaaadcaadaadbddbaadbbcddcaacbaacdbbbdcacadbccdbcacdcababcbcbdaddccdccbabcaaaddabaccbbbacdbcacdddaaababcbcdcadcaccdabaadcdbbcbdcccbcaacbaddacddcbcdadababbcdaaabbbcaacbbbbcdbacaadbcababcabbbbacabbbaddbaacdccdcdaaabadbccccdbdbcdaadacdccaacdcbddbabbbdaccddaadbdbbdaacabcddaadabcdccccdccacdddadaabbbbddcaddabddbbdcaccabcddadbcbdadaadcadbbcadcababbacdbbadccaacdbbbcaacbbbdadbabcadbbdadbabdacddddababbcbdddddaddbddacdacdccdacabbcdbbcdbaaccbbcbacdcaababcbdaddabcdbcbabdcabdcdadaacbaabcaaabbbdcabcdbdbcaaaaabaddcdbccacbdccbcbcdddbadbdbcaddabacacbbcbbacdcaaddcdcddcbdddadbadbddddbaadddaaababbbbbdabadabaddccbabbbaaccadaabdcbbdccaaabcdcbbcddbddbccbcabbcdabdcccbdadcbdbdcdaaaddcdaabdbcdabbcbacdcadaddbdcaaddddbacdddbaacbcdbbcbcdacdbcdcacdbaddabbddbaacbacbdcabadbddacadbaddcccabcdbcdbcccdbbabdbdddcccadababdbdcadcdbdbabcdcadaaaaccabacddbddaacbacaaabbbacacdcdbacaccbdbbcbadacabdccbccdccaaabcbdcbabbbdaddbacbbdbbcbdcaaccabcdcddbcbdbbadbcacddcaabaddbcabcbddaacdddddacaaccbdbdbcbaadcaadadaadbdacbbbaccadbdcbbcbcabcadbabcddbbbbcbadddbdddaababccabbccbccbdbbcdbcadbddabbaaaaaaccdccddccbaddbbcccdabdcbabcadbbdbbcaaadbbdddcdcccbaadbbdddcbcaccadbadbbbacbabbaadcccdbcdcbaadddcaddaaccaadadccdaadcbbcdcbcadcaccdbcbdcdabaabacdddcbbdbcddbdcdcbbdbcbaddccbdcaadaaddcbadbaacaabcabcdbbbdccbcbdaccaabadcaccddbaaaadaadbacdacbadaabccdcabdbacdacaccdcbcbacbabacbbcabbabbcccdaddacbddcbbbabaccbbdadbdccbcdadaaabdaadabbdcaababdabbdbdcbcbddacddabdbcdaaadccddbabcabcbabddbdbdaccccbadabbbadcbaabcadccaacaccaadacbdddacdaddcdcaaabdaaabdadcaaabcadabccdbbbbddbccbcdbadbdcacbdcbddbddabcaccdabbbbbdadabdbcccbcdccddaddcdabdbadcabbacccadcdcbcddcdbdcbcdccbddbbdbbabcabacdaabcdcbbbdaaacaabcadcbdabddbcaddadbbbabdacacbbadccaabacbcadccacbbbbbbbbadabbdacabcdbccdcbcddbbadbcbdaccadadcadddcaddacdabacbddddadabdcababbcaacdcacbababcdbddbcbbcddadabbccbdcbbbacbaacbccbdabcdbdbddbdabaccbcccadcabaadadcabaacaadcbcdaaacccacdabaddbaaabccdaadddadbbbbbdadcbdaaadbcbddcbcacdbadabdcccdacaaaaccabbaccabdcacbbacbadbbdccadacbcddabdbcdbdadacacdaadaadbabdbcdacbdcbadaabadbdcabdddcdbddaaabcaaabdaaababaccdddcbacbbcabdcaddbdcaaaccddcdddbbdddbbbbadccbdacbacaaacdbadbcacdaacbbdcdabcdcdcacdacbdddbcaccadcbaacbccbbdbcccdbdababccbaaccdacccdcadcddadcabacbbbccdacabdcdbdcccbccbaadccbaadaaaadacbdcacbaccbadcddbadaaabbcdddbcadcdcbbdbcacaabcbacabdcddaabddacbdacdaccdcabbcdaaacbdcdbdbdcbaadccdbacbcdbcabbccccbdccacbcbbcdacaccbaddaaccdadcaacbcadadbddaddbabdcdcdbabacaddcbcaaacbbaccbacddddaabdaadcccdbababcaabcbabadccbbbcaccacbacddccacbddacbcdcabcabaddaacaddaacccbbbdaacdbcbbbcadbbdcdbacdcacadddddbddbcbcacccdbadbaaacbaabdabbaabacabbabadddccbadcaadadacddacaccbbbbcdadaccabbacbcdadaccabcbacdbbccabbabcdbabacacbcbbbabbdabdadacbdbbacbdbdabdabbcbbcddcbbbdaabbcbdaacccbcccbbddbcbcdabdccbbdcacbbccaaddcdaaccbcaaccdaddcdacaccaaddbadcdcbdaaaadadcaadcabcdcbdccddccdbacaddcaaccddaacbcaabdddbddadabaaddacadcdacddabbdaadacbacdbdcaaccdccbdcadcccbdacdaaadcbcacadddbbabcaabadbbdadadbbadacadbaaddbdcadabddddccaddbcdbdacbbdbddaaddccadaaaadaabaadbccbddbdbcccaaaccbbccdcbbaaaccaaabccddbdcdbadcdccbcccbdddadaaaaccccacadcbdbbbdaccaabcbccbabccabaaaaaaccdbdadcaddcabbbadacaddcaddcdadadbaabadcccdabbababdadaabbbdaccbcaacdcdbbcbbbbcaadcacccdbcddccbdccccdbbcbbaadbcabbaaaccacaaabdbbbbdbbbcbcacbcaaccadcdadcdcdaabbdbccdcbcaacacdacccaccdbdbaaacdaddbddaccbadacbaadabdcdaccbdbdaaddacddccdbadacdacbadcdccbadbaaccbaadadcdbbcdddcbdaccdcdcdabbabbccdddbadbcbabbdccdcddadcdbcbdbbdcacbbcbccbdbbccaddbcdccbacbadbaaaadcbcbdabbccabdadccccaddbbbcacdaaddbaaddcbbdaabcbbadadacaadccdddbbccdcbbcdbdaddbcdabcbcdbdbcbbdaddbcaadbdbcccdbabacaaabaabbcbcbdcdacbabbdccdcbbccbabddbddbcbaadcdbdcbabbadbaaaaadcdbcdaadcbdbaadabcbcacaaaabdbcabadbaadbacbadddcbbccbbabdadbdcbbbcbdbadccbadbccdbcbdabadbbaababadadbdbabdcccaaaaadbbcdabbbbbcddcddcccdadcadbaccdadbdcacdcabddcadaaabcaddbaabaabadcaabdccbaddacaabddcadabdacaadaaabbbdacddcabdadaaabbaaaabaadddcbacdadabaaabdbacbbccbccbaccbabccbbbbdbddcbaccbadcacdddcaacbcbccadbbdddadbbbaacbdbcdcdccaaccdcaddcaacdacaaccacbbcbabddbcbccbdbcaabbccddadbabbdbcadcabcbddbdadbbbaddadccddbacdcabcabdbbcddadddacbcdababaccccccacbcccdbcabadbdabbcbddbbdbadddcbbadcccccbcdabddaacccddaaddcddbdccdaccaaccdaabdcbcaaadbcabbcbdaabacaccccacbdcbbddccdddbdcaaccbabbabddbcbbcabdbcddddccdddabcbcacacaabbaacdcbbccbdbdaddabaccacbcdacadbccbdddddcabdacddccbcbbbaadcdccbaaaadcbdbaaabcaadccbdcadbaaadddaabbdbbcabdaddddbddcaaaadabacbccadaaaacaabdcdcaaccbababcadaddbcabcccbccccbcadbadbccdcdcdbdaaacccabbbcbbbcdbbbdabddbcabdadbbdcbccacdbddaabaddbbacdccacaaabbcabdbdbbccadbcabdbccaccbddbaabdbaacbcbbaaababbbdacacacdbbdbaccbdaddcbcacbadcbdadbaddcdabbbacdbadbdccbdacabcccbccbbabadcadbdcacddcacddaaacadcddccbadcabbabdbabadbcbbcaccbcabcccbddbddccccadbdcbabacbdaacdbddacbdbdbccabaadaacbbdaaabacccaadbbaccbbdbabcdbcccabdbbbcabacccaccbcabaabaaadcddabccdcccabbdcbcacabcbdcaccdabbdaabcddaabbddbbadbbdcbabbdcaccacacdbbdcbaabbbbdcbadcccbcbcbaabaaadcabbaddddcccacbdcacddcdabadbbccaadbdadcbcbaaaadbdbdccbcccdcaadcbbcacbadabdbdbddbcbbabcbcbacddbabdcaaccacbadbccdadaaadacddabbdcbcdadbbaacbccddaadccddbcdbadddddbbdbcaabccdadbabdadcddcdccbaadddaacbbbcdacbabaabcbbcaadbaacabbacabacabbdcadadcbdaddbaadcdbddbdabcbcdacbbdabbcdccacbaaaadadabbcabcbbaddabdbbdcadcbccbdabdcdcaadabdccdddcacadbddcdaaddccadbdbaabaacdbcdbbddacddcdacdbbabababdabbbdddddadadbbbcbcbdccdddbacabaaacacadccadaadacacabbaddaaccaccbacdaaccaaccbbbccddaacadbbbaccaaaabadacaddbdadcbcdadcccbbbacadbcdbdcaccdbcbdacdbccdccabcdaadbbadcaaadbaaabbaadcccabdddcabdcdbabcbaabcddccaacacddacccccbddbdacbaabdaaaccbdacbcbbadddbdbabdbaadbbdcbddcccccdddbacdacbdcbbcdccbcdddcadaddaadbaacbbadcacbbdbabdcbadaabcdddbadacbbdcdabccaabdadbadbdadcbdaaabddcabccacddbbcdaaabaabcccbdcaaccdbbdaabbdbcabaacdcbbddcddabbbdbbbdbbabdcccbabcaacabbacacaccbdacbcaacdbbdaaccbbbdacbbbcdbcdadaddbcbcabdddadcdaacbabdcaacbbcabcbadcdcabbabdcacbcaaddbaccbdccabcbaddddaacbbdacdcacabcabcbdbbaabdbaaaddccbccccbdaabdddacdcaaccaabbcbaaabcbaacbbcccdaabadaaadaaddbbbcbbbcbdaddcdbccddcaadcdcdaacbaadacaabcddbaabcabcaaccaabaaddaaacdacddbbabbadbccdbbaacddaaabdaaabbadaabbadbccbdbbcdcdaccbabdbcccdabbaddabbbbdacdbaababaacadcbbcabddbacbdbaaaddddaacaccdccdbccccbbaabcbcdadddcdbbcbcddbcbbcabbbcbcddacdaaababadacbadccbdbccdaadccaaadbdacadccadcacddccbddbdddbddbbdcdccbacabbabaccbdcbbaaaacccadabdccdabadabbcbddaddccbbadddccacadcdaddccadcccbdbddabdbcddcdcdaabacbddbdaabaadbbdabcacdabbaddbbdcddbabbaabdadcacddcaddbcabbddaadacbdccadbadbcbbdcacbaaaaabadacdaabadbdddcbcdbbcabddaabbbabdcbccbcdabdcaaabbbddbbcaacccbbdcaddbddbbdabbbaccccddbdcddbddbcaabdcaddbddcacacbdacadccdacccacccabbdbbcbaabdddbdcdccdcbcbacdbdabdacdcadaddbacabbbbdaacbdcdbcdaaaccdaaacdacbbcabadbcaccbbbdcbbddbacddaaddaadcadcbcdabdcddbaadacbddbbabbcacdcdcacacdcdccabbccadbcdbdcbcbbabacdbbdcaaadcadddbaddbcacacccaddaaabadaaacdbbdadcddbcbdcbadcabbbcdcacbccadcbadadbccbdacdbcdbabaccbbbacdaadacbbaabbdbcbdbdcddabcccdddabddbcbdabacabdadabddbccbbacdbabbdbbbdbcbcccdbadaccbcbcddbbbabcaacddabbabdbcdddcaccabdcdccadbccccaadbacddcbbabaacbbabacbcaababddcabcaaadabbbabbdddbbdccadcbabcdaacdcadadaaddbdddcacbcccccabdbcbadbddddaabcaaccadbccabccbdbbadacbbcdabcacdcaabcabddbaddbddddcaacacadabdcabbadcdccdcacdcabdadaaacabdcbccddadccaddccacdbdbaadbadaaaadbbcbacabbdbdcaadcdbaccddaadacabcabaaabddbaddbbadddbbbadbabdbabcaccdaadddadabbdcdcddddccabdbbccabcddaccabbdcabbdaddaabcdaabaabaacddacabcdddccdadccbbdacabacccbabacbdbbcdddadcdadcbddaddacbbaadcdcbccaddccbddbabcbdcdccccbdaacbddacdaccccdcaccaaababbdbcbbcdcdaadabdadadcdbabcbbbaddacccdaccabbdbcbaabadbddbddaadabcdbdcddbabbccbadaabdbadbaaddcdccaaddddbddcbcbbcdabaaadcbbaccacbcabbcbcbacbdacbbacdcbbbdbcabbbadacdacaacadbdabdacaccaccddcccdddadcdbdcacbcbdcbdbbabdababcadadcadbdcdaccbadbdbcadacbacaabcbbcbcbaccbadcacacadbcddcbdbbdccabdbcabdadacabdddcbdbdaddddabdbdaaaddaaccddddbcbcacbbdcddcacabcdabcdddaddbacdabcbdabaccccddcbddddadcddaddddaaabddacdcaaddccaddabbaaaddbaadaaacbddbbbbbbbacbccbcbccadbaddbdacdddccaabbacdcabbbddaabdcdccacabbacddacbdccbaddaadaddacdbabddababdacacaaddbbbdcdaacbbbcabadacbdcdbadcababdccdbdbcacdbaacddaccbbccacdbdcbbdbddbadadddcbbabcddccbabbabbabdacbacdabbbbbbdcacabccdbdaddbccdbdbccbabcdaaabaacbdaadcccbdbcdbabaaadbcabbcbbbcaaddabaabdaddddbbabaadacacacacccbcbacabddbdadabaddcdbaaaadbaaaabbcbdddccacbbbaccacbdacbdabdddabbacdcdbdadccbbbcbabbaadbaaddbcbabbcacbdabacbaabccaccccbadbbbaccaccaaddcbdaddabadddadbbcddbaddcaabadadcbdbacaccbabcadccdcdcdcdcbaccdddabbddbdddaadbbdacdadbcadacbbcdabbccbacdbdcdbdaadddcddadabcbaddbddaddadacdbbcbbbacbcdaadadbbbcacccaabccbcadbdabdbddbccdabcacbbabbaababcdbdcaacadacabdadbcccacddbababdcddbbabdadccdcdccabacbdbcdcdcdaaadaacdddaaacbcdabaaaccbdbbabcacbabadcabdabbccbdcbdcdaabccddaaacdbccacbcbcddcbcbacddbbcbbccdbababbcaddbaddaacbdadcabcbaccacaabaabcbbaaadadbdaddababaaabdaccacadcdccaadddbaabddacbbdbbabccdadabbcaacbbdccacdcccddbcccdddddbdadcadddbcacaccddaccbcbdcdcacddcabbacbbdcabadacddcdcaddbddbadbcacacccddbacdbdbadcbccacdaddccdbddcbdacbacbcabababdcbaadddddbddcdaddbabccacadaacbcaabcacbbadbbbaabdaccbdcbdbdacbacdadbaaccdaabbdacbbabababbbdabbbaccadbbabdadcabcbbcccaacbcdddacdaccabadacbabddccbccacbacabccdcdcabbccabdbbbcaabcdabbcacbbcabbdacbdcbcbdaaaaadbccdbaacdcaabbabbbadbadbdddcbbdcadbdcbacddcdbdccbacabbabccbbccaccbcacabcdabcaadaabcbdcbccdaadbaaadacbbacdcacaabbbbbdddcdddadadccdccdbbaabaabbabdaaacdadbdcdcadaacdbabbacbaaddbaaaaadababababcbaccdbacababcbbdcdaababdcdaabbcdddaababbaddddcdbcabdbadbacaaadddabcacaccacddbabaabbdccccddababaddddbacccddcdcadbcbdadaacaacacbcdcdbaabddbaccbacdbdcaabbbbddbbdcabaabddcbaadaababcdcbddddaccabadaaaadcdccdabadbcdbcbbdbcccaaadcabccaacdaadacaccdccabdabcacdbdabcdbcadbddadcbccbdddbbdcbcbbbdccdcdacddddbddaaaacdcabcddbacbdbbbacaadbacbddacadddadbcdddccbbccadcddbbbbbcddabcdccdadaaabcacddadddcabbdcaddcdcccadbcdcbcaddbdadcbaaccdcbaacdcbbadacdddccccbabddccacdacadcdcadbadbbadcaacbcaddbcccbbbcbcacddbaccdacabcdddabcacacddddbbcaccbbccdcbddbbadcddbcddbacbdbadcaadcdacdaddbcaccacbabababdacababdddccdddaccbcbbaabacdbbbddababadbbdddcddbbbccaadbcbbcacbadcaccdadcccbddcbcbcbdaccbbddabbcacbccbbcbabdddbccaadabdaddbdbabbdcdccacccaaaccbddbadbababccbcdbddcdddacddaaccbdadbcccbccabbabaadccacbabccbcdaababdddddcadcacadaaddddabcccdcdbbcbbbadbbabcabdbcdadabcbbabcbcddaadccabcddccaacbbaddbcdbcccacdcdaccccbdaababacbddbccdbcadcdbaabcaaaaccccaaabcdaaaccdacbabaaaadccbbbdaaccdabcacbcddbbbacbdccddaabbdbbddbbddbadacbccdddbbdbdabbddabcccaadbaabbbdddddcdbddcaaccaaadcccdcdbdccbbadbdcdcbdcaadcddaadaadbaacbccbcdbdadbdbcbccdddacbaaacbdaccdabdbbaabbcccbdabbabaccabcabcbcccaaccdbacccbdddaacccdabbddbbddaacbcdbccaddbdcbbcdccdbaadbacbabcdbaabcdaacdaaccdabbbddbcbdddccbcadcaddabaaacadcccbdbabadcdbcbadaacaabdbbbdacadaaccbcababaacdabbcdacdbddbbadacaaabcccabbacbbdbacbdbbcadbbbacdcbcbdaacdcbbdabdcccaabbbccbbdbcbbabcbaabddbaaaaabccbdaddcadbbdcdbddabddbddccabbcaaadaabacbcbcabdadbddabcaaadddccbdbddbcdbbcbbcdcbabcccbcbcbdaddcdabadadcababbbbacddccbdbcdadbaaccabadcaaadccaabdcadbabaaaabcbdbdcdaccbacbadbacdbbbbbddcdacdadcaaabadabdaaabbbcbdadabbacccabdadacdbddbddaadcbdacacadbcbabcdaddadbccccbdccadcccdbbcacaacccbbcaacddbdcbbaabccaaaacbcdaccdbddabbbbbabcadcbcdcaaaadadabdddcdabcdadddcbbddbdbcdabcbddcadbdbbbaababaabdaddcadadbcdbdaccccacddaaadbcdabcabbbcbcdcdadcaaddddaccaabbbcbababdaaabdbbaddabadabdccacadddacdbacacadabbbdcdcdaacaaaddcdbdcdcacbadbcaabaddcccdcbaccdaabcababbbabadbacadaccacadcaabdcddabbdccbbcabddcabccbcdabbacdbdcdccbbcdaabbccaadaabaaccadbbdbccddbbacbdcdcdccacbbdbcbbcacacaacabbaaacccddddacabbaddccaadaddaccdaddaadcadcbbdbcdcdadadcbcabdbdbbdcbcbccdcccdccacddabcdccacdbaaadbdcccadcdbdaacbccbcbcddcbbabbbabcccabbabbdccccbcdbbccabbacbcccccdacccadabbcaabbcdaacadaccbdbcadbbacbacaddcbabaccacdccbcdbcaddcdcbbacccacccbaaabbddacdabbcadccdbacdcdadcdbcabcbdbcbbdbbaadcabbcdabbdcdadcbbababdcbdaddadaacdcbcbaddbbadccdcaaacbdabdabccbddccabbbdbadbabbbabdaaccdcbcaaabcacadacadddbaddabccbbbcbdcdabaabaddbdadbddbddbcccccdcaadbbbaabadccacddbadababdadacdddaadbcdcddddbbdddcdaccaadccbcbcbdabccadacddbbacbcdaacccbabcdbdaddcaddbdbddbbbbdaaabcddabcaaaacbccdbccdcdaacbbaabcacbbdbadcaacadddccddccdaabadaaddaabbbbbbccbdaccdaacacccbbcacacbbabbddcdbbbccccbccbdcacbddccacdbddabcbdddbbdcdbbccdbaabcadaabcbddacdbaacdccccdaddabbcbaccccbabdbcabdbcdbadcdbaacaaaadcbdcdcabaaaabcdddcddaaacdaaabbcadddccabaccabaacadbddcddbcbcadcdcaddbdbccccaadbddddddaccbadbbacdccdbddadcddccbabcadacdacbcdabbbbcbbbddaadaadbdabaacaddcacdcbdabdcbddbbdacccbaccbbdcccbabbabdaabdcacdacacacbddadbcabdaccacbddcbdacdbdbcdcadbcbadbaddaacbacbaaacccbbbcbcbbbcbbaccdbbddadddaccdaaddcadbdbbcaabacdabccdcbdccacdcaddcdabadcbbabdddadacaabcddbcabbddbdcccdbbcccaabaabaaaabbadaaccaaddcadabbcccbabbaaabdbbadddddaddabddcdadbbbdddacadaabbcacdadabacabaddadccbdadaacadbdacbcdabdcdaaccbbcbbabbaabadddbaddccbcdcbcdbdadabbddbacbcdcbbbccbcccbcdbccaccdcdccdadaaacdcaccaaabdabdccabbdaddaccbdabccadccabccaddcbdacdbccdbcaccdbdabddadbbcadaaddddcddbddbabaaacccaabacbdbadbaabacbcccadbbbbabcdbdadcdbaadcdcddbcddbbabbabadadcbbdbabaababddccaadabdacbdbbabcadbdbdbcbddadabbabdbabcbacacadbaddacbbabccbaacbdbccbdbbdccddaddccbcabdcadaaabcbcacccadaccccccababddacddbcdccbaaddabbcddacadccdaadcaaaddaddacddcbabaadadcccbacbdbadaacbabbacdbcbbbbaacddabccadabbbabadbbadcbdaddccdaadcbcdcdacbdbdaabdacbbbbdcbcdcbbdbcbbbaaacdacdaacbcddccdbdcdcabcababacccdddbccbdbbdbdadbbdabbbcbcacdcacbcaabccddabdbaabcccdacacbbacdadbdcdacddccdcadbdadbdcddaabcbddbacbbbcdcbacabddbbcbbdbcbcddaccbcbccbaabbdabbabadbdddaacbcbacbccdbcaaacdadadcddabcdddbaaacbabccdcbcacadbddcacaccaddabcbbaabbdcaaadbdbcccdaabbbdcccbdaccaddadbbadcbbdbddcaaccabbbcdbbdcaaadbcdbbacbdbdbccdabbbcadabdccadadcdaabdcddcdbcbbddddbadacadcabdaccbaaacacaddcbaaadaccacbadddbbadcdcbabadadcbcdacaacbbacddcdadadddbcacdcaadaadbcccbabbabadbdbadaacddbdabcccccaacaccadcabbccdbadabdbddcababccbccdadbaacbdbaddadbdcbbdcbdbbadacacbadcddbbadbcaadbbcabdbcdccadabbbcbbdcabbaddcabbcdaddabcddabcddaaccbdbbdcdddddaaabbdccddaacdbbaadacbdcaabddbbcbbbdddccbcabdaaadaccbdacbaadabbcdddbccaccaaaacbcdabcacbaacccdbcddbddaacaabcbbaaaabcdcabbddacacaddbabbbbdabccccadddaaccaddbcbcbddbcaaacbabbacbdcadbcccdcdccbdadccbbdbbbaacbadcabdcaabbbbabbbcdddbbbdacdabadaabbabacccaabbbbdcababadcdacbaaadabddaacbbbdcbccdccdbaddbccbddbddbabbbdcaacccbbcabbdbdcdccbaabaddbbadcdaadbcccddddaaadcadddbbdcababbdacbcaccacacadbaddcaaacaaacabadbddcccadcdacadbdacdccabcdccbdadacadbcdcbdbaabdbbabcbaccdbccbbdbdbbbaacadbacaadcabbacbcabbdbcdaccbacbdbaadbcbdaacbadbacddcdcbdbbaaabdadccadaadcdbbcaddddaabccccddcbbdbaaaaabacabccdadcccadbcdaacddbbcabcabcababccdccdbaaddcbcaddcdacbdcdabdcdbcbcdbbccbcabdcbdcaaccddcaaddbcbbabdddacacdcdaadaacdaacdcacaccbadbbcdcbbacbcdbbbccaddabdbbadaddbccdbbabdbcdbbabbadcacdcdcddbdbddadaaabbbddcbbabdccaacbaccbcaaadbabbccaabdacdcaaabdaabbbaccdcbbdcadbbabcddbbdbcdddbcacaccabdbcbcddcbdcccdccbacacdadbccbbacdccbdccbcbaccdcddaccdccdadacacbddbbcdbcdbdbdacdacbacbbaabacddacdbdcaabcdcbdcaabacbdbbcababbbaaabccdccddccabbaaadbdbdbddbbcbdaacadaacddbdaabdbbadcabbcbdcdabdccdddadaaadbadbcacdbaabbbdacdabcbbdadbdbacbdbdbcdabbacdaadabadbccabcbadaaababaadadadaadadccbbbcccacacbdcbbcabdccbbadddbdddccabddbadddacbbcbdaadddbcaaabaabacadaddbacccdabccbaaabdabbcabacbdabacccccaabbbbdccdabdddcbcabacabaddcbdadbdcdbacbabcdbaaccbdbabddcabddcbdacdabaddbddccbccdbbddadbcccaacdabadccdcdcccddaaaacdbbcdbccbbbdcabddcabdcaadacccdadbaddbcdbabdadaadbabbacbbbddadddddadacacaccbcbccbdcbbdadaccbdacbbdcbabbcaadbbbdbdcacacabcddaadbabbccaccaacbaacbcbbdcbdccbabbaadabbccacaaddbbaaacbbbaaacbaaaaababbdcadcaccbddbadadbcdcddbddcdbcabbbcbbdbbdbdbabccbdbcadadbaaaaaaddbdbccdaddbdaaaadbababbdaccaaabcccbdbabbbcaacabcbcdbddcaaabdbdadaacdbbcddddcadbbcdbbabcbaddacacadbccbdbbccadcbcbccdbadbadcccdaaaccabbdbcccbdbacddcadbcaabbbbadaddbacacdddcbcdccaccabdcacdccdcbdabbaaaaccabdaacccbbbccacacbdcdbcbddbacdbccdbcbcabddbadaccdbddabcadcaaddcddaccccbcddabbbabcadbbdddbbabbdababbcacabcabdcbdabaadcdbbdbacabbddbacabaaaadbdcdadabdaaaaccbddbcacdbdaddbdabcdbdccbbcdbdbbcabbcbbbcbdbbcccccdbadbdcbdaddcdcdbbbcbbcccaabaaabdbddabcdddaaadbbacbcbacdacbdbbdbacccabcbadddbdcdbbcccbcdaccdcbaddbacacdacabdddaababbcadbacdabbdcdddddccbbcbbadcaaabbdbbbbcbadabbaddcbbddcaddddccdabdadaaacbadbacbcabdaaddbdbdcaacadcababdadbdbccdccccddabcbacddcdddcdcaadcaacabbccbbdaaadcadacdcdcadcdabababcbdbacbaaadaacddaaadcbcdabccdacdcacbaabcaabcbaacdddacadadcdcdbcdddcbdcdabbaccdadcbacccbdadcbcaacaacadbccbadadcbbdddabddcbaaccddaaaaacbaabaaabbcdbbacabbbaabbdbbcabbcdaddaddaacbabaccbddcccbcaabdbbaccbadaaddadbddbdaadddcaddacadddbdbabcbbcadaacbcbdabdcbcaadaabadccbdcabbacadabdddbbbcbbddabbadddaaccbaaacadabcacddcaabdaababccdadaaddbdabbdddcdbdcaacaddcadacddbbbccbdcddcbacbdddcdaacbaddbbcdbccaacbadbbcbaddbbdabdacaabdcababcbacbacbcbcbbcccadddbdaaccdabbdcacbddbbaccbcbbdcdcccacaabdadccbacdacaccbddbbddcdcabadbcdbcaaacdcbbbaabcacbabcddbcbdcacdadacadabbbddabbbabacbcacaacacdcdbcdbddbcadbadadcdbdaddbcdbbbbadddacccbbdadcccacdcabbbcaddabacbcddcacbccdcbbabccddcbcadcbcccdddbbdbadccbacdacbcbcacdcdadaddccdabbdbbbccaacbbdccadcbcdcbaadadcadcaadbacbbcbcbdabadbaabdcacacbcbabbadcbbacbcabbdbbbdaaadcaaacbacbacddaadbabbcaccdbcbbcbbaddabdaaaabcddbcabbddbacccbdbacabacbddaabaaddcaaabbbaddaacdcccaababaaaacadcbcadcaacddcbadacdccbccdddcbcadbacbadcbcaddbcdcbccbbaaddcadaaddbaacdccaddcaddccbaccbccdbcadabadbcbbdaabdbdbbcbbcbabbaabbabdbccbadbabbbcddccddbdcdcddcacaadbdcdddbdbbccdbccddacbddacaabdddcccddcadacaddbbaabcadacddaabddbccddacdabcddaabbdcddcadccddcbcbdbcadbcababadcbccddcdbbccdbbbdddadbaaaddbcbdcdaadbabdabdccaacaaadccdbdbcaddbbdbbbddcadbaacbcbdbbccbaadcccccbabccbacccdbdcaacadccccddbbdbdbbabacddcbbdcacbdacbcbdababbbdcddbaabbcbbbdabaccbcacbdcddcbcdcbcddcbbbadcdddbdadcdabcabdabadbabbbcbccbdbcdcabadadabadccbbddddadabcbcbabbcbdabdacaccabbdbcaacaddcccbddacadbadbcaadbcccdacbcaddaccabbcaacbccaccdbaccacadbabdbbcbabbdaaaaaddbccaccacaadcaaaabdcbcbcbccabacacbaabdaaddbbcdcbcadcabbbcddccbbcadcbbddbbdbbccbbddbabcccddddbbcbcdbbdbcccddacdacabdabcabbcdcadbbbbdcaaddcbbbcaacdaaabaccdcaaaaaabdbacabbddaadbacbaadcbccbaababacbbadaaacdacdcaccabcabadbbcacbdcabbcccbacbdcdbbbccdcabdbacdbdbbabccaabbccdbbcccddbbdababddcbcbdbacacbcdbabbcacbcaadbacbbaabbbcccbdcdbcacbadacabccaacbddddaddbbbbadccdaadbacccddccdaaddcdadcacdabdcacbbdcddbaaaacbaddddbabbacbbbcbbabaadbbddaacbadbbdbbcabbabddabcadadcddbcacbbdcdbbcdcdcbacddabaccdbcbdabdbbbbbbdbcadbabbbcbbbdccacbdaabcddcacdadbcacccadcdacdbaabcdbbcbaaccbdddcdadcadcdbddabcaabbbdccdcdbcdddbcbddabacddbcacaaddacbdbdbdcccacadcdcdcdadcaadddbbabbdbddcdbcadbaccdbdcdbbbadccacadbcdbbcdabcabaadcaadbccbbbbcadabaaadbcdcbabdccdadddcdccccaadcbbccbbcddbdccbabdacbacadbbdadbcacdbbabbbcabbaabacdadddbbdabcbcaadaccadbacabdbbbdabdccabdcaaacbdaadcabdcdbbadbbcbdacaddaaccbcbcdbccbacdcadccaadaaddddddbbdbacadabbccbabbbbabdddbddccacdbacabaabddacdaaaadcdbcacdcdbbcdcbbdadcabbadcadcdbdadccdbccdddbbacdadbdddccabbaccdccdacdddacddcaadaaaacbadbcddcabaddcdbdcddddbdbaddbbddbccaacdcaadaaddbcaccdbabddcddcbabcdaccacbcccacdbaacdcabbcdacadcdbccdccbccdcbaaaaaadcadddcbdaacdabbbcdcbddbdbbdddaaacdcbbdadaaabdbaaddbbcdddcbdbbccdadddcaabcdddcdbbbaccbadaaddacbbabdbcbcbdbbdabbccaaabccbccbaddaaaccaddcbadaccbaacaaacabadcddbabcccdaddabdaadabbaadaddaddabdacaadababdadbaccaababaccddbbcbaabdbadaccabcbacbabbdbddccdcacdaccacccbcbcbabbccdacabadcbcdbccbcccacccddddcaccaabccaaaaacdaabddbaadbbadaababbdaccaadcccaabccddaadacccdcbccbdabccaccadabadbacbbaccacbadadddcaabbbacbbadacadbcdaabbcdbadabbbbaccaabbcbbbdcbbdacbabcbdabbdacabbadabaabcdaacbaccbacabcbababbaaadabdaaddaccabaaacdbbabdbdcdcabdaddcbbbaabaadabaddaccccccababaddbcddcdddaddbcdcdaadaaccdddabccdbaddbadcdbddcdbcdbbbbbdabcddadcbdacdbcacadcdbabbcbacabdadddcdcabaacccbcdbaacabcddabcaadcdbadadbddabcbbcaaabbabcabcabacdabbadadaaadcbbbbaabaaacbbcdabaaadaadcbabbbbccacaddabbadddacadadcabdbadcbacbbcaaccabbcdaaadadbdcacabcdbcdbcdaddcadbcbbdadcddccaaadbdcdbcbcdabacdbbbadacaccbaacbdaddbbcddbdcaccaabaddbccadbddcaacbabbcabdcdabbbddabcacaadbbaacacbcbcacbaaaacaaddcdcaabcbaadcacacbbcccbdaacbabdccdaaccabccdabbbbadacacaaaccdccbaabcccbdcabddccdabbccacbacdbbaacadcbbddcddbbbddadadabbdaaacbaddcbadbacbaaaabaddccdaacccaaaacdcabbdabccaddbcdababadaaaccadbddddaacbcdbbbbcbbbcbdbdbadacacadacdcabbbcaaaccabbcbcbddbbcabadaacdabbdddcacbbdcdbbcbabcacdccbabadaabcbbbdbddcaddbcacadadbbcbbadbbcbbdbcbaacbbcbaadaadacaabadbdcbbbcdcabdbbbcacaddbcacdcbbdbdadaacbabcccdcbcacaacccadbdcbcacaabcacbdacabaddadacbcdbcabccddbadbaacaababadacaadabcaddddacbbaabbbdddbbcbcbadbacaddbcabdbbccddabccbdababcddbcdccbddcdcbcbadbbccabcaabdbadbabbddbbadddbdbbcadbcdcadcbcbcdbbcbdadbaddbacccdbabbcbcadbabcbcddbbbbccdabbcbbaaaaaaddbadcccbdbbcacdbccbacccdcbbaccaacdddcabbcdbcbabaabddcddabdcacacbaddbcdbcdcdaabdacbcaaadcccacadcbadcbbddcbbcbcdacbdcaaabaaadacbbdaadbdcadbbacbadaccbaadbcbadcbaadcdabdbadbdccaacddaabaabdbacabcdccabdabdbbbaadbcdbdcdbdccddbdaabdbcbcdabdcdddaacdbbbaadabacbdccbcdbdbdbcdcdbbbcbaabacccaddaaabdddaacabacddbadbbcabddcacbdcacdabbddcdabccadddddbdbcbbbccabadbbbcabcccaddcdbccdcadcaddbcdacdcadbcabcccbbdadcacabdcbbbaabaaccabdaccbcbdbdcacbbcdbddcaaabdaccaaccbbdabbcadbdaddcbaabcccbabaabbdaacbbaadacbbaccbbcbbbbcacbcbddabbbdcbdcbabaaacbbbdbcdcaacddccacbadabcabdaadcddabccddaabaccabbbacdbdabbbcbbaaabbbccbddcbdbbcbbbbacadcbacbcbbababcbcabcbdccaadacaaaaadcdbacacbaddbbaaabdcbadcbdbcddbadaaabbcacdcbdbabcabdcacaddcabaccbccccbdaadbadabacdadbbcaabbcdddbdbbcdddccbaabbddbcddcababacacbcbcccadabcabaabcadbccddadbbaaddabdbbacabbcbbaacdbdaaddccacbbbbdbaccaddacabdcddcaadcadddbdabbacaaacaacdaaabcbbbcdaaccdddbccbbaccddcbdcabbcdbddacadbbdccbbbcaccacaacccdcdbbaddccbdbacbcadadadaccdaddbbaccdbddcaddadcaaabcadacccddadcdcdccbcbcddbaacababdbbdcddbddcdbababbbcadaaabcbcaaabacaaccbbddccacacbaacaabaaaacdabaacbcbbcdbaacbbacacbdaabcbdadcbdaccbcabdcccdbdcdcaccdddbcdcdabdddadbdcadbabacdaadcacccdbaddbbbcdcbdcbabcbbddddddbccadcaccbcaabaddcadcbabdccabbbdddbdcaabdccabdaaacabccabbcabdabbacabbcbcaadadcbbcbcdadbbdbcadbddcdcadccdbccaacbacbdacdccacbbacccadcbbaccdacdcaacaabcbaaaaccabdabdbbddbccdabddcbaabbabcddaaacadcdcbbbbbbddccabdcabbacacdcdacdcdcdbccbbacaccbacbccacdbdbadaaaacdadbaccbdaddcdbcbaddbacacbdadddacbaddacaabbbcdcabbdabbbdabcbcadadadcabcbddccaccabcdcbbbdcbbaccaddcbacacabbcbcdbbadcdddcbdacdcdbacbdbcdbabacdbbaacdbbaadcbbaaaacbaddabccdbbbaacbbdccddaabbacbdccabdbcaccdbddcdbdbbddcddcdcdbacaabddcacbcaaaacabddaddddaacbbadbbddddcbdbcaadbcacdcdcbadcbbdadbbccbababdaaddbbddbdaaaddbddcacccddadbbbacacadbdccccdddaacaacdacdbdbbbadcddbdbbcdcdaaccdbcbbcaadcbbcabccacccdbbdcbaccdbadcccdbaadcbdcaddbbabbbabdbbcbdbddadbdbbadabaabdcddbbaaccbdabddccbdcababdaabaaccbbcdaaabbcccccabcdcdabcabbbbbdbaddbcccaaddaacbcaacabdbaacacbddbabdbddacaabacabdbaacddccaadabddabacdabccaddbbadcdcdbdabbdaabdcdbbbdbbaaaadaaccabcbababdabcbcbcddcbbcaddcbcddabbbaaccddccdccaccdacabddbcbcdabbcccbabbacdaddcccbcbbaccbdddabaaaacddddbbadddbdddcacacbabbcbdbabdadbbbbbbaadaddacbbbdbbbabccabbcdbacacabcbadcccbdbcdabcadbdcdabbadcbbadaacbbadadccbbabbcbcbcdcdcabbbdcbccdddaaddddbdadbdcdccbddccbacbaacccdccddaddcadcaacbddaaaccbccddaaacabcccdbbccadcbbacbbdbcacacacdcdddbcbcbadcaccddddccacbccdcdbcadbdddcaacbdacacabbaabadbbbbbdbddbcdcadadbbcabddccdabacdbdabbddcabbddbdaddacababdccabcbbcdbdabbacbcbaabcdbddbccdcadcdbbadaaaadadcaacadbbdbabcbdccacbcadbaccbcaacdbbcadddbbabcdcacddaddbcccdadddbadbbdbadcdcdbaacbbdacabbaddadbacbacbbbccdbcaaadcaccbbccddcabbabcbdbaddcccdabcbcbababcdaacaadbddcdbadcbabaacdbdcaacacacccdcbcbdcdacdabbbacddaabdddaabcadddcbcbcdcdccdcddacbdaccaacbbcaccccacabcdbaaaadbcadcaadbdbcbbbbcabaacdaaacbaadaaccaacbdbcccbdbcdcbdbadbaaaadadbcbcacaddddbcdaccdcdbbbccbccbacaaddacddddacdcdcaabbdaabcdbbabbcabaabdbdddadbbcdbccddbccbadddcccdaaccbdcacbcccbbaabdabcaccbabaabbaaaccbcbbbbabddcadabccacddaacabaaaccaccdbbccbadcccbcabbcdcbabccdacdbcabccaccaaccbbdadabddcbcbdddddcbbdbaadcccbcbbdcdaddcbcdbcbabcadcbabbcddbaaacbbdaccaddbbbdbbbcacdddddccdbbcdaacbbdbcaacccdcdbbdbcacdcbdcacadbcbaaccddcacacbdbabdbabccbaddddacacdacadcabcccbaabbdbcadbcdbbcbbabdbcccddadaadcdbbdbdacbddcddbacbdcadabccaddaddadbbdaaababbcdadabcdbabcabdabcadddaacaadbdaaccabdcabddcadcdacaacaabbbdbcaaabcbabcbbcaabadaadccccdddadbdbddccccddcccddcdcdabbaabbcccbbcbbabbdbaabdbdadadacccccbddaacbbddbadbbdcadcbbcdbcbddaacabcbbadacbacabbcbbdbccdaabaacabaaabdadacbddbcdcbcacdcbdcbcbcaddbacdbbcdcdaadadaddacddacaabbdcaaacbcadadcaadbcbcdbbacbabcdddbcaabdbcdaaacaabbcdabcddbcdbbcadaaadbbadddaacbdccdbcccaccdbcdbbbdbaccaaccbdcacbadcdaacdbdcbbaccdcbadccbdadcadbcaddcddabccbbcdcbaccdabbccccbabbbababdcbccccbaccdcddbadcaaddaccbdcdaccdbaaaaddaccaadacabddababcbcaaadcbacbbcccbdbddabcbdcdbdacbacbacdcbbcadabcadaddbadccbbaccccbbcdcdcbbddabddcaddcbbacbadbbbadaccbacdadcaddddccbdacdcaadbcdcaadbdbccdbbccddaacccbabbaddbdcbbbcdadbccbbaaabaabcdbacdadcadccbdcdddcababadbbbaabbdbddccdaaddadbdbacbdbbccddcadaccbdabbcbcabdcddaabbbddccbabaadbbbbcdaaabccbdbdccadcbabcbabbcadabaabadbdcdbadbcdabbcddddcacddbaccccbdccbaaacddddacbdbdcdbaabcabbbaabbbabcdbacdbcbcabacdbccbbbdbdcbdbacacdbaabcdaadacbddbcbadbbacabccbccaadbcacaaabbcbccddaaccdadbddacddaccbdaacbbdcbcdcbcbccddaaabacbdcdcddaadddadaccbcbbcbcdadbdabacabdbabccadddcccabbbacabacbddbbaacbbcabbabdabcbbabdbdadabcbcbbaabadaabaaaaacdcbaacbdaacdddccadadadbcbdcbbadaccdabbcadacbcaaabdcbabcacdbcccccdcdcdadacccbdccddcccababcaddcbaccdcbdcccbacaacbcbacdccbbbbaadcddcbdbabddcbbbdcdccdddccacbaaacadddcbdcdcadcbdcdbdbbdacccbcadbdaddcccddacdbdaddaabbbdcaabaccbcadddccbbbaaabaccaddacdddbbbbbbcbaaaaaaaacbbcdadadbbbbddbbdabbbadadcbaacdbbccadbbbccdcadbbcccaccadcaadaaaddcdbcccdbacadcbaacddcdcadccaabbdaabdadabdbcbcabbcdbdbbcacabdbbcdbcbcdbacbdbbbacbccdacabcccdcacbadaacaaadccacccbbabcabacdbcadacdbabadcdacdabcccbddaaccdbcbadabbacbdabbbaabdcdbcddcccdaabbadbbbcccbbdbdacbdddaaacccabccacaabbbcaadbcbaabbdbdbcddccbdbaadcacdbabdcdbcaddacbcacaaaddbdcaccbadbccdbbbdcccdccabdbccdcdbddccacddcadbcccadacbacaabbcadabaacabbcdbcbcbabbcdaadcdbaaddbcdaadaccbbccaaddabcbccbacacccdacbbacabdcdcdccdbabbabdadaddcaacacacdddaddbdbdadcabdcdcdadaaaabadcbcdaabccbaaabbbbcbbdbbcacabbaaaadadbcccdaddbddcdbdabaacbbbdcdaaaddcacdacbbdacaaaaccdbaabacbdbadbcccabacabdbacbdbbdacbbaacadcdaabcbcbbcdcbdadabacbaddcdbaaccabdaaabcbdcabadddddadcacdbcabcccddacadbbdcacccabadcdccaaababdccdcadbcbdaabddbbdbacadbcbddcbcdacdacdcbadcdcbdadddcbddaacbcababaadbadaddacbcaadaaabbbbdbaddcaadaaaccddcdadbdcbccaacdacadcaaacbaccaccabcbcbabdbdcdcddbcabacbdbbbaacddbdcbcadabaabbcdcbbdbbaccdababcabcabaacbbaccccccbccadbabccdbabdacadacbbbcadaaaacbddbbdcdacaddcaaacbbabadbdbcbbdbdbadddaccccdcbbdcdccacacdcdbbabbdaddabdddccdcdbbdacdacddbdcabddbddababadadaaaacaabacdbdbdadccbdadabbbdccbdbbacdbabdbdddbadbccaadabccadcbdaccdababbdcbddbabaadcbaadaabcaaddcbadbcbabaaddcbbaadccbbbcadcadbccdcabcbbbacdbdcabbadccccabbdaccccddcacbabddacdccbbadababbdbbdccadbaadbbccdbaddacaadcdbdbdaacbdbdcbabdbcbdbdcbacdadbadaacdcacdcbcadbaddaddccbbcacccdabbdaddbaaaabadbacadbbbbbacddacbdcbcacadcabddbdaacbcadcabacdbdcadbbbcbbacbadacaaadcddacdccbcdacbcdddaccabdbacabddcaaaddbabaabcbdababaaacabaaaccabddacbccabadbdcbadadaacbaaaaddabddccbbcccccadddaacbcbcbdbbaababbaabdbdccddacbbddacdadbbdbacbbcaaabbcbacabcbadcaddaddabbbccabccbdadabbcccdcbadddcbabcaaabcdabddccdccbaabcccabccaaabcabbdcbcbbbcdabbaaabdccbcacddbbdcabcdcabddabcbaaddbbbdcacdddadbbdabaaaaacbbcabccbccdccccacdccbcaabcdadccdcbcadbbcbdcddcadaadcccbbdbcbdddbbddcbacdccbacbaaadccacdddaabacbbabbabbddacaacdbcdcacdabaddababacccdabdbcccdadabbdccbdabdccbaccccdadcdbdacadcdcbdcdddabcadbcccbadbcbdcacddbbabdbcbcccbdbabadcacadabadabdacdcbddbbbcbbbbddcabdbcbbacdacddcdcccdaaddacbdadababaddcccdbabcddbbcdcddaaabcccacbadcbbaacdbbddcbdcaadbadabbacadddccbcdcdacbcabdcdddcbbcdacdbdcdcaacdbacccbacdaacacababbcadbbdaabdabcccdaddbadcdbddbacadabddddaadbcbdbcacabddaddaccbbbaaabddcadbabbaaaacabbabddccbccbabcdaddbabdadcdbacdabdcdaccdcaccdcadbcdcbcddcaacbaabbbadcccbababcddadacddbdabaacdbcdcabaaaaadaccbdabcdabadaacaddabbcddbdccddbacbabdbdbadcacddaccccadddaabaacbdddccbbcdbddbabbaaccbbbbdddccbbccbaacadaabacabadcbbacbcaabbcacbdacccaaacaaaddbbdcdbddcccdcadbcabcaaddaabadddbddaaadabdaacdcabdbbadbcccbacccdbacbdbcdddabaddabacdccdcccadadaaccbaaddbcadbcaccdbacdcdccbabdbbcbacbabaccbbaddbbbddaddaccdcaacacbcadcdbbcdbccccbcdccadcdaddabbdcddddbdcabbabcaaddaddbdbbdacbcbbdccbbccbcbbabbbcabaacaaacabbdcddacaccdcbacdcadbbdcbbcaaabbdddacabbaccccbcbdacadbcbcbbccbcacddcacdccdbbbdbddabadabacacbdacbbcaadaccbcdaccdadcbcdbbadbdadabcadaaabaccacdabcccaaddbabbdbcdabccdcdcccddaacaabbcdbdbcdadbadabcbbddbcaacbbddabbdacccadcabcabbcbabdadcabccadabcbccdccbadbabcdacdabbdbbadcdabcacaadbccaaccadcccadcaabdccbdccaccabbdbcbcdcdcbdccdddcdacbdddcabcbddadddabddccbdbdbbcbccdbbcadabaaabacdbabddbdbbdabbcbabcbbabddccddccbdaabbacbdbddacdbdbbbdcbadbabaacbcccbadccbaaddcacdbadcbaccdbcbcbbaacabcbcbddccadcaaccbabbadabbdddccacabccabaaddcdaacccadaccbdaccccacbabddaacaaabcbcacadaabcdaaddddcaaabdbbbabadbcadacddbdcaadbcdaddccbbcbbcbdaccadacdaddddbdbbcbdadddaabcdccdcbbcbcdccaccacbabcbcabdcbaddabbadddccdadcaadbbdbdaacdddbacdbdbdadcdbabbcdaccbdcaadbaaaaaaccacbcdaadcccddbbccccaccbabaddddaacdddbdacbcdadadcadabbacbbadaaadbacaabbdaddcadbccaadbdccccbdaaccbcdadcddbaadbcabadcdcdcaccaabdaaadbdaaaababccaababadccdbccbaacddbbcabcabddbacbacddaabbddcbaccbcddabdccacbabbadbdadacccbbdcbadaabacddbabbabccddadbabadcbacacccbbacdaadcaabcbdbcacccdadcaddacbdacbdbdcdcdddddcbabadbcbaaccddbcdcabcdccccbbbcbbbadaddaadbcbcabcdbbbdbdbbccddbcabdbbdadaddaccbdadcbbdcccaabbbdcaccaaabaabdbabacccacadabbddbbcacbbabdabbdacacdcccccbbccccacddcddcbabbdababdaaabbacabbabdcbdabbdcbacbccaadbddacdbdddcadbbacdbaddbabcddbadcadacbbacbccadaaaccdcaadaabcaabdaaaaaacbcccabcaccbcccbbddbacaadbadddadadccabaaccddccbdccacbaabbbbdccddaadabcdabbaabdcadbdcdbadcbbaadcbdacdcabdabdbdbcbbbadacdcbcadddbbbcbabccbdabaadabcabbadbcbabddcbcbdbbbacdbdaababbddbcbbbbabcdbcdcdabddcabdcdccbaadddbbdbbcdbaacbbdabaddbdbddcaadcdcaccaddddddabdadbadbcaccbabcbbdcadbdababddabbcacdaaddbabaadabaacacadcddddcbbcbadaabcbcccadbbaccaabddccdbddbcddcdcaabccaabdcccacbdbcbbbccaddaccabadadabccadcdccaaacbddddabbccdcbbccdddbcbbbacdbcdbcadbbdddabcbbbbbdbaacdadabbbdadbbbbcbdcaadbdbacdadbcabddaadbadcabcccbadcdaaddbdddddacccdbcbaaddbadbdbdcaaaccacdbbcbbdadbbbacbbabddcdccccbadcaaccdadcaabaacbaabbcacacdadbaabdcccdabacdcccbcbbccdbdcadcdaccbcaabcdbcaccddddbddbbabbadaadbaccdbacbadbbcdbdbbabdbbccbabcddabccacaababbbcacbbcbbbacacacacbabdacdaadcacdcabddcdcacaadccababcabbaacbbbdbccbcccccabdacaacaddcabbaddabdbbcdbdbbacacbaabcbaddacadabaaaacdbdcdddcbccaadcbbddcabdaacccbccaadcaddbcbbcdcbaaddbdbdbbabbacaaaabcabbbaddaacdbadccdbacbcaadccaabbdcabaabcbddadbcdacbcdcccaabdbadbbabbbaadbdcdcbddccdcadbdcddcbdacabdabcdbbddbdaddbddddaacccbdaddbdabcdbcabdccddaddbcbabdcdcabbcaccbddbcadbddbcddccbbdcadaaddababcbabccdadadcbaadbbbbaccbaadcccadcdbbddaadbcdbacccbaaaabadbccddbdabcbbbdcacabcbadbadacdaccbaaadbbabcacdadabddbadaccadddabadcccdcabbcdaabbbbbdbbaddaaadbadcdddadbddaaacbcadacdddacaaddbcddbbccbdaaddccbbcbcdcbdbabacddadcaacacdbabaaadcbcbccdadddbaaadcdcbababdccdbacaabaabdaaddadbaaabaaddcacdaababacdcdabbddddbbddcbcdbbdabaadbdcabaddbccacbbadaadbbcaadbdbaacabcacaabadcacaabbbddadabbbdbdcbacdacccddddaacbbdcaadacabacdcbbaddabdbdabaacccacdddddaccccdcdaccdccbaccacbaabcbaacdbccadccbddacddaabdbcbbbdcccaabdcadbacaaddbcddbcdbdddbdadcccabddabadbbddcdaaacdadaacbddcacbcdbccddddbccccdcdccbcacaaabbdabcdbacbaaabdadbaddcdabcdabadddcbbddaddcbccccdbcbbbaaaddabcbbcabdcaddbbccccdabccdcdaddaccbbbbccacddbabbabbabddcbcdacddcaddccdbdddbddccdacdcdadadbdddcdcbdabdbcbbdbdadaabdcacddbdacdbabbcaddccaccdaadbdcccbdbaccbabdabdccbabdccaabbdcabdaaaadacbbcaccccdcdcacbadacacdacbbcbaddccdbddcdbdbaadaddacbbcaaddcbbbdaaaddbcbabacbcdadbdbcdaaddaaaabccadabaadadbaabbadacdcdcbaaaacbdcacdbcabcbdcbdcddcadcccabbdbdaaaccaddadbdcabdcabbcddbaccaaaddccabdaccacdbcbddaaacbabaabdcbbbbaddcbaacddbbdddcddacadcdddadbaaccaabaacdccddcadadbbcdcaabdddccabbaadaddadadcacdbacbaaccacccabcbadccacbcacdbababdddbccacdbdbdbcbacdbbddcdbbbddbbdaccdbadadbdbbbdbbcdacabbccabbaddcbbaddcbcbcddaadacdaabaabbdbcdabcbaadaaadbaccaddbaadccacdbcbdcddadddcccdacdaccccccaccaabbdbbdadbadbcacccbadabbdaabbabaaadccdbcbcdbcabcdaadadcbdcaaabbcdcacabcaccdbadbddbbccaacdcdcaaabbdcbacbcbacbcadccdbddadccbddbaaadbacbadbadbdccdccabbddcbbddbbcaadaaaabbcccdaabbaddcdcaccdcccbadcdddbaadcccdbddcadcbacbaaccbadcaccbbcabadbabaacacbcbababbcddbabddcbaaacbbacbdccbbbbcdaaaabadbaadadaaaabbdaacbaaadabdccdbadbcccdacdcdbaacbdabccdcdcbbccbaadbabbaadaabdbaaddcbcccbabbaaaacaaabbcdaadcbccbaabcbdaaaaabbdaadcdbbdcabddcbbcddddddcdcaabcabcddbcdaadabcbaabadbbabdaccaaddcdbbadcddddbaddaddbbadaaaabbcbbcbbbbbcdadbaacbbacbbabdcbadababdbdaacdbabddaadcdaccbdbbadcdbaacaabdccaddbababcccaddacbbbadabaacacccccdbaccaacacbdbdadcbbcbddbbcabbcbbbccddddabbbadcccdcbcaadcbdbbdcdbdcabbbadbacbcddcadcccdadbddadaaddcbadcdbcdbcacadcabdcadbabcdacbbbbcaabdacaccdbbdadbbaacccbbdaaacdcbdbbbacbbddddbccaaccbbacbcccdbbbcdaaddcddadbadbcbcdccbbcdbddbcdccbdbacbddbbdacbababaddbdbddaabadbdadabbcacabccdaddadaabdbaaaaaddbaddacbdbaababdcabddaabdacdababcbabacddcccbabcbaaaaacbabcbbcbababcdaddcadcccdabdcdabbdddbddddaaddcdaabcabadaadbacdccdbcbdabbbbcadcdadcadcbbbaadabdaddacdcabaadbddbcccbdadbcddbcdcddbcababbdddaddddadbdcacdcbdadbdccaacdbaadbdcbdbcdabaaabaddcabdadabdcadccacdaadaaadbcccbcabbcbcdbbdadddabbbddcacddbacadbadbbccaadbbcbdabdbacccdcadbbbacadcdddbdadabcaadccaaadacbdcbdaaabaacbaaccbcbcbbdadccadcbbdccdaaddddccabaddccacddcdacddbcbdcdabcbbdbbbbaaaccbcbcbcbbddcdabcbbcbcdcdbbcddbcdaacaacadbbabdbcacdbbaadccdbacabadccbaadcbbbdaacabaabaddcaaadaaadbbadaccbaacadbdcdccccabdcdbcddacbaaaddbabcbbdcbaadccabaaaccbbbdcdcdaccccbdcddbdbcabdbaddabcabbbbbbccdbaddacaddbaddcbbdabcadbbcbddcbabbadacbadddbbbaadcadcbadacdcbcbcbbbdcbcdaccaabbcdbdddcbadaccccacbdccbdbdbdadaddabcbcbcbdddbbaaaaaccdadbdcdabcbddbbbdcbbcdadcccbdababdcadccadaaaacbdccacbdbadbbccbccbbadadaabdbddcbcaaddbdccababbaadbcdbbbaaccacbbbaadcaaabbaadbaaccccbbacbcdcdaaaadcddacbbacbdabcddbcacdaddccbaadccbdccdacacdaccabbabbcbadddcddbbdaadabbddaaacadcdaaccadbdcdaabacaddbbacbdbddbacabccbcbbbabcdbaacdbacaabababddcacaacdcccdddadcbacddbaabddcdccadcabcbcaacabbbbdcbcbbdccacbdbbadabacadcbbbaaaccacbacbbdddddaababaccaccdddddabdadacddaaadbcbbdccccccbccbcaabcdcbcbadadbaababbbbccdccbbbaccabadacdbbcaddcbddcdcbddcdcddcbcaddcaadababbaccdbdbaadddcbbdabbabaaadaacaddabbdabdacbbdbbaaaddcaccadcabbcccbbddcacabcbbdcadddaccbacbabccdbcbbcddabdbadbcbccbbaaaabbdbbaadaaaaadddacbdbcaccbaabbcbcadbbacaaccaaacdadbddaddbbcaabcdacccdacbbbaaaadbccbabaabdaaacbaacadcbcbdaaabddbccccaadcdaacbccbaaddcadccddaddabacbccdadacadccdabdccbdacabbcbbaadbacdccdcacbbbbabcbcbbbcadcadbccaaacbddadcdabdaaacbbaaacbabadabcdbabcdaabaddaccccdbaadbccddcdbbacdabdcaabbbdadbddccbdcdbdbcdddbbbaabdbccddacbdbdcaabcdbdcccbabbadbddcddacbdacadcacaadcaccdcaadddbbcdacddddadaabcacbaadbcbcdccaadcacddccdadcbdbbcbdadacdbddabbcbdbcadacbaababdaaacabdccacccadabdaccdbbbccdcacacabcdacdccbddbadbcadadbcbbdabcdabaaccbaccaadacbbdcaadbcddbbdbababababcabadabacbcddaaaaacbbacccdabbbbcbadaabccdbcccddbabdddacdcbbbddcdaddddbacbcdcadbcabcdabcddcccbacabadcbaadccabcddabacdddcaccdabbacccdcdaddddcbccadabdcddcbdcbdbcaabdbbccbaccadcccccbdbbcdaccdcccaacdaddbbaabcacdbddbdddcacdbdbdcbcbddcacadcabbcdbdcdcdaddcbcacbccdbdabccccabbaadabaadbadcadbacbaadddbdbaacbbbadbddbccccdccabccbcadbbbdaccacbbaaddbaaacaaaadaddacbccacaadddadacbbaadbabacdacdcbbabcbdcbdccccbcdcadcaabacdbddcaccbadccddbadabddbacdabadbbddbcccccbabbdcdcaadddbbbaddadbadcdadcdbddaccadbdbdbdabdabbbcadaaaaddcbdcbbdacbccbbadacbdddcbdbdcaabcabbadacbcadabadaadcddaadbcacabcabdbbddbacbcdbabbcaaaabaabaabacbbdddbbddcbadacabbbbdbdbdaadaabbacbcadddadacbccbdabbddbadcbcbddbdcddcbaddbabdacacadbdcccabcdccacdadaddaccdbcddacddbcbabbcacaccbcabcadcdddcbcdbbdabacabddddbdbabdccbbbbadddbbbcaabcdcbadcbbabbccddacdcaabadbbabbddccccddababcabacdadcdcadabcadadbaabcdbcbdbccabdddcdbccadbbcaaacabbbbdaabbacadadacccbbcbcabbbacacddcdbacccbbbadbacbdcadcbcccdbbaabacdbacddcacbbbbabdddbbbacccccdcdaddcbbbacbbcbddacbadbcaaadcbddbabbdababbacbcbdbccbacdacddbbdbdcabcbbdaaabbdbadabcbcbacbcbddabbdcdccbbcddbcdcbbddadcbddccdcadcdcdbcadbdddcaaaaccaadadacbdabaddbddddadcdbcbbaadbcadccbbaacccbdcccdabdabbacbaacaabdadbaaaabbbccccaacbcbdaccddadccdbcdcddbddabbdacabccacbbbacbcbbccbdaabadbdddacbdabccbddbcbaacaaadcbcbcaadbcaacddaacbaaadcbacddbdbacccbcabdaaccddbdccbdbbaacaccaabddcdacddaaddcdbbccaabadaadcaadcdddbadcabcccaabbcacbdaddbcbabcbbdcbaacaddaadbcabbdacadaddaddacaccacdbacadcbadbdbacdcbacabcddcbdccbcbbbdcddaadaabbdabbccaccbbccbbbbdbcccbdcbabaccdadcbdcbbbcbcaaacaacbabacadadacadcbbacdabddacdadaddacadbbccbacdbcaccacacbadbbabbccddbccdabaacbaabdcdaaaddcddbccccccabdbbaadcdbddddaacbaaccbbddcccbaaddacacadabcdacddabbdbbdacdacaacdcbbcacabcdacbccbddddcdaccbcadabbcdcabbdbbddddcdccbadabdccadcdbdccabacdababdadddbabcaadddbbdccbdcbcdaacdbbbbdcaddcdcdacadbccbbbbbbdccbcbabdccacbdbadadcacadacabbccbcbcdbaacbcdcaddbcbabdaccbcbccbbdaaddcaabccdccbaaabccbadbababadbdabdbcaccbbbdadabddabdbbcbacaadcbbddbadcbdccacdbdcbdaadacdbcbbccaacbdbbacddabddbbdaababbccdacdadbddacacccaaaacaacbabbaaddddddaddcddcddbadaddbdddabbdaaddaaadadadadddaddbbdcacdccdccbbbbbbcbbbbaaaaacccbcacdabaccabcacbbadbaabcbdaacbacbbaadbdccadbcbddcaacacbbbdbabdbbadbcabdbdadcdbdcbdabbbacbdbaabadcccabdababaabbdcccccdcacccacaacadbaababdbccdaccabccbcbddddabddcbbcabbcdbdacbdbacaaaaddcabbbbcaccaaabbaddddbbaaddaaccbcadbdaccabdddcddddaadbabddcbacbdcacccbbadccbdbaccaaaacbdaabacdcbccbcbdabcdbcabbbdcddcbcaaaccccaabacdbcbaddababacdbbdbcdccdaabcbdbcaabdbaabacddddccadcaacbaaaadaaaccdcbaddddbdbabcdbdcbcdadcdbcdddddadaaddbbdabccbddadbbcacccdbaddbbcddaadadbdbadcbcbcdabdbbdcbbdaacccdbdcaadbcddbdccadddaaaaddccbabdbadadbccabcdbcaaacabddbacdababcdbaabdbdbaacaaaabccbbddbcccbbadadbbdadaacacbbcdbcddabbbccbaccbcaddcaababbbdccdbabbdcccdcdabbdbddcabcdcccadbccccdcccdadbacddcbadcaaabdcadcabadaaacbbccacadbccaddccaaaddddcddaddbcdadadcbacdaabdbbdbdadacbccbdbdbcadbaddbbdbabbddbadbabbaadddadacdddacbbddcabcdbbadcbabccdcacccbdaacbbcadddcddcdbaddcabbdcdacadccbcbcaabcddcdddaccaddcdcdadadcacbabdcbbaccdccccdacacaabdbdbacabcaadccbdbaccaadbabdddbabdadddbacdccbdacadbacdcaaddcdaccaadcaaabdcbbabcccbabdbbacaaabcdbbbbacdacaddacadcbdaddbcdccdbbcabdbcabcdacabddddcccbbcccbacbadccdadccadabdaadacdbdabccdcbcbbaacdabbdabccacbdcdcababaadabbcacaaaabaaadcbabdccdbaaacddaddaddccacccdbdadbbbabdabdabbaccbdcabaabbaccccbdddaacdbabbbdccdacdaabbbabaccdbcacbccdabdbbabbdcaadcbbbdacacddabbbccabbbdababacbaddaddbdcccbbbbbcaaabccdbcbbabcdcaaacbddaacbcbaccddcdadcbaabadbbcaacbcbabbcdadbcaaccbdbacdbdadadcbcbacdcdcabacbadaabddccabadccbdcddaaadbdcdaaabdcccbcddbacacdbcdabbaadcdabacabcbcbdddcddadacdbdbaccabbcdccbbdcbbaaacdbbadbadacbbcdcdbaacbbcbaaaddadaddaacbcbdddcbabbbaaaacbcbdbddbcaabcccacbbcbdbdabdaabbbcaabcbccccabaacbadcdccbaaaadcbadbaaddcbcdcdcbbdccadcddcdddbaabbaccbbabbacdacbabdcaaacdaddbacadbaadddcddccababbcddacdadbdabddbdcdcccbcdaacdbddcaaaacddbdcacdcdccbbcbdbcbbdbabadbdcdcccaaaababbdaddaccbdabacddbaaabbbaadcbdaabccbabdbaadccdabcbdacbbcdccabbdcddadbcbaacabccdcddadbdabaaccaaddcbdcccccccdadbcdbcadbcdcacabcaaccccccdacddbbabadccdabaccabdadccbdadbacadbdcbbaddcddbababadcbdcadcabcdcadbdbddcddddbbccacaccdcdcabccaddbbacabbadcddbadacdbcdcdccbcccadadbcbabcabdcbccabadddbabcddbadaaaacaabbacddbabcdbbaccdddaaadbdaacabbcbdbcccbabcbaabcaddcaabcbddabdaccdbcdcbdcdacadacbbacaccaaabacddcdccbbddbaccccdbbcdbcdbdbbadbccddadaaabbaddbbabbbabdbbdacdbddaadbcaaddbbadaabdbdbccdcbadbdaadbdddbbdddcdbcadcbdabbabccdacbcacdbaddacabbaadabbbaccbdaadcabdcddabdbbbabdcbcbdbcccddbcbbaddbaabbbadbdabdcdbccbccaccabccdacbcdbabdabbadcabbabcaccdcbbddadaddddcabddabbabdcbaddadcbacbdbbaaadddcdcdcdbddccacbdadbbbcbbacccbcadbcdadcaabacdbcccccbdbbdbcaccbacdddadcbadbdaacbaacdaaabcbcadabdbaccccdccbcbdabcdddaccacabdaabcacaaccdabbbcaacbdbddcaaaacccdababdbddddaabddccdadbddbacadaddaabbdcbccbccadadddacdbcddabbbdddddbcacdabbadbdacaadaaabddbdcaccbbcbadbadacaacaddadbdccdacdadbbadbcddbdaddadcccaabbdbbabdddcacdcadbddbcbabdcccacccddcccbdcbcacccdaaddcababcdadccccacabbbddbabcabbdcdddaabbbcbcbbcdddbadabddadcdacbabcbcbcadcbcabcbabcbacbddbaaaddbccbcdcadacbbcbbdbbdadcccddcaddcccddacdcccbcbccbcbcbccbacdcbcaabbabbbdbbdddbaddbccaadaadcaadabddbdddcadaaabcdbddcadbaaaaaacdccdbdadabaabddcdadacdbcbdcbaabddddbabbbbccaddcacbbcccdccdaaaddbdabdadabbdabcddabadcdbdaababaabbcdddcbdcbaaddcddacbcaacccccccbbbbcacdcdbaadcdcdbdcdacbccacbbaacbbdbcddccddbdaaadbaadbccbadbadcabadaabbdbadacbcdddaddcaccbcabbdbcdaacddcbcdacaababddabcaddbccdbccdcdcaabcabdcabacaabccdaaabbdcbacaccbcbbbcdbaacccccdbdccdbacaabbaabbcacddcbcbbcbacdaddadabadcabbbdadbdcadccccbbbacacbddddcacbbcdadcbbabccbbddddbabdddabaacdddbcbdababcbcbdbacaddacddcccaaaddaaaabbddadcacdaacbcccdcbdacdcadadbddaaaabcadccabcabdccccdbddbadadbdaabddabbacdbabadbdbbbdccbcdbdbccbcababdadadbacbadcbddccbbdcbcdccbbbdaccbbcadbbddcbdadaabaddddacdcbdcdcdccbdbdadbabccdccbdaacaaabbbddccbaaadbbdcbcabcadaaddadcbbcbdbaddcdbadcdcadcaaabcbdcbaaabbbaccdcdccbcbccabcbcdbaaadbccdadcccbbdcbcbcdbdabaaabaccaddacdaccccbbbacdabaaddbabbdaaabcddaaaacddcadddccadaaddcddbaabaccbcaadbbbabbcaacdccabccccbcbacbddabaabdbcbadbcaadbddbabdaccdbcabbcaabcbbcbaacddbbbcaaabbaddaadcacdbccdbccccbdabbdcdbdabdabdccbaccbdddccbcaadcddaabdaadddcdcaacbbcaccbddabbcadabcdcccaadcbccdaabcdacbcddcbbbccaacbcbbacddbacbdaaabddddaaacaadbaabdbbaccaddcaccbdababacabbadabbadabdcaadbccbdadacddcbbcaaaabccdddcabaaabcaaabccdabbbbbbbdbbcaabddbcbdbdcabbdbcaaabdadbacabadbcdbddacccddaabddcddaabccddddcbcbcbadbcdabbcdaccdbcabcdabacdbcdcaadaadbbaacabaddcdaddccbcaccdcdcadbaaacabbbbccbdcbcbacadacdddaabbadbdbaabcaadddbabaddcacabbbaaddccdbadcaacabababdadadabdcbdcaddddcdbdccbcdbbdcabaddabbdccbadcbacbdbbcdddcbdbbdcbbadaddcaacacbbabdabcdcadbbcdaccaccaadcdaadabbcbcacbdbdcaababcccbcdadbbdbaacdabccdbbbbadaaaddbaacacadaabdadcddccbbccbbacbdaacdccdaccabdcddacdddddaacababdbadcdbabdbadadcbadccaadaaccdbcdabddcabadaabdacbdadbacdaadbccbaababcaaaadbcabcdaabbcabddbbbdaacaaadcddccbdabbddaaabccccabdbacbccaddadabbdabccabbadadcacbcadcddcabbbdabdcbbcaabddbdcbcdcdbdbbabbcadcdcbccdbbbdbcdadcdcbcddacbaabdbcadcdcbabccddcaadabdddbcbbaadabcbaabbbabbddaddcdddbdaddcacdcdaacddcbbcdddacabbcaaaabbbadacdabdbadbbcbdabbcccbcdbbdccdadabdaadcccbbaaddabccbddabcabcadbbbaadbdddabacdadcadabddddbaddcbdbbcdcdcaccbaacbadbddcbbbdbcdbbcbaaadadcbadabccccdcdadbacdcbcabcbdbcdddbdcadbbabccbdcacbaaabddaaabbdcdaacbcdaaaaccccbcbababdbaadcadcbcbcddcadddcbabddbbacbabcbccaabbbdbbaabaddbacdacbdbccadbcddccdcccbbcdabbacbddddbcbcdacdbaaaacdcaccabbcadacbbabadcbbbcaabdcccbacdccdddccaccbdcddbadadbccbcdaccbcddddadabdccccddadbbbdcdadaccbdddcadcdaacccadcadabaccdbbdcdbcbbbbacabcabcdcaddadcbcbdbacbdcacdbbddbdacacdddbcabdbdabcabcdcaabcbbcdabbabdcbbccbbdbcbdaaaccbcdacdabddabbbaaabadcabbbddbcdacbadbbacbacdcaacddbdcdbcbbbdadabbabdbbacdbdbcadababbaadccccbabcababbaddbabcdcbddbbdccadbdbcdddadbccddaadcddcbabbabbbbbcdbacccbcbbdddbacdcdaddadbdbdacbacddcdbcadaadcbabbcdbaabbcacacadbdaabbbbcabdcacaaaddaadaacabbdccadadaadabbdcbdaaccdcadababadbdaacaaaacadacadbdcadcccbcaaadbbbcdcaacdbaabbdccadbbcbdbaaacbbcccdaaaacadccbccdcddccadccbcdcbbbcdbcbdccbdbddccdcdadcbbcdabaacdcdbcdcbcdcdaaabddbabbadacaaabdbccdadcaadcbcccbcabaadccabdbbcdcacdaccbdcbdcddddacadbbcaadbdcdbccccaabbbadccdaacaabccdaddcdabcbaabaddcdccadcbacdbbacdddbddbbaaddbbdcbcccddacacababaccdddddddadcddccddccbbbbcadccbacdcaddbadcbcaddccdddbcdbacdacccdcbbcabaadccbdbddcccbbbcbbacadabccabccabbbbdbbdaadbabacdaacbddcaacacacdddaabcbdaadabdbdddaddccbcdbccdbbcbdacddabcbdabcccddbcddddcdbbdbcbaacbdaadcddccdccabacdbdcdbbaaaadaaacabddbacaadadabcaadbdcabccbddaadcbdbccbddbcdaabbddaccbcdbcababcaadcacadbcacaadadcdddaddddcdaaabacbaccbdbaaccccabdbdabdbccddabacadcddcaddccadbdbbddbcabbccbcbcccccacdaaaabdbaadbcdcbabcccdcbcaacbaddcdbaaddcabacbccdccabcbdccbddcccbcccaaccadbbdbbdabcadadabbbaacbbcaaddddacdcdaaabddbdaaabdbbbdaddcbbaaccdbacbbabaabcbabcbddaabcaccccdcccdadcbdccdbcabdadcdabbbbcbaaddacaacabbadadacbbcbabbddabaacaabdbabbadacbcbbbbccaabacabacabbbbbddabccbbbddccdcdacbaacdacdbddbdbddccaaddbbdddccdbccdbbcadbcbdcacbbabadcbcbcdbacdabdcdbdbcddcbcdabaccacadddccaabbccdaccddbcdcabdaaacbbabbbadddbadbaccdaadcdadcbaaaddadbbbddbadabdadacabdbbababadabddacddbbddacbbbaabddaddcbaadaacdbcccdcaacbcaadbbabaccabdbdbdddbabccdadcdcadbaacdbcacbddbddcbaaacddcaadbcbbddbccbbcacabdccbddaddddcbccacdcccbcaaadbabaccacdbaadadcdcdaddcbadcdaacbdaacabdbddcbaabdbadcdccdbbcdacccbbccdcbccddbadcdbdadacdcbdddccadaabbbddbccadbcdcdcbcaaaddcbdadaddacbdcbcbbbaccbdbacdbadbbdadcccbddcbaddadacaabcbbdbaadcbadcdcbabdbddbdbbcbbaddbbadadaddabdcaadaaddcbdaaacccadcabccdadbbbbcbcbadcbacdcbbbdaddddddabcbadbbaabcdddcccaddddaabbbcaccdccadabbcccaaadbccdcccddddcadcabdcbdcabccddbcaaabbcacaabcaacdbadbccdaaaaaacdbbcbbadadcadacdcbcacdcbdaabdbbddabacdbdcdaccdddabadbcacddacabcdadadccdbbadcbdddddbadabdbbaaadbdcadabddbbccdcccdbbdbddddbbadcbbbdabdddabcdddabddbacadbabadbdcbcbdaacbdbddddacacaaaadddbbcabcbcccacbabbdbccdbdadcaccacddaccadaacbbadbabcbabddaddbddadbcbcadcbadcdccbdadabbcbcabdbdbdbbaacaddcbbdccbcccbacabccbcbbdbdcbcabbdbabdcdbccbdbbbcbbaadaccdacaabcccdabcdadccdcadaaabcdaacdadabdaccaccaaaacdcadbacbcbccbccbbadbcdbcacccccbbdacdadcaacdbaacabdbcdbabaabbcdaaaccacaabdccdaaadabccabdbdbbbcaadacbcddcbbdbdbdababaadbdbcdabbdbdcdacddacadccbdbcbcadbbbabdbcdabbaccbccdcadbdabccbddcdddccdbccaaccacdbcddbcddabbcbccbcbaabdccdcabdadbdadaaccbcbddccbbcaadaddbdcbcbbaaabdddadbdbabccabbdaadbccbccdaacbdcabbdcabbbddddbddabccdcabbbacbddbdcbaaaaadbacdbbbbaccddbddddcdcbcbbbdacadddccaccbdcaadadadbaccbcbabacdadcadadcabdccadbdbbcdbbddbbddacacdccaaccacdbcdcdcaabbbdddcabddccbcbcacdadaaabcbdbbaccdcdaaadcabaaadddaccabbbbcbcaabadcbaaababdbdccacaacdccbdaccdddacdbaabdcbdcacaddcdccdbacbbcbdcdcadadcccbcacabcbaadabbaaadccdacdacccbbddcdadcbaccddccabaabcbdaadadbbbdadacdadabdcbdacbccaccacbcbbbdcbcbcbdacdaddcdbabbdbcccdababbadbcbcdcadccaababdccacaabaccddbccbcdcdabcaddacbabcbbbadcbbddbbcccbccbdcdcababacdbcdadcabdbbabacabaabbbcaadadacabaabcccbddbbdcdcdcbbadcbdcbcacaccbbaaaaaaddcdbdcdcddabcdcdacdaaddaabcbcbdcacadbaacbbcbbddaaccbdabbcdcbcabcabdbadcdaaadbcbcdcbcaddabbbbababadcccacabbddabbccabdabaaaaabdcddcbbcadabdaaddbcadbbbaabbddbbcdcaabdbdcadadcabdbbdaabacbbacbddabcabdbcbbcccccaadaccdccbaaadddbbaabbaaccbabbbbccbdcbaaaabdbdabccaadabdadcdcadbddbaccaddcbcbbbaabbcadcddccdbdbaaaabacdaabcbcbaabacddbbacbdadcdbbcacbaadaaaadcbacdbbacacbbbaacdcacddcacccbadddbdbcabcabdaabbbdacaaddabbddbdbbbcddcacababaabdcbcabccbacbdabdbcdacbadcbaddaccddbbbaccbaadbdcdbaadcbdbcbcddbddcbbcbdcadbaabbbddcdddcdadbdabddaccadbdbaaaabbaacdbcdccddcdcaaadadddcddbabbcacdcbcaadabcaadabbdaabacdbacddcccbbadddcdacdcbdaaacadabdcbbcbdbcbcbabbbabdbdcdadbabcddccacbcbdbddaaabacdbacaaabcccccabaccaacaddddbccdbabaaccdcacbcabcdcabddcbabdabdbdcaadddcbcbddbcabdcdacbaadbccdcaddbdbcdadaaacccdbcbdcabdcbdddcaabcdbdcbcbacababddcaabcacbacbabaabaddcbccbbbdcbbcabaaacdabdbdcbadcbbcbbbbababdacbaaccbdbdddcdaccdabbbcbbbbbbcabdccabcdddddcbcaaccaadaacdcbdacbddabcdccbcdbabadbacacddbbaaddabbacacacbccaccbbcbbdcacdcaabcdcccaacacbcddabdbdcbcbdabcbbcabdbcdddadccddcddcacbaddddcdbacddacdcbacadababddacacbaacbdbdbbdbdbaccaddabdacbabaddddbadbcabdddcacabcabaaddabdcbdabbaccbdaadbcbbbaacaabcadccdbddccdabbacdcddbaabacbadaaacadadadbacacdcdbccdbddbdddcbbdcbbadaddbbdbddccabcccaacbadbdddbadcabadacdadcadddcdabbacbcacabddcdbbbabcbcdddbacabacbaadccadcbaacdaadbddacccbadadbcdcabddcbcaccdacddcbddcaacdbabcbcddbbddabbcabcaadcdbadbdbbcddddbdbbadcbacbcacbbdaacdcaccaccabdcddabbdadbccaadcabbaadddcaccadbddcaaccdbabdcabcccbccbccddbcabdcacdcccabcaadccacbcdaacccabacaccabbaaadaccaccabdbbbaabbdbadaabbddcadcdabdaaaadabdabbbdcaaadcabdccbcaaaabcaddcbcbdadcabbabcbddbabadaaaccccadddacbcaccbaaacdbcacdaacbbbacbccdcccdabbcabdcbacbaccddabdbddbdbadadaddaaaadabcbbcabccddddbcdaacdccbccdacbdbdbbcddaacdbaabbdabaaaaacbbbdbbbaaabdbdbbbaccbbdaacdbbaabcccbbadcddcdacdbabbbabbdcabaabdadcbdaccabbacaabddccdbbcbdaccadcabccaddbcbbadababaddbbdbcacbacbdcdbbcbbdcdabdcccbcbbbaaaddcbaaabaccdaddcadcabcaadcbdacdcbdadcabcabcaddbbadacadbbcbcbdccaadccbcbdcccdcabdbdbbaadbaccdcccbbcdbdbdcbacadacaabcddadcadbdabbbdcdbdbdbacaaddcdbbabcbcdbbddbbccabdabccbbdadccbccbabdddddaacbabdadccddababdddcaaccdbadbcbbabccddbdccdaaaadaaabbcdcbbdaadccbdcbdaaaccbcbaccbdabdbaccbdadbdaabbbdaddbbddbadcdaccabbcdaddadaccdacbadddddbabcbddbcbbbddcbadbdbbcbdabdabdbcbdabbcaacbbccbbabcabbbcdacccacbbaaabdbbdbdacdcbbaadbcadccacabbdbaaccabccababaaadcccbcbbaddbdadcbccdbabbccaaddababbdbcdbdbcddbdcdbadaacabbaaccaabbacbdcbdbdaadcdcdbcabadcdddaaabdcadbdbdadddbcdbaabbacacbdddaacdcbacddcabcdcbacdaacbddcdbbabaddbbcbcbcaaccdaacadaabadbdcbcdbdbbbadbbadaabbcdbadaaddbdbacbacbabcadbbdcbdcbdddcadacdcaadccddccbddabaaacbbdcbdbbbcbbbdcacdcbbcaabcddbbdcadccbabbbbdadcbddcacabcdbdbacdbcabdbabaddcdcccbbababbbcbdaabccdcdcaddbcbddcbbcaddabcaccbbddbabaaccabdcaccccaacaccadacbcaadbaacaccdddaacdbaddcdbcbcbbdcbbaccbcaccbaadabcacbcadacbabacbbcadabcadaadacaacadbaadcbdccdacdbdcabbcbcdcabbbdabacbadabbbbcdacbdacbdaaaaccbdabddccbaaccabdddaadaccbbaddddccdccbbdbaabaacaddbbcdbcccacbbaccdbdbdccbdbbdabbadabccdbabbacddbbbbdaabbbbbacdcbdbbaacaabcdbbbaccccabcabdbbadabcbddaabdbacdbccbdbddcaccdbaabbabdabcbdbaaadcaadacabacadcbdbddaccdaaaadcadccabccaaccababacabccdaaadcddbdababcdbbcdbadddbaacacbbdbdcaadabaabbddaadddaccaacccbacbcccccbadcdaccccdadcdcbcdabcaadcbdaacdbbdabcabbbccbacacacbbcaabcdddcbccdbcacbaacabacddbdcdbcbbcaddccbcaabacdbbbbabddddccdbcdcaabcbbadabbbdcacbcbbcadabbbdcdaabbdaccbdbcdadcdacbabdcbcdbdcaacadcccabababcacbbadcabcacccabcbacbcbcadbdcabacbddbbbbbabaccbcdadaddacadcbcdccddbadccbcabbdddbdcaccbaadbdaccbdbdacadcbcdbbbcbbadbddaacacacbdbdacddaadddadbdcacbdccdadbbbcddbbdbacdbcdabbcddbcacabcdcdbaabbacaccbbccdccdcbdbacabaccdbbdacdddcbbbdaacbcdaadabbacbdbaddbdbcbaabacddaaacaccbddbcbbabacdcdadccdaacbdbcbdadcdbddbacbaddcccadaabbccdabcdccddbbcacbdcaddaadddbdaacadcbdbdcbbbbbdccaaddcdaadbcbdbbbbcaadcadadbadabbddabcabacdcabccadbdcacbcadcbbbdcdbbcbbadabcbcbdccddddbddbdcdacaddbbdbbdbdccddaddddbadadabcdcdcbcdacdabcadaddbbbbabcbcccbaaccdcabdaddbbabadddbdadcdcaabdbbcdddccddccbabbccdbbaddbbdbaddddcbacaaddbaccbdddbaaacdadcababbdaaaaadababddddbbcaddccbddbaaaccdcbcbdadadcbdbbbddadbcdbabdcdbbcdacdbbadbdddcbdbdbccbcdbaccaaabdaabcdbcaacadaacadddcdcadbdcccaccaadcbdcbdacdaaadcaadcabaccdaaaddcbdabcdaddabdabdbbaabcbdddcdadcbdabbbbabbcbcdacdbbddaddaaadcccbddacaaabbdabcdcbaadbdaaaddabacaacbbacdbaddcaddbccabacbbbdccddacbbaadacdbabaaaabddddaadbbbdabdbbaaadbdbadababccdacdbbbcddbabbddbcccdccbcabcacacbbcacccdcdcdadaccdacaccbbabcdacbddbcabcdcddbbbaaacaacbababbbabbbbbbaadddbcabacbacacacdabbddcbcacaccdbcbdcdaabbabcdbcabdbbcdcccaadbccbadbbacacddaaadaaaccbdbccabbdaadacbccbbddaaaccccacdbadbacddddabdcabbaadbcabdacdaccbbaddabdbccdbdabddbadaabcbdbcaaccbcbbcdbbbabbcdcdaaadcdccacbbbccbbccccbddcaaaadacbcacdabadabdacdaccbccbadcbdcdbcaadabbbacbbabbddcaacdacaabdcccdccbdbcaaacacadbbcaadacdccbcbdcbbdabdcdcbdcdbdcccaadadabdbdbcdbdcabccacdadabbacbbaadadaacabdcdaccdcabaabaadcddadcadcbbbacaaddbbdddcabcbbabdabdaccbdccccaababddbcacbdaaadccbbccbcabacacccbccbdaddcbbbdcbccabdbdbbdcaabbbbbcadaadacadccbabaacacdccdbcdbbacddaabcabbbaaabadbbdbcaccaccddbcadcbbdaabadabdddacacadadcadbdaababbdbbacadcbccaccdddcbcdcadcddddabcbdadadaacccadbbbddcddabadaadaacabdbabbdaacbaabdabddababaaaddbddbcbdcdacddccaadaacbabcbdbddccadaadcdbcbbdccbcdddaacbbcdbdbccababbaaabccadbbaabaccabbaaccbdbcdcbaabdacbdacbbccbaabdbdccccddcdaaacbdbddbaadcbacadbaccacacacbcdcadbdacaddddcbcdadccaadcbbacdcddaaddcaaabacdccccbdcaaacacbcbcdacccccdcdcbbcaccdcacabadbccbddacccdadcdcbccbaaddbccccdbdbdbbcbcacbcdcdbbacaacbcbabadbccbabbacbddcaccbdcaacdbadbacadcadacbbddbaadbcddacbabbabdaaabdadbddbbcadadaddaddbabdbcaabacccadcddcbabdbcbcadabdabdadccccbbbcdcaddadbaabccabaacdbcaccabdcacbaacbbccccbdbcdababdccabbbacbcaadbcdbacddcbbcddbacacccbcbbcbaddabacbacdcdbbadadbbadccbdcadbdbdadacacccbcbaabcabdaddacabcbaadabdcdadbadabcacbccbbadbcbbcdacbaddbdbcddbaadddbccacccbddaaabbdcdcccacdbdbbdaabdbddbbcccbabdbbbcdbbaacddcbbaaabcadabbacacaabdcaccacbacccbabbdadbddccaaadccdaabbccddbdbbcbacadbbbadddacdbccbbbddbdcbdbaabbddacbccbacbddcbbddddabdaabaaadbddccbbaaadacacdccccbbddcbcddccbbdcadacacdabbdacdccacabcaadbacbbdbcbcadbbbadddddcbcaddaaabbdbbcdcbaabacbdbbabbcdccbccddcbbbcadacadcdcbbdacbbdcdcccacadabdcacbbccaabadadddddcdcdbcdddaddbddaddbcacaacbabcbccaddaadaacddbbaccddbcddddcdddddddcdcbbccdcdbdcacabbcbadcbbbacadadbbcddddacbdddbdddaaccabcacaccbcaabcabacbaadbcadcbbacdbdadadbcbccadcdaacabdaaaabdcdccddcdbadccddcabbdbadddbdcaccaaaadaabcddaaacdadcbdacaabbccabcacddbbdcdbcaccaacabdccbbcdcabcbbbbabbabadadcbdccaaccdcddbbdcadbcaaababcbcbabbabbdddbbbdbdbacdacbaacdcccaddabcdaddbaadcbabcbcbaddcaccbbaaabaacdcddbbdbaccdcdaabacbcadacdbadcdcdabaaacbddbacadbccbacadcaabdbbacaabbbcaadbabdcdcacabcacacbacdcdcbaadbacbcbbbcddaabdbbbdcbbbabcddbcbbcddadbbbcacdbdabacbcbbdbaaacdaabcbdbdacdcccdbcbcdcbbbcbdbdcacbacdabcabbdbcaccabbbbabcddaccddbddaaccbbabbdcbbccdbacddacdcaaacaabbcaababaddddbacabbcddccbaadcbcbacabcadacbccbccdbaccddbbadbcdcbadddcdbabbdbbdbbbabacbabbccccbacabbcaabbacaaababbddaadadbccbacabaadaadbccdccbddbabbbacaddbaaccbdddbadccdacaccdbcbabbbdadcccddddbccaccadacaccbcdcbdbbabbdabadbdbbbdbbbcbbddcacdcccbdcbbabcdbabcdcbbcdcbdaaaddbcbcdcacddacdbdabadbbaaacddaacbadbcdcdcdddbabccabacbbcccdbbacdbccccaabadadcccbbdadacacabcabbbdacccaabdbbbcddddadacddbabccadbaaabbbcadccbdacddcabcaabdcadbdadabaccaaacddbcbbabdcabcaacabcbcaaccccacbabdbcbcddbdaddbddccddbdcbacbddcabcbabdcbbddbacdbddccbaaddbdbdccdbacccaacdadddbcaadbdcabcadbadbdaddbbcbdacdbbcaabacaabdaadcbdabddbaaaacacdddddbacabadaadababdbacdabdbdbdadcdbaddccdcaaddbddabacdacbadcdcbdddadddaccbacbbdabbccadcdbdccbdadaaaddcbbcddbccdabbcbaabbccdcddbddbdaadaddcdccacbbadbcadcddacbbdaabccccdadaaaacbdcdbbbcbacdacbabdbcacdbbbbcdbcbbabacccacaacdbdbbdcbcaaabddbccddacacbacbacabbbdbadddcbcadaaaaccaaccdcbbaadacddbcacbddcbbaaddcacabacacdbcccbbcddacccacbbadcdcaabbdbaaacdcdddbacacacaadccdadbcdcddabaaadbcbcbbbbadcadcbdbacbbccbbcdccaacabdbdcaacadbcbbcabdbbdcababcbcccabddaaddcaaaccaabaccddcccbbcddcddcbadbdccdbaabaccadcddccaddbdabccbbdbbdcdbdabccbbccccabbdbcddcbddbcaaaaabbbbdbaaabdbaacaacbbabcaccddbddbbbcbbbacbabbbaacbdcdbdcbdabcaaaabaddddcdbdbcbdbdadbbacbcbaccbddababddcadbdacacccbadcbbabdaddbbacbddaaabbbcbdaabdaddabdddbdadddbbddcbbbdabbccdacaabddddccbcbdcaadbdcdddadccadbccccabdcbdbcccdbbbbbadbddaacdcdbcbbadbcdcaccaadbadbaddadacdcadadaaacdcdcabcbdadcdadccbabadcaadbcaaaacdbbbcdcccdcbaccbdadcbccbacadbcddadbacdbbccbbabccdabddacdadbbcaaabcdacdadcddbdaadbabadadbdcbaccbaccbaddadbdccbdadbacdbccaddcdbaccaabbccaccbbbaabdcaaadcaacdabbbcaabaacadbbadcbcbdccbddaccbdabccccdcabbdcaadbbcbccbbccdbccbbccbbbaaadacbbaabdccacdcddcacdaacababcbbcadccacbadcccdccadbbdbddcacabcabadbcaabadcabcdddaaaadbccdcdcdbcdbadbdbadcabdbbdbaadddaddbddbacdacbbbcabdabaddcbcaabaabdabbcdaddddccdcbdbccabdbaccabddbdcdcdcdccbbcbbcbbcdddbccaddcccaadddcbcbadbbacbdabbaaabcddbbdcaccbcccdbcabdcbabaacbcaadaabcddbaadabcacdaadaadaaabdaabdbadcadbdccbdcccbabbdbbdccbcbdbbcdbabccbcadbaabbddbddadacabcbccbddadbabddbdddddcadcbcdadcccabdaaadaaabcaacbbcbccaacddcbdbcbcdacbabdbbaddbcdddcbcbbabccdacadbdcadbaaabdcbcbdbbdcdbbccddcaadacaaccddacbaddababdddccbdadadbdccaacdcbbabbabbbacadacdbbadbbaaaabdddadcddcbddbcaacbbdbbbcadacbacadcaaccdadadcaaddbdbccddaaacaddbbdaadadcbaccbaabcbadaccaacdddccdbaaaaccaacadadaaaacbbdbaaadbbcabddcbdcdbadbdbbcaabcadddccabcdbaaacbddccdddcbcccbdbbdabcdbdbddaacdbadbacabcbbabacabdccdcaddbcadadcccaccbabccdadcaadcaaddbdcbaadcabbdddccbdabdcdcaaaccacabdbaacbdaaabccccaaaddcccbbaadbddbbddadbcbbcbbbdbcccaaddcdcdbabbdcdcabababbbdcdbcabcddaabbbbabbdcccdbbadbbddbcccdccabbbdaadbacdbbbdaaadcabcdbbbcadcccaabadcddadadcacabdabdabbbddccdabadabbdddcdcdcdbddaacdccacadcdaaaabcdcddcbbadbcbddbcadbdaacdadacacbccacbdbdcbddbbadcacddbcdaadcaacadddbdccdadbdbbbcdacaacbbcccddaacabddabbccadaacbdabddbdbcccacacadddaadbcdcbbccaabbdaabbcbadbbaaccbaadabaaaaadbbaabccbdbadcbdcabdaadcaccacadbdbadabddaccddacbdaaabddddddcdacdcbaacacacaaabcddaacddbbcabdcaadcbcabddcdaccacdbdbacddcdcbdaabdbaacbbadaaccbacaccbdadbdbacccacaadaacdbaddccbabcddcbccdabbbcdacabdbbddbadddacbcaaccabddbcaddacbbddbddcbccbdcacbbbdcaddcddacaadcbcbdaaaabccdbbacdcdddbdaabbbaccbcbddcdbdcacacdadabdabcccbcaaaaadddbbacaddadbadcaabcabdadccaddbdabbdcbdadbdabaababdadcddbdbbdbacbcabccabcdcbddaacddbcdaacacaccacccdcbdbcdbdccaadbcabddbbbbaabbbabbdcdadccdcdccdadbcbcbadbdbabacbdcddabddcbdabacdbddacddcbbdabbaadbdadabadbdbaaccdddbbbbccacababcadadbcbacacdcbabbbcdbbbdadacbccddddccccdaadcdccadbdadadcbdbacbabbccadbcaacbcabbbaaadaddbbddbddbddbcaabbdbcdbbbbcbabaabbbacbabcddabbabacccdccacbbaddbcadcbcbcbaacadaddcabccdbabcbadaacaadbadbcacbcdacbcbbdccbbdababcadbbcbcabacbcbbbacdddcadacbdabbabbbdccdabdcdddddcbcacdacdcbbaccaddabbabcdcacbdbbbbbdbcdbaababcabcbacdddccddaddaabacdadccadccabcacaacdccbdacabdcccccbbdbadaccadaaddbaaacccabaaddaccbbababaabcdadcaabadaabcbabdaccbbbbcccabddcddacbcdaddabbbaddbbabdabddbacaaaabbcbbcbcdccadbbbadcbacdadabbdccbcadccdccaacbcdcccabbdbdaddaddcdbbcadadbdcbbdadcabbbdabaadaabacabdbaddddcbbccbbdbadbdaaddaabcaadabbbbddcdbccdcdcdbddbabacbabadbabddcbdbdcccdcbcbabcccdcabbacdadbbabbbdbcdcddcabccbcabbcbdbbcbdcbbbacacacbaadabdcbcaacbccbcbdabbabddccdacadbaacaaddbcbcccdbdaadadcccbaabccbbddabddbdaacdbcddbdbdabdcaddabcdaddcbcbbbbacdcbdcaaaccbcccccacdaaaccdcadcbdcbabadcddbcabacaacccddacddbadcddddabcccbddcbadccdbddacadaacbbaaddddaabbbadacaddaaacbccbabdcbbbbcdcbabbadcdacdddcdabaabaabbdcdaaaccaadccdcbbacbdabcccdacdadcbcbcdbddabdabbcaadbdadbddcadbbdadaabccdacccabdbcadcdbdcbcacdcacbbddadccacbcbacdaadaccccbbddaddbaaabdabddcdbdbcddaacabadcbcbddcaabbdddaccbddacbbcbdacbacbcbcddaccbbdadbacbccdbccdddcbdbbccbbacacabadbcdcbddcacccabcbddcddddccdbabdcdbbacaabbabbdbbddaabcdbddcbbaacbbbcdbaacbaaaadccadbcdcdcbccbddbacbcdcdcdbbbaaaadcbbaababcabbcbcdaccdcccabddbddabdcdacbdbcdccddbbdababaaddacbadbcdccbbdbdbadcdcbcbacabddbcdddddbdabdcbbdadcbdddcdccddaccdcdabccbadacbaaaaadcababdbdacccbdbbdadbddbbcdbbccaadbbcbdaddbbbbadaaddbbddcdccddbbabaaaaaddaacbbcdbcadbabcaccddddcbccdbabcdddbadbddcabcadacaacdddbcdbcdbdcdbaccddabdbbcaadccbbacdccacdacaaccdcaccdbcdababaacaaddcbabbcbcdccadbcadbcdbabcaddaacbcbdbbcdaddbcccbbbbaddbbbabaabdbdbbddbdbaccaabaabcbbbcdaccdaabdbabdababadbbbaccdbdbbacdcbdcbbaacdddabcdaddbaaaabbcddddabacbabcccabccddccddaacaadcdbbbdbbdabbabbcbabbcabbacacdcaadcabbadcdcbdddbbacbdbbdadaccccdaabdcaacccdbbbdaadbdcdacbaddacacddaadacdccbcadccdbcaaabcacdddadcaadccdcdadabaaccacdaddbdddbacdbaaabadacadcbcbddabbddbdabcbccbadabcdbadbbdcbababdbaacadbddacadbadddcbbaacabbacbbddbbdadcdacbcadcdcbbbcbaccbbadddcdbcddccccacbaabcdbadadbabaaaccabccdaddcadccdcbdaccacddbdcbdbdacbcccabdaaccdcdaddbabbdacdcaacadabccdddbaacccadccadbdcabbbadacccccbbdccbdddddbaaadadaacbdcdadbacbbbdaadcdbbdbdcbcbdccadddbacdcbbabbacaabcdacabcbdcacbcdccbbbbcccbdacbbdabadcdadddbcbcaacbaaacccdcadbabdabccddbdbddbaccaaabbdabcacdddbcddcddaccdbbaadbaacdcbbcdcacdcbcdddbaccbbcdbdccddcbddccbcabcaddbdaabadacdddabbbdbadbbbddbbbbcdaaadbcdccdddcbbabdbbddbccabbbccabdccdaaccaaaacadaaddcbdcdbcddcccbbccdccaccbdbabcdcadbcbbaabadabdbddddabdaddabbadcdcabccbdbcadcbcabcacdbaddaaaaccbaabaadabdbacbbcdaacbdcdadcaccacadbdbccbdddbbbdcbccaccadcdcaadbcccbcbbcccadcaaccdbbbdcddccacdcbcdabdbcdbdacddbdaddbaddccaaaaaaadddaaadcaccbdacdbddbcabdccacdabcbcbcccbbaaacbcdaabddaddcdaadbacbabccdbbccabdccbbacbdccbdbbabccddcadaaacaaacdaabcdcccdbcdcaadaabcbaacbacaacddcadbbbbaabaddbdbbdacabacabaadcbbaaaaadaacaacadddbabdbaacdaccabadbcbbdadaccabaadbadadcbbdacbccbddabbccdbadadadbbdcbdbbdaddcacbbddcadcccababcaccbcbcbccdbdbdccacddbaadccbddaacbdbacdbbbcbcaadaadddcbbdbbaadadadaaabbbacdcacdddbbadaadbbcabacdabbadddbcacddadbbccdcaaddbabdabbcadcddcabcbabbdddbbcdaccdacccacaddaadbdcbdadaabccabcbaaaacdadbadccdcccbcdaaddcdcccaadddaddcaddaabdaabccabccdcdbdacdcacdaaabdbbcddaabbcaabdbcbabadbcbabbbacddbbbbabadcabaadbccacdacdddcbbcbcdccddcabcaddcbacaaacbabcabacbbbbdcabbbaaccadccbaababcccabcaacaddbdacbbcabbddbdbbaaacacbaaabcdbbbccdaadcadbaaccbabccdbbdabaccbabccdcadbacbabadcdcdccaaaadabaddccdaabaacddbcadcbdabbadabbbacbdbdcbcdddcdaabdadcddaaaaacbbcaaadcdbbaaddbdbabbbabdbcabaadcdddbabdbddbacdbccdbcbcadcccdcbcadabaccbcaadbdadcbaadbbcbaabdbbcaacddadacbcdbcbbaacaddcbcddaacbabcaddcccbaddcbbcbabbdbadbbdadaaaabbacddcdbaccacabbbbbabcbdbdaacddcddbbcddbcdaaadcccabccbcabdddbdabcdadcadbdbcdddbbcbccbaccbddabcbcdcddcbbdcbdcaadcaadbaddadacaccdbcacbbbbbbdccbbddadbddbadcadddbccbdbbaadbdccabaddcddcbdacabbcddadaabbdbcdaadbacccbbdabbdabadaccddadcbcadbbcdcccaadcccbbbbccdcaadabababadbbdadacdbdcbddbbadddabaabddccaddbabddbcbdacabacbacabcabacadaaadcdaccbcbacdcbacdcccbddabcabbcadbcacddadbdadbdaaddbbbaacbaddabbdcadccdaabbabdcdcbdcaadbaabbdcadcadccccabdcdddbcbbbbacdbddccbcbddddbcdbcaddbbbadcbaadabddbbccbadaabbbbcabbcddbbbbacbdbcccadccabdbdacabbaccccaacacddbaaabddabdcdbbdbddaaddccbbbdbdcdaccdbddabbdabddbabbcbbaacaaadddddcddbadddbddacbcdcdbdcbbccbbbacaaadbbdcddadbbbbdbaadbddbabcddbcddbddcbdcbacaaacdddbccbbacbabbbbcbaabdcaadabbcccabdcaacdabdbcdcdacadbcbddbbdbaaaaacabbdaccaaadaaccdbcbdcdcaacccbabbadcbaadddddbcbbdabacbddaddadccdcadbabbbaccbccccaabcccbdbbbcdacbdbcaacdcddddadbacababbabdbdbaaaddcccababadadbbdaddddbbbacbcbaaadbbdbadcdabbadbbcbadaccaacabdacdccbaabadabcbbddddaddacacbbdcbbdbaaabaddabcdddbbcdbbaaddbdadcbadaaadcaadaabcaaacaaadaddbddbddaaacabaccadbbdabbcdcbdacacdadcbbbbbacdabcccdaabccddabbdcdccacabcbbdccaaabcddacabbbbadacacccbcabdcdbbbbddcdaddddbcabbbddbcbadcdcdcabacabbcbadbcddabababcbbbbcbcbbaaddacbaccdaccdbdddbdbbaabdddcdbaaaabbddacdbaacdcbdbcacadaabdacddbaaacbbaababbaccddbcdcdbdacabbbddadbadbbaabdcaaddddbdcbacdadabdaacbbdccbcabdccddcdbbcbcbcddcdbacccccbddbcaababdcadccbcaccabdcbaaccddbdccbddcacdcbccbdcdccdbbadddcbcdbaaabbadddcacdddbdcbcbddabdcabdbbcbcccacbbcabacaacbbdabbcccdacbabacadbdcccacdbbdacdadbaacaadaacabbcdbabdddcacdcccbcaadaadddadabdbaddbaaacadddabcadababdaaabdaddccdbddbaddaadccbdddbcabbaaddacacbbcadbdbacccbbcabcaacddabbdabddbccbcdcaddadbdcbddddbaaadcdabcddacbaabdcbaaddbddaaccbcabbaadcdbabddbccacaddaabcabcdabababdcaabcadabccadaadbaccaabbabdaaadabcadcacbadbadbacbaabdccabcdbbbaccaccaabccbbdcdaaaadbdbcdcacadbbadcdbbbaaddbbbacadadcbbcdbacadadbaaacbacccbabdacbacbbcabcabbdbcadbcccdcdaadaccacbcbccccdcdcabdbccbdaadddbbdcccdcbacacdaabdacabcbbbbbdcccadacdcdbcbbcdcacbddadcabbbacdbdacaccbdddabbdacccbacbdabbdddbabcacdabadaacabcaaccadcadbdcdbdcdcacaccbabbcdcabdddabddccbbccaccdadbbbacacbbbbbaccccdbdbdaddbbacbaabbaadccbcbccbdabaddddadadaadcccccaabcbbcdababadddcdabaddddcdbadbaddcbcacbacaccabdbacabdabccdbbbdcbbccbadaaadcbcaabbbbddcddabbbbaaddbdcacdbcddbadacabbbaddabcacbabdbddcddcabdababcccabacbbadacccadaddbdbbdddbbadadadbccccdbbccaadacbcdccbcaddaccdcacdbccdaddbccccdbbcddddbabdcdcbabbccabbdaacbbbadbadbdcbdadadbbacbcadcbcbabcccddbaacdbdcbcdadbbcabcbabacbddcdddddcaccbccbdbbdbccdbaadbaddccccdbbcacccaaabbbcdbababcccdacdcbbdbaaaaccbbbdacbadaadaabcabdabcbacbbadadabaabbcdcabacbbabaccbacacbbdddacbacbddaaacaadbbdcbdacbcbaadccacddbdadabcbbdaadbadddbbdccccccdaadbacbcacbbcdcdbcdabbaaccbdbacbcbcdadccabcbdaaddcaccabddaaaacbddbddbcdbbbcbdbcddbddbdcbacddabcdaccdbdccabdbbbdcddbddbbbaddacaccabdcccaadddcdcadbcacdddbaccdccdacacabdabdcbadcccacccabaacacdccbdacaaabbaadcbadbadbaacbbcbacbbbdadaddacdbaccdbccddaacddbbbbdcddacaddddcbdcdcdabccbccbaacddadbdabddbbbbcbdaddbdddadadddbddacbbdcaaddabbacacdadbdaadccdbdbcdaddcabacdacdbadaacdcdabdacaacdcdbdabacddccadbcdcbcccbcdacabdaabababbcdbccabacbbdcacbaaaddccdbcdcaaccaababcdabdabcbccdccdcadccabaadbdcbdccaaacabbcdcadadaaddcdbdbbabbbcdabcdbddcbabbccacdcacdccccadddbacdbcbbbbcdaabacaaddbdabdbdcacccabacdacccacacadaaaadadbcbdcccacadacdaaacdbabbcddcbddadbbdacdcbcaccabccbdbbbcdbdaccbadadabccdbbacdbbbaaccaacacccdcabbdcacaadbbcdccbadcabaddbabbccbaabbabbcabbdaaabcbadbcdccbacacaacdbacccddaaadcdcbdacdbdabacbbabdccbbaabccbbbcccabacdaacdacaabdadcbbaccbabbcdcdcbcbcacdcadbaaaabdbaabcdcddaaccddaaacadddadbacdabdaacdbababaababdcadbcbdcbdacddddaaddbabdacddacadcabadddacbcdadcbccdcadabababdbcabbabbcdcbadcdcdabbbaadcbccccbdbcdaccdaddcbaabaacaacdcdbdbbbcbdabaadaaaadbbcbdcbaacbddbbccdddaadcdbadcbaddabbbcbbbadababcbbcbabbaddcdbcdcbacdbdbcbaccddbbcdbbacbaaccdcbbdbcdbdddaccbabcabcdcdaccccdbdacabdbbadbbcbdaacdbaadbccbacadbdbaaaddbcaaacaddcaaacbcbddbcbacbdbdccbbdbbbacabcdcccabcbaaadabaabbaaaddccababacdccadbaccdabbbbababbcadcaaccabcbcbbbddaaaaaacabdabbaddccacbcaabacccdccdbaccdbbbcbcacdaabddcdddddbdbcbcbcaacccbbcdaadaabbacdcbaaccbacbbdccdbacaabdcddbabbbcbdabcbdcbdbddddcdcbcbcddbbbdbbbaabcbbcdbcdcacabdcbccddbddcbddacbaddacacddabdddadabdbddcdddcdddacccdacdabcbadaaadadabadcbbcdcabdbbcdbcdacacdacbbdbdbaaacbbacdbbbccabbbacadbbcaccdcbddacbaaccdcaacabdabdbacacbddadacdadaababbabcbbddbabbbaccdbacdaccaccddabcbdaacbbdcbbbaccbddabaccccccdddbcdaabdaccadcaddabcaaaccadbdaabcdadccdbdcbcbbcddcbbdabadddcdadbaccbdadaabcbdddbabbddccdbbdbccbbbbadbdaabdbbaacbcccacabcdcdaccaadbabcbccaddadbdaabcbbbabcbdcbcaddcbcbbacdbbbcdbbadcddbcccdbcaccddbacacadbdbbacabadbacbdbabdadddacddbcacacababcabbcbddbabcaacadbadbaadbdbacabbbddbbaacbccbaabbbdadaadadcaccdcdbcdddddacdcdabdcddcaddaacbbcaabadababddcaabdbabaadcbdbacacdaabccbbdcccbddcdadaaaabcadddcaaaabcbbdcdbacaabdddbdbbcdbdcdcdbbdccadcacddaddddadddbccaccbdddbcdacaaccaaaaaabacbcdbaadccdbbcacbccccddbaabbcaadaccdbaadadccaaacadbccbcccddaabbcbbbdacabbdaadcccacdbcbaccabacbbbccacadddadbadbbcddbcdabadbcbcbabbacbdabcddcaaddbddadbacbcbdcabcacbbdbdddcbacbabddcacdcaacdccacadcdddbcbcccacdcdcabcbdaadddbaaccaadadabbcbcbbdbbbbbabcdcaccddbbdabbcddaacbcbccdcbbaadaadcdabdcbbcddaccdbbddddbabacdcaabbbaacaccabcbdbcaaacccccbacdcddadbdcccacccdbcdbbddacbdcdcdbbacadadbcabcccbbbddacadbdcabacaaabbccdccdddacaadabdbdbbbdcaddcabcccccbdbacadbbbdcdcdcabcbdabdccbbdddbbdbbdcacaabcbabcbcbcacbaadabbbcabbbbbcaacdbdbcaaddcacacddddbdabbbcdacbbabbacbaaabbccdaabbadadaacbbccbccbccbbddccdaadbdcdcdcdcabbacaddbccacaadadbabbccaddaaccadbccdbcbdcccbaaaaaacccadccabbaaababdaacacccdccbaadbdacaddbbcbdbdaaccbdbaabbcddadcddbbcbabdcdccadccdcccbcbacbdadabdbaacadacbacabdadbabdbcdacdccaddccdabaadddacbcbadbddaaaadddcbbcdbcadcbddddcbbcbbdaaddbcbbbdcdaccbcdaacddccddbdccbaadcdbdadcdbcdcaccabacdbaddcbbabadcccbddaabcdddcbadcccbcdccccdbdcddacdbbdcdcaabaccaccbbdbabdbcabcdcbabaaaacddcadacbccbbccadabadcbabdcacdcbcddadaadcdaccccaacbbbdacbaaaabdbcddbccbcaacbacdbbcbbdadbaaadcdcddadacbdccbcadcaadcbcaadddacadbbaccbddbaababcccbcaaacadbacdaddcbddacbbddadbdbcacacacacdadacdbdcdcacbaabbcdbbbdbcbddcbcdcdbdabcdacaddaadbdbbabbcccddaaccbadcaababdaaaaadaccdbacacdcddbdcadddbbccdbdcbaacdcbcacbbaabacbbcdabbbbcdbcbadbaadaccaddcccddbadbbacddbbbbadbbcacacacabddbabdcdccdbbadaddaabcdcddaadbdbacdabaabaabbaddbbdbacacaabbdcadabcdcaddabbbadbbabbdabbdadacdadacabbcdbdcabdbdbbbaadccbaacadaacabadbbcacacccdaccadaacdddccbddbcdcadaadaaaddabbabcdddbdccacacaaacabacdcccddbcbbcabdbcaaacddcccdccaccdbddccddbdcbddcccbbbcbddadddcdabddbdadacbcbcdabaccccaacbbdbcbdcacabadcaddbcddbbbccacacbabdbdcbbdcdbbbadbcacabadbcabccacdcbbbbbdadadacbbbbcacadabcdacdcaccababcdbacbbcccdaddbcbdbdaccbdbcddddcdcccbbdbcaccbcacbbadbdabbdcdadaadacaadadaddddaacacabdbddabbdaababcaddbccacbcbcadbabdbccdcaadadbdadcaccdabacacbbccaccbcacaacdcccaccdccdddbacdcbcbaacccbcdbcccbacbcadccdcdabcdcdbbdbabbcbdbcabdadaabdbcdbabdabddbcabbaacbddbbbcbbdabdcdcbadbddddcadbadabacdcaacbcbbbcdbdbbdccaaabcddabdcdccddabacbdbddabbcccbaccdcddbdabbabcdddaccabaaacadbdabdaadaadbbddbbccaddacdcabadadadddbadccdccdabcacbaabadabbddccdaddabaadbaddcdabddadbadbadadbcccacabaddcbdaccccdbdcccdcbbabaadacdccdcbbdbcdcbbbaaacabcacaadacbdadabcbbdacbcaacbbcadccadccccacdcbbcdabcbbbaabddaddddddccbccacdcdcdabddaccadbbbacbcccddcbcadbadacbabadacdbbcdadbcbbddbabccbcaaaddcdcaabcdacdcccccbdcbaccddcadbccdcdbcabdbbbaaaacddcddacbccccaddcdbbcacbbbadbabdbcaadcbcdaaddbabcbbacbbadadccccdbabadbbaccbbacdcdcdbcdcddadbbabcabaaacabcadbaaaccaaccdbdccdadcbadcacabaccbbdbcdadbadbbcabdcbbaccbadaacaadbcadbaabbadccacbaaacdcdcabbacbbaaddbcbdadddadabcbaadacbbcabbdbcbbbdcdacacaabacbadbddbaadabadcdcbdcbacdcdbcdbababbcdadbaacaacdaddabdacbaaaacdcbdaccabaccabbaababbabbdddcbcbbdaacabacadddddddaadaccdaaabdbadabbbdbcbddbadbdadabdbbdbaaaadabcbdddccabdacdcbcabbabcddddccabdadacbcbcadaddabdadabbbbbdbbabbddbdcadddcbbbddabadbaacbadabbaccacbdcdabbcadddbababbabbcbbbabcdcdbcacccbaabbcdccadbccddadccbdabbbdbcbbbabaadacbaabcabaacdcbccdbdcaddbbcbbcabccdccaaacaabbbcddaccdadbccacccbdcbdcabccdaacbbccaddbbdcaabcdbddacabbdbcbbccadacabacddbaddaccddbdcddcbddbaaccdddbabbadccbdadabaaddddbabacbcbcbcadbcccaacddadcbdcbcdacbdbdcdbacbabaabccdaadcdcbaabbddbbbbaccccadaaadbaadacdddbdcaccccbdcadbbbcccacdddbaabaadbcaacabdbdccdddabcacabbadaacaacdcbdcabdaadcccabddabbdbaabacdbdbdadabaaabbcdcaabccbbbaddacccdddcdddcbccbcbcbaddaabaaddaabbdddadaaccbbcdabadcdddbcbcdacaaabcabbcabcddddcccddaabdbdbaacdbacaddbcdaccccccdabaddacdbccdbcbdbbacaabcbcabbaadbdaaadabdbacbcaddbcccdddabcaadcbbbbbdcdcbddabcbaccbcaadaadbbadbadadadababaacbddbdbbaaddbbacbdaddcdadcccddaddbcabbcbcddcaddbcdaadbdccdacabacbadaddadcdacdbcaabdcbdbddddcbacacaccccdacbdaabaccbadbcddcccddcdcbbbdcbbcccbbccdabbcadabdddadbcdcddcaadbdbcbacdaabaccdbaaacabadbddddcabcbddbdbcdccacbaabbdbccdcdabbdcdabcbbccdbcbccdccbabaddbdccbdabddcdcabdbbadccbabbdbdcdbaddbdcbadadaccccdbbdccddabacbdabaabbdbadaddcbdbcbbcdacbadcddadabccbcddccabbdcdbdbbccdbababcadbcbacdbcabcccdaaacdcccdcbdcbacbabbacdbdcacbdaccbbaccbdccccddadaacadcabdcbcdddadadacddcddaccacbbdcbadbacbadcabbdaabdbcdabdbacacadaccbbccbcbbcaddbbbcaaacddcbcaaddcbbbbbabdcdbcaadbddacdccdaaaddcdadbbdaabcbbdbccdadcdbabaabaabaccbccadbbbbbcacbccbdbbcdcdaadbbbdcdadbaccabaacadabddbdcddcbdaadccdadabccbbacddbaabcccdbbadbcddccdaccbbdadbdccbcaabccacccbaaabdcccacddcaddaadbadaaabdadaadbccbbaadacbdbccaabacbcbdacddadccddcdccbadadbaaadcbddcdccdcbbbacbbddcbacacccdadbadadcbbddccbadbbbbbaabcdacdbbbccabccbdaacdbcadbdddcbdaddabbbaccadbbdacadccdcdcbdcacadbdcdcadabbaacacadbaababdaadccbdccddbbadacbbcabbdccbdcbbbdaaaddcbcabbabcccbacaaadcbcaaadaabcabdcabadabbbbcacabbbddcccdbbddcccaccbcdadadabcabcbbcbcabbadcbcbaaaddbabbdbdbdabbdabadadcddbabbcbbcaaacaacadcdcacbbbcbccdccbddaabaaadaacddbccadcadbbdbcdcabdadcddadaccabcddddbbbcaddabdccbaacbcaabccdabacbdacbddabbcbbabcabbbdaccbbcbdbccbabaddadbbcadbcdbdbacaabcdcdcabaabadcdacddadabdbddaddcdbbacdccbaaddcabdaabbacadccccdbabaacbbcaadbdbacdabdbcbbcacdccbcbacbcdabdbbabaacbdbcadcbcbadcbbdbddcabdaadccbdacdcadbadaddbdbabdccadcaacdbaadbbacdcdbbbdddacadbccaddbbcadaccadbbacabcadbcadbdacaaabaadcbadbcccdabcddbcaaddcaaaaabcbcdcddbabbdbbadbaabdbbdbbddcdbacaddadbdaaaacadccdadaabaccaddbbcbbcabccbbcbadddcbbccadccbbddacaabcbcdbbaadcdcbaaaaaaaaadcdbcdacbbdddbdbdadacbabcdccacaddbdbccccdabbbcacadcbabaadababbbccaadbbbdaaddbbddcadcaaccbcdcdaacdbbacdcbaccdcbdbcbabbdacbdddcdddcddadbdbdaccddaadcccdbaddcbbcbaccdcbbaaabdacbddbbbbdcbddaabacadccbcdaaddbcdbabddabcccccadcbacbbbaacabaaddbacbababdcacddaccadbddddbcdcacbaabbdadadaaaacacccccdacdbaccbdccbaadbcdaccccdadadcacaabdadbdabccaabcbcabbdbdccbccabbbddddcdbaadbbabcbdddddbcdcbddcbbcaaaaaacaaaacddddcbaddcbabaaacddbbdcdcdbacbbacbadcdadabbcadaacdacdbdacadbccbdcdcdabccdbbcbcbbcabbbadbaddcdcaaddabccadadacaddaadaabbdbbddbacaabdbbdbdcdcabcddbbaadaabbdbdcadabacbdacdbdcdcabcbbcaadadabdbaaabbcddbdadbdddbabbbaaddacbdcdaabddacaccbddccbdaacdaadbcbcdcbbadbcbddabbdcdaacdddddacdcabbbbcddaddaacccadbaabdcdbdddaabddabaacbdaabcbccabdbcbbabdadadacbdbbdcaddbacdacdbaadbbcdbcadbadbccacbbdacdbdcdbbdcbcadacabacdbacaadaacaddbdaadcbbbbacbcdaaabcbdddacbaadacccdaabbdcaabdbcaddddcdcdcacccacacacacddccdadbbdddcaaaaccabcbccacdadaddddcbdcddacbdccbaaccabcadacaaacaccdcddcdaabcaccbccccabadcdbabcbcaacabcbcaaccddacbacdbdccbabdaaacbccbcbcabcdcbcdbbbcadaddbabcaabcddbdabcdcbccdabcbdbccaaddbcddaabdccaaadacbdddcdbbbddccaddadaadcddbbadbdbbcadcdcddbadcbaccaabcbbbcadbabdacbbddabcbdcbacbdcadadbcdaadaddaabddbdbcddbbcdcdadbcadcadddcbabdddaaddadabbabccccadccdbabdbdbadcaccccbcbcdcdddbcbaaadbdaaccbddcbbccbdaacbabdbccdbcaaaaacaddbaabdbdaaddbddcbdadaaaabdcabddbaaaddaabbabcadaaaccccdaccdadcdcccbcbddadccbdcbcaadbabdccbddabddbbaacddacdabdbdcdbaabcababbaaabbdaaadadddbadabacdabbbdcbcdcddabccdcdcaabbcbbabccaabbaddbcbddbdaacaaacccddbcccbdbccccbdabdbcbcdbabdcdbdbcddcaccbcdadcabcacdccdddbabdcbcaaaccbddcaabccadbaadbdccaaddbcddadaaabbbcadadcbbccbddbbcaabbbddadcddbdbaaadbcbbcdcbababdcbddcdcbbaabdcbdbabaaddbadababacadacddbcbcadbbcbaccdcbabcbbdcdcdadcbaddcdbbcddadaccdbaabcdcabadddbbccabdcdacdbdddccdcdacaddbbdbbbabccdacbbacccdcaddbaddadccbaddabcbacbbabccddcddcdbbcbabddacbcccdddccbdacacddccbdbdbddbccdcddbdadaaadabbaaddcdcdaabcabadbaabadaacabbcabcddcbaccababdccaaadaddddcbcbadcbcabdadccbbadbaaaaddbbcbacbbbccaaadaabbcdbdcadcacdccdaddbbccccbcacbcadadabacdcddbaccbdaddbbacccdcbbabaadcbdcadabcddddbbccbdadaaaddbdbcabbacaddacaabcaaadacaaacdabdcadbaacadaacbbbdcacddbdcccacaaacbaabbcbcdabacacccbdccdcdaacaadaadccabcdaaddcbadaddadbadacbaddaddccbbaacbbcbbddbcaadaabbbbdbbcaaaabccbbaacddaadbddbabbbabdacdddbdcacbabbbaaabddbdaaabddacdadabdabbbaacbaddbbadaddcbbbdcaaaccdaabcdadaccaaaabcdaccdbbdbacabdacbbacccacbcccbacbbcbcccbadacdcbcdadbbcadcdadcdcacaddccdbdccdcadbabadbdadabcbaaadacccaaadacbaacadbbcdacaadabdbdbacaabdcacbaacddbaabbdbbccdbcbaadbbddcacbacbddbbabdddcabbddbddcddbddacccbaaabdcadbadbccaabbddcdccaccbbddbacbddbbabacbcdcbddaccccabddcadbabbcccdabbacdcbbbbbcadbcbdccacdadadbdbcdadcbcadbbadcbaabbacdacbbbcababdbddddcadccbbbcbddadccacbaddadbacabacbcaaadccccdcdccaccbcabdbcaccbdadbbcbaacbdcdabbabcdadacdbdabcaabdcccbadcbcbccbcbcacbbdddcbccddcdddadcadddcabbdacddccbabcdcbbcbadbdbacbddbdbadbcbabcbbabbacbdcddabdcaadcacdbbddccaadbcdcbdabacdbacdbccddcccdbdbbdbdbcbabbcdabdccdbbaadbbcbbbdbbacdcdaccaccdcbdbcbccabdaaabbcdddaddcbbbcacccdcadcccacdbcadcbbdaabcdbddadacccaacdcbbccacacdbcbbaaacbbcbdddcbdbbbaacdddcccbcdadacbbbbbcbbaadddcbbddbbddcbdcabadcadcbacbacdbabdccbcdccbabcbcabccdbababcbbcadbbabdaaadbcbbbccadadbbdaabdcbcdacbbbdacbdccaacaaddbdbcbbacccdcdddbadbadacdccbbbccddbccdabbabcdaccbccdcdbbacdcccaabbbbaabaccbdbbbbcadcbccabddacbccababcbcdcadababaacccaccadcaababdbdccacaddaadbdccabacacdddcccacbacbaacdbaacabbcccbcdcbbcadbacbcadcdaabdcbabcccdcacabcddcbccdbddcdcddcbbccdbbbcccdaddcbadbbcadacabcadacbdbbaabbdbabdaacdbbcbcdcbddaacbdaabccabbaaadadbadbcbabdcaddcaaccabadaadbdcdbdddccccabcddcacccccdaabadcacbabdcadbaadbbbcdcddabcddabcaddccadcaadbccadbbdccdaacbcdccbaccdbddddacdcadbccbdddadadcbdcabdbdabadbbccccabadccbbcccbbddcaccbcccbacaadbaacaabbcccadccadabccdbdadadbcaadacbacbcbcbccaccbbcacaaacccaaddadacdabadaddddbdaaccadaaacbdcbbccdbadacbcbacacacabcccbccbbaddbacaabcccaddaabbacbacddddcdcadbabdbdacbcdadbabcadcddabddcbdadabbdadbccddbbddbbcaaaddddaaacbbcbcaaddacbbbbdbdaacdacbbccbacbcddaddacadcabdacaddcadbdabdacdaabcdccbddcbbcccaabaabbcacdcbbbcaacadcacbcbcbbabbdcabbcbccdbdbcdccaacabdddbacdbcbbddbddcabadcadccbacdccccbbccdcbabaacbbbbacdccdddadbcbbcaaadaacbcdaabcdaaaddbcbabddcabbababcbbaadcdbdccbddbdbcccbdbcabaabdcbccbcbaccccdbddddcbccbacbacbbdcdccddabdcdccaaacaccccdddacbcbcbcaddbabdcbbccdcbdbccdbdddabbdbdbcaddbbcbcaddcdcaacbcbadbddadcbcdbcbbccdddacdaddaccacaabcdbacbcddcadacadcbbcbabcdacbdbaddccddddbbdbaadcababccbdbaddcdcadabbbadabcccabccdcbcbccdbabcabacabccbddbccadddcdbcbbbcbbaadbbbaddbacadaadcdcbdcdadababcccabdabbccccddcbaaaabaabaccbccacdddbdbccccccbdbdbdcabcbdcdbcaddcddccdabdabdbbaacbadbbcdbcbcbbdaddddcdadcdbccabbccabddbcbbaaccaacaadccbbdbdccbabacabbacbbcabbbcccdbaaddacdcaadcbddaadccaaaabcbbccbadccdccbcbdacddbaacccdadcaaddcaaddabcdadbdcbcddcacccadbcabbbdabbdcbccacdcbbbacdcccbbcbcadbccaabaaccdccacdaccddbbbacaadddcdcdbcdddcbcdadaababbcbccdbbdccbadcabbcababcbcbccacccddaabacaabbcbcbddbddcbccccdccaacdaaddcdddacddddcdacdcaddddadccaabcabdcabcdbadabdadcaaaadaacddcbcaccdbcbcbdddcabcbdbcdddbdcbddbaabacdadaddbcdacdacdcddaaccaccddcddadbaccccabdbbbbdbcbcdbaadddcabbdccbcdbaacacdcdbbaaacadadadacadccaadbbcabadbcbccbddcbddbccddbddadbadddddaccbadcdadccbcdcacdbcccdadaacbbddadabcdcbacdcdbdaccdcdaabdaabcbdcaccadabdacabbbbacacccbdcbcaaacbddaabaababaaabbdadbbdcbbdbdbccdbcdbbadcbadadccacccaaacbdabccabcadcbddbacbdabbabddccdbbaabdbdbadcbddadbbcadabbdabdbaadbdadbcddcaaacbdbbbaadbdabaaadbbaddbcabcccdcacabbadccdddbbbbdcdcaaadaccddbcdbcaacbdacdcbccacdccaabadbaabdbdcddcdabddbbbaabcddabbcaccddbbbcddbabbcbbdaacbacccbcaabaaddcadbdbddaadbcddddccccdcbddadaaccbbdaacccaaddbaddbbbddacccbcdadcbbdccdcacdbdbaccacbaccaabdbbdbdcaabdadabbaadbcbcddcbccccdddbbbabadaaacbdcdbdddbdcdbdcabdbcddcdbbbcadabdcbddabdacdadacbbaccbbccbcbacadadccdadaacacacbbbbcddbbbbdadaaadbbdbcdadcbaaabddbcddbcdcddbacbdbdcbbccdaccbbdbbaddbddbdcdacddbdcbcdcacaaacabcdccadaaacdcccacabddaacbdbcbbacaccbccccdddbddabdbdabacbbadcbdaaacbcdcacdbaccdcddddbcabbddccbbdccacdbdaabdcbccdddcaccabbabcaddbcdbdbbbacbadbaaadacadaadbbaadbacbadbacbcadabdcbbdaabbcdccddbdcadcdbcccaadcaddbbbacadcddbcdbadcbcacabbcbdadccdcaccbbcdcdacdacabbccccbbbadccababcdaaddabcbbacdbddbadbbcdcdaaabbcbdacdddbdacdddbcbccbcaccbbddbdacbdacddddcddaccabaadbbccbcacbbcabbbddaaabadccdacbbbacbbbbacbacccaddcbadbbbcbdcaacbbcdbaadaddaccdcaacacbddcdcdbccbdacddcdbadaadcddcacdbacbbcbaacbabccbadccdacabdccaacadcbddbbcbabbacbddccacacbaddabdcddccdbabcabcbdddcdbddcaaddccdaaccaaabacbbbdccadadcadaddcbdbbbdbdaaabbbcbaacdcdaacdbdaaabacdbccadadcccaabaccdbadcaaabcacbcbcdaddbdcddccacdcbdbaadbdbbbcaddabbaddcbbbdcddcbcbbdbbcbbdbcbdbadacacbbdbadacdababaabadbdabaddaaabaccadcddacccacddcbcbbcbdccccbaccbccccdcabbccadbaadaddccbbadadbcacaaaadbaaccabdcdbdcbbdabbadcbdbbadadbcadacabdacabdbbcacccddadddaaddcaadabcbabddbaacddcacdbcabcddadcbbbbdacbccbababccadcabbbaddccbbcbcbaccaabdbaabbdbadacabaacabcdcdabacccbbaadccbaaddddccbdadbcddbdcbcacdcdadcabbcadbdbcabcbcddadbadabcbaadaaabdbadcaadddcacbdaaccabcbbddbdcdcddaaaadaaabddadbbdccccddaccdcdccccbaadadccdaacaadddaacacddadddcacbdbddbdbdcdcdcdbcacdadcbaddbbbccccddcacbbbdddcaacccbddcbaababacbabcdbbcdbbacacacddccadaadabacbbbacaacbabaccacdddaacbbcdcadddddaaabacbdbdadbabbccacbcddaabcaabbdcbcccbbccbbadccddbcaccaabcdcadcbcaacbccdaddcbcaadcacadacdacddabcbdccbcbabbdadabdcdabbcabddabbdbddbcacdbaadacdcbdbdcaadbdcbddbabdcbdabbdccadbbcdacaadddaaaddabbbcdcdccccbbbabdacaddabbbbaadbcadbdacddbbcddbdddbbbbbccaccdacdbbccbbbabccdacbbdbaadcdcabcadaddcdcdadadbbbdbcbadddccddcdccbaccdbbdbcbdbcdabbddabbcdddaaaadddabbcbcbabcdaaacabbcdbbbdbbabacbadbacbddcabccbcccccdaccbbadbabddcaabdcdabdaabddcdbacabddbacbbbdcddbbbcbdbdacbbcdbbcdadccabcadcbdbadcdcabdaacbababbcadcdcdbcaacdbadcaabbddddabadadcdcdcbddddcbacbdbacdccbbadcbcbdbacddbbbdaaddaaaaabdabcbdccdadadacbccabbcadadcabccbdaacadcbbbbcddadcadacbcbbaccdbcdbdbaabbdbddabcbbabaddadadabaccddbdddbcbcadbdacaadadcadadcabdbabbbdabccabbdaddbaacdddcdaaabcadbbcacbdaddbdaaaadddcbadacddcbcabbadadbdcccacabcbdabaabddabaaddabaccccbabbbadcaccabcbccccdcabcbbcbdbbdbcdddcdbdadccdbcdbbdccdbbabddcbaaacacdddacdaabdcccbacddcadabbaddcaddbbaaaddcbdabccbcadaabaabacbddcbacbdadaddcadabdcccdbbbbbcddbaaacbcbdcbabdccadcbdacbbbdccdacbaccaaacdddaadaddaacabdaddcbdbdcddcbbcacabddddcbcbabdcddbcbbbcddcccadccbacbbdccadcabbcabaabdcdbaaaaacbcdbddbbcbcdcabbbcbbaccddbacdbaadccdbdcdccccbabdbcbdcdccaacbccdbddabbcdcbdaabcbccaacdbcbbcdabbaddcbbcddaacdcaddbddababcbccdacccbabbdbccccccdaaaacbbacddddbccacbcdddcdacacbdaddcadcbcbcbcbcbcbbccbaacacaccdcacdcdccadbdccbbcdcdaacabbdbdbddbabdabbaadcaadbdabdbdbbaaccbbbacbcbbabdbadddccabdcabdadaacabaccbdbbcddbcbdbaacbcbbaccabcbcabadccddaaaadddbadbaaabdccbcaaddcacccbcbbdaabadccabcdbbacadccbabacabddcabcdbbcdcbcabcbcdabbbacdadadbdcbcddbbdbadbddddbdcaabbacabcaaabaccdabccacdcddaabcaaccabaddcbcbdccdddadcccaaaaddbdabaabaacdcbdcacddadbdcccccaadcdcdccdddbadccdbbacabcddcacabadbbcadabbbcdcdcdbdcccbcddacdcbadddabadcddcdbccaccabcdbcabacabacddbdccdbddbdadddacbcccbbdbdabbaddbcddaacdcbabadacccdcaabbdbcabbbcadcbbaaabadcddddadbbdabbaaaaaccbabacdadcaccbadccbbaccbdcdddccdcacddacdcbddabbadabccdaababbbbbcabcddbcdddcabaccbcdbbdbdddddaddcdcddbdadccdcbabbdabacbcabdcbddbbcabccadadcacddaddcacdadbabcbaacbacadbabadbaacbdacbcabaaabddbcacbadddabcdbaaccadadccdcbabbacdcdcddadadcdabddbcabcbbadaccadbbccddddbddcbcdaaaddddddcbcbccdbcadcdddbdddcbcbaaaccdcbddbbccdbcaccaacacbdbddddabaabbddabaaaadabdadccbbdadcaddaccbaaaabcdacdbcdbdcdcaccccdcbaacddadcbcacbabbdabbabadcabaacbadcbcdcdabddcdcabcbabcbabbbcababcadddcaacdcdbddbacdcbccdaacadbcdcaaccaccacbabbcadcbcadddaddbacaacaaabdaccaacabcbdadaadccbacaaddccdbbbdbcbcdacaaaabaddddacdddbcdbcdaacbdadbccbadddadcbbdaacbaddccdcdddbcadbbacbbcbbddbcbcacccddbabadcddbccadbdcdbdaabcadabaacbcacbddbcdcccccacccacbbdcdccaaddbabbbdcbaccdbbcaaddaddbbaaadbaaaccbcbccdcbdbbdccaacdcbbbbbdcdabaacabddadadcbdbdccddcacacaaaaccabdddbdbbbcbbdddbcbccbcdbbcbcccddadccbbcbabcadcaabcbacaddddbbcccbbadacccbdbccdbbbccdbacaaabacccdcbcbcbcabcaababbabbdcccbbabcdacadaacdbabbdaddacaccdddcdabcddaacacabdbdccdabdcdbcbddabdacdbacbbddaacddcbddddcdacabdddaacacddccddacabcdaaddacbbbcdcdabaadcdddacdbcacdcbcbdcdcdddbdaccabbaadbbbccdacccbdacbabaaabdcaabdbccbcccbdbacbbaccacadcaaddccdbaccbdcabaaabdbbaddababbacddcadaabdadbabacbadbbdadacacacbdcabdbddcbcaaadabcaacbbadcabcdadcabbdbaaddaaacbacbacbbabadcaaaccabdddcbbdcbacbbdaddcdacbcabaadacdbacbaadddaacdcbdcbcdcaaabaadbbaaadcaadbbdbabbcbbdaadadbaddabbababadcddcbccddcbadcbcacacbdccacaadddaaaaaacabaabdbdbbdcacbcddccbaaddcdddbdbcddbdaddccdcabbdcacaadcbcbdcdbccdaabbababdccdbbccbdabccdbdacbbcadbcbcaabdbdbdadddccdcabdbacdddbccdaccbcccdcaadadbbbcadadbbddccdccdaaccadbbdcdcbbabcacaaaaabaadbddadddadccdcdddccdddabcbcccbbcbabadcacccadaccddcababcaabddabcabbabcacabdddadbdaacbacaaadbcabbbccbdcddabaadddbcccdbccaaadaacbaacaadcddbdbdbbabcbdcdddacdbbccabdadadadccaccabadbacbdccacdadccbcdcaccddcdbdadadbdcabddbddcdcaacadabbababdcccbcddabdaccbbdcddbddcbbaddbadbdaaabdaaabdbbbdadbabbbbbdbabcbcaaacdaadabbbacacdbdccaabcddbbbdcacdcdadaabadbcbaadbacdaccddcdddcdcdccbadaabcadacdcdcadddbbdabaaacddcbccaacdbdadcacbbbdcdcdacbddacdbbdcbcdcdcdcdcadcaaabdcbcdcaddbcbacbddddcbbbcbacabbabccbbbdcadbcdadbccabbcabccaadbdbadaadaacabdacdddccdcdbadabbbbaaadcdbabbdcccbacdacddaccdcddbcadcaadcdcdbabababcbccbbcbcddcccbcaaadcaadadacacacadbbdbdbbdccbdccadacdbcbddcddcabaadaabcabcdaddabdbccdddadcaadabdcbcabcaaccbbcadadabdaccabaacadbaacacaabccacdbccccaacbbbcdcbcaddddbababbdbdbacdadabcbbabdbcdcdabbdcbdccdcdbaabacbcdbabbababaadcdaacbbcadadbaadcaabccdacbbddbccbcbdadccbbbbbcbbdaccbbcaabbacdacccaadcccbadcdacddbabdbbbbaccbaaabadbcaaddabacbabccdcbaabbcabbcccabbdaccdbabcaabbacdacccadaccaaadaaadbbadbdcabddcdbdcdcaaccdaadcdabbaacbbddacbbadabcdcadccdbadcabadbcdcbaddcddbaabcbbacabbaabababbacaaccacdcadadaaadacdbdaddbabdcdabcdccaddcdbdaadbaccacbbabdaccbdbadbccdabdabadbbbccdadbccbdbbcaaacabadcdcddcdadaadaccbaddaaaabbdcdbbdadddccaadbbabcaabdcdadbacdccaacdcaacbdacbaacdbccdbcaadcccbaacdbcaadbdcdbaddccbcdadcddcbaccdabddababbabadacbbbbbbaabbcbdcdcabbabdcdcdbbcdcabadccabdbbdbbbabbaccbbaaccadbbbddbbcdbaadcbdaddbbdccccdddcababcddbddcadacccadccddabacbdcdddccdbdabcaabcdaddcdddcdcbaabaacaccdbabaddddcaadaadaacdacdcabbdcdadcddaacddacdcaaddccbdaccddabacacbddcbbccbbcabbbcbdacdbdcccdccaacaababacccddacbdccbabcccdbdbccabdadddccbbacdcbabadbbdaabcbddacbabbcacddcbbcbdabbcbadbabddcddcbdadccbaabbdcdadddccdcddbdddacdbdcaacbadbcdbcbcdbcdacbdcbdabdbcdadbbdddabacadbbbdabbcdddbacdacdbcbcccbdabdbaaadcaccbcdbccddbabdbaccddcabaabbcccbcdabbcdcaccbddcbcacbabcadcadddaadbbbcdccdbcdcabbddaddcadcdcdaabcadbcbdcaacbbcdbbcdbadacadaabdcdaabbabbdbccaadadbabddbabdbcbcddbdaabbbbdcbaacbcbdbbcaabadaabdcbbbaabdbddbbaaaaaabdbcccacaaddbaaddaabcbcacacdaababcabcdbbcccadcbccbbdcaddbcaadbcdacbabddabaaabcdbccaccbacbdbdaccbdbcbacdbddaddddbdbcbdbdbbdddacddadcbabcaacdadbdadbacdbcbdcbdbbcdbaacbcbdabdcacdbcdccbaaabbbaaddcbdbcaacccdabaacaabaabdbbabbccddbccddadbccbbaccbcdcbadabdbabcacccaccabcbccbbccbbcadbadadcdbcbcbdbbbaaaacdccdcadacdccadbcabdadcadcddccbddaaaababcddaacdacabdddccdadbddcadadbbadcdcbcdbbaccaacdabbddabcacbbbaababbababcadadadbcbcddcdbcabcaacdbcaaadcdbabbaadacbcddaaaabccdddbaccbbacdbbdbccccaaaaddbccaddbbaabcbdababdbbacddbbcbcdacbabbabacddbbbddbadcadcdaaaddcbacbdcaccbbcaccbdbccbaccaaacbdcbadcabcddaaaccddadbdaabaadbbbcbbbaccbcbdcbaadbbabbccbcccbccbdbcbacdcbdcbddddccabbdcccacabcdacbcccdacbacaaaddaacbdaadaacacdbdadcbdacdbcccdbaacdabbabccdbdcccdbbcdbddbbbdaccaabaadaaacbdcadcaddbdddccddddaaaaabbacbccdaaadcbaacaaabccbcdcccaacbbbbddabdacabdcabbacaaaaabdcdddaadbdabaadabddccdcacaddabadbcbaabdcadcadbbdcbaaaaddaccddbdaabadccbbbbbbdaaccdcbbdcddcadbcaddabbcddbbabcdaaacdbcccbdacdaccddaacdccdbddcabdcbcbddbacdcddbdccbddbcaccbcdadddcbaaaabccccdabbbbbaccaadcbbbaabddccbdaccbdcbbcbadbcdbbaabbddadacaaddccabaccabcaccbabcddcbbadcdacaabbaabadaddbacddcdcaddcadaaadbadacacaadababbbddddabbdbdabbccddaddcabbabadbbbbbddbcbdcccbdaadddcdcacacadbabbcaabdcddbacdccabadbbdcbadabdccbdacdadccdccbdcdabacbabdcaccccdcbcbbabbcdcabadbcbcdadddbdaabcbdbdbcdccddacabcaacbcadadcdcacdaabadddadccdbadcbcacdbaabadadbbbbbcccbadadadaabdcabdabbbbcccacbdbbabcdbdaabcadabaacaccadddbbccddccddccbadbcccabccccccbdcaaadacbdbbbadbabbcbccdccbabdcdacbcbdbadacbcbdcabddbccdadaadaadcaacadabaccddbacabadadabddbbbcbcccbadcdccddbccaacbcbabdcadbdcacaababcadbbbaadccccdbddbdcdacdcddcbabcdcbcacbbddbbbabbdaabbddcdbacaddaacbcaadbddabdcdcccaadcddddbbacababcaaccaccdbbdcbabbaaccaddcaacbdcbcbdaacdcadbdaacabaacdbbbbcdcabadabcdcddddcbdbdacabdbcabdccabbacdaddacacdbbdbddacdcabacbdbabadccccadcaadadccbdbbdadddbddbbacbdaabbabdcabadaabadcdbcacbcdaccaaacabdcbadcbdcaaacbbddbccdbacacaabddabcacccbcacadddbcadcacdaaddcdbbddacdddbcbdddbacbdacbacccdbbdbdddaddbbcccdbcdccbcddbabcdcdabdbcddcdddacadbccacbccdcbcadcccbdadadccbccaacdcdabbdcdbbddcbcaaaaadbaadbccadacbcddddccccabbcbcddbdadbbaaddbacaaddcaddcadcbadcddcabbdbadadaabcdbcaabcbccaddbadcbabdabdbddacdbacababbbabccdcbaabcbccbadacddcbaccbadabcbadccbcabdbdacccadaaddcbadbbcacdbdbcddccdbcdddbddbdccaddbadacbaaadddaaabccadddbbbaddccabbbbddcbbadbadaaddaaccdadcaddbbbddacdcbbaaaabaccbaaaddcccbabdccbcdacdadcbccddcbdcaacdabccbbacbacdadddbddaccbabbbdaaababccbddccaadcabcaccdbccdababbdcbcdabadcaddbccadaadddadbdbbdacabccabacacaaadababacbbbaaccaaabbddbdddacdacdccbcaddaabbbcddcdcccdcbcdbdabbdcbabacddcccdaadcbbbadddbcdbcabddcdcccdcadacbcacdacbcabbdcaacbaacccdbadbbccbdbdccaadaacdccdcbcaccdaabdcbaaabddabbdaccdbaaabbcadaacacccbcccbbdaddaaccdbbdccacbcbabccadadbadbcbbdabbabcccddddadbacdbbdcabaddaccabdaababccbaccbcabcabddaabbaaccacccabcdddcbddcbdbadabdacbcacbbdcbbbdcacdabacabbbadadadcdacdacaaddcbcaadbcbcbbacbdaccadbbbbcaddcbaaabbacaaaaacaddbdccdacdacddbdcabababdbaacadbdacaccbdadaabbadadbacdcdbdcadcdcdcbadbdaaaaacbdcbabcaadabcbbabadcdcdcbcbbdcdbbdcddacbdbccbacadddabdcaacbcbdbbdabdddaabbbdaadbbddccbcadbdbabaabaabbadbddbaacdaaddabbdacbcacccdbcbdbcbbbbbddcbadddcdbacacdaabdcdddadbaadbdabdcddcccdbbccbacbadbcccddbddabdabcdcdcacbcccbcacbddcbbbbcbacabcabcccaadadbabddaabdbdcdbccaccddadaaccddbbdccddbbcbcdccbddcccabbadacbbddcadabdddcaadabbbccacdabcbcaccddbdabddaaddbcdbabcaacdbddacbaaacddbaaaabcdccdcdbabbbbcaaacbcbddabadcdabdbbbbdcbdbbcccbddadabbdacdbbbcdbccbbcbabdccbcbcaabababdcbbdabaccdaaacbcddcdabbabbccbdbdccbddbdaddadbaadbcbbcdbaddbdaddbadbdadbadaccbcadaddddddbdbbacccddcccdbbccdbabdbbdcacacacbcdcdabbcdbbacaababddcacdadccbccdcababddcdcdcabdbdbccbcbbcabccdcbaaaccadcaaacbcbcbbddcbdacccdaabddcbcdccaccdaccbdbdddbbbccbcdadcaaacbacbacdbacdcbabacdabcddcbabbacddadacbcbdccbaadcbabdaacbccbcdbaccaddaaaabcbcdaaccaabcbbabcbdcbcbcdbcdcaccbbbbadadbadacabacccdcbadcaccadcbcccbbcbdddacdbabdbdcabbdcaabbbcabcbbbcadcdaddabcacdacdbadcaabcadacbdcdabddcbabddcabdaddcbbbababaccdccdcbabdcdbadccacbdadcdbcbdbdabdcddbddaccababddbdcaaaacababdbdacaacdcbaddddabadcbbddbccdaaddcdcdbcabdccddccbabbadccdcbdddddaadbcabacdccbcadcdcaccbbaacaabdbddbbccdcacdabccadabccbbdccdaccaabacbbcdcbbbddabbcccbbcadadbdddbbdadddddaddddcaacdcccdbbcaadcccaccbbcbbcdbabbabacbcbbcadabcabcbccbbbcbbbddcbbdbbaaabbbddcdabbdddadacacdacbacdabddddbdbddaddcdacdcdadaacccbaadbbcdacdbbdcabddcbcddbbbdccadaabcbbabdabadaccddcdbcbbcbdaddcccdadddbcbcbdabbcbdacaadddaabcbbabacdcbccdcccbdcaddcdbbbacaadacaacdaadcaaabdabbdbdadaaaacaadcbcabbdcbbdacdabdcdaacaabbbadcddcadadcadbcaacdcdaabbddbaccccaabccacbadcbcabbacdddadbccabbacbbdbdabbccaabbddbabcdcbdaadacbdcaddabdcbdadabaadabbdcccbcdcaddacdabadabcddcccbdbccdaadaaaabadbadaabaccacabdcacdccbdbdddbddcdadcdcbaddadcbaabdbcaacdccddadaaacabcadbdbcbdcbaaabacbbbdcdbddcbcaaadbbcbbddbdcbbacabdccddbbbbabcdbdadccdcbdcadbbabacdabcadcbdabbbcccadadabaabddbadaaabbdddbcadbdcdbaadaabbadaacdadaabaccbdaaacbbbcbccbbabdaaabbcacbddcdbbddddbdddcbbbdacdbddccbbacbdbccbdcbbddbcbdbddacbabcbabdaddbbbddbadacdbaaadbcdacbddbbcdbbabbdcaadbdcacabdacbddcabaaccacabddaababaaddadbcccdbbcdccbbabbddccbcdadcacdcbadccdaaccdbbcdbbadacdddcbacabaadabccccccacccdacddbcacbccbacdddccabdbdbaddaaadcdbcbccbbbbabacaccaccdbaadbbcbbbcdbaddbdbcadcbbaddcaadacabdcadbdacddbbacaccddbbbdbbcddabdbddccaabacdcacbadddcbabdcbaaabaddcacdcabcbbadbbaddccacdbacddccbaacccabcdcdbccbbbcdcbcddbabaccaabcadddacdbccbcccccddcaccccaddcbdbdcadcaaccababdacacbabbabaadacddcbabacdadadbbadaddadddadbbdbbcaccdadbaacdbadadbcaadaabbaadddbbbbddbcbcddcaabbaccccaccadaddcbbdccbdaabbaccaddcbdbbdadacbcbaccbbadbdabcdbbbbbdddabdacbcdababcbcbcabbdacdaaabaaadbaabaaababddcdcbbccdbcadbaabdbcbddcbbcdbbbdccccbadaddaadcdccacbadbbdcddcbcaacbcbbcaddddccbbacdccccacbaabcbdadcbdcccdabccadaddcbbaaadadcbbaccbcbadbaaacadaacadbaaadadaaccbccbbaacbdacbbbdadcdaddddbcccdbcaccddbccadadbbbcadccccadcadaabccddccbcdbcbddbdccbdacacccdbbcccbaadabddabcdcdbdcbddacabcbadcadbabcbddbdcadbcbadadaabdbcdbdbadbccaabddddbdddcccbdbaadbddcdcabcdaddbccadcbabacdbbcbdabcdcccbdcaaaabcddcdcbcddaccaacbaacacbdabddcacacacabdbbadacbbcaacdaacdacaaddabdbcddbadcbbcdacaaadcbcdbbaadbbddcdbdccbbbbcbaaccaadcbcadcbaccccdbbcbdbddabbaaadabcadacababdcbacacdccbabbaaacdccbdbdddaadbcdbcaacbbcadabbdbadbbacddaacadddcadadcbbabcbabbbbabababbcadbddabccbaaaacbbaaaadaaabbdadbccbcacccbadcbcaaddbbcaacabbdbdbabcadadcdccabcdccddbdaddbacadbbaddacaccdaabccdbbadcaadcadaacccbacbbdcbabcbacbcdbbbcbadbcbaabbbbdbdaaabcaaabaacaadcbcbadccbdddabacbadabbbdbbccbbdbddcddcdbaaddcabdcacddaabcdbdbadbcadbbddabcccaacdbcddcdbccadbacaacbbdcccbcbacaacadababacbcdccdabdcadcbbaaabbbadbaaacdcbbbbcddaaccdcbcaccccaacbccbacdacbbccddbbdbbcacdabdbabacbaddcaaccbccbddcbbbcacdabccdcdbbbbccacaaadbacaaacaadcaaaadbdddcddbcccdbbcbccbddbaacadccbaaaccbccbdcdbdabbcababacadddbadbddabdddacdaadcddbdcddabdbcabcdcbbaacbcabcadccaaabcacbcdbbbcddbbcaadcbbccbccadcdcabacaccbaadbbcdbaccbcbbadcddaaacbdbbbaaabbadabdddbddbdbadccbdadcbbaaaadccdacdbbcbaacbabcdbabbcbbdbbbaabadbddabbbabcbbdddbabadaabdacacbdabddcbbcbcadcbabcdddadacdccbdbccbcddccdccdadbabbddcaccabcbbaaaabbcaddaababcabbbdccdbabdaadbccadacdabddddadcadcacbadbcbdadcbdaddddaddddacbadadabbabadcddcdcaabbcaacdcddcccbbdddccaddadcbbccdbababbaddcdbdddbcdbbacaaabcbccdccbaccbdbcbdbabadadadccabdbccccbdcdbdbcddacbaaacbddbdbbadbbbdacdccaaadbbacddbdaadbabdbadbbbcbaadddaabdcbbbabadbcdcabcdadddacddadbabccbabaadbcccdcdabadadbbacdcbcdcadddbbcabccdbddbbcaadddccbdcbccaacdadbbadcabaadbdddaddcbcdcbdacdbbdbddbaadccaadbdbbbbbacadbabcabacaabaababadbacabbbcbadbabcbbadcdcabdccdcbacccddcaddadbbbabdccddbbaaaccdaccbdbadcadacbdbbbabdacaccaaaacddbcddbcdadbdcabdbddcbccbbdaacbbcddaaddabbcccadddabaaaccaadaddaaddacbdbabbcccccaddaaabcbacadbdabbcbdbabbbddccccbcddadcbcbcbcbddadcdcbacdaacdcabdbacbadbbcdbbadbbccbadddacccbcabaacdddaaaacaaddacdbcdcabaabcbdaacaaccadbbcdbcaaccdbbbacddacbcbdbcbbacaadbdddadddaddcadbbdcabbdbbbdccdaaadcdbdacdcbaacdccccbbacabadaadbcbbbdabcbaabacccadddadacdbbaabacbbbbcababdbcbdbcbabbdcabdcaadddbbccbcdabadabacbbdacbbaccbdcdaadbbbaaadcbdddadddabcacaabdbdbbdadaccababccdbcbcabaacddaaaccccbcacabcbaddbccdccdddccdacabaadbddccbabcbadbbddbbdcdbdbcdabbdcdcdddcbbcbacdcacbdaacbcadacbdadbbadbdcdaabbcddcdabbccabdbaacdcaddddcccccdacaababbbdddbbcaccccbcdbdacbccbabbbabcaacaccccaaaaabdbdcabcdadbcdcdbcbbdddccbbcaddbdcdcacbadacccdadcdddbbddccaddaaaabbabcccdaaabbbcaccbbbabccdcdabacbbcaabcdaddbcdacbccbcabadabdcdbcbaadabbacbbaabbddadcdcbdabadbbcbddabcbcdbdbaaddacaabdbddbbbccdddacbbddbccacaabbacbacbcadaddbdcdaacbbbdddbaadbcaaadbbaabccbddaaadcdbbdcbdcbdddbbbbaddbccbdbdaddcdddaaddccccddbbabadbabdadcbabcacaaacaabcabbdbaacddacbbcbcdbccdbbaabcbcaabbcdddddcdcdccaadaddbacaabcadcabbcddaabaadccbccdaaddcccadbababbdccdddcbaaaaaacaacadbccdbcdbaaaccbacccbdbbdabcacddbcbbacaccabccbdcbdababdbbadabbdbbdbcbabbbddbaccdaacacbccdbbaaabdbbbadcddbdcccdbacabddaaabdbbbbbaccbcbccbaddcbccacbbbcddacdbcabbadcdccdbbcadcdbcbdbabcdbcdbcdbcdabdbadbdbaccacdcdabccabaddabacaaddbcabcadccbccccbcbccdabcaaddadaadadccbcacdbcadcddcdbbadcaadadbbccbaaddddadcaaabaaadbabdddccdbcaabbcbdddcbaaabdbbacdbcbdbdddadbaabccabbcbcdbbadcdacbdcaababccbbbabcbccdcbdddbabccacabbdbbcbdbcaadadddbddddbccddddcbdacddcccbdbacbbdcbdbccdbadbacdadabdccbdccaaabadbdadcabaaadbdbadaabcbabacababdaabcacdabdcbdbcbadcbbcadccbbbadcbcdcccdbdcadcbbabdcdabbaacbaddcbcbbbaabcbbacccacccbbbaadbcbcaccbbdaacddcbdaabdbbbaadcdcacadbcdbaccccbbabaaaddbabbaaccdaccdaabdbaacabdabbbddadbbaccacccaddcadacbdcddabcddbcbbabbabbbdcdadadccccdcabdaacccaadbacdcacbccaddaddabcbcddabdacdccccacaabbaccbbdacabccddacaddacabcbbdccbcdbddbdabdacaadbbbdbbbbdbcdbbaccaccdaabbdccdcccadaccacddaabbababaaddacbcabccccabcbccadadadadbddbacbcdabcbcccdbbcbaddcabccaaadbabcdabdcdaabaccdcbacdcdabdbbcaacbabadcbbaabadacbacdccdcdaacdaddacadacacadddddacccabaddadcdcdddcabccdbaaccddcdbdbdddcacacccdbbbadadcbddddbcccdacaaccabccdcababbaadaacbabcbabbadaabaaabccccaacccdddaccdddddadababcdcdbdabbddbdcbcdccabccbdbbbdbaddcacdabbccacbbacbbbdbdbbccdabbadbdacdadbcdcaabdbabdddcaabaaadabaadcdbacdcabdbcbbcaaaddccbccbaabbadcaaabdbdccdbdbcbdaacddaccbddbdbaccbccabbccbdadddccadcaacabdadccbcaccdcabadcacbbbcdadcccadcacbbaaacbcaaddbbdbdcbbbbdadbaadbbadddaacdbdcdbcaaaabdbabcdaacacdaddcbdacbabdcbbcacadacbdddababbcadccbddbbccbdcadbbbaacbdccdbdbdbdbadaadbbbbacbbadcaacbbccadccdbcddcbbaccdaccaccbdaddaabbcdcabadbbaccaaaadcdbabbcabbacdaabcccabbcddddaccbaadbbadbddbbacdbbaaaabddbabadcaacdbabbbcbdbbacdbbbbbdcccdabadbdbcbbbabacdbbdaabccacdcbccacbacdddddabbbbcadabbabbadadaacccabacbdbbaadbbddadaacbcddbacacbdbadcabbaabcdbdabbdbddadacaadacadbbbddccabdaaaaadaabbaaaacdbcbaabadbdccdabaacddbdadbdcbccdbcddaacdabddbbaadddbddaccbdabddccbdbccaccbaadbcbccdbacbbabdaddaacdbdbcbcbccdddbddaabccaacbcbcccadbdacbaadddacabdbdbbdddaddcdccadccaaccbabaddccdcdbcbacdabababbadcdcbaaddadacdabcaddadabbbccbcdadbcaababdbacdadbdbadbbcdcbcbacdbddbbcabcacdbbccdadadbaabcaacddbbdbbbcacddbdadcbdbcbddcddaacadbcddddbbdacdbcccbddbcdccbabdddbdaddaaccabccbabcbdbacdcbbcbaadadcdbbcaabdacddbbbcbcdaabaddbddccbcdbcbcacdccbbdcdabcaaadbbabccadabddaadadcdadaacbccabdcbabcbaddabcaddadbccbbdcdccdcdcbbdcdaccbccbadadbaaaadadbdbdabcbadbcbbddacdcaabbdccccadcdcadbcaadbbcdcbdcbabcadacaaaaddcdaaacaabcbdaabbdddbdcdaabcbdbadbbdadddadabcadddcababbaacacbacccbaaaabbacbdadadbddcccdcbdcbbbccbdcbcaabbcacdababbcbcacccaabdcbddbaaaddcdaddcabdbcadcdaddbacaabcbbaaadadbbbbabccccabddbccdaabbccacbdbbddbbabacbbbacbbdabdbcbdbadbbbbcabcdcabccbdbcacadccacbbdcccdcbacbaabbbcbbdbddccdbbdddbbddbaabaabbdcbabbcaadaacdcbbaddaaccdacbbaabcadbbacbbadaddcddbcaddbacbccbdcadcaccadaaabadbdadadbbadadcaccdcdbaccdabbcabcddaacaadddbcdcdcbcccbdcabcabbbbdacdbabcdcddadabbbccdddaabcdadddadbbdcbcdaadcbcabcccdccbdddadadcbcdbaccbadaacdacddabcacacacbabbccddccbcccbbdadaaadabacabcdbaaccbadbabaacddcbabbbcdaacdaadbaaddbabccdcaddabbdbccbaccaaababbcadccabbbbcbbacacddbcaaacbbcbcabdbdbacbcbdbbdcbdbdbabbdbdaacdbabccbadcadadcdaacbdbaacbcadbdbdccbcbbcabaaddcbdcdacbdccadccdbbcadacbcbbdaacdbbadaaabaacbbbbccbaccacdaadadaaccdbcddbbbcbcdccbccdaddbcbacdaaacdbdcacacaabdbcdbbadaddadcbcbbacccabdaabbcdaacbbdadadcaadbdcbbcaabdddbbaacadbaadddddacabbbddacdaddbccccdbcbabccabaaccdaacadadbcabdaaaabdccaaaccaccacccddbddddcccbdacacddcbababbbcaabacdabacdbadcdddcaddcbdabcbaaadbadbcddababcdabcababbbaccdbbacbbbacdbbdbbadaacdacbbdccdbaaacccbbccbdcaacdcddddaacdcddbabbaadaabbcddcacbacabbccdcaddddbdcabbacbddbbcbaadbbbcaddcadcaadcbbdddccbddaccbcdababcbdcdadccbdaddbbcaaaaccaadacbcaaddcaaddbcddbcbcbccabcbdccaaadbbbdcaadcbacbdbaadabcbcaaadddbddbddbadcdcaaacddbadbcddbacbdadccdbcddbabdcdcadbbccaacaddbbcaaaddbbbabbbaacdbdbccccadcbadbcdcbaddcbaadbdabadccdbcdbacadaabcbdcbbbccbbcdaaaaccacdccdabcdbadbcabadbdabdccacccdddccbcdabccbcbcddddabbbabdbddbccccbdcabcbdabbbccdaabababcbdddcbbdcaddbacddabccaacdbaaddbaabbbcdbdcaaacccdbcaabdbddbbccbdbabaadccbcaabcabcbcacacdcaadbdcdddbdabbacabbcdbabbcbbadccdcaaaacdbcdaadcdcdbdabbcadddababbddbadbaddaddcddcdaacddadbbaadacaddaccdbdacbaccadaaabcdccdccbdccbcddabaaabacdabbcadbdaacbbadacdbbdaaabbcaadcddbcabcbcccadadddccccbacbbcdadcaabaadacbccdadcacdcadbccaadcbbdaaccddbdbdcddddcdabbaabcbbaddbbdcaccadacccbdaadbadcddcdbdbbadcabddbabbbdbadccbaaabdddaadacdacdbccdbdadcbbddbaacdaaadcbcaacabdcaabdcdcccadacacbcadabcdbbddcdabcabbacaddacabdcdabddabaccaddbbdddbaccdacadcaabcdacaabdaccdddddacbdddcccbcbccaabdaadccbddcbaaaacabacacdaddcadcdaadbbbdcdcabbbdaddcbbdbddcbbddbbddadbdaddddadcddbbdabadabbccdcbabbabbaabacdaabbcbbbdaaadbccdcbdcdccdccdadacaacbdaddcbbbaaabbbbbacccdbbbddababaadbddcacbcbcddcbdbabbbccbcdcacdacdcbacddccaabbdcabaadacbacdccbdddbbaadbcdbaaabbbdbaacdcaddccdbbdaaabcaaabccbbccddbdcabdaadaccadccacaddaccbddcaacddcbcddbdbdcacbdababadadbabdccadaacaacdbacadcaadcdcdabbabaccdddacdcaddcbbcbcdadcdbabbabcdcadcdccbbdaabbadcdadabddcccdaadbddbbacabccabcbbddadcdddcccacddcbdcbcacddbbccadbcbadbacadabcbcdbcdcbaccadaaabadabddcdaabcdadcbabdcdabbbaccaababcaabdddabbdcaaddbdcacacbaabddbaddaaaabbacbcbcaaacdadaabadbcdbbbbaadbacaaccadcbdcbabdbaabccbdbaccccbdaacdccbbadaadaccbcbdaddcddccaddbdcbcbdacddbccdadbaacccbcbccbcddabcabbbcabaaccdbadbadacbbcbabbacabcccbccddbdaddcbddcbccbaabdbabbbddddbcaabccdcabbbcdbdbaacdddacdacdccaaddcdcaaacdcddbbdaaabdbbddabdaaaabcaadbaccacaabdbdcadacdbdabbdadccbadabccacacdacabdbaacabbbaacbdaddbdaabdbbbadabdadaacdacddbcbbcbbdabbbdacbdabacaaadbcccbbbbaabbdaaacadaccbbbbabdcaddaadcadabbbcacadbbcbddadcadaddbcacdbdccbddbdbbabcdcdcadcdddacadbdbdddacdcabbbbadcdcabcccbdadbcdabcddbbabdbcbabdbdbbbcdacaddcbcbacdbcaacbbccbabccddaaabbddadddbccdadaacdbaadcaccdaadadacaacaabdbccaabbababadabacbaabbbccddcdaddcddcacdddccccabadaccadddabdbbcdaccacbdabddbcadcabcbdcdaaddbdcdbcdbbadadbdddaabacabbdaacdbdbbcaaccbdbbadaadabcddcddabacbaaaabcbccbabadbdddabbbccbbdddbbcbcdbdabcccccaacacccaddcccadadcbddbbcdcddbbdccccdbdabdbadacdbccacdaadbbddcabdcdbacacbbbdaadbcbbcacdbcaacabccabddacbdabbccbbaaaaccdccbcacddccdddbbaacadcaababdcbaacdadccbadbdbbacdcccdcbdddaabbbcbcadbbdbdaaaabcaaacbcdbddabacbcdbdbacddcdccbddcbdcbcbacaadbadcdabccbbadcdbaabcabbddcbdadbbdcabcbacccbdabbcdccaabcaccdaacddddcbdbccdbcabdababbdddcccbbcaadbddccbdaddcddabaacbacdcbcdcadbacccbacbcdcccccdcbdcadbdcdabacdcccdcbaacccdaddcabbccbacdbcdcddcbdaddadababccaabcccbdccbdccdbbaccbbdacaacdbacbdccbadcdaddaaddabcdbadbbcccbaddbacdbbdcadbaaaaacacdaacdcdbbddbbddacadccdacbdadcbdcacccacadbbcdbabcbbadaadabddacdbdbcdaadadbaabdbcadaabdbcdbdabbcdcabcaadabbcbabcacccbbcdacbcaaabcaadddadcccaabcacddcddaccbbcadbcbbcdbbaacbaabdbabcddacbbdbacabbcddbacadadacacaababbdbdbdccaadabddbddcaddabcacbdaaacccbbadabbbbdbdbaabbabccabdcbacdbcbdadacbcbdadbbcddacdcdbbaacbcbdccaadbcdddaddddbdabccbccbdcdcacabbdacbbcbdbddbcacadacaacbdadcabbdcababaddbbdbaccaacaababcdabdabadadbacdcadccddbdadaadcccabacbdddacddacdbabddcbdabbccabbbdcaabadcababcacaacadcaabbdaacdbcbacbdcbbcdccbaddccadcaacdbbbacdadcdcbadddddababdcccabdadacdccbcdabbcccdbacdbcbacaaaaddabcacadbdddcccaadabcddcdcbbdacbdaadbadcaaccbccabbccccdbbaabacacdbaaacbbdcbabdacbbbcbaadacaddbccabccbdabbacaacacddadbcddbadadbccbccddccabddbccdbabacabcbcdabaacaabdbacaacbccdbcdaacccabccbacdddcdaabdcabadbbaddaaabddcbdacbdadbdbcdcbadadcbbdbcbdcadcdbbdabdabacdcccbabcabadddabcbabbddabccdcabacddabcddddaacdbdcbacdcbccdacadabdcdbcdbdbacbaacddbadcdbabdcbaadbdcccadbbaacbdcdcbdccbacdabaadbdabbdcbcbabbcdcadcacbccadadbbabaacaccacbbcdcbdbacacacaababccddadcdbdddcbbcbabbcbcddaddcdddbccdcaaacdacaddaabdbadaccbbaddaddabcaabacbbddbbaaaacadcddabbaacabddadbabdadbaaacbbcbddcabaaddbdccdddabaabccccababddbcacdbdbccbdddbabbdcdbcccddaaacccabdbabdaacacbdcbbbbddadbdaddabdcdaabbaddbaadcbdacccabbddccdabddbbadbbbccdddbadcadacadcdbddbaccacabcdcacbccdaddccccccabaccbabbdbddcbdabadbabdcadcbaacacaaddacbaaaaccbaabcdabcbaaadbbccbacddbaabdbcbdddcbcdadcadddbccadaacdabbccbcadcddbdbabdcabccbbdbcadccdacdadcdcdaacddacaacbbdbbddbaabadacdaadbbababcbadbabbcacccdcabbdadbcddddbddcdddbadcdccaacabdacabbbbdacaaccddbdddaccbbbdcaddadabbadbdddcddababacbcabaabadaddbaaadbacaababaddcaacbccbcddbddcaaaddcdbdbcaaabacdacbcacbdcbbcddcdddddababaaaabadddadbbbccbcdddadacdccadcabdadbcbbcdccadbbadcccbacbadaabdddccaccbdadacddbddccdacdbccaaadabcdddbcddadbccaddbaddabcabddaabcbcbaacaadbaccbcccdabacbbccbcbdbbadbbbbdcababbcbaabcacbbdcdbadaaaacaccacadbbacbbdadcdcdcccddbaaabdaccdbccdcaabbdbcaabacbbdcdbbaacdaccaaacddabbbcbbdcdaadbbdbcaaccbcdacacbaabbddcaaccbbcbcbddbddccdaccbbbbdbacbdbbddbcbddbabbddbdadabddbbdbacabcbcabdadddacdcdadcbabcdbdcbbabcaabbcaccdcadbccabbdadaaccbcbdaccabdaacaaabddabdcbaacbcaadbbaabddabbdbbbccbdbbacbdbbcaddaaadbccbccdadbabbacddacbbbbcdcdcbbabbcaabacbbcdbabcadacccabdbaaddbaaaaacbddbacaacacdaddbddccacbbacbaaaadcbbcaabacdbcabdaaadaabadbcaaadddddbbcbcdbcdadaabaadacdabbbdaaddaaacdccaadacabaccdabcddadacbcdadcbcabccacdbadbbadabcabacaacbbcdbbdbccbbbcdcababdddcbabbddbbcdcbdcababcdccccaaadabddcaccdddcbadaaddbcaaadcadaabbacbabacdccdaaaaddcbddbdccdbdcdbabbcadbcdbcdcbabdbacbbccdbaccacddbaadaadcccdaccbaccbbbacdacaaddccdddcacadbbbcadcacbccddbcbdcbacadacbbbbadcdbbcdccdbbcaadcdcaaccccdbadaadddcacddcdcbaacbcbddddcbcbdcbdddcdccdaacaccaadacdbbabbcdcadbaadbabacaadbcaadbaaddbbadacdcabadbcddbabaadbdbdcbbaaaabccadbdcadabdbccdacccdbdccdbdccbabbbdbcdbaadacbcabdacadacbabdbbdabbaaccdbccacddbcdcbcdbcdabadcddddcabbbadaaabbbaccdbdaabbccaacaddbcaadcdccbbdcccbddccabaaabcdbbccddcdabbbbcaadaabddccbcadcddabcddddbdbbcdddbdaadccacaaabdcbbddbcccabacdccbcbbbbcddadcaabdbacdabbadbcaccbbabaabdcbcacdbbcbcbadddcddcabbbccdadbbbdbbcaaacaaaaadcadbdddbdbacbabdaccddaabcdcbcdcadbddadbbbbbbacabbbbbbdcddabcccadcbaacddbbddddabdbddccbddabcccbaccbccbdacbaddbabdadcdcaabdbbcdaddaacdcaadccdbabccaddcbcacbcabdbabddacadbcbcdcccadcbddccbcacbacaccacaaaabdcbdabdcbcabacbcadccbdbabdaabccbabcacadbcacbbdcdbcccacddbccbbadcabdbbbadcbbcabbccacccadbbdccbabaacabdbcababbcadabccdacabcabaaccadcdbdddcdccccdcdacbbcdaadbdaddcaadddcdcccbabdbcbbcdbacdadcbbbcbbdaabacbacdbbccacbbadabaadbbdaacbddbddadcadbdbcccadcbcabcadacbbaccaaddadcbccdcdcadacddbcbccbcadaabdbccdddabaaccacccddabccbadacdcccbbaaacbaccadbdcbddbbdcabddaacadbbbbbbdccddacadacabcababdcbccbbacbccdbbcdbaacdbbadccbdccaacbaacaaddcaacccbcbdbaadcddaadacdcdcbdcaabadddacdbbdcccbacbcbdcbadaabbaadccbbaaddabdcbbdbcbddbcdddbbdcdddddaabcdadbddddbacaabccbadaccaaacddcbbddaaaaaddaabccbaadcacbdddcbddabbdbccdcacdbababbbabadaacbcdccbdbdccbdacdcbacaabbccdcaccbcdadcbbbdcdccaccbacacbaaabaaaaaaddacbcbccbdddabcdadcdacbaaabbcacacadcaddccadabbdcdacbdcbaaacddadbcccbccccddcdbdbdacbaadbcacdbcdbdbccdbcdcbdaccdbbddbcbbdccccadcacdbaabcabdbdabbdbbbaabadbcbaabbbaaacdbbdbdccabdbcccabcccbddcbaaacaddabbccacddbacaababbcdbbcadabcabccaabddadabdcbaabcdbdcdacbabdabdddcabbbdbccabdadbaccdaababcccbcabcbacabccdbdbadbdaadccdbdcddbbaaadadbdaddbdbccbdacacbbbadadbcdddbcddcbbbbbcbcccbdddbaaacbbabdacddccaabdbacbbaabcccbdcbadcdbabbcbdadcacbabadbdabadbbddbdbaddaacddadcbdacbbdbbbaddcacadbdbabcccdbdbddacadcdcabcbcbbacdbccdcaccbadcacdabdbaccbabdcbaadcddaddcdcbdadcadcbbabcbdccaaaaadbcadcacdabbdbbabcdcddcadcdddaacbbcdabbbbdcbbccddadcbccbdcdcbacdcaaaadbdbacacaddbbdadbcabcbdaadaacaadcdacdaabbdaccacacabddcbcbabccbbadbcabcdaaaddcadaabaadcdbcdabbaaaccdaadcaaadcadbabdabdbacbcbbddbcadabdabdddbddabcbbcacbbdabdbabdcbabbcadcaaabccbacdabacdadacdabddbaaccdbbdadbabdabbdaaaaacaaadbbbaadabcacbdabddcadbabbcabddaccbdccdbaadcbbaaababacccabbabdabccbdbbbabdacaccdddddbdabaabbbccbcbadcbdcdbadddbadcbccddbdcdcddbddabddabcddaaaadbcababdddbbcbaadcdbbccbcbcdbdddaccdcddbdacdadbaadccdbbbacbbbadcdbbcdbacdbaabbcdacaaddcdcdbbdbddbbdabadadbddacadcbaacdaaadadaaaaccdbcaabbcdbddadaddadcacdaddcaaccdccbbcabddccddbcdcdccbabcdbadcbcabbddbdddabccbdddabbababacacaaabbcbcabbbcddbadbbccdaccaddbabcbacabbbcaadbaadcdcddccdaacbcdcaacdcbcdabbabcaccbaccbccddabbadcbacababdcddcbacdcadabaadadcdabddbbddbdcccdaabaabadabacbdccabcacbcddcaddbbbbdaacaccadaaabdabcaacccdbbdcabccbddbaabdbdbccdbdaadabddddbdabbdcabcbcdcaadbaddcbddbbcbaccbdbdbddcabaaabdcabbdcacbcaaacbabadcbcbaadccdcacabcddaccbacccaaadaccacccbcabcbbacbcdcccddccbaccdadcaccddadaadabcabaddbadadbddacbaadcdbdcaaabcaaccdcaabdddbbdbcdadccbbccaccacbbaaaaaacdcbdaacdaddccdadacaccdcccadcdccccdacabddddbcdababdabbcccbadbaadaaabacabcbcbdccbaddbbdbaabccbdcbdcbcdaddadcabcdacdaacbbacddbbaaccccabdbbaddccdbbdadcbaddbdbacccbdcacddbbcddadbdbabcdbbbadcbdcdbdbcaabbbabadccbadbddccdadbabbacccbcdcdbdcabcabcdcdbbacdccaddcacddbcaddccbaaacdbaabccaacadbcacdadabadacdcddcaaadbbbbadabcdccaadcbcdaaadcdccbbcdddaacaddabccdddbaababdbaccaccadccadaddababcadbcdcdabcbacccdabcbadbabaabccdabacaccbccacbcbccbccaddbcdbbbbccaabbdcbcdddbcabbcabdaadbcdcccdbdacbdddcabdaccadaddbcacbccacdbccaaddacbccccbddbcabddbadcbaaabddbaabddabcaacbcbacdadcdddbdabbaaccddadbccddbacbbddaaacdddcaadaaadcabcacbaaabbcdccbabaaddbcbbdadadbbababdccbcbddadbcdbbbcdaadccbddaadcdcdcbddbbddddcabacaadadadbcbbaaaabccdbbaacaddadadddabbaaabadbccaccbabcacdbdaaddcbdcccbddbcaacdbccbadcbdccddcaacbbacabaddacbabbbbbdddcccbbbbdabcdbbcaaabaccbbbacbcccbdbdacdbbdccaabcdbdbdbabbdbbdbabbacddccaacacbdccdbcacbbdcccddadbaaabdabbbaacddbbcbabbbdbccaacaddbccaabdbaddcbcdcccbbbadcccddbcdabbcdacccdccccaaaddbaaccdbbabcaaccdcdabddcdcdaaadbcaacacbcdcbaadbbbdbcacdcdaabddbbacacdcbaccddcbcdbdbddbaaccbdacdbbbbbccaadcacbdcaabdacdddcbadbbcbabcdaddbbbbaccbadbcaabadbdcdcdbbcbbbbbcdadcaaadacccbacaabacdddadccddbabaaaabacacddcdacbccccbabcbacacadcccdbbdcdbcaadddcdccbddbcdabaabcdacbdbaccaddaabbdbabdbadacbcaaddccbbaaaddcaaaccddabccbcdbcadadadddacaaaaadcdcbdcdbddbacaddaacdcdbaddddbddcacdcbcadccaaccbbccaadcccdcdbccdccaaacbdcbdaadbadcaccbcbbdbdbccccccdaabdbaddcdacdcbcdbaacccaabcadabcbaacdcabbdbcbbccddcbabbcddbddcdadccbdbadbbccdcaccacdcabaddcbddbdbaabcbaadbdaddbcdbcbdadbadcbbbdbabddbcbaccdbcdbbbbacdacbbcabdbaddcadddbbcdabcbcbbacccaabdacbdcdbdcadcabcadbdcadacaaabdcababbdacccdbddcbdccbbdadbdddadbbbbcbbbabaaddcabcacccbddbaacdaddaabadacdcbcdaacdabdcdbacaadbaccdadcdbdcbbacabadbbddabbccdabdacbcccdaccabacdadbbbcbdcbdcbbcbdccbadaadaccaadbbcdccdbcdbabcbcdadabcaaababbbcdcddbcdadcbaadbbbdccaddccaccbaccbacbabbadadabbdabccccccbbccbaccccddacbcccbccdbdaaabaccbbcdacdabacaaacaacbbdccdaaccdaabbdbaacabddabbcaccddadabdacadbcdadcaccaaddcaddaaabcbbacccccbdaabaaaabdadbbabdcaaddbcbacacccbbbbdcdccabaaccaccddaababdababbcdbaabbcbbdabacaacdadbabbbbabdbdcbdbcdbcdcdddaaacabdddbaabaccdabdcddccddbacbbacdccdadabbbacbabaadaddddbccabbadbbbdbddccbbcdcdddbaddbbdcadbbcdddabbacacbbbbaccdbbcbadbccbdbcacabacccbdcddbcbcddaabbcddccdbdbbbbbdcbcbbbdbbdddaccdbaddbbabcdbbbddadbcaadbbabcabbdadacabcdcadcdacacbccbcaaddbddcbbadbdbdacabddbacaaaaadbaadcacaaddcddccdbadabcabbacccbcddbdcbbbcaaccdcaadcdcbacdccbbccdadbcacbabdbbbbabdcbccdddccbacbbaabdddabcaccccacbdcbdcbaddcacbaaaaaddcbbbbdcbccbababacddcadcaabbcbdddabddcadcccbcaccddcabcdcdcdacaacacaabbdccbbadbbadbcdbabaabbbbadadddcdadccbcabcbbdaddcbcdabcbbaddbcdbadabcdbbbdccadaaacadaabdcccdccbadadbccbccacaabaccbcbccccddbdcbaadcbacbccabacdabaccbacbdadabacbddddaddadadacabaaaccdcbdddcaabcbabcdbadcadbcadadaaaaacccaccdccdabbcccacaaacdaacbddcaacacbbaddbccabaabcddabaddacddcbbcdaaaacdadabccdbbcadbdcabacddadcadadbdbbaacbcabcaacbdadabcccabcacdbbadbdccbaaddaadcddacaaaadbcdaccbdccccddcbaaddcbbcbbcddcaadadbdacbccdaadacbcaaccdddddcaacbbaccddbcbddaaabcbbddbcccbcbcbbdbaacdddaabaccdccdbbddbacdcbabdaccbdbbdbdccddbdcaacdbadccbcbbddaadddbdbdbdbbcbcdbbaaadadbdccabbbacdcbcacacadbbdddbcbdcabaadccadbaaccbdcddbbbbcaaabcdadadbbbbabccdbcbaadcadbdadbbbdacacbccacdcbccbbbdbbadbccbccddcdadcadbdddcbaddbccbabdbacbbcbdbabcbdccaaadbcadacacaddddcdbcccadbcbbbccadcccbdcabdccdabacbaacaaabaadbbdcccadbbacadacbcacdbabdcaddbbdabcdaadbaaabbcbaccadabbccbbadabddbcdcadcbabcacaabcabadbccdcdacdbdaabcdccaaabbdbacbddbcdbbbbacbadddbbbbcbaadbbbcdcccbacddddbbddacaadbbadddbdddabdcbbcaabbacaabadabcccbdbdbdbcdcaaabbabbdccdacbccbbccbaccbcbabccccbcddcdbcdbacbdcacbbdddccbaccddcbddacabcdcbbabbacaddadbbbbbbbacdaaaabdbbadbddbccbcadcbcdadadddbcabcbbdbaccdacbdaaaaabcdbacaccdacdabcaaccdcbdadbdbcaacdbdbddbccaacccbcbaaacaaababcbdaccdbcdadadccddbcacabccbbcbbcdccacabbddadcbccbaddcbaacbdaccdbcadbccccddabcacbcddcdcdabcaadcbccbcbbbabaadaaabaacdcbdcbdbacbacbabdbdabcccabaaacacaabbcabbaddbbddccdcaabacbadbbccdbdaaacdcabccbababdabdcadcccdcbabbbcddbbccadcabbcccbddbbdcdcdbcdcdaadddbcdcdbdbdbcdbdbcabbccbcdbbccbbaadcbabbbddbdbacdbbacdcdacbddbddbadbbbbdabddccddaadcbbbabbccdbbbbccaadabbcdaabaaaaacccacaaadabcacacdbcdcaddbcbbccdbcaabccbbadadbbcadaadabbbcbcaaabbddcdbbbdcbddcbabbbdacabbcbcadcbddbacabbdbdcbbccaaadcdbbadabcdacabcbddaccaacadacdbccdcccddabdccbaadaddbbdbbdcccbadadacbcdacabddabaddaddbaadbbdcbbdaaabcabbcbbabdcbbcdcdaadccaaddbabcbaccdbbdaabdaadddabdcbcabbccbbdaacbadacdadcccdcdaddbaaaacabcadcbddababddabbadcdabaabddbbacadadcadbdadbdcaddbabcdcbdbcaadccdabdadcbabdddcacabcaacddcdddabcabdbbdcadbbcdcbcaaddaddcbbabbccbdcccbcddadcacdcbbbdaabaaaaaaaadbdcbddcaacdaabcbddadcdbbabdaaacdbaaabbbaaabdbcaabdbadbacbaccbabcccabcacbcadbdacadbbbccbadbcdaddaaababccabdacdccbbdbdadccdadcacdcccccaadbacdbddcbdbbbddcdcadbcbcdacdbaddababbbbcaaabcddaadcccdcadcbabcdaaaadbbdaccbdaabcdbaababcbcbcacbbdcabcddbdcbacbcabacbadcbaaaaabbdcdcbbabccabbdaaadabdcabddcbcbbcbacbccdcdbdadadbbdbacadcccacddddbcababbbcdcdbccbacbdbabaaacddbaddcaacddcdadcdbaadccbadccabbdcacbcdaabcdbddaabacdcadddbbcdaaabdacaacccaacabdabbddaacbcdacddbcaaacddadbacdbdbbacbbdcbddbccacdbbaaabdbdccccbdacabbcdacbcddbadcbdcacaccdabdadcbacaddcdadcbbdcdcadbbacbccbdaaacaacacacbdcdabcccbcddacddbcabccadacddbbacdbaddbbdabdabaaabdcaccddcacadcaacbcaadabdbbabddcacddadcdccdbcbbcbdcbdcbdacabbbddccaababbdcdbacadddcbccdbaaacbcbbddbbaaaadacbaabbdddccdbcaccabacdddabccbcddabacbdaaadddbcccccadbacddacdbbdabbcbbaacbbdbacdbbdbbdcbdcaacddcdacdacbabccbacdabcddddabccdabddbbbbdadbbdaadbcdbbbdadacaaabddcdbccaabacbbacabbddbadadddbadccadccbbbadddddbbddabacbdacbccbcbbbacbccdcdccadbcdbccadbdaddadcbcdabcabadaaddabdcacbdaacadbddddbbbbcdcdadccdaddcbccadbabcdcaccbddbbbdbccbdabccdcadabbbbccaddadacbaccaaadcddcadabdabcacbbccdaaaddaabadacbbbcbaacdcaaacabbacabdcbddadadbbaccbbdbabcbcdaaabcbcaddddbbaacccccdcbaabcadadcdbcacabacdadcdacdcababbbdbaaabbdbaacdddcccdddaddbcdddaacdbcacacbcbabdadddbdabdaabdcdaababbdcbacbadbaaccdbbbbdbdaabbbddabcdbdadbcbcdddbbcadccccacabcadcccaaadbcadabbddcbcbadbabbccbbacccbbcdcbcaaacddadacbacdaddaabcbbbabddbacbbaacccdbdacddaccdadaaacdbadadcdababddcaabdabcbdabcbddaccdddcbdacbcbcccababababadcaacbcbcbdcdaabbabadabbbbddadbacbcbdacbadcabcdbddbacacdddbcaccacabacdcbddcccbbacabccadbbbdbbcbccbacbdcdddbddcddacdcbddcdddbbaacaccdbadcdadbddccdbabdbdacbcabcbcdcdabbcbdaaddaabcabbdcadadcdbdabccdbcabacacabdbdbdddadcdbaccccabaabbcdabadaddacbaacdbcbdadddbdddadbdacccccdccaddbbaadacacbbbcbcbbcccddababbaddadccaddbddbccabbcdbccccbdbbcdbbadaabddcdaccdbcdbaddbabadbcaccadccacbaacaacbdcbaadcbdaddcacddbaacddabcbddabcacbbdbacacacabbbbddacaaddadcbbcbabbbaaaadcdacaaadadacacbccccdbbdcdcccccaacdcdacdddcdcdabadcbbabbcaaddbacadacbdaaaabcaaaacdcaabbbddadaadbcccddbcbdaddbcdacbcaacaadbdbcdbadbcaacdbbdbcadcaadbddabdbdddccabaddcbbccccabdbaabcdcbbcbbdadacdbbadbddcbacaddbaadaccacdbdabcccbccddaccdaacadbdadaccbccddcbccccccdadbcbcdddadaadbdaacdaccabdddcdccdadaaddcbbcdcbdcdbdbdddbbcdabbdabbbbddaabdcaacdbdcddbbbacddcbadbadaddadaddbddbbabdccbbcaaadcdddabccdbbbadccbbbabcdabcaadbddbbbdbdcccdaaaababbdbcdddddadbadaadadabbaaadcbdbbbbbcbdabcdccabdcddadccbdaadddbcccdcaabdabadcccbbbacaadbdddbbcddcdddaadcbdaadcabbbbdddddcaababcdcbacacbbabcbcaddddbddabadcdacbbdbaabbcdaadabacdddbbcbcccaaaddadaccdccabdacacddccacacccddcabdaddaccdbccaaabbddcabbdcaabbcbbbacdabadcbcbdacddcacaddaccddaddbbaaacdabaccbccbdcdbcaaaaaadccbcdcaaddddbbdcadabccdbbcddccdaadddadabbbbcababdaabcbcbbbdadbabdcaadbbcadddcbcbdacccdbdcbdddbdccbbabbbccbdcabdabadadaacabbcbdabaddabcbdaddcbbacabdbccdabaccadbcbaccacbdadcbaccbacbbdbcbcdabcbdddbbbbccbbcadababdaaddcbbdaadabcddababacbdcccacaadbabdadbaccbbaaccacddababaaaadbaddaaaccabcbbcbaadcabadbababaacacabbabcdabbdbbdbabdbcbabbbdaddcbddacdcaabdbccdbdaaaadbdaaaaaadbcdcbbaadbccbdbbcbbdbbdcbcdbaaadbabbcbddacdaabdbbaacbdaddbccbddadbbbdaaaccbabbddbbbdbdbbdbdbcddccaabbbcbccdbabdbcbdaaadacdcbaaccbdabadddbaadcbcdadcdadabbbcacdcbdacaaabddbdbacdbcadadaddabbbdbacdbdaacabbabcadaaaccabadddbcdcaabcadcbbbdabbbcbcdbacbcdcbabdbadddddacddadcaccbbdadbdbcbdacadcaadccabdddddbddadccbdaacddbddcdcdabbdcddbadacabddaacdbccccddbcbdbdacbccbacaadabbdadcdaaccadacaaccddcbccddbdabdbdbaccbdbacbbabbabcddabdddcbdbbdddbdaaddadacbdaccbcdcadbcaaabaaabcbbabbcbbdcdbcbaabcdbddcdabcacdcbbabddcadbccdbbaabaadbccaaabaadcbaaaadbdcbadadcaaacdbbbcabbdaadddcaaccbadbabccbddbaabbadbdabddaccacacdbabacaacdccabbdcbbbcbbdcccabaaccaacaadcdbbdbadbaabbabcacaccaccaaacdcbadcadccdcaabcdcaddbdbadccbacadbadaaacbdacadbbababbdcdbdcabbcbaacbbbbadaadbcccabbdacdabbbcdbbcdcbbcabcdadbacacbacdadcbaadcdcbaadaadcdbcddacbbcaaccdddcbabbdadbbdadcdcbadbadddbaccdddaaccbabccdaabbdccdbddcaabdcdaccabadbdacadccacbccabbdabcccacbbcccadabcdcdabddabcaaddbbdbddcdbbcbadbcabdbdccccbaaaaabbccacaaccdacdcaaabababadbbcabbdcdccbdddbbdacabadacddcdabbcabadccaadadbcddcbbaccddbccddcaacbadcbcbcdacbabbbcadcacbaabdcbcaaddbbcaacbbccbdabacbadacdbdbbaccdbabaacadbcaccbcbbbbaaccdbaccdbbbaacbddbbdaabdadbdbcdcacbbabbaccbbdcdcadcbbabadddacccdddcacacbbdbdbddcbdddcdbaccdaabaabdcababbdcadbdbcacbdbcbbaaaaabbbdccddabbabcaddccccbdcadddcaaddbabcabbcacbbbddcddadbbdbcdbacbcaaabdaaacadadccccbbbbcabddbddcdcbadddcdaddbdcbbbaabbaccbdaacdaadabdcbadccadababbbaacddaabbdacaaddcbacdabadccbbdcdccddddadadcdabcccbbacbabaaddddacabbcddbadbcacbccdcbbddadadadbbddccbaabaadddaaacdbbbdaaccbdaadcbdbbacdabaaddcbdddccdacadcbacddddbdddaacadbacbaddcbbbacdbbcddcdabbacdcadaabcacaabddacadcbadddbddcadbbbaadddaacacdbdbcdbadaccdbbddbcbccabdcabdaddddccabaadaddaaaaccaccacbabccbaadadccdcadbbbcdbddcbaadbdbddbcacacccbbadadbaccddacbddbbaadcacbbdcaaaadcdbdcbdcbbadcbdbaabacaabaccddadddddcbdbabbbccdbcdcbddcadbbdababbddddcbadbacababccaaddbdccdbcdccbabdaccddcbcccadabadcabdcabaaabaccaccbdbcdddabbccadbbddcbaacadbadbcadaacadcccccbdbbdacccbabcaaababcdabababaccabcbcaccabbdbaccdccacdbddbaddcccdaacdacdbdcddbabdacccbaadbbbcdbdcadcdaddbadadadaaccccbcdcdadbdabcdacaaaccdaadaadcdbbacdbaddcccdadbdbbcdaaddccdbdaabdacbdcaaadcaadddbcabbdccdbcaaaacddcdddaaccbcdbbacbcadbabcabdbadcbdbccaaaddcbcbcacdaccdbadabacccbadbdcdaccbcbadbdcdccbddbacdbbdbbbcdbbdacbbbabbccacaccbdabbdababbdbcccdddccbcccdadbcdacbdcdcccacbbcddbbdcdccdacbaaadabdbbcdcacbbabadbbbbddacbcddcddbdadccdbbaaaadbdbbabdacabcbabccadaadbdbacdccacbbbcdcccbdcabbdbcbbdadabccbddbcbcdabdadcaccccccbcaaabbcdddddcadbdccdabbaacbacdbddaddaadbdbdccbbddbdccdbbdadbbbaddaadabaadddcdbdbbcadbbbccddcddaabbccaabbadcdddbacadaaaabcbbadbcccadcdaccdddccdbbddcbcababcaddbdbaddbdbdabcabdabdcbdadbcbdbdabbcdabbcbdbbbdaabbcbbbadabadcaabdbbccbcbabcbaabbdcabaddacdadccaabbdacadaaddccbadcbaccabcbcdcdacbadacacdcccadcbacbbbaadaaccdddddccbccdadbbbbabdadadbbcaabdcdacacdddabdbbcadabccdcabbacdacccdaadabdbdcbadacbbcbdadadcbadbcdbdabbaccadadcabadbbbdcdacacdbcbdbbddaddcbacbdbdbbabbbaddccdbadbbabaacacacdccccbcbcdbbacaacbbadccaabcdacdadbdcbadaaaaadcddcddcbbaaacbcdaabdbbbabbbcbdddaadadddcbddaabdaaabacbbabcbbbbbbcbaccbadbbcbdabdabbcacacacddacdabcdadadbacadaddcbaddccdadaaabccdbddcbbcccadbdabcdbbbaddbdcbdbdcdbddbcadaacabcaccccbbcdccbdccaabdbadcbbbaabdddadbcbacbdcaaaaccaabacdabcaababddaaddbaddacdaacdacbbbabdbaabdabaaacadbcddbadcacdbbddaccbddbccdcdccccbadadbabdcbcaaadbbcdbcaadadadbccbddcbdbbbadaadacaacdccbbbdbabccabddcdcadbccdababbcdddaabddcaadaadaddaadabbdabccdcacbdccbbaaacaccacaabaabcbacadbddbcdadbaacdcaddbcccaddbdbbaddabdccbbcabbddcdddbadbcbcdbbcaabcdbdaaccaacabdcabbacadbdbabbaaadddadcacdabacbbbacaacaaaacbbbacdcabcaccddccdccdcbaaabbddccdbdacdadaaacbcddabcdcbaccbaadcccdcdcbcccadbdacdddadccaabbbacadccdbbcbcddbdbbbbbbadbcccbbdddaaadbdbccacabaccdaacbdbbadbdccacdabddbbbabcaaddadddbbdaacdcbcdbdddbdbdcacadbabcdacadadaddbacdabcacdccabbdcaacddabdccadadcdbcdddcddaadcdaadbdbccabacadbdcdaabdadbabcbccabdbbdcbcbdacdcadbbbbdcdbddaacdccbcabccabadadccccaadddbdadabdccdddbdaacbcdbdccdbcbacdbcdacadaddacbcadbabbdadbdcccdddaaadbcababcacacbdcabaabcbabcccbadcbddbddbdbccaccccbcaaccabdbdcdbddadabdcddcaddbdddddabccbabbdcddcccaaaaaaacadaddbcabbcccdabddbdbddddbdbdccabbbdbbadaccbacdcdbaddcdbcbbadacadbbccdacdcdddccddaabddbcddbbbbbbccbbccdccaaacbbbcdaabbacadbaaddaabbddbcdcbacdccadbcbbaaacbadaaaadcbacaccdcaddacccdcdccbdabccbdacacbdcccaddbdbaddbbccbccdbdcadabbacbbdbbdadabcdbddabbdacbbbacdccccacbaddbacabbadcdbccbaaddddcaddbdbadccddcdcccbbcdcbcbcdbdbaacaaaababdccbbdccbaaddaadcbacabbbbacdbbdabbaabbdcbadbddaacdbbcdddaadcabaabcadcbddccbcbdaddbcddcdaaacbacdabbdbdbdbdcacdacdcdbbdcabaacbcacbdbcccbcadcccdcabababdddbabccdadddccdacdbacaababcdddadacbddddacacccbaabdbcacabdacbbadccaacccdbdccbdaaddabaadbdbbcdbcabbdbdbbbbacddcbbadadbbabdcaccbcbdcaaaadaaacaaccabdbcbdabccdabcabbddacccbbddddbddbaccaaaddbbadbacabbddaabadbdaccbddbccbddaadadccddbbcbaccbbdaabcbcbbcadcccbdbdcbabccdcacbbdbdbacdacaccdacdddaaccabddbdabcdcabccdddcdcadbabcbcdcdddacbbbcbaacadacdcacdcbadbaabaacdacdccdbdcbacddadccbdbdcddcdcbbaabaccaabcdbaaadabbbbcdcddbadddcdccabbacdbbbdbaaabcaacdcaadbdccaacbcbbcdabcddcbaacaaccbbddbdbacabbdabcbbaacacadabbdcddbbaccbdabbccaddbacbdababbbbcbacdacaddcabcbbccdcabdabacdaababdcaabbabddacbbbdbbbbcaddcadbcdcdbcccacdddcbacdaccdadccdacbabaaccddddacdacaadabcabcaacbcacdaddcbdccccccdcdbbcbaadbbaaabaaaddddbdadadbdbcddabbcddadcadbccadcaadcbccbdabccbcccdbaddbcaababbdacccacdabbcbccbcddddcdbadbcccdcddaadaccadacadbcdbaabcddccddadbaccddabaddbaabbbbdbcacbbcaaccacacdbdcacadacabbadaabbabababacbdabbbdcccadbdabbbdaddadaadcaddbddbdaabccaccbdcdbcbcbacdcccbdacbbcdabddabaaccddbbdbaabacbbacbacabbdcddaaabccaddbdbaadcdddaaadcacdbbddcdacbbbcaccabddbdbdcabaacddadbdbdbadccbdbdcbbaccdcbddddddbccbabbcdcaadcdaabcabaccccbdaabcdacbbbcdadddacdbcdccbddcdbadccbdbbdddddabdbbbabacdabadbdbdcbcccbbbdadbbadcbdbbcadbcdabcdaabbcccbbdadcdacadacbbdcaadbcdcabbbbdadcdcabdadbabbacbabddcddcddaaaacadadcbcddabaddcdbbbdaabdabadcddbadacdccdbbacbbbbadccdaacdadbbbacaaabccbcaadcbbdbdabaabddcabcaddccdddadcdacabbbadbcdcccbdadcadcccabbbdbddaadbccbdadbcaaccddcbdabdadacabdbbcacabbbdcaacbbabcdcddbcababababdcaadaadbcadaacababccdbccdccbccdadcadcadacbdcaddcdcccdbbdbcabdbddcdccdcbacccdbddcaadcdcbacababbbacbccabdbbcadcbcccbcbbabcbdabacaadcccbbcbdadcdacbcbdacabdacbcbacbdccddbdbbacabcbdbcacdbbaccdacbaccaabaccddbbbcdaaaacadddbdabddadcbaadccbaadbdbbdaccaaddbcdbabbbccaabdbbdabcaddcddbdcdabdbbdbcddbdcdcdbadcbbddacdbddcdadbaddcddabacbdccdbaaabbccbcbbabbbcbadcbcbdbdbccdbaaabacbaaddadbbddbccadaaccdbddccdcccbddcbabacdcccdaaacbccbbbdbcacccaadbdabbdccdbcaadddbabacacbbbadcbdcbabdcabadbbbbaadaaacaaadbddcccdaaccdacdbbadacbadbcbabcbbabdcdddabadaacbaaaabcbbaccccdbdaccbbacdabbdabdbdabadbaabddaacbaaaddbdacadbadaddddadcbabcabcabcdbccacbcdabcbabccbabbdabcdabdbcccdaaacccddbcbaabdcdbdcbbdddbcadabbdadabcbdabacadbdcdadaccaabcddbdadadadbcbdddddaacbbbaccdcbaadaccdbcadbddbdbcbacbadaadcbcbcabdacadcdaabdcdbadaacbdcdadcbbbbcaadcdcadacaaddaacbadacbcdbcbabdbbcccbaccbdaadbddcadadbdbcbbdcdacdbcacddabbbdaabccaaddbaaaabaddbdabbabbcddbcbbcdadbaabdcbaacbdcbccdbddaccacccadcabcdbbcdacbaacdbcadadadbccaccaabdaabdaacbcabccbabcbdacdccbcabbcccbddbbbcbcbcbacadccdcbdbdcbddbacadcaacddacadccacdbabaabdddcccadcdbcdabbdbddabaaaccbdddcadcdaacabddaaadcdddcbbadaaccabbdcdcdadcdcbaadcdcacabddbdbdacbaabbadcdbbbcbcdaaaddccbdddbabddbaabddabccbacbbcaaadabccdbadacacdbbacaacdbbcbcbacbdabacaabdcbbddbddacbbbacbbddcbacabcdddacbcbdcacbbbbacacddbdccbcabdacbacdddbbaddcbccacbdccdbcaadbdcdccdbdcacdaddadbaaacdccdcdcbaadccbaabbcbcddacacbcdbdbbdaaccdcdddacbbbcbccdbaabddbcaadcadbdcdaaaabbadcdaadbabcccccbcabacababdbaabbcdccdaaadaccaddbdacbccaaccbcabaacaabbbbaacbcdbcdbaadddbbddadbadbccdcbabbadadbcbcbaacbdcdcbacdddbccbdccadcdbcabaaacbadabcbcbacdcadbdaaacccddadbabbbacccbcbdadaadddadcdbbbdadaddddaccaabbdbbaabacbbadbcbdcabaaabdbaccabacbcaababbaabaaccbddcadbacdcbcddcbdbadadddcacdbaccccdcdcadcdacabbabadcbbcaddacdabcbcdcbacbcbccacccccbcbccdcdddcaadcaddddadcbadadbaabdbadcbdacbbcbadbadcadcdbdddabdacdcddacacadbaddadadcabbcbdabdadbdaaabdcbabddacbcacbbdccdcbaacbcbddbbdaacdbdbaadbdddbdccdbaddbdbcaadddddcddcbaadadbbbacccccdbbccadbcbccddddcbbddddacabbdbdaaaaabbacbcdaccadbcbbaabcbdbcabbccbdbaacaabcdccccdaabcbdcddbbadbcabbbbabbdcadcaadabbccdbdccabbdcabcabbdacccacddcccadbadbadbbdaccbaacbacdccabcdbdccadadaadcbcdbcabcbbbacadaabccacadacbbbaccbacbcaccdbcddccdbcdaaddaccdbbbbaacadcaddacbdbabbacbacadabccddbbcaabdbdcdaddacabbacddacaacccdcccadbbbccdadcdcbaadacdbccbcddcddbbddadaadcabcbbccbddaacdbbcbdccbddadadcccdcadbcaccbddacaacbacbbdaadabbbadaddbbcbccddacaabbddcbadcccdaabdcbdcbcbaadaadadbaadbdbbaacdddddcccbaddaacbbcbcccbcddcbcbccdabddbbcdbdcddabaddcccdcabbbbacbddcbcaabddcacbcbdcddbdbcbdaadbcbbcbacaaaccbbdbdcbdabbbadbdcdccadaabcbcbabbabadbaacbbbacbadbbbbbacbbdcccdbbcadaadabbccbddccadbbccccdababbcaadbbadbadaaaabdbaccbadadcdbaacddbadccdaabcbdabdbaddbbcccbcdbdddbacccdbbaaaabbcbddcdddbbdbaddccdcadcadddddadcaabcaccabbddccbbcbbdccbbddabdbaccaccccdddaabdabacbacbcdbbcbbacbacdabdabdacaacacdbdabbdccacaadcacacdbbbbacdddabccaccbadbcdabddbabcbcbbccdaadadcabdabacdbbdadbbdaccdcbdcddbdaababccdcdccdbcbdcbaabbdcbdaadcdcbcbadcdccaacdcacccaddbadbcdcccddabccbcccddbaabacbcabbaadabdacadbcaaaddbcadcdcaacbcacddadddadacabbcbddbcaccbbdbbacadacdcbbbbbadabdbdbbccadaaaabaabadbcdcacbdaaccccdabaaddababccdcababdddaccdacdbbbbbbbaabbbbcbcbdadabacadbabbbdbbdcaccadaddabccadddcaadaddaccbdbadcdabbdaaccdcadbdbbcabdbcbbcbcaadcaacccaabbccaacbcacddacaaaccabcdbdbccacccaadcdbdadacdbbbddbddbccbdcbacbabcccadbbaaaddadbababacbbddbbccaadcacdadbbddbbdbdabcddcdaadcdcdbccadddbcbccaaddcacabcbcabbcbddabcaaacdcbbcbaacddddbbbdcacabbdabccaabccbacadbdccabadabbbacaababdcabbdcdcdddcaacdbadaaabcddbdbcdbdcacbadbdccddbdcbacdaacdaacdaadcaaaccdcdadcdbacaadbdabbdddccbabadcdaadbdcaaaabcbdbacbbcbacbacadbdcaabaccccabacbacccdcdbcdadaccadbbbbccbabbbbaddddbbdddbcccdacbadbbbbabdabcbaaacbcdccdcdcabbbcbcbdcdbababbacbacddadbaaccdccadbccaacbddcdbbbdabbacdcaaaddcbaadcddaadcadbccbdcaddbaabdccddddacddacdbbddadabcdcdcdbbaaccddcabbccddabcdbababccadaccbcacabbcbcacddbbbbcbbbacccacbaccdcccabbddbccaaccdbbcaacbdabdcadbadacdbaddbdcbabbabaabbbabacaddbabddbdbadcbcabbcbcdaaddcddcbcddaabdddaacbaadaabcbbdadddcddacbadabadcaacdaccaccaccdbccdbcbcdccdabddcaacbbccabbdbcbcccadbdccdcaccabcdcddacbcccccdbddccccbdbcacaabdbcbbbbddbcdaddadddacbacadddcbabddddcdaaabdbdbadbddccacbbbaacbbcbcbcdbbccbcbbcbdcabdbabdddbcabcccdbcbcaccbccdcbddabddccbcddbadacacadcbdddbbcaddaacaabbcdcaddbcbccdaabacadddacdbdbcadacadbbadddacacabaadbdbbcbbcccdddbbcadcbbcdbcccccacccbbaddabaadabcabaacdddcdcdbadbcadbdabbcccdacbcdaacdddbdaadbdcababacabaabdbbddcabccabdacdabdcdbddccbdcdcccacccabadccacbdcabcddadcccddcbccadacbacadbbdbbaadbcdbdbbbcbaadcabdacbacbdcadcdbbddabacddbcbadbccccdacbddbaabddadbbaddcbacababacbaabcacbcdbaddbacdaaccbabcbbabbbaaccccbbbaacabaadbccbaabcdadcbaccacabaabcacdcbcaccddbcddcdcbdaccabacbcabbaccdcaadcccdcbddabcbcacddcddbbdadbdbdbdbbddadbacbaabadddcacccbbbcabbbabcacccabbcbbacbbddacbddacddbbddbcbbcccbbbdacbaccbccaddaabbcaabddabbcbbbbacdcdaadaacdbacacbaaadaadadcccadccbbbacbadacaabbdbacbaddbdcabdbabbccdaaabcdbcbcddbbcaaddccdbbcdccdabbcbccabbdbccacacaddbbacaaadbbbdbcbbaabbabdddabaddcdbcaacdacdbaabbaccbbdbccddbabdacccacaabcbdbdcddcddadacdcabcbdacaacbabcccadccaccbabbcaacbbddaaacabbacccdadbddbccbcccaabccbacdabdaacaabcbbabdaabccdccadcaaccabcdadaadadcbbaaabbacdbdaddbddcbcbcaccbadbcdddcdcacccbddacddcbbcabbaccdcdbaadacbddabaacdadbdbdcbbaadbccbaaddcacbbdddbaaddadddabbbccaaaababdbacaabddbddcacbccdcdadacddbbdcbccabdbabcccdccbaccdacbbbcbdacbacabacccacdaabcabadaaabcccbbcdbbbcdbdaccacddadacdccbadacbacbcddbdbcbcacddcdcdcbaabbbbcbaccabdcbcbcbbdaaabdddbcabacabdbaaabbccdcdadbcddaccbbabababdbacadabbaaccbdbccbadcdcbdacabdbcadccaccaccdbabbacbcadcadbadcdcbabbcbbbccbdbddadbaacccaadbcaabdbdadccacabcbabaccbbdacddccaccbcaacaabdddcabcadddddddbcacdbaddbabdaccbadadcaaaddaaccbcaccbadacdadccbbacddbbddccbdcaaccabdacbabbcacbbadaaccacbaacbbdbcccdadcaadccbdabddbddcbcbcdcdbcbbcacaabbcbcadbaacddcbccdcdccdccbaddcbccbdcdbdaccdddabbccbccbbbaddadccbaccccaaaacadccdddddabbcddbddbbaddccaaaacbadcdcbdbddbdcabcdcbcbbdbbcaadabcdadcbaadbadadcabcdcdbdabbcbbcdabdacadbdcabdacdcbdcbcadaadddbdbccbdababbacabbcbdccdbdaaaccdbbccbbbaacbdbccbbdbdcbcdabdbaaccbddddbdacaaaaaaacccdccbabbbabcdddbacadbcbabdcbadaddcbbacdddbcaabadbcbcdbcacacdccadccbababcadddaabcbdcabcbdadcdcdcacaddcbccadccacddbcddadbaabcbadbbddcdabcdabbdccacbabcdccaabcaaabdcbbbaddcccacabbacaddbddbdbbbabaadabdcbaaacccbacaaddaababacadcaabcbcdbbcdddcbcdcbcbcaadbacdbcaacabbbbadbcdbcadddbcdcdccdaadddccbabcaaabdcabbaaddcaddcbcacbacdcbbaadacdcbccaaccccdddacbbaacdbdbacbcdcbbacdcaaaaccbcdbacadcaadcbbcaacbbadcccabcdddcbcddbcbcdacdbcbcacaadcaabccbdcccacddcaabdbdabccbacaabdacbbaaddcbcdcdcbbbcabbbbdbadcbbaccccdadcaabbcdbdabbaadacababaccbadabddddcaaaddccdcacbcddaaabaaaadabaadddadddcbabbabbbccbdbcccdaacbbbbdadadbbccaadacacabdbddcbaacbcdabaacaccbbbcccddbaadbcbcdccaddcdcdabbbcadbcbaddaccdddbdbcccabaddbbccddbcdcccaaabaaccababbcacadddbcccaacadcababdabbcbaacbcbaacbbdbcccacbccdbaabbcdbbdbadbabbdbacbdcbcdabccacaccdcbcbdbcbdbcbdabacaadcabacdcbbdbddabdcbdabbcbddbccdddbcccddabbabcabbcaacddbccadbdbcbbbbdcbaddbcddadadbbcdbaabbccbbabbaaacbacbcccbcbbcaaaacdadbbdccddaabadabccdcbdddaadacdabcdbadabbbcaadccabdaacdbbbbaadbcbdbcadabbaccbaaddadbcacbbcbbbabdacbbdcbcdccdcdaaccdbcdaadbadcddbbadacddbcdbcddddabdddcbddbdcdbcbabaccccdcadbbbcdabcbcbbcaadccccdbdddacbaaadbbbabbcadddbddccbdabdddbdaccccacabadbddbacbbdcaaddabbddacbadaadcccdccbccdacbcbcddbaaadacddacaababdaacdcccdaabbbacbbddbaccaabadadaacbbabdcbdcacddcdcaaadcaaacdbccdacaabdcbdcdaacbdacbababbcdabdbadadabddbdddadccdbadcdbbbabcadcdaddcacdadaaaddbbbadabadadadaadabcdcccabcbdcbdabddaabdbabdabcaabbacccbabdbadabbbbcbacdcccdacabaadbbbaabbdbaacbabdabcdaabdabcdcddddabccbbdccccabcbbabadbcbdabbdabadaddcaddccbcccbccbbaccbbdbdbaadbbdbccdabbdabbdcbdbcdbbcaaaaabcdbbcaaabdbccbcacbaabcbacdddcbaabacbbcadccddacdbbbdadbccbcaabdddddaaaabdbcdacdacdabdaabbdbbcacdddcbdabddaadbadcbdadcbcbbcbcccbadcacbbbacdcbcccabaadacdcaacbcdaacadbdbdbaadadbadacaddbabadacadaaddcbadcbacddcdaaddbdbcbddbddcbddacbbcdbacbcbbdcababadddbbbbdcbbbbcdddcacaddabacdcbdbcacbdccdcbcacbbddbddbdbadabddbbddcdbaaccbbbcbcacbbbcddacbccdccadbdaabcbabdcdacbcacbccbdcbbbcdcdaccdaacacadcdcbbabdddcabdadabcbcdbcdbdcdaabdadbcbbcdadabdabddaadbccdbbcaadcbbadcccaccddabdababacdbdcdbdbdabcdcaddacdabcbbaacbbbaadbddbdcdbcdbbaabcccababcccdacbbdaccacaccdbcddadaaaaabbdccccbdabbbabddbacdcdbddcdacbdccacaaaacbdbbbcdcccdbbbbbdddccdddbabbbdacbbbcbdadbaaadacdcbbccbabaaccbbdabadbbbccabbcdddaacadcbddaaaaadbbadacdadcdabbbaaacdadcababaadccdadddcaabbccdbdadaacacbdcdcbadaacccbccabdaaacdaccbccdbbdbcddcccdbabbbbadcbdccadaacbaadcddbbdcabcbbcdabcdaddbccbcbbcdcddbdbbccdadbacbcbdcaabbcabacccbbccdddbcacdbdbadcbbaabdabbccbdddabadaccdcccdcdaababbabacbbcdbdadddbbbbabdbadaccbcabdacddddccdcdabcbcadbaccabbcbdddabbbcdbbdaacbdcadacabddbbaacddadbcdadcacccbbdbcdacddbdddbbdbadcabadcdcbdbbbadaadbcadddacabdabbcddaaaadaccbdbdacbbcaacdbcababddaccdaccbbaadbabbaaccbdcdbcbcdaddbbbdbdcacbacaccbcaaaabcdbdcbcbbdaddddcaddddddbaccccbbbddbbdcbbdccacabcdbcccbbbbaacacaabddcbbdbcbcdbddbdcdadaadddbdbdcbcaddbdcdcdbccabdbdbdcabbbcccccbcaccacabddcbbdbbbbbaccdccaaabddbcdaadabacccaacadcbadddcbdcdcddabbadcbddacacaabdcdbbdadcadcdbababacacabdcaccdbdbcccbbbcaadbdacbdccaacdabcaacdadadddaabddacadccdcbaaaaacaccddbcbbacbdddccccdaabdaabcdabdacbdccdccdbbcdbcaacdbdaaaadbccbababcdadbcbacadbdbcbbbabcacdcacbcbabcdcacbddabbbbdaddababaaacbdadabbdaabcabdadcdbddcbbabcabbbcadcbadbacdadbdadbddabacdadbadababdaaadcadaccdadacccdbaabadbaaabadbccccccdcdbbbccabcbadbcddbcbbccaddbadcadadadddcabddddacddadbcdadddaaccbcdddbbdaaaaccbcbccbbbdcbdaddabaddbbbbcacadcbbdaddabdaabadbcbbdabcadcbbcbbaaabdcddddcbdbbcbadbcbaaaadcbddbbddbabbccabbdabdaabadadcacbccdbbdcaabaccbbbbacbcdbabcaddcdaccbbcdadaaadabbdcdbbbababcbccccababbadbadddcbdbcdbdbdaaacdcaacdbbbbdadddcbdccddcdcdacbcabddbacdbdaabcbccaaaabdbdcbcddddbbdabaddadcdacbadacdbdbdcbabdcdddddbbaaccbdbbdabdbdcccaaadccdcacdcbbbbacbdaabccbdabbbddcadddbcddddcadcabadbadabdacacbcbcaddcabbadacdcacddaddcddabdccdababbabccadcadabcbddbbbacbbcbcacdddddbbdaaabcbcbccccbcbcdddbccccbcddcaaabcacddabdcacbbcdbacddacaddcaacccacdbbdadadddabcdbdccaabadccbdddddbaacccdbdcadddbdccaabcdbdcdcbaadbcbdbbaddbbdbcdcdbbacababdcddbbdabbdaaccabdcbcbabdabdcaabccbdccdbccacdcadccaadcacaaddcacbddbbadbcdabbddcddbbbcdcbacdcadbbababcdbacddaaccaaabcabadbbdacaabdadacbdacdacddccddbdbaadabcbdbcdbcdbbaaaccaabacabbaaadbbcbdbacaabccadaddadaddbcaaaddcabbdcbbabbbadcabddbaacbdcbdbadccacbabbdbdccdbbabbcdcbddbdcadabccbabadadaaaabdccbaccbbdabcaacdbdbddcbbcabcbbbaacbbbcccadcaabcdcdcdabbbcbaabcbcacdaddbdbcdbcaadccdcbdabddccbdacddabbccbdcaabadacdbadcaadbdbbcbdabbdababbbbcacaccbdacdcbaacddbcbdaccabcbadbbaddaadbaacabdbbbcabbadbaaaddbbdccddcaaacbbbacdccdacabdaaabaccddcddcaaccaddbddbabaccbdadccbdddadcabcdcdccdbaadabcbaacdcabdbbcababbddabbcaaddcbccdcbcbbaaaabaabaaaacccdabbddaaadaddbaaaaadddcbcccaaaaadacaacccaccbdacabdcaabaddaccbcbacdaccddabdbacbbaacdcbcabbdcadbbdadcbcdcbaccdacddbbddbbbabaaccdbcacacdccaaadbbadaabacddbdcddbaabbbcaddadabbacccdbdbacbccaddadacbbadbacaccacccbbcddbabdcbcdbcbbbcabccabbbaddadcbdcbdacacdacccdbddccddbdbaacababdccacdabaaabcccaaccaaaacdaccbdcbccdbadcbaccbccacbdcabaabcdbbddaaadbcbbcacbccbcacaaaadcbcccaabadbadadcdcbddccbddcbdaacdcbadaaccddbdcbdaacbababcbcbadcadcaacbabaaaaadcbaabaacdccdddaaadbaccbbaddaadcabadababcdccdbbbdadbdaddcdadccacdbdacaaddccbbbdbbdbcbbdaddbadcdaacbadcbadbbacbcddcaaabcdccbbdabbcadddaacdaddacdbdcbaababbbabcacccabbcdcdccadbabaccbcbababcdabbaddcccdbbadabadcdbaadacbcdcaadaccbcbadcbdacaadababcaaadbdaccbcacbdaadbcabbbcdbbababaccdcdcabbdbacadbcacaabccbdaddadbbbadbcbacdabdabadbdbaddcdcdbdadcabadbbcbcddadccabaaacabcdaaaabcdddcddddaadbcdcaddcdcaabaacbccdbcbbbabcacbbbbdcdbdbcabbbbadbbaacadaddbbcadbaccdbbadcabbbbdbcbdaddcabddcdccbacbaaccaaadaadbadabaaccdcbbacbcbcdbccbbcacccaddcadadaaabbcbdabdacbadcadadcdadbbcadababbbbbddaccbdaacadcccddaabacbccdbabbdadcbcccccdabbabbdaaabdbbdaacbcbadadbccbbacdacbbaccbcabbbdcddadddcbbaacbccbbbccabcdabbbcacbcccdbcaacddcbbcbbcddbdadbacbababddadbbcbabacdaaadbccabcddddcddddcaacdcabaaacdaadbcbdddaadababcddbbccbadacbabddbabcabddbcbccbbdabcbabcbcbaccbbbadcccaacdbccabcabcdcbbddbbadabccdddadcaccddcdacbccdcabccbbbccacbdbdbcdccbdabaadaccbbcbadaadabadcdbaaaabbdcabdabbbdacbcbcbaaaacdddbbbcadacbadbdacaccaacbbbdbdddcdaaaddcddbdbdccbbcabbabbcdcccccdbadbddbacccaadbcdcaadbccabbbacdddadccbdaaddcdbdbacbcdcdadacbdabcadaababcdddcbdbaccbdacaaadbbbcbadcdcabbbdabdacbbabbbaddadddcbdabdcdaccbbaaccbcdbdcdabbbdaddabdbacdababcbbacaccdcaadacbaacabcacdddbabadadbcaddabcabddccbbdaacbcaabbabadbdbbaadacdbdadadbacbcdacbcdaaaddabcdbadacadddcbcaaadacddddbbddacaabcbbcbbbcbabaddbdcdccdcaabcbaabdadadcbaaccadcdabaabdabaacbaacabbbbccbbadcacabbdababbadccbabacbacaacdbbcbabdabdacbddbccbcbdadbbbbaccaccdbadadcccbdddbbbdccbdabdbccdacbcbcdaabdcdbdcabcbdaadadccbdbabadaadcbaccdbacabdbcdcddcbbccbdacddbbbccddcadacbcbcccddbdcddabaaabbcbacbdcbcddcbdaddccadbddddcbddaadcbccbdbababcabbdaaaddbcbdacbccddadddbacadabcdbadcddabbaaaccdcddacbdaacddaccbddddacdddadaacadddbacbcabacaccbdbdaadabdccaddcccccbcddcbbcdcbadcccacccdabacbadabadcbbdbdbbbacaaadbdbacaccabcdcddcbbadddacaacacdcabccabcdadbbddbccabadddbddabaacabacccaacadabbdbbddaaacabccabcbabbabcadcaaccddcbabcaacbaacaddbbcccddccbbdcdcaacbacdcdadbbabddbdddcdbabbdbaaaccaacabdababacabacdddbcbdbdaacdcbcbcadddcaddcbadccabcddcabbcbcaaacbbcbbbbabbacaabdcbcdbabcaabbcbddbcbbcabbacdccdaccbdacbddcbbaadbdaaadcaacdaabcbcaccdcbadaaabbccbabcdadaacdcacadabadabcaccbdadccaabdcacbddcbcbdabddbacacabadabdacadcbdaacabcadbddcbccacaacbbcbdbbdcddacaabcbabaadccaadbbbbdbcdcdbbcccdacddaadbadcdaadcbdcaabaacacaacaabcdabaaacbcacbadbcadbdcaacdaabaabbaccadddbbadaadadddcbbbdcacdcbdbaadddddddbacaabcbdcbbdabadacbabcddcddadadddabbadbdbdadcdcaaabcabadddaadbbaaccadcdbabbcdaacdabcabcadccdaddddcdbcbbcdcacbbcccddcbdaabddbbddbaacaacadaadbacabdbcaaacbbccddddacbdbabcaababaadbdddbacccdbcbbbbadcccdcadacbcbbaccacbcdcddddcdcbdcdaabdbbaaadaadcbbcabcbdbdbddcadcbacdccbbdabcadbcccacddddbdccaadccdbcbddabcabcadaabbaddbbacbbbbaacbadcabbabcbcbdcabadabcbdcbcacbdbcdbdbdccccbbabdbbdaadcabbcabadacaadbddbddcadabdacabaacddadadbccacacadbcadacbdaaabbdbbdbbcddcacdcbcbadabdadacbbadaccadadacbaaddadbcaaacaddbccaabdaaacbaabccbdcbcccbcddbddabcabcccbadabbdbbcdbcdabbabcadadacccddadadadcaaaddcccbbdbaccbabcabbdbdcdacddbdbcccbcdbabcddbaabdabdcbaacacbaacdbcbaaaccabcbaccddccccdbccacbaaddadbcbccabddaccaadadccccbbccbacdabccbdabcdaababccbaabacdaaabbcbdbbddccbaccacaccdcbbdcabbcacddbbbcbcbdcaacacaccdbadaabbcdcbdbbbbdbbcddbbcbadbbbcbcccdbadbdadaadcccdcacbaccbbababdbcbababcdcaabbbcdcddabaccbdcbaaadbcddaaacaacbcabccbdcabaababcaacaadbcadacdaccccabbbaaaabaadcdbbdcbcbdacdcbdbcdcdbcacbcdbdadbbdbcbbcacdbcddadcbaacdaabaacdcbccbcbcdabadccadabbbdabdcccbddabaadbacdbcbadbbaaaacacbdabcaaabbdaaddddbcadbbbdccabaaaaacaaabccaabcdcaacdbabdbadcaacbdcacaaabbccbaddcadbbbabcdaddbbaccdbbadbdddadccabbadaadcbaddbadddccccddadbddaabbcdacbddabcacccabcdacdacabbacacbcbdaddcdbbdadddadaaaacabbddabcaababddacacdddccbbddddacdbbcbbcadcababbbcacababdddbddaccabaacdaaccddcbdbcbbbddabcbbdddadabbbdaacddccbbdcaccabbccbcccdcaacdadbcdacabdcadaacbbbbcbbbdbdbddbbbdbbaaabdccbdcacaabbdbbccadddbabdbaccddbaadcaabbdbbbdcbcddbaddaddcdcbaadbbbdbaabaccccabbbdcccaddddaadbbdbbdddcdbbcbaaaacaccaccaadddcacabacbcbabadadcddcaccdaccabcddbaabcdbaccddcccdbdbcdddbcaadbaaaabaaaaabdbadccaabbacbdadbdbdaaacbdbdacabaccdcbccbcccdbaacbadbaaaaccccdbbccbdadadbcbbdadcbbdbabcadbabacacaddbcddaddaddaadbbbaacacbbababcbcbbcabcbccbcaadcdcbdacbdbbccdacaacacacbdddabcacbbbabcabbacbccbbbaacccaddbdbdacabccccccbcacaddcbbbbccbdccabbadcaacdabaadcdcdcddbbabcbbbdcbaabaadbaccdbbddbabdbbcacccaabdacdccbdacaacdabcbadabdabbabbbacdadcdcbdcddcacbabbccabbccacbcdbbcddbacbbcddcbcdbccabdcccadcdabacdaabacaadccbccabbbddcdbabdddbadbbbaabbacabdcdccdaccbdddbaacdcbbcdcbcccacdbcacbdaccdcadcccbcbcbcddcbabacbddbdccdbdccacbaaddbdcabbaddaaacdcdccabbcadcdaadabcabbabcadcdcbdadaddbacddbdacacdbdcbbacbcaccbbacaacddacabbcbcccabbdbaabddbccdbaccbdcddcadabdaacddcacabdbaacdcbcbadcbddaddcbadbccbbabbcacacabadccbdddbcdcbdabdddbcaadacacadbdcaacbcbcadaccdbdbdadcbdaabcdbacbacbddbdacbbaabdccdacabdcdadcddbcaadcbccdcbbabcdabddbdcdaaccabdccdccddccacdcadbbbacbcdaacdbcadbccdccddadcbbccdbdbdaccaabcbbaadbcbddabaacccdacaabaccdccbadbabbbaacbadbdccbcaddcbdbadbcdddabadacaababbdbacdcddcaddbcbcaacabcaaddadcbbbadcaadaabccbcabcdaddcbbbdcbbcbcdaddbacaacacaddcaadabdaaaaccbbdadcdccbbdbbcadcddbabbabcadadcbcddbddccabdcdcccbddbdbcdcdbcccdbaccdcabbadadbdcdbcadcbbbdadbdbacabaddbbddadccbccdcdbdccddbdbabcccdcabababbccbcaaabdacacaaadaacdbbdcccadcdbbdadadcccdbddcbdabbcaadbcbdccbbabaacaddcaabaaacbadaacaacddccaccdcbbccacaccccdcddcdaaaabbbaaccbbabdaacccbcbdbbcbadcdcacccabaacacadabdbccbadccaccdcadcbbcbddaacdbcdaddcabdbabdbaddaabaccadbdcdcbdddbdddaabaabbcbbbbdacbabacadaabacadacaaccbaaadcbbbdbcbdbadcdccdcbdcaacdabbbbabcdacdcacbabdbabbbbacdaaccccbbbacccbdcdbdbdababbbcdcbdadddddbcaabbdaaabbaccdddcdbdabbccbacacdaabcadbdbadbbdddbbccbbbbacddbddcacbaadadcabccabcbccbbbcdaaaabddadbbcdadcaacdcacacdccdbcdacddadcaadbdcbdadbcbabcdcbadaadccccaabdccdbcadcdadbaadaacaaddaaccaaddcbccbdbbdadcbbbdbcddacdbcadaabdcbaadbcbaacccdcddbddaccddabaacbdccacdabcddbabadccbcabcbbbdcadccbcbcbadaabcababccdacacbdbacaadddddbaadccbcacacdaabcabccadbbdbccccadcbcdccdbadbccdbaaabdaabaabccdcacddbcabbadccbccdcbbbaacacddcabbddadbcdbdbdccdcbbadabcacbacabcacadccdddcccaddaabdaacdaacbbacbcaccaadcbbabbadcbdccdadadbacacabdcacabbcdccbaddbacdddbcbdbdcbcbaaccacadcadabcbadbbabbdbdbaccdacabccbdccbdddbacbaaabdccbdbbaabccccdacccbdabcdcabdcaccdadaddbbdbbabdacdabcaccacacabdbdbaadadcabcbcdcdbadcacaddabacdddabcbacaccdaddbcbccbabdadabcacadaacaabdcababaabdbcdccadbabdbacdcdcccdaadbdcccaaacddbcbbaaacdcccaadcabbdacddddcadcadbbabdaabdabccdbabdadabcddcbdbbccbbcdcddcadbdcbadccccabadaacabbdcbabaccbacbbdbbdbcadbbdbdadaddcdcaabaabadabccbdbdababcbbcacbdbcbdcdcbcdaabcdadbbddcbbdbbacdcbcdbaccbdbdbdcbdbabadbbbcbcdbccdbdccdddbcbdbdbbddaabadbccccbccaacdbaababcaadacbdcbabccabdbbacdcdcbdbbddbbbcdcabcbadcbdcbcbcccdccaabcbdbdbbcbabcbdcaccbadbcbddadabdbadcdcaddbaccbabcbbabbaddbbcdadccbdbbbcbddddcdadddcadddaadcdbcbddabbdadcdddacbdcdbcadbabababbcbbaacaabdadbcbdcbabdcaddbabbcdadbccbabbdacddcccbdbcbdaacaabcbabdadbaadccdbcdabdbadcbbdcacddabdbcbcdacadabcbcaabdcbccdbbcbbbdacadbdbdddbaabacbacdabcbbcddcaaabbabbdcbbbdddadabdcbacacacabccbcdcdcbcddacdabbcaadcbbdadabcddcdccbcdabcacabcbabaccbabbbdbdcacbcdcccccaadadddacbdbaccdcdacbcbdcbbdaabbbdbccaabddadcccdcbbdcdcaccaadddbcccadaacccabcdbabdddacbcdcdbabaababdcaccdaabddcabdacdccddddbcabdbaacaadddcdbbccadabbbacbaadcbdbbdbadbacadbdbbcbadabaadcbddacccccaabadcdddcccbdcbcbcdddcacdadcbcadbdbdccacabdbcdadbbdbbcccbdadabaaadcdbbadadccdbcabcdabbadadcdccdaacbcaadbccddcccbcdbdaddcddbbacaddadaacdcdcbabccccacccacddbaabddddcbcbdbaaaaddbdaabadbadbcdbadacabcacaadbbdccbdcbccbbadbccdddbbabbdadcddaccadbbdcacdabbcccacbccdcbdccadcdbadcaccabbdabbcaabbbddabdcabadbaddddadbdcbababaaabcdbccdcaccacacadcaabdbcddcdcaabcccaadcbaacbddacdddacbacdccccacacadbdcbcdcddaabdcdccdbcccccacddbaadccabdbcabdbcbbdcbcbaccabcbcdacdadabaaddbadbcaaacbccdaccdabcdaadcbcbccabaaaaabbdaaaddddabbaaacdcccbdbacaaaadabbadcdcccddaaacacdbcbccabcccddcdadaccbadddcbbbdbaacaabdbdababcbadcdaddcdbdddddadcbbdbcbabacdbbcbdaaddadddaadcddbcbcbccddcabbabacabbbbbccadddddddbcdcdaabaccacbbaccbbadcabbadcabcddcdcbababcacacdccbaabbbabcccacbbadbabbcacabcabaddacdadccbdbcaddbdcbacdccdadcaabdcbdaaabbdbddacbdadabaaaaaccddadbbcdadbccacdbadcdaaabcdabbcaddaddddbdccacdaaccaacdbbddabaaacbbabcaabbcbccdcdaaddcdadcabaacdcdcbcdcbbaabcacadbcbbcbadcabbbbdabddbdcbbaaddbababbdbccacbccbbbdbddadcbcccbbbdadcbdbbbcacbddcaadabbbcadaabaccbddddcaacacdcaddabbacbaabacccaddadbbbbdabdadcaadacbdabdbbacadccddcabccccbaddcabbcbdccbabdadacbaccdccbdddaadbaddacdabdcbcccdccdabadacdbdaccbcbbbbccdbdaadabcdbacacadbacccdcdcbabdbccbbdbbcddccabdddcbddcdacadacbadcddcbbcdbbccaabbaadcacbaadacaaacaabdbaddadbaabaacdcddbadddcbccacbabbdcbadddabaaaacbaaacaccadbaddacddcaddaadadbcddddbbbddcacbaccbadbbdaddacbcbcbbdabbadaaacddadcacacbabdaabddbdaaaccdaacdddcdabddbadddadbccbddccbddcddbbcaababdacacccccaabbbbbacbadccdccdddcdcbbcdacbdbbdccdbcdcacbaacaadcaaccabcdbadbaacbaadacdcdbcbaccabdcdcbdbcacccbaddddacdcadaddccacdcacbcdddcccddaaccdbdbadabcddbdbacadcabbcdbdbbacbdbaacadbdacdddccabaabacccbacbbbaabdaababdbccbadddadcaaacdaccdbcadcbdbcaadadabddabcadbbdadbbcccdcbbadacccbacbdcbbdbbbbcaddbcabbcbabbdacdcbddbcdbcabbdccddacdabacbdcdcbbcbdcddbcddbbdacaccbdcadcbbaccdcacadbbbababdcdccbdbdbcaccbddbbcbcdaabbddbdbddcaaabaccddadabadaacbabcddcbbdbddbdbdcbdbbbccaabccacdbdcbadbdcaadcdadcdaaadbdcbaabdbcccabbabbcbdbcdacaabccbabbbcdabcacdbdadacbbbabdaadaaadcdacdddbdcabbcdbbcdbcccaabadabccdbdbdabbaadcbddbcdbddbaccaaccbabacadbcccddbbabbbdacccbacbaaccacccbcbcbcbdbaacdbbbdbadbbcaddcbcccddbabadaaacccdbdddcddcaacdddaaddccacccbdacdcdccccadbdacbbcbacbbddcdaadbcdacadcdcdcabcabbacbcbbabbdacdbadbdbddabbdbbadccbdcadcabcdcacabaaddaabbdbcbdaabbaaacacbcbadbdabacaaadddadbcbcdadcccaabcddacbdbadbcacbbddbccccaccbbdbccacbadccadcbadccabbdacbbbccdadbbcdcdbabddcabbacbcaaddbcbbcdadcadbbadadaccbdaadddccacbacabbcddcddbdcdcacacdcbbcadbdbccddabbdacbdabdcbcaaddddcbdabbabcacaababcbabcadcabdcaaaabddcacbcadcdbbacbaadbbdccdcddcdddddacdaadaadbdbcacacaacbdcaacbddaccdacacadddcdcaabcdcbaacdbbbccbcbdabcaadcacaaddddabadaddcdcbdbcadcddddccacacaadaddbadbdbabdacbbbabbacacaadcccddaadbbcaacbacbacbcdaaadabbbdddaaadadccbcbcbcbccdababcccbbddcabbacbcdadddbbaccbcccdbdbacccabcabdabbdddbbccbbddbacbacbcdbdaadaadbcaabbbcddadcbbadacbaabcbcdbdbcdcabcbacdbabbdbddddadcdbcbbcbbaaacacbcacbdbbabbdabccacdcccbabaacaaaaaadaaababbabaaccaabadccbadccbacdbacadadacbccbcbddabaaddabbbacaabdbbdcaccdadccacdcadbaacdbaadcaacacaabdbbddbbcaddddacccbdaaadcddcadbbdabdbdabcdddbbabbcdaacabbbcdcabdcabbadcacccccbdbbaaccbddcbaddcbcbcdccabdddcbaadacbacacccbabbcbdcbaaaabaadcbaccbaddacbbcdaaaabbbddccacbdbbbdcbbcccaabacdcadbccacbcbadbdcacbcbbcabcbbaaacbcdcacbdddadbbcbdaaaccddadaaacbbacacbacaaaabcccbaddbabddcdcddddadbabadacabbcccbbadbcdababadbbadacabdcdcddcabdbcababdbcbabaadadbabaabbadadbbadddaaacbaadaacabdaccadbabbbdbddcdbacbacacabdacdbaccdaddbaadaaddcabacaacbcadcbddccaaaaadacbabbcbcabdbacbddbcaccacbabccddadbadabaacaacbaaccccddbcccddbdcacdbddbdadcccdbacdacbbadcbabaadbcddbcdaacbcacbbabdbdaccaadbddbbdbaadcbccdcdcdbcdcdacaaaaddacddcbacdcbdabcacdcaddddabbabccccddbcbdbaadbbdacbbdadaabdadacdcdaadccccccbaacddbdaddddcdbbddcabadaadddaccbbdaadbcdabadabcdcddacaababcccbccbaaddacbbacddbacccabcbbbdbdbbbbbcbcbbcdabdbabcbbbabdcbbaacaacbcbdaaddbcabacadccaaaaddbdcaaddbdbaabbaadbaacdbbdcaccdcddcbaaabaaaccbbaddcdcdcaaccbaccdabbcdcddadbdacbbdccbdabcbdbdcbbbcdbccddadabbdabbcaddbdcabbcaadcbcacbbbcdbcbdcdadddadacbdcdaabcccbdacaadddcdaabcbcdbdabcddbdddbadaadbccdaacbabbabbcbaddbcbcbcadccaccddbaacbccabcbbdadacadaabaccbbcbccbaabdbdccacddaabcacdbcaddabdbbdcdbbdbbddcdbbcdabdbdadbcabdbdacdbbbdbabbddabadadcbbacabddbcadabcdbaadcbdcccacacaadddabaccddcccadabadcbcdccdbdaabaccbddaaaccadbdaadcbddbddcddaaccbacddccaabbcccdabaccbbccaadaddbbabaabdcbbcdbbbaddcccbcdbdbcdbbbcdaadccdadddbbacddbcddddbdbadddaaccdddcabccddbabdccbccddabcacaddaaacdcbdbaddaabbcababdbccdcbdcacbbcbbabbdabcdddaabcdabccaadbccdcdddcdddadcbbdcdacccaddacadbccabcddadbaaaaadadabcaddabcbdbccbcddaacdbadaaadbdcdabcbcddbccdbabbdbbdbdbcacacdcdbbbcacdddbdbacadddcbcdababadacddcabcdaaadcdbcadbadddcbbacdcbaadcdddbaaabcacdcacdcccbdbbcddbdaaccacdaacacdbcbccbaacbdaccaaccadcbdadbccbcccbaacbadbdbdaabdbdcdbadbcbbdbdcbcbddabbbcccdbbbbbbbccccadbccccdaaccccadbcaabcbbbcbaddaccbbaadbcadcdcdddbdbdbbbdcadcbddbaddccbdbbcdaadbaddbdcbcabccbbcccdaaadcddabcdbddbacacdbaddcdabcaacadacdbbdcdcbadbddbdabbdadadaddccdddacbadaabcbbdabaacddccacacccaccdbaaddddcabadcbdacaacaadcdbdadcbabdbabccdbdcabddaddbdcdabdddabadbabdccaacbacccbbcabadbaddcadcbacccbaaabdbbccbbcbaacbbdacbcbaddacddccadddbcadbaddcccacacacdcdbdcdabbdaaccdadadbacddcddabcbdbacbcaddbbdcbcbadaccbdbadbddbdbdababadbdbdccbcadaababbdcddcacdbadbbaddcbadaadddddcbacdbccddcdcacbcbabccbadbaaadcdadcbcccdcdabcdcbadbacbdbadcabaabcaaabaaddcdbdaaccbadddbdcabadcaccbabadabddaccbdcbabcccadadabcadcabdbbadaadcaddccbcbcaaadabcacdbbdbaaccaaddabdbdbdabaaadccaaacbcbacddccccddbabdabdbbdcaacbbccdbdadaaccdcbdcbaabbbccbbbccdddbdabbddbbbaabcdacdabdadcacacdaabcbadbabcbdcdababacaaccaacdddcdcbadbacdcdbcdbdccacbccabaddaacbddbcadbadaabdadccdddcccbbbdabccdadbccbadbbdcabadcccbbadcdaadddaabcddadcacddaccbcaaaccccbcbabcddaaabbcddddacddcccbcbbcbaaabadbabaaccbacaabccabddbbdccbcdbcaddcbbbaddcdccaadcacaaccbaacaddddaaccbcbbcaddbadcdcccaadcdaccdacdabbccacbdacdcddcaddccadbdaddaabdddddaabdbbacabdddcbadccdcbbabbabbbabadccacbbbdacbcdbabcbcbbdbbdbaadaabaadbaabaccccaadacdbcdacadbadcabbcaaacacddddcdbaabbdcadababaacaddcdccaabdbbcdacabdbdccccaaabdaaaadcacbcbaabcacbaccbdadcdbcaddabccddbddabcaacaccbbdbcabaaccbdbbaabcaddcbbbccbbcddbbabddcbcdadabcaccbcaccadbadcacdbbdccdadaddcccccdcdcbdccdbdcbdcdccdaaacdbbcddbddabacbaabccccacbcdbcbcddcddcdbbcbcaacacbdbbccdadddbcbcacccadbcdcbdcaadaabddbcacdaacddbabacbbdcbbcbcbdccddbbdcdadbbbdcabccbbabbadaacbadcbcdadcbabcbdbadddcaddddcabcccbbcbbcddccdcdcaabdbcaacaabccccbdbbbdbbbcabbdaabccccdcaadcdadcadcbadccadbbcdbacbbdbdcdbadbbaadcadcdaabcaabdbacbcaaaccbdcbbbccdbcaddbaccabdbaabcabbbbdcdcbbdaacadaaccaaddcccbddcbbadcadbbbbdcacabcbabcbcabcadcddcabaacdcabbdccccadabbdcadabaaddbaaacbadccccaaccdaccaaacdadcdacbdbddcadddcaabbbabbadcccccacdcadadadcbabababddddbbdabaadbcddbbacbcdbdaddcdbbdccbbacdcdbbadcdacdcaccabdaddcabcddbccdcdcacdaadbadadcacbcabbbcaadadddccdbacdabadcdddbcabcbdaabdaacbbbbbccddcaddaadaabcccbcbbbdabddaaabbbcdbbcdbcadbbacabcdccdcbcbbdcccccdacccabdcbbdcbadbadbcabbabbcdcacdcddcbabdbcbbccccabbbbdacdadcccdbaddaaadbddcacbcccbcabccabababacbbcadbabcdbdbdacadbdabbbdbcadadddabdcabcabbbddbcacacccbadbabdcddbbddadccccacdaacbdbcdbdaaabddcbcaddcdaacbbbdcdcabaadccacbbacccaaabcdabbcdaacdbacadadadccbdbbdababaddadacabdbdccaaacaddbbbbcaccacccacadbbcabadbbdacaaddccadadccaadacddbadcbabcdaadbcaddabbbddcddaabccaaaadbabaadbaabccbdcaccdcbddabdadcccdabadbddbdbddbcaaddbdabbaacbcbddcbbacabdabbcadcddcdaadcbacaaaaaddcaabbdbabdabcddacbcdcddacbcdcbadbddbdbbcbbccbbacdbdabcabcaadbdacbaaacdcbaadcdcdbbdccbcdbdcacdbcccddacaacacdaadbacbddcdcbcccdbcaadcaadaaacbbaacdbaabbdabddabccbdbcddcddcdacdadadbbddaaacacdaadddbbadddbbcbbdddddadbbbbbbaaaacccbdabcbadaabbcccdadbacaddddcacdcaacddbdbcacdddcbdcbabbacbccacbacaaabccccaabaccacccdddcbacdcdcbcbbaaccccdadacdbaaddaaccccdbacbcbbdbdaddcbdcbbcdcdbaaccddbdbdaddccbcbbbdbcbacbacdbbddcbbbccdbabdadacccdbabbddbdadcacdccdcabcdbdacdaabbcbcbccbdbacdaccaacaadababcdabdcbdbcaadbaacdbacddbdbacabcaadadbccdabcdcdbcbcacdcbbbbadacbdcbcaacbccdbbdbabbddcccaadaaacbbcbbadccccdbbdcaaabbadbaaccbadbaaadbaccdccbbdcccdddabdaccbbcbbbccaaacccdccbcacacddcdaaacaacbaddbbbbabdadaabdbabcddbcdcacabcbabbccbacdbadbcccdcdbaccccacddaacacdaddddbbddabcbdcadcdcadacdddaadddbcdabdbbbbdbdabadacbaddcbdaaacccdbbcacbccbbcaadabbcccdbdabdcbcdbbabdccdcdabdbabdadcdabbacaacdabacadbdacbbccaabccdddbbcbbbbcaabddcaccabbadcbdcbbdacdbdbddacacaabccabdbcdaaddbaccaacabbcbbabddcadbadabdcdccccbcacdcadbbdbaacbadcbddabccdcdcbacdbddbccbcbdbbbbbdcdacaaccabbccbdbbadcdbbbccacaccaabddbbacccdccdabaaaadbacacdbdcaaddddadcaadbdbaddcbddbcbbcdbabdccabbcddddcbaacddcdccbdcaadbdddabaabcdbbaadadbabcbdacacdabadaacabaabbcacadadbdcccdbddaacbdbddbabacadcdcddcacdadabaaddadbadddacacccadbbacdadcbbbcbdcbbcdcccaabbdbbbacbcacddddbccbbabdccdddaccbcddadbabbccabbcadcaaaababaacbabbaadadbacdacdbbaaabbbdddacddcbbdacacdddbaaddaaabdadcaadcbdadccdccdacddbaabcdbaacbbacbaaaddccacacccddccbccaadcdadaacdcbcdcccabcaccbababdccdcddadcdadcabacaccccadcabbadacacbcdbcbcbbcbacbacbbcdcbdbcbcccbdbddcbaaaacdbacadbdaaacbaaabbcaccbdddbaccacaabbaacbdadbacbcbbcbaaabbdaacadcaccbaddbbbbdbdabdcddbadbacbaddbcbcdccdbaabaddacdbdcdadcabbcdabbbbbcadbdbdabcaadabbdcdaddbbcbbbbdbbcdbabaaddbdbdababadcdadcdcbaccdcadcbaacddcbbcdbdaadabddcdaadbbaaddaacabcaaacacbaacacdcdabcbdacccbccabaccccaadacbadcdadbbacdcadddcacbcacbbccdaddcbccaaabcbcbbacaacbcabacbdbbacbccdbbbbbcaacbdcdbbddacbacbaadacdccaabbdbaddabcbbccabdbbccdabdadbbaddccddcdbbacccbabbcbcbccdbbcbaddabdccccadaabbcadbacdababddcadbbddacccccdacdbbbadacdaadcdcbdcbddabadcbcabdbdccbdcddcdadbbbdcadcdabdbcbcccccdaababaacdaabcddabadddcadaabbdcadacaabcdbddcadcadddbbcabcbbcbdcbddcacbbbdccabdccaccdbcbdaacabcbbdccaabddaacdacbccbbcdccabbdcdcdddcccdbddabdccacabcbabbadabacbadcbbddabadabddcbcdbaabccbcaacdbacddddbccabdcdaaacabadcbbccdcdacddabaaabacdbddabbdababacabbbbbaaaadbabdbacbdcacdbdcdccadbdadccbdadabcccaccacbbbbccdbbacbadabbdcbbbcbacacaaadcbdcbabbabdabdccbdadacccddbbbacaadbacbabbcbddacbcbaaaaddbccbbabcdcdddacaabbdaacddbdabaaacbcccddbcbcabaccbccccabbcaddccddbbdbabcbcbcbcbbdbdcabbabcacbbbdddbcbabcbcdbbbdddbbaccdcbcbacddaabacaccbdddcbccdabbcabacbaaacddcbacbbbbdbdbadaababcaacbddacddaaabcabaddcdcabdbabcabdccbabcaccdaabccacdaaabababdaacccbbadabaaaadbacdbdccbaaaddcbdbadbadbcbcacacdadcaddbcdcccdddaabbaaccbbabbadccbcabcaadaccaacaacbdbbdbaaabdadbcaaccddccbddcdbdbbabdcdacbccccbabddbaacdabbbaccabcdbbdaccbabadacbaaddaacacbdddcbccbacddcbcddacbdcdaacccbabbcadbbdabacacbbadcabbbbaddbdabdbcddaaccbbaaddbbcbaadaccbbdbbbadadbcbbaaddcdbcdacccdcbcbcdccdbadbbdcdbcbcdacddbcddabcdaabadbadadbcdadadbcadddadbdddbaaaaccbcbaddcbcbacbacabddcddadadcdbcbccccbcbaddddadbcababdaaabdaadcccbbdbcbadabcbbcacbddbddccbdcbdacdcccbbccbababdbcccabdcdcbcdddccdbcccaadccdcaadbaddcbababbbcbdaccdcdbdaadddbbcbbbbaabcadbbbddababcddbcbcaabcadacabdbadbabcadbbdddbcdbccbadccbabdbbcbcbcdddcacadadcadcdbbcbaaddaabdadcdadadcdcbbcaadaaddcaaacadcddcdbbcbacbdbbcccbbacaabccdcadcbadddadabbdcccbcabbcddbcacdcbbddbbcdbbdbbbdddbcbcdbcadbdaabdddddababcbababccdddccdaaddbcccaacaabccabbacccabddcabdccbabdbaddbccbbcabdbbcbcdcadbbdddbabaacdcacbadddbbdbbcaabccdbccabcbbaacdcbcbdccddbbcdacdbbabdacacccaaabdbaccdaadabcdcbbcbccaabdacccacdbacdaaddcdcdacdbacbbbaccbcccddbcccbcbabcbaaccbbcaabadbcccbccaaaadbddabbaacccdbbbcadcccbdddcbddadccbcbadbacabcccccdcccaabbcaddaccaabbbbbdbcaccacaacbdadaacaacccddbcccbcaababdbdcddbddcbccbcdbdaddcdabcabcdaadcdabbbcccababdbbdddbbcdbdacabcdacacabcddccbbbadabdacccbdcdacaccabdbcacdcadacdcadccadbbcddadcddbdaddcdcdcbdbcdbbadbccaddbdbcccabdabdcdbabddddbdbaddaacbcbadccacbcdcbdadaddbccabcadababdbadbddacaddabdacddabddbbbadbccaabcabddddaabbddbbdcbdcadabbdbaaacababadbcacdbdbbbadbabaddcccbbccccccabdadcdacaacdbcadbbbcdcaabbcdbdbbddcaddddcabacadabccbdcbbabdbdbacacccabbaddcddabdbcbcacbcccacddcbdbdccaadcbdbdbbacadbdaaccbbdbdaabcdcdbdbbbcdcadadbacccddaadadbbccaaaddcddddaadbcacdcdcbabbabbabdacbaddbddcddabaabbdadcaccbabdaabbbaccadccccacadaddbdbddabdadcdcdadcccccadabdcdaaacdaabdcaccbbcbccdacbaccadaddadddbbcccabcabbabccbddcdbdbdcabdbdacdabddbbacdbaacdccbdcabbcdcbbdbddcbbddacdcdcacabdddabbbbcbaddabcddadbdbddaddccabbbdacababadaabbddaccdadcaacbcaaaaadcbbdaacccbbacdabdccacaccccddbabdacabbdbaabbdbbbdcccbcdbdcbacadbdbbbabddbbabcbadcddddcadbbcbbcdabddbbdbcdbbcdddaaddcbccccdcaabcbbadacabaaababaccddacaddcccabacdddcdcabaaddcbbabdccbcaacbaabaddadadadbcbcadcdbddabcacdbbdccbdaccbcaacbbdaaacaccdbaccdadbbaaccdcbcdbadcadadbdddaaccccdddcabbddcaabdbcabdccbbcdbdbbaacbbbddbbddcddbcbbacbacbbbabccadccadbcdbacacbddcdaccddbaddcdddcdbccdbdadacbbdcbababdbdbacdbdbbccadabbdaccdbbccdcacdabcdbdcaaddbbbbddbbaddbaccaadcbdddddabadcbadcdacbcaddbaddcadcacadbcbbcdcccddddaadacdbcdadbdbaddbbdddcdcacccddbaaaadcaabdacdddabccdbcbdcbbbcbcaaddcbdabbdacaacdddbccdbbdcacadaadadbdabdbbbccbaaddbbdcccbdaaccbbbabddcdadccabbbbcbdbddadadaaabcbabcbdddacdcdbdaddbabaabccdbdacaacbbacbcbbdabcabbacabccadccddababddbbdbdbccabdabcdcababcccbadaabcabccbdaadbbcacdbdadaadadaccccacdccbbdddacacddddbadacadcdbdbccacbbbbbcacdcbacbdbbbdaacadacbcbdacddababdabdcbaabbcbadddadcdcdbdbabdbbbbbabbdbcbbdbacbddcccbbaaacdbabdacdcdcabdddadbcbbadcbbdbacbdcdcdaccccdaddccaddbcbcabaaacbaacdabbcdbcdbbcbbbbbbabcbbcdbdcaccdcdadddacbacbdbdabbdcaccdccaadadcabdbadbddbdcbcccccddbcdbcbcdaccbdbbbcbbcabdabbccbbdadbbdbdaacbaabbbcaaccbcccccabaccdbbbaacdacaabaacbbbcabcccadaccdbbbbbacddbbdcbcddccaabbaadaabbbaddbcbcbcbddadadabbdcbbaddcbdcaccccbccaddbcdccbacaadacaadbcbbddbdbdabdcacddabbbddabddaabbbdacaccbbadcdbaaddabccdccccddddbcacabddcbbbbbcabadccdaddbacdbcdabdacbbabbbadadbcbcbabcbadbddcdbddbcbcacdaabddccaddcaaacddadacbbcdbadaabcadcabccbdcccdbddbdaaccdcccbdcdddccacbaddadcbacaabcbabdaaabadcbabaaddcabdadbaccbdaadddaadabbddaabcdaacbabbbcddbdaaabcadbcbdcdacbbcbbacdacdbaacacbcdadbcaddbbbdaadbaccdadbdaabaddddaaabbcbdccdbccccdacabbdcbcaccdbdcbdcaacacccdcdddcaaabbbcdcadcbdbbdbbcdcbcccdacabbaadbabaaccdaccdccbbabddbadbbbbadabdacaaccbbdadaccaddcaaabdcdadbcbdacdbcbaaaccddcbaaaabadccdcaaabcadadbbbaaddccabcbbdbcdbabdaccdcdadbdabacdcadbbbcbacbcaccdcddaddacccbcbddcdccbbbbdbabbdacddccadcaaccdaaabccdbcbacabbcaaabadabbcdbcaaaaddcbadbdaaadccdabcbbbbbcdddadccddabbccbaadbbaaacdbacbcbabddaaaabdbdaadbbaaddccdaddbdcbacdadabcaadaacbdaadadccdadbbcbdbaaacdadbcbcacccbaacdadccddbbadabaddbcaacccaaaccbbcbdcdcbabadcabccaddcabadababcabdcbabddaddddcccacddbdcdcabdddbbbcdcbddbcdcacbdcbbbcaadaddbcdaabcbccdbcbaabdadaacccbcdacadccbabdbdbbcbcbbadabcdadddbbabdbdbdcaabacccadbcdabaabcdbcdcaabcccabadadaacbbbbcbcacbdaaccbbcccdaadcddbabacabccbcdccccdabaaacdbcbdcbdddacbccbbdbccbddbdaacbaaaccdddbcdaadbcdbadddbaaddbbbaddadbdbaaaccbcbcccddbbcbcadddccccccdbabcbacbddcbadbbccdccbabaacadccbddacdbdadadbaacadcabbacbaadcbabaaacaadabdacbcdacccbabbacaabbabaadaababcdadcbadacaabbbcabccdbabcdbacadbadccccacaacbcbdbbbabacbddcbcacdcbcaaddabdbbdcbdbccdccacacccacdbcddbcabbbbbbaacbbbdaacbcccabdbabaccdbcdaaacaabccdddccbbbcababbccdbbabdbbaccccaabbbaabcabadcdcdbaacaddbaadabacddaadcccdcdaabadabcadbcbadaaadabcbaddbadadddaacbbddabacbdbbadabdbccbdadcdbbdbadabdadaaacdacbabbbcdbacabcaaaaabdbabadabaacadbdaadcbdacbbcbcddcccbbcdadacabdadacaaaabbccdbaccbabadddbabadbbdaaacaaccacdbddbdacbaacddcddbdadaacbadccbaddbccdccbbcdcbadcabdabbcbadbcbdbbdddbacaaacbbabbcbdaadbdaaadccaccacccdaabbbcabbbccdadcdbabccabdccaacbdaddadabbdcddbddbddbbdcbbaabaccbbdbabbcaaaabccbdddbbcadabaaabbbdbbdbabadadbcadcdacacdcdcdacbdabaaacdbdacbacbdaddbadacbbdabbbadccdbadaddabbdccbdbbbbbabcccddbbcdbccdcdccccccdcbdddbddadccadcddbaddcabcdbccdddadadbbbabccccaaccbccadabdddccadacbdabadadadbcdabcbcabbbdabcddbddcccacaabbaabdccabdabaaaaacaddabcbadcccbddaacbbbacbccdbabccdbadccacabaacabcbbaadbaacdbccacdbdddbaddabcbccbaccbaacbadaddccbabcddcabbbaaaaccbccabccaabbccbcdbddacbbabaadbcaacdbbaaacacaacaacddaddadcaacddacbcabbcdccadcbcddbbcdcabcdcccbadbccdaacdadbbbbcaadbabdadacbcdbbbddadddcdbdaacabcabbdabbdbbddbddddbcbcabdacabbcdbbbcdcbadadbaadaabcabbabdbdddbbbadaaabbaccccabdadcbbbdabcbcdbacacddccbadbcdddbcbabcbbdcabddcbbabccaaddcdadddbbaccddcaabcdcdaaadcdbbccacbadabcacdcccdcdaddcdadddaabbdbcbababbbddcdcbbbdaabaaccccadacdabbadaaacbdddcbbdbddbadbdaaaabbddcaacbcbadcaadbddaadccbbcdcdcbdccbadcbddbbdaaacbbbbdbdcbabbcdcdbaddbbabbdcddabbcbccbcdaabcbdcdacdddccabacbccacdccbbcabbdacccdadbdacbbdabbdbcabbbdbdcbcddbbdbaaaadbbccdbdbcacdcccdbdbabaaddcddcbbcabcaabdccddcacadcccdbddbdddcddddabaccbcaadadbbcddbbdcdcbadddcabadddbbadaabccbabbcdcbaadbacdcdabdcdacccdaacccbddbacdddadacacbcabaaabbcbbdadaacbdbadcaadbdcdcbadbbadaaccbacacbbcabbdadcbbbbcdbcdbcdcbdbbcdadcaaaaacddcbababbccbbabdbaabbcbdaadabdabccddcacccdaadbccbacbcbbdbdcdccccaddcddddaccaadcdcaddcadbcacbaadbaaccdbccdbbccdcccadacaaadacbbbcaddaadaabdacbdbddbacbcdbdabddadccadcbdddddcbaadbddbabcddaddcddcabcbaddaacbabbbaacbaccbccbdccddadccccadcbababbbccbcdbddcccdccabdcdadabacdcddcacbdaabbcdbddbcbcabbcddabadcccacdadbdaaccaaaadcaaddcbcadccbddbdbcdcdccdabdcaadadccbcbabcbacdcccdccaababbcbbaaabdacdbadbdbadccabaabcbabcbaabbaabcdbabdabbcdbdaabbddbddbabdadbbdbbcdadacbbbcdadcdadccbccddcabaaddbdcdddcdaaacaabddacadaacaaaabcbabbbbcccaabcbcccddbccdccabbbcbbdcddcdddccdcbdbaccdabcacdbbbdccabbcadbcdcadddacabdcadcacbcbddbaddbabbddabddcddbcacdbdaadbadcaabbbadbcbaaaaabbabdbdccddadbcbdcddcadcbbcbbaddabacbcdbccabacccabdbbddadabcdcaacbbccdacadbacbbdacbaaadddcbdaabcbdbcbcdacddadddbdcdcbabacbcdabccaacabdcadbaccaaadaadbbbccdccbdaabdccbcdadbabdaaabaaacbbbaabcaadaaaddcbdbdbdbaccadabaaacdccdbaccacacdccdcbddaccaadbadbadcaaaacacacccddaaabdbddbdbcabdadbdbdcdabcdcaccbabaaaadccddacaddbcccacaaddababaabaaccaacbcadbbcdcddbabbbdacabdaabdadaddbcddcacdbcdbdbccbbdadcddcccdabbcdcccddabbddddcbddcdaacadccaccbaaccbbcddcdadbbcbcdcccadadddadcaddabaddccdbbcabdcbcbdbacacddacdcbddaaaddcbcbcbbbbdaacabcddadaabdabbaadccbbcbabbdbddbaadabdbdbbbaaabcacababcbacabdacbcacbbdabbdcbbbbbbbacccabcdabbbccabadccdababbaadcbabccdcacbbdbcaabddccbbcaabcccaddcdbadcdcbdbcccddcadadacccddccdcdadcbcdcbdbbacadbacdadbcddbabdccddbddbaadabcbbcaaaacdcaacdbccdaccabcbdadcbcadbbbbabccabbadadcdbcdaccbddcacddbdccbbdbbbcadcdcbdbbcdbdbcdcccbcdccdddbbcbdddcdbbacabaababaacdccbdaacbaadbacdaccbbddbdbbaddcabdccbdbdcdcbdbcadbbbbbacdcdaaddabddacacaacacbcdaaaacbbbbdbbadbbccdccacbccbacbaaddbadbbcbcdaabacccaadcccdcdbcacaaddcaacaacbadccbbabbdddabbdacbabbbbdccccabbcababbbdbabcaadccccdaacdcadcbddacccdacbcacdbcbaabccacbbdacaabaaabaacabbdaddcbaaaccbcabbcdaaccbbdcdaabaaccbcddacaddcdbdabcbbdddaabcdabbdbdadadaabddccadbccadcbcdcabcdcbcccbbbbbbbdadcabbbadaaacabbcaacbccbddabbbcaaadbcbbcbbbccabdddaabbcaadbccdccdaaaccaadbdacbaadddcdbbcabbcbdddabbdddcddcbacccbbadabcdcbdbccacabaccdbdbbacdcaaccddabdcbbbbadddcbbcabdcbcdbccdacbabdbadadbdabdacbccbbdcdcdcadbccaacadaadccbabbbdbdabcabaacbabcbbcbbbcdabccabcaacbaadddabdbcccbcccbdbccadcbbcbcccabbdacbcbbbabbcbddcadacadbcaacbbdcdddbddbdbadacbcdadacbbcdbacccbbbdacaabbdbcccacbdcbabdaddbbaadcdccdacacbabcadababbbdcbdcbcacbbabcaacccbdbddaacbdcaddccbadcbbababcacdaddabbbbcdbadabcddddcbdbabccccbddccdbdddccbadcabbbaacddbcadbcbbdcdcadcdacdbbadadddcbbabccaccccdcdcbcbbbabdbddddbdadbcbdaddcaabdcbabcadbccdcbaacccdabaccdbcdcdbcbabddbadaabbcabcdcaacadbacabcbdacbbacbaabbacdadbdddcbbbcbaaacabdcccbdbcccbadcadabaccdcaacdbbabcdcadaaadcbdbddadadcccdabcccdbcbabaadadddcbcbcbcbbcbdaabbacbaaddcddbddbaadcdbddbabccbbcbdddbaacabcdaccdbcabdbdadababddcbddbcabbcacacdbabdcacdbcbbcccbadbbddcddbbbabccaacaccbddbcbddbccaadccddabacbadbcabacdccdabccbbdddccdacdcccaadccaadaaaaabcadcccbaaccadcbadbadcbdacdadbbcddcabdacccacddacaaaadbacadacbdcacbacaddcccdacbabcbdcdacbacdbacccdadccaccdbadcbccbbddabcdbabcbbcbbcdaacbacddabbcbddbacbabbabcabbcaacabbaaaabbcdddbcbaadccadcbabdcaddcbdbabcdadcadadabcdabbbdccdbcccadbacbbddbcdabcdcabbbabbacdddccdcbcbdacbddbdcccbadadabaccdbcccabacbabbccabdacacadccdbbacccbcaabbacacbbaaddbddaccaaacbdcdcaabcaabbdbbcadaccbbbacbdbbbbddaacbcadccaaddcdcbacbabadccddaababdddabbdacccababcbadbdcaddbdacbdaadcdcdbaadccadbdaddadbcbbbbcbcbccacaadddddbbacaccdcdbacddabcbcdadadcbacbbbbdacbaabbcdcaccdbbacbdcbddadbcddacacbbaaadcddacdddbdabbbdacabdbabdcddbdddcbdddacbcacaccbdcacbddcbcdbdacabaccdabdbccccaaadccddcaccdccbcadcdbadacabcdbdcbbdaacbcdaacacdbbdacdbbccbdacaabdbdaaabbcbaadbacbcadbbdaccabdadbbcbbcddabbadabdbcccccbddbddbdacbcbabcdabacaadcbdbcaacabcadcbacbcbcacbadadbdadabcbdbacaaddbdbddbdacbdbbaadccbdadbbcadcadcbbcccddddcadccaccbcacadbbbdcddaadacdbdbadbadddacdcbcbcadbccbcaaabcabcbcdcdadcaaabdcbcdbadabbccdddcdcacaadbdbaaabbbbbbbcbdabdcdbdddacaacaacadaacaadcdaccccbcdabdcabcdccbbcbcabdddbccbabbdcabccbccbbaccabbcdcbbdccabbaabbccbcaabaacbbadbadbdddccaabdbbcdabdcdddddaddadcdcbbbdcbcbabdcacddaccbaddbdbaddddadbcaaadbacacacbaddadadbcbdcbdcabddccdbccbbbcdcdabdcabaabadadccbbdcbacbcbcdcbdcbcdbdaaabbabdcdcddbdcdaabbcddcbcdcdbdbaddcbacbaabdabddcdcaccacadbabaddcddcadcbcbddcdddabbaacabaaacbddbadcabbdadbabcbcbcbbcdbadbacbdbddbcccbdcacdbdaccbbabbadbbddccaccdbbdcbbdaadbaacacadaabacbaabababdcdbaaabcaddaccddaadaccdddbcaddcbccdbddbbbdbbdabdabdabababbccaddcaddbcccddbcaabaabaadbcccbcccabadacbdddbbdcdadbacbbbbbddbccabccbbcdabbbcadddaaaccaccccdbcbdbaaaaacbcdbabaddaddabadcdaadcbdccaadcaabcccccbcabbdbaacdaaaadbbcbaaadcdacbdcdaccacdbbbdbabcbbaddbccbabcadaacacdbccbbacccccacbcaabbabddbdbccdccaacaacbaabdaaaabcbabadccccddadbddbacbacbadcbcdcabbdcddadaacdbddbbcdccdbcaccdddcacccacdcbbaaababbcddcccadcadadcbbbccbcaccabbbdadccbcddddcadcaaabbdbdacbaadaadddbdbadcaaacaadbbbdbabcdbcdcbdbdbdccccadbdcbddbbccbddcdbccabdacbcccdaacbabddbadcabcacacbdcdcbdaccbbddbdcbbdbaabcbcddccabccadaaaacdbcdcccadabcacbcaddcccaacbdbdacbdadcaabddddaaadcbcabcabdaddcbdbdddaabcddbadacbcbcbcaacbbcdcddcbbaaaabbabadaabbdbdccbdcbbaddacbdbbbacbddaaaacbbddcacadbbacdbadcaccdabbabdcabdcacdccbcdccbdcdccbcccaaacaccdddabdbcccddacbadcababacbdbdcbcbdabcadbbabdddbabbddccccbddccbaccdcbdbdbabbdbcbaaadbcbdcbbbdddabbbabababbbaccacdccdbaacacadddbaccdbccdbcdddcbdccaabbcddbcdbccbddcdacacdbaacabbdcbccbabadbcaacabbccbdacbaaaccbbbdcbcdcdacacbddbddabaaabdbbadddabaabdadddbabcddbdabbbbabadadabbacbbcbadcdaabcbbbabadacdcbbacddaccaadcdddaadaaddaddbaabadccbbbbccbabadbdbacbbbaabaacacbbababccccbdcacbabcabddddccbcabbccbbbbdbddcddcacdcccdccbdddcabbadcaacbcdccbaddccbbbaabbdbbaacdbbdcdcdaacbadcdabbbcdbccbcbbdadccbcccadcbaaccdddadcadccbdbdcbdcbccbbacddbbddcbabddbcdcaddcdcdbbdbbdaacdcacdbbcbcbadadcdcabaacabbcbdcccdcdbcabdcdccdccbdbbcdcbcbacabdacbddbbaabcaaaadddabbabdccabdabdcbabacbdccdccbadcddcaddbbbabddcdccddbccbabdccdcddccdbaadcbdcbbbcabadbcaaaacaddddaacdcccacadddabbccababcacddaabddacabdadbbdbaabcaaadccbccddcdbaabadcccbdddabccbbddbaabadcbdcddaddbbbdcadddbbcacddaddbaabcaddbcdabccdcaadaacbabccbdbcbadbacdadddbdacdccadcccdbcbbcdbdcbcbdaacdcdbcbcacccadadbaddddbdabababdaabaddabbdbcaaaccccbcaababcdadccadcbddcaabdcbadbbdddabdadbdcacabcabccccdcacdcaddcddbcbdabdcdccadbacaacbbabbdbbcacdbadbbbaabacadbacdacaadbcbcbdcbddbbaaabadccadddadccbcccdccadcdaddddcaaacadcbddcdabbbadbbcabacabbbbccadddbdbddabadadbdabddabdabadbcaadcbcdbbdbabaaddbadcdcbacbcbdacbbdbaaadbcbdddadbcaadbbbccbaabbbaddcbabccabaaacddcbaddcbdacbcbacbbadbdcbdcadaddcbcadcadadaacbbbbbdbcbbcdddcdddbabbcbababdcbcbddadaabdbbdddbcbaababadcaccbccadbbbbdcbcaadcaaaadddacababacbddabaabacddcbdbcdccacbbddcaccabdbbcabcbcaccddbbacaccabddacdccdabaadbccdacddcccbaabccacbaabddcadcaddaabdddccdcababbdacaaacdcbadcbcbbbccdcaddcbcabdadcbdcabaadbaacbcbddbaccdcaaaaadcccbadcabbdddbbadbdcdcaabdbababccdbdccdbbcbdacabdcddacdddbbabdcddccddcdbcdbdaddaaacabcddcbddcadbcdccdcdbbcababcabccbcaaddcbcbaddbddbcbcbbaccaddcdaacdabacdddacbcacbaddcaacccacdddabbcbddbababcdcbbdbcadadacdbdddaccbdaadcbdabacbadcbdcdcdbdbbdddacdaaccaadbdcabbacbddacccdbaaaddcdabaddcdddcadccdcaaadadaddcdbabbbaccbabcbbbcabbbaacdbdbadbaddacbdbbacaccbaadaddabaaabcbadddcbaabdacbccdddcdacaadbadcccaddcccaacdadacadbdbacbcbbddaddbdbcbbbabcaddbbdaacdaacdcbbacdcbbcbbddbbdccbdcdbadacdcadacddcdadaabbbacbadcdaaabaabacabdbbcacabdbccdaadddcbbdcadccaccadcdcdbaaccbcdcaabcdaacaadbbdadabcdbaadccdaaccbdabdcaacadadabcdddcdadcbabdbcdccbcbbccbcacbcabdcbdbdcdbabcaccccdaacdcdadcadddaccddaadaadbcbdcabbdddddbdcccaaacbbcbdbdccddaadaccbdcbacdbaacccabdcddabdacdcdaabdabccdbabdaabbdaaadbddcadbbbbdbccaccacadcddaddbcadccabbbccbdcdbacddddcbbadbcbdabdcbbadcabdbaccabbdbcdbddbbdbbdbabbddcdcacbcdcdcadbadbbabadccbbddaadddbcdcdcccdcdbbdbcbbacdacacddcdadddcdccbddccdaddaaacacabbacbbacbdcdbddddbaccadaaaccaaaccbcbbdcddccaacacadaaddcdbcbabacbbdcdabadbccdaccccacadcbcdcdabaababaccbcacadaabbcbcdcdaabdacddbbcccbdaaadbadccccacddacdddaabaabbbcaaccbacbcabdcacbbdbcabccdaccadcacbacdddddcbcabdbdabcbbacdcbdadcdcabcccbbaadcbddcbccacbbcdccbaacdabaccdddcccbbcabaccbddccabbcbbcbcbddbdbabcbccbccdddbadbadacbcbddabccccddcbccdddbbaacbdbadcdcadacdcabbbabbabcbbacabaaadabddbaccabadaaacccabdbbacacdcaadcbaaadabdddadadbacbdbcaadaaabcccacbccbbbcdbabbdbbbabbbddbdcabcdacdbdaabddaaaccbdcadabcadbbddcdcbcadbbcdbdadddbacbacbdbdcccdbabadacddcdaaacabdabddabbcdcdcadbcabdbdcddbbaaaadbdaacbaddbdddacacccddcaacaabcccbbbdbaddabcddabbdcadbdccadadacdcaacaccbccbbddaddcdcacaacaaadccccbdcbdcabdbbcbdbdbdddbacbaddcadcaadbababddadbdbaccbcadaabbdcbcddbbabbccddbddcbbcbbdbbdcdbdbbbadcbcdacadbbacabadacdccadcdccbdadadbcbdacdabaadddabcdbadccabadcbabcbabccccbbbcdbdbbbbbbbccddacaddcadcbacbbacbbacccbaabadbbddddaaddbddbdcbccadcabcbcccbbbdabddbdaaadbacdbcaccbbdadcddbcbbcddcdadadcbcaccbabdaadacbdddcbaaccdcdbbadaaaadbdbddddbcdcaaddcbcdcacbadbdadccdbddbcacbbcbddabcdbddaadbccaddbcabadadcabbabdbbccadcdadbbccadbaccdacbddbcbcbddcaccbcdccbbdbdbababcbaadcdabbccddcbbabaddcddcdabcdcddacdabaadabccadbcacbcacaadacdbbadbacccdadacadbdcadcdddabbcdadcaacbccdbdcbccabadbddabaddbacdbbbabdadbacdbacadaaddbbdbcdcacddbccdbccdcabddbccdaadaaabccdccadaabdcccdaabcbdcadcbcadbcdccdddaaadcbdbbbcacadbcacbaabadcbadadaadbabaddaaabadbbcccccbcabbcaaddccabdadcddbacbbccccdccadccaccbdabaddccdcacbaadbbacdbbcbcaabaddbbdbbbabbcbcadbabacdacdddddbacadcabccbbcaabaabbcddacbadbcbcadddabddcbdddcadaccbbdcbbcabccdcdadbdcbadadabaacccdbdcadcdaccdabccbccdccdcccccdaabcdadddadbbaccbcccdbcdbbdaacdadddcdbaadcbbbcdcbabcbcaddaaaccbcdbaabdcadcacdcddddacdbcbbcacdbadbaadadabdaaabbaacdcdcbabcbbbdccbbbbaddcbcbacdbbbadbdacdacadbcdbcccbccccdbaaacdccbbccaddcdcacbdccbcdaddacbcbcababcbabacbadbdaccabcababacbdacaaadcaddcbdddaadbbcdaaaddbacaadbaaacdbadbddcacadcdadcccccdddadbbdbbccdaadddcadacbcabcdcaaabdaadcdcabbadbcadcaccbcaddaadacddbbbddbbcaddbbacdbaabbcadddabcbcadbdadbadabddbddccdbdcacccabddbadbabcabaabdcbacdabaddcbccbabddbdadbbbddbdadaabcbbdbcdbdcabacbabdccaadbdcbdbdadabcacdcaadaddaddbaddcbbdbccbaaddabcabccaccbbccbccdccbbcbaabaadaadcdccaabdccdadbcdacccccadcabbbdddcdadcbcaddcaccdbadabbdcbadbbadccbdccadddaabbccbcabacccadbbcacddcacbabccdcabaccdbccddabacbcbabdcbbddcbdadcbacaaccbcdcdcbbdbbbaacaccbaaddacabbbaccbabbadbabadadbcdadbbccccbbdbbbdbdaccbacdaccacdcbadabcaaddcddabdabcaabbdbbbaadadbbaaaaacbdaabcdabdcbaacccbadbccccabbccdcbdaabcccaccbdcbcbbddaddddacdcbbaadacabacadddcddabbadddbabaaddbddcdaccdbaacbbaacddddddaaaccdcdaddbbacbaaacdaccbbbcbbdabaaccbdcbccbabbcdbcaacacbdbdbcdbabdddadcdccbabdcaaabddddcccacccdaaadadcaaacbaaccdbbdcbbbadaabbcbabdcdcdcaccbcddabdbdcaadbbbdababbaaaacbddbbbdabcdbcbcaaaccdcacabdcccccdcbdbabccabcddccbacdcacdaacdadccbbcdddccdddbadcabaccdddcbadddacbcddadbbcdadcabcbaddcacbbabadcbdadbdcdcccbbaadbdabcbcddadacdcbabbadcaaadadcabcbbabcdbaabaaadacdcdbccdccbcbdddabaadacbdadaddcdabdabdabcbdadbcdccabcabaadddcdcdccacdadbbddbdccdbaabcbcbaddabbaccdbdbacadbdbcdaabbccccacbacabcacdcccbadcbbbdddaddacddbadcbadacbccabcbaabbdcccbdaacdadbdbababbdcddacabadddbcbbbbddddabcccbdcbdcbaaadcdcacadcbcadacdbdbcddaddccaccabdaacdbaacccbcaabcdaddbccdadddcbdaabdaacdabaabbccbcaacabcaaacabbacdcdbacaadbddbddcbddbaaddcdbdcdcbbaaddbbdcdddacbbbbdacacdcaadbbaccdcccadaccddbddddddcddbbdaaaabacbaacabcbdadcaaddcabdaabdcacdccacdbadaaacaacdbddbacabcdcdccbdccddabcaccccaccdbbbaccbcdadddbadbbbcdaccbbbadddcdbbcabccbddbcaddababcdaadabbdddddcbadbbbcbbcbdbabcabbbbddaadaabdccacbbdbcbcddadcccddbcdacdacbbdcdcbcaacbbbbacdcbcacdcbcdbccbaddbcdbcbccbadcabbcdddbaddaccccadccdababbddccbddcdbbbabdcdcbcbbccdadccbaadbddabaccaadbdbadabaddccccdbdbbddbbcabccddbdcacacbcbbcbbacbcacbddcddcacdbaddbdbacdbbadaccdadbbdcdcdaacdcddcabaaabcdcddcbccacdbccadabcadacaacbbaadccbcdbbdadcadaadcdbdddaacddbaacdbbabdcacbcddcaabdcbaaccccdbdbaaaddcdabbcbabadccddccabbddbdbbacdcaaacdddccbdbccbbaaaccdcdbdbdadcbaabccdbcdbdbdccbacdbbdacbcabbadbcdbddaaccdbbbdbdacbccabcbccbbadbccbcacdbdbccbbacdcadacbbccbddbabdbaadcddccddcdabbbdadaaaacbcacccaabcddccdadcbbcccacabbbacdcbacbdddcbcaacccbabadacacbaadccaabddbadadadcbaabdcabbbddccbacdcdaaddcdcddabbdbddacadbdbbccddbddbbabbbabdcccacbdbcbbacbcbbadcbaacddaccbcbbdbdbbdbddbbbdacadccabdbbdabdacddadabaaadbdadadbcbcbccdbcbbcdadccbcccbcaadccbdbdddbdccadcbcddcdbdabbaababbbdbdbbccbaaabcacacaabbdbaccddaaacabbaddadabbdbdcddcbcbdbccadcdddadccbabadcdddcabadcbbcbdabbaabbcbacbbdabddcbadabcabddbbabdbbbcbbbcacabdbaddcdbccdccddaddddbaddddbcabddcbaabcdabdbabadbdbacdabbcbbdcbddccddbabdbddaadaabbadcdbdcbdbcdcccbccdcbdcadbaacccacabcbdadbdddbcdadddaaccabbdccdcbacdadababbddacbabaaabbdbdaccccacdbbcbacbbadddbbccabacaaabdcccdbdddaacbcabcaadbccdcadbcacaadadbcdcddcccccbdaacbacbbdbabddddcacaaccdbcdccdcdbacdbaadabbccaaaadbdccdbcdbdcacadbaabcadaadaabbcccacabddcacdcabaadacccbccbddcdbdcdcdadcbcdcbdbbacbaaaddbbbdcbcbcdabbdcaabcdaabcddbcbdcbdbabdcbccbdcaccaaadcbcbbadabdccabdadaccdbdccbbccdabddcadcaabddadbdbabaaadcdddbaaccbdbdacaccadcdddbbcdcababcacbaabdbdaaaabcbacddccadbddbbcaaadbcabddcccbcbdbcdaacbcdcddcdcdddccbcddccbcdcaacacdbbdaacdcabcdbbacccbddbdbdbdadabbbcdcaddcaddaddaddccbaddabcbbddaccbbcdbaabdccddcbcbabadbacaacbccdabcdadddcbddaaaadadcbbadbcaacadcbcabcbbddbacabcbaadddabdbaccbadddbbbddaadbddacdcbcdbcdcbccbdbbcaadbacaabaadadaccdabdcabadbcbacdaadbbaabbdbbbadcbddacbcccabcbdbdcddcbbbadcadcccadddcbdaacdadbcbdcdbaaaaacdccaabbabcbacadbccccaaadacdaaabcaacabdccdacbddabbadcbbaaadbdcbbdadddadddbbcdadcabbcaaaadbbbcdaabbbabbaacbbbddabdbcdabbabbbdcdaaadabdbccbbdadbcaadddbbbcaacadacccaacaadcdcbcccadbbbbbbccacdddbacdacbcdbddbdadddbdbdbbccccbccaadbbddaaddcccbbaccaaacbdbabdbcdcacbbacbcdbccaabbdabbcaabccdccbcaadcdccaacadacacdbdbcdbacadabbacbadcbcadccbdaacdbcccababacadadaddbadabbaccbadcaabadbaaadccbcddacccbadacdcbdcbdbcdbbadacabcaaadaddbcacccabccabccddbabbbacccacdbacacdbaccadbccddddacaddacadddcbdaddcccdbdbadcadadcdbcaddacdcaaaabdcdcaadcbadabbbddbabdcbcabbbbadbaddccccddbdcadadccdadbbcbdaadbcabbbacccdccddaddcabcdbdacbacbabdaddaabdcaacacaacbbacccbcaaddcbdbdbbbaaddbbddbdcacbdacbaadaddbddabaaaaacabcdbcbadacccbacdabbaacaaaadbccccaddcabadbcddbbadcdabdbbabbbbcbacdabdbbaacadcaadaddcdaaabbabaaaaacaccababccbaaaaaaddcdccbcaabdbdbdbbdddbbccadbaaabaddbccbdadaaabdcbbdaabcdbbbbcdcaabdabaabcaccaaadacbdaaabdaabddcdcbdcabcabcdddbbddcdbcdcabaddbabdaabdaccdcbcadaabcddbabbabcccdacaacbcaadcdcdcdcaadaaadaabbdacbddbdcdbdabdaccddcdacdadacccbabcbbdcccbabccdccbdacddcccbddcbcdaaabcccdbdbbccaddadabddcbddbbdcbcccabacbaababcdccdbbadaddadaaadcbbdbcaaddcccbbaabdbdbaccdddcadbbdaaaaaabaccddadccadaadaaddaadaccccbaccaacaabdcbddbbcbbacdbddaaadbbcccccaddcadadbcdacbdbcddcabddccacabdbdcdccbcddbacaabdbaacaadadcaddccbcddabacaadabcdbcdbcabdadaadbdcbaddbabcdcbbdbddbdbdaaabdbbcacbdcdadddcabdcccdabccaddabbadcbbbcbcaddadacaccbccbacaababbdabdddbdcdcbadcabbabdddddcbabbcdcbbbdaabcaadccdacbbadabababdaaccbdaabbcdcabbcabcdabaddacacdcadbddbbacabbccdbddcabcdcdbbacbdbbadbcbccbcdddcacaddbabaacddabbcaacbbddcbcdaadbaccaabbacddaacbcbcadddabcdaaaaadaabbabadbacccaacbbddccbdcadccaabbdacbaabbdddbaaacdddabacbbcbbacaaabcadcddaaaacccabadaddbbcabbbcbacbaacddccbdcabcccaaccadcbbdbbbbcbcccdbdccccabcdacbabacadbbbaadbaaccdcaddddcdcddadcbcdbcbcbaaadaccbdbdcdacabdbcaadbbabdcbcabadbcdcdbbbadacdbaaadbbabbccdccdddbaaabacaadbadccabaacdcbcdbdabcbabcbbcccacabddacdbdbbbdbbdcbbbacccdaaaacccababbccddbbacdbabacdbadcbacacacdccdbaacaddcbadabababbccabaabadccadaccddacbbdbcbaddacacbabbdcdabdcbdccbbcadcabcabccdabdcdbcccdbbccddcaddaadaddcbdccadbccacddcabaaaadacbaccbdaabdbcccaaabacacadbddcbccabcccbaadabdaacbbbaaacaddcdcddbccbbdbabcdcbddccddaccbacaccdcdadcaccdadcdbaddccddcdabdabbbdbdbdcdbabaccbdadaddbcabcdabdddcabddadbacacabdbbbcccbcccabbabbcbacaaadccbdddabddbdbddacadbabdbcbcdbddabcbabbcbcbabccadacaaabaabbbccbccabcccadbbbaabdcbadbabaaddcccdaadaccdbdbcccdcdcabbcaabdadbcbcddcdcbbdacbadcddacaababbdccccdcbbdacbcadccbdabadccbcbbdccacddacabcdbdccbcbcaaabddbbacaacdadaabababccaacccdccbacacabbdabdcadcaaccbccdbdaaccccdadaccaddcaacddbcacbdddcaddbcddddccbdaadddacbddcbcabacabcabddbdcaaacaadbccbdcccabdbdccccabaddaabaadbbccddbaaadabbabaaaadabdbaadcdaabdbbabbddddaacacccdcabcacbbdddabccbcabababcaadddbddccccbddbdadcdabcbcdcbbaaaabbdaacabddabbdabddabcbbaacdaacaaaaadaaddddacadcdadaadbcbacbcadcbcdcadaccdaddbadadcacbcddaccccdacdddbcddabcdbbadadaadacbbadabdababccdcbcbaddaccbdadddcddbcccbaadcbbdacddbbcbaadbcbdcbcabbbcddcbbbbadddbbdcadbdddaacbaaccbcdacddaadbabdcbbdacaaacacbbadabddabccbbddabbaaacbbdccaacacdbadbaccdbacbccabacbddbbdcdbcadddddbccacacbadadccabaccacbdbaaadaddcdcdadaabdabbaadadbcadbcbcdaabcddddccdaaabbadaddabddbadacbccbdbacbddbdccddbacbcdbddcbbdbccbbacccabdaaacdabcaccacbbbabdbbbabbbdcbbdcccacdabcadddadddcdaccaaadcbbcaddacdddabadccbabdaacbdacacbcbddcaccccbaabbaaddbbbacbcddcaadbcccccaacbcbabdbdbcbdbaddcaadbbadaacdbadcbadaabbcdcccbcacdcddababcdcadcdcbddacbcdcdbbdbddbbcccaabaccdaaaccbaadcbcaacccbddbcadacabcadcbdbaacdcbabbbddaacabacabdddadaaabbcaaadbccbdcbdcbabbdcbdaabcacddbbbadccbcabbddbcbbccbaddccdbdccccbaaccbbbaadbabcabcbaabdadacdbacddbbaccdbccbaaadaaddacaccaacbcabcabcdddcaabadbbccdbcbcbababcdcbacabcbaaabbcddbacbcbcbccabdacbdbacccabdbccdcaddbbcacdcbabaaadccbacdadcbdacaaaddaacbababbddababcbabbdcbacddddaddabdddcdabdcabbcddbdccaddbdabdddccdaccabdcaaabcaaaccbdadcbabbddbabddbcacdacdbcdbdbabcbaddadcadbcbddcbacdbddbdabdbcbdbdcccddbbacacdabbcccabbabcbacdcacbcdddbabddccdbabbdaacdbddbcdccdbdbcddbabcbdcbaadabcdddbbbcbabdbcbacdacdbccacdddbcdddbcaacbacdabbadbadcddaaabcbadcbbacacdcabdbbadaccbcbccdaadddcacdbabbcbaacdbdcbbabbbcadadddbcbdaaaddadaaddbdbdabdcccaaadbabcaaaddbdcbdbdadcacdcbcbcbaabdddddbbcbbaaaadcadccccabcddbdbdbbcdbbabbbdabcaabacddbddaddccdbaabbaadcccbbbdbbcddcacaacdbdcccdcadccbcbcbbaaabddcdccbcbcddcbadbdcaddcccaadbbddcbccaccbbcbcdacccbbcbcdcdbadadbacbdcbbacaadaadabbcccbbccbddadacabcbddbcbbbadcdbcbdadadadadbbadabdaabbcadaccdbbbcddcabdaaadddbaccadcadccbccccaabbcdcbacbdbbaabaadcccdbbaadabcbacbdabbcdacdcaaccaddcaabacdacdbbcdbcaaccdddbaabbacdbbcdacddbabcdadbbbbbaadddbcaccbacbddabbaabcbadaacabaaccbdacbbddcbacdbbcaddacddbccbcbcdbcdabacccbdbadbccbbaabdbbdadccccbabdcbbbdbdcaacadcaccbbbbabddaaadacddbacccaacdadbadbabaabbdadbddddbbcdcaccaadbbddaccacabdcbccadddcbdaacdadbcacbbabddcdbbdcdadbbddacdddbdadadcabbbbbbddacabcbcadadcaadcdcaddbbadbbbdcccadaaabadcddabbacbbacbbbacbbcbaaabcbcacaccdcbcccdccaccabcbdabbaccbbbabccbdacdcdabdbbccabdcabaccdcddcbbdacdccdccbddcbadcbdcbdddbbacadcdabcacacacbacdadcccaccbbbbbabbaadacacbcbddcaabbabbbabacdbcdabdbcddddccdacaabaddcdbdabbabacdadbbbdbcacdbddcdaadaadbcdcdcccbbcbdaddabaadacaabdabbabbdddbddcaaacbddabddbdddabdcccdcacbcadddbbcadabbbbbbcdbdbccadaccacadaacaccdcacabdccacaddcadcbbdacbcbcbacaddacdcdcabdcdddabbaddacaadccddddcbaddcbaadcdaccdcdabdabbabdabbdabbbdcdacadbaaddacbcdcbdadcabbbccbbddadcccaaacbaddcdbccddcbadbbbbdcbaaacbadcdacbdcdaadbbbaadabbacdcdacbaccbbabbccdddaaddbbccdcaadccddcabbcbabcdddbdabcdcccbbbcdcbbbacdadbbcaaccddabbdaabdccbbbaabcbbbdbbddccdaaaadaacbccdcacbbaabcdacabdcbbddbbbbddbbcbaddabcbcbbcdbbcaadbbadccddbadbcdbddacddbbbcbddabacbcacabbdddbcacbabcdcdcbadcdcdcbcadddbcbccdbbccdaaaacbcbddacbcaaccbddacaadcdaabadaccbabbdcbdbcbaaadbabddabcdacbbdddbabcaddcdcabdcbdccbabcdddacadaadcaabbcdbbccbdabbcbbbadbdcadacdcbbabbcdbdcdaabcbdddccadabaadadcdcaabcaccdccbbbcdddcddabdabbbcadabcdbdabcbabbaccaddbcbaaaadcdcacababacbdacdcddbbbcddbcdacdbccaaadbcddadccdbcddcbbdccccddbdaabbbdbbcdccaaaacadadccdcdccadbaacdaabbcbbaabbdaccdaaccaaddbbbbabcacccaaadcbbabaaaddabddadadbcbacdbdcddcabadbbbaaaaddcccbadabdabacdcddcaacbddbaacbdbcbdccbacdbbcbbcdccbccaabdccddabbcbbadddcbaaddcdbdbacdddaaadbddbccdcddadcdcddbbcdcdababcabbcdabddbcdcdddcdcaadccdbcacdbdbccbcaabdbbdcdccdbacdcbbddadadabdadadbcbcacabbbdcbaccabcacddbabddccddcbbdbaddccccccdaaddcabbbcccccdaaacbadcbbdaadcadabbbdddabdcccbcbdccdabadaaddaccdbadccbacdadaddaddaacababccaacabbbacdccacdddbaaadbcdbaacadcdcbabaccabcbadadbaaddaaabcadaccddccdaddbabdbdcdcdcbaadcbbbdaccaaccdaacbbdbcbacdacbcdbdabbbdbcdbcdddacbdbdacbccccbacddddccbdacadcbbbcbcbabcaabacadbcabdbccbbdcaaacdaccddcbccdcdcbdbaadcccabdcadbdcbccccbadaabaadcbcaaaadaabbbcbdaddbdcbdbabccbccdacbccbdaddbcccbdbdbcbcccdacccbbdddacdddcbbbddaddddadadcabdccddddcbadbbccbcbdddbdbcaddbadcabdbdccbccabacbccddcbcaccbbaabbbbdadbacbacaaddabadacdadaadcdddbdcddbacbbaadcabbdadaddacbadaabdcbaaadcbacccabbcddcadadbcbcabdaabbdccdadbdccbbcbadcadbadaddaccabdbcacadcbbbcdabcacdaadbadcddcccadccdddacacdadacccbaadaccadacbcdabaaccadcabbbccddbbbddcbbccdabdacdacdcabbdacbdcbdcaaabcbccbdddabcdbaddbaacabdcababddbcaadabbbbaabbabbcbdcccbccbbcdabacbdcdbcabcbbbcdccbdcbabaabcacaddccddaabcdbcbdbbddbddcddcbcccbdbdabcbcdcbbcdabacbdabbdcccdcbdcdccdadcbbcbbbddabbccadcbdddaaadcaadbdadddabbdbdcddcacbcabbabccbdaddabbbdcbcaddbcaacccbadabbadbdbccddcdabadddcdacbaddbcbbbbddbbaaacbdadcccdcaddcbdddadcccababdbbdabaadcddbbadbbbdbdccabaabbcbacababdaaabaddddabcbbdadcacabcaadacccbcbaadbabbcdacabaddaacbdccbdcbddcbaaddcacdbacbbaacbbacadcaddbadacbacaabdbbbdcacababadcddadbcabdcbccaccccbbacaadbabccabbbddcdcccdcabcbdcddaddcaaacbcbbcaaadadbdacadcccbaddccbcdbaccdaaadbaadcbadbbbcadabbbcadaadbdadadbcbdadbcaabdcddaccdaddbdcccbabacbcbaabdcdabddccadcdddaadcdadcbcabacddaabdccadbbcccabdcaaddddbabbddadcbacadcacacaaadadabbddbbcbcdadbaabbdbaacbbadccdcabbbdabbdaaacbaaabcbbaddccdcacbadddaadcbdcbbcdccbbaaacbdccddbacdbcbacdaaddcbadcaccbbddaddaccadacbdbdadbdabdbadddaaaacdcdabcabbdbabdadabddddbccdddadbacdadbaacdabbcdcdcadbbbdcbbcabdbdcccabdcabcdddbcdddbbbbccaababdbbaaccbbdaacaddabccbbdabbccaaacbcbdddaddbadcddadcdaccdddaaddcadadbbbbccbbabdcbdacbdaacaabbcacabadcadcadacccdbcdcaadabccdadbdcbcbbaaccbadcbbaadaaacdcdaddcabcbdccabadacaadcabaadaccaaaccaabcbcdddcbadcdbcdbcbbbbbaaaabaaddadbaaaccabbcbcdacabacacbdcbaddacadddbabdcbbcbdccbabccdbcddaccbabdcacdcdcdacabcbcdaaabbaacbcddcccbabaabbabddbbbacaccbbdcbcadbbcdbaccabacabcddcadbaadbbdaacadddbbddcaadaddbcadcabacadbacdbdcbaadadcbbcdacadbbbdcdbbadddacdaccaaddbadadcccbabcbbbaabdabcabcbbdbcabbabbcdbdabdbcbacbacbbadcadaddacbdddaadbcbbdbbcbdcbbacadaabcdcbbbbbdbaadacabcaacccbdcabadabbbbccbdbcbdadaaaaaabbaacbabacabdccbbabacacbabbbdadcacbdbadaccacccbacddbadcbbdaadbadbacbadbdabaacdabcacbbbacbcadacbbbdcacdacbbccadbabbbccabcbadddaacaacdbdacbbdbdbabaabccdcbcbbaadaabdccdadccccbcdbadacddbacaddcddaccaacccabbdadccdbdccddddcbbddddcacabcbdacddcbcabddacacdaacbbdbdcbcbcdababbddcdcabdbdcaacbaaddbddcdacbcccaaadabdbdacbbccbacccbaabccdccacccbadabbbdaadcaaaccccbacbbacadccdcbcadbdbababbbaabdcdadcddacccacaaaadcbdcabbcbbbdbbddbaaadaddcadadcdaadccddccdbdcbadacdacdccaabbbbadbbdbbdaabcccbbdcdadcdcdcaaaddbddacddccaaacdcdacbbdbcbdcccbdbdcccbacbcbcaccacabdccdbbbddaacdcdbbdcbabaaddbadbdcaacdcdcdbdcadaabddcaabddacbbbaadbbbddaddbbacadbbdcddbddbaadbcdbabbbbaaaddcdaabddcdccabaadcccbcccacaccbbaacccdbdcaabbacaaadbcdbddbbcabdcddbccccacacaddbbaaddcbddcbcabdcdcdabdbcdaadadbccaacccaaacaabaabdcacabdabcadbadaaddacaadcaabddbdcccccdabdabccbacaabbabdadbbcbbcbacaacbbddbbdacacdcadbbdacdcbcdccaaabcddabdcadaccdcaacdbbbadbcacddacbdaaddcccccacabdbddacbbdbbaaabbccddadabdacdacbabddddacabbbbabbadabaacaacbacacbabcdcadcddaddddbbbbbacbdadbaadcbaabdccabcbadaddcaadbbabdcabbacdbdbdabcddcbdbadddbdddbcdbbaabbcbaaaddcdcbbccacbadcbaadcbcacacacbdaacacaacbdbabbaacadacdccbbbcbbacbdacaccbdddcdbaaddacbccbcccdbcbbcacccccdadadcaabbdddacbbacabadcaacaabdadaabcbbddcdacbddcabdbbacaccaddbcbccdcbdaaadaacdadbdcddbacbddbacdbcdcdbcaacbacdcbdbddccbcbaabcbaabccccdddccccbdcdcbcbcbbadcdacdbacdbaccabccabbddbcdacbcddcbdadcbacbbdbccadaaccbaadbabacbbcbbdbbbabbaabcadaaabbcabaaccaacdacdddcbaddddaaadcbbbbdcdadcbcbdabdccdcbcdacabdabdaddccdadaaddacbcdbdccdbdbbcabcbdcadcaababdaabbcacdadbcaadacccddcdbadacbdbbadcacadabadbbacbcccccdcabcdacbaddccdcabbabadbcdbcddacbddddccbddbdabbdaadcbababcdddbdcbbaaddaaaddaadbdbbcaacddcbcdacaadcbabbbcaacdabbdaaadaaadbbddaacdaccdbccbbbdbdddddaddbdcadbadabcbcbadcbaabbbcaabdbbcbdcbbbbaabbbbcbbdcbbddddacbdddbabcababbbdaaccacbdbbddcccbccabacbbbbcdcadaacbbcdaccdadcdbbbbacaadaacaadcccccaabdbdbcdaacdaabbdccadbcdbbcbadbabdcccddcacaaacbaaacdadbbdcacbddcbdbbcdaaacabbbaccdaddaacbcabaccbabbcdbdabccccabbbbdcbbdddacaccccaabdbbbabccbddbbcccacaaaaaabbbdcbddadcabdaaccadadbbbdcbbdcbccbaadccbdaabcdcccadddddccabccdaabdadabddbaadaadcaadaccbcbdaacbababcddcdbccaddabacabcacccdadcadcaacaccbbadccbaadcaaababcaddbabdaaaaddbbbcbdbaacdaccbacaacccbabaabddbbdccacaadcbaacbbcbadacacadddbcdcbcbbddabacacaadbcccbbdadbacbccddddcdbbdddcabddddabcbcacdcabcacaddcdbdccbcccacbaadabadababbabaaaabdbdacbcacacacdabbbabbddbacbcdbbbabdcccacddbaaddcadadbdbdaccbbdcaabdddcbbbbbcacbadbaacbbacaaacbbdddbadcccdcccbcdcdacccbcbcdbbddcccbdbdcbaaababbabdabdbadbadaddcbcdaabcaadbcbbdccaadddbaccbaaccbaabcaabbbbddacadcabbbcaccaddabacbdaacbabbcdcacbccacabadabbdccbdadcccbadbadcdcbdcabbdaabbbccccbcbccadaddaacababaddbabddbcddcccaabacccbaccdcadcaabccddaadadbadccbcabcaabbaadadbbbacdbacabcddacbbcaadacaddaaacdbccccacdaccbadcbaadccacbbdaabcadddacbabbbaadaadbaadabdddabcaaadadadabcdbdbccbbadcacabcdbbbdaacdadbddbccdccbdbccdbaacdccabaadbbbaadccabdabacaabacbadabadcdddcabdaccbbcbbabddcbdaaadabdcddcaddbcdaabbaaaacbbabcbbacccbaacadabadbadadbbccbdbcddddcbddcdbcaadacabcabababddcaacaaaadccbcaaccddabcdcdcacdaddaabbaaacbdaabaccacbadcabbddabaabdcddabbacdaaacacacccdddcbacdacdccbbcacdcabdbdaaadadbdcbdbaddbadbabdaacaccdadbdbbbdcacdabadcdcadcbacaadadbcbcadbabadbdcabbbaaaaddabdddbcdcdaaccaacdccaadadacabcdabcadbbacaddadccdcccdcccadcdcaccdcdbbcbddbcabadcbabcabbbddabdbdacdaddcccbbcdcadacdaccdddbdabbdcdadabaacbadababdadadcdbcbdbbdbcddbabcdabdcbcdbcacabdcbcaacbdddacdbcccdddbcacbacbcccbcbcbbdadddbbcaabcdbdbbdabbbdbdccadddccbcbbbddadadadabbabddbcdabccadcddbdbbddbddcddcccdaddbccddacbbdddbccbddbbbbcdcabdccbcccdbcbbaabbbccbdabadcdbbbacbbccaaabbbbcccbaabcaccaccbbadacbbbaddcbddbaadbaadcbdbcddbbdbbdbbcbaadbcdbdcbbcbadaacbddbabcbbcbccdcccbddbcccddcbbaccbdcaccbdbbbcdbcccbcbccccbbbdcaabaccabbcabbddcadbabdaaddbaccbbddbabdcbcddabddbbcbbbabbacdcaddbccbcccabacadcddcddacdbacdbabbdacbdcccdcdddccbbbcccdcbabacccacadcdccbcdacbdbbaadaabbadcdbbcdcadabdccdbcdabbcadcacbcbaaacabbadccdbdaabccdcaacbbbdabcbbddbcaddcacdbbbdbabbcbaddabacdbadddcdcabadcbdbaddabadbcabbdddbcbcacbbbdabddabacaccbcabccadadcbcaacdabcbabdcaacdacbbccddddbcdcbddccbaadddcbcaaacacaacbbaabcdcbdabcbccbdadaabbbdcbdbaadacaccadbaaddcaabdbabdaddccdaccbbcabaababccbadcadbdacbdacbbadbcccbdbbdccaadcacabbaadcbabacabbdcaaaaabdacccbdcbcabdbcacdababbbcbddabdbdacdcddabaabaccaccbcdacbcddbcbacaacaddabccdcbbdcdaabbcbacacbdaddcdadaaaabdbcbaadbdcabdaaaadabacaaccdabddabadcbbbcaadbddacbdadaacadcbcdddbcbabdddbabbbdabaaacdccddbdbdcaabcaddaccbbacbccccbcbabbacdaabdabaacbdbaadcbcccbbdccbdddbbdcbcbaacdcdaccaacbcdcacdadddcccdadbbdbbcbdacbbcdbcbcdbbaddbdaacabdcacdcbdacaabbbcbbbbaabdbccccbcdcbaabbcabdcdddacccadcdabdbabdcdccbdaadcddbaabdddadcdbcdbdcbcacdbcdcbbdcacabccccbbacdcccbcaadcccabbaabcaaadadbadbbbadbdadcdacbcccbdacacdbcdccddbddacdddccadcadccbcdcdcaddbbaadaddccdaaaacacdccadcabacacbcbcdaddbdcbaaaaabcdabacbdaacabcbbccaccccbcccbcbdcabaaaaacdbccccdbcbcbdbdcaabbcbdbaaaaabbbcabcccbababcdadacabaabcbcbccbabdadcabacbcdbccdbcbdbacbdbaadbadccadbdccdacdbcadaccadbbbddadcdaccbbdcbacdbbcaddadbdbacabccbcacdabcbbaaddaabddcdbcabbdcbdaabcabbbddddcddaddababcdbddddbcabcddbbbababccadaccadddbdbdbacaddadaaacdacaaddccbaddbcdadcaaacdbbbbbadabcbbdabbbbbdbcdbbddcccccaaaddcdddcbcddcabdccdabddbdaacadbdbbcadacaddcddcbcbbddadaaccaabcbdadaddcabcacddbcbabbbbdcbbbbdcddcbddccbdccbbddbdbabbaaabdcdaccacbadcaaacddadcadacadbbcdbaaddabdcbbadaaabdcbcccaddbccdbcbbbabdcbaccdcbadddaacbbabacddcabdbcaddbdbcdcaabbdccbddccdadbdccbcababddcabccacabdccddacdcbcaaddaaaabbdadcbbcbaaabbddbadccaaacadcadcbbacdbcdbbdadbcddaaacdbcaaccdddccbcbdcbaaabaccabcccacccdcdbcbbbabdadaddabccdbaacccbadabdaadbcadbbdcdaaabdbbbcaadcabbdcbbbccbdbcabccadabbcbbbdddddccbcabacbbbdbcdadabcadadaccbabbddbbbccbabcbddaccdadbaacdaaadccdbbbaaccbdbaabbabaadddcbaddcdcabcdbabddaadacddbdaaadaaabadabadacdacbbbabcccccbbdacababdbabbaabcacbacbbbccbdbadcdcdcbbdcbdadcababddaabccabaaacaddcaccdcddbcabdbccaabadcccdabcbbbcbbbbccbabbbccabaabacbdcabbdbdbaadacbccbacaaadcacdbbbbacbacbdddcaaabdcdacbddcabdcabbddcdbdcbbababacbaddbddbbdcbbcaabadbbcbacbabbabcdbcabbdacbbcccdaaabaaacacbddcdcdcbcbccabadaddbcbcacbacdcbddaacbdccabbbcadddaccacaabbdccbccdbbbaccbccdccddcaacbcdcadcabcaabacddcdbdbdcbbdcaaacacdbbdbcaaaadbabdcbcaadcccdacccbadbdaadbcbacdbaadcbaadadbbbddabcdbdcabdcdaaddcabbccababcbdbcbccbdcbacccdcdddbdcdbcbdcbacbccdadddabbdbdaacdcddacbddbbbccaaacbbcadbdbcbddcccabcacacdbacdcccdabbddccdbcbddaabadbdcbacadcacbbbbbacdccdcccdcddccadcdcabcccbcbdabdbdcadaaabdcddbabbaacbdbabdbbacbaddaabacabaddcdccaacccdbadabddabdcacadaadbaaddcccbcbadadbbacbdabccdcbdddbbbccaacaabdbcadccdadbbadbacadcbccbadadbdddccacbcbbabdbbdbaccdcdbbbbbdbaccaabadbabcaadccccacababdbcabdbdbdcabbdaccadbbcbcdcadbbbbaddacbabdbcacaaacbaabcaddbdaabdaddccdbdcaaccaacbaccbcacacbcabcabdbacdcaaddacddcbdacdbdccbbdddcdbaabcbccdbbabdbccacdbdaccdacbbddbbbbdbdddcadcaabdcabbacacaddcabbccbdaadcacacbdaadddccabddcccbbdcdadadaddaabdbdadccaaaddcadabcacdabbadbdcdbbcacddccbcaabbadccacbcabaabcaaadbcbdbacadbacdbbbcacadbbcbcdaddbcabcaaadbaabadaccdcddcbddbadacbbdcabababddbaacaaabbdadddbcbcbcddcbbabbdcdcdbdbccacddcdcccbbabcaadbccbbcddabddabbddbcddbcbcbaacccddcbcadcacdbbbccbddaaddabbadababcbadbccdaddbbbdaacaadbadbdaccdacdcccaccdadbdbddadaccadcabdaddbdcdadadbbabcdbcadddcacabdbbdcdaccddddbbbbcbabbbddbbabddcbdbcdadbcddbcabcabcccbcdadacdbbacddcdddcaddddaadbbaccbaddbadacabbabbaababcbcbcaaaaaadacddbbbccaadbdaccdbdbabdacbbcabadcdcdaadbaabddaddbdaddaaaabacbacdaaaccccdcbcccbabcbacaddbbbcacbccbdcaddcbdbbbacbacdabadbbdbdcccdbabadddcdbabcdbccaddabcaacdcbbcdabadcbccdcbbbadadcbcdbdbacdbbbabddbbdcadddbabcdaccbcacbccadccddbbcaacaabcdbabacdacbcacdbdababdbcadcbcdccdcadbddcadcabdccdaaaaacdcddaaaccddacbcabcdabdcacabdaccdabdcccbcbbbddadcbbcbabadcabdbacdbdabaaaabcacaabccccdccaaacccdcabcdddcbaadcdbcaabdbdaddacddcbdacbacdbccaccbbdcbcccdacbdbbabcdbbabcbbbdaddbabdbdcaacadbdaadacdcbddbabcccacdcbcaacbdcccdabdddccabaaadcbbccbcaabdbaaccbacabcbbdddcacdbbaccdadcbdbcdccbddddbaddccbacdbccbaacbddcdbdaccbadddaaabcbacbbdacdcddadcbbcdbdabaccabbbdddaadbbdaddcdaaabcddbaadabddccbacaadcadcdbbbcadabaaacacadacaaaddbcbcbaddcccaaacdbcadcbbdabdbdccbdccdabbcdcadccbcdbadcdbbbbbcadbcaadccaabaadddcdbcccdbbdcadbbcdadccdbaabaacbbabcddbabaccccdadadccadacdbdcbabbbaccadccabdcacbddaaddcbbabbdadacbcdccadbcddcdbdabbaadcacabadcdccdbcacdcbaaabbbabbcddccacddbacabcbddbcaccbacbdcccbddaaaacccbadbacadbbdbdbabaddddbbbddbcabdabcbcbabcccccdadcdcccdadbdbbadbadcbaadbdcbccdbcdacdddddcdadddbcacdacbcdbaccbcbaabaccccdcdbcaaacbabdcddacdbbdaddbbdbdccbcaadddccccdddacadcaadccccdabcdcbbacbcddbaddcccbaaadcaaacaaabdbddabbbbaccddcaaacdbdbacacddbddaabaaadcdaabdacacbdcaabbaaacdacacbbcbabbcbaabadadcbdabacbaabbcdcdabdacacbaadbdaccdccdbaabccccaabdaacabdddbbcadcdcdcdabcaccbbdbcdcacbdbacbdbadddddaaddaacdcbacbbaaadcabbcdcbdbccbdabbabbdaabbdbdcdbadbabcbdbbbdacdadcbcaadaabbcabbdbdcbbdacacdaabaabbcbacbcbdaadbadbbbdabcdccbbcbbdbcabcbadccaacbbdcccbabbbaaaddabdacaacadaadcbcdbaaaddabcdaccbacbabdabdbadcaaacaabddcbacacdaddaaababaaddaadbadbcbdddbabddaacbcbbbaabddccbcdddbbdccbabcbcccccbaabcbacbbadbacbbbadabcdcaabcabcccddcaababccbddcaabdaadbdbadaacccadabdbdaacabbdbadbdcaccdcdbadbccbbccddaaaabddcaddbdbbbddaaabbbbbabbccbdabbcbbbabaadabadbcdbaaccaaabcdaaacbbcddacdcdaccbadaddbaabdbaacdcdabcbccdcddbbadbaaccbcacaadddaaacabdcacbacdcacbdaadbabbaaaaaadbaabadabdcbaabacacddcddcdbaccbddacadcbaccddbcbabacdbacbddababdcacccdcbaabbcdcbbdbaacaadddbabbaddbacacdaccdaadaabcaacddcbcaccdcddacbadbccabaddbdaaddabbccbcbbabbdcbcabbdcbdacbdaaaddbbdacbbcaaaabbcdbcaddcdcbcbccddaccbddacaacabcbbdbddcdbccabdcbcacadcacbdcddcddbaccabacadaacccbdbdcacacbbbadbbccaaacbbccdcaaccdbaccacabdcccccdacddacadbdccdbcdcbcbbbbbcdabcaacabbdccaacbbbcbbcadbdadccbabaacccbadbdbbddccacbdabcadbcbabdcbadbcaadaabddcaaaacccbaaadccaabdcbaddaccdadacccaadbbdcaaabcaabdbdcbbdbbbbccaddcbddacbadbccccbcbcacacbccdcddcabcdbdcbaabdbdcdcccacccbdbbdacabcabaccbccdbdbdbcdbbdbdadbaccbddbcbbbabbadcbbcdcddccccdabdbacdabbbbcadccddcdbdddabaabddbddcaacadcbccbaaacacdbaabaacbdcbcbdbaacabbddcdadbaccbdcdddbdbdccddacacaddabdcdcddcaaaddaddaabbbbbcbbcdaabcbababbcbdcddadcaaabbcdabacabadddcdaadaabadbdddbcacbabdcbaddcddcdacbddbbdddacabdbccccbabbcbcabdddcadccbcabdcacddacdcbcdccbacabddabacaaabbdadddcaccaddbabbcbbaccaaabacccdadacbdababdbbbdcaacdaddbdabcacabdbcadcbdcadabcdbadacaabcbcdddcbaadbabbdbadcacaaadaddaadabcccbdcbbdbcaababcdccddcddbcacbaaaddbcdbccdacdbdbcdcaddbccbabbcbcadbbbcbbbdccdbbacdbbdddcbcaaacadabcaadcdacaabcdabbcaddbabdacbcbaadbdccaaadacdacadacdaabdaccdaaccdbcaacacacbaadccdbccdbccbbababbabddbbacbbcaacbbbddbdcddbcdaaaacbdaacdbacccabdaabddacaacddddcdccdcaddbcabdabcbbbdaadbdbabccdababcaabcbaaabacdbacbacdabbbdacccbdbabccabccdcacdccaddabddabdaabaddbbdbadcacbbccaadbcaadbbdddbaaadadbdcbcdabcaddadaccaaddabaccbbaadccbcdcbbbaabaabacbcbcdaccddcdbdcccbababdcdbabdddddcbcbdcacaacacccbabaacacccabcadcdcddaabababcccadaccdcdadbcccacaabbaacbdcccbbddcbcccadacbdcdabdcdccbcdcdddccdbccdacdddbcddcccdababadcbbbccbbadbcccdaabdcadccbadddbcdcadbaaadbaccbcdabbbbcbccddadbaaaccbadacbcdabdbdbabdddbbaddaddacbcddbcadbcbddcadcacddcacbaabcbadbcacdcbadbcccbdacadbbdcdccddcbcdacbccadccdccacdaaaabbaaadbdadbadcbbbdbbcaaaaadaabccbdadbcadacccaadbbccaabcacdcdbabaaaddcbbdbdccbbadcbbdbddccbcadadccddddaacdbccadaaaddcdbacacdbddbddcaaccbdbdddbbdacbbdcddadcbacaadaacaccdacbdadcbbcaccccabadbdccccaadddddcabccbaadadabddabdcbacadbccdabbbdccccbadbdbdcbbcacadbcacccdcacadccdbbbcbdabdbbddbdacdcbcadbbbbddaccbaccccccbcdadccccacccdaacbacacbccaaabccccccabcbcbccccbbabbadbcbdbbaabdbbbbdcbbbbccdccabbbddcddccaaccabacdcaddcabcaddcddaaaaaabbacbbdddcaaccdabaadddbcbcbcccabdbcbbbbdacaadacdddaddbcbcdbdbbabcdcdaccbcccbaabcbbbdbdddadbcaadbcddadcabbabddabdbaccdbbdbdaddabbcbbbddddadadcaaabcccdacdccdbdaabababbcdbaababbdabddcbabddcbcaabddbabddcaaaababcbcddcbcdddccbdabbdacbcbcddacbbadcdbcacdabcaccbbbccbdbdddacdbbbdbacacdbcdcbadbdcdcdcaababdacabbbbcdbdbaddaddcdaabdbcccbcbcbabdbdbaacccdccadaddaabbdcbcacccbddbcdbcdbbcabcdcaacbbdcdcccdddacbdcbaaadcaaddcdaadaaabcadbbcaaccddabdcbaabcdadccccbcddacdadcddbbacaddbdaddabdaddbccaadccccdcaaaaadcbdcbacddabdadddcdddcddbbadcdcadaacdcbacaaaddbcccbcbddcacbcbcaababdbbcacadbccdabcbadddbaadbbbddccbbbacdbbdbbcdbbdaaacadbcaadabbbadaccbcbccabccaadddddaccdbbdbabdabbadcadbcdcacbcdbdaaccddccabdaadcbcddbcdabdabdddadbcbddbadadacbbcbddabdbaabbdbbadabaaccacaabaabcaacabaaddabcbcaccbdadbdadaccdaaaddcadcaabaddcdbbdaacbacdbdbabbbadadbbcbbbcdbccdbddbdaddbbacccdacdcccdcadabddddbccbbbdbadcabcbbcdabdaadacaccaddadcddbddbaabddabbaaadcdaddbddaccacdcaabadbdbbdccadaaaddddabbcacccabdccbccdbcddbddaccddcbdbddbababcbcdddabaadcbadadcbabbbdacbbcdaacabadbcbdbdcdaaacccddbcaaabccbaabadbddcdccababaccdbddbbabbbccdbadccaabbabdaccbbddbacabdccdcbdccdadbcaaabddaccdcdbbbbadbaacbdbcbacdaaccbacdcabdbdbddbdaccbaabccbadddabbdcabbcbcaccbaabcbabcdbcdbcddaabbbbaabddacdcdaccacacbbdbbddacacdadccadbbdbaacbcdcbacbacbbdaaccacbbcdccdbcbacadcdcabddaabdbaccaaaadadcdbcdcddbdcdbcaabdabacaacdadaccccaabdbababaaaddbadcdadbabdddcacabbaccaacabbaadbdabdaccaadbaddcabbaabcdcdbbcabdabcaaaccabddbbadcccbbddbdddddcddbaaabccbdabccdbcdbbddbcaccbdbdbdccbdcdaaabcaacaddcdcbdbddadbcdbacdcaadbadbbbddbcbbdabbdccdddbabbacbbcccbcdcaddacacddccadcbbdccacbdadbdbcbdccabccddbdbaddbccabdbbddcddcdcccbdcdcbaaacabdadbcbdcdabacbbcaadabcaabddaabbcabbcbdadaacbdbcccbadaababdaabbcdcaccacbcdbbbbbccbcbaddccccdbbbbdccbadbcabbbcbcbcdcacbbbdaccbbddccdccdadbaabdcdbbdaaaadcbdcdccdddccddcbacaddbbbdadabdbbbadbcaacdcaadbaadbcdcacccaacbbbccbdcdacaadbbddadcbddadbcacbddcabacbdaadbadddabcdaacdbadbcabcdbaacadccbbacadcdaadbadcbadaddbdbdbddccadbcddcabaacbcbcbbcdccddaaaddcaaabdcddcadbddbdcabcccabaaaccddaaabaababcbacdabdddcbcbbbabbdaddabdcddaacdabbabcdabdcbcbcbcdbabdcdbddbdcaabbaadabbadbcadbabcdaaccabcccdbbdccaabbabdacbbaccdbabcdbacccbaadcbccbdbacbcdbbaccdbbcdcdadddcabbddabdccaadbbacddcccdacddddcabdbacddbdbabaccdbbdadcccaaddcbcadccdcadabaadddcdaaddcbcbcdcacdaddacdbcbdbbaabbdccdddaaaaaacbdbaddcccbcddcbcabccaacbdbcdbcabddcddaaaaddabcbabacdbabdbaddbababaaacdbaccbccccdbbbbdbbcdacdccbdcccdcdaaaabacdadabadddaaaaabcbaaaccbaaacabccabaaadcbcabaababdabbdddcdaaddbbcadabcdccbbadcccccbbaacdaaabbaddccdaabcdbaacbabacacacdcccadbdccddaadbbdbdbbdcbcddcbdadcddddaccbcdbacbaaacccaccbcdaccbbacbccddcdbddddabcabcacccdbcaacbaabdbabccccdbdbdadaaaaaddacbddaccccccdbdddcdbdbbcdacbcaccaabcdcbccdaaacaaddbdadaccdbbaadddacbdccadcdcbababcaacbbccbabcddaabcdbbbbcbabcdcccaaccadbcabbabbdadbdbdadbdcccdaabbddacabdcaaaabdbbaadacbddcbdadcaaadbbddabbcdbdacdbcdbcaabbbcabcddbaddabddcbdcadbddccdddcbcabdbbcaccdcadbcccccaaaadbaadababdcbaddcbadbbdcccdcdbcbdbcacaadaddbbccdcddadbacccbdbdbbbddacdacddbdcdaadacdccbdcdaddabdbbdcdcbaaaaaaacdbbabcacddadccddacacaaddabadabcabdbcaaabbcadbbbcaacadddcbdbcaacadbcbcddabacbbcbdacdacbdbdbcdcbcacddcaaaaaddadabdaaabbdcdabbbcbadbbdacaaabdadcccdcdbacdcbcbcadcdcabacaadccccbccadcddabcacadabdcdacdaddabddcaacaaddddbbbabadcaadaadbcabcdcdbaacdcbddbbaabcaddbcbdccdcbdaacdaacaacbacdadbbcdcaababcdacbdaacdabddbccaccadbbdbabadaaaaddaddadabcabbbacabcccbcdbaadacdbbbcdccbbbacbaccbdbbdbbddadaccbccbacacabccdcadbadbcdcbccacdbcccdbbddbaaddabcaacabbacdcdacddccdcbccdcaadbdcddcabdaacadbccaacccddaaadcdccabbaacaddaccddbbbbcbadcdcaccbdbdababbbcbdbabbabccccaccbbcabbbababdbdcbbbdcdcddabccacddddcbdcbbbbbdcdacabbcadddccdcdbdacbbadaacabddaaacbdaaddadcdcbdaddbddcbaabcdcccdbacdadaabcaacacbcdccbaabacdccdbccccdaccccaababacbbacddcddadccbdcadbacdaadaacbddcdabcdcdccddcbaabbbacdbaacabbdabaddaadbbbaddcdaccddcdcdcbabdcddbabdbbcadabbcddadcbcabadcbadbcaadbbbaacabadbbdadaddbddbccbbcacdbdaabdaccbbbbbdcbcbbbbbaabaaabaacddbabbdccadaadcbdadbadacbbabddabbdbdacadbbcbdacaaaddadbdaddaabacaabadcadccabbbdbabcdcabdcadccadcdcdbadbbbbdbbcccacddaccbdcdcaccbbbcddadaccacbbaddcddccdbaadcacbbcaaaaaacbdcdbcdbcdbccddddccaacdacddbccadcdadcabdabcadcaaddaaacbadcdadcbccdcccbcbdbbbcbadabbdcaaaaacccbabacbbbacbdcadcbdbdbcbaddccdbbaacdcabcdbbbbdccbccaaacccabaccaaadadcbbdbacddcadcaaddbccddacdbaabccdadabacbabbcdbccdbdcdadacbcacadadcbaccaaaabbadddcaaacabbccbddcaadcaddbcaadabbcdbacaccddabbcabaccadbbbbaaddbbbacaaadabdbcdbdbcaddcaadacabdbddcbcccacccbabbbacabdacbacdccbdabbbdcbabbdddbddabcbcacaabbdbcdbccabbabddcacacbccdbcccddabbdbdcbaabcbccddbadcbcbdaccabbabdbadabbdbdbdcbcbcbccddcddcddbbcadbbbabaabcddbcdbadacccdbacaddcdccadadcdacbbaabcbbacaabbddbcccddcadcdaaaccbbccccddaaccdccadcdcbaacaaabdaddbaadcaacacddbdcdaadccabaadacaddbbcbacdbbdcaddadcbbdcbcbbbbdaacbbdcaddbcdcdcdaaccdaddcdcbbadaabdbbdaadacbdbbabddcbabdccaaaabacacadcddacadababcbaacdcdcdbaccabccdcdcadcdabdbadbaabbdccbdadbbaaaacbaddcadbbcdaaaddddbcaaababbbaccbadbcadacbddcabbcbcdbbdaacbcbccdbdaabaabbbbcccbadadbdbbadbdabdbcdcadbbbbadacaadadbcbdddcaabcbbabaccaaacddcaacbdbdbbcbadbbbdadbabdababcbaaaaabacaaccbcdbadccbcaaaccdbbdddabccacdbddcabadbdacacaaddbbdadaacdbadbcbccbdabdcdcdddabccbcbbcaddcdbdadabdabaabdddcdacddcbcbcaddcadaacadddccadbdabcddbbcbddbbacbbdcdadaacdccbddbccdcddcdbcdbcdbdbacbdabaaaabcdbbadadadcaddcacccbdccacdcdddbccdbacbbddbcdcdcadbacbddabcdcddbcadacabdcbddabcbbdbbcaaaddccdcaddabcccccdbdbabccdcccadaaaacbbbcbabbaddcaacaaabdbdcabbadcbcaabcaabddbccacaabaddcdbcbcccadbbccbddadcabaddddadbadbcdbbdaccadbabcdbddcdbbdbacadcccabccaadaaccaaccabcbccabbcccbccabcdcbadcbdaacbaabbbacbbadbbbcacdbbbbaadddaccaaddabccbcdcacdbcdbcabbbbaaabcdbdccbddbccaaccbddaaabcacddccadaaddcbdbcacdadbdccbbdccdcccbddbcdddbdccddddcaacdadabaadacaaadbabcaaaacccbdabbbcadadabdaaadcbcdcbadaaddadabbcaccaddcadcdddbdbddcbabbbdacabbcadbbbcbcdbdaadacabbdacaaccdbacbcbadaaababdaacddbdcdacaadbbbbaabddbddbacdbdddbddbcddbbccddaaadcbbbbbdcbaaaabcacdcdacabdcabccbbbaadbadbdcccbacddcbcacbdbcbdcdacdccdcabcdabcccabcdabdaabbaaaaadabbbbdaccacdaabbdbbcbcbcabbdaacdabbdaadcbabbaabbadccaccbcbcbbccdcdbbdcdbabdbabccdcddacdaaacdcbaabacdadcbdcdaccbaddbccaabdcadcacdcbadbbaddcacdbadbbadcaaacabbbccbcbcbabbccbbcabacbcbdccdbbcdadccaccbacbabccaccadcdacbbbbdacabdcccaabddbabaaacccdadabdcbdcdbbcbabbdbbabbdcdacabcadaaabadbddabccddbabdaaacaadbdabddbcddcdaacaacbaaccdacbabcbdbdadcdcadddaaabbccdddaadabcddcccddadabbbbabccbabcbbcdccacaccdbabddcdadcccccbbbadacacadbacddaddcaabdbcbaadacbdbaaccbadbadaddcdcaccdaaaaabbbcbcaaccbccdadccbdcdcaacacadcdadbbbacbdaacbacacdabcbbbccdcdccaabadddbbbbbbcacadddbadbabcbacdacdcddbbadadcdbdacdcacabdcbaabcddcddcaaadbaddbbabadbacbdccccbabaaacbadacdabbcaabdbbadabcabdcdcdacdacdaaabbdbadbbbbcaaabcdacccbcbcadcdbaacdcadcbbcdddbcadbacbcddbaaaaaddacbcdbcadabbbabcbaaadbacadabdabdcccbddddabdcdcdaaacdcadcabbacdcbabddbcbccdbdabbdadbacabbcdbacbbdabcddddddcbdacdcacdccaddddaddadbdbdaabddbcbddcadbbddaddabbcddddbbadbdccbcddabcddbabdcadbcbabcacaacdccdaacababbbbccdacbadaadccccaddaabbabaadcbccbadaccacbddcdabadddcaaabbababcdcacabdbabcccdcccbcdbcdbbbbaabccabddadbcabdbddbbadddcdbbbacbaacdabcbcbbddadabcadacbdbdcbbaadcdabaccccabadcdabccacabcbddbddabbccdbbadbabdadcaacbaccabacbaaacbddaacdbdbcbdadbaaccdabdadabdaacbaddddbbcaccdbdbbaaacbacbaaadbddcccbccababaaccbdbaddbcdcaacdadcadacdcacaacccdbbcddbddaddadbadcadddbaabcbdbaabdccaddccddbddbacbdccdaadbccdbadcacaabbadccddcaaaacbbcbdbbadccccbcbdbcbcbcbabaccdccaabbcccaddabddbaccbacbddbdbadccdcdaacdbccbdddcbbcadcccdadabadbcabbbddacacddabcbdabbbaddbcdbddbdccaaccbdbcdccddaccdacacabdacdbdabdcbbddacbdbdaddcaabccdbbacbdadaabccdaddddcdbaabbddcbbadcabbbdbddbaaabbacdbbbaadabbddaadcddbbdcaadbcaaccaccdacbaddccabbcdbabcccaacbccdaaaaabbbbbccbbdaadcdbbbdacabcccdcbbdcbcbabaabdaabbcbcdcbdacacabcbbaccbdbcdbabdbdcdacddcddbccdbaaaaddbddbbabdbbcbbcdcbbccabdcdbbdbbaadbdcbaabccddbcaadbbaabacdbdbcbaadadcdcaabbdabcbbabdccdbabbabbcdcbdcdadbbdcdbdbcadadaacdacbbcddbccdbdbcdacccccbaaabaccbdcadcdadbbaabcaabdbacabcaddbdbcdcdabbacacadddbabbddcddbacaacadacccbaacbbbcbadccbbbdbddadabcdbcaacaddadcabcadbdabcabbdabdbbbcdaadcacaaacaaabccddccdcbabdbcbddddacacadaccaacdcbbddadccaabdbddccbbaccdcdaadbaabdbbcdadddcaacaccbdbbaaddcacabadbdddbbccccaddadddabcddbdbdbacbacacbdaacaaaaddddcabcabccaaabcdcbadcaaabdddcdadcbbbaddcbcbbaaaacccabacbbcabcbcdcdbcbacdbaabbcbcaacabadaabaacabadabbbccbcbcaccdbadddaddcdcddaaccddabdacdabcbdbabdbcdbcadbddcaddddbcdcdbacbcbdbaadcbadcdbbaabbcbbcaaaadcdbbbdcbabcbcdaccdbbddcbbdbdcaacdddaccaddaccabaadbdaacabacbabbdaadbddbcbdaacbacdcaabdbcbbbaacddacdabcbcbccaaaccdacbabbacbcddcdccdddababcbbccbbccabbccbcbbdccbadaadbdddadbccdbaaadbdcacccaabbcbbddbacabaadccabbcbccddadddddccccaacaacccbbcdbbadddbdaabcacdaddcdddabbcaddabbaccbadacacacbaccbadbcacbaaacdcdbccdacccdbbdaddababddddbdbdababaaaabdcabdbadcaddbabcdcbcbaabdcdbbbbdbacacddacabddbaacdcdbcbccccabcdbbdcbabdbdbdaaacdcadbddabcddddcdacbdbbdacccbbabaabacbcbcdbabcbacabdbbabcaabaaddccdcbacadcbccccbbcdcbbcbacabacbbacdbcacddacaaadbaabccdacbabddbdcbaacddbdbcddbbdacbacbdbbbcaaabbdcbacdbdacabdaddbbccbbccccabdcaadabdbddaacdcbbbbcaabbccbdcbdcbcddacdacbbdacbabbbccddabddaccbccccadacbaacbdddcbbbbabcbbcacbddcddddbcdbbaadcbcdcdbbaccaddabcdacbdccdbbcddbdabcacbcdbadacdbbcabccabdbdddabcbbccbbbcbcabcaabadbccdbaacacbcbadbbbbbabcdcadcdddaadadcacadcacacddbdbcdaccacacbbbcaacbcccdcbaaabdacdaabadcccdbabbddabcaaaabdbdacbdababbdcaddacccdaabcddadccbdabddaabdbbcdadbcbaddaddbcbaccdaccdbdcadcddcbdccddaccccbbbbcccdddbcbdddbadaacbdcddbdcdacabbbbabcbcdbbdcbacabdabcddbacdadccbbcadccddcdcbcdcbcadabdcaccbaadaccdbaccdddacdbabbcadcbdbbdcabdacadbbacaaaaccccacacdaabdaddcabbcdcbddabacdcdddacdbbddcacdbcbcddadaddbbbbcbabacbbdbabcaacaaabaabadaabddddccadbbdcbcdadbbdcdccdbcadbadbdabcbdbcadddcbbdbdacbbcaaababbdddcdbbbacccdabdbcbdcadadbdacadbbcbdabacbcddadadabbbbcddcbaabbcaabcaddcdcbbcbbbabacabdacadcdbaabdddcaccbcbcabcacdcadcacdcbcaddbbacccdbacbcdcbcacdcdcbabacbacaddcadaddbacadddadacbcbccadcabbdbdaccbaabcbaacddadaddbaaccabbacacccccdddbacccabcddbbcdcabaddcbdcdbbbbbaabccaabdddacbacccbadacaabbadccaccbccdcaabbaacacdbdbcbabddccbbabdddddbbcacaccdbddbabaacbabacddbcabddcabbddcdddcccbabbcbaccaddabcaaaaddabacabdadaadbcdadacddbacabdddbcbdbdcddbbdccdabdabbbccccbcbcaadacbdaaaacdccccbdcbbcbadadcdadcabaddddbbaaaadcbdcbbbbadacaccbdbbdaaabccccddabcacbbcbccdcdddcdcdabccaccddccccddbaadbcdaaddcdbaaabddbdcddcddbbaabbcdddbcdaacbdbdadacbcccbadbaccbaaadaabddbddacbdccdcddccaaabaabddadbcccccaaababaddaabbbdbccbaaaaccdabcadbcddcabbdbabadccdccbdbbacddbcdbcaaabbcdbbabbbddbcdbdbbbbbcdbdcadbcaccaadcdddcdbdccacbbdadbdadadbbadbadcddbbadaaaabbbddcbaaababaaddbccaabbcbbcdabcbdcdcbcdadcadabacbdaaaddcbdaaadbcacbcddcdbcacdaabdbccacdcdcdcaccaabbcddbacbccaccbbcbccaadddaadadbdbcbccabbdbbcbccadddaadcacaddcacccbcadbdcadbccdcbcdcbccbaaabbadacbadbddcaacdcacbcdacbcdcbbdbcbbacbaadbcadcdbccdcacdbbabdcdcadbbadcacaddaabcdbdaadadcbbddbabbabddcddcabdaacaaddbcacacdadbddbadbadadbcdbbddadcdcbdbdcadccabcbdbaddcdbbcbbaabaabdbdacacadbabaadaddbcdbdbabbbaacadbbacccdbdacddabaaacbcbacdbcbbacbabbabccabbaacdadbdadbbddcdcbbaabddcadcbdacaaadadcdbcbddbbcdbddbcaacdbacadcddbaaccdbcbdcdcbcaccaccadbadddcbdbdbddcbadddaabdaaabcabacbbdbdbcbcdbbbbdbabacaaaabdcadbabbbaadbcadadabccbcbbddbbaccaadbdcbdbcdbadcabadaccacbdabbbbadcaaaadaccbbaddcbadddacdbabbaabbbabcbadaaaadadcdcbdadddddaabaacbabcddbcacdacaccdddacddcbccaacaacdacccadbbcdaabdddbddabdcabcbddaabcadaaacabbddbaadabbdaaacccaabcccbaaccdabdbdbdbabccdbbbadbbaadcdccabcccadcbbbbddaddbabcbbcacaaabdbccadcadabaaabadddbacbabacdbdaaadadcadacadcdaacaabccabcbbaaadbacbcbddcdbabcdbdcdbbcbdddbabbbccdadbdadcacbbdcbaabcbcaabcbabdddacdbbbadbadabcdaccabccadccaabccbbababbadbcabdadcdadcccbccbcdadbdabadbadbbacbadcacaacccdcabdcccadadacbbccccdccaddbcbbbaddaadbccddaddbccbbadcaddccddccbdddcadbbdcdbdcbaccacddbcbcbdddccbabcacbabcccbdaabdaccabcaccdadaddbcbacdddaabccdbdcdcadaddddbbcadbddcdbcabacdcbbddddddbbccbbdbbbbacaabdcddacddccdcbaccdaaaaaabacdcccababbabdadbacacbbdbaaddaaaccbbdbacabaacbacadbbaaddcdcacaacbbdacdcabddbbdabccadacacaccacddddaddabcddcabaccbcaaacabdaccdacadccadacccccdaddcbdaccdddcbdbadcacbcaaabbaaccbcbcadcaccdacaccaddbcdcbbadbdbbdaccacabddacaabbcbdbacddbdaddabddacadadbbdbacadcabcdbaaaabbdaabdadcacaaccbcbdbcbdcaaaabdcacccabbcccbcddcababcacaaabbacadccddcbacacabcbcbbdcdddaccbddabaadabbbabbdbbadacbdcdaaabaacdbbacccccbcdcaccbbcaaaaacccbddcbccdccdacaccbcdbcadbdabbdadbabdcccabbdbadbdcdbacbdcdbdabcbbadbbcbcbadacacbdabcbacbbbadcbddabccbcacbadcacdaddcacdadbbbabbdbdabccbcddcdcbbcadbadaaaabbbcbacacbacdbccbabccbabadbbadbadbdaaaaccdbddddbddccdaccbddbcadbabbdbdaddacccbdcbbadbabdabdccdcccbcdccccccacdaaabbbaabbbcadddccbaabbdaaaacababbcdbcbdcbaaaaaacbdabbabadcccbcdaababaddacaccaaadcaaaaacabcdbccbbbabababbccbbbbdddddcddbadcdabacbdabbdbbdbabcbbaaacddaadaddccddcdabdbddabbcacddbcdcbccbcbbdabccdcbacabcdcddbaacbcaaacddbabbbcacabdbdcddbcccdacddcaaaddbcbbcadacabdcadddcbbaddacaadacaccabcabbbdabdcdcabdbbcddabdacbbdbccccdbccaabddabdadadaacdbaabbbbcbacdddbdaadadcbbaabbdcbdbaaaabcdcbbbdcdabaacdcadbccccdaadddcadddcbbdbddddaccccadbaabdcdccacccaacbcaccbaabbbbaadcdacbaaaababbdccccaacdabaacacccadccddccbdbabbacdadcbddbdcaacbaabbcadbcdabadadbcaacbbbdadcabdbdbcacabcdcaacdaccbdccbdbdcddbabadccdbabdbacdaaccccddccdcaabccadabbaaccaccbbadbcaaaabcdcabcccbbdbacbdbcacbabbaaaccaaacacadbbddaaacbccdacbbbdaaccdbbdddbccadaabcaadcbbdbdbbbcadbccbdabaaddacbaacdbdcbbbacbdcbbddcbbaadabaacabbdcaaacdbaacbddccaabccddabcdcacabcacabccbcabcbacadabcbcccbbbacddddacdaddaaaddaadcbaadcadddadcadbdcbaadccbcaabccbcdbabdcbabbddddbcbcbbdbbabbdadcdaaadbcddbaabcaaabbcccbbacacadbdabccadccbcbabcadbaddabdbbdcdbaabdaacbccbabdccadcdbddbbbdbacdaadcadbcbaacdddddcacaaddbcdbdaccbbbacddbcbdcabdbddbbdbdbdcccacdaabadacccacaabccccddcbbcacbdadaddccaabcdcaabbbdddadbdcccaacdbcdbbdbbcdcbccdddbbcacdcdcabddddcbcbccacdcbbabaadbabbddcaabbaadbacbdaaacbdcbcbddbccccabdabdbadbbbbadbcccdcbcbdbacbdbacdcbdbcdddaccacdadcdccadbdadccaaacbbacdacabbaadcadbbadaddabcccabdccddcdaddcbdcdcacccadbacccaabccdbddcccbddddcbcdccbabcacaddbdbbabccacbbccbdbbcdaadbdbdabdcddcadbaadbabcbaacdcbaacdacccdacbacbadbbdbbdaacddbcabbadbbadddbabbddddacaacdbbdacbbacddcdadbcbcbaadbaaaccdbacbbbabddbbbbcddcbadaddbcdcaadccabaaacadddbbbddaabcddbbadaacabbbaadadbadbccadbcbcdacaddaaabcdbabccbcbddbabcbbdbbcacaaabddccccdbababacbdddadcdddadbbbcdcccacabccdaddabbcddadbcbcbacbdbdcbcdadcbadbcaadaaaadcdaddacccdadcdcdcbdaccbbdabcbaccacbdbdbbdadbcdcbbbcadaddbdddddabbbbdacabcddbdbadbdbcddcbacabcbbccdbdbdadcbdddbbccdbddabbaabdbddcaacbbcccddacacbcaaabcbcabaacdbcaadbbcadaacddddaaacabdcaadbabbbbbbcdadbdccabadcacccabaccdbbccbabdcbbdcbacbacdbcbdbbbcdaacccbcacddaddcadcacbddbbddddcbddcccacbadabdcdaaddbcddccbbbcabaabbbaacdcbcddaadacdabccbddacdddbbbdcccbdbcdcbccdbddcbabcadbabdcabacacdabcdcbdbdaadccdbdddccbbcdaaabcbbddcdaacddbbbbbaabbcdbddbddbbabbccacdbcccdaddcdbbaddcdbaddbdbdddccbbddabcdcdcabdacddaddccdbaadbcbcdddabcbbdaaabdbbcbddacbcdabbdcccddcdabbcaacbccaccabacbadacbadbadabbdadbdcbcbccabbaccccbcbddbcadabbbbcbcddcddcabbbdbcbcccadadacadbbadbdbdbcbdbdbababacbdaadcccbabcdcbdacbdabdaaabaadadcadbabddbbdadcbadddccbbbbdbacddacabdabbbcccccbaacdbccdcbcaddacbaadcbacacddbbccdabdaddddcbdacdbaadbbbcbdddbddbadacadbabcbaaddcabaadaadabdcccacddadbbdaddcbdcaacccbcadadadcccdadbcbccaacbccabbddccbcbbaaadacabddcadacbccbbdcbccdcabcbadcdcbcaccaabbbcdabbcddbbcbbdbcabbbadcbabbdbbcbcbdacdbbdddcbbacaaadcdaccadbbadbccbcbdadbacdbaaccacababadcbadcbdcdbbcddabadaaccadbacaaddbbdcbbdbacbbbdccabbcccdcdbdbbacacbaadcbdddbcdcbbbdcccddbbadabbaccaadabddacadaaaccccdaddbacacababbdddbaabddacdddababbaddcacdbaacadcdcdbcdbbcdbbbdcacbbabdcbbbbcdaaaacdcddbacdaddbdaabdddccbcaccbadccbddadbdcbddccbadbaaddcdbcbaaabcbaccddcaaadbbdcdabdbbdcabaabcdcdcccbcdbacdccbcddbcaababbbbabbccbbddadaaabddcbbbbabbdbbbabdddccddcddcbccbadbbbcdaaadaabcadbbbdacbbabbababcccbadccadcbadcacaabaaabacabdbaaddbcabacdbcbbbcbdbcacbcacdbacbddbddcabaabcbdaccbdcdbabaacdbcaabdbaddcccdddcdcaddbaadcbcdcadbddbdbaabdabcdaabbbabccddddbddcddacddbbabbcaccbcdcaddaddbaabadabccbabcdcbcbdabdadccbbbbcccbbcbadbabdbadaccdacdbdababcdbdbbbadcdbbcddddccbabbcaccbddcaddbccbcaacbabaaadacdaadababaabbbdabaddbababcaaccaccbcdbadcabadcadbacabccbdaabddcbddcacdacbcdccdcdaccbcaccbcbcbbccdcaadbdccddcadabddccabcbbabdbddbacbdacdcaadcbadccdcbacabbabacbdacabaaadadbcbdbbcbadcadcdcabdaccddcbddbdacdaccbdddddddcddbcbaccbdbabcbddccadccddcbccddabbaaaccbbdaddcabbbbccbbbadcdbaaddbcdccabadacabdadabdcccabaabcddabbaabbddacccdabcbddbbabdacaccbbabdbddabdbcdddbddadbdbdddbadababadbaabcadbbdbbbbbcdbcddcbbacaacdcdcbbabbabddcbccaccbababbcdbbbbcacdaddaaabbbdbcbbbabccdaacdbbadbadabbddaddddcbbdbcbccbbbbabacdccdbbbdcaadabbaadabbaaddbcdbccaccdaacbacaccadadcaadcdaddcdccadadbcbbdcaacbddccadcdaccbaacdadcacdbdbdbaaaccadddcbabdabacbacadbaddbbbdbadccadacbaccbdadccdbccdaaadadaadcaccddcbcbddcbaabbabdabcabbbdcbbabaabbcaaadbcadadabaabbadccddcbdadbddbddbaadbcadabadbacdbbaadacddabdcbcdbabcdabbacabacccabbcabcdadbbabcacdbcbbbdbbcddccbccdcadbbadacbabacabcaddcdcdcdbadbddcbabbdabcadadaadbcabcdbcacddbddcbaabbbdbdcdbdabddaadccccaabccbabccdcabdbccadcdcbdabdaaaddbcbccdbdddbcbadaaabaaacdcbddddccaabdcbbdbbacdbbaccadabcccadbddabaddbcdcadbadcbbbcdadcabddbdbdcccbcccdcdcccbdddbaddaaaccdbccaadabbaabacdaccdaadbdcccadcabbdbcdcddcaccacccbbdcabbbacccccaacdacabcdadcccccacbabacadacabccbaabbacbcdcbabacacddddcadcbaddbacdbcbdccdacdbabcabdcdbbdacbaabaaccbadcacdddcdadddabaabbbdccccbbdcbaabdbaadbddbbcdaaccdcbaabbddacaacadcbbcbbaaabababbabdaabccbcaaaccdbdcaadbbdcbabcabcccdaacbdbbbbaaaaadaacdcbdadddcbadabbbdddcacddcdcbddcdbaadacdacadacbcacbaabaacbbadddabaabcdbcddbddabbbacdbacabbbbbddcddacdbccdadacbdadbbbdacadcaaadcaccbacdbbadcabcddcaacdcadccbcbdabbbbdcdcaaddbcaabbbaabdaadbbcdadacccdbacacdadadccdbadbadbdddbdadcccdccdccaccbabadacbbacabdbdacbdadcccdbdccaadcdababbddadadaccabcccabbccbbdbaacbdccbcbccdcddcbcacadbbbdbaccaddabacdaaabaaabccddcabadcdcadbabbdccdcabbdacbdaadbbcbcadbbbaabadbbccdcacaaaccdbcbdbcdcaabacbadbaacccdadcccdbbadcbbbdcbdddaaabcbacddaaabbcdadcadcbacbbaaadcddcbadbbbbaabccbadcdaddaadabdddcaddbbaadbbbdaaddcbadbccadcabacbdabdabbaadbadcacdcacdddacdcdcbdbccbcbbbaddcdbacccdccccddaabaabbcbcbbaddacbcdabbbbbdcacccbabdadddccbdbcabdbabbbacdddaacacdabcbdacaacdabcddbdbbbddaddcaaacdcbdcbdabbdccbbbbccdabdbcbbbddcbddbbcaacdcaabcaadcaaaaddbaababcbcccbaacaabaadcbddaadbdcdadacabbbdbadbcbacadaabdbdcbdacbbddcdbacaaabdbdcdbcaacaabcabadbaabbabbccaaabccccbabaccadcacbabcadbbcacadabccdaacdcdaaccabbbdcadbdbdabdcacacbdbbdacdabbaaabbbaccabdcacccabddbaacaacaaaccadccadbadcbcadcabdddadaccdcdbaacabaabadbdbccccbaadddbdaadcbcdcabdcabdacbadcdacbaddcbbbccacccaaadbacdabdacbddcdadccddcacdcdbbbcabbdaabdbabaddcbcbdcaddbcabcaacdbadccddcacadcdcaccbbacddddbbacadabcdaadbddcacdbcacbbcacbdacaacbaadddbbccadbbbadcabadddbbddabdcaccbbdbaaddcadccdbacdcacbdaccadabdcdbaddbabdadddbcbddbbddacdbbadabdbdaadcbdaabdaababdadabcaaccdcdadbbbccadbabcaddcbababbcddbbccbcaacabbabaccbdbdacbbcaababdcabcdcbacbddcabcbbadbaaaabddddddcabccacacdabdcabbcacbcccbbdaadacbdcabaaddbbacdbacccbbddcaabbdcbcdcdddcbaddcaaadcbbadaccbddcccdbdcdcaababacbccdabcdabbdbbbbcccbcccbbdcaaaddadcccbbaaccabdabbbcaccbaaddabbbadaadddcddcbcdacbbbcddaabcdcddcdbcbddbccdbadadbadacbaccdbadbabdadccacacccdcccdacaaabbcbaccdddcaadccdbacadbaacaadadddddbddbaccdacdcacdacddbdbccaaacdbbbacbdcdaaabddaaccdaaaddcbbddcdbdadbbcddaaaabcaddaaadcdcdbccbabbacadaaadacbccbbdcdabccabdbcaccbbbacdbaaabbbbbdabbbccbdccdadbaacbbbdbbbdbbbdbcaccaadccadcaccbabddcdbcddbcbcdaccbbcacbcbcbdbaddbdbbabadddcaadabddbdacabccacdcabccbaabcaaddcaaccacdadbdbbdcacacbdddabdbaabcdcdacccbccadbcbaacacbbccdbacdbdcbbddbdbbdadbbaaacadbcddbddadbbbbccadbadbcddaabdcbadadaacdbddbdadbbbbbcdccbcbacaadcdccadcbaddadcbcbcdcccdbabccdabacdbacdcbcabadadcaccaaabdadabddbabdccbacbbbdcbadcdbdbadacbadbaabbccabbbccdadaacbbbaabddddbababaaaacacaaddbaadcacbcddccbadbdbcaccaacabbacbabbddacbcbbadcdadbdbbddadccaadbaabdccddaabcdcbbaaabddabbbaaacbaadabaadddcdddacbbcdcabdaacacdcdbacbacbcadaaaaccdadadaddacccaabdadacccccbbdcacdcccbdccdadaacbbbccddcbcdabbdbadacbdcaacadbbdcaaaadbcbdacdccdddaadcacacbbbdbabbbdcdddabcbddddbcbccbbadaaabaddacadcccbddaabbcdbbdaccdbbbddddddcbbaaacabccacbcccbdadaacacdadcdbbcdcddacbadbccaaccdcadccadaccbcdcdcdbbaadcdacbcbbcbbaabcccdabccddabdacccbbaadddaaacbabacddbdbbdbbdaccadbacbdcacadbcccbccacdcbcddaadddbccdbcbccaaaaabbdccbdadaccdbabbbbbcababacdaadcbacdaaddaabdbbbcaadbdadaacbbbccdabbadbaacdcbbadbdabbaccbcbbbccbbcdaadbadacdbcbddaccaabacadbbaacbddcccaabaccdaadaacbacccaccbdbdddcbaaacdcdcdaabaccadbdbdddacccddadbcaadbbcaabbacaddbdccdabdcbdccbbbbcbdaccbaccdbaacacaadadbdbccccadcaacccabccdaaaccadccbabaacdccabacddccdddcacbacccaddbadaabaaacadddbbcabcaaaccbbbadcbddcadcdbcdddcaccddadabdaabbdccdbacbdbaaadddaaaaaaccbdccacbbcbbccdddbabcdcbcdcbaacabdbdbbdacbcddbbdabdaacaaddddbabdbcdadbbcdccdcacabdcabaddcdaabbcbcbbcbdadddccdcbdbabcacaabcdcaababaddabdcdabdadaaaacabdddcbcbbbcbddcacbaddcadacadaacdabdbcadacbcdcbbacdcccdddaaddaaabadcdbddcadabadabdcbbbcbcccadcbcdaaaddaccacddacbbadcbdacadaadcdcdcccdacdbdcacbdbdadadbabccbdcdadbacbcacdbbcdcabbcabdadaacbcbaadcdbdabdcdbadbcabbccdcbcccbadcbbbcdcddddadabdadbddaddabaabacbdacabdbcbdcbbcdbacabdbdbbcccdcccaaaabadcbadacbdcabcbcbbccbbdbaaaadabdcaabaadaccbdbcdbadbbcccbccbdcdaaccaccdaddabbbacbbdbcaaabcbbabbaccaaccdcabbacacbaddadcdabbdcacaaaccdadbabbaaacacdacacbcccdbdaabcaaadbbdcaabbccacccabaddaadabdcbbdabcdaabdabdbcccaacbdcddcbcadaddbadcdadcdabcaaacacdbdccddcbddbbdaddbbaccaacccddccaaaccabbbdbabadcbccdcdbddaabdcbadbbaadcdccbdabbaadbaaacdbaddacbbcdbbdbdbdacdccccddbadaccdbccaaabccdddcddbbbcbabccbdccdbababbcabbabaadccccacbbcdbbababdaddbababcdcdabbadabaaacdddabdccddbaccccbdcbbacdccddddacadcaaabdddadcdcacaabbcabcbacbacbbbcdbdddaccaaaacbddcabcccdadbaaaccacabaaddbbdabbbccaabcabaacaaaddccadbabcdadadbabddcdccadbcaabcabddbadacccbdccdbdbcbaacbbadabbbccbbbbbcdcddaddbacabbddcddddcdcadabadddaadcbcdbbcbbbbbbadcccadbbabbddbdbbcbbabbcaacdbccacbcbccccbbcacbadaccabcbcbdaddbddbaccddddabdcdcdcbcdcaadbcbcdbcadbbcbbbddbacddddadbadaccdccaacdcddcaddbadbaddcbcccabadbdbbbcaddbacddddcaacdbcbbaacbdccbbaaddbdccacbdcbcacdcdbbcbaddaabbdcdcbdbdcbdacabcdbdcbcacdbcdcddcabdadcbbabadbdaccccbbcddccabddcbbcbcabdbcbcdacaaadaccdcaabcaaaadcbcdbccbbcbcbcddcbadaddadcbccbcabbccdbbadbcbdbdcdcabcdcddadccdcbcdccabbbcbaadaddaccbbcaadddbaddaddaaabccacaccdcbbabddaddbcabbdbaaadcbcbcbdcdaabdbbabbbcdcacbdacbdbdacadadabddbddbdcddcbacaabcabdaacaadbccdbadadccdaaddbdbccbcadbdbadbccbdaddddbaddcbdbdddccdbdaaabacbbccbcbacbdabacacdcdbbcabbacdbbabdabdddccaddabccacacaabdacdaddcaccdbdccccdcbbbbbdcbbbccdcaccabaacaabccacdbaabadbdcbcdaabdabbdbdacadcbdbacdbdbbacbbcaadbbbbcddcbdbbbddadaddaaaadbdaacdadbcbdddaccbbcccdaabcdbdacdcdbadcadcdbdcdbcdddbccadbdddaacbadaccabcbabacdabadbcabaabddbaaabacadbbadaabccbaaabcdacaadccadbabbbdbaaadadaaabbbccddadbdadccdabccdbbadaccabdbaaadbdbdabdcaacbbdddcaddaaddbbdccbacbcaadddbadaacabaaaadabdddccbdadcbbbaddadaaadacddaabccbbcbbcbcccdadaabbacdaaacbdbacaabccacdcdcbdbcacbaaccccacdddcacaadbbcbbdbbaaabaddcdcddbdabadacbbcbadaadbcdabdaabaccbbccccabdcddbcdbbcbcacbcddbbabcdbcbcaabdbaabbbcbadabccbbcdcdbcaccadddccaacadcbcadcaabcbbcabcdbcccdcaadacbacbddbabdadcdaabbcbddabccbccaaacddaabdaccccabdcadddcbdcaaddaadbcacccddcaaabdddcacdbdaabccdacadacbbccddcbabdabbdadddadddcaadabdcbbcccbacaaacccacacddadbbbbbbbbbaacbdddccabbdaacaabdccdbaadaabdbacbaccccdabcbbbacaabbccaaccdacbacbbccbcadbdbdbccbcdddaaabaadbccccddaddcbcbbbdaabacadabbccbdcdacabdcbadbaacdccbbabcacacbabaaaaddacadaabacdacccdbacdcbdadabdaddacbbabbdcdacbbbacdcbcccaaacaadcdcddbcddacbaddcdaabbcdabacdbdccddbabdbaabacbcbaaaadabccbccdbbdbbdbabaadabbbccbdcbbbabdbdcbacabbbdbdacdcaccbdccbacccadaadbdbabdaddadcbacabdcdbadbdccaaccbbcdbbaddbbbacabcdbabdcabcbdddabadcbbdddcdaaccabbdaabbbbabcaaaabcaacdbdbacbcccdbbdabbaaadadcccaaabdcbcddccddddcbaddbaaccdacbacdccdacdbcddbadbbbaaaddaadcccaadabbdcccacbbaaddaacbdbdcddccacdbaaddadbddbccdccdabdddcccbdcdbbdabbaaddcabaaadacdaccbddadbabbbdcaabdddadbdcbbabcabccaacccadaacdbbdacbaadbdaccacbaccbdbcaadcbabcbdaabdaccacaccabcabcdbaaaaabbbadaacadadccbdaabccbcaaacdbbcccdddababbacabbdaabadddabbcccbaddbddbbaadaabcbdaabadcbadcbbdbacadcbbbcdcacbcbbddcbdcadcdadbaabacdcbbcbccddcbaadacabcddddddacacddbcbcdbddbddabcddadbadcddbcdccdcccabcaabcaaddbbdcbabacabaaddacbabdcddaaddaddccbddccdbbcbadabacbdbcccbaccadacbaddbacaadacbabacdcccabdcdcccdaccdbdbddbabbadcdbcbdabbaabcddddbaaccbdbdcbdcacaadbcbcdddcbdbabdcaabbaababbabbdcdddabcccbbdadadddbbadcbabccbbdabbcddcbaaabccddcdbddbcdbaadbabbcdabcdaccbbacdbddadbbdabdbdadbdccccadcddbcbdababbcabccbabdbddcbcdddbcdccdbadcbdacdacbbdcbabbdccbcddbdbcdbcabcaddcbabddacabaddadadddddcaabbccaaadbbacacbdbcacddbadbbdbbbbcaabdbddacaddadacdcbddddbdbcbbdaabccdaddacddabadddbcaabdcbddcbabdbacdcaddabbacccaabdcdadadabdcdaadaddcbdcdcbbcbcdcdbcacbaddbadcccabcbccdbcbbacaadddaacccdcacbdcaadbcdadacbacbacaacadbdcbbddababdacadabbacccdbdccacdcbcadcbbdccadcaccabbcccbaddcdbaaaaaacabdddaaadacaddacadaddcbacadaaccadcddddddabcaaccbbcaadcbdbdbcaaabddcdcaccaddbabbacadabbddbaacaadacabccbdbccbcdadaacbbdbacccacbbbacbaadccaabcdcdabccabbadbbcdbdadbcbadabdadbccdbccbcbcdaaabacbcbaddcbcadabccacddcaaabcaadacbbcbccabbbddccaabcdbcbbccaadadbcbadbbabacbacdabdaaacdccbdaaabcdbdabcbdbdbaadbddadadaddabadcaacacadbddadbddadacdddbcacdbdcbbcabcbacccacbddbdddabdcdbccdcddbbbaacaacccacbbaddbccabdadbbcddacddcddbbabbabddcddaacaacdbaddadbabacddcaccdaadadaccbcbdaacaaadcbdcdabdbabbabbcacdacdabdbabbaabbdacbcbcbcacbbabcdcdbcbbbbaadbaadcbddadabaaacddaaacdcdababddcbccbdcccabccbaababcddcadbadabadbadcdaadbbcbaaaddbaaccbbcabdbdcaadaabdbdbbbbadacbbabddccbbdabbadbdaacacddccabccbccabbddbaaddcaadcacabcabcdddbbaadbdcacabadbdcdddbaddaccbcddcacdaabcabcbaddaccdabdddcaaddbddcdabddadacdaacabddbbbdcdabadbcddcadbcbadcaabbdbcbdaaadbaacbcdaabadcacbdacbdabbdcdccdcaabccadcdccddbbabbdbbbddadcdccacccdbabcbaccbcbbaabcbacbccddcacaacdbbbbbcdcddbbdbddcccabccaaddcccccdcaddcbacbaacbabaabcdddbddcbddbdcbbdbcdcddbccbcbbccbabadbddccbbcdcdcabcbaabdbbccaddaadbcdccddabadcbbcdcbccbbdbacadcbabdaddacadabacdcccdadcabbbcaaadabcacabbcbacccdaccddcabdbcdbbccacabadadaacdddadbdcbadcdadbaacbddcaccbdbadbdaddaadcdbddacdbcdddbababaaccadbbcccdaadbadcdbddaacdbdcadcddbdcaacacbdabdbcbdadbdaacbdcacccdccddcbddcaadccbbcacbddaccbdbbaaabaabdcbaaaabdbccdcbdcacbcdbddcbadddcdddcddddbdbccdbddcabbbabbabdcbbbdaccaddadaabdadcaddadabbcdcabaadbadaacbccccaddcdbdbdccbcdcbcaddbdbcbcdbcbacccadadcacddcabbccdadbdcaaacbdaddaddccdccdbaccbcaadabacccbdacaddccabdcbdcaaaddadbbcddaddadacdcbabdadccccbbbabbcadbddbbcaadbadbccbcaddabccbddcdacadbdbbcdcaabbbdaacaddcdcdbddcaacdcccacdccababbdcbbbbccdddcbcdaacacaaaacaacaaaabbbdbdbbdaccbdadbbbdadbababacbbcdaabacadaabbadcbbcdddadacdddacdcdcdaaddbcbdccabbdcbccacacaabcdbcdcbbddcdbcccbdcaaacabccabaadcacabdbdadccadccbdbadcbdcbacdaaddacbcdbdbdacbaacdbcbcdddbcdbbcbacdcdbadbdcbcbcbdcddcadbaddddabbbcaaaccbddcdbacddcddbadcdbdcbcabdbcccdcbcbacdddabaddbbcbbcdcbabaadacccaccbcdaabaddbbdcdadcaddaddccabdbaaddccbaadacccadcadcdbcaaaaaaaaabdbdadcacabbdaaddadaacaacbbcbbdcdddddbccbaadaabadcacbddbadbbccaaccdcdbbaabccbabdbaabbccdcbabaadbbccadcccddccaabdbddaacbcdcbcdcddcddddbdccbdcdacccddcaadbdbbdbbbdcabbdcbcdaadcababbddbccadacabcbdaabbadbaaababacaabadcbbbabcbbccddadcddccdbbddadcdadccdcbcacdaadabcabbaccbcacbdcaabacddbcaccabddbbddbbbdaaccbddbacaadcbbcbbabcabbcaabacaddabaabbccccdabdadbdcddbbcdbbcbadaabbaacccdcbccadddddadababdcdcbdbabdbdaacccaadaaddccdadcccbddaadcbabddaadabcababbcbacdacaddbcdabbddacaaddbbabcbccccabbbbbcdacbaacdbdcdcaddabdadbadaaaabdbdbbbbdaccadcbddbaacadcdadbdcacccaabaccdaacbdacbbacbbadadbbbcdbacddabadaaaabdcaabbaaccbcdcabbbaccbdbbdadbadccbcbcbcccbacbbdbacabdcbabaacccddbdcdcadbaababcdcabdccbacaadbcdaccdadcbccdadbcadacdadadddddcaaaaaaadbcbddadbbdbcbaacbabaddccadbabdaacdbabddbdbbcadbbbabcdcabbdddbdaacadbaacdbbcdcbabbcabdaccbbcbacccdbccaccbcbaadbbbcbabcdccdadbadbdaccaaccbbdcccaddbcababbbbbbaddcdacaddbddbcbdabcbcbbcbbadbbbaacadbcadadddccacabdadbbccbdcbbddbaccbcacadcccadcdbaabdbddccbdbcabdadcbccbdcbaabbdccabaabaabadabbddcbadcbadddcccacbdacadabacbadbdabbacdbaccbcbdccdacbcbbdaadaabbadcabbcaaacaaabbaabbdbddcbbdadaaacdcacdadbbacbbcadddddaabbcacbdbdcbddbbbcaaabacdacdaaacabacacddbbaddccacdcdcbcbdaabdcaabdddcdbaaaadbddbcddadcdddabccbcccdcbdbaaddddabbbdbdbabbcacacbccdcbcdacbdacccacdcdcbbbadbaddbaaaddcccddcadcaddabcbadbdabbddcbbbcbbddbbbabcdbabcccbddaaabdbcabddbdcabccaacbddaccbbaacadbabbdbbacdcdbabcbcadcdadccbbadbadcdbdaaddcbcbcaabdcacdccacadadcccabddccabdcbbadabbbbabddcbddabdadcdaddddddcaabcacdbacbdaddadabbccccabcbabaaaadcbbdcdabcaabaddbaabdabbdcadbdbdcadaddcddcabcbcdbcdbbcadcdcabbbbdbadbdbaccdbacadbdccddaadbbbabbdcaccbbddaacccacabbcdbcddcbbbabbcacdcabddbadccddbdacdbdcdabbdbbdcdbccaadbabbdaabdabacccddbcddbdcbcabaccdbbddaccaadddacacabcacbdacdabbcaaddacdadbdacbbaddaddbcacbbaaddbcddcadadbbcbdbdbcadcbbaaddaadaaabcacbbddaaddcdbcbabdacdbdcbacbbdbbdbdccdaccdcdddbdbbbabdaaddbccccdacbbadcbbbcbdaaadcacbcddcadccadabddcababdaddabadcaadbcdcacdbcbdbbcaabadabcddaaaccbccdcaaccbbbbddbacbdcadbcbccbbccdbaaaabcabaccccdadadcccbdaaaabddbbaabdbcddbaabbdacdccdcdcacdbaadbccacbacddacbaadcabbcacabccdddccaadabdabcdbabbcbdbbdddbdbbccbdaacbdccbdcbbaacabddcadbdcbaddcdddbbbadcdaadabbcadcbadacbbbaabdcbabcdddabcababbcdccacbacadddacaabdbbdccbccbdacddbdbdaabdcaabcacdaadbcacbadccdacaabccabaacbbccabcccdaaacabcdbdbcbbbdbbabdbcaddcbddabbdcbdcadbacdcadddabadbdcaddbdbcccbbabddbaadadcaddcdbccbababbacccdaababaccbbcddacbdaaaabdbbcbccdadbdbcaccacccbbdbbbadbdcdddaabbcbdbabbadabcccbcbbadddbcbabdcbcbcabdcabbccdacbcbbacdbcacadbccabcaddcaacabdbbcabbcccccdbdcbdbcdbbbacdcdddaaadcbabaccbcbddbadbdcbbccdacbbaccbbddadacdddbccbacabaadbadcbabcadddabcbadbbbdbaabbbabdbdcabcbcbdbbcaccbcbcbbdcadbcbcdaccbcabddacbbcacabdadbdacdbddccddcdcaadadaabbccaaaaabcbbcbacbadddccbbabacbcddcbbcccadcdddadacdaddacccacacabbcbaadbaccacbcdadbcdcdcdbabbbcaccacadadaaddddbbcbababccadcbbcbccadcadacbddcabdbbaccaabadcdabadcaaacababcddbcbbbaddbbaadaccaadacbbcddbdacdcbababdcbcddaadadbbdbcbddbaaadcdabbbcadbbbccdbdddcdaaaadbacccaddcbcabddcbdddabddabccbacdbbaacdbaadddccbdcabdbdadcaabbcabcaaddaccdccbaddbacbadbcadaaccddabaaabcadcabacbbbcbcdabccbaaaccdbdddcababacadacaaddcabcdddcdcabbaacdabdadadabdcaabcaadccbbcaaccadcbbddbddabcddcabaaaddbcbabbddcbbcbadaacdabbbcbdcbccddbcadbbdddbdadbcccddcbaacaadacacdaadadcdcbacddacbbdcdacdbdaadacadabdcbdbbdacbbddaaadaaacdddbccbbdcadbbabdaddbdccadcbabdccbaddaaddcbdaadaabadcdbbcdcbddabdccccaaabbcadcbbbddaabcddbcdbcbcbbcaddaadccbabbcbbdaacdbbbcabacccbdaddcdaddbdcaccacbcbbdcdbcaaabbccacdbbbadacdbddcadccabdcccadccbddcbbdccadbccabbdbcbaccdbbdabbcbcaccddbdcbdacdbaabdbabdabbdbbdccabcabdaccaaabacdbcabbcaacbdabacaabbdbdacbaacbdcadbbddaacadccbbccbbacbadaacdabbcadbcdbcabddcaaaadccaaddbbaabaddccacabadaadddccadbabbcbabacbdadcddbacbcdcbbcddcacbbdacbdcdbadadcaabbdabbcdabddcdddcdcdabcbbdbdbcaddcabbddbadacaacdcaccadbdaadcaaaaacdcaacdcdadbbbbcbdaacabbdbddbbaadcddbccabbddaadbadbbbaaadaabaabbddcacabbdbacaaababbacbdbdbdabccaadcbadcbadccbbaadcacdacddcbabcbcdccabdbdabddacdcdcbdabbabcbbdacdacddddbbbabbacccaabadabaacccadddadcaadbbbacacdbadcbbabdbadcaccbbdbbbdcdbabddcaaabbacaacabddbbdabdcddcdccdcaaaaddadbbdaaacdaaacbdccdbdcbbaadbbaabdcaabdbabdbdccababcbacabadccbcbcdcaacddaabaacdaabbdbdddbdbbbccbbaaadcdddcccaaabbbcdcbdbabbdabacadcbbddbddcbbbacbcdaabcddabbddcdddcddbabcdccbbbdcbacccbcbbdaccabcbbdbbdaaabacaccbaaddadcdcbbddacdddccbbaccbdcacbbccbaadbcacbbdccbdccabcdabddaadbcaaddaadbccacabcccaacdcaccbcddaabacbcdbddbccbabcdccaaddbbbdbbcabbcadcdaddccdadcabbddaaddcddcbbddbaabdacdadaababbcacabaccbbbadacdcddadbdbdcdbbbcccddcbcaccbcdabdcabdbdacbacddcbdbbdbabaadaadbaddcbdcdadccbdbcdccacacdbbcbadbaddcaabccdbdcbddcaddcdbadaaaccdcbcddcbcbacaddcdcddccabbbaccacbcdababbbacdcbadaadddddbbacccaacbadbcdbddddbabccddcdacabdccccadabdddbaccddcdbadccaccacdbbabdbaddadddbabccddcccdcdcddccccbbcaaabcaaacdcdadaaacbdcbdadcbababbacdabdccddbadbcbbadcacdcbdbababbbbcccaaacacadcacabcccccadcaaaaaabbdbcdabbcacbaddcdaaabddabddcbdabbaadcdccadbdacdcccacddcabbdabdbbcdacccdcbdabbcbddcdbdbcadddcdabcbabbadddcddbcdadbcaaccabbdcaadcdccbadccbadbbabdadaccaddabaccddcaadcccbcbabcbbdaabbdaadcbbcacaddbaddabcdbcbbcddacaccbbddcccadddabbbabdccddaadbccaabcbbaabbcddaccbacbcccbcacacadabbbbbaadddcbbabacdcabcacbadaaccccdbaccaabdbacadddccbdacdabbbdcdaddddcaccadcabcadcadbdccdbcbbdadccccbbdcdbbdcbcdadaaddcdbadccccaacaabccdbbcadbbcdbadadacaacadbdcbdacbabaabacbcaaabbcabddcacdbdbabaacbdacbdcbdcabcbbbcdbacdbddbccadbadadccccccdcdbcdccccaccadbbaaaddacacaaadaadcbcadabdcccaaccbadaacaaadbdbadddddbcbcadcccbcabaadcdcbadccddcabdbbcdbbaadadcccbcdcbbabacdaaabaadbbabaadadaaccadbaaabcadaacbabcacbadcbacdcbdcdabaddaddcddaabcbabdabdadddcccbdaabbdcbcadbcadcaadacacaababbcccccddbddcdbcababbdccabcacaacadbdadddcdcbdcaacaaccbbaadcbdacdcddbbbbdcdbacbcbbcbdcacadaddbbbadccdbcdaaccadaccaaaaaddcbdacdabcccdcbbacdbdbddaacabcaccbddbbabbbdabadababdbcababdcdddcdddacabdccaaaadbdcadcccbdbcddcccadddbcdacbcbbbbddadbccbbdcccbababbcbdcdabbacadbbadcccacdccabbdacdabacbacbcadaaadbddbbccdcabbddbacdacdbbacabcabbcddbcaacbdccdbbabdccbbbbbacddbabbdddccdcabaddaaaccacddbbbbabcaacdcacbddacadaabaabcbdbddbbabaacaabcccbcaccacadcacdbbaacdcdaaacaccccdddcbadcbaadbacbdddbadcbccdbabcbdbcdcccdabacdcabacbdabdcbcdabcacbddcdacbadbdabbdcbbacbbdacbbcaddddadbdbccaacdaccddbabbaaabddcdcdcbaabbaacbbddbdbaacadccbbcbddabacbccaadabcaccbcadbbbaadbbaddadbcbabcaacbbbbdabcdccbadbadddcddddabdbabacccabadabcdbccbbddabdbaabadcbdabdabddadbadaccbdcaccdbcbabccdddacacabcdacbdbaccbbcacaacbaccabacddbbaccdcbaaacdcdcbdbcdcdaabdcdbcaccbdaccbbadaccaddaaaaccbabdbdacbddcddbbbccacdaddaaadbbcbccadaabdabaccbdbbdbaaacbbddadbbbcbdbdbbbdabbaacdcdddacdbcdacddcaaacdcbdaaddbddbacbacbcbcccccddadddcabdcadbdcdbccccaccacbbccbbbaccbaccddaaadabbdcbdbdaacacbccbadcbcbbadacaabdcddaccabccbcbadddbdaabbdbdbbbdcadacccccddbadbbccdddccbccdadabbacbcccbacdaaaaaddbcbaaadbacaaddbdacbbcaacabbabdabbdbaccbdddccdadbcabacbdaaacdbdbddcacabbdbbddacadaddccdabcabcacbcbaccdddadbbcbbbbcacccdcbbbbdbbaabbcadcdacbcbbdcbdbcacaaccccbcddacbabacdadbdacbcabcacadbacacbacbaabccccddbabbcbcccabbbdccacbdcbaccccddbbdbbdcadbbaddbabddbbdaddacbaccbadcaddadbbbbbbdddaaccaacbbaadabacacbaccabbaddadddbbbadcadcbdddacddaacaddbcdbababdcadbbcbaaadcbcdcabbadbccadcacccbadadacdacdcbbadbcbcaadabaaccdcdaaaddcccadbcdcbbddbccadadbddabcbdcbcccadadbdbdcdaadcdbcbdaccdabdcaaddbccaaacbabadbacbdddbbacbaaacdccddaadabdaddbbaccadaddbcbbddabccacbdbcdbbaacdcdcccababccdbdcbcddbcbbbdbdccdcdddcabcddadcbdcccdbcdbbaaccbdadcdcbcaddbdddcbbadcabaccdaacccaacabbbdddabaacbccbcaabcbbbcbadbbdcdcdbbbbbbdcbbcabbaddcaabcdbbabacccabbadcdbbccadbcdcabbdaabbaccbabcbcbcadaccddcdbcdbccaddcacdcbccddcabbaadcbccdaddcaddcdcbbacdbbaabbdbbcadacadacadcdbacccacbabbabbcadaccbabcadbccddddbbddcaadadddbbbcadadaaccdcdabcaddcdadccdbcbcaacabccdacbcbbbdbdddbabdbabcbababdccadaaacabadcdddddaacaaacadcdcbccacdcdaacabccdcbddadabbdcbabaaadbddcbabbccbcbdccbbadcbdadbcbabbcbcbabacdaaadbdadacbcbbcadbaddddabddbcbcdcadcbbbbabccaadabaddbccccccbdacbbcacadcbaacabaddadcabcacbaaddacccacccabcabccbacbdcbdbbddadaadbaacabbabbcdadddbdbccacaccbddaabccbaaaaacccdcadcdcacaaababaaabddabbbdcbdcbcaaaabbddaaadaabdadddddccbbcadcaaacbdcddddcbbacbdcdabcaababddddbbacdcddaddcdbbdaadbaadcbbdacabbaddbabccbcadcdbcbccddadccddcdcdacdabbabcbcbbdcdbbcdaacbcccadbaacdccccaaaabccabdcdbdcacbdabbdcdccbcbabcbddccdbdcbdcbcbcadbbbdbdbdccbbabbaccccbddcbcbcadcbadaddcccdddcddcacacccddadbabdacdaadbcdaaabcbbdabddbddcbddbccbacdaabccbcddcdbcdddacbdccabbcadaadbccaadaccbddcadbccbdbdabcddbdacacbbddbddcbaacdbcbaaababacccdbadcadbcbaadbcdcabdaccddcdbbdadcdccdaabadaacbbbcbcccdbbcacbcbdbddbadaadddcbbcadddbbadaabdddbbcadaabbcbcccbdcaabbdaccbddaddcbadcabcbddbcbbdbbcbdcadadbcadcbbbadaacbadbcbcbcbaadabababcdbcccbdbdbdacdbbdddbbcddbccbadadbadadbdacdcdabbbcbdbdbaabbadbdaaccdccbbdaadbcdbdbbaccbbddadbadaaadcadabcdccbdbaaabdabcaaabbbbddbaccbacaababdacbcbadacddcbddddcacdcbcddaccaaccccaabcaaaccaadbcdabbbdadcbcabacccadbbaabdddaadacbbaababbcbbccdbaaacdbcadbbabacdaccacdbdcdadaddcdcabbcbbbaadacbdaacdacdaaddbcabcadccadcccaaabbabadbdadcbdbadbabbadcacddaccbcbddadcdddabcdbcbcddaccdbbcbdbcbcacaabcabcbcbdacaadcadacdcddcaabbabaaccaacaaddacbddabdaddddcdadbddcadbcabacbbdbdbbcadcadbdaaddabacaadbaacbcaaadcadbdbbbcbdaccbacaacdcccdcdddddbddcccaabccccdabdcbdcadabccdaadbadabbaccccaddbbbdcccbaaccbabdcbcadcdcdbdacbdadaabadadcdbaabccaabacaadddccbdabcacdadbcabaddabaababcabccdadccdbadababdbaabaccbcbbbaabacddabadbdaccabacbabcaddbdcbdbccadabaadadbcabbdccbbcdabdabdddcddcbabcdadbdacdaabddcdddaadaddacaaabacddddbdbbacccabadbcabcadcccbbcdaabcbcbdacbcaadabdbdaacabddadcadcaddbbaddbbbbadbddbaccdbbdccadcbcaabdcdaaadddbcdcddcaaddaadacadbcbbcacbddcdaaabccbaabcadacccdababaabdccacdcdcabadcadccbbddbdcdbbbbabbadcdcbbcadbccccccbdcbabddabcbccdccccaddbdabccbaaaddaabddaadaabcababdcdbabaabbdcadcdcadaddcbacbcbdbbbbababcbaaababdcacdccbddcdccaabcbacdabaddbcbbbabbdacdcbdcdacddadadbaccbabbaacdccabbbbdbaaddabbcddddacbddbbddaccbacdabaabddbbbabddabdddaadaaadadddabacbdbababdbaaabdabaccacdbacacdcadbddbbdccdbbabcdaddddcaabcbcdcabadbbabaddabdadacbaddabbccddaaacaaaabadabcacaabadbbcccbdddbbdacacccbaadbdcdddcacaaadbdcbbadcbcbddacccdabcaacbabaadacaabcbdccbcdddaddadbcbbdaacccbabadaaacccbaacbbabbaccbbbcbcdccabdabaddddaabbdbccccacacddacacdccbaaabdacdccbbdabacbaabdaacadaaabadbbcbbbccabbabadadbcbabbcbcaccccdcdcbbcaaaabcdabbbaaaacddacbbdbaaaddaccbcdacbdaddaddbcacbaabddabdcadbbbbcabaddbadcbdabcdcccddababcbdbabcabadbbcbadabbaccaaaaccdcccaccdadbcdadddbbddaadbcaacdabdddbaadbbcbcddcbdbdddabbdabdccddbddbddabacbccbdcaccdcccdcbbddcaddbacccadbcaacdbbaacacdbcaabdaaaccbbbabacdcbabbcacdaadbcbbcdcddaaaccaddabbcddadabcdacbdbaaacacdcbaaaddbccdabcdbbaababccbbcbdadcbaadaadddcaabdcadacadcacbbaaaddadbcddbacddbdcadcbbabaabdcaacbccddacacaaacdccbdbdbdaadcbbcadadcdbccaddcccdacbaaacbcdcaaacbccbddbbabaccadddacdacabccdaaaabadccbbdcbddbdadaabcccbcbacacdadcdcacdaacbabdddbadacaaabdddadccddbacddbbabdabcdbabadbdacbabdbddabcccbcbbbdbdabbabdaccbbcddbabdbccaababdccbabbdcddadbdbcadcdcdacddbddcabbbabddcabbaadcbdcadcbbdabaaddaabdbaacdaddbcccacbcbbbaadccadcbbbbccbacccabdaddbaccadcaaaadaaaabaabdacccdcaabcbbcbbabccabaaddbaacdadbcabbbbdaaacacbcadbbbcdddaadaccabdaacdcadaccaaaabdcddacdcaadaadbdbbadaabaccabccbdbcaabbcaccdadaaadbadbaacbadbabdbcbbccbadcdbabacbacbdcabaabccabcdbbcbdddddcbcaabcdbcbbcccbabaadddbadbabbcdbaacbdbddbcdbababacdbcdcccccdcccccbdcdbcccdddccddbaaadbbbadacbccdcaadbadccaaacbcbcdbabaabbbcbaccabadcdacabdaccdabdaacaccdaadbdaccdcbddadcbcdddbdcbacabddcbbcddcbaadbdaadddabbdbaccccabbbcdbcdcbcababbbbdcbbcadadcdaabcbcabbcaacabbcbbddccbbbcaabdcacabacaaccccaddcdaaabaadccaddddabdcddabccccabacdcbbcdbdcdcccaaccacadaccacddaabacccdacddabddbadbdaddadccdacbcdcaaddbcbbdddcabbddaccbccbadddadcbbccdddadaadddccbcccadbbabaadcdddaacbbcdcadacbccadcbabdbcbccdbcbddccdbabbbbaadaabdbabcdaccadcdbcdacbbddcbdcdcbaadcbbbcbadcccaaabbacaaccadbdcacadcdbdbcadccacadadcdacbcdbbaabdbbbbdccaacbbabacbccacddccabbddcbbdbcabccaaddadabdacbdbbdaabadbbaddcdcdcdaaddcdbcadbbdddcdbacaacadacbddaadadcbdccddaccdabaddcabcdabacbacbbcacdbddcccdabddccdcaaddcbdccdabddccaddcadcdcccbdbbadccacaadcdadbccbadacdccaaaddbccadcddabdcdcbccaadbccdabdaccaadbbbabcbababcddbdcbdbadcabbcdcdcddacccbaababdadcaaadbaadbcabdcabbadccbcbaabbaadadddaabcddabdbdadbabacaccbacbadaddacddbbcdbcaccbadccbabbdddddcacabdcccdcdcdaabaabcddbacddccddbbcbcaabacccbbdccdabdaaaaacbbacaaaaabcdadaacadabccbcbddbabcdbcaabdaabbcbabdddbabddbaaabbcacaadbbaabbbdbdccabadcaccbacbabbdaccdbabccbaaaacdcbadcbdbadcccdaabdcadcddaaacddcbddaaccacababcaccdaadbbdadcbbaadbcccabbbcdbcdbddbcdbabcddccdbcabdacbbbbaaadcbdbbabccccbdabcbcccbdcdbcdbcbcbaccdbaacddcdbbcdacdcdadccbabbbcbcdbdbcadaaacabadccaddbbcdddcccdaccaccbddccdabbdbbaabcbadadccaaaaacbbabccadadacccddddcbdcabbaccdbcddaccababdcbbbdbcbcaadcccaabccabcadcabddcabacabdacbbbddbcbadbaaaabdccbabdcacdddadaddddbaccabcddbdcbadbaddaabaacadbaddbdcacbbaadcaccacdcbdbcbabccaaacddcaaadcdbcbddaabadbcaccbacccaabcdbccdcabccdaabccaaabdbadbcdabcacbbacbddbddcddbbcadbcbdaabcccdcbaadcdbbaababdacbacabcaccdcbabcddbdbaaddcbcacadbcbdbbdcbccabbccaabcbbabdadddbdbacbcacbdddbbbbbccbcabdcdccdbbbdacbbbbbaddacccacbcccbdcbbbcdcccbccddcdabaacbcbbacbccccbdbbaabacbcdacdcbdbbadccabbbbbcbbcabcabdccccddbabbbdcacbdcaababcaadcacacdccccaccdacbccaaddddcbbccccaaacbccccdbbbdcaadcdabbabbdbdacbbacacbcbcabbabcaccddacaaaddddadbaabbcaacababaabcdbcadbaaccdcadcbddacbddcaccdaddbbdaabadbaabdbcdbabdddcdbddddcdabbadaddddcbddbccbdccbacccaddbbdcdcadcdccadbbbaacaababddbdbacadbadcabcdccdbcdbddaadbabbcadbddddcdbdbbbdbacbacbbcacacaadbdcabcabcdbaaddaaaabaaacaadddcdadaaaadcbdacddbdaabbababddbcbccdddabaaccbbaadaaccbdcbadcbdcdacbadabcbbaabaadcbdacddacdabacccdacdddaccbcdcabccdabbcadbcddcbadcabaaaadcaaababdbabaacdabadaacddacbdbbaadcccaabdcaddbaaabbcaacaaabacdadccadacaadcdcdaacaadbabcadbacbcdcdbcdcbbbdacbcdddbbcdbccddcadcbbbddbbdccddcbcbbcbcbadcadbaccccaaddbbdbcbbdbadcaaacabbacdabdcbacaddbbccdbcaddacdbbadccaabcdcaddcbbadbddaacbcacbcbbccbbdcdbabcadbacbabadbbdaacbccababbaccacacbcdccdaadaacbddcadbbdcdccbadabccababbccbaddcadbbadabcbbacabbddaaccdcdcccdacdcabdadcbdcbdbacccdcaabadbaaccbcaababbdadadbaccaaaddbdaacccbcbdaaacacacddcaaaaacbbdcdbbcadaadaabbddddaccbbbcaadcbabcaddabdcdccacddbbadbcbdcaccdddccbddabdddbdddababbcbcaaabcaacbacbcacaabaccabbacabccddbcbbadacbdbccdcbadaaccaacabbdbdccbcccdbdbbbbaddbddaddaabbbacdcacbbcdbcbcaccbdacbccbcddacbcaabacdaacadccdcbcdddaddbddbbbbaccdcbdbdbbcaccabcaaccbdaabdaaaacddcdbacbbaadccddadabbcbcdabcbcccbdcacccccacaabacdaabdbdbadaabdbcacddaccacbbbbacdbbbdaddcdcdabadccdabbbcccccadbabbcbdbbacdcaddaacdddbdbadaaccddcbcacdaaabbcadcdccdbbbbbcbbbdbddcbadcdaadcccdbcdadcddcdaaadacccccdcccacbacbcdbddbbccbddbabccbcdcccbcdadaadddccadcbaadcbdadbcacbcaabcdccbcccdbadcdcaaaababcaabcadaaaacbbcddaabaabbaacdbcdbbbdbcdbacbbadbadaaadbadbbabacddaddbaddcddbaadcdbdddaaacacdacabcaadaadadbccbcdcbbbdccddaaddcbbdbccaaadcacaaddbbcdcbcdadbcabdaccdacbbbdadadcdadcbddabdcbddbbccbcdbbdcbdacdcbbcdddabacdabdbdbdcdbdadcaacbddadbbcbddabaccdcacbdccadcdddbcdacacaddccdcccccdbcdcbcbbadcaacdcccabadbbbccccddccddcababadcaadadbadccbaacbbddbadbdabbcbccccdcbdcabcacbbacbdbdacacdcacbddbcabbddbcdbadadabdaacbcdbbdaacddcacdbbdacbbcaccbbcaadacbacacbdadbadcdcdbccdaccabadbcdbabcdaccdaccbdbbcdcdbcdcccdaddadabbaaaabdbcbcccabdaacaacadbadbdaadbdaabbccbcacbddaadbcabbcccadccbddcbdaaaaddadacdbdbbcbbaaadbdcdcddccacdccbcbcbbdacbcccbbccbaacabcdadcddbabdacdacbbdacbbadadcacabbdbdaabacacacacbabccadbbbaaacabcccacacbadcaabcdcbcbadcdddccccababbdababbbaabdccadbbccdddbdccbaacdacdcadaacbcaaccdccabbbabbcbdabacaaacacadbcaddaaacbaaaaddccbdbacaddbaadddcdaabcbbdadaaaccdbbaccdcddcbcccccdbcabdacdddccadaaccbcdbbdaabcdadadddbcdbdbbabbddcaaacbdccdbddccaaacbbaacbdddbcbbcddbaabddacbacabcacdbaacabddcdadaacdcdbbbdddadbdcdcbbbccbdabbccdccaccccdccdccbcbababbbabbddbacbbbbbaddbccbaaddabdbbcddcdbaadddbbdcddadadbaaccdcdbcdcbaabbaaddbcabdccccbcbabddbacbdaccaddccacbcdcdbababbbcabbcdbbcaaabcdbddbcaaccbbbdbbddbdbbbcdcbaaccbdababbbacbbcdccbcdabadadbbddbaacadacbdbccccbddddbaaccacbcdddcdbcccdaaadaabcbcdaabaccdaabadacbdbacbbdddbbdcccabbdbcabccbbacbccbcdadbdcbacbdcbcacddddcdbbbddbacddbaacccccaacdbcbcbcdbaadcbbcbddbddcddcbddbbdaabbcdccdbdbcdcacdbaabacaccdabaabadcdcdbbdbcbaaadaddaacdcbacbbdcbdadcbaadbabaaccdaabcbabcacacccaddabbbaaaddccccdbcdbbaadbcbbacbdccdabdccabcdbcdccaddcdabcbddccbcdabdacdcdcddcdbbcdcabadbdbcbccbdddacccbacbbdcdabaabaaadccdcbbdabdabddcdaddaaabcdaddbcacadaaabcaaadbbadcdbcdabccdadcbadbcdabcbabdbcbdabccbdddacbababdaadacdcaaccdabbcabaaabaccabaabcccadbdbbaabccdbadaadaadcdabbcbbcbdcbbdbadbbaadacdaacabcadcadbcbdadbbdbacbdbbcbdbcdaaccabbadbdabbbcbcaaaccacbbadbbbdddcacdaaadabcaabcabddbbbadccdccccabbdbcccbddcddbccbaacadbcdbdbcddbddbddbacdcbdccdcacdadcbaaaaccdcbcbdaccddacccdadddcddbaccbcbacccbbaadccbdcababadabdcdcaccdbacbddcbcbacbaadcaccdccdcdacdaaabaadaabdccabaabcddbaabadddbabdbadaabababccccdbdcaccbddbccdccaaaadcadbccdadcbcaaacabadbabbbbddcbabacbadcbbbdadcdaaaddcbddcacbdddadaabcdabbaadbdaacbdcabcbbdaaccddcdddcaaddccadbbbdaccddccbbaccabaddbdadaabcdbdbddaacccbbbadbccddcaccdcdcdaadcabbddbdabcacbacdadbdabbbcbcaaccbacbcdbdadcaaddcabadddaccaacaddcbdccdbdcdcdbcadabcbbcbccbcaabaacbaaaacdabcddcdddbabcddcdcabcbadaddadcbdcbbcdbccdaabdabdcaddbbdbadbbaccbdadadabbcdadcddadaadcdadacbdbddddbdbdcacdbbacccdacbcadcacbaaddacbcaaddcdabbadbcbcbccbcadbbddcdbadbcdacbcdcadcdcddcbabcaaaabcdaaadadccccadccabcacbbcdaaaacadbcbcdbabbcaddcacbbccdabcadddadbbabbddcbbadaccbbabddbdcaddbcccdaddabcdacdbddadabadccccadcadcbddacdcbdabddbbdcabaaaccdcccddabacbbbdbabcaccdbbccccbccdcdbbcdabcdcbaaadcbcacacbcabbadaaddcabcbabdabadcacbcdbdbadcaabccbdaacaaddbbcbacdbbbbbbdcacbbccdbcaacdddbacbbacacdbbbcdccbaabbaacbcdaccacccbbbbabddbcbcccaadabbaadcdaaaddddbbdabbddbcccdabccadcdcaadbdadaaaacbcabccbcdcabccdbdcbabdcbdbcaabcdbaccaddadcdacdaaacaaacdbdbaacacabccbcadadaddcccdabbcccaabbabcccadadabcdabddccccddaaabdabdcabadcadccddbdadbdbadcabdbbdcdcaadbdbbcacdbcdadcbadcbdbadbdaaccccbdbacbcdcaddaddbbccabdbcadabbddacacbbbabcbdbbabcbddccbdacbccdacadbbcdbabbcbbabacddcbcbcabbccbbabdcadbbbadabaddadbdadbacadadcadadbdcddcacdbaccaaabbdddccbccacbadbdbaccdbbadbbaaddbdadbcacabadaaaababddcdbccccdaababcddacdcbadbbbbccdaaccdcadbbccdbccbdacabdabddaabcdcdbdacdbcbcdbbddcbccbddbbcdcdaabdbdcdcbbbadbccdbdccaabbdacbabddbadcdcdbaabcaddacdabccbcbabaccababccbabaddbacbdccadabbbadabdbcacaabcbcddcaacbadaaddcdbddccdcadabdaabaddabbacccacddbdcadadddcaccdbaacabbbbcddddbcbcacdabbccacbbadcdddddddcdabadddccacdbbaacbdaaddbbccdabbabbdcadabaabcbabaadacabdabcbdccbbddcbbbbdadacccadcaabcbaabcabbadbcccbadbddadcccbbcbddbbbcdddaacacdaaccdddbccbcccdccbaabddcbacacabbdccdadabdbddabccbaadbabbbbadadacadabbaadbababbacabcddadacddabbbbdadddbbdacdbabbbadbdadcabccdaabdacacbcbdcaaccadbababcaacdcdbbbcbaccdacccdbbaddcdcbdcaddbbdcaccabacbccbbaabaabbbdcadddaadaadbaaaddaaabaccbcaaaccbbaadabbdcbbbcabbabbdabbabdacabcacacdaacbdacdaacbcccbaccdddbadadcabdbcbbcbdaabccbadabbcdccabcdccaabaccddbdcbcdbccbcacaadbdcdbaacbabbbcacaadcdcdbbaaabbcccdababcbbbdaaaaadbddaaabdcdacabbcdbdcbabcbaadcccadadcacccadbbdcbdbbbaacdaabbabbdadaddcccacccdaacdaacbadacccbbddbaadaccacdbddbbcbaababbdabcdaaaddabbccdcadbcacacbaacbabdadddcdaaacdbdbdabbcccacaacccdbcdccacdbdbddcbcadbdcbaaccbbdbcbcccbaddbbddaacbcccabbadddbddbadbcdbacdcbddaaddcbaacbacdbdbdbdcdabaaaccccdbacccdbdddacdbccbbcadcaadbbbbaacacbbbabcdbbddcccdcaaadabbbabdadbadddaaccccbadccddadaddcdbdacabbacbddadbcabbcbbdaacadaaadddbbcccccddabcdcbcacbadaaaabaaaadcababcdddcaacddaaadaddbaadddcbaacbcdbcbccbddcdadbdddbbbadcbacbdbbdbaabaccdbacdbddbcccbacdbdccccacadbcbdbbdbcccabaabddddabcbacdbbdbcbbcacdddbdbccdcbccbddcbbccdddaaacaddcabbaadddaacacaccdbccccbcadaaccddaabadbdbaaaadddbcddbdddcdbccaadadbcbddbcbcdcbccbbabaaacbbbbaccdabcccdcddccbddcadccabadbcadcdcabbdabbbdadcccddbbbccddcbdbdbdcdbdbcccccbcdcccdabcbdaacdccdacabdadcddababdbcabaaddbdbbcdbbadaadcbddcccbdacbcdaadbbbadcdddcddcbcacaaaadacdcccaddbbccbadadadbcbcdacbddbbcccabdabbabbbdcbcbbdabcdcdabcabdcbccacdabaccacababdcadbabbbdaaabcccabdadabcacacdadbcabaccdddbabcbcaccbbdcccbacbbabbbdbabbaaababbcdabbabaaaacdcabaccdbcadccaabbdcaabccdbccaacabcbcdabdddbaaabccdabdbbbaacdaacbdbadcdbcdbbccaabdbcbbcbdacdabbabdbddababcdacbcaaabcbaacabbbddccdacbdacccbaacdbaabcbddcdbbcdacbdaccbbacdadaaacacbcdccdbacaaddadddbcaddabccbcaaacddbdbcdbbdbdbdaadbabcdabdcccdccdacdacddcccabacdcddabcabaddbcbccadabcdbdcddcdaabcaccbcdcbcddcacbcdadacaadbccaadacacbacbadccacdcccbdbabadadcdbccacabbbababacdbaacbaadacdbdcbbdacdddbddaaaaaddbbccbddcdcccbcadbcabbccacccdbbcadcbaabdbcbbdacbadabaccccbcccdadbdccbddaacccbbacdabcbddbaabcbbcabbaabcdccabbcdbbbbbcbaadbcacacddacaddabaacaaacddaacddcadacdddcaccdacbdacaabdcacaadabdabcbccaabccccabbcadbdacccaccdbdbdddaddcdcbaaddbdadbbbbbaccacbadbadbaaacaaddabbbacdcccbabadabdcccacdbdabdbaddbdcbddaadcadadabcabaacadaacbcdccbbbacbbabbcaabadbcaaabacaababbabddcbbabaddaaccddadacacbaaadcaddbaaaabaccbbabcbbcccbbaabdcbaddbbbdccbdbcadadcdbdaddacbabdbdadadbbbbcaacdcabaabaabdccacccbdaccbcdacdbbcccdcaabccbdadcdcbbbcddcacdccbcdcbcacadaadcbdddaccdbaddddccbbaccbcdabbcbddadabbdcaacbbddadcabccaadaaabcdcaddbccbdddbccbadbdcccdabbabcdabbacdcabcaabcbabdcdbccaacdadaccaccaadccdaabdddbdadbadcdaccaaccdabcdcccdbaddddddbcdacbddabbbadbcacbccbcdadbbcacbddbdcddbbabcddbdbddddacacbcaacabdcddbdbdaaadbadccddabacaaabacbbdddccbadcabcdadccdcaaabaaabcbcdabbccbdaddadabdddadbcaadddcaaabddcaccbdbdcdbbdabbbddaadccdbcdbabacbddbdcbbcddcdaddbcacdbcbadcdbaddaabcddbadddbcbaadcbadbcbcbadbaccbacdacbaabadaabcbacdbbdbddbdbdabaddbadaacdddcbaaacccbddbbbdabddadbbabadbcabdbadcdbaaaacccadabdbcabdcbddaccdacabdddddbabacbccccbbcbcccacdbacacaaccddcdbabbabcabdccdcbcbadddbbacbadacbcabaaccccddbbddadddbddbcdadccacdcabbaaabdacaddacdcccdcdbccacdcbadcadddcbbddddbbdacadcadcbccbcabcaaaabbbccbdddcbdbddcbaadbcccacacaaaadcdcaabdbddacbabbccacbddcabddadadbacbabdabaaadcdcbbdbbcacbbaadbacdbdcadbbcbcaacaacacbdccbdddaaaaccddbdcdcabcdacacdccbdbbbbcaabacacadcbcbaabbcbaabbbdabaacddcddaccbcacaacbaacacbabcbadaddbaacddbcdcadaaccbdbcbaaddadcaaddbcbcdbcddbcccccbdaccbccdbcbcbccdcbdabdabacdcdaddadcbdcdaccdacdacaadbcddadbbadaacdbbaccbccacbbabcbbcccacaabbabdbbbdbcadcdcddccabdccddabaddaacddabcbcbdaabcdbcabdadbdadaaddbcbdadbcdddacbcaadbabbacacacbcbdcabcddccdcbbbcbccbaccaaccabcdaacacacadaaccadcddcadccbbabaaacbbaadbabcbbdcaabcbacccbdccbdbbbdcdaddbdadabdabbabcbbddbbdaaadbaaddaccbaadbaadcdccdbbbddadcbbabdcbbccddbadddcbdbbbdaaddbbbcbdbbcbacacacdbacccabcdacbdbacaddbbadbcdbbdcacaacbabbadaabbddcadbdcacccdcdcabaaddbccacdbbadbccadaccbbdcacbddadccccbccdaaddabcbbddbdcaddcbcdaccdddccbbcccabccdbccdcdbabbabbdaddcbcaadbdcaabbcdbddadcbdddccdbadbdadcaaabbabcdbbbabcbcabdbdcddcbbdcbdabbbbbbacdabdbbacbbabdcbbcdcacdabdcdddbddbdaabaaadaccaccadddbcdcaaacbbcbdbccbbdcbdaadabdcadcacbcbdaabacdacaaccbbcbaadccbdddcabdaacbacdddcbdcadcaacdaccdadcaacbdbabccccbbdccbdbdaacbcdacdcabdbbbdccdcacdcbdacddbbdcabdaddbbdbacdabadcddcbadbddadddbdcabcdbbabcdabbddbdddaacbaaddabdddbaadbcbcbcbcabadbdbcabbdadaaddbbcddadaacddabaacacdcdddbddaaacaadddabaddaccacdcacdddcdaaaaddbaccbcabddcaaaadcdddcaabacdabbbbcacadadddacababaaccabbccdbbdcbaabddbbcbcbacbccdddcdaaacbbbdcabcbdddbddbddaaabcddbcaaddaddaacdcbddcbcdabadbbaccccdabbbbdcaaabcbdbccaaccdadbaaacaddaaabdcbacbdaccbcccddddaddcdbbbdadcdcdddbcbbcaabaabcbdbbcbbccbbdaabdbcddacaccbcaccadadcbbdbdbadcaccbdbdbcdbccbaaccccaaccbccbbddadbaabbaccdaacaddbcacadccdcdbadaadadaddbabdccddbcdaadacdbbbbdabaabaadcaaddbbbbbcccdcdbaabcdbccbdabbbdacbabbbbccbbcdbadcadbbabdbbbccaaccaacdbaacadbcdccdadacdbadadbbababbddbabbcdadabcddadcbccdabddbccbabcabcdcddcddacbbbcaadddadbdabdddbabbabddddabcddbdaccccbaddbcbddacaacdcadadadbcbdbbbaacbcddaacbcdcdddcbabaccbddacccaadbcaadacadaaabcccdadcbbabcccbacdccdbaababbbcdbdcbbbcdabacccddcbdddccbbdabaabbaaddbbbaabcdcacbabddabacadaaccadaccdaadadacdcdbbbacaddbcccabbcaadaddcdccbdcdaaccdabbabcacbabbacdcdddccccdadbaccaabbadaadbcddcddccadbbbbbabdbacddddaacaaccaabdbabbdcaccccadadcdaaabccbabdcbdaaaaabbdbdacbbdbbdbdbdcbabdbcacbdbbdcdddabdacbcadcdadadcaaacaadcabcacdabcbdbdccdadddcabbdcdbdaaccdbadddbccadabaabdcabbdabbccdcddaabdbdddcccdadcbbcadbacbdbbcbbdcdccccdcabdbccbaaaccdcccabbbadcbddbbccccbcaabacbbaadaaacccdbdadbcccdbbdbabcacdbadacaaacccbbbacccbadaccacbccbdcaadaccacbcaaabaaccccababbadbbbacadcbddcccddddaacddcadccbddaadcbbcadbdcabcbcdacadaabdaadcabbacddcbdbbbbcabbcccbbbadddddbbaddbbddaabcbdacbdabcacdccbcbdddbdbcbcdadcbcbcabdaddacdcdbcadbdcacddabaacadcdacdcadacccaddadaacdbbdadccdbabbdcabcddccbcaddabccdaabdddbcadacaabccabdabddcdacacadbbbacaadaccddcbccadbdddccddcddcabddbcddbadacadccdacdbdbcbdadcaadbcbaabdabbacdbbdbdbdddcaaacbdadcdddadabdadabababbdadcddadacddccbaacbaddabddbadbcbdaccacbabaaccadabadcaadbdbcdbaaabaccdccdcbbddaaaccbdaacacdcbbbddbdccadaacbbabbdbdddadddcdacddbcaadddacddcdddcaadbbaabcdcadcdaadaacdbcdbdbccccbdcdbccaddbaacbbdabbbdadbdccadacbdadcaaddbddadabcddcddbbbbbdbaaabbbcbcddbaadbacdbdbdcbadabbcdcadabcdadacccdcabbdaabdcacdcbbbddadcbddccdccaabadaabdcdbdacccacccacdcaddaaacadbdabcdabbbbccccabdcbadbcbcacdddbaaaaabaabccacacdddaabdbbbdbbcbddbdcbcccabdadcbbbdacadcacdddbaadbcadaddbbbcdbbaddaddcaddcaababddccdddacabbcbdbddaaccdadcadadcabbdbbabbcdacaddacbaaccccdcdbbcdcbdacadabdbddaadbadacdddbdddadbacbdadaabbcbbdaaddaabdbaadacaabcaabcbbdbbcbddbddabdcbabccacacdcbdbdcaccdbbdabaacabcacabcbabddcaacdccadabccdcdcabbaabcdbdadbdbbdabcabddbbadbcdcdddaaaaacbdabacacdbadaadaaddbbacaabbadadacdaadbaabccadaccdccbcaabdcccaaccbccbddaccbcaaaaddddcbcaabaabcadabaacadbcaabaccdcccaddcaadabcbdbcdbaabbdabaacdabcbcbacdbdbbbaaadbcddbccbabbbccddaaaacddccaabbaaaccddccdcbcbcbacdcdacddcbcbadcbbbabadbadbacbabcbacdacdadcdccbccbaacabbbabbddacdbcacbcbbaddacdddddbcdddcbacdccacabbcbdcdddcbcbbdcddaddcacbdbcaaabbacbadcbacccbdcadddcccccbccadaccdacbdadccdaaddcccbbccbaaaadbcbddcaaadbbcddbaacdcdbbabacbabddddcadabacabbddccdbddcabcacbbadcccdbccadabcccddcdabbaddbcdcbdbbcddaccdbdcadbbcccabcaabbbccacccaaaadcbbaacddbcabbbadbaadcaabcbadbcbdaababacadcdbaccbdbdbdbcaaaddbbcadadccbcbadadbacacccdbbbbdccbccbadbccdbdbabadaadabdddacbdbcaaaadbbdcaaacdabdcbbacbbacccadcdddacbadcdccdccdbddcccadbcaaacccaaaadadaaaccacdcbbaadadacbdbbaabdabcacbddccbababbadaaacccccbcddcbbbdbbcddabbbadcbcbcdccdccdbcccdbbbbabbbbbbbcaddddddaddbabdbcdbccdccbabcaccacccccabbbccbabaabaaaacccbabbcacdbbcbbacaccaacacaaadcadbbbcdbbdbcdbcdccdcacbbabacadbcaabdcbcccadbdaacccdacddbdbcdcdcabdccaabddcabdadcccbbbdccdcbdabaaccccbdcbcddadabdbbcccaadbdbacdddbcdbcccdbcbacadbabdababbbcaabadcadaddcccdcdcadacdbadbbbbcdccbbaccbacbbbaadddabcacdadbdddabaacadaaacbbcdbccacdbdbdbddcdbcdcaacbacdadabbdaacccbcbbdbcadcbbadccbaadabcadbabbbccbccdacbdaccdbcabcbadbcdaaaabbcabaaabcaabdccacdaddcaaabaaaadabbbcdbadbdcabbbcdadbcddcbddbcbadaaacbdcdcdbabcbddcaadadbbdaadcdadcddadcbbbcbdbccbabbcbbccdcacbabdbdccbcdacdcdddcccccbaaabdadadcccdcbbcacdbcabccaddaadcbacbcbbbcbadbcbddbacaaaabbbaacbccbdbcdddcdbcdbbdadddabbcdcdbcdadcccadbcdbacdcdbbadbcdaadcadcbbcacbccacbbbcadbabddabbcdcdacadcdadbccdccaaccabcddacdcadbdcccbcccaddcbbdaadccadcdbdbabdcaabccddabacdacdacdcddcccdbcbbbdaababdccbcbaacdbcddabbccadbcdbabdadbbcadaaacbbdcaadcbbacbdcddcbbdaccbbacabdabacaddbcccbcbcddbcadcaaabccccacbddbdacdddadddcaabdbbdaacbbadbbbccaacdbdabcaabcbdaaddadabccdddcbddbbaabcabdbadadbddcbddcbccdcbbcbbbdcabcdcbcdaadddbbaacbcdacadabcbbbbcbdddbaacddaaddbdcdddcdbcaacaadbcabdadbbcacbadbdbaaadbabacadbdbdbbdadaabcaabbbbccbccbdaabaadbdbdaababdadbddbccbbcabbdbddabdadddabbaaaaacabaccaabababdcaacbacdbabadcacdbbbbacaacadbabdaabcdabbdcbcabcaccdaacddaaaacabbacbdabccbdcbbddbadaacdcaacacaabbdbdacabcabacddbbcbbbcadaadbbbbcdbddbdbaaaccdacdacbadbdacbcbdbadbadbabadbaddadadcacaccccacbbddbabadcbdbccbaaadadabcddadbdbbaaaabaacacdadbcdcccbdcdccacabdddbbbbcbabadccddddaddcddaacabadbcccaadaaabbbdabddabbbcdabdbcadbdadbdabcccaccddcadbbaccdaadadabacadbbbbabbbcbbddcadbbcabdcdbcddacdaaddadcbacabbcccdcddadbccccdbadaddaccbaccaccbcdbababdadbbbccddccaadadbccbcbccacbddddccadcacbaccaccbcdbbdcbaccacdccacccacbccadcbadbdbccadaadadbbbacdacdbdbdbcbcdadcabbcaaaccbbaabaddcaccccacaaabbabaacbcabaabcdcacdbabadadcdabcabacbbcdabcbbcdbbabaadaabbccbbabacdabcabdcacdcccbccdbadaabacddbdccacbaadbdbdbddadbdbdbcbcdcdabddbaadbaadbabbacaabcdccdaddadbcaadcbccaadaccbdccadcbccaaddaccdcbadadcbbaaaaabbccaccbbddccdcacdaddacccbbddcccccbdbdacadcccdcbdbabdabddbcddaadadbacdbdbabdbbcabdbbccbbccaddcddcddddbaacbddcadabacadcbdcbbccacacbcbbdbbddbcdbbdcbddbcbacaaacddcdccbacacdddabcdccacbddcadbbddccdcdcbbdacbbadacdcaabadcbbddabaacbdcbbbcaadcaaddbcaadcaadcbdcbccadbdcbabcddbacbaabdaddddbddcaadcbddbbbdddacadbdbdadacbcaccaacaaaacaadccdbcbacccaadacaaacdddccadbababcacdcdbcaccabdccbacdaadbdaacbadcdbacaaddddbbccbdccdaddcbbbacbcbdbaadccdbbbbbbdbdabbdbabaadccabdcabbddcdcadddaadbdddddabaddacaaccabaacdcadaccdcdcccdadacbdaddcdccbaacacbabacbbaababcdcbabdcddcdcccdbbaabacadbbabdbabddbbaaccabbcbdbbbcbcdbbbdcadddbcaabbadcaabdbbdbbdcdbccbddbcdabccbaaabaadbdcddadccadcbdcddabbdabcabcddadcacadbaaadcbcbacdbacbadaaaacaaacaabbadbdabbcdadaababbdaabdadbdddbaaaacacdbadcbaccacbcbcccadacdaaaacbacccacbcdbddaaabbbcacdbcdddcddbccdcbcddcddaacadadbddcaccddacadccdbdcadabaddbadcdaadaacccdbbcbaadaaadbbcbcbadaaacdcbdadddabbaddccdbacdacdcbabbacdaabbdbabdbcdbcbbcaccdabcbbbdddbccdcabddabbddabcabaacbcbaaabcbacdcbcdabadaadbdcaabadadddbdacdddabcaddbccbcccbbacccdabdbbdabbaaaddddbbddacdcdcadaadabbcacdbbdbdcabaaccdcadabbcdbacbcdcccbccaccaaabadbcaaacbcbcaaabdacbcacacbcbabdbdabddbbcdaaadcdcdaaccbccdaaabbcbadcdbcccdccabccdaacdcbddaccbbdaadbddbbdacaccdddaccadadadadcaaaabcbcaaacadcbadabcaadbcbabadcbbdcbbdbadacdbcacdbcdbbbbdcbcbbcabbacdaddaabdadaaaadbccbcaabacdbdbbadbbaccdaaddcdbbdaddbcbddcdcdcbdbabaabddbccbccaddcbdcbbdddcdcdbabbbacacacabdcadbbdddccbbdbbcccacabcdcbddbaabcabbcbaabbbbdddccaccacaacddabcbabaacccdabccbdbadbbccadcabdbbabadbaaddbdcbbbaaacadbbcdcbcaadabdaccadddaadddcabdbdababacaadbcdabddabddcabcadbbddbddcacddcdbaacbaccaacaaabdaccaadaacdbaccddbcbacdadccbbcddbcdddcbcbbbbdbaddacaaaacbdbbcadbdadbadddbbddcdcabbadcbcbababadbdbaadcaabdcbbdbcbababccbababccdacbbcdcadccdbabdabdbcdddbdabcabaabbcbcaddbdcbdbbdbdbcbbdaaabddaaddbcdbbcbaabbcbbccbbbbddbbaadaadbcaabdadcbdbbcbdadcbdcacadaadaacbbdcadacbcddbbcaadddddcddbbcdadbcccbcabadbcabbcacbcdcabcbcbcaacbacabadacdcdabbcaddcabaccdadccbbcadbbaaaaaadcbdadcdadadcabccabccadabdadcdcbbacdabcacacdccdaccaddbddddcaacccbccbddaccdcbbddddadbcddcbabcadcccdcdaccabacddcadaaaababcaabcbaaaaccccbaaaccbacbcddcdaacadcadcbaccbbbcaaacbddbdadaaabbddaacddcbcacbacbcaadccacdcdbabbcaabcaacaccccdcadddbbcbabbdbaabdbdbbdcbddcbdaadccdddbcdccacbcdbddadacbacbadabcccbabbccdbaccdcdbcddcdcaccadddaabacbbaddcbdbcccbaabbdaadbdbabcadddaabcccacdbcacdbccbdcbbbbbdcaddbdccbaadcabcdadcaacadbabddbcadcdbbcdcbcdabbacbdabddccbcbcaadcdbbdbacccaddadccacaccacacdcdbaacbbcbbccabcccbbdcbaabaadaaddcbdccbccadbcadccbbbdbacacbbbabdaadbadbcddbcabbabaaaaacbabdcabbadadabbdaababcbaabcadacadbcabcbddcdcdcbaacccadcaababacdadabdbdbabacdbadddbbdddddaaadaacbcdbddbdbabadcaccddbaddbbacabcbabdabcddacbbdbbbadcdcddabcadcdddacdbdddcaababacadddccbccccdccbaaaaccaccacadadadccbbbbbbbdcacbcadacccdcabccccdacdabcaacacdbaabacddbbcaabbbdacccdbababaabbccaccbadbddaaaabdcabaacbdacbaabcadacaabbdcbddbccdaabababccdbabdcdacccbdaadbaacaacbaaacccddabbcadabaacacccaabccbabcadacabaadccaadcacbbbbaddbcaccbabcbbdbdaabbdbabbbcdcadccbacadaadddddaddcbbdabbbcacccdabaddaabdbadbacdccbbcccdcbdccdbdcddddddccadadccabddbbccdadbbcccdadbaabadbbdcdababaabaababcacccdbbbcdbdabddbacdbaddabcbccbddbddabaacdcaddadbccdbdbbbaabcacadcacdcaddcdbcaddbabcbccdccbaabbddaadbdddccbdaaccacdcdbaaabacbcdbbbdabadaabcdbdbddadbbcbabbdbadaaabaccbcdbcadbddabdaabcbbaabdbdcddacabcabababbdbbdcdbbdcabdacabadaddbcdbddddccdbcaaacbdcbcbddaddaacaacbcdabcdcbbaabaacaabbdccccbcddddaacccccabaaddbcbcddccddccacccbadddccdabdabbcbcbbaaccaacdcbdacbaddacaabdcaabccdadbabbbdcbbddacaaaaadcbaaccdbacddcbdaddadccdadaacacdaddaaadcdbbbdabbccddabdaacbbbaddddadbbaabdcccdbddbdacdddbbadddaacaccbcbbaccbbcadaccddbcdcbaccdbaccdcbdbbdabdddbbacdaadbdbacbbbddbcdbccabddadcbbbdadbdcabdbcddcdcbdadbcaddaaabcacacbcbbcaccbacdadbbabcbdbdccaccdcaacccccdadddccabdbdaddadcddddccbdaccaaadabacaddddddddcaddabbcbbcbcabacabdababbadacaadcaabcbadaabbbcddcddbaacbacacababdaabbcaacbaaabcdcbbaacbbababbabcdccbabcacbdaccbdcdaacaaacbbdbcabcdadcbaccbbcdaadddbccbdbcbbbcdcdbacabaccadacbdbaaadadbdabcbbddacdabcabcdcdbcdbbacbddaaaaddcdadacbcbcbabbbcbbdaccadaacbabbacddaccdcbcbabadddabcdbcabccbaddcadcddccaadabbcbdaadbadbbdadcaabaabbdadcbadaacbcadbcbacaacbccdaddadcdcabdaccbbdbacbbbdabdaccdcddbadcdabaabbcbcdaaaaccbdaddbbcabcddddcdddcbbcccdcccacdccdcbaabdbcdbcdcbadcbdcdcddbbbbccbdccbaaaaabcabacdacccddcdccadaccbaabccabdbadadadaaacdabbaadddcdaaabbadadbbabbdcadcbbabccadcddccdbadddccaddcaacacbdacddacababdcdaccdddcdccaabaaaadcdaaddbcbdbcdcdbddbdabcddbbacdddadbaaccddbbaadadbdcbbabcccacaacaaddbaadbaaddaaabbaacddabcacbcbbddcbbcdadadbabdaaddbbdcabdabcbdaadcbccabbbdbdbdcabccbcddbbdadcddadccccbbcaadccdcaacdaabbbbcbddbdaccbddaddbadaabdacabbbaddbacdacbddbbddabacdcbbbcacdadabddbdabcdacbdababbddbaabbaddcabdabadcdcdccdcdbcaacdcdddbbccdbabbddcddcddbaddbcdcbddddddadcdddcdaadbbdcdcacdaadddddbdbcbdadacaaadcbdcdadcabddbcdabacccbadabadadabcdbbbbacddbadadcbacdababcababaaabdbaddbcbcbcbdbdbdcddaaabadbbcbabbaddbabacbaadcabcdabcdbbadaaddccdcaaadacbacccaabdcabcbdbaccddddcccbacbabccbddbbabcbacbddcdddbbaabdddadaaabdabccccdddbabccaadbacaaacacaaaaddcadacccabddcccdabcbbaaabdcbbbaddbadbcaadbcbbbaddbddababbddacbdcadbdabbbdcccccabcddcabdbdcbdcbbdaddaddacabcdbdbbbcddbbccdcabacddabadbcbcbaddaddcbddcddabaddccbaaddaccdcdddbbacccabadccbdadcaabacdabcaccccdaacdabadcddcccbdbdadaacdbbccdcacbcdbbbdbbacbaadadbbbcccdcdbdcdadabccdbdbcbdbabcabbdaddbbbacaabaddaaacbaccccdcdddccbdbdbdcdbadadbddcdcdadcccdaaacabdacacbbdadaabdbbcbaacdbcadacbcbaadaaaaadccbaaddbcdddacbccccccbdbdcbdddbdbaadddccaadbaacbbbbbabdccbcbcccacdbabbbcbbabaaddcacabcacbdbbbadbbcadddbaacbadbbbdbcabbbccdcdbcadadddbaccdabdbdcdbcdabbdabadabcccadcaaacbcdcdbdabdddbddbadbdccbbddbccbaccdcccdaabbddbbcccdbacdcddcaaabdcdcbaccddabcaacadbabddcbccdbdcdbcabdaddccbaacdddcaaadcacadbccabbbccbaddddcbdcbdcbdaddbcaadadcdbddcdacbacbadabbdcdadddbbaacabacbacadcccdacdbbddccbbabcbdadcdadcbacbcbcacdcdaccacdddbbcbbbcabddbbdbbabdcdccaaadcdcddcbabdbadcadbddbbdcacbdccbacbbdbcaabdcddbcbacbddcdccbcdbbacccbabacabcaaccdddaaddadabdabaabadbbcacaadaacbbbadadadddbaddacbbddcbaabbaccbdaabddadbadadcccccbdadbabcbdbcddcadbbcadadbcadaabacabcbaaabbabbabdcadabaaacdacabaddbadabacdbcbcccabbaddbcccabbbcbccadcabbdbdcbacabcaddbdddaadccacdbcadccdbdadcdaacdccabdcbbadddadaabccbaacbcbbbcdabdddbdccbabaaddaacbcacaaaabcaabcdcbacadddbbdbbbbcbdcbdcbccddcaabbbbdacccbadcaaaaadbacdadaacaadccbaabcbbbaaccbcbbadbdcadcbbcdadaacccdcadbaaccaadaababbbbdcabdbdbcaadadbbadcbbbbdabacdccbbcadbacccccaaddaadbdcbbbbadabdcadcaaacdddadbdbdddbabbbadcabcccadbbacadcbbddbadccacccbdaabcbddbcdadcaddddacdcddcbbdacbabcaadcccddbccabdbbdcbddaadbcdcbcdbdddabbbaabdacacbcdaddcccdcccbdbadbddbcdbdbabdbacbadbadabdbdaaaabcbcdcbcdbcdcabcaaaadaabddcdbbcabbcabcdcacaabaccbbcacacdcbacbbccbbbddccdcbbcdcdbbbdbabbadaabaddbadcdbbcbcbbabdbbcdacacdbbbcadddbcbcdcbbcacbbbcadcdccdbdcbcaadcaabdddacdbacbabbddbddabbdcaadcccdbcabacbbdbdcdbcacddccdcdaaacdcaadbbbbabcccaabbabcadcaadcbcdcabddddbaacdbbdbadbdacdbdaabcbddbbbadcdbddadaacaccacacdacaddadabbcadddaaddbcaacddabacacacbdcdbbaadacdbdbcabacccdccdacabbbcacaacbdaacdddacadcbadcccacaccaccaabddddcbdcbbbdaddcdbbacaaacdcbacdaddacacbadbcccbbbacdddbcadaccbdcbcdcaaaabcbcbcbccacdccadcccadcddaabcbabcbdbcacccbcbbcacdcdbcadababcdaadcbbdcdbaaaaabaabdaacddbacbccdcbcbcbcdbadbbccadadcacabaccdabacdbadbccccdadcacbbddbdaaddabccdcbabcaddcdcccddddaaabdbcddddaaaddcbcbcdaacabdababdcdcdcbdbdddcbcdbbacbcbdbcdbbcabacaacddadcacdcdabacdaadbaddacddcdcdadcdcbaabbdcabdbddaadaddcaadabbaaabddaccdadabadabdcadccbcaabcbdcdaabcdcbdbddcacadaddacabdcacbbdbccdcdddbaaddbcaccabbabbabcbacbadaddbbaabdbdaddbadacbdddcacddbbbddaccaddaadccddbdcacdaaaadbcaababcdcaabbcacabbbcbbdcdbdaadadddddbaddcaccaadbbbbdbcacadbbdbaaacadcdacacbbabcabcccdaadcdbaabbbaddcabbddabacbbababadbdbbdddddacddabbaabadbbdcbdccbbbbcaadbbbbcdacadcbabccaaddacdcbaaddbaaacbbdacdddccaddbcdcbdbcdbaaabccccbbacddccbdccaabbccbccdddbacdcbbdccbaabcbdbccbbbababaaadbaaaddbbddccccbaabcbdbbacccbbdabcdabddbdaccbdbaddacacabbdacdbadbdbadacbaacbcacaaaadbacdabacadbabcabcbcccdcbcdaadabaaddbcaddbccbbdbaabdbbdcadbbbdabcdddabdbbdcdacbdbbccacaaabdbbbddbdacdbadcaacadaaabdbbdacbdddbbbcaabccbcabdbadcabcbaaaaddddacadbcbbccaadccbbdbdabbaddadbabcdadbbbaaacbbdbcdacdccdbcdcbbaaaacbccbddddbbaacabadbaadcaccdbdbbbdabbacdbbadcaacccccddcababbbbbbdbdbcbdddbaaaabacdaacaabdbddbacddcdbabdbaccbddbaccbccbdacbbcbbbbccdbcaccdcacaaaadaabcdbaddadcbbcccadacbbabbcbbbbbbbcdbbbaacbcaddaccccacaccbcbbbacabbbabaaaccdddaabbbaadbcacdbbdcdddcccbbbcaaadcbbccddcbcbdabbdccababcaacbbddaadbaabcddbbadaacbabccdcacdabbbddbaacbabacbdbcadababacaddbaaccaacabaddadcccabacdbaaaabcabacaddbdcbdcdbbcdbbdaadababbcdbabdbcbdccadbbbcacbdbcbdccddbbdddcdcacccbcbadcaaccaaaacaccccbbaddabdacdbadbdacadbcadbdcaccbdcddcdabbacbabbabbcdcabbbabdadcbcccdbabddaabbbdaccaaaaaaabbdccccaccbccbcbdcabcadbaadadcaccddacaaaaddbcbcdbadbcddbdccccacaddabccddbdaccabbbccbcbdbaddaacdcddcdcbaadacbcbdbccdddabcbdbdaccbbdddabbaabacdaacdddccabdadacacacdcdacaddcdbbdbdcabababccaadadccadbdabdadadacccbbdcdacbbdbdcbabbddbaadcbcbcbaddbacacadbddcabaabccdcdadcccabdbcdaabdccdadbdcbcbdabbcacacbabacdaccabbdcdacbadcbaadddbdbacabdcabddcabdddbcabbabcdadaaddbcabcccbccacdadcbbacdddbabaacbbdaaacdbbdbdcdbaddcbbdaacaaaacbdcacbddbdabbddcbdadaacabaadbcabccadadabacbcdcdacdaaaabdccdbdcbaababcbbdacbaaabacdbacbdcbaaccdacdbbacbbdccdcbdcccacbddaddbbddacbdcdadaacbdadcdadccbccadbdccdcadcdcadbcadaaabbabddbdcbcaabdbaaccababcadccbbbcabaadcddbdccbdbdbccbacabaadadbbbcccbbbadcbccddaccabbcddaadcbbabadcdacdabdbcccdbbcbbaddaabccabccdabbddabaaddbaadbbcacdbbbcdaddadbdcdabaadcadccbbabbaacbdbadaaddacddabbabdbaaddbdcdcbddbadcbbadaaddababadbcabccaabbddadbbbcadbcaaaaacaadddcdbadbcccdaabadcdbbaacbdaccddaddbbdbdcacdbddddacacdcadbbdcdabdcbaaccbbdcddabdabdcbdccbbddaababacdabdcdabdbbccdcabcbccaabcdbadccbabacaadddbcbbcbccbbbadccaaaaabdcdaaacbdccacacbcbadabccabccadbaddddaadaacdadbacbddabaaabbddbddcacbbcadbbcbbdbbcdaddbcdbdbcbbbdcadcdccaddadcabdbabaaccccbdcdddbabcadcabbababbbbcdbbaaadddcabcdbdbddacdcdddcbcbddadcbcabaddaccbbcaccddccacbabaadacadcdcbcbbbdcadcacbbdbacaacccabacbaabbddbdcbdddbcaadaaababdccbaacababdaaadacbbbddbbbcdcaaadcacaabcacdacbbaababcbcbadbcbacddacbdabccbcaaddbbaadbccababcbadddaccabdbdcaddccabdacccdaccbdbbbdaaddcbdadddbdbdabcabcbcccabccabbcbacbabccbdabbdbdcbdbacbbdddddbdbabdbdddabdacaabdcacbdabccaccdbbaccbdcaabbccadbadcbbcdbdcbbabdccbbccabcbbdddbabbbabdbdbdbdaaaabacddadaabaadbbbbaabbbacdacbddaccbabbbadddbbbbabdaaabcdcddcdcccdddadadacaadcbabcdaadaadcadccbbdbbaddbbbaabdcdcaaaadbbabbdaccddbcacbcaaabdbccbdbbcdddccacbdbccabdacbabbaacabadcdcabbaddcabacbbbcdcdcddbbbcaddbbdadacbaaacaddaacadbcbcdcdcacaabadaddccacdaaacdabaddccbaaacdddccdbbbbdcbbbababdbcadabddcacabcabdabacbcbcabdcbbacbcbccdacdcdcabaacdadbcbbccbdadbcaaaccbaaadaadabbcdbaccbdbdacbbcaadacdcaddacbdcbddbdabcdbababbdcacaccbbaddddccaccccbdcdaaaacddcddbccbbacacccadadcbdccdcbaaaaddbdbcadadcaacadbbccccabccccbdddbbdccaddddcbbddbbccabdadacadddbacacbacabbcdacbcdacdbaabddabaccdcbbacaddabbdbdabcdcbbcccadbcaadadcdacbaaaabbccaaacbadabbcdddacccdcbcdbcbbcbbdaadcbdcdcddccadcbdcaccadccaabbbbbdcadacaaadcdbcdbdbbddadbbcabdcbaabbabcbaabaddabbddabdbbbcbadcbaaadcbbbcaacdccabbddbacbabbbcdaabaddbaabdcbbabbdbbaadacdddcdbbbabddbdbcbacaccadccadcdbcbbcbddbbaadabbbbdbdccbbdbdcabadbbabccbadabbdcacadbaadadcbbabdddddbadbaacdbbccabdbccdaaddadcccbbcccdaccbbcdcadbdcaddacdabbabbccaaabbcdbdadcaaaacadcdacdaacbbdcbcbbdccbacdcadaabdaabaccdbddcccbcdcbbbcbcddaabdbdabdaabbbcccbabacdbabcbbdcbdacababdadbbacacacdbdddbcbddaacabcaabaadcdaabddacaaabdccbaabbdcdcbbcdddbabdaccbccbbddbaaabbdcaccacbbbbbbcaaaadacbabacbbdcbdbaaacadabaaaccbbddcbbaadaabcdddddcbabbcaabdcdabcdbacacaccbacaabcabccbaacacacabaacaaddcadcbbcdcdcbdaaacabccbdbcccacdaadaaacbaaaabbbacdadddacdcbbccddacacbbcddabdaccbcabdbdddadbdddccdcbbccbacdcbaadaaddbdcccabbdbacaacdccbbaccabadbbddddbbbcccdbdcabcaccdcccbbbdbcbbccccdcacccaaccbcadccaadabbdccdbdbcacaacbbbcbaaddacadcaadccdbddcdbacdcaddabadcbbbbcdbbcbaabcabaddccacadcddcabbccaddcaabcddacbdadaabcadbcdcadbbcdacadbdacdddccadccbaccdaaaaadacdabbcbcaccdddadbddacbdccbddabcacacacacacaaabdcaabdbcdcbaabbabcbbdaaaabaacdcaabcbadcdbcadabacaaabdddabcbcdbbbddaccbcbdbaddcbdabdccbbcbabddcdcaccccbbcabdcddaadbadaacdbcbacbaccadcbaaddbcadccaccdababccbcbbbadbdcbddcabaabdccaabcaadabddccaabadaabdacadaacdaaaaaacbdcaacdcdbbcdaacbdbbabaabbccdcaadbccaaaaacdadcbdbbcdbdddcbbbcacdaabdabaddbadaaaabddddaaaacacbcbcadcbbaaacabbcdcdccacaadadadcbcddbdbcddacabbaddccdccbabddbadadaccacdccaadbdacadcdbaabdaccbccbdbdabaabcbdcacbabbbdcadacdbddbacdccbbcacdbbababbbcddbdabbdccdddabcdcccddcbdcdbbbbaccabdcadbbaabdadbccddbcaaccdbcabdaabbbdadcccbabaabbcdaccabdacbdcccaadbbdccddabbdbdbcbbdadadacdbbddccabbbcabadcbacbcdcccdccbbdcbbbadbdcbbbbcadaadcaddbbadcdbbaaccbbcdaccaadacdcdcaddcddbbbbaabbdddabaacbccddabaaaccdaaaabbdbaacacbbabacbadddaaaacbccaadddbaaaddccacbbbbcbbcdbadbddaabdadcdcacbbabcccccadabcbdbdaabcaaabddadbabdddaacccbbccbbabadadacdccabaccaadcccbcacdbadcacccbcdcbbdabbcddbcabacdbbcdcbacaacbdabacdbaaccacdbddbadcccadcabadabaaabcadacbabdccccbcaddaacadcbaabdbdaddccccccdbcadcbcdbdbadcbcccbcaaddcacccdabbcbbcdaddbbaabbbadbaddbcaddabdccbbabbbbacbbcbbccaaddbbbddbcaccccccdbdcbcdbcbdaadbccbbdbdbcbbcaddcbcbccbacdcbbdcbdddddaacddabbacdbddcbadcdbcbccbccbccddbadbabbbbddaabcaaaadaabdabadabbbcdbacbccdddbddbdadaaaccbabbdbcdaddcdbbbbbbacbcabcbacccacacddabbabbabbdcdddadbbbdaacdcbcddacabdabdbacdcaaaccadddacbccdbddabbcaabbcddcaaddabbbadbcbcddbbcdbdcadaccdcdcccccbdaddbddbabbadaacadbbbdccbbdccbdaccbaadbbccbdabccbdaabdbbdacccdbdcccbacadcaccbbcadcbdccadcacdcadadcbadbdbcaaddccaacdaaccacdbccacaddbccdadcbabcdccaacbdbdbbadcdbabddabbbcbdcdadbaccdadaadaabcbcdadaacdacbabbcddadbccadbabcdcbcbaabbaaacdddcbcacbcbcdaabbdbbbcabaadacbcaccccbabcddadacabcadbbababdbccdbbacdbccabdbabcbaaaccdddddbccdaacadcabbddadbdcbaccbddaadcbbcabbadbbbbbdbcabcbbbbbbabcabbbcadbbbaaadbcaaacbaaadcbcbcbacdccbbbdbbcbbcacabdbbbbdbdcabbdbbbcdabcccdacacaadbdcdbcddddcdbbdbbbcdbaadabccacaabcacbaadcadadccccacccbdcccacbcbdbcdabcaacccadaccabaddbaaddaadbdaadcbbadbbddbcabaabcaaaadadaabbaaddbdbbdacaaabdaddcdaababcacdbcbddbbdcbcccabacbcddadadcdaccbcabadcddbcdbbcacacdbdaddbddadbbdcbbbcddbdbbbbbccdaadbdcbaadcbbdbbcbddcaacadcacddbbaabbcccddcddddaadabbdcbbdbbbdbdaaccacbcdbbaaaccaddaccbbbcbcacbbacadbccdacaaddcbbbaabccdddcacaccbbdaabaddbdbcccbabcadababdaaaaabddbaadbacccdcccacadbabacdbabbcdcadadcdcdcbdaccdccccdabddbbacaddddcadcdacddabdcddbcaaddabbadccddbbccddaaadaccdbadadacdcbdaadbbaaabcddaabdaddacddccacccbdbcdcaccbbdddbadbccccbdcddaabacccacdccbcacccbadcaadddddddbdbbacdaadbbadbadcababccaddcdcdaddbabdaaddbabbdcccbdbddccbdddcdacaccaaccdacccddbcacdbcddbddcacbbbacbadbcbbcabccbdadcdcbbacaccccbcdccabaacbaddacdddadacbacaddbaabadddcacdbddcacdbcadaabcbdcabdbcbbdcdadcaabcbaabcddbbcaadbbbcbddaaccabddacabcbdcbcbdcdbcbbacdaabdcaccabccbadaaadcbdddacacdcddcbadcaddacbdcacaddcdbddacbbdacdbdadcbdaadcbcdbcbbcbbadcccdabdabddbbbbbaddbdccadbaddacacbbbcddbdddbbdbadbbbccbdcadbdbbccadcddcaadcdadabcdabcbadddabdccaaacccddabddbacbcbbbdbababdbccdacbdcabdabbbabadababbddbcabacbccbaadbccdbcbccacdbbbaacaccccbcbdbbdcaacbbcbcdacabdcdccbabbbbbdcdbaddbddcadcabaccbcbdcadccbcddadbdacdadabbadbdbbccdcbdcdcacbaabccbcbacdddcdbcaccbbbbcbbadbdcdabadbbdadaadcbbccdbbdcabbdbddcddaadcdcbdbbbcdadaadacacdcbbacacddabdadbcdbaaaacdaccccbccddabbacbdacaccadcdaccbaacdbccbbbabaabaadcccdcbdaaabdbccdbaaccadcdccadbbcddaddabcdbaabbaabacabacbbbcaaacdabcaddaaccbbcacdababcdbcdabbdcdaaabacbddbbaddbdadbcacaacabadccacddcbcacbcacdbabddbcdcccddddbdbddddbdabcbbabddbbcbabbadbbdcdbdcacdcbdbbdbadddcaddababacadaadbcbaaadaadccbcadbdaaaddaabdcadadcdddccdbddadcdbdddadcdacadcaabbdacddccadbdcdbabdbbdabaadabababddaabbddacbdaaddbccdbdcbbaddbbcddbaddddaccddbbacbcdcadcadbdaadadccacaacccaadcbbcadccadbbacadcbaddaadbcadbbdddacadacbbcdbbcbdbdaacadcbbcdbdacabbbcdaaabbabdbabdddadbaacbdabadadcbabdcdcbbaccbccabadadadabbbbbcddcdddccbaaabbdcdabaabaacdaaabcaabcdddaddaadbaaababcbddacbcaaabcddcbcbacaadbaaddbcbdcaddcbbadbadbcdbbcdcaddcdcccdbadccadbcacdddbbdacbbcbbaddcdccbbbadbbcdadacbbbdcaddddaadcdabcbbacadcbaddadcdddbbccccdbdaaadbccbbcccaabcbadabcdccdcbcbddccaaacddadcdbcdacadadbbbdbdbaccbddcbdcacdaaabbcbadaaaccaabccbcddcadabcaacabacbcbabccabbccadddcaabbadccddbcacbdcdcbcbcbdaddacdacbddddabbadbccadbdaacacdcddcabdaccbadbbccadccbacdbacccbbcadccacbcdaadbaaadcdddcddaddccdcdbcccacdcabbbcdacdbdacdabdaccbcbdddbababbbdbabcccadabbdbdcdbcbdcadaccdccdabacdccbbcdbbcddcdaaaaccddcabcdadadcaddbbacbcdbabdaccaaabcacbacbaabbcdbbcdbacacbccbbcdbababccbacdcaacdcdccbdcacbacaadbdddbcccbacbbbbcacbcbdbbdcaadbaadbdbaacbbdadbcbacccdacbacdbbabbabcdaaaccdababcccbbaabacbddbddcccdabcdabcaccbcacbbcdbddbcbddabcbbdbabddbbdcaacdbcddccbcbbdcdaddcbcaaabbbdcbbddbdccadbcacdbdabdcbdaabaabbadadbdccacbbcaacdccadbbccbdccbdccdcaabcacbcdddabcdcbdcbaccbdddccbccddabbacbadbcadacbacccccaabbcaabbdabbabacbcddbacbcddcacaaacabbbbcaabcdccacbadbccacadcbdbbbccccbdddaabbbbddaacdabadccaddddbacdaadbbcccbdadccadbaabacbdccdabbadddbddababcbbddaabcdbacacddcbbacadbbcbbdbdadadaddcaadcabadcbcddcbacdcaadbdcbabacaadabcadacdbacabdbbcdaacdbacaaaacbddbcbaaabdcccccbaddabcdacaacaaabcdabcabaaddadaccdcaacbdadcbddbbddbadccabccbaccddddadaacadabcaddbdbbacdcddbbdddaddcadabaaadcaaccddcbdccdacabbacabbddcbaadbcccaaabcdbacbcdcdabaccabbbbdaabddccdbbddddcadcbcdabbcdcccbcadcccadbbbcaddbdbddcadccadccaadbbdaddcacbacdabaaadcaadbcbdabdccababddcbdacddddcbaacbcdbcdbbbbdcdbbadbabdccccbabcbcddcbbaacacdabadcaaccdcbbaabdbbbdcbbddbdbdcdaaaabdacabdaacabcabcbdbbcabdabccccbbadadadabdbacddabcdabbcbdbdcbbbcdccccbddcaabadccbcdabbbdadabbaddbdadccccadbabcdcaadaddcabcbdbdbdabaacccbcbadadacbcdbabcbddcabadddaaccbccadbbbacddbbddcacbdbcdbbdccbaccdcdaabadcbcabaddbabdcddabbacabccdbbcdbbcaadcdcdcadcddbcabadaabcdadaccbbcdbbaadacdacabdccabaddbaadaddadddcaaacbdddabbcdcdbdcadcdabbccdcdabdbccbdbaacbcacbcbdcdcdadcabadbccddcdccccdccccbdacbbccaaddaddcdbdbdbacadddcbaabccbbcadadbbbabdcbbbdaadcbcaabdbccadacbdbbadbbddbdcbddacddaadcbdcacbadcbadbcdbacadbaadabbcbbcdbbcaddbcdccaddbccbcbccacdbbbcaaaacbbddaadcdcbdccddbaabddcaccaacdcbcbdadadacdabbdcabcabadddbadbbdcbbbcdccaaaccbbadadabbccadacacacaaacaaaddbabbbbbadbbdaadcbbacbacdccbddacbacdcbcaacaabbacbabcbbdaccbaabaacabccddccaacbbbacbbddbadbccaabadacadbcdcaccadbaccccadabbbaaabadcbbacddbcbbdbccdadcddaaddccacddaddbbddcdcbddaaccccaaacdbdbbccbbdbcdcbddabdddcdddadbdbacabdbddabbddacbacccdcbaadaaadaccbcadbdbbddddcacaadddbdcadbcbcccacddadadcddbababbdbdcabbdbcabdacdbddcadddddbdddaccacddbdcdcabdbdccbacddbbacadbaaaaddcaccaaabcccacddcacacaddaddbbccacbccadabacddccbabddbccdabbaadbbbdbcdbabaddaabbccbbccabcbacbbbddacaadbaaadcbbddadcbbdccdaccaabbabacbdcdcdadbbcdddcbdadbdbdaaabddabdaccbdbbadcdccdbcdcabbccabccaccbcbccdddbbaaddabbbabbaabbcbdbccdacbbcbddbdcbddcacaddbcaadddabbccabbbdcccbbddbbaadbddaaaabbbcaccabdcdddccaddaabcbaddbddbabaaaaccbdbcbddadcaaadbabbdddccacdddbcccacccbdcdbcabccddbcbcbdadcdaacdaabbdabcabcacbbddccdddcaacaabbdcbdbaccadaabcccbddcaabdaadbdaababcbccbddabbdddbcabccbacacabbbdcbdddbbdabcddcdadddaddbdbcbacabbbccdacddcabaabcdcdadabdabbdabdbdbbccbbcdbcacdabcacdaadbbbcbbadbcbdcacdadadcacdbcaccdcdcdcbdabdbddaaccdbcdaabbcbaabcdcbccbabdadaddcadaabbcaaaacbcdcdcaddadbcaaacccbbabcbacbacdcbaaadbccbbcaacccbbdcbcaddbdccbbbbdcdbadabbbddcacacbdddbdbdbdaaccdcaccbdcaccbdadbaabdabcdddcbbaccbdabdbbabddcdcdbcbcabbccaacaacbbbcacdadaddbcdbbbcabdbddcbadbdbcacbccdcaacabaddcccdaaabccccdcddaacdbddcbacdaaaccbcdbdacccdadcbcabababbdbcdaabcdadcbcabadabaccadcbbdcbadbdadbdccacdaabbbccccbabbcbabccaacbdadbaaadccbbdbddadadcbcdacddabcabcdabaadbcbacdbbddacabdaabdcbcccdadabbaabcbdbcaccbccbccaacbcdcddbbbccadcbacbdadbbabcdacadbbaaabcbdccdacbcbbdccaacbcaacbbbbbadccbcccadaabbddbdcaaabcdacccacadcbdcdabbabccddaddadbdadadcddbdddbabbdcbbbcdddcacbdcbdcdcacadbaabccbbacadaaabcbbbbdbcbcbbdbbcaadccbaadbacabbcbaabdbacadcbcaddcacabadabccbdbbbdbddcdbbcbbbcdaddbadbbcbadbcdcadaadcbabacaccdcbbbbacdcdbcadaccddcadabcaaacadabdaccacabccbccbaddbadcbabbacbddccaddddddccdcbcbaccdadadbbbbcbbdbbabbcbbccaaaccbbcbddcbdcaabbbdddbabcbcbbdcbacbdbbacabdaddbcdbcbcdcdcdabcacaabbacccdcaadbacabacaddbcdcddbaacccbaadaabdabdbaaacdcabcbcbbbacddacbdabdcdababbdcbbcaaacccbbabbcbaaaacbbabddaaabcddadddabddcdddadcbcabacbdbcbdcabbaccdaddabbddbbadcacbcbacbbacbcbbddddbaadccdddadddbbdaccabcadcaaadbbddabcbdaaccddcccabbdcabacdadbabdcccbbdbdcccbdaaddbabcabcadcccbdacdacccadcacbcccdbbdbddcbaabcbcabcbadaaaadadcbccaddbddcccbacaadabbabcbcdbbcbcdcdbbbcddbccbcdbadaaaccbbcbbbacdacdbaacddcdddddcaacacddbabbbababcdbccacbcbbbabbdbdcbaddbdaacbcdcaacbccbdbcabcbbabcdddbdcbadddaabababccadbbdabadabaccacbddbbbaccacacabcbbdccbacbcddadacdbdabdadbcabcaaadcbacacabbbbbbbdbabcddabbccadcbddadcbdbdbddaddadbaacbdbbaaccabbdcdddcddbababcacbbddbacbdcbaadbacbacdcbdbbbbcadbbbabbdcaccddbbbabaabbddcacaadaaaabdcccdcaacbdcbbcddbaabadbaddcdbabbbbadbccbaddabccbcdbdbbaaabbddabadaacbcbbcbccccbaadccadcbbcdaadcdbadbaabdddaacddbbcaaabcbdaabbcaacaccacdaadabbbdaacddbcddabacbdabddbcabdbddaaaabbdcdadbbacbadbadacabcbdbaccabcbbcbcccddbccaadabcccbddcadaaabcdbabcbdcadbdadaacbbadbdcdabcbddbabadbabddaadbcbbddadcdccdaadbbcbbacbcaccadacdbcdcbbbababdddcbcacdbaaaacacdcbdcbaaabacaabacbdccbbcdccdddabbdcdcbcccbadbcbadbabbbdcaddcdadcabacdacabdadcdbaacabddadabbcbaddadbcaaaaadabcddcdbddbbdbdbdacbdbdabaababadbabbcbcccbaaaadbdcaadcaadcbabcaababdbdadccbcabcbdcabaadadadbaddbaacdcbbcddacbadbbcabdcbbadacddacabcdddabbcababacdcbcaddcadaaddadbcacabdadddacadadbaacbbcbadacbacdaabbaadbaabbdddcccbdaadcacddbacbcbcbaadcbdabbdbcccbabdcbabdcdddccacddcddcbcbdabaadbacaccdbbccabdcdcaddcdadaddbbacdbdbaaacbdabcaccbadaabcdbadccbadaabbcdacbddbbacbadbcddaacaacaaacbbbbdccaccddbbdcaadbccdabaaaddaabdcdbdbaaabacdbddcdcdcbbcbcdabadbcacccacadbaacddccdbcccaacabcbcabdacbdadccdcbcdbdaacbcbbacabccdaaadbbadcbcadbaccdbacbbbbadbcaabbabccdddabbacbdccbcbbacccbcddcbdcdcadcbadbcdbacbaccbdaddaabdcaccdaadbbcabccccbbadabacadcabccdadddddbdacbbddbbdabaaadccabccabacbddabcdabbcadbbbdacacdddabdbacacadacadbcbdbcbaaddccdbbcbdabaddddcaaaababccdcbdbbddddbbbaadcccdaaacdcdabdbdbbbbcdacbcadadbacbcaadbbcdbdadacbbcbaadcdccdcadcaadbdbbbbaadabdaadacabaccdbcddcabdaaaaccacdabbdbadaddaadcacaabcaadbabdbddadcdabdbcdcbacbadcbcaabbcbacccadccadcdaccabaaadbaabbcdcbcdbcddddcdcacbacdabacbbbaadcacabdabcacbdacacdcdaccccbcccdddbdcbcaabdabdcadadcdcdccdbcdbaadbbdacbccdbabcbdbdcdddbadacdbbccdbbacdddbadbcabaddacccbbcabbcbbabbabcdddccbbbbbbababccdcdabadbabacbbccaabacacdcddadcacbabccdacccdddadaccabcddabadcdaaabdcbddaacaddbdadbabadabdacbbaadaabdbcacabccccbcdcdcadaccdbbabdadcdbabbcaadbbabacdddbabadcbbbbccdaabcabcacbbacdcdabdabaabaaaddbccacabddbadbbcbbabbcdcabadbbdcdcdbbbbdacbcabbbcbcadccbacadcbabdaacdbabdbbdccbdbabdbabacbccadacabcbaacbcdadbacdcabbdaaaddaaadcbcacdccdaaadbdcbdabaacbbabbabdcaacbbcaacbaacdbdcaccbabdabadbaddaccbcbcdbdcdaccbbcaaddbbbbbcdbdbaabbdbddaadabdbbdacdbcaddbaaacdbcdcabdaaabacadaadcddcacaccbadcabcaccdaaaabccccccbcddaadbacabdbdcadbacccabddcaaabaddbddcaccaadbbabbdbcbadcdadadabbdbbdaabdabaacbdbdabcdcbcdccbabcbcadaabadcddcabdcaaacadbabccaaaabaaadddacdbbdccaacccaddcbdbbddacdbadacbbddabdcbbacdbadabccdbdcbcdaaddaacccdbadaaacbbcacaababddcaadadaacccdbbbaabcbdaacdabbdadaaadbacadbabcaabbbbbacbaabdaabbcdcdbddbbddadabacbcadaccbabbddadadddbabddbcddabdcddcdddcaddddadadbdcbbaadabbadbbcddbdbabbdbbbddccccbdddacdadbdbadbaacadbadccbabaaacbbbacbbbdbccbbcdbdadbcadcdcbadcaddbabaaacddbccaabcbdadcdcacadbccbcdabdbbddcbddcabbdccaddcbbaadcbadaabcabddacccdccabdadbacdbbdbdbddcdcdbbabcaabcbdbadbbcaababdacbcddbadbbcaccbdadaaccbaadacdddadadaacbccdddbacacbdddaadadbbccdaccabbbcacddbdbdcbddddcbcdbddadbccdadcddadddbabdadcbcccbdbcdaaabbccbdcbcdcbdcacabdcbcbacbbcbccccdbddabdbcdbdaccccdcadbbbcbbccddaababadddaacdbbbbabdacddbadbbbabacdcadbbbdadccdcabccbcabcadbbacaabdccbbddbdbddcdcbcbaacccbcacbacdabcbadbcdcdabaccdccabadcccbddacacbdcadaabbdcacddbabdaacccdcdbdadcddadbaaaccabcadddadabbcbbabccbdbaaabdcdaacbcadbbbaadcdcabaaddaaacbbaaadbbdbdcdaccaccbddacbdbadbadcbbaabccabaabdbcdbcbdbbacdbddadcddaacdbcdaaddbcacccbcbadbcaaadadabcbbcbadabbbbdbdcbcdcddabbaadcbdbdbbcdbdcddbcbcdaabbaddcaccdacbbabacbdbdcdaaccbdccaaacdccdcbbbaaddcddbadccacbbbdacabbbccdbbbccdaaaccbbdbdadaddaccaddbdadcbaddabbcbcaccdbcdbacbccaccdbcaaadcdbbdaabdabcbbabcabaacadacdcabdaacdbddddacdccbdbdcccdbacbccccdcdadabddadacaaacccbdbaaccdcbdddcbddcdaadacdcadccdbbdbddcacddadbcbdbbabcbcaadbdaacddadbbadcbdcbbbbbdabccacadaadbdcabdbabddbadccbbccdcacbbcaccbbcbcabdcbacbbcddcaccddcabdaadcabaacdabaddcaadddcbaacaacdcbcadaababacabbdbddcbcbddcbbaabcabcbdcadacbcdcccaccadcaccaadacccaccccabbcbababbdabcbddacdadccacbacddabccbdaabadabacbbdbababbbbdaadadabcabccbbcbabcbbdaccbaccbbbabaabbbccadabdbdadadbcbcaccaacbdbaadddcacbbcdccaacbccdbdbdacbbcacbacacbabbddddaadbcacbcdbcbbbcbadbacdacbcacbbbcbbbddacdbdbbaaabcdbccccbabacdabadaddaaaacaddcbcbdaaabcdcbdbbbdbdbccbacbcaaadcaadcdcabbcddcdbbdccadacbadadacaaacadbdbcdabddadcccdcccaabaaadcaadbbaccaabcdcddcbdbadbdcacaccccdcbdababcabcdccbdaccbccadccbcacdaaacbaaacabdadbadddaddcaabbaacabbccbadcaacbcdabaaccbabddaacbbaaddcacdbccaccabadaabbbcaddccbdacbadccbaacabacaaddabcbaacdcccbacaccaabaaacaadcadbbddbddacbdcdadbdddcbabdcdbacbcdbaadabadbcdaabaccbcbcbdbccaabdadacbabdccddbcddccccaabaaabbacaaabdacaddcdddacbacbcdddbccdbaabccdbddcddcccbdaabbaccbdbabcabbaddaacacacbddadcadddccbacaadacaabbbbbcadbacbbdabcbabdaacaddadbdcddaacbbaccdabadacdddbcdbcbadbbdcdaabbabcbcabacaaacbcdcacdbaddbbbbcdcdcdbddaaaddaccbbbdabbaddbcacbbaaaccaaccbcdacdbcaacaadbdaddababacbaadcdcbaccbbdbdbabcbbacbcccdccacdcbccbdddcdabcccabaddbcbccdccaabcbcbcaccdabcbacabcaacbcabcadabbabcadbbcadcbcabaaddbccaddcddcabbdddcbcdddbaccbbbdccbbabdadddbdbaabccbdbbccaabdcdbdadcddcbbbbdcadcddcaababbdbbddbdbbddccdcdabdcbddbabdacdaaadbcdbadabbadbccadcadbaaccdbcdccaadbdaadaddcadacdbaadbdabcbacbbdbbcbbdcccbabcccdaddababccdaddccaddcbcaaadaacccbaaadbabaabbbcaababbabbbdbadddcbbbcabbbdbadcdaaabdbadcdbdbaacacbdbdbaaaabcdacbcaacabdacaababadbacbacadcddaadbadbdcbacadccaccccbdbdddcbcbcdacbbbcbabadadbbacacdadaaabbabbcddaadbcacbdbdcbcdacbcaddbbbabddacddbabdbccaccddcababbcbdcaaacaadbdbaaadbbcbdbdbbccacbaabddbccdcdcbbaccdddbdadccdabdbbbacdbcddadddcdaaabdaacbcaddcdbaaadbdbcddadaadbcbbcddabdcdabbabacbdacacbccccabdcabcdadacdbbbdcadddbabacdcacbbcbadaaabcadbbccacddddcdadbcaaadabbacbcbbadddadbcaaabbbbcbadacdbdcaccbdcccbcdbbabcacbbacbabdcddcdbaadcdbabbcdacdcddabdaadbbcadaabdddbdbdcddbcaaabcbdacdcddbcabccaddccbddbdaaaacddccbdbccbadbbcdbddbcbbccbdbbabcbbcdccacbdaccccaaddbbcbcbabbcdbbacadccdbbbbadccdcbabdcababdcbaaacdabbacacbbacbdbdbdbdbadcccabcdaabaabcbbdbbaacaacbcbdacaadadddadcccdcdcaacadbadcaacbcccbbacdbacbddbadcbaaaccabaddbbabcdcdcccbddadabcbbdcbccdccadbaadcaaccabdddbcacccbaacbdaddcbadaadadcbbadcadaaacdaccddddccabadacddababbadbcbbcbbcabbaabacdacdadabcdaccadccccaabdacbbccdcbccdbbaabbaabdddacdabbcdcbcbaddbacabdcddbacbcbdadaabccdabdabdbadabaccdaaddaadcddaacdbaccdaccdbcbdddbdbcdccccadbdaddbbcdacddcbbacbbabcccdbaadbdcabaaacbbabbacdbdbbccbbbdccaacbcdbbaacacddddaadbaabbccccbcaaabdabdbadacbadbadbbdabcabccddaadcdbddbddcbabbcbbbbdcccbbcaccbddbbdabbdbabbddbcdbbddbabddddccdcbaacaabcddcbcacbbcbcdabaccdddaacabcadddbddbaaabdabbbacbcbcdaaabaadadccdccacacbddababdbdbdadcadabdaccccbcddadbbbabbbdcdaacdbbcabcdacddaccdacadcaccdacabadaaccdcbacabdbcddbcdcadbacacdbdbbacbcddcbbccdddbdddbbdadbbbbcbadcaddcbcbbbcdcacccbdabbbadccccdbabdbadbdcbcbbdcddbdccdcdcccddcabcaaadddcbbbcbbbddbddadddaabbadbccbbdbddccdddbbadddbadbcbcbacaccbbcbcaccbacbaabddbcdbbaabbacbaadbcccadccaaccbccbaadbdccbbadcabadbaddcdcdbdaadcbcabcdcbdbbbcaaaddaababbcbbdcddbaaabcaaaccaabcadccccbdaaddcaaddbbaabaabccccbbaaabcbdadbcdccaccddbdcadacdcbcacbbdbdcbdadddacaacbacbcbaddbcacbdbbbabdabbbcbccbddaddbaaadacdbcbccaccbcbcdbcababbccaaabaadabdabcdbcdadbaaddbbadcdddddcdaacdcaddbdcddccadbbccabadbcbabdaadddcdcbbdcbbbacacbdcabdcabddcadcdbdbadbabdadcdabacbaddbadddcbaadcaaddddacccabccbcabaaddabbcccaddbcaacabbdddbbdabcbacdacbabababcdddbddcabcbabdddcbadbdccaabcabddbdbdadbcbcbbdccbcbcdcacacdccbdcccdadbabdabbdcabddcaaadcaaaddbbadbacbbbbacdadadacabbbdbdcbaccbcccbdcbdadbdbdbdcbbacdddccaccdaccbdcdbaddaaaacbdabbababaaaddadbacddcacaabbdddabdcddccdcdbdabcaadcccbcbbabcaabbbddcdbacdcabcbbddddccbbccdcadbdcdbcddbdbdbabcadcdaacddcbcdcbdbbaddcdbabdcacbdbdacbcddabcacdbdaabbdcacbddbaadccbaccdcbbbbccccaacdacbddbbcaabcabaccbcdaddbbddcbabbbadcabaccaadcbdcabdbdddbccbdbcbdcbadadbbabdcbccaacdcbcdbdddcbabacdcacabbcaddbacdddbaadcaadadcbadcddccaaaabdbacddcdbbbaadadccccaacdacccabbaacdcdabccccbccbcaaddbcbdcbcbaaddaacacbbbaccbdbdcbdaaddaabacdacdbdbddcdababcddcabbdbababcaaccddddbdbcdadccbadddcaccdbabbcddcbbbdddabaaddbccaaaadaacbbacdabaddccccddbcaadccaadbbaabddaddbccbdabbcbddbaccdaacdbdcdbbaacdccbdcbcaadccbbaacbddaabbbdacbdcbaaacbbadbbaacadbdbadccacabcccadacdddcabcdbdcccbbccaaccccbcbdccdcaadaccdbcacadbbbabcbdabdbccddabbbbdbcabdcbbbaadcccacaaccdbbcadbabcadddbaccadccdbdcdbbcadddcdbcdbadbbcbdbbdcdaddbddadabbdbaadabdbacbcbbabbcadccaaccbaacacadddaddccaabbbbbcbcbabdbcccccadbcdbbbbabccddcddcbdbcaabbbbbabcdccddcadccabbdbbcbbcccdbccddccbcacbbbacababcaaccbdbdaaadaacddbdcacccaabcdbaabacadbabaabbdcdbcaddbaadacbabaccccdcdcbadcbddcddbdddcbacbddababdadacabbdbaddabdccacdbccdcabbdbcbadbcdddbbbabdcacdaddbabccaaccdaccdbdddaddcadabcdbddbccbaadbcabdbaaaaabadcabbbacaaaabbdcabaabadcddabadacdccbbcacacccbbbaccadbdcdbbaaaabdbdbdbccbaddbdaacbaddddcddbaacacdbcbbcbbbaacbdccabadbacadccbdcccacbbadcddddcabaccbaaccdddcadbcacccbdbcaacbacddaaddaacabdacddbddbdcdbbdcacdcadbbdbadcbddaadadccdbcbdbadaaadbcdddddbabadcadadcbdbabbcababbaacccbcbbacdaccdddbdddabdaacbbccbdabddcaabbcbdcddbdaadddbaabdabbbdadcccccbacdbbdadcbbabbaacbababdabcbabbaccbbbccbcadadcbcdcdadbbdadcabadddcacccccdcacacbbadbbbdccbacbcbdbaabdabdabbcabbcacacdadbddcbacacaacabbdddbdbbbaaaaddbcaaabdbbccbdddabccaccccabbadabcadcbbdbdacaabadbcabdaccdddbaabbccbbaadcaadadbbabcabddbddbbcdccdbbdbbbdbcabddddcbdaddabdaccdaacaaadabdaaccdbcdaddadbbadabbdbdbbbadbbbddcddcccacacddadcddddcbaabaddbbacadddbbadcadbbbdabbbbaccbdcacacdcbbabdabacaacbccacddacbaadcacaadcbcbdcbdbbdcadcdbcadbdbcacbbbbcccdcdbbdcdacadccaabaacdccaacdadcaccbbbbcdbdbadcacbcbbccbacddabdabbbccbadabaabcdaddcddacbacccacbbbccbacbbbabdbccadcbccabbabaabdcbbbdcdadabcabccccbcaacbadbcccddbdccdcbacabddcadddbaccbbaaacaacacabcadbdbdaaabbabbcbcaacaadcbbaadbcbacbcbadccccddcdcaacadbbaabbaadbbdbaccabbcabbcdcbdcadcbcdbcdcdacaddcbdcacbadabcdcddccacabaadddbdbcaddcacadcdbabcbcacaddbbababcddabbcbdcbcbddbbacdcdbcacbbbccdadacabdbadcbbdabdbbbcacdacbddcddcccbbdaddcaddcaadbddbbcadbaaddcabbbaadbcdabdddadcdabcbdabcdbdadabccbcbdbdbbcbdaacddcbdbccbdbababccddbadddddddcbdcccadcbcadadaaadcbdcadbdabddbddddaacaccccdccbbcbdcabdcdccbcccdabcabddcccaaaaaddbbdbbabcbdadacabbdcdabbbbbdcddcdbacbbbcbdbdaccaacaaaacabcdbdbcdadbdbcacdacbdacbcaaccbbdbccbaaadbddbccbbabdcabbbabbabbcbccaacacdadaddbbbadadabcbbdccaabbbabaabddcabaabbdcaadbdcbbbddbadcdcacaccdbdadcdbdcbcbbcdbbcdacbbcddcbbbdadadacdbcbcbbddcabbdababccddcddbdcbbbaacdbcdababddddbcbbcbcbabdbacccdadabcadcdbdccaddbccbdbabbaabbacacdcccbbccacdddbcccdacdbbadaabbaddadcdbaacbaddacacbdbcaddaccabbcdbcddadbbccbcddadacbcdabccbcdbbdabaccdaccbabbcbabddbcbaadabaddcaddccddcbdccbcbcbdbcdacaaaaacdadbddcddcbcbadbcdaccacabacaacbddbacbdababccdcccbdddacadccdccdcbdbdbcdcbdbdcccadcdcabacbcddcaddcdcbbbdbdcbbcbcddacbdcbbdacaddababdadcddbdcbaaabbbaabadbcdabbdccdbbabbcdbdabdcdabcaccabacdcbdccccbabababddaccbcbbbabbabdadcbccbbcbcacddaadccbabbcdcabaacababccaadaaabbddbadbbbcdcbddccadabcccdabacabacbadccbacacabbcccbccacabcbacbcbcdbbadbcbcbcaadcdbbcbbdbccbcacdbcdcdbbccdacaaacbabcadadddbbdddbcadbcbcaccbcbccaaddccdaddcadbcdbcddcddcbabdddcadcabacaccabddaccbcaaaaabdcdcddbbcbadddcddcbbddabbbbacbcacddccddaaaacbcaacddcccaacdcaabcbbbdabbcdbcdccccbcacccaabcabbcbcbcdbbbbaddadabcadcdabbaccdacabaaabbabdbbbdadbabdcacbabccdcbbbbbdaaabcbabcbadacbabcbddbbbdabbcdbcbbbbbadcadcdbdaabcccbdaddbcaccdcbdcccaadbbcaccacbbbacbadbdbcbbccbbbadcddadcaababbdaccdddbaddbabdccdccbcbbbaabaabbcacdbabbcaadcdaaacbdbcdaaabdcadcdadcadcacacadacdbdacdabcdaccccacdbccdbddabdaabcdccdacccdbbdcbabcacbaacbcabcbdcdcbadbbdbcdaabbabbbaddccaaabddcbbcccbcbdddcdabbdbbcccdacdbbbaccdccccdcbadaacccccacacdaaacaddbadcacdabadcaaabdbdacaabcaddcadadddaabbdcbddbccbcddbbcdabdaaadcabdbdadcabdcccbddcccbcbddacadcddacbdcdaaacbccacccddbaaacbbbacbadabbdadbddbdaaadccccbbadaaadcaaccbbddacbcabdddcbbcbcbcbabdacbaadcbbcadcbaabbbbacacbbccbbbbbbbadcdcddabbbcbddacdaccbdcaccbabcdbadadacbdcabcaadbbaaccddbbbabcabddaccabbbabacbaabbaaaacdbdacadbbaaaccababdbbbcaabbaddbdcacbdbacddcbddbbdacbdccbcadabcddcbcabccccbdaddadabcbddbaaabddacdcdbbbaaadcadcaabcdbcaacdbdcbcddcababaabcadbdaaabdcbdbdcbcacdcbbadcccaabbbcdabdaccaacbdaaccabbbdddadcdcdaadcabbcddacadcbcddcbbaaadcadabdcbdcbaaaaabdadabcbbdbcdbdcbabaaaacccbadccadcdccacdcbabdddddddcbbbbdababbdaddaacacdadacdcdbaacaddcdbbcbcaabddacdbdbdcadcbdbbcbdbdbbaadddcccabbbabbdaccadddacbdaababddadabcdcadacbbbdaabaadcbbaaacaabacbccaaadbaaacbaaacbddbabbabdacacddcddcdacaacbbcbcaabdddadacaabccbacaacdcdadacdaaababadccdbbcbbccdcbcbaabbbcacadcccaccddcdaadaacbbcdcbbbdabbacccbbdddadcacdcdabcdbbdcacacadccddbcbacabcdccabbadcccadbcabacabbdaddadadbcaabcbccccacddddabccddacdaccacaaccabdccabbcbadabbdacbbbaddddadcdcbdbbcccabbcdcccabbdcdcbdcbbbaadbbbdaabccbcdcaadaacadbbacbaaadccbacccdbdbccabddaddddbdabbabbcdccbdaadccbaaabbbabbbccbabbaabacbabdddbbddcdcddbdddaabdddbbbcacacbadcbccbccccbacbccaacdccccadbcaacccacaaaadacdccbaabccaaabaccccccdcdbdddadacbddbdbbabddacbcbaddacbacddcdbadabdabbdbddaccbaadbbbbaccbbbcaadcbabccccdabccaabbaddacccabdcbbdcdaadacadadadbbadaaadccdcdbaddcbbccdacadcbbbcacaabbddabbabccdadcccbbcdcddbabdbaccbbcabaddcbaddbcccdbdabaaacbcadabccbdabdabcacadddabadbaddaaccdbacdcaaaadddaabacdbbdcbdddaddcbcdbdbadacdabccdbcbbaacbcbcdccacdbaabababbbbcaaddcbddbdaabbdcbcbacbdbaccdcbbbadcbacaadacbaccddbdcbcaaabdcbabdabccaabbbbbdccdbbbbaccbdbbcbbccccdcccbdbddbaadcbbcdadccbabccbacbdbcaabacabcbdbcbdabbdbabdabdadaacdccbcdcbdddbdcbbcadaaacacbccbccbcbbddbacacabcddbcbcaadbadadbdbbcadadcbabbaddcbdcadbababddccdacbcbaccdaadabbcadaabddadcdacbdcccbbddbabaaabaccbdccddbcccadcdbdcaabccbcdcbbcadacbcaadcaaaaadcccadbcadcacaccacdcbcdcacaccadacabcdcdbdcddddcaabdadcbbcbacadacbdaadddcbcbcdcccdcdaacbabdbbcacdbabbcbadcadbabacdbcbccddbcbbdbadddbcadcadcabcaaccaaacadcdadccbccddcbdbaaaacdbccacaccacdbadcccaacaacdaacbddaaccabadaaadadabbabdccbcdbbdaddbbccabdacbddadbadaddbadcbcbacccbccaaddacdbcbdbcabdbbccadcaaacadcbbadbccccbaccbcbadaddbcabdcdadacddbabddacddaaddcdcddbaacccabddcddaacacaccadaaabaabddddbdccdbcaddcbdccacbdbbaaddcaadcacdbcadbddbcadaaaabcdacaaabbcddbbbbdbabdbaaccbcddadaccbccbbbbcdaaccbbbcbbbadcbbcaabdacccaaccaababbdddaddbcadbcbbbcdbbcbbadbcabcbcabbdbdcbdabbdaaaadaccacbababdddbdcaabcaaabcbdacddbdadabcccaadcdabccaadacdcbdccddcdddcbacdadabccabddbabddcbcdcddbdacdabccbdddbcdacdbdacbbccdcdcdcbbbbaccdadcdcbdddabadbadccdddcdcbacddbccbdaadbdddaddbcddcbbbdccdcadabcccbccdabcbdbdccdbcbbacaaaacccccbcdaadabddacddbdcbdbdbbddbbcbabcbadbdcabccddbbcdabdcdadacaccabdadddcdcddbacdaaddcddbbcdbcdbcbcaabbaaabdbcbbaaccacddcbaddccbabddaadccabcccbdaabbbaabcadbabcacbddddbdcadbbdbdbdacadacccdccddbaacadaaababadaddabcdbcdabdcccdacdabdbbdabaddabaabbcbbcccdbbabdacdcbacddbacdccabbbddccdbbccdbaacbbacdbcbccaacccacbdbaccbbccdcbcaddbbaabcbbabcdcdbaadcdadcddaddccbaaacbbbcaacdcbdbaaaccacccbbdacdcaccdcccbbdccaddcadaadacdcbcacbacadacaadbaacbdbabdcbacdabcabadcbbcdbddbcddcacdadacddbadccbbbddabbacbdaddbadcdcccadccbdcababaddbaacdccabcdbdabbdddaabbdaccdddabcbbbddaacbbdbdbacbabacacdbcccbbccbaccaccbcdadcdaadbbdbacdcbaabacdabddddcdbadbccabcdbdbacabbcddaadddddabdbbdddbdddcbbbacbddbcadddaadbdcdbbcaddbccbcbbacdccaaddabcddbcadacaddadcacaacbaabbcacccdaacbaccadadcbabcaaccbbaaccaabcadccbdaacbcbcbdbcdbbddaacbbcaadcdcbdbacbdbbcdbcbcadbcdcdcbcaabdacacabbacaaddbcabdbaccabccaccdcabccddcadbdcccddbabbbcbacdccacddbadbccbcacdcdacaddcbccbadbccdbccabadcccbddbdcaccdcbbbdddccccadadbadbbbcbcdbbcacbbbdbcabdcdadcbcacbdcddbaddcaaddabbacdcaabcdcbadcbddacacdddccdcabcdadaddbbcbadadccbcdcdbbbbcbaaccacccbccaabbccadabbabbcddddcabacdbccaaaabadcadbabbadaaaaaadccacacbdcbddccdddbaadacaababbddabbdbcaadabbcabadadabbcacbdddcccaddcbadddaadddbcaacdbaddaaddaabaadcdadadabbbbdcdddcbbabdbdcdaddbcccbbaaccbdbdadabdddbdccabbbdadbbcbadbccbcbabdccaccccbadcabbccdaadaddbbccdccddbabcdaaadbcadacacadadddaaaaadabacbacaaacaabadaacacbdcbacbbbbbadbbcdbbbdddaadbadcacccacabddcccaadcbcbdcbcabaaadbdabbcbacbaddaaddddcddaacaaadcacddcbdccaccdddbcbbcbccbaacdcdccabbcdbdcdbadbcddbbadabdabbdcbddbabcddcacbccacddbcdcdbddbbdddbbcbdaaddbdacacbadaddcacdbddadccbcbbbdddcacbcbbbbbbbbdcacdddbdbdcbababdccbccbadbacbdaabcaabccbbcacccacbdaadadaaaabdcccbdcbddcbacdcbcbbcdcbbbbbbadaccddbdacbadbaaabbcabbadddaddacadbcbcdaaabcaaddcaddbcdcbacddbbacaadaadabcbacbcacadcdbddbacbaaadddacbbdbaccabdbcddbbadabdcdcbccbadabbcbdbabdbbbcbdadcabdcdcabbcacadcbadbbcbbddcbdabcacccdbababbabbdcdbaccbcbdcbaccadaabddccbdbdaabaabccdcddbbdbbbbcbdcdaacbbadbadddacaacdabbabdcbcbddddbdbbdbaacbccbcddaabcbcddcdbdbacbcdcadddadbbabbdbdddabbdbcaaaddabbbbaabbabaadbdcbaaccadcbaadbbccaddddbbcbacddcbbacabbcbdbdaccacbbbcdddcacbdbabaaaaccdcabbaadbabadbbccbabaacadabdbddbddaccacbddbbccbbcdcddcddaaddccdccbccadacaabcbbaadaabcbcdcabbadcbbcdbbbbbcbaadacdbaddddbcbdabbccdbacacdcbbdccaacddbaacadaddbbdaadbbbbabbaddcbcdccdabcdbdbaadaacabddcabadaadbdccbcbaccdddbccbcbbaadddaacbcabccbaabcdbacbcdaccdcaabcacbbbbaaacdbacbcdbcdcbccbbadcdaddbabdbabcabccdcaabbbbbbdbdbdbadcccbadbdbadabddcdbbbcdcaabbcccdaaaccddadccdbcabacadadbbabccbcbdcababddddcbadbaacabcbcddcbcadbabacbbdaabdaadabddaddddaacccdabdccabaccbdcdbabbabcdbccbddbacbbcabdbbabbaaccdcbdbadcaaabdabbbaaacabbbaabcdcaddcbaabcdaddaacabbbbcaaaadbbdddcbbdcadbabccacbdccdcccadcdbddcdabbcabcbaabcaabbaddbcbdcbdcdccddddbabdbbacccacbcbcaabaaacdadcddbcabcccdcdcbdcddbabbdabacabdcccdbacdbdacbbbdbcbbbddcadbcacbdbbccbbdbacabcccdbbbcdbcddcbabccddddbacbbdacccbadbbadaccababbcdcbcaccaaabcbacbdccddaaabcbcddadcacdcdaabbcadddcccadbddbacaabddabbaabdcdcbddaabbddadbdcaaccbadbaaaaaacbcdcccbddaabbcdbbdcbbdbbddbabbcddcacbadccccbcbdbabcbbadcccdbccbacadacdaaabbbdabdcbaacaadbddbbbadddccbadbacbbdcccbdcabbcbcbaacdadacbdacadacbddabcacadccdbdaddccddbabdabbabccadcdbbdbabbadadcdcaddabbddcabcbbdbabcddcdadbbcacabcccaccabdabccdddbcbcdbbadbdabbbccabbcbbbbaabbbaaabdcaabbbbddccddbacdcccddddccdbcabddcbacacbdbbabbcabdcdcdbcbddcaadccaabacbcbacabdbcbabdddbdaccbcbccdaadabcbbbdadcdddabbdcaadbcaabbbbcddaacdcdbdaabbbbcaaaabdbbaacdddcbdadddbcaddcbdaddddabbbadcbadddbbcdccbdbcabcbccdaddbdddcdbcbdabaabdacacbaaaaddcacddadddbccdaddacdbcdadbdcbccdbdbcdbcaccdbdadbbbcadbbcabbdcdcbdcbadbdcccddcacddccabdcacabcacbdddbdbdabaddcddcacdbbcababacaabbbcdccaddadccdbdabdadbcbddaaacdaccdbdadadccddaaadbdcdadaccddbdcbdccdccbcbacbcccbcccbabaacabccadabccbcccbbdbbdccacbccadbdccadbdadccccdcdcaddaabdacbabaccdddaadcdcdcbaccadabbbbddbdbdbcacaacdabaadccbdcaddaacdddcbabaaccccabcccdccadbcdcbdddddcddcdacabcabbbcbdcdcccaccacbbbabbdaacbccccaccadcbdbcdadcaacabaaaccacacbaddbddabdcddcbbdabccabadcbccdbcaddaacbadaaabdacacccdacabaddcabdcaaacbadadaccbbdbaadddbcbaabdddabbdaccaaacccdcccacdadacbcacababadabcacddaacbbaadbdcbacbadbadcbbbdcbadcdacbaadabdacadaddccddbdadbadcbddbbaaabcccbbadabbbadaddbaaaccdcaddbbbdcbacdbdbcdcbaacdbcddacbaaabbcbbacbbdabdcabddcbdcdcbabbdbaacbaaddbccbacbbcddcddbbadccabbcaaadacddbbcabaabdbbddacdccbddacdacaccbbdbcdaacbdcbaaccacddadcadddbbcbbcaaabadbddbbdbabcaccabcacaaacdaacabbddbadacadddcdaacacadbcbbdcbabbbdabdabcbdccacccabcdabadbccbbddaaaacdbdcdbacacdccbbdbbcccbddcabddccbccbadcbddbddaadddadcbdcdbbbcdcdccbbbacaadccaadaadbcbaabbacdbdadacccaaaaaacadacabddaabdcacbdbddbbcbbbabdbccabccbcacaddcdbccadabacabdcbdabbddcaacdbbbccdbabbccabccdbdbdaddbabaccddadbccabdbaabbcbabbdbbcbadbbbbbbbcabddcabcaddacdbadbbccddadcadbbaccdbacabbbadbcddddaddbabddaacaddbcdbbcbacdabbdaaaabaaacbdcbdbcadddcbcddbbdbbcdccdcacdcabaadaadbccbcbacdcacabaacbdbcbbcadbcdbacaddbabadbcadbacbccdaccccaabadccbbdbdbdbdcbdbcaccbdcbacccaddcdbdccddbcbadadcdddccacbdbbaddccdbdabbbbaaddaccdcbbdabbbadaabdbcccdcbbabbdddddcdddbcccbbdbdaaccaaadabbddccbcbbdbdcddbbbcdcbcbacbcbcdbdcdcadcccabcaddadcabdcbadcdcacbbbccbadcabddaccbbaacdbbbacaccaddabdabdbcdccaabaadacbbdaccccdbacaacddddbbabcbbabbcbacdcbcddabaaaaddcaadbadcdcbcbcbddbaddccccabdccbbcbdbdabcbddbadcdaadbdacddabbabadddbdbbbaddcdaaddadaaadabcadddadadccbbbbabccbbdaaaababaabaaaaaacddcdaccadacdaccdccacbcdacdaaacbdbddaccbbdbdadcaabccadaabcbddcbccabbacdbddabcbcbadbbbbadabdcbbddacccbccbcacbcacabdaacdcabcdcddcaabdabadabcccddabddacbdaaccdaaabaaadbababcdbbbbdaddadbcdbccacccbdbdbdabbaaaaddadbddbaddbbaaaacdbdbaccbcacbdddbbabbbaccbadbddabdddccabbabacdaacbaaddaddbcaacdddbdacbdbcdbaaaabbaccabadcdbaaccdaacaacaaadcbadaacdddbbbdcdcbdbdacabbdccccacadabaaaadacdbcadddbaddabcdbbdbacccbcbdddbbbccbbddaadacccccaabdacabaccbdbdddbadcacdadcdaaddadacddccbacdbbccccaacbddaacbbbacbacaaadcaaadbcabbdcbbaadbbddcabadacdcbbcdadadabaaaddbcbcbbbabdadabdbcbcaddacbacacbbdddddcaabbdccacbaaddaaaaddcabbcbcbcbcacaccdaababcdbcabdbababdbdbdadccabbadcaacabadadcbabbcabcaccdcccccddabcbdaadaababaccdacddadbddcdcdbdddacabbbaccaacbdddbcccdadbaaadbaccdbcdbbdccdaaabaaddcdacdadcacdbbbcaadcbcccbbadcaacacdbdddaaaabbddbaadbaaabdabbccbdaadabadbcabcdbbcacdcaadcaadbcddaabddadcdaabccbcacababcbaabddbbccbaabcdaccaddcaaccdbbbcbcbaabbadbababcbdacbbdccaabdbcadaabcbdddddaaacccbbaacdacdaddacdbbdcdbddccbddccaccacddbdadcbbabbcbbbacaaacdabbcadaaccbbccbcdcdbaaabbbbdbabadbddbbbcbaabbddabbadabdacaccbbdbcaaabcacabdacbadcacdaabdddacadccabaabdbbabdbbdddacaaacbbddbbcdcdcaacccccdccbdbdbdddabbaccdacaaddccacacdaccbbdbabcbacdaaadcacabcaabbddbbbcbbabacbdcacbadcacddaacdccbdcdcbaabbdcbabddaacdbcaadcddcddbbcbbbddadacddbbbcaddaaacdcdbdccaadccbbaaddacabacdddbcacbbbaccabbacdcccbcccbbbacbcabcbddadbdcbadbccbcbbbaabcdbccbaccaacabdbccacaadccadcddabbcacbdcaadcdbddcaaacdccbacbdbacabddabddbacaacddabcbdbbacacddadcbdbdacdcdbbdbcaabcabddbbcacdddcbdcddddbdcbdabdabbcdbcacbbbadbdbcdaaadcdaabacbbaccddcaababaadaddbaaacdbddcacadbaadbddaadccbbadacabbbabcbddacaccddddbddcbcbbaaaacbbacaccbabbaddbabcacccbbbddddabdadadacbaadbbccbabadaaddcbabcbcaacaaaadbccadcbacdabdcccaaaddcdadbcbaddcbbbbcbdbcccabdbdcbdaababbadbdddadbadcbadcdbcabcaaabbacbbaabbabdaacbcadddcbaccccbdabbccacbaccaddbabcaadccbccccdccacabaabaccabaccddbbdccabbcadbcdbcccdaadddccbdbdcbbdbabbadcbcacbddabaaabaccbaabbddaccdabcddbbbaabdcdcdccdcacbdaddcdcbbcbdadaddccaddcddbaddaaaacdbccddbbcddaccaadbaadabcabaccdaccbcbacddbbdaadbaabdabdcccbcbbcdcdadcbcabbdbdadcdaadacaabbddbdbddcccdbdbdcbccbdaddbbcaabbddccadbbacbdaabdccbaccabcababaaabdabadbcdaaaaccabacbccbcaacccaadcaaaccbbdcbadbcabacabcabacabadcbddcdbbbacacdcccdcbddababaccacabdadcaabcccddcccdcaaddaabaccaaaddadbdbdacdcbdbcccaabcbabacbddbadbdaacadabdacadcbaaaccccbdcdbcdbdbbbbadbbbbdbadaacdcdbbddcdcbabbcbcdacbcccdbdbbdaddcddbddaabdabdddcddcaccccacdcbcbcaacdabbbacbddbbdbdbaadacaacadacccdacabbacdbdaabdaccaacbdbccbabccabcbcdaadcbdcbbbcbacaabbdcdcaaadcaadddcdaaabbbadacdbabbbbabdbdaccaaadaccaabbcabcccccdcabbaaaddbbdacbdabdbdbdccdcaaccbdabddcdbccbdaacbdaabaadaabdaccdbcabadacbdaccbabadcbabcdbcccccaacbbbbdbabcddbdbdcabbaccabbdcaaddcddddbdabddadcadddaccadacadbddddadbacacabccdddabababdbbcbcdaabcdabaddcddacdccbdcbdddcabbcbbcdbcaadcaccbbaddabacdbaaccbabbadaacbabcdbcbddbcadcbbdbcadbcdaddddbaccdcbbbcabdbdcabadddadadaddbbabbbdcdaacdccbcbadcdcbbaacbbddcadccdaaccddcbcacbddcbbaccadbdbdababcddcaabcdabddbbbbcdbbabdadbaadddcdbddbcbddabbabbddabccbacdcdbdcdadadbabadaadddddcbabcaabbdbaaddccbcbacdacacbcbaacbbbadcbcddcaccbbcdcacdcdabaaaabbcbadacddbbabbaadacbdbbacdcaabadccaacbcacdbccdaddadccaadabddccccbdcadcbcdcbdaacbabbadcbbcdaddcadbbdddbbabbabbbaacaabaacacdcddacacddcbcadbcdcbabbacbaccdbacabcadcbacbdcdddccacbcbdbddbbdcacaadcaacdcdabadcabbcacbbbdbcacdbcbcacadabacadbbdacdbbcababbaaccdbbcdabcbccbbabadabbacdddcbddddbbcbdaccdcacddadbddcbbdacbacddbdacbbbbcdcccabcdccaacdadabcbdbdaccacdbaccddacbabccccacdbdbddddcdbbadcbbdabdbbacaacddabbadaacaabcabbdacdbccdacadbdabbabacccbbdaddbacbcdaddaddbadcdbdbdaacadcadcdcdcaaaacabbbdadbdaaddacbddccbdbdaabbbdaddacccdaaaaccdbbcbacbdadccbdabdcaaadbbbbccbadabdddbcbdaaccdddcbdcbccdbcdbdacbdbbaccadabcddbddaadcacdbccdbaddbacabdddbccabaaaabcacbadcdddbdaaacdddcaddcbddaaccddbcdbbdbaabaadacccddaadaadccdbadcabcbccbbaccacdcabbccbbcacccaabcadccdaacbabbbacbaaacbbcdadaddbcacdbaddaaddbcdbcbcacacdcdcbbdcabbdabcdbcbcdcccbdbcdaadbcaaddcbbdcddccdbcccadbbcbacbcbddbdbdadcdbdacbcccdcbaaacbcbbcdabaddbdbdaddcaaadaabbabdbccbccabbbdddcacddcdaacbdbaddadacadaacacdbaabcbbbcbdbdccacacdbaacdcbaacbaabbdcbdacbdaabddccddaddaaabbdccbdadaaccabcdabaccadbccaacadbdaabadccacacccbbacaabbbbadaacaaacbbccbccccacccdbabcbdcbacdcadcbcadadcbdaabaaabcbcdbccadcaaccdaabbaadddacbccbdbacaaaccbccdacbbdadcacadaccbaabdbbacaacbbabcabbdacadaabcaabcbcacabdaddbbdccccdbccbdbbdddbbdcbaabbdacaadbdacbcdbababadcdbbadcbdacabcccbadddbccdbcaaccdbaddacbdddacdaabadaccabbbcdabbbcccccdcbadacadbbcbcbacaacaacccdddbcbaccccdaaabaabdabbabbbdcbccabacddbddadcddcaddadbcbcccabbbaddacbacdbddcadbbdaaaddbdaadaabcbabaadcddcbacadccaddabbcabacbcccbcdccbadaacbadddddcabcabbbaaabadabaabbacbdabdbdaadabadcbaadbbaddacbaaacddbbacbddbbdbbbabbdccdadbcbddaaaadcbbabddaccbbaaabaacaaacbbabdbabaabdddacbaaacdbcaadcdccaaddbdddcbacdddadcbddcbcacabbbbbbabbbadacbaabacccbbadacaddcacbbcabdcddcdcdcddabcdccbacddcacbcbabbddbbbdabdcccdcbbabacdcadabaadcbbdbcbcdbddcdcbdadcbdacbddbddbdbdababaddcabbdddabbbcbaccaabcbdaacbabdadcbbbbdbbacbbbcaddbbbcdcbbcccaacdabdbdaacdcdcaadbdbccacbbddadabbcabdbdbccddbddccbdbaacdddcadacadcbccacbaaccdcbcccabdabbcadaadbdddccacbdddadbcbbbcdbcabbbdcaabddabcdabbdabdddadcacacadccccacaccdcdabccbcbdbabdbaadacadcaaaddbcbdabdbcdbabdbdbdbbdacaabdacbbacdbbddababccadbcaaaacacacdccaacaacdabdbadaaccdddbcacbddcacabadbacaacdbaccbdcdbddcaddcadbccbccbdabcadacabbbbabbccdadabdbcbccabbabccabdaddbbabbcddabbdbcbdcdbdcdaddcaacbbacbaddcacabbcdcddacdccddaaaadbdddbabdbcadccbccdaacdaadbcdddcbcdbcababdcbcdaacabdbcbbadaacccbcadabdcabccaccbccaacdaaabdbdbbcaadcdcadadacbbbcbbdcbdacbbbdaacbbbaabbaaaababccdacaadcdbaadababdccbbdaabcbdaabdbbcccaaadabdbcdbaadcabaaaacaadccccadbcbbcacadbdacabadbbbccddcbcacaccdbddadacacccbbbabbddaddbcadcbbcdbdadcacadddabcddadddccbcddaabdaaaaaacbadcbdaabdacaacbabaaabdbddcdcaccdacdbadbdadbbbcdbbbdbbccbbdbbabbbabbdaccadbbcdddadacdbcccccabcdaadcdbaccdadbddddcaccdbdbbbabdddbdcbddbcaddcbacbacdcbaabcacbcaaaccabbdccdcaacadbbacbdaaabcdacbbacababcbdacdbbacddcbaddabdbacdcbcbbcbccbaadacbbaadbccbcdabadadaddaddbcbaacccdabbabbacbdddbacdbcaadddcadddcccdacbababdcadcdbacaaaddcccbcbadcdcccacdbacadacddcdbbcbaabdbbaddbdcaabdcbbdaaaaccadadacdbacacbabccabbacbdcbccccadacbdbacaaaccbcbaacbaabdddaacaabdbaadcbcaaaabbcbddcabbdbbbacddcddccdbccacbdbcbadbbccccacbbddccadaaaabbdbdababdbbacbbabdabddbdcaaccdaccaadcbcddadbcbcbdbccaabdababadbdacdabccacaabaccdbbcdddccdcababbbaadcdacadbcbcbaaccbadacdcabdaaaccdabbaaabaccbbaaddccbdbbbbcdbbbbddaccdaccbbddbaccabaabccacdbddddacaacbacccadddbacbcaacbdbabbbcaddddbadcbabacadccbcdabbbbddddaabaababddccddabbdcaadabbcbadadbbbbdddbaacdaaadadbbdcaccacdddabccdddbbdabbbddddadabcaabbcadbbcdcdcdaacbbdadccddccbddacdadcaddcaddbdcbdabbdadaaaadcdddacdcadccbbcbbcccaacaaaadddacbaaaabbccbbacadbabbddcacdcddacccddadbdbdcdbdcabaaacacadaacaaddadababbacbdbcacdcadbabccaddacacdabcbbaaadcbdbdaaabcbabdccbadcccdbdcbacddcaddbccacbbcaabbcdbdcaacdcbacdbabaacdaabadacdbcbccacbcabdabdacadddcabbabdcbaabbddcdcddaaccdaadabbbcbbcdbdadddaabadbdacaabbadcacccaaaddcccddbdcccbbadbcbddbcabdccbaaccbcbabcccddbadddcbcccdbaabcdddabbbabdbbddccbcdcaacaccbcaacadaccccbbaadcddabcdbadbbdbbddbadccaacbbabbdaacccbccccbbbdcdcdabdbdcccbdcabbdadaaaccabbcdbccddbacbbcdbdaccbcadacdacdadcbccbbdcdcbdbbdbbadacdbdbadadcacccbcadbacdcaccbdabcbacadddcbbcababcacbdaaacbacdcddbdcadacbcadbabcdaaaddbadccaacdcdacabbabbdcdcdbdaadccaddbdbdcdccbdcdcadccacbabadacbabacbddcaaccbadbadcbdcbabddacbdadddcaabbdcccadaacddccabcdaccbbadadabdbccdacabaddcabadbbaacacbbabcbbdddbddcacabacdccaaabaccadddabbcacbdcabbdaaaaadbbbdaddcbcbddcddbbadccbbacddbbcbbbbcbcaaaabddabbccacaacdbbdaadbdddccccdbaaaabdaabcaccdcbbbdacccdbcadbdcdcbccdbbacadaddaababcbdabdbbabccbdabbdaadbdbcddcbbaccbabbbcaabcbccacacaabdbbbbdddbcabddcddbcbcbdadcdbcaadbcdacbdabbaccbcdcddacdababdbdbaadbdaddcbcdaaabdbcdccccccdccdcdaccadadaadccddcaacabdaabdabbbcbcdccbaacbadbababbbaabdabdaabcbcbccaaccaccbcdccdcaacaacbddcbbddccaabbbabaabcbddbdaabdcddcabaccdcadabcbaacabccacccccbcaabbbbbcdbbaaadaddcdddadacbbaabdddadbacabccddbddcacbdcbcbcbcadadcdbdcdaabcccbcadccdacbcbaddcbccccbcaaccddbddbdddadcaacadbbcacbaccadcadccbccbababdacabbbdbcccbcbdaccbdcabccbdbadabbbbbdaddacacdabbcddcdddddcbddadbcdbbbacabdacacabcadbcccbabbbabcbccbbbdadddadbaaddcbbbddcacaaddadcaaaddcdddccaacbddcabbcbacacbbbccaccccabcbbbabacdaacadcaabbabcdcaddbbabbbabcddaaabcbddacdbbacaadbdcbabdacbcddbaacbdacdabdacbddcdadbaccabdddbbcabcbbabdadacdccabcdcadadcccbbdcaccabdcabdbaabbbdcbadbcddddbabbacabcdddcdbbabddacdddbbddcbacabbcbabbdcdaadddaddcabbccbaaddccbcabdabdddcababddbacdbabdadaadcaccbbbcabcaaaaaacbddcdbddbccabddbcacdbdbcccbbbbabdbacdbbacabccdaacaaabdbcadaacdcdccbdcccacdddbccccbbaabddabcdacbdcaadaacbacadabcdaaadbaaaadcbbdddaadccdbacbcbcccbcccadcdaaadccbaacbdddbdcdbdbcabcaaadcbdadcaadbcacdbbabccccdadbbbdbaabacaaccaaacacaadcbdbadacaababcdcbdbdcbaadcdbbbbcbdccaadbcbcccacdbadcdddabccaadabbcccbdcdbbbbcdbdcabdbaddbcacdcaccdaacdbbcbadaaddaaacccacdddabdddacbbadacdccdacdcabbcabacacdbcaabcaccdccdacacbcdddbccadcddbdacbadbbaabccdaaccadcbccccbbababdbcbdcbcccdcddbdcaabcdabdadbbacccdbcdbcddcbcdddddbcbababbbbabdccbdcccbdccaabcaadbacbaccbbbccbccacbccbacbbaabdddbbcbacccaacbaaddbabcadbabbddacddcabbbdcabdabaadbaacbcbcddcdbcbcbadbadccbdaabcdbcacbdacdcdcbadbbdcbabcbcbccbdcbdbadaddcacbbadccbdbadacaccddcadacccddbdbadabbdcaadccddadabbadcbbccdbbababaaabbbacbbbccddaaadcdbccdddddccaabbdaccadcdaaacdbaabdddbaacbabadcdadabaaaacadbdbdbccddccaccccdcacbcacbdcbbcaccadadbbacddcccddbabdbadbaaacadddadcacccadbdabcadddddbadabcdcacaccbadccadacbbdcacaaaaaccdabbdccbbcdacbdbccaaaaddaacddcabbcadddabaddcdbcbdbddbadcacccdacbcdaaabbcbddadbaacbadbbdbcdcdbaaddbcabcbabccabbdadbcddbccacddbcaacaadcbcbccbabdaaabbddbdcccdcadcbaabdcdacaabcbcadaddbbddaccacddaabacacddcbbbbbbddbaacdcaadcbdbcbbddcddcbcabddbcaabbdcccadacbcdcbdaaadddbbacbbdbcacddabacacabdddadddcacaabadabddcbdcbddbbddcbdcdcbacbdadbcabbdcbcbcbdbddadababddaccaaabdadbcacccbadadbcbdcdcdaccbdddcbdcadabccbdccabadabadacddbbbacadddcdcacacacaacadabbccaaccbcdaddbcaadababaddddbcbdaddbccadbcaadaadbbdaaacbdabbcdadcccdaccccdddcbcabbaadcddccbabdcbcadcaadcdcdbcbaabdbbbadabbdcbcabcdabbabbbdaddccddadbbccacdcbcddbdabdaddbcaababdbbadbaddbcaaccdaabdacddcbaacbcddccdccaadddcbccbbaaccddbdbaabdaaaccbabccabadcddaaddbbcbcdbdbaacdcacaaaaddcaaacbbdcabadbdacacbdabcbccbcbcdadcdccabdbdaacdcbcabdadabdcdabbdddbabaadcdbadbabcabaacbdbaddbacdcbcbadbbdaccadabbdccaacdddaccbacbdaadaacdbbbcbbadcabadacbcaccbcaaadbabaabacdbcdcaccaddbcddddbbabcabaccadbbacdadbbccabdbdbbaadbdddcbdabbcccaccddaddaadabbdbbbbccacbaddbbcbdcadbddadddbbbbabbacbbdbdaaddaccdbbabaaccbcabcbdacacaccabbcdcdcdbdadbbdcababcaacbdbcababcaacbbacdcbbbcdbccdacddbcdbabcdcabcacdaaabcbbccdbbddcdbadaabddbdcbbdadacdcccbdddaccdcdcdddbddacbabcdcbbdbdbabbaacddbcabdbcacbdcdcdcccbbacadcaadabcbcccadcbabcababbdbaababacdccdcbdbcbcbadccbcdcccddbbdbdacccdbadbbbdbcdbbccbdcbbcdccdcbaabadcbdddbcacaacbbcdbbdacbdcadaddbbbadacbdcbdadddbbacbcaccabacdbaaddbaddcaaccccbbaddabbcccbcbddcbacaaaccbbdaaaadabbdabddddabddcadbdbcaacbdcbcdccbdccccbbadccbccdadaddbaaabcbccdbcdbabbbaaaabdaabccaacddacbaaddbdbccabcbdbbaacbaccbbacccacacbddcdacdbdcccabdadbbaacdccdaadbaadbcaabbbdcabdddbbdaaaacabcadddabcdacbbabddbbaccdcbacdabbbbdcadbcdccdbbdabddabcacadccdccacdaabbadccddbbcdaccadbbadbaacdddcdadccccacbbbbcbcadcbaaacbddcaddaaabaacdccdcdcbbacabccccbbcbbabcdcaacacacddbbbaadacccccccbbcaaadbcdaadcdbdcddbcccbddabaabaadbccbccbacabaabbdbccbcabcbadcacdbbbacaccbbdcbaacacdcbacbcbaddbbcdadcdbdadaabbabacaaddbddcabccabdadbadcccadbcabdddbcaddaaacabbddbbbbdccdcadcbabbabdbcdbabdccddddadbdadabbadbcbdbcaacddacacadadbabbdcdcdbbadccabcdbaabcadbccdddcbababcddcacccbbbabbbbaacdbbacccccccddcccddccdbdaabdcaddcadabaabdcbccaadabadbaabbbbcacbacbdcbbbaccbdbaababadbccdaaddddabdadbbccbcdcbbcaaaaaaaaaacabbccadddaddacccaaadbccbabddcbcbbadddbbcdcabdcbbdbccbaccdabaacbbadabbdbbaadbbdabcadaccabcbadbbccbadbdbabbaaaaccccadddbcacabcbddadacdcddcdabbddaacccabacaadbababdbaacccdaadccdbccdbbaabcadbacabbacdbabaacccadacbdbcdaaaaddcbccadabbdabcdbdcbdbcbccbdacabacddbbdbcaabaabddbcbbbcdacdbcaccdbcdccbbadabadcbbdaabbdbdbccbbaadaababbacadbbcbaacbbdacacbddaabbdddcccbcdabcadcdccadabbbbddcbdacaccdcadcbdaaaaabbddbbcdbaacbdcadddacccccadbdbabadadbcddbbadbdbaddbabdccbbdcbbbcdccdabcbdcaccbbabcadbdcdaaccdbcacaaacccdbadcbdcacabbadcdaaccbabbadddcddcaabadbdaacacccccbdbabacbabadccdadddabcdaaddabadcbdccdddddbdaddddbdbdccbdbbbaaabccadbaadddabcacabbddcdbbbadcbadaacadaacddcacdbbcbbbaaddccddabdbcbddcdaccaadcbbbbadbccdbdaacdbdaaaccdcaaccddbbccabdaaabdbaacdddaddcdcdbacbabbcdbbdaacbdbdcbdabccdbbdabdcaddbbacbddddcbabaadacbccaabccaadcbdbacccdcdbcbdcdbdabbaddbacadcccbadbbbcaaddcaccbddacacbdcadadcbaccddcdbbbcddddacbbcdbbbabccacbabcaccdbbdddabcddcddcbcacadabadcccdaaddddaddbabababdacddcdaccdcbcbaacbbadaaadccdadddddadddcdcbddcabdaabdcdcaabbbdcdabbbcdcdbcdadbadbbabacadaadcdacbbabdaddbacabcccadbccacaccdcdacccbdddddcabcbaccddcdddbcabaaabbbbbcbccbabbbdbdddcbcbabbbabbcadcbddcaccabbabbcbccdddcddbccbdddadcbccdbbbbcbdcaddccbbadabadacbdaccddbcbbcdacaacadadacdbcdabacdcddcdcadcbbcadccddaddbdcdbdbbdbbabdadbbcccdbabbcabdacaabcdcbcbbbdcaccbcabcdabbdaabcccabadcccdccbdbaaabdaacaddbdacdcdddaaabdcdbabdaacdbaadbdbcbadacdcbaaddccccccbdcccabcccabddbdccadbbbcbdacadadbcacbcbdbbbdcabbdacdabcddcddcdaaabdabddbadddcadcacdcbcabdbadadabcadaaacbabcdbbdacacdcdababdaabcdcdaaacdbdcdbdacadaadbbadccbbdacdabbcddaddacdaddcbdacbdcbaabacbbdcadabdcbabdbdcdccdcdbdcbbcdcdcbcacbdcaddcdbababdcbcdcdaddcdddbdbbddbdcacdbaabadbabbbacababaccdbadacbbddbbccbdacdbbbdbdbaacabcddacaacacaacdacabaddadccaadcbcdaabbacbacdbcbacdbabaccdcbccadacbccbdcadcadcaabbaaacdddcccccbdcacbcabcddaddcdcbcddccacdbaddadacdccbabdccaccaaabbdbadddacdcdbcbccbdbadbdcdbaabbdabbbbacddbcabadbdccaacaccddcdadcddcdbaabbacdacdabacaaadbabcbcdaabcacbbbbdddacdcdddddacdbdadcdbbbadbaaabdaaadccdcbdbbbbdbdcabdabaaacdcbdcbacdddbddddddaabbbddcdcbbbddccccdaaacbbaccbdabdadcbcdbcbabcdbadbcacbdcdccbaaaadbbbdddbbacbadccdbbdbabbdddaadbbdabdbaccbccbdadccdbdcbddacbadbddddddbdccbadcddcddaadcbccbccdbadbcbdadabacbddcbabababacddddaaaadcaadbdacdabcbadbabbdbbdddabdaadddccabbddabadcaccdbcbbdcadcdacbaaccacbbccbdacaaabcbadddcbadcccbabadbbcbdcacbcacbcbbacdaadccddadcccadadabbdbadaccbcbabdcbaacbcdccdcbaccbbdaaddbaccdcdbbbdadaaacadcccbcbdbdcaddbbbbdccadcbddacaaddccbbcbaaaadacbdaabaccaacbabbcbcbcbbaddcbaaaacacbddccbcdcbdaaabaabacacbbcbaddacadbdcdaccacbdddaccdbabdbcdcdccaccbbdabcdcbddcddcadcadcccbaaadacaacdccaababadaabcaaaaabcddaaccdddddcbdcaabccbccbccdcdbdacdcaaadccadcbbbccaabddabdaacdadddbbccdddbddcacdcbcabbacddcdbcddcdddacdcccbbaacaaabadaacdbbaacbdacabbcabcbaaaccacdacadadacddcabaddcacbbdcabcddbcdbaccbabdddbaacdccddabdddabbdbbcdbbcabbdabcccbaddbaaccabbccccaabcacdcddbcbdcdbcbdbdbcbcdbaadaacdaaaddcbbbadbacacdaaccdbccbbbbabddcaaccbaabdcabacccaddacaadabccbbaacccbdbcaddaacbcabacacbdbbbcbddcbbbcaccaaaaddadaddddcdbdabcbdbadabdddbccbdcdadbccccbacadbaadbacdacaddbbdabbbbdcababadbdbddabcadccaabaacbcacbabcbccabcdddacccccdabbbdacdaccbaddddabcdcbbbccdbcdcbabbcadbadbbabddbbbcdbdccbbcbcaddcbbccccbaadcdcbaddcacddabbcaadaabbcdadddcbdbcbdaadadbdbcbdabdddcbccbccacaddbdcbbbdbbcdbadadacadbbcbcbaabbcdaddbcbccaddcddddaabddaaadaabcbadcdadbcdcdabbdacbabbadadddcadacadcacabbcaccaadcbcaddbddcacacccbcddbaacdabdacddcbbccbdbabbcbbbdabbabdcbbccbbbdcdcdaccdaddaabdacdcbbabacdbdcbaabcccadbbbadbadbdaaabbcdbcaaacccbaabadbaabbbbdcccbbcbbadbababddddddbabdacdbaacbdaabacbcdbdadabcdaaababbbadcbbdbdadaabbdbcaddaccbacaabcdbcdbdbdcadaddddaaacacbabadbbaadbbcabdcdcbccdddbddcadaaabccbcacbbabaacddadbdacbbcbbbaccccbdcbbabadcddddcdaccdacaadadabacdabadbddcbdadacdbacbadaddcbdcdbccdcabdaadbdbcacbabdcbbdaacbbcdabacacddbcbbdaddbdaacccdadcbbcbadbccbdbcdcccacaacdcbcbdbcbcdbdccacaadbadddccdbddaacaabddaccabcddccddbdcbabcdddaaabbcccdbbbcdbacadabccbabdbdcacaccacaadadbacacccbdacabbcbdabcdbbacbaacccbcaadbabccddadbdcbdbdccacccbbbdcbcbbbacbababcdacabadbbddacbbcbadbbbaacbdbdbacdbbbdccbadaaacddbdcdaadbcbbabadbbaadccadcbadbbcdbdccadbadbdccadbcadbbbbcaccdadaacbacadbaaadbadbadaabaaacadaadbacdbbaadbaabcabbcabbddbddadcdbdbdcaabbbaadbcdabddaddcdbcacadaabcabcbcacdbdaadcdadcaadbcccadaddcbcdcdcadbdabcdbaaccdccdcaccbdabacacdddadacdcbabdacdbbadddddababdbbddbbcaabcbcdbdabacbbacbdddcbdccbbdbadcabdbccabbcbdccbbcdbcddabcdcacbcaddbbcdacbabcbdabcdabdddbccadabdbaacbbcacaccbcbbbbdaadccccacdbbbdadcadcdcbbcdddaddbacaabdcbbdcbbdbdbcddbbaccdadbaaccdacccabbdbadadbcccaddaabdcdbccccbbccdaadadacaabdbcbbabcacdbacdbacabdcbbabbbabdbacabcdcacacbbadaaaaaadcaddabcbadadcbdabacbcbaadaacacbaccadccbcaddbabddbaddbabcabbcdadddbbdbbccdbccbdacbabdacabcadddbdccdaacdacdbbcdbbbadabcdaddccbabddadcadbbbdddcbaccbbddbbdadabbbadabcbaaccaaaaacbccaabbbdadcdabadddbcbadbbcdaaacdbcdddacdcadbcbddcdbcbdadccccadcbbbacbccdcabcdacdadababcabcdcaddabccaabdbdcadbcaadddaabbdcbbbaadbcbabddccdbaadacbbabacbbbadbbaccbbcadccbaaaddadaccddcdadacabaaadbcdaacdddddadbbaccddbadbdadccccaaacdbbddadbbbbaaacbccbaccbadbccbaabbdddcbdddccccadbcbdacdbbccdbdcdbdabbabccadbcdbaaccabdcaaabcaccccbbaddacbbbaacdcdadbacbbadbddbddddcdadccdabbaccabcabadcddbcddaddbdcbcacdaaabcababdabbabadcdccaabbdccddadacbbcdbdbbcbdaaadaaacaadcbdadadacbcadbcccaaddaddcadadccbcacbabcbccdbdadacddbbbddbddcdabaadcaabdbccaccdacacddabbcdddaabddcadbbdddcdcccccbbccbccabcaccddacdbdbccabddbbcaadabdbacdcdcccbbadcbabcdcabaccbbcddbcbcddbcdacabcdadbabddccdaacaddbddddbaadbccbdccacaaccadbbadbbdbbacadbaabdacadbadddcaccdbbbcacdddaddcabbaaacbcccccbacadddcdbdccddadbdaadbddcdbaaddbdcdbdcdbccddbccdbdbcbdbbbcbdcaabdcbbdcdddcbbcaabdcbcccbccbdabaccdbdcdccabcabaddadbbdabbccaadaacbbddcddadbdcdaaabacadacddcbcbdbdacdcccbabbaadcacaddbdbdacdabaadbbacadaaddadaadaabadbbabdcacccdbdabbacbddcccbddbaaadaadbdccbcbdbadcbbaabcdadcadcccdbabbbbbbbcbacccddbdddbcdccbdcdadaaccccddbcbaababbcdaddcccacdcdbddcacabbdbbdaddacbadadaaadccccdbdcdcdbdbcbdbbcdbcbbdccabadddbcbabbcddbccbaccbbccdabadcddcdcadaddddddaccdcadbcbdacbcbacdcbcccdaaabacacdaadadbcbcabdbcccddccbcbcacaacbcdbdbbbacabddacacabacbbabcdcbabcddcbcdcbcdaddaacbccbbaadcbdcaccadccccbadddbcdabdddcbbdbbccbcccccbddaddaacabaddadbcbbbbbbbdcddabcdbacbadadccccdbdbdbddacbadccddbdddbadccaaacaadbbaacbdbcccbaabbdacdcaaaaccabbdbbadadcdacccaacdbdbacddaaaaddcabcddabcaddcaccccbccaaadbcadcdbdccdaadcccdabacdddbaadadbccbcbbabbaccaaabdcadbbccbcbaaccbdccbbdaabbacbbddabcabaabacbbdcbcababbbcccdbdccdccdbddadadacadcdaaacbbcddaddacdadaccbbbdcbabbdcaabcddadcaccaacbaaadcbbacbdcbdcdbcbbababdacabbdadcaabbbdbbdbcdcdbdcdcbabcababbdbadacbadbccaddcdcaaaaaadbcacbabbacabbccbcbacbcaadacdabcdccaaaaaccaaadcacabacdadbdcdaacbcaabaabcabadacadbacbddabccaacddaabdbbbcacbadbbbacddddbabdaaaabbbdaaadccbdbbccbbbccabcadcdabadabcabbbacbaaccdaabadddccdbaadbddcdaacbacbaabacbccbdbbddddcadbcbaadcadddabaccdaaacccabccaddbabdccddccabcdbbbddaacdcabbabaccbaccaaccaadbaaabcadacbbddbccbcbabcadbadcacdadccaccabdaddccbabbbccbdaddaaacaaacbadababdcbbabdabbbdcdcacacaadbaaacabbcadccbbbbcdbcddaccbbbcacdccbababadccddadbcabbbcdbdabbaabbbabdcbcaabccaaabaddbbcdadcadabcbcaddddcdbbbadaaadccdbdcabacbdadaabccbbdbadddacbdccdbaddcabcbcccacacababcabddcacdabccdcdaacbdadbacdabddaddccddcccccdaccaabadabdddbcbdcaadacbccabdddbbaabdbdbabddbaccddcdbcabbdcdddbccadbcacacaaaddbccddbddbbbcadccaabccdadccbdbdcdcadaabddcaabbaabddaabcbdbcadbdbaccddabcadadabccadbbdcbdbadacbdadabbadbabbcbbdbccbaccdadabbccbcdbbacbcadcbbcaabbcbdcabcababcddbbddaccaabbbdcbcadcbbaccdbccdcaaababbdbcdbccbcbbcdcdaaaadcaacdbcbcccdcbabaadbadcccbbaadbaadcabadcdccabaddbaccdcdabaaddbacbbddacabcccddccccbbbcaacbdabccacbdababadbbabcdcaccbbcccdbababcbcbacacddaddccdccbcdbaaabcbacdabbaabccacbaaacdaaccbcaddadacabcaadcaadacddcdcadbcababcdadbacbaaabbcccddaadbbdbbababdcdaaabbbbcddcabcaddbbaacacdacbbbcbddadccaacaaadaccdbdccbadbaadaabdccabdbacdddcddbddbbbaddaacddccdcbbdcbaabddaacbdbdaddbdaccdaacadbadadabcaaaabaccadcdddbddacdddadbcacddacddbccaabacacacbdbddbdadadbcdbcbccbcccaccdbdbdadbbdbdabdcdaddbdcdbdcbacadcaacbcacbccbdccbdaabcddcccadbcdbdbdaababdaabccdcdcbbadbbdbaacbdcaadbaadaadccbccbdabdcddcddcbdaadcdbbbabcdbcacabdbddcbabcdcddacacabcccccdcddacaacadbabcbcaddacccccdccdcdabaaccbadccacacccaddcbbcdcacbddccaccddbbaabadcacbbcdccdcaabbbadbcacbdadbbccdabdaccadaaccaabaddcbabacbacbdbacbbcabdbcccccbcadcacbdbabdaddcdababaadccaddbaaddadccbaaadcddacbaccbbbaaddbbddbcacacdacbacdacbacadacdcaabaccccccabdabdbdbadbaccacbdcacbadbcadabdcddaccabddadcdaddadcccdaddacbbbdbcaabcddcbbcdaabaaccdcccbbbabbbbdaabcbaacbdddcaccbaddcadabcbdcdbcacdacbbadbacdadcbdcbacbaabbababaddbdccabbbbcabbdccbddccbdddccaddccdbcdcddcadccbbabbbacccdaababcbaadacdcddbbccadbddbbabcbbdaaacabbacabddccadaddddbcbbcccdbbddabbdcaddadbaddccdcbababcabbccabbabdbdabdcabcdbddabaadddcddacdcdaccdcabcadadadabcdbbacddbacddbcccacbcbdaaaccdbcdaadbcabadbbbdacbabbddbaaabbcdcdbcacdcaaadcbaadbbdbaddcbacdcaadacbadbcabcbdabbacdcbccabdcbaccbdabcdbbbcbbaccdbdccbcadcdbbbdbbcbaabddabadbbadcdcccbbdbaabcddccabbbbdbbccddbddbdaddddbacdcbddbbdcdbdbacabbdadcdabdbabddbbcddaaaadadaacbdccacbbcbcaddddaacdbacaaacbacbacadbcdbabacbcbbaddbadabbbbcdcdccacdbacdccaaadbadabdccddcdadddcdddbddabadbdbcacadccadabccdacdccbaccdbcdcabcdadaccbcacdccbdaabaadcdaacaaaccdbcbcddcddcbcadadcdbcacaccdbadcbcbbbbbbdabadadcccdacabaacbcaadacbbcbcabbdbbdbcabdccbcaadbddbdcbcaaddccbbdddcbaddbdddbcdabbadbaaaddaaadcdabaaabadbdcaaaaccbabcaadaabdbccddbbbccacaaccdcbddcaabbbdabacbdabcbdcbacdaccbaaccaabdbddaaaadbcddccdcaccdabaaccdaddadcbdcabacbdcdddccccbdbaacaadbaabbddbdaacdbddddcbacbbadcdadbccbacbdbccbbcaaddaabdbccdaaabcdddcbdbdaabcabdbadaddabaddcdcabccbdcbbbadcbaaadaacbdcbacbcbddcccabaaaabbabdadbdabdcbdbbdaacacabcbdcbcbbdcbaaccbdacadacacabcbddbadcccbaacbbcbaabbbadcbdbbbdcdaccaabdaaadbdcadddddcbdcddddbbddcccbbdaddccadcacdaacacaacccdccdbcadcdcdbacccacabbdabbadbccddcbabadcccbcbcdabbcabadabbcbcacddabbdaaacbcccddbbbdbabcddadcddbcabacacbaacbbabbddbcdaacdcaaddddbaddadddbcdbbadcbcacdcbbcaabbddbccccdcdccccbdaabcdccdbdaadbbbcdbabcdabdbadddaaadcccbbacabbadcabcbdddcdccbaccdbdacabaaadabadabaadacbcabddacbbcddabacbcdadcbdcccdcabdaccabbabddadbacdaaaabcadbababaccacddcbbaacabaadccacadabccccdacbaaacbabdcaddddddcdcdababbabadcaccdddaadaaabdadbccdabdcbcccbdccbbabaadcaaabdcacaccbbadbbbcadcaacaaabbbabccbadddcaaccbcdddbadadcdccaabcadccdacdccadccbcddddcbdadbbdbdbbaadbbabddadbddabacbabbaabbbaadcdddbaaccdacdadaadccccaaacddbacabcdaccaacdabbdddadacbdcbccbdbbdacbdbbbbdcdadaabccbdcaacaaaccbbacabaabbcaccbddaddcdaadbcadbcdbadabdaadcaacdcdcdddbaaacdcbdbdbdaabcddabbdabcdaabdcadbbbcacbcacdbdbbcbcdddcbdcabcdabccbccdaaaaaaddbcddbdacbdaddddccaccaacadbadaccbbabdbcbddcbcccbdabdbbdcbbcbbdaacdbbddbbccaacccdbbadabdaaacccbdbbdcddaabcaaaddbdcabdddcaddcabbbaadcaaacbbdcbbbbbdcccabbaacaccadbaaaadcbdbddccdcacccbcabdaaaccdadcddacbaddaccddcabcbbcaadbbabdabaaadaaacabbbbaabbacadaadbdcbbccdadaaabbabcaadcddbdbaaddabdddbaccbcbddabcbbaddddbdccddbdbbdddabbccbbabbbbbabcbacdbcddadcdbcdbddbacbbcccdbbccacdabccadcdaaaadcdcdbbbabacbbcdadbddccdaccdaddcccdacbcacbbbaccbabdacdcdcddcbcbabbcbddcddabbababcdadbbdbcccacbdabccaaddaacdcaabbbaacacabddbadddccdbddadccddaddbccdcbdccddcadccabcbdbbdddadbacdacbabbbadcddbbcbdbbbcdcabbbaacccadbcdabbcbbadacdcccadadbcccbabcccbdbcdbaaddbaabadcdbbcbacddcacaadadbaddacccdaabccdaddbbbdbcdbcacadacbdadddbaddcbcaddaddbcccccbaadadaacbbbcbbcccacaaccaaabcdcacbcababacaddddddbacddbcbdcbacdcabadcdababaccdaaddaadaddbccdcaacacbbdcadcbddaabcdbdbbdbcbcacaaadaacdbcadacbcdadadcdaccdbbccdaacbcccaaacdccbadcacbadcbbdcacdaddbbacdaccdbbcbddcdccdcbbbcabcdabacdddcaddaadaaacdccbccbaaabdcacbbbabbccabbcaacdadaccadcacdbcbcbadcbddbcbbcdbbabdcccdbdbabcabacdbccaaccababacabaabcdcacccdabbdbdbadaadbdaadacbcacbdddcdbcadbaabcddcdcaccabccbcdcbcbacccdacdcdacacbbbcaacbbbbbaabcababdadcdbcbccddabdcabdbddbbbbcbcbaccacbddadcabbbbbdacaabcbcddcdbaddabdbbdbccaddcbbbbddcaabdccacbdbacdcdaadcabcdcbbabdcbdbbcdcadcadbadddaccbddbccbadcdbccccdcbcbdaabadcabcdcbdccbbbbdbbbbcccbdbcddaababcdaacabbcadbdcddabdbcdbadaabcdbbcddbcbccbabaddcdaadbdcbaacccbddaaacaadbcbcbdbdbdbabbcbcaacaccaddcaadaababdbccdcdbcccddccdbaadadcdcbbdcddacdcbaadbcaaccdccdadcdcacddcccacabdbcadaccdbccbbdadabcdbcbaddbacdddcddccccbabccdbacacddabcdcacccbdaddacacbacdbdcabacaabaabbcbbcaabccbbdcbcbaacdbbacaadbcddbddacbbcbbcadbcbdacabbbcabdcccbcdbdababddababcaabaabaaacdcbdbaccaacbcacdaccdcbdbacccbddcaddbaccdcacdcccbcadcdddbaababacdacbacacccacaacabacccbcacdbbbbdbaacacbdbdddcdbbbcbdaabdcbbdacadbdbdbaabbbadccbbcbbdacbdbbccdbbdbbdbbddbcbbdacdcdbbdacadabbccdadbdaddadaccddabcdcacdcabcdccdbdbaddbaacabbcccbcadbadaadcbdddbbddccdcbaababdcbcadbdaccddddbccbcbabdadbbcbdcaccddbaddacddccbaacaccacacddbbdbcbdabbcacdaaccadcdbababbbcbaddaadbccbdddddabdcaabdbbcadbaccadadbbacbcdbddabbcdcccccdbdacaabdbbdbaccbbbbacabcbacaccbdadadabadcccdaaddcbdacadccccadaacbdcacdddabcdbaabadcaabbbdbadccddddabdbaadbacdbbbbdadacdbccdbcdadbaadacbdbcaaddcbdacabbbddadbaacbaacbccabcbdadbbbbdcabccbdabccbdbbccabddbdbabdbccddbdbdcbbcacdbcadbbaabdbbcddaabdbcbbddddcbbdaabbccaabcdbcdcddaaccbbabdbaabcbcbddaadbadcdccadadccdccabbbaddbbabbbabacadddacbdcddcaacdbccbabadcbcdabbcbbcaabaccaadcbadcaadcbbddacdcdbbaccacbbcaadddcbbcccadacabbaaaabdaccaccabdbbabaabbadacdbcdbaabaddcaacccccbcddabbcbdabbdbdcccbaabbacdaccccadcadbcbdcaacaddbcdabbdabcdcdacdacacbcabbdaababcbdacbbcaaccaacdcbcddbbdcdbdadaccdadbcbacbcdcddbcccbacdacbbcbcdababaaccaadbabdaabdadbaadcaabcacbabdbbacbdadcdbbaabddaacdcccdbcbbacccaddbbdcaabadbabcbdbaacacacaaadabcccadcadbacbcdabbcbbdaacbacabcdbcbdbbcbcdbaadbdadbbcbbcdcabbcbdcaabaaccccabdcbbdcbbbaadcbbcbcbabacaddbccdbaadcadddbdddbccdcacbccbddddcbbbccacdabcbdcbbbcabcdbddcdcddabaababcbdcdcbdacbcbdcdabcdbcdaccbdadbbbbaabcadbbccccbcdadbabdacabbcadddcaccabbabcbdbabbbbddcdbadbbacdcdadbcddbacbadaacaaadaabdcabcdbbcbdbbdcacdcdcdbbaccbcacaadcadbbbbbdcacbacdbabaabcbbadabddcdcddbcbcabbdbadcbcbdabcccdbcadddbbdddbadbacbabcaddacdcbbaccdabcddaaababcdaaaabadacbcdaddddcaadaadaccbcaaddabbbcabacccdbaadbbcccbdacacdccaaacccaabbbadbbbcdcddcbaadabacbdacaabaccbaadcdacbabacdbbabcacbaabdbbbbdbcbaaabccbdaccbacdbacabbaaddbddbcacabdcbbdbbabccadbaccccbdbdcadbabdbdbaabddababbaaababcadcdbdababbacbbabdcbaacaacdcaccdccbabdbbcbbbbbabcabcdabccdadbacaadddddbccbadadbaccdaacadcbbbdbabdbdbbdabbacbabbbabbacabbdbbccdbaccbbacbcccbdacdcabaadcbbdadbbdddaabccaacdbaadadcadcdaadccbabcbbabccbcdabddbadbcbcdbdbdbddbbabbbabcdcabdbbbcbbbbcbcbbadbaabcacacdaacbdbdddcbbbaabdbdbacddbcdccbccdddbacccaabddcccaabbddadacbbccddcbbbcdcdaabbaaabddbbdcdbccccbbbacdbacaadabadcaadbccdbbbbbcbbcbacbdcbaacaaabdcbacaacccaadbbbadaddbdcadbccdbaacabdcaaaaccddcccdbddbdccacbaadbcddddacadcabddbccaaaaccbcdddddcddadbabcaaacbaadabddbabaadaabbcabacbbaaadbdadbadcdcccdbddabaddadcbadbdaabddaadaccdabadddcdccbababbdbccdbcadcccdadacbaddadbcdcbababccdadbccaaddbdabddbdacbacacacbadbbddcbadadcddadddcddcbcacaacdacdaabccbbadbcadadaadbaccbdcccdadddacbbcaccabddaabcccbbccddcaacaacdcdddddbbcccbbadcbcbbdcaadbadddacbbacddbdccdabbdbdbbcbcdbcababcbaacacdbdaccdbbcdaddacaddaabdaaabdcbacdbbbaccadcacbdbcdccabcbccdbbbdabddcccdbbdbcdbbbcaddabcddbacaabdacdadaccbadcabcaaaddbacccdbbbbccaadadcccbbcdcaadcdbcbbbcbbddabdcdadbabdcaadcadacddaccddbaaadccabaadbabbaddbdaaccadbddbdcbcdbdaacccadabdcdccabcdbaaabccdaccddbadabcbcacdbcabbccccdcccdccdaddcbdcbcacbcbacadaacadadbdabadabaddadccdcbaadddbacabadbcaccbaadbbabbcdaabdadadccdbcdbcdadcbcbdcbcbbaaaabaadbddbcacbaacdddccbcdabcadddccaabccaaaccaaddabcbdabcacbbcdddabddacccbbadcddaaacbccacdbbcbddcaabcadcabcacbdccacccacdbbaaacbabbbdabccbcbcbacbdcbdbcacadbddbabddcaabcadacaabccbbbdcaabbadadbdbbdcdbccbddddcddbcddadadccbcabaccbdadbccadcbdddcdaccabbabdccdccbbabaacccaaadbacbcbbdbdcdddcbbcccaccdabdccbccbdacdcabababacacdcddbccdbbcbbdadddddaadbaddabbcddaccdbcdaabaddadaddbddbbbcaabbacabcdacdddcbdabdabdccaaddcaadbdcbbaddddbbbcdbccaaaababadbabbbcaabccbbbdacaabcacbaaadcbabdcabbbdaabdaaddcbabbccbccbddcabdacccacaabcddadbaadbcdcbaaadcdbcdbcdbadbabcbdcbdbcdbdaddcabbcabcbacacacbbcccdccacdbabdaadbcdddbbacdbabdcdbcacdbcbcddaabdaccddbbacabadcaccbdcdaaacccdddadbcbddaaaacabbbacaadcbaccccccacadbabdabddcaaabbcccdcbbbbdcdbdbcacbdddccdbbacbbaabbdbaccdcbcbabdcbccbabddacdbbadbaadaddbbcccaddcbbabacccadbadabbaddbcdcabbcabccabcdbacdbdbdddcbbadcbbdbccbaadcaacaaadcaddccbcadbcdbbaacaadaccabacddabacdbbdccacacdacbcbadacdddbbdbaacdadcaddddbaadaddbabacbbdbaacdcbccbadcdacaaabdccdcbcdadbbcdadcdacabcbcabdccadbdbdcaaacdaddddbbccddcdacbcbcccbabbdaddadcddcabadabccbddcdcacbddadcaaccddbbdddadddbbaaabbcccaddaccbbdcacabbcaaaddbabadabaadcacaccacabdcbbddccbdaadcbaddcabcaabccbccdccaabcdddcccdadbdaccdbdccdcbbcaaddbcbaadcdadbdbcdcdbaacbcbadacabaaccdbcdacbaacababacdccbbaccabdbbcbdbbacdaadcaddbbdbdbdcdacaaddccdddcbcdcdcaaaabbbbcabdaaaabbbdabbbdaabcdbacdbaaadddcaaacbcabdccbdbaacbabababbadacacbbbccbbcaabcdcdcccabbcbdcddbababcaadccdbbabbddabcccdbbccdbdccccdcbcacccdabcdbcbbcbcbabccaabacaaabbccadbcaccddadbcddcdddacbbdaacdcccacdaadacbaccddbaadacbccbbbdccdadbaaddabcaddcaacbddbcacdbabbaaaaaaabdadadddcaaaadaabbddaacbcdbccbdcccdbacdadcaacbcaccddbdbabcdadbdabdadcaadaddbbdcddbdccbabcbbbdddcdcdcadccbbbaaddbabaacccbcadadbabdddaacdddacdabdaacbadaaaaadbcadbdcadcdcaaadbcbdddcdaadcddacbbbccdaadadcabbcddacbcbbcdbcdacadadbdcdccbcdcaaccdbccbbbcabddabbcdaccbadabbddbcdaaacacddddbcdadbbdcdcdcbdbcbbbdcbbbdbadccbdcbaddccddcaaccdadadadbaaaadabaabdbaaabbabcbaacabcbacbcdaddcbaacaaddbcddadccaaddabaacbcdabdbaacbddbbabcdcdbcabaacacdaabaadbbbbabcabdbdbaacbdcbddddbabbddcacbabcacccccdcacaccdadbdcaccbccbbdbccabcaacddcaccccbbcdcbcdcacabdcabddbdcabacdddddbabbbdcbaabcaccaddbbadcccbdccabaacbaccadddbcacdbddbdcacdcaaaacadbccaadbdbacddbacacbccddccabccbbcccdddacbdbdacabbcabcdddbcabbacaadbacabadbcdbbcbcdacdacbddddcddcbaaaaabccdddcccbbcddbacccdbdaaaddccabaaacacbbabbbbabbdaabddcbdacadabdbadacbdcabccaadacbcadbbadaadccadcbcdddbdaccaabaacacbadaadacadadcdbdadaaaabdbcdbbdcdadcbdddaaabccadacccdbcccbdcacabcabcaabaaababacbcbabdadcdacbacacabacdabbbcbcabbabbdbdddcdbbddacbccdbaabadcbdcdbddcacdbdaaccdadacbdcadaaaadbdddddbcddabbbadcacbbdabacacdbbdbabddcaadbddcccbbaaccbaadadcaadadddadaddcdbbaacadcdadabacbdcdcbddabbaacdccacdabccdabacccaccbdcaccdaacbcdcaddccccdcbaabbaabbdaabacbcadbadbdbabccaddddddcbdccbcbbcdcacdccbcdbbdcdbabbcdbdbccababbdbcccbaacdbadcadababcccacccbcbdccbdccdacacbaabdacbbadbadbadbccdcbccabbdddbccbaccaaaacbbbddbdbcaacbbcddddabdcddbdbbcbdbdaacabbdacdaacdadccbcbadcacbddbdddccddbbadbcdbbdcaabbbbbdbdcbbdbdcaccdccabcdcabaddbcbbacccbabaacbdcdccbdadcbdadabdaddabcdcdcadacadbdbadabcbaaacddcabdaabacadaccabbcbdaaabddabadbabbcbbdcbbdaddcaaaaaacccbbbcacdadbcacaccbcbabcdcbdaabcdabbbbacbddabdcacbbbbbdaadbdbbbbabcadaaaccaaccadcadadcdbacbcabdddbadadabbabacacdccadacbbdacbddcabdccdddcbbcaacabbabbbdaaabddccadbbddabbbdaacccdabcaacdbdadbbacaadcdcbadaabdcacdbbdbcbccadcdacdbdaaaadacdabbcdddcbccbddbbbabcaacdddadbccbcdcacbadcbbaccdbdbababacbdadbdcbbcbbdcddddbbdbdaccbbcbcccdccacdcabdddacddaccbacabaacbcdddbbbcccbcccbabddbcdbcbcdcdccabbdaacdaaccabcbaccccccadadbdddaccdabbcbaabcbdcaadcddabcbdadcdbcaaddbabbbcdbdbababdbadddabcbbcacbdbdbaacabbacaaadabbaccacdcdabbbabdaacacdaaaaacdaacacabdcadcaccaaddcbbcdbadcbadcdcbabccccbdcdabcaaacdbdabaaacaddbdaabdaddaccabaadbbcdccdcdccccccbddcdbbabaddcdaaaabaaccbbddbadcdabbdccdcbabbdcbadaadaddbcbbabccabcbbbbaaabccdbdcdbdcdcdbbbdacacdccbaaaaccaaccdbdcdaaabdbadbcaddcaacbddcdabcbabbddccababadccbaaabbdabdadbbbbaaaccdccbcdbacaacdacccadabccacdcadbccdabaddcccacbcbcdbacbdaccbabbcabdbbaadbdbbbadbcddddbbabddccbdaddcabdcdbadabcaccdacadddcbacccdccddadccaababcacadddbcddbbddddabdbcbbaabbbbdbdbccccacbccdabadacbbadacbcabcdaaaabcaacbbdbcddddacddcbbbaaaacbadcadccdcabddaccdddbbcaadbbcdacacdabdcdddbdbcaacbbdddcddbaacadaaabbcbcdbacabbcdbabdbcbbcadcbacaddddbbaacadcbacabdddcacdcbbacccacdccacdbcdaccdaabbdcdaaccbbdabbaaaadccbcddddbcccbaccbbbbddbcccdbccadbcccbacbaccdbccbbaaccbbdbbbacabbabcddcdabddacadbbcacdddbdabdacdbadbcbcbbcbadcdbcadaccdaadacbcdbcaaacbbacaadcdddaabdddaadbbbdaddbddcbcdcdddddbaaabaaabccdbabbdbadabaaabbbbbbcbdaccaddadbddacdabbcdccbcaaadbcdcdabddddadabcadadaabaabdcbcddbdaabcbddbcabaadbbcdbbaccbccddccbabcccaccababbacdaddcabcccaaabcbbbdcccacccbcaaadadabaddcadabdcbbcbcbdbbdaaccbadcdbcdbbcdbadbbabadbbcabbacabbbdcdbbccbabdcaabbbabaadbaccccddbaddabbabcbdbadbadabdbacbcdacadcdbaacabdcaaacbcabaadbbbdcadaaadbbdcaddacdbaabcdbcadcdabbadbdcabdaadddcdbdabcaacadcadcabbadbcdcbcacdaddcadcdaacbccdacbdddddacacabcddacacdbccbbcacdbccbabbbbddbccadbcdaaadadbcbcddcadcccbdcbcdbaabcccabadbdcabcaddabdccccdddacabaacabdbcdabdbbcaabdbcbdcbbdbcdacacadcbabddcacbacadbaccacdaacacdadcababbcdccdacdcbacabcabdaaaadabbabbccaddcdaaccdcdaaacabdacacdabbddccaaadddbaabcbdaacaadcabbacdddacdbbcbabdabbbcaccccdbccdaacbdcbbdddbabaccadaddddbbddaabbdbcabdcdabdcdaacddcdcacdacadcddabcabdccabbabbcaaddbcbbaabdcacaadcacacbccadcbacccdbccdccaaabbabcacbcccbbadddcadccdabcbaadcabcbccdbabbabaccddbbacabdaacbcbbdcdbaacdddbbadbcdcaabcdbcdaacaaccbabbddccbccdbdcaacabadacccccddbaccccdabbccadbbdbdbdbdaadcacbdbcbdcbcaadbadadacaabddbbabbdaacdbccccbbcabaddccdbcbbaccbacdccdaaaabcacdbcbccbbbaddabbcabbdbbbdadcabdbddcbcbabaaddddbdbcdbbdaacddbdcbdbbbbadbbaaabdabcbccdbcbdbdbbaccdbdcbbbccdcbbacdccbcabdcbcabbaacbadcdabdccdccaaaaadcabbbbdccdbbbacbdcdcdbadbcdcdababbabacddddddcdaaaaacbacabbcdaadcbcdccddcaadaaddbcbbbaababbaddddabaccbdcabadadddcacbddbcdcddcbbbdddabcabcdbbcdccbabaddcacdabcaadcdddbadcbdcbdaadcdcdddadbcdddacabbbcbdaaadbbcddbccabbabbabadbbaccccdabbbacbdbaacacbbacdbdbdcbcccdcadbbbadcbbcddaabcacbaabdbcbdadcabacabdbdaccaabbcadadabbacbbdaabaabcadadbdccbdcaadaddbdccbacdbdcbdbdcbdaccbdcbdcdacbddbdbbddcbdaabbbacabcacdadbbcdbdacbadcbdcdccbacdaabdbcaaababcadccccdbccccdbbabdbbcbbcadbcdacacacbbdcbcccddabadbcdbcacdaccaddcdaaccbbbbdccbddaaabaacddbcadbbacbbddbaacabddbdcdbbdcbdbadaccccdccbccbacbcdbcdcddbaadaacbdbadaddbcdcbbdbbbddbcbbbadaabccbcccaabddaacdbbdabcbdbacbbddcbccdaddbddcdbbabbbdabddbaaaaacccbcadcbbacadcdddcacdbcccddbbccadcaccbdcbdbaddcbcbcadcbaacdbabcacaabcaccccbadcddacdcdabcbcbcbaabbdbbadbccdbbbbccddaacacdbcbcdacdaacacdbcacbcdcdbddccabdbbccbcaacdcddcaacbddaadbdadcbaadadababdddadabdcbcabbdacdacacbacbbaabacbadcbaabaddbcccdddcccbbbbacbcccdabccababbccdcbbcdabcddbdabbadacbbbcdbdcccadcdcccbcdbaddcbbaacbacadacbbdcadcacaaacbbbbcdddcdaadcabdaacdcdbadddbccdbcdbdbadccbabcbacccbbdababbbcbbadccbacaaaccdaabdadabcbadbbbadadbcbcaaddbdddabdabcbacaddbabaadbbacdabbcacdcaccbcccbdbbbcabcdccdcabbbdcddccdbaabcadcdadcdbbcdcabbcdbcaddbaaabbddcabcbacaacbdcddabdcaaccbbdbdaadddadcaabcabcbdcdcdccdacddbabddacbabdbbcbbabbccaacadccabbcdadcbaaddabadbbacaaadddcdadcdccbdabcbbcabdbdbbbadcdbaacbcdaadcdccdbdaadaadbbdcadcaabaabdcadcaababbccdcbbdbbdccabdbbaddccadcdbdcddaacdbcbdbdadbaabbccbdbccdabcbadcabaacaadcaacabbbadcbadddbddabddbdbcbdaaddaaadacaabbaaaadabbbcaddcccbdbcbcaccbdacaadccdacdbbdcbbdaadccccabdacdcbdddacaacaadadbaacadcadddcaaabcaaccbbddcaaacbababbbadcdcabaabdaaabaadddaddddcbbdcdcbbcadbbddddbdcabbccdadcdadaccdacbdbdcbcddbdcccabcbdbdabddabbdabcccdabbbcbbbabcddaddadacbdabbdcabcbcacdacbdaddbdbcabddcaacaaabcbbababdaacdadbacbabbbabcadcabadddcaadcabbdaabacdcbccbbcbcbcdcaacbcdbcccdcdbdbbabddabaccabcaacbbcbdcacaacdacabbcdcddbaacababcbcddbcbdcbbbcaaabbbdcddbaadcdaaacbdaacbaddcbadddcccbbdacaabbbcbbbadcddddbdacbbdbbdbcdbcbbabcaccaaababcaaaddcbcaadcbbbdaabdcbbbadacbadcdaaadbdbabdcccaaddcdbadcbbbcaadcbacbcbddadcbbaacabbbabbdabdbcabdddaacaacddbdbbdadcadcbcbdcaaacddccaddaadaaacdbcaaacdcadaccdcbbabccdbcabdccddacdbacdcdabdadbabcdddccccbbaaddbbcbbbbbbbcbcadaccacccadcdcdccdaccbacddacbadbbbdccadaabbdcbcdbabdcddbddcabbaccabcaabccdddddbcacdaabaacdcbaaccdcbacbdabdddcbbdacadaacddcbbdcdbdbacccdcbbaabdbccbacaddcaabdcaacaaabcdaaabaabaddbbacdabcddbccdcddabdddcbbdccddaabddcdbabbcacdcbccddbcddaacaaacdbaaadbaadcbdbcbdaddabdccabdcbaabdbdbabadadbbdcdcbcabaaabbdbbaddcbbcdcddadcddbabdccdccbcbbadacdbbbbacbaaddddbbcdccbccdaaddaddbddbbbcbccbaacbcdccabcbbdadcddaddbaadabcccbabccaabcbcadbdcdbbccddbcacaacdbaaccadcbbcadadccbbbdccaaacbdbcbccddadccabbacdcdadbadddaddcabadbcadaccccaccccdbadaaaabcdadcbbddcadcacadcaaacaabbcbabdadcbabaadaaccbbcbbababbbddaccdcbaccbcacacadcaaabbbbbaaddaddbcbdadccacdaabbdadaaadcacadbddccdcdadcbbbabcccaccbcbdaccdcacadcdccbabbabbaaccabdcbdbacadbaddcddcbaccdbacdbbcbbbcdddacddcaccadcadbdbacdababaaccbcabacbddbbbadaccbcdbccdcbddcddddadbdabbccadcbddcaccccdddcddbccaddbbcadcbabddadddbdbddcddacdabdacbaccbdcacdbaddaadacabbcdbbacadcdccbabacdcbbcbaacbbddcacabbacabcadcddbdbdbdabbdaccaabdcdadbbcaadcdbbddababdcddbabbbcaacdddbcdcaaaaddccdbbacaaacabbddbcabcbcdcdbaadcadcbabdacbdacadbcabbaacacaddadbaacadcddacabcdacdbcacaddddbbcabbdabdacdcdaaabadbdcbbaddccdbcbdbcdccacadadcdadabdbbacbacdacbcbccddbabcbdbbaaccadabbaccdbaaddbdcbcaadacbadaccbbcdbcbabaaacbbacddccbddcaacbdadacbacbabbcbadbdaacccaaddabddbaacaabbabbbbdabcadacbcadcdccabbcdcaccadaaaacccbaabdcbaaddaddcabdabdddccccbdacddacdccaabbbaddabcdcbbadbcbbadccbbcdbbdaccaddadcccdaadaabbbaddbddccdbaabcddccbdacaaddabbbaacadabccbdcadabcdcaacbabbccbdaddbbcaddcdacabcbbbdbcabdbaddcccddcdadddcdbcaccaccbccabdccabdbcdbbdcabccdddaddadaabaacccdccbacdaabbadbbbbbcabbdadccbddbdacdcdbdcbdbbadaaccccdbadddaaadabdddacaaaccadaaacbaadddbcddbddbdcacbbadbacacdbdbadcbccddbdbdbacddaacbcddcabcdcabaccacdbdccbcdbabbccddbdcbabddbcccddbaaacbddcbbbbacdbdbddacdadadcadbdbbdcbaccdbcbbadddbbbacbabcbaccaacbbcbabcdbcabdddcdaccacbbccbbabaadcacadadcacddbdaddbabdacdacbacbcdbaccbbccbaddcbbbadacddcddccbddcacaabcbbddaaababcccababdbbaacbccdaaccbdcbbdbadccabadadbcbdbdddbdacbbbccaacbcbbadabdcadabaaccdddbbabccbddbaadaabaccbadaddccacdbadcbabcadccccaddcabaadabadabaacbadaadddbdddbaabcdcaadccbadccdacadcccdbdcadcddaccbadccddbbdbcccbadcacdaacbcdddcbaadaadbdbacdcbbcbbbbbcbbdccddcbbadadaaabacbdcdcbacdcddbbddbadcbbadcbdbadaccaaacaacaccddddbababacaadbdcbaacdabdacbacbbabcdcbddabcbbabcbacacccddadaadadbdaaaaaaadcbbadddbcaaccdbaccbddddbcacccadbdbacdbcdadbbccdcdcbaaabdacabcbaaadaaacdcdbcdcbacccaccdbdddaaaadcdcacaddaddbcaddbabcbbcadbaadadadadbcbbbdccdbbbbddcdcabbbbccaccccdaabbadadbcbacbcddabcabcbabcadccabdaabdcdbdccbcaddbadddbcabbccadddcaabbcbaccdbcddadacabbcccbbaddabbbacbabaabbbccbabbccdbbaaaacdbddcacddcdaacbadadbdccdcacbbdbabdaccaddacbdccdaccbddcdcaacbddbadbaaddccabbcddabadbdaadaabcddcbdcdcabbbcddcdaaaabbdcddddabdacdacbcdcaccbacaaabadccadacaddcadacdcbbacbbaacacdaddcbbbbbaacadaddccacaacdbbcaaacaaabcbdbdbbbacacbddbaabdbdccbcbddbddbcaccaccbaabdbcbacdadbbdabcadaaaacaadbccbdaccbcdddcdadbadcadcbddbaacbbabbadcbdddbddddddbacdcdbbaddadccdbdabbcacdbbbdcaccaccddbcddcdcabaccbbdbbbcddaadcbddccacbbadbdbdcdddaccaaabadacddbccbcadbccbcccbccbbdcdbddcdacbddbbaddaaabccddcadaadbaaaccbabcacddbddccadbacaccdddabdaabddacbbcaacabdbbbddcbcdbdccbccdbcbbccdcbadddccbbcdacdaabcbadccdbddbaadbadaabdccbddadadccadacbbcbbdbddadbdbbdaddbbabaacadcadbcaddbaccccadcbcddbbbcddcbdcbbcabdadbdabcdabddbbacabdbdabcbbaccbacaabcaacbacaacabbbabaadabcdbcdadbbaccdcacbaaadcaccbbcbddccbaacacaabcbabacdbbbdccdacccbccbabdacbddbccccbdbcacdabbbbadbddcdbdcaacddccbbdaddcbaaabcdbaaabdbdccdbdabcacadcadacacbdccdccbaccbdbbdaadaabcccacbbddaaccaccabbbacbabacccabcccaddcaacdbddbdcdabbbaaddbbcdbdcdbabacbcbaadacdbdbccbdccdccdacdacdcdadbaddbbcbdcbaabdabdbbdbcdcbbcbbbcaccbadbcabcbdcbcacdccdbacbcbcccaddacbbbdaaddbdaddadacdacdddbaccdccbdbaccccdadcdaabcdadadadbddcacbdaccabbdccdbccbababbdcbaddcddccdcdacadccbdccdabddbcddccdbdabadcacdddddbddaabacbbdaadaadcddcabdccbbcdacabbdcddaacbcaddbdbbdcaaadbccadbaacacaccbbbbcdcbdbbbbdaaccdbaddbddabdcbadcadbacbbbabadcdcadbcacbacabbcbcbcdcddabbccdcdbacdbccbbddbddbdbcbaadcbdaacddbcddcbaabcacbddcddcbdbacdcdcbbccdaccabaadcddbdadbbbaddcdcabccbcdddbcadcccabcaddbbdcdbdaaacbbdbbbdaddacacdbbabdcdcbccbdababdbdabcbbbbccdbdacbbadadcabbcbaccadbccdcdaccddcaabdabdcdddcddbcacaaabccbabdcdcddbaadddbbacbaadddaabbccccdcdabdccddbbcbacabbbccabdacbcaccbbbcdddcbbccdbbbccdbbbbcddadaabddbbcccbccbbddcbbccbaacbdcabcbbddbbcdbacacdbccbcdbbcacdcacdbadccadaaccbcbcbbabacbbbacadadcdbcbacbccabcdddcdcaddbddddbabbddcbdcbcddbdcababbdcaabcdddadabdacdddabdbbdaadbdadacdbdacdcbaabacdbdaacbbbdcbbbadbbbdbacdaabacacaddcaccacacabcabcdacadddcabababacbdcabaccbbbdaddcbbacbcadbbbdccddbbaaddaacaacccaaababcdadcaabaacbbccacccaacdbdbdbddcbdbdbbdcdacdaccdddbbdaaaccbbbbadddabddcbbdabdbcdababcdbdcbcccdddddbacadacbacaacddcccacaacbbdbbdabbdccdddbabccadcbdadbdacdaaddabaccccadcddbacdaacacbbddbbaaddcbbbabcbabaddcbcacbdbcdacadcbbdadcdddbdbdccdcacbccbdcbdcaadbccaaabdaadacbcaacacddcadccdcdccccbbbdddadbbaaadbaccbbbadbabbdbccbbdcdcbbcbaaaccccababbbdadbdbdaabccbbabcdbdabadbdbdadabdaaddcccbacbcabcaabbcbabcbbcabdadaddabaadcbaadaacaaabaabdcbbdcbbbdadbdaacbcddadbddbcabcabadabbccbcabcbcaaacdbcbccdcbbadbbbddaadcacacadcccaabbddaacaddadbaaacaddacdcaadccabbdcccbbddbdadcbdaaabbaaacdacdccbadbdacddaaadabcdadccdcdaaabdbccacddbbbadbddcddacadbbddabcbcaadbbbacabcaabccbbcdcccbaabbdbadbcbadabccbbbccddddbcdbaddbadbbcaccdcbcbdabdaabbbdbbaddaddacaabdaadbbabbaddcccbdcccbcbbcbdabddccbcaabaabcbcbadacbabbdaacbdbbbadabbdcaddbbadcdcdbaadcbccdbbdcbaaacacccaaacdcddddcccabbcabdbdbbddcdbdbcdcccddbabcbccacadcbcadbdbbbaddbdbdaabbcacbaaabcdaccddddbddbcadbdbdacbbacabccdbddcddcdcabadcccbcaacccacbbbadcbbdcbabaddcbbdddddcccbdddbaccacbbbddddccdbdcbddbdccdcddacaaabcbbadcccbacabbbabbacbcdddadabcbaddccddcdaaddcabbdbdcbadbddaabcacadadadccdabababacbabacdbcddadbdbdcbacbcbabcbdbcddccddaabaabddcaacabcdddbdccccbaadcaaaadaaaaaabcbcdadcabbbaaddcbbccddcdcababbbaddcadadbdddccbbccdcaabbaaaddbdcbccbcdcaadbcdcbcbdcbaaacacdddddbdcdbdacaadccbaddadddbbaddabcadaddaadacbbbbdaccdbadcaaacadaadacdbbbcaccbbcbaabdcdacbacdcbccacbcdcdbadbaaadacdbcbccccdcccacdbbabddccbccaccdddbcbdcdddabcaccbdaddabddcddbcadbbcacddcccccdadccdaaaaacbbccbadcbccccbccdbcdadacaacaddacbabadbdabbdadbcaccbcbcdabdaabbdabcbadaadddccddbcacaaadaaaccdccdcbaabcadddcaddcbadcbaccdabdbcacbacdcbdaddbcbbcdccacaccbcddcbcaadbddaccbcbcccdbaddcabbcdbbbccacabbadbababccbadbadbdddbabcdaaacdcacbbdadcbbdcdcbcdabdbdcadcaabbbbdbccbdabddabdddacbdaaacbccbadacdbdbbcbcabcbaaabbaadbcbddddacbaacdacadaacbdcbbbadbcccacdabdacacdaddcbacbcdccddaabadaaddacdbcccdcbabbdcadcbcddbdababadcdadbabdabbccbadcbcaddbcdadbbbaddbcacaddbadccbdcccdadbabdcdadbdaabbcbcbdccbcaadcabaaadcabcdcddcbacdadabacbadbcdbbccdcadbbcbddddbbacdabcbdcaadcaaddbabaaddadbaccbbbdcabcdcacdccbccdacadccbbbcaadcaaacbcbcaabdbbbdddaabcaadbdccacddbaacdddbdcdbbbcabbdbbbabdcdbdbaabadbababbddbacccbaacbabbaaadcdddddadaadaaaacbdabcbaacbddabaabddcdcaddbbbdaabcbdabbabcbbdadabababbabdbcbccbaddcbadcbcbbbcadccccdcccaddcababbdaabcaaadadbccbcaaddbdcaacadacdbcaddadccadbaacbccdbabadbaddaadddaaacadaabdbcabaaabdbdbcddddbcdcacdcbddcadcdadcbdadbadacabbddbdbcbabbcddbbdbacadcdacaddaaadbdabbccdacabdaddcacadbdbbcdcdddabcccbdcadbcaddbdbbbddddcadcdbcabadbcaabcbcddccbbcacabaaccddbdbaabddcaddadabbccadccbdbbdaadcacbddcabbdaaaacdccddcccaccaddcabcdbbcddaadccbaccbbacbcbddddcacabbddbadcacaaddadccbddadaacaadaccbbabbadaddcddacbccadbcbdabcdccbbdacbadbdbcacabdbbdccbaacccccaacccdcaabcdbaaaddbcbbadcbdadcabadbdbdaabbcaabaaadcccdadddaacdaabcbddababcaddcabaccacdaccccdadbcbbbcbbddabcccdbbcbddbccbdaacbddbcdaacdbcddbabbdddaaadcbacdbacacacddabaacabddbaaddaacabcccdcdbdbccccdabbacacbacddccaadcdcdcdbbadccbcdbacccbcbdbacbbbdcbcacbddadabbdcadabbbcddbddacabccadddbdbcddcaccdcdbcddaadbbadccadbbbdccddbcabcbbcdabccbbcabacdcacdddbdbcdbcaadbacdacacaaababaacacbaadcdacbbbbbcababdbdbacacbbaadbbaddddccbbbdbcbcddddbdcbdaadabbbdbbaadbbacaddddacdcdaaaacdcdbdbcdccddbbdbccdbbbdacaadbdabdbbadacbbddbbbcccbbdaaddcababcbbdacadcadcacbbdaaccacccbcccbbabcbaccabaabdacccdbcaadcdcbcabbddcbabadaaaacbbacbdabddcccaacbdccccaccddbabdbdbcbcbaaadacbacacdabcbbabacdadcbaadacccbcbcbdabbdbabcabbdddddddadaccdabdccadcdcdcdcacacdadddbcaadaadccacdbdcaacbbadbcdcdbcdabdcaadbdcbbdbaadaabbaadbcdccaddcbdbadbacdbbdaadbaaaabccacbaaadccabbbccadbcccdbdbccabbabdbbddcbcacdddabacbcadabccddcbddcccdadbbdddcbbbcaacdbacbdccbbabbbdcacbbdacdbcdcccadbdabbdacbabadaadccadbdaacbadbcabddcdccdbbcbabcbaadddabdaccadcddcbddcbcbdcaacbabcddaabdacbcdcaabddddbddbdcbbdbabcaacacdcabdbadaacbbaacadaaddabcbbcacccddadbccabcadcdcdbdddabaabddcdbbaaacbbcababadcaddbdccdbddcacbdbaaadacaaadacdcabcbbcccbccaccbcbdcbdacbbcdacabbaddabdaddcacbdcaddcbbcacbacddbadbcdbddcadbcdccabbdbdbadcaddddbcaadadccdaccbbccadbbdddbaabbbbdbacaacacbdcbdcacbcaaddcbacbdbaadcdaccdbbbcbacbddddacaadaccbcdccbddbdcccacddcdacdacacccdbbdbabdcabbbadcdacadcbcaadbacbbcbbbdbdabdcdcdbdadbcbdcddbbddbbccabbcbdddaacbdaabdcabcabdaacabbaabbabcbaadcabaadabbadaccdabbaabdadcdaabccdccadaadbaccdcbaadacbaddcccdadabbdcdbcadcabdbcaaabdadcbbcddccaccdcbcabacadbcccbbabcddcacddbadcbdbcbcdcabcbbcddcdaacabdaacdbddbaacaabbdcaababdbaabdddbadcbbcbbbdbdaaccdcadabccdccdddccbddcaadbdcadabcbdcccbccdcddabcbbacdacdddcbdcdbbcdaccaaadadadbdccadbbcdbdbddddaaddaaabdbddcbbdacbdcdbcaadbbcadcabadadadabbaabdbbcccadbbdadbbbdcadbacabdbccdbadbbddbabaacaacddadcaaddcdddabddaaabdddccbdbcacabcdaacabbaadbbaddbbcbddbabcddddabccdbadabcaccacbadaabdccbccdaddddcabcbaabacbcbbcaccabcdcbcbbbccdbdcacbbcdccacccacdcbcacbacdccbdcbbdcbbddadacbdbbacadaacbbdcdbabadbbdadddabacdaabbccdcbdcadbadacacaaabcadaccbcacddaccabdcdacdcdacbdcaccdabbcdcadddddcbbbcdbdbcdbbbdcdcdddbbddadaaddcbdbcaabdbdbddcdcbdaddbddbcbddbacdaabbbaababddbcbbcbabcadabacaabcacdaaaadddaccabdbbbdcdccbbaacacabbdadbaccbbcdcddbadbcacccadacdcbbccddcbdbccaccddcddcccbdbccabaccdacccbddcbddcdbcaddcbacaabdbcbdaabbbdccccaadbbadcdcdcdccbbabdbccccbacbbbacacbaadddadddddabcbdbdddbcccaddacaadababdbaccbdbdbdbbbaccddadddccbcbdacacaaadccdabbabdcdaacccbaadddaaaadbaccabadadbddcaccdddabddcaccacabaacbcbcbccabcbdabdcdaababbadbcaadacbbadbdadbccbbbcdadbdababcdbbbdaabaaaabcaccacbacaaadaacbbcbbadbacabadcbbaadccabdddbdccabdcbaadacdaddccdaccbbddacaaddabacccadbbdcbadaccdcbacbabdcdcacdbbbbccddacddccaadcdccbbbdbacbabaacccccbdcacbbbbccdbbddbdbcaccbacbcacadbcdcdabbcbbbbcadabbdcbdcdabacadcddbaadaaabaabdacbcdbbdbbddacbbbbcdbcadbdccddaabdaabaaaccacaaaabddccbdbbaabadcccadabbdccccbbbdcacadcabdabcdbdcbdcccdbdbccbbccadcbcdbcbacabaababbbcbbcacccdcddccaaddaabcdbddcbddabacbabadddaddddccccdcbbaaacccddabbdcaabdcbcabbaadaabcdacaadadaabdddabbacaacbcbbbaadbaccadcbbbbaadcdccbddbcbaccccbbbcdcbbbdbbbbadadadbcbbabbcabdbdbbddcbbdbaabcdddcccddadcbbababddabddcadbcdaababbacbabdcbbdacabdcabbaccbcccbbccdabccccadcccadcaaccddbdcddbaabcaccadbacdcccddbdababbbbdcdbcabaaccdccaabcacdacdbdbbdaabbdcbddadabacadbcbcababddbbabddddcadadcccaacbccbccabbcbcbdadcabadbaaacaaacbdaaadadddbcadbaccccbddaccbadbaacddaacaadbacaabbdabacaaddddccdbabbadbdadadbdcabdbcddabaccdccadbdcbcbddbabbddbbcaaabdcadbdddabddacaddcdbbcacacaabdbcabdadcdbbdddccbabbaaaabaadaaabcbdacaddccddcbacaaadcbbadadbddcccddaaacbbbccdacaaacdacbbdabdadaacbaccaddbcabcbadacbdcbdbccbcdcdbcabcbcdccddbbddbdaaccaaadbacbdbadbbdddbacbcdbacaadddcdddcadabbbddbdbdcccacbdadccabddddadadcbcbbbcadddbddaabcabccdaacbdadbbbcbbcccdddabcdbaabaaaabdbbacbadbcccdbccacabbbdbbcadbcbdccadddcbaaddcbdbadaddcbcbcdbbadbcacdabbcdcacdbaacacdbadcacadaccbbdcbacadacdcddbdaddacbdaddbdadaccbaddbbdcbbccddabccaaabadcabcdbdabcccbaccdbdaabacbcdddadacaccbabbbdcdcddbddbbccbbcdbdbdacdbaaadbbadbabccbbddccbaaacbddcaadabbcacdcbadccdabaaabbccbcdacacdccbcbabbcabbcaabaacadcdbcaabacbdbbabcccbccdbbdcddcadaabbcaabdbabcbadbdaaccadabdbbdbcadabddccbcdcaaddcacddadcbacbcaaadcdcdadbabbadbddcbbcbcbbdbdadbdccbadbbcaacdddbabbddccacdcadcbdcbdddadddabadaccdccdddcbcbaaaababbabacdbabccbcdadbcabdbccdcbbbacbcbadadcbbbccbbaddddaacdbddbadabcadcadddddbdbbabbaaabcbcbdcbcddccbcccddddadcbabdaaabacaaccbdddaaaababaddabaacabacbdbdababaaabdaaabbddccaabdbabadaacdddacaddbdaabbaccbacccdbabcdbdaacbacbddbdbccabdbbbcaacacdcacabcbaadbacccbcaddbacbcbbbcddcbdbcdbaaddcabdbbcbaabdabbbcbabbbabcccdddacaaddaddcabdadbddaaccdbdbcbcabadadcdcdccaaabcbcabdbdcddcbacddbbdaadaadbcddcacadacaacdabcbbcbbbdaccacbcabdcaccbaaaddaddbdaacdbdbdbccdaabcccbcbcbadacabccdbcbccbabbdababdbcacdcabbacddcdbccddabcacdccaacabdcbcbbdbcccabcbacdcbccbbbacacbbcbcadbbdcbbcdabcdddadbadcabbacdbabadbdcbbdbbcdabbaacabddabcbcccccbbddcacccadddcabccabcadcdacccabbbbdadddbbcccadbdcbbcbcbaabdbabcdbcddcdddbabccbbbdcbadbabcbcccdbacbbccabdddbcddcdaaccacdcacbadcccdccbbacdacbcadbdbabcdccadadacacddddcbacaaaaadacdacddcdaabdbdcdbbdddbacccbacdbacbbddcdabacabaabbdabdddaaabbdabddbccaadccacbcabdcadcadcddcdcdbadacddcaadaacbdccbccdbcacbccdcabddabbbacacadaabbbdddabadaddddaabaabddbaabdbacbcdcccaaacbcadbbcbcadcbcccbcaabcbbbacbcbbacdaacbacddacddcdcabbddccaddccdcccbacccabcbcccdbbcaddcbdacdbddcdaabddabcaaccbbabdbdacacdcadddcbcadbddbddcdcdacdcdbccbadcaadbccdbbccbcdbbbbbbaaacbcbbacadaccbacadbbcacdbdddabddcdbababcdadbacddabaadcbabcdcccbdaccacacaaabbbdbacdabbadcddadaddcdcaaacccbdbccbacdbaccddddaccbbccbbbdabbaaddadbcadcdaddddaadaddcbdbcbaaddbbdcabaacdaaaccbcbccccadddcacddadaadcbbccacbaaadcbbdbccbcbcdbabbbcbcdbbbacbcddadcacadbaccddddacdabcdcddcbbbdaaacaaddbccdcdbdcbbcccdddacaaacddbaccdbcddaddbbcdababdaaabdbadadcbdadbaddccdbaadbcbaadbbbccbbccdbbbaabdccacbcacacadcabbdddccadaacbccadcaaacacbdabdaadddbaddddbaccdcddcbbcbaadbddbdccdcacaacccbadbbbaacbaabccdadcdadbddcadcabcaacadcccdacaccccdbdabccdcdbcdbbbcaccadcaabbdcacacddbccdbcdbbdbaaacdbaadadaccacabcdaaadcaadcadddcbcdbacddddbaadbdbadcacadbbdadddbabccacddbaddabbabdbdcdcccddbbcddcabaccbaaabdaaacbddddbacdabacaacaccccbacbddaaaadccdbdbcbaabccddcaabadadabaccadaddbabcaabaacaccbbbabddbbdabbcdcdadbadddddadacacbbbcadcaacababbacdccbcaccdacbdcabcbaabdbbcddaccbabccacdcadbacbbbbddbaddbabbcbbcbbcdabdaaabbbccdccdbdbabbababcdcbdbcdcacaddccacaddbcdbcbdcbdbabcaaccbdbaaabacdbcdaabaddacdadbdbbbdcdabbdbdbdddbdbcdbdcccddbabcdcdbbbdaaacbadadcddcccadbcaabbabddccadbbbaccbddbadabbabaaddddbdbddbbabcdadbaccbbdaddbbaccbcdbbbdcbcbbdbdbabddbdbbbdbbbdadbabaacccaaccacdbdbccadbbbaccdadbadbbaddbcddbcccbcdbabaabccacbcabdadbbccabadaaacbaadccbcccbacbddaccdaadacabacacbdbcbcadabcdabbdbdcaacdacacacaddccbcababccdadabdadcadbcccdacacccadadbcbddcadaabccdccdddcdbababdbdddabdcccdaababcddbbdddbacccdbddcccdddababbbdcbadaccadbccbaddbadadbccccadaacadcadbadaabbddcaadaabbacadddcbbcacccdcabbdaadbdaacddacbbabbadbacbdbbadacdccbdcbdbbadadccadccaacbdcbdcbcbccbadcdcadacbabccbcabbcbcdccaaccdbdcbbabbaabababbcdadbabdbccdaabcdccbdbbcabbaaaddcdbccdbbcaccaddcaaacbabdddcadddbccccaaaddcabcccdadaadcadbbbbadccdcbabdbaadbdbbabacbdcacbddbaddbbcdcbbcacbcbddbdbccdcbbdcbcccbbddccddaacbcccbdddadabbcbcacdbbbbaabaabcbdddcddaddbabbbbdccddcabbdbdbbcadddddddccddcadaabacabcdcdadacaccbaaddadcacbdcadbddbadcddcbacaddaddccbccadbbcacacdccadbabacddbddbcccbddccdcbbbbdcdaaccbbaddbaabbaadbddbbdbdabcddbbcdbbbcddcdcbdcbddcbdabdbacbbdbccbbbadcdadcbcbcddccaabdcbbdbcdaaaccbbbccacdcdcacaddbadbbaaaadcdacbbdbbdcdbcddbcdcdaacbdbaadbaaaacddcdaabbdcbcddadcbdadbacbdabadcbbbdcbacbbbcbccbbbdacbddbcddbddbadaadcdbbbdcdcbcbadbaadcacbdcbdaddabacdbbbadcabacbdcabdaddacbbbcbbabcaaccdaababbbdbadaacdbccadaaadbdbcdabddcacdcdadbdddacadccbabcbcbbaadbbddacacbacabdbcdbabdcbdadabcbdbcadbddabbbcbadddadcbdccacdbdccbbbddaaadaacadadddcdacacdaacdcdaababbcbaacaadbdabcaabacabaadbaaddadaabcababdbaabacdcdbbcababcdadddbcdabbcdaaddbcdaabccbdadbddbdbbcdbababacacbccddadabacdcbddbaadccdacdadcdadbdddabbccdcdadbcadccbbabbaadababcbccbabcccddcccbcacdacbdadccadaaacddddbcaccdccddbbdbddddabccadbcdadabcdaccabdbddbdbacdacadabcccbacaacacbdddcabcbdbaacbdadbcaddbaadaabaaadcbdabdaaacbcccbbabcddcaaddacdbbcbdbbcabdddadaddbadbcabdcbdbdbcbabcdbddacdcbdbcccaacdadbadddcbaccacdcdabcddcbbcdacaddadbcadbadcaadbdcbadbaacdbcdbbccbcdcaddbdbadcadcdaccdaccddacabadaaabacccbbabacbccdddddadbdbadabaddbdbdbbdaddcbcbddddcddcbaacddbbbdabcdddaacccdcccaddddbbdabcddccbbccdccaddccbbaacdcdabcdddcaaacbcdccababddccdccddbbcbabdcddbdbacdddcabcddaadaadcacabcacabdbcabccbccccabddbdbcbdbdcacdbdcbdacaaadccaaadcbcdbcdcacbbcccdacbdacbcdadbabdaaadaabadbdcbcddccdabdcbcbccdaccaabcbadbbaaaaddbbaddadadadccabadccbdbcacdbdbccadcddcccdbdaadbabacddbccbdbdddcbcbcbacadbdaadccddbdcbacacdaddaacdcadcbbbbabdddbbbddbddcddacbacccdcbabcdcddcacccdbbabadcdcdadddbccccbaaacabdbbbbcdcdbbcbdbadabbadaadcbadcdcbcdddbccbcdbdddbcbbcbdbcaddccadcbbcaaacbcbaddddaadcabaabcabcaacadcdbbcbcccadaadadcddbdadcdabdbadbcadbcdbdddbdbacadbbdcaadadbadddddabbbdabdbcbdcdaaabbbadccbcdbcdbddccabddaaadabbbbcbbbdaaddbabbabbcababcccdbadcbddbbcdcbbabccdbddbcabacdcdaaadadbbccddbcabaccadcddaadcabaabdbadbdbcacbbbddcbbabdcabccdcdbdacbcbddddabacbddbacacdaadbaaabdcccbccbdaacbcdabcbabdcaadbaddcadcacacacbbdbbcadacbbaabdcbccbcdbaaaccabaabaabddbcdbbdbdacabaccddaadcabaadccaccbcdbaddcadadaababadddbcdccacaddbbdadabbdcaadbbddabcacaadbbcbbcbcddbcccabbdcbcacccbcdbcbbabdbbacbdbabdcccaaaaddddcadabadbbcccabdbaadbdacbaddcbabbcddadaacaacbbdcccdcddadabacbcbccddccccdababcbbabbdabbbbcbdcbcdacbccabababadcabaaccabacadbdddcdaabdabdbacddaadcbcbbbbddacddcaddbadadabdabbcdcabddbabaacbadaacdccbdddcaabbdbcbbacdbcacddaddddacaabcdbadadbcbcabcbdacddbdccddbbbaaadccabacbccabcdabbcacabcbddbacbcadcdadbbcdddaaababcacaaaadaccdccabcccbaaadbcbbdbddbabcadcdddacadcbdddbbcddcaabcbbbaadabaacbbbdadddbddcdbabaddddbcadbbbaabadadbdabaabbcaacabacabdababbdadcadbcdbbccabcadcbcdbacaacacbbcadbbbbbbcabdcdcacdaccaaaaabbdddabcbdccbbbadcbdbdbababadbbcaacddaacbbabccacdaaabdaadcbcdabbbdccbdbcabdadccaacddcddcbbaccabbbadabddcbcaacddadacbdbaadbbbbcbdccbdbdbcbdcbdcddbbdaccbbcaadbddcdaadbbbbdcdadbaabaccccbbacbbabccacdcbcbaadddbbdadbcdabdccbcaddcccaadbddbbcadbabdcdcabacdcabdcbcbcbaccbcacdbbabdccbdcbbddabadcadccaccbddcbdbbdbabdcadaacbbbccbaaccbcababaccdccccbacadbacdcbaccbdbbdabcabccdbbacdaacbbccccdacbbcabccabcbddbadccdaacaabcdacdccdcbbacaddabcacbabdddbbaaaacaacbdccbcdddaabbbbcabcaccbcdcddccadccdbbaaccbbaaabaabcccbbdcaabdbadcdcacbbbcacdabcccbccdbbabcabbabdbccddbcdcadccbdcabaccddacbbdacabddbaccdcabbcbcbdacbcaadbcccbadbcabbaadbddbdacadcdacabdabcddaabdabcadacaaacccdbaabbbcdbabacccacbacbcdddcccabbabacabacdabddbbdcbddbaabacbacccaadbcdbabcaadbdbcabadccdbddacacbbbbdacbdacabdbadccbacdacbdcbbcbdbbbcacbdbaccaabdddabacadddbccdadbadabadbdddadbbcabcbdccccbaaacbbddaadacabddcdccbdcacdbbacabdddbaadcbccbadcacdddadbcadcdaaccccaccccbddbdbbdbdcbdaaddbbddacdcababddbdcbaadadbdabcddcaaacadcaccabccbcbccdbbaacaddabadaccbbcbccddcbacbbcbddaabdcbadbdbbdcabdadadacbcbcbcbbbdacdabddcdcddaaadbcaddbbddcdcaccabdddacacdccabccccdddcbabddcdaaacbdccdadbbabcbbdadcdddadadbcdbcbbbcbadacacbcabbcdcbabcbaadcbddbaaacbdcaabdbbabdadbadadcccdadacaddccdbbabbaddabcbadbdbaddacaadcaccbcdacaddbdbcccdbccbcccabdcdaacbbbbdccbddbbcacdbdbdddcccabdaadcddbbdcbaadcaaacddddadbdddccbadabcbbbabaacacdcbbcccaccdcccdaaadccddbbccdddbdaddccdcdabddbcadbcaaacbbdbdbbcaadabbaaabcccbdbdbabbdaccbbadddacacbaddbdbcbcbbbdccddcdbccacaaccabbbabbdacabddcdaadcadccacabdaabaadacdacccbaaadcdccaccabcabbadccabaccccaacdaacbabdaadbcdaccbaddddadbccdbdbbabcabaccaacadcaccabcccdbcbaabaacaadbcaadddcbcdbdabddbacdcadcdcccdcacbaacdbbabddbbaaccbacaaabaddadbdcabcbbdbaddddcdccadccbdddabcdbcbabaabbbabbdbcbacdbdddaaacbacdcccadbadcdaacddcddadabadcbbbcddbddacddccbbdccbdcbdabdabdacdabcaaacbccacaabaddbaadddbddccabdabbbbddbacbacadcddadaabbdbcccabababbccbcadaadadacadccdcddddcbbdcabadbbaddddacbbabbdabcacbccccddbcbaaabdbcacdcaddbbdbbbbaccbabbaaabbbcbbcbbcdddcabccbacbbdabadccdbdadaacbbcdbbdcccccbaadbcdddbddacccaadccaaadcbaaabdaadaadbcacdccbaccbbcbbabbabbdaacaacdcbbabdcbabcabdcbabbacdacdbbddbbbbccbddadcbdcbaacbccadabbbacbdbbdcaddcddddabdabaccdbddadabddabcbdaabcbdbddabddcababddaccadbacdbdaadbcdddadaacccddcaddcdcbcbcdacddbdbdacbcabdbdcbaacacbacccaacdaccbcddadbabdcbcbaaabadaaaacddbdadaaccbaaadccadacbcdaacdaabaccbdbcccbacadbacaddbbdcbcddadadbcababdaadadcbbaababbacdaaaccdbcaadbccaddadaddbabbcabccbbbadccbdcacdbdaadbdadbadaabdbbaadbbbbaaabdaaddddaabcdcbbdbdcdbcabaccadccbcdbbcdcbbaadbacbadabbbcccabbdaaadcccdcbcbdddbbbacaabccdcdbacbaaadaddcbccdaabdcacaddacbabddbcadddadaaaddcdadbabccdaadbccbadacccbbbbcbcaddbaaaacdbdbbbcaccabbddddcbbabcdbdddccababbaacccabdddbdabbcdbdddcaaabbaaabadbcdadccbacdacdbdbacadaccddadabadadccdaacbbddccacccbcdaccbcadcbdbabdccaabaabbdcdbbcdbbccacadddbddccbdccdcdddacdaaacddcdbddcacacdacacdbbbacbbacdcccbcdcdabcdbcadadcadbcddcbdacccbbdadccbdcddbbbbaccdabccdcaddbddbdcbdbbbaabbacabcbbbbacccccdccdcddaacadddccdabcbccdbbddabdbcdcaacaaccbddbadcbbddaaacaaacbacbcbddccbdcadcdacacadababdcbbbadbddbcbcdcdccaddbacddbacadacdbcdadadcaacdbccddcadddbbbaabbbbcacbcddcbbaabdcbacbadabcaaddcaabacadcbdcbbdbdcdbcccbacbcdabdccbdddcdbccbdbbdabbdaaccadcadadacccbbaabdaddaccbbddbbdbdbcdbdcccdcaadacbccbbbccbcaaccbcaacbdcbcabaccbcdcdacdcdcadcaabcdadbbccaaadbbbaccadddacdabcadbcdbccccddacdbbccabddbdcadadaacccbdbcddaaabcbdddadcabdcddbabacbbddbababaaacbadbcbcaaadbbbbbcaacdcdcadabdcdacacabbdacadadbbcaadbbacdaccabcaaaddbccbcbcbbdcbccabacaccccbcaaabbabaadcaaacaaaddccbcaccaaabbccddabbacbdcbaccdbabccdabbbabcbccaadbbbaaaccccaddddbaddabcddaacacaadbaaabbcaaabbaadccddbbadcacadcabacddcacbcaaabacccbbcdccbddccdddaaaaabacbcbaabbcadaddbabbcddbcaadbbdabdbaaaabaacbbdcbccabdbccddccdbcbbbcdcaadbcdbcaccbbcbaadacbdbdbdbbdacddaddbdbaaaaadabdcbdbbdaababdbdbaadadbadcdcbdacbddabdccddaabaacdbbccddbbddbdbccdacbabbdcaabcdcbdbcbbccdbbbccccabdadaaccdbcdabbddccdddababccdcbcbabdaaccaadbdabbadccaaadaadaaddbadcbcdccdacdabdddadbabddaaadbcbaadbcacacbdbcabdbdcbbbcdaccbccbcaacdaadcddbabccabaacddbaacadacbddbcacdbdacabcabacbcbbbdcacdbdccdbaabbbaabbbdbdbcaabdbadaccbacadcddcccdadddacbbcababcadcabdadcdccbacaaaccbccbcbaabbdadcbdbcdbbabddbbcbbbadaddbbaccbbdacaddbaaaadadabadadcdccbadcaadcbabdcdacadcbcbcdbddddcdaaccacddaacccbdcdbaaacabbdddcaccdcdadddbcddaacdabdbacdbadabdddcbaccbaacabadabacbaadbddacbbccbacbcacccbcbbccccddbadadcccbbcdcadaddddabacddccbbbaabcabbabdbdbdbacdccddccdcccbdcadaccbacdddccacabacacbbbbcccbbacbbbcdcbdbdabdadcccbccbbbcdabdbbacabdbadbaddbddadaddabcdcbcdcbbdccbcbcdddabbcadbdaaabcbdcabadddaddcacddaababddcabdddbacdbdcbabbabdbddbbdbdadbbcdcccabccabbadcaadabcbbadaddcaacbaabddaadddadccaccbddbbcbcabbbdabbbadccbabbaabdccaccbcacdddbbcdbbccdaaacababbcdabcadbcabdcbadbbaadccbabdbcacbbdbbcababbcabdbbbcabadbcdcacdddadbacdacbaabddbddbccbddbaabbdbacadcabbddcacbccdabccdbcacaabbcdbcdddbdaaddbdcaabbcbbbbbabbbcccaaccdadabbbddacaaddcbcbddbbbaaddddaacadacadcacadaccbaccdcdddacbbccbcabccccdddcbdbbcabaaaccbbbdbaadcbdccacbdadadcdcdcbccdacbaddcbbcbbcabdddcabddcdbabccabcbbacbcacbabdbcbdcdbbcbcadaabbcbddabbbabdaccabcccdcbccdbcbdabddbaaaddadaaaabadcadbaadcccaabcccdadadccaadbcbdccdadbacddaccbccbbcabccccdcdadaddbbdcdadaacdadcdbaaaaabbddaddddabdbbcbbcbacdbcbdadddddaabddaccacbdccdcacbadaadcbcadddddcddddcbaabadcddcbcdbbadaccacabcbbbbcaccdacacabdbddaadbdcdcddbabacabdadaadabaaadadcdcbaaddbcbccbbcdadccdcdacbadadabcadabbbbdbbdadcdcaaadabaadcbdaaddadccddabaccadccdacdbdddccdccdccbaccadaaaddcddadbdcccacadacabcbacaddadbccadcbaccbacbdabdcaadbbacdddabcbaacdbccbacdcdddddccbddabbdbabcccbdabdbcddcddbabbdacbdcbdaadbccbaacacadbacdccddcaaabcdbadcbcbabbaabdaabbcccabdcacccaadcbdbcbcbbcadadddadbacdcdcbddaccaaaaddbadadabbdcadddbaabdddadccbbbccbdcdcabacabcddbdbdaadacdccdcbdaabdccaccabcacbbdbabbccccaacbaacbabaddbbcaacdbcccdacadbcacdcaccdcaadbddcbbaaccdaccdbdddadcaadbbaaadadbabbbaabcbcdabcdddadbaddbdabbbbbbdbadbdabdddaabbddbdabcdacbdaaacacaabbdddcbbaaaacdaccacbaacbadacddbccabcddaabbcaaaabadbbacddcbcddddddbbbcbbdcabccddcdbacacdadacdacbbbcbadbcccbccaababccdaddddddccbbbcbcbabddcbcdcccdcdcdbbdacddcabdccbbacadbcccacddaacdbbbbacacabcabadbcdbccbdabcbaacdbaabcabdcdccdaabccddadcbdadbdbcdaabcccdbcbaddcbadbccacdcadabbddbccdbdddaacddcddbcabcbbdcccdbaccadabaadcadcaababadcdbccbccddbacdbcbdddcaccbdaadadcaaccadbacbbadccaccabacdabbcacbdbbcacbcbabcabadacabbadaaaccccdbacdbacddbcdbabbdcdbbaaadbacabdbabbdcdbbabcdbdbbcbcddbdaccaadbbcadbcdaccdddbbdbabddcbcacddaabccacddaababdbccaacdacadbaddbcbdadcdbddccbdbcbbbcaddadaaabbacddbbddcbaccdddadccbcacabdabddbcacacbcadbcbdbccbaaacbcdabcadcbcdaadcacbabdaacdbaadccdacdccbcdbbccaabadbaacbadbcdccdbabbbddcaadcdabdbddcbadacdaacbbadcbcdacddccbddacaaaabbdbbdbcacdcabdddbddddccacdadccbccabdbaaaabcccbbdddcadcbaadabbdbbcccdbbadcdaaccbbbbbaadcdbbbadcccdbabdaddccacdbcbdddbdbabacaadddabbcdaaadbcbabbccdbbddccdadbccbbadaadbadbbddccabbcabccabacbdbccccbdaaaadccdcdaabaadddaacacbccacccbaccdbdcbadabcbcbbbacdaacbcacdcabdbccdacbdcdccdbbddbccbbabdccabababdacbccdbcdcadabcccbaccabbdacbcccadcdabbcdbddddababdbddcbcbbcbddacccbbbbdbddbddacaddaaaccdbcbbdbcbbabcadbbcadcbaddccccaddbaabddaddcabcbaaadaabdabaddcbcbaadccdcddcbdbbdaabbadddacdcbaabddcbcdabcabbdbaadbbcdaddcddcbbbbdcbccdccddbddaaacddcdabbadccccabccbcdbbdddccbbdcbbdaaccbacddcbdcabbdaddcdbaadddcacdbabaccaacdabbbadbbdcabcdacacdadbdabdaccbadbdaddcaccacbacadcaacccbbbbabcbaabdcdbbaacccbbddbadadccbbaacccdccbccaaddabcaabdcaccccbcdabdbdbbcaaccbbcbddbbccbdddbbbcabadacdcbbbdcabbcabbadbbadbacdbdcccbaacdbaacdddcdddddadcddbbcdcbcdbdadbbcadadbdbbdbdabccadcaddcadcbdbdbcccabadbbbcaacddccbabccbccacaadacdbcdcccdbccdbbccabbacddddbcdbcddacccabdadcaaccdaadddddcacaadacbcdcbdccaacbdabdbacaacddbdaadcddcdbbcdaacacababbbccdbabdcdcadacaddbbbccbbaddcbbbadabcdcbdbdddbacbadddadbdadabdacdabbaaaaaabcabdcbbbcadbadcbcaddbadaacccdcbcdaccaaccaddabdbcccdbdbadbcbcbbdabaadcaccbcbcbbdccabcaccdbaabbdcbaaabccaccddccddabdbcadcaabcdcdcbbbdddcadaadccbbdbbdbdabdbbdabcaddbbabccdacccdcadcdccbbcbddbdcaadcdcdcaddccdabbcadcddcbdcadbadacabdcadddacbdadcbcbbabbbadbdbabdbbbcddbddbbcccadbccaacaadaacacdcdaabdcadcbcadccaababbbbddccaabacccdadcadbdbcadcbccabbdccdcbddbcbdbddacddcacacbcbababcddbbdaddbbbdadaabbbabcaaaadadbbdbdbcababbbdcccbcadddbccbdcaaacbabcacacccbaaddcabdcccbacabbccadacddbcccdadcabccacccacbbcbdacaddaadbcddcdcaaaaaaacdaccacbcbdcbccbabddbcbabcdacccdcbccbabddbbbccacbcbccdcbbcdcbdcccabddbcabdacbdcdbccdcddbbbabcbbdacdabcbcaaabadacbbaaccdcbdbbabaadaddbcdacaadadacbdabcdcbadbdcbacbaaccdcddadacaabbbdcdbaabaabcddddbbababcaabddbcaadbddcccaccabbbcdcaddbaacbababbabadcadcacbcdaadcdbacbbbbdbcaadabbcdcadbabdbdcabacdaddabcabbdbdbccbddbaacacabcadcddbdcbdccbaaccdaaaadbcadabaddccdbabacbcdcbabdcaabdacaddadbdcdddadcccbdaccdbdbdbdadddabdadadabcccbcdababcbccbbdbbcbbddbddccdccaabbabacdacdcccdbaddbabdabaaddaccabdbcdbdcadcabbbdccbdbcbccbcaabdabbaadabcdbbdcadcabbbaacabddccbcabaadccbcddacbdddcaabadbcdddabcddcbdbadcdacdbaaccbbdbdacddadbdacabaaaabcabbadadcdccadcaaccabcdabcdcbabababdadaaccbadbddaddccdbcdcbcdddbcabcbdaacaaaaddbddbaaabbbbbdaabddcaccdadddbddbadbcbccacddcdbdcdddcdbcdcadaabcdcadaaccdcaccbcccacdcdbcdbbbcbddadbdadaabaadbacdabbacacaccadcdabcadbcbbbacdcaaaccddcbccbbccadadbcbaabaaabaacdbcaadbcddadbadbbbbbcbdaababdaabcdddbdcddabbddcbccbcdabdcbacbbddbcabddbccdbcbccdcddcaadcaccbaabccbcbadcacdbbbbdbbacaccaddbbbcbcbbccaaaccdcddabbcdbcacdccbddcbabaccddcbccddbbacccbccababcbdcbdbabacdadccbaddbcbcacaaadcbbccdcaaaccdacbdbcaacabdadaccddaacbdccdddcaaccaaaaccbdccaabdcccdcddaacbaadbadadcabbbcabbcdbcbddbccbabbdabddcdbadaaabcaadaadbadaacccdbcbababbcabadcadaaacdabaabcabbacbcdbddbbbcdcadbbccaacdbbdccdadacadaccaccccccabcaacaabacbbbddabcbadccaaabcadcddbcadcccacbaadcabdcddaccbdddcdccaaddcdcdbadcbccbddacbdadbdbbaddccbdabddacabcbdccdddabbbddcbbacacbbaacadcddadbabccdabbdadbbcdbacdbbdabaccadbdbddcccacbacacdcabccccddadbdabacdbabacadccdbbdcdacbbadddadddbbcccadbdbcbcdaccbcbbcddccdbdbdddcaddcbdaacbadcbbacdddcadddbdcdbdbdbcdabdcdcaddcaaddabaadcccadbaadacadbcaaacaadcddabcadbccadbdccccadcaaabdccddcbbacccdcaacaaababbddcbbccbbaadbdcbddbbbcbaaddcadbdbaacaacabbdbbcbcbcbdcabcacabdccbaacbadbcdbcbdaddddacddacbabddcbccccddcbbbccbcddddadcbccddabbddacadcbdcacbdcacbaabddbbacadbccbbccbaacddaaccbbaabcaacccaddacbcabaabcbcabdcaaccccaabbacabbdcdcababacddbdcdaabbcbbabcdabbadbbdddcdcdbbcaadbabccacaddaddbddbdcccddacaadbcadadaaabadbabbdddccdabaddbcaaddcaadabccbccaaadcaaabbcacacddbaadccccabcbdcdbbabcabaaadcabddcacdddbaadcccaadcbaadccdcbcaadbcaadcaabbcadcbbadaaddcddbaacbbacbacdcadbbbbdcbdbbddddccacadccadbcddbddbcbccbbadbcbaccddccacabcacadbacbbaadccccdadbbaaabbbcbdababddbcdcabcdaabccaccdccadcdbaadabbabbdccdbdaadacdaaabcbddbccabbbdbdaacaccbcdaddcbabcbbadadcbddcbbcdddccabdbbdaadadcabdaaabaabdbcbbcacbddaaadbbcddcddadcadcdccaabcbdcccddababdccbaddaabbdcddcacddbacdcdababcbcbbcadadabcdcaadbdacaddaaacabcddabdabacadabccbbbdbdcdbcbcdadbaacdbbdacdaacbbbbacbaaadbbdcbdbbbdccdcddbcddcbaddcddaccdbababcabcbbcdbcdadccbbccbacabdabaddddcccbbbddcabcdabcdbadcbcbdaaccdccddcccdcdaabdcdbabacdabbddcdcdccaaadcdcababcbccccdbbbdacaadcbaadccdbacbcdadcacddabbbaaadadaaacbcdabccbaaadddadbabdabcaddabbaddbddcbabacdbbdddabacabbbaddacdbbbddbdcacdaadbcbacbcdcbcdbaabacdcdcdbcbacdbbdbdaadbccdaabbdadabbdbdddaababcdcdcbaccdcdccadbdccabcbbbccdcccbdcccacdacbdabaacccdbddcbbcaabbbcabbdcdacaabdccdbabbdabbbcdbacdcddbcdcccdabcacbbcdbcddcdbbbdbcbdbdccadacacddddadcadbcccdcddbbaccabdbdaabdbbbcaacbdbdbacbaabadcabadadbaacacbbcbdcdbddcbabdbdbcbaaadbddbccacccacadbbdbbdaacacacbabccabbdaddcacabaddaddbdddbbdadcdbdbbccccadccddcdaacdbcdaddcddcaadbdaccababcbcdacccbadcdacadbdcdcacdbcddcacacdbcddddacacbbacbcdbaacdaacbadaadadcbaacacbdabbbbccbbcadcbaabccabacddcadaaaacaddbbdbaddcccadbbdcacdbdbcccacbbaadbacbabbbbacbcbdbcadaaacbdbcdaacdabaaadcbdddcabcbccbcbbbcadcaabdadabdcdcadabaccadbbaabcccadadcccccadbdbabcccbbdbdcbdbdacbddcaaacbaacbadcccdacbcbbccaccabbbdbccaccddcdbabdbbbcaacdccadbdcdababccbdabbdbadabdaacdcabccbaabbcbbcadbbcbacccdccdddcaadccacbdccaaacaddbddbcaaabdcdaacdddbbdbdababbcccaccaabbdbdabcbddcddcddacdabdcdcdaaaababbbdbacabcbcacaabbdadcacbaabcdbbbbbbbdcddbadcdbbbdcbcbcaacdacdadcddbdbcbaabbdccccaadbcbbbcaacabababdacabbacabacdccbbadacbdbcbcabbdbcbddadaddaaacadbbbbdcadbddcabdacaddabdcdbbccdaddacadaabbcccddcacbcaccdcddbaccbdcbabbacdacdabdcbccadbadadbcdbbadaaadacddcaaddadcadbaacdcbbbbcbcbabccdabcbbadaabbbbccddcadabbbaabaaabcdcbdbccbadacccdddabdcbabacdbbaacbaddaaabddcddccadaccabcadcbcadaccccaddcadbdaccbadaacadcaabcbcdacaaacbbcbdcaaddcddaabcccbabaaaaadabdcbcadacdddacbacdbaccdbababdddccdbccdbdcccbdadddcbbabbbdcbadddddbbdcadabbdadcddbbccacbcbcdddbcbbcddbadadacdbabcdcadddbbcadcacbbcdacbabdbbabcdadbabaacdadabaccdbddbcbbbabdbdbdcbbbaccaacdcaccaabdcbcaaccbbcdbdaaadaddddbdabacadaabadccdbdcdbdbdaaadaddbccbcbbdbabdadbbccaabddbbccbabddaaaaabcbdbacbaacbddbacdcbdcbddbcadbbccadbcdababdaccccdbdcbcbbdaaaadddddadacbcbadcbbddaddbbbabaaacadbdbabdaaaacbabdbcabddcbbcaadabadbcdbbcbbaddbaddbdbdbbcadcbdddcbdcccbccdcacbcccbacccacdcdcaccbadcabdbccadccdcbabdcacddacddacddbcabdcddcbbbaddbbadccdacccccacacdbcbcadccbabcdbabdbbbcbaaddddbadbabdaacaabccacccbaabdacbddacabbbcccbadcadbccbdaaccccaabacabccbabacacdabacddbcccbbbdcabacadbcdadbabbcddccdcbddbccccaccccaacdcdbbaccabaacdbddddbbddbcbccaaabcadcbabbcbcadbbbadbcbaacaaaadbdadadababaadcbcbcbccbcbaadaccbbdcadacbdddbbddddcacddccdbdccdcbcbcbacaacdaaaaacaddcbccdaaddcbadadbbbcdbcadbdadccbddadaabbadacdcbdaabbcaaacaccacbcadabbdbaababdbbbbbaaddbbdbabbccbccadcaccdbabbdccbcbbdcdcadcbbdbadccddbbaaadcbcbccacdbacbaccbcdccdadbabbdabacacdaaaaddccdabdbcbabbcaadcbacdabcbdcddcdcbdaadabdbacbadcaacccadcabbbbdddadaddacdadbdbbacdddabadddabdadbdccdacbbabcbbabdadbdddddccddbcaacdabcbdababdbcdaccbbccadbaddcbddbddbadcddacbbbbbcddabcdbbcbcdaadcdaacabccacbcbdaaccdbdbccdbbdabdacdcdcdcdbbbaacdddbadbabbababbabdaaaaccccccadddccabbccacdabdcdcddbadbcdbaadbcabccaaaacbccdbbddaacadaaabdcdcbbdaabcaadabbacdbbcdbacdbcccdbcbadcabaaddcabbdabcaabacdcbaccabcbcbabbcbaadcccacaabbadcadbababdbddddddaaddcbaddabaabdbddabddddccdcdccadadabcbbbaadadddbbacaaabdbdaacccaccdccccdcbddcbbcbdabbdacbcaabababbcdcabdbcabadaaabbcccbdbcbddbcbadabcbddbacbcbddbddacdcababdcaaddbbccbabacccacadbdcaaabababdaababcdcdddbcaadbcaccbaccbcccbbadccaadbbddcacadabbccabaddccbbadcdccbadccccdaacadcdacdadacdddaacabcccccdbbbbdcbcacaddcdbdbadcbbacbbbabcadbcdbdaddacaddaabacbdccbbbdabadadcdaadbcbbbaabbdcdacbcbadaddbaaabacbcccbccdcdbbaabdbbdbddcdcdacdbbacacacdbdbbbabacabcaabbbadddcdccabaabcbdbacbbbcdbbcbbcccdbdbaaaaacccbadcbbbbaadcccdddcaaaabccccabcddcdadbdcaccaddbcdcabdbabdbacacdddadcdbbbbdcdcdabbcbcbaadbadbbddbcaccaaaaaddacbbdbcccaadccababbbadcbcdddcbcbabddbcbcdbbdcabbabdcadccbabbbcccdbbdcdccbdacbadbcadbcbadbadaacabaccbccaacadccdbddbbbcbbdbbdcadaccabadbdabdcbadcbdcdabbaddbabcabdbdbadadaacbbabddaaadbbbabccacbccbabadcbbddcbcdaddaccabaddadbabdcbbdbddadbdcddbcbcababddcdacbcdadbadbcbacdccdcdabadacbdacbabdaabdcacacdabbadccddcbaccaddddadbcdcddaabcdcbbcbacaabcbdcacaccbbddabacbdacdaadbdddbbbcbbbcabaddadccbbabdcbdabbbacddbbddcdaabcbbcaabadadbcabaddcabbaaacacacbdabddbccaabbbdbdddbbbcabacaddaadcacaccadaccbadaacdbadddbcbaabbcbbdddaabaadcaabbcbcadbdddcabcddaadabbacbcdcdbddccdabbdddcabcbbaacadcdaabbaccccbbbbcdddabcaacdccaabcbbbdddbdadcdacccabccbcdddbbbdccbdcdaabddbbccacbadcbdcdaaadddccdbddaaddbdaababccdbcdcdbabadcabacbddacdbcccdccaddcccddabbcaaddcbaaccbccdabbcbaadabdbadbddaaccddbdbdbbdaccbcabaadbbbbadadddbdabbabdcbaadcbbddcdaaabdbddabdbccdbdabdddaabbbaccddcadadadcddadcdccbddcbaacdbbaadcaaaaaaabcacbdabbabcdddaabcbcbcbcadaddcddaabbbcabbbcbbabdbaddbcadaabbdddcdadbadbcacdcbdcaadabdddcdaccaddbdddcaddbcdabaaaddaadadcdabddccbcdaaddbccaddbcbcbcacabadcaababdbdacbcaaddaadddcacadaabbbbdbcddbcbabcbbcdbbbabbbdaaacbdadcbccabdcdabbbcbabbabdccdcbabbdcdcccdcdcbccadbdddbdcdcaacbadabbdbdaccbaaaaddadadaabaabddaccdcbcddcaadcbacdbcccdbcacadabddbdcbddddddcbadcbaaabadcdacdabdbcabaabaabbbadbbacabbbbdccaadcdcaddcacccccddbcddadddaaadaacacbaaababbdbabaababbabbdbcddacdcabbccbbbaacdbcababdcdbbbacddabbacadaaddbaaddcddccacadacabccdcadbbdababcaadbabaaccccdcadbbddadbcacdcdddcbbcbcabbccbdbdcdacdaadccdbccaababcadabbbbbadbddcaddabcabccacccadbabbdcccbddacbccdcdcaddbaacbdddbbcdddbddbbdbcdbdababcaacaddcbbcabacaacaccddabbabadbbcabcddacaaccbdabbcdacbcabcbbadacacdbcaddadbabbdaadddddcdbdbbcccbccbaddadcccdacbbbcddadadcdbbdcdcadcddacbaabdacadcdbbdbcbbcabcbbbbbbcccbdbaccdabbcaacdadccadacdcbccbadcaabadcacbabadadbddaddbcadadaaaccdcbbdaaaddaaadccccbadddbcaadabbdccbbccabdcdcbbabbcdacccccabacbcadacbaccccdcadbcaacacdcadcbdadcddddcdababccdabddbcaddabcbbbaddabcccdcdccbdcccdbbbbddbbcbdbbdaccddabdbbccbaabbbaacabcbdaacddddbddbbdddddbabbacaabbacddbbaddccdcddaacaabbacdbdadadbcbdaaabcddcddcbbddbcbcbbcacbcabacacbdccddacababddbbdbdaadabdacdcaddadbacbabbdaababbddcbbdaabccddabaacadbcdcbbaccabbbbbaccbbdaaacdbccccbabacdcaadacadbabdcabadddbcbcabcabcaabaaccbaacdbaacaccbdccccddccacabbdbbbbbaccdacccccabcbaaccdaddcdcdcbcbbaaacddcbdadbdadbcdcabbbaaacaccdcccbbcddacdbadbaabbcbccabaabbacdcabacbdddbdbcddcbcadbbbdbaacacabdbcadbdbaacccbcabdaddbdccaddadabdabbbdbbccbaaabcdccaddcbdcadbaaddcccaacbabdcaccdaaaaddaaabdcbcdaddcaadcdddbbaaddacaacbaabcacccccccddbcbadbdcbcbdaccbdbbdabccdbcdccdabbbadabacdcbdacdacdbcacdaadaaabbcbabccbddcbdabacacdcddcdddcacababaaaabcaddcdcaabaabdccbbbccdaaacccacddacbcbcbacadaadadbdccdbbddbcdddccbdddcdaaaccdcbdcdbaabcaadcaababaabbdbdbdddbdaadbcdccdadacdacadaadddcbcdabadabcaadbcbbcdadadaabdbcbaddbdacdccbacabaacbaadcddcbbbdccacbccbcddabbabbdabcaabadaadaddbbdcccbacccabaacadabdbdaacbddccdcabbccaccdccdbdbbaadbacbaacbbaaabbbabacdaadbcabcaddaaddbcdbbaccbcccbcbdcccaccccacdaaadadddcbbdbbcabcbaaacbdadabbbcdcabbcacbdbbcdccbcbcdddcdabbcdacbdbbbcdddcbcdcadcacbbadacdcacabbaadbdaddbbaacbcbcbbaadbbacdcddcdbaaacaabaccacccabbbbdabbcbcdbcdabcbdadccbdcbbbdbbaacdaaaccccdbacddcacbcaadacbbacbadcbdccccdbbaddddacccbbdacbdadaacbcbccdcbbcdbcdbdabaccdbdbbdbcbccdcadddcaddbddaaabcdadcdbddcacddcbcddbdcababdbbbaccbadcbabddacaaaddbcbbdacdacabccabdbadcbbadbabaddddbcaacccddbdbdbadaccaaabcaaaadcdadcddaacbababaaacdbbcddbccbdcaccdcdbbaaabcccbadaaadbabadacbbdbbabdababbabccacdaadddbbadbacdaabadbaccdbacdbdccdbaacaddbcdcdaccadabdcaacdcbdbdddaadddcadcbadbcabdbcdddaabbccdbcddcdbccdbdbbdcbddcbabcbbdbbabaddbddcdacbcbdddcaadccacabcdbdddddacbbdbdaccbbccadadcbcadbadcdbbdabdaaaabacadaabbccacabaaabdaacaaaaaccdcdbacbdccacbacbbccccbcdcaabbddaddacddacabbaabaaadbabdabbdccabbabbdbccadbcdddadbdbcbdcbdaddbcacdabbabbcbabdaabdcbabbcaddaadadacbadbdcbddbcbccbaacdabababbdbabddccbadbbacdcdbbdbcdbbbdbadbadbabcaabbbbcdacbaccaddabddddaddcdadadddccccdbdaaddccacbdbadbddbccdcbddbccdcaaaccabcababbbdababdcaadcdaaadbdbabacccabadabdcaabacbaabbacbbacccadbbaaabccdcacdcaccbacaccbbdadcbacdbbccbbadcaaddcdbcaabcbdbdacbacbabcbdbdcddcababdbbdcababbdcddbaacccdaaaddaaaabdbbabcbabcccbabbdcabdccbdbccadcaacbaaabdcbdcbcdbadcaabbbcdddaadbcbaacbaadbaddddcbacbcacdaadabcadbdcadbcadbaccaccbdbbadadadccdcccadbadcbacabadbcdaabdadadbaccddaaabcdbbabcdbadcbababacdadcacaadcbdaaaccbdadadaccccdacdbbaacdbcbccacccdcdcbcbddcdacbaacddbbaaaccadcdbcbaccadcdcdadbbadadaabaaddbdccabccdccacbcababcacdabdcacbbadabaadcbbbaadbcdcbcccbdccdbcbddacdbbccdddaababcadadbcaccdacaaabcaabcbcdaaababadbaddaaacadcabbbcadbccdabbddbdcadddabbbdbbdbcddaabbaabcdbddadcdcaddbbacabcdbabbccbabacbcddbcaabbabdadadcacaabbccdcdcadabcddbdabdddbbdbcccdcbddbdaccccabdcdbcbaadbbdabdddaaacbbabaddcdcdccbdccbbddadaacdddbadbddbbddadcbdadcdbdcbdccbbaacdbdcadbbcadbdddbdadadbabdbccacaaadddadcdaddbacdcdadccbdcbbbcddbdcbbaccdaadaacbdcdbbcbdcabacdccaddccbcbacaadaddbaadcccdcdbaabadbdabcbddcccddadcbaabddaadddaadcbdbdbbacacabadbccddccacbcdabcdcccbaccabbdcbbdacadbacddbaabddabdccadcaaaacaadbbbadcdcabddbbbbbdcabaaaccdcdbdaddbaacbcdccddcdccbbdaccdadddbbabaccaaccdbadcdbcdbabdbdbbdcccccadbaaadcbbacadccbbdccaaaddcbcbccbacbdcadaacbdcacadbdadccbadbccaabaaabbdddaaabdbabbadddccccaaccdadadddcaabdcccababbacbcdcbaabacbcccddaacdbccccddbaadacbccbcbdadabdbddbdbabbdddacdaacabcaddabacaadcbadbabadccbddcaddcacbcdaddadbcbacaabababdcabcbddcaabbaaaddabcaaddcbdbdbdbdbadbddcdcbbacdbacbacbbbcddbbabbdbbcadadbbdcabcdabbadcbdadcbcdadaabbdcadabbaacddadbcbcdabcabccdcdbabbaddccbadcdabddcbcabcbdaacadbbbbddacdcbdadabacaaaadbccdaddcaaccdcbaabbdcacdadbbddadbddbccbbdacbdbbcaabcddadddcbbacbdbcbbadddcbbbabddadabdaabbdaaccddddbccbaccacbbbdcccddbbdaaccdcabcabacbbaccdaadbbaacdabddcaadabcaadaabbcbdadadcabacacbacababcdcadacacdacabcaddbacabcbdcacddacbbdbbaacbbabbabcaaddadbdaaadcacbccaaddcabcddbababacaacccdcadabcacaaccabcbaacbdcbccddabbaaacdbbbcaacaadccaaaaadaddacdccdcbdccdccbdbabdaadacdbbccaadbbdaabbcbdaaaacdccabdcdcaccaadcddbcccabdbccbcabbaabbcaccbbbbbbdcaaddcbbdddcacbbabadacddccdaadabacadadabbdcacbbbbbbccabadacbdccacdaddccccdbaaaddaaabcdabcbbadcbaacbabadbbdabbacccdacdaccadbbcabbdccacbddbabdbbbadcbbbdcbadbcdbdcacbbaadacadcbacccbdacadcabbbbcdbbdcdccbbabbccccabaabbdbacdcbcaadaadacabbcaadadabccaadbdbcbdccdbcdcadcadcdbbcddccdbabbcdcddabdaaacbddcbdcadacdbcaaccacbacacdcbddccbbbcbcbcdaaabadbbbaccacbabdbcdbddbabadccdcdbbabbaaddddbdcaaddcdccacabccbdcbcbacacccaaaccddbbadbabaabbabdbbcabdcabcdccdacdcbbbbaaacadccdcbbacdbcabcbdabbcdcdcacbbaaccbccdccbbcaabbabccccacbccdddaddbcbddbcdabccccbbacbdcabbbdbabadbbddbddbbabcddbccccccadabdcddbdcbccbacbbcdaacabaadcdcbbbbbcdcdbaccacdbbddcaccdbdadbcbdbdaaadcddadcacbaabaacccbadccbbbadbdbccdbccabcbaacacdbbddcbbadccdbcacdbaacdbacbccbcbcaacdbddacdcdacabdcacdddbccacccabcdbdaddddcccbdabaaacbcbcaccdbcaaabaabbadacdaabaadcbddcacbaddbdccbdddcaaccdaccabcbbcdbbbbcaddbbcbcaaacbccddcabdacacdccbccabbbaacdcddcaccdbbcaccdccbaddbcbabbdbaadcbabaaadcdccaadcbcaccddadcaaddcddcaddcbabdbccaacbbcdcdabdadbcbaabaacadadacddbdcbcdcdbaddaabdbbcdcadcaadbdaabdbaddaccdcbdcbbcabcdbbabdbdcbadaddaddcadaddbababacbaccdabaaddcdbbdcbacdaabadddadbacaccbbacacbdbcdcddababcadbadbbadaccabdcbdddccaaabacbbbdbcadaabdababdabaacdcabcddaaddcaadbdbbaaaaaaadadcadaacccddaadadbcdbadbabcaacaccdaccbcadacbaaaaabacaccaaabaccaadadcbabadaaccadcbccbbcdcdccadddbcccdbcaababcaddbbbbcbdcdadcdcccdbcadbbbbcdbdccbcbbddabdbddbaccaabdbdcbcddabcbccaaaaaccbbabcbbbcadccdaabddadcadbadbbcddcdbdcbadbacccdcaaccddcbdaaadbaabcacacbdabaccadbdbcabdbdbbccbbcddacbaabaaccaacdcaacdddcadaaaccacdabbacdddbbadcbbbcbdcbabbddbdddadcdddacbbdcbcbccbadddbcbcdcacdbbadbabcbbccadcaaabababacbdadabccadddddcacaddadadacccacddcddcdcbccccdcdaacadcdbdcdcbadcabbdcdccacdbcbcdcdbacbddacddcdcdcddbbbbbabadadbadcddbabdaacaadccbbdddbaabccddaadbdcdbccbccadcaccaccadcbbbbbbacacddadadccccbadccddcdcbdabdccccadaabccadadacbabbcddcbbcbbbcbcadacbaaaddbcbaaaadbaccbbdccaaaabcccbabcdaddddbbacdbbccbccbbbbabbcdddbdbabaccaaccacbbdbcbddcbadbdcaacdbdcccadaaadabbbdcbddddcaccbdcdccdccbbcbdddbaadadbdcdbaabdcbdccddacccdabacaccaccdcccacccadbbbcdadadcbacbadcdcccdddacddbccadababacaabdababbbbddbdaabbcbaacddbdbcbccbbadbcddbdaaccdadbbbcccadddbcadddbbabbbbcbddddabbcdbadcdccacbbdbccbbbddcbacaadaabcdccdbdbcbaadbcdcbbcaadbadbdccaacbdbacabcbcdbbdbcbadabdccdbdaaccaaabaccacdcddcdbaddcdaccaabddcdbabcaabbdcdadddccdcdbbdabdadcbbabddadadbbcaaabcbcaddaccaacadccbdacdccabbbacbdbadcdababaccbaaaabdcaacabbcbcbcaacdacadadbdaccccbcabcbcdabacbdbbaacacbbdbcacdbababbcbdcdacbacdadcbbdaabacbbadccacdacaaabdcdaddcabbbbbcacabaadccdbdaacabbbdcbcadacadcbbaddccddcaadaaabbacddcbcaadcaadacacddccacadadaaabcbbabdcddbbbbbabadcacdcdcdbdccaacabcaacbcccacacabaadcdbdabccbbccbaaaacbccdabddccaddbdacbbaddcbcdaaabdbaaabbbdaadbbadbdabccbbabcaadcccddcdcaccdabaacbbcccccacbacadabadbbaaddabddbaaadacdbadcbdaaddaabcadbddaabdabbcbcdcdcabacabdabaddabdcbabadbdbacbbdbaabddabcaddbaccbdcccbadabbbdbdadcaabccbdccbadabdccddabaccccdabbddacaabacaddcadbdcabaaddcbaadacacbddabaabddbacaadadcbaabadbadbccdacaaabacbdcbbdcbbabaccabdaabbbabdbcdbabccdbbccbaaadaccbacbaabbababcabacdacbbcbcbbbaacacacaadacbcdbcddbadbcdcaaaabcbdacccbcdcccababcbcaaacbcbdddcccbddcddcabbabcadacbabbdacbcddcddbbbadaaacadabdddadaaccaddbcacbaddcdacabcdacccbcabbddccaabbcbadcbccbbcdbdbbbcbadbbbababadaaddacbaacdddcacbbcadddcdcbdadcacddcdcacabdcbbacdbadccdccbacddadbcdbcacadcbadababcdcdaccbbbabaccaadacaccccabdddbbacdcdaddcbbacdadcbbdcdddbcbdddbbdbadaaadbaddabcacabadaccdcbddaadaacaccbadddcdbaabccbcabdddddaddcdaaadcdbcdaadddcdbccabbdacdcdaccbcdbccaddcccbbabccbdadcadcdabccbdbbbbdcabbdacabdadcdbbacaabcacadbacdccacaaacddcbdcaabbaccdcccdcdadccbbcaacacbbdccdacbdccddcccdadbdccadbadbbbbbcaacbacaacccccddbabdcbcbbadaddccbdbadbddabdcdcccbadbdacddcabcbbcababbbdccacaadaabdcddccbbdbbcdadbdbaaacbacaacbdcabaddbbddcbadbbaddbcaaddabdcccadbbbcdbcbddacdcbabaabbadcbdaccaabdacbacacabbaaaddbacbdababcdbaccdcbbaabdcbddbbcdddadbadacdcdbcbccdddbbabddcaddbcabcaaddadcddcacddaccdddbabbaacdadddacddaaabcdbcabdccacbdcdccdacadccaddcbbabcbadaababacabcddcbddbaacddacbcbddbaacabbbdcbccdccdadbbdacdbcbdadcddadcbcbbadadddccdbcadcabbbadcbadddbbaccdaabdbcabcdbdddaddcbdccbccbdbdadaddddacacabcbccbdddbcbbacacdcdbabcccdbcbcdaaccbbdcbbbccdbccddcdbaaddbdccadadcababacadbdadcaaadcbccdbcacbadbbbaadcabadbacbacacadacbdcacabcbaacbbacaadccdcdddbdacccbbaadbcaaccdadbaccdcadaddbbbbdacdcaacdbadcaaccabbacbddbcacadcdabdcccbccdcaaaabdbbbdaadbbcbddadcadcacbccbbbdcbcaaddaadaaacdbdcdaaccbddccaccbacbdcbddabbabaadddbcdcdccaaabccdddcaccbabcbdcadcccbbddcddbcaadccdacddbbcdcccdadabbadbdccbcabdbcdabcbaaacdadbdbbcbaaaabbdabcbbcccdacddbdcabccbbaccbaddbcabcaaabdaddcdcccdcaabbaaddabdbcccdcbcddbbabbccbabbaaadacbdabbbacadcbddadbcdccdcbbddcbabacabdccaddbaddadbdbcadcbccaaabbbdbcbdaccadcdbdcaccabcddbbadacddcccdadacacccdcbdaddacaaddadccdababcbcdcabccddadaddcdacaaccadadabdbbdcddddbccabbaddadaacbbadacccbbddaddcddacddbadbddacbabcacccabaadadcbabdcbcdbbcbbdadacabadbbacaaccdbcbbaacbbcbdabdadaddcdcadadddcdaabacddcddbadcbaddcaacadabbcaacdbacbaaabbddcacdddacddcabdcccadbdadaccddacbbcddaababcabbaababbddbccddbdccabacdbccaacbadccbadaddddabacdbbbcbabccacccccdddcdaaaaacabcdbddbbbddabcbacdcadacbbbdcdacbbcabbabbadcaabddcdabbabaaaabbbadcdaadccbcabcadcabaabddbddaddabccdacacadcbadaddaaaccccddbacadddcadaabcdacbadbbbbcbcaaabdaadabbacadacbccddacbbdacbcdbdbcbabccbaabdbbaabbdbabbadcaadbabcaaccaccdabbccbabaacbdbacacacbadddaddddbbdbadbacdcaddaabaacadbcdadacabaddaadcbaabbddcddccbacdbbdaacbcbabcddbcaddacadccdaacdacbaadaaacdaaaadcadadabdbabbdacaadcccaadbcbdcabadbaccbccadabbbbbccdcccabcaddcdacbabdabadcaaccabdccbcbcbbbaaadbdabaddadacddabdbbcbbbddbbbcccaaabcbaacaabdcdccdadcaaabddbbdabddbdbdadbddcdbbbacddbdacbaccdbadadaccbcacaccdcbadcabcacabaaddacdcdccaaababcbbbcadccbcdcccbdaacbabbbadcbcabacdbcaadacdcabdababcccbbdabbccdbacbdaacacabaaaccbddccdbadbbddabaaaacabdbbabcbcaadcabacacbbbdccaddaadbccccdabcbccbdaaccdabbdbcdcdaccdabbaaadccadcbaacdabddcccccdcccbabbdddbabdcddbbcbbabcddccaccdcadaddaddcaabbadbcbbadaddbdccdaaccaababdccbacdabbcccabdadaddcdcdabdaccdbbdcaadbdaaadcbbacdabdabdabccdcacacdcbaadbabcdacbaadbabdaaaaadcbaabadacdcaccbddabbdbcabbddcbaddaccddbcbddbbabacadcaacaccbddadabadacccdbcdbcdcdaabbbbbdaaaabdabaacbacaddcbddccbccccbaabbcadadcdabdddcabacdcdcbbaadaaccddbcbaaacccaacddcdbcbdacacbabddbcbcdccdabbbdddbacadabccbbadaaadbddcbacbacadadaabadcadcccbcdcddddbbbacbbbbbdcdccccccbdddcbaaabddcdbdcbaaaadaabaaddccadbbdbbdbbadaadbdbabdadcdcdacdabbdcabbabdcbbddadcdcccacdcbabcccdcdbdaadabccdacacbdaaadddccdcbbbaaaadccdabcdccabbcbddddabbbacbbcbcacbbdbcbdaddaccbdadddddbdabddbaddbddcbbabddbdadbaacbaacdaaacbabbbbdbcbabcaabccbcdcaaacdbbbbdbadcaadadaccbaccddbccbabdddcccdabdbacacdcdcbcbccbbabdabdbadaddabdacbacddcadcbaabaccdbdbbbccbdcbcaabccdabcaddbcdadddcbddcaccbccdadbdbaabaadbccadbaadcabcdcabbabdababbababaacbbccaacbbcadcccdbdadacbabadcbcdbabcaaabbbcbcabbcacbdddccdbdbdaacacdadddcbacacddacaddccabacbdcbcaacacaabdbcabdbcbcdadbabbcaddbdadbacdcdddcabbdcbdbcdbaccdaddababbdcccdaddcddccacacdadadcdaccadbddaacbbbadadaabdcdacccbcddaadcdbcdadbcdcbddadbdbdbacdaabcdcacaddbbdcaacbbdcadabaacacbcabbdbddbbdccdbabbabaadbdbaccbcccdbaacddcdbaddadadaddadcaadcadaabdacababbcbccdacaccaaddcbccbaddaaaddbbcdccccdacdcddcbbdbaadaaabcdabadadadcbdababdcbbddddbaacadbbacbcdbacdcabbcdadbdacdbaadbdddacbaaacdcacdccbbaababdbdbccadcbabddddcdcbdcbacccbaadbdadcaddbaccabdbddcbacbddaaadcdaccbddcbbcbddadcadddaaabbccabadabbcaddabbabbcdcccaaccabacdccbddbaacbcdacbcddbabdaddbaaabaabaadcbbccabddabdaabaccbadbbcbcbacdbbdcccaccbabacbddabbbccbadbdabbbbdbdcdaadaadcbdacaccdbdcbdcccccccabbaddbcbbacbacbdadcaadbbbcbbcacadddcddadccacadcacbdabbbbabbacabaddcababbbcdbadaddbdbaccaaddaabadbddabdccbbaaaabcbbabacadcddbcbdabccbabadaadcdddcdcaadadbadcbbccdddcdcccdbcbcddadacddddaacdacccaddaddbbbcdabbacccbbaabbcacadcacbadcbaaacadbdbcbbdbabadbcbadabaadcadaadbdaacdbccaddcbaabdaccadddddacadcadcaccaadbccacdadaabcaadacdbdccddcbbbbcccdacdbacaccdddbbcdbdcbdbbaaadbdabbacdaddbbaccdbaddbbcdbdacdcbccbacdccbbddbdcadccbdadbaaaabaccaadcacddddacabddccccbdabdcdabcbdabbbbcbbdbbcaabcaaaadcbcbddbdcaccdacbddbaadccbbbbbdbbcabddabaaaccbacacbcadadcaabbaacacdddaddacaadddcccabbbddccdcccabbcdbcdadbcdaddcbddbbbacdcbaccabcabdddababadbcadabdbddcaadaadaaabacdbbbbbccdaddadddbdbabdcaaaaccdcdacaadcbbcacdacacdbacbccaddbadaccdcadddbccbcacdcbadbbddacbdabbdbcabcaaaccdbdcbcccbcaadbbccbabddbbdddadbbadcacdaabdacacbcaacbaaccbddcbcdacbabdcbcdbcccadddcaaadcccdacbadcdbdbdbdabaadacbdcdbadcbbbdddbbcdccdacadabbacacddabbcaabdabadddbcbdcbbbdadcabadcbbdccacdbdbcadcbbcdccdabdacccaabbadcbbadddacaaddbbbdccbcacbadacbdddbccbadcddbbddbacdcacdccacaadadacbbbdadcddadcdddcabbddbdcacbcdcadccdbbbbcbadcdaabddbbdacccdcacbddcadccaaddccadcbabbdbcaabbcbbaccaabadbacaabbbccccacdacbabbdbcaaaddcbcadccdbaabbbbbabdaaacbbddacbcabaaddbacccabdacdadbcacdbcadadabcbcbabbbaaadacdddaabbaadacaaaacabbddccabccadaadcdbadbadacdcddcdadadbadcbcbabdbccaacababaaabaabddbccbddbcbaccdbcadadcabdbcdccbaccbdabdaccdbdcbbabacabdccbbddbdbccccbcdcabbadbbddacdaccdaababbabbacdcdaddbaaaabdabaaabcabbaacdcbbbdaabadbbaaaddacddadbcbdbddbcddcbcdcdccaadaaaacbbbddbdabcbcdaadbcbdcdbaababdbcdacdacbddadbbcbbadbbadbcdadbbdaddcdaccdaabacbcbadacbcadacbddaccadadbdbdababccaadcbcbddacdbddabbcdcadaadcccadbbdcabaddcaacbcccacacbdcdcbdcbcbabcbbcdbbcadbcddcccadbcddbbccdaaaacbacdbabaaccacbcabcbcddcbcaabacdcbaacbccdcabcbacddcadccbcdbbaccaddaddddcabbcabcbacdbcaabdcabdbbbddadaaaccdbdcaacaccdacddabadadabbbcdadacacccbbabcbcbabcbbaabaabcadaddaadccbcdcbdbdddddbcdadbabddcaddcacabcdcddaababbacababbbdbdbaaccdaccdadcaadbccbaadbaacbbabcaaadbdabaccacbacaabcbbdbbaacbddddadddbacdbdadcbbabbdddcbcdbacbcccbabccbdbacabbadcbbcbaaabcbdbbbbbcacbbbbabbcbdcabbbcaacdddabbbcaabcbbdddabccaabbdcdcbddddcdbdadcdcacdabcaacbaacadacbdbccacaccbbbcabacbbbacdcaabdddccaadcbdbccdaadaabbdbccaccdaacbaaddcddacbbaddbcabcadaadadbbcacdbcdabbdbadbbcaddbcccccccdcbbdadcacdcbadddccaddcdaacbdadcdcbaaacccaccbcabdbbacdacbdbdabaaadabaadabaaddbddcdadbaddadacccbccdaacbddbaacbbcdabbabcbadcdbadacdcdbcdbdbccccbbbcdbcbadacccdbaddbbbdbdbbbacdcdacaadcccacddbcabddadcabbbbddcabdabddcadcbdbbacbcccacdbbbdacccbcddaccbadaadbdaacbabcabddadcabbcacbbdcccdaadddbaadcdabdddaaccdcbddcbdaacacddbcccddcbccaaccbbccbccbacabadadbacbcbcdacddcbcadcabbbacabddaaadcbaabacdbcdcbcbdcddacbccacbcadaaabdbccdacbaaccbcbccdbcbcabbacccdbaddaaaccbacddcadaacbadbadcccdabbbbacbcbabacdaccabaadacabdccdddddaadcbacddcbcddddcbabbaacdcdaccddadbaacbdcaaaddbcbbadaaccdaabaaaccbbddccbabdcdcccdabbcacbddaddcacbbabcdddbacdabdbaddbdbbcabbaababdcaacbdcbccdacaddbcbdddcdbcdccdcadbbbdbdbcacbbbbbcbaabbacdccbbaaadccbcbcbaaaccbaaadaccdbbccacadababdbcccacdcdadadbbdbdcbbaadbacbbddaddadbddcaacccdaabdabdacdccbbcbbdbbaadbaabcdcdacaaacacaaccccbdbcdcaaaddaabadcbbdaacaddbabdabdaacdcaaacbababddbdcdbdbadcadccabccdbadbbcacbddadbddddcbdccdaaddcbabbdccdacacbdadaacadbabbadccacdaddaabadabbbbabaabcbaaccbabddbaaabadaaabcabbddcdddcddaccaacdacddaaadcbddddabdadacdbdbdccaadcdbcbdaaabacdcacbbcdbbccdcdabbcccbaaacbdcaacaacbaddacdccbcddddadccadbdaabcabaabcbbabdabcdcaaaabdbcaabdabadbababbbdbbdacacacdadbccddcccbabadccadddbacbddccdcbadbadabcaabcadccaacdadddccdcddabacadaccacbbbdabcadacccbcdabbcccaadbcacbdcaabcaabaacabdaddbaddadabacccbcabdbccdbcdbaccbbadcaabcbbbdbbbddabdcdaacdcacccdabcdbbdcaaaabddaddbacddacbabcabdbcacdbaddbcdaddadbcbacacbcadbdddadacdcbbbcdccacaacdbccbcdcdbdcadbccdcadbbcbabbcdbaadcdcaccadabbdabbbcdcbbacdacacdcccadbbbbcdabccaccbdbbdcbabcbddcbbbadddbcaccbabadbbbdbdbbdbcabdaddcaadabbcdcdbaadcbbdbbbbaadacbaadadcbbacbdacdadcabdddddaaadccdaaabbdaaccbccbbbcbbbcbdddcaacbbccdccdaaabcacbbaadacaadabcbadcadddccbdbabdcbbaadaaaccdabcddbabbccbbbcbacaadbcabcbaccaccdcddcaaacababcbbaacddcdbcbacbaaacabcabccbdbbcdcacbdddcbadbdbaaabddcbbcacacbccbdacccbbbbaadabdbbcccabaadcdababdacbcaaccccdaccbbaabdcbadbabbacdbcccaabcacadddacdacccbabaaddcaacadbcbbdbacbbaadbbbbabcdbcbbdbdbdbcbbacddcdbbaaacaccabbccacaacdbddaadcadbccdadbddbadbdccadbddcddababcdbbacccccbadcaabaaaccdcaadacacccdbbcccabcbbcdacaaacaaacdccdabbbcddbbadacdbbdaddcbbcbccdcbdcadcdadcabcbbaccaadcaaddcbadadacddbabcddddbaacaadbbbccbaccdbacddaabcbcabcbdaacbabcbcbcdbdacdcddacacdbdbaaaaccbcccbaabdadadcaadcbbababaacaaabddacadbbbadabcabddddadccbbbcaacdcbdbcddcbbacbdaddabbcdcacaadcabcbdaadabbcbdcbadcaddcdcacadbbabbbaaaadcccababccacbadcacadaccddbabcbdbdadbbabdaddbdccdbdddbcaaaccddcdadbacadbbaabacbcabaacdddbccdccdcbdbccbabcaddcbabbddcdbddbcabbbdbbdaccabbbcbddcdccdaaabcdcbbdaaabbddbccdddadcabcacddbabdadabbbabdcabdcddbcbcaacccbaaddddcdcccaddbbcbacbccbabdbcdabadadacbdddabcbcbaabaadccddacdcbabaacdbabaddacadbbbdbadacccacbaacacabcdbdbdcadabcbcdbaabdbcbdbbdadcacbcdbbbccaabbadddadacddaadbcbabcaaddcdbbaaacdbddcabbbdadbaadcdddbdccabdbcbbcbcabcabbccbcbddcaacadcccccabcdcabcdbaaabdbdbbbdcbcdadccadcbbaaccbacccacacbbbabbcbccbadadddacbbccabbdaccbdddbdddbbaddcbdddbbbaabbdbadaadccddaddacaddcadaccbcadbddccdddcbaabbdacadbddbabcccddabbbdadbbadabdabcdbdcabbbdccaadddabdbacbbccbbacdddcbcbccacbacabaaddbcadbadccdaaddadddccbabcbdcbcbccaabbbaccdcaddcacabdddbbbccccbdcaadcbabddbddaadaccdccadcbbabbacdbbddadbacadadddbdcbbcbccadcacadbadabdacadaaaacaaabdbcdddddadbabcdacbdbaaaaddcabbadcdbcabbcccdcddccccdbdaacbdbdabcbbdcaaccdbaacadcdcabababbcdadbcabbcbdddccbdbaacddcaadadabcdadcbcdcbbbdaaacddcdadaddcddbbcdddcccdccadcbaaaabbdddcaacccadaacddcbbccdbdbdcbddcaaccbabaababdccaadaaadbdaddadcccacbdbdbabbddacdaddddadcccbbcaaddddccbdbcbcbdbbddabcabaadddbbddadabddaabaabdcaacbdaccbadcdacdddcbcdcddaabbcabbcacdbcbbbccdbcabccccbbadbddcccbcadacdcdcabacdccbabddcbddbddaadcbbccabaccbdcaacbddcadababaccdcdbadacbddbbcdcbcacdccadbacdcdddbbcdadbddbbacaccbbddbccacdcaadcbbaddcbacaabacdccbbdcabaacdabdbaddcabadaccbdbbccadbdbbbacbaddaabdadbccadabacccccdaaabadbaabbcabbbdcdaddacbddbdcbcacddcbcacbabbdabccadbbcbddacbaddbcbdcccdabbdaabaddcdbbcadccdabaddbcddccbbcacbdbadcbdabccaadcbaccdccdabadadaabcbcccdaabbbbccddccddbdaadacbdbdadcbbbbbadbdbbcbaccdbdbdbdcbadcacccdaaadcdcacdddbdccababdadcadbbbcabbddbcbcabccadbcbccbadbbaabbcbbdbccaabbcdbdcccaaadcbacbcdcdaabbcaaccbccabcabbcbdaaccdbadcbcaaacdccddbcdcdcdbbbabcadacbddbbcccbadbaaddcbbddabddaadbdadcdbdbcdadcddbdabcabcddaacabddadaddbcdbdcbacddcababbdbbadacbaaddcabacdddbbccddcbacdcdbabcaddacccabcadbbcccbbddcdcacbdbaabcccaacaabcdbbcdcaaccbaaccccddbabbdaadadbdbdcbaadcbacbdcbabdacddbadcbbbdddbdcbadbcbdddbdddcbcccbacaaabbbdbcacccbbacbdcdcbcbcdddaacaccccabccbbcbdccbadccacdddcddadabbabacabdadcaccdcaadcbbbbbcbacbcdaddbcdacacbdbdbcbbadbddddbabbabacadbcdabbcbcaabadadbaaadababcccdbbabbaacacdaacbbaabbdbbaaacbcdabbaaacdcaadabcbbcacbcabaccacbadddcdcdcbbabbbcdaabccaccabaacbacdaccdaddddcdddbbcaadadbadcaddaaadcabdcdbacdadcadbdbdbcdbabcccdcccdddcabcdcababccacccddbdcdcbcbaabddbbcbadbdbbdcbdacadaabdbddccdadbcadcbdbdaabbbbddcaaaaacdcbdccbdaddaabacbacbdcbadbcbbdadcbbbbdacaccbbbdccdbcacdbdccaacbbccbdccdbcdcbabacdabbadbdbacacbbcacdbbabcaacaaaaccbbaaacbbddcaddccbbbadacbcdcaacabbcdcbaabbaadcccadddbbcbdddaacccabdcddcdccdbadabacacbcadbcdabbdcbbdbdbbdababbddacacbadcabdcaddbcddbddbdcdcdbaadabcdabbccbcbaaaadcdbbdccadcbabbddabcbaabdbadbccdddbdcddcbbabaacaabbadbdaccccddbbbbbdcdcbddccbababbadaabbbcaadccbadcbbbcdccdcadadccabaadabcdcdcbcdcbacdabdcaabcbadbdcdcdcddaaccccadccacccbadccdadcdcaabadbddbdaaadbaaabbbcbbddcaaccbddddabddccbbdcbaacdccddbcaacbccaadbcbbbbdbaddaddadbbccbbdacbbcaddcbccdaccdadccbcbdabaabbcccabadddacdbabacbabccddcbbadcdbcdaccdbcdbbdcddaadcbdcadccbadabccaccddbdbabacbdcbcacdbcadbbacaccbbcbccddcbbcadabbbcbaaadabcdbdabacbcbbbcdaaaaddcaddbddccbadcbbacdddbbbccaadbdacdaddbaccdbcadbcacdbcbbabcadcccdaaacdaccbcddcddbcaddbcddbbdbcbdbddbbdccbdcadbcacabdbbaacbacdacbbaabcadbbbacacdaadccbabbddaadbadadcbdcadbdddcaacddbddcbaaaabcdbdcdccdddbabacaaaccacbbbdcdabcbccbbccadbdbabaddaaaccacbbaaabdbdaaadbabcbbcdbaccdadbdacdcdbadcbcccacadbcbdabdcccdbdbaddadcadacbaabddbbdcbbbcbdabbaacdbdcbaddcdaccadbaabdddacadabacadaacdbaddcbddbbadcbdaaaccbbdcacabbbdddbcadbbcdadbbaaabcadcccacabcbacacbdcaadbccbcdcaadacbbdaabdbcbcadcdddaaaabcbcabdcdcdbdbbbdddcbdbdbacbbacaacbdadcbcdbadaccdabbcbdbbaddbccdcabbdcdaddbcabbabddabbcaacdcccbdbbdacdbdaccdacdbcdccbcdccdadbaaabbbaacccdcdabbcadcaaabcdabcbbcabcdadbacacadbdbdcccdadcbdccaabaaaacccadcbcaddbbadaabdcabadadadcadbcbcbacccddbccccbbadaacadadcdaddaabacdabdbadbdadbbabdadabccbacddccbaddcbbbddbcbdbdcddbdaddaaadbbdbdcbcdbcdcbcadacabcdaabcadaaddbaddaaacbcbabcadacbcbacdddcbdabccbddccdaaaccbcbcbbadcbbbaacdbabcaaaaadcdccbcabbdbacdaadabbaaadcabdabacbcdaccbdbaabdccbcbcbdaddcaabdbcbcdddbbddabaddddabccaaaadbdaddaadbbdaababdacaadddbcdbcdcbcdddbdacdcddaaacbacaabdadcbaccbccacdbbdbbadccabccbcacdcccdaaadacdbcbcbaaacaacdcaaacabdddbbdcabaabddbcbbbaadabbbbbbbdbdadcbbdaddbddcaadbcbcdcbabdbbbddabdcacdbbddbccdcbbacabadbaacdbabbbdadbbacbabddbddbbaabccccbccacbdacddcdccccbdbabcdddddcabcddadaabbbaddbdcdabcdadadbcbdadbbabbdbadccbcbdacaadbacdcdadacbbbbdacdcbdbbbbdccbbddbdaddccaaacadabcaddbccdccaadbcadcbddddcbbcbbcacdadabdaabcddcbccdcaadaacdccddbbccbbacaaabbbcaccbdddcaddbbdacbdbdbccaacaadcdbbadaadacdaacdddddababaadadaddddaccbdbbaaaccadabbacddaabdbbcabcbbadbccbdccbdbbadaabcddbdbaadbadbacdbaabddcbcbddccacddaaacdacdbdbaddaccabdbaddaddcaaadcbaccbcdbcddcadbdaabdccddbcbcbacdbcaacdbdcbabcbdbbaaddbcacdbdddcccbdbadadbcdabbddadcaaaaccabbadcdcbbaabbdcdcbdcdccaaccaabbdbacbaaaaaacddbbacddcccbdadbaadbccdbdcacdabbacddccbaadabbaabbcadabcccaaabccadddcddbdbaabcccabdddabacdcabbcbddaadbaaaddbddccdbccbcdbcbbdcccbdbbbaabdcaccdbacabbbbcabcddacaccbbdddbbabbabdcbdbcabbcbdbabbbdbabdcbdddddaadbbcdddbdbadcbadcacadbbaabdcbaabdaccbdccccbacaccbaddcbdbdbbbaaadbdbacbccdcbcabcbbbadacbbabbbbadbdacddcbdcbaadcdbbcbddcbabadadcdcadbdcbadcdbadbadddbbdcdcccdcaaadbabddbbdcbdcdaacdacacbbaaddcdbcdbdadbcbabacbdacabccbbabbacaccbbbdcbaddaabbbdbacddcdccaadddccbdaaabbacbacadbaacddaabbcbdadadccbcadccccdadabcacdccbdbbcdaabcdddcbbdacccbadbccdddaccdabddbbccbbaacababbadcbdbbaddaddbbddadaaaaacbcbccbaccdddbcdcddcbadccacddaaacccabcddbacacbcbcdbbdbddbaaabdbcdcccadbaacadbbbbdabbabdabdaacbcdccddbcdcbbbccdccbacabcddbbbdddbcacaadcbdadababdaccbcababbcaabadbccbaddccabcacddaacbdbccccbbaaadbadabdcddacaadccbababaacabdbddcbcaddaccbaaccdbdcbabaadadbbadaaacdcddabcabdacdbadacbdaacdcddadaddbbaaaabddcbcdcccdbcccddcdadccbababdccabcbaaccccdcbbbbacdcdaabdabcdadddaadbccadbacaaccccbaadddaaddbcbdcbdccbacacbcdabbbdaacaccbdadadcaabddcabacbaabadcdbbbddcadcddcbabbaaccddaabdaccbacdadcdcaabccdaaabaccddbcdaabdabdacaadbbccdacddcbbddcbccdcaabcbaababcaabdbbbaaacddacbcbbcdcddcbdddacbcdcbbcbcbbddaabbddadaacbcbbacabbabbadbcbbccbbabaabbcadbdcccbacccaabdbddabdadbdadcbaaaddcbaacbdcddadadabcdaccbddcabdabccdbabbaabdbddbcdabccbbaccbbcbacabbccbdccdacccadccadcaaadaccdbaaaccabddbaacbbaaaddaabdcbdcaaccbcdcbdabbaddbabadddacdcdddcccdddbadbddadcadcabaddbbbaccccadaaccacdcacdbdaacdccabccbdccadadcbbacdccccddbcdbcacccdcbdabdaaccaabcaaacbbacacbbaddddcddbcbddbacaddadcaaaccbdddddababccaccdabacddccbadaadacbacacdbdcdcdcabcabccddcddbabaaddcbbacbcacbcbdaddcabddddbaabcdacdbbbbacabddcdabddbabddadadbcdcbbcbbbbdcccadcacbdadbdcbabacadadaacbdbbbccadbdbddabcadcbacabcdbaaabdacdbdbcddbaaccbccabcacdacdbaabddbcbbbbdbaacbdbcbbacacacdaabbcaadabaddddbaddbddaabcaacaadacabdcdcdcababbbdaddabdbbadaacacdabaadacacababaccbbdddacbbddbcdccbbdddcdbdbbcdbcaccbcaaddbdcdacadaadabacdadcddbdcdcacdaaccddddaddaccbdadddddadbacddaaadccdcabddcabcbacdddbddbadbdbdadcbddbcbcdbbcadadddbdbbbbbaadbdabdaabdadcabcbcaaabaaabadcdabaadcbdaabdbcadddadcbbaccabababddbcbbbbcbdbaadbccddacccacaacdabdbdaadaabaacaaddbdbccdadcddccaaaabccacbccdddcbdbbbdbbdbccacdacbddcbbcbbadcddcababbccdbdbbbabdaacaaaacacaadacbacbdccbbdcaadddbcaacbabbdacdbbcdacbcdcbbddaaaccacbaadbcaaddabdcbcdccdaaabbadadcdcabbadcdaadcdbddcddbdddcccbbaddbabccadccddacacbdbcdaadadddbdcdddccbacaaaacccbcbccaccdcddcaccbcdbbbaabbaadddcbbcbddbadaccacbaccbaabaadaacabbcbbdbbadaddcccccddbaacaacdcaacbdccccbdbcccbadcccaccbcadbdbdbdcccccadbdcdbbcacaaccdbcbcdcddcccbaadaadccaacbddcbdbbbbabbcccccccbcccbcddadcabacddcdcdbbddaccdaacddddcaddaaacabdabbcdaccbbabcddadadbcaacdcabdcaadaaddbdccdadabaababbddcdcccdbdccdadddcdaddddacdbccdbbdaaaccdabacaddadcabababcdcbcabdbadaacaacbdabbaadabbddbabadbcaacbcbdcdbbbadaacbabbaadbdcdbabaacbdbacdcabdcccdcdadacaadcacdcccbaadbcacdacbbadacdbddaadabaccabadcabbdabcbabcbabaabccbbcbbbabacabccddabbcababcbcdbacdcdabdbbbaddbcddcabcdcabadacdadacacdbacaddbcdaaaabcaccaaacacddaaabdbcababbcabcddcccbbddabbccddbdcadccdbccdaccadacabcdabdddcccbdbaaccdbbbcdaccbbcdbaddcdbbaadacbbadbbcacbaaadddbaddababaabbcdccdccabadabdaacaacbdbcdccdacabadaaddcaccacdbadabaddddbcbdccddbbacabadaaddbbcdacbcccdadcbadbbcacadbdbdabbbaddbbcbdddbacdcdbbcabaadbdcdcbddcddbaabdcaccaccbbaaaabcdcaddaaccbdccaabbdccaccbcccdabbcdacccbabcdabaacbbcbadbbcdbbccdbcdbaadbbcbdcacdddbabcdbacddbaadbcddbaadcdabadbbacdcccabbcadcbbabacbbcdbdcbbcccbcbccddaaacbacacaaaddadcdaaabbabccdddadcbdccadcdcdcdbdddbcbabddbddabacbbcdbbcddcdbcddccacddcbdcbaddccdbbbbcdddcdbabcbcdaccbabbadabdbaadbddbbcdbcdccaccbbccbacbcacbccbdacbadabacabdbabbaddaacdaaabbddcadaadcbcbccbdbccddbdadbdadbbbdacdbcdbaddabbccdcbcbadabaacaccaccbbcaaadccbcacddbbdbddcbcbccbccbadacccbcacdcdacddbcabbdabbcdcbbddcababdadccabdacbccbdbddbbcabcbbdacbacabbccccaacacdadcbacddaabcbbacbcdccdbbcbddbdabcbdbcdcccdbccdabaabdddaacaccbdbdbdcabcdbaadbcdcbbcdacddcabbaccbcaadadbbaaaabddccdbabdcdaacacbcaababcddbcbbdaaabbcaabbdaaaaabbbccdcbdcbbdddaadcabbbbbbadacbdccaaaadbddbacaabbabcdacdbdcacacbcbbbadadbdbcccccbcccddbddbcddaccaaaabccaacadbdccadacdacaaddaccbddaabdbbaddcadccabacadcbdacacccbcdadaccbbdbaabdccadabcbdabdcadabdaccccacdaadaaababcccddabadbababdddadaadabbaddccdacdadbdadaabddddaddcadabacaacccdcdcadbcbaadddbcacbbcbccbbdbdadcadcabcbbbdbbbcadcddcdcdbdccdbddaacddadcdccacdbbdbbaabddaaaccadbdcadbcbdabbdcaccdcadabdadbccabadaaabdcabdbcacdcbadcbbcccdadaabaaadcbacaaccadaccabcdaabadddbccbbcdaadbdcabddcbbaaadabbababcccbcdaaccaababdcddbccccdcddacadcbaadbcabaaaadddccacdddccacabdabbbabbaccdaacdccdbcbaddaaacdbbccdddbaabdbcbbabbdccbbaacabbcdcadbdbcabcddccadcabbaaabcdbbacacabbdbbbaddacdbbdcdcdcbbaaccadacccddabaabdcdaacbdaccdacccccadccacdcdacbdaacdcddaacdcbcabccbcaacbddadbdcdbbacaaabdbadcabbcdbbddaccaccacdcbcacbdbadbbdabbccdcaadcdbdacabdcdaacdddccdbdcbcadbbdaabaaaacaddcaadbdacbcccdbbccbabccdbcdcabcdcbcddabbcbcbadacaddbbaacdbdddadcddcbccacccdaadbacbcdbcddabbbcdacdcddacabbcaadbdbabbcabcadaadccaddddbbbadacbbddbadbabacdabbbadcbacbccadbbbccdaddbcbdcdbbabbbbaaacbdacbbabbacdcabccbbdaadbcbaacbdcabddcadcdcdcaddccdcddcbcbdbbadcbbbcdacccbabcdcbdccbccabcadddadbcacacdcaadcaaccabcdacaddcacabcccbbcdbbbaadadadbaadcadcadcccbaacacacbaccacbaccbaddacdbdccbbbdbdacaaddcbbadaabacadddcdccdcdbcddcbdaaadddcdbdcabbdbaacaadcadbacdcddabddcadabcacaabacdcdcdaabaaccdcbcdbaccdcabbaccaccbbbdbabbcbbcdddcbcbdbcabcaacbbabdabcdcdcbbaacbabcdbaddababdaabacabddcdacabcbccdaacccabbaabdbbacdddddcaccaddbbbcdabbadcabbdccaccacaabccdadaaccdcabaadbbcdaabddabaabdccbacacbaababdaadaabccadcabbdbbabdbcdcdabdacaccccabdbaabbccabacaccadaccadababbcdadadaadadbcbbcbbadaadaccbaccccdcaccbbdcddaccddadcccccababcbddaaaadbbadcaabacbbbbdadccaacadddbaaddbaabccacbcdcdacbdacdddbaccdbbcddabaacacadbbacaabaabbdcdadbbcbadabbddaaddcacbcbccdbadccadcdacaaabaabddadbddaadabbaccabdacdcbdbddacdcbdbcacdcdbbdbcddadbabbcaaadbacaddaacbcdcbbacccbabcdcaabacadcdadcbadcaddaabdacdadaadaddadabcaadaddabdcccddbdacbcaadbaadaaaabccbadcbcddddbcbbcbaddacbcadbcbdaacdccaccbccadaddccbbcbdcbadcadabdbadaddbcaabaddabbcbcdabbacdddaacbdaacadcbabdccbabddbbadaaddcbbdcbcbdbcdbdbbbcbdbbcabbdbaaaaabcdcdabbcbcacccacbdbbdadccdcacdbdaadbddabddaccbdacdbbabdcaabbbdaaabbcadcbbadcbccadddadccadacbbcaabbadddbaacdacbddbadcaadbbdabcbdbdddcbbdbabdbbddcdcdadcddccabbadadabaacdcaabacacacbbabdaabbbaddbbcbadadbccbdadccbadabdcddcbaadabdcaadcdacdbccbdaabbadadabadcabcbdcdbdddadabaaacbbacbccbccadbddcadadabbccaaccdcbcdacabdbddbccadaddccbaadbdabbbbaccadacdabdcdcdddcaccacbbbccbbcbbcdcdbccaabaaaaaaaadadbdbcddcabbbbdccdbcbbadccbdaaaadcabaabccddbdcddbdbcdbdcdadcadcbcdbcacbbdbbacacddddbdaadadaddbcbcddbbacdbcbaccaacdaabccaaabbcccccdbcabbbbbbaddadacbdbdaddadbadccbabccbccdddaaddadcababbbbaacaaaddabcdabcdbdabaabdbbbabbdabddccabccccbacbcdacdcadccdabcdccacdcabcdcaccdbcdacbaaaccdabcdcdccddacbcccabadcaabcdccdcbcddbcaabdcbcbddaccbbdaadbdaddacbcbcabaccbaddcbadddbabdaddcbbddddbadbbcbbbbcbabdcbdaccdacbcdcdcadacbabccbcddbabbabdbbacdacbbadadbdbbbdabadacbaaabadcadaaccbadaaababbccbabbbadbbbaaadbdaabcbddcbbabbbddcdbcddaadccabdbbaacdabdccbdcdcbcaaddbcdbaacdcdbbdddbbabdcccccbddcadbcdcddcccadacacabcacdaddaaaaaabaadadbaccbabaababdddadaccacbdbccbccacbcdbdacbcbbabacbaadacbbacddadbccdbdddabbabdcddddaccddddbadcbbadbadbcabcbccbadbaddaacdcbaccdccbacadadcddbcbbddbcaacaabcdbcbbdcacaddbcdaaccbbccbcdbabccbbccabcdabbcddabbbadcddadcdabcacbddbdababacddccdbaddacdabcadadaddbcdacddcdcbcbaabddcabdcbdacdcaadcdccbbcdaddcddcdbadccaabbdbdbdadddadcbabbdcbaccaadacdbadbaccbcccdbddccbddacabcbcaadaacacdaaacbbaaaadcaddaabbacdaaaadccbadbdadbaadcddabbccadcbcbbddddbcbcbcaaaabdcdbcdccbdbcadbbadbbdcdbdbbaccccbcbabcdcbdaacaadabaabbdbbccadbbadbadcaccbdabcdddbabcadbadbcacddaaaaabcaccdaaaaaadcbdbddcaaddabcaadabbdbbcaccbcbdaabdacbbbcbbdaccbbdacabacdcdcdcbcaabccadadabdbabdacbbcdccabcacbddcbcdbdaddcbdcbdbadaaaddbdbddbbadbdbcbcbbdadcbdbdadccbcaddcdbcabcdbdcbaabbcbbbcdcbcabcdcbdacbadaddaccbdbdaaddbabbcdadbdbdaacadabcaabbaccbbdcccaddaddbdbccacacddccddddddbdccbbddccaadaaddccadaaddcaddcadcaaddbabcbbdadddbbcbcacccccacdbcabbbadadbccacccccbacbdccbdccbacaadcbcdadbaaaaccccccdbaacccadbdbdaabdccadbacdbdbbcaabdcabccacabcddccdacaaadacacaabbbadccaccdddcacbbadbaddbbcbddaabccabcdddaacbabcacacabbaccbdadbccbbabdcabcbdbcdaabbbacccdabadddbdcdbabcbbbaabccbadbdadcddcbabdacadcccbabdcaabcbdddacbddccadbdabcababcccbcdcababdcacbaacbaaabbccccbadaabcacadacabdcbbbacadacddabacaaadccbbbacccdddddabdddbdcccdbdbabccdddadbcbcabbacdbcbcccdcdabdbccadccdacccdbadbbbacddcccdcbdbdadbaaddcaaccbcaacdabbacdcaabbdadbcabacdccbddcbacaabaabddaadbadccabcbabcabcdabdcbabddbcbcdcdaddbbcaaabbcbcdbcaccbbbaabbaabadbbaddacccdacaabdcadaacbadbbcaacabbcbdccbadcbbadcabbabbacccbdcddbacdaabcaccadbcddcaadbabaaaadacccbbabbcddcbbdbcacbaccadbacbacadacbbcbbbaabddcabddcababaddaabcdacbacacddddcccccabccbaaacddccddabaaabbabaacdadcaadbbddcdbabcddbbdaabbadddddaccdabcbcbdddcbaabdacbcddbbdaacdbaddbacbcccaaddcdbbcdaadbddcbaacacdddcdaacbdabbcaacbbddbbaabdadaaccaadcacbdaddccbbcbcddbccccaabcababcdddddcccdbdccbdcdaaabbcddbcdcccadbaadaaaabacaaabbbabddcdbbccaddadbdbbcaaabddabcdcccbaaabaacbbadcbbdaacbabdbbabadbcdcadcbbdcadcccddbaddcbccaacdcdbdbdbaddacbbabdddbabcbdcabcbdbcccabdcdcccdcaacaaddbadcaadbabcbcabccbacaaaddaccbcbacabdaadaaddcdddbdcbbdadddbbdaacbdaaadbacbadbdbcdabcabbaadcbbbbabbcccdcacacbdbddbdaacbcabcdaddccbddbddabbbbddcdddaddcabcacddadccdcacbacbaabcbbccacbdbcdcbbcccdbcaaadcddcbbacdcabdccabbcbadaadbcbadccddadaaddaabbabacbdddcdbdbbddcdacaadbbbdaaacbccdbdddddbacadaabccabbdaaccddaadabbabdccaccadcabcbadbbcdbadbbbddccbdcaaacdadcccdbadadabcaccbdcbaababdbdbadcddcbccbcccccdbdddababbadadbdcbbdabbbadacdbdcbaadbdbadbbcbdbccdabddccabbccacabacadbcccdadcdbdccabbcccadcbabbdcccaadabadbaababcbcccbaddaabcbcacbacbabcdccaabcbcbacadbbbddbcbbdccbadccdcacbabbcadaacdccabdddbbadaddcadbbcccacadbbacdadcddbbdcdbbbdcacdcbcbbbdcaccababdbdcbccabdaacabcadddacabdaadbcdcbdaccbbadaabadaaaabcbccdbcddbdbaccdcbadbaaddabcbcadbaaddbcbccadacaabbddccabccccddaacabdcacbccbdbaccadabbddcdccdadcdacccddcdbcdcbdddcbdaddcbddbdadcabdcbacccbabadccdadddcbbdaaccabdbddddbcbddaaacdbbbdbbbcbadabcaadbacddcbacbabddbbddbbacbcbacacbdaccbbaaddbdcbadbccddcdaccacacbadddbcacabcdacbcbadacbbadbcacdbdaaacccaabcddccbcaccbacdabcdabddcdaacbbbcdcddaaaddcadcabbccbabddcacdccbdadbdaccacbcdcabccddbbabdbdbbacbdcccbcaaacaddcaaacdbdcdaddddcabbacdaacdaadbdbcaaddcabdcdddcacbbdacdccacdbdbacacadabbcabdadaacaaaddcddcccaababbdadbbaaaabdadadbdcbdccbacaacbbacaadaaaadbcaccbadacdacaaabdacddbdaccdbaccbccdaaaddddaababbaddccaccaddccbdbbdcdcabaadccbdacdddaaddadabacdbbabbcacbdbbddabccbddbcdcddbccbaabcccdccaaadcaaaababdcbaccbbdcbcccbaacdbcdcaddbdbbdcbbcadbdacddddbaccdbccacdadcaabbbdbbaaccdbbacccdaaacdbdbdbcbbbbbcaddccabababddacdbcdbaccbdddbdbbbdcbbdbabddbaadcdcccccbaadaabbbbadcdcccaadabaababccdadcbbdcdcdabcdacdaacbbabbaddccaabaaabbdcbabcddbcbaabccdbdcbcddbaccccadcdacaaaacbbaccdbdbabdbbcdddbcbbaaccbddccacbabaadcbcdcacadbcbcbcbcbdacaaabcabbbaddcaaadabadaccabbbcbccaccaabadaaababcaaaccdaaddcabaabcbabbabccbcbadabbbdacbacdddccbbdbbacacbdaaacccdbbcdbcbacbbdbdddaccaddadbccbbadaabadbcbaaabdacaaabcbbccaccdabbbcdddcdabdddabababdbdadacaaadadabcabdddbdcbcbbbacbcacbaadbcdbbaabcbccabaadcbbbcbcacdadcacbcbddaddbcccacccacddaaaaadddcbaadcbbcbbcccbdaccbabcbddaadbbdddaacccbccccabbabcbcabaabacbabbdacddddcbbbcbbddcababddabcbabadbccacddcaccbadcccccddbddaabbccccbbaadaaccacabbbdcdaadbcadababaabcbdcbcccdbdbbbabddbdacacbbcaababddcbdbacdaabbdcddcaccbdccdbdadadbbacabbdacddbbaacbcccadabacbccbdaadbdcbdbaacbdabcbbccabbcababddbabdbcdacbbbabdbabbdccbbcdddddddacddddbdaaacdadacbacbdccbdabaadabdbdbbbcbacddbcbaacbcbccbcbccddcaddbdbdababddaaacccbaacbbdccbdaddcacdaacadacacbbdaddaadcdcddbdcbdcdadbadcdaaccbbbdcbbaaabadadcadccddddbdcdbbaabdbdbadbbbaddabddaadddaacbcbbdddbcdccdccbddaddabdddccccdbbaadcbcabbccddcaabbdccbccdadcddccbbbbbdcbbddcbccbdbadcccbacabbbccddbaccdbcbcbbbadcbdcccdbaddcddbbacaaccbabdbabdddaaaabccabaccdabccdccaabddddaaabddcabcabdbbdadcaacbdaacccabdbbaadbadbcabddaaacbdddaddadadbbabbdcabdcbccbcbbdcbdbbcbdabdbdcdabdcbbccddbadccdbcbbbacbcbcddabaddacacbbaddadcabcdbbbdaddbaaadcbddaacccbccbccaacadcbdaaaadabaabcdddadbabccdcaacaaaccdabadbdbdddcdbdabbaccaddbddabdddbbcdacccdcbaaccbbbdbabdacddbadcadabdcdddcbcbaaddbcbddacdcaadddccaccadbbbcacbbdccdcaddddadadaadadbdcaabbdcbaddaaabaadacdccbcaabadabbdccbbcccbcbdbbbdbadaacacdadddddbdbbbdaddbddbadaaadcadcbadadcacaacdcdabcdacadbbbdaaaabbadcccaabbaabbdaacadabcabdbaadbcacaccbbbadcbcbadbdababccdbaabdbdaaabcabacbababacddbbbaaaddacbdbdaaddbcdbdbbadbdacdccdddddcbcabbbabcabcdbbacbcaccadaabcccaadaaccbdddcaaddacabcbdbaaccdadddbaacbbacbcdaddacdaccabdddcbddacadacacaddddcdabadacbcccdadaacabcdcbcccbbbcdbbaadbdcbbabbaaccccbbcddbbccadcbaddabaacbcabcabccbbdbaabddcbdaabadcddbaabdbdacbaabcddbbdcbcccddaadbcdddadabaaddbbddabdaaaacdcdacdbdddabaacbdcdbacdaacdccaddcadbdaddabcccbbcddabdccaabddadbaaacddcdadbadcbacdcbcacabbbcbdbadacbdccdbcaccdadaccadcaaddcdbbabdbdbaabdbaaccbdacadacdcabdaabaccdcaabdcdbdbbdbabacbaacbdcbdaaabbcbadaaaaacbdbcddaacbbdcacaddbaccdccbbccaacaadaabdccaccddcdbabadccbdcaabddabdaccbbbcbdacbcddbdcdcdbadadadacdbdbbdabbdcabbbbadbaababdcdcacbdadadbbcbacdccbddbbabdddcbcbabaddcdadbdbcdcdcdaccbcbbcaaaacdbcbcbacdaaacabbcbbddcbcbdddbbbcddbddcaacaaadbabaadbbdddbaacdcdbacbadcbbbccbdabdcdccccbaaabdabdaccbcbbbbadddaadcddbcbccbcacbddbaaacdadbadadbcaccabdcdbbdccddcccaddaabbbdbcdcccbaaccaaaddcbdabcdacbcadddadcdcbacdaadcbcabbabdbadddbabdbacbccddadacacbaadadcdbdcbadcdcccbbdbbcdccbaccdbcadcabdcccbbcacaadbbddacbacccdabadaacddaddcdabcccbbcddbccdaabdbdaddcdaccbdddbbdcaddccccdcaaabbabbbdcbbadcaacbdbcbbcaacdccdabbbdbaddcacabdbdbdbdaccaabdbbdcabacbcdadbabacbacbcadcabdbbddbaddcbcaacdacccadcdccbcccabbbacaaacdacdaaccacdbbbaacdadaacbdbdaadcbbcaabcbdadcccccdbaaaadcaaaabacccddbbdbbcbcdcbbadbcdacacdcbccbaacdadacbcbbadcdccdaaadaacbbcadacacdabbbdadddddcdbbddcbbabcacaabbabdaccaddcbaaaadabadacabdcbdacdcaadbbbcccadabbbdcaddbaccacdcdcadbccbcddddcdbbcbcdadccabcabdddbdacdaddbbdacbdcddaacdcbbacbcccbabcadbabcacbcdadbdbdadccdbdaaabacdddaccdcaaacccadacccabcaaabdcaccaaacabcdcbcdcdadbacbaacdbdbbbdbbdccaddbdcbbdacadaaacaddadddcacbabcbbccddaccbababdcbadadaccbdaadcdbdbadcaccdcbdbaddadcdccccbbadccdabbbdbbaccacddbcbadccdbcdcbcaabdbaacddcbdbaacabcbcbdccadabacdbcddcdbadbcdbddcaadddaaadabacddbcabccbdadcccbdbdbdaabcbabbbdbddccbbccddbcdcccadbabadbdbddbaacddaddddaaabcdabaaadacbdddcaaacacdccadcbcbbdcabcdddddabbabaacdbbabacaddaabbabdcbcbabbaacdcacaabbddccabbcdccadbababdcddcbcbbcbdcbacdabbbcabadbdbadbdabadaccabccbcdabadddadabbbdcabdbdddabdcaaacdcacdcdabcbbbacbbdbccdacdbdcadbaaadcacccdcddadaddbdabbccdccbccacbadbcddbbabaaacbacbabbcadbacbbdcccccacacaaaadbbaadcbacbbacbcdabaccddbaaccbcbbaadccddacdabadbdccadabccabdcbbbbabacdbccddbcccadadbacabdcdaddcdbbbacbdaaccdacadabdcbcabdcbddaddccbadadbddbdbdcbcdbabcdbadddbbabcbdaacdaaababcddbbacdcacbadbbcacaaabaacabadbbaccdbcdaacbddabbbacdbbddcabbbcbacabccaccdbadbbaadddccdbcdacddaccaccbbdaaabbabcbaaccdccaabaccabdabcabcabccbcdcdccbadaacdccaadbaacacaddbbdcaacbdcdabdbadbbcdbdddbaaccdbabbacdbdabdbdaaadbbabbccdcbdadbdcabccbabcbdbdadaacbddccaadbcdbbaaaacaaabddabdbbbabdcdcabccaadbabdbaacaadcacdbbcdcdacabdaccbdbdababdddacbacaddabdbcdcccbdcaacdadcbbacaabbadcccbdbaccdcdccccddbadaacccaacbbdddcdadacdbbbbdbcbcddaadbabddaadcbabcaabbaccacbbaccbcdcbcbdadbdbabccbdcbadaacbcdacbcdbdababddadcabbbbdbdcaadbaacbbdbabaabbdbbacccddbacbabbabdabbcbbccadbdadbadaccdbbcdcabddbadadcbcbcccdaaaacbdbadbccddbbdccdbdbcddabccaabdcacbcaccbdcccacabcaabcbadabbcabdaabdbccabdcccddbbddcbdcbbadbbabdabccbdcdbbdbdcbcdbabccaaadbbbacdabadccbabbbccdbcdddacbcbabdcadcdacbdaabccccaacdaaadcdbcbaccbdaccbdbcddbaddabbaabbdbbdbbbbdaacdcdbcddcabbbcbaabaaacdcabdddccaccbdbbcaabdbddbbaadaddcabccaabbddacdadabccbcddbbdabbbbccddcaaadacdbcdabdbbadbdaabbadbbaacbaabdccbaacbbcbcaadabdabcbaaaabbcdcadabdbabaadcabaccdbccbccabcdcaabbdadddcacbbdbcddcbaaabaaccdcbddabcbccbcdacbacbdaadddbbcaccababbbbddbcacbabaadbadcbbacbdcabddacaabacdcbadbdcdabacdabacbdbdccdacbbabdbabacaddcbdacabdadddaddacacccbbadabdcbccbbbcdcbdadcbbdaacacacabcaccabcbaaacbacdbccaabacaaadababcababcadbbbbddcddcacabbbbdcddcbaacdadbccbbdabdabdccbccbdaaadabaaaabaaabbddacbcabbadacdbbcdcdadbdcabacbcdcbbbacbccbdbdbdadacbdbaddcccbbabcaaabbdbbcbdbccbdaadbccdccbcdaacaaababdcdbabcdcbdccbdbabdacccddbaadcdddbbbaddbcbcccddbbaddccccbbabbbdbcddddabccddbbbbadabbcbccbcbbbdbddbcccababdcdbcdccababddabadcaacdccdcbaaabccdaabcccacdacbaaaccdbcdadabdcdcabcdcbbacbbccdbadbcccbaccacdadbccdccdbaabdcccdbbbcdaacdbcdadcdcadabccbaaacdbddacbaacddacdbcbdcdddcbddacbaacdaaaaacdbbdcbdcbdcdcabbacccddccdbbdcbadbdacdcacaccdadbabdbacccbbdbcaccbbbbdcccbaccbcbadddcdcaaddcacabccababbabcdaacddababcdbabcabcabcbbadcbccadadddabddbddbbadcaacadacdcabcccabdbdacdbbadbdbddaacbdcbdadbddadcccaaaabcbabaabdadddbdbadbddcbadcbabccbdbaccadbdcbacccdbcbacadbcddaadbaaaccdccbcbaadabadbacbbcbbcaddbbbaacaddbdcacbbbbcdbabbadadaacdabadabcdddbcdabdacddddbaddaccadbbcbbdcbccbccbccabcaabccbbcacbbacaaadbcbadabcadbacdddbcaadbaadddaddbccddcddaaaadabcdcaccbdddacbcbbccddcadbcdaccbacacddbccdadcaddcabbadbbdcdcaadacaacabaccdccbccaaccdcaccdcddaacaaacbbcadaaacbccdabadcdbbbdddbbacdcbcaadadaabcddaccaabcacaacbcacaccbabdcdbbcdabdddacacaabbaaccbbbacdcabccaabbddbdaadbcaabbcbbbabdcadcdbbadbccddccdaccdddddcdaddcdcbbdbdbcbbdaacdcdccddbbcaadddacdccdbaadccbdcbaaaddcccbcccccbcacbcbbdbadaacaaaddcddcdbcdddbcdcbdabccbcbbbbccadadaddbaccacabaadcbbddbcbcdaaddaaabcddadcdbabcbaadbaacbcbabacdadccbbdaccdcacabbcddbdadbdcbcacdaadbadcaaddcbddbbcdabccddcdddabccbcaabcadcacdbabbccccccdbbcbcdbbcddacadbbbbdbbdbabdbdaccccbcdbbbdbcaadbcdbdaabadaadcabdbdcbaaadbaadbbdddcbabbbbbcdbbcacbcabacccdcdddcabaccbbcbcbaccccccabaadbbabdabcdacadddddbbbcaccdbdccdabdccabbaabaabbadbcadbadaacdadbababdbbbaadcccdcabdcaaccccbadbcbbcbcdccbbbcdcdbdcaabaccccdddbbabaadbbbbacacabcaddcabaccaddbbaaabcccdbcbddbdaddbbabcabaddcddccdddabbbaaddbdbddcdbcddaadabacccdacadcbbdcdacdbcddacdbdcdaacdcaddabbacbacbcdacdaacbaabddadbbabdaaccdabaaaadbccaccaabbbbddcdbccaadaabcdcabcdadacbbddbbabcbabbaabaadaddaaabadabacabdcabdcdcbadddddccabbdcdcabccababacdcdbcabcdaacbbcdbaaddadbdbdbcaacddbbbcbdbadcacababcbdbadcdaaccdcacacbaacabddaaddbcccccbacdcdacdaacdadcadbcdadddbbdcbdbaabbbbcddccdcdabbcdbcacacbaabdbcdbbcabccadaaaadcbcccabcdccadabacbabbdabaadacdccbaaddadaddcbdaabbaccbdaabcaadcdabbabccaddcabaccbcbadcadacddcdadddbcbbadcaddaacbdbcdcccccbabacdabcbccdbccdbcbdbcdccadccdbdcddcbaacbcbacbadcbbbaccbbbbcdbacbdcacbabcadaaabbdacadbdbcdcbcadcbaccabdbdcabcdacdabddcdccaddbdbaccdaaadcdaaddcabaabaabdcabcabddadddabccbdacaaccadcbcbcbcdccddddccadbbddddbbccadbbdcacbaddddacacbbdbdabababbaccdbbccdccbdbbbdddbcdaaddbbcdcddbdacbbdcdcbcbddbabcdcbccacacdcadbbabbaadccabdbcaabdbcbbdaacbddacaadcbcdcdabcdcbcaccadcbcaddbddbddacbababbaddcadaadbadbbdbdbabcdbbaabbccaacdddabadddbbddacdddcbacbddaaccdcdabdcddccddaadbbcacabaaaadbbacaadacdbacaddacdaabbabcababcbadcbadcbbcadaaadbbcadbdbbbbcabdabbccbabbcadcddcdbddbcccddaababdcbcbadccbbdabcdcdabaccacadaadcacbabaddbbaccbbbbcabadadcbcbcadcdcccdcdadcaccadacbbacbabbdbcbdcbcbbdbdcaaaadbdadaaddcdbacdcdabcbcaacdcdaadcccbadccbccdacdcdcbcccbabbacbccbdabcadcdddbbabbbddcbaabbabbdbbbbdcabcbcbdaddacddcdadaaabddaccabcdcaaaabcdbbbcddaaddcbddcadadabcbdbaddccaabdadccbbbdadacabaabbddacbccacacaadcdccbbcdbdddadddaaddcbbabdccadcdbcaddcdaccccadadbbccbacdccdaccaaacbcbcbbdbbbaabbadddadbcaadaadbcaadccbabbbadccddbdaccddabacccdbdddbadbadabaccacdcccbabdddacdadadadbadccbddcdcddaadccbcccdaabdcdccccabaddadcddabacbbcbcbbbcbdbbbdbcdddccbbdcccadcddaaaadcbbcabdabbdcabcdbcdcbacddacaaacbbdddcddbbbccbcdbbccdaccbadbbbbcacdcaaadaabdcbbccdcdbdbdbbabcbabcabbabbdbbbdcdbdcdbddcadccdbdddbdcbddbbddcdaddbdcccacadbadbbbcbbaddcbccadccdccbdbdbcaccbccdbdaaacdcadddacbadabdccbbabbbabbbccacaabddccbadadbdababdcdcdadadbdccaacbdbadcbcaadadddbccbcaccdccadcbabcbccbbacabbdbbdcdbbdbdccdbdababccdabdaccbcaacdbcdacdacbadacccccdbddcdbddbbbcaaadaaaddcaaadbcccddbcbbaddaadaadabbacaacbccdbcbbbcdaadccdcbacabcbaabcbdacaabcbbccbacaaccdaccaccabadbdcddcdcabcdacbbabbbacabcbdbaccabbcabdbacdbdccbbddabaaabdbbcdaacdccdaddaddcdabaabadcaccbdcbcddcbdcbccacaddccdaaaddadbaabcccacbdaabbcabacbabddbcdabbdcadadbdbabbccbdbddadadaddccadaccacaacabdadbaaacaabbbaadcadcdbaadaabcaaccabacadcdbdabbcadadbacddabcabddcbcdddababaadccadacadcbdbdccbddaabaaccadbbaabcbaaddccdbabddcbddbaddbbabdaccdccabbdacbcdabaadcccbdabdbabcdaaaddbabaadccdcadbbdbbdccbadcbcbcaabadbddccacaddbcbcdddbbadaaaacabbbbdcbddacbdbccccbdabcdbdddbbacadcaacddbddbddcbbbabcacccbbccdccacdccbbbcaaabdcabaaccdaaabbdaacbcdddbadabacdaaaabdacdcbacbbdbbbccbaacaadcacccaabccccdaadcbdabcbbbcdadadbacbdcacddadadcaabcdccccaabdcabbdcdaabbbdadbacdabccabdabcdabadbddcbabddcaacddcddbdccdacbddabdabbbaccbbddddaabdcdbdaaccaaaabbabacbcddbbababaccbadcbcbadccdccaddccdddcbbdaddbcbccadcdcccdbadacbbcacbdbcdcddadacddabcdabdcdddcbdbdddddbabcababdccdcbcbdaabbaaccdcacdbdddbdcadcbddcbdcbacacdcbabbbadbdcddbbdddabbacbcddacaadbdadbbadbcbcddccbcdadabdbdbcabcaacdaaadcbbdccaadaabbacbabdacbcaacdcdcbadacddadaaddacbcbadbdacacadcddbaabaadbcbddbaabacccaadaabcabcbccddbbacdccdacacababaadbccccaadabcddbadbdcdadcacbdadbaaccabcbabdbbbabaaacbcdcbdcdadabdbaccbaadacbcabbcadbabccacddbacabddcdaacdabacaccadbbcccbadcabcddbcbdccbabcbcadcbccdcadbcddbdaaabbbcbbbdbabcacdbdcbdccaabbbabcdabdcbcbacbcbcadadccacdbbadccaaaccaacadcdbddcabdaccdcbabdadcbacbbbaaddcbdddddddcccdaadbcdcbcaabbcdcddcacbcaddddbddcbdadbbcbcbdcdcdaaabbcaacabacdccacbbdccabbcaabcbaacbacaaadbbadcadcdbcaaaabdbcabaacabbcddbdbdbcccbdbbabccabacdabacdbdadadddcccccbbdcdadcdcdaddabcbbdcdddaadabcbabddadabaaaddddccddcdabbaacccadabbabbacbacbacaadcccabbdbdccdacdaaaacbaccdbabddbccdadddbdcbbcdcadbdabcbddcabacbadcbacbccbccbdaddadacdbbabbcddcadacbdbbdabdbdccadddcabbaadddaaacadaaddacdcbcccbcdacaabbcccdabcdaabdabccbadaddadbddccbbaddcbddddacbbdaaddcaccabbccccadabdcbbcdaabcdcacbcdcbbcacadadaadccdbbcdbadccacddaaadcddbbddabacbadcacdbacaabcaccaaabadbbcbcdaaaddcdcccbababbddcaaaacddcdbbcdbccacbaabdcccbccccbbabdadbdddcdcdaabcacaaabacccbdbdcacccbcadabadccbcddacbbcddcacabaadaabdddddbcbddcbbadabdbdbcbcdcdabcaabbbacadabcabdbadaabbdbcdaadbabbcababadaaddccdbbabbaaaddacadccbcadbdbbccdaaaabbdadcccbdabdccdcacdcdcdbaccdcdaaabcbdbbdbccadcbadccaaddcdbaababdccacccbdcacdbdbbadbbdbbddcdabdadaddbcaaadaaadcbcbbbcdaccabbcadcbdacbdbccacaaabddbdabdaccdcbbbaaabbbbddbccbabddcacbaacbabcaabcbcbcacbdadcabaadaccbddcdbbaacddbaaadddddbdcbbdacabcabcbcaccaacccbccbadbcdcbdbadddccdccaaddabbabdcccbdbaddbacbccadbdcbccbcadcabadcbbacbccaaabdadcacbdabcbdbbbdcdcdcddbdbcbadabaadabbdababcddbdacaaabdcccccdbdcdddcbaaacabbbabcccccadcbacbbbdadcbadabbdcdcccacdbcdcacdadbcbcccacbdcbcccadabaccccacdbcbacaaabdcdaabbaccabcacbbbdacbdcdacdbacaadbbaadbdcbaaacdccaadbdcbadadcaaacbadddbbbcbdaaaaacbadcacbdbabdcbccaddddcdcbccabbbadddbbaaabdcbcaabcbbacaaaababcadadcdbccddcddcdbacdbbcaabccbccdcaaddccbabacaddcddcbdcdbcbdcbbdcdacbaadbddadbbdbdacaaddacdaadaadbadabaabbdcdbcbbabaaaddabdabccdbbadccdcababcbdcbdaaaccdcbdabddabcdbaaccabcacabdbdbabbdcdddbdacbddcaadadbdbacabbbccdabddabbabbbacbcccabcddbcadbcdccaaacddbdaddcdcbcaaacdcdbdbcabbddaccadddccdccccdbcdcbdcbbbacabdcbbbddabbbabbcbadbdbdadaacaabdbcdabdaabccdbbaaabcdababdbdcdaadddacacbdaadccdddacbdcccbadccbaddaddcaaabadcdabcdbdbbbdbaacbcddcdaadcbcdcbbabdaccdaaacbabbdbccbcdbbccbcdddbcdaddbcacaaabacbbabdbdadccdacdbbddccbbcaadabcabbbcccdbbbadcdbdbacacbddaabcaabadcdbdcbccaaabddccccbdabcbaddddabdcaaccdbdcadbbbcaddccbcabdcabadcbbbadacbadbdccacadbdbbdddadbcbabddbbbcaddcccabaabcbaaadaddddbbacbccdcccbdbdbbcdbcdbdacbddbabadaadaaddccaadcbbdcbacbabaacbbbdadaaaadcdbdbaabbcddbbbbdadccbcadacaadcaabdabddcbddabcdadddccaddadadbadaaaaaadcdcdacddacbaaccbbbcddacbbabbbbabcdbbdbddaabadbcaaadaadabbdbaabcbbaabacddcdcdddbccbcbcdcbcbcbbdbcadabaacbdbdbdcdcddaddacbdcdaadcbbadbdbcabaadcbbbcabcbdbbcaddcdccbbadcbdbbddbaccdcacabbdcdddcdbaaacaadcabbabddacdadccaddbaddabbdaaaccbbdacbbbdbacbdccbcacbcdbdcdbaadcaaacbccbdaccdbcaddaaccdddaaacadccabbbdacaddcbbaccbdbaabbcbaacbacdaccccdbbbcadbbbddabbbccdacbadbdbcbdadcddbadadcbdabbcaaadcbbcacbbabbcdcbdccadbabcdcacdaaccacacdcaabdcccbddcacdaccccaccbbdddaacaaacaaddadabcccbaacbadcaaddbdbadbacbadacbbbbbabbddababaadbcdaddbdddacaaacaabdabbccdbbdbcdaaabcbcccabcaabccdbbadacbbdcdcccbadbddcbcadcbdcdbbabbcdabbcccddccdcddcbaddacacacddcadbbcbbdbbdbbccdcddbacdcbaaaaacdddbcbbacdddbdaccabdbddcabbbcbcbaabdacaadcabdabcaadcbbccdbdddcdbacbdabcaaadabbddcadcccacbbdcdacbacdbdcaddbbabbbaabadddbadaacdcccdcaababdddabbddadadabcdcaabdbbdbdcaddcdccdabcdaabdbabdbccacdccccabbcbdccbadbccbbbacadcaaaacccbbaadabbaaacbbddddcddbccbbdcacbdccadcbbabbadccdcbaaabbddbaabdbcbddbaadcbdbdacccadbdcdcdcdcabcdccdbbacbbacadddddcdcdcdacdaacdbdbbccbabdbdaabbccacdabccbacccdddacbdddcbccbbdccbdaaaddcdcababaddbddcacdbbdbabccadbacbaabdbcbcdacdbbcbdddaaacbccdacaaaaadabcadcadabdbdcdbbbbdabcbdaccaacbddddabadabcbdabddbbabaddaaccabdbabaddadbcbcbbadbacacaababdbadbddcbdddabaacbaadcbdabdddddbcbcbbbcbbddbbcbccdccbbbddaabcdccabaabcacbbaccbdbddbbbdbbdadaabcbcaadaaacdccbdaaccbabcccdaadccdcacbccccdcddaaddbadabccdcaadacaacddddaababccbbccbaccbcdabbbacdcbdcddcaacbddbaadcdacdaaccbccaaccdbaadbcccabbdbbbadcccbdcdcabaadcdccaccabddaaaabaadbbdddacddacdddcaaacdadbdddcadddccadabddccadcbbadabddadacdcacbcaccbdcaccdabaccdabcdcacdabacabdadccdbadbcaaddccbbbabaddbbccadcbdaaaacbbaaddccccbaaaabaddbcaaaaddbcbbddabaabdacddbcbbaaccdbabddbcabaaadbaacadddcbbbdcaaddbcadbabbacbbabbaaccabadcbddabaaccacaabdcaabddaadabcaddbcddaddabaabbacacdbdbddbbdbcddbddbbbbabacbaadcbacaababacabccbbacadaccccababcdacccddaaddcddabbcaacaaaadaddbcaacbacaccbdaddcbbcabdbbdcdadabdadbbcaabaabcaaddbdaabbdbabdabacadcadadcdadaabdaabddcbccacddacbccddadbdddbaadddacbcdadabcdccbbddcbccaaabcdabbbbdacdcbaaccbbdcabbdabcadbbbcacdadddcddcadadacdbabbcbbaabccdaadabbddadaddddbdbdcaaccbdaadbbdaabcabadcccbdddcbbbdabadcbcccbddacbacbbdcdaacaddabcadccdbabacabaabadadacbddccbadabbdccabdcbacdabacaddacaabbdacaaacdabdbadadacccbcabbddcdbabdbacbbacaadbcbccaacddbbddddccacbadbbcbbccbbaacbabcbcccabdcadadddccbbdaddbccacdbbbadaadbddbbdbdddaccccadbbdcdbacacaddbcbddacacbddacbbccdbacabcdddcabbcddabddddacbbaabdcdcabddccbdaacbdcccadcdbbbdacdaabacacaaabacddaccacdabdabbbdcddcbabbbdcbbcaacbabadadabdccccacdbcbaabddbbdbcabdadbabcbcbbaccddbcbcbabdbabcbbaabacaabbdccbbccadbabbcadadccdbbbabdadcccccccdaadbabbacbccaacacbcddcdbbcdddcacabdbacdacbadbdabbdaacbbcbabaddcbcbaadacdcbdccddbaddbbcaaabdddbacccadcdcaaaacabcbadaddccdabddbbdccbdaaaaacabcbcaaacbbdcbbcacdaaabaacaddacddababcaccdadaaccbcccadaabccccdbddcaabaaadaacacdbbbcabbdcbacdccbabccccdcbacbacbaadabdadccaaaacddabbaabbacdacadbabacdbcacadbaccdacdabddcaadccabbadcbdbcaccbbabaaccbacddbbbbcaaabdaccdacbbaddcabdbbbcadcdbcbadabccacdaccadaacaaacbdbccacdabdadabcbbdaacdbccccccbcbdcbdbcdbdabacadcdcdcccbdadbbaddddddbdbcccbbbcbcdabdaabcbdcdaccadcdcddbcdaaabababccdbcdcdaaabbcacddddccbaaadbbbcdccbdcbadadadaddabdadadcbccabccdbddbbcadaccdacadcadcaddbaaadbabcbcaaaaddadacaaaaabbacbdbaaaddccbadaadddcabbcaddbdbcbabdbdbbadaabbbbdccbcdcabcbdaadabdddbdccdaadcadadddddacdcdacacdcadaaaaacbbbbcdacddacacaabbbdcadadcabdbbdabddcdbaacabcbbabbcbbacccacbdabdcabdcbcdacdcbbbcbbdddadddacddcbcacbbbddbbdbdbadbdadbcabbbcbccdacdbdcabbccabacbacdaaaddddcdddacbccadcccdcdbaaccacbaabbdddcdbabacdddbbbbbcddadabacddacbbbdacabbccddbdadcbdcadcacacdcdddcbcdaaaaccacdabdacbaaaccdadabcddadabaacabbcccdcbbbbcddbcdadccddbcaddcadadbcbdcdbdaabbaaacdbdabbcababdccddababdddbbcacabbbbdbdabbbbcdbbdcabdaabdcdcccdacaabcdaabdbadaaadabdaacabcdbbcccccadcbacdcacbdcbabadccbdbccbcbddcaabdcabbdbbdaabccddadbbacdacacdbcadbbdddbcbddbcdabddacbadbdbbccaddabccbdcbadbbabcdddbbbacdcbbdaabdabddaccacbdabcddcbadbcccbdddbddcbabdccccbbabbdcdbccabdabcbacccabcacddcdcbccdadddbdccaaddccbcddddbdcddbdabdccbadcbaaaccabdabbdcdbbdbbcabbddabdbaddcabdbadadbccccbcbdcdcbacbbacdcdcdacbacbbbdbddbdadddcbcbbbcdcbacacacdabbcbcdbddbaadcdacdbcabcdcbdbddacadacaacdddcadaadbdddbbdddddccabddddcbaacbcbbdaccaccccbbddccbdbbddbaacbcbbbccdcbbabdadabcaacbacbddcdbddccbbdcdbcddbbbbbcabcbbbcbcbdbabcccccabbddaabacdabaccbbbbbdaacccddbcadbacadaacabcadbddacccdcabaabbbbddadacadbdcbbbaaadbbbbbacabacdcddcbbccaaddabcccbbcbaaadbdcabdbaccadabcbaddcabdaabddababccbcbdbcdcdcaaaddaaadaccccddbabcccabcbdaaddacabddbaacaabacadaccadadadcbabcccacabcdcdbbdcabdbcdabdaddcaccccbaaccaacdcdabbcccaaddabbcdadacaacbdcbadcacddcccabcacdacbbccbcaadbbbcbdabdadbbdddbdcdbddaabddabcdcabcbbbcdabacccabbcbcadbadadddbbdcaabbbabcadcdbbccdaaddabbbdabbbbdabcdadadcbadbcacbccadcbdbbbabdabdbaaddbccbdadccabadbbbbcadbacbccaccabcccdccbbbdccacbccabbbcbbcbcaabdcbccbcabcdcccabcacdaaccaadcddccbaabbdddbacbccaaccbcbdabbdbdbcccbdbaabcbbcdccccdcbbcbbccaaaacabbddbddbdbaaccdbcbdbaabdcacacdccddbabbdbdccbbdccccacddacadbaccdddbdacdacabbbaaaaadcaacabcdcacabbdbccddabbbbbddabdbccddccbbdacaccbadadcbddaabababccbdbcacddadbabbbcbcbccdabdacdaaadaabbaacbcdadaadadadbaccbcdbbdacddbbcccacabdcacdcacbdbccddbddbdbdbcccdbbdbbcddddbaaabcbaacbabcdddbabbbadccadaabcaaabacabaabbdccdccdccdaaacbcadccdcababaacabcaccdccdcdbbcdacccbdaadabcdcadbbcadcbcbdccbccbdbaacdbbbbddbbaacbcabcbbbcdabddbccddacccadcbaaaabbcdadcadcdcacbddaaaaaddaaacdcdabccabbdcaacdacccbabccdbccdbdcacdaacbddaaddabdaadcbbbccabbbbadabdcddccdbbbbabdbadddaaacbabbdabbaabacdcddbddaadabbbcddadadbacbccdcabdcbdcddaaccabdbdbdacddbcabaddacdcbabdcccbbdadbbcdababbacbabcbcabbccbdabaaccbabbcabcbddcdaabdcababaacaaabbddbbabdbcccdcddbcccaaabccabbcbcccdbccbbabbaabcacacdccbcbaadcccaaaabcdcdbcbddcbdacddbbaabbabdadcdacdcbaacbdcdaabaddcbaabddddacbdcbcbddcddddaadadbccdbacdddbacbabadbcddbcbccadabadddccdcbaddaaadcbddaccaababcbadaaabcabcdcddbddadbccbbcccbaadddabdcbbccdadbabbcddaaacaccadaadbaacacabcccdbddbcddabadcdbdaaddababccaabadbdccddbcbbbcdabbcccbdcddbccacabaddccaaccacbdbabcdbbdcbcbdbbbddccaabadbabaaaacaccddddbbaacbcabbacdcdcdccabaccabcbddbbacacabaddbabbabaaccdbcbadacdddaadabadccaaccccabcacbcaabdabaadbccbadddcbadddcccdcabdccbcacdcbbdbbaacdcabdbadbcbacacbcdabdaabddcacabdcbaadbbaacbdabaddbaabddaacdababdcbcddbaaaaadcababcababdbbbbdcddcbcbadacbadaaabcabacbadacddadccacddbcbbbcbabacbbbbbdaadaddccabdadacaaacaacbdcdbcadaccbbcbcbdbdcbdcbcdadccdddbcdbddcddbddacaabbcbbabbbcacbbcaabddcdcddbbdabbbabdadcdbabccaaddccaababbcbbdbccbbbcbbaabdabccddbbddcdaaddccddabdadaabbcbaacbcaacccdabcbcbbcdcdbddaddddcbcacdbcbdabcaccdcbdcbadbdcdcabadaadccddabbcabcabdbcbbcadcbbacaddcbbddcaaaabbcadccbdabadbabcccaacbbdbddccddbcdbbdcdaadbbabbbadaadbbcbccadabdbabbdbbbcaddcabacdcaadabdacdbdcbbddbadabacbbacbbaddddaabdbbcdbacbddddbdbbcdccbadbdbdccdcdbcbdadbdadabbddbabbbaabcbdbdabdcdaccadaccbcbdbadbdcccddcddbaabdcbdbaddcdccdcdcdcaaccbcccaabccadbaadabbdbdcdddacacbdacbdaadacbadabadcbcdddcccaadcdbdadabaaaadcaddbaabbadcacacabdacdcdcdcccdbbaaabbcbbbbcdccdccdbcdabadabaaadcacdcbdcccbbcababcaaacaddbbddcaabbdabcdbdaccddbbddddbacdccacacbacddcbaabddadcbaccbabaabbdbdabadddbabadbbadaaacdbdaddcadcddacaacccbbdadccadaaaccabbdbcdaabadcddcbaaccdbacdcdcbacabdadbcadcbccbdacdcdaaaabddccbddccbddcacaddcbbadaccdccacbcaddbccddbabbdcabbcabdccbbadbdcadddccaabdddcbadcbdabaadddbdccadddbdcdadddaadbbcacacdccabacacdbadbddaacaacaddaaaabbdbbaccadbcbcccaaaacddbdbbacccbdbcdbddbdcacdcacbbbcacddbbcdaccacacbdaddbdbbacaadbdbacacacdbbdcbadbdcdbadacacdbacacbbcdddddbacacdcddddabaddcbcadcacbcbdddcccaddbddcdcbdbbabccaacddccaadbbaaccabbaabdabacacaacdcdddcdbaddbdccadcbcddccccbcacdbdbcbbdaabdcaacbaacccbccadabcbbcdaaacadcdcabbadccbcaaaddbadddccbddcadababcbddacbadcbbdddcaaccddddcbabbacabacbcbbbadbaddcabddaacbcacbbdcccbabcbabbccdbddbaadaaabcacdbddadbaddacaccabdadbacdbcdcdbadaaadaddddacbbcabcdabbbbbcdccddabbacbdccdacdcdcbbaabbbcccaddbcabcdacbacccacbcbbccbabcdbdbdaaaddadaccbaddcadbdbccccddacdbddbcccdcbccdabaabdbabcaabdbbccaaddcbdddacbbddabbcbdcdaaaaacbbcaabccdcaaadbbcbcddddadcadabccbaddadabdbabbbdadcddccbcddbcccbdadcbbdaabcaacccbbccddccccbcbbbaacbbdbcddcbbbacbaabdbcdccdabdbbadbbbadbccdabcdcbbddccaabababbaabbccbdbaabdcacddcabcdcdadcdcccbbcadcaacccbaacccdbdacdcdcdcbbcaaacbdbbdcbaaacbcbacbaadbcbaaaabadbdcadacdddcbabdcccdadaadbcdbbcaacccbddadaaaadbddbbbbcdbcbbacabaabcddbaccacddcabdcddbaaacbaadcbdbcbccaaaccbacbdcaaaaabcdbcdbccdaccacbdbcdabbaadaabbbdaabbadacaadccdacbdbabaddbcbaccaaccaaacbcddbcbcaaaabcacbbcdbcdacbcdcbbbcdbdddcbbccddcccdddbbcbcaccbcaaddbdaacbbcdcdaccdadbcdbccdbccbdabdaaadaccdbdcadcaacbddbcbaadccbaabdbdaadcdcaaabdbbcbbaabddbdcddbabdcdcacdabaaabcbcaabdcdcabdbbaabdbbabddbadaadadccbdccdcdddabdcabcbabdcadddbdbcdcdabaacbbcadacacbabbdcbccacaccbbbadbcdccaccababacddccbadbcddccdacdacbacaccadcdaabcadacddcdbbdccddabbbbacaaaaabaddcabacacbababaacddaacdbacaabdbbcabcbbdcbaddcbcacdaccdbcabdddbcacaacbcacbbacacdaadaddcccddcacbaaddacbacbdcababacddacaddddaacccbacababacbaaabadddacacadcaccacadddbccabdcdbbaacdbcdbdcabdaaabcabaacddbbdaccacddacdadcadcacaabbabcdbbcdbbdbaccabacdbbbcbcbdbbabbccabaabdababaddbccdcaaddccdbdacacaaccbadbcadcabacdabadabadcbacdcabbcabcbccbbccdcbcdacbdbbaadacadaccbbbdcdacddbdcdacccdccdbccdcddbdacdddcadadcbcccaacbaaacbacdcaadaadcacabbbddacbdaabddcabcadbaccaabdabadadaabdacdbbbadcbdcaacbcabcccbdcccaddadaacaccbbdcdbadcccbacabbaaccaabaccaccbbbdadddccbbdcabadcbbddadaabbdaaacacadbcabbddaddcccacadabacdcaddcbbdcdccccacabbddaabbccaabcacddaccbacacbcdcaaaaabbdddbdabbbaaacbdaaccbddcdaadbcbbbaaaacbbbcbbbabaaccaacbabdccdccddabbdccbadcabbdadaccadacbccdaabdcabbbcbccaaabbcdbcadaadbabcdbacdaaaadaddbddcbbbcccdcacbaddcddcaaabcbcdacaaddaccbacabccdbbbcbdaddcdabcaccbbbcdcabbdabadbaabcbbbcacdbabaaaaababdaaddcbabdaabcbcbddbdadacaabddbcacbccbadbcbaddccbcabcccbcbbddcbbdbdbaaaadcbcddbbadcadbdbbccaacccdaadddabcbbadbbdcacbabacbaadcccaabcbdcacccdbbaccbdccbbbdabacababcccdcadbadbdbaccdbcbcacbcbdaabbbbccdadcddacaabcbbabbdbbbcdaacbbabbddcbdbdcbbcabddacabaacabaadcaaacbdcabaacbdcddddadbcdccaadbcdddccaacbabcbccadbdacbccaaaabcdaaacbdababbbbcbacaddbcdcbbddadbbadcbdcbadcbcdccbcbaddababdccadbbbbadaaaaddcdbcdbdcbdbbabbdcaaadccdabadcaacbbcbbadbbabbaccdccdcbdbcdcbdaaaaccbababcaaddccdbdacdccadcdabbcbdaaadbccbbadcdcdccdcadbbbdccbdbccddddbaaabbdcbcbbacadacacbcbbcbadbbcbddaddcaccaabbbbaabcaaaddbbbdbbccbcbcaabbadbccacbcaacdbdcdacbdbadccbdddccdadadacaacbcbccbdcbdcddcbbbcbaddabacbbdcbbbdaaacccbcdacadcbaddbcbbaddcabbdbacacabbddcdccabbddcdbcbbccdadbbbbcccdccbddadadddbdcddbcbddbbacccbcbbcbbdbdbdcaaadcbccccbbacccaabcacbccbacccbccbadaadddcccbcccdbdbbcaacadcaccbccccddababaacbacdacdbdcddccaddddabaddcbcdabcbccbaaccbdbdbccacbdbdccadababadddcaddbcadcddcbccbcaddbadcbcacacdbaaaddbcaaccddbbbdcadbcdadabcbbcbdcdbdbabbccdaadacacddbcccbaccadcbabdbddbababdbaacaabccdbddcdbcacddcbaaadabdaddbabbabcbdbdbdaacdabccdcdcacdaacbcdaadcbacabcaaaccddbcdddbdbbcbbcdddaccdaacdcdbbcabdaccbcccbddaabdcaabdaadcaabaadbbdcbcababaadabddbbabacaaddaabcaadcbaadabdbbacbbbddaaadcacdbcaddbdcccdadaccbdabbaadbbddaacdcccabddabbbcdbdbdaaabdbccddccbabacddddbcacccdbcacddbaacababbbdacbbaddabbbcccbadcbacadcbdabcdcaabdadacccdbdccdbbdbdaccdbbcbacadddbdacbacaddabacacaccddbcdcabdbcddbbdbdabbcddbabbaaaabbdcdbcababbcdccaccabbcdcddcabddadbbadccbddaaaaccbdcbbabaabbaadddacabcbaddbcdcaaabcdcbbcacacbbbcdadccbcaadabbcbaaadcaaabbccdacbcdccbbcccccbabccbdcacdabbacbdddbdbdbdabcbbdaaaabbdbdcaccdaadbcccbacbdbbddbddadbbbdccdbadbbbacacdaadbaaadbbbccadcddddbddbcdbaabcddbddcaabacadaadccbadbbbccdbadddaadbbadbbabcbcbadccbdcdabdcdaaaccbdccdacdbadddacddaddaaddccbaddbbadbccaaabcdccddbcbbccbbdabdcdabddbccacccdcbdabdbbcdaaacadadaacbbdadaaaadadbdcddcadddbabcaccadadddcdbccdcdacbbdacdbcddadcbcaaaadabbccddaabdabadcadbdaddbcccbcadadaaadcabcabdabdddaaaadcbdccdaaddbacdcbcbbadbbdacbdabaacdaabaadbdbdcdbcccdbbbabacddbddbcbbbcbccaaacacdbabcbdbbdaaccadabacdbadaadaadccaabccbddcbaddddadaaddbddabdbdabaddabbdcbcbbdabcabddbddadaadcbdaaaabaadbcabcddacbbddaadcbcdadaababccadbccbdaaadaacadbddbbaadcbdbdbccacdabcbddaabcabbdaacdbaacacaccdbdcbdccabdaccdccacdcadbbaaabdabaabddbbaddacacddbbcabaabadacaacbccddbdbbdabaadbddabcddcdcdacbbadbbcdcbbaccaabdcddadbacbdddbbddcddaabacdacddadbdabcdddcacdddabdbdcddbabacdbdcbabdaddabbdcbdddbcdcaabadacbcbacadccdacabbcdbdddccbdccdbbdabcdcbadcbbacadbccdaadccbbddbdbcbacdddadadbbbddcdbdbccbbaaadaacbcabdaccacbddaabccaabbbbddddbdccddcdadaabcbaccbdaddbbdaccadcbaaadddacaccabadbbdcdccaaaccaabbabaddccbbcacadcdbddbabadbdadcddbddabbdbdbdabcbdbddcaccccdcdbdacacbbcababaccbddacaaacccaadbbdddbbabaacdbbbdadccaacadcbabdbdaaaacddadcbcccdbacabdacabadbadbcaddaaddcbbddbadadbbdcddbddbcabbcdcadacddcaccdbacbaabdcbcbbbdacddabdbdbbdadaacbdcbddbbcacaadcabaaabacbcabdcbcadabddcdcdabdbcbaabddadacaacaabcaccaddcdbbdccacadbcbbbbbcabdddaccccddadbbdbccaadbdddcaacdcbcabcbcdbccdcacadabcacddabdcdbcbbdbbbbdbbdaddabdadaabbdcbdbdabbcbbcdbddcbabbbcdaaaddcabddcccddbdcdbbdaabbbbadcbbdaacadaadbcabddcddadcbbcaaaabcdbdbbadcddabdbdabcbcdbdbadbddadcddbdabbcadbcbaddabdcccadcdccadadbacadcaccabcbadddbaddbdbdbababacdbaaadcacaddcabaddcacaadabbbcddcbbacaabddaccccdadbbcdcddbdbaccddccbdbcbcdccaadaddcbcacbabaddababbcdaddcadcdadddaababddacacaaabdacbdbdbadcbbabaabcccdcbdbbccccbbbaaddbcbdcddddcddcdbabbdabdcdacdaddbdadabcccdcbbadaccccbdddccacdaaddabbccaaacdbbdcdccbbcdcbadbcacdbdbaadbbacadcccaadccadaadddbbabaaddccadbbdccbcccdcacbaccbabcdbbcbdcdcdbcbddcddaaddcddaccbaacdadadccdcbdcbcadbbcbbdbdabddbdaccdbbaabbcaddaaddacbbacbaabbbbbcbadadccbabdbacaabcdcaddcdabccaccddaccbdabcbbbdbccabbadadddddbccdcccbcaaaadcdadcaaabaacdcdbdbacaaaccabddbddbdaacddaddaccbacbacdbccdcbcaddccdcabdcababaddcddabcdabbabbdcaadcddbdbdcbdbaaadbcaabdcddaddbbadcaabadcaabbabdbaaaacdabdbcacbabdacbcddabdbaabdaabbbcacbbcadcadaccbadcbcdcbadbdabcaadddbacddabbdbbdbdcdddcbbbcabdcacdccbadbddccbccdbacdbddcdcaabbccbbcdccaccdabdbdaadcbddcacbddccbadadaacbbacdccabccabaccabbcacddcdbabcbbcbcaccabbcdacdabdabacbcaabdbddaabbabddbbbcbdbcccaacccbbcaddcbddcdcabbadbbcaccbcadabbcbbdbadddbcccdbadadacbbaaccabbcadcadbbbacaddaadcaaaacbabcadaabbbddcdcbcdbabacbaababacadddcabbbaccccbbdddabcbdaadabbbccbdaabbbdbcacbccbcccdbdccdbbaccaadcdcdcdaaaccdcbccbbddccbbcdbccaddaacacdddcccabbdadbaccdaabbaabacaaddbcddbcdbacddacabdbcaadbcabbbdadbcddaddcaadbccdbadbccdbcadcbbabbcbbcacdcbdbbcdcaabdbadcadcacdcaddaaccacbdbbbddccababccabbcdbaadbadddaabdbacbadcdcacdbbaccbabcbcccababacadccbdbdddbdabbdbadbaaabddcbcdbdcadbbacacddddadcbaccaaaacdadbbdbcddbccdbdcbdbbbbcaadcadcdaddcadaabbcbbbcbbabcbbdbacbdbaabadbabbdadbdcdcddbbdbbdcdbddacdcaababaaabcbdacdbbacdabbdcccdaccdbacadadabcbaababaacabcabccbcdcdbcaccdbdaaaacccabbdbcabcbbadbabccacbbbdaaadcacdabdccadcbbdadcccabdaccbdbccbcbddcbdbbccdcacadbaadaacbccdcbdaabbdbdabbbcaaaaaaccacddcadadbbcbdbdccddcaccbabbcbdbdcbdcdbdcacdcbabbcbdbdbcdbddbdcacbcaabadadccacdddcdbadcdabbbcbcadadbdbbcdabdcbbabcbbcbcaddaaadbabaaddcdacaaaddabbbddabcdcadabbddacadbaaaaabbcdcbccabacbdaadadaabcbcaccdabbcbcdabccdadcbcdbddbcaabdbbdbcccaadbbcbcbdbabddbccddbddaddacbaddcccaabbabadaaccadbbbcacbbddaddcbcbacacbdccbaacccbcacdabcbcbaaacbcbcabaadccaddbabacacdbabcbbdbcacbbcbbbacbabbdaadcccbaaccabcddddccaabcabbaddcddddaccddcaabcdcaddbcabdabbacbcccaaadabccaaccadcabdddbaadcacacccddbcababbadbcbdaaaaabbabcadaaddcbcbadddbccabcabbbbadccdbcddcdaccaacccddbbabacbcadddcacadbaacadcbadaddaaabaadccdbcddcbcabccadcbbaaababacdcdadadbdabdbabcbdccddaaadbbabbcbbdbbdacddaacdacbadacccddaaccdbaddcbacbdbcccdbcccbddcdbdacbccdcdddaaabbcccbaabbbdccbacddddadbdbcdaabacbcdcdbbccbcdddabcccaaadabdbdbbdccbdbabcacbbbcbcbdacbbadbadbdbdbdcbadbbaacacaddbdbbccbbaabaddabdacdcdccccadddcccaabbccbacdadaaacaccdccbadcbaaabbdcddcbcadadddbbcaadabacccdcdbddadaacdbbcbadddccccaccabcdcadcbbcddcaacdababaabaddaabbcabbccdabdbadcadccdbcbaaddbcdbbbdcccdbcacadaabacddaaddcbbbcbcacbaddcaddbdcddbcccadbcbdddbdbdaddbbcbcbaddadcdcddbaddbbbcdababcbdbdabdccaaacdbccbcdddddcbacdaadcdaddddcadcaacdbbacbdccdcababccabccbaaacaaadcdcabadabcdaabbcbbcabaddacccdacbaadddcdbacadcaddbcadabcbaacadbddcabababdabcdcabddbcbbabbbbddcbcbaabcabbacbacddbdaaccaadbcdaaadbcdcdbccdacaccdadbaccdbccdabccabadbdbdadacccbadbcadccbcbddbddbabdbdcbadaabcdbabbddddbdbbcbdbacbdbbaaddcbacddbbabccbbccdbcababcdcdacdcdbadbbddbdcbdcaccacbabaaadbcbacacabdacacacbcbadaacadcadcddbdaabddbdaabbadacbddaabddacabacaccddbddbcbbcccabdaccddccdcbbdcabcddddbabddaacaabbbbdbcabcdcaacdabbcbadbcbcbcabdaccbccaaddddbabbdbbdcbbdbdbadbdcbdbcacbdaccdabbcddcacbbadcdcabbccdbbcacadcdacabddcddbdcadbbccbbcccddbdcabdcbbdcbdbcbcbcaacaddbcdabcabacbcdaaccccbbcbadcaabbcdaabddabccabdabdbcaacddacababccaccddacbcadcdabadbbbbbbbcdcdaaadbcddccdddadbcdbaabcabcdaabddccabaabdadcccaddbcaadaabdadbaddbccdbcacdcabccddccbcbbccaaadbdcaaccaaccbbcaacacdacdbbbaccbbcdbbabcccddadccaccaabdcbdddaaabddbcbbbbdbbabdacacdccdbbbccbcdddabababcbccdabcbbcacbabdabdaddbcaaddddbcbdbaddaddbbcabaaaaddabbacaccccdabccdccdddacaddaccbbacdddaccbdacdcdabbbbbbdabbcdbbacaaacadcbdddbccaacdbcbcddcbabadbbccacbddbcbdbabadbbbdcacdcbcdcdabbadaacacbbacdcddbdbbabcdcaaacadbdbbddbaaabdaadacacbcacdcdabccabaabcbabbcdcacadaaadcbcdaddacabbcbaaadcdcbadcdcdabcaaddcbbaddaaacbdcabddabbdabddbdcbcbbdcbabcdbbcbaacacaaccbccaddacacbdaddadbbdacacaabbacaaccbcadcdaabbacdcbddcbdaaadbbdbdcbcdbcdacacadaabcccddcbbaabdaccddaacbaabdddcdcacdcaacbbdaccaddbcdcbbbcdddadbdcaadaaaccbbaabdcacdccdddbbaadcdadcbddcaaccdbbdaadadccdcdcacacdcccadbabcbabaadccdababababdbacabbddbbadaddcbcbcbadaccccbbdaccbcdbbbadacbaaacdcdbbdcbabacbcddbdaacbbdaddadbccbbddbdacacdcaaaaccbbacbcbbcdaaccbbbcadcbdabbcdacbcddabaaccdabcbcdbddcbbddbbbdaddcdcdbcaadadcccbcdbabcdabdbcbadbacbbacdcdbaacacaabdbdaaabccdbddbbccbcaddbdabbbbccdcaddadbbcdacdcadaadaabaaaaddbcbcdadacdabccdadcdacaacaabaaaaacbabdadddcadcbbddcbaabccabbbdcdcccaaadabcdbcbacdcbdaabacddbbbabbcaabbdddccbadbbabcbcdaadcbcaabdacacccdcccaacbbccbbbbbaaadacbbddbaabcbadbaaccdabcaacaaaaaccbbbaadcacdbbabacabdcddbdadcddaadacaadadddccbcdbabddbcbbddddbbdcbaaddbaacbddbddcbabacaaabcdadcdadccdddcdacdbddbabaacadbccdaacacbadadacddaddbbcacadaaabaabcccbbbcabadaddcbdbbdcabbbbcdadadccbcdbcabacdddadabdcddcaddcbabddcccaddcddcdacbaacabcadbbbdadcddcaaddcbcdbbcaabdcbaccababbddabbbbdbdcadcdcdbdddadbdbdbdbddaccadbbccbaabdccaccbcabddacbabcbaddbcdadcaaaabccdbacaccdcadddaacbcccddbcabdddcddabdcdcacaccabbaacabddccbbbaaddadddacbdbacaacccaaddababaaaddadcbadadacbccdddbabcaaccbbccbdbababcdadcdcdddbaacbcddddddccaacdaaaadcbdaacbccbbccdddadccdbbcdbaddcccbbadcbabadaadcbcacacbbbcdcbccbaadbcacabdaaadabcdbabbaaacddcbdacdabcdbbdacaacaadddadbddcacabbaadadacbcaacdacccdacacdaddbbddaaaadcadddabcabcaaccdabbaddbababbdbbbabbdccabadaacdcaaacbaabbcbcadcaabdbcdaadbdcdcbcdcbadcbccdbcacdddacbaaabdadaccddbadbdcbbaaacaaaccdadaaadbdbbdddbcbdbcdacaabadacbcccaaacadbdcacddabccaaadbadabadcdcacdaadcbaabdbcccdadbabdbcbaabacdddcdcaddbbaddabcaadaccbadccadcbbcdacdddccdccddbddabbaabcbdbccaaccbbdadbcdacbbadabbbdcbbbbaaadbdddaccdabaadcdbdbdccacdabdcbbbbacddacabddcaaddcabadcbbaabbbdacadcddbaabcddaacaacddaaaaabcadbdaadcdcaddbaddabcaccadababacbcadbcaadbadbdddcabccdcbcbabbaaddbadbdbdddcabdbddddcaccbccabcbacbccaabdacddcccbbaddbdbbcdcddbcdccadbacaadcbbdccdcbdcabcbdbddccddcdbacbcbdccabaccddacbabaaabccaccdcabcccdddbbaabcbadbbdbcdbbadcaddbbacccddacddddbccadbadcacdddbddcaddbbadcbaadccdbcccbabcbcbadaaaacbdaaabdcadcabdcbcccddbdaabdadddddbabaddbcbbcbdcdabdbcbabcddddcbcbdccdbdcbdcbddccaacdaacdbcaaaacdaacabbaacaaddcbaaababbcccbaddcbdbccabbddbacbdcbaadddbaaacbacdddaddcdacbcbdbaaccaabddacdbcabaaabccdabdccbabdcbacaadadcbccbaaaddadbdcaccbcdbcccabaddbbcddccbbadcbdbcadacbcbbaaddbacabbbadadadbbcaacbdbabbdaadbccccddbdacbabcbdcdacccbbbcdbdbacddbcadbbadbcbdbccdaabdbcaddccdabccddbbcbacbcbdcdaddddacaaaabdbbabaaaabacacdbddbabdddccbcbbcccbdbbbbcaabdbbabbaccbdbbcdbddacacbbacbdcaadbddadcbcccbdbdbadaddbbaaaddddcbccccacbdcadcbcbcbdcbadbbaadcbdbababdcccdaddcabadacdbddcbcdcccbbbbdabbacbdbdcdbaabcdbddbabbccbdbbdcaabcbcdcdcdacdcbbbabcdcaaadcdcbdcbcadaddbadbccccbdbdcbbcbbdbdbdcabcacdbcccbaacbbddbbbabdcbdaccddbddbddcabdaacdababcdbdcbdacbaccacdddaacbbcaddabcabbcdcbcacaaaccdcadcaaccbcdcdbacdbddaacdcacdaaddccabbaddcbcdbdcbdcddcdbabaccbcdbcdabcdbddbbdaccdbdaabbdcbaacbbddcaaccccaacbdaadccdcdcbdcddbabcadcaaadacaadcadccdcccbbcdbbddadcdddcaacdccbaabccacccdbaaaabcadcaaacbcdadbcbcddccbcdaadcbdcbacbccaabbbbaacabdcdaaabccacbcaaabdcdbdaddaadbabacabdadcacbbabaccaacabaacbbcddbacbdbcaddbbadcddabaaccbbbbdaaddccaadadcdbdcddccadbccdbbcbdcdaadbdbbbadbbcbcabcaacbdddadcadadaabadbcabacabdadcdcacbddacabadcccccadcaddcbdccccbadddacbabdccdbdbcdcacaabbcaddbcddddbdacbbbcaadacacacaddbdccdccdbdbccabcabddbabdadbddabdacddccadbcbcccadacbcccbbbcbbcaccabdbcdbcacdccdabdbadddaaadddcaabdcccdacadcbcdacccadabccaaccdbcbcdccbacbcccbccdbbdadcabbccacbbddbdbcdadcccdccbdbaaadbaddccbbdacaabbbdbabaddacbcccbddadcdacaacacbbbaccadbacdcdaaccaabccbdadbdbdcadbbbdaacdacabaabbcadbcccabdcdccbdbccbbcdbcbbccadaddbdadcdcbbabcdbccaadbccabbcadddaabbcdadbcdbbcbbdbdababbdcaddbdddbdbaabddbdbbdbadbbadbbaadccbccbdadbbbbabddbcbddddabaacddcdcdccabbabaabcbbbaddaadbdaadbaaaacddcbdacacdcaccbdbccbacbbcbdbadaabbcbdbcbcaaadcacaadadbbcdabddaacaaccaacccdccaabcbdbcbbdbcacdabbcdadcbbbcdbbbdcddacdbadbadcdbddbccdcaddccbbbcbdcdddadadbadaaabadcabbacbbdcddbaaaadcdbadccaababdbccdbbccbbabbcbaddddddcacdbdaacdadccdddcabbbdcbddcbbbbbdccccdbbadbcbcbbbbccadadadaabaabbcdbaadbbddbddcadcbbcbacdbdcadcbddcaabcbaaddcacadcadbadbddbcadccdbabdddbbbbbbdacbcdbdccdddabbccaadbcabbddddbddcbabbcdcdbabcdadccbbdddacabadadadbcdddcbccbbddacdcdbbadbcadbacdddcdcabbcabcbbbcabcabcabacbdbbadadacdaabaaaddcccacaaaaaddbdaaabdbcabcdcbaadadccddbcadcdabbdddcdadcdaccbbccaabdcdaacdbdabcdbbcbdbdbcbdbcbccaddacaaaaccdccaddbaabdbadaaaaacdddcdcbcdbbabcddbaddbaadacadddbacdacbbddacadbbbbbadbccbabdabbdabbbbcaacdbcddabaacaabaddddacdacbdbdbdaacccdcaabdccbbdbddabcbcbdaacbcccbcbbdaaadbbadbbbcdbdcdaaccabacacbccddcaabdcdbaccadacccbacbadddaccbbadccddcbccababbaccaddbbccdbabbbbababdadadabbdbbcdcabadabbdcbbbaccdbbdabadddccdbdbcddccbcaaabdbaccaaaccbbddadcbacabaadacadaaccaaaaaddccbbcdbddadabaddabbbcdbaaaadbabacdcaabccabaabbbddccbbcaddacbababcaaabadbccbcbaabaddbcaccacabddcddbccbacabddbbadbaabddaaddccaabdbcadbacdbdbddcdcacacbaaddbddacabcbaaabbdcadcaaabadcbabbcddbbddaaabcdddadcabccdabcadaacbadabdbcccdabcdcacababcccdaadadcbaccdbbdcdbdacddcccdaaccadcaacccdaaabccddcabccacbaddcbdbadccdcddacdccdaabcdbdabcdcbbbddaadbcadcabccdbbacacaacddbcbcbccbcabadddabacadacaccbbcacdbccbdbbcacccadbccbcaccbcbbaaaabddcacbabcadbadadccbbccbdcbdccbcacaacaaccbcbbbbdcddddbbdaacbcdaabcbaadbcbacbbcdbaadabaadbcbcacacacabcbabbaadcdcdbcbcdccdbbabcddbbddcbcdcadcadabddbccbbaccccdbdadaccadbabcddbaacbcdcbbbbcccacddbcdcbbbdbacdcaabdbaddcdddcbdacbbcbbbcdcdacddacbbbabdcbddabbbdaaadaaadabbbadddaadbabbcbdaaadadcddbccdccddbbbdcdbdbacbadaaabdaccbbcadaadccdbbddbadbdacaccbbdacddbcadcdbdbadbdaacadaacadaabdaabdbcacdacaaaccababdbaccbdabaccddadcdadabddccbabcadbdadaacbaabacaaacddcabaccaaddcdbbcadcdacdaacddcdacadbbddadbacdcaacaddaababddcabacccadbdbbacbccbdacadcaabcbddbccbcdabaabcccbbacbbdacbbacdbdaabacbccadabcadaabdadbbcbabbbccadbcbdcacbbcbabdcdacaaccbaaacdcadbddbaaabcddaacdababcccbddcbaccbccaccdbcacbbabddddcbcdbddccdadddbaabcbcaaccacbcaaadadabcdbbbcdababdaadcddccaacacabbccccdcdddbcaacdcbbabcdadbacdddcbcddadbbbddccbbdbcbabcbaccdacdadabcdbdbabcbaddabadadcdbaadabbaddddacdacdabdaaabdbbcbbcacacabaddadcabdcabcdaaabaccdcabaddcbaacdcbbacbdbccccbbdcacbcacddbadcacdbdaadcdcbaaadddbdcabcbaabccacbabdbbaaaabddcbabccccbabcbdcdaadabbdabbbddbaaadbdaaaccdbcbdcacccddaabacbaacbbacbdbabccadcbbdbbbcdbcacbdbdaaadccdbbccddabdbaaaccabbccbddccabbbadcdccacdcaacbdaacadadacbdbabcadbcbccdbdddbaddbabbcabadbdbccccbacdddcbccdcccaacbbcdbdaaaabdddadaccccbdcaddddcacbabccacdcccbacddcacbbadbbdcbdaaacdccbcbadcbcdbbdcccacbcbddbaadcdacbddbbaccccbbdabccbdbadccbbbbacdbbccccbcbbbdadbccadbccbcdaddbabccbbaddacbbacbdddaabdabdccdaddbbcabcdbdccbcbbcbdacdbcacbccdaccaadcdccaccbbcccabbbdaddacddcbccddccddcaabdabddaaabbcdadbbabadddddaabdbcccdccdccabdddbdbababcbddabcdaaacbadcbdadcdcbcddcadadddcccaaddcddcacadcadaacbdcbccabadcadcdddddccaddacbdcbadbcaddccbbbccddadccababbdccdadbbbadcdbdcccbadbababdbbdbdadabdaacabdaddddacdbdcbbaaccbcccbadbddadbbddbdadcdaabaaadcdbccdcadaadcadcdbbcddddadbdcdbabaaadbaddababdbdadcbcccddbddcdbbacdbbacdccabababccbccaabcabcbbcddaaaacccdcbcbabdabdbddbcaabdbaaabacbbbddbbaaadbdcddccacadcbdbaaccbcadcdabdabdaccadcccdbcccaccaaadabdccbddbacdbbcbbcbcadddadadbbbabdbccdccbdddadccacdbaaabcbdcdaccaaaccdccacacbcaaddcaadccdbbdbacaddaccdbccdccdcaaadcddbdccdadbcbdbabdddcbabdcccbccabcadddaaadabadcbacababbcacdbcbbbbabcbdbcabaaddcdacaccaaccbadbacdbdcccdbbaadabbbcdabbacdbcdcdbddbcdabbbbadcdcadadaaaabbbdbdaccacbcadacbabcacbbaaadcbcdcaccddadbdabadaabcdadbaaddadcacccdcbdbcbdbabbaabaccdcddcddcdbccabadddddabdbcdbccabbbdadbcabdaabdddbbddabcbdbacbdbdbadbbccabbdbabdbbadbadadbccbacddbdcdcdaaccbdcadddaacadbabdbdacaaabddabdbbadabbdabbcdaacaaabdadacbbdbdcddcbcbbcdbccbbddcdccbbdbabbadcadbccbadcdaacbddcbbadbadcbbdbabcaaddbbbadbccbdabdddabddaacadaddcdddabccbdbbaadbcdccbacccaddcddbdbcdbbcdbbcabababcbcbcacdcbbaddbddbcdbcdddabcabddaabaaaddcacbbdbcdbaadacadbccabaccdcbbcbcbbadaabbdcbdbbdabacdcbacaaaccdabaabddcdabadaaaaacacdaddababcaddddcabcbccadbdadaabbaadadacbabcddbbccabbaccdcaadcaaadbbbbcddbcddbdddbcbbabacaababcdccacabcdacbdbbcbdabcadddababbbbdaddacddcdcdaaddccdcdbdbccdccbbbbadbadacadadbdadddadabbdcbdbbccccadcdddabccdacbdcdccbacdbbbabddbbcbcaadabacccdadbbdacccabadbcbbaccacddddacccbcdadbcabcbdbdabaaabcdbdacccaaddcbbcdddbbccbddcbcdcacbdddbbadddbbbcacdcbcdaddcaadbdbcbbbabbbdacbcbabaddbadbacccbddcbcdbcbaaabddbcaccbcbbcacdbbbdcbbcacbbbcabbadbadbabdccaaabbababbbbcdacaadccddcadddbcaaaacaddcbadcdcacdbdaaaabdbacbadabbbcbcbaaacdddccccaccdadaaacdddbacaacaccbaabbadaadcdaaadcddabdcccdaddadbacccdacbadacdbdbcbcccbaaababbdcababbcacccacacaccccbbddcdbdbdbacccbcdcbdbdccdaaaddcddcddaabbcdbccadadadddcdcccbacbcdcacdccccddcbccdcbaaccdddbcabaccdbaaacaacaabbbabaabccccdddbccaadcbcbddbbdacdcdcdbccdbabccbbacbdabacdbbbadaacdbcbacbccddabcaababacbddacaaacbcabdbaacbaabcacaadbaaccdbadbcccdbddbcbbccdadbdacdcdadccabbbcdbbbdccacabbcbbdadbacacacddcabaabccaababcdbbabbadbbbcbbbcdabcdaaccadccbbdacddcdccbdbcbcadddcbbbdddcbbabbaabbbabcadacdbbbcdbdbbadbddbcddccdcbccddaccaddcacbcddbdaadadbbdbbdadbdbbcaccbbcbcddaadabdcbbdaadadcbbdadccdabdbbccaccabcdcbaacdacadddadcaacbbcddcbabccbdcbbdbdcdaadacbabdbdbcccdbbacaabbaabccacbcbcbbbbdaaccbdcbdabdaccdcbbddddbabcaaaccdbcdbcdbabcdddddddaacdcbdddcadbadadabaabdddddcaabddabdaccbccbbcddabcadacaaadcaaacbdccdcdadbbcbddadcbbdbdcaaabdcccdcabdbbbaadbadbaaddccbbbdacbaccdcbaaacadbdaddaacaddbadbccadcbbbaadbdcccaddaabdbbdcccbbbaaaacbccabdcacdaacadbcbcdbdddbddbddacbaadbbdadaaadabaaabddabbdcaadbbbdaadacbabcaaabaabbadbbbbadacabdccabccbbadabdbbbbdcbcbadcddcbaaccaabdbcdddbadccabaaddaaacccbadbaaaadcbdaccbbbbdbddadbbcbdbbaaddcdccabaaabacbbdabcbbcdcddacaaabcdcaddaabcdadabcaadacaddadcbdcbadaabbdbcdbababaacacaccddadbdadadcbcddbcbaacdadbcccaacacbdadddabcdccadaacddddcdabcaddacaccdaabdcbaccbbcbddbdbabcaadddacdcadddcbbadadcbcccbaabadcbccbacabbdddabdacbadbcababcddabbacccbcbaaccdbbaddcbbcddcabddbbabcdbcdcaacdcabbbadbaadaaadcaabbacbbdbcacdaddcbacdcaaaabaccbcddccddccbdbcaddcdacdddaaddaacadcdbbbdcabbcdbdcddcabcacababbcdbdadaccaaacabcdaadcadbcbaddccddddaccddbbbdccbddbacdcccaabccddbdcbdbbacbdbdbdddaddccddbbccdbdbadbbcdcaadacdcdcdccbcddccbbcabadddbcbddadabadbdbbdbaacbdaddcabadbbcdcaccdaabbbdbbdccabdaacccdbdbacacbccacadbadabbccdabddacbbbcdcddacacacccdbbdbbccaddabacbcaccaadccbcaccbaabcbacdbdacdbdbdabbbdaadbbcbcccbaadcdcdcabbacabbadcddbadcccdcccabcacacaaabadadcbabbdddbccbddbbcbddaddacdaacabacdabacaddacdcddcdacccdcaabcdbadbdccaacacaabccddabbbaabddcbbdcdaabbdcbabdaaaabbadbddadcdbbdadddcbbdcdcaabaabdaacaddcdddaddccbadabaaccabadcdbbdbdcbacabccabdadbadcdddaabbaadbacbdabccabacacccadbcacddaaacbaccadbcbccbddbadcacacacaaadccadcdacbddddcabadadbadddccacaadcdbacdcbaddcdccadbcdcdabbacabacdaddcbbccacbcbacdacaacabccbddbdddbbbbabbdadaacbbdbcdaacdacbddbbcbadaccabdddbaadabdcdcbccacbdbacbcbbdcbddabbaaabbdbdcccdcbcbbbaaacddbddcbbadbbdcbbbabcaabaaabbdbbbbcdabaadbddddddadbbccadcadcaaaabdabaccabbcbbbacbbcbcddbaabdabddbabaddcadccccdbadbcdbbccabdcaabccdaccacabacbbaccdcadddbcbcbcbcddbbabbcdabacccdbdddbccbbdccdbdbdccaabcbaaddaccadcdbdcdccbaccdcbaddddbcaaaaabbcaacbbaadbbbcbbcabacbdbdddbaddaccdcdbaccbaabccdddabddbbabcbaacbabccadadcabbccbadcacbcaacdaabdabdbacdccaacaaddadddcacdaadbbbcbdacaabadcdadcbacbadadadbbccaddbdcbcdbaaaacbbdacbdaacddcabddabcdbcbdccadacacbabcdcbddccaccccacbaababcccacbadbbdbcadbaaadbbcbdcdbadacadbbdaaacdabdaddcacdddbbabcbbbacbadccbdcdbbcddcccbadabdcaabddddacaccacacdbbbdaddacaddcdabcdcabadadbdcddaabdcbbcabdabacccbcbdbaaadabbcdcaaabcacdadabbcadbddccabdccadcacbdcaccbabbabbddacccdabcaacccabcacccadaadaaadddbbabccadccabdabccabbdadccadcdcaacdbbacbdcabbbddcbdcdcbddacbcbccbcbddcbdccbcdcdbdcaacddadbadcacadcbaabdcdababaadcdbcaabaaaacaccadaaabbdcddcbccaccabcdacccbabadbdbddbbbdabaaddcdcbaddabbdbaadbbdaabacdaadbabcbcaacdbdcddbbdccaadbaddcbaacacbababccbacadcdacacacbddabdbdadaadcbdabbaadabcbbddbbacbdcacdacabacadadbaacbcbaaadbdacdbbbdcdbdabcdcccacddcbbdacccdcadadbcdcbadcabcdbbacdbdcdabbdbddbcabbbbccaadabbbbbadddddddadaadaadbdabbbdaccdabccdbcbddcbdbdbacbdbabbbdccddddcdadbbacdcacccabcbdbddccdabbcdaaccaaddddabbccbdcdbacacdbddbaabacadbdaddaddcabbdbdbacbabccdbbcaaacddbdbbcaccbaaabdaccabcbaababbdacaddadacdbbdbadcaaddbadcacacaadaacdbccaddcbbccaccabacbbbaacadadbdbcdccdcbbabadccdddcbcdddcbadacdbdbdbcbabccdabcaaddbbdcdbdaaadbdbdadcababcdbadbdaacacbbccbabccdbaacbaccddacdaaabacdcbdaabbcdcdcbcbdcdccbdccacdcaccadbaabcaadadbdddcdbcbcdddacdcdacccaabaadddaabcacdddcbccbcbdcbdabbacbbbcddcccadadaddbccabdacacdddbaddaabbdddbabaaaabdbdabbbbaabdcadddcbaccddacdbbbddcccadaacbdddccdcbcdbbbcdababbccababaccaabccadcaadbccddcaabdbcdccdddabdbaacacaaacdcdcdaaccbcbcaccbdabdbdacbcadbdbdcccdbcdcccddddcabddcadcdadacbdbabbdbdadbdadcbadaabcdbbacabbbbbbacaabcaadabdddacbadbbcabbbcbdcaabdcbadcdcbcbbabccdbcbdddbbccadccadddccdcddcbcbbbdaadcdcccbabdaddccdbabcdbbbbbbbcbdddccaccdabdddacdadcbccdacaccdbdbdddcbbabbddaccacdddbcacbcabcbaaaccbcddcdaabaaaabcacbbcdbcacdbcdbccacacdbcbacacdcaadadbbdcabcaacddaadbdcccababacdcdddddbcdadadbcddaabdcdddadcccddadbcaddaabccccdbcbcccadadabcddbdbdbbdcccbabaccccdabbcddaddabdadbccbabddbbcaaaaacdccbbadbaadbcbcadcabacacdccbbbdbcabacaabbcabdaabccadbaabaabdcbcdadbabbdbadbbddbbbddcacadccacddbddcdacdcddcdbccdaadcdbbadadcaadbcbbbbddccbcbacdbbdbdccdadabaddddcbdddaabadadccbdacdbcbcaddadcaddadbddaaaaddacabcbdabcbdcbdcbcabcaaabbbdcdbbbdddbaddddcdddaaddcbaabcccbacccacddbbacccdbcbacaacdddbcabdabcdabbcddddbbaadbbddccdaddabcbcdcadbdbbcdddbbcaccadbccbdccbbbadddcdbdaaddacabadddbbdcbdbabdaaaaadacbbabdbcacbcddcbddbbdbadddacbbcccdbcbdccbaccddbaddabbacabdddcddbcadbbbbbadabddabaabdcbcaadcacaabcbdcbcaddbbcbbcbcdcdddabbcdbdacddadbddcabbdcbcdcdcdacadbbccabbcaabaaaadbdadacbaabdbdbadbcddaabdabdbdaabbadbdbdcdacbaaddbcdabcccbabaacacbbcbacbcabcaaccdbcbbadacdbbbaabbbaccaaccdaccbcbabacacdabbbbdabcadcaaacccbadcbcabdcbcdbdbdaccdbdbabaadbcdcbdbabccbbdacaddaaddcaadbbbbdbdbaccbddddbcdbcdbacbddbdabdaadddccaacbbcbbcdcdadcbabababcdadcaadcdacaddbccdccacdbbbbcbabccdbbcdabaddbaddcdaddbaddbbaadbcdacaabbacdaabaccbddbbcbdbbbaaccbdcdabcacbadcbacdbcdacdbdbcabdcbbdaaadddcddcdbbaaadddbdcbcbdcbccbaadacbccbdbdabadbcbdcdbcadbdacbbbccabdaddcdbdbcacbcadccccacaaabdabadbbadcccdcddbccdcbdcacbadbccbbcbddcbcbdcdcadacbccdabbbbdcabbcabaacaaadabcddbbdacbdabbcacddbaacdcbaababcccbdbaaabdcbaadaacbddcabbdaabbbdadacdcccbdddbcbdcdcbddbcdccdcbcabcadadcbcdbacbabdaabacabacbcbabbbaadbbdcacbdaaddddccbabdccbbddadadcdbbdabdbcbdbdddabbacbbadbddddbddacdddbbadcbaaddcbcaabaabbbcdcdbddabcaacbbdaaccddcaaadbcabaddcdbddacbdababdbaaadccaadbaadacddbacacdbdbadbbcacddacbdcbdcdbacdaaadcacbbbaaccbdabadcddbcabaadbadbbcbcdbdbbdbcbcdcdddaacabbbdabaccbdabdcdcddccbbccdcccdcdddadcaaabdbbdcdbdccbdadcdabddcadcddacacacacddabbbcbcacbdbdbaccbcbbdcdacaddaacbdbddbbcadbcacbcdcdcdcdbbbcdadccdbadcacacbbdbcdabccaaddbaaccbaadadbbdccdccbacbcacaacdcdbdaddccaccadbdabbdacaddbbccdacddbadbdcdddccbcddccaddaaacaabbcddddbbdaddabdddcaccddcadbcdccbdbaabdbbdbbabbcabbabdbdaabdbdadcbcccdcccacbdaadbaabbadadccddcabddabacbccbacaddcaaccdaadabbbcaddbadbcdbadcdaabaddccbacbbccdabcaabcababcdaaadcbddbadbbacacbaaddbcdbbadccabbdcccdcbaabbcaaccdbbcacadbcaaddbcccaabdcdaaaabddbbdccdccdbdbbbbaccbccbdabcddbadbaabdbadbacabcdadacadadababdddaaaccbdbcabcbabbadcdaadbbddcabcbcdaadddacabcacdacabdcaabdcdcbcbbbcdbabaacccaaccdaaccdadadacddcbccbdbbdbacbdbbdbcddcacdabdbcacdcaaddbdbdccbbaddcaddbddbdcdadaadcbddaacdcbabccdbbcdccbdcbcddbdbddbaaccaadbdcbcbadbddbdcdabadddbdbbbbadcbbbbbccdabaadadbcddaaabcbaacbbacdacadaccddbdacbcbcbcaacadcacbabdbadabcbdcbbdabdbdbdabbdabcadbacbbbabadbdacadacdcbdcdbbaccddabcaaabddbacddbdaabbdbcbabdcbbbbabbdbdbbacbdbaaabbaccbbbcccadbdadaccddbabdbbccaddbadaaaaaadacddcbdbbdccaadadbaabbdabdccacabdcdcbcacadcccddcbccbaddcbbadacbadacadabdddbdaddddaadabbcabaaaaddbdcabadcddbacdaccabcdddbaaaaaadcdbdacaabbcdbdcbbacacddaababbccbccbaadcbababdbadcddccdbbaabacbcdcdcdaccbdcddabcdbdcacdbddabdabdcabbbbbbadbbbdaadcaaccbbcbdcdddbdaccccddcaacaaabccacacbcdcaaaabcdbcdcaddacccaaaadcaababdccbdccbabacccaccdcdbcbcbcdddacdabdacbcbabdbccadcddbcbaabdbbcdcddcadcdadbbabddbcddccbacccbdcadacdcddcbddcbccdbbdddaddccbdbbaadabbbbbbcaaabdaabbbddcbdcbccaaacdadacabdcddadcabbddbbbbdabcdbacabbdaaacabbcadbcccccbbbdbcccabbcddaddabdbbbdacabdddbdbdbcbbcbdbcdddabaabdbdcadadbcabcbcdaadacccdbbcaacbccaddbbacbbdbdaddcaddcbadacaadcaacddbbbcacccabbaddcdababccbacbdddbdaaddccbcadadabccabbcdbdddcbbccaccaacacacdbbbdddaddbcccaadcdbbacbcdacdbacbbbbaadbcbcdaacadbdcdbccaacdbabccbcaaaaabcbdccdcbbdcadddccbbbdccddccabbdbdccbbbdbcbacbaddbccddadabcbcabdbcadacbcdcadcabbabacddcddaacbbbddcacaadacddbbdbbabaabddadcccbbcaacbcddcacbbdbdadbbdcaacdbadbcbbcadcacbdacaabdbbdcbdcccbabaddadbacaacbdddacaccccaccaaaababcdccbbcaaaacbddacccabcaadcbdddbacaadadbcadacddabbdcabdcbabdaadcccbdcabcaadbdddcbdcddadabacbbdccdcbdbacbcbdaaadccaddddabcdcdcbcbdbddcdcadcacaaaccacacbccdaadbacaabbdcdbabdbbddbbbddcaaddcdabccadcccbacbcaacccdbbadaabbbaccadabdacdbccbdccccdccbdbdccddcbadbaabddacaaccccbccaddadcabbcdbaccadcadaaddbdcdcbdaadcbbcdcbbcbbabbaaadbcdddcdacbbbdbdcbcbcdbcbbdcacdacccdccaaabddaadcbcaddbdcaacdacbcaddabdddcdbdcbdaccbbcdcdadbbcadbdddbbdbcbdcbbcabdbbdadbbaaaaadddadbccabcddaabaadddbabddbbaddaabcdabbcbcacbddbcbdacdbdaddddcaacabccbcacaccabdacacacaabdaddbcabbdcddacaacdcbcacccbbcaacadbabdadadcbaaccddccaadaaabbcdccacadcccadbbabcdcabcdccbdbbccacbbaaddcabdddacacaccabdcdaaaddcccddabbdbdaabcddbcbbadacaacacbbdccaccbcadaacdabbdaaaccadaadbabbcacaabcccbcbbabbabbdcdacadcabddadaacdcaddabdbcbacaadcdddbacbcdbddbbabbcdbbacccdcbacbccddacbcdaccadaaaddbabadbaddbadccdcadddabcdbbacbabbbbbabccdcdcacdbadbaccbadcbcaaccdbabccababddcacbdadbaaaaccdcbdcaabcdcaabcacccbabdbdbbaadaccdabdcdadddbdbabbbcbbacbabddaaabdbacbdcaccbbbddbadcdacaddcbcdabccdbdabbcccdaadbddbdbaddcddcddbaaacdbdaaadaacccbccddddaaddcccccbdbdbdadcccbccdaacbadddaabadadbbdcbcdaaaaabcbbabccddbabbbabccdcbdcaabbddbccbdccdbcddbaaaadbbccacabacdbbdcaddadadccabbbcbbbdcbbbccbdcadaacdccbcbcbdabaabcbcadabddcdbcaacaccdcbaaadbabdbcbdbbdacaacdbdddbabddccccacdacabccabdbbccabacbabcccaddbbadcdcdadcdbaadacaaddabacdbcadbdaabbbaaadbbbacbdcbacccbcbbbdcabdbbcbcbdbabcdaadccbbaaaadcbdcbbacddcdbbbadaacdbcadccddcaadbadddbdacbaababcdaabddcddadbbccddabcdaccdbbcacabcdacadbacbaccbccdccdbadbdbbadbbadccabbbbccaacbaadcccdbcdacbacccdbcbbbadcaaccababcdbbddcbcccddcccccbdabdcbbababaccadbccaacbcddcbaadbcdacbbdddddcadcbabbaccbbcabcbdccddaacaacbcabbaaccacadcbdbcaaaccacdbdcbabacdcacabbbcccaaabcdcbccbccababcaaddaccccbbddcabbadcdadcdbcadbadcbaabcdbabacddccbaabdacdcadbccccccdccdbbbcdcabddaddbadacddbbadabdbbcbbcacdddacccaabdcaacadcaddbbcaaaacdcaabacabaaacdbcddcbbbbadcbbdddcdcbbbdbbaacdcdabdbcccccabdadacccbcbdcbbbabbaddacadddaabdbddadcadadcbbcbbcbabdbcddcbdbcddbcadacdabddcbacaacbabacabbcdbbcbacbadbaadabddadadcaaabbacaaaccacddddcadcccbaaccbccacbcadaddcbdbdcaabbcccdbadaacbaccdaaaabbcbcabcbbcdbbddacabbaabccdccdbcdabbdacbaccddacccccabacbdbabcabcccbcddcdbbabcccbdcbcbaaaadcddadcbaaaadbbaaaadbabacdbabccdaddadbcbacaaaddaabcdbdbcdbacaccbbddbddabcaadccbdabaaacbddaccdcdbcbaaabadcaabaadddbdcdadadddbcbaabddbbbacddaabdccaacccaabadaddcddabcbddacdccaaabbcbdacdbdaddabadcabdcaddcabbcdabcbacdbddbbdaddaacdcbdccabaadcbdcdbbacdaacbabbdabcdbacdbcadcdacacdbddcabdadadbcbbbcbcdbcaccbbdabcaabaccbbcbdbadadcdadbaabaccbdbadbddabcdcccdbdcbdbccaacbcacdcdcbbdbcacccaccddcddabcbbdcaadddadbacacaaacbbcbacdccdcddadaadaabcbaacdacabdcdaabacacaaabdaacaddaaaccacadddadadbdabbaadababadabcbabcbbaccabdcbdabdbdcddacadcbbbdacdcbcbccababdabdcdabbbccdddabbaacbdadcdacaabaccadabdcdbdbcdccdcbaacaabadbaaaabadbacbcddcabcaccbbabddabbcaacccccbbbdccdaaaddbbdbddccddabbbcdccccaaccdbcadacbdbccacbcacdccccaccbaaddadbbcdabdabcccbccabaaacdcabdabcdcaddadbcddabcbdcccbaabccdcdbbdddabbddbacaaccbdacaaaaaacbabbccbcacdcaaaadcccacdcbcddbbcccdcdcaaabaddcdaadaacccddcacbcabadcbabcadabbdcabdaaddadcdcbcbbacaccdddcdadaadccaabbbbcdccbbbdddcbacaaacdbabcdccddbcdadcddddcdaabbccacbbacbbaaadacccdbdcaacdaccacbdddbbaaccccabacadbdabacacdcbccdbdacdcbaaadbbdbaacdacababdcbcbacacbdaacadddadadccbbacdcdddaadddbbcddabcabcdbdbcdacacbaadcddbabaadbdabbdbdcabccbbabdbbbadddcacdacbbdaccbadbbbacdddcdbdaadcadddaccbdcabcacadbabcbcbbbbbbbaacaadaaaaccdbaccdacacbdcbbdaccdcbdcccadcdbbdccdaddbadaaacddbbacddcdaadcbcdcbdcadaababbacdcdcbbbabcbaadccbbcabbabdddcaadadccdbccbabccbdccaddcbddacddbccbcabbbccbbbaadcccbadaabbdddbdccbaababbaddadabacddbdcdaaccdcbbadbbcdbcbadcaddbacaadadadadbdacdcccaacdbbacbccbddbbacddcdccdaccdddadcacadccdcddbbbcabbbcdcdbccbbabaaadadcbbcaaccbdcdadbbcdbcaaacabaaabadbcdbadaacaadcabddcaadcdccbbdddbdddcabccaadcccabbdbdcaacadbaabbdccacbcbcabdacccbdcacbadadbcbbbaccadabaddacadcdbdbdcbacacacacdbcbabccabddcacdabbbdddbbbdcadbcadaabaacbbcdccdcdadbdbcbbdcdbdbcabadbccdccdadbacdadcaabccbdcddcadbdcabbcacbccaddaabbacdcdcdcbacddbdacddbcccaacbabbcaddbbdcababbbbdcbabbdbadacbbdabdaccadabcacbdaccdddbdabccabbbdddcbadaacabdbcddbddadddaddcddabbbbdaddcddabdbaabdbcdbadacdaaadacbaccabbaaddaddbbabbadacccbdabbbadcbcdcacdddddbcdddaaaadadaadcddabcccddcccddcdadbbcaaddababbdcdbddaababbdccaaabbddcabcbdbcacaacacbccaccadacabddddacbbccabcbadbcaadacaccacdddddbccadcbbaddddbcaaddabcbadbdcbabacabdcccbcddabcabbdcbdcbdccacdbbcdccdbbcabcacaddcbcaaaddadbbadbadacadddcbdbddacdbbdaccdbcbcbaddcaabbbbadccbacdcbcbcccccccaacbccacdbddaadabdcbbdcbacbaddacbccdcbdaabcababbcbbbbaccbaddabacddddcadbbccbccaccbaaccbbdbdcdababbadaaabacbacdccbacbbddacdbacbaaabbabdbabbadbacdabcbcaacbaacdcdddbccdcbacaadccbdbddbacbbcaccacddcbabadddcccccbdacccdcbcdcdadccbdcbcbbcdaaabcccaabdacacabdabcdadadbdbbdacdcaadcbccdabbabccbddbabcbdbdcadbdcbacabcbcdcaddbbcdabbbaabdddabbbdbcdddcbbaabcdaccbbaadddddcaacbbccbdbcbbaabdbcdbabaacdacbccacdcbcdacccbaacaabdccbcbbcabdabbcdbcdbaddcbcdbaccddddcbdcdcaaadbaccacdddacdbadaacccbacbbabccacdcbbccbddbaddabcdbacdaaadcbcbabcbbacbaaabbdadcbbbdcabcddcacbdbddcabcbbaaaddbdbbaaacdbbbabbacddddaaaabaddcacbbcbcccaaabdbacdcbbbcabbadbccdcbbdbadbacccdcdbcdaabbccabccaadbbcadcbabadddcdbdbbcabaddabdcccdbccbdbadbdaabcdbddbbbdbdbabaddabdbdcdddddadbdcadcccddbcbbdbdabbddabdccadcdddddccbabcbbabbbaddbdbabcaccdbcccaaacaddcbcacdccccaacbcdbddbbacccbdbbddccbccbcccbacccbabcccdaccaddbbbbdcddcbcdbdaacabbcdcacbdbabaaadccadbbdbcccccddbdbacbbcbabdbadcaaccbabcbaadadbdbdbcbdabdabcbdcbdbdddbdacdbccbcddabaabbbbdacbcccadabcdcdaacbcbcbacdabddbdadcadddacdcdaaccdcbbacabaccdbabcbacdddddbccbbabbbbbbadabbccccacaccaabbadcdccbaabacadbcadddcdcbcacabacdbcadcbbacdbaaacabbadcccbacadabbbbcababaaadcdaccdbdbddabbacaabbdbadddcaccbdbabacabadaacccaadcacdabbbaabcadbdcaaadcbbccddaddbdacbbcaaddbacabcdaabadbcadcabdaacaacaadcdbbdcacacddddcdbaacbbddbaaaabcbabccdbaacbaacbacddbaaaadcadadadbcdbabddddcabbaacdaddbbcacabbdcabdabcacabadbadcccdbcbabbbbbdcabcabddbbbaacdadcdddcdbbabddabccccbaadacbdcbdccadbbbadaaccbbdbaacbcbdaadccdcdacddacdabdaccdbdbdaabcddddccadddaaacbbbcaddcbaacabccbdbabadcbadbbddccdacbcbcaaccbdbdbcddccabbbbabddbcbaacddbcdbbbbbbaaaacdadddddaacabbcddaacbccbdbcdcbdcacbaadabbbaddbadbbddadbacccabcdbabdaaabdcbbacacddcccdbaccbdcaabcabadccccccdddbcbdadccbccbaacccaabbbcdbacaccdabcbccadadacdaccdbbbcbabdbbbbcbbdddbcdddddbabdcadbcdacdadbaaddccabbbbbbbaacdaccadabadbaaaccccdadbdabababccabbabcabdbdbcababccaddbabbababdbcabcbadaadabbbdbcacacbbbabcbabbdadbccbdaabaaaabbcbdbdcccbcbbbbababdacbcabadacdabdddcbcbcbdbaabbdabaaaabcdcdadcddbcddadaabbcbdcddacbcddbbbdcccbcacdacddcbdcbcddbabdddadbbabacbacbddcabadbcaacccbadaaccacdcaabbdcbbcbaaabccaddaaddbadaaadadcdadaaabdbacabdacacdbaadaacddcdcaaaccddbacdaacbdcbddccccdccccabbdcacaadcaddbbdabacbaccbdccacdaccaddaadadcbacaaacccddbabdadbababdbacbacdcacacbdcddcaddbddcaaadadbaaddbcbdabdaadbcdbbaacbcabbcbbdadbbbcccbbdcddbdbdaadbaadbbadbbacacacdadcbaacacccaccbdaccaaaabddcbbbabaadbbadbdacadacdaadabbdbbcbbcdaaccbdabdaddbbcbcdbccdbdabcccdbaaabdccdabcdddddcadaddabcdbcabccabbaccbcbcdbadcaacdcbcddbbcadabaccddbbaaacdccdccddbbacaaadccaaadddbccacbabaacacdbaabcabbdbdbadcacbddccbbdcbbbdcbdcdcddcdaadccddacaadbddbdadacdaadadbbcdaccaadaadacbdcbbdaacccccacddddadabacadbabbabccdabddabddddcdaabaaddacacdadaaddbabcbcddcbbdbbbdbdaddbbcddaddcadcbbacbdddaddacabdbaadcacddadacbdbcacbddacddcdabbabcbdcbbddbadbbcdbaadbdcddbdbbbaddaaccbdacbaddcdbbdbbabbddbaddaccbbbdbdbddbaacadababddadbbaaacbaddacbbbbaacbadbaacbbabcdbdadccbacbaaadcbdbbdddacbacbbcaacbbccccdbbdbbdcdabbdbbabcddcbadbdabcbcbababddabdbbaddacbcbcddabadddaddaccaaabadbcbaccaacadcbdbbbdabbcccccaaddbbaaacdaacadaabdbdbcbdcbbddabdbdacdaabadcbacadcbcbdabcdcacdbabacacdcacbabcbadbcdcacdcadcaacaacddacdadcaadddcdcadbcadbadbdbcbdbcacdbccccbbaabbdddccbacbacaabdcaaabdcbcbcbcbbaccbacdbbcaaaabbbdcabcbbabbcddcddcaccabdddcccdbcbaaacabdbcbacdadbccbaabccadacccccdcccbbabbdddabdbddcdbdcbbabaadbaacaadaabaddbbcbabdbdacbcdddddacdaaabbaabdbcbbdccdbababacaacccbcdbbbabddabcdabcccabbbbdbabaaabaaabcabacddbdbdcbacdddcbdddadbddbdadddabcddbabcacddabacdbdcdcaacaadacbabbabcaaacbdaacbdabbdbbdaddcdbcddbdadbcaaccaadcaababadabbbccbbdcbbcbdcadbdbbaabaddccacdbdbbdaadbabbccaadadbcdbbbdbcbcdcbbbacdccaacbcababdaddbccbccbcaaddbbbbccddbcbdadbabdddddbbcdddaddacdbcaddbcbbabadabcccccbacaacaadddacbbdbadbbaabbddadddbadaabbaddcbbaacbddbbcbabbadadbcaadccccadddaabbcaadadadddddacaadadbabbddcbdbbcdbbcccbdabcdbaacabbaddcbbdcddbcabcdcaadbcdcaddddaaadbdbbaccccbcbdcdaacaabacadadcbacaabbbbcbccacabcdacbcdababccbcbadbbccaaaadabbbbabcaaadadbbadddbbaabcbddacccaccaaacdcdbabccacdadbdbbbadccaabaacaccdaddabaacaadacdaacdcdbdaaaabcbcabdaddabcddbbdcabbdbbbcccabcdccadbdbdabacbcadbbcacbcccacacbbbccdccadbbaddabadbacbcdccdaabcdbdddcbbbabcdcdcccccacadcbcbddaadcbbbcbabbbcaccbacccaaaccacaabacbccbcbddcbdcbbbcdcbbdbaabdccbbdcccaddbcacadccbddacbcabcddbabcaacbbaddbbcbaccaaabdaaccddacccacdaaaacaaacaddddcbdaadbdcdcbdbcacdcdbaaacbbbdddaabcaabccdbdddadcaddcdbbacbbcacbadcbccccbbddabadbbbaacdbdbbddccaddbccdcacbbcbbdadabadabbcddcbbaabdccbaacdbaadbdcdcdacdcdbccabacdbdbcccddbbbadaadbaccbdaaaccaabbddaacabcbccadacdbbadcbbabddabdacbbcdaabdddbcbdcdaadabcbabaacaaddcadabcadcbaaccabcbbababbbdbbccdbcccddcbcaabacbaabdadacbccdcbadbbaabdbdcbbdcdacbaccdcaccdcbccbbbadbbccdddbabcadadbcdbacccbcbadcdccbcbddbbdabdbdddbdbaccbdadcaabddbababbbbcacabdccbcccddbabadcbcbbdbdacdabcbcdabdcdbbabbdadcdbdabbccbbcbcdaadbcbcccbaacddcbaccabadbdadbbddbadccbcbcbacacbcdadcabdacbcdaddcaaaccbdbdacaaaabbcaaddabadaaccbcccaccacddabbbcbcbdcbacbbdcdcbbdabaaaacadccbabcddadcbdbdabbddaccacdaabaabbcdcccdbaabbbcbaacbdbaadaacbddaaadacaddabcdaacddbccacbacdbbbcdacaacdacadbcbcabbaddbbbdbadbdbcdccccdbbbcbbbddbaddabdbbbccbbadcaadbccdacccddacababbacdcdbdbbddbbaabbdaaacbbcadcaaddbcacdbcdbccbdcacdddcabbbbddcdcbddbacbbdbccbdabcccdcadaaacadabcbadabccbbddbbcbbdaadaacabdbabaaccaaddabacabacaddbacadccabdcbbddabcaccddbdccccbadacccdabcdcbacbbaccdbcbacbdaacacbbbaabcbaadaababacdcdcacbcdbcdcbccbdabcdcbacbbbadcbdcbbbcbdaccccaccddadaaabccbdcdbadcabddcbbdcabadbdadcadcbccacaabcacbdddccacdcacaabdccbdcaaacdbcdcbdbacbdbcdbaadcdcdbcbbaadabbabcabdcacaabddcbbbddaacaddaacbababddadcadddbcaddcaaacadddbcccdbaacacccddabbbbcbbadcbdacbddabbdbbdbbabbddddabcdabcacadcdcdbacacadcddbbcdbbcbbabbcddadbdadcbaadacaabdabcddabdccddddacaaadabdaaabcbbacdcaadcaaabaaaaadcacddcdbbbbbcbcaabdacadcdccbdbcddaddabcbbcacaaacadcacdddcbadaccaccdaddcaaacdadbcadbadaccdadbcddabbabbdbbabcdbacdcbbcdbbcbccbdaaadcdadaadbccaacccbaabdabaabcbcdbbcbdcbaccabaadcadbcccccbadbabadcdbcaabdaddaddcdbbddbcdcaadaccccbdbbcacdcaacbabcdbddadbdaacdabaabaaccbdccaabdacbbbdbaccdbaddbcaaddccababacccbbccababbcabaabddbbadcddbabcccbcbdacbdcddadaccbcbadabcdddbcaaccbcbbacbadadabbacabbbbdbaddaacbdbdcbdcadbbdbbcbbbcddadacddccccdccccdbbdbbcdbaaabbbdabcbbcadacccccabdbdaacdbadbbbacadbacadabdbaadcddcabadabdbddcbdbdddcdbbdcaabbbdcbccdbccabbddcbdbbaaddcdacdcdabbdadcbdcaaabbcccdbbddcaaaacabcdcdddabcbaabbcaabcccbadcaccacbbddacbbacbbcdbcdccdcdcabdbdddadaabdabdbcbdabbaddcbbabaacdbdcdccbdbacadaabacdbaabbbbccddbddbcdccbcaddaaacbdbacbabcacbbcaabaaaddbddbcbdacaccbccadccdddbcdaaadadaacacbacdbbcaacddcaaddacadddcabccbdabaddadbaadbadbdcdbdddddacbadcaddddcbdcbbbdccccabadbbbdadbbddbdbadcdcbbbacabcdcdcdaacddccdcbdbddbbbaddcabcacabbbcadacdbaadacaabbddaadbbaccddaaabdbcaadbabcbcdcaccbaababaacadcbaaddbcbcaccbdbaaddaccbabbdadbccdbdcdadaadccccccdcacdcdabcdbcbaacdcbcacadcabacdccccbabdadbcdacddcbbdddaddacbcccdbbcdcabbdccaaabaaadccdbcdcccadcaccabddacdbdcaaaaabbcaaaddaabbcdbabadaacdcdbcacbcacacaccdddacddadbdcacdacacdaddcdbbbbbcddadadcbabdbaabbaaaadcaacbbbabcbddadccadbddabdcdbabccbcdddabbbdaaadcbdcbbcdccbdbdcbddadbcdbdccabccbabbbcdaacdaabbaadccccadbadbdcaddccdaaaabaacbcabdababadbcbaadabcccbcdcdcbadcdabaaaddabddadcbbdbdadabccadbccbabcdacdabdddaacbdcdabdbbacaacdbbbdabdbcdbdbaaaabbaabbadcdaadbcbacbdcadddbdcadccddaaacabccddcbdbaacbacdcdbbaaababbccbddbabaabdcaabdacacbabdcdacbacddbadaaadbbbbddaabdddcbdadaddbdcccccacbaaccbcbdcacccacdbcdddcccbaacaaddacbaaacadabdbdcbddbdaddabbcadabcddbdddcdcbaacdabbdcddacddbadbdabbdcdcdbabacaacdbcbcccbccaccdacdccbbbcccdabcdbdbcccacadcdcbddaaabcbcbbcaccdccccaacbdabdcbdcbaabcbabcaadbdddcddbadcddcbbbbbdbdbcbacdadabcabaccabbacddddbdbabccddcccbccdbbddcaaaadcbddcbaabacbcadcadbacdabdaccdaccacdcdbbdbcbcccbdacaabccdabddabdbaacbdaabacabadbbacadaababdbcdcacaabdbddcbcdcdbddadbdabdcdbbbdbdddadbdbbbdbcbddadddcdabdcacbaabccbdaddcdabddabdbdcdbbbdbdbbdabccbcaccdacdaacbccabbdbbcbbacdbdcacdbbcacbbdbbdbdddbacdbdbdabbcdbddcddbdaacaadaccdbddadcdcbdddbabbdaaabddddbcadbaabacbcdccdbcdbccabdccbdddcddcbbcacccadabacabcbbbadaaabcdcaccbdcabcaadccaaabcccbcaccaabbccdcdcbacbbbdbcbcbccadbbcccadccdddaacdbdaabbddbccbbddcaddaaaaccdcacddaaadccbaacaccdadbcbabcccbacccdbcbdcadcddbcdbbaccddaabbccdbddcbaadcbbbdbdbdcdcadcbdcccbbddacbcdadcbbcabadbcbcabdaacabdcbddabacbbbcddadcdbbcacbdccdbabcbcbccdaaadbbdccbacdbacbacdbbcabacbcdcbbdacbbcbdadddabcdbaddcbaacaddbdbdbcdbcbdcccbaaccdddcbbbcabcaaadbbdbccdddabdadbaadcbbaaaaaabaccdccbddcdabbdadccddcddbaacbbaacdaaddbcbbdddadbbaccdbabadcaadbdccdaabbbcdbadaadaaaddbcbddbcdbcddacaadbaddbdcbbacdddcaadacbddabbcccddcdddacbcddabcbaccadcbbbabdadbdcddbdbadddbaaaaadaacccdddacbbaadccdabccbdcccdbddacaccbdbccdbbcbabccbbdcaadabadbcadabaacacbdbdbcdaabbdbcbdcaccdbadacaabbcadcdbdcaabaddccacaaaaddbcaddcadbdbaacbcdadbdcdcaddcccaccbbbcccbbddbccdabacddabcccdbacddadbcabbdbdaabcbacbbbdbcdcbdbcccbdcdccccdcacdccbccdabaabbaacbcdaadcaadcccbcbacdabbaacbcbbbacbaadcdcabbcdbbdacbacbdbcaccacbbbcabbbcbabcbdbccdbdacacccdabdccdaabacdcbbdbcdaddbabaccccbaacbdaaaadddaacadacbacacbbbacacabdddbcbccddbabaadabacbaadacbddbaacacacbcbbcbdddacdccdacdbcdcdabdcababadaacdbabaddbacbcdabaddacdabacbcadbcaaaabcdabdaccacacdcdbbdbbadabbddbbcbcdcbbaaddbcbbbbababddcabddbbacdacaaabdcdbaadcdaaccabccdddccbaadddcbcdbcccadcabccacbddadbcbcacdaccabbcdaabcdbdcaadbdcdcbcaaddddcbbccbbddbdcdbdacdbcadcdbaaacadabbdcccaaacbadccbadbbdbbdbaccaddaabbbdcabbdacacabdcbbcdbcbcabcdbbbdaadbcbcdbdcccbbacbadcdddbcabbccdbabcabcdcaaccbabacdbcacdbcdacabddcdddadacabcbbabbadbbdaadbcadddbbcbbcbdbbabcdadcbcabdddcbcbbbaadcaacdcadcbabdbabddaabcabbccbabdbaaacbabcaacaddaacddbcccbaaabcbddbdaacddbcdabbbdcddcbccddcdcdccacadcaddbddaabaddddcaccbcdcbdbaaccbbcbdaacbcdbccbacaadbccaabcaaaadbdadabadaddccabdbadbbbdaccbdaccccbbbadccaadcadbdbadcdbdaccbbaccbbcbaacbbcdbcaaddadbbddbcdacbddbcabcdbcacbaabdddbacbcdddbcbaddcaaddbbacbdabbdcbccaaddabaadbddacbbbaabdccbdbacbbadccbabadabbabacaccbbdddcbbaccaabdabbadbdbcddcdbcbcddccbdddadadababacbcacbcbdcccabcdcdccdccaddbddddcbcdabcdbbdcdcadadacaaaabccbaacabcdaaddacadaaacbadbdbaaccaacbbaccbbbaabdadbbcdcaabccbdcddaaadaadccbddadacadbbdccdaacbcaacadbcbbabaacabadccbabaaddbbacadabbabacdacbbcadbccbbcbcdadaddcccaadbacdbddcdcabbaccbdbccabdbdccbbbcbddbbdbadabaaadbabcacbdbbabacadcdcdbdcbaddbbdadabbdcacabcdcddaaddbcbdbbddaaacdabdaacaabcbbdacccabcdddaabadddbcdcccbccbbcccdadacbbaabdcacbaadaacddbadcabccddcabcaacadaddaadcdadbcaccaabbaaddbadbaaddadcdcbbcdaadcdabadacaacbabbadadccccbcabaabcbabcbbcabadaadddcacacdabcadadcdbacaacbdbddcbadabbcccdbacdccbabcbbabcdcddaaaaacdaadbccbcadabccddcdcdbbdbdbabaaccaaddddacbaacdacdddacccaabccccbdaccacccccaabbaccdcabbdcbcddbcbccbaadcddaccaaddacaacbdbcbcaabbbbdbbcdbcdbbabbadcbdcdabdbcadadcbdbbcacadbadcbcbcdadddddbbccccdbccbbcaddcbcbaaabacbcaaddddcccdbdbcbcaccdcaabcdbbbcabdddcbcabddacccbcadbbabcbcbccaabddbadcbdbbddddaadccdacddbcbacacbcbabcabaabadcabcdcaabdccdaccbdbcbcbacacbbcbbbdddbbdcbcdcabbcaddbbcadadbddcbdccacccaddaacadbddccdaddacddddcdccaabaacbcacdabcdbccddbdddddbabbaabbbadacbaacbdcccdcbdbabcaadadaaadbbccdcdbccbccbcaaabbcbdbdcdbaabcaaccdbacaacdcadbadacacdbdaccaadcdbadbcbdccdbbddbaddaadadddcaabbddbcadaccacdacccbadccdcacacaabbddddbacacacaacaacacbdadcdcdcddbcbbcbcbcddbccbccbcaccdcacdbcbdbbbdbccbaadcadaaaccdadbccadcabaabbdcbcbaddadadbacddaabcabbdddabcbabadccabadaacccdcababacbdbbcdbbcbdcacdbcdccabcacdcacbbdccdbbdcaaababaddbaadaabccdbbbdaaddcbdabaaabdbcbdbcdcbadcabcdabccbacbccbbbbbaccdcbccadddccaccacccdabaadaaacbbcacdacaacacdabcbadcaababdccbdbbbdcdcbddcdadccadabccdaadbaaccbdbbddcbddadbacacaadacacbcdaddcbccadcdbcbdbbdaabbaabcbddabccbcbdcbaadcbbdddbddccaccaababbcccabbdddcddbbccbbdacdbaaaccddabbddcddacbdaabbcaaccdbcbcabdbddbcbdcbbadbbabcdbdbadcbdddcbbcdacadbcacdaadbbdcdbadaabcddbadcdcbbbdabccabaabdbaacbadaaacbdaccbcdbbdcbbbcaabadcdbdaababbdabdaaadaaabcaaddabcccabdcaadbabccbdaaddbcdacddacacadbacacadcdbcddbdabdacbdcddaccbbdadbddcaccaadbadcdaacbbcdacbcbadcddbccbbcdadcbacdcdddadadbacbcdbdccadbabccdaddcdbdcdccbaccbcddadbdcccdcbabbbadaacbccbddddabdbbcbcddbabadbbaacaacbcddbdaadabddbadaddbdabbbcddcaddcdbcabaccccaabdcacadacccdaadbaccabacdccdcbccdccacdbaabdcaccbccddbbcbccaadaccaaaabbbacbbbdcbbdacbccabbcaddbbcddcdbcaabcbbccadcdbaacdacdcaacddbccdabddacadbcdbccdacddabdcbaadbacbbdccdaddbabdbaaadcacdcdbaabcbbdcaddacadcbdbcdcccaadddcddbaddaabddbaaacaaaacaadabdabcdddaaadbcbadbadcadccbacccdadcddcbabdcaacdddbaaddbbdadaaddbaaadbcabaabbadddacaccbcddbaccccbdddbcdaacadbddcaaaccdddabcddbcdaacddbaadadacbbadccaaaadcbaadbabcdadacbdbdacbbcdcbdbbdbabbaadccbcdbdcbacbacbcabdcdddabbdacdbdcaddcadbddbacaaaadddacbcacbdbacbbcbcaacbcdbaabbabaabdcbdbdadcabbdcccadaadcadaacdcdbabaccbdccdddbdabcccdbacbcbbabdbddbbdddaabcaccabbbaccadacbccccaaacdaaabbaddcccbdddabadababaadbbbadabdbdabbdccacbbcaaaddabcbdbdbbbacdbdabcddbabbaacdcbddcaabcadacadbcabadbdbdbbcabacdbbbcdccdbaaaddcbcdcaaacbaccbadccbbaadacdbacaaccbdcbdcbadcaccdbcadbadcaadbcaaddadacbcddbcccdbabdaccddcdbddaabcacccaaccbdaccadaabdcaacbdbccdbdcaddccdcabdccdcddccdcbdbaddabaadcbbcdbcdcacabacabbabdcdcaddcdccdadacbbababbccdddbdbcaacaaacbcbabdccbcadadddcbbddcdabdaaccdaaddcdbacdabbadbcbbabdccabdcbdcabdabbbbadddacaccccadaadbddcbccbcacdacbbaadbbababbcbacddcbccdbacbaddacddccdbadbccadbbacdaaccccccaabdaccaabcdcabadbdabbbbcdddacbabdbaccbadbccabdacdcbdaaaaabacbbdbbdddddadcabaaababaadccbaccddcbaabaaadcbaabdbdaaddcbbcadbaaccbddbacdbcdcbbaabdadccacbbccbacdbbdbdbcdccbadadbccdbadddccddbaaabbbcbbacdaabaacabbcbaccadbacaacdaddbdabaaaacadabbddbabdcaddacaddbbabaabdcddccbbaabaaacacadbddccadcbddbacddbadcccdabacbcbbdbddbddcbdcbcbbccbbcaabacdaacaddacdcacaabcabcbbdbcccaaddbacbbbbddaaadbcbddadaabdaaabcdbadccdadabbcbdcabcdabbabacaaaaabcbbabbaabddccbbccdbaddcccccbcabbcaaadaaaabbdbdaadabcccaacacbdcadacddbbacddbbcbdaaccacadaadcccddbcbaaacdaadbbcdbadabaaaadacdcddbbcddacdabbbcdbdddbbadaaadaccccbcbddbbaadbadacdadddcccbbcaddabbbaacdadadcbdadcccbcabccdccdbcccdcdaccdadaabdadabaccbbaaaaaccbbccadbbbaadadbdadcdbadbcbcdacdaabdbcadbdbccadcadcdddbcbcdaaaabdcdadadbbdacddadcccdaddcaabbadabccadadcdccaacadbacacabcccddacdabaadcddabdbadbddbaaabddbcddcabddabaaaaddbbadddbacdcbabbddbdacdadcdacbdbbbddadcdbbdaaddcddcaaadcacbdabcdbaacadcabdaaacbbadccddacabbaabcddcbbbcdcccbbdadddaccababbbdabbbccadccdcbadbdcaaacdbddcbdcacbbcdcbabcddcaccadbabdacccaccbccacdddbadacacddccdccdbadbaabaaddaacddaabcdadbddbadbdcbdcabdccdadaaaddddddbaabccbbccababdbdadaacbcbcbbdddabdabaccadacccbbcdbcaaababaadcccababcdccaacdcacabbaaadddcacdacdbcbccaaadacdccbaaabbcbbacaccaccabdddbaadbaaddbcdccababcccbabbccdacacbacbacabadbaccdcaccbbcadabaaccccddbabbdbcaabbddbbcddbcaccaaababbbbdcababaacccdbaccdcaaccadbbccbdadcbbaccdcbdababcdcccbddcacdaccdbbdabbcdcbdbdbabcbdaddddacbbdabaabdaacdcccdcbdbbdddabcbabcddbdbbaacbdadabbcacabdadddcbdcbabddacdaaccdbbcbdabdccadcdddbdcbcccbadcaadddbbddbdaddbccadacababbddbbdbdcbacdaaddadccadccdbcaadbdacababaacccadbddbdddcdbaadaadcbdaaccaaaccbcaacddbcbdaacbaaddacbcdddadccccbcdcbbaccccadbdddbdbdaaaddaccddbdccaccdacddcaabcdddabdacabcbacdaccdbdddddbdbbaacacdcacccaadcbcddcbadaadbadbcaaabcbbdbccdbacddabbacbdabcaddccabcbdbaacdbbaddcccccddbdcbbbcbccbbacabcdacadcdddcabcbdbcbccdccaccdacdbbcdccbaaacabdadcbabcccdcbccbcbbbcadbdadcdbbabaccbdacacabdcdbbddccbabdbbadcacbacdcdcdbaaadaadcdacbbbadacdcbccbcdbdaacdbbaabdaabdbbadaacbbddabcdadabddcccbbcbdabcabbcabbbcbbdaaccaabbaababdacddcbabccaccdcbbbbabcbcacaabdbaabdcabaaccaccbbaddcbdbcbacacbdbaaaccaacaaadcaabbcadcdccdbcdcbaaaddaabcdcccbcaacabdabbcbdcadcccdaabbdddbcbdaabdddcdcdbadbbdacbdcabccdadccbbaaddbdddacadaaadacbacccadaaccabaabcddabdacccdbdacbcdcbbccababbcadbbaaacbbbacdbddccbabbadbadbcbabaaabaacbbddbaddcccbcdabbcbacadcdaaaabacbacaaaacadacbbcadaacaddbbccadbdabaaaaaccababcbacdbcbaaaadbbbacddcadbaaddccdbddabcccaadddcbabdcbbdaabddabcbacdadbabbaccabdbcaacbbbddbddcadccddccbcbaacacdabdadbbccbacadbdabaccbadabcbacabcbbcbacaadaadbcddcdccdbdabbbcbdcdbdaddccbabccaacbbcdcaabbcbaccbddcdcdddbaadbaabcdaadddbdbdadccdbabcccbcbcabcbcdcadbdaaadbdaaccabcaaadddadacdaddbddddcacbbbaddaaddcccbccccaaddddcbccacdbdbddcdddbbccacaddbabcacddbbdacbdcaccadbdcadacdbbcdcadccaabbdccacdcacddaacabbabbccacddddcadaacdccaaabcbcacdcddcabbdabaadaaaddbccccaadabadccbcdcbcdabcadaddbabdcdbcdbbcabddccbbadaababaabbbdabbcabcbbccbdbbccbddcdaaddcddcaccbcaaaaabacbbccbaabccbbbcbacbabacdbaaadbcadaadcdadacbacacacabbcbbdabcdadbaaacadbdddcdccacddcdcddabaadababddbadbabaddccacacabbcbdbddbbabbaddaddabddddadcddbbddcdaccbacbcdcdbbdadcbcacaccccaacbbcbbccadaadddadacbacdbacbdcbabccaacaaabbddacdbddaacabacbbbaadababdcadcddaadacddabbbcdcaadccdadbbadccdacddabbdabbaadcacddbccccaaacdccccbaabcdacbbaddaacbdadcabaaacadcddcdadbacdacdcccdbabccbdccddddbcbccaadaaabdaacacbbdcdccdacdcacacacdcdcddaacdacacdcbacdadbbadccabaadbadbccddbbbcdcbdcabdcdddcdcacdcdbacabdbcdacdbccabdbdcbcabdbbccccbcbdacbaddadddcdcddcdadbbcdbbbcccdcccdcdabbbacdaabccacabcabcdbbbccadcacdaaddcbdcaddbbbaccccdcaaadbabbacccaaaaddbdbabccacacbbdcddcbccbbabccbddbadadbaababbcaadabaaabcadccbccbcbccdbcccadcbdacccccddcbaaabababacabbdbcdabccddbcdcadddbbcddbbbdccdcabadabdcbbabdbbcdbdbabccbbbcddacabbbbdddbbdadbcdcbcddbabccaddcdcbbbcddbddcacdbdaaadcdbaddcdadbbdccbadbaabcdcadbacaccdabddcdbddabdadcaabddbcccdbbaaddbaaabdacbcaadabcdbbddbaccbbdacdabaacabcadddbbbcccacbcddbcaddaaadbbabaaddacccbaabddccdbbcdabdcbdabbdbaaaaabcdcbcabcbbccbaaabdbadcaaaacbbabacddddbadbccbcdbadbaaaabdadabbbbadabdccbddaadbdbbbaccacdcacbbdcbddcdbbaaccdcccbccacbdaaaacbacddacabadcbdbbaaccaadbacbabbadbbacdccbbabdcdbbcdbbabdddcabbcabbdadcaabcacdddbcbacbadcdcddbcaacbabccdddacbcddabacdbcbbacacdaaabbbaabdbbccaadadaccdbdccbcacbcdbbbcdbabbbcacbbbdcdabadcabccdcadbbdadcabacdbaccaddcacdcbaaabcaaacbbbcadbddbcccaabdcbcabbccddbdccdccbaaaabcbcadccbbdacbbabccccacaaabaacbcaaaddbdbaccddadadacabcbbabdbdddccbcdacdccbbbdcdddbaabddaddbdabbbcbdccbadcdcbaddbbccdbbaddbccbaddbababaacdbbcbbadbddbcdcbdbdcdacddbccbcbcdcabaddbddacaadddabcddbdabbdbddaacbdbcbddbbcbccddcbccbdbaadcbdaacdddbbadcccbbbdbdbcadaabaaaddadbdbadbabdcbbccabcbbaaaaadadaadadbbcccadccbcbbcbccbaabddbdaddbcbccbdaaccacbbcadbbabbaddacadabbdbcccdbdaaadbdddbcbdbbcadcbdcdacccacbadcbdbdcadaddcbbcbdccabcabcabdaadaddcccaaddbabadcadadaacbdabbaaaabbadbdddcddcdcabddbabcbbdcadbdcccbbcbccdbcdbabdaabccaaabcaabdaccaabcabcaccdbacbdccbdccbdacdcbccbcaadcdddbaddacbddcddcbacbdadbcbcbdbacbddadadcdacbcaaadddddcacdbdbdbcbadbbddccbadbdcdabcabccadbcadacbccbcadabccdccbacaddbbcdcaabaacabcdbcabcbbddddabccddcdcccbcbbadcaccbbbbbdadddaadcaabacbccabdcaabbbadbcccdcbbccddbbdadccbbabdcaacaddabdccdbaddaacbbccbddcdbddccbdbbbcbadabbbdcaddabaabacbccdbacbbaccdabddaaadcdaadbadabbbcccdbddbdbaadbdbaaacadcbcaccbbcaadbcddbbadaabbadcabacabcaaadbdbbcbadcddcacbdbcdddcdbdbccdadabbaddadbcbbcddaadadabbcdbcbcbabbadddcadddadaaadabaddcdcbccddadbaadbbbdaacacdabdccaadddaddaaaaadbacaddcaadacbdcdadbbdaadbcbabdbbaabcbadbabcddaacaaabdcddccdaaacbbddcbaacbdcdccdbddabcdcababdbcbdadcabbccdcddcbcdcaaabdaacddddabdcbbaaabdcbbcdccbcdbaadccabbacdacbbcadacbcbabcbbbbdbdbdaccddbbaadbcbcacadadbdadcaddbcabddbbdcacdadbabddcaadccccddcddbbacbcbcdddaadbdbabaabbdbabdadababadbccdaccaabdcbdadacdaccadaacaacbaddbaabbdbdddbccdcadbbdcbbdcdcbbabcdbbaabbadbcccdbabcdbadbacbbcccabddaaadbcddbbdbdaaabadddcbccaaabacdcaadcdcbcacacacbcbcaacbdaabdbadbddbcdcabcbbcbcaacddabcdbbcdbaddadaabbabcaaddaabddcbbdccabbcddbcddcbbbdbdcbbbbcbadbacadccdddbbabccbccdaaddaaacabdcacacdccbdabbacbdddcacabbbbcdababdaacbddbadcaadcdbdbdcacbcabdbbaaaddadacbacabcbddacdcabacbbdaacadbcaddcaaabadaabbacadaabcdddcdbdbbaadcacaccccbabdaddbdbdaacdbbbabbcbcaaddadadcbdcdbbdcbadcadaabbbcbaaaccddcacbaabbdacadbdcaccdcdacaaaaccdabacbaaacdadcdbbbcbdcccccdcbddcccddbbddccbabddbabcccacacdcdaacaaabbcadcccddabbbbaaabdbbbdbacdaaaadccdacbdccabbcaccbaabdbdacbdbacbccadcacabcbbcaabbcdddbabacbbccbadbdddcdbbabbabccdcbababdcbadccdacdbbdbaadcbaacbacbaacabdadabbcabdabacacaabbdbaaaabbbdbddabaddcabbcaddcccbacacabccccbcdbaacbdcbcabcdbdabcdaabdbaabddacdcacbcabaaabdcaaaabddbadabaddbcdacabddadbdcccbbcbaabcbbcdbcdaacddcadaccdbabbdccbdbccacabdcadadddcaccbabcaaacbcabcdadcccbddccabadcadacccdbcacccddabbcdbbbaddaaabbccbcddbadbdbcbbcdbdadbccdcabaadbacaabcbdbbcdccaaddaabaadcadddddabddbbdadcbdbbccaadacddcbaabadadccdcacaddbcdcddddcddbadddcbbdddcbcacacacdbdadacddaabcaaaccdcbdbcdccbaaadaabdcabaabcddaabaaadddacabacddaadbacadbbabaaaadbaddbbbddaddcaddabbbadbbdadccbbbabccdaacbadaaadacbcbbadabbddddcddcccddcabcadcdabbbcaabbbdbccadbbddcbcdaadabbacddcacbcaaaccbdbcddcbccbbddaaabddddccdbbcdbdadbdabdadadbbdbbcbcccadddbabdcadaabcdbaaacdcacaaababbcdadbaccadcccbbddadcababbaddbabcaabdadcdbdbbaddcabadbbbaacababbdadcddbcbbbddaaccbcaadcbbabdcdcbbbdacdbddbbdcaadbaabcabbcbcdddcbdacaccbaaadbdcdcaadcbbaadabccdbccbcbccaaacbccdbbabaddcadaacddbdcdcbacbbcdcbbdabccdadbbadbbdbbdabbddaaccbbbbdaccbabdbddbbbdaacaabddbbbcdcbabbadaddbdcbcabacaaabddcbdbacbcccacccddadddcadcadbdbabaadadabcabddbbcadbdcadaddbcadadabadddcccdcddcbaccdbddddbbaddbabbaadcdbacdcdddaabaccaaabdbdccaadbdddabcacbcabbcdddaaadabccddddbdcaaddabdadaabcacdbcbcbaddadcddbdccccdcccddadccdacbdbaccadcdadbbbcdcddadcdddabacbbabdaadbabdbdaaacbbaaddcdabdaadbabdcccbdcdccbacdbaaacabaaadbacdcdbdadbdcbaccbadadabbbccccbbdcdabdaaabcdaaccadbabadbacbdadacabdabcadbcdaaccbdcbbaddabacbdababcdbbccabddacadbcaccbadaacdcdbbaacbcadbcbdcddabdbbcbcddccaccadacccadbdaabcdaddddacacbddcaccbbcdaaabbbacaaaaadcbbabcbbdbdbdabcddabdccbdddbdacbdabcacbbdbadcbbabbbadcdbadbcabdbdcabddaadcbcdcaaadbdcbdcdcddcadddcabccdaababbadccbcbbbdabbcddbaddddadddbdadcbdbbacbbcbabdddadbbdabadadbdccdbacbdcdbbbaabaaadababbbcacccaadaddadbaccacdbacdaadcababdcbbdaddbdaacaabbaabdcbcdcbcaabbcabdcadcbbbdcccddcbaaabbccbbbcdcabdabbbbbaacacdaabaababdcaaabbbdbaaaabdaccdddcbbbbdbaadacabdbbdcdccccaadacddadadccabcdbcddaacbbabcacbcabbbbbacbacdcdbdcabdddddadccddcdbbcacbcbdcdcbbdadbccddaaabacbaddddbbbdcdbaabcadbcbcbcababcccccdbbddaadcacddadbbcabdacbbdabcadbcbdccaccddcacdcddcaacbcbdaddcbcacaabccddcdcaabcccdddccabcabbdddbaaddcdacccadddcbcdabbabccccbaabdaadccbcbdaadcbcdddddbdbbbacddacbdcddbacbdccbbccdacadbbababcdabacbaaddabdbdcbbdbcdbdababaaabbdabcdbcdbbcdddaddbcbdcacccccacbbcaaacaabaaadcbbbabbcdacdccccdcccdacbcbbadbcdcdbbaabdcdcdacccdacdacbbcdccdbbaddddcbbdaabcacbbbdcaddaddcaccccdbadcacbadddcccacdcdacccdccdabcbadabaadcacaccaadbcbccababaddcabbaabcabdbdcadaaddaadcdabdababcbbabcbcbcddcbaccdbcaabbbaddbcdcabcdbcbccbaabbabdcbabcadbdbcaaadcbacaacbbbcbbdccbdcbbbcabddbcddddacbaabcccddbabbdcbddbdaadddbcdbcdabccadcaacaacccdccdaaadcccbdbcaaacacadcbacaaadbaccaacaaaccaccadddcbcbcaaaccbcdcdadadbcadaabcaacbabacaabbdbbdddbbadbcbcbddbbccababaabaadbddbcbcaddcadcdbdccaaabbcadbaadabdbacadabbddabcbbcdbbdabaccadbcabbbcdccddccabaadbadcaadbcddbbdbbddacdbcaccbccdbddbcbbbadbacbcdabccbdbaacbabdabbdacddddccdbcabaabddbacdaabcbdabdcddbbabcabccdaacdaacbcddbbaabbabddddbbacccbadbaadbdbcbcccaddbbdcdddbbbbcdcddabaaddcadbcdcdaaddcacbbaabdadbbbcabcadbbdcabcddcbdcadbaddcbcddddabbdcccdacbcacbadccdbdbcdbcbaddaabcaaadccbddcdbccbccababbbabacdabacbcbdbaccdaccbddaddcdadbbcdccbdccccbcbcbccbcdaaaddabaddcbddabbabaddbcabbaacdbbdadcaaabdacbacaabddabbbbdcdbddadcacdabbbcadacbcddcbbacbddbdcbbacaddbdcaddcddabbcddacdbbbbccdbaacdcbaccbbbbdcddbbbcccacdaaacacbccdbcdabaaacabdddcadcbaaabccccabccaadadcdbdcadddcdadabbcdadbbadddaabdbcdcccdccdbcabbbcababccbddbadcdddbcddddbbdbcdabdacdaacaddccadcbdddabdabbcdbacdabddabbaabbbdcbcbbabbbbbbbacdbddcdbbdadaaccbdaaacabdccbcdbbcccbabbbacaadcdaacccdcdcbdbccbdacdcdbaaaccaccacdcadadacbbacdbccaacdaaccabbadacaacdacbbaadbddcddddcdacdcabcbacdbdaddbbbabdcbcbabcaacabdddababbdaaaadbbcbabbbbbbdddaccbbcdbbadbacbacaccacdcbcdcabdbcadcbdbdbcdcadcabaddcdbdbdbbbdacdadacacbbddababacbbccdabbcdcdabcbdaaaaccadcabcdaaccbbdcbbdccbbaadaacbccdbddbaabaccbaccaaacdcdddcdabadacadadbddccbcadaabcabcadbabaddaaaaaaccadccacbdbddaddddabbbcacbcbccabaacdbddacabaacddbdbabdbbdbbbadccabbdabcacabbdbdbadabdbabbdcbdadbadcdcbabbcbdcbadababbadcbbcbbdacbbcdbbaabdcddbbbdcbacccddcadadaacdcddddabdcbbbdcbcbaacdaddcbbcbbcadabacabadbbbcdbcabcbcacdcbbccdabaabdcaacbacdabbdcddbbbcbccbadcaadaabcccacbcacabdcbabadccaccdbdcbabcbdbdbbdbcdccccdadbbadbabdbcdddcdbdcaddbbdbbdbccbdbadcbdbaadbabaaadddaacdabaddbbaaadccbbdccacbbbcaacabdddddabcddbdbcdcbdbbaccbcbddadbbaadaccaacbcbbcccdcadcccccccbaabcbcabccbbcbabdcbdbbabababdddcdbdaaabaaaddcacbcbcacacaaaccabbaadabdaacdabcbdadbbcacacabbaccdbbbabdcddaccbaacdbddbcbdcccdcaacaddbdabbadbbadacadccabcbaadaadbdcdbdaddddacbadabdcacadccccdbabaaabdbdabbcacdbdddabccaabdbabcbdccdbcdaaccdbcccbaacddabdbccacacccdadcbabaadaddaadbacabbcddbdabbbdbddaccddbcdaccabbcbacbccccdcccdacadccabacbbadccaabadbbacbaddcbdbdbbaabcbcdcdddaabcbaddccdddcbdacaadaaddbbccbcaabaadaabbbbaacaacaccacaaddcacacacdcaacbcacacbcbdbbaabdbcacabcddcacdcdcdccbdaabccadadcdbababbabdbbbdccdabadadaadaccddccccaddadbbdcaaadabbcddbcaddddccacadbddbbabbdacaababaadbbacbabbbaabdbcadadbaababdbbdbaadbbacacacdddbcbbbcabbbcbaacdcbacadcccccabbdbddcbbbbdadabbbadccddadacdccaadcadbbbcdaadbabccdabaacbadbbdaccbdbdbacacabbcaaabdbaacdbcacbacdcbcccaddddacccbaadcadcabbaaadcaddacbdcdcbbdcadacdbdabcdbdaadcbccbddcbadcbccbabcdcbdbcbaaaaaacabaddbbabdbccdacccbbadbddabbdbaccaaabacdccabddbcbaabcacadaaadcdcdcdadcacdcbabbcaccbacbcbdbabaabadbdbdddbbcadaddcbbcaabbbbbdcbbdcacadccbaccbbacdcbcdaacdcadddcdbcbbaaddacaaadaaacbccbbccbcabbcaaddbbabcabdcbabdcdbbcaacdaaaccccbbbbdcddaccdbaaacdddccaccbbbbaccbadaadbbaabdbddacdacddcdcdaccbacccaddabdcdabaaacabbcdddaadbbdbbbcddbbdacdcbcaabdbdadddadaddbcabbbabbbdccccacccabacacbdbdddcdccdbcadbdaddabdcaadbdcdbdcacddbbbbbacabcdaaddbcccbdddbdbaaaabcbcbbbbdcddbcdbdbdbbcbabcddaddaacdbcabbdccbcbadaddaaddbcadaadacdbcdccccacdbddadbddccacddcdcaaadccadbdcccadcabbbacddbccabdacccadbabcaaaaabaabbddadcccbcacaacbbadcaccdcbdddcccabcacacdacadcaddbcdcbabddbacdbccdcadacbacbacdcaabddcdcaabdaabcbcbdddccdcccdcabaaccaadbdcabcbccbcdcdbdccacdcbcabbaadcdbcbabdcdccbcdabadadcaddbdddcbaddbbadcacadadcbaaacabbcdbbdddcbacabdcddcabbccaacabcbabababdcaacbaadaadcaacaaccabcdbbdbccdbcccbadcacdbbdcaadacacbabadddbdcbccdccbacabacbdcccddccdccbccdcccabcccdbbcddbadbdbcaccdcddadbcdbccdcbccaddaccbdcbbaddaadcddbcabadacbdaabdbbdaababbacdacbcddcdabaaccacdaaabaabadcdbbdaddaccacacbbddcbdcdadcccaaaacbaabdacdbbbadabccbcbdbdaadacdbbacddbcdaadaccccddbdbbaacacbcabddbaddabadbaaabaaaadbbacdabccdcbcdccbbadcdbcadaddadcdacdadbcbdbacacddabccbbcdabbddadbaadabddaadacdcbdaaabbcaaacdcdddacabccdcbbdcadcdccdaacdccaaabcadcabcdacdbddbdacbcdbacddddabbaaccddddbdccbacacdbadbdbadbbbbcccadacdccacdcadbaaacadaadcbadbdbddadacbddcdccdcaaacbdaddcabdcdadcddcbdcccdbcccbbcbcddcdbcacabbbbaaccbdcbabaaabcdcdbcbbaccbdccdbdaaccbabcbdaaaadcacdcbccbbaaaddbdbdbcbacdaadcbaccddddbddbccbcacdabcabacbddaadaacbbbddccacdbbdbdadcbddddccdccaadadcbbadadabccdababdbabdcaabcadacccaabbdddcccacbcdadcdccbdccbbbdccaaaadccddaacaadccddccbbbaabdccdcbdadbdadacbdcbccdcaccbccaccddbdbaababbccbabdcccdacccbadaccaccbdddacabcabbcbdcdbdbacadaacabaacaacdaacdddccdbdbaddbbabdcadcdbbbbabdbabbccabdbbcbcabccdcabcaabbaccaacdadbcdbadcbacdbabcabcdddaadbcbadbcbbbaaaabdcccdcdbbabdbbcdcadccbacdbadabbacacccdddcdccbdbaddaacbbcbbbdbddabcdabdabddbdadcccdadaccdcacadcabcbbabaddcaddadcdcabcbdabbbbdbdbaccccdbccdcbabdabddbccdcadddaacddaccdbcdcdaacdabbcbdaadbadacbdbcadbacacdbbbcbcbaddbcdcbadbdcccbcabcdaaaaaaabdcaccddbbaadacaaadbccbdbcbdadcaadacaccddbdadcadbbdabadbaabaccbaaadacaccbbabadccbadcacbdcdddadbdcaaababdbcdadcccaddaddccadcaabbbddaddcdddcacadacbbcccabddacccbbcbabacccdbcccdddbaaaadbbcccddaabdbccbaddacbbacdbcbadaababcadcddcbacbadbbacdcbcabcccadccdcabcbdddbcbcdabacbdaddcabcaddbbdbabbacacccdcacdbbbadcdcabcbbacdccddbcdcccacddacaaadddbdcabddcaccabbdcbdbcabcadcaddbccaaadcbbbcabbddbcacacbbddccbdcdcdcdbddbbbbbabcbdddaacbcabadbacaabacabdcddaaddadacccaacbabcbbadaabdbbcddbbaabbbcbbbbdcabcadbaabdbcdccdcdaaabadaddbbdbaddcdbacaaabccacdcdbacbbbdddccadaaaabbdcdcabdcaddbcabcccdccdddbabcababdcacccbabdabcbccadabcaccccddbdcbaccdaccdccccabbcbabdaaaabaaddcccccddabdbcdccbbbbcdbbbcccaabccacdbcaaccdcaddbdaaccdaccabcbcadabaddadcddcccaccddbbdbdaadbdcdcdcccbadadaacdddababcadbadbabbaaccdcccbdacdcbbadacdbdbaacaacbcbaacdcccdcdbddabccdbdaaccbdabdcaccdbabadcccbabbbcddcaacaddcabbdddacccacabacacbcbdbbddbbbaadcbddcadaacdbbaadcabaaccdadacaabcdbbabdcdcdcacddaacbdacdadadbcccabccddcaadcdccdabacacdaddbaccbbbcabcbdcdcddabdcdbabbdcdbbbbbaabdaaabcacabcbcdbdaddcababbbcdbbcaabcddbacbcbbddcbcbdbbcbdbdbbacaadccaaccbbcbbaabadaabaddccccbbccccaccbadacccbcbdaabcacdacacdaadccacbabcbacaacbcaabadcdcbbddbdabaaaaccaadcccadccaaadddbcbcabaacacddaaadcddbbcdcdddaadccdacaaabdaaaadbdadaaadddcdbcbbccbaddaaaaadadaaadddddaaabbcaccdcbccbcccdaabbacbcbbddbacacbddadabcabcaaacbbbbcbadbabbabdcdadbbddadaabcdccbbcdccacccbcdaadddddcabcdbbaddcddcacdaaacbdcdcbababbbdddacdabccbdbdadcbbaddabdaacbdcadaacccdcabbabccccabbbcdbddddbcadacbdcaabbbccddcdcadabbcbdccdddccbdadcdcbdccbabbbbcadddccdadccbbbdccaacaaadccdcdcbbddacacddccdadbacddcabcbcadbabcacaabdcadbadbabddabddabadadcaddbdadbaacabcbdddbcaaababcaabaaccbabcdbabbbcdbdaaccbbcbcdadadddbccbbdddabadaadbbdaabaabcaaadccadacadadcdcadacadcddcdbaabaccbbacdabbdcdadbcdaddbdbdabaaaabcbcaddccbabcbcccdacdabaccccbadbbacbcadcbccabbcbddaccccaccbdaaaaaccccdcaccccaacbdbacbacabcacadbbbcacdbccccdaaccaaadabaddddcdbdbbdbbabdaaddcdccdacdbccbcadabacbdbdacdcbbacbdaaacdcabcdbbabcdcabddcdbaaacccacaabbaabbcdbacabdbcccbdcccaacddaddcaccacaacadcdadadddacbcbdbacdbabdcbadbdbdbcdbadcbbaabcbcdabccaababadcccdbdaaababbccbababcbbdaccdadddcdccccbcbdacddcacccbbabaccbdabbbdadbaadcbdbdcaccbdacccbaabcdbacdcdcaddbdbadacbaabaaabacddddcbadaacbaacbccabddaddbdacbabbdacdadaadcbdbaabaaabcbdacaaccccccbcabccbccaacdcdbddbcbdbbbbaaacdadacbcdddabcbdaddadbdbabcbababdcddcadbdaabbcccadadccbccbacbdbcbcbbddadaaababbccacbcdcbddcbbdccadaccbbbcbbdabdbbaccbabcabacbbcbddbbaaddddabccdcddaddcccadbadcddbaacbbabbbbdcbacaddacbcadcaabdacdcccddaaaadbdaddcccdcdccabcbdbdbabcbabacbddaacbaabaccbdbbdcbcdacbcacadabaadacdcdcbcbbdabbacacdddccacdbabaaacdcbbcdddcabdabacbbabbabddccbacacbdccaccbbcbacbdadbbadabccacdabcddbdddcccaaddbcbdacbaabddaccdabbbbaabbdbbdcdbbcbbcadbbcabaaadcdacddacdbabbadcdccccdacddabbcaccdbcbbcacdbcaadacdbabbddddcbadbccbdbcdbcbdabcaaccbacbdaddadbcddaccbcadbdaabababddbdcdccacaadcbccdccbbaadccabcaaacdcbdcaddcababddcddaacddcccaddaaabccaddbccacbabbcbddbcbadaabddbcdbbdadcbcabacbabaadabccaabcacaaaddabaacdcadcdccdaacddaccacdbadaccbaaddcaaadcacccbadcacabdbbbabacbabdbabcacbadaabbacdbcbbacbcabccbddbbccacbaccacbacaaccbcdbadddabcadcacadbdbcdccbcdadacababdddbbddadaabcddcacdaadaaabbbdddacddabadcacdbacaaaddbddacccadbddcadcddccabbaacddcdadbdacdcbccdbbcacbcadbdabacabbbdcdccadddaaabdbaabbbbccdcdadcbdbcaacdccdcdcdacddabddbadcadcbaabaddddcbbdbcbbdbdabacaccbddbadacaaabdcacbaddcbbabacdbdbbaacadcdaccdcadbbbabcaccacbaacaabcadccaabcdddbbdbcdccbbcccdcbabaaddcddcbcbdcbcbddaddaddcdcddabdcdcdbcabbcbbbbbcacdbbcbdcabcaddccacbbdaaddaabddbbbcabcdbdbcdbdcbcacccdcbbcbdcabccdabdcdddccdbccdbbdadddcbdddccbdcaabadbcadbababaccbdacdaabdcdcadadaacbcbdcadbabacdacccaacbdddbbbddcdccaaadabdcbcbabaccacdacdbcddcadbcadabbdaddacdcddbbaacdcacadaaccadcbcadacbabdbbccdbaaadbabcdadccadccbbdabdcbacaacacadabbabcdddcccccdccdbcacddcaacdbcbbcbbbbdcddcdaaabccabccbbcacddddbacadcaccabcdccdcbcacabbaccaabaccaadaabaccdadccddabbbdcbcdbbbcbacddadcbaaaaacacdcdbaadbbabdcccacacbadaaadaabccddaccccbcdbbababadbcacbadccacbccbaaabaddaddccdaaaddbdadbbddacddccbaacbbcdbdcdddbdabbcaadddbbabbbdbacbcabaacaadbbbcabbdacdbdbdbdbbcbbcdcbacdbaaaaaacbcccbdddabcaccccddbddabadacaddaddbadabbccddacdccbdcbccbbcacbcabdcdddbbbdabbdbcabdbbcdadaadbccbcbbdcbacbcdbdbacabcdccaabddaddcaaccacaccbbaabbdbacccabdbacdcadacacbcaabadbdacdddccbcdaccaccaddabdbdbadacaddcdaccccdadcadacddcbdbdcbbacaadadacaacdbacbdabaaddcbdcbcdabcabbbcdccaabcdbbdadcaabbccdddaadbacbdabbdaacbcaccdbddcaccddadadadbddbdbbbcdccdbdbcbbdcddcbbcabbddbccdadbbbbcabadbabcabccbaabccbbdbabaabacbcdccdaccaaacadabaadaaabbadbdcaddcacbcbcacaccdbbccdaacdadcdddcdcbaadbcaaacabaacbcbbabdbddabdabdcdbacabddcdccaaaabacabdabbdcddcacadccdabdbcaccbbcccbabcbaddacdcabdddbdaaacdddababbabcacbaddcdddaaaabdbcdbcdccccaccadabbaabbbabdbbcbadadddcaaabbaaddccbcbdcaddbbddcabadbddcdcaacdbbbabdaabcbdbcabddcbabcdacaabbbdcdbdaddddadabcdccabcccaaacdcacacacccbbcbcadbbcdcdaaacdcbcaabdccadddbcbcdccacdbaaaaddddddbbdbadaabcaaacbbcbbbbbadddbcbcbcdacbbbaccccdbdddcddabbabcbaccbcabccaaaddbbdacaddabadccbcbadacbaadadbbacdcbcbcdbbdbdbbbbabbacadadcdaaaaddcaaacbbadbbbddbbdcbbaaabbcacdabbddadbdadbbbbadbaaadabdadddcbcbdcdbdbbacbaabdccdddbabdddbdbaaccccacbdcadbadccccacbacadcadadddbabaaadaddcbcdcbcaadbabdbdcdddbdadbcaaacddadccbcadacdbacbdcbccbdacadadcbcadcddbdaacacaddcabdddaddcacadcbadababccdabdadcdbadcdbcdccdaddcbbcbacbcadcdbaddcaabdbccbbdddcbdddccbbdbacdadcaaddccccdbbbccdbabaadcababaabbabbcccadaadabdbcbddaaabbbbbdaaaddacccdbcaacbaddcbacdaacaccaaddcddcaaaabddbdbcddbdabbdadccbcbdcacbdbbcbbadccdccacabadccbbaaddbdadddbacdaaaaacadbabbabcddbaabccdcdabbdadbbccadabdbbcabaadbaacdbabdbcdcddccaacabdadbbadabdbdbbbcaccbcbddbbacabdbdbcbacbcbabbdadbcccdcbbbddcbdacdbbcdabddcbdcaacdbcbdbaabcdacaacdcacccaddcdcacbdacbccacbbaabdabbacddabdabbcadadbcaddcbadbaaccdbbbcbaadbbaaadcaadcdadacdcdacacccacdbaddbbdadbccdaaaccdaaadaacbbccdadacacabbbbccccbdbabcaabadaaabacccbdcbaccdacbabdbbdaaccaddbcbaddaacdddacabbbcdbcbcabbdcbddadccaabbdcbacbabbdccadbbadaadadbbdbdddadddadcdadbbbaabdddbabcacbcadbabbcdcabaacbddadacbbcbccbbaadbbacadadbabcaaaacdbacbddbbbaadbcbbbcacddcbddbbaabcaaadaddbbcabaadccaaccbbdbacabdcddbaadabbabbcbbdadbbacccbdbbbcbbbdddaaccccabcbabcdcabccadbaaadcabaacbdddcabccbcacaadbdcadabccbcabcadbccddddcddabccabdbaddadddaddddcbabdaddbadbdddbaadbdccabcabbddddaaabcbbacbbcbcdddcbbdacbaccadbdcabbbdccbcaddcbdcaabdcabbcbadbcadddbaaadcccaaddbdddcdbbbacdddcdccbbcddaaaccacbcdaaddccbdaabbaaaccbddadcbccacdccdbbcbbadcdaccddacccbbdadcbaadadbbddacbcddbabcdbbdccaadcbcadadddaadcbabdcddbcabcbddccddadcbbbabdaddbbddccbddadcdccbaabbcdbacdadacacaddabdcaaabbddabcdaccbdacdbcbccdccadaddaddcbbdccacdabccdbdcadaccddbcdaaddcacccbaaaccbddcadddbabcbccccdcbcbbdbbdcbaaaaccabdcdbbbbcdbbcabadbcaacdcbcbcabcdddacbcdccbbaccbddbbbacabccdccacabdbdbcdabdccababbcaddcbbcbaccdcccbbdbabbccabadbacaadaaddcabaccbadacaaabaacabbdacaabcadcccdacabddcbddbacddaacbdcbabcabacbcaadaadcddbccdaadcdbcadcdbccbccbcdcccdbbcdbbbcbcadbcaaacaadccdadcdccdabbccbbabdcbabcadddacdaacccddacdbbdbcdacdaacacccaddbabcdbdabcacacaddaabadabbaccacaabdacccabdcccacbacdbdbdcbabaacabdaadaaabbdcbcdddcaabbcbcacbaacdbccacbbacabbadabbdadaddbaddccdbcdaaaacddacaaaaabaaaadbdcddcdcbabbcacdadbaaaacdbcbababbdbccdabcaabdcabbbadadcdcdddabdababacccaddcdadbbbbbdddabbdbcaaacadcdcacaacbdacccddadcdbacbccbcdaadacadbbaacaaabdbdbcbcccddcdbbacdbddccddcbaddbdbdbdcdcaaadaabdcdbccdbabbbcdcacddcaadbdbadcdacabacbcdcbadaabdbdbccdababbbdcbacaadbcbbaddacaaadacbabdabbdadacddcdabbdddcdcddbacdcabddcdcaaabaaccadbcccabccdbaacbaaabcbccaddbacabbacbddbddbccdaababaaddacaddbdbbcbcadcabddacaacadbcbccdcdadcdaaacdcdcaababacaabcacdbacdbcccbabbcbbbabbbbccababacbcdcabdcabacacdcdbacbbbacacaadbdccbababdacddcaaccdbaccabcddaababadccbadadbdaabccbadcdbdbbcbbaadcdaacddaddacaacaacacccdcdcadbdbccabdadddadbddddadacbbdcbadbcddbcdddabcccdbcbddccbadcbdccbdabcddbcbaacbadddabcdccddcbcbaaababbdcbaaadbaddddaddbdbaadabdacbcadadcabdcaadcabbcaacbcbcbbabcdaaabaabbdbabadbdaaabaaabbacbbcaabbdadcddcdcddbadcdacccaacddcdccacddaaaddaabdbcdabaccdcddcaaaccdcbcccacbccdbabcadbdbcdbcaadcdccabbcbbbcdbbaabcccadbdacbbbacadcaccacddaccababdddbbddbaabaaabcddbaadaddcbbdcdaabcdbbabbdcdacdacbdaccadbcbbcdddbcdbcdaacdbcbdacbbcbcdabbcbbbccbbcbcbddcdbcdcdadaddcdbbadcbbcadcbaabdcddabcbbaabcccaaadaabaadbdddbbcaaccbacaccdcdacacabddbbbadabdbcbdbcaddcbcdddbcacadbabacacdbadbcabacdadadcbdcbbbdacddcddbbcbddcadacadacdbbdbadbdaacdbccabcadabdbbccddbbdcbaaaadcdbcdddccdadcccadbbdcacacadcdcdabcbdccbbddbccaabdcacabbdcdbbccadaddddbdabcdacbabbadcbcadadbcdcbdbbabbadacbcadaadadddabacdbcaacaabcdbdbddacbacbbbbdcdaabdaddabaddaaabadccadadbccdcadaaabcddbaaddadacadbcdaaadcaccbcdabcddcabaacdbbadddbadbbcbdcbabbcdadaadbaabaddbcabdabddbdbdcbcacccbcaabbbabadaaabccdbbbdcdbbaacacdcacddbabdccdcacccbbbaaacbbdaadcbbbdcadcddadbbadbddccdcdbadadaacdcabbabaabcbaccddadcdbccbbcaadbbbdaccddabdabcdbdbdacbbbcabacbbcdcccadbabbdcbcbcdaabaaabddcdbacdbcdbcbcaaaccccbdcadaadcbcdddbabdcadddcaadaacabaaddcdbcbabdcccacbacdacddadbddbacdcbbcacbbbacaccbdcbaddddddbbddddbabdacacbaaaaacbcbcccdcdbabccbdccbcaabdaaabdcbbddcbdbbabacbdbbcbacabbbabbbcbcbcbaaddcdababacbbdabbbacbbacbdbdcbddbcbcdcdaadbadddcdbaaccaadccdcbbacdcabddabbdabcddcbaaacbdaddadacdaadcccabcdacccadacdaadbdababdabadcdadcdcacdcbccabaacdcdcabdcddbaddabbbdbdcbddddddbbdaddbdcaaccdbaaccadbbbcdbcccdbadbbbadccdabcabcaddadadbadcbaddbababcbcddcdabdcdcccbbbccaccdcbbbadacbcbaabddbccaadadbbabcaaccacabcaadbdabbaabaabbaaddbaddaaabaabdaccccacdabbcbacaadacbabbdcabdadbbdaacbbcadbccddbdbcaabdddbbbcddbbdabcccdddabbaccadccbbbdaccbcdcabdbcccdabbccdabadcbbcaccccddabbacadccdcdcddcaabcbadcbbadccbcaaabcdbbdbbbccabaacbabbdaabbbdcdaabcddbbdbcbdcbacaaddcabcddcddabbbaaddaacddadbcdadddaadccddccaabbccdcbddcabbcdbdaaaddddbbbabcccacbdcbbdcdcbbcaaaabdabadabdadbcddbabaacbbbaabaaabdddbaddbdbdddbabcaccddbbdbcbdcdddacaabbabccdacbabccdcccdadddbcbaabababadbbdabbccbcccabbbbddcbbbaddddcacabdaacbccccdcdccdabbdbcbcaaaaadbbbbcccccddccaabcaddcddddbbadcaadccbbadaabacbbdddbcaabadabbbccddaabadbbdcdddbcccadbabccaaabcbccdcabcadcabadabcadacdcdbbddcadccbbbdbababcddcbaaaabdbbcdbbcacbbbdbddbddacdbadadccdcdbbddbacabaabacbdcddadaaaaaddbcaabbdddadccabdcdcbdbccbdbddbbdcadddddcdacccbcddbdccacdacbdccdbbbdddadbcdbdbaabbacbdbddbcabdaabbddbaccbbbbbcbcdcdbdbcbbdcdaabbdbacdccabaaaacbcbddacdbdbbbbccadcdaccbabbdcddddbacdbbccddcccbccddcddddaccabbbcbcbadcbcabdaaacdbbbbbcbbacbcaddbaccabbaabbcccbbabaabaacbbdcadbcdaacbdbccdabababddddcacbabddcccbbaccaaddbcaaddbbdccccaadbaabbbbaaccbbdaabdbacbacbbbacadbaadcddbddbbbbcabadcaddcbabbabbacddcccbcdccbabcdbcbcccaaacbaddcbcdbccccbacddaabcdbddabbcdaadcabbdddccddbbbbcdcbbcabaddcacaccbcccabccaadcbcaaddbabbdbbccdaadbcdbabaccdbccbccdacbdcbccaacbbddddacbdaddaddccddbdcacddadaabccbbbbababbcbcbabcaaaaddbccdabdbccccadccdbbbcdbabbcbcccdddacabdcacadcbcbcdbaccaaccbadbbbbbcdabcbbacadcabbcabbcbdbcbcdcbbbabaccddcaaaaaaacdadcbdbbcbbbddadadaddaaaacaabcaccbbbaacbdbccabcdcabaccbcbddddddcbccddcaacddddcacdaaddaccccaccdcbbcddadcadcbbddcbdacacabdcddccbcaabaaaacddadddddadaaabbccccbdadabdaadbdddaadbdbabccdabadddbcdddacddaabdacbacccdbbaacdbdabadbadbdbdbdacbbcdbaddbbddadaacdbdcaaadacdadacacdabcbddcbddbdcdbdabbcbaccaccadbdacabadaacadcdddadacbcbdcdacbdcdacdcacdccaaababcdcbcdddbbddbcaadadbaaabccbadcdadbbbcdccbdaaaadcaccdbabdcbdccacddacbcacaddcaacabaddaababbaadccbaaaaddaacdaabcaddaaabaadcbabaaacdabcadcacdddbdbcdcddbdddadaadbccabacdcacbbbacbcdbccacdabcadabddcdcaabacdaadbddadcbddbdacadbdddcbcbabcddaccbbbccccbccccadcdabdcbdcabdccdabbbacbdbdccdccbdcaadddabaadcbaddbadaddddaaacacabcccdbbcbdcadbddbdabdabbdcdbdabddccdbacdbcdabcacdbdbbcdacbbcacacbaabddccbaaaacdcbcbdacaaaaacdbaacdcabacddabbbbbcdbacaabcccaaddcbabbaacacbddddacccdbbbadabcbbddcacdcdbcabccdcadbdcdcbdccbbcaaccccbbccdcaacbbadbbaabcabdcdbddaaacbabdddadabbcdcdcbcdbabaccaacaacdacabcdbdaaacaaabdddcacbcbcadcbaddbbddaaaacbacdcaddabddadaaccabcbddbbccbcadddbcddabaacaaaadaaccaabbcbdaccadddcacdbbaaadbdabdddcbddacddddbbbaddddcabcacadcaddcbbbbccdbddabbcdcbdaacdbdcbbbcbccababcccaabbaadabdccddacbbacbcabbdcdbdbbdcadbcbcbccddcdddacdabcdbbdaacadcbdadacadadccbaabcdbcdcbacaaaaaaccaaadcdccdacbacbdbddcacaccdbddbbcbbbdbabdcdddbddbbabbabbbbaadbcdcbcbdcddbdbbbadaccddccacbdcccdacbcccdbabbccccddddacdaabdbbcccbbcaadddbbcacadddccaddcbcabbbccdadcdaaacdcccacabdcacccadaccdcccdbdcccadadaaaadbdcbdacbddcbdaacccdbbdaccbcbaaddbdaaabdabddcacdaddbbbcabbbabdddbacdbdddcacbdcddacdbcddccadabdbbaabadccacdbdbdacccababcbbcaabbbcabcacccaddadacbcddbcddadabbcaaaabbbadcdcddcaabccabbabbcadcaccbcdbbaabadcbbbcaabddcaccabaadaadcacdcbcbcbddcbacbcbaddbadadcdbbbbdacbadcabcaadaacdaddbcadbccbbdccdabcbdaabbadacbdccbdbddbcddabaabcabadbcabdccdcdbddbaddabbcbdcbbaadccddabdabcadadbcabcddbacabbabbacacaccdabbdbaabdbbddbacbadaabbcabaddaadbcdaddbdabadabcbddbdbbbbbcaacdaccbaccacbbaadbdbcdacbadcdbacbabbcccabdccbabbcaaccdbaaaadbdcabcbacdbccaacbaccccdbcccaccbcadbddbdaaacabbcbcaadaddcdbdbbdabadabcdddadabdbbdcbdaddbccdadadcdaabaadcdaddccbaadabdadaccdddbbabdbacccbcabcddbdccbbdddbccadbadcbcdcbadaaabaddbbacabcbbdaabccdbaccabaddbabacbbbdcdadabacdcaabddadcccdcbbccbadadddbbdabdbadcbbdbabbcccbcccaccbdcacacdcccaccadaddddbadcbbddacdadbcdcacdccddbdbbaddacddaaccadbcdddbdcbcbddccdddbcaaacccaabbaabbcbddcaddbccccdbaccccbbbaaabbbadaaddcabcacbabcaaccddbdbadbbbcccadadcacbaadbacdbcccadacacabbdbdcabbdcbbacaaccbbcbdacadbccacccbccacadaccccaacdaadbaadbdccabbbcbcadadacdaccadabbbcacacbacdadbdddddaabbdaaaadcacaaddaabbcbbadddbababbdaadaadbacdabcddcbaaabaacdbdccdaccacbcdbddbacaadacdaacdbadbbbcbbdccdccadadbccbccdcbbdaacacdabbbbcbbbccaaabcaabcbdbbdcadddcbcccdccbbbbcbcbddbcddcbddabacadbbbdaccabacdcbccdddabdabacbbbdbcccabbbdcdcadddbaadbcabdccbcacddaaccdacabcbbabbaacacadbabbcddacacaadaabbacbccabccbbbbbdcabddabcdabdacaccbcdcabdbbababbbcbadaacbccdcdacabbbbbabcaaddbbcdaddadabbdacaddbabaddcccdaacdcdbacadbadbddcbdabbdababdbccbbacbdbcbcabcdcbdddbaababbcaabbcbacccaacaaababababcbdaaddacddabbbacbaaddbadcabbbbcaccbbdcaaabbaabdaabacabbabbcaaabcdcdcbabcbabbdadadbbbcbbbacbbaabcdbbaddbdcaacabcbbbcacbcaddcbaaacddbccccddacdbcdcdacabdcdbbcadbdacdabbbbabbccbcdcacddbaacabbdabaddbcbdcadbabcbcdddbcadbbbbbabadacbaccddcdbdbbccacdbdccdbbadbbcacdbcddacdabbdbbccababbaccdabadaaaddddbbdcbcccdbccbbbacabdcaadabaadcddbadddcabbbdbbbadabddcddddddcddbbacdbcdaadbbbcabaddaaabbddbacbbabbdbbccddcdbdbccdaabdabacccbcacbcdacbbddcccbabdbbbcbcbaabcddbcaabbbbddcddbcbbdbccccbbbbabddbdbadadccdcbdcdacccbdcccadabbcbccbaccacdaccbabdccbabdbabcadbdbbdcdbbdcabdbacdcbabdacdccccddaabdacdbcbdadbccbdbbdbdcbaccddcddccdabdbbbddbccbccdddabacbbdaacdaadddbdddbbbbcbbdddbbcdbaacccdcdcacadcadcbcdbccdaaaccccbccbcabdbbddcdddaabadabdaabbbadbdcbbbcacdccdbacdacbddadbbbcbcaccdbbdacddbbdccccbabdaabacccbdaaaddcaccdcdbacbcaadcaddbadddcadddabbdbbdadaadcbdcdbbdbbbdcaabadbcdabbdaaccaacdacabcdcbadccbdaaaccbcbccaccdadbcbddabcaaddbaccbddabcbcbabdbbcadaaacadabdbccbcddacdadddbcbbbccacacbacdddabcadbadabdddcabacdcabccdbaaacacdadabaacabbaaabdccdbacaccaddcbbacbdccbcbabbacbcdadabbdccdadccadbddbcdaddcdbcdaacaddddcbaabdcbbdcbaadbacdcbabdadaddbadbbabdcddbaddbdbddcddcdcbacbacbbcaaabacabbccbadacdccabdaccbdcdaaaddcbbccdccdbbcbaddbbacdcacddcadabaaacdbaadcbdbbdddaaaccdcbaacadcadbdcdbcababdabbccccbcadaacdacbcddccbdccdacccddacdbbccddadbcddcdbbacadbdbaabcdbbbbcdacdcbaccbbdbbdcaadbacabbbddcdcccdccdbccbcddaaadbacdaacbdbbccbddbbddadcdaddbabbbccaadbddaaadbbacabacddbddcabbccdcbadcdadaadbccddaaabdacbdccbdbadacccacadbbabbbacaaddababbcaaabdcabdaadbabcadbcdccadcaaaddaddbabcdaacacdacaadcdbadcbadcabacbbddbdaacabdbccbadbcdbddbddccdbbdcaaaabbacaababcbbdddcdbcadacaaadccddadadcbcbacbbbddcdaddbbbbdaabccbbbdabdcbccdbbaabdcbbbdddcdddadbbddacdbcaaabdddacabcbbaacabbbddbdddbcbcabadcaacbacadabbacbbdacbbbadbbdcbcddbbabbdccdcbdabbdbdbacadbbdadcadabdbcabdbbddbbbddacaadcacccaacdcacadabbcccdcddaccdadcbcacabbcbdbbcdacbbbcabbccddccaabbaddabddadcbdabdbcdcaadaddabddcbbbccbccdbdcddbadbddbacbaacdadaadaadadabbcdcbcdbcbbbdccbbadacdadcdbbcabdcadccbacdddbdabbdadabacdbbbadbbacdbbdaaadccddbaaddbbdcabbcccaddbbcbcadbddddaababbdccdabbddbbbbaccbbacadadcbcdaadaadabdaabddbcddbadbdccaaadcddcdbacadadaccdbbbcdadcaaaccddabacbcdcbaaadcabdabdcabcacbdaadaadaababdaabbadabaacbcaababcabdddaadbdbabddabacddadbdccadbbcdcdacabdddcacdbdabccadbdddcdbccddbddcbdccbbbadcaacadaaddcadaacbbdddcadadcaabbbadcbadccdddcbbbabdddbdacdabdbcabbabdcbcbddbbbabcdadbacaadccddddcadddcdddddbbbadcbbbcbaddbcdbaddbdddabddbcdaabaacaddcdcabbccacdcbcabcadbcaaacddccbbddddacdccdcabaacaacbddaddcacbbbbcbdbabbacabbccababdcdbbdbbccacaccaddacabcacaacdcdbdcadbdddcbaccccddccabbcdbdccdcddbabcadabadacccdcdcdbbacdabbbdccdbdccbbdacbbbddabdccbdbaaacdccbcdccdbdbcabacacaabbaddbccbdccccbddadbaadacdcdaaccdcacdababaaddcddddccabdacaacbadabdadcbaaaadcadcabdcadacbadcadbcdddcbbdcccaaaaadcbaaacbdbddaabaddbbcbbddbcddcbbcadbbaaaaaacbbcbacadbabcacdcdcdddcddbccaacaacaabcbacbdbdcdabddcadcadcbbdaabccacbaacbcdbacdcddabcabccddaaddbcadababdcbbadabdbdbaabdaccbbddbddabcdbadbacbddbdbdbbdbcbddaacdcbacbabacdbcabbbcbabcdcdccabbbdcaaaddbabbabdbcccbcbcaadbdcacbcbacccdbcdbdcbacbcddabccdbdabadcddadddaabbabaabaabcacdddadacadcaacdcaaaaabadcddacadbbcabddccbcabbccbddbdbadcbdabbcccbabadbbdcdaaacadcddcdadaabacbdaacaaccbaddcdcbbdcdbbbcbccadccbdcbccadacacdbdadaaaaddaadabbdbaabdcdccbddbaccacbadbbadcbcddbccbcaabdbcbabddbbbbbcabddcdaabccddcbaaaacbadaaadcccbcdcccdaabddaddbdccccacbcbcbdbbdcbbabddbbbdddaddddbadcbbabdbadabbbddabbacacaacdccbdabdcbdddddbaaccdddadbcbbdcdcdddabaddcddcbdbbddabbdccdcabaaaacbcbadcabdcaaaaddcbabbaaaccbdcaaadcabcaacccbacdcdddbbdcacabaababdccaabaaabcbbcdddccabcdcbaaabacbccadccdaadaaaaddbbcbdcabcabdcbcabddababcbcddbdadbadadbcabaaabbdcaaadbdbccabacbdbadccbdccbcaccabbbdbaabbbadbaacdccaacadabbbcdccbbcacbbdaabddcbcdbadbbdcacddbccbddacddaabdbdbdcccacabcbaaacadccdabadabddbddacddbbbdcabbcdadbcbbbbdccbadccbbbcdcabdccddbddbbdaddcbcbacaacdacdbddbdbabcbdccabaaadcccdcbbdcbdddcdccdcdcddaccadbcadacdbdcbcbbaaadcdbbbadababddaddbddcdbdcacbbdabcbaabbddadcdcbdcbbbdacacacbbcbbddadacdbaabcbcaabdcabcabbaaadccadcdccddbcacbccdbadbacdddcabdbdcdaabddbbaacabdccdbabdbccbcdccdaadcccbcadadcbcbcccbcacdcdcdcacbcbdbaccadaacbadacddcabdbdacbcddddcbbacaaaacddbadcaaaacdcdaccdaabacddaddbdcbccbbdbdcacaacbbbcbbacbdabaaddcbdabdccbdbadadbccbbabbcdbaccbdbdcaabdbadababadcabcbabaadcbcdbdaaaaaccadadabdbbdcabdbabbacadcdcccdcdbcadbcbaddbbccbbcdbddcbcabbbdcccbbbdcabbaaacdbddbbabcadbcbcccadbcacdcbdcdaadcddbcdbbdbaacaaddadddcaacacabacddacccbaddbbdcbdcbbaddacbdacbaacadddbbcaadcacaccacbacbbacdcddadbcaccbbddbcdabbabacbbabaabccdcdcabaaaacaabbabbcbdaacbbccdacabdbdbdccacccbddadbbccdcaabbdcdbbccaabccaadaaccdbadacbcaddcaadbcddadcaabdaabdcdcccbaacddbbbdbbbcadcaadbddcdbbdbcdcaaccacabcbaaddaadacddabbcdadababaccdcbdacaadaacdbdadbaacccadabdbabbdcaadbbdbdacddccdbabbddbdddadcddccacaddcacabdaadcbdababdcbdcbbccbabcacdbbcddabcdddcabbbaddababccccbdccccaaadaacddadcdbaccccdacacbdacccbbbbdcccbcabdccadabcdddcbdbcaadddcbbdcbddadcddbaabdcdadadbcdddbbabdcdcaddccdbaadabbddbaabbdcbdbcaddccdccbdccacdbcbdaccadacacaadadddaddbbbbaadcdbaacabadaaacbcdcbacdaacccbaacbbbbcaccacadadcbcccbadbccbabdbdccabacaaddbbdddaccbccbdaabdcdbcdbccdcbccbaccbddabddbbccdacddddddadadaaacabaddaaadadbdadccbabbbbabbbbcaddbabaccdbbabdcdcbcbadabaacddcbaaacbadddcdbcccadbbdbbdcdcddaacadcdccdcdabbaccbcbbdcddbbdcaccbbdcbcbadcadacabbadcdabddbabccdcbbabcccbdcccabaccbcbcacbcaddccaadbaaadbbddabdbbcacbcddcbcddcdaaaddacabcacaacdabbddccdbbcdadbbdaaddddbcdcadaccbdbcadbaccbcbbbbbddacbabdadbdacdcbbbbcccbadbdaaddddccadcbaababdbcbdcbcdaacabadbbbabddaccbacdccbaadbabbbcccbbbcddadbacabacabcaadbdcabbadbabcbbdddadacacdacbbacccaaaaabcadacdbaaadaddadbbdbcabacbacbbadbddcdaadbbabdcddbbdbbcdaadababbadbbaccbdbadbddbccacacbbbbcdabbbadadbbacaabaddcbbcdaccdbbbdbcaabaacbcddcdbbaacddabadbdbbccbdcbcaabacdabdabaaccbbddbcbbbcdacdbbaaaadbbbbabccbdaadcdcdbdcabbcabdcbdcdccdccadcccadcdaddabbcdcccacadbcabbbccaabbbdaddbdccbabdbcaabdbabcadbadddbcbbbbbcdcdbccccddadcabadcadbdaccaddbbabadcaacaacadadaacbbabbcaacbbaddbdccdaadadcababdaadcbccdbcddadbdbddabbbbcccdacdabcbcbbbabcbaaaaacbdbdbbdaddaccccddcddccbccacaacbbaddbddbadcbcabbccbaacbacdccbdbdbbbaccbbcbdbbacddaadadcaacacbbcdcccbdcdcdcbbdcbdddbcbdbdaddbdabcdacbacbcdbaadadcccdadbcaadbbaacdddacadbdcdabbbabcabcddacabdccbdbcabdbaacdadbbdaaacadcaccabcbbdccaaadbccadccaccacddbbdcdabdbbadabdaadbbacabaadaaaacdcacdcccdbabdbcacababdaabddcacababcccbdbbbbdacbabbdcaddacdadcdcccbacbddadaddbbdcadddaacbcdabbccbbacccaccbdbcabbacdaabbbddabdbbccadabcadaadbcccabcbbccccdaddccdadbdcbbbbbbcbcdbcacdccccdbdadaccabcadaacbcdcbcaadbbabaccdaaccabababbbcaddbadacacadaaddddbababbcdccbcbdbdbcbcaccdcdbbccbbddbbbacadbccadadaaccabacdcabdcbdccadadbdbbdbadbdddbcbbddbbacdccbaccdcbaccdbadbbcacbadbcddbadbdacbaccbadbcdbbbcccdbbaabdbbdadcccacdcdbdbbbdaaadbaccacabccaddbaaacdbbcccbbacccbacddaacdbcccadbbaccbadddadcbadabbdbaaacccbbbadbbbdcccdbadcdddabbacbbdbddbaaccacbacadbdbccacdcbcbbaccdbcababdaabdbbdbdcacccadbadabbbcbdcdcbbdccddcdbbabaccaddaddcdbbdadbacdcbcccddddddbcbdbbcadbbdadcaaaabcbcbdcccdbbbcbccadabdddbabdacaddcadbacbccabacabacbcadbdcdcccdcdccdbbcdbcbaddddbbbdbaaaacddddabddadcdccaadbbadcbaaacabccababbadacbbdbddacddbbbdcabdbcacabcadacccdbdcbbcddcabdbadcbaddcccadcabbaadaabcbbcadccbcaadabcdabbccbdbbaccddddddabdccacbaadccaadbbabdaacacdcbdcdcaccaddbccbbaccbbabadcbadaccdcdaddbccccbcabbdaabbcaaababddbcdadcdddccadddcbcccdaaccbdbddacbcccbccbadbbcbbdbcadaabcccabbcbbbdccbaddbadaacdcadabdddbabdbbacbaaabcbdcaccdaaacbcacacddabcbabdcaaacbbcbddcacabbacbcdacabadcbcdbdabdaadbdbcbddacabcddadabcaadbdadabdaccddbddaddadabbbbadabccbcbdaadacbccddcabcbaadbbdcbbdaccdddccdaabcabbadccbaababbbcccbabddcccddaacbddacdabcbddcdabbcadbcaccacaaaababcbbadbbcbcbccbcbccccdbabbcdaddcaadcaacabddbdcaadadbdbabbdbdbadaadababcbadaaddbdaacbbcddadaabcbdaddcaccacbaacbcdbbbbbbdbbbcababaadacaddadaddabdadddbcdcdcbcacdaabdabdddbacdcdbacdaababbbaadbdabdbbddbcdcdabbaaacccadaccacaadbaacaccdaacabbcbadbcddacdccbbdacbcbacbadaaadadcabddccadbcdaabdccddbdcbccabdadcbdbdadbaddbdbddbaccadaaddbacccacdbccccbcdacaacacabcaacabdbdadabdbdbdbccbcdcbbbbaccbbabdccbbdabdcaccabcbdaadbbcddacbcabbadcbdacaacbbbcbcabbbdaaaaacabababbdadcbcdababaacdacbaccaddabddaaacbccccbcdbddbddbbcaccbbddbbdbdcbbcbdaacdbcbbbcdadaaaabcaaacdbdcabccdadaaccadacbbbabbaabcdcacbcabdaadcdaabcccbabbdbaacccccacdbbdaacdddcbbcbcdcaadababbcdbddddcbddbbbaabddccdaabcadaddbadcbcdddaaccbaacccdbabdbcdbbbccaddbddadccbccadcabbdcdbabdcbccabcccaadaadacdccdcbbcdabadacbacadcaaddaaccadbdbabbadccabcddbbbbbdaadbbcbdddbaddbcbbbbccacaddabdbbaacddcddbaacbaacdabbbdbddbcdbbccabaccbbdbdbdaaacdccadaaaadbcabacbddbdbbbcaccadacdaabddbbbaaaccaadcbdcccaaabccaabbadbddddacbadbabdacccdadadcacbdcabccadadbcbcdbccbbdcaacdddabccaccabcadccaabcdabcabdbcadddadaaadacccbddcabacbdadadbcbcadacdcdabdaabdadccabadcaadacabbbbaaddacccacdaadabdaddcdadddbaccabaaacababcadaaadbabbbadccabdcddaaabdadcadbaabddcddcaddcdadaacdabbccabdbbdbddbbaabcaacbabcddcaccadaabbbdcbacddacdcdcbbaabbbcddbdaadaaabcddbcaccdadaccabccbbacdccbdcdcdadaccbddababcaabdadbdbbdabdabbbaddcddaacdcbadadacbccdbcaccdccdbccdabbcbbaddcbcbbbaaddcbbababbcccccacccccabaaaabadbacaaccbbbdbccdadbdbabdbaabbcdcddddcbcdaadababcadabdbbccbabdabbcaaadbcadaacdabacdcbbccaacbbbdbabddcbadbadbccaaaaacbdccccbcadbcaabbabcdcbdcddaaacdbacccadcbdcccdbacddbacaabcddbdbdbbdaccbbddcacbdddbddccbbaaaabcadcbcbdaaddcbacbabadadbdadadabccbadcabbbccdcadcadddbaaaabbddcdccadddadcdcbddcadcadaddcbbcbbbbbdcacadbaaabaadabddbcadaccadadbacbbbdbddacccaccbdabbcbaacccbbcbdcaaccccbbbbbbccbbacaddbdbdaccbcabbddaaccadcabdacdcdbdcabadbccddabdadabcbaccabcbacbbccbabccbbabdabccbcdbbcbadcbcbbadcccaacccdbbcbcbdadcadadabacadbaccdadbbaadacacdbcdbcbadbbaababadddccaabaddcaacbbbcbbdacaaccbcababccbcabdaaaccaabacbcbbacbadbccbadcdbabcbadbbddbdccadaabcbcbcdbdddcadaaaabbdbcdbcccbdddbcdadcbbccdabbbdbcccbbdaabcbdbaacddadccabcdbabdcddabdbbcbabbbbdddadbadcaddcadcacbdddadccaaddadcbbdacdddbdbccbdbdccaddbacbddbbcdadcbbdbbaaaadabccbccbddbcaabdaacdccacdcbabdaacbcccabbddcdccdbcbcadbbaacdabcddaddadcdcadaddabdcdcdaaabccaadbacbabcddabaddbcadcaadacdcddacabbcbccacdababacacbabbdbdabcabbccbdbddbbcbdacddccabbddccdddaddcdadacaccbbbabcdadbbababdccaddcddabcddacbaaccdbcabbadadbcbdacdccbbddcadaddcaddcddacdcabcacabacdaaccbbcddbdccdabccbbdbdcaabbdadbddbbacddabdcbaccbcaddaccdbcadbdabbaacdbadadcbddbadcbbbacacaaabcaddcbcdbaaabdabccdbdaaccabbbcaaadbddccdbccadbcbcabbbccadbabaadaabbbaadabbbaccbdbadbabbbddabbcddbabcaaacccbaabcadcccadbaabccbdacabccacaddbdabaabdddcaabdcdbabccbccadbbdbbcdbcccacdcacabcccbcbbdabdbdcaacbdddbadabdbabccdbbabddbddccddcdbccdccbdbabbccbdcbacadbdcdadbccbbbbddcdbddcbaaccdbbdabcbaadbaababdaccddccbdbddcccdccabdbdbbbbbaacbddadcbbccbacdbddbdabdbcddbbcbcdadcbdbbdaccbbbdaadadacbaabbddaabcdddddbbadbcaaadbbcdbabadccaaddbbcabdabcdaaadacdddababcbbcbdaabadadaddcbbaacabdcaabbbdaababdcdddacdcccabcbdabccaabbdacdbdccbdbbdcdbbddccdcbdbbbdadaacbdacabbcaccacadcadbabbabaaadaabaabdaaddcacddccbaaddbabcbddccdabdcbcaadaaacabdbbbacaabbacadadccbbbaccabdcacadbbbbaaddcdbbdcdaacadacaddbcadadaddaaadbcacddadbbacabdabcacbcadaccdbbbcbdabbdcccbcacacbdacbbddbbbcdadadbabbcdbbaacbbccbadbcadbcaacccacdabaaabaabcabcbcdaccccabacbccbaaabbcbbbbdaadbcbcaabdbcacaaccbabcccadddccbacacbadacbacaabbcddbdbaddadcabdcddbbaaadbddcdcbbbaabdabbaadbbabbbcaadcaaabadccbadaccadbccbacacccbdadbcbaddaaaacccdcdccadcabbadcbddcdccddcadbddcbaaadbaabbcbccdcdbaaadbcbadaccdaaddbcccaacadaccabcbcdbdacadaccadbbcbddbcacabddddababbcdcadbdcabddddbaacacddcdbdabaaacbabadcacdadabddddbcdadcbccbdabdaadbabaaabaddddbbadcaacbcaacdaadcaaaddcbdddddacdbbdcdabdcbcabddbcccdaaaadabdcdabbbbbabdabdbcddbdbcbbcabaabaacdcaabbbadcdaadcdddccadacaacdbbbdbcddadcccbabcaaababaacadbbdbcadddbcdabababdbaccaabbcacbdcccddbdcdbbcaadccbdcabdbccbacdadacbabbbabbadabababcaccaccddbbadcbbadabddcaabcbbccbcabadcbdbacbabccacaaaacbbcccdadddaccccacbaabdcccbabdddadaaadcaabcccbdddcdbbaacbddcdaccabbacaaababdaaaacacbdcdbdbdbadabcdcaabcddaacbdddbcdaaadadbdacdbdadadbdbccbaccabbddcacddabbdbbddaaccadcccbdaacaaabdbddcbcdbdbdcbcababddbdbaadbdabbcbddbdbdbcbaadabdcdabcabbadbbdcdabcdcadcbacbcdcbdcccdaddaddcbabcabccbdaacabbdbcabccbbabdbabbcbbaccdcdcdcadccdaacadbaabbbdbdacadcaabbdbcbcacbbadbacdbbcdaaaacaacdddadccccbbbdbacababcdbbdaacdaabdcccbababdabbacabbacbccddbccaadddbcacaddcbaabbccdbbbaaadaaadcadcabbaccbacdbdbddcbbdbabbcaaabdacbaacaadabcdcdabbcccabadacbcadaacacddbacacdbdccccbabbbbacabdcbdabdcccdbaccddbcddbcbaacccacdacbbaccbacabdbbaadaaaccdbbaddccccacdbccaaabdacbacbcaaacdcabbabaadbcacdbdccdbcdcccabbaadabdadcadcadccdcbccbcaadcdbbbadcacdbacabbbdbdcdcbbbaacbbcadacbbaacacbabdabadccdabdddddbdbdbcdabaccaadccdaabdaadadadadaaadbcbaadaacccdbbbaabdbaaaccaadcabdaabcdaccdcadccabbddcaabaadcbddadbdcaaddaadbaaadabbaaaddabbbacccdadcbdbbdbbaaccddbbdbbbcdbcababbccbcdbbaddbcdacabaadcbccbadababbbbccbcbcbcaaddabcacbddccdcbabbadbddaabcdbadccccddbbcabbccabcdadcdddcbdcadadabdbdaddccabcabbacababbcadddddddadaccdabdbbdbcacccacddddcbcabaaacdbdbabcbababdacddadbaaaadbdadbaabbbbaadccbabddacabbacbbdbbcaacaddbcadcbbabcdddcdadbcabcaadaacdbdacbbbdcbcbbdccdcddcddddbcdbdcdcadddccdbabccbadbabcabacbcdabcaaabadbdccbaaaddcdcabddcbbcbabaddabbadaadabdcdbddbbdbcdcabdbcacabbbdddddaaaaaabcabbabddccccbaaccacdddbbbcdabbcdcbbbacbbdbdaccaabcbaabcbcccacbcdabdbdccdcbdbdccadadbddddcaccaadadaccdcbbabcdbdccdaacaadbcbacbabbccabadbbbabcacbdadbbadccbccbbaabdbbcbccddcdbdbbbccddcdcdcdbcbaaddaacabcbadbabadabbddcaccaacdbddacbdbacbcbcacacdbdcbbccdccdccbbdddbacadabbdaaacbabbdddcbddadcbddadaccaabbccdbadacaddcaababcddbaabdbbacbaddbccbcadcddbbbadaabbbabdddcdabbcbbddcddddabbbdcaadbadaddbadbdcaccdadbbbbbadcabcbbdadaddcbdcaaccccddbacbdbabdccbdcccbcbadadcadbdbababbdccacccadaddbdddbcdddbdaacaaddcaddbdbacaaccaaaaddaabcbcbdddcdccaccdcddaadccbbaaabbadbaaaaabadbaacadadbbbdcaaaadabbccddcddabdccaccdbaadaabbaacdaadaababcdbaddabdbcddcdbdccaccadcbbdbdabdaccddddadcbcacbabdbababcaaaadbabbdaabaddabcdabbdcccdcdbdabbdadbdbcadbcbdcdbdabcbcdabadaadaaadddbdbdddddacdaccababcdaddcddbcadbadddcccdcabdbbbbbddaaddaacdbdbcdbdddbabddabddabcabcaaadadbcddbdbcbbdbdbddcacacbaddbcbbbbbbcdbbabccbddbccaabcbdbcababcdbcccaaadacbbddccacbcddbcaddbaadcbcabdadbddadcadddacbdcadbdcadcaacbaccabadbbaccbdbaddabaccacbdaabbbbacddddbadbcbdacccbdbcdaacbaadddabbdaacdcccdcadbcdbcbbcbabcccdbdbbdbbdcabdddcdbdcadbdbcabdabdddcbddacdcdacdaaaccaccacacdccdbdbaddddcbaacbcaddbdcdcccabcdccccbcbcbdbbabcbdccddccbbcacbbdadacadccddbdcbcbddbddbdcbbdccaddaaaaccbddccbbabcccabdaaccddabaabdabddadcddccbcdabacddccaadcbbacbbbddddabacbbbbddbccbabddbbddcdcbbcbaccacccdadbdbaaddccaddcbcddccacbaaabdacbbaaaaaddbdcabdcdcabdbaaacdcbadbadcabdaaaaadbdacdbabcdcddbccaaadbdacaadbdaadbbcdbddaabcdbdabdddabbcccbdbcdcbaddccaaddcccccaacadbdbdcbbacdbacabacdcacdcbdabdccdbadcddcddbbccddaccbcdbadbbdccadbbdadacbbaccdddabbccdabbadadcdbcbacdccacacbaddacccaacaabdcaadbcbbadcdbbbbddddabaaaabcddababbcabdabbbcbbbdddbabcbcbcbccbbbcacbdcdcccdacbbdddaddbacbcadbaadbcdaddbaabbdbbdbbdacaccdcbcdaaaacadabdaacbdccbcddcadbdddddbcdabccaaacadccaaacdabdbbcdacccaccbdcddbaabdbdabcaaccdccaaddccbdddaaccdadcbccbdddcacdbdbdbdcabdbcbbbdddccbcaabbdbdbdacaabbadabdcdbdaaadacccaabbbbbcdacddcabbaaacdcbbdabccddbabccdabbdbccabdcddddbddddccdbdbacaacacadcaadacdbadacddbcbabdbdaccccabdddbdccbdcbbcadccdbadbdadabaacdacbabbcababdacdcbddadabccaaddadddacdadcdabaadcbdbdadcbdbadbcaacabbcccdccbdbdccddadaddacbdbcdaaadcbcbabcdbcdcdcbabbcacdaccabdccccacbdbdbbcdaabdbdbdaccacdccabdacbbabdccaddbabbddcdbcacdccbddddbbcbbbacacbdbddbbbabddacbacaaddccdcbabcbdaccadabaacaadbbabbaabbcddcadaddbacdcacbbcbacbacbacdcddadabaacacaddbaccbcdbddaadbcdadbccddcabbbcddddbccdacaaccbaaddbdcdddcdcaabbbdbaacbaacabadcaaadbcadccbdbbcbdacbcbacbbaacabadbcadddcbaaaccdcaadacccbdabbabbdcdcddccddaadccaddbbabddaabccbcbacbadadaababaadbdbacccccbcdaadadaccbdbdbdbbbadacbaabdabddbbacbcbddbbabadddabadadbccacbdccaaabdbbcadbadcbdacdaadbadacabccbbbadcdbadacdcdddccdaacdadbcdbaaccbabcacdcdbbcbcbcababbcdabbdcdbdddabbaddcdacaacbabcddcbadbcdbcbccabdacccacadccdcaadbbccadcbdabdcacccbdcdbabcaacbdaaacbdacbadbccccbddcbbccbdaccbaaddadaabbcacaddcdbaccacadddcabbbaaacacaadcacbdddccbaabdbacacdacbdadababbcaabadcbbbbacbcccabbacdcaaaccacaaccbdaaaccabddabbaccddacddcacbbdcdbbcddbbcccbddbadbabcccbbcdbdcadcabaaacdddcabacdabbdbcccbbddbabcdccdbbabccdbaabbbadbacbdbacadbdcdbcdddcaddcbacaaccabcaacaaaccdadcdbcccabccbaaaddbbbdbdcddbbddbbbabdbbcaaddcaddacbccddbabddbccbdcdbbdcdddcdabadbaacddccddccdcccdaaabaaddbdcbcbddcacbbbdbccdddcadbacabcaacbccdacdbbbdbcdccbbadbbbbbdbcabdbbababbcbabcacdbddaadaaddabcabcddbdbdbddaadccbbcadaabdacbbccdaabaaccdbdbcdcdababddbabacdaccbdbbbcdbddaccdbdccbbbcbddadabbaabbbcadcddbcbbbbadbdbcacbacddbaadabccabacabaaadcabcacdaacadcabcdaadaaabbdcddcccccaaadcdbaccadddbdbdbabbbccadcadabcacdacdbaddadadddddbdbbdaadaadaacacbccbcacadbdabbbaaccddabadaaaabcabcdbacbaaadbcbbdacacbadbaccbbcbdbbacaadcdbcadcaccabbbdcadabaddcbbbcaaaabdbdbaccdcaccdabaaccaaaacbbabbdbcccdbdcaaaacbcccbadbdcbcdcddbcbcadccacabddcdbabbbccbacaaccadbabaabccabcabddbaaabddbdddaabbddababbdbabbbcadbcbcbbcddbbbcbbbdcabdcabdccaadcacccabbadddacadacadbbcdbcbacbddcdcbcdbdaccbddddadacbdaaacacbcbddbaadbcddbacddbddabbbbdcddcacabbbdbcabdabcccdabdcadabbdbdcbdcdaabcbcaccbdabaddbccdbcacacadabcaccabbcbdcdcaabcbcddbccbaaadadbccabbbcbcbdadaadacdabdabdcabbaaabaaadcbcdccaaaccbdaaabbdcddacadbacccadbbbdadbcbcddaccadaccbbdcabccdacadcacadbcbbdcdadcdcddbcdcaaabbcdadbabbabbbdababdbddbcbbaabcdabbdadabdaaacabcbabbccaccccbdcacbbdbaccdcaddacccbcadabababcddcbbbbcadcdabadbddbcbdcaabdabcabbccaccaaabbaadacaaabbbddacacbbcdccbbacbdddcabcaabadbadadcaddacbacadbdbcbdbcdcdbdbbbbdcbbcadabaaabcddcbddadabacdcdabadacabcdcdbacadadddaabbabadaaadddaaaadcabcbaaddcacabbddcddaacbbbbbbacdcacabbddcaddaddadbddcadbcadbadcdbbcbdbaddcddddbacbbdcccdbabccddbbcbacbcccccbbbdcdacbabcacbbbdabbadbacbaaaadddacadcbdccdbbbbdaadccbadcccbbbbddadccccabdbddbdbbbadbbdcdbcbdcbbbcadbbdccaabcabcadadbaacccdbcccbdcccaaaccbbdabbaaadbbccbabdcaacbdbbadacbbaccacaaddcdabdbcadcdaadbaadbbcbccbdbabcaaccadbabaaccabaabadaabbadcbabbdadbddaabcbacccadacabdbcaaaccaccabdcaacbbbbbbddcbacdadaddaabcbdadacacbdccdcbbaaddabcbabbdcabbdcbcbbcbdcdbacbdacaddcddaccdddcabbabcdcdbbabddddbcbcdabaaccdbadccdaaaaabccadcbacabddddccbdcccdadcbacdccbadcaabaddadbcbaaccacddbdcbcbacadaccbddddacdccadbbbcdcbadbdaacbbabbbccccaacbbdbaabcabdddcccbbaaacddbdbcacdadddcaabdadacadcbabcbddcbdcbbddaabaacdccaabbcdcdccacdacdaddbabcccddcdadbcdacaddddcacbabaccdbadacdbdcbccaabacbcdaccadbccadccbcaacdaddbadcddadbdbbcabbcbacdbdbbddbbbbbbdbbadddaddcabbbaddbacbaccdddadddbdcacddbcdbdbacbbcaadabaaddbdcdaabbdcdbcaddcdabaaccccccddcbbddcddababdbaacadcadcabddcadbacdbbdaddabbbadbdddccbdcaccbbabaacaacababccdcaacbbdbaaaaadadbbbcbddadcdcadcbcdcaadbbadbaabdaabaacdcacbcbaabadbaacaaaabbadcadbabdbcacabcdddccdcbbbbddbaabcddcdcccdbadbaabbadaadcddacddbabadbddabadccdddccbabcacddcbadbcbacdadbdacbddbadadbcbbcdbcddbbcddddcbcccbcbadbdbdcdbabbaacdbcdabbaacacbbccbacaaadddbddbacadbddcbbdbdbabdcaacdbbcccaabdccababbadcbacadcdbcbbbbdcbcbbaddcdcaaadddcbcacbbabbbbbcabadcadcdcdcbcdabdaacbcaddccdbcbbcbbabbaacababcdacdddcdbcddaaaaabbbbdcabcaddddadbcddddbdcddcdbdbdacdadbaacadbcbacabadaabacbadcbacdbbbdddddcccacaddbdcacccacacbbbcddcadddabbbcdcdbdbdaadcdcddabdcbaaddcadbdaabdbcaadbbddacdbbccbcbcdbaccccbcabbcbcdcbaccadccdbbaddadbaaddbbacdbcdabadaaacbccbcbbbbbbaaccabaddbdbadbcbaaaabadbcddddcacdcbdbddcbaaabddcdbcbdddbaccdcdabcbcbccbabaaaacadadccaadcabdbbcacaaaabbcdcdabacabddbdcddbddddbbacbadcbbaccdaaddbabaaacaaaccccddcaadbddcacbbdddcccbcadadcabcdacdaaaccadccadadccdbbbbddaaabbdabbccdaddcbdbbaccdabbabdbcdacdabcabcdbaddbcbcaaaaadadcbcbbbbcacdadbbccacbbcccabddbdbbbcdbcabbdcddabbcccadbbdddddbbbaaadddbdabaccacaaadbaababdcaadbbbccdbbdccacdaabbbabcccdaddadcacbcadcdadddbaaaccbacbdbbdacccbddbdcdbadbccccdcacaacaddbaacdbbdbbbcdcbdacbdbaabcdbdbccdcacbccbdbadbccbdddbbdadadaadabbacdadbcccaabccccadabbbcdbcdbdddcdcbacbabdbccddbdbbdbcbdadbcbddabbcbbabccdacbbbdccbbacbabddadcbbcdbababcadbcbacbacbbcbddadbbacddacbacdcdddbcbdbacaaacaacdbabccdbbcabbacbacacbdabaabdcaacccbbdadbbcdabcbcbdcacccbabdcbaccbdcdbbacbcddbdccadaacadacbcddbcdacdddbbbaaccadcbdcababbadbacddbccbcdadbbbcbaabababadaddaccccbbbcbdacdccbaacdbbccdcdbcdbdbbbbbaccdccacbbaddcccadacaabacbbdcaaaaddccbdacbaadadcacdcbddaccabaaadbaddbabdcdddcabdaccbbacccccdcbabddababdcdddcdbcabbaccacaaadbdabcdcbdcacbbddadbcaabcddccddccccabccdadabccdbabccbadbbddddbaabbcdabcacaabdabcabbcadadcdddbbdcdabddddaaddcdbbcddcdcccbddcacdcabbbabddabddaddcaabcdadbbbdddddbbabacbcbabaaaccbbadbddbadcadddbcccbacbcadadbccbbaddddaaaccababcdbdbdccdcdaacdcbbbdccdabcbbbdaabdcdcdbbbddadbbddcdaaaaabdccbbbcbddaaadbacdbbcaaccddcbdcccdaccbcbccdbbbccbacdcccbdaabbddabddbabaacabcddcdccdccaaacbcbbadbacabcaadddddcccaadbcaaacbcdcccddabddcbdbbaaaccbadaadbbdddbcdcaaaaaccbabbcbbcabcbbabcaacccddbcbdadcacdaccbabccadcbacaaccaaacaadcbabcbbdbadcdbaacbabccddcbdabbadbdbbacadaaababbccddddbcabccbdbdadacdbcbdadccccbdddbcbacccccbbcddadadbcdbbcdccbaccbbdaadaaacddadaabccaaabdbbacaddccdbcbbcaabacdccaaadcabcbabdadcaaaadaaddddcdabadacbbaddabddadbbabdaddadbbdadaaacabcdcbdcdbbdcdbaaadbccbbddcdbdcbabccbbadcaabdcdddcdadbddbbbcaaddbadbabaaccacadbdaabadacddbdbdacdbaccdacddadcdadcbdcbabcaacdcaaaaadccdbbdcdadddcbbdcaabddbbcaababccbdaabcdbaacdacbddacdadadadbdbcbadaadddbacbbcbbcbbaabddaabbbccdbdccaaacacdcaaadbdabdbdabadaabbaddabacddddabbbcdbddddadccaadcdacdcdaaaccccdbcabbbbaadabbdbbccdcbddabbbdddbbbdcdcdaacccdbcacddaadbdcdbaddccacbdbcdddccadcdccadbacaaddacbabcaccccbabbaddcacdccabbdabbcbddcbcadadabccacadcbabcadbaccaadaacbbdbbddadbaddbaabbbdbdbadbbacbccaadbcddbcbcbbabddcbaaadacabccdbddadadbcdcaadadadbddccbcacddaaaddbbaabccdacaacdcbbacbacbbbadbdcdddcddadabbbdabadccbdccacddbbbadcccccbdcddacdbbbbadaadbaabaabdabaadbbcdabcbcdcdadcdabbabddbaaacbbdbbdbcdcdadbdcadccbddadaabbccacbcccabcdbbacadaccdcccddacddcdcbdacbbcdbbdbcbdddcbbcabddbcbcccaccdcbacdbdcbcadcbccdbdbcabdabbcabcdabdddbaabccadaabadbcddcbbabbaddadadbdccbbcddaadcdabbabbbdaaaababddaddaabbcacbbabdacbaacacbacaddcddcbaddbcdcdaadabbcbcbacbababbbcdbdbbdcadbacddbaacaddbbdbdabdaabcdcbcdbabdbcabdacabccdbdadbaabbdaacbddcdaabaccdbadcaaadacbbbcdbaadaacadcaaccbcbbbccbdbbcadbdadabdabcdbcdcadbcbccbcabadcaabdccbbddbdaacccbbcdcbadcaaadbdbabccbbdcdddabcbaabdbaacaaddbacacaabaddabcdadbbbabddbcdcdcccddacacaacbacbcbddcbcabccabadccbbabaaadcbbddcdaaaccbaacddcbccccbdaaacdcabacbdcdbadcadccccddbccbacaaacdddcddaaccbbdcdcdbaccbcadcacdccdabadacaddbaaaabbcadbaabcccbcacdcaaadcccbccabccdaacbbddcdbcdbbbbdaabdcdadcadadbabdccabaadcbbccbdcdbddaaaabaabbdaabcdbdddaacbcabcabbcdaaadcbbaccdccdadacbbbacbaddaaddabbcacdaddbacbbdcdbbdccbcdaacbcdbabcabadabccbacdbbdcacadbcdbdbaccbaabacadddaccacbcccacadcaacabdcddbadcbaabdbdbbdabbdacdcabccabddccccddbdadacadbbbcaaacccabdbdbcccaadbacaacaabacdcdcbadcbcabbdbbbcdabaaaddcddadabcaadbdcbbdaccbadabdabbadccacaccddcaddaacbdbdadcabcbcabcbbdbaaacdaccbddcaccbdcddddacdbacbcbacccbcbaadcdbadbdacbcadbbbdcdcaaacbcbdddccbbacdbccbaddaacacacddaccaddbcdbbbdcdacbcccbdccdcbaddabbddbbadaccabbdcacdaaddacaccbbcddbbccbabcadadadaaccbddcdcaccdadbaaddacaabcbadaacbcddbdccdbbabcccddbdcbbbdacbcbdadcacbdcbadadcdbabccaaccbadabbccbadaaadadcbdacbaadddcdddacbadcddadbaaddbbcabadadbbccddcabcaacbdadbbcdbbaacdbdbbaadabaddbbbbcaccbbdabbdaaacdccdaacdcaaadaacbccdabcacbdbcdaabcbcbbdbabaaaddacccabcbbdcdcaadcbcbccabaccccccccbccdbbdbdbabababaacdbddddadadabbccdadbdbcdbbbbcddacccdccdaaacbbabbcadabcdcacccdccdbdcbbabddbddcaacddacbcacddadbdadaaaccdacacccddadccbbcaaccbdcdbddadadbacbaabadaadbdbccbdaadbcbdbbcddbbaabbdbbbddbdcaaabdabbcbbaacdbdaaddbcbaacabcbbcacdaadaddadcbadcaaddaabaddcadbbbcccbbdcbabbadbaabdccacccddcacaaaacdcbaabccbcdadcdcbaadadacadadbbacacddbbdcaaaaacbcdbcdbbabcadacdaddbcdbcbaaabacdccdcabdbbdcccacbcdbaadbacbdacacdcccdcdabdcabdbaacbaadacadbdcabbadaddabcacaacbaabaddccdbddbbacbddbaddabaaabbadccadabbaaadbadbcdcbbdcbabcbccdadcbddbadccadcbccdccdddddabcaccbbbbbbacaaacaadcbcdbddacbadccbacbbcbaadbabbcaccaccdabcddcaacbacbbbbbabccbccadcbadccbadacaaabbdcaabaccabadbcacdacaaadcbbccacbacdcdcaadddbccdbabdcaaccccbdcacbcdaabddcbabdbdcbaaaabcdadbbccbccbacbdbccdddbdabbadbbcbddbbacdabadacaaaadbbcabbcddacccccaaccbaadadcabbaddabbcbadaacababbdacaccccdccbbaccabaddbcdbbbccbcdadbbaabdaacddacacadacbcabddaadababcdbbdddbbaaacdcdadadaadadcbbdcbcaacacdbaabbcaaadacadaccabdabcdbaacababdcdbddabaccaddccbdbdabdabcdcbdaaaacaaabddadcbddaccdabcccdbcacddcbacdcbbcbdcdaaddcbcababaaadabddcadcadddacbacdadbbadaaccbdbdaacbddbcaacbcdbccdcabbabbbbdcbdcbacbbcaccddbbbdacdcaccdadbcdaacbddcddacdaddcdbcbacadcaadacdcbdaccbacbaabddcdbbbdbdbdbbccaaddabbaccaccbccdaaadaabdccabaacdcbbdbabcbabbbdcbddaabdbcbccddbabbcbadcdbacacaacaccdbdcbaabbbbbcabdcbcddcdacccdabcdadcaabdcacbdaaaadbadcabbbbdbdbcbbaccbdaaddadbabacaddcacadcbbbadcaacccbdbcacaadabdbdcddadbacbaddbacdcbcbbacddbdccbcccabdabcacabbbcdacaaaadbcacddadddcccdbbadcacacdddcacccddcacbdaadcabdadacadddbaabbddbaabaabccbdbabccbabcbdbddacaadbadacabcabbbacdbdbbddbbaaddaaadabbaabaacadcdaabbdcdbcababdbdcbbadccbbacdaaaddcdccdccacbcdbaddbacbcbbccadadabaccdbcdbcdbccbbabaabdddadaabdabcbcabccbdacbbbacbdacdbcddacddacbacadcbabdbdbaccabdacaadcbbcabbddbdadcdbdbbacccdcaddbaddcbbdbacbdaabcbaccbaaaaabdbdacdddacabadbdacccbabbbbadadadbdbdacaddcdadababdddcaacdcdcacdbbdcbbcaadadacbabadaaaccbdbcbccbcdcbdbbcddccaccdadbabbcbcddcaadcddacbcaddacbacbcbbabcbcaddbdbddbaadcadcbccccdbddcdacddacadbbbbaaaabbddadacccdbbcbbcbaabbbadcbccdbcccbacacbacbbccccbdacbadcbababdaadaacddcabddbbbabcadaacaadacbcdbcabdcbcbdacaddbaaacdcabbcdaabbdabdddaabaabcbddcbcdbcdaabdcbcdddbbccccdbbbbbaacabbdbcdbcdddaacbcccbdbcabccdccacdddacbcbdcaabadaaaaadbdddcabbcdddadacaabdadbcdcadabddbdaacdbcdbbcdbcbaaddcdcabadcbadcaabbadddcdacdcabaabdabdacdcbdabbaadcbbdabddaabbbdbdbabddbbdbbaabbbbbacddbadadbadcbaacbbdccdacbcbccdaddaccdbccacbdbcddbbbbccadacbccccaacabdaccdcadcdddaccbccdcccadbcaccbadabdcacaadbbcacddccbcbaacababcddbbaadaddaabacbddcdcdccddcddbcbcbadacddaacabadabcaccacaaadbbacbbaccbbbcaddbaadbbdbdcdbadaccbbdabbadbaddbccbcdbacdcbddbaadadddbadcadcbbbbccdbdbcbdaccbbadaaacaccbadcaddbcdbcbdbcbccbadcddcbaaabdaadabdbabdaadbbbcdabbbaadbcaadadbdbcccbcccbbaabbaaabcabbdbdcbadacabdacccdbbcdccdcddadcdadccbbcbdcabbabaabaaddbcddaccabaacbbdccddccacdbcdcbbddaadcbabaccdcbccddababdbcccbaaddbaacdddacbaccadbddccacaacdcdcaadacbbaddaaadccaadbbdcbdaccabbacccbdcbbbcbdbcbbadaccdcdadbaabaccacbdcdcdcacbbcbcbabcbcabbbdcaaaacabacdcbbdacccbbbdbdcbcadacddbbdcadbcccdbcdcbccaccdbddbabbcaadcbabbccdaccaaddbacdbcdbdbcbababbbcadcddaccccbabbbdadadacabccabbaaaacbdadcbacacbbabadabacdbdcaabddcaaaacbbdcbdbabbaaddcbdadbdbcddddbbcabbbdbbcaacdcbddbcaabbcaddadabbbddaaaddaadbbbbdacadcddbaabbcccdaddbddbabcdcabbbacbdbbbcdcbccbabddccbdadaadaaccddaabcdacdbbccbcaacbbdccadcabccbbbabbdaccddbdcadcbdabcbcdacddadcdccbbcdbdcaabadadcdbabccccbddabcdcbbacacaaddadbabcabdaccabaccdddaddbcbbaacaaabbddababacadcdcbbccbbbdbcaaddbcdcaaaabddbbdacdaaabacccaacbbcdaabbbdcadccbcdaaadabcdaaddbdadcccccaaddbdddbaccbbacacbdccccccbddddbccbbbccbdbbcabcaababcbcbccddacaddadbcbdcbddbccbabccbbacaabdbddbdcadaabbddaacabcaadcbaadddadaccacbaabaadbaddcccbbbbabddcbbadbcdbdbcccababadaabbcbbaabbbbacdacaacccaadacaccaabacbcddcdabdacdbccacccaddbcddcbdabcabddcccdbdbbddaaabdccabcbbcccbbddacbbadaadaccbbcbcacddccccabbdbabaabcbdcdbcbdcabbcddabadccbbddbabcccbaadcbdcdadcdddaccadddddddacaaaaccabacdacaacdbcabdaacbaddcccddacabdbaabbdabddabdbdcddcabccbccdaddabdcaccddaccbccabadcdcbdbdbccddabadbacdabcbdcbabcdcdabaaddadcdcbaccbbcababacbdacbbcdaadabdbdddaccdcccdabdacacaaacddbadcbbcdabadbacaccadbdacbabbbcdcaabdbaadbdbcaaccabacbabbcadcccdaabbcacacabadbbccdbccbbbacdbacbcbadddacabcaddaabddbcccacbdcdddddbbdaacbabddaccacbacdccbcadbdabccacdbbdcdbddbbaccadcccdccdabbdbcacaacdaadbcdabbbbdcacdacdabbadbaacdccddcdabdaddacdcdddddbaadadcacbbdaddbbcbaaccdbdabcdccacdbbaadadcccdcbbdacbabbabdbbdbcdaccaadcbddbdbcdccacccacbabacaddbdcbbbdadcdbacdcdcadcccacdabccdaddcbbabaaccdbaacaacddadcccdababbddaccdadbbadabccaccbabbcdcdbbcdccbbdaccbcadcbdaddbababcacdacdadccabccabbcabdddacdcdabbabddbcccbabdaadabccaaabcdbbadcddccdcbaccaadcdabdaccddddbdaaadbabaddbadddabccabaacbabacabccaaaabddcbbccbabaacbadabbcbdbdaccddbaaddcbcbbadacabbbdccbacccbaabccddacadaadbddaacdccdaabcdccdbbcabadcbaaccacbcabddbbdcbacccadaccbadaabdaabaacccacdcccbccaabdbacdccadaddbadbdabaabababdaccdbbdbabbccaaddcabacaadcadbdcaaabccbdcbdcbaddcddbabcbbccbccbaddbaacabccbdabadddbabaaacdccddabddddcbcdcbadbccccdaadacaadbcaababacaccaacccaabbadbcaaabacdcbdddacdbdcdccbadbccddcadaacbddacabdccbdaacbbadaddbcacdccbcbcdacacccddaccdbdbdbdaccbdddcdcadbcdcbdbdcaccdcccadbccdcadadbabcbbcabbadcdcaaacacbcaadbacaaadaadbcbbcbacddcaddcddabbbacdadaabddcbbbcbccaccdbbbcacbbbbaabacdddadbbcbccacbbbccbabccbcbdbaddcbdddabdcbdadaabdddcdbddadaddcacddddbadbbcdbddabcdcdcadcdaadaaddbdaccddcaaddcccbaaaacccdcbacadcadbbccdbddddddbabcddcbaabdaadcbdbbacbbbcdabbbadcccabadacbdbadbbbddcdadbbdcdaababacccccaaabbbbcaccdcdbbcabbccddacdccbbacbacadddbcaabddadadcadbaccdcdcdcbbdadbaabdccdddddbadacabbcbacdacacabbaabdcbbaddbbcadddabdcddcaaaddaadbbaddbdbaabcdbbabaadacdbcadadcdcdddaabaacaddddcacaabbaccbabacbabdaadaaabaadaabbaddcaccbbcddbaaadbabdadadddcbddbaddcdcccaababbadadcabdcbdabdabbcdbcbdacbacbbcadcaabcabbccdaaccdddaadabacdcaccccabaabccabcaaacccbbaccccdcccadbbdadabaadccbcdbdbabdbcdbabcdddddabbdcdcddaaadacdbaaaabdadacbbbcdbdcaacbdbbabbabbbccccadddcabadadccccbaccbbcdcdaacdabaddaaabccdaababdbdccdcccbcbbccccdadbccbabaaccacdddadacaadcbadcbcddcdccddadabbdaacbcdbcdbccadabaaaccabacbbaddbdadadbdababaadcbbddbabcbcdaaabacbbadccccadaaaccdcaacdaaccbcaabcddabadbcdabbbcdcccaaacbcbcabcdbdcadbbcbccdcccbdccddbbcacddabadadbcdaaddabdcddbdaacbddddabccbabcdbddcabcabadcbbcadbcaaccadadddcbcdddcbaacccdabdcacabacbbcdcaddcdbcdadbbbbcbddbcdaaaadacaaacadbaddadaabcbabbbddcccddacccbbacddcaadcdbcdabaabcbdcdaaccdbbcabcdacbddcccdaabaabdbccddcbddabaabdbabacbcaadbacdadbbbacbbdcababccdcdcbdbadadadbaaccaaccadbdadbcaabcacbddbdbcbbccddaaddaaccbabcbadacbddcdcadaadadcacccdbcbdabbbdcbccadcbcdadbabccbbdcacddddcbddbbccdbaddcbbcdcbbdbdbdbaadaddcdbbcdacdccbaabacaadacabdaadaddabadbcadbaccaccdadaddaaabcaabdddacabdcbcdcdadabcbddddbcacbccaaabcadddcccdaaaddacbcaadbdaadccdddaabdcdbcaccaddaddbbdadaaabbdcdcbaabdccbcaacbddcdcdddcddbdacbabdbccbbbdcddcbacdbdbcaadcbdcdaabbbdbbbccacbdabcddbaacdadcaddcbdcaacdaaacbdbbdacadaacddbaaacbabacaabccabdddaadddbdcbadddacdadcbacdacaccacacbaadcbcdaccdbcdbcbcdaaacabdaaadccbadbdbdddbabababaaadccdabcdcdddaadaaaacaacdbabcbdcccabaabacdcbacdbbdbbccbcbdcbccdddaccdbbaddddbaadaadbcacccacbabcadbcbdaacaccdacccdbaddbcbbbbcbdddaadaccbaddcbbcddcddbacbaacbdbbadcadccbabcabacccdddddcadadcaabcaadbbdbcbaadcacbdcdabcdbdacbdaadbadbdcbbbcadcbdcbabbdbccbdaabbaadacacaaaabbbdccacdcbcdaacacdddcbbacbabacccbcdddcabbccadcacbadacbabcbbcadbaadcbcbdacadadbaccadccbbdcbadbbcacbccbcbaddacbdacacdacbaddaabdddacaaaacccaddaacbbdabadcccbdaaccaaacabcbbacbcacacddbccacbaaadbabdbccddbbbbacaccbdabddbbbcabbddaabbbdccaaabaabbaabadbdabdcddbcbdcadddbabbddaaaddadbcabbbbbddbcbbbdaaacdcabdcdcadbbccdbcbdcccbbccbdcdacbccaabacbcddcdacdadbccacdbbbdaaaabcccdbbcbcbcbcadbbddcdddbcabdbcccbcccbcdcbbddbbbccccdddabddddbdcabbcccbccbaccdcccddccbbcaaadaadaaabddcabcaacbbdbaacbaaaacdbdcbdbbdccadbbdbacadaadaaaadacdaabbbdabcccddbcbccddbccdbabcabcbcbcdadbcccabdcddadccaacdddcdcababcadcdacbcddababadcdcabbdcdbabaddaaddbdcacbccdbbcdbddaaccaacdbcbbdcbbccdbaddddbdbdaacacadddaacacdddbbcbccccdcaaabdabdbacdaaadbddbbddcbdaacdaacabacaddbdbbcddcddbcdaddbaabbdbabcdbdbbacddcdddcbbdbdcdcaaccbaaaacbddaacaaabdbbacdbcdcdabbabddbbdbdcdcdbaaacddaacaaccdaaccadcbbdcbccbbbacabcbccbcbdbabcabaaddcbddcadabadabbacddaccbdbbdaaabdbacddacdddbbcbaaaadbdccbabcdacbcabbcdbbbbcbaddccbadbbcbbacccbbaddabbabbcbbddaaaacacaabdadbcbabdbbacdcdaadbadaddbabdbbbddcdddbcbbddbabaddccddcbdbbddcababaddacaaccccbddaaabcadbbabaadddaacbcbdccadabddadacbabbddcdddcddcdababacccbbcabbdcbacacbbcabdbddbbcccaabcdcddacddccacbaacadabddddccabaadadabdbdcdbddaabcbdbcdabdddcbddabdbacaaaabcaddddacdcccaabbcdacccbdbbacdbdadabcaaabcbddcdccaabdbadbdbbddbdcaabcbcbadaadbbbddbbbaccacbdcbadaaabbdccbddbbbddcbbbbbdcddacbcccbbdcbcadccbdcacbaabbadcdaabcbdccddbacbbccbadacaabaccdacbcbbddbbaabcdbacbacbdcbaccaababddbdcadcddbcddabdcacbbadcccabbaacbdbbdddbabdcbbbcaacbadacdcbdabbcbaccdcbdbacccccabbcdaabadcabcbcccbababbbbcccdcbcabacdcadcdbbbcdaccccbbbbdcdbadbabdcadadaacbcccdcabbcaddaccccdaabcbdaabaddcaddabdbbbabdaaaaaccbbdbcccbcaadcabcabbcdddbbdcbadbdbbbbcbddbdcadccbdbacbdaabcdbddddadadabdaccbdaadbbcdbcdbcabaacbaaccccdcbabdacabbcadabdcaadadadcdbaaaaabdbacdadbbdcddccdbacbcadacabdcdcacacdbcbcaaadddbcaaabaacbcabddbbadbccbdadacacddcddaababdbcbccbbbdddcdcbdbcbdcdbdadbddabcadaccdabbaadbaadcbcbddacbdacdddcaaacbbcaadbaacacddccdabcccdcdbcadadadbccabdbaadccbacdbcccbcddaadbabbdcadcdcbbabbccdaacdcccbbcbdcabcdcacbbcdccbabaccdadaccaadacbcdccdddabddbcddcaabcdbbabcdbdbbaabaccddabadabcadcddbbbbdabaccccdaadabccacaadcadacabaabcdaabbdaaaaabcbbcbacdbdcddcaabbccddaaacabcabbacdcbcabbabbddaaaaccccccacddbbbcbacdabaccaddddbbadcadbcdbadbabaadaaccbdcbcdaabcdcaccaccdabcaacadbddbdbcbdcccacdacbdcbdcadbbcbcddbacdabaaaabadcabbadaadbbccaababacabbcdaabaadddbcdbdaacbbabbdbadbbbacdcbddacadbaccbdbdddccdcaaadbbbadaaadaababadadcabdbaaaddddcbbccccbaadcbdcbdacbbadcdaccbddacabababccabadacddddbaccdabcaadbdbbcbcccabaacbdbdbdabbaaadaaccbdcbdaabdabdcccacbbcabaccdcbbbbdcdcbdcaddbcadcdbacdcaadbdbcbbccacdcdbccbbddabacddbdddcddacaacaaddddddbaaddcdcacdcdbdbacdccbcdccadcadbbbbabdbbbbbbbbbbbdcddbcababcbaadaaaaacaadcddaddbdccaacdccccdbbbdaabdcdbadacdbabccbccaabadcacaddbcddbdcaacddacdbcbbdcdbacbaadccdbbbcbabcdaadddbaddccbbccabddadacabdacaddacbcbcddbabaccbdcadacabaacadddcccbbcdacbaacdcddacdabcbdbbabcdbbbdabccdccaadbaadbcdbccbbdccacccccbaccadbddcbccddbabccdabbcbcacbbacaaabccabaddaddcccbabdadbdaccaadcddbadcbadcbbcccbcbabadaaddacaaabaddabddcdcadaccddadcdcacccabbdacbdcbbbbbaabdcdddbbadbccdabcbaabdbbadddbacdcbcaaadacccabacdbcccdabcbaddcbdabdbbcccdadabcacdbcacdbbbabcabcbbccbdddbbbccacdcbdbccabacdbcbbdbacacaabbadcbabbcdbccbcbadddbdcabbbadadacdbacdcaabaacbbacbccdaccbaaabcabbdaadddbadabdcaacccdadababcccaacbccbbababbaddbbcccdbcadbdacaddacacdbbccddbcabcbbddbbaabcabcbbcdbdcdadcdadcdacdcbaaaadadacadcbaabdacbdbcabaaaccdcdcccddbbbbaddbbcbbddcaabdbbbcacdcbdbabcddcdaadbcadcdaaadddabcdadccccaccabcdabbbddbadddadccdcacadcdbdcbbabadccdcababacaddbcaccccdcdcbdcbcaaaadaaabcdbbadccbbabcaaccbccdbbdaacaaccdacdabbaacaddabcbbbacacdbcdcdcccacbacdcacaacdaadccadbabaddbbdacabcbbbaddbcadddbcbdbbabdbacbdddabbbcddabdbcaccaaaaacdadabdcabccabbdcbabadaccacdcbdbbcbacaaddccbabbcdcaaccccdbcaabdadccbaabacadbacabccacdcddaaccbbabbdbacabdbbbbaaacbccbbbaabacbbdcbaaacccbaccddddccbcdadcabdcadbdabbdccccdcdddcbdcbcbbcccbaaddbaadbddacbdbabcabcbddccdccabcbdaaadadaadadcacdcababcaabcddadbbcbcbbccadcbcbbdaabcdcdadbababbbadaddbdabcbbcccbdbbcaaabccdbaddbccacabbaccaadacdabbaaadadbbdabaccadbdabdabcdcbdcbdddddaacbbadbababababcbbcadcbababdbdaadaadababcaadcbbdabdcbadbdaaddbcbadccbacccbbacaccdbadbbdaccccddcbacbbdbadadddbdddbccdbdbcaddacbbdabdddbabdbaabbbbacdadadccdaaacaacbbcadaacdacdccbdcbabdcbcccdcacaacbbdabcabbdccdcddbccbabbabaccdccbbccdbaacddccddaacdababbcdccccbdbbbdbaacddaabdadcadbccdacbcadabcadbbddcdcccbacdcaccbacbbacababbaccdadabdddadbdaaabdadbcaaddaaacadacdbacabcccdaccbcabbabcccbdddcbbbbaddbabcbcbcbbccccabcdcdbccccbadaddabaacadbcbaddabdcccaacddadadacadbbbdbbdbdbcbdbccaacdbcbabdcbacccbbdadbdaacdabaabcdacdcacbaddaaccdddcdcadccbdbadbcbdcccbbabbdacbadacadccbabababdaddabacdcdcadbcdcabadcabbcacbacadadbcabdadcbaacbbdcdaccadcaccdbaadacbddbdccbccbccaccaadcabbdcdcbcadcbdbdcbcacaabccadbbddcaabacdabddcdddaddababcddabbaabdccdbbbabcccbccdccadbbdaddbadcdddbcabccdccadbccdadabdbdddccbdadcaccdbbadacbaacbbbccacbaddbccbaadabbbcdabdbdbbccccaadadcdcccdaaaccdbaddcdbcabaadcdcdddadbdacddbabbbccaaaccccbddaddacccacaaadbcdddcccdadcbddcbbcabdcdcadbcaddbaadbddbcbbacbabccdcbbbdadcdddcdbbbccdaabbdbbacbccdacdabcbbacacbbaabadbbdbabacbddbacacabdacdabddadabcddcaaadbacabdabccadabadbcadcbaddacccdacddccdddcdaccbccdbdcdbaadadbaccbabcdabdccdbdbabddcdcccddbacbbdbdabaaabcabdadbcaddbbdbaacadbbcbbababdacabbdabcdadadabaaaadcbadbccdcabccdacbbccbdbccdaccccbbddcdbabcaabbabccaaccddcbbcadbaabaaabdcaaacddcabdcabadbadcdadbadbddddcbaabbdcdbadbbaadcabdcadabdaaaaccbbbabdccccaddcccddcdacaacdcaabadcacbbadbcdaaacdabddcabbcbbadbcccbaabbdddbbbbdbbbdddadadddabcbbbdacaddccdabbcdbcacdbaaadaabacdbaccddcbddadcdcdabddccaabdcbddbaccacbcdcaabddadddabdadcbdcbaacdbdaabbaacdbcadbdcadddbcbcccbacddabbbcddddbcdbddbacbdddcaddbaddacbabdcbbdadcadbbbcaacdaddcacaacdddabcddddddbacaddbacaacabdbcbaaabbcbaddbcbbbccadcbbccbdaccbabdbdacbbdbdbabcaadcabcaabcdacbadcdaabbbabacbcddacbdaababaaabccdabddbccaccabddbcaacababdadcdaabddbacacdaabdccccbbbadcadabdbbcccbdcdadddabcddddbadccbccacaacdbccaacacdaaaabdddbcbdcaddaabbcabaadacbcbdaddacadcbdbaadbddaacabdccdcbbdcacddbbccdbbaabcbbaddcacdbacdacbdbccdddbbbdadcadacbccabbaabccddbcabaaacacddaadcddccaaaacaddddaaaadcdddbacdbbaacccccdcadaccbbcaccbbccbbdcbacbbbadaaacbadddcacbdbdaadbcbacabbcdbacdbababcaadcccddcaacdcbcdbbcdbacadbcabbadcdbbaccbcddbbadcdddccaadddaabcaccbcddddcaaabbdacabbddbdccaabbcccbadbdabccdbdaccbddbccdccbacdbbbaccaacabadabbadcaabddbbbbbbbdbbabadadcddabbaadabaaadabdcccacadbccaacddddbdbddccaadcddcabacddaacaadccbccbcdbbcaddcccaadbbdcbbdabccdbddcabdaaacccdddccbbddaaaadcdbccabadbcbcddcddcaacdddaaddadacbbbacdcabcaacabbaaaacacdabdbadbabaacbadbdaabaabcbdcdacdbababdbdbdcadcdabddcbdaabdcadabbbdbcbccbbadbcdbdbdadaadbdaabadcaaacaccdcccdcbddccddcaddcbabbccaabadaaababadbacdccdcabacdddddbdadcabbabcdcadcbcacdccddbcbbbbacbcddbaacdbccdcbbcaadccbcdbbcababacdbddbaaadcdaaaaadacccddcbaacabadbdddccacbccbbddbbdcccaabdacdabbcddcbabddacccbbbaaddbccaaccbcbadcbdbcbaaccbbacabcaadbabddbcaadbccbaabccabbacddcacaccdddccabaabacbbabccabbbdbdbbcdddacbcdabbcabbbdbaccdbacbabddaaaccdaadcbddabdddcddcdabdcabaaaaacdddbcbdcbaaccbadcdbabaaccddcadadaccdcaaacdcbaddcdcccbbccdcccccabdaccbcccdadabbdbbccdaddadacdabaddcaabcbaabbcbcbaaadbbdbbabbbbabdaabaddbdccddddddddcacdcbbbadddabadddaaaccbabbcadabdaaacccabdbbaddcbcadcdcbacacadcccbbaadaaadddcadcaacdbcbaabbbbdabccdbcddadbaabcadadaccbadcadacbcabbdbacbcdccbcbdaccdabababcabdbbcdbcdaacabdcdbacaacacabaaadbcdddcbabdaaaccbadbcabdcddddcdbdabdcbbcdcadddcdbabbddddadabcacbaaacabbacbddbacccadbddbdababaaaccdddcabdaabbddadaaaabdaaccadbbbddabdbddadccaabbadcaaaddcdcddabdaabdbbacbcbbcdbabcbcdacddbbcbdacabaaccdaddbdadddaaadbdaabdbbdbccddabdcbcbbcddcadbdcccbabddcddcaacbadccabdaabccdbddcdcaacaabdabdbbabdccbdddcddbcabbddbcbbaaacbbbadbaaddaabdddabdbcacbbdbdccaaadccadbacbabacdbdbbddbaabbabbccddadcacbcaddaadcacaabbaabcadbcabcddbbbccdaaddacdbbbddbdcacbbbbdabbcbbcbabacbddddbabdcadacadcdbddbaaaadacdacabbabdbbacddbcccaaabbddcacadabdbabadbadbcddaccdabcacbccbcccbbabacabaadaadacccbdbabccdcabcbcbbadabcacbdbdacbbabdcccbcdccdaaccbbadbcbdbbbacadacbbbdbbdadbcadacacbbdbdadddcaabbaddacbcccdacbaaabcddbcccddadcacdadabbdcbadcaacbccdccbcdcdcadcacddcbdacbbbcdaababcccddadaadacdbbccbcdcabbaddcdbacadbcccddbdbdabdbbcbbccdcaabacdacdaadadabaccadadabdcbcddaaadcdbdadbadbcddabddcbbdddcadacaddcbbbdcadaddbabcbccbadcabcaccbadbcdcbbbabbaddcaadabbacadacccaabbcaaadcddacdbcbdacddabbdbabdbbbadcaabdcbcbbbddbabddaadcdaaacaabcacbbdabbddacbbaadddbbadbcddcaccacdbdddacababcddacdbddaadadbdbcaaaacadccddbabbdbbcddcadbaadbcbcdddddcdddbbcdbdabcabcdbbbbcbaacaabdabddbccccccbabbddaabdbcaaabbdbbcacabcdacdccbcabbadaacbbaaddddcaddcabcdcdaadddcdacbdcacbdbbddbcdcbdccbdccbcaaaadaabdbdbbbdbbccabbcdcaccdcbdacddcdccbbbadabbdccbbabcbdcbcabdacccdaadcdbcbaccaacbacddbadddadacddcacadacbddabadddbdaddbadbdcaadadddcdbacdcbadbbbbaaabaaabcdbdcddcaccaacdcddcdbbabbaddaaccbdddcccadbadbbddbccbdbdcabdccacbaaccdbcdcdbbdadbcaadbacdbdbbcccbcadbbcaaacdcbaddadcadabdddccbaddbadcaadabcdcbbcbdaccaddbddcabadacbadccaccaacdcaddcdddcbacbdbbabbdadcaacaabadacbddbbcaaccddaacdacdacacabbcaccacdaddbcabbdabdccccaabbbccdccbaababacbcddaaacdbbccccbbcdbbacbddbbdbcdbbbadbabbcddababbdbccdcdcddaacdbccbbbdbabcadccdbdabdaacbbcbadcbdbdbcdcbaaabcadacddcbcdbbbaabdaccccdccdadcdcaadadbadadcbcdabbbadcccabadcddbdabcdbcacaabcbbaadbaadbacbbaaacadacacbacbaadccbbaaabdaccbbabdcbaddbbccdccddcdddaccabdddabacbaacddcdadcbdcbabdcdddaaacdacacdabdbdcbcbcaccbbacbdadbbbabbdcabcbabaadcdbaaabacbdacbabdadccabbdabcabdcbbbbbcdddbdabaadddbaabdababccddaddbdcbddaaacbbddcacbcccdcdcbabdcaccddcdaacaadbdddbbdbabbdcbbaddccabbbbbdccdaadbcdcdaabcbdcccbbccbcdbdcacddbccdbbdadcacacccaacddabaccccddbaadaddacdcabdbbddbaadbaadaddacbadadcbabcdcabdcadcbcabaccdcabdcabbcddbabbddcdabcdadcccbcdabdabdcbadabaaabddcbbbadcadaaadccdbcbbddccbababdccbacbbacbcacdbacdbdbddbccdcccabdbadbdddcdbbcddbbdbcadbbaadddbbdacccabcbbadcbbcbcdbdbbcbbabaccddbdaadacccadaccdccddadbadabababcdcacadbbaacaabdddbdcbbbcacbdcadadcdddcbadddbdcbdaabadbacdcdcacbbdcbcdccdccdabbbbcdcabccdccccaabddccdaaaccbadcbaacdaabbaabbacbdadccdbcdaaaabbbbdcadccadaaaddccbbbacbaaccbcdcadcadcdcbccbdcabcbccbaddbcbdcdcbbabbbcbccdadcabbdbdabbdbcadbddcdabadadcbdacdcdcbdcddcbcdbbcbbcbcbbbbaaabcbbddcddaddddbdcdbbdbcbcdcbcbbddaaddcbcbbdabdcaababbadacacdacdabbbbadadadcaccccdacbcbaccaabdaacbdcccdddbbabccadccbddaacdbbbcadbdbaabaddaaddccacbdbbbdbcdbdbbcdbadbdccbbdcabbdcdddabcbbdbbadabddcbdabbdaaaaacaabaaabaabaacdacbabacdbcbcdddddacacaddbadcbaddaacdbbbcbccddcbbcdacaabdccacadbcdaabdddaccbcdabaacdacdadacadcacaacdabcbccbcdbcaadacadcbbdbbbdbcbddabaaacbdaacbdcbaabdaadddbbcadbcdcacadcadbbdabbabdcaccaabdbadabbabddabcccbaccbbaaccccdabdbabccbbccddaddcbddbaddabbacdbabcbbcaccdbddbabdbbcaaadcadbaacdcdcbaaaaccacbcaabaabcaaabbbcbdacacadacadcdadbdaccdbacdbaddacaddbcbbcbacacabacddaadaccdbdbbcbababcabbbddcaddbcabbbadbbbaabbbbdaabcbaddbcddcacbababaddbccbbaccdcbccbbbadbbdddbdcaabadabadacdcbcbbbccdcccbcdbbabdbdcdbaacddcbbdcbddbcdcbabaccdcabaddadaddbacabbcbaacbcdbbacccdcdbcccbcccddccbdacbddcbaadadcdbcadadcbaadddbacbcdcccdbcdcdacbabdabcbdabbdcccdccdccbcaddabdcbbbacadabddabaccccdbdddcdbaadbaacddcddbbcdccaaacdddabbaabdcdacaaaaacadcddbccbbcaadcbddbcbdcbdacacbccccdccbdbdacbccbcbdaddbcbbaaaaaadbdaccaaadacababdcacacbdaaaaacdbacabccdbacbaaaadacabaddbaddbccbbdddbbdadbbabbbdadcbccbaddabbacbcdcbcdbadcdabbadbaabdcaadbacbadbbabaadcdcabcabcaaddbbccbadbabdbdbadbabcdacaadaccacbadaddbaacdadadddbadccdbbbbccbadabbcbcccaabdacdacdadcdcdadcdcbdcbcaddacdcbbdacbbcaaaccbbaacddddbadadadadadbcddbddbbbacabaadbccbcdcccacdabcdddadddbaabaacbbbaddddbcdaadccdcadbaaaabddddacababdbcbdbabbdaabbabaddaabbccbcddcaadaadbdbbccccbbcabbababbcadccbccbacbaccccaadbacdaabcbdccdabaccaaabadaabddcbacdadacaadcbadacbadaacdaacaaacadabcdbcbcabcbdcccdccbdaacaccacaddabadccbaaddcaabdcbdaddbbbcaadcbddacadaccbcadbbccaabccadaaccabbccdcacbdbcbacaccbcbadcdcdcbcdbdbbdcdcabcdcbbacdcddcaabaabcbdcbdcaacdcbaabbcbaddacdbccbcdcabdcdcdcbcabbcaacccdacaabcbcdaabadcdbadccacacacacdaacdddaaccddadadacdcbadbdaacaacddadabacdbcabaadcadbbaddacbaaadaadbccdccaacbdccbddaddabdbcbadcaacadabbadddccacddbbabbdbababddcbabdbadbabcaccaddbcbcbcbbcdbcdadacccacbdcbcbbbdbdcddccadcbacbcabbccbddcadddadaabcbbdacbddddabdcbbbaadaddbaccaacdaabcaaddaddacdaccabacdbcccdccabcabbcadbaddbcbcccdbbdbddacdacdccdcccadcaaddadcabdcadabccddbccdcbadacbcabadddaabbdbaddcabbdaabacbcbcaaaabacacdaaabbccbddbbcaacbdcdacacdbadcacadabacbcbbbddbcadbadddddbcacbbbabbdddacdadcaccccccbbdaabcdadbacacbadadbabdcbaddcbbccdbdbcadcabcbbbaaacbbcbcadcccabdaadbcbccaaddddadbdcadabdddacdacdbddcadbbbddcbbabbadcbccadacbdaabaddcdbadacadbabadbdabccaacaccaccdaacdbdbbcbabcdccbcadaccadaabbbadaacccbbbdacadaadbcdacdadbdbdaabcaccdaddabcdbbabcdbbcbaadbcbdbcadcddcbccacaacccdabdcbdccccdadcbcadbdacddbcaaacbbdaadabadacaacaddcdcdadcabbbcaddbbabdabddbaabdbddbadccbacadaadaddabbdbdabcbbddcbadddbbacbdadddabdccdbcabdbdbaacadaadbdccdcacdacdccbaaabccbadcddabbcadbcbbdbacaacbdccadababdddcdaddbacbacabaaaaddabcbbabdcbacaaadbcddabdbaddaadcacabddadababacaababacadcbccadcccbccdcbdaddbcddbdbaaadcccaadaddbccdacddbdbdaababddbbccbdcccbaaabdcddadccdcadaabdcaacbccbacacdbdbcddacbcaddacbdcbcbcbaababcbccaadaacccdbabdabbbacdacdaacabcadaaaccbcddcbdbcaccdcdddbddccddccadcabbdabdcaabcbdcabdbcccaacdddbbacdbabadababaaabbababbcaccaaadaadbcaadbdddaddddabdcbbcabcaaccaccddbabbcacaaccadacabaabdacccabbdababdcbaaabdddabcbdcdaaadadcbabadaddcdbbdacdadaabdcbabacbcbbbccddababbaccbbabaacbccabdbcaaaaabdaabdabbdadccadbdabbcdacaaccadcabbbabcccdbabaadabddacbacacbbaaadcadcbbddaadcdadcabddbbaacaaaaabdccccabcbccadaadacacbdaddcbbcbbddbddaccbaddcbadddadabdbccacacaadddabacbdaccadbababcbadcaaddbbdabadcbaddbacdbddcbdccacadbccdcbbbaabdbcaddaaaabbcdcaadbcdaddccaacaacacbadadbdbbacdababccdcbbcddaadaaddabdddcdbddbbcdbabaddcbaaddbcdcacbdbcbbabdbcccdaccdacccadcdcbbbaaccbdcbaadcccadbdbbdabdccbaaacadbdaccabdcbbdccabaadacaabbdabbdcababddaaaccbcdbbcbbaabbccdcbaaadbabbcbadcbacbabcbbdaccdcaabababbaddabdbbdaadabcddcaddadaabdaaddbdaccabbbddaaddaababddcdadbdaccdcacbbabdbccbacddcabadbabdbcbabddbcbbcaccbaaacadddacabdacbacdaacccaddadadadcabcbaddbcdacdaddbbbdabacadbababbcbcacccddbabdcbdbcdbcdcacdbcdaaddcdddbbcdbabbcaddababddcbbdddcdcaaddabcaabbddccdbcdadacaaccaccbbbdbbacddcbabbaddabbcbccddcbbbcabbcbbcddbccbbcaaadddaccdbbaaabcaaacbcdacacbbcbdacbdaabbdccaccbdabbbddcbddbdacacaacacdabbadccdbcadbccbbbcadadadcbabacdccadcbdacbadcaaddaaababbadcdadaaabadbdddbcababbccadbbccbdaadaddbdddacbdbcdcadcdcaadbabccabdacdbabdbaacccccbbdaadddcbcadccaadbbabaaccdcdbcbbbcdddcbcbdadccdcbbaadddaabbcadcdbdcacaabbabdcbdbbaaccadaddbddcaadcbcddcbbbddddccdcadbdddabbdbabcccddcaabddddcbdbbababaaacbadcabbbbaaacdcaacdcbbaabbdabbacaacdbbcccacccbdaacbbcdcbcdbaaadccbacbaaacabadadbbbdbadbccbadbbbbcdcaccdbcccaabdadccbddadccabbcdacbaadcbbdbbcdcabacacadcbbadbbbdabcbaacbacbbacaddacabbbddbdddcacddbdcdddcddaacbcbcbadabdccdddcabbbbcabcdcdccddaaababbccababccabdcddbdcdbdcbdccdbdccbcaaaaaadbdbaaaaacbcaaddbdbaacbaacbcdcdbabcbdbdccbbbcdcababdcbdbccaadaddaabbacddbccbdccbbbcacbacbddcdcbdbaddbcdbadadbbccaddabcbaadaddccacdcbccacaddbddcdaddccadacbcadabddbcbdddbdabcdcaacbddbbcbacbbabdcbacabdcdbdcacaabbbccaaaadabddcccbcaccadbbbacccbbdaaccaadababbccbbcbdddccbbbadbabdcbcbccdaaaccbcbcbbcadcacaaaacacbbcdacbacbcacccdaccbcdacdaaacddabccbdaddcaccccbbbcdccbcccbadbddbbccacccbdaabbacadbaadbadcbabadaadbbbbdabadadabcabdacbcbdaaccccccdcccabbbadbcaddccaccabdbddadbacacdbbcbdcbccacddcbbdbccdbdcdcadcdaacccacbbcacddccdcdbbdbcbdaddaddabcddabaabbdccdadcbcbddcacdcdcbaaaacdbdbcaccbdbcaadabadbbccbccabbdadbbadbbbaadacdacabdaacdaadbbcdcabcacdcacbcadababadccbccabacadadabcaaacdcabbcbdbbaabbdcabaacdccdabdbcabdaabbbabbadabbcdbdacbcbcbdadbabcdbadcbcccdccbbdcabddabbdccabacadadbbddbaabdbcccbbadbaaacdaddbbaccbadcbccacabdccdccbcdcbacabbdaaabdddbaacccbacabcdaabaaadabdcbbacdadcbabbbcbcdbdcdbbddcadacdcacbadaaaaccdaaadbccaabdcdabbbdbbabcaacbaccbccbcaacabdbaaadbccdddadaadcaccddcbaaadcdbccbabaaddaccaaabbbbdaacbadcdadbdbcabdbaaacccabcdccdbdbaadccdadcccbabaadaacadadacdcccacacbdaddcbcadaadcbcdaddbacbaaacdcaccbdbbdbdbdcadcabbbacbbaccaabccbddacadccccacbaacdbbbbacdaabcdcbdabdcdcddbdabbdddaacbccccadcabacbaabbbdadadddcaabdbcbbaacdabcbbdabaddcdcacbbdbbccaabdaadcdbcabccddbbadcbbbbabcddbddacddacacdbaadbddcadbddbdabbcdccbbccabcacdbaccdacdaccaaadcdbcdcdcacdadaadacbbabbddcdcabadcadcbadaaaabcdddbdcaadcaabacdcadababcbcdadaadadacadccbadbbbddaabdababddbcdcbacacbaadcccacddbbccdbcdaaacdcadaddcdababadcbbdcaabdbccdaccdcccadccddcbbaccdadadbcdacbddadacabcdacaadbaacbadadbabdacacadccbcccadddaccdcaacbcbdbdaaabacbaabbcacabcccbdbbbdcaacabbccbbbdcadbdabdcbdbddabccdaccabddbccdbbabdcbddbbbaadccbdbddacdaadabcbacdbdadbcdbacbbddbdccdbbdccbacbdaacbaabacbcaddccabdcbdddaaddadbbababcbbadabadbcbbcdddadcacdbcbddaccabcdbbaccddbccabccaaacdadadccadbbbbdabcdaabddacbdcaabadbdacacdbccaddbbcbacdbacbcabdadcdcbdcaadadadddccadbabbadaddbddbcdacbcccdcbaabaccdadcaccbcaaccbbddaabbaabcacbbbcdcbbdabdacaddbbcabdbdccbcaccbdbcdccadbbbdcadbdddddcabdaaaaabcaddcbaaccdcaccaaaadcacbcdbaacacbdbdccbdbabaddadaadcaaadbdccdbabcacbdcababcababbcdccdabbacccdadbcaadddabbbdaabbdaccccdbcddcadaaddbcaadcdddcbcbabaadbbcadddbbbccaccbacabbdbdcdabdcdddbcaaaacaaabbbdabdbaccaaabbbbbccdbbcbbabacdadcaaadaabcaccacbbdabadcadbbacbbabbbdbccdaabdabbcbcaabdbcdddcabcdabcaacbabbdbcdbbadaddcdcaddddcdbbaabdcbccbdbadbbadbbbacbdcdcbaacbcadccacbadadaccaccbddabdcadaabddbaacbbddaabdcddcbcabddccbbdddccbadcdcdbbabaaadcddadbaccbaddadbbbcbdcccbbadbabcaccdddbdbcaadbdaacdbbbbdadcbadabbdddccbbdabcacacdcdbddacdcadcdbabbacaacbdaacbabcadbdbadbcdbacacbddcdcababdcaccbaabaacadbacbbaacdbaaaddadbbbcaabcdabcbdadbbbdadaaccddaabddcbaccdcadbccdbbaacbaabbbdaaaabaadccadcbabcccbdcdbccdacbabbdccbddbcbabcbbdcacdabcdcccbabcbbccbabcbbbcdbabbdcadbbbbbbdcccddccddcdacdaddccbcaadacbcbddacccbbdcccaddcdcdcbddbccacabaccbddbaacbaccbbdbdcdddddadadaddababcdaaccbcaadcdcccacdadbbadaaccbddbdcaabcadcdacdbcacbbdbbabacddbdcbababbaabdabdaddbddaadddaaaababbaddbddcaaadbbabacbdbbbabbbbbaaadbcadddcdaadbccdaccaaabdddbabadacdddbbabdaaccbcbaaacadccacbbccacbcbbaadddbbdaacdccbccbadabccdbbaabcbbcbbddcbdbddaddadbcdadbbcbbbbdabacbdababcbabbbdbcbdccadbcdddacabadcacdcdbacbcadacadcabdbbdadbbcacbdbbbdcccbbbddbddccabdbacaacbbdddabccbacabacdbadabbbdaaabcdddccddcdbadadabdcbadacaddcdcbaaacaabcacccabadbbcbccccabdadbbcaaccdbcccbbdbdbacbaadaacbbdcbdabcadbdabcacabdbbcdcabbbaddcaddaaccbbbbccbcabcacbccbdccddabbbadcadcaacdddacabbbcccdadbaabababdabdaccdbddadccbbcbdbdcdbacbcabdbcbdccdaacbabcaaaacdbdcbcaabdacdbcacacbacaddcabcbbbabadcdabdacbbbbdcabdbdcbbdaacabdcabbadddbaabbadccadbdaacddbbdcbaaabbadddcdbdbcdadbaabcabcacbbdcddccbdadaccdccbaddcacdacbccaddddbbcbaacdbdcaabaabdbbabdbbaaadddcbadcdaacdbabbddadcccaacbdbcbabaccbcccaabaccaacabbbbcbcbaabbacbccccddaabbbabbacbbdcdbccaacaaccababaacccddcbcabcbbcbcdacdbadbcbdddbcadddddbcbdcbadabbacbcbcccdabaabbcbbdacddbcbaaccaabdaddccbbacccddbdbdddbcdcaabcaccbbcbabdbdcaccccdbdadbaadadadbdcccabdcadbbacacbbacbddadbbabdadabbcaadcccbcbddcbbacbddacdaadddcdacdabdadbbcbaaabdbadcbccbbacbbcabdccbdddddbdbaddabbacdcdcddbabbaddadbcdccddddababcbaddcbbbdadacdbadccdbbadccccbdccadaadcccdaabdcaabcdcacadaaabbaaccacddbbadbbcabccabbababbadbaaacdbaccbadabbbabadcbbbbabcaabbacbdaacbaccddbacdcdaccbdbcccbcbccdaababbabbdcddcdacbadbbcddcdcdbbccbdaabacbdbbdadabbdabbbbaccbdaabaddacccbabcccdcbbcccbcaddacbcbacabccababcacacabccbdbddcbddbabbdddcbcdbcabdbaabdcdbdaccbdbbdabbbaaaaadbbbbabcacdbdaabaccbccddcdccaddbcadddabbaacababbdadcacdaacacccbaadccdbcaaccdbddccabbcdabaaddbbccbdcbccdcabcabbdabcadbdaadabacacaccaabcbbdacadccbccabcbccbdaccbccaabbdddbadbdcbdbaabbbabbcbbbaabbacaacaaaddaacbcadcaabbddadacbaddbccaaadbbddbdcbcbacacabadcccdbabadadadbdaccbccccbcbcdaaddddadabaabdbbcabadbadddccbabbddaccdbbcbccdddcdbdbdcdcabbadbcbbbdccbdcaaacdbcacbdaddabbabbabcabdabadacddadcddabdbadacdccccadabcdcbcdbaaccdbbdccaaacaaccccbdbcddaacbddbbdcaccbaacccaabbcddcddaaaabdcaabcdabbddbdbbabadcadcdccbddabaaabbbbbdbadcbddabbbacbdcadbcadacadacacdbcabddcccaacbbbadcbdcaaccadcbbcdbcbdadaadccaabcdcdcabcdabccbdacccaacaccdccbacbddccaccaacbddbabcdcabaabaabdaddbabdcbcdcccdddcacccdddadaadbaaacaaaddcbcccbdcbbbbabbdadcdadcdcbacccdbcdccadadbbbdabdbdacadbcbbabbacdcbadcaaadbddbaccacadbcdabababaaccabbdbacadcbaabdddddbdcacacbbcbadcccbacaddcdbbdbbbdddcdaaabbccdbbbbbcacbdcdadcacadccbaaabdadcbcbaccacaabdcabbdbdadbccacbbdababbdcabccbcadbdcdccdadadbcbddabccbcbaabaadbdcdbbadadcadddcdbbdbcdcbdabdcbbbbbabacacdbdbcadaacdcadaabccbccdaacccbcdaacacbdbcbdcccbbcccdbcdcbacaccdabdbbbcccddbddbaddbaacbadbdabadcbdbcbdddccabdaacbdaabbabacabaacacaaaadcdcbaadaadddddbabbccdccaacbacaacaddddadccbcccccdadcdcadadcdbcadbdcabadcbcbababbbdaababacdbcddddaddbdacacbbbacabaabdcbdcdccbbcddadbdaabaddaddcccacbcdcbabcdadacdbcbaadddddcacacadbbabbccddaacadbdaaddababbccbcdcadbadbddddbddcdcbdcbdcbabdbacccaacdcdbdadccddabcbbcdcbcadccaddddcbabdcaccbbbcdbadbbcdcbaabdddcacbbcacacdacdcbbcabdbadccadcaddddacbcbbbbbaabdadadcdaabcbbdccacddddcaaacaccbabcaabbcbdaadbaccbbdaacbdcccdddbabdcadccddbbccbdbacbdbcdadaaacddabcdcadbccdcdcbcaacddabdcabbddcbddbcbbbddabcbbdccbdabdaccacbdcaacbabdaacacaaaabcabbaacdcdbcbabbdbbdabbbbadabdccdaaabbababbbaadbcadcdbbdcdcdccccddcbbabdadcdccdccccccbabbbbcbbbddddabacdadabcdcbaaadccadaabdbdbcacdabbdcccabbaaacdabdadacdddccbbbbdacadacccdccbacaadacdccacdcabcccdbaabcbadcadcbcdbcaccbdcdacdaccddcddcabbcadddabdacbcbabdcbbdaacacacdaabbaccdcdbdabccacaabccccdbaccbaddacddcabacbabcdacadaccdadaacdadccaaccbaddcaabbacdbcacbabcacbdaaadaadbcbbadcdabdabaabbcaabddaaccbdbddccaccdacacadabbbdddbaabaaacdbcbababbcabbbbacaacdbbaadbbbbdcdbacccccbcdcccbbcdadaccbdcbbdaacdbcbaaddabbdcbcbdaabbbccbdbdabbbccabddcdcaadbcdcdbdbaaadccbbdcacdcacbcbacaaacdaadcbacdbbaccdaacaaacdbcbbaccbdadbdccacdadcdacdaddaaaaababccaadabcdcbcadbdcadabdacccccdbaccbdddcbabdbabbcabdcbdbbbbabcbadacbbaadbbdcabdaabdcacdbbddddbdaaacbbaddadcacdaadbabcaabccdcabbcbdcdbdddcdabccaabdacbdbcdacbdbccaacccababbbcdcabaccdbbbbdbccdaaacabcbbdacbadddcabbbcbbcbccdcabbbabaadcccdbadbcacdbcaccddadacacddbddccdbcdbbdbbbbbdcdaccabcdabbdbdbadbababdaccbdbcdadcbdccdcbdbdccabcdcddbcdbbccbcddcaacbdbacbcbcabbabdbdcabaddbadcbdbddadcaaabcdddbbdbcbdcbcdbbdaddadccabbdcdaddccdbbdabcdbbcdbddbcbabbbbdcadbacadbaadccddabcdbbaddaaaccabddaccbbdddadcababbdacbdbcbcacbcdbddcbcacccbbbcdbdccdabbadbbacadcaacabacabbdbdaaabaacdccccaabbcadddaabcbdaacdabcbcbcaadacbdccacadacbcdbdccdacddaaacadbdaabcabaabdccdbcadbaaddcbbdabcadbbbcaccadbacdcdbcabacbcaacabcdcadabcabaaabcdaddbdaadbdcddabddbcddabadbcaccadcabababcdcdccccaadbcbddababcabcdccbbabccbaaabbdccabdabcaddcadbabddbbdddaadaabbadddbdbacdbdbccadccdcbbaaaccccabcbbaacbcadaddaacbaabaaaaccacccbdbacacbabbdddbbbbdacdaddcbdddcbbadbcdcbdbbcbbdcbbcddaddaabadbbdcbccadabbdcaadabcbcaddbddccacdbbabcaaccdbcddccdadbaabcdcdbbdbccaccbdcdccbcacccabcaacbcaacaabdbcdacbcbdaccacbbcbddbbcbcbaccaadccdadaccabbcddbcbcbdbcbdbcdcbbdbcddbcddadcdaaddadaacaacdcbcddddcdccbbadbddcdbbababacdacccabaddbdccacbcbcaaababcdccaadadabaacbbddbdbaaccaacdaccdadddbcccbbcbdbaacdcadccabdccabbadcaddbdcaaabdccdaacbbdcaccabbcabbcacaadaacbbdaddcccabbdcaadbcadcadbaabadaabbdaddbbdbbabdadccbdcdcccddaacbdabbaabcdccbaaababcccbbcdcabbccdccaddacdcaabaabdddacdbcccabadaabcdbbbbbbbbdccabccbcaddaacbacbadbccbcadadcbdabbadccccaaabdccbcaaababcadbadccaabacabcdcccddbbbbbcabbbbbcaddcbcabdcabadbadacadabdadaabcbdbbccabcdbaaddbbaacbaaccacaabbddaaacaccbbbbcccbdbacdacdcbabcdccaacadcadcdcccbcabbdbcccacdcdccacacbcdcdbaddaabbaacbaaaabccdaaccdaccbcdbcbbbacbcdcbacaacdadabcabbabbaabaabbdbdacbdcdcbacaddbbddcbbbbabcbdbcaaddbdabdacacacbaaddddbaabddadcbaaccacaccdbadadabcdacdbcababbccabddaddcbccbccaaabadcdddcbcabdabbccdcdacdbcdcabbadbbcadaaadbacdccdbabddbdcbdcadccdacdaacabdcadbbcdccbccaccabbabcbbdbbdcabcbcacaccacacddcadcaddcbdacaabbbbdddadbccaabdbaaabdadbbbaadcccdadbacabbdadcbaabbbccabdcccdcacddbcdbacbdadababacbdcccdadbdaacabdbdcadadbdcbbbaaadacaccdddcdbadaadbbabcccaaccaabbcdacddcbabbcaddbddcbbcdcacbbccdbaaabcdabaabcdcaddaacbdcdbcdadbaabaaabcacddccacdcbcaabdbcbcddbaadccaaabcdbbcadaadaabacdcdabdcdccbccaaabaabbacdddbdbccaaaddcdbcbaabcbacadbadaadbaddabadaadbdccdcaccccacacdcdcbbcbddcddadccbadbccdcabdbbdcdaacbbbcddbcacdadadddcbbccbcdbaddbcbabdcbabdbdbdacdaccaccabccdbddaaaaddcdddcdbbacccbdcadbacccbcadaacbcdbdadadcadabbdabcbcdaaabccdcbcbbcbabbdadadbdacabaadcbdcbbabdcccbcabaddccaaccbddaddcadcbbaabcabdbdbadabbaaabbcaabaabccdacbbbaabbbccabdaaaaabcccccdbcdcdbbcaadaacadaccbdcdcaacabaabcddbcaacbccdadcbccabaabdabddbddcdbdcacacacaabcacaaacbcacbbdcbbdaadcabcaaddadabddcadbdbaddadcbbababcaabcbabbdacdabdbcaaabadabcddcaccaddaacabdababbbdbcbdbbdbacdbcdcdaacdcababddacbccbbacdbdacdbbcdbcabadaccaadccddddaaddabdbccaaabdbaccbaacbcabdcbbdbdddcbcbbdcbdccaadccdddacdbdbcabbccadabcabbbccadddccaddadcddbacdadbabbdccaaaacdabcccaabadcabcdadddacacabcadbdabdbbacbcadbddcdacdccabdcbacdabcdacbadaaddcabcacdccabdacdbddddbacdaabdabacadaacacbadddabbabcdbdbcdbdbddcbcaccbbcdbdaddbadcbcccdbccadbcabcbbbcbadaaabdbdabddddcbabcadacacaacbdcbaabcbaacbbdcdadbcaddaaabdbccbcddbbcabbbdaadcdbcdddcccccbcaaadadabdcbabddccdccdabddbaacaddbbaccacddcaabddcdbdccdcdcbbbdddcccdbddbbdcddddbabacbbdccdcaacaaccbbadbcaacabadabcddddabcccbddacccacabacddbaddbbbcbddacbdaaacabacbbcdbdacbbcbacadddacaaccbddbdacbdacbdbcdbaaddbbabdbdddacdbbadbdabaacacabbcabcadaddaccdadcacaabccdaadbccaababdddbbacdacaabbbaacccbccbcbbcdabcabdbabbcddbbaacbcdccdcadbcabadbacacbabdabcabdccccdacbcbccacdbdbdcbdbcacabbdbdabadcdbaabbddadcaddcbaaadbadccaacdbbcccdadbaabdcabbcbdcbcbcbaddbaaaabaddacccbbdabbccdbccbaabacbaaaadbbacbcdacacdaccacdabcbbacdcabbbacbcbacbdcbddbcbddcddccbabdcadbdabdddcacbbbbdbcdacbcaacaccacccbdabccdadccdccadcbbbddcbcabdcadabaddcaabddbbdddcdacdadbcbdcacacadbcbabbdbdddbbdbcadbabcaddabaaddadbadcddcbaacbccabcbccbadbabcadabdbbcabcdaaaabcbdcbddbaadccdaaacaabcbccadbdbababdcdcbadbdbdddddddaadcdbabccdddaccdacddcdccacadcddcddddacbdddabbacbdbddcbcbccabbbabbdcddbcbacdcaaccbaddbacacddabcbdabccacaabbddccaacacacbbbbbadadbcaccbacbcaddadcaacbacddcdbadcaadbdcababaddbdaabbaacbacdbdaaacbcdcbcbadcbbcdbcbbcbcadbbcdbcbdabaadcbbacabbcdbcbdcabdbadbcccddbaaacabcbbccccbdaaccaabadacdcdcdaaddbcbbadbdaaababacacbcabdcabbabcdaddbbbabbababbbbadcabdcaadadcbdcdccbaabddcbccdacddcbbcacacbdcadcdababacdbccccdcacbcabbdabdcccdabdcddabcdacccdcbaaacccaaaddbaadabbccbdcdcdcdbcdbcdbcddbbadccbaadcdbaaaababcabcdcdbabbadcbdcccdcacbdadbcccbbcccbadacaabbdcbbcaddbacdaaabadbcddcdaadcddbddaadababdccdbdcabdadcbdbacdbabaacddbabbccbcaccdcbbabadccdaacccdbdabbadacacbadbdddadcacbcdcbbddadcbcbbdbcdbcdddadcbadacbbccbbbaccdcbbdbadcbcccaccdaccbcadbadbdccbcbcdcaddcadbadbddaaccacabdaddbbbcadbcddabadcccbbcdbabcddccbccbaadcdaacbcdbadbcdbacdbdbddccdcaabcadacdcbaddcbbcbbaacacbaccddacccbcaddadacbccdbaccddcddbbbaabcacccbdacdaaccacbaadcabbbaddcbdddcaccadabccccbdbdaabacdccbbbbddddaccabbcbbbbacdbadabddbadcabcddcdddadcbacbbbacbddcdddabbdcabbadccbbabcccadaddacacbbdbbaaaacbcadcdbcbcbbdbdddcdadadbbcdaaddaadddcccbcccadbaaaccbbbaacdcadcdcadabadbdcabcaadbdccaddbaabddbdcdacababdbaabddbbbbdddbabcdaadcddaadababdcbaadaadaccdacbbbdcdcdcddbcddabcdaccbcdccaaccbdcabdcdaababbcbcddcabbdcbbaaaddcadaaabbdbacdacbbaadbaabccacbabadddabdcdcdacccccbbdbabbabacccbdabdaaacaccabdacaadccbabaabbbbdddcbdcddbbdcbdabadaccbdcbadddddcacaadaddcccccdbcdbbddbbadcbbdcbccbcbbbadcaadcbaadadbbdcadbcaccbbbcbbabdbbbbcbabaadbadabddcabbccccddbacccddddbaccbabdabaaadbdcdbccddbcdaababcbabbaccbbdbbbcccaadcbadddcadccabddbdccdbaabdbdcbdcddbabddbabadbdcaddbadbdbbdabdabbdcccadbcbcbbaacbbbcdaccdbdcddadaacadcbcbbbcdcaabbcacdcaccbbabbcacaabcbcaadddadddcbaccabacbdcdcadcdbddddaadaccbbddbbaaccbddbdcacbdbdcbcbbcaadccddbcdbbcdcacdababaadbbbacadbabbdcaabbbccaddbdadbdaaddcdccacbbbacccaccdddaacddbcdcabdccddbacbbdddbbabbdbbbabdccdcbcbddbdccccabbdbadbbbcddacbdbbccabccbdaacadbbccbacdbddacacbcbbadcabcbcdbadcccdcddbabbdadccbcabbcddbbcdaaaadccbccadccbcccdddacbddccdabddaabdaacdabbacdcacdcdddadaababccbdcbbcdaaaacdbbcdbaadaadaaddaddabbcccccabcdacbaadacabcbcbcacbbcdacbadcdacaaccacaddddacdabccaaabaaaabcccabcaccabcccadbdbbdbabacdbbcdcacccbaacccadbdbcddaabddadccdacdcbdbbcccdbadbaaadbcbbdaacbbccccbcdabdbabdcbbaacdcacadbcbbcaccaaddbaacabdcccddbadcccdbddcaadbdbdccdbdddccdbdcdcabacbddbdadadbbccbbacbbbdbbddacbdbcbbbbacacdcaaddaabdacbdbcacdbacaaaadaccadddddaccdadaacacdacdcdddcdabbccbbddcacbbbbccdcddbdbbdbacaadcadbdccbddddcacbbabbcdcaddcacaccbcacddcbdbbbabdabaacddddbccbbaddbbddabdbabdabdabadabbbabbbabcddacdcbdddbccbdcdbccdadbbabdcadbbacbddbddcabcbadbbbadcdccdbcaddbbcacaadcaddbbccaabadcdcbcdddacbcacbdcabdbdcdbacbacdcaaaccbbaacbcabcdbcabddabacacabbddbddbcccababcabdcbabcbbdccaddbaabaabdcbdbbaabbdbacadbccdcdccadcbcacccabbbcaacddbcdcacadacabbacaadcccccbbcddcdcbbdbbcaccddcdbdddaacbdadbbcdbdaacacaaacacbaccdccbcbddbcddbdacdcdcdaccccabccdcbabbddabbccddacccadaaaabccaabcdddbcbabddaabccaaccacdcdbacbaaabbdbbbbabbccddcdcddabbabcccbdabbdbcbabbdacaabcccbbcbacaccdccdbcdacacdcabcabbddcadaabdbaadbcbbabdcaccbbddddacacbdbaadadcdcaacbdbbbaabbacdbabcbbcabacabbacbbccadaaddcbcdabdcbccddddcaaddabbcbabadbdbdabdadbabadbbaaadabdbdaabcabacdccddaacbdbbcacbbbabccaabccabbacaacaacbacaadbacadacdabaddadabacdcdacbdcbdccdaccdcdbddaccbbbadaabbccbbcdcaacaadbdcbcaaddcaacbcdbdcdddbbbabdccaaaccbbadccdbbadaaacbdcddcbcabdacaccccbdbcddaddbcaadabcdddadbdcdcababacbddcdaabbcbccddaaaadadddaabbaaabbcccadabddacdacbbbcdacabaaadbabbccdcdcdddaaacbdbcaddacbaadababdacbdcbdbdcbbddabadbbbcbccdcbaadcaaddccaaaadbcabcbcbbabcdbcbbdadcadcbdacaadccdacbbddbcbbbcbdaabddbacaacbdcbcdaabaabbbbcaabccaccabbbadcaabdbaacabaadcdccbbadccdccdbddaacdbdacdbddcbdddddabacccdaabbdbbdbbaacccabbdacaccababdccbadcccbbbbdaddbbacacccadbdbbadbdcbddcaadbcadabcbacdccacdbccabacccccaacadbbccaadccbbdbdcacbcdaaddccadcadbdcdddbbbbdaacbaaaaababbadbacbcaadaabaabcacadcadbdbadbdabaaadbaddcccdcabbdbdddabcdaddaaacdabaadddcdabcaacbaabddbcdbcdabbccbbbdddcdaaccabccdcddababbadcbaabddcaccbabdcbaaacabbaddbaaadacbccadbadbbbbcdbbddccabdccaddaabbdaddcabbdcbacdacacadcdcdaccaaddaaababdcccccdcbaadbdbcdacdbbcabdabbccbddadddcadaccaacdabaaccbadbbdcbabdcabddabaddbbacbddcabccabcdbbadcaaddbadbdcacddcbabdadcadbabadcbacdabddddcdbcadbbdcadbddcdddcdcbbcddadacbdcccbddcccdacbadadddcadabbabddddbacacbddcbbdbbdcaabccbaddacccdbcbdccbcbcabddacadbdbadcbbddcbdddcaabdbcbdcdccbdbbccacddcabcabbcabdabdcbabcdaacdddbdacdabcbccddacadcdcbdbacbcdbadbacabdadbacadbcbdaaddabbbbdabbaabadcbccdaddbdcbcdabaadbddaccacddbdbdabccddbabdbdbccdccdbaabccacbabcbcbadaacbbbaabbaabaadcbabbaddadccdbbcdbdadadccdccddacddacdacaabcccdbbdcbccadbaacabababbccdadcccbdccddbcacaaabbaaadcccdacddbbbddddcacaabcabbbbddbcaaadcaddcdbabadcadadcadcbddccdabdaacdcdaaaabbadbaacaccdadabddadbddbcbcdbdcdcabdaabdcdddbccdadadbdbddbadbcdbdbaabbdcadbddcaddbbdccbabdadddbbcddcbdbcbdabdacabdbaaaccacbaabcdccbacbadacddbaddcabdcdbadcdabbcabbacbcbbdcccaadcacdcdabaacbbcbbcdccabbcadaabcbbdaacacbbbabcdddccbbaadaacdadacbabbdcbadbbbbabdccdbcbabbadbbadddbcccaacbaacbbcaccbcdacdddcdcdaddacccddddbdbdadbddbabadaccddcdaaaccbddbaaadbdadcbbdbacdccbdbaccacdaadcaccdbcbacdabacacbacababadcddaabdadcccaaccdddbcbbdcbdcacccaacddadabbdccacabdbcdcdbbbabdccddbabdcadacdcadbcaccddcbcddcacbddabacaccdcdddbbbcbacdcbbdadadbdbbbbcccddcdcadcabbbbddacdabbbabacbbcccbacababacdcccccacbacdcdbaabccacdbaabddbcabccdcdcdcddcbcccabaacddbaaacacbbdcdadbacacdcaadabbacbdcdbaabdbbcdadccabbbcdbddcaabbaaaabddaacdccaccaabddaccbacacbdccaddabbbbbabaaddcdbbdccbcaacdcaaacdadbdabbcbcaababbbaaabaaaccbddabdaddbadbdbddbbccbabacdcadadcaabcadbbadbdbccdcdcadcdaadddcaaabccdcbaadddcacbdcccccbccabdacaabddbcaabdbadababdccbbdcadbcccdcbcbadadaccddcdbcddaaaaaabbccaacadabadcdbaabcaabcaabcdaddbbbbaabadaadbbbaaccbabadcdadddacabacbcadcdcccdbdbddbcadcbcbacdbcbdcccbccccdcacbacdabdaabdcdaddbbaaddcdabbcdccbcbccaabcbcbabccbdcbdddbdcccddabcddbadcacdcbaabaacdddadcdcdddbcbcdadaddabbdcbcdbddbdbdababddabcacbcaacacbcdbbcdadddbdcacbddbcddbddbaccacbdddbdccbccacdcdcddbddbdbbadbddabdddbdaddcbadbdadddccbadabacaddacbcdcadccaadbadaacaaddcddbbdbaabddccbbbbaadddadbbdabddbaccbacaaabdddababadbadabddbddcdddcbbbababdbacabbcbdcbaacadbaddbbdbcddaaabbbcdbcadccdababacbabcdaccdccbdddacbbdadacdcaaaaddbdbaacbbcdcbdddcbcbbddacbbdbddcdcdadaddbddbcadbabcaacbdadddccacadbaccdcaabddcbcbdbabcabaddbdccadbaacbbaaaacdbdbabcadcbbcbabcbbccaabacaadabdbdbdadaaccaabdcbcdcddadbdbacbdcacabcdacdddbcbaadccbaadabbcdbbbadcdccdabbdadbddcccaadbacacdccaccacccaacbabacbabbcdbcaabdaabccbdaaddcddcaabbbacbcdcdbaccadaabdacabaacbbbdaabccccdacbcbadbabaabcaadabacbbbbacdbabcdbccbbbbbaddadacabbaaccaabddbaddbcadbcacacadaacadaaabdddbbaacccddbddcddaadababcbcbbaacacbabccbddacccdbbdadaddcbaabcaadcbdaabbdabdccdbbcdaaacbdbaadacbdabcdbaacababaacddddacadbabaadbbaaddacacdadaadbbbdccbdcdcccbdaddabbabadabaaddabbcaabbacbdccdccbbddcddcbbaaadbcbbadbdbdaaacaaabbbcacbbbdddccbbccccbdcbaadbcdbdddbdbabbbddbccbdddcacdccabdacdcaacdaccccbdccbdbcbdcadaadadbcdcbdccabcdbcbbbabdbacdddbaacacddcbbddbabcdadaababbbccdcbbdbbadcbbddaaacbadcaadbdbcccbcabadcdccaaadabcccadadbdabbbdcddbdcbacbbdadcaddbbbbbbdadabcbcbbcbadddadacbacdddbbdccdbabacbdacacbccbbcadadbdaadacabbdadadbdcddbacbbacadaddcdaaaacdbcaacacabacdbbcacadbcbbaadbbbaabcbabcaabbdabbbaaddbbcbdacaabbbcbabddcdddbcbadbaaddbdbdabdcdcbcbaaadbdaddbcbdcdbbdabadddbddaabdaccadaaacdbdcdabcccbdcaddaccddbacdcaddacbdccbbdbdacbcbcdabdcacbccadddddbcccbbccbdbadabbdabddbbdcdbbbdccbddcaddbccaacbcccbcabaadccbabbccdcbacbdbbcdbabbbaddccbaadaccccbccccbcdbbcdadcccdccbbcacbacaaadadabaddaccbacdabbaaacdcadbbcbbccbcddbbaacaacbabadbdaddbbbdaddcccbbacaddddacadcddabaacbbbcbcbdaadbbcabbcbcbbaabadcbcabdadcddbddcbdccaacdbacccacababccbcabddacbbadbddaaacccdbbccdbcbdbcdbddaddcdcbcccbcdbdacdabcdaabcbcbbdbaddccdacbcbaadcadcbbcaadbdcbadcbbabccaddadaadacabcbcacdadbdbddcbddcbcbadcdccaccbbaaacbdbdadcdccccdbcbcbbacccbbdbbabdaaadddbbadcaacaacdcbaadbdcbddcdcbdacdbadbdbbcddbbadbbacdcdbbbbbdcbccdbcbacbcdbacabdcbacaaabbcadcbbcccacaaaabdadbaaaddacbbdabcbaaadbaccbdbdbbacbaccbaadcacbbdbbcddacddaddacacaabdbdcdddbbcabbaabcabbbcdaacbcacacdbccdcabdcadbbcdbcabbcacadbdcabcbddcdddadbcdbdcdbbabdabddbdacbdbccaacadbbbadabddcacbbbcbdbdbcaadcccabacaacbaacdbbaaabbbacccbbcdcaccdaacabbcacbacdbabbccbdbabacaaabdacbbaabdbbccdcbcbcadddcdbabcbbabccbdbbaabacdaadbbbbabdbdcabbbabcacdbbcacbaadabacaaaabcddbdbcabadbaabdcdabdccadbaccaaadacdbdbcdabbdcddcdbbbcbcbadabdcbbdacaabcadadcddabdaddbacacccbccccbaacbdcdbdcddbbacacbcbcccdacdadacbdbbcacbdbbddbadbbadddaadacdbcdabcdcbdaacbbbbaabcbccaddcadccdcbaddaacdbcaddcbcddadcabdccaccaabbdaaccbaacaabacbdbcaadcbadabbaaadcdccddcaacacbcadcbacccaabbdbcaadcdaaacccabadbdddcaaccdacbddcddbacccacdbddcadbdddaabccbdbabbbccdddbbabcbbbcbcdbcadbdabbbbdcddbcbcacabddbaaacbdbbbcbdbadabcdccaaadcbadcbabdaccbbddccbadcddcaabbabcbddbacbbddddbbacbbacbcbbbbbdaccdabbcbacbccbbcdcdacaddcadbaadbaddcacaacaddaadbcdadccbbbacbdcabdadbaddadbddcbcbdcbddbbbaababbdbabbcdbccddacaacabcdaddbbaacbdcaccdadabdddcaacdbaccbbaccaabcabaddcccddcccccbadbadbbabbbbaacbdbdabcdabbcbbdababbadcddcddbbcaacbbbadddbacabddadccbaadbbcaccbbdcdbabdccdaabdccbaccdcbabdbcbdbcdcabbcddcdcbbdcabccbaadcdbacbccdcbabdabbbbaacdbdcdbdccddbdaaadcdabbbacaaacdcdccdcddbacaaddbccabdaccbaacddcbbcbbabcaaabdbdbbcaaadcaacdbccccccabccabaddcababdbdcaaaadbaacacadccabdcabcbddcccbcabbdbddadbdbabbcbccccacaadbabbbabccdaddbdbdabbcacbbbcccdabcbdabddcadbaacabbabdabadaddcbabcdbaccddabdbbbcccabacbbabaaadbdaccdacdcbdddbcbcbaaddbdcabdccccdababbcbaaaccbaadadbccccaccbbcdddbcbbcabacbacbcbbacbcdbcdccdcabddabdacdabddddadcabccacbcadcdcdacdacabbbbcbbaaabdcbcbbbcddcaadabacadcdcccdbcadbcddccaccacdddcbdbdcccbddbcaaabcdcabdabddccaadccbcabccdabdcbadaadbddddcaddbcccacadabdbcddbcbdccaddabaabccbcadadcbadcbabcbdbcdbcaadbcabccbbacddcdabcdbbabdbccdaacadacacdcaddccdbbcaddabcbbbdaaaacadababdcccdaadaddacacacdaacdacbdacbaabbcabcddcbcbccdccddadaaadabaacadbacaaccadcacbaabdbadbcabcdcbbcdddadcabacdddbdbaddbccacaccbccdcccacdacdccbbbccbacadaaababbacddccbbaaadccbadbcbcbddadcabcdcccddccdabaacabaababdccbccaccdbcaacdabacdbdaabaadbcbbdbbadadacaabbccdccbcdccbdaaadabddddbcdabbcccbacccddbcbcbbdbdcddacbdcababbcccddabbbcacbddcdaddbccbcbcbcacdaabdbddcbdbcdbdaacacadadbdadbbaddadcdababaddbaddccacaaddababaabcccaddabdbbbadbbbbbcdbbcddabcdddacbcdcdcdbbcdcdcdabbdbbacabbbabcadbadbdacdcddadbabcadccdddbbbbbacbbcaabbcdcadcccabcdbcababbcadccaccdaabbdbabcabdadaacacdbbcaaacdadabaabccaadddccdadcdcdabcbdbbddabccdacbdadccccbacaadbabddcdbcbaacbcadabcddbcdcccadcbbabccdaadbcabdcdabbbbadaacdcaccdbabbadccbbadcbcacdbdcbddbcbacbacabaddbdbaccaadcbccadbcabcacbaaacbccacaddaddcbacbdbcbaabdddbcdabcdcbdccdddadaaaacbcaacccccabacbbdbbddacbcccabcaddadbbaaddacbadcbacacacadbabdbdadabadbccadbdbaaabbbacacbdbddacabaacbdddcbbacaabdaddbdcddbbbdcbadddcbcbdaacccacdbacabbdaaddbaccdcbddcbababdbcbdadddacbcabbaccccdacbbdadddcbdbbaacbadbccbaadcdacdadbcbabaaabddbabadbbbbbddbcdabcadcdcbbabdacbadcadcacdbbadaddbbcaadcccccdadcddccccbcddacbdccccddbdbdacccdadabadbbbabccaacdbdabbccbdaacdbccbaddbbdddcababdbdbcbcdcdccbdcbcaabcdabdcbacacdbcdbbbbbbcccccaacbdacbdabadcdadccdabbdadbccbcccdcbadababbaadadaddbaadccbcccdacddcbbccbbaadddcccabbbaacabcadbcdbbaabbddcdbcbbbaacdbbdadccccdcbddddbdccbacbddabbccbddcbcccddcdcdcbacccdbcadcbbdccbdcdabcbbbbcccdadccacbddcabcaabdabbdbacdccbbdddcccdddadcccdcadbdbaabbcbdbbbdccdcbdaabdbcacbccbabcccbacadadcaababbdcbcadcbadabdbcdbbaaadcbdadbcbcdaabdbcaaaacbddadbbdaabbaaaabcacdaacdbaabcaaaddabccaaabdddabbbbabbbcaaadddaabdcbaccaaacbcccbbcbcdbbcdaaacbcbcbdcbdcaaabaccadbcdaabdadbcbabacbcdbbddbbcdbcbadabadcacdbaadcacacbcddcddbadabccdabdbabbdcadababdcddacbbcbbbaccabaadcdbabadcdddabacabaaddadcdbcdbbdbcbacaaabadaadddbacdccccaaaabbdddbddbcbacbdbbcbbbbbcabcacadbdadbcaabdbdadcdcbccbdccadcdccdccddaaadaadbcbcccbbbccaaaccadccdbaccabcccbbadbdbcaadbcdacbcbacccacabcbbbcabccbccaabacadadcbccdddccbdbadcddbcddcdbaadaacaddcacbbcdbabdbaddacadccccbdacbbddcdabbdcbabbddadcbdaadcbdccbdaaadaadccccdaadccbadccccdadbbdbdabdddcdacbacacccccabddbbadcadbcacbacbabbdbabcccddbdaccabdccadddadadabcaddbcbaabaaccbdbdababcabcbcacbdabdbaccacacbdbaddbaaccccbdddbaacbadbdaddaaccccbabcdcdabbbcacaccddbbbcdadaabcbaaadddbdaacdaccdbddaccabbabbbcbbbdbadcbcaaadccacdabdaccdcbccadcadddbbbdbcddcbabdcdbabddbdcbacbcacbddbaaacabbdbdbdbcbbdbcbcaabcbaabadbadddcabbaabcdaccbcabdcadccaadccaabcbcdaacaabcabadcdcbcbcddbaadcacadddcdcccacbcdadadbdaacdcdddbbbcccaddcddabaaacccdaaaadcabccdcabccabddbdbdbaaacdcaccbdbacbbaacbbdbaadaccdbacddbbabbdbbcadabdcadcdabcbaacababcabdadbbcddcababcdddbacbddbcdcbcadaabdccabddbadbcdbdccbcabbacddadbcdadcadbacdbbbcabacbaabdadbcddaadaadabdbddcaaadabdbbccdabdaadacaadcacdababbbcdaddbdbaadcdbcdcbddcddcddbddabcadbdbaadabababdbcababcbcdabdbbdadabaccccbcdadccdadbaabdaadadacddaabaacddbbdadbaaddcacccbbcbcabdbaccadbdbcccabcbbdcdaadacdcabbcdcbdadbdcdadaccadaaabdcbdbacdadddcbcbbbcbbdcacbbdadcdcccccabcdbbddcacacabccbcbbcdaadcccdacabbdccdbddacdccadcacdadbdcbdaadaccbacbdbdaadadbcbbbdcccadadcccbcbccaaddacdbaddcddbbcbdcdbddbcbdbdbbccdcccbdccdaddcdbddadacdcdabccdcdbcdbaaaadabbcbdccdbccdcadbcccadabdbbdcbadacdcdcdaccdbcbbdccabddbacbcadbadccbacacbaccabbdaddbdaaaddcadcccadcbabbdcbbbddcdbbcbadbdabcdaddaaabcbbdcccbdbadcbdbbaabcabbbcbdbcbacaadddadacdcbdccdddbcdddcdaabbbacabadcbcdaabccbcccbbcccdcdacccaadcaddacaadcddbbbbdcdaddaadbcbdddabaadcccbbddcdaabcaadcbcdddaadabdbcbdddbbbddabbbdcabdcaadcbabdcddcababbcbbddcaaddabcdaadaadacdddabacbcdbcdbbdcdacbcbaabbabdadbbcccdadbbcaaaddcaaadccadcccbcdddacbccbbcccbccbaddcacacdbabacadaccbbaacaabccdbdbbdaddaacacdaabaadbbdccccaacabbaacdaacdbbcadbddddcabbaddacddcdaccbddcbdababcdbbacbbbccbcabbccacddadccaacbaddbbcaccadbcddcaccacbcbdaabcccdcaddbcbcacbccddbbddbdbaabcacababccbbdacdadadacdbcbccbaaadbbaabcbabcabddccccaabcabbbacbbccccdcdbcdbbcdbacbbabcbbcadcdbbcacdbabbbabaccdbbcbdbcbababadbbcbaaaaacaabcbbabccbbaabdbccddddabcbcbadbbbdccdbaabaadbadaaabbaddddaabcbddabdabcbbddcbaacdaccacccddddbabadddaacaaabadcbbdccddcccbbaccddadacccbaadbcdcaaaadadcdbbabddadbcccdbbdccdbbdcacacdbccadccddbaabdacabcbddadddcddbdaddbbcaaadbacbcdabdcdbbdcbabaaabccbbbdbbbdbcabccabccdcadcaabcdababbbdacdcdaccdbcbdabaddbccdadacccbcdbaacbdcadbdacdcbbcdaabbabacadacbbccdaddccabddcccbcaaddbcabcaadbddadbbccbdaabaacdbcabdbabacdcdcadbbcacacbdaddcdbaaacacadadcacdabbdbdababbcbcdddcbdabadaaacbaacbcadcdbbbcdacbacdbdbddcbacadcbdcdaddcdbcabaddabcccbaabdadcaddabdacdbacbddcbcbbcabdbbcaccccdbbaccaabbabaddabcbabccccbcbbcbdacdbcaabdacaccbcdaabbdbbdacbbadbdbccbcbbbabccdcaaabbcdbdbbbcabaddbadaacbaaacaccabaaaabadbcccdaabcbbdabaddbccbbcdbbdbdddadbcaccacabcdaaaddcabbaacdbbaadadcbccccacadbabcacdcaacccccbccdbabbbccadccdddbbcadbdbaacdccbcdddcbabddbdbbcabbaaacdddadaaddabbaaabcabbaaacdddcdccbcccadcbdabcbcacabccbddabcbcdadbbdabbacbcabacaacbdbcdccaddccaacbcabaadcbabdaacbcbddcccdbaccacdcdddaccbdadddcddacbcaaddcbacbbbdbaacbcabbabcaddcdbbdadadddcaabcbdbadaabddaaddbcaddaadaccddbacbcbcbbacbdbcaccbbcaccdcabbadacabbabdaababcaadbbbddbbcddabbddbdcdbbbbbcaddbcbbbddcabbbbaababccbcdcdacadabbacadadbabcabcacbcbcddcacbcbdbcaabbaaadcadbcacccabcbbacbaacccaadacccdacaccdadbcccdcbcccdacacddcadcdbbdccbcacddcacbdcdacabacdbbaddbbacbdccaadbcccdbcdcdcbbbbcaaaddaadbbbcabacabaadbaaddcadadbabcdbdababadbaacdbcbbccadabbcbbbbbabcbabbbcadabadbdbbaabaccacacddaabbadbcbbdbabbdacacacdacaabddaabcbabbcadbbcbdaaacdbbcacaacdcabbddbaaadacbdbcdadbcbaaddaabcdcdbcadcccdcbdddaacdadcbacdccbddcacbcbdaabdaadbdccaddacddbcbccaddbbdacddacdcacccdcabaaadabbaddccbacabcacaadcccacdbcbbdbbdbabccbdbbcdbbaadacbbbbddcddaacdcbccbdbdaabdcdcbdccbbadbddacadcaaccdbbaccccccdabbbacadabadbabbccacbdcbdddccdcbbabcaddcccdcddbbdaaaccbaaaabdcdbabbcbbccbbbdadbdcabdccadadcbccacababbaacaaccbccbaacbaccabaaadacacacbbaaacbacbdadbbccbbacbbdabbcbbaccbabaadaccadddcbbdadbbccdddacccdaccbdaaabccdcccbbccbabdbaaacbdbdcdadacadcbaaaabbcbdbdcaaacaadaadaababbdbbdaaaccbdcadadbdaadddbbddcaaccbbadbddcccddaacbcdaabcdbdacdbdaddbaabbdacddabbdacbadbdaccbaccacbbadbdaabaaabadbcddcccbbcabdacbdadacddbcadbadccccdabcbccabcacdaaadbcdabacbbbcbaadaddacabbcadbcdcabdddccbacddbccabcdacddcadcdadbcbabddbacdabbbcdcddbdcbcccabdaccadccabadddbccdddbcdcbaabbcbbcdbadadbbcbadacbcdccddbabccdbdcccbbcdacddddbdcdababcbcccbdacbcaacbdbdacbdabccadbbcdcdbaabacbabbcccdbddadadabcbadabcddabccbaabbdbdcbccddcdadccbbccccbccdcccbbaccbadcadcdadbabacbcaaacbbcddcaabbdbbdbadcabadcbdbbdacbcadacbccdbbcdbaabcadadbcabadcbbdbdacacadaaccdcbcbdbdcbdccbbcccbcdbdabbbbbdabbadcbcabdabcbaabacaabdbcccadcddbdcbaabaccadadabcdabbbaaddcdbccdcbcddbabcbcabcbdbbbbaddccbdacabdcbaabdadcbddcaadbadcbdbabdbccdcdacabaddababadcdbdabbaccddaaaddbccdacadacabdacdbbcdcabdcbdcadabcbcdbdabcccdccdbabbdcbcabdcabaccddccbaddbcbaccdbdbcbddadcbcaccbdbdbaacabcbacdccbbcadabbcbcaacadacdababbacdbddbaacbddabacabbdabccaddabbbcdacacaaaddcbcaddababdadcbbdbbbbbcaabdaacbcacdadbcaddcccadcccbaaaaaaaccdabaaacbcbcabcaadadcccadaddabbabcbbacbbcacdddbcbdbbcdcdadcaacacbcbbdaadacbaadbaccbaddacabbccbddbbdcbdcbdabcbdbbbbdbbbadbccacccbcbcaaddbbdaacabcdcbccdcccdbcdadcbabbacdbcdccacaadbdaaadcabacaddcddaaccbadcddbbccbdacdcbadaddbbabbbacabacdcdddbabbacdbacdaddcbbcabcbaddbdacdabbbdccccbbddbaabccddaacbbaacddacbcaaacadbbcddabadbabcbbdadcadaadbbadadacbaccadaacdcccbcacbcccbbccbadabddadcabbbdcccdcdddcbcabdaccdaadaddcdabdacccbdadcccccdadcccbcabbabaddacadbdabddbccadbacddcdadcbdcbadcdbddacdbbaacddbaabdbacadbabcbccdbdaabdababaccdcbabccbdccadddccbacaaddbcaccccdddaacccdadcabcccaabbdddababaabacbcddbcbbadcdaddbaabdcddcbddaabbcbddccacacadddbddacaabddabdddddcddbbdcadaaababcaddcddbbbccdaddcbbdacdbccdacabadccbdabdbdcdbddaabddcbbaccdcbbdddcacdaaaabccccddbabdaddbbaadadcddbbcdadccdaacbaaddcdcddbcdaacadaacdcbccbcabbcababcbbbacdbddcacdcddcbddcabbccbadbdbdddddcbdcadbbcbddbabbaadcabdaccacadbcccdcccaacccccbdbbaadbdddabaddbdbccaddcbcacacdcaabdbcbcadbcdbdddcdbcbddbccbbcabadbaccdacacaaacbcbabdbccbdcbdcccacdbcbacdabadccdcbbaadbacdccadcbbddaadbacbacdbccdbacbcdccbcacdbbdadcadbdadbacbcdddddbdbcccaabcddabcdccabbcadcaaaadcbadbbdabbacaabdbbdbcabaaabdabccabadcbddddabdadcddcbbacdbcbacbabdbdddbbdbbacacadaccbaadcdbbcbdbbdcbcbccbacbbaadbdcdabbaddcdabcbdadcbcdbcbdbaacadacabddccbccdabdabbbaaddaadbcbbaccdabddbdbbaaadcabccaddcdddccddbaaacacdaabbabcbbbccbcdbccdaabccbddabcaacdbdcbabbbcaaaccdbdabacccbadbcabbbacbacbabbddcacdcadcababacabccbacaccbdcdaadcdacdacacaddbcccbbcdcdcdabbcabdccaaadbdbaacbccaaabbcdbcdadcadccdaccacacccdbaddbccadaaccacababbbaabbcbdcdbdbbddaddcacadadaccaddccbbbabbccacadbcbdccbbbdbbbaddacccbadbbccbbdbaabaccbabdbcbbacbdacdbcbadbbdbcbdbadaacaadabdcbdabdcbcdcbbdcddaabcadbaddddbaabbddadcadbccaacdcdadaaccabaddabbcacbbaddcbaababdaaababcdcacaadabccadbbaacbbcbcbcdcccdddbbadabcdaddbcdacbbcccdccddcdadaaabbbbdbcbaadcaacbcabbdabdcccbccacacdbbdcbccbbdbddbdcbdbabadccabcddbddabbbdcaabcbaccadadcabcbacdbabbcbbaccbdddcbadcadcadcccdadbcccbacbbcaaddddacccbbcdadbdabbabddadbaccaaaccddcacdcabdccdbccabbcbacbbdcbcadaadccacadadcddacbcbdbadddddcbbaadcbadcddbacbdccaaccabddaddbacbcabbadadabadbcbdcacabcaaadcccccbcbcddacdbddbcbccbcddadbcadbcaaadcadcadcccabaabcdbacbbdddbbaacaaaccbbacddcaabdaddababdabbbabdcadadabccdbabaaddcaaccbdcbacbbaaaabcbcdccdcadabcaacbcaaacbddacccdbdbbdcabdaaacbcacdcaddaccacaddbdacbdbddacbbdcbabcbcccacabbdbbcbaadaacbdadabccdccdcdddcbdacabbbcaabbbabdcaaddcbacadadbbcbdcddabbacbbbdacbacbcdddbaaabccbdcacdbaabddcadcbddaccccaddcbdadccabcaaaabbbcbcddbabdacbccbbcbccaccaaabaaabbbdadbbdbabaadcbddbcbbacbdadcabaaadccdabadabddccacdcccaddcbbbcadbdccdbcdabdaacccdbbbcddbcbacbcaccaadcdbcadbdccdaabbcabdcbcbabadaabadaccbbcbdacdbcaadabbdcbddcbbcdcdddcdcadccbcbbabcddaadacdaaaaabbbadbcbaabbabbddcbddacabacdaacbabcdadcdbaabbcadbadbdbbbddacadcdabadadcdcaccdabddddadaddcaadabacdacabdadaabaabdccaddbcadaccddbabbdaacadbbdaaadbbaaccdadbdacacdabaabbababdaccdbdadccdabbcbcbbbddbcbcdbbdcdaacadaabdbbadbcddcaacccccabaacaccaaabadcaacbabbbbadcddadacddbcabdccadbbaaaacadbacaababbcddabbccdcbccbcddcddabcddacdddbdcbaccadbabcabbcbbdbdcababccadadbbdcdbacaddbccdcabcacadcadbadccdbdddaaadaadbdbdaabccccdacbccadcddbcdaaaddacadbbbdbcbacadbbddbbdadcbccdadbcbddadcdcaddcacdadbcbcdbdbdaddccaabdccdcdcaacbaccacabcdddabbcdcbdccdaabaaaaacdaabcdcbbcdbaaacddcaccacddabccbabadcbaaccaccaaccdcbaacacadabccdcadbadbbabdccadccacbdcdbdccbccdbbddacdddbcabbdbababdcabcabdadddcabbcdabadabcabadadacacaaccddddabdddcdcdadbacbdabacddcacbabccadbcaccadcabcbdcbdcdbbbcadcdaadbcabbcaaccaddbdcacabdcdcbacaccbdbdcaaaacbcaccacabaaadbbcdbcbccaaacaaaccddadabcbccadccbadccdbdacbcbcabbacdddabbbbbabdaaadbddcbcddddcacaaabcbaaaddcbbdcbdddaacbaccbddbbcdcabcaaadcdbccccbbbcbcadaddacdaccaaacddbbaddcaabbadadbdcabbaabcdaddddabdabddadbdbdcdbdcdbcdbabccdcbacadbbcdcadabacbcddccaabaadddaaddcccbbcacdbabccbdcdadbdcabaacddcddbdddabcdabdacdbcdcdaccbcdacccdabdbabcdddcbabccacddcdbddbcdbcddddabcabcacaaaddbbaacdbdcdbdddadcdcdbcdddbddcbacbbdcdacccbdbdbbccabccabbddccdddbdaacdacbaccaaaabbdcadcddadadaacdccaadcacbcabbabbdcbdbbaacbbbdaccbadcbbdbaadbcddabcbdbaaddcbdccabcbbbabdbcbcdcdcaadadbbbbcbcdcabbcccdcadabacbaadcdbbabaacdabbbdbdacdddadcdcdbaddbdaadbabacdcacabbbdaacddcdcbcbbcdbcbbdbadcbbcbbbaabbdcabbabbccdcaccbdcbbadddbbbbbdcaacaadcaacccdccdbaccbdbddbcacaacadcaaadaabaddbdacccdbdabddbdaadccccdacbccbdacddaacbcbbabdacdadcbccbdcdcdabbcccdccccbaaccbcdddddddabaaabaaadbdbcddaddbbdcbdcacdadadddbcddcdbacddcbdddcbcbbcdacdcaddcdcdcdccdaddcddbdacdbaadbaaadcbaaddcbcccabdbdbdaadbcaadbabbaaabbccdddbacadbadcdbcbddbbaaccadcabcacbdccadadcccabaddbaccccacdbaaaddadbdcbbdbbdcabccbcbbbbcbadacaadbabcccacdcadbadbdcbdcabdcadcbbcdcadcacaaddbdcadbbbbcbddacbccbbdaacdadabacbaaabadadcadabbdabcaaaabdadcbdabdbbabcacabbbbdbaaccbadbbbccdcccbaadcdddccaaccacaacadbaaadccbcbccaccbcaaadadcbdaddcadcbdbabbcaddddbacbaabdcbbcacbaaaaadcccdbbcaacdbbddadbacdcdbdcbdcaddbbcdaddddbcccadacdcabbcbcbaaabadbdbddcbcdbccdacdbcccdccdcdbdadbbdcdcdcbacaccbcdcdabbccadabdaaaaaacaadaacaaaacbddccadaabbcddcdadbbccabadbdbccddacacdadadbadaacbabcdcdccdacabcbacdaccbacbaadcccaadacdbcbcbbddabbabdcabaabbdbcdbbcccbdcbdabdcbacbcdcadaddbabacacdcdbdbdcaaaacdddbcacdaacbcbcccbddbcdaadbbcddbddcababadbdbbccadcdddcabbacdcdcaaacbbbcbdcaabbcaddbdadaadcabdcbcdadbbadbdbdadbbadcdcbbdcdbbcccddbcbbcbababaadabdbcacddcaccdadddcbdacbacaacccdccaaddaddbbbcadaacaaadcbcddcccaadcacbcddbcccacdccddabdcddbbdaabbaddadcbdaaddaaadabbaadacbcbcdadbdabbcdccaadcdacdccabababbddacbcddcccbdbcaaddabdcadddbaddadccadbdccabbdcdaacdbcbddbcacdbbbdccdcaadcbdbcdaadddaacbbdaadaccbaabddbdadacaddabcbcbdddbddcbccdcdbccadaaadcababbdbadbcacdbcdbdbcccddbcabccdddddabdbccacbddcbbbbcddadcadbbccdacdbdabacabbdaaddbcddccddbbbdddabbdcbcbcacccaaababdabcdbdbcacaadbcbaddddabcdbccbbcdabbbccdcddabdcdcabaabbdcdccdabbddddbabcddddaadbcbbabddcbbaadbaabdadccbcbddaabbcbadbbabcbdbbabcccaccbbaaadbbbabadbddaddcabbbccbbaacacaadbabccbddbbcccdbdccbacccbbbaccdaacbcbcddbbacaccdbdbcacaacaccacbdddaaabadcbcabaacbdcdabbdbcacacdbbbdbcacadbaadcacdaccdddadbbacdadcccdbdcaaabccbadbabacbabdbbbdaaadabddbdbbdbdaadbdbdacadccbcdbaddacadaddabdbbaacbadbcbdcbbdbabccbbbacbaacacaadbccddcbbdbddbbcadcdbcbadadcbcababcacacadbddddaddbcdbccdbbacacdbbccddcaaacadbddaddabcadcdbdadcccdbbaabcadcdcadcbdaddbaaaccdcaaccbdbbdacaaabdddcccbcbcacdbabdadcddddcadbbabccabbababbdbbbbcbacbabdddadcddcbcbdcdbdccbccacabcdabcdccadcabadbabacabbcbadacddbcdabddaddcdbbaccdccaacbbdbadcbcccdabbadaaadabbcddcadccababbacdcbdadabcdabbcabdbaccdadbcabdbdbadcdcaddaddabccddbcdaacbdadcacabcacccadddaabacbbbbbdabccdbddcaaabcdbadaabbdbdadacbccccaaaadabcbdbadbdcbabdaaabcaddaadbbdcbacdbbcddabdcacbcdcacdabacaadbbcabcabbcbdbcbcaabadbcdcacbdcaacdacdcdcdcdbacdcccbaacccaadaadcdaadcbdabcdaaababcdcbbcadddaacddaadcabadcdaccdbdcaadaccbdcdbcaaddacbbcadddbabbbaddbbacaadddabcacddcbcacddabaabcdaaaaccbbbadcdabcbcbabcabbdbcdcadcdadabdbbcdbcdcabbdaacaaaaadccbccccbdcdabddacbddcdddaaddcdbdbdddbaaaabbbbcbccbaabccabdbbbaababccddbadacaaadcdccaccdbbbbcadccccdcbdcababdbbbabcdaccddbdadcdabcbcdabddcccbaadcdddaddabbbbbcabacadbdcdcbdccadbacaaddbdaabdcaaccbddbaaacbcbcbdbbcbbbabbbbcbcddbccbdddaddbbadaddcdacbbcacacacccdabbacbcabccaabddcbdcadccabaccbcbaadaadbaddbcaabaabaaaddacdbbabbabadddbdbdcdccaabccccbaddcbacbaaccabadbbdaaddabbbbcaccaccdddcaddcbdaddcdaadddbdcdcdcdaddcadadaccbdcaaabdcccbacdbaaadbabcbaacbcaadcdbcdbbbdcbbcbdbbccababadbddabdcccdddabdddcbcccdacabbaacdbaacbdacbcdacadcabaaaacbaaddaaabcddaacdbadcccdacacbbaddaacdaaaacabcdbbcaddbccaacacddbdcadadccabdbaadabaccbddabaacacdcabdbabbdadcbbbdbddabaccccdadbdabbacccccdbdcabcacbbbdbcbbadaabccdaddccdbddcdbcbaadcbbddccbaadbdcbdbadadaadbcabddcbddbdbacdabaccdbddaaadaccdcbbdbabbacccadcadccaabaababcdbaccbadaaccbbcbcadddbbcccbaaddcaabdbcdbabcdadcddbcddcddbbdcdbdcccddaddbaabccabcdbbdcacdcdbbdbaccaacabcacaadaddaacbabcdcbcaccdbbdcdcddbbbabcadcdbabdbbcddcabdacbcdccacdadcddcddbbacbdbbdbacccdaaadbcadcbcccccdddaccbbbccbcbccaacbdbcdcabadbdcaadbdacdcabbacacaadbccacaaccdbdcacdddcbbdadbcadbaababdbcacadaaadcbbbbdbdbdacacddabbacdadbcdbbacbbbdccccdabdcccaabadccdcabaabbcadcbbccbdbcacbbddbbdabbbdbaacabdcdcacbcdbbbcbbadccdbcdbadcaacbcaccaccbbcadbdaccacdaccdcbacdcdbddddacbaadbcaacddcccadabbcdaababdbcbcbababdcdbacdccbdcadcadbccbabccccbdbddccbadbdbacdbabcabcadaaacdbadbdbaaadcdbddaabdacabbcabdcbcabcadacbbabdbbabbbdcacabacadabdbdcdbaacdcccbcaacbaababadddbabdbbdccaccadaddaaacdbcccdbcddcbdccdcdbaccbdaababaaadccbbaaccbdbbbcbcbdcbbdaddabadabcbcaabadccccddcccdcbdcbdaaccbccabbaddbabbdbabcdacbbccbbcadaabcddddabbdcddaadaaaadbabacccbacddaacaddacbdcbcddcdadccabcbbcaacddbbdadcdcacdccaacbadbbcacbcbccddabddbbcbaadbacaddbdbacaaacdcaacabbcdbaddabccacbdddadbabaaadcacdddbacaacacccdcddddcbaacbcbccccddaddcdaacbbdacabbdcddcdcdbcabcacaaadadadcdbdcacdacbbaababccbdcbaccbddabbbbcddcacbcabdddbbabdaaddccdccbdabcdaccaacaaddbdaabababadbdbccdbdbdbcbdcacddbabadcdbdbcdbaddddbabbdcdbcadcacdcbdbdbdaacacaaddacaddadbcacbadbbccdbabbbcbbadcbcbcbccdbdbbacacbccbbadbccbacbaccbbdadbcbccaadddbcbbadddcbdcdccbbacbbcbdacacbbdabbaabadbcacbdbadacabbadadcddaccbaddbbcaaaaaadbbacdaaaddaabcacbbbcbdbbcabdbacdabccbabcdabdaacacbcdacadaccaadbdbcbccaaaaacbcccbccddbadcddcbcccabbacdddddacacaacbadabdbbdadcddbadbbdaddadabadbcdadadddacbadaadbdddaabdacaccaaadacdcdacaccabaaccdcbadbabaaabdcabccbdcddccddccdcdbdcdaabcdbdacdddcaaddccdbbdbbdbdcbdbbcadbcbdbdcabcbabadcacccbaccdccaaabbbacbdbaaddbddbababcabacabaccccccbdcdbacaabdcbbdcddcadcdbadaaccbbbbdaccabcadbbabadbadacbbcbdabccbbaccaadbcccacbcbbbbbbdddabacadccdbabcdddaabaabdacbcadacbccdcabccddbabbdbdbdacccdaadabadbcbbdcabaaacadbbddbcdadbbcbacbdadcbbdbcacbcaaacaadadcbbddcaadddadbacddbadbdbddcdbbdddaccdccbccccabcbbdbdaddccdddcdcacadadcacaacaabdaabbabccdbaaadbcbaaaccbcdabbccbdccdbbbabbcacdaabdcbdaacadcbddabadccbcdacbcababccdbacdcbadccadbadbddddabacdbcdddbdbaadbbdbdbdbcbcbaccbabcadcdcccbabbdcabcacdadcbdcccadcabcaadaaaddccdccbacdbabcbdbbddbdabddbbbcaabaabcadadbdddddabccbaadccbacbdcdbcdacaabcadddbdbdbdcdcacdcaacddbbbbacbacbcdddbdbacdbadbaccbbbbcabbddbacbdbbabbaaccdcdabcadbacbcdddaaadadbadabcdacdddadaddcbdccabadcddccccbddccdbdabbabddabddddcddbacadddcacbcddcbcdddbcdcacaddacdcacdacadbcbdabccccbaaadcaccdddbabbcccbbbdbcdbbbdbcbdddcabacdbccaadadcaaacabaddbbdbadabaacdabacbcadcdcbbddadaaacbacaadabcbcbabaddbacaccdcbabcbcbaacdcabcbbccdccdcabbcdbddaccbdcdbcdbdddbcbcbbcdccbadcbdbdcdcbcbabdccbbddbcbdbccadbdcaccdbdddbdaaabbbdabccbbbdcbdaabbaaacacdaaaccccdcbadddbdacbadbadbabcccdaaadbdaabadccaaabbabcacacaacbabcacccdadddcabddbdcbacdcabdaccdacbaabbdaaddcaadcbacadbcbabbcdbabcbadbdcadbbcddbbcadbaabacbacbbcbcbcbccaacadbcbcbbbacaadcbddcdccabcdabbaabbbaacbddbadadaddbcbbbdabaabaaaccacacdcbbbabbbccccdadcabcaaccbacbdbabddadcbbbcbdbbdddcaadbbddcaaddcaabdcdcccdddcaaccdabddabacddbdbddcdbcacaaacaddabcbbcdaaabbbabdbcabdacadbbdbcadddcaddcadccdabbaccdbdccdbdcdcdcccdbcbaacadabcadbdbbbabcdacccaadaabbbdbbadccbbcadccabbabdbdccbbcddcabcacbcdaadaaacbcdadacdcbdcdcdccbbbabdcacdbcdcbdabbabdccadabbdcbabdbdbccdbdadbcbcbdbacacdcdadbcdbabdccdabaddddcbcdbcdcaccbdaccbdbbabdabdbccdaddddddabdcabcbacdccbdcacbdbaacacbaccbacccdbabbcbacddacdadbabdbacdcbbaaabbbccabbdadaabbcddaadaaccadbaaabbbdcdccbdcdbcdbaadcdbdcdcddcacbbcccccddcdbbddcabdbbbaabaabdbbccdcddabccddcbdbcbaadcdccdadcddcaabbabbbacbdaacccabbddaadbabdabcadadcbdaaadccdbcadddccbbbbdcdadacccbdcabcbcaaaaadccaddcdababcdaddaddaaccbaddbddbacbccbbabccdadcdbbcbcddbbdadbdacdccdcbddabdbbbacdbadaadbcaacdacdcadbadbbcbccccaacdbcbcadaacddccaddacbdbcdbdabaabaacaccbadaaaccdbbcaabccbabcadbdbadbbdacdbbaddadacddacacddaaadaccbdcbdaaacbabddcbabcdbddddabaaddccdbdbddccdcbcababdcbacdbdabddccdbdbcbadcbbbbccdcdadddcccabbdbcddabcaabbdbddddabadadbddbbdaabccaaaaddbbddaadcccbadabdbcaabaddcbcadbbacdbbabbccddabaadabbdddabddbcadacabaddbabddbabcdacaadccacdcbacdaaadbddadccdaccbcdbbbbbcdaaccadacabdccbcdcbacbadbaabaadbcdbcabdbccaabadaacbbcacdbccbbabbbbdccdaadcbdaccdcadabcddbcbcabacacaabdcdccdbbcdddbdbabbbacaadbaabdbbcbddcdbddbdadcbcdcdaadccddabdbcaccaaddddcdadbdaadcabaabdacaabbdcbabcbccabcacbdabbabcdaddccbdccaacdacacccdddcdccccdacbbbcbdaacadcccbbcdcbcbacabaccddcbbcabbbddaccbbadddabcaabbcccabbcbacacccbcdcdbabdbaccadddccbaacdadadddbdbccbbdcddaddcdbbccbdaaccbdbbbdaadbcbbacbaacbccbbabbcdaadaaaabcbbdcdccbcdababdacddababcbbaddcbbacaaacadbbbdcbccbbcdaadddadbccdbdadacdbccbaccacdadbccccbccdbddcbdabadbdabcdaabaacbcbcababdcbbabaddbabaabbdbddbcdaaaacbcaddbccdcddddddbcaacdabdcccdddbbacbcdbadcdaddcbbacabddaddcddcdadcacabdbbabdbabadaabbdaaddbcbcbcccccdcdbddaadcacabdaaacbdacdddadcadcaaaacddcdccddbdabcbdddaadacbbbbacdbdddccdacadcbbbaaadaaabdacbadbbbbbddadddcdbcacbcccddbcaccaccacddcbaacadacaabacadddcabdabacccdacbbcaacdcdbcadabdccdaddbccdcdcdcdcdbcdcbcadbcbddcaabacadccdddbaabacccccbcdbaaaddcdcccbabacdaadaaacdbacbddbabcbadcbbbddddaabdcdcabadcbcaaacacdcbacdcbcabacdabbacdadcdbbbaadaababdcdaccdaaaaabbbdbdbaaadccbdadbbabaadcbcbcabadcdbdacdaadcbbcabdcaccdbbbdcaddacddddbbbdacdbdbbbdcadcccdbaaaddbddacababbccdbdcbdcbbabbbaabdadaabdbbadacabcdbccaaabacdcdadababbadcdcddbdddbdddcccbdaaddacabaaccaddddadddacccdacbbcbbdcddbdacbacccaabddddaaacacbbdaddbdbdacbccabcbbdadccdcdbaacbbcbabbdaaabcaacbbcacacacbaabcbaddadcdbdbbbabbdcbbcbacdabbadbcbbbdacbbbbadddcdbdddacabddabaccbdcbcddcbbacdcaacdbdcaacddcdadcaabbabbdcbcdbaadbaadcbcdcdbaaccaadccbcbaddadadcccabcbbccbdbccdbcdabdaadddcccccbcdcacdadbbabcabaaadacaaaacbabbddcbbbccdabbbacbadbbdadcdcaccbddbbaabcbabddbcddcbbcaadabddbdaccbdbbcccbbbadcaabdbabadbcbcababbbadcabcbabdadccacaccdcadbbcadcadaacccddccaccdbcaabcdabbcccccaccadabacdbdbbbcbabdbdbabaaabdcabbbabcadcdacdddbbcdabcacbaabbadddcdcaacbdccaacabbbcbbdbcddacddddcdabbdbbcacdbabdbdccdaabcbdbbdadbcdbaacdbcbcacadddbdcdbaddbabacadccbabdbacbcdaadbcbcdcdadbdaaccbbaddcabbccadaddadaaacdbdbbadcdbccdcbbaabbcbbacbcbacbadaaaacdbccdadbbacbcdcddcdcccdcccdbcdcccddadaacbbbaabbdcbaaabdbbdccbacdabbdbbcbbccacbbdbbdbbbdbaddaacadbdbacabdbbcbadcbdabacbdacdcbddddaaadcdddcabcacacbccaaacbdcaaabbcdaadcbcadaccccadbccacdaaababdddadaaabbcdddaccbdbddbbddbdcbcdbdadcadabaddccccccbbbcdbaabdcbbdbdddcccaddcdbcddcabddcdbbdbccadddcccccddaabbcaaacacccbccbaaaaccaadbdbaddddbbddbcdcabcdacdddabdcbbcbdddcccbcadadaacdbdcdcdcdababacadaadcdabdcaacdcccddcbadcbcdcbcbbdbbdacdcbddabccaccacadccbbbaadbbbbbababdcbbabdabbadbcddbcdadaadaadcbaaadaabdaccccaccbacbcaccbcddcbbaaccbdaadadaabaabdacbbddacdcbacbccaabbbcccaabdddcacbdacaccbacccbbbaaabaaaacabdcccaabbaadacadbcccacdbdabcddbbcbaaadddcaaaadbcbdaaabdabdacabbddabdbcdbadababbabbdbbccddbdbcacacbaddbabbbdcddaaacdbbdbdcbacdcbbcbcadddbabacbaadaabcabbbcccadbadbacbdddacbddadaabaaaacdcdadaaccdbcdbdcddabbccdbcbadcbcbdbcccabcbbbbbcdddaadadbdacadadbcbbacbcbadbdcdaadbcaaacdabcdcadbacabcacdbbbcbbdddddadccbdadacddbdbabaabbacadbcdadaadccbdbaadcadbcaadccdacacbabaaddbbacbadaabdbdcbaadaddbcbaddabbdbddcdcbccbddcddddabdadcdabbdacbbcaccbcddbbcdcabaadaddddbaccdaacddcdabbacddbddddbddccacadbdddadbaaaccdccdccbbdbbbdcbdcbcabcbcdcbcabcbbddcbdcdccdabccdcbadacdcaccccddbadbdbbcaadadddcabcccddbbbdabdadcbdccadabbacdbbbaabdbcdcaccbcbcbcbaacccaddccadabddacdaaccccdbaccbddddcaabacbdbadcdcdaabbcabcdcaccbaaabbcbbdacdbbdbaadabbdbbdcddaacbadcbdbbaaccdabbbacdbdddddccbcbcacdcbabdddadbccbdbdaaadcacdaccacccbbbcbdadacaabbaabdbccababbcbbddbdaddabbccdccabadbbcdadadbbcdcabacbdbabbcdcadaadacccbabbdcabdaaccdacababacbaddccddddbaaadcbbbadabcdbddbbbddcadcacdbdbcddcabdccaacaabaabdddcdaaaccbdddbdddabbacacadcaaddccdacacccbdbbabcdaaadaadbabbdcadbbcddccaacbbddbdcddabbcbdddcbbdbbaccddcdcbdddbcabaacbcbabdccabbccdddabbcdbdbcdaddddbcbcbcaddcdaacdccbddaddaabadccdaaddbabccabbcbddcacacbdcdccabcdacddbdbabcdabcbcdbbddcddccdcbbcbbdacbdbcdcdddadccabaaabdababcacaaadaadbabaabbaacbdaccbccabcbabdadbccddcaadbbbcaabdaadcadadcbdccbbcadacccbbdddcdbadadacbddbdbcbbdccdbdcdadccbcdacadbaddbdbdcdabdabddbadcbadccdccbbccbabbdcbcabbcabbbbbcacadaadcaddabaadbbaadccbabbcaccdbacbcacabcaabbddddccdaababcabaadcababbababadabadcccbdcaabcbcdccdccdcdbbbdbcbcccbbdbdadacdcaaadcaabcbbdacbadddccbdbccadabbadddcbbadbcccbcadbaaacccaddddcdcbacaddabadacccbcbacacbccbdbcabccbaddaaacabacaabcccaaabdaacaddacbbcbdcbcddddaccbbbddacdbccacbacabdbabccbddabbdbddccabcdccbdcacdcdbcdcbccdbcacdbdbccbcdcbadadcbbababcdcbaadbbcdbccdacbadaddadddbabadbacddbbdacddaccbcbcbdacadcabaadddacbbcdcbcabbcacdadbddaacbabacdccdbadcaaddbabcbdaccdddbadcacdbdabbcdbcbaabcbdbddbbaddcaaddbdddacadcddaabccbacaddccbbaaacaacbcaabcdadbadbcdbcdabadcdbacdcdadabccdbabdddbbaaddddbbdabcbcaccdadcbaaccaabbcbccbcbcbacdacccaabbaccccaddddacdabdaddcdbacddabdcddaaddcbbdacbbbadaadcbdaddaadcacbacdbaadbbaacdccabbacdbccccdaaddaaccdccddcacbdabcadcddcdbacdacabdacbbcaaddccdddabbbabddacabcdcadcbbcbbcdddabdacdbdbcadcdcdbbacacbacadaccdcbdabcabccddbaddcbcabbbbbabddcbdccccabccadbbbaabacacccadaddcacdccdbcdccbdccdabbaabcacbbccdadcccbbdbbbccbdcbaacddddbdddbdbdcdbcbaabbbddbbdcacbbcccddcadadddccbbaadccdbbdcddaddbcbdbbabbddbcbbabadddccaddcabdbdccacadaacbdadbdbaaabbccccdbbbbbcaddbdacdaaabcbddcaccadccadbcbdbdaddbdbcacddcccbbcadcbbbaccdcaabcacabadccadaabbbbcdacabbacabccaddadcbdbdbcaadaaabbdbdddbcbdbacdaadabdbcacdadbbdbbddbbbdbdcccabadddadcbcbbaadaaccdbcabacaadbcdacddcccbabcbdddcbcdbdcccdcbcaddacccdaacddbcdbaddcbcdadbdbdccbdbdcbbdaccbbbdabddadaadbbadbaaddddcabbbcbadcdbbdabcacdadcbaadaacdbaccadcbbcddadacaacbacadaaacdbdcdcadacdbbbbcdacbaadcabdccdbbcbbdccbdacddbbdbadcdcacdacacdcbcccabbbddcdccccaabbbbaaaadcbcddccdbdbacbcccdbdddaacaaaaabcdacbdcdbddcddaadabddadbacbcdaabadaadbdddabbbcbcaabbbdadcaadcbbdaccaccbdabcbbcadbaaabcaddcaadcabdcbacdbabaccaaacbbbdcdaaaacdbddcacaccccddbaacadadadadabccacdddccddbccdddccdbbbaccddcdcdcccabcbbdcabaacccbdbdacbdbccdadbcacdabbbdcccddcbbcdbdbcbdaadbbaabdaacbbdbaaadcddcbbdacbbcddacbddcabccbaabbbacabcccccacabcdcbcdaddddddddcacaabcbabccacaaccddcbddabadaadddadbbbcabadabcadbabbbbddddbcddadddbbdadacabcdbcdacddadcbccddddcbacabbccbabdbdddddbadbdbcbbccccbcdcbcccacbdadabcadbdbbbbaacdbbaaadbccadabdabbbcadbadabbccdacaacdabdcdcdbcbbddbbbadcaacabccdbcadbaabacdcddcacbabdccaacccdaadbddababbcdacadcdabdbbdbddcdcacdddcbcbaccaaadddbcabccddcbbaacbbcddabacbbdacbbccaabacdbbabaddbcdcaccbbadcadadbadddaaadbdaaccdbacbdcdabbbbbaccacccbcbbcbaabdbbdbbadcdcbbbaabcabbddbacbcccaaddbadabbcdadaddcddcbbcadaddaaaacaddadadddbdbaabbabddcaababcbdbdcbdcaaacdabaacbbbdaabdaadacbcdaadabcbbbaccddbcbbbbcddcdbcabcdcbadacaddbaddbbccacccdddccccbdbacdbcccdabdbaadbcdccbddbdaabacbacbccbcabdaacbbbacaaacdaddbbcdbdccbacdacaadbbdddcadccbdcbcabcdbddbcdabcccccabbbdbaabbbaacdbcccbbbddcdaabaaccbbcbcddacbddcdbcddaaacccbaabacdacdadbbdbbdacbcdadcbbacdcccdcdcdbaacadcdadbbbbacbacabbabccddddddddcdadbbcadccadbdcaddbaabbbcdbddccddccbbaddcadbbbddbdbbbbbbabcdccbddcbdddaaabadbabdcbddcdcdaaddcacabbcaccdcddacaddbbbccaabaaaccaadcdaabbcaaadbacbadbadbaadacdbacaaadbaddbbbdbbbbadcbcadcbbdccccbaccadcabbcdcacdbddbabcaadddddccdccdbdbbacddcdbbdbbbbcbbdbbbcbdaadbadaccddabadbbbdccdccbcbdddbcbccdbcdbbddbbbbcccadbdcdbdcbabcbacaabdabaadcbcdcaaddddcbbbdaccccdadacbdbbbdaccbbbbbbdcbcabacccbccaaabbddcaccdbcaddddcadcdbccbabdccbddcdbdcbadbadaabbdbddcdcabbcdcbaabadbbabaacddabcaaaabcdaacccbccbcddbbdbcdadbddddcdbbdbaababaabaacdcdcccabbbcdcbbcdbadcbdcbadacabadabcbcabcadbacdaaadccabdddddcdcbccdbddbcabbdcdcdbcbabdddbcbdadadabadcacddaddadaacbbcadcabcabdadabbcbccdccabadcdddacdcccbbbdcacbaacabccdbdbbbadddaaadbacbccddabbbbcdbacdddccbcbddbdbaacbbbdcaaccddabddcbccccbacacddccddcdcaccdaaacabaaaacbdccacdcdbbdbddbbbbacacabcaddddacdcabbadbdaacdaddbacdadabccdaccccccadaadcdaaaccaccbdddbbbddbdbadddcabbaaaabbdbdadccccdaaccbabdcdbbbaccdddacbabdbadacdddabbbbdcdbcdacadadcadabccddaddacbbdbbcdddbabaadbacadcdbdddbbccbcacdbddcbccdaacbddbdbcdbabcdcabcbcbdcbccaccaacababadbadabcdaaccbbbbbaddbbdbcbdacdcbcdacbadadabcdadabddbdddadacdbdbaaccbabcacdccabccbdbddacbcbacaacacabaacdbcaabacbaadcdadddcacddaddcacbadbcbcbcdcaaadbabbadbbcabdcbccbddabacdcbdaacacadbbcacdaaaaddbaccddaabdaccaccaadbadbacdacadbcaadaaddcdddaadddbaccacdaacdabcbadbbadbbdcbcbbbabacdaadbadcbbacbadcaadabbaccdbcdcaacaadadacabadbcccbcacacbcdcabbbdbacdbdbabacbbbbcbddbbaacbbbcbbcbcdcacadbbdcbaddddaabdbcdbaadcbdadccaadbdccabcdabcadcddccddaaabdddcdbaadddadadaacbcdccddbdcabdcbddaacdbcaadcdadadabbccdcdaadcabdddcadaddaaaaccbbcccdccbdabcbabdcacdacccbcdaaacccdbadbcbdddcaabccbadddabcccdddaabdbbaadddcbcdabcbbbbadcdcbddadbbdbabddaacbcccaccddcbadcbbabcbcacdabdbdddbbabcdcaaaadcabcbcbddcdddadccdcaccbdadbcaccaacdbaacbdcdbbadabcdaddcacabbdbdcaaaaccabbbbddaadbdacabcdbacadddadaccaddaccaacaccbadcddcadbaacbbccbdaaababcbddddacdcabcbcddadaabcabaddacddaacabaaadbbccaaadbcacaadbcbccaacbbbcddabccdaacdacccdbccccabccccbbabaddcbacdbcccbdcbbacdccaccdcadbccaacddabadcaaaacbccaddcaabaadcacdbdbdddddaabaadaabdacaccbbcdccdcccccbabdcacccadadcbdbdcbcbaabadcbbdcccaccdcdbcccbcaacddbcbbaabdcbddcdcbdaabccaaaabcacadadddaccdabdbadcdcadcacdcbcaacaabadcbaccccbcacccdaccadadcdcbbbdbdaabacabaadacdcbcacdcbcdcdacadacbcdddadbccbdbcccaaddcdbadccaaddbcbdbcbdbdcccbbcbaccaddabbabcccabdbdbadddabdbbcdcadbbdcabaacaddaaccdabddacdabddcdbbabbbdadccadbadbcbbdbbabaaccbbccddbcbddccdcabbcbddbdcabdcacdcaacccdbadbcdadbcdcabbdaacbcbbbdabaddbdbcdaaadbbcbcdabbaabdabcdddcbdaddddbcdadaacdacddbabbbadacacbbcbadccaccacadbaddabccccacbddaaaaadbbbdbccbbacbdcbbddacdddcacaaadcaabacbaccdbacbdddbdaacabbbbcddaabbbacabaddbaabbdabccdbcadcdbddbaabcaaaacddbddcbcacadcdbcdbbaaadadadcdcaccaddbacabcbadbacadbbbccaabaddadccccbcdcbacadcdadaaabcbbbcbccaaddaaaccdccabdccabbdaaaaacbdbbcaadbbdcbcbbabcdbcccabbdabdccdccbbdcddcaccbcbbadbababaaabdcacccdcbbcadddcdccabbaacddbbcddadaddccaabdbcbabbccccadadaaadcddcbdddbcadbdadbddddddbbbaabdacacbcbdbcbadacbbabadcabbbbccccabdcbacccbdbabcbcdcdbcccaaadcaddbabaaaccdabdbacccbadabcbbcdcaacdbbaaacacdddddcbccbaabbdcbcdbcadadacaaadaccabcdadcababbccbacccbbaddbabbdbccbcddbdacadbaccbdbaaabddcdacbacaccbddbbcdcbadabcdccbacbcdbcbaacdbcacbcabcaaabbcacbadabcdcdcbddbbaddcaacdbcbcddcaacdcddbcdddcbbbbdcbccbdbadbbbdbdccbaabbbadbdbbbdacdcaaccbcacadaaabbbaccbcaddaddccbacacddcabadcbaddacaddbbdbdbcdbbbdbbabbcdcbadacdcdacbaadbccabdbccbbadcdadbbbcbbaaaadacdbcacbdaabdaaacccaaadcaaadaadadacaccacccbcccbcadccbabcbacbaacbdababdcdcaabbbabaadacccaddbdbbbaabdcddcababbccdbadbabcccacaababbaaaaaacbbbdbccaddcddadcabcabbbccccaaacdcaacbbcbdadbadbdcabddbaabcbcdcbdaccddaaaabbddbcabcddbaaaddcadcdacbdbbdbbbdabcbbbcdcdacabacbaaaabacbaaabbdadcdabbbdadcbcaaabcbdbabadabdaabcdcaaadccaccadbcdbdaccbbabbabbccbdcabcdbcbdaadbdbaccaaddcabbacddbbabdbacddbaddaacbddccaccbbaccadcddbadbaaadcadbacabaccbbccbadbdabdabacadbadbcdacabdbdaadbcbbdddadbbdacddbbccaabaaccabaddacbcabbcbdbabbbcbdcadbdaaabccabbcbbbaacdcacbbaacdbbcaccbdcddcbdacdcddabadadabdbacacdbddbcbbaaadddaadadddccabcadaacddcabdbdbddcccddabbababccabccacdaddccbddcacacccaacddadbdacabbcadabcdbacaaacccabdcbcbcbadbbcacbbacbddcadabaccdddacdbbdccaabcaadaacdacdddcbcaadbcaacbcbdacdacacadcaaacdbaaaddaacdcadbbdccacddddbdbcacdddbbcadcbbbbcdddbaacbadcbcbacbadcdcdaabacdbabdaddabdcaabacadcbdccdbaaadbddabccddcdadbbabcaadabbbdbcbccddbdbdacbaccdaaaabbbdcbbdbdcbacabcaacadabacaaaddacacbabacadddaabcdcabcdcbacdbadadddcaabcbcaabacacdccbddacadbcadddcacadcacbcaccccdbacbadcdbaacbacbddacdacaaccadcbabadddcabbccbcdbcadaadabddbdbaabddbbdddccabcdcacabbcadacaddbdcbaccbbadcaabdcacbdccddbbbdcdbdabacbbaccdbccdadbdbaadcaddcbaabacbcadadcdadabcddcddbddbcccdbabbabaadbccddddddbabdbdaadcadbaddbdaabcaabdaaabbdbdbcadacdaccabdcdbbaddcaccbdbdcbdaabbdbcccadbccbaabadadadbbbbbbabbcbbbbadbaadccddaadcbaadacbabcbabcbdaccdbdccdcdaabaaaddbccdcdacdadcacbbbcddbcabccbddbcbdabbdbcaadbcddaabbcadbcccbaacdcdbbbabbbcabbaaadbcbbbcaaacbacabdbacdbbcccdbadccdcdacabdabcdbbdbabbcaddaaacabbbdbcbdcccdddaabadabccbaadbadaadcdccadbacabadbacaadbdbccbdadddadababbdaadbdcadcbbadcbbaacbdbbcaacabcdddbdccaacbdcbacbbaccadcdbaadbadbaadbcdcabcbbaddcbacdaccacadacbcdabbbdababbaccabaaccbbabcccbaacaccacaaacdcbbbcbdcdbaabdcdabbccabbaccddbcaadcabdbcdbbccdbccbdbdccbacaccabaacdcaadcbcbddbccabbbbdddbcabccdcddddbaaaccbcdcccacbacacccadadacddbadbdcbababdbdcaaccadbbcabbcbddddbdabcaddbbdadcdadaabcaccccaabdcbacaaacddbabcdaaccdbaddaabdcdadcdcaadbabdaacdbbdccdaacddcbacdadadcbbdddacabbcacdadbcbdcbaabbcbacbddbaaadbabaaadabbbccccabdbddcbacadbddcdcbacdbbcabbdcccddadabacaabdcdadbacddabcabcdbcabababadbbcbbdbcddcdbacabbcbcdaabdcaabcbacdabbacddacacaaadbbaddccccababdbcaccdacadbdcaacabaadacbcbbadabcdbadadcbdaababbcabbccbadbbdbbbbbcccababacdaabdbaccccddacbabadbdcbcbbdadcbccdaabcdaabaddddadaaabaccbdddddbcaddcadcbaabadbcababbbdadcdcbacbdcbacdcdaaaaadcddadadcdcaadbadabddbbddbaaaddabcdcbdacbbcacdbdcadbcababcadadbadcbdbaccccbacaacdcdbdbbacaabddabcadbdcaacbbaacabdbcacabcdababdcdbbbbccaacbcacabdddbcabbbbddddadcdacadbaacbdaacbbdbabacbdcacbcdbabdcddcbcbabacbbdaaaabacdadbccadaadadbcbbacdddaabbbabdbacbbbbdbbbdabcbbcdcddbbdcaabdcddccabdabaabdacbdbcbcdbaabcabdadcddcaabadcdaaacccdbbdaacbabdcdbbbbbcbaababadbccccaadbadddccadbacbcdcacbbcabcdbabcdabcbbaddcdabbddccbabbbcdaddaaabbcadbacaaacdcacbddcbdaabacaddbddabacaccbbdcdbbcaabdabcdabdaaaddbdabbabadcacbabbbbbbabbdaabccaaabaccddbdcccaddabbbbcccddcbacdbaabdbdbcddbdcdccacaaabbacdddbccddacdcddadbbcdbaabadbbbbccbaccacdaddcaacdcbddbccbbcbbddddadbdbdcacbdaaabdbaddbddcdadbddbaddccbbabcdabbcabbacbadcacdcddccacbdbcdddbdccbcbdbcddabbbccbacdbdabdacaddbaccbdacacadbdabcdbabcbbbdbcbdcbdcacdabcdcdabbacdaaaacacaaabdcadbddabdcbbcbdacccacaacbcdbbdbcbacacdccdaabacbccaabdddbabbbbdcabcbabaabbdccbcbccaccbdcabaadbbcbbacbddbacccabcddaacabdbacbddbcdbbccdabcbaabdcdaadccabbaaccccbacbdcadbaddcdbcbcccbccbccccbadabacaadacbcbbdacadcdddacaccddbbdcbcbabcacaccddcacdbadbdacdaacddcacdacdbabddaccabccadddddbdbdbdbbccdcbdadcddcdcbddaccddbadcddbadbbcccdbdbbbaaaddaaadcdaddddccccbcbbbaaadadbdcadcabdcbdbbcbcacadadbdcccaadbaadbdbdcdbbabddbddcdbbabcadcabbcabbdcabbbdacbbdcdbbaadcabbabbbdaaacbbbccbccbcbdbccccbaaadaabdabcbaaaadbbbababbacdcccccbdcacaabbacdbccbbaabadcbbbdaacdacddbbcbbbbbadccdaaabdcbaaddabaaabacdaaabcacdcdcadadcbdbddadabaccdddccdbabdccbcbbbccbbbbbcbbbdcbdccdbaaacbacdaccbcaadbcabddbadcacacdbdbddcccbccadccadddcdbbaacbabdabdacccdadabcbcdbaaddbcdadbacdcaabaccdcaacddcacdcbcaadbbcdacdbcccdaadbdccdacbbdaaaadaadcabcdaccdbddccdaaadaabcdcbbaabdcdaadababdcddaadbdbcdbbadcadcdcbbddbccadcbdabdcccaaacaaddacbbdacdaacddaddaacdaddabcdabaaaacacccacddcdaaabacdbbdcdaaabcbbcdcbdabacadcdadcadbabaccdcacbdcbdabdcaabcbadbaaacabbbabbcdcdbbaddbddddacbadaadaddbdcddcbabcadcaaabcaacaddbcbddabcdabcbcdadbbbccdbdcabbabdbaaabcbaaaddcabaabbaabdddddbadaadbaddbadaaaddabadbcdcabccccbcadbdbbabccadabbacdbcbdaccbddbdccdcacdcbcbbdaabadadddaaaabbbabadccaabdbdbbbcdccddbddbacdcbadbbdaaabaabdbcddacaccabaacdcababdaaddbbabddcddbdaccddbadababdcdbcacabbcdccddacddaaaacdddbbdcdabbcaccccdadbcabcbdadcabccdcacdcccacdcdbacbdbcdddcacdbcdcccacaccdbacdcabcccbbdabbbadcdababddaccbccbdadcdddacddcbdaaccbacaccdcdbabcbaddaacabcbddbaddaabbdabaddbdcdbcaadaacdcdcddbcdcbbdbcbabcadadbdaaccdbddadabdbcccaadaadcbabbdabdcdcacdadbcbbadbbcbcddcdcacdddbabcbcadccbdbdacdbccabbddadbcdcbaadbadaacddaabcaabdcaadcccacaacdbaaddaaaaddcbdddaacbbddacbdaacbaaaaddbbdddcdbdbbaddacabbbcbdacbdaaacdcbcbaababcadacbaaabacadcabbccabcddabdbcbabdacaacddadacbcbbddbcbbcdbbbddbcbacdadcccdbdbbdbdbaccdbbbdbdcdbdacdcccdbaaadcdcaaadbcdbddcddcbdabaddcdcdccbcdcbccaabaaccabbcbabcbdbbcdbcaddcabcdbcdbcdcddabcacadbaababbccdcccddcbbaabbccbacaabdcabbcbbdccbdbdccdcacababaccadacdbccddcdbdcdabbcbcdbbabcdccdadaaabbdcacbbdcdbcdbdabccbddccddadbabbdadbdaaccadddaacaaddcabaadbcbbcdcdacdacbbbaacbadccccbabbccbaaacabacadaddacbbdcccabdaacaccdacaaadacccbcacdaddbcbcaacaacbcbacccdcbdcabbacbbccbddabbbcaaccaddbbcdbaadbdbddadbbdadbbdbbcbadcdaacddcbbaacbdccabacadabdcbdbcabdbcddddbbcadaabdcbcbacddaabbdbbcdbaadcbbdcdbcacdabccaabacdcacdddcdbcbacbbbbcbcbcbcdbdcbaccdbddccacdaabdbaaadacbcabbccbacdcdbccccadcccabccdbacbbacbbcaccdababdcabdbbacccbdaadabccbcaadbaabaccbcccbbcbbaddadbdccbcdcbccacadcdcbccacddabdacccaabaddacbbaddaaacddcbcdbccdcccbdabddcaaaabbddcaaaaaabdaccbbbdddcadcabccbbadbbadcdcddabaadccbaabbbcaabdbcbbcbddbdccdbbbbbcacdbadbaaaaddcaabcaacaccbaddacddcddbdadccabbcbabbbabdadacaacbcaccacbacbccddcadcbdaacacbdcabadbccabbbbbdbcadbacbdbddbbbdcbcbabbadbbabbdcdacacbbcdbbdabddbcdacdbbdddbadabadabbbbbbacaaadadccdcbaadaadcccdbddbbcdabdaddbddbcdcadccddaadcbdcbdaabbbdacbbabcabccaabbdcddbcbcdcbcadccccaddcaccbdcdbcbcdabbbdddbaddacdabccacbccbcdcdabadadbcabcdddcbdaacddbdccccadbdcdababbadbcccdbbcbcccbabcccabbcbcbbadddaacbbaaabaddbaddbccdaccbddaaacadbbdbbabbaaadadacabccbddccdababbbaacccaaadbdabcacbddbbcaaabdcdbddbaadcbadadddbadbcbdddbaddbcdcacdbacdcccbbcbbddcbcbbdbbdacbbbabdddbacadcbadabcaaccacdacccbbdccdacaacdcdcadadbbdcbaaabcacadacdadbbaabbcccddddccdbbcdbdccdddbadcbacadabaaaaabddbdaccbaacaaacaaabcddbdaaadccbbbbbdccbcdacdbcbaadcaddcabbabcadcbcddcddcbbddbcaaadccaaacbaddabcbacaddbbabbcdccdbaabbcccbdddcbaabdccdddbcbbcbdbdcbacababcacbabbbbaaaaabbddcccdccccacdadcbddbcaccdadcbcdcdcdacdadcbbdcbbccadcbddbacdbbddbdcbbcdaccdbdcaababccccabcdcabbacaccbdbcabdadbdbdacddababccabcbacadddccbbadddaacdbbbcbcbabbcbdddbcdcbcbccbbbbadcbbcccbbdcacadccadcaaaabbbdaaacddaabbabbcabbcdcabdddbcddbacaaddcdddcaddccdcaccdbbbdaaabbddabbbbaadcbdddbacaadcbcdcbaacaddcaadadddaccaacdadccccabcbdbcbdddabcdcacacbabddbbadbccbdacdaaacaaddbaadcccbbbdbdabcdbbdaabcccbcbbdcdadbcdaabcddbabdbaaacdaddacdbbbaabdcdabdcbcbaccdcabbabbbababadcadadbddbdbbcbdacabadbcdcadccabbccaaacacabdcdbccaddbdbbdadabcdbdcbabaaaccabbaccdbbabcabcbdcaadaccdcbbbdbaaddbbbbadadbcbdbdbcbdccbcaddcbbaadcaddddaabcabbcabccbbdbbdcabaaaddcacbdbabbbbabacbcadbadddbaccaaacbdcaadccadddaddbadcddcdaadbcbacdcaabccdbddabdbcbbdbaacbadbbdcddbcacaabbaabacbcdbbacbaacaccdbdaabaaacdcdaacdaaaaadcabcbbbbdbbddaccabbdcbdddcbcaabbaccdbbbaaacbdcccdccaaadbbbdbbbddcadadbcbcccbbbaadbabbbccacbdaaddbaabdacdacbbbabbaacbaddadcddbbdddacadbabbabccadbbcabccbccabdacbcccdbcabcadacdbcbdacddddaadccccdaacbaababadaadabdcbbdaacadbccdcbcccdbcabcbccacbcacdcccbadacdaabcbbcabaaccbbbdacbcbdcccabccabbbcaaaacbdbccaabdcdbacaaabbcadcbcccbacadccdadccaacbaccadbdacacabaacadaccdaddbaddbcadabbaccbbbddbaadbdbdbacccdddbcdccddaccbabddbdcbdcdbbccbcbabdbbcddbcbabbaaccccaccbadcacacadcacabdabadbcabdadbdbddddbdccabdcccbacddcadadaaacbdcaaabcbdadddcbbbcdcdcbadbccacaddbddbabdadabdcaaadabdacddaaaccbbadadbccdcbbadbddcabacaaaaccaaccbdcddcbcbaccaaadaaaacbacaacaaaaabdbdcdbccbccdbbbbbabcabdbbcaddcdcbdccdacabcdbdadcdacadcaadbaaabccdadabccaadaadbdcddcbddacdcbabbbabbacdaadddcbbdbdbbcddddacbcdbdbbcbcadccdcdbbcacdbbdbbdaaabcccddaaaacddbacccdbdcddcdcdacbcaccadcdbacbbcaacbdbabcdcacbcadddbabdabcbaddadcddabadaddddcaadbabdbadcddadadbabbbbaddbdbdcbbbddbbddcadacccbaaaddbccbbbaaadadcbcdcdaaccbadccdddbbccdabacbddbccaacbbadccdaabbabaabadcdadcdacadcaddaaccbbabadbdabdaacbbcadddcdccadcbdbccdbddcaddcdbccdabcddbaadbacddbdddcdbbacabbcaaaddcbbdaadbacbbbccccbbbcbaddcbacbbdcbbcbccacbabadbcdcaadbacabbcddbcaabdddbbcbbdcdbdcdacdbadccaaaaabdbbccccadacacdccbbccbbdacdcbdacaaabbcbccabbdccdaacdbdcdbccabcdacbcbadbccccbcdcbbbdadbadbdccaacbcdabaaabaddaaccdbbadaabdbaaccdcdcabaaaddacbcdcbdaababbdbcdbdcccacaacaaaddaddccbcadddbcabbbcdcbaabcdbcbcbacbbbdcbdacaaadbabcaadacddcdbdababccbcdbcbcbcbdacacbabbcaccbdcddbddbaccacdbbbadabadcadaacbdabddaadbcbdbdbabbbcdbdcdcbabdcbaaababdbcabaccabdacccbddbbabdccaabbbcbacdddbcbcdcddcdbadbdbdbbabcdaaddcacccccabcccbcccaaaacbbdbdcadabbcbaadaaddacacdbddaaacadcaaacbddaadaddcacadbddbcacbbbdabccccbacababddacbddcbdacbbcdbcccbddacacdcddabadadcdabbdddcdcbbccdacbaddddbcaabaabdbdadcddacbdaacbbabccaccdaaaaadbdbcdcdacadaadbbadaacaabdccadbddbdacbabdbbbbaabacaabcccddbdacdbcbdadcdbcdcacdcdbbccabbbddabdbcbadaacbbaadbccadbabcaccadbdccbdcaccdccdbbabdaccdcdaaaaaccdddbbdbdabbbddbbbcbabadcbdddddcccbadcbdacdabbbcacaabdaadbddcdbbddccbdddbcbcaaabdbacbbcdabcaaaaddbcbddcbbbcacdbcabcbabccaacacbaccdacabbadabdaacddbdabbcbabcbaaccbdccbaddaaaccadbabbddbaadbcccadddcbdacacdadcbcddadaadcaadaabcaadadccdcdaddadbcdabdbbadadcaaadcaadbbcbacccdccadaddccacadadbaaabbbadddbabccbbcbbbacbaddabccdcacdcbdcbbacbddccdbcacbccbbbabcacdacabcdbaabdbddddadadcbdddcdacddbabbbaddcbdbddacbdddbccdbddcdabcbddadcbbbdcccccdcdaccaccadabdddcbcbccdadcbabaacccbdabcadcaabccaccdbcabcddbbccadcbccdababdacbbcdccdbbbcdadabdccaabcbcdbccacddabbbddacbdcbdccacaacaadcddbdaddbbddbdbbcdbdacbaaadaaababcdbcddbdcababacacaccadcbbcdcdabcdcbababdbdabbcacdbaabaacccdcdbbaadbcabdaccccadcacbdcbbbdcdccdcaadcbddcdadbdbdbcdbcdaabbbbabbcddabcdacbdcbbdadddcadbacdddddbdaddbaacdddbaaccbdadadbabdbbcadccbbdcbacdaadbbbcadbdaabaabbdcabdcddcddcbcbbddccbabdacabbdaaacbacdcccbbcdcdbcdcbaadddcbcdddccacbdccdcabddcbcbbbbccdcddacabbddcbdcacdacdcbcbcbcadcadbacaaacccdcbcbdbdadbcbbaacdbbdabbbcccdabbcbacbcaabcaccdbacabdbacdccdcccccccdcdbbbccacababbdabddadadddbbbabbacaadccddabdcdbcaaaccdcaabaaaaacbdddcbbaacbbbaccdbddcbabcbbadadbdabdcddcbadacbacccabadbdbcbbbcaadaadbcacdbdccaadbdbabcdbccbcbbcbdcdadacabadccbdbdaaccbcbcabbacddbabdaaabdbddacbbccddbaadacaaadbbcdcbdcdcdabaadddccbddddbacbcdcaaddbdcbaabcababadabccdccdcbddbdbadcadbcbbaadcacdcccbbababdaaaccdbcbbbbbaadcddbcacdddaabdbccbabbcccbbaadbadacbcbcbadbddcdcacdbabdccaaddbcbaabcaaacacddcbcaaacaddacbddcbabdbcbbaadabcdbadbbaacdcdaacaabddacbaaacacabcdbdabdcadcbccbddabbdaabcaaaabaccbdbbbccaaadddacbcacaadcdccdcacbbdbbcdcbadcbbddbddcbaaacadbadbccccbcdabddccabbdaaabdadbbddccccdcadbaaabcbdbccbbabaaacadcbcbbdbdbdcbaadbbcddddcdcbaacadabbabbbdbaacdbdcabaccadbcdcdcccbddbbbcaacddcdccdbbdabacccacbddbcbbbdcabaaaaadcbcbabacacbbcbabcccaaddcacbaaddccbbcadcdcdacccdbdddcdaaacbbdcdbbdaabcccacdacbabdbbdcbaabbadbabbcabaaabaaaabdaacbcbddaaadbddaaadbccabccbacaabacdddadadbbcbcddbccacabdbcbaababcbbaabacccddaccadaccdabaddaacadcbaacacbaacbcddcccccabcacbbdbbcbcddcbcbdcddcaabbaacdcaccddaaaaddabbdcadaabdccbdbcddbbcdddddbdbabbaddbdbdbcbddcadbccdcdabdbbdcbccddccaaabdadadabdabbaabcabadbbddabdaabbadccbbaabdbabdacaabbddbbcabddbdacccdccbbcaabdadadbdacdbdaadaadcdbbabadcdaaacbadddcadabbcdbbdbcadbaddbacacdacacdbcdaabacbdaadddcccbacadaacddcadbbcacbccdbccdadcbcccbcdbccbdadddddcbbbdaaababbcdccaacddccdbcddbaabddccdbbbdbbbcdbaaadcddcdbcdabddacbccbbccdadbacbcddbdadcbccbbacccbdbbaadbbcbdccbddcdababdacbaadcaaabccdbddccaaadbccdaccdaccbbdcbbbcdccabcccbbcdbadcbbbdbdcdbacadaacaaddbbdcadcbacbbccddbccacdcdcacbdabdbbabbadbdabdddcdcadadccdbdadadacbbacadadccdaccbabcbbbdcddbaddbaaaacbaccdccacddcabddbcbdaaadaaababddcddddccbacbcabbaadbadaabadcbbabccbbbcdbbbcdcbaabacaabbcddddaaaaabbabbccbdbaabcdbbcbdbccdbcbbdbaaabdadadccddbcabbddadacbbaccbbaddcadaabcaaddcbbadccbdbdbaccaabacccdddaadcccdddbbaacacdcbdadcbdcdadbcddbcccadaabcbbdabcbbccacbcbdaabdbbbabcdbbdadbcdabccddbbcbcabbcbdbbccdacbdbcaaccdbdbddcbccdabccddbbacadbaadbdbbcbbdcabdadbabbdcbccadaaddbadbdabbaadbdbccbbdcddadcacddbbbddcbadcbacaacdddacacbdacdadbaddacdbccbbbdddaadbdbabaaaaaaadbabbcbdacbdddaaaaacbcddcabbdcddbbbddcdcadadcbcdabcacacdccdacbdbabdcdadddabadddcaadaacdbddabcccaddaccbcbabdcadadaccbaccdbcccdbbcbabbcbbacdbcdbbdbabcacbdcdcbcbdbacbcbdccbbdabbbbcbcadccdababbdbabcbccbdacdccbcdcaddbdddbbdadacdbabcddddaabbabcaabcacaabbbdaaabbadbdacacbbcabdbbbaabcadaaaadbcbcdcbcdbbbacbacdbbcdbcbdbccaaabdcbcaadddccacbddcdcadbcdabbddcdbaabdcadacbabadbdcbaadaadbbbcdccccabdacabdbdbdacddbbadacabbabccdbcbabcadccbbcabbccbbbcdccdbadcaccbddacdbbbaabcbccbaadaadabaacddbbbcabcaabcbcabbaaabbcadccdcaadddaddccdbadbabbccdaacaababdbbbcbbaabccadbbdaabbdbbacaccabdbbabbbadcdbbcbababccddabcdbbbaadabcacdcaccdadbddcabacaaccacaddccdaabcdbbacccccbabcabbbdabacacbddbbadcbdcccdadacabdbcaababadabcaaaacabccdacaddbabcbcaaadbacdbdbddccbaddddaddbddcbcababdcbabcabdadbaaabaadbbdbabacdbbcdbdcccbbdadbdccbcbaaaddbcddddbddaadcccbcdcdacccdccacbcbbcdacbdddccbdbccbabccdabaddcdabbccccdbcdcbdaababdabaccbdddbccbbbcbcdbbdcdbcccbacddcdbcccdbbdcddadcdacbcbacaabdcdddbcddaabcbbcbcdadabdcddacabcaacdccdcddbdbbcabaabbdcbabbadbdbaaaaabbdbbdbdacbdccdcadaabdcaabbdddbbaadbcdcaaddbcbcbabdccbdacdbdadcdaacbaadaabaabcdcacdbddabadaacddacbbcaaacbddabccbdccdaadadcaabcccdadcdcbacdabbaabddddacadbbcacdacadadbdcdcdadcdcadcbabbaddccccbbcdaaccdbcccaadbcbbbdcbacdbbdbbabdcbcbaddcdcbddbaaabccbcbbcddcadaddaccdddadadbcdaddbaddbacddbbcabbbbbcbdbdbddaadcaccacadcddbcacccbababbcabcddddddaddadaabdbbdcbdadbbbabbcabbcbbcddacbdcadccabbbdddaddcbddddbccdccabccdaaadadcbaaccbaaccccaccabdcbcdbdaccddbdcbcaadbbdbdbdbcdaaadaacbcbbcacaddbbdaadaabbbdcabdadcbbdbdbcdcdbbbdadbaabadcdabbbcbbcdcbdbdaadddabcadcddcbbdccababccaadcdacccbddcabcacbaabddaadbbcccdddbbdcdaabbbcbabbdbabacbabbdbbadabdcdbabdcbcaccbabcddcbacdbcdccdcacdabccabaabacccccbbdddcbacdaddabcacaaaddbdaabdcbaacbddcccadadacdaaaadaadbbbbbbccccccbdddabbddbcbccbbcdbdbbaddbdddbbaaaddacdacaccabaccaccdbaadacbccbadcbcacdbadaccbadababddcdadddbcaddbccddbbbdbdddcdadcdcbbaccccbdccccabadbadbccbddbbbcbddcbdadabbcaaccccabbababbadbbdbddabaaacdabdbcbcbbdcbcccbacaccbdbabbbcaababaddbbbadcabdbcbdcaacbbdacbacbcddcbcddcaaabbcadddcccddcbcbcdbcbadddbdaadcaaadbccabcbccdcaccacbaabdbbdbdcddbabdcddbabcdacbcbdccaaabdbcdbdbbbdbccacccbbdabcadaacadccabbadbddcccaccabcabccdcdaadbbbadbbddcbdbcbbaccddbccbbcbcdddbcdcdbbcadabbdacadaddbdccaabbcdabdaaddcbdcaccdbdcddcbccddbbcccadbabdbccabbcdcddbcacaabaabbcadbacdabacacccbacadcdbccbdadabbaaadbdddccadcdadbdbbbadcbcabaacaaccbcdbdcbcddcbdaadaabcaadaccbdcdbbbbdaabccabbbcbcdcdcbaacdbdbadcdbaaccbcbbccbadacacbdaadcadacbbbdabddddcbbbacaadddadbcacadaacddabdaabbaddacdccbacbbdaaaddbddddcacbdaabaaaadcaaaaaabcbdaabbddcabaabcbbbcdcacaadacdacbadbdbadddbcadbcbabaabaacbdccacddbdbdacaddcccadcccccbbccdadcbbaaccdddcaadadcacabadbaccbcdaaccbaddaabcdccbdaabbdcaabbbadcbabadbdaaddcdcbcbdbcdaabcbabcdabcbbbaaadbaddbccbadadccbbdaccbbcddbacbbbbaadaabbcabbaccbcddadaddaadcabdcdcaacbdbacdaacbabbcbadcbbccccbcababbcacbcbdaccaddbbbdccdbabbdacddcbcadcaacbaadaaacbabdbddbbabdcdcdbadbadaabcabadaddcbacacacdbacabcdddacddbdccacdcaccbccdbacadcdbbcdcbbcabbaaaadcddcdaccccdcddcdabbcbbdcaacbadccdacccdddadaadbcbbcbbcbaadbaaaddcdcdcddccbbccdabcbdbbdbaaabaadbcddcdabcdabcaabddcbdaaccbaccabbdacddbdbbdcaccccaabbcddbccbcaabccbbacbcbbaddddddaccacbccbdaacacbcddaacbcdcbbccdcacdaabdccbaacbbcdbaddcddddcaadddccaaaaacdcdbdbbaabddcddcccdcbcbcdcdadcbbabcdcbcaccbdcadcadbdadcbcdcaadabcdbadabcabacbdbdcabcbdcabdadbadabaacbbacaabddaacccadddccdcbaaaacabbcbbdcacadcdbddcbcddbaacabbaddcddccbcabcabbdcbbbacacdbdcdbabcccbadbbdaabccbbccdabdaddbbcacbbbbddcacbcbdccbdbccdadaadbcdcaaddbcdbdcbdbcbaaadadacdaadcdacdbdcabbdbaadbaddcccbcbaadbbcbaaccbdcbadcabbaccacbdccdbdbccbddacbabdccabbaacdabbbcaabcdbbadaccaaddccdbadccdbadccddcdcbcccbccbbacbadabcaddabbdcdddaaccbcdaccdbabaadabcacadccabbacaaacbcdaddbacdadcaaaadcacabbcbacbcabcbcdacdcbbbbcdcccadacccdaacbbcbddddababbabdcacaaddaacbddadbddcbbbadcdcdcacbcadbbcadddcbcccbcbbddbccdbabadabdcacbaaddabacccbdcbbcbcbaddcbcadbbdbdcaaddacdbbcdbccccbdbbbacbddbdcabcbdbbccbddadabaacbaababaaadabaccccdadabcdaadabcbdbddadccaaacbcabadaacbabdccdcbbddaadaaabdcaaabadbccdabcadbbddcbdabbbaabddcbdbadddabdbdabdddcdaddcadcbcbaacbcddcacddbbcbdbcabcdacdbdacdabbdacdddaddcadcbbcaadbababbbadcbaabadbdddacaabbdcdaaadabdcbadadbbcdbbcdccccbdaaaacabcadbddcadccbddcbbdddbdbbcabdcccccabdcdaccdadbcccadcdadabcdacbacdcbddbdccbbcccbacccbbaabbcbadbbbcccbacbcdadacacbabcbdbdbbbdbbaacaddacbcccbdbbcbacbbdbdacaacdadaddaadadccdcdbdcbbacaddacadbccbccccdacdccdadacbbcbdcdccaaaccadcdcaddbbdaabcbccabdadcabddcabdcdcdbaaadbbdbbbacabacbddcbdaaabaccadcacabdccccdcbccccadaabdbbcddbabbababcbcdcaabbdccbdaacdcbcdcbabbabbaaadbacbabaacdcacaacbadadbdbdbcbbcabdadcabbbccddaabdbaacdcabaaabadbbcdccbdcacbdbbcdcbaccbccbcdcbcbbccbcddababbadbbadbcabcbbdaddbdbabdacccbdabcaccacccbadaaccdbcbdbdacaccabddacbddcbddbaccdcabcaacacdddddbbaabadbcaacbbcdbcbbabcabcdbabdaacabbaadccccdaddbadcbcbdaaacacccbbbcbaababdbbddbdddababbaadccdbbbbdbcbadacadbaaacadbbcdabbddbdcaddaacccaacbaddbbcaddadcdaaaacacbacacadcbddbcaccacddadbdcabcdaaabcbcabadadabcdacbddcbbacdbcaaabbbbccbbabbccbcbddcdabcaaddadddabbbdbbdcaabdcccdbcaddbdbccbdbcbdddbbdddcddbbacdcdbbddabcbdacdbcaaddabbbccbdccdbcdaabdbdbbdcaadbadadbabddccdbdcdcabbaadddbcbcdacdabdbdbaccbdbacbbdcdddabaccbabcacdcaaadbacdcdbbbbdcccbadadcbcbdaddbcbdcdcaaacacbdcdabbdcdadcbbbdbdacbbaabcdcaacbbdbddbabbacdadaadaddbbaaabdbbdbcbccbdcacccbaabcdabddcddcdcdbcddadaacbdbbadbdbbabbabacdbdaaccdbdadaccadbcacbdccdbadcaddacdbdaaaacdbbcabbdbabbbcdbcbbddcdadbaaddbdbcbdbbbccddbaaabacdaccabadcbabadbadadadaabbcccadddbbcabbbcaadabdadbcccaabddcdadcddacbcbacabdddbbadadcdcbcdddcaabdddbdadcdbadbcdbdbdadcccabdcdcbaabbccbddacacbababdddbcdbcddabaaccacbdacdcbcbdccacbdccbbddcabcdbbbadbdadbabdccbddbacaabdccbcbdacbcccccdcdbdccbcccaaacabcabacbaabadbbbbdddcddbbaccadacbddcbdcbdccacdbddddbcbaacacaaaacbbcbabddbbbadbcaaabacbcaaaabcaababbcbbbbcbccddaacdaddbabbaabaddbcbacdadabddcaadcdabdbadbbacddaddbdabcdaddddaabbaaccaaddabbdddcbacdcbdbadccbabcaabcaaabdacddcbadddcbbdcaaaacbdbbcbdddbbddddbdcbadddbdbdccbcddddbbbabacadabcdcccdabdadbbabbbdcacabbbcdcdababdcaabcdcbdbbbbddcddabbcabddcbcacbbccbaabbcbaacaddddcccabdcbcdccdbdccccbaabbaddbadbbdddacbccdcadbccdbcbdcbdaacadacabdcbaacdbcbdcbbcccadbcbbdbacdcbdcabbbbdaabcdbcaccdbaabbacbbdcdbaabdbcbbbaabaaddddcbccbabdddddadcacbadadabdcbdddabdcbddcccbdbcbbbdbccdcbdabdddbcdcaaabbbaadbcdadacabcdabbdbacadddabcababcbbcadbdacaadcbacaddbcddadcbbbddcddbdbdbccaabbadaaabdcbbadadcadccbaadacddadadaaddcbcbbbbcbaccbdbbccbaaaaababbdcdbddddcadacccdccccdbccadcdbaabdddbdcbbaaccdabbadaccadbbaadbccccdcdbbdcadbdaaaccbdddbbaddbdbdacdcdbabbbcddaadabcbcdcaddbadddcdabbadddcdcaccabcdacddbbcdccbbbabcccbbaccdbcabcbdbaccbabbcddbcbdabbcdaaadabbdbdbabababdcbccbbadbdbdbddbabdadcacbdbaccccbddaaadcdaacddadcbacdbdcabbdddcacddcaccbadddccadcddabbcaddbbccddcaddbabdddcaadacacbccacbccadcbbdcdccccaadbacdddaccaadbaadcdbddcddadadacdbcdddcdacaccbdcacdabbccdaabadcbccbcdddaccdbdaabccbdcacacdddbaaaadcbacbbdacbdcaaabdcbccddddddccddbcadddddadabccbbdcaddacddbbacbdadadaacddbdcbbaaabbccdbacdbcbcbabacadcadcccaaccbdaacbcdbddababdabddbdccadcddaabdacaddcdbaddbcbacadbabaaabbddcaccdbddcacbcdbbdccdbcaacbbccabcccdcabdcbabbbbacaadcdccbaddbdaadacbddbdadbdacabdcadabdcaaabadbccaacddbbcbdcabaacdaaaaabccacdabdddbabbcdccadacdbaddabadabadbcababbbcbacaccbadabdcdabdccbcacbadbcaabdcadbdcbadcdbacabcbcaacaadcbbcddcabdbaadcdcbdabdccacbbdddaaabdcddcabacbdadbcaacdcdabaabdbadacdadbcbbabaccbabbdaadcddbadbddcabbcabddabdcbbdcbcabcacddccbccbccbcaabdaddcbdbcdcccacabdbddcabdadacabbddbccdcabbabccdadadbbadadddaddccdccaccbabcddbbbaaaacbcbabdacddccbbaccaddaadbcddbdcdbdccababaaabccbbbdbdbacbccddaaccaabccdacacdacddbbabbacacdccbbbaddbadbacbcbdbcbadaaaddabdbacbbadcaabaabaddaccdabcbadbdcbcdacbbddcabccccacbcbdbbaddbcbbbabdaacacbbdacaacbbdbcaadbaacaccacddddddcbbadbbdcdcaddbcacbdacdabbdbcbbacdabadcdabacdccdcbbcddcdddbbdbbaccbcaaacdcaadbbdccccdabdabccddcccdbcbbddadbdbbcbbbdabcadaddbbdbaaccbcdbdcadbbbacdddddccadbdbbdcbdddabdabbdacaacdcaaadacabaaddcadabddcdbddbcbdbdccabddacadaacdabcbdabaadcaadcbabcbbdabddbcaacdcacddcacbbcdcbcddacdcbdcacdccdcbbacaddddaaccbbdaddbdddcbcbdbdacbbccabcdbcbddbcbdbaabcbcbabbdaddbcaccaccaaaadcbcdadbccabdcaadbccaabdcdadabddddaccdbdacddddbdbadccdbbabdaccbcaabcbbacbccbadcbcdcdadbddbdbaaccdddbaacdbaccddddaacbabbdcbdbcdabddaaacacacbdcbdbbaddacaaaddbccbdadbdcacddcbaddbccbbdcaaabcbdcdbbdadabababcdbaddabcbbcdddbccacbdaacbacbacaddabbbbdcddccbaaaacababcbbbcbcbdcccbcdbbcdcbcbbadaaccbcadacbcbbdbbbcccaddacbbaabababdbbbccddaadbbdbaddcdbadccabccdaddadabdddabcbcacbaddddbcacdbccdcccdbadbccdcdbccacbdddccacbcbcacadacdddbbcbaabbbdaddcaabcadcbbacbacbbabbccbdcdbcbdcadadbbdcdacbbcaddbcdaabababccababaaacdacdcadccdaccccabbaadaaacadbadbbabddaadbaadacdbcccaabddbabdadacbccbadcbbbbbcccdaccaaacddbbbbddbaddaddbdacacaddcaaaabdadbcdbacdbabcddcdcdbcbcccccbbbaabdaabaabcdcdbcadcddaacbaccbccdbbcdadaddaacddbabbcbdbbaaabadbdbcbdbaabbbacbcdabbccaabcdbadaacaaddcbadcdaacbccacbbdaaadbcbbabdbbaacddcbababdaacaaddaccdbbaabdaccdadbbcaaabcbdbbaaccddcdabacaddadcaadcbdccadbbcacdabbbacdcdbddcbccaddbbccccabacdbccbaadacdbdccdacdcaccddccacbadbdddcacbcbbcccbbccdddcdccababccbdbccaaacddcbdccbcbadaacbdacbaddbbcbabbbbadbadcdbaabcbcadcddadddaabcdbbcdcbabcccbbcdabbdbddaabacbbadaaddcdaabbbccbdcdabcdcbcdcbcddcabddaacabbabbddbadaccbadccbcbcbaddadaadbdcababbababddcdaccdcccaabbbdccabcabbdcdccdcadaabdcacccdbdcaabbbdabdacdbaabbdbbadacabdcdbdaaaaaddbacbdbccaaadbccbccacbccbbbaadbcabdcbbcbabdbcddaccddadddacbaadabdabbbdbcbbcaacbdadcdbbdacccbccbcbabacbbccdcdcbccdbbacbcdbaaccbadcaddaabaabbacdcccbacbbadbabdcdaadcbbdbccccacacabbcbadcbaddbbacaabddbabccbdabbbdacabcdacdbbddcbbdcdacdaacbbacdbcaacdacadddbabbadacadcbcddabccdbacbdcbabbcdabcaaaaabdacbdadcbbdcdcbdbcacaddcbbccabcaaacbbccdbabcacbbdcdabcbabcbaccdbbbdcccdcccaacddcbdddadcdbaccdcdcbcacbcbacadaacccaaccdabbbcaadacbbcdcddcabcadaccbacabdaaabdaacaaaaddddcbbdbbaaadbdbbdbbcddababddcabbdabddddbbcdbbcddaabcdbbdbbcaaaccababcbcabacacaacabaacaddcbbabcadcddcbaadbdbcdbbdcdabacbaabdbdcadbabbadadadabaaacabcdbadbdcdbaadccdaaddccbabcdacbccbcdaddadcdbabbcaacdacdabbbddcdbbbbbcdcdbdacdbacbaaddadbdddcdacadbddcbabcacbdbaaaacccbbcabbbadcccaacabccddcbbdadabaddddddcdbbdcaabdacdbbdbccddbcaabbabbcacacbbcdadaaacacbcbaadccdaadaaaddbbdaabdaaaccbccabcdadcdadbbbbbacbabbbdbdcacbcdbaddcccabddbcbbabcaccbcbbacddcbbbaabacaadccaadbcbaabcddacbddbdabcbcbdbdaaacbdadaddaabaaabacacacacaddcacaaddabacccdaaadcdadbdaaaabccdaabddabdcbdadccbcaccaddbbcdadadaabbbabccaabaabaaaccbddddaacbdaccacdadcdbddccabddaddcacdddbdbdaaadddddaccabaabacbbdcdabccaccbcdbdacbcbbababcaaccacaadbbbbbcabbcbddbbadabcbccccdccbabdbbccccadabdacabddbcdadadabcdaccaddacdaddbdcdccaddadcaaacbbddbabccbcbdbaddbabcbbadccdcacbbbdddcbddbcdabbcabadccbdcbbdaacddccdddacccdaddbbabaabbbdbcdcdccdbaadccccbacdbddbbbddccbabbccbaabbaacbcbadcdadcabccdacdaccaaabacdcbcbcdaccdbdcdbdbbdadcdbcbabccbcbccdbcbcdcdbdbcdcccddaaabcccbcdcadacaabddddddbcbcabdaccadbdcdababcdacbadddadadaaabbdbdccbacaadddccdbcbadcbccdababcbabcdccadcadabccccbdcabbcbcabacbcbdacaadaadcdbdbbdcdbaaabcabbbddddddbdbaabcdadcabddaccdcdaaddddbabcbaccaaacbddbdbdacbcdbdbdabaaddcbabbaaabbadadcbcaccaadacaddbadaccabdaccccaadbaaaabbacabaddbabcabacdacabbddbaacbddbadacadbadcaadbdcddddcadabcdaadccabbdabacbcbcdcabcdcdbbbbbdcbdcbbcabdcacddbdbbabbbabbaabdbdadbdaaddbddbaddadcaabdaadccdbdbacbdbacbbdadabcdcadbdbbaccccbbbbabbcbcdcdadaaddadcbbcbbaccabcdddcbacddddddbacccdaabcccbcbcbbddbcbaabdacddbbcacdbdabdcbbccdbccacadcaabbcccccccaabacbbccdcbbcadccdbbcadcdbbbcabdbacaccbcacadddcabdcdcdbccabdbaabcbbaaaacaaadbacbddcbbbbcdabacabbabdabdcadbcadadbbdacbabddadbddbbcbbbccaadbbbbbdbdabcccaaacabcbdccdbbbbcbbadcbacbcbdbbdababddcaaddbdbdbcbacccbbcdddbdbacdacbcccabdcbdbaccbaddaaadabdabddbbbadaccdcdbcaabddadcbbabdccacadcbbbdddaadcbbacbacccabbccabcaadbdcdaabcbdbccbbacdabdcbbdabcddacdaaccbbbacbdabcbddabddbdabbcbddcaadabbaddabaadbbccacddbdbaddaccaccbddddcbcdabacaccadacccbdabacadabaccbdaddaadaacaadabcdadbcbcdaddbadddabaacadbcadcabbbcccbcdbdcaacbbddbddccbadbaccbbbabcddabdcbabbdbbbdbddcbdcdbabbcdbbabbbcdcbbcabcccadbbccbbaadadccbdddaadbbcbadababcdcaddcbbbbdccdbddcbdbdbdddcbbcacdabbadddadaddbdccddaabdbcbaabaacccacacdddaddbbabdccaacaadbcbdbcdadbcbbbacadcbadabcccaabdbbccbcccddbcbaccababaabacaddcbbcbcbccbcacbcbbbcdddbcadaadaabdcdbbcbdcababcdcdddcdbbbcccadcbbdacacabccdaaddababdbdadcbacbdddacaabcbbdcbdccadddbddbcbabadcaadbdacaadaccacbbbcdcbaacdcababdcdccdaabaabdccacabcdabacbacdbacadabbdbadcdbabbdcccbbbadaaaadadcbccdadcacadcaabadbaacddaadbcaaccadbaacbdabdcabbdcbabbcbdadbdcdbbbcbbcaacbdabacddcabccaccdaabdbcadcabccbcdbbdbbbbadbdccbaabadabddacaabbcbadbabaddbdacbbbdbdbdccddbccadcadcaaacaddbdccaccaaabbaadaccaabdabadcdcaccabddabbcccdbabdaccddddccbaacddcbaadaaabbaaadaacdcaaccdcbddbdcbbacacbdbacdbdbdaaaddbaabcacacdbcdbddabdcdcaaaacacabbabdbcadaadbcbbadaddbadabccdcaadabcdabdcdabcaadbaadcccbdacdacbdddbbbbabdadcccbcbaabcadbdacabbcacbacbbadbaabccdcadcbbcdbcddcbddcbadabbddbbabbddbabbacbdbddacdbdaaccccdacdacddaadbcacbbbabcbbcdbddbadcabbabdabbbccadbabadaacbcbcaddbdcddacbaadabbdbabbcdbcdaadbbddbdabdbdadcbcbbbdaabbdadcdbbbdadbbcccadddcdccbddbcbbaccbcaabdbcdacadacbadccccbbbcbcdcbbcccadaccbadccdbccbdabbccdacdacddddcbdbbacacddddabbdccdddddabbbbdcacdabaddbcacaccbdacabcddacbcacdbadcacbbadcaabcaabaadbbbcbaccdcbdbbbdcacbcbadbabaabbaddabbacadbdccbabccdcdbdacddadcabddbddcacbddabdacabbaadabdabadaabadaacaccdaccbbaacaaabccaabcabcdccdccaabbdabaaaabbddbadbccacaacbacddcbaaabbddcbbadababbadaddcbacbbbddbbcabbababbbabcddabbabdcadbbdcbdbadbccbcacbbadaaddcacdcdcbcbcdcaabcbdababcbbabbdccbddcabaadcacaaabbdbaccddbaccadbbcdbbcbaacbadcbbabbbadbdabaddcccbdabcbbcbcbdddabbdbcacdbadaccdccbdcbccadbbcaddbcbdcccadcdbbaabcccbcbdabcdbddcabdadbadbaddddbbbcbcdaddabdcccadaccaddbbcadacbcadacabccbbdbacdaddcdcbcbcaabbadacacdddccabbbaadabaababcacddbacbcddcabddabcacababbbddcdbbcddcabdddacddbbadcaaaadcbbbdadcdbbcbdcbdcabcdadcdadcdcdcccadbaccaacddcbbdadbababbaabcdaaccbdaabbacdddcdbcadaddaaacaabbaacaaddddbbabbdbbaaccbbaadadbcbaacccddcabdcbacabbbadddaaddbcdbdcbcaaccccdcadcdaaaacaabcadabadadccdcbcaaddbbbccdabcbaacbbbbcbbbccbddbabcbcacbbdaddccdddaccaaaddccdabdcdddccdbcadbababdadbbddadbcbacdacddaacdaabbdddcdacbdbdbcbcdbbcdbcbaacbbdcbaddbcbbccdbdaaccbdcbdaaadbaccaacacabacaabdcbbaaccdcabacbbdaaaabbcccaabacaaadbabdccbacbaabdadbbaacdadbdadbbcaabdacababccaacdaaddabddadcdabbabddbbbcdcdaadcabdbbdabbbdbbbdcaddacbdcdbcbdbabdaabadadbbcaddaadddcbdbdadbcadbdabbabcbcdbdcbbadcdadadbaababbbcddbabadbdcaccacdcaaadbacddadababdcccbddcdadcbdbabbbdbdabacdcdcabddaddbccabcdcdabcaabbcdcbbbbabcbdbaaabbacdaccdcadaadbabcaddddacccbdaaaaabcbcacaddddbcddddbbddcaabdcacbccabaacadbbabccbadacdcccadbddcbabdaadcdabbbdacadbdbaaacdcccddacccbdaadcbdcbabacbbababcacacbadcabbacdbcdacabcaadddccaddabbcdbcdcbbbdbbaadacadcbadaabbcdaacdadabcaabbacdaaacabcaddcdcdbabcaabcddbddaabbdccdbcbcdbcbaccadccddaacccdcbcbdcbdaadbcdcccaaddaabbaadddaaaadadccaacdbcdbdccaaadcdacbaaddbdddabdcbaaacdcccbbbbcbbcdbbcaaccbbacddbccdcddacbdcbdbbbdabdabdcaadbbccdbabaadcacbcbddbdcdcdadbbdaacccacacbdadaabdbdcbdadcabbdbdbbabbdbcadddbdcdccbbcbddcbbbdcbaddadacdccdccbdacabddcdbcdcbddbcaaddbbacbbcdcddadbabbdcacbdbddcbdbcdcacbaccdadcbaabcdbbbbacbdbdcbccbccbbacbdacabccbccbbaadbdcaaddbbacdbbabbbadaddcccddadacbadcabdcbbcdddacccbdaddbcaaaaacaabcdadddaaadbabcddaacbacaaababadacbddbadbccdcadadddacdacdadbbaabdcdbcdadaaacccddddabdbdcaabcaaaabbabdbcbacdbbadbcbcaadbadbcbdcaccddccadbbbbbadbbbbbcbdadbdcbabbcccbcdbcddddadacddccabadcddbdcacdadcdadbcabbddbbcabccbbacdacbcdaccdddbbcdbbbbdcbdbabdddabdbacbcdcdcaddbbaacbaaaddaabcbcddbbbcdbbaaacabcabcaadaaddcdacdbcdaacddabbcaacabbbdddabbcccbcdbdadaccbccbbddaccdbbbbddbadbbbdbdcbcadaacbabdaadbcbbadbabbccbdabdddcaccbcaaacaabaaddbbbcdbbaccbdbdadcadddaddadbdcbaaabaadbaabbaadbbcddacaacdbcbbbabddddcbaccadddddccbbbbcdccdbbabddbabaddbcbaabcaaacaacddcaaabadaadcabbaaddcbcbabddbbddacdacadcbbdddbccbddacddcbaabcccbcdccabbddcccbddbadcbbaabcdbddacaacaddcaaababdacbdcddbdababbbacbacabdcaadbaddbcbadbacdccacbbacbbccaadddbccdccccdabddbdcbdabbdacdcbcbdcdacbbbbcbaabdabaadcbacaccdbbbcdbcccadacddcbccbbabbaddbdababccababbdaaaddccabcbbbcabbdddbabcbdddcdbabcbbaacbaaaddabadccaadbaacbcddbddbabdcdbcdaadbbcbcadcabdcdcdcdcbbddcdbcaddbaccdccccccbdcbccddccbcaaaccadcacbadbccdbdaacbbcccbdaacaacddcacabbcbcadcdabdaaadcbbcadadcdcddaaaddbcacbaddabdcbababdaadbdbabcadbbdbcdcdabcdddadabcbcbbaccbacbaadaacaadabacbbacabcabdcacbcaaddbccabcdbbcdaacdaccbbaabcaaabaddadcaadbcdabdbbccadcaaadbbadddcacddadbbcbadcbddaabcddadacabcbcbcadddccaacdddcbbaaacbacbcaaacdbacdcaadcddcdabbcbdabdcbabcbbaabccabccccdbbabcadbbdddccbbcadacadbccbbbcacddbbcbcbdccabadcaaacccbbabbcbacdcabccbacdadcdacbbddbaabbcdbadcdaadcbdcbaaacacbaadbacdbdbdbbbbdadcbbcddadcabdddabcddabaabbcbdbcaacacdabdccacccacccaacdcaaaccbdbbabbdcccbdabadbdcdaadbaccdaaacaacacacacacacbabcaaadabdaaaacaabddaacaaadacabcccadabbbcdaacbcdccacdcbbddcdbdbcbbcdcadaadddadaaadabbdccaadabcbbaaccadcdbaadcdbacdbccadabcdbccdcaabbbabacadcdbabaddacccddbacacadcaacdcccaadaabcddababcaaadccbdadacaacadddcacbccbadcdbcdbdcdbaabbcacbcddacaaaddbbbbbaaddbdabbdabacaaaacaabcadabbcdbdacbbccdcbacdbaaddaaabacbadcddabccccdcdaacdccdccccaabccbbccddbaabccddadccccadddddbabcaacddcbbbbbcbbabaabdbcbddabdabcdacbabbcdbbddccbcddadddbdbaabcdcadadcddcbddaabdaaabbaadcaaaddbdcdcacdccbaddcddbdaadbaabddbbddbcbacaacabbdbdabbdaacdabbabdcccbbbcbdccdaaaaaccbadbbbcbadcabaabdadcabaadbdadcaabbcadddcabdbdcabbabacccbabcddddacabbdcabaaddbccddbbbbdabcacbaddbdbbccbcaadcaddadcddbdcaacabbbabadbcacdcbabaacdbabccbccccddabaabbaadaabdacadcacaadccaccdabacacccabdcdbddbacaacbaacacadadadcbadbdaaaddbddcdddbbacdcbacacaacdcccacabdaabcdcaadbbddaaaaabcbaadbdacabbdbacbccdbddbbcacacdbcdddcdbacbdbcdbdbaadadbcabccbbdcbcbaddddabbbcbabbcbaadabdcbacdcdcdadcaccdbaadddbcaddabaccdbbaacccbdcaabcbbcbcddddaddaacdbbbbdabdcdaacdabdaabadbbbaacaddcdddacccbadbddcadbbadbccdaadcbcadabaacabbadaacacdadbaccabdcdadcbcbddccccdccddaababddadabddadcbccdabcbbbbbdddaabadbbbbaccbcbacddaadbcaadabdccbdadacdacbbdbbdadddbabcbaacaaaaddbabbacdccbdccdbacaddddbbdcadbbbbccaddbbcdaaddbdbaddbaddabccdddabaddcaaccddadaccaabbbccdcbcabbbbabacaaaadcdcdddbdbcddddacdcddbcaaabbbbdbabdcadbaadcbdcbccdcbacbbaacbcddacaccbcbbabcaddcbabbacdcbbadcdabdbaccabdbdcdbcdcdaaadddddcdacbdcbcccdaadddbdcadcaabbbbcdacbcaccacccdacbbcabcaadaccddbddddcdbabbabdadbabdbddacbaaadadaadbaccbbaababacdaddcdcabdbccdcccabdbbaadbadaabbaccdddbabacddcaddcabdaaccddbcbdaadbabbabdcbaccacaddbaacdccbdaddbaabaabaccbbcdcccdaababdccabcdaddabadcbabdacdcacbbbaaddadaababdcccccccbbcbdcabaaccdaabbccaddbcccdddabdcabdaabcbbdaaabbbcabccadccdbbcddccabbcddcaaddcbbcbbbdbadbdaddddbadbcaaaabacbbbdbacdaabbaadabaadacdccdbbabcbcaddabcddbbacbbcdacabbdcddabcdcdadacdcbdbadadbcbbbddbadcdbcccbbdcdcbbacbcbbabddadbabdcbabcbbdadacdbdcaabbcbadcdacdcabcbccbcbdaaaadcacdadddbabdbbaadcbdbaaadabcaabbccbbccaadcbbbbdbbadbbcccbdabacaddbdbcacbcdbcccabaabdcacbccaaccbadccaaacabccccddadaabcdcdabcbcbbdddddacaddbadaccadddcdcccdcadacdddbbabddacbbbaadbddbccaaabdddcdaabdcadacbabcbcdbacadccbdcdbaabacabbabbbdabbbdbbdcdcaaacbdbcbcdbacaadaaacdaddcadcddabdcbdadbaacabdbdbdbcdaccbacbbdabdcabcccdbbcdcabbbbaadcdbaadbcdbdbababbcacacbdaadbadabadbabdaadbbddccaccdaccbadabbccbcccdcdaadaabdbbcaacccbcdcdcbddbcddaaccdacacddcbaabbdcdaacbcabadbbccbcbaacdcbbcbacaacdbcdccbddadcbbddcdbcdbbcaabdddbcccbadbbcbcbbcdcdacaacbabaaadadabcbababaabbcbaddcbcbbccbdaccbccbbbcbbbbbabdabaaabddbaadbaddaccabdddadbbdbbcaaaccbcaabadabbdaddddbacbabacdaabbabdddbbdccdbaadcccbcdbdddbcabbdbadcaccaabcaacbcbbcaacbacbbdbdbdbdcbdcbdcbccaabbbcbbaddbbcbcbbabcdaacddbbabcbcbdddcddbbdbcbbdabddbddddbcdabddadadaaacbcaccacdcbabddaacaaccddaabbcdaabdcbaaabadccddbcddbbadaddaacacbacaadabadddbacbddaddbbdcacbabccabcdddcbcbdccbabbcdbcdddbdcdaabcacaaabccaadcdbcccccbcddbcbdaacbcbdcaccadbabdbccabcbbabdbcadccabccbacbbbbbdacdbcacbbdddddadccabccaddbacdaddbdacaaaaddbaacabcbcadcaadddbadabaaccaaaaaaabacccbdcbabbdcbabcbcdacbaaccddcacccaaaadddcbcabddcacadadabadbdbccdaaddbcdccacaabbdbcbdbabbadadbacaabccdcbccdbdccabbcdaacdcbacaadaaddbdccaccdbbdbabccbbccaccdbacbcdbdcabacbbccdcabaaadcbbcbbbcccddbddaaaaabddccbcdbcbdbdbbabddbaaaabccbbddcbddabbdadcdaaadccadabdddaddddddcbdbddaddbcacbadadbcaacacddbbaddabcdcdadabbbadcbcddbcdabdbacddcabaadccacaacccdcbcaaadaabbdabcccbadcadbcdccdddadacdccdaccaaabcddbbbdadccbbcbdbbdbaadcacdccdbdbcbaaabddbccabbdaaaadbdccacbdbaddbcddbdcbddcddcbbaddaddcbbdadcabdabdcdaabcccccdcacacaaaddaabacddddabcccaddddbacadccccbcacdbdbadaddcddcaaddcccdaaadadcbcaaccbabadacbcdddaddbadddacbddaadbaacbacccdbacbbacabbdbacbadbaaadbaaaccaccbacddccdadacbbcbddbacbaadccbaddaaabadbcbcccbacbbbcdcabccaadddaddbdbdbbcbaadcacbdbbabbbdcddabcacdacaccadbaabaddbcbcbcadbaabbcbbdddbbdacbbaadcacacbbbbadabcccdbddddcdbdcabacdcaccacdbdadbbcadadcccccbaddccabdbaccccdbbccbbbdadcdaaaddbbcadbbcacdaccabbcdbddccbcdacacdbbadcaadbaaaadabbadbcdaacbbdcaacdbabacbaaadabaaabddaccaaabcbcadbcaaaddabbbabbadcddaddaddaabcddacbdbaacbdcaabdcccbbdbcbbdcabbabbaccadaaddccddccadacadacbacabcacbcacbdcdcbdaaccbcbbbdacccdbaabccabacbdaacbdabcddabacbabbccbdcddaacbcbccaccddcddbdadccdacacdbbbaaabbcacdccbbccdcdbbdaccabdaabcaacdcdbcdacbbddcccdcabdcccbdbadbaddbbcdacdbabcaadcbddbbdccdbbdaaabacabcbaabdcaadbadaaddaadbaaaddbcccbbddbcacccdcddbbcaaddabcbbddbcdaabbcdabdcadadcdbddaabcbdaaadcaddbaccaacbbaacbdccacdcbbcbaddccdaacdacbbccbccaabdaaddaabddbdaacaaacabcbadaaaccccacbcbddaadaacddacabddbcbbabcdaaabbbcabbbddcabaadcdcdcbadbbaabaddaacdabbdacadbdbdaddccaddccdaaadcacaabacdaddcabcaabbabcaadcbdacccddcdcacbaaaabacccbcbaccacaaccbbcdcbdccbaadcabdadadbcdcbaddcaadcacaadadacbabdccacaddbdbdcabadbacdbbdadbdcacdbdadcddbbdaccbaccccacbbabdbbbcaaaadcdcdcbadbdadbaacadbacbbadcdbbdbcbbcabbabdbdcdcaabcdbbbdcaccabcddcbaaabdbabbbaaccbbbcdbaddbcbdbbbacdabbccccdcdcdabdbcddccaabbbabacdbcbcddddcbbcacddbaabbbcacaccbbaadcabdbababacaddbdcccbdcddaddadbabacbacccaddcaaadadacbddbdcadcadccaabddbdadbbdcdbadcddababaddbadaaadacacdddbcbddcbccdbcbabdacdcadadcbbcbaccaaabdaaaabaccbcbcaaadaaadcddaddabcdcdbccabddbcccbcadabdcbacacaabccdadccdbddddccbdcbbdcabdbcdddcacdbabdccaaddabdaaacbcabcaacbcadbbadbbbbbbbdccddbbbbbdaadcbbabbadabacaacabccbbdaadcdbbccbbbcaddcadddddcbbcdacccaccddbacaddcdcbadadaddccaabcdbccdaccbbddbddddacbababcabacbdaaccdcbcabacaacadadabbadbaaabbdcbccdcdaccbddddcacddcaccaddddbcaabcbbcaccdccdbbcbdbdccdcbabacddbabdbcbaabbdcaabddbbcaacaadcbcdcdbccadbcccbbddbdbacdbdccbbcbbccccaadbbcadcbddddcbabbbabaddadcdadcbbddcdaddcdcbbbccdbaabcbccdaadcbddbdbcbacdacddcddaadcacdaabcdbaaddbbddbadbbdbacbcccddbcadcbddbbdaddaaaddbdbdbdcdadadbbdcbadbccadbabcdacadcacdbaaacddddddabcbbbadcadcdccddbdbbbaaabaaadcccdacacadbdbbaaccadaaddbdcdbbbabaddcbdaabccadddcddbdcdbcbacbdddbaabcbaaaddbcacacdabdbcdaddacdcbbaccddbdabdbccbbdadcbbbdcbcadadaaadbabaaaabccddbbbccdbdbbaaadadbdaccadadddbbbcbbabdababadcadccdcdcbbccadbdcddbbdadadaccaddacddcbcdcadcabcaddcbadbbbcaaaabacbdcbddbacaaadabacaddbddaaacacabcadbdbdabcbcabddabacbcbadaccdbbabacbcdcadacdbcbddcbcacbdcbbdccabbcbacbdcaadaababcdadbdcbdbbcbdbbccabbbabdcaddabdaddddcacbaddbabcaabaacdcacdcbdaabacbcbbcbdadddcdccaadccbccdbbaacbbbbdcabcdcdcdbbbcbbdbddcdbcbdbcbaddbdbbccdbadbadabcacdadabadababcdbdcadacdacbbdaccdbcadddbccdbcbbbcacdbbdddbdadbbbccdbbbcaadddcabaadadbadacadbbdddccaabccdbbdcbbdaccaccddccdbbabddadaddacdaccbbdbabcbaddddcbdacbbadddbabbacbdbccbaadddbadacbdbcccdacaccacddaccdbabbbcdadaacddbdcddbdadbcaaccacddaabbadaaacabaccabcaaccaaabbddcdcdcdbabdacadaacadacdcbadbddbdbccabdaccbbbbdababadddcdbbdcdbccacbbcbacabbcdbcdaabbbacbccaadddddbccacacbacdcdcdcacbbcccbccadcdabdcdbdbcddbbcbdbddcaabbccadbdddbdbadccddbcbacccdcdaacbdddadcbabcdccdbcdcddcddcbdccdcbacbaabaaaaabdbdaacbdcdcbaccdadcbdbaaccbadbaaababbbbabbbbbbdbddddddaddcbaaadabcbcaacdabcadbaddddddaabaadbacddbcaaccacaddabbadbadadcdabdccdabdcacbadbabaccbcccddaadbaccacacdcccbbccdacacdbaccacdcccdcdddccbddcccccacbababbabbbcdbbddaaddcbdbcbabaddcdbacbabbacbacbabcdccbadbbdbaccdbcbadcbbcbdddbdccdbcbbbcdddbcadbadbacadaacbadcaacaaabccaacabadadabddabddbbdbbabbbadaddbadabbdacdbbbdcddbadddbdbbaccdacabbadacdacaabadcbacbaaaabaaaaabbcdbbacaaadcbbccbaaacaabadabbdbcadabbaababddbaddccbbadddabdacdccaddaacdaadbcbdddbaaadcbdbdaccbccaccdcdabdbddbccdbabdcbbddbcbaaddacbcdaddcdbdacdbccdbcacbbcbcdabadbacadadbabcdacccbbcaddcdaaadabaccabddcacaabbbbcdaacdbcbaadbcdcbdccbddabccccdaaadbbcbadbcdcbcabaabdaddbddccadcbabaccdaababbacacddcbdbdadbabddbbcddadcaacbaabdcdadbbcdbdcaddccadcaaadbbadbdbcddcadadbbabdadcdadabddddadccadbccaadbddcabcdcbccadcdddcadbaacadcaccccddababdadaabcaaabbbdcaccdaabddbdccdcaccbbbcaddcacbbbaabcbabbadadddcdcbabbcbdccaadabbdbdabbcaddcacabbcbddddbdcddabdcbdbdbababacdabbbaacdacbbadcacdbbddcadcacdabdabbabbadabdcaabbbdcbbdddaadaaaacbcbbbdbdbcaccdabcdcbddacccacdcbddccaacdcdacccbdccabbdadddcaacddbbcaccdccdcdabaddadacbdccbcddaabaabbcbbabbabcbacbdaabbabddcbbdaadcdadacbcacdadbbabbdabcdaccbabbcbbddbddbdcddcdbbaabdabdaaadaadbddbccdbaccacabcbdcccdcaadabdacaadbbdabdbbababccbdbacbbababcddcccdaabdacdabdaddcbccacbcdccadbacaacbddbccbabacdcaadcdbaaaccacacbadcbbcdadcdbdcdcadaabcbdcdbbaaabdaccdadcbdabaadbccabaddddbdcadcccbcbaadaaccbdabbcbdbbbacdaabbdcdbdaabdcabdddbddaabbddcddbbcadbdcbdcdaabbaaaabcabcdbdcaddddccbbacacdbbbbcbcbcdabcdbaaadcccccdacabdccbdcbbdcaddbdbcadcddaaacdbcdbcaacbabdaabddbbcacbacbadccddbdcabcccaadcbbadabacacdbabcaadaacadaddbccdddbacacdbcadbcacdbaabddcaabcadddbbccdbddddddcdcccacaabbabccaacacbbbcaaddcccadacdcdcddddcababbddacdadbabacdacadacdaadcddddcadddccaaadbdcadcbcccbcbdbabbacababdcabcdbccbbcadaaabbacbcddacdddbdcadcacabacbbdabbdbabadacbcbcccdcccbbcabccdcadbbccbcbbbcbcddacdddababdacccaacdbabaddbbddbabdcccbdadbddadcccdcabbbdcddacbabaaabaddbddbbbababdcccbccadcabaccabccdcaddbabaabdaddddcbadadabddcaaacbdabbaacbbabcabccccbdbabacabbddbcccbcbddbbdcddaaccdccabccdbbbadbcabacacccbddcbbddaaabadadcdaccdcbdcbabcbbbbacbdacdadddbdcbbcccddccdbdddcdbbdbaddcdadccdccbaacadaababadaabcacbcabdddabdaacabbddabddaaddcdacccdbbaddbaaccabbcaacbaabbbdaaacdcbacbaaacddccdcbaabbbdbcdacbdbbaababdcadaacbcbaacccbcacdbcbcadabdddbadabbdcbaacbcdbbabbabaabbdbddbcccaddcdddaccbbcdbacbababaaabdbdadcdcccdabdbcbcacccbdaccaaccddcddadcbbcbbbadcbbccdbdadcdcdabdacdcccabbdcdbdcacdcaacdddaadbccccddcbdbbdbbdababacccbaccacdbddcdbdcbcacdccabbccddbcccdccabcbaacdccbdcddbdddccdabaddddbbdabcadddadadacadaddadacbdbbdbacdabacabbcbcadcbdadbcdabcbdcdbbacbacbdbaddcdddbbadbbccabaddddbaccbbdbaabbdddcbbcbbdbabaddbbbacbbabccacbcbaccbbdbcaadcaccaccadbdbccabddddbabbdbcdbdbadcbcdabadbbdcdabdaaadacbacdacbccccaaaaacabbcaadbabbdcaddcbddadbababaddccbdcaadbbcdbbcbcadddbbaabcdbabaaddabababdcbadbbdabccbdcbddbaacdbbbbcaddbdcbabbdbbdccccbcbaadcdadccadacbbdbadccccddbbaaccbabddcdbadbbdddbccbbaddbdaabbcbccdadcadcaaddbcddbcdaaccacbcadbdcbddbaddccadddcabacbdbbaccadbadaddddaacacbadcbabadbbcdabcdbcdddddaabccbbcbddacdcbbaccacbacadddadbcbaddddddbbbcdcbbcdcddaabccaadabddcbbacbbbadacddacbccbdbdccdaaababacbddacccbaadbbbacbaaacdaaadbcdaacdcbdbdcbcdcaadaacbcaacbdabadccbabadccacbbcdbcaaaadddbaacddbcabdddcdcacabcdcadbbdadcacaacacbdadcacbddbbaccbdcccbbdadddcbbadabcbabccddbabdcacddcddcdddcdbbcaabddacadaddcdacdcadcadadbcaaccbbcbcddadddcbaaabadcbbdadabbbcbcadbabcadbbcdbbbdddccacbdddcbdacccdcbcbabadbbabbacccacbbcabcddcdadabdcadadabbcaacddadabbcdccbdbaadbabbdbbddccdcaadaddddccabbadcabdabdddbbddcdadbadabaacabdbcaabdddcbbbadcdddaaabdaabbdcdaaadadacbcbbdabcbdabdbcdcbdcbadbcbaadddabadadbacdddddbddcaddcabddbbaadadbdbabddbadabdcaccccbbbdcddadddaaccaccbcadbcaddbdadacbdaacdcdcbdddcbcaaadaaddddcdcbaaadbbdcdadbddaccdbcdbccbcadcdadcddcccabddabcbbdbcddcabadccbabaccbbcbdbbbbbcaadcccadacbddbcdacbdccdccbbbbbababcdcbabacacdddccacbdbaabdbcdbababcbaadddcaddbaaddcbdbbbcddcbddaddcbbbcbabbdaababbdddacdbbbccadbcbbbdcdbcdcadadbccbbaddabadcbaadabdabbdaccabddbbcccabbdccaabddbdcdbacbcddcddccdbdbbaaddacbaaadaabbabcdcdbdcbdccddcbcdabbaddbcdbcdadadbdabdcbbacbadddccbddbaaadcdbabcddaacbbabccaabcbcbccbbbaacaacdaadbacccbaaddcbbcddcaaacbbacacccadbcdacbbabddcabcdbbcdacbbcaddcaadbdbbbdbcadccacaddabdcacabcadcabcacbaabddacbcdabbacabccbaccbdccbacbaabcccdcbadbabacdccaaddbcccbaccdbdbbacbdccbddadbbccabcbadbccaccbdbabcbbcaaacddadbcdcacdbacaadddbccddddddaaacacbccabdcbdadbacbaadddaaacadbdaccdaadbccdbbacadabcddadcaccabdcadacadbcdbccdabdbaaabaddcbbddbacbbccccbabdcdbdcbdcacdabccacabbdbadbdbaddddcbabcbdbddbdbaccdcacaccddddacccccddcaacabbdccaabadbddadbdbbbbcbacacdcdbcdcbabbdddccabdbbccaddbdacddbbdaddddbcadbcddbdddbaccdccdbaabccadaaccacaadcabdcbbbbccbaacdbccdcddcbabbcaccdbacaaabcdbbabadcbcccddaccccddcbdbbbdccbacbacdcccdaddadaddbccbbacdcabcacbddbdbcddbadbbbdcdbdbbcdddadbccaacbddddddddbdacbcbbbabcbaaacccbdbadbbbddaaacbaabdbcccdbaaaacacddadabdacbcddcdaabbcbbaaccccaadabcbbabbbccacabccbadccacacbdacdcbbbccaacacabddaddbacbcadaddcccbdccbbdbdbccabcaaadbcbcaaabbabadadabdbdacacdaadcccabacaccdcdcaaabcddaadabacbcdbdadbabbbcddbcabdddbbdcadccaacadbaaacddbcabdcbcaaabdbbdcabdccbddcbbbbddcddcbcacdddabbbabdcacbadabdbbadcbcccddbbccdbadccbcacbcdbddbccdccddbcddacbcdccbaabadddacbdadcdcddcacaddaddabbcbbcbcaadbcccbadaacababdacbbbcabdccbaccbddbcddaccddaacaaabaaabacbadabcbccbcbcdcdbabaddccdaadaccccadcdbdbdcdcabcbadcccaaccabdcacdadddcdbcbabcbccddcdabddacbcaaabccbcacbcabdcbbaabacdaaddcddbbbcbbaaaadbbabcadacdadbcbbabaddabaabbdcaccaccdcdbdcdbddcbcdccdccbcacaddbcbbcaaababaadbabcddbdaacacbabbbcaadbacbcaccbaabaaadaacdcbdadcbdbcbaaccabbddbbcbcdcccacddacbbdccbbcaaccaddbabadbbbaddcabcddbabcaddcdddcdcbaddacabcbcbcdbcababddabdcdbccccccdccdbacaababbdbabaaacacdcdaabbbccaabbbccdcabbdaddabdaccaaccdbcbddbdabdccddbdaaaadaacaddaabcbcdabbdccddcbbcaadcdbaadacbbbcadbdbaababccbcadbbdccacaccddddabaccaacdbbcadcacadbdcaaaadaabcbaaadcccbdaabdbcbabdbcdcbacbacccabadbbadccaaccbaaddaadbdcacbccbbabbabbbcccbbcaadcaabcbcddcdbcdcbbdbabccaddcbcabaacdbbccdbdbadcccccaccdccdcbdaabcccadcaabdbbdabaacbcdaadbcabbbcdabccbddbbbbbcbdcddababbcdcacabcbcaaddcaaacaaccadcdddccadbbbdbadccbbbbbbcdcbacdabaacbcbbdbcddababbbccabbbdccccbccbdacaaacadcaadcdcddaaabdcbcbdadacccbbcbdbadbdccbacabcbadaadadadabadbbaaacccdabccbdbbabddbcdabadddbcabdcbbdbddabbcbccbbcbcaccbaddcddaadcccbcabbcbddbabacadbcababddbddadccddccaabddadadbcadbbddbacccaadcaaadcadbcabdaaabcdaadbbcbcaabaddaadadaabcccdbbbbdadbcacdbbdbabccaaabaaadadbabdbcbcccbaddbdddbdbabcbbacbadbccaaadcddddbaabbabdbbdbcbaacdbadbbccbacbaaccaacbdbabaacbddccacaacbabbabacddbdbcbabdacccaccdbdadcbbdadcdabddbabbadcccddadbabddbabbdababcdadddcabddddcccbccdddcdbabdcbcddbbabbaabdbbabaadcbabdbbdcdbacbbdacccbbacabdabbacbccbdbbdadddcdcdcabadadccaaddbbbcbbacbdcdabccaccaacdcddddadaccdbdbcaabacdcacddddbbadacbadcbaadaddccbbccbaacdddabbcabdaacdbdbcdbabacdbcddbdabdababcbdadaabdbbaabdcaddcbbdbaddaacabacdcdcbddabddbcdadadaacdccdbcccaabaddbbbcbbdadbbccbddbcddbbcdacbdcbadcabbadccbddacddbbabcbdbdddbadbacaccbcbcbadaadcddccbccbcabaddcdcbbbaaaaddaaabcabaddbdadcacccdbbacbcdabdcacbdcccadacaabcacbbdbbbdcbbdcaabadadacaadbccadcbbccccacbcdcacaabcbcbabbcbaccdacdbccdcbddcbadbdbadcdbdadacabbdbbacbcbbdddbaaaadaaddbddbcbddbdcddcadcaadabddbcdcadbacadaccdacbbcbacaccddaadcdabbccddbcbadbdccdacabcbddbaddddaaabcddbdbaddbadbcabadcbaccbbaadaaaabbabbbdbadcbdbbdadacabacacadcdacaabdaadbcbdccccaaadddaccacacadaadcddbbcdccdaddcacadddacbbabbdbdbbdcbbcdadbcbcddaabdcccabaacdbaccadccbdcacbcbacdcadacdcbaabaaacdbcacbdaadadacbdacbadbbddaccbcccdacdcccbcacdbdacbdbadaabdcddcdcdababbdbabcccaadbbaddcadacdddbbbbbabdbbccaccdbdbabcaacadccbcadbcbdaccabcddbdbabbdbaddaddaaabbdcbddccdcaaabbabbacccabaadbbbbaaccbcabcacaabddddcdcbbdbbdccbdbcccdaaabcacacadaabdadabcacaadcbcbcbdacdadbbcddbadacccddbcbdaccacbcadbadcbcdcdccabdbacbbdcddbacdcccdbbadcbbcadbdcaaadcbbadcbcbdbcdcacabcacabcadbaaddcdcbbaabadbdcabadcdcbadadddbdbbddcadbcdcababdccbdbbbddbcccbacaacbdacabbdbacdccacdcddbbcacaaddcdccddbdddcbbacdacdcddaabbaadbabdddcdddabcbcbbadcbcbcdbabbcadcbdbbadcbcbaabbbaddbddaddccbdcbcacbacdcbcdccabdaabbabbcccadbacadaabcacdcddccdabdadacaadccdcdbcbadabcccbdcdbcbdadddcdcdbcbbabbcbadaddabbdaadbbcbbbacbbdacadbaaaadadccadacbacdacbcbccabdcdacdbdcdbacabbabccccbbbbcadaabccbcddadbbcbbacacdbadddcacbdcacadbdaadabbaaadbccbcdbbadbdadbaadbaadaacbccacaaddbababdcbbdadabacdbacadbdaadccddcdddbaabccddabdcadbdcddabadaddbccdbadbabbcaabcdabbbabbdaddabbadbdddbddbdbbbcddaadadaacbcbbacbaccdadcbaacacdcdcccbdbaccabddcdabbbdcdbcddccdddcbccbbccdaaabcaaaccddbabbdcdcccddbbabaaabbdcbaddcccddbcaabcddbbbadbcdaabbbbdbdcdaadadaaadbccadabddadbbcadbcabadabdddbadcaaacbbbddaddbaadcbbbdadaabdbbcababdbbcbcacdadccdbddbbcbdacdcbdcbccbdbadbbccccaacbbacdcdcddcdcdaddcaacbcbbaddbbbacdaacdbddbdbbddabdaccabdcbaabbacabcdbaaacdbcbdccccdcdbdbdbabdabddbabdabbccaccabbdabcddddcaddaacdadbdbbbabbcdbdbbcbabddbdabaaabdabbbababbdcdaadabbbbdbddacabcdaaddbdbcadcbbdbdbbaaacccaaabdcaacbdadaaabbbaccccabccaabbcadaaaabccccbcacadcbaacbadaccaaddbcbbdabbadddccaccddaadaaddbdcbccbbacbddcbddbababcacdbcbcbcabcbdadababdcbdaddabaddcbbaccdaaccacbadabdccdaddcbaccbdbaaaaadcadcbdcaaadcdbddaaddcabdaadaabbbabbaccadcbbadcdbdaaccacdaaacbbdcacbacaacaaadaacdbdaacdbcdccbadacddddcdbccdbaddabcdacacbacdaaddacdcddaabbaacddbdcacddaabcbbdddabdbaabcdddccdabadddddbdadcaaadcacccdddacaabcaaaccbccbacbbcbcbcacaaaaadcdcdbdadaacbdcdaacddaaadaddbdbadbbdddccbddccabdaaaccaccdaccbbcddbcbaadcdcabbccddcdbdbabbdabdbacbcbdaabbcabbbaabbcbcaccbddadcabdabacaacddcddcbbabcaabbbabddcbacbcbabdacbbbccbdcadabaddcaddbccaccdccbcabadbccaaabbdacbcadacadcabdaaabddbdddadaacddbbaacdccaaaccddabdbabccadbabacacbabdcaddbdaabcaaaddcbddacbaacdcdabbadaccbdbbbdaabdcdcdcdaadbdbddaaacadcbccbbddabccdadbdccabcbabaccbbbbbabcabdabcddcbdbcbdacdcdcbcaadcdbcbcaabcdcbccababcdbcddbcadcaccaaaddccccbddbcacaabadcdbacacdbdbdddaacdbcadcdbcdacbadbccaccdcaddaacdaddcbccdcabbdbbddadcddaddabaabcacddbccaaccbabbdbccdbacbcdacbdcddaaacddbbbbbaacddadcddccacaaacaabacbacbdccdccadccdcbdadcccddbdddbbbcddaabcdacccaddccdcdbddbbcdcaacddacbcccccddbaacccdababaabcaccaabdddbacbadcaacbbdbbccabdcbbcadcbaabdadaabadbabbbddcdbbabdacccccadabccdacabdccccaccbcbcadcddacaccdcbaccdadcacadcbabbbcdddbcbdbadabdabadacbdcbdbdcdbbccdabcddbcbdbbddcdaccdcabdacacdbddaadbacabbccccdbdabdbcbdbbcaccadadbdbbbcbcdadbcccddbaabbdacddaccbbbddbaccbccdbdacdacabaacdcddbbbbdcdbbacabacbabaabccbdccddaadcaacddadbcadaddbbaaaadbbaaaabbddabccaadaccccdbdaadcbdbbcccbabababddcdcdcdbaacaacccadbbbccbdbaaaaaccaacbcaacaccadcccaaabaddacddddaaddaddbcbddcabdaadadbacaadacacbdadddcccdabccdabcbcaabdcccbbaaabdaaccacccbdaacaaddcdbbcdbabdbdabdccdcbccadaccacbacaabbccccbbbbdccbbdcbdaabababcbcdccddcbddbbdacadbdcdbaccaabbbdababccdccdacbbcabddbadadaabcbcaababccaccccdbccbcabbacababdbdabbdccadbaaadcccacabacccddacdcdaacabadbadcbccaddbdaccdacccddbddaabdbabdbdadacbbdbcdddaadaaaddcadacccaccabdcadbabcdccadbdacdaabdacabdadabdbadbcacdcadadcccddcaccacbbcbbcaaaadabbddbbadccddaacdccabadcadbaadbdbdcabcdcabcbbcaddcaabbccbbacbcabccabbbddddbddaabbdccabaacbbddabbaaaccbacbbbbcdbabcdacbaddcbdcdbcbddbbcbcdcadbbddbadcaaacaadcaabbbabccbcddddcbbbcabbcbdcbcddcbadccdcabdbbdcdccaadadddabcdddbbdcbbbdcaacbcadacddcccacbabdadcbcdacdddabdcadaaccadaabbacabdcdddadbaddabcbcdaaccaabbbbddcddcacbdbcabdcddbccbabadbcadbbbcdadacbcbdcbbbacbdbbbccbbdcadcccaacdadbddcbdbbcabcaccacbdaaaaaababdddcaaddaddbcaabbbcbbdcabdbaacdbaaccaacbcbadbabcabdaacababdaababddbbdbaabbddcdaddcddcaccccccadbdcacdddcdbcbbcaacabdddccbdabcacaddcdbadbadaddbdbacdadaabbdbbddadcdadbcabcdbcaddcbacbbbabcddcbcdaaacccdccabcaababaddacbbddcdcaadbbacdacadbdacdbaddcddbaabaadcadccdccdcacbaddcacbdcbccbbccaadadcdcdcdcdbcaddcabdbdaccacdaabcccbcbbacadadcccbccabbccbaabcdcdadbadbddcdaaddbcbbddbcddcacadddadccbddcaaacccbccdcadbddaddddaaaaddaabccadaddbcabcaabcdcbacabacdbdcccbbdbcbadbbadccaddbdcadccbbbabacaabdcddabddddbcbacaddcbbbadbbacdbcddddccdadbbbccacabbbddbdbaacaddbccdbbbdaaacdbabcacccbbaabcbddabdacbbdbdcaadddcdaddbcccccaaacaadbbbccdccdabbbdcadacdccdcdaaaadcbbaaddbbdbbddacacdabbdcadadcbcaadccdaaabcdabcaddbcaddddabddcbacbabaabcbccbaadcbbaaabccabdbcbcdcadccdcbabccaaabdbcbabcadddadadacdcadcccbdacacababbcdabadbbadddccacbdacaacbbcaacbddcbbccabcbbacaacbbcccbbcdcdbabbccacdbbdbdadaccccadcdbbcbcababcabccccddcaccaacdccdaadbccbbdabacadddbacddbbccadbcdcbccabcdbaaaaaccaadcbddaaacabdccccadbdbcbbccaccdabbbbddddacdbbcbbbbbcdcccdccddcbadaccccddddcdaabaaaccacbdcaccbababdcdcbcdcacbdadcdaadaccbaacdaaacbaccacbaadcdcbdbbbbbdcadbcdabacaabbcbbaacadaaadbddcbbdccaadabddccbddcaccdadbdcabbbcabbacccabaddccbaaabdcdbababcdbabddbdbcbaaccabccacbccabdbdaaadcdaabbdcdabaadbaccbabaccdabdbacddbbdaadbbbcdcacbbdaaaaddbacdbdadbdabababcaddcdbdbabcddabcbabcbddbdadbdddaccdccaaabadacabdbbcccdcabcbacbcccaacddcdcacbcaadacbddbaaaadabadabcdddbbcbdacacccaddccaacddcccbcdbcbdcaacbdbddabbdaabbacdcacacadbbbbdacdbcccbbcbbdabaabacabdacbdbbdcadababacccdcadcaaddaaaabcaccdcbccaabadaadcaaccdabadbaabdabcbadaaabadabcacbacdaddaabadbcaaabbbdaaddddccdaadbbcddcbaacacdaaadabaaaabcccaadbbbdbcbddbcbadaaccbaadabbbbaacdbddaccdaacccbcabdbdbddadcadcdaabcbbdaddabacacccdbcdcdcccbdadbbccbcadaabcbacabbbacaabccabcdcbbccdccacddcaacbbaacdaacaadadaabbddcbaaaaaadbddbacacbddbaaabacbdacdadbcbacbccababcbcbccbdbacbbbccbacdcaacbdccaaddbcbccadcabcacccbaacdacadbdccdcaaaadaacaababcaddacbaaddcddacaddcbacbdccacdadcdacbbdbddbbbaddadbbbbbcbacbbbcccbaaacbaabdbdcdbdddddabbadbaaabcdcacdadbaaddccbdcddcdabcaacaaabccaccdbddaddcdbccaddcbcacdcbbddacabaccdcdaadacabcaacdbaaacbccabccccacaabddbdccbcbbcdbbabbaccbcabcbadbacacaabadbbdbccbbdbbccddaacbcbacdacddcdaaddaabacbaaadccdddbbbadccbaddcddbababccdbbaadbccadcbcacbacccdcbccdbbbbdbcbabbabcbcbcccbaddcdacdcabccbbdacbabccaddabcaaadbabdbcbcddcbdcddacddbaddbdccaadbdbdbbadccccaacdabcddacbadbcbaccdccdcbbbccbbbaddbbdbaddadaadbaaccbaacddbcabcccabbadadcbdddcdccdbcbaacdcabbcbcadbdccbaddcaabdccdcdcdcbbabacabadcbcadccadbbcaabcdcdcacdaccbddbcacbcacaabbcdaaadcbabdbdbabbcdbbddbbabbaadcbbbbbbacbbdabcccdddbabadddcbbbdbdddbbadbbbabbcddddacbbdbbddabdabadcbdbcbddccccbaacdddaddcdbdbdcdbcadddbbcdbdcbacacbccdacbcdadbbbabdbccbdddbdaaaacadacbabbcdcdbdcabcacddaadbababdbdbbcccdbdbdcacccdccdcdcdbbbbdcaadbdaadaabdcbcaadababcccabdbdadaaddbabbddcdcdbbaabdcaadabbdcbcbbdbbdcdbcacaabcdbadbbcaccdbbabcbaaabbadcbbdcdbbcadcaccddcaccacddbcaabbbdcccaaaacaacbcbccdccbccbbcdcdbdcdddbacbaacdddbadabcdbcaaaacdbcbddbacbbbddddacdcbaaabdabadbabdacbbbcccddcdbdaddcdababbbbbaacabbaabbbbbaadbbddddabcccbdccdaaaacbacdcbabaaabddbdadcdcdbabddadcdabbaadbddbcbdaaadddbbccbbacbbbaabddaaaccacaccbcabdddbcdcbaabbcdcbcacbbcdcadacbbbbccbbddbabcdddbacaabcbbddbcadabdbadbadcdbdcbddbdcbcddcbdcdcdaaadbacccbdabcbddacbbdaaabbaacdcbbbcdaccbacccacabcbabacdabdbababadaaaadbaddadbbdcaacdbdacabaaacaccadbcbacdbccacadddaddcbddcccdbabbadbbbcddcccdddadbaaddabbcdbadbccddadacdcdaaddbccbbcdaccbcbaabadbbccdbcbaabdbdccacbddccdaddaddaacbdcccddaacdcbbdcaadddaccccddacabbaddaccccbacbbacbdadbcddaadadabdbbddcdccabccaccbdabcaadabbbaccdcdbdbcadcbbcdbbcbbcccadaadadaabcbccddbdddbcdbcbbbabbcaccbdaabccacbabaabcaddddaccbcdccdbdcbcdbaddadcddadcdaabbdbbdacbbbbbaaccccdcadbcbbbaccbdcccbdccccbbcbdddacaddcacbaccddcacbadcbdcbcdcccdabbdcdcacaabdccbdbcbbccbcbbbdbacbcdbabcaacabcbbcccddbabcbbbbacdbbbbdccbaccdbadaccaabbdbbcddbddabcbadacccccdadbacaccbbdcbddaddaaabaabcabcbabdcccdddbccbdcadadacbbbccbcbdacdadddbaacbcbadabcdcbabddbbaaabbddbdbcdabcccbacadaadabccbbccdbadacdbbccbaadcdcddcdadbdcaadcabccbcccbdddbacaadbadbcacabdcbaabadabbababdbcbbbbaacbddabdbbccacbcbdcbcaccdabbdcadccdcbabadbbaabbdccacbbcaddabacdcdcadabaadccdbaccdadcbabbaadadcddcdcddddccbcdadcccbaaabaadabadcddbdcbdbbcdbdcacbbbcddbbabdbbcadbbdddbcbddbdcbbbacaabbcddbdbbaccabbddcbbabccadbcabaaabdbaddcbddaabadcbdcaddbccccaccbdbcbbacdbcbaddbcbcbbcbdbdaacaccdbaccadbdccacacdadbabacbcccdccddadadccdaadadddbcbbaaacdcccdbbdbabbcabbcaddccdbbbdabadacdbadcdccadcbddbbabadabbddbaadcbccbacdabbddabcbbdbadddabbabddbbccddcdbccbabcbbcdbcddbcaadbbdcbdcdbdccddbbcbdabcadcaabcaaccabbbcdbadabbcaaaaccbcdcbcbbababacdbcdabbcbabcdacbacddbabacaccddaacccdadbcbcdbbcdbabbdbddbcccdbaadccccbbccaccdbdddcddddadbddcbbbacacdabaddbabbcdcbbcccaabbadaccdcaddbdcdbcbdbcabbcccbcacbacdbacccbadabbdbcbaadcbabaabbbbbbcbdaacccbcdaadddcbdacadbbcdcabbdccddbaaddbbbdcacabcdccbccdacccdbbcbbcdbabdccbdaddbccdcadaccaaabdbdbaabddadadcbccdcaadbaccaaadbcdadcbbdddaacbcbccdbaadaacbdadacbdbadddacacaadbbbbbbcaccbdcbdddcabaaaacdcbbdbdbbadcacbcbbbcdbdbcdabcadbacdbdcdabaaacbdadccdaddaacbaacccabccadaaadaabaadcbbabadadadcabccacdabaadbcbdcbacbbbbaaccbcbcbcdacdaddcbbccbbcbdcdacdddabcbbbcdadbdbbdccdcdcabbddbdbbcaaccbadbbbbaaabdbbdbcdaabcaadbbcdddbcdbadaaaccadabcbdabbcadcacbbdbcbbbdbdccadadbbbcccdbbbcdaaadbbcacccccbcaddaddcaacddbbbbaaadbbbbccdabcadbcddbdbadbdbbacadcaaddbdaadaaaadddddddaaadbbaabadccdbddbddccadaacbbcabcadaabdcbdccaccbbcbaddbdbdcabdcadbbacccaacadcbdcbbaacaadddcbadadadbacdbabaabddcddaabbbdabbdacabccdcabaddddcdbdccaacdccdacadbbccdbbcddbadbdaccbaacbdaabbdadabdabdbbbaaaabbaddcacddabacbadcaccdddcbacbbcdbdbaddcddbabaccabcbcbccaccbcbaabbdacbdaadddbcdadcaacbdadccbadcacaaddbdcadbbacaacbccdbabbcaaaaaacccbacacbdbadabbbcabcbcddbbbacaaabbdbadbacbacdcabbaabbaccdaabcddbddddbccaadcbcbbbcbcdccccaccddbdabbdbacbdccdabdbacbabddbaacccdacbacbaadcaabdbbacaacdabaaccdbccdcdbadcabccdabbdcaabdadcdcdacccddabdabaddcaaabbbdcaaabdbddcbdbacaaabbabcabddaacbbaaadaadaacbcdabbadcbcbbbdddbccdccaaaaddbdacdcbbcadbcacddcdcdaabccbbccdbdbdacdacdbdbddcadadcccddcbcbbbbbabddabdaaaabdddcdaccabadcbcbcabdabddbabaaccddbdacadacbcbbdbdaacdabdbdaaddaacadccbababdbacbcabadcbabacbbcdcbbbbadbaccbcbacaadbabbaacadcbbbbdbcadbdaadacdadcccdbcdadbbadacbdbdacaccdcaabbcabdbbbbcdbdadcbdbdcabbccbbbbcaddbacdcbbbdbaabddccdabcbcdacbdccbdabcbabccbdbcaccbbcbbadadbabbdaadaccaaadaaccbcdacbcbbdbbdbcbccccabadbdbacdcbbdcbbbaabbbbbaacccbbaddbaacbaadadddbbdaddabcbbccababbbacccadbdcabddbbdddaaadcbcbcaabcddccaadadaddbcaabcadacadacdbababadbbbdbacbcaddcadccdadccdbccbdabdadbdddcdcbabadcbcaadaabbadddcdddcbaaacadbbbbddbadcbdcbccdcbadcbdbcabdabbbcbbbadcbbdcddaaccccaabbcccbdcaacbdaacadbbaadabdbabadcadaddabacbaabcdccabcbcabaadcadbaddcbcbcbadaabbadbaacabbbdbabcbbdbdbdbaadaaaddddadddcbdbdcbcadaccaccdbbaadcbbabdbcabbcaaacaddaaadacabcbbcccdadbcacdaadddaababcaaabacaadbbacbbcbcbbaadabccdbdcaabdcadbadabccdcbaaccbbcbccacddbcbdccbbaacacadaccbdccaadcabcccdccabdccbdbcccbcdddccbbbbcdacdacccdaccddddccdcbdadccdaabdcdbdbdadadbbabacdbcbbaaabbdcbbaaaabcbbabdbbcaadcaacbaabcbddcdcddabadccdacaccaddbcccbbaccbbadacdaacddbadcbdbcaadbcddbbadcbaadaaadddbbdcbcdaddbabdbbaaadddddcdaaababdbcccaadbbbacaaacbcaabaadacbcbaaabcdbbadacbcadbcbdcbcbccdbcdccaaddcdcacbadcbddbadbbdacdaadddaacbabcaaadddaaacdacdbdaababdaabbbccdacdcdbbbbddcadaccdaccbdddbccdadbccbabbddbcbddcabddbbbcbdacdaacaacbbbadaadbabaaccbbcbadcccccbcbdacddbccadaaccaacdcaadbbdaabdcabacadcddbaadbddddddddbbdacbcdacdadddcadddcaaadaadcdacadacbdbbdcaaccbaaaccbabcdccddaaacdcabbccdcdabbacdbabcddbbdbcbdacdddbacaabcdbbcabacdccdcadcbcaaadaaccbcbdbcccddccabcddacbcbaacddbcadbccadddbcadccccddcbcdbaaacaddbcabdabdbbbdbaadbcadcbcdaabbbccaabdddacccbcbbbaaddcacadcdbabacbabdcbabddccaccddabcabbdabdbbccbcdacdacbaabcddbacbcdaabaaabaadacbaccddccbcccbaaacddbbbacadccbdcdabdcccbccddabdaaacaabdadacdccaddcbbcaddbdbdccbaaacdaccabcacacccddcbadacbddbdbcadbdaaabdccaabdadccabbccabacdbcadddbdadbdaccccabbbabcbdabbcadcdcaacbabccbbcbdaadcbadcaacbddadddabaaccbbbbddacddccbcbdbdbcacaabbacbbbddddabaabcdaacddcbbdaddbbacdcaaaaddddbbbcbaadaaccadbabcabddbbbbddbcddcdbcaaacacabbddbbaadcabbdaddbbabdbbaacbaddbccacccccaaaadababccdcadacdbcbccbdcbdbcbacddacaaacacbdddcacdccdbddbdbdaabadccaacdabaaabcdcabdcddbdbccabbaadabbdbddbccacbaabacdbbcdbcacaadbbbacacdcdcdcdcbdaddbbabccccdcababbddacbdccaaacdbddcaabbbdddadbdaadbddbdcbcbcdcadaccadcbaccacdddabbdaadacbcbabddbdcdcbccabbdbadcaddaabbbadbaadbccabbaabcbccdacbbaccdcadaccbababbaacaadacaadcacaaadaadadacaacbdadddadbabbcabbaadcbcacbbacbbbcacadbcdadbbbdaadcccbaaaddbbbadbacadcdbbcccccdbcccabdddaaccddbcabbaccdcdaadacccadccdbacdcdadbcbccdbdacbacbddbdcbdbdcaaccaddbacacbddbcccbdcaccbbddbdbadbddadcabcbdcbadccbadcacaacaacabbbccacbaabbcadaaddbaaacdbbbcccdbabdadadcbadcdbddadbbbdccdbcdadddadbbbbcdadacbadcadbaaacccdbacddbabacabbdadcaaacbdabcbbbccddbbbbdbdadacdadcbcbdbdbdcababcbcadaaaaaaadaddbcdbdbdddabcbbdbcbbbbbaadbccdccbcbacbcadcbbbdcadcacccbdcacdccadbaddadacbdacadcbbbcabbbdcbdccabaabcbcbdccabddacdddaabcadaccddddbcbbdbbbadadaacccdabdbbdaacbabdcccaccccbadbcbdcaadadacbbaaddbcdabcaaaccdbabddbaddadacacdcbddaacdbbcbcabdbdccbddbabbbacabbacbadccdbddbaacddbdcbadadccbbcbadbdabdcbddbdacababcababbacdbbccbaddacccbabacddaaabddabdbbbcbcdaadacbbdcbaddccdaaabcababcbdaccdacdcadbbcdccabdcaabacaabbccdadcbacaccbbadcbbabcbcbbdaaccbbbaaaaadcdaabbacbbdcaaccaccabcbcbdbbdaabccdbbdcbcacdddacadcdbabbbddcaadccbabbccaacabbcbccccbbcdcabccacddabddbdcdadcbadabccccddcdadaadaacacbcbabdabbabcbcadccaaabadbaaaacbbcdcddcaaacddcbddcbbbbdbdcabdccadabbbaccdbbcabcacddbabdaaccbdadbaacaadcbaacddbaadaabcbbbcbdcbdcccbbbabdaacbcacaabbbbbbadccbcadcdadbabaddabacbdaddabbbddccdcaccadcddbadacccdbdcdacbccdbcadcacbaabdccbcaaadbccbbbdbbaadcabbbbdcaddabcccccbcccbcdccccaddaadddbabdabaccbdadcacdbcabcabbcacbabacbdcddccbcddcccaabaddcdccdcbcabdcdcdaabbdccacdbadcdccadbbabbbbaaadbacbaaabaacacbddbcaabcccbdaddcdbdacdccccacbcbdcdabaaabacabbccdddbaadaadbccacddaddaacccacbddaddbcabcbbaaabaacaccbbccdcadababcbcdcdbbbdabbccacbcbdaccadaddbbdcabcdaccdbdddaadabaaabacabcdabaaadcdccbdaadadbdcbbdcccbddcbaacdcabacdcadabdacdbcdaddbccaccacbbbbabbacddbabbcccddaacacdcdbdcccccaddcddcbdccbcdbadacabcbaacbdcddcadccddaccbacdbbadcdbbacacbaccdcbacbcabbdbadcaabcdbbaacbbcbdbddacbbccbdbccbbadadddacbbabddbabdbddcbaccbcddddbcdabaaaacdcdbdcbdaacabaaababcacaabbdbacdbcbbbbdcacbcbcbbaabbcaabcbbdaccadbaabbdccabbbbdbcacdbcdaddcbdcddcacbbdbcbadcbcadabadadbdadcaddcdabbddbdabcccacbbacaddbdacadbbabcbcbabbbbcbabaccccabcacbbbbabbcccdcdbaaabbadcacacdcdaadddaaadababccdaaadbbdaabdbcbccbadbbcabaaabbccacbbbdccdbdcbcccabaccacbbbacaadcabbcbadababaabacacbaacbaaddbcdbddacdcabbcbabddaabbdccbaacacddddadccbadddbabdbdbacbaaabcbcbbdaacdbdabbaaabdbbbaaaaaabdccacdcababdbcaabcabaddcbacbaabcdaccdccaddcdcadcacacdcaccbdbdbaabacccddcdadbcbcadccddcccdaacbdcaabababcccabcbddadacabddbaaddbaadddaadcdcabbabbbbaabdbabadacccacbdcbaaaadbcbadbdcdcdddacbaacdcaacdbcaacdcbaccbcacdbadcddbcbddcddbccdbaacaacccabdcbbbacdaabaabdbabdbbdcdcadcdddbcccaabbcacaaddbcddbaabbbddabadaaccadbdbaccbabadabadccbdaabbcdcccddccdadbbccdbdbacacdcaccbcbdacaaccdacacdccabadbdaacccacdbabacadaabcabccddaadadcabcacdaaaaaadbccdbcaddbaaccbdaadbdcadccbddccdccdbacddddbcadccadddaccbdcdcccdcabdbbabdadcdcaaccbddcccacdddaacbbdbcdddabaccabaddcccdcdbadbacddcaccdcccbadbdacbacbccddcaacbdbaacbbbaadccbccddaddbccdabcdaaddbabdbdcdaddcccadadbbcbabacdabdabbaadddabcabbcbdbabaccdbbddabacbcaccdbdbcddcbcbddbaccddccadccdbdbadadbdaabacbbdbdcbcbbcabadadbdbdbbddbbacddcbdadabccbadccbbbdddbaabccaadbacdadacbbacadddcbbaccabbdccbbcdbcdcbddcbbdccbbbabcaddcdabbccdabdacbbccbacddbadacadabacdddbbdcdbbdddcadcbaccdadbacbdddbadbabaabadaccbdccaccabcabcbbbabacbadbcbdbcbddaacacacdddcccabbadbdacdbacdbcdbaadaccdacaddccdcaccbdbccbbabaddcdbdadcdddcbaabacbadbccdcaabccbbbbcdddcccabbdabcdcacdddbbaddaaddacacbdcdddbcaabccbbdccadbdbadbadcbabbddbbccdccdaabdabcbadacbbcdaabdacbacbbbbcacddbabacdcdbcdcbaadbabbcaaddbadbdaabcbacadadacdbcacbdaaaacdbbdccdbdaaccaaadcdcdddababbbabadbcbdddaddcdcaccacabacbcbdadbbcbaadddbcbccbcddbaaadabdaddababaddcdcbccaaadbdddcdbadbabcddbbdbcaaaddddcdbccaaccdddbbdcdaddaabcabbbaadabdcdbaadbdcbcdbccaabadacacabbbaaaabcddadbacbdacbacbdccdadabdaccaabcbacbbbbcadcdadacadcadbcabddadbbbcccbbccccabccdbbdccacbbcbcbaacdabaabcccbbbcaabccdabdbccdddadbddbbdaccacadacbbbddcbdccdbadbbabacbbdbdcacaabbbaaabacbdccddbddadbbacaadbaaaddcdcbccbccccaaddddbaadcccddcaadbbadcaccdcacddadaddddabcdcdccacccaddbdcbbdbbbcadbaabdbdbacdaaadccccbacccbcdbbaacdbbdbaadaccdbbbcbccaddddbddaccccddbbcbccaadbccdddabbbdcaabdccaabacdbdbacbdbbdddcabbacbdabaaacbbcacaaaaaccdccccbdacacbdbcdbcbadabdabcaddcbdaacddcadddabcaaaadabccdbdddaccccacabbdadacabbaababdbbbdaccdabcdadcacabbaaccdbdcccaddaaaccdadbaaddcddacdccacabbdcaacbbaabdbbdccbbcaddbdcbcbcbbdcdcdcacdddcbcdcaabdaccaaddcccbbdddadbdbadaadcbdaacaabddcdcddcddbbaacdadbadbbccccddabcacccaacadcbccbaadcdbdbadaadadddccaabaccbdbabccdbaadddacaabcacbdadddbabbddddbddddcaabdaabdccdccbcaabcabddbdbbdabaadddcdbdaddabdbcaccbcbcbbbcacdaacdcabdbaadbaaaacdbbdcaaaabbcbabcbadbbaccddacccbdcacbbbaaccbbcabaadbddadbbcdacbcacccccbaabbbdacaddacdcdcbbaaadbacdbadabaadabcddddadaabdbdabdccdbdcbdccccbdadaadacdbbccbbbbdbbacbadbbdabacbabcbbdbcaddcdcdbddbaaaccdbcadacbbaabbabcabbdbbcbabcbdccabbcbdddacdacabbabccbacdcdaadacadaaadccbacacdddbabcabbbbaababdabbdadbdcdbacabbcadddacacbcccbcddcacbcaadbcbdadaadbbcaaaaacdadccbcdbaabcbcccdbdccacdcbacacbadaadabbbacddccbbcdababcabcacacacbacbbadbbdabdcbcbabccbccabaaaacaddacbbccbabaabccdaaaacabccbabdbadcadcdcdcdbbdcddcaabcababdcdcabacaadbbbbdbcbdbdbadbaabcbcbdcacdbbccadadacaadcddadaaadabcbaddacacabbbaddcbcdcbcbdccabbdcaabcaccccabdccdbbbccccababaacabbbcdbabddcbdcdbadbaaddabbccdcccbdbcaabcbdabdacccdadbadaccdddaddabbbbddadcdbbcacbbcbcaaadbdacbaadcddaccadbdbabbadaaacadbcdbaabbddbbcdbccccacacdcdccbddbabbacdbdbddcaaadbbcacaacdacadabaadccdcbdbbbcdabadacdaaaacdddbcaabadcdcdbbccbbabaaacaaddbaacdcddbddcdcdaaaaadacdddbcbcbdccbbabdcbcccbcbccbacdbdbddbcbbccdddbaddddadbcddddbcabdabccbacddcdbadbbcddadabaadcabadbaaadccccaccccadbacbddbbccccccacaccabcccccaacddabaccccbabbacddcacaaddbddaccadadddaccbabbaacaadddabdadbaddccdaabbbdcbddcaccadcaaadbabdcddbabdbcaadbbcdadbacaaabbbcddabcadacdacdddadacccdadbacacbcaddadddcbcbbabcbcaadadccaccbdbaddbdbabadcccabccdbcdcabbcccdaabccadcdbddbbacdcdddaabacbaddccddadaddddcabcaadbbdbabcbaacdcdbcdcacccdbbdcbbcbbcacdcaabbbcccddddccbbbcdccdbacdddabbadbbabdacaaddddbccbdabcadcbaadddacadccacbcccdaacbaddcdbcbcaadaadaadddacbbcbacabaaacaaaabdabdacdcdbacbccdbadabaccbdadcdccabbccdaddcabdcabcaaddcccadadabbcbcddbadcddddbcdcdcbcaccaccbcadbacabbbdcbdcccbcadbaccdbbdccabbbddbbaaadcbbbacdabaacdaaaadadcbcaabdbdcdaaacccbadbbcadbacbdbcbcdbdcbacbccadaccacbabcabccbbaaadbcddcddbbadcbdadbccaacbbbddadbadbaacdcacacacbddadcadcabcbbababbadaccbaccddcdbaaabaccbdddccbbdccdbbddbcabdbbccdbbddddbaaadcacccbdcdcdddacbabbdcdddbcccdaacacdcbddaabaabadcdddadcaabdadcacdbbcacbbacdbdcadadaacddddbcdaacbcdabcacdadadbbcacdbdbdccbddddcaaacdccdccdccccdddbcabdbddaaddabadcacddddbdbdaddbcabadcaaccddcbaddbdbbdcdaacaabaddddadababcdcbdbcbabacacbdcdcdbcdbdbbbacabdcbdbbbbbbccbcbacacddbdacccadddcbccaddbcdddddbcadabcabcccacddbdccddadddaadaabcdadccdbacaabcdaaacaabadbdcacbdadabacaaabbcbddaccaadadacdddddddbcdacadacccdbccbdaacccbaddcbabcdddaccabaaadbaddcdbbaddadacccdcbaaaacbaddbcbcdabbccacabdadadaaadbbacbccbacdbbdccababbbcadadccaaaadabbcaaddddcdabdbccaacbcbbadacabbbcdbdcaaabbbbdcaaddbdbbdcdcbcbbadbaaaacdacaadddabcbdacbddccbabbabbabbbbbabaabacbdacaaccdddccaddddddbcbcacbacadcdbdadabbbdabbdaadddddbaadcccbcccdbbdbddbdacbbbadcbbabbccdbcacadbcbdcababaccddadadbbdbcddbcacccdabbcbabbcdbddbacbadaabbbddabbcdddddcbbaddddcccccacacbaaccdaaaabaaadcbcaacdaaadadccacbbaaddddccddcdbdbcdadcdabacbdadbacadcdcdacdbababaccbdaccbcaaacdbccadbbaaabcbdaacbacbcdbbacbcabbabccbacacacacdddaadcaacbabbbabccabadccdacddbcdccdacadbcdbdddddadbdaadcdbdccddaaacaabcbbddabdabdbddcabdbccbadcbccdcacdbbbadadccbaaadaccbdbdacccbacacdaacdbbdacbdbdaacbbadcddddbbcccdddbccdcdbaddabbcccbdadbadcdaccdddcadbddaaabbcabaaaabadcadaddacadacccbdacbabccabdbbcbbaaccdcaaabcbadaabaddadaadcbcdccdaaaadaabdaabadaaaabadcccdbadccdaadddabadbdcbbccdcbbbcbddaacbacaadbdbbcdbdabdccbbaaacaddccacabcbacbadaccbdbdbcddbcbbcdbbcbbcbcaddbccbaacabdacdcaddacabcadadddabccaccdaadbdbabbadaaabbcbccdadcbbbdaaadaacbacdcbcacbaccadccccbbccdcacdacdbbaacdbddacccdaabbccadbcadbaabdcccbbccadddadddcadaacbcdcdadbabaacbdbbabdbbddcbdabdccbaacacaadddbcddbdcccdcbdcdbdcacbdcddccbacacbbddccbcdbcdcaaacbabbcabbaaabdcbcbbbbbaddbcdcaabddbbcdcabadccdabcdbbdcbdcacacdaabbdcdbccccadbbddaddaddddaaaabdbabbdcbdbdbdadbcdabdadccadabadbddcacdadbddcdbdacdbadbaaaadbcdbadaacbddbdddbcdcccadbbaadcdaddbdaaadddcdcdcaadccccdbbcbdbdadccbdbbcdccabddaacacbcbdbdbdcabbacdacadacccabdbbbbdaccacccdbabbddddacccddcdaabddbcabdbbadcbcaccacbaabcdacbbbbaadbcdcbcacccddbbcbcdcadbadacdcbddddacbaabddccadbddcdacabacdacaabdbbcdabcabcbdccaddbabbbddacaacadbccdcdaabbdadbbbbdccdbccacadbddcabdabbdcdaccdbacadbbacdaaacdadacdadcaaccdccbccbabbbadadbcbdabadbabccdcacbcdaaaabddccccccbdaaacbddddcacdadbbddcddaacbbaacdaabbddcbbaabddcbdccddbdcbaadadbdddaadbaacacabdcdbcabdbbaadbbcbcdbbcacadbccbbacdccbbacdbddabacaacdbccadacacbcbccbccadabbddddbdadccabaccbdcacadadcaabcdbcbdbabaccabcbcabdbcacbaabdccdabbadcbabcbadadcabbabbcbaabbaadabcccaaaacdaaccbcacbbacccbcaddbddbacadbdbaadcadcabbdbdbcbccbbcdbdcdabaaabcacbcbabdcaccacbcccabccdddbdbcdbcbacadccdabcadccacccdabcddbcdabddabccdbdcdaaddbdbdddcadbdbddcbdabcbcdddbccdcadabaccacacadcccaacaaccacabcdaadbcdbccbccacaccbacaccdcbcdbaccbaddddbadaacacddacadcccaccbadbaaacbdcbcddddbbaabcbcababccbcacaacaacbddcadccdaccddabababdcaccbddcbcbadbccddbbccdccaddcbbbddbbccbcabbdbdbdcdaabccdadbdadbaabdbbadbdbbaacbacccabbabaabccdacdbbaabcdaacacbddcdcccccdbbbccddccabbbbadbbdaaabbbbcdcbdbcaccddccacdbddccaaccddbaddddabcbdcddccbcaccbdcbadccbbbcabcbcacbcbaabdaadaaccabdbabdccbddcbacbdbbbcdddddcdcabcdbccdbaddcbabdbdcdabacdacbdcbcbbbcbdcdabdabbbddddddbccddbbbaabccdaacccddadcbabdbcbcdcbbbcdcdbbacbbdcccaabbacbcbcadbacbcaaddadaabcbdccaadabbdacdacbcbcdcbcdaadbdacddccbadcacbcacacacdaddbbacaabdaacdcdabbbcdadcdccaaabbabcacbadbbacbccbcdccbccbdccdadcdcccdddcdbbcbabddbcdbdcbcccacaabacdabdcddabcddbadcdaaaabcbdbacbbcdacdcaaddcacddbacddddadabacabcdcaadccdbaaaacdbccbccbdababbbbcccadbcabcaccdbdccbaaabdacbcdbaacbaddadcabbbcbaddadbdbaacbddcbaabccaaccdaacdacbdbacabbadadcdcddcddaddcadddccbbcbbacdcddbddcacdccdccdcbbbddabaccacbacbaaabacbbababbddcbdccdbbcccbdabcdcababccababaaccbabaaadbdccadabdbdcaabbabcaabbababdcbcddaabbbacbadaacdbaccdcdbcadbdcadcdacbdbbddcaccabacbcbddacddddbdcccacdddabbbadddddddacabcccaddbabbbdbdccbdcbdcabadbbdcaddbbacbbaabadbaddbdbdbbcaddbbbcaaaabcbdbbcabdcacbabcdadbcbadcbccababaccddcacbdaadcdddcdbcbadccaadcdbdbcbaadacabbaccdaabacdaddbabbaadcdacbcbcbcbcbbabbbaadbadbdcbddcbbbbddcaacdadbcbabcabacdcddddaadbbcbacccccccbabbadaaccaccaabbdcbaaddbdcddccabbcaccdddbcbdbbadbddcadadcaddabbabacdddcaaabbbcabbcabdacbbadcddcdcaabbaabbcbacdabcbbdaacccccacdddccabbccdbddbddbdadaabcaccddaadcdaddbbaddddabdbcddcaaadcddaaadcbacbbddbdbdcbbbcaacbbaaabbbdadaaacacbaaabdcaabdbbdccccbaadccaabaaadbaccabcddadbaccaacadabaacdbbdaddccbbcbacdaaaabcdcaddddcdadcbcbdacbbcabcccdcdbaddabbacaacdbbdcacaacabaadacdcccacbdcbcdacdbdaabadabadbcbadddabbbccdddcccbbacdadaaddacaadbbddbbcddbdababbcaaccacacacacbcddcddbdccbaadbbbbadcacdadbcbaaaddbacdcacdcddcabdaaaacadbddddcdbbddbadcababccbdacdbbcddacdcdadadcbccdaccddacaacddadcbaadbbbcadbbbdbaaccddcacadbdcaddccdbacbcadccdbadacaacaacabadcddaddbcbbbcdabcbbccbddcccabacadddddabbabacbcddbadbdbbaacdcdbaadbdadaccccabacaaccddcadbbacabcddccbbcabadabcdbdddcbcaabdacaccacbdccadaddbdbdadbdbcccddcdacabbadccbdabddabddadbbadcdcbbdcbaaabbbdcbcacdddcacbdadadddacaaaabdbdbcacabbdcdcbdabccaacacacddbcaacddbdbcadbcdaaccbdabdacccbaccbadbbbccdbbdcbbabdcdcdcddadbacccadbcdccdcbcdabcbbdabdcdbacadbddacaddacacaaabbccbddcbbbdcccdbbaabbccbcdbbaadabccddaaddaddbadbbdacdcdcbaacbdbdabdccabccccdcbadbdcacbcccbcddbcdcaddcdbbaaaccdccacbabacaccabbdaacccabccbcdcbbaaaaaacbacdcdcbbaabbbbabacdcabadaacbbaaccbdccddadcdcbbbcabdabbcaadacdaacddaadacddcdaccacaaccababacdbdbabccccddbbdbdcdcccdbcbbdbccbcbdbcabbdbcabbcadadbcabcbbdccaaaabcdbacbbcacddcaacabbaccbadaccaadabcbbababbadbcbbccacadbcbcbbbdbcdadbdcacddcdabdadbdcbcaadbbacddadcbcbcbdaddaddaabcdadbcadccbdaabdcdccddbaadcddcccbabdcabdcdacacabdcaccacbbddcaadcadbaadbadacccaacdccbccabbbaddbaaccabdaabcaadbbdbaacccdccccdbacbbaaabdbadabcccacabcccdaadabbbacdbadaaabdbacdadadabdadddcbbdbaddacaacbcbcacbcddcbbddcbabddadacddcdadaaaababbdbbdddcacbdabbabacccdbbbcabcdadaabdccccacbbbbbbadcabbbbacaddccaadaaadcddabaabcdaccdddccaabcccbdbcdcabdbcabcdcbccbbcbcadcaddbcaadcdbacdbddbaabbcaacccadadadacaccdbbbdadaadbabbdcbcadabdabbbbbabcacbdbadbdcdbddbcbbbbdcabdbddaacdadcbccacbccadbadadadaaaaabccddcbdabdcbadbacdddbbdbdcbbabcbcdbdbcbdcbadddcdadbcccdbcddcbaaadcadcddaddcbcadbbcbaabcbdcdcaaadaacdccddbaccccaabbccdcbddccbaccbabacbdabadcaddddcbccdaaabdddababbabbdbdddaaabadabbbadcdaaacdadbcbbbdbcddacddcadadddcddbadacdccbcddbbacabcbdacabcccabcababcbabacbbbbaddbddddaabaccbbcbdcbdcdbdcdddcdacddbbccccccddddabcbbaabacbcddcdbddababbbdddaaacabaddcccabdaabbdcabaadaccccbdabdadbddddbabcbadbdbaaadadcbaaadcdbdaddcdbbdcbbcbdcddbbccdcabacbbbbbabbaaacabadccaaddbbccdacdaadbddaabcdacdcbccacaadcacdbcadddabbacdcaabbdacbcaaabccaacbbadaccdcbcadbbddddbabcdabacdacdacacddcdaddbcaadacadcccddaacbadbdadabadaabbddbbcbbacccbbcddacbdbcaacdbccacadaadcbbabbacbbabdbdbabaadbbcbcddcadbddcbacaddbabbcabccddcbaabddcdbbaaabdacccbdbbdbabadaaccdbacdccdbcabacccbbddaddaccdcdccbacbdaddbcaacacdddddcaccaccccbcacadbccbcddcbcddbcaaabadaaccadacdcadadcadcaabaaadbcbccbdcdbcccccacaabdbbbdcdbddaacaadaadaabadcacadabadbcddcbaadbbbccadbdbacddccddcbcacbaacbcaadaabacaabacdddaacabddddcadccdabbddaaadcdbaadcbaccbbdccddbdbcbcbdadbbddadbdbcbadaabbaddbccbdcbbcccdaccabbbcdddccbdcadabcbadcdadabbdadcbaccaacaadbbcdabcbbbcbcbbdcbacbacdbbdbddacadcabdcacbadddbcdaacacbdddbacdbcaabbdadbcdacdcdaacaadccdcdccacdabbcddadacdbbbcdcbdabadaababaacbcaaaaadcadcdbaccaabccbaddbddddacdcdbabdabdcbdaadacaaabdcccdbdcadbadbacdcccdcdbdbdbbdccddccbadbbcadcabbdabbcaabdacbbdccadadabbddcdabddcdcadaabdaccbcbccbbdcdacbcdcddbdbdbbabdcccbbaadccbcbabcbdaccadbbdccdadcbcbbabcbcbadbadaaddbbddaabdaccdcdadcdccadcbbabacddbcbddabcdbccdadaadcbcadabcbadbaaaadacbbdccdcdcbbaaacabbdccaabdddbadaacccbabaabcbbcabbdabbbccadbbcdabaabbbaadcdccdbdbddcaabcdbddbbbbbdadcdccadacaadbcbcbdbdddbadcacabdbbaaacdacdbbccabcdacaacabdbcaacabccadbcdccccccabaccbdabbbdcacdacddabadddaccbccccabcdccccbcddacccacbccdacdbbdcacddcacacabbadbabccbccdcbccdbdcccccadbcbccadbadddcdabaddddbacdbabbdcbbddbccabdcccaadcaaaabdabdabbcdcbdacbccbcabbcccbddbabbadbcadcbacaababccacbbaaacdcbacbdabbbdddcbcbcabaababcadddbcddabaadbcaabcbaaddbdbbcacdcaacbadaddaaadcdaccabbcddbabbbcabacddccdbdababcbdcbcbdbdbabbdccbcccaadcaddabbdbbbadcdaadbdabacddaadcccdcbdbdabaacdcadbacddadcaacdaadbabdaaccaacdbccbdcadcbdacbdbdcccdcbdbdcddcdabaacdadcccabddcddbacdabdcdcdddbaccabadaaacabbdaccddacbdadcbcbcbddabddabacccadaaacddadbdddaacaadaddddcccdddabbacadcddbcdacbccddbbccdddcbcdcbbddabcbbabddccadadaddbdbddbabdbcdadcaaccaadcaadcaacadbacacdccabcdcdbbcacbdddbcaccdaabcccbcdbbbacdadbcdcadadabdabccdabbbabdccbadcbdbaccdcddbdddacdacaacaacabacdbddadbccbabbbbbbdddbcddacccdbacdbcbabbabcacadaabbbdddbdcacbbbbdcaccabadabcdddddcccddcdcaaadaccbdabdcdbbcbbbbccccdcbbcdbbcccbddadabcdbcadbdcccbdacadadbabbdacabccabccadbacadbdabccddabcbccaaadbdacdbacbcaaccadbdbbabdbbaccbbdddbaccbddaabbddbcaacacbaabbccbadddcbdcdbccdccdbdcdbaabbbcccbbdabcdddcbdccacbcdbacbbcaacbabaabacdcccdbacacbcbbbabbdcacdcadccbbaccabcaaacccbdbaabbacbabdccaacadaaadacacaccccbabbddbdcbbddddccbadbbdbbcaddaaaaadaccccaccbcabccabacbcdbaaadadccacabcddacbcbbbbddcbddddabadbddabdbabccddcbbbbbbccbcaacbaaacdcacdcddadccacacbdaacbabbaddbcdbdcacabaaadbbbdddcacdcccabbbbcdaccabdbbabddccbdcccaaacdcbacdaacbdadcadcbbddacaddcbbdbdadcaaaaaacbbdddaaabbcaddadadbaacbddabcabdbccbdadbadcdcadacabddcddabcadcccacbdddccbadacbcacbdccddcbacccaaaccadbcbccbbbdbaddbbdaabbaddbdabaccacccbcdbadbccaabbbbaabbbbcbaacccbccbcacbabcaddcbcccdabcccaccaabdabaaccaaaaccaaaabadabcddccbaddcdbcaccaccdcbbbdcbbadbabaacbaadccacccddbcabbbbbcddadbcbbdbdabbbbbbdcddbaaddbababbccaabbacbbdaccbdccccdcadccccbcacbcdabcdadcabbdddcdabbcddcddcabdacbbdcbaadacadbadcadbccadcdcabbdccdcbaacbbdccbaaccdcdaddcacdccacbbacdadacbdbddcacbbddabbabdcaacdbdcadbbbccbccbabdccabddbbcdddcaacbabcbaababccbdbdbbbbbdbcdbbdcdcbccdcdddbaacaacdaaabacdddcdaccabadcacdaddcbddcddbabaacadbcbdddcbcccdcbddbbcddaacabacacadbddcbbcabacaadcdaddadacbaacccbaaacabbdabacaabbcacadacaadddbacadadabbacdcdcdcacbabcadadabbcdaabacbacadcbccdcddbcddacaddaadabccdaaccdcbaddbbbcdcabccbbcabaccdacaaadccaccccdcbccdcbadcbdcadbbdadbbbcdbbdcdbadddadabdcbddbabacdadcdbddccbabddddddaaacbadbccbaaadbababcabcbcdadccdadbdbdbabdaaabadabddbacbbadddaacdcbdabdacaddddddbbbbcacbaadcddabacdcbaabbbbadbbdbacbdcbcbcbdbcdbdcbdcdacdcacbbccabdbdcbdbbabbadcdbadabbbbbcbaadaabddcccbdcddadccbddadcaabdacbabdcdcdddbabdcbaaaadacabbccbdbbbbbccdcbacaabdcbbbbcbbdabcadadabccbdcdcabcdccddacbbcccbcbcbaadacadccdcbacbcdccbadadbabbcabdadcbdcbbbcddacbddabaacdbacbcdcabacbcdcabddddbbcacbbdabccabddcdaabdadaccabcddcaabbcacddcbcdcbdabacadddaddcbdaaddacaaccbccbbabacbaabbcaaacabaabdababccabadabbdcdababdabbbddbadcdacdacbbabdaccddddaadbddbacacababaababbadbddbcbddbdddcdbcbbbbabdacbcbabcccadcbadbdbcadaabcacaddaccbdbaddbcdcabbdcababaaaabcadcbddbbbabcabcbdcbdccabccadcdccbacdaadabcdaaccbaccdababdddbbdbdbcdbcbdcaacdbaaaddcbabaabcdbdaddbddadcbcbdcbdcbbacababcdacadddbbbdaaabacaaadbcbdacbdcbbcddcabddadddddabababcdcbdbbdbacacdbcbbdabcdcbaaccdbaccbcacbcbbdddaaadadacdcdbcdbcdabdcbcccdbbcbcacadbbcbbbccadcadabadbacbdccbbccbbbcbadbbcadcbdcdabccabbbbccbdaaddccbadcbccdadbbcbdaaadabadbdbcbabcabbdadcabccccddccadcdcaabccaabdbdcbcbcaabacbdababddcadabcdcdbccababadacadaacdcddcbaacacaddcdccdbcbaadadccaccababbbbbaaadbdbbcdacdbdccccbdbbdccabbbaabbbacdaabbdcbcaaabbbbcaaddadcacadbdcdadadaddbddaddabbccaabcdcabadabaccdcacdbdaaaccaaadabdddcbaaaacadacacdbbddcdcbaababcdacbcbacdddbdbbcbdcbcdcbdabccabdcddbbacadbaababbddcdbaaaaacdaddadcbbbdaacabcdcacdbaccdcabcaccabaddadccbbabccdcacdcaaddcaccaccadcbbabdaadbddbcabbbddaddbbbcccadbacbdaccdcbcccabbcbbbcbdcddadbdacbbcbbadbadcddbdbdcaabcacacadbcacdacaacbdccbcdbbcbcdbbbcbaddddbdabcbcdddddacdacbaabcabccdababaabdbccdacddacacbbbadababaddbcdcdbdbdbadcacdabdcbccacccccabccababcabbbacbcbadbbaccdddadadccdcadadbcabcacabdacdbdbabcbddcccabaddcddcdacccbbdcccbdcbbddaabdcbcaabadbabddaabccdcddcdcadbadcbbddcaaccbabadcabbcdacbdcccdbbbdbaabdbacabddbbddbcaacdadadcbccdcddbcbbcdccbaaaaaabdcbdabddaaacdcbabaabacbddcbacbbbbbabcdcbdabccdbadcdddadbddcdccbabaddadcdacaacaabadccdabcdacacbabbacadbdcacabcabadcdaabaabcabadcaadcaaccaaacdbacdccadbabbacbdcdbdacdbdcdaadaaddbaddddbdbccabadddcdabcbbcabccaabdacbbdbaccdcacdbbbabddbbdcdbbbbabcdbcbdabdabdabbdbccdaccdacaddbacccccddddddbacdbcbdddbcbaadccbbcbbcdadcbdaddbaaadddddbcdccdcbcdbbcbcdcabddbacdddddcddbbcdcdbbdcccdcaabbdbdbbcbbdcccdcabccddbcccabdadabababbdbcbcdabadbbbabccbcbdbbcdabbdacbadccddbcdcaccdbddabaaabdcccdcaacbaaaabddcacddddbdddabcbdbdacddddadcaaacccdaccdcbcadbbcbacbabdbacabdccbbccdbbcadbdcdaccddabbddcaaadbbaaddcadaccabbabdbabcabbcadcccbdbdabdcdddabbadaaacbbbaccabbbbabcddaaacdccabbcadaadcbcadacaaccdaddccacaddccbaadabbacabbdadabbbdbacbcdacdadbaddadbbcadddccdbadaccccccccbcddcbaaddacaaabccdbccdaacababbdbaaccacdbdacddbadadabdaddcbadadbcdaccdcadddacdbabdbcaccbbbddddabdbbaddbabdcbccabbbbbbadbcddcadddbbdaadaddccbbdaddddcdcbabcccdddbdadbacdadacdbabbcbbdaddbaaabddabcccccabcbcdbdabbcbaacdabaadbcdbdddaaadbacdacdaddbcadbbacdddbbdaaacbbacccdbadbbdcccccdcbbadccbdcddbdabbddcdbddbacccdcdacdbadcbccacaabdbddacbcdacbcacbbcabdcbacdddbbadcdaaabbddaaaaaddadcabcdadaddcabadbdbbbdcdddacdbcbbdbaaacbacdccdccaacabadbdccacbbacabadbdbdcdaaacaabdbbdcbbdbacadaaacbaabaacabbdbbbaaddbadcabaddbbcdaccddcabcaddcddaaccacdccaacbabacbcccadbcdabbdcaabcdbddccdcdaacacbbabddbcbcaaaccdacdacbcacbdcaacbdacbbaaacdcbabbdbcbdcddabbbbcacabdccaacbccbbbcbcacbadbacaccdcbdcadcbddcaacbcaabcdadcbdcbbaacbcccdadccbccbbdcbcddbcccddcaaaadabccbaaccadbbdabbdbbcaccbdccbacccccabdccadacbdaaacabcdadcccacbbcaccacbadbacadadccbcdcabbacdacabaddadcacdbbddacdbdddddcbcabaaacbbbaadcbbdbcbdddbabddbcaaacdcaadabbddcabbabbccbacacccbbaabcdcaaabbcdadabccbaccdaabbdcbabccccbabddadcdbcddaadddcbbbcbdacaddbbaddddadaccbdadaabdddabdbccbdabbccbaadbbcbacabdbadaacabaadccbcbdababcdcbadcbbccacdaddbbcabaccdabadabcdbadcbdcaaaabacdabbaacbabbcaabaabcadbcdaacabdbaadbcacddbbbccbbdcadccaccccaadcabccbdbccbbbbbbdcbaaacdccdacaaacdbdbcbbaaadaaddbcdcbbdabddbdadbaadcdcabaddadddabadddcaabbbababaddcbbcbddccaabbdaacadbdcabbccadcdcdbadcacadcbdbbccbccabdabcadbdadbbaaccbcadbbadccbcacdbaadcadbaccddcccacdbdcccdadbdcabaccccdbdbcccabbcabdaccdbdacdcadbcaccdadaaabcddacabbaabcbdacdcdcdadcbabbcacabbdbdcabcaaaabbabbcccdacacbdacaccabdbbbabccabbbccacbddabdbdccdbcdaaddcaccbdaabcbbcacccbbddbcdccbcbdcacbcccdcabaddbddcbcdbdbbccadbcddacabaabccadccddbacbcadddddcbbcadadbbdaabddacadccbcbdaacadaabcbddadbbbaabdcacdaaadcadbcbcbcdadacacabbdbaabcdacdbbdaacbbcdacbbbcbbddbabdaccacdcbdabbcbccdbadadcccdaccaabcdbaadacdbcdcdccbaddaadacbdbbacbcdabababdccacbdadbddbcacbddacccbccbcbdddccbcabbbcddcabacbccbddaaaccddbcbbbcdadcadbdbcdbacadccccbbbabbccbbbabdbbbaddbdbcabbddddccacaabbcbbcbcdbbbdcdadccbdbccabdadddccddcacbbdbbacdbddddaabcccbacbdccadbbadbbdabddcbcbccadbacccaabbbdbadccbaacbcdbbddccdacbbacacdaddaabbcabdccdbdcdcccabadacabaddababbcadabaabddacabddaddadcdbcbbcbdadbbbbbacaaaacaddccddcdbdacddacddccaaadbaaaddbbcccdbabdadadddcbabbcbddddcbcdacabadacddaccdabcdddbbbcaaacdbdcdabddcbddcabaabcbadbbddbbacaabcadcbbbadcdbdadddcdaadbcdbabdddacdaadabcbbacdcacbacdbdcbadadccbdccbdcbacbadadcaadcacbccbaabccbcdddacddacbccadcbabadcaccbaadcdadabcadababcdcdbcdcababacdabdddcadbcbcdaddcabcacbbbddbdbdcdabaacacadddaadcaaaacadcdabbccbddddadbaabadbadbdbbbcdbadacdaadbabbaadbcdcdbcaddcddcdbddaacddabbbdacaddbaccaacdbdbcdcdbbbcdacadccdbcaccbdccbaacaaaababaccccdaaadcbddcacacdcbacddcdaccabcadbcacdaacddbabadcdddaddbccbcbdcdbdadccccddbabdbacdababacbdbbabcadacdacdaddccdcadcaccacdcdbcdbdbbcaccbcacaabddadbcaaabbcbcdccdcdcdcbcdbaaacbdcbbbbbabdaacccdaaadabccaaddaaadaacbbbbdddddbaacabccdbcabcccadcbacdbcabdabcdcdadbaaabbbcbabcabcdbbcbcdcaccaacdddddaccaadccbcdcbbacacddbbdacddcddbbbcababaacbddaaccababaadddccbbadbcaadadadbcdbccaddaadbcccbbacbacdbbccbcbabdadddcdadaacacdbccccbcdcccbdbbbdcccbbdbacdbddddaaaadcabdbcdabcbabcddaadcbdcdcaaacccdadcdacccabbadbbcccdbccaabccadddbbcadadaabdcbbacacddbaadcdbadcccbadbbcbddbdbccbabccacbaaddbbadbbdadccdaabddbbacdaddcaccacbadccaabcbacbbaaccaaabcadbcdaaabacbacacdadbbadcaccccdabcaabaabadcccbbcddaabccabbcadbccbdccadcbbbbdbdccbbbcddcaaccdcadbdacdbbbdbbccccddaccadcbcddcadcbcbdcbbdbddabdaacdabbdcbdbccacdacccbddccbacdcdabdcacdbdcccbacddabbabcbdddcccdddabccacabdcbabadcacdcbddcbabbcbcbdbbdbbdadbaadcdbbdcbbaacaacbdddbdcababdbddcbdddccddbaaabddcadacbaadbdcabbaddcaabbbcaabbbccddababaabcdbcbbdcddbbbcdacdabcabacddbdadccdbbadbbbbcdbbaabacdadddccadcadaaaccbdbabdddddbdcdadccacbaddacbdadcacbdbdbbdbbadaddbaabcaaaadaaaaddbcabcdacdccadbccbbdbcbdddbcbccacaabbaaaabdadbdacbcddaccdaababaadadccbaabdcccacbdbadcdabcbbdcdccdcbcbbddbcbcbcabcadcbbddbbccddcdccdbcbcddbddbcbdababdadacaaabadcaadabcdabcddcadbdbaadadcddacaccbddaddbcbcbbbcdbdcadbabbbcccccbdbcbcadcdcdabdbabacabccabcabbbdacbbbadcbbbbacaacbccdbdadcadcccbdddcdbdbbacdaaacdcbbdaacadcbbadabbbbcdbcdaddbdaabcbdccaccdbdbcdcbddbcccdcadddbbbabcdddcabadabaccdcbacabacdbbcacaadaddddccaacddabbcbaadbacdbbabcdbdbaadbccaacdbaadaaaabacbcbddacabdacacbdcbddcccdabcbccbcbabadaaddbbccccaadbbbdcaaabdadcbcaaacabaccbadbdadabdabbdaabbaabbcacddabdbbbaabcdbbbcabdbdcdaddccbaadbbcaabbdcaccaacdababbadaccbcddcabbccadccacadddadbdadcccbadaaabcbacbcbdbcabbdccadbaccabdacabdcbbbbbdadacdbddbbcdddcdbbaacbadbcadcdddadbcacacbaadcdccaadddbbbdbddabacdccadabdadaabcbcacbadbbccddaaccaabcdaacbddcbacabdcaaaccbbcabbddbcccdcabaaabbadabdbcabbbdacddabcccbacbaabacbabdddababbdccbbcdcabdadbdbbbdabadaabbaaabccbccadbcdcaaacbcbcacddbcdbbddbbcddbcbdcbddcadabccdabdabbddabdcbbbdbadaadcddddbadbbababdbcadddbccdabbcadbcccacdadcdcdaccdbdddbbaacdbcdaadbadcccaadccccaadbcdbcbdaccdcbbdaaabcbbadbdaacdbcbbcddaacbdcabcdacdaaadadbbaaadcabbabcaabdbadbddcbbccbacbcbdbddabccdddabbbcadaccdaccaddaadbbadbccabbcdacacbddcaaacbaccbcccdacbbccaacadcdcdbccaddddaacbabaaccccddbabbcdbaacbcddbadbacbcdcdcaddccdacdbadbbcbbdcdacbdcdccbadaaddccbbbbbbbcdccbabdbdaadababcccbacccaaadbccbdcaacabbbbcbacdcabbaaaabacbbcdaaaddabcacadcacdcdacccbbdbacacdbdcbdadabadaaacaadbbbbaaadbdbbaaabbdbbacacdbacccdccacbabbdcdccdcacddabdabddabbacabbdccacbcbadbaccdcdbaadbcacacbdbddccaadbbabdccadbccdddccbdacadddcdbcaaacacabbccddbbccbbbdabdddbaaccdbbcdabdacaaccdababbbaaacadbbbcddbacabcabbcdaadcdaddbabaddbbbddacbbadbdacdaaadcdcbadbdaabdddccdbcdbcaccabaacaaccabccbbdaacabcadccccadaccacadbcdddadbcbdbdadddddacbcdccdadbacadaaacabccddadcabcabdadcbabacbbcdcaadadcdddadadabcaadcdbacbccaddabccbbbcaabddcadcacbcbdcdddabaabbdcacbbbdbdabddaadaabbacccacbbabdccbdcdaabadddbddbcdcdbdbcaaaabccdaadbabdcddaccdccacaddbdabacdcdacaaaabbccbaadbcabaaaddddbabbbbccacddacbcccacdddcbddabcbaaacacbabbbcccabbacaadaccccccbacabdbcbccdcbddcdddccddbaccddccacbdcdacdacbabdacaddddaccbdaaacbabbdccaabbbacbacadaccdadacdcaadaaaccccabbabdbaadccdddaabbbadabaddbdccbcaabddacccaacbacdacbbcddcdabcbaddbabadcaaadbcbcdabccbdbcdaabaddcbabbdadcabcbdcacdaccadabadbdabdddaadcdbcbdbcababcadacaabbbcaccdbccccababadcdddddbaabdbcdbcbdaddacccdcaadcddccdacdcddaacdbcabbbccccbbcadcbdabbdbcbdbabbcaabaababdbabbaacdbccaadcbbcdbdacbdabbacccdcaabddadbddddddadbaaddbadbdddbbacacdccdaccdacaadbadcacccaccbcbdabbdbacabdbdbdcbcadacdccbddbbbdacababdcdddbacbaaadbdcabbbdbbbaacbdcbcddbdcdcdcdcbbdccccbbbaccdaaacdcacadaabdcaaccbdcddccccacbddbddbcdbaabbbbcdcbbbdcdbddddaadbccccadcadddcddbdbdddbaaddacacccdbcdccddabccadadbacaabcbadddcdcacaccdbabdbaddcdcdabddcdcccacbcbcabcaabccbddbabadadadbabcaccadbddcaddccdacabacaaabbccccabcdbcacacbdbacacacccdaacdccbddccbabadabbbcbdddccbabaacdcadaacbcccbacddddcdbadbaadbaabbaabaddbdcaddddababaadcaddbaddbbdcacbbddcdbdaccdcdabccacdabdaddddacabbddbdbccabaaccabbdcbaccabbdcccccbbdbdabbbbaacdbdbbbdadccdbabbbbbbbcaabcddbdaaccaddcdaacacdcccccbdcbaadcdbbbdacbddcdbabcdbacdbaacadcaaadaddddddadcbcbbbaccdaccdbbabcdbcddbadcabadbbcaaaacdadcadcbabddcdaccbabbdbddddabcbabddcdbadcbbdcdaddccdaadbbcabcacbbacadbaacbaaabcbacccabbcdcdbbcdbcddccadbbbbbaadddbaccabbbccadaacabdacaacaaabdcbcccdcbabdcacabddabbbcaccabdddadacdbcdabbccbbbdbaadacbaadcccbbadbcbdaddcbdabdaccaadbcdaadcccdaadcaabddcdbabbbdccccaddddabdabdccbababbcbcaaaddbbcdaaabddbacdddcdaccccadacbbaaaadbbaccbacadadaadcccbdbdabaccccabbcdcbdacccacacbddbcbaccacbacadcbbadddaaabbadaadddcbabbcdccaacbbbabbcddbbbacddbbcddcadbdaccbcadbbbcdbdbdbabccddaadbdddcaaccbaaccdabdccacdbdbbcbbbcacbbbbcddccbcaacbbadbbcccbcaabdacdccddbbadcccabcdabdaababddddadcdcdbcbbcbadbdccaddcdcbcdcccddcdcaccbabbbaabbbcbbbadbacadbabbdbdcbcadbabadccacdaacbdcadcadabacdbbabbccaacbddccccdbcaaaaddccdcbccdaabdbcbcbdccddbbbcdadddcdbbaaaabdacabcdcdcccaacababdabbcbdcdadddbcccacbbcddbabccaccbcaccadabacddbcaadccbbdbcaaabdcdadbaabbddcabcacdbdabbcdbaaadddadcddcacacdcdcabcabbbabdabdddcbddaabcdcacbacbadddbbccaadabbccbcabbcdbacccdcbadaccbbababaaabccacccacabadaabaaccddbabdcdbdccacbbdcddcbaccdbbbbcdbbbbbccdcbadcaaadddbcdbabadcbdbabdcacaccbaadacddccaacbdbcaadbccdcbdacbdaabadcbadabdcdccbcbccddbbcadacaccbaddadaacbbdadcabadcacdadbcdaddacadaadcdaacbaaacabbbbacababdbcaaacbbbadcbdadbdabdbcbaddcbbbcaaadcadcdabadadbbccbbcabdcbaabdbbacbcdaabacbbbcabcdcdadbabbacbdbdcaaddacaddbdcaddbacadbdbadaddcadaaacbdadaabcbabaacbcacdabcabcddcabaabddbdaabdbdcacadaddcbabbabbaddcbdbdbcaaadcddcdcaabcabdcbbbbbabbddbbbaaaaadddcbdbdbcbdacbdbacbcdcdddccbdaccdbbabcbdddaadccdddcbcaccccccdbdcdcdcabacdabcddbcccbbaadaadccbcdbabacdbadacbddbcbacccddacddbcaccdbcaaadcbcbbacaadccdcdacadcadadcbdacacadcccaccadcacbccdbbdbdcdabadcaaccdcacdcbcabbdcbaddabaccdbbccacddaabdacaaacdbcdcabcacadcbbcbcccbbdbdcdccdadbddccddbdbacdcbbbbaccbbadbcbadbdbbcccdcabdaaabdaaababcbadbbdadacccabbdcbdcabdaabcabaababadcacdabbdabbacdcdabaadabccbdadbccbbbacddcadadcaccdbbdbadcaddcbcddbdbdddbdbadadacccdcaacdcabaabbacccdcbbcaaddcbbcadcaddacdcddbbcccbbacbdddaabaabbcbbbbcabcdaabdccacadbcaccdbbdadaaddbcdacbbccbcabccbacaaccabaabddabbdaccbddacacbdcaccdabccddbaccbdabaadaacbddaaddabdcbccaabdbcabbacccbcbdadbbdbcdbbdddcaccdabbbbbbaddbccccabcadbbbdbbbbaaaabcbdabddadcaaaccdacaadacaaccbccddabbacacaaabbdabcbacdbcabdbaaaddaccdddddbabdbdcabccacdacbadbcbadabdcddbadaabaaddadbdbbdddcbadcaabdaaadbdbabbcdbcaddbcbdcbcaabccbacdabaacacbbcbdddbadcaccabcccacaadccdcadbccaadddbdcddcabbadcaddbccbcacbdccdcbdcdbbbdccdccaaababcabddcadadcdcaaddddcdbddacaadacaccdbbbbdbdadcadcccbabbaddbabdcbdacadaabaddcabacacdcdbbcdabababaaddcbcdcdbbacabadbbdacbcacbdccbbcaacabbbbbcddbadcbadbbbcbccbcbbbbdacdddbbcdcabcdbdbbbccaabdccdabdbaacdbdadaaabaddbdbcabacaccaaddbbbbabaaabccdcaabdddddbadddacdacdbaadccdcaddbaccacdbbccddcabcbdadddaabbdbbcaccaccbddadcdcadcbcdababddbbbabbdcacdacacbcaaccaabddbaccababaabadbdbaabdbccaadabaacaadcbdbbdbdabcddbabaccadabbdabaaaadaaaacdbcdcddbdadcbaddabcadbdadcbdbadabdbbccaadcaabccddadaaddbabdadbcdaaacddccacbadcdabddacbddacdbacddaddacdbddacdadaddbaadacacaccacbbababbabddacacbcbcbdacaadbbacbddcdaabbabacdbaadcababbadbcddbbddddadaadaaadabddabdbcabadabacdcccdabcccaabbaaccbdcbcdbabcadcaacbabbaaadcaaabdcadcaacddbdbdabccdbcddcabbaaabdabcddddcdbcccccbbdacadaaadabcbbdadccdcbaddcdbabbdccdcdbcdadcaadbcdabcacadabdcdbbcadacbbbdcccddadbcddacdbccaaccdddcaabdbcbaabdbddbbbcbbdddcbaadadcbbbabbddbacadcbddcccbbdddbdadcccababbaadcbadcdcbadabaababcdacadcadcbcaadbadcadaddcdadbabdbcacdadbdcbbccadacdbacbabdbbcabcbdadacdabbbaadbbdddccaaaacbdbcdaaacddaabacbbcdccdcdaaabddaadacbabddbbdacbcdcccdcdaccdadabbdaacddbcbbabcdcddddcaacdcbccddddbbbcbbbcadbbaaaddbdbcbdbbbbdbdccdbabdcddddbbbccabcdbcbdccadadaaaaacbcddbaddcbbbcbbaabdbbbcadbabdbabccbcabadaaccdaaabdaccccdabbadabaaaaadcbdcbaccacadcaacddcbacddabbdbabdccbccacdccadcdbaadddcdcbcdaccdbbcabccccabaadccdbacddccccdbdcdaaadacabbaacbabcaabbbaaaaaacbacdbacdcdabacadbacdddcababcaabcaacaadaaabacbbcbcccccdddbccbccbcdadcccdcaccadaaddaadcddccbcbccbbcbcaadaddcdcbdacbbdbdccbdcbdbdcacddbbccddaddbadddcdbcbdbdcbdbbdadabcadcbbcbabcdcabddcbdddccadcccaadaaaadcbbadcabcdbdbadbbabdcadadccbdcdbaadccddababaadcbadacaacbabdbcbddcbbbcdcdcddccacabbddabbdcdcdbaabdbacddbbdcddabaacabcbbcbcdabaaaddcaadcacbbbbccdbcdcabdcdadaaaabbcdbbddaacdbdddddbbdccbdbbbbaababadcddbbbcbdaaadddacbbcddddbdbbdadbadcbcdcdbbdccadabbaadccdadaacabccbdadaddbaaadbddcddbbbdabcdababadbabcbcadaaacadbbaaabccddadccacddcdddacbbbcbbcdbccbbbdacabcacadbaababacdabbbacaaacbbddcdcbddcccaccaacabadacdddcbdbbddcdadcddcdbdbbbdadadbaccdcabdbdbddbbacddcbabccdbbbcbbdcacbbacaadcaaabcadcabadbadcbbbdaadccddbbaabaaccbbbacbaabbaccacadacbacdbcdbabadddaddacaccdabaddbacbdccccacadbbbcbabcbaaccdcacdbcccbadcaacabcaccbbadcabcddaadaaacbbdbcaabcaddcdbdadaddadbdcadbdbcccdddacbbabadcaadbbbcdbabaaadadbacccbbcccdabacccacacbadcacaabdacbbcbadcddcbdadacaabcaaaadcbdaccaadbbbacdbabdddcdaacadbabacbdbaddccbdcdadaabccbbacdbaaadaabcaaacdbacbbacbcdbacbcaadaabcdcddacaadbbbbbdababacdaaddacccacabcadcdbdcdcacaacdabbcbdddadcdbaddabaccdbbabaabcbdaadadcbcbddbbbcccacbddbbbcababdacabaacaaabbbdcdaddccccdcddadadbdbcbcbcddcaccbbbbbdcaccacaaacacabdaaccdcdcbdacbdaddbbbdccbbccbacccbcdaabbaddcbbcdcdabbccdcbadaabbbccdabbccabbdbaabaccbcbaaddcbdbddbbdbbdacddbcbdbacdabbdcbbaaccbdbadbaaadbaccdbdcadadcaadabdccbbbdaaddbacccbcdbcddbbdbddbbbdacdcdbadbcbcdddbcddaddbaaacdaabdcacbddbabcabaaaaaadadcbcadbbdbdcbadabaadbcbaaddabdbadaadccbccccdccbcaaabababbbdbaddbaaccbbdacddadbdbbcdddbdabdbcddcbbadbddbdcadbccabccdabadcbddbbabdabacbdcadcccddaddcadcabcdcaddbdcdaaddcbbbaccacacbcadcdacbdcdbddbcddaacccdbbbcabacbccdcddabdcdccdbbdbcbcbdcbbbccccddaabbbddbaaddaddaccdcbbbccadbbabdcddabdcdcdbadbbacaaaccbadbccbadccabccddaadbbdddacbabaccccaccdcabbddcaccdbbcdbbbcdaacbdccbcddbbdcadcbccbbadacdcdcadddabdbcacdadbcdbcdcbabcccbabcdcaaabcdbacbadadcddcadaccbcbccaabbddccdabcbaaaaccdcdbaadcdacdbbdacadccdbdccabbbcddcacddbababdcdbddcdccbccbbddaccdcdaadccaadaadbddaacbcababdaaaadabdbbbcbadbacbcbdaddadaccdbcaaaabcaabcdbbdcdbbcacdadacbcabddddaddacbcdbdcadadbcbbcccaadaccbddbcdacdabdbadbbbdabaaaaaacbccbaddbbcdaadbcbbacdccbaadcdbcdbacdaccabadaaabbddbdbbbabbcbcdadabbcaadacdbbbcbddabcaaabdbbcabaacddbbbbdacdabccdccaacddadcbbabbddbcbaaabdbbacdbdaadbdcdcdadcbccadacdaabbccaddabadacbbacdccbbbcdabcbbcacacaccdaabadccaaadbbdcdadcacabaaabdccacacacdabcbdbbcbbbbdddbbbddacacabdcbccddaabbdbddcbbaadcdbbcdcdabacaaacbcaddaddadcbddcbbbaaaccddabdccdacacdbbcaaddacaacabadcddadabccdcbcdcacdbcabbbabdabdcbcdbcabcddabccbdaaadcbdabcaacbacacdddacddbbcacccdbbaadcabddbbcbdacdbdaadcbdaabdaadccdccbdcabddabadbdbaccabdccbcbbbbbcdcbabbaaabdaabbacbbaccbdbbdbdcdbdaddabcccaaaabdacadcdbabcaabadacdaddabdbddccdcbbddbacdcdcbcaaaddacabdccdcbdabdbdccacdabdabccddaccbbbccdbbddaaadbbcdababbbdadcbbcbbadbcccbabcdacdddddacacacdaddbccbcdbababccdadacccdacbdadcaaabacdbbcbcccdcbbbddcabcbacadabdcaacddcdacacdbbdbaaabcbcbbacbdabdaaaccdbcbaacdacdabdcaadbcdbaabdddaaadcabaadcabddabdcaddccacbbcdcdadabaddccaaddcdaacaaadddcdbadcaacddbdccbadcbacdbdbcabddcccababaaaaadcddcacdcdaaddbcddbaaadbcdbbbadacadcadcbaaadaaccbabacbbbadbdbccbaabcdadbbbadbcdbabbbccacadbaacbdcbadbdadadbdccbcbadbaccdbcdbccabbbbcdaaaabcdccddababccdccadaaacacbcabbddadcbbcabdadbddbdccaacacddbadbbabdaaddcdbdaddadcbabcaddccbadcdbabcddadcdcabdbadcdadbbdbdcaabacdcddbddddbbccccbacbacbbacdbccaccababaabbacdbbdddbdbadbbcaccdbbbaabbadaadabddacdabaddbadccbcabadcabdcbbbbabbaadacbbdbbdaababacbacddccbcbaccbcccdaccdbaddccaddbddccadabcbdbbacdacdbadcdaacaaadcbcdcacdcadaaabdbbcdbadbcbcbbaaaaadbcacbdbaaacabbaaccdcdbbdcdccdddbbbcbdaabdaddbabbdbdccddccdccaddbdacabdcbcbaabbcccccbcdcdadaaacdaddbdcbccdbbcaacccacccdbadccaadadaabbdaccbcbabbadbdcbdacabdcabcbcadcdccabbdabdabccdbbddbcadadcacdcdbcdbbddabbabcaabbacdddacbbdabacddacdcabaacdcbdcaaaaaccccddaccaabdacddddabdbcbdddbcabcbcabbbbbbdbbcdcdcabccddaaaabdccddbbcdcbaadbbcddcaccddacadbcdccbbdbcadddaddaabdcabbcbaadcdabaacbcabaaacdadcdabdbbcdcdcaacbdbbbacdcdacdddcdadacdacddacdbdbbbddbaaadccccbbdadbcababccccbaaabdccddcdccadbadacdcacbdbdaaaddcdacbdcdbbacbabbaabbacddabaddbbbadccdaaadbcacbcdcbcbccbdddacadddbdcbdcbcdadddcdcaacdbdaadcdbdaadadaacbbacadcbbddadbdaadbcdacaabbadaaadbaabbabbabbccaababbbbdcbbadbcdabaacdbcdbcabddbbabababacbcbbbdddbacdaaabdbbadbbdaadabcbabcaadadacdadaabcbbdacadccabccdaacddcbbdabdcdddaaddcbdbabdbabbdbdacbdcabadbcadccabaccdcdcaccdcdcaabaccaabdddbbdcaabcdadbcaaaccbddacdaadcbbdaacdaaadaddacbddcabbbbadddddcadcacacaccadaddbcddbddccadbdddccbcccdcacdaccddadaaaddddcdaabccddcdddcaaccdaaaccdcbcbcbadddccabcaababaccdaccdccbccdbadddcbacbbdabbcacadadcbccdbadabcadbbddaabdadcbdbcccadbdbbaadcbccdbbdcabaabbdabbbaacdcbccddcbbdbdadacccaabdccbddabcaaacbcaaacaaabaddccdbdabcabdccacadaabaabbdadaaccbbabdbdbcdbaccadabacdcacbcdddbaccacacdccadccaaaacdbaccbaaccbdacdaaaaadacababcaccbabdbdbacabbbcbddbcabbabccdabdabbccbdbdadbababdbddabdaabaabbbabdcabbdacbddadbabdcdaacadcbabcacabadacacbbcdaaadbcabbabacdddacdcbccddbbcbacbdbbbbdaccbbbadbdbbcaadcadbacdabaacdbbbcdddababbacdccbacaccbbabacdabcdccbaccaacaddbbacdabdbabcbcccbdbdabdbcdbbabcbccaacaabcbdcaaacadddbaaadadaadccbbcbadddaccdabacabccacccdbadaabbcaabcbccacabadacaacbdacbdbbccddbadddbaabbacdcccacbbcaabcacbccabcddaacbbdcbdaaadcababdababccbadcbcbcaddcdbcbbbbcdabbabbcddcccbbadbbbbaaaadbbddaaadbdacbacdaaaacbbbccbacbadaddcaddcbcabbdacddaacaddbcbdacaccaabccdccbcaadbdbddccaaddabdbdaacaacaddaccdcccadbaaadbacddadbbdacccdabadcdccdcbabcbadbabdbbaaddbbdccdcdabbdbdadbbbcdbaaabcaabbabccbadcbaaaadbbbcdcbdbcaadadccacacbcbdcdbdabbccaadaaacbababccbbccddcacaadcacaaaadcadcddbcbbcbacbbcddcbbbccdbdaccbbcddaaabaacbabdacaabcbbdcabbdcdcbabdbabadcccbbbbddcabcddccccbadddabbddacddbbcbbaddababbbccbdccabbddbcbcdaddaccbacbddcbacabaccdbcdcdabcacabbbdabbbcaabbacbbbbcdacdbaacdcddbbadaacbbbbcabbaaaaaddaaabbacdcdcaddccdbabbbcbcbbdadcbdddbcaabccdcdbbbccaaddabbbabbdbcccdddcdccdddcacdadabccadadcddddccdcbacabbdabccbbcbcbcaabdccbdbccdcbadbccacbbdccacabaddddaabaaccdddcacdbdbddcbbacddcaccacbadbcdbaabbcbacabadccdcdaccdcabdaabbdbabdbdadabcdddadcabcdcdddbacbdcaabbcddbcdbcaadddddaadccbbbcadcdbdaaadddddccacabdabbddaabccdcabdabcbcbabbacbbcdaaaabcabcaacdadcdabcbccacdacdcccdddbcacbabcdaddccacaccbdaacaaaadaabacadaadccbdddbbbdccacdcddbcccaabbdcdddbaadbbccacbdcbcdbacdbbbbbdbadcdcdbcbbbbacbdcbdbbbbbbcbdbcbdddcdbdccbdabacbdadbdacaaabcaccddcbbdbbaadcdabbbabacbbdadadadaddadbbdccbcbacdaacaacbddbdbadcaccdabacadbcdcaaddccacbdbcbdabccbbbaadbdcaddcbabaadaabaaadcbadbabbdcbddacbdaaadbbcaddcbcbbaadddbddcacdbdcdcaadbdabbcddbbbbabddbcabbbccabccccdaadbdddaccccadaddabcddbccbccbcdddddadaadccdbdbdbccbbddbdbcacdaccdcdaaacaababbcbdddddabddcaaccabcdbcdabcddaacbcbdadaadddddccaabcadababbdadbaabdcacdacdbbbbacbcbbccbbbbaababaaaddcddbadbdbdabdcdbdacccacdbcccbbabadbbbaddadccaabcaddddddcdcccbdbbbcbdcabdcabbbdccabbcdacabddaadadbbdadabacdbbacdbdbdaaabdacacbdabacbcaababcdabddbbccabcdbcacccdbddabcdbadbcbcaaacbdadcdaacdbbacbdadababbcdbaccbdbaddcdcddabddaababcccdcbcdcaaaabdacdbccccddbdcadcddbcdcaaccadbdadbdacacbcdbdacbcddadcdaccbddccacbbccdbaadcbdcdbbadbbbcccbbaddbaaaabbcaacbdbdccdadcbcbcbacdabbaccaccddcadbabbbdbabcacaabbabadcddbdcacbcccaaadabcaabcdacdbbcabdbcdcaddacbabbbccbacdacaddbadaadcacccbcaccbdabcbdaabaaabaccbcabbddcdaddccadbddcaaabcabcbdbaadacdbdccabbddcacddddcbdcacacbbcbccbdabadcbcdabbbcbcbdabccddcaccccbbddabbaaabdaddccbaccccddbcbbcabdcdabcdbdcdbcabacdbdcabcabcdcbbdbdbacabaacbadbbbdddbcbbbddcbcbabcdbcacdbccbbdddddcddddbdcbdadbddbdcadddcdacacddcbdcacadbddacddbdcacbcdbbbcdadccabcdabacbcacbabaddcaddaaadaddbddbacccbbccdcbacaacdcdcbcdacdbddbabaabdcddbacdcdbddacddcbacdbabbcaaccabbbbcacbdcbccdcdcdaaddddbbaccbdabadbadaabababbbaddddacbddbbacaabdacbbabcbdbddaaaadadaacbbbdccbcbdcabacaddacadbbdbaabbbdddabaadcdadbcadbabaaddcdddaadcacacdbdbccdaadacabbbbababbbdaacacbcacdbbdaddcbbddcddbcdbbcdaababaacacbcaddaccbabcabbdccacbccbaadbccadabbddcddbdcdababaadbbddcdcdbcacaabaddabacdaacbaaabdacacdcbccdccaacbabbccbdbbbddbdabccaaacadcbbdcadacabdddabbabbbaabbbbdddaacbabddacddaddddaccaabbbacdbccabddcbcabbbbacabbabaacadcdaabaabbbacabaabbbbbaddbddbdcdcaadcabdcdcdcaadbadccadabccddacdcccdcdbacbdabbbdcadaaaacacbbacbdbaaabdddbdcaaddabcbbaadadcbabccaabcbadadbacdbdddcddbbacccddabbbdbcdcccaccbddbdddaaadcabcdbbbbadaddcdbcabcaacbdbdcaacdabbabbccbccdcbbcbdcdbadccadccaaacacddbbcdbdcbbdcaccacbadbbcbdccddabbbdcdcdbbbbbbbdbbbcaccdadccaadadcadbabdbbddbdccbccacdddbaabdaddbabdbbdcdbbdbdbbdbabbbabbcaadbdabbabdaadcbbbddbcbdaccbacdaccbaaaabaaacaddcdaadcabbbbaabcdbababbacbddcadcbbdbdabbdaabdadbcbcbdddccccaaadcbcdbcbdacddddddbaaabcadddddadabddcbccbdacacdbadabccbcccddcdabbdddbdccdddbbddbcaacdabacacbbdbcdbdbbabbacacdddabbacbabdabcbbcacdadbdbbdcaadaddadcdbabbcdbbadbcbbdbccbbaddbcdadcbdabccbcdacdccbbaaddbccabbdaadbaddcadddbcbbcccdadbbacdaaaadcababadadabdcabdcacaccdacbbbcdccaaddddcdadadbccaaccbabbdcacabddccdddcaddccacbbbacddcccadcbdbacccbabbbbbcdadcdabdbbcbcdaacbcbcdacaddcadddcbddacbbdbaadacddccacadbaadcdaaadbabcbabdddaadacadbabcabdcddcbccdaddddbcddbadcbdaabcdcccbbdbdbacbacaabadabdaccabaacacddcbacddbccbaadcadcdacabcacabbcccddaccadabadbddcaccadaacbacbabddcdccccdbbabaabcdddcdbccabacabbcacdabcddcadcabbbbabcabbcaabcabcacaddacddbbbdbdddbdbaddcabccbbddaadcbccdcccdacaadccdadcdacbabddbbdbacbbdbabbbcadadbbddacdcacbccadcddcbcabccacbdccbcaacaabcdddaadcbbcdbcdbbabaabdccaacdabccaddbcabaacdabadddadbacddbcbabccbbbacacbbcadbbaacdacabacdcbaabcacdcadcdacbadcacbbbacccdbdadacbabcbddddbbacadbcaaccbabcdbbaddcbbdbabcaacdacdbdccaabcacbcaaacacdbbdadcddcbadbbbdadbbbcbbcddcbddabbabccbdccdabcabbddccbabdcdbadcbccddddadbdcbaaccbdcbbbbcababbcaddadadcabbddcddaccacdbbadcadbdaacdbbcbcbcadccddcbababaabdabdacbcaabbbdbcaddcdadbdcbbbbacdddbddcdbccacbaddbdbbcddddcabadabccbcaaccaabbcaacdaaddabbdabccdabcdbcbaacddcdbbdadcdbdbadddccbcddbdacadcdcdbbadabbdcaadddcdcdbcabaaccddacbcddcdbcbabdabcbddcccdabbcddddbbadccbbccaadddaabdaabccaadbdcdccacbaccabdbdbccacacccdabddadbaddddacadbcbcbaaaaabadcbabadcbdacbdbbdacaaaacbacbbdbddaaccaacbcbdcbdddbdcadacbcdcbacaaaddbbdaadaabcdaddbbdbdadcaadbabdccbadccacdbaccdbbcadcdaccdcbaaadbaddcbdbdbbaaabbacabaccdbdccbcbccbacddaccdaaacddbcdbdcbcdbcdbbcccbaccbcabdabdbddaaabbdaadcccdbdcddbcaddbaaccaddbbacddaddbccbccadddbcbaabcdbabaddadbcaccbdccbdbbdbbcdbcccabaadbaabdbccccbabdcaadbdddbadaaaacddcaaacbbccbdcabbbbbbdcbbacdcacbabaacabccccaadbabddaadbbcacbcacadcaaaadbacacaaacdaadbdcaadccbdbdbdccbaddcdcbdbbbaacbcbacbbbabdabcbcbdccabaacbbdabddccaaadbaabbbbaacaadcaccadbbccabaccaadcdabaabcaadbcadaacccaacdccdacaaaccdaacbcabaaaaddcdaaadddccabcddbbccbbcbbdbcdaccadbcccbaddcaccbbbbabdbbdcadddadbbabdddbcbdcbbacbabbbccacaabadbcdadbbdcdacbccaabdbacdadaabdddbcdcbbcababcacbcababbbbaddbbdabbdbbcbcaadcdbaacbdbdbbabcdaaadbdbaddbccbadbcbcdddbabbcadcadbcdcbbcdabcdacaaadbabbbdbcacccbaabdadbdcbdccddacdcccbcaacdcadabbadbdccbbdadaccbdccbbcbccbbacabcbdbaabbacbabcbaabcbcacacacabcadccbbabcbddacbaaacbabdcdbabaaaabdbababddacabddddbabdadadabdcbadadcccccbcaacdcdaddbbcadbacdbdbcbdaddbcaaaaddaadcbbabaaacadcbadcbdccadbbacdbcaaaabccdccaabbbbcccadbcacdcacdccdccaccadbadabccccbcbccdaababddacbbdabbdaddcbdcabccacabadaadabdbdccbaddcddbdbadcdcacbdbdadccaabccbcdbdabbcdcbdccccbcaabbbdabbdcaacaadadbdbcbbaaddcddddabbdcabddbbddbbdddbbaabdbcabbaacdbacbabdcabddadbcdcadbbbccabdbcbaacabdbaaadbcbaccbbbaadbacbaccbccbbcadadcabbcddbccccddddbcdbaabcdbbbbdadacbdadddbabbdcdbbcbcdbdbdbadbdbdacdbcdcadbcadcbadaaccccdabccbbccbcdbbabadaadbccbcdbbbbaadadccddccdaacabddcadcbaacdcddbccccbbcadbadaaabaccadcacadcbaabcdbcccbacbdabbbccbcbcdccaccaadaaccbdabdcbcdbcbdccddccdccaaddadcaccabbaaccccbabbdbaadaccbccbaadcddcbcbbabdbddbdbbaddabaccdaaaccaaabcadacadcdadabcdcadcaddbcabdbcaadacbdadaaddcaddaabcbaaaaccbbddbbccadaaddccabbbbcddcabcbbacadbccaaddbacbcdcdcdbabddcadcdcabdcbbadcaababddadcdcbbadacbacbcbcccbabaabdbbcdcbdabcaacbaccdbabdbbabbbadccbaaadaaadcbbaccdccdcacccdacdccdacbadbadaaaccadbdaaaacdbacadccdcacbcddccdbbaccabccbcddbacdaacccabbdcbbdabbaccbbddbababacdbcbcbdcaadbbcbcacaaccabadcaccdbccdccdddbdaaacaacdadbcbbbcccbbbdbaaacaddbbcaddabccacbcacbabdaccbdaaabbadbbbcdcacabccccdacbcdbdbdacbbbbbccdadccabacdcccdcccdcccbcbbcdabcbcabbdbbccaccbaddbbccbbbdaaaccddaadbcacbadabadacadcbaadddcdabaaabbdbabbdabbcadbbbcabbcdddbdacdcbbabadbdbdaabbbabcbbcddbbbabcccbbdabbbccabdbcbbadacbccbbddacbdabddbcbdadccaacadddbacabcddabaaddddadccccdcccbdbcbbbccabaadbabddcdbcbdcabdcbbbbaaaccaaaabcbbbaadaaaacbcddbbabaddaddcbadaaccdbadbbddabdaaacaaabccbaacbabbabddbabbadabacabdaccbadcaaadddaaddbcdadcdadbdddcabaacadaabdbaaccccbdaaacbcbccdbadccdddbddbbaaadaddcbcbbcacbacdcdcdbdbaccbbbcdcdbacaacacccdacdacdbcaddbdadabcbdbacbddccbbcbbbbddcddddcadbdccdcbcabdabddabbcdaadabbbadbbccdcddcbdacbcabdddccbbbddcacdabdbabcbbcabcabbacbdccacbdacaabaaaaadabaaadbabcdccbddcdaccdddcaaabddbcaddaaadcacaccdaddcabdbbcddbccdaadbdcbacaaaabcbdcbcacdcaaccdbbabccdbaacadcaddabaacadbabccdaccbcadacbcdcbaddacbbbbdbaacbddbbdadacbacdbbcadadcdbbaccacbcccbddcdadcbcaaddabddddbbdbcbbaaabadbbcdcadacdbcbabbbbcaabbbbbdccabdbcdacbbaddbbcbabacbbadadaadacaacdcdcddbadbdbbdaaccdbbcddbbadccacdcdaddbbdcbdcdbdbdaacdcacbaaddaabacabdcabadcdccbdbababcbddbbbdcacaacbaaabcbacabadcdbbadcdadbbdadcbbdddaadbbdcccdacdbcbdbabccbbdacaacbbaadacbdbcdadcabadacbbbbabadccabacdbadadabcddbdbbadcccacdadbcdabacccbdaabbaabbdbdacdcddbaccaddddabccbdadabacbcbccbadadddcacacdadacabccadddcddaadbcbbbddddbbbcdaabbcbddbdcbabbbaacbcbabbdacbacaaddbcddcddcdbddcdaadaabdddaabcddbaaabaadbbbdddbaabdadadcccbdaaacdcbdadcdaccdcbdadbabddbdaaccdcacbdbcbbddbddbacbabdcdbaccaaabdabcdbbadbccabdbacaaadacbacdaabbbacacdaaccdbcdaadcbddbdadbbccadaacdacdaabbdbadabddbabdabbdbccabcaccbadaadacaadddabcbbdaaabccbbbcbdaaaadbbbbcabccabbbbcbcdcbdddadcbccccbdcddbcaacbddacbdbcabdacbddbcdadcaaaacbabaacabddabbcdbddaabcbcdbaaacacddbdccbcababcaaabcaadbbaccadddacddbdbcbccccddbcbddccddbadabdadcbbcdbcbdcbccbaccdcbbddabbcbcbcacbbbdacdbbadcbbabddacacbcaacadbacbadbcbdcadcabbabadbdbbaddcdbdcddaacdddbbbcbbcdcabdaabaccdccddabdbdbccbcbcbdcccbdcdaaddcdcdabacabddbddabdccabddaacdbdcaaaacabcdabcccaadadbbbcaadaacbcbdbabadbdccbbbdbaddbbdabdbacddabaaaccbbbbcbababcaadaabddaabdacbadccbbcbbddccdbacccdbcbccdcabccadbdbacaddcacbbdcbaddcadaccadcbadaadbbbdabddbcbabaadcdabadccdbbcbbadbabcdbccbacddddcdcdcbabdcbbcdaccdbabcaadaadbcbbcaadbbacbbbcbbcbbbdcbcbcbdcddbdcccaacdbbbdbdaadddabccddabaccdbaaacbbabdabaacdbdabdbdbbbabbbadaabddaddadabcacaabacdadacbbccabbadbdabdbacaddaccbbdcaabaadddadbbddaabbabdcddbcdcdbdccdacddacacbdbcccbabcaaccacbbbbdaabaddcbcabadcccccacbaccaabddacbbcbabcbccbdacbdcacabdaaacabacdacacddccdabdbbcbacbcdacdabddabccaacddbbccdabcbaabcadbcbcdbdacbcacbcbdccabbaabdadcccdddddbddcaadddddbabdabdbbababbbcbbaaaaccbabcbcaaccabcacadcdadbbdcccdbadccbbacdbdabdaaccbdbbcbbccdbabbbbadadbbcbacadcaccddccbccacaaadddacdbacddcacaacacaaaddaddddbdccaabadddcbdcacdcbbcacbcbaddabccaadcbdcbdcdbbccabcccdaabdaaabddadcadcbbdbdaddccddccadabbbcdcbdbacababaccbdcbbdddcacdbbabcdabddaabbdaacaabcabababdbbbbcabadbcbabbabdbdcdaaacbcdbdabdcddbcadcbcbdaabcdbaaabcdbbbddbadbbcdbdddcbdbadbbdddcbabcccaabcbbcbaadacadbdbdbadbbdcbcdbcdadcbcddbbdcbdddabaabddccdbcbccbbcdbbcdcdabccadcdabdcdcdbcbdcaddacaaccbabaadbcabcacdcdddbbaaaddacbdabaccdddbcbbabaaabccddbaabaabcdcadaaddcbadaaddbdaadccacadbdcccddccabdbbbbbababbadbdddbcdbdcccabddadddbcdbaadadcabaddbcaabbdddcddadccbccdcbdacabacbdcbbccbbcddcacbdbcaccbcaccaadddddcaaabbbadacdddbdaadacdcbcbaccccabdcbdcbabadbacbaaacacabdabbcbdaabdcccaabbaabccccbadbcaadaabddbacaaddcbaabcccdadcddadcbbbbdaccdabcadbcacdbccbbddbdacdccbcccdbcaddcbdbcabbcddacadddabadcdcbddcabdbddcbcdcddddcdbbacaababddaddcbdbbaaabcabacddcdacdbddcabdacbbbabddaddacbacbacdbddabaccdaaaddbbdccaccabdbdbbcdddaaacbbddddbdcdbacddadcacabaaabaacccccacaadcbcdcccbcdbaacbccadabbcbcdbdcdcbaaabbdcbdcbacdaddaacadbbbdccddbaacdcdaabdaddababacdaddaabbbcddcdadccabdbdabbdcbccadbabbdbbaadccdccbbbabbbcdacdddbbbcadcdbccdddbcdbccbdccabcabbbbbcdddcbcbbaacacccdcdbddabacccdabbbabbbbdcdabddbcaaadbdacbccacbbbabddaddbdccbcdacadbabaadcddcdadacdcadabacaccabbccdbcdadcaadabdbccdccdddbbcdbdaccdddacbbacadacdbbccaabbcddbbabcdddbcaadabbbdddddacdddaabcdcabdcccdabccabcdadcdcbcaccacadaaddcccbacacdccdaabcbbccabdabacbaaddccadcdcddbbcdbddbabdbdcccccbcdcddbbbcabdddccaccabcdcbabbdaabbbabacbdbdbcdcaaddacadacbacaacdabaaaacdddcbccbcbccaaadbacbccdacbcaabdaccbddbaaccbcddddbddbbdaddcbcdbdabcbbdcdabdabccdcbcaabcaacaabdaaaaabdacdcdcabdbbacadadcdabddbabcacabbdcdbbdcbdddbbaccdbbccdacbacbbcbbaacbddacbabcbadbddacaaacaadcabaaadbbbaccdcddbaadddbbccdbdbbccabddcdbaadadadbbbddaaadbaaccbbaaadbacabbcdacaaadacaacadbadcbcdaacbdbbdacdcaababcbcabaddddbdbcbdadbccaadbabddccbaabcccdccddccdccbbddaadabaabaddddbdcaaacbdddabbdbcdccbdbccdacbabbdccccbbddacdabbbdbbbbbcdbcbabacabadabaddbabacaaaabccaadcacadcaaddcbcabadbcdcabadabdaaccabbabcbadbbadaaaadcaccdcbbcacdbbbdadcbaacababdbdcccdbdcdccdccdddbdcbbcadcbbcaaaacdabdcadbdaaaacaacaaaddaabcadbcbcacbdbdcacbacbbcbbbabbdcdbcaadcbaccddadbbcbcdabaabccacacacbbbcacdcdaacdbbcbbcbdcbbadbcddcdadcdbcccdbdacdccdcccddbbabbbdcdccaabccbccdabccdbddadacbbcbbdbbddbbdddddccbacbadbccaacdcbdcadbdadcdcccdcbcaacacbbabbdaddabcadcaaacababdadcbdbacbdcadccaababadcaacadcbcbdbacddccdcaccbdbbcddddcbdbbcadaabbbcbdcabbbccbcaabaaaaabbcbbadbcddbaadcccdacddcbcacddcaadaacbcacbcaddaaadabaacaaadbbcadbadccbcbcbacbdcdcbdaadbbabadcdcdbabacddcbbdcbdcbbbdaabaabbdcccbdaacadbbaccbbbabdaccbcccbcababaccbccbccddcddcbdddccdadccddddccbbadacbaaababacdbdcbabcdabdcdbdcdcbcdaacbabbcacbabcbccbbcadbabaadbcddcbccdbbcdbacccdbbabcaaaabbdabbbbdabdbbabaacaacacabacaacaddbacbdbcbdabadcddaacaccbccbabbcccbdadaacdccdbddbaaacacddcbbcbbcabccbaababcabcdbcdacabcdcadadaaaabaabcbcbababdcbdbdbbbcbcdcddbadddcddbabbacabbdcacdaddaccbcbbaaacdddacccbcbdcaccadabdcdaddababcadbbbaaddcaaabdcbbbbabcdbdcdaaaddbbadacbcbccdadbaaaaddcacaabbdadbbcdcaccbaadcadbaabcaacbacaadcbdbcadacaabbcdcddabbadccddccddcbacaccaacbddbdacdbdcbbacdcbccbccbdcdaadcbdbddbcbadaabbcbadccddcdcaddcbbcaadacccadbadcdacacdaaaccaacadbcdabdccbdcacddcdcacbbaacadbaabaddcdacdabaadccabcaaabdddabdcbcbaddcadabdabbadbcdbadcaacbdaaaadcbbabdbccbdccdddcabbcdcbaacbdabbccabcdddabdaabaabbaadaccaadcaaaccbbacdacdcadbddaaaddaddddaaccbdbcbdddbcdcbdcaaaaadbcbdbccdbdbddaabbaccdbacbbabddadaaacbcabcaadabcadbdbccbbcddddabdbddbbcbdccbadddaddaddadccddcaacddbccaacaacadbdddaacbabacbcaacbccdbbaaaacacccbadcaaddacdabacbcdbbdcbaacabbbaddbadddcbcaaddbacdaadcacdbaddbdadabcccabcdaabdbdbccbddbdcccbddcddaaddcaccbcadbdcabdadbbcdaaaacbccccdbbbddbcbdcabcadbcdcbdbddddcacbadbaacbcaadaacacacbdbdbdacdcadcdbdbdcdcabbaaacbadbccabdbcacbbacaccbbbdcdbcbccbdcdcdcadcdcbddbaabbdcbbaabbdacaccbacadcccaaacccbcdadcdaaaccacbddcbacabdbcdbcddcbbacccbbacaddbbcdbccacbdbadadcbbabaddabacbbdddadabadbabddbaacaacbdbabcbccabaccdacbaadbddadcdbbccaabccacadccbdadbcbcbcdbdadbadadadbcdbcbbaacabcbadccbacadbdcccbcbaacddbcaabbbdbbacdccdddcdcbcdadbccddadaadadcadccbcbddbcbbbcdccddbdcabdcbbcadcdbaabadabcdbdaaccabcacabbdbabcdbdccccabbcabccbbacaadcbbadbdbcbcbcbcdbbbbbcacbbdaddddabbbcaacadcdcdaccccbdbacbacdbccdacdcdbabcabddcddbddbaabbdadbcdbaadddadacbadbcbaadaadcdbadbddbdaabccacaaaadbdbcbddbdbcabaccadabbdabbcbcbbbcddcbadccabbabdabaabbcabbccdcddddabcddbdddbdcbadcbcbaaaaadabdabcbaaadbabccabddaaabbadaccbabbababbdbcaadaaccdbaaddacaaabbbdbadbdaadddbbbcdaccabbbbaccccabbdbcdadbdbccdccaaaabcdbddcccddcddccbcadaddcacbaacdcaddacbaaacaabdddbcaaccbacbadbdaacbccdaaacdcdbbddcabcccaddaabcaacccdcdabddacbdcdbcadddaaddddbdddbcdbacacbdcbbbdabddbdaadadabddababbaaadbdabadcdcbcdaaaacacbdcbcdcdacbcadbadbcbbcabacbaddaccbaccbabdbbcacabbcccdcbabaddddacdaacbcdcddcdabddabaaadaabcbbddcddabbbbcdbcbcacccaccaaadaaaaabbddcabbddddcdadddabdbaaccbaddbbaacaadddbdabacddbbdaccdbcdaabccbabbcdabcababbdbadccdcacccdbccccdcddcbdbaaacbaaccbbbaaccaccadccdaaccddcbaccdbcbbadacabcccacaabdbdccacdcbdacdcbbaabbaccddcccdcccbcbadcdcdbdbddacaddbaccdbbdcacbdacabddbadccbdcdbbcdadbbdaaadaacddcabbdacbbbddbdbcddabaaacadddddbdacbaabcccdcbcaaccdbddaadcdbcadacbadbdbbcdaccbbbbdacdaddbcbdaddacdaadbddcabdcbdaaaadbaadcaadacbcbadbdccdcadadcccdbcdadbccbdcddbbbdaabddcbbbbabbdacdccdcdcdccccbdcdcbcbacaccdddcbdadcbbaadcdabcbdabaaaaaccdaabdbbddddaddcbddadababdbadaabaacabadbabbcaacbdacbaaabbaddbdcadccacabcbacdcabcbabdccabbaddbababaddabacaabbbdbadccaaaaccdacbdadbcbcabaccbcddbbdcbcbaddbdbcdccabaccbbccbdaabbbddaadbaddcdabdacddbcacaddbabcabacbbcabbccccdadcadcddccacaddddbbcdbbddadabaaaabcacacbacaccbababcacabbbabddadcbbacccdbdacacbaabdaaabdbaaabbcbcbaabaabaddaaadcaabcaadcccaaddddacdadabcdcdbacadbbcbcbbadcadadbacabcbaabbabdcadcaccabcccabcacbcbcabacadbacbcbaadbbadbdabbadbbbabbadabbdccccbbbbbcddbdacdddadabcaddcaadcdbddaddcdbcdddccccbcdacbcccacaacdbdddabacddaabdcbcdcadbcaccdabddbbbccdcddccbcaccdcbaacbdabdbcbdaaadbbbcdabaccbdbdcaabbbadaacaccacbcbdddddacdadadcbdccccdbadacaabdbbcaadabcccaabdcacdaccbadabdadbdcdacbadacdbbcdbabadddacdabdbccbadcbaddabbddbddddacddbcbadbbdbacccbcbcacadbacccdccddbbcabcbdadacbcdabdcadadddccaddacbcbbbcdbbcbddcacabdbccabbccbbaccabcbdcdcdcdacbdcbadcdabcdcccbadbccbbdbddddbdcdbbacdcbdabddcbdbdaccadbbaaadbbbacadbcccaaadcaaaabaddbbdcbddabcddadbacacccccbcdddbaadccbdabbbbaaabbccbbcdaadbbddcbdababcbbcbdbaddbbbabdcbcbdcaaabdbcbdbaacdabcddacaccdacbabbbdbbabcaccadcbcbbacbaacbacaddcbababacccaadcadccacbbbbddbddaabbddabcaddcaabcaabbcbacadcdcbdcabcadcacdccdadbdbccdddacadbbdbcbbaddabaaccbdacdddcbcaddaaabcaddadaacbddbbdcdddccccabbdccddcaaccdbdcabacaaadaacdcdadcacacaabbadacbbacdabaababdabcbddccbadcacaabbdcacdbbcacadddbaadbbaaccbccbcbddccbadadcdddaadcdaddddadcdddaaccdcadabacbbbadadcbbbbdbadcadbbaabdcdaabbadbcaaabcccacaabaccddabbdcccbdccababdcbaaabdcddbcbadabccaaccdacacdbdbddcacddbcbcabaddacdadacbbbddbcdcbccccbbaaaabcccacbccdaabdbbcdbcbacbcbbaadabcbabdbadabbbcbdddcabaccbadbdbacabcdacbbddcdabcdbcddddddbaaaadcbcaddbcaaabadaabbbabddbdcbbbaabbbdddbcdcadcdbacbcdcdcdccbbdbccbcaaddbdbdbaaddcbcbbcddacccacccbbacccdababbbbdbadcadcdacddcbdcdbcdaaabadcdaacaccacbccdcdabcddacadaccddabdadddbaabbbbccddacddddcbcaaaddbccccddcdbbdabdbcbaacbccbabbcdcbddadbbcbcabdbdcbbcadcbadabbdccbddbdadbdacbdcbccaacaabcaaaaccbddcabadcbbaddcbbcaadbdbcbbabbcddbaacdaacadadcaccbaacadcaddcdabadcccbabdacaacacbaccbcacbaadccaadacdcaddcbbdabbcddaabbdcabccdaacdbbcdaabcbbcbcdccddabacbabbbacaacbdbaaabadccccbcdbdaacacbcacaccbabbaddcadddbdccbbbdaadcbcbabbbcaccdacddcbdacdabbcddacaddabccaddbcdbabbbbdacbabcddabadbbbbbbbadcacaaadbdabdbbbaddbccddcddacaadcaaabadbddcdacbacdbaadddccaacbdacaccbbabcadaadadabdabcbbbcdcbadbdcadcbbbcabadbbdaccabdbdaadbbccaaddacdadccdabaaadccdcbcadcddbdbaabdcdabdbadadbadbaccdcddcbaabddbdcbbcbcbcacbcddadaaccdbcbbdbabcaddbdddcbcbcbccacddaacccccbaaccbdcdaabaaabbbccdabccadddacacbacbabacbdaaaacaaabaabcccdcdacbdaccbbbbcbbbabdaddacdaaddcadabddcaddbcdaacdabcdacaabbcadcaacbcdccbadccaacbddcacccddbaabbaadcacabcddcdadaabadcacdbdcababcbddaabcbadbccbbddaaacabcbcdabbdaacdaccccdcbbbccbbccbadabccadbbaabbccadacabdcbcccbbdbadcdacaacaabbaaadcbccbadcddabcacadadadddbbadabdbabddbcbaadcbaabdccdbbcbdacdbdabaaadadcddbadbdbdddbbcbcdbcdcbaccbdbadcadbdcbadaaacbadaaabbddcaaddcdababdbaaadacbdadbbbdacbacadcddcaaacccdcaadcddcdaddcbaddbbbcaddacaaabccdcbbadbbaabdbabbbdaadacacbadbdbdbcddcabdddddccddcbbadaaddcdcabdcadbcacaadbdccdcdcbacaccbcccaababcadbbdacdccaddddbbcdbcdabdcdaabcccbcabaaabaadbdaabdbadddddcbcbabcacdacddbaacdbbccaccccdbacddacdcbdaabbaccaabdbdddcbaabcdbaadcdbcbbaaadcdccdaadcdaaadcaadbbdabaddabcaccaddddbdbaaccbacbbaacbbddaaaddbaccbcccaabbcbdbccaaaccdcdcdacaaaadcaddcabaaadcdddbcbdaabdaabddabaddddbadcccbabcdcdacddbbcbaddbddaadccdbaacacbdaadcdbbcdbdbcbdcbdbbbbbbabccabdbdbbaaadcaabbcabbbdbaddbcdbcbababbacdaccbbdcbcbcdbaadbadaaddaaaccacbbcbbdbcabbabccdaacdccccbcccbbddabdaaabbdccdacdbbdadbcaddacbdbdadacdaabcddbddacaaccbddcbccadcacbbaddbabbcacdbccdddcaabccbaccadbadbcdaadbcaabcdcddaacdbabbddcdcdddadccaacddadaccdbaccbccbcbaaccddacabdcdbaaaaaabaccdbbbbdbdaadbcbbcacdccbabccadbcbdbbdcbbdccabdcccaabccacbaacbcdcdcabbbbacdbacdbdaaadccbcbcdcaabbbdaccccbacdadbabbbbaacaaaacabbaaadddadddcbcdbcababdbbaacbaaaddaabbdbbabccbcdcbbdddccacabcddbadbdbbaccdadcbddabdacbcbdcbcbabbcadcbadddacaaccddaadbddaccbacbaacacbcbddccabccacbbbadbabdbdcdacdcbbacbbacdcbacadcdcdccbbdccababdbbacaddbadbddccaddabdddcaabdcabbcbcabdacabdcbbbddabbbabbcaaabacbcbbdabacadcdddcdacadcbbacacbabdbbdccdcccbdaddaccbbcabdcdacddadbcbcbaacaccdbcbdaadcbcacdddadbdadbddccdbaacddaacbbacddbabcdcddcaccdcacdddccabbdddbbaabcdccbadbdbcbbbaaccbcaadddaacdaaaddcbbadbbadbcdabdabdcaaadbabacbcdbcbaababbddbdccaddbddbcbdcdbcdbbacaacbcdaddcacbacacababccbdacccadbadbddcddbacbccaacdadcdbcbbbbbaabdbdbbcbcccadcccadabcbadcdcccbadbbaacaccdabcbdccdaaaadcdddbaccdcaddacbbdcadcdabadcdbaaaaddaabcdbcddcbbdbacbcddcabaaccbbabbdaadbbddbdcacddcbdadadbabaabaadaabbabbddddbdbcbcdaccdcacccbcacaaabaacbadbcbbaabcadbccdcbabbdbadaacbdcdcbacaddcdccbacaabcdbaacbcdabcbbbcabdabdacaaacdccbdadbcccccbbbdcddcbcccbcdcbcdbacaddacadadccabcdbcdacaddbdadaaddbadbdbcadbcddadadbbadbdcdaaaabadddaaaccdbcbcbaddacaacabcbccbddaadbddadccaabcbcbddbcdacdcbddcdcbcbcabddbbbcabcdbbcddbbbbdacdcbdcccdacbdabdbbcbadbabcddcdcacccddbbabbcbcaddcbcabbcbcdbdacacccddcbdbacdaccbabbaacdbdbabacdbaaabacacbbaccacdaacddbdaabdbbddaabbcdcccacbcadcacdbaaadbaddddccadccccaabbccbdcbddacbbacdbcbabcbccbcdaaacbacaddcacccadaacddcadcdcbbaacdcccabcbdddbbbbacaadbcacbaaddcbbbadcbdaaccbbccddbaaaddaaddccbaacbcddbdbcdabcdbaadbdacccbbbccddaadbcabcadacacdbdacadcddbcbadddcacaccdcbcbcddcbadbaccddaaccaadaaccabcacacdbbaaccbbadcaaddcddadcbacbdbcbbabdacdccdbdcbbabcdbbdbdccdcddcaacacdabdaaadcadbbdcddcaccbcaddcbaabdacbddcaadacdaccbabbcabbdddcdbabadadadccbbdcbcbdbcdcadccbdcdacbdaaabdbdaadcdcdddbacbddddacacabbadbbbadcdabbbabbbcdddbccdcabdadbcbabcaaddbdbaabccbbbdcccddadcbabaabcbcdabdcbdadcabccdadcaadbdbccbbbdddbbbdbbdddbbcbdccdbbdbbcaaadacdacccbbbddbcadcbbdacbadcdcabbbaadcdcbddbabcaababdbdcddaddddcddbaddadddbccadcacddabadcabddbdbacddbddacddadbcadbabaccdbcddcabcadddacdddacacdcaddbdbacabcdbabddbccabdbbcadbdbddbbcdccdbcabacdcadcdabccdbabbdccddbbadaddddbbcaabbbbbcccdabadbbbdaadcbdbdaabddbbdbdadacbddcbcbcdbacbaadadcabdaaadbcdacdbadbbcddccacbbaabaacabadcdacbadcbcccdbcdcaddcdbbaddddcdabdbbddccaddbcadbdddacabcabcababddbcabacccabbbdacccbccaacdbbaadbcbcadbcbadaabddabbcdcbbdbdaccaaaaaabcabbacbbbbbbdbcbdbcbddbdadacdaddaadbcbaccbcbcdcddacbddadabdbaadddccaaaacdacabacadccdcadddddcbbdbadabaadcdccbaacddbbcbdccccbabaaaddbacaadbaabacaddaaacccdbbbdbddacbcaaabacdbccdbccabdaaaadddadaabaadcbdbdcaaacccdcccaaadddadaacbdddadbdbcdcccccbcababbdacbdcabbbbdabababdbbdbdbccdadbaaaaaadbcadacabcaabdbcdbcaaddcbacaabacacaadadcbaabcaccabadbbacbcadbadccbacdbcddaababababadbdbdddadbcbbbcbbcadaddddddadabbcbdcbaacadbdcbbbaabcbcdbdabbacadadadaadadddbddaabbcaadddddccaaddddbdcdabacabbbddccbabddadaabadaabcababdadacddabacaaddbdbcaadbddabaabcadacdacbabacbaabababaddaddddbdadbbccdbbbaccccbdcdccadccdddcbbbcaaaaddbbabadbcaacdacbacdddcdddcbcaaaabbbccbcaddababdabaabdcbaaddbabdcdbbadadaabbdacdcbabdbadcddbbcdbbccabccaaabddbabbdcadddbacabaabadabaaccdacdaaaadccdadabaaaaddccccadcaabaabbcacaadbbadadaddbcbcccdcccabbdabccbabcadcaadcbabaaaaddbbbadcaddbcdbdbddcbaadbdcbabdbdddbcbdbbabbbbbacaadddbbdbcbddddcaddcbdcacbbbdddcabcadbdabcdcdccabdaadbcadbcddcaadbdcbbbccdbdcaacddcbcdadcbaadccabcccaadadcdabdbbbcabaabdaacacbcacdbbcbbcdaacdbdbcdddbccdabdbaccacadccbaabdbbdaaacccccbabbcabbcdabcdbaccabbcbdaddbcaadddacabbcccdcbdbdacddabdaaabcccbcdbdcabdbbcddbadcaddddbcdcabcdddacdacddbcadbbdcbadddbcaaaddabaacddbdcccacbbcdabaabcbbcbbaacdabaaaccddcbddcdbbdadababacdcdaddcccbbbccaaadcadcbbcaddadbaadaaaddaabacaaaadaccaccbcabccccacabbbdabdcacbcaddbddbccadbaddccbbccbbcddccadcdcbadcbdcacaadcbbbabbaabdadcddccddbbdccbdbbdbbdabdadcdddcaacdcdcacacbcaacbdabbcabccdabcbbcacaadccdcaadcbcbbcccbdcdbaddcddabdbbcbdbcadbdcbabdcbbadccbcaaaccbdcdabddddbbddbcbbaccbddcabacbcccbbadacdaacabcaabbbaddccbdaddbbcaaaaadbddccdcbdadcbdabdacbdcadcddbbcabaccdccdddcadddcdccbccddaabbaabddaccabbdcbdccbadcaaabcbbabdccddbdbbdcdbddcaccabbbcdbbadcaabdbbdbaccbaacbddbccbccdcdcadaabaaddddcbadbaaacdcabbabccdaabddbdacddbaabcaaabadaccacbcacbbdadaaaabddbaaccdcabdcbdbabbadaaabdbbdbcddbddacddacaaabdddddacbbddaabccbadcbcbdbdbabdcbbabcdcdbbaccbdacacdbcbadcbcaadadabcabbdcdbaadddbbcdacdadcadbddaacddddcadccddddbdaabbbddabdbcbdacdabbaabadaabbdbacaccdcbcbccdadbcdbcbdccbbcbaabacdccbaddabbbaadbbbcdcdadbaaaadcbddaabbcbbcdbacadbbbcaadcdaccccbdaaababdddbbbbbaccbbbabcbdabbcabacbaccccaadcbadccddaacdacacdccbbdbaccabbbadcaaaddddbcdbabddcbadabcabcdabcccaacadacdbcbcbdacadaabdcadabbbbdccbcbaaccbdccdaaddcdadccabadcdadbadadadbcbcaacbabcdcbcddaadbbdcaaaacccdbabadbdccaacaaccbaadddccbcddbbdbadcccdbddaccbdbadaacdccababddaaaacdacdbbcbcacdcaccdcdbbabbbadbdcbcbcabcdbbaaddcdcadaccccdaabcbcbdabdbaccacbdbaacdababacbcbcdcddaddbaaaacadcbdabdccbccaddbcbdbbaddbccabdabcbdccacccccdbbdabdccabddaccacdacbbaddcdabcaddcaacdbacadbdbabcbcbadccbcacccaadccbbcccadcaadaacccdbcaccadbabaccdbbacdbbacbacabcaaabcbdbacacbadcbddccbacbdccacabcbadcdbbcdbadcdbccdadcdccabdddabdddacdacaacdadcdadcacdacabacddaaccddccdacbbcaadaccccaabcdbbadbcdaaaccbbaababcaacbddcbbbdbcbcbcabdacbbccdaadadacbaaabbdaccdaaccbddccbbabdbdbaccadbcdbdaabdbabacabbcbbdacdcdadaaaabdabdabccbcbbbccacbddadbdcdaaacbddbccbddbccdadadbdbaddbcbbaadcdbdbbdbadbccbdbdaaaadcaaadbadabadbaabdbaacbbababacaddbccadbdcdaaacdaacddaabcddaddbcaababaababbcbbaddccdcaddbcabcbdbdaadcaadabbbbaddbacdcddacbdbbddcbddcccdbdcddadacaabbbbaacbdadabbcaabbbccaacadcdacbaabbcdbbcacccdbcbddacaadcadddaaabacbdabaddcdbccadcabadbdbcbdcdaccdcdbcabbdccacbacbabbcaddabdabbaacbdaaaaddccdacdddbcdbcddccddbaadbacaabbcddacdadbbaabdbbcbddadabadaddaadbddccbddbcabcbdbabadacadbdbdbbbdbbaccacdddcaabcccacacbbabbcbdcacaddbaccbbdacaccbacaddaabcbabdabcbddcdbcbbdaccccccaabdadcddbddcbdaaabcacacdbdcdcabaaaadccbbddbdcddccadbababdadbacdaaddababddadcacaccbbaddaddaababbccbdabbcaaccbdbbcbcaabaccadabdacdbbdabacadddbcabbabdbbcbabccccdaabdccdacbbbcccbcbccadbcbcadbddabadbadcdababbdccddadddcacdddbdadddcaaccaddcbddbddcccdbddacaccaaabcaabcddbacdbabacbacaadacaaadaaddbcbbcdacdaacaaadacdabcdbaabbabdcabdcdccadcdaabbcaccdabacacdddbaacdcbccbccccdbbcadcccacbddbabcbaaabdcadccbabadadaabdcadcccaccbcabadadcaddcddbddbdcdaacccdbdbaaaaaadacbcababaadbcdacadababaabcbdbdcbacdadccacaddaddcbaaaacccbbacbdbcccaaccdbadbabadabbdacabbccdcadabdadbbabcbddcbbbbbbbbbcdcabddcabcbdaddaadacdccadbcdaacbaaddbcbbbbcbababccbbcaacbaababbcdaddbaaaabdcbbcaacabdccccbdbbabbdacbbcacaddddbdbbcbaacaacdaddadddccacbbcddaacbbdcbcbdacddaaaaababaaaadccaaccdcccbbbcacaacdcbddabadccdaacbaabadbddcadbddcbacbcdacbcdbaabaabbabdaababadbddcaacbcdcbcdcbdaccacbbdbcdbcdbadadbdddacbcdbddcabadbaabbcaabccbdbdcaaadbccdadaadcabaddcddcbbccdcbaddcbddddbbccbdaadcdadcddbbdabaadbbddbaacadbaaabcccdaccaacccaaccdbcdaadacacbcacbabdacaadcdcaadcdccacdaaadcbbccbbbbacccdbddbddddcbdaaaaaaabdcacdabadcaacddaddacccacdbcbcacadabababcbccacccdcddbcacdadcbddbaaddddacaddbcabbadbdabddbcdbaabbcadcbadaaacaacddcbabbbccacabbadbcdabbbccdacbdbdbdbbcbdcddadbadbbbbccdcbacbcdbdabdacbacccbdcadcdbdbbbdaacadcbacacadadbcbdabbcdbbddcbbaadcddbcbccdbbcbbdaacbaaddbadbcaadaacacbcccbddddbabddcbbdbbcbadadcaddbabdcadbbbbbacbccbabddabbbaccdbbbbbaacbbdaddcbaddacaabdcacacbbcaadbddccaccdcabadddacbbbbbbbbcdcbcabdbbbdcbddbabbabbaadcdbcdccccacbcdccaadcadabdacdccabddbabccdddbbbaccacaacbbcbcdbbaddadbddadaddddaccacaaacbbacdbddbbddbbbdaabbdcaadaccbacbdcabbabcdabbbdadbacbdadbbbcddabdbbcbddbcdddacabacbdddaaaccbbccbcaacddccadccabcdabadbdcabdcddacddadacbbaadabdddcaaddbcaddcbbcaddbbaabaacccdddccbdbdcadcdcadacbcdcbdcacadcaccbdbbababbdccdccbdbcdbcbdddaacddabdcabacdadbdaadcaaddbbdbbdcdadabbbdcbbdbaadcadabbabbbbabdbcabddbdadcabdbbaacdbddaccdbbdaddbccdcadabdccdbbaddcdacadcbbbbcccdcdbbbdcabadadaabcaaaddacbbaadaabdaabbcabbddbaaacacacdaabcaaddcdaddadcdbadbcdadbbdcdbbaadbdacbcdadbbddadbbcadbdcacbcccdccdadbccbddbbcaadbccacbcdadadcabaadddbbcabdaacacccbcbbdacbdcbcbaadadbccbdaddcaccbabcdbcbcabbbccadbaadddbbddaaccaaccbcbdacabadbdaccbdcacaabaccdabbddbcdbcaaaaaccbdbcdabccaacaacbbaaccaadabacdaacacdcdcacabaabcadacdddcbcabdcabbbcaccabddccddbdddbabddacbcdcabcacacaabbababbdddbbdbcadcaabcdbaaadabbcdcddbaddaadbbbbccddbddbabddbccacdbccabcbdccabdddbcbddaddcdaabbbdcdacbbdabbaccddaaabaadccaacacacdaabbabcbbacdcdcddaaddcbbaaacbaabbabacbadbccdcdaabdbaaddbcddadcddccbbbbdaadccbccdacadbbbdcbdddcadacbaabacacdcabdadbcaadbcddbacbdcdbcdbacadbabaddabcbdcdcaaaaabbddddddccddbbbcddccbabadbcddabbabaccaacbbaddcabddbadbdabbcabcaaacdbbabbacbadddbdadacddbacbdbacbaabddddcddcadcbabadccbaaadcacdbbcdaaaccbcdddccbabbcdbbcdbcdbbddcddbcaccadcdaadaddcbbabbbdbdabacadbbabdacbbabdbaabbadcddbdaaddacdcccccbddcddaabcdcbbabcddaccccdadcbdccdcbddaabbbcdddbbdcddcaabbcbdbbdbbacdbabcaacabdbaddaaaccbcccdcdccddddacbdaaacdcabcbadbbcdabdcadabbbbcbaaaadccccddcdcacbacdadcccbbcaabcbbddbcbbadbcabcbcacbcaacbaaadabdadcccbbadddbccaaddabadaacababdcbacaacdcbccddbcbcddccdababcacddcbcacadcccaaccbbccbadddcbdabadcaaaabacacbbcbccbbcddcacbabcddcbdddbcdaacbdacdbccabdccabdacacddaabbddaddccddaccacbaaadbacacacabababbaddccbdabbbccbccdbacddccbaabbacccccbababdbbcbaadccccbbababbbbdbdbbbabddccdcaacaaabaacaadcccdbdbdacaadabcbbacbccdbcbddcabcbbbcbdbdcbbcbacddbdabdbcbcdcdccbccbcabdaaddbbbbccacbccabaadcbaaacdbdbcbddabdddbaddcadcbddbdbccdbdccdbdbacbbbdbccbbcdbdadcaacaccdaddbcdbbdacdaddddcdbacdbacdbbaccabdcacddcaabdadcbdbadcdcddcddcdcbdbcdbacaddbdcddcddbcbdadabababbbdabdcccdabdbcacdbbbcacbcacadcdababcccaddbbdccbabdbbcabbadccdaccadadccdcbcdbbddaabccdccbbcbbbacacbdddcabcbacdbaabacccacdccbcdcbccbaddbcdaabaabbdbbabacbaccdcdacdcddbbbcaaacdadddbbaddbadcbcadbcaaaddaacdacdcadadbdacddadaadadababaabbccddcbdcdbaccadbdcadbdcaccabcdaacdacbccdbbdcdcdbddbdccaaccacdbdcbdacbaccbaaacacccacdccccdbcbdaacbddcaacbdacaaadcbacddcddddbaacdcdbabadcadbddaacabdbdbabcabdccccacacbbcdadacddbdcbdbbaacdacbacdbbbcacbcabaacacaacbdacacbbaabdcabdaadbcacddbccbcacdbcadcadcdaabdaabdaabbbdbbdbbdbcdbabdcaddbbbdbbdccbdcacdadcdbdbdbbadaaaaccbaddbddcddcbdddbadbadaccccdcddbacacccaabdbddbbdbbcacbdadcdaaadbbbccdabbbccddabbbaabaccdabaadbdadbbcccddbcaadbacbadbaacccadacacdcbaaccaaccdacbbcbdacbcaabbadbaccccbabcacccdcbdacdddaaccdcadddbbcccbdbaddbdaccdcbbbcbaabbacbaabcdabcdbbbbcbdaaadcaccbbcaabcdbcabcbcbbdaddbcbbbaddcaaadacadaacaacdcabbbaddccbbbbcdbddddcacacbacabaabcbbbcbabaddccacbacdccdaccacbbcadabdadbcdbaadbddcdabcaacacbdcccabdcbbcdbadbddbcabbccccdbabadddcbcaababdacdadbcacaabbddcaadcdcdabccadcbddadbadabddcabbbdcbdcabdddbabcabdddbdccdbddcdbddaaddcbcbcdcabbabddbbadbdcbbaccadaacbccadaccaaadcdddadadcadbaaabdabaadbbbbcdcaddbbaaaaacdbccaabcccccbbabcbadbcbbbccbabbbbccdddaddbcccbbbabddbcbcddcddadccdbbacbddbbdaaacddccaabddbacacdddbbaddadadcdabccdddcbadadabcbdcacaaaababcabcdbdcaaccabdbcdabdccababcbcbbadadbcdbdbdbdcdbacabcbbcbbcdbcbddadcaccbcabddababcccabcdbbabddbbbdaaaabbadccacabcaccacadcccdabadaddcadbccdcccdcadadddbbcbbbdcbacaacaabddcadcaadbbcdbddbcdddbabdddaaabddaabbcadadabdaddadacaaadbcaaaadbdaaaabcbcaabdbbcccbaaaacddcbddddbbabbbabddbddcbdaabbabbbcbcabdcdcbdccdcdbdbcacdcabbcaacdcdaacbcabbddcacbbabcaacdbdadbbdbbbacdbccaaabdbdadbbdbbcdbdbcccbbcdcdcaaabdcabaadcacbdbadcbdcbddcbdbccbdbadcdcaccaddccccbdbdabcacddbadcdbdbddbccbacdbdabbcbbacabcaacaabdcacbbaacacadadbbccdcbadcbcbdacccddbbacbacadcbbcaddcccdbcbddcabddcccaabbcdbdbcdaaabadabcddacbdbccabacccaccbdbdacdbcbcbdcbababbacbcdaddbaabdaaaaddccdacbcdbcbdbabdcbcddaccbabadacaddaaacadcbcbacddcddaddabccaababcccdbbccadaddcdcaddbacccadcdcddaaacadbcdccdcdcccccadabbaaabdddcdcbdbacdcaabadcdbbbabddbdcbbccabddabddaaabddacbcbdccdbcaabacdbddacacdcdadcdddddbbbcbdaabacabaddbddcdabadbbbdbccabbbcbbcdcbacdcdccbdcabbdbbdbdadbddbddbbcabdbaaadbaacadcbcbbdddaadbccdbbadacacdcacbbddacdcdcbabddabbccbbccdcabbabccdddbdddaddaccddcbcccbaacddbacbcccdbcbababacbbacacacdadbbacadbaccbcbcaaddaadcbadddddacddccddcccdaaacbcbbadabcddadbdbbadcbcdbbbccbdddbadadcddddcccadccbdabdbcbbbcadcaabdabdadcdabaaacbbdcdcadcadbcccbbcabbbaddcbcbcacaccbadcbdbadddbacddccbbdaabbcdcababdcccccddcbbcdbaaaabddbdbbacbabacbadddaccdaabababbccdadbdcddabbbbdbcabacdacdaabbcbcbcdddbdababcbabbcccdcabadbacbbbaaddccbbaadbabdcccdcbcacbbaadbbdbcaacdbbbbbcbccacdaacdacbbcadccbacadbaabbcadcddcbbbadabdccabcdccbbbddaadbbacbacdccbdaccddaddabdcbdcbabacccbdccbdbdaabccabbbcbccbbaddcdbddbdbcadaadddcddddbdcbadbcddadbccccaaaabacdccdcaabcbabcdbadcabcabbbacbddbcaadacacccdcaaadbbddaccdccaccabcbbddddddadbcbccdbbdcbacdadccccbadccbddabccbcaaadbcbdccdcabacbacccbacbdbdbcbdaadbbbcccaaacdaadbcbbbbccccccdccbccadcdaccbbdaddabadbcbaaaaabdccddddcbdddcdadbdbbcaaaddaacaddddacbacddddcdcdacadacdbddbcadcbccabcdaccacacdaaabddcbbabbbcddaaabdcbadddccdacccbcddbccdcabdaaabbcddaddadbccdadcbbbdcdcaacdbddabcbabddbcaacbdccbdadaddaddbddbabaaabbbdacbcdaabdabbbcabdbcabadadacbbbdcbaddaadcbcddacccdcbaaadbcbdacbdbcdddbaccabcdabcacdbcdadccbbdadddadaaadccaddaadacbaabdadadcbcdaadcacbcccdddcbacdaabbbdbaabbaabdabddaacccdbabdcbaabccabcacdabcdddbacbabadbddcbdaaabcccdccbbdcbbcabdcbdabdacddcbccccabaaddabadcddbdccadbcbabbccbadddbabdabbddaababdadbaadcbadbaccabadcadadaacaaccdcdcabccaaaabacbbaccdacddddcbacddcbcdbccdcdcadaacaaadccabcdccccbcccbdaabadbccbbdbbdcaaacdbacccbbccccccabcadbbdbdccabbabdbbcbcbbbacadbdbadcadaacbbdababbabaabadcaabbaadbcabbccbacdbbdcbcabcdacabddacddbbcadcabadbadcaddcbbadccaaccabdabcdabddbbbabacbccacacbadcabaababcbdadbcdbdbbcccabbcddbadcaabddbcdcdbcccdbabaabbddcdacbccbcacaabacccddcbbdabbadbcbdaabacddaabdcdaadbaabcbdbadcaacdacbaacaccdacbcaaabdddbadcccbbdaccbaaaababcdbddadbaaadddaddbcbcacccddabdadbcacbdbccacdbacbdddbaaaababcbabacdbbcbccaadcbbadacdcaddbcdababbbdbcdbcabbcbbabdbbcdaadacbdabadbcccdcacbadbbdcbcdbdcbcaaaaaabaddddbcdbabcbdcadcdcbdccabcbbaccdbddabcbabbaaccbbbabacbcabcabbcbaabcadbacaccaaadbcdaddadbcaacaaccdbabcadbddacaaabaaaddacaddcaaaddccdcdcacbddacdbdbcaaabadcacdcaccaabbaaddcdabdaadcdcdbadbbdbdcddacbcaaccdabaaabaddccaaadbdddbbcdcbaacbcdcbcbcbbbccdabbdcaadccccadcddbabdcbabacdcbcdcadbaabcaabdabbacbbcdbaaacaaccabadacdbcddcabaaacbcccacbdaabdddcacabaaabdadadadcadaacadabcdbabbcdbadcaabcdabcbbdbbbaaabdacbccbcabbbdbddbcdddcbcdbbacadccdbccbdddbccadbbaadabcaccbbbdaadcaaacdacadddcdaacabdaacbdcadabcccadbacdcaaccbcbbaddbbdadddabdccabacbdadcbbbbbadadbbdcacdbcbcacbadddbdbacbdbbbbdcaccdacdbcbdabcbdbbbdddbccdcbbbdbcaadcccdcbcdaddcacccbbdbccdbcccabbcccbdacacdddaadbbdbbdbccdbacdaddcbcdccdbdcdcbccbcadaadacccacdcaccdadabbbdcdadcdcdbaccdacbbabbbbddcccdccbdbbcdccbcacddddcbddccbaccaddbaabcbcdcdbddcbbdcababaddddaacdcdacdbacccccdcbbccbbbddcbbcccdddcabcdcccabbdccdcdaccbcabbdcccdbdaddcbddccbdccccdddcacadcddbcdcbbaddacbdcdaabdbbcaddbcacaacccccbdbadcacaddbcaabbaacadadcdcbbccdcbadaacbdaacdddcacadbbddabbaccacddcbbbdaacbdcdadcbaadccbdabaacbbdacccddbabdcdaadbcdabdadddbbbbdaddddbdabdbadddccabcddbbaaacdbcacbbbdabccccaacacdaadbbbacdbaabbaaabdaaddddcabdcdcdcdabadaadacbdbcbdaadbccabccbadbbcaccdcddbabdaccdbbaadbabccddbbbabbaaddbdcdbbcdcaabcbcdccbdbaabcdbcddbadbcabacabcdccdcaaaadddcacdcadbabadadacbaddcbdddbaccbcaaacbbcbadababcdabbababacaaaabccbcddbcdccbdabaababacdcdccdccaddaaaccbadccbaddccbdaddaacabdbcbacdabdbcbbcbcacacadccabaaabcaaccaadbabbcbaabdcaaddccdbcacabbbabdccaaabacacdbccbbcbaaabcbbcdcbbcbcbabccbcdaaaaddcdbbbcbbdadaabcbbabacababdacadbadccbcadadaabbdadaabdcdadadcdcabcddcccdaccccabbbabdbdbcdacdaadbdaadcbccbdaacabcbadbadcbbcbdbdaabcdbbcaddbdcbdbdbaccccbbbdcdcdbbcccbdacdbbaabdcbacddddcaaaddbbcbbacabcbdbabdcbababddcabbacadadbacbdaaabbdcabbaabdcbadadbacadcadcacbabdbadcbdaccbaaadcbcbcaaabbcbbaccdbcbdabbdadaaabccadabbaddbddadbabccdccaadcbbcbbaacdbdbbbdccccbcddccdbcbdaadcdddcadddaadacdaddabddbdddbbaddaddbaccbaddddcaabcaabcacbcabcdbcadadaddccbaacacbdcbcccacbbcbdccaddcdcaaccdbcbcacbadababccacdbacbbcdabdaadbbdabbdadaabbadbbdacddddccbbbbaadaaabdbcaadaccbbddcaaacdbdcddaccbacbdbabaddbadbdacacdaaaccccbdacbbabacabddadabcddadbbadabdadcbaacbcaacabcbbdaadddddddacddadadaacabaccdabbcbbdacbddacbdaadbaacdbdcccdbdabcadddddcaadbbadcbcdadbabddbbabdbdcbcadadcdbbddbaabaaacadadaadcaabdcbdcccdbcabdaadbdaadccdadacbcadabccdbbdcdbabcbbccddbbcbcbaabcabbbdaaaabaacdccdcbaccdcddadbdcbaddddbcbabdbcaacaadbdbaabcacabbbacaaacdccccdabddbabbcdbcacddcadacaddccbdadcbcaabccaacadaccdbbbadaaccdaddcbbadddcdcabdcdbcdccaababbbddddcbbdddcdbcccdacbadbbbacdddbbcbbdbddddbaddbbaacaddccabcccbbbbddabbbbdbacacacdddcdcdbadcaadbaaadacadbcbcddcbccaccccdccccbbcbcbbddcdaaccddadcdcacbadcdbdcaacbdacbdadbabcdbcdbacbadcdabbcbacbccccdcdbbabccddbdcdbacbbbbccaaacddabcbcacbaccacbcdadacdbbdcbddddadbbbcbbbbdaaabdddbdcbddbdcadcddccdabcdbdbccbaaccdacdccabdbdcacdabadadddadadbabcccbdabccdddaaddabacdaccaabcbacdadbbaddbaacccbbdccbcddbaababbcaaabdcbccacdacdbbdcaaddbcabbdcacdaadcaddbadcddbdaababaccdaddbccbddbccbdcbbcbbdbbacccdcacaadacdacbbaadaacbcabbdabadcdccaaddbabcbccaacdbcddaabababcabacabdbbabcdcdbdbbccbcddddbcdabbcdaaacbdccbbdabdbbabddddabdbddcbbcabdaccccaaddccccabaacdcaaccddbcdcacccbacbabacdabadcdabbaccdcdddadaaddbcbdbbbcaacdbcadaaaaadbbabcacbbaddabaaccbabadaaccbccdcdadbcbcabbcbdbcddaddbcdcdbaabdcbbcdcbddcbccacbbcccacddbbbaacbdaddcccdacadbaddaacbbcbcccbbcdabcadaadbaaadccbddcbdbccbbbaabbbdcbbbcdbcbadbdbddacdacdaaadbabbccdcdbaadabbbcacbcdaccddddaaadabcbaccadcdbccadbcdcdbbdacdadbbadbdccaaabbdacdcccaadbcbbcabcbccaddbadabdbccacacbdccddabcadbadbdddacddcadddacdbcccaaadadadcbdbbbbbccaadbbbbcabcbcddaddbaacbcdbbaccdddadcbabacbddbadbbcbbccaddcabacabcdbadcbbaadaabccaaadcbacbbbacdbbcccacbbabacaadcccaddbbaaabaddbadadbdcaacadddacbddbcdccdcccabbcbdadcdcdaccbcdaacdccbaccdabcbbacacbcaacbcbbcadaacbcadcbbbcabdcacbaadbabbdacdaccddaaccaddbcbccbaaaaacaadcdbbcabdadbbacdcacaddcbdccdaacbbacbbcaacbabbbcdccdcbdaaaaacaacaabcddabdddbddabcdacbdcddbbabbbbbcdcadaccddcdacbadabbbcdccabaccbdaaddbacbbbbbacdcbdcdbaaaaddcddbabdbaacbddaccdbadaabbababdabadadacccaddbacbbabbababdbcbcbbbbbdccdaaccbbcbbdccdaadbadabaccdbdcadabcdddadaabaabdacdaccdbbdbddacacbcbabdbbbaabdaddcbcabadccddacdacabbbcaadcdcbdcccdacbadccdacccaadcbcbdadbcaaccbcbbdbdccbccbbddcdbbbdadbacbccbcaddaacadaccbbdadbcdcabadddcbddbdaadcbaddaccabbdaabcdcbcbacbcdbdaadccadccacdcccddccabcccadcbabdbacaabbacbaaddabdbaddadbaabcaadbadaadcdaaccbadacdcbcdbbbddddcabcdcdbdaaccabddcadababbcbcdcdcdbaadadaacddabddcbaccbccbbabcadbcacbabdbdcabbbacdaadddabbbadbadddaaccbcdccbdadcccccddcdbbbbbdaadcdaccdbdacbabacdaaadbcdcbbaaddababbdbdcddadddadcbcdcbabdbcaaabcddaabbdddcbaddbccddbdbddbbbcbcacdbadaacacddaaacddcaacdadaadcabaaabddabcaabbdabcadcaddcbbabcabbdccacdbcdbcdbdabccacbddcabcadcadbccabbbdbaacabcdabcccbacdddbdadddddbddddcdbdcdcdbcabaacdbdcaddccddaadbbabbbbacadccbbcddbcdaabdcaababacabaadcdbcabcbdccddbbcdbdacbbddbacddcdaaddddbbcadacdabacaaabcaaddddbdcdcbdaacddabcacbaddbabdadbcbadbbcdddcdbaddbccdbaacbcabacaaadabacabdcaaacbcbacdaabdcadcbaabdabdcbdbaacadcadddccbbdbbcabdcdddbdbbcdddddcdcbbbbbccadbccacacdcacbabcdbaacadcbcdbbdbaccdbdacdcabcbcddadbaadddbcbaadcacabacacbdcbbdbbdbaccbabaddacbdbacabcaaaabdadbbdabbbdababccadababbaababdbbdcababbddaddacaddabdbdbaabccbdcbccabdbddaacaadacbdbcbcbdccdccabbcccbcddbbbccabcaddaccbdbbbacadcdbcdaabdddcbcbbbdccbbdcbcbaccccdcdabacaaacdddddbcbbacdcaabaaaacbcdacdacddbbabadcbcbabbdbcdcbdbcdbcbcdcdabdcbaccccbccccddccaabbccddbaabdddcaaacdccbcbbdadcadabaccbbdbddaddabaddbcdbbabbbdcbcbccbccccdcbcbddbcddbdddbadbbbbdbabbacdbaaddddadacbadbcdadcaddbcddaadbbcaaacaccacaddcadcdbbacbadadcdadbcabcababbcddbdcdcdcdacdaabcbbaadabcabbacbdddaabcadbabcccacabdbdbaabdbbbccaddababbbadccbbbdacbdbcdbdcaaaacdcbaadccddadbbddcaccadadbdccdddbdacdcccabdacccdadcbdaabbdccdabadcbcbdddbcbddccaaabdcbdabdbdbbbaabcadcdcdaaaacdddcbaccbabccdbadddadaadcbacdbcbacbcbaabccccddabcaddbbadcbbdcbcdcabaacdbbcdcdbbdccbccacabaacdccbabaaacdacddcbbbbcccabcadaacabbcdccabbdcadcadbcacdbbcbcacdabdabdcdbababcaacaccbbadadcccdaaaaadcaaccddbdaddaadbcdcabccddacbbcdcdbacccdabdbbadcccbabdbabcbcaadbbbdaaaddcdcbabbbdcacbcdcabdabcdbcdccdcaacaacccdcbdcdbdddbbabcbdcbdcbcabacbbccbadddccdaccbdbccbcddababdcbccadccabbcdacdbdcdbddaadcaabccbdbbbdabcbcddcaccbbccdaabacadcaddbccbcdcacaaaccdbabbacabddbcabbdbdcabaaaaabdadaccbabbccadbdbbcbcbbcdbabadbcbddbdddcbcdddbabdcbbaccabbbbcacacbbddcaddccdaccbabccbdbdbbbbadccddcbacdbacacccdcbdcacbdcaabcaabcbadbabcbddbaabbcdcababadccaadbabbbddbadcdccabcdbbdbbcacccaccabdadcdcaabdccadaacddacbdccbbdacbbabddccaabccacabcccbcbabaccbabbadbcabbbdccdcdcbbcbdddaccacacbadabccbabbdaababcacdbdddbbbbcbcdadcbabbaccdbbabbbcbdbccbcbccdbabccccbaababccddcccadcbbadccccbacbcccabdbaacccdcccbcdbdcdddaabaaaadacaabbdacdcbcddacdacadaccdcbbadccabccbbcdaddbbcbdcbaaacbbdcabccbadacbcdccdcddadddabbddcddaddababddcacccbdabbcbbbaacdcabbbdcbacdbdabcdcbccddcbdbaaadaadddbbdddaadcbcdccdbcccbbbcbabccdabcbcddccdbbadcaaddaabcccacbdccbabccabbbaddabbbbbabbcdbacaccdcaadcdaccaabaccccbcbdcabcadaacabbbdcccdabbcdcdbbbcbdabdcabbbbdbdadcbabaaabbcaabdbddacbcaccaadcabbdadcbdbcabcbacbaaddcbbcdadbcdbdccadcdcdcadaabacdbccdcdcabddabdcadddbccdcacbdcbbbddddbdccccadccbadddcccbaddacbdcbbdadddadccaadadccdabaacabcdbbdbdcaccddbaadadccbcbcadddbcacadacaaacdadbbdabaccccdbdaadbbabbbbcbddcdcaabbcdbababaaaddaabcaaacdbdbdcbbabcbcdaddbbdadadcaddcdddaccbabccadbadadadaababcbcdbdaccbaadacddbcadadaacdcdddaababaccbbdbcccdccddabdbdacdaddcadbaadbccbbbbbacbadcbbabbbdcadacccdddbccaccdccadcbddccadbabbadaaddcdaaccdbaddaddbcddcaaacbcdcbdbbdaadddaccdacccbbbbcbdccbabccdaabdadaacddcdccdcbcacadbcbcabbbdcaabdadacdadcbaadcaadadcbcaaabdbbacdacbbbacadabcddbbacbbbccbddcadadbbcbbddabdbadacbccbabbbbabbccddacbcaaddabdbdcaccaacbcdcbaaabdbaaccbcdbbdadabccacaaaacdcdbaaccaabacbddadbacbbcbdcaddaabacaadbdbbdddabcaaadbacabddcacdacacabbaacabdccdcddcbdbbbdacbbadbdccdaddddbbabadabdacbdaddaddaaddbbabcbdbcccddcdcccdacbdacabdddaadcadcdddabcdcdacbcbbdbccaaacdbacbccccbbcdccacccdbbbccabdddabcabbacccbbbabdcccaabdcbcadcddcccddbacdaaaddbdbacababdcbdbcaacaadddbbccbcdabcbcaaaddadcccbadadaadccbcaaddbcbbbbdaabcbcdaddbcbaabddccaddacbcadaadcbdbbdbbcccbabcddcbcddccdcdbbaabbcdacbbbadaccacacabbbddcacddbddbaadddcccdcabdbdbbbdaadcabcdabdcadcbdbbbcabadcdadbcaaaacbcbddcdccabadddacbcbccbdbdcdcabbbabadadbdbddaadbcbdbdcbdbdbbacdddbbcbabcdcdbcbdbbaacabacddbbaddbccacbbbdacdbacbbccbcdcdcdbdaddaaddaacbdcbacbacdccdbcacbadaddbdadddbdbdadadbcaadcdabbbcdacbabacaadbdbcddccdadabddbddacbbbcccacccaddadcbbaaaccbccdcababdddabdbaaadccdddcdddaaadabdccbcddbbbadabacdcbaddcabdacbcbddcbcbdddccbcbccdabccdbbdcacaccaccdbccaabaccabbababaaddcdaaaddbabaaabddacacddabcabbaddcdbcdcbbdbdcacdababaacddacdbdaaadbbbaccabccdabcbaadabaadbbadadbaabccbbadbababdbdaccacbdadbabcbbdbaacaddccacccddaabbddbcdcdabdbbdaabbcaabdcabbbbabdaaacccadaababdbbbaccadcabbcaadcdccbbcccdbcacccbaabadacbaccadcaadaaccbaacbccadbdaabaabbbaaacdcdcbbaabdcaddadcdcdaddbddabbcbcadbaccadcdcaadcddcccbcbdddcbbbbaaaccdacaabbabadbaaabddcdbbbdbcdadbacdacddccbcdadccccbcdcadcacdbcacdbcdbbbdbbcccbbbccadabaaabadcbcdaaacadcababcddacacbbdadccbbdcabbadcbbbaddadadcadcbabdbdddcccdddbdbccddbbabccbcbdbccacaadbcdcbbddabbcaabcbbcccdcbccdbdacdbacdaabbcbabddddabccddacccbdcdcbaacadbdabbbdcbddbacaababbcaabbcdabdbdcacdddbcbdbdcabbdccacdbbdbbdbcbdbccbabaabaabacddacadaaccbaccbdabdcabcbdbacdbcbabddbbcccdadbbbcbbabbcdcaadbadcabcbbabcaccbcdabdcbbbcbbcdbdcaabcbadbbcccbdccbbdbdddcaaddadcdcdddcbcaccadaacbbbbbdadcbdababcbabbaacdcbadbbcdabdddaccbbbdddbbcaacdbabacbbdbcdbaadddbaacaadabbbbdaacdbccdcabcaddcbadcbbaabdabcadccacaabdbaccbddddbcbbdacdccbbdddcbcaadccbdcdbbcdddddacdcabccbaaaaabdccbdbbbdbcbcccdddadadbccbbdcbabacccdcbccdbbdbbbadabbaaabddbbdbaaaaabcbccabbbccdacbcdcdbbdadadabdbcccdbadbdbaccdadbaddcbbbcbbbdcadcdccccbdacbccdaacbbbaddccadbaaddcadadcddddccadbbaddacacaabadbcddbacdcdbdabcaaaddbdaaccbdddabcbcbabbadcbaabdbadacbdcddabbcbdacbccaacacbdaddbaddddacdaabacdaccbadbacbacdacdbccdacbdddcbdadccbcccdaacaabdbadbcacabacacabcbaddbaaacbcdacdcdbcddcacacddbcdcdaadbcaabaaabdbcdddacccdadcbddadadcdcbcdabcaaccabaacdabbcbbddbbcbadabcddcbdbacbcadaadaaccdabcbdadacaabadcbccaaccadcdcdadbbcaabbabcaccdbbbbaaabddbcdccabccdddabdadcbddddcadbdcdbdcbcacbabdbddcacdddbbdbbacbabbdbaacaaabdcaaaccadbcdcaadacacadcbddadcbdddbdcbadacbdbdcdbacccdcadcdabdabdbcbcbcccabcabdbddbbadccbdbabdbdbbcbbdbacadbcddbdadabbccdabdbacdadaabbdbcbaadccbdbabcaaaababbbbcdacccdbdccddadabdccdbaacdcadadccccaabcbdbcbcbdaaadcdacbaadbbcbcdccdaacdadaabaaabdbbdcbadcdadbbdbabccddacabbbdccdbbbdddcadcccdaabdccccbdbcabbdbdbadcaabcdbadabccadbbbacdcbccbaddbcccdadbbbddbcacbcdacaccbbbaddccaaacbaccccbcbadcbcddddccadaacbbacbcacbdabaabcbbccabdccbcdcbcadccdccccabacbbbabcdacabcbcdadaddbddbaabdccdcdaadbbbdbddaacbbbabcbbbaccaaaccdbaddcdccabbcdcccdcddaddbdaddcddaccaadccacdddccbbbdabdbbcbddbacaacccaaadddcabdbbaacdaacadaccdcdabcccdaddacbdcbbbbadcbdcbbdacacdababcbbcdcdcbabbbcbaabcbdddaadcbdabbddbbdaccbccadabcdacadddabacabbcbdadbcabbdadbbbdbbdbcbddcbabbcccbdacdcbbbddbbbcbddaccddabadbccadbdcabdabbbbbadbdadcbbacbcdddaddccacdbccbccdcabdbaabcbbdabbacbcaaccdbccdbdbbcdcadbaaaddabbcdbbaabbccdbbddbbabbccacabcdcdcbbbdaadbdbcbbdaccdcacdcbaccadbacabcdbbddbacacbdbbdadbdabadadadbcdddabbdbdbcdcacdccbdaaddbcaaacadbbadcbcbbccabaacbbaaabddbddcddddddcbbadbbbdaccbbbbbbababbadaacdccadaabdacbcddadcdbdadbcaabcbdbacdcaabcabddacdabcabbbdaddbcbbbcdbabcdabaaaccddddcbbaabcbbdaccacaccdcacbdccbbbddbbdccbbdcbddabdbcadcbddcadadadcdcabbacbcaadbbbdbcbdbcbadbddbaacbccdcccbccdbbaacabcccbadabbbbbdbcaccaababdadbacadcbacabcaddbabbdacadbabadabcdacabaadccadcdbabaaaccbcabaadccdccdbcccbcababcbadabbbdbbbcbacddaaadcdcacdbcddccbadccacacbaccddbcaacbcccdbddbaddcadcdcdbbaadccdacbabcaccccbdbadbacccdddbbacdadadcbbbbababdacadaccbcadbbbbcadababbababbdddccddbadbaccdcbbcaccdbcddbbacadcababcdaadabddbabbadbbdddabaabcadddcaccbbaddcdaabbadcdbccadaadabaaaabcdabaaaacbbbbcababbabdbbaccccdabcdaaddacdcdccaacabbacbaaabddddaacadddcbddaaaaacbcdbacbbdbabbcadaacabdcccacaccbabaccdaabbdcabcabadcccdaabbdadccbacaababbbcdcdcadabdaaacdaadcbddcbacabccbadbaaadbcdbdacccaccbdbccddaadacdabdbccbcbdbadcccbadddcadccbbdaccbabaadacaadcdcddcbdcbcddddbddbacbcbbddbbaddcbddbacacddcbadbcddbdcaccdbdccbdaccaadaadcdbaadaccbdcabdccbcbdbadddbdaddaddcbadbcccabadadadbaacccbdcccaddcddcccadbacaacdaaaaabdaacdcbdbdabcdbbaacddaacdbcdcdbbdbddcdccbadaddabdbbbcaaabacbbbbadadcdaadbabbaaccacbbaccbacbaadabbdacaccdadbabdcddbbcbbccbbcccaacacacbdddaadbbcddbdabcdaacbabddbccccddcbacbbbbdcabddbcbaddbbdccbcccbdcbdaabbbdacbddaadadccbbbddddcddbbddabccdccbcddbabdabbccdcadcbbadbbbbbbbbaaabcbcbabddabbcacbaaadacbadacaaddbcbdcddbdbdacddcabdcccdadadbdddbcacccbdddccdcdababdcaabbaaccdcbdbdacaaabaabdbbdccadccbdaccabbcbabddcdadadbbadbadcbdddbccbaaaadbcaacbbbdacadbcabdabccdcdcddddbccaadacacdcccadcdcddadaddadaaabbbbddbdbacaddcddcadacddbcaddbcbcacbaadadacbcbdcdabadbbdcbcdddcbcbcdbcdbabacbcbddccbbdbaaabddccbbbbdbbacddacdbdbbbacddcaaadadbbbcabcccdaabdbbadbddcddadadbdccbccbbcdcbbcdbcadcaccbbadadbabbdbbaabbdaddbddbbbdaccaaabddabbddacbbbacbbdacbdcdbccddccaccabbacabccbcddacdccaccaacbbbbccbcbcaadaabdbcccbccdadcbabbdbdaaadaabcaadadcbaacdaacababcacbbcabaacddcbbccddacddacbadbcdcdadbbbdbccccdcabadccacabbcdabdbbdcdbbbaaadcaadcbcdcacbcdbaadaadcbcdcccdccaaabadaddbcadacccacddcadcbcbbcbbbadbccdbaaddcbcabaaacbbdcbbddadadcdacdcbbdddcbdaaaacacbbcdcadbdbdccbdacdccbcbcaddcbdbdbcababbaadabbbccaacdcbbacbdbadcbbcbcbcdbcdcabccbcbcabcdcdbbcbbcccbacacdcddaccadbacdbcadcccbaaddaacaadddddaddbbbcaabcdbccabaaaabbabccbaccbdcbacbdcbcddbddbadcabcbcbbdbbcdbddbdaccbdadcbbddaccdcdddabcacabbaacbdabcabbdbcbabbcaddaaaddbdacaaccabdcbdcdcaccccabdbdaddbcddbcaaaccccadaabaadbcaadbdbbdaddbdddacccccbcbaaddbdadaabaaaaadcdbbbcadbaadcdbcbcdbdaacbacaccadcdadbbcddaadbcbdaaadbbbbaccbaacbdabaabacbbcbabbcacbcdaaadaaddbdbabdacddcdaabbbdadcddcbcdbbbbbbbdadbacaacabcdadbdaadcccccdccbdccdacaaddabccbdbacdcdaabccdadccccdaabcdcadddacbabcdbcdbcccdacdbbdcaabbdbaaabadbcadacbcccdbabacbbddbbddbbdabddcaadddbccbbaabddbcbccbddacadcbbbbaaaaadabdaadbdaacddbcaacdbbabcbdbcddbaacbaaaabcabbcabbbcabaccdacaadddbcbcaccdcbdbdcbbcadadadbbdddadbabccdaaadbbcdabbdbabaccababbbbbddbbdddbadbcdccdacdcddddbddcdbbabacaabbcdbbabbaaacbcdddddcbccabbcadbcabacaacbbdbccaaaaaacaababababdcacacaacabbacbaaddcdabddaabbcadbdbdaaaccdcbbacadabcadbcadaabdbbabcccababbddcdcacbdbdcbdccdbcdcbcdacaabbbcdcbbdabadabbdcaaabdaaaccccccacbcbddcabaaddadadccbaddcaababaadbbacdcddbcdddcbdcddccaabcaccdababaccbdbdcaaacabcdddbbbadccbdacbccabbccbbaabdbaabbcddbabcdcddbbabbababbccbbacaaaddccadcbacabbbcaaccbacaaaadacacaccbaabcabcaadbcacadddddabbdccabcdcbbdbcdddcddbcadcabbdddddcdcaddacdcbcbddcddacadbcdacdcaacddcadcadddbccdbbadacdcacdbabbaacadaaacbcaaaddbabccadacbdbcaadcadbcbbcbbcccbdccbcdbcbbbbabdabbbdbbaccccccbaaaccabcbbaccacaadccccaaacdbcbdacabbaccaddcadbcabadcbcbaaaadcdadddcabbbbbbabbbbdadcccadabdbadddbbbccaaacdbddcccacdbcbcdcadbcacacadacdcbaadcacaddaaddbccbcdbcbdcddaccadbabdabdddaabcdbabbcbcdddacbcacdccbcadcaccbcbbdaddbaaabbbaaddbbccabbbbbdbabcabdccdccdbadbcababbcbdadbbbdddbbabbadadabacbdcabdcdcbcbcbaadcaddaddcbccdcbadbccaaaadcdbdbaccbbbaacabddbaadbbadddcadadaaabcbdbaddcbddbadcdbadbbdcacbcccbdddcacacbddaadbaacadcbabaaabacabccccbccbdccdcaadbabbaadcaaababacccdabcdabbacadababcdacaacdddbdccacacddcbdcbdabbbbaccacddcbddcbbbacaaccacccdcbddbbddcbbababddcdcddbcaddcccdcdbdaacdadaadccaddbdbadbbddbccbcbccaadaaacbcaabcbcacdacbbaccbaddcdccddcbcdbdacbaaccdcbadccadadddbaaaacabbcccabdbccdaaccbbcbcacdbacbdcbbaadbdabadbbbbcbcdcbbccacaccbdadbbaaccbdacaddbbdcdcbdcacdbbbdbcadbabddbcdddcdadcbbdcbabaaadbcaacbbbdaacdbacbccdabcdccbcaaabccacadadcbacdaacaddacbcddcddbcdaadcbbbabdbcdaadbabcbbbababbbadbcdcbacdbbacbdcdcddaaacadcccdbabadbbddacbacbbcacdcdabadabaaabdbdaabdbdaabadcdadacaadbadacabcacbdbaabdaccddcbbaccaaabaadbbcbbaccacdbbabcdabaadbcbccddaaabbcaaadcaadccbaaddcddbbababaaaacabbbdddabcddcdbdbbdcbcddacbdaadcdcdddcbaadcacbcbcccdcbccadccacccdddbaccdcbbcccbdabbbcdbbcadabbdbcddaacdbcddabcbcccccdbcbbaabcaadddaccdabccbaaacadbadbacdbdcaccdcbdcdadbbbcaccddddcdaacadbbaaaadbadbadbcbbdbcbccbabbbbacdddcbabbcacabcddaabdbadbbdacccdcccaababbdbddabbdbbbaaadbccbadcadabcdccaccbccaabddcabdaddcdddddccbccbdbcbcbccbbbbccddccacdcccacaccbdcabccdddbddabdaddabadcdabdcdbbbababccdbaacacaabddbdccbaabcbcaaabcdcbbabababbbcbaadacabbcbacababdaadbcbcaabbdbddbbcbbbabcddaacccddccadabaacdbccadaabbcbbdbbaccdbdcadbcaabcdcddadccdccbccccdcbaadcdbbcccabacacacdbcabbdbbccdddcdcbcbdddbaaccddaadcdcdcbabcaabbccdabbbdabcdbdbbcbbddbdbcdaaabbcaccbbadadcbcaabccbdbccbcbbaabbddcddcddcdbbdaabcdbbbcbbcadabcbaccdbccdddaccaccabbbbaaacdbaadcbbdcbbdccdaadccdcdbbbdaacbddcaddbbdaddddacabacbddcddabcdbbcbcbcbdcdddcbbadcddaccacabbbcbadbaccabcdcdccccacdadaccbbbbabaadaadadcdbbccbcacaddacaaaabdcbdcacaadbacddadcbbdadaababdaaccaabddcbabaaabbbcdcddbacbbdcdabadcaacdddcddaccaccbdcababbdabacabcbdcddacabcaabdddcacaadccddccadacbacaaabacbcddcbaacdcbcddcdbbabacbbcadddddbdbdddacdbdcccdbcdcdcbbbcbdbdabddaccbbcbdbaaacacabdccdbbccaaacaacdbdccdbcccaacddbaddbcaacabcacbacabaccdccdadacdbbcbaacdadbdacdcbccddababaddbdabbcbaaabcaaddbcdbcdbccacdbcdbcccdbcadddaabacdaaddbcaccbabadccaddaaccdaccccacbaaabdbbcccbdcbdbdadcdcccabdccbcbadaacccdddbabbaacbcbcadabaaddccbadccaadcbcbaaabddbcbdbacdcddacccbbaddaabbdabaaddabbaacddbccbdbddaadacdcbaccaccbcadabbccbbcaacbccdbcbcabdcadbbdbbdcdacdaaacaacbbcdcacbadacbbdaccabaacadaabcaccdbcccbadcaaacabddcbdddaccbbcaddbdcdcadbadbdbbdaddbbabcdbdcbdbdbdacbbbcbbbcccbabbdbcacccadabbdcabbacabccaddababdbadaaaaacabaadcabcbcdaaabdbabaddccbbbadabccadabdacadcadbcaadaaadacdaaababbcbbddadbcbbcddadbdcdcaddabcabbccdbbcaacddcabbaababcabbabbbccabcababbccaddacdadaacbccbddbbcacadcabadabccbacbaababccaccbdbadcaddbdcdadbdbacdcabcacbbcbcabadcbbbbbcbadbcbbadbababbcdddaadabcadadabdbddbbdadabdcbbdcaabddcaabbddbababcdadadddcaabcaccbabccdabdcdbaacacbdabdabbdaadcccbbdaadabdcdcccbaadaadbdadcaadcbabdbaaaacdbcdcddddddcaddaaaaaaaaccbaabdaacadbacabdcccbbbdabbdadabaaaaacaadaddcbcbbaabbaacaaddcaacbcadcaddacdccbcccbbcaadaabbbdccaaaabdabcaabbcdcddcbbcdccacadbadabcddcadcbdbbdcaacbdabbccbcbadbcadabadcbbbddcadbdccbcbbadccacacaccdcbbaddbaccbaccaaddcbdbadcaabddddaddddbaddddbcdbadbcabdbacadcaaaaacbcadacbcdadadbbaadbadbdccbdbdadccdadadacaaccaddaccbdbadbabaddbbcabdccbabacbacaaaddabbddddbdbcbbcabbcaaddbbabdaadbcbbabadabccbcddcabacbcdabcabacadccadddacadbacbccaaababdddaccbdbbcacbbcbabcaadcabbccddabdadadddadabdddbcddabdbbbdaddbcdadddabbbdcaddcabcaaaddcbbddcbbdabccacbbbbacabdabcdaacbbbbcddbabdabbabbcaabadcabdcbaadbadcdbdbcbcddaaaccddbdabbccdadcabacdbcbaaadcccaabcbbbdacccbabcdbdbaadcdcacddbdaadcbdcbcacdbdbbababccabbcbcaccacdbabddbcaddcaacbacadddcdccdbbdbadacbcacadacbadddacdcbbdcddccbacaadbbbccbddcbdbdacbdbbdbbdaabdbabbcbbadaddaadadacdbdcadddccaccbdbdcbddddadaaacdcaccdadadcdcbacdadcdcddbbcdcdccbbdbbcacbaacdccdbbacccccbbdabdabdabcdadaccbdbbbcaadbdabddcaaadcaaabcbbdadbdbbcaaddaaabccbadcdadadccdcaabdbbdddbaadcadbbbacdcbaaaabbbacaaaccdaabaabaaaadaaaacbaccdaadbccdabaaacbcbdbaccacdddbcccacacaadcdbbabcbdddcbcaadbdabcaabaadababbdbcacbdaaccdbaddbccadbbdddbbbcdbdcdcabadddacaadccadcbbbbcabcaabcadcdcbddaadcbdbcaacaaadddbcbdcdbacdbaadcacbdadadcbbdcbdaabacccbcccbcbbcabccbbccdcacabacdbaacbdbbcddcdbbcbaacabbcdbdbdbcdaaabcbcacdbddcbcdcdcadaabdaadcddadcdcacbadcacccadccbbcbdbcaacabacadbaccadbaadbcdabccaccddccdccadbbabbdbcacacbabbddbabbccbabddbbacbdddcbaddbbdabcdbcbcadacdcaccbcadbbaccacaabcddbaabdabaccacdddacabccccddddcbddccbaabbdcadbcaddaaadbccccbadcbaadabababbaabadabdabadaadbcbbccccddbbadcdaddbdbcadcdccbbabacbcccaccdabcddcbbbabbbcacbcbabdaadccdacaccaabbcbaabbadabadcbcabbdadbdbcbaaaacaaaabdcdacbabaabcdaadaaacbadaacbbbbbabacccdadbdddccabbbdbddccccdadbdbacadcdbacbbbacdccdddbacbcddbadbacdbadddbbcbbbddbdcdcbbdadabdaccadaaddcdaddcdaacdcccabdacddadbbbbdbbcdabcadadbdbbaacbcbbadcdaababcdddabccddcacadbdbaadbbdaadcadbddcccaacaccacacbabcbcdadbabbccaadbbababdcbdaabdcbcccdbcccacdaaccbabbcbaaccccadcaaddbabdbdbcacabaccdcdccacacaccdbdccbbaadddcacacccbbaccdcccdcdacbdbdcdddacbacbdccaaaaacdacbacdbbdbcccadcdaddcacacbbaabddadacbdaccadddaabddbcbacdcdbdcdacddaabcacaadddacdaadaabbcbcaadddbdbcacabcacdccdddaacadcbdbacbdaccddccbadcbdaadbbbbcbcbbcadbcbdacacadbadcddadaadcccaaacababacdaabbdaccbacdbbbcabaadbbbccbabdaaddacbcddabdbaabbddbccdcddabccaacdccbbcaadcbababcabbcaabaacbacaabdacdbdabdcbabbbcbdccbdcbbdbdabbcaccadabccdbdabbdbbaacdcdbbbbbdbccbdcaadaaccdbbcbaacdbcccdabababccdadcdcccdbbcabbcbcdccbdbaaaaccadcdbabcbddcbbacbdaacaabcdabcdccacdbabccbaaabbadcbdabacbcdbabcadbdddaadcbbcbcbdcdbaccdadaddbdaababcbcadcbaacacddccdbbdbdbaccbadbacbbdddddddcaaaaacdbbbccbcdcdacabbbcbaabdabccadcabddccdddcacaaccccccdbacbbdbbcbaaadbbdadcbbdbdbdbccbadabbddacdcddcacaadbbaddbccadacdacdabbabcccccbdbbdcccbcbabadcacdccdadbdabaadbaaadacdbabacdccacadaccdadcbdadacdccdbacbdbdcdbabcadabcaccdcbaacdbdcaaaddbddbccadcddbddadccccaaabdadadbdbcdbdbdaccdbbcbbbbadbcbbcbdbdcdaccdbbccddaadbcbccdaaddaddabcdadadcbdbbbdaacdacdcaccbaabcbdbaaaacadabacdbabaabdabbdaddbdddaddbdcadcbadacddababbabdcbaadccddbaccacdbcbbbdbccdcaccbcbadbadcdccdacadcbdcbbcadcdbbacbccddcadabcbcdcdabcdacdcabcdbbdabacacccbcdcabddbbdbddabddbbbcadabbbdcdaadbbbcdadcbaabbcdccbdaccdadbaccaaaaddbbdccbcabcbabdabcdbaadbcbdcacdabbbddddbabcadcdadccbaabacbccbadadadcbdcbcaaaadadcaccbbdbbbabaddcaacbbdacadcbbacbbadcbdbbbaaccbbcddbddacabbdcbcaaddccadccabbccababcababccdbaacdaddbccdaadbcbbdadbdddbdbdbdadbadbacacadbcacdbcacacabcbbdcbbcdaadaaabcacacaccddbccabcbcaadcbbcdddccaaadbbbaaccaaabbaccdddacabaacaabbbdcabbbdbbbcbadccbdacdbaacdbadabbbdbddcadccaabaddbacdbcccbbaddbdbbcadaddddadccacdbcaaacabbdccbaddabadcdddbbcddbbbbcddddcaddadaadcbadaacbcaabdbdbdbbaccaaccccdbcddaabddaabcbacbcbacbdcdbdbbddaabadbacbcbbaaddbbacabcadaadcbbbdaadcdcaabcdddadaccabddacaadcdddcbddaacccbccadcbbbacdacabbcccbbdaddbadcdddbbaabdcacdadcdadacaaacbddaababcacbddbabcaababbcadabbdbacdbdccabbaddbaaddcdbbbabbddbabcccccdcaddccaacbcbbcaaaccdbdaabddddadddcaaccdabdbbcadbacddadbacbdbabcbdcacaacbabccddababdbbccbddadccddaadddadddcdacaacdcdbcdddbbccacbcbddacdbcddaccaadbdddcbaaaccccbabdcdbabdcccbabdbbabbbbabdabacbbabdadadabdacdaaacbddacdcdbdadbbadccaddcccdcbcbcbbdadacbdadcdccabbacaccccbaacdabdacddacdccdccddabbdccccbadbbcccdabdcddbaabbabcbbaaaaaddbddcdcccacccbcdadddcdbcbccbadbdcbabccbbbbdccbacdbccddcadcbbaabaacdaabbcaaaacdcdcbddaabbdbcbcabcabacacdcccaaacaabbdacddaababaacacbdddccdbddaaabaacbcbbcccbabcbabdcbbaabbcdadaadddbdcdbbbddabaccbaccbbddabacddbbcbbcabbaddcddadabcacbcbcbcdcacdbcbbccbbbdacdbabddccadccccbcbcdcccdbdcccacaacbcbdbaabbdacacdbaadbbbadacdabaccbadbcdabacdacdaaaadabaaddbdaccacbccadcaadabccbdcdbbdaddcdbdcbbaacbacaadbddaccbadbdddddabbbbabccdacbcabdbddadadbacddbdbaccabacbccacaaacaadccadadbbacdcdaccacdcbadaadbdadcacbdcabbaddccaccaaaccdcaadbadcbbcbbdbcbdbcaaadbbddcccccabaadbdbdddaabbddbaadcaacddbccabcdcbbaabadadbcbccddddbcbdacaddbaadacbabdddadadddaadbcdbcabbdbbbddcbbcccbaacdbadcbaadbadbbabaadbaadbadddcbdaaaadbdbadcdcbabdbbdbdddbdacdbccbdddaccadbabbdbbbabbcdcadbacdacacbbabdccbddacaaaccacabccddbadbcddcbdbaabbabddbacaabccacdbaabbcacadcdbadaddacdaadacaddcaddcbddbadbddddcdaccaaaaacccccbbaaaaacdcddcbdbcbddaaddbacaadbaabcdbaabcbdaaddbaccccbddaacacacbbbdbddbabddbbcdddcbdcbbdacbdaaacabbdbcbcdaddbaacadddcccddddddcdaccdababcadbaacdbcacbccbddbbcdccbdcdccbccbdaadcabbccacbddbaaaaadacadaddacacabccdcdddaababacbbbdabaccbcddbcabadddbbaacabbbabbccadabddcdacacbdbdcdcbdacddbbcccdccbadbbaadacccbabdcbbdbbacccbddccbcbcaccbacbdbabcbbdccdaaabdbdbdcdcdbdbbadbaadbbadacdaccdbbcdabddddabcbbcbaababbcbccacdcbdcbbcaaaaabdabdbabbabacdbacddddcddbadaacbcbccdbcdcdbcababbbdadacabccdcaacbcacbddcadaccadbbdddaddcbcddcabdbcacbbbbdbccbbdbcadddddaacaaacbbadbbcddadacccadabcdbbddcaaacbaabcacabaccaabcaadcddbdcbbdadbabbbadcaacbccbaaacbaddbbabadadbbdbdccdbdacaaaadcbbcdaadcbcacbcaaabcbdcdadabcaabbdbcbdbaaabcdcadcbbdddcbadddabdacdaaaacddddbabacabacbadbcbdbabdcbaaabdabaabddadcacdddcddaaddbbcdbbddccdacabcccccdacdcadbaccbbcddbdcacaacbacbcbcbaaacddcdcaacddadacbbaaadbdcadaddaaaabcccbbbccadccaaabbabadcacbcdabccbcacddcdcdbdaaaacdcababcdbdbbabbdddabccbbcddbababddcccbbcbabcacacadccdcdbdddbadddbcbcbbbcddaddbcbcaacbadbbccaabcbbddbaaacdccbacddcacdcabccbcdbdcdbdcbbabbadcbaadbccacbcaddaddbddcdbdadadacbcdcccbccbdbcbabadacbcdadabbacadcaccbbadbdbccbcddcbcababdacdacdccdadabbbccccadacdabbbbacbbabacbbaadcdaccadbbdbdcdbcadcccacbddccdaadcaaccaaddadabdcccaaabccbbdcdccbbdbccadbcbbdacbdcadcadccbbacabacabadcbccabcddadcbbbbaabdaabadcaadabacccababacbdcbadbcbdbabaabcabccadaacaacbdccbcaadcacacdcbddbccccabccccbdabddbacbdbdbadccdbacaacadaababbbbcaabbbcbdbdadbddcdbdcdccddddcccbcbcadabddbcdddabaabcadbabadbaccbbddbdaddcbaacbabdddababbbdcdddbcbbcdcaddbcbdaaadddbcdbbdaddadccbcacbdcadbaacccabbaacdaadbdabdbcdcbdaaabbcdbcaabcdaaadadabbdacaccbccbcaacdcacbdadbdadbadbbcabcacbcbddcddcabacbabacadabcbcccaadbbbdbcbdcdcdbabcababccdaccdaccbcbbaadbcdcaabbdbcbcaadbcdbbccbcbccddbbbacaddbddaaaddaccaabacbadcbadddacccbcacdaddaacdcbbadabdcadddacbbddbabdccadbadaccbcdcdabcadbbbacadaaaddcdbabcdcaabbcbbddcabddcdbbddacabadbcdcdacadcaadcdbbccdacacbddbbbccbdcbbdcbdcccbbdadadacadcdabbddbdabdcdddadcbcdbcdbccacbcddcbbdadcdadadcbdbddacbdbaacccdbcaacdcaddcaddbdccbadacabadcabdbdcdadbbdbbcdaadbdbadadbcacbaabcbbcdaaabaabbabcdcabccddadaddacddcdbbddbcaabcbcbdbacdaacdacbadccbcbdaccdbcdddaabccbcbccccbbbabbaccbdbaabacdbcaacabbbccddabccccdaaccaaaaaaacbccbdaddaaaadcddccccabcddadcdcbbdbadbbbadaddbaaabbabacbdccbbdadbdcbcaabaabdadccadbaddbbaabcabbcaaadbbcacabbacbdbabdaddbdacdacadadbbcdadbbcbdadaddacadcbbdbcbabccaaacdbcaccacadbbacabbbccccdbadbcdccdbadccbbddacbcdcdabdccdbdaccaabcccacaabadcdadacdaabcddbcabbcdaaddcaaaabbabbadbaababdacabbcdbdbcaaaddadbdbdcaaaabbddaacaccdcdddaacbaacccbcbaabcdabbabddbbabaadbbcbbddccbccaaadcbdccbcbbdcdbabddddabbbddcdcdbbabbdcdbaabbddaabdaaaadadcbdaccbdabcbcdbdbbbbddabcdbbdbabdcdaabdabbacaadbdabcdcaabcbaddbbabdabadcadadbbcbcbcaadabdaacdcabccbbcdcacdacbddcccccabcaacbdaaabdacbccadbabcacabdcdcbdcaaccacacdbcbadadcddbbdccaaacddaccbcdcbcdddaaacaddacacdddddaaddacdcbaadcbccdbbbcddcbbacbcddbdacbdbdadadaacdbbddcccaccbbbcdccbccccbaccddddcadaccbacbdccbacbdcaccccadcbaaddccbdabdddbdbacaacdbaacccbbacdcccccdddddaadadbadadbdacdaacbdbaccacdbdbbbbcacacddbbbcdcaccbcdcadbdacdcbbaabdaadaccdcccadacadddcbccdbddacabcadabcbbdbddbcccdcbdbdbbbdddbbdddcabbcadbcabcbabbdabdcdbddadcacabacacaadddadacbabcbcbabacdcbaadbddcbbccaddbdcaadcabdbbbdabbcbbaaadbcccbaaacadcdaacdcdcbaddcabdabbdcbdcdabacadcdabdccaaabcacacbabacbabbababcaddcbdddccbaaccdadcadabbbadccbbccaccaacadbdccddbdcdaaaccbaddcbabddaaacddbabdbddcacccdcdbaddacdbdcdcdacdddacaaaaadcccbdddcddbcaddcbaddcdddacdabaaddadcbaacbadbbaadacdddadbacddadbacccddbbadbdadabcddbcddaadacdcdccdbdacabccbbbadddbacbaadcdaacdcbaabaaadaaccddabdcbadccacbbdaaadadbcbbdbccdbadbcaccaabddbdcdacddaccbbabbbddabadaaabbaacbddccabcdddccbacaabcadbcdadbcbabcdcadbaaccbdccabdcbdcaadddcadbaadbcbababdbbadccaccdcddadbaacbbdbdcbdbdcabcccdccbadcbabddbccdbaacdadccabbaaabdbadcacacacaadcababddccbccabccbabacbabbccdccaccdbcdccbcaacbbddacacbbaccdbdadbcbacbcabbaadaaacdbbbaabdccbadccaddbcdddddcdabdbbbdbcadccddabccbdbaabbbdbccaaacbacdcaacacddddacccdacaaadcccabcbcccbbbbabcbdccbbadbdddaabdcccdaaacbcbcaaaacbdbdbabbddcaabcdabdbcabadbccaccbbddbccadcbabdcadccaccdcbadddcadabcabacbbcabddbdcdbdddaddcbccbbbdccbbdacaaddadbbbbbcdddabcddabcdcdadbcbccdcdacaabadaddabbdaabccdbbacbbccbbbadacabcabaddbddadabbcbbbdadbdbdbdabcdddadccdbdccabcdbddcbdaadbdbcbbdaddccbdaaddadbaccccacacbdcdddcbddbcdcccdaaaabbbadabcabdccabdbabdadcddcbcabbccdadabbbaaadbdbccbacabddbdcbaadbbadbadbcddcdcbdcbdadaccaddbcbdabdbddcabcacabccdabaccdcbbcddbddbababbdbbaaaacaaacacbacdabccaaaddcbbbdadccabdddabaddcbdbbbdbdaadacbcaddccdbdbcccdadaccaccbdababccaadbadbacbbabdbabcdcdbadcbccaadaabddccabdbbabbcbbdcbacdacbccccbcbbdbabcbadadcdaadcabacbbabadddababacbbbdbbbacbdcbcbdccbaddddabdddaddadbbadacccaaccbcccdccabddababddcbadcabaacccbbaabbdcbadbbadcdcabacccadabbaabcccdadcabacdbadcacddbdcbdcbdcbbddbcccbabdabdcabdbdbcbaacdcdcaacabdaacbcbdbbdaddbdabcaadababacbbdbabddddcbadbadddbdaacdbdccdabcbcddabccccccbadadbbbadaacdcadbacdbbddbdcbdabcdbdcacbccbacbddbbccabccdddcbabbcacaacbdabaadabbbcdbbbdcaaacddbabbaabacdbacbddabddaccdaaaaddcbbdabccacbdddabdaddcabaccacacbadbabddcbabaacdddcccccbbbcbcdbadddadbbbdbaabbbbbdcbdadacbabbbdaadabddadcabbddbccbddacbcdbbddcbabbcdaacbacbcabadacbaccbdcaaddcabdcdccccbabbccdbaddcacddcabcbbabbcdbadbbacabdbdabbddbbbdccbadbbcabdcccbabacbcbacddddbbcccbbcaaaabbbbcbdbaacbabdcbccdbcaaadccdaacaacadadbbbdbdabacbccbbbaaaacaacccbcbadbbbdbccadadaaddbddadbabcdcdbddbcddcbcaaabcbbaaadbacadbdacdddccbaaddbbbccaaacdcbdcccbadadbdabcadcbdadbccdddcdbacdddadaabdbbcdcdadacaadaacbcbccddddcbaccadbdaddacbddbacbcccdcacacddadcccddaddbacaacacaccdccaabacbacddcbdcabaadbaaaacbdccdacbcadbacdcdcacadcdabcbcacacaabaadcbbaabdddacabddcadcabbdccaabbdbcbcbdccabcbbbcdbbdcbbcaacdccadbdbcdcdaacbaadcaadbaabcdadbdaabadbbcdadabbbcadcddbbddacddbcbbcdadbccadbaddccbbadccdbaacaababcbdadbdacbabdbdcddcabcacccaaaaaaccdadacdbbabadbdccdcaaddaabbcabdbbabcacbaaaaddcdabbdddacbcadcbcdbcdbdcbbaabdddaccaaccdadcbcaaaacbbcbcccbcadadbddbbabaaaadbaaabbdcadcdcaaabcbabccacdbaccdadbdbadbcdaadbdaccbdbbbadaaaababacdcdaadacdaaddbcbbbbbcadacbdcdccdababcccbbcbaaaccbdbddccdcddadbadbdbbaadacdcabcccdbccacaacbcdbbdadcdadcabaddddbcdbdddccdacaabdcbdbaabcdabccdbbdadabbcbdbdbaabcbbcabcbdbbdaddaacbdacdbcaabbbcdcaccbacbddcdabcbaaccbbabccdbaadcadabdaaddaadadabbcabdcccdbccdaccdbcbdcbcadcbbccdcdcbcccacaadacccdacaadaabdaadaacdaacdaaaaddccabbbdbcbaddcdaacddcbccacbdcbcbbaadbcdbbcdadabaabbdccdabababcbcdaaaacdbdddaabdccabbbcdcacaddddcbdcdcbbabadbcbddddbacabcabcadbbcabdaabddcdbadbabaadddaaccbbccbcdccbcbcaaaacbdbbbabaaacadddccacdccaccababaaaaabacbabcbdddbdcbbdbabaacbacddcacacadabacbbdabdadcbdbdbacbccdcbacccdaaaacdaddcdddabdacbacbdbdcdacacadabccbccabadacdbcadadbdacaccacdabcdbcbadaadbaddabdaaadcbbccbbbbabbcaddddbccabdabacbcabadbbabcabacccccdaadbbacdbabadcadbddbbaccbbaddababdbadacacdbddcdcdcbadcdcccdbadbcddaddaaadbacaaabbddbbcdacdacabcbbcdcdbcbabadcdcbbacbbbcdacaaadccabbabdaababbcadccbdbadbbdbcdcaaaadbadbdaabdcaccbadbcbdbbbcaabaacddcdcaaaaabcdacbdcbbabcbabdadaadacdcdacdcabbaccddabdaabababcdbadcdbddaccacdababaccccdacbabacbbacdcacbdccdccddcdbdbdacadaccbcaccdbbbaaddddacbdcddcbbcaaabbbbbbacabddcdadcdbacdabacbdadbdbdaadbadabcdaacccddbbbbcbdbadcaddddbdbdbdcabbccaacbbdcabdadbccdbcdacbaadddcaacdbdcbbdcbdabdbacadccacacccacabaacdcdcdcabdbdadadcabbdcaccdcbcbadadabaddaacbabaabadcdcdcbadcccdadbcddabbcdacabacaadcdbdcbbadccbccbaccccdcccbbdaabdccdcbbaaabbdbbcdbbcdadcabdcbbadcbcbdbbcbcbcbcbcbcddaccddcdcaabcbcaccddcbaaaddcdcccbcddabdbdaacacbdadcacabdaaaccadbaacacaadcabbcdbccadbdabccccdacbaabbadccdadaacbdabcdbdbbaabdbddcabdbaccabccadacaabdbbbadaaaddbdadbabdbbcbaabdadacbbdabccadccdcbcccdaacccdbacbddcacdcdaacdbdbccccdddaacbdddcadcaaccbadacaaccbbdbdbcccdcccddddabadbaaadaacdccaadbabbddcdadcbaddcbddadddbbabcdcbbcdacdccaaaddbccbbbdcddacaaaacddabaaabdcadccdabcbdbaabadabaacbbcdbadbbdbacabaaadabcddcacbabcddacbcdcacccccaabbbabcddbaccbdcbdcbbadabacbcacdddbddabcadddcbaabcdbcababacdbdccdabbaddbacabacabbdadcbdadabcbdcddbdcdbadcccaacddcbddcbcaccdcbbabadbdaddbbbbcdbdccdacbbdbaadbacacaaaddbacdbbacadaccadbdadcabddabdacddcbdbbbdccbaaacbcccadabadcaadcbbccbbbccdaddabddbdcadbbcbabadacbadccbdacccdbadbaadbbacaccdbbdbccadbabddbaccabdcbbacdadadddbcabcabdbbbdccacbcabccccbdbaacaabcacbcbdacbdadbdcbbadcbabbadacdaacbcaddbbcdbccdbdcbdbcacccadacabddacccacbddbacdbccaaabadabbbccbbddadcdbbccbbadccbacddcdbbcdbdcbdaadaacadbadaacaadcbbaadacdabaaddcccccdcaadbbbcacadaabacdabddcddddabdaabcbbcdbcdabddbcbdbcadccbaccdadbbddbcdbccddaabddacbbddbbdbcaaddbdbcbbaaabdacccdaaacbcaddaccbdccbababdcbccaacdbcbbbdacdcdadcaabdaaadcacbdaaacbdadabadddcbcabbdcdabbbcdadbcbdbdbbaccddaabccddbaaccacbdcadbdbdcadbbdaaddabbbbbadaccabcaaadaccadddbdbddcbadcbdbbdcadbccacdacdadcbcbcdbbacddccadcdaccadbcbcbbbaccbccbbbbcdbcbbbbddabdabbdbabacbdbdcbdabadccbdbababaabbcbbabbcabcdcaaabbddbadcbdbcadbbbbbccdccabbcadcccbaaabbdabdcdbcacacddddbcbdbacddccabdadcaadabcaddbcbbdaddcdddbbaadbddaadcddddddccadacbacdcabbcdadacbcccdbbdadadbccbcbcbbaddbddadccdadabbbbccbdabdbdadcbcabbdbbccbdaabdacbbbabdcbbdbcbabcdadddcdcaaabdcbacbccbcbadadacbaaacdadbdddbcadaccdadacbddbbaaadacdbbddbcadbabddacddbdcbcddaddbbadbbaabdbbdcbccdabdaadbddbdaabcbbdbbbbcdcacbcacccaacdabcddccccaadbadddbbbbddaccbdaaccbbadcbadccbddcdaddddacbabddcadcaadabcddbdbbcbcdaccadbbcdaadbddbaddbbdcddbcadadcbdbccbdbacbcabcddadbccdbccdcbacdbbbdbdcbaccdadcdccaaccadccbacacdadabdbccabaccbccaddccddabdbdbbddaadbccaabcbadaadbcdccbccdbcacaaddbdccdaadccadbbccbdbbadabcddaacabcddcbaaadcbcbadabcdaaadaadcbabadcbbadddbbbcabcddaaacbabdcacaabbcbbbdbcdddcdccbbddccbcdbcadacadaccdaaabadccacdddcdbdbddabcbcbaacdcbacadbbdaaaddcdaabbbdbbadcbaabbbbbbbaabbdcdaccbbabaaddbacadaccdbcbddabccadccccbcacdcdddcbcbcccbccabccdddcbcdbdabbbdbadbadcaddabbcbdcccbbabddadacbadcbbbaadbabdbdcadaadaddbcccdabaabbadbcccddadbbbcbaadcbbccacdcacbdcbbcdbcbabaddddcdadcdadbaadacbbaadabdaccbaabbcbbdcdacdbcbbdcaccdbbcbdbadadbdbcabcaadabbdbdbaccdabbddadbababdbcaabbacbbcaddcacabcdccbbbaaadbccdbdcacdcacadabaabcbddcdaaccdabbbaccbbbddbddddaabaabbbddabaaaaabdbcdaddcacbddcbccdcaccddbdcabbbcddbaaddcdabcadaccbcadbdabdaaadcbbaabddddacdcddbdadccdbacddbdddccbddabcbccacdaabdcdcbbcccdbdadccbcabbcdcbbaccaadadaccddcabaaabddbdbcabacbaddbaacdadcabbbddcdbcdbbcddbcdacabcaadcdaaadbdccababacadadbcdbbacdccdbdccbadabcbadcbdbacaabdddbbddcacabcdcbbdabadbcdbbcaacabdaabddaaccddbdccbcbbbadbaddbacbbcddbabacdbcdcaabadddbcdbdacccacdabcabdcddabadbdaaddadabbdadcccbabdbaaaadabcaccaadadcbadabaaddbccddbbcddcbdbbbadddbdcdbdacaaddcbbcaabadacbbbcddbabaccadccdbcddbddacbcbdaccacdaaadddbbaaccbbdccbabadbadacbbcbcdcaaccbcccccbdacdacbddcbaccababccccdddacaddbddbbbdcbdccddabbbaddccbdccbaacbacccdaaddabcacdcacbaaadaccaaccababdaaaccdadbbadbdddbdcbaabccdcbbcabbdbbddabcbcdaaaccadbcbbabdcadbbacdcbdadadccbdaaadadabcbdcadddbbaabbdddaabcdbdbadcaacbcbcdcbadbabdaacbaaadbacdadccccccccadacadcbdaccaaacbdbdbbdaadccaabddcbaabadbcdacadbbbdcdabaadbabbccadadcdbdbdccbdcbbadbcccdcccbdcaacdbbbaacbbacdccaddcdbdbddcabdbcbaabcccccdbdbbabcdbdbbcddabbaaccabdcdbbccadbbabccdbdcccbaaabcababbbdcadbabaacdccddabdddbabaabcbdcaddcacbdbdabcbdacbaddbbaaaabddcaabcbdddcdabcbbdaabdddabbcdbbdcbaabbaccbcbcbddbcdbdcbadaadcacdabdabbaabdadbaaababdbcbdddbbdaabbaddddadaaddddaacdcbbacdbacbdaaadcbbdaabddadbdbbdaaccddcddbdadddcccbcbaabddddbcbacaabcbbcaccadbcabbadbdabcbdcdaabaaccaacddaadcdddadbddbdbaacbcbddcdcaddbbaadaacbcbaacdddbdaabddbaaccddcddaccccdcbbdacddbcaabdaddaabcbdbaaaaadcbbbcccabdbdcddbdbadacbcbbcdabdbadaadbcaddadbbcaaccaabbbdbacbdcbdbabaacbbcccccbdaacbabcdccaaccdadabacacbccdcdddcbddbabbcaacddcbacdabcabcadadcccaabbcddbbbdddcadcabbadcadbacbcbcbbcdbadaccbbaaaacbdccaaabacdabadabdaddccacdaddcabbdabdaabdadcbcadcbacdbbabadacdaabacddccdadacaaccbdbddcdaaaacdbddcccdbcadddbabbbcdcdbddddbccaddbadaaaacdcccaabbcacaaabbdbdccabbdbdcbdccaaddadbaacaabdcbcabbbdbbaabdbaabadcacddadabdacdcbdddbcaaccccabacbddaabdbcbdbdcbbdcddddcccadbdaccacacccdcdbddbadcbbccdbabbaadccbbdbdabcdcbadbdcbdaaddabdcccbccbaccccaaadccddabdbbbdccbbcbccbbdadabccbdccabbccbaccccddaabadaaddbbccccbddadacddabbdcbddacbddbadbadcadcdcccdadadaccccaaaccbcdacacaccaddcccaaadbaaabacdacaacbbcbcdbabcddbdbdbabcaadacbadbdbddcaaacaaacdbacadbcadaabacaabbdcdacbaadbcbbdcccbbacdcababacaabaccddbcabbbbcbadddbdaacdcbaccacbcaaacdcbddddaabbcaccdabadabaacacaadaaabdcbdacacddccbbaddadbacccacdcaacdabbdaccbadbcdcddcadacbccadbdbdaaccdcddcdaaccddbcdccabdaccadadbdcaddcccbacccccbbaabaaacddddcddbbdadaabdbaaadbddbacaadbcaabacaabcaacbaaaaccbcdaaacacbabbbbcdabacaaddaccbbbadbacacabbdccbdacacaaadcbacabadbdbabababcccccbabdcacbbaacddabbdbccacdbdddbabdaadbdacdbbbcaadbacdccabbcbcdcccddccaababbdcacdddbbccaadcbdcdababdccadcdaaacadbdbabacdadadbddddbacbbbbbcadcdccabbcbaaccbabbabbcddadadaadddaccbcacbcbbabcababdaabbdaabbbbcdccdcdaccdabbddbdddbacdbcaadbcacadbcabaadadccbcdaabcdaaacadbbdcadaaccccaadbaddadbdbadbdadbcaadabadcbbdbaaadcdbabcadcdbbdabaddcbdaacdbdbaadbdbbaadcdbcdabbcdaccddcabbcdadcbdcacabbdbcdbaaccdacdbbdadacccadadabacbdcbabddacccbbaadcaaababaccbccdabccbdadacbbdbdcbadaabbadcdbbbdbdcccdccaacbcbacbacdaacdcaacaddddddcbacdbdacaabbdbccabdabbdaacbbacaacaaacacccaadacccaabaaccacddaabdbabacbddddddadaaccdccdbddbcddccabccdababbccdccccdacdbdcdbdbcadabccbddabaabbabcdbddbacdabddabccbdaadabaabaaddccdbcbbdccbadadaacadcddacdbcbaabcbcdbbbbcabdcaabbdbcaaaaccdcdabddcdabcaccdbacddadcaaacdbcaddbddbbddcdaadbdcacddadccaddccdadbbcdabadcccbdbbbadcacbcdadbddabcbcbbbacbbbdcbcbbdcdcdcdbbbcbcaadacaabcbcdbdddbbaaabbdbacdabccbccabbcddccdcbaacdccddcbbddadddaabacabbbdbcabddcddbacdcbbbddcadbdcaadccbbcacbcbcddddaccddaddbbddcbcaddddacdabcaacddcacacdcdacadbbaadddadbdbcaacddaddacdcadadccccadcddacdcaccabddaccdbdcccdcdabddcacbcabaabaacdadaaadabbddcbbbdcaddccdccadabbdcbbdcdbcbcadcdcbdacbbcdaccdbcbbbbcddbbbbdcbccdcabacbbcbdbdabccbcddabcaddacbbdbbccadddddbdccbdcccddbadbbbacbacacdcababbddddddadadacabdbbbabdcbbacddabcaaaaadcdadbcbdccbaacbdcccbabaabbbabbacacddcbdbcbbbbcbbddccacdcdcacaaccacbadbcccbcbcaabdbacddbccbcbcddbadddabacbadaaabcbccacaabcacbcacdcdaccdcbcacdbbcaabcbaccbbadcabbabddbbdbbddcdabbbcabddcbdcadcbccdabbdcccccdcbcababdddcaaccababcacbcacaacdabccbcdaadbdacabaaaccdaadbcadbdbcdbddcdbbbbacdcdadbdbccbdcbcdcacbacdabcbadcabdababbddcdbcdddcaaaccbaccdaddbbcacdadcdbcabccdcdccccbdcacccbbacddbbbbbadbcbbbabcbcbbbdbdadcbdcbcdccdaaddbdaacacccacabbbdbdbdddcbacdcbdabbcdcadccbaabbdbbcbcdddaacbdbaadcbccbabbbbdbcaadccbaadbadabdbcccabbabdacddbdcbdabbdddbddccacdbbabbbadddacaadabaadccadbdabacccccacbabbacacdcccbcbbbcacddabbcddddcbbbabcdcdbdaddadaccddccabdcdaaababcdbcbcabbaabadabaccddcadcacdadcadadcabbdabccbacddabaabbdadcaaacaacddddbddbadcabbbdaddcddabacaaccaaddddadbbdccdcbcdbabcaacbbabdadcddcdcbdcdcbaabdabbcbbaddacdcacabbadaacadcbbbbabbdcadddcdcdbbccbbddadcdaddaabbbcadbdcddddaddcadaddababaacbcdccccabdbbbbdbbbbbbccaddcbbcdacbbcdccbadcdbdbaccdcbcdbdacbbaccacdccdaabcadcdccdbbbbdddbabcbbcbadacbcadbcddbabbabdddacddacddcbaccaaadccaabdcadacbacddabbdabadcbdcabbcdbcbcbaddcabbdaaccccaabbdbcdaadcddbcbbadbccddcaaadddacddbcdababddbcdcbddbcddcbdbccbadddbccbacadddbbcdccacbdabaaccabbddbbdbaacbaddacbdddccadcbccacaddccccaddccadbdbbabbadccbbcabbbbaabbbadbcbadcbbcdbbbcccaaccbcdcadcaacccabbcabcaddaaaccbcdbdbddcddcbbbcabdacadaadbdbbabbaccaaadcabddbdcdcaabaaacdddadadcdcdbadacddbaaababbccbcddcdbbbbadbddacdacbccccbbabcdddaaacbccbacbbbdbcadbdaaadccbddaabacccabcbbcccbddcbbbaabdababcaaadbddcadcbdacacddbccddbdbbcddccdacddbbacdbddbacbbaabdddacdbcbaacddaabbaddbaadbcbdccababdabbbddcdcaacbcadbdddbaaabdbdccdcbaacdccacdbcacabbabcaaccabdbcaabbacddcaaacccabadadcddcbaaaacdacacbdccbccbcbcabddcdabcaacbcaabcadbdbcabbbcadbaaaacbdaabbbdacccaadbccddbacddbccbdacbcacacadcbaaccbdaccaacbccbbbbddcdcbddaaaddaacbaaadcadcdbdadaccbbabcaaacbcbccdccaabacddbbcbbacbbcaddbcddbcdbcadcddcbdcddcbcccbaccacccadddddbbcdbcabcbadbabbccdaddabcbdcdbabcbaadaccacccdacddabaccdcaccbbcacaccabdacdcabdbbadbaaacbbbccbdbdcbabddcdcabbbdaccbddddcacdbdaabbbbacabddddbaacdccdacdbcacaabdcbdacbadbdcdbbbbdacbdbcacaadcbcaabbabdbbbbaacdbadabdaccdcadbaaaaddcddaadabbdabccbdccabbaddaabbbbcabddbccdaddddbcadcadbcaccdbdadcababaccaaddbbbdddadbadacdbaaccddabdcdacaddbaadbadbdaccbabcdadbbabadbbddaaadccdbadbdbadbdbbadbddbdbdccdabbbdcdcabcadbccaaccddbccdacabdbadabaaccbdcbbaacaadbddaaddcdbacbcbbdaabcbcdcaaccdabacdbdddbdcbbcdaddcbcdadddcbcbccabaccbddcaaaaaadbdbccbdabcadabbcabababbacccddbbabcbbacdcbdabbdadadcbcbabdbdcbabcdbaddaccadccdcdcdbbaddaccbcabcbcbcacdbcdbabdaddbadabacddadabdbbaadbadaadcbdbdccdabacdccbccdbdbacddacaacdcbdaaabbcdaaababacdbbdabdaabbababbdccddbdcdbddabbccccaddbbadccbabcadaacdbcbabacdbbadcabbbccccacbbcaacbbdabcbadcbcbddddcdbcaacdbcdbabcacbbbbacacaabdccaacbdccbcbcacdddcdbadcbacccababcdaabbcdbabaddadbabbbababbabbcbddaadcaababbadcacdbdbbaccadbccabdadbbaddabacaadaddbbcdddabbbbbacaaacbdbbbbbdbcdabdcbababaddadbabaddacbcbadcadbabcbdcadddccbbaddcdbcccabbcadcdaaadccabddadbccccbcababbabbdcbbdaccccbacacadcddcbaaacdaddcdcbdcdbbdcbbadaaabbdcadabacdbdbcbcdacbbdadabbbdcdddabccdacadbbacabadbdcccdbdbdadbabdddbcdbcaabdcdabaacadacdabcbaabadddbdcbdbaaabcadabbaaddacadadcccbaadddcabcacacdbbcdcbbbcdaabbdbbbbdcaacdddbcdcdcabaccdbbaccbdbcadbdcbaddadbaccabdbabbccacbdbaacbdcdbcdabacbccddbcbdcadbacababccabdaddaacdacccbbdddbcdaabaadadabaccaaabdcacdbccabccacddcacbcdadcbcccaababdcbbccccdacbbbaddabccbbdabdabddbcaccbdbbccdccadbaaaacdbadcdbdbcadabbbabcabcdaaccaadddaacddccabbccccbdbacbcacdcdcbcadcdbabccbdbbcabdcbcaaadabbbbbddbcbacacbbdddcddabcbbdcddcbbccdacadaadaaaccccacddaccbacbacbddacdcbcdaaddbdbdcacbbdbbccacaacdaddaaccdacdacdbdaccbadcbbdaabccbbcdcadcdbadddacdbabdbaacddcdcdacacbcadcdcdaacbcccbaaddcdabadccddddbdbaabcacbcdccccaaacdbbbbccadacabbbddbbaccaadcbaababbacbddadaacbdddcbcadccdbcdbcaddbdabdbacbbccdcaccbdbadcdabccddccadbacccccdddccbdbcddbcdbcbaaacdcdcabccaabbaaacbcaadadabcdbaadcbabbbccaaadddabbbcabaddacadacccbdbbbaadcbacdbddcabdbcbddbdcadbaadddadaddacbccabbcccdbdbacabacdcaddcdddaaacbdbcdbcaaccdcabdbbaacccbcadacdbaacacddabbbdcccadaadcacdcdbbdcadbbdaacbcadadbcabdddacbccbaadcddabbacbcacacbcbcacddcdadbdacddadbbcbddccabbccbabdccadadbbdbbaacadbaadbaadacaadabcbbcaacddddbcadbabadccdbdcacbbaadadaacbbacddadcdbdcbdcbdcddaddbdaaacdddbcaadbaddbaddbbcbccaabdbcdabbaacbbcabcbcbbdcccccabbdcadbcdcdccdabdacdcddacdaadacadddccdcddbcacacaacbdaacbbbbbcaccdbbbabbbbaadddbddbdddddacabaabbadcaadaacdbdaaaadbcbaadaaacabbccacbdacdbddcabbacccbacadbddaacadccbbbddbadcddddbadddcacbbcccabaabcacccdacdccbcadbbdbadbbabccbaaccacacdaacbcacdddcbbbbbacabaaadcdaddaaaccdcabccabcaaabacaddadabccbccbcdbaaadcbcaaacbcdbbbcaccdcbbcaabcabadbcabcbaaabbbbcacacbbcbbdadaacddacdcaadcbcdbdcacacadaacacdacddacddacdabcbdcddaacacdabadbcadaadcdadbccacdcddbcdaacaabadbbcdadabaacabbbccbbaacbdadaccddbadddcacddbcadbdddbcabcdcdbcdcdccccadbdbcbbbaabccabcabadcccccacdccabccddcbaaaddbbdbbcbbbaaacccbabbdcbadabbcbbbbabdcacbdaabcbbccaddbabbaaccdabbbddbbcacaaacaabcbddcbbcbabcaccbdcbaadacacdcacbbcbcaccccbbbcbabccbbccabbdddddaaabcacbcbbaaabcaccbcdcbddaddbdbcacbaadccaabaddbbbdcdbbdcdddacbbdbddcdabcaddbbdbacabdcaadcbcddbdbdcbacdcddaacbcbaddcdcbdacbbbddbcdcbdddbbcccbcaddbbdbbddbdcaccabadccadccacdcacccacabccabdbacbadacbbadacabaacccdddcbbcadbabcadccaabcaaabadcccababbdccbdbadbabbabdaaddbcdcdddbbaddaaacaaabacbabadabdddbcdaadcbaabdcadadcdbcbbaaaaacbccccbbbbaabcaddbcddbdadacbbccbaacaaaddabcdbbccbaaadbcdadadadbbdddcadcbdbbdaccacbabbdddcdcadcaadabccdbdabcadddadabdbacbcabbaddacbccbadddbdaabcbdcbabcdcbbdcaaaaaaaccdbcdcbdadacaaaacaaddaaaaddddbbdddababbddaabbacbacbbaacbadacbddaadaacadabdddcbcdbdacdacbacbddacadccdbbcdddbcbabbaabcddaaabcacdbdbcdcbadcbadadcdddcddcbbadcabbcacabdadadabbdabdacdcabdadaacbabccdcacdadabcdcdbaaacaabbaaadcbdbddbddaabbacccdbaacccacccabbcdabbcbbadcadadababdcbcbbdcddbcacdadaddbbddaddabbccdbaadcdcbccbbbbcdaaadabbabbbbdaaaddaabdcbdbabdcbaabcbabbdbbccbcdcacdcaabaaadbdbbdabaddbcdadaccbcbadbacacccdadbabdcdaaacccbbcdcdbaaacdcbdccbddcadbdaaadddbcadbdcdddcadccadacabbcccdaaaaaacadbcbddadbbcddcbabdcdcccbcdbdcacbbdbddbbdaadadaadddbdddbcdacacdddacccddbbcbbbcadccbbbacdcabdbdccddacaacdbcdcccaccdadbcaddcacaaaadbabcbadadccbaaadcdbccbacbddcabbbcdbbdacaccbdadbccbcdcadbdcccbaabbdcdcbddcaabdbadcdcdcabdcdcccaaabaababdabbdaddadadbaaabbcaacaaaadbccadbcaaadaabcddcdbaacababbcbbbabcbdbdaccaccccddcabdbdacdddddcacaddcbdbbabdaacbcaaccbaadaaadbbbddcdadbaaccdccbcaccbbbadcacaaaccccadadbabaadcbcbbadaacdcabdadccaacbabadddcaaabbdabdbcacdabaddcbcaccbcbdaacccbadbdbbbcdcabacdbdabcabbacdbadaddbaaabdacabdabacddccddcddbdcaabcdcdcdaacdabacababbdababdacdbababdadcbabbdbdcaadbacddbdbcbaacdbccacaabcbaacdbbabbaddcbddcdabcbccabdadcdcbdddbddaacbacdcdbcbccadcdacabaaaddcdbcabdcbdadbcbcadddaaaddacaadbadcaacbbbccccacdcbbcddbdadaabaacaccadcacdaabadccaabccabbcbaaaabddacdcabdbddbcdbbbacbdabbbacadbcbdbdaccbdcbdacbcbcaccbcacabbdbbdbbabbcbabdbccabcddbaabddaadcbbababbbabadcaaabacddddddaadadccdbcbacdbcbacabcbbabdaaacacddaccabbbcbcdbdbadcdcababaaddaacbcaacbcddbcdadddbbbacbccaaddcacbacdccabdbbccbddddcabbccabdaddcadacabcdabbcabcdcbacbacdbaabaacdadbdddccaddddcdcbcdcbdacdcbcddccbdaaadadcdaadabbbbadaacddabbdbddadbdbadbacaadcdadbcadcccacccdaacacbcbacbbacbdbbcacaabdcaabcbccbadbbacbbdcdabbcdacdcdacadbcdbcdbabbdbacadacadddaadbbabbccccbdbbbbdacacdaddbbbcdddadcdbdadabccacaddbdadccbccbbbdbbbaaaddadbcadacddddaccdcacbdccddaacacbdaaddbccbcddbbadaadddcadbbacddaaadcabadabdbdcadacccacccaddcbdaaccacddadbdcbdcaccdcabdbaaaabadccdbcdbabcadcadccccaacbcbaaddabcaaaaaaddacbbbaabddabdbbcdaaaaabdcdbcabaaaccddcccadccdccadbabaddccbcbdccaddaabaacadbddcbbabbcacddcadcbddbbaacaabbcadccadabddcabcbbbadbbdadbaadcdddbacdcdddaaadddadcbdbaabaabbcddabcdaddbbccdbabdabcacccccabcdcbbacddacbcaacdbabaabbbbdbddacdaddcdcdcacabdaccacaddcccacccbbacbacbbadcbbcccacdbccdddddcccababbbcdddddcbddaaadaacbabddbadbdadaacababcbddcbbccaddbadddccdccacbdbddadbdbacbbdacdadadadbcdadcbbabdcdcaababbbaabdabdddcddbdccdadbdcdaddbbcbcbcdabaabdbcdaccabbccbdbacbdbdccccdabbdbdbadacccacaddddbcaddabbcbcdaadabbabdacbaadccdcdcdbaacdcacaacbcbbbdcdacdcaabbcdcdbbaccddbdcaaddcaabadbcbabddcbbacbcacbabbaadcadcabacbabbcddacdcabdadadbccdbbbbcabbbaddaddbddbbdbdbbbbcaadaabcccadccbccdadbdbdbccabcaddbbddbccdbcdbaadbbaccacdcbbcadddddaccbdddddcdcdaabdbddcbdbcccbdcbcadcbbbdcbccadddcaaabacddddadcadaabbbacdbcdadbccabdaddcbacbbacdaccbbbadbadadbacccdadbcaccacddaacddcaacbcaaccaddcddaadccabdddadacdacbdbbbbcccdabcbbbcccbcdbcaddbdaccaabaadabdcababbadbcdccdbdabcbcdbabadbaaacbdaddbaddcdcccabacbcdbccddccdcbcacdcdddaddbcacddbcbdccbacabaabcdddbcbccbdcdbdccacddbdaddbcadcdcacbdabaccccbddcacbabcabbcabcabaabaddabbddbbaccccccdcdccccddabadacbdcccbcdbadaadaaaaaacaddadddccbadcccdccabcacbaaccaabbdbaabcdddbbaaddabadcbbdcccdadcaaabdbaadbadabccdbaccdadbbccdbcdabdccdbbaccacabbccdabbdbcadacbbbbbbcaccaaddbddcbcdabdcbdaaaacbadbacbcddddcbcaabbaadcbacaadccccccaaccdbcdbcbdaabaadaacbcacccccbdbdddbddccddabcbbbdbcddcdccaabdcacadbbddabdddbbabcadcbadaadbdccdbccdaaaacbbcddbcdadccccbaccabbddaabbbdcccbdadaacabbadbccddabdbdbcadacbdabadbcddbcabdbddcbcaaddbccbacbcbaadcdbcdbcccdacbdcddddbabdacdadadbabbcacbabdcbccdacbbdccddcddabaadbcaadcdbbaadadcbdaabdaadcbccdccbbbbadbcadbadacdadcdddcdadaddabdaccdcacdcdacccdbaacaadddbadbbbccacbdbbabdddaccaacadadbddccdbdbabbcdcacbcbaccddacdbbbaabaaabaaaadaccadbabbbcabdabacdadbbdcabdddbbacbbcaccbcababadacabaadadbbaacaaaddcabbcacaccdaabbaabacbaaadaccddbdcbcccdadbdbaabbccbcddadcdddbdbdadbcbabbadddabbcccddaadabdaadbdabcaacacddaaddcadbacbbddbaadadcdbbbbadccdbdabdccabbabcbccddbddcadbccadddcbabdccbcbcddbdabdccbaabccddcacdbadabaabbdcaaacdbbcaabbacdaadbadbbcadddacacdcdbadbbaabaaabbacddcdaaabdbccadacbcacdaaabcbdddbdaabcacccaacabcaddbacabddbadaddbabbaaddbbabbcbaaabdbdaaccacbacccbaabadadbbcbcacadacdbdbadaccbaaccdccadcdacbcaadabadacacddbcabcaddadacdbbdbdbdcbdaaddbdbabaacabacabcabddaadcabdcccacadaaccdbcaaacabbdacaacaaccabacdaacdccabaabdaaacccabcddcaccbdcaadcacdbcdcbcacccdbddcaabcbcdcaabdccbdbadadcdcdabaaacccddacacbdbacadcabdaacdbbdcacacdaaaaaacaaddbdcdcabaacaabbaadbdccdbaccdbadadcdcaadadbadadbabdbdccdddaabbaaaaabbcaccdcccacdaddcccccdaabcdaabdcaddbcdacddababccdabdcddcabacaccbcbdacdacadbadacbbaccabcddcadaacbbcbbcacadcaadcdcaaadbcaaddabcadbadbbcbcbdbddcdbcabcddbddbabdadccbbbbbabaaabcaabcacacdcbcccacbdaaacdacaabaabcdcdbaaacdcccadacdcdbcddcddadbcddddacdcbacdcadaadbadbdddacdbddacbcbccdcbcdccabbcbaddcaccdcdaacccdacadaaaacaaddcbacdcdabcbccbbddabbdcccadcdddddcbdacbddbaacccdccdbcdacddcbdcdacdcbbdddadaabacacbbbdaaaadacccadaaaaacbccbaadbcdbacdcabbdabdccabddabaddbbdbaadadbdaddcccdddccabcbdaaccadacbcdabdabbcbcccdbdcadaabbdbdbbcdaaabdddadacdacbccabaadcdadbdacacbdddbbabbdcadaccdacdacdbbbdbbdaaaabaddbadbbdaaadabbababcdaabbaccaabaadadccbdbcbbdacbabcaddbdccaabbacacadbaccbcdccdacccdddbadbbcbdcbadbbccdadaacdbccccadbaacdacdbaacdbdcbbdbbacaabbdbcddcbcccbcadccaaccaacaadadadadcccccbaaaaaabcbccbbdccddcbbcdabdadcccaabacbcdddaaabbdbbababdabaabbcccbbbdccdacbabaabdcbdacdaadcadddadbaabcdcacdaabcbbcbaaccbbbcdabbadcbabbbdbdbacdddbaddacdbdaddacdabdddcdbacadaaaadacaadbaaaddbddddacdacbadabbacbccbcbbabdbdaabaccdbabadcacbdbcabbadbdcbacdaacbacbabddbaacbbdcbdbcddbddaddadadbcbdcbcadddadbcaccacabbbaabbbdcccccaccbdbbccdcadcbaabdcddacadababbaacacccbdadacdcbdbbaadbadcdbccccbadccdbdbdcbdbaaaabbabdbcacdbababcbbdbddabccbbdaababdbdadbacccdbabadaccbddbdbbccccaaddacbbbadcdbacbdabbbdbcabdbaababaddcccdcbaacadbcdbdabdccdccbcbbcbabbbcdaccddabbaaddbaddabaccdacabbccbabcddcdbadcdabdcabcacddaabacbbabcbcacbbdcbccbbdcaacabbaacaaacbdacbdcdbdbbdadcdacaaccdabadaaacdbaaadbbaaadccdcacbbccccaaddabaccbdccbdbbbbbcbabbcbddbddbbdaacddbbbaddbcbbabdbcabadbadbbaccacbadacdddcbabcabdaccccbbbadddbcadbaaccdbbababadcacbbdacddbdbcccbaddbcdbdcdcbdadbaaadaddbbcbbcdcababdaadaabcbabcdbaaadccacddbcddaaaddccadaabcbbbcbcacccabdccbccacddbcdbcbaacdcacabddbcdbbabaacdbcabdddccdbccaddaaaadddbccabccccbcabcacccccdabdcbbbddbadbcddcadcbdbddcddddbabbdcbbbbcbddbddcbcbcdccbcbdbabbacacddbcabdbddcdddaddaabbccdadbdbbcadcbdccbcaaddcbbdccccbcbbdadbcabcdacdbaaabddcacabadcbbdcbdbccadbddccdbddbdbbabdbccdddabdcdaabbcccdadbdcbacbdcabdbccaddcdcbcdccdadcbdaddaabacdbdcadddbdaaaaaadbdabcbcccaaddddbcbacbdbaccbdaacbcaadbcdadcbabbabcabcddaadbbbdadbcbbbcdcdbbaabaaaccdcbaaabdbccbcbcbadccdbdbbdbbdabaaadaddabcbcdbdbcadaaabbcaacabcdabccabdcaddadbadabcaabbbcdadbbcabacadaccccbabcbbbdcccabdbdacdbcbaddcddddacbacbbcdccdddcaadbbdadbbbdabababddbdcacbcdadccdbbacbcdaccdcadadbdcdccdccddaadcdabbbdcaacbdbcbabbdbaccbcacabcccacbacbababddccdbaaacdbddbdabacbbacdccbbacabbaabdcaddbcbcdcacdaaddbbcdbabbadcdbbdbbacbcbbcddacddbcbdddbdcbdbbbcbbcabbdbadadcdcdabbcbbbbabddcacadcabbcdcdcbbdbbbbdcbddcacccdcabbdcaabdcdacbdbbabbcdcacdaaabcabddadbcacabbcdbdaccaddbdbcddcadbcbddcdbdccdcabbcbcbacbaabccbbccddccbdabacacabadabdbbabbbbccdccdbbcbddacdbbbadaccbdbadadaabaaacccdaddbcdaadadbadccdccccabacdbbdbdbbdadbcaabddabdabcbcbccabbaaacacbaabddbdacadaacacbccabaacdacdddacacdcccdabdddaababbcbadaccbdcdadbaaaaccdccacacdacaaaddbbddbdcaddbccbaccbbbbaabbbcbbbdbbaccadbaabcdadabcdbaadaaaacbcccadacccbcadadababbcccadaccbddadbcaabbcaccbccddbcaabadbacadadddadbdddaabcabcbabbdcccbaaccaabdaddaabaabbdaaadcacdbbbcaaadadacbbcbbdbcbbacaddaabbcaacbabdbdcaddacadacacbbbbaabccabcbddcccaadbbbbcabdabdaacccdcbcbbcabccbcaabaaaaacaddcbaabadbbddadbcaacdcccdacabbcacccabacdacaaccddadabdbacbbdbccbcaddddaccaaddbcaacdcadaacbacccaadbdaadbaccccbbdabdcbdabdadbbcadadaaabcbababcccbabbdaadcaccbcadcbcccabdbdbdddacaddbbbacbdbccaabcabcbcbbcccdabbcdcdbbadaadaabcdcacbbdbdbccdccababcdccbababcbdacddcbcaabcbcadabdaabbbaacdbbdbbcabdadacbcbabbbcbbabaaccdcadabddddadddbbdcbdcbccdabbadaccdaddabacdabbdddcddccadccddbabbcdcacaccbcaadddcbbaacdbccaaaacabddddbddbabdbaadcdccacacdaabbabbcdcadabadadcacbacbaccaaaddcdcaabccaacddbaddabbcbcbdadbccbdddaadacbbdddadbddcdbcaabdabcadbdcaccadcdccaadcccbadbdaabbcbbdbacabbdbbbcddcbddaabdacbdbacbadadadabcbdacdbbbcddaaddbddacabbccbabbaaccbbaadcbcaddcdbaacbbbdcbbdcddaaacbcadbaccdbdbcccdaccaacaacacdbdbcacbabdcdbdddbcddcbbccbdbcddadddbadbcadbbabaaddddadcdcabdbabdaabbdbaadaddacdbbacbccadddccdccacdbdcadbaaadbbdaaaadcaaacadbbcdcdadccabdcccbcadccccaacbdbdacccacccaccbdaacbddcadbdddbabdadabbdcdddbbcdbcbdaccddbdcadaacbcaabcbacadbdcbacaacbdcbcbbabcbcbddcacadddababddbbddbdcccaacbadaabddbbdbadbcdccabdbcbcdacdbcbabcdcccaabcdccdccabacdddcdbbaaadbddcdcbdcdbbaacbcbbbcdbdbccbaacbacccdbabdccadbdadbcdbbccadabddacaaaaabadbabcabdbabbbcdbabacadbacdbccbcdaacdccbbadaaadbccbdcbdbbabcabadaaccadcddbbddbabcbccdacccdaabccacbadcadbbdcbbbaccddbdacacaacddddbdbbdaadcabbbabdccddababddbcccdbbdbacaadcacdabccdabdababcbaccbaccdbcddabbcbabacbdbccadaaaacacdabadbacabcdcbdcbddcacbdcccdbbabddcbbbdbacdcbbaabbdadbcadbdcbadbbbacbadacaddacaccdcdacdbdbabaaddaacbbaacdaadcaaaabcbabdbbdccbcbbddbcbbdcabaadcdbaaccbcabbbcbabcdbaaabdcbddccaacdbaddadaccbdcbcbbacbbdcbdccaccbcdcacaacbadadbbbccbcbdcdcddacddaadccbaabbccdccaaacadaacbbaaaaddabbcddcadcbadcddcaaaababbddabdccacdacadcbbcddbcdccbdabbddcccddcaaacdcabadcbbcdcbacbaaddabcaacdaabcdddcbdccddddadbbadcbddcdacdcbbcdccaabcacacadccbacacbbcccdbabdadbadaddbbbdddcbbcccddaabaabdaaaaabaacbcaacbcaadcddcbcaabbbddcaabdcaaaadbbabacbadbddbccabdddbddacacaabcccbadcbcabdaacddcbccdcbdacddbbbcdbdbdcbaccaabbdaaadbdbcdabadccddcadcbccccbbbccbbcacbabbdacddacdbdcaacadcdcadddacaaddbacbdaaccdccddccacddbadaababddbcbcddbbbadbcbabacbadbdbdbcdcbcbdddbddccabdbdaabbacdaaabaaadddabdbaaaabdabadccddcccddcbbcacaaccbaadadababdbbdabbccbcabaadbbcdcacdabaaccacbdbcaabcadcdaabaaadbccddbcabbbadcddbadcacddcbbacdcbcccddbacaacbcbbccababcccbbaddddbccddddabaacbbacababdbbcdcadcbcddaabdbddddabadabccbcbbcbdcbacdcadcdacbacaddbabdcdcdadddaccbcddbacdadddcbcabbbcdcbbdcccdcdcccdadaccdbaabbadabbcdbaddaaccbacdadbcadbcacccccdbbabacbddacccadacdbdcabbcaacaaacbccaccbcddaaabdbaadacdddcddababdcbcdddddabcbcabcbddbbcbbcbbbaccdcccdddddaddbbbddaccccbbabbadccdadabaccbbcbabbdccbacbdddcbbabbbbccbbbacaadcadddabaccbcccacabcadadcbbcccdcbbdbdabadbcccbacdccabdcacabacbaccbacddcaaabccaadcbaadcbdcbddabcaadaaadacbaaaacbaacaaaadabcccccbdaddbbbdbdbbdcdddddabcabacadddacababcabcacadababcbadcabbdacaccaaaadbdbdddbbbacbdabbdaddcbacaabddbdbbdaabacbcdbccdddaaabcdbabcaaddadcdcdcdaddbbdabcabcdbacacbbdddbaddbcbbdcdbccaadadbaaccacaaddaaaabcabaaadbdccccadacabcbacdccbadcaaddddcbaabbcadadabacabaadccbddacbddddbdacbacdabdddaaacdadbaaacbabccdccaddaabcbddcccacdcdaabcddcbdcbabbaabbdcddddcabbdaaccabbdbbdaaabbcddcbddcbbcccbddaaaddadaabbacbbddcacdbacbccbaadabcbddcdcdddaddddabcadbbdbabadbabcdbbcccbbcbcbcbdcbdcbddaacdccdcaccdcabbddabaaddccdbdaddcaabcddccdacaddccabdccdcdbccdbbadccadbbabdbccaacadddbdbcdddddcaccbadbbdcdbaadcccbddadacbacddcdbccbbacbdbadccdbacaaaacbcacdbabbcbbccdaccbdbaddcabccbdadcdddbadaadbcddbdcdababdccccacababccadabcdcddbddcccadabbababccbbadaadaaaadabcaaccabcbddcdcacdbbcbbdadbdaaabbabdddababbbdaddcdbcaadddcabccabccddaccbbbdcddaacaabadccddabdcaacbadaccbbacccbbbaacdbdddaccbacccabcbcbcbccbdadbcadbdbbccdbdacbbababbbaadacdbdcbccddbacbadbbbaacddacbbbabaadacaaabcabbdbcdaaddcdaacabbdcbcabbbadddaccaaaccadbbccdddcbbdcabdcbcdccbadadbadbbabdadddbbdabacbcaaabcbbbaccdadcbcbaadbddccbbaadccdabcdacddcbadbdbbadbaabaddaddadbbcaccacbaccdbdddbabaadcbcdbbbcbddcdccacbadcccadabbacabbcabcddbbbadbdbcaddbbccdbdababdbcdbdcacbcdbcadcdaaddaaacddbdbbacdaccddaaddbcbbcdaabbbbacdabadabbaabaabcdababbaaacddddaacaadcdddbccaaccdccbccdacdbabbacabaddddababacbdbbdcacdbbbbddbcccccdacbcadddbadbddcaacdbccadadabccacbadcacbdaabdaaabdbbaadddcbbacbdabdccbbbbbbddaccadaddcdddcbddacbcabbaaaccacbabdacdbdcaadcbbbbbabbacccaacaaaacdddccbbcddbabadcdccccacbbcdcddbbdbbdbaccabbbadbcccbcacacbbcbbbcbabaccaadababcaaccabdddccdccdaacabacbcacbddcbdcbcdadcadcbbdbadbdbdbabcaaadaaccddcdaccabdddbccacdcddccacbddadbbcbbbccbdcdadcbcbdbdbcbaaaabcccabccdbabadbbbbaccdacbcbadddadabdbccaabaadcaabdccdddcacddcdacdbcacbdacaacdcaacdcdaddbadbdaaabddaacacbcdbbbddadcdcaacababdcbbbcccdcdddaaccbbbbbbccddddcbdbbccaddbbcdccbabdcbbbadbaacadddbbbaddbcbbadccdbcccadcbbaadcacccdcbccdbdbddbbcbcbccbaabadadaddabcdcaccdcccdbcacabddacabcdaccaccdddbabbaadddbbabcccdbdddbbbaadcadbbbbcababbcbdcdcbcddbdcadaabcabcabbadbabbcdccacdddbdbaacdbaacbaaacabdaccbddacccbccdaddacaaddbabcdbcbcdbabbacaccbadcdbcbdddbcddbbdcacccabdaddccbcddacdaabdabaccddbadbabdccaddddccddbaabddaacaddcccdbcbbddddddadadcbbacadcbaacdcbcdcdbaccdcddddcacdabddacbbdbbaadcdcaabdacbbdcadabdbbcdaccbbbcaaacbbddcbbadadbdbacaadaaccccdcacccadbaccccbdddbcacdbcdbcbdbbdcabddccaababdacadcabbdacccdadcccdbcbbadcaddabbaddbddbabaabbccbbcbddbcccbbbdaccccaadbbabdbbdccdbdbbcbacabcdccddcadbbddbdccdabbccbcacabbddabdabccddddabcdbcaadccdaabbbccdcdacdabcdcadbdcbbbadadbaddabbbdcabcacbccbbcaccdbbddcbacabaaddcaabccccdaccbcbcddcaaadccbbcaaaabccdbcbabaadbbccdbccbbcabbddbcbbbacdcddcadacaabcbacdcbadcbaacdabbcdddabadbabdcbcdddcbdddbabaaddacbddcdccbbdacbdccdbcaddaabcbabbbdbacdcdcacbbdbacaaababcabbbadcdcbdbadcbaadddbddababccddcdabcbadcbcdbddadababddcbbaacaacbcadddacccddccdaddbdabbaacaaabcddaabdccaadbdddaaaabbcccbdcadcbbddcadbbaaddcdbbddddbdddbbaaabcabbcdcccabdbdacbadbbabacddcbdabcdacdbbbaccdababddbacdcadbccdddabbdbaacddddbadccacdddadbaacaabbdcbdcacabcaabbabdacbddbaacdacbdcbcbbcabaddccbdaaacdbddcbcaacbaaccdbaabbbcccdcbdabbdccacadddacbcdbbbcabbddcbaabbdaccdcbacacacddcbcddbcbbcaccdadcbadbcabbbdaccbdbbcadaadbcdcacacacdccacdcbaaababbbbacadbcdbacbaabdddbbcadabdcacbbbdadadbdcaacdbaaacdbddabdbabcaadcbdccdaaaabcbaabcbcdbccbabdbcbbcccbdabbdccdbabcabbcadccacaaaabdbacacccdabdcadddaadcbddaabcddcbdcbdbccaacdadcabddadabdddabbabcabbcccbbbbdbbbccbcdbcbbbcacadaadadacdddcdcdaccdcbabccabdcababbbccbcbdbaaaaadaddcddacdbbadbddcccbadcbccbbbbcdcccacddbdabbbbcdcdcbbccaabacbdaccdbbbcbdbcaadacbacbabbcabacaadddacdbadbbabaaddcaaadbcacdbadaccadcacddabaacddabcbacdbacbdabcbaaabcabcccbabbbdcabdccbdbcdccdbbbdccdaadcccddcdbdddddcbccacaacdaabcbdaabaaacdcbbacccdddbaadcaacaabbdbcbadbcbbcbcbbbbacbccdbddbdacbcbbbcdcbbcbcdcabbacbbabbcbdbbdacabbdbdbabbccdcdaaacacbdacbccdccbdbdccdcbbdacdaddbcbcbdbbabbbabcabadbbbbcccaadcdcaacadadbbababbadbbbbdcdabddbddaadacdaadddccaaacbadcaadaaccbcbbcbbdcdccabdbaccddacacbcbdbcaaddabcccbbcabaaabbcaabaccadddabddbbacbabaddcabddccaabbcaddccddbbdacaaccdcaabbcbdbaddacaacbbabbdabbccabdcabbcabcabbbcbccddbaddccadbcaadcabbcddccaddadcdccdbddadcdaaddadccacadcbccaacadccccdcacbcadddaadcdabaacdbaadadcddbccbcbbdcbabdaadabbdcabdaacabbbdabbccbadadddcbccbcbccbbcccdbcbaacaccabdbaabbbcdbbcaacaddbddcccaaacbcadbdccdbbcacdbadcaabdaadcddbdcbadccccabbcaacbdaabbbdcdbdddbacaacbbdaadcbbdbabadbabdbabccacdaabdddbbcdcabbdbbbabcaaadaacadabdacdcbccabadcbcdcbcbdbabdbadbbbabcabababbdcdddcdaabdadaacbbcdbdbbdccabbcaabdacbdcaaabddcdccaadcbcbcbccbaabcdcdbdcdbddadcdbabbcdadbacdccaadddbbbcbacaacdadbcccaddbdabccdcccbdcccacabbdddabbdccaccdcdacdcbcbbccadddbdcbbabbdacaaadbbadcbaacbcdcaaccadcbbddaaaadcbdcababadbdbdcccdcbbbbababdadadbbdbdcbcdbbbabccacaacdddbacdcaaaaabbdabdadbbabcbdabcdbccacababcdbaabbcabdbbbccdddcccaabdadddbddcdcaaacbbadabdbcbdbbddbadbaddddabccdddbacadbbcbbbcdabddbadaccabaadccdbbcddddaaccacadbbbbbddacdbaddccabbbadddaacdddccccccccdbbddabcaccbaddadbcccbbdcdcdbacdcbdbbaaabdcdbbddadccaddcddbaddcccadddccbabdadbdaaabacbaabdcccadacaddcbabbaddbaaaabbddbcbbbbdabaccabaccaaccdcbcaacbaadcbcbccacbdbbbaccdacdbacbdcabbaaabdababaabdbacdbabddcdbabbbddadbbdbcababbcabddadcacddbaabcccdadbaaadbcbadacbbaacbdbdabdcadcccdacccdbdccabdbadcacdadaacddbdbdbcadabbadaabcccabccadcccadbabacabdbaababdbbabcbadccadbcbddcaadccbdabdaccaaccbccdbbcdbadbaddbccbbacaacdadddbcbdbcaabdccabbadcacdbbcdbabaacacbacccbbadbcdaadbbdcbcabacddacdccacbaccccbdcdbaabbcaaadbdbccdbdbdbbbadcbcaaaccbcdaacbccaabcabdadbdbdaadadbaddabccdcbbaccccdbbcbbcccbccdcadadabcdcdbddddadacbbbdbcbaaaaabacabaddaabcbcadabacacbaacbcbdcdcdbadddbcbaabdcddbdcddcdabcddacbaaddaccaccbccbacbbabcaacbadcbcccbcacdbcbadbbbadcadbdbabcdabddbddcaabbccdbcbacabbbcadbdcdcdbacbccdcacbcbcdccadadddaddacddddabbbbddaccddcdddaaabbbaabccbadcacacadbdccabdccbadcacdddddbdbbaaacbbaabbaadbbbbacdacdcacdadcccbdbaabacdaadbaacbbadacacdaabdbdbadaccaaccddddaaccccaddbbdddabbdadbbcacbccccababdddacdaadcccadddccbccbaadbbadbdcacdacaccbbaddcbadacdcaccbdacabcbbaddcbadcaccbdcaaacdabddddbdcdbcdbdcdddbacbabadcbccaaacaabbaddcdbaccdadddbbabdcbcadbbbbccdcbbdcabbcabadcabcabbbcdbcccbbccdabccbcdbbbdcbabbbdbdbdbdacbcccdacdbccababcbccaccdcbcdaadddbbcbbadabcbbaaacddcadcdcaaacdaabccdcdbdddbbbbccdaabadabaddcbcddbcdadcdcadbabddcbcbbcabbdcacadadccabacdccacadccccdddaabcabbcadadbcacbadadacabbbbaacddcccbbbdacdbaadbadcbaabcbdcadbcabacbbdadadadbcdbbdccdcbdaddbdcddacacdbcabcdbdcbcdbdbadacccdbbabaccacbaacbbbadaabacdbddbdcccbbbddcbaddcddaaddbbdcdaccdcaacadddddadaadcdddcadcdcbbcadcbdbcdddcdccddbdcbabdccacadddacaaadaccbccdabdddabbdabaacddbbacbbdabcdcdbaabbbcabcdadbdcbacdaacdcdbdbdbddaddccbbabcabaaaddbbbaabdddbcaabbdbdbabbacdbcbddcbddadccbbdccbccbbcdcbbabddbdbdcccbcbbdbbdddaccadacdabbcccaddadcbcdbbcaccdaaccaaacccdaaaacbddadcccadadbaaaabaaadbbddaaacabcbacacabbbaadbabcbbddddbdaaabdbbadcaacdababaacdbadbaaaabcadaacdbdbcbbbddadaaccdbadcddcabdddaabcbbcababdacbbdadccdcdcbaaabddaccbcdddbbcabbbcbdbbacbddbaabbbaddabbdbbcacccadcaabddbcabaccdbacdbabbabbcdabacbddbbddabadaaadcddbcbccbddadccbbcdcadabcdaabdcaccdbcaacbaaacddbdbdaadbbacabcdaadddbdabdddccbdbbbdadccdabcbcbdcccccaabbadddcbccacaaaccdacdcadddaabbccaccdcdbabacdbccbadddcbaddcdccacbbaabddccccbaabadacbdabaadcdddbbdbaacbcbdcddccacdcacbddaaddadccaacdbaadccddcdaccbaaaacbabbcdbacdddccabdadcbcaaccadcaddcdaccdacbbadcccbdaaccdadabaacacabdcddcccdbaaacaddacbadaddacdccdaadadccadbcdcdcdaacbadbdacababcccccbbcadcdcdaaddcdccbbdcdbddadddddddcacacaaaccbcdcdacacdcdcdbccdaababddabdbddcadcdcbcadcacdcdbdaabdbddcccdcabbaaabdbaddcbadaccaccaaccdcddcdccbcadcdcaabcaabbdaaaacabcddabcacadbdcbccaddacbacddbbbababadabbcabaabccbababdbbccbbccaaadbbccdcacdcbcdbcacaadabadaddcabdbbdbcdacaadaabdaaddabbdcbcaaaaccbbabcdabdaaabdcddcdacccdacbbbaaabcdcdbbacaacdbdbdadbacaddacaacadaddbabcdddbbcababcdbcdbdaccbdacbcdbcbdacccdaadacbadcaabacabddbccaacbabcacccbabadadbabbadabbdccaacbaaaaabaabdadaaaaacdacbbaccdacccababbbdcdabccdcacabdbdabbbcdcabacdddbbadabdacbbcbaabaacbccbcddbbcaadddcbaacadaccbdabbccabacccdbccbaaacaccccdadaadbcabbdaccbabcadabccdabbadadadcaabcdcdacbcbabcacbcbbbbadaddbabbccdbbdcdacccbdddaaabddacadbaadacabcbbdcccdbbccbabdbbddaabacdbcaacbdacbdcbbdcacaaadbaacdddabbbbddddbcdadbbbbcababccbacadbbadbaaaaabcdbcdcbadcdddddcbacaacccdcdddacdbaddcbdbcddbbdccccbaccdadccbaabacaaacadadbccdcdbbbbdcaccbbbdcabcdcbadadbcbdddcacbaacabdcddcdcbcbaabcddbabdbaacccbdcdaaabaccbdaccccdbcacaaacdbbbabbcdddbacbcbacbccdadbcbbdcadcbacadadbbdaacdadaddabbcbcbbbcbdcacdccccdbcddaddcbdacbccdaabbadcdabdbdbcacccdbabbacacabbcababdbbdddbccaadbcbabbdcddaccbccacddbbcaddbcaabbabcacbdbabccbbabdddcbbaddbdaabadbdbcbadcaaccdabdacbbccbabadadcbbcbccdbadadbaddcdadbdcdcdbbbcdddddabdcbadbdbcccacaccdccbadccbcaadacaaccaddacccabaaccccadbbdbaccaaccbbbbbababcdabdcbdddbabdadbababbaababcddacacbcdcbaadbaacbdaadccaadccdccabbbbacbbdcbdddaacbbbbcbacabbccdcdadcadbbccbabacbaccddcaaabdaadcddccbdabdaabcdbcbababdcdcdabdbdabccacbccdcdddaabdacabdaacccddccacbddaaacdabcdcabccbcbacdbbdaacdbdcccaaacdbadaaadbbdbdbdabccdcdcdcaaccbcddabdaaddaabadbdabbabacbaabcacbbccaccbdaccdddadacbcbdcbcbcbbbabbbadcaaacadcdddaccbbdbbacadbcaaadadcabadcbbbcbaababbabaddccadbdcbccbaccadadbbaadacacccddbaaccaacabbcdabddddbcabcbccccbaaabaabcdaddccabacdadaabcccbbddaacdcaacccaaacaddbccdccaadbbcadadbdbbdaadbdaacabddaaadaddccbbaddaccddcbaadabbcccabacbaddbdcbbccdcbdadcdcdcdcbcaccbcccadcbaaabcbbabddbbbdcdbcdbbaccdadbccbddbabaccddcbdcbaadddbdcadcbaadcaccbccbcddbaadbabbcddbcbcbdadacadabaabbcbacadcdabcaddbbcbbdcbcdddadacddadcdadbdcaddadcadbccadacabaabacbbbcdbcdadaaddcbaabdabcbdcccaccbaaccdcccabccbdbcbbdadabbacbbcadbccdcdcbbbccaadccabadabdddbabaddadbbdbbccacacadbbdbbdcddbaacabadbbaadadabcbabccaddbddbbdaadbdadbabacccababcabaabaababcbaabdbddbdbcdaabcabdadaaadaabcadaadabcadccddbadaddbacabcbddadbdccaaabaaccaaacdcaaadacdcaaaacbbcbdbddacaaacbaccdcddcbdabcadabdaacbbdcbbcbdadbbbdcbacdbdacccbdddddbcbccacdbdbbddcabcdabbccccaddcbddcccbdbcdddddabcdcdaddcdadbaccbacbacddbbcdcdcadbddcbdccccacdbccdcbbdddbcabadcabbdaddcbadbadddbdbdbbdcdabbdadabcddccbbdddaddaabbdaacdabdccbbabbaaadaaaababdcbaddbdabbcbaccdbaacadccbbccbabcbdbcaddabbaacabbbbadbbbaadcdabcbadddcbaccbbcbdcbbcbbccdbaabbccaadacdacdcdacabcacccbdccbdcaddaabacbccabcabadbcaddccbdaddbadbdabaddaacbbdcdbaabcbaddbbbaacdacccddcdadaaddbbaaacbabbadababbbcccccddbcddddbcadbbbaddaadbaacdaababdbaaabccdaaacbcbcaaabbcbcadbddccdcbcdaabcbaccbdbdacacbcadbbcdaccabbbbcccabdbdabcdbddbdbacbbaabbcddaddbaddccaaddbbadcdbdcbbabddddcaccadcccabcdaacdddccdbabddbcacdbdaaddbbdbdadcaddbaccdaabccddbcdbcdaadcabcccbabcaaabbbbddaddbaaccaaadbbcbdcadaddbdacbbdadacabaddcddccccbabccbbbcdccddbdbacbdbcdadaaaadddaacbdcdadcbabadaabbbadbdadadbccadbacbaccccbcacdbacddbdbaaaaaabbcdaadddbdbaaadabcbabaddcbccdbaabbddabdbdbdbcbabcadcbaacdbbbcbbabddadacccacbdbbccbbababadbddaccadcaacbccccabbbbdbcbabccdaaaddcabcbaadacdbcaadbbddbbdaaaabcaacddcdacdaaadcddcbdacdbcabccacabdacdbdaccdcbaadbdacbbdcbdaacacddcadccabbddcbbddcdabbaadacabbcdcdbaabaaaddbaacacbdadabdaddadcbacdacbbabddccbddacbcccabcddcadbcaccbaadaacbcbcddcbbbdddacbddaabbbabbbccbbdadcbbaccdaabadadabaccadcdddacbdbdaddbbcbcabdbdcdcdbddccdcbdbadbdaccbabccaccbdaddccbaadbccaadcabacababaacdcddabbcdcbcdabdaccbccdcccddaaacadabdcdcccbabcbbcdbabbcdbccddbcbbbdabadcddcbacbaacddbaadbbddaabdcbddbababccdbaddbdbacdaadcdcacabbbccdaaabccdcbabaacdcbacacaccddbaaabcaaabdddacbdbbcadcdcccdccbaccbddcccadcbdcdaaaacbccaadbbdddbccabbaaaddaddadcdadaabcdbddbbababdcbaccabaaabdbbcdccbaacacdadcbddcbdcdcbabcdaaadacadccbbdccdcdaccbaddcbcdcdaaccbcdbdcdabaacccabddcabcddbcbbddccabccdcbdcbdbdabaccbddcbdbbdbaccdcccadbbbdbccacbbaadaccbcbccbaabbacdacadbcbdddddaadcaccdbcacbbdcccdbabcbcddcddcbbdddbcbcbdbbcbacbaaaccababcbcdbbcbbbcdddbcdcddcdbcdbdddcadbddacccddddbabbaaadbcabbbbadabaccddbbacacadbcdddbdccccbadddabcaadaaadadcbabbdbadbaabbadcccbcbcdaddaacdacccadbcdbddaadcaccbdbacddacccaacdcdcabccadaacaaabcdcccabcdbbcaadcaccdbcadadcabcdaadbddcddadbccabacadccacabbdbaaccadcadacacbccbbabddcadababbbbdbdbdcbcadcbbdcabbccbaaddabdcaaccbdcbaaaadbaaccbccacadddcabbbcbacccadcaddddcdaddbcacaacbbbacbbcbbbccacccdccbabdcabcaadccbbaddcbbdcabbdcccdcddddddcbddbabdccaddbabbcbcbcbaacbaabbbdaaacccbcadcbbcdacbbdbbccccadccbaddbddadadaadbcabadbddcdacabddbbaddcddabbdddcbdacdcddadcddddccdadcddcabbdabaccadccbabbcdbaccaccaadaadccacbccbabcaddddbdbdcacccddabadacbbaaabdbaadddbdbddaaabccbbabaddcbddcbdbbcddadabdccbddbcccaadadcabcccababcdabadaaaadabaddbdaadadacabddacdacbbaabddccdacaaddabadadcaacbccaacccadbdcbbacccbdadabcadbcaaaadcbccddbbabbdcbddacaadcdbacdccbccbaacadcddcbbadbbbbcbabbcdbbdcdaacdccbddbdbaabcaddbcbababaabbdbcadabcbddbaddddaddbdadadabbcdcaacdbcbcaddcbacbaabbaababacadbdcaabbccabddabcaacbadbacccbcdcacadddbdccacbacabdadddbababbadaddddcdbdbbabbbabdcabcbaababbdbdbcccbccabbaacabaacacadaddabccaababcbbbabbbbdaadddabbabbbcbccdddddaaddabbadacbadbccccccdcbabdaaababddbabaadccdaaabdaabccdacabbcbbbdddaacdaaadacbcacbcabbdabbdaacddaacccadddbbbacbbdccbcddacabbccdbbabccdaddddadacabccadcacbdadddccbbbcbdadbbcbdbcbdbdbcadabbcbddbcdccbaaaadcddccbdcbabcbbdadbaccbddcdbcbbbbbccdaabaccdccddaaadbacbbcddcbcdcbbcdadbaacdbadcbdaadaabcbbacbdaccdbacbabcdbacddbdbadddcbbdbcdcacbbcabcabcdcccbacabccbcddbcabcdcccbbbbcabcadbbabbcdbbccdcbdbcbbddbdaccbaabbbbdcabacacdbcbdadcdcdbddaadaaacbabcbcdccdcacbbbddddbabcbadcdcbdbadaacddbadbabcdcbdacadcacadcbbadbccddacdbbacbbabdcdcabdadbbabbaaabcabccdaacbbaabcdbbbcdcabcbddddabacbdbcccabcbdbdaaadaddbbccadcdddacddccbcadcbaabbdabcdaaddcddacabdcacacaaaddcccacaacbcaddbcdaababaabcccadcbddcbdacadbcdbbabbbdabcaddbdccdabdbaddaaddabdabcabaadbbbdacacaddadbccbbdbdcadaddabbaacacccccaacadabbcabccadddacdbcdaaccbacdabbcabdbbbbdbaabdcdbbbadaadbcadcbadacacabadaacadaddbdcbaddabdcaacbaadbdbcbbbbcbbbaaadccbdaabcccddccdbabbabdadbcaadcbdbdcadcddabaddcccbdddbcccdbcdacaabbcbbdccbdcaacacbbdddaddaabbabdccaacdcacaabcbaaababdbddcdbcddbbdbcacacaddaddacbcdcdccddcabbcaadcdabddbbbcccccaccbcadccddddcdddcbcdcddcabcbdaadcbdbbabdbacddabaacbdcccbcaadcabccbbaddddadbacaaccbbaacbabaadbbdcdbaaabadccdaddaacdbadddcdcdaddaaccbcbcdadabccacaaddccddcbbbbbcaacdbdcbdbcdccadaddcddbcabcabbbcbadadbdbdbbcdcbdcabadabcdadcddabcbdaaadadcdabbcaadbbddcddaccbbbadaddcccdcbbdddbccacaadcbddaddcdbdaacbaaacdaccdbdacdcdbcdadcbccacbcbcdadccccdbcbdacccbaabdbcbddbdbadcadadabbbaccdcbbaabcbcadbaddddaccdacadcddbcdadccccacbbcccaaaccbdbdacbcacbbcaabaccacabbcbdbbcabcaaddddcdbdccacbdccbdababccadbddcbcbbaacabbabdbadcdbcbbadabbdccbddbcacbbdccdbcaaadbccdcddddabccdacddacddcdaaadacaaacbbccaccddcdbccdcdbabdbbccdccaddabccbcadccccbcacddbbabbbbaacdbdbadbdcbcdbbadbbadaadabbaabaacbccdbadcbacacbbbbccadbbbcbbddddcddbdbdacbcdbacacbcccadccddbddadaacddacbadcbccccddbcabddddbcbccdbbbcacccccaccbbabbbdbbaabacacdcbcbddababababadaddcabacdcbcacaabdabcdbbdcbbaddbdaadbbbcacddaacdbbddbadcbbbbcbdccccbbbccdcbddacaaabbbaccbaadbcddbcabdbcbbbacddaabbcccabdbbdcccbdabababbcdcacbbbadabcddccaaabacbdddcccccbbabacbcbbbdbbbbbdbbccabbbacbabbdcacbdbbdbacbccbabdbdaacdbbcaadddabddccacbdbcbaacbbbcbabadacbdcaacababaaacbbcacbbccddbdacbadcacbadbddaddbcdacccbcbabbabddbaadccdcbccbaaddcdbbaccbaacacdbbdbbcaaacdddaddcdbcaabbdccaccbacaaabbaccaadcdcacbcdcbadabdcbcdabbabccaacdadbddcdabbcbdbccbdbbacdacacbacbaccbbaddbcbbbbbcbbcacadddbbacdbcccccbddddbbbaabdcadbacbdaabbccbaaddaddacaacabdddbaaabcdbabcdddcdccaaccadcdcdacaabcdbbcaccdbcbacaaacdcdbcdabccbaacbcccdccadaddcbabbbcaaacbcbdadbaabaaddddaccdadcabacbdcccbcdcadcbbbbccdbddbdcbbcbaabbacaadddccaabdbdbcadabdabddbcdcdcccdbbbaaacbcbdaaaddabbddbbcbbcacddcccccdcadccdabcacaabadcdcdabbbcbdbcbaacdabcbaaababdabdbbdcaccabaacbbaadbccbcccdbcbcacbddcadcdbcdaddbaabbaddbddacbbbabdabaccadbcbbabaddcdabdbaacbacbdcbbbcaabdbcbcadddaddcdcbccabbbdcbabaabcabccccdddcbdddbdbaaccbddabadcbbbdbabcbbddddccbddccdcddbbbddadacddadcdbccccbddaccdbdcbbbcddabacbdddacdcbdcbdcbcbbcbddcadabbdaddbbaccbcbcbabdbaddcbcabbbdabadcbaccabdbacbccadcccddadbaaccadcdaccdbaabaacacacadbdcdabbbbbcbacdccdabbdbddbacbccccccaaddadcbabaaadabccbbbbddbadcccdbaabcdabddcccadcadccbdbadabdcbabbdbbbbacaadbbdbbbcabbbadaacddaaabccbcdbbbabbcdcababcbcacbacabaacaccaaabdbdaabacadbdbdcccbacaadcaaaadccaaabdcbcbaabbdaddababcaaabbbcdbbcccadaacbbbbdacddbbbbbaabadcbbbddcbbccdaaaaabddbcaccccccdbbbadbdbcaabadadccccdbcbdcddaadbbbabccccdcccabdbcacaaccdacadcaabcaccbcbcddadcaccdbddbcdcaacadcbaabcdcbbcddbbbbdcadbcaddcacaddaadcacbaaaccacbcabbdabccbaabdbaaacaacbadcbabdaabdcaadbaabddbbabddacbccbdabdbccdbdbacdbaddcdbbbdabddabccdadbbbbbadcbbbbcdabadadccdaddbddbdbacacdcdcbbbbdbdaccdcdabdabbbdadbcbbcdcdbacddcbdbddbdcdbaccaddbccbbcdbbcccdacacacdbbabdccbcadbbabbddbdbdccdadbbbcdabcacacdbcbdcdacaddddbadacadbccabdcadaccdabacbcabccabbdcaadadacbcaabdabbcddddccbbabbabadbccbbcaabdcbddccbbbacbadbadcdbccdbdddbdbcadabdbcbbdaabddbcbdbdcbdbccdbcdbaccbacdbdbaaccacadbbcaddbadaccadcacbadccbccbaddccbcdcacbddcddcbcdcadbcdbdadbccbacdcaddddabcbdcaadbabbaddabbdbdbcacbdbdabcdbddbbabbdabdabbddaaaadbbddbdbbbbcbcacbbadadbdacaccadbadbcacbdcbbaaaddbdddbcadbccccccabdacbddabbadacaacbcabbabdcbdbcadddccddccabcaabcaacddcdbddacbababdbdcbbbabdcdcbabddccabaababdcaaaacccaacbbbdaaccdcddadddcadcabccdbaaaccdaaaabddbcadbccaabcbabcadbabdbabcacadcdadabacdbcbadabdaddbabcdbccbbcccddbadbdabcbbcadaababbdcccbbabbcddaddbbacbdaabcdabbdbdcbaaaccdacaadacacaccddbcaadacbdabcbdbaadababaaacaabcdcccbcbbaadbddbcadaddababcbbcdddbcadacbdcdabbbdbdadbbcdadbcbcbcbbbcaadbddcdbacbcacaadcacbcbdadddbbdbbadddbaabcbcaaaadbabcdcacdbcbbdbcabcadbddddabadbaaaabadbabcdaaddcbbcddccbdaaaaadaddbbdaddadbbcadcdabacaaaccbcdccadacbcbdcddbabdbacdbbcddadadccbbdbcdacaaadaacbacbbddbdacabcbdbcccbdcddcacbcaabababdbdbbbdddbadcaabadadcdcdbcdacbdddaddabcdddadadbbdbbdbcdddbbacbaaacbdcddcdadaaadbbdbaccdccaadbdbdddaaacddbddbbbdbdabcabbdabadbaaddddcdabcdbdcabbbbaabadcdbbacbdddbcbdbdbdcacdbddacaaddbddbbaacadbdbdadaaaaadaacdbaddccdddacacddcbbabdaccbdddbdaddabddbbdbdbaaccabbccbdbbccdddbddaadabdbdbdabaabdabccbbaacbdbccdbdddddccbadddbcbcacabddbadbcaddccdbcdadacbbcbaaadacdaacaddbcccbbdbabbbbccbcadbcbcbdccbccadbbdabbdaabbaccdcaacbcbaaadbcdcdcdbdbcbcbadbdddcbdbcadaccdcdadbbdcacbcdbdbdcdaadaabdcabbadacaacccaacddbccbcacbcccacabcadccbdadaaaddcbcdadcbcbcaadbacddcbbccabddcaccddcacadadbccabaabbdcacbbdaaccaaccacdbbdddadbacacbbbadddcaaabbacbbbabcabdddcdbacaccbcbbdcddaaaaadcaabbdddbbbaccacbadcaadbdbcdabbbcdcbabdccbccbbacdcbbcdbbbccabaaadbdbbdddbdcacaababcabdcabcacdadddcccdbdabbaacccabbabadbabdcaacacddbcdddcaaaadbccabdacdaabdcbcbbaccadbadcdbcbbaacbaccadcdacdbbdaabdcaaacbaddbccacadbabaddadbdbcaadcdbdacbabbabccbbdadbcddbbabcddccabccbbdbdcadddbaccdaabcddbadcbddddaddcbcaccaabcdbddcabcbaccacdbdcbadaabdaadcaacabccdcdcdcdbcdbdaabcccddcacaddbcbcdbbadbacbaccddcdbcaabbccddbcdbdddcaddabdccbcadcdabbdcbbddacbbcababdddabaacdbdbccdcbbddaccaabbdabbbcdadadadbacccdaacabcbccaabddcaabcaddbbbdcaacadcbdacdcbdbbaabcdbcabbabbadbbbccddcbbadbbabdaaaadabadccddcdaaccddadababdaadbdabcacbbccabbdcbcddcddbdbcdcbbcaaadddadcbaddaaadbbacdcabcdaabcddacaccbdcdcdadbdccdbcdaaaaddabdaddddbdacdbbcbbcdacdbdabdcbacddbcabdddcdbdadccabbbaddcbcbacdbaccbacccbdbabcbabbaccbdaccabcbadcdaccabcbdaaaddabacdcabcdbcdaadcadcbdbbbcaabbacdbcbacddaacacbcadddbdbcddbcabacbcccbbcacdcccdbddbbbaabbbddabbdbddbabadbccbababbbcbabbadbbaddabaddaccdddcadccdcbdcccbdaacaccabdadbbccdccababcdaadbcbbadcbcacbaddccdbddcbbadcddcddbbbdbabdaccdaadcadcadabbadbabcbbdccbbbaccbaddcdddadccbadbacbcbdaccbcdadccabbcdbacbcddcadcdbcaddaccccdbcdcdcaabadcaaadcbcaaabababbcacbbcccddadbdbacbdadbabcabdddaddcddcaadbcaadcadbbbdbcbcdcacdabacbbcabcdbbdcbbdcbbdaddaadccccacdbddcbaabdcbdcadbcbcbabbaaaacadbbacbbbaacaabaacccbaabcbaccbcbcdbcccaabcdddbdabbdbbdabddcabadadbcbdaabbbbbdbcddabcccbcbbdcbdadbadbddccbbbabacacbcbdaccdccdacdbbcdabccaaadcbbbdaaaadbdddaacaaaadaaabbadbcabadbdddcdddddadcdcbcdabcccbcbbcddaaadddcddcbbbbbaacdcdccadaaacdbabddaabaabcbcddaabacadccacbadbbbdadbddbbaabbbcaadbaaaaaabcacdaccababbccdddcdcddaccccdaabcabdcaadccbaababaccbbcbaabbbaabdabdbbabccdadbbddcbadbcbadadbdaccdaaaddbaaaccbcdcbdcbadacbcbbdbccaadadddbcabacbabadbaccaddacbdabcaccccccacdbdccccccbddcdaaacacccbadbdbdabbcaaddacaaaddcbadcbbccccabccaaaacacacdbbaabbbaaaabdcbcacdadaadbcbdabcbdabbbaabaacacdadabcabadbbbbbaaaaaabddcbcdbbcdbcccbbbacbcdabaabaadadccdadcacbcbcabcccdaabccbcacabaabdbccbaaadadbadcccdbabdcabacdaddaddadaabadabcdadabcbdadacccbcccaddcccabbbddacdddacbcbdaddaaddccbccdcacdcbccddaddaabcaacccbdcadcbdadaabdaadcbcccadddbcacbdcdbacccaacadbababdaababdbbaadbcdbaabdcabbcabaadaddcdccacdacccdccbdaacdacdaacdccaabbbacdacbcabbccdcaccbaadcadbcdaadcbbdcddabdaabdbcaacdddaccdaacbdbaddaccadabaddcdcddbdbdadccaaaabddbaaadcaadbabdcbbcccdacddcbabdccbbcdcbabbcacbbadacaadbbbcbdcbbabccdbddbabcaddbddcadbbbbacdbcdaccbaaadbbddcdbbdbcaadbdabddaadbccbbcabadaaddaacbacccbdcabcdbdddcdaddccbadadcbabcdbdcbaadbbababbcbbbcccbdbaabcdcdccbdcddcabcbbcaabadabbcacbaaaaddadaaccccaabcdcaadccababadabbacacbddcaccccbcaaccdccbbcbdcdddabdbabbdacbbccdcacadbbcbdbbaadccdaaaadcdbddaddbcadcbdcacdcbdaccccdadadbdcbbbccbbbacaabddacacadddaaadcdcbaababddbabcadacccbcccddacacbcbbaabcacddbbcbdddcacdcdaabcdcabaccdbcccaaaadacdbaabcdadabdaddcbadaabcbbbdcabbababbdcbbdacdcacbdbddaacbaaabdadcdaacbccddcacddacababcabccbaabaddcabbabdbbdccacddcbdbdacadbbabdbdccccddbcabbaacddcccdbddaaabddacccadacaacdacdbacbbcaccdcacdcbbddadaaabdddcabababdbddcddadadbacacacaadcacbbdbcaaccbbabaadcbbaadbcbaadaccbdaaaaccaaddaccdaaaaaccacbcacbccadbbbbccddccbaabacbcdadabccdabbbacbcadaabcbdccabdcbddbaccdacbddccacbaaacbbdacbdaaadaabbddcdbdbbdbaacddbddbabcbbdbaadbccddbccbcaddbcbaacdabccdcdbdbdbcbdacacbbacbaacbbcbcbbaabacdbcadbbbabdbcdadcdbbbcacbdababcbbbaccadbdaabdaadabbdbbcacdcaabadcacabdaddcdadaccaabbdbcddccabddcdbabacccdabcddddcbdabdcaddcccdcdabbbbcbccdccbcddaabcadbdcadcdcacbbbccbdacbabaaabbacbbccdbdbccaabaaadbabccdcbaaccdccaccbbbdccaadcbabbacbbbabdbaccbbcbdbcccdccbabbccdcbdacdcbbccbdcaaadccdbbdbdaabaabdbdaddbabbbcbaacadbdbbccaacbcabcdbbddaabcaadbdabdbdbabcaaaaabacdaddbaddbccbbcaddbcbaadcbabcccccabcacdbbdbdcbcdaccdaadcadbccdccdcbaddbcadbdcdbccbdaaadcdadcbbdcabccddbcaaadcbbcbacbbbcacabababbddaddacbbcbbaabdbddbacbacaacaccacbcbcddbaaaabdbdaccbbddaddaddcbccaaaacacccdcbbbdddcdadaabddcacabbaadbbaccdbbacadcbbbcadaaadcbbbdbcadaabdadbdacbbadababdbbbbdccbbacccacdcbcddcabaddaccaacdbccdbacbdbdcbcadcdbaaccddcdadcdbaadbcbadbcdbdbdbadcacddaddadbccdcabccdddbbddadbbaadcbccdabbabaddadcbbcddadddbdbaddddcaabdbabcacacbacbacaaacacabdbcbdbdcacccaaaddacdddbbacabcddcaaacaadbbaaccbddbbbdabcddaadccddaaccdabdbbcdbcbbdbcaacbbbacbaadcdaddbbbbcdbbbbadcbbbaaccdcadacdcccbabacabbcaadbddcadabdacaadacdabbdcbbbddbbbbccbaadacbcbdbccaacbbcabddddaaabbdabcaadcaaccbbcbcddaacabaddddcdaaacbcbacddbdbacaacdaabacaacbdbdbabaacddabcdbcbcdcddcddcbdcccbcbaccdcddbccddddcdbadbcbdbcacccbacddadccdadcdadcbabaabddbbacdaacabdcabaaacbbccbaaabbdcdbbaacacdddbdcdacdbbdabccbabaddbdddccbdadbddabdbbcdadbaabdccccdacbabccadcbdacccbcdaccddbbbbccaabdcccbabcccbaaacdbdcacbbdccbbbdabbcacbdbcdaddcaaccabcacaccbcacaccbcddbdcccbcbaaddbaabdbdabbaddabcaabbabddccbddbaaacdaaaabacaccacacddcabcacbdaccbcbaddcdbdabacdbadabbabbcbcacaccddbadbbcaacbacddcdbdbbacabdaaadadddabbcadbadaacaacadaacbdcabbdbaaabadddaadacbadddacdbbadabdbbbbcbddaaddbacdadbdcacdbcdbadbdcaadcdddbbccdaaaddbbabdbccdccdcccacaabccdcbccabcddddbcdccacbcaacabddadcbacdaabacaaabacbcabbbbdcbdddaaaabdcdabaabaddcaccacbbdbccdaacacbdbddbbcdaadccdcddccbbbdccaaddaccdaacacbdcdababadbccdaabdcaacdcbbdbacbcdcdacbcadabaaddaabdabdaccaadbbbaabbcbcacbaacdacadcaaccbdddacaabbdadcbadbdcdcbacdcadddbcdcabcddacbbcdadccddcbadaacdcdbddbbddbbcdadddacacacadcdbcccdccccacdccbbddadbaaddbaaadacbbccacabcccdbbadcabbacdddcdbbbddaaabcadcbaccacabbdddcbbddcdcbbbbbcbadaabaadadbdddbbdbcccbacbcdcbddcdddccadcddccacdcdadcbacdcadcbddadcdcabdacbdcbdcbddddacbababbcabccbbdbdbaabdadccaabcccbacddaccbcbbaaccaabcadbcdbdaccbdbcaaaaccaadadadbbaacaabacacbabadcddbcbcbdabaaabbcdbdadacbabdbdbcbdacbddbdbbbaccdbdbaccabccadacddcacbdacacbabcddddbabaddbdabbddcbdcacabdddcaaacadcadabddcbdbbbccaabccbdbbabaaaccdddcbdaddcbcdcdaadadaadcbdabcddadbdaabaabadacdcabdbbabacadccbddacadadaabcdcccbdccddddcaadabadddaddbaaaaacbcdabddbdacabbdadddccdcbbccbbacccbdbdbabaddbddcabbaddbbbacbddaaacbbbddcddddccadcadbaacaaccbadabccacccbbdbadbbaadbbdabcadaacacadadddbbbbbbdbdcccabadbdacdbcccaabcbcadaadaacbcdaccdcbbacccbadbccdbdabdbbdbabccdbcaaddddacdcbdabddbbaddbbadccbdcbbbbaaddaaabdcddabccaddbddbbbbbddaabbcddbbacdaaddddccadcbcabbccadcabdcdaacdcdbdacaddccadbdbbdbabdbdaddadcccbcbbbccdbacbbcddcacdcabaabcbbbbbaccccbaacdcacbdcdcaabadbbaaaaddacdadabdccbbcacabdbbbabaabdbcaadccabadbbdcdbddaadbbbdcabacbcdcbcbabcaabaaddbcdadccaccbdbbacacbcccdadbddcadabddbcadaacadcacdaadaddddddccccabaadbabbacbddcbdabaadadabdaccdabdbbaaabddcdaabbcdaacaddcadacaccdcdddcacccabadaaadcaabccacabccdacacdaaacbaacdbdddcbbcabaacacdcaadaaabacbccdddacccdaadcbdbacbcdaaadaaabbbdddabbbcabccddbabaaadacdadbacabdadbdbdccabcaabbbdbdddcaabccbcdbbcbbcdadaaaddbcbdadbdbbaccddababbcbbcabccdabaabddacaddccadcdbdbdaabadadddcadcddcddacaabbdaaccdaabcadddbaadbbddbdacaccabaaadcdacbbcdacccdcabdacdcdbdabcdddabcbcadbdddbddacdbbdaccacbcadcbaccbdabbbbbbaababdacbadbbdaadddabdcbaaaccbadaccbbbbcaabbaaadadcacbbdcbcaadbccdabadaabccbaccddbbacbdcdbadcabdadcdbbaacaacccbdcbcbcaabdbbddbbaaadccdadbcadbbacdadaaccdcdacdbaaddaccdcbdaacaabbcbaadbdbcddcbbdcaddccabaccdbcddcbdbabbacdadaccdccaabbdadcaccbcbacbccbcccdddbbbadcacbcabccbacabcbbbaadbdddaccbdbddbddcddabddadacaccaaaddcbbdcddabbaacadddbadcdcabcccaddbabcbaaaddbbbadbbbbbdddcbbbcabbbaddbbddbcbbbaacdddbcddaccbbabaccbcdabddcccbaaccbbcbdddaaadcccccccdbcdcdbdcadacbaddaabcddbcabccdadadbababddcddacddabdccbbacbabdcdcccbacdacbdabdbabbbbabbaacbbdadaacbcaacccacabbcdcaccbaadcacaacbcacadadbbdbdbaababdbdbacaaaacaaabbbbcccbddaccbdcdbcbabadbabdaccdbbddcdbbaccaabaabbddacddcaabcbbdadacbddcddcbaadcdbaacbcdadacbbbbcbdbddbdcbacdddaddcadcacbbbcadcaccbdbccbdbbabdbdbdbdcdbbbbacdbdccddcacddbdadbacaddcdbabbbabdbcdbadbdabdadbbcabacdbcccbbabcadddddcacddbddaddacdbbdbaadbbacbdbbdbddacaadcccbadcadcccbddadcbacccbaadabcbaaadbbdabbbdcbddaadadcdbcbdccdabbcbdaacacabcdadcbbdbcbdbdadaaccbacaddaddcadaddbacaabdacdcadbccdbbddcbaadacdbcbddbdbdcadbcbbbccaadccbadaacaaddacabbcbccdaccabacdaababadcacaccacaababacadaabacbdbcaccbbaacdccbdcddbbddbcbaadddbcbcbabdaadbccdbccadababcadabbbacdbacaacadaaacaaccadbdbcbbbbcdacddbdcdabbbdcbbcccdbabddddcabddccdaadcdabbadbabcdbbdacbbbbdcccddbcdbbaccddbababadbacaadbdcdcadddbdbbcadddacbbcaddabacdcbbbacdaccaadbcacbbadcbbaccaaaacadcdccddcabadccbcadbcbbbbdacbcabdcdcbbadbbacaaacaabcbcdbccccabdbdabddbbaaaddadccbcadbadbdbcabadcacdbbbaccccbcccdbdadaadcdccbcbaddbbdaaaadaadccbbbdcbaabadbbacbdabdbddacaabcadabdcabcddbbdabaccdbbdbdbdbcdddbcabcbaccccbbcdbacbacddcaccbacbbacdcdcaaaacddbbbbadcdcdbbcdaabbdaccabbadccdadcabbcccaadcddacbbcbccbcaaaacbdcccadbddadcbaabdaabbdbdbadaaddaaaaadcccacbdbccbabccaccddcadbdbbbcaaadccdbddaadbbbacdbaddbdbbbadbaaadbbcdbcbdccacabcdbbbadccdbdaabbaabbddadcbddadaaddbddcaabdddccacadcbddbaaadaaacaadaabbcbdccbcaccadabdacddbcbbdcacbbabcdacbbbccbcbdddbabcddbddcbaccbbbadabbabcabbbbbcdabdbcbaddaadacbaaccacbabadcdbbdcdbcaddcdcabccbbdccaccccccddaccadccadbabacbbdccabdcbcdababcccdadccbcabcbadccaaaadddcacccaddaccdccbbdbddbaacdcdbbabbabbccdbaaddbdcbdbbcaadacacdddbbacdccaadcdcbadcddccdbabbdcbbbbddbbdccdbaabdcbcddaabdaacbdacacdcbbccbaabdddcdaadbcdcaabccdddbcbcabdcdcbdcdcbcddddbdacbcadabbcdcddbbacdbdbbcadcbddddbcdbdadbcacaabbdbdacbccbbccbbdbdbcbcccdcaacddcdcadcacadacaddcdcabdbbcbdadbbdabcbbdbdcdcddbbbbcdbbaacadcacdacdbaddddbdabadabbcddacbbcdbadcbccbdadbabcaaddccaabaaddbcbaabdbdddbbaddddcbdabcdcbccbaabbdaddaabddbbdadcacadadcddbccbabbacbbddbbacdbbdaacbbaddddadcbdababaadddadbbdcbdabdaabdcbcdbbacbcdacacccabdcddcaababcccccacdbbcbdcdadbcacdaaadbaaddcccaabcacbbbdcbbadddbcdbbbbaabaabdaabdcddaacccbbbaccdaaadcabbcccbbdbcbacdadbdacdcabdbdcaacdaddadbdcbbabcdabbdddaabdbbddaabdaaccbddccabbccccbaddadcbdddcbbadcabcbaadddbccbbbcbbbadacaccdaddaacbdbadbdcaacacbccbdccaacdaccbbcbdbdacbcbdbcadbaddbdbddcbcbdcacdaadbaccbbbcbddcaaababdcadbcadddcacbddadaccadcdbdcbbdbadddbdccaacacaccbacacabddabddabbadacadbdacadadddacabccdbacbdaabacdabbababcdacccdcdacaadbabdcbbdadaccadaadcbbcbabdabacdacbdcacaabacdcadbbdabadabbdbcdaaabbddcbdbacaddadaadcbaacacbadbcbcaccaaadacccaadcdcddabbccbcdbaadbccbcdcadadcbdbabccdcbabbdcacaaaadcbddababbbcdcbadddccbaaaaaccddcdbbbccbcacbdcdccabdacacdadbdbacbaacacbacdbbbdbbbcaadacacaaadddadcccdddacdbacddbaddbabcabaacbbabdbcddadabbaacdadadaaddcaadbbdbdcbcbbcbbabbdccdcaaddbdabcccaabcaabdabcdabcaaacbdcdbabdcabbacdaadbbddbaaabbdbccacbcddbbdcccabdccbcbadbdcacbaaabcdacacbbdaddbbdccdcbabadddaabbdcaabcccbabaabaabaccbbabcddabddabbbbbacddaccbdbbaccdcadcddcabbbbaabbdabcabccbbaabacabddabbaccacdcddcbdbadccdaccabcabaccabdabcabadabaddadadaaaddabacdbdcddcacbbbabbdbadcddbcdcddcbdbbdbddacaddcacdaabcdbabdccdddbccbcbdbcacddbaaacbcabccacadddbaaddbadbcaaddababadbbcadcdbdbbaddaddbdacdcbbbdcadbbdaabdaabcdddaddbbcabbbdcbddddcacbdbccabcabdacdadccdbcccdadcaaccdcabbbbcdcbcaddbcbcdbbdadbbddcabbbcaabacbbcbdccbadadcbcdccdbdbbaabdadbbdccabbbdbdacbabcaccacbacbbbddabdddcacbccbacaabadcadcddbdbbcacabccbabcadaaadcaddcbcacaccaddcdcacbbcddcbbcababbacbbbbaccdaabcbadabadcbdbbdcbbcacbcdbdccabcadbdadaccabadccbcddcdcdcccdcadacbcdbddaaddaabcdabcadcccccdbddcbcbdaccdacdbcadbbbdccddbcdbdaddccadcbbdbbdcdbddbbacbbaabcaaabdcbdcbcdcadcbcbcaddddbcbccdaabdabccbbadadabdaadabccaadaaacdbadddddbbaddbdbbaaddbcacbdbcdbbdcdaabdbccbdcbdaabbddddbabdabcdaabcdbabaccdccdabdbdbbdbbdacbccdcbbcbbbacddbdbbccccaccddaabbbcabacdbaadaddbcdccccdcbbbbdbacdcdddbdbcdbabcddcccccbaaacbdddbbcaddbbdbacbcbaacbaddbdccdcbdddabbdaadadcabccabbcbcccccdaaaacacdabcbdbcdccddbabdcccccacbacaaadbcacdccbaabbcbddcddadddadddccdcdacdcbcacdbcbdccbdabdccadaacdcabdccbcacbdadabbdaadcaadbaddbdbbccdbabbabcabcdcbddbacaddbbbaadabadadbdacaccbccdcadccbabdbbdbdcbbbccbbbdadabdbdbbcadadccaabaddbcdbbbabccdacbbdcaaddcbbccaccaaaadbdbbbbbcdaacbbcbadacddcbbadddcdcbccaddaddabbcccccaabbacdddbdcbccbcdabdddadbacaaccccdbddbdbcccaccbdccdcbaadddbaaabdbcccadbcccaabcdbbdbdbccabbbacbbddacdbbbbcadbdaadbbcacadbdacadabcbcdcbccdaaaadccdcdcacbdbdacaabdbabdcdcdcabcdaacdcadcdacabaccdaadaaddcbadbdabcbabddcbbdcbbddcddcbdcbcbcdcdacbcabbacabdaabdcabcabcbdccbdacacbddabadbcaccdbcccbbbbbccccddbaacbdcbcaaddbbcbcddacacbbaaaaddaadabccaadddbcdbabdcdacdadcccbcddaacbdcbdbbdbacdaddbdbddacdcacdddabaddcbcaabdbcbaccbbadbaaaabdddbcacdadabdcbdbaaabcacdacaaadccbabadbddabbaccdbabbbbbaadabacbabcabcdababacadbbdbddbdccbabaaabbadcacaaadbbdaddabddbbccbaaaadcbcdbbcccacbccdbbddccaabccbbcbbdbcccdbbaabbadacadcbdcdcabdbcbcccdcaadcdbdaaabcacadcddabaacabbabccadaadabcbdbdaaaaaabbabbdbcaccaabcdcbabadadccbdddccaaabdbdabccadbcaabddabcdccbabcadccabcacbbccaaacaacdadbdbaadacbbdcddaaabcaaddcddcbaacacdbaaacdccbdaabbcacdbacdbaddbaaacddabcdadabadaabdadadbdbabcdaddadcbccccbacccbddcdcbabbcbadbcdbbadbbcabacbdadcccdbdbccbaddddbbabbaadacbadbdcabccabcbcdacadccccdabbdbcbabaabdbaddcbabbddbdaabddbbdccabccbbaabdacbddbababdaccdccbacacdccddddaacdaddaadbaadaacdcdbdddbaacadbcacdddaddcdddcbcbcbddbbdcaacacaaadadbaddbddcbbabdcacaacacacadadabcdcacbcbdccbcbdadbcaaabbcddcbaccbccaacdadccabbcdadaabacbaccaccdcccadaddcdccdddbbadadbcdcacbbdacbbadabccdcbdacbabbccdbccdcbddbccabdaadbddaddbbbadabdbbcbaccbdadcabdccadddcabcdcdccbccaddbcccbbdbabdaccbddaadcdccdbabdaadacbcddaadbadbdbacbadabbcaaddaadbaaddccbabcbcbbcabccdcabcbccbcbcacdcadcbcbbacadcdaabbcdcdbbccabdacadbbcbacadacacccdbcccccbbdcaddcbacdadbcacbdddbddabacacadccbcbabaaabcaddccdbdddccdcbcadddbdbbabdccbdcaaaabccacbbdaaaccadaaabbaccabdcbcdbdcddcabcbbdbdcbbadaaacacdaaacaccbbcbdddaaadddbccaaacccaccbbcadbccbdccdcdcddcddcdbbdccbbcabbcddaccbbbcbabcabcabaccadcdbcbbbdadaccbcbbbbcbdbcbcbcabdddaabcbdbbaccdbcdbdacccdddacbcddadcccccbbddddcabbaddbbdacdabbdcacddccddbcbabbabaabbbbccddadaabaaaccdcaccddddbbddabccddbabdcabadadbbdbabcdbcbaddadddaacccdbdaabadcddcbbcdbdcbbbdddcacabdbdbcccaabcbaddccbcbadccddbbdbddbcbccbbbdaddddbcadbdbbabdcdacacbbbcdbddbbbabacadbaccbdbcaccadabbcadaacddabbdbccbacaccbaadbbcbadbdddbababaabdccabbaddacbacbabddcbcdacaccbbaabdbbacabaaabdccadcdbababccdcbacddcbadaccacacddabbbaddcaacaadbbaddbbcbbccbbccbacddbaccdbcabacccbcccadabccdcbbcccdcdbdabbdaccdccbacaddaabddbdbcbaabcddbcbcdbcacbbbdaaadbacccbcddbdaccdbacbcdccdaddccdccacbccccbccbdbdaaccccbcabbcdccbcbdddabccdabdabdabdcbbbbcccdabdbbaaaadadadcbcdccababdadbacbadbbbccaacbddbacabcdbdabbdabbbcaabaacbdbbbacbbbdbacdbccbdccbdaddbbbddcacddbabbddadabaaddbcacbdabdbdbbbccdaacdbbdcbabddaabaabcacdabdbbdababadcaaadccddcdaddcaaadcbdcabbcbabcdaabdaddabddddadcccdacccacdcabdbbcbdaaacbabdcdccccabcbdddcdadccbaabccdcdbbdadccdccddabdbaabdadddccbcadbbacbaaacacabaabdacaacdabaaacbdadadabaaadcadbdbcbddacddacbdacabccdcbccbdbbaaccabbdcabbcadadbccbddddadddacbcacbcadbdbddddcdadaaddbabdcdcdbbbdbaccccaddbdbbccbdbaaaadcdcbccbcadaacbbcbcbcacdbacadbaabcdbdbdccbdbaabaaacdaddcbdbabdbdbadaaaddaaaacdabbacbdbbbcacadcdddbcdccaaadcbaacccabcaaccdaabbddcddbcaccccaaddaabdaabbdcbadaccddccbaacbcdbcacbcbbdcccbabcaabadabcbbadacbbdcadaabcbabdaaccdbdaabadadccbcbdabbdcdbcdabdcdcdbdccbbcdcdadcaaabbbdcadaddadcccaddbdacaadcbccaabadbbdabcaccddaabdddbbdcbcbcbabcbacbdbdbbbdacaaacabccaadabdbbcadddcdcccdaacacbbbddaacabaccbbdbcdbbacabbaaacdbaccbaacbaccdbadcabbdadbaccaaccadcdbbacaacadddadddadaddbaccbdbacdddbbabbbccddadabdcacbdcdbdbbdbaaccaaacddadbbcdcdddbcbdacbcccaaccbcdbbddaddbaccddadbbcccbbccadbdbcbabacdcddbbaddaddacbbddbdbbdbbdaadbbdaccadacaacbdbcbcdadaacabadcadddcddbcbdbdcacccdbbdccdadadadcbbbbabdbddaddbdbbdddcddddccbcddcbcccbdbcbcacbadababaccaacbbadcbabaddaabdddcbabcbaabdbcccdbbcbbacacdcbcccacbdbcaadcaaadccbbaaccdaaacbbddddbdaabaddaabcbdbacacbddcdabcadcbbbdbdbbbacaacdbdddacdabbcaabdaaadcabbbbcdacdccaadddabadbdaccddccaccaaccdbdddbabacdbdaabaccddbcbaacbbbabdcdbcacdbbccccdbbacabdbaadabaabacccbacdadcbdacabbdddadccacadadbdcbddbccadccccadddbbbcbbacccbcabbddabababacaddbdcdcdccabbccbcbbddaaabbddbbaddacdbccbccabccaadccbdbdabadcdbbcdcbdbdbadababcbaaaddbbbabdcadccbabdbbbacbadadbbadccbddbbabbaaacbbbcbcccdbcadbabbccbdbacddbabbaadcaacbadaddbdbcdcbbabcddcdbcbadbbabddbdddcccbbabbacacdccbcacdccdadddbabbcaccdbddbabccadcbbadcaadbbbdbaabdbdcddacbdbbbacbbdcbbbbbddcbcbcdbbdbcbbdabcabbddbcaacbbdcabdadacaaadbddbdddadadbbabbaccbccadaaabbaabdbacaadabddbccbdccaaabccdcbaccbbaacaacddaaccbcbcddaacddaddddddaadcdddbcdddbdcaabddbbdbbbdcdacccddcdaacdcbbdadcaccabdbabbcbcacabcaaccdbdaddcaaababdaaaadbcdbbdadadcdbabcadbdaaabdaacacbdbacbabdcbcbdabacdadbbbabcabdbdaaadbdcdabddcddabaabcbbbbbacdbabadabddccbadcbbadabaaacbbcaadddbbabacdcbcbcabadacdbccacadddcbcbdddcbbdcbcbdbbbdabaabaabdbadccddbcacbcdcbadcdddaccababccdbbdcccdddbdcdbabdcbabcddcdcbbbbcacaadaaccaccdbcbdddcdabcacadbdabbdbaacbadccacabbbccdbcacbbdbdadaacacbcbdacbdcbcacababcbaadbacbacddccbcaccddcdcbcdcacbddbcbcddacdcbcdbbbdcbcbaccdcbdabaccadccbddadbacacbdbbdbcadaaccaccbbcabbabcdbcdcccabbccbadbacdaabcccbdbcbbaccbdaacaccbdbbccaccaabadcbccdaaabccbbcbaabcadaacaaabadccdcccbcdccbddbbcccccbbcbbdccbddbacccddbddcbdddacbdcdcddaadbbbdccddacdbcdcadccaabbbaaadaddbdabbcbdddaadbababdaaaaacdbcdddbdaadbcccbaadcbcdaddbabcaaadcbbaadabaddcaaadccabddcddcdccbcaadddcbdacbacaadcbdabbaabdbdcccacbddcbaccabbcbccbddbbabadcdaaaadcdcccbdcdcbccabdcabbabadbdbbbbcbcbdbcaadacadddcabddbbbbcccdbaccabadacdbcdcacacaadacdbcddddbdbdccadacdccddbadbaacbbccddcdcddbbacbddbababdbdabdadbcacbbbbbdccdccbcbbacbaaabdaddcaabbacbdabbbadcacdabdcdccdbcdcbadccadcaadbaacddcbdccbdbaccddddcabacadabbacadccaddadddccdaabcbdcaadcaccaaddbaababacddcbddadbadacbbddccdacdcbadccbbbbbcdcadbadbdcdbcaaccbcccbbddbbbbacbcdcabdbdbcacacbabdbdcdbcdccbddaabbbbbdaccbddbaaabaaccacdccdaabaaddacacdaaddbacbaccddcdadacdabbbbcbcbdbbbdccadbddadbcbdaccaddadaabdbcdcabaaaaabbacbdddcdddbbacbcbdacbbcddcbcbcbcadcaabccadabdbaddaccaabcdbdddabbcdadcdcdbbacdcbacadcccbccaacbdadcccaccbcacdcacacbcacbdcdbacddbbddacdbdbabcddacabcbcaddbdacdcabcddbccccaccddbacddcacbcbbbdbdacdcdadadbbdcbcbbbbdbacdacadbbacaccbbccababbcbdabcdadcccdadaacabbadccbdaabbcacacabcbbbaacdbcadbadbbacbacbdcbdacabdcbabbaadabdbbcbdadbdcbcddccaddcdacaccdbdaaaddadcbbcdbdadcadaccadbbbdbadbddacacdcbdbdbdcdcbdccacdbbacbccadbdcddacaaaccccbbdbccccdcaabdcbcdcccbdddcdcaaacdcadcdabdbcacbccabbdcacbdcbdbbddabcdddacdbbddbbabbcddbdcbadbbddcdbdbbdbadcbbbadbdbdadcdaadaccbcbaabadcbddbbbcdacdcabacbadddcccccaacdbabddcbbacbcbddbcaaaacddddadccbadcaacbbcadccccabacacbdaaadadcadbdccddadaddcbbbdbbaaabdabcdccddcadacbcacbcacacddbbbacbaccacbbabdddccadbdbacbaccccdacaddabacadbcccbcbdbbbbddccbbbbabccabcdabaacabadcacdbccdcccbbdccabdbbdcacdbabaabbbccacdaddddbadbddbacaabcbadbbcaacabdacddadcddabdddcadbbdbbbbdcccacdadcabbbcbdaaaacabbccbacbbccacccabcddcccccdbbdbdabcbacaddaaaddcdcabcdcabbdabcadcbddbdcbcbbddaaccaccbdcadddcddbcbcddbbbaacdadaabaabddaddddccbdabbcdbdbcacbabdcddddbdcacabdccdaddbbbdbadbccadddadaabdbcdddcccbdababcdbbccccdbccdcccdcbbbcadcbabacdcaaaacddcaacccabbccaaadaacbcabdabbbbbadadddcabdcdbbbabaadbdbdbabadbaccbabaadabccaabbbbdbabddcdbbcddabbbcbcacbdcacddccbcbcbbccadbaccadcacadadbcbbddabbabddcbaabacbcaacbdbcacbdddabccccaaddbaabdbccadccdbcccacccacccdcdccbbabbdcadcccabaaccbaadccdbcaccbdbccdacaaaaaadabcbccdcddbddaadadbccbdbccbacaccdcdcdabcdadbbbdcadccadbdbbbcccaabdbbaaabbbddcbadcccabbddaccddbdabbccacbcbbccbcabddcdbcacdcdacacdbbabbdadaccaddacccbccaadaadabbbababaabbaccacaaabacacababcbcadbdcabbcbabadadcadbdcabbbcacaddabccdcdabddbdadbdbdcbcacaadcbacbbcccdbadccbddadcdcaddbddcabdaadcbbdadbadabcaadbdbaccbcbbadcddacadccccccbddaadaacbaabcddadcbcbcbbbdcabcdadbcdcdaddcbbdddacbdccbbabccacccdacbabcbbddbacdaabcbabbbdccdbbacccdcadcaddcdadcbabbcbaacbddcdbbdaacabadcdaabccdbbbdcbacadacbdbccbccccdbacaccaaaaabdccdaddacdddcccbadacbcabcbdaabacbddcbccddadbdcadcddadddabbcabddcaccbadbccabbddddbbcabdbcdaadababacaaacccacdcccccadbaaabcabcaabaadcbccbcccbbaddabdbcbbbbadcaccabaccbdbaccbcacaaaccbcadaacdbacbbcdcaabccadbdaccbacdacbbcacddbbacdbcdbadbacabdabaabadabcddcddbddbdabddbaadbacbacdadcabbacadccdaacabddaddabaaaabbcdbdabbaacabbcdbbadcdbbbccbcdcddacdbbcdabacccccbdadbccadcbcaababbcbdaacabdbbadacabcdcbccababccdabaaababacdcaccdadaddcbdbbddabdadaaacbacddbbbabbcadcabdadbbdcccbdacccccbbbaccacdcccaaababbadbdadbbccbcabdabbacdbaaaacdbaaaadbaabcddbcacacbdbdccbcabbdcccddbbddcdddadbbdacccaacacabaccddcbaadabbabcccddcddcddabcacddcddbbaadbbdccabdbcadddabdabbacccbcdadacdddbbbdbadbbdaddacabbdaabdadabdbbbcbcbddcddccdbbaccbcacdcdddacdbcbdadadbacbcabcbbcccacabcbdbddbdbacdabddbbbcddcaacdbbcddbccbabdaacabddbacbdbdddaacdbaddbcbcabaaabccacaaccadbdabbacaabdcbccabcbadbcbaddbaacbcccbcbbbabdadcccbdcdabcbdacaadacbcbabababcbdbaabddcdaabdbbbdbadabcbacaadaaadacbadddcaadabdbcbdcbcbddaaccddaaddcaddcaccbadbadbbbcbcdababbbcdaddbbbaacdcdbaddaaaddcaccbadcbcacbbbdcbddadcaabccaacacdabbbabcdaadadacddadabccbdbbcdabbbcbacadcbcbbcbccdaabdbbaabcbababacabcbbbbccdadabccbdcdcccdcbdddcadcccdcdaaaaacdbdbbdaddaacbbbbbcdadcdadaadccbdacbbdabdbbdadbabbddbdbaacaacbdaaddcdddababaacbaddaddbddbcddadcdcdabcaddcccaadccaadadbcadbdacccbadadcbbcbdaacdcadacbdbacdcaddbadabddbbcdbaaaaaaadcabcbacdccacacabccdddbcadbbbabccdddcadabadacabdbccabbbacabdcccdbbcbdadccdacabddccacccddaabdcadbbdddbbdcaaabadaaaaacbcddacddddaccdaccddadbacadddababbcdddaacbbcabbbbcaadbdbdacaaaabbbcaddbcdccccdbbadacbacdbdbbdbcdbbaacaaddcadaaabdaadbcddcaccdcbcabdccadddccabdabbcaddbbaccbdccdaaddadcaadddcbaabdbddbdddcabdbdbbacdbddadadcdbbabbddbcddabdccbdbcacdbdcabcabbbbbcddcdbdabbcdadacaaddcdaddbaabcccbacbbaaadacbdccdacbccddbdccbcdabcdcaddbdacccacdbaababaddcbbcadaadadccbdcbabcbadccdcbdcbbccdbbcccbddcdddcadbdbbcbcdcbcdcdadbbdbadbdcabcabadacdbdbbdcbdacbcacdbdaabbbdabcdabbdcbccdbccbdddaadaaacbdaddbbdaddcdddcbaddddaddbcccdbcaaddcddbcdccbbccdacbcbbbbadbaacaaabdbadaaccaabdadbcdccccbdccdabcdcbdddadcbbdddacbbddaabcdccbabcabbcbaadaaaacdadbbaacadcdaccdacaaaacdddccdaaabdabbbccdccadcbcdcccdbabddcababbcbbdadbaccdbbbadbbcdbcaddbadcbdcbbddacaccbdddacddabddcacdbbccbbbbabadacddabbdccddaddcddaddaccbadbdabbbbcdaacaadbcbadabdadbbbddcdbdbbbacdbdaccbdaaaabadbbbadcbdadaaacdbcdabcdaadcdddaccaccddacbcdaabddcadccbbbabbdabbadadbbcdcdbabacccaabdaddcabdccdcabcaaacddcdcbdccdbaccdabdacaadacbbbaadbbcbdbdaabcaabdadbabdbcccdcddcacbcddacbacccacbbccbabbccdbcaddbbccaaabccbaccaaacadbdbbdddbbcbbbddbbbbcbcccadbdccdcdbcaaaccdbdccbabdbbccddcbcacddddacdacaddbcccacbccaaaddabcdcbdacbccabbccababdbdabdbdadccdcccccabcaaddaacdaacaacdbcccadbcccacacdbdbaddcddbdddaadbaaaccbbddccbcdbbabdbabbcadcccaccbdbbcdcadbdaccadabdcbbbdcaabaadbddaddcbcaabbdbddaadabdbacadddbdcbcbaaabcbbadbbabbcdcdbccaaabddddcaadbccddadbcdbaadcaabcdbcbdabbcddbbdcddacddcbaccbbbddccabccaacbcaabccdcdbbddacbacaabcccbcacabbacdbaabdbccabbacaaddbaccccbbaaacbccdccdbbabbdcddccdddddbddbdadddddaabdbdaadcdddcabddcacabddadbccccddbaabbadaccabdcdddabcdacbdabbbdbbdaaddabdabbdcdaabcaabddcbbbcbaccaabdcabbdcaccbbddbbbaaaacabbbcbdcbbdbadddabadcbcbabbacdadcccccbadaccaacbdabadddbbdcdcbbddaabbcdabbddcbdddacbbbaccbabbbccabaabaccbbadcaaadbdbbddbdbbccdadabaddbdcbcaabacaacacaccdcacccddaabbddaabdccbdbaabbcbdacaabadcccdaabdaaacbcbddbbcbbacbbdbabcbabdaaccabaacdadacbccadbdcdadadbadaaccdbabababddcdadcdbbddabddccaaaacbbcbaadcdcbdadcacababddcbdbccbaaabdaaaadbbcacbccddcccbabacbabccaaaccdcbdbcbbaadbadcccdaadbbbdcbcdcaadbbbdcadbcabddbababcbdadccbaddbcdbcdccaadbcccdcddacbbdaaaadbbdabadcdccddddaddadcdcbdbbbcdadcddabddaddcadacacdaabbdddaaccacaabcbcaccbbdbaadcddcbabdabbbbbaadbabbcadabcabbdddadcadabadacbddadbbabdcdcadcbaadaadbccccbacdccaccddbdcccdabadbbaaaccadcdaadddadcdbabcdbbacbbaacdccdcbbabacdbdbcdadccccadcaaccddabaabddcabdacacbcbdcdcacbabdccaadcbbbcdcdaabaaaacaabaaddcaccddadacbbdaabbcdccccbcdcdbbccccbdacbdcaacccadddbdadcabbddcdddcdcaddadcbaacaacdabbbddbdccbbdccdaabaadabaabbabcaacadabdbbabdcddcbcaccacacdcabbcbbacbaaaaabdbdbcdaccbadababbbacbdddcdabcabbadcbbbacdadabdcbcaddbaaddccacbdcdbdcccbaabbccdcaaabaabcdbacddcbadcbdadbcccdadacdbdcdbdbbdcadcccbbbbcadccbadcbcdbbcdaadbdadaaddbbdccdcddbddddccbbaaabcdacdcaadaabdbdcbbddabaabaadbabccadcdaadbaababdadbacabcaccccdddbbbccdabbdccabbacdabbaacdbbbbdbcdddabdcbbaadccddbbdaddcadabccbdddababcdbadcacaadddcabbbadbdacddbcadcdbbbcadcdbdbdbcbdcbcacdaadcadabbbbbdbacbcdcaddbbdbbadacdbcbbaabcabbbbacadddabaabdcdcbbaacdaccadbbcbddbddcadccaccbccdbaabbcdbabccdbbcccdccbcdbddcadaaacdcbbdabacacadddabbadccaaabcccdaccddcabadddbdbadcabdccddcdbbabbacbccdbbdaadacbaabbbdaaccccccacadcaadbdbacdbddddbdbbbdacbbcdccbaccadbddbdababcdcbaaddbddabcddbbcababbddbccadcbbbbbcadaadaacadabbcbbdbadcacaaabdcbcdadcbddbcaaacabbaacadccadccacdcbbbcdacabacddbabacadcdabaacbabdaddbaabbbdacabbbbbaabcbdbcbadcbbacacaccbbadddaddcbbbdbbbacadddcdacdaadabccbbdddbbdcbaddaddcabcacdbabacdadbbdbbdbdbcacdccacbcbcaadbadabbaaccdbdcbacaccdbacadccdabdabbdcbddbcabcbddadddbdddbdddbcdbdbaadaaaccadcdcaadccddabcdddbdbacdbbaaddcbcbabbbcbccdddcaccbccaaacbabadccdacdabdbbadaabbdccdbbcacddaabdcbaacabcbdabbcacaddcaabbdaaaccddcaaddaadcacdbccbdcbbccbbddabaacbdaddccadddadabcccbbcccbcadcccadaadcdadabdbbabcdccadcdcdabdccdacdcaccccccddbabdaadbdacdddaddcccddcabbabdcbcaddaabdaaabacdbabcbaababadbdccaacbcbbdccccdccbcadcdadbdbbbcdbcbdccdcccbcaaccbadccddaadcdabadabdcbddcbddadcbaaccddaccdbbabdcaddbbdaddcacbadcccbcdbdbaaacbcdbcaacdbbbadbbcdabbbaadcddbcaccdccadabbacddcbaaddddadbabbadacdabdbdaaddadabbabadddabbdcdcbbddacbddaacabcdcbbbdbbbcacacadaabcbcacaabaccddcabbacbabccacababbcbaabbdaaabadcbcbbbdccdaaccccabcccbdbccadadcadaccabdaacdabcdacdcbdadaccccdbdcdcbacdbdcacbccbbcdbdbccdbadbccaaaadccdbadcacbdadbddcbaccdbaadbdaddabdcaacadacdacabdcdccbbcdccbdcdcbccccadcabcbdcabddbadbaaabbbdbaacdbcdbbbdadcdcccaacaacacbbbcdbcdcddbcaababcdcaddcbadccbcabbbbbbbdcbdccadbccdababdbccaddacbcdaabccabbbabccbabacaaadcdadacccacddddbcdbcdbcacbbabcdbdacadddbcacbccdcdbababacbbdbadcdbacbdcbbbbcaddcdcaacbcaacbcdbccdabbdbdcabdddddadcabcccaddbbaacadbdcdabacbdbacadacdcdcdcdadcacadcbccbcccaadbdbacdccdddbbbbadaabaddacabddcacbaddabaababadabcbacbccabbdbddabddacdadabcabadacdddcbdacabdcaacaddcbcdddabccaacddbbadbdddaaaaacdbbddbbabbbbadbcabbbacddbbabcdadcaddccbaaabcddbaccacacabdbcaacccdbcbdddabdbbdbccacbbbddbcaadbdbcabbdacccaaabddcbdddaacbcdbcddbddcbbddabdcddccbacbdccddbaddbddcdbbdbaddbabdbbbbbcadabadbabdbbdbabcbacccdcdbcaddbbccbdcdbdcccabcbaaadbbbaccadcdccacadbbbdacbdbaabddbbbbcbcbbcbcdbbcbbddcaacacacaabbbcccdcccaccbcabdadcacadbcddadbdcccaabcccaddbbbcaacdcabcaacdacbbabcabcdbbbcdccaabcddadcdabdaaadbbaabdadbbdbcdbacccbaadcadcddabdcaacddacbbbadcdadbacbdccacbdcdcdaccccbcbbbcabddaccdcdabcbddabaccdddacaadbbbdaabbbaabaaaacbbddacaaabdccabdbbcbacaaaacbbaadcbacdccdbabdacbacddadcccdabccaccdcbcdacdabaddacacabcaabdcadcaadaacbdbdbdcacbdbdddbaadcdbccabbcdcacbbccbbbdccdcccaabdbabcaacdcbbcaabbddcacbbdbbcbaddcbccdadadacdbdbccbddaddacadbbabdadccdcbcabbbccabbbacdcbbbbbcaacbaaddbacdbbdabccbabaccbdadacbdaaddccbcddbbbdcdaddbabaaabbbcccbbcaabdabdddcdbacaddcbcabcaddbaaacbccbbdaaadcbbcdcdabdbabacbdbbacdbbababbbdcdbacccbdabcbbdaacdccbcacddddcdaabdccbccccabdcdbaacbdabadbcadacadcbcaccbccdccaabcccadcaabcbaaacacbabaaadbdcbaadbcbdbadaccdddbbbcccdabcbcdacdadbcbabaadcbbdccccadabaadabbaaaabbdcdcaacacbbbcabcaadddabaaadcbdacdddbbbaaddbadadabaaabcdadabbaadcaacbbaacdbbbcbbadaddaacbaaddddbcbadbaddadbdaababddcacddacacddbcdcaaddccaacaddaacacdcdcadabaccaddcaaccdbbcdbcdccaadadcdbadaddcbbcdcdaccabaddcbccbaadbcbddbdbaccbbaccadbbaddddbbbbdadbdbaabbbccbbccadadbcdcbddcdcabdcabcbacaabdabcbcbcbdbdbdcadadccbccbbbdcddbbabcddccdacbacadadcabccccbaabdaaccdbacbddcbdabbcbcaaccdcdbddccacbadcaddabaaabcacaaaadadbdcabdabdcabbdbbdacbbbdcbacddadcdbbabddcdbcccdcabbbbdcadcdccabbdaabadbbcbbbaddbacdbdaacbdaaaaaaccbccaaaabbccaddccdcadddcbccabbbadcaccabddddbdbaadcbdcdcadadbbcbcbcdabbbdaccccbccacdabccdddbdcbacdcdaacadababccddbaaaabbdbbaddcccbacadcdbabcacccbbbaaadccbbabbddddadcddabcbdcbdacbbdacadbbacbddcacccccbabacadbdbdacdabcaadcbacbabbccbdcdcaddadcdbcddcbdabbadbaabbdabadbdadcaacbcabdbcbabdccbcadaadbbaadcdbbacaabbbbacbbdadacdabbbdcdbcaabccbcdbbadaccbdbddbaadcbbcdbaccadcaacacccbcdadbcbdcdcddddddaabcdddcbbbadcaadcbaabbcaaccdabbdbdcbccddabaadaabcaabcdadbbdcccadaddcbbcdbcdddbcbddbaadbddbbaabcaaccadacbadcaccbaaaaabaadaddaaacadaacaabbccacbabddddadbdccaccadbaabdddadbdadbadcbbddbaddaddbbcabbcacddbdcdccbdcaabadcbdbbbbbcabcaabbbdbbccdbbbacdaabbbddacabacaccadbccaabbcbcbbddcaabcbdcaacaadbcdbbbcdaadbbdcacbbcaddbcdccaaddcabdcbbcaddbbabdcddabcabccbabcdbbaacddbabbcddcacdabbabdcccddcdacdbaddabddcbbcbddcdabbccbccdbbdbdcdbccdcabcaaaddbdcccdaabaaadbbacdcbaadababcbbaccbbabcacccbaacadddcbbdacdacccacbcbcdcaabbadbcdddabdacccabcdadaccdabacacdcbcacabadaddbcacbdacabcccaacdbbaaaabaaadbdabdbbbadccdddcabdddddcdcbdbadbcccbccdaddcbdbbabbacdbcdbbaadddaddbdbddbaabcdcdaabaacdbcababcccaacbbdbdabaabaacdcbccbacbadccacbcdaabdabcdbabcaabbcaccbcdbaababccbacbabbabaacbdcbbabcdcaccdddccdbdbdcdbabbbadbbbdcdabbbbabddadadcaccbcdabaabdbdcaccbcabcabdbbbbaddbddbaddcdcacdacacbcdbabdaacbbabbacbbbdabbaacabbccabbcbbdbbacdcbdbddcccaabcbbbdccbbdcdbadaddddcacbdcacabcaabdcaaccaacbdccaaccabbacbcddadacacacaabdcabbcbdbabbadcaabbcadbccabccbadcdcddcdcbdbddbccbcbcdcbddcadbabcdbdcaadbdbdcbddabbdcbdcddbbacdbcccbcadbbacdbdbbcbbbaaaddccacbabdadaaabbacddcacbcaabbbdaccaabccabacbccbbcbabdcbdccabddbbdadaddaccbabbbacbabcacccbddcdccaadcdbacabbddacaaadabbccdaaaadacadacccaccabacbdabdbbbdccdabcdbbdbccbbacadaaccddbcdbabacaddbcdbddabcbcacbdddbacacbbdcccdcbccbdacdcdabacbbbcabcdbdaccbdcbbbdadabdccdbaabacddcdcbaacaaadabbdaaadbcdabcbdacacdaadbaacbbcbaddbdbadddadabbddaaccdbcaadccaddccdbbddbbbcabbbaabadabadccabbcdbaadcbdbcacdddcdbbcabcbcbcdabbccadccabdadbcbcbcbcddddbbdbbdcbadccccdacdabaacadcabdcdcdbbdbdacaabddaacaaacbddadccccdabdaddbccbbbaddaadbddcabcddbacbdcbaccdaccbcccbddddbbbbddadabaaacadaabdddadbdadcadbbadacadbbbdaacdddbacbbaccdbadabddaaaddcaaaacbcccacadabdadbabbaadbcdbbdadbabbbbadbdcbacbbcdaacabcbacdadadadcabbcadaaadddbbbacdddccdadccaacbddcabadcbdbbccbdcabcdcbcdabbaccdccccbdadbbbcbadcdccbaacbbadbdcaaaacdaccacadbbcaccdbbdabacacdabbdcccadccddabcbbbbdacdbadcbaadbdbaddcbadaccabacabdbddabbbbcbddadbcbbbacbacaaabadacadddbccdcaaacaaccdcababcdbccbdadcdbacacaabbdaacdcadccaccbcaddddccabdacadcdabcdabaadddadaccabcbcddabbbaacaabbbaacbdabbdddbdbbdbbbaaddccabadacbbbcdcacbacadccbbbaadcdadbbbabbcbcdcbdcaadaccdcccbbaadcdacbaadbbadcdbddbdabdbaacadddacdbcdacbababdcabdccabdbacbcabcbbbacacaadcccbddaddacddbadccaacadccbbadabacdacbccbdbacaacbbbdccacaabbbcbacdbbaccbbbbdbadacaabdaadddccbcbdcadddbcdadccbcadbbbcbbdbccddcccacbadcabcaaadbadbcadccbdbacdbdaacacaccaddababbddadbdaccdddbaaddddabdadbdaaacadadbbdabcccaddcccddcbbaadacbbabccdabdbdbbcdbbabddcaddcbcdbadaabccbcdddbdacbcabbdddbdccccaabcaaaaddadcddccabadddddddadcccdddabcbacddbccbdcadbaabcdacbbdacadbabbbdbcdbbadcdcbccabcbcddbdbdddccdccccccdcdcbaacbbcdcbdcbcdaccdabacabddcacacbbaadddadcadccdacbdddbaadbbccbcdcdbcdaadcdbadcadddaabccbcdcddaccdbbacccdaddcbbcbbdcdbdcaaabadbdcbdddccdbdcdbcbcccaabacbbccddbbbddddcacbcbbbbddbccabacbbabacacadacbbddddbbcdccbaadccbaadbcddcabdddbcbcddccdadaddbdbacbccbcbdccaaadbcddcabcabadaacdaaccabaccabaaadbdbabdaccbadaddcddddadbdacaaddcbdabbdddddaddbaabaacdcaacbbcaccadabbcbbcdadcadabadbabacadbccccacdbcddbbdddbbabbabddcddcabcccdcdbccadbcdaacbbdddddcdaccddbcaddcccdbdbdbccbdaabcdbadbcaabbaaddddbabbaadcabcaacdddcbdbacbcaddacdcdccbcacaddabacccacaccbbbcdaacbaccdccdcbbdbbbccbdacacabdadccdcaaabbbccddcdbaaaadcdccbbaadaccabbddadbdadccbadcbbabbdcdcdcdcccaddabaaaaabababaaccaacddcbdccbbaacddaadcccddbcbaabaabdccaaaabadcbbdcadcaccbbccbbccdccdcbcbccdcbaddcbdacacddcbbccbddaabccdcbdcadccddbabbbbcbabbdadaadacdddaddadabcadacdbacbbcacddaadaadcbcdaaacbbadcadbbcccabdbbdacdbdaaaaaadadcccbcacddcdbccadcaddbbdadcbbcdaddaacacdccbcacdbadcacdaaaccccbbddaddacacabccabcdbcbcdbccdcdadbddadbcabaaccadacbacdabcadcbdcdbcdddadbdbaccacdbdccdaddbddabdabdcaacccccccbacbdcdcacbcabaddcabddabbddadcbabdcddbcbaccdacabbddbbbbdbdabbdaccdadaabcabbbdcccdcdadabdcccadadbabbbdbaacbabdcccacdccbacdaabccbabbdbcdacdcdbaaaabbabdccacccabbcdbdabaaaacddacacdabccabcccabaadabcdbaaabcbadcdccccdcdcaaaaabbbbbdcabacacdcbdbabbddabacbcccabccaccdcbabbcbcbabaaccccaddccaabbbbaacbcaabdbaddbccbccacacccabcddbaabaacbdbbabbbbccdaacccdddbbaabcdccbbbcbacaddcbacaaadddccbaabcaabbbcdccdadbcbdcbacdbccbcccaccbbdbcacbccbcbdcdccbabddadacadcbbdbadaddcacdbabdcddcddcaacbaabcaccdbacbcdcaaccbabddcdcacaadbdbcbaaaaacdddacdcdbbbabbadacdbddbbacdaabaddababccacabcbbacbcdabdccacabbaabaccacbaabdabcdcadaadacccddddbacdcdadadcbdbaddacbdbdaccdacababdaabccbcccbcbcddbbadaacbdbaddadcadcaadccdaadddabbcadbbdacccabbadcdbcbdcdbbacccacdbdacdbbcbcddadacbdbaacbccdbdacaacbcabdccaabdbbcbdccaddccccaadbbcacdaccbabdaacabdbbdaddbabccdddaabdbaccdabacdbddccadbdbcbdabdabcaabbdbcdabadcabcdcbbaabcabacaadddadcadddaccddddcaadcdabddbdbdcabacbbaccdddddbadadaddbbaacbabbdbbdccaaabcadcabccbcdbccddddcbbcdbabacbcccdaaccbadcbbcbabdcabcddcddddddadddcaccdcadcbdabaacadacccaabaadaaddcacbccacdbbdabbbbddcacabbbbabddcdccbacbbadbabcbacddbcacbdcabcabbbaccbaddddcccdbdcccbdabdbdabaccdabdaccababdcdcccaadbaabbccaababccbcabcaabaacbcbacdabdbaaccbbbbbbdcdcdadbdbbcccbabccbcccccddcaabbbcbbcdccccddcddcacaadddaddcdaacbcbdcdddccdddcbcbadcabbcbabbacacdcbddbbcbbbcccdababbcdbaaabcdccbbabcabadabacbddabacacccdcacbbbdcacdddddbdadbaccbbadadddcbcdaaabccdcccbbdcbababadabaabbaddbcdcbccbdcaadcccbabacddbaabccabadabadabcbadaaaaccdccbdaaccddcbdadaaabdbcaddccbcbaaddbcadccdcbcacddabcdddbdcddaadcbcdabbadddbaadddcbcdcacaddbadcbbdcdbbcbdddbcadcccdccdabddbcbcaaacbbbbadbbdcadbcbbcccbdddccacdacaabdbbaacabcbdccaadbabbacdcbcababcddbdbabbdbaadcabcccdcabacaacbbccdbdbcabddaccadabddcdabbbaddcabbadaccbcabbbcddbaabdbbacdaccbacabcddacaaddcdccbccadaacabcccccdcdcbdcbbdcdbadaacbcdabddadddbaacccaddbdaaaccdacbddccdcddcccbdcaccccbcaabccabbdbacbdadccacdccdbdcaabaaddcbbbabbbcbdaddcadabadbcdbabbdacdbbdccdaddcdacbadaadadddaacbbdaadcaabdcdacbabdbbcbdcbaddaabbcabcbacaaddccdccacbbddbccbdacbaadaddabaddbbcdbdbdddbaaddcbddcdcaccbcbadbbabacbdadacdbddccdabadcaaaabcabadcdaaadacabccccbdacacddbaccabccbcddaccaadaadcdabbccbcaddbbcaadbaababbdcdbdadabdadacbabaaacbacbcadacccaddacdaaddabbbbaccbcbbcbcdaaddaababcadcabcdccdcdabbabdcacdcdcabcadaacdddbabcaddabaacddcbdddbbdbdaaaacccabddcbbaddcadadadddaabdbabadcdbdadcbcdacbbccdaabcadccddaacbcadbaddcdbcacddbbbcdaabaccacbdabcbcadacabababaddbcccccbbabbabcaacacdcaadcbbcbdbbcaacbddbbaadadddbaccdcdacaaaacdcccaddbdbbbababcbabadcdcbcccaadbbacddbaddcdbacabaddcdabcdcdacadacdaccdbcbdcddaccdbbabbddddcbcddaaacaddacadcdcbbcdcddbdbccabcbaccadbadacdadadddbdaccbbadaacabcbddaabdbbccccccccdaadaadbddcaacddaaadccdbdcaadcbdccdadcacabaacbcdbdcbcabcbdbcadcbcabadaddbdcaaccdcdcdbbbadddbadbdabddbacbaaddbcdabadbbbdaddadbaccdbcccadcaabccdccccbadcbaadcdabdacbabdcbbbbdadabdcbdabadccdadbabddabcdddcdcbbcdaccddcabbbaddcacccdbddcbcbaabdacdbbcbbcddadacaddcdacdccaabacadadabaaaaaaaadcbddcabadcbadbcaccccbbdabcbddbaaccdaaccdddaaadacbababdcccdbcadadcddbcababccacabdadcabcaccdacbbbbcabccaabbabdbbcacaaabadbacdbcbbaddbaabbdbbbaacbcdbaabcbddabbadbcadcdadabcabbdabcccaddacdddbdbcadccbcccdaabadbabbdbaaaadcaabcaccbdadddbdcaacdabcabbccdccdbdbbbbdddabbbbddcabdaabbdbbbcbcdadabbbaccdddbbaacabcaddddbbcddcbbdcbbcbdcbabadcbdabccabcdacabdcccdccbbdbacaccdccadcbbccccddbccdaaaccbaabacaaabadcdddddcdbbdcbbdadacbdbcbdaacaddccbbdbadaacbdccccbbcaacdacbcabdbbbaddacbdbbdcbaaadddcbacbddcadaabbddcdabccadcbddabbababdcccbcddcbbadddadcbaabccccdcbbababcaccaddcbdaaababcbcadcdacabcadcacabcbddbcbddaadcaccabbdbdcbbddcccaccbcbccacbcbdbdbcbbcacdbdcaabdcccbcdddaddcdbdbcacacbbbadaadadcbaddaabbbdcdcaabcbbcbdddbabdcbddbaccdbdbdcbcddacbdddbbdbcbaaaadabcdcbdaddcbcddcbbccadddcdddbcddbcbdadbddbccdbaabccbddcbacbcacbcaccbcddccaabaaadaaaabdbddbacaacddabacbdbddadaacadbdacaabdcddccdbbbaadcdbccaadccbbdbbabbdcdaccccacbccdbdaccdcbcbdcaccdddaaaadcdcacbddbcacdabbaadcdddbcaabcbaccdbcbadcaccbabacbbadcccccbbdadccbaaaacaababdbaccbbcbcacbcbbcbcbabacdbbabccddddcdbaccbcdabacdbccbcdcabcadcdadcbccaccdbbddaccbbbccbaabaccbbabdbdbcdbcbbbdabbbabddcddcaabbcdacdddaaacdcccbacdacdadcdbabbcddaabbdbccdbacddbbcdcacabdcbdaccabaaadbcaddbbcdcadadaccacabacdddcbabbcabbbcbbaabbbbcadacabcbdddcddbcabdccbcbcadcbbddbabcadcdacadadccbddcbdccbadbbbbdddacacaaadbbdbcdaddabdbccbcdcababacaddabaadcbcdaddbdcdcbcabcabdccdaabdacabddbabbbcbbcdccaaabdcdadadadaddcdbdadbdcdcccdabcbcbdccadabddabbcdbacdadcbadbabbadcdcaaacabababbaadcadcacbabdcbddcbdaddbadcdaadbbdadcabbdaaadbbbdbadddbbcdcacaabcadaddabdcbdddcdcaabaadbdcddbdddbdabbdababbaaddbabbdcbbcddaaddbadaabacbbbdadcdbdbababadabddbadcaadcdcddabcccccbbbbadaddbacddbdabbccdbccbdabbcccaaabbbbcacaaadbbbdcdaccbacdcbdaccabbadcbabccaaaaadbcccdbdbbdcddbbcadcbbdcdccabbbbbcaacbadaadaaccdcdcbdbcacaacabbccabddbbdddcbcabdcaabbcdbccbbdbcbcbcacadbdccdadbbcccbdcabadcccbcdbcbccbccacdbcaaabcbcbbbdadbaadcbcddddabdccdddccacbacdaaacdcbcaaacddbbcacbcccbacaddcbdccacbbabbdabcdcaacdddadabbbddcdbcccbccaadbbbdbccaccabcabcbcdacbaabdbdcacdcddbbdccaddbabbbcadbccbddbaacdcdcaddbddccdbddddcddcdcddccdccdacdbcddbcabddadbadcbbcdacbcbbcaccdadbbbdabdabdadacacbbbdbbcacbbbdabbddbacbbbacabcbccbadabcdaacdbcdabdaaaaabbabbcadccbacadadcacdbbdadaabcabdaabbddcadbcabcbcaddbaacddddaadaddaaadbaacccbddbbdbbadabccaababcaadbcbcaaccbcbcbcbcbdacdcaaabbccaddcbbbcacddddaacadbdacacabdadcaacaaaabbddcddbaccddccddcbcdbddccbccbbbadcbccaabdbabadaccaabbdbbbcabdbbbcbbcbddcadadcdcadddadadacdcbbadcabcddbddacabbadacaacdadbacbcbbdcccbcacabadddacddbccabbdaaacdaabcacdbccddcadbabbcbcbdcbbacbbbcaadbcdcaaadadcaaababcaadcdaadbaaaacbaacbdaaccddcdacacbbacdacccaacccabacadbcdbaaadbadadacdabbdadddbacbdcadcacdaddaabcbcccdcbbabadcaacccccaaaaaaaaabbdcbcacabdddbbacccdacbcbadcaadcddadcdabcbaaacbaaabcabacacdcbabaddababaccaacaddaabbaaabcadabbddddcbaabcaccccaccdbdbdadadaaadcddacabadadbccacaddbbaacddcdddcddbcddbdcdababacbbbcccdcddaabbbbcdcbacdabbbcccdbccbaaaddaaadbbaaadbdcddbccbdababcddbcddcdbdbddcabddbbbaaacdcbcbaaaddddaababacbacdcacaaaabcbacadbbbadddbabaccaaaabbdccdcdcadbaaddcbbcdcabdcdabbcccccacdbccbbacdbabbbadaacacaddcdbabbaacdbacacaccdddbadbaccaabdcbbdcdabccaacbdbcaddaccddacdadbcadcabdacbdadcaadabbdbabcdabacdbaddbaddcadabdcccaaadbabdbddbbbcabbbdaabdcbcaabacadbcdaccbabbadcacacdccabbadcacabbabcdcbdcadadabdbdccdbcaaadbabbbcbcddccbdbcbadbdbcbbbbddcdddbaaddddcccdbaaabbadbccaccbaaacbbadbccabdaaadaaacbdadccccdaccccadbadbcdcccdcbbddbbcbdcacadcdaaadacabaddccdaaabcaacbbdaddaacdccddaaabcddbdcaadbadabaabbdbcadcdcdabdccdccdcadaababaabccadaadcbbbdacbdcbddacabdccadbaddcaacbcbaaaaacbacbcadabbdaccdcaddccabaabdcdabdddcbbaccdbbbcbcbadddaadabcdccccbadcadcbbcacbdcdccccccbaabbddbacdaaccbdaccbcdcabadacbdabcabadaddcadddcbccdbddcdaacdabdacacbcacacdcbcdcacadcbbbdaaabbadcdbbbbcaaacabacdcbadcbacdcbddcdbcbbbaaacbbbaccdabcbdaddbabcbdcdbdddbddabaacaacbcbaababaaabdcadabccbbbbdbaabbcbbaadcccbcabdcbabcaccbcdbaacdccabbbcdddbcabcdcdaabbdbbacddbbabdddaaacabbdabaaddddadcdcddcaddaccbacdaacdadaadbbaadcacbccdbcaddabcacdcdcdadacaccdbdddaabbbdddddabadbbdbcdcbabcddcadbbbdabaaaddcacabcccdcaadadcabacbbdabdddccdbbacabdaadbdcccbcacadbbabacdabccbabacbbacabaacddcbcbcdcbcccdadccbdccbddacacbbccdcbbcadddacdabcdbdabbdbaabacdcbdddadbcdacbcacabcbabcddcaadcbbbdcbbbcdbddadabdbdacdaabcdddbdbcbcbbaddbcbddadaccdccbcdbcbdadabbcabababbadbccdbcbadbcaabaadbdccddbbabcbbdcaacbaaddbbbaadcabaaabaabaaadddcdcacbdaadccdcdbbaabcdbbaddaabcaccadcaacdaccdacaacacdcdabbacdcaddbddcbbdccbccbdbdbddcccbbcdadcbcadcbdccccbbbddabdacabbbddabccdbabdbabbadcabbcbbbdadbacbcacbbdacadacaabddbdbdcaaabaaddbcddbabccadbdcdcdbaccabdcddbbdaaccdaaccbaccccccbcacdcbcbcccacabbccbbddbbdaadbcaccdcdccccbbabcbddcdcdbcbabbdaadbbbbdddabdcbcbabcdcbacaadcbcddcdbcdcdccbddddccdcdcdaaabdddcbcbcaacdbbdbdbdbacbcbccddadcdcaaccabdcacbbbcbbaaaaabcdbccbbddcbcccdbaccdaddaacbdacdcddaaccdcbcacbbabcccbabddddadbcdacaaccadcabbcdabdadaadacbababccbcbdadcbdbdadabbdbadacaaacbcdbcaaadcdcbdcccdbaabddabadcbabcbbaddadabbcbdabbaaccdabbbdddbddbbadbdcbccabcdcdbbadcbabadbbdabadddbddabdccacaaacbbddccdaaaaaacbcaddcbabbcadacadbcbdbcdadcaddbccdbddcabddcabcddabddabccabbdbcabddcabdbdcadbcbdccabadababbcadbbacdabbdccbadbaaddbabbaccaaacbdcbdbddcabadadbabcdccbbdadccdbbdbabcbbcbdbbbdbcdacabdccbdbccdacbaddbbdaccbdbaadcdccabccbbdbbbddaaddbdbbdddbaaabacacbacbacbbdbbccccabbaadddcaaabbbdccccabdbbbccddcbadbcadbbdbadcabacdbbadacaccdddcbdbbcaddccadaccabccdcdcbbacccdacbcdcbbbadccbaaccabcbdcccdcabbbdcdbdbaaadccacbcbabdaadcaddcabbdbdbbacadaccdbbcbdacbdddcacbbbbdabbcbdbbbdaccaddcacbadcdcddacbadbdbcdaacbaddadcbbdcddaacbaaacccdddcdcacdbdacabbcaacaacbddcaaddddcdddacaabcbabaacccdccbbcabcadbdaacbccdaababdadcdaaacababcabbcbbcacddadcdabacbdbddabdccddcacbdcbabcbaacbbaddadbddddddbdbabdbabbabbddbdaaaabdbbccbacbaacdbaaaccdcddaaccdbcaaaabbbcadadddaaddbaacacbababccabcaadbdbadcccdaaaaadddbcabbbbbbabaccabcdcabbacdbaaabdddabcaacacdabbdbccadcdbbcbabadbdabbccdcabccbdcadcbcdcabacdccaadccbabacbdacaccbbaaacbdbdcdbaabbccaccddbadabccabddcdbdccdbacbaabcccccccaabdcccdadabbddcdaddbddacaccdadadabaacdbdaaaaccaacacbdbaaccaacccddbdaddacaccbaababdaaabdddddcdaddadbcdaacdacbbcbabdccdabbbdacadcbcabcbbdadbbabbdcdddadbbabbbdadcbcbcddbabcacdbccacbbdbbcabbdcabbdaadbbaaaabbcadbadbcddadadcccdbbcbdaabaddccbaaadbcccbaacbcdcbaddbabdcbadcbaccaaadcccdbabcccdaddcabcadbbdddaadddbabcbcdadcdcccccaaaabaacbccddbbacaccaaddcbcaabdddcdcababbabcaaaddcbbabcbcdddcdcacbdcdccbbabbababdcbcdbdccbadcbcadcbcbccababdaddbbaccdccbdbaccacbaadacbccadababddccbbcacadddcbdbccadaaadabbadcadbcdccadabddbcbcdabbddabcbbcccaccabaababadadaacadaccbcaabcdbbdbdbaacdcbcbbddcadbdccacdcdcddababadcbddbdbbcacdbadcbbbdabacdcbcdcdddbbbddcacaccddbbccdacddcbbddcacdcdacbccdcaddbddbdbaabccadadbbbdacdbdbbdbcbaddadbbdddbadacdcbbdbcbabbbaaaaddcbdcdcaabcacddaabbadcbddbdbcccaddcaaaaccbccdbbbdbdcacbcbbbacdbabbdabdcccbcbcdbaabddaddbbbadbcacdcdcabcdccbddddbdcdbdcdaddcaddcbdcccdabadaaadccaaababcccdcbdacaacdccabddaadaacacbdacdbbbdadbacdbdbcaabdaacddbbbdcbdabbcdaabacaaccccbdabaadabcbdbbacbbcadbaddcdcaddcdbbdbbbadcadcdccbdcbcaadccbdcdabbccdadbbbaadadddbabacdddbcdabbdbbbaddddbccbbddcbaaddbbcbcddcbbbbdbaacccaaaccadbababcadbabababdacdbdbacccbbbcabdbcadcddbdaddbbabbcabcdbaaddabacadcbaadcdaabddbdcaabddaaabaaacbccdbdcddbbbaaccadadcbcaaaadabcadbbbaabbcbcaadcbddabdbdabdaacaabdcabadabbabcdcddcdabacbadbdadadbcdccabbccbccdcaabacbcdddbaaccdddbdaabbbdaccbddcaabdbdabcaacdddcbcbadccbdacaccabcdbbdbbbccacccaccbdcadcdadccbabcaaaabacbcaacdadbdaabaadabddbddabcdbcbccbabcdddcabdadbdcacdadbaabadacdcbbbcabcabdaaaacacccddccbcaacbcdadbccdacbbaadbbbdaacaabcaccaddcdadcbbcddbdddddbabbdbbbbbbabcaddaacabbabcdabcdccaabadbcdacaddcacdcbaaaddaacaaadcccbddcaddcbdccaaccabcbdddcdabdccaddbddbcadccddbadcbaddaddbababcdcbccdbdaddddcbdccaaccaacdaacadaacbdcacbdabcdcaddccaddbbdbccddddddbccbcdddadaccacaacbccddccbccddabaadabbcabacccbcbcbcaacaccaaaaddaaaabdcdcadccccbbabcbdccbcdaabcabdcbdcbaddccadaadcacdaccadbadacbbdcddbabbcaabdcabdcacbbbcdccbdbccbdbcbbdcccdccdbbdaaabdddbabcbccdccbabdbddbddcbbcbcccacacddddaabcbaccbaacbcaabcbdbcbababbcaddddcbcbbacbacddaacabdcbaaababbcdcbcabcdbdabdbadbcabcaadcaddbaddcacaccdadbacadcabcbacbcbdcdadbdbbcdccbccddbacaccaabdddaaabcbaabddcccabacbbacbbdcabcbccaabddccbcbaadcaadcacadbbbdcdcadadcccbbcdacccdbcabbddbccddacdabbbdacbdcbcbcccbabddbaccacdbdccccaddcbdcaadbddbbcdabddaabcbcbacadccbdcbdbdcadbddbbbdcbadbbddabaacdbbcadbdbdddacccbabbaadccacaccacaccdcdabacbbadbbacdbdcdbdbdaaaacacadacbdacdbdbadadbcdbaaccabadabccaadacdbdbbbaabcdbccaadcadabcbbbcdbbddbaadbdcddbdcdacccabcdaddaaddbdbcbbddbaccaccdbccbbabbcbccbcbdcbbdabadcbccabdaacabadcaacccbccbaaccbbdaacadcdbaccdddcdabccddbccbacdcddaacddccadbadbdcbcdccabcbaacbdbdddcbabddbbbaddaddadadacbddcaddacbacccacaddddadaaacdcdaacadbcbbdaddaccbbdbbacbcdbadaacdbcdabaadaddacdbccacdbcdcddbacadbdaaaaacbbbdabbadbcbcdcbdbcbcacbbdddabacbabbdacdcacdcccadccbcdcdbddabcadcbbccdbaacaaabccacdbadcdcabacdaabdbbcbbbabcacdbbcacdcadddaabaaddbddcbbddddcabbbadbbadbcbdacacbcbdcbdabbabddcaddcbbdabcbbaacddbbcabadadbdcbbddcccbabcccdacdbbcacdccdadcbbcacadabdbddcabdddaddbabbbcabccbddbabdaccaddcaaadbdaccbbdbbcdaacbdcaadaccbdcdaabbbcbdbbcbcdacbaaabcbbccbdcbbcbacdacbbbccaddcdbccccdaaadacaaaacbadbccbcaabcdbcbadcdbadbaabdbadbdadacabdabddbddbcaacaacabccdbbabdcbdbbdcdbcaaaacbddcddbddacdbbcadbaabadaadcdbdcbbdbdbbdcdcdbdbbadabaadcbdbdcaacdbbdddaabacdcbaabcbaaacccabcddacadcbcadcdbabbdccccdcbbbadacabdbbbddddadbbccabbdccbdddacbaccbdaabcdbacbdabaddadcdaadbddaaccadbaccdccabdbaacadbccbdbaaaabacbddcadcdbbcabcbcaabdbbdccbdacddbdddadaabcdcdacbbbdddcacabababbccbadadcaaccabcbbcadbaaaaddbacdcabcccdcbdddacccdbbcaacadaabdaacaaccaaaddaacadccabbaaccdbccaccbbaddbaccddbacadbabdbbaadbbaaaacadabdddbacadbadcbdacacccdcacabcaccbabdbcadacccbaaadddcbcdddabacabdaccbbacbaadacbaababdccbdadbabbaccccaabacdabcdaadcdccaaaccbaddadbbacddbbbaddbdbaabaaddbcbabcdacbbadbcccbdabbaaccbccdbcbbdbdbbadaaaacadcddbccbcacccbbabcdabbbbbdcaccacdbdadbbaccbbdacabcbdddabdadbaaccbbcdbdbcabcbbccbdbbaaaabacadccbbdddbcbdcacbdaadbdbacbbcaacccbcbabacdddcdbcbbccbabbddbcabaacacabadbcaaabaacdddcddcdaabcbabddddabbcbbcacadcdadbdacbdcdcbcbadcabadbdcdaabcbdcdbcaacaaaccddaccbacadccdbcbcdcbdbdaccacbcbccbbacbccdbddaabaddabbbaadcabcaddacaadaabcbcbcbaadbbabdbbbcdcbcadcadbdddbadccabcbaabdcacbaaadcbacbcccbadcdcacbcccadcaaddcabbaadcdbddcdcdaaaddccacadabdcbdddcabddbddcbabcbbbccadcbddabddaccbaadacaacbbbaaabdaabbbabccbccccdddccabdcdcbadcdabdaabbdabcbababbddadddaaddbdaaabdcabaccabadabaddbbdcaabdaacddccccabdcadabaddcbdddddaacaabdadbbacdcabdcdbabbcdaaddddbcacdbbaaadaaabbdcabcbcdbacbddadcbbdbcdcacddbaddaaaddcabaabbaccbabbcdcaddabbccdadcdbbacaacbdbbdcbcbaddccbacdbccadccddcdabdaddcadadcdaddcdcbbcdaaabacbbdbcddaababcddbdbbabadbbbcabdcadbcacaddbbcaaabcbcccccbadcdaaacdddcdddaadcbddcbdccdbacdabcabbbabbabcaabacabdabacaddccbababdbcadcaccccdcdcaabbcdddcadcaaaaadbbdbcbbacdddbddcbddddaccbcdbaddddcabcbcacdacbbaccbacabccddbccadadadbbaddbdbdddddcbccbadbbcbdcabcbddbcbbadbcaadcbccddbdbcbbdbbaccdbbdabbaabddccbbcbcadbbaaacdcaababdcabaabdbdbbabcdddabbbbccaadddddbbacbbaaacbabbcdbdacdbcadddcaabbbadadaaaabcdcddddbddbdaccacaacccdadabacadacabcbabbabbcccddaccbacbcdadbbdccdccaabdaccdcaabdcacdabadbbbbcabaccccccdcabacdccbdccadbbbadcbacbbadabbdbaabdddadabdabbbdddaccbccdadbbacbbdbbbbbbbacbbbadcacaabaacdadaababcbbcadbbbccadaaacbdaadbadbaabcbbaadccbcbacbddabcdbcbababdbdbabbccadbcccdcdacacacbcaccaabcdadbbacdddbacacdcddbccbdddaaddacaacccbabbcaaaaddadaccdbacdcbbaadadaacbdabacaabaddaadaaccbdcbadbcaacccdadbbaabbdbdaadcbcaaccddbbcadbcddbcbbbcdbbbabdbbadccbccbccaacdabdcbdcaddddbdabdcddcaacabaccacdddcbdabddbcdddaaddbbabbddcdcdabbcbadacdabccdddbcbbadbaadabbcbdcaaabacadccdabaaabddbdcbdbaaccccadaadacbcacbbcabddcadcabcbbbbccdbadcbbdadabdcbdcacbddbbbacabaccbabbcdcddbbbaabcdbddabddcbcbcccccabacacdbbbbbdbdbdcbcabbdbcdaacaabbcddddabddbbbaabaacddbdcbbdaddaccdbaccccaaabaacbaadabadadaaaabbcbaabbddbdbaccabbbccdddbcddcddddcccbcdbbcaadcdabbaadbdccbbbbabdadcbcbcbaddcdddadbcccbcabddbdcaadcdcbbaddadddacadcdbaaaaccaaaabddadbdaadaddaadaabbcbdcbdadacdacbaacacdbbccbadabdaacabaababbacacdbccbbacaaddbacbcbbcbbdbccbcdaddccaaaddbdbabaabddaabcadaddcbcadcabddcdcadadbababbbacddaabcdbaddcdaadcccdabbcadcddaadcdbacbaddddcadbcbcdbabacbdbcdcbcbcbdcaddbaccbacddcccddbadacddadadcdcddbcdbabaccaabbaadbcdacabcbcaddbbaacabbbdacbbbddbcabacadabdbbbdcacaaacaddcccadacacddbcbabcabdbbadbdbaadbbbdacadcccbbccaadddccaadcddacabbdabbdabbaabbdbbbdbadadcdcbbdaaadbcbccbdcbaddcbccadabddacaacacdbcdbbbacddadccbdcbddddcadadbbddccbccdcdaddadcaabddbadadadadbbabccbaddccccdadacdcadaadaccbbcdacdbdbbbdddccabcdccbccddcaddcdacabcbcaddbdcccdcdcaabccddbacccdcacadaaccdbdcbcbccdbddaabbcbbaccdbacdcaaadacabccbbcbbcabbdacdcdadaddbccdbccadcdaacdaccadabacccaddabadbaabdcbbaadcbadbdadaadaabaaccddbcdacdcbbcadacabdcbaccbdccababadbbaadacdbadacbccaacadbcbbdabacaacdbdbdcaaaabddcdbdaabdbccccadabbcbadabacdbbacbdadaddabbbdaaabcddadccbcbcadadcbabcddabaacdaaaddbcaaaddacdabbcdabcacaacddabdccbacdcbadcabaccddbbdbadcbadcdcccaacaccdbcbcacccacdcadbadabcbddbbccdcbdcbbdcdcdacbcccbaaabcdbbadbdbcacbccbcdbcbdccbbcdadbbcaaabddababccdbcccddbbddbbbabccbddccbdadcbdacdacbcdadbabbbbcdbbacbacbaacdddaddcaacbadcdbdbbabddadaddcdbacbadccadbbcacadcaccacacaaabbbbabcacadcaccddadabcdccbabcbaadbddadbaadadcbaacbccbbbbadadcbcbcacbcababbabbabbddbdacdcdbadccabbdbcaddabcadabbacdadbbddabdacbadcaadbabdcccbaabaddccabbccdadccaadbdabcaacbaaadbddcabdaacbcaadccbabdcbbcccccddaadacbabadddaadbdbabcbbaadccaaddacdbbabdaaabbdacdcdcdbbabbaadcbdbccabdccdbabccdbcbacdacacdbbacadadbadabdbbdccccdbbcaddbbacccadddbddadbbcddbaadcadabdbcbcdcbdddbddcabaabbaabdadcdacbadcadcaaddbbbadddacdaaabaabdcbaabcddababcdacccdacdacdcbbaacddabdbddcdbcddcddbbabbbdcccdadbbcddaaacbdccbbbdabadbacbdccabaadcabcbabaadccdbababbbcbdbbcabcdbbabdbaaabbbcadcacbcdbcbbdaabcbcbbcaabdbdbbbaaacbccddccdbcaccabcacadbcbccbacdbbbdcabdcbddbcacbddbdcdbdbbccbccacbdcddccacbdbadaacbccdadbadadcaaadadbabcbadbdcbbdacaabdcddbbcdcdbbbadabadbcaddccbccdcdcdbdccbbcdcdccdadcacddbbabdbbbacddbaaacdaaccdbadcddacacbcaddadcacbadbcaacadbcbcccccdcbbdaaabaddadcdadadacccacbacacaaddadbddccabacbdcabdcabaabbcaccaaabdabadadbdabdddbdddddccddcacbabaaaaabccaaabdbdaccbbadddaccbbdbaddbbacdcadbbbcbcbbcdddaadddbaadcbdcddbdbabddadbbcdbbabdddaccacdbdcaaccbcdabbaadddcbbbdbcdbdbabbdcaabaaddcbcdadacadabadabbbcadcdabcaaabdbabcbddcbdcccbddddabdbbcaadbbabadcabdcbbabcabbcbbbaabdabddbcddbbbddcaaddcdbdacadcccddddcccaacabbcaacaddaaabbbdbcbdcacadbdbaaadacbabbccbbbdcddacdbcbdcaddcaccbadacbaccbbaacacaabbcabaaabbbaacaaacbbadabdbabbdadbcdccdcaaabcdaaaccaaccdcadaccaaabbcbccdbdbdbcbbccdabdbdaabaaacacddbbaacbdbbcbadbaabdcbdcaadbbdaabaaabbaccbccaadcdbdbdabbbccbddcaadaacbccaaadccccdbdbabaabcccbcbadcaadcbadadbccabbbcdcbcabccdabbbaccaadbbcbcbdbcbccbdcddcacabcadcdbbcddbbdddbcbddcadbcdcccadbddbbbbdbaadbaccbabdcccabbabcbbdbccddbbacdcdddcdcadadccadbadbbadaddddcdbcdcbbacbabddaddbacabbcaabddbcabddadcbddacbaccbabdadabbdabbdbbbadbdcbcbdcbbdbbcbddbcbdbadccdaccdcabbbccaabdddadaddcdbbaddcaadccadbccdabbbdccacdadbaddcaadabcdccddddccbaadddadcdbdcbadacdbadcadbadcdadddaacbdbbbbaccccbddddbabbdcadbcdacdadccabccbcaddccadabcabbdbaadcadddbabadcdccabadabcabdccbbcdddcaabcbcdbbabacaacacacdccbcccbdcadbbacbadaabadcdabbddbadbcccadddcdbacdccdadaacbabcdcbbbdbbdbcdbdcdaccddaadadbcdccbcdacadddaabbbcbabbadadcabcccacbccdabbdaacacababdbcacdadddbadaccdbbdacddcabdadadcbbdcadbdbcbcdbababcbbdcbcbabddcdbbcbadacaaaababcdaabadabcabdbbcbbdaddddcadbcdbbcadacbabbddabbabdbdcaddcbbaccdadaaddacaaabcabdaddbdaadcaacacbcbabcbbadcbbbcddcbdcdcccdbabbbbbcacccdddcbcacbdadbcabbaaaaabddbabbadaddabdcdccdabddbbbdcadcbdcdbddaabcacabddaabbcabddaadaacbadadbabdaddcccabdbbdcaccaaaccdaccbabbadcccabcddcbcacacccbababcbdabbcbadcbdabddaadacabddaaacdbdbdaacacdacddbccaaccbdbdabbbbabaabcddcbbabdacdddcdabbcbaadadacabddabbaaadbacaadaabbbccdbaadcabbdbbbbcdbbcdcbbabbcadbaaddddcbcaacccccbcdabdccccaacdcccbabcdbbbbadaccbddbbbaddabccadacbdaccadbbaddbbdcdbacbbbcacbdabdabaacbaadaddaaaddaabdcbbcccadadbaadadbbcacbcccbbbacaaacdbdddabcbacabacbdaabcacbddbacbabaabdbabaadbdcdddddbbbbababdaabbcbcbaccaaddabaaabcbbccabadbccbccbbdbcdcacaddbbcbdaacccddabbabaaaccbbdbdbaaabdcddcccddaaacddcadbabdbdccabcccbacdaccddbcacdacababcddbbccddbbaabbdbadabddddaaccdcbdadcdaddadbcdcdcbdbadbdcacdbcdbcacbcdadcdcabcdabacdaadbddbcccdbcbbdbdccabdaddcbabdaaccbacababdbcddbdccbbbdbbadddaddadadbdaaabadcbdaddbaaddaccabdabddacbbbbcaabcdadcdbccbccbdbbbdadadccabadcacbaacaaabbdacacdaaccbddccabaabdbbcbdbdabacaaccddccdbcdbbbaaccbbcddbdabcbdbddcacdabcccabbdacabaaadddbcbbdbdccbbcdbdcdacccdccbcabdcbddcaddadccddacabbabbabaaccdccdbbaadcbadaaaabcadcddabacddacddcdddaacddddccdcccabdcdcadabdbcddcbabdaadadddaddcaaababbbbbbabbdccabbdbdacdadbbabcacdddddcbacccdcaabdbdbbaacabccabdacdcbdbcccabaaddcbbccbddcabdddaadcbaccdcabddbcdacdbabacabcdcacabadbacdcdddcbdcbabdaccbbdddcddaacdacaadbdaacadccabccdadbbaacddaddaadcabcccabcacaaccaccadadbddbcabccbbabcdcdabbbaadccacdcccccdcaccdabcadbaaabbdbcddbdabaccbababbdbddcdcbcdbddcdcbcbddbdbacddabdbcdcaccaccacdbabddaddaccdcdbbbbcadadaabdcbcadccaddbdbbbbbbdabcdabcabdcbaaadabacdddcdccabbbacbbcadbbbcbbbbbadcddbcadbdcbcdcacdcbbcaaddcbdddcacababcddcababaacccaaacbdcbabcdbdaadabddadbcddacdbcbcdbcaabbccbadccdcbcdaadbbadbcdaccbccbcddabcabbadadbcdddaadccdccccabaacadddddaadaadcdcdbbcdacbababcccbdadabaaccddbddaccacdacacdbcbccabcaddbbbbdacdddcabacddbdccaababaaccacccdabaadbdacddbcadabbacddaaacaaaaadcaadbcbccbdabbbbccdcadcbacdbbbadaccccddbadaacbdadbdbaaaaacbcdbbabdbabdabdccccbbabcdbddbabdaddcccbabdadbccdcbadbbdacdcaabcadcabadababdabacbdddbbddcdbdbcbbbacadcadcabddcccabdbaadbaaccbacbddcabddaabaaddadbbbcacddacaadadaaddaaacbdaacaccbdccaccddacddbaaaabdcbcdbcaddccadbccbbbcdbccabaadcbaaaaccaadcbdbdacababdcdbddbaaccbadbcccbcdbaddabababddacaabcaaaadddbaabdaaabdaaabadccabcbdcbddbacccadbdbcaccdbcbacccaabcdbcdaaaabcbddcaccbacdbbacbdcabdbacdccacddddcddbababaddbbbbbcdaccaddaabcabbbaaadbbaaadbbdbcdaddacacaadbabacaaadcddcaadbbcddcdcbabcaccccbbacbbbdaacccaacbddbabcbdaabdcaacbcdcbccbcbcdddbddadcddbacdadbbacccacdbdbadacbcccbbabcadddbababbdabbdbadabbddadcddccddaabcdabadddcabddbdccbdbcbadabbdacdcdccadacacadadbbcaadbbcabbdbcdcbbbcaaabdddacbbadaadbabbcbcbbadabcdbacdcdcddaacabdddcaaccbccbccdabdabbddcdbbbcbabacadccabaabbadbbbdcdbcbbcaabdcadbabddadbccbbbcaccababdacdddbabcbcddddbddccbaabdbacbaddbcbbbdcdadcaccaaadbdadcdcadddddccdbadbccdadbbbacbacccbbcccbcccddccddacadccaababccccbacdcbcacbccdbacaddcbdbbddbbbaacdbaacbbaacdaaddccaaabaabddadccacddccbcbaddbbcacdbbccccbcdacbaabbcccbbcdaccbccdcaadbbabdaccbcaccadcbadcdadddbdbcdbbadcbdacdaddadbcbbcccbdcddbcaababbbdcacbaadcccbbcdaabccdabcdaacbdddbcdbcccddccdaadaccddacdcbacdcbbbbcbabcbddbbdccdcbabadcddbcadddcadddacdcabdddaaabcddcbddcdddccbabbabdcdccadadbaadcaacbcabcdaadbdddbbdadccbccddabbbacdbcdbbdaccaaacabcdbccdbdcbaaacdadcdbccbcdcacdccbacaddbcccbdaaddadbbbbdbcdccddacbdddcabbacabddcacbccdccccacdcadcbdcdacddddbdadcdabaabcccabacadcabdddcbcdacbccccccbbbaadddbdcaabaaaabbdadcdbcababbdaabccdccabdbcaaadbdcacdccbbbdbcaacbdacabdcbaababcddacabdbdcaacddbbabaabdbddddbcbbbbaccaccddcbadbdcaadcbadacaaaccccbcdaabddadbadcacacaddcaccacadcabdaaaccaddcabcabdadbabdcdbbaadbabdbddcaaddcbcbddcbcbadcadababdcdbddcacbbbcdbbacddcdbdcbadbabcbbdacdbacaadbacadccabacdcbbcaaaacbbcacbbcaacdbaabccbabdcddadcddcdbbccdcabcccbbcbbadcdddbbdbdbcadaccccdbbbcaddcadbcbcacbddcdbbadbaaddaaabdaccaabcbdccbdbddbddbcacbbabbbcabddccadbcbbcbdcbbcabbbbdaaaddbbbdbcdcdadbbdbbaaddbdbbdddcabbbacadaadacccbcdbdcbbdcbbabcabdcccbccccbdaaacccacccdbadaadababcabbddbbcbabcbddacdadbbcabaddbbaddaabcdcbcaacadbccddcbaacbacaadccdcabddaaacacdbbabccdccdcccbbcdcaadddbdbdacdbadcbcbdbddcaaddcdaacdbdddccddbadbdbabbbbbadbccbcaabbcdbabdcadabacdabbabcabbccadabadcbcacddbababdbdacddbaabdbcdbcddcbbccdbdddbadcadbacdadacbdddbadcdbcacdcbaddaacabddbdaacddbbbdcaddacaadaabbdabbbdbbaadcaccdabdcdacbdbaadcdaacddddbdccadbcbddbaaabddaaabdadbddacddaadcddcdbbbacaaadbcabccbcccdaacdabbcbbabbabdcdaabdcdbbdadbdbdabdbaadaccdaabbcccdaccddbcccddccaadcbcbdcbdaccdbcdbbdbcdbcabcdddaabbccbddbabdaadddadcbccadaddcbdaadccbacbcbdcccacdacabacdbbdcadabdccdaddabcabcbbadccdcdbcabccccbcababcdbaaddcdbbbdccbbcccdaaacadcbbcccacddcadbaccbdcbbcbdcccabcaaadcacbabdabdadabaddcccdcdbbcbabbcdadbbaadaaaabddabdbacdccccabbbddadaabddbbdcaddbacabbcbabbdadaacdbdbbaccbaddcbabccabcbbbacadbbbcdcbaaababadbdcccdabddccbdddbaaccdabdcddbddbdabdddbbacdcaaaabdbdbbcaadcdabaddcbcacdbbadcababbcdbcaacabdcccccaaadabbdaddbcbcbabadadbbcaacacdbbcbdcccacaadcbaabccbabadacdbccbdacdbccbcbdaddddacaadabaccaccddacabcdabbdcabbdacbacbbdcbdccdddcbbdcdaaabcddcdccadcddcbcdadcaddbbaadaccabbbaaadbddbcccdcdddccacbcdaabdcabacbcbdabcdadddcabdcdbaadaaadabbcabdbcbbbaadcbabbbdbccbacdddbdcadcadbddabcadcdbcbcbcdbccabacbaabacbbdadaaadbbcaccbbdaacbaccdbddadcadbbbabbcdcddadcdaaddacabdddacdbbdcdbbacaadabdaabcbaaaaddbbbbcacacadcdabcdadbdbcbcdbdcbabaadbbbbbbcccabbdddcacdbbdbcccbadaaadddcaddbdccdcaadccbbaadbdcbabbcbbcacacdbdbdbabcddbaabccbdbacdbadabbacdcdabdbcccdbdabbdabccbcaadaadacddcccabdaddaccdcabdbddcbcbacbacacacaadcccbbdcaabdbadadaacacbcdcaccaabbdcdbacdccaccddcabbcdcaccbbddbdbbbdbdcbbdcadbdaaacaabccccbddbcbbadabaadbadddddddcaadccabcddcbccacaadbbabcabdbbcadddacabcaacdacbcabcdbabbaaaaccdcabccbbdabccabcaddbaabbadbaabcdcbdbaddadadcdbdbcaaacdcdaacaabccddacdaabdcbabbbcdbcdbdccabcbadaabcdcacaadaaacdbacbbabbdaaabcddcabbadaddaacacaadccdadbaddbdabadaaccacddadaacadbcbcaaaccbcddccdaddbccbabcacaabbddccdadabcdddbaacaabcaacacaacbcbcbdddcdbbbddaddcabdbdcadccbbbaccadbabbbbdddbababdcabcccadcbddabdcdbbccabcadadcddbdcbcbabddbdabcbddddcccbdddccbdcbdcabbaadbcccaabaababadbabdbdbbbcdbcdbacbdbbcbbacbbaabbbccbcababbaaacdbbdacdaacaaccadacccbcadbcdabbdcccdbbcaaaaaadcabadbadbbcbddbcddbbcdcdcadabbbbbabbdcbacbcaddcacdcabdbaadabddccacaabcbacacbcacdaccccdabacbcddcdbddcabcdcdddcaababacbcccbccacbbabbbcdaddaadadccdadcdaabccdbcabcdbbcacbbabacddadbdaaaadcbbbaadbdbdcbbdbcabbbbabdcdcadabbbbdaabadcaadccdbabbbccaddbcbdaacacbdddddddacacaddcccbdcaabdbccdbcabcbcdccaabbcbdcbddcbdadcdccbbddbbaddabaccadaacdbacabcadcabdacdababacaccdacbcbbddcccbacccaddaaabdbbbcdbddaacabdcaabadcabbdcdbacbdcaadcacacabaddabbabbdccaacdabcacddbadccbdaabcabaabccbdddbcdbdaabbbcacbbacccdccdabbcdccddcacbdddccabbabdcdaababadcbcacdbbbbbbbccbbddadddbbcbbacadddccddbaadcddaaabcdaaacbadbdacaabccbdddcdaccaaadccbddaaccaddbbaaccdaaaacaaacdbdbcaadbbdccdcaabadaccacbadaabaddddbdbbdccabdbaadcbbaadbbbbdddcbcddaadbcadcdbababcbbbacbbdabadcaabaaddcdcaccbdbccaccdcbdbdbddcdccbdcdadaccbdbcadcbddcdbccaabcbcbacadaaaadbbcbdcdbcbdcaadbccaaaadbabaacbdabcbcdcacacccbaabaaadcdbdccbaacbddbbaabbbbdbbacbcccdccbddcccdabdadbcddcbbcbadcddacacdcaddacacccbcbcadbaddababcccccaacccadcbaabddacbdbcccddbdbcbcadbbabbcbbdadccbadbaaaaacbcadcbadadaccadbccbdabdbddaaddbbdaaacdbadddaddaddcdbbdaacbbcbccdadaaccbcabaacbcccaccdbcbbdccacbabcbaaaaaacabaabaacccdabcdbcaadcaddcabccdbbbaacbbbbabcadaaacdccccbbcbbcaacdbdaaabccddadbacbaabdbbcadababdcbaddcdcaadcbdbbaccbbcaadcdacbdacbbdbdcdcaddcccbbdbaddaddcbacaacbdbbddddaddcbaaaabdcdbcaadbbcdbadbacaabcdcadbcbabaaabccbaaccbdcacdcaabaaddbbdbaccabbccddaccacadbabbaabccacbcacbcadcaadcadbcbccddbbaaddcdddcdbbddcbcaacabcdaccbcdcaddbaabdcaabdbbcadddbcbddbaabdbbacdbcabdabdaacdadbaadbccdccadcabbdabdccacbccccbccbbccdaaabdbaddcbccbdabcddccdaddcacdadbcacdccddacddcbacccbbcbbdddcaccbcbabcbddbacbacadcbcaccadcababbbbddcbccdcdbbdcdddcdbbaaacbdabccdabbddddcbcacaaacabadddcacccacbdbaddaaaadaabbbcababcbadadbdaacadaacbbcbacaccbcbbdcaccadcbbbcdbbadcccdbdccbacbbcacbbdbcddbbcbdddbddccdbdcdabbdcdcccaccaaadbdcbbcddaadbabdaabdcbacbdbbdccccdabccdaacbacbcdbcdabaabbdcbdabbacccbcbcacacbdcdbdbabdbcdacccbacdadcbadccbbdacbddcadaadacdcbdadccadcadcbbaacabacbacbddaaddcabccabbbddccddababdbcdcacdaaaccaaadcabbcaacccddbdaccdcbaccdddccdddacdbbcabbccaccbddcbdabbdbcbcaccdbbbcbdabbcbdbdcdccaadcacccbcddccadccbccaddcbabaddaadcaabaaaaddcadbdccbbddbadbcbcacdadabccddaaccbcccdbccaddacbdbcabcbdcbcccbadbbbbcdcdbadbbbdadcadcacdcabddcccdbbcacccdcccbdcaaaaacaadccbcabaddbccdcbbddcacbabcdadcabcdcbabdddbdcadbabcdddddbdbbbdcacbdbabacdacbdcaaccbdaabbdcdcdaaabdcbaddbbaaddbbacbcaadaccddbcabcdaabaacaacbacadacdbbacbbcdcbaabaccccacbdacdabcdccdacccbaaaadcbadbbadaabddbccdbbbbcabdccbbaaabccdadddabcdccdbdcbadabccaabcaaadbcbadcdcacbcbdcddcaddcacbadacbabcbcaadabccabcaaddaaaddbdaabbdbdccadabbdcbbabdbcabccccaadbbbdabaaccbbbbdcbbadcacbbbcacccbbddbddcddccdcabaadaadcaabbdaacaabadabadbaccabcdbcaaaacbbadaccaacdcacbabcabacaabcbdcbabaabcacacbacbaacdacbbabccbcaddcbbbaaddbaababcbcaccbcccdddaaaabadcdcbacdcdbdbdaadbbcbbbcabaadbcaaddaabdbcdaadbbcdcaadcbaacaaacdacbdccacadccaabdccbbcdaddadbbaadcccbacbadacdaccaabaddadbcdbcccdddaddabcbabdbcadacabdbbadbdbaddbbcddcbdadbbbcbadbdcbcaacccbcadcaccdddcaccccdddadcbbabcbacbbdabdbdacaabccbbcddcdcbabddcadabadcddccababaadddcbcbbbbbbabcdbaabdcbddaddcbbbabdbbcdadcbaacbbdacacddabacabcdbabbadcacdcdcbdcddcabcadcbcccacdcbabadbacdbacbacdbbdacaccbcbadcdcadbaabadddbbddcdcdbdbadaccdbaccabcccbaaccaccacddddadabccddbabbcaadcdadcabdacabacdaddbdbdbbdddaadddbdadbcabcaadabccbacdcdaadcdbcbadbdaacabcabaddaddcabddccaaacabcacbdcabcdcaabbcddadbbcaddcdcbcdcccdcabbcdcccaccdbadbabdcddabbbbccdbdbdabbcdcaadbbccddadbccaabcbbdbcdaacdcbddbccbddbccccddddddbcabddbacddccababcaaabcabcbaaddcadcdcdacbbbacccbaabaacccbaccdaccadbcdacccdbbddbcdcbdccaadadbbacbdcadbccaacdcaddccddcadbdacccaddcccbdabdddbadcabdbcbdbaabaaabcdcaddabbaccbccbddaabacbcddcbccccaabcbaccacabadcdbbdbccdacbbccccddbabacbdbbccbcbbddcbddbbcccbbabdcbdadacadabbcadcbddbcdbdbbbdddabdbabccacbbbdddbcbdabdbbbacdababbcbdccabbbddaadadccbdbdadbcbbdcccdbabaabacdbcacbdcbabccbbdcaccabcccdaccdabadacdbcdaddbdadbccdbbaaabbcddbaadccccbdbdcdcadbbababdabdababbddddadccbbdbbbcbbbcaccbbaacbcbccdbbdaacdcbddbbbcacbaaadacdbdbdcdabdcdacbdcbcccbdccccbddbcbbddadaddadbcddbaaababbbdaabdcbdacbcdddacacbdcdbdacabcdbaaabacdadccddcccddbcbdaccabcabaabddababacbbcaccdbacbcabacbdbcdbdadadaccccacbdddcbacdddaabcadcdcadbaaddbbbbabccbcbdccaacbcbdbcbcbdccacdcabdcbcaacbacaddadbddbbabbbaabbcddccbdcadddbdbdddcdddacbabaddbbabaddbdcdcdcbdbbbadbbbccdcbadbcbbdabaabcacaabddacaacbbcdcbcbbccccdbacbcddbcabbdbadacabdccddbbabaadcaddccabbdcacacbdbdaacbabbadbabcabcaabcdcbbcbaaddaccdbaaadbacdccabadddcccabccdcdcbabbbdbabdabdddcdbcdaccdadaacdbbabbdabacbcaababdcacabbbddbcbcdbaaccaaaaaaadcbaaadddbacdbadddbdadbccacaaacbadddadaabbbdcbbcbcaadcbcbabcbbbbcbaacdaaacadaababdcdaabaccbbddbcbdbabbcabbabadcbbcddbcaaadcbbdabccddaabaaaabacabdaabacccdddbddcadabadacbacaacadbbdbcabadabdbbaddbcddbaaabbdbbddcdcadcaadbbabbcccddddbdbdabbbacddbbcaacccabcbbbababccccbdcdbaaddcabbdabdbdadcabaaabbbddbccabcdddadbcdabddcdcaacbcaddabcaaabcababdcadbcbaabcaacabadabccbadbbddccaaabbcadbaaaacaabaabcbbcccbaddbdcdaacdcccbbdcdbddabdcbdbdaadabaddbdbcccbdbcdbcdaabccdadddccbbcccbccadabddccadaacbcacdadaccbadcdcdcddabdaabcddcaaaacaacacabbbbabcbdaaaaadadcaabbccbaacadcbdbcccbbdcacccdacadababadacdababcdbcdacacaadcaacddccacaadccbbdcaccadbbdacdbbcbcdcdababbddababbcacdcbdaddccbbabccabaabddbdacaadbdcbcaddcccbbdcdacadcacbaadcdabaabadcbcacbcbaacabdcdacabaccdbdddcaccacdadcbcaaadbdbbbbaccdbaabbbcaaddcdbbacbbbcabcadbbcadcdbadccacbcdcbbbdabadcabacaddcccaacdddbbdcdadcbbddacdacbdccacbadbbcdacdcbacddbdadcbaaabadbcacdabadbbddcdcaabababbbaccadcbcaccacbdcdccabbdbcbacdaaabbadcbcaaddadddaddbadcbbacccdcabbdadbdcbddacdbbbbbbbcbbabcbcbcabcdadabbaaabdacabdacbcacbbcccdacabddbdbccadbbcdcbcacabdcbdccbacacbaccdcbacadbbacbbbcdbcadcbdbadbdaaaccbdadaadccadbdddbbabcadcadbdaacbacbcacbaaacbabdcdaccccdacddbccaacbbbdcadddcbacbabddaacabdddbbaabcabbcadbbccbbdcaaccbbbcbddddbbdacbcdccabbaadcadaddddaabddcadddadccacacdbcdbabbacacbbdaddadbbddddadaacbbaabbaaaddaddbbdccbcddcbccbdddadcddadbcdbcbabddbabdbcdaabaaddacdabddcccccdabdbbcccbdbbdcdadabbccdadabdddaaabbcacccccababdbdacbbbbadabcbccccabddbccaacccbdbbdcbaaacacbccdabbabcdddbabdaadbdbdbdddccdcdacbacbbccbbacbbadcabbbdbbccadbaabbcdcdbcacadbbaacdbccbdcbcbccdadddcdcdbadaaaccdababbdaadbdcbadbccbcbaddbdacbccbbdbabcccddacdaaaaaddbcbdacaacdcdaacddaacdbdddbaabbabddddadadcddbccdcddcabccabccaabcddccabbaacccdcdbcbbcbddcccddbacbcdddccbdddcdcbbacacdbdaaaabadddabdbbdaacbaccdccdabdbaaadaacdbcdababcccaaadabaddcddbaccabdabdccccccbadbdddcdcdcdbcadabddddcddbaacbbadcdaadcbbdcdccbacdbbcbcaabacdaaccbadadacdaccbcbacabcaadababaadbbbbbcbccabcacabbccbbbacaacddcbcbadbbcdccbcbcabcdccadbdbacbcbcadccdbcdaacabdcdcdddabdbcaadaaadaadacabadddadadbddcbdadadcbbbbaaadddbbdcbbbbcdadaaacacbdaacdadbacabcdcdbcbaabddddbbbcdadbacdaddadccaadbabacbbbaccddccaacdbaddcadaaddabdaacaaabdaacddacdddcdaaabdbdddddaadaacdaddbadaacdbccaadbadccaadbdccddbadaaacbaadccadccbcabbbcdddccbcbabdabcbcdcadaddbbdbaabcdababcacabaabdccabdaabccbbdadbdbacdbcdcdccbdbbccdcbdccbdbcabccbdbcdbdaadcddaccaaacaccbcddcacaabacacbabbbcaabddccbcadabdcdccdbcdbddacabcaddadacaacacaacacbcaddcddbccdbbcbabdcdbcdbdcdbcacbbdbdbbbcbadababadabdcddaadabdcaadcbdaacaccdbadcaaccbddbddbdbcbcbccdcbdbdcaaabaccddabadccbcddbbdaaabbacbabaccddadbabbcadadbabcaaabcccbacbbabddbccaadaadbdcacdacdcbbabcdccaddaacdaadbbaacbadabaabbacdccbaccadaacaddaaabdbacccddcccddbacbcdacdcadcdcadcccdbbdccccdbdccbdbcbacbadbbaacdacaccddcadbcddcddbadddcacdbdbbcbdbccabacabaccdcbaabdddcabcaddbdddcdccabbdadabcacddddbbdbbcdacdcaadbabdddcbaddaabcadbcbbdcabdddaddacdddbdcdcadcccbdccbcbbdbdbdcaaacbaaccbbaddcdcaadacbcdbbcdaccabdadabbccbbbacdcccccddcdbdbcaacbbbddadabadaacaddbccbaabcabccdbdaabcbbaadddcaccdaabbccbcdacadaaacdbbddbbcbbadbdaabcacccdaaccddbddadaacadddcacbacabdadaadbddbbdacdcbaaabdddccdcddacbbcacdcaaccacddbbcdcccacbacadabaacbbbbababadacbccbbcbbbdbdddccbdbdadbdcabccbccbcabcccbdbccacacbaddcadaddcbddcdaabaaabdadacaaacadcbaddbadaccccddbbbdaadabbabcadcbbdbacdcaaadbbdddacadbbcadacaaccdacdcdbdabccabdaabbbddddabcdcaccacbbabcdcaaddbadbdccbbcadabbbcbcbddbcaacaadaabbbbddacadacdcadcdcadaddbdbcdbbdbbbdbbbddbdbbcdbbaabadababdaaacccacdcbcddccddcadbcaccbbbdbdbcddabddadabdababbbadcdbddccdabaadcadadbdabcddacccbbcbdcaccbbcbbccdacdccbacccbdbbdabbcabcabcbaabacbbabddabcdcbcabbbcdabaaabccddacaddbdddaaadcbdcaaadabadcbacacbcadbcadabccaacabccdccbaccdcbccbddcdbbbbbdddddcddbdddadbdadcacaaacdddaccacaddabdadcadabcbcaabbccdcbdbbcabadccbbccdadbbccdacbbdbdacdaaaaabaadddabacaddbbccbbabaabbaacbcacbbabbabbcaadcbcaaadabddaacbadcccbcccbbbdcbcacdcbbcbdccacadacbcbcaabcbadacdadddbdcddbbaaadabadbabdbcbacddadaabddcdddcdbcddabdabdbdcbdbdcbcbadabcdcabdbdcdbdbbcadbddbbbcccadcbbdddcbbcbdbbddbcdcbcddddbdbcadcbaacbccbbababdabacacbbacaabaacaaccbbbbaabcbcdcaddbbadbdddbbdddadcdcbddcbbcdbdcabdbacaccddbbbcdccaabbcacadccadbcdacdbbbcbadddaccbcdccbdbbaacdaddaadaccbbacdacbdacbdbdaaabbbddaadcbcbdbaacddabbdbcbbcbcdadcdccacbcbccacdadcddadcacbadcbbcbacdddadcbaaabadadacbbacdacbcdaabacaccbbcbaadcbadcdacdadabbbbdcdbbbadacaaccbcbbccddbadabbadbdbcbbbabcaccabcbcddddbcacdbbbdabbbcbadbccbabddadaccabdccaaaddbbacbcadaacaddaacdaacacadddadaddcccabdacdadbdbbcccaacaddbdbdaacacdaabcdabccacdcadcdabadccccccbbbccdcbdaadcacaabaddbbddcbdadabadcacabccacbacbccabbabbcdddcdbdddddcadbadaacdccaaccacdddbbdbdcacacaadabbcacbddcddbbbbbdcbdbadaacaddaaaaddbbabcabdcbaababddcbadcbccadabccbbdcaaabcaadbdabbdddddcbaddaadbbccdaaaacbdabdadbddadccccaccadacdaabdcbcdbcaaaadbaadcacbdcdcbccbcabbddadcdbdabcdaaabacdabbddbbbbdaacccdcbaddabdacacacbcdbcaddcbddcbcbcdaabbcdcbbcacacdabdbccadcbbddabbccbccdbdccdaacdbcaacacbcbddbdbaccbccabacbaacaabacccdbbbcabdccabcdbcbcaccdccdbbbacaddadddbcabcaabbbccdacddabddcadbabaadacabdbdccaacdbbcabcbdbcabaccadcbcacccddcbcdadccdaadcbbaacadadbbaddaccddbddadddadaacccddcbbccccdacdabdbcbacdbabdbccabbabdcbabcbcddbbcccabaccdcdaccddbdbacdacdcdddbbbaddddababadbacbccadabadacddbbdccbdcacabbccbccbddbbcaabccacbabdabdbbcaacbbddcbaaccacaababdcdbadaacdaccdddccdbdabbbbcacabbaddcbaacccabdddbdcaaadaccddccdbacabcbccadacddbcbdccdcdcbdddddabdcdbdbcddbaaabccbdadbddbccbbccbcadbabdbddabacdbdccacabbcbcdcccababacbccdbcdccdccbccbbabbddbacbadcbabdaabdccdccadccaddbaadacdaccbaddabdacbadadccabbcccdcbddaabdcbadacbaccdabcbcccbacbbdbbabcabbbdaccacccbccabaadcddbaadabdbbcacbbdacaddbdcddbdaadabddcbcaacbccddbddabcbbcaabcbdbbbabdacbcdddddcaacaabdbbccabcabacabddccaccadbbdcbcdacaccbddbbbdbccccaaaacbdddcddddcbcdcdcccdaacdbdabdcbdbcbcabbdadbcbcddbbbbdcccaadaddccbacbccdbbccadacaacadbabdbabbacdcdbcbabccdcbacabcacbdcbcdcdabaccacacdbaccccaddabaadcccddbadccccbabcdcdcbbdcabcdcadbcdbcddaaccdbcbbacccaddddcbbaababacaaccbbadddbdcadbccbbdbdcddadacabadbdaddcbaadaacdadbcaaccacaabaaabcbddaadaaabddccbdadccbabbbadcdadccdabddbcbcbadcdcdccacbbaabababdacbabdbdccccccbcbcacbccbbabbaadcbaadbbacccbabcacdacabcbcaaaddacdccababcacbabadaddcacbadcbadcdbacadabcdcddadbbcbcabbcbdaadcaccbddaacabbcccbbdbbddddabbdcbcbcdaadcbcaacddaacadaaadaaddabdbbdaaadabcaccdaccddadbbdcaacaaaaddcaddbcccacbaacddabcaaabbadcbbddcdaddcabcaaacdbadcdcdccaabddbbdbbabcbabacbdaddcbbbadabdbbcaccadcbaaacdacbdddcdcccaabdaadbdababbdcadcbcbadbdaccdcdaccbdcaccbccdbbbaaabacbbddbdacddcdaacbddbabaadbdbbdcaacbdcdabbcbcddacdadddccbdddddabdacdccdadabdbbdccbcbacdccaccabaccadccdaaccabcacadcbacadccdbcbdccccccbcadbcdaaddaabcccdadaabdcccdcabadddcaaaadcacdabaaccaaaccbcccababbbdaddcabbdbdbcdbbcbbbdcaccbbbcacbbcbbadacbacbdbbdcccbacdbcdcbacdbbdccdaabbacbdbacccabdbcaabcbabdcdddccadcbcbadbdaaddbbcbbdabbcddcdcdcdbaaaaacabcbccccabbcbdbdcbccdaccccbcbcaaaaadadccdccabcacdbacbdbdabbcbacccddaadccadbdccbdddaccbbbabccdcababccddacdcdacbcacccdbbdddaacdbcbbcbcbbccbadccdbbbadbcbcdbabcbddaccbdbadcabdbabdccbdbbcbbadbacaaabbabaacdbadbdbdbcadcadabdbbbbccdbccbacabacbdbccdbcacaabccacdbdabcabdcbcbdaddccabbabdcccbacbbaacabccbabccdcbdddbcdabcbadcddbcbadabcbdbdbcabdcdccaaacbbccabcbcbacaddbdbcbbbccbdacadcbccadacaadbcbadcabcdaaccaadbdccdbdabcadbbdbbbbbdaaaccccadaadcabdcccdcdcbddddccdbabcaacdadddaadbddcdadbccbbabcccdccdbaaaabbbabdbdbabdcbdaccdabdaabbadcaaadcabaaadccddadbaabcdddcaaaaaccdabcbacbddcdddabbccababcbddbbacaabdacdaadadcdbbabcbddcbdcddcdaddadaabccadccccaccadbbadbccdbabbdcbdacababdcaddbcbabbdcacdcacaaadbdcadbaacdcdaaddabdddccbddbcacdacbccdbabbcdccaddacdacabbbadaabdcbcccbcbcbbddadcbaaababbcdaddcdcadcdcccdcacbbccddcacddadcdccdabdbadcdacaaadbcdaddacdcccbddacdbddacaaaaabccbcdccdddcdaaababdacbdbadbaacacbdacdbbcddcbacbccacbbdacdbbcadbaccbbbabdddcadcddaaabcbcbadacddacaddcbbcabcaabdabccdcbbbdcddabcdddadaadcdcdcbadbccacadbdddccacbcdadbdaabcbbcdacbdacdaaaabdcbbcdadcaabcbddbbdbbaddbdaccbcdcacddbdaddcdcaaaddbccbcabbccbaaadcbbddccccbccaacadbccbaadaacdbbcbabcccabdaccbbcddbdbddacbacaaccddaaccaaccbadcbaababdaacadccbdacdcabdabaacdddddccabdddcabdbdabbcbbbbaadaaaadcbdbddadadccbddbadcbadcddacbabddcaacdcbcbbadaadacbbcccbdcdccddccbdcdbdbcadadcacbdaaaadbaccbacbaccbbbcdbcdadaacabccddbacacbadabacdcdcaacdbdbcacbddbbbbdabdbbbcdcdcbbcbcbbcdbcbaaaaacbbacddadcadbdbddadadbdacaaabcbdcbcaaccdababbbbbcbaabccaccabdbacadbdaccdabaddcdccdbcdcbddbacdcccdbbbbdcdccbdabcbadccbadcdadabbbbcddbccdbacbcaaaaadabcddadababcadabcadabdccdaccdbbddbdacbbcdbcbbdcdaddbdbadbbaadcccbcbadbddbdbcacdcbbaabbaabaaddbbacccddddddbacbaaadcccccbdbddbcddcabddbcbaccbdcbbbdcdaaadbccacbcdbabcabdabacccddccbbdbaaaacbdcdacccbabdbbdbccdcbddaabaddaacdcaabacbdabdcbcdddbccddaadbacadccbadcccaadbdbcadaadbadccbaaaacaddbadccabbcabdcdccbdcaddbbcaacaaaddadacaaabdddcdbaddcdcadcddcadbcbaacacbacdccadbbcdabdbdccbddcbdabcdbaabbbbbabcbaccacdcaabbbddddbcbaccddcbccdddbcbdabcbbcdbabacbabddbbcdcdabbcbbcacdcdadbbacbbadadbabbbdcbcdbbddcbbdbabcbdcddcdbcbcbaacbacdacdcbbdcbbbcddcccdadbacabbdcaddcddcaddaabdbcdcccccbbdabcccdcdbdabacbcbcbddacbbcddcacabdaadaabacdbadbcabddbbacbbdbcbcbbdcddaaddababdcdbdbccaccdcbbbaabbccbdccadbcabbadaacbacadaadcaabbaadcbbcaadbbdcbaadbddccbbbdbbbadcabcdcababdddccdbcabdbaadbaddaddabdacbcbcddadcadbcaddaacccaaddddabbdcdbaccbacabbcaabcddddcaccddcbaacaabcababadaabdbcddcdcadcdadaadbdddbbcbaabaacbbdadbbabdccabdadaaabdabaccbabbbbaaddadadcaaabcdbcabbabcacacdabbcabdddddcadaaddbbbaadaababbbdddbbdcaaccaabbccbdabcadcdacbbdcbbcbbbccacabadcbbddbabccdcccddbdabdbdaaccdadcccaacbcdddbadbbaccbdacbbadbddddcdacacdbbbcbbabaddacaaaaaaacbcdbdbbdccbcaaccdccdcaddcadbccababbabbadcbabbccbcaadbdaaaacdddaadccddbccacaccdaccadbcbcbdaabcdaaddddbddbcaabaccacdddbddcccacbdcacbcbdaabddabbdaabdadabbcdbaabdbbddddaacdccaacccadacbcdaabdacdbbcaddddcacaacbddcaaccdaabdbaaabaaaddadcddddcbdbacdbaaddabbcbcdcadcaaaababbadddbddcaaccbcdccbdadcaacbababaddbbdccdbadaacabcadcbddcaababdcbcacbdadacacadcdcbbdcaabbbcaadcbbcadcdadaabacdbccdcbcacbcacccbbacadbabcaabddddbaaacbabbcacadbdbbdcddccdadcdcdddabcddbaacbabaaacddbbbabbcabccdcabddcccddadbcdccadbcdadbaddccbdabdaaadabaaabdbbdbabaacdaaaccdabccdbacdbcbbbccdadcbabcaaaccbbbcacbaaaabbcbadccdaabdaaadcacaddbbaaacbabccdddbdbbbaababcadacccbbcaaaccbbdcaddcdbababbdacdcaadbabbcdbbcbcbaacccddcaacdaccadcabbcadababcbaacababdbabcabcdcccbaabcbbacdacbaabcdcabcdbdddaaabccadccaadacacbaaaccacaddcadcadadddbacadbbbbccabcaacdbbcdaadabbacbdaaaabbcabaddddbacaaacabccbbdcacbaadbbbcbabbdbcabadbcdaacabbabbabcbbadcdcdcddcdbbbbbabbadbbbbdaabadcdbabbcacadaaadbcbaabbdadddbbbbddccaadcbcadaccdcbbccdddbaabddccddacabcdddcabbaabcbbdbadadcbbccbbccaccadcbbabbccdaaccbdcbcaddabbadadccdbcadacadcbbbdccdbdddacacabaddddcddabddaddacdbdbaaabccbbadbcdbddabcacdcbbccacdcdadcddaddddbaaaddcdcdddcccdcddcaaddaabdbcabdcbcbccabcddbacaddbbbdbbddbaddbddacacbcaaabcaccabccacbbadabbdcbcbddbdacdcddbddacdcdcbbcccccbddddcbdacddbacbaddcddcadcddbaacdabbdbbacacbbbcadcdcdcdccdcacddbcbcddbcdaccbddddcbabbcccdbdddaacabacccabadcbadabcdcabacaccccaacbcbcacbbabccbcabbdacaabccbbabddbbddcbbcddbadcaacaacccaacbcadabbdbdcabaccabbcbadcbdacaabcddadabadbddacaddcdcdcaacaccacdcdacacbbbadcdbbdabbbdddabababcbdcacdadacabbcbbdaaaabacbdbddbccccadbddddabcbcdacbbdadbaadcbddcccbccdadaccbbdadaccabcccbdbcddaaccaaabcbcaabaacbabddcabdbcdbdcdddcacbacbcbccdaddcacaabbbadbdababcdcbbdaaadadcdadbccdbabadcdbcccbadaaadccdddcdbabbacdbdadaadcadddccbabbbccacddbabcbdcaaddabbdddaddabcaaadacbbcdcbddcaddacdaaaccaacbcbacdbddacadbbbdaaccddccdddacabddcbcaccbdaaccdcaddbdbbbbaadcabacabdaacabacccaccdadbcaddbccddadaacacadacbbabdbaabdddaddcccbccaddabbacdbdddbcdabbacabacadcdcbadbbdddbccddccdabdadddbddbacdcdcdccadcdddacdddbbaddaccdabcaababcbdadbabcbbacbccddcaddcdcaacdadaaabcdbcabbddacbcacbdcbcbbabdbaaddacadcddaadccbacacddabcbcaaaaabdcbccaddcbbdcbbcdbdacdacddabadaaadabcccbbbcbbacddacadcdbaccddbbadcaabdbbdbbcaadcaababdabbdaadabbddcadbadabcbabcdcdadbcbbcdabcdddbadbdddccdbccababdbbaaccbcacaabccccbabadbcccacdbcaddacabcbddcccccbdccddaadabbdacdacaddadaacdbaabcdaaacaabacabdcadcbdabbcdabaadccbbbdbabbbdaacbccddcadbbdbbdacccbdabccaabaaaaccdabcadadcbaacddaccdacdbaccccbdddaadaacbdbadcdcaaddcdabdcaccababaccbadcacadcbcaddcacbdccbcacacaaabccdacbacadbddbbccbcccaaddbbcadbccadbdccdaacbcdbcbabcacaaccbbcbcdbaddbabddcbcacdddbbabccddbcbacdbbabdbbbdadcccdcddbaaacbcdaaddbcddbbdbbdcdbabcccdabaccddcbdccacababcdcaaccacdbdbacadcbbdbcdcbbacaacacbcbabcacdddabdaaacdadddaaaacdccacbbddabcacdcbacababadcabccacdabbbbacddccacaddbbddaacdbacdccddcccacbdadacdcbacbbbabdaabdcddcbcdadcccdcccbcddacbcabccbdcadccabdbacddaaddbdddbdbbacdabcabaccccdccdbbbacbbbdcabdaddbcdaddacdcbcbcbcabdbdbbbabbddccdbccbcaddadbadddccccdadccbbdcaccbddcbbadbadcabbddadcccbddcdaccdadbbdbcabdabddbdcaadcdacacbabdbaaccccbdbdbbccccaadcddddcdbaccaaabbabdbbaadbdddddbdaaabaacdcdddbcadcccddcbacabdbcbcccccbbaadccbcadbdbaddcdccaacacadabcccbbcaddbbbbcccdcbdcbccdcaadaabdcbdbacabcbdccadbdbccbdbbddababbddacbacaccbbdcdbccbcdbdcaaadbcddcaaadcbdcbcaabdaccacacbcacddddbcdcaaabdbcdcbbddcbbdcaddbcabddbdbdadcddbcabcbaaaabdacdbdbdcdcdbdbcbdbbbdacbbacbaacbcaccbaaccbdaadcbdacabcbdcabccbdbbaddbaccacadddccacbacbbcbdbdbbbddddbccaddadbcbcbbccbccaabccbdbdcdcccccbcbcbcbcacddaacbbcabbbdbbdaacabaaaadcdbbabadbaadccabcacdbaaaaaaadcadabdbccccddacccabdabbabaaadbcdbabbbbbaadcbabddabbacbcacdcbcaaabcaaaadbbbaccadcdadcdabdcdbcaacabcccbdaadbbcddbadbacbcadddacbbbccabdccdcdcdcadbbcacabdaccbadddddaccddbdbcddaccddbaadcbcabdccbcaaaaccaabcbbbdbbabdbdcdabbbcccdbacdbbbbbadbcddacdaaaddadaacacbbcbbcbbcdddbabdadaaddaabaaadbbcddbaacbcdaacabaddbbcaaacabbdccccdaaddbddbcbddcacaddccdcbcbdaddacbccdbbcacbbcbddddabaaabaacdcddbaacdbbdbaccbdabaaabdacbbcccacdbaddcccdbaadabcbdcddccbadaddbaacbdaacbadbcbbbaabdbdcbbdbabacaabcbacacbcdacbcbcbbacbdcbdbdbbdcdbdabdbdcccbcaadaadcbccbbdcabbdcabccdaaddcabccbadbdadadcadcabbdddbccdcbccbcabcbbcbcdbbcdbaaddbbdbbabdcbddacdaacacddbdcdbbadacdbbbdccdabbdadaaabdaaaabbdacbdacbacbbdcccbbbdabbaabdbbaaaaacdbacbdacaaacadbdddcdddbbababdcbddbaadcbbcaccbbbcacccdccbdddcccccbdcccacbbccacdbddabdcccabaaabbccbadbccadbbccabddccbcbcadbaabacaabbccaacbdddaacadcdaacccaabbaadbcadbbcbbcdbabbdadacbabccdabcdacdcdacdcacdadbbaddacaacaacdaaaccabaaadcacabcccbbcabbabcccbdcdbddabccadaabdadbaddbbabddbccdcddcddcabaddccbbadacccccdbbdddcadddcadbbdadddacbdcbabacdbccbccacaacbacbadddbdccbccbdccaacdcaccdbdbababbbadcadbbcbdddcbaadcabbdbbbbadcdaabaddddacaaacbcacbcbdbdcbdbcdddcbcbbdddbbbbbcacbbaccaddabacdccbdabdcbacacadcdbddddcbdadddbcadaddaabccdaadbbbbadcdacabcdcbbcdbccbbddbdbcdbccdccbccadabdcdccaddcbadbdaabbcdbcbddadcbdbccaccaacaccdcbddddbdacacbcabddbcbcbdabcbcadbbcaaaaaccabbdacccbdcaadadadaabdadcdacccdcdaccbbbaabadaabbaabbbabdaaabdacbbbbbaadddcadadacadcdcaacbddadcadacbcdbbcababbccdcabdccdbaacdddcbabadbbaaccccdcaacbbbccbbdbbcddadcdbccaddabaccabadcdcddadccacdcddcdbdbcbbabcaaccbbcaabcdcbbbbbdcaaabbdddccbcbcddadaabccdddbbbbdbadbbabbddcdabcacbcdcdcaddcacdbaacbdbdacddbbcbcccbcdcabddcccccdbabcbcbccaaccbccddcccaaccadababaccbabbaccbbdcaadabcdcdadabbdccbbccbaacbcddadcadddabdcdacddcbaaccadcbddcdbdaabcbcbcabbdcbcabcccddcdbdcabbdccabacbadddbdadcccbdadcddccaacbbccabbaacaaabdadcccbcbdaacddbbadcdbaddacddcbcddbbbbcbdbdbcacbddacbaacdadccddaddcbcaddaccccdaabaccbdaabaabddbcbcadcacbcaaaaadcbaabbbabaaccadcbbadaadaddcabadaddddbbcdcbccbdabadbbdcdccaaaaabcbcabbbcddcdccbbcacccbbabaabbbccaacdcbbddabddcdaaddccacbddcbbbdbdcdcbdbaaddbccdbccdbdbdcbaccddcbbdcdadbbcaccccbbacccccaccddbbdddddcbbabcbbbdadbabcadcbabbdcbddbcaababadccbadccabadacbbabccbcbabbccacababcccddaccababdbcabcccdccaccccbbdbbcbababdadbcbabddcddcdbccdadcbcbbcadaddacabbdbcbadddbbbdcccaccccdaadccdbbcbbacdcddbccadcbaaabbdddddacabbdcddcabbbbcbaaaabbaadacbdabadcabbcdcdcdadbadcbbadcdbabbcbaccbdbddccbacdabdadbcaabccabcbcdabbcbddaabacdcdcdbbbcddbabbbccccccbbcadbddbdbbdcbaddcdabacddaabbbccccbacdcadcadadbbbdabbcbbbdadcdcaabbdcbcddabbaddddccbcdcaadaabcdcadbdccbcbdcdbdaadcdddaaabdccbbaadbcbcdaaaddccaacacddbbbbcbbbadcbbbcacabcdadaaaabbbdbcbacbdccdcacbccddbbabcccadadcbcccbdacbcddcdccbaadcabadadbbdbdddbcccddcdbcabdcacdabbdcdbccddcabcdbacbabdccaacadbbcdaccadbdaccdcdaccdabdabcdcdaacadadbbdcdbdabcbadcccaddddabbcccdabcdaacbbcbacbbbccdbccdbdccdaabaacaaaddbbcbabbbaababdaaabdbcadabcbdbabcadabbbbdaabcdbdaadbccababdccadbcddcbbccadcdcdaaaddbaacbbacabdbbdbbdabcdabbdacdcbbaababaacabddddadcbbcddadbccaaaabacabbadaaaaaddaadaadabdadddbcadcacaabbcccdcabbacddbabbcdbabcdbadadbbcaccaccddbabcddaadaaccbdabdadccbccddbbabdddadbdbdcbdbdcdcdbcbdacddcdbdaddbcdbbddbaacccaabdbccdacbbbdaaaadacbdabcdcbcbacaaadaddadadddbbdcabaddbdabbaddaadaccdbbaccbbdaabcadabacdabaabccbcbacbacddddaaacadcddacaaadbaddbdbddabaababbddcadabdcccabcdcccbcaaacbdbbdcbaadcdbddccabcaaaabbcddcddcabaccccaaaabdbccbdaacbaaaaccccdadbbabbbcccabcacdbdccdbabbaabdcdacbacbaaaddacbadbacdcdcdcabbbcdbdcbcbaaadcdcddabccadbcaddccbdbdaaacaddcabadabdbdcdadcdcbdcadbcdaddabddadbcbcccbcaddddcccbcaabadaddbaabbdacbbaddadcdcdbdbbaacbacacaddcdcadcccbadcdabdddbddaadbbccadaadcdbcdacabbdcadbabcccccacdadccbcaddccdacdadcddbcddbbbcaaadbaddadacbcccadacdcadddadbcdacaaccbdaddbabbbdacdccbadcbcaadbdbadaddddcdcddcabccadbcabacaddccdacaaccaccdaccbdaddbcccbbbacbaccbbcbabadcdbbbabaddbcaacacccbadbdacdcddaaaabcccddcbabddcdcdbdbbbbbccabbaadcbddbccbdddddbabbcddcacaacbabdcdacabaacbcbdbabacdacbcabdbadbccddbdbdcdadbbdbcabdcbdbbdcbdbcbcaadcbacbcadaccabdabbccdbbcacdddcccdaacacbdbbcbacadccdbaabdbbadbadabccacaabcdcaadadadcddacaccbcaaadccacdcbbbadadcbdaddacbcaaacbcbdbababaacbcddcdbdcacddbbbcadadabbdacdabadcabadbcdcbbcdbccaaaaacccdabdcbdaaddbabdaadaddadddabbdadcbaabdbdadbcaccdcbaacdadcbadddaddddcddbddccddbcadaddacdadabacccabbdbaddcbbddacadccbcadacdaadbdbaacbbabdbcaacdbbcababccacbdddbcadcbbbdccbdabdbccaddcaaabbdcdbccbcbabababbacdbaabdbbdacbccdbbabcbabdabbbbaddaadcdbadbdaabbadabdacbbdcabbcbdadbbcacbbbbdbabbddcdcaaabadbcbbbcbaacadccbadabcbccbadcdabbdbcadadaabccbadcabbaaacbdacbcabdcbdababaddaaabcaaaaadbaacaacadcacdbbbddacbaccddaddabbccbbdccccacbdbcbddacdbddbdddadcabdcaaabdcbaadbdcdbbcdbbddacbbcbdacadabcbdacbbcbbdaddbbdddaddadddbdadddccccbdbdcccdbdbcbadbdcbcadbaaabcbcadabdcdcbbddcbbbcbbbabbdbaacdacadcdbbbbdbacbccbddddccdabacbccaacbabdcdbbacbddcdcadaddcadabbdbaaacdbaababdcacbcbdbaccdcadbaadbaababacbddcccbbabcaadcaadacdddbbaacdcbdddcdadcdadddbbccadbccaabacacabdabbcbcdcabbdbbbdadccbddbbaaaddbbacdbdcbddadcbacdddccccbdaacbaaaabdabadacccdbbabacdcbcacccaabcadddacbcdadcadbbbdadccaccccbbadbcaaabacbdcdaccabadccbacadaabdcabbcaddadabcccdacdbcacabaacddbacaaadbcdbaabcdaadbcdaacbdabdaabcabbcdccccdaddcacccaaccabcbbbdbabdaddddccddaccabbbaacdbcdddadccdacadbdcbbbbbccccdcbccaaadcddccdababcccacbbadadbdbcdcccccdaddadabcddcbaaaacabddcdcdccdaabccbbbbbabdccbccdbbccabbaccbacaabbdcaddcaaabdccbdadbdddadcaaaacbabadcdcbbdcddabbbcdbadddacacbabcbbcccbcdcadbdccdbbbbdbdbddcdacdaacccdadbbabdbadddcacabbdbddccacdbaaccbdcccaadaddabbacdbbacbbdabdcdcaaddabdcabaabacbabcdbadddcacaaddabbddddabadcaddbabbdccbacddabbccbdcbaccbcbdcadbdbdddababbbdbdabdbbbcddadaccddaababcddcaabacabdccacaddacaadbddacdaccdcbdadadadcbbcdaccddaccbadabbdacadccddaadddbcdcaccbdcdcacbababddbbdbdabbdaabbaddccabbcbdcbbcdbcdaaacaabcdbdccbbbdacdccbdaaabcddccaacbbaabcccaacabaaccbabdcdbabcbabcdccbbcbacabdabbabbddaaaacacdaaabdccccbdcbdcccaabccbddcdcbdaadbcabbbccbbdadacbdabcbcabdccdbccadbbaccacbdbcdcbdadaaabdabcbababdcaddabdabdbdddbddccdcbbdadaaddcbacacbacdcbcbaadbbbbbbcbadcdaacacbcbbcdddddabdbdbdddbddcabacadcdccccbdadddcbdccaabdcaddbcaabcdbcdbdbbacdabccacabdcbdbbccbcccaadbaacaaabbcbaadbdacdaddcdcdddbaadcbaddccadddcaccccbaadcdbcbadcbdbbbaccbddcaadcacbcbddbcdcabdbdbaaccccbbdcaaaccbabcbccbbcbbcabcddbabdadabacbbaaaccadddabdddddbcadddbbaacabccacdaaaaaacccadbbdabbabdbaddddbcbcbdbcbdbccadaaacdbbacdcaaabaaacacadbdaadbcaacbbcddcbadaccabacadadbbcaddbabaccadccbcdcdbccaacacdbbbbddcacaabbcdbaacccadccdbdcdadcbdbbdaaccacabbbaccacccdddcccddabaadadcbccbbdcdbdddabccbbcaccdbcddbcdadbccbbcbdbcaccbbacaabcccbbbabdaadacbccbadccdccbdabbcbbccdbdbcbdbcbcbddcadacacabcacabdadddaddcddadbbadccdabcbbababbdbcddddbdcbbccaadbccdcbbdbbdbbcdacbdcabbddcbbbbbbbcddbacacdbbbadcddcbbdccccdcdbabbccbcdabaacdbbcdbdcdbcccbdaaddddbcacadabbbdcacabbbaabcabdbbaddbbabccdddabddbccbdbccadbdcadacbabbcbaaccdbddccadcbdabccbabcddccaabbdaaadacadbddadbbadbddaaabcdcabdabbccbbccabbaaabddbdbdccdaadcbaccdbcddbbbbaabdacadabddaadcdcbddabbaabddcbaabbabaddcabcbdacddcccbbbcabcbddbdcbcbabddbaabcbadccdacabdcabdabaacbbcadacbbcddccbaacaddbaadcdcdcdabcccccaabccacdbcbcaddcaaddcacaccddcbccccbabddaccdbaaaacccbadcabadabcddaacbbddcacdabaabcdddcbcaadbacbbbacabccacabbadcaccbaabaccddcbadbcdadbadddccabadaaacaabdaabddbbbcacbcadacdcdadabaabdddbacaaacdacbacbaadcdacdcbcbbabbcabcaccbacdcaadbbcaabbcdbcdcbcddbaddddabacdddbcadaacdacdacccbdccaddcaabbccdcbbbcccdcdbdbcbbadccdbacdcccbcdaaabcadbababdadddacbcddbcacdbabcaddbbccbdbcaaaacdcbdcddddbbaadddbbdbbaacddaacbddbbdcdddcbabacababaacaccadaccbbcbbabbcbbabbdcabacabdadcddcdbacaadbcdbccbbdcdaacacdababaddaddbbaacdcdabcabbdcadbabacadccbcddddbcaaddbdaacdbbdbbcaaaabbbabcbdbbccccdbcbbbacbdaadbdcaaaadcddacaabbbaccddccadcbcbcbdaacbacacacaccbaabbbccccdacacbbbdcbddadcadccaabddcacbdcdcdbabbcacadcbdccbdcabcdbdbcaadcbababbabcdacacadbadbbbaacaaddccbaccdaadacdadcddabcdcbcabcdcdcabacdbbabcccdcdbdcbbccaddaaadcbbaacbcbbaabcacadabdbbbdacadcddbdddbbcdbaabaccbbdbaacccaabcdbcbdabbcbbabadbaacdabacdacddccdababccbabcbbcbbccabbaababdbdcbbabdbbccdaacaaccbcccbbcdaacdaccabdaabcdaadacdaadacccaddbabcadcdcbaacbdbbbccabdcdbdcacbbccbbabdbbacbbcbdadbcbcabcacbbbbdccddbabcdabcdbcddcddddccababdbbadacddaccddaddaddacbccbbbaabcbaddbccdadcbacbdbadaabcbacaccababaabccbcacbdacbbdbacdccbccbccdcdbbcbdddbcacabdccccaabbaabaabbdcdcccbabaaabdaaddbcacabdcdccbadbddccdcdaabcadbdbaddcbabadcacdaabdadacaaabccbcbaadbddabdacaddcdaccbacbcdcadbaadacdadcabdcbcbcbbcbbadddaacadbcddbbcacbabbccbdacddcaabacddbccacaaddaabdccbbcbcacbbdbadaadcbccbaadcccbdbbbcaddcccdbbadabcbaacaccbbaabdbbadbbbaddbcdddcbbddcbaaabbddabbaddbacacbabcbbbcdbccabdbdcccdaadbdddadaddbddddccabacdcaddbbbdbbbcbcddddadaaaacbabadcdacbbcddadcbcaaddcdbdcdacbadcbbbbddbcabcbcabbcccbaddcccaddbaabdcaabbabdbbdddbcbbacccdbdbcbdcacacdacccabaabccaaaacccbadcaacabadacdcaddabbadcbabcadabdbaacabcaaddbcbbcbccadbaddccccdbacbbcacdccdabdcadcbddabbcbcddcdabaaaaccdabcaacddadcbbdaacccccdadaccddaacdaddcbbbcaabacacbcccabcdabbcabbadbbaadbbacdaabadadbcbbaacbcacbbaddcdbbdbbadbdccbabddbaaacbdbcbaddcbbabddcdbdbdaabcdddcadacbbcbcbaaddddccaacacaabdbbcbacccbddddcadabcbadcbbdcdacaddddbbddacabbcbaacdbdbacbcbbcddccddcdddbcbdcabcacbdaababbcdcaddcbabccdcdbcccbbbbcadbaadcdbdcdbaddbaaaccdabadcabccabadaacccdaddcbacccacdbbbcbdacabaddcbbcbcbadccdbdddacdcddbbbdbbbbcadaacaccaaaddabcdcdaadaacdcbdacbdacdadcbbabbcbadcaabcaccadaddbddabcacdcbdbaacdcadaddcbddabcacaadaaccadbbaadcbddcddbacdacabccaccbdccabdddccbbacbbaaadaaadacabdbaabccbdbcddaccadabaadbdcacaaabadddbccacabbbaaccccdbdabdaddadabadaabdcabcbaccaacbaacaaacbcdacdbbbdbabbbabbccabcccbadcbcabdcccbbbabdcdcccbbcbddbaadacaaccbcdbabcdddabdcccaabbccccdaddcbbadbbccbadbadacabacdcacdabcaacadabbccadcdcddbadddddcbcdadbacdddcbaaddacacdcbdadbadadadcbbccacdcababaddbcdaacbaacdabbabcccbcaaddbadcadbbccbdadddbdddbbbbbccbaabacbadcbdccccadcdbcabadccdbcdacaabaccdabadacacadacaaadadbdadbadcadbdbdaadcdbaabddcadcdddccdccdbbbcbcabaccbabacbccdbbcdbdbddadbdbdbdbcdadddcdaacdbdbaacdbdcdadbcddaadbcabccddadcbadaddccdcbccbcbcdbdcacdbbdaabcdbbabdddacbadabaddddadbccdbacccdbcddbddcccaadccbdaccbbabbacdcabdccadbbddccacacbddbbbbaacbccabadaccdcccaadcabadbcccdcdaabcbdacadcbccdadddbbbbccdaddabacccbdddcdbdaddbbdbddbbcdccacdcdabccccbcbbdaadacdbcbcddccbbcaccddbbbcdddbbdbdddccacbbdbbbababbaaccacdacbbcaaacdccbaaccbccbabddbddcaaabcdccccdccabaaabccbcaddcbddbbabbddbdbcccbcccbbbcbcacbcdcdacccabdadadabadadbbadabbbaaaaabdaadbaabdcdcacaadccccdbbabaaabdbacdccabbaddcacdaddacbdbdbbadacbbcdbbccdaaadddcbcbbaaccadddbdbddacdcacaadbdcaaaacbdacdcbcdbdcbdddacccacaddbacaaaddddacdddabcddbaccdabacbcbcaacdadbbdccdcabddcbaabacaacdddbcabdabddbbdddabddacadbcabcbbcaadaaaddabacdbddcdaadccababddddcadccdbbcacdabcbbdbabadbbaadbcabdbccbdadbdbabccdbcdcbaaacdddccbbadbdcadbcbbaacbdddbbbdbbdbacbcdacbacbcaddacadaacccacabcdacdaadcbbccacccabdbbcddcacbbadadabbbaddcbcbccadbddcacdcdcacccaabdddaabcbcdbbaccccddcccdabadaddcbaddcbababcbbbddddcaccabcddbcbddbcaacbcabcddddadcdcabdbccacdcacdcdacbdbdcbccbcdddadbaccdbcdcddbbaaabbdcaccaacddcccccbabaccaabddaaadbabcacdbacbdbadbdcdbcddcabdccacacbbabaaddadcccdadcbadddadbcddcbdddbabacabacaabbbbbcbcccdbddcdddacaaabddcacaddccbcdbcbdadbbabadabcabbbbaacaaaaaacaccabdcbacdbabdccbaddcbcbbcbbbbbdbcbdddabdbddabbdadaadbdbbdabdcdccdcadbcdaaadcdbcdbababbdddcdccabcdcdddabcdbcdbadddaaddcaaabcbcadcdccddcaacadbbcbdcbdaadbbdadcbddccababaddcdaabaacdadbaadbcbabababcbdbacabcdbbcbcdababdbcdacbadbbbcaabbcbdabdbabbdbacccadaacacadababdcbadcddddbdbcccdddadbcbcabcdabcbbdbbddbcdcbacdcdbcccdbdbbdddbdcccbadbdcdccdaacdabaccddaacadacbccadccdbbaacdbaddbabdadbacdcabddabcdcadcddacaddbadbacaadbadadacbdacaadadadccacaaabadbcaddaccadcaccabadbdbcddddcacdbcddbbbdbaadddddbbddbccccbdbdbbdabdaabacbacaabbccaacdacbbacbdddddbcabdddbabdddcdabdbbccaacdcdaacdaacaabaabbbdabacdddcadaaabbdaabccbcbcdbacabbbccdbdbcbdcbdcbadcccdcadbdaddbcabadabaabacacacdddbdddaabddcacbdacadbdbdcbadacaadbdbacdcaccdabadadbbbbadbddcaadddbcbdaacddbbdcabbccbbaddbacadabdaadcbacbadcdcbaabcccdadaacbadacaabccdbcbdaaadcabdaddddbdcabdabdddabbbbabbcdabdcbccbcbddaacbcdaaadbbbaaaccabcdcdddddcbdbaccddbdddddbbcbcdbdbcbaaabcaacbccdcdaccbdbabccbbbdbccddddcbbabaacddbccacabbbcccabbbcabbbdbbdccaabbddcdcabbbcdbddccdbbabccaaddbcccabbadacaabbcddbcdccbdbbcdaabdadbdaacdadadcaaacaadbdcdbccdaddbdbdabcbdadcddbcaccbbcdcbddcdddbbbcdadbaccbdbacabacbadcdaaddcdbdccabdabcdbcbdbcacabdbaabcadbdccbdbcccdbbabdcbcacdcbaaaaacbabbdbcabbadabbccccbdabccbacaccddaddacadaadabcbdacbddbcabbaddadacbaaddacbadacacadcdadbcdcbdcbcbbcadbcdbcdaccaddbcdcdacddbbacbddaaabdbcbdbbcbabbdcbbaaccaaabdcdbbdacbacadaaccbcddcbaadddcadadcdabdacbdcccabacdddcbabdcadcbcbcadacbdbbbdabacadacacdbdcccdadcccddabdddcdbdbbbcbbdbdccbddbbbcacabdcacdcdbcbdcbbbacaacdcccbbabdadcbbddaacdddabcdcbadabbbacbbcacccbbaccaadaabcdcacabdaccbbaccddbccbdccbcdadcbdadddcbbdbabdaadbccdbdddcbbdacdcabcccccdbdabadcddccbacabddacabdcabdbbcbabccbaaabaacadcabcbacbddbabbdaccbaadadbaadccadbdddabdcbdacaacaddabcdadbccbcacdacbdccaadaaaadcabbcbcbcbbcbbdbabadabccbacdbcddaadcbcccabaadbcdcacabaacacbaccccdcbbacaadaadccacbddbcaabdbdaadbadcddbbaacccadaaccbadcbddcacccddaaadbbbdddcdddcdbcbadaddcbadddbadbaacccaaaadddddcccacdbacddacabddabbddcbcddaaaabddaabaaacadbccaadaaadbaaacbbcdcabdcbbadadccdbdcacacddcddbdadbdddaddabbbaabcbdbccaddcbbaaacbaadbaacbaccaddbacddbbcddcadbacbdcacbdbcbacbdababaabccacbaddacabcaadcbbdbbdccaddccdbddddcbddadacdabacaaaddccdbacbbdacbdbbcaacddcabcddcabdcadccabbabbdccccbdadcdcbabcabbdabdadabaddbbabdababbcaddccdbdcdddadbcddccdcdddaccbdbaccdbbbcaabddaddaaddbaaabbdcbcccbacbcbcbdadddccaccdbdcaacbadbbaabbbcbdadabdbdbcbadddababbaddcdbadcacbaddbddccbcbdbaaddbdadcabdcbacbbdddbcabbaaccbdcddcdddcadcaddbcccbabddbccacbdbbacabbaacccbcbacbdcbbcbcababcbcababbaadccadbdcbbdbbaadaccbcdcdcdabcbcddabbaaacadcdaadbbccdbccbabadddaccdaadbbbddcacadbaacbcccccddbbcaaaddaaccdaddacacadaabbabccaaacaccabcaadcbbdbbabbbccbddbcbdbccacbadaddbddccbaabaaadaacdbaacdcbadbdccdcdcdccbbabbcdadcdabdcbabcbbcdaadccdcdcaaccaabbccdcdbcdcccccbcabadcdacaddddbdbbadadacbdbbabcdddabdcbddddbbdbcadabbdcadbabdcdbaaccaacbccddadbdbacaddacbcbdbdcdadacaddbbcacabbcbacaccbadabaadcddacbbcccdcabbcaabdddbadbccdaacdbcdbddbbaddbbdacdcbbadaaccbbbdcbdcdccaddcdcabdbcabaaadddaccdbccbadcadbdacddbcdbccbcaadcacbdadaaacbcccacacccdcbcbdaaabcbacbddbdbcbdbdcdccbadaadccddbcacccabdcbcccddacdbdbbbbbbcbbabbcacdddbbcdddbbdaadabbbccaaaabbdbcacccbbcbbcaaddddacacbbadbabcbaccaacbcadcaadadcaaaadbaabaaaaaabbbdadacdaabcdccbacbabccbddadadcadabacddbcacaccadbacdaabbbabddbabaabdbcdadcbaaabddbabcbaddcaaccaddddcdbdacacbdabcadacdbdabaccccbdcabbcbddbcbbcdacdaadddcdabbbdcadadcdbcacaacbaabdaabdbcbadcbdbbdbadcababcbcdcaddaddacbdaaaddbbdcdacdaccaccabdbdddbdcdddbbcbbcccbbdbbdcddbbdccddabaacabbadadcaaaadbabdcabacccdaaabbdadbbcdccaacdbaababdccdaddbabaddbbdbcaababcccbdbcdddccadabcbdaabcaddacbbdddbabbcacbdbbdcacbdcbcdddcaccdddbdaabbbcdcbabadccddccacddbcdbcbcddadbaadbaddcbdccabcbccbdbcbbddbcddadcccbabbcabcdcddddcabdbcbbabcbcdbbdddbacdccccccddadababaadabcdbaccadddbaaacacacaddccdcaabbdcadabcbadcaabbdcdcbbdbbabdddacadaabbddabbdadcbadcaccbaaddaaddadcbdadacbccacaadadaadbcbcdcbacdacadcddbbdbdbcdcacabacaddabdbcdcbbcbaabccccbbcddcbdbdbbdbadcccbdaabaadbbdccdacccbcaadadbdabbadcdbabccccabacbaccbacbcbbdabbcddcaabaaabcadcaaddcdccaadbcadabddaabbaddbdcabccbdcabbabaaccadcababdadddadddcbadbaacdcbccdcbaaaadcdbdbccbcabbddbdbcdcbdbcbdcdacccdcdddbcaccbaaddddaaabbaddcaadbccddbbacbacbbbadabbbcdccbacdaadcdccbcbcadbbbaccbadcadbcdabdbcabbcbcccbacdaccbcddbdcdddaddccaaabbbaaaaacacddadbacddbcdaabadadddcbbcaaadccdabddbadbdcadddddadbbacdbddccdbacdbadcdcdddbcbcadcbbbaddccbdadcaabcbbacbaadcccbdcdcdcddcbbdcccaaccaddcbabaddddcbbdadabdaabcaacbabdbacccaccdddbdacabaccacacadbcaacacdaccbbddbdadbdbacbdbbdabcbcddcdddccdaadabbbdbbdbcbddcadacadbdbcacbcbccabdcacccbccbadbaacadabbcbaabdbcbdbbadbdbdcbbcdcddababddaccdbdaacccbbbdddadbcadcdcaacccdabcbcdbbadabdbddcdabdacbabbcccabbabccbcddbdbbcbcccbcbcddcacccabbcbbddaacacdacacaadddcbaaaccddbdddbbadadbaccdcddddbbcbaaabadddcccadbadbdbbdbcaddcbbbbacbcaadbcadbcbddaadbbaccdbdddadccbbbcaabddbdbbcbbdbaccdccddbadacbdbdabbaadabadbdabbcacaabbbaacddcbacdacdadbcbabaddaccbdabdbbaaabddcdccdcddcdddbdadcacdaadddcbdbcdbdcaadbabdbdbdbdadacddbabadadddddcccbdcdbabcbdddaadbacbccdddddaabbaaabddbabcbaddbdbbcbbccaaacdbadabbdcddcadcbcbadabaaaabadbdddbcccbbaacbaccbacdaababbaaaccaaddadddacacbababadbcadcddcabbaadbdcbaaddbdcaaccccbccdcaabbdbbabbbcacddadaacdcdaacdbbdabadbccdcaccacdcacdabccaddbbaacbbbaadddadbdddcdacbbbddadcdbaddbdaccaabaddacddabcacddbbccbbcdacccdcdbdacabbdbbccaaaaadbabccdccdaaccdabdccabbaadbbcddbcdcccdcaadbacdabadbaddcdccdcdaacadbcbcbacbdbdbccabdcacbaccccbdbccaacaadacdbbabcdcdcbbbaddbadcdbbcbacccbacadcabdbaaabdcbccdaadbddacbccdcbbcdadaacacccbddbbbddacccaccaddbdccdbaaaacbdcadbaccdacbababcbcccbcbccabadcabacbcbdbddbabbbbcacbaddacaadadddacdccaacacbbdddaccdadcdbcbbddddcbddbddacbadaaddddddccccdacbadbbdddcddbacdbbdaccccdbdcbadbdbdacbbbbacccccccccacacbacadccadbddaabababcdaabcbbbccdcdbaddaddccbbddababdabdabccadadbbddaddadddbabaccacacadbaabbbbdaccacbcddbbdcdcbdcbcdbabbcdaacbdbaaabbdbadcabcdcddddbbccdcacbdcbaabbcaddbbbcbbbcaadabbcaaabcacddacccaabaadcdbaddabbbcccdcaadccaaabadadaddddddccabaaacaaccccabbdbdcadaddcbbbdcabccbdbdbbccdddcdcbbbcbbbbdbbababcbabababbccbddbcaaddacaaabbdcdbcdbdbbaccdbbdbbacaababdcbdcddbdcdaccddcabadddcccaaaccbdbccbcdacbbbdbcccbadaadcdaccbabbbbdddadcaacbccabdabcadbdcdcdcbbbddbcccdaccdbcacaccccabdcadbddadbbbabddcdcbcbcdbddaadbbbaddcadbcbdbbdaccbaabacccbccaddcdccbabcadbcadababacdbcdbcdbccadababdbbcbddbbbabaabaabccbcaccbaaadacbbdaaaabcbdbddcadaaaaaadcacbdadccbcdbbdbcbcdadbbdabdcdccacbadabaddcbdbabdbbdaabddddddadadddcaccabaadcadcdbdacdbcccbabcaadddabcadaaabdddcdcacbbdabbcaccaadcbadccddadaadddcdddbdacdaabddaddbadcdcbdddbcacacbcdbdbddaadcaacddcaaabaaddbbacbbbadcdabbabddabaadcbdaacdccabbacabcabcacdcdabcaadbbabbadaabcbadabdbddadbdddaaaabdbdcdabccaababcbdaccbadaacaadcbcacbdbdbdddbbdbbbccddddccbdcbaabcbcabddacddaddbcbbbddabbaddbaacbbdccbaaddcccbcbaadcbdcbbddddddcdbaadbcccccbabccadcdaabdbaaccadaccbdddcbaacdbdbadbcdccdbbaacbcbaadbccbcacacbcbdabdbdddcdabadbbcabdbdadcbbdbcbaabccbdabcaabcaccccaacbddccbbacdbccbdcabbbaabddacbcabcbccccadacaaaadacbcbaacadbcabdaccdbbbbddcdadbbdacbccbacddacabddcdcbdbccbdabbbccaacccabdbbacddaabddabbdbddbdbaabcbabbaddacdbdabdddbbdcadabacdbaaccccdbddcbdcccabcbcddcadbbacadbdbadbcbabcdcadddcaaaccdaddbdccdddbcbddbcbcbacbccdcddcabbacbddcdadadcbcddbbccbcbdabbaacdcdcbdbadabdbddccdcbdbdacdcbdabcbaaaaadcbaabdcbdbdacdadccdcbaccccdccdcdddaddcccbcdbcbdccccbdbdabcddbcacbdaacdcbcddabaacdccadbdababacaaacbdbbcdcbbabacaaaaacbadcbcbccacbdbcbcbdabccddabbdacdcddbcbcabddccbcbcbabdaacdddabbbabdbbadcccbddcdbcdbcbbaababcdbdcacacababbcbaaabaddddbcaacdadcdccdabbacbaabdccacacdbbacaaddadbaccbdcdbdcbacbcdacccaabcbcbddacdaacacdbcbbcadcdbadbadabbbabbadccdbacbcbadbcdbdcabccccccddaadadacbcabbbacdbddbddacddcdccadcabbbdadcdbbbdadbcdcddcababcdadcbbbccadaabdcabacbcdabaadacbabbaadccbaadcdaaacdcacdcdcaadddbadddbaabadcbdbcbbacbccbcdcddaaabddacbcdbcdbabdbdcbacbabdcdabdaccbcbdcbcbdcccbacadbabdbcabdabbabbaadbbabbcdaaaababcabbdbbbbdccaaadaacdcacaabdcdcbccadbbdadaaccabbaabdaabccaacbacaddacadbdbbddcabbcbdbdabbbcdbcbadaadddcbcaabbaccaaddadcaaaccdbacacdcdaaddaadbacccbaabdaacadaabaadcaddccddbbacddbdcdddbddbccbcccccddbacdbbaddbaccacaaadbadddacddaccbbabcabdadbbcbbacddaaabcdaddaaaabbdbddababbadccabcaaccaacbbbcacbcbcaacbbbacaacaaadaddbdbaacababdacbadcbbddacadbbcdbcacbbbcccabcbcbdddabcadabcdbdbadbadaddbaacbdddadccaddbccabdaaccdcdccadbccccaccddbacbbdacbcbbcdaccadcadcabcddbcbabccaadbabaccbabdcbccadbbdaadcbdbcdcbbbcacdcacbcacdbcabbbdcbbabccddcdccabacbcabcbddaadbbbcdabcbccabdcccddbabdcbcabaddabbdcacddbcbadbaaacdbaddabaaadadbbcabccabbbccdbbaaccbabacdbbcdbdabdcdaabbcbdacaacddbdbbbcdcccdabbbdbbadbcabaaaccbbabdbcabbaccbdbbdaabaabbaccddacddcdddbcbdacdccdcdadabdacbadaddbadbdbabcabacdbccccccccbbcacbdabdbabdbaaabdcbadcbbcdcdcdcddcddaccaddbadbcbaddcdadadababbcddadddccccabadabdbcaccccadbdacadaabdbbdbdabddccbabbdbdddcacaadacadccdccccaabcacbcabaadaccbbbcabbdcccadaabcdcadddbcdbccbdccaadbccddcccdaadbbbbcabdcdbbbcdbabbcabbbdbdaddcdbabbcbcacdcbbacacdadbdaccbdccccbacabcbcdaabaaaadcddaadbbabaabcacabaaadacadcbacddcdddaabccbdddcaacacbaaacadabdaacbcdcbabadaaadbabcccdaccbaadabaacbcadadcbabbabbbdccdbaadccadadcbdbcabdbddababaabbdccabbadbbdbcadcbdacbcabbdaccbcabdbcdddcbadbddabaddbabadacbaaccacaaccaccaccdcaadabcaadbbddacdbddabadacadcbddaaaadaabdcacbaccabcbbbaabbccddcdcbcccddddbadcbaadbcadbcacbcacdcbbbadddbbacdaacbaddcdadcdbabdcacdcadcdabdcdbdaccdbccbcbcccacdaddadbdcdbcaacdbdacdbabbdbdcbabcadbdbacacadbddadcacccadcccabdddcadababbcadabaddaababaacbdaadbbacbacbcaabbbdcacdbcadcbcdcbaacddddbadbbddadacdabbbdacaccdacdbaccbacdbdccbababbdabcbacabccadcddcbacbccdaccbaaaaacabcaacdbcaadcbbdcbdbdcdcbcdcccacadbabbcadcbcdbcabbabcbbaacacddbabbcddcdcdccddddbabbaacacbcccabcdabcabacacaaaddaabcdcbdbbcdccbccdcbaabcbdadccdccbdccaddacbdabacdacadbaacbbddaccaccdabbbccbcdcdbccabbbddaccdacaacddabaccdbbdcacdbbdadacbdbbdcbdcbabdbdccbbdccdacbaabbcdddcdababaddadddaddbabdbadcddadbdbcbadccacdbbccdcbdacbadbcbbcbbbbaaccdaabacababcabbdaaadccabcadbbcdacababacbbabdbdaddaaccddcdbcdabdccdaaaacbddccacacabbcadcdcdacddcddcaadcddcbdaabbaadbadbabbddabbcbdadcbbbcdadcddddbdccdaddacccdcabbbbabcaaabcaddcaacbbabacccacdacbdbadddddaaabcaccbaabdcddbddadbcdabbabddbababcbdcaaadbbbdccbccbbbbaccbabccccdcbddbcbabdbdcadadbddadadddabbcacbcdcadccaddddcdccdacdbdacddbacbbcddbdcdadcdbabcbccdbccdddbadabccaddbddcccbdbcbacbacccbbdababacbaaccdbbdccdcdbdcbaaabcbdbabbdcbadddbacbaccbdbccadbbacbbaaaabccacbdabcbbbdbbadcbdcdddbcbcbbdbdadadaccbabbbaddbbcbddcacacddcccbbbcbaddbaadcacbdaacabcaddcdbadbdbdbacabadcbcccdbcaabadccddbaaadadbcabaaacbcabcacabcddcbaadcbddbcbcccccddaddbccbbbbdbcdbbddbdbcaaaddaaabaccdacdbcdddaabacddcabadbabcabdadcbacbbdccadcbaacaacdbbbbbcbaabdcdcddcabcdbdadabdbabbdadddacddbbddbabdaaaabadddcbbaaaccdabacdaddcacabbdbcabaadbbbbabbcabbdcaaabcaaabdadadaabdbbcabdacdcdbdcbcaccadabdddacaacaaddbbcaaddcbaabbcabbbccaaaaabbacdbddaaabaccdddadbddacadaababdbddaddacacacccbdbadcdadcacbcccaabccbdccdadbadbdacbccddabcdbadbcbcbdbbbcdbabadbdcaabccbcadaacdaabacdbbbabddaccddddaccacbabbccbdaaadacbdaacddbddacddababbbcbcbabdacadbdccbbcdaabcaacbcabcbdbcdcaaacddbcabadabaddbabdbcacbbdadacadcdacbbbabcacacddbddadadaacaadbaccadcabaddaccacacdccbcdccbcadbdbbabacdccaabbcbbbcbccabbdabbddadbcabdcbdbddbaababacbbaabcacbbacacacbabbbbbcbcbbadadcadcbcbdabaccdbcdabccbdacbcddabccbbcddacaaabbdabbaccdacdbacbbbbcdbdbbcccabbcbcddcbbacbbaddccdbabddcbcdaabcacbdabadbaacccaaaaccbacccdbbadbabcadcbdaaadcdbdcaadcdadabbbcbadbcacbddcbcccacabdcbdcddbdabcccabbdcbbabbbdcbbacaacbaaacbcbbbabddbdcaadddbbdccdbaddaacadabbcaadaaddcbbaadaaddbdaaadccdacacbbbbadaacdabddbcadacddaabbdcacdbababdaadadcbbdbbdbbcdabadadbbddcabaccadcdadabdcdcabdddabcdcddcddbadacabdbcaddbdabcbbbabdabbcdcdcdadbadaccdcccadbcaaacacbcbbcbcdcbbcdddadcdcabbdddababdbdcbdbcaacbccacdccbacadbdbcbabbcdcadbccccadacadaadadcbbbdbcbdbcadddadcbdabacdcbbadccdcbcacaacaaacacaababbaabcaadcabcbdbcaccacbbdcccadaaadbccbabddbbcdccadbdbbabbcadddabcaabcdbabcddadccdcbacccddbddcacdbadaaadaacdbdabadcdcbdadcdbaabbdbdcaaabbdcbadadabccbbbaabbbbdcbcbdbabcbaaaadcbdcdddcdccbccaddcdbddadaddbbabdcaaddcbddaadaacadaccdabcdabacddddddbaabdcadbcdcabbbcaaaccaacdccacaddccaacbbdbbccabaadcbdbaabbbbcddbbacdbbdaaacbabbcaacbdccccddbdadccdbcadcadcbdbcbbdbbdbdacccaddbcacbaddbdddbbdbabccbdddbaaaabddddcbbbcbaacbbabdcbcaddbdadcdaddcaaaaddcaabdcaadabdbabdbccbcdcbddacbddaaccbccdbbadbaadaadabccdcbbddcabccbbcbddbcdacccbdbcbcbbcaabaabccddabcddcddcadacddcbadadbddccddcacbddadabcacbadbccabdbccdaddcbddcadbbcbddacaabdabbcaabdabbbbcaabbdadbabcdcaacaabdbcddbabbabdcbcabcdbabbdcbcaabaddcaaacdcbcaacbbbdddadbaadaddbbdbcbcccdcdcddaadadaaccbaaaabbcbdadaabbbbababcdadaadaadbdacadaadbaaabacabadcdbccacaaccaccbdcccbaaadbbabcdbdccbdacabdacadaaadaacccaaaacbcaaddacabbdcdbcaadacbbaabdcbdccbadadcdcbbbdbcdcddbbbccadabccaddaacacddaddbddccadabbacababbaadddacbbaabcddadcdcbddcbabccbdaddacbcaaadccaacbaacabcbdaabbaabdcbcadbdabaddacdbdadbbadbcdcdbbcbbbdcabbadddcbbaddacdcacccbccbdcdcabbbdbbcbadbdddbdcbaccbbacccbabadcdbdbbacadabbabbabcdcadbccbbbcbcdcddaadcccbddabccbcdacddcaabdddcdabcdbaaabdbbdbbbcddbabdddbaaaadacacbdcaddbcdbcddcbcaaacadbdacccdbcddbbdadbaaaaabbcccdacddbaacabbcaabddbcaadcbbcdcbdbaacbbbabdadcbbbadccadabdabadaddacbdbbbdcadbcbddadacddaadbcbcdbdabcddababdccaacdcdabaddddcccdcbbcbdbbcabcacbcdccccaabccdbcddccbacbaaccbdabddbcacddaaadcadbbddbdbddcdaacacbcbadaacddccbadbbdbcbababdacbadacbacaccdaadaddcbbbacabbbcdccabbdabaaaccccddbabcbbbbdbbcbbdaddbaccbbbbacabacdcbbabdaacacbaccabbcdaacdacbdcaaacddacbcaaadcddbaabccddcbdbbacbbcdacadacdcadbacbabaccccbcbddbcaacbdbbdadbccdbcdbdbcaabacbcabaccbdccacbadbdaadccdcddacccbdacdddbabaaabbbabccbaaccbbdddcdcddabdcddbcbccaabdbccaaaaaabcbadabacabcbdddbcdbdaabccbdbdcadabddbbbdcdcdaaaabcadbacaaadbbaacccbabccbbabbaabcdccddcddacaddadbaabaaddbdabcabbcadacadbaaddcbcbcbdacdcbccbbbcbabdabbacaddadbadbdacdaaabccabbabcdcdababdbdbcaddcbbacbdcdbdabdddaadccddcbacaccccdbbdacaacddaccaccbdbcdbddaaaaccccadcdbaadddabcacaaccdaaabbddbbbcccaacbcbaaccaabddcaaadcdadcbcddabdcddbbcdcbdbadbbbcdbaaacbcdcdbcdcacacddddbdcdcaddbdbaccaaaaadcacdccddacbbbadbccadbccbacaccdcdbbcddcdacddacadaddddbbdcccdcdacacaacdaaadcdddadacbdccaadaaaacdccabacdabcbaccbaaabbdddbcadcaddbadcbbbdadbbadcdcaacdcddaddbbaddbacccbbccabacbbdabccacdbbdadaddbabcbcddbabcdbddacacccccadddbdacbacdacaacaadbacbcbbdbdbdcdbabbddbbbcbcdbbaadbdddbdcbcddabaaabcacbdcdaaacdbddddbbdcdbbabacbbdabacbaaccdbbaabbcabddcbddddddadcbbcdabdccdbbdadacabcababbabcbabbdaacbcbbdacddcbcdaadcdbdcdacdbbcbbbbbadbadbadbacdcccdbbdcbdcccddcabacdcddbaaccaaadbadcdbababbacbaabadbddbbdddbcdabadbcadbdcccacddcddabcbdacabcddccbdbaabdbdccdbddcdcacadcadcdcdcababdbabbabaacbddadabbbbbccaacdbccbadcadcaaaccdabcaacdabbdccadaccccbadbadadbdccbcaaabacbbbbcaaacbdbdaaababbaaccdaaaccadadccccaccadcdacacadbaadcbbbaadbcbcaadcabcdddadcbcddcbacabbabccbcdabbabcbbdaadcdadccddbacbaababdbcbadcbbaccaabaacddbabbcdbdbdadbddaccaccbacaabbccccbabadccbcbdcbccccdbdcacbdcadabadbdbddcbbcacbddaabccbdcaddaacbcbdaccddccbdddddaaabbaddbacbcdcccacbddcbdcaddaadcccadabdbcaacbcdcaaadbcacacbdccdaddcbbcbcbddaadaabaadccdbcdbbcadadabbaabcddababdbdabbabdaabcbaddddccdccddcadddacbbadbcacdbacdababcbcddcbbdcbbadbcacdbdbcbbcdbdaadaaadddadcaadbbdcccaddddccabddcaaadacbaaccbcaabadcccdaddabbbcbcaabadadacbddcaaaacdbbdadddadcdcbdcccdacbdbcdcdbdabacbaabcdaadadacbabacabbacbdccababcabadacddbcbcccbabbcddbcbaadcbdadbbabcbababddbacddbbdbacddcadccbdbbdacbdcbbccccbbdbddcdbbadabaacdaaacadbddaabbbcdaacdccadcadbdacbbadcdbcbadacddaacddbdabadacabacdcadccaadadabccdbadabaabdacddabbacabcbdaadcbbddcabdaccddaddcdddbabbbacaabbbbdcaccdadcddbaaddbbacaabdcdccadadaaadadcbdbcabbacdbbdbabdcaadbddccccddbacdaaaaaaadabadcbddbdbaadaabcacaaadacbbbdabacccbcdbbdaccbdbabaabdabacbbabdccbcabbdcbccdabccbbdaabaaaabdcaabbbdccaabbbdcabcddacadcdabaddabadbdbddbddbcacbadabdbbacdcacaddbcdadacbbdbaccbaaadacdababacacacdabcdcbbadaccbdacbcbcdcdaddabdacaddddcddccdbdcddadbbabddbadbbddbcdcadbcabbcdacabaabcabcabddbdbcddcccbabbbbacbacbdaabbbcdadcdccbbdbbbdbccbbdbcadbbcdbabdbadadacdcbcbdcabbabcddbdcbbdadcaddccabccbdcbddadaabdcabacbabddcbccbabadbdadadbbadcdacbcacdbccabaadaadddaccddbdaadddadbdddbaababbbddbdcadadacdbbbabaaaacbaaadcacabaccacbadbdcabaaadcbdccabcadccacbbbbddbdbdabaacdbdccbbbbddcadabbbabdabccdcaadacddbbccaddadcabdabccacbddacbcabdccdbbbabaaabddacaaddaaddabdccbccadbdbccddaadadacacddbbacdadcaacdbbadbaccadbcadbaabbabcdcbbdcacbaddcaabcbbdabcacbbbdababddbbbcddacbabccdadddaabdabacdbaabccddabaaadadbcaddbcabdabdbbcdcadaaabdddbcdcbdccddacabccaaaaddcbacbabbbcdccbaaccbbcdbabcbcacaaabcaddacdcadadadaacbadbbdbdcaadabccdccadbadcbacbdbddccdabdbaadacccbcabadbcbdcccdcbccdbadabbcaacdcdacdbbcbabcbaacacaaadbcccbabbbacadccadcdccbdabcbaaabbaaacdccddcbbbbbadcbaaadacbcdccdabdbcadcbabadccacacadadbbbabdabacabbaccaccdbabaadbaacaacbbadadadaddcbccbcbbacbabadabcbdacdbcccdcbccdaabddcbbddacbaabbabbacacadbcadacdbacbbccabbdddcaccadbaadadcdabaaaadcacabcccacaadbacdaaacccdcabdccddacbdddbddcdbbabcccdcddcabcccadcccbcbabaddbcbdacdcaadcabbcddaadaabcbcbddddacddccccddabccabbdddcbcbabcadbdaabacdbaaddcbdbaadaaaadaccbdaddadbdccadcbcbbdcbadbccbadcbdcccbccbcdddaaacacdabddaacbaaabddbddcdcbcacabbdddbabdaabcbbdbdddbcbbababddcaacbccadcbbbccccabdddcbacacacbdccdbbbbcbacadaccaacbdbcbaadadaacbbbdabbdacdbbbacdbcbdaddcbcbddcaadcccdccccddbcdaaabaccadcacddcbbbcdbdbadaacdadaddbaadacadaaccadabacbcbbacdcdcacbdbbbcabbccdaabcccacabbccacaabcbadadcbddbcaddbcccbaabddaacbcbdaacacccabdbbbdbacbbabcacabdabaacdbbacbdddadccadbcadadbbabdcaaacbdabdadbccacbddcddbcabddaddcababbbbbdbddcaaaaacdabddadcacdbcbbcbdbdbbcbbbacbcccabcdacdbadcaacdaacacdbbdbbaabacdcdcadbdcacaaacccdcaabbaddabcddadddaddbcbbddcabcadadcbbddbcdccabbbadadbbaacdadbcccddbaaaacbaabdcabbdcbcdaabaaacadaabbbdaabbbcbdddcabbacbdddddccdadaabbbcbcbbddcacbcdadbcdadcbbabcacadadadadddabcaccbccabdacadaadbddbdaddaadbddddbabbaccbbaccabcaccadbbdaaaccbcbbaaacbbadaadbcdabaaadaadacadaabdbbcbaaabdadacacdbbddddddacaacbaccdabaccaacdcabcdbddbdbadddccdbdcaaadcbaccaaaadadacbcaddbcacccaabddabaabddacbabadcadabcbabaaacbbdaadbaaacadcabadbcadbcadacadaccadccaabcaaaddcccbadbabdaaccadacbbaaacdadbbbcadaadbabbbacbcdbccabacdcdadcdadcbdadcadbcdadbddabaabcbbddcdcbdacbadddabaddcdbadbdacacdaaddbdcabdccababacdccbadbaabbbdadccaacabcbdcaddadadbbdcbbacddaabdbdabdcbdcddddcbaabbcdddddbddabdcabdbccaabdaaaadbbdcbcbaadcacacadbdcdaccdadacabacddbdaddacabdbcacaadccbcdccdddcabccccacadadaabbddbbbaabcdddaaddcabccbdddacdcaadabdcddcdbddaabbabcbddccdddddaaabbdddcbbbdcdcbacdaaddcaabcbccbdaddbdaaaaacadbdadbdbabcdbbdcbaaabaacaacdacdaaaddbcbbaccdddcbdcabddcddadbccccaaacdcabdccddadbbadddcddacdbcabcacccdbaacbccbbcbbabaadcbbadaabdbcddbbdcdcddbabcabcdababbadbbcacadbcddcacdaaaacaccbcbdabbaccbccbadbbcccbbbaccadabcbbcbbabcbccdaacaddbbcbadbaadbdbaacbbcddaadbdbcdcabacbabdaacaabddacabcacdabcbacbdddccbbaabbddcdcbcdccabaababcdbdadddadbadbddccacdbcdacdaaabbbacaccbbacbcacddaacaabbbdadabbcdacddcbccdbcbdcadadbdbabbbbaccbaccaacaaacbbabdbdcbcbadcdccddbacbbbacccaadbcdadccbdbaadcbbacbacbcabbdcaababdbababbbcadcbbdddccdbddbccdacbcbadccdbadacdbbdbcabacdcccddcbdadcddcbdddccddcbbbccbddcacbdbdadabbdabdaccddbccdabcbdbbcbaddbcaabddccaaaacdabdacbabacdaccddddbcbdccdaadabbbdcadcabbbbadaadcdbadaaccddbaacbacacadacbdccccddcdbbbdccaacbcaaacacaaabdcccaaccdbaacccccdbcabdbbcadbccbadaadddddbdbbccdaabdbabcddcacdadcbcdddcdcddabadddcaadaddaabbbdababccccdcbcbddabbcddcbaaabcddbdcdcadbabcabddcdacbbcadaccddbabdaabbabcbbadabdcbbadaaabadbcaabacdbccbbbcdbbcbcbbbccabbaababccdddbbbbcabaccdabddaabadbcbbbdddbbbbaadcadcdbaccadbdcdacaddcaadaddccdbddaaabddccbadbcdbaccddcacbbcaaaabdcbbcdaaddcbdcbdbddaaadbacbcaadbcdadcdddddccaacbbaaaddabbcbdaacaccdbbaabbbcddcaabcacabbdcdadbbbbbdbaccaacacbaccbbbcaadaccadbdcdabcdbdaacdddabcbccacdaadcbaaacccacdbacdbdbcadaaadcaaadddbdbacbbdbababbccbbddcdbadadbdcadcbbddbdaadacbbacbdbadddcaccdccadabbcabbcabdcbaacaacbddaddabbadacdbdacbdddbabbcdaddabcddaacdccbdacbcdaacbcdadaccbcbddcabaaacacabacccdccdbcddbccdbbddadbacdaacccbddaabadddaacabdadabaccadbdbbaaaacaddabcccbccaccacdbaabacdbcbabccaadcadbbccbdcadcbdcacadbbdcdcddcbaccbbbdadbcddbddbdccdbbabcdbbcbcaaccdcbdbdcbdcadadcbddccaaadaadbcacdaddcbaaddaabbaabbcaddaabaacdddcccdddcdccdcdcdbdabbccbccbbbabcabccbbdddcbbbcdcaacdcccdacabadcbcbadcbbacabcdcbbdaaadaabaadcccbbcdbdaadbcaaddcccadbabadcbdcaabaabaddabadcbcabbacacabdcbbacccbcbcddccaccbaabcbbababdcdcbbcabdbddbbadccbdcbbbcbccddacdbddcbacacadbdbbbacaabadacbaaaaabacbdaacadcbbbbacddcbbaaacdaacdbdcbccbabcdddcdccaabcddbbcbbdbccdabbbdbbdbadbacccdcbcadacadbacacdddbdbbadbcbabacdadcbadabbaddcbaabaacbcccdbaabdcacabdcddbdadcddcccdbabbdcacaaabdabbbbbbddaabddcccbaacbbdacbbccccbccddacbcbbdaabbbbccbccddadcdbbccbcdbacdabbbccacdbaacccbcbabbdcbabdbadcadababadcbaddabacccbdcddaaaacadbadaccaaddadaddcaccdcbabaaabdadabcbaabbbbdbbcbdacbaccbdcbbddaccaabdcdccbcbacdcccadbbabbbcddbddbcbddcadbacbaaaacdbbcbaccbbdbbcdcccbccbbcabccaacbacddbdcbdbcacaaaabccbcacacabbacadbdadbaddcaadbaacbdccbdcadcacbaacdbdccbdaddcaacbacadcbccbdddaabcaacddcddcbbadabcdabdcdbbdcaaaaaadbacbcbadcdcabdddddabbdaacdcdacbdadaabadbbaccacabdccddbacadbaaddababaddccbdcdcbaabccdbddadbbdbcabaaddccbddcddbbdbbaaccbdccdacbadccdacbabdbbaddbacacbccacbbbcbacacdcddbadabcacdddcccdcaaaaacaddbdccacbcdbadaccbddcaddcdbdbcccbcdbcbcdadbddacdadaaaaabcddcacbaabcdccaccddabcdccddbddacaaabacddccacabbdcacddcbacbbcacbdabbdbdccddccaddcacdbbabcbccdadddaababaacddcaacdbdccbcabccdaabcbcbbababcbbccdaabbbddddbdcdccbcbbaaabbbacdaadacabcacdabaaadddddcdcacdadbababccbccddadcdaabccbdbdbccacacdbcbcbcbbacabccbbbadcdddbcaaabcbbdbabddbaadcdcccbbdccccccacbbbccabacaddcddbbddcbacdcbbabbcabdcadadacaaccdccdaccbdaacaabddaddcccbddadbbdbdabaadddaabdadcacbbadcdcdaaabcdbccadbddcbcacacdbddbbbbaacdbbbabcadcbcabbaddcadcdcdbdccbcdcdabcbabbcbdaddbddaccadcadabdbcdbccbcdaccababdbccaddadadacbadbdadddadbdbcaadddbbacbbdcbbdbbbabadadaacdcddabdcacbccacabaacdabccdbdadcabdbdbdbcdcaadcbcabcccdbbccbbcdaaaaacabbbadcccdcaabbcbdbbbbbdaddcbdcadcdcadbccdbabbbbaacabacacbcaaaddaabcabcabddddcddadabdbdcaddddccabbdabdbbcdaabbddcaadbdaaccbadaabadbbcabccbdaabcabdccacdcabdcdcbdbccacccdbcddadbcbccacbadabdbaabaaababcdacacacdccadbcccdcadcabdbbccbcacacbbabdabdcccddbbaadaabcdacdbdabaccbcdadabbaccbadcbbcdcbaddaabbcccabaccdacadcbddcdbdadbadadadcddcaabccbbcdbbcccdaadabdbbcacddcbddaccbdbaadadbbabdcabadbbbccbdacdccbdaacddbbcacdbdadcdbcaaddaabdacbcdcaddbdddcdabbccdcbaabaddaaaacaadcdacadaacbbcccccaddcadaaabdbcbdddddabcdbcccbaddadaabcaabccbaacacaabdbbbddbacadcddabbdadcbdbbdbcadaccbbadcbdbbdbcdbadabcacccaacaabdbccccadbdaaaaddaccdcbbdaabdabdbcbbcccabccbdddbbbacdcdcaaaddaaacabacababdcdccaccaadbbccccbbdbccccdacdaabddabddbabbdabdbadaccacaaccbdbbbcbbbdbadcccbbaccaddddacdbddaaaaacaacaaadacaadbddaddbccccaabadadcacaaabdacbbbddbcdcdbdcabbabcbdcaadcdbaccdbacbbabcddabdbcbbacdddcbacaadbcdbacadcaacbbcaababbadcadaddbbcbccdcdbccbabcdcbabbccabddccdbaabdcdadddcbcbadaadddcbabbcbaaccabdabbacacbadcabddcbdcdacdbdaaccccacabcbbdadcdacbbcbcdccdadaacbcdcbbcdbcacddacddbcaabadcccbcaaaaddbdbbadaddcabccdbdbbabbbdbbabcacaaaccadaddcbcabcdddaabbdcaaacadcabcacaacaadaddaccbcbadabbdaabbdddddddcddacbbddcdabbbbcddcbbcdbcdbadcaabbcdadaacaddcdbcbdcacbacccbbcabaabddddacaddcddcddacacaccddbaccadcacadadddccbcbabdbcaabcdbdadaccbcbcdabbcdbcbbccdbaaccabbadaadabacbdcabcdabaddadaabcbbdbdccdddaccdababbadddacdcccdbddbbdabbccccddcabaaacabacccdbabddddddcbbdabcdabdcabcbdcaacadabacbacabdadbabaadcacaddddbcdcbaacdbadaacbacaacccbcabddccdccbdaadbbbbabcbbdbaadbccccdccadaacadbbcdbbbabddabbbcdbadacdbdaddaccbbcbacbaaaacdbbaaaaaaabccacadaadaddacababbddcabdaaaabcaddadaadcbcdaabccbdaabcaadaabdcaacccdaacabaadcabdacbdbaccbddcaccbaacdbdacaddbadadaccbdbacccdccadabbabccbbcaddcdcadacaabccbcbdcadcdbaaadbcccadccbcabcacbbabdddddcadbdadcbbadabccbaadabcdbcbccbbdcaccbacbbbcbabbcddbadacdacdbccbcbccbbbbadddcbbbaadbbcdccadbcdaadcdbadccaadababcabdcdbdcccbbaabdadcabcacabdcaabbcaccbddacacabdacacbaabcdccddcbdaaabcbaaaccdbbaacabddabddacdaaaddcdddacbaabbccbddabddcccbbdbbddcaacadabcdacadcdccccbccbaccaaaaaacdbdbdbdbbbcadbbacbcdcbdcaaddcbaddddbbdbbdccdadbdababbdccbdcbbcadcdbacbdaabddabdadaddcacbdccccabaaccccdcdddcdddacacacddadacaacaaabadcbdbbdaacccacddbaacdcbadbbdacddcbdccabaacdacbdcccbcaacbdabddaaddbccaabaaaccdcbcdccabbcdaddbaababdaddcddddcbadbcccdaacdaaddadcaaccddcadbbccbcadcabcacdacdbbcbcbbcccbbacdbacadccbaacdbabccbccacbdbdacddcaddacccbdbbddbddaaacccababcdbdcbcdacccbbbddcddabbadddadccacadcbaaaabddddadbcddadbdbacadaabaaacadacbccbcdaddabcddbdbbcbbaabbdcbdaccdbbdbdaaabaabbdabbbddaccbdbaadcadcadcddaadaddcccabbbcddcbcdccbbaccbbadaadcbabcccdbdabcaacddabcddcadacbbcadbbbccdbccbbbaddaacaacdbcdcccdaabdabddcbbadbbabbdcdcaabcabbdaaababdbaccdcccccbdcdbacdcddbdbdaabbaadcaadddbdadadbccbaddadaaddcdbdbcbbabdacabdccadadacdbabdacbdcadbdccdccbbbdbcccdcabcacdcbbdbbbbcbdbcaabbbdaaaaadccdcacccdadddccbcdabcdcbdcccdabdbbbabccbacbcdbaccaabcacbdbcbcdbbdccaaccddccbcdbbaddbdbccddbcdaaabbaaaacadcdcdabcbcadcadccccbacbbdcdbcbbdccacaddbbdbaadbabaccabcddcaadbdaddacddbcddaacbbcdadbdbcbddaaccccbbadaacddbccbcbddcdaacccabacaadcbbabbddbccbadcddaadaacabaaacbddddbdadcbcdbcdcaacbadddabaccaaaccbccbacabcbacdbdcabbcaccdbcacdcaabbacabdcbccabbbbdcddbbcdbdddbcbacdcadbcddbaccbbacddddcdadbbccbcbacdaaaccbbaddbdaabaabdcabdbdaddccbddcbbdccadaccbbbcadbabcbbcdbddaddaaddabbddaccaabcccaddbdbadaaacbadaccbaacaaacbaddbacbbadabcbbbbabdadbcbacabddbaadacbccdbabdddccdccdaacadcdddbaccdddbcaabdcacacacababcbaabccdbacaccbbbcdaabbbbaccaaaacacaacdddabbccabdcadbbdacbabcadbcbacccadcbacbbbcdddbddbbdccddcddacddaaccbabcdddabbaaadbaadbccbadbbacbbdbcbdaacdaadccccaabdbbcbdaacdacaabbcabcaabccddcbaddbacadbbaabcabcacbbccdcbabbbbbacbbddddbcddcdbcaadcdbbadbdaccabacdcacadcaababccabdadbdbbbadccccbddaddaabdadccbdaddabcbcaddccdadabacdcdcbccabadddadcacacbbcaabdddcaabcdbccdbbbbcbbbbaaacacbdcbcaaacacdacccddcabdcbacccbbdabadbcacdaaadadbccaaaccabaadbddaabacaadadbdbcdbcdacccdbabcdccdaaabbacabcbbdbdacbacabbbdacdacdcdbcbcbbbddcbcbdabcaaabdbacacabdaddaaccdbbddddbdadddaaabdaddbcddaccdddddcabdaaaabdcadcacbccddbdcabddccababcabbccdbbcbababcaccabdadaadadbcbabcabbbddcadadadbacbbccbbdabcbbddadbcdadcdacaaaddbacdacbcdbcbbcccddabcdaaabbdbbacbcbcabacdddabacbdbbcddaaccccbddbbbddbdddbabcdbcdbaabccaabdbdbaacdbdbaaadadbabacccbdddadccbdcdaaddaddbcabcccbddbbdbbbbabaabbccabdbcabdaacbcadbaadbbdddccdacbacbcddbdaccbdbcbaddaadaaddacaaababdbdbdaadbbdcbacbabaccbaaabbbbaaacccbcdbabbbccdabbabbdccbcdbdacdacdcbdaabbbdddcbdbddacaddacccdadbbdccbaabcaadadddacaaccacdccabaaaadbaaddcababbdbcddabbadcaadbbccccabccadccbcaaadacdabdbbbdbbacbccddddadcccbabbabbcdbbcdadbcabacdcadcdbaccacacbdbdcccaadacabdadbaaacdabccdbdcdacbbcbadbdcdcdabaaabcbbcadbdacbcdbbdddaddcdcdbabccbabacadbbaaddbccbdaddaddcabaaddccbadacaccaaddbaadaabddbbbaacaddbacbcaaabbcbaddacdaccdcdccdbdadaccbccdacabbaddaaaaddaadcdcadbcddcdbabbdbacdaabccaaccaaaabccbcbacabbadabbbbdabbcaacdbadcaaadbbbacbbddcbdddcdaacdcaccccdcddcabddabbddddcdaacdcdaaacdbdddadacccdccabdaddbaddacacccbddcbdccccaaabdcaaaacddadbcbdcbbcaadcdbaabcbbcaccbbbadbdcddbcacdddcbbaddabaadaaabbbccaadbacdaccccbaadadabcddcdabdbdaccbadaccabbccadbbdcaaabcbaacaacdbdbbdbabdcabaadbaddadbbccbdccacaaadadbdbbbadbbacbdcbbbbbaaaccdbadaaadcaabddcbbcbdbcdacaabbbdddbacdbadacadadbbdacadaccdccbcbacbbbdcaacaadabcaddbdaaabdcdbdaddcbacdaabaadbcdbbccaccadddcacdbcabdbcbccbdbdaaaacbaccadcaababddbdacddcdabdcdadacbcbbabccccadddcbabbabacddddddbcbbbbdabccddbddbdbbbaddaaaaabacbddbbcbbdbcacbbcbccadaccaaddcccaadbabadcbdacdabcccccccbddcddddcbabcadabaddbbadbbbbdbcccaaccddddccdbcddcbccaacccddbbadcddacdaccbbbdbcaadacdaaccdacbbcbddaadadbabcabbcadcaaabadbaccddbacdabbccbaccddcaabbcbabcbdcbddabcacbcadddadbabdbddbcadbcdacabaadbdadcaaacacdbdaddbaabbabbcdbcabadaddbcacbaababbcdcaadbacdccddcccdbadaaddabababcdaabcdcbadacbaacccaaccdbcdcbccadcbccbdbbababddacdbcbabbdbacccdddcabbdbaaddaaacdbbcababdcaacdacbaccdcabcbdbdccbbacaccaadcacccbbbbbcadacdcbaaaabdcbacacadadcbcddcbbabdcdddaaddadddcdaadaccccdbadbbbcddcadbabcdbdbcddcaccdbbcdacbcbbbbbbcabdcdcdabbbddaccddbccbcacacadabadcabbaabdbdcbccabadcabbbaadcbabcddaccbdbdaccadcabbabbdbddccdddddacaadccddbddcbcdcdcadabcccadacdccbadabddbcccadcabadbadadbbdbdacddbddadcdcbddaddbccaccdcdcbcddbdabcbdccbbbaaccdbbcbbadbaddcbabbbbbdcdaccbacbbdacbbacdcbdbdbacccacbddbdaccabcdabaabbcdddcaddaacaaccdabdbccacacdbbbaaacadcababdcbdbcadcbdaabcabdcdabacaccacbcccdcdcbdaacbcbaabdddbccdadccdbcaacbdaaccbcaaacaccdbdababdabbddbbcaadbdbdbbbabddcaccbdccdbcaadcabaaccabdcbaacccddcdbbbabdabbdbdcdcdaddaadcbbcabbdbdbdabcbaaaacacdbaddaaadbacbdcbbcaabbcbddabbaabacbaddadabdbdbbacccdcccabdcdcacbbaabdabbddddddcacbdadbcbbbadcbabcbabdbdddccccabbbbaadbbadcdadccdbcabcbaadaaabacaabbbacdcdddabaaaaadabccacbbdadbbbabccbddcaaacdcdbdabbadaaccdbcadbbdcccabcdcaabcbdcacabaaabdbbbadaaccccabadacaadaadacdbbbbdabaacbdbbbbbcbcdabbdbadbcdbdcbaaaadcbbcbaddaacbbaabaadacaaaacddcbacbcadbcdccbdccdcbcaabcbccdcbcbbdcccdacdcbcccdacbdcaaaccbaaddcbacbbcdbcbacdccaccdacbbcdcbbcbcdcababdcdaaccacadaabadacbacdaacbdacccbbbdddacabcbbcabaaddbbacbbbcdaabcbdbbcadccadcdccccadcdbcccddaabacaabbdcbdbcbacdbddabbdabaacddccacbdccaccbcbcbabcdabbabdccdacccddacacadbcadcbabcaabadcdccdaddbdbadddbbacccccaccbbcaddaacaabcabddbcbcdbbbdccccdadcbacabbaaaadccadbdcddcabcaabdbdccbdaccbabaacbbacdaacacdaaaaaaddcbabbdcaccdcaaacdbaaabcacdcacdbbabcbdacacbcabcbacbbcbdacdadaccbddacababdccdacbdcddbacabacddddadcbddbbdcdaddadddddaccbcdbacadadddaddaaababcbdddcbcacccbadcabccdddddcccbabddbbadcddbdbddbaccbaaadcaacbcacdccddcbacdbcbddccabccdcabbbadacbaadbaadddbbcabdcbcaabdabdcddbcabddcbaccccadbbabbabbdadcddabadbdcbadadacddbccadabcccdcdbddbdaccabadcbbaddbcddbbbcbabbbaabadaaabababadbaadbcdabccbadbbccabccaabbbdbaacacccbccadcaccabbabdaccdddabcdabdbbdccadadbdcdacbdccbadccaddaacacbbbabbadccbbbbacaabaccdcbaaabcbdaadbaabcdadbbdbddccaaabcacdaadcdcbbbddbacaabbdbccddadabaaccdbccbccaaacbdbdcdadbdbbacadadbadbcadbababcbcaadbbdbcabcddabbbdcacacacbdbccccdcbdccdbcbbcbbddabacadbdaabcdabdcbccdcdadaaddacddcbdbbabaddaadcddaadacdddccdddbddccddaddcabbdccabaadbacaabdacbbdaadccdaacbbdbcacdaadaaddbcacadacbdbddbaacacbbbadbcddbdbcbddbbbadccaaacdbbdbcadcababdcccdaddcbdbdcabddcdccaddcbbdddcbabadccadcdbddcccbaadbdbbcbdbbbadbdccddacadaddcaacabccddaabaacdbbacdcdaccbcddddbcaabcaaadbcdcdbcdcbcacbcadaddbcbcdaacaccdcbcbdbacabddbddcaabbacccccbabbaddccadcadddabddbddcdacacdcbbdabdcdcadabbdcdcbdcacbddcbdddbcdaaacbbbacaaacacaabadaccbdcadccacccaaaccdbbcdcdbaadbbdddaccdccdabcaaddbdbaaacbddabcabccabbdaddacaadbbbaccdaaccaaaadbbcbddaaadbbadbaaacadbdabcbabcdbccbdabcbdbbdadccbabcbdbaaaaadccddcdcccacdcdbcadcadcbcdaaddbccbbcadbbaccbaabbcbbabaccccbcdbcbdcdbadbaadabbbcbcabcadbbdbddabcabaaacdadbadabbcaaabbacdddcbabdbdcacbabaadadbbbcbaadbdaabadcdabddcdcbdcddcbbcadbbdddaccdbbabbcbaadcbbdbccbdaaddacacbddbcdacdbcabccabbcabdaadcdcdbdbacdabccbacbbccacabcaadbcbbaadaadaabdbbbddbcacadabddabcdacdacbabbababbaaccccacccacadbcaabdbabdccaddccbdcacbacddbcbabbcabdacdbcacbadbcddbddcdcbddbaabdbabcbdbcbdccdaabdbccaadaacabcaccbddccadcaacddccccbcadabbdaccdbaccccbdbbacaaccccaadacbabbcadaadcbbcaabbadbdaadaccacbaabbcbcbccbdccacabcadabbbabcacabababccaadcbcdacdacadcadadccabcddcacbcdcabcbdbcdabdaabdacbaddcddbbddbcbabbdddbbddacdcabdbbbcbbdcabcdcbdbabccabaacdbdddacdadccccbddcdccaccabbacdbacbcbcdddcadbabcaaaccacddcacadcbbaaaacbcdacdacaadadadaadddcbcdcbbabacdadbcdaaaaddcdccaadacdaccddcadbbddcccabdbbcdbdbddaacbcadabaadccacdbbbaadbdbbaddddcabddbddbddbddadcaacabaabdacbdcadbcaaccbccdadcbddcdbbabdbbbdbadcbbabbaacccdcdddbcaadbbcbacdadbabdddadcdaadcbbbabdaacdabdadcadaaddacdbcdbcacbbbcdcacbadacaabbaabcbbbbabdbdcadcaabbbbdcadcbddbdcbbddcbaabbcdcacdaaccaadbaccccbcbacdccbdbcdacaaddbdcdcacccbdbdbcadbccddcacbbaaacdccbcddcbdccbcadbacbcbcbdcabcabbcbababcaccacbaacaddccccadcacadbbdbdcddabdaabdcdbabbbcdcdacabbdbabccbdbacdadbbcccacbcabbbdddcabcdaabaaabcccdcdcbbcdddcbbcabacccbdcdadabcddbcbbabdbdcddbbbcdacabddcabdbcdbdcabcbcaadcbdacbbadcbcbcddbaccbabdddccadaabcadcacddabddbababcccdddbcbbadbbcaccaaccbacbdbaaacaddcadcbcabadabcdcbbcdbabbadccbbaadbccabbdbcbbabbccccabaadbbdabcaddbcdbbabcbcadbcbbccccaacbbdbabbbabccaabaadbcddaddcccaddabacaccbdcbcbabbadcdaadcdbcdddadadaabcbabdbccabbdaaccbccaccadbcdbaadadbacbdcdbaaaccbbabcadbdacdbdccabdcdbdcabdbadcadccaabaabcccbccdccdccabacbdbdadbadbdcccaaccaabadddbabddabbaaddbccccbaddbddbddcbbcdcaadbdbdabdcbcddddcccbcdcbbdadcddcbddcbdbddaacaaabcaccacbdacbdaadabdaacdcbcccdbdacbabadbdadccadbcaadacbacbcbdadbbadbbbacabaaabbddacacdabddbcbbbdbbcbbaadadbacaacbcbadaaadabaddacdaadcbdadddbccaccdbdbdcbbaabdcccddabccaddaabdbbdacbabbbcccaddadbcadcabacddcddbdccdcbdcdcbcacdabbdbdccccaabbcabaaadbcaaddaabdbadddccaadbbaaaabaccbbcabaccaadccabbcadadbadccbbccdaabaaaacdabdadbababbadcbbaabdbbbaaddadddabcacccdcddcacabdcdaddacabbaccbaacddadbdacaadaacbcbacabdcdabcbcbaccbbcbcdbbabbdbcbdbdbadbdcbccadbdacbbbadaababbdacadcabccadaddacdbcbbbdabccbdbbbaacdababbdaabcbcadaaddaacbdbcadaadbcaabaadcbddcccadbccaabbdbdcbddacccabacaaaaaaababcbdacdddccccbcbbbdddbbdacdbdbacbbabcdcbbdaddacdadcadabbbbdcbbbbcdbaacabbbdbbdbabaabdbbaabcbcdcabaacbbcddabcbadbabdabacbcacbcdcbaccabdbacbdaadbbccddaddccdddaacbbdddadddbccbcccdaadddccabdbcbdacabadcccbccdbdccaaacadcdaadbcddccaabcbccabadaddcbaccabddbacbaabacddcacbbcadcddaaadacacdacbbbccadcabcbbbddbaacbacacdbadacddabdcdcbaaccdabbacbdbdbaddabcbcdcabbbddbddbaabcdcabacdddcacbaccbabddbdadabaaacdbccdbbccddddabbbbaaadacdcbddddbcbadcccdacbcbdbbcdaaaabcdbbacabdcdcccaccdaddbdbdacdbadbadabcdcaadcddcbdcdbdccdcddacddcdcaccbaacddcbbccdbcccdaddacdaccbdabdbdcdbccbbcbbddacacbddacccdcdbbdaadcabcabcdaadbadaccdbccdbdbcacdaadccdbddbddaaddaacadbdabddbbdacacacdcadbacbaabadcbcadbcbbabbbbcccbdacccdbcacbbadbcbcacdbaddddcdbccbabbaabcbddabdcbacddacdaccacbadcdcbcccaaaaabccdacdbaaacdddccdcccbbdabbcabddbcabdaaaadcbdbdadcacaacbcbcdabcccbaddddbdccbbabbabccdaddbbbbabbaaacabbbdaacaabcbcbcbddacdaadaccaadcbbbbcbaaabcabdaaaccdbabaadabcabdcbcacbcccabbcadbaadcadbcdbcccbbccdacbbaadacbcbdccdcadbacbcdabcaacadadbacadacccddbbabbbcdbddcbbcdadacdaadcaaccdbccacdadcdcdbccbcabccbbdcaaddccdbdaddcbdbcacababbddaaccdbcadcddccdcabacadbcccddddcaccaaadcadabbaddbdcdacbadbbdacadcabdcadcdbcbbcccbcbddbabdbdabddbccdccaacaacddbddcdccadbdddcabbbdcabbaacaaaadaaabbcaabccaddbbadddadbcaaaaccdabcddcccdadcddbabbbdcdccbbaacdacababcacaabcbccddcdabbdcdcdbbcaadcabccdcbdabdacaababcadddacaabbcabdcddbadcbdacaddbdddbababaadabdbaddacbccabdcdbdcadccadabbacadbbccabdcddcbbccdccddadbabdcdbddaddcbcbcdabbdacabdbddddbddccdbbcdbbaacacbccacdadaadacddcacdaaccbcaabdcababadcbaddbbaccadacdcbdadbddbddcdcbacdbdacdcdabdabddaaddcbbacdccccccdaabaddcabcaadbdaadacadbcacbbcacbabadcdbddbbaadadccdbbbccadababdaaaddddabddaccbdcaccbcbaadadbaacccdcccbcdcdabbadccbdacabcaddaacbaddabddbbccbdcabdabcdddaadaddbdddacbccccbbccbadccddbcacdaddaccddadccabddcadccdccdcdcbbbbccbbdacdacadadbbddbadaccadccbabcaccbbbcdcbbadabbabaabacbbddcddcaadbdabaccdcadcaddddbbacdcdacdaccbcbcacbcddacabbcbbbaadccabcdcdbbbddddcabbcaccdccdbcdddbbcbcddbbacdcbdcbbcddaccadababccacdacacdddcdaacdaadaacdccabacdadacadbcdcdbaddbacbdbaabbcdbbccbabbdcddaccbdbbbaaacdcbdadbaaadcacdadccbddaccabdbbaadbbdacdaabcdaadbdbcdabaddacaacacdbbacadddbbbdddbacbcbbdcbcdcccbcbccacaacbdcaacabbcadbaddaddbabbbbdcadddcbcdacbdcdabbcccbdccadddbdccbccdbbadccccdabccddcabbddadddccaccbaccdaacdbdabdbabcdbacdabdaccabdcbdcccacddbbabcdaabdaabdbbbbbcdcdbcadcbcddbddadbdccaadcbbcabbcaaadaadcaaccbcbbbdbbbbcdbdcabbbccdadcdaddbbcaaccbcdddadabbdbccdcdabbadbdbabccacdbbaadbdccbcbbaacccdcacdabbbdcdcccccdbabdbadddcbbabcaacaacaadbacaaabbcbbaaadddbcadccacdccabbdcaacbdcbdbdbcabaacabaadcbadbccdacccbbaacbbcdcdabccdaaaccbaaacddcbcccbcdccdbacacacbccbbacaacdaccdbcbaabdddcacdabdbccbbabaacdbbdadbdbddddaacabacddadbdababcbdbbdcaaddbaddacdaddddaacadaddcdadadddabaccabbdbdcbacbcbbccacbbcccbcbacdcdaaccacbdbbbbabcbddaacdcacdbccadccbbdacdbabbaaadcdbdddbcdaacddbbacdddbaaacdaaccbbaadacaadbccccabbdcdcbbbdccacddacadcbaddcbdaabcdddcdaabcdddcccbacaabcdcadbdabdaabbabcbaacbbbbaacaaabdaabbaabcdabdaaddcabaabbadbdbbcccdccaabcaaddacccdadcaabbadacddbbddbbdcbadcdbccdaccddbacdbddcddbdccccdcdabbdbdbbcabadaccddcdcbacdcaddadbccaaadaddaddabddaddbdccdaddbddadadadcdababaadaacbdbadabbcbadcddbadabdadcdacddabbbdbcbbdacacacabbabbdbdbabcaacbaabbddbcdbbbaabdddacabbcaddbacacbaddbaacdaaaacddcccddacacdbabccadbabddccbdccbdacbdbdcdadcbabdccbabcbccbcccbadbbbdbccddcacddddccadaabdbdbddcdbcddbcaabcbdacabbbcbcbdbcdcaadddcccccbdccbaadbccdabcabbdabbaccbcabcdabadcdaacabaabcacdcaaabdcdabbaccdcbdbdabddccadabbcccacdbdbaadcddcadbcaadaaadaccbbcdcddbbcdbdccddbacddadcccbcdacccdaddcdacdddadaadccbbdbccacadcccdbcbdadacabddaddbdddadbabdbcbdaaababdbddbbcbbcbabdcadbddddabcdaacacdababdbcccadadbbcdbdaadcbcbcddbdcbddbcbcdbcdaabccbabaabdacccdbabadacbcdaaababcaddaccaaadaabbccacbdcccbcdaddcbbbdbabcccbccadabccaaaabcdcbcbbaacccbcaababbcbaddaadddddabaaaabdcbccaccddabcaacdbbcccabbcdbcdbbcbcbbabdabbbbacacacadcddbddcacdbddcccadaadababaabbbaadacddcadbddbdbcdbbbbcacbccbdcaacaccbdbbbacdacdabaabdadbaddadcddbdadaacccaacbdbcddcbacababbaabdcccaddacadbadcbbadcbcbaaaadbbaddcccccbcdbcaacacbbdbdddcdadbddbcacddccabcbadbbccaccabbdbcbccdcdadbaabdccdccbbaaacbbddcccbaaaccbccddaddaabddddadddccacbbbadbbcbbbcbadccaabcdaaacaccaaccdddaccbbcababcccdbdcddddcbbcddbbcbbddbdcadccadccaadcdddbcbdaabdadbaaadaaacdbbbabcdadcdccaddcdaacdbacddabaaacbdbbabacbbaabadaadbbbaabddcbcadcbdaddccbdcccadbdbdacdddccddbcccdcacbddcbaaddbbaadbcbbaacbdbbabdacdbdaccbcdaadaddddbaabbbddaabdaadbbacadababccacdbacbabcdbbbcbcdbccbabcdacbcdcdbacbddaaddcabcaabdbccdadbabbbadaacacccbbdaddaadbdcdccdbadbddbdabdcadcbdbadcddccacadccbbdadadcdadcacbaadbcbcabbbcddcbdcbddccaacddabcdaadbbdaccccdccbbacdaaadbbdacddbaabdcdbbbbddacbbbcacdcabbdbabcccbcaabddaaadccdbbcccbbddddaccbbadaabdcadccabaacbcacbcadcbbddbcddaabbbdbcdbcdccbdcdccdacddacadcbbbdbccaccdadccdbbadadabacdcacbbccbbacdababacbcddadadcbaddddbacabdabadbbcabdcaacdbcbdcdbcbcadcdbabbabbcdcccdaddbdbbaddbaadaaacbaaccbdbabcdccbbccddcadbaabbbabddadbaabbdcbccbcccdbcbaccdaabcdcdabacbdddaabcbadbabccaadadbcdbabddbdcbcdabddcbabbaadccddbaddaacccdbdbabbbbdcaccabdcdbccbbaacbcdabbaadaabaacccbbdbcadbdbaaaacdbaabccaccbdbaccbdccaabdcdbabaccacacdadbacddcbcdcbcbbabaaaccabbcbcccdbdadbaadbcdbdbaaadbddcdabbabadbdadddbccacababdadbdbccbbbdbdcdacabbacdddbbccdcaabdadddccdbdbddbcaacccabcbcaabdcdbdaaaacbccacbbbbcbccdcbacadacdbbaddabcddabdbcbaacbbdaacddbacacbcadcaccdacbcbdbddbdaddacbdbddbbbcadbdcbdabbacbcadacdbbcaadddcdccacccbbcccdadcccbacabbadacaddcabdbabcaacadcadcabcadabadddbdbcddadddcdaadbbddbbdbcccaacccbcbdcdbcdcdacbaadacdaccacbcdbdacbbabacbcabbcdcbbcadbdccbdabddabcdbbcbabcbaabdbcbaadacbabacadbdcabccbbcbdbbbbdabbbcdbcbbaaaadcbbbbbbbabadbbabdbabccdccaddccbcbbbdbaabcadddbdacadddccdadbbdcaaacbaacaacbcdcabbadbbbacbabbcabbbcbddabcbcbddcbccadaaddbbabaaddcacdacabccbddccbabbcadbaaadbddabacaabcadbaacccbbcadddaaddabbadbddcaacdbccaadccbdbdbbbadadbaccdabbcadbdcdabdcbcdbccdaddbacbaadaabaaacadccacdcdbbbcadadaacbcccabdadbddbaabaaabacbacdaddddbbbbccddabbacbdcbbbabbcdadbbcbbbcdcacddabddaddacaddccdcaaccddcccdbbaabccbbbabddadbcbcabdabccabaccacbbadadccccacbdabdacbbddaadbdbabbdcbbcbdadcdacabbcabcdbaddacbadabbbbbabadbcccbcabcabcbddddbcdbbbbadbbcaabdcccabcdadcdcbcdacbaadbcadaabcccddacbbadbbdcaaccbbaadbcabaddcaccabdbbacacdabddcddbddbdbcaddabcbdaccbadbbdbbcdadbcaadbdbcadcaabbbcdcbaabdcbabbacbaaddaabcdcdbbcdcaddddaabaddcdaccaaadccdbdaaccbacbabdbccbcabdacdccacbacdbacdaccddbabdbbdddbbddabaacbbcbadacacdcddadabcdacbbcccaaadddcdcaaababdbadddabaddaaaacddaabbbacbaddadddcbdabaccadcdbbcbcdbbdbbaddbdbddccbcadddadcacddacdddccccdaccdbabbdcbcbbcabbadadbbababbcaaddbdababcbbdcdabbcbdccccbadacacbaadddbcabcdddbcdccbcddbcacdddcacdcbddddbacaccbaaacbcddcdbdcbbcdcccdbcdcaccabbdbdcacaabbdcaddabcadbaddaddddaabbbcdbcbdadcbdbcccabdbacbabccaacabacbdcaaadaadbadcdacaadccccaaaaccccaabdcadabbababbbbcccacbabacbbcdcadddaaadbadbabddcadaddbdddadabaccddadddbdbabddcdcdbacbdbaabbabdcbabbdaabdacbdbcccdcbcbdcdbcdcdbacdcaabcdcdcbaacdadabbddddcdcbabddddaaadcbadccccdddbbddcbdcdbdabbaacdbbcaacbdaababababdbcaadcabddbcadddcdcaccbddabbbabadcbccaadaacdcdbdacbdbcccccacabdaaabdbacddbbabbdcbbddbadaaadbbadadcdaadacbaccabcbddbcddbdbcbabdddcbccaabbcabdacbaaaadadcbaadcccadbaaccbdccaaddcbbaabddbdbdcbbcccdccccadddbaabdcacccdbccdabcbaadbbccbccabacbaacacaabbcdbaaabaacaccacbbbcdbacdcbcaacbbdbdcdacdacbadbdcbcdbaabaccadacacbbccccdadabcddbcbddbbccccbbabaacdccaccdbbcdcaaccabbbddccadddaadddacccbcdcbdcbaddacbbcdddbbbbbbacbcbadcdbbbbcccadcacdccddaddaddcaaacccabddadcccbaddacccbacacadcdcbbbaddaacdbbadcbbdaddbdbacabccabccdabddddaacadadddcaadcababbbbadbdaadcaccacabadcabadcaacccadddccbdddadbadabcaaadcdadaccdbbccabdcbdcacbbbcaadccdccabddbcdccadccdcccbacdbbaddabbdaccccbacacaccabbdabdbbbbdddbcddcabaccaaddababcbcdaabdddabacbdbdbbaddddcbdabbccbdcdbbdcbbabbdcabbccaccbbabccccdbadccaddbacaabddacdcdbadbdbdadccdacbabacdadbccbdcccccbdabbacdaabdcddcacaadadcbacdabbddddcbdbdccddaacdadbaacdcbccccadbaabbbaabaaccbcdddcadbdcabbdcadcdcbdadbcdabccadcaacddbdabccabdacdddbdccacbbabacbccccdbdcabbbaacabacbddbbcabababdadbddadacaadbbdacdddccdcdccdadadaccbcadcccdccadcccdabdabbbacbbacbadacdbbcbdabdbbbabcddbacacccbaccaddbdbdbccbabacbcbacababcadacaddbabdbdbabaccdbbbdcabbabddbddccdacbcdaddbdbdbbbadccaacbaadbcaddcadaccbcdbcbbdaddcbdddcabccbacbddabbcdbbbbcbbacddabbacdcbbdbacadacdbcdbabccaccbcadddddbbbdbcdccdadbabddbbacbdabdbbcbbddddaadaabdcadcbaddccaaaccbbbbdcacdbdccabccdddacaddbadbaddddbbbdcdcbaaacbcddabadabcabdbddddcbbcacbdaaadcaccbdabcbadbdbacbbbdaddbaadacaabcacaaadbbbccdcabbdcbcbcbcbbbbcbccccacaacbaccadddaccaaaaaaacbabccbdcbdabacbcbdcadccabddcdaddbccbbcaababaccaabbcdaddacabadbdaaaaddcabbdbaddacbbbccacbcdddcabcacabacabddabbaadcccbbbdbdadcacacabaaacbbacdcccdbbdddadcbbdaaccadbbcacacbbddaddaadbccbccabbbaaacbaaabbcbcdbccabbacadbdacbbddcccabcbabcdabbaaadaaabddbbbbbabacdaaaabccbcdacbdbacdabababbbbcdcccacaaadaaacbdbdcacbaccdcacdcbcbbbcdaaadcdbbcbadbbdccaaaccacacdbaadcdaaabcdbacbcbdaddbbbcdbddcdccaadabaabacdaadddbcabcbbbbbaabcbbddbbacddbabcabcadcbccccdabaaddccabddaccccbbdcccadddcbdaabbcdacdbddcbadcccdadabccbbacaadcccaacadadacbccdbaabbadbaadddbdbadddccbadacadccbaaadbbdbccabccbcdcdbccdcdbccbcdbdcdbdcdcaabbadccdbacbbdaadaadbaccbbcbaddadabdddcdcbaaccbbbbdbbbddabdadcccdccbabbacadbbddbbaacccacadadbcabbcbcdccdbbaacadbacdaabaacacccdaadbdabcbbddccdbbcacaaabcabcdaddbcbddddcdcbdacaacdbaadddbbddbbacadbbabdbdcaacbbbbbcccbacabcacbadccaabddaddcccddbcbbabcaaacdcacbbabcdbcbabcdbcbadaacabbaadcdaccbdaabacbcbdbdbcbacdcdbaddcaaaaaaacbdddbbbabacdcaacdcbcabdabacbcddcbdcaadaaadcdcddcabcbbcbcadbaddcbdabdadbdddbbbadcbccddacacccdddababbdcaccbbdacaaddbdcbcabbcacbdbbbbcabccdcaacaacabbbbcacabcdacbbccdccabcaabdababdbcdbcbbbdaaadbbbbcdcdccacdcadbbaddacaaccdbbbbcbcbacacdadacccbacdccbbdacbbcbccacdabcbccdcdbcbbaacbdabcccdbbcaccadabdcbcbbddcbdbcdbddddadcacddcacaaacdcbacadbbdcbabbbcacaabbcdbabcdbacabdcdccabbadacbcaabdbbabaacdbccccddacacaddbdacbdacdddaddbbadadcbdccdbacacaccaadcdcdbacacccdaddacdcbcddbbabdadcbdbababdacbbdcdcdbdcabaacdbbcdcbcbadbbaccdabbcddabdcccdccbdcacaaccbdacbaabcbbabacdbadbaabdbbbdddccaccbbbddabcccbddcccdadbcacadbcdabdbacdadadbadbdcaccdcaabddbcddddadacdcccbdadccabcbbcdbadcaabddccbdadcbbddbdccacabbcacbabcaadbccacbdccccdaadbdbbcdcadcccdaccaabadcdbbbacdaaadabbdababbcdcdccdcbccbcdadbdcbadaddbbbacdacbabbccdcabcbbaabadbaabaddbcbabcbcababdbdddbdacdccccbbdcadbcdabdcddbabcbccccbcabacdbacdbaccbdcdcaccccddcbacabbadabdbababcaabbdbbabccbdbdaabaddcaaacbacbbcddadabbdabaccdbaadaacbbbccaabacbbabbdcdbcabbddcbaaaaabcabaccbbabcddcbddbbdbbbabdbcbbdacabacbadbbbcbcabdcabddabccbacddaabaabadbbbccdcadbbbaadadbaddaaccacbbddbdbadccbaaccbccdcacccacccacbdcdcbdbcbbaadbaaaabdacdcbbdcddbdaadbbcdcabbdabddcaacbabbadacaabccacaacccbbbabbddaabacacdacbcbcbaabdcdccdcccddcdddcacbcbaaddbacbbdbadcaabbabcccdcaaabcccbbbdddccddcccddbccabbaccbadaaccbadadbcbbbddbbdbcccbbbdaddbacaaabaddcbadbbdbcbbabbcabadbbdaabbdabaadcddacdacbacadcbcaabadadcddabcabccaddccabdadbccbabbcaddbdddccacbcbddabdacacdcabccacddaaacabcbbabdabcbdcbcdaaacabbdcbcccdddbdaccdbcbdaddccbdcccacadbdadbbbdacaacddbcaaaacabaabccaadabbadbdbcbccdacdacdbcaccddadadbaabadbaadabccadcbadabddadcddbcddcbdbbaacbccbbdaddaaccabbadcadaccdcabdacbccbbbdabdbaddbbabdcacadbadccabadcaacbbaadccacbcadbdabacaabdaccbdcdddcbcbcbcbbdcbdbbccbccccbdbaabadaaaaabbbabcadaabbcacaccddcbdbcbcbaabbdcbbcbccdcbdcadcdcaadccbcbbdcbdadcdddcbdbcabcbbbcbcbabdbbdcaddadadddbbdbbdaddccaaadddddcbddabddbbcaaddcbabaccaddbcbbabaddadaabbbaccbccacbdcbabbbaccbbbabcdbcccdaddcaababbaabcccdbadbabcabbccbccdddccdbadadacadadbbddacabdcdcbcccadadcbaadcacaadabcbbdccaccadbbaabcbadbbbaaacabdcbacdaadbdacacbdcbbcccbcbddcccabaddaacbdddbbcabbacdaabababbacaddaabbcccdacbdadbccdaabcdbbbcccdacccccbcddaadcadaccdbdabcddadbdbbbdbcbbbbaabdbdbabdcddcdcbadbcbdcddaccbadbdcdcbbcbaabadacabadabccdcaabdbbadccbdddcadbddbaabcacbcdbdcdddacddbdbbbcbddbdbbabcacaabababdcdcdcbbbaaaaacdcbbbdcaaadcddbcbbbbcbddaccbbdaaabcacaabdbcdbbddadaadcddadcbaaadadbcdcdbdcabcdbadacdcbccacadbddacadacccbcbcbdbadadaabbddccbcaacccababbadbdbcdcaacaacabdcbbbcaccdabbbccaacbcaadaaaccdcbcbbbcaccacdcddaccdcdaacbbbcacddbabdaadadcabdcadcbcadcdacccbaaaabaddccaccbbcacdcccdaaadacccbccdbbcdabdcaaddbdadcdbcacaccaabcaccccbaadddcbaadbadcbaabcccbabbaadbcbdcbccaccaabcdaabdcdabbbbaacabbdabcbdbabbdbbbbcbbcabaadbccaadcadcdbcbcbcccddcdcbaddbcabbbccddaaaadadaadcbdbdaadcdaacaadddddcacacaabdbbcccdcccdacccabdbcbadddcbaddaadbdabaaaccbcadcbdccbdddcbbabccdaaddddbdbbdcdaacbbadadcabcbbdadddacdbcdbbacaacadabdddcababdacbcbcbbbababbdcbadbaadadadbccabcdcabcadcabdaabaddbbdcbbcbbdccaadaabadbdbccbdccdadadcdcaddabcdbcdcbddacadccabcddbaadaccbdabbdbaacbdcbcadaadbdbaabadaaaabdabdbcbbabbccdaacdbdcdddcdabdbcdddabaabdaabdbbcabcbacbcacadbcdbcacddbdbccdbccbaabbbacaccddadbdadbdbdacaddbcacdddbdaddaccaadcaccabcdbccddddacdaacbcbadadbbbabcbcbadabdcccdcacdaadbcbdccdcabbccdcddbbadcaabdcbccadcbbcddbcdbbdabdabcbcaaacadbaabcbdacbbbcccbdbdcaabaabcbccabcaddaddbaaddbcccaaacbdddadddabbcdaadcacddbdacdbbbbdaaaabbdccbbbbabccdbbadbdbcacdccdbcadadababdabcbdacadacabcbbdabddbdbacbbdddaaddcadbccdbcddadaadbcacdbbaddabcbcbdbddadcdaabbbaddccccadddbcacaadadaadaaacdccbccddabbccabacaccdbdacdcaaacbabaddaabdcbbddcbcbddcccabdacabdddcadbbbcbcdbccdcdabbadcaddbbbdaaddcdaccbcaaabbabbaccbbbbdbadccdababccdaaddcaacbdabcacdbaabbbcccbbacdaddccccbcbddddabdadcacccdddcbbadcbbbaccabcbdaadbbadbdcbbccdbcccdabcdcdccbcaaaccbcaadabacddcbccbcddcacacacbaddadaadccbaadbabdcbacabccbdaabcbabdaaaccbcccdddaaabcdacddcdcbbcbcbdbaccdadabdabcdabacadccdacbdcbddbbabcbdbaddbddcbbbddaaacbbcdbdbcaaacbdbacbaddbbbcbbdadcadaddcbdcaccccacccaccbbdacbbaaacdbbcaccbacacdbabcbbaabdabbcbdbabcdcdbacbccdbabbddccaccddbbcdbcaaaddcccacabcdbccabcabddadbdcaccdadabdbbcbbcbdaccadddbbbcdbbddbcdbcbddaabdcbccdccadcadcdbbadbcddddaaddcbaacdbcbdddaddbbbccdbbbcbadcabbdabddbababbcbdbaabbdcabbadcbbcbacdccbbcacbcadaaddbacdddcdbdbacabdabbdcbdbbbacaabbdbccdccbcdddadadbcdaddcdadddabaddadadacbcbcdacbccaabdbcddbacdcccbaaacddbbbbadddccacdcacdbaaabdcdbaadbdbbabbddbadaadadbaaaadcabaadbbbcddcbcaccacccdcccbcdaaadadabdbbdbccdcdacadbcadccbbcadaadacbadcccbabaabacbbdccdaaaabdabcdabddadbbddcbcbbadbdcacdddcabacbdaacccadcbbdcbacacdbdcbdababbcaabbadbdbaadaddbcaabbabadaababacbbbccdaaadddccdacbbaacdbcbcababbdccbadbccddbacdaacbbdbcadbdabbdbcabdcbcadddddacbaadbbbcbadabdadaacacbddabaadcbccbbccaaadbdccacbbbabbcbaacadcbdcbccabdcdddcdabdaaadbadabcdcbdcddbdaabdcbdadbbaacbbcdaaacdccdbadcdbbcbcadbcacbccbdcdccbaaadbacbacbcbadbbcbbccdddaccdcbabdbacdbaaccaadabdcbabaccbbdcccdcbcadddbcadababdacccddcdaaaccbdaddababacaadcdbcccbccbdbdbcdaadcadadbcbacadaacbdcbdadcadaadaccbdcabddccaacacccdbabbdabdcaacdcccacbadcbadacddcaddacacababbaadadaabdadacbcdaccbdacacccbbbcdddacdbbacdadaaccbdbcbcdaacbdcdbbabbcbdaaaddcaccbdddadaadbbcadbdcbabbbabadbbacdcccdacbddbbccbccabdaaabbdcaddcbdcabacccddddbbdbcdabccadccabcbbabdcaabbbdcbaddaaabdababadcdcccddcddddcdccbdbbbdaadababbdaccaaccbadbcadbaabcbdcbbcbbccabaabcaaabbddddbdabcdabaacbabbbaddcddaaadccbadddaccbbbbccabbccdacbbdcaadbacbdcdcbcbbcadcacbcabddadbbbbadccdcdcacacacbabcdbdcdbaaadbabcdbcdbcdbdbcbcabddbdaaabdcdbbadadcdccbdddbcbcdcdbbbadabcaabadacddaaabccbcadbabdaadcabdcabbdbcbbbbaadaaabbcacadbadacabbbcabddabbcdddacbdcccbaabacdaadbbabbbacbbbcdcdbdcdddddcbdcdacccadccaaaccdbabaabccabadaacbacbcddbddbbabacadbbabdbbadbabbbacacabadabbbddaccbbbbadcaabdabcddcbaddadbbbccabbacccaaadabbdaaabaccbcdadddccbdcababccaadabdadaadbbcabcabbbbdabbccbbdddcddacdaccdccdbaabaddddaaddcadcdccdccbcddbdcdacacadddacbbbddababbbdbdcddbaaaaddcbbadcbbbddacbacadcdbcdcbdbbbcbcabcbbdcaddcaabadcdaabdbcaaaddbbccdabcabdcbdcaaaddadaccccadbccdadbdddbbcbdabddaaddcbbadddadbaaacccbdbbdcaaccdbcabdbccbacbaabaabcaccbbcbdaabaddbdcdabbadcbddaccbdadcabbbabbcadbdadbdbabccbbcbbccccbdaddccaccaddbcbababbbbabaabadddbbbabcdacbbbcbdbcddbaaaadcdccdadcdbaacaaddaaabadacddcabbacadaabbcdccaacaaabdddddabbaaadbcccaaacbdadcbabcddaacadbccabdaabddcdaabdcaaadaacccaacabcacaababacbbcabbbcdcabcdcadadcacdbaabbdcacddcbbccdaddbdbcadbbcdbdcbbcccbdbccdcdcbdbbcdbbbcdbbadcddacacbdddabbaaccbcdcbccddbbccddbdacaddcabbbbccddccacdcbdbddbcbcdadadaabcacbbdadabdbdabbacbacbddaadbaabbbbabddadbabdbaacddabccccbabacccbaccdbcadcdcbdaababddbcdbbadaabdaaddcbabcbbdaabbbabbadcacbcabbbaaacadcabcadacbdbdaccbacbaabadbdbbdcdaabbcacdaaccbcacabcddbdcbadcdcddcdddbcaabcbcbcbbabdabacdcddbcbaacdbbdcbcdaababccdcbcabaddcdacdbccccbcdcabccabbcbdcdcccbccddcbbacbbabbaadbaddcbacccdbaadbbddccdbacdccabddaaaabaacdbcdcacdddbbddcdcbdacbadadddccaacaaddbbcdacbbcaaacccbcdcccabaacbdadcddcbdbcdaadccacdaacbcbcbdccabbabadcddbcadaadaabbadccdabcdcbbcadaaabddbdcacadacdccdbdcbaadacbbbaddbcdbacabbccbbbabaadccaabdbadcdcdcdbadbbaadaacdcaacdabbcddabacacdcbbdccddbaccdcdbbbddaaacdcdbacdbbcaddacdbdcddcbccbcaabadccabcacabbcccbcababcdadabcddccdabbcbaddbcdbcabcdcccabdcbcacddadbbaaacabbdbcdddbddccdbacbcdbcacdcccacaaddacdaccddbaddcdccddcbdbcccbbddbadddddabdccbddbbabdbcdcddcdbdadbbdcdaccbcdccdbdcdabddcadaaddbddadddbddabdaccacdddcccacabbbbabbdbdccddddacbacccccccaadddbcadacdbbbabdbcadaaccbdcababbccabcadabaabdbabaacbddccbacabcadaacaababbdabdbcbabcbaaacbcdaacacddcacadbbabacacbbcadcdcdcaacbcaddacbddcdbddbdbaacbcdcdccdcbdaabaaddccdabbabaacddcccdbababdaccdbaacbbcbcbcddbddcbaccdcbcccbbabbcddbcdbccbddddaadbdbaacacbddbbdcacddcadbdcdcdbabcadccbdbbacacddacabaabbbbcdbcbddaacdcbacccadbccddacabcdbbabcdbcbcbcadadaabbabaabdabdcadbadbdacabddacdcdbdcaadadcbaddaaaddbaddbcbbabaccbcadccddbdacabcaacbccdabdacbdadacccdddaddacbbcbbabbdbdccbacbddbacdadddacbaccbaddadbcbbabcabaabcaddaccbddcdbcccdaadcababacacaccbcbcdbccdaddabcbdaddbdcdccbadabbacccccacddbcadbbacbadbddcbdcbbcaaaddbdddacbdbdadabccaaddcddccbdbaaaccaaabbdbcacccaacbbcccbaddbdacddcdacbbbbbcdaadccbdabaddaccdbbdbbacddadcbccccdabcadacaabbbdbbdbbcbccdbcdcbcaacbcbacddaccdccccbcdcdcabdabcabacbaadbcbdcbbbcaaaadadcaabbabaadbbabbaaacaabadccbcbbcbbbcbddaadcbdbdbbaadadaabbbbcadbadaabbbadcbcdbdcddaacdbcdaacccbcccaccccaadacbadbddbadcacdaabcddbddbaaadcdbacdcbbbcbccccbbbbdacdbcbdadabbaabccbaadacbaadccbddadabbdabaacdcdbdbdcacddbdaddbddabcbbaaccacaaaaacadcdcaccccdabbadadbbdcbbbccadcbaaaddbcbbadbddbbdcdaddabbbabdadaaacaadacabbdddbbdddbdabcadcbdbcdccbdaddccabaccddbacadccdbbacbcddbdccccdbabbdbcccabddadaabddbddacccdddbcdadcdabbdaaddcbdbabacddaababcbcbdaddaccbcadccaacaaacadbaacdcdacdabdccddbbbdaaacaacbcabcaaaaaadcdbbadacdbddcbdcacbaccadabccbacbdadbadbcacdcbbdacdadbcccdccddaaabacababdccbcccabdabccbcadcddcdbcbacdbcdcbddddcaddadbbcdcdaadbddaabaccaaccbaaaccabbaccbddacabbdacccbddadccdacacaabbaccdbdcbcbcabacacbabdbcbbbcbabcacdadbdcaccadadabbcacbabccbdbcaacbcaaadcdddbabbdadadadcbbdddcdadbcbacacbcbaadbadaddadadcdbdabbbbcbabcaadbcabadcbaccdccdcdcbbbcdadcbcbadddbaddaacaaaacabcdddabcabbdaddcdbacadcddcaadcdacaadddabdacbbcbbaababdbcbdaaccbcaddbbddcdcdabaddbdbccadddccdaacacdabddabacbbcccababddaccdbdbbccbadcaaabaddddbcaaddadcacddbdbcbaaabacccbbcaacbdcaddcadaaabcadcdaaadbcdcacdadcccdadddcdabcccbbacccbcbaadcdbbddbbcccccbcbcddaadbbcdcdbbcddabadbcabdaaddbdbcdbdbacdcdcbccaadadcdbbdddacdbabddadbdacadddccadabbcadaddbabbbcdadbddabbbaacadbddaadbbdacdadabaccbdbaacadabaccdabbcddabbabaccdaabbdcbddcdcbddcbacbcbdddcbadabdbabbababaddcccccacddccdbcadcbbaddccbdadddaaacadcabcbdabbaacdbdbdcaacdbbacadacdccbabdadaadcabcbaaddbdbcdaaabbbbbccbbbcddbcdcaaabccaccdccacbbabbadcdcacbdccccdacacdcaadabbdbcacaacddbacbcbdbbbdcaddbdbacdbdbacbcddacabbdddacdccbcbcbbcacbcacbdbabbbdcbccbcaaabcbcbddcbcbccccaaddbdcdbddbbcabaaaaabaaadbadcabccaaccddcbbbcbcbcacaddabbdddaadbaadcdcdacbbdbaadccbddaabdcbadcbbabcaccdaacbbddaadcbaccdcdcdbccadccbbdbddabacadcdbaadaaabcbaddbacbbacdabbaccddbadcbababbddaadaaaadabbcacabbaabbccaacddabcabadccdacbaabaaccbbbabdaccdcccbddbdcaccddaadbbcdabbdadddccdddccabadbdccbadabcaabdcbcddbcbdbacbcdcbaaaccbadcacdccdbbdcbacbdbccbdcbbccaabbcccbddbcccabdcadbccabbbdadabacbccaadbbdcbbabddaadcbbcadadddbdbccbddabdabcbaccbabdabcdddabbabbdabcddadabcbbbcabdcadbababcdbcadcdcacbbcddadadbabaabbdaaacdbcbadbcdbcbaadadbddcbccdbbdcbccbaaccdbcaddabcdbabcbddddbcdcbcddbdbbdcbcdddbacaacbcdadbaacacadccdbbcbcbbacbccdaaccaaaaadadadaaaadcbabbcacbdadaacbacbbaadcacbcdcdbdaccdbabcdbddcaadccaadccbdcbbcdabbaddacbddbdccaabbcdbbddabadcccdabacbdddcaaaabdacbdccbcdacacabdadadbcbbacdcbcdbabdcbdcabcbabbbcdaaadbdacbcddcccdcacdcdaabbbccbdcbcddadbddbaaaabccaacaddbaddabdbbbdbaadacabddaddbccddadbcbcabcddbdbdabacccbbdbbcaddabdcdaccbbacadbbddcbaccbddbadcabcbdcaddcadbaddacdaccbacbdcacdcddcbcdcabbaabbbcddaadbcccdacdacddbdacabcacbdccdaccddbdbbbcbacccaadadcbdbbacbaabbadabbadabbaacbdabcbbcccbadaaadbbdbcabadcdbadabdcbdadacdadadbccacdccacbbcbbdbabacadaddbcbdcbccdbbbacbcddcdbaaccdaabbdacccbdbbcddcbbabaaddbcdbcadcdcbbdcddbcccdbdddbaaaabdddcbcabdcbcdbcbdaaccdbaccabcddcaccdbbdbadcbaabcbcdcdabccbdaaacbdcdabbdacadadbcdabcccbddbcacdbbcbbbbcddcabdbbcbbcacadabbbaacbcaabadababdddbcaaacccdbbbccbcccbcabcdddadddaaaacacbadcbdbadacbcabddddddbadbcabcdcaacccaadbaaabddbdbdaacbbcdddcddadacbaddacddadbadddadcacacbcbbdacbdcaccaabadbcabdadcacaaaacddcbdbcdcaadadcdbbbddbddddaadbcdcbcccccdadbaccbcbabbcccaacbacadacdcccbcadcacdddacdccdcabcacdabbadccbaaaddacccdaccddddcddbcdcdcdaaccbaccbadccdcabddaacbccbddcbbabbbbdabddbaccccbbcbdcbaddbdccbacbbcadaacbbbbabadddcdccbdbcdcbdbddcdbcbcdaddcddaacabadbaadbcbccdaddadbdadddccdbadcbdcabddbdbaaccbbbaacabaacddadbabdbdaccbadaaadccddbdcbbbadcdcdbacaaacbcadbaddcdbcccdcdccdccdcbdcbccdcdcdcdaacbadbddccdbbddaddbbaccbbddbdaccbdddacccbdcaabbbdccdcdadaddddbddaacbbcbbccaadacabbaccbaabcdacbdcadbadcacbabbddcdcbdcdbbbbdabdcacadddcabdbdacaaaabcacadaadabbbdaacaaabbbccacbcabbbaddadcacaabadccacbaadacddbdddcdcdbddbcbabcaabaacacaacccaabbaddadadbdbacbaddacbddcaadcddbadacaabcbbcdcbbacabdbabadaaccadbdabddaddbbabacdacaacbbdcdadddaacacbbbdbacddbbbaaabccbaaabdddcdacadddccddabddbcabbadccaccabaacccdbbbdbdcddccdddbabdccdcdabccaabacbbacbacbbcadcdadcbaadcbadddbbcbcdbbcdbadcdcabdbbcacbabdabaccadabdacacbbbaccabcaaacaddcabbacbacbcbccabddcbbcdddabbdcabdbccacacdbcadbcdcbdcdbddaabbdbcadabacabcbabdbdbccadbddaccaacdaaabbbdbabcbdadbbccadaaddcdbccaccdbdccdcbcbabdbdacbdccddbbcbbdaabbdcadbcadcadaaccabcbbacdbdabadacabadbdbcbcbdaacdbbbbaaaacddbccbcbaddbbdbcdbdacddbdbddbdbdcabacbcdbdaabbdbdcbbbbdccbcbaaccadccbcdcbccbaccbbcbdacbabbcdacdadaaadaaacbdadbdcccddbbdcbbdbbcdbdcaddadadacaabacbaabaaccbcdaaabcbaccdbccbacdbaaabdbadbddddacabaaaccbbccbcdbddcabcdbacbaaccdbcdaacbcdcbcaadbdbcaaaadacadcbacbbcdbdcdccaaacdabbdcdbacbcccadbbabdccaacacdbddddbabdacbbcccdadcabaaabdbdccccccddaacdbcdbbcbcbadacaccbcccaddbbcbbdccdababbcacaaabcabbcaaaddbdcbddbccdabccddcbcaddabbdcbacacccccacdacaabcbbacacdadcadcaacabdababbddbdbadbbbabbdcbddcdacbdddddabbaabdabadbbbdadadcdabaabbadbbbdbddcaddbadbbbbacbccddaabcabbbacccbcdbbccaccddbadbdaacdbbbdbdbbddacabaaddcaaabbabccddbcabcdddddcadcacdbcbccbcabbbbdccabcbdbadaacbaaaadadadcabbbdcdddcacddcdabcabbadabbdddddcabbddbcadbdcddadabbaabdaaddabccdadacdcbdcdddaddcadaaddbaabccdbdbcaadacdbcbcadddcabdabaaccbcbbacbbddacbcbadadaccbaddacddccbdcccdccbdbdaddbcbdacaaaaddabacacdadacdbabdaaadaaabaddcbcddcbcbadbabbccaabacccaddcadbacabcacadabbdcacdccdbdcaaabcdddaadacaccddbdcdccadccdbdaaaaaaadbccddccbdddcacdbadcabbdbcdaaadacadcddcabcccababbdbcbbabcdacabcaadbddbcadabdbbdcccabaabbcacbacccacdbcdbbbcddadabbbadbabbdccbcdadcdbbbacbbdccaaabbcabbbccbbdcbabbdbccabadbcdcaaaddcbcacdbabaddbbbcacaadabdbddddcbccabcccabbccdaadaddddcbcacdcacdcaccbdacdacbacabbdddbadaabaaddbcbaabdabaccbbdbacdbaccabcdabcdcaabcdbacbdaddbdbdbbacacdababddbbadabbbcdcdccdddbbddabdcabbabbccccccccbabbaccdabaccbbaadabcaddccbcbbbaddabccadacadcddadbabdcdddccbddbcabdaddcdcadaababbbcaddbdcadcacbaaacdbddccdacbbadbdbbcadbabdbcdcbabaccbdcaaadaccdcdaddacbbcabbcdcdbaddaccacbcddaaddacdbabaabddabbdacdbabbcbbabcadcaabdcbccdadadabdbccbadacddddbddabbabaaacababdabadadbdddbccbcbbcaaddbacdbdadacbdddcacdadbdaabacacaaaddbbcccbadddcabdcaccaccdabdabdbdbcaabddcddbabcbddabababcbaaacbcaacddbbacbcaaabdbdcaaabadddccbcddadabdbcdbaddbabdcdbbbddddbaddacdcabcaddcaccadccccbdddbbbaabcadcddcaddacdbcdbbcdbcdddadabbbbadcabbbdccccdabababbddbbacadbacdadccbbadadddabddddaddcbbbadabddbcccadbaadaabdbaaaccbdbabdcccbdbdcdaccccbacbcdacdbdcabacaaddddcbdbdbccddaddcddabcadaddccbddbdcbcddacdddbadaaacabbdbdcabcdbadacdcbbadcdadcaadddbdbcadddcddddbcabababdadaddccbdddbcaaaaadbddbdbccbddbaccaababbccadddbcaaddcacbcbcaacbcdcbbaabcacdddddccbbddcbccaddaadbccddbdccccbdddcccaadddaabdabcccbdaabbdcadcabdddccbaccbcdacabcddccddcbdccdccbbadaaccabaaaddcaabbadcbcadddbadaabdcccabcbdcabcdbadddddccadddaddbdccacbbccbcaadacbdbcaaacdcbdcbccbcacaaaddbacabacabadddbbdbdabccacbccaacaadddbcacddbacbadbacdabdbcabcccabbbcbbddabdccbabadccbdbddabdcbbbcccbbddbacbbdaaadabaaacddcbdbbbbdadcaabddbcccbddbddcadbbbaadbdbbbbbacbdacaacdbdacadcabadaacccaabdbbaabdadbacdbddccbcbbaccadbcccbdabdbbaadddacbbabadcdcdbcadddbabcdbdcaccccadccaaaccbbcadddbbaaccdaddbdcdddacbacdccbdbaadbababdabbababcdcbadbcadbdcacbdbcbbcaabbbaaacbacaacdbcaadabcdacacdadbcadcabdbaabdcacddbdababdbaacbcbdaaacabcdcddabcdbdabbaabcbbabadcbdcbdaadbbcbcbabdacbdaababaadacddacbbadcdaaccbdacbbbbaabddbdabdbdadaacacabdcbcdbadbbcabdabbbaaccadcbbabacaadacaaabcadcdbadbdabdabcdacaddbbcbbdacaaddbdbcbadcacabbbadddbbdbadbaadddcccdbcbcabccbbdadabadbabaccaacbccbdcdbcbabcdcbaacbccaadccbcaddcddadddbdbdbdbddcddcbdabcbbabcddacbacabcbacbccacbbbdcabddabdaadccbbbaacccaaddbbbccccaabdaaddabaccccdaaaacdaadbccbbdcaacbdcaaabcbcdaadbbdddabaacdddcadadadcbaaadaddbbddbdcbabdddbdbbdcaaccdbaabdbbccddacbcdbbccccdbcacdcbcdadadcaacaccdcabbbcccacddccbdbdbdbcccdaaabacdcdaadcccdddbccdcdcbcbaccadbddbcddccdcdcacdcbccdcdadacbbadcddbbaacaadddabcdabbdddccabbbabaadcababdaccadddabcddbbbcdbddbdccbdbbcdbbdbbbacaccbdcbacbaacbbdbcbbbcaccdaccbbdddcdcdcbaadddbbbdaadbbbcccbdccbaadaaacbddcacabbacbabbdcccbdaaaccbdbadaabaacaaddddadadacabdcbcddadccbcddadbbdddbaaaaacbaabadaaabdbaacabacdccbccabbccacbdaadddbbdcacddcdcaabcbacdbaaabbabcdaaddbdaadbcddbdadcdbcadbddaabbbabccbbacdaadcacbcddddacbbdbcdacdbadccdcbcabcadadcbabcccaaaddbcbdacbbaaccacdccdaadcccddadbaaccbcdcdccbdcbbbbbbdbdabdaddccccadaddaaadbabbcbdbbbaadaddacbbcbcbbdacaacacccaabaabdadcaaacdadbddccbcbaacaabbcaddcdadababacaaaacabbcbdbadcccaddcbacacaccbaccbcabacccbcbbcdcdcbcaacdbcdabaddcacaabbcbdbbaccadaabdcbbddabcdbbccacbabdadcbcadcdabcbbadccbacdadbacbcdddddddadbbcbababbaccccccabdaccbdaccbdcaddacdcdbcbbccdbcadaaccbcbbaddcabdacbadabcccddaaccacdbcdbdaabcaadbbdcaadddacabdcbbdbaccccddcbbbdcbcbaacdbdaabdaaaadadccbcadcdbccbacadaabccdccdcabbcbcccbcaabccbacabacdbabdcacccdddaaaacacdcdcbbadbacbabcababbadcbaadabbcacbbbcdcadadcddaabdaaaabdacdcddbaccccdbdccdbdcdddadcccdcdaddcdabdaaccacbdaccdacbdbaddbdcdbcbddbbbcadbddbdaaccbcbccabbcdbbbbaababdbbbdadbccbbabbccbbcbccccdcbbddadcbaccaccdcccdbaabccadcbaccaacaccccabbbaaacbdcdbbabbcaaccacdcbdabcbccddcacdcdcadcacabcdcdaacbccdccacdbabaacbaaaacababbadbdaaddadbcbbdcaadddcbbcddbcbcbbddbdcbaabbdbcccbdbdbdbabdbbddbdddabcbdaabdccaddaddadaccbaacbddcdddbcdbbdbbdbcbcdbdaddadaaacacdadddddcdbdacdccabbdbbccbbaaadcbacbaccdddddcbbdbbccddadbdcacddadaacaacacabcbccbadcdbdbbcbbbadaccdcbaacdccddabcbadbdabdccdacbcabcacbccdbddaccdcdadaacbadacbcdabaadacdcbcabdaddacbdbcbacbdcadbccadaccaabdbdabdbdbacacacdcbbcdbbcdacbdcbcccdaddcaababdcacdcaccdcabbdbaababaddddabcbbbcccaccacccdcdadcdccdaacbacbdadcdabcdbbdddaabbdcdbdccdccbbbdbaacdbadbabbcaddcbcaaacacdbabacbcdabdbaccddbddbdbbdbbbddbbacacdacbbbaaddcaadbcdccbabcabbacabacaabbbbbbbcdcacadaacccbcccbaaddadcbacbadbabadbdcdddbdcdaccabbcdabbbbdadbddadcacabcaacaabbcbacdacadcdaabcbdacaddddaaccacbadccacbaddccabcbcbbbbcdbdadadcaaddbcdcbbcacdcdadaadaddcdccbabcaacacabbbbdcbcaadbbdadacbbccbaabddcbaabaccabaaaacbbabbbadaadabcacabddddcaadaadaaabcdddaacaccacbbcbaabdbbdccbdadccdbadbddbdddddcaaccbbcdcdcabaaadaacadababbbdbcdaaacccacdadbabcabbaadcbccdbabaddbaacbbababdaaabddadbcdcdccbacbcaddaadcdabdbcadbadbdcbcdccccddadddcbbaabbccbbdcabcacbccabddcaabacbaccbbcddbbcddbaabadcbcddaaabacaaacbdbbacaabbcdccaadcdabdbcdcbcabcadbabaababbbcccdcbbbaabbcccdcaddcabcdadaabbccdbbdbcbbcbdcbbabbcadbdcddddabdacddadbdacbddacddcdacabcdddddbabdbbbbabccccbbdabbaaabbdcbacaabadbddddbddaabbbadcadcaaddaadcddccbbaababccdabadccddbadabcabbabcbaacbaddcaabbaddadbabbbbacdcdddcdbcdcdaabbdadddbaaacdccbbabbdcacdbcacbdacbdacadccbabbbdddbcacbbaddbddadddababbcaabcbcbbbdcdbddabdabbbddcbacdacbcbcbadbccdcbcdcaadabcbbcaccabdacbccbcdbbccbdbbbaaccababbbbcbcbcacbaaaadbbcbbaababcacadbcbadcaabcaaadcacaacbadbdcbcccddbbcaacddddbaabddccaabbbbdbbadddaadccdcaddbbdadbbabacdbdbddcdbaddbdcccddddbbcdbcacaddcbcdabcbbbdcbbbbccdddbadabbdbdbbaddcaadbdaddbdcabbbbdacddadcddadbcbcaaaaabdadbbcbcababadabcdcabbbabbdbaaddbcbdadddbddddbdcdbddbbacbacabacaccabdaaccabddbbddccbcbbacbccbaddadcbadaccccabdbadddcbdaabcdaadcdabaaadbaccdacabcdcddcaadcdcadbaccacdbbbacbcaadaccccdcbbccdcdcaadacadcdbabdcbcabbbdacadaccdcbabddaabaacdaacaabadadbddbaaccccdcabdcbaaaaacaaacddbacbcaddaddbdbdccddcacbcabbcccdbabbdcacddadccbbdccbabdbdddcdaadbccacdbabcddbabbbdabccaadbcbdbbcbbcdcdccabbdacbbbabcacbdcbcaddbbcbcdddadbaabbdacaacaddbddbdcbbabbbcaabbaadadacbccdbabbccdbdaaaaacdcacbddbddccaabbdbaadacbbaadbcdaddabbdabccbdaddcbcadbaaacdadacbcdbbcbcbcadacbcbacabacaddddbcdbcdcacdbcbaaabbccbdbbdadddcdacacbbbacadcbddacdbccbcadcdaacababdbddbbdbcababccbbbcbaabbaabcbcbbabdaaabaacbadbdabdbbdbdbbbcddccacabdcbdbaabcaaccacbcbdabdacbdcaccccbadaaccacacbccbcbaaccdcbcddadcddbababdccdaadddddbcbabddcbcbaabbadadbaddbdadaaabcccbbbbbabcbaadbbbbcaadbaaabaadbcadcbadbacaddbaaacdaadacdbaddaccdcadcbbbdadcdbdbcccbbcbdbbcbbbccabdbcdbabbccccbdaabcdbcbcaccbdacddddadcddbdacddcadbbbabccdccabacbacdddbabdbbcbacdacddcabaadcabcccaccaacbaccdaaabdaadcbbdcacbcdbcddbdacadbcdcabadbabcddadbabcabaddbcbcccbadbdccdddbdcddaccbcbdccbadbaabdccbcdcbddbbdaadacacbaabccbbbdcccabacbabccaabaadbcccddabbbddabcaabbdaddabaaddbabbbddbdcbbdddbbadbbadbdcaabccbdcdbbbadaaaacddbddbbcadddbbaadadadaacbcddbaacccdbcababdadacaacdbadbdadcdbbdaddadbccdbbbbcdaaccddcdbbacbadbdbdcbbbaddccbdacadaadbabacacbaaabbbddbaabdbaadcaabcdbbcdccdaaaccacacbacaddcdcaacaadadbbdcabaababcddccbaabcdddacdcccacddbcdcadabcadbabababdbdccabadabadabcbaddcabcbaadccccaacdcccbbcccdacdbcbadbbcacccccdcabcadabaadaadcdddbbcacadbbcadacdcabcdddcccccdccbcbdbaacabbdaababcdacdaddccbbbbbadbbdaadcdbbdccbacbdaabbccdcdbbabbcccdaacdabadacddbdaccdbacbcacdabadaaabcbbcaddccaadbbacbdcbaabbccbbaddbcbbbacabcdccdabdbaabbcdbaabbaadddaabbccdcbccaabcddcbdacbbcbcadbcdacadcbcbcdbbacacbbbccdacbdcbcdadbcaabdccbcaacbbbccccbbbbddcddacccdabadbbccaabbddbdadadcabdaabdcddbbacbccdbcaccccdadcbabbbaaabddbaccbdaddbccaacaabccbacccbaccdddbbcaaddadbbbbdaccacbabdcabdbdbbccadbaacbaacdabcbcacaddcbabcbaaadabbacccadbdbadddabdcaabaabdccaabababdbabcdccbabaadcacbbddaaabacbdcaabcddaacbaaddbaddaabcbacacbbdddcabcbbdcdccbcdbaaccbbbbcbbbbcccccbabddbdbdadbcbccddcddbcbadaddbbcbadbdadacbcdbddcbcccadbdbbbabaacbcdacdcdaabbcadccacbbdcbdcadadaaccbcdbacbdccccbdcabbdadcdbabaddbdacdbdadaacaadabaccabccdcbdcbbdacbadbabbddcbbbbcdaccbcdcacbacabbcdcbbddbcdabcbbbcddbdcadadacbaaacdcbaadadaaabcadabaccbabcddcdbcdbadbdbcdbabaccbcbdbcbdaddddacbdbcdccbbcabbbbaabbcadccaaccbcdbbbcaddbdbbbaadacadbcddabbcdbbbacacaccbbbbcddaaddbabddbcaccdcdabccacdbcadacbbbbcdcaaabdccbdabcadbbbbcbaacabdcbcacbcacacdbadbcccdccdcbdcaadbdcadbaabbddbbaddcbdacdcadacadadacabbaaaaacddddcbbdcdabbabcdbbbbaaaddabdabcbbdacdaddbbbabbddbaabbdcacbbbadaddccdbcddddbbcdcacacabcdcdbacbcddaacadbdabbdabbbccccacbdbdcbddaaabcbabdaabdcbdaabbbacbbddcccacdbbbcdacbdbacdccddbabbdddaabaadbadcddcacddbddddbbbcdacdacabbcdbccbabccadbcdbcdacacbcccbabacababbdbcbaddacbdabbaaabddcdcacacbccdcdbccccbbbdabbdaccdcbbbadcbddadcacbaddcabdacdbcbbcdbcaaadccabcadbdabaabcbbddccaccdadabbabdadbabddadcaddaacbbdcbcaacaacacdaaccbaaaccdaaccdacbabddbbbaabdcccdddbddabaacacbcdcabacadcccdacaccacdcbbccaaddcdbbacccbacbbbaadcddbbcaabaaadbbaddcccbabbdccbacbbcbabdccddbadcccdbacdcbccbbabbadabcdbddcacbadbbdcdbbdbddbdabadbbabbacaadbdbadddabdbbbbcbcbadbbccacbcbacadddaacdccbdcaccbbbdcdcbdcdacddcbcbaabbccbbcaabbaabbcaccbaacbbbcaabdbbacaaaddbbbaadbdccdacbacddccdbacdbbcaabdddadcbcdcddbaacdbbbcabccbddbaccbdadccacababdcddadbdacbabdabaccacdbddadbdababaadcbdbdbbbdcbbbaabcbadacddbddbcdccaccdbddcacdbabaccbacbaababcdbccabddbddaabdccacaaaadaabbccdadabdbddddddaaaabddddbabaabadabaadbcddbadabbaaabbdaddaddbbdcaadbcdbbadcbaabbaadcbadaacbdcccbddcbbcdabdadcbabddadddbcacababccadcaaacbdbbddcaadabddcadcccdcdcdaadbcdaacdcaccdaccdcdbcbcaccdbbaadacbccaabcbaaccbdbbdabadcbbbcaaccbaadabadcbbcabbbadbacaaacbdbbbdbccbdbdbcbacbdaacdbbcacbacbcdadccbacaacdbadaabacaddbccdddbdbcbbcdccadbadbdaacadcbdcdccadacbcddcbccdbddcaadbdccbddabccbddacdddbcdacdadcabbbabcaaaabaaacdccccadacbacbcadabaabdabdcbccbaddacdcddccbcbccabcacbbbacabcdbbcdcbadacbbdbaacdccccbbdcabbababcacbbdbcdcdbbdabbadabccaccbacddbcadcbdddadabdabbcbabaaaababbdcbdbdabcbcccacabdaddcaaccbbbcbbbbbddbbdabdbdcbbacabdacbcdaccccadabcabaadddcabbbaaabbbcacdadcdbaabccddaaaaabcacbbdabcdcaabbbbadbaccbdabccabacbdbcbcddbdaddddbdbcbbadadbddbdacdccdacddaabccbdcaadcbbdaddbdbacdcdcddabaaaadcdccaabaddbdcabdbbddaadbabbcddbadbdddaacbddcabbaadbcbbbaddcbccadadbbccddcbdbcaddccccaabacbacbbadbbdbcaabdddbabbaccbacacbbdbcacbabbcdcddadbbbadadbbdbdbcadacccdbaaddadadccbbaddccabdbbbabccdbbcdabdcdcdcabdacdcacbdbcdbadadaadbacacddbacbdaacaaabaaddaddbcddbdadccdbbdbcddddcabcaddbcbcaabcacbabdcdbdbcddbbbbdbddccabbcbdcaacdcddacddabcdbbabcdbccdbbbdbbabbcdadbdacacbbbbdabdaaabdaddcccabbbbadaabdddbabccdcabcbadcabdabbbdcaadcddaccabcaddbcaddaacadabdaadcbbabaccbbdaabcacacbadcbdadccbabbccdacbaacdbddaabaabadcbabcabcbdcbcabaadcdccbcbcdadbcbdcbacdbbcaddcbacadbaabcdbbcbbcbbcddaadbaadcbcbdcdcdbadbdacaccdddbbdcccaacacdbbbbacaddbdacdabdbbbadddcbadadcddcaadcbadbdaabaababcacdbdcacaccbdcccbccdbcbdaaacaabbbbbcdccccbcbcbdbcadabbdbbaddddcccccdcdbaabbadccdbddadcdcbacadbbabaabdddaabdaaacabaccdaccdbbadbaadabdcabbdabcaddcadaddcdbcdabbbccbcaaddcbdcddcaabddbdbbaaadbaacdbcacabacadacdabdaaaccaddbbadacbbacbbcacaadbdcbbadccbacbbdaaabacbcbabaadbbbcdadbccabbdddaaaaabcddadadcabdcddcddbdadbcbbcacaccbbacacacbdcaddcacaddabbcbbcdddaacbdcccdbbcdddcacbcacbcbacdabdadadbacbcddadacbcadbcdabacbadbddcbdcbccccaaddbbbcdbcbaddadbcaaacbcbbbaadcadababbdbbccdaacdcacbcbbcbddbbbccbcabbdbaccdccaddddbcbbbcdbddcddbdbacabbccacbaaabaccbadcbbdbacbbdacabbabaaabbabacdcddaaacacacdbcbdbbbdbccdcaabccacccaddbccccbddabcbaccabccbaaccacbbcacbabadbcbcdbbcaccaccacdcdabbcbbaddcabbddacabbbbbcadcdaaddccacadccbdcadbbadcbbdbabaccbddaaabaadbdcbbbcacbcbddbaccbbaaacbcccbaadbcacbcbcaabdcddabdbcadaccbddcdbdbcbdbcbabbcbcbbaadbccacacaccddbcadadbdddcbcbbdadabaacadbdaacbccdacdabcabbbccadcccdabcccccaccddccbbcddaabcbdaabbddabdccbabbcabbbbcdbaadacbddbcadacdbdacdddcbbbbdbcbbdbbbccaccadccccdcdccabdddccbababdadbadadcdaaddccbacdcdacabcacdadadbbbcbcdcacdbccccbbcacbbdbbbaccacaaccbddbcccacadbdcaabcdadcabbaabcdbcbcabddadcbaccddcddcabbdaccabdacaabaaabcbbacdabbcdcabaabddbbcccacdbbaddacbcacdbdcabadbdadaadaaccaabcbdbadbabdabbcadbdabbbbdcbbbbccccbbcabaacbdbbbbcdcadadbababacdacccdbadbbabdbcbcbabadadaacdbcdcaaacbbdbaaaaabcdddbdacdababacccdcdcacadddbcdaaacaddccbdabcbcdbacdbacaacaccabddacbccccdbbcccbcadbaccadcabcbdaadcaacccaabddcbcdcbbcadcbcaccbacddcdbddaadbacdbaaccacbbccaccdbbdbdcacbddddacbcdbddbcbdbcddbdcdcdbcadabcbbababdacccdabbaabbdcbdcdbcbcbcbdadaddbbdcbbdababaabbdaaaddadadadccccabdddabddabacdbcddcdbdcaaacddbaaddccacbcdadadabccdccadcbdbbdbbbadababdabdccdbbbbaddcddacbcccaadabdbcabdddcbcbaaccabdadbbbbccdccbadbbabaacdcdcadbacbdbcbcbcabdaabdbdcbcabbcaabbadcacdcdcbaacacccbbbccdbadbcdbcacdbaacaacadaccabbddbbabacddcbbbccbdddaabdaabaabcdacaabcacbbbcacaabcdbdbdbbdbbaddbccbbacbcbacacbdcdcaaddbabbdccbcdbbabaabadbcbcaddcdcacababdbdadccdccbaadbdabadbccbccdabacbcdcccdbdcacdacccdbbbdcbdcddcacacdcccddbadaadbddbacdcbccdaacabacddabdcbcdccacdbdacadbcaacddadabacdbcdbdaccbddadabdadcdaacabbcddadddbcabcdcacabccdbccadadabbddddbbbcccacccbdcccbdbbadcbdcaabbacbdacadbbcaaaadacbcacdcccdadbcddbdcaaaabcabaccdcabacaccdbcbbdadccdddaadacbccbdcabbcdadaacdbcdcccacabddabdcbaaabcbbbbdcadbbdcaadddcbcbaacabcdbdbdaddaddadcbaaadcaaabdccadcbdcbbdcbadcbbdbbcacddcdacdcbabdcdccccabdbabcbcbbcbadcbdacacbcdcaccaccbcbaddddcdbbbbbddbadacacbacbcbdcacadcabbaaccbdddcbabdadcdaaddccddbaadcbbbdabaabbdbabbcdcbabdabbaacbbadacbcacbdcadbadbacccdabdadccadcaaccbbbcdcabacccbcdbabadbdbacbbcddcbadbbcadabacbacbbccdbacbdabdccbcdbbcddcbdaccdcbbcadbcbcddbdcbccaacbaddabbacbccdcacbbddbdbcdddcaccbcadbcbcacdbdcbaacdbdcaadddbbaccdbccccdabadaaaaabdbbbccbdddbcdcadcbccbcbdacdcccbbdadadbcabbababbdadbadcabaaabadbdbbbcbbdcccdadaacabdabddbbcaaddcdcabdbbaabcbddadbbdcabddbbcabaddcdacddabdadabbcdbcccdbaadabdbbabcbbbaaaaacdcdddbbdaaccdaabcdbddadacdbdcdabccdbacdddddbbdbbadcbcdadbcdbddcdcbddadcaacdbbadcccaaacccacadcbdaadaacddabcabbbbcacddcdcdaddcdcccabbcadadbddadbcadcdcbdccadcbdacaabcbddaaccaccccabbdbbcdbddabaacccbaaddddbdababcadaaabcbdacbbacbdacdabbcdacbddcdabdbcbcadcccabcaaaddddcddacdcccabcbaddadaddbbdbabaccbbaadacdadcbcbcdccabdbabadbcddddbdacdbacadabdcbbadbaddddcccabbdcdadacbdbdaacbdcaccacdabbbdcddcaaabcaabddcdaababcddddddcddacadcdcdcadbcaaabacaccdaddabccadaacaccbadcacadbccddcadbaddddcccacbdaabcaaddcbddacadadadccaadcbcabbdddaabacacacbddbbbcbbcbcddcaddbccdcdbcacdbdbcbdbdbccdcbcaddbcaccadabccaaaacccadddbddbdaaccabaaadbacbdbacdcadbbbcdcbbbdbabbcadbcccdcaabbdddbbaabbdcaaacabdacadbdacaacdbaddbbcaccbbcbaabbadbccdbadbdbadbbcbaabaacaddccdccbabbdbabdbaaddbbcaddbabccacbbcbbccbcdadcdcaaacacadccaaabbdaadbdddaacdcaaddbbdcaaddcbbacdadbcdcababbdddcccabdbdbbbcadbbcdaaacdaaacddabbbccabadaaddacacaabdcadbdbaadddaccdbadadddababdbbbaacadbbbbbacdabaddadcccdbcadcabbacbcabcdaababdabcdaccadacabccbcdadaacbbacaacbdaabbbbaaaaddccbcaaacbcbbaccabbbddcdbbaaaabcbcdbbddacccddaddbaccabaaabdcaddbbbacabaabadbddbdabadcadcdcdadaddaabbbcbabcbacbcaacadccacccdcbcaabdabcbcbcbdabaddcccdbcaaaabdbabbcdbdaaccbdaadddbaacdcbcaadddbcbbabaabdbdaadadcaddbabcdccbbabaabadaabbbbbdacbddccddaddabcbdbddaacdbcbdccdbddbacdaacbccaccdbbdadbaabdbdbccccbacabdcaccdbdcbbabdcaaccddcdcbdcdccbbbcbabaddcacdadbddbabccabadcabababbcdababddbaacbaabacbcabdbcdaccbccdcdcaacdacbcdabbcaacacbdccddbaaaaaacdbdaaaabcbbbcdbcdddbcacbaadcdbaddddbbabddccacdacbcbdbcbaadcdccdcabadbcbacbaaabacbabddcaacbdbdbcbdbbbcbcbdcddbabccbdddbdcbdccabcbbbaacddcabaccdabbbbabadacbbccdbcdcdcdabbdccddabaadddcabdacdddacbdbdbddcbdbaadaaccdddbddcaacbdcdcdcbccbcbadcbbcdbbbddacbabdadbdccbbdbcaccddbddadcabcaadcadaabdabcbdbdccadbdcccacdaacdaacaabadcadcbbadddbccbbbbaacbadababdccbdadcbccbddbbcdddbbaabadcdccddcbcdbcadcaacdbaaccbccddcabdaccddacbdcabdacdacdbddbdbbbdcccdabadaadaaaddaccdddbddbcbdadbcdcdcccbbbcccbbccbcdcaadccaddbbbaaadddaacddbdcdaadacdbababbdcaabaaadcaddbbdabcaaddadbdaacaabbaacbabaabdaacabdbddbacabbbabdcdcddddccaaccacbabbccdbcbdcdacdaadccaddbccdacbdcdabcabddaaaadddccdaccddbbadbadcdccabcdcabdddbcaadacdabdaccccccdcadcddbdbdacbbaacddbaccbcbcacccdcdcbbbabcdaccddbddbdbbcacbbabcdbbbbdbadacdbbacccaabadcdbbcbcdbadddcbdbbaaddcdcdbbaabdddadaddabbcbbbbbcccaddaaadaadadaaddcdbaabbcacbbdbccdcccacacadabddcddcacdaddbdbbdbadccacacdacbcddaaabdcbbbbdccdccbdbbdbadbbbcdcdddcbdbbcccaddadadcbbacbcbddcdabcbbabdbaabadbacccbdcdabacdaacbbccacadcdbdbdaabbacdcabccdaacacdbaaaadabadcbdacacdbaacacdcacaddbbcbddcbdadacbdacbbbcbcdbbcdacbdcbbccabaacddabaccacdadaccdaacaadccaadacadacdaaabdacbbabbcaadcaddbacdbbcdacdbabcdbbbddaacdcaccdcdbdbcacadbabcdbccdcbdbbaaccbcbadbdccabbabcbdbbcdabaddcdcbadbadabcacbddacdaadbbabbddbbaaddbbbdadcadcbdadadabadcbccdcacaadddcaccbaaaadabaccdaadccabbccbabcdbdbbddddcacdadbaabbbcdbdbaadbbaccbcbbcdbdaadaaadbadddddcacdcdcccacaaabcdcddabdccadbadcacacdcbbcacbdaaccaabdbcabbdbdcadadaddcaccadddaddccbaaccbbcdcccbddacbabddabdabadbacabccbadaddccadbacadbabaaacdbdddddacbabbbabdaabcbdccccadbdcaadabaddadbabbdacdbaddaddccccdcdabccbdaaaaddcbcabbdcbbbddacbacadddabbddccbbadbcdcadcbcddadddaaddcdddcbbcbdcbabcdacccbdbbabaadaabacabbacccbaadaccbacdaaacbabbdabcadbaabacbacbbbdbcbdbccdaaacdbcbdaccaadbbdddddccdddcbcabdcbcaadcabdbdaacdcbbdcbdadcdaaababddbaaaacadbbaaacddaadbbababcdccdabaadacbcbcabbabcacdcadcbddbacccadbbcbccccaaaccbbcdcdadccdadbaaaadddddabdbcdbbcdbdccacdbaabbadddddbbdadaacacbdbcacbdbdcacccbbdaabbcabadaaaccdbbcddbdbaacbdacabcddabbddcbbdbabbaadbcdbdbaabdadbbdaaabddccdadcddbbbcbbdccbdcaaabdbcacdcddbaacdabbbbcbaddcccdabbdbdbbbacdaabbcdcddccdcdcaccbcddcbcbbaaaccaacdabdcdbbacdbbbbbbacddbbdddbdcbbbbaacabcdcaccdabaccaccdbdcdbbadbadccdaccabccbdbabcdcdadcdababcaaacdbdcccdaaccaabcacbbbdabaccadbbdabdcccabdcbbddcaabdbabbbcbbadbbbadacdaacdabbdccadddbcbaabccdaabdaadddcdccbdbbbcbcabcdadcbacbaadcbdbadacdbcdabbcaddccadbcbadcdaccaabbaadcccacbdadcaacadcaccddbdbcddbcccababacadcaddcdbdcdabbdbadbbdcbbbaccccbcbbdccbaabdbaddbaccacccbbbadbddbdbccbadbbcabddacdbdbdcdbaccaadaddbdababdacacdadddaacbcdaabaacdbcddaddadcccadbbbddbbbcadbddbcbdbbcbbcbcbcaabbbccdbdbabdcdacdbacdcdbcdbcdcadcbcabdabcbdcbbabbbcacaaacddccbddcdbbbadbcadaaaacdcbdbbbdbcdacabcadbabcacacdddaccddaaabddcaaacbbaacbdcadccccacbdddaadadcdabdadcbcccadcbaababddbdbdacbddbacdccdabbbbcddadcabdaadbdbcbaadcbbdbbdadbaccbadaaacbdcaccdbcdbcddacbbcbdcbbdabbaadacabdbdbcaadabbcabacbbbbcddbdcdabcaadddcacdbadddadccacbdddabadacdbaababbadcaccdbbdddbcadcbdddcbcdbdadabbbdcabddcdcacdadbcacbbdbbaabacaabdddccccdcacaccdbbcbbadbcaabcbaaaaaadaadcabadcadaacaaddabdabccbaaacbbbcaaadaadddaccaddbdddcaadcbacbcddbbdcadcacdacccbcdabdddbbbdacbbabacbbbabbadcaacbbcdbbabbdcdbcbacaddaccccdadbbdbdbdaabcadadcacbabdaddcdbcaccababccadcbaaacaabdddadbcaccddbbaccabccaabacabdbadcbbbdaacdbcbaabddbabcacacabbcdbdbbcdaccdbdabcbbbabaadddadbaddcbbadcdccadcdaabcadacdbddcaaccabbbccdbbcaaabbdcbdcccaadbabaadcadaaaaddabcbddbcbaddccadbbdcadadccabdddaddabaddbbcaaadcdddabcdbbdbdbcbdbccadaabaaabbbbbcbdcdcaaacaabdbacbdaaccccddbccdbacddcbdacbadcccccacbdbaaacadddabdbccbccdbadadbaccbabaabdacbcddaabacacdcdadadbcacdbacabcacbcdbcdbbdddaddbaddaccdaddadcdbddcdcabadddcdccaacdcbdcbdcbcabcbbbcaaabccbdcbaacbdaadaaadadcabcddaddbbdbbbdaacbcabdacacdbdcdaccacccbcbdcbdaaaaddccabbbcdbdabbcbbaccbbbccdcaabccdcddbabbbbaadcbcababcadbaddcccdacbbdcbabbbaacadabdcacdcbaddcdbbbaacaabababcadcccacabaabdabcdabaaccaabbccdccbdccdcbbacacacabbcacbaaacddbbcaddaadcdbbccdbaccbbbaabadcbbaaddbdbdbacddbbbaddabadacddcdbaadaaadabdbbdaaaacddbdcaadddaaccdadcbadddbbbaaabddaddddddddcbbdadcdcabbdabdccabbdccacabdaacbdcadaaacccbbcdbadbbbbadaaadcaccdccbbaaaaccbcdccdccacdbcaccacbdcaaaabdbbabdcbcccbcdccbccdbadababddbcbcbaabadcbdcbcaaddcbcabadbcccbdddcbbbcaddbccdcabdabcdadcbbbcbccadbbcbcaddbaababdbaaaabacbcadbaadabbbcaccbacdbdccbccbccadcdcddacaaccbadbcaacaddddbacacbddcaccabcccbdddabbdbcaccbaadaccaacbdbccdbddcaaadabccccbbbdcabadddbdabcbcacbabacdbabadcabbbaccccadabbcdcdacaaccdadbcbaadadbaacabcadccaccabccbacbabbbcdaabdcdcaabcbacdadddaaacabdadcabdaccadccaddbbdbcaddbcbdbccccaddbcbbdcbdcdacabcdcadbcbaaccdcbcdcbcddcbcccddcaacdaddcdacacdbbcbcbbbdccbcdacbdbdbbdbaaddcccbdcabcbcdbbdaaadcdcbdacccddcbcccbbcbdabdbabcaddddabcbbadbbcdbccbaacddbacbcbadadcacbdaaddababbbabddcaabdcbbaccabdbdbddcacbbdbbdbbadcdccdabcacbddbdaaddbbbbacbdadcadcbcdadadcaabbcaaabacbccdabaddaacadacdadbcaacaddcdcacdabadcdabacbcadcbcaadbcddbacbadcdbbcbdcacdcacccbdaacbdadaccaaaaacaaaadccaacbccdacdabddbbddddbdbddddcbdddcbacdbabddaacbbbabbbccaaabdaddcdabacbadabdbabaaadbbdaddccdcacdcbdbaacdaddbcdccbaadbcbdcaabbbbcdbcddaadcbcaddadccadddcbbaacdcaacdcaacddbdcccccdadbdbdbdcdacbbababbcabcccdbdadbbbcadacbdbbaccbdbccccdbbbdbbcdaacbdacadabcdcbadbbccdabbcadacdbdbabbacbddacdcbcaddadcddbccddbbababcdbaddaaacdcccddcadbddddacaabcddcabbbdcdcdbdadbbbcddcbcbcbcacabbdbbdcaacddabbcbcdacabcababbdddacbabacbdcdbbababacccbadbababbbdcccaababbbcacbdaddaccdccdaacbcababdabccbcabdccdaccbbbdbcacaddddbcabdadacdbccbbabbcdcbdddccddcaddacccdcbdbabdbabdadbbbddabdcaadcadadbcdadcdbdcbbadbbccbcbabcacdabcdbbacdbdcacacaadccccddadccaacddcabcdadaabdacbacccabbccdbbaaabcabdacdbdcdabbdbdccdbcbbdbabdacbadbacbcbbcaabbcdbdbbdcadddaadbaccddcbadbadddaabbaaabdcbbcaacddcbbbabbdcdbbcdbbbcadbbcbacdccddbaacdcabdacdacdadbbabbbcacdcbcddddbbbdbbadcddabbaadabcacaadbccccbccbcddaaabddacbbddaaddddbcdabdcabbddaaccddabbdcddddcbbadcbccaaaaabbcbabadbabaaaaaccaabddbddbccabccdadcbbcbcdaddaddbbacddbbcbbdadddcbdaddaaaacdcbcddcddbdddaaadabcbcadbccddbaccbcbdcdbdadadaabaacdacbbaaacbcbbdcdadadbbbaccddacdaadacbcccdcacdddcadbcbabaddddcabccdbcababadcbadcabacbbdcbaddabdadbdddbcbbcbcccadbcbddcbabdaddddbdacbcaacbbaddccbdaddbbdadbcdabcaacaadcdddadaadcadcddcacbbbdbabcbcccdddacbddbadacabdabbbcbacccdbadbcdabdacdacbbdcbddabbddbadccabbdbccabddcbadddbccadbacabaaaddabdcbababccacbbcadcaacbdcccacbbaddbcaacdcadbddbaacdcbcbcbbcbbddccadadcdbdbaadddddbccbcbcccbcabcdbadcdbcdaadbcbcadcdcbbddbdcdbdaacdcdddddccbadadbcbaaccdbbadcacdbdcdcbcbddaccaaadaaaddaccbcaadbddddcddabbcdddaacccdabbccccdaacabddcdacdddabaacdcbcddcaaadddcabaabdaccbbcccdddaabdaaccacdaadacaccbdabdaddcbcccbdbdbadacacbdaabadbdbbdddbacccabaccdddbbabaadbababdddcdddadbcddbadabadbbcdbdaddcddccaabadccadaaddccddbbbabaaddabaadbbcbbbbaabbbbbbbadccbaadaababcddbccdddbbbcadadadaddcbbccabbadabcbaabddcbccbbaaabbbcbdbddacaadabdcababdcddbabddcaababadaccbabdddbbabdcddaabdaccbdcbbcdadcacdccddbbaaabcbccdadabbbacdbdaacaacadddadbcaddbbdaabcadcdadccbdaccacaaabdbbadcccaadbdcaddcbaddbbbcbabacbbcabaddbcdcdddcbbabdadbaaaadcdddcabcbabaacddcbbbddbcdbaaadbbbaccddaadbbbbbbccbdcdaddccccacbcdbbbabcacbacbcadcaadcbcadaadcabddbcbdbcdcadbbbdbabaaddcbcccddcdcbcbbdcadddcbccbbcbbadbaaaaccbdabaabaaddbdbbcdbdcbacdadaddccdacddddabbdaaaacddabbadbcbbabaacabdddccadcabacadacbbbacbacabbbdbaaaccaaaadcacbaaccdacaababbbbddcdadbbcddabcacdbdacbcadaddbcdabdabcadbbdbdadddabbdbccccdcddddbbadcaacbcacadbbcbcbbadbbdcacaabdbcdcccbbdabddacabaacbcbbdddabcddccacbacddacbcbadaacccbcdbbabdbdabcdacddabcadccbacccccacacdcddbaabacdcbddcdbcdaaaaabdbbcdabdbbdbddbcaddcbddddbabddaaddccbddbccabcdaaaacddacbbadadcbadcdadbbbbadcddccbacdbcdccbababdcaadadddadbaaddaadaddbdaabaccbabccdabbaadccaccbcbaaadabbadcaadaddbbadddabcbbcdababccdddbacdbcccccdccbcccdabbdbdccaababadddcddcabbabbadbadbccbbbaccaddaabddddacbbacbcdcddaaaadcaabddcbbddcdabaabdcabbccccdbdbbdbcabbbaddddacdddabdbcbddaccddaabbdddbbcbdababdbadaadabdbadabcadcbccaabbadadcbdcdccccdbcccabcadadbdbbcdacbcabbdccbcccaacdcbcbdcccccabdcddccdaddbcaccccdacddccdbbbadbacaababadccbbbaacbdbddabdaaacbdacdabddcbdddcdabcaaaddcdacdbbbbccdacdaaacaabcaaccdccdcbcdabcacaacdcaaabdaacbaacabcbacbdcaddaaccdaddbcadddbaddaddadddbaabbabdaaabadbcabcabaccbbdbaadaccbcdacaadbcbbadadbdddbdcdcaaabcbdcdbbdbccdbbadccdadaadcdbbcdadbccbacdbbccbcccdadcdcbbcdacbcadaddbcdcdbcdcbbacdababadcbdddccdcdcddcbdbadbacabccdbbbcdccdaaddccddbcaaddabbbcadbaadcccbbddacddacbccccacbaaddccdcbcbdadccabcbacadbcbcadaaabdbabdbcdabdaddbdcdacbdbbddccabbadccdcbdbababbaabbbbadaddcccabbacdcbdabbbbbcdbacdcaddacadcdbbbbdaaacbadacbcbacbcdbcccadcdbbdbcabcccaadbddacdccdadaabcdddbccdcdddbbcdbdcbdacabbcbcbabbabacdacddaacbccbddaddcccabacaddcbcbdbbcadddccdbbdacbbdcccbddaddcbcdddcccdbbadbdbcccaccbabbcdddacbbacddccaabadabdbdcbcddbbadcddcdabcbcdbdaadacccadadacdcaddccddbbdcbcdcacadaadcbdbaddbaadaaddddcacbcdabdbdabbabcabacddabbdcaddbbacddbadabacaccdccddddacadcbaacdbccddddbddabbdbacadadccdbccacdcabbbadabbcbaacdcbdccdccdddacbabdcddabacdaabddbbdaacadabcadaaabddccacbaabcaabadbaabbacccabbabbcabdbbddddbadabaabbdbcbaadadabbcbdcadbddabbadbdbadbcdbccadbccbcbcbddcccbabccbadccdaabdccdbddcacdbcabbdcacbadcccccaddcccaddbcdcccdccacddbbbbbaaccadbbdaabdbcacccddcccacbcccbbddcabdcaacdacccacbdccadbdbdddbdbadbaccababcadbcaadddbdaacdcccadcbadcbdccabdbccabbdbcaacbbbacdccbcbddddadcbbcaadacbadbbbcabdbdcbbabbcbdbabaadcbdabcaabbdbabaabcdbccabcacadbaacdacabccccbbdadccbadabadcdaaadccdddbdcacaabdbbabcdccbcdbbacbaddccdadbdcadbabadbccddbdbcdaacacbcadbbdbcdcdadadabdccbbddcacacacccbbbdccbddcadcdbadaadccdbccabbbccaaaadbcccaabdadacadcdddddbdabdabcbcaaccdadbdbabcbcdadccbbadcabbbcdbbbdadbdccdbdacadcccddcdabdacaabddbbccadccacdacdcadcbcdccbdababddaadabcabaabdbcbcbccbdbbdccacccdcdacdcddccadbcccbbccbbbbdcabcbaacdddccdb