ddddbcdadbbcbaacdcdadabddacbadbddaddcdbccacadbdbdaadbbbaccbabdabdacbbbcbddcabdadabaabbacacbbaabcdadbbcdddddddcbddbccabcadbcccdddbbcdddaabdbbadcacbccbdcdbcaaabdcdadbbbdabdbbabaadbddaabbcbabdbcbcdbdadcdabdcabbdcababbcdacaabccdbbbdadddabdddbddaaadbcacdbbacadcddbdcdccbdccbcabacacaabdddbacbaccddabcbacaaacdcdcbbbdcadaadbaccaabccddcdbbcbbcdcdcbddaccacbbddcbadccaccaaccdccdbbbdadccccbdbdadbcddbcbcadbddaabaabcdddbaddcabbbcbbadadbadddcaddabcabdaacacadbccaddcaddaadcacacdbcacabaadbcadbbaaabdcbabadbabbdcacbdaddbcdbcdadbcdbaacdbbaacbccbbaacaacdbabcbdbaccbcdabcbbadbcbdabddcbdcccbccdbcddabcccdbbcacabdbddcaadcadccddbbbdbaaacddccabdddcbdcbbccbdcbcccdcadccbbdddabccadddacdccacddbbbdbdadcadbcdbbcbadbabbdbadabbdcbadbadcbcbccdbbddcbddddaddccdccaabaaddbdcababaabbddabadccbbdddccaccdcbdbdbdadbcdcbdddddbdbcbbddcadcdaddabbcbcabbcaaadccbbbabdcbddabaacccaccaacaadbdbbdccabdadddddabaaccddddacaadcbacadbaabdbbaaaabbcdcbbbbddcdacdcacabddabbcbdbaabcdcaaacabacacbabbdaaadadaaabbdcdaccccababbbaaaadbcdcbdacbabddbdcccdadbcacbbadbbbddacbbcdccbcabcabbabbdacccbdaaaddacbabdcaabccdbddbbbbcacbcccdddccddbbdcdccbbcccabbdacccacccbaaccdbcacadadddddccadddaaabacdccdbadaadbdbccccdcbdadcadaaddbbdcccbcbbbdbbabddcbacadcbaddccbddabbccddbaacadddcbbbccbacddbbdaabbabacbacacbabcbbadccdddccaabdbbbbcdccaccbbbbaccadcdbbbcbadbdabcbbcdbabcdddcbdaddabdbdbccacddbbbaacdabddccbbcabadccaaaadcdbcaccbddccbdacbdcddacccdacdbadbbddcbabdadabdbddbdabbdcdbbbbbbcbbbaccbabdbbdaddaaccbcdbddcabccacdadcccbaabcdcaaadbbcdcbbbcccbabbcaaaccadadbdacbccbdcdcadacbbcdbbbcdbaddbbdcacdbcdcdcdcaadccacbcacbabdabcbadbcadcdaccdcbdacbabbcbacadccabdabdbdddbbbcdddbabdaddcddcadcbccabdcdaccccdbdababccdcabdbcbbdcdbdbccadcacaaaaddcaaaabdbddaacccccdbbbcbcccdcbacddadbabdbacbddbbcbaaadcdadcbbcdcdccadbcacaacbbcccccbaddbbccbbadaadbdcaaacaabdcbaabdbcdcabbaabaddacdacaabcaddbdaacddadaaaddbbcdbdbbcaddaacccbdcccccadbdabdabdbabdadddaacbacabdddcdddacdcababccacdbbddbbaadbbbcbadbaaddbcdbcbcbcdbcbccdcaabbcbabcccbaddbccbccbbdcbbcdbadabcdaadbacdbadcacacdbbbbdbbbcbdcdbabbadcadbdbccacdccabdadbaabdbbbabddddaddaaaccdcdcdbaadbbdadbbbcbcbcbaaaaaccabdbccaaabdbddaacabadcbccdddbcbbcadadacbdadbcbcbdaaabdbbdddbdabccdbcabddbababcaddcbacdaaccdadbcdcabaaaacadbbddacdddddddcacaacaddcabbcccddacdcdbdaadabdcadbcaaaababcbacbbddabcdbdbcadbdbabaabbcaddaadabccacccdbcbdbddbcdabbbaadaacaacbdbdcadbabababadaddabbaacaabbcadcabddcccdddcabcbbddadbacaacbcabcdacdddaadadcbaddacbadbaccadadadbbddddabadddbcaabdcbbcbacaacbbbabadcabaabdccabaddddcddbaabbcbdcddcabdbacdbbdbabbcdacbabcdbccbddccbcdcdbddccaaaadabdacbdabbcccadddcddccdabbdadadadcdcdabdddacaabcabcacccdddacdcbbabdbdcccdbcdddadabacdacbcdacabadabbbdbdddddacccdbdacdbcdbcdbadcbaccbbcaabbcdcbbbdaabbcdccdddbbacdaccdcbccdaaabdbdaccaccdcbddbdbdbdbdcbcbdddddcddccabbdcccaabaadbcdacaddddbbabadcddbdbacdcbcabbcacadbbdbaccdaabbaabbabacbbcccdbcbcbcbaacacddaadacbabdcdaabccaddacbdbdccccccbcddbadcdbbacbbcbdaadcaccdaaababccccbaadbdbaabdaddbacdacaddaadccbdaccdcabbddababbdbccaaddaaddcbdcdcbbcbccbdabbcaadacbaadbacabdbbaccabcdcdabaacdcdcbabbdbabdadaacbcbdcddacddaaddabddbadaddbcdaabbbacdcbddabddacabdbadcbbcccddadaaccadacdbaadcdbbacacbcacbbbabaadaacbbcbddadcdddbabbddaacbacddcccdcabddcabcaadbdbcdcdcbabcbacbaaabdbbdabacdccccddbdbacbabcaddadbccccadcadbdbbbaabdbbcabcccccbdcdcdccacaaddcadabbcccaccdddaababbccbcddbcbcddbbdaaabcbdbcbccadaadbdaacbcaaaaaaccacbdccdbbaddbabcdaccccddaadcccaccacdacdcdbbcbccbdcbccddbcbbdbcdcddaddaaccdcccccabadacabcabdbdbbcaacdacbddcdccdbaccdccaacdcccbccddbadddcbddcbcacbcbbabccadadcbccaaaccbacacbaddaacddabdbabacccbacdbbbcccbcddcccacbacdaacdbcabcacbcdbbccdaadabaccabdcbdccaaaadcaccbddaddadbbabacbdabcacabcbaabacaddcccabbdcdddadacbbcddbcbadaadbbbbcaaacccccbddabbdcbcacadbabcacbdacdcdaabcdbbcbbaacbbcadccabbdbbadcccddabadacccbdaadbabdddbdccbdabcddbdddaacdcdccbdbadddaccbbbdbbdabacbddacaccacbcaabaccbbacababadbdacdcdabcdaabcabbbdbaadaaaabcbbccccccbbcbacbcbcdcabbdcbabdcdddcccbcadadddabdddcdbbdcbabaaadbbdacaccbdaabccddcdbaabccddaaccdbbcddbcbccbacbdadbaadaddadcadcaabccdcbccbabcbcadacaaaccccbcaccdaaddcaadbbdaccbadcacbbdcdabacdcdabcbdacddbdadbaaaacabbdcbbdbbacdbcbadddabcacdbdbaddbbcccacbacbcaabadcaccaddbbabccdbdcdbdbacdcccbcaaacaddbadbdaaacdcccaadbccddcdcdbdcbbcababccbdcabbbcadcacabbdcadcdabcbcdbdcbdbbbdcaccacbdbddbabcdbadcacabcadcdbddcaadadbcddbdadddcacbbabbcdbacdcbacbcabdbbcaabaddcdaaabdadabdccddcccdbbbbcddcdccddadcbccbcaaadcdccbcbcbdcbbacbcdbbdabcddcbdccbbacddbcbdcdbdbbabbaadccaccccbaaabbddacbcabacadbabdbdbadcbbabbbbbacbdcbbdcbdcabbddbccccbddbcddbdbcdcdcadbadbcababbbadbbcabdaddacddcdcdbabbabcbacccacaabdddadbaabcabcacbbcdbcaadbbbdacbbbbcabbbacabcabaaacdaaaaacccabacbcdcbbaabccccdcccbbcdcadabdcdcadcbdddabbddddabbddcabcbdadcbcbbddacdacbdddbbccacadcbcaccddcdbadbdbcadcadcdaaddddabcddbaddacabdcddbdbcbaaaabcdacadbaaddbdbabccccdaaaddababbbdcdacccddabdacbcaacaaacbcaaadbcbcdaccbcaaddcbbcbbadddcababddccbacddddbccacddaaccdbbbccddaaaddccdabccdbbaacdaccabdbbddbcbcbbdbbddadbcbcacbbcdcbdbcacaaaccaaddccbdabdcddabdccbdaaacaadbbacbdcdbdddadbbbabcbadcdcbacbabcdbbddbbdbbccacabcbcdccadacbaccdadcddcacbcddcbabacbadccadbdaadbcdbddbcccbadaacbacbcccbcbabbbbdbdbaadddadbbacddadbbdbbaccaaaabcdaccbcbbcddacddcbbabaccabdccdbaabacabbabdcdababaaccadccaadcdbadacacdaaabaabaddccabdbcbccddccddcbbccaccdbdcccacaaadadbdbdbccdacabdbbdcacadcaacbbbbdccaabddccbcadabadcacadcccbdbadbabddadbdbbcdadacdabdaabaaccacbcbcadbcbcacaccacbaabacabbddbdbccdaccddbbacabcacaacdcabcaccabbbadabbddcbbaabcacdbbcccdadcdacddacabbbacacaacdcadccbdbbdbcbacbadbdaaaabddccaddadcddcadddcddcccadacbbbaccdcaddbcbdcbcdadbbabccbbbbcadcbcaaabaaabdbbcdddbbcadabddcbcaddcbbaddbcacbcdaacadcbcbadabccbdaaacaabaaccdcbcbadbcacaddcdadbdcdbcdabbabbcdaacabaddcbbbdabcdbcabbbcbbccbbcaadcbaaddacaccacabbcddbadbccbdddadacdcbcbaacacddadccdacbbadbaadcddccbaabdaddddddbdabccbcbcddcdbdbdbbbaacbadabdccdadadabddacadddddcaccdcacdcadaadbcadbabddbbadbbcdcbdcdcabbbaabdcaccddcbbabacbcaabdbabdbaaacdcaacbacccddacbdbbccdcccacccacbdadadccadaddacaacbabcbbacaadcccaabbbdcbbadadacadbcdcdaabbbdadaadbbcabbbabadcccbdacbaccaacabcddabccdbcababddbacdbcaccabdadbcbaabdaabdaacdddcdddcbabbaabcacddaccccababaaabaccaacdcabbcddbcaacdcababaadbbbacbdbbabaaabcbaabdcbaabbadbaacabccbddbcaddaacaccadbbdbcbcaabccabdbdbcaaaccacbbabdaacdaacdababbdcaccdcadbcbabcbbabcbdccabaccbbaabdacccddccbcadccccaabbbcddcdcbddbabaaabbdbcdddbdaaddcbcdabdccacbcdadcccdadabaaaaccbbbdacdcdcdbaaaacbcdaadcdadbcbcaababbadadcbdcddacddcdadabddbaaababbdcaaabcabdbbdcaccbbdccabcbcdbddcadacadacadbcbadddabcdaabdbdcacdcaaaaddbbcddaaddddbdbdbcaaaacddcbadbcadadbadccaccacbaadcdddbdadbcbcadddbcabcacccddbdccdacdcbbacdcaadcadbaababbadbbbdcbadbadbccdaaabbdadcdddabcccbbdcbbbddccaabcddbdacddacbaaaaccbaacbdacdbddabbbcabacdcabcdbcaddcdbcdacdccbcdcaabadccccccbbabccdacbbdaaacdbcadbadbbdcdaaadddddcdcddaddbabcdbbaacdcabdaaabdcacdcbcbcbccddbbbdacdbccbdabcaaccbbbccddabddddaaabaadcccdbabaccdaabcaacaddabcacbdaadcacdabcdddcadddbcccadbcbbaaabaaabbdbddcbdaacdaacbababbccbabbdabbdaaadcaacabbdbacdbddcbdcddccbccbcaccabcadabaabdcbadacddaaacdaddaaaccddccadbcaacddcaabdacabaabbccbbbcdaabcadcadddcdccdcaacbcdddabbbdabbcadcabdaaddadccadadbcdcccbbaacbccadaddbddaddcdccacdcbabdbadaabdcabdaaabcdbdaccaaadcaacdcaaccbcbcdbaabbdbbbdddabdaabbdcaabbbdaabbcabbdbcbcddddbdddbbadcbaacddcdcbaadcddbccbbddacbacdcbccbccaccbdcbcaabbbcbabacbabdbadbccdbacbcbdcaabddddcdabccacddcdadcaaaccdcdcdbcacbbbbcdcdddddcacbbbaaaacbcbcbaddcbcababccaabbaaababcbdaaadcaababcaaddcdbdbaccbccbadbddddadcbcabcdacabddbcbccdaabdccabdaaacaddbbbaaaddbabbdcdcddabbccddcbccdbcddbcabcddadddddabcbdbcdbdbdbadbdadacadacdcbbdbabaadadaabadacaadaaabbaadbdbbbcbaabbccdddacacaaadcccbdcbabddbcbabdcbbbbccbcdacbdcaddbbdcbdddbcdbcadcdcdddbcdaadbbabcccdbbcbdacaaacbadcbcdcbadadcdcaaabbbbbcdbbaaaacdadbacacbdaccacaccbddcdcaacbdddddccbcbbabbbccaaccbddbaccabaabcdaacbbcaccbbbdabdbdcdcaaddbddcacaddabaadcbbccbcbdbbdbabdcbbbdaacaaaccbcddabdcbddcaddbdacabadcbdcddbaaaccbbdaddcbdbadbdbaadaaddcbdccdcbbcbcabaabdadbdadbdbbdadabbbbbcddddadcadbdcddddbbddbccacbddbdddcbadccbbdacabccddbcbdbbabdcccbabadccbdbabddaddaddbabbdbbcaacababaddbdadbccbabdaadbcdacbcadcacdbbabcdbbdddbcabdadccdbcdcacabddcaaabddacabbdaddccbdbbdbadadcbbbadabbdbdbdbdccaaabccddacbbaccbabcbaaaabacabcabaaadbdaacadcbbbbcbcddcdcdcaaccdbaccaaabcbccabbbdbdccaabddadbcabbccdcdbdaccdaccdddadbcdbdddababddddabacbadbdddabcbcbacacdccddbbabddaabbdabbbabdbbdbaccaddbdcbcdacdbcdcacbcabaabdaabbcabbdcbbdccddbdddbdaabdbdcbcabacbbccbbacaadcbcccaacbddddccdbdaccacdabbaddddcddcbbcbdcdacbbbdacbdbcdddcbddaabbdbaddcbcbadcababaabbbcdbdcbcbbbbdacbdcbccdccdccbbddbadabacaddcdcaaacdcbbbbabdddbabddbddaababadccacbcbcbbabdddaddaabbdaddabaddcadcaaacdacdaccdcbdddadccaaacbabcdddbbcacdddbbaaddacdadddaddccbbabcacababcdcbdadcacdddacabbddcdcdcacadaabccaaccabbbbcadbdbaabddcccddbdbbdbadacacdbcabbddbddcdcdddddaccaaaddcbbcccdadcddabadbddbdaabdcdbcdabddcdddbbbdbcbbacbcdbacbdaccabababddcdbccbaaadadaabbacaabbdbbbabdacbcdaaccaacacdcaacbcabbbccaacdacccdcdcbdcadbbbddabddaddcddcdddbbccbaccddadbcaaabcbbadbacccadccccbcdcabddadccbabdabaaabacddcdcabdcbddcacdcdbcadbbabaddadaacaddacbddcdaadbdacddcbcdccbddaacbbabbdaacdadbbbacbdbdacccdcddddddcaccddbbddaaaccbddcbbcdccbdbaababacaabdbdbaacbdbacddaaacaddbacdbdabccdccccdababaaabcbacbabbccabcdaaaaabccbadacaaaccdadaadbaacccadacacdcbcabcbaacdccccddbbdbddccadbaaaadbcacdddccbdabbddaddcddbdcbccccdbadabdbadbddbddaadddcbccdcdcaaadccaddddccddbbbbbacaabdabbddabcdbddabbbbacbbddcdccbdcaababdaadcbdaddbdbaaaabbbcdbbddcdacdbdbcaccadbadabccbccadabbabaacdcdbacbdbaadacdccdcccacccdddddbdcdcaaabaacbadbddaadcbdadccdddbcadbcdcadddcddccbbccaaddaabcdcdcbbcdbacacbbccadaccbbdabbcdaacbcdcddcdbcccdaaddccccbdccacddcaaabdcccbbccccaccddaababadddbaaadcdcabaaadadbabccbbbacdbbacacbbacbcdbcaccbadadaadbccdddcaacaaaaadcbcccbbabcbaadcddabdbbabcabbdbdabcdcdaabddabbcbbbccbbaabdbbadadccabaccccbcbddbbdabbbabcbbdcddaadcdabbaddcccdbacdaaabbbcbbbaadddcaccbbcdcccbcdbdaddabbcdbbdccdcabacaadcaadbbbcabcdbacbbcbdccaaacadbaaabccdaadcbcbaaaaacdacdbcccddabdbdacbcbcdadbbddabbcabccbdbadcadbdaaadbddaddcabdbbbcaacbdabdbcadcbaddcbdbdddcccbdcdcadccdadccbccabacdabdbcdcdbccaabcdcdcaaacdcbcbbccadbbadaccbbdcabbaaadabbabbcbaddbcddadcabadcbccdacacabcadbddcdbcaddcddabcdbcdbccbaaabddacabcbcbdddabccdacbabbcbdbbdbdbcbadbbbbcbbbdbcdbabcbaddaddcbdbbcacadacacccdbabbddcdcbdcbbbccdbcadaadcccbdbcacdbdaadacbdbaabcccabbdabccaaaaccddcbadcaaccbbbabcdcaadbbdddabddcaadcbdccaddcacbddbddbbbcadccddbccdccadddadbabcabadcaddcccbacbadddaccabccbbbabaddaabdabaacdadabacdadbadacaaacaabababacdbccbcaabcacbaacacbabcbaaaabcbddbcbbabdbccdadacabccdacdacadaacdbbadadcacbdbddcccddbdaccabbadbccdcdbcdaabbdddccadbddcdaaccbcdbcbcaddcdcddbbbcaabaabbcdadadcdaadabcdcaabcbdacdcbbddaacdcdabbabdbbccadabccccaddaabaadbdcadcdaddaabdacccadcadacadbdbcdacbdabddbccabcddbbcaaccbdbbbddbdbcddcdcdabaddbabddcabbcbaababdabddddcdbaaabdddbabcbaabcaddbcabdddcbccddadbbadabcbcdcddbbbcdbaacbababacdbdbdacbddccdcdbbadaabdbbbbdbaddbaadccddcdbbadddcbcabdaddabdcaabdabddabccbcdccabbcaacbadbbbacccbdadddbdabaccacbabbbcadbcadbdbcddcbabacccaaadaddbdbbccdabbabcdccdadbbbcbadbbdbbdacadbccccddbbadcacabadbbbabdcbaabddabcccdcddcdcbcadadbbcbbbaccdccbdbdcdddbbbdcaadadaddcddadabdccabacbdbadcddabaacbaacbbaddcdcacadddddabbaabababdaabcbbaacddcaaabccdaaaadccdcadcaaddababccabdcbcbabbddddaacababbacbbaacadabaacbdddacdbadbabacacabbdcccbbbdcbcaaddcbcaaabaddbdadabcbadaacdacaacbbddaacdddacdadadbddaaabcadaabdaddbcccabdbdddaabadbccdabbcbdccbaccdbaaccbacdabcadddacdbadaabacbabcbddddbabdacdcccaacaaccaaccacdabdacbbdddbcabbdbdccdbaaacdaacaddbacacaacabaabbaaccaaacacccdbacdcccaadcbbdcdcdcbdaaccddacbcaddacbbcadabcdddaabaccdbbaacddddbdbaddabbcbbbdcacbacbbddacacacadbadbcbddbbacaadadbcccbbbadccaaddcaacbddbaccbdabbbbbaabbccacbabaadcccdaabdaccaccdcbccbdddddddcccbdbdacdbdcdacccddbbccbdbbaddcbdbccabcacababcbabadadcbaaabdaaadaacaacdabcbabcbdccdbddabbaadacaaabcbdadaccbccccbaaaabbdababcbcdcdabcddcaddbbddccccabbccdbccadccbcbdbdadbdcdbbcbaadbcdcdcbbbcadcabcdbdbdbbbdbdabdbabdcaccbdccccaaabadddbbbbbccabbbcadadccadaaccaddabdaadacdadddcddbbddbcaddabbccbacaadbbdbdabdcbdaadbaadaacbbbaaacbacbcaddabbcabdbbcacdadcadbddbcbccbacadbadcbdadcbadcdcacacabddacddbbddccbcccaaaabaaccdbacbbbdbccbccbaacadcaccbddcbcdadddbbabadabbbdbbbabccdabcbadcbdacabbdacdccacdacdbcabbcbcdaadcdcaccbcacdcdadbdbbcaadbdccabacbccdccdbbbbaacddcbcccacbddbdbabdcdbbacbbbabccaadddcdaccddbdabdaaadaccabdcbcdcadacdddcbacccadcdbcbbabbbabdabddaaabaaddadcaccbabccbddbbdbbbcabddadbdadcbaaccbcacacbbbbdbbbccacabadaacabdacadbbcacddacdddcbddcdcdccaacdaddbdcacabbaabccdadccaabbababcbadcbdacacbacbcddcbbddbabcdcadbaddbaacddabaddbbbdaadbacacbddabcdbbaadaccbbdabadddcdcdccddabdcbbbbcadcbcadbccdacadbdaacbbbcacccbdabdbcbdcbabdbbbcacbaacddcbcaacbbbbacacacddaaabbdbddccbadbcabbcbdcaaccbbdbcbabacbabdcbccdddcaaabcccbcbccaadccabaccbcbddadabaccccbaadaaaabdbbbdadcabadbacaaadbacbaaaccdaabdcabcccbacacbcbbdabbbababdcbbccdcbadbbdcdbdcadbbabccaddabddbcdadabccabcbaacbdcdaabcbdacdbdcdadaabddadacabccacacdcdacccabaaabbaadcaccbadbcaacbcbaddbdddbbbdccbcbbdcbadccacbadcbcdbbccdaabbbddaddccadddbcdbaacadbacacbbbbdbddcaabcccdcbdbacbbccbbaabdadcabaddbcbbbadddadbbdabaabddcbbdbadbaaadcccbbcaacddaabddcccdabcdcaaddbcccccdacbaabdbbabddcbabcacdcbcddcbbdaacbaabbddbddabcccdaaabacdaaddacbabcaaacdabddccaaaaddccbddbaadcdbdbcbaadcaccbabbadbccaddbddccbdacabacabcacabccaacbdcabaadcccdcadbaaabcacadbccbbabbacdddbdabbbddacbdabbaadacbdcbdccaaabbbbbdcdbdabdcdbababbdccddbdddcbdaaddbbcaadabddabdadabbadbbabcccbcdcbbcccdcabcdcddbacdcccbacabdcbddddaadabbcabccaacddddadcccbbbcccacacdabddcdbacadaccbdbcdbadacbcdccbbdcbabaccddbabbdddddcdbbbbacbbadabddacadbbaabaadadadbcacdccabccccbbcddddabdadcdcdcdbddacaccaacdbbbcbdbaccbaabacddadddacdcbddadcbcaaacaadccadbdcacbcddbababcdbcaccaadaadddbcdbbbbbbabbbcdddaccdabbadabdcccddaddcdcccddbbbcdbbdbdcdabdcdcbcdddbcddbccdbcbdabaadbbccabdcdccdcdcabbbacaccaacaacbdacdcaaccccdbcaddabcdddcabcdabcacdbbcbcadddabbabcddbacdcacadadbacbccacbcbcdddbddccacacadaddbbdabaacacdcbdbddddcdcaaddaabbbacbccccdaadbddcdbabcccabcdcadcdcdcccbdccdccbadbadaabdcbbcddcccbbcbbbacbdddabdddbaadaadaadddcadaabacbcdabddaddbdacccbacbdbdbdaabcbcccbcaabbddbbbdbadbabdbdcbcdcbbdccbcaababbccccbddddcddddbdbdbbdadbdcdbdbcbcbcacccdcddddbaacabccaabbaccbdbcbcbdccabddadbcadabcaadcabaabcbccddddccbaadcababbcbdabadcdccccdcacddcbbddacbadbaaaccbaadbcacadddacdaaacaaabdaaccaadcdabcacbcbdaccccbacdababbcbacbacadbcdcadbdcdbabaaacacddbdadddcdccbbbdbbcacdbdabbdbdcccaccddcdcbccdbdcdaccddbbdcddacdbdbddbccdbdddbcabccadaddcaacbbbaaaaacbbababccddcdbcaaadcdbbdbabccadcbcdcaddabbbabdcbbdccbdababdbdbdabdcdccadaabbccccaabcaaccaabbaaadcacccbcdcabbdccdadbbabbbaabaccdabdcdacbcdccccbddbbdacabaaddadaddddccdccadbcabcabbbacbcdbbdababdbccbabbbccacbcdadcdcaddccaaacbccdacddbcbadaccaccdcadcdabdcabddcbabcacacacbbcdabbaadcdaacdcdddbacbdadabcdbdabdbaddbddcccbdaacdbdddabdaaadddabcbdccadacaaaaddcbcabcaabaacbcabadbdadaadcaabddcccbbdcaaddabbcabcccaccdcbdaadacbabdbbccaadcababbbccadaabddddbcbbaabccccaadbaabccbddaacaaadaddbaccaabdadbaaadbddacabbdcabdabbcddbdbacccacaadbadbcdcbdcaaadccabaacdbdbabaaadcccccbdaabdbccdcabccdcadbccadadbaccbbbaaaacadadbabccabddddbccdbdddbddbabbccbadbdcacbbcaabaccdaacabdaccbabdddaabdcdbbadacabdcaaccabaabacbbbddacbdabdbbaaabdddcadaabcddaaabbbbccbabccccbadcccabaacdcbcddcbdacdbdadaaabdbbdbddcdadccddaddbcdcaacdacdccddaddbcddacdaaddbaaccddbdaabccaccbadbccbbabaccdcbcdbaabaacbbbacccabcdbcaacabbabbdbaabdcbbaababdccbadbdcdcbbbbdcdcadbacdbbccdccbbddbcdaccdcdcbddddbcdcbbaaabadddcbcbdbbcbcbdbbaddacccadbccabbcbbadddbcddbabacbddccadabdbdbcbbaccbbacdcaaacbcabcabdabaaadadbcddaddbbdbbadbcadbdbcdadcccdbdccdcaadacbacbccddabcacacacdbdbbadaaccdadaaaaddaacacccbabacbcdaadbcdccaadcbaddbbdccbaaabaaadcccdbcadbdccddbcaadadcadbbbcdcbcacddbaccadbbdcbbdbdbcdbbbcbbbabaacabbbbacdddcdaacdcaabcabdaaddbbcdbabddbddcacbacbacbdbbdcacabbdcaddccdacdbbdabbcdadcdcddbdbbccbcccbaabcbbddaccdcdaacacaabcdbbaacbbdbbacbbdacbbdabdcacccbdbadaabbcdddcdbaadbcdcadbababddacabccdcbadbcdcddbdbaaddcaabbdbcbacdbcacddddacbdbbbdacabadddddbaadaaabddaacbadaacacaabddaaddacbbabdacbaabaadddadbcdddadbdcaaddbcdcaccabacddccbcdcccbcdacdddbdbdbbabbcddababbbbbbccdddbabadaadbdcdacabababdabcbdcbbcddbddddbbdaddcbcccaabbbaaaacdcbbcbbcdabdbdcdbdbabcabdadcadacdccdbbdbddcacaaaacaadadcbdacdbaacbdbbdcabaaadcdbababbccababdddbbcdbbddcadacdcdaaadcacdaadbbbbddcdcacbcaccdaabdcadbdacaaddcacbcdbcacdcbcacdabbddbdbdccaacbdacbcbdbcdbcaadadccababbacbaabdbcdacbcbdbdadabbbbcdbbccddcdddddbbdbaadabbdddcacdcabbdbbcbbbbdcadddbaaadabccacaabbccdcddbcbddaacaddccbbddcabdabadddbbddcdccdbacabbbdddcacbbdcdcddbddcaacaccdbdddccddaadcabbbcddabacaaaddaaabbacabbacbbcdbddbaabaabbccdaaacbadcdacabcbbccaaadbbbdaabcdcadbbdcaacddcaccbcddadbacadbababccacbdcbcdbccddbcadaabaacdcaddcdaaacadcdbcbcdcaacabdaacdccbbabacbccbacbdbccaadbbabacdbdbcbcabcbadacbacdcaccacaddcaadabdaddccdbacbbdadabdabcbbcaacbaddaacddacbdcccaaabcdddcddbdbdaddcdbaddcbcacdbccddbbddbbdabdddabbdbcabbacdcacbabbddbddbddbdbddbdcbabdaacbacbcddaacccbaacadaadbdbdbccadadcacabbdacddccbdadbadcbbbcacaabcdacbcaddddabbbdbcdabcbbadccadcdccccdaaadcacadadbccaddbbcbacdbaddabdddcccdbcbcaacddaddcbacacabdddcbadabcdaaabcbcdadbdabaaabbcddbccbbccbdbdaacdbaccacbddbdbbcacabcacdaabdaddbbacdbdaadbbbaddbbbcbcbaaadcbabdadccddaabcbdaaacbbbbccdddbcbadacdcabcddddbdcdadabcaccacbbbacbaaaaadbadcdddcdacabaadcdddbdbcbcbcbdccdcdddbabddbccddddcbabdccdcdabbccadacdabccdcbbcaccbbdacabbbbbbaabadbdddaccaabdbabcddcacbcbbdbbdcaadcbdaddddcabdbbbbccddaabccbbcdbbdabaabddbcabacabbdadacddaadbddacaadacbbbaabdddabdcadbdbcdbdbbcbccdcbbbbcdbadabbabcdaddaacddccabcbcbcbddadaaacbabaddcdbaddbabdabcddbcddcacccccbdcbaacdacbdcbcadbacdcbbbabbcadaaadaaabbdcbbabbdabbbbcddbcbbaadcbabbcdbdbdcdabdcdbbdcadacabacabbbbcbdbdcbcddbcabcaabbaadbcbdcdcbbdcdcabaadaaaddcbcdabbcabcabaccbabddbcddddcccbbbbbcacdcbbccddbbaababaaccccdabbacbadaccccaabbdaaddabcbdcbabaaccdcadaaadaabccbabacbcbdadbadbbbcddacaaacccaccdabcadbbcbbbabbaccbaacdaccbaabbbabcccdccdaacabcbdbdaaabbccbababbddaccababaccbcdbcbaaccdacbcdbcaaddcbbddadbdbdcaadaabdabaadcdacaddaacddbadcabcdbbcbdabbaabadaaacbccdcbdbbacaccadcdacdcdddbcadabdbdacaddccadaaabbadcbacaccddcbdaddbddaddddbabcdddccabdaadcccabadaadbcaaacaabcadbccbdadbcbddccacdbabbaadadbcdbaaadbccbaaaacdaccbaccbbbcbccbacdcbabbabbbccbccaacaaabddddddbdbababbcaaacbaccadcaabdbabdadbccdbcdccacdadbacddccacbbabadbdbbdaddddbdaacbdbcaabbbabaacbbcccacdacddcccccdabcbaadbccdabcbbbdcdbaabdcdacbadacccdcacbcbbadcdbdbdbbccabcbdcdbbdccadccdbcabddacaccdcaaadbabbbccdadbaaccdacccaccabbaddbccdabcccdaddacddddaacdbcadacdaccdbdadaddaabddabbccdbbabdbbdbdadddcdcddadddbdbbcdbbcccbabaacadaacbabaaaccbbddcbadddccbaddacccbcdbdaabdadaaadaddbacbddcdbdbcadccacdddbaadbabcdaddbcbaccbdbbdbbbacddccbadcadbbdcaadcbadcabbddbddcaaacaacbbaacbbbcdaacabdbdcacdccaadbcdbccbcdbdccddbabadbadbcaabbcccddaadadbabdcbadaadcaccabcdacdccbcacbbadbccccbdcbdacaddcdcddabcbdcbccdbcbcadcbbbdadbdbaccccabcdcaccdbdcabbacdaaabcddcbbbdadabccdccacbacbbbaadccbdaaacadcdcccdccdccdcabaabbababdddabbcccabbacbbbacbdcbcaabadcdbbbbbcacccbdababbdcbaddadbcbbaaacaddddaadbbcdbaabcbbcbcccccadabbdcdbcacddbdacdacadcccbaccddadcbbdddaaacddcccdabcccbdaabddadacdcaacccdadcabcbbcbbdcdadcbccbbaadaadcacdbcacbabbdbdbabdccdacbcdabcbacbabdacbbcdabcddcddbbaababcababbdcababdbbbbbcbdddbcaadbbbbbdcaacdddabcbccbdbdabbbacbadcadcacacdcbdbdabadbaacdcdbacbbbbcbcbcacddabbacccdbdbcbbacbdbcadcbacbcabdadbddbdacccbccaaadcbadaddcbadacdbdcdbcdddbddcbabbbbbddbdbbdccbaacbacdbacbadccadbdcababaddccaadaaaaddcdccaadcbcdacadaadbbaadbacaaacbcdcbbbbbcccdaadddabbcacdabddbcbbcbbcdacccdbadbdccadcbcdacabddccaadccbccdbccbbadaadddabcdadabdbcadcbdabbbaacdbacbababcbbcccdadbccadbcabdbcaabaddcbbabdbbbdacdcbbdabcdbabdbbadcacbdadaabbacbdcbddabcdcaacabdbbcdacabcdababcdabdbccbdabadccdbbabdbcdccdcdaabcddbbcdaccdabdcbbdbdcbadbccddacabaacccaabaadcadbcbdcaccdddacdaccbaadbcccbcbddbbcacdcacccaadbcdbbbacddaadacaadbdcbbbadbbdcadbbcbddbdbcadbaabbdccbdaadbddcbadbdcabbabdcbdaabadbdadadddddbaacacbcdbdbbbcacbabdabcbabbdbcbadbbbdbabdbccbcdbbbdacdababadcddacdccddbcbcdcdcdcddcdddaaddcbcbcdaaaacabdacbcdcbacbcdddbbdcccdbadacccbdcdaaddaddadbbcaabdcaccbcaccabbcbcadbaccbbbcdcadaaccdddcddbdbdcdacaabadadcdcdbadbbbdaadbbcbbaccbccaaccbbbccdcccbdcbabdbacddaddbcdbcbacbcddbbbadbadbdcdabcdadcaaadbcbbdbbdacbbccdbaaccdcaaababcdbdddaacdbcdacccbabadbbbbccbddabdccdbdbdbbcbbcdcddbbdbddbdcaacddbadbadaaaabbcacbdbcaaccbcbbaaacddcadcdcdababddcccbddbcdbdccdabdddcaddbabadcddcdbbcadacbbadabcaabaddcbacbaaadadacdddabdadbbcdacdaddacdabdccbaaacabbdaaacdcbdaabbacdbbabcdaaddabbdddccbddcdabaddcbdadcdcdabacbcbbababadabddccababaaaccccccabbdddbacbcabaddadbcddacdabbcacdadabcabacdcadbcabbabbbdcbabcbbbacbadddcacbdabbcbdcdbbadddbbacaadcadddbacbdbaacbdacdabccbacabddaaacaabbadccacaddddabcacccaaabcbbcbaacdaddaddbabcccacccaddcdabaddaacbccdbdaaaddcddaccacaddacaddbacadcadcccdbaaccbbcaddbdacaababdccaaaadacbddcabbdccbbacbcaccbbcdbddbdbcddacbaadcddabccbbcbbacbabbdddcdbababaabccbaadcdbaaccdadacadbddcbabaddddcaaaacdbbabadacdcbddcabcdccdbaaadacdaaadbcdacadaccbacaccbbdadcddaddaaddadddadcabacabbbdbbdaabddccaabaadcdacbaabaccdacadcaaacbcbaabbbbbacabcdbcbaadacbcbdbadddadccaadacdbbccbaadcddccddccdbbbdddcccdaddcbacccbdbdccaabbcabccbacaacbcdcbcaabcdadadcdcacdabaadccdbcbbccabdccaabbdcdccbdadaddbdccbcabacaccccddcdbadacaddbaddadacacadbdbdaabaaabbdddcabacaadbabacadddccaaaccdadcbabdccacbabdddabcccbbacbccaaadacbabbbcdacbaccbacdccdbdcdaadadbbbdcbcbddbdbbdabcdbbadccbcdaccdaadabcadbbdbbadacddaddbdbbcaadcbcdbdbbdbcccbccaccaddccbbcbbbbbdbdcaccdbdbdbcbadabddccdcbbdcbddbdbccdcbacaaabdcaabbaaadddacaaadabdbbbbaaabdabcaddcdcaaaccdccaccbdaddcbaaacadbacdbcadcdddbddabcbaadddaacabcbdbdcabcdadddacacddcccccbbddccddbcddcaddaddbacbcccabcbccbcbaabdbccbdabbcbcacdcbaadcdacaaaccdbbbbcdcdddaccbdcbccbccabaadbbcbbbabaabacdcabbdcbdbdddcdddddaccdcbddddccabddddcaddbbdadbabdcbaacdddcabccddcdcbbddadadccbabacacaabbdbadbaaaabddaaabccdaacadcddcaacccddbcddddddcabaadddbdcabdbcbbcbccbacaaaddcacdadcabbdbcacdcbbacdbbdcaabcdccaabbaabcacbbdacbabbbbbdcbabddbccaddcbddcaadacaddbcadcdaccbdddccdabddbbaacbbbbcaabbacaadcccdcdbcdbdddddbbaacabcbdcdcdabcaccbabcaccdcabdccdcbdadaadaadacddadaadbcbbccaabccdabbdacdddccdaddcdcbadbabdacaaacdcaacbaababcccddbbacbbacdbdbcaaaaaaadadabadadbdcabdcdadddacaddbbbdbcddadbbabababcccbcdbbabbdbbdddcbbababdcdabddcbbbdcbbadcddaddddbaccabaccbccbbbbbcbbddbcabddcbbddadbaccdcbdacbaadacdbdabacdddacdcbaccacdabbccdacddcacaadabdcaabadbaaabdddccbbbddbcadaadacaccacbaacacaacbaddcadaddcbaacbbbcdbdbdddbbddaabdcdccddbcbacbdabcaccccabacaaccbcaaddccabcaadacaabaaccaacaaabbaabaaddabdacabbbbcdacadaadbadbbabcaadbcbacbcdabadbdadcadddabcdcabbbdccbbbcdcddadaaddaaddaabaddbcbbaacbcadbcdadaaccbadbbbddbcacddbacbdaccaadcabdaacaccbbccccbaacddcdbdbdacadbdaadabddddadbcbcdcbaaaabcccabdddbbcdabbbbbcddbddacdcdcacdbcbbccdadbdcaddbbccacddcbdabaddbbaddbcbdcdbbcbbaccbbbdbcbbadadacabdbcbddcbdbaaacdddaccabbccdccabcdbabadabddddcbbcbadcadaabcddacdccdbdcbcbccbabbaccdadcccbaaadbcdccabdabccbcbbbcdaabdaabdcbdccbaddadbcdccbcaaacbbbdbbdadbdacaacdacabaddaccadcaababbdabdacadaaabcadaaaadbcdcddbbcbdbdcbbbbadbadbbccbaaccadbdbdbabaccbdbbcbadaacddaacbbdddcaaaaccdbdabadbddcbdbadcddccddbdacbccbabccdcdccbbbcbbadcababbbcabadccbbbdadbcbddbbcbbbcdaacbacbbabcbdcbdabdbcddbbbbbddaaadcabddaccbcdcdbbcabbdddbcdbcccaadbadbddcdaddaddcabdcbbdddddbacccaadbabdacabcbbbcacbacdaddbbcdbdbaabbcabaddcdccadacdacccbbcdaabdbdbaaaaacbcdccbadcbdbdddcdddcabddcccbdbcabcddabdaccbbcbbbadcadddcddadbdccaaddcadcacaaacbdcdcbaacacdcbdbbbdbdbcdacadaacbaacbcaccdbbcabcadddccaacdaabdbcadccaabacbdacbdccacacdcbcbadcabadabdabbdbbcabbcabcadaaddcdaadbcacacbcbddabbbcdcaddaabccdbabddddadbbccaacbddccdddcbbcaabdababccddbdbcadadbbdddcdaadcaabbccdabcdcbccaaadcdaccccaaddadcaddabaddbbccdccaadadadbccbaddadabccdabdcdbadcabdabbadabbdcccbcdaddaabcabcddaaabaccadcbcddabddcccacdcabbadcaadcbbdbaabacaacbcaaddcddddaabccdbbdcdaaaabbddcbcbbbcdbbbccdaabcbdcabcbaacccbdbddacdaabcdaddabacbbcbabacbddcaababbdaabbabacaabbdbacdbabdbaccbbcdcadcbadddacbcadcdabaadabbacbcbaadbcdcbaacdaabadacccdaccccbbaaacabcdbbcdbabbbcbbddddbcdcaadaaabddbacbcdabdabaacccaaababdbdcbdcbbdddddaccdbdccbdababbbabddaacddbbacdabaaabcdbabbaaacbcdadbbbaadbdddddcbddacdbdddacaccacdbaadabddcbdaaddddcabdbdbcbcacbaadcddcbdbaacccccacaaadbddbdadccbcbbdcbcdcaddaaadadcbabadaddaadddadabcaadabbddcdbaaabdaabbacaaaabacdbdbbbabccabadcbabccdbbccdccdacdcbacccaabdbcdcbdcaabddbccbabccbaacdadcdddbbcbcbccabacdccbbcadbaadadabacbcdaabdcadddcbcbcacddbbcbdbcaaccbaaaccccbbcdcabcbbbcaabbcbdadddbccacabddaacbcbabadcdbbddbcadddbabcadbcbadbabbacbbbbddddcbbacabdbcbaccbdabccacaccdcadbbbcbcaacbdbdbdbcabbacadbbbabdbbacdbdbbbacaabcadabbdddbbbacccdaddbdaacbdabcdadddcdcdbdcaabccadccdaddbbaddcbdcbcadadcabbadcbccaabdbdbbcbbcbdbaadabbaccaaaaabdadadaabadddbdbcadacccacabccdcbbdcbacbcbbacabccbaccdccbdcadaddcbdacdabbdadcdbcccaaaaacbcbaccbaadacbcdbccbbcdadabccdacdcbbdbddaadbdbdcbdcadccacbbaaddacaaaaacabcbcabdbddbbddcbbbacbadbbdcaabcdacbbacdbbbbdbadbccaaccabcbdadbdabbabdaadccaaddbcbcbcdcbbbacccdaadaabaabcabdccabbcadbdcbdcbbdacbaccdbdabbbccbdaaccbdcbddbdabcdcdddcbbbaadddabbbcaccbdcabbabbdbbbdaadabacbdbabcabdcaccaaacbadbaddbdbcacdabadacaacccbaabbdacbcccbcadaaaabcbbbcbbdbdabaaabaabbbabbacdcbbcbbdbcaacccddcbbddabdbaacdcabbbaccbdaddbbcbaacdccdbadcddacbaaaccbdbbacddabdbbdacbbdadbcdbabaabcbdadbdbaccdcaaadabdcbcdbaacababbadbbacadcbccbcabacadcbadbbabdaddaaaadbbdcdaddbdbbdccaadddabcdcdbcabdcacaccdaaabaabacdcddaadbacbacbddcacbbbcbaaddcccadbaddcbbdaabddbcabdcbdcbcbdcbcaabcabbacdaddcbbadbcabbbcadbddaadbcbcddcdbccddadcdcdaacaabababadddaacdbccdadcbdabbdbdcabdddbbdcadabdbbbaddddcaddccddacbbccabcdcadbddbaadabcbbadbcdaabbbbbbabdddbcacbbbdbddbdacbcbadcbccaadbbcdabcbcbadcaabcbddcdcabcccddbaacdabbcdabdadaddbcbccbabcbddbaaccbddbdddbbbbdcaaadccbbcdbdbaaaaadbcdddccdbddcccbbdbacdbdabbcbdbddaaacbcdbadbddbcacdbadadddddcacbaaadcccabbbadcddbbacdcaccdadcaaabaacbbbdbcbaacdabaadbdbacadccdbaabadbbabdcddddcaaaaaaabcbababaacddccacdcdabdabddabcadaacaaaacbddbdacccbcaaacbdccdcdbbbabddcabdbcababcbdcccacccbbddbbcbaccbbcccdabbbacaddddddccccabaaacadbcbadadbadaacccdbcddccbddbddddddbbabdacbcbbdbdbadccdbbbddcbcadccdcadcbbcadaadabccbadddadccaabacaddbdcadbabdcaccbadbbcbccabdbcaabbcdcadbcaccccbdbacdaaaaabdbadcbabdabbbbcbbcacdddacaddcbabaaadcdcdbdbdaacccdcdaaabbccbacabacadacbdcbdbcaabaadcbcaacbaadaddabbbcabcbdbcbbcbdbbcaacbaacdadbddbdcdaccdbbaabdbbbabaddddadbacacddcbbadcdccaabdcbaccbacdcabbbbcdcdcdcddccddbbddcdaacabdbdcacdaccabbabcccadbcddbcbcbaacddddccdccdccbcadcbbccccbbccbcdbadcaaaccbaaddccabcccabdbaababdabaacbacdcbdddbdaddadcdccccbccddaddddcaaaacbbdddabdccbdcdddbdaadaaddadacabdccaacaddddcbcadddcddcddccbcbbaaddbdbcadcadbaaacadcbccbccbcacdaacacbaabdccbadcbdcbdbbbabccadaccbaacbbdacdadbccdaddbbcbdcacdadddaadabdadadcacacababcbacccbcbbaaccbcaadccacaddddcdbdadadcdccdcbcdaaddddbaccbdbdddadbabbdbbaacbdaaadcbacbbccdcbacabbccadcdbdddcdadcbddcaddcdadacbaabacabbdddacadbabccadabdabbcdbdccdabcbbdcbbbbdaadbdbccbccbdcdacaabbdddbbbcbcdabbaccdbdccdcdcbdccdacaddcbabcbbdbdcbdadccaaaaabbbaacbcddcdaaddacccccccbcddcbcccbbabbcbacabdbbcadcaadbcabbaaddbadbbdaadbcbbbabcbbbaddabbabcdbdcbddbbacccbcadccdaabdbacccbdddcdcaabadcdcbdbaabacaaabcbdddccbccacbcbcbbaccdbbaddbcadbbbbbcdbcbbcbddacaabcbbcddddbcaadbbddaccdcbaacdbbbdbbbddbcdaddbcbddccaccbaaddacaddadddadaabcdabdcabdbbaacbcbabbddbacbccddbdabddbbaccbbadabdcbadbabddddddddddcacacdbadcdcdbccaddddccddbabaccccbbdddaadadbddaacadbdcdabcabaababdbbadcadccbbddcaaacbacbcbcaaddcabaccdbdcacaaadaadbccaddbbcdacdccbcbddcdcdcbaaacaabdbcaacadbabaccdbcbbbcadddbbcadbaddcbdbdbdcbaacdbbdacbcbaaacccdbdadcdbcadddcadacabacbbbadbdccbadacaabbaabadbbaadabacacacbbcdddbdddbcaacbddbbaaaaccdbddccadcdccdaadccaaccccaaacbcaccddddacdcadbabddacadadadabaaabccbcbabbdadbcaccbadcdabddbcacbbcbbbdbdccdbdccbababadaadbaacdacbcaccbbdadbdcbaabcbdcdcdaabacdbbcabdbdbaddbcaadbbaccacddcbcddcbcabbddcbdddacabddadbabaadcadcabacddaddbbadaabacadadbdbaacbdcbaacabdccadcdabacdbbbdddabbbdbaaacbcabbbaccdcdcabcbcaaaddcccbacdcadccdbcddadcadacdddabcaaaabbadadbcccddcbbcbaabdbcbdbddbdbbbabcbcadbcaacdcbadcacdabadddadabacaddbcdccccbdcbccacabcaadbbbcabbbadaacdcdcbddbbbababbcddbdcababaddbbbaccabccdbbadcbcbdcddaabbddddccdbccbacccbdaabcbabddcbbcdddcacacaadbddcdbbbbacaaddbbdcdbddddabbcbaacdabaabcabadabcaadddacdccabcddacaaacaacacbabacccdacdcaaaacacccdbcdcbccbaaacabbabdbcdcdddbbadcbccabdbdabbcbdbbaacbcadadcbdccbcacdbbccdddccacccddbbccabcbbacabaacbbabacddabacddcabcbaabddbcbacdbadabaabcbcbabddcacbcbbabdbdcadbcbacbbcdadccbbaaccabdabcbbabdcbbccbbcdbbaddcdcdadbacbccaaadbadbabbdadbdadcddccabbbadccdbdacbabbddbbadabdccbadcbccacccddababdcdabccdcadacbdaaadcdcaccacbdbacbacabddcdaddcdbbcccbdbdbacdcdbcbccaadcddcaabacbaaccbccbaacbadcdbadacabbbacbabbbdbcccadcbccddbadcbacbbabccdbcdbbaaccbaddcbcadabbbccddbaacacbabdadcdcbbdacdabaaadbdbbabdcacdabccdbbacabaccbaaadcddcaccabdcdbdabaabccbbbbdacdabcddcdbaccbdbddccbbcccaaddadbddbcbbcdcabcddabbcddaccbaaaddacaabdcbaccdccbaadadbabbacdcccdababbdadbbdbcdcacccbacaacdbbcddcbbccbdaaadcacbcdcdbcdcdadacccbadaddacbddaadacccbcadbaacbcddadadccabcaddabbcadcbdcacbbddbcacccbccadcaadbbcdcaadccabadcbcabcdcbbcacadbdbccdadcdcaccddbddcddbbcdabaaddabcdddbcdccdbcaadbaccaacdbbcdabbcbdbabbdadaadcadccbaaacacaccdbcdcdaadaabadacccbcdcbcaccbbdbcadbbabddbbbddbaadcdcbdcdacbdcbcacbbbaadadcccbaadbdabbbacacdcdaabcdccccbdbddbcaaacaadbdddbbdcdbddbcdbdbbcdbbbaabddbdadbcaabcbdaaacacddccbaaaccaabadbaddadddbadcbaabbabbdbbcbbdbaadbbaacbcdadddaabddacbabcbcdacdddbdacaccddcbbaddddabdabbadadccddcacaaaddccdbadccccdddbcdbdcccbddadccabdaadadacccadcdbcddcccdadaabcccaddcdabcbacccbacadbcaabccbccdcabbdbabddacdadbccbbdbabbdddcddcdbcdbbbbcccabdbdadcccabcaacacbbcaddabdccadaaababbbbbbabddcbddcaaadaabcbadadccdcacbabcdaabccddcacadaccaaabcccbaadbaacdbbdbcdabcdaadaabcddacbcdaddccbaaababddaabaaddbaaacddaadbbbcbbbacbabadabbdccabbbdaccbdbabbbadccaacbdcadbcbcaccbaadadbbabdccadabdabbcccbacbdbabdaddadabbabbabcaadbdddaadbaacaacddbdbdaccabddbacacddabcdacbccdddcdbddcbbbbdadbbcacaabdacdbbddacdddbccccacdaabbddabbdbcbcdacddcadaabaddacdbdaccabaddbbddaaddbbabbddacaddbadddbcbdcacdcabadbbaadaccdcdddacdaabbbbdbadaddbcbacaadbbccaabadaccbbabbcbaadcadabacbddacdcbadddddddcbdcbaadcdcadacadbdacccacaadaabacbadcbdacbabdcdcacdbcaddbadbcacbdcabbcacababaacbbabcaaaaaaacbdcaadcbbbccabaaaadcdaaccaabcadabcbcdcabbadbbdabaaacbcbddacaddabbdbcdbaadbabaacbdbcbdcbbdcddacdabdcaacbcbdbadacbdcbbbcdcaaadbabbdbbcabdcbdabaddccbdbcbcaddbdbcdbbaddcabaaabbcdaaacaadbcaabdcacacbbbabcccabdaaccdcaaadcbdbbdbadcbbccacbddadaaaddbbcabbadaccaabcbbaacabbaaccddbcdadbbbbabddbcddbdccdccccdbbbdbaacadccaccacdcdacadacddadadcacdbcdbadacdcaddccbdcbaadaacacbdbabcddddcdcaccbaccdaabddccdcbcddccdbaaccccdcbdbbabdbbccddbbbcabaaacbaacadddddcaaaaaabdbcbdabbaacdbadcdcdadcbbbcdbcdadbbcabbddcacaddabbdadbdcdadccccdbdabdbbbbbaabddabdcdbbdbabdddcaadbdaaddadabddaadabcababdbcbdabacadbcdcacadbbcabdccadbdabbdbaaaadaddbbbbbdbbcabbccaaddbadcbcccacaadcdbddccaddcaaaddcdabcccaddcbdbbadbbaaadddcbcdacababcaccbbddcdcddadbccabbcdbacaaccdcdadbdcadbccacacdabbbbcbccdcbbcdbcdcadddabbbabadbdadbdbbdcdcbccdbcbbccddbbabaadadbdacbabdcbacccacaddddcdbacddcababbcdcbcdababbdbccdadbddccbbcbccdcacbaacbdcddddadaabbdadcaabaadccabadbdadbcacddcbaadabbabbbadbaacbbadbcdcaaabababcaddaabdacdbadbcbbbaccaadaccabacdbbbdbdaabbdbccaacdccccddcdacaaacbaddcdaaaabcdccccaddccbddddaacbbcddacbbddbbbbdcadcacdacbbbacaccbbdcacadccdccaacbdadbcdaabdbadcbcabcdcbbdacddacdcdbbcadcccacbacbccccacaaddaddaddbdbcdbbdbdbddbbacbcbcbbdcabbcddbdbdacccacccccbccacbbcbccbcaacddabddbbbcbabaddcdcdcbadccbdabcddcdabccaaaacdcdcaabccdabaaacabacddabbbdddcbacadcdbdbaccbdcbddcddadddbddcadcdbcaadbbdaacdcbacdababbdbadabdcccaababccbdbdacdbbccdadadbcacbdabdacacbdbddaccbadbacdcdccabbdcabaadacbcbbccdacdcbccdddbcadcabdacdadaacaccaccbbdadccadbdddabccccdbdbdadabbdcbdcaadbdbdcadbbaadccacddbababbcdcacbcbcdcadcdddbdcaabadadbaddcdaccccccbdbdcacaabdbdaaacddbbdbcbdcaaccdadaccccadcaaaccbababddacbbbbcdadacabaadbdaddddbdacccdbcddbdcaaaaddaddadccadbdacbbadccdadcdabdadaaadbcdbaacbabcdccbaccccabddddbbcdddabddbccccbacdaddadbbcccdbcbacbacadcbacbadcababaaaaacadcaccacacdcdacdacbddcdcddcbbbcaddbabcddbdaddcdbacdbdacbabadabadaadddbbbaacacaaabaacdbcaccbabdaaababdbdddccadcaaadcdbaaabdacabadaadbbcbcdacbabaddaabcabcadcaadcbbadcccbbabbbddcbddadcaaadacdddcbacacddccdbdadcbdccdbdabacacddbaadcccacbcadbccbacabdbdccdcbcadcdcbdddcbbbacabbcacaacdbacacacbaaccabddcaaaddcadadaddbbabcaddadbaabccbbccdcdcadaabdbabdbbabbddacdbcbcbdbdacadcbbdbabbcdddbacacadabccabcacbdcbbbdcbbdcddaddbcabcaadbbcccbdcabaaadbabdaabcddbbcbdcdaddbdcabcbaabcaddbbcbaadccbdabbdccacdcabaddcddcdabdbddcaabadccbcbacabdbbbbccbcccbcadadcdbbbaaadbacdacacabccdcdaacbbcdddbabdaaddddbcacbacdaccbcacaddcdbbcabbaadaccdcdddbbddcbbcadbcdadcddbdbbbdcacbccbcbdbdddbadbbbbbccbcaabcbacdbbbcbdccdccbbdddaaadbaaddcbbbaddbcbbadbaacaaaccaabdabacccaabdbccbbdbacadbbdcacadababccccbdddabababccbdbabdbdbbdccdacbcddbbaaccadbaacadbabbaadbacaaddaccdccbcbdcabbcbdadaabcdaacabddbbaaccdcacaaddbccbbdcadbdcddaccbacbccacdcabadbcccabbcbadbdccbaabcddaddaddadcabcabbdbcbdbbcccabbdaaaacbdbcbddcccbcbcdabbaddaaddccdddbcacdbacbdacbdcccccbddabcacaabcadddadcccaddcbadbcdbdbbdabdabbaccacdacabcabcccdadcccddadcdbdabbbbddaddbadcbdbaadbadcddcaadbdadcccbbbcbadddbbbbbddaccdbabbddccacdbabddcbcabbbdddcdabddbccbcdcdbadccdbbccadcccbaaabadaccdddbddbabaaccdbbaadababdbbaddbbcbbadbdabdbaacbbdbbadcdddbcdbbcabcaabbcdddbbbdabbdcbcbdacbaccbbcbcbdddadbbadbccdddbaadddcccbcdcbddddadcadccdbcbcbbbdadbabbdabccacabbbcaadadacaaadccdddbcaaddadcdcacabaaacbdacbaccdadabaabcaaadbbccdccccddbdbadbabbdbbddadbbbddabbabbdbcbaddbdabcaabdccaccdabdcabbbdcbbcbccacdacadbbdcacccabaadadbddbcbbaacabcdacdcadacabdcdcabdddddbdbbcdcadaddcdcdbdbdbddddbddbcaacaababadcccaacadcbacacbadbbbadaacbcdaaabbcdacabaccbdcdacaabbadcddacccdcddbaccdbcbbbdbcaabdbcacbbbbbddbacbccacaacacaaaddababcadbbdbcdbdccbbaadcdddccabdcadcbaccbcbcaacbadbdcddadcaacadbaccbcdaabdacaaadabadddabdccabdcadbacbccacadbaadbccdbaaabcbcaaabcccaddcbcabacaabdbdbcbdcbcbccacbbcccaccbddadccdabddccbdcdbbbabdbddbbbbaacbcdbbbcccbcaabcaabbcacbcabbaccbcccabcbdddabbbacabbddacbcaddbbcbccbcacacbccaabdadadaaadaadaacdacccbbacddddabcccbdbaacbccbdcbcadbccccbccbaaacaaabcacbbcaabababdaababdcbbadacdbcdcbccdbbcbcdbdcbaacdadbbcdbbacbcbdadaacccdbaaacbbaaccbdbcddbccccdbbabdcdbccbcacacdacadddbabcbcabacdccdcbdadcdabbadbaaccbadbbdcddbbabccbccdbbabdaddcccbccbcbabbaadbcdcaadaaadaadabaddcadbadabbbaabadadcdddabdacddddbbcdaadadbddbdbcdcbaaaccbcbdbbcabcbdcdadabcccbbbdbadbdcbbaababcccbacdacdbdaacdaaaabdddbbbbadbdbccdddabdbdcabcbbadadbddaddaccbaabcccabccbbdcdbbdcadddccdcbdabcbcabcddadacbaacacbcbcdcdacbcdbcbdcadbbdddbcacdcabdbdbbbbccdbccabaccbcacbcaacbddcdcbbcbcadcaabcdbdccdaaaaddcbcbbbaccbccdacdcbbbdcccbdababcdaddbaacdacdcbaabadbddbbddabbdcabcacbdcdcaacbccaababbddaabbdacbcaccdbacdccdabcbcccaddacacbddbdbacddadbdccacddbcbcbbccbdabadddadaccabddaabcdbcabbbacbdacaabbbccdacbdbdbbaacccbabbabcccabacdabaddabdbbdcacadacaddacaccdaaddddcbcaddbbaabdabddbadadccbabacbcbcbbdcdbbdccbcabaccdbcbbdacbdcdddacaccddaaaadbadcccccbdbbaadbcbaabcabacbbaccaaadadbadbdaaaaadabdbcdbccbbdabcbcabbdabcbabcaddabcddbcccaaacbccadbcaddcaabababcabcdbccbadcbcaaddabdbcadbcdddaddaadaccbcacdbabbdadbccadccbcacaabcabccabbbdcbbcabdbbacbddddddbbdbcabbdcbdcabbdccddbccdccaddabaadbaaccbabacadddaddaccbdbcdbbabaddaabcbaddccbbddcdbdcbbcdccdacaaabcbbabbdacabcadcdababcccbdddcdcdcdbdaaaaccaacaaccabdaacbccdcddacdacabcbcddbbadaaaaaaddbcccbdbbbacbdbcbabcadddcaabbddabbacadcadbdbadbcaabacdbadccccaccbbcacbbcadcdddadadbbdddacbadbbcdcadacdbccabdbadcbbbaabccccdcaddcccdbbbabdaaddaccadabdcbcbbdbacaddccacdcdbaabdaaaadadccdbbdbaccbddcdcadcbbacbaabbbdabdaaddbbaabbddaaccbaaddbccbaccccacdddcccadcdddbdcbadccdcddccabdaddadbddbcaaaacbaabdccbdcdacabbadbccdabadcddcadabcdaacdaacdbddabddccbbbaaaabcdddcdaadabbcdbcacdaadcbdbcdaadaabacbaabbbdbcbcdcdccccbccabbcdcaadbadaadcbadacbddcadbcdcacacabdbcaddaaaacdccbcadccdccdcacdbdbaacaabdcabbdcddbcddbcbdaccdbadcbdccadddaaaadbabbcdcdbdcbaabdcdddacddaadacbdbbdccdabacccdcdcdaaabcdaadddccaddcacccdcddbdcacbadacbbadcccacbadccdacdbbcadcdcbadddbaccbabcabdbadaddbdadcbcdcddadbadbcacdbcadcadcaacadbbdcabcabbaacbbaadcbccdacbcccbaacbdcdadcddccadadbcdbdcbcbdddacddaaddabadbadddccbadcddddbccdddbbcabaaacdcbbcbcbddbccaaacbbbbbbaccaccdbbdbacabcabccccccdaacadccccccddbadaaaabdddbddaadccbbdabaadbdadcdbbcbccbbccacdbccdcabcbbcadddadabbddcadabcabaccaacbdcdddcabdaabbcdcdabbbbdadddddaadcadcabdabbbccdccdcbbdbbaccbcabccaabaacabcdccacdddbddddbdaddbadaadccdaaabbbcacdcdddbcbdcabcabbcabdddcdcadbddbaaacdcadabbadabcdbcdaddbddcacbcbaaaabbccdaadbbcdddbbdadbbbbdbcbacacbacdcbcaacdbdaacaabdaaacdbbbacbcdddcbabccabacdcddccaccbbaabcccbaddcdbccbadcdadbcdaaadcbccabdadaddadccacdadbdadcadaddaadbcababbbcbbcabaaadaadacbdbbcbaaadbdbdadbccccbacabddacabadaaddcbccacacdcabbcacbddaaadbbcdaadcdccbdbabbbcbdbddcbdcbcacccabdccbabadbbbcdbaadbacddcdbcdbadcdcabdaddaacddbcbddccccccabcccbdbcaacadadbcbadabcdcbadbacbddddaccaacabbbcdaddcacbadbcdbdbbdbddbbbaddacabbcddaccabbcddcacbbcbadacabbcabdbdddbcacdbabcaadbaaabbcacbdcdbccbdcaaaacabaaadbdadadaacdbccbadbaadbcdababcddaaddcacacbccaacabbcadacbbacbbabbcbacabadadaadbbaaadccdbbbcbdaddbbbacbaacbcdaaadacdcaacddabbcdcaacdabaabdddaaadbbadddcbadbacccdadacadbbbbdcaababcddbcaddbccacdddbbaabcdbabbacdbddbdbabdbbcaaadcbddacdbdaabbbcdabbaabdbddcdccddbbdbabbddbabdbadcddadcddcbdbbcbcdddcaaddaaabaaacbacbabadaccbacdcbdadbabdbbdcaadbacaaaddcadcadacbcdbdcdcdbcbdabbaccabdbbdcacbaaacdcbdabadcabccaacccdcadccbabcbbccdacddabbcdcbcdaccdaccdcdabadaadbdbbcbdbcacacacacaabdbabcbcdaacdbcbbddcbcabbbddcadbcbccbbccacadcaaadbadbaaabbdbbdabbcbbcccccbdadbcbdcacddcbdcdddaddadabaddcddabbdacccadbadadbccbcbadcacbdcabacadbbabbdabbcccddbbacdbaccddcbccbdacbdadbaacdbcaddbdddaabdadcccbaabaaaabbcadcdbdcddcbadbabcdcbbcdccdccccbabdacccacdcdbcaccacaacbbcadcbdbacddcccabdabcbaacbbaacddbcccccbbacdcdbaaaaaddcbdcaabbcbbcccbaadadaabddabcadaaadbddaaddabcabddbcadbaabdbaacbdbbbbcbddcbcbdcaccabaaddbbbdbbcdabdadddcacbddbacabcbdcadbdddbadddabdcadabcacabcaaabbddcaabdddbaaabbdacadcaccacabaabccddaccacaccadcabaadbbadadccdddadcbcbaabdaaddaabadccddbbbbbbcdadccacdcdddbdddbcbddcccbdacaacababcddddabccbcbbbbccccbaaddcdcbaaccaaaabccbaccddcabdbbbcdcbdcbdccccdabdbdacbbdbcbdadbdacdbdbcddcacabcbadacdaccbcddbcbabbdbdaaddcabaddbbcccacbdbbbcccacbbbadbabbbddbbcaabbbacaabaddbdbcdbdddccdbcbbbbdbbdbaacadbcacabcbcdcdcbdbadacaabaabbadcbcddcbbcbcbbbcaddddabbdbbdaadbbacbcaaacddccaacddcccbbacbbbbdcababdcdddccccbcbdaaadddcbccdaaddddaaacdbacdadacccdcbabdcdbbcdcdccbddaadddabbaadcabdccacbbbbdbbbcdcccadccdbcbaaaaadbbbcaabbbdbcdaaccddbdcdbdadcbbcadddabcccbbbbadacbbcdacbdccbcacbccabbadbbabbbdcadcbdbcaccbbcaabcdcdacbbbcbaccadacadbbdbacadcbaacdcabbdbabddadaacdcccabaabdccccababbbdbaadcdbaacccccdddaaabbbbabaccadcdbacdbddaadcbaabadadacbdaadbdaccabadaaddcbaccdccdadbaccabbcaaadbbcdbcaddbdaababcbdbbbdbddbaddcbabcbbcacbcbbcdccaddabbddaacddcdacaccabcdbdaadadccdccdbacbdadabadaccbddbcbcbacdacbaccdcccbdccbaaadcaaabdbcabdbdaacaaaabccbcdaccbdadbbbaabdaacbbaaaccddcdcbadddccbbabbabdcacdbcdacccabababcabaabcdcddbbccbbdccabbddadcdacdbcabbcddddbcaaaddccddccbcddbaaadaadccacdabcdcdcbabcdbdaaabbbcccaddabddacbcccccdcdbdddcaaaddbcbdaacacbaddbcdacadcdcadcabccbaacbbaabcabaaaccbacbacbaabacabaacadaaaddccdaaadcbcbacdaacadacdccbdcbacdadbcbaaaacacccddccbddacacccbdbbbdbcabdcabbabbcdadcbdacacdcccaababdaabbdbadcbdacccbcaadddcdcbdbdcbccdaaabcddadccccbabbcccdacddccabbadddddcdddcacbbacbabaccbcaabadcdabcdcdacbcabbcccccaccdadccbbacdbccdbdcddaabadcaaadbddcccdcbbcadccbdbccbcadbddabacbdbbdcacaddbdbabcddddcdbaccdbddaddbdaaddddbbcdaaccaccdbdcacbadddbcbbbcbaacdcbdbbabbbcccadabcbcbdaadbdcdbacdaaabcbcacbbdccddddcddcaadaacbcbdddadbdabcbcaddadabadcddbdaacdcacadcbcbacacdadababbbdaabbdabaabadbccbdcaddadbdcbdcdbbaccdbdacaccbacadabdaddbddddacccccdabbdaccbdcadcadbccbddabaaddabcdcaccccbcccbdcddaaddcaddabbdcacacacabdacbbccddccacbaacdbcdcadcbcddaaccacccccacdddbaccacababbcdddbdacdddaabccadaadcdcdcdbaababadcaadbcddcababdccbbadbdcabacdaaddcccdbbdbcbaababacbdbdacbdcbbaaaaadcbddbcaadbbaaadbccccbdbdbdaabbaacdbddacabbdbdddcdccaccbbbbbadaccbdbabcabbddddbdddcccabdddbcbcbbddaadabccbcaacdbaabaadacbdbdbbbbddcaacbbbabacddaadacabadcdcbbbcacadaddaadccaaddbdddcaadacabcaadcbdccadadadbbbaabdaddabaddbcadcabaaaddbcbaddabbdddabcdbbdcacddadbaabccaadadcdbddccdaddbbaabbcdbdcddccabacbdcacbddccdbbabcacddbcbcaaaaccbccacbcadccbdddabdbcddccccadcbcddbaaabacbcbdccddddaaaadcdadcaadbadabbccabbcddbdbabcadcbbabbbadadbcaccaaddacddcbabaaaaddbaabbcdacbbadbcddabdbddcbbacdbbdcccaddacbccaccccdccbbbcbdcabaddbaacaadddccbbbccccbccbdbcdadccdbcbaadbbddcaddaaccdcbbaadaaabbbbcbababaacdaadddbbddccacccccbbadcdbcdadacaadbaddbcbababcabcacababddbcbbcddddbbbbcabdcabacabbdcadaaadbdaacbadbaddaddddcacadbadbbcdcddbadbbdaaddabbadcccdacacbadbbbddbcdaddaccdaabdbcdcaaacaccadbccccccbccddcbcacdcdadccabababdaccbcbdbabbdcadbaabcdddadbdccdbaccabdacddacbbabacbdadbcdaadbbcbdbcdbdbbaccbbcabbabdcdbdbaccabbacadddadbbaadddadbdcccccdcccadcbacddbbbadccbcbbcdbccbcadcaccbbddbcbbbdadcdddadbddbcddaaabbddacbccdabbbccdabccacaabcdcdbbbbdaddcadbcaddbacdbbddcabddcadbaaacdbdabdaccaaacdbbacabbbdcadaacbadcbdabbbaaccaaddbbbcaaddcabbdcbcccbdabadadbbaccccbadacbcdddabbdadbadbbbcbdbbdabdadadbbbaadbdddbcaacabcdbadcaadcbdabcbbaccccabbcacadbcaabdbdccddaabbdbacbcbbbbabbddadaabcdddcaadacbaaddbbbbcdbabdbddbdcddcbcaacbccbacdbcbadbcdabddbbdabccbbbbabdcdbaddcbbaddbacdcbbcdadbdababbabcbcbabaabaaccbbacccbddaccdccbabbadaaaadacbddbcddcdcdaaaaabddbadadbcdbbbaadbcdbccbaaabababaabbdadacdbaadbabcaddcadacdbaaccabccaabbccbabacbadabdcdbaadacbbccbccbdadabdbdbabbdcddcbdbcccaadbabdbcbcbabdacbdabdcccdccbdbacacdabccbcbbcacbabadcbbcbdadcbacbdddccbbabccbcacdabbcdcbbbaababcdadbccbbccccbaadadcaadbdcaddabdccdbacddccdbbcaadbddcbadddadbcaaabcbdcdacabbadbdcdadabdacbcdadcbcddadabcbdbcbcdaacccabcdcbbbadababadacbdcbccccaaababbadaabdabccddccadddcdacbacccccdccbadddccaadcbdbdcacadccddaaddbcbccadcbbaabdabcbaccdadbdbacacadaacaabdcdbbdccdabacacacbaabbdbbbbbbdaacdacbbccccadaabbaabbccbdbbcdbbbabaacdabddbacdbadaddccbdbdcdadacadbabcaadaacbdcccbccbccbacaabbadbccdddaddcddddcddbabbdcbdcccdbababcbccabdacacbbbddcbdadaadbcbcbdacccadaaddddbbadadccbddbddcadbbbcddbcacbacddccdcbcdcbadadbcbbcdcdaacdcbdbadbcdddadbbaddcaadbaaccaddaabddaabbdadacbdbbccdbcdcddbbcaacdaabccccabcabdbbacdacabdbbacbaacaaabbcddbbdbdabbbdbcabccbdcabcbccddbdaaadbbddaaddcdcaddadadaaaacbabadabcaabddbcccaccadaddbaaddbabcadbdcbbbacaddccdbdacccacadcbdabcabbadbbababbbaacdaaaacdbdcdaaabacacdbcdbacadbddbabddbdabcdbadabcabcdddcbbdaddbaacbadbdbdddbaabbdaccaadcbcdaddaccbbadabccaccabdcaddabdcbdbabcbdbbaadcadadababbbddbacaddccadbdadaccadcccdadbccaccabdacdadacdbabbbdacccacaccadcabbabbcbabbcdbcacdbbababaaadcabbdbcacaaccbadbbbabbbaadcddcdadbdaccbadddbabccaacbcadcbaaccabcbddbaddabbbbdbdcdabcbccaaaacbdcbbdaaccacddcbdaddbccbbdbbcabbddabccbbdcacadbdcdcaabacadddadbbddddddbcbbbdbbddccacdacddcbacbbaddddcadbbabddaabacdaabddabacbddcccaadbcbdbaaaaddcccbdddbbbdacdabababcdadcbdcdacabcbcddbdcbdcdbbbccdadcaadababababaddbacdbcdadccadcbcaabcdccddcabbdaccbacabacdcacadcadbadbacabbdabccdacaabcbbccdccadbcaddbddcbadbdcacdcadcadaaddaddbbdbcbbaccdbbdaccabbdadcdddcabdbcadcabcabacccdadbaadaddbbadabdabdbabaaabdbdbbaadcbacbcabbbddcacbacbdaccabccbcabbbdbabbdaaabcbcaacbccbabbbcdbdbcdcbbccadcabcabdcbcdaddadccbbbbcdabdcbccacbcabaaabddacbdadaabacbbabcacdaddcdbabaadbdbdacacdaccbdccadcabadbbbadcbccabddbddabccdbabdcacccbacddacdcbbbdcacabacabcaacbdbccdcddbdcdcbbbdaababcbacabcaaccababdadabbaaccdccbaaacbddababcbacbcbcbaababdaacddbadcbbcbdcaccaabaccdbdadbcdadacdcdddaabdaddbcacadddbcbcbcbbdbbabbbadcaabbccbadadacbcbcaaddbccaaddcbcadaacdddddacdabacabcadacbbabaabcaadaacbbadabddcbababdcabacbaaabdbddbcbbdcbcdcacbcaccbdabaabcdcabdaccbacbbacaccadacbdcddbabbcdbcabbcabadbbadabcabbbdacddbbcddaccbcddcaccaacbddaacbdcacbcccbabddadbdbbababaadbdadcccbbccdaacaaaadabaaaddcaabbdddadcbcbdaddbdaaaaabcbabdddacdacbaabcdcdbdaabcddbbbaccaddbcddaababcdadcccdaaaadcdddcdabdcaccbbbaacccbbdaacdcbdbdcaaaadaaabcabbccbcbdbbdcbdbdcccdcacbcbabddddcbabaaaaadbdddaadbdcdcddbcdbcaddbbacccaacdadaababbadbadaccccbaccbbcbbdacccbcadbbbcddaaaaddacbddacbaacccadaddacdcddcbccbdcccaccbbcdbbaddbddbcabbaccbbdddcbbcbadcdadadcbdabccaccbbdbccbddcabbdcaadbcabdccbbaacdadddaccccabbabddaaddcaabcabdbdcdcbabbbcbdcaacbcbccbbbadcadcacabcaadbccaccdcdaddbcbcabbbdcbabbdbbdabdcadccaddadaababbdcbbaaadbcbdcaaddcbdccdaacbddbdbbddabdbcbbcdadddabccadadddbdddbaadacdcadaaacdddbdccbbcaadacacbbbddcbadaddaaddddbcacdcdcaacdcbddbcadbcbdcbcdddcccbbbbbcdbcbddcdbbdddaacabaabdcdacadcabcabccbdacdbababaccccbadccdaccaaccbddcdabcbbccacddbadbbbcbaaadcabbbadbbdbdbbbacddadbdbbaaccdbdaabbcacaabdabddcccbcdbbcddcbcbdcdbccdbdbccbcdcbcbcbbbbdacbacbdccddcbbaadaadbbcacbbddadbcbacccdbcabdacdbbdbaddbcbdcdcdaddacdcabdbbbdbbacacbcbabbadacbcbdcbaacccdaabcccdbccbcbccddbdddddddabaddabbbcabbbabadbccaaddcaaacbcacaacdccdacbbccadccdccccadbbdababaccdddbdbdbcabdabacababddcbdabcaadcbacbcbcbaccbcbcbddacbbcdbbcdcbbbbaabaadcadbdcbabadcacdbacdddddabacadcbddacbcdbcddbadccbbdbbcaabccbbbbdcbbbddabbabbcadadcbcaaccaddbddccddbbaddccbddbcacdaddacaaccdbbadcbcbcbddacdcdcbbcbbadddadcdbbcdabdacbdadbddaadcccaabdccdbcdcdabdcdddcbbbaacabaccadcbbabacbdacdbadcaaaaccbdcadccdaddacbdadabbccbbcaddbadabcacbabbaadacbacaacdbdcdcdccdcccddbabcadcaacccaddcbcadcdbddddcdccbaaadbbccacacdccbdddbbabdabcdabcbdbdaccbbadcbadddbcaccdbadccbbccaacdccbccbcdadacbbdbcabcccdcadcacbbdccbcdcbabbddaabdddccaaccdcdacdbabdadbddddadcbddbbcaadbaabbdbbcbccdaabcbdabcddacbacdcadadcaaddcdabccaccdccbadaabadabbdbdcdddbbbdcdcbbaaababbbcdcdbbcddcabdcbbcbbcbbcadadcdcdcbbbdaaabccaacbacbddbdcbabcdaacbddcbdcacbdadddaddcdccaadabbcbbdbccadcbbdddadcadddadacaccbabdccacdddacdcabdcdccbabadcadbabacdcddacdddbacaacaddcbabcbbcdaaadadadccbbaacdbbadacabcaacbcbabcdccddcccdbbabbdabdbadadcdbacbcacabcdcbcaaddcbbbdbadabcbacaacbdaaacdcbccbaddaacbbadabbbdbdcdbccabccacdddccbaababccddcaadbddabaabddacdcdcccabdaadadddbcddcdcdaabcabbdcdcbbccabccaabdbcacccdbdddddaaacdbabcabadaadaacabddbdcacabadbccbadbaccabbbbddddbccbacdbdcbccbcadcaaabbdbaacbaaddbdcdbabacaccadbccdabcbcaaadcaccaccacddcaccbcaabbcadadddbabaacbcdadcdccdcaadadbabbdbbbaddbdcbcacccdabdcaacabdacbdcaabbcadbbcdbbdaadcbddaddaacaaaccccdaccddbdaccabbbadbcbdbaabaacdcacbdcbaadaddcdbdcbacbbdbcadbcdcbcddacabcdddbcaccbadbadbcccddcbdacbccccccddabdcddcaacaaddcdacaddaaccbbcdabbdcddbcacbaadbccbacbcdaaaacaabbccdcbcbcbaddcbacdbdaddccddbaabcdbdcbccaabddcdbccbccacbabdadbaabdbcbabadadbbabcbdbbbdddcbcbdbacacbbddaaccccababadadcbccdbcacddcccddabcbbcdacbcdbbbddccaacadbdbdccccaadbdcdcbbcbccbadcbdacdadbcbbddbaabaadacbaacdbdacadcadccadadacbcbbddcaccdcbacdbbadcaabadbaaabddcbababdcacabddbacaddadaccabbabcbabacccbbcbdabbcbddcaddbbbdabdccbbcaabcadbbbcccbccdcdabccaaabcdabccbcbabaacdaaddcdcaabacddbcdbbbbbcbcdccabbdadabdcbbbcbcbcdbddbdaabadadcdddcccbcdddadadbacaabcdbadbdcbbbcbbdacdacaaabbddadcddbabccdbaacacbbdddcacbacbddcaacddcaccabcccbbbdbcdacdbabccaccacaadcabadaabbbdaadccaabbcbdddbdaabcddcabcdadbdcdcdabddbacbbdadcdaaaababbcabdabadadcbdbaacbbcabbcdcdcdadabcccccbbacabaddbccccdbdbcabbdccdccacbddadaddacaccbaaddacdbcbddcadacaccabdbbaddaddbaacbcccccbbdadbcdbcbabadbcbcbadbcaadacaaabdbbcbccccdbcacddbdbcbdccdbacbbabbdadbbaccbacbcccbdbcaaaccbbdcddbbcaccaaaccdccbdcacbabbddaaacddddcbadbabcccaadbdcbbaacdddcacbdaddbdaddcbadaccaccdcbbacdbdcacaacbabbadbdddcadadaacbcccabdbdaadbcdbdabbcdababccddaccaadbdbccdbcdbccabbddddbbdbdcbdacbbcbaadbdabaddadcbabbdcdaddddabbadcddaddcddabdaaccdbccbbbbbccdbddaaabaabcbbaccacacabbbdbabcdababcdcabcacaccccbdaaaddbbcccdaabacdbacdacaadcdbbadacabddcabddaabaddcddddccbcdcdaaaacbaaddddcdacacacdbbdbbcdacdacbabadaccdccdcaacddddbdaaddcdccadbcdadcadaccccabddaacbaaadabaaacccadccbbadbdbdbcbccaaabccbcdcaccdadcabcbbaddcdbacdbccccdddadccdaadcdcababaccacbdabdcbbbcbdabacdbbccbddbcaadccdcacabdadddacbbaccdddbbcaddccbddbcaabaccadbbbadbcdcdcadbdadbddabddcadbbadbacbdcbbddcdbbdbaccaddbdcdbabcbaddaccaaaadbaddcbbacbcaaaaddabbcaccdbcbbdadbbdbacacbadbdbbbcbadcdbaddccbdcaadcdcbcdbdacbdcbdacccddadaadcbcdddacddcaccbcdadcaabccddccbdadcdabaadbaacaccbdadcadaddbcdbcbdbcaabcddacabcbdcbdcdcadbadccaacbccacdccccddbdadccbdbcabccaacbcbdcbcbdccabddcbcbacdbaadaaacbccccbacaaccdbcbaccdabdcbadacbdbaacaadcdcabcdbbbaabdbccccbdcddddadbcabbbacdaabbcdcdddbbdbcbdbdcdbbbbccdcdabccdcdaddcaccabcaabccbddccbabbdadacacacaddacadcdddadaddabcbbcccbdaddabcdadcdbbcddbbaaabdbadadbacbaaadabbccdcbcbdcdbccbcdddacbabccdddddbaccdccdbbbcbbaacdacbbbbcadbdadabaaacbabcadaddababcccdbaddaacaddbabccdaabcbadbabbddadbccabcbaaccccccaaaccccaccdbbabdaadccbcddbdcbcdacaddbcddbbddcbbbaadccabbbabcabbaadadababccddbaddbadccdcbcccbdaadcaaddcbbcbaacbccabccadbcacbdddbbccdcbdcabcbbddcbcdaadbddabbbdbbbadbbbacbaabbbabadbddcddabaadbdccdcaaacddcddcaccadbaacbaccacaccbcdcbacaacbdacbdbdabdcdadadadbbaaddbdccadcdbcadacddccbddbbabcddbdbcadaaaadbdabdaccabbdbcdabbcaddcaaaddcdcbddaadcbacdccadcbcaadbbccbdbcbdbdddcacbcdbabaaddbacbacdddabccdcadccddaaabcaaaacdabadbacdabbdaddcccacbaccdccccdccdbdcbddcadacbcbaccdcddddbacadddccbaabcbcdaaababdcaccaadcdbddadacdcbbccadbdddadddbdbcddcccacbbacabbbaccaddaddbbcdccacabdbaaabbabcabcaacadcbdbddbcbbbbccabbaadcadabcbcddababdbbddbbbbadbabdbbbbddadcbccbcbbadaddaddcddccbccacddabaadaaabccbdacbccddbbbbcdcadcbdccacadcdaccdadaaaababaddcaaccaadaadcadbcbddaabbdcccadbbabcacdbbcdbdacdcbdddddbddccddbdddbaadcbaadcacdbdcacdaababdcbabbcacbadabdbbdbccccaadaadbbdaccdddbcdaaaacdbcacadaaabbbacbdaadaacabcaadcabcabacbddcaabadbdcdcabadadabccbcdadcabcdacdbcbcddadcbdbbcdacbddbabcdcccdddacbbbabccbbddcacccaaccddacbcccaabdbddbdbadaaddcbaddccbdbcccdacdddabddcdcdbbccdddababcaccdcadaacddaacbccbbccaccabdcbdcbcaacdbabdcbbcbdcbdacbbccaaaaddbcbabbddabbadddbdbadabbbbaddcaabcaacbacacdadcbccaacaaaacdaacbcbdbcbcdabacdaaddcdcaabddabcdadddccabcbbbabaddabbabdcaabbcbcdcabbdaabdabadabacaabcbbdcbacbccdbaaadcaaadacdbacabbbbadcbbacccdcccabaddddbaccdaadcadabbddbdcddcddbdcbabacbadbbdbabcdacbabcadbbcbbadbbccdacbcabcbcabbbbccdcdadddcddddbcabacdbddccabaadcbbadbdccbabdbcabcbaadbdcbabccababdaadbdcbccbadbcbacbacbaccaabdaccddcdcdbbabbbdbadabcddabcbadbdacaacddcbdabdccdbcdddacdcbbcdcadddcabcdcbbdadcaadaacadcdcbbacdccccddcadccbcdcdabbcbcdbcbbbbacdadbbcadcdddccabbaddcccccadcbdbcaadadaacbcdbdccadaadbdaabdaaacaccddddbadacdddadbbcbcbbdbaacbabbadcccdcdcdcbbdabcdaddcadbbdccdbdbbbaaabcdbacdcabcbcbcdcbddddaddbcbadaddcbdccccacdcbabcbcccadbabccccbaaabdddcddacdcddcccdadadacddddddabccdadccbcbbdcddbdbbadcbbbbccaccdaccadcccabdadabbcacdbdacaadbccddadacabcadbaccaccbccbbcddabbdcbacabddbadabbadaccaabcabaabbdccbbbdddaddcacbdbccbadcbbbabbddcbabcaccabcdcbccdbdbbddbcccbacacdadcbbbddaacccdbbbabdccdddcdbcabacdacbcbbcbccbcdccbabcdadbdccbaabbcabddaadcccbbbbabbbdcbbdbdcccdbdbdccdcbbdaaacacdbaaacbbddcbaaadbcbadabdcacbdccaaccaabacdbbadcdabbbadbcdadcddaabcadaaccbdcbaaabaccaaacdddbdbdcdbdbabadbdcabcdbaddaaacacbcbcabcbdaddcdbdabbcaabcacaabaccabadaddddbabbabddddadaacababcabbdbabaabddccdddbdaddaccccccadadcbbaabcdddbbbbdbacbcbbaaadbbddcadaacdaababdccadcdcddbaadcbabdabbacaaacaaabacbcbbdddacabcaaddcbbcddcadbaacaccabbbbcdacaadddbbabddbbcddccabcdbccddabcbabbcdaaaaabdabbaadabccccbccbcadbddcccbcbcbbbbbdcacbcaabbcdabbabbdadddccdcddcdbdbabdadcdbacdcccdcdbaacccbbacaddcbaddabddaacaaaddabcdbbdcdcacadddcbbcbcbcbdddcadabccaabbcbddcaabdbbbddaccbdcbbdcaaabaccbcaccddaadcaacbacdaddaddddbaccdbadacdccbbdcacaaabcdbdaadbdbdbbccdcbaaccaadcdcccdadbbddbbbadbaacbcbcaaacbccbccddddbcbbabcbcabbabbbdbadbdbbccddcaccbadcddcdacbcacbbabcaddacdaacdcacaaaddaccaddbbcaacdcddacbacddbccaddabadbbacbaddbaabadbcdabddbaabbabdadacdaccdcadacccaccacbabcdcacdbdaaadabdadadaaabdcddacbbcbcbaddabddbcbadabcddacccaabbdbbacddabccbdcbcdccaabcdaaacdccddbddbbabdaccbbaacbdcdacacadaadacbaacbabaddbbadaaaddbbcbbadbcbbbcabbabdddcdaccababbddacdbabdcbdccbbdcadacddbcdbdabdcdcacbbccddcaacdaadcdcbaaccbcaadccccacdcbbcccbdadcdacdcdcabcbacbcabccadbdcddabbababcbaccabdcaddaabdcdacbaadddcbbdcacadacdcaadabdbbaabaaadcdccdbabdabdccadadadaaccaccdcdadcaadabbcdcbbcdddbbcaacbddbcbacaccbabdabcaaaccdcddccdbbddbcddcbdcbdcadaaadbddaccbbddbbacadddbbbcabbcabbbbcaaccababdbabdacccbcdbbaabaaccccbaddcdccacaadddccbbdaaaabdaadcbbbdaadbbcabcbadaacdbaccabcbdbbbcbcbaabaaabcdaabbaadbdabaccdddbbbccbadddcbcdaabddbabcbcdcbbbccdaadcdccdbdbacddccdcbdcbdcabaacccbccacdbcbcaddcdccdcbdcaddacadaadacbccdddbbdbabdcabcbabccbaccadbadbabaabbdadbbcccddcadcdbcadbbbbdcbabbbdacacdbdbcacccbcdbdabcccdaabccbacdcbaabcdccdacaaaabcacccabdcdbccaabddbadbcaacdbbdacaabababacacaaabdcdababacdbdcdcddbccdddcdbacdabbddbccdbacbdbddaabdbddacacababbddddddcdaaadabadcccddbacddaacbbdcdbcbabadacccadacbccaacadcdbdcddadadccaabbbbcdbadbabbdacdcdbaaddcadbaaccbdadbaccaddddcbabcbdabbccadcdadbcbaaacdccdaddcbcacbbacbddcaaabdbdbaaabcbddbdaadbcaccbdcbacbdddacdccacdccdcddcdadbabddccabcbcabdabddcccadbadadaacbcdccdbcbccbcbaaaadcbcddaadbaaadbaddcccdddccddbacbdbabddbddbdcbcabddaadadbaccddabcdaacadcabcbcbbbcbabcbbbaddbaccbcccbdaadbdcccbbccbabbcccbacbddabbabcbbbaaacdbbbccbaadabcadadccdcdaaddadcccdbacbacadcbbaadbbadbdbacbbcdacadcacdacbddadacacbaddcbdcacbdccbcadcaabcdcbccdccaabbacdbacdbacdacabcbaadcdabaaabbbabcadddccadaadaacbcbddcbcbaccabccdbcaccbadacaccbbadccacbabaddcccacaaadcdcccdacaacdcbdbbabcbbcadcbaccdcaaccdddbaadbadadbadccddaccbdaabccadbcddbcadbcdddcacdbbcbcddabadccbbddbaabdbcdcbaddbddacdcbaaabccbdababddbbcadaccdcdaacbadbaadbdbaccacbccbaabbaadccdaabdcdddbbdabbddbccdbabdcabdaacccdcaddbdcaaaadddcbabbacddbabcdaddacbccdabccdbbdbccdcddcccdaaadbbdccbcaccccdddbdaabbcaacddadaaddcacabcdbaacbbccadcaacadcadacbabbcccaabaabacaabbcaacbaabbbaccdccdbdbacbaaadccdcdaacdaabaaacdbacbcdccbcdcaadbcdadacdababaaacadbbcadacbccdbdbbdacadddbbdbbcdccabcbbaccbdabbddddabcdacccabcbbbbdcbcadbcddbcbaadcbacdacdbccbabadbcccdabacccbcdbccadbbcbbabaccaaadccbacbacdacbbbbbbabdbaccbaccbacbbcadadbccdcccadbdccdcdccabaccbbdbdddbbdabbdccbcabcbccdddcbacddacabdaabbdcabcabaacdbdcabadacbccbdbbbadbdadcdadcbbaaabbabababbcdbdcdcaabdbabcadaabdbcbaabcacddbdabcbcbaabadcbbadadddcbcabcdacdcdabdabbdbbcabcddcdabaadacddabbdbcbadbbcdaacacdbcddbbcbccbdaccdadbdddbadbadcbbcdddcaddadbbdbbdbabbcddccacbcdaaaadbcadcbacdcacbcbdddaddcdcbaaadbdcabaaddabcdcabadaccacdbddbaaaccddcbabddddbddcbcbddcccacbcacbdcdccbbcbbbbadacbbbccdaabdccddbaddcbbbdbcadcaabccdccaccdddddaadbadcabddcdcbccbdaacdaabdcddbcdadddcacdbcbdcbababdbabcadcdcdababacbadbccdadbabdaaddbbdbaadbdabccbddccbbdaaadcbdaacbadddcbbdddcabdbcbacdddbcbbdaabacbadcbcdccbaccccaaadddcbddbcbbcbbccabbdcdbcbacaaddddbaacacaacbdaccadddaadcdddccaadbbabcbdcaadaadacbccddccdabbdacbbbbadbbbaccbccbbacacdccbdadbcbaabbddadbddbbccbbdbabbacdcbdcaabbabcdbdcbcabaccdddcaadcacbadbcbccadabacdbcdcccadacacdabcbbbcbadbacbcbabadbacbcccacccdbaddacbabaccaadadcddaadcacbbcbbaadbbbddccaababdddabccddddbcadbdbdaaddacddddbbabadbbbddbadbcdacadcbbdcbcbadadccadccacdcdbdcbabdbddcbbbdaacacbcbbbdccadcccbbbbaaaddbaacbdbcccadacabdcdcdcaabccababaccccadddacdddabcbdccddcbbbabcbdcacccdababdcbdbaabbbaddbbddcabcdbdbcbbababbdbbcdadbcdccbccbddaccbdbdaddadccdbbabcabcbcdbdcdbdadcbdcbcdaccababbacbdcbbaabcbacddcadbdcccdbbababadbaccacaccccdddbdddadddcbcbacdaaccdbcbbddbcbdcccaadaaabacacaaaadccccabbcbdcbbccabbccccdcbadddbddabdadbdbdcbacdabdcbdcbcacccbdbbadcdcddacddbbdcbbcacbadcbaadaadbdbbbadadaabbdadbadcaabdbacbaadacdcadaadcbccbbcdabcddaadcdbcccdbaacccbacbdabbacdbdcaadabadbdaaadacabcdcacbdabcdacdcaababdacaccbdcadcbcdaaddbcababccccdaaabdbadccdcddababdcccdbccaadabbddbccbdadbdbdacbbbbdcbcbdddbcddcdbacbcdaadbacacccdddbadabcbcadcbbbbadabcabbdaccbbdaacccdbbdbbbdbdacabbabdbddabaaabdcaabccdacdddbdcbaabcacddbdbcaaabcdbddcadddaadabcdbbdbbcacbaabbccdbbaadbcbcbbdbbbbdacabbcadcabadcbaababdbbcadbacaacdabaadccaaabadddcddbbbdaddabddbdbabbdcbdbddcbbaccdbcaabcbcdacddadcaadcddbcdaadbacaabdcaccaddbbcdcbdcccccaacccabbbbcabbbdcdbccadaacbdaddcccaababcbdcddacdcacbdbbadcdcbdaddbccbbcaccaddbacabaabdcdccbcadcbbbbbcbccaadaaccbacbbacbdccdadbcbccbbbdccdddabcdbbdcccbdacdcabaacaccdcabccbccbabcadabdaadbdcddadccbcbcabbcccbcaacaddaddadbaccbdddbadcbbbabaddbcdbcddbbabcdbbcbaadbddabbadcbaccbaaaaacbddaddcaabbabcdddbcddabcdacbbacadbbacbcbdaddbaacadaaddadabdbddbabacbcdadccbacbddccadcaadddbbaddcadbccabdabcabcdadbcbdacdbabbacdaccdaaacbcacacbbccbadddbddcbcaacacacdadcbdbadcadbbddabcddcccdcbccaabcdacddaadacdbccbbcacaccaaddaacaddacdbdcababdbdcbadaccccbbbbaadccddcccbdaaddbdacadcaacabacbabaadccbabcdcabcccddbbabcaabcadcbcdcccacbbbdbdbddbcacaacaabacdaabbcdbaddcabddacbdcdbbcbbacaaddbcacbbadbccddbaaccdcdbbbacacaddbabcdcbcbbbabacbdcbaaabdbaaadbacaaaacdaaddacdcabbcadccabccbdbabbcbbbaaaadabccbdcaacaadadcaacbdddaababbdabcabaadabccddcadabdababcaccaadcaadccccdcdccaaacbbdcbdcdcbdcdbcddacbaadcbcaddbaddbcbcdaacccddabbbdcccdaaabccdabcccbabdaaccbdddbccbcbdddabcbbbccbbadcdabddddcaacccbddcbbcddacbddccdccabbadbbbcddaacccddabadbcbdacaddaabadcaddacdadababadadaddbacaaabdbabacbaabdadcdbacbbaaaaaacdbddcdddacaaaabbdaadbaabaccddbabacbdccbacddaabbcacccddccaacbdacbbcadddccbccaacabdbdbddcdbcdabcababcccccaddcaacbcaddbaaacdcbbdbcabbdbadbbaaadabbacdbdccccabacddabaacbbacdcbbababaaacababdbabcccdaccbadbbadbdacbdadbbbbadbcadcddcacdbaaabacbdbbcdbdaabbcdbcacdbdddacbaadddccdbcacdcbdccabacdcbbdbdabaacbcbaddababcacadcabccdacabccbdbaadcdcbcdcaadcccacbdcaacddccadbcddbaddcbacbddddbdcdbccbbbdcbaadcbabdaacbdccaddccccbbddcacdcbabbbcbbaabcadadbdbcaddcaaaabbbccbcbcbddabdadadadbaaadccacaddcddabbdcbabbbcbccccccbaaddcadcaccdbdbaadbadacdcdbabbdbbacbacddbbdbcadaaccababcbbadcadadaddcbbdabcbcdbdbdbacccdbaddccdaccbdccbcbbaddbdccddaadcbbdaaaddccccbdadbcadbcacdacdbddadabaccdadcaddbaddbabddadabddcccbabcdcbdadbcdadddaabcdacdbadaaacddcaddadbdcbdabcdcbcdabcbbbaaacdaaacbbbbbdacadcdabacddddcbbbbbbcadbbcacccddcdcbabbcdadaabdadaadaaabdcaddabccadabcabcbdccadaddddbdcdacdbcdcbaabcdbbdacabcaabbbabcabbaccbdcacdcbaadcbddccbcccabcdabcaaaadcdbcdccdabbcaccddbccdabcdacbcdadbbcdbbadbacaabccaadcbbdccbbcbdbaadadabdbddaccacaccacbbacadcbbbbabdaabbdbdcacdbdcadaaddabcaaaaabbabbdcabbaabdcbcabbccacccacbbaccaaaadddcbcabadbbacabcccdabaddcabdbbadaaabcbdbdaaccadddadabbdabdacbacdbdcacbdbaddbdddbdbcbcaadcdaaaddacbcbdcbcbccddbbbdbabdbaddadbcdbdadabaabacaabddaadbbbaabdbddbaddcbbabbdadaddbcbadcadbadcdaccdbccdcbcbcbcadcadabbacbdcbbdbaaccdbbcdabddbacdbdcadbdccaddabbabcabccacbdddaccdadbaddddcdbcdbabcbbbdcdbdadbaaababddcbbcdbaccdabccdbbdbccaccbadaaacddbadcaaddacdbacbbbcdbabcdbdccdbccbbbadbbdbbdbddbaaabaaabbaaddcbbcccaaabcadaadbbcbcccdddbdcddacccabcdccaccacacddadcbadcbbdadbcacbbdbacbbcadbdccdacdbcabcddaabbcabddaabbdbbcacbaadabaadbaabbccadcdacbcbacbaaacbccaaabbdbbcabccbddcdbbabaaddbbbdccbdcbabacbbaadbbabadccbaddccabbdadcccdcaacdcdaadaddcabadbacbdbbddbdccadccbdcdadbccadabdbdadadddcbccababcccbabababacabbdabbacbbcdcaabbccababcdbcbaaadacadaaadbbdaaddcdabbcdbccdbaabdcdbaaabbddbcdaacbababaacbcbbdbbdccccbbbcaaddbdabdddccbaadbbacbdbdddcddbdbbacbabddbbbaccacdadbbaabdbabddaccbbdcbaddbadddcdcbbadcbcbacdadbaacabcbdadaaddcbaabdbddbdcbbcadccdadbcabdaabdcbbdcddacddadaddabcbbbbabcbcbcbccaccdcbcccbcabbbaacabbacbaadacdbdbbbacbdcdabdbcaddcaddacdcbcaddbdccaddacabbbcaaaadaddcccacabbdcaccdaacdadcbabddacabbcbbbcdabbdcbdadabbcacbccabcdcddcabcdacccacbaaccdcbcdbccdabddbdcbdacccccbccabccbcbacadadbdacbbadacaddbabdcadcadcbcadbdacdbcdcdaabacaaabbbbadbaaabcaaddaddaaccddadccaccaaacdabbcccaddbcccabaccdddbcbcdddbcbdcdaddabbccdbdadaadcadadcadacadbacacaaccccabbdbbcadccdcbbbcbdacbabaaaabacaabcdaddcccbaacccadbcbdcacbaabbdabbdaccbddadbadcbabdbdacbbcbcabbababdccdbaacacabddcbddcacccccbadbabbcbdabccbbcbbdddcaccaaabbcddababbbbcdacaabdaaacdcaadaccacdbbcdccdbcacbbddcbcbcddcdacaaccaaadcaaaaaaabcccbbabddaaaadcbccbbbcbaaaaadadbaccabbcbacaaababdbddddaacdabdacaccddbbcadbccadacbcabddddcaacaddabdbdadccabdcbdcacbbcabaacacaacaccdcbadacccdaaddbbabbcddbbbbccbacdacabaacbaaddcdbbcddcddccaaddbbcdadddaabababbbdacdddaddaabdaccabddddccdddcadbdcdabaccbacccddcbccdacbabcacdcaacdadacaccabdddbadaacdbbacccbdbdbdaadcadbbccbbbaaccbbcdbabdcdccbddccbacaabbbcabddaadccbcbbcdcbddbcaababcddaaaabddddcabdcaaddcbacaabcbddbddddcaaadbdbaccaccadabcddcacaadcabaadadabccddabbdbdabcadbabdbaccbbaaddbcbcbaadacbbbadcbacbdbabddaccccbddbcaaabccddcababbbacadbbccdbacbabadbcdaccdddddbcbdcbbbddbbdaaaacbcacbbcddbdaccdcabcaacaddcdacdaaddcbcbabcadabbcbbddabaadcaccdbdbbadbdcacacbcbbdcdcbdccdcdccaadaddadddabaddbbacaaadabdababdcdacbcdbdcdcddacdcccacdbdbcaddbcabbccdccbaabdbbdcccdaddcbadcaababcdbaaddbaaaddcdcbacacbbdbccdbbbabcdadadbcacbbacbcaadabbaadbcabbabaaabbbdabbdcaccaadcacbacbdccabdbbbacacddadacacbcdacbcbabdbdddacccabbccaccaaaabadbbadbdcdcbaaadcadbccbbadbadcdddcdabdbbdbdadcaddaabcbccdcddacdcdadabccbadabbcaccccbbccbacaacccdddbabddadbddacccadbbdccccadcaabaccdbadcabdbacaddababaacaddaadcdbccbaabbddcbbdccdaadcdddacbadbaddadcbddccbacddcdcbabbbbbddbcbbacccabccacdacdcaaccbbddbcdcdacacdcccadadcbadddbdbcbcaccadbadbbbbcdcdcabdabaaaabcbddddcbcaababbddacabbbddbadcbbcbaababcdcacdbdcaabbdacbaccaacabdbbaccbdcbdaaaabbdabacaccccdddbcdabbcdbaaddcccdadcadaccbddbdbcaddaacccddacccdccadabddbdbccbbbdbacaacccbbdbdddacbbabaabcadabbddbcabddcccaaacbcaacdadabbaccaaaababadcbadddadcabbcdbadbbccdccabdabbabaadbabdcdbaddabddcbcdccabbadadacbbadbccbbddaabaadaabaadcabbdbadbbdddbccbbacdddabdbabbaddddbdbadddcbbcadcaabcacdcbdbaaccccccdacdadbcacdcaacbacdddccbbcabacacabdcadcddacbcbdabcccbbbadbdcddbacdcbacbcddabcdbdacbdcabcccadddaaccaababcdcdadacdcacdccacabaacbcdbcdabdcbbabddccbcdaddbcbccdaabdccbdcbdcdbaaadcaccddbadbddccbbcaabaaadabcddbabcbacddacdabcbbbdbcbbbdbcbabcdddadcdccbaacdcbcabadaabbdbccddbccdacddcadaccbdaabcbcdccdbccccccbdcadbcbcdaadbadaacdadddbcccaacdabcbbcdbdbaddcdbcaddbbbadbcdcbcabbcadaaadbdcbbddadbbdaadadbcacadcaaccbcacadbabdcdcaddacdadadaaabcbcbddbdaadbcabdddbbbdacababcaaadbdbabbdacacbcdbaaaacbbcddbdabbcaddacddcdcccbbdabbddcbbcabaacaccaccacbdcacddacbaadbdbcdabaaddaaacccdacabbddbabdcadaaaddabacaaddabaddaaccbdcbdacbdccabbcdadaddcddbdadddacabacbbcdcddcadbbccdaccddddadbdccccdcaccacddababdccddbdabbabbaadccdabbbabcbdbbadaacdbadbabaaaadcaabddaacbdddbcdbaaabdadbabbccbdbccaccbabacbcbbabdcbcdccacadcbabcdccbdbdbbdcdbcacdabadbbadacbdccaacdccacbcdbccaacdcabaabcabcbacbbcddbcdacadacaadabdcdcacacabaacddaaabaadbabcdcbdadcacbbbaaabdacccdbccbcccccbdcddaacabababccdbaabdacbdabcacacbddddcbcbcdcabcbcdccababaccddbbabcdabdaddbbadbacaababaabccbbabdcaddbcdbbddbbccbbbdcdbdaaccdabcacccbbcbdbcbdacdbcccdbcdbabddbdbbabbdaaacddcacabbbdadcdcabcaccbdcadccddddcaabcbbaccdacacbbcdcaabcdccbabcbaadcdcccacbcdaadbcdbadaddabbbadaadadabccadcadaccdcbcaaaccabcdbcabbaadaaadcbadbacabaaddaabbcdaaddcacdabaadbbcccccddbaabcdbdbbcbcadabdcbdccaabadcadaacbbdadbacdddabccdbcadabdbddabadccbdcbdcddddadabdacaaddcccddccddbdccbaadbdaabbcccbdbcdddddacdbabdcbabcdddacbbcabcccaabdcbbdbadbadacabbadabaacaddcaddddbbadadaacdaadabadbbcdcacddddcaabadaabdbbbaadccacbacabacdbdddcdaadcddbdaddbcbbaabaddcdaaddbdccbbcacacdccdddbbddacadabbdacadabdbadbadbaaadbcdddddcdadddbdbacddbbdcdcbaabcbadbccbacacbdbcbbbdcdcdbbbcdabcadacdbddccaaababaccabcabaadadcaccddacaaccaadacbacacbcadddbadabdbbdadacbbaaabdbddddbbbbcdacccbadbdcdbcbbbbaccabbadabdabdbdbddddbcaaaaadaaadcbaccdcdbbabcabcabadcbbaabdaabddccdbcbacdbacacdbbcbbcdabdddadaabababcdbcbbcbdabaaabcbccbcccbaadacaddddddbbccdccccbaddddccacdbdccbadcbdccdddaaaddbdbdcbcbcdcdbbcacbcbccbabacccbabcbbbbcbddcddbdadadbbccadacddaabacddacbbaccabcdabcddcddbbccabbaddcdbdaadbacabddbbbabccbadbacbabddbccbabdcddabbbddaaadccdcdabbbaabcacabbcaaadacdcaaabbbabcbbabbdabdbcbadbbbccbdadcbbadccacbbdabddbdcbadddacbbdcaaabbdbabaddcacdacddadadadaddacacbbdcbcdddadbdbbbbbaccaabaabdbdcabddbbddcadbadacdbbbccbccadcaacabdbabadabcddaddddcbdaacbcabacdcababcaadbabbbcdcabbcccdcdcddbbaccbccacdcadcccdabcbdaaaccacaddbbbcbdcddabbbbcacdbdbdbbdabbcbdcdacabadbaccacdddacacccbddbadaddaccadbdabbdbdcadddbccabacdcdbcddbddcdddccddbcdcdacacabdcaaaccbabaccddccdadabcacbdcdbaadcddbbdcbadbbddaacbdacadddabccbcbdcccadbbaccdcdcabccbdcacbbcbbaabbaadcdacdddaaccaaadaabbabcdbccbbdabdcdadbbcccdbadbccccbccdcddadadcdaccddaaddccbcbdadaacbadacbdbdaadacaabaabcdacbcbddbaccbcccbbbdccddcaabacbcdbdccbcbadacabdbbcabdaadaaacaccaabcbbcadcacadabcccdadcadabdadcdccbdaaaaddcdbdbbdbdcdacbbcbbbcadacbdbbddbdccdbbadabbbbcabadccccaacdcccbbbdaccdbbdbaadcdddacaaddbabcbaabbbcadccabaabcddadcbcdbadaccdcdaaddcdcbdbacdcbcadababaacabcbbcbacdcaaaccacabdddbabcbcbcddadcdbacdbbabddaadcaddcccaaabacbbabdbcdcbbddcaaccacbdaaccdaaaacddbcbdbaaaaabcabcbcbaccbcdccdcaaabacdddcbaaabdccabccdcccaccddcacacdadddbcbdabbaaddccbcbbcbcddbaacddcbdddcadbabcbdabaadddcdcdaddbccadabbbbdddbbcaaabcacadadacbcaaacadaaabdadddbbdaddcdaaccbcbddacdadbdbcabbdacdacaddaccdbabdabcbadadddabddcdcbcbbdadbbbadbdbdcdacdbbcdacdbabdddccccdbcaacdbabdcdaacabdaabbabdabcaabbabcadaadbaababdcbadbaaaaadabacdadabcdaddbbbbabbccddbdbccaaabdcbdadcccaabbbbdddcdaadabcaddacaaadcbaadddbdcaaddabdbbbbaadddbdcdacdccbbbdcccccdcdcdabbdddaadbcbbaddabcdbacdcbaddacbabadbbddacdcbbabaabaaaacdcbdbbacbabbdccbbbbdcaacdbcbadcbcbbcdaaccbdabcddaccdaadddcdddaadcdadddbaaacccadaaaccbdcbaaaccbdbdccabdddccdabacaccabdddaccdcaacdccbdcdddababdacbcddbdadbabcbbccdaaadbaccccdcdaaccaabaaddadabbccdddccabbbaccddccccbdbbdaaacadbbbcbdbdbacacaacbabccdaadcadabcbcbbdcccdbadbbadaacdcbbbcbbdbddaadbdacacdccabbccababbdbcadbbcdbaabadacdaaabbacdbbabbbbadabcbbcdcdcadcaadcddaadbbbbcdadccbccbbbacbcdbccadbdaccbbdbdbdabaacccbcaaabbdbaaacacbcbacdbcccdcddacbdcdbcacdabdbbadccaadcbcbbbdbcdcabcdbdacabbbccdcdaccdccbababbcbdacbdbbaaababbcbaaaccbcbdaadcccadadddbabbdcbcbbaabaccaabcbadbbbbabbabaabdcdbdabbdabdcddccbabdbadbaacaabacddddccdcdbbbdcaabddcdabbacbadbddbccddaddadbcaadaccadddabcbdbabddbcabaaaacaccacabbdaabcacbccdabdabdccbcbdaadaddccdbdbacdcdcbbbbbddbbcbcccbbaadcbabcbadabbdaaacdbbbccaddbacbddbbcbdacddabbddbddabdacabbdbdbdbcccdcacadaaacbbcbabaaacaacbaddabdbabdcddcdaabcaddadadaaaabbcbcdcdabacdcdcaacbbacacddbbcdddaadabdbbcdaadcabaaabadbaabdcacccbacbcdcaaabdddbbdaacabbdbabaadccbcdbabadadddaccaaaabdcbdabdbbbbbbdbaadbadadabcadbbaacabdcddddcddcabdddaaaccabdbdbadaccbbdabbdabbbcbabaddaccbacdbabdabdcbacccbabbccaaacadbcacaaacdabbbdddccccdadbddbcabbadaccadaadbcacadadcdbadbcdcddccdcdabdccaccbcbcccbababcccabcdcadbdccccccbcdcdcdcbbbbaaacbababaaabbdcbcdcabbbcdcbbcbcaaadadbdcdabbbdcccbadccbaddbbbaadadbdacbdcbaabbabdbcbacdbacbbbdacaccacbccbcdbcccacdaccadaddabdabaccabdaccdbcbbbddcdcbaaccdbbcaabdaaabacccaabcddadcdaacccbbbddcbadbbcacdabddbccbabdcbcabdbbcacabdbdddcadaccdbaaacaabcdccadcbabbacacaccaadcbddbbbbaabdbcdcbadabbbdacbabbbacbcabdcaddcbbadadcadbbdcdbbbbcabddbaaadaacddacdbabacabdccbbcbaaaadaaaaacbbcdaddbcbadbdccddcbccbaacaddddcdbaadaacdaaaababdcadbabdcbbbabaadaacacdddddccccaaadaddbcbabdbbbcbcddcbcdaaabbcabcdddcabccbdddccdcbbccabbacabccccadabcacdcdddcccbddcaccaddbcdacaddcddcbcbbcdaacccbcdbccdcbacacadbbdacbadbabbdcacddbcadddacacbaabadaccaabbcbdbbccbaababbadcdbddacdcadcbacbadabdcccadbaabbbcddcabbdddbdcddcaabdcbcdbbaacaadcbdcacbbdadbcdbdaaacbdccdbadcdddaabcbabcaaddddddcabbabddbacacdbbccabdccaabdaaacbdccdbaddcbcabbdcbdcccbdccccadaacdbbdbaaaccaacbabddaaabacdccdacabdbdbaabdacbbacaddcbbaaccdbdacbdcaabdccaccbcccdcccadcccccdcbbaddaccadacbdaadbdbbcdaaabadcdcdbaaccdccaaadabdadcdaababccbaacabccbaaccccabdbbbbcbccdcccddaaaacadaddaaddaacaacbcbdabdbbdacaacbbaababddbcdabbaaaccadcaccdbbdbccacdddadbdcacadbbcdbababcdbaddbdddcdadcccbadbabaaddcbccccbbbabdcdbdbbdaaaabbbbbdcddadaccbaadadacbbadadabaadaaabaddadbcdcbdbddbdcbbcaacdabcaaddaacddacbbcdbabaddaacdaaddbcaaaaccacdbdadbbacbaacbacdaaabadadcccdacccabddcdddcbaacccaddacbccabadacbbababbcdaaacdabdcdadabbcdcbbdaddcdabbaccdcabbdacdcaadbbdadadcbccadddaddbaaddcacabbddcdaabcbbabadcbbbbcdbdddccbdacddcbdbddcddccdaaadcdbaadddadbdcbbcdbcbbbddadadcdbdbadabdbccbaababcadbaddcabccbbaccaaabcbdcababbababbadcdcbcaabbcaaaaaabbcbcaadadcdbccdaadaabadcbcdacdbcccaabdddbdbaaabcadddbdcadddabddbccdbdcbabaddcbaddccabbabacbddddaccdcbdbabdcdaabdbdadbaccdbcdcaaaddaacadacabcaaddccdddbbaabcaddcdabbbdaabbcdacbdabaaddaabaaadbcbbacdccaaaabddbdbcccdcbabcbbbacabacbcdcdbadaccaacbdbdaabcdcccdcabbcbcddabbcbcaddbacdbcccbaccdbddacadadccdbbcbbbbbadcbcccdcccbbbcbcaadbaadcacbcdccaabdaaddbacbabacbdbbbdddcdbdadcbddcbcdcdabcbbbbdddabdcbaababaaaaabbcbbcbabdcadabbdaccddbbbcbcbaabacccdddbacbcbdadcddccbabddccaaadccadabdcbabacabbcbcdbbabaaaadcbdabdddaaacdabbadcbadddcbddccbbbccbbaccbabbacdbdabdbcdccaadacddddcbaabbabbbbddbbdbcbbdaaccacdcdbacbacacdaddaacbdabddcadbdbdabbdcbbdcacbcaabaccdcdbcdbadbdbbdabbbbdcdbdaacabccadabdbdbddbcbbdbbbdbdbbabddbacbccddabcdbbacadbddddbdbaddbccaaabbcacdaabdccdbaccdbcdcaddcbbddccccadcadccabdaaabaddbbadccacdaaddacbbddcaaacabaaadadcbdacdcabccabdccacbdddabcbadcddaccaabddbcaaaccdcdddcdbcabdadcddabcdcaadcccaccacbdbaadbbacbdcdbbaacaaddddaddaccaaddbbddccdbadaddddbcadcccadabbcacdbbaddbacacddddaadaddccacabdabbcbbcadccadcbacccdddacdbcbbccbabcccdbcdadabababbddcabdacbbabbdcbadccbbbabddacbddbbbaadaadaddcbabdccdabacbbccbabcdaacbddaacabadbabcddcbaababbbbdcdccddccdbbdcacdcdbdaddabbadcdbacbcccbcacacabbbcabdcababaabcbbcacdcacadcbdabcbbdabcdacbbbcdbdcdacdccdbddcaddbddaaaabbbabcbdaaaabcdcdbbbacdadcbcadcadcadcaabcdbabcaadabdbabbadacabccbcccbcaabcacbbbcabaadcdacbddbccbabdccdacbaccbcaabdaaddacddcaaacddbdcdcaabdcbabbaacdaacabccbacadacadcdbaccbcdadbbddcbacccacbadcabbcbbaccaacabbbdcaadbbccacbdbcacdaabccbacadabbaababcbacbcdaabcdadabbbbccbabdccccbadbaaaaddcddbdbddbbdddcdbadbbbdaababdcbaabdacbcbaccbcaddbbbbdbccdcbdabcdaaabbdadacbcbcbbacccaaccadddbbbdbbccaadacabdcbbcadbbdcadbabccadadbabccdddcaccdadbbadabadcaaabcbababadcdcaadadabdaddbccaccbdaaaddaccbcdbccccabbdbbdabdccaabadabcaccdcdabdbddaccbcaccadcbddadcacccbbcabadabaaccacddddbaccabcbdcccbcddcaacacaaadaaccdacdbabcbdaddddadbcdbaabcdaccdcbdbaacaadcdadbadcdcbcbcdadbcabbbcddbcabbbdddddcabaaabcbacaabadbcdbcbcdcbacadbccaaacdaaaaabaddccacbaacdbcddacdbbaccbacccbccbaabacbcdbbcbabbaaddcaccddcacbadacdbddbaaabcbcbbcabdcabbcbddaadaacaaddddaccaabbacddaabccaccbbdacbdbcddaaaaabaabdaabccdcdcabdbbddbaabadbadbacbdbddaabbbcdddbbcdccacdbcddbababcdddbaddcacabbbcddcbaccababacbddaaaccbaccdabaddbcdacbbaaaacdcbcdbccccccbcdcbddddabbacddcaaaacaaadcacbbbdbabdabbacdccabdababbadaaddbddbbadacdaccdbadbadbdcbacbdbbaacbacbcdacbbbdbaaddbdabbcbdbbcabcdbacbbbdaaaabcdbaaddccaaadcbdbbdbbaaccbbdbaabbbddbddacabbbdbcbdcbddddcddadbcddccdaacbdccdbacddbcddacadbdaacbdcdaaabbdcbdabcabdddcbaddbcbaccdbcddaacaccdacdaaaaacadaaaaccbbdbdabcbdbdcbadcccbadbcadbdcabcabdbabcdcdbacdcbcdadabcbbadbaabbdcacbbabdbaadbbbbcbcbdabaaadcaaabdccabdadddbadbacddbbbbdacbadcdcaaaacbdcdbbbaaacaaacbddabdcbcbcddbbbccdabcbccacdccaabacacdbdbdabbdbadaaaccacdabbbcaabadccabcaacaccbcbcbddcbddcbcbacacbadbaacdddcdbcbcdabdcccbccdaadcadbcccbadbdccdddbdaddabcccbabaddbcaaaaddbadcbbbaadcbbcadcbbacbbbdbbbbbcacacacadaaacdbaccabcdcaddbaadcaccbcbaabcacbbccddddddbaaadaccccadaddacaabbcadcaabaabadbcbcabbbcaaacdccbbcdcadaabcacccadbcbdbcbbdacacaccacdcdbadabdbbbaaacbcdabddcdbdadcbacdacdccdcdddcacddcacaccdaabcbacaabdadbccdccabbdbacdcccbdadcccbdbccacdbbcacacbddbcbbdbabdcbcddccadbdcddccdadbaabdcbdabbacababbcbcaabcddadcccddbabadabbdbdbaccdccaadadccbccbcbbddbcdaaaaabdccabccdbbcdcdabbbcaddbdaabbcbbbcddacacaaadccdadbdcddcdbbbaaadbddbcaddabcaacbbcdcbdbcbccadaccdcbbaacababcccadbaacbddacdabddadadbcdbabbdaabcdcaacabaddccacbacccdcbacadadddcadcacabcdcdbcaaabdccdbadbbcdbbbddcddccabadaddddbadcdcdbbcaddaccdaaaaaddaaccbabcdccbbbadcdddcdbadbaaabbcbaabddaddcdcaaadadddacccdccadbacbdbcdadbcdcbbaacdcbdaccacdacaadccdddcbbddacaaccdcaddacadacbdadcacaddcacdadcccbabcadcbaaacabcadbdaacacdbacccdbbaddaaddcccadcacbbacbabcaaccbbbcdccccbbdabccbdaabbacdcbbdcdacabddcbbdabccaddddbbdbbadaccdabadccbcdbdadcbdbaaadcbabbbbbcdbcdaaddcaddcadcdcabbdccccdcddccdaccbbbbaaccbaacddbdbaadcdadbcdbaaddbbddcbaaaacdbabdcabbabdbdacbbdcddbddcdcbddcbbaaddaadcbcabcddcaaadccbcbdcccbcaccdcdbabcadcdbcdccbaabcccbbccbcbddbddbdbdacbcaccaddbaacbabcdddabccdbaadbccdbcbacbaacccbababccadbbadbbacbbcdaacccadadccbcbccbcacdbddbdaadbbddccdabdddbbaaadcacbcdcbbadccbadaabdcadaabdbdcccdcacaaababbbaaaddabcbacbbdddbbccaabcdabcaaabbcbbacaababdbddddacacdcaaaaccbccdacdbcbdacbcaacddcaaccbabcdabaabcdddbbcaacddcadabccbdbccadacbbcadbaccdbaacddacbdaddddabaadabddabccccaaccbdbbccadbdbcaadccbabddbdaccdbdddbcdddcaaddacbbdadcbbaabcdbdcacaccdbabcdaabbabaaabaabbbbadabbbbddabdddcadcbcbcbccbbdbcbbabbccacdccbcdbbdbabcaccdaaacbbadbcacbbdbacdbbdcadccabcbaaabcacabcbbadbadcdbdaccabbbbaccbadcdadcdbbbccddcdcbddbdbcaaadadadcddbdaabcabdbbdcabcbbaddcddbddaddaacabcccbabdaacaabbbdcbcbacbcddcabaccabaabaccdcaacddbacaadccdbaccbdbabccddddbacabadbdcbdbaaabcbdcccdaaddccbadadaacbaabcbaabacdcdcbbdbabaaadcdbdababcadccadcabbbbbbbbabbaadaaabcdabdbccdbcabccbbdcaccadddcbbcadabadbaaadbbaddbdbaaaabbcacadbacaadbcddabddbccdbaacbdbbbadbcacdaabbbaabcbabdccbbcddbbcabbcddddacbabbcbdbdbacbdabcaacdcdaacabdaddadabdbdccdacdccdadbdcbacccdaabcdcbbcdcaddadbccbcdbabcbdcccbbbbdacacddaaabacaabbccbaabbbcdcacbbdbcbbdcadbcaaaadcbdabccbdbaaccaacadbdddbdabdadabdaaaaacbacdbdcdcaaccbdbcaadbaddabcadcaaccdbcbbcddadacdaabbbdddaddbdcbaccbbadbadbbacadddccddacccdacaddcdaddbdadbabbcbcccaddbacbadbbdcdaddbbadacabdbcdacbcabbdaabadbcbadbbbabbbcbcacdbabbdabbcddcbddcdbcddddcdbabcdcdbcbbdddabaadccccbbdbdabdbcbcabddbcdcccabbaabddadddddbbaaaccccbcadcbcbcdcacbaacbdbddbbbbbabacaabcbddbbdbdcbdaadbdaccbddadabcbdadbddddadccdcbdadacbbbacadbcdcaaaccaadcdaccbdbbdddcacdabccbccbdcdbdbacabcaadabcaadaadbcdacacbdbcdcccbaddbcaabacadccddaddbaadcdabdabbaccbcacddccdccacacacdbddbddabadabbaadadabbdacddcdcdcbdbddabcadabaadcddbdcabaadcdabbbacccbbaabbccdbcacbcbdaacaddbbacaddbbbbdabdbaccabadcddccccdcaacababbaddccaadabdcdcbbcdcbaccaabdadacbbcadbcbbaaabcdbacdbcdddddacdbcbadcccaadadbacdaaadaadadacabcdddbcaadaadcaadacdbadbcaccccbccbcbdddacccdbadcbbdadcdbadbbdaccdadbaccaadcbbbbdadadcbaadcacdcbdbdbbcbdacdcaaacddcbcdadabdaccaaacabcbacbabadbbbcdbcddcbbcaacadacbddaadccdcdccbabbadccdcbcbbcdaaccbdccddaabadbbcddbacadadbabbcaabdcbdbbcdbddcccdddcbadcbcbbaadddccacaabdcaaaaacccbaaadcbbdcbadbabdcaacdccddcacbcbddbccaaadbbabdbbbcbdaadbcbcbbbadccaacbabdcbcbdddbacbadbaadccbdbbdcdcbcacbcbaadbcdadacddacbaadacbacccbdbcdaddbdcadbbcbcadddcdbdcbcdcadababaabbdaccddbdacdbbddacbbcccbbcacbbcabababcbccaccdacaabdbcdcaacccaaadacaacdabacadbaddadcbbbcaabbacccadaaaaabdcbbcddccdaccdaaacadacbbdcbdcbdababacaacadaabaabddbbdabcdbdaddccbbbbacabdbbddbcbbcddaacbbbcacadabcbcadccddbddacbbdcabbcbcbabbadadabbbbcbccdbbbbcbaacbcabcdcddcdddadcacdccbacdcaadcdaddacabcddacacbcbbcaaacacdcdbdbdcacddddccbddcbddccbaacaadbcdbdadaddcdbccccbdaddcddbbdabdacdaabdbcaaccdaaadadacbabddcdbaabaaaacdddadcdcabbddddadcaccbccbdddcaabbcdbacadadbcadcdbdcdadccbadbdbcbbabbbdbcbabcbacbacddbadbcbdcbcacdabdadcddabaddcdadbabbdcdbdabbdbbacbccbcadbabaadbdbdaccadbcacadacbaadabdacacdbbccadbaaddadcdadadbbaccddcaabddacdbdaaddcbbcccdbbccbadcdbdbacadadcbacdcaaddbbbdbbdcbdcddcdbbbdcaccdbdcabbdabdcccaabccabbaadddbacadbcacdcaadccdbcbbdccdababbcbacdabacacacbacbdaabcdacacbccacdbcbdabacdabccbacbdccbdaabbbadcabaadcdcccbdbcdbbbbadacdbcdbabddbdbdadbbacbbbdbbaaddabaaaccabaddcabcdadbbbaddbbdbabccbacbaabdcdcbcbcabbbcbadddbdcccdcddbcdacaadbbdabdbacabadbdbbcdbdabdbbccdcdcbcaaadadbadbbcccbcbdcccccccdbacabbacddbcaaddbbacdaddaabacaacababcdaabacaadaaadbdbadbadaadacaacccacdacdaccdbadbcddbacabcccdcacccccaadccbcbdabdcbcbddddccbbbadbaddcdbaadabdcddbcccbbbcbacdbadddaacccbaddddbbacddaccbdacbbcaadbadbacdbabddddcbdccbcabbaccdabbaaaabddcdbacbadaabdcadcdcbcbdaacabacbcabcbcdbacacdddbcdaccbabcbadbcaaaccadcdcbbccdacabdcddabcbbdccbacdbbbcbbaaacdcacaadccaddbacdcdbddbddccdbcccdccdcabbbadddacdacaaccabcdcbcadadbadcddcdacbdcbdbdacdccccadccadaddcdddddbccacbdabaccccbddaadcbaabaddaccbddcdccacbbaccbbabcddacabbdabcbbbdbccccadcbabaadadccabbcbccbbcdaccabccadcbcaabcbcaabbdaabdaabaaaddbaabdcdbaccabaddcbacbaccacbcaacbcbddbacbdaadbbbadbaaaacdcbbbaacdddbadaaddcadcdbdbaaacccaddcaacddaadbcbcadbacdcddbdcaabcadacabadaddbaacccdababccacbbadaaaaccdcaabbccabacdcdaaddaacaaacbcdcadbbbcbcababcdabacbaaabdcaaacccaabcddcdcddcdaabbbcbaadcbbdccdccddadccdadbcabdcabbdbdacbaabacbdaadbdcabccdaddadbacaadabcdbcbbaccdbbdcdcddadadbccbaaadcdccababdcdccbddaaabaaadabcbbbacabddadcbdacaabcdbaaabdbdcacdacabcccadacbdccdcbbcdcacdbddbabbabbddbcdadaabccbaccbcaadbbccbcbbbabdddbcaaddcddaaacaaadcbaadadaabcaccbccadadcbdacdcbabbbadbdbddcdcccbbdbddddcddcdcdcabdadbbcbdacacdcdbdbbdbbdbcacccbacccaaaacaddaadccbdcbaddcddccabdccacbaacdbcddacabddcdcddddbcdcdddaddcbabddbbcddbcdcaaaabbcdaadabcaacbcacbddabbdcdadadacbacddcacccddacccbcbcccacdbcdcdbddacaaaacdaacdaadcabaaccacbcdaccabddacadbdbdacbcccaccdabadacbdaccdaabbadbacdbabcacbddcadddacddcddcbabacbccbcccccddadddbadddbcbabcdbbbdcbbdabcbddadcbaabbcdaadbccddabcccbbaadbbcdccdddccccdbabbadabddbacdbcbaccdadaabaadcdcbaacbbabdcbaaaacbdddccdcabdbcccbcccdccadbaabccaadaabdbcaabaadddabccddcacadddaadbdbbcccabdabbdcbdccccaccdadbccdcbcabbcbacdabdbbdadaabbcccdccdddbbaadbdbacacccaabaadbadddbcbdcddccbacadbbdabacadaadbcadbcdccadabaaacbdbdddaadccdaadbacdcaacbdadadcddcddcbaaacccaaabaaaddbcdbcccbcbaccbcdcababccdcccbccbbacacbaccbdcdcddbbcbdacdbbbacbacaaaacbdbdcbcababdcbdcdbddcaabcbdcacbcbacbdbcadcdccccbbccdaadcbbacdbaadcccbaacdadcadcaacbaacbabdcabcdbcabaacadcacdbabdcdabdbaccadadbbdbcaaaabaadcbccbadbcabbdddccbdccacaddbacbcbbcbdcbbccbacbcacddbccddddccbbaccaddcbcdaccaacbadccdcbbdbdbbabbcbadaccaaaacbbdacbdbddbaddcdcdcbcadddddbcbbdcccacacdabcdbabdacabdadcdddcabaabaddccbcbcbdadbbcbcbaaabadadbbbabcadbcbddcbaddbdaabcbbdaabadaccacbcacaccdadadacdabbdbabdbdbcdddbbbdddadcdabcbbdddaacddbadcdbabcccdbacccbdacadaadbbddcabacbdccacbdcbadccbcaccacddadbdcbabacbaabcccddbabacacaabbcddbcbbcaacddacadcbbbbbbcbbddcdacbdbaababbccabcdbcabacdcdaacbcbbacbdcbabdcaabcdcbabacdcdbddabbddcbdbcddabdbabaddacbadabcdbbbbbbddcbcaabddbcdbccddabddcddacccaddbbccaddadddaaacddadbdcaabbcabaccbbabbcadccbcbaddaacdccabcbadaddbababbcabdadcbcdbccccaaccacdddabdababcaadababbdccdcbcadccccbacdcdadadbbddaadddddbdbacdbccacdbacdbadbbabdddbbacadaaccbddddaabdadcbbcccadcbbbaddbcacbcaddbacbcbacddadabcbdacaaddbaaaadcdbddcacbdcdcdcdadcbaacacacbcaabddccaadcbcdaabccbbcdbbdbbdadcacccbbbabdccbcacabcccbacacccbdbdadccaabaccbdacbdbabbaacdddcadbcadaaddaddbdaaaccccdcabbbaabbadadbcadcababccdbddcdbdbcdcbdbacbcdbaddadbcaabccddddaadacaabddcadcaddcdadbbdbaabdcbcaaddbddcbbcdabcbbcbddadcbbcbdcdccacccdccaaabbdcacdaacaabcddabaadaacadadacddcaccadddcccadabaccbacdaabdbbcacdbcbdcbddababdbccacdcbabacadcadbacadcdddccaadbababbcdbbdbdbcacaadbbcbdbcdcadccdcdbdacdddaddcccaaabadbbdabdcbdaacbabadcbbdbaccdcabdcaacaacbabadcaacbbadcdaabccacaabcdbdcaacbdcdaaddbadcccddbbaadbcaacbdcbbabcbabbbbddcadacdacbdadccddcabbcdadaaaabadddcbdabccadbaaddbcdcdbadbbabbcbccbcdaabbabcbaabbbabdccaaaccbcccbdacdbcbdadabbadccbcacdbbcdacbabbacccbdccbdbbcacbcbadbdbadcbaacabccababdbacbbdaabccbcbdacacacbdbadaccacbbaddddcbbbaadbcaaacccdbbadddabbbaaccdacadbddbcadcdcccbcdcdbcccbacdaccadbbdcacdccbdacdcadadcdcccbdacacbdabcaccdacccacadbddbcddaddcaabdbdbbddbbcdcdadcccacabcbbcabdaabcabcbdddaddadbadcddccbddaccababbbcadcbdaabaaaccddbacbdcabdcabcbadccbaaccacbaadbcabdbbcbdbbababcbddcbabdccbadccacabccbdbabddcabdbacaabdbbbdccdcdcbcbadbccacbbbdccbacbbcabacbcbacacbcdcccbbacacbaccadcbcbaaacaaadcdbcaaaaddddbbacccdaadacddccdbabccbcddabaccadabdbacbdacdddcbbbaabbaadccdcacabadbacacaadcabccabadadccddbcabddccaddccacadbabdcadcbaadadaadacadbbbbdbbadcbabcbbaadbaaacdcbcdcaddcbbcbdbcadcbaccacbddccabbdaddcaaacdcccaccccbdaabcabbccbbabdcbdaadcaabdccdabdaaaaaadbcadbdcdababbbacbdcadcabbdcddddbbccbddadbadaabdababacdacaccddbbbdcacacccdaccaadbdccadcdbadbcbcbdddacdcaacdbbaabcbdacdbacdddcbdaccbbdcabbaacbbdababcddbbdbddccdcacbbbacccabddaadcccdccdadcdadcbaadadbbabaaadaacdcaadbdcdadcadababddabacbbbcdaadcabdbdbacdcbadbbbcccbadacccaababcbbccbdbaccaccbcbbcaccabddcbccabbccbaaaccaaabccdcaaabaadbabcbcbbcbcccdcacdaddcdbbcbcccddbddabbbbdcddabbbabbcabccdddaacaabaadbdbbbacbacdadddaadbacbddcccdddcacadbcdbdccbcdaaaacbaddbdbddabcacdadcadbcdbabddacdabdbabccaacbcaabababddaaddbbcdcabcdaabaababdbcaabbaacdaacadddbdacddbbdacddadddccabbcdcabdadddddbdcbdcdddcaaccdbdccbbabcdbddbddcdccddbdbddbabadacacdbadcdddaaaabcacdccdaccdcdbcbadbabddccdadbdabcaccbdaaadbbdddbcadbcaaabcbabdcbccdbbcaaddbdccbabcdaccbcbcaadacbadcabdccaaabbcabaaddcddbcbbddbaabcabbddbcacccaacbbdbdaddadcbadaadadcaabacbcdaadaccddbacaaccbcbadbbabccadcbcacaaddbbcadacaadcabdbbdddcbccaabcdadabcdccabdabadbbbbdcbbbaabcdbcbacbdcbddadcbaacbbdbaaadcdddbcdbbbdacbbbcdccabadaabacdccddbaadddbcadbcabdcbcbddcacaddcdcacccbcddcddbdcbbcdacdcabcdadbbdbdcdcbaadbcaacabbaddabbbadddcbbaadcabaddcdbdddcdcbadaacdcbbadabcdbaccabdbbadbdcddbacaaccbbbbbcdbdddccaabdaddbcdbaabbaabdacbdcbbccbbbccdbddadcacdcdbccaaccdbdcbdabbadaddddcadcadbddaaddddddcccacbddbbaadbdbadcabbcacabcdccaaacccbbabcaccccabbcadbddacddaddbdbbdbbcdabdabdddcddccbbccaababaacbccaadbdbbabdbcccdbbdbdacbacabdabbddaaddaabbcbabddbbcccbbcaccddcaccdaadaccaddbdbcadccbcbcacdbadbccbcadcdbcbdccdcbddcdddbaadcdbabaabcdbdbdcababaaccccaababcddcbabbddcdcdcdadcccabbdbabbdccccbbdcdcccbdbadcbdaaaabaabccccaacccbabdcbddbdddcbdcaacdbbbcbcabdcbbdbaaabccbdadbcababdcdbcbaaccdabbacaabbcaccdcaaddabadbdaacbbdcccbadccddcdddcabbcdacdcaaadccbdccdadcdaaacccbbbdcadcacddcbcacbdbbabdcdbbbcbacaadbdbbccccdbadbcbbadcdaabcabdbcdcbdbabaaabcbcdcdccccaadbabacbabdbaaccbccdcccbbbddcbbcbcbdddbbbccabbdccadabdaaabcbbdddbddbcddcbbabcdbdbcccabcdbccabaabcaadbaabdcbabcabbcdadbcdccbdbbaadddbdddbbdacbbbcbaaaabdadbbcbcdacddcbbaaabcacdcdbbcdccdcdadabacaaadaddbddcdbaabbddbbaccddcdbabccacbdcdcddbddacdcbadbdcacdbcbadcdddbcbcbbdcccaaaaadcaccacadcadbcbdcccdabbabdbacdbdaccadcdbdcbcbcbbaadbdaccaaaddadbddbbcbcadbdadccddcddcbdcdbbbaccaacdbbabdcbcbdccacaacdbcaaabbcdcbccdbcbbdaacdacbcdcbcaaddbdaabcdddbacddbbbabbbdbdbbbcaadddbddccbcddcbbdabdbccbdcbbcabbccadcdcbaaabdccdccdcaddbaaddbbaddcadccadcdccbcaddcddddbadacccbcadcdcdbdbbcaacdddaabdabddccadbbccacaddbbbccbddbdadbdddcbaacccabbacadaaaaabdacbbcdacccbabcadcacdabdacdaadaadbbbccaaccccccbcddcbabaccccbdacdcddabdbcbacbcbbabbbbdcbdabcddcdcbaacdbaacabddacdcdcbbddbacbbddcaadcdbcdcbbadbbadadaacdbdddcbbadacbaadaacabbdbabdcbdcddccbbbadbcddddacdbcbdababcbcaadbadbdaadcbcbacbcaccddcbdadbbddcccbaabccccaaccaaaabacddaaaaacddadbbacdbaadbdcccdddbcadccadcbabccadaddddbccabcacccadccddcadcdcccdbdaabdddacadcadccaaccdbaccdcbaddcdbadaabcadbcdccccabcaadddbadabcccdabababdcddbdbacbbacbcaabcbbbdacdcbabbbcabbadbadbbdcabdbbcaaccddabdcabaaaccbcdccdbcacccbcbbabaabcaadbccadcbdbdbaabdabbcdcccacaadddbbbbdcababccabcaddcaaabbacbdaadaccaddaddacaabccadacaadcdbdadcdcccdddccdaaaababcacccdbcbdaccbdacdcbcaabdaddbcccaccbdbbccabbbbadadbdbbcbcbccddadbcbabcbcacaaaacbdabdbdddbbbbacddddbacbccddcbaccadbdcdaadccbbbcccadababcdbacdcbbdbacaaccabdcbadbbabacdddcbdccdcabdcbcbbdcaadcaaaadbbadaadbaabdcdddcbcbacdcdaadabdabddacabbacbccbdbabcacaddabbcacaadddcdbacbbcaadcbaacdbadbbccbaaabadbdcacaaabcadaaabacdbabbdadaaaabbcadcccdaccabdbddadddcbddbbcbcabddaccbbdbcbdadccacacbcdbbcdddabdbdaadbdabdbaacadacdbaababddcbdadcbbaccdcadbcdcacdcbcdccdcdadaadaaccdddbddcbaccdcabaaccbbcdbdddabbddabcbabcdaabdbaccaabcdababdcdbadcacdbbabacbbdbbddacacbabbcdbccddaacaacccccdbddadbcdcaabddcdbaaccccadabdcaaadbdbabaacadddbcdcadacbdddbacdcddacccadadddaaabccdaccabccccabbccabbdcabaaacccdbaaaaaadbdddbbabdccccabdcadbabcabbbdddbdbcbccacdbcadddccdbacdbdbccbdbdbddbacaabdabdabcbdccadaacdcdccdbcacbdccabdddcdacbcdbcadcbbdcdbbcddddacbbabdaabcadadbdbccadadaaccbadbbcaccddbdababadbbddaacabbaadccccbdcacbcdcbcaccccbbcbdbaaddacddddacdcbddbadaaaabdaacbbdbadbadbdadbdacaabaaccaccbcdcddaaaacbaaadcbdcddaccdadccdbddacbbbaacaabcdbcbbcbbdbccbbbcbaaacbacbacadbcdbbbbbcbbbdddabdadaddbaaabacdbbdbbbbdcdbcbaacddadcbbdccdbabbaabdddcdcdbddabddaabdaccdcddbbdccabaddadbddbdbdadcdbbdcdcdacabbaaacaaccaacdcbdcbcaccddcacdcbdcbabccdcbddabdabdbdabaaacccbbdcddddccbbaadbbabdbdcabbcdbbacababcdabbdbcdddcdbdcbadaabdbadbdbbadadbaabdcaacbaadcccadddadbdaddcbabacdccaadadacaacdacaaaabccacbabaadcbcccabaaadcbdbadbcaacadccdbcadaccbdadadbbdbcabcddcddbaccbddabdcdbbadbbacbcddccccbacabccbaccbcdddcbdaddcbdadcccbdbddbbbbbcbabdddadcbbbcaacadabdaacbbaaccdaccbcacabacbbcddaadababaccdddacaabdddabcbcccaababddbdcaadacddbabccccadccacababadbaaccbbbbbbddccddadacabbccaadbcaaacbabbabcbcddccccddcbdbdbccbdaaddccacddcdcbcbcbaadabcdbbbdbabcaaccddcdccdaabdadadbcacaaabdabddcbadbabcaabaacdcdababdccaaaabdbabdcabccadcacdaaadadbbccdccadcacbdcadcabaccdbbddadcaaaaacdcadbbdcbddcbddcaabacddbcacbdbbddaccacdaccaabaadaccbdcbdbcbcacddacdddbddacadccbccaaccacdcdbddbabadbababdabcccaabddcccbbbabcbbbccdcddcbbadbdabcccdabbccbabbbababaaaadbadababbdacbccdabcccacabadcbadccccacbadadcbadadabaabcddcaaaabddababdcaddcbabdaaddadbdaadcbcaddcabbbbbbbadbaabccccbdadcccbbbddaaddadbabbcadbcbdcbccbacdbaccccdaacaddcaddbcbccbccbcabcbacbccacdccdcbcbdbbdabadbbcacbbacbcbddcabdbdbaaaccdadbddabaaadadadaddcdbaaddbadcdaadbaaabccccaccbadbdbccdadbddddaaccadcacabcabbaaabbcababaccadbdbaaabddbadbaddcdbcbddaaabdbadcbdaccabdcddcddbcdbdbaaacbdbdbcabbaaaacbddbdddbcccabcdbccacaaccbaddcbabbbabcddbccadbacbccbcbaacccdccaadbaaabcbaaddddbddabbcadcdadbbabaaabaccddddabddbdbcbcababbaadaacbbbacbcaadabbabcdbadbcdaaacbcacacdcacdabbbccacbacdacdabdabbccbaccbaaaacdbdbadacbabddcadbabdaacbbbcbbbccbbbcdbbdcaacddbcdbbdbdbbdbcbaaccdacddcdbdbbccdddabbddddaabdbdcbbaacacdbbbaaadaacbcbabddadbddbddaadcaacdcaaaabcddbaaccbbdacaddabbcbcddbabbdbbabccdbdaccabdbcdbbadbbdbbccdcddcdcdcacadddccbaccbaddadcccbadaddbdcbabbcddadacddacbbddbdcdacdbacadadacbdbcaacbccbdcdcaddaddcadbcdbadbdbbdcccaadbdcabcddcadcdbcbbbacbabbacdacbdddadcccadabacbdbccbbabbddcdaabcaaccbacacdaddaddbaddadbacbccbbbbcdbbbcdabdbacbabbdadbbccadccaaaadcababbccbbbaadacaddbbdbbacbadbcabdacabdcaddaadcdaabacbacaddbbcaccabcdccbbbccbddbddadacdbbbddcbadcacabdbcddddcabbdacaccacbcbddbdbacacadbbdbabbcbbaacaddddaaabbbbbcbbaacabbbcdaaadbaccbcacaabdcaccccaadbccbacbbcdbcddbdacdbdbcbbdbdbdabdcdcaaabcccdbabcdbbbdcbbcdbabbbaccbddddcadbdabcdddbbbaddaddaccacdbabcddadbbdcdbddcbbadbdcacbddccbbbbccaadcdbddcdcdbbadbdccaddcaccccabbdbadbacadbbcbcaaaddcccbcdbbdcadadadabbbdccdabdaaaacccbcddccabbabbddbaccdbbccbabacdaabbcacabbaacdadbcadbdbbddddcacbdbbaddccbbcaabcacababbbdcccbccdcbccbdacdbcbcabccbbabadadbabcbccdbaabdccadcacabbcabaccbbbdbddcdbdbcbcbbdcdbabbdabbaaadbbcdcbbbccdbdccbdadaccdcbaddcacadcabdaaddacdccadddcddcdccdacbcccbaabdacaacbdaddaaacddcdcadbddbcbbaabaacbcbdcbabdbdbdddcddbdccdccdabacdcbacbdcdcbcbcbcdccdbcdbdcaaacbcbbdccbdbdddcdccaddcacdddddcbdcbdcbdbbadaddcabaacbbddacbcaadaddbbcdcbaadcaadcbdaccadabddbaabddcaabcabccabbabbabbacaacbdacabdcaabaccbacccdbddcdadccdcbadbaabdbcbccaadbdcadacdccbadcdbabaabccacdabaaddacdcbbdddbabddaadccccdbbcbddbdacbdacaadcdbacdacbccadbaccaabccaacbbcccbbdaacccccababbddcaabdcacbabadaaacaaddacbdadcccacbbbccbbddbbaababcdaccbdabcaccdacaaaccadcdadaaabddbbbdccbaccbcbcdbdddbdbddcadacacbdbdacbabddbdbddacccacbcbdaaacdddcdcaadcbdbdbcaaabdcdcdbcddcbabddbccdbdcdacbdccbcddacbcccadaaadbaccbcbccacdaadabadcbabbccddacbadcbcddaadccacaacaabbddcbcacdaabacddcabaaccdacdabcacababdccbcaddadacabbcdddbdaadbcdccdbdabcccaacdcaddccbadabaaabcbdaadabacddcccbcadcddcabaaccccccabbdbbcbcdbdacadbbddbbddaabdddbabdbdabddbcadabddbaddcccabbcabcbbbdbdaadacdacaadaaaaabcdcbacbcacdccbaccadbcbbbabcdbbdbaabcadbadbcbddddbdcaaabbcdcaddbcaccddabcdbbabdbccdacabdabaacdaabaddddbbcabbddacccdbbcdabccbccccacbacbdcbbbacbbbabbdbadbbbdacbdbcdbdaaaaccbacbdbddbdbcadcabdcbdbccacbdcdbbcbdddcbaccbcaaacababdbccbccabbdbaadcbdaccbbdaabacbddcaaacdadbcabaccbacbcbadcdcabcaccdababbabbbbbabcddacbcaabdcddbbdadbddadbcddbbbdbacaccaabbbbabcdaddbcdcddcbdbbdabcabccaaacddbbdabdccadbbaaaabaccdccacdcddcacadaaccbbbddcbabbdbaadaabdcbbacbdbccdbabdbddcdbbdaacadabacbcccdbbadbcbbadbcdaabacababddddabadcadadbdcacdbdaddddbdbccabbbaadaaaadcbadabadaccdddddcabcccbbdcccbdacaadbbcbccabdcccccbcdadcacccbbabdcbaadaacaabdaddaacbdcbbcabdbbcdacdcaabddabbcddaaabdddbcdaccccbbacccbadadcdccddcddacaaddacdcccdcdbdadbaddbbccbcbbdcacaddcabaadbbcbccbaadabdbaadacbccccbbbabdbddaddcaacdadbdddcbcdbbbbccddaaacdccccdbcabccdcdccdbbcabccbaabccaadadcbcdadabadbdaaababdaadcbcbdadbdaabbdabcdbaabdcbcbaacadbcaccccdccdbbabbdcabccacbcccdacadbcddcacccbbcdbbadadaaaaaaaadaabdcaccaacacadcabccabbddccbccdcddbcbacbdcaabcbaabdbcadabbacbaddcabaddcaaaddddbaabddbbdddababcdaadbdcbdaddaacdadccbaccbacdabbbbbccbbdaacabddddcbddadcaaacabbacabacacddaaabbcbababbabcaaabcbdbddacdccdbaaadabbabdbdbdddbbadbabdbbbbbdcaaaaadcabbbaddacdcbbadddcbcbcbdaadbdaadcadcdcacbcaaddcdbbddadddcdbbbbbdbbdbbdabadacddadadbaadbdbacadadccaccdcdcacdaadabaadddbadbdbdcbcbddacdabbababbddccaccddbbaddbbbbdabdbbdccaddacaaacbccdadcbbbdbadbdbdcbcaaaddbcacdacbbbadcabdacbcdacbccbbadddaaabdddabddbaabcbdcbbccdcdbdcabcaabbcabbaadbbcabbddadcdbbdbdbddaacbbaddbadabddcdddccbcabaaaaaddaacccacadcddcdcdbabbdbbbdcdabcacddbbbbcdabacdcbabbdadcaaaddbaacdcdaabdcaccacaddbcbddbdaabcbdddbadbcbdaacddbbaaadcaccddacabddabcbdaddaadaaacdbbaaccddddbcbcbdcaaacdbdbbdabbabcbcdaaacdabacababcdaaadabbaacabdbbdbddabdabadbcabcbabbddaddabdacaadbdbacbbbdcbbaadaaababcaddbbacacbacdabdbaddbbbbabdbdcdcddacdbcbddcbcabdcbcaccbccabbbadbcdccdcadcaabadbcccacabbaacabaadbbdbdacddcbddcddaccacaccdbddbbdadabdbdbaddbaaccbdccccbdabbadabdccdabaacadccbabadcbbaadbcdacdcbcacddbbbbbbdcadccaacbadccbadbaaabcbadaaaabcbdbdadaabbcbbddbdacdcacadabdcbcdaaccbcacabcdcbacaacaaadccaabcbbdabccdacdbdddbbaaddccadbadbacdaddbdbbddaccdabbabdcddadbdbddbdbacdadbcdbbabdadcdcbadccbacddcddccddbcabbbcacccdbabcdbbcdabcbbbccaccdcaddcbdcdcadcadcbbcdabbabdddcaabcbbcacbbccbccbbadbccdbbaccbbbaabdadadbdcdcbacddbdddacaadabdcbccabbabddcddbaadbcbacdcccdacabacaacbccdaadaaaabbcdabadbbddbadcdabcbcaacdcdcdaaacdbdaddbadbcbabbabaaababbaabbbacdacaabaddbbcacdbacabdababaddcdddddabbcddacdcdabaccdaabdaabbdadaadacacddbdcccbbccccabaadaabbbcbbcbcbdbccaccdcabddccdccbcccadbbdbacbadcbdaaaabbcdcdcaaaacddbdbbdaadacbdbcacdaadddaabdbcdbdcddddabdccbbdbccbbdbbaabadddccbbaabbbbcbabcddcccbaacdaaccbbcdacbbabbabcabccdaadadbbcbaddbcdbcaacdbacdadcbccddacdcddbdbbacdddddabbcbcacaacbcdcbbdccdcdcddabccdcaaccdcccddcddbbddcbddcbabddccbadddbddddbabcacbdaabcdabbbbdbadaddcadcbaacbacdbabcdcababcabdaacbcbccaddabcaaaaaabaabaaaadaabdbbccddbacdbacdbacccabbbadacbccaabadacbbdbbcabacadbaadbccdbbadbadcabdacaabacddccacccccccdccdabcbaabadacadaccbaadaddbbbababcadcdabcbbabcacaaadadddbbbddddabaccbadcbbbbcdaacbadaaccbcbcdadbadcadbbbacdcdbbadacbddbbabbcbacdcadbdacabcdbaabaaacadabdaabcdccbbccacdaabadddddcbcdcdbaaabadbcdacdabbdbdaaadcaadbabbabbacacccccdacdcbbcddcacdcabcadacacadaccccadadacdccbcacdccbcbdbccbdcbccadccccacacddabcbbcdaadcbdcdcdcaadbddadbabddcbcbdbcadbbcacabacdbdccaabbbacdabdccbacbcdbbdcddddbdacdaccccacbdbacaadabdcdcdcbbcabdbcabcacdaabcdbcdcaacdbaddcdcbbdccbdbcddcbcbbadabcdbddcccadcbabcbabbbbddcdaadcbcabcbaaaadbddacdcdadaadadcbdbccabccabbadbcadbabacacbddbbdaccaaabcccaadbcbdcacdbbbbaaacbcacdbaadabdddaadadcbbdbdbcbcccdddabddcbabcbcabbababccaadadacaabbdaaccdcaacaacaabbdcabdcabcdaddccadcddabbabdcbbacdaabbbaacdbacacdadabddcbaccaabcbadddcbabddaddccdcdcacabaccbddcbddbbacbbacadcccdaacbcacdbbaddbadaccbaaabbcddbcdacdcabbbbccddcbbdaddabaccaddabaddbbabdbaaaaadadacccabccdcbdadacaaadbbcbabdccbcddcdcdcbcaaaabdaababbdbdcbcbcacaddcdaacacaaccdcdcdadddbcaabbbcadcdcccaccacbacccbbccaacabdccddbdddcbadcbaddcbddbbcabcaacaabdaddadcabaacbaddaaacdccccdcbddbdadcddddbddadbdcbdbaadcbddcddbdcddbcbabdadaccabdcdbadcbdddbabdbccaccbcbacbcbcdbbaabadacbccacbadaacccbbcbaddbdbcccbaadadaadbabbcbbcadaccaabbacdabaacbdcbbcacdccdcadbaddddacacacaacdddaabaaddccadaaabadacbadbabdcccbdbbccaddcacaabdadaabdbaccbdaccccbbbdcadddacbcbdadbcaccddadaacdbbdbabbddabccddacaddbadcaadbdcbaccddbccbdbcabcbbcdcadcaddaaddddbdabacccaaacacdadadaacacaadcdadacbcdcbdbddacaabbdbcdbcbddccddcbcabdaacadbaddbacdbdbcdbbcbddcbdcbdadbdaccdbadacdabacadbbbaadddbaccdbabdddcaabbbcccbaddaadddbaacccbabcbddcadaabdacbdddadaaadbbddacaccacdbdabbccbbdaddccbbdbbadbaccbdcabaaaabcabcbabcbdcbbcdcaadbdaaaacadccdcaccaadadddadaadaddaccbdcbdbddabdbbbacbcbccdcbbaddddbaacbacdcdacdaaaacddcbddbcaabbcadacbdddaccabcaadabdbdbccbaaddbcdbadabaaddbcacbccbbccddcacdcbabbddaadbcdddccadadadabbbacaddbabccabaddbcbbcaadcbbdadddabdbbbbcdcaddddbacdaadbcadcacdaacabbaacdcccadaacabcaddddbadbcccaadbcdadaaaabccbbbdbabcdddaacdddbcbbddadcadcdbdcadcddbccadddcadcbcacdacaabacdabcbbababacdcbcbdbbcbacaacacccbcabddbcaaddbdcddababddaccddaccdaaaabdbcdacbacbabbaddccbbacdcddbadaabbacdbcdbacddddcddadcbaaaaadcaabadbcaaccbddacabbadabdadbadaacddadababbdccddcddcbdabdbcbdaddadadaaaaaabdcbcbccdadacddbbddaadadcbdababadbbbcabdabcadcccbbacdcbcabddaacbdaaddaaccddcacaadabaacdaddabbddaccacbbddcdbddadcadbdcccbbcdbaaaddbdbbbcadbcbdabcddacccddaddcccbaacbcacaacbdcadccbaaadacbabadbabbacdbcccdbdbcbcdcadabbcbaccbaaabddaccdccbdadacbbabbbabcaacaccccbcadcdabddddbdbcacacdcbbbdccdbabaddbbbcabacbdcabaccabcacadadaaacccddadacbbccaacabdbcccaaaabbbacbaccaccabbacbdcabaadbabaaaadbbbbddbcdadccacdcdadaabdbbccabacbbccdbdccacbdcbbdbbbadbdcdadcdcbbcdcabbccdacdcbbcdabcccabddddaabdbdaabadcadabcbbdcdaaaabcdaabbacbaddcbcdcacdcaadaabbcccddaabaaddabcbbdcbcdaabaadacccadddbbdabbdcbdacbcbcadccccaacbaaaadcbccbacabcbbaadcdbcbddddcdacccbaaaacadbbbcdbbcdcbadddccaadcbcddbcbcbbcdbcaadbaddadacddbdcdcdabacaabdacdbdbbbabdbdadbdcbbdcddbdbacbdcadbcbadbbcacaccbdaddcdcbadccdaaabacbdccbbdabdbcbdacbdabcbaadccbababbbccdbbcdaaddbdcdbaccdbaababcdabbdddcbabbdcccdcbbdaaaabcbbcbdaccbabbccbcadcddcdadddcbabacdabbabbadcbbddccaaaccacccdcccbcdbddbbdaadbcaddccddaccbaadcccbbbbccbbaabbbaccbcbaaccccbacacddcbaacbaccaddabbbacbdbbbcabbdccccddadbdaccadbaaccdaacccbcbaabcabbcbaddacadaacdbccddbccddddacbbaacaccacbcdbdabdddaacbbddcdaabadbdadbdbacbbbaddbaccaabcbdbbaadabdccddcacdadccdcbdcaaaabacdddcdcaabcbaaadcdbbddacbbddcddbbadbdbccccdaabccabcabbbbcdacdcaccabbcbbbbbdabacdacddccdcbbbbaccbabacbcabdbdcdadacacdcdabdddaaabaddccdacdcdaabdcbdabccbbccddcbaadccaabaccbdbadacdaaabdbbdabddddaddcacaddabadabdaddcbaddcbbdbbcdacabbadcabacdcccdcacadcbaabdbdccddbcbccbbcccdbcaaccaaacacbdaddcaccacdccbccbaccccacaacbcbcdabcccbdbadbcbdbddbbacdbdbabcaaaaabcdbddcdacdadbbbadbdabbcaaacbdbdadadbbbaaaacadbdacdcdaccccdcbaabbbbdddddababcddddbdcabcbddbcacdccacccdacbadbaabadadbbbbdcdbdabccaccabddcccaaddadccacacbdcacacbbdbbbdbbcadaddbbcabbaacaabdbcbdadcbbaadcadbbbdbbcdbdcbbdbaaaaabacbcbabbbcabddabcbdadadbacdbbaacbcbaaaddababdbcaadadcdbdbdadccddddabddaddccbddbcaadadacbaadacbcaccddbabdcbccccbdcdbcbdbabadddbcbadcdacccbcbcbdcbabbacaacddabaaadacacdadadabadccabdbdcaabcadaadadcadabccdcadbdaadddaadaccbddbcdddadaabadcbcdcadcddadbadcaacabbbabbccadcdaccdadbabcbccddbabccdbbcdadabdcdbbdcdbcaabacbaddddbdaadcaadbcbcaadcdaaccddbbbbbaacbbaabdaabaccbbadcaaaacdaacadbacaccabaaccccacbcdbcdcaaabbbadccaccbddbcccaabaacdbbbdbddbcdddccabdbbabccabdadabbbdcacdbcddcbdabcdcbcacbcbbcccbdaaacccdabccbdadcaaabbbccacbdabcdbbbbdcadcacabbddccbccdbcbdaaadcdcabbbddacdcdbaaaaaadbaadbabcccabddaacadadcbbbddaaadaccbadbbabcaccdaccccbabacbcabaaaadadcadabaccccbdbbcddabccdacbddbccadbaaddccbcccdabadaadbacdbdccdcbcbdabddcdcaabddddcdbbccacbabccacadacabccabbbccbadbdbddacadbdbccacdcabacbdbcaacdadaaddbcdccdbbdacacdcadddbcabacdabcadbbacdabbcbdabcbdcadccbcbbbadcbccbcacaacdbbbdbcabccbadabadddbbbdbccbdcacacaabdbabdbaaaccaddadbacbbcacacadcaddcbbdadbbaccaadbcaacddabcbdbacbbbaacabcacbabbacabacbccacccbbadaadcccdbbbcddabadcbdacaadbaaabbcbdbdcabaaacbbcabcdcabacdaddabdbbbbbaababccdaadbcbcdacdcbdaddccddbdabbdbdbcdbaadbcdddacccccccadbacdabdaaddbbabbcbccccbdadccabcacccccddcbdbbabdcdcabbbcddbbcbacbddcbdcdbaabbdaaddccababaaaacbdbadbbabdcaccbbbabaabdcaadbbacdabbccbdacbbbdcdbaddcbabaadcdbddccdcdadcaabbcdcbcdbcbdbdacdbddcdadcdaacabbbacbccccacabbadcabdddcabcbdadadacacdadbbdaababaabbbabccaddcccddabdadbcaccdacaccddbacbbadadbdaddbbbcbbaabdabcacbbdbbcccdbdabacdbabbcdabbcbbbaadaacabddabaddccbadaccccccaccddaacbbcadcdbdcbcbbdddcdbdddadacaddcbdbabddcddcbcabcccddbcbdcaaddbbcaacbabadbbbbcadbcaadaaaccdcccbabbadbbbcddabccdcabbbddcbbcacdcccaddbbdcbccdaaccdccccbbdddaabbdcbcdddbbcbbbdadbdbddaddabadccbadaadadaccacbbabcdbccbddbcbacddbdbcddddcdbdadbacadabababababdddbaadacadbaadbdbbabdcccabbdaabacdccabbddbdbdbdaccacacddaaaccdccdacdacdbadcadcddaabcbdcdbcbcddbaacbbdcacbdbadadcddddabbdcbcbadadabddcddaaaddaacbbbdacdcdddcccacdddddacadaccaccbdbdcbcabcbcbddbbabdaddcbcbdaaddccbcdbbdcdabaddcbcbadccbbdcacddaabcadaabdbabaaaaaadbabccddcdadaccdcbadbcdacaacbdadabacbbcbbcabaabccaadcbddbadabbadcbadaaaacabcaddcdddddcdaadaabdcddddadddbbaccdbaddbcbdcdddbabddabcdaadcabaacbacddbcadacdaddcadcdcdacacdababdddcbddcbccdbabcbdadbbdbabbcbbddbcabbddbccacbccabdadccddaacbccdcaaaabcdacbdcccbbababbdccadbddaaadacdbdcaabdcdcbaadddbbdcccbbbdaccadcabaabcccdbbdcdacbbbaadcbbaaadbadbbdcdddddacaaccbdbacaccadaabcbdccdbddbaadbccbddacaaddcdadcdcdacdddaabcdabbcccdaacabdabaddbadbdcacbdccbdddbdacdacdbaabdbaacadaaaccdbcdccaabcaadbdaaacaacbdbdddaadccbabdbbaaddddcddcccdabbbaadcdbdbdddabcacccbcacdbdadbaadacabbddbbacadaddabdaaadabcbddabdbbaacdabaaacacabbcdcacaaccdcddcacbdcbcadbcccabbddcbbcdbdccdadaccaccabcccaadbabaccccacccdccabbdbbcccabbabcdcdbbdbdaddcacbadbabdcdccdbcdcacaccdbdbbdcdcccbdbabdbaddaadbccbcdccacbcaddadbcbacdcaccdbbcdccdbcbabbbdcbadaaabbdbdcaacacdaabacaaaaabcddcabdbbbcaabdcaaccbdadacbdddbdbcbcadbbadaaacdccccabddccbbbbddacaddcdadbbadbbabcbddccabaddbbadcddddaadaaacddbccbcabaacadcdaaddbcbdaacbcaddbcadbbacbbcaabbddbdabcbbddbabbbdccbaabacdcdbccccdcaabdbabdddcbcabcdbccbdcdccddbccdbcdcdbccbdbdababcddbbcddbaacdcbcaacbddaddbbcadbbbccccdadbcbabbccaddcccacbadadcbcbacdccbdcddccdbaccabddacbbaaccbcabaadaaacbcacddadaaddbbaaabacaccbaadccbabbcddccaabcccbaaddccaabdccdaadccbbaccbcdcbdadbaaabbdcdcdddcdbbbbabdccaaabbabccadbcccdcbddcbcaabacdaabdadcaacadcccddcddaadcaccdbdaabddcdaccbbaadbadbcabdbbabcdcbdacbbacdbbcdacacabdababccbabbbdddaabcdbacabddbaaabcbcdacbabccdcbaaadccbccbbdabcaacaaacbadbbbadacbacbdddcaaddccdcbcccbcccddcdbcdcdcacaacbdcbdbdbaddaaabbaaadddcdbadaccbaaaacbaccdaccabdcdadbacbddacdddddccbdbbaaaabadbdbaabaaccbcbacaacdaaabbbadbdbccaccbcabbaccaccdbbcaababdcaacdbdaabbcbadcadddbbdabdcdbdbcddcacaadddbbbadbaadcadcaccaaabddaccddbddbbdcaccacdbabddbbbbbcddbcbaadddcaabdacadbbdbbcdcabaadaccaabcbcaccaaaabaaaabccdaaadddccbcadacbababcbbbcdccdcccccadaabbcbabacabaabaabbbbdbdcdaddbdacdaccacaabdaabbcdadbcbaaaabcacdbadccbadcaacaadcbaaadacbbddcdbdabaddbbbdccaabcdadcbcddbddacdadcaaadcbddcadcdabcccbbddbbcbadbddbcbbcbcabadbcaccbdcdcbbdcdabdcdaacacddcaadbddccccbbacbbaadabdacbabdbdcdcbbcbacbdcddaaddacabbccabbdbdbbaadcaabcdcdcdacbcccaddccacdaadabaadcbddbdbcbbbbdcadcbddcbcbadddbdbdbadaaaabddabbcbaacabddaaddccccddaccbbccabcadbdacacdcbddbaababbcdabbcbaadccbbdaacbdabcbcbacabdbcbdbbcdadbdbbcaabdcaccdcacbdbaadcddccddbadddcccbadbdbbacccdcbddbbddbccaabccabbcaabdccbaaccabbaadccabcdbaccabcdabcaabccbaaaadcadbddbdcbbcddbdbabddbbdcddbdbbdbbacbcadbbddcdadadcabbaccadabdcddcbbbdbcaacddabadaaaadacbbdabdccccbdbbbacdbccccbdbdddbdadadacdabaaababdcdadcccbdaaddbccdbdadbbcbccabbbddddbcdddaddbaccbddabcadddacbcabcbcdaadccbdbcbbcdabdbaabddaadbdaccbadcbdcdbdcddcaaaabadcadbccaabacccdbdacbbdaaacdcbabcdbbbddcdacabadaccbdbbcdacdcacdacadacaccccbdcaccdabdcdddbccbddaaabdcccdddbddbccdbdcacbbacdaadbdaaaadcdbababcadadcdbddaadaadbacaabbacaadbbbacbcdcdcacaddbdddcbbdcbbcccbbdcadccdcbbcbbcbcaacbcabcdaacaaadcaccadbbdaabdccbbcaabdbccdddbabadbccadbcabbbdbcabbbabbcddbbdbdbdabdcdbadadbaadcbbdbcbdbadbcdaccadddcddaaaabbbdabbcbaaaaccacddbdaaacacabaabcacdbdcbacdacdaddcacaddccbdbdccaabddbcabaaacaadcbdbbbdccdccbaccbbdbbbcdadccbcbcbcbadcaccaacdbcaddbdcabbdcbbabbdabbadadcaddabacdaccdbbacddabcddbcccacbdaacdcbcbcdadbddaacbdacdbaccdcbaddcddbaacaacbcccdcbbacbaaddcccddabddbbabadbcdcccadccccaacacdcbaddbdccaccbdddccaacaaacdacaccaddaaabbdaaccdbdbabdcddcddabdaacadcbbbbcabdbccbadabccccaabcdcbcdaaccabbacdabcacdbbcccdacaadabcabbbcbbddcbbdcdbcaacbdacabbbbabcacbaaacbbbadccddaacdbacdaabddddbbabdcacbcabcccbccaabcdacaddbbabbabddbdddbdbaccbdbdbabbacccbcdabccdbdcdaccddccacbbcadbddcdabcbbddadbcaacbadbdaadddabcdcdbcbaccbbdcdcdddcaababacbcdcdbcbaccddcdbdddbaccaababcddccbcddccdabdcdcdddcddbdcddbcbcdcaaadaaadcddaddacbdcdbddccadaadbadcadcbaccddcdbbdaacdaacaaabbcccabccbcbbbbacdbddddbccdcadbddaabbacbbcbdcccbccdabcaddadaaccabdbaacdbaaaabbbcdbaacbdacbaacdcbabcbccdcddbcdaadadcdbdbddacbdadbaadaabdcbbdbbdadaaccaaababaaccdcaccbbbbdaacddcaaaaccbdbccadacbbdbacdcacaaaabdbbadbcbcbdcdbcabbababcdaddabcddcccbcadaddbcaabaccacabbbacbaaccadacddcdadbcdcacdbacbbbdbbcdacddacbccbdcbabcadddadcccbddbddcccbaddacabdabbdbaadcdadddcacabbdbddaddbabaabcdcbacbcaabbbdabbbacbbcaacdcaadbdadbddacaabbddbcaacbbacadbbdcdccbaadcbdccbbabcccbcdbadaaddbbabccccccacdaacddaaddbddcdabbdddacaaccbcbdbdbaacacbaadbccaaaaadacaabcbccdbcdbccaaaddabcbdbabbdcbcacbadcdccaabddddcdcdbaabbdabdbbaaaabcbacdbacaccabdcdadbdbabacdaaddbcbbdcddbbbddaadbcaaadddcccacdddddaababdbdadbaabaadccdccaddcababccdacbdaabdbbacbdbaaddbcdbbbacabbaaacccdbddcbadddccbdcdcbbadddaaababdbdccdcddbdacdacdcacdcdacacbbccacdcdadcddabaaadbcaaddaccdddbadccbbbabaccdcdaccadadbcdcbcabddcaddabdddbbbadcbaddcaabaabddcbaaccbdbcabbbaacaccbbaaaacdaccddcabdbcbbccddadbaaaddbbaacaccabdddabddbbddcbdbbadbacdcacccddbdbacadcabdadcaacdabdadcaaadddbbacaccdbdbdccbbbacadddbcbdccaaadcaadbadcdbdddcdbdaacbbbabaaaacbbbcacbacabcddabababccbccbbcbdcbdbdabbacdbaddcdadcbcbdccbacadaaaaacccadabbaddbadabbbbdbccccdbbcdacccccbabdbacccbabdcdbbaccababcaaabddbaacacacadccacbadccbbcaacadbcbdbdadbcbdddaabababadcdbbdabbcbbadccbbaadccbdccadcdaabdcaccdccaadccbbdcbdbddcaadcdbcbdaadaadacdcdddcdacdaaddaacacbacdbcbcdddacdddddcadbacaacdcdcddaadcdbbdccbcaddcddacabacaccacaaabdcaacbdcdaadcbdbaaacccdbccbccccddcbddbdcdacbdabdddaacccdbadcbbabaacadbdbbaadbabcacabcdbcccdcdacdddcaadadabacdbbdbcdabdcabbbbcbcaacbdcdccdccabcdbaaaaaaabbacbdcaccdbdaaabcddaabbaccbbbbbbbaaaabaddcbdddbddccaadbaccccbbbcccdacdcabbcddbdbbcdacacdbbddadccbcbdddbdcbdabdcbcdbbbdddbacbdccdbbbbaabdbbdabcbacbaadbbabacaddcccaddbddbadbbcbbdccacbababbccadabbbbddcddbdbabcbbcacbdbccdabbbccaddbabaddacdbabbcbabdbbdddbdbddbacdbccacbbadacaacdaddcdaccbcadcbbaddbbacdaaccacaacadaaadbabcdabcbabaccadcbddbbbabdddaabbcbccacbaaaccaadaddbdcbaadadbcccdcbddadbbabcccaaadaaccbcdccbbdcdacbdbcbddddcbcccbaacbcacadaccbdbdacacdbacdcacdabdabdadaadcccbdbbccacdbdbdbcadaddacbbbacccddaabddbacccbcadacacdddbbcdbccabbcbdadaacdcdbcbdbbcaacbdababcabaacaacabcbcdddbaccccbccbaccdccbcddccacddbcdaadbcbdbcbacbbacabbacabdacccbacbdacbbacaccdbababbaaaddacdbcbdadbdadadaadaaddbbcdaaacdbdcbcaccbadaaaddcacacddcaabcbbccadbdbcbbdbcabbbbbdacadbcccaacabccadcdabcdababcadcdbcabaaabbccdbdababbadaddcccdcabadabdbbddaaabaacaaaacabddbbdaabadddabcdbccbdcabcadaadaaaacdcabadcccdcddadacabcabdbccbdbadcaabdbcaacddcadbdbdcdbbcdcacdbaaaacdbbdcbbddbcbadccddddbcaadbacabdaabcdcdbbbacbdbbbaadcacbdbbdbaccbaabbcdcdcdaacbdddbaddaaddbcacccbcbdcacdbbacbbaadddaddcbcadcbcacbbbadadabacdbaabbbacdbbdaaaaaaaacdbdabacacccaddadadaabbbccbddbacddccdbbdabbdcdbaaabbadbdacddbbddbabbccbdcddbbabadcdbdabbbddadbcccdbcbacdaaabaccaadbaaddbbcbccabbaacdcccaadcbabcabaacacacdbbabcabddadddcdbdaaddaddbbddaabbbdcadddbdcbddbdaabdddbbaddaadddabbbdbbbbaabaabccacabcadcccadcaaacdacaacbddcacacdbaabbcccdcdbdbcbdccddaccadabcbcabddcdcacabaabdbabadbbbcbdbbdcbcaccabaacdbbbbabdadaaabdbacaadddddadccddbbbdacaddbbbaddcdadddccdbacccbbddcdabdcdbddbbcdcbaaaaabaacdcabbbcdcddbbcbcaabcaaaabadaacdaddacccaddabadaabcdbcdbdddbcddcbdbacabadddbccddddbcbdccadcbccbbadaabbddaccabcabadbbcbabcbcbbbdbacaacdbcdabaddcacddcdcaaaadcdbbcadadcbcabadbcdccbadcdddbabdbccaacbaababcdcddadbcddbdddacbaccdbaabbcabcacbacdcbdabacaddcbdbabacdcaacbbabaacbacdbcbcccdabaaddbdabdbbdccdabcbaadcbabbabaadbcbdaaacabdcdbcccbbdabcadcdbbdcccbbbddaadbbcdbdbcabdaacddaaababdcacdddccbbadacaddaaaacddacbbadbcbdbbdddbcdbdabdacaaaccdddcccddbadbcaaddbaadbdacccbddddddbabcaaababccabdbbaacddbdaaacabaabadacadadddbbabcdababadbaadbbdaabcdaccadaaadbdccacbddcdaddbcdcdaccaccaabdccbcddbdbababacbbdaddccbdabbccccddabdddbdcbdbacabbbcdbcdacaabddbccdadbccacbdddddaddcdccbbdcbbdaddcdbdabddddcddaadabcddbabbccbbbaadccccdcbdadbcccaabaadddbbccacadcabdadbacbccdcacaadaaabaadccbddaccaacabdbbcddcbbcacdbabaacddacbbbbadbbdcabaddbaaacbcabcbcdcbdbaaadbdcdababdddcacbbbccdaabdcadcadaaaadadbbdabccbadbaddabaaccccaacdcbbdcbbbddbcabaadbdbcddadbadbadabcaacdbaccaacddbdccbdbcaddbabcbcbcdaaadacaacabaddaacccaaaccbdbddccbbdcdabbbcdbbdaadcdcdbacacccbabccacccdbbcdadbcdcabcdbcddabddbcbdccaacbbccddcbabdaaaadcdbdbcbabbbccdccdbacbdbdbaccbcdccbcccadbbacbcbdbbcddbcabcdcdcbbabdcdbaacaacddcadbdddacdccadbbbdadccdacadcabadccadbdadcadbacbaacadbacbcaaaaadbdabadaadccbcbcdbbdadbadabdbddcdcbbabaabbdaaddcbabbccdbadadccadbbbabcddacacacbccabbddadadbcccddcbcbacdbcbbbbaabcababbdddacdbcabacdccacbacccccbdbdcadbdbacbbbbcbccddccbdbbcbcdbdcbdabccadaadcddcadccadabcdadbbaddaabccabcdcdcdcbacaddbdadbadacaabbbacabbabbacdabcaaccaabcacbdbbbdacccdbbcadcadabdbadbadcaacacddadabdaabaccacccbddadbdcccbdadddabccdbacbbcdaaacddccbcbddccddcdbdadbbccabbadbbccaabccdcbdbddaabdabdccbadccbcdaaccbaadacbbdabdbbbacdaaccaabbbbbabbbdabcbaadaaabbbdddbbbdbddccbaacacbdbcdbdbacccacaccacabdddacdbacdcdcbcddcbbadcbbdabdcdddaccadacaadbccccdababddabcdcaacbdcbdddaacbabaabdbbdbcdabacabdbaccdcaacbadaabbbacabccccdddccaacaacbdacdaacdcbbcaaabbdcbdccbbaadddcadddcacaabccadacdcadbbcaadcccddbcddadadabcdcdaccccaaddcaabcdddcbdadaaaccaabbcaccdacdbbcadddcaacdcbdccbdbcbcadaadabdaaccadbbbcadadddcbccdabdbbdbaabdcdabccbddbadaaacadddcbbccdccdadbbadddcccdacaaaccdacbbcdccdcabacdaaccdacdbdaddbccbddccbbdabdbbacdbcdcdaadacbdbbdbbaadacbbdadcdbbcddcacadccacadacbbaabbdcaccacbcdabbcbabcdcbbabaddaabbcbacabcbabdacbababaabaaadccadadadabcacbbbdbaabbcbacdaddacdadcbdccdbabacdaadabcdaddccacbbdcabbabcaddcccbabcddbadadbcdabdcbdcddddcbcabccdbaacaddacccdccccaaabaabcabcabccdaddbabdbbcacbacddcabdaabbacbcadbdbccdcdcbacdcbbbcdccdcdacdddddacccbcabcdadccabacadcdddacbcdbcbaddaacadbddcdcdababadadaabaadbccbdccaabbbbcbdcbcccadbdcbaabbcbcaacbacaabbdabcbcbdddbabdabcdabacabbccdbcbdababdbcbbdcccbccbcdacdcdabbbabadcbbdbaadcadccdaccdadaaaaacabdcbbbabcdcbbaccadddccabacbdaabdcbcdacacdcaaabbbaabbdcbdaccbbbdabbaaaaddbdcabccbacabbbcabcdbbdadaabcbdddacacaddaabbddabdbadabdabdaadbcdccdaabdabcccbabaacbbbccbcddbdbdaacaaddabacddcacddaaacdbccbcaddccbcdacccdcbdaaadbbbcaadcbddadbabdbadacabdccbccdacbcbbaaacdaccdcbaacdbbbacccddaaaabbdccaaaabbdbdbcbcdddcbabcaaacdacdccaccbdbacbdbbcbdbbdacdccaadbdcbacbccccabccddcbacaadcdcaaacbdaadcaacbaacbadbdbdaabbbabbbaddaadcbcabbbacddaacbccddbcbcbbcacbabbdabdacabcdbcccccbccdcdbcdddbcabdccaddbbdacaaaabdadcddaaabaddbcdcadcbaaaaabaabadaacacbbbabbadbcdabcbbacdabcbcacbdcbdaadcdbacbdadacaaabbdbacbaddccdcbabccbddbbbbcbcddccdbcdbacaaadbbddbabbdcdadbbaababcccabdcccabdaddaaaaccdbbaacabbabacbcbdbabbabcbcadcabbdaacaaccadbbbccdbabcdbccbbcdcdcccaadaabdabbdbabcadbdccaabadcdbbcdaacadddbdcadacbbcddcadbdabdbdbdacbbdbabaaadbdaacdbcbdbbabdbbccabbdbddababddcddaccdaddbaddbbbbaacdacddcbbccbabcdabddbbccddcabaaababcabadacbddddbcabdacaabdcaccabdcadcabaccaacccbbbbcacbcbdbbdcccbabdacbcdcbaccddacacacacaaabaccbcddcbaacadcaabbcccdddabbdaaccdbbbdbbdbbccccdaaaccaabdccbbbcdadaaccbbabdbadbbbcaabadccacbbccaadcaaccaadbdbddcbbccbcabcccdadcaabbbbadabacacbdabaabababdccabdbddabdccdcccbcaacdcdaccddddacdaddacbcbdabdbdddccbcdcbcbbadcdacbdacacdabbbbdbdbbcddbbbbbacaabacdbaabbbbdbaaababbaaccbcabadbbddabccadddacbbddaadcdabdabcabbcdccdaacaaaccdcbcdcaabacdbdacaadcdbcadaddccadaadbbbdddcdbaaddbbbacabacaacccccbbcacabcadbadaaccccacaabddcbacdcbdcbabddbcdbbcbbdbcddccaabadcbadcbcacbdaaccaacbaaccaddbdcbdbddcaabcbbaddbadacbabbdaaaccbdbbbcaacbacdadcddabccaccdbbcbccdbcbdadcabbddbaacabdcadabccbdcbacaaacaacabacbacaadccdbcbcccccaacbdbbcabcbbacacdabaaadaacbdbcdddccbaccbdbcaacdacbccdbddbabccbaabacdccadbcdcdacbabbddccdadbbdcdadbbcdabacbdcabdacbdbcdcddcbbccbddbdbbbccaadcbacadcddcbbcaaabcdbaddbcccdcadbbaaccbcbdcbbcbcaadcbdbcddbccbadaaadcbbdddcdadaabddddcbcdbacaaacbdbcacdabbddbdadddaadccabcacaabddcccbcaaabdaccbcccbddabdbaacababdddccbbabbacabcdddacbaaaacaadaaabcabbddbddbacdcbcbbcbcdadaddadcbcdbdcaaaaabdcbdccaaabbdaaadbccadcdddbbdbadaadbabdbaadabadbddcbccdadacddbcadcaabbaaacaabdbdbaabdcaaaaabbbdbabbacbcadacbcdaccccbbbbdbcadccbaddcbbdcccbdbcdbdcadadcaddbbdcbbbbacaddcadbcabadcdabadbbcdbaaddcadbdaacdacdadcabacaaccbcaaccccdabbbdbccbdadbaadbbcbddddbdaaabbcadbcddbdcbcbbcdabdcdddcdddcbdcdbddabbbdabbbdaddacabcdcbbaaccbabaddccadabbddddccdbbbdacbcdaaccabdcabbbccabadbabcbacaccaacbccddaadcbbbddcabdcadbabdbccddbcdcddbabcbdbcbdaacbcdcaadcdcaaaadaacbddbdabadcaacdbbdbdccaadddabccbdbdddaaccaacdcbabaccdddcabbaddbadaccddadadbdbcbbadabcaaaaabdbabaccddddcdbccacbabbdbcdbcddbacbccdbacdcbddabbaadccbcdbaacaddcbadbbdadacbcadbccbbcdddcaabadbcbcaddbddddcccacabdcbbbaacdcaaabccbcdcdbbdddccabaadcbbccacaaccaddacddbcbaacbbcadbbbdadababccdacddaaddbdccbddcbcaabcbbcccadcccbcdaadbdabdcacabaadcaadcdcdcaccacddaddbabcdaccccabcabadaddcdccdcdaddccdbcaccacdbdcdababcacabbadbccaabbdbacaaadacdbbacaabbadabddadacbdadccbdaaaddacbbaabadaccaccdbdbcbbdaacbabbdcdbaaccabbbacadcadabaccabcdaccabdbcccbbaacddaaacadcaacccdbcaacaaaaacbaabdbcdcdbabadccbadabaadacadacbcadacadbdabdcdcbbaacdaddbbbdcbccdbacabbbbbbdadbcaddbacacadcdbdcbcbcbccbdacbcbdaacdddbcbdbacddddaacacdbbabbacdcbccbadccaabdaaaaccbdabcabcbdabdccbbdddbaadbbbcbcdbddddaccadbdcacbcddbbcddbbdcaabcccadddccbccdcbcbabcabccbbdbbdacdbcaabdddddaaaacaacabaaccabdacaaaddbbadcaabacbcaadbbabddbdbaaacdaabbdbddcbcdbcabbbccbddabccccddadabdbadaccbbaacbccdbacacdcabdcddcaabadaacdbbcdbbaaccbdaacdbbbdabdddbddacccddccaabccdccbadbcccadadbddbaccdddcdbddcdaaacadaccccabcacaadbdcccdaaccabbcabcabaccabaadddaaabcadaaabbcaadcbbdaaaadaadcaabcbcaacaacdadccbbbbdbdbccddadbaadcbabcccdcbadddbccdbdacbbaaaabdaccbbdbabbbcadcbaaaaadadaaadcaacddabdadbccddaaaaadcacccddccccadbdbabacaaacaacdcbdadbaabbddcacbdcbacabbcddbaabdcccbcbbcabbabbcdadaadbadbcbbadbbbadccbcccbdccdbbabccadaaccdaaaccabcabddbddbcabcdabdbdabbbbcabccaccababbbdcacbcbbdbbacaccabcdaaabbadcbabcdbacdacdbabbbcbdcaadbdbadcccdbbadcdbccbddaaaaddaccdcccbbaddabbadacccdbbadabdbaddcdabbaaddaaaadcadbdbacddcbdadbbdbccbbcacccccbacdcbaadaacdadaaabcbdabcbdaadccccdbcdddadcabdbcdcbbddcbcadddbdcdcbcddcdcdcdcdcddbdcbdcabbdadddcbcbdabdbdcbcdbdcadbbabbabcacabbbdbdaacacbcdccdadddcabccaaaaabcdcdbadccbddacaabccbadadcbcabdbcbdbaabaabacabbacdaabdbdbaddbddbcddcddddcbadcaabdbaaccbcdccdadbbbcbbdbdacbdbbbacddaddbdcdbaccbcdddbcdadabcbdcccbadbdbcbaddadabaabadcbdcdcddadaccdbdabdbdbdbacddadabaccbddcccddcadcccababbcbcbcadcbababcabbdaccddcdadacaabcdccadcdcadbddddccbdabdccbcdcbdadddddddacbdcccdccccbdcabdcaccdbcdacadccccdaabdacdaaaadbdcdaaacabbcdaabcbddcdabdcdadbdccdcbddcacccddcbacadacbbbcdbccddcdddbbdacdaccbbbbbddbdabbabaacadbacdcadadbbdbbbaabbaacdadaccdbbcddbbbcccbccaacaddddacccbadbbcbdcbbbdccbbbadcbddaacddbacaaadabbdcccbcbabcdcadccdaadbcddbbbabcddcbadccabdddadbbdaadbbdacadaabcccdaabcdbbbabbbcdbdabcabcbbddabcaaadaccdccccbaccdbabacbcdcadddcddbcdbdcddccdcbadcdcaaddbdcddaacccbaccabbaacbdddaabcabdcadddcbaaddbbbcddadadabcbacdbdacaadbbcccacbadcddcabbdbccdcbaddbabcdadabdcbdabbbdbbcbaaacbbccbdbdcbddcabbbccdadcaadadaacdccbdccabdcbcccaaaaaabccbadcaccabdabbaabbcdcbaccbaabcbbcacccbccdbccdabdcdcaabbdccdcaabbabcbcbadccdadadacabcdbbbccbcccccbaddcbabdaddbddcdaababbbbabcddaddaacbbcadddbabacddcddbdccbddbdbbdcaddbccdbadaadcccaadaadbdaadbddbbddbcadabbbbbbdbabdbacabdaccbadcbdbaababcaacabacccabcbaabbbddbbddcbcabcdbddbddacabadcdccdcddbacddabdbcccabddcbbccbccdcddcdabdbaadabbacccabbcadbdcbbbcbdccaabacdacbbccabbadcbccdbbbccddbcbacaabbdccbbadaaddaacaabccdaaddacaddccddcbddbbabbdbacdcacabdccbcadacaacddcbcdcdcdcdcaaacdcbcabddcbabadbccccdcddccaabadaccaadbaacacbcccaaaddbbacadcaabcddabadcbacabaaabbaacddddbbbacbbaacccdbcadbdaaaacaaaababdadccabbbcddcdcdbcbdcacdabbbcdcaadbcbcadbccaddaacbdbacaababbbcbcbdbdccbacadbacdbaacbdacddacddccaccdadaabcdbabcaddbccbbdddaadbdcddbcbdcaccccbbadcbdbdadcaacadbabdccddbabcdadcdccbabbbbaddcdcaddcadcbdbabbbcababcbbbbaaccbdcccbbabcabcccccdcabcddddacaabcbaaacaabadadacadccbccbdddccbaacccccdbddbcbdaddaaaddacdbbcccaaaacdcbdabccaaacdddbccbcccbddcacbdccabcaddccbdbaabbccbdddabbdaacccacbbcdabddcadaaaacadbbbcadaaccaacdaabbcdbcaacdcdbbabcabbbcabddcdbbccaabacbacbadcdaddcbaacaddccbdbccabcaccbcbcbdbcadbdcddabdbdadcaabbbbdbaadcddadabbabacacbcbcacdcaabdaabccabcdbbdcdbacabddbdcbababbcbbadbbcdddddddacabdbaddccdaacbdaacaabcddbddbaccbbabdcbbcdadccdacdbbccbaadbbddbcadcdabbdddaaacdaababbbdbcbcabbddcaccccbcbadacccabdccddcdbdcdcaacccbcdcabdbaddbadbbcacaccabdbbaaacccbaabdbccdaccaaadbbadbcaddbddcdabdadabccacbcabacbdadbcacddbbbcacdcbdccddbddcdcaabdcadabbddbdaaabdaccdabdabdcbbccacbccadbaccdabbdababcdccbbbbabdabccdddadaccbadcaabcabacaadabbbdccacdccddbdccaaadccadcabccdacadcbbdbbbdcdaaaababbcabcbcabccdcbcddccbcbabbdcdcaabdacabacbbdabbbdbadadaaaacbadbdabdbcacaccdcdaabacadbdabaabacccbcaaacdcbbcccdbcbabbaacdaaaadcbaabcabbccadaddcdcabdbbcbaccbabdbbbccabcacddcbdbadbdaabddabcdabadddcbcacddadbaaaaaccbbdabbcaaddcaaaadcbdbdbcccddddcccabcdaabcbbbbbbcbaabbadccdddcdabbcddcdccbdcacabdcaadabbcaccabccbddcbaacccdcdddbdadbbcdddabbcddaabcdbacddbcddbaadbdbdcbaabbcadabaacdbbcddddadcdacabdcacadcdabcdaabcdaddaccbcdabadcdcbbdddcacddbcdbbbdbdbbddddadaaddbdccabcbbcbacaacbbccabbcbcbbddbcbdcadccaaccbacbdabddabbdddcdbacddcaabadaaddbdabdaddabadbbdadcddbddbaadabbccbdacddbdccaadcaabcaddcabccdccbdbbdaddadbabacdababdbbdadcbbdccbcacacddbddbcbacbdccddbdcbdbdadbdcadddddcbcbaabbcaaacdcdaaabbdcbbdcdbbcbadddcabaddcacccdccacadcaadaaadccdacbbaacbbdbcaadddbcdacdaccbdccdcadadcadacdbbdaacddccacdccdcccbdcbdadaaabcddccaaacdadcbdbdbdbaccdcbccccbddcdacccbacdadaacbaadcdbdcaddabdbdabacccdbaaddcaabbdabbaaababbacaddbddaaaabbdcdaaaddbadcbcbcdaaccccacbdcbaaccbcccbbcbaadbdbdcaacbaaccccbbcdcacdcbccbbbbaabaddadbdbccbaddaccdbcbacaddcddbbcddcaaabdbccdbcdacccaaaaaabbbabbdcadbaddacacddadbbbccabdbcadabcaddacbcdbaaabbddcbbabdbcdbcacdbcccadbacbdbdcdbddddbbbdababbcadcdcbdbaabdccaaabcdcabcbcaaddbdbbabbdbbbdababbbdbaabdacdaabbcccabaddbdadadabbcccdbcdabbabdacbabdbaaccadbdcabadabaadbbdabbdaabccbbcadbcddcbaccbabadccabcdccadbbbdcbdbdaccdcddcbadcbdcbccddcbbbabcccbdaaaadbdcbdbbddacaadbbdddbabcdaacbbccdcdbcabaadacadccdcdddddcdbdcdcbabcbaabbcbadbcdcddcdaddaacaadccddcbbbdabdcdacadbcadcdadccddaacacabcbdacdabbadaddbcbbcbadaaadadbbccbdbcbabdccdaddaaadadcbabdcdcddbdddbabbccdcacddbbccbbdababbacbcaaadcbaababbdddbccddcdddcdddddaaaacbbcddabbcacccadadabccddbcbbbbdacdabccabcccdcbbcbadabacdbccbdbcccdcbdabdbadbcadadacbcdcdbcaaaaadbcdbcdcdcaaaddcaabacccccacddcacbcbabbccbacaccabcccddacdbaaddcbdababdbaddccdabddcdcdadcbdaadacccaacdaddccbdddbdbacdcbbcccddcdacdcaaddacbcadaddaabdbcbdddbaaadaababcccabbadabdcdbdabdbbbabccabdaacdabdbabcaddddcacabddcbaaddddddcccbbbcacacdbaadbbbbcbccdcaadacbcccdbbcdbbbcbdaadbabbdaadaccbabcbcadabbcbbbdadbacddbbdccbbcaabbdadcacadaadbcacddcbddacdbadaccbacdddcddcbcbaccacbdddbcbbbabaaaddbccaacbbacaaccdcbbcadbbbcbbdbbcbacabaadadbbcddabaaddbccbcdabcddbabadcccbdaacdcdacdbdcaadbacdaadbaaacabacadadcabadbdacaaaaaaccccbccddacddadbabcbacdbcdaddacddbcbccaaccddcbdbabadaaadbababcbdcabdbcaacbaabcddbabbdacaaadcadbaadaaadddbcabccadddcaddbccabacaaaabddabcbdcaacaccacadacddacdbdacbbbbabddacbdaabaacacbadbbbacbddddabacaaddcabacdbaaacbdccccdbbbbadcbdbddcddcbacaacaabbbdbdacadccccabcdcababaacbadaccababbdddaaabddbbdcbaccaadaadbbcbdaddaaccacddabcabbbbbababdcddbdcbbbbacdabbaddcbdcacccaccdbbcbbbbaaacccbcaacbaadadbcdcaadcdddbacacbcdbccdbcbddbabbdcaadccbbaabdcadbbaabaadadbbcadabbcbcaaababdcabbcddbcdaaaabaadaddaacdbcacacacabbccccccbacbcdbcdcadcaaaddbcccdccbadababdcdacacaadcddcabacbcdbbdacdbdcadacbcbcdbcaacabdaccadcdbcaabcdacbdccbbcabcccbdabadcadbbcdbbdbabbadccadcacddabcdaaacadcbdcbccbbdbaacadcaddcacdbddcddbabbadabcdacdbcadbcccdcbdbcddbbcaabbdbabcdabbacabccdccccddbbaccacadbdbadbcbddbdbdabccddbabcbddbdddcbbdcacacaadbadcccacaccdabadddcddabadddccdadbddabcbbdbababbcbdccadddccadcbbcadaccabddbccdbabbdddbdaabcaaacdddbcddaaaacccabacaaacdbadcabdcaaaddcdbbcdccacbdabbdbccbbbdcacdbcacdbdcdaadacacccbbbbbaaddbbdddcaacbbcbdcadcdbbbdbcbcdaaadadbabdaaadbbdacddbbdabddcdddaaaaccbadadddbdaddbdcdcddacdaddacaabdbcbbacbbddbccbcddbcacbcadbcadaaacbbaadbcdababcdaddadadcbaabbbbaaacdabbcabbacbddccccbccbddccbbbccaacddccdbacacaabcdabdcdcdabbbdcbbbaacbacabdbddccadbdababbbaabbddaccbccbabdcdcababddcdcabadcaaacbcbcacaccacbaababcaddbbaaddbdcbbabdababdacdabcadaaaaccabbbbbdcbbdacadddcaadbbcbcbabbcbacdaaacbddadbacdcbbbcacdcdcaddcaaccdcdadabbcdbbbddacbcdcbdcbadbbdcacccadaaabddabbacaababacbdbbacacacaabdddabacdcadadabacdbdcaabacdcbbaadccbccbacdcdaaacdbdcabdaaaadaddbbdaabdacbaacdcbacabcabdbbbdaaadbadcbbcbbdacdcbdabbccccccbcbdbcdbdaaaccadddcaaadabddaabdadaabdcccdcaddbbddbddbaadaadccadbdbccaddacbadcdbdddadbdadccaadbabadadcabcacbadcadcccbccaaaaccbbbcbacabbcdbbbddcbbacdcdbdabbbacabbdaaabbabbcbcababbcdcbbcddbdaadbdccdacccbdaabadadbacdcadccbdddbcaadbdacacadcdcbccccccacdabacbcbaacddbdccbcacccdbcbcdccabddbbaaacdacbdbdaaacabbbdbbbdcaabaccadbccbbbcbacbaabcddcdadccabdadbccdddacbcbadcabacabcdbbbaabdbadabbacbcccddbbaccdbabcbbdcccdadaacddcdccdacacadaddbbadaadadcddadadcabdcababcacdaadabbbdbccdcacaabccbcdddabdddaccdbdcbdbbbacadabcbbcaadbcbacdaacdaacbabccacbaacacccbdacacabaccbdacdcbbdbaababbbdadcbadcacbdabcabaaacaccbbaadbbbcacaadaccadabbbdbccbddbadabcbbacabbbbdabbbbbaadcdcbcbbabacbbcaadadcdacdcdacaabcddbbbadacaacadbcbccaddcdddabbbcabbcaabbbbaabbbaabaacadcccdcaabbdaaacddaaadaabccabdcacaadaaaaabbccdaddabaddcabbddccdcbbccadadaababbacaabccdbdacdbdcdadaaccdcdadacdbdcddbaadabaabaacadcbcbaabcddccdaddaaacddadcaadbbbbdadddabddbadaadadaddbbbdacbcaabacabdaabcccbcbadbdcbddabdcbabaadbadaacdabdbaabadbdaadcccdacacdcaccaacacbaaddbacabcbcccbdcabcadbddadacbdddbdbbbdaacacadabacdcdcbcdbbdddacacdcadaabacdbcaaadccadbabbbbbacddccdacadcbbbdcccddacacbcabbcdcbaacddddbcaccaacbcdadadadcccbbcabcdbcacbbaddadadddcdbddaabbbadbdadccccbdcccdccbbdbadabbaddabadcddacabbaabdbacadbddcdcbbddaacbbcdbcbccaaddcacaabdddadbdacdaaabacbccdabdbdccabdcdcadbbcccbaccacdcccddcabaacadadcadcbcaaccaccabdbdbbcaadcadaabdddcbcacadaabcbbcdadcaadbacacdbdadbbcaadaababdbaaacdabcaddcbdbdddddbcdccccdaadcaccbdadaadbcdabbdcbcaaacdbbbabaababcdabacacaadbdbcbdaabdacccccdcabacbcddbddcabadbaadcabbacdcaccdcbdcbdacdccbadccddadbdaaabdcbcaadaaabbbcdcdacadaacbacbddbbcddcbcdbbacbbdcddbbbcabbcabccaacdacdbcbadbadddddbdaababbdbddabcbdaaaccadabcddbaabdcadaccadcdbddacbdbddadaddacadbcbbbcbccadbacdccbbdcdbbddddbbccabacaadddaddcadddacccacbdcbbdabdddacabccbabaabbdcdaadbaacaddaabbdcbdaabdddaacaacbddbaddadddbbaccaabacadacaddadbcaddabcaaaaacccbbbddbbaabbdacdabbbbddaddcbaaddaddbcbabbcbcacacaadabdddccaccbcccbaabacbaaaccdbdcaacdacccadacabdbbaaaabddbbcadacdbbacbdcbcdaacacabaaabbbcacbaabcdcddbcbacbbabacacbabdcbcdcbbbdcbccacdaaacbcbbadddbabcabbdcdcdbddbcdcdaadbaaadadbadacccddaadccbdacbbcdcbbdabdcaabcaddacabccbaadaabababaaccddbdbabcbbcddacacadaddcabdbaaddddccddbcdabdddcaaabcadbccbccddbbadbdccaabbdbbbbddcbacaaabaaddcabbdbddbcabcbacccbbddcabdcddacacaabbadbcbbcbacadddbabaadadbbdbccbacbdccdabccbdaabdcadcbbadcbbdadbaaaccdabcbbdcddbbbcdabdbcddcdcbccacbddcbacbdaddbccbbaadbcabbabaccbdcadcdaadbccdcadaadabccccaabbabdaacddccbcdbbcbbbbcbcdbacbbbddccbbadcacdcdbabaddbadaaacbacdacddcddbdcbbaadcdcabaccaacdccaadabcadbcdacbbaaddbdbcddddbbabbbccdaddadacaccdbaddabdcbaddbabbaabbbbddcddabcdbbbacbcaabddcbadaabbcbbdadaadcdbdbcdccbbaadacdbacddaddabdbdcccbaaabaddcbbdcdcddcaacbbbbccaaddbaddadbbbdcbbdbcacccbccbaacadadddbabcdabccdbabcbabcbccdcabddccaadcabccddabcbbbaccddabdcaadaccddbbdcbabdbaabdcdbcaacaadbbddbdacbbbaaccaadcdacdbacbbcbdbdddabbbbdcccdcdbcbdcdaaddaaabcccdcacadacbacbcbccadcabccabaabcaaadcdbdbbabddabbacadadbbaaacadcbabcbaaccddbccaacaaddcbabbdddcbddcdcbbacadbbadbdaabbbaddccaadbbadaaacccdcbbbcdaabadddabcaccdadcddadcdabcbccbadababbbaaacbaaddadbdccdcddcdcdabccdbdcacbcdaacbcbdbcdabcbdaadddccdcadbdbabbcdbbccacdcacdbcbccabbbccbdaadbacbaadcbbabdbcddcbadcbbcdaacdbdacbbcacdacaaacadbbababdddccdadbadacaaacacacaccbcabacdaacbccbacbcdbcbdccccbababbddaabaacdabdcadbcabadadcadccbacdbacdbcaabdbabbddcbbadabacbbdddccddddddaadbccacbbccdcaccbccbccbccadcacccbcbcbdaabbdbcabbcacddadbaadaccdaaabbbcdbddabcbcaacadccbbcdadabddadbadbcabdabcdadbddacabdbbddaddacbbbbdbabaaadbcdbdbdaacdbadccacbabbcdbacdddabdbdddcbccddccbbdadadccacbddcbabbacccdcacbddbdbaaacbaabbbaabcddbabbddbbdcabcbadddbadbbaaabbbaadcbbbadacaaaacbbcdcdcdaccadbabbcdddabbdadadbabddcdabcccdadadaccaaaaabbbdccbccdabbcaddccdaacbcbcbbcccdcabaaadadabacdbdabcaaddbdabdbdbcdcacdcdadbdcbaddbdbcabaccdbcddcaadbdccbdbddddabbcbdcacdbdabdadbcdccadadabbdcbcddcccabdbdbcdabddadbcddcbcdcccacbabbdadbaaccddcbababdcdaacacbbaaadbbdcadacdbdacabbacaacbabdcacdbaddcdccdbaaddacbacaadabbbadabadacdabccdbcddcacbdacbaaaaaacabacccacacbcadbadabcaacdabddacbcdadbbddaaddaadcabdacbbadcbadacbdbbcdddbcdcddacdbaaabbcbaddbbaddaaddbdddbacdbabcababacdccdddbdcdbcdbcadaacbaabbdccddaaabbbccbbddcabbccbddbbacacdbabbcaddbaaacddcccbcbbabbddabbbbcbddbddaabccbdbdddbbcbaaaddbaaacbcccadbbcdbbdadbddacbaaaddbcddadbabdabcbcabdbcbacdadbabddbabcbcbccaabcdadbbbbcaacbadbccaaadcaacabacdaaaabbcbacdadcacbcccdcaadabbdbabbbccbdabdacaacaabdcbdccbbbaddccdddbddcccbbaddbbbdabbddbadccacdcabadbdbcbbcacdaabcccaaddbddcdbbadbdaabdbbbbbacabcbcadcdbdbcacddaabadabdcbcbadcaadcddbddcbddcdbaadbcbcddbcdbbcbcdaddcaadbcbdbbcdbcdcbcabbcacacdbbaddcbbdbdddacaadcacccacdabbbdcbcbcaadbaddadbcdabbbccdddddaaadabaabcadbcbdccababadcdbadcabadaaddcadddabdccbbdbbcdcabbaddcadaaabdaddbaccdacadcbacdcccaabacdccbbbcacadbbdbdabbbddcadacccdddaadbcccacbadababcccdcbcbdadadbbddcadddaaaccabdbbcacabdbccddcbdbdaddababcbbbabaaadcddbcacdcbacacbcaaacaccacabdcaaddabbdccddabbccacbbcbcccccaabacacdcadaaccbbcabaabcbccddbbbcdccbcbdcccdddcddbccccbaabacdacadcbcbdbcbccaddbbbbdadcaadadadbabccbdbcacbcccaacabaccdddbbadabdbadabcdaabbbcbaaccaccacadcdbcacbaabadbabacdddbdbdcddababbaabcdbbcdbacabbbcadabbcbbbbdbbbbdabacbdcbcccbcbccdaddcdcccbbcabadadbbccccbdccbdccdcdbcddbccaccabdcbdcbadbbcbbbcbdddaaadcbcabacdacabcaabddcbbcbabacdbbccccabcdccbdaccbdacdbbbdcccababaaabaaadcbdcaadbcdadaadabbacbdaacabaaccdcdbcbdaccbcbdaaababccbabdaccabdcaabaacbcdaacbbcddcbaaaabbaccdaddacadabbbbddcadcaadbdcbdadcaabdbacabcabababcaadcbbaccdcacddcbddcccdcbccccdbdcbabadaccbbccadacdbbdcaddbcbbddcdbbadabcabcdaaccabaabadbadcabbbbddddcccdddaacddabdaaddacdcbcbbacddbbbaccccbbadbbbccbbaaccdcbcdcccddbcddcdbcaaaaddaccaaaabaddadcabdbdabcccbcbcdacbbbadacababbacdbbacbdbdbcacbddbddabcacccadabbddacaabdcbdbdacbbccadcdddddcaccacdabddcdcdacbacbdaccbcaaaddbbbdadbabcabdbdadddcdbbaaccdababbdddbdacdbdaadbdbcaccdbbbbdabcdcabcaadbbacdababacacacbdbaaaabcddaabbbdcacadddbbbadcbdaddcdbccabaabaacdddcccaaacadacdddbbddbccaadbbddabaabccaccbadbcbbadbbcabdabcbcbdbcbaabbdcbadaddbbabbabbbbbbacadaccdcbbcacaadbcbabbbcbacccdacacbcbbccadbbccdcbaaccbbcdcaacbccbbbccbdacbbacccdcbbcabcaddcabcaacddcadcacbbdaacacbbbbbdbbaabbdcbbbbcdcddcadcaddddbcbccabcabdbdbabdadcaddacbaabdbdaddcdbbadacccaacdbbddccbdadbdbbbabccccbabcbdabbdcdccdbcabcbdbcaadaadcdbcdaccdcccaacbccbbcbcbdbcddbaddcddcdcaaabaadbbbcacddcccdcdcbbbcacbddcbbacabcadddbadbaccdaadcbaadcdbaacdbdbaabddcdcacbabcdddabadaaaadcdccdccdabdbccbccddbcdbdccccbdbbdabdbdacdbaddbbbcbbbccdbdbdcabaabbbcddddbdcaaaabddaddcdbaaabbbabcabcbbbdbcadaadddbcbdabadcbaaccbdbdbbcacbcddababcbbbcccadacaccdbaacccabbdacdacababcaacdadadbcbdadbdbcacabadcdcdcacbbdcddccbcbdaababcdbabdacbdbadcdccbbcdaadabbaadccbaaadbaaabddacbccdccbabbdcdddadccdabdbacdcbdcbcacdbcbccaabbdbccabcbcacdbadaaddbddbbbadacccdbccbbbaaddabdcdcbdbadabcbcbbdabcaccccbcdaacbcbaadaddcabccabbcabcbacddabbdaaacbcbcbcdcbcdbbaacabcdbbbbaacaaabddcbaacaadaccadcccbcdbababcadbcdbbbaaadacccdaccbcdbcdbdadaccdaccaababcaaaadbaddbadacdbabacbabdbbcdddbadbccabdaccddcadcaabdbaccccaaccdcaadcddaaccaccdbbbcbcaabdcccbdbaabaabdcbbacdcbdadbddbccadccbdcdbaaacddbbdabacaccbacaaabaccbaccdabdbcacccaaabbbbcaabbbddcdcabbbcdbbadbbddabdbbbdccaaccbdacbcbcdcdbddaabccaaacdbbadcdddacdbbccbbbadbbaaababcdaddbddbddaaddbbdcdbadcbdcddabcddbbabbbbaadacbdbcbabddbddcbccbbdabbcadbadacbbdacdbbdbcacbbabccccbabaadabdabdabcbaaccdabbbdbdaadaccdbdbdacccadcbaccddbbdbaadbcbdcacbdaadaddccabdcaacaacbcdaaaccccabaaadcaabacbddcacbadccbaacbdaddcdaabcadccabaaaccdbaadadbadacaacccabdababddbcdabbabbbbcdacbdabbabbdccbdbdccbbabbcaabadaccbbcadccbcaaaddccdcbcacccbbdacdabcbbdcdbacddbbdabdbabaabcadbbccabadcacabcaaadcaadadcbdaddddcbaabdacadacbbcbdbccdadabdddaccbabbdbdabbdadcabdcbcbbdcbdcdbacccbdbbdcbbacaabbabacddddcbbabbbdbdadbaaabcccdbbbddaabbdcabbbdccadadabbbabdaccbabaaacabddcdcdaacddaaaaddaacdabadaacbabacbadddccccacdccabcdcdcbaadaacbccbbabcbbaadcccadccccdddddcababdbdaccbbddaaabdbcdacbabcdcbdaabdbcdabdbbacbcadadbddbccdcdadbacaacbadcacbbcddabdcdbbbdcabaabbadcbbbdbbaccbaaccaaabadaaaaabcbadcbbadcbbacccaabccddaaacaccdcbbadcccddacaadbaadaccdbbdacabbcaabdbbdadaacdadbbadbdcbddddddabbaabdcccaabddabbdbcdaccadaabdaacdccdaacbaacdacdcbdcdddcaaabbacdbccbacbbdbccbadcdcdabdadabdccbddddabccdcdbdbacdaccaacaccbddbdbddcadcddabdcbddacbdbbaabdaaacccddcabcdccbaadbbbdadbbadbdddccbccdcaadaddcdbcbbcddbbdcdcdbdadaabdaacbdbcabbcddcaaddadaabdbacbbbadbcabbdbcacbadabbadcdbbabccadcccdcdddbbacbccddcaccadccbbaaccabaacddbccaadacadbbbcadbcdcabcbddbbbabaaacbccadbdbadabcaddbccabbbbdcdcbdacababacddaaccdddcddcdbbddadacbbdbdcddbcbcdbadcaadddbbadaacbbbbabcccdacdaabadbacdccbdcddddddbcdacdbbbddbbcbdaccccbddabcbbabcbcdbabacccbabdacdbaddbcbaabcababdbbbcbbaacdddaacccaaccdbdabbdddbcccaddcabbdbbadcdcabbaacabdbcacdbcbabdcbcbbbdcbbbbaaccdabaaddcdbdabacbbabadcdabcaadccdadbababacdbcbbddaabdcdbacbdbcbbcadcddabcaaabadaccbccbadaaabcdaabbccbcdddabcddcbbbcdddabaacbbdadbcccdaabdddcbcddcdbadaaacdcaccabdbaccbcdbcdabdcacbbbbcbbaddaaddcacdcddadaaddadbbbbabbdbcacabcabcdbcadbacdcdccdcacdddddddabbccccacadcdbdbabdbcccadabcdbcdaacacdcbdadccdabcddcbacbcddadcaddaadddaccbcdbcbccaaabadabddbdddabdcdaacdcbbbdbbcdbcdabbcccacdacbbaccbaaaaccabdadcbdcbacbbdacabbbdbbabcbaabcddcbddadcbcdbcadbabbdbdaabbdadcaaaddcbcbdcbcdbabddddbbaccadbdbcbbdabcaaadaaacbabdbbacddacacbcdbaadadcaacaddacddbdaddaaaaaaaabcddabbbbbdcddabdadcacbdccaaadaabccddbdbdbddbcacaadaaccdbccbcccdaacdaaaaccddaccdcbbddcbccdbbddbdaaaccdccdacaddbddcccdddcdcbbdcbbcbccdaccbdbacbcbabdacdcaaacadbccabaacdcbdbcbbdabdddadddcacbdbcaccdcbdcbacaaadbdadcaabbbcaabdbabcbdddddbacbddbdcbdacabddabbbccddaaaaadbabcdccddaddbbdcaddcabacdddddabbbccbcdccaddcdaabccaddbadcdabdadccccabccccacbaadaddddcbaabdbbbcdcbddaddbabbbcbdbbddaaaddcbdcabcdbccdbbaccdcccccaaadbaadacadcddddccabadadcabbadcadcbccdacdbcbcabdccbadbbbbaccccbbcccdbdbacdaaadddcbcacbbbcbbbdccabadbbccbcabddcaaadbdabbbbbdaadcaabdabdccacdbacddbddddcbddcdadbcdbbddbbcadaddccacdadccabdccbdacccdaddadadccbcddbdacbbdbcddaddbddababcdcacbbddbccdbaaccbbbcdcddbbccacacadcdbdcbbdaddcdaadacbdadcabacadcbbcbcadbbbababdabaacababcdcabbdbaabacbcadbcbcbbadcacdabcbdbddcddbccbcbcdacbcdaabbcdaadabdbbdcccdbbddcdccbcbacaadabcadccabccbaaadccbbbcadcaadbdccaccaddcbdcabbcbbcbcabdbcdacdaccbacbadbcaaccaadaabaddbcdacadcacadbdbddadadbbabbbbdcdcacbbcadabbabcacacdbddabcbbacabdcbdcaddccbabacbaaacdcdbcdbbcadbdaccdacacbabdacaaddcadcdbdddbaabacddcdbdabcaccccdcadcccddaabbbdaccabdaacbbabdbcbacbbaaaadbdbbdacdbbcbcbacbbbbabbabccdadbdaccaadbbacbabadbdaabcccbcabbccadccabdbbdbccbbacdddccbadbcdbddadacddabdbbbcdbcaddbdaccbbbcababcbccdbbabcccbbbddbcbccbabababadabbccaabacccabdadaadddababcacccdbbcaddcadbdbcddddbdabaccaacbcdbdbdaaacdacacadbcddabbaabaaddaadbccbdcbaddcaddcadacdccaaddcaaadaaabbcccadadcccddacabadaabdbacaadaadbdcbddcccbcaddbaccbdbaacbbcdddaadbdacccaadbbbadcaddcbabcaaddacbaaabcbbddcdacbcabadabbbbcdcdbdcabbdbaddbcbdbdaaadddaddbbacccdbbabcaddddddbcdddcbbabbcccccadbbadddadccacdadbaadddcbbcadbdcdbcdadabddbbadbabcccbacbdaddabcbadbdcaacacadbabcaabaacadbbabbabddaabcadcdaadccbdaacdccbcbbdbabdccadaaaaaacdcbdbcababddcdababbddcbdaddcbadbaabdccacbaadabacbaccaccaabacabcbbaababccddddddaacddbbcbabddbdccccbacdbacacacdbbcbdcdbbdadaacccbbdbabadddabcbdbcbbabccbbbaaddcccdadcdadaabbccdacbaacbbadcaadddacbbcaacabbbbcdadbaaaabbababcdbdbbcababbcddadadacdbddbacbcabadddcdacbcbbaddacbdcadbccacdaadaaadccdcbaddccaacdacababdccdddcddacacdabcaabbdcadadccaacdacacadabbaaaccaacbdaacdadbabddbcaadddbccdbadabcdcdcdbbdaadddbaabbcabaabacdaaaaaacccdaabddbacabaadabcbacadabbdabcacbdcbaccbababcbbddcbccabddcacaacaddbadabdaabddcacbbbcbcbdaddcabacbdbaabaaadaccbcccadadcadccbbccbbbadddadcdddabccdbbcbccabaadaddbdcadacbdabddacbccdcbacacddbbabadcaacabadcccdccadcbcdcddaadbcacbacadddcdcdadaaaddadabddbcabaccbadabadbaabccdbbaaabbaaacbdbccdbabdbaccbacbbcaacbabccbdbbacddbbbacdaadadaadccdabdbddbbcdaccbcaddbcaabdaaccbccbbddccccdabcbdcddbaccaabbdcddbaaabdddcaaacaacabbbdcacaababdaabdcaaadcaaaabbbccbdadbdaaabadcdbbcaaadaaccdcaabcddbaacaccdcdbcccabcdaacadcaadcbbbcbcbbbabbddccbbadbacbbdcdabdbbdbccdbccdddadbabbaacbabadcbddcbccccaaddcbbaddddacabcbdbabcbccaaddbdcdaadaaacdcddcacbcaaaccdaddabcdbaabaaddddacdadddcacdbcbcddcabddccaadcbbabaccdbaadccaacbaabdbdaddbadddbbadbcccdacdccdbacacddaccdacdacaabadddabbddccdadcaccaadaacdadddbbdaabcbcaacdcabbccbcabdabcbbdcababcbbcabbcaccccadaabdccdccccdbdcbdcabdcaddabadadccbddadbcbdcbaaacdccacdbaccdababddaadbccdbbdcabdaacddbbbbabdbbdbdbabcbaabdadaaddacbdddaccccabbcacbbdacbbdaaadabbaccbcadaabbaaaacadddaddcaddbbdbacdcaddccbdddaadbadccbcccbcddcbddbcdacbddbbcdacccbcddcbcbdcbbcddbddccbadbacdabbcdacddccaaadbbacbddcbabababdcabccacdadbdaabddadcdbcdacdbcccbadbabcaddadaddcadbdbacddcddddcdbabbcbcbcabcccdbdbbbccbaaddaaaddbdbbbcdadcaddaddcbdbacdcaaaaadbcaddcbbbbbdaccbdadccbcbcbdabdbadcdbaabbdbccbdacbabaaaadaaccacbdaccbdacacabbccdbdddbaaadcdddcbcacacbddbbcdabacccaccbdaaccbbcbbbcdddbbadacdadddcbdacdcbbabbcdaacddabbaadccdcaccccbcbdbbabbbccabdbbcbddcdcbcdaadadcaaaddddcbabdadabdcdcdadcbbccbbdabbccccdccbdabcacbdabdddadabbcccbbdcbcacdcbaaabacbbbbdcaddcdbccddaacdbbdcddadddcbacccdddbbadbdcdcccacddcbdbddbacaadcbcabddabadbddcdbcddcbaadbddcdbbadbbbccbdbdbaccddaabcbdcaababccdbdaacbdddaadcbccbcbbddcdbcccababcdadaabdbbcccaccdddabadbaacacbaaadabadadcdbcccbdddccbddaccdcddcbdbbaabacbbcbdabacbdacabccdcbdcdbcacdacdbcbcdbaddbcabcbddacbbacbdddbcddcbcdcbbdcddcbbdcadcdcbcacddddbdbbdadbdbcccadabdbcacdabdbbddcbbdcdaaacabbaaacdbdaddabcbbddaaccdbabbdbabcdccacccdabbbdddaacaabdbdcacbdbddbaadbaabaddddddaacaabbbbcaabcbaddbccddadbddcbaadcbcdcbddbcdcacbabdabaaccdadbacbcaacbbbabadddaccdbbcaddbbaaaddaadddbaabbbcbcdbcccbddcaddbadadaaddadadbaadaadccbacaaaaddbcccccabcbcbdabcdacdaacccdbdbddddbaddacadcdddcabbcbabbcddadadcbdcdbacdddacabdbaddcdadadcbdcbbaddcdadbccddbdcabcdbcbcaccdbabdacbbcaadcbbcacadabcbbbdcdbccbbdacadadadcacadabbccdbdabaadadabcbadcccccbbccbdbddcaabdcbacdcdccccbabbaccccddbaabbdddcccddbabdadbaadbbaacdddabadadabadcadcbccdaddadcadadccaaccdacdadccaaaccbcbbaadcabddddbaaddcbabbccddaaddacbaabcabbcdcbdabbcadaabdaaaddaaaadabdcccbadacdadabcdbabcdcdacdaaccbcadcbcbbdadaacdaddcccbdabdadbbdbcabbbdccbaabcbaacdbbabbccbacbcdbaadadbdccadcbdbcdddbdbbbdccbbbdcacadadddaadabbabccdcdabdcbbcadbddccabdbbddccaaaabbdcabccbddbabcddaacbddbadbdadddbbbadbbdcdadcddbbccdbbdaabdabbdbcbadbddacbaabbddcacdbbaacddbbcbaaddabcccadccdbcdcdaabdcbdddcadadbbadbabdaaabacdaccaaaacdbbdaddbbbcadaccdadddcaddddbdaddcadacbcbcacacacbabacdaddbcbacaabaacaadcddcbaadbbddacabdbdcaabdcdaccaabaddbdbccbbdacaacbacbbbcdaabdccbcaddbcaaaacdbacaaddcabdbaaccaccdbabbccbbbcdddcabadbaaacbbcbbabcdbcaabcaaacaaaccbccaabaaabbccaabbaadddcbbaadabacababbcacadcbbdaaadcddbcbcdcccdcdabbddcccadbbcccbbdbaddccbabacbdbcbddcbaddaadcddddcadcaacccbcbacaacdbbdcbcdbabdbdabdcbddadbdcdaabaddbcdabdbdadbcbacacddbdadaabbbbbcbcacaacddcddcbbadabaddbcddbdcaaaccbaacdacdabdddcbbacdabaadcbdbdbadcbaccbdbabdabdacddbbbbdcadddccbdbddcdabcbcabaabddabbcdddddaacbbabccdbcaddadccbbabdbbcababcadaddddbadacabdacbbccaadbaccddcbaadadccaadbabacbdcdabacbcdbabdbacbdaadccaaaadccacbdcdabbdabbcaccaddccddadadadaacdccadabbaacbaccccaabbaacbbbcbdadbcccaacbdbacccaacacdcaaabbccbcdadbdcabadcabcadcdcbabacbbcaccdbacaddabcbabcbcabcbbdabdaadbdbcddbadbdcdacaadcbdbaaacbbbcadbdcacbdcacdbcbaabaaabcbabacdababbabddaddbcccbcccbdabacabddbcadccadbcaddaaaaaccabcadadbdadacccdbdabbcdaccdcdaaccdcbdbdbadacadbcbbaccdbaddcabbbbbbcabbccbccdbbacbcccacbbbbdadacdbaadddbaaaccccdbbbdacbbbbaccdacdcddadadccabbbbaaabbbbdacdabaacaccabcbdbacbccbdbaaacdbccaddaadbcdddbdbdaddbcaaabacbbbbbdddcadbacbbdaaaadbbccbcccabcabbacdadaadcbccaddaababadcabdcaabbcccaadbdcdbcaaddcdcddbabacccbbcadabbacdcabddaadabdabdcbacccabcadcbdaddadcbbabccbdaccdacdbdabcddcaaaadddadbaadadbacacddbdbbaaabbbcbbdbbddcbdbacabcddccdbcdcdcdbdaacbdcbdaddaaabcddaabacadddabbdbbaadbcacddbaaccacddbadcdacbdacccccdcbccddcdcdcdccbdcadbbaacdccaccdbabdccdbccbdadcbaadcbbabbacbadcabdadaabdcddaacdbcadcacbcabcbbcddbcbbaacdadbcddbabacbcabdaaacacaaccaacbbbcacddbbdbadcbadbdddadcccbacabacbdbacccddbcccdbaaaadadbddbaacacadbcaabcabdacbadbcbdccbcaabdacbaadccddccaaacbbbbabdbddcbabddccacddddcdabcbdbbbcaddbbaacdbdccadddddccbdacacbbcccaddadbdcacbcaaaacadccaccccabcabdddddddabdbdacacbcaacdbbbcdacbacddabcbacaddccdcadcdccbcabacddbcbbcdacddcacbbdcbdcdbaddcddbaccdacbabcbadbbcbbcccdacdacbcdccabdbddaabbcbdbddcddabbcdacdbadbccadcdcadbadacdbdabccabccdbcbaabbadcbbabbbbacaccbbabaccbabbabaadcaddcdacdcaacdbddaabbabccdbbbdcdbcccadbcabbaabbadabdacbbccccadadabccaabadbaadcaddddccaabaacbadbcabacdbaabcdacbdbcabcacaaadabdabccacdcdaaccbdcdccabcbaddcccccbcddacdaccabcbcaabbbccdddabbcaccababddaacadcdbdcabcbcbbadacbdddabccbbbbbabbccababddabbcdaadddbccccbcbaaabbdcaddcadaccdabbdcbdccabdbbacbcacadaddadbbddcbcdcadcddabadbbbbaddaadacaabadcbabcadbadccdbcdcbccabcdcbddaaadadcaddadadbaadbabcdcbcddbacabcacddabccdcaabaddddbbbaddcdbbbddadadbbbaddaabaddcbbdbdbcccccbdadaacbbabcaaabacacdbcbbcaccdabcdadaabdcdadabcacdaddbcdbabbbcddabbcabddbabbdbbaacaabcadacacbcacdbacadabbccbdadabbdbdacabdcdcaadcabdbbabdbcdcbcbdbbccaadcbbadbcadadbabdbdcaaddcccabbdddbbbabcccddbdbcdabbadbdcdabbaadaabbcacdccbcbaabbabbbcdadbaddacadcaadcbcdbaabaaaacbddcdaacacabababcbbbcabdbacaabcbbbdbccacadadcbaabcbccadaaaddcbacbbcdddbacbcbabbbabaccacadbacddbbdbabcbbacdaccdbcdcbdbbdccbacbadcbcaaacbabdccdaaccbdddaabddbabddbdbacdaadcaabcabcdbbcbddcadaabbdcbdccbbcbadaaddbccdaccbabdcdddcbbcadccddddcacabaadbbdaabadccabaccbdbacabcacdadbaadbadcacbbaacbbbdadbbdddabbdbbabdcbcdabcdcdbcadaabacccaaccaadaadcacbaadaaacbdbdaaaacabcccdccaccaddcddbcddbcabbddaabcaccdaaccbbdbacbaabaadadccabdbdbacadbcacbcddbaaabdcaaddccddbdddcccabbcbacdbbddbcbbabbabdbcdbcaccccdbcdcccdbdddbbbbabdbccdacccdbdbbdbaacbccbdaddcadbdcdaddccbacdbbaabaacaacaaaddacbbdbabacdcdddbccdaaaaadcbabbdddaabbadbdbbcadbbdaccccdaccbbdbdcadccbdbabcbcaacadcbbaacdbabaddabadcdacacaccdbddaccbddcacadcbccdaaaccbdabaccadddcaaabdadbabdadabbdacaadbaadcabbbabcbbdbdbbdbdccbcacadbaccdcacbbdacbcadacbbbaddddbbaabcddddbadcbaaddcbbdbabbccdaacaddccbddbddbdcccddbcabcbbcdbaadbbdbdacddbbadbbcdbbcbbdbdbcbbdddcccdacaddcdabbadbdcdacbdbbdbbadabdddadbbbcdbabbcabcacccbdacabbcdacacbccdbabcddccdcccabadccadbdaccabdbccaabddcdcbbdaadadadcbbcdcdcbbaacbbdaddbcdbabbbbbcaddccbdccadaacdccbdaabdddaaabbdadbaadacbaaacabbcbddcadcadcbdcabdccaacddbdddcdadaacabbaadbdcaacddbdddbbdacbcadddaadbbcaabdaadcccbcdbcbddbcdcbdcdaddbdacdcdacddcbadcbdccaaaabbaadbdababcaccccadcdbccddbcdadbcbabdbdbbaacacacadcaddddadbddaabcdadadbccccbdbacbddddcbaddacbcbbbbbaadbbdcbbbcbadaaaccccaacdaccaabdbadaadbdacdacaaabccbaabbbacdacccdbabacbabdaccdacbadbbddcbccdbcdccdababbbbcdbdbacbccccbddbcdbbdadaacadccdbbcabbbbbaadabccdcdddcbaadccadbdbaaabcdabbddcddcccbaccddccaccccaadbddbbadbddbdbcdddadbcbbddccbdabccdabababcdababbddbdbadcabcaddaaccbbdddcacbbccbcbbcacaacaaaccccdddddbddcacdddaccccddbcaaddddababbdcbbcdaccabbcdabbdcdddbacdcadbaccccaabdcccdadadaacadadabddccbccdcbaaacabccdcdadadbaabbbbddaccbdaaaddabaddaccccaaabdbcaaaccccbbbdcbadcabbbddacccabdccacdcaddadccadcdaaccdbaddaddaabaddaabdcdbbcbabdccdbaacccbccddbcbaadcccdacabacbdcbcbdccadacaacdcabbcaaddcdcdccaaacbcbaccbacaabcbbddddbdcdcdbaababcaaaddbdbccddbdbaaaabcdcbcaabababacacabbbdbcacadcdaabbacbddbbcbbcddcdabadbcaabcbdddcdcddaaaadaddddddcaabddbbaadbcbabdcbacaccbcacbcbdbbabcddbbadbdddddcdaddacaddddadccdadbaabdcdcbabdabddbdcabdadcddbbbdbabdccbddbacbcdadcbcbbbaadbbdcbdaccabccacabaabbdcdcbacccadddcacaaaadcadbbaabacaddadbbccdadcdddacbddadaccbdccbdaccddadddcbacadddbbacabcbbdcddbaaccdcbdaabcdcadddbabbcddbaaccbbbaccbadabaaadcdcadcbdabcabbbbccdbbabdcaabacbbaddadcdaacbadddbacdcbcabddddaaddcabbbcdabacadbdaacadbcdcacbabdcbacdcddacdacacbbdccbcccbaacbdbddcababdbcccddccddcdbdbcddadbcabbdbbabbdaacaacccadabdccbddcadababbdadbabaabbbdccdcaabcabacdcbdbcccbbacbaddcaddbbbcabcdbbcdaaaacacabddbccaadcdbaccbaddabcbbdbccacccdbaacabbcdaadbacabcacbdadcaccccdaadbcdbbbbdbaacaaabadcadabccccbdbbaccddbddddbbcdbbabaaacdadbbabcaabbaabcdbccacbdcdcdbdbcaabcaaadcdcacbbdacadcbcadbbdcbdcdbacadddbcaddcdcbaddadcbdccadccbacbcdacdaacdbdbdccdcacabaabccabcbbccccbacadbaabcddccaadbdbbbababdbbcbccdabbbcadcbcccadbdbdbdaabcabbccbbacaccadabbcbcdcccdbcccadcacabdadcbbdadcdacdddcdadcacbdaabbacbacdadcccbbaccbcccbbdbbaadcabaaabaabacdcdacaadbdaacdcddbaadcbaaddbadbbabbadcbabbbcdadbddaaccadcbabacbdcbadbbcdbbdaaabaabdbccadbdcccbdbcdcccadbcdddcbadadaadbacddcdcaccddbdccdbabcaaccbdbbcacdadadcbaabddcbcbcbabdbbdababbabdbbadcbaabacddabcadbaccadabcdbaadccabbbbbbdabcbbabadbcabaabbbcbaccadaaccbaacaaddbaccbcdbbbdaadcbbbabdcbdabbddbaadacbaaddacbdadcddbdadbbbbbdcdcccababbdbbcdaccdbaacbbdbdbdcbdcdaddbdacbcbcbadbaddbbacadcccbbbbbabdaaacbccdcbddcbddccbdbcadabcaaccccbaacaaccdddbdaacbacbaabbcccadddbcdbbbdbacccdbcdaadbcdcdabdcacbadadacdbbaababacacadbbccaaccdbbcbcaaaccbcbabaabcccadbadbbcccbccdccadaaacdbdddbdbdacdadcddbbadcabdcdcbacdccbbddcabcbcaabdaaabcbcabcaddbddccbcdccdddbcaccbdbcbdddaddabcaaddccaaadcbcbdbddcaaadcbbddbccdabdcadaccddadcbccbbbdcabddadabcbdcddbbcadacaddbcdcccdddcacccacdcbccaaaabbcbdabdcbacaccbaadbdbcbcdcabadddbabbdacdcbaaabadadabdaddbcaddbababadbaccddbdccacbcadaabbdcabddcaabcdcacaadcdcbddbabddbdbbabdbdbabdddadbbabcacacaabdbacadacdbcaaaacbbcbcadacacadbadaadbcccdabccdabaaadaabdbddbdddddbadccdaabcadadddbcdbcdabaabadbbbabddddccacbaddaddaddddcbbbcdcbddddaddcabbacbcdcaccbdddbabccddbaabdccaaadbbdbdabbbacabacadacbbbcccbccaaccbaaccdccbbaddcdcccdacdcbacadacbddbdcaaacbaabadbddbcbccdbcabadabbddcbdbcccdacdccbabdaccbcdabacbbaddbabbcbdcbabccaacdbcccddaacdadaddcdcadbdcccbcbabdcaacdaaacddaadadbaacddcabacbdccbbcaaacbddabcabdadccdbddabcbdbcaabadddddcacbacabbbdbbcabdacacabdbbddcbccabacbcbcaaadddacccaddaaadbbbbdbdaabcaccdcaadbdccdabddccbbdbbdbaccaadcaadcccabcaddaaccdcaaaabbddbcdcdcadaadacdcbddcaacbbdddabcabcbdabcbcadabadadbaabbadabaddbdadcaccdadccbccaabbacbddbdcbdbcabacddaccdbcddddaabbdabbaccdaaaddacadaddabbaccadddcdddbbadabdadadccbdaabcaaddccbbdddbcbdacddaadbaaaddababdbccddcdacddbbaaadcdabadcabbbbccccaccccdcbbabbbdaabdcdbcdbcaadaaaabddabbbcddbcddccbaccadabbcbadccaaacdaaadbbcaaabaddabccbddbbdcbabcdbcaddaabaaddcccdacbadcacdcddcbdaccacccbacdbdddcbbaadbaaacdadbabddabccdabdbbaccdabbbcdaddabbacbcccdaabcddbdcaaaccaaaddaddbcbdaaddbcacdabbcacdaccabaabadcdaacabdcdaddbbccabcbaccaddaccbcdcbabcdcaaacbcacddbbbcaabadbaacddadcabbdabacacddadbbddabcacddbadbbaddabaadaccbcaddcbbdbbacacdbdacbdadbcbabacaabbabbcdacdccdcdddbdbdcdcacacbcadcbacbababcbabccdbcbbdbcccddcbbcdbaccdcaadadbcacacccaaddcbabadadcacccbdbbcddacbbadbbacbbacdcadbcbaacddcccbaaacdcdbcdbabdbddabddbdcacaacddbdaabadbdcadbadacdbbdcbccabdbbabbaacabbcdaacabbcbcbcddbcbcdccdadaabddbbcababcbbcdacbbbbddcdddbadbccdcdcbcdacaabacacdcddacabadadadabddaccabccddbaddacddaddacaaadbdbcccacdcddcaaaccabbbacdccabaaabcbbcbcbccbcccdadddcbddadcdaadababacdccdcacbdbcbddbbbcbbadcbdcbdaababbcacbdcccdcaaaadbacdddccaddbdbcacbdbcadbbabcdcaaabdacaadacacdadcaaadccddcbcbdcdbcddbbddbabaddccdccddaaaabdacaddcdabdbbbaabbdcbbddaadabdddcdbcadbaacadbcddcbcccdbdddaddbacbadcadbdbccdbbcdddcbddaaccacbbcacabdbbcabacacaadbdabcdcddacdabaadddabdddbcbbadccadbcaadcacacbbdabbbacccbdaabccddbccddcdaadcccdabddcabcdcbaabbddbbbabdabbdaabdccccddadaddaccbbdabbabdabccccdcbdaabaabcbcdabacaaabdccdccadbdabbcabbabddbbacbcbacacccbbdbdcdbdcaadaddcbaadaacdbdabbaaccddccccbbacaadbdccbcaabacbdaccaacbbcdabddbbcccacbdcdcaacbcccdcadccddbdacaabddbdabcababbcccabddbbaddaaabcccbcaaadbdcddbaaabababacaccbddbddadbcdbcbdbaacabacbbaabadcaabacdaaacbdacbdbcddaacdbbdbaddabcbdcbaaccaccdbbacbcadcbabddbdcdccabdaacadbdbdddacabacaacdccddccbbbbcdaacccdbbadbbdacbcaccacbbcabcddaaacdaacbaabcdaadaccdaaacaacddacccaadadaccaddcacaabdbdbdaddadaabccadbbdbaacbbadbcaabcaabadadbbdcaabdccdaddddaddbdaacdaababcaaabaaaccddabadbccababaccbabdcccdacccacdabcabaddcccbaacbdbadbcbcbdccddcdadbadbdbcdaaddbabbcabbdccbdabaababbcaaaaddccccaddddbabbccbdcacbcbddbccabcbaaccabdbbcbddbcbaabbabaabddbcadaabdadabbcaadcacdacdabbccacadaadacbdcddbcdbdcadcbaadbbdccdacabccccbcbdbbacbbcbbbaddaaaccdcdbcabbdddabcbdabadabdbabdabcdaaadbcbcbacbcdbdaabbcccbbbbaacbdacaaadadddcdcdbbcdccbccddadcaaccbadbbbdadbdcdbabdddabacbabbbdccacbbcbbddbbcbddccccdbccbbdacdccbbaddbcaacdaadbdccbdcaacacbbbcbbdcdabbabacdcbddccbbadcbdcbdaccbddaaababcdcdcddddbdabdddcbabbbcbbbdababbddcaabbabbccdacdbbddcdccacccddbcdbadcbbbaaddbbccddadbcdbaddddbaddbaaccdddcbdadbcbaadadbdcbdcbbbadbcbaaacaaaaccdcbbdcbdcadbbaadbbbdbacadbacdbdaaacccabbdccdddbcdadcdcddbbbbabdaccdccccddcacdbababbabababcabccbaaabaabdacbaacaabdcdbacadbbccadbaadaadbdddabbaccddabdcdabcaaabcbdabcccbcdbbacbdacdcdbcdaadacadadbbadacccdbdbcbdbdabcdccabbbdbddbcdbdccadbbddaddbbbaadcbbdbdbbcababacadcdaaddacdacabdcddcbdbadccdadadbccacdaaddcacbdcacdbdcbcdcabdcabdcbabacbcdcdaccdbdcbaabaaddaddbbaabdbbdacdcdbcdcdaccaababadbabcdcaaabccaddddcbbddaddaaacbacdcdcdccddbacbbdccdaabbddaccbadaccbbacccbccbdabcbacadcaddccbaaadcaccaacacacbbacaacdbdbdcadddacccacbabbacbaccacccbdcabccddcccddabbaccaddbddadbdacbbbdccbcaabdbdcadcbbbadacdcdddbcacbddacaaaacacbadbbdababdcdcbdacbbacabcbcbdcbdabacacbdbcabbdcaaabbbcabaddccccccbabddddacbbccddadabadbdcdaddcabcdaaaaccdccdbcdadbcbcccabcbbcaabcbcdbbcddcaadadccbdcdabbdbbcbddbcbaabbcdaaacdabddaadbaccacabcbbdcdacbbbcadaadcbdbdbbabcaadadaabcddcdadcbccdddbbcbabbcdcdcbddabcdadccdabbadbcadccdbbccabbaaadcdbdbcbbddbcdccacccabddbcbccaaabdcdbaaccdccbcdccdbdcdbbbcadbcbddbdcbcdcbdcdcddbddabdccacacdadbbcddddadaabbccacdadcabcbddaaacbbddbaccdbadabcccbdbcdbddacbacdddcaacccacdaabbdabcbadcaddddacddbacbacaccddcccdccabbacaacbcbbbabdcadbaadbdccddbdcdabcdaccccbbbcccdadbaaacbbbdaabaaaaddbdccabdcbdbaaccbabacaacddbacacabcbccabaabcababdcbbcabaddcaabbdaacdacabddcabaaacaddaacdabbcbbaaadbcdcdbcdadcaabdbdadccabacbcaaaaddcaaccadbcaaccdcdcacdcdaacddbdbabcaabddbcadabacddbaadddabacdbbbddbdbababcdabccbdaacbbadbdcbccbcddbbcdbdabbaddbdbcbadbacbacbcddcccdddbdabdcabacacddcdcbccbdbdacacbcbbdbbdddccabdcacddcabadaddacbdcbadddabadadbdbaaaccdcbddabdababadcbacaaaccbaaaacddcacbbaddaabbadbbcadadadabdabccdcccccadbbdabcacdcdbabdcaabdadddaccdaabadbaccaabdbcdbabccbcbaddbcacabbaddadbdcacbdacccbcadabddddbbdabcbabdcccabbbbacdaabbcdbbbbcbdcbdbadcabcbaccccaaddaabbddbbcddabdcdddabababacaadbbaacadaaccbdcbbabcbcdbdbddacddabdddcacdbdcccddddbcbabbabcbcbddaacadbdcbbcadccdbdcbdacbcbadbbaccaaddabcaabbcbacdddbacacdcbcdaccbdadbcddcdcbabbabacbcaadaaadaccdbaadaabcdabdbdbabaacaccbdabbadcbacabaabaccadcdccddccbcddbbcacacacbcccdcdaacdabcdddbdacdcadddcbdacacdcddbdccdaabbdbacbcdacaabacbbabbdadacadbaacdadbbcbccadbbbbacacccbdbdbdcbcabbadbbadabaaaaacbcabddabdcabdbaadbbcaabbbabacacbacacbcbabbbaacdcbaabbacdccaddaadbcbbdbdbddbabcbabcdcaaabbbdbcdcdadacbcaacaabccbacdbdddbcbdcddccddacbaabadbadcbdddaadcbabdbaddbacaddacbadbbddaddbccbbcacaacdddcddaacdddbcbbccbadacdacbbcccdadaabdccbabbdddacadcbdacacbdadcdcdcbaacabddbcdddbdadddddaaabdccdaaadbbdcbdabbbcbdaabcaabdacdaccddbddabaccabddadaacadbddcbaacbaacadbbdcccddbacdbcddbbbdcabdcdbcdcadadbbddbbaabbcdddcadabdadbcaaadabdacaadbaacaaabcacddbbadcbcaddbcaaccbcaabdbdccdbbaabcadaaccdabdcdbcddbacacdbdcbdbcbcbdccdbdcccdcddcddcabdbbcbbaaacdcacbdaabdcddddbbabdbbadbcdbaadbdccbbbddadabbdbdddbbdccacadccddabcccabdbdbccadcaaccdcbdbaacddbadaccdbcadaacbccabaddcdadaaaacdbcbaabbdacbcddcacdcdadbbacddbbaccdbabccbadaaaabcbccaaddcbcadbdbddcddbccadcbddccbadbaaabbbdccdacbddbbdddaaacddadcbaadbabdcadcbbbdddbcdbccccdcbbdccdbbacdabcdacdbddbadacadcabbcbdcbaddbacdabbbdacdcbbdaccbdaccaddadabbbddccbdabadcdbbccdabdbbadbbcdcaacbcdbabcababcacdccabbacbdccaacdbcdcddbbddabdacaabbbdaccbcbbacdbdaabbadbbdbddccdcbdacdbdcbadddaaaccccbdabdbbbdcabadcacbdddcdcddccdbbadcdabbaccddcdcccacdbbcddcbcadaababddddddabcccccddaabaddcdbcdadadabdbcbbbbdddccddcdcccdcbcabbabdbbabcaadcdaadbbabbddcadcddcbadcaabdcadcbdcbbddccabdbbcaabddbbdcdccdbcbaabacbdcdcbadcaaaabdcaabcbacbdacbbaaaddbacbacdacdbabbbcbacadcdaadcacbccabbcdcbacdcbcdbdcdaddadabdaccbdcddabbbadccdbbaaaabadbabbdbabadbacdbcbdababddcdbccaccccadadcabbbabdaababdcaddcdaabaabcadbdcadbccbcbbaccdbcadcabdcbddcaddccbbcdbbaababdbacdbbdbabaaccbbabdcabbddccdccdbaddadaaacdddbdccbacaabdcbbcaabbaadacdccadbbcdcbdbccbdbadadddabcabadaddddbadaaddbbcdbcbbbabdbaddabaddbabacbbbbdbdccdcaacbbcccdbdbcbcbadcbcdcaadcbaabcabccdcdcccabdccbdcccdaababddbbbadbabddcacaaccabadccdaaabcabaddacbbaddddbbbadbbcadaccdbadaadcaadadcbacdbbddbbcbbcdbdabcccbabddaddbccbaaddcacbabababdcbadabaabdcadaadbadacbbaabadcacbccddcacaccdacdbabcbddbcbdacadcdcbdcacccdbbbdbbdddbdcbabacacbadbddcaaccaabbdbbaddcababccdcabdcaacbdbccdcbdbadbbbddcbabaaaaaccaacacaabbdbaabddadbcbabccdaddaadbaadabcadbbdbaaccbcbcdbabcaddaccbdcdcbbbdbddcbaacccadccbdcbabdacdadacdaadadadbcccdcabbbdabbbdcdcabbcacbdbddbbcbdcbdababbdcbcbdcbddbccbadabcdabbdadcdddbadaaaacdabdcbccbbaadbabbbcbabaaabaaddcccaaaadbdbcdabbdaddbcadcddccbbadbbbcadcddcacdbbcdabcddcbddbbcbdacacabdccbbaacbbaccccbbcddbdabbbacbccdcddcdbdacadbbdadccbbbbdbcabcddcddbcdabddbccbaddccddddacbddccacdbccdbacdcabddadcccbabccbaadbdcbcabbbddaddddbcadcabbcccaabacdacccabbaccbaaacdbdcaaabbcbddbccabccaaddadcdbcacdbbacadbbadadacdacccacccdabbdbcbddadcbcbdccdadbcaccbabdaadcbbbbddccabacbbbddbddbdcabadaabbcabcccbccaccaddcaadbbdbbbaabbadaacccccadbadbcbdcabdbbccddaadddccbbdadcbadadabdddcaaccbdabbcacabcadabdbddcccbadccdbdbdbcabcadacbcdbccbcdaaddbdaaadacbaaadaaabccbddddaabdabcacddcaabaccbabdcaabcbdacaacbcccdbaabbbabacbcbbacaddcacdcdbccdaaadcbababbdcbaabadbabdbddbdddbabbdcdacaaaaccbddbcaccbbcaaaacadcaabddabdccdcccbbcbaaadabbadabaaadcccdaadbcbdcdcbadbcabcbcaddddbdcbbbdabdbddbcabadcddabacddacdcdbaccbcccdddccdabbcbdbbdcabcbbdbcddbcbbaabcddcacbddadbbaabcbcbcbcbcaadcbcddabbbabbaadaccabdacccbaccaaddcacdacdadaaddabdcdadbbacdcdaddbabbdbbabbaacabddcccdbacccaabcdddabcccaaacddcbcbccdbddbcbccbddaddbbbdaccccbcccdcbcbcccdadccbcdaccdcbaabacaadbccdccbaacabdaaabcbdcaccdaaddcdbccccdadadabaaaadadabcccacdbabcdbbcccbcabcbdbadabbdcbddabdccdabcbabcbcdddbddcabdadccdbdbcdbadbdadadacabdddbdaababddcaccabbcbdaababcdcacbcbbdabdacdbabdabacabbdccbbbbcbdbdcbcdabacabbacbcdbbddabdbaccabcbabadbbaadbabdaaddcbcddbaabcacaabdacacabbbabbccdaaadbaccddbbcacbbccbbbcbccdadabcbbacbdabcdadabbbdadabcadcabbbdbcbddadbdbccaabacabbdadcbdcdabbcabcabdddbadddcaddbccbdbccdbbdddadbcdadcabcbdcbabdacccadbbccbcdcccdcadacbdbdcabbaaabdccacdbaabaadcbbccbdbaadcdcbcccdadbaaddbbaacbabcacadddcadacbcbdbcadbbdadbbcbbdcaccdadddbbdcdcddcdbaaccaaaccdccdbadcdacbcbaadacbbbaddbddcaaaccaacccbcbdacabddddadabbbdaacadcbddacbdcccdcccbcdaaaaabbccacddcaddccaddadcdddadbdddbcddcdaccaddbdacbaaabddbdbaadbdcdacdbdbbacadccdbdbabddcacbbacdabdaacadacccabddabddbbbdaaaddacdaadabccdbdcacbbbcccadbccaadbdabacbcbddbbacadbaabdaaddcdaabacababaaadadddbbcdcdcadaddcdabcccadcbabdccdbdbccaaacbdacdbccdccddbdbbdddccbadaacbcdaabdccabacbdbdacccbcbbddcdacadaccbaacadbccccdbadacacaabaaabddbcabdcacbbdcbdbbdbcacdbacbcabbdbdaadcdaccaabddcadbcbcbddcddbbdddcccaaddbdacadbadcccadbbaabdadbdabcdadacaddddbdbdccdcccccdadadaaacccbcabbaaddadccccddcccbdbdcdadcccdcbbcbabddcdbdccbcbbbcbaabaadaaddacbaacacbadaddaaadddbdbbaccbbabdddbbdbaccccdcacccdccbcabcddabbccaddbdabcdbabbaaacbcdacabdccdcbdbbcdbbcbbadacaccbddccbdababbbdcdbddcbdacddddcadddbaabcbacdabbacadccdcabbcbbdbcbcdabadbcbcbdaaabbcccdbdccabababcbcbccbdadbdbddcddbcdccabddadcdbddbddaaacbadcaadbbcadabaccaddbadaaacacaabbdaaabcdbadbbbbcabadaaccdabccbaddabaaddbacaaaaaaddbccbabaacabddadddaadccccbbcababdcdaccacbaadddbabbaccaddccdcbdbbcacbbcbadbdacddacddabccbbccccdbacdbbcbcabaaadcddccdacddabdcdbadaddcaacbaacdbbbbbbddbbaabdcadbbdaaabaadaabdcdbddacbaadaddccbdcdaaacabaabbcdbbbadadabddcabbcdabdcaabbbbcddcdaccdaabacdbdccdcbdbabcdbacdbcadabdcdcdabbdaaddcaaaccaadabaacdbabddddcdcbadadbadcdbdadadcadccabcbbcabdddadbbcadddaddccbabccdddbacadccdaadcabbbddababacccddabcbddaaccbaadcbdbbbdbddacaccabadbcbacdbddabacddaaadabbdaddacbbcacbdddacbcccbaaabbcadddccccbabacabdcccccacdbdbbccbdadaccbccbcbcdcbcaccacdccbdaabaadcdcbabbbccacccdbbaabcccbcadbdbcccccbdcdaaaccaaaaaccbdaabcbaaaaadaacdaacddbacacbdbbcbcaaababcacccaacbbadcdadcbdbcddcdbdcbbdddbcacacdcbbbbbabbdbaabbdacccbcdbdabbdcadaddcbdaaaaddabdadccacddbdaabacbbdabbcbbccbaadabadbacccaadabcdadaabbdbccbcabdadcbcacbbbabdcaadaaacabaccdbacbcacbccadddccbacbaaadddaacbbaaddcabbdcbcdbccacdbcdaabababcdbcbaabcbaabbacacccbdbcabcdccbaabccacaadcadbaccabbcbbcddaaccaabdbddddcadadcdadaccdbbbdccadccacbdbbcdbbcbcadadcacdbbabacccabdacdadcdcacddcbabdacabddcbdadddccacdadcdacbcacdbbaadbdbdddddcacaaccbaacbaddabaabaacddaccdddacbbcadcbbadcbbcbdbbcdbcdcbdbdcbccaddcaaddabacdaaccabadccadcdddbdbdcbbccabdbabadacdaabacbaaddbabddccddcbbadbaababcdccbdcababcadbbdaacaacccaababddabdaadcadccdbdacacbdcabcdcccaccddabbbaaaacadcccdccabddaccbabaaacbcbaabcdacdaddbaacaaadcbcccddcbacaabbbccabadbadaccdcbdcccaccdbbaabdbdbcbccdaabddadaadabcaaadcddcccbdbdccccddccaabadcbbbddadabcdaddadabdbbabbaddcbbacacacadcccccdddcbcbbaaccddcabbbadaadcccdddbacdddddacbaabddcbadbdbddbabbaacabcbdbbbdcbcabaddbbadbbacbddaaddbadcbcadbddabacadbbbcbadaadcaddbcbddcaddbbddbacabaddadbdcbaaaccacdabaaddbacdbcbacadbccbacbccbdccdaaadacadccbbcbabbbdcbcdadbabbcaaadbcaacdadbcadadbaccbdccbbcbcbcbbbbadbccdaabcbccbdaabcdbcbdccbccbaccdddadcacdcdaddddcccdcbacdadbbdddaaadbbdcbddbdadbaacbacabbbdbaadacbbddacadcbbadacddaaabacbdcbdaadadcbabcbbbcadccdbdcabcccddbaabbddbcdaddcbccadaccdaaabdddcdcbbbbdabbdbcaacbccccabdadcccabbbbbccadbcbbbcdaccdcbbcacbacdccbdbdacadbdddddccabdcacbbddcbcbabadcdcbcbcdaaaaaccbdddbcabcdabdbbdcacdcccbbdcacbaaacabbcdbcaaddbcabcabdddbbbccbbbadaabddbdaaabdcdcdbacbcdbccacccdbbadbdacdacddbdcdaaababcdadccbcbbaadbcddccbbccabaadbbbbaddcbbaaacacdcbcabdacacbdacbaccdbbbccaabccbbbdcdbaabdabbcbdaaabdaabbbdccadbccbaccdaccadcbaddcaddccaadaccbbdbabccabdcbbddcdacbdaabdcabbbcaacacadacbdccbbaadbccbcdacaddbaddaacddccdcadcdbbbadddcccacbbbcbbccdbcdcabdadcabdddcccdbcbcdbddacdaddcccaccaaaabbcddbaacbdacabcbbabddabbcccadbbadaacbcddacccbabccaaaadaaaadcaccddabaddadbbadabacacadbdcdbdabaaccacbcbcdbdccaacdabbbdcadddcdddacbbcbbccddaababcddabcbabcbaddbbbbbcbdcddbcadbbaccbdacbabcacbbcbbdaddadcdaadbcaabddacccdaddacbdabadcacdbbdacabbbbcdddcdadaccddacacdaaaadcaacababdbdcbdbcbbcbadbcabdcbaccbddcabbbbbdbacddaaaaadbbbdbdcdbabbbdbadcabcddbddaabadcdcccacddbcbadaddccccdbcccabcdcdcaacbddddbacbbabdbcdaaaaadababcabdaaadcdbccccacbcaacddddadaabbbdaaacbadcbccbdbbddcddddadaaccaddaacdccbddddbdbdccabadbdadcbdbcccbbddacbcaadbbaaccbaadcadddccbabadcbabbababadcdbdbabddbaadbcdcabdcbdaacbaccaccbcbccbdababdcdbacbbdbaabdbcbbabababdabdbbcdaddcbdcbcbaabdadccaccacdcbbdbbccbbdacdbddddabbacddbdaadadcaabbbbadabcbacdbacdbdcccadccdccdacaddbaabcdaccbcbbcaccaaacdcdccabcddcbaadbacaabcdbbaddbdbcacbabbbcccaccadbaabbdbbcbaaccabdccacaacbbabdacaddababbadcbcbcdaadaadbdbadbababccaccbcbdaccabbdddbbaaaccacaabcadccacbccbadbacbbdaacaaabaaaaddacbdabcbadbbccbbacdbaadcaccdcaaabdccabaacbcabdcbacbaccdabbdddadbddbacbcbdbbccbababccacdddbaacadcdacdddddadcacddddbbccdcaddcbbdbdcbdadcbdbabdddbadccbdcdbaddbbdccbdadbccababbadadcbaacbdabddbbbbcadadabdbcbacbcbcbdddccbaadaacbbdccadcddabacdaabaabacabbabdaadadbbcbcccbbbdbddbbaaddbddddcbbacbcacccdbacddbdbdbbcdcadbcadacaddccbbbadacbbcabdcaabbbaaddacdbbadaccadadacabbbdaaccaaacbcbaaabaabddddcdaabcbddcbaaabcdcabddabcbaadbabdcbdaddbcdbacbbddcbbdcaddddbcdaabbcdbadbdddcddacaccabbaacddcabbdbcacdccabdbcadaccdcaaacbdaabdbabbcaadadacbaddccacdcddbcccaadbccbabcdddcdaabaacbddcdbcbdbaccabcbbcddbdadbccccbbcbdaacaaddacbbdbccdcacccabbcbbbcdbdbcdcacadddcababcaacccbcbdadccaaacbdbbacbbdbabdccdadadbaadaadcbcadbcacaccadcbacbbccacbbbdaaccddbcbbacaadaacdcacdddcaabadacddbabaccdddddbbddaddbdaadcbadbcdabaacbccdaadbcdacdcbcadbaddabacccbbdcadbbccbdadbbdadcbaabcddacbadaddbcbdcdcdbbdcbcbbdbdaaaccadcddbcdcaadccdcddabdbcaaaadcabadcccabcddbcaabbbbbabdaaaacbadbddddaccacaacdcbadcbdabcbbbbbdabccccdabacadbbacccddddcbdacccdbaabdacbacabbbbdaadbddabbabacbbbdddabaaccacdaaacdacbabcabcbacacdbbacabaabddaabbbddabddcabcdacabcaaacbbbacbddadbcadaacbcbabacbbddcdbbbaababadbbcbbcacbcbcaccddccbddbbdbaaaabcdbacbbbccbcadddcabdcaaaacbdbacaadadcbbdcddabacbaadadddacbabcdcdccdadcadbacdaaabbbbbaadabcdcadddddddaddabdabadadabdbbaccdbcccbbcdcddaacdcadddaccadaaabdcbbddccbbbadcddbcbcdcbcdcbabaddadcbbbcaabdbbdbbdddccccabaabaacaabddcbdaadcbddcbcabbbcadacadbddcddcabcdaaaabbcdcccdcadbcadccadbcbdcdccdcdaabcdbdbbaddbdaaccdabacdaacaddcdcbcbbdccbaddcbcccdbdcbbccbcbadcabcccbdddccbdbabddcbadbdccabcbbccbbcadcccabcbaadcaaaaadbcbbdcdacaaaadaacbdabaaaadcdadaaabacacbcbadacacddcddcdaabaddbccabbdacbcaabbbbbbdcbcbcdcccdadcdbcbcaabbbcbbcccbadbcbabacacdbccdddcddaacdbcdbaccddadacbcbcdabbbabaabdcaaccadcbabbbdbcbcdbccadccdcdbaaaadbcbccdabacbdababacabccaddddccaacdaddbdadcadcdbcbcbdccdaadcbbcbcccdbabbbbdcbddcaccbadacdddcababacbbacddbdcaacccabbdbadabcaacbaacbbcbaddccbbddcccdabbcbdcccddbccbdaccbaabacddccbaccabcbdcddaddcdbabcdadaaabcdacbbbcdaddbaccacacacaccdcbbdddabbdcdcbaabdcbdbddacdbbdaacbbadbccccbbddbccacaaabbabacbbbdbabadbdadddcddbdbbbcdaaccdadbabccbcbcdbdcccacddbaaababddcabacbdadddcdbbcababbacbbadbbcdbcdababadcdddabadcadadcddadcbddaabccccbccdcacccadbcccdbababcdbabbcbcacaadbdbadbbdaacdabccdcdcabbdbbcdddaaddddacaadbdcccabdbccadbbacbdacdbccbdbaadbcbaacacdaacddacbcacbbbabbddaacbdcddccadbbaaadbcadcbdbaccacbdbaadddabaadbbbdaddbcdccdabdcacacacabdcadadbaacaaacadcbbcaddacadbacaddbcaaddbddcaccacaccdcabbdbbaaaaacdadcbabccbacddaabccacddadcbddaacdbccdbcadadadacbbabadccccaabdbbbdaabcdabddccdcbabdbdcbbdddcacadddabdcbcbddddadcdddbccdabbdabdddccbadcdaddddabddcbadcddacdcaccaddcababcaaadcddbcbbbdabdbccacbcacdcdddcbbaacdacbddacacadbbcccadcdccdbdccacccbadcbcddaadddacadbcbbaacaaacdbabdadddccbccacabadabadcdbcbdacbdcaadbbccddbdccdbbabaddbccabdabbbcdaaaadddababdddbacbbbddcaaabacccdcaacadbdabdccacadbaabcdacbccabbbddccdacccdcccbbbacdaaddaadabcdbccbabcbbcbdadabbbbacccdacdbaadccccbdacaadbcaabbbdadcaaddcbbbaabdaaabcbabcdaaaacddbcabdadcbacacbdaadacbcdcccdbbbbbacbccacdbcccacbbcabdccdbbdcbbdbccacbccacdcdbadbccabcdcdbbdabbadccdccabdbdabacbdbdcdcccbcdccbaddaaabcccdcbddcacababbbcbbddcbbabcdbadcddbbcdabbacabadcaacbbcdacccacccdddbcdbddabbcdccddabcbcdbabdacdddbbadccccabcabddddcbaaccaacacbcccaadaddcbacdcdbbaabbbcacadcdddadbdbadbcdccbbbcbaaaddadaabbcdccbdbbdcddabbdcacdcaabaddbadcccabdacdacbaabbdbacabaddaabbccdbccaadacbbdcadacbcbabdccddcdacdcddbbacccbbabccaaaccaddabdbbcabbbadcbbddbdcdaccbdcadbabcaadbbcdadcdbdcbabacdccbcdbbabccabccabaccbdcccdcdcbdadbcdabdcadcabdbddabdaaccbddbcbcaccaaddbdbdccbbdccaddaaaaaddccdadccabdcbdcdbbadbcccdbddcbbdacbbdaacbdabaddabbddcabbcadddcbcaddbadddbddbadbadcbcdcdaccbdaddbccbbcbdababcbacbaddcbdadcdcddbaadabbacabbaabcbacdccabcabcabdddcbabddaaddbcbdcacbcdcbcddbcacbbacdbaabcdccddcbadddccbdbaccbcabacaabdabcabdcbdbdbcdcdccaadddbdaaccaccacdacaddbbddddbaaddcabddccbccbacaabdcdcaaabbdccddabbbdbbdbaabbabcacabcabadcbabacdcacbccbbbacadadbaacbbbaaddacaabdcabbadbacaddacacbccabaabbbdbaaccdddcadccbcbbcdcacbcacbaadaacabacdcccdaccbcaddacbddaadddacadaabddbcacbbdddbdbdbdadbccdbdbdcdddacaabbccabdaccbbbdbcbabccacdaacbdcbcbdddcbbcdbacadabcbdbcbaddacaaccdccabcbbbcdbcbacbdadabddcbaaccaddddcdaccccdcbdbdabacbdadabdabcbdadbbbcaccabcabcabadbcacabaadbbabbdbacbcdcaccddaddadcdababbbcaacaabcaacdaccabdabacdaabcadbabaabbabbbddbcbabbcdacadcacaabcdbbadbdcbdccbddddaccddddccdcabcbbaaacaccdbdcdbaabbaacdccdbcdcdbcabcbbbcccabbbacdbdbdadbcdcbbdbbddddacccddbdbcdadbcaccabbccbbddcadbccdbbccadaddadccbdaacbdbcdddaccddcbacbbaabccdbcdcbbbddcbbcdddbcdcbaddababcaddddbcbaaaabdbdacababdbbaddcddcddaaddabddbaaaabbaccbadccdbbadcacdcbdcdaabdcbaddadbababadacabacacdacbdcabdaacccdbacbcbddbcbbaadcdcbbddbdaadbadacbbbccbbbbdcabbbbbadbbdbbddaabcbdbcadcacccddbdcccdddaddbabcdcaacbdacdaacdccddaaacdddbbabdbcdadaacdbdaabccdddcacccddbabcacdadcbccbdcbadbbcacdbabdbbcbdabbadaaaadbbdccaadadcdbbcbccaddddacbcbbadabaccaaadbbddbcaaadababacaddddacccccdbacbaddbcbdcacbaaccbcbabccddbdddbbadcaccbacacbcdaabcccbcbbccaabccbcdacdaacaacbacdcdadaaacaaacccacbddbbdcacacdcccbbcdbcbbcbcacdbcdadbbdaacabadaccbdccadcbaacadadccddaabddadadadcaaadccadbacdabdcbacbcadbdcbdacdabababcdabacaabcbccdcdbdbcbbccbdaaccbbbcdacaacbabdbdcbacddbacccdbdcdacadcbacbdbaaccddbdcabacbacabdcbbbdcdabbbbccbdccdcdbdadabbadcddaabddcccdbcddbdbcccbdcaababbaaccabcbdbcbdccadcaccddccabccaabdddaccdcdaddbaccabbbbddbdccacdcadcdaabbbbadbabcbbdadddbccbdbaabdadadddcbacccdcbacdbabbdaadcbdccbbacbdaaadaccdcbdbadbdbababbbaacdbbababcbbcacdbcbddbcbaccaaadcbdacdcbabbbdbdbdcbcbbbcadcccccacdadbcbdaacdccabdccaacdcbbdbbccaaabdbbcaadacddcadbcbacddccbdcdbabcdacaadacbdcdcdbacabbbaabdadabdcdadadbdcbcbbcdcdcdcadcccacbbdcdadcbbbdbacabbddacdbdaadabbadabaaabcadddcbbdaabdacdabadcccccdddcbcacacaacacbbdcdbadcabdaaacadacddbcdddbbddccdcbdcbaadbcaabaaacbcccbdbdcacbcbadcaaabcddccaacdbcabcddcacdadcdbbbabacdcacdcbbbbabacdddddbbaabaccbabcadbcaadadbbbcdddddaccadbdaddbacacadccdcdbcbdbbdaabbcdbddaabcddbcadcbcbdbdddadccbdbdacbccdbabddbbaabacccaaaccbcbcbbcbddddccdbabdddbbbcbcdacbdcacdcddaadcdcbcddbcbbcccabacaabcdbdcbdbdbabaaddabbbbcbdbccccbdcacabbbdbdadaaddcdadbbacbcaaccadbdccabdddddabdababcbbdcbaccddddbaadddabbadbbaaadadcddcdbddcccdddbabbcbaaaaabbcbdbabdbcaddabbcadacbcddcdabbbdbbdaacabbcabadcaacbbaccdcadacaddababbbcabbadacbbbbacbbbbacbcaddaabbcbaabddddddbaccdccadacacdcbbbabbcbccadababadcabdcddcadccbbcbcbcaddaddbabddbcbabdbbdcccbdbccbbcbaadabccadbddddababababbbbccadbbccbdddbcbcbbcbbabbdbdcdddbbbabdbbddbdbbbdbcabccadccaaadddaabcaddddacadabdcdbdbdabbbdbbbacbcbcbbdccddadbcbbbcdadabcdbddbacbdcdddcdacaacaacadbbacaaccbbaabbccaadcccddaabbccaacaaabaccadabcaddbdddadbdcbbbdaabbbdbbcabdccbdbbababacaabdacaabddbbdbbcbbadbaacbbcddbbccbcaabdcaacabacdabbacdcadddbabdbdbdcacabdddcadbdadbbdadbcdbaabadcdbcbdabcccbadbccbbcbcbbcadabbdccaacdcccabaabcabaccbbccbbddcccaddabadbcaccbcdadabddbdbdbccdbaaaccdbbbbdbbadbaacacaccddcdcbadcdabdcadabbccbbaaabddbbdcadbcbbcadbccdaadbbddacdcabaadbdcacdacccddaabcacdccbccaddccbadcddbdbacaacbcdbdccddbbcabdcabaddadcbbbcdbadbbccdadddaccababddcbcdccabccaabbdabbccddaadabdcbcbdcbbaabdbbbcddcabbbccdaaacacabaaabdacbcacbbdcacdadacdddbdbacaddbabdabaadacddcddaddccdcdbdaddadbaaacbcdcaacbabbacdbcababddadbcddbddcaadacdcccccdadacbddcbbcdddcbcdabdddbadccdacdbdcbccaaaccdcbbbddbcadbdcabadbbcbcbddbbaaaadddddcbadddbaabaddcddadcaadbdccbccadddcbcccabccbadacccbddcbdcdddbabccaaaccabcddcbccdccdacbddacaccacdccccdccbaddbbdbcdbabaacbadbdaabdaaabcbbbdbabdddaddbcbbcddbbdbccbdacbbdbdaaabacdbdacabadccaaaabbdbbbdaacadcabdcdcacbcbcabbddaadddbdadbaabbdbadbbaaadbccdccadabccbaabaddacbdbdaaabcdbacdbbdbddbbdabbabadbadaaadbbcbccdaaaadbbccdaccbdbabbdadbadaacbaaccdcdbaababdadcbabadcbaccabcdccccbddabccabccaaaaccabaccbcdbbcadacaabdabdaaaabdcbdaabbabbbadbdbdacbddaadbcddcccbcadabbcbbbbbbdadabbccacbbccbadbcbbdacdabbccaccabddbadbccdbaaaadccabcadcbccbaabccacadbbdaadbaabdcdcdddcbdabdcbbcddcbbbacbaabaabbbacccdbbdabaccabbbaccdddaddbdbcbdaadcbbbbdccababcbddabbacddacabddbdcabdabaadcabaccbdbdbabaabdcddcdacccbacbbaddacabdcdaaadadddcddacbddbadbaaaacaababcbddcbdbadacdcbddbbdacddaabcbdabdaaddcdccbddbdacbcabaaaccbbadddcaacbcbcacabdcccbcdaccbacaddcccdaacadcabbcccdcbabcbaadbdddcdcdbbdaadbaadabbbbbacbcbcabdababcaacdcabdcdabadcacbbbadddaadcdbbdaaadaacdaccbbdbbbcabbadbbddcccabbadbcdcbcdbacacaccdaadcddbdcbcabacbbddccabbcbaabadbbbaaaadcabbabbdacddcbdcadbbbdadaacddabdbdbbaabcacacdbddbabacaabdabddabdaadadaddcbaddbaaabcbbaadadabdccaddcaaabdccaccaadcccdaaccdcbaaabbcbbadcbaaababcbcbcbbdccbbcbcdbbbaadddcadacccbcbadacbdbaadabbbbddadddbadabaacdbdccbaccaaacbdddbbbccbabddbcbcadddbaabbbdcbaaccdccbbbcbdacdcdcccadcdcccbddcaaacacddcdbdbaaaaddccabcaccdbccbccdbabaddabcbdbcaadbbcdbcaabcbbddcbcccabbdaaccbbdddcdcdccdccbcaccccbadbbbccbdaaaddaacdacaddbdbaacbcbacbaccbdcbcdabcadbadbbbacabcdcaaddbccaabcddcddacccabbddcbdacdcbcdaabddabbcbbddbbaabbadabdbdcacabdcacbacabcdbdbcccdabadadadacadacacabadbdabddbbaadddbbbabcccadaabbbaccbdabcacacbcccbaabdacddcdcbcdbccabccdbdaddacddadadbaddcdacbacacacacccbabdcdabbabbcccbcabcbbcbabcaabddccdcadccaddcdcadddabacabbcddabcdccaddcccdacacbcddacccaaadcccdbdabcbdcabdacdbddadabaaddbabdacadbdbdacbaabddcdddccacaadcbcdcccbdacacbbcbddbabacacbdcccbbdbabacdcdabbbdbdabbbddadbaababccacdacdaddacaabbbdbcacbcbddcdbdbcddbcbaabbbcccdccdacbbccabcadbbcacbcadaccadbcbcacccacbaacddadaabcbcbacbbccaabbcbacbddbbaadccbdcacccbbbdbcbddbdccabbcabadbdacbbaacdaaadaaaabccccbcdbdabaadcdaccaccabcdbabaabdcdccdbcabbdddcadcbbccbcbddccddaaacbcdcaacacacdcccdcacbddbbadbcdbddadbbddabacdabbccbdbdaddbcbcbdbdddbabcbbccdadabdbadbacbadaddcabaabbdbaccaacdbdaabcddccbdcbbdadbabdcaaaddbcdbbdcaacdacbcdccdbbadcdbcabcaabcdcadaacbcabbbddaadddbcaaadaabdcabdbcddcddbdacdaaaabdcbddcbddcdbcbdbbadbdbbacbccaaddccccabdbbacaadccbbadbbabbabbcaacccccdbacbdcabaadbbadbcbacabbacddabcbcbdcabaaadccaabccacadbadabbddddaccbadbcccccbcdbdbdbbccaabaabbacaaaddbccaabdabdcbaacbbababbdddcddcaaddaabdbbabbabaabbbdabcadddaddcabddbabdcdddbcdbdaacbacdacabacadbbbcadaabccccbbbbbdbbbcbcaababbdaaacaacaaaccddacdcdbdcbacbaaabcdcbbccaacccbadcdabbcdbdadcadbdcddbccdabbdaddacdabdcbccbdcddacbadabdddbdcddcdaacdbdabbaaabcbccaddacbdbcbadbadcaaccbbbccabcaaadcbdccbabbcddbbdcbcbbbbcacbaabbadacdccdccccabcbabcaadcadbdbbacbdbbccccbbcbadbcbcbccbddadccddaaaacdabbdbdbbbdbccbaaccdacbcccaacbccddcbaaccddccccacacddcaabcbccbcbaadcabcdbccaadabcaccdbdbaccddccbdccdccdcddbdddaabbdbcdbbacdaabcbbcaabdaadbdcbaabddaacbbdabbcbcdaaddaaccbcaabcaabcacadaabdbdadbdbadbacddcdbacbccdacbbdabcbbcbcbdcccdcbabaccadcdaddcdbcaaddbbdbacccddacdacddbdccaadabcbdaccaacabacadadacddcccbcaacdadadbbbaababbaccbaadbdadacdcccbdabddacccadbaaabcdbbbbdacdbabcdbdbbdaabdbaaabccccddbccddacaadcdbdbcdcddbcdadaccccdddddaddacdbcabddcabbcdcdaabcddcaabadcccabdabddadbcbaaacbddbbddbaaaabdcabadbabaacccdbadcdaaacdbaacbdcabbbcbbbccdccbdddbcacbdcababbbcabcadabcbbaddabccbabacbacdcadbacabbcdbcabbbdadbabddcdaccdaaaccdbadccdccaadddaacaaccbddcdbabbbdbbadbdcbbbadaabadcaacdbbaadddddaccadcccdbabadbdcbdadbababbddcbcddbbaaacdcddbabbdaccacccaadbcbcdcccdcadaabadadadbdabcdddbbdbcabcdbccbcccdbdaddbbbccaccbbaabdabadaccdabdabdacadabadaaaaaadcccbcccbddacbcbdccabdbccccddccacbaddccddcbdaabbdcdbaadddcacdbdbbcbcacccdbcccbbadbaadcbabadaaadbdbacadcadaaadcaaaabdabcbdcabdbcdcdbcbddaaccdadacdbdabddbacbabdddbdaaccbbddabbbdcbadbacddccadabbadccacdddadbdabdbbaacabbdddbadcaaaaacbacaccdccddabdbbcaabddcccdbadbdcdabbbdacdbacadcbbcdcdaaadbbaaadcaacdbaabbdacbbbddacccaaadcbcaaaacaaabaabbadacbbcaacdbaccddddcacabbcadabcddbcddcbbccdaddcbbcbdcabcdbadaadcbcabaaaaacbcdcbadcbccaacacababddadcaccbcbcbdccbaccbcdccdaacbddcdcbabdaadbdacddbccadcddaddcaabddacdcadaabcbcbcdddaacddacbccdacbbccccabcddacadacbaadabcadbacbadcbcadccdcdcadbdddabdadaabcbdbbbaaabacabcbbbcdababaddacdbbdcaddccaaadbbdabcdaabdcdbaadacaaadcbaacbbacadaccaacdccacbbcdadcadabadbdadaababcccbcacccbbbdadacabadccbdcddbabcbbcaababbbddcdacbbcbcddadaddabcddbabdcaaacdbcdacdadbaaddccbacbaaddadcdbbbdacaaacacabcccbbddcbbdbabdaadbbcdbbbcbdcdcddbddacbbcadabaccbbcacccdcdbdbcacccddcbdbbbccbaaccbcccbddcdbbdcdcacacacbbbcbdadbaccabbdaddaacadcbaaccadcdcdcddabcbacbbaddbabcddccbcaaaccaabbdaccadcdaddbccdbaabcdaaacdcdcbaaacdabdabcdcdadccadbbaadbccdaaabbadccabbabcbbbbddbcabadcabbdaaaabadbacbbdddcddaaabdaaaaacdbbaaacbbcddbbcadcbaddddbdccdcbcadcaabcbccdcbdcbdbcbdcbacdcacacabccdbaccccdcdbaaaccacacbadcacadccbacaadccddbdadbcbbdddcacbcaccbbcbacdcadbcabbcbdacdbadbbdadbacacabbbaccaabdbcdcadaaabcdbaadbbacdbaccaccdadcdadcbbcbbcdcddaacbdbcccbcababacacccbcbbcadbdacdaadbabbcabadbdcaacadcccdcbdbcbbbacaaacdbbaddacdbcabcdddcaacaadbbdcbbadbcadccdbaacdcccadadddacaacdcbababaacaadddaabbacdaccddbadccdbaddadaabadddcaabdadcacacbdddabaabccbaddbdacabcbacabcdbaabccdabbaaaddacabccbabbabdaacaaacbbcadccbcccdddbbbbbdddaacdbaddaabddccddbaacaacdbdddadbbcadcbccbdbcababaacbdbddaccdcadcdadddcaacacabbaaadaababbcdbcbaaacdbbbcbcdcbddcccccddaadcdbbabcaaaacababaababbdadacddaacbabdbdadddccbbabbbccbaabadbccaabdbcabccbadabbaccccbcdcdccadbddbbcaadbcdcaccbcdabddbdabcbdbadacacbbcaacaaddaaddddcdccbcdaaaaaabaabcdadcacadcbccbbdabbbbabbadbbddababcdcbbddbacabcbddcccbabddcabddacdbcbdcacbababcddabdddcdacbbcabcbbdaaaadbcaadddcbaacbacbaddcaccdbdccbacaabdaacbbbcdadbaddbddcbbadcbbbdcdbabaabbababbaabddcbdacacdcbcaabdaddcbddbadcbbdbbadddabccbacdcdcacbdbcbbbadddbabbbcbbababadbdadbdbdbbbdbbddbddcbbcaddcdcabcaaddaadbcacaadadabadcabbababcaddbddacaabddcdbaaaacacabbdcbcccaccaaaabbdccacddabbacccbabaacddbaccabcbdcdccacadddcdbcbcbbcacbdacbbacbbcddaaddaddccadbcacdbbbdaaabcccdaabddccccbdbbbacadcabdcdaccababcabadcdbaaddbddcadacaddbaddcabaacdcbadacaaccdbcdbcdbbccbdaadabcbbacacccbbadcccccbaddbdcbdbbcccddaabdadcccdcbcddbaabccddcadbacdbcaaadaacadbacbdbbbacddadbbddbbccacbabadcbbcbcdcdbdbbdcababacadabbadcbdbcaabdcaccddacdddaaddcaccbdcdcabddbbcabaccddcdaaadabbdcbcbbbacbacdaaaddbabdddcbaccbdccabcaabdcaacdacbbbddabdadbdcbbbbaaddacabadabcaabdbaabaddbbdcaccbccacbdbaaadccccadadccdcbbbbbbccccaccbabcbbbdbdcbbbadcdddabbbdaaaabbadbcadbaddccdabcadccbdbdccadaadbbdddabddcacdababcadbddabcaddddbaadcbcbccdcaaccacdcbccdacbcbbcdbaacdacbdcbbcbcdbacbdbdbddaccdacadbbbdbdadbcdbbacaadcdaddcbdbcbabcabddbabbcadcadbaadaaabbbbcadcadcdccccaccdaabbdbbabcadbcddaaddddaaaccddcabbadbcdcdcddbaacdbbcccaccabdddbbadbdbccadadbadacbbcacdadacaacaacdcaaacdbbcabaacaccbbccbdbbcbcbabbcccdcdccbcbcdbdaccddcadbbaaddabdbcbbdbdabbbbbddabcddccddcdcabbbacdccdbcbddbcdccbabdacabbcbbccacdacaadbcacbbbbdabacbccabaddcddcbaccaabccaadcacacbacbcbadadadddbbaccbaadccdcdbdddcbcdcdddbabcbbabcbdabbddbaabaacabbdccacadcadccacaadcbdacacbbabaccccadbcbadadadbdcbcbaccdddcbaaabacaaadbaccdaadcbdbbdacbbabdcccaccbdaacabdcddbbaccdbbdabcddcbcaaabaccbbdbcadbcbdadcabaccbbabbacbcdbcbaadbbdcdbdabdaadbabcacacaadbdcbdaacdbdacbabacaaadbddacababcdddcddccbbcaddcdcdabcdbbccbabaabcdcdcaacccccbcacabdccdccdbccaabddbcaabcadacccabaddbdbcbaabacbbadbacbcbddbcdbcacbadbbcbdcababbddbbdaadaddcbabcaddbcadadacdcbdcdaaccacbcdadaaacacadabcdbdbbbdddcddbacadbcbabcbadbbdccbcdbccdbbaadcdcdacdcdacbbdacacdadabddbaaaadacbabdcccdabbccbbabbcbaacddbbacdbcaaababcaaababbcbadbdbbdcdccbbddbcabdbacddabcadbaadbbaddadabbdddcbacbacbadbdbdadcbcbddddbacdcacdadaaaaddbaddcadbacdbdbdbbbdddabcabdabbbbdadccdbccbddbcabadbcacadccbdabbbddcddacdddaddcbbcddacdacadcbbcbbddbacbadaccbadacdcbccddcdbabdddbbccadaacaabbccabaaaaaaaaaadcccbbbdddbaaddadabcbdaaddcdadcdbdccbcbaabaabcabacbddabbbbccbbbcadcdacbcbdabdcddbadbcbadcbbadcbbacbbccbaacbbccccddacdbbcabccacacbcccbdaaacbccdbdaccdaacdbabbcaccadabdcbdabcdccaacccddabbaaaadccaccadbacddcbadcabbadcbdadccacbdcdbacdaddadbdccadbbbdaccaadccbabbbaddbcbaabbdcaccbcdaddcaabdbcacbccaaddaabbcabdacbddacabdccdbbbadddbbdccdbacdcdadaababcddaaabddcacdcbcbcdbcdadcacaccdcccbdacdaabbbddbcabdbbccbcacddbacdcbbcccdcdbbacaddadabdaababbbbbddadbcdcdaadccbadaabdadddcdccdaacdcadabbccacacaaadaacacaddadbdcadcaaddadaacbabcdbadbdadabbbcaacbaddaadccaadcbdcaabdabbabbdabdadaabacbbbbbabdbcadaadbdccacdaababbbaaacbcdcddccdbdbbabdaaccdbdddbabbdbdbabcacddbaacdadbacaacbddddbdbabbcabbdababacbcaabdcdacddbabbcddaabcacbadaaaddcbbcccdabbbcdaacbddbdcadbccddccdcbdbdbdcdbddbdababcccadadcacdcbaabaacbdaaddccddcacdcdccbbabaccdcccaadaccbcbabacdcdbcbbcbbcdccddcbaaccdcdcbabccbbacadbbadabcaadddcbacbbdbabddaabbddbbbccdbbddbdadadacbabdabdccacaaddaadaacbcbccbadcbbacaacbabcbabccbaabbadcaaccdbadadaadcccabbcabccdbccaadbacddddcdbdbacabcadaccbabdadbccbcbccdcaacbdcdcbdcddaacabbcbaddbcbcccdcbcdacccdcbdbdddcbbcddaacbbacdbbcaccdcdddbcbcbbddcdbbaaacdcaabbacaaaadcbdcdddbcdbbcbcddadbcaadddabcacabcdcccaacadcabdcccdbaaddddbacdaabaadcddaababbcbcdadbadcdcdbcabdaddaaacbdaadcbbbccaacbcdcdbaacdbacacdcdcdabbdddbacabcabbdadabababadddaddbbcabaabbccbddacdabbcaddbacddacabcbcdccaaaaccbdaddbccacbbdbcaabadcabdacdcbdacddddbaccacdbddbcbdbdbddabbdcbdcabacbdbdccbaccdbdbbabdbaddbababccdaabddcaabadcddabccabcdcbbcacdaddaacdadbbaadddbbbaaacacbaabaadcbbdbdcaaadbcdbbbdcadbdcaccacdbdbddacbbabadbcdddbbadabcacddababbbbcbacaaaadacdbaacdbacbccadccdabbccbddbcbbcaabaaadbccbcdccdccbdbacabcaadcccadbdccadcacbcaaaaccbbbacbcbbcbadaacabcdcbddbaaabbbdbadccacdbdacdacdbbbddbcccdccaaaabbdbbdbcdbcabbcbddcddabadbbcccaaaddddbdacbbdcddbcdacdabdabbbcabbbabccbabadcadbbbadcbcbcdcccbcbdaddbddbcdbddbbbcbbbadbadddddcddddaaacccadddccbbbcacaaccddbbcbacadadcbccbaaacbdcccbcbdcbaacacbcadcbbccdddbcdbbdaadcdcddbcacdcbababbacabddcccaccddcdbcaacbdcaabaadabababbcbccdbacdbbabbcaabacabcdaaacdcabcbbbcaccdcccacddacbbbdaabcbddddbdcaabdaabdaaaaacaaacabcbccccbddabddcccabaadddaccbabcdccaaddbbcbcbccccdadbdcdcdaacccdbccdbcbccdccbabcdcbbabcdbbddcacabcbabcdcabddcbabbdcaaaddabacadcbaacdbaddbaccbdabdadabcaadbbdaacdbacbdcaccdbabdabacabcccdacaacdadcbbbddabcdaabcbadccdcdbbaadadcdabcdbbbdbddcddbcdadccaacacbdaaacbbadaccbcaadcacbcdddcdbbcaaadadccaabacddbdbcbccbdbadbdacbbbcdbcacdcaaddcadcacbcadccacbaddcbbddbbdccdbacbabbaaccaadcabcddaaabccdadbbcacdadacabaadbbbbcbaabdcccdaccaaadabcdadbbbcddcdaacbbccadcbbbcbcdcbaacbbcdbcaabadadcbbdbcccbcabaaaacddcabdcaadbbadbbdcbdcaaaacadacdbbdacccdbccdabbccbdcccbaabbddbddcddabbccddacdcdbabbaccbaaabbdaaccbdcdbbbbacdbddaaaabdcabadbcabacadaaaabcbabaabccbddccbddddadbbdabcccbdcadcdaabbacccddaabbddacbccbadbaadccdbdbcbdbababdccdcbbbdbaacadbbabacabbdcddbbcbbcbdddbcadabdbdaabdbadbbabccabcadadbbabbdcdaabcdcbddcbdccdbbcdbcbacbddadbdadbcbbaaaadbbaabdccbcacdaaddcacbdbbdddaccbdbbbadacdaddcccaccbcacaaabaaccdbaaacaaacacbadbcbcbdabadbdbaacbdccabbaabbcddacbccdcabbcbabcacdbddcbbcaccddccdcddabdbbdadbabacddbacbccabdadbddbabcbcbcccabcdadbabcaaadaabbbcdabdbdcadadaddabacdbcaadabcddadbaddbadcbcdadaccaddccabddaadcacacaddbdaaaacdadcdbdcbdbdaccaacaaadcaadacacabdbcaccbcaccddbacaddcbcbbaadbbcadbacdddddbcbdaccbcdabcdbcadcaaabadbabdadbbaddcbacbacadaacbbbbadbdddcaadbccccccabcdbadcbbadcbabcbacabcaccbcadbccadadacabdbccbaaadaaaaaabdadaaccacacbcaccacbdadadddbdabcaaaacadbccabbcbabadcbdaabcccabbbcdadacadbabddcdcdacaacdbddcddaccacabdbcbbcddacadacadaadbcbdbadddbcdaccabcbcdbacbaacccaaadcbdcaaaacadadbacbdaadbcdcddacaddadcbabbdccdaccbddabaccbcccddddabcbaccddacbbddbaddaccadddababdababdbccdbcccacbaadacbbaddabbdcdcdcabddcadcdaacdcbacacbdbddbacdadbddabaccccabdabbcbcbadbcdbdabccbcbdaaabccabadcddbbbaaacccdbcdadbadadabdacaccdbdbccbbdacacbbcbadabbdbbadcdbbabddabbcbdbcadddaaabbbaaacbdaaaadaabdddacdacaabbbdbbdcdbcbccbdccadbbadbbcdaadbdcdadbcbbccbbcbdbdaccdbccdbdbdbbcaacacadcadaadabcddacababddacacaabbcbbbacbcaacbadbabacaddaddabdaaabdccbbdbcccacdaccbaabbcabaabacabddcaadddbdadcdccccabdcdbdbbadcadbcabcdbacbaaacccaddccccccccdacbcadbaabbbbaadbbbadaacabacaccaddbddacbcbcdddadbdadcbaccbadcaaddbdccbbddacbcaaadcdccccbcaacccaacadaaadbdbacabbbadcabddbbcadccdcbbabdbcdadabbbbcdbbbdbdcaacdabbbbcbdccaabdcbcabaaacacdcaccdbabcabcbabcbacadabdbabaadbcacbbcdaccbbacadcbbcccccdcbaaaccacabdbdbbccbaabccabcbbbbcccbcccabacdcabcacdbbabadddcadbadbdaaadddadabcbbccdddacdbddbcddccacbaaadcdbabadbddcddabccdbdacbbccaaacbbbaaddcdcacdbaaadabaabcccdccaaadbadaccaccdbbabaabdddadcdcacabbbbadcdbabbababcaabbacdaccadacacdcbadbbdbaddbdbccaaabadcdaccbdbdabacdccabddaddcadcdacddbdcdbccdccadaaaabbadbadaabbbbdcabbdbdbccbacaddbabacccdadcdaccdcbbccdbccbbbbbdcaccdcbcdbcabbcbcdbddbddddcdbcbbacbbdcdaccdbbbaaadaacabdcbbdcdcddbbcdbdccbddbccdbabdaccbbbbbbacdcbcbbdaabbcbdccdcacdcddaadaaccacdacbbcccacadbaacbcdcadadcdcabacccbdbadaaaaaaadaabdddabbacdbccbdbabcbccdbbcddbabbdaddbcbcbcacbdcdbaadbbacbbbdcbcdacaadbdcbabccabadbabdbadcacbcdddbbbbadbdacaacdaaadddcddbdbbaaddbbcdacbaababaaddadbcdcddbcaaabccddcadcddaddcbbbaddddccbcdaaabdcdbbcccaacdcdabbabadcbaadcdbbccdbdbadabadbaccdcdccabccbaabdbdaaaadbdbcddcbbabdcbaddaadccbbcdadbadbcdcbcdccababcaccdbbccaddccbcdadbbdcdcbbbcdcacddcbcdabccdbbbadbbaccccabaababbdbdcaabcacddadaccdcbdadadaadaabbbcdddbbbbaacddccbbdacdddadabaddcaccaaaabddbdbcacdadbadbdacaddbabbbadbdaddadacaccdbcdacabbdbccddbdbabcaddcccbddcabccdbbddcbbcaadbccdcdadbcdaacacbcacdacacaaccbdadaacbcbbdbbcddddcdbaadabadbaadacabddaabbaaddbaabcabdccbadccddabaabbdbdddddcdabacdddadbbddabccaddcdbabcadcdaaabbdbdcdadbcbbcbcbddbaaaacdccccbdcaccddcadcdbddaccdcddabdacbbbabcacdcddcbcdcdabdbdacbcaaadacabddbdbaccbbaaabbddddacddbaaaabacabbddabccbcabbcbaaabdcddcccabaabaddbcacdacbcccadacdaaacbccbadcadccdccbccaaddcbddbacacababccbcacbbdcbabbcdcdbbbadcabbaccaaddcbbdadddccdabdabdaacbcdccdbcadaacadbdaccacdcddbbdbadacbcddbabadcccacbbbdadadddcbbcdcdcaccbbaaddaadbddbbabadbabccccbbcbdbcabcbcbadaadacccccdddacdcaaaccbacbdcbddbdaaabbacbbdabcbaaaaabbcbacaccddabcaccddbdcbaaadbcdbcdbbdcaccaadcacabcbdcbbccaababcdbaccdccaccbdbabbcaaccaaadbbaabbaabbcdbcdbcbddbbddbabcdaccddbbcdbbdabcdbdccdadcbbdaccddbddcdbbccaccbcdccacaaabbcbdbdcccaabdcddbcddaabbcaddcbbcaacabbddbcdbdbccdbadcbadbabadbcbacddacddcbdddbdbcbacdcbdcbbcbacddcdbdcacadbcdcbacccdcddddbacbabddcbdcaaacacbddcdbddaadcdadacaabaaddbcbcadadcacdbcbddbdabbdabbaaaabacadbcdabbbcadddcbdbdaababdccccbdccbcaadcbbcccbdacbbaaacdbbbadbccdccaaadccbbabcdaadcdbdcbacdadbdcbbcbcccdadcdcaadcbddaddcbdbaddccdddddaddcbcbacccdaabbcbacbcbababaaacbdbacdbbccccdacdbdbbddaaaacaacadaddcadcdcdbcacdbaadabdcdccdbbbdaacacccacdddbdadabcbabdcabccdbaccdaadddcddaadcacabcbdbdbbcabaaddbdbbddcdaacaabbccaadaadacddadbccbbcabdbabaaaddcbcbdddcbdadcddabbdbbcdbcbabdbabdaaacbbdabbabdcdadadbdbabccdbaccabcbbbaccadcdcababdbcccadacdbcaddddbbcaacbccdabadaaabbdadbbabcacdccddbddaabcbccdaccdddacccaadddadcbbddbcacddcddcababcbdcacbdbbaacabcdabbbaacbabbdaabbbadbdaddcacaacbabcdaacccabddaadccbddacdbaacadbcbbbdbbadbbdaacabdcadcbacdddbcadddadaabdadbdaddadccdcdccddacccbaadcdaabcbadabaadcdbabdbbacdccbbacbcdabdbcbcadaabbcdcadccbaababacbaadcbdbdadaadcccdbccbdbbcddcacacccabadccacacbbaacdbccabccabbcabbbabdacacddaddcbdaabdabaddbdaacaadaacababcaabaddcadbcccaadbbcdabcaacdbcbadbbcbabcdbaaddcaccccdcbbbbdabbbbcaaadabbcdabdbabdadacadccdddacddbbdccaadabdbddbcaaaddabbbbddaaaaccacbbdabcdadddcccaaddccacabacddaaaddbddaadcbaddaddcbccdbdaababbddbbbcacbabaccbcadbbbbddccacdbcaccdbbcdcacccbcccdaacaaddcbcbbcbbcabadcacbaaaabcadbaadaccaabccdbcbdabaadabddddbcdaacbdcddcaccacbbcaaadcbdabccddbbbaaacadabdbddddacbacbcabdaddaaadbcdadccacdbdddcddcdbacbbbdbbbdacacddbbcbabcdadcadadddaaabdbdcbabdacdcddcdbabdcbaadbccbddccbaccddcbacbdcbbbcbdbabbcbaaccacbcccacadadadcdaaacbdadbabbbdcdaccdbadaccccddbccccadadabdbaaabcdbbdbbbbbbbbaabadbdcaccbabaacabcaddacbbccbdcadcdaccdadaababdcdbbcabbaabbbccbaaaccbdacaaddbdaaddbcababaccabdcdbacbadaccacdaadadbbacaaabadacaddcbcbbcdbcddcadcbcadadcdddacaddcbbddbddabcdbcdbbbabdddcbdcadcabbcbcaabbbcabbdabcdcbdbdcaaaacddaccbbbbddbccdbcdccdadadaabccabdabdcdacaacdcccdcdddabbadadbdcbcddcbcdbadddbcabcbacacbbcdbabdcbdbdbdcaabdbbccbdcadcddbcbcbdcdacccbcadbbbcdcdaaaabdcddaabdacbacdcacdddaddaaaccbcccacaaaddcdaabcbdcdabaccabacaccabcdabdbcbdcbcdbbbdbacdddbbbddbbadcbbdadcdbacdcbaddcabbacaccbadcacddcbdbcddcdaaabdbbddaadcbdcaaaddadaadabbabbdabcaacabddbcccddbcbddbbdadbbbbbbadcbacbdcabdaadbdcadcdddaacacbbadcbdbcaaccdcdbdcacadaacdbcbcbbbcdbaadbacabbcadbddacaaacadbbbbcbdccacadcdadbdcaaabbdaacddbdbabdbaacacabbcbdcbbdabaabbacacbabdcabbcacbbbbaddcaddabbdbcbcbbabcccacbcdcdddabdbdabdcabacaabdbaadbaaaadcddbadaadaabcbbbadddcbdddcbacdbabdbdbaabcaaddbdcbbdbdacacaacbacdcdcabcaacddddabdbacbdccabcbaabaadaccdabaadcbdcddbccdddadcbabdddbadacaacbbdcaaccddddbdcbcadcdcccdccdcdbbbdadabdbcbcdabcbdbdddbabcddcadaaaacbdbddbadacbbcbbacdbccbadcccaacbbcdadbadcbdbaaabccadccbbbbdcbdacdcadabbdbaddacdacacacbbbaddbdadcbadbaabdbacddadcdcbabcdddadcbbcbccdbddbadccbabbbdbcbdadbcbbbdaaddbbcbdaccbddbdddcdccbbaabadbcdccacbcbabdadbdcaddbabcdbbacababbcbbcbcbccccbababcacacbddcbccbabacdbcdbcdcdadbbccbbbbbcbbcacdadbdcdcabaabdbbcadaabdabbbacdaccbbabcbcacaccddaaccccccdbadbaadbbcdabdbcdbcacadcbdaadcacabbaadcccbcacbbcdddadbccdbabddcbbdbbaacbacbddbaccdabbabacdbabcdbdbdadcbababbcbcccdbcddaadadbcdccbacaadadacdbaaabbaaddcbbbdcdaabbbcdbbcbddcccbdddbdadabcdccbcbbdcaccddabbacbbcabccaccddaababdcccaacbccbccbbacbcbadcdcbbabcdadbdbbcbdbaaddbbbaddddbbdaabaacbbbcadadcacbbcbaccddcbccbaacbcdbdbacddcdbbcccbcaacacddbcbaacabcdccbccabbcadaabbdadaacdbcddbacdacdabbdaaacbddcaabaaacabcddabccbdbcacbabcbccaccbcdacacadccbaaccbabdbccaabdabcbacddacdbaddddcaaaddbaabcadabbbacbacbdabbbdaaabcadccbccbcdcacacababacddbaabcbbbabadbcbaabdaadacbaacbcbccdacadcaabcdaacdccbbccaaadabdccaccaadcabdadddbdaababddabdcacdaabddacbcdbadbaddccacbbaabbcbcbdcdabcbbadcbaccadbbdaddaaaccddabccbdcdabcddbbadabbcccbabcdbaccaacbacbcdddbbddcaaddadbddadbabdabbababcaadcbaadaaabdccdbddddcbdadaaddacdadcccdccbbacdccadcdabcbbacaaccbaaaddcadbcbbaddadcabcbaaabadaacdaadadcccbcaaddadaadccdcdbcddddcacbadbdbbbacdcbcdbcabddbadbadcacaccabdabbbdbacddbacbdcdaacbdaadcdccaabcacabbcdcdadaaaccaabdcabbdccacbbcdbcbccbdbacccdccccdbdcacdbcbbdcadabcdbbdbadabddaddaacaaccccbcaaddacbbabdcabdacaadabbabbdbdddabaaabbcdbccdbacabaabaaadcaabcddbcdadbacadadbcddcbcbabdaddddacbdadaaacbdbcdbbbbbcbdccbcddababdbccddcadcbcacabdaddadbdaccddcaacabcdbdaccddcabcabcdcbbbbddaddabbcaddcdcdcccabbdaadbdbbbbcaabcbcbcaabadbaccbcccacbddacabbdadbbaacccdabdacabacddbddcdadddcacdcadcadbbbbccdabbcbaaacabdadcaddcbbaabaaadbaaaababdbbcabdccbaadcdbdadbaccabcdcdaacdcbddadcabbadbabdbbdcbbdadddabbccdbccbbdacbabcadddbaddcdadccacdcbbcbdbcacdcaadbccdbabdcdbdbabbcaaadcdccacdcbcaaddcbdadddabaadabcdaabdaccbdcbcbcddacbaacbbcbbcacbadacabdacddacdcabccaacddbbdcabdbacdbbcadaadbbacbacaccddbdaacabcacbabdacdddccabbadaccabcbcbabdaaaadaadbddadccccbbbcdbcabcdddbabdbadbbaacdabddabcadcbccaaccdcaacacdbaccbbcbccabddacabbbcacddddaababccabaaabddbddbadbadbcaccaddddcbdbbabbdcdbdbcddbdbabbbabdbbaacaddddcdabdaadbdcdabcbaccbabccdbddacbadaaabcbadddadbdddcdbccbbccaacbaabbadbdbabbccabdbddbaabdbaaaccdbdabcabcdccdcdbabcbdabcbbccabbaacddaacbcaabcdaddccadbbdcaaacaabccbbbcbabbbbdbbbaacadaacbccddadccbddcbcabdcbbddbccbddadccaabcaaabbdabbbdaadddccdbabdccabcbaaccbaaaabaacdadbaccdbbbddcdcdcddcdbdccddccacddcdbdaddbcddbdddbddddadababbbbbbdbbbdbccadccbbccbbbcddaabcdaccbadbacdbadcbcaabbdaacbcadabbacbdaadabdddcdccabcacbcddacdccadcdcacaabcccddddccaaabcddaadbddbdacbacadbbbddbaabdccbaacacccadcabaaabdaaabdaacdacdcbbcbdbadbbbbbddcccababbcaacbaacdaababdcbbbbbccbaaccdbdddadddbdacbaccadaacadbccdcacdacddaadbadcacbbdadcabddbcadcbdcbcbabbbbadbabaaccdcbbdbbccabaddddadabdcdbaddccdabdbcadaaacbdcdbdacbbcdbabaaccddaadbabddbcbdaabdabcbbccaadbcbccbddcbaabbcaadbbcaaccdbccacbcccabacadcbaabdccbcccbcdabdaaabcbbddabbabbbbadddabbcadcbcabbcdbaccbcbacdcacbbaddaadcdddbabcbcadbcadbbbacdbabaddcbabcddcdbadbbcbadbcbbcbbbbaabddbabdcccbadadddccabbabaaabddbcaaacbbbcbbbcabbdcccccabddacacbbbdacdacdabcaddccdbdcdddacaaaadadcdbcaabadaaadcdbacdccbdbadaccbdbcdbbdccdcbaacbabccdbbcccabcaaabdccddcaddbdccbdcbcbcdacacbbbcdabbacadbbaaddbbbbccdadbccabbcabddccbcbbcabcacdbdbcdaaacddbdbaccaacdadabacdccbbaccacdcbcbddcbdcadcbabaacabdaaacdbbbccbbdbddddbbcddaadabcbbdbadbaabdacaaabcabcdcbbbcdacbaaaaabcbcddacbbdabbdabbbdbaabadabdacdabbccdaaabccdbbdbdcbdbdcbacbddddddabadabcbaadaaaaccdbcaabdcdacddacbbcdbcacacdbaacbdddbdaabbcccadbdcbaccddaddddbdaadbbccdbdcacdccdcddbbdcbccabccaaddbadbadddcbbdaabcbddadcaaddadddbaddadbaaccbdcdbcadcacbdcccdbacbababbcadacdccaaaaababbdabcdccdcbcacdcdbadcdaacccdacacddaddcabaabcbcacacdbbbbdcccabddabcdaddbdbcbdbdadabcdbdcaddcadcdcddbcacbdcacbddddaaabbcbacbbdcdcbdbacacaaddabbaddadccacbdddbcdbddddbddcbacccbccdbcaabdbcbabdbadbbccdabdadcaacbccbabcabdcadaabbbbdddbacacacdbcbbdcaccdcdbbcdbcbbacbdcbbdbcaccdaadacbcbdcdbabbabcadbbbdaddddcacadccdbbaccddcbcaadaaabadadadddabcbabdadbdcadbbaadddacabddbabcdccbadcbacabdbccddadddbcdccabcabcaadcdabdcaccbacaabcaacaddaddddacdcaadadbaabadbccabcccdddbbbdbbdcccdcccaaadacbbddcadcccdddacdabaccbccbdbcddccbbcdbbadacbdcdbaaaaadccdbbaacbadddbcababacbcbbbbadabdbabbbcbcccadabddbbdbacdabcdcadcaacabbddcacdababddccadbaacacdbcacbcddddaaabbadbddbbcbbcbcdbdcbccbdcadadaddbccbdaabbbdbcaaccaaadbabdbbdccadbbcdcbccabadaacbbadacabdccaaddaaaccaacbccdadaadbaccadccadbdadbddbdcdaaaabddcdbdcdcbdcbbdaccdcccacacbbabbccaadbaadcbbaddcbaddccbcaaddbdbadcbdbcbccbadbbddbbbbacdacabccabdaddaabbadbabbdddbcaaacbbdbddbaddacccccbbcacdcbaacbdcdcdbddddcccbaaadbbdcdbacbaabcddbbbccbbddaccacbcdaaaabbcdadcbcbbdcacccaabaaaadcdcdcbcbdcccddbaabdaadacccdbddddbbcbdbacadacacddcbbddcabccbdcacbdcbadbadcbadaddbdbcddaabbdcabdcbcdbdddbbdcaccadbaadbabdacdcacaadbbcdcbaabbccdbaccdaccbdaddddcdacacbbcccaacbcdabdabaaadbdaaddbcbddddbccbcdcaccacdcddaabdddbbcddcabdaadabdbccdadcbadcdcbaccdacbcbdccdadbadacbcbbbbddddcbacabdcadabbbabdacbdcaadabbcbadaddbadbcddcccdabaddbdbabdcdbdcaddcbcacdbdcabadaadbacbadabddcaabaaaaaccbcdbaccaadabbaaddbddddcacaabbbcdcabbddcbbddddcaaddcbacaadbddacbaacadbdabbbbbbdcbbbadcdbcddbcccddaabaabaaacbdccdbcbaaddbdbdcbcadabaabadddbcbcddbdbbbdadbdaaabcbdaaaadbadcbbcbdddaababccabddabcacadaddcdbbcbdbdcbcdccccddbdddbdababadadabbacdcbadddbbacabdcacccadcbcbaadbbdcadacdbddbacdaabbdccbbaccdacacddbcbacddcaddbdabccbcbbbdcbaacaddadabaacacbdcddbcadabcabcacaaaacabcbbacccbccbacbcbadcbbcacadbdaabdaadabacccbbcdbccccadbdcdadbdcdbdaabaaddcbaadbccdbccddcbadddbccacdbcccdbdccbbbdcbaaddbdabacbdaadcdcbaccaabcaaadabbcbddbdbbccbbdddabaddadcadbacdcdcbabcddbbdabdcddddccbbdbcaccdbcacbcababccaccddbadbababdddcadddbbaacdcbdadbddcbacccdaddadccdadaacbbcababaacacbadaacdbdddbcbbdacccbccdddcbcabbbbdcadddddcbdddcaaccbcbdddbaabacadcbabdadbcacdcccccbdbdccabdcabbbaddcdbdcaaabacdddacaaddcadcdbcacbaadaaccadacaababbbdaaddaddddbbbaadcaadadaddcaddaaccccadacbbbbcddacabaaabcbcadabbaddbdbdbaacbbdaddddddbacdccbaccbdbacaaadbbbadbacdddabdcddbbaccbcdacdcaddcaacdbadbbadddaabccaadcadacbacdccdddcbdaaddacddcbabcaaaccbddddbbbaaadbbaabcadbbcccdbaadacdbddabadbddddcdddcddaddbdacbcabdccaaadacadbcccaaadcbcbaaacbbbbbcbddddbacaddcddadaccaadcababacabccbcadadbabaddbaacbbcdaddbaacaddcbcdaaabadbdbaacbcccdccdbdbaaddadcdddbccbabbababbaaddddaabcdadaadbbdbccdbbccccaaccadcabcdcbccddbbbcacabddacbadabaadbabdccbdabbbcdcdadbdcbbbddacdaaadcbbbddbaaacdacacbbccacdabcdbcdcbddabdaaddcbbdbdbbdcddddddcaabcddcccaabcadbabdbdadadbcacbbdbddadcacabdcaabcabbacaabaccabcaadbabbcbcdabcabdbdddcacbaadcddacaadcdbcabdbdccbbdddcbdcbabdabbdacbcbbbbcdddacddacdbaadcaacdabbaddadadcdaaacdbcaaddbccacaabadddcbbbcddabcabdbaacdadbbddbbbbcaaacbbcabaabdbbdbaabaccccacaaddbbbcaaadabbddcbaacdcdbccccaabacaabdcbcbcbbacdababadadcdcbdaacaabbcbbcdbbadaacadadacacddccdccbbaddaaacacbacbccdcaabddbbcbdadbdbaacccdcbabbbbbbcbbadbddbddbddcdcbbbabddabcddcbaaaaacccddbddabdcddabcdcbbdcdbbaccaadbabbcadcdcbdaddcddbaacdbdcadaaacbaabbdbddadaabbccccdadbdababdcabaadbccabcdbddbddaacacbbcccbabcabcbcabccbadcaadbcaddbaddaddaadbbdbbaacabbbbccbdcdabbbdcaccbcbaddabdbacdacdaabaddaaccacbcbadbbbcdbddabadabdcdacddbcdcaaccdbcbbdccccddbadcbdcbcdddbaadaccaacccdbaaccabbbabbcabbbaacdcbbabcdcabcabbbbabdbaaccacdacaadaccdcdaccbbdabaccbadbbbcbdcccdbdacbccbbbaaacdadccadcbaabcbcaacbbdaabdbadcbacbddcddbbbadaaadcdaddbcccccdaaacaccaaadbbbbaacadcaacbbcbaccabdbbdcacbccabdcacccbbaccadccdbbcdcbccaddccddcadabcbdbdbbdaddaaaccdccaadbabbbdbdbbcaaabaccdaaaddacdaaddabacaaabddcdadcddabaadcbcadbaaabaadbdacaadabaccbbbccabbbadabcadadcbcbbbcccccddbbddddbdabbbcbcadadcdcbacddbdbcaabccdcdcadcabdccdacbccdadaacdaabdcabaabbdcddabcdacbdcbcaddacdbadbbcdadabdbbadcdcadcddaaddcdaaaddcbdcdbacbbbaaccdcbbaaabaabcadaacddcddadcbbddccadabcddcdbddcacaacbdadabbdaddacadaadbdbdabcdbabddbcabbbddbaccccabddadacdbbaaaaabbddabbbbbcdcbaddcaddbccdbdaacdbdacdabdcccbabdcbddcddcbdccbcabbaadbadbacbdbcadaadaacacbaababcaaaaadaaaadababaabdbbbbbaddcbacaabaadacbbabaacbdcacdacbbcabbababaaddcbcdcbccdcbacbababbbddccacacadbbdadbdabcdbdadaddbbddbaacbdbbabcdccbbbaddcdacccacddcdddadcdcbddcbbcbdcdddbdabcaabdbccdcbcbdacbcbcabddbcabdacdbdaaabcbbcabbadcbccdbcacbbcaaacdddadbbacaaaaacbbcacbcbddcbaadbababcbcddaaabadaadcdccacbcbddbdddabdacaacddcaaabbadddcbdbdbbbdabccccabdbcaaacadababbcaadbdacdcdccbbccbddbbdcddaccdaaccbcdbdacadbaabacbdacbaabcddacaacaddccccababcddaddbccacabddcaccdaccbdbcddcbcddbbbcbbacbabadaddddccabbabdacbdaaaacacdaccbcbbbacdbaddbaddbbaddbacdcdaabddaddcaacbaacdbddadabbbcaaccddbbacbadcaaacbcaabcbdcdbccccbdbabbcabadcdaabaaddcdcdbdccbbcbdadbbbbbccdadaabdabcdddbbaccbcbacccabbcbcabbbdccbaabbbabbabdabdacbadabbadbdbdaabcdcdabbbadbabaacaaaccddcbcaacaaadadaddcaacbcaddadacacbaccdcdbabcbadabaadabcdccdddbbcbbbddbaadbdacccccdacbacdbbccababbbbcbadbbbddcbccdccabbcbdbbddbbcabbbbacbadcdcbdbdacddbaabcddddbdbcbddabcbaadababbcbccdbcbbabbcacbcacabbcbcbabbacddbacdbabaadcadcbabddbcbcacaaaaacadadbbcdccadbbdbbdbbbcadbddbbbbaccaccccccdcddabddbabdadcdbbccacbbabbcbbbcccacaccdcaccacbddbdaabacadadddaaddaddadcbdadcddababacadacdaadcbcbcddadddcddcdbbdcacbdabaabbacbabddcabcbbabdbaaabbbacadddadbaacaaacdddbabbdccbaccdaaadbbababaaabbdccaddacaadbabaccaadbdadcdacbbadcacbcbcddbabcbacbbddbddcbcadbbdbcdddaccacdcdbdaaaacbbdcbdbbdbcbcacbacccabbbabdbaadadddadbbbcaccbcaddcbcbbabadcbdadcdcbcdbddcccbbcbadbaccacacaaabcadadadcaabbbabcbcadbaaccbaccbdddaccdacbaccdcccdcdcdabbcbdddcbabbbabadddcbaddccbdbcddbbadcbcbcabdbcbbdddbacdcdabaddccdacbbbadbbcacccbbbccbbcbadcacdcdcacbbddbaabbaaadcdbdaabcaadabcabaccccdabbddccdabdccabbbdddbbcabaacbaababbdbabcaaaacbaaaddcbcdcbccccaccdcdccbdcccbcaaaadcccaaabdddbcccbcbcccabadadcbcdacabbbbbcdddbbcaadcddcdcdcdcbbbccdcbcbacbbcacddbcacaabbaaaddddcbdaaddcbddcdbccaaadcbdcdcadbdadabdadddcadaccaacdbdcbabadbdbccdbaaaadbccbacddbcabcacdbcacabbcdddddbbccdbbcbdacdaadddbcdcdcaacabcddccdcbbcdbcbbabbbaaaadbbbdacdcbddcdbcbcbccbddaadddbccaccccadcdbadcccddabcadcccbbbbccdcdccdbbcbcadcaaddacdcbdbbddddcacabbcddbaccabacdacccdbabaacdadcbddbadadaabadbccdccaacdabcdaacabacbacdcdbdcbdbbdddccccbbbdbbdadcbabdabacddcabbdbccbacacdbbabbcddccbcbdacdadcbddadabddccdacabbdabcababcbbaadcdddbabadbadbbdcdacbcbcbbbcaddbaadaaabdadabacabdddcbaccbcbabaadacabdadddbaacbbadccbaddbdcccddccbdccacdacbaacbacbdcabccbcdacdabbadcbacabccbadcadaabbdbddbabcbbdccbdcadaccabcccaddcdbaaadbbaddadcdaabccacbdbdaccddcdbbadacbabcbaabcaddbdcdcacdaaabddcdbbadabdbabacdbbbdcabdbacaacdbdbaabdadadddbcaabcdbabcdadadddcdcdbbbbabcaddaabcccccdbaaadaccbcbbabdcdcdacacaadaccbbaaaabbadcaadccadddacaddbcbcbabcbaaddbccbadbadabcabbbadaaddadbdcdabcacbadbabdaccddcbcbcbacaaacadcbddbbccabdbaacbcadaacbaaacbccacdacddccaaacaabddadbabcdabcdbcabbddbcdcdbcabcdbcbdbcbcdaaaaabbdacacdbbbcbdbabcbbdaabaddddbdbaccadbcbcbdbdadbdcaaaaaabcdcbcbcadacdcdaacdcadccbadbcbcbabdabbcbcbbaaadbdbcdddbdbdaabdbaaddcddaaccccddbadabdbbdddcdbcbdcbdbacabdbbcddbacadaddbcbddbbbabbbcaacdcbdbaddddbaabaadbcacbbccaddadbbababcbcdcaddbccdcbccdaddacabbaabdbddbaddbdddaacdcaaabcbaabcbadabcbacbaadcccbaadaacccaaddddccabbadcbcccadddddacbacdacbabdadcbabaccccbabbaccabdaccacaddbbbcacacbbccaabcccdcacbcbdadadccaacacaadccbacabdcabcaacdbdabdcacabdccccbacbccadaacabaccadbddcbadabacbacaadacbdbbbacbddbbbcdaaaacdaacaacabdaacadcdaabdaacbcabdddabcaccbaccdaadbcacddabaadcddaabbdadbabbddabcbcbcbcadbcbddabbbbbaaacdbcabbbabdacbdcabaaabcbbddacddacdddbaddddaabcccbaacaabaaccbcabbbaabadccdbaadcacaaaacaabacaabcccbdacabcbcccdcacbccbcbabacaabdaaacaacbbbbcdbaaccbdcdcbdbdabadacdbbacbaddadadccdacbbacbddcddacccacbcadbdcdbdabbdabcbcacbadbdcddbadbabcaadddbdcbbdccbdabccdacaddccdbdacdbbcaadaabbadbbbddbdbbbbbbbdbcdbaaaaddbadbdabccbbbcbaaddcdccabcbdbbdaabcdccbbcaaddbacadcaccdbadcacbbbbdadccdacabcaaaadbdacaacccbdbacbbdaadcddddcabccbdcabdaaaccaacdddcddababcccacdbadabdcdacdaccdcacddacdcbadbbdcabdcbabcbdacbdbbacbaaaddadabdcbccbdcbdcddbbbcddadcdcbacbaabcdbcdccbdcdcbdbdcdddbcacbcdaddbcbbdcccbcbbabbcdbbacdddadcadbccabcadbabacadddbacabacdacaacacababababdcdabbcadbccbcbbccdcbdaccdbcbadaabbdddbaddbdaacccbcbbaddbccdcabaddadbcdadbabcbaddaaacaaabdabcadabcdddccaabdcbdddaabddacaabbaaacacabbaaadaccdddacbbaadbccdbdddadaaabbdddcbadbdcbcbacadcbabdcbadaabbcddacaddccdbddcbdbbccdabdbdcbcadcbbcbbaaaacabccbcaddbbdbbccbdddbdcdcacaddcacbcdcbbdbbbddcddacaabadcacbbccbadbbcdcaccadbacdcacbcddbdacaddbdadbadaaaacccacaabaccdbaadaacbbaababbbbcdaabadaacddddadaccddaccdccbaccabcacacbcbbdccbacabcacdabdaaacbbdadbabccbdacbaadbcdbdacdbaadaccbdbcbaaaddbadaccbbdcbcddbcccaaccddadcdaaababcbdddcdbaabbbdddaaddacddaddadacbbbccdbcacbcabcabddbaabcdaccacdcaadababaabbcbcddacaaaabccbdaaddbdcababbcbbbcaaadbbdbcddcdccccaadbabacdadadacaaaaaaabccdacbbcbabbcbddcabcbadbaddbbdcaddddbcbbbbdadbbbadabbdcaaabacdddcdcbacbbccacdbcaaaaccaddacadcbacabdbdaabcbabdbcbdcdbccabbaccabddbbadaddbbaddbdaabbcdadcbbacccbdbadbcbcadbdcbdbdcadaaabddabdcaacbcbaaacdbaadaccaacbdccccadabddcacaaacdbaabaaaaccbccdabaccbccdabcababcdcddadaadacccadcdcadbdbddccaccabdbbdacabaadbddacacccaadadaaddbbadabddcaddbbbdcbacdbdaddabddbbadadcccaacbadcccbdbbaacddbacabcdaabcccadcabdddabcadbdaaacccbdcbdbadcabacdadbcdbdbbbcdcadaccddbddddbbcbddcdcbdcdadadabdbddadcdacddcaababcbdabbabdbccbbdbddcbaddcdbacbdcdaaacacaaacadcadadcadddbbddaaadccabdcbacdaddacbbcbacadabbccadadbbaaacaddbdacdabbabbbacbaccaadccaadcbcdabaaadbaaadcacdcbbcbbbcbcdddcacbdabbcbcddccadbddacdccabdccabdabdbddcabbddcdaadbcacbaacdabbbcdbadbbcacccbdacbbccaccdcacdcbacdddacaaaabbbdcddaabddcadabbcbccacddcbbcdcdcdbadccaacbccabcccbabbcaadabaaaaccbcccbccaabbddadadbabbaadbbbcddaadcbcbcaaaaddcbbdcbaccaacddcddacacabaabbcadbdcddadcccddcdabbdbcbbccdbdaaddbddcbcacbcabaacdabbdbdcddacdbbcdcdaabddacdacdcbaccbbbddadbcabadcabadacdcabdbaaacacaddbdabcbbcccbabbccddadcbdbcabdcbbcbaaadcddbccdabdabaacbaacaaacccdbcacddabbaddcdbaacadcadaaabdadddadababbbcacccdaacbacdbdbdadbbaccbbdcbaabbaccdaaddcddadcbbccdcdabcdaccbabacbdaccaabcbacddbbbadccbbbddddbbdadccaadcbdbbabcabaaccdacdcabbcccdbbaadcacddcdadcabcacaabcbbacadacdccbdccdcdbbbaacdbcdbddabaddcddbdbadcbcbcbbddabcbcaabadddbdaaadcaccbddbaddbdadbddacbdaccbaaddacacdccddbacdbdbaaccdaaacbccdaabcbbddabdbacacbbccadcccadbddcccbdccaaccdddcccacbcddbbdbabbacbbbdbddbbdccbbbdcdbcdcdbcbcbbadbdbaccacdbbaaacdbdddbdaacbbbacdbbaaabccbacacbdbbcacdcbaaddbbaaaaaabadaadabbccdcddabbbaacabbddcddaabcdbabcbcaabbacccabbdcdbdccdaacdbcababaabdbbdddcadaddbcacacbabaaacdcaddacadddbdbaccadcccabaadccabacadbbaaacaaacbdcbababbbbaadbbccacddaadbcbdbdbcdcdcacccbadabbccbcbdbdbcbcaaacaacdabccbbbbabbabcdcbbccdabccbcababaababacbbdcabcdaaacbddbccbaacccccacbcddbcdbdcbcbaadadcbacbbdaccbbddbdaadcbacabacaaccdaddcaaadcbbcddaabcbbdaabcddbabbacaccdbabcacaddcdbdacaabdadcabbbbaadbadcacccccccabacdcaabcabbbcbcacacaacdbbabbabbcbddabaadbddbbcacadbdcbdddbaacdbbcdcdadabdddacaccabcadcadbbcadcbdbccbccaddcabdaabcbabaabcadaabadacabbaaacacdbaabadacdcbdbacbaacccbbadbccabdacdcdbabadcaaaaddbbbadabadabddadadbbbbdaccbcbbcddbcabaacabdcacacddbbbddadaabbcdcddbccbacaabdcdaddaacdadcddbacaccadbdcdcacdcdaadddadadcdbcbbbdadbbddbcabbcdcccdabdddacbdcdaacddbddccddaabdddcacddaaccdbabdcccdbcdbbcdbaddddbbacbdcacbdbbdbdaabdadaacccacabbbdabadcccaacadadaaaacdccbcadcaadaccaccaccdadbcdddadccdabccdcdabdacbbabbbbdabadbadddcadabbbcbcdaddddddbbcbcccdaaaacaaaadccbdcaabdaddbcbacaabbcdccaadcbdacccdaaddbcdbbacdaabacdadabadcbdaddabccdccabacbdcdbccbdcbdcccbbaccbccaacacabcbdadcbadacaaaccdcccdccabcadcadadabacbbadaaaabcdaccbcddadabccdcdcbcdbcdaaadcddddaaddadaabbdddcacdabdcababcbdbdddaddbadacdaddacdbcdbdadbdbdacabcdbabdbcaddddbbbbabdacbabadddddbbdddbdcbabbcdcbcaadaccacddbbadbcbaddcabaacabcbdbdcddacdaadbbbbdddaccaababaccacbcbccadbdcdbcbbdbbdadcdcbabbdbccdaaccacbdadbdbbbcbabaabaacbbdccdbddbdcdadbacaabcdacbbcbcbababbbbcbcbcbddabcdccaadddabbbbbdcdcbdccdacadaadcaabbabcdccaddcacdcaaddddbddddcdddcbbccdbbacbdaacbcbacaabcbcaaaabbddcbabdadccbcdacdaabaadddcadddacdccddcdadabbadbcdabdabcdbbdcccddbcbcbabcaddcbbccbbcabcbcdcabcbcddbadabcbabcaadbddcbddacacbbcbbaaaccbdbdbcccbcbabaaabdccbadbabdbaabcccbcdbcaddbcbdbddddbbddcbbcddcccdadddbacaaabaabaaddaccbadbdbdaadaddacdccddcdbbdadcaadadcabaccddbdbcbdcdabdabbbbcbcdcabcdccbbdababadcbacaacbacaddabbddacddabdddbababcabcbbdbcdaccaaacdbadccdbbabbadadddcdcbdcacbcacaccddabddccddcbbabdbbacaaacabccddbadccbcdcdbdddacdcaddcaaadbdddddbacbdcddccddcbabbacbadcddacdacddcdadddcbdacdcbaaaadbddabdaaabcabcdddbaaadccaacddbdbadaccacdbaabbdadaadcbdcdadbbcdcbbbddccbcbadbbbbccbbcbcddaaaacddbaaabcccbdadabbcddcbbcdaabbccadbadddddbdaaabbbdbbdacabbdcbdbcddbdbdaaaccdcdccddbbbabdcdbbbdbaccdbdcbcadacdcbabbdcbbccbccbbaadcccddbabbdcdbcaccababaddccabaddbcbcbdcdcdcccccabcbcabaabccaccdccdddbccbadcbacbadbacdddbdcacddaccbacbadbdbadcaaabbdbcbbadadcdabadcbcdaccadbaabdcaacbbbdabbcccbbaababbaccadbabaddbbbccdadddabbadbaddaaddcbcccbddbccacabaddcbbddcaacacbaacaadaccdcbbbacabbbcdcbacccbbabcacdbbcdacacaaaaadbacbdbdccdcbbcbaabdcabccbaaaadaaadbaddcdcdaccddcaddcbcacccaacdadacadbcddbcdbbbabcbcaabbdabcbbbdbbaaaccbdbddcdcdbbbadcbbbcbcddbdaacdbdbadddadacbbcbdabbdbdbaacbcbdbacbadddcbaacddcbabadabbaabacdcbcacbaddccacadbcbcadbaadcddcaabdaaacdaacbccbdbabdccdcacddabcccdbdaadbbaddddbcdcdaaaddbddccabbcccbbdcadcaddacdaabdadaccdcaccbcaccbdbcccdcbdccdbcbbdadcddaaaddccbbcddccbddcdbddaddbbcaabbbbddacdddabcdccdcacccdaacbaaddcdddbbbcddcbdcbcdaaaacabcddcbdcdcacaadadddbbcabdaaadcbdaaabdbbadaacdbbcdcbdbdcdcaaadabaabdadacdbacacabacbabcdcdbbabdbbbdabccbdddabcaddbcaabdbccacbbaaacacdbccbaddcbbcbabdbbbdadbbdadcdcdbcacdcbacbdabdcadbbccddbbdadccbbadadbbcacdadbbcbbacaadcabdcdcacbadbbcdcadcbadcbdcdaaacaaddbaacadabcbbdaccbdaaaaaabbbaacdcabcadabacdcddbdccaacaacdbcccbdcabdcbdcbcbcbccabcdddbbbaabdaabbddabadbbcbacbadcabacbaaabdaacdadadbdddadbcabcbadcdacddbcaccccaadcbccdabcabacdddadbacaaccbbbacadaddacdaddaabbbdadbabcaccdadacbbdbadddddbbddcdababbbcccabaadbabcccbcddbacadcabccbddabbacabacdacdbacbacccccacdcdccddbbbdccdabadabdddbbbadadadcbbcbaababacbcbadcabbaaadcccdaacbaddcdadabadbcddcdbdbadcdbaacabaadcbbacbddcabdcacdcacaabaadcaabbdbcbcddccbaddcdcbcbcbbbabacaaaaacaadabcadccdcbaadacbcdadabbcdbbcacbacababbdadabbbadbbcdcdcacaacabbcbcdabcbcddabbdbbcdbaadcbacaacbaadcbcdaaabdccbdbbbabaabadddadcacacbbcbadcadcadcacdbaadbdcbbbddcbbdcbcccadcabacbccaabcadbbcccaacbcaaadacbdbaacacacccbadaddccaccccadbbcddcdbbdcdacacddcbadcbcacaaabdddbccddabcbbcdbcbcaaddddacbdddbaacbbdddbdbdbddcdccddcdbdcddadccbbbbbdacdcbcaadbcbcdbddcbadbcdabbddbacccbbdabdcdbcddbabacaaacabcacdacdaccadaabaddaadddabbbccdddabbcbcccbccadcbdbbadcccdbdbdbaadabbaddddbdddbadababbdbccacaadabdcabcabdbbabdadbbaaacbcdacccbccccbaccabbcddddcddcddcddacccabdddabaddbdcddcbbdadadccbddcadcbacbdbdbcbbabbbbbddacdaccdcdaabdabccdacdadbaaccbdccababdbcbcaddabaddbcddacbabbccdbabbabdacabcbccbddcaddaaabddbbcaacccaaabaacbdadaaaaabbcdbaadacbcbdabdbdbbbbcbdcaddbbdcbddadbaabacdaaacabccdcbadccdcadadddddaacdbaacdcaaabbdcccaccdbddbabdadddddcbbaadbbcabdbdacabbddacbccdadbdbdabaccadbcabacdcbdbbcdbdcbbcaacacbddcdcaaddcddccbacbbbbddbdbaccaacacbacddacadcbdaaabcdbabbacadaadcbaabdccdbcbbcdbcbabddacacddcbbddabadbdbadbdcbbbdccbbaccdbbadcdaabdcbadadcbadbcacddadbbbdcdccddcddbcbabaacaccbdbaddaccdaababbbcacdabadddbcadcdaaddddddbcbbabbccbcabbdddabadaaabacaabbddcdbbdbdbbbccbcdacbbbdadacadbbbcccbddccdbbcaabadacbbddadbcadbacbcadcabdacbacddccaadbdcbbcdbdccabbbbaaaaacabadaabbacdcbbcbbbcdbdcaacbdadcbddabbdaacbbcaaabbbbdababdbbbbcbaacdbbaaadccdbbacaaaadcacbacdbaaddcabdcddaaadcbacacaaacabbcbabdabdcbddacbaaadaacccddbdbbaaacabaaddbcdccadbdaccddababcacabbddcddbdcadcabaadcccaadbccccdbdbbdcaccdddbccadbcdadbbbbbcaccdabbaadbaabadcccbcabcdcccbdccaccadccbccadcdadcddcbbccadddacccbcdabadcbdbbdabbdcdaaadbbcaadcadbcaabbcdaccdbbccbacdddacaaddbbdbbcbbddbdcdbdcadbbdbbbcaacdddbaaacbdababbddacbcdaabcbcbbcbcdddbababdbadcbccadbcdccccabaddaccdccbcdadbcaddcdbaddacdccdaddacdddccbdbbcdacdddbadadcbcaccdbdcdcccaabdacaadcaaccaaacbabaadcdbdadbccbadccbcabcdbaacdcadcdaaabbcccadcbcacabcaaccdbbadbdcadacdccdadccacccdacdcaadbdbbaadcaabdcbcdbcacccaaacbbbbbbaadbacbacddabadcbcbbabccbadabbcdcdbccdddaacaadaadccccdadbadbcacacbdcbcbaacdabcdbdccaacdacdcbccbdbdacdbcbccbbaaddddddaaabdbcaacdcbcccdaabacdadbacddbdbbbbbbccccbbdadaababcdbbbbaacbbbbcabcddbcbccabbdbacdbbdaacdacabdcdbadacdbbadadcbdacbdbddddcbbcbccbdddabbcacabacdabdccbacdbdabbacdcdcbacbccbaabadbdbbbdddadbcbdccbaaddcbbaadbdbbbdbacdadccadcacccddabbacccbbdadbdcadadddadbadcbcacaddcbccdbbbcbbaccbdbacbcbbbccdadcbbaaccacdcbbdcabddacbbdbdbaccbdabccdccabaccacdaaadccdbaaddabcbbbdbcbaddaacccdbcccdabcbcabdaacaaddcbdbdccabcdccbbababbddbbdacabaaabbdaabadbcbbdbcdbbcadbaacbabddbdbbabddbabdddcdbccccccbdaabccbcddbcbaadddccdadabcacbbcbcddbabcdbabddbbcbdadccbacdaddaaddacbbddacdbccdbbcaadcadcadadddbaaacdbbaaccadcbcadbcccacaabaabdccacdcdcbddbacccbccdbabdddcaaababbabdacacdadbadbcbadbcdbdcdcaccccdcbdddddaacaccdbadbcaddddcdabbbadaaaccabaddccadabccdbbbdddbbabddbcdbdbbcdcabcdddddbdbbdcdadadcbaadabbadbdbaacaaccadacbabcbacbbaaaccadbaccbdbabbabdadbcdaacddabcaaccdacbacddadcacdcccbccacacabdabdcaddbbcdcbaaaaadbabbdddadacccacdbdcdbbdcdbccbbaaccacdbbdbbccabccababbcadbbdcbaccdddcddcbbdcddccaccdcbaddbabbbacacdabcaabddddaaacbdabbacacccaadddaccccbdacdaacbcbdccccacdbcdbbcaddccabaccbdcdbcdbcdadaadbcbbbcabaaacdacddbdbcabcbabddbbcbbcaddaabcdbabcdbddadbbdbdbaccadccbbbdabadabbbdbcbcdbaacbadcdbbbddcbcbddbdbbdcdbaaacababdcdcbbcaccddddbaaabddcaadcdbdaabccdacdcbdbadaacbddbdbdabcbccabadcadcabcbddacdcdbdcaacdcaddcadcbbdccabcdcdddaddbdaabccaadbacdbdbabcdbaadbbacbbabcdaaaadacddcbabaaaabcacbbbaaddcdbbbcddbcadccdcdbabcbadbdaddbacbddddbcdcdcccdaddaccacaaacabdcbcbcccbbcdabbddacdccbcacaabdacaababdbcbbbaabdaaabcbdccabccccababbccadcdcdcabacccddbddabbabbdddbcadcbdbdabdbdcadcbacacaacabcccabacaabbdcbdaccbacbadccbdbdacadcdabbdccbababdacabbcaaabcbcccbbdbccbddccadcccbaabdbcaacabcaddcabcccaddcacabcbbabaadbdababcaddaacbdddababdaacbdcccdbbadbcbadcbaacacbacadddaddbcccbddbbcaacabaddcbabddbccbbdaddcdcbbcddacbcddbaacabccbaadbdabaacaaabbcdbdccccbcaadadaaddacbcdabdcadcababddaddcdbacbdbbaaddabccdacbbabdadbcbacbaddbbbdbddcccdddcbbaccababdaccabaabacaacbdbbbadccbcbccaaadadbbcddacaccbabcdcdabbcdadcdaddacabadbdaababddaadccdbcdacbadbbabdcadadcaadabaadcacccdcaaaaaacdbcbdaaaddacdcddbbcddacdacccaadddaccdcccdccacaadbcaacaddddabbcaaabcbaccacbcbabdbdcbbadbadbdbcbccbdcbbbaadaabdcadcacaabcacbbaaadddabcacdcbddbbaadccdbdcccbcdacbdcbcaabddcaddcdabacccbcbdabdcaabadbcaabaaddcdacdbcbdbabdbbaaadabbbdacdbcdddabdbbddcadaddbcccdacdcdadbdaacaddcadadaaabbacbaacdadbbbbcbbbbbcbcdaaacaabcabbccacadbaadabcacdabdaaddccadcdcadcdcadbbccdacbccbacbdddcbbcdbbadccdddbbaacbdcaadbabacdcbacbdbdadcbbbaadbbdabcbabadbdbdddbbacabbdccddddcbdbcacbbccbcaddbabddcacaddcdbacdbdbadadddddbddddcddaababbddbabaaaaacaadcccbacbcccdcbbcbddacabdbcadacdddabaaacacdbbccdbbbcdacbbcdddaabdbaccbcacaacbccddacacbaccdacdcdabdacbcaaabbbadcdcbcbbaccddbcadabbcdadadccddabbccdcbdbbcbdbadccbabbdacbabaabcbdacddcabbdbccdadbbcdbdbbccbbcdbdbbacbcbdabccadbdbccbbdbbdacabdbacaabcaccdcbadcbbbddabadcbdaaaacbcaacddcdcaaccddbbbddccdaadbdcbddcbaabcacbaababcccbacaacdabbddbbdbdcabcdcbcacabddbaaabaabababdbbcdcdacccddbcccdcdacbbccbcccccdadadcaaccbcaacbabaacbbbdcabadddcdbddbadaddcbcadcdbdccacadbcbbbbacbcdabdbbcbdcaababcdddccddccbdbdbcababdaabdcbbbbaacdadcbcaddbbddbdccabaaababcbbbbdaabdbadadcbcdbbaaacbacdddadaddcdcabbcabbdadccbabdbbbbababadddbbbddaddcdadbadbacdbcbbcccbaabaaadcbcdacbaacaabbdabbdbbabccbdbaddabdccccaaddaabdcaddcadabccababbcddaaabccbccacdadccadcbccaacbbbcdccdcbbdbdcddadbbbbddbbdacaaaaadabcadcaccaaaaccbdccddbccabcccbaabadadbdaabbdaabcbabcaacacbacdcdcacbbabcbddabaccacddbabddbaccdcbadccacbbacbabbbcbbdddccdacbcbccddaccddacabaccdbcadcadaacacdadaacbdadcaccaddcaacabbdbcdacccbddcadcdcadaaaabbdbddcaababdddbbddacbdbbbbbcdcadacdaabdacddcddaadccdaddbdcdaccaccaddbdaaccddacbdccbadccccbdddadcaacadbbbbbbaabcdddccbcbdcaacbcacadbbcabaccbaccbbacacccbadbdbdcabdbbbddacdbbacbbbadbbdccbdcbcdccddacaccacccbcbcdbababdbacbabbbaccdabcbcccccababbcdcabbcacdaacdacbabbdaddadbbdcadbadbdcdbccadabbbbaccdccbccddcbdaadcadacadcabdbcadadbddccbbbbbdbdcaadaaddddbaababcbbbbadcbbacadaddaddbbbaadcbaddbccabcdddbcaabdabbdcbcacacbcadbababbbccbcadabddbdacbdddaddcaaabdcbcdbdbccaaaabdacbdadabdabdcccbddaadaacccbdcbccbbdabdaabbaadaddadaacccdcdaaacddcdadcdbdccadddaaabccddbbcbcbdacacdccddbdacdadcaaadbcccddacbbbcbaabbbcbcdaabbadbdbcbdbabbddaddadbdadbabaacaacadbabaaaabbacbddabbdccacccbbdbabbccadacadddbdddcadaddacddcccaddcabdcaabcaadabcbdbbddcbabcabcbbccaadccdddbbbbdacccddbcdcdcddbadcddbbdbbdbcdccdabdcabdcdddccdabdaccdbbdcdbaaacccaccbdcddcacabcabccdbabccbddcaacccbddaabdaccbccdbacdcaddbbaccbbbcacdddcdbcaddcacbbcdcdccaabbbadcbbcbdbaadbcadcdaddbacdbccccbdccacabdbcdbadaccddaaacdbaababacdddbddabaddabbbbcbdacbddccadcdbdbcabbccbdabaddabdbdaabccdadcacaddcdabcbbbcadcccdddcdaddddabdccacbabcbccdaabaddacccbabcbddcbaaacacdbdbcccdcacdaddacbdbabbdcdbccbaaccddabcddabbddcbdcbcabbbbdddbdaccaccbacacbaadddcadddaccbbddabaaabaaadccbacadbcabcaddbdcddbddcbadadbabbbdccbdddaddcbbabaaaabcdabdcbddccdccbcdcaacbddacbbddcdcbdcdcdbdcaddbdacacdabbababddbdddcdbabccadddacbcaaaadabddbdcabaaaadcacdbbccababbbdbdbbddddabbcdcbcccabdadaaacdccaacdaacbbdbbcaabdbaddcbcababbdddcadddcdbabccbaacbbcaccadbbdbbbdabbadbddddcbabacddbbcdcdccacbbcbcddaabbbdbddacadcaadccadadccababddcdacadcbbcbdcbccaddccbbcdaabcdbcdbccaccabaadcabadcbdaabdabadbadcaddddabbbbaadbbcaddbcbadacdbabadccccababbaadbbaaaadbdbbbcddbbbbcaaddddadccabbbcaaaababbdccabacbdadbbcbdadabaabacacacdcbbdbdbccdcbacbadcdcacddbacbbabcabaabccbbbdccabdbacbcaccabccabcdbdacdadadcacdadccaacdbabaacdddcaaccbabbbcbbbdddccccadaadacccaccddcddcdaaccbbdbdddbabaabdaaaadccbdaccbaabacdbccbbdddacddaaabacdbacdabacadcbadcadccccabccdccadcbbbdbdabcaaddbddddccbcbadcdbbccabaacadbaaacadadbbbabddbbdbddaadccbdcbbcdabbabcccbbaacdaaaccacaacbdaaadcbbcdabadaddccbbddbaddaadbcdbaadbaabbdbdbbadcaabbdabadcdabdbadcacadbbabcbdbcccbcbcabdcbdbcbddaaaabdcaacdadbbdcadabdaabcbbbdbbdcaddbacdcacabdacdababbacbdbccbaadaaaccadaaadbdaddabccacbcdaababdbdcadbdbdcaadcbcacdabcacbbcdcdddadadcadbbcddaacbdacbadddcaabddcddbbbbddbcacbbdbbabacbdaddccbcbaccccdddadacdaacdbbabcddaacaddbcadbadaacbdadbadbdadaadcaaddababaccabbaabababdbbcacaaccdaabcadbaddbddbcdbbbdaaccabaaabaacdabcbdadbcdadcccbcdcbaacbcbcdcddccbcdacabddbacddaaccacbcbbbbdaabaddbcbdcdbdcbcbaccbbccbbcdaaacbcbadcacdcadabbdcadcdbddaddccaddbcaccadddadabcbbdabbbcadcddbaccaccddaabddbdcdadabbcbbbdddacddadcbbcbaaacccabddccabdabdbaaccbaddcdbaddbbdbccadcbdcddbadccccbcdbddcbcdadcadddcbcabbaddcadacacdbbdabbaabbbbcdbbcbbbccaabacbbbcacccbaadbdcdcbbaddbacadaddacacbaaaddbbddccdabacdcbbdcdaddadaabbadabbaddaaabdcacdcddbcccdbacbcabbbadaddaabbaabcdcddcbbbbacacdabdaddccbadbacdddcdbcaddabdccbbdbbbcbdcabacdbaaaccddcaddcbcdabdcbacddaabcabcbcaadcadddbbbdcadbccbbdbbcadaacdaacbaabcdabdbcbcdcadabbdbdddcdcbbabbcbdcadbbaccaaabdccdcabddbcccdbbcbbbacccdaaaabaaaaadcaadccaacadddadbcdabdaacacbabddaadccbcbbdadcbbccdadccadadbaacbdacdaccdddbdacccbcbbaccabacabaaccbdcacdaadcabaddbdaabdccabbccbbbbaaccbccacbbcbdcabbcccdbccabccccccacccdadaadddddcaccdbdbdddddbaadacaacaacabcbcbdcdccacabbcccbaccdcaabccadabbbdbacbddbadadabdababcbdcdacabcadccdddaccdcadcbcdbcdddacabaacadaadbbadabbccccadaddacbdacdabcaddbadcddbbccbcdaadcdabbabbaaaacbddddaddbacaaacdabcbcbcaadddaadbbbacbcaaabadbdcbbddccaccdccbdcdaddcbcbbabbadaaabbbddcdbabddaccaaaacdacccbcabacacadabbacbdbbdacadacdadbcbdaabcaaabccdbcbcbbdcdaccbacdaccadcabbcbddbcadaaccbbccaaaacddabbbadbabdadacaccdbbbddcbdabddcdbbaacbacadbbabbccdbbbcdbabdacaacbbadcacacbddbdcabddbbcabdbaabcbcddccaddcbbcbadbabccadcadabbadadcacccccdbccbbaddadcddcaccbbdbcccccdabdbcaaccacacdcccdbdcbcabdcaacadbabaadddadadbbbcdccddabdbcabcdcddacadccbdadcdcaaaabbddbcacabdaacddbadddbdaacddbcadcabcabdbadabcddbcdddbccbdddbbccaadccbabddbbdbcaaadcccaabccdaadbddcdabaadccbaccbacbddcbaddbadccddabdbaaababcbbdacddddaacdcaddacaddcbcacaadabcabdbcbdccdbdddcdcadddbabdbcaacabdaccbcbadaaaaadcabadacadadbcdacdcaadaaddccacdcbdabbcabaaadcbaadaaacdacccccbaaacdacabbdcacadacacddadbbadabcdaaaabcadaabadbcbacddcbaddcacdbddbdbcbbcacbcbabcaabccbcaadbbddbcbcabdcbcbcacbbddcaaabadbaadcbcabdbcbbbdccdacddbbbbccacbcbdacdbcdbdbbabababbbbabadbdbbabbcacdaaabddbaacddbbcdcacaaadcbddabadcdbbcacbaaadbcbaadabdbadccbcabcbbbccabadacbbbccdcbdcbbaaabcdacdacddbdacbddcbacccbaabbbcaaadbdaacabccadcdccdddcdcaccdbbacdbaabddadaaccbcaddabcacbcacdabbddbcacbaaaaddbbbbcdbcddadccdabdddcdbbdddbbdacddbadacdbcdcaddabdcbbbbddbdaccccadccbdbcbabcaadabcdbdbdbacdddadbabdbdaabbabbaaacccabcddcacdabbadcbbcdbccdacddcddcdbdcdabbcbdbcbacddbdbaaabbddbbcabcbdcbdddcaadbbcabacccaabbbddaaaaccadacdbbadabdbbccbabbbadaccbbcaadabdabdbbcddaddacdaddabdcadcdbababdbbbdbdcaadaaddaadcdcadbbabdcbdbdbdadcddadcaddbdacabdcaabbddccdbbbbbbdbbbabddcaadddadbcaddcddcdcbdadadacaabbccabdcddabdcdcdbdcabbcddbaaadaadabcadbbccbdbccdaaccbcadcbaaadbbdaaddbdabccdbbbcbcbdbdcabbcdbadbccacbcdcddacaaabdccddadaccbaddaccadbbbbacdabdabcdcadbacdbadbbcdbaabbccdbacadbccccbdadabcbdddbbdaccadcbbcdddcbccaaabcaabddabbddcccdbbbadddbbdcddccbbcbbdbccdaacdcccbdbccaccdddccabdccdbdcbccbaddbddcdbccaaccaadadbabbadccddaadbdcdacacadcddbabbcaacabcdabbbcbbacaaabdaddcccbdccddcdaccbdbcbbadabbacaadadadccdadbdcaaadaddabccddaaccacbbabbcbacdbbabbcbbdbcdcbdcbcabddddbdacdbaadcabcdabbccdaadacacacccdddcddcccbaddccddcdddababdcadcbdbdabbcaddacbaadbdcabadbdabbadbbcbccccdaddabdaccdadaddabaccaddaaaaaccacdbaddbacdcbabcaaacacbabcbbdbccdcccbbdaddcabcbbaacddbabbdadbaccbccdbacbadcadbcbbdacbccbdbdacbccadaababadabbbdcbdbdcddabbccdaabcacbdbabcbdddddadbccacacbddcbdaacabaaaadbccbdabcbaabbcaccacbcccbcbcadcbcdacacdaabaccdddbccacbcabdbbdcaabcabddadddcaabccccdacaacacdddcddcdbbccbcdbadddaaadcbcaddbdbabbbcccabdccaaabddcbbdabcdddcccbbbcdcaddcccdccdbdcdbcaccabbbcbccdbbacaaddbdbcababcdabdbbbabcbddddddbcbdacbbdbccbbddaabcccdbacbdbaaacdcbabbabbdbcbaaacdaccbbbddcdcabddcbdbcacadbcdaacadbcdcababacddacccbbabadaadcacabdccbbbcdcbddccddacdbdcaabaaaadbbdcbcacdccccbbadccccbdcddaddcbdadcddaaaccadbcccdaacccccbaabdcaddcdadbdadcabadbbbacdadcccaababdcbddcdcaacbaadaaacaabcaaadbaacccbabadcabccadcdcbadcdcdbababadaccbacdcccaabcdacbdabbcbccaaabacdabdabdcdbbcacccdbcbcccdadbcbbacddccbadccdccaddbdaabadbcadccbbaacbaddcdcdbcbaccacddabcdacaaadcabbabbdabcdbdadcbcacccbabbaabbcbcccbcbabdaabaacddcbabaddbcbaaddcbccacdbcbcbbddcdcbaddcbcaccccdbcccadddaaabaaccbabbdcdcbdabbccbcbcbbadddcabbadbcddcaccbcabcaccdcdcacccdccddcdbabbcadbcccbdbddbacdaaddbcdcaccdcbdccabdcaaddccbddccdaabcdaacacccaaadcadadaadadbabbcdbccadbcbdbaaddcdadddadbbdccacbcacbacccdcdaaaddbdcdabbaccdddadccbdcddbdaabddacdcabdbabcbbcdacabdcdcbccdabcbcdaacdabbcabcbdccbaaacaddcabcbacbccbdcaabbdbcabddbbbaacaabccdbadcbccdccbdbdcbbcadbdcddccaabcddcdddddddddccbdababcdcdcdabccccdcadcbddcbdbcbdcdcdbcbbcdccbbaccbbdbadadcbaabbbbcbcadbbcdbbbccbddbdaddbabbdbbcbcdbcdacbabccbcbcadcbabadddabadcacaaadacdbcacbbabcdaccaacddbddcbdddbcbcccbbacddccdabbbbadbcbaaabacbbbdbaddaaadbdddababcabacacccddacabdacaabbccbcadcbcbbdcbcaaabacacdacbdcccdcaabdbbacadcdcbddaccbdbbaccacdbabcadcbcddbabbadddcbabbcaccaccdcbccddccadbbdcbabbbbabadcbdbcadcdddbbdabdbabaacddabbcbddbdcccccaaccdaddabdadacccccdcbcdbbbcaaabccdadbdcdcaccdbdbcdaccbbacdadcdaddccccadbbaacddcddbbcdadaabbcdddadbcbbddaaadaaababcdaaccdaccdccacdcdcdbbadcacacaabdcaadbbbaadcbdcabaccdabadaadcacddcbaccbdbabdcbdcaaddcabcddcbcaaadcbbbddbaabbddcbcdbcadcabcbdcbdddcbbbadbcccacdbdddbbabcdddccadbaadbdbbdbbcacddadacabdbbdcddcbdddcaadcbdccbaacabddccadadccbaaaddccbdbabdbccaabacbacaabbdcaacdccaccabdaacbdcaadbdadaacdbddddcbccabcaadbbdadcdbdbdadbbabcddacacbadbbacacdaaacbababaddcbbaddccacccacadcdcddabbaadcabcacbcacacbdabadcbcdddcacdbcdbcadbcdbccacabcccccdcbaadbdcdcccbbbbadcdcbcbaddaabdbcccadadbabacabdaaccaadbcdaccadacbcbdaccbbabcbcddabdcaccaababdaabbabaddccaddadabbabcdcaddcbbacdbcbaadcaacbadccdcccbddbcdbbbaaaddbcacdbcbdccaaccbdbbcabaccabccddcbababaabbcacabaddbccbcdccbbcaabaddcdbdabdadabaabaabadaadbaccdaacbcdaacabbadcadbaabadbcbbcabacdccdcccbbdbcbaadbbddddcabacccbcacddbabbabccddccdccbdcbbcbddadcdbddadcdaaacaddcabaabcbdcddccacdcbbaadcddbabaacbcabcdddddaccdcaadabdadbbabdbbaaabbbddbddccadbbbbbcbcbdacaddcdbcdcabbabdbdcacdbcddabaddadbcbbcacbabcdcccaabdcaacbddbcacadaaddddadaccdcdabccadcdccacdbabbaddcdbacbdaddabbbaabaadcbddaddabaddddddcdccacbbccbcdbacbbdabbbdaabddbbdacadacabbcdbbcaacaccdaddadaccbbaaacacccacbabccbaddcbbadcbcbcdcddbccddbbbbbaaaabadabdcbcacbbcaccbabdaabbdaabadadadabcbbbabbdcaccacbbdbaaadcbdcdcbdddbaacabdbcacacbbdaccdcabbdadbdbdcdbbdbdadbcdddbbdccdacadddccbdadaaaaaadcadbddbcababccaacbcacdbcdddabaabadbcacccabaadadaaaacdcbabcadcdbbacaddacabbbccaabcdcdabbabcddbccbdccdacdcbdaaacbcacddccdbcbcacdaaabbdaaacdccdccaaaabcdadcdcdddcdbbabbacbbdddacdbcabaacddccddddbbaadbacdbbddcbddacbdbdcbcccbddbddbbbabdbbcddcdbdddaaadcdaaddbbbbbbbbaacbdabbccadcacdbdacdccccdaddabbaacacdabaccbbdcacbdadaaaacdbdaabccddbcccdacccccdcaadbdddabccbcbdddaabbdaacdbdbdbbcaddbcccdbadccdcbaabdbddbbbaddbdcbaabbcbdcbcbadcdbcbcdabbdccaaadbddccaacacbddbdaddaddbccaccbcadcaccadabddcdbbbbaccacabaabdbcadbaaccabcccaabbcbcaadbdacaacbcaadbcddababdccabbcdbdadbabaabddcbdbcccacddbadadbdacaaaadcabdcbdccadacdacddddbbdddccdbbdbadbbcdcbcaabababccccaddabbcbcdbabacbdaadadbaddadbabcbccdbcbacbcbacacdddbcaccbacdcbdadabbaacddddaacbdbbdbacbcabcddcdacbabcbccbacdacaccbddddacddaaabdddccaadbbbaabaddcaaddbdabdddddcabcbdaacbcddcabdbaccbacdaaddacbdcdcbbcccbbcadbcacaacbbbcdabdbbcacdabbbdcdcadbbbcbcdabcbacbbdcdaaaadbcdbaabcaabddcccadcbdbbcaacddabbaadadacabadcdadbbdbcbadcdaacadcddacbdacbcabbcddaccbabdcdcdcbaccbbbddadcaabdcddccbbbdcbccabbdbcbddbadbacbbaaacccbcbcbcacdacadbdacbbdbdaadaacaacdbadbbbdbcadcbcdaccbcddcabadacbcabcdacbbbdadaddacbcbdcabdbacbcdabcadbdcddabcbdbacaaccbcbbabcbaaddcdbacabbadcadcccccaaacaaaadbbaadcdaccadaadddbacbaddaaddabdccaadddacccdddbbacaabdcbaccddaaabbdcddabbcbcbcbaabdccdddabddbbacbcbbcdbddbcddbadddbdbbdcdddaabccacadaaddcbacbdbdcdcbccdbddacdbbbcdacddbacccdbaadddccdaccaabbbbacaaadcbcddbbabcdacdaaaabdbadbccbdabdabadbaddccdccbdbdbadcdccacbbddbcbabacbadbddcabaadbcaccbdaacaabddddbdbcdccdabdcdbacdccbcbaaccbcaddbbccadddadbddbdcddddcaabdbcadbaabaaccbcbdcacdbadaabcabdadadbacdabdcdccadddabdccacdbcdccadcaaccbcddcacbaaaacbacaaddaaccabbcaacdddbdaddaabbbabcabbbddacdbdbbdadbcaaccbccbadabbaadbdcbdbabbbacbcadcaabdabdbcbadcddbbbdbcbaddbcadababdbbaadbcdbbdbcdbcccacccdabacabbbccbcabdbcccbbdcbdbadaabbaadcbdbdcadbbcbcbadbaabcdbcadbcbbaabcbdcbaaaaadbabbbdcbdcddbbddccdbbbcddcaadbbbacaabbacddcdddaddccbabbdaccdbcadbddabdacaacadcccaddddcccdbabacbbbbbbbbdcddcacbdacddcbdbaaabbdacbcaacdddcadddbccbbabccdbdbaddcacaaadacbbbccddbcaaacbcccabddacdbacacddadccbccbbbabcccaccaddcacdddcabbdadadcabaaabbcdddbacbcadadddbcadbdbcccddacddaaaacdaabcbddcbaddaaabaaddcccbaacccadabdccbccdbbdddbcadaadbdbaadbbabcbaaadaadaadcbbaaacbcaddddbcbdbcdbaaddbdcdccadacdbbcdbdbcbbcddcabdcacbbaccdccbbbbbababdcaccabcbacdadbbccabddbadabacdbdbbbdbcabbaadbabdcbaabbcdccabbdbdbbdbcbadababacbbadaadcadddbdbdacbdbbaabacacacdccdccdcdaaabccbbbddaabbcbddabccabbbdcdaacdbdaabdabdbbdcadcbbcbadbdbadbddbdacbccaaadcbccbcdbbabadddccbabdcdabdabababbbcbcdddaacbbbadcddaccdaacacacdddbadcabbababaddbbacaacbbcbbccadadcddbaababbacdcaabcaddcabcbaaccbdcbcadaddbbcbdbababdadaabbacabaccacdcadcbdadbbdaccdcacbcbaccdadddddcdbabccadccbaabaadaacbdcbdacdcddbaddbdbdbcaccdcdaabbbcaaddbabdcbccadccbdabdbddddcaaaadbcbdbbddddbacbaaaccdaacaabacbdaadcabccbbdbcacbcdcdcdbaaddbbaaddcbdadbbccddadaabcabcacbacdbabdbaabaccccbccacacaddbcbcbcbaacbdaaaadbbdbaababdcbcdadbacddccacbddcdacccbdbcbaddbdaddbabcbcbbbdbbbcbaacbddaaacdbddabaccaadabdabdcbcddbbbcdbacdcccdccdaaadcacacacdcabbcbcddacbbdccbcaaacdcbdacbaacddcbbbbaabdddbccbbddbdacccddbcbacbdacccaaadcdcbaadddcddaadbbbbbdcbaaaccddddacadabaabdacbbdbbdccddddcbdadbdcbaccbbcdadcbdbdbcddccddbcddacbaabbbcdacbbddcaddbbbdadabdbccbbacddcddaddcacbccadbbdcaddaabacccbbcbaccabccbacbcdbbdddbacabadcdadadaddcadcacccadbdbcbdcacddaccdbcaabaaadcccdccccdcdcbaaddaddabaaaaacacbcbbabccbbaacccbddaccbbcdbacbdaadbdaddabdacdcccadddadbabacaaaacbabbabcdcbbcdddccacbcaccbadbadaaccabcbddabbddbdccdbdcbbbdaacadacddbcadcccbbbdaaacadbbabacbccdbbbbccbcacbcddabbadaadabaabadacbddcbcdcaabcbcbacdadcccbdcabbaaddcacccaaccaddddcbcbdbadbababadadadbadbacabacdbbdadbccbcaddbdccccbcdbbbaadcdacadccacccadbccadccacbcdbbddcabbbaccbdaadbdcdcccaabacadacbbcbcbcbbddbdadcdabddcbbbdddaadccbbadbadaaadbbadaaabcadbbbdbaccbbbdcdadbacdbbcdcacbdbaaabbdabbacacbbbcdacacaadaaabadccccaccbbbcddaadbcaddabaacaaacccddadacacbabcadbabcdcbbbbdbbbcaccbbbcacdacbbadcdddbdcddddadcdccccccbabcadbcaddabdbaccbbdbabdddbaabdbbcccbccbbcaacdbaacacaacabcacccabcadadccaacdbdcdaaccdbccccdddbbaccbbacaaadcaacabbcabdcaabcaaccccdcbacbdccdaaccdcdbdddddbdaccacdacbdcddadbddbacadabaabbadbaccacdbcbbbadddcdacababcdacbbbaccbbdacddcaabadcaadbaaabddcbbddbbbbccaadbdcbdccdbbdadadbcbccbbacbbaaacadbadadacddabacdaacdacaacdacbcbaaacacbcdcbbdaabbccdbaacaadcaaabccbddcbddddcddbaccbbbacbbcaabddaaddadbdabdabacbacbabdbbaabbbdddbdaaccdabdabdbccbbcbdbccdbccdcddddabacabcdcabcbabbccbcabbcdcdbccbaaabbdacccaddbaacababdbacdcbbbbbabcadabdbcdadacacbdadbbbdbdcdcabddbbdccadadbadacacabbadbdddbdbcacabcbadadbddbbaccbbbbcbaabddcadbdcbacbbbaadddcdaaaccbdbccacdaccdcccdabcdcdccccbadcddcabbdabacdccbcbcabcddcabcdbdddaddddaccdacbcbdbbccaaabdbbbdacdcdcaaaacccdccbbdbdcabddbcbdcbcaaadcbacabcdbcdbccadacdbcbabbbabdabcabcdadcadccbcaaabbacabcdddaabadaabdbddccdddaacccbcadcbdcbacbbdbadcdbbbacbcbabddadabbbababaacadcacbdcddbdddcaaabacadbcbbddbcdbccaadbbcdabcccadbdabaccdaaccacdbaabaaaabdaaccabdbabccdaabbbbdcbabdbcdadcdcddabaabbaccdbadabaaccbdaaabdbbbbaccbcaaabdbdcacbcdbaaaadadbbaabdbcbbabbcdcaacacbbabbabdcbbcbaaabbccbdbaddccccacaccddddcccbacccaabbcadbcacddaccbdbdcacbacdbdadcbacabadbcaddadaaadcbabbaaddddccddcbdbdbcbaadbadccaaccbcdbcaddbbcbcbbcbaccaabacdccaaacdcdcdcacabbdbcadacaadddadcdbbaaabbadccddabcdbccadccbbdababddabaacccacbcabbdaaaaabaaabdbbbacdabbacdcabbadcbbbcaadbadcdaacddbbadaacbcdaaccbdbddbdabddcadbbcaaacddcbcccabbbcaadcababccabdbacdcadaaaaadcaaccadbcdddcbbacbcbdaccbcdccacccaacbdcddabbdacababbcccbcddabbcaaccbccbcccbddaaadccbacbdbcdbaaacabcdbcdabbcbabddaabdadbdbdbdacddcdaadcdcadbdcdcccabaddbdddccbcbcbaadcdbbdabaaddacdaadcabcbabcccdcdccbdbcdadaabddababbbcccbdcadaaddcccccacdcbddbdbdbabaadabcdbacbbcabcccdaaacabaaabbbabacccccbdacbdabadbabcbcccdbadcbbbcbbbaacccccbbadaccbdbaaaaccccacbacdcdabadbdadacabbbdbdddbdcddacbaabacddcaabdacaddcaadbbcccacacbacadcdadccdaabdbdbccdabdbcccdbacadadccddcdcddccccaabdbdcdbdcdaaadadaddbbcbbaaddbbbabacdacbcadcdbcdbbbbbbccbddacadcbcdcabbcdbddcbcbcacaddadabbcabbaaababdbdbbdbadbbacadcbdabbcbdcbbcabcaccdccdccccbcccccacbcdabddadaaadabbccddbdacddcdbbccddacbdbbccdbadccacbcdcbbcdaabdadaddacbcdbbacbcbbddbbdcccdacbdabdababacadcdddbadaddabadcaaabcbadcbacadddcbaaddcbdcdbdababddbddabbadcccbbbdaaaadbdcbcccdbbbacaddcaabbabccbdaacadcbddcccdbbbacbcddbababbaadbccabbadacbbacdbacabcbaadabadaadbaacbbabcddadbccbbadacddacbadccdbabcdaaabdcabbdaadcaaadddacbdcbaccabaacbcddbcadddbdabaddaabdbbbdaaacbbbcabbdbdbdcbdcccddddccaabcdcddadadabaacdbcdbdaddaadadccabdbbcbdacbbcacbabaacaccbacaabcdacaadcdccdbbaacbacccdadaacbacaacaddaccbddaccbddcddbbbccdcbbbcdbcccabbacddacbbaabbcabbdaccddbbdcdcacdccdadbcbbddbaadbdddcdaadabbcdcbdddddaadabadddbbdcccdabcdbdaacbabddabadbcadbcaddaabcdbdacbcacdbddddcdbbcacdbddddbcbddddbabadcdddbaaddabbdcbadaddddbaccbcacaddacacbaaccbccbdddccdbabbcaacadbddbbdbcbadcadbbcabccdbcdbadacdabdaabaccbbcadaddbacbdcaccabaaacbcccaaaadaddcdacacbcbacbabaccabbccdbdbbccbbdaaddbdcbdbcdaadbabdbcdddddbcaddabdadccdddccdcdbaaddcbcbddadcdadddcccdcabbbcdbcdddaccccdcbdaaacbccbcbacaadaddabcbddaccbacaccbbababaaccaaabcdddccbbdabdaccbaccdacdddcbdbbbadbdbbdacabdadcabccacbaacacbdabbdddcaccdcdcaddbcbaacddacbcabdcdabbcdcdddddaccbabcaaccbaacccadaccadbcbcdabbbddddbababddacaaddaabacdaaadccbbdccbabbcabcaacadbacdaabdbdcacaaddddcbaacbbbdcdbbcaaabaaaddabbdaacacdddcadbadadaccbcbbdaacbdcdbaacbacdcdccdbddcacccaddaaacaadabcabdbdcaddaadaacabdccbcdaaddcaccaadbbbcdcbbcbcdddcabbabccaccdcadcbbbdbcbcabcccdaadabbadccbdabcbbbcdcbdccbddaaadadaadadaadabaddbabdbdcdadcbbcdccdddbdccacddbddaababacbbbbcddbabaabddbcabdcdbacadddccbdccacbdbadaacdbddbcacddccbdbacbbcaaacaadacbaccbbcaccdbcdbabaccdbcdaabbddbbdbbcdabbddcacaaadbcccbbacabccdcbbbadabbdbbccbaccaadcbdddabaabaddcbbbadbbbcbabdaccdccbcdddaacbaccaabadadbdccaadabdadcaccaccaddcadabbbabaadbcbdcacbcdaacaccdbbbacbaadcdbdadbcaccbabdaadddcbdadcbcdbaccdbdccbdadbbdadacdbbbaacdbcdacccaabcccddcaabdabcadbdaccdcaaaacbbdbcddbcbbbccdcdbbcbdbbcadaaadddbabccadbbcccbcadbdccabadcdcaaaccddacddbacdacddcccaadbcabdabddaaabbadcbcbcacdbaaaddbbaadcdccbdaccddbbaaaccaaadcaacccaadbcadaacbaaaaccccbdcbdbbcadacaccdadcdcbcdbcbddcacccccaadcdcbddabbccacabdababaccacabcbccbacdadbdabaccaddabdacbdbbababdbaccdcddcdcadcbaabdaacdbaacbddbababcacaddabccccbaabadddddabdcbddccabcbcaadbdbabdbbadadaadcdacbadbbaabdbdacdbbadaddcccdcdddcbaaaccbacabdcbdccadcacdccdaccddccccabaacbddabbddddaddcbbcddbbccdaddaabddddccaaaccbcaacddbbddcbacaccacbbabcabccddcdcbaaacccdaccbdbdabdabdaaaaacabbbcabbdbbdadcaabbcdbcabccacbcbcbdadaacbdababbcaaddbaadbcbaacdbbdcadabccbaaacaccdbcaaadcacadadcadacaabccdbcccacbacbbbcabdaccdbbadbdacdbaccbbadccadabcbdaddcbacbccbdbadcbdbcaccabcdbcbcbbcaaabbcbdbcdddbcabbccaabacaddbcbacaaacbbcdabbcdccbbabbaddaccdbcdbdbcddabbbbaabdaddcaccadabbccabbbacbbcaacbdbacabcbcddcbacbdcaacaaccacacacbdbccddcabbcdcdacddacdcaadaccdcacddaaddadbadbbcacbbcdaacadbadbbdbdcbabdaaacaacabbccaabcdbdaaccdadddbacabbcbacdadabacccdaccbdabadacdcadadbabccbcccdbbadabbadaccbaadaabbbacddcbbdabbbcdbabdababbaaaabcbcabbbaabaacbcdaadcddddbcbabddbbdddacdaccdcbdbaabddbacbdaabaadabbacadcdcbbbacbcdccdcbacdcdadbabdabcbbdbcacaddddaacaadbdcccaadcdcbdabbcdcdadcdbdcdccbabaaaababccbbbbcacddbacddbdabdaaccabcacbddcdccdccbdadcdaddbdabcdbccdddbccabadcddaabbddcaabcabccbabcbcaccccbdddaaadcbccdaacdacbcbabbcaabdaabadaccddddbbcbdcadbbbcaddadbddddbbaaccaaabdacbaaaabbddbcacdccdacabdabdbacbcaddacdbacdbccbdaabddaabdcaacdadbbabccadbaaaaaacbbcddbccdcdabaaadbbcdcbccddbaadbaaacadbbdbcadacdbdbdabddcbbddcadbbdcbbcaababcdaccbdacaacdddccccacccbdbdcbabbbccbdaabbbcddbccdcdcdaccdcadbbddbdbaccdacabbdbcccadbaaaaccdbdcddcacabdadbaabccaaccdcacbabcaaadddddbaacbddcbbcbcbbdadcbbdabacabcddcbcbaddcaadccbadadaacadadabdcaddddcccaaabbcdcddabcabcaaaccacaccaabcdabaadbadbacbbabbbddcdbcddaaacacdacabcaabddcddabbcabdbcacdacadcbdaadbbbadcbdcaacbbdabcbdaddbcbbcaccaccaaabccdbdcccccbbcdcccaddabdcccbdcadccaccdcaaddbbaaccbaabdaadcbcbcdbbaccbbabddcdcbbcbaddddaabccbcdcdaaccadbdcaddbbacbdbdaaccdbdabbacadbacacdaaccddcacaccbacdccccdadadccaabbddccbabdadcdbdbdcdcdbbbcadabccccacaabdbacaabadbaaacccccdbadcdbcaabbabbccbdbccbbaaabbdbcdbcddabbaaabddacddcbdbdaddabaacababacacddbbaaadbcaaabbabbdddcaccbbbadabaccbaaddbcddcadbddbcdbbdcbdbbddbacaabddadacdadabbadcdaadbbadbcbcbdacbddabdcaabbdbcadccadaaddacabbaaccacbcbdbcbdcacdcbccdccddddbaddabdbdcbbaadbddaaaabbdcdacacadcdbbdcddccdcbadaccbbabdbcdcbcbbcdcdbabdccaacdaaabdabacaacbbcacdcadacbbccbbdbdcabaddbcabaddbdbcbbbbcdaacbdcdabdcbdaacdabdbdcaaaacdcbdcadddbdcdbdccbcdbccbcdccddcdbbdccbaadcbcddbcbaaabaaaaccadabadbabccacababdaacbdcccbbdbbccdcadcddabdabdabbaccddbbdadcadabbbbdcbbcbaaddccacbcbadbcdbddcdcdabacbaabbbccacadcddbccdcccbcbbacabaabbadabcbcdcccaadaacdcdcbbadbabbddddaddbadcddccacabbaddadbccdbacacadbdcbaaccbcbcacaccdcbaaaacbdcadddaacdbacaacabaaccbbacddcbbaabbbcbadcccacdcbbbddbdbdabddadcbbdcdaaabadccbdcadbcccaddbaacadbcaddbcaccdcbccbabbbaacdcbdbadccbacbcaaccbcdcdaccabbbccacbbbbabdacabdcbdcaadacbccbaabcdbcbbccddcdcacdaddcacbdbbcbdcbcbabcbdaaaabcbcdcaaabccaacbcddbbdaabdaddccbcaddcdbdadcaaccdbdaddaaaaadaabcdbdbdaccabacbacbaacadcbadcadbcadaadadddacdcbcabcdcbbcddacaaabdbabddcddddadccbddbdbcbccddbcbaccacaacadbcaacbbdabddbbddccbabcacacdddbbdcbdacabbbdcadacddcbadbbcaabcdadbdcccadbdcababddbddcdaaadbdcdccaaacbccdadcbbbaccaccaaadcdbccbcaababbdadcdababbaabdaadbaccccbdcabacaacbabcbcccbbccdcaacbdcbbcbbacacbadbadddbacacaadddbbaaadcacbcbadcdaaaadbbcbdccbcdcdbcbdcbbcabcaabbbddddbcdbbdaadadcbcbcdacacbabcdabcadddbcaccbaddabacdbadadcdcaccbcbbddadcbdabaadbabadcdccdddddadbdadcbbabbaabdadbcadbcbabaadbdddcddaabbbbcdbcdacdaccddbdbdbddbccacbddcbddacdaabccbcadababddcccadaddbdbddcaacbcdbbacbdcaccaadbbbaaddbbdccdddbabaadbdbacbbbddccaaabdbbddadddabbbbdaaabdbdacbacabdcbddaddcacbabccacdbabcdccabaaadbbadaabbdbaddcbaaaddbbbdcddbccbddbcbcdcbaccbbcdabacbbddbadabbddcdbabdddbcacccabcdbdbbadcacadbdcadaddcccddddccaaaccadabadbcdabcccabdadbbccdbdbcabbccddabdabddccccdddbcbdaaadabcaccabdbdcabdaadadcbadcbacbbdaacdddcabbcdcadadccdbbbdcbcaacaaccdcadbababcbcabddadddbbcbcddadcdbbdaaddcaacdbdbcabadcadbdddabdcbcadcbabdadabbcdcaadcbabbdcaddccaacaaabcabaccacbdbbcbacccaacabdabdccdacadbaadcaadddabbbadcdbabdadbbbcbcacdcadababbadcadcdabcbdbddaacababaccadbcbbcdcdadbcadabcccbabbdbadccbabbdbacbdbbdacabcddcbbdddabcbcbbacdbcbccddbddbbbadbdccdcccdcbbbdcadcacaddcbaaacaddabdddbccbddcabcacbacdddcabbddbababacbddbdccaaabbaabccbcdccccbcbdbbddbbcbbabaddbabcdcbdcbaaacccddcdbadcababdbabacadbbbabaaabdadbdcadccabbacbaddcdcbbabbcaaddcdccdabaaadcddcabbbcbabdadcdadabaacdcbccbdcbbdcabcacbccccbbdbbdaaadbdcddbbdaabbdcbabbccbcaccbccacddcbccbddcccdccdbbdadbcbacbdbcacadbbcddbcbbbaddcccadbbcddbcaccadbcadacbdbddbbaacccbdaccddbdccddadcbaaabadaddaddadbabddbcdcdbbbbadddacacaddcddddacacddddcbdbcdccdacadcdbcddcddcbabbbdacacbaabbcbdaabbbcabdacbcacdcbaabadcacddccddabcdbacaddaacabbddddbacbbddbdbcbdbaddcaabacacdaadbcbbbbaccdaccbbababaccacdccbddbdaaaaadaabbdcbbcdaddabbbaaccbdbadbbbcbbadbdccdcabcddcbdcbacdabdaddbbabcddcdcaaadcbddbcbadbdcbdcdaddbaaccbbabcdbadaaadcbacacbbaddaadabdaabbbbbddddadddcdcbcddcdbdabdacbadbccdbbbcacaabdaaccbaabbdbbaadcacaccdbbcdaaaacbabbdbadadbdcbadbbabbababadbbababdddbabaaaadcabccaddacccaabcdbdbacbccbcdbdbbccbdadabcbabacdaddcaccccacacacaadbcbaabccbbbcbdcbdcbbbbdcabbaaadbbdcbabbaaccadacdcbbaadacdabaddbdabbbdaccabcacbcadcccbdbcdaabadadaaabccbcdbbdadcddadbdabdbacaaddabdcbcddcccddaadbbdcaabcbacbdddbcbdcbbcbaabbddbacadaaacdcccbcbbbbbdcaadbdcabadcbdbacdcaddbcabdcbbcdbdddaacbabacbabcdbdbbadacbdbbddbaddbcbbbdbcddcabadcddbcdccdaabadbbdbadababbbbcaaaccaddccdddaccbaadbdccaccbdbaabdcbcbcacccccaccdbaddacdcbbadaaadadcbcbbddaaccbcddbdbbdbdcbbdcbbddbcbabdabadbbadcdababcababcdbadaacacaaacbacdacacdcbcbbaaabbacaaaabcbdadbdbdddbdadabbcbdcbdabacbcaaccbcaccbbbbacadccbdbdcaacbbbdaabaccaadcdaccddbbacbdbdbdaaacbbaddcdadbbcddacacbcbcadccabadacdccccbdddaadacdcbaaddcdbaabbbdbcadaabadabccaadbbbddaddaabbadadbdaccbbcabddacbcdddccddcdbbddabcabddccbbcbdddcacdcaddbbadbdbddcdcccabbcccccdabbcacdabdcadbcbcccbaabbbdabadbdddcdadbabdaacaadadbdadbabbdaddaaadddbbcdddabbdddbabdadabbdddcdbcaccdcdcbabbcdbbdbabadbdbacdcbaacaaddacdbcdddacbcaccbdbcbdbdbadbddaaadabbdacbcbbbbaacbcccdbaccdbdabdcdadbabbdacccbcacbdccdbcbbbcdbadcabbcdbacabacaaccdccbdccddbbcccdbdaabcaabacbcabdaaabccbcddcbddaaabdbbcabdcccaddaaaccbacbdbbabcbdbcaadbdbdcaaacadcbcdacdadacbbccbbadbdcddabaaadddccddaddbcdcacabddcdaabadcbaadbbdbdaadcddbbdbbdcdaaddbbccbcbbaaccddcdaaccadcccabdbaccadacbbbdbcddbacddcdddcbaddaddcacbbcaaaccdbaaaaaadaddcaacdabbccaccdbdcdcdbcbbbdadcaacbdcadbabadabadabdcacaabdaaacdcdaaabcddcccbbdcdbbdbaccaacdcbdacbdcacdadbbcacdccaaacbdcdacbabcbdbddddccdcbaaddbacbadabdadcdbcabdaabddbdaabbcdcdcdbdabcbaaaddbcbbbbbbdacbdbcacccdddcbcbabbbbccaadbadadabbccacdbcbaccabbdbdadcbaadcdbbbabcbbddabacddadcccacabddcbbdbdaaddddacaabbdcdccbbdbabdaccabddccccdccccdcbbbbcdaabdccbdaaaabccadcbaabaccacbbbddcbdabbdbddcbdcddddabdaabbbdbcacbbcddaabababcbbaadbcdcdbbabaadbadaacbcaccbaabcdcbdadddababdacdbbadaadccddbadacabcdccbbcacdcacddabcabddcbcbbdbabacaddccdddbadbcdbaaacdcbdbddaabbcccacdaaabbccbacbbdbbddbacabcdcbcbbabbdabadbadcdcbbcdacaabbadcbbddccddbdbbdabbdabacaaabaccbacbaaccbacbdbddccdbdddbbdaddbccacbcbadaabdbbbdcddacaadbddaaaabaadbaaabacddabbdaddcacdbcccabaaaaddddadaaadcbcdcaaaacbbccdbabccadaaddcabdadadbabaccdbcabdbcdacabaddaccccbdbdbaabcccbacadcaababdadaadbbbbaadcbccaccbbcddbacccdabaadcbcbcadaacdccccdddcdbcdbdadabbaaccabbaadaddadccbcabbdcaabaaabdcbacdaacbbaacccbbacdadcccacdddcabbdcadbbadddbbacccaaaaadcdcdcdcdacacbdcadddccaccabaacacddbbcddcadccccaabbddcdddabbdcaabdcbddcbddcccaabaadadaddcddcdbaaccbcbadbadacdabbaabaaadccddabdbbdaabaabaabaaadadadabcabbbcbdddcbcdbddcdbcabbdcabdbdacaacbaacdbbcaddbbbcdacccbcaaccacdddaacbbdbbccbddcbabcbbddacbdbadacbcaaabdacbbbdcdcacbcbcaabdaabadabcaddbcdbaaadabcbacaabddcccbbbdadcadbcacdadccbdbcadcadbcddbbbcadbbbbdabdcdbacccbbaacccbadccaddaacdcccacbdcdaabcccbddaabcddcbcdcddcbabcbdaabcadbbaadcbddcbcaddabcccdadcabdbcddbdbbdcbaabddaacddbaddccadaacbbacadacddaabdabcdcbdbbdddcaabcdddabaababdaccaabdcbdcdabbdbdadbcbdccabbaabcaabadbcbadbabcdabbbbacbcddbadbcacddccdddcbccbcdbadcddaccaadcadbcbbcdcabcdadccbabbdcdcaabccccaaaacdcdabbacdacabdaccacdddaadcadccabbbccccccadaabadcabcdacaddaadadddabcddaadabdbbcaddbbabccadbbdbbbdabcdadcabcbadbacbbdcdbadbcbbddbcaaadbbbabaddccaccddcaccadbcaaabcbdbcbdcccccbabcbaadabccdccccdbbaaddcbcbddbaaddabcdddbbdaaddadbbbccdddbaaaccbbdbcdacdddadadcabacdbbbcaabcdbbaccbddaacccaaddcdddabdacbddbaaddbbaddabdacdcdcaabadcacadbcbbadccacacaadbddbdbbddcccbbbbdbcadabbdcaadacccbaddbcacaabcbdbbadccdddaddbdbdacccabbadcabcdcacbbcbabbbbccdbaacddbcbdbadaacdbccddddaaddbccdacacaddacdcdbdcaaddabdaacdaaabbbdbbdbcbbcbdcbaadddcaabbbbbdddddabadabdbbaddbbcaabbabbbcabadcddcdcdbdbcacabacadddabadbaddadccaadbcdccaabbcccbaddbdcbbabdccacbdacbaddbaabcabdacdcbcbbaccccbcbabcccaddbddbadcbdaaddacdbbdabbdaccbaccdbdacbadaaadbcbcabbbaaddacdaadccabddaaaadabddcbdadddbcbccaadaacdbacbbadcbcbacddabcaddcdbbbcaadddddccacdcbcbcacdbabacdabdbbcccdcbbbbddbcacccdaccddcadbdcdadcabdbddcabdccdcbdcccbcaccacbaddbabccbdabbcababdddddcddcabaccddcdcabcdbddacbdbaddaabdccadcabcbbbcccbdacabdbdadbbdadbdbbabdcddcaaccacdaddadccacacadbcdcdccacadbddadcdacacddcccccdacbaddaabbbaacccbcadddcdbbabdabcbaacbbbbdbcaaadbbacbaababbcbaacdadcabdabcddccdacdbdbddaaaddabccdabcdbdccdaccccccddbacacbabaabbabcaccacaabbaabbaccaaacdaacbbccddcdcaabcdbdaacaabcadbcacdcaadbcababbabaaadcadbcdcaadadbbbccbcacbadbbdbbdbcccdaaabbcbbdabbcabccddabaacaaaaaacabadbcadccadabbdbbcbbcbcaccaccccabbabdbbbdadbcacdbdaacdbbcbbbcdccdcdccaaaccacabdbddcabbbaacdcbabbbadbdcbddcbdadabacacddbcbdccaaadaaaaadcabcbcacaadcababaddbadaddcdaabcaddabacbabbacdccaddbbdbaacccadcbdbdddbdcbbddaccccabbbacdccdbdbdadcacdadbbaaabcaadabaacabdccbcdbaccdccbbadacaccaadcbabddbcbccbaacbaadccbddcdcdcacacdabbcccbddbdacacacaddbbcaccdaaaabaaacbacaddaacaaadaaadcacbacadaaabccadaacbccbdcbcbacddbcbccccbbbbcabacccadacabcbbadcbadaddddbdbcbdaccccbacdbaccbbabbaaabbdcdbcccccbcacbaddbbbbcbabcdbccbadcdcdabddbaabccccccdcdacacccdabdccaacddadcaccacbcadbdccbdbdbbcbdcdbcaddbdcddcdbdacbdddbcaaadddaadabddbddaaccdddcbcbabdbcaccddddaaaadcbcbcccacdcbcdbacdabbaadaadadcaadbbbddcbcacbaabdbbcbdbccaaccacbcdbcdcbbbcbbaaacaddbaabdbbdbaccdcbbbbdcaccbadabbbcbbbdddabaadcbacddadabbbbcadadabbccacaabdaccbadcdcacdbbccaaddcdaaacbcacaabdadcacbdababccaaaabccacddadbdbdcddcbacaacdacadaccccaddcdaccaabbbccbdbccdabaddcdbddbaccbcdcdaddbaacdbbadcbdddaaabcbcbdcaabbacaacaadbbaccdabcdbdaddabdbbdbbccaadcbcdcdcddbdccdcbbcdbbacaaaababdddabbabcdcabcbbbbccbdbcbacdcdcacbcbbccaacdacaaddbdadbacaddacaabccbbbbcbccbaacaacbbbcaddccbabacbabddcadcccdbbaaaadcdbccccbcddabdadcbdaddcbcdcbacdbacbddababdacbcbbacddabbbdacccdbacdcdadbaccdaccdcdbdcaadbdbbcddcdcddcbccabbcbabbacbdcbdddaddcdbdabbaadccacbccbbdbccaaccccbcbdcabbcaccdcdcbcbabbcaababccdaabbcbddaacaadaabdbbbcbdcaaddabbaaacddabacdcaaabacbdddbcbcccccaddbbccbdcabacbabddbcbaaaabbcbcbcaacbaccacdacaabdacaccadccacccdbdbcabbaccbbacbbcdcddadadbaabbcccbcabbdcabdabdbdddcbcaabcaaccacacdcadbbabbdbbbbcdbdabcadcacbdadcbabbabdbcbababbcaacabababcdaccabadabcaabbbaaaddbcbbdbadaccadabcdbdccdbdbcddadbdaadccddcabcacbddcdcaddabcdadbbaaacaaaadbdbacaadcabbcabdadaacacdbdcacdcabadcbbadcacabdbbcddccabcbadbdcbddccdabbdddbccbcddcabacdbccaadcbdabbbcaaddcbacbdaabaddacadbdddcbbdcdabcabcdadbdcdabbabacadabcacccdccdbaccadabbadcddacaacbaddcbcababcccbdddcaacadddbabcaccacaabaaacabcddbbcdbababccaddabbaddbcdbdababdccdaadacbabcabccbacaccaccacabcbaaadcbdbdbdbcdccdbbbbacdbccdadcdababababdcbcadcddaabadaaabbcadbcdcbcabdddcbcaadbdcaddbbbbbbadddbcdbcdaddccdbdbbcdabcbbdabddaddcbbdbadcbaacddabcdaababddcbdcbdddbddbcbadbdbdbdadcdbdbcbdbdcdddadaabadadadabbcabcbcbcdcccacbbbabdccbbbbbabbdadbcbccbdddbdcabacacbcbbbbbbddabddaaddcdcbbcbddbabbddcbdadddababdacdccbbdbacabccbcaccaaacabddbdaadbcabaacaabdcaaabddadbcaddcacbacbdbcbacbcbabccddbbcddccadbddbaaabaacbdaadaadbbcbdbbbdcbbdbbabdcbbcdcbcdddbadacdcaddcbddccdacabccacacacbaaabdcacdccbadbddaabcbcacbacbdbbacbdbdbdccaadbaaccdbcaacbbccbddcdbbbaaddccacacbcdababbdcbcbaccbbbabddccddacabadcdbdaadbccbbacaddadbabadbaabbabdbcddabadbcbaaabadbabbacaadbadaddcdacadbdcacccbdbabdccaccbaabaaababddabdabcaabadabcdadacabccaabdcbabdccdbddddabcbabbadbdcaddccdabadacccbdbbabdcaaabbbbadbcaaaccabaacbaddaaabbccbbdbbbacacadbdcbcbacbcacaddbbcdabdadadaccdadbaddbbcbdaadacbbdbbcdcbcbabccccdcbadcacadaaabbddbacbbabadbabcaaadadcdcaacabddcadaabbbbbaddcaacdabbddcadcbbaadacabdbbbccdcbddbbcadbcdcbcadacdacbbbdcbcbddccabccbcadacdbbbcccbddbdccacacbdacddddabaccaacbddbacbacdccacacdbacadcdbdbabdcdcdbbdcbdddcbaaabbdbccaabcacccaabcaacbbddabcdadaccbdcacabdbadccaaacbccccccaddabbdddacdbdcbdbcacbbaccadcdbbbbccdcaaadaadbcacccbabbcdbacadcaabdcbbaabadddcccdcbdcacadaaabbccbddacadbbbcabaadadaccdbbcaabaacbdbbccaacdcaabdadcddcdacbddbadbaabbbcadbbadcbaccadbdaaadacbcdaabdcbaddaadacbcdbbacdacacddcdcabacdbacabdcdcdadacaadadcdcaccdbcccbcbacadcbaaabdaaacabdbaccbacccbaddcccacccbcabdbbabdaabcadadcdaccbcacbaccbcbbddcaccbacadcaaccabcacccdaaddccadabcdbbccdcacbddcabaadcddbdbbbbabbabbddbaabbaaaadccdaddbcbaabdbabbcdabbbabdddbaacbdcaababbcccbdcbaabcbddcddccccbdcadadadcdbbacadbcbdaacdcababadbadabbcbbddbbaaddbcbbacadaadaccabcaddbacbbccbccbbaaaccdcccdabcbabacdcdacccadddacdacdabcbacacaadccbddcdbccbccdaaccbbccbaaaabcdcbddbacdcbbcbcaacbdbcccaadadcbacbbacbacbbcdaaddadccbddbcbbbdbbdcbcddadcddbcadddcacabbdccdaacaaacaaaaabbbadaddacccbbaacbddcadaabadacabdcddadcbcaabcbbbabcddbadddcbabaadbcbabdddacdcbabacdccbacadcabaccadbacdbbacddbcdabcccbbacbcdabbcbdbadadbddacdccaddacadbacacdbdadbabbcbcdbbcbacbbdddddaadcadddddbdbbabbbcddbbbbccbdbcdcaccdaddacbbbbdabacdddabbbcccdbabdddbdcbbabdbbcaaccdbbaaadbacbbadddaddadcaccacabbbadbbcddadacaddbdadacbaccddabdacbdccaaccbbbacdbadcdbbadcddbcadaadbcbadaccdbbacbbbcaabbabbbadacbbabacaccbccbbbadcacaddbcabbdcdcbcddbcdacbdddacccbddcaacdacadbacddbbbcaccbbdbcbcdcabdbdacdcbddbdddbbaacabbadaaddcaacacabbdaaccacdbbbcacacbccaadccdbadcdcdcbcabccbacccaababdcabaacbadbddbbbbcccccbdaccdbabcdbdacabcccadadacdcbcbccdabbcabbaaacbbbbcabdcbcddbccbccacbabdddddbcbaaddaadbbbadadccbdacdaddcccdacbbbdcdcbbbbbddbcaabaddadcbccaabadadbbdbdaadddadbbdbddcddcdaacdbbbaabaadaaacdccacabdabaaddaabacdbccacccccbdcbbbdbdaddabdacdcadaacacdaabaddbdbdcacccbacacadaaaacdbdcdccddacdbcaacdadbaddbbaddaaadbcdcddcdabcacbaccddbdcbaacccacbbcaadccccacaabcaddbcbbbcbacdcaabaabccacbcdcadababbaaccbbdbadbbcababacabcddbbccbabddcddabdcbdbabdabdabdcabbdcdcccaabbabdabccacdccaaaddccbaadaacabddbabbbcaabbaababcdbbaabadbcaaaccbcdcdaaaaaaacdbadbcdddcacadacccacabdcadbbbaccdbcddaabcbdddbabcbacaccdbcdccdadabaabccddabbbdbcaccaadbdaabaabdaddddaadadabdddacaccbddbdbcddcababcabadbbadabbbbcdbddacdcdcbdbdbabccccadcabadacdaccddbccdacdbdbadcaabdcaddccacbaabbaadcbccadccddccbabddcacaaabdbcaccbcbadcdcbdabacbcbcaacbbcdbddcadadcccadbdbdbadcccdacdddbccbdbdccbccdbabbdbbccccadbbaddddabcdabcbdbcbaddcddbbdcaabcdcaaadacbaccbbcbcbadbcdbbbcddaabacdbbbbdddcadccddbbddacbddcdabbabadbaccbadaddaadbddaabbaaaadaccbdacaaadcacbadddaddadbdccaacacaddabdbbccdbccbdcbaccdcbcdaaaacbcdcdcbccbddbadadccacdccbbdddbbadcdbacbdcabccdcbcaabdabacbdaacabbccbaaddcbaaadbaddbacbdbdabcbaadabbcbabadcddbbcccbaaadbdbadcacacabccdbcacbabdcdddbbcdabcbddcbadbaddbcbcddddccaaccdaccaddabdabbbbbdcbdbdbdbadbcdadcdcbacbcadbbbdbbccdcbbaccdbcdcdabbbacdddaadcbddcbaaacddbbbadbabccbbbcbadaddbaabdcdcbdbbdbcacddbabbbddbddcbdbdcbaddcccdcdbbacbbcbbdbacbdaacabbbbdccbcccdcbbabcaadcbabbaabbbdddadabccadccaccccaacabbccabdbdddadadabdadadbdbbdabbcddabbbcacddddccbaddacdabaaaacbcdcbaaddaccadbaccbddbbbdccabdacadbdbdcbadaabacdacaccdcacabcabcbabadaaadaadaaddbaacbdbdaddbcbcdcadacbabdcadbaddacabcddbbdcbcbbaaacdbdcbabddbadbdccddcdbcccabccacaacadbacdcabcbacbbacdcbcccccababdcdcdbbddcdcaccbccdcbacbadddababaaabcdcdccbdbababdcdcabaacabaacbcdabddcbccabbcabcdbbcdddcabdadbcdbdbaadbdbccdababdcadadcbacddacddaddcdbdacbbbddbabdbddccaccaccbcaacbcdbdcacbabbcdddacddbddacbabaaaabdbcacbdaddccbabacabdcaacdabaacaabdacccdddcadbcbcdaabcbadbcbbdabcdbdbacccaddaccaaccbcaacababbabcdbcdbacbdcbadbcdcbcbbaabcdcacaaddcabcddddcbdccccdbcaacddacdccbbdaacbbbacccddaccbbbabcdacdaaabacbccbdbbdbacdcacccaddddbcbbcdaaabdaabdcaadabbcbcdcbaadbcadbadaabdccbadacbdbabdbacccbddbcbdcaadadcdbabaddccbadcbdaadadcaaaddacabcccacdbdaadbabbcbbaadbccadabdddcbcabbbaababcbdcbdbbcadbcbadbcaacccbabcbccddcdddbdacddcccababbabcccadacccbcaccbcdbacaabaccaadabcbcccccdaacbccbdaaadcccbdaadbccbabbcbcbdaaacbddaddddcdcbaaabbadcdaaccaabcacadcbddbdcbaabadbbdaabccdbcaadbaccbdbdcaadaddcddbcdaaabacaddbbccdacdababbbcdacbdbcaddbbdcbcaddcdbcdddbcdadbbcbdcadddbdcdbdadccbdbdddcddccdaaddddbbaaaacadbbacaccbdcccacddbadbbbbbabbbcaccdbbdadddbbadcdadbdcbbbcccdcaddcabaccbaddadddbaaddbdcbacabcabdacdbdacaaddcdbbdcbadabbaabdacdccddaadcdaadabbcdabadabccbccdbccabaabbacdddabbcadbbacbaaadcbbdcbcacaadbabddaaddddbaddabbbddcbdbcaabcbabddbaddacbdbccccadabadbdbbdcbdabbabdaccabccdbdcbaddbcbbdddbcadadbccbccadbcadcdbdacdddcccbdaadddddccccaccdadaaaccadcbbdcbabdbddbcaccaddcabcddbdbbbccabadbcbcdadacdbacabaadcacdadddaaccabcbdbdddbbbadcbbbddbdbbdbbdbccdcbcbdbcacacdabdacaddccddcbabcbacbbdbbbcbccddbbbcabcaddccabbbbbbaccbababcdcdaccbacadcbbdbcdcdacacadadbcdcbbacccbadccbcdcdcccabcbdaccbbcabbadbdcaccdadcccbacaccccbdcccddddaabcaadcabbdcbccdddddccbdabddbaaaacabbbbcdcadbbbbddccacbdccccbccccacacdbcccabbcbdbbcbacddaadcacbbababbaadcdbccdbcbbbdabbcbdbcbacdcbcdabadaacaacdabcacdccabcddbbcbdcacdbbdaddcddcbcbacdcbccbcbddccacdadbbddacbdcdbcbacbcdcbcbccbbadbcddaccdcccbacdcacabddabacbbcddbaaccccabdbbbbbcbdadcbddadbdbdcacdddcaacccdacbaddaacddababdcdbbccaaddcdcbaadddaadcddbdcbcdddacdcaadbdcccbdbdadbbbddccacbacabbbcadabddbcbcabbbbcdcbbbccddccdbdbcabdcbcaddddddaddbadadbcddcabcdcdbdaddcabdaccbdabbcadcbddbbdcbbbcccadadaaccccaabbdabddaccabaddcbcbccbdcbbbbdaaabadcbcdbcacabdbaccbdadbcdcdabacadbddbcdabcacbdbbcacddacdbcdbaaaaabdacbcbcbbddbbccdbbdcbaccbbaacacdbaabddbbcdbccacaaddbcdbbbbdccabaaababdbbdcbdacdccabdddccabcbbcbcbdcdccaaaccbaaccaddbcdbbbccbaabbdcbbaaadaccddabbacbdacdbbaacccabacdaababaaddbdddbbbcbcbadaabdacacadbddccbdcaccadcaaabcadddaddbdaccabaacaddcbcccadccbaaaccaddbbbcdcaddcddadddcaaaaadacdbddccbbcdababdcdcbccbaaaaacaabdacadbcbadccbdaacdddadddabdccaddbcbaacdbdbaabacbabddcbacdacdbbcabbdccadadbcdaadbadcbbddacaabbdaaadcbccdcbcdbcbcadcddadbbcbccbbccaccddbbbabdcbbbbcbabbdbdabcbddabbddcbbddbacdbaacbcddacbacdaccaddbcccccaddababccdaaaaaabdaabadbddbbbbcbabcadabadabdbacbabacbcaabcabbaacaddabdadaaddacbddabcbacccaabcabdbbbbaddcabddbabcabcbdcbdcdbbcdaaccaaabbbabbccbabadcbdbddcdbcaacaccabddcddbbaabbccddbddbcacddcbbdaccbbdbdaabaccdaaccbdcddbccdcdbcbdabaacdbdcbccadbbaccdaabdcccddadbdaddbbcbcacaadcadadcaccbdcccdbbbcbddbcaacadabcaadaabbcccddccbbbbbbbcbadcbccacacccbbbdccdddddadbdccbcdbccbccbbccbacabccbabccddaadadccdcdbdbddabbcacabadcbbddbdbccdbcdbcdcabdbcdacbcbcdcbcbabcacbaabdcdacdacacddacaadadcbabdbcbacbaddbabacdbacaacbaaacadcadacbacccdaaccdbbbcacccaccbcadbdbbbadccdbdbcbcaadabcacdcdddcabddcdadcddabbccdbbbdcbaccadbbacaacaaadaddbaddcbccbddbadddacdcdbaccdabdccddbbccccdbbdbdcbadbabdadcbcdaadacccaacdcdcabaccbbacddabbadcbaadaaaddaaadcbbdcdccbdbdabcadbbcccaddaaccacdccaadbcaaddcdbaccadabcacabbacbdabaaaacccddbcacbdbcacdabaccbddbadacdabcdbbbccbdadcdbdabcbdbcdcadcdbabcbcddabaaabaacdcdbbcbabbcadcbbcddcdadbbbadaccdcadcdddcdddddcacdcadabcccbcbddaddcaabbbbdacbcacbacdadabdaddcdbbadacaadddabdcaacabdacbddbdabacaabdcdcadabbdaccbcadccccdcbddadabadcbbadbddacccadbbddbdddcddadabdcbaaadbbdaabaaddbaadccacdcdcdbbbacbaddabbcdadadbcdbdbbadddcaabcdacdbaaadbdaabcabbbdaaaddcaacdcacbbabcdabcaaacdbddcaaccbbcababadcdbccddacdcaaacbbacdddcbaadabaabbddadcbacbaacaabccaababaaddbaacbbbccbccadcbcbdaadbdacddbcadaaccdcdabdadaddccdadbdbabddcaacbdbadddbaaabccddadbcabdbabbdbacabbccacddbcccccbddbdcdccbccdadadbaadadadcbdaabbdadddddcdaaabbabcbddbcbdcbcddbdddaccccbadbadadabcaabcaddbdccdabadaccccbdaabcaaacccaaaacbbabdadadbbbadabccacadcbddccccdcbbaccbccbccaacdddadcbabadbbbdcdcbbcbccdaabaddaccadacddcbbbcdbabcdcbcadbbabbababbacbdbbaacdaabaaccddddcbcdcababbcaabcacdbabdcdbdaaddacdadcbbdbaaddaacababccdbaabdababdbbbcddaddaddcbccaabacacbacdbbcdadcbbcbdadcdadccabcbccabacbcaddbdcdbadadbacadcdccdcacaaaddaadcbbdcbadcbadadcdbdaddbbdbcdcccadcabbacbbabdcadccdcbddadcccabccadaddccabdccdbdcbbbdaacdabaaabbbacbddcbddbadcddacddcdaccccddbbaaadcadbaabccdaacccddabbbdcbbdbcadabdcaabdcbdbcbcacccbabacbaaaadddcdbcdbbbcaddcbabbdaddbdddbbabdbadadabcbaccacdbbacbabdbadbccbdaaacdcaabacadababcdbabccbccaddadacbcababddddcaababbbcddbdbbbbadababdcadccbadcbabbdbbbccabcbcdcabdbdbadbcaaaabdaadbbbadcdadddbadcccaacaaabbacdacccccabdccdcccaccbbdcbbdaabcacdababbdbcddacadaaaaaddadccdcbdbdcdddabcabcdbdaabaadbcbcddcababadcbbbbdbabadacbdcbaaddcbcadddcbcadaccbbaccbcbbaacabccadcadaabdccbacbadcacbacacccccdcabddbbcabadcabacaaddaabaccbccdcdbabdbaadbccbcadbcccabcdbbccdacdacdbabcdbcbbacbcdcbadddcadcdbbbbccacbcdccdddcdccbdadbddcdabdcdaacbbcdcbccacbddddaaaddcbdcadbbccdadcaadbdaaadbddaabcabcbacbdcdbbadabbbabcddcaaacbdacbacdaaaacabbdcaaadadaaccbcaaadbbcbababdadcbbbdadbadaacabdabbcdabbbadbacbdcddccdcddcdddacbdbbbddcbbbabacdccccddbbaaaabacabcbcdcdbdbadacaddacdcdabbbbdbadbccbabccbcccbdaadbbdaacabbacdaaadddcbccdbabdababdadbcbdcaabdbacddabcacccbaddbdacdbbaabbbacbdddbcdabbcabacbdbcbbadadabcbcabcdbbddcbcdaaaccadbbadcacbadcbccaaddcbdcacaadcbcabadbcdbaccbccbcadacbcddcbcccdabbddaaddbcababccacbbcaadaccaccbacaccaadaddbdbdddbaccaabcdbdcdacbdccaccddabadadaabdbbbdbdcacabcaabddccabccbdabbacdbcbcdbabddccbddacddacaaacdbadbcbbacdddaaadcbacdcbadadbdbaddddcdabaabbabacbadbcdadddacbdcaabdacabcddadbbacbdaababbdaaaadcddcaabbaccdaacadbcddaddddcdbbcbcbbdbcbaadcacbaabcadccdcdcbddbccdbdcdbdccdabdbcbcdbccbcacaddcbdbccabaadccccbacdbaacdbcacbdbababddaabbcadccaaaaddaaddabadcaacbdcadbacbddbdccbcbabcccbcdbdcdbbdddbbcddacccbcdcabdbadccddacaccbbcdbdcdbcdbdbaabbabacbcbcaccbcaddcaddcdaaadbacccbcbbbcddbdabcaccbaadcacbbabbdbdbbadcbabbcdddbdcdcbbadacdccdbadaaacaadcbcbddbddccababaccbcbaadddbbbcbddcddbddddbdaddaadbcddcacdddcbdbcadcadbabcccdbbbaaaccbacbacbaadcdcdccabcbcacbccaccbcccaddaddadbcdabbbcdcccdbbadabdcaabbdddcdaadaaadadbdddbbbacbaadddcacdcddbbbbdabaaaacddbbaccdacbadcbbccaccdcdccccbdbaadbccbcadbacacdaaccbdcccbcbaddcbdccdcadbbaaaaccdaaabcdadaaabcadabcdbbdabcdacbcaccaaaaabbacaacdbadcaaaaadaaccbcabcdcbbadbdcbbcbdaacccadadcbcdadadcbdcbadbccccadcbddddacbaadacabaaaacbcaacbbcacdcbacdccbdbdbabaaacbcaaadcaccbadadbcbbcdbcababcaadcdaddadbadcccdcadcccdcddddadabacacdcaacbccbdcabacbbbbddbbdcdddacadbaabbdabccaadcdcbcbbaccbcabccaaadcabccbaacdacaddbdaccbddacabcccccdbadbbccbdaccadaddbddccbbcdcdcbbaadadcdbaacacdcccaabcbbbbcababbdadcdbbccadbbccabcbbbadacbbcbddcadcdacadcddacbbbdaacadbbcaaaadbbbdaabdcdcaadbdbcccdbbdbbccbbdadbcbcddcbabadbccbbbcdcaacdbbcaaddbabadbdbbcacaabcdbdddbbabcbbcdcadbcbadabdccdbaadabcdbbdddacdbbabaabdbadcaadacadcddccdaaaabdaababcabcadbacccacaadbcdadbdacbaadbacdcbadbdcddbdadcbacccadabcadbacdacdacaababbbdbdbbaccbacabddacbcacbbaabaacabbdabcdabdaadaddccccbadccaadbccdbbdbbdddbacccadbddcbdbacdadbbaaadcbcaaaadcbbccccbdadcbddabdbbabcbababbabcacdaaacbbcadbdaadaaddaacaccadadaadbacacbbbbbdcddcaccdcabacacbccadcadddabcccdbbadacbadcbcaadbdaaadcbccddbabcabaadbbddcddbbbcccdbcaaaabbadabccccbcdccadcbbccbdaabdcdacddcdabdaddaacbbcbbcacbdbacacabcdddbabdbabaabdbbdcdabdbabddddcdccabcdadbbdcbccacdbbccccacdaabababcaaadabcacbaadabbcdbcbaccdabbbbbdacccadcaabbdaabaacdcbccbbcabbbbcbdabdddcbaddcbccaddabadcddadcddadcdbaacaccbcbdbbababdcdabdaaadaccdbbacdccdaabaabdaadaaaababadccbdacdbbdadbbcbaabddbdbbbadcbddacacbcadacddabaacbabcbbcccddbbacadbadccccbcdbdcdacccdddbdcbbbacdbdcbdcbadabbddaddcaabadbabadbacbdcdcbbadcaaccabbababbbcbccdcaadddcdbaacdbcadccdddabcbdcbcbacaccaabacaccccdccaaaadccadacdcadbbbacccdcddcabaabdadcaddaddbbabcbbbaccadccabbccdcdcbdddddbbddccdaabbbabaccabddcddccbbbdcbdddaccbdcbdcbbddadadabbbdcaacabbbbdaacbbacdbddacccacddbdcaddacbadbaaabddddabdbdbcabbcaabdbabddbcdccddcbcdbccadbcddadddbdbacddbcbdcddbdbabcadbacccadcacbcddbbccacabccbbdcdababbaccbabcbacdddbccbbbcbadacddacbcaabcdbaaabcbbbbbacababcbdadbcacbdbbbcccdababcdbbdadbdcccaaddaadabbcccaadcbbbbbbabbbbadcbbbaaadddbcdbbdddadddaaaaccbcabcbacdcdcacdaacdddcabdbcccdaaddcbadaddbcbabbcaabadadbabbccddaaabadabdacabcadbacacabdbacadccbaadcadbdccaaabdbdddaabcccccccccccdaabddaacbadbdddbdbcabbbbcdddababddbcbbaddcddcaaabcabadccddaabbdbabcdaadccbdaaaccaccaabbdbdccbbdacbccabbcccabcccbaddbacbddacbcbcdbccbdadcabbacdbccdbdbcadadabadbcacbcbddbbbbcaacdacbaadbddabbcacbdbaddbaabcbbbbcbcacccdddbddcdcbdbacddaadcccdbbaabcccacabaadaddcdcbabacacaadcaacdbccacbdbdbacdbddcaddacddabbbbadcddacaddbccbbddadcdbbabccbbcddbdddddbbdbcaadaccbababcacabaddadbbbcdccacaddcdddabcddddbcdbcadbdbadaadbddbdcbacdadbccbaddbdcdcadcbaaadaacacdddddddbdccddbaaccdadbbddcbcdabdcccadbabbaaaaaabaccaacbddcccacbadbcabdaddaababdddcccbabbbbdadbbacdaacbdabcbccdddadddccbdbbbccdcabbddcddddcabccabaacccadbbdcdaddabbdaacadabbacddaabdbcdbddbcaacaddbdcbcadbaaaddbdcdbcdabcbcddccdcdbdbcdbaaacbabbababcadaaccadcddcdbdaddbbbdddbddcbdcacdabcabddcacbbdddabdbccbdabdaccdacdbcaaaabccacabcadcdaacdaabbdcdabacccccbdddacabbadbabbadddbaadbccaddbbcbdbadbccdaddabcacddbdadbbaabcadabcdaccdbaadbbcccccbccabdbcabaadadcbacbcabbaacddbdccddadbbbcabbbbcaacdbbbadbccbcacbabdcdabcdacabcbdccbcdbdcaccccbcbccdaaadbbcadabdcdadaadbcbbabcccadbcbccdccabdbbacbbbdbcddadabbbadacacccdbadddabccdddcdccddbcdbaacbdbcbacbcbdbbddccadbccbaccabcdaabadccabbbabcdabbdcccdddbbcbcabccdbbbdcabccaddaacbcacdacaadabadbddadacddcadaadbdcbcabbbbcbdcbadcacdcdbacaddbaaaabbacdccaaaddbddaabbcdcccbbcbbbddadabdcaccabdacbbddacdbcbaabbacbabcacdcaaccbadccaaddcccacbccdddbccbccdddbddcadcdbbcbaacdbaccbbbdbccccadbadacbcacbdabbdabddcaccccbcaccaaddaccbdababcadabbacadddbccbbdaccbadccbbacabcadcbbcbdacbdabcbbadbcbbdbdbccacdccabbbcdbaabacdcdccdacbcbcdbadbdbbacababbbabcacacdccbbddcbbaaacddccdcbdadadaddaacacdccacacdcbcdccbdaddbcdbdaadbdbdbadcabaddddccadcacbadccdbdbbbbbcdcaddbddcbacbbaababacadbaaaddcbccddaddccddcaddadcddcbdcdcdaacbdbdbadbcbddacdabacdbabbabbbdcbaaadbcbcdcabacbbabcaacccddbacbcbcdadcbcdcdcdcbaccbacadddbaadbdcadbbdcddcbabbcdabbcdbcdadbbcacbdbbbcbbabacccbbcaddbbacaabdcbcaadcdaaabaaabddbabccdcbbcbdcdddcdbcaaaccaaddbbacdcacccbacdaabbdbdbcbccdabccdbadabccdcdcdcdbdaaacbadacbbbacacdaaddacddbcbaabddacccccdbabdbbbcabacaabadabacddcdbbacbcaacbadbdcddbbdbccccbcdcdaabcdbddcdadbbcadcdaaddbbdbbaddddadadbaadadbdaccbccdaacdbcbdabcbadbbabdabadccdacdaacdcdaababddacaabbdddaabccbccbabaacacbcabacdcaabcbacdabcaaaacaabadccadaabbddbcacbbbabddaccabcbdaddbdcacbaccaaabdabcdbbdbbaabbcdcccccbaabdcbadcbcadbaccacdbaaabbcdbbadbbadccdadccbcbabaaccbcddbaacacbabacddbdbcdacbdbaacddadbddaccbbbcdaaacbabcadbdacaacbadcdababcbbbdcadbaaabbcababaaacadabcbcbadbabcddcddadcbbbbacbccdaaabddcbabdbdbddddbbbbaaddbdadcbddddcadcdbcddcaadcbaddcbadbbdaaacbcdaaaabdaadbdaaacdcbddbccbaadadcaaaadababddccbcbabaaaddbacdcaabbcaaaddddbabccccbccccbcccbcbcaababbcccacadbbacdcbbbadabbacdadcacbcbdaacabddccccbbbaaaddbbbcadacdcaacdbdaccdadbdaacacccdcadabcaaddddbbcdabacdddadaccbcbbcaccbbabcabbcdccdcaabdddccacdcdbccadbababbdaddbaccbbcabbaaccabdbabcdbdacaaaaddddcbdabbabbbbcaababbddcabbacaacddbdbaaadacbccccbdcaacdaaccbdcacbaaaadbcbccbcbbdbcdabbcbbabcdbbdbbcbdcdccabdadcaadcddbcdaadacbcdbccdccddabbbdabdaabbbbabdcbcdabdadccbcbabbcdaddabcccabcbbcdddbbacbccdaaaabcdadcbbbcccbaaadbcbabdbcdaadaaadcabcdcaccbbbdbbbcbacdadcacadcaadcdddccbcbdddabaabbdabccbbbdaacaadabacacbcdabbdddabbbadcadacbcadcacbadccbabdacbbaabbdabbbccccabcdbdcccdcdbbcaccbadcdbbadbddbcbbcbcbacbcbdaddbdaaabbaddacbcacbbaccccadcbdadbbccccbddaddbaddabbacddcabbdabacddadbacdbccbbaabdbddcadabadbccadbbaabdbcbaddbbbdcacdbbdabdcbcaaabdadabaaddadcdbdbddcccabcdaddaadccbadcaddabcbbdddbaabbcbbbcdadcbcabbabbccdbddadbdaacdbbdcddcadacbbdabcdbbadaadbbabcbbdbcbcdcaaddbcbdbdaadcadbdbdaabddcdacdbdcdbabcbcacdacbbbacaaadcaccdccddadabbaacbdcbacdaccbbacdcacadabdcaaddaababadccdddddddbdddbdabccbbcabbcbacdddcbccdadaccdbabcdddddccacdcdadadcdbdddcddcdbbacbcdaabcdaabdcadcdbcabbaccdaaddbbdcbabdacccddaccadccadcbbadcddbbaacadaddcbacdcbdcabacbdaaaababcdadbcbcbbabbbaaadababdcaabadcbddddbcdbbabcbbcdbcacdcdaadaaddadadbcadcbbbcdabbadaaaaacdbaadbcaaaadcadadaddaabdacaaccdaccbcbabcbdddcbdcaacaababcbacbbabcdcdcbddaddcbbcdcdbbdabadbabcabdabbccdccccbbdadcaddacbddabdadddccabaacdbcdddccbbbdadcdabadbcaccabbbdcbdacabcadccdcbcdacdaadabdbcdbddbdbbcccbaacaaabcbbdbdaddaddcbcccbbaaadcbaddbacccaaadbbdbabdcccacbaccadbbdbddbacadacdcadcdaaccbbbbbbabdddaadcaabbdcaabcabccbbabbbdaaccdaaabbccbcbdbdccaaddbbcdadbacbcdcbdccddcabbbcdbcccbbdacdaddaadbaabbcdbaacadaaaabbdcabcbacacdacbbdddabbcbaccbbcdbbaacbabccbadbacddbdcbbbbaacddbbcddbabbbaddbcdbcabcabbbacaaccddcbcacdbbacbdabdbcbbccadaadbddababcdddbdbaabbcbcdddadcbcdcadbddacddcdcccbacdddbbcbadcabbaddbadbdadbadcbcabaabdddabbcbbaaaaccaddbaaaddaccbccaadaacbcdbdbdddbdbaabdcdaadbbbbcadcccccacddbaddaaddccdaaabdbdcbabacdbcbadbcdcdadccddaccabbabccbbddbcdaabbcdbcdbaaadcbdcdbbacbadaaccabdabcabcabddddbadccadbbdcbbbadddaccdcccaaccaccbcccabcbdacbaccbaacbaaadabcbacbcdabaaabbabbbacddadbbabdcbbacacdabcaadbacccdabcabadbdbaaaddaaacdbbcbdddbcccddbcaadadbbacacdacbbbaaaaacacdbccaacdcdacddacaacdcdcbdababccacabdddddaadcccbbbcaaacdbadbdabacdcdcbbdadcdadbbcabbdcbcbaadcdddacadacacddbabbbddcdbbbacbdddaaddccbbabbabdadacdbbcddcdbcdaacaacbcaaaaaacaaabdbadbbccdddcadaccacbbbbbdbbdbbadddaccbcaddbadccacbddcbdccaadbbcdbbacadacadddbaacdbaddddabdabdaaddcbbcbbbbdbcacabcadbcabccadadbacaabccbccddbcbccdaddbcdbcabcccaadcdabdcdbacccaadbaadbdcdbbdabdccccbadbbccabbcaacaccbadcbcdddacbdbddcaaddacaccaccaaccbdaaaaabddbaddbbcdbdbbaabbacbdaacbdcdcadaddaaabcbbabacdcbbadacaabdbdddabdbbdbacbcdcadddabbddaccbddadbccddabbdbcbaadbcbdacdabbcdbaacdbaabbaadcddddcadaacbabddbbacaccbdacdcbabddddbbcabacdbbcdddacddbddddbdddadabdbbbdddadacbdcabadcbcbacabaadaaccadaddbccbbdaaaddcbcbdcdcccdabbbbadbacddaacaadaccccddcdbadcadddbcabbbacdcddccdddaadcddbdbacddcadcdbbcadacbddcbcbbadbabdacaabccabcabbdddaccbbdcaacdadbcdadbdacbcaaaaaddbdbccbbdabaacbcbcadcdacccbdbbbddcabadcaabcbddbdbcbdcaccdacabaacccbccdbabadbabaaccaacdcacaddbbcbbcacababacadaabbddbdbccbacbadbdacdabbcaccacbababdbcaaadbdbdadbaaaaabdbddddcccacbabbabdbcaaaccdccdaaadccccbcbacacaaabcccadabcbdbddcbaabbdcabbcbdcaaabdaabccdabadacbabacdddaadadabaadbdbcaadbacaccbbacadaacbbacaacabbacabdbbbbccddbcbccacbdcddcbdccabadddabadabdcbbcbcbcbbcbbcccbbbabdbabbacbdbbdbabacdcdbdabdabccbbddcbcdbcabcddbbccbbbaacddcdccadbdbcbadaacacaadbbdbbcadaacacccbdcbacbdbadcbbabaabddcabadbacbddcabbdcbbdbbccacdbadccdbcbdbbbdadbacbbdccacdcacdbcdabbabdadbbcdbabdcbdcaacdccbadaaacbdcbaddaddcbbbaabaadacccccaabcababcadcabbacaccdaabbdaddddcdbabbbbbbdababdddbbcbcbbbabbcaddcabdbcdcccdcbcadccdadaacddabaddddcddaaaabbbbcababaddddabdccbabccaabaadcabdadbcadddcdbccccddbdccaababddbbabadacacbcacbbbbcbcbcbbdcbbdbdccbadcddabcbdbbbdbacaddbaaddcbabbabdbdabaaabbcddcddabbdbdaabaadccdccddddccbdaabcdaaccabcdacadacdcbaacaaccadaccacbdacbbccbcdbacdcacbdadacddddcdbddbdcbdbdbaacbaabcdbdcccbccbddbdadbdcdcbbbadbaaaddabdcddbddcdaccaccabbdbadbbbadcdabbcdcbcdcabdcddccdcadadacbaabbbdcaacdadcbdcccdadabaacdaabbcbaddbdbacddaaacdddddddbcabcddbddcbdaacccdcdddcaddacbcbbddcbaabccaabbddcddbcddbbcaababbaccbbdccdacadbbbbbbccabaabadadadddabaacabacbdcbdadacaaddcadaabcaddcacddabaacccaadcbbcbcdcccdcbddcdbbacbbdcbadccdbdccaaaadcbdddbddbcdcbcadacddcdbacbdbacdbdbaadbacbbaddbaccacaacbbacdcdbddadcbbdadbdcddcdbbccdacbdabcdcabccdabaddcbccdcbbaccbaacacaabaccbdcccbcdcadaddabdabcaccbdbcaacdcdaccdbacbaabdcaacddddacccacacabaacddddbaacabaccbdcacaddcbbdacdacdabcbaabbbbbdabdcabddacadacbdadcbdbccbcbddbdabbdddddcdbbcbddbbabcddcdddaddbddaddabbabdaacbcbdcddaacbabaccbaaccbbccababaaccaddadabdadcbbbbdbabcdadacdacbbdcadbbdddabccbcbbcadcdbdcabbbabddabbbbbbcadcddcdbbaccbcbcadbbaadcdcbbcbadcbaaabaadccaadddabcdbdbbbabdbabbccccdcdcbbbdddacabbcdadbaaabddaaddbbdcdabaaacddcdbcabdbabdbabacaaddbcbbbacbcbbcbbdabbacadcabdcdbadbddbadcdcdddbaddcaadaabacdbdadcaaddbddaacdddccdbbbcadabbaaddbabaabaaccbbcbabbdaaaabbadadaaddbcadcdbdcddddbdadcadbbdcabdcbddbabdacbaaaddabdcdcbaadbdbdbccadbadbadaccabadbddcdbdcdcddaddcdbabcdbbccddbcdcaadbadddcbdcaaacbccbdaabcadccadbbcbbbbdaddabbdccbbbaddbaadaaddbdadbbcaacddcaaaabccddccbbddcdbbcaaabbddbabdadabcdbacbdccaabcbbdcdcadbabccbdccdbdbadaabddaaadcccdbcadbdbcdddcbbbbbadcbcdddcacbdbacabdaabcdcabbabcbdadcadbddcaddbaabdcbdbddcdbcbdabbbbabdacacdcbdaccbaabdbbdddcaacbcbddbdcbcbacbacabdaabdbcdbcbcabddcabcddacdddbcdbcdcababdaaacdbddbccbddabcbadcbbadaacadadbcbccaadabbacadcbcbdbcaddacdbbbdcbdacddbcbaddabcddccabcdbbdadadbdbadddbcabadacbacbcacdaaaadbbaddadbabbddbcbbbdbbdbacddddccccbbdddcadbccabadbabcbabbdaddbadabccadaaccbdcbdacbadabbaadbabcbdabbaaaadadcbbddabcdcdaccabcbdbbadaddccacdbcadaddbcdbabcdacbadabdddcacabddbbcacbabcbbbadadcbdacdbaaadcddbcaddbbdabcbcccbccabcdacbacacabdcddbbdaacaadcdabdbabbdbdcaabdcccbbbdbcbadcddbbbccadddabddccdddbacdccbbabacccaacbadcaabddaddbdbaabdcdacacddbdbbabcaddccabaabcbccacabdcbccbacadbbadcbbcadddddddadbdcbcbdadbbdbbdcabcccbaccbadabacaddbddadcbacacdcbddbcdcdbccadbcbabcbadbbbccccdcaddacaaadbababbcdcdcacaaacabcadccadbbaddbbdcdbccdcbbbddacdbbdadbbdacaacbbbaacbbaaccccccbdccdabdaccdacacddadcbbdccbabddbbdaadbddacabcbadcddadcadcdcdadbddbaacaddcbcabbadbdaaccdabbbaadccdcdcbbdcccddbaabdbddaddbabccabdaaacbbcbdaadaaabbcdddabaabbdddabcadcbcccdbbdaabcbcdcdbddabdcddabbbcbadbabbbdaccdccbcaccdbdcdbdbbdcadadababbcabaccbbbdbcbbcabdbadcaabadaadbbcbddaacdbcddbbcdcacbadcababdabdbcacbdabacabccccdabdcbcdaddcaabdcacdbababacddccbcbbdddbcbaabbdadbbadcdcbddcddbaabcbdbabddaaaacbbbbbcdabacabbbabdccddcbddbcadcdabbcbcbdbcadcbbcbacaadbacddadddadcbbaaccbcaadbbabdadadddacbabadcaacaaacdddbabcdaacdacdccbdcbdbdccbadbbcbaadcdbbbccbcbbdcabadddbcabdcbaddbabbcabcdddbbdadbbcdbdabacbacadcdbabcbbdacaaacbadadcacbacacddcabacbbcaccdcbaddcacbccbdacddddaabacbbbdbcbbaabcbdbdbcacbacbabdbadaaaabcbccadbbcddbccbdabdbcbccccdbdacbcbbcadabcacdaaccbadbdccddaaccccbcdcacdaadbcddaddddbdbbcbdaddccadcbaccaddbdabccacddbdadbdbabbacdacabaacbcabcadbbaaccddccacacbddccaabaadabaccbddabdbdcbcdddddbabbbbcdbcdbbbacbddabdadcbbccbcaaaacbacdcdbbadddcbbbadaccacdbddaabdcdbdbbcdddabddbababcabcddcdbbabcccdacbbddadccacabcabdcbadbcdbdbadbacdcbdbbdbccccbcbdcaccacaddcabdddccdbcdccdbccbdcbbabbacdcabddcdccccabadbcababcaccddcbbaadadbcbacdbadbbacbaaacbbadcbcbcbaaccbadcdbccbaaaacbdaaaacbccabdabaaddcbaacbadbcdaccccdbdabccaabacdcddaddcdabbacdbcacdaacdbdbcababdccdacbabdbddaaabbcdcdbabddcabbdbaddbaadaadbaabacbcccdccdabacbdacdbcacbdcbcbcaadddbabcabcbddabaabddbcbbccbbadacdbacbddacacadddcaaacacbcdcbdacabaddcadbadababdaacdbcdaaaaccdaabcbccaabbbcbcabcaadcdcaadcbdbbbccdaabbcdccaddadcccacddddadbdadcacbdbadcacdbdcaaaddbbcbcdacbacadbdacbddcbadbbdbadccdbcaaababcbbcdcbccabbbcdbdbbcdacdabccdaccbdccdbcbbdabbcbabdacbddadccabddbcdcbdbdbbdcadcdcbabdabcabadacdcbccacadbbbacacbacbaddbadbabdabaabccbadacabadcdbadddacacadacdbdcabcbacdcbbabdccacbcbdcacadcabadddccdbdaccadabddcaacabbabdabdacccdbdcabbddbddabadacbbbadbdaadbdddbbcdaabbadadaaddabdbbbcbdabadbdcbbcbadbcadaccbbbbbcaaccbccaacddcdbcacdccccbcbbddadacddaddcaacbaadcccbaaabcdbaabdacdbdbbaacdadababcaddabcdaacaaccccabbbabbacbccccacdabcdbbabddcddadbddcbdcddabadcaccdbcacabbbaccaadaacaabaababadbdddbaaaadccbbacccbddabcdaaabcdcbaccabbdbdcbacdaadcabaabdbaacbdaacbbacbbacddcadacaaabbcaacdaaadaddddbdaccdcdbacbbccabdccdbacbdacbadcccacdcddaacadcacddabcdcdababbbdcaababaccbdacbbadabdbbadcbdbababdacaabcabaaacbacadabbcccaaccddcccabbabcaaaabdddcdcacbccbbdadadbaccdcaddbadbacacbdddbdccdabccaccdaacaaaddaabacbdbcadcababacadacbddaccdacacaaddacccaaababdaadaaaacbbcbaddacaabdbabddabacbcddbdacbbcaadadaacdbabdbacccaccdbacddcbacaaaddbcdabdbbdbacbaaddddbbddbaaabbbbdcabbabaadbdbabdbacbcadaacdcdcdcaabbaddcaabbbdcabcdaddddabddbbdcdabcdacaacabbaadccdcbadaacbbcdddbaacabadabaddddbacbdccbadddacacabbacbdcdaabdbbbbbcddbcaaadcbdbbaddbcadbbcbbabdcdcbcbadccdbacabdcaaaabccaabaacaabdadcdbaaaadabbdccacccaadbaadcbdaddbacbddcdcbbbadacbcbababaaaabaaccadccdddbbdccabcdbbabacacbccbbbdcadbaaadacdccacadddbaaabbddbdbcccbccbdccdaddbcabbdbcabdbabddccdddcbaccbdddadcaacdccbdcdccccbccdbadbccbaabdbddbcacacdddcbcdccabacacbdaccacbdababbbaaabbdcaaddacabbadadddbbaaddcadacbcacbaaddacaaabbabdbbdcadaabbcbacddadabbbcadcbbdacabadbcabbbcdccababbabbbbdcdcdbdbbabcdbdcdaacccbdaaadcdcbdcabbbdacbbdcacddddcadbabbbaadbddcbdbbaccbcdadbcaabddcbaabdbabdccccdcbddcccadaabdbdcbaadccccccdcadacbdcdaaddacadbaccbddbadddbbaccbabbbdccdcabdddaaabbdbdbdcabbdabddbdcadacddcddacbadbababacacadbdcabcbdbbcadbdcadaaaadbcbcabadadbcdcdcabacaacbdaccabbaaccbcddbbacacaccbaaddbadaaaabbacbbdaccbbacddaacccbbbbdbdcdccddbbdbbaabdbdbdadddadcbbacbdacbddacdbbabdcdccbbddbaacbbaadbabdcdbbabdabccccddbddabdadcbbcbcddccbbdccdbbadaabdbbacbcaddcddadacdcacddabdcdcbccccbdcaccccabdbbdcdadadacacdaddadcbcbcabaadabbdacaaccbdbcdbddbdddbbbaabbcccbaacccdadbdbcbaabaacbadcbbbabdcccccbbdbccbaccdcbabdcaccaabdbdbbcaabcdbaacbcadcdbdbabbcbabbcacbcddcdaccbdacbaacbccdaabdabbaadabaaadcdddcdacaabdaccbddbbcbadbbbabdcddddabcccdadbababbcbcabdcdabcdcadddabdbcccdbacabdadbbabadacbcababcacdbaddacdcaaaacccaabadbdaddbbcddabbdcdcbdacbddccaabbdddccaccacdaddbdddcadabdddcbbbcbcbbbcdbdbcbcababdaddcdcacabdacaadbbbbcdbbccabccbcdabcdbdddbdccdcdbdaaaadccccbbcaacdccaabddbcaacadcdbbaaaccabccbacbbcaabaddaacadbccdbcdadabbcababbcacbdaacbccccbbaacbadbdaadbcadcabacdaddaaaacaadccacbdcabccbcaabdbcaabbaabadcdbbbdbaccacddbadbdcccdcbbacbbdbdbaaadaacdbaaabbdaacdbadadddcadcadaaaddbaaadbccdddddadddcbdbcbbaabbcbacdacacdcbcdbdaddbdacccdddcbcccbbaddadcacabccacacbcbabadcdadcabcabbbdddcacccbabdaaacbbaccdddddadaadcbddbadbcbabbbbdbcbaddbbbddabdbcddaadaddccabddaccdaadbdacbbbbcbabcbbbcbbbaddbbbddcbacddacdaadccbcbaacadbbbdbdcbbcadabcaccabbadbdcacbaddacdaaabcdabccbadbdcadbcddabddbdbcabdbccdacbabddcccbadcadddbdccdbacbddccabbbacdacdacdbcdbccccdcaadcdcbbccccbccdaabbcbcdacbbccbdbbbbbcaccbcadaacbadaddcccabdcaaacdcabbdabccbadcdbbbcdbdaacacabbbaacbdaacabcaccbccccbcdbcdabcdbccacdddbccdacaacdabdbdbbdbcbcdacbaacaacdaadccacaddaabacbdabdcdbdacbdbaddcacabdcaabdbcaddabbbccabcbaddacbbdacccaddbbdcaabbcddcdcaadcaacaaaccccaaabbcabdaaaabddcdcbbddbcabbdcdbcbddcacdcbbcabdbaccbcddadbadaabaadacabcccdabdbabbcbacddccbbdadacddcbcbbcdcbaaaccbaababbccdadbbbdbdccbbbbbadaacbcdadcddbcbcbcbbbdaaaddbbbbbbdbbdabaacdbbcbcdacacbabbcccbbcdcdbbcbaabddddcaabcddcddcbbbdccbcbdbddaabcdabdbaacabacaadddacbbccbabbcdcadbdbaabddddbbbbcbdcdacdcbabbcacdaddcdbdabbaccaccbbaccbbcbbcaadaabadbabdcbabacabdddcdcaaaaaacbbadabbdccdbbacdbbbbcbddcdcadadbbabacdabbcaaaccccdccabddcabadcdcadccbcabbccbccbcbacacdadbadcdcccacbdcbacbdbdddaddabccbadcddcadcaddacabbadbabdccbdbdcdcababbccbcdcbbbbadbccabdaabababccaadaabbcdcccadadabcbcadadbbbccabacabcddaabdabbcbbaddcbcadaabddadaacdbdabaccdbcdbaadadaabdabddcdabccccadbcbdbddbcbadcbbaacbddbadbcbabbabbcadcbddbabbcdccabcbdadbdaaacadcddcccaaacadddccadcdddacababbcbbcddbdbdcbdddccaccccbbbddccadbbbdacdbacdbcbaacabbabbacddcdacbacdbcdabdcbaabcbddbcdaadccdcdaaccabdabdbabbbbccadadccdacddadccabcbccadbabaaaaacaadbbbadddbcaddbcabcbaabaabcbaadbaccbdcbadbcdbbcdddaacbbabbccacdbbabccdcabddabcabacabdcdacccbdadabbdabbadbccadbbbbcbdcaaaaadccacbdbdcbabcbddbddcabcbbcadbaadcbdadcddddbdacaccbacabdaadcbbdcddddcdccaaadbcddbaacdcbabddaabddcabbbdddabbddababccdbdadbdbdcabbaccddbabdaddaacbcaabacaaccaddbdabddabaaacccacbdcaacaadddccdbbccabcabbadcadcbcabcbbbacabbcbaccbabdbddcacbdbacbabddbcbddabccdcdcaacdcbabcdbcadbaabbdcdbbcbbadddcadacbccbddcddabccdabcbcaacbaacccbbbbacddbbdacccadcabbabadcbbbbbddcbcaabbdbbdaadacaacabdbbaaadabbccadacbbabddaaccdacbdccddbacbdaccccbbdcdbbdcccabcdbcbccdcabcbbbcadbccbbababcdcdddbccaccccdddbaadbdcbcacbbbbdcddcdcbbdaaacbcbcdcdaaccccbabbbbcddcbdbdccbddccbbbaaddabbbdaacacbccaddabdadcddcaadcbbaddadbdbbdcbddbbbadcccccccaaadabbaacddddadcdcccddabaabbbcabbcadbdbddbdccdcbcddbdccbabbadcabbddddccdbacadaadcabbddcabcabcadbbdddaacbcabdabbbacaacbbbcbdaabcdccacabcbcacdbabadaaddbbbccbcdcbcdaaabbcabadccdcacccccabdacdbbadbbdbabaacabbcccacbbacdbdaacccbadbaabdbabdadddbbdbabbaabaacccdbccabacaacddcadacaccddadbdbcbadcaddddacbadacddbddbddcabbadcbccacacdadcabcbbbacabababddaabbdcbcaaccbbaadabcacbbcbaccaacadccbacbcabacbacaabddadadacabbddbbabaccbbcbdbbabccdcaaddacdabdcdaadabbbbcdaccdddbcadadcbdbcbcabaadbdbbbbadddadccbdcbdddcbabadcaddaaaacaddaaccacdcbdbdccabbaaaadcbadabcdbdccbaadddbccbbacaccbcccbaaabadadcdbcdcbddbaadbddcbaaaabdbcbadaadcacddcbaabbddbcdbdcbbddbcddccbcaaccdcbdadcbccdbabdadbacdddaadaabbbcbaabdddcbaddabddcadcaabbbdccbaddbcacdcabdcaabbbddbcbbadbabdcdbbcddcbbdcbcbcdbaaddbccddbababbaadabbcabcabcaaacbaadbbcbcdbadcdabdaaddbbaddccbcadbacabaacbbdacbcabdcbaaaaddbabdcdccadcddddbbaabdabacbacbccacbdacddbbddcccdadcadaaaabbdaacdcbccbaacbbbaabdadbbccbbabadacccadacdaadccabaacacdacbccccbbabaabdcdbaddcacaacdcdbdaccbdbbacdacabdcacadbbcbbddcabddbdbcaacccbcddcbcdbaabaccbccdbdaaddabcaddcbbbddaddcbddbbdddcaddbbcabccacaabbddcaadcacdcabbbdcaadbddaddccdcccdadaccccadadcacdbbaabddcbdbcbdacaadcbccadbdbdadacacacbaacabacbaddccbcdbcdcaccbbaabddaabaddcadbabcbabccadcdcbcacccdcccdbdaabcaadbcaccbadccbcbbadcccadcacbabdcdddaaabdadbbbbbbabdccbdabcccbaaddadbaabaadcadaacaacdcdacdacbbabadbddbacaccacaadddaabdcccdadbdbdbccccdabdbdabddbdbdbdcdbabcdacacbacddadcabbddccdbbbbabdaccabbdccadcaababaacddbdbbbacbccddacabccdbaacbcbadbdcdbbcaaabdcbbacccadbcdcbcccdbdcbabdabcacdcdccbbbbdccabdbcbdaaccadcdccdddbcaaccbbcdbdacdaacacbdaaadaddbcbbcdcdbbbcaddadbbadbcadddabbdaaacbbcdcdaacddbcccdabdddaccbaacadbdcbadbbbabcadbbaddadadbbabdcdadbddcdcdaddabcdcaabbbbcadbcdaabdbdccddabbbaabdbbbabdccdcdabdbbaabaadabadbbccacadcdcbddddbcdcacacbcdabadcbcabadadadbdabbbaabbadcddbcccadddacdbdbadacbcbbaccadbbabcdcacdcbdabdbabbadbbdaadcdccbdddacdccddcbcddddccdcacbcaccadbdcadabcbbabbcbbbadcccdcdcbaddaaacddccbcdccccbabacdabbbabdcbdbabcaabdaaabbccbabbbabcbcbbdbadbdaadbbaacbbbccbcaccbdadccaabbcadacbadaaddbabbbadccdccdcdacbccaacaadcaaabdddadbcabbabdcdbcaacacdacdabbdacdbbcaaddbacdaaddbdadbbbbacbbacabdddbaaacbcdcaacdddacbaacdcbaccadadaabdbadacbdacbaadabbcbbbdbcbbaabcddcdddbaccaadbabdccdadcbdbcddabbaabddbdccbdbbacbaaccdbbbadbbcaddddcdcdbcdcbacbcdbcabdccbdbbdacdbbacacdadddccaabbddbacbbcdbcacdcacabbbddbbcbabaacacdabbcaaddbdababdddcabcdaddbcacbaababbbcacabcdddaaaacddbcadbcdadddcccbccbbdbbbaaadddaadbdacabcdabcccbaabaaacacbbadbaacaadadddbddddcbabbbbbacacdacadccdcbcadcbcbaccdbadcadbbdbadaacbdcdabaacbbbbccddcdddcbadacaaabccbbcbcbcacacbaacbaadcacadbadaacddbdcaaacaabbccaccbacbcbbbcdabbbadbcddcbabcbabccbccdaccbdbdbbadcaadabacdddbbaadaccccadbcabdbcadbacacbabaacddadbccbacbcdcadddddcddadabcbcdbbbabbdcbcbcadabbddcccdccdcadcadaccbbbaacdccaabaadcbdaacdcdcbbdbccdcabbdabaabccddccaadaaddcaabddbabacaaadcdcadddacdbabaccbbccbcadbbabcddaadaacbaddaadcbbcadbddcdbbbccadbaccdccbcacacbcbccbdbdbbcccaadbbbabadbbabdacaddcacccdabadbddcacabdcdbddbababcccddcdabbabaacbaddbbaabccccbdbbcbaaaacadcdbccaabdccadcbaacbababacadaabccbaddddabaacbddacbaadbacabdbadcbcdbdcbadaddabaacaadccaadcbdbdabaadcbaccbbaddccdbccbcccaacdddccdbcddcbadcdbadaaaaccdaadabbdadcaadcbbadcaaddbcbbccaccbadcdddbbaadbbcaaabadbaccadcbaacbbdddabbaabdccbbccdacdbcabacdacdacaadaabdcaccabcddcbbcbaabddbbbdccbccbbacabbcadabddaabcbbbdcacbbdcabcacadddbccabcdcddaadbaadbdcbcbdaabcccabcddcdcdcbbdddbcacaadaabcabcbccccaacddabdcadcddbabcbdaaabccabdcadbaacdcbcccabccdccddddcacdaddadacabadddbdcadadcccbdcbcddbdcdcaddacbccbbbabdbabcdccdddbbcaaddbaacbddaadaacdcdbdddbbbcdcbbacdbadcbbaccadbadcacabdcadbabdabdcaaadcbadadbcbacadccbcbcbcaccdccbbbbaadcccbbcccdadccbdcccbbabbbcadacddbcacbdaabbdcaaacaadabbdbccababbbdbadbcaccabcdbdcbdbbcadbbdbddddbcbcbcbddbcacdddadadadbaacadcdcdaadaadcbcaadbbddccbcbccabababbaabcdddbdadbbcddcddaccccaaadadcbcacdbaaddcbdbcdcabdbcbdbadbcccbbddadcddbddccccabddbddcaaaabbcabdbbcbbdcccddddaaccaccbcbbcbccbdcdcbadbbcaabbddcdabcaddaabcabbbdbbbadccddcadacddccdabcaccdbadadaaadabbdddcacacaabbacaabdbbdccddccadcdbbbcdbacdcccdddacbbdcbcacabacccdbaddbabdadccbbacbadbccaabcdbcaabcdcbddbdcbaabbcadddcdbcbaadcdbcabbbbaaaaacccdabdaddadccbcddbabacabcacbddddcddbcaaddaacbbccdabbbcccbbdbddbccbcdacaaabcbbddacbbcdbdbaacdcaddababcddacbbadcdaacbbccbadbabbbcdbdcaccbacaaadcadcacddbddaabccdddcbbdcacbcbaadbcbcbbbccdccbabcbccbaadaadcdcbadbbcaadcaabccadcccdcdacdddabcbdabaaadbbddabcbacbddcbaccdaaddbbcdbcadadbbcaddcbccddbdcdcdbdaccddabcccdcdaddababaaadbcbabcdbaaccbacbcbbbcdcbdbdbdaacabcabbabccbbddaddbadddddcddbcbdcdcccbdddbbaababcbabaddcdacbcaccbdcccdddbaabadabcdccbcdacdbcdddcbaadabadbbadbadddaaaabacbcddccbbbadbaaccbdbcbdbabcaaabddbdacaacadccdbbcddacbbbbaadbbcbccaadabdadcccbbdabcbacdbaaabcdadadbadaabaaddaaaabdbaabacacbdabacbcdabacdaadbbcdcbbbacaaadbcbbdabddbbdbacbdddccdabcadddbaddcbdcdbbbdbbaabaabbadaaaaadbdccbadcbddadccbaabcbaddaabcbdaabbaaabdacbcbdacaacacdbdbbadacbcdabacdbbcdbddabdcabdcadbbdaaacabbadaacbcabcbcccbaabcdbbcadbdddabbbdacdaadcacddddacdaddbcddcbadabbbaadbababadaaabdbbabcbbbdadcbcaddcdbacddbcdddabbddadcdbdcdbddaaacdadbaddaadaddcbbbcaddacacacddddcbbaddbbbadbbbbaddcccbacdabcaaadcbdbbcaadddaddbccabcadacdacadbcbbacaadcaadddcacddbbbcaadcacccddbbaddabcbaaccababddcccbcbdccdabbddbaaddaaadcccdcbbdcbdbcadacacbdddadcdbbbdbbbdbbcaabcdadaccbbdcbdcacdccdbccbacdabdccacaaddabcddcaddbbdbadbadbbbccdcbabdbddaaabcbaaaacabdbaaabcddadbccabbbddcbcdddaacbabacabbacabcbdbdacbdbaabbdbaaadabacacadddabdcbabdaacdccbccddcdaddbcddccccbccdccddbcbdcacaacbcdbcdddaabddbbaababdbdacbbcaccccdcadccbcdaddabdbacdacdaacccacdabcccbaadbacabbccaabacbcdaaccaaddcbdbcdcdabdacadcdacdaccadaaccbcbccddcdaabbbadbcbcdbdcabadaadbcdadcbbdbcbcdbadbcddcbadbaacaaccccbccdbdddbbbacabdcddbadcdccaadcdbacbbccddcdacbcdacaaadbacddadcccbdbdaacbacdddcbdadbdadbbcccdcdcabbdacbccccbaadabacbbbbcbbbacacabadcaaaaacadabcdaccaddadcbdabcabcabadabcaacabcbaabdaddbaddbadccaacdbcccdabbcbbbbcacbbddabacaabcddddabbdcdabacacdadaacdabaddacbbcadcacaacdacaabaabaadbbcbaaabcdddacbbcbadcccaaddabcbbdcbbccaddbaccaaacdaadddabdccbbdcdbbdcaaccdabdabddaabbcdbddaadabaccbcbdacbcaabaabbbcbcbbaddaaacbaacbccdcaabcacccbdaabddabbaacbacbbbaabcccddcacaaabbadbddadabcbdcbabbbabccacaaddadcaccdcbdbadbdadababdbcadcbcabdcaacdbddddbcbacacddddcbddbcbbdcabbcddcbcbdaacdabcddabbbbbcdadadccaacabbccbdcdcadbdbadbaadddabdabcdbdcbdabadabaabbddcdbddcdcdcbbbcaddabbadbbabcdadbdbccabbdabcbccbbabbcadcbaddddbbbbdddbabcccabccbabddcdddccdbacdcdddddbbacadcccdcbabcacdaacaacdbdbddcbbcbdabdcaccdddaddccacdcccdbccdddacdcacadcaaddbddacacbabddddcbabadddccbdcaddabcdccddbddddacdbabbcbdcbdbdabcdbdbcbadabdddbdaadcdcccaaaadcbdaccbcaddcaddbcbdabbccdabbacdbbacdbccdadcdacdabdaadbbdbcbcbcccaacadcdacaadacdcbdaabacaaadddbabcbccacbcabdabcbcdcbbaddbbdcabcbbaddaabadbaaabccadaabcdccacdaccccadbdbdddddbddadacbdadcddcabcaaabbcbcdcbbaccbcacdccabcbcbdbacbaadbdababddbddbdaccadcbdcdbdadcccababbbbcbdababcbcdcddbddadcabdcaabcbbbcddcdbdcaddbcdcbcddddadcbcbacaaccabddbbddaccacbddddbdacbadbbdcbccabdcadbcacbbdcaacbadacadaccbacbbcacddbdaddaabababdbcdcadacbacdcbcabbaabbbdbbbcabacacacadbdcdaadaabaccbdbbbaacbdcccdcabbcbabcadaababdbcdddddbadbcddbaaaddddcbcaddacbdbdabdcbbbcacbdabbdbadaadcaadcdcababaccddccbbbacbcbbbddcdcdadacdccdaabcacaabbadcbaadaacdcadcabbcbacdddacddabdabdcaccaacaaccdabbcbcbcccbcadddbcbadcaabaacabaaddcaadcbddcbbbaacdcdbbbbddbdbadcabcabdcdcaadddccbdcdaccbddcaacadbabcdaaabadccbbacdbacbacbdabcaaabacddbdbdbdcdaaaccdbcbdddbaddbcdcbabbbdaadaccabadabdcbbacbadacbddaddccdcabddbdbbadaccbcabaacdccacacdccdccbbdcdddbddddbdadcddaaaacaabccabcdcbbaacadbadadbcbdacccdbaacddbdacadabacdddcacbabbbacdadbcbbccadaabbddbcaaaddabccddaababbaabdddcbabdbcbdcddbbddcbdaacdddbddbcdaacdbabbbcadddadaaabcbcabbcbcbaadbbdaaaddcadcbaccbaabbdbccbbabbaddddbcdcbdbdbabcadadcdabbcaddcbbabcbcabccbbacdbcbabdcabbddabcdaabccdabacbbaaaadddaabccbbcbbaadbaadbbadbbcbdadbdccdbbdcbccdbbdcbdcbddbdcdbdcbbccccbdddccacacaccbcbbdbabcddacdbabdbabadddbcabacccbdcadabaabdcbcccddaacadddbccbdadddaabdccbbacaadddaaacdadcddddcccccdbbcbcacaaaacbddbababacaaacdcdadbddbaaacdbcbddddbbbbdbdaaacccddcadcdacaddccadcccddbbcabbccaacbadbabdcbcdaaaccdcdbabcbaabbbbaabcababbccdbccaccabacdddbacbbbcbdbbcbcaccccbabbbdacdbbabcdaacdccdabaccdddbabbdcbbcbdcdcbdcdbaaabcbcbcabcbbacccbbabacabcdcababdcddbccdbdaaabcdbadaccdcbdbcbcddbccdaaabdbddbbcbbbddddbcaabcbcaacddddcadbcbaacbabadacddcbcccbdbdacdcccbcaddaadbccacbcdcdaabbdadcdadbcdbabcbdccabadbdcddadaadbabdddbaccbcabadaaabdbaabdacdbddacdacbacbaaadabdcbcbacabdacdbdbdcbbdccddabbdbdcbcbaaabdabccaccdbdcddcaabaddadbaabccccdbcbbacaaacabddbddbcaddbbcdbabdaccdbcccbadbddbaddbddcdadadbbbccbaddacdbdaaaadaacdaccbbddcbbbdaababbbbcbbcdcabcabddbbadddbbaddaaddcccbdcacddaadbdbdabbbcccbbddacbdbbdadaddbaddccddddbaababccaaccaabdddbacccdcadbcaabbababbbcdaaabdccaddbcacccbcabbdacabbbdaadcdddbcacaadabbdbabdabaccdbcdaccabccadbccddbdbbdbcbcaacaddddaaaabbddbabbadadccdaabdaccbbcaadbddcbbdbbcccaadbaadadbdcdcabdacaadaddcaccbacbcaacbdacbcabbaadbcddbaddabacdcdbaadaddadcbbccaaddadbacbaaabaddddacdbdacbaacbddabcdccacbdacaadaaaacbbcccabaaccbadbaaddbaaadcdbbaabadbbacdbacbaabcacbcaccadabaabcadabadbacbcbcabddaaccadddacbabadccaadadbabdabdabdccbaaccdaabbdcccabcddbcbddddcbcdaadbabaabcbacadcbababadbcddbcbaaaabccadbaaabcbddcdbbbbdaaccaadbabcaabbacdbcbcaddbdbcdbcbaadabaadcadadcdcdadbcadddadcbbbbdacaaccaccdbdbbdaccadddbcbcdbdaddbdcccabdcdbbbacabcdbcbabadadacbbcbbdbabadbadbdabdcdcbbbdabcaabcaacddcddbdaddcdccadcbaddcdbacacdbabddbddaaccbadccbabbcbdddbddadaaabcabcdbdaaddcbaaaaddddcabcaaccdcccbaddbcadbddbcbbdcdcaccadaaaadadcdabdaacdcabdbdbbcaaaddacddbccbbadccccbbbdddcabdabdbccbbbaadabbddbcbbbaaadcacbdcccbbccbdbbcdbcdbabdacccbdccdccddddcabccadbdcbdcaadbcaaaaadbbcaabadcbabcaaaaddcbccdbdacbbdccaaddddbdbaacdbacacacadabdcccaaaddaddabadbaadbcabbdadcadbbcaccccbcdaacacbbbcdddbcabdbadddcabddbaaaabacbbbcccdbcabaadbbcccbdbdcccdbacabaaacdcdcddaabbdccaaccdaddadaacdbcdaddbdccbdccbaabcadbcaaabacdcabbbaddccaabdcadbaadddcabcbcbbbaacaacccbcbbcabcacacccaacddabccbddcbddaccdbabbbcddbccdcadaabddbddcacddbdaadcccddbacccbcadcbbccbdcaabacdcaabccaabbabcddaabddabdadbaabdbbdbddcadcacacaaaacbadaaaaabddbddcddcaaaccabdcdccdabccaccacadbdbbbdaadbaccaaddabcdabccbdacdbddcadcdaccadaacdbabbacdadadbadddacbcbcdadccdbdaacaccbabbdaccbaacddcdbddbdbacaddbaadadcdbdcbcdaddacbcaddccbbcaddcccaadacabbbdddccccbadacddbbbbbacdbbcaccadcaabaaadcddacbbcbacdccbdbccaacadbcadaccdbbcbddbbaacdaabbdcaacdcccddbdabbacdbccbcbddbbaadccbcacaacdbbdaddcacadbccaacbddcbbccbbbcdccaabaacccddcabdadbcaabbdbbdcacbdcadbcabbdbbbadccadacdccbabaccccccbcbddddbbdcbddbddacbcaaddcdacbaccdcadaaacdcbcdbacdcdaabdadbdcaabdcccbcaabadcbbcdbcbcddbccbabcbbbcdbbcabbbdbbdabdddacacdacbaadbacbcbddbcbcaddaacacabbbadddcdccacccbcadddcbdaacadabacabbccbbacdbcddcbaccddacccdadabaacaacdcdaddbcaccbacabaddbacbacadbccdbcddccbcdabbcbdccccacbadddaaacbbcccacbabacadabdbcdcabdbdcbaabdcabdddbdacccdacdccabdaabacdccdcadadcdbdbbbaaadacbbacdcdddaaadaadddbbcbdcadbcbbdadaadbabddcdadbddcacabcbbadbcccccdadddaddddadaaabcbcbccacbadcaccdadddbcbcccbacbaadbaababaccccadbbddddaacadabdcddacaaccacadcdbbccabcbbadccbadcbaabdcbbcbacdadddbccddabcadadcdabdccbdcadcacbdadbabadaabcdcbbcbacdccadacbccbcbaddababcabbdcbcabdddcdbddbbccadbdadadaabdacdddddcbabdcbcccdadbbddbdabccacccaccdcbddbdbdccccadaabdcdcacacacccdbbcdcbbaaddadbdaccdbdabbbccccdcdbdaadcccbabadccdccdaccbadacabdccaabacbddbcdcbacdbbababaaccdabdccccabbcabaccbadcadbacadbcbdddadbddbcbcbcbbadcacabbdcbbabccdbcbaadcbbbdacbaadccacddcaddabbbadacdddbabaacdbaaddbdaddbdbdadccadabdbddbabdbdabcbdaaaddcdaaddabaaadbccaabdcabbbccccabaddcdddbabbcbcaddaaaabcbddaabaabcacadabcbcbabcbbcccccbcdcbbacbdbaadcabaadddacaabaddaaccaddcbdbdaacbcaddcbcabadcdbcbbadadcbbbbabaadcccaaacbaccdcaadcccaaacccdabaaabbdacdcdacdddabdbcbaadbdaddddbccdacabacbcbcadcbddaadccbdbaaadcacdcaaddaadbdbbaddababcbcdadaccbadddccaadaacbbaddbacdcbaccbcbcdbccccaaacbaaadccaddddcbadbcdadbbbabbbccabacccacacbcbaacccadabcbacdbdbababccbddddbdcdcccaabbbababdacacdaacddddcbcdcdcadaaccaaddbdbdcdcccbacaaacddcaaacdbaacaaccbabddaacbcaaadadddbddadbadccdbdddccdacdbdabbdddcbbdbacbdadddabbbababbccbcbaaccbdbabbdbdadbccadcbdccabdadababddbcbcddadbdaabcbdbcddbddcadccdbdcccddadababbcbdccdcabadccaaccdabbcbccbbcbbaaabddbccbdccbccadbbbbcbdddaadcdcddadacdadaadbbdcbdaccabdcdbadbdacadccbaddaddbbaaaabccbbdaddcdcabbbcbbacdccdbabadbdbdcadbabbacbbbbbdacaddbddabbabcbbdcdacbcddddbbdcadbcaabcaaadaabddcdadabbcbdccbabcbcbcdcdbcbdacdccbcabdbbadcabdabbbdaadbdabcdaddddccccacdcaadbcabddcaadcdcccbbdaacadbdaabdaccadcbbabdaddddcadaaacbdabccddbabcbcaabaadddaaacccdabcaadaaabbcbaccbdbcaacbdaacacbcbbbabadaabbadbbdadcbbccbcbdcbdcaabbaaabccadaacccdbbddabccbcdaadacccbbcccaaadddddcbbadddadcdccadaddcdccdbddaaadabccaddbdbbccadadcacaadddcbbdcdbbaddabcbadadacadaaccaddbdbbbcbabbabbbcdbcdabaaddabdcbdabdbbbbdbbbbcddadadaabdababbcabddadbaddaadbdcdabbbabbbbcadccddcacaddddbbcabcddaaddacdbcadbcdadadacaababdabbacadabdbacdbdadabcdbdaccabdbaddababbbddbbabdbadadbccbbdbabdcbdbbcbbbaddcbdccbdbcacddabadabdccaaddadbcbddcaccdbccbcdcabadaaadadcbdbccadddbaaccbaaaadcccdcadadcaacbacdccbabcccbadddcccbddcccadbadbcdadcbdadcbbdddaccdacbcaaacdaddcacacccbdcdcababbbdadabbbcbdcdaadcdaddcccdacdaccacabaabaacbbbbadbbdcdccbccbbcaacacbbbabddacddbabcbdaddcddaddbbdcaacaabbccabbbadbddaadacacadaacddddbaadcbaacababbabbbcddbdcacbaaddbdbbbdccdbdabddcaadadcbbccbbdbabadcbdbababbbcacbaadaddbacaacdabdaaaabaacaaaddcabaacbbcddcacaccbdbcabbbccabdcddcabadccabbddbabdbaadcacdbacadacdcbcbcbbbccadbcdbabbddcbcccacddabaaacabdbbcababacabbcabbdbbbdddcaabbbbacbacbaddbaddadddaabdcdcaabccccdacbdcccdaabdccbcbacdcadcdcbbacbaadcbdbdaaadbdaddbbabbaaabdcccbbdcddbabdcdadbcaabadbdbcdbccacbccdbddbadabccbdcdbadcdbbdbcaaaddccadcbcdbabddacdcdcdddbcbbacbadcbcdcdacdcaddacdbdbcadbdccbbbbddbabddbacdacdbcdbcbaaacaabbcbcbbdddbbabccbbddcddcbdcbbabcbdbdbbbbdacdaadbadbbbccdbadcbaddbddbbcacbacaacbddbacdbacdcaddbdcddcbcaaaaccacbabaaadaabbdcddabdacdbcccbcbdacdaadaadacabbdddadcadadccddbabdacacbcbbbbbcaaadddcddacabaaadcdbbabcaabadbdddbadacbaddcdddbdaadbdcbddbabaacbcdaccbaddcbcdadcbdddaabbbcccbaaccaabdacbbadbcbbabddadadbbadcdbdcbbbcadacdcbadadaadcaaacbddbbbacdbdabbacddbbdccacbdacdcbbbcbaadbdddddccccaabaadbddbbccadccdcbaadcacccdacbbbbbdabbaacbbbbcabacddbacaacacbbccbacddbdadbdaaaabdbbcadcbaccacabbdddcbbadabcadbbaacbcbbbacdddcbaddaaaccadcaddccacadaabcdbbbbdbdbabcbdccdadadaddcdbadaddacbaddbbbcadcbbdaadbabbddccaababaccdbdbcbcddbbbbbcacddbbadcdcccaacadbdbadbdbcdaccaabadccabacbaadcbdddcadbddbdccddccbdabaccacaccaddacbddcabdcdadbcdbdbcccdcddddcbddabdbabbabacbbccbdcacdbabacdccccccdbdadccdbcbbbcabddccbaaabbacacdddbcdbbabdaaadabcbbccbcdaaaadccdbadbbcacdaaaabdcbcbaaacddadadbcbbbdccddbcdbbcdabcadcdaddddabbbcdcbcabcaacbaddbdccabdbdddbccbabacdbadccbcbcdbaadaabaaaabbccbdddcccabbdcdabbcdaaddddcbdcabbcccabcdabddbbddbacdbddcbbaacdaccaccaacddccbdbddbacdaadaaaadbbdcddbabadabcdcadbddbddabdaabcbaababcbbdcbcddabbcabdccabcacdaababcababddbdaddddacaaaadacbadbcddbbbabdcaaadadddadcdaccadaddccdcadabcaaababdabcadcbbdaadbadccdcbbcdaddbdabdccddabbbabcabbadabcdbbaabadcbbabccadaddacdbdcbcabaaadabcadadbbcbbbbddbbcabdaccdbdddcaababaacadcabadddbacabbddcbacbabdcdbcbaabaddcadbacbcbccadabaccdccacdbadbaabdbcadaadcabdaccbddacaabdbbdcdbacbaaccbaacdbbcdcbaabbcabdcbadaabdcdcaabadbcddddccaadadcdaabccbbdaaadacbcdbcdaaddccaacbdbacdcccbbbbbbdcbadaadbddbcadbadccbdbbaccbbdbcabaccbccacacaddaaabaacbacddcaddcaaccbacadbaddbddbcdbbacdcccabbacccababdabcdacdacbaabdccbcbacbcbccbcaabdacdadcaadbccaccdbbcaadcabadcacaaccbcabdcddaccdccaddaddbddbcaaadbbcbdaddbcdbbccbddacaaadcddcaabccccdaccacbdbacbcdbadaabcbbadadadcadabbaccbbcddabbabddbdbbbcbaddcacbadccababbbdbbacbddbacabdcbcdddacddcccbdabbcdaaaacccbdbdccbaaddccabbbadaddacacbaabacccdbbbdabccbcbcacadbdaddbbbadbadbbccdaccddcdbcacdddaacababdcdaabdccababcddcdabdbccadadaaacaddcdbccabbaadddddabbaacdbdadadacbdcdcaaacbdcddbbdbbcacbccadaccdcdbdabdbdcdcacdcbdbaacbcdaaabccadbcbaabbbdbaacabcbacdaadabbbabadbaaccacddbabbbbbdacabdccbdaacdcccddacabbcacdbddabdcaacbabacdaabbaaccadcabcacaaaaacbbaccaabacbacbaadaaadbddcdbcccbaccbaaabcaaddacbbdbccdbcbacddbddcbabbddddadbdcdcadbacbcdccdbdbadccddcdbccaadcabcadadadbbabdaddcdbcddadbdcaddbdadcbcbabbbaadcbabccaaacbcabbcadbabaacaddadbadaccadbbabdcabbccbdababdbababcadaaccbabaddddadcdbbaacaadcbcbbcbabcbcdacadadbcbdcadddcaddbbdbaacbcdbdaccdcddcdbbccbdbaccbaabacadcccddbdadbacbccbddbabbddbabccbdbccaddbbacabdbbaaaccaababbaddaadbadbcdcadbcdbccdbadaaabbbcbcdbbbcdcbbdcbdbbcbaddaabcddadbcccbadcbcbaacccdbcdcbcdcabccdaaddacdacddaccabadbdcabdaaaaddccacbcbabacbddaddaaababcbbaaabacaacbbbacdaabcbaddaaaadcaddcdaabcaaddacaacdbababaaacbcababbabbdaaaacbdcbdcabdbcccbbaaabaacbddcbaddddadbcaddbacadddbbbccadcbbddbbbddbcbaccadddbadbdabcdadbbcdccbbbcaaababdddbcdccadaaabacadaaabaadbbbbccadccbdcadabaabddcccdcbdbabdabcabaccdacbdddccbcbdbbddcaacadabbcbdbdaabadbcbaacadadccaaccdbddbbcdcabaddadddbddccdbbdcacaaaaababddaabababbdccbcaccdbabcbdbaadcdbaaabaccccbacbaaadbcccbbcdbcdaccabdbbadaaddaabddbadccbaccddbcacbcdccabcddccacccaccdbdadbdddadddaaabaabacacadcbbdbddddcdcbbccaabbadadccdddadacbcaccaaccabdbdbbbacccacbbdadccccbcbcbcadadacabcaabaadabbdcacccbdcdaacaabbbadcaaacbabcbcbdcdbaadddababbcccbacadccddbbbccdddbddbdddcddccddbbdbacddcadbaaacbbcccbddcbdcbcbddbadbdddaaaccdaaddaccbacbaabbaadaaaccabcdcbbabaaaddcaaddcccdddccadcacabadccdabbdbdabaadccbddbcdddcadbddcdadcbdcbaaaaabcaccbddcabcdddbddddcbacdabbabcddabdddcababababdddcccccdcaaaaaddcabcdbdcacbdcdbababdccbbacbdccdacaabbcccdaaacadbcdacbacbdcaacaadaaaccdcdaaadabaabbcbcccdddaaccbbabadbccdcacacccccddbdadaabdabcdcccbdadddcdbcbbdaaadcccbdcdbdddbaabbbbacabdacadcdbcbcdcaacbcbcbbddcdbddddaacdbccccbabaaaaababdbbdaadbbadaddbabaccdabccbaccbdddcbcdabdaadbaabadacdbdcbbbbcbabdcbaabcaabbcdbbdacbbbbcdddbabdddcbacdadcbcdbdaddcbdcdaabdaadbcaacbaccaaaddadaaaddaaddbddcabdbadacbacdadbabcaadabbdcccddcdccddbbdabbdcdcdbbbaccbcacaaacaaabcddabddcbccdbdadbdabbacbdbccaabdcdcabcdabdbcadaccdcbbdbcbcccaacabdbdacaaddddabdadaccdaddabbcabcccacaddbcacdabdbbacabbbccaaddabdaaaaadaddacbabbcacdcdabccaabaacbcadcabbddaccdbaacacdadcccbddcacccdddcbbdcdccddbabbababdbdbabbcbbbdaaccabddaacddbcddcdddacdaccabbdaaaccbddadbaddbabbccacabdbdaccacadbccccdcbcbdcaabdabcbbbadadabcadabbabcbaaaadcdbcccdbbaddbbccacdabaddbbbdababbbbbcbccddbdbbdddbbcbdaaaddabdcacabdbdbcbdcddcbdadaacabacdbdcdccbdacbdddacdbaaacaddacabdbbdddbcdcbaddbbcbccccdcdbcabbbcacbdcddcabbbacbaadcbaadcccdbdbabbbcccbddcaccacdaadabcdbcabaaddadaadbdbbdbcdbcbcabddbaddcddbaabbaaaddbbddbaddaccbcbabcdbaadadbddaaaacbcadcdccdaadadcadddabcabcbdbdcddcaaddadabcbdcaacabcbaaabbbccbadadabdbabadcbcdcabdbddbaaacdadcddaaabbbaacdbdcdaacbcbdddbcbacbbbcbbdcbadbcabbccdcccbbaaacbaaddaddbadbbbaabbdbccdbdbaacbcdcbcbdbcdabcacacadcdcacbcbcabaaacdbdacddbcadbccabdddbbabcbadbaccbddcddbaccbdcdbbabcbadbabcdbbdbdbcbaadcccabcabdddcddaaadbddbbdacddababdcddbacdddabaadacbcbdcbbdbcddbdbadcdaccdccbdacdcccbcbcbabccbaaacdaddbbcbdaddcbabcdaabdbcdcacdabcaabdccacaaacababdacaccbddacccdadbccdcadbadcbaaccbdbccbdcccdccbcadadcbacbcabdbababbdbcdbdadbdcdbbbccdbbbadddcccbccbabacdaaabcbdaabcabaaddbaddaaacdddcaccbbcdddbbdcdcbcaddcadccbcaacddcdaddadddbbdaaaacabbabbcbbcbacccaccbabacabaccdbdbbbcbdabbadadabddabbdacdaccbdcaabbbcccbdadabddbbbdbdaacccbcddbcdabadcbbbabdddabadaccabbdbcbdaabbddbaadaacbbaccdbdabacaadddcbcbacdccbddacbcbbbdcdbcbbdbdadbbacdbdcdacbccdaadabaddcddccaadcbdcdaaabbbbaabbdcbdacbcdbcadadbcdbcbcadcdabcddbabccbacaaddcdadcaaadbdabddbbdcdbaacbdaacdbacaacccdcbbbcbdddcaadccccdaacaadadcbccaccccbbdcdddabacddcdabbdcbcbbdddbcbcaacccbdaadbcaabdabbdcccaaabbbcaccaccbbddabbbbbddadadaaadcbcadccadcaaaddadbdbdbacdbdcdbdacdaddbabbdddbdcbbcdcbadaddacbccbadddcadccadbaaabdbdcdaacbadcdcdbabdbcaabbdaaabadbcbdcdbbcdbcdcdbcdcabdbdcbbbbbdcdccabddcdbddaabdcacabbdacacdcbcdcbcddbcbcdaddacaaababaaadadcddcacacbabdacadcadacbdabaacbbbbbcbdacaaccdaacaaaabcbbcddcddacbcbbbcabcaacdddbdcddddddbdbadacddbbcadcccbbbbbdbbddcabbcdaaddaadabdcabbccaddadbdcbcaacdccccabbbcbdadccabbdadbacadddacbbbbbacadccdcabbcadabbdadaacccdcbbaaacdccdcdcbbbcaadacacbadbcdaddbaaccccadcaabdadbdaddaaaacacdcbdabddabdbbccbccccddbbaababaadadabbbdcaacccbbbaacbbdaaadbdabadadaccacdcbbacbcddabdccdccacdaacbabdbbcaacdbaccdccccdbacbcababaadbdacddbddbdbadabcbdadbcacbdbdbbabbdaddbbcbcabbbbcccadbcdaabccaddcdcccabdaadbaaddcbdddaccacdcdabccdaacadbdabbddbcdabcbbbaddcbbcabddadbcdbabdaabbcbacdcbbcdabadbcbdcabbaacdabcbdcaacadbcdcbcdddcaacdadadbdcbddbdcbcddccbbddbcbaacbadbcacbdabccacacdcbaacdabaccdcbbbccacbdbbadabbcdcdaccacccdbdcbabaacadbaddcbcaddcbccaaadcbaaccbddaaaddadbbbadabbdbccccadbbcdcacaabdabbdbdaabbbdddcaaaadccdbdacaaddddaaddbdcdbbcdacddacddddbdccbcbabcdcaccccddabcdaaabbaabbbaadaddadabbacdbcbbbbcbdbcbbdaaabbacdddaddbdddddddadbaaaabbadcccbdcaccbbbaddbbdbabddccdaccbadcbabdcdbaccaddbabcaddccaabcacbcabcdccaadacbddaaddaaddacdbdcaabcacddcdbcbcdddbbcbaaacbbabccdaaddcdccbbdcdbdbdbcbdbcacbcddcdcbadcabbbcadcddbdbddacaacddabbadcabbacdaadacddcddbbcbdcdcbdcbdcaadcddabdbbcbdaaacadcccccaddbddcbbdbdccdcdabbbaddcabbbdabdcbbbbaadbddadcadadabadcbdaccaabbacaabbdaadbdccbddcdcacbadcabccbabccccbdcaddacabcabcdbdabadcbbdadaabadacccdcdbdacbdccdaabaabaabbccdcadcaccadbdcabcbbbbccdaacbdbdacaaaacadacabcaccbbddccdbbbccbdcccdbdaaaadbcaadabbcdbaadcdcabadcbaaabbdbdadadbaaadddcbdacbddbcaddadbcaddaabccbaddbbbbaabcbabbdccacadccbcdcaadcadaddbabaaaabbcddabbbacbddbdbaaddbdcdadccdacdcacddbcbdbdddccaccdadcdcdacbbdacccccdccbbaacccdccaadadbdbddcbbbcbbdbcaccbddbccddadabadacabbcdabbbbcdbdaabbccbadbadbcaadbadbbdbcbadcdaaacdabdccddccdacddcabbcdcacbcacdbdadabcbabacabcbcbccacadaabcdabadcabbadabbcabdbdabacadaaadddbbbbacbaadcdddccacdbabdbdbdcaadabbccbccbdcbcbdbabdaadcdadcadacaadccbcaccaddadcdcddadcaadaddbbdcdcaddabbbbaacbcdbdcabaccacdbcddbabaabccabaacdbbdcbabcaacccdccacbbaaababdccdcaaadaaaadcaaddbdccacdabcdcadbaddadccbacccbcacbcdacaaabbbacbdcbdcbbcbadbdaadbbbbdccdbcdcbbbbccbbdabacaccbdcbbdcdaaadddbdcadbaadacccacadcbacdbbbbababcadaabdbaccddcbdabbaadabdbbcccabcbbdbbacacadadcdabaacacaaddddaacaccccddcdcdbdaabbcbccbaaddcbbdbcbaabbcccadabacdbccaaddabaaacbdababbdddbadcabdcbadadabccbacbbacbdbbaabddbbadcaccbccdbbacbaccdbabdbaacdcddacbcabcabbdcabdbdcacddabcbdbabdccccbacbccccbaadcaddadbbbbccadcabaaddabbbadcdabbcbadbbdcdbbdbbbbdbdbcdcdbdacabdbcdccdaddacbaacdbbcddaacdcddcbbbbaccbdaccabdcabacdcccbdbdbacbcdcaccddbddbdcadbbbcaccbbdcaaabdccbbadccacacddddbcaaaabcaaacdbcdbcbdaddcccddadaaccadbbcaccdabdcbacabbcbdcacbccabcbccdcbcadadccdacababbaacbdbbcabcddbcbbaadcabcabcbacdaddccccbdddcccdadaddbabbbabcacabdcbdcdaccbdbaadaccccccdbbacbddbdbadadaaababbbbdaccdbabadacadcdbaacdbdccbddbaccbdadbcaaccdcbddabcddaaadbcdabaacaddbbcdddabdaddccbaacacddcdbabddcacdcaabdcdbaababacdacbbddbdcdbcbcbddabcabbaabdabcbdccbbdbddcdacddacabddddadbcbaaddcaacadaadbacbbcdccabbbcdbabcaabddacaccacabcddbcdadbcabbaaabaccaabcabbcbcdbaaaccacabdabbddbdbbbaaccbcdbdaaabdabcdabccadaabdbcaabbdaddbbcddacadbadabdabcaddcbdcdbbbbbbdabbdaddaccacacabbcbaadabbbddcbdbabbcbddddaabaaccbbbdacabbadabadbbbcababdaccdddcbadaaabccabbaabdbbbaababddcdcdaabddbababaaddddddccaccbdbabcaccacbbbadabdbcbdacaabcdacabdcacacdddabbdbabbcdaaaabcbcaaadacdbbbaacddcbadbaccdbddabcaaccbbbdabaacddaadbbdbadcbbbcadcaacddacaaaaccdccadadcbdaccbaddabccbcdcccbbbbccaddccacbbdcacdadaabdcbcbabddacdddabcabbddbabadcabadcddcdbdcbaacabcaadddcabdddcdbadcdbdbbccbadcbdddddbcaabcaadbddaacadbccaacadabdbadcaacbbbdaacaccdacdbabaddadabdbbcddbaaabdbbbaddaaabcdbdbcdbbcaaacadaccdbacccabadaacbbbccddcdaabbadccdcadaabaacbcacacdabdbdbababdabaadbbdbcddddbddaddadabcacdaddabbcaddbdaabcbccbcadaabdcdacddadcdcaacccddaaccdaabbbadbcbdaacaaaacbcacbdcbaaacbbbddbabbbcbbabdacbcacbbddadccdcaddabdabcbdbddcbccdbcdcacdcdcabbadbccabdaddcadccdadddcdbacbacddabccccaaadacdbbddbadddbdadaacbaaababacdaaddaadbcbacccdcdddbadcacbaacadccccabaabaacccbccabbbaaadcdbdacaadbdcadcababdccbcacbbabbdaadabbcadbaddadcdaabaacbdbcccccbbadabcddbbccbbccbcabadccacddaadbdccdabccccbcccdbcbdddaabddbcbbcaadbdacadcdacccadbaddcdcdadbcbbdbbccaaaabcbbcbccdabbaababbabbddbcdcdbabdbddcdddbcaadbccdbbdadaccdddbccbaddbbdcabcbcdbdcddcbcaddaddabccccbabbaccbcddababbacddbdbdcccbadabcaaacccadacaaddcaabdaccaabacbabbdbadadbccccdccabbcccacdbabbaddbcdadbbdacdacaabdbadadcdccdbdadcbbccadbcdadadbbdbcbdcabaaadcabcabdaadbcbaaabcdabbbcabcaaabaddbdadbbcbaacddbdacadcaabcddadcddbccdbcbadaccababacccabddacddbaddbdcacdbadcaddbbcaacdbcadbaacbbbcadbcaabbbbacabcdaddbbbadbdabdbdaccbcbccccdddccdccacbbaacadadddacaadcbccccbdabbdccccbadbaddadcadbabbbabcbaadbaabcbccccacaadcdcadadbadaaaacabacccadcdacccacbdbbdaaaddddbdcdbacbbbddcadcacbccbdabdbbacbcbbbdbbabdadabcdcccdcccbacdadcadcdbaabdacacbcdcddbccbcdaacadddbbbbaddccbdaccadacdabacbbbbbcbacabcdcacccacaaadaabcdbadaaadbabbadcaacdabccdbccbbcdbccbddbcccdcbddcabbdddccabbcccaadadcddbdbabdacbadacdcacdcdababdcadbcaddbdabdddcdbccbdccddcbaaacaccbdbacbbcbdccccdccbdcacbaaaddccddcbbaddcdddbccbdcdbcdbdccddbbbbdcaacbdabcacdbabadaabbcaaabdacdadbbaaccbcdaababacdadacdcaccbbdcbbbdaadbacbdddcddaccbacbdadcaaabadacbabadaabddbbdddddabbacacbbccbdbacbcbbbbcaacddddccdcdcbdbcacbbbcabdbbcaaadbcdabcbcbcbadadbabcdacdbdcddcccbdcadbaaadcbdbddbadbcadcdbbabdaaabdbdadabbadddddcccabdccdbabdccdcaaaabacdaaaadbcaadaaaabbaccbdbcabcaacbbbccdadacbdcadbdcaabcbcadcaaddbbacddacddaabbdabbbbcdbaababbbbbcadacbbccdadddccbcccacabcdcbddbbdcdbbdcaccaabccaaacbaaaaddbbdbbcdcdaaacccaacbcadbabbbcaaaacaacbbcccdcccadaaddacddcadccbdbdbdddbccddddabdccbbabbcdcabdcabbbccccddccaabcccdcdbcccdcacaabcbbddcabcdcddbbbbddbddacbcdadccaaccacdddaaacccbabcadbbcdbbbdbcbccdcdaabcdcacdbbcdddcaccbcdcdabcaddddabcababcbbaacccbabadcbcaddacbbdbcbacdaaddbbbadbaccadacbdadcdbcddacdacabdaaadaacbaabcbdddadddcacdaacbabbabbbbacabcccccdbbbadcdabddcbddcdadbbcddcbabccdabdcdbadabddacbacacabdaadbdacbbbadbadccbaccdadaccaaadaacbbbcccccbdccaacbbaababddadccdbcbacaabacbdccccbacbacbbcbdaccbbaacabababdabbaabdcccaaabbaacacacdbaabccdbabcdcccbadcccdbdcbcbdcdbadbaabcdcbcababacdbbbdababadbcdbcbaaddabacbaabacdcdcdacdacdbbdacacdbbcabdabcdbcbcccccbcbcbaaccdadababdcaabbdbbabadbbddabbccdbccdcbbbaddccabbabbaaabddccabdcbdadcaddbcbcdbcaaacbabbabbcddccdbcccdccadccdbcaacdacaacddbbadcbdaaccbdccaaacacbddbabadaaabaddddbcccbacbacadbdbddcdadadcacabcbbccbcdaccdcdcccaacacabdaddccbadddbaccdcdcbdbcbaaaacddaadababbcccccbccdbacddcbdacbdbacacacdcaabdcdcdccbbddcbabdaaddbcdcbcdbccdcdabcadbbaadddabdbdacdcbdbdddcadadadabdcbddccdadbbaabccbdcbcaddbadbccabcacbccdabdabddaadcdbbddaddbddcacdcaadaaacdabdadabaadcadcdcdbacaaababbddddccaccdcbcddbcddbdaccacaaacdccdcbdabdcbdbaaabdabdcabbcaabacacdddccbacbacddcdcdccbdcabacdbcbaaccdccaaacadaaacbbabbcdbbcacbaadacbbbdaddbbbbaccaccacabcaadcccabcbdcaaddcaccabababddbcbdcdcabddddcadbccaacbcabccabaccbdcacccccdccaddaaacbddbbabaacacccacddbaccbcbdaddddbdcaabccdbbbacadbbaadadcadcacbbbaddbacbbdabcbaccaaddbcccadacdacdbabaddcddcdbcccbabdccbddbbadacddaabcaadddabdbbaadacaabbaadbbbdabbbacdcbacdacdabcacdcbcccbbadcccbcdccdadbadbbcbcccabbbbbadbbcdabddcbadaccbbcbbcdbcbaadacccadbdcbddbdbbcdbdabbbcddbaccacbdacbcdbbbabdadadadbbdcabdabbdcabccddcbbaccabbabbdbcabbacccaacbddcbbdbdccababcccaccaababadadabcabaccbaccadddcabbccaddddaaadaaabdadcbabacbdaadcabbbdbaabaaaadcdaccbbabadcbbbacadcabcccadbacadbdcdacdcdacaabadcbbcadacaacdccdcabbaacabdadcaccaabacbccdadababadacbadcababdcccbabbbddaacdcabdadadccdbbbcddacdabaaccddabbdccbacaabddbacdadaabdbbaaabddadbbbbccddbcdadbaabbabacbbacdcddbcbcdbbdbddbadbbadaccdddaaccbaacadccbbbdccbcadadddbddddacabbbcdcccbdbacbdcdcbcdddcbbcabdbaacdabddacbbdbbdacbbabcadbbbbcbbcbbabacadccdddcbcddacdcbbcdcdcbaaddcbccbdbaccdacdcdbccbbadcbccdababccccadddaccacbcbcaaabcadcdbabccbbcadddbacdbaddccdcddddccbbabbccbbcbacacaaddadcdbbabcbbbdacdccadccabddadddababbadccacdbbbababdddadadaacbbbaddbcbdaddababbddbcdccccbbbdcacdaaaadcbabcbbcbdcaabdcbcbdabccbcababdcaabbddaacabbbbdcddbbdbcccabdaacbacccccbdaccbbdbddbcaddcacdbcabbbaaaaaadbccccdcdcddbdabdccdbadbbadcadccdccbcababccbbadacbcabcdcdadbdcaacadbaaccadcbaaacbabcbcaccbcbbbdbccddcbaccbdcabaadadcacacddbdcddabdbbccdddcddbccacdadaddadbbccdbddaaccbbccaccadcbccdabbcdacdcdcaaadccddaacabbbdcddbddcadccaacbdbbaabbcddcacddddcbcbddbadacbadadacbccbcddddcbbcbcbbadbcbbcdaddccadadcbddbabcbabbdbcbadcadbddcbccbbbbcdadacaccbaaaacbcadcddccaaadcbccddbcbdabbcdabddbbaddbcbabacdccaddbcbadacbddbbaadcdbaaccbcddcdddcbdcadadcbcbacbacbacdadcdcdbbcbddcaddadbdaddbabcbbaaacaacadaabcabcaaaddbcaacadcbdacbcbcdaaadcdadcaaabcddbbbdcddddabcacdababaddbddadbbcbcbdbcbdabaccddcdcbcdbcdbbaabacaadccdcababcdbcbbacccabbcccadbbccabaddccacdcbcdbddbdbcadcbcaccdbddcaabaaabbbccdcddbadabcbccdabcbacddacaccbbbaccdaddadbbacbddaaabdddacddbabcdccdaaccddadbdcdabccddbbcacbbbdcddbbaaaacdbddddacdaaabaacbcccdacbbbbdbbbdddbccadddcbcbcbbdcacaabacdaadcdccaabcaccaddaababbcadbcdaadabcdddbbcccdabacbbdcbaccadddbbbbdabdbdbabdaacdbbbdaabdccbadbdbdcadddaccbdcdddaddbbcddababacabdababbacccbdbbadaabdaadbcddbcddadbaacddaabbaaccabbcadcacadcdbbcaabddcabcacbcdcdadddccbddcbcdccdaccddbcdcadbcccccadcdbccabdbdbcdaabcaccadbbcbadcaccbdddabcbaabaaaadcaabcacbbdbbdcdbadaacdbdacdddaddccdcddabcdabacdaaddcaadccacaccabdbbcbadaccbccbadbaacdcdaadddbbaaadddcdccaddcbcbbbdcaddaadaabaccabaabbbdcaacdcbdacdcaadbdbbcdcbadcccdbaabbbabcadabaccdacbbaaadddbcccbdbaaabacaacaddababdabbccbdabdadacacbcbbbddbdabbdbacbbddcbbbcbcbbcccccbbcabbadcacbbadcaddaacdddbbdcdcabbddadccabbaacabddaaaaadcaaaccacbbdcbddbddbddcccbacbdddbddaaadbdcabcbbddcccddcbbcacdbadacdbdabccddcdbdbdbbbccccdadaabbcadcdbcbbbddcabdcbbddaaccbaccaddbbddadacbbabbcbacbaabbbdbddacacbddcaadbccbcacaaddbbbbacccacdddbabcdddbccbbbccabaaacabcccbdddabcbbcadacbbbcaabdbaddcababaaaaaaacdabacbbaddacddabcbdbaccbbbcbcbdbbbaadacdbddbbadbdddcaabbadddccbcaadabddacccdbbdbddaadcdbcccbbddcacbbaacbacddaddbacbababddcadadbaaaaddbbdcaddcbdaccacbaaaaadcaccacbdcccadcabbcbbcbbddbacadacdbcadbadcdbbcdaddcbbcbccacbbddbbaaabdbccadbddddcdccdddacbcacabdccaabadcdbbacbabcacabbcbdacadcdabbaaddabdccdabcacddaabadaacdaaccdcabcddbbacdbbdcaadcdababaccadcabdcccdacdacdcaaabcbdaababacccbdcbccaacacacbabcbdcccadadbcddadabcccccccbbcaaadaacaadabbacdbbbadabdcdddbaddcddaccbddbdbaaccdaacdbaccdbdbbcdbcababbdcdccabddbaaaddadbaccddadadbbaabcdcbadcadbcbaaccccbbbccadcddbdddbacdadbddaaacdcbcbbbadcabcaaddcbcbacaccacaccccddcbcabacbbccaaabbcdaccbdbbacdcabaacacadcbcaccabcadddaddcaabbbdcdbaccaccbbbdbadcccccbdcabbbdcbbbcbcbbcccbccdbcaddccbdcaddbbddaaabcdadcbaabbcbcabdcbdbbdbaacacccddbbdbcadddacdccaabcbdabcabaadbabacacbcbbddbbcacadcbdaaddbdabcbccbccdaaddadccabddcaccbcacbcabccdddbaaadaabcabbcbbaadaccadbdddbdaabacbaadcbbaaadddbddcacbabacccabbaabcaccacacbbbbddcddbcadadbaddcadacbadbabdcbcabdccbcddcbdadcddbabdcaaaabcdcdcccccbbadacbddaaadcbccacbdacbbcabdbcababdcbdabaddbccccbbbaaabacabcdbbcabbacadbaaacddbddcbdbdabcdbbbbbcdbcbdabccacbababbbbcbbbcbabcddcbbddaacabbbcbaabadcacdbacbcbcdaccbbdababbabaabcbddabdaadbdabdaaaacaaaabcccabaacccdacbbdadcabdbbbddbcbccabcdbbcddddcaddadbabddccadcbaabaccdbcaccdaabbacddadccdbabadddbbddbadaabbbccddccddbbacbdccdbddadbddacddaddaaaaadbdddcdbaccccdddababdbbadabcbbcacbddabdaaccbaddcccdadbaccbaccdcdabdccdbacadaadabdcaabcbcbadddaccaccdcaadccbdbdaddababbbdadbacdbaddabdabcacccbcbaaddabcdacabbbaaaccbdbacabbcbbcdacaadadacadaccdbbdcacdbbdddddccddaadbcdaaabbadcacbccdddcbdccdaaaacacccbdcdddbbaaadcdccddcdadacbabaabaadccdcbcdbbbdbccaaababbdcadcdaccabccbbacadcabcbacbacbadcbdadcbababbaadccdbcbaddbdcdddcaddbbcbbbbcbcbaaadabcadcccacccacdacaadabbbadaaddcaabbbbacacdaacbccdabbabaccccdcacdacdbbcdcababddadcbbaccacbaaaccacbccabcdbdbbcccddcbdaadddadcddabdcbddbcdbbdccdccdcbaaaddaacccbddbdbacccbabcabacdbcabdacadcdabacdcbdcbabbcbadcdadbcccddbaccbbacaadaaddbdacbcbabadcdbccccdcdcabdcbbcccacabadabddcbdbabaacaacaacdbbdbccbdbcdccdcaaddccdcdddbbacdcaccdbcdcdadbdcdcaaadadccddbddbcdbadbbccaddbaaccabadcbadccbbcaabdbcabdacddbaabbaaccadccbbdcdbbccadbcadbcabddadddddbaadccdccdacdcccbbcbbbdbacbdaabdbbdccdbcaacbbcabacaccabdbcdcbabadcbdabccdbbcbaabdadaabccbcdddacaaccaaccddccdbdbdacdbccdddccddcccbdbbadccbacdcddbcbbcabcdbcdbacbbacbdababbcccabccdccccbbadaadbdcabcabacdacbcbcbadbcbdddcddddaabbbdddabdaacdaddcdbbcccadcdadcadabababdddcccadccdbdcdacbcbbbbcbbddcdddbddbcababaacbbcbdcbaaddbbaaacbcdaabbadcaaadbcbbbcdcaddadbdccdaaacbaddcddaababcdcdbbcbbdadbcdcbccdbccdcadddadabbccddcdabadbdbbacdacadcdccdaadadcaacdddadcdaacdbdcaaadbdcdcaacdabdaabdcbcbabcadaaccbaacbaadbdddbbcccaccbbcddcaaccddccabbbacacaabdbacddababbacaddaacacaacccbadccddbacbcacbccdbacdcccdddcbdcbacabaddccabddbcbbbbdaaadcaccdcbddabcbcddacadcdcbdddcdcbbbaccbdbcbaaabadabacdcbcaadabcddabbabbcbcadaccdbdccdbaabbdbdcbbadccdcbaddddbacabbcaacaddcdbdbdababddaaaaccabbcdaccccdcbdbadbadcbbcbcadccaacdbacddcabbdaccddbddbbdccdadcdddbbacbacddcdddbaccbaabbbadcdcbddcbcccadcbcbddcdcdbabccdbbdadbcddaacaddacaaccaabdbaaacddaccddacadcdbdabddbdccabbbcadabbaabcccbdddccabadccbbadbcdccadbdacbaaddaccbbccbacdaaddbbddbbdbdbacacccacbabcdcccadaccdacccabaaadcacadacdddddacacbdbdbddbbbdadddbddbacccbbaabbdddbabbaabacdabbacaacccdbcdabbadababdccdaabddaacddcbaccddaadaadaaabdccbdbbdadbbdbaacabbbbbbababdddccadaaaaaadcbcbabacbbccddadcbcadcbadabcbbccacbaddadbdcccabcdaccdaccadaacaadcaabcdbbadbbbdccaababcccdbccdbbcddcddcccadbadcbdabddcadcbacbcbbbdbbbccdaadacdbbdbdaaacacdddacbbcadbaaaabbabaabbddbbbddcabddbdcdbccbdcdbcbddaccdcccbacbdbbccdbbbccabdbadccbdcaddcacadaadabbddccadcbaaccaacddcabbcddbaadbccababbcdcaaabcdacbcbbadddccacbccaaabddadbabdbaccbdcbacabbadbdabcbbcacbccaabcdcacdddbaadababdbadaacadbddbbbbbadcccbcbacaabaddbdcbacbbbaabbdcababaabacbcccacaacbdcacaadaaaddbcaababbbddadabdcddaaccbbbcbcdcabdcbccbcdcddcbdbccbababbcbaccbddccabaadabbdadcabcabaadaabcacddacccaacacbcacaabbcdaacabaccbaccdcaccaccddcdbaddabccabbaaabccddcabbcdbddacddacbccabaacddacacababbabcccdcbacdadadaababdcabaddbaabbdaadacccbacabcbdbabbacbadbcbdacbdbadcbccadccbccbdcbdbadbbabaacbbcdaaacbababaddabdaccbdbdcadbcdbaaddccbcbadbddbadbacddcdbdadbbaaddaabcaddbdcbabdcdacbbdbadbccbabcdabccabddbabdbacabbbcadcddccbcccbbacbcacccbcbdbabcbbcabbbacbabbccaadccbcacaaaaadcbcbcbcbdaadaddcadddabccacbbbddccacadbabcdbbcdaadbbaccbcddcbaadcddbabbaddcdcabbcbadcdbddcadbbaaccdbacdabcbcbdabccbbaabdbbcabaabbdbddadbbccbacdadabcbadaacabdcbbabbcacbaaaadcbdcadcdadacdaaaababbccccdccbadaddadadddaabdbdcdcdadacddabbdaacbbbbbbacdcddbababddccbccdddbbcbabcadbaddadccdaabadbddbbcdcdbccaadaaabcacdbddccbbabcadaabdcbbaddcbbadacbbdccadacacacbadcacbbdcadabaddaabccacaccabcbdcadbabbcabcdcdddadbbacbaabdbdcaabcddacadcbccdbbabcbbdaadaccabdbcdbdabbbcdadbaccbdabcdddaabbbddccbacabaddddabcacbbbddbadcdaabcdccdaaaadcacbabcbdbcccdbaddbacbbccbbdbcbbcbcdabddabcddbaacaadccadccadadddddbdccabdbddcdababbacdabcdddbbcdbbdcdcdaccdbbcbcbddcddcdaccbcbbddacabcaadbadcabcccddcccbabdccbdadcdbbcdcdabcabdbbacbbacaaccbccdbabdcbdcdcbcdcabacaaadbcadcabddbbcbadabcbcccccbaccbbacacddcbdbccbbbaaddcdcadcdabcacbcdddcaaaadadcbcabcdbaacccabcbccaccddcbadccdccddaabadbbbacdddbdbcadaaacacddbdabdbadaddcacbbaacbaacdcbacdcaadcbcdacadddccbdbbbabbccbcbabbbdcaddbdbdbbaaddadcccdcacbcacbcadcadaacbaddccacabbaddddcddcddcacdddabbacbbccccacdadbadcbdbcbdaadcadabaddbdcdadcbaaadcbbbbdcabdbaaaacdbdaddbcbcccbbcdbdbbbddccbddbbcdbbcbbcdaacdbacdcdbbcbbcbcccbaadadcdadabcbabddaaaabcadccbbcbcddcdcadaaddbdbcaccbbdddadbbddbbbddbbcabcbaabbdabccabddbcadabdabaadccdcccdabcbccbaaabcbcdccacaaaddbaaaddcddacccdbcaaacdacdccbacadabdcbadbdbcdbddaabccdbcddcccddbacdccbadbbdcaaabddcaddcbcdbdbadbadcaccbbaddbdcdddbaaabaadccbadbdbdadccbbdbccaacacdcabaabcacbcdcdcdaabcdccabdddbcddcaadddaabbdddbdccbbaacacacbbbcaccdbadcdaaddcdaaabdbabdccdddddaaabcaccbaaaccbcdddcddcaccbbdcdaacccbdccbacbbaabbcccdbaadaccadabbddbcdbbcbcabccbdcbdcabddcbbdbcacdcbccbbbcaaccababdabababaababdccdcabdcdcdccaaaadcadbdcadbcdcbcbbbaabadddaaddbabdcdddabbdbbacdcdabdbdbdbdbdddbdbbdccdbddabccdbdbcbbadcadddacbadabcbbdcdacdcbbadddabdbdacabcaacdcdcabcacbdbddaccabadacbaabdcaccccdaacabcaccabadbadcbbabcacabdabcbacbbdddabbacdcccaaacccabbcabcbccdddcddcabcbaddccacddacbbbaabcdcadbcdbddcdaaadbbddbaababacbdbcdbccdacdbcdcdddbadbaadabdcbcccadcdcbdbcbbbcadbcacacddbdbdccbcdbbcbddabbcaacbabdcdbbddadcbabaabcdcabcdbbccbdacccbcdabcbaddaacbadcaaabcdddcbadcbddaaaccbccabdaadbbbadcdcbababaaadaaddabdacdcacbaadaddcbbaabcdadacdbccbbcbdabccddccdaccdddbbddbbbdaaaacadccddddaabcdadccabcdaacadbbdbdcadaccbbdbdbbaacddcdbbdcdbbcdddadbcbbaaccdcdaabbdbcbdaabdbbcaabcdadccaccacaabdcbbaadbdcaddccaadcdbaddbdacbacdbcabcdabacadcdcbadadddacadbdadaadaaddbcacdccddcaadddcdcaaadaccacadabbaadbcdabbbcdcacbcababbbcaddbcdbcdcbbadadcadccdcabccccccbadbaabcdcccbccddddcacbbcbccccddbddbdccdaaaaccbbcbdddbabbdcdababdddcbcabcbdaadbdbcdbbcadacadabdabaacacaadabdbbacddaaccdbddbabadbdcdabdcdbaaaacadcbacadccbbccbcdcaaddabcdbabbacadbbdcdbbcddcababbdabaacabcbcddbabcdabdcdcccacdbbbdcbcbaacddaccddaaabbdaadbbbbaaddbdbbaaabcdbcacadadbbdccaabbbbabbdcadcdaacacddbcdabcddcadaacddaaaddadabccbdbddcbdaddbbaabaadaadccdadbadbcaddbaacbddbdcbbaccdadaaabaadcacbbcddbbbaccdbdbddbdcbdbccbcdbacacacddcaddacaabbbccbbababddccdcccbaabdcdcccbbdbaaabcbbbabcaaddcbaabddadbbbcbbabddddccdcbdbdcabccaddbbacdaddbdcaccddabadbcbccaabcdccddbdaabcdbaacacbbbacdbbabdadbbdbbbabccbaabccdcabbdbcccbcabdbcaadaabccbcbcddabdaaaccaadaccabdcbdaacbabaacaaaaddcaccccacdcadaaddcbbdddaaccabcadcbdbcaaaacdabdddccddcbbbdbdcdaabcbccbabdbcddaacbaddbbbcacdabcdcacbcbaadabdcbaacdbaaabdcbaabacbbbbdcdcacbbcaaddbcabdbbbabdddacbcbdbcaadbcdadbadcaaaddcddcabdacbbabbcbccbabcbbcbbbdbdcbabaabdbdbaabdbcacbdcdaabddbbaccbcdcbaadbbaaaadbaacdabaabaaccbaacadbaadababcdacddcbacbaacbdacbdcaadddbddbbdcaadabdbcbcbabaddaacbbcdaabdcddccbdcaacadacddbcaddbbddcaddcbadcbdabdadbdcdddadddccbbddaccaccccabdbadddbbabccaadabcbbadaacbadacbdbabcbbacaccadbadcbddccbbdabcaabbbbacbdcbbadddcdadbcacdcdabdddccacdadbbabbcaddbbdbcadcbabbdadadccdabbbcabadccdddbccdbbbcddddcdacccccabcdcbbcaacbcbcadcdcbaacacccacadddcadccdddbdadbbaabcdcbdcbcbaaadcbabbabcbdbdccbccadbbaaadbadbbcacbabdcaacdaadaccdacddbbbabaddacaccbaacbbccacbbcccddbcdcacaadbcdadcdbbdddbbccbbdabdcdbbaacadbddbddadacaccacdbbcadbaacdcdadcbcabadacdacccdbbddcddababacbdacaddddaabcbbbabdccbbcccaaadaadbaadaddaccacaacadbbdccabacccbdddabdddcdadbcadbdcabbdadccdcaddcdbacacbccbbacabbcbabcbbbdbdccbaabbdaadbdaccacccbcbdacaadaabaccdadadbdcbdabcdababbbaaaaaaccdaaaabbbdcbcadbbdbdababcbacbabdbdaabbbaacdbdddbbadacddacdabbbccbdbadaacaccbbbaadcaadcbababacccacdcacddcddabdccddacdddabbcaccddbdacacbadddaaabdcbdcddddbdccbaccddabcdcbabddbadbccbadbcddccbbdcabcbbddbacabaaddbcccdaccaadbbbdadcbdaaabdbbacddbccdcacbaaabbddabdbdcdcacddaaabbccdcdadcdcacadccddcaacddbacbdbcbaddcaacaabadcbdaadbdbcdccbbcbdbdabcbdbbdbddabbacdcdcdcccbdcdaddbcbbdcadbabbbcdabcdadccddddacaccbdccacdaabadbcaccdcdcdacaaacaaddcccbcccdacbcdbacaddcaabdbbdcbbdbdcadacbdbcccdccabbbdcbdcbcbccdddacbdacbcbcadcbbbdadcbccccadbdabcabdaabbdbbdbacbbabbddcdcccdccaddaccdaadacbacaddacbbbcaacbccbcaaaccddcacadadaacbccdcdaddabdadcdbcddcacccbcbcdaadcbcbbdcdacabababcdbbccacdcdddacccbcaacbbdcaabcbdadadbdbccbdbcbbacdccacabcadbdcbbcdaaacbdacdcddbdadccacadddaccbcacccbbbbcccaddcbcaabcbcbabbddbdcaabaaabcddbdaadccadbddcaddcdabcabbddddbdadcbbaacccaacacbcaaaabddadcdcbcbdcbcbbcacabaddbdadacaaaaddcbabbdaabbdaddabcbaddcabbdcdaddcbbacbaccddbddbdbbcbdbccaaaddacdbdabbacbbcbcabdcdbddcbaddababdabcbadbbbbcddccbabcbadacbbabbdacaaddabbdacdabaabbdacadcdacabcadaadcbaadbcdabbbabbaabdcdccabcbabbcdccccabddaddaccdddaccbbcaadbadbdccddbcbabcbcbdcbbacbaaaaadbbcabaadddccacacadbbabdcdccababaddddabbbdaddcddadcbbdaaccbadddbbadcacdcdddabbcddcabaaaadbaabcdbbddcabaacdacabdddbaabcdcdcdadaaaaacbcccbbaabaddbbabaabdbadcdbdbdaccdbacbccddbccddddddbdbadbaabdcdcddbcdcdccadaadcdbaddbaadadcdbcbdcdacaacbbaccddccbaaddcbcbabbcbcabbbbcdcbdbacdbbbaaccaabccdacbabacaadacacadacacbcbcdadbcacccaaababbbddaacddbcabdaabadadbbbcdabcaabdabaaaadcbbcacadbcbaadbbaadbcbbbbbbccaddabbbccadbadaddbcbcdacdcdccdcbdcaccdadccbcdaaddbddcacbaccccdddccaaacbccaabddcbbdadaabaccbaababbcddddacbaacabadbdbcadaacbccadabccaadddabacddbdccdbaccdbddbcabbddddbddabdababbdadcbcadcabaaaabbbadacbbbcaaadcddaacabcbccabacacddbdddacdbabadabbdbccdcabcbddacdadcbbddbdbdabadddadbbccabdbabaacbdcbdbbcaacdcadcdabdbccdadbbaacaabbbcccdabcbbbdaaadcbbadaaacadddabaaaacbcacadcccbbdbbdbaacdbdccaaccddbdddacaddbbcdacddacbbabddbadccbccdadacccdbbcddcbddacdabcbaaacdbdcbbbaddacbdddcdbbabbbddbbbababbdbdaabdbcdccadbcaccdcabccbcbcaaacbdabcbdcadbacdcdcadcdaabbbcdaadabaccbbdbdddaabdcaacaccdcbbaabbacaacdadadbbabcaabdbcbccbddcbbbabbadddaacadddcaadcdcabcdcbddbcaacaccbdbcbcadaddccbacabadcbabcaddacdaababadabbcbbdaccbdabbcdaccbadacddcdcbdcbaaaadccaaddbdababbbdacabbcaccdcadbabdcbaaadcaadbadbabdaabaccdbbaaddadcacacacacddcbbdadadabadaacaabaacccccdbaadbabbddacdcbabdaacaabdbbdbacdabbdbacacaadadbaabccabccbdcbdaadbacddddcccbddcbbdbcaddaddabdabbcaaadacccaccbcacdbadcccdcbbdadadcbbcddcacbdadbbadcdbbacbbdadcabcddcbdcbbaddcbbadcbaaabccabaccaabdbacdabcaddcbdabdbbbdcbaacaccbdbcbbabaaacdbcaaadbaaabdacaacaabcbbdabcbbdbaccdcbcabdaaadbaabdacacdbaddccadabbbbddbcaabadcbccabcdcbabcacbcdacccbaddcacbabcbdabdddbccadbdcbcdbbdbadabacbbbacbbdcdbbdccbccdbadddbabbddababdcdabbbdcbdcdbbdddbaddddcddabcddbdbdabdbddcdbdaacaabdcbdacacdbdbcbcacbdddabcabcdcddbbdcbdaacdbcdbbbadacdaccaacbbbcddbadddbdaabdccddaddadbdabdbacdbdaddacdacdcdabbcdccabddabdcdbdacdabdcbbabbbcdaacbdbdddabbabacabbcddcbcccabdcdbaadbcadabdaaaabcbbbdcadbdcadabdbbcabddabbdacbcadbdabcaabbcadddddbdbbdbcbcccddadbaddaacacadddcddbbdcabdbbabaddccabdcbccacbdabbbaaaabdabbbdaaabacaacccbbabcddaaabcbaccadcbdaccdadbbdccbdcbdbbcacdbcdbdbddccdbbccdbdcbaacbcbddcdabadbaabcddcdccdcccaddbaddcdcdcdddcbbdacdabccbccaacdbbacbbdadaadbdbccdcacbddcdadbadbccddbbdbdcabccacdbabccccbcbdbacaddcddbcbdadbdbdcbbdbdbdcdcabbaaabbcadcbcddbadcddaacbaacdcbcdbcdbcaaaacdbaccaccbcacbabdcdaccacabcbadbcbaddaacadccacbddbadacaadaccaadbbabdcdaaddcabbddbbbacaacbcccdccadddcbacadababaacddcdcbadaaacdbacaccbbcdcbbcaaccbbbdcddadbddcaadbddbdcdcdcbbacbcacdacadacaabbbaccabaaccdadccdcbdddaacbcdaadbbadcbdcabbcdbdcabadcaccabaaacbaacbdbcdcdcadadbdbcdbbcdabbdcccbbccbbacbcabadcdcabababbdcbdbccbacdadaaaadbdbbaccbacababbaaaaddbdbbacbbcbbcabccadbbcbddaadbdbabdcaddbcbcaacdbabaaabcdaacdaaadbbacaaddbacccabcbbccaddcdcadcadcadcbdbddabddabdbddacaacaaaadbdcdabccabcdccdddcbddbacabadbbacbdbbbabaddddadcdccaadcacaaaacdcbadbdaadccdddaccccbababaadcaddbbccbddcbccdbacacbccaccabbbaabadacabdbcbccbcbddadcdabddacacacbdcccbaccdacdbdabcdddbccacababacbadadacdccdcdabbdadaddcaaaaadacdbccbccbcbcccdbccaacdbaddadddbdddacddccddcccaabbddaabbcdddabddabcdadbccbbccccbdabacaaaadbcabbadcdaadadbdddacdaacdaacddbbdbcbdccdaaadaacccbbcddcddddadcacbbcbdacabcccbdccddaaaacdcbbccccabadaaadabddbcabdaccdcdadbabdcccdddaabadabbcccbdabcccccdbcccdbaddabdbadcaccddcdcbcdadadacbcbacccccacbbcbcaddbccbdabbaabdacdbdcdddcbddbccbcbadddcdbdaddbcdcabbadababbddcdbbdcdccabbbacbababcbbdadcdbacbcdcddbcdcbcddcaacdaaddabadcbbaadbaacdbdaddaddbbabcdbadbadaacbbbcdcddbacdbaacaddcdddccdbbcccdddcdcdcaacdcaaabccacaccaadcdbdabcbabbabcaccdbcbaaccddccadbbcdcddbbaacdcaadbcadcdcbcababdacadaccdbdcbadbdbbbbbdcaccdbdaddcccbcbaaadcaddabdddccdadbbbccbbbbdcaacabddbadbdbdabbccdbbbcdaccaabcbaaaadbbdccbbcdbcccdbcbaddbdcbaabccacacbcdadbbbbacbaddacadddaccbcadcbabbacdbdbdbdcadcbabbdacadbbcbadcbaddcdbabcacdcbcacdababacbcaaacaaaadabbaddbbbdbacdbbbaccabcabddbacbdddabcacadddaabbadbbbcbbdcccdbbddbaccbbbbbbdbcaadadaaabcbadbbacbcadbcabacdbbbbdcccccdcaccbbddccbacddcadcbbddaabdcacadcbcaabaadcdccdcdbdbdbbabaddbdcadddbabbaccdddcdcbdcbbcddadaddcdddaaaacdcccbdabaaabdbbbdcdcbcadddddaacdaadccadaaaabbbbdcadcbdccababccddddabddcabbaaacacacadacdbbbdaaccabdcbbdcbcbbcbdbaccbaadaaadbbddaddbbacbdbaacacdccdbbbabbacdadbdcabccdabaabaadcdbbccabcdddaddacdcddadbbacadbadbdcdbbdaccdcacbccddbdaabadadcabbbcdbbcacdbdacbbababdcaadbcabddccdcbadddcdcdaacdcddadccdbadaaddadadcacadabdccbbcdbbacadabdaabbabadbbaabdddbcbbaadadbcbacacaaaacdbbacbdabdacaaccddbaacaabbcaaadacddddadcbbdacabbdcbccccabbdcbadbabbbcbcbdcabaaaacaacbcbaccddabdacccabdabbddcdbbacccbdcaadcbccabdcdadddadaacacadbcbdaddcbbbabaabaabcaaddcdcccaaddcdbadcaaabcabdacbaccdbdbcaabccccacbaacdbbcbaadcbdabdcdcaccdabdaababacdcabdccadabdddaacccbdabcdbddabdccbbbcadaddccbcadcdcadbdcdddbdaddccaabbdadadabdcbddbdbabadccbdcdbbbcbdcacbbdccccddaddbbccddddbdccadbcddcacbcacccabbcabacddccacbbcaddacdbabadbaabaacaddcbcddabaabababdcbbdcaabccbabbccacccbbbabaddccaaacaccbabdacdbcdabacadbabaaccbadaaaaaaabbdcbdbacdacdcdbdcdddbddabdbdaaadbbaccccbcdcbaddbacadbaaacddaadddadcbdabaccdaabcbbaadbbabbbbaccadddaaadcccddcccdcddcbadcabddcdcbaabacccdaddbadbbddcadacbbdbcbacdccddbcbbacbbddbcdacaddacbbadcbcdadcdcabbcdaacdadabbdaaaaadaabdbcbcdabacabbaccbdcdacbdbcbaaaccdacbbadbabbacacdbadbdacdbcaccbdadbdabcdbbabaaccbccaaccacbbbdbbdcddbdddbddcbcdddbbcadcaaddcbbdbbdadabbbdbbddcababdccaaadacbbdcddbbcdccdccbadbabbcaccbdbadbdcccbbdabaccdddccdbadcdbddbadbbabbadacbdbddabcacadcddccbabbacddaadbadacbddaadcbaccdcaadbbccdadaddaabcaccdbaabdbddabadbcddbbadbcccbdaadddabbcbdcabdcbcdcacaacabbbcddbaadbccacabaccdbbcacdcacbbaccbabbacccdabdabbdbcdccaaadcdbaacdaaddcddbadcdcdaddbdcbadcbbabbacbcabacccacdbcdbccbcddbabddcbddcddacbbdcacccbdcdaccbabbdddadadbadacccbcdcdcbcddbbbbabbdadabcabbdccacbdaddadadadaaaadcaccabcdabddabcbabdcccadbbcacbadabbadbdddbaacdcdbdcddadbcbbbcdcabccadadbbbbdadbacbacbaadbbdbbbabcaaabdccbacdcbadcbcabababcbcabdcaccbdcdbddcbacddaabdcdbacbbbbaddccbcadcdcdcbaaadccdcabcbdbbabdaaaabcbccaaaaacdbadcabaabbcbcdababaaacbbbcbaddadaabbbcaadacdbadbadadcddbbcacacacbdadbbdbacaddaadbbdadadbbbcdaccbbbcdbcacccbcaaaacdbbddabbaaaddcdcaaacdbdbddcddbcbaaccdcbbcddcaaccdcdabdbcbabacbccdcbbacccabaadbcdcabbbaacbbcdadccbdabccbcadadcacbbcabdabdbccabbcabaccdbabbaaababcbcacbcaccaabcbabcbcdacccdcdcacdbcdbdbbaddcbdddcdabaddbdacdccaacdbcccdbdbdacdcddddcaacbbdacddbbbddbcddacaaaddcdbdbcbaabcdccccbcbabcdbdbdbdadabdabcddccbadabdababcabcbacbbddbccdccccbdadbcdcbdbcccbbdcbcaacdbdcabbcdaacbcccccabcccaccabbcccbabcddbdddddbcbbdbbcdacaaaaaadcaacdbacadacdacdcaadccbbccaadcdcaccadccbcbdbbddddbbacdabcdcbbcbbbccdcdaacdbddbdcbbcabddadcdcddbccdabdcdbccbdaddcdbadccbcdddaacadbabccabdcbbbbaaddaadcdddadcdbbbcdababaabbbccabbbcbadbdbcddcdcddaabcdddcabaacadaabbccbdabdacbababbacbdacbdbadadcbdcadcddbbabddbbadadadcbabddcddacadcbabdbabaddbabdbdacacdcadacbbabcdcbabbccbcaabdadbdcabbabccdadcabccaacacdddddbababbcbadcbaadacbdabdddaacccdbdddcbdbdcdcbaaddccbbcaccdadcbbabaddbbccaaacddacdcbcadcbbaccaadadcaabbdbcbaaaadadaddcdcaacdbdcdabadacacbabdadcbadcacbacdcddaaabbbaaacdcdaddbdcacaaadcdadbaaaaacccbbbdcacacdddccabbcaabacabbcabacbccdbaaadcdcdadcbdabcbacdadccdabbadbacaacdcbdadbdbcacaaddbadadcccdacbdccacacbbdcacaccdacdbdabcdcbdacdcbdcddcdcbddbabacadbaabdcacbdbddcadccabdbdbaccccbaadbaccbcbbbccdbccadaccbaccbbcaadaadabbddcbcbacadacdacabccaddaabcdbcacbbaccacbdbbabcbaacaabbcdadcbbbcdbdbaabbbdbbcabadabcdaccdbbcadbcbadcccbcaccdbaadbbadddaddaaacdacbccbdbacdadaacacadabbdbddbabbdccaadcccddaacdbadadcbddbbacdcdcaddadbcbdcbcdbbbddbcadccdbdbabacddcacdabbacccccdcdacdcdadccacbbaccadbabdaddbdaabdaaccadcddbacccbcbddcdacbadadcdcccbcbcddaadddbbacbdbbdbaabadbaaaadcbddbbddbdbbababdaccabccccbdbccaabcdbbdaacbbcbbadcbddccaabdcddcdbbbddcabbaacadcdacbbbccabbbccaaddcdcccdcdbbbadacbdcdbcdacbddcccbcbbaacaacbbddccaadadaadbdacddccacabddadabdadbbccbdaababaaaaaaccabbdcdbbdddcaaddbadcaacbaccbcdcdabbacddcddddabdbbbaaacdacadcaaadcdaadbbabdaacbacdbdbdbcacacadccabbdaddbabaabbcadcabaababdbbdbcaddbababdcabcabbddacbdbbcadcbdbdccdddbabccbbbbddddabdccacbccdcbdbbcaaaababbadbacbcdcabbbdcaddcbcbbbdacdcadcaaccdbbcbdbacadadcccdbdbcbcacdcccbccccbdabadbcabdabbbdbcdacbaddaddcbcbcdcdcaabbccccaaabadbcbaccacaaaadabdadcaadcadacdbaddacdcbdcdcaaccccbddddcdbcbcbcbdaddddbaccadbcadaadbbcbddbacaddbaacdcbabdcaabddbaadbddabaccaaacccabcbaabbccabcadbbaccbcbcadccdaaadcbdcbabbddbccbcccbccadaabdcbbbaacabacaabbdabaadbcaaabdccdddcacababbbbbadccacacdddddcddbdddcabbbbaacdbbaccdbcbabdbcdbaacbcdadcccbbabbcbbbabbbbddadacdcccadaaaaccaadabccddaaaacdbccdcabacaadabaabcddabacadcbacbcbdcdaaddddacadccadaadadbcaddccaadabcacbbbbbbacadaddadcddcdcdabacbbdaadbbcbbbadabbdacbcbbdcccdcdccddcdbdcabcdbabacddbccbccccaccbdbdbaadaaaacdccdacbcaaadcadcdaabddaaccaacdddddbbbcbddcbbccddaaabccadadacbabacbacbaabdcbcdcdbdbadababddaabdabdadddbcbcabddaaccaadbacccbbcbaddbcadabddbcdbdbdaaabdcdbacaacbcaaabdccbcbaadaabbadbadadcbddcadcccaddbbbbcaabccccdddaaddbabbddaacdbacaaaaabbcdabcaccdbaaacdbbdddccdbabbbaaaabdcbcdccdbbdbdcbbbcbbbcaadcbddcaddbaacccbdbbcccbaaadbccdacdcbcddbcaadbdccdabddabbbbcbdddbccdadaabcccabbadbdabdcbddbbdccbadaacdaccdabcdcaaadabccbacadccdbadccbbdbaabaaabdadccdcabcbbaccadbbdbbbadbcdddacdaabbaaddacababadacbdacbadcbcadbdddcbbddbccbbbdabbabacaadbdcbbadddbcbdbadcadcbccdbbbbbbabadcdaaaaaaadbcadaabdabcdccbaadbbccddbdacddcbabcbdadbdbccdcbaccbcbbcbacabdbadcabdaacabaacabdbcbbbbbcacadacddddaaccccabcdcacadaabbcbabcabdcbaddacdabbddbadabddddbcbaacabddcaacabddddccdbbcdacaacddacdaccccbdddcdcdddcddadabdacaaaadcaddccadbbcbdaaccbddaccdadadcccadbaaabcbcbcbcdcccdaacbbcadcdcaccddacdabacdbbdabcadbbdcbcbbacabbccadbdabbaabcbcbcbacdbadacdcbacaacbdababddbaccabdaadddddbbcadaadaacbcabccacbbddcbabbcbdcaccdbbacdbcadcaaddcbbaaacabbacadcacaacdadcacdcacddadaddcdaabccaddbdadbbccbcdbcbcdcaaacdcccdbbdbdababcaddbcdabbadcbdbdbbcdcabbddcccccacadccbbaccacabdccbccbddaadadbdcadacbabdaddcbdbcdaddccdbcbccaacbbbbaddcdddacdadddddacdddbbbcddadabacbacdaddccacbaaacdddabbacbdcadddddddcdddccabcdccadbadcdbdabdbadbcbdcbabadcbbbccdbbbbddaacacbdcccabbdbaabbdbcccacacccbaabddcddcbdbbdadbbdaddbbbcbacababccbcbaaacbbbdacdaaabdbbbddabdcbcdccbbbacdbbcaddaaaadcdccddacdccbbbbddacbcbbdabccaaaabdcdacdbabaccccbaadbabcdcaccadaadaccbabcdacbccbabadcaddbabaddbacbdbbcccbcbdbbbadddadbaacaddadaaacdbbcbacadbbcbdbbbbcaacdbdcccdcabcaddbcaccabcbcacdbaaddcdaabcaabdaaabcabccdbdaaddbbcacdaadaaaaccabbbbdcdabcaacdcddcbaaabbdcaaacaaccaabccdcdabbbddcbbadddddacdaacddabbcadbcaacaaadbcdcdabdbbadabdccbababdbcabbcddbbbacbdcdcaddcaddddddcaaacbaccbdacdbabaadaaccadcbdbcbbcdabdbacddcdbcacddabadabadcaaccbbcbdaadccaacaccbbcaccabdabacbdcacbadccadbbdadcdddcbdddbccaaccabacbdcdddaccadadaaacdbcccdcabaaaaabccdbadabbbbbbacbcdaadaddaddbcdabddbcadacabadccbcbacdbdccbbbcaadddbbabccadbdcbbcacddacaaccdaadacccbabcdbdcaacabbbadcbbbbbdbacddddacabbbbbcacbcdcdcadabdabbccccacdddcdbacbdddbdbdaddbcdddadadbccadabadaaababacdbbacdcdaaaaadbbcacdadaacabdcdadbdccddccddccaddadbdccbbbbbaddacdbbdaadbbacddcbacdaddbcdbbbbbddccaacabbaacbcadcadcbbcdbaadbacabdcabbcdcbcdabcbaddbbbaaddbcccccbdddccccccdacdcbbdcdbabaddddcdacacdadbabcbaccbbdcadcbdddcbcccdbbcbdcddbbadddbadabbcababaddbdabdabdcabcbdcaacdcaccbbdcdacbacdbcbbddcbdbdccaaabaaabcdaadcbcdbbacbabcbadbdbdacabcbaadcabdaaacbdaccacbbbdacdbcacdbbcabbbaacccbbccccbdbcdccbbdccbabadbdaadcbabcdcacdaadacbcbbcacaaaccccabbbdcccdcbddccaddbbcbcabdcdbadccdddcdaaabdcbcaacaddacbbdbbbddcabcbdaacaccdcabcbaddadaccacbcbbdacbbcddaadbbabbcadcbdcdbdbadadcbdcdacccddbadaacabdadcbbcadcdcabcccacbcacabddbdccadcbcaabdbbabcbadcbacbdaddcddadbdcbdadababbdbcddbdcbaacdcccadaacbcadbcdcacabacabbccacabddacbdbcacdabdacaccbdacbbdbacbcdacadddbbdcdccaaccbcdbcacbcbbccbdacadcbcddacbccacdcdcbdccabbaaacbcbabdabaaccbaacbcdacdbddaaadcddbdabadbdcadbbcbdbaaacdacaabbacaddddcdbcbdaccacdbcbddcddaabcadabddbbccdbbdabbbdacabbabcdaccccadbbcbadacdcddaadbdddbdabbdddcbccbdacaaababcddccbbbcbcdabdcacccdbacacacdbddaadadbbdcdaccdccccdccbaacbccacbccccacaccccdccdaccadcddbcbcdccacadbbacbbddaacbdccadbdbacdccbbcbabbcbcabbdacdadaaacdabdcdbaabaddcbcdcabdcdcbbbbaccdbabacbcaaadaadcacadacbbcbbbcaacbaacabadcdcdbcabccdaacadbbbabbaddcdbcdcccabdbabddbaabccabcbcaacddcacbbcadccabbddcbddbacbcdbbbcbdccadccdcdadcbaadcabbdbdbbbccccaaaadacaabcdcddcddbdcdbbcccacbbabdadcdadaaaadddbadabbbddcaaaccacdabdababcdbabdbdddabcbbbccdbccbcccbcaaabcbbcdccabbaabadcaacddcdabcbcadcccabcaadbaaacaadbdccabdccacbcbdbddbdbbdccadbcbcabcdaccbcabacbabdbbadbdaacccbaddaddbcbaacbabdbaddadbaaacabcddbbbbdacbdbbabadbaadcccbbddbcdcabbadcaddadbcbabaccbcdddacbacbbccadcbbcccacddccabbdcaccbcbbcdbbcaabcacbbccbcacbccccdbabbcbaaabbcbddaacbcadddaadbbaddbbccddbcbbbcdcadcbcdddbacddbbaddbaadcaadaadadbabcdbbdadadcadbddcbdccabaadcaccbcbcdbcbabacdddbbadbaadadcdddaddddcbdabbabdaaabaddcccbbbdbcdaccadcddccdaaabcacadcaacbcdacacadadaabbdbcdddcdcbcbbcbacccacaccacaaddcbacaccddcdbbcddcaadcbbcababbbdacbccaadbbacdadbbcbcaabcabbcdbbbbddaccacdbdadbcaddbbdbcaadbabbdbacdbdabdbbdcbbbcabddcdabbcdcdaacbbcccbaaaddacbcddddbcdccdbdcdaddbccadbcbdbddacacabbdddacbdddcabbdadbcdadcaddaccbdababcbabcabacabbdaabacbbbbaccdabbdaccbacabbbbdaadadcdabbdabbdabdaddcbbdaddbababcbcbdabcbbcabbbdccadacdccccbabaadadacadbabdaabdadaadbaabbccbbbcccbcacccbddbabbababaaacacdcaddadcadaabacbddacababbdccdaaccaadbcbacdaadabdacdaacbcacccdcbaaaccdbbadadddcdbadbabdcbdcadbbcaaaacabaddddbbbdccbcddbccdcaabbdcdddcadadbbcdcdabddccbbcdabcabcaabcbddcabaaddddbbdcbccdcdabdddbcdaaaddbbdaaadcaadcbddabbacddbcdccacaddcbdbcadcdcdadcbbaadacbabcdabbdbadababaddaadbbdbbaabcaadacccaaccbdaaaadcbdaaaddccccdccacbbcadbcabdabacaaaccadcbcbdadcabbcbadbaccdbacacbcacdcddaddbddabcbcdcbbdbadcbaabdbaabbbcaadaddbbadaaccbdbaddacbddcddbbabadbbcdaccbdcacbbcbaaddddadccccdcdcbaddacbaaaddadbbdacabbaabbdcbadcbbcdabccbacdccbbccbcccacbdbcbacdabcacdacddccadcccabbbacbadbadaddbcbbadbbdbddbaaaabcdbddcbbcdaacbdcdbaaddddbdddccbbbaabbcdccdbacbcdddcbadbdddbcdaadcddcccaddaadcdbacccccdadcaadcdccacadcaacccddbabdbcadcadddbbbabcbbccbdcbdbcbcccbcdcbdbcbbbdcadcaaaabbdaacbbababadcdacabccadbaacacdbadbcbdcdcdacbcaccdcaacbabbbaadbcbbbacabacdcaccabbbbbddccdccbbddcbbaaabccadacbcadacabccdbccccadabdaadcdddaabaaaadbbddabcdddacabaccccbddcabdbbbacdcaabddbbacbdcbcccbbdacccbadcbbdcddadcbcbbbdbdbcdccdadddccdcdaabbcaaccdbbccaaacdcabcaaddbcdaadcaaddbcddbbcdaadabdaaccdbbadbdcdbbacddbcdbdddbbabaaddbcbcddbccdddcbddcabbbbcdbbbbaddcbdcbcaaccbcdddcbabbcbdccdbbbcaacbcbbbdacaacbaaadcbcbcbdcbabaacbccdacbcdaaccababbdbbbdbaddcddccdbdcdacbdbbdcdcaddcccbcadaaaadddcddcbcaadcaccbbdabdccaadbbccdbcacdaddabcbccaaacacadccaccbaddabdbbbdadbdcdaccdbacaadcdcadbccbbdbabcabcbdbacbadabbdabbdabcabaddbcacccdabdacaccdbdaabbcabcacbaadbcaaadacbcdbdddbbdacbcbaacdababdddbbbbcadadcdcabccabbbcabdadbabadbbbaadadbacbcadccabdddadbdbbccbcbbdbbbbabaadcacdbbdbabaadadabcacacbabadcdbddacbbaaaabaadcacbbbabbbaaabcbabbbbcccabcdccddddaadcaccdcbcbaadddcbddbbbacaaddbbccccbaacacbdacadddcbbdaadbacdcabcccbaababacbacbccabbbcbdbbbdbcabddacbaacdcbbaadcadabbbcbbdbababbaccbbcdabbacaadddddcaaddaccbcbdaacdbddddcdadccacbbaaddcacdacbcabcbacdddadbacbdbbdabadddbbbccbdbabdbacbbcbaaccccddcbbbbbaddbacddacdabdbbcbbdbddaabdbccabbdaacdbccabdacaaabadbbcbaacabbbdcabbbbcbcabaabbaccccdbcccdcdbaaaabcdabaccadbabcbcbbdbaabaddcacdddddccdcdbabdcaccaacadabbcdadbdcadccbddcadaccdcaabdaacbdaaacbdadaabcdbbacaadcaadaaadbddabcbbdcccbaaacdddacadbcbddbbdcccabaaaabdaabaabaabdcbccacacacddcbcabaababdabaddbacbccdbcacdbaadddbdadbcdcdbadbabdcdbababbacddbddddbbdacccbacbadddcbccdcbbcdbcddccccacddbbabbbdbacccbbccbbcbccdcbdabdcacbdaacbbacbbabaabbbacadbcaacadcccdbaadaadcabaabbbbdddcbbcbcacacaacadadadabdbcbdadcdcaddcacddbdbbccbacdbccbabcdcdbddcadacabbdadcccdbcbcdcaabaccddcbbaabbbdbaaacccbcdbccdcaddcaacababdadbaaabcdbcbcccdddadaaaaabadcabaaaaacddcdbdcbddaadbbbdbdbdaabdadbddbbdddcdccadccabbbaddbccdaccddcbbbbdcccbbdababbdadadcadcabcacbdbcbccadbaadbccbabaacabcabaaddbbddbdcdbdbcbdadadabdbbaaacaabccabacaddddbbdbddadcbbdcbbdbacdaaddaaadddcbcacdaacaadcbdbccabcbdaabadbaaccadadadcbcdaaddadbacaacbbabbdaacaaccdacbbcdcbababccaaddcdcbcbcccdccdbbbabcbbcbbcbbdadbdbacdcadccbdcbbbdbdabbbdabddcbdddcbcaacabbcaadabddccdbbbcdadbbbdaccbddaccdbcdbbdaccbbbcdccadcdccbcdcaacddbdacaaccacaaddddddbabaccbcccbcddcaacacddbdbcccacaccbcdbcacbacacadadaabbaacacdaaaadccabaddaabdaccabdabcaddccbccddbbbddadacbbdadbdddcadcacdbcaccdcaadcadbccacbbdccdababcbcababbabababdcbabbdccbbcacbccabcbbbbdbcbbabbddaacababcbadbcaaadcddbdbadcadaaadcaaddacabdcdcdabcbbcdcdcccdcadcccdaaaaddadbadaaaabcbaaabadbddbdabcdadabcacdcdddabbdacdaacdbaddbbcbdcbdcaabacdcacdaabababadbbacccabdcbccddbccabdaccbababbdcbdbdacdbbcccdaaadaddbcaccdadabbdbdaabbbddbabddcaddcdbdcadababdcdbbbaddbdbcbaadaddcdbcbcabcbdaddddbbaabbbdacccadccbdaabbadbdcbaaacddcadaacbbcbdcdbcdbcddcacddcdcadacbccddcdcccbacabbbddacdaccbbcbacdcdabcdcdacaadbbadbbccdbcdbbbbbbbacbabccbbdaccdbdbbabdbcdccbcdbaabcaddadbabcadddbccdaaacadbcdccacbcbdadccbcbbdbcadcddaccccaccaadcdacdcbcabbcdcadcdacbababaaddddbbdaabccdcddcadabcccbdadbbbcaacdccbbbcacdbccdabddcdbdbcddbabbacaabacbdacdbcdccbbbdcdaabbcbdcddcadbcddacbccddbabdcbccbdaaadcaabaddcbcbddacdddaaccdddadddbbbdcdbacacbdacccbcccbdabdabbbcbcadcabdbbcabcbadadccddaddddccacdcbcdcbbbbabdcdcddddbdcdacbbdbbccbddbddddbdbccccacddacbbcdbbadbacabbcbaddababbbaccabddbdcadaaacaaddabbacddaaacbddbcbabbddbdbabbdccabdcaaabacdddbddddadcccadaddbdbadbabcbbcdcbbacacdccaaabcdcbccadacabdddcdbbcddadcaabdababaacdccaadbdcababddbcdcbcabddbbccbdabdbabaddadcbbaaaccabaaaabcdbacdaddaadaddabbaadcdcacacdadbaaaddadaacadabbdcddaddcabcbbbdacccbccdacbbbacdacbdabbadcdadabbbdbbbabcbdddddbbacdcabcacbcacbababcccbdadaccaaaababbccabaaadaadbcbbcaccaaadddabadaacbaaaccccccbbbbdbacdccbbbdcacbcdcbdcaacdccadaacbaccbacbacbadadcdbaadcbdbdbaddabbbccbbbbabaabccaaabaadcddaccabababbabcbbdaddadbcbcdbcbacacbbbdcbcbcacbacacadabccdbdbccbabaaacbabddbccdbabcdcbbaaaccbadbaaddcabcaadaadcbbabcbbaddacccdbbcccbabbabaccbbacdacdccdcbabacabaaddabdcabcdaaadccdbddcaddcaddaabbbcaccaddbabdcbacccbdbddcbddadddccaddcbbcdbbbdbdadcbbcdaabdacabbdcccddadadcbadcbcdbdccbcbbdaacdbcccadcbcbcaaacbacdbaccdaddbbdcbcbdcabddbdddbabbccbcbacbdcdccbccdabbdbadbdaaccacdbcaadaddbcbbabbdabdbbbddbadbbabcbbabcbadacdcdddddddccbadbbdbdadddbadcbddccccacabcbadcacdcbbdabdbcaaabcacccadacdaccabbbcdcdabbabaabdbdbbdcdcbddddcddcacacbccdddadaabbbdaabaadbccdbcbaaaaabadcdccacacdbcadcdddcabcbabbbdccbbdbaaddbcbdcadadcdcaccdadbddcdbbccaabddabccbbcdbbdcdcbabdacdbdbabcadaadcacbdacddcbaddcbdddadbbdcdbabcdbdabbdadadadbdabaccccddddddcababccbaaabdddbbbaaddacdcddabcdcbcddbbbbbabadbdbabdbddabadadddbcbcbabbdbcacdcdaddddcaaaccbcdbddacccaddaaabcbacabdbdcdddbdaacddbbdaddabcdddbcbbcadbccaccaccacdbbbbdbcabcdabbacdbbcaaabaabaadbbaaddcdbadcbdccccdcadccaaadcbbccdabbccaabcdaabcdbcdcddbdababacacacbacdddccabababaabcccdbacdbabadbacdccdddbbbbbadddaaddbdbcacddbbccccdcdadcabdcbabacbbddabacbdaabdbbdaaadccaadabccbdadbcdcaadabaabaaacbbcacddcbaacabcabbadadbdacbaaabcddbddbbcbbadaabccaadccaacbdddbcacbadacddcdbaaadcdbbcbcbcbddaacbdbdccacbabdaabacddbbbadcccbccccbdbcdcbbbdbcbabdbabadadbdadbdbcccbcaaacdcccdddabbcbccbddabbacdbdabcacbcadddbdabbcccbbcabddbbcbbadbcabcaababaaacaabdcbcbacccbcadcbdcadcbbcacadcbacddbcdbdccbbddbacabdbbbbbabdcacccbcdcdcddbcccbcadbcddacccadbdaacddbadbdbbccbdaaaaaaadddbbaddaadbbdbdacccabadbacbaabbabbdaccddddbbcabaabccbdadbdcdabbdaabcadacccaccbbcbcacbbbbbbbddbcddadaadaadccdbccabcddaccdcaacbdcdacacdccbcddbcdacbdbcbddabdcdbdbcbcacbdbbddaacaabaaccbacbdbcbacddadbbdcaaadcccddcdaaabdbbacbdbbbdbbbcbdcdbbabadccdadbdaddbbaadadacbbcbdaabcadcbcccabacabadbadaaaccbbdaccbadbacdbcdbadbabbbbcbcadddabdcbaddddabcbbbccaababbbbdacabcadbabaacdabcddcaaabdccbaabccdcadccbbcbbaccbbadacaabccddcdbbbccbdabdacbacddbcbadccccbcdcbdcdbaccdcacddbabaddcdbcdabcbbcddabaddccaabacdcaaadaabbddbacbacdabdccdbbbaddcddbdbdcaccbccdcaadbcadcbaabaabaccdcacdddbacdbdaaadacaaadbacbddbcadcdcdbbbbdcadacacaadbddabdbbababbddadbcacdcccaddabbbbcdbcabacccbbbabdbcccdccccabadbaddccbbbbbaccbddadbbabccacaadcbaabccbddcadbccabadcdbcbdcabddcabbdbccbabdbcbaadbcaddadcccccccccbdabcbdacdccdabaababdbcbadbadaaaadaadbbdbadaaacdaaddabbddbababccacddadadbcaacaccadbbbbbabdadbbdcdcdcdcbbaadaadacccabcbbddccabbaacbbbbbdbdddbdccadbcccacbccdcbcbbccdbbcddcccacbddcacbcadccbabccbabadaaabadaacdaadddacdadbaacaddcabbcdbdbdbcaaccbaadababbcdbdccacddbdddacbacaabbdabbdccadbaabbddbbbabdbacccbacddcdcaabcacadcababaadcddacbbacbbabccacacadcbaacccadbddccadddcabcadaaacccaacbaacbdbddadcaccbbcddaccbcbaddabdddcbabbdbbbbcddbcdcdadcabbaccdbcbdaaaabcabdacababbcacaddbabaabcdbdcdcbaccddcbccccdaaabdbabdabcdbbabbdaccdbbadccccdbbdcbbdbbbbbcbcbadaddbcaadbbbdcacacadabbbdaaccdcacabcdbdbbbcccbadaaddcbbababadddaddccadacaddabadacdbbbbabbadcaabcaaaabcaabdccdadcdaccacccaabdbcdbbccdbbacbadcabadbabbdbdababcccdcbdcdabdcddcbddbccdcaacccdddcabdcbbbddccbdbbaaababdaddcbcbaaadadbacbdcdcdccdacbaacbaccdcdadbbddcbdcdbddadddddddcdaabcbbdcbdddcdcbdacdaddbacbbcdcbdbbdcdccccddbbcddccdabddcbddbabddbcbcdabcabdadbdbbadcbbbdadabacaaaddadbdbbdcacccadcbaaddbdaccbbaacacbccbabcbadcbcaabddaababaadccacccadbbccdbaabaccdddcccabbbadcccdadabbcbdbcbdaddadabbddabddcacbbddbadbbabcacacddbbbdbacacaadbdadcdbcdadbbdbaaaaacdddbabcbbbadaaaababdbbbdabbabcdddcccccabddbbddcdabdbbcbbbcbcbbbdccaadddddaabdcbaabbaddcabcbddbabccdcccadcdbabacbaabcbbbcccabbbdccbacaacaccaddbccdbdcabadcacdbadbbddbcbccdaadaacbdbcabcaabcbbdddcadadbdacadabdbddaadaadcdadaacadbaaabbbadaaabbdadaccbdcccbbcdbbcdbcadbabdbacccacadcddcbdcdcabaacdadacdabcacaabcabddbacaaccdccaabbadbcccbacabccacaaaadddccdcccdddcbbcaadcadacbdcdcddcacbaaacddbadbbbcbddcdcababdcdbddccddaabbcdaadbbdadbcadddadcbdbdbccbddbcddccbbaaccbdadddabbdbdabccabbcbbbcdadcadbacddbbbbddbadbdbbdadaabccccaccbabaabddbbbddcddcdaabcaaabcbcddaacbdddbdabcdaaaaaadcadcdddcccaccbcbdcccacdcdabacaddbccbbabdacacdbbbbaadbcdadccadcbbcadbcaaccdadccaccdabacdacbbbdaadaaacabcaadddddacbcacdbddcbacddbbbbdbcddacdbadbddcbadbbbcbbccaabacbbdacdbaddbcbaddddccbbcaccaabaaacadcddddcdaaacaccabcbcddcbabbaabdacbcdacdcbacdbcaabcdbabbbcdacaacdaaccaacdcacacdcaabbdccdaabccbddbccbdbaddcbaccddaccdcbbdaccaabadbccdaadadbddcdccbaccdaadddbcbccaccdddacdbddabcaacabbbdbcaaacdbdccdbacaaaaabdabdcaccddcacbdbcbcacabbaababdaaabddbcaddcdaddbabdddddbdcbcbcabcbcbcccdcdbbdaccdbcbbcdadacdbdbdcadccabbcbcabaabcacabcddddccbcacbdbddddabadcbbaadbbcbbccbabcbdbdddcaddbcbccbbdcdbbcbcadbaaacdaccabdaccacaabadbcdcdcccddbdadabdbbccaadcddaaadbccccbabbaaabadbabdbbbacadaddadbacddddaadccdaccddcdcadabcbdcbbacdcbdaadddcccaddadcccabccdbbaaccaccdadbadddbabbddbccbaaacbbcbcadabcacdbdbaddcadcdbcdcdccdcbbdcaaddcbdddabacacdacbbacbaddbbcbdddcdcbdbdbccddbdbcadaaacaaccbbdacbaaaabcbcbabbdadddcadbaddbaddbdcdaabddcbdcbbbbcbcdadaddddbdccdbababccccdadcacccdadbcddcdbbdaddabbcccdaddcccadbaaadacabaaaacadddbdadabadaaadcbdccacabbbadbaddadbcbbcacddbdbccbbdcaddbbadddbcccbdcccbaddadacdcabdcbcdcbcdbabdaaccdccaadadcbdccbddbcaccacdddcbabaacccccbddabcabadbbabcabcbbbdccbcdddddbccdcacabdbddbcdcbadbacbabbaccdccbdccabcbcdbbdabbdcabaacabbccabbdcbacadaabdcadcbdcdacdccabbacbabbbcbddbbdacbbacaacdadabaaccbadadccdaddddabbbccaaddcdacdbbdbddbbbbdcaddbacdcbacdbaccadcbcbabbdbdaaaddcdbdcccaadddabdbccdcabadcdadacdacaaaadbddadcabcacddcbadcaccbbcacdcdacabbdabaaadccaabcddaaddcacabbbcbcbabacdcaabccdadaadbbbdadccccdddbdabaaacbcbdaddcddcababacdacbacbbdaccbabcddbcbbbcdadacdccccadcbdddbdcbdddccdadbacbbbccddabaacacdbccbbdbabaacdbbdcccbddaadcccdaaadcdbadabddcbcdaaadcdbdcccaaabbbbcababdddbcbcccabbabdacdbcacbcabbcbcbcadbdaacbdabcadbadbacbcbbbdadacbdbbacbaaddcacbaadacdcabdcbcdccccadcdcbbccabcbaacaaacbcbcbcccabbdacbbddadcaddbacadcbcdcdcabcbbcdbbaccabdbcbcbbbcbccbaddcbdbcbcbddbbbaaabbdcbddbbcdcdadbacbaacccdbaabccbbaacbdbdbcdbdbdddaaabcbaddabbbabccaacabbccbadcbadaadbbbdcbbcacdcccbaddaadcdcbcbccbdbbbcbcccdcccbacbdaccbcbaacadaccddbbcccdccccdddaaadddbcaacaaaadcacbcdadbaddabbadaddbbccbccccababcdbdbdbbdbcbacbbbdabbccdbadaddddaaccddddadbdbcbdbacaacbddbaababbbadabcdddbbdabdbcddcdbbbcbbcdddcabdaabdbcbacdbcdbbbddddcadcaddabaddbccaccdccbbadbccbaabdcadcccadabbdacdcbcbcddddddbcbbdcbcbababdabcbbcdbdddacbcbddaacddccbddccdddabacdcccadddcacaaabcddaccabbccadadacbacacbccadcbcdbbbdcbaacdcaaacdadadadcccaabddcbcacbacbacadbdbabbddddaacabdbadcadbcaccadccdbdcbbcddbabdbacacbcbbbccadacdacbbdadbdccddadacbddadabadbcbcddcddabaadbcdbcdabaccaabbaaccdddbadccdadbccbcdbdaacccbcdcbbbadbcaaadbccdcdabbbcacdaccdbababacaadcadcaaaadadadccdbdddabcbdbcadbdaacbbdaaccdbaadacbbadacdbdbbbdbabdbcaacadadacabcaadbcdbbabacddbadbdadcbaccddcccddcacdaddccdccdddaabbddcbadaacadcbcaacaddbadbcddcacabbdaddbccaddcdbddabacbabccacdbabddddcdddaaacdbabdbadddcdacbdcbdbbdbcbccdaccbbacbddbccabccbcbbdbcbbcbbacbdcccbdbbddbcbbdddadccabdccbdcdabdaccbcddabbddbbaacbddbaccdcbbcccdcdccadadadbcddaacdbbcbdcacdcccbddaddabadacacbcbcdcdaabdabbbbadcdcddddbbdbcbaaddadacaaccccdbabbcdbdcabdbcadadddcaccdcdbcacbcacaadddadadddccdddcbbdaddbbbdbbddbdbdcdaaddbcbddcdddcdbcdcbcddcbccdccccdcbbaccddbcacdaccbaaadbcbbccbdcacbbaadadcccdbcdbdccbdbbbbbdcccbcaaabdadaddacdaacabbadbaacdbbdcdbadacbbcbdaddcaadcbbcbccbbbbddccbaddcccacaaaccccccbabbcdbaabbbcdacdcabdcaddcaddcadbbdcbadcabbcadddbadccdadbaccdbcbacbabaddcccccaacdabddcaabdbadbdacaaccacddccabaabddbdaaaadcbbcdcacbdbdbbbcbaccaddddacadccdcdcddcacbdbcabdbaaccbccdbabababbcabbdccbcbbacdcbbdaddbadbbbacaacdccabdcddbaccbbcadcabddccbbacdbadddabdddbddabbacaabbccbbcdbbcabaccbddcdadcdccbbabbddaaaacdcccabadddbdadcbddcacbabcbbaaddaabbbcccccdbccbccdddbbdcddbadadccdcdbdbbadcdbaaacbcbacbaaaabdbdcaaadacdccdbacbcdaddaccccddbdbabacbadbcdbabadacbbddcbadaaacabdccdaaacdcbadabbcacdbadddaaadabbbbcbddabbabdbcdaccbbbbcccbdccddcaacccddbadbdbbdccacbaddabadacaaaaddacaddacbcbccbbdadcadccdacdbaadbcbdccabcaddadbababccadbbabdadaadbdbbccadcdcacbbacaccbdabdcbadbadddbdbbddddcbabdbbbdcbcbadabbdcadcccdbdaddcddadabaaabbcbbaaddaacaccabdadaadcacdcccdaddbdbbdcadbddabcacdbabacccdddccaddbdbbaaadddbccddcbbaabbccdcccbcbddcddadbdcbcbaadcbcacddbbccdccbcbadcbcbabbcdcddbcdabcacabcacbaadaccaaddababacddcaaadbcdccdbcadabdaadbdbcdccdbcddcdbadacaaadddddcddbaddbcbcbccaabcdbbdbbadcbacdccdcbacbacdaaaabacbdbcdaaacddcabccbcbbcdcddbcccddabdbaaabdadaaadbababcabbccabdabbdcabccdbacbdcbddaabcdddcdbdbddddcdaadaaacccdccbaadddddaabddbdbbcdcaadbbdbcacdabcaaadababcbbdcdaccdabdcaacdddaaacdcddcbaabcbbcdadcbbbacaaaadaadbacccbbbaddcdaabaabbbaabddbbdbabdbabbcbaaddcadddbbbacdcddcbadadcdbddbabbccbaabddbacbddcdaadcadbcccaadbdcdcadcbbadadddabbdbcddbbabdbbacabdbacadaaacaacddadaadcdcddababaacadcbaabcbcbcabcdbbcbbdcadcbccbccaccbbcdabbacacdbcccadcbcdcaadbcacdaabdbdddaccbddbadaabadcbcdcdcabbdabbccbdcbabbdabaababccccabcbbacccccacbbabbbbcdadaccbbdacbcbcbaddcdccdbabcbbaabdacbbcbdabbacacbdcbaadbacccbccbaabbcbcadacccdaabaacccbcbabbcdccacabaddbdcdadddacbbdbbaccbbbccccadaaaccdddcbdbddddccadcbdaacbbdcdcdaaacdbcdddaddcbbcdbaabbbbacabbbaabbdbbabcabababcababadccbaaabbbabacbadbaccacaadababadababbcaadcdcbcccdbbadddaadacacbbabbbabbcbdcccccadadbccadadcabdabadbbddbbcbbdddddcbddbcaddbcbcbbabacabddbbbacdcbdbaacaadbbcbbbbbbdbccabbccbcdbbdcaadbddcaccabadababccbddcbadabcdbadbcddbddbbbddccbcabdaccaacaccccacbccaadaacccabdcddbdcbabccbdbccdcacdadbcaddacbcddacaddacacdbcadbadddbaaaaaaddcbcdcdddbdabbaadddadccdcbababbddbddaaabaabdcddacacbdccbbbdaadbaacccaabcbbadabccbbbacbaabbadacabbcbabccbbacbaabaabacdcdaaabddcccddbabcddcbbabdcdabdcbdccabbaaddaaacbabcccabdcaacadcdbaccdbbdcaccadadbcdbaccdbdadccdabacbaadbcaddadbaabcbbcbbbdadcccacddababbcababccbdbaadcabadcdcbabbabacdddbadddacabcccdadcccdaabdcacbdbdcadcdcacccdbcbaaaacccbcdadcaabccbdbcdcdabccbcbdcccdcadbdbcadddccadcbacdcdaccdacbcddccdaabddaacbadaccdccbdaaddadacddabcaabbbbdddccaccdcabbdcbdbbcbbabddbdcadccbcdaccaaaababacaaddbacabddbddcbbddaabdaabdcdcabbccccbbbbdbcbcdccbcacaaadddbcacdabbdbdabcbbabcdccddaadaacccbccdacdaddcbbbddbcbbbbbddbcccdddcdbbdcbdacdbbdcaabdbbacbbacdddbdddbbdacbcadcaadbacacaadcddbbbbddcdbbcaccabaaadacaddcbabaaacbadcdabcccabdacbcadcbdbdbacaaacbaacddbbadabaccabddacaccdcdbacaabcddddbcabadabdddabcbaabddcaddbabcccddddcdaacdbcdcabcabdbbddddbddbbbaaadadaaaabddaadacddccdbccaacdcabaddddadadaabcbccccddcaabacbadddbddadddadbdcbcdcdbacdcacbaadacbddccdcacadacddbccdbdbcabaadcbbabcacadddaaddacddabbdadcacdaccbcbaaadcbabcacbddbacccabcabaaadaaddbcbccbdcbdaabcaadacdcacaacabbddbabdadbbccaaacdadbbcccaadcaddacdbdbaddabadaaacacccabbdddabbbddbcbccbcaaaadbbccbdcadbdaaaabccaadbcbcdbadcabbccbbbaddbbcaaacdccdacdbbadbaacabbdbddbccbcaadbdbdadbabcdbbbbcdccaaadaadacbbdcabcbcbbaabdacbbbcaadcdbdacadccbbdcbadacdadddbbaabddbdaddccdcccaddcdabddadbbbadbddcbdbabcdbcccdabcacdacbbaadaabdadacbcbcddbcbccbbbabbcbbacbdbbacbbdddaacdbaacdbdbccacbabdbdbcddadbdccacdbccabccddabbbbcdcdbaacbcadbbaadcbbddababadcbcbcaccbccacccdcbaadbbccbdbbbbdaaccdbaadcbcadabdbbcbabdbbdbbcbcdabcdbabccadaadbbdabbcdaccabccdcadaaccaadddbdaddccbcacdbaacbaabbdddccbacbbbadbdddaccbddadaaaddbccdbddddaaaadcbabcaddcadcacabbaaadadbaaccccddaddcdaddaabaacdcaadbdbaaadbcabdcdadadbbcaabdaddbdbdbccccbbbabbddabddcabdaaacdaaaacddccabddcccccacbbabbbbdddcbbbbbbdcbccabaabadbddcbcdabbcbaadcddbaacbacadbddbaaacaaddcadccdaacbbacbadbccaaabbadaabbbdddadddbcadabddabbcbdcdbdadcdbdcadacabacbdcbabaacddacaacaabdcccadcccbbbdbadbcddbddbcbdccabddcdcbdddcacdcaccbaabaaccdaacddccccadcabdbbcccdcbbddbdcabddacdddbdddcccacbbdcacbdbbbcdaaccbcdcdcaadbdadaaddbdcbacacbbdbabaadbccbabcdbaddbccadccacddbcdcaaaabddcbdadcbdcadcdcacbcdccaddaabaaaccdbbaaabaacdacddccbdbdcadcaaacbdbacaadccdcbddbbdccabbdbcaabdbcbbadddccadadaaddcaabadcdbdcbbbacccdbbaddbcabbdddbaddccbdadacddccbdabadbdbdbacdcddadcbdcbcacdbbababcaccaddddcaaabddcccabacccbdbcbdcdcabbddbaacdadabcbbbdadacadbdaaccdbbbaaabcdbbadcdcdabbdcaaddacabbbacaadbdadabccbadddbbaccdcbddbacdcddddccdcaddcdbabadcbdbbddddcabcdaacbbccaccccaaddacbcbabdacbdbcaddadbdbaacabbddcdccadbdaaddcaacaabccbdcdcacdbccadadbbbdcbbaabcdcbbaadcbddbaabdacaabbaddbccabdddcccdcdbddcbcdcbbdbddcbaddbbdaaacdcdadbbcacdcbbbcccadbdcacddbdadbabbbbbdbcbbcdddbaabacbcbacbbdbbbcaabaccdaaabcbaaaaabcbbdadcdabccdadbadadcaaadbaaabdbbcaccbdbbaadadcaaccbbabaabdbdbaabccabaaddabdaaddaddabccccabbdddacbbaccdaabdbcccacdcbbadddacbaaaaadabacbcaacdcdcaddaddbbdadcdbacccaabccacaadcdacbaaadbcaadbddabddbaccaddddadcbbbaaacdcdbbcbcbadacbacbdbcdbaadcdabcddadadcaaddabcbababcddbacccdddacabdadadaadabddbcbddcccbcdabdabcbcdcbdacbcdcabaaccddbdddbabbccabccccbdadbcabacadcdbbaacbdbdcdacbccaaacbbbbccbcadabcdbddbcacdbdcabdccbaacadaddcdcabcdaddcadcbbdbcacdbdbdaacccbddcadabbdcaaadaddccdccbaadabdacccbdbdadbcdcccabcbddbdbbaacccacacdaccacbaccacdbccbadcbccbdbddddddcabdbccaabcdaddcdbaadcbadbababbdaadddddbccdbdcbbababcabccaabcbcaaadadcdaacdaaaaadaccacbadcadaccbcaabbddddbbadbacddbdbbccdababccadbdaabdbbbcaadbadccadabcbaaddcabdbdcaccacabadaacaccacbacaabdcbbbbcacadadbaccccbdbdcbaccddbdccbadcbcbccdaacabbcaccbaadbbbccdcaabcddabdbddabcacadcabcdcaabaddcccabbabcbcabbccadaaaadaacddddaddaddcbcaabaaabcaaaccdbaaddacbcbccabdbadcbdcadbddaacaabcddacdbcbdbdadbdcddbbadbdacbccaaccbcaabbdccccadbdacdaaabbcddbcadcbdadadbdbacacbcaaadbbaadddcdbacbadaaacbdaddbacabaaccbabacddabdccbddbbadbddbdcbabadbccbbbacbabddbbbcbdaddcacbcacadbcdbaabccdaccbcdadbbabaccdcddcdbbaabadccadacdcbbdbdadaccdbbdacaabaababcadcdbbdcbddbdadbcabaddccaccdaadaaadbbcbbccdadddbcaacbccdaabaadaccaadaaacddaddadcabbbbddbaaacccacdbadabcdabcbacacabadccbcddbbcdbcdcdcbbdabcbdacaaacdcbadaaadaaadbbdadaccabadccbaabddbcbccabacdcddbdacbbddbbbcdadaccbdbbacaabaaccbbcbacacdcbcadaccccbdbbcbbdddcaabbcaddabcbddcdaadadccadbaadcadbaacabdabbabbdcaacbdcbcbbacabdbbbdadcacddcdaddacbcdbaddbdadbadadaddccaaddacbbabadbaacdbdcbabccbbabdddcddbdbcddbabdcdbbbdbacbbcdddcbabbbdbbcdcdbabadcdcdcdacddacbcdabdaaccaaccbddadcdbdcacbacababaabbcbabadccdddcbbbadbdacdcaabdbbdcabaadccadaddacaaacdacabbbcdbbdbabcbdbbcacaaacbcbcdbadaddabbddbcdcaaadcbdaaabaadcbdbbbdbdbacadbaadbadbdccdbadccabacdbcbdbbdbbdadadbaaddbddabbbbdabaadcaabcdbbaacaadaaddbccbbbcabbcdaccacbbdaddbdddbdbcabcbaccdbadbaddcacbbbdbdaababbbabbdbdcbddbcbbaacdadaaadddacadbacdbddaccddabbccbccacdcccdbbddbdcddcbabadcbcaadbdbdbacccbbcbabcdbdcbbbabdcaabcdbbbddcbcdcacbdacdbdacaddbabbabbadddbdccbbbcbdcacdcddadbabdbcaccbaabacaccaadbbdadbaacabdbdbbccbaccbaaaadabbbacadbdaaadbbcacbcadabbdacabcabdcbcbccddaadcdddbbcabdaaccbacbbbbdbccbdbbadaccbbbccdadcdccbaacbabaababdbdaddbbaccadaabbbaacbcdbbacbbabacbbdabdacdcddcdacbddaacbdacdccddbbccdbcdbbbacbaddbbcbcbcdbbaabdadbcdaaaccdbbacabbccdadadadcdbbadabaaabaabdaaadddaccbbddbbdaccccadbaccdcaddaccdcabcccbbccbcbdbcabccbadddababccaacaadadcccbbbdabbaaadaccabcaaadacadbcdacaccabbcaaccdadadddaacccccbabbabdcdacccdddabdaadbadabaacbcbaabcbdaaccaadcbadadaacbadddabdbadcaaaaaacccadbbbbbabcadcbbdccddccaadcacccddacdacdababacadcdbabacdccdacacbddaddbdddabcacddcabaaadbdcabdcbdccdbddaddbbbbcbbdbbaacccdbcbacaababacabcdbcbbacdaadacbbccddddcdabccaddbbabbcdaadccadabcbdbccbddadccabdacacbdcdadbbbbbddccaaddbddaaddabcbbcbccaabbbcbbcadbddddbbcdbccacbcccddbddbadddaabbbcbcabccbacbbbaaabdbdabbaccddbabdabdbbcaccbbccbccadaabdabdababcbaabaacabbdcdcacaaaabbdabcabbdaacabbbbdcbbcacaabbbacaaabbdbbaaadbbdbcbdbcbbaadbcacaccaadbaccadaadbcccdcbaadccbababdcadcdabbdccaccadbacabbadcaccbbdbdbadddbbbcdcbdbacdcccbdbdcabccbcabaddbaadaddcadcabaabaadbddbdbbabbcccacadcdacbcbacbabcbabdadcddabccccbcabbacadcdbcbbddcadabcbbaadccaddbadbabaccbbaddcbababdcabcacbdbadbbabdcadddabcaacbaaccdbaccaccdadabbdccddaaddccaddcaaaabbbdccaacddcbaadbdcabdbcdbccdbdcaacccdddbdacbcacabacdadddbcbdadcaaaaadccacabbbaaddadacdbdaddaccaddbcdddadadcdccbddbdbdddacdabdddadcdacaaacbbbddbacbbadccacabbccdcaddcbbaccabbcbacccacaacbbbbaadbdaaaddbbadabaabcdddacaaccdcaadbddbcbdbdbaaacbaddacdcbdccacaaaadddcaaacbbdaabbccbbaadbddbddbdddcaadcccbcdabcddabbcbcbbadbdbccdcbbbabccacdcccdbddbabaacabdddbdabaadaacbabbabdcbbddcbcbabccaccaddaaabbdbcaddcbabadbbbbdbabacdbdabbcbaddddbbccabadbbaaabbbcaadbddcbcadbacdbcadcdcaddddbaaacddddccacbdccccdabdbbcdadadadacdddcdcdcaadcabaadcdadddadbacabdadbabcccbbbacbbbbadbcbccdbcbdddccbbbadcabcbdbaddcbabbbbcdccbbddbabadbdbcababbccabbdbbbacbacabcccaadccabbdcdbaaacaacdccddabcddbcaadbdbbbbdabddcdcbcbdddadbcbbadabbbbadddbdaabcdcaccccccabaccbddddccadaaddddcbadacdddabbbbadacdadcadbcbbdacccbdbdaccababbcabcbcababccbabdaacccdaabddbbccaddaadcbcdbaccacacddaaddddacbbdaadccabdcdcabbbbdcabddbcbcacdaadbaccbbcaaddcdccbcaadadbcabdcabbcaadaaddccbcbbccddccacadadadbdbbbdbbaabddcbbbaaaabcbdbcbcabcdaadaacacbbbbacbbdbbdbbcbdccbcbaacabbdadadaadabbabcbacabaddbdccabbbacaaadcddccabbcbddbbbacadcbbadbdadddccbddccaacddacdbbacbacbcbabccaacbbaccdacbccacabbaaabddbbcadbbaaddcdbdaddaddcabdcbcdbdadadccbabdddcdacacdbacaadaddddcbbbacadcdcbdacaccbaadadabdbcabcccbdcdacbdbdbabaacdacabdaadabbbdcdbbbaaccbcaaaaaaacdccbbcbddcabcccdbacbcdcdbcddddbcbccbaccabdbacdccaabddbbbbbbddcbdaccacbdbbcdcbdadcbbbaccaababbaacbbadbcdcadcdbbadabbcdddaaaabddaabbacdbadbdddacbcbabccdcbcdcbcdbbaabddddccacbcaaddbababddccaaabcaaccdaaaadacbcbadbdccaaddacdcdacadaadbbabddbdbacacccadddcabcaddadddabbccbdacccbddcdbbdcbadbbcdbdabbabccbaabbabcbcaadcabcacdccbaaaabbaccbcbddabcdbbcccbddabaacdbddabdaccbacabbdabddaccddccabbddbadbabccddbbbbcbbdabdbadaacabdddbcbdaaabadbbaddbdabacdbaabcdcbbcbbbdbddbbabaabcdbdddbdadbdbddadcdddddbbcbadbabddabbcdcbcbcdbadcabdddddbdaabcbdbdabddbcabdabcaccdaddcaababbacbddadbdabcdcccaccdabaccbbcbddbaabccdacbacdddccaadcacaadabbacdabbaadcbdccbddaadbacbdabacaaddcbcdbcbdcbdcdcbcacbdbabdccbcddacbddcccaacadcdbcabaacdaaadcdadbbbdadabaadcabcdcddacdacbcbcdbbdbabacbbdcaabdabcdcabadaddcddababbadcdccdbbaabdbcbcbacabadaddcababdacccbabcdddaddcbcadcaaddaabddbaddbadbbcadccdbdbdabdcabaadcadcaadabbbbabdcaabbdcacacdcbaabcadabcabbabdbbacdaddccddacbbaaddcadbdbabcbabdbcaaabacbacdbbbbdbaaadacaaabdccababccaacaccdaaddddbbddccdcbcbbcdadcabacbdbbbbcacabcbccdbacbddbdaadaabacdcdbccbdccbbaaaadcdbddccbcbacdcbadaccaababbdbcabbcccacdddacabaaacaadcacdcbbddbadbdbdacdcdaadbcccabcabdcdbddbacbbadbcabacbbdbadcdcdcbccdabdabcaaaddabadbdabbcaddcdbacbcbbdcabcaccdccdcacaabbabbadaadbabcdbacaadaadaccadbbcdcbcbcdbbdadcadcbabcdcddcbacccccdbdbcdcbddacacddaadbdcbaabcadbccdcdabbbbabbdbacdabadacbbdbcdabdcdbabcabbbcabaadcaddabbadaabbddcabaadcaaabbabdaadbbddcadcdbdbcdbdbcbaabacdbadabbdabdaabdaaddccdbdbcbddbddbdcacdadcbcaaaadbdcbcbbbbadddabababccabadbdcaddbbddccabdcbabcacdabccdccdadaacbcddbadaacabcccdaababcdabdadccdbdddbbddcaacbbbbacaccdcaabcdabacaccabbaaccbbacabbadabacabbabaaabcbadacbbbadadcacbcadcbbadddccdbababdcbbdbcaccbcabcdabddccbddbdcccdddaccddbddcddaaacdcadbdcabdddbdddbdbadccbdaacacdabcabcaddcaaddcaabdaddcbbbdbddbdaacabacbcabaacdabacadcacdcdcddbadcacabdabaddbbcbddadcbaaddddddadbcbadacacccbaccabdadbdbaadadbcdaadcaaaabdacdbabbdaddaabaacadccdcdadccbbcddcdcaddbbcdabcdadcbcccccbbdccabcbdadaaccbacccbacdaadabdcbabdadcabadcbcbbccacbcbdbcddbddbdaabbbbdadbaacacdbbacdcdcbacacabbabcccbccacadabdbbbbccccdcabbaacbcacadccbcbacbbdcddaccbadbcacbabbdcadcaababcaadbcacacbacbbcaaabccdbdcadabbaaadaccdaadcdbbbdbdcbdadcbbcaadddbcbdbbacddbccccaccadcbaaabbbcadcacbdcadddddbdddcacdbbcaddcbcddbaabcadcacdaddaddcaddcbdadbbdacaacadcaddacadadacbdacdccbabcaccadbcaadaaacdbbcadacbbbbcdbdcbcdcacdaabaabadbdbcbbcbbbcdcbbddabbcbbddaadbcddbccdbbdcdccdbcaadbbdcadcabaccbbdcdadabdbbbdddacaaddbabbcddadcccbdbddccdacaaacdabaddbaddaaaabdbbdbbccabbdaacddbdaabbbbacaddacdabbcbdababcadcdcabaaacabbacccbacbbbabaccbabbbcdcbddbdccbcbdaddabbbccdabdbacacaabccbdabacabaccbddbabbdbcbcbdacdbbbbdaabdabadddacbcbacacacdabcbccccadaadaaacdadaaddbbadddddbbadddbdbabbdbbadcaabcadcdacaaddbadbbcddcdbcccaadbccabdcacccabbdbddbabcbbbbacddccacbbdccdbddcbbdbbdabbacadbbdccdbbcddabcdcadbdcccccdaaaabdbdbacdbcdbbdbcccbddaadaabcdcbbccddcbabccdcddcbccdcbbabbcdbcdaaaccdaababcbbacbdcbabcddbbbcccdaacbbdddaaabdccabddbdacbbcadcdbabacacaacabddaacdadddaccaacbcdbdadaaddcacdbcabacddacbabbbdacdcacbadddabbaccbdddbbdacdcaacddbadddbcccabbcdbccdbbadcbcdbcdcabddddababacadacbaccbdcdbbbbdbbccccbcdbccaabcbbddadcbababdcadaaadddcdddbbcbabcbacccabcdcccccbdcaadccccbcabbabacdcacacddcadbcbbacbbbdbbcadaaacadbbddcdbacdbbdadccbabbdcbbcbaccccabbdcdcdcacddbdddcdcbadacadbadbccdccbdaaacbdaadccdadbcabbbbcacbbcdacbbbbcbddcbdbdcbdcbaccbcddadccabddcadbbbdaabacdccadbbdbdabdbbacaddaddddacbddabdacbbddbdbbbaaabccdbaaaabcacbbadcbcdddbcacaadcbaddbbcaadddccbdabddbbbddbacbbccdacabbbdcbdadbdcdcdddddcddcadbadccdaddaabbbccbadacdacdaacaaabcaaacabadaaaaabcdbabdddabccbbdbcbbabdaddabdbaaaccbabdccaadccbbabdbaddbdbbaccadaaccbacaacbabbcdacabcacdbcbaaababdcaccdcabccadadcddbcacbcbadbcabdddcadbdcccbabcbbcaaababbdbcbacdbacdbccbdcdbdbdabdbcaababadabbdddbccbdcbbbaadbabddaaccdbbddabacbbddaaaaadcbcdccacbcacccaaaabbddbcbbdaccbaadcdabbcddcddbdacaaaaadadacbbcdaddaacbabadbbcdcbcaaddbccacdcbacdacaadabcbacbbdcadbadadabbaccabbbacbaaacbabdddabdccbdabcaddcdaccdabaacdabbadcaddacacbbadbbacdaadbaccdbcbbdadadbccbcdacdccbacaccdddccddbbdabdabbaddabdcbcdbcadbddabadaccaacbdbaacbcdcbdbbbdcdaacabddbbddacdcdbacdbdbcbacbabacadcbbccddcbcaacbadcccdcabbccabaaddacbbcbbdcccdadcddddabdddabddbadbccbbaabcbdbcdbddbabadabcadcbbcccacaadbbdbcdddcbbcdaddabaabcababadcddcdbbcabcacabdbbbabcacabbcabbabdddaacaccbbdaccdabbdacbbbbccccaccaaaaacbdcadbabcccdcbbddbaddaadcddabaadccbbdccbccabdddaaabdcccaaaabdcbdbbbaddbcdcadbbcdccbdadcaccdbbdccdaaadccbabcbdbcaaccdabacadaadaaadbbcdabdacbdabbcdddbadacccdcabbbbdccdcdacdcdaaabacacabccbcccbacbcbbaaddacdabdcbdadadabdccacdddddccbbbaddbdbcbdbdbdcbcccbcbabacaacccadadddadcabcaddbcdccdadbbbabbccddddbbcbcbdcdadaddbcbccbadabbdcabdcadabbbdbdacadbccdbdddbdaddadbdddcdcddcddbaaddbbdaacacccddcacaddcbcadbbcabaadddccabbaabaabcabdaddcbcddcdcddbccdbabababdadaaadbbcdaaabdabcbcadadcccbbadbbccdcdccaaaccbaabdccddabacacaabdababacdbbbbbdccacbdddcdbbbbaaccdddadbdbadcbdadabbabdacccaccdaacbacbbadaccdaccccdcadcabdddcbbadabdcadddcdccdddadbcbbaadabdcbcbddbaadaddbaddadccaabacacdbcbaaaacadbbcaabddbbcadcbbbabacaabbdbaaccbcdccddababcccbacddcacbacbaccbcddbacaccbcabbdabaadcbadcdbdbdaaadbabcbabcacdbddbbddbcbabccdcbaaaccbdaaaaabbaadcaabcccbdcbbaacccddbdcabdbcabaabbcdcbdbbadddbdccbddbcadbdaddccccaacbcdacbdbbbdcdcdaacbcaddccabacabbdcabbabcdcdbdbacdaabccbaabcdbadadbcdaacbdcabbdcbdcaacbdcbddbacdcadaddbbcdbacaccdacbcdaaacccadcddcadaabacaddcddccbdcabccacacdddabcdaaacdadbaabddbbcbaacaacbdaabddbbdcccdddbcbdabcacadcaccdbdcadccdbacbdcbabdcdabccdcadbadddbdbadbcbadccbbbddcdbcddccabbdabcbccdbbdcadcbcdcbaabdacbcdaccdbabcdbdddbaadbcbaabcbacdbabbaadadbaccdbbcccdddbababaaddbacdbbbccabaddbdcbdcdccbbcbbcadcccacbdbbabaddbbbbcaccbabbcdbccaabcdbcaacccbbccacddaacaddaadbddbaaccbcbaccacbccacbbccadabccbbbbccdaadcbdccabcadccdcaccabddbdaacaadbbcbbacbdcbdddcbaaccbaadaaddcbdaddbcbcbaccbbadccdaaccacbadacacccadbdcbccaaaabcabcaabcaadbbdddbdadacadadbdacadbacdccdddcbabdbbadadbbdcabadccbdabdddaabddcccadccbdadbbccdbccbacbbbbadddabaadbddccbdadbaabcbadbabaaacddacddabacddbdcdbbbdadacdaaaacdaaadbccbdbacbacaddcbbdcdadbaacacaccbadabdaaabdbcbcbdabbaddbddabbbadadbbcaddbccddabbacdbadabdaccacacdadbcddbbdcadcddccddbbbcdacbbcbdddaccacddcddcccbdbbddddadbdabccbaacadcbdaacbcddbbbaadcacaddcaaabcccbbcacbdbaacbbdabaabdbaabcbbacbbbbddbbbbdbcdcaddacbadbbabdbcbbbdccadcadabbdcaaabdaccdadaabaadcccddcdccdadcadddaaccabdddbbbaabdcdaabcaaaacbdaadbcbaabaabbddbddcabbbcbacccaadcbcaabcbbdbdacbacadbcbcadcacaddabacdbcdaaaaaabbacccadbaacdadcaadbccaccdccaddaacadacabbdbdbcdcdcbddccbdcdcbdacccbdaccddacdbbcddcadbdadbcddbadaadadaccbdddcadcddadbbcdbaadbbcccadcaadbdaddcbcddcddbadbbcbcaabbdabbddbbdbdabdbbddadcbbadcccacbdbcadaadadbcbcddaacdcaadaccbcdbbbadaaabaacbcaaacbbaddbcdbddacccaadbabcadddabbbbadacdcaaaccacddddddacbbbcdabadddaabadaacadddbbcdcaaccdabacccddbdccbbcbaaccaabbaccdaccbddcdaaddabcccccbbddddcdacbacdbdccdaadddbbbbcccbbccabdbcdcbdbddaddcdcaabdacaaaddcbbbaacbccadcadccababdabdadcbcbbccdadbaabdcabdabdaddbbcbdbacbcbdacdbaccdddbbdbbdbdbccbbaaccdbdbbadaacdacddbcdaddabacbadddadacbabbadabaaadadababccdbdcbccdcadbadccaddbdaccdcabacaddbdaabdcccdaddcabccadabdcababbcddcacacadabdbbdcbaadbbaacacbccabbccbababdbdaadbdbcadbcaabcddcdbccbbdaacaabdccdcccdbadbdddbcdabccbaaccadcdcccadbaccaddbdbbdccddbbaacbdcbdccabcbccdcbdcbdabccbdaadbcbdcadadadbbaabbdaccdddbbbccbccdcaaaacdbcccccbdddabcccbbadcaabcbcbbddaccadadccaaccabadddddcadadbbdbcdcadcdabbbcabcbbaaaabdabbaadaabddbbbacbaaaccdcbbacdbcabbabbadccccaabadbdccbbbcbcacdcddabacbcdbbdcbddcdcbdcacccadacdbdbcbacabccddcccadaabcdccbcaabcacacacaacbbcabbaaaabbccdccdcdadbbbadcbccacbbcbcbabadddcdbacadacbbccaaadcbbabaccbdbdcaacacbcacaccaccadcdbadcadbdddaccdabdacdadbaadcdcaabdacdbcbdbacaaabcbcbbaccbaacbabbacbaaadbbbddcdcbbbcabcddabadaaaabbdcbaccabbdbdcbccaddbbccbdbccccaadaaccbbcccbadbaacdbccaadbacbdbccaabbabcdccaaadbcdcbaacdbcaccabccabdbcdacdabdbddbcbaabcabbdbcbbcdcdbccbcadcdaabbdcdacdccbdabdbbaabadadbbdabccaadcbbdcbabdbbbadcdaacaaddabdddccacbdbcdbcbacaaacdbaabbcdcddacbbaaccbabccaddacbccbaddbbdabcacbadccccadacdcdcdbccacaacacccddbcdcdbcbdcbdaccccdcdbaabcdadacaabbaabcbddcaacddadcccccdcccacdabacbaddabaacdddbadaadbadbbdaddddcbbadacdacdcbbabcbdccaccdbddcadadbcddbcaccacbbbabbbcccccbcdacacdcdaccaccbccaaaaadccbbcbcabdbbacdabbcaccdcbdcbabdacbddbadcdabacdcccbbdbbbbadacaaccabcdadaabdbddddacdcaabacacacacbdccdadccbcbbacbddacbaaccbbbcbcdbccbbacaaaccbbcbbcacbcdcadcbdabadcaaacccaabcdadbcddbdaaacddcdaabbcadbaccadcccacabbccbbcbcdcbdcbcbbbdcccbabbdaabbaabdbacdaacbdccdbdbaccbbabbbaabcbdbacbadccddcbaaccabadadcccdaccccdbbbdbddacdddbaaccdbbacdbadddaaacdabbbabbcbabaacccbbbabbbaccbdbabdbadbdbbdacaccbdcadadbccdcdcbdacdbabcccacdcddbcabdbabdddbdbdaddbbccacabdaacacccdcbbdddaadcccdccabcaadaaabadcacbbbccacaccbbddaddcdadcbdcadbcaaacabbbaadcadabbdaacdadaabdcdabdbacbddbbabbacbcacbaaddbbadaaccbddcccdddacbbdbbbcabaadbaccabbdcccabdbaccbabcbbcadcdbddbacadbdaccabcaacbdbcddbcbdccbcbbbbddbaacdacdccbcabadadddbadcacccbcdababdcbdcccacbacbdbccddabbcaacbddcdabddbacbccdbbaccacbaccabbaaaacbddddadcdaacaadccbddcabdacdabaaabbcdcdbacdabcbbaaadacbdadbcaccdaccbbbcccddcddbcdcdccdcbbbcababcbaccadcabcdcaaaccbaadccccdabdcdddaaacaaaabaabdacddadbddacccbcaddbccadcddbaabdabdcdddaabaacacdbacccccadccdcbacdcbdcdbddddaaaacaacdcbdbdcaddbdadcbccaadabcaaddbaaaabcaacabdacddaddcdbdbcddbcaabdcbaadbaabddcdccdccdcdacaabaadcbcdcdaabaddcabbbdaadabdcaccaadbbbbccaddbabaaadccbcdaddabadbaadbabccaaadbbabcacddcbdcdaacbbddcddccbcabbaacbdbcaaaabacacabcaabcdaccaccbcbbcacdccacbadccdaccdcbddddcdaabbdcddcaaddabbdcadabdbcccbddbbcaaddaadbdadcccbccbcdcadaabdcdccbcbadaadacbcbcaaaaccdbdbbddcdcdcdcaadabbbbadcaadcbcccbbcaabacbbdabacccbccdcbcdbcddccacadcabddbbbcbbcbccaddddadccccaddddabdcddabacdcbddcddcdabdccccbadabcdaacaaadbdbdcadccbbbccaacbccadabaaaddaaababccccdadaddbbbadddabcdcccbccbdaaddabaddaaadddbdcdcdababcddcacddccadaaabbabdabbbddacbdcbaadbadaabcbbacbbcbadcbdadbbacdadcbadcbbdbcadcdcaddacbabddbaacbcbdcaacdbacccddbbddbcccacbddbbcccdcbdaaacacdbabaabbdbabdbbbabdabccaaaccdcadbbbdbadaaccaddcccbbaadbdbacbcdcbddddbdccdbddccdcbddccdccdcdabddbbbddbbaddcbaaccbbabbacbdacdcdccacabbaabbdbaddcddddadccbacaddacccddcddccabadbdcbcdcacaddbaadabcbdbbddadcdccadcdacdacddcbbcdcaabccbbacddabdbbcdcababbdccddacbacbaaaaabdbcdbabdadbbbcadddacccbddaadddcbddaddaabbddccdcacddcddbaabaddabbaddbdabdabdabcdacacbbbbdabcbbbdcbabccaadbbaccabddcadddbcbacbcdabbaccdddccdaccacbaaadbaadbabcbbcbbcbcddacabddacadccdaabdcddcbaaddbdcabccbbadddbccbaccaacdaddbdbbaaadbdabccbaacccbcdcdacdbccdddabbccaabdbccdcabaacbcddccbcdcccaacabdacdbabbccadabcdbadaababdbcbabcdbaaddaddcaaababcaaddcaacadacacabccbbdbbccdccbbbabbaaabccacadbcbbcddcbbadbdcbcccaddabbdbddababccabcaddbadaadddaabbdaabaddcccbdbdacbaadadbbdbcbdbdaadaccdddcbdabbabcbaaacbacaddaadabaaccbbbdbabadabdbdaccbaacdaddababddbcdcbaaabadaabddbaabbbabbccaacbdcddcdcadbddaadadabcbbcbcbbdddadacbcaadbcbddcccbabbdcbabcbdbadaabccbcdaccccdbbbaabdaadbbbdbbbaaccacbcabadacbbcacaddadcbcabdccaaddadadcaddccdddadaaacbbddbcacdddbabddadcbbbbabbddbbabaddbdcbcdbddbbcaadacbbbacacaddabbacbddabdaadcaccbbcdccabdaaccadcdabdbbccdddbcbcccbaddabddcbbcdbacdacbdadddcaddbdccdaccadddccddcbadbbbdacbbcdbddcbddaccacabddacccbbaacbcdcabcbacaddaaabdbadbbdaaaccadaacacaaaccbbadcdbdccbadcccaccdddccbcbcabcbdadadcccdbdabdabbabcaacbbdabbdcaacccdaabbcdbdbababaddcddcbbdbbbabbdacacddaadcdcdbbdaccaddadbcbbabcccccadabccbcdddccadccbaadabbabcbdbdadcbadaabaddacadbcdcdccbbdcbcbcbcbaacabcaaaadaaadcddabbbdadbacbaabbadddacbacaacbccbbdccabdbcbccdababcddcbabbddcaadcccaccbddcdbcbcaabdddbbdabccaabdbbddcaacbdacdbbccdddbdadcdbdbcdddababbaddcdcbabacdbcdccadbbcabddbabdaacacddddabddbcaaabbdbaddbbaddcadababaadababbbbdbddacddccccaaabbbdddddbacbaddaabacaacdbcbccbaabaadccddabddbacbacadadccbbbaadbdabcbdbdadcdbbcdccdddadddbcbccabccbaaddbddabbcabbbaabcaaadccacddccbacabdcbadacacccbdddaddbabdccbbcbbcbaddcadbacadadccacddaadddadabcbacdaacdbcbcaadadaadddbcdbacadccbbbdbbcbbabcdaaabbbdccadcccccdbbddcccbdacdbdacababcaccbadabcccdccbcdaccddadabadaabdbdacacddbcdbacbcbaacacaddbcbbdbbabccaadcdcbbdbcdbaabcccbcbbddabbcaaccaaabbdcccbcabaabcbddcabaccdbadccabddbcddbccdacddbaccbdadbaddcdccdcbaccabcbcababbcbdcdcaccdbddaaddbbdacddcdcddbcbdadbcbcccdaaccdcdcdbcccabcbdbcaabbabcbaabdbcbcdbbacdcdcbbcbbbdacabadbbdabbcdaccbbcadbdcdccccacbadbcbbcbbcddaadddcbabdcaccdbaddbabbcdabbbaccbbddababccbadcccbddbdbbabbbcdbadadbabbacacddccabbbabadcccdcaabcdcadacddccaccbccddbccdcacbbabacbcacddcbbcaadabbbabdddccbcdacbbbccbcaabaccacdcaaaaabcbbcdddaadbbabdcbabbdddabbcbcacbbbaaccbabbcddbccbbbbaaaacabccdccbcbaccaabccdbccaabadabbdddabdccbaacccdcccbccdaaadbabcabbdbacbbbdccacaddaccacbabaaaaaabddabdbbaabaaddcbcbaccacddccccacdcacdbaaddcbdbdbcbbcbaddaacdcdabcbbbbacccacabdbbadaadddadbadcddcbdbdbbdabcdbcdabdcdccadaccaddccddccdadddbbccadaddddbdaaaaaabacbbaaacdddcbabcdaacbdadcadacdbabdbbdcdbdabbdddadcabcbadcdbbadbabadcadadcaaddbdbaaacadaddadbcddccdaaacaadadcccbadcbcbadbabdacbdbcaaacbabdcddaabbddacbabcbcaacdcdddccddaaccdaccdbaddddbcbddcbabbcbbaccdbcdbbaaabbacbbbcddccccaabcbdacbdbadbdcdbbcadbbccbbcbbdccdbcbccddbbcbbbaaaddaccdadbdcdbdcbdcbcabddbcaabcaccacccdbaadabbdcdcaadbbcdddcadcbaaaacaadabdabbbcaacdcbdcdadbddbbcadbabbddccddbaaacdbdadaaadbcbcdcddbacaabbbabcbdddbbbbcacbaddadadcabbaabbdcacbbdbadbbbddccccbbabddcabadcddbddccdcdddcdaaaacdbdbbbabccababcabdbacdadbbccadabbbbcbcdbbccdabcacdbabcbabbcbdbaddcaadacbccbdbaabdccddcaadcbbcdaabbdccbbbdacadcdaaddccbbcdacdacdbabddacacaadaadbabdadcdabbaadbcccbddbcbbcbbdcaacbabccaccbbbccccdbbadbbaabbdabcdcbaccbacccddbdcabbbbcbcbbcbaccccbdababdcbcacddadbbcadacdabcdbddcdadbbdaaabdccbdcababbacabdbabbcabcdbcadacaccbaaaabbbbcdbbccdbccaabadcccabacccbbbddcdbbaacccdcaadbddddbdbbccadabbbdaacacbcbcddbacabdbdadcacbbddbdbcabbbadbaabaccaadcacbcccbbbcccaabdcddaacacdaacaadccdadcdbcadbcabbbcbbbbcdcadccdcacabdcdacdadbbabdabccbaaacacabdccdddaaabbbbcabaaadaaabaaacadaaacaabbcccaccddccdacdcbbdaacbccdbdaaabaddcbcadbcdacacbbcddcadbdcaaabacabacacbdcadabbabbabcabdddaccbcadbcbdbaccccaabbcdcabddcccabbacdadaaccaabbcacdbaabdccdaddaadadbdcbadacdddaacdcdcdddacaddcdbbcbabaacbadbdbbdabdabaaadcadaccbdabcababaadddbcabcabddcdabbdacaaacadbbbbacdabadbdccaddbbcbcbaabdcbdbbbadcccbdbcdcccbaccddbcbcddadcccbdabbadadaacbcacaadddddbaaacccddadaccaaccbabccdabdbbbcbcabdbdcbbdbbcbcdcbaccabcdbabbccdbcaaddabbbdaaaddbbcaadaddadcabdbaaabdcddbdcaccbabcabaadcacbbcbbdabcbdcdaacdbdabbbaddbcdbdcddbcaccbadabbbddccdbcacbbccddadcacbbbddbcdcbcadbcccdbdbcacdbbcbcdcdbaacbbbcaacacbbbdbcdbdbbbdbdcbbdabacddbdaadbccdbcbaccacacdbcadcbbadddbbabacccabdbddacbbbcbadbbcbbcdcdbaadbcdadabbbadbabadabaabacbacdbaaccbbadbcabbbbdabcdadddadddddcbbbaacaaaacbcacbbbbcbdccbbbbccacdddbdaaadddcbdadaddbdaccbcddaacdbcadcbcdadbcbddcaadbbdadcdcddcadbdcccbbabdbddccbcccdbcdcadddbccccdaddddbdbacbbbbdbbdbdacabcdbdcabadbaccdcbbacdbdccdaaadcadccbdddbcadbdadadabdcdcaaccdcbdcddcdbdcdaadabdbdbdbcbabcdabdbdcdccadcabaabcdbbbdbcadbdcddcbcddbbbaddcbdcadccaccbacdcccdbccddabdaadbdaaddbcbbddddbddadcbcaabccdcbbddbbbbddbcadabcbbbdcbaabcaaaddacaccbbcbadbbcddabcccdddabcccdacdbcdacaabbbbadbcabbbbbccacdcbabccbcbcaddccdcadddcddacacaabcddbbadddadbcbbdabddccdccabddbadcdddaabbccababdcaddacaacdccadcccacaababcbbddacadaddaccacdcacabacddcdadacdbaaaccbbbbcdbaacdcdcdadddddcccbbaaaaabaaadcccaadccdabaacccabbaaccdcbdbbabdcdddcdddccaadabcdadddddbdbacadbaabcabcdcaddbbacbdbcdbccbaacbbdbbaccdabccbdbbddacdccccbcbcddabaabbaccddcdababaacccbbcaabdccbcdabdcccbbcbdbbbbccdadcababdbcdababdacbcdacadaaadababbbdacaabaababcaacbbacadaaadbdbbbcbbbdaacacbcbaaaccbccdddbdbabbadcdbccabbddcaccdcabcacdbbdbcaddacddabacaccbaabacdccaccbaaaabcabbdbbbdaabcdbcdadabbabbdbdabbddcdbbbbdbccabdbcaacbdcbaaccacbbbbbcdaabbcbdaaadbabdacadacdcdccabdcbadbbbdabbabbadccddcaadadabbcdddaaadbccdcabadadaaaacdaaccbbaaaccabbdcabcaaaadacbddccccdbbbddadcddcaaabaabbcaacbbbbccccddddbabcddadacdccbdabdddacbbbbdcabcaddbbaaabbcccbbacadddbacabbbacbadddaaabcacbaaaadbcccbcddcbcacacbbcaaddacdacdbbbbdbbbccaaccbddcaacbcccdbdbcacddcbdcadacbbdacbabcddbabdbbdcbadccbaabdaababbddbbcbcaabcdaaabacbbadcbabacddadaaacbcbbcaddadcdbccdccccbacaddcacacccccbacabdbdaaacacbbdbcadadadccbadabacdbbdcacabbaadcdbabbabcdcbdabcdddaaacadcabbddacbabaccdcbcbadbcdadbabacbbcabadbabccbbabddcdcccdbcbcdcadbbbccdcdddacbbdcbbdcabaaccdbdbcdccccbccbccaaccaccbdddcaaaaacbaabbcbdbddaadbcadbaadcbdaaabbdadcdbbadaadcbaccdddaabccdddbaddbbbbaddcbbdbabdacaaabcaaacacbccaaabbacdabacbabaacbcccbbdddccbcaddbcddccccadddcaccddbccbdadbdddacacbcddaccbcacdddbcdabcdcbadacbccdcddbbbabbabcadbbcabcbbbdbbcaaccbdcbbbcdcdadcabcbddcbcbdbababacdccdbadccdbcbccaccbdabbbaacbacaccbcadccccdaacacdbbcbbcdbbddabcdcddabcdbacaddccdbdaaccbacdadcbdddadaaadaaadbaacbcccdbaaadddbdcbdacddbccaccdbbddbaaddabacadbaacbddabbbdbdbaadbcabbcbcbacddaaabcdccdcdaabdbbcdbaddcccbcbaacaacdbbcdcbaaccdcaccabddaacaccadacbbdcadccaaadbabaabcdcabacdbbbcdbbcdcdcdbbaabaddbcabdbdbbababdbbbcbabbbaddccccdcdcabdadbbbaabbbbaaadbbbddbddbdbbbbddccccdabddcbcbddcadbbbbbcaccbcddaccdccdbabbcabaaacadaaddcdbdcddcadbcbaaabddbbbaacbbdacbdadaddbcbbaddbbccdbbdcaddcddccbbabbcbddabdbaccadacdcacbccaaaadcdacbcacdcbcaaabbdabbdaccaabbddadadbabbbbdabcddabcdacbaacbdcdbacabbadaccbaabdccdabdddaadcdabcbcbcacbcabbabbcdadbcbbddbbccaaccccbdbbbaacdbcdcbbdcbbdcdadccddbaaaaacdbcbabccbaacbbddddbbdcbbbcadcabdddbbcdcaadbbacccccaccacbdbabdccbabdbdddadbaadddbbadaddddaddbbbcdbbacaddaaaccddccacacbadbbccddacbbcbabcadabcadbcdbddadadbbabdaabbaabbbacddcbaccbaccadaabdcbcbabbddbcadaddccddcabbdbadcdabccdbbccadcbacbabaabcdbabdcacdcadbcadcbdcadaaacbbcdcbadcbadcabcdaaddbdcbacaddcadaabcbcbbbbbcccadddcbbcabcdabacddbaccaddaddcaaddadbabcdddaacabdaaabcdabdbbcabbdccdabacdabcabbaaddaaaadcabbaaccbacdbdaabcacaccabdddabbdacbcccdaaacddbaacbbdbdababccdcdabddaacdddbabbaaabbaadbcdadabddbcdbcaaababacaddddcaddbabaadacddacdbaadaadabdbcbabaccacbcaaadaccaabcddccdadbccaccdabddacddadabacaadcaddbaabadaddabaadaacdcaddddbcddcbbaacdcbcbabdadadccadcccdcbcbcbcccdddcdddabaccaccbcbcdcddcbdacccacdbbabcaacdcbcabbcaaaaacbcacbbacccbaaacccadbabbabbadcccbbccacbdbacabcaccaddacdacdcbaacdddbadcbcdbdabbaaadbcccbbbcbbcacbcdbdbdccbdcddcacaacdaaacaddcbbccacacccaddbccddababdaddbadadbbacbcabdbcadbbcaabdbcbdcccdcaaadbdabcabaccdccbabbacbccbcdcccddccbdadcaabcacbacbbdcaadbddadbbddbdccdcbdcaacdbbccdbdcbadcdabcabbadbdaabddacbbbcddddcadcaabbdaaddadbcdbadbbbbbcbcbababcdacadcaaccccacbbbbdbaaaaccbbadbbddcbddcccacdcaadbaababbbbccacadcdcdbbcaabaccbddccbdbbcadaaaddbbbbabbcbddbaaadcacddddcbaabddbccdcdccaddddbacbabbbcdabbbbbadcabcdbcacaabcdcaddaabddccdbadbacdaaccbddcdaaaacabdbdcaaddcaacacbaacaababcababbcbcacddadabcddaddbbddcaddcabbadbdccadbbccdaabcaacacacbccbbdacdcbbcdcccdbadcdcddadbbbbbdccddccaaadddddcaabacdcbadcbcababdaabccadbadadcdcaccbcadbabbbbbdbbbcbcbbadbabbaacadbadabadbbacdbcdcccddbabccdbbbbcacadaddbdddabbdbdabbddbbbabcacadbcbbabcccdbbcbcccdcabdadcabdcbbabbbdabcccdadaddddbaadcdbddcdabddbacabcdabbdcabdcdbcbabbdccadbddbbaaccaccddcdadcdaccbbccbcddabcbcbdadddbdcaabccabadbbbadccbbbabdacccdadcbdacccdabadabaccabccdabcdcbacadcbdcacdddaabbddbbbbbbadacbbdaaaccaccbdadacbcddcaadcacdcccacadcbdaadadadcbdadbabbdcccdaaddaddadaabddbbdddaabaaddbdbabaadabdbbccbaabacbaaababcadaacbdddcbbcdbdaabdbcbdddcddbbcaabcdcccbddddcabacddddcdbabcdabbcbbbadbccddbddbbdcccddaaacadcabaabcccdcbdccaadddadccadcbdbdbbacbadcbcbabdbddbbcaaaccbccbddbaddabdabaadddadcbaacbcbdbacbdbbdcbdbaabcddccaddbacbabbaadabddcdbbcbcdaddaccbbbabbbdddccbabcaadccbcdbcababcccbbbbabddcdcdbbcbaaccbbadcbccddaacadabddaddadacaaadcdaccddaadaddaadbaadaacdcdbbdccbcbadbaabdbdcdcaccbccdbcbbdbaacabababcbcbcdacabbbbcdcccadbddbdccdadbbbcdbcdbcabbdbabbbaababdcddbdaabacaaaadabacdbabdaaacadabaadabdcabcdaaccabbcadadbdbaccdbcbcabbaacddacbabbcbccbcdbdcbadadadccdbddadacccddbbadadadadccbdcaabdaddbcdcbcbdcccadcabccdaccaadddbbabcccbccbabcccaaacdbbacbcdaacdadaacdbbabbabcabacdbdaddbdbabbacdcbbacabbbcdaccdaccadbadacabcbcdcdddccccdaddcbabdcdbacdccacccccdddadbcbddacdbcbdccaaabbbbdbadaccadaaabdcbcaaadabdcaddbabdcadccaabcdbadbbadacaacccaabaacdbaaadcbdacccacaddabbcddbacbcaadbccbadaaaddaadaaabdaccddabccbdbcaddcbaabdaccadacbabdbdbadcbddbaddcdddadacbcdbacbdcdaddddcaabadacdccbcdbbbdadcdbcdcbdacbbddadadddbcbabdcbbbacbbdddcbdaaabdcabccbbbbcbabbcbadccccbcaacadbbaddccccadaabbcaacacccbbbacbaccaaaadbbbddbddcbabdcdadddabbdbdcdaaabcbaadcacdadbaccdcbbccbdbbdccaabaaddcaadcdadbbadcbaadccbcaabdbbdcbbababcababdcbcdadaccbbbcbbdbdbaccbabdbbdaacdcdabccacadbacbdaccaaddcbdccdaabcdcdcaddbabbdcacbbcbcdaaaabdbacccbcadacdbabadadaadcaccaaabbbddacbabaacdadbcadddabaaacbcaaadcbbdcdadcbbccdcdcccdaaaccbbdaabcbcaabaacddcacccdcbbcabddbcadbbdbcdabdadcddabbdcaacbaabaccccbcbdcbadddabbbacdcccbddccbdcbdaaabccdaabbddbdacdcbcbdacdadcadcdabbbadbdcccdbabaddacddbcdaadcddacbbbddddbcbbcbadccdbdcdbcbabccccbcadbdcccccdadbddbbdcdacdaccbdcccdcabbdcbaabcdcdacdabadbbbdcacbcdaacbcacdddbcbdcadbdcbcbdaaddacccbbcddabdbaaadadbcacbcddddbbddadcaddcabbadccdbaabccbbbbbacaacddbcbbbabbdabccabaacdcbcbdacdaaccccdabaaadaacaaabccdbddcaddacddaccbbcbcadbcbdbaddddbabdacbdbdbaacaaaaacbbcdcaddabcbcaababcbccdabcdabdaadaaacdddaabdccaddbbadbabaaaacddbbcaccbaccdddcccbdcaccdcddbddcbacbdccddadaccacacbbbccbaadcdabbdcadcbbdccbaacabbacaddabaddcacdcabdabdcbbdccbabcddbacacabdaccacdccaaacaaddacbacadbbddddacdbbbacdadddbadadcdbcabbdbccbbadacdbdaadbcdddbbdcddadddcdacaaadcdabbdddbdbabaadaccdcbddcaadacbccacbdbddbccdccadcdccabcabacbdccdbcdbcadbdadacdccbcdaaabcdcdccadacdcaacabadcdbdaccadbbbdcbbcdcdbcddaacddbacbdcadaabadbbbbbdacbabbccadddacbcaacdcadcadabbcdcaccabbbabddcccbaddbdacbccddaabdcddcacabbcbcbcbbccbbdacaadbdbcbbcdbddbbddcadcbdbcadddccbdbdaaadbaabdadbcacdbacbcbadbcbbccbdcabdddadacccbcacbaadcbbabaabddcbadbbaaaccdacdcbbcddccaaadbbbccaaadbdabcddbbdaccdcdcaacadaacadabbbbbbbbabbdbabbacbbcbcdbcdddabcdbbbccdadcaacdddbacaabdadabddcaaacccbacdaacadbcccbbdcbbccdbbbbabacbdaabdababddabcdccaddaaabaccddbcaacdbbdbdbcdacbdbcdcbdadabcddbaacbcdcaddaddbcdcbcadabccdcdcbddbbcdcbadabbbccadbbadbabcbdbdbacabcccdbbbbcbcdabacabdabaaaabdddcbbcbabcbcbaaaabccbdbadddcbbccdbbbbbbaadbbbcadddcbacaaaaabbbccbddbdbbbbabbabbaabcadabbccdcbcaccbdddcdacbcddbcdaccdcdadbaddccacdccaccaccbbccacbcbdbbbaabdccacdaccadadacbacbabdcdabdabacbcdbcbcaacdbcdbadaacdcdadcdbddbbbcdddaaddcdcdcaadcaaabcabddbdacbabadacbaccccabddcddcdbbcaccddbbddaadbcbaaaabbacaaddbaddbbcbbdbcdccaadabdbacdcdbcdcccaacdcbddadbbbddbddadbcabccbccbbaaababbadacacadbbbcacddaabbacadcacbbcdcacbddcaabddddcddbacddcbaacdbdccbdbcbbaadabbaccccddcbdbbbdaacdccababccbcabbadbdbbddccddaabcaddcaacccbbdcddddaabbacabbabdddcddddabadbdabccdbcbcddaadbacdbbcaabcabccbdbbbcbcabacbcdabcbdcdbccaadaddadbacabccdbcccbaacdcdbacccbbcaacadacbdcabadbddaabcdbaaaacaaddabadaaaccacaadcddbacacdcbbbdbbabdddabcaaaabbccacbdaabccdddaccbacabbabcabdadbdaabcbdcbdbccabdacdcbbbacddbbcaccdcabdcdcbbcbdcdcbdbcabacabbbcacdbcddbaaadbaaaaccdddaaccaacdbbaacacbcbbcbbcbbdcbaacdcabdcccddbacaacaddbcbbbaaccdbadadaadadbbababbdbacccddbacaddadaccbdbbdbdddabadadddcdcdbdcbdddbadbabbadabaabcbaacdbcdddcabbdacbcbcccadcaacdacdacadcabbdbcdbdbdddcaabaabbcaccbbaddadbaadccacdbacbaacdbadcbaabacadbbadcbcdcbabbcddabcddabdccadcbbbbcbababababacccccbdbcadbabaaaddaabbcaaddbdabaaccdaadccbdabdcccccdbdcbadcbbcccaccbbbbbbcabaadaddaadddcbadbdcdbdbbcddaadbccdddccccbbaabcdadcaccaacbdaaaaddabaaaddaccadaacdbabddbdcacbbcccdbacadcbababdcccdaddaadcddcdbbbddcbdccdaddbbcadadbdcdcacabbbabbbdbdbcbccabacbcaacdacacadcddbbcdadbcbcdabddcbabacdacbdbccbbdababbdbccabbbdbddddabddcbcabcadccbbdaddbabcbabbdcdaccadbddcbdcbdddccbadccaaaacbdcccaabbccdacacabacabcadcdadbacdcccbddcbdcdaaaacdababcddacacabadaddbdadacdcbccbadccdddadbbccbcddadbdabbbdbcbbbcaadacabdbbadbcdbccdcdbacdbcbbcdccbbbbcdcbdbbddabcadcbbdccdaccadaacddcdbabbadcccadabdccbacbabaadcbaabcdbacbadaabadccacabcccbcddccaacabbccabbcadbcaadbaabbdaabdcbddaadabbacaddacbcadaabbacdddcdaadcaaddcdcccdacdabbccdcacaaadcbbbaccccaddaabaddcabbdacacabcbaaddcaadcaaacbdcbabccbcadbabccdacdbdccacdbaabdcdbcbddcdcdcadccabddddaddcbacbdacddcdbcdaaddbbcaabacbbbadacaddbddcbabdcddbccacdcccdabcbbdbcdcdcbdddcdcabbabbdcabcdabbadbdbacaacdbbcadcaadcabdaaadbadbdcbcdbdbdccaacabacbdcbbdcabacacbbaaabbcddcccdbdbcacccbaabcbacacbccabdaabbcadadcddadddaaaaacdcacaacdaaadaaddbbaabccddcaadacabacbabadcacbbabcacbcbaabcccadacabdcdadbcaaaadcbccbddacaddcdcdddabdabbbdddbdadcbadbbbbbcccabdadadcdaaaddbddcabdaadacddacabbcacbadddccdadbcbbbbbdcabcbaaaddcddbbbaacbbbaacbbbcacbbdabdbdadcdcabbabcdcadbdcbdcbdbbdccbadabcddcadccacdbdcbbbdaccaacddcbdbbcbaadadadccbaaababbbbdcdbcdcbadacabcdaddbcadbadbbaabbbcdaadbaccccdacbccaacdbacbdccdddbacdcacbadcacbadbaaccbbddccdadbabcccdccdbbcabdadcccaabdbccdbdbcbabadddbcbddbdbacabcbddaaadcaaabddccbcddabbaaddadddcdcabdcbbbcbbdaadacadbbbcbabbbaddcbcadbbcddcbdcbdcbaaadddcacdbccbdcacdbcdaadbdcacdadbdadcdcaddbbcbccacdaabaacbcdbbadccddcbadddacbbaabadbdcdccaabaabdbcdaadccddadacccacbcdaaadabcbbbabbcddddadcbccacbcdddadbdccdbbaaccaaadcddaacdaabcdcbdcdbbccbdbdcdddcacdbaaacbdacdaaaccbabdcbccccccdbddbbcbbcaddcdabaababaabacabbdcdacdcbbdabccbdacbadbddcacddbbdbacaaabacacdcdddcbdabdbcddbccbccaaadacdadacaaaddcdcabdbcaccdbbaacbcbadbbbdbddbbbcdadaaccdcbdcdbdaabbccadbdcddbccaddbaabbcbbbbcdddddbcbccbcdabbddacccadbdacaacbdcddcdcabdbbdaaddddcbbbaadbbcdbaaaaaacadbdacadcbdddbccbccaadbbcaddbbccccccadbdbdcccbaddabbdadcddddcadcbdabaddabdbbbbdddaddbaacaaaabcbbcbcdabbbdbbddabbbadcaabdbacdaddacbbcbdcbabcaaddabacdacbcbbbdbccbdacbacaddcdbababaccdbbabdcadcbbaabddabaddbadcdaaddcdbdcbcacbbacdcacaccbdcbdbdbadccccbccddbcacdbcccdabbcabcabacabddacbbbabbbdcacbcdcdbacddbaacbdddcdacddaccccbacadbbddabcacdcaaadbcdbcddbbdbdbdcdbcbbddaccdadbdcbdcdcadabcdacadddbdaabbdaddbcdccdaddadbcbaacbcdccbbbdcaadcaccdbabcbbcbaadbbaadccddabdcbaddaddbccdaaacabbdcddbcdccbabdbabbccaadccbdaabbddcbbbdbaabcaabcbddbadbcaaddbcbbdbdbcdcdcdaaadcdacdbdacbdccddbbcdcabbababbaaaacdadbcbabccbdccacdcbddccbcbdaccddcccdbddbddacbaadadacdadbdacbcacbbadacbdabcaaddccbbabccdbcdaaccbdddbaddddaabbdacadbccbcdacdadcbacbdaadabcccbabbddbdcaaadadcbcaacdadddcaabacabccccabcaacbddcdabbbcbdbcccbbcadbdadbdadbadccbacccdcdcabdcadadbbcdccadbaacabaabacaaacaabcadbdcaadcbbcdbadbdaddacdbcbbcadaccacbbddcccbcaccbdbdacacabcddcacabcabdcbdcdcdbaddabdbaaacbbcacbccbbdabcbbbabbdddbbcbbadabdcdbdbbacdbddcacaabdaadbacdcabdccdccdadcabaaaadcccabbcbcaccdccdbdbddcddbbdbdbdbbbbddcaabcbadbdaaaccdcddabdcdaacbcccbbccabcbaabbbbbcddbbaacccdadddbcbbabbcadbcdacdcccbbbdabcdbaadcdddcdcadccbbdabdcdaacccabbabdddbbcaaacaacacbbbdcbdbaddddaccccccadaacacbcaabddddaabacdabdacdbacdddbaacbbdaaaadccacabaabcacbddbdcbdcbcabbccadddaaacddadbdcdabdcaddcabbdcaabbbdaaaabcacaadbadcbbddddacddcbadabddbbacbccbacacaaddacaaababdbcddcdcbdddcbadaccdabcbdaaabcbcddddaccacdadccdcdcabacdaabadcadbbbbcabbaccbccacadbbcbaaddcadbbdacccadbdadaccabacbbaabbcbacaacccacaaadddbcddbdabdbbbdbcabdddddbadbacbbadcbddacadaacbadddccdddabddabdcadcbccaabdbcccbbcdacbdbbaccdaadddaacadcaaaadbcbaccaacdabcacaaadcaccabdacbacccbcabdccadadbbcdacccaabbdbacbcabcaadcaacabdcabdbcbbcabadbdacabaabbaabddbdbdcdbadbdddcaabcdcbbddcdbdccbccbddbcdddccabacababaddbcddbabccccddccbcadbcbdabdbcdcddccccddcaddabcdcadacaaaacacbcacbaabaabcbcbddacadacadbbcccccbcadcaccadbbaaddaaaacdaaadcdbacaabcbdcbcaaaccaaabdacacdaaaaaaaadcbdaabcddbcdabadbdbabccdaacdbbaabdcdcaabacadadbcbabcdacdbcaacababbdacbabbccbadcaadcbdddccccadbbbcccbbdccacbccacaaddcabcdcbdadaacddcdcdaaaaaccbcdcddbccddadbaccccbdccdacddbccdaabaabcbabbdcabaabbdaaddccabcaaabdacccbdaabdbbdddbcaacbbcddbacdbdbbcbbbccacaacdcacdacabcdbddbdccbcdcbcbbbacbccdcbcabbabbaddccacacbcabcbbcaabddbcaadccbdcabcdcabdacbacbccbbccabadadbbdaabdaaaccdbdddaabacbbbcacbdadbdbcdbccacaacbacdcdaccadaacaaacdbdacccaddabacbcdddddcaadaadaaabbacadccbbacaddadbdcddaaaccbbbbaccabddcadbdddacccddabdcbbdacddbbbadabdbdabdcbcbcbaccaaccbabdbbaaaabdddcabbdbbdbdcdcdaacbcdcccddbbbcaadaddbdbbbacadcdadaccdabcdbdbbbdbbddacaacccacacdcbccbadbdcbdaabdaacdcadccaddaccabddaadacdbbdabbbadcadbadcdcdbbbacaccbcbcdacdbaccbcaaadaddcbacadadacdccdcaadbcacdabacdadcccabbdcababdbaacadcadbdbcdbdaadcccacdbdccacbdabbdcaaabbdbddbdcdbdabccbbacaabcbcdbccdacdbacadddddccbbacdcccbcaddabcacbcbcbddcdbdcaaccdaddbdacdccbdbbddcacdacdbcaacbcaacbdacaabaacabababbdcaddddaabbcddccadcbcddcaccddabbcdcbdabccdccbbaddcdbaacdbadacbbabcddabaddcdbaaadacaadbadcdbdccdbcbdcbbdcbccbacdbaaccccadddadbbcbbadcdbdccccdaddaadbbbababbdcdaaaabbbdcabbdcacdabadbbdbcbdcbcdbbdccdbcaadbcdbddacbbcaadbcbbaccdabaddaaabcbbdaabcbbababadddbbcbbacccccdbcdcabddaccddcdcaadbccdbdddadbbcacbcacaccbbdbcdcdcddbdbdbacdcadaddacbcdbddddabbcabacaabadcdccbbcaccacbcccccbcaaabcbaddbacccbbccdcccdaccccbacbaadaccddbdaadbcbadbdbdaacacadbcbcdaccccbbdabcbbcbdcbacadccbdbccaaddcadbabcbccdbcddbcdbddbcbddbccdbcdbbcdcdccbdcaadbbcccacddbccaadacdcabdbdcadbcccadcbbdaacdbbccaabcddcbcbabacbdcbddaabdcbcdddaccdcdcbaabcccdcdbdcbcabdaaabbabbcddccbadccdcaabaacadaccddbddacdcbacbacccbccadcbbbdcccddccbcbbbacbdbdbbbdadbadcddaadcadadbcddbbbdcbddadbabbadbdccccbcaaaaabdddabaabacdabadabadbadaacbddbcbcabbbcbcbcbdbacdabcacbbdabcdcbccadcbdcdaccbbadbdcaadabdaadcdbaababdbaaadaaaaccacccdccaababbbbaacdbddacbcccaccdadabbcbabcaacadcbadbbbdcbadcbabcddadbdcbbbcddaccbbdabacaaacccdcdaccddbdadbdababaacbabdacdcdacbddcdcbbbdaacdcdcddcccabaacbcbcacdadabbbabcabccdbaccacbdcaabaccadcbdbaabdbbdbabbcbccabbdddcdcadaddbcbbcbbdbcdcdacdabcdddddddaababbaadbdaddbbbcdbabcdcaaccdaccbbdcbbdcadbdcbdacaddbcbbdacbadbbdddbbcacbdcbabcaabddcdccbcddcaaaabdcddbbdccaaaaadcccddddbcdcdbabcdccddcdbacbdcacbcdcbcbdabaaaddcddaabdcdccbdbdbabadaabaddabcabccdccccdcabccaabdbcdccddbaacdadbbcbcccdddbbadadcddcbbacbbccadddcbccccdcadbadadcbdaddabcdbbccaddbbacbdbabccddccaabaabdaadbcaadbbcdcdccdbcabbddcaddccabbcccddacbadacdacdbccccdaadcaccccbdbdccaccbdacdadbbbbcdacdaaddacacadcdcbdcccbdaddbddbbabaabaadcacacccbabddcacacbaaaacabdddaccdbcaaacbdccbdacabcdaabcabcdaaadddcddacdadcccbbbddcadaaabcdaccbbcccabadcddcabaccacddaadbdddcbdcdcaacadbbddcadadbadadbbcbabaacccdacdacdbadacccddcbbbccbbacddbdcacabbbbccddacabdbdbddbaacdacadcacbabcaaadcbbabccdaaaccccdddabdaaccacdaccbccdaaadbbabbbddcdababddaddcabbddbddabcacabbbdacaccddcdbbaabdbadaadacccdccbcccbaaadabadcbcddbcbcccacdbcbabbbdbaccccabbbadcaaacaddcacdccbcddbdadbcbddabbcadbbddbcabacbccdbbacbbcbbdbcabbbaabcdaadbaaaddaccbbbbddbbbcdcdcacbaabddcacbddbbdabcdbcdacdaabacadabcddcdadbcdcccadbcbbddbbaddabcaacdddcdbdcbaaabaadaabaaaddbaacadadabbacdbbbbdaadcadcbbabddcccbadbcbcbbccbddcaacbddccaccdbaaadbcadccabacabddacdaaacbbbbdbbaccccabbadbbbbdcabacccdcbaaabaadbbaacddaabacbbdadbaaadccddadcadaaaccbddcaaacdcbcaaacbdcadddbdcdccbdccaaddcaccbadaababdcdaccdadbbbbaabaaccdacddabccbcaaadabdbbddadbdbdaaccddbddbbdbcacbdcdaabaaabbcaddadcadbbbddbdbccdcbbbdacbdcbaacbacaadaddaacaabaddaddcadadddbbccacadcbdcddadbdbbcbdabaadacdcbccbccbbaacaaacdddbbcaccadbaaaddbcdcbacaccaddcbcacbbccacabcaccabbacadcbbcbbabbccbcdcbdbdadccadabcacccdcdcabadbdbdcaacbbccaaddacadddbadbccbabadccbbbcabbbcccabdacbcacbdaabacdcbabaaadbccbaccdbbdaccbdaacaaabbcbcdccbcbabaabbddbbadbcccacdcadabbdabdabcdbcbaadbaccacdabbdabcaddcaccdbdddbbdcacadcbbaabdbbdbbcdcaabdaccbbccbaaaaabbabaabccbddcadabccbaddccdcbbacbcdacdbccabbbcbbdbaaccdcdacdcbadcdacbddbbccadaaacacbdbbdcbbadcbdcaacabaacdbacbbcccabadcdddacacaccbbbaccbdbdbcbcbadbadbabdabbddcadacaddbbcacdcaadaccaddbdadbddddcaddbaacdddadccccaabcadacdbbccccdcccadcaacddddcbbabdabaaddbbcbbdcacbdcacbccddbadddadaacabbdcadaccdaadcdacabdccbacadaaacbbdcdabccbccdbacbbddcacbdabdaccdcbcddbcdadcbacaadddabbaaabdcccbddcddaccadddadcbcbccccbaadaabbbbccbdcbdcaaaadcaabacbbabdbabddbacaabbcdaabdcbcddadabadabaddababbacaabbdacaacadcbadbadcddbcbbbbbbccdccdbbdcddbcbacbbabbdbadbadcbddacaddbddabccdacacddacdadadaaacbcbdcadacbcdacdaadadbdbbdaababadadbdaddaddcbacccccaadbbbcdcbaaacbcbcddadccbaabcabbadbadccbdbccccdacdbabbdcccccdcbcadcbabbaaabdabcdcaadddaccdabdabaacbbaaacaabdcdbcccbdacdbbccccabdbcccdcaabbdbdbbbbccbacbddcabdccbacadbdabadcababbacadcbdbdabdccacbdabcbcbbaaaabbbbadbbdabdbdaaaddcccadcaacabddaaabccccbbbdcccbaadbdcabadbcbaacdcaabdcabdbcdccdaaabaddcdbacaadacccbccadaccadcaaddddcadaccabbdbacddcbbcdccabdcbdcdddcaaaabbcaccbdccccccdaddbaabdcacabddacabaadaaacbbcdaadbccbbcdadbcbdadbacbddcbcacabdbbdcdccaddbdaacabcabdddbadcbbccbdcadaccbccaadbcabccbccacaacdacaabcabddacbdddadbadbdaabacccbacbcbcbbacdaccbdcdcdbadcaabccbaabcdaabdbaccbcccdaaddccadbaabbdcadcadabcdcbaddbadbbdcbdbaccabdabdccddcbaaabaadcddabcddcdcacadbdabbccbbdddcbcbcbacdccccdbbdbabaccbcbaabccaadbbdbbcccdcbadddaddadbcddaacaabcccccacaaaacaddacacacbddcdddbdadddbbcdaacdbbaacbdbbaadbabcabdadbacacadbdddbdadabdbbdbdabaaddbdaabccbabcdacaadcdbbabdcacaabbacdadddacaddcccacdddbbbdcbbbdcdbbcaabbbadaabcdcacccacbabacbcdcabcdcbbdaabcdabaadaccbdcdcdcbbcdddbdcdaacbcbbacacdccabaacdadbdbcdcbddcbbcbbbbbdbcddcbdcdadaaccacddddddbcbddcbcddadccaadadbcbdbdcdcaacaacaaabddcaddadacbbcdcbddbbdbcccddcccabcdaabcdcdddbdbcadbcbbdcdbcbaddbcbdacdddadcacdbbccabcdacaabcdddddacbcaddcdacddccbbcdbdcdbddbcadbbcbdddbdddbacdddcbabddcccddbdcdcdccaacadcdcacbccbdabdadccaabbbbaabaabccbacdbdabbaddcabacaaaacdccbbdacdbacaccbccbadcaabccdaadcdcadbcccababcabccbdcbbdaaccadbbdbccbdaadacabbbdacaabdadacdabdabdacbdabcdaaabacbbabddbddacdbbdddcbbacdaababadabbdabaaabccbccbbdbbaccabbdccbbcbadbddadabadaacdbccdcbabcabbaaccbccbdabcacccabababdcdcccaadabdccddadaabadccbcbbdbdabbaddabcbcabcdaacbddacbdbcaaaadddbacbbbdddbdbbdabcacbabaacacddccaabccddccddbdbdabbcbdbbbadbbcddaaaddddcbcdbbacdadaddacddbccabcdbacdddbdacbadbdbbadababdcdcbccdddddabdcbccbcbbabcdbadddabddaacdacccdaccbcdcdccbaaabbddbdbbaadddbcadbcdbbccaadcccdacbacdaadcacadddbbbbdccadaaadddcbadbaadaaaadbcabcadcbccdbbbdddccadbbccdabccdacbbdbcacbacaabacadbaadbbbaadbcccdaabdbcdabdcadaacbcdbcdbbbaabcadbcabaadacadbadccacccbddbdabcbdcabdbabaacddddaadbaabccdbdbcdbabdbabadbccbdbdbddaabbddbbbaabbdcbacbbdaadcdcbacbdcdaccaddcbadaadcadddacabbdaccbdadcddcadbdcbbdabdaabddbddacaabdaaccdcdacbcbdbbccdadaabdacadbdcdabcabbcabddcadddadaaadaccadcbbbabbcdaccbccdcddcbbcccadcdaddcdabbabbbabdddbccaccdcbbbdcdabdbbdbbcacadaadabbbadbabacdccdadbababadbaccbdcaccccdbacbcbcbabcaaabdcbddcdccabdcacbddaadabccdbdbbabaacadaddabcaccddadcbdacaaabadccbcdabccdabdcdcddbcdbcaaabcbccbbbbdabcdcbcabadcbadbcadabdcdbdaacbccbabbdaacddababcbccdcdcbaadbbbababdcdacacbdbbbaabcdddcabaaddbacbcdccdbbaabbaacdbcdadbbabdbddaaccdabdbdadadbdbdadbbcdaabacdddbdbadbacbdbcadbacadbbbaacdaaaacaadaabdcabacdcdbbbbbcbbbcaccaacbcdabbaaccbdaaacdbadcdbcbaccdcccaabadbadcdcbbbadaaadddbcbbbababcdabbbbdbdcbdddbbabcbbdbdadcbbdcbdbcbdcbbbddacdadbdbdacaaadbdbdabbbdabbdccdbacabbddadbdbbabadabbdbdcbccadbcbabacdadbcccddccbacdbcacabacbbcdcbadbcabbadcaadbdcdbccdbbaabaabcbcbddccdbaccabbcccdacadcdbbacbddbbdcdabacbdcdaabcbddbccdabbaadcccaccbcccbccdddacdabdacdbacadccccabaccbbdbbdddcbddcddadbdbadabacccacaabcabcddbcdabacbddacbbddadbbdbadaccdcbabadcbdbacbadbcdcbcdbbbdaccdcadaaacadacbcacbdabcabbccbccaacbddccabccbdccdbbbdcaadacddccaddadbbbbacbabdcbcadbbbbaaacbdcdbadcaabdcbbbaddbbabbdbbacdbcbaadbadcaadcdacbbbccccaccccdbddbbdaddcabbddbadcdaccbcbcdbbdacbbcbdccdcddcabbcbacbcbaabaaadcababaaabaddbabbddcaabdadbccdabcddabcaaaadccbabcccbdddbcadcadccadcccaadbddaaddabbcbacdcbabdddccdcdadabddbdadabdddbdbabdcdbacddbbdabcadaacadddcacbadddccaabccbcaabaddabbcbaacaabbadcbdababaddccccaccbbaadcdbdcbcbaabbdcbcbbbbcdcaddadaaaacbababdbccadbccaadbaabdadabddbbcacaacdcbcabcbcaabbddbcaaabaddcbcbadacddadbaccbbddbacabdbdbdbcdabdbccddddcbbbccabababbaccabbbabddaccbaaacbddcabaaaccaccbbaadabbbbbadbddadbdabbbddaddcbabcccbbdabcacdbddbddaacadbcbcbbbabbbaccbadbabaacdbcbaccdadabcbdddbcbadbbccbadaddaadcbbcdaaddbabdcdacaaccacbcdcbbdddbdddbcbcdcbbacccdbabdbbddcddbabadcdddbbccdcadbadcdbaabcdadabcbcbacdbdddabcaabbaaacbadbbdcbcccbdbbadbbabcacdcddabcaccbaabaaadabacadddccbbbdbddccbdccacdadcabaabddaacdbbdddcaabaddcacdbbdddbdaadbddabccdacbdcacbadabbbbdbdbabccbddbaccdbbaadadbddbaaabbcccdddbdbadbbaaccadcdadcbcccdcaddbdcabbbdbddaaaaccddddcabccdcabccbaadabbacccacdbdbdbcbcbabccdbbaaabcabbbccddcacddcabbddcdbbcdacbdbbaabaaccbbdadabbdbcccabacaacaccaabddacccbadaaacabbaaacacbdbccbcbcdbbccadacbccdacbcaabbabbbdabcbccaacaccbcacabddbcaaadbdccdbbbdcbcabbcbcacadccbddaadabbdcbcabbdcdcdbcabbcddbdcbaaccdbdccbbaaaadbdcdadcbabadddbbdcabdabbdbbaadcadadccabaacabbbadbbbabccbcabddcdcadadbadcdaaddadacdcdcbadbbacbdcdccabacbcacdcaaadcacbdddcaacdabddcbdbacacdbbbacacdabacbcabcdacddcdaccdddccdcccadbaddbbdababcaabbbdcbbcbbaaaadbacccababcbbbaabcdababbabbdcabbcccdbbadbbabdbbaaabacdbaabaaaaaacdabdadbccbbddcdbdccbccacadbabdcaccaadcddaacccbadbadcbcdccacadbaccabbabbdcbbaabaccabdddcdcbcbcddaabbbcbabbcbbdbcdacdddacaacdcccbbdcdbddbdcaddbbcdadacaadacabdbdbbbbbbbcbcbdadcdaaaadabccbcaadaadbcddbddaccbcccaadadcbbcdcbbbbcbddadccbbbacbcaccaddadddcbaaadcdbbccdacababcbcaccbcaaaabbbbdcccdcbbaccadbdbbabaaddddcaabacbabddaaadccdbdaaaaabcddcdbdbbbcbcdaadccdacccacbcaacdbcbbbdacbbdbbacbbdbdcdabdaacaccddaddbbbcbdddaabcacadaddcababdadabaacabbcbaabaacbbaabbcabdbdadbadcdcdbdaabdcdccdbaccbdcaadbcdabbdabbcbaacbbcadddcdabcbcbcababbdcbccdadcaacbbcddabdaaadbbababdabcadacadaadaaabddddadcadbccbabacbccdcdabcccdcbacacaaccbcbbadccbcadddcdaaacdabddcbccbccdcdcbddcbcdbabbaaaacaccdbbaacbacbcadbcdaaccaddbacddadcbdbddcbdccdaddddbcdbdbdabdccbaddcdadcaaddcbdcccccaabadbacaaabadaaccddbcddadbbbcdacbddacdacdcbcadacabaaddcddabdcdcabccddbcddabccabbbcdcaccccbbdbbccbabcddcabaaabbddcbbbbacaabbdbbdccbcbcaddddaacabcccddaccccbdcababdcacbaadbadbdcacddccbdbcccbcacaabbddcdbabbcddcdcacdcbacdacaacdadcaaddacbcadbaadbdcbcadcdbdccbaddbdbcbcaacacaaabccbaaaacadcddbbcadccbdbdaaccccccdbccaaccbdadaaabaaaadddcbdcacdbcdabcabbabdcdccbaacaaddbadbabbbbccaaddcbabccbddcacaabdbadbbdabcbdccacbbddbbdbaccddadacdccacadcacccccacbadabbcbcacabdcdabcdbbdccbbccdaccadaddbadbccbccadbcaddbdabdccbabbcadccbbdbacabcdbcacbcbabbcddbdabdbddabbabbaddcabacbcadcdcdcdddabdcdaacdaadbadcadacddccdbcbcbabadbcdcacbaacbacbdbbbcccdcccbbbbcccbdccdacdbddcacdaddcbdcbbdddadaccbabbabcdadcbabbdddbaaddcbcdabccdacdabaabaacbdbbadbabcadddadccbabbdcbddbdccaccdcddbdbaadccdacccbbbaabdbacdccdbbadcbbccccdbadaadacbabccacbaddadccbbbcabbcabcbbccadccadacabbacddabcaccdcabdbcaddbaadaaddbbdcaddaadbaddbbcaaacddddabdacbccdcaaacaccccbabdddbdddbbcccddabddcbadbdcbbcdccdbdbddcbbbdcdcadccabdbddbcbdbdbdadbcbadbcdaadddcdbaddbaadcbcabadddddcbccbaacccbdbcdadbdbdabaaccbaaacbdddabbbabaccacdacdbbccbbabddddcccbabbbdcbddccccdbabdbacbdadddcbcdddddbbbcbcdacdcddbcaacddcccbbcdbbacbdbbbdbcdbbaabcabaccccdcacbddbbbbcacaacadbccccdaadcadabaccbcadddabbbcdabbaabacbacdadddabdcbacdcaddcbacaaacacbbabbdaabcbcccdaacbbacababcbdccbbaacadcdaddcdaadcabcbbbadbdbbdcbaadadbbdbcaaacccadcddbaababbadcbacdacbcdbdcbdbdacaddccdbcdaccbbdabddcacdcdcbbacbdadcdccbdbddacdcccbbabcbcdddabadaddcdadaadaabcbbcccbdcbddbbdddbbdcbdcbcdadbabaabaacacdcbbbbccddaacdccbddbadcdbbcacaaabddddcbdccadcaabaacbdacccdcabacdbabcbaacaadcabbbcaadababcabdccdbbcdbcbabbcdaaccbccaacddbccbbdbbcdaaacadabbabbbbbccddbacdaababccacbbcaabacdcdababaddbdcacbbcbbdcaaacdacbdcaacbbcabcdaacdabccbdabcabbbbbbbabadacccbcbaacddadcdabbbdbdbdbbdbbcacbacaadaccbaadbccdbacbacabbdcacdaadbdcabddbdadabcbaadaadcbcccdbdccdbcdddacbcacaddcddacbcaaddbcaaaadcdcdccadcabcbaacbdbaccccbbadaabacbacaabbccccbbdbdbabdcdccddccbcabaadabdddbdbacccbdcbcbaddcaaabbddcaccbacabaadaabdbddbbccbcdcbdaadadbadbdabcccabbacbdacddbcbaacbddbadacaccaccdbbbabcbddbdcdddbbdccdcccbdcdacdbcbdddaddcaddbddcdadddacccdadacdccddaaadacadbadbacbbbabdcdcdadbdcddabccdcabddacdbddabcacaddacabcbcaacdbccbcbcacdbbbabccacbcacaaaaddbbabaabaccdaaadbbabbcadabcbbbdbbdbaaaabccccbaabbdadbaabcbacbdabdaabddabadaddcccdaabbcadccbacbbbbbaccdbbbccddccaadbbdaddcbdbacabadadcabbaaccbcbcaabbbdcddadabaaaadabcadbbabadcdadbcddddadcdbadcccbddcdaccdcbbaccbbbabccdddadbdcadcbdbddbacadddadbdaabbccadbabbddcdcdaaacdbabdaadccaabccaaccaadbbcbabbdbccdbbbabdbababaddcbcbcabbdcdadcbaddcbdddcaddbcacbaddaacaaabbbadbdabdcbdcdccdccaaadbcaccddcddacadadcacbdababdbdcbdcadcbcbabbbddbaccccccddcdbbcdbcdbbddccaaaacddbcbbcdabcbddcccbbddaacdcaaaabddbdadbdaacabadcbababbcaacadaabcdadaadcacdadadaaaaacacbbbdadbbacaddbdacbcbaddbdabcbacbcacbddacdddbdabbddccddcbaddbdcdabcbbdbddcbbadacbcdcbbcdddbdcabbbaddddbaddaabcdcbcbddcbcacbaaaddaacaddddcbadabcbabbaadbcdcdbcdabdddcacdbcabaadbdbccdaddcbcdaadccdadcdaacacbcddadadddcabcdcacdaabbdabadbadccdddadacdabbdaddabdadadccbadaadcdadccbddcbdbbbabbcccdddccbbacbccbdbaccbaabccdbccadadabbaccadcdcaacccdcadbdbabbccbddcbaddadbbaaaaabacccaaadccccbbcdbddabaaccbadaddccdbacdadbccccdbdddcddcabcbbdddaccddcdbccbccbdcdbcdaccabddddbbadadaaacddacbcbacdcdcdcacdacadbcbbacadbddbcaaaaaccbbdaccbdbbcdccddaabdddaccdcbdbbbbacadccadaaabdbdccabbcacbbcdacbaabacdcbaabdcaabadaddddddaaccbbbaaaacadbababacdccdcabbcdabaadaccccbbcbacdbbcdddbbbddaaaaabcbcadccaddabacbbdacbbcbdbcddabaddcdcdbabaaccdbcdcbddcabcbcbdadbdbcddacddacbcadaddccadbcaddbabccbbcddcdadddbdadcdabacbaddcbccdbbdbcbcbdbbbddcaacddcaaadbbcbabbabccbdbccadcbaacaccdddbbbacdbaacbadcbcccdadddbdbbbaccbccaaddacaabcaabaabcacaadcaddacccbbbcabbaadcdcddabdadacdadcacdacaccbaaacadbcadbbadaacbcccdaacadcdaadababbcccacccbaaabdddcaacaadddaabaccabaaddddbacbcacbdbbdaabbadbcadddbbadaaacacdacaddccbadbacaacdadccdcdbcdcdaacbabdacbabaddccabaccabddccacbddbdabccaacdccadccdbabdbcabdcaababaaabacdbcacdcaccbcabbcbdccbadbaaaabbbdbacdddaaacdaadbbaccdbabcbbdcdddddabcdadcaddddaaccabababacbcdcccdcabaacbcbaccbdccaddbbdcdbcbaabaabbdacadaddbaaaabdadbdaddbadcdadaccdbddbbccddaacdacdbaccbaababddbbabcacdabacbdbccbdbacadbbbacadabcdadbbbacaddddbcadaddccccddbacdcadddcdaabaaabbbcbdaacdbcacdccddddbacaaddddccddbacdcdddacaccdcbbaadbcbacbdbbcbacbcbdbacacadadccbdcaddccdcacddcbbcccadcdccbcdcaacabcdadcdcbdcdcabcbacbccadbdbbbabbcdddadbbbcdcdaaddcdbaacdccccdbabaabadbbaabaabddbabccadbcbcadccbacccacbbdacbdcbbadbbbcdbdcddbdccadbdcccabbaccdadcbddcbabdcbcdbaabcaddddddadadaacbaaadabcbdaaaaaadaddcbdaadddbdbdbbbdcbccadcddbddbacbcbbddadddaccbcabbbacdbaabbabbcdcbccdadaaacbabcaacadbaaadbdbcbbccbaabdadddacdabbbdbbbbdddabdcdabbadcaabcaaabadccdcabddcbdbaaddbdcabdcdacaaacacdadaacbaabbbadbdcdccbcadacadaaccbababaacdabcabcabdddbcbabbbcbadbdddabdaabbdccdabcabaddbcadbbcdcacbbbddcadddabdbccadcddaccdcabcadbdabacbbbabbbaddcbddbcbdccbddbdcdaccaabbbbbabccabadaddbadcbddbbbddadddbdadbdccacbbdbaaccdddabcabcbccdbabacccddbbcabdaacbbabdbdaacbaaadbacbbcbdcaccbacaacbadbdacbabcbbadadadbdbbccadbddbcccdadacadcdcdacbdcbccabdbbacbacddbdabbdacdaaadddcaaaaccaadaccaabaccdacbcccbccbcccdcdaddacdbddaadbccaadcdbbaacdbbcbacbbdddaaddcddbcdbbdcacdbbdcdbbacaaccbaadbddbacdbaccbdcbabcbbaabaaadccdaaccbdabdcdbdcbdacbbbdadbaacbccabadbbddadcaddbdadadbcaabcacdaabdabadddbbaccdddabddccabcdaddadaacadacbcccdbcccaadaabddddddabbdcbaddddabddcacdcbbdacbcdbcdddccddccaadadbcbdacdcacadacbbbbddadddbcdbaccaacccbaaaaadbbbcaacddddbadaddddaabaaddabdcdccddbdddbccadcbbcabbbbdcccabcdcdabcdcabddadcbacacddacdbadbcbdcddadaadbccbadabcacbacbdccdacaadcddaddcaddaaacbabdbcbcdbbcabcbdcacaddcadbcbbaaddacdaacbdbadcccbabccacabcbcadadcabbdbddaadcdbdadbdddddcdbcbbcdcababddbcaacdbcbbcaddcbbddbaabbdbbcabaaacbaababcddddbadcbbcdcbaabdaddcadbcacadbcaaccdcdbbcacccccbabbcabddadcbcdacaacbdddadacdadddddbcadadcadacacacadcdcaccacbbacbddbccccbdbddddacbcdbbabbccdacacdbdcabbdccccccbaacbddbadbdbdaadccabbcdacbbaacdcababbbaaacaaaaaaabdcbbaaaacbdabdcdadabdaacbcbdbddbbbbabaaadddaabbbbadbcadabcdddabaabdacbddddccdddbdbaaadcdacbaabccbbaabadccdbbbbbcdccbcddcbabccbacdddcddaccadbbdbcaabbadacbcbaadaacddabbdccdbddbcdbbbacadbcdddcaacadbdabcbccbbbcacabaadddbbaaabbabcacbcabaddaacabdbccddbacbaadcacbdddddaadbdbcbcbddadbadadddbdbabdbbbbdcdbdddabdbabaaccdcabdcdadcabbdacccdcbddacabdabbcaabbccdaacdadabdbddcbaaabcdaabdbbbdddbdacbaddabacbdaadcbdcaabcdadbbaaaacdcabaccddbaadcbcbaddcbbcbddaddbccccddbbdabcdcababdbdcbbccabbdbbabbbdaadddddabdcddabcdbabdddaaabadaacaddaddacbdaadbaddbcabcbcabaabcaacdbacbaddadccbdddbaccddccabcbcbbbbdabbccbdcdcbbbddacaadbbcccaaaaacbbcbcdcbdadbdcbdbaadacdbdcdbdaaacccccbcadacbbcbcccddabbcaabababdaaabcadaccadaaddcbaaccabbccdcddabbdadddcdabdcdaddbdbabbbdbaccadaadbcbcbaaadbdaaddddadcbbbdbbaacabbdcacdcadbccdabcddccaaccacdabbdacbdddacbddbacacaadbddddbbdcddcccaaacaccadababaddbbcabbbadbddcdbcbaabddcdbdccbdcbbdaddaddbcbbabdaccaaaacacaadacbdbaabaddccccddbdacacbbdccccbbdbcbdcabcdcbbbbcbccacaacdbddaddcdbcadccccccccbcadaabaaaadbcddbbdccdbcdbbdabcbcccaadadcacbabbcadbbbdcadcbadbadbdddabdadbabcbdabacbabddabdbcaccbbbddcdaabbaacbdccbcddbcbbbabaaccdabbbcbdcadbbacbcbbcdabcbacadbbbcdbcdbcaacaabbadacddccbccdaaadbbabadaacbdaaaccdcbacadaddbbadcbcadcbbcaadbabdabcddbcbdcadcdaddacbcbdcbbaacdccaccabbbcadcabbdcddcccbacabdbdabbabdaabadbcdbaccaacadbcabccabcdccadccbcbdabcbcaadabcbbdabddaadddacbdbababacbaddbdbcdbacddcbabaabbccbbbccaddcbdabdccdacbccdbbdaaabbbdbbaaaadbcdddbdaccabbbcddadddccbcccdcaacdddddcabadbbccadcdbcaccccccdcdabcadbbdccbdbdbdccdcbdccbdaccbbcacbacbddaaaacdbcabcaabdcdbcccbccdbacadadaddcdaaddaaabddadbaccbdccadaaacdabaaccbcacccbadaabaaaababacbaaabababdbcbbdbbbababacccaabdcbbacddcdcdcdaadaccbbbccccbcdcaacaaacabdacadacbcbdbabbddcdbbdaadbccacddabacaadcdbbcdbababdcbbbbbaddbdcbababddcaabdbabacacbddaddabacdbccacbbaaaaccabcbddcdabbaacdabdcbbadddadcbcbddccacbacacddabdcbaccccbbaccacdacbacbbcadbcbccbcbacbccddbbddabbcddcbcdabcddadbaaadbadaddaaadcdcdcadcdbdadcbabccabdabaabdabbbbabdadaacabccaddadacbccadcbcddbcdcbabbcdcaddcccaccdccadadabcabcbbbbdbcdbbcbbbddcaccaadcbccbcdaaabadaabcbbadcdaaadccdabbbaadbbbcdcabcbdcddadaddcdbdbacbbcadaabdcbaabcbdaaadabccdabaaadaddacbbbdcdacccadcbdcdabbbdcbcbacacccbaabccacccdababcbcbddbcbccaddddaddacadcdbbadcabdbdcdcbdadcccbcdccddabacdcddbbbabbadabbcddaaccaabcccdbdadbbcdadbacaabdadbdccadddadadbdaabddddddcdcbcbbbddcddddcdabdacdbdabbdacdcdaaccabbcacbcaadaacdadadbcdbdbbcabacdaacabcbcbcadacabaccdadadabdbcbadbaaacacddddadbdbbaddacadcacdbcaadbbdcabdaadcbabbaaccacbdbbbdacccbcabcaccdbdbbcabcbdbaaacadabbabbbbbcadccdbcacadbaadddbdacabbdcdcbccadcddcaaaacbaddcaaabbbdaadcabacbabacacdbaaabdcdccdcabdcdcbbcabdaadadccbcdbdababcacbbaabccddacdcdccbdadaccbdabbaccbaabdbcdbddcbcdbdcbaaaaacddddbcddaadadabadcadddacababccdcccccacadcdbbadcbaaacbdbcdbdbaadbbbabbacddcacaddbaadccabbbbdbcbabbdadadcbcdaccbaadcbcdadddbacbdcaaabbcdbbcabbbacdcabcbcdbbcbdbcbcdacacacbacacdaadaabdaacaddcdcbadbadacacdddbaabacbbbcdcdbddbccddbcabbbccbbdadddcbabcdbbcbccadcccddbcbbddbabaabccaacbcbbaabdcdbabbdbbacdacdbdaaabbaabcbdcacdccbdaddbbaababaadcbabddaabaadacdcadaddaaacdabdddcdadcacdccaadbddccabddbacbddbddacaddabbadadbcccdacdccaaaaccdbbadbdabcbcdaabcbacbdabadbddccbdbcacadabdababdbadabbabaccdcbbcccadccdabbdbdaadabccbbdcaccdbcdccabdcbaacdcbbcaabaabccbaabadddadcbcaadbccaacbacbdabcddcccaaaaccdbcadaddcadcaddbadbcabccbbabbcaccbbccccbbcdacdbdcabbbabcaddccbaaccaabbdbacbabdacdddcbccbddcaddbaacbcdcacbabdaaacdcadbbccdbdcabaccbddcaccbcbabadaaccadbcabbabdbdbcabbcbdcbdbdbdbdcccacccabadabddccacacbcdcababbcccbaabbbdaaccdbcabcbbdddaabacaddcaccbaddcbabcdaccdbcbcbadcbdbaabddcddbcaaacbcbdaacddabdbdbbdbdcdbddbdbdcbcacddbacabaaccbaaaabacbbccbaccabdabcacbabacdbacddbdcaaccbaddbbdbbbabddacbacbdbabcabcaacbadcadbccccaacbcdaabcdbccbcabdcccdddbccdaccaacabaaddaababcdcccbbdcccdaddddadaaabbddddaaabcddaaadcbbcacaacaaaaabddacadacdbccbbcaccbdcdbcabcaddcbcddcbababbabbacabddbaacacbcacdcacdbbbcdddbcccddbdaddccdccddcbadacbddacaabbddbaadcabddacdaddaccdbcadacaaadddcacccdcdcbacacdaaacbaddcbabbacabccaccabbbbcdcacbdbaddadcbddcbcccddcdcdaadcaababdbbcbbcdcacdcdcabdacbbaaccccdbaccddbccbaacdbacabcccdacdcccaccbabbbdaddbaccccddbdaaddbabbbddbcbbbdacabadbaabcbbaaabbabddacddccdddacbbdbbaaccbbbccaabdaaaaadaabcdcaddbbdabdccbbacbaaccbdbbbbbbdbbaddadbdadbdcdcbddbdddcccadbdadabacbccacddaddccdbabdcbbcdcbbadcaacaabdbdddccacbcacdcdcbcbbdabdbbacdbacbaddaccdabdcacdccbaaabcccacabaaaddddbbacaacabaccbacccdddbdddbdcbdcacccbbbacabccdcccbbcbccbbdcdbbcaabcbabccbaabacccbbcccdbbacdbbcdadbdadbdccdbabbacacaddadcbbcdbcbcdcaaddddbabdcbcaaadabcbadcdcbbdcbcbdaccccbdbaccbacbbbdbabcbbbcbdaabadcdcaadcbabccbdbbbccbcaccccbdaaddbabdadddbcbacdacacabbabbacddcdccddaadabbcccccddadbcadabaacdbcddaccdabdadaaddacdaadacabbaabbccbcbcdbabbbdacccaabdabbcccccdcacaadcbbcabcdbdcdcaaacbaadacbdbccbdbbccdaddccccdaaacccccbacadabbdaccdacdcdcadaaadcbcccbaddaaddabadbdacddabdbaabcbbdccaaabddcbbdcccaacbaddadbadbbdabbcaadccccdcbcabbbbbbadccddbddadddaabadcabcdaccacaabacabdadabbdcbbaaddcdbbbbabdaacacbadbaadbbddccbcbbbacaacababcbacdbbddbccccbbcdacdbcabbdaaaabccddadcbaaacdadcabaddabddbbddaadbdbbdabccabacbbcbbbbaabbacdcacacddacbbdddcdaabcdcacdcbacacdaadddcddaababccbcbbbcadbcbbdacaccbccbadabaacbbbddabcbbcaaadcaccdcdbdacaddcdacabbadaaccabadbcbcbbdbbdbacaababbddcbbdbbaabcacddadadcdbbdaabacbabdaadcabbaabcaabbcaaaaaaccaabcbbdaaaaccabdbddbbccaabacdddcadabbabdbaaaaacdcadbbbbbddbbccbcdcdbbcaabacbacdcddcdcccbadbabcccbcaacdacdaaaccbbcdaabadcaabdcdccdaaadcdbbacbbcdbcbcdbddcccaadbdaccbdacdabdbbdbdcbdadbbddbadabdcaaccdbabdcbcabdddaddadcbcddcaddbbabcaccadadaaddbadbcdccdddccadcccdcdbcdbaccccbcaaddadccdcdabbaaacaddadbabbaddbcdacaddacbdbacdaccaabdaacbbaccdbcdabcabbbbbdcabddbbaabaabbacbddcabddadaddbbbacacacccbbacdaaaddcaacacabdbcddaacabbcabacdbadacdccabadcdabdcbbcbabdaabaacaaababcbbddbbdaaaddbcbbaddadcadccccbcdcdabacabcabddbcbcaddbbbbcadcacbcdbaacacddcbdcccadbbdddddaacdabaaadbdcdaabdabbbaddcccdabcdbddaadbabddddcbbdbbcdbbaaaadcbdababbccdaccadaabdcccaaaabdbcdbbcdabdbbbcadbbdbcadbdbcdacdbadaadaccabbcdccacbaacabbbbaccbdbcbbaabdabccbddcdacdbacaaccbdddabddbcbbdadcbddacbcaccbcababbddbcddcccbdabbcdcaacadcbbbdcacdbccadcbdbadcabcbaaccaababaaadbdccbcbdaacabbdcbcbacdabaaccdacbbdbbcaaacbddcbcaaabbbacdbddababccdadbbcabaacddbbabcabdbacdcadacaccabbdadabddacabaabdcdddbdbbdadccdbccddbadbaabcbadbbaccacdbdcdddcaaacdbaacabcbbdabadcbabccadaddbabccbacacacacbdcccbbadbddaaacdbbadbaaccdabdbabbddbaaddcbdcdabcadcacacbcddcbaadbcbdbdcdddabaddbaaacbabccbbdbccaabcdcbdaacbadbdccdaacabaddcdcccdcccdcdccaddabcababdcadccbacdcdbcccaaddadcbbaadccacbbbbcdcccbccbabdabadbabaabcbbdddcbbaddcadacbbdbbdbacddcbbaddbdcdaccbaabcbbbbbdbdbbbaacdbbdddadcaaccddbacdaaababcaddacddbcabddddacadadacabddaacacadbaccbdaacbacbdbcbdbacaacbcadcbdbbbcdbcacabbcacaababbccdbacdababadcdcaddbaaaccbacbaaadadddcdcadbbbdabababdacbdadbaababdbbadccddbabdabcddcacdddaaacbbadabdbbcabbdaadcdbbcbdadbbbcabdaabdabaaaabadbcbaabbaadccbabbdcdccddaadbbbdbabdbcbbdadbbbadcdbadcdccbbccaaadacbbcdbbbabcdcacdcccbcdbdadcbaadddbddcbaaddcddccabcbddaadaddcdabbaabbcbcbbbbbbccddbccacccbacdcdcdcddddbbcbbcbdddaadccddacbbbcadbdcbccbcadabababddddbcdaadbbbaacbbbdbcccbababccaccbdbdddddacddabcacbcaccacccadddaacbdabbdbacdacacbcdbdbadbacddaaaccacdcadadcaaabaaabbbdaabaaadacbbdadcacbdbbacaabbddddadcdbdcbabbccccbcacaddcabbccaadacaddddcdbccabaaaaaabdbbcdcdbbbdcddadcadbaccccadddccabddcbbdbbabdbabdcccabbaccddcccccdacdcdaadbddcbcaabdabdadababdaccccdcadcdddadaaddcacbbcaccdbaddbcccadaaabcccbacaaddbadacdcacbcabadcbacbadcbdccbccdbbcbcbdaacdddbcbdaadbdbcbbbcbcabdbabdcbccdcdddaccacdbddadbbdcadbbdbbdacaadcdcbacbdaddddbbacbacbdcdcdddaccbcabbbdcaaabdacbcbdbdcabbbbccadacacacddabbcbccaabbacdddcababdadddcbcaaadbbabdacdbddabdbbadcbdbbbdcbdbaabbcddcdbdacdabbcbbaaccddcbddbcdaaaadcdcddacdbccdbcdaccabcdcbdbabbabacbaabbccbbddcdcbabcaabbbbcccbabcdbbbcccbcaddcbbadaabadaabbccabcaabdbbcbdcdabcbdbbcdccadadbddacacddddbccbabddaabcacdbbddabbdcaadbaddbcabaddddbbccadbaccbcdbbccabdcacbdababdcabaccddcbbbcbaabbbabdcccabbccdcbacadaaccbcbacbadcbccbcaabdddcdddbcccbbaaddbbdaccbbdcccdabbabccdbabbacbddbabadbabbddbbdcabdbacbbbadccacaadaadcadaadddccddddbabaccacbcbbbdaadabbdbaacabcbdcddbbadbacbccccddddadbdadcdbdaadbccacaabaadadcdbacccbbadacdbbabbbacdaabbbddbaabbccbbadbadbabddbcaccccddccbdcaacdcbadcbdabbcdcddcbcbbbddadacbbcaccbdaddccabccabddbdcabcaccccbcaaadbdadbbddcdacbdacbccccbbccbdadcdadcaccdabadddcccbbcbbbdcdcaadcdbdaccdccacccabdcdccdbcbbccaccbbdbcbbcddbdbbdbaccacdaacdccccddccdcacabcadcdaccbddabbacbdccbcbdbadbbddacdabbbbadacbcbbcdbacabccddcbcaabbdcdaabdabdccaaccbbddcbacbbdbabaabbacbcbbababcdcdacbcdcbcacaacdcdbccccbddcadcdbbaacbbdbcaddbbccaacacabccccbaabadbabbdabbbcbccadcbcdaabdbcddcdbcddcbaadddacddcbbacaaacddacdbbcbabcbdcbbdddbccdcaaadddccbcaabaaabddccdabcbdcccdbabdcdbaaabcccbdbdbaadadbcdccbccaacdbbddacbbaddaddacbdcaacdabbbdcabadadbaacaccdcababcadbdadcbddddacadaadacdbabaccabaaaacbaaadbbabbabcdbdaabaccdcacaaadbcaccaacbdbadccbbbbcabcabdabcdbcaabaddaadabadadbcadaacdbdaadabdbdbabcabacdaabaabcbdadccbdcbbcdadadacdbbaddacaaaacbbbcccadaadaabbcadbbdcdcccabaaabdaddbacaaccababbdbcddbcccabbdaabadddccbddbcaccbdddbaddcaccdcccbddbccdbdcdbbccdabbcbcadabccbcbbdcccbdcbcbdcdacdbbcadcaabbabdccdcbaccbdbdabaaabbdaaddbdabccdbdacbddaccbbcbcdbdaabcccccadbabcdddbbdadbdacacbacddcacdabdabadcabcdbdbabbcadcdacbaaaacaaaaabccadcdabbbbdbdadaadbcbcccddcddcbdbbadacbbdddcccbcbbbbccadbacabdbdbccdcdbcbbcaabbdbacacddccdabccbabbdaddadaddbababdbbddbddacbcbdbabcbdbcbddabacbcaccdadadacdbaaaaabdadbacadbddbbbddbcdcabbadadccdacacbdaacccdddddcdbabaabcccbcdbbbadaaaacacbadadadcbabacbbbbbdbcdcdbbdcaccddadccccccdacdbddcbcddcaddadaaabddaadbaaabcbcdcbcdaadcaaacaadcaaadaccdbbbadbddbcdbddaacbbcbbbcccaccaaaabddcacdbddaaacdabbbbaaccdabbaddcddadacdbcdcddddabdcdbdcabddbbbcdbbaddbddacbcadcbbbcabddaddccdbcadadbdcaabaddddbcbcabcadaddaddabcadbdaaccccccadcabcaccabadcbabcbccaabccdbacacddaccaaddbcadaccbacaabbdccdacccbabddabbdacbbcaacbddddbccbadabbcaacccbdbcbbdcaabdaaacdaabdcbadaacbdacbababbaddabdaaaadbdacbdcbbcdabdabdcdbabccbdddbbdccaddbdcddabbaccadbddadcdcbdaccbdbcbdbdcdcacbaaaddccdddbdabaadbdbbcabdbabbddaaadaabaabbdbddaaaadacadbbdacccddbacbddcbbaccabddadcdcaabcbcabadcadcdabdccaaaaaabadcadbddcdddbbdcbcacabbacbaaddcdcaaacccdccdcdbccbcbbdcddbabaacaadaabdbaccccaccbaaddaaacaabacdbadacdcaabddadacdcddcdcbabaadbbdbcabbbddbaccabaddbbbddcdadddbabbdbcdcbcdcadacaacadcccaacacccbcaccddcaaabbdbaadbadababdbbacbaaccbacbddacaccaacbaccaddabdddcdbabdcacbbcbbadbbaccddcaacdccbcacadcabdcdaacbbbaadaabcddadbabccbbbcbacbacdadbcddbacbbaabaadacccbbbcbcddbbcbdccaadacadacdbacbdadcddcbcddbbacbccdbdcccdccacadadbcdaddcaccdbadaddcbbbdcabcdcaaccdadadccbdcbcabccccdcdcadabbacadddabbbcddabcdbaadccbabaddcbdacacbcbdabcccdbcdbcaccbdcbbabccacbdcdaadcdcccbcdaaabadcccacacacadbdcbbbbdbbdbbbcaadbaddabcaaadddbcdcaadbcbdaaaccddbcbcdbabaababddcccdcccadbacacdcbdababdcabaacabdbccccacdacbacdbcdcddbccacbaadbbcacdcdddbaabcbcbcdbadcabdaacbbabbcdbbacdcbddddcacadbaddacaaadcbddbcabbcbbbdbbcdacaadccabcdadbbdcdcbababbbcccbcbcadbdcdcccaddadbaddabaaacadacdababbdcddbccadadcccccbadddbccccbadacadccacacdcccbcaaddbcbccaaaacdacbaccabdcaacdcbabcbbcbadbabaadccbbcccdcbcddccddbaaacbbacdbcdbacdabdccbaadddaabaddaadbbdcabbbcadacdadcdacbcdbbcabdcdabcaccaaadcdddbbdadaaabbabdbcbcadabbdccabcdbbcdcacddddacbaacaadbcbbddbdcbccbcdcdbabccddcddcadbabbbdaaddccdccdcccadcacbdcdddbbcbbdbacbbadccbddbdbcaabdcbbacdabcacaccbbbcabbdccdcdaaddaaddadadadcacbbddbadccabddabaabddccccababcbdbccacdabcbadbabcabadbbbcdcbaaccdbcbacdbbdbbaaabbadcbbacccbaabcdbdddcdcbbadcbabbbdacabaddcaaacbdcadddacbacaadbbaccccdcccdbdbbcddcadcddabccccdcabbccadbdaccbbdcabbddbbcbbadadbccbaaacacabdaabddaadaadabaddaaccaabcdcacbddcbcddcaadbcddbadcdadbccdcaccaaaddccbababdcbaacbdcaddabaaaabbcaadccdbacccbadaccbbaabacaccabacdddbbcbcbdccbbbbaacccdbdddbddddaadddbbddacaadbbbaaddbccddacbcbdaaaaccabbdcccabadcdadbcbcbcadaccbdbdccdbdcbbddcdcdadbabcbcaabaccdbbccbdddacbaadccdcbabcbbacadbabbbbbabaddacddbbccddcbcdbcccdccdabcaadccacdadbadadbbcddababadbcababdddadbdcdcccddbcdcccabacbbacbadabaccdabcaccbbcbaaadadcbdccabccddacdcdbbbbabaabbbbaaacccbcacaccdcdcbccaaabbdabacbbbaabcdaddbbddaacbdcdbadbcadccbacbbdabbcaaabbccbbcdbbdaadaccbbcabdcdacdbddbbaadbaacabccdbabcadcdcdcacdcccdbbaabcaddabaadbdccbbbdabdbcacddccdcbdacbbabcddbbdcbaccbbcabddcdbaaadabddcbdcdaacaddadcaaabaadcddacbadbbcabbcdcbbcccadcbcbccbcddcabcbcbbdadaddbbbabdbbccbbaaacbccbdabbadcccccdbaadadcdbadcddadbcbdcdccccacbdadbaddcbdaadacbbcbdddbcbccaaddbaabbdbdccbbcdcdcddabaddbbdcdbbcbbdcbddacdbcdcbcccaabaaaaaddadcbbaabbaacdbdaaabdabbabbbcbbccacdbdbddcaaddabbabbddcadbababbbcdddcbddddbbddcadadcdadddbacdaabddbbdaddaabababcadbcbbddbabdbadddbbdadacbabbabcddcbabaabdacadcabdbabbcacaadabaacbddbabacadccccbacbdbcbacadbdbabbabacacbcbdbdcacbdcbbbcdbacbcabbaadcdaadbbacddbcdbdbacdabacbddabbbbdaccbabddbadccdcbdaadccddddaddcdadabaabdcaadcacbcdddcdbcbddbcadcccddbdbdbdabcdccddbdcdbbbcbadbcadddccbabcdddcadbcbdbbddabdbdddacbbcaadcccadbbcddbabdbbcbacbcbbccaacabaabbbacadddbabcdbcbaccbdcbcbbccaddbccabadddbddacbbbbabaccdaacbddcabcdacddbcdddccbbcadcbbadacccbcddbaabccbacdbcbadcbbabccdbcadcbbbccaaacdcbaacdcdcacbcbacdcdacacdbbacbaccbccadddcbcaaadabdcbdccabbcbadacadbdbbbbabccbaabbadadbaaccabaccaccabcbbbcbdabbccadcabaabacbcbacabbdcadaccbbbbbadccbbdabaaaddcbbcbbcbbdabbaddbaabdadbbcbccccdcaadcdadaabaabbaacdacbdcdbddaaacccdcdabdaaabdbacddcbcbdabadcdacccdddddbcccdbdabadbacbbdbcbccaaacabddadcbdccabadabaddbcbadacccacaaaabddbcdddbdaabdcdacdacdcdabaccbdcabdbdcbbabbdaaaccdaaabdabbdcbcacccbcdcdbdbddaaccbbdacacbcacdaabbaabccdbccbbacddddcbcbadbdbbbadbdcbbbdaabcbbcccadacdbacddcaccdaadbdcbbbabbacbddbbccbbbccdaacccabddbbcddababdabdacbccacccbcddddbdaddadcdcabcacaddccddbaabbcdcbaddabbacccbacdccdcaabdbbccdabcdbdbdccadcdadbcdddbdcdccabcadccdcdaadabababbdbdcaaaadbbaaabaacbcddadddcccadccbdcdadabaddbbbdaadcadcbabcdcdbcdbbdbabaacddbbaaabccadcbaddcdbcdbbbbacccdcaccbacbcdbbaddcccdadbcbcaddacccbcddbaabbdbdcbaaacdbbbcbdbacaadadcabccacbaddccaadcdcbabbbdcccccbcbacbbbbbbabcdbacdabaccbacdcabcbaaaaadcaccbabbdbcaacccaabdcbbdcaaabcbbbcbdbdbbdbdcdbdcadcddbdaacabcbbacddbddbbaaacbcbcdccbdbadadcbbcbcdbbcabbddbbabadbaadcacccbbbbbcdbbdcacaaacbddacaccdcaabcdddabbcbbabddabdabadcbcdcbcddbbcbbacaabcbddacabacdacccdabbacbbcabdacaaabaacbbccadbaacadbaddbbabdbadcdacccababdadbdbabccbcadacaccddbbcdbdddbdadbcdcacdcaadcabdcaacbcbcddcbbababcbbdcacdbaccdbdcbcaacccbacccabdcbccbadbdcccadcbdddcaabdbccacaabddaaddacccbbcbaaacdccbcddcbcbaccaddcbbcabdcccaacadcacaddabccdaaaccbddcdabbdddadabcddacbcacacadbdaacdadaaabbccacdacadaccbbdadaaaddcdbdcbcacbbcbbcdcaddbccbbdaadddbaaabcbcaadaadbabdddbbbcdbacbcabdbdcbdaaadabcbdcddaaccdaccbabababadcddbaaadaabaabdbcdccdbbbdaaababcdacbcdabbbbcadbbaddbaddddcaabacbdbdbcbdaaabcbadddcddbdbababbccbddaabdadaacaaddacccadccbabddbbdbbbaacbcaaadcaaacddcbabcbccdabdadaaaacaaaadbbbcdddababcdaacdaaddcbbccabbdaddbdcaadbabbcaaababdbdcadbacaacbaabaccaddddaddabddaadbbabcdaabccbbdaacbcdccdbcbadddbdbadbddacbbadbccaadaaaccccaccacbabddcbcbcddcdddccccaddacdbbddbbcbdddbdbbadcbadacbbdcccadcdbabadcbbdcbbccdbdbacdcbcadbbcbadaddcbbdaadbdbabdacbccaadbbdabcdbaddabbcdbdbdbcdaabaadcaddbbdbcbdabbdbbccadbdbabcbadbcdaabbabcbdadbbacdbdabaaaaccbbccccaaaadacbddccbdaadddaaaaccacdcbdbdacbdabaddcdcaacacbdaabdbcbaabcaadbccbabaccaaaaabbaabaadcdbadcccadcbcbbcacadcbabbacacdddbaacadcddaacadcddaabbbbcdbbadaaabbddabddadbcbbabcddddbbadbcacbabaabdaadabdccdbaacaacdaadcbdbacbaaccccbcaaccabdbcabdacddddaddbddcdabaabcbbbabdaccaacbddccdbaddaabcbacabaaddcaaaccbcacabcabcdabbdcbbaacddaabbdbbddbcccadcdaddccccbbaabadaacbccdabcdadcbbdbccbdabbbbcbaddcdaaabdadbdcddacbababbbdcbdddbccccdbbadabcdaaccabdcaabdadbddabbbddadacbaaacddcbbcdddcdaabadcdbddadabbaadcacabbccaccadbddcbbcbbbcbbacdcaacbbdcdcaadbaddbdccdadbbbbcccccddcaaadbadaccbaaaaaabcabdaaddcabdbbccbdcadacadabddbadcdbcaaaaadacdccdaaadaaaaabcaccacabccbcbcaacbbcaaccdbacccbaacdcddcacbcbacdccdabdccbacadcaabccbbbabdcbdddabdccbaacdacbaabcaddddcdacbcdcacabcbbabcbccdccccdacddcdabaaadabbaddcbabaddababcdcdaacadbabddbdabdbcdcabbbdcacaddbacdbbccabbbbcaaacbacabbabdadbbbcbdddccaabbdddbbdbabbcdaaaababacdadcacbbaccaaacdbcbadbacbbaadabaaaddddddbdbcccabdcccbcbcacbbcabbdbbcdcaccdaaaadabdcdcbccbabcdabaacbdbcaadbaadbddbdbabacbdddbbdaccbccbadabbdabbabddcbdcbabbccbddccddbddacadbdaddaddbcadbdcbbbacacdcbcdcbdcdcbdaaadacdbbadabcdacdbddddddbddadcaabbcdaddcdabdcbbccccdcdcbabbcdbabbccabdbdbcdcbbaacdaacaacadcdccdadbcadcddcddbaddacdaadaaabdddbddadadcaaccbddbccccdbcdddabcbabbbbddbcaccaddbcdcddadcbbabbcabbaccdcaabdbbababadddadbdadbcdaacbcadabdaabaaddccddbdabddbbcacdbcaabccbacdbccaddcdbdadbdaadbabddbabbbaccccbcddbabdcbabdcdbcccbbbabdcabbcaaaaaccadbccabdaadaaadbdaaccaaacaacddaacbdbaacccbccabaadaacbcdabdaacaacdaaadadbdadbdddadadbcbabcdbabaaddcbcabadbaaddccbcdacbbbbdccbbbdaacadddbaddbbadccbdddaacbacbdacbdcbcccababccaaadcccaacddadaaadcabdbdaaddcbdcddcdbdcbcccbbcbadbbbcbbbaabddbbbbaaadaccacbaaaddccdbddadddbcdcccbadccdcbcaaaddacdcacbbdddbbbddaddacbbddddbdcadcbabbabcbbdbdadaadcdadcacbdabcabbbdbadbcabbcbbddaaccacabdcddddbdaccddadbadaabacabadacbaadcacbddadbadbdccbaacaaaadbbddcbdaacdbdbdadcdaabcbacdababddbddbabaaddbbabdbcbcbcbcbbbaacdabbbadbdcabcccbabddbbdababccccddacadbabbbbadbbdcdaaaddbbaacbaccbdbcdcdccdbcbccbbcabdbcabcdcccbaccbbbacbcdccbbacdcbbccdcbbbccdababadacaaccacbbbdacccdcccdbcbdbcababdaabcbccbaaccbdbbacadbdcdcddcaddccddbaaccadbbcccbcdcabbaccccbdaabccbbaadcccabbbdadcdbbadcddbbbabccabbbbcbcdaccccbaaddbddabadbccbcbbbbacbacdcdcbaadcbccdabccabcbcaaababcccabacbcdcdcdddbcddccbdbcbadddadcddcaaccadcbaaddcbacadcadbabadaccabbbacbcbcccdcabdcccadbddcbbcbaaadcddacbcaadcadcccbaacdcbdabdaaddcdbbdaaaddbcadccccdaddbdaacabbdadcbcbcabccdcdcbbadddcababdccdcbdadcaabadbcbccddbbcbacbcdbdaccdbbaaabcabacccbbcdbbcdbaddddbadcddcabcddcbdcbdbdadddacbddbbbdddbdbccdbddbcddcaccbccddaabccbbabcbabdccabdddabadadbadbcadcdcbbdbbaabcbdccaccdcbccdabdbdaabccbdbaadbabbccbaaacaabbaccabbdddabccaaadccdbcccbdbccabcbacbbaccbdbcdadcddbdbdcadaaccdccbdddadacaddaaaadcbbabdaacdccccbcbbaccaaccadaadadbaadcaadacacabccdbcdbbbabccbcccdaacddadaabdcbdabcbcccadbcabcaabbdadadabcdaddbbbdcbdbbbdcbdddccacadabbcabcdadddacaabbbddababdcbacbadababaddbbbcccdbdbdacabdbaadbbdbcdbaacccccdcbadddadcacbacbcdbddbdddbdaccdbbdcbadcaabbcbaaddcdcaccacccaccbabacacbcbcddcbcdccccbdacadabccaacdcadddcaabdbcdaccbadcdaabdbaadcbddcaaccdaabdabcacdabcccadaacbacaaadcaddbbadcbbcbacdcdddcbddabbbcbabadcaacaabbbaaddabadcbccadbdccbcdbcbbdddddcbcaaaccabbababdaccccccacbaddbdbdbccbcacbbbccccaadccbbcaddaccbacadcdcabcdcaaddbdbcbbdaccaccddaddbadabcaabbbdcaacdcaccabadccabcbbbbcccdabacacaccaabbdacdacdbddddaaadaabdacbdbdbacabcbcccadadbbcbbbdbdcdcbdcadbcaacbbabcdbaabcabcddbcadaadddcdaddcaccaabbdccddbcbdddaacddcdbabddadbbcacabbdbdbccabaacacabcbdcbbbdbbbacdbbdcacbbccacbadaddaaadbdbbaacdbadbadadabbabdaccaaaacdcdadcbcdcdbcaacabaadcdaccccbdadbddcbcaddadccabddccabdcccadaaadcbacddccacbdabbbcabaaacbadbdccacabbdbdcbdacdccdccbabacbcacccccbacdbddccadddabdbcacddbbaddcbddaadcbcbaccbdbdcaacccbacaccaccdddaadbbabcacddbababadcbcbcdcdbddddabddaacbdbacbadcacabccbcbcaccababdcdbbcabbdbaaacddcdcbddbccbabdbdacdbbcbabcbdaaaaacbacbbcaacaddacccbccbacdbbcabadacddabddabccabbddacbcdadbaaabadcdbcdccbbddddbbdccbcbdcddacdbcdbdabbbddadddbaabaaacadabdacdcbcbdadbddabcadabcaadbacbdbabcddadcdbdbbdddaadaabcadadcbcacaabcddabcbcddaddabdcadcacbccbaddcacdcaccadcabccddcbbdcacaadbbbcdaadcdaabcaabdbcdccbaaccbbaacdbdcccdcadbdcaccabacadacddbcddabcbdbdbddabddcaccabaabbbdccabbadccbdcbdaaaaccabcbaabacbdabddabaaacadaacdacdbbabdcadcdabdbbaabbcdccbabcbcaacdbbacbcaabbcccbbdadddbddcddcbdcadccbaaabaddccabbaaadbaaacadbbdccbaaccaccdddbaccacdcccabcdcbcaddabdbcdacabbdcadcddbaaddabddcacacaababbcaabadbbdbacdddadbbdbbdaaddbbdbcccababcacaddacddabadbbabbcbddddcdbdaabbabcaadbcbccabbddadabcddaabadbdbacadabdccbcbcacbbbbbddbccbcaaadacccbdaadbcdcbaaacaadacdcbcddadbbcadccadbddacbacbabcbcbdcadbcbdcabbcdaaddcbabbcbbdacdacdbcbcccbccdcbacbcaaadadccdcdaaabbabdcbdbddddccdbcacadbadaccabbadaacbaccdbcacababcdcbbcbccdcbbddababaccddcdbbdcbaddbcbdcacddcbdcdcccbcdaacbadaadabccdbbcaadababdbcabacbabbbdbdcacccbaadbdccaacdbdaadacacdaaaaccabddababaabcabdddcaddabadadadadbcbaaccabdadaccdcbccddccdaabbcabdbbbbcdbbcccdbbbbccdccbbabdbdcbbadbadcacbcbbddabbddbaccbddadbbadcdabbcdaacacbccbcbcdcddddcdcdaacdcbbacccdbccdbdcbdcbdcbdccdccdbccadcbbdabbccbccdaccddcacdaccddacadcdbacdaabdbbbdcacaabbcbccdbbcddabdcadbdcadacdabdacaaadbdbadccddcccadbdbdccdacaabbdacdaddbdccadaabacadacdbbcdddcbcadadabccdadbbdcabdcdcddddbabaaccdddbacddddddaccabdbdadcbddbdadccbcddbacacbcbbcaadbbabcabcabcddbdcbcacadcdacaaccdcbbddaadcdccacdbddbaacabacdbbcdbbdcdcabdadbcbaddcdcddddbddccdcccccdabbbdbbadadacccdabbcadcbcadcddbcabddcdabddbddbccddabccbacabbabcaccbbadcbbbbaaacddddbbaaccddddbcbcdccabdbddadcbaaaabcccabadccadbadabbaaacabacaabdbddabcaababdcabacbbcaadcdcbacddbabbbcdcbbabdcbbabbaabbbacabbacbbcbbacbbdabdbadcbdbcdddadbdcdaadcababccccaababdccccaabbdaabadccdadcdcccdbdacbbbbddbcbccaacabccaaaababccadcddbdcbdbccbdbbabaadcbdcabacbddbaddcbbacaabbbddbcdaddccbcdccbcacdbabacbbddbaabaaddcacdabbbabbdadacaccbddadabdaccbacbadacbdbbcacddbdddaabadccacaababaddadbbdbdacdccbaadcdcadabadcccdcabddbbabcdccbddacadcadcabacbdbbdaddbccbaaabcabadbaccbadababaddcccdaabbdadbcbbccdddccbdbccabdbacbccdcbccbdbddbdbcbbdbcccbdacdbcbcbdbabcbbcaaddbbacaccadadaddcbddbaadadcbabadabbcdddbdbdddcbddcaccdcdaaccbcddbaddccdbabbdaddcbdbdcbbabcaddadddaddbbadccdaabbbdccacdcdaddcacacbbadbccacadbaaddcdbabdabaddbddacbddbcbcacabaddabbcbacacdbbadbcaaabadbbdccbabacaacbddbabcdbbdaaacaddcaadacacacbccccddacdbabbbaaaaaadbaaadddacbdbadcabcbacbbcacbadbccddacddddaababbcbabbbadbcacaccdcbbbdbddacdcacbdbcaacbbaccdcbddcabaaaddccaadabcdcaacbacacdacccaddcaccdadddacaadacacccaaddaadbbdaabcdbcbdbaadccbdcbabbcdadabbccdbdcdcadadacaaccbaabdccaccbcdbacdaaacbdacadabacccacbaaadacaabbddcaabbabacaaadcabbbccdddbcccbccdbdbbbdaccabcdddbbcaccdbdbcdaabaacdababcaaccbdabadddabaaadadddaadacbcdaaabdbbdabdcbcdcadcdddaadabcccbacdadddcacdbdcbcaabcaadbcbddadddcadcdabbaddbdadcabacdaacaddabbaabdbcbbdaddbdbccdcdcbbdadbbddccabdbddaadddcbbbccbcdadcdccccccddacbbaccbdacbdddbcccdcaabaadbbacababbbddddddcdadaabdccdadadabaaddcdabcaacbaabcdbddbbdacbbacbddcdacbcbdacbcaaaabbaddccbbabdcaabbbbbdcddbaaabdaaacdaacbbbbbddadadaaaabbcccdaccabababdbabcaacdacbdbaaddabbaabdcbdbbabddcabccbadcabccbdcdbdbcccabacacdadddddddddcdddbaaabbbbcaddcabdccccbabbdccdbdabbbdacdadbadabcaaaaccbbaadacdadbdaddcbdcabbbcaadbabdbaacccaaabbdbbddacbbbabbaadacccadcdbaacdbaddbaabdbbaacabaabdbbdcddbddbcbddbadcdddbcddbcabbccccbbccbaacbbabbdddbaaaadadddadbbddbcacdbdaadbbacacaacadcdacbbcddaabddbdddbcbadbbcbccdbbbbabcbbbaabccdbdbcaacdaaccdcbcdddbbccbbbcaaddaaadcaadabbcbbbadcaacdcccddacbcdbdadcadabbdcbdcdbccaccabbdcbbcbccaadcaabdcaacadccbacddabbcabcdbddadccadbccabdabadbccccbabaabcbdacadabcaadbacadbbaaaccaddacccdccbcaddbacdcabcacbbcdbabcabcadcabbaaacdaadacabdbbddbdcccbbdbdabbacccccabaaaccdbbccdabcdbccdbbacadccaaacbbddddccbcddcbdabcdbcdccadacadadabbdbdadaaaadacbabcaddbdccabaaddbddabbaccbdaabacbcbacacbddbddaccacbacbcdcaaababccddbddacdaddaddbabbbabacddadbbdcdabdbaacbcbddcacbbdcacabcdbaadbcdbbcacbdbddccadaccdbaabcdaaadcccbbabddadbcbcaacdbccbadbbcbaccbcaddadccadcaccdbbcbbdbdddddbdaccdcadcdacbbdbddabcbdabacdacaddcbcdbdaaaccbbacdacbbdddbaadcdbdccbdaccbacdcbcdaadbdbdccdacbcbbcdabaccbabdbaaadcbbdcaabdddaccbaadbacdbadacbacccbaccacbcddcdabddbcadddcccdccbdacaaacccabcabaacbddacdcbcbcdaaabcbccaadaabdcacbacbcccbbbbbaacdbaaaabddbbdbadddabdacbdbcdcccabbaaaacabbbcccdadbaccdbcddaadbbdbaddbdcbdbdcaccbbccabdccddcbccdbabbacadaaabbdccdbbbadaaadddcacdaabddcaddcadcdaaabacdbabccccabdddacbcacbccabadaadcbcbcbacccbdbbcadcabacbbabbaccaccbcdabbdadbbcaaaddadcabadbcdaccadbabbbcdcbbadcaadcaadbbbaaccbbcbdcddaacddcbaddcddacbaddbbaacddcdcbbadacdcdacccaddcbdacbbbaadbabaacadbadddbcabcccbdcdbaadbacccabbbccdababbabbcdbacdcdadccadadbaadadcccdbdcaddadabbdbddabcbdaddadcdacdcddaddbbacaddddbddccadaadbdadbacbaadaccbcbcddccbaaacdababaacbdddadabddcbbabbaaddaddacaaabccabbbdbcaddbbdddbbbcbccccccbbabcbcdadcccacccbbddbdcbddbabaccbccbdcbadcdacdbacdabbcabcdaadcdbdcbcbaacbadadbacadbdadbcaadcccbbabacdbcbcdbbbbbbdccdadbbacacabcaaccadabccddbadbcdacaaccacdcaddbbdcaddbbddcdbacaddddddbdbbddbdccbbbdccccccabbccaaddccdcbbdccbbaabaacaadbbdccaccaadbcababdcbcaaaacdaccbccacdbccacacdcbabdcabbccaaacbbdcccccdbccccdbaddccadbccabaabdddcabaabadbcddbddbddbcacbcbbbccbaddacddcdaabcbccdbaaaaddddbabbbdbabaabcddbbddaaabcbcbdcabacabbccabcabdaabcdbdaddbbdbacdcdcdcaaabccdcccabddbaacbadbaadbddcbbccbdddbcbcaddabbbdbaadbcbaadbacbccacbcccbcbccccaabdadcaabcccdccaadadacdccdbbbdbbdcccabddabbaaccbabbcbaacddbaacddcbcbddbaabcdbcccbdccaacdcccdabdbddccbadccbcbcccacdabddabdcbdadcadcacdcbbcdccbdadcbdddbbccbcbdccaadbbccccbaabaacaabaabdbcacdbdddcccaccccdbcbabaaccbadbbacddcbdabccbaabbccccbbaaadbcdccddcbcbcacbddacadaddacbbddcbdcbaacdaadcccddddccccbddcdacbbbbdbddbdbdbccbbadaccbdcbddadcadbcccccbddaadabccbcabbcbdbdcaddadabcaacaacaddcddbdbdccbdccddaaaaadcbadacdbaccdccaddacabdabcdaccdccadbcadcbcdaabcbcbbddbbabddbcdcacbabdcccdbbadbaddabababadaabccabcbadabaaabcdcdbbadaddacbaabaabccbccddbabbabdabcdcbbbbadacddcbdaabdccdabbdbccbdadadccddbddccacdbdcabddcaaababcadacdcdaccbacdcbcaaabdacbddbcaccaddabbdaaabcabcadbbddddbddaaacacccbcaacbcdbbdbdccddbddacaadccaaccdbbcadabbccadddccccddbadacabcabcdbdcccdddbddaabcccbcdcccccacbbbacbabbbaaacbaacdbbabbcbabcdbddbbdaadaaddbbcbcbadcaddcdcdbbabbcacdcdbddccabbbaacaaabbadcbdcdcdaadcaabdbdbaadcaabbcaabdbdbaaadccddbcbddbabcdabaacaabadbcdacbdbcbacbbdbbcddabbcccabbdcddcdcacacbdabdcdaddddcbaaadddccbdaddbcbddadcdddabcaabbdcabcacbbbccaddcdaabcaccbdddbcbacdcacdadcdacccbaaacbcbcdcadbdabcccdbabdabdbcbcbadcddbacbccbcbbcdbabbdcccddcbddabdcdacabcacbccbccaaddabcdababcbdaacddacdbdddccccbcabbcaaddcbbcabbaccdcaddbcdbdabadbaadcbbdccbbadbbbabbaaaaadcdadbadcccbadaababbcbdbbcbacabdbbaabadbbbbaccdadcdcdcabbcdbdccbbdabcbcdddcccddccbbdadadbcdadcccabccbabaaaabdcdaccaccdabacbbdcbcadaddaabcbdabbbccbcccacbdbdbcdbcadbadcaddbbbccaaaadbbcdddaaababdcdaadbccdcbadadbccbbbaddcdaadaaacbacacacddadbababcccbcdbabdbcadabbacdacdcaaabdbdacbdbbccbcbcabadadbcddabdbdabbbbcbbababcccbaccbdbaabbcccacadccdacdacdabddaadcbccbbddababcdbccbccabdcddaaabbdcccabadacababcbbdddcacddbacbbbdabaddcbcdbdbbdadbabdbadcbdcbccbbabcbbcbadbdacdbdbdcdbacccdadaccbabbcccaabdcacadbcdddbdabbddbcdcdcbdbdcbacdbcadcaabbcdaccbdcacbabcaadcccdbabdcaacbdbcdacbccaddbabadaaaadbcbbbdbddcaabbcaabcaaddacdbdaabcbddcccccdcdbbbdcbacbddaadbddbccddadcaabbbdccbbcbacdddcbbbbabbdcaacbbcbacccbbbcdcaaabdbbddbdadbaabcaddcddababdadaaacdbdcbbaccdbcaacddaddabdbddacbdccddabcabddcaadccaacaaaacccdaaccdcccbbcdadacababcbacdcadcbbabcbbbadbbcdabdbaaabdbaaacaacaadacbaddbbddadcbddddaaabbacbdcaaaddccbcbcdcdbccbbdaacbaaabbbdaadcabaabdbdcccadbccdcdcacbbdcdabccccccadccacaddcdcbdbdbcabbcddcddbcababcdbcabdadabddccbbcbabdabdaddadbcbacccdadacababddcbbbdbdbbdabdaacdcdacadbcbcabbbbbcadbaccdabcbababdbcabbbabdbcaabdcccbadacdcbbadadbbbdddbdbccbdbcdadcaddcbaccaaaaaddacadbbdcacadadbddabdcbdadccacbbadcbbccccbaddbdbbbdcbbdacadcddaaacdaaacbaddaabdbdbcbbddaacdacccbdbabbbdcabbaadabcdcdcbbcabcdcdabaadccdddbbbdadddbbdacbbcddbddbbdcbdadabbcddbbbcabbbddadaabdabadcbcbbdacddbddccacbbcdadadcbdacddcdcacbbcddaccaaaabacbaabbdbacbbcadadbdaacacadccacaaadabddddbbcbdddcbcbbbcdbaacbdddccacbbdcdbdbdcaacabdaaabcdbcbcccadcdccaaaccdbacaadbdacbaddadcdbccdadccdcdbacbaccaacaabadcdbcbaaacccddccccabcadcbdcdddbdbbaaaaacccacaabbdddadbacbbaaacbdbdbdbcbbdadbccbddcacddbdbdcbaadabdcabadbdcadcbbdcbadaccbdcaaddbabacbbbcddcccaacdabbacdbbcabdddbcbcbccacdbacdbabccbbabcdcdabdabdccaacaadbaadacaaaacdaadababdabcdcbddbcccdaccabbddaadaabbaccbbbaabcbbcddbdcacbabccabcacaaabdaabaaaadbddbacaacdbdcbcdabcaaaabdadcdbcabaddabdaadcaabbcddbabbacadcbdbbadcbbacddbacaaddcaddcadbdbccbdcdcccaadccdaccaadabdbdacadbbacdcdccbdbdcdacadbbabbacbabbcaaddabcbdcaadacddabcbbabbadbaacccbcbaadcacbcbdcaaaccbbacdbbadadcbbbcacddcacacbaabbbabacccbbbcacbbacbbcadcbaadcbbbbaddbdcdcbbbaacbbadbdadaccdbbcdcbacbdaacacbddbccbabddaddadccccccdaadbabccdccaaabbbdaddbcddacabaddacadaddaadaaacbbabadbaadbbaadadbcdcbcbbadcccccdcddbaabddcbcbdcaddadadaaddbbadcacabcdbcddbcbaabcdcbdaccbcdabbcaddbcdcbcdcddacbbabdcbbabdbbdcccbcabaccbadcdccadccacdcbdcbaacadccabcccabcccbabdadddabaadddbaddcdbaaddcbaaccaaaccadcddaddbcdbccdaaabbbbdcbadabbabbadccddbcbcbdbabbaccaaacbddaabcccabbbcacbbcdabbabadcbbdcccaaacbdccbdcbbbdaadadcbdaabcbddaaadadbbbbdcdcddbcdacbabddbdbbbdacddacdcbaccabdcddabdbacbbdddbbcdbaddccbccbabdabaccbdccccadddcddcacbabcbbbdcacabdbcbabadbcddbadbcdbcccadababcbddbbdbcdcdddccddaaccaadbabddaacbaacaacccddabcccadaccbacaaddaabbbcbaccccdccccaddadcacbdaddabcbcbacbddbaadadacdbbcaadacdbcdacbdbddcbadbdcdbcadaacbdbdbddcadcbdabdbbbbcdddccddbcdccacadbadddbdbaccdbbddbdabbbccbdbaabbdcbbdbdddcbabaaaadcccbaaddbcbcdbaaacdcdbabababccdcccdddddccdacdabbcccacaaacdbbbbaacbccdccbcbbababdddabbdcbaaacccdcddaadbdadbdcacccbaaaccdbddadcbddbbabddaacbcadabdcbaacaadccbbcbbdaaaaddbcccaccbcccdaacbbbcdbcdddacdcbddbaacccdbadbcabbbdbcdccdbacbcbaccbbcdcbdcabbbcccadaadaacaadcaabaabdbcdbaaccbddbaccddcbabbbbbdaaadaadbaabcbccbcaadccbbbccccaacabddcbdacddccdcbaccacabadcbaaadcdcdcbdaccbbdbacaaacdaaabdcbdbacbcacbccabcdbbcbdbcacddaaccbcbddabadbabcbbbdacbccdcdaccaacacbccdaaacadadcdadbcccbbcdcaddccbccbdcaccdabaabcadbaaccdccdcacaaccdccdbbdacbdcbbadcbadddbccabdbddcdcbcaabcacaddbdbabcdcaaacabacdddbbaabdacdbbbbaaacdccddacaddbaadbdddacaaaadbabdcbdbcadbaaadaaddbcabdabdabbbacccdabcacbcdcdbbabaddadadcaddabaabadddcdbbaacbaaabaddbdbddccbbbcccccbdaadbbbcadcddbadcbbdadabcadcdabacdbdcadcbdbcdddcbddddabcaccaacbcbabcbdbbabaccdcbbbddccdadbcbacabaadbacdcbbdbddccabadcdadbbabbcbdcdcddabacbcddacddccbadbddaccacbbcadacbcdaacabadabbccbadcdbccdbcabacbacbadcccabbcdcdbaaaaabbaaaaadcbbbcdcbbcbbaddcadbbaaacdacbddbbcbdabacddbaccdbbbadccddbaacabdbacccaaacbcaddaccbaaaddbbabaaacadbdbdaacbdbbcbaaadddccddbdbdacabcbccacccdbadbdddddbcbbbadbcdbcddbcccdaaaddbbadadcabcdaabcccdaaadaaacdcdaabdbaaabbcdbdaaaabbddbccaccacbbbdabbbbcbbadbbbcbcccddbbbbccbdacddbbcababbcaacacbccaacadaabdcacbbbdcdaddadbcaacdbcabadbcbaccbdcbdcacddddabcccacbbabdbcdcabbaaaaccaddcbabcbccccabbdddbadcbbcbdbcdacbcdbaaaddcacbdacccdbacabcdbaddcbacabdadcaaadadcbaadbbcadabdccddbbccbbccacdacdbabbadbcdcbbdcacbbcbdadadacdbbbdbdacdcacbdcdbbadcddbdbaccacbddadadaddccbadbcdbbdccacacaccbaadcaadcdbcdcdbdbbdaddacbdddabddabbcdbcabdddacdaccdbbbbaccdcabadcbaadcbdcbbabcbccaccbdbbdcdcbbdcccccccbbacddcbadcdddbcbcbdcdcbcdadbdadacddcbbcbdcddbccdcbbabdcbacaddbdcdaccababdaccdaccdacdabcbabdabdadabdbbcdcddddccbdacbdddbccbbabbbdcccbdabaabcdabcabdacbccadccbacbcbcbdbccdbddcddbdddccaadacaabdacbbdcbdaabacbbaadbbacbabbbdabdbaabbddbccadddabcdcaccbbbbddaddcdbbcccdbbbcccdbadabdccabaadbdccbacbadabcdccacacccbdbbccdaddcbdddbbbbbcbaaabccadaacbabcddacdaadcbabababdcaabdbddbaddabcbbdaadacbabbbacdbbdcbbbcccddaacdcadbbddabdaccdbdacbdddccbabcdcbcadbcaacacccabbdcaacacabbdccbddccbdbbaadbbacaacaaaaddbaacddaddddcdcdaaddccbdbdbdadddaabacbdbdaaccaabaddaacaaddddcdabbaabcdabbbacdcabcdcccadcadccadddaacbacbcddbdabdcddabbcacdcabbccabdcbbacbdddcdaaaabccbcaaacbbbcdbbddacdbbabcdcdccccaabdcbdabddcbbdbabccaacdddcddcacdcdcbbcdcdadaaabbacddcddbababdbcaabcbacadccbbbabbbdbbbcaabdbacdaacadbdacadbaabdbdccdacdbabbcdaabbcbcaddcaabccdcccdadadacbdddbdadabdbbdabccadacaaacbdababbacbdadabbddaabacbacbcaadaababacdaaccadaaacababdabcdbddabddbbdbcdaddacdaaadabbddcbadaaaadbbcbdadaacacadcdccacadbaddccacdabaadcaaaccdcbbabcadaaccdbcccbacdccaabddaadaaaaaddbbaacbcdcdcdcbddbbcadcccbddabbacdcadcdcccaaaccabdddaaabcccbcbccbddabbaaadccdcadaadbbadaaddbbaacccaacaadabbbcaadbbaaaabaddcabcadbcbcbddccdbddbacbdaaadbcdaadbbccadbaccdcbadaccabbdcccbcbdbdddadbcbadbdddbdddbbbbbabbcacaaabaaabdbddacaabbbacdbcabadbcdabababacdbdadccddacdbbbdabbbddbccdbbdbddaccbcbbbbbccdadbadabacccbdacdacbcbbadcbdadbbcbadbbadccdabcadddccdbaccbdbcdaabaaadcbbaadbbdbddaddaaddbabcdadabbcabdccdcaccbacbbcaacdacdbaaababdadabbcacacabbbcbcacacabbcbaddbaaaddaccbdcacacaacdccacbadbaaaacdacbdacbacdcdcdbaadabdbbccbbddcddabccabbbbadabacddadddcadbbbaddbabadcbdcbcbadbadcabcbbbadbbddcbdbbcdcdaaaabdccaadaaaccbdadbddcdaccddccddadbdbacaadcabcdadbccdcccacaadcaccaaabddccdbdbaddabacdcbacabdabaccccbdaaadabacdacdcaddcccdcdddaaadbacbddcbccddaacddddcabdddabdbabcacdbcadaadcdbcacdbcddbccbcbbbcbcaaacbcdcbabbbccdbbcccdaaabddcbbdbdccabcdadaabccbcccdaccbddcbddaccbadccdcaccdbbacdbbaddddaccbdcdadbcacacdbcddcbacbabaccbadcdbabaaabacddbcddbddbdadbcddbdbbbacdbaccabdbccabcbadcaccdbabcbdabaadbaadbdbbbbcccbccbddcbbccabdbdaadcabdddcdbcadcacabcabcbacadbddbcccbdccabbaabdccbcacadcdaaadababdcbdbacacaabbbdaaaddaaccdbdcccbbadccdabaaaaccbabdabbacababcabcdabddcdaacaadbdaaaacccdcabccbdcccbcaabdaddbbdcbacaabadadaaaccbbacbdadabdcbbddacdccdddcbbcbbddccdadcdaaabdddacdacaacbcbdabbbcbaadbdccbccdcdddacadaadcccddcbdaaacccdcbaabaccbdcccdbbaacaddbbcdddacccccdbabbabcbcdbdbcabdacdadacdadbcdccccbadbdbbadacccbbdbacccdccddaddbbcacbdcbccbacabcdbcacdbbaaadacddddcbdacdbcbbddadadcbcabcabaaaacdabddaabaddccdbdbaabacabbbdaaddabaabdabcbcbbabcadcddbddacbacbadacacdcdadaadcabdccdabcbbcbdbadbcdbabbbabcddbbbcdcaacbbbbacdcccbbbbaababcddbacccbdbdcbaadccdcdadbdddaccbaccddabaddadbbacadcddbbccaccabdabbdbbbadccaaccddddbccbaacaabdbccadbcabbcaaaacbccbbaddadbacddbbcbccdaaadacabbcdbbcbbaabadcbbdbcddddcdacaaacaabcaacddaaccbacabaddcdcaacbccdacaddabddbbabdcdcdcdcdbdccbacbdacabccacdbdaacbddaaabccacbaccbbbbcbbbbdadacbcbbdbdadcbccdddaaababbcdccaaaabaacccbbbbdcccbbcacddaadaaddacdcacaadcdcbbabaabbdccbacbaabddccdabbdccaaccabbdabaabdcadcccdacbbdadabbaddaacbbddcdaaacadcadcccdbacdaddaadbddbccdcdadabaadacddabdabbccadbddaccaaacacbddbbcacbcbbdcbdaabdbddcbdddcccdcacccbadaabaabbbacccadacabdccdbabcadbbdbddabddbddbdcddcdaacacbdccccccbccccabbcbcaccbbbaccddcbcdacbdbcacbbdacdcaabddbccbdbcbbadcaadcacbdccbbdccbdbcbdcddacbaccbbbcaabaabdabcbaadacbbbdcdaddcbbdccaddcbbbcbcadaddbcdaaadacabaccdbcabdababaddbacccdbdcaababdaabaccaacccdcbdccccbadaaaadabbbbccacaaaaaddaadbbbdadbccdbbabbbacdcddabcdaccabbcdacddbdbccaabadaddbbbabdbccddbdbbdcdbcdacadadbdbdabdddcabaadbaacddbbdbbbcbdcdcbadddadddbaadbcdccbcdbccdddbdbddcdcdddbdabcdbadaaacbccbbbacabacabdcccaacbdbcacdbabaadcbbdabbdadadaadcbbabbccddabbbbaccbdacbacbbdddccbccccbabbbdaacbccbabacbbdaccdccbdcbaaccbdacddaccaaabcadcbccdaaaadcaddacbacbacdbcdaccbddcccadadbbcaadccccbcdccbbaddddbcaadddcccdcbaadcdbdccacbddddbacabdbcbabbdaabbbacbccdcdaaabbcdcbdaddadbcbcbcdcabdbbcddbbbbdbcbddccbbadaddabbbccdabacabbaaabbbcdbdcadbdadadbbcdbcbacaddacbdbdabbbcabddddbbaccdbbaabcaccbdcbadadcabcadabddcbabdbdcdbdadbddbbcdbbddbbaaccdcdabaccaacdbcbbdbcbcbadcacaaabbdcbbdccdbacaccddcdbdbcdcdcdccddbbbddcabbcdaaaaadcdddbbcbbdcbdcccddcddbdddcbbabccaadcbabdbbcdcccaabdbddcabbbbccccdbbcacccadccccbddbdbdbbbdadddabbaccbbbbabbdabcabcabaacabadcbdaadcbbdacbbcccabbccadcdcdaabbbbdabadaabdcbccddcbababcdccbdbaabccddbdaabcaccdbacacbddddadbcaaacddabcaaacdccdbcaababbbcbacdacdcbaacbcadcdccddbbbaccbadadacdddbdbbcaacdabbabccdbcdddcaccabcddadadbccabdbdbdddbdbadcbcacacbddcabcbdacabcadacddadbbcdbbbccbabbbcdccdbccacbcbbadccbacbadaabddaadabdcdbdbddbdacbaababbcadcdadcbdcadbadaadbbbcbcabbbcdcbadcabccbbbbdcccbcadbbcdbcacaabaadcdadbdabaccbccbbdbccccdcbbdbbccabaaadbccdacbddacdcbdddbddbaacbbabddaaadccdcaddaddcdacbcddcdacbbcbdbddbbcdbabacbbbcbbbdbcdabcabbbdbcaacbddadbbdbcdcdddbbcabdddbdcacddaddccacddbdbcdcbdcaaabbccddcdbdaaaadadccdbbcabacdcadbbabbaaabdddcdbddcdcccaabcdaadadcdbcdbbacbbdcdccabaabddcbdcaaccdcabbcacbbdbdbcccaacccbddbdbaabbabbacccbaccccbbccdadccbdcdbbbbdcaabadcadbdabadcddcdcaadcadadcbcdbdaabaababccabdbbbadccdcbbccaabcacbacdbbddacdddababbdcdabbdddcdaabdadcddddabacbccdcbcbdadcacdddcbaaddbbddbdcdbcadaaddddbbbadabbcbdabdcccbbbabbdbddbdcacabaacbbbcabcacbbabcabcddbababacabbcabddccbcddcabcaccabaaacccbdaaccbcbdbddabadaaddccccccabaaacbbddcbddaadaaadabbdacabbadccacbbbdcbbcccbdbbcaaadbcbcabdcbacdcabcaddccccbadbbddbdabdbbdbbbbcbacdbabdbcdbcacbaadcddcdcacadbccaaadcdacdabdcdcbacabaabbacbccadddbacacbcabdbaabdaaddcdddadacbcbaacbcdcbabbdcaccdccccbdbcaaaddbbaadddbabdcaacdcdbbdaabcaacadcbdccbadddccadabdbbdbdaacdaacabbaaabdbccaddaadaddacacdaaabdcdbcbdcabadcbdbcdbbcbcdbbcdcdbababdbabaaacdbbcbccadaabccaacddccbddcbbbbadcbcdcdbcbdbcadaccabddaacaccaaaddbcccbaddadccbaddabbadaacddbcdccccabacabccddbadabbdabcbbdcdcbbbabdbadbacabcbbdcbcabaaadcadcaabcbababacaaabdaddadbaddadcddbdcabddbaadbbabddcadbbadabccbacdbadabcbabbcabaacacadbcdcaabccacdbcbbadacccdbaabacabbcbddcccdbdbdcabaaccdcdcaaacddadbbadbacadcbcbbdaaadcdaabdabdcaddbcdcaadccdcddaabcddccabcdbdbbcdbcdcdcaabddcdbcddbccddbbaddbdcdcbadbbadabaccabbdcbbdcdbccdabccddabaaccaccbbacbabbccdaccbdabbcabbddadcccaabdcccdaaccacaaabbaabcbbdbadaadccdbccacddcbbbcbbaddbdcbcdbbcadbaddbcacbcaabbbccaccddddacadaabadadcdabcaccacabcbabbababacddaaadddbdadabcbacaaddddbcbcbbacbabbccabbabbacadadadbcaccaaaccadddbacbbabdcadcadcaddcababadadcdbdcdacbcdabcaaabbddaacabcadbadcbbddadcbbababbacdaadaddbcdddababacdbccccacabcbcacccdbdddacdaddacadcaccaaddbaabccccdadbdabdaaddcbccabdbaabcbcdadaabcbcacdadacccddbbdbcacacccadcaddcaacaacbacaddbddcaddcbbdbabbcddcdcdddacdcacdadcbbaccdccbbbbabaaadccabcadabccbddbddadbaddbdadacacadbcaadddcabadaadbaacdaccacdacdabdcbbdcdcaddbcbdcbabcabbdacdcadbabbdcabcabdadcaaaadaacdbddcccdcccdbdcddbabdaddbdcacadcdbcadcbbdcdcabaabcbcadbbcbcbabdadababcaaababacbaddcbdccccacacddabccacadddacdabbbbcddbdabaddbcddbbaccaadacddadddccdcddbcdbadbdcdbabbbaccdcbddbdbadabddcbccdcccbaddbcacccaabdabadaaabddaddabaadacbbaabbcadcadddbdcbcabcadbddcddabadccbbacadaaabbbcbcadbdbdcacbdcacacabdacbbbcdbccdccaabcbddbaddcdcbadbcaabbbdcdacbcbbacaacdadbaaabcdaaabaabdccacbbbcaacabbbdddccbadabaacbbadcdcaabccbabbbccaacccacbdcaccbdcbdbcadabbbaddbcdabbddadadbdacdbadaaddbcdcadacdcaaabcacadadabbcacadbcadbdacbacbccbbbdcddbcabbdcdadcaaabdccacddbcccabacbdcbaddbbbcbdddcbdbddccadddbbcdcacbccdcbcdbaacadbbaaacaaccddabadbbcadcdacbcabdcaaaadddcabbcccbdacccbcdbbbbdbdbcbcdabcbbbabdddbcadcbacbabdbcabcbdbadabddcadabbbbddbbcaabccabbadddbaabadbaaabaaccdddbacbbdbacbdbcccbdbbbcdcccddbcdcabddbdcabacabdaacdacdcddacdbdcadabbbdbcdbcaadaacacddcbddbbacbaddaaadcabdbdbbdcdbdccadcaccbdbabbaaacbacccbddcccddaaadaabcadadccabaadbaadddccacacbadddccbcaabbcbbaacbcacccbbacddbaddabbdbbddcdcdaccbabcdacbdbdbadcdaabdbcdccdddcbcabbacdcddbbcbcbdccaabdddcdcacacccadaaddddabcdddbadcddaaacbdbdccadcbbbcbbbddbaacbccdbaadcaccbdcaacddcbabbcdbdaabdacbdbbbacadcbcdbcddbaaabbcbdbbcccddbbcdcaddcccccbcbaaaaabdaaaaaccdaabaaddbdbdbacdcbcadaaaabdadbcadcbacdddddadbcbacbabcccbdacaadcaabdbabdbbabbccddcbdbccacdddccdaaddcdaadabcbcbcbddbdaddbacddacbbadaaaadccdadddccbcbcabcdcdacddbbbbaacddccbdaddddbddcccaacbcbacbddbccdadddacbbcdaabcbbcbcaaccdadcddbcbacccddbdcdaababddccbcbcdbadbccccbdadcacccbcdacacadbcbacbcddcbbbdcadcbbddabdcdcdacbcdbaddbacdaabcacdcbcabdbddaddcdadabbbccbbaaacaadbddcccbaacaacdbacbcabbbbdcdccacbbdadbaccdbdccbababcdabdcbdccbddbcbbaccdcaddbaccbabdbbbdcaacaccaccbacddadcbbadcbdaabbacacbbcaaaaaadccbdbddbabddbbbcacccdccadcabbcbaabbbbaabcadccbdbddcdaacdabdbdaabbbdcadcabbacacbbcccdbddabdbcccdbadbcaccdbbbbdddcdccaabdcdabbcddcdcbdbddcabddbabcbabddbcaacbcdbcbbbdbbccdbcdadbcddddaccaddaddabbacbccbbbbdbaccbbdbdbabcdaacbccbabaabddbcdbbccadccdccbaaddcdadbbcdcbabddddbddbdccaabbcdaccacdcbcbbbdbdabcaacadacddacabbbcbdcdbdaadbabddcbdcdccccddbabcdabbdddccbdcddcbddbdabdacbcaacbccbcabcddabccacaacbcbdabcddcabaadcdcccdbdcdcbacadbdaacbcdcdccddbabcccacbadcdcabbaaccbcadcdaddbdbacdcacabcdbbcaaaadaaadbdbbabdcdbddccadadcdbacbdbcbdcddacbbbabdbcbdabcbdadbcacbdbaccaaabdcddddbdcbcaadabaaadcdbdcacacbcabbbbaddcbbbbbaadcccadaadcbdacabdacbbdaacbdadcabdcbdacadbbaaabacbbcdbdabbbdbbcadaccccdcbcddbdccdccaaadabaddadaabbddcbdccaddccaddabddbabcdbcdddcbcdbbadbaccbacccccbbbcbadadbbdabccbcdccdbcbdaaaaaaaadaaacaaabbbcdadabcbddacdaaaadddaabaccbcbbbadadccbbdcbbaaababbbbcdbbcbabdabcbbabcbdacdbadbdbabbbbcacbdaddaccccdacabdcbabadddbadbcbadbaadaaddbaadbdbaadccbcdbaacdaabdcdbddcdadacbcddddccdbacdcbaddbaddadcdcbbacbbdddbcbbbdcddaacbccacdbbccabddbbbbddbddadccbbcbcdddccdbcbccdbaccacdccdbcbcddddcaacaaacdbcbaaaabaccadaddbcbcacbcdacdddddcbbcabbcccddcabacdccdddbcbabcdabacaaabccaacddcdbbacabadcdccadcdbcdbdbaaaddbbbbdddbcaabcdcbabbcaacbbccbbdddbbaacdabdacbcaadacdadadcbbddabdcdcbdacbabcdbbdccdddcaadadccaabddcdcbbcabbacadacaaabcbccbcdddccbbbccabccabbadccbdaacdadaccbacdcccadcdcdbbcbadbadbcccacabdbdacaddacbabccdababdcccdababaadbcbcbbbadaacddddabddbacbaaccaaabcbdcbbaabdcadddbabbabdbcdcbaadadcaaaabaabcdcbbdbbddddcbbabdddbcccdcdbccbabcbcbdcbbadddcadbadacbccaabbccbbcddbdbcdabcdbadbacadabaaacdbdaabcdbdbaaaaddaacabccbcbdbcddcbcaadaabcbccadbcbdadcababbbacccaaabaddbbbaacbccbaacaacddacabdaabbbabaadbacbbaaddbbaacaacdddbaadcbacdbbcaccbbcdbccbcbcdcacbabdaadcdadbaddcdbcdacbbdddaacdadddadbacdcaadcacabbddabcbcdccdcbcbaaacbaadabcccdadddbaccdbaddcdbcbbaaaacbabaccdcdbbacdadaddaadcabbabbdccbcdaadcbacddaaabbdabacccadcddabacabbdcaabdccddabccddcdabdcccaddddabadabdabdcbddbbcddbbaccaccbaaadbaabcdddadbaacdbbbababcdcdbdbddbbadbbbdbdbcaaddaaccaacdddcdaabacdbcacaccdccdabaabdaddcdcabdddacbacaabddbcbacacbadbcbcbcdcaddbbbbdbadcdcbdabdcbcadccbabcbacacabccbabbdbbcaaadabbcccdcbbadbdcaadadcdbacddbacacabcaaacaabdabdacbdacdbcddcabaadacdcadbccdbbddccbddabbcbdadcbdccabaadbdbabbcdcbbcaadaabccdabdacdbabccabdcabdaaacbbabdcdccdbabbabcbbaaccddcadaabcdddbcbbccbddaabdcddbbbdccadabcbbacccddbdabdbddcabdcbbcacacaadaacdacabbcbbdccdcdbaccbdabacccaabcddcdbdbbaaadbbbbddaacacbbaccdbdccacadcdbccdbadaabcbcbcbcdddcdcaabbbcbccbdacbbdcadddabdabdbbadcbbabadacdaaabaabaadabbbbbcdabbcbdddccbadcbbdadacbdddcbcaabdcbabacacdbdacbdccdcccbbbccadabacaaadccbdbddbbdadbacbadabbddbdacabdbdddcacdbdcdcdbcdbddabbdcabcadadbcbaadacbbdcabbcbcdbbadddaaabacbbcccbcdadadadaabbcbdcaccddbcdaccdcaacdabccdddacdccdbcccaaadadbcdbcadbadacbabaabaddcbadaadadbbdbacbddccacaabbdacbbabaacaacbbbddbacaacbdcccccbccddbaadadcaaadabbdaaaadbaabdcaaddcababcdaabadcabaaaabacbbacdaadadbabcbbadaabccbdcaaaccbbbbbdcbcbdbcbbcccdbcacccacdddbadadbbaabacaaadbccbdadcbbdbbcacddacabdddcaaacaacaadddacabcbdabdcadcaacabccbcdbbacbddcabcbccdccbaddbddacdddccbaddcbcbbdcabcababcdcdcdbadabcdddbddbcdbabbbcacbacaaabddddadcaccabadabddadcbcbddbbdaabbcdaacabbaccbdacaadccdcbddadcabcbccdcbadcdcbdadabbaacddcaddacdcdbcbdabcadcdaaddcdbbadbbbaadcdabcdcaacaaabdbdacbaddddaccdbadbddbdbcbadcbcaaccbbdcdcbabcdbabcddddcdaccdaacbbbcbdaabbbbcacabbcccbbbbdaddadcacdcabdddbcdbabacaddadbcaddcbdbbaadcbdbdbacdaddbcadaaaabdacaaadcccbbdcabccacbcbdddaaadcbdcccadbacdbadcdbcbbadccadbdbaabadcaacaacacdabacdbadcacdddbbcdabbaaadbacdccdcadbaacdbddccbdcbdbaddcbccadddcddccbdbaccacccdaaaadabcaaaccdaabacccaaadbcaaababdababadbddbabacacdcacbadbbaabdbbcdbdacbcaaaddbbdaaabadcccdcdadcbdbdbcdcbcaddccabbaabdadbbcbabbadcbdbcddbadaaccbdccadcddcccbacdccdbadaabdcdcbcdacbdcccdbcbcacadbdbabacaccdcdcabccbcbcbbaadadaaaadabcaadddbaacadaaacdcbddbdcbaababcabababadabadabcbbcdbcbcdbabcacdbabdaaccdababbbacadddcaabdcacdbaadbabcbbcbacabacadcdddacdddbbaabcdbddacabaddbbbbccaadaddbabdbaccacdbdabbabcaccaddaadadabbbbdccaabacabacdbabcadcaaadccdacbdabddaccabacdccacddcabdabadbccdabdbcdcbdbacbbdccbddabddbaddccccdcdccdbccabcdbacabbbaabadcdbacacbdaadaacacadbadcabccdadbbabccccdccddccdabbcbdcbbbacddcaaababddaccaddcdaabacabadbcbbaddcddabdcabbabbdbabcaabddbbacaddbcacbaabddaccbadbbcbaccadbdddcbddcadbbaaacddbdcdbabcbacbadcbdcabdccbdddbbcbcbbcdbbabddaacbdddddaaccaaaadcadbcdadabbaadcacbbbcbaacaaacabccadbabdaaacddaaacadcacbadddaaccdaddcdcbcaddcabbacbdabdcbaaabddadaacdacbbcdcddbacddcbcacacadccbbbdbdbadbcdcdcddbbdcbcbabbcdcbbdacddadacaccbbdccadbdaadcdbbdaccaadbbcbdcdbcddabdccadcccddcccdcaaaadcbbdccbabcddcdaccdbdcbbbdacbadcbdcbbbdacccadbccbbddbbbbccadcaaabaaaaabbbdadadddbbcdaadcbacddbabbccccaabcdbadbabcbdcbdbbdbabbcabdbbccdbbcaaaaadcdabcdaccabcdccddabdadbaabacdcabbacdbccaabbaaccaacdabbdadccbabadbaaabcbbbdbadbadaacbaadabcaaacdabbbabbaaccbdbbcabbbaacdcdcadaacbbccabaabacbbabbabadcabbccdbcadbbbdabddcbbabaabdbcadbdbdbbbdaddadadcacacbaddaaccdbacdadcbdaaaccacdbdaaaaababbaabddbcbaaaacbbbbcbacdcbdcdbbbcbaccdcabdcbdccdbcdabddcdaccbdadaabbbadcdbbbcdabacaccadcdcbbdbbcdbaccacababaccaccdbcccbabbbbddbbdacdbdcbadcbcaddbdccbbbadbdbadbaccdbdaccbbbaaaacdbbdbcccdbaacdacacbcaacadddbcaabcaabdbaadddbccaddcadaddcbbbaaddcbcaadbbbdbabbdcaabcacdabdadbaaadaddcadabbdbdaddacbbdabacaacdcabcddcdcaabddcdadaccddabcbbcbaccbdaaccbddabbcadbcdbcccbbacddcdcbcaababacabcdadaccadcacbaaabbcadddbbcdddabbcbdcbacdcbdacdbbccdabbaccdbdbbccbccabbddbbddadbcddbdddcccdaccaacacdccbddbcdddacdcbbdddabdcbdbcaacbdbaacccaadaacaadcdddcaadbbdcdbabbdccabdddcdbbabccccaadadddbddbdddabaadaabdcdadbbdadbcadddcbdcbcaaabcbacbbddcbbacacdbdcbcbaaaddddabdddaccbdadbbcaacbcbdcbcadabdddbbcbabaabcabcbddcbaadcccddaccccaccbcddbbabbcadbbabdcaddbbdadddbcacdbcddccbbbacdcaabbadaddddbacdbabbcbaccbbddcddbbacddadbcabacddcdcdabacbbbdcbabcaccacbaabdbdaaaccdacbddcbbdbbddabccaacdababdccabcbdbbaccbccaaacbabdcaacdabaacbcbadbdcbababacbcaadbbababbccddaacbcbdadcccbbadabdcadabacbdacdcdacdcdabcaaccdabacbdcbadadcbbddcabcccbddaabbcbacaccabbcbdbbcbabbbbcdacdddccdddadaaabacababbccbdcdaddcdabbcacdadbcabdbbcabaacdacdddcdbaddddddadcbadccdcccdaacbbabdaabdadbcbdbcbbadbdcabccacccaccdababbbadcbbaddbabbaabaaabbdbdcddbdbdacbcdcbbcdcbcaddbabbcbbaddbbaabaacacbababdbbcbcbcaacbbbbbacaadadacbbbacdbabadacbcadadbabbdabadccadcbcacdbcdddcdcadbbbcaaaaaacabbcbdcbccbaaacdddcbbacdccaddaaddcdabbabbdbdacccbddddbcccbbddbdbabbbccaabcccdcabcbbdccaccdacabaaaacadbcbdabaccadcaaadddbdccabddabbbcaaadbbbadadbbdddaabadddcacdabadbdbadbadabdcddabcbaaadbdaaadcabbdbadcccaacbcdddbdbacbbabaaacddbcaacbdadcbcaddadabdaaacbdaaacaaadcdcdccbdabadbcababcbddacdabdcbbdcacdbddbadbccccdbcadbdbdacaaacadbbadbadadddbcddccdacaddcbccaccabbbadbdacccacdcddcabdcdbddccabaaaadabcccddcdccdddbaccbcaccdaababccdaabccdccdbbcdbcdbccccdbdaabccbbdbccacccdbddddbbcabaabcdcaadcadbcdcccbbbddcdddacadbabcdbcabddbbbdacaaaaccbbabbccbddcbbbbcadabccabdccdddddccaadbdddabdaabdaddadabcddbaddcddbcbdbaaabcbdabddbcdacbbcbdbdddaddccbbccddbaccdbdaacdbdccadbcbddadddbbbabaacacadcbbacbaaaabdadcbdcabababadddbdcbccddaaaddaaaaaccbdcbbaaccaddcccdacacbdbdbcddabbbcbddaccbaabbadabadbdccacdaabcbcdaccddbbbbdbbbaccbbbcdbdaaaabdbbbcaabbacadccdabbaaccdbaaacaababbccbbdbbaccbdbccbadbbbcaaacdcacddadbabaccdbabdcadcdcccdccdadbdbadaddcbacbbbacdcacaaadabbbdaddbacabacddbcdbdacdbcddbcdcdbabcaaadbcaaacbbddbbaabddddbbbbcdacadddbbcaaacbbbdacbaabcdccdccbcaaabccdaddbacbcbdcbabadcccadccaaddbbdbdbdbdacaacbdcadabbbabadcdbbcdbdbccabbaddacacbdbbadcbbbbaaaadaccdacccacbbaacdccbddaadcabacabbbbbbccbdadcadbaacabbdabbcabaadcbcdbabdbadaabaccacddacadccaccbaadbaaccdbcdacbbbbdcddbadadcbaacbadabadcddcadabaccbbbbccdbcbdadbabcbcdcabccbbbaaaccccdadbaaabdbcdcadddcdcccaacdcbadaaccabbbdddbababccacabcaacbbbddbacddaddbcdccdddcbdacdbabacdddbbadbcdabbcacbaccddaabddbaacdadbbcccbccbdbcacacdccdbbcbdcbbbbaddcbcaacadcdaacbaaadadcabdadddbbdaadaaccbdccccadcaabacbbbcdaddbdcadbcdccbdbcaaadccbacabaadbadbabcbccbcccbdccdadabdccbbbdddcccdccabdaaaabbcbdcaaaaaadcccaabdabaddddbdacdcbbadbacbacbdddbddabbdbcdbacccbdddaadcddbddcaccdcaaddcbdcbbdadddcabccacabdabcbaaaccbadcbabbaaacbabcbabcbbcddbcaccaccdadccdaddaaddccbbbdbcccbdaaccbdacbbddccbcaccabbcbddabccbcaadbdcdcbcddcdbacabbccbaaabcdcbbaaacdbabdabacddbcaaddaddadaddbccaababdadcadcbdcbaacbbcdabbcacbabaccadaacdccbbacccdbccbcbaccbbabbbccbdcbdbbcacddcacdccbadcdaaabdbacadaacdadbcbddbaadadcdcbdcdadbcddbaabaabbcdcdddadacccacbccccccbdadbdaacbcdcccdabaddddccaaddbcadbdbbbcbaacaddcbadbbcbdbcccaadbddcadcbcaaddabbdaabcddacdbacdbcacddabbabadccabbccabaacbbabccabcbbbdbccdacbaacccaaccaaacaccccadddbaaaccdcbdacbaaccabdadccccaadbadabdbcadddcaabbaddadaacbdccdadaabaacbbbbaabcddaabbddbdccdadcadadbaacdccdcddacbbddbccabdacdbadacbdcdcacabaaccacabcadbcbacaddbccabbdcbcabccabcbaacddbcabcbacbbbddbaddaadaabccdacaccbdbddbbcbbdacacdaccbadcccddabbbcbccdbcddacadcccdcdacdadcddcacacabddcccbaaaabbaacdbccdddcddaaabcabdcadcabcbadacddabbadddbddccdcbbaddabddbccabdabaaacddbccbbdbcbbddcbbcddbbddbcbbbdbabacbcbadcccabcbadbcccbccdddbccdbddacdbbccdbcaaccdaabbdabbcdbbdbbbcbabbdcbbadbdbdcaacbbbcbdcaabcbcaccdccdbabbbacdaadaabcaaddaadaadcdbaaaacabaaacbdbacdacabadacaaabdbadabdaaddddccbdaddbdcacdccaaddaababcadcaacacbcccbbcdddbbaccddcdbcabddcbaadaabddbacadbcbdadbdcdbbddcdcbaccadadbdddbdcdabddbadbcdbcbdaabccabdcbadbcbdbcabdabbcbdccbdddbadbddccaddaddcccdbababbbaabbbcccacbbbbcbdacddcbbacbcacdbdcddbacdcdccddaccddbcbbcdbbdcacbdbbcabddacbdadddaddabdcbbbbcddcbabbbbaddcdabcdbcccbaddacdddaadacbadbaaccadbcbcabbbabdbdbbbccabbdabdcdacbabcaabddabcacaaacbddbabccdccabaadabacdbbdbbdbabaccddabbadbbbacbcbdadbabcdcabcccdcdbaddbdbbbcdcbacabdbadabdbcaabdcbccbaaadcdcccdbbdabbabbadbdcccaccbacbacdbaacccdacbdccdaadbbabadddcbaadcabbdbbcbddbdbacddaccccdcdbcaabaaadcdcdcbcddddcccbcbaaacabbcdcbcbabbcbcbbdcdbabcabcccabbcccbabaadddabcdacbaaddcbdadaacaaabccabccbcaacaabaaadbcadbabacaacbbdcadacbbabadbddccbbbbdbdcdbabddcdbcbaacdbddaacaadcaddaaaccadbdbccbccbcbbabccbcbbdbcdbcdcadbaabaddbdbabbbabcbdcddcaabacacbbcabcbdbbdbcdcbdccaccddbbcadbdcadddcbbdabbbacbddacbdadcaacbbdbbdadaadacbbabcaabbbbabbcbdbcaccabcbbacadbcdcbaabbaccdaaaacadabdacadbabdcbccabbbbabcaccbcaccbbbbadccabcdbcddbbaacdccbbdbddacadacaaaaccdbacddadbbddadbccabccddcdccdabbdabbaccacccaccabccbcadacdbddddbacccbbacbbdabacbdacdbadcbbdbbddbdaacadcdcbbbcbaaababcaaccbacbdddcaaddcddbbabbadcbccbcdccdbbbcbcbadcaabcbaabcbdaadaccacbadabddbabbbabddbabdcbdabdaacabcbcabcbbbbddbcdacacbbdbbdbddddaabcbbdadacddddcdbcddbccdcadccaadcbcbaaabcabaccddabdccaaadcbccbaaadcbcdaadadbddccddcabcdadddadacbccddccdcdcbdcbcbaabcacdbddddcbcabaaacbdbcddcbabccbcaaaaccbdadabcacdabcdcdcacbdabbdbacbbcaabaadacacdacccbbabcbabacddbacacbbdaaacaabcdacbdabbdcabcdbccdcdaabbbadabbabadddaaabdadbabdbbddbbbcbbaaabbdcdaaabdcbcdbbbaadccbdaacbcbcccabbbcbbbbcdbddddabbcacbaaaadacdcaccddccdcabbbcdddccdabbdccccacbcbcbcacdacbbcdadbadaabbcddbdcbcccbccdcaabadabbbcdaaaabbcdcadbabcdabbddcbbcbadaccdbbababcabdcaaacdbabbacddbccbdbacaaaddadcadbcddbccbdbcbcccbbcdadcdbdbcbbadbdabbcdaacaadbcddddabcabcbdadbdcacbaccdbcdaddbdddbdadcbdacddcccabdadacdcadccdcacbdddbdcadcdcaaccaaadbbcdaaddcbdadabcabadbadabbddbddcdaddbaadbdbdbcccbddbabdaabdddadcbadaabdbcbaddacadbdbabbaddabdadbcccdacaadcbdcdcbdadcabadccdbacbcadcaddbaacbacdaaabccdcddbcdabddadacbcabdcabccbacddbdabaddddadbdcbabdaabbcdcababbdccaabbababbbcadbcdbabbdabacabdcbdaadaaaadddddbbaabddaabaadbcacbdbdbddabcdacdabbddabadbadabcadacaadbbaacdcabbdabddaacaacdbbbdbdcaacabbdcabdbdccbaabbbcddbaadbccaabdcddbcdbbcdbbabccbcdbddbbabdddddadadcccdcabaadadddbbadddcacccddbddddbadcbdaacbbdcbaabccdbdacacacabcbbbadcacbaadcbddbcdcbdbccdabdadcbbcccdbbbbaadabacbadaabaabcaaabbaddadbbacadbbdcddbaccacdbdcaacdbadaabdaabdcccdabadcaddbacbbcdabbacdbcbbbcdbddbcdcbbcadbdbccdcbdbacdaacdbacbabbbcdbbaaacacbdcdcbabdacdadacbacbcddacbbdcaadaaadcbadbbdddaaadaddcdadcddbaabcdbadacbabadbbaddbacaaabbddaabdbccacaccadadcddddccacbccbdbbddbdbddaadcdcacaccaacbdacddbaaacbbbcbbccaddbdaaaabbabbbaccbbcacbabdadbcdaacdccdaddcaabaaadbbabdacacbbcdcaaccacdcddabccdadbacbbddcdabbbcccacccdbbcbcddcbaccaadcadcdcbcbdaccdadbbdaadacbbcaacbdbdbadbbabbbbdcabdcddaabbadaaaddcabadcdccacbcbadaccdadbbcdabdadddabbadacdbabadbbdaababdbdabddbdcaabaddacaadbacacaacbcbabbddcdddcdddbabdcddcbdbbbcaabbbddadadcccabbbabcacccdcdbbbcbdcbcbacddbbcabbaddcbdababdaabcadcbabacdcbcccaabdabbddbcbcdccbaacabaadbcabcccabadccddbdcaadbcbaccacabdbabcdaacaabdcdcddcaaccbacbdbdbbddbaaacdcbcbcccbcacbbaabcdccbbccbdbdadaacbbccdbcdacccdbcdbbdadddddadcdbcdacdcdaadddbbaadcaaaddcbcdacadabbbabacdbcccddabcacadacbcbcdaababcbbbcbbacdadbcdcaaabdbdaaaacaaaaddadbaacbbabdacdccaddbbaddbacacadbaddddadcbddacdbbaabdcbcdcbabdbbdbaabbaabcbcdcdacdbcdaccbdcbadbcacdcbccdabbabaddadbcababacccdbcdaccdbbbcbcaacbcaaccbaaacddccbaacacacdcbbcabcbdacabadaadaddccadadabdbccaacadbdadbbdcbbcbbbddcbddabdcbbcbcacabcbcdacbadcabcaabaaaacddddabbadbdddcbbbddaaabaaddabbccdbacabcbddaaacdcadacccbccbbcbcbaccdcdbbbbdbbbadacdbddaacbabdbdbdadbadcbddcabdabdcbacabbabadacbcbcddbbcdabbadcbaaacdcbbcbcacccdcdcacbccabbdaacdccacacccdbccabdbadbdbaabbabbbbdabdcdabddbaddbacacaddcbbcdcabcbbacaadaabaccaadaccbaaadcdbbbdcbdcbbbcabbbabbbacdaddccbaadbabacdaadcaadcacabdaaadcbddbbdaddadcbdbbbaccaaababcacbcdaadbdcbcdcadaacdbbacccdbbbccbabcbddadbadbcbcacaddddbddaabcbcbcdbdbcacdcddccdddcaaabadccabaaccbdacdbccdaacddbccbcdadccadbddaddadbbdbbdbdcadcccbdbcacbabbdabdcddacaaabcbbdbacbbcbdbcbcdbaacbccbcbccaaadcbdccbaaaddaccabbdabbdcdcdcaabcdacadbadcaaabddcbdaccaaacadcdacbaacbbbbdbdcdbcadabadbccdcaddaabaabbdddcadbdacacbdadacdbaaccabbbaadcabbdbbdbaadacdbddadccacdbacaddbaacbcbadcdcaacacacdccbdcbbdaccacabdcbadbaabdaddbdbaaacaadadcdadbdbdcdbaadbcdcbdddadbbbcabcadcacadaddabcacccacbaaccbabcacadbdaadcbbadcdcbddbdabbcbbbccccdcccbbaabddbcbbababdaccbdaddbbbdcabcdcabdcacbbadbcbcdbddddcddcaabdaadddcccabbbccbacbbccabdbcdcabbaabcdbababacdbbbadbdadbacadbddaccaabbaddcdddbcbabbbdcbabaaadacaccbacbabaddbaccacddacacdddaccdaaddcbcbbadcdbcdccacaabdacacaabdbbddddddbaabcbcaaccbbabaaabddcbaddabcccbccdbdcbbaadcbcbdbccbbabddccbcbbdcadaacaadcaadbbbccdacbbacadbdbdabbcabbdadddcacddadaacbaddbbdbaacdabbddbddbbbbddcbccadadaabdacacdcdaacdcdadbbccdcbadbaddbbdddacbccddcbacbdcdddacaabcaaddcbadabccbaaaaddcbdabccabcdbdccabddddcdddccdcaddccbbcdadccdadbbbcdcccadddbaacacbadcddababbabcdbaacdcdcaddbbdbbcadabbcccbabcbcccbbccbaaacdbbaacacbdccdacadcccdbdcbcccabddbbadbdddaccddbddbbbcadbcbcadbabddaabadddbadcdcabbacbacacaaabccacbbbdacbbbcdcabcdaababaabcdccdddbadcccbcddcbadaacaddbcadbbcbcbadcdbdadcccdaddbbadadcbdbdcacababacabdcacdcadbddcddccbabdbbdacdabcdbdcabacdccbbdcbcbdadbcccbbdbabacbbacddaccadbaababdbbacacbdccbcacbabacaadcacdababbcabbcccdcaacbcbabdbaabcddabaabdbadbbaaadadbacaaaabddacdcdddacdcabbacaddccccdbaabaccdcbbcccbcdbbbcddbaddccbbddddbaadddbaaabacccccbaccccdbbdcacccdbdbbdccbaadabacdccdaaaccabbabdccaddccdbabaaaaddacaacccdddccaaabddbbdbabbbacbddbdcaddbaaaacdcacabcbaacdccdaddcabbbcaadbaccbacdabdddabddbcdaaabccdcabbccdbaddbaacdbabcaccaadaaccacbabadccccaccacaacabccdddadaaacacaaaccaadbacdaadbdcadcbddacaadddcaaabccdcbcccbcddccbdabadadadaaaacabdccbacdbcbabbdbaabdbbbabadaabddadaabcbbdcccaadabbbaacbbdaccdbdbdcddaadccdbbccddaccdbacadbcddbaddbaabaaadadbccbdaadcbdbdcdaddadddbcadaccdcbdadabccddaacbbbadcaaaacbbddbcacaabccabacbccdacaaacaaddcdbddadbadcdbcbbbbcccabdaaddcaddacabbacccdabadaabbbddbaacbdbbcdabdbdcbbbabaaccabdbbabcdabdbdcdbbcbbaddddaacacadbcababaadabcdabaadadddccbbaabbbdccdadcdbadadcbcdcbbcccdbdcddbaaacddaaabadcccacabdcaadacbcacabaababaaccddcdcbbaaadcbbdddabbcabdacabbbacabaddabbbbcadbcbdbbddbcdbddbaababadddbdacdabadbdddccbabaadaaaaaccdadbbbcdbdbdbcdcbccabcbdddddaadbabacabaddbcddbddcbaabbcdcadddcbcccaccbcacdcaabdddbbdacdbdbbacdacddcaabadbadcaaababbdcaaadacbcbacaaaccccbaaadcdbdbdbcdcbccbbacabccbddddadbcaacaabcccadabccbdadccbacdcabcdddbdacbbcbccacaadcddccbadbdcacaacbadddbabccdcabdddccbcbcdcdbdccabdccbabcacaaacbcacaccdbbdaabadddbbabbbaaacacdcdbcdabbcdaaacdacddddaabacacabadcdabdaadabacdddbabadbcabccdcdcbbbbcaaaaacabdadbadabcddbbcbddbdddcdcccbdadddcaddbbbdadbdbbbdaddadbdcccdbcdbcdacbacdcbdcaccdadccaccbccbcdbdccbcdcdbcdcabadbcaadcdadadaacadaaaaabdcdabcdacacbccabcdbbaaabdcddcabbbbbdacbcbcbabaccdbccdbdbbabdadcaddabbaabdbbdbbdcddbadaccabbcadacbcdaadbdcaabccdbacaadbbdcaaacaaacbccccdbbcaabaabcbbbddadccabbbadbdbdcdadacabcbddcaaaabdbabcaaadbccacbdbadcdbadadcaccbbddabbcdddcabbddccadabcaacbdabcdcbdcaadaacddaadbbabcdaaddbdbcaabbccdbadcbdaccaacccddcbacbaadaaaacbcccccdbaddddbadcacacbccbbaacdccbddddbbbbcbdbabdaacdcacabcaadbdcadaadccbccdcbcdbcbbbdbcaccdddbbccabbdbbbddbcddbcbaadbdbdbddacaccbaacbcddbbaabdcddabbaddacbdbbdbadddaddadccababbdbbdbbdbcdbbbcadabbaaabadcbccdaccdcadccdccbbaaabbbdadbbaacaadbbabaccdcdabacccbabbbcdbcacdadcdbddbadacccbadbabcadabacabbabbdbdbbabdbdddaadaccbaabddabdcaabcdcdddacabbddadbbccbbccdaabcdaacddcadbacabcdadbbadbccbddccdbddcadbcabbbdddaddcdccadcbbabbaabcabaadadaaaadaaacdbddccbccbbdcaadcadbdbddacaadcadcccccbacaaacadbbabadcbbdaacadbbbbbacaaadaacbaabbabbadadbcbacbbbbdcdccbbddbaaccbbcacaaaaadbbbaddbabbdbccccbabbddcbbaccacdacdacccabbbbabbcdbaccdacacbbdbcbdabbbcdcbaaabdbbcadacbdbbbdacaadcccacbaccabbabadcacbacccbcaaacacdccabbacadbcbdadccddbcaddbcbbacccbdadccbddbbadccbabcdccbdbdddcddaddbbbbcbddbabacaddacddbabbbcaaddaccabcdaddbbdbaabcadbdbabaacbabadcdbbcbcbddcccdbabddadbbcbabcbcabbadbdcdbdabbacccdacdcbaaacccbadcdcadcddccadacbacacbbadddbdcbddccacbbdcbdadacdcabaacaabdcbabadcdbbaccaaadbdddcbabaacacbabdbaaadabdbabbadbcabcddcabbdcaacbbdbdbddabaaacdbdccaddcdbacaaacdccbdbdcccddcbdbbcabaddcacccbaacaacbacdddcdadccbcababddcbaacdccadacabcbdbddcdaabdcacaccdcbcaccddcdcbdabdcbcdbbbbbdddcdcabdbdbcbdcacdbacbcaddbcddbabcbbbcbbbaababccadcdcbcdadcaadccdbccbcadddddcdcbbabbdaabcdabcccbddccbdccdbddcabdaadccbddabbbbdcbadabcacbcbaccacccadbbcaacccddacbabdbacdbbbaadaaacabadcabbdccccaddcbcbacdaaadaccabacacdabddcdbcbdaaccbaacaabdaddabdbbbdcdacbcdbdbddaacadcbcbdccdccbdaadddbbabcbbdbacbcdcddbbcaabaaaddcdddddbdcbacdcbcadabccaccbdccaddbbccccdaccbcadbbdccaadddabccabddbcccaadaccacdaccdbbcaadbddadcddbcacabbddbccdacacbabcddbdbdcbbddcdddcdcdbacddacbdbaaddddaabbabcadddcadcdbddbdddcadcadcacbcdacdbaacdacbbbdddcbdabcbbaabbbbaaaccbdacabddcabcdcacbcbdccddbabcdaddabcbdbacacaddddccbcdacdabbdbacbcdbabababbbdadddccbaaaaddcaabacddbbcadcdaabaaacbdcdddbbbbaccdbcbacadcabbaadacccaadbadaccabcdbaacdcaabcbbbbbadacbbaacddbdbbabdcbcabcbdbabddbbaabbdababdbcacdabbabcccaaaccdddbbaaddaacdaddccbddcdbacbbccbacbbaacbcbcdacbbcacbabcbacabddcdddcabbbbccccbaaabdbaaabaddbbaccddbddbbbdbacaddcdbabdbdadabcdabadabdddacdbdcccbbddddcaacacbdcddabdadabadadbdcccbcccadddadbacbcdbdacdcbadbcbbcbadbdbdabaacabcacbdcbaccdbbbdcccdbdcaacacdbadbabbbdaadabcddbcdaadccbbbbcbbcddabdaaccccbbadbbcdaabaccababbddcabbcdddbbaccddcbcadbbbddccddbdcbcadbacadaaabbbccdaadbcadadaaacdaaadabbcdbcdcccdcdcacbcbddccdcdbccbbbddbabbdcabacabadbbabdabccaddadbacccdcdcccbbbcccdaadaaabbddbadacbadbbabacdabccccdddaadadbcabadcccddacbddbcbddcddcbadcbdcdcccdabadacacbdddccbcdabaacbdddcdcccbbbdbcbbacbcddbacaacdbccdcdddcdddacdddadaacdbabcaabdacabcadadcdbbadccacabbabacbdcddcaccccabcadbccbdacdcbbabcbdbcbadcbabdcaadacbcbabdddaddababacaccbdcdbdbadbdcbdccdadbabcacdcbdbacaadcdddbdccacccbacadbdaddddbbdabcdbbcccabbbdddabbccaadcdcabcabbbacbbcddbaadadbcbdcdbdbccacbabbccbbbcbbaccbacdbcbabdbcbbbdbaadcdabdabbacdbdcddbaaddbabbdabddaaaadbcdcbddbcadddaccabccdaccbdbbdcccddcdbbbbadcbbbdbbcbdccdcbadcccbccbbcabccdbcbadcbddaddbdbcdddcdcaddccbacdacccbcacdacccdaadbadbccdbbcbabdacdcbcdadbacacdcbdadbdbabcbacddadadccbdccababbddcadbdccbdcbdcabcadbdabbaccacbcbdbccabaaabbcaabcdabadcaccdbccbabbbbababdabcadbcbbdaacdabaaacacbacaccccbabdaabccbdaaccabccdcdbbdacbbaadccbcccddabcdbdbcddbbddaaaabaccbbbaddcaacbcccbbbdcddacbbcacdaddcbdccdadadcbdbdadbccccdadbbcdbdabcbacdbabbbabcbbdbabccaccacabcaaacdabccdacacbaddcaadbbddacabddadabacccaacaacdabdbdccbcccddbaacacabdbacadddbbbddcdbadadcbddccdbadabaaddbaddbacbabdbbcacdccacaccddddabcaadbdddbaaaadcbacdbabcdbcddddbdadcccababacaccbccccbccccddaccbcdaabadbccbcddccbdaddadcacdccaadbcddbabccacbcbbcddcbaababaaccccbaaaacdcadcadcbdcacbbacadaacaaadbcaadbaabcacdccdbbadbbdddcaccaabaadcbabcaabccdbbcddcaccabbadcbcdbccbabbadbbccbabbbcddccdacbbaaacbaaaaccaadcadacdaadccbbddbcddcaaadcdacccdcaccbcbabbcddbcdcddaabdcdcaddbbcdcbaaabacddccbcddadbabaabaabbacccdaaddbdabbabbcdaddcbddadabbaaadbbbdaaacbbbdaabccbdbcdbdbddbdbcbcdbabbadccaccbbdddcbacadcbadbbabdbcddbdcdbcddabbddcdbbcccdbdcbaadcdadacacbccbbaddddbcbbdbccccbdbdabadddadbabddddabbbabababdcdadbcdacbaddcccaacbcaddcabbbbcacccdbaaababcccdacaacbdaadddcddddbcdadcdcddbdddacbadbbacddacccddcdcdabdcacaadccaddbcddddbcccbdacccbcbccdbcbcdacbcabccbcbbbaccddbddbaaaadddcbbacdadccbdcadcabcbcaabcddbabddcbadddaadcadbddcdcbaccbbacbcabaddadaacccacdcadcdbdaadcccbddcdacaddacdcbbacbcbbaccbbddbbcabdccbaddcbbadaadcdabbbcddbbcdbcdacabcccdadbaabbdadddadbcabadbdcadccaabbccadbbcdacbbdcabbcddabbcbcdbbbcdcabcacbcddbcadddcccbaabdadbcccdaabacbdcadbbcccaabaddadbabbbccdbccbccbbdadbadacadaabdccccdddccacaaaaadbdbbcadbddcadaadbaadcdbbcbbdacbbcddbbdacccccabcbbcdcacdababacbabbddadadaaadcadbbbccbdacbcdbcadacdbccbaabdbbacdaabdcabdcadddddbadaacbbadbdcaaccbaadcccdadbccdcbdcccddcdcccacbacacdaaaaacadbaabbbabdbbbcbcbcdabbbcbbacabbdbdababcaacbcdabbaaddccaabdabcddabcddbbbaddcdaddccabaadadaaddbbccbabdadadbbcdbdacdcccbdaacabcdcadadbbbddcabcccacbccbbabcacddcadbadbdbaaaacabbbaabcdbdaddbcbabcccbbbaaacccbdcbcbbbcddbabbbccdcbaddbdbdbdbccdbcbaacbcbccbadbdcdbdbaddbcadbddcbccacbdaaccaddbdccdbbbacacccabdcddadabddabdabdcabcbdbbaccaacccccacacbddbccbbabccbbcbcbcdcabaadcdbddaacbcbbbddccbaadaaaaacabdbdbdbdbabbddcacbccbaccdbbdcdcacacccbacdbdabbcdccadcabcbcbdcacbcbccdccdaadbdbadabacbcbacbddddbbbdbddbaaacddbddddbacbdddbddabcbdbdcaacbcccdbbbbbdcbddcabbaddbbadccddbddacbcdcbcdbdbbbccbbbdacbdcaccabadcacabbcdabdadccdddaacaaccdcadbacadabcacddccbbdbcddaadccbdcabbdcaacacbcdaddcabadcddbaacddbbbdbadacbcbbbdabbbcddbcdaddadaacadadddbccbbcaddbbabccadaabbadbabbccdbcdabdadcaacdabdcbdacbcabccdabdabdcdccdbcbcbbdbabdbcbbcdbbabcbabaccddadaabcdbbabbdccddbddbdacdddcaddbaaddbdcaaadcabcacabdcccdddbbbdabcbccabbbcbaccbcddbddaacdbdacaadabccaabaddbacbdacbaadaabcbbcdcddaccaddacaadddacbadbaadcdacdadbacaddabbdadacdddcbabbbccdabbcbbaddcdcaaddbdbbcbbaccddcaaacbdbbbdddbaadcdddbddbaccaabdaccacadbbbaddadbcbccdbccaaaabcdaccccacdbaddaddacbbdcdaadadaddadbdacabbdbbcacdccacddcddbabcacaaccbbddcaacacabbddbbcdcaaddddddbcbbcbcacdababcacababdccdbbcdabdddbabddcadbcdcbdcaddbdcdaadcbdbaacaacccddccddcdaddddabcdbbcbbdabbaaccccdbcabacbcdcdabdcbadadddaaabccbdbcaabadbbacaadcddbdacbbcbdcdbdcbcabcbaccdaccadcaadcdbcbcadacdbabbaacbdacaddabccaaccaaddcaacacbaababccdabdcbcddccbcdaabcbddabdcdcacbdaadcabccdcabcdcccaabdddcbbdbcbbbacddbadbbbbadcbdaaaaccaaadccddcabacddabcabbbbadacadaabcbdaacbdbbdabcdadbcccaacbcbbcdbbccbbbaacdddacbcdcadcdbaddacbbbdaddcbdbacbbbbcaddabbaadddcbdaccdabcdbbddbabbbabbdcddccaaacabdbdacdccaabcbdcddbcaadadadaabddddcacaddcddbdaddddbdcaabbccaccabdbbcdddcabaabddbcdcddbcaacbdbddbcdcbbddaabddaabadcdaccaacbacabbbdbdcadadaabbddcabbacccdccdbcbdcbdabddabbcdbadabcbbcccddddbbdbbddaacacdbbdbcbbaacadbddadcdddcccdbdbadadbbbaacbbbcdadcdacdcdcddabdadacbbcbdbdcdcbadddbccdccbacadbdadadcaadcadbdcbbbdbaddbccbcbdaccccccbccdadcdbdccdccbdbdaccdddcbddcabcbddadcdbcaacaadabbccabbbaccbbaacbabdaddacbdadddcddaccaddbdaabadcdddcbbabababadabcadcdcabcbbbacbddbddcbbbdcdbcbaaaabadbbccaddacbcddccadcdacdcdcdcbdbcccadbdabbdbcbabcdcccacabccbbdbccababaadbaacacabdcccbaaadcbaacbaaaabbdbbbdccbddaadcbacdadadbdcaccddabaadabadcbddbaccbcdabababdabccabaaddbbbcabdabcbdbcdcdacbbabdcbbddddbdabcccaacbcadacddbaddccccbbcacdbbcbadddaccdcadabdcddaddcbbbaaaadadccaccdabddbcdbddacadcbdbcacbccbbdaddbadaccbbaddcdacabcbbbbcbcbbbbccaaaacbdbcdbabdabdbcdcabcccaabccccbbaabcbabbdcbcbbaadcdadbacbdadccaddbdcacdcbcbacdddbcaadabcacacccbabaadbacdadbcddaccadbbccdcbaaadcbcbcbcbcccbddccdcccbbcbbdbcccbbaaaccdacdaaccbdccaacbaaaaaccbcabbdacdaababdcdddbbadadcaadcbdadcabdcbbbacaabddadbbdccbbdbcbdcbdadbdddcccbbbcddacdcaacaaaadadbbbbbdacbddbcadbcaccaaddbbdcdbccaabdaddccccccaababccdcccdabbcdbcaacbbaacaabcdddbadcbaacdddadacaacaddbcbdaacbabdbddcaabaddddabbacbadbdcbacacacbdaacdacbbcabbdaaccbbbdabbcbcdbcaabdbacabcccaddcdbcacdacbaadcbbbabbccadddcabcabbabddabdbcbaacddabcaccaabddcadadcbaacbbcccadcaaabbaaaaadadcaabbaaaacadddacdcddbbddabbddaaddcbddccbacababbadbaccaabcbabdccaadcdcabccddaadbdcbddcddddccdabdbdabdcbcbdbdcaacbdaaacddcccdccccaacaccabdcacacccdacacdcbdbacadcccbdbbadaaddabcbddddabcaadbcadbbadcbaacacdbaddddbddbcddbbcaaadabbdbbcdcacdbabbbbcaaddcacacdcbaccadacbbcdbbaabbcaaddbccdccbcdcbdcccadcdcacdbdbdbdcacddacdaccbadcbabadccdcdadadddbdccbcdcbcdaacabbcabccdccdbcadcccddcbcabcbcccdbddbcbdcaadcadbcdbbddbabaacaacddacacdaddbbdbabaabcaadabbbdcacdaadabddbddbabbcbcacdccdcadcccadbdacdcbcacddbabdccccabddbdacbdaabccdbdbbcbcbbcccabdabadabcaaadcddbbccadcbadaacacdaacacdccbbdadaacbcbcaadbacdcbbcdbdbadbbbcccddaabdaacbcadbdbcadaaaccadcdaaacbddddbdcbadbddccbbdaacdbadabdcdccabbddcbaddabcccabcaabdcdcbaaaaaacccaccadacbcddbdbbcddbcdddbbdaccdddccddbbccddacddabbccbbdbaacbaccacccaccbcbbcabbcbbddbababbcbadcbddbccdddcabddbdbddddadbcddbadbadbbcdcaaccdbcccdbadacbcacddbccdcdadcbdbdbccbbabaaddccbacabbadaacdcdccdddababcccbccdbadcabdcdccbaadbddbbbcbcabbcadaabddbdaccbabbdcadcacaabddbaabddcddcabbaaccccbddadabadabcadaadbabdbadbdbcddbcbdadbababdbaccdcabdddaabaadbbaddcabadcdcbbcbbbacabcbccdcbdaabdcdaccbadddaaadbdcacdcccbdbcbadccabbaadbbbbbccddaddbdcdddabdaccabcdabcbabbdcdbbadbadbccbcbabcdbabcdbcaadddbcaddcacbbcdcaaacdcbcbadbabdbbbadcacbdddaccbbcddcdbdbbcbccdadbbccbddcabaacdcadcdadbbabcbddcbcdacccccaccaabdacaccddacabcadcdccadcdacaadadcbdddbabcaccccccaddddadccdbabacbcadbbcdcaaabaaaabbdcabcbbcabbdbaadacaccadbccabcbbaccdccaadabbccaccdabcdabacdabdcbcbbabdcdbcbcddcccdaadccabcaddddbcbadbcdcccbbbadbaaaccabcbdcabcddadabdbcdcdbacdbccacbdacddadadccacaccdbbadbddbcdbdccccbbadaccbdbadbbbdddbdcbdbcbcabaabaaccadcbdaddadcaccdcacdacdbabcbcdcbcdcccbdbdbccdabcccacdbabcddbccababdbacdbcaddacbabcabbdcbdbdabdacdcadbbccabdccaccbbdcacbccdbabdbbbadacbabdaadbdbaacabbacdabddaccbdbccacccaadcdcaccbcbaaaccbbababdcaccbaaccadbabacabbdcbddcabcccdcbaddbdacbdabdbbbbcaccbbbdaaaabdcbccadbdabcadbbacbaccbbdcadbbabdbcdbdcccaaadaadbdbadbbbdccbaaccadbbbcabcccbdcdbddbcaadcaddddaacdabdacdcabddaabcbdbaaddbabccbdcbbaabaabcddcddbaabadbbaccdbaccccaaabdcdbaccdddbbbbdcbdacccdacbdbbacdbbbccadbadcddaadbddadabaacbcadadcbcabdacbbcdcbacaabccbbdbdcacbccbcbdbdbbccddcddcaadbccabacbacabdadcbaabacdccccbbbdadcdbdcbdabdbcdcbbcdacddcdabdcddbadbcbdbdbdaaadadcbbbacddabaaacdabdbabdadabcadcacdacdddabcdaccbdadbcabcacbddcdbbaadbcddcccacabcccdbddbdadbbbadaadacaababadacccccdcdcddbbcdcbdddddadadadbcaccabddcadbbbbadddbbdbadadabcaabcbabcbcdbcccdbdccdaadcbccdbbdbdcadccacaaacdcabbcacdcbdbdbcacacddcdbadbdcacbaccabdacdabcccdddaacacbddccdcddddabbaadddaccbbadbddcaaccdacdabcacbbcdddcaadbbdacbaaaadcdddbbccdacdcbcaaacdccbadccbbddacdcddddadcddbabcaaadddacbdcdbbaaaabacdaacbaabdccadbbddccdbbdabbadcdcbdcdcaccbaddcddbadbcbdcbcacaaadaadbaabdaccdddaabcaccbcbcdcabcdaddabddbdccbddabbbbbbdcaadddbbbcbddcabccacacddaadacacbddcbacdccadbaabcadadddcaaddbccabccbbcacbdcdbbabbcdcddbacdabcccdcddaddabccdaaaddacbbdddadaadadcaddcdbcdddbdcdadbbddcabcadccddadbccabbccbddcbcacbbccbcabcdaadccaddcddcacddddadcbabbbbcadcacbabbcccdbbcdccbaadaadcabdcddabaaccadddbbbdabccddacaddaadacdcdbbbbacbdcadbaaadbbddacaadcbacabcbbaaabcabdcdcdbddccdccbaadabcbddcaddbdabbbabccaadaccbdbcbaddaadddddbdcdddaddaddaabcccabdaddddabbaabbdbadaccabddbbadcdddbbaabbcdddcbaddbddadbdabcddbccbdaccbcbacaacddccdcadbabbdbabbcbadaccdcccdcccaadabdbcaaacacdcbacbbbcccacdddadcadacacaacdadabcbddcadbccabaacbcbcdabcddaabaabbcabaccadabbdaaddbcbcdaacbccacaddcbabbaddbaacccdaddbdcccaaccbbdabaabbadcbaaddadcabdcdcdaadcabbdcbdddabbbcdacaacbacddbdacdbbdcaadbcbbadcaabadacacdbbdcbdaaabbccbadbdabdbaacddcbaacdccbddcdbcdbdbdabdabaaaaddcdbaabcdcbbbabcbbaaaddaaabbdacbcbaababdcdcdbbacbdbadbdcbbbbaabbccaabccbbddcdcbbdddddddbadcaadccabcdabcacbcbaabcbcbbaaacdcabcacaaccaccdddbcbadbccbbbdcdcbabaddadccbabcddbcabaaddcadbabbabcbabaabddbbddadbdadcaabbaabcbcbbbabadadbbadacccaddccdcdcabdadbadcbcdadcababddddddababdacdcbabccdadabbbdcddadbcccdbacaccbdcdcababbabcdbdbcdddbdcdcbbadbbadbdbcbcbacaccbcadcbbdccccaccababacdadacbcacacddbcdaadadcdbbbacbcddaabcacddbcccbccababbbbddcaddbadbdcbcbacaadbcdbdddccbaacaaabdbccbddadcdbacadbcabccbbbadbdbdbaddcbddcabdcaccbddbaaacabbcabcaacdcdaabaabaaacbcaddaacabbabbcccccacdbaaddbbcddbdcdbabbbabddabdadaaccccdabaccadaaabaacdbbbcbdccaccadbbcccaacadbbcbabadbcbcabbaabbdbdddabbacbdcdcdcccaadcadcdaacbcbabdaddccdacbbbacadbbbbdbacdbdbbacbcbcbcbabdbbbbccccccaabdbcaaaabbbccddaacbdcbdcaddcddccadcbbacddbdacdccdacddbbccaadbabbcadccccdccdbadabdbcacddaacdacbddabccdbbddadacabbaaabdddcdcdbcbdddbbadbaabdbcbdadabcccbcccbacabccaccbdcadcbabbaabcaaadddbabccbdbadcadcbabbadbbacbcacabccdbcdbbdcbcddabacaadccdbbdbabbccdbaaacaddabbcdbdcbccdacaddbcaacdcbdabbababccbcccabbdcadddbaadddbccddcbbadadaadcadcbdbbbabbccccaccadacacadabbbdabbacbdaaccbdbcabccbabdcbbddaddbbbcbcbbdddcaabbdddadcddacbccdcccdcbbcabcdccddbcacdbaacddcdccbbdaabdbdabdabaabbbaccbccdbccaccdadabddbbadbbdcbaccdabaacbbaddcbabadccccbdccbabbbccabbbadcbadbccdbbccccdadcbcacdbbcbacdaabccdcbcaacdcadbdcbadbcbbcddbaaabbadccaabcccacbacabbbacdccdddbabacdaacddadcadacacabbaaabadcbaddcccbddcccadcbcbdddaabcadcddbacdbcccaabcddbcbbcbcbabccdcbacbcdcadadacdcacddbcbddcdaacacccddbaabaddadccbcbbbcabdbcbcdcacdcbcadacadaccabccbacadacbabaabdadcbddaddaaaabdbabacbbcbddcbcbacdbcbcbccbdaadcbbbcabccbdbabcbcddaddbddbdbdbbbbcbacbadaddbdcaccbabbcccdbdababcdabadababcdaadddabcccaacacabadabdbabaccbdddbddacddcacddbdccacbddcbdddabdaacccbcbaaabaaacdadbcdcdabddbddbcbbbaadadccabbbbbadaadbacddababcdadccbbbbcadaabbbdcacbdcbdccaabdbdaddabccbbdbccddbbddbdddddcadbaaadccaabddcdddcbadbbaabaabcacdddaadbbadbdcdcbdadadbabdadcdbbddbdbddcbbadcaccaabaccccaabdcbadbcccbcdbacacbbaadbdbbddccbccdacbabadcddadcdcaaaadbbbddcbaacbbdacaacbabdadaabddddcbaccaccbacaccdbcdaacaccdbdcaddbaddcbbaaaacdbaddbbadcbbcadcddaaabaaccbcaccaacadbdccbadcccdcccaaadbdbbddcbbbcdcbbacdbaabadaacdbddbbbacccbdcdbbaabbdbbacdbbbcdcdcbacadcbdcdcacbdacbbadcdaabbcbaabdbaaddaddbacdaddbccbbdcdbabcbdcbabcbaaaccbbabaddbccdbaaddadbbbcddadadcdaacbbcdccbdbddadadccabdcbdcbaacacbaccadbabcbabbdabbddbdcbddcddcababdcabbbbadacbdddacbaddadabdbdccaaabdbbbccbdabadabacccddababbdacbcccbaddcbcdbabaaddbadacaaabbaaddcbdbabbccbaddabbacaaaddaadcdbbbbdaaadcabbaabcaabbdcdbdbdcaabccabacdccbabdbadacdbcccadcbcbdccddbdacadcbdacabbabaccabdbdbabcbdabadcaadabbacdcbbddcdbaacddabdaacabdbdbcddbabacaadcbdbbabbbabcdbadcbbbbcdbbcbddcdcccbdcddcdbdcadacabccaacccbbbbcacbbacdadbadcabccaddcbccadcaaacdacbdaacdddccadabaaacdcbbcdcaddccabbbdcabaababcacabdbbbcabbadddbabddababccbacddbbabbbacbdddccbbabbacbbbddaddcbdcdccdaaadbbcabdaacabdbbabccabcbcadcadcdbccaacbaacbbabdaaacdbbcabdbbacddacccadacbabdddadacdbdaaaaddacdabbcadbcbcadaccbbdabcadcbacaddcadddbdccbddadcaddaddbccddadabcdabddccbcdacdddcdcdcbbdabacccdabdaaddaccaabaaacbcdaddabbabddabdabaadbbbcaacdaaadbbcdcacdbabcbcadcadbcacdddaaccbdabbacdcdbccbddacdcbddbdabdccbaddaacbdcdbbcbdaddacddabadacbddabdbaacabbabdbddcadddbdbbaabccccaccacbaaadbdbcdacbbaadcdbcdabbdaccbbcdddbdbcdadbabacbdaadacbdccbbddbdabdacdadaabadbdcbaddbabdcbddabcbbbcdddabaabbaddcdadaddbccaddadbacabcdbbcdcdbddbdcabbcbbdaddddbbdbaddbcbbdbdcaddccbbbbddbaabacbacaaadaadbacabbaadccddaabcacddacccdddabccdaccdaacddcabcaccdcdabcaddacccabbbccbaccddccbadcbdbdadcdbbadccdbdadadaacdbadddcbcddbacaccdccdbadcddcccabbbbccbcccabbdbacddbcaacaabcacddcbadabbabadbccbabbdbcccddbabcbdddbadbcaacbbcdbdbcddaabcddccabdbdbbbbaaadcbbbcaccdbabbadadabadbaabaaaadccbdacacdaccadcababaadabbdadcabcaabbadcdddcdbacdbddaabddbbbabcdbacaacdaaacdbcbdaabbcbabddadacddccbdccbcabcaadadadbadbbbadcccbcadacdbbcacdbdcaccdadddadbaadbccccaaababcabdbcbdadacdccccbbddbbcabadbdbccaaaddbaabbdbaddbabbcaabdaacaacbdcbbbabcdcbacccdcdbbbdccbccbbcccdbdcbddcddbbccbacbaddcdadbacbddbbdccadccbcbaabacbbadcddbdcbbabdadaabbdcabbddcbcaabdcdcbbcdbdbccdbdbacdbddcbccabdbdcacbcaaaaacddcbcbcabdbdaabacddcacdcadddbbdddcddcabdcccbcdaccaaacabdbdbaccacadccbacccdbadbcdbdbccbdabbbdadcdbbbdcbbaaadcccacdddbaaabccbbdbddbddcccdbacdcdddaacbaacdccaccbadbacdaaaaccbbadadbbadcbaacbdcbacaabcccaccccdbbaddbcbaaccdaddabdbcbdabbcabcaaacddacdccbcabaacbcbdcaaabaaddaaacbdbadcdbbbcccadbcdbdccaadddddcbccabbadddadbcccbdabaddadaddbdcccccbbcabcdcbaaaabbbcdabacaddacddabaabbbbabdcbcbcdcaccaadbdcbaddcbccdcabacacbcacccbabbacbbcbacaadddabbdabcbacbbabdcacacdcdbacabbabbddddcdaabbbbacbccdccbbaabcbbcbbbadbbbcdcbbbbdcddacbbbadacdcdcccccccacaabbcbdcabdbcccccbdbcbdbddcdadcbddcaacadacdadbcdbdadbbcabcbdcbbaaabdbbddbabadcdcdddcddcccadbdbbcbbdaacdcbaaaadbacdbadaabaacbdbdacdaacdbccaddabadddbabbaabdcdbabcdbdbcbbdbbbddabcaabccacaabadadbbdcbddcabbdcbdadbababcaccbbdddccacdccdbabdcadcdcbaaccabcbadcadababacbabcaabaaadccaacacacabcddaabaddacbdbacaabccabddaaacacdbaaacdbbccacbbccaabadcbbdbcdddcbaadddababbdbcccccbadcbabbcbbcaccaacabbaccbdcbadbbabccbadcacdcdcaacbdaabcdcdababbcaaddcabccdabbbcaadbcddcaaaaadaaacbdbdcabcbaacaccbaccdbccabdbbbbcdacbdccbcdbbcdcbaabcaadaacddcbaccccdbdcdbdbcddabcdcacbbbbbbbdddbabcbacdddabaaacabadbbdbaaaabccdbdbdcadbdcdadbcddbcbbadcdbaacbbcbcadbcdcdddccdbdcacdcccbddccddbbccbcdbbacdccaababadbacdaaadbdacbabdbbaadacbdadacaadaddcbbbdcadbdddaccdddbbbddbcabacadaacbcabcadadcbcdacdabbaabbaacccbbadbdadcabdaaacababbdbacbdbabaabcdabdbaabaccccbcccaaabcccbabadabcaddcaacaabdcbacbcacbcdbabcbdacaccbaaacabbcdbadaadbdbdbdbaadbaababcaaacddcdddbddaddbabbdaacbabadadadbbbacaddaaacadbcdcbdbbdcdbdbcbcdbadaaccdaddcbbcabdddadcbccdccaccbabbcdcddacccdaccbaabbddbbcdbddababadbabacbcbbbbbaaddcdcaaaaaabbaaddbadbdbdcbdddcdababcbadccacdbdbcdacadabbdaaddcdadacdacdbcbaaabacaacddabacdbbccacaaabaaaaaaacdcacaadbcbaadbdddbaaaaddccccadcabadccbcbadcdcacadbdccaaccddcdbbdbbccbadcccddadbcbdccbacdbccdadcacbcddaaabdbadbadcdbdbbadbcbcbadccbbcbbabbcabcaacddcadbcddbcbcaaadcaadbbcadcaaabcdccaccddcbcdaacdaaaacbbcaaaadcdadacdadbcccccbddaccaccadccbacccdaacadbacdcacccbacbdddaccadcadbabaacdcdaccccdbacbadadcbacddccddcbabcdabccbabdcbddccdccddaaaddaccdccddadaabbcdbcdbadbbdcabaaacdbccbcabacdaabbddbddaccccdabaaaccbcaadddbacadccbbcadcbcabbddcdcbadbbabaadacdaaaabcaabbbdccbdddbbdcabcaddabbbbcaddadacddbbdbddbdaaabaddbbdbdccccdacdcbadbccbaadbccbdacbaccccbcadddabdcdcdbdbcbadcddaabbccdabcacdacadcbbccbbaadadabcacbbaadccacbbbaccadadcbcdcaddcbccbddacabddaddabaadcbbbcbbddbcbddbbddabbbcaccaddadacbbcbcaacacadadbcdcdcdccacdbbdadcbbacbddccddbbcadcccccadadcaaadbdbdcbaadbaacbcbadbcccaccadbbabcbddbdddddbcccbcaaaaccabacabaaaadcdaabaccbccabbdaddbccbbbbcccdbbaaabaaabbddaddcacddccddabcdcdbdddbbbcabdbcdbcccbbddadccdcbdacadddacbcaddcaacdddbdcadccdbbddbccdbaddbdbdadbaabcdbdbaaaacdccbbbbbacacdacdbbccdbbcdcdccbbdbbbdbababcdbbaaddabaaddaabacabbdcbaaaacdcbccadbbbdaccbbaabadabbaddbabdcbbadcbdcdadddbacdcdccaddddcdbacbdcbadcbbcdaaabcbcaaadadbaccdacbdadcaadadaabbabacaaabbbbaabbbdaabaaaddcaddbadaacbadbdbadcbccaccdddbdcddacdabbdbaacbbbccadccdbddcacabaaccacaccdabdaabbbabbbcbbabcddcabaabccbcaabadbcadcaccdbdcaabddcaddaadcababbcdabaacbbacdcddccdbdccdbcdadcbabccbbbddcbdbacabbcdaccbcbbacababacdaacacaccaaddcbdaddbabababbbbbcdbabadbcadcbacbcdbadaacbacdbcddcbcaabbddacadccbdbdabacdcabddbbccdcdbcdbadcbcdadabbdddcddbbacbdacbcbcadadaddacadbddaadccddcbccabbbbaababbdbdbbacdcacdccbbabbcacaabbcdccdadcdabbcbbdacadddaddbbbaccddabbcaddbbaaaacbdaaadabaaacabbddadacdcdbdaccadbbdadaccbacdbdcabababdbdadaaaddddcbcaaacbcddaaabbbbcdccddddabbdaaaabcbcabbaaacadbdcdbacbaaddcbbcababaaabbaaddcbddcddcbcdcddddcbabbbdcbdcabadacabccdbbcadcccaacbbcababcaccacaccacbadacdccadadddddabdadcddbaaadbdddcddabaaabbaadbadbdcdabdbadcdddcbcbcbadcdbcdccabdbcddcddcccdbcddddbccabbacadbccbaadcaabccaccdddbccccaddbcdaddbaabdacdabbcbbcaccdadbdbacdcbbbbbbbaababbaabaccdbaadcdaccbcddccdacbadcdbaaccdbccbacdaadddcbcdccabccdbaabbccdbbacbcdbcabccabadaaaabaccaddbdccbdccdbddccaaabcbdbbdccbbaddccdccbbaadbcbdaacaddaacbadacddaccaadcdadcbacaaabaddadbaabcbbbcaddbdcaaccbaccddcbacaddacbddddacccadaacdbadbacaaccccadabbcbdddbaadbadcacdbabccdbdaabcbacadccbbcdbabaabccabddcadaadbcbccabdbcdcabdbaaaabdaccaabacdbdbaddcdbbcccdbbcbcacbbadbccdadcbdaaaddabdbdbdddddacdadacaacbcadbbccbaccabdcabbcaaacaaabdaadbbdbcdcbaababdbdcbbcdacbccabcdabccdcdcadcdcacdbbbdadbbacdbdcccbadbdddcaadabddbdaccbdbbacacdacbdddcdbbbcbdbdbcbccbababcaadaadcdcbaddcaacdadcdcabbcccddcaacbbbaaadbbaddadacdabddacbbaccadabcccbdccbccdccaaacacddacdbcdcbcbacdbacdabbcaabbddcabbbaadccdadbaabdccacdabdcbcacdcdcdbcddddccabbaacaacdbcbaddadbcabbbdccbcbacbbaababaabdbbadaacdadbaddabcadabcbadaabddcccadabcaacbdbaadcdbdadbdaddaadcccabcaabddbbabaabcbccabdcbcdbcaaadadddcddddddaccdabbbaccbdddbccbbdaadbdabdbbadccbdabdbcdcacccbcadcaabdabadddddddcabbbbaadaadcdbcabbdccdbdbbcdcdcdccbadcccaadaaddacbdadcdaddacdaabcacaacbcbadcabccabcbddcdddaddabbbdbdbcbbdcabadabbaaaddbacabbbbcaaabcaddbccaadabbacbbacacbbbbcdcaccbccdcabbaaccaaaaddaaaacbbcbacdcaadbccbabbdbaddaacbabdabcdcaacabdccaacbcdccdcdadacbdbabbccbcdcddbcabcbcbdaaadacbabbaacdccdbadabadaaccddbdddcdbcaaacbbdadacdccbbaadcdcddbbdbacccbdabaacaddcabbdaaccacccbabbbcddbdbccabdbbabcacaadbbbddcaddbbdbbababcbbcdcbddddbacbdbcddddddaababbcbcabdcaccccdabcbcdcacbbabcabbdcaaacaaabadcbdcccccdcaabaabaddcbabacbcdddbadcaddcdacadcbdddcadddaddaaacacdacabbddcbabccaccabacabaaddccdbbcbbddaddcbddddbacaaabaccbdcabcbabccaaabbccddbbbaddbcbcdadbbacbbcdcabdddaddbddddabcbaccdacacbababdacadcbcdbdbdcbdcdcaacaaaabccacaaaaaaddbabccccdcbdbdaabaddccbdabadccdbddaccbdddbbdadcdddbacaaabdbacdaacbccbcadbbacbabbadaadbaaadabbbdcbdcddacbdcadbbccdaaddbababdabbcdbbaaaabcdbdcddacddcdacabcdaabbadbbbddadbdaddaadcccccdbadcbcbacddcabbcdbdcbdbccdadbbcabacaacabccabbbdccbcaacccabddbbdcdcbabcdcbcdadcccaadbbddcccaccbdcbbbbaccdccddaccbcccccccbbdddccaaaacccdbdbbcacbcacdabdadcbddbadadababddbabcbddadaccdbccacbcaadacdccadbbddacadaaaddcddbadadccacddadddcacaacbddbbbcbbdcccbbdabdddccadadcbbbcccacddacaadbdcabacacdabdacbbddddcbbcadccddacdbadbdaaadddadbccbadaccadcbcacbdbcadcdcdbcaabbdacaaabdddcaaacabccacdddabcbdbaadaccbacdcadbadadcdabdabcbcdccbdbaabaccbbddcacaabadacaaadabadbbccddababccbbdaccbadabadbbadcaaabdddaddbabdcddbdcbabcabbccdcacbdbbdabddcaaadacdbbbccccdcacbcbdcbaabadcccabcdcabdddddbcbaacdddaabbccabbbacccccaacabbabcabacbcbabbacdbcadabdabcaacccdbbaadbbdaabacbbbcdddcaacbddabdcddccdadbbcaddbddbcbcdddcdbcbaaaaaacbbacccabacdbadadcbcdcacdddbbbbcccadbcbacbabcbdccabdbbcacdbdbcdaddaccdbadcdbbcacbbdcbadabdcabdbcdabaabdbdabbbddabacbcbcacdcbcccdaacbbcaabaaccdacdbcdadababdccacbadcccbddddcaacddbccdacabdbcbbcccbcccbdddbdaaccdaccbaccabcccdcbbaabbdcbadbcaadbdacdbabaaaabdabbdcadcbbbacdabbdadbaccdabbccacbbddddcbbbdcaacbddcadcbcbaaacdcdaaccabbdbddadaaabcdaababdadcbabbdcaaabacacdbacccdcbcaacabdbdcdcddabcdaccdddcbcdaccdadbcbaabbcdacaacddcbabbddccbbdcadbccccaabbadbabddcdabbaaaccbacbcbbdacdbbbaabdbaabaccdcacabccaddaacbdcaadcaccbbbccbabadacaaaddcaabcdccadcadccabccdabadacbbabdaaccabcbabaacbbcdcbadccabdbcadacbdcadccabadbccdacdabbaabbdabbcaabcbcabdabcccdccbdbddabccadbbbbaccbcdbbcbcdcbadcadbdadacccdbbdbabdcbbbabcddabdbdabcabbbaddabbadacdbaabcdabdaabbccccadabcbacbadbacdaddccbbaccaaddbdccccccbaaddbcabdbbbadccbcacbbbacdabcadcdcdbadaadbdccbcbbccabcabdcdbaddcddbaabdcdcccbbbdcaabdddabbadbaacacdabccaabadbcdabadababbbabaccdcabcbcbccbabdbcaddccbdbcdccaabbdddddcbacacbbadbdbcabcbdabdbdabdbbbbddaccbbcdadcabaaaadacdadabdadbdaababbcaacaccbaadcaabbadabbacbabbadcccbaddabddcdbcabadcbaddcdbabacdaacaabcababdcbbbdaabbaccbccccdcacadcabbdaaccbaabbbaddcaabbcabbbbdacdadabdbdaabaccddabaacadadaabdabaaaaadcaccaccdddabbdbccadcbaaacacabcccadadadbcacbcdaccaabbbaccdadbdbdcacccadaccbcbbdcdbcbabccacabdbbbabbbbcdbbaacdbaddccdcacbddabdbccaaabadcaccadccccbddbbccccdacbacdccabbbdcaccdaaaddcbabbadbadbcaaccacacabdbcbcaabbccbbbdddabaddbccabcdabddbddcbcbbbaacccadbaccaacbbbddadcdbcbcdbcadabddcaaacbcdbbabbcddaaccccbaadbabbcdcacacbbbbdcacacabaadbcdcbabdcabdabcdcabcbdcdcabdbabcdacdabdbbadbbacacccaaacbcdcabbdddcbbdabcbdddccddbdadbddaabbcababcddcbddbabbdcbabbbbbaddddadbddbbacdbadaccdabddcdcbbbdcdaabaacdccbbcbbdcbbaadbacdabaaacdaadbcbbbcddacacaaddbdaaccaddbddccabdacbacbabbacaabacbbbbccabbdabdacdaadbdcbcddbabadbcdbabacddcacdbabdddbadbbcadbcccacdcbcbdadaadbcaabdacbacdbadadcbbabaaaaaddaccccdaddccdadcbbaadabcabbcdcbbdcabcacacdbcacccacbdabdababadbdbcbadadbddccdbbdaccddbcbcbcdbcaaaccdcbaddccdbdaabbccabadacabacadcbccdaddcdadacdccaabcabdbaadabcabcbababcddaddadaccdbdbdbbdbbaaacaddaadcacddacbcbadaccbcdaadcbdaaccbcbccadadddddaaccbbbabdbddcccdcaabaccacdabcaddbabcddadbaadabcacccbcdabbbcdcbaccdddbcddaaabccccdbdaaaddcbbbddcdbbdcdbaacdddcabdbbbabcbccdcbbdabdcbabcbcdcbacbdcdaaddbbdadbcbdaccdcdbdccaabdbaabcabcabaaabbbcaaabddcbbcbcdadbcbbccccbdaadabdacccbbccaacaacabcaddcaadaacdabacbbcdbcbdbcdbdabdcadadbaabbbbaababbdcbacadbccbadcdabbbcacbcdadbbbbdbaaabddcbadacadacddaacddcabcaaddbbddadabdcdbbcdacddacbdaaadcbaddcaacdccbdbadbdbacddddcacadadbcacabdddcbdccbdbaccdaacbccdbbdbbdbbbccccdcadcabacdcbabbacdbdabacbddacdcaabccabcdbccabbbbccbddccbabcdadaccaddddbddddbbcabdacbbdabdcbcdddbaaddaadbabbacabdbcabdbbabcadadddbdccdacddcbaddcbaaabbcabdbcdbabcbacdaccbccddadddcdcabbaddacbadacdaabbbcaccaaccbdbaadbcaacbdbaccbaaddbbbdaaddabdaacbbdbacdcaadbcaadbcdaacdcbddcbcbbacacaddddacbcaaccbddbccaacaccccdcdbabdbcacdccdbacbcdacbbaaaabaaaabdbaddbbdbbbcddbabcbcabccdbcabaababcaabbcdaacdbdaddcbbbdaacdabbbabccbccdddaadcbaadbcdcbddadacccdaaaabbdbbbdbbacabcaddddaaddadaaaabdcdabdcaccddbacacadadbbccccbcadababddaadabcacddaddacddcccdadcddbbbcabcdcdbccdcddbbdadbbbaabcdaadcdcccbadcdacddcbdaacbcbcbbabbdbcabddddcaadadcaccbbbbcbbbdcbabaddabccdaadbbccbdcbdbaadcdbcdbddbcdbdaccdadcbbbcdaabdcdbbbcbcbbaabcbadcbdbaaaaddaaadaccbdadbbbbdadaabdbbdccdacdbcdccdaabbcbacddcbacaacbccdddbacabbbabaaddbcddbcccdbbbcddaaabcdddcaccaaabbddcbbbacacaabdbabcbcbdacbdccbdddabbabccdacdbbdadabddacabaccbacaaadbadabdbbdddadabdbccccbcdbdccbcbbdccccccddbacccdaaacdadbaddaaddcaaabcbdbdcadbaaadadadccadbbbbcbbdbcabadcbdbbcaadadbdcdbcbccacaabcadabdbdabbdabcdbcacccaddadbcdaabcddaaabdbbdbbbbcbadaadaddcabcdddaddadcbcabbddabdabacccbdbddcabcdabacaabcabdbacaaaadabbaaacddabaaccbdaacdcbadacaaaacbcdacdbcdbbcaadaddcdcbdaabcddbdbabaaacaaaaccdabdccbbaababbdbabadacbdcbcbdcacbbaccadadbaacabbbacbaccbadbbabddaddcdcdbcddabadbbcbccbdbccadacbcaacabacdacdcdcddccabcacacdacdcdccabbbadccccbdaacccdcdacaddbaddbaaddacddcdacbadabbdbaccbbbbabccabbaddcaccacaaabbadbaabdacbbadbcbadcdbbcccdbbacddabbdddabbcaaccdbbcabcddbcbbadddcdabcdbbbbccdbbdbacaddaaacadcddcbabaacdbcbbdbdabdcabddcbacbdcbadbccbdcccbdabaccddbbbbbcbdcddaccbcbbdbdddbabddbcbaddadbbcdcababbacacabccddbddcaabcbbaaacbbdadaaadbcbdbbacbdabcbdbaabcbcbbacbdbaaabbbdaaacbcaccdccabdadadbaaadbcbccdcbdabcbbdbbddacaacdcbbdddaacbdbddbdbdddadccaaaaadcdbabcdaadaaacbacdacbaabdbbdadcdbadacbcbbdacabaaaccdcbccddbbcbaccacccacdbdcdcddcabbddcaadabbdaadddabdbbacacccbcaacbddadcddbacbcbadbbdababbadcbaaacaaccbacadaccaacccbcbacdbacdabdabbdadadaddddbcaacdcbaddbcadcdbbddbaaaabadabcdacddabcdadaacbcbcabdbdcccbcababddbdbcabadabadcbdaadacabdabdddbdcaaccccdddbcabadadddcdabaadccbdddacccaccaadaaabcbadcacdcacbddbacaabbadcacacbcbbdbbaabbadcadbcacbaabadaccbcbddddbdcbdcddbabbcacaaadadbbbdcabbcdaabcbacdabaadcccccdbacbadaadcdcdccdadbddccabdcccbabdccacabaadccabbabbcaabdcdbaabbccadadcabcbbcacdcdbcbbdbaccaccdccdcadbbbabaabbbacaabbcaaacbdadadacabddadcacbabdddbbbdabcabcdbcdabadadbddccdaaccadbdddbcccbbaaacadbcdccacbdccbcbbdaacaaaccbbbdbdcbcccadddacabcdddddbadcaadccacddcbdcddbbbadbbadddaaaddbbbabbbaadabcdaddacddbbbadcbadcaabbcacaaadbcdccabadbddbcababadaaacbcbaccbdddabcbdccbdddbaccdcdabccdabadbacbbaabaacbbccdcabcdaacbcbbdbcbddaacbbdabbcbaaaabdadbabaaabaccdcabddcbcbadbacacadcacabbcacbcdacdcbbdbbdbdacbbdcbbdbacadccddcddcbdcccddacdcdbbababcbbaaddcaacacbbbdabcccacddbdaccccacddadddaadbbcdaabdbccdccdccccacbadbcbcbabddcbbbaabcabdacbadbdbbaabcadccbcdacbadbddabbadbbbdacbcdbabcacaccbdbcdbddbbaacdaacacbcdddabcbdacbcdbbdbcdccabbbbccacadaadcbddadaccbcccbdccadcdccbadadbbdbababacdccdacdbabbcbabaadbdcadccaacaccbabcdaaddcdccaaaacbddddbbcdddddbcbcdcaccaadaabbccddaadccbbabaccacbabddacbdadacdaaddddcbcdccddacbbdcacdbacdbcbcddaaddbbdbbdcbcaacadcdadaabddabaaabcbcdaadadacddcbccadabddcdbbbdadcacdaadaabbaabababddbabcdccadaaaaccbbdbbcbdcdcdaddadccaacdbbbcaccacadcbbbbdbdaaadaaabdcccabbbaabcdbdbbdbdaaddacdddaadbcbcdaaabaddbcbbbddbdcaaabbdbdbcaababacdcadbdddaddacdbaaaacaccadaadccaacbcbabcbabdbbadcbbddbdbaacaaabcdbddcdddabcccdcadccbccddbcabbcbacddcbabccacdcbdcbbbdcaccdaabcddddbdacaaccdbddbbadabacdcbcdbcccbcdbaaaccccdabcccbdcbcdbcdadccbdbcaaadbcdaabcdaabdccbddabadcadcccbcbcdccddddadbbcabbcbaaadcaddbbddddbaacaaaaabbdddaadabbbbaadbbabcdbbccabbcdacbbbdbaabdcbddaacbaabcccbccbdcbbddcabdccdcdaaccdddcddbcdacabcbbadcbcdcaacbbcddbdababbadbddbddcadabcbdadadcdaadaccbcabcaacbdacddbcddbbccdadddbbdabbadddabddddcdadaddbccbccadaacdaaabdddaaabbdbdacabcbdbabbdbaabdabdaaddbbaccbdbcbbddbddadcddcaddcacdcbcbcdbdbcbdccdbaddbbbbbbdbcacbdcbbacdabcabcaacaabdbcbcbdadcbbcdddcabdbacbdccccddcabacadaccadcdccddbabbdaacaadabccdbbabddcdcbaabdbcaaaadadadcdbbddcbcdadccaddccdddababddaacdcbcccdbabaadcadbdacdbbbcadccdaddaabbabcacccdbadcdddccddcbddcdbbbbadcddbacddaccabddbaaadccddacdbaccdbabccdcbbcdaddadddbbcabbdcddbbdadcddcbabbbdcdbdadcddbddbccbcddbdbbccbcdcbcdcdaadcbbddbabddbccdadcdbbabcbdccadcadbddbbababcdabadbcccdbdccabcbddbacccddcaacacdbddbcabdcbaabcbbbdadbaacadadddbaabcbbcbddbacdaadaaadbcdbaabdbbbdacdddcadbccbcacddcccddbabacbbcdbdbcccacbacbbabcdadcabbbdabaabacddcaaddbddcbcddbbcddcacbbddadcadaabcacbdadaccaacacadcdcdabbcdaabbaaddddabccaacbbbbbccadaadbbacdcadddacccadbcddcaaddbadabdccdcbbbcccacacddbdbddbaaddabdbacbabcdbbdadabdbcaaddcdabbccadcabbccdadadcdabbacacdbccabcbcdbbaadabbbdaabdadbbdadccccccbcdaccdacbcabcccdabbdacbbacaabcbcadbadcbbadcabcddbadbdadcbbddabcadbbdaabaabccbbadcdabaabccbbbbadadadbdcbabadbadbcdbccacadcdcabccdabacccbadbcccdcbcbbdcbcddbcbbcbadacdbacbcadabbddadbdaadacbcbadaacabdcccdddcacbadcccacccacdabcbdacbbdcaddddadcbcaddcccdbabbdcadbdbbabdccbbbcbbcadbbbdbcbbcadcabbcdcddaacbdbbcdbbaddcccbacddcadcacaadbdabbdadbaaccdcbcdbbcbcdadcbcacaaaadabcbcbaadcabbddbcdacdbccbcddbacbcbcbbbbdacdcdbadccadddbcbddabcaabadaaacccccaabcccbadcbcbadabdadbcbdaddccdacdbccbacbcbbbdacdcdcdacaaabbbccbabcccacbbddbcaabbcbacbaacbcaddaabdccadcaadabcbbababcbbabbdacddcbddbbddaaaabbcabccdacaabcddddabacdbbdddaddbacbacaccdddacaacbaaacaddabaccdaccaddcbcbbddbcaadbacacadcaabbaabccdbaaddccaabaccdcbadddcadbbbacddadaabddcdbbcdcabbacdcbdabdddbaccaaddabcadabcbdbcdbadcadcdabbcdcdccaacdcbbacbcbcbbdcccccacdcbcddadbbdaccadcccbdacdaadbacbabadcbaadbacdccbbaaddcbaaabdcdbbaaadddadabbdcdacabacdbdaabbdbddcbbbdbacdcbccabcdbacbbdacaacabbdabbdabadbbabbddabaccbdacdcddcddbbcdbbbcacbadcabbbaacdacbaddcbdcdacaabcbdcadbcdadaaadbcaaddaaccdbaddbdbdcddaccdadbcaaddbbcdcbccaacadccccbcdbaccaabbdccdacacdcbaaaddadcbbbaadcdccbcdaccccaaacabaddbadddabbabaabbbbcbbdbabbadabcdaaadcdaacccbcdabadcccbccaddccddaacbddddaabcabaccabdaaacdaabdddccacabcbdddcbacddbaaabdcdbdacbcbbbbcadadbdddadcdcdbdadcbaddcbaadbbbaacbdbdbabaacacdbbdcdcccabcbbccaddcacaadddbbbbccadabcbbddaaaadcaadcbabbababaaaadbabcadaccdcdbcccdaaaacbcbbacaaccacaccdadabbcadcbbdbbcddbaaadcadcabbbabbddbbbcdbbcbadddddabcbddbbccbbbddadbacbbdcbccdddcbdcdbccdccbcabdcbbdbaaacbaddcacaaddccacbcccbaaaddaadcddaaadacdcbbdcdacddbbcadcdbddccbacaacaacccbcbdcbbacdaadcadadabbabbdacddddacadabcacabaacccddaaccbabaacaccbcbcbabdacdabdbbbddcdbaccbaccdbdcbbadcdbbbcaacabcbadbaaacdbadcadbbaabbbbdcababccbbbccbdccadddbbbbcdbdcadccdddcccbbcdadbbcbcdccddddddbaacbaddcdccdbacddddaacdbacaadadcdcabbadbcddadccdaaaacbcdbbdddacbacbcbabbacaaaccdcdbcbabcbdcccadccbbabbdabadbbcdbbcdccdaabcdbcbaabdacbcccacaabbddbddcacccdddbabdbadcabaacbdaadbcdbccdacdbdbdbaddddbddbdaacaabdbbaccbabbcbcbcaddbdcddadcbbabaacbbcccabcccbdaaacdccabddbcddacdccdcdcdbdbbbbaaabbbcdadddcbcabcbdccadcacaddabbdbacdcbdacdcbaabcbcdcccdbbcaccbdcdddadcdcaaabadccbdcbbabcadadbdccdcabbdddcadbdabadcdbadabdddabdadbacaadbbacaddcbbcacbbdccddaccabbbabbdcbcbcadcbcdcbabaaacadcbdcddcbbbbcbcadaabcdaccaabccdbaacabcacacbcdabdcaadaadbacacabcddadccbbbcabccdbcdcbbdbdbbababdbadcbbbcbabbadbadcdbdaadccdbdaacbdccbcdcabbabaadbcbdbbaccdcbacdccadbccbccacbacbcaabbdbcabbaabbbcbaddaaaddabdbadddccacbaadadbcbdddbcbcbbcbccdccbcbcbacadabdccddcddbdcaccadddcaddacdbbabddaaadababbacddcaddbadbacabccddcbcbdccbdbdcbbaacdccbdcaabadcdbdcdcbbccacdbdbaabcaddbacaaacbccdacbccacaacbaccbdaacbacdcacdaaddbabbbbabcaacddcbbbcabbbbdcacdbcbadcaacadaabdccccacdabadddccaadcadbccbcaacbbccdbaacbabadabbadddbdbcbadcdccaaadcaabbacbaacdbdabddcbbbabdbcdadaacaabacbdcbcbbdbbbbbcdbdbbcdbabbdcddbdcdcbdbcbdccaccbbbbcacadbdbcabcbacabaadbabaccbddacaacabbccdacddbdbdaccdadcddccaacbcbdbbcacaadbbddbacdabbdbdccdacabdbccaaaccaaadcacdadbacdbaabbcbabddccaadddcaddcccbcdbadacbdbaadcdccaacdbccdcadbdaaabcbdababaabbacbbdcbbdbdcbacabaababadbaabcbddccdcccdcabbcdcdbcbcccaadcbaaadcbbbdabaacbcdaddcbbbcbbaacabbcaccccbdccaadcccddcbaadcbaddcccdccdaadddbacdbacbcdcbcaccdbacbcccadbdcbabdaccbbdcabcdabaddacabaabbcccacdaaadaaacccaccaddcbadadddadbbdacbcdacaadccddccdcdddccaacddbbabccbbcbaadcabdadbcccaddbcccdcbbdbabbabbddabccabbaabdcdbcdaccdbbdabcdcbcccdcbcbaccdbdbacbcbdbbbadbccccccbbdbdaddddddbacabcbccadabdaabcdadbbbdcdcbadbcadaddbbabdadcbccabccccbddccdccdaccdbbdaadbcccacddbabaaadddcaadabdddaadddaccbcbadccddddcabdcaccbabcdbbddbcadadabcabdcdaccbdaddbbccdaddcdbaaadbddadadabbcdbaaacacdddabcddcccdbccabdbcacbccdddbaadbcbcbadadcdcdbbbdbaabbabccbddbacdbcdbadbacddccbdbacacaadbbacbacbcdacdacdcabbdbbbaddbcdabbcbdcccbbccdabacdbdbddddcdabcbaacbaacabaadbcabbcaddabdcdbbdcbabcdadadbdcdcdabbcabdcaddbaddbcaacbaacaabacbdcadadacabccccdddbbaabcadddaddbaaabdcdaacbbddbbbabcbbcbcaabbadcabccccdbbdcaabbcdabdcaaabdacacdacaddcdcbdbaacaaccbdcabddbdbcaaabaabaccdbaaabbcdacbcbabbadcabbcabddbbbbcccacabdacabbabadcdcbdddbdaabdcdbdcbcddbababacccdddddbcbddbcdcadbbccccdbcbddcdadabdbcbcaabcbddcbbcddaabddcdbcdabdbdccaabdbdddaacabbddcbadadcccdabcdacaacdcbbcacccbbabbbbdddacacabcabccacdbddccdbacbcacbcabdbbacdbddbadbcccdabacbcbaabbdcaacdcdcbabddcdabcabadabdaddbbcbdbbbbcbacdababbdabcccbdcbbccadddddcdddabcaddabdadbddddabdccbabbbbdcbbcacacbcddaccddcccaaaccacbbccdbbccdcdccdaabbccaddcdadcccbcacbbaabbdcabcadbdaacaccbbaaccdbddbbcdbaccbbabbcabbdddbbcdcbccbbdaaccacddadddcdacdabdcbbdcbdcbdacdadbdaabbbbbdcadbcaccbcbacdbcdbdabadcbaacbaaaccaaaccbcdbcdbbcdabbadddbbbababbbcddbcaddadbdbabcaaccbdaddcadddbdbbbbdadccccdabcbcdcabbacbabbdcbaaadbdccbabbcaddbdddccadbccdbdabcdcbdbaabacbbaaccddacbdbcadccbddcbddbabbaadadbdbccabcbabbdcbabbcbabadacdadbbabdbcbcadcadbabccadaabdbdaacbbcbacadbaddbbabccadadcbbdcacaaaaadacccbcadaaabcababbcbcdbdcabacdbdbbcccbcadbccdddbabbbdbbcabbbbccacbddcdcdcabbaaccacaaddbadcacbcaadbadacadcbaacbaccadcbbabcccbbcababcdcaccdcdcacaacbcadccadacddaddaadddcadaababdddbbbdadbcacccbabbbcaabbabaadabbabcdbaddccaadcbaaabbdcdbbacdacabaddbcdbbacdcdcddaadadbbdaccabbccacbcbbdccbbcbcbbadbdacbabcbccdaddcdccbdbbdabccabddcaddddbdadacbddaacadbabadbbabdbacdababbabbaaddaccbbabacacdccdcddbacbcdacbadcacbaabbabaadacdadacacadaccbdababacaacbacbabddcdccdcbbbcaaaabbbcdcacddcbbcaaaaccdcdbdcbcdbdbbcbbdcddbdacaababdbcdcadabdbbabccabdddbddcbaaaabcabbdcddbcabcbdaabcccbbcabadddcccccddccdcbabbcccbbabccacbdbbcacacbcdcaacbcbdadbdbabaccadcbcdaadaabbcbbbccbbcbbdccaccbdaccdaabdcdadbccbcabbcadddcbcbbadcbcaaddaabbcdcdcaccadcbdacddbadacbbbccdcbcbdbbdaccabaabbabacccadcbdabbcdbcbddbbcdcbadabcbbcdadacbdbcddbbadbcacbddbbbdbccccbccccadabcbcdcdbcbddddbaabccbdcdbbcacddcadbadbabcbcbcbbdbbcbaddddcbdcacbbbaccddbaadcabccdcdabdccdbdadcbcdabdbabcdccbaabaaaabaabdaaabccbcccddcbdddbccbcbbdbddccbdbcbcacbdacdaabcdcdaaabddbacbddbbacbaabaccbadccdabaaddcdcbcaddbaaadcbcaddadbaadcaadccaaabadadacabdbcbdbbaadbcdbbbaababaddbdacbbabdbcbaaddbcddbccaccdcbdbadcccadbabcbddacddadcbdbcbaacdbdcabdbaccdbbcabbdbbbabccdccccdddbcbdddcacaabbabbccadabdbcbcaadbcadacbcaaaaccdbdacddccbabdaddcdaaadbadbcabbdbccaaadddadcccdcdddddcaaaababddacdadadbaacddbcbacbbbdcbdcdcbdcddcaccccdacddabcadbbaadcdaaaddaaabaadbbcdabcaadbddadbbdcabbbbadbdcdcdbccccdccadaabcbabadadbcdbbbaaadabaabdcaacddcabccadcbcabdcdcbbdaacabadbaccccccabcdbcdddbbadcccdbcadbddcdcbacacabddacddbcbdaacddbccbbaccbacaccaaaccdcabdabcbbabbcdddaabddbdbabdaaabddcdabbdcacbdcacaccbbdbabccacccbccaadccabbdddaaccdaccbaabcbdccbdbdabbcabdddabaadbcadbdadbbdbbdccdcccdccdcdccdaadcdbbcdccdccdabcdbbcacbcccdbbacdccbaddcabddadaaacadbabdccbdccbcbadbcbcddddcccbbadbcdcddcabaccaabbbbccbbdbbdcabdaccbddaaccadbdbcbacddbddcbcadacaaddddcdcdacdaccadbabbcbacccadabbbbdabdcaadaaadbabbadcbcbdacddaddcadcccadbaabccabbdbbbbbaacbaaddccdbdbbdbdddbaacbddcaadadbcacdadcabadbdbdcbdbcadaabbcaaabaadbdcdbccaaccdacbacddcbcbdccabccbdbdcbbbabcdbaabddcacdbccacccdaaabcaccbaaccabaaadbcaacbaddcbabaaccccaadbdacdccbcacdacdcdadbbabccbaabcccbdccacbcdadcacdaacbddacaacdcbddbadbaddacdabcbabcccccababcdbbcabdcdbaddbcadbadcdadccdacbacdbccccbdcabaabbbacacddbdcccbabddbddbbadbcdabdddacbaadabcacabcccdbcdbadcdacbccacbaababbbaccaaabdddbddbdabaacddadacccccdbcbababbabcccdbcddbddbddaaadcabadaacccacabdbaaabcbcaadddcaddbcddcdaacbadccadccddabddcaccbcddadaadbdbbabbbbdaacacdaddcdaaadcdabadbaaacaabbdacaddaabddacdabdbadbcbdbadadbbdbcbcbcbabaaadcbdababccbdcdbabbadccbbcccbdbdacdbdbabcadcdbadbaccdbbabdbcacbbaddbdbdaadabddddaadaaaccabdcaacdabdccdbccdbbcbbabaaccbbcdcaadbaaccbbadcccaddccbcdccacbbbdaccbddbdabaabbdbcaddacbdbabcbddbadabcbbabdbadddbdddaabccaccaabbadbababdbddadaccabaaddbbbcbbdcbcbcdcccbadabaccdacdbbcdacbbcdacadacccdcbadcaacdbbaccaacddcccdccccadcdbdbbabdddbdcbdadaabbcadadaadaadcadcadabbbaacbccadbbbabaacbdbdbbcbadaacbbdaabaccabaddbcbaddbdcdbbccbdaaabaaccbcdcddacdacdbcabbccbcbaccccbbaaccbbddccddbdcacaddcddbaabdaacbabacdbacdaacbdbaaddbdbaabbcdabcbcabbdbdccacacacadcddadadcbcaabbcbaddcbaccacdcddadcbbdccdaacdbbabdbacabaacabbbccbcdcdcdbbccaccddcbadbabbcabbdbcbababcddccdbbcccaabcccabbddbbabdbddddbbdaccabaccdbbdacdbdbddadacdccabacbacccadacbcddaadacbbcdbdcdbcbaccdbbcddbacdabcddcbcdaadcbadddabccbccbdcacbdbcdacaadccdcddaddcbaddcbabcdbbdbbbcbdbbdbdabbdcbbaadacabbcbbddccacbbdcbbcdcdbdbbdcbaaccdabdbcccdbcbacabcbdaddbabcabdbbcdbccabdbbadabbdacaadabaabbdbcbbbadbbcddcdbbdadcaabddccadddbbaddbacddbcccaadbcbcdcaaacbddbadcbbabaabdccbabacdacdcadacabbdddbbccbaabdabddaadbbbdbdcdaadbcbddcdbdccbaaadababbadbbbbdbadabaadadbcbaadbbdcbacacadababaddbcadabcbcacdddddadabbdbcacaaddcccacadcbcddcbcdbdadcdcddccbddbdabccadacbdadabcbcbdcbcccdababbbabaadddcadacbccbbdbaadbaaabbbcdbbdcbdbbdcbbaaacdadccdbdadbcddbaabdcdcdbbaaaddaaacdacadccacdabbdacaadcababdcddbacbdabacabaaadcabdbaabdccabcbdcbbcabdabbbabcbaaaacababdbbaaadabacadcbacdcccdcbbdabccbcbbbdccbccaacadddcdbdabdaadbaddaccbbabadbabddacdabdabdcbdddbcaacdadbdadcbacbbcbbbbdccbbccbaadabbaaacdccdcaaccbbdaaddcadcbcdbdddabbadcababdcbadddbbdccdbbcacaaadcaccaddacabbdcadbdddcdaaadacddcadccddbaccbabdcddcdbdcabacdbddabdcacccbcbbdaccbcdddbcbdbdcbdbaadcdcbccacaddcbbcabadcddaaacbdccacdcccbdbcacbdabcccdccdbaddbaacaddddbaadcccaaabaccdabdaccbadacaccaddbacccbcaaacbdbbdcddcbccbadcddbbabcabdddadbbbdaccdcaddabbbcaadaddccadddcaadaccaabadcbabdaadbdcddcadcbddcadbaadaaddbadaadbaccadabacbcbddadadacadacdaccbbdabbccdacddbcdbabdddacbbbaaabcccbadbcaadddabbbcabbdadaadacddcaaacabdadbccbcadbdabcdaabddbbaddaadacdbcdbbcbcbddddbacbaadcbbdbbdbdabdcbdacaaadcbccbbbdbbdcbacaadabbbaaabdddabbadabdaaaaaabaadccccddbcdacacabadbcdaadcdabdcaaaccabddaccaadbcdbdabbbaccbacadabbbbdbcabbbdbbadbccaadaacbccabcddcbaadabcabbdddcaddbbcaadcacdbbddcbaaabaaccdaacddddddcbcadadbcaacdcddcabaacadbacbcabcbbaacacdababbdcadcbcabadcbbdacbbaacdcdcbacadcbbabdadcbdcabdcbddaabdcbdbcbbcccbabcadbcccabcadcdabdddbbbdbddadbbcacdbdbbbdccbcaddaaadcdaacccbbbdcababdbadbaabcbcdaccdbddaacbcdcbcaaacbabbdabdcaadcdcbcccbaccbaacaacbbddccbccdaddcdabdbdcdcbbdbddbcbdbccccdcdaaabddcbadcbbaccdccdbcbaacddcadcadaacbcdbdccddccacaabdbddccdbdaabaadcbbdabbbcbaadddbbdccbbbcddadbcdcbdcdcbccdbdbacaadbabbadadccaaabcbbdccdcbadddcbdbbcabdcbbabbdbaccdaccabcbddadccdbdcaabbbddaabddbdcdbadbcbaddcbabaabadacdadadcddbbcdbbcccbaaaadddbdbcbdcbcdbbccbdccdccbbdabdaabdddccbbacddbccabcbbddbbcdcccbbcbdccccdcbaddccccabaadccadcacbdacbcdccabbcccdcbdbccbcdbdbadddddbbdbbdccadbdbddaaaacbabacabccddadaabdadabbcaddbbabcacddabcbddaacadcdbbbdbbdbaddccaabdcadbcdcccdbbacbadacbdcccdaddbccdddaadcbdcabbdccdbddcdbaaacbacbcacaddddbbadabdbccdcddbdcbdcbcddddbdaaabacdaadabadadadaabbdaccdddbbaddddbcbdadcbbdbbcccaddddabbacddbcdbdcacdbbadddaabacabcdcabcdaddadbdcacababaaaaaabbadbaabdddcccccbccadbccbdacaadacddabcbadbdaddbdccdaabbcacbdcccddcbacdbccacadaddbddcccdccbabbaaadaabcbcbadbdbdccaddcbddcdddcccdcbbacaabbabbbbbdacddaadacdaddacdacabcbbcdddbaddaabccaadcaddccabbcbdadbbbddbdaddbbdbadcccabdbcbcadcabddcdacbaababbacbcabadccdcdadadabadcbcbccaadbccaddcdaccbbccbdabdcdbbbaacbcddacdcccaadaccadabcddbcbababdbdadcdabcdbbbdddcadbbbdacbaacddacdaaacdbaabcbaaabaaadbcdcbadadbbdbdcbbdbdcdddacbbaacdccadcddcacddbbadcadcadadcbdaabbbaadaaaabcdcbbaaabbbbabdbcaaadacaabcbcddcbbddadadbabccdcacadacbcdddccbdbaacabccdcbddbcccbacbccbdbcccccccbcdadadabaddbbdbddddabddbbadddccdbbabdabcabcbcbdadddbbacaabbaaacdaadbbcddadcbbdcbdbdbacaddacccbadacbcdcbbdbddddbdbbdccccbcdbabbdddbcddadbdabaacbcacdabcbbdbacdcabdcacddcbbabdcccadbccbcacbcdacaaacccaddcbcdaadaccccadbcbddabdbbacadcbaddacccdbcaaddcadccdabbcccbcaabdadbcbbbdcdbaaacccdcbddacadddbaaacbdadabcaddacadacccdccbdccabbabbbcddcbbcdcadbaacdadabbacdaacddddcdccbcaacbaccbabccccaddbddcdccbccaacbbdbadabadcbcbbbacbcdbbdcddababdcbbbabdacbcadbdcacbadcabacaddccccbdcbbbcdccddcaaabaccabdacddaacdcdbacabcdccccdcadbccdaaaaccabccbcbbccbbccadcacaddbbbadacbbacbbdcdacdaddaadbadabbdabbccdaabacabcadadcabdbababdadbacbababbaddcaaadbccbadadbcbdadbaacdccabdabbabcbdbcbbcdadddbbcabcccbccadabccccbbcddabbabdcdbadbdcbaaccbcbcbdcdddcbaacdcbcabadcabaddddddacbbdadbcbacaacbaaacbacaaccdddaacddcbcbaaccccddabcbccbbdadcbacccaabaddaaacbdcbbcabbddadacccabcddddbdaddccbabbdcbbbcccbabddacacabdbbbbdbcdbdbbcabadcdccbbdddadcdbabaabbbcbdaacdadabacaabcbccbacddccbdadacabdcbcbbacdacdcdcadbcbbbdbcaaabcabbdacadaaabddccdcaadccccdbcdcccdbcddbbaadbbdabcadcbdbccdddaabacdaccabaddaadcaaacbbbbbabccbdbcaabaacdcacabdbdcccbaabadddddbbdaabccbcccddbbdcadadadddacdabaaacacadadddcbbaadbadcddacbaabdbababcccacdbbaddccbaacaccaababcdbbccdbbabddcdddcbdadbbbaaaadcbacdaddddacdabdccbdcbdabdccbbdbcbabdacababbaabdccddacaabbcadadaacbbdcbdbcdbcdacdaaddbadaacabaccbaadbdddcacbcbcdaccaddabbdacdabddaddbdddbbdabacccddcbbcdbbdcbabdccbabcaabaacdabbbcccbbcdbcaadbabaddcaaddaacbdccacaaddacaccbcddbaabcdbcacabdbcbaddcbaaabbbaccaabbbadbbdccbdbbbabbbddadabadbbbacbcdbabdccbddaccadbabcaacbcaccbbcddacbacadbbbdcaacacbabacbcdcccdccbbccdcddcdcbbabcbcababcbacaddcdbcaacddddbbbbcdcaccbbddcbbaaddddbbcaabbdadaacdaccdcdccddcacbabbaccbcbbadaaaabbbbccaaccccdacbddcadbcccadbcacbddccdabdacacadadaccbcadadaccdbbaddbbccadcabaadadcddacbcaacbcaababaacbccabbcadcbcdaadcccadcbcdababdbdcdbcbbdcbadcbdcdaccddbcdcbccdadbdcaacadaabbbddbcbdadbdabdbdcddabbdbaaadabbabddbcbdbdcbdcbabcddcdabcabaadcdccbcbdabdabdaababbcbaadadccddbbaabadcacdcdabbccdacccbcaaabdbdaabaacdcabbcbbcabbbaccdcabdbcddbadcababbcccdbacabbbdabddcdbaabbddababaacacbabdcbcbbaaabdbaddaabbbbbccacccdddaaaacdcdadaaadcdbbccaadbacbbbabbdbcddcaabdbdaccddaaabdccabdacccbcbabacccbbcbbdcadabbdddacbaadcadccacabdcaccaadaadadadccadcadbccadcaaadaddcdbdacabaaaacdcbbcdbdddbbaddaddddcdbdadacbacdbbccbdbdcdccbbdcadbcadaababddcbcbcbcaacaccbabcdddcdbdcdcadbabaacacdccbddbcbacadaccbcddccbdbacdaaccaacacacadbcbcadbcdcdcbbbacabcccacbddabcacacaccabbaadcbbaddddcdddccababdcabbacbcbbbacccadacdabccdbbaaacbabccdadabcadaccbaabcdbdaaadadcccccabcbdaaadaaddbdcbdddcadcccadbacadcaababdacaabbacbaadddacadcddcdabcbaadbcdabcddbbdbbaaccbbadabdccddcdbaaccbadcabbccaaacbddcbdbbcadbcadaccaccaddabbdaacabbbbaddcbaabbcacdcbcccadbccbbbacbdaadcaadabcddbdbacbabacddcdbacdabddacaccabdcdbbcdaaacbcabdddbdaababdbacaaccaaacdabbaacccaccacbbcddbbacdabcbcbcabdcaddabddaddbbbdccddaaabdabaaababccacddbacabaaaccadcbdaacdcacccdabdcddbcbcdbcccaddabbbacdbabdadcdbddaddccbccbccdbccdbadabdacdbcbaabdcaababcbbadaabdacdbbdbbabacccbccdcddddabacddccacdddcdabacdcbaccaaccaaabcaccadbcccabbddccbccbdcccdcbdaabadbbacadbaaccdcbdbaccddbbdabdbccaacdaccddcbbadaabaccadcacdadbbdcabbbccbbccbccabaddaabcbbdbadadbaacbaddcadbdadcaadbcbadababaaababcaabbdbbacbbbddcdbdcabdbaccbaacbcbdaabadabccabaabbcaadbcbabadbaadcbcadddacdbdbcccdbdcabbbcacbacdcbbadcabababdbbdbdcddddaddddaabbcbcdddbcbbdaaabcbbbacdccdadbccbdbbbaadbbadacaaccbbaaabbcbcacbdbabaaaadabdbbbcbddcaccccbacdaddcbdbddcccbddccacdaabbccbaacaadcccccadbddacbacdccacabbbcabcbbdaaddbaabcbbcdbcbbcbadcdaddcacdcbddcabbcaabcadababaaabbddbdbcccbdaccdabddcdabccbbbabacbabddbdaabdbbcbbaadccadadcdaabaaaaccbcbddccdcdaabdbdbdcdbcaaccbbabaccdabbbddbbadabbbaddbdbaaadcdabcacaadccbbcddccbacabbdadbbdcaabdacabaccbcadacacbcdadbbbcdbbddcadcabdadacadbabcaaaabcaadbbbbddadcdadaaadbcccdbddbcbadbdddbaadddcbadabcdcddacbababddcccbbdbbabcadbdcbaaacbaabcdcaaaabddaabbbdcbdddabcdbdadadbdbdadaaacdbabdabcaadbaabbaabdabbdbcdcaccdcbbadbcabdbbddbdbbcccbaaabdacccbcadabccdaacacdddaccdcbcdabbdbbbcbdbaabccddabbcbdaaccbcbaaabaacbbdacaabacbadbabbacdacabcdbbacbaccaabcbcadbcddbdabbdacbcaadcccbdaacdcaabdcccbbbdbcdbcbaaccaaaddcdaabcadbdddaccddbdcabacbddbbcdccccdddbdaaddcddaababadbdcabbacaaabcccbdbcbcdacbcdabbcbccccdbcbdcccabcacbbbaccbadcccdbccdacdbabaaadbcbcbdababadaccbbbacaddcdcddabddcdcabdadbdbbabbaccdbbdadcdabbabdbdbdbaabacabbbcddcddbababdcbddddabbdcccdcacadcaabbddbddddacabcbbaabddddaccabbdaddbdbddbaaaabaacccadbcadabbacaadaddabcccdddbbdbabbcdadcabdcdaabbbbdcabdcbbbccaabdbacbdcaabdccacaaadcdabccbddacccccccccbccddcdccbcdddbcadcadadacbdbadaacccdadcccdcdbdadbbdcbdbcacaadccdaadcadcccbadadbcbbdaddaabddcdabbbdbddcbbddddccaccbbbbbbcadcaababbbdddddbacddcdbaaabddccccdcdbdcbdbbbcddbdbdadaabdabbacdbdccbdaacadbbbaaadbdbbdadaadbbcccabbcdccbdbddcadddbcdaabaaacbcdbcbcddbdbadbabcbacabadcadcdbcdbdaddbbddcdccbbcdddadacadccccddccbcccdaaddddabbbcaadabbcabadaadbaabbcbccbcacbbccbcaddcdddacbdbbccaabdbabdbabcdcdaabcaadaabdacccdbadacbcddadabdabcbbdbbabbbbdaccddbcabcdbabcbdddaaaaddbbbddbbbddcadbabaabcaabddcacbcbbbcdaadacaabccdabcdbbcdcaabacdcdabbddccababdbbbdbbddabcbccababdaabaabbbdbcbcadadacbddddbcbacddbbddbdcddbbbabdcdcacbcddbccdbbabbcabbaabbddccabddbaaddbbacbbbbadcbbabdccabdbaadaccadaaddaacdababdccdabdcabadcbcccdbdadbcbbcddbbbdbdccaacacbacdcbcdbddabbccbcadaadacccaabbdbacbabcbddabcdadadcdaddddadbacadcaaabbabdccbdaccdbccaadbabbadbbcacbbdccacaaddaadbcdaaaacbcaaabcbdaccbcbcdbcabacbccdcbdcccdcddddcaabcddbcdddbabbdaaadccdacbcdcbcabcdbdcdcbddabdcddcbcacdbabdcdcbcaaaacadddadbccddacdddaaacdacdbdbcadadabdadbdcaacccabdcadcdcccaaacadcacabaaadabdabbdccbadcdcadadcabbcbdaaadbbadacdaacaccdbcdacdaacbcdcadabcaabcdcdbbddbbacbcbaddabbdadbdccbdcbccccdccabcbacbcacdccccbcbadabaabcbbdbdaacbacdcdddadccbcdddcacbbccbaabadcacdbaabbdccbcbcccdaddcccbcbabcdaddaccdbbccbdcbbdaccdabadcdccccabcaacabbbbabbadcaddbdaccdacbdcbdabadcdcbbccbaddaababadbcdddbaadbdbabdacbbbddcbccdbcbdcbddadbddddddcacdcbbdadccddcaddbaddaaaadcdbddbabbabdccbddbdccccbdbcbcaddcddcabaacdaadcaaabbdadcddabdaabdadbbcdadccdbddcdaaaacdabbaacadbdbaabdcdbcbdddababbcadbddbcdbdacbcbabbacddaaabbabacccdadabbbddbdbdbbddccaabbbcaddbbaddbccadcadcadaaabcbadcdabdcabbddccaadacddcbbcdcacdcbdbbbcaadbdcccacdccddbbdadbaddbcdccddccaadbcdbbddbcbbabcacabbdddcabcdccbacbcacbadabdcabbaddbabbbcbbbdaccdcacdcbcdbdabcbbbabcbbcdbddadbaccadcaccdcbdacddaaacdbcabadcbabbdbcabdcdaaacbaddadcabbaaabdbcddcabcccdcbddcbabcbadadabdcaccadacaaadcbcaacdaacacabcdddbadbacaaaababbcbdbdacdaadbadcadacdbdbababadacdadccbccadadbabacbbcccabcbdddaccabcabacdccaaddbdacbbdddabbccabdbaabdbaddbccacacbbdabcbdbdbdddcccadadcccaaabdaababcabcdacbbccbaccccbbdbcabaaadabbbadadccdbaddadcddcadbbcbdbcddaccdccbbbabdcaabdccadabadcdccadcaaadbaccaaaddcbaacbadbcbccbccbdcaacabcbbddacdccbcbbbdbcdaabcbcaaaadcdadcaadbbbccadbdcdcbaadbaabddbbccadbbcbcbdabddacdaaddbccdbdbccdccdcaccbccacabcaccddcdaddacacaddababbccacbbcbdcbdabaaccaadddcabdcddbccbcaaadbcddddcadbdbcdbbcaccdbdaadcbadbbabbaadbbbdccabaacccbdaadcbabbcadaaaddabbaccccbbcdabdbcacbbcdcbdbbcbaaccbbadabdccabccabbbacdacbbdabcccdddbbcdbdbbabbacccbbdbadbaddbcbbdacbaacbdddbaacbadbbdcadcccdacabadbcccaababbbaabcbccccaaabbacaaaaabbcbdadbaaaccadcabaccbdcdbbaadbcbabbababcccdadcdccaadaadcbabaaadddcbddbdbdbbaabdabcbacbbacdaadcadabacdbbabcdcabddadccadcbccbbcaaaccdcadddccdaaccabdcdbabbaccadcdbdcdacabdcbbbcbcabdcdcaddaccdacacdabdcdbabdbbcbbdadcaadaaccacddddbbcbdacdbacbbdadacbbcdcdaacbdddcccdcccbdaadcaddbbacadbabddbdababbdccbababbdacacdaddccaaacdabacdccdaacacbbcbabcabdcadddcdbbbadabbdbcdbddcdccbbbdbaacabdddddcbbcbaccbcaabacbbbcdbcadacdbbaaaadddbbaddbaccabccabccaaddbbaccacbcaaddbcbabbccbdcaccdccacaadbddaacccadbacbbabdaacaccacdadbabcbdbadbdaacabcdccdbadcdcbccbbddbbcccddacbcccdcdabbccacdcadadacbccbbbccdababbcdcacaaccbdadacbaddcbdbbcbbdbcacaccdabdadcaaddcbbdcadddabcbbacdddaddabcdacbcddaadbdadacdbaadbdbacbbcdbcdabddcaaccacabcacbaaadcdbdbdccadccbadaabccbaadaccbccbadaabacccdbbbcaacdbbabdcdbbbdbdccddbdbbddcbbaaadacbaccbacbcabccadaabdaddadddcdaaaccdcbdabbbaadadddbdbcbbdccdbccbcdcdccdbcdddbdddaaabcaccaacaaaabbcaacabcaadaccaccacbdccdbadcbbdcbbdaddbcbaadababdddbbacaacadbdcccdadcdccdaccbcabcddbdacaaddbbcbdaddccdcddaddabaacaddcbabdcaadcacbccdbabaddabdaaaddcaaaaaccadcdddaadaddabdbabccccccdcccadacbdaacaddbccccbcbcbbcacaacababcdaacbcbbcacbadcdbacacccdcbcbcbccbbdbbabddcabadbdacdcbadcaccbbaabacbbbcacdbcbbababbcddbbacbdadaabacdaaadddcaccaabcbbddddcabbaccdbccabbccddccbddadaadcaccbcdbdddbdcccddcbccddabbcdbbdbbaacbaabdbcdbdbcbcccbbdccbbdcdbcaddbbbcadaaddbbcddadbcbaabbcaadbdbccddabbadcbbbadbacacaadcccdcadbdbcaaaaccacbcbabcbccabdbacdcdadcbcdcabacdaababbcadcbabddcaaadbddcabcacdcbdcccbdcabdabcadccddddaaccccdbddbccdadccacccdbabdccbdcdaccccbbcdcddbbdacbadaadbbdcddaaaadbbcbdacbdadbaadaabcccddcccbaaddbcaddaddabdbccbbadccabbdddbacdbbdddcbcbcbddcccdbdbdcaadcdccaadbabdbcdaccdcaabdbcbdbbbdaadbbaaccdbaadbcdaddaaacdcdcdbaaaccdbbaddcbbbaaadcaddbcabccbdcadcbdbbcaccbdbacdcacdcdacababcbddcbbacccbaabbddbacdddadbbdaddcaabcdcbdabdbdbccabbbaadcdabbacbccadbbdddddcdbbdccaabaddaddddbaaccdddbaaadcbbcbacbbdcabdabdbdcdaadadbcdbdccbbabcaacddbbccdddaccdddbbabbbaadccbadcbdcaadbdbbdcdacccbbccccacdcbdddcadbadabdcccddccbcdcdacbcccdccbbbcaabadaaabccdadbdcacbdcddbcbcadbbddbbcbdcdcdbddddaccbdbdddcdbbccbacacdadcabacacadabbacbdcacdcdaddacdcbbbaddddbbabdacbaadcbcacbcddaabbacdbcabbccbcbddcacaaddcdacaabccdbbbaaacdbdacdaaaddcacabbcbabddacdaacbcbbdbadbbbbdbdcabbdcaadabdcbacdcaacccbbbcbaacccaabcbdcadbabddadbcadcabadaccabdadddcabdccadbbbcdbbcddbcbbddbccadbacadbdaddcbaacbddcabbbddcaacadccddbcadbdbdabbccbdbadaacccdabcddacddbcbabbabadcbadabcbdbcbbbadbadaadacbddbdccdddddbcdcbcbaacdadacacbbadcdbdbdacdaadabdbccbabcacccadabdcdacdccdcdbddadbbaddcaccbcaadadbccaaccdcbbabdccabdcdbbacbcbcdbcbcabaabcdddcbcbbdbbccabbcadbdadabadbbabacacbbaacccacdcddadcabdaccdacdbdcdaadcbaacdddadbdabbdacdddbbacadcdaadcbadbcabbbbbcccdcbccadbbcabadbddcbbaddadaddbccdbaacbccbbcddbabbabdcdbccbdddcddbadcdcddaddbbbddacbadbbabdadddccddddbdcabdaabdadacbcccddbacccdbcccbbdaddabddadbdbaadddaabbbcccccdabbcccadbaaaaadadbcadcbddddacadbcadccdbddaddbdabcdcdaabccabcdadbabbcdbcbcddbbaaddabdacabcdaadcccddbabdddadbbbbaddddcbdabaadcdcdbbbccddccdbadcadcbdbbcbbdabdadbdcbaccaccccddbabbdcddabcabcadbdcdbbdddaacbaacbbdbbcdbdcddddaadddadcadcbccabdcacacadbbbdaacdccddcbdbadddccaabcdbbcdbcaabcdcbcbdaadccabbcdbaacccdbbbcaaaadabdcbcdbddbaaaccdabcdbddddbdbcaabbabcbbbcdcbcdadbddbddcadacddbccbcabcaddaddbdcbddddbabcbbcddccccdaadddaacbcdccbcabbacddaaabababdcabccdcdbddadccacabdcdbbbbbbbbcbdbdacbbaccdbcaddabbdaadddacbaacdddaaabaacaacabbbdaaaabbabbcadcccdadccddccaaaacbddcdddadccadaadabdbdacdbcaabbcaccdcdbcddbabdddcdaaaabcaaababcbacaadbddbbdcdbccaaaccabadbbcdaccaadaccabcadadabaccdaacbcbbddadcbbbadbadaabcaccabccbbabdbacdaabdaadacbbddabdcccadbdaacdcabccaaaabdcccddabdadbbdbbdcacadccababdccddcdbbcccbccdaaccadbabddcabcdcacddccacdbbcabbadbcadbadddbabcdbcabbddabbccbdcddacdbabcbababdbccbcdbadacbaacddbabccbbddbaabbadbccdaccdbccaabadbbcdcbbabdaadcdddddaccbdcdababcbbbdaccbdbbbdadddbabdabacddaaabdddaadccccddaccdaddbaaddacbdbabddacdbddbbbdacccdbbdacccdddbacdababdcacdbcdddcccabcacdbdadddbbcbcdcacadacacccbaacdddadadcbcbdaadbcaaabdbbaddcbbccbaabdddacdbcdbcdddcaaacbcbbcdcdacbcbdbabbaaabcbdbbbcabbbdbcdcddcdcadbdbadcbbcddaddacdaabacccabdcdbdaddaaaabbaadcaabbadbadaadacddbdccdacddbcbccdddcaccccccbaccadcaabbdcbabcccacdaddadcbacdbcaccdabbcbbbaaaacabbaacbbbddcbdbabdacbbadadbccadbcccbccadadbddcabbdddcabadcdddbdacaabbcbdacbadcdcacccddabcabcdadcbabdacbcdbadabdbbadbdddbadabddabdccdcdacbbabacacdbadcdbddddbbdddbddcccbcdbddccccdaaccddbdcbadcdbaacccabacabcdacbbbabcbcdabbcdcdcabdbaddbbaddaadadbcbdcdbaccaccabcdbbdbbbcdaccddacddcdaaccdbaaaaacacabbcdddaadbabbcdaacbaacabcdccbbdcdacaaaadcccadcabdcddddbadcddcbcdcdabbaccabbdcbacddddadacacaacddddabddbdddadbbdadadaaabbccadaabdcacdadbcbbbbdcaacadbdbcbbbdcbdbcccddaddaacadcdcbccdbdcbbcdccacbaccbcbbccaadcccbbdbdadbacacaacbbcdababccdbacdadbaaaddbbacaabdbdadccbadacacdaabbcdabbdbbccdbabadbbbaacdddabcabcbaabbcddaddddacaaacdaacadccddccbdcbdaddadbdadddbbdbdacadaaaaaadddcdabccbdcabcbabcabbacccdbcbcbdcbdccbadcbddbcacbbbdcadacbbcadbabcdcdcdaacaacbbcdddabaaccddacdddabbdccdaadaabdbabdbcabaddbbdabcdbbadbbddcdacdbdccbcaaacadcdccdbbdcdadbacdaacbbaddbbcdbbbbcbccacddbdadcacddbdaacbadaaddaddbcdcbcbcdcbcaddcadbcccbbddbadcbccdbbcdaaacbbddcbbdbbcbadadabcadabbcdacbccbbbddadabdcabbbabbcdaacdbbcabdaddbdbaabdaabaddaddaddcacdddacacabacddacbbacddbdcbdcdddcadabdbcdcabcaccacabbcdbbdbddbcbdcbcdccaaacccbdcdddaadcbaaabacbbdbcbadccadcbddacbcdbbadabcddbcdcabdddbdbbcadbbacbbcbabbdbdacabdabcdbcbabcccbbbaacbcddabbdbbbdbccaabccccbadabacdccadadcdccccaddccdbbcddccbddbcadbabcdbbbcdbadcddbcbcdcdadaababdbbaaaadadacdcaadbbcbcaccdbcbbbcddacabbddadbbacdddcdaadcdccaccbdadabdcadacadbdacabcbabdcbbbadcbddcdaaaaddacddcddbcdcaaadbaaddcdbbbaaaddbaabbdddadacbbddbdcdadaabacccbdcdddbcaaccadbadbcdcaddbaabcbccadabcabbadccaacbaabbdadcbaacadadbcdbdadaabdadbdccadaacdddccaaccccbbccccbacbdabcabcacadbdcdacabacacbbcabdcadddcbdbdcdbaaabdbcdbbdcabaccbdabdabbabcabbbdcacdcacbabcbbbcdcaacbbcdacaaddcbbbdaabacabdbbaadbbbbcaabaabdccaacccbbccbaaabdbdddaaadabdbcacabbbbdbddadabcaccddbacdbabdbcaadccbcdcaabddcbcccbcbdccabaaaabdaccacccdabbcbabcacdbbddadaccabacbcabcaddbbbbcdddabccdcbaccacaaaccacacabbaddadcdbcdbdbdadaadbbadadccdccdadaacdcaacaadbacaddcbcbcdbbcaddbacdddcbccaaacadcccdddcabdcddbabdbdadcdabcbcacdbaddadddbccbbaaabbaccabdbbbbcccaccbcabbcbaadadaadbadbbabbcbabbdacccacbbdbaaabcddcdabcadbbdabbadbdadddabcabbbcacccbbcbcabccaaacadbddacdbdcccaddaacbcabcaaddccdbaabcbddacaaadbabadddaacbbcccabdccaaddbcbbdacbbcbcbccaabcacddcdddcaaaddddddbdbccdacaddacbdadacdbcbbdbdabaacaaccbbbccabbbbdbdabbababaccbdaadacdaacddcadbadbadaabdadbabcabbdcccbabbbaadbdcadcacdabcdddadbcbcbbdbabaadadbddcbdaabcbdddcabcadabaddadbdccbbdabcadbcdcdcaaadddccbddcbbbbbdccbcdababbaabccbcdaddcdaaadacbdddcabbddaacbaadcaccccdcdaabbabddbbbdadbbaadbabcdbaadcddcbaabdccccdabcbccdbbdccabdcabcddabdcdcaddcbcdcccbcbbbccbbcababbbbacdddbccacbdbcacaabcdccbbbcbaadaacdcbdbdcadbdbbccbbababadcbcbbcbacdccbbcccbcbcbbdcaccccbacbabaabaddadbcdaaaabdadddbbdbcbdacaabbddcbdbdbcdadbccddaacdbcdbdddbabdbaabccaadcaabdacaacccbbdadacccbadbcdcccddddbdcdcacbcbdaaddcdbdabdabadbaaddbdbabbabdbcdbbaccaccddbdcbbbbbdddbabbbdabbcdacdbcaddadbcccdacbbdbcbcadcbddabbabdddbbabacdcdbbbdabdccdcdbcddaaadacccbbacadbcacaaacccccbadcdbabbadacdbbcaddaacdbaabdcaddbcaacaaacacbddaddcdbcacdbacacbacbadcabdaacccabddcbdcbbbdacaddddbbddadaaacdbcdabbddcdbddbcdcbdaccccbddacacaddabccacbdbdaaccbcbbbbcadccbbadbdabddcbbbacbdcbdddaabbbacbaadaabbaaaaacbddbbcaabaccadcdbadbcacaddcbacddccbcaabbcdcbbcadcbcbcbddbacbadddccddaccbdddcabdbdccbdacddcadabbdddadbbadbcbdaabaabddddacbaacbcddcbbbadaaddaaadaadacccabdcdbaadadcdbacdaccbdaadcaaabdaacccbadbcaabbdbcbdacbdbaccdbabababdddbcacbcaddddbcdbbaadaadaaadcccaabbcdcbcdabddaacdccdcabcbbaacccadabcdacbccbdbbbcacbaadbbdbddcabbcdcddcdadddbbcbaccbddbbdccdbcddbcccbdccaabcacbcbaddaccaaaddacdadbcddbcccbcabbdabbcbdadcdcbcdcccdccccacddbabdccdcbcbcbadadbbbbcdccababbacbbdadbdbbcdccdadccbdbaacadaadddabcbabdccdcddcbddcabadbaccadcbbbcdbcdbacacdaabccbdabbbcaadddbcdbcdadddbcadadaddcccdccaddbcbbbabbdadabdaaccbbbdaaaccdcbdbbbbaccaadbabaccdcbbacbcbbaddaabbbcbcbbdbcdaadaacccddcdadcaacadacaacdadbcbbdabcaccaacccadabdbacacbdbaacdcadabaccddabaddaaadbcbbdccbdbddbdddbbcddbcdbdcabddaabdcbdcaaddddcdddadbdbbdcbdbadbbdaccadabaacbbbacaccadcadadbdbcbacbddccdbbccdadaacdabbbcabbbabcadcbbcbbadbdbbacbbbdcbdbbdacbbabdbccdddbddabadacdacbdccbdcbbcddaaabccaaabacaccbaccbabcbbadaccccdbdaacbcadcacbdbbbccbaddababacdaaaaabaaacdacadcdbacacabddadccacdadddcabbaccacbacbabdbacbadcdacbccacacabdcadabddcadddabbbbdbcbbdbadbbcbbbdcadbcbddccdabbaddbcaaabaaadbbadcbbbdabdcddddacbcdaccacaddcaaddbcbbaddaaddcababdcabcacaccccbccbbcadbacdcbababdbddbdadacdbcabbdbcabbcbddadabddadacdbddaacddcddcbdbddcddcdbdababccdcaadbcabaaacbddbdbbbbbdaacdbcbaacbddaadaaaabdbacdbdabcddaccbadacacadddcbbddbbbdadcdbadaddbbaaabbaccbdabbddddcacdcbaabdbbaaaadabacaaababaadccdccaccdbccbaccadbbdcddaaddaadcbbcdbaacddbccbdabccadabdbccadabcdcbadabacdbcbdacaaabaaaabbdddbdbbbdaadaccbccabbacdcdbadccbdcbcbadabbbcddbddaacbbcccdabdddbdadcdbabbbdcbcccadaadbaabdbacaccadaabddcccbcdabbccddcddacaaaabdcaccccddcdbdaaaabcbddbdcccbccacdcbadbadddbccbacdbdcaaddccbbbdcbaaadbadddbdcaadbabbcaddaabacdbdaaaabcbdbcddbacccdaaaaabcdbbccbcbbcaaaaccabccbbbbcdddddcbaaccadcaacdbbddaabddddbdacacdabbbbccbacdaddbccddbccccdbbabcaacdabdacbccddcdbadabababdbbbbdbbdcbdbacbcabdbbddcdbbabaabdcacdabcbdbbcbbaaccbdcdcccabddbcddcccdaabbacbacdcaabdcdabaabaddbacdabacbcdbcdcdcdddaaadbdacabdacdccbbdbbadcbaadcbabccbcdccdabacaaacaacdbdbadaddbacdbcbacacbabbccccaccbbddcaddaacdddcdaadbcbcdbbdcabacdcdbdbdcacacdacbdccdcadbdcaddbddacbdbaacdcdbacdbdcccddbddacdddcbabccdcdbcbadaabdcadbaccaaddcadddcbadbbcdbadcbdcacccaadcdbbbcbcadcaadcbcbaddcbbacdabbabaccdaabaaccbbabacbbdaadcbbabcaaacadcabbadabaccbcabccaaccbddbcabdadabcdacbabbbcddbddcddadcdbcbabcbbabaacdaddccadcaadabaabccaddcbdccdacbaacccbcadaadbddcdabaacdbdcaadacacbbdadddcabddccabdcbcdbdcdcababdbdddcbdbbaaacdcbcaaccaccbdcbdcaaaaacbbcaacabababcbabacbbaccdbddcbcacdddababaddccbaaaccdcadababddaadbdacdbcdccbaabaaddadcabdcacdabadabbdddccddaaddaaaccadcaacadacbddcabaadcdbbdbcaaacbdbbcbbdddbaccdadadcdadaddccdccaaabccbadadcdacabbacabbcacdacbbccbbdbabdbcbbbcbdcbbddadaddbadacbdcdbbdabcaabbdbcaaacddccbabdbbabaacddbcadcccdcaabadbbdabacdbbadcabcbbbbccdbbbabbacdcbcaaadcdbdabddcddcdbacbbccdcabbbddcdbbccddbabaacdaabaabcccdccbdabadcbbccabacacbabbdaadadcdadbadababaadbaabcabaadacbaccccbdbdabacabaacababaababdbbdbbcaccbbbbabbbcbcabddaaacdccddcdacbdbccadaacbabcbccbaddacaadbdaadaaddaddacbbbdacdaddbbbacabcaccdaccadabcadaaaccadccabaaabddaaaaadaabcaadbadcabacdbadcbbdccbbcaacdbccaaccdbdabcaadcbdadaadbcdbbbaadcccdaaadaaaaadcdbddaadcbddccccbbccdabaacbdbccbbcdcbabbbddbabbaaabcabcdddcadaaaaddbbadccaadcaadbbcbbcabdbcbcdaabbbacbacabdcbadcacabbbbbadcdbdababaacaaacbbcccdddbdcdbcdabadabdabbcbaddcdbdcddabbbadabcabcbabdababcaddacabcdcadadccaadcbdbddacbbacabddabacbccdccabadbaddcadbcdabdbabaccdbddabbaacaccbcbadaddcaabccbaaadaaccbbaccabaabcbbbaaccadcddbcbdabcdbadcbadaddacdacbdddbbbbbbdaddacababaddcaaddddbabbbdbbbcadbdadbdbdcddccabcabaadaddaababcaacdcdcadbcbacbbbbbaabadcddbbddabbddbddccacbcdbcbccccdddbabacadababadccdddbccbbbddacbcdcbabbdbcbdcadabbccacaaccccccdbdacdaaddcbdabbdddbcadcbadacddbbcddbdacbcddaadcbbadaccbcbbadbaadddaaadadbcaddaacbadcdcacddadbdcdbbdacaacabbdcbadcadbcbacdcbcccbdabdbaaabcbcacbcddadbdbccddcbcdcddcbcdcdacbbcdabdbacadddcbaaacadaaabaaaaddbbbacdbcccbbdbabdabcaabdacccaaaadbbacaccabcdacbccbbbcabbadbbbbbabbcdacadadddabddbbadabaadccaabdbcdcbbdbadbcbadaccadaadcbabcdcdabdabcdabdcaaabacbcabdabaaaababaddabaabbaaadaaddbbdbadbdddcadaaddaabaaddacdbacbbdcacdababaaaabadddbdccaacaacdddabbdaabdcabcbbaccabdaacdbabdaacabaccabacdccacbdadbadbdaabdccaaaabdccbbadbdacdbcdcbacaaabdccdbcadbabbbbcdbbcccbacbbaacbbadbdabaccadbcabaabbcaaccbdaabbabdcbcccbcaadacbdacbabdcbbbcbdcddddccaacbccbcadacabdcbaabcdcadcdddcdcdbbacdbbddccdccaddddabbcabbadbabdadadcdacbdacccbbdaadaccadabccbccbaabcdaccbccdaaabbdbddbccbaaaabbabbaadbcaccbbaadaddabcbbccdcdddadadaadcbadddbbadcaacdaaaadddcdbadaacbbdaccacccddaabbdbaaccbbbcbddbaabbdccacacbaabbdcbaddddddddacbaaacccbbbbbdbbdbbbbabaacbdbacbadcadbbcccaabccbbbaccbbbccadabadadadcdbbaddaabbaddcbdcdcbdabdcbbddccddbbbadcccbccddbabdbbcadcaababcdcbdbdabbacdcadbaadaccdbcddacaacbbcbbcbdacacaadcaadbccadaaabbcbaadadacccaabbadcbcabdbcbdbbabbcaddcddbdabcdacbcccababdcbaaabdcbccabbdbbbdabdcadadbbdcbbdacacadabbddbccadcdcdabdccdbddcabaddbaadaabacddcccaadaadbabadbdcdbdbacccabbbccacbddadadadadaaddbcaabbccbdbdbaabdbcaacabcacaddacaccacaabbcccdbaadbdadddcbdcaacdadadbbddbcbdcccacddcccaabdccaccabdbdccdabcbaadcbbccdcbadaacdcccbdcdcadbaccaccdbdbccdcdaabdcdbcdcacacccbbaabdabdccbbdbbddacdbbacaabbbbbdadacbabcadbbcdbdbcdcdbbacbdbdbbaabcdddcbdbaadcbbddacbcbdbcdaaccdcccaacdcadababddaacbaaddbdbacdcdccbcaddddbabccccddbbcddddccadaacccdacdbcbaaadcddadbadabbaadbbbbddcacacccadaacdadddacbdabacababbbbddaccdcbabddcdddbaacabbadcabcbddbbbadbcccbdbddddaccbbdcdbaadaadcccabcdabdbaccdbcaddbcbcabdcacbcbdabbcdcdacbbdbbcbcbbcdbdccdabdacbdcadcbbacbdcbddadcacdbaddaaacddbbcdbccbdcddbcaccbccddbadabdccdcabdcdacddbbabcddbdadaacdcdadcccabadacbddabaddbccddccaacadbcbacbcbdbaccbbbccadbcbacbadddbbabcccdcaabddbadddccbcbacbdcdcccbddbadacbcbacdcddaacdbadadadbdddababbdcbbccbccdcadaacadacacbaabdaadaddabababccabdbdbaabcbdcbabdacddbaabacacbcadcacdcabcbabcdccdbabcabdcbbdadbacccdbdaaacdbabaccbcacaacbabdbadabaddbcdacaaabadaadbacddbbadbccddbbcaacbadbdbabbdbdbabbdddbadacdbcabccaccdccccacdccacbcdadaddadabaababdddaaddaccdabccabdadcbaaaaddbcdadadbcacdbdcbddccddcbbcaccbdabbbcaabcaddadbdccabadadddbaacddaacadacddacdaaadabcabacbadbbbaaabccaabaadcdbdbccababaadcbabcbdcabbcaadabdbaccdcdaadaccadacdbbaabdadbaddcddaaadabcadcbbababdabaacccacabaadbcbaddbbdbcabcbbbacbacdddcdcacbdabbadabcbadaadcadcccdbbcccabaaadbdacdddbcccaabbcdbcdccaabbcaacddcbbbbdcaaccadadaaacccddaddcdacdbcbcbabaabcccaacdddbaddacabdbdaaddcbacaabdbbddadddbdacdadcdbbadadcccdcabbdbdcabadccabacdabbbbabadadaaddcdbcdcdbabacaddcdbbacdbcddabcddabbaaacbbbbbcabdaacdbbbddbbbcbaaddbaddacbbbcbdadbccacddcaaddbcbcaaccaadaadcdbaaabdddccccbdcabcacdadcdcbdddcdadacbdbbababbcaaabbabadacdbcadcdaabccabbaadbcacdbcadcadddddaacbbadbcdcabbbaddacccbdcacadbbcabdcbaddbccbabdacdcaddadbccbdaccdbcdacddcdadadbdadcdddadddcbdcaaccaccdbdbbacdccbdcbdaadcbbacbbbaaddbbadcacddaacddaaacadaabddddbaacdcdbdbbaddbbdabadcdadabdbbabcdaacacacdbdacdbdcabdbccaadbadabcbaadacbcccaaddcdadaacbabcaabcbbbdacccaadabcabacddddbddbaddbdacacacaabbcaacdbabdbabcaaccbddbcaacbdaadcaabccaadabdccbdcadbbbbcbdbaabbbdabadbcadbcdcbbadbadacbbabbdbdbaaadacbcdddacaaacbbbdbabbdaacbadacdcaadacddcbbdbcaaaababcabbabddbabcccabdbacdcdadabaabacbcbbcacaaadcdbcbcaaadcbbccbbbaccdccdcaccaabdddccadcbdbadabcacddabadbccaaaaaadccbbabaabacddbcaacabbddacacbdaccdadccaddadabcdadcdabbabadbcabbbbcadccbbdabdcabcaacacaddabdcbbbacbabbdbdccdcbdccadbdbcbacadaaaacabddcccdcaccddacbcdacbaabcaabaabcbacbbbadccdacaaadcbbbacbabdaddbdcbcaaaaacacdbcdddddacdbbbaacaaabbbbcdabdddbbcacdcabccadaccdcdbbdbcabdaabcbddbabaaaabaabccbacaadbcdbdadcbcaadbdbbbaaabbcdbacdabcabdcaccbdbbabcadcacbabbcacccacdbadcaaaadcdcddccbbadbccacdcbdbcccdacdbbcaccdaccbadbaaaadcabcbcdcccdaadcbcddbdddbaabaddbdbbadcbccbcaacdbaccaddaccddbbdbadcadbddaacdbddacddcdaaacddbbcacbcbadbdbadcdabcdbabbbbabdcddcdacbadcdbcacacbbdacbcabdbdccbcdabbbdddaadbdbcbabbcdaaacacdbcdaccbacaadcdcabccdbcaacdbdaaabccdababcdbacccaccacdbcbabacdaaacccdbaaadcbaacddbdccabccbbacdbcabcaccdaccdabbbbaccbdacbdabdacdcdacbdccbccabdabcdcaaacdadbdaddcbadbbbdcdbbbabcbacadcacddcdacdbcacacacbabdadacacabcbbbddccbaacdbacbacabbcbcabcddccaabcdbadccdaadaccdabbdadcbaaddbadcacaabdbabbdcdbbbabbaabcdbcdccbdcbdaccaacddacddbabbbaadbcbbbcaaccdabdadcddbbbdaabbbadcbbbddcdabdaccddbccbdddbbaabcdadcbbccadcabdaadaccaacbacbacbdbcbbbdacbcdaddaddbbbddbaadcddbbccdadccbbaccabdaaaadadcbacbdabddbdbbcbbdbbcacbacaddcaadcdcdbbababbcdbbaccccbaacabdacdddcdbbcbdcacaccccbbbbdaacaacbcbcabccabcabbbabcbdbbdacaccdbccbcbdbdbcdcddacdbaaccdbcdbcaacaadbaddacbcbbdbabbdcbaddddabaaabbaaaacbcaddbdaddbddabdacdddbbadaabadbacddcabaacadbddabcadbddbaaaaadbabadbccbcadbdddacdabccbdbbababdaacbaaabbaaabbdabdcabccabaabccdabadbcbaddadadcbaaddcdbabcdbdabccaddcdcadbdbaaabaccbcbcaadcdcbaddabcddacbabdabcbccadcbdcdbddbcccbdbabadbacaaabbabbaddbcbbcdaadaabdaacdcbddbdbcbbabaccaaadacaddabdcccdcccbaddaadddcbccddacbbbdbdadcbcabacacbdadaabaacadbaabbadabddcdadcababbcddcdbdccbbaadaacbbbbaabdbcddadccbbbacbcdcddbbaacbacddccbabaabdbaabbccbcccddbccdccbdadabadcdacddabaaabacccbdaacbcdabdcaadbabcdabcbdacacddcaabaaccbcaaaddabdcbabdcbcdbbcbbbdaddbdbaaabdcdabcdcccdbbaadabddabbbcbcddcaccdccbcaadddbaaaccdcbacabcacaacacdbcbbbbdabdbbdaadddcbbadcddbdbcababaddcddcbadaacddcccbbbcbcdcdcbbabaaacdccbcacbbccacdcbcbbacbcdaaaddadbadcdacadacbdcbdaacabccdadbdcbaacdbdaabcaadaaaccabccabcbabadbaabbcccddabadbcbbdbadacbdcdacbbbbcdbcdcaabccbcacccbabcdcdbcccbbacadcbbddcaaaadcacbbcbacacbdacadbcbbbddadcccacababbadcbadbbabbbccadcadadabadbdcdcaabdadcacacbdabaccccadcbabdabdbabaacbadcccbbabbdaaaabddacbddcadbacaaabcdadabdcbccaddcdddbdddaacddacaabbbcadcddabdabddcaabaccdcdbcadacdbaaaadbcaadaacacdbabcacaccbdddcaccbbaabadbdbdaaaddcbcbccbbbddccbdabdabaccabccacdadaabdaddcaddbccacbdaaddaaaacbdabaaddbbcbabdbbbdcbadabaddcbbacabcddbbabdddadaaacbdcbccababbcaccbbdadabbcaacabacbabbaacddabdaddbaadccdddccbddbdbbbddacccbcbbadcaacddbabcdbdcdcdccacdaaaaacabaabdcbdbadcbbdcdddadbcdaaaddccabdaccaacccbbdccdcbcacbbadbddccdccbbaabcabddacddabaacbaaccdabdcdddbbabaabdaabccddcdacccdaacbddbdacbdbcddbbbcadabaacbabddbcabdcabdcbbbbabaddadbabbcbcdbcccdcdbbbdbdacdaccccdadacacbbcadacaadbdaaaacabbcbdddcddbddbcccccbbbbbabadcadddadadbdcbcbdcdadcdacbddabcaabacaabdabbbcccddacbdabcbcabcbbdddbddcbccbacdcddccdabccbcbbdbacbdbadbcbddabaabdadddcbbdddbcdddcccadaddcadcaabcdcadacbcaddaaacabbdaaaaadbbcabbbccbbdaabcdbacbdabbdadcbddbadcbabbcaabddcbdaaccaccdabdbbdadadcaaabcabcaaadcbadcddcbadacabbacbcddcacabdbdaddbbadbcbddbddbaabdaaadbbdbbabbcbdacddadcdaacabaacaaadaacbadabbbabdbddaddbccbbcbbabddaccacddccdbdbbdccacdabbdcadbcddaddaaabdacdacdddbdaddbadaccccbbcbaadcaadbababadbcabbabdddbadbdbcbcaccaaabddcbaacdcabbccbbbccbcbacbbddbabdcccdaacbbbbbdbaddbabacbbbdaddcccbbdacccdcdbbabaaabacadadacdccabcaadcbbaccbcdcbdabaddadbaacbcacabbbdccbccbaaddbcddcbacacdacadbcaabdcadcbbadaaaaadcbdccbabbbbbbaaacbcdacbbcadcacdddaacbccbdcdaacbdccdcacbcbccaddadccaddcddabbcaabadddabbdbbbddaabcbdbccdcdacdbadddcbdabbcbcddbccbcabdabbbabacdbaacbdbadaaaaadbbdccaabddacaddbdacdaadbdaddbbaccdbacdadbdacccbaddcdbacccacacbaacbbbccacbadabacabbbcbccbddacdadaacbdddbcccdbacdccbbbaddaabdcdbbcdacacabbdcbcadbbccdbaaadcdccaabaaaddacddcbadbbbaadcaaaaddcdadcbabbadddcccbabbbdaddaaabbadbbcbddcbaddddcddbacaaacbbcbdbbabcaacdcddccabadcbdbddabaaaccdcdcccaccdabcbcbccdcabdddbaddcabdbabccacbbcbbddcdcbdcadbbbbadccaabdbabbdbccdbabcadacdcccbadcaaabadbbbcccadbbcbbdbbacddccdabaabdaccaabbcbcddacabccbadcdabcdaabcdadbacaddcdbcbabcaacdacbcadabbbcbbcabacbddcdbabbdadaadadcdaaadacccbaaaabddcbabbdcbadbacacabdbcabdbbbccadbaabdaadbcbcbdbabdbcbbabdabbbbcdcbabbccbdbababacaacadbacbdcdcadcbbbdcdacdaddadbabdadabddccdddbaddaddcdbaadbacbacdaddcdadadbacdaacabcbcabbcbcbaabadccaacabddacadbcccbbaaaccccacbaddccadcbccbccddaabbbabbcddbacdacdacaabcdcbcbcbbabaccdcbaccdacdcdcdacaabdbdabbbcabbbbbdbbcabcbdccdabbbaaacadcbacadddabcbabacaabaacddbccccabbcabbabbddbbaacbacbadbaaaacaaadaabacccadbdccdbdcdcdcdcccddbccacabcbbbcdbbcaccbacbdcacadaacdddccdcbdbabdaaaabaddcdddbdccadbccdcdaaccbadabaccdaddddbddddbdaadacbbdcbcccbddbbbcadaddddcdcbabcbbacdaccbbdcbcbbabdacddbdabdbcdbbddadaacccbcdbcbbabaadadbcdcdcdddaaaacddabcbdaccadaabdaabbbcdddddbaadddabdccadbaccaacbabbddbcbccbcddbddcddbcbdbbcdcabacdacbaddbbccabccaaccbdbacdadbdbacddacbcbcaaaddaaddbacaaabbddaacbbdadcdcdbdbbdacddcddcadccdaaccdcbbbbadcaadbbcacccadbbdcbadadcccabbadcddaaacabddbacdcddcbcdcacbcdbdcbcbdababbbccbbcbbbaacadcabbbaabdbdcabdcbdaaabdcdaabbadaacaaacddaaccccbbabdcbddbdcdccdccdcbcdbaacddbcccdbddccacaacadacaaccbbbcacabbaabbbbabcacaadbaddaabaabbbacccbdcacccddcadcdaaaacaaaabdaabddbbdbccbabdddbcbaaabdadaccdaaddcacbbaadadcdabbbcdbddabccdbcabcdadcacabdbaadccbadccdccdbabdbdaaadaaaadddbbcaccaacbacbbbbbcaabdccbcccadaccdcdcabdddccdadddbdbcabcabaabccaddddacaccadbacdacbbdcadababadabccdbaddbdacdccdbddddcccbacdbcadaddbdbdcacaccbaaddaabdcbaaadadbaadbaccadbbabccbaccbcaadcdbbabbbcbbdbbcdcbdbbbdddcbbaabdbcccdacbcccbaacadccbcaaadddabdaadadcbbbcacdbbdadcddddcabadddbdbabdcdccbbcbaabacdccccbcddbdadbccbdcabaccdddadcdccbcbbcbdaabbddabcdcdbdbbddbbdccdcdacbbdaccdbbbcdabdcbdccbcaacabcbdbcadacbbdaabaadcdbdbcddacbddaddcbccdaabadbbdbabaaddbaabcccbaaacbcbdbadaabadaabcaaacbdcdcccdacddbcbbcaabaacbdbbbabcddcdbdcbabcabdbcdcbdbdcdbdbdbabcddaccccbcdbdbbccdddacbdbbbaaadddacadabbdcddacbdddadccccaccddcbccccbcacbdcdbacadbcdadbaadabbbddccacbcdabbabadbadccddcbbdcbddbdddbabddcbccadbbaabcbddabcaaaacccbabacacdacbccbbbbdabbbbddaaaadcacbcaacaddabcbcbccbaccbcdacbabaabddccccbbccddbdacbadccacbdbadcbdbccccddcabdaaadccddacadcbbddbdcababdbbcbdbcdddacaddddaacdbbbdccaabcbcbbadbbacdbabadbbbaaaaacdbabdbaaaccbbbcadbdacdbcbaadcccdbbbaacccdcabbaabcabcdbbaacbcccabcdadbdcacbaabaabbabbddcbbdcaaacdaaacdbbdcccbbcaccbababcddccbcdcbbaadbbaadabaccdbbccbbcabdacdcdcccbddaddaddacbdadbccdcaadcdabcbccccacddbbabcbacdcdabcdcbbacacbcbddaacbcdaddbadcdaadccacaccdbbadcabcbabdcdcdaddbccabcbcaacbacbdbbababddcdabbcbaddaddaabcacccabddaccdacdcabadbcbdbbcccbdccdcbacbaaddccbcbcdcbcbddbccacdcadddaddbcabddccadcdcbdbdbaabcadcbcbcccbacbbcadaccbcdbcbbabdcacaaacdabaaaacbdbdaaddadbdccbccacadadabcbdcababdccbabbabcddbcabccabcbdcbaddddbcbaacddbbdcbaacaabdcccdbcdaaaccbcddddbbbacbbacabccbdaaddbccaccdccdddbccbbbcbbdaaccbacbcbcddaabbbbdcdcddacddbacadccaacccbadccbabcbcaabbccaacadaabdaccbcabddddadddbcadddabadbddcbbbacadcddbacabdbbaaacdacadddcdabcbdadcccdadaabddbbdbbcbabccaaaacbaccbcbabdadbcbdcbcaddbccdbbcadbbbdcdddcaddabadcacbcddaaabacadbcbdadbaddbdddccdcbccbcadcbbcbaadbdabbadcbabdadaadddcadbacaacacdbadccaacbacadbdaacbdabaaaabbccdaddaacabdccabccbdbdbbbaddbdbdadbccdddcaccabcbcdabcddabdacdccccccddcadaabbcddcabbaaadbacbdcadcccdabbddcbbbdddbcbaaddcaabcbacdddccdccaabbcddabcbabadccbcadcaacbcbdcbcbbddbdbcbcddccccbadcbadacbdbbdabbdcadcdccccdcddddcbaabdddbcdbdcbaccdaabdaaadcddabbbddbddddcbdbaddbdacdbdbdbddabdbdabbdcadbbcbabdaababbddbdcaddcbbdbbbdddadbcdcddabdcbbdddcdbaacaccacacacbcbbbacabdacadcabaacbcaacdcaadacadabaadcddbcdcbdadacadababbdacacbdacddcdbdcddcabdcbaccdbbcbabbddacadcdddadaccdaababcbbadaabdabcbddaccaadabbbddddacbcbcdddaaccacbdcccdcdddaabdbbbcddbabaaddadaabdbbcdaddacdadaadccbaaccaacaadcccdadbacbbddccbadbcaaaddaaadcdadaaadbaddadccbcadabcbbbabcaaccadacdccbdbbbcadbbdbaddddcbdacdbccaadadbaabbdcadadbdbbaabbabbbbaccabdcabbddbbddaccaabddcbdcbbbdadadcbacabdbadcbccdbdcddcbbdbaadcbcacbcdabcabbbdbbaabbbddadadaccbcaaccbdbaccbabdadddcdcaacaaacbbcdbaaccbaaddacccaabbdaaaddcaabdddaacbdcbabdcdbcbbbacbadcdcdddcdbdacbabccbccaabdbbccadbcbbcababacbadbabadaddcbdcaaccdccdbaadcdcbcadcbcbaccbdbbbbcdbbdcddbccccdaaccbddbccbbbddbdbdcdccbdbdcdbdbacbadcbdcddbdbdaabdbadbcaaddcdabcccdabcabcaccbbbcbdddcdbacdadddbdddabbabcbaddbdcabcaaaccbbcdaaaccdbdbbaddbccdaccabdcbbddbabdcdcabcbdabcdabddcbabdbdbadadabdacadbcadcbdddbbcaaabcbabaadabdacbdbbbddaadbbbdaacbcbbcbbdbbcccbbddbccdcddacdaddbcccccdcacbaabbdddabcbcbabdadacddaaadbdddddadaabbababacadbcdabccbdccbbdadabddaccaddbcdcbccbbabdbadacdddcaacddcbcacdabcbaabddcdbdaadcdabbbcccdadbaabaccaddbbacbbcadabcbbbddabadacdbccdcbbdcbadacbacaddbababbadcdaaaacbbbcbcdcdabcddcaadaccbcdcaadbbabadcaccacdbddacddacacaaacaadbabddaaaadaadccadcaadcdaccbcbadabcdcbbadacdabcdddcbdcdcadcabddddabdabdbacabbbdbdadbbaddcbacdddbdbcddadadbccacbcaaddacbddcddbadcbbbadadbbdaaccbdbbcbaaacabaacbacabdaaabdccacbaadadbddaacaadabaddcbcdaaacdbacbdcdaccccddcdaddbbaabcaaddddbdcacadcabccaddddbbddcbbadccdcdbdcdaadadadaabbdabccaacddadbdabdaabcbdbbccdacbbdcbcacdabccdccccadbcccddbcbdabbbbbdaacbbcaccbccbbbcbcbdabcabbadcdcddaacbbbdaadaccadadadabbacbddabaddcbbbcdccadcbadcaddddacdddababcbbbdcbcbaadbcbccbdaaadcacabadbaccababbadacdbbcbbadabbacbbccdabaddcabbbcbdbdbccaaccaddccadbdcaabbdacdabdabdabdabdbdbdaaaabcadaccbaddcbabccdbadddcadadabbbabdddcdaccadbbddacbddacabcbdbabbcabcbccdadbabdabbdcdcccdcccccadcbbbbcaddbdcdaabcdddacdbbdbddccacadaacbdadcbddccddacadbbcacaaaadadbcacdbbbdbbcaabbbdbbbaddbcabdddbddaacbdacadccaabcbcdbccbbcabbcaccccadbdcbbddacdbddcaacacddaddbdabaaddacabcdddbcabacaccccbdacbcbadaaabbbddabbbacdcadcbbccbddcbdcaacbbadddccaadbbcbcdcaddaabacccbadbbbdabcdacbbbbdbddcccbadadbdccadacabbdadcacbdbadaaabdddbddbccbdbadbcddbacbdadbcaacdbddaaaacbadbddcdbbacbdabcccadcbacacdbbbacacabcddadaacdbddcadadadadacbddbdbaaddacdbcddabccabddccccddccbbaacdcddccabbddddbacdccccbddcaabccdbbcbdbddccbaaadbdbadbacbcacbdbcdcadcccbccdaaababcadbdbbbabccccdbcacddccdbdbcbddcddddaacddcabdaacaddadbccddbbbaabdbbcbcdddbbccbaaddbadbbaabbccbccccabadbbcdddaccabdbbdddbccabadcdabddbcaaabbdddabacdaaddcadbabbbadcaaabaaadaccabbadbbdbabcddccbbbadaaaacbcabcdbdaabbbbcdabaccaabadbccbddbbbabdabadcbcdadcadadacadacababdbbcdbcbbacdcdaadadccccbacdaabbccdcbdbbacddbccccbccabcaddabcbbabdaabaabcbddbcddccaabcbbbbccccadadcdcddabbccbdaaabbcdcababdbcbacdaababddbaacbccaacbdabcabbbadacdacbdbabbdabadddbccacdbcdabdbaddadadbcbdccdadddaddcdddcaabcdaadbaaabbbdcabbabcccdcdbbcdadbdacccdcbbbcabcaacbbcdcccbcacbcbbccabacaccbbccdddabccbaaccbccabdbdcccdacdcbacdcadaabcaccaabddcaaabaaabcabbdcabbbbbababbacdcaabababdbbcaccacbdccadabbbbbdcdbacabddddacaccbdbabbddbddcbbbcadadcbabaccccaabbbdbcbacaabbbbbdbaaddabdcabcbabddbcbcaccddcadcdcbadbdbbbdcddcaabdbdabdabdcaacabcaabcccbdbadcdabdabcbadcaccdcaabdbaddccbacdcbcbdbaadabbcbbcaccdbbacbaaccbccdbaacbbabaddadacdbadcdddacdaabadddbdcadbabdbcddaddadbcababaddcddabbdbdccabbdbbdcddcdbdbabacaaaaadbdcbbbcdabcadcdaacbcdadcbcaadbbcccbaaddbdcbdcccdacbaaadacbaddadcabcdaacaadaadcbdabadbcbcddadbaabcbbcbcddbccbddaadacdddabdacbdacbbacdadaaadbbdcdcbabbcccadbccdbccacbbdaddaccacbdbaadadacbdabcbbcdbbacdacacaadccbaddabddaadcdcccabcbddaaadcadabdddbdbdacbbcdaaababaccaabcdaaaaabbacddcaacbdcbcddbbcbabdbadbbadbaccdbaccbcaacbbdbabbbabddaabcdcccdabcacbbdccbaabbaccbbabaaabcbccabddbbaccbcbcdccaccadabacbcbccaccadbcccabbdcbccccdbdcbbdbaadbbcddcadcbcdbabbabccdcbacacdbacdbdbcdacbcccbcdabdbcaaaacdccdabcdbbacacbdabdcabbcdbacaadccaadcacdcdbacaadacdcdccbbcaacaddabccabdbaddddcddadcabdcabccadbaccabbaccdabbcadbbddaaadacadbcccdccbcbcacaacdddcbdadcacadddbbdcbaccdaccccabdcccacbdbbdbdbadcacbcbbbaabddbbccccdbdcacabbbdcdbdbbdcdddbddabcdbbbcbaaaccbaddabddbcccccaabddadddbbdadcbacabbabbcaabacabacadacbdadcbdddabdcdcccacaaddbaaddcbaabdbdcccbdcdddbacddaadddcabaadccabbbacababbbdccdddcbdcabdadbcbdbcadccbbbddbaadbcacbdbcdaccbcccacbccbdddabbbadccdababdbcbadcbbdaadcdbbbadccbadacbabbbadccbccacbbcdcbaacadcdacdbcabbdabdaaccbbabdabcdbaddaccddccddabdcdcdbcacbddaabdcaacabdaadbdcacbbbcaddabcabaaaddcaabbdbbdddcdaccacbbacbbcbbcdcaabbadccdadcabdcbabdddccccacbaabcbadccabddabcdbabbadbccbadccdbaaddadbbccadccbdaddcbcddbdbacdbcbdbccadccbcddacbccababcadaadabaaacdacdaddcadbcacaddcbaababdcabccbaaccccadbcbcdaaccddbbdbdbdbadbcbdbcaabdcccdcadbdbcbcaabdadcaabdcbdbddbababacbcbcdbdcbbbcdbddcaaabacdbadadcdbadacbadbabacdddacbdcbaaabdadcbdbbbddccbacddcddcdadacbbddccbdcacccbddaccbcabddcdbdbdadbcdbddcbbdbbabadddddbdbdbaaadcdcdaccccdbbccbadcccadcaadadbddadcddbbdbaabcabdcabacdabcdbabaabaadccddabccdccaadaadadadcdcbacacacdddacdbcadbbcaaddcadcadcbacdacbdabadacccbdddbccbdadcacaddcbbcddbbcaaacacddbccbaaaccdaabcbccaabbcdbbccddbdbadaadcdcdccaacabcaccadcbaaacbcdabdcbbbbbbaadcbcbdbaddabbbddddcbdcccdbdbddcadcacdcdabbcbccdcbadacbdbdcbdacbbdbdbcdcbbbdddacbcacadbcdbcdbbdccbdaaaabdbbbdcdadccababcabdaddababcabddbbbdccbbdbcdcadbcbcabbabcabcddbacaddbabbbbdddadaadcdacaccabbdcdbddbacdbaddcdccabbdbbadadcbccdbcacaaccdababdbcddbcbabbdaddacadacaabdccbdccbdaccdaacbbbdccddbdaaaabccaaacdabbbccadcdcbccadbccaadcdbcbcacbdbacdacabadbadadacddcdcbbcbdcacadcdbbccccdcccaabcdbdbcaccdbdccdcdbabacdabadddbabcbdbdcaabdcccaccbaaddbabcbbdbdddddbcbbcdbddbbaddddccacabdcaadddccabacdcadadccdcacdccaddcbacbbadaabaaddaccdabacdcbcbbddcdbbbaaacaadadbbddddbcadbabadabdbdcbdabddcbacdbbacaabaddcaacbbacbaccdadabdabacdaccacddacabaddaaabcccbcbdbcabddbaaaabccbacccdbcbdbacbcbcabcabbddcacabbddddacddabddcccbabadccdbacdddcdbbcaccdabbcadcdbbacccadcaabbbbbdccadcdcacdccadcbdbbbbbdadbddccadcbaabaadcaaaabbdbddadbadddddbcbacddcbadaddbdbddcacbbbaaddaabcaddabcdabaaccbaacadbbcdacdabadbacadbdaadacbabbdbcdbccdccddcabdcdccdddabacdddcadbdcbdbacadacdacacaccccaacbcadacbcabdccbaaccbaddabcbbacadbadcdcaaacadbcbbcbadcdacdacabdaccddadbdabdacacccbcacacaaabacbbdcacdddccddaabdacadcdbabaaadbcdddbacabccaccabadbbbbbaabbbdbbadabcacbbbddabdabcdabbdabbdbddddadadcccdacacdcdcdabcbdbcadbacbdcbcadabcdacbbbaddcadcaaccdddbbbcddccacbbbbdbdbcbadacbaaacbdaacacabcbcbdccabdcbbadcabdadcccbcbaadacbdddbabcaccbbcabcdccbcdcbacaddcccaddddddacbdcccdddaadabcaaaaaaccabcbabacbbcbadcbccbcbdacccacbdbdddccaabdaabbbddbadacbadbadacbdaaaadbdddccbdadaaaadadcbbbaaabbcadcbacdcbdbaaabbadcaccabbcadababddbacabcdacbdbcdcbcaddbbabbcdcbbdcbbaadccaddaadccdbdbaadbadcbadccdbcddbacbaaacabacbcbbcadbadcacbdadadccaadbdbbaccabdaddcaddabaccbadababdbbdaacbdaacadacdbccdbddbcaabccaacaaddbdbaabddacaaacabcccbddcbadaddbbaaaccbbcabdcdabddadcdbcacbdcccabaaabccccdcaadbabcddbdddddbabcabbaabaabdcbbcbddaaadcbdbabbdccddacbcbcdbbcaadaadcdbcabdabaaaccbbdbacdbdbdbbcaabdccbcdadabaccaccacaccbbaddbadcbbcababdddbcbcdababcdbaaacdcddccbbcbbaccaaaabcdccccacbacabccbadaadcbccbbbccddcbcbccadbcacdcccaacabccdbbdbcdacdaadccdcaadacbddcbcbbbdbbbbcacacdbdaabdccccdaadababdcbcdddbdaaccaaccacbbbbacaccbbdcdcdbbaaddbabdccaadacadabbcbccabbaaadbaaddcdbaaacbbbadabbacacbbaadaadbdccdbcadacbcddabcababbabdcbdbcbacdccbbacabbddbcadddcccabdccbbcadabbcddbaaaccbddabcabdaaadbcbcabddacdabbadddcadccabdccadcccdaabcccacacaccabdbdcdaacbcbcbdabaccbdadcabcbabaabdaccbccbdaabbadabbbdbcbcbddbbbbadbcaadadbcddcaaabaabaadadcabbbcaddbbbaadddbcddbddcbacccbccabadaccbdadcdcadbdddaacbadcdddbdbdcbbbddbbdabccadadbdabccdbcdaaccaabcdacccccbdcccbdddddcddacacabbaaadcbdcbccadbabcaaccacdcaddcbacacbadabddacacdbcaaaddbbcadcdbadaddababaacccbbbcbcadaaccaaaddbcadbbddddcaaaddacdbdcaddacabbbadcccccdddcdbdddbcbbdcadabdbddacdaabcdacbbacdbabcbbcddaaaacbcbaccddcbddadadaddadabdbbdbccccaabcbbcccaacccabdabbbbcdcbaacadacabadcbadabdbccbbcadbacdadbabcbccddcadcddcadaaacccdacbbaaadddccacbcbdbaacaaddacdbdcbdacdbcabadabddcbabcaccbaccaddadacaacacdcbccdbbdadcdbabcccadcababbbdacdbadbaaddacacabbcddddcbdddcddccaddddaaacdacdaacaaabaccabddbdbdadbabdacdaddbccdaabdddbcdbbdcccbbdbcbcaadbaabdaccadcdbabcaadcccacdbcacdbabbcabccccdbcbaabddbcadccbcdcbbcbabbbbddcbaddcbbbbcbbcdaadbddadcccbdcccbcdcdabdccaccabbbadaadaaddcbccddcbabcbbaaddcdbdbadddcbbaaaccadcddbababbbbadbbacbbacbadaccadbacacddbdcbbbbbcbddbcdcaaddcdbbddaacccdbbdaddacdcccbdcdacdadbaccbccccacdbcbdaddcccdbdcdadbdddbdcadbccdaaaacabbaddacdbbdbdcaddcadddbabaabcadcccabcdbdabcdbcbdcaadadccbbcccabaadcabaadcbcdbacaadabaadadbbcacbdcdbcadcadddaaabcdcacadcdcddbaaabacccabdacaadbcbcdababdabcadacbadaaddbcbcdccbabcaddaaabaacaddcacaddbccdadbcdbbdbdcaadccddcbbabababbabcacbdcdcdbaadbbabbdadccbadacdcadbaadbbaaacaccacbdabdacbdaccddbdcdccbccdcdacbaaaabbddaaacbcccabbadbdbbababddbabddcaacccbbcbcdddbaccabdbdbdcacadbccadadcdbbbadacacadccdabdcddccdabacdcabadaaaaadadcabacdabacdbdbdcdccccbadcdcdbccaccadbaabddabdcdbabaabcaaadacdcbacbdddacacabbcccabaddcddbdacbbcaaadbcaabababaaacbddaaddbadbccdaabacbdccaaabbbbaabbcbabdaccaadddbdccdaddbacbdbabbbddcccdccbcabdabdbdbaccbcabccccbdbdabacdddbacddbddadabacddbbacdcbdcdaccadbacddccdaababacacaaadddcadbcaddaadbddabcadcacdcaacddbaacaddbcccccaacbcacbddabdcabaaabccaaccdbdacaababdacacdcaacabbdbbacacddbbcdaadcccbbadcaadbdadaacbdabccdddcbdababccdbabadcdabcacaddacaacaaadcdbbcbbcdbddbbabdbbabdacdbccbccddbacdbbbaccacbbbdbacbccccabdacaacaddaddcbbacadbbccabcddcdbcdbadbbcbcbdabacacababcacaaacaddddbabcadadccbacbabddcdacaaddbcdaaccdbadbadcdabaadacbbdbcccdadbcdbccbaddbbdcbacbbddddbbbbacdcdabbacbaadabaacbbdbbdcacdbbdcbbaacbdcaccbdcbbbcbdbdcacbbddacacbccbdcabcacbbbabbbbdbbabdccbdabbaddcccabbdddaadbacbcadddadbbdaddbbcabdadcaacbdabcdacacbabbdabdcdddddacaadddbcabcdaabbddabdcbbacaaacaaddcbdbddccdbacbbabaaabcdacbbddddacbbbbbadacdbdacaabdbcdbbbdbcadacccdbacbdcdacbdccddcabdaaadadccbabcccbddbacaaacabdbabcabcbabcdacdaadacbccccbdbcbabdadcbdbccbcabaadabdcddbbadbbdcaacdddabbabadaaddcabdcacadddbbddcaacccdacbdabbcdcbdaadbbcaaabacdddaaabdddbabdacbacaaaacccdbbddaacadbaccbdbdcdaaddabcdcbdcbcabcababcaacbadacaacccddbcabbbcbbccacacacbbdcccbcbdabdabccdabccbbcbbdcadaadadbacccddacbdcadbaddbbbacadabbcdccbccbdddadccbabaccaddbcbcdcbcbbdacbdcbadcaddddaddadcbccaaababbdbaabdabcdabcbddbcacaaaabdbcadbcaddbdbdbbdacabcdbbacdcdcacbbaabaabcaabdbabccdbccabcdaacabdabadaadcdacbbccbdaabbdacdaccbcbddcacbbdccddbadbaababdcccabaccabdbacdcdaadbdcdcabacddcdadbccbbcdccbacaabdbddabbdcdadbcccadaddbadabacbbcdcadcbbadbacbcbbbcacdbdcbdaaabadcbabbdccaacdbcccaadbcbdbcccbbcdbdccbaabcdbbaaaaddccadcbccaabdabdbacbbcaddccaaadaddaadbdbacbdbdabdcadddcdcddbaaaaccadbacabbbdbaadbbcbcdddadacbbabdadadbcbadbcdcbcadcbbdddbcdbcdadbdccddddacbcbdbbacbdabbcdabacbaaabdcacacbcdadcaabdabcbcddacacaacadcadbdabdbcaddacaaccddcccddcdcbaccbbccdccadaccdabdbbcddabcccacddddccaddaccbdbccccaaabcdddcdadddbbbcaadaaccadbbccadabdabccacacddccbbbdddbcdbbadbddccbbcaddbbcadbbccaadadcbdccdbabdaadbbbdabacbcacccacacadabbcacaaabacacbadaadaaadaadbadacdaaadadbaabccccdccdbabbcbdddabbccdbcabacbcdbcaadcbdbbbcccaabbbdcadbacabaaddccdaacbbcdcadbdcdabcdcacbdbbcacbbcbccbbcadacaaaddadcdbadbddacdabbbbacabbddbdaadbacbababcbdacccdaddabbbcbabcbdccdbadbbbbddddcdadcbabccdabbabbadddbddadbbabddacbbdcdccaadcddacaccdaadcaddabcaaaddcccddccacddaaabcacbcabbacdcdadabcbaccdcacbcacdabdcacbdcabdaaadbdcbacbdabcdcddddccdbdabcbbabdcbccabaccbdddaabbdadbbbabcadacdcaacdddcbbccddbbdabaccbadcacbacddbccdcbbacdccccadbbdacbabccaccddabbcdacdacadcaadcacdaababcdacdadcabacbcbdcbcabbbbdbbbacdccaadddbabbabaccadcadbdadacbbdbcacdaacdcbaacdbcbcbcbbdccabdaaaabddccbcbabcbbccccadcbdaccbcddaabacddbbaabcccccdacccbaaadabddabaacabbcbbbcdcddcbbaccdacdbdbbaacccdbbdaadddccbadccadbdaabddbcaadbdbaccdbcddccbbdbabbdadbaabcacbabdbdcbabdbaddcccbaddbdbdbbdabacadcbddacadabaacaddadcadbdcacabdcdddccbdadbdcadbbbdacabadbadcbdaaddaadbdbbaaccdbabdbbdbccddcdbdcadbabaaacbdbdadabadabcdccaadcabadcddacbaccaddacbcbddbadddaaaddadcbaabcacccddcaacccabcbbdbdaddbcdcbbdaaabbbadddcaabbdadbcdadbcbababaadbdadbbddddacdbdcbacdaccdabcbcdbcaabacabddbabcdadccccdccaadaadabaabbcbdcbdcadcddacbaacacadacdbdcbabbcaacddcdbccddbaaccdcadbddbcacacadaaadabdbcbaddabcdccbddcbacdbbcdadbbacdddbadbbbbcbadbabbdddaccddaccacadbddbddcadbdaccdbbdabacacadcabbadacddbdbcbbbcbaaacbadbbdabacbdbcacbbdaadcdbababbdbbadbaccbdcdcbdbabdbdbddbbbccddadacacadbcaaaadcdcaacddcbdadcacadbbdaaddadddababbdbbcdcbbbacbbaabbbcccabdccbbdddadccacbdacbbacccadcaabaadcaacbaccbdccaaddadaadcbdbacbcdaddcbaabcdcdacdcabbaabccaccbcbcdacbdacbacddaacaccbdadbdbacddaadddcbaaababbbdaacdadbadabdacabadddcabcdddadabbcaadbaccbcbaacabdccbdbaddcdbdbacccbbcdcbacaddddadcddcadcddabadbdbaabacbaacdcdbaabbddcbadaddccccbbaaccdbacaacdaddcbdadcddcbccdbddbaaabcaaadccaacacdbcaaabacccddbcbcabacdabcdddccabbbabcdbbcacadadbbabccaabbadadbdbaaabbddadaacabaaaacbdcddababccdcbcaaadcdccadbdadadaaccdacccacadcaaccdddaaaabcabaacbaacdbaccacdcbacdcabbcadbddabcadbacabcadaabdaacbaacacbcdabbbddaddcacbdcdccacbadbdcbaaaaaabbdabdbacbccabdbaadcdbcbababaaddcacdbcabdbdadcbcbcbaabadacabadcccccadbddbdaaccbaccabddaaadbbddcbdaddaabdcacabbcbbaddddbcbabbbddbdcdacccaadaabdbcabbcbacdbdabdcdbacddaababbacadabddccdbaddccbcbabccdcacccdaaacadcccabdadabaacdbdcddadaacadccbdcccaccaaacccaddccdccdccdbcdbabdbbbacbddbacbadcdcdaadddccacccaacbbbacbbcdbbcdabbcbacbdcacddadcacdccbaacbbababcaaddbdbdaaadaaaccbdcadaabdcddabbadbbbcdddcbbaddbcbbcdbdcdbcdaddbdddacccccbaaddbdbcaadccadcaadcbcacacdcbadaccacbadcdccbbccaccdbabaacdbdbaacbddccadbadbaaadadabbbbdbadacacbadcabcbadcabcabdabdaaabaacabdaacbcacadbddacacdcdbaccdbdbbbaaccaaaacbdbdaacbbadacdbddccbadccabdabdcbdaadbcccbcacaccbacbbdbbaacdacdcbcbacbbbcadbaabccbbccadacabbdcccacaacaddbbcaaccaddbbbcbabbaadcccbcdddadadbdcddcadbadbcacccccdcadddbdbdbcaaaaabccaddcdbabcaadddbadccddaaddcdcdcbabbbccbacbcaaacbdbcabcdcadcdccdbcdababadaaacddddcccababcbadabdccddbcdaabbccddaacdccbcbdcdcccbdcbcdbbbacbabbbbccdcbcbcccaabbbdaadccacdbdadcbcdbbabbabdcdabcadbaccaabbcbadcdbacabaacdbccbdbaababcbcdcddabadadcbbaccdcdbbadbbccbacdaabbabdaccadbbcadbbdbdaccbdaccccbbbbabdaacddbcacbcacabacdadacdaccccdcbacaabbadbbddccbaddaadbaabbadabbadccbbdcbcccabbbdbbbbacbaddadbbaacdddabccbbacdbacddbbcdaddcccaccacadbddbbbababbccaccddbccddcacadabcccadcccdcdaacbbdbdbadbdacaccaddbccbbdaddcacabddcbcddbcbcdcaabacbbaaacacdccbbbbabdbacccdaababccadbdadbcdcddcbcdcdcdbdabccadadddadacdaccbcbbdbaaacbddbbcccddbdcbdccbccacaabdccdabaddddbbddcbcbabadabadadbbcacbbadbbbdbaadbdbaacbaadbaacbaaaccadddccddcddabdcdacaaaccccbbadabbaddaaccdbdabaaddbbddacbabdaabbcddbbdccbbdabbcdcbdbcdaaaadbcaddccaaacbdaabcdbdcdcddbdbabdbaadaadacbcbadaacacddacaacdcdabcdddbddcacbcaddccabaaabacdcadbbbdabbacabcbbbbbadbdbccccddcaddbdaacaabadbbdaddccabaccaddabbaabbbbaabdbbbbddcccaaadccbaaddcdddccaacccacbcddcdabdbbcabbbdabbdcdabbbcaccddcbdcbbdbccbbaddbbaaccbbbaabcddcaabcddcddadcacdccbbcddbbddabccbdaaadddcaccdbbbcbdaaabadcbbdacdbbabbdaacbacbcbcdcbbbbbcddddccbabddcdbdbaacabbdabdccacabbcbacddbbdbacaaacbcbccacdbcbdcccbcdbacdacbcddacbccaacabcbbdcddcbdcaadabdaacaadabbdabdbbdabadaccaacabbaddbbddcccdaadddbdbbbadabdabcacadcaaabdaddaadddaaaddddadddbbdbacacadbdbbdccddcbcdcccabcadaabbddaadcbabdcaccdadaacacddbdcacbbcbccaacbabddcaadccdaaddbbbcaabbbdcdabbcdbacbbbbbaabcbbcbcaccdabacaadcdcccddcabaacbdccdcbdbbcaddccbbbacdaadbbbbcdbbcbbcabaadcaacdccbabcdcdbdcdabcabdadddbaacacdbdaaacdbbaaaadbdcaddcdcacdcabcaddcaabadcbaccdaacaddbdddabaaadadccdadbccbadaaabbcbbcdacdbbbcbdcbaabdcbbcdddaaacadccbcbbacbcababdcdbbabbbdbaaccabcbccddaadadbcdabbbabddbbbaababadabdbcabacaadaacaccdaabdbcaaaabacaadaacddaaaadaaddbcaccdbcbdbddcbcbaabbbbbbaabdbdabadabbbbdcabbdbdabaddcbdabcbcabdabdddccdaccbaacccdbbcacddcccbdcbaccdabaddbadbababccacbcabcbaaccdddabbdbdadbacacabdccbadbaaabcabcbbbdbbacaddcbbacccabadcacaadccadcdbadbbbbdbdbbbbadbbddcbdccbdadaacbbdacdddbbbbdaacadaaaaaccdadabdcddddaabbdabadbdcbbdbbbacbbdaaadaddaadcadbbdaacbbaccadbcdabaaaaadccbcddacdcbbaacdbabadcacccabdcadbbdadddbbdcacaabbcacdcdbbdbdabbbaacacccaaaacddbbcdbbcbaccdacbcbcdbddbbaabbcddbcdccbbadaadadcdadbdaccccabacaadaddcbcbdddbadacbbbaaaaddcaccacbdbbbccabbaadcdbaabdcdccddbddcbbcddcadabadacdcbddadbbbdbcacdddccdbbccbaaabbbaaabbcaddacaccbabaacddcadbbadccbdbbbbbdcdbcddcabaaaabbccaaccaadabadbcddcdcbcacaddabbbabddccbdaaddcbccacccbbdccadacbadcbcdbabbacdcccaddbabbcdbdbcbbaccbbbdacbdcccadbcabccbcbdacbbdcbddcbabdddbcabbcdbabdadcacbadcdbadcddcbbdabddbdbabbdcabadbbddbbbddbddcbddbadccbaadddabacdbdcbcccdddcbcdbbaaccacdddacbdbaacbabbdbabbadcdbdddccadcacbabcacabdbddcdbdbaccbbdbbbddbdbdcdcabbbaddaddcabcadcdbbaacccbcaccdbdcbdbcbaaaacdcddddcccddadcaabaaadcabdbbadcacdbddaacaccdbccabcadcaaabbdbdacbaaddddacbaddaabaccaacddabcbacbccbaacdbddabdcccddcadbcbcbcbbdacdddbacdccbcbbbbacbbcbcddaddaddadacaccbabcaaccaaccdccacadcbbaabdcacadbcadbbdaabadaacaaabbbbabcdbbdcdccaccaddddcdbdbdabccddacabaccbabdabbcdbcddcbcdddcaabdccacbdbbdddddbcaaacddcdacabbacabbddbdbdcdbdbbbdadcccdabcacddabbdbbbabccdadbdabbbbaacbdbcbbcbbabcbcdaaccadabbbcdddacccdccccacdaddaabdcbbddabacddcddcbadccbccdcccbbabdbbcbcadcccacaaddbdbbbdccabbdacdacbaacaadcdddaadcbadadaddbbcaabaacdcddbcdbcbddbbbabcabadccbbbddddadbbbadbabcdbddbccbcccabbdaaacbbbdbdcbcdadcadadbdcbaaacaabbbcccddcddbcdddacbbbbcaaddabccbdbbcdbbccdbdbdbdadabacdcccaaadcdadbbbadbdaaacdbbcabadabccdddaacdcacacbdcaabbbabacbcadbdacaccdccdcdcbbacbbbcaaaccdcbcbacbbcababcbbadadcacbaaaadbcaacbbcdbaabacadddccdcbdcabcdabcbbddabdcdacaabacacccadbdbccacaabdabbabbddcadcdcaaaaaabbbdbcabadaddbaaaaaacdbbdbbbbcdaacadcaabacaabdccdcdacaabddaddcacbbbadcbcabcbcbccbcadaabaabbaddcdbcbbadacddbadaccbcdccccdaabcbdccbbaadacbccbdaacabccccbbacddadcbbdbbaddbddbcbddbbddcddacdcaaabbdbdccdacacbcaccbccabcadbdbbaacbdcddbcbbcddcbbcdcaaacbddddadcdacbbccaacbbccbaacdabbacbccabbbabcdbbdaacaaacadcadcacccbcdcaaaaccbaacaadcdadcbabdabddcdaccdaccbaabcacadacbbbbcddbccbabddcbcccababacddabcddbacadbcbaacdadcdccdcabcaadaaccddbdabdbccdbcbaabdddccdbdbbcbcbcbcbccabbbcdadbbbbdcbabdbacddcdaaadcacccccccdbbbbbddbbabcbadbcaaabbcadcabbdaabbdaacdbbacdaacacdadddababdbabadccadabdcdbcdbbdaabcabcaccadaabdddcdcddcbccbbababcddcadacbdbdbcdbbcadacbbdcababaacdddbbccaacdaacddbcabbbaccccabcbabaaabdbcdcdbdccadccdcdbbdadacabaddddbababaacbdddbdadcdcbaddcbcabaaaccdbaccadadcadccdcbdcbcaddbabbcbbdacdabadcbbabbbcbdcadcbdcdcacbadcaacdcdcadacbaadaabbaabcdcbacdacdbbbadbbddcdbddcbadbaabaaacdcbccacdabcdaaabccccdcdbcbaadbcdbaaddbdbbacbcccddcaacdcaddaabbadacaabadaccabdbcdacbababbdcdcaccbacdbabcccdcbdbadaaadbbbbbdbacbcdcaabcdbbcacacadccdbdddbcabccaaccaddbbbaaaddcaadbcbbbaddaadaaaaaaaacdadaadacadaccbbbcabaaddaabdbcdbcabdcaaabbdbdbbbabdbcabbcabbbbdddcbdcdcbcbdccabcdcbbbcdcbaddcbdbacbddddabaacdaaaabbdcbaccbcadcbadcdbaabadabadbdbacbccbbccdbbdddddcaaadccbaaddbcadcaacdaccabcabdbbbbddaadaccbaaacbdaabbdadaaadcdbbbccbacdcadbdccbdcaaddcdcccbabacbddccccbabcbcdbabacbbdabcaccbdbdcbcacbabaaccdabdbbbaaddcbabaababacddaacbccaaabadaadbbaccddbcabcbddabcbaccbacbccdacaddccddbbdbacccbaacbadaabadbcabdcbaacdccbccadbcadadbaacadbadddaacbccdaabacdddbbcaacbdcababaaccbadcbadaadaccabccacabbacabdbbadbadcdbcdcbadbcbcabcdbaddbbbdadbadccbbaadbadbdbbbbddbdbdabaddadaddbbdaddccdbdbbcddcabaadcbccdbcaaabdccacdaaadaddcacdadbccbcddaabcadaddcccdadccacdbbbcaccbcbdbbbbacdaabaacdbcaccdccadccdcabacdadcdacbbaddddadbcccbaabbacacadccdacaccadccdaabccaaddacbcddbdadcdcaaccabddcadadbaddccbaaadaacbcdbadaddacaaacaadaccaabcdddcabccdcbacbacabcbbbdabbbdbbadbcdaccaddadabcbccbbdbabcaacddaaacdbbbdccddcdbabcbaadabcccbacbdccabbacaadbbabbbccdccccccbddacdbcdddbbdcdaacdcaaaadadcbddccabaccdcaadaccdbdabccabadaabcbabababbddbdbdcdacbdddddbdcacacabcbaabcbdddbabcddddaabdbbbdbccbadcaddadcbbabdbbcdbccdccccbbbcabbbbbccccbcddcdbaccdadbbbacaaccbcacdddabdddabbbdacbaaddbcaaabddcaddadbaaacaddddaadbaddcadadcbdddbcacbadbadddbbdbadabbcbcadcdcccbdadcaccaaccdcddabcabadbccaaccbddcbdabccdabcbaaaccddbdabcaaccbabdccadbaabadaaabbcaabcbabcbabadadcabbbddcccdbcdcbaacdaaacdaabddbcacbaddbcdcaabcccbabbaadaacdacbdcbcbdcadddbbcdadbbdacbbcacdaacddbabbbbadddccaacdacbdbaadcaadcbcabdacdcadbabbcbdcbadbacacbcdbdccdacdcaadbbdddcdbaaacaabcddbaaabbcbdacddcaaddcdacbdadddbbbabcbaabcabaddbdbbbababddcdbaddaaccdabddbabddcadcbbbbaaabcdddadddddbdbadbddaabbcbcddccbdbcbbdabaabadaaaaadaccddadcaaaacbbabbdbdbdccccacacdbdcadbbdabbcabdcdbcacdadbadcacbbdbdcbcbbacbcddbdddbbdccdabcdbaacbdbbbcdcabaaabdbacdbdddadcbbbcabacdaadacddcdabbdaddaacabdccbcacccadddcbdbbaadbabacaaaaacbdcbcaadcdadddadcaaabcbcddacdacacdadcbcdbbacbaadcacacbddadbdadacbdcbbdbdacdbdbcbadacddcbbdadaacbdcadbdbdacbcbaccaaddaaaaaabcaaddcbdccbaccabbbdbcabcbdadacdadbbdacaddbbcabdabaaaccaacaacddbdcdcdbbcbccaaccadbdaaacbbbacddacbcaaddcabbddbabbdcacaaccbacbcdacaddabdcdcacababadbcbabdbacdddcbaadbabdbacddcadcccddccbcbbcccdbdbadaabaaacaadbdacccabbaadcccbbadccddbcdddbdbacdcaacdcbabdababcbbddadcddbbaababdcddbdbacbadcababdcdbdaccddcdddacdbdcbdbabcbbcbacddabadabccbbdbaabacddccbbcdcbdbdcccddcbadbddacdcacbbaadbaadbaaadddacbbdbbcbacbdacbadaadbadbabbbdcddcdccdabadaccccaaabcbccbabcababacaddccdacdcbacbcbbadbacabaadcbcacbbcaddbbdddbcadcacddbcadbbdcaacdadbbbdcdcbbcdababcbdadbabbbcabdaabaddbabbdbdaabacdbacaddaacdbbdcabdccabadbdabbdbdaabbcbbbbbbbbadcbaaabadbbdbadcdadabddaccdacdddcabaadaaadaddcbccbadcadbdbabadbdbccacaabacdbcaacadccdcbdadbaddbaddddabdbadabaadaccdcdadbbcdbdaabcbccdccbbdcbdbacbcddacdacbaaababdbcbbdbcbccaabdaabbcdbcccbdcaccdccdddaaadddcbbddcaadbabaaaadadadcdbaaacdcbccccbaccbdaccdabcddaccdcddbddddccbbcbbcdccbdaccddaabbdbdabddaccbbabacbadcacdcdcccddddbdadcababacddcbbaccccbccaccabbdabbcbabdbadabbcaabaabaadccddcdaacbadbcbbbbbdbababdadddbcbddddbddbabbadabacaacbadbacdcaaddadddcbcbacdcaaccbadacddaadcdaaddbcadaccaaccdcaccbcbaadacadccbcccadadcbaaccbabbddabbacccbacabcdbdbacadcddcdabbdddbdababccdbadabdcaacbdabdcacbddabccdabbaaaacdcbbdacddbddbaaddcbcaccaddaaadaaaccaaaaaabbacababbdaabbabdbcddaabaddacdcaddbcbcdcdacdabbcabcaddbccacaabcbccacbdcddbbcacddbdadbdcbdacbdaacabcccdcadaccdcbdcddcbbbdcbacacabdbdaddcccccadabacbdcdbcadbdaabddabbdaccaaadbcaadacdbabcbdaccacbaadcccbabaadddbacabbbaaabcbbdacaacbabcbadaabcbbdcabacbdcadcccdabacaaccadaaaaadbbbcdadbabdadddddbbacaaabdbbbcbaacdcbdabccdadcbdacbbcdcbddbdbabbdacdaaacbbdbcaddddcacdccdbadcdbadccddcbbbbcdbdddddababbaddcbbccdbbccccbbbcdddbcdddbcbcdbdcbbabacabccddbaddabbadababbadabbdbadbabcdcabaaaadcdcddcddbdcabccbdacadaadddaaadadbcbcccabdabcccdbdbbcadacdccabaaabadbabbdbbcbcadabdbcdbddaddcddabcbabccaacbcbbdbaacaddddddcbcddcddcacabbddbacabadddacabdddacbcbbbdbbabbcbabbaaaccbddcbcdbcbccabcbccbbcddbcddadbccdcabcdabcddbddcbbbddddbddabbcabaddcababacdbacddbcabbdabaacddbcdcbcbddaadcdcdabbaadaccadddabacabdabaadbdadcdcdacaaddbbccacbbddacccbdcddddccdccaccbcbbdddcaccadcabbdbdaaadbbaaadcbdcdddaddacbcbabcccbccdaadababccbbcacdcbdbcdbaaaaaddccbabacccbaaaabadccdbabbddcdbddbccbadcabdbbcbbbbdccccbdadcabdbccdcaaddccbddcdbcccbadcbcddbbaabbdacaabadbcbbcdcabdacaadcddaccacabaabaddccaaabcbabdaacacbdcbaabbdbbccddccdcdbdbcbccdddababcaddbdcddcdbccdacbcdcdcaacddaccbcbbabcabbbabbbddddcbcaaddccbbaabaaacabdaddcaadbaaddaaddabdaddaccbacaaaadddbdbdabbdbdbcdacbcabcbcbbddbddcdcddbcbbbcaddcbcbcdddcbadccbbbcadabcccadabdaaddbbcbdacaacbdcbaaccdaadbacdddacdbccdbdcaabcbcdbbdcacccbbdccaacddcccddbcaadbbaadacddccdcdbacbbdcccdacbdbcdbdccadbcabdaddacdbccaadcacccdcadbbbdaaccdcdccadabdaadaabcabadbacbcccacccaccccaadcccabdbccacdbdacbbbdabaadbaccaddbbaaacdadcdacdabbadcdbbcbcacdcbbcbbaccdbdcbdcaababddbaccbcbdcdabbbacdadbbaacbcdbadcaabdbacacbddcbccacdcbcddadbccdabccbabababbaacadddaacbbabbdabdddaadbabdcbaacbdaabdcddcdacaaaabaddccbbaaddbacadbcdbcdcbdbcdccadacaaadaacdacacddbdaabdadddaadcbabaccdcbddbdcadabacaddcdbcadcbcabcaddccabcadcaaddbddbdbacbadabaaabdbdaacabbcddbcadbbcbddababdbdaabcadccbdccaaddbcbdddacbdcabaadbbddabbbdbcbbbdbdcdcaabbbcdbccdadddbcbbbabcdbddcdacddbcdacbbcbccaabadbcdbadbdbcbbbcaccbbbcadbdcbbbabdcdbcacddbcadabdadddabcabbcddadcacdadbdccabdbcdbaaabcaadaabbdbbbcabbababdccdacabaccdbbccbaabaddaddababaaccacbbcdbcddbaabdbdcdcccdcbbaacbdcdacbcdcadccaccccabbbdbccbdbabccacdcdbcdccdabcdbdaaddaccabddabddbcabccacacbdbccdddccdbcadacbdccbbaacbbbabaccbdbbccbdbbbdbacdddbdbcccccdcbbabdddaccbdbcdaabcaaddadaaaadbccabccadbaddcbdbaddbadbccabbbdcadacbdddbcacccdbbaddbcaaddadacbaabcbcacdcdbacabababcdaddbcaacdccaadbcbadbcabaadddabccadaddcbdccbbabaaaccdcaccbadadcdddccbcdbbddbdabbcaddbcbbbabcbabaadcdcbabbddabdbadbbbbdabbaacdababadcaabccbdabacdbcbdbabaaabdcbdddbddadadccdbabbdbbaccbcbaaadbacddbbdddbddddbdaacdbcdadcbcadbbbdaccacbadbbddddcbbabaccaaaddcadbacbdbddabbacdccabdcbcbcbbcaabdabbdcdcbcadaaddcaccaabbbadcaddcaadddbcdabcaabbbcdaccdabbbcadaadcacbbdddcdabcaccadcaadcdbcddcdcbacddadbcdadbcdddadbacccbdaadbcacdadcdcadcabcdbcbcacbcbdadcabadbcadbccabbbabaacacabbabbdabadadbccccbdcdcccdccabadacbdcdcdcacadcbdbdbcaccdbbbdcabbbdaabaaadaddbccbbaacdcbacdbbacccccddbcaddbbcabdcacbccdacbaddbcbadcaacdabadabaaabbddbdabbdaccdcbdbaaacaadcaacdcadcbccccdabbbbadaaabbbcdbccccbadabbcbbddddaccccddaabccadcadaddcbcccaaaaacdcbddcadbdadbcdddccddbcbbaddadbbacbcaadcdadbdcdcccbacdddaabbcccadcdddaccccdbbadcbbbbacabbaaddaadcbdcbaddbcbcbccaccabbadbccbaddbbbdaacaddccbcccbbcabcdcaaaababcacdadbabdacbbddbdcdcdbabdccdcdabbddaaabbbabaccaadaabcbcbddbbddabaddbbbdbbcabddcacababaabdabdccdddcacbbcbcdbcdbbadadaadccaadacdaddcbdccddbcddaaabcdddbbdbdcacdabaaaaaabcdcbcbbdabccdbabbcdbbaabacbdccdbbcaddbbbbdcaabacadbccadcabcdbbababccaddcdaddcbbbacabccddcdadbbbdbdbcbccbbdcaabbccbababacdbadaaddacbdddcdbcabddcdddadddabbbbabbcdbcbbcbadaaacabbdbaccbacabcadbbbbdabdbbcbcbabbcadcbcbbcaacbdbacdcccbabcccacbbcaabbcddccccdbabaadbdcbacdbdadbacbcacaacaddddcddccbdbbaabcdaddbdcdccbbddcbdbbbccbadcdabdabbacaaaadcdcbdbaccbdaaacaaadccdacbcdbdaabbcdadabdbbbdaccdbadddcacbdbcabcbddddddddadadadbbabcdbcdbacbbbcacabcabcbbbdabcbdddbbdddabaddacbbdcadbcadadddddabcabbddbbdcabaccdadddaacabcccbadcdacbcbcbddaccbbaaddacbcadccbdddbcacaccbdaaabdadbadaaddbacccadaddbdabadacdbabbbdcaaacbabddbbbbbacbccaaddcdcbbddacbabbacabcbbbdacaadabcacbcdcbbccdbbdbdbcadcbbdadcadddbcdaccbdbccddaddadcaaaacdadbadddcbbacaabaabcbcaacbbdbdbadbbbaccccacaaccccdcbabadccacdbbaaddbccddcadacdacacabdacacdccddacbcbbcaacdcbbadaadbbbcabcaababdaccdabdcaabcaaabddccaaacacaacadaabddcabdcbaddbdabdabdaabccbcbdacacbbdbaaabbcabbbacbacdcbcabdbdacbccdadaddaaaccadddbaabaacbddbacadadbbdaddccbaadbcbdddadacdadcbcbdcdccbdccddcbbbdbccabccdcdcabcaabdcaddbcccabadccbbcdddcaacdcddbdbcacddcbdcabbcdddbcddcddcdccbddccaacaccaabcaadabdcadccbadcbbabbddccdbadddaaabbaacddcbbadabcaacbcabcccdbbddaacdbdbabbccbadccddcbdbabdbdcdddacbadabdcbdbdabcadcadabdccbdacaccaaadbcbccccdcababccbbaacacdabdadbacbdcaadbdbbacdcadbdaabccaacdcdcdacbccadbbbddabcacbabcaddabaccccaababdcbcbdbccaacccabdbacbadbaabcdabbcacdddabcacbdddaadbcaadcacdbbdbcccdccdcabbbaaaddadbacabacadbbcbbbacaaddccdcbadbcaccaadbbdddbadaaccddbdadddcddababdbbadabcdadadabcbbabcabdbdbbbddbccbbcbaaacccabaccdddbdbdccccbbddacabdbdbcdadcdcdbbdcdbdabbbbdccdcdbccacdbbccaadcababdacaccccbcddcabccaaabacbbdbdacaaadaaaaccdacbcaddaacbbbcddccaabdddbbbbdcabbaadbcbaacbaadccdaacdcbaadaaadcbdaacadcbdccdbabdcaacdbcbdddaacdcccdaddcbcadccbcdbcdadbadbbaccdbabdbdbccbccababbadbcdccbccddaaaddacdaadadcbbdcaacccbbaaadadcbdabdadadbcccbbcbbabadbccbadccddaaabcdddadddbabdcabccbabcbacdccdaddbbbbbdccabdcbddbadcacaabbdbcabbadaacbbdcacdcbdbcbbacccdabcacbdabaacabbbbbddadcdbcdbaabaddcaddddcccadaccbcaacccadacbbdabacbadaadbdcdcbadcdddbcdacadddacadbbbbdcccabacaccbdbcacaddbdcadbdbadddcdcacbdbddbbdadbaabcbcadaabadbacbdbaccabdbaaaacbbbbadbddcadacdcbccbaddcacaddababbaadcddcbaddbbbbacbdcabcdadaddbcacbaacbadadacdbddddacdbbabcaaaacadcabddcdbdbddadbdbaccdbcbbacacabddabdbabcdddbccdbbbaacdcdccaccadbaaabadccbcabcbaabaaabdacabdddcabdddddcacdcababccacddccbdabdcbbaabaadbabbcdacdccbbdbabcccbcdcbbbbbacbdddccccdaacbaabcbbadacccdaabcbbacbcadaadcabccaadbcdcabcbbaadbbdbcbddccbbabccdcadbdabdabdcdcadcddbccaadbabaddbaabcaaaabbaddbdbccddbcdbabaccddddbdabcbdbbbcbabdcaaaccaacaadddacbbdaccababcdbdccdcbdcbbcbbcaaaabdbbbcacdcaadbbddbbdcbccbdcdddacadaddbccadcabdcccdaccbdcddbcbddcacadaaaacbbdccccbbdaaddadbcadadbbcdaacbcbbcbbcbddacdcddaddbaadadccbbdddbddcacccbbaddaacaaaaabcaadaccdbdbbdbaabcdccaabcbbcccdabcacaccbaadbccdacdaadbcbaddadcdcaddcaacbbcdabbdacababddcccdcdbdcbadbaabaccaabdcdabccaaadcabbddabdacadbbccadcbbdbcddcacaadcdcdaacbbddabdbcadadcdbcacaddaaadaadacdbbdbbccbbadbcddccbabbddcaaddbbcdaadabdaaadddcadbdaddaaaacddacbaccddabadadbcabbdbcdcaabdbcadcaadddcadcbdccaadcccabbddccbbabbbdabbdddcadcbaaacbcdaccbdaaadcddddcdbbbbddcaccdbaacabbaccddadacadaabbccabccaaccbcdababcbdacbcdbdabaacbbacbbbabdddaddbdcbaadcbabbbacaadcbccbbcdddcdbdbdadaaadabdbdcacaadadcaabddbabcdddbdbdbbcbabaddabbbbabcbddddccacaaddcddabacbcdaabaadccdbcbadaacabaabaddadddaccabdaddcdadcabbbadcdddcdbaacbadadcdbcadbcbcacaacabaacbcdccadbaabdcdabdbabbdbcaccbcdcddccdcabcabddcbaababdcccbcdbddcbdcaacbbbadaabaddaddddadabdbadabaacbaadbadabdadbbaacdbddccccacaaacdbadaadcddcaacbcaaccaccadcaaaacddbbdcabcddadbbbddadccbdacbbdcbbacdddcdbdcbbaaaaccbbccaacaaccdbcdbbbadacdbdbcccabdcbcbbdbaaabadcadbacabacacacaadbdadbaccbdacddaabadbbccdabdbcbbdabacdaccccabdcaabcdcbdccbabbaadcddacbaacbddbaccddddcabbdccddabbbbaccccddaddcbcacbbdaaddcbccadabbcbcdbaccbddddacaccaaddacabaadbbddcbadadcdacbccbdcbbdddbcababcbcdabddbdababdbbadddababdabbbacccbbaaabbbdbdcaaaabdcdddcadcabcbaddddcbbdacccabacdbadacdbcdcaaacccabdbcaddabbccddbacdccdacacdadddbcbdbcbbdddabcbddcababadddaaabcdaddddcaccbdddbcbbddbadbbbdcdadabaabdbcdabdbccdccccacbbaaddbcabccbcacbcabbaddcbcbadddbbcddccbabcadabbdcdbccbccdccccabdcacaddcbdaabcbcbdabdbadcbccbdbcacbcaddccdcbbbbaccabcbcaaadcdbbabcacabcacadadbdcaaacddcacbccdabbaccccbcddcdcdbdbccbdddcdddbdadbdacabbabdaddadbdddadabdbcacdddcbbabcaacabddbabcbaadcbdbcbcaabaddddbbccbdccadadbbadbadcccadcbbdacacbdbdaccabcbdaabcbbdaadabdbdacacbdabbcddddbdcbacabbbbbcdccaccdccdcbcbcaadcbcdcdaccdbddabddaadadccdcaadaccccddcabccccbddcabdbcdddddddbbcbcdcdbdbaabdbaabbbbcdcddbbcddbabbcaacaccdaabbabdcadbacdbcdddbbbcadddcdbbcbaddaadcdbabaabaabaddccbbacbacaacccaaabbdcbbbcccddabaabcbcdcdaccaaabbabacdccabbabcacbcbbaabadadcbadccdcbdccaabbdcdcabccaadcdbcbdcdcacbbbcabdcdacbcdddccccbdcaacbddabbbababcbbbaccbaddaadbbdbabdcbddbbcbcbabcdcbdccadccadcbcddbbccbbddadcbbbbdcbbaccdbddcbdabcdaabcdabccddbbcdcdddccdacbaddcbbbabccdcbdbaaaddbcccbadacaccbaaacbcbbbdcddcadbcdcdacccacbadcbadbbbcdcbcacdbbcaaaabbdbacdacaadccdbddaddbacccbcadbacdcabbcaccdbbcbccbbddaabcdbbbdbddabdcdaaccddbddbcdcadbccabcdcbbbdacdabbcbdacbcccdacbdbaaaaacdccdbdddbcccbaddbcabddbdabcaacbbccbadcabddadadbaddadbdbaaddbdaddbaaacacdabbaadcbbbbaacbddcadbbaddddbddcaabcaababacacabcaddcaacbdccaabababacacdbaaabccbbdbdcdcbdadadaaadbacdbccadbccacbbaddccdcbdadccadaadadcadcdcdcbcaacdcddddbbacaadacdbbdccdbacaadbabcbbccdadabadbabdabdabdbcdbccccbdcbbaaaacaabcbacaadabadbbaadcadccbcdddcadcaaaccdcbaaddadbcbababcdbaaddabaadccacbdabcaccbbdaadbbbaddcadadbcbacbbdadbdddbabbcacacbdcabbadbaaacadcdaddbbddadcadbaaccbcddccabbccaccadcbaadbbbbaaccccbbbdcacbabdacdbdacdabbbabdaaabbcacaaabaabcacccaaccabcaccdcdabaadadcbcaabadadcacbadcccaaabccccbacadacccbacaabbdabcdabacddcbbbdcbbddccdcbdacadddcdbcabccbccacdbcabdabbdbcaadcbabbbbaacabdadddbbdbddddbbbddbcaaaddcddacdaacbcbdadbdddbbacadacacaadccdccdbadcbdbaadccbdcdababcdbbbddcacdacbddbbdbcadcbdabbbbdcabdadbdcddccdddbddbbacddddcbacdbdaacdccacabdbdcddddbaacbabbadbdacdcdccaabccdcaacddbbabcadcacdcadbdcaaaaaadccaddccccadbaacccaacbbdbcddbcccddaaaadbccbdcacbcbbdbabbbccbdcacdbbbbdbdccbdaabcbcdcaabbbddbdbabadbbacaabdddaacaaddaadbacdabcacbcabadbadcdacbaaabdbbdbaaabdddddacbadcdbdccadbabdcdabcbcabbbaccabbddbdbcdcbbbabdcddadacdbcbcaddddbdcabadcbbbdacaacabcdabadcddddbaacacdbbcaadcabdcbdadccaacdbdadcabbbbadcbcbcabaacdaccaddcdacbbbdaddbacbcacabdabccbabcaccbdaabacbadbccbdcacadbbccabbcdccbcacdcbdbcabbcddbcdcdccacbbbaddddaddcadaaacdaacadaadacabcbdcbcadbcadadcbbbdddccbdcbcccbbacbadbbdbcbdcbdbbdaddccabddbabdacaaccbcaddbdaddcccbbbbaadaccccbdacbbcdaccdbcddbcbdbadccbdbbbdcacacdcbbaaaadacdcbdaaadddddccabbccaaddadddccdcdcabdacbcbabbcdbbaabdcbdaddadcbccbcccccadcbcaabccabbddcdbcbdbbbddddcbbaaabbcddddacdbcbabdccacdcabbbabddddbaddccbabbddadcabbcdbbcaabcabbdabcbbbdccbddbdbbbcbdcabccdcbbcdaaaccbdcbabacccddadccdbdadcaadabdbbabddcacdbbbcdcaadaabdacbaadcaccdbbcddccbccccaaacdbcbaadbcbbcadbcbcdacacabbadbaabbcddbbcdcccdcdddcbcbbbbaabdccdbbdcbadaadcacadcccddbbabddbacadaaacacbccdcdbbcddbadaddaacababdadddcdbcdcdbaaddddbddccbccdcdaadacadcbdbdddcabdacbdadbdbbabaaadbbdaadaadaccbcbdbaabcccaabcbbbddacadccbdcdadcddcbdbacadacabadcdaacabbabcbacadbbcabbcbcbcbcacbadccbbdcdbdbccaccbdddbadcddacdaadddbdcadabcdbbdcaaabccccbbadcacbcdabbbbcbbcadcadddcdcaaaaadacbcadaaadcbbbdbbccbbbaabacbaddadacdcadaabdcbacaccdddbccdabbbacdbacabbbddcadbacdaccbcccaaaaacbadddababdcbdaaaadcadddbbddcbdabaacdcbabbcaadcdccaacbcbacaccaaccaaaccbacdcccccbbccacbbadabddbdadcaabaddcbdcdcbacaccadabbbdcbcacbadddabaaddcdcbccdcbdbabbdbcddbcbdbbbcddddaabcbacdcadbabaacbcbdcbbbcbdbbadbabcabbadabbdadddadbbcdbcbddbbaddacdddbdabccacbdccdcccaabacacdddcabbcddcdadcbdadbbcbddcbcaababdcadaabddcadccadaaadabbaaabdbcaaddbaabacbcddcdccadaaadabcdacdbacccadbcdbabaaacabdcacdcdbdbcdddcadaaacdddddddcabcccabbadcdabdccabdabddabdbcadaacdbaccdbabacacbadadbcdadacdacadcabbaccbcddbbdccaadcdccddacbbbacabcbcbbdbccddaccdadacacdcbaddddbbddabbbdcdbcaccacddcaddbbdaabdccdaccabdadadcbaccbcbccbbcccdddbddbbcddcabaaccdcdcbacdadcabacdaadbabdacddacdaaacbdcbbcdddacaacadabdbcbdacbacbcabdcadbabadabccddbdadabaaabcbccddcaadaabbcaaddacbaacabbdcbcabbcabaccacdcabddbadbdcccbbccaabcbacbdaacaaddacdccdbbcdacdaaaabdbcabadabbdbdaaaddadcdcddcabadaabadcbcbbdabaaaacaadaabaacbdaacabddbbbddaabbdbdcdccddaaddbcadbdbaacdaddbdcacccbabaabaaaacaccdcdaadbacdaabbacdddadabcdadbcdaaaadbdbdbbacaddbbcbadbdcdbcdcbccdcdccdddaabdbbbaccdaababacbdbaddbdaaacaccbbabdbacdaccbdbbdcbabcaccddcdccbcccbdbcdacdcababacddbdaaacaddcadddcddabdcaaaadcacbcdaaacdcccacbbbdacdaccdadcabbadcabacbdccbbcacdbcbcdacddbcacbbdabccdbbcdbdbdbaadaddddcdbcaccccdcdcddaddcacacbbabcddbbbcaacdcddacaccbbccdbdddabdbbcabdbcaaababcaadaabacdbcdbbabdaaccbcdaaaabcacadbcaddcabcaddadcabbadaacaaacbbdbacbbadbdddcbdcdaccdddbaadaabdbccdccadacdbcadcadbaacbcaadcaccaaabbbbbbbbdbacccaaadadcdaaabcbddbbdcacaadddccdbbacadccddccbacadcbdccabdcdbccdaadaacabcdabbaacbbcdbbddbddcccbcdcbacbabbdbbcbdbadbadaabbdacaaccdabdccabcbbbbcadabcadaccdccbcbadbadbcbbcdcdaaadcdddddbdbbcabbbcdabadccdabdcccbcdacbacbdacbcadbdccaccbadbdaacdcbbcabdbbabddadcacacdabacbcccaaadaaacddcddcaadcdccdbdddcddcdbacbcbdaddcbcaaddaadcdbcacacacdbdaaddbdbdaacbdddaacadcbddddaadabccabccbcccdaacdabccdbaaadacdcadabddbdcdcbaabdddacdcdaadadcadaaaacbdaaaccccadbcdaccbcabcccdaddacdcabccdccbdbccdacccdaaabccdbbbacdcbbbcababcacabddadababbccaabdbcabbdbbccdcaaccbbacdbaccbcbdaabcbcaacaabbcbaccbcdcbcbcdaadabbbcdbbbdcaccdcaabbbacabdcbaabbdbbcacbddbbbbdbcabccacbcbacbbcbdaacdbcabddaaaadcdabbddabdacaadcddbbcccadbcdddcbacccbcbdabadcaddabdcbbddadcdcdacabbddccbaaabacabcacabddbdbadaadadbccadabbcbdccbbacccaccbcbabdbbcdaccaadbccbcdddcbdbcacccdabdcabbadccbddaadbcacabdccbddacbcddacdbddcddcadadadcadbbcddadbaddbdcacbdccabaddabdcbcddaaadbacbcdddaaacbcbadcbbcbdcdbdabccccaabcbcbdbdbccabcbacdaabbcabacaaacacdbbcbbabdadaddcddabbcbbcbadaacccdbbcdccdabcadbbdaabbddbcccbcccdcacbdcbabdddacabcaabbabbcdccccaaddddadccdcdbdcdcddcadbcdabaadbdabaacccaadaabccdccabababbcbacdcddcdcdbadbbccdcdcbcaadadabdaabdabbbcccabbbbbcadddadadbcccbabcbcdccbcdbcabdabacabadadcaaaabadcccddbadccbdabdadddadcdccccbbcbbadbcaaaacacdcbacdaaddbcbddcadadabadddaaccdadaabcdadddbdcacdadbdcadacbcdcdaccabcbacaabbcbdbcbcddadaaccdabbdbaabbdbbbbdcbbcccbcbcdbadbdccbdbcddadacdbcbbacacabbdcccaaadabcabdaadcbccaaacbccbaccbbacdbccacbcccdbcacababbadabdbbbcdaadbccdbadbaaababbacdaadccdabcbacbaddbcbacadaadbdddcdaccdbaacdcdbdbcdaacdaddbcbbcbbdadcdbacaddabbbcddbabcadccdadcdbcbddacbddbdccdcccbbcbcdbbcacacdbdcdbdaccabcddcdbaaddbccabbcbdabcdcaacacddbbbdbddddcbcddcdccbddbdcacaddbadbdcbdccdddacaadaacabbacdccacbdbdbbadbbdddbbcaadacdbccbbabdacbacbdccddcabddbadcbbcaaadcadcddaddccacacbdbdccadcacacabccaadbcbdccaacccccccbddaaccbcadaccbccdabbcabdcbacdbbcdacaaabcbacdabaadbcdbcdddbadbccccdcbdbaddddcddbdbdabbcbbbaccaccbabbcbdcdbcdacdbcabddaaaacbcdababaaaadacadaaadadacbbbbcbaacdcadccaccaddaacbdddaacadacddddcbddbabadbbaacbddcbbbdbcdbabcbacababdacaddcacacddbdbbdaadddacbbcdccdbbbcbaccabbabdcccadbcdbacbdadaabaabcacaaababccaaaddcaabcbabaccabadcdbacaccccdddbbcaccdadbabaadccbbbdcacbcdcdadabcbdadbcccabdbdbaddddbbcbbaadadccabccddddcbbbacbbdddcbddadabaaadbbadccbaddddddaaacdcbdcbccdacbaadbdcadbacbcbabcbabaaccaadbbccadabbacdbabbbcaadadaacbccacbddabaaacdddcdbaaadaaddbbbbbadbdbabbaabbbdbabcbbddddbcacaaaaadbaacddadabbdabadacbcbccccaadbaaaabcbccddbdbadbcddcccdbbcccdbcdccddaaabadbbbbdddbccadccadcdbacdaadcccdbbdcaaddaabcdcaacdddabcdbadbdacacacdaabcddcabcdcbabacbbcbcddbdacbdbabbcacbbbaccccbbdbcdcaabdadddbdacdccaadacacddbcabbcaadbcabdddcabbcadaaacaccccdbdcacddcbcadddbadcbbbbbcbaabbdcbdbcdaabbdacbcccddbbacdcdbbdbaaddcabdabdabdabbbaacddabccabcbaacabddbdadcabbbaddbbabdbdabbbbdaaccaadadbbbccbadcadbabbdabcdcacacbabadbdcabdccdaacabbbaadaacdcddcdcdbacdbcadbdcbcbaddbcbcdbdbdbdabdddbbaabcbdacdbdaccbdbccdbabcbacdddcbcbaadbbaabddacdaaaaddaadcdabbccdbddacdcabbacddaddcdabdbadbbdadadaacacdcadcadcadbcacacaadcbdccbaacadabddbaacadadbbcdadacbacddabbccbcbcabaabadadababcdcbbcbdaacdbdababaccbcbddbcdcaababaacbbadbbcababbcabbaaaaaadbbbbbacbbbbdbababbadcccdcbabbdddcabbccadaddccbbcdabdcddddbcdddaacacabccccbcdaddbacddbababdbdaaaccadabbadaadcbdbbbaadadadacacacdcdbaadcdccadbdbdbcdccccacbcaaddadaaabddbcbcdcacdaabddbdcddabaabcdcbbdccdcbadccccccddbdcbdacdccabaccdbcabacdcccadbbccbbcbbccbcadbcadcabddcacbdcbcbbdaadccababdcbdabdbcabdbbcabadccacdddddcaaabcddaddbabccdbbabbccdabdabbdcaaccbcbcccbbaadcbadabcbbbadccbadabdabcbcbddadaabcaacccdaadcbabddbaacabbcdcaadbcabadddcdcabacbbacabccadaadadaccdbddbbbddddbdccbadbddddbdcdbdcabacdcaadbcdabdbcabddbacbdcababdddaadaaddabbbccdcabdaacdbbcaacbaaadbdabdcbdbcdacbbaddaabddaabcdaabbbacbdcaaaccaadcabacbbdbcaabbcaadadcbbaadcdddcbacacdaaadcdbcacadbdcdddccccdbcbdaadacdbddbccaacbacdccbdbaccdbdaccbadbbddccaaccbbaacdbbbccacadbbcacabcdddadcbbbdacccacdbbadccdcbadbbadccdbcabbcbcabaddadaccadabacabbdcacabbddddaadbcdddacaabaaaabcaadaabcadbcacdbbdadabcbcaadddababcccaddabdcdabbdabddbaacbdbcaddadbdbdcbcdccbcbcacccbbbbdcccccbbaabbdcdbbbbaccddadbadccddbbcbabbdadcdabdacdbbaabccdcaacccbdadddbdccacbbccdbaacbaabadcaddadbbdccbaaabccdabdacbbdcbbadbadaabbbabccbabaddcbdadcdaabbacccbbbacbaccdbcaacabbdbbbadabbabbddacabacdbcbadcaaadcdddbaaacadbdbdadcbababdcddbbdddacdbcccddaaacbcaccbaddbdababbdaaacbdcababdacddddbabaddddabbddababbcbbadbbcdadadddbdcdcaadadbcabdaddadbddcdbaacdcbcdddcacdccaabbacdbddababcaadadcacccaabbccddcaaaabbcacddabbbacaaddaddaaaddbbcaaaaacdbcabdccccbbabdcbcdddbccbdcbadcccacadccacccbadaddcabdbcdddcacccdcccacbcabbdbababbaaacaddbdcaaaacdadccbbbccaaaccddddbaddbbaddcbdbbdaccababbdabcdccbaaadbbdbbbdaddacddcccbdbdadbacadbddcbcbbdcbccbcaacccbdbdbabaddbbdcbdccababdcccdadbaaaacaabcdbabbcbabddccacdcaaadcbbbbdabcdcdaadacdbdbbdbccddcdabdcddbdccdcaaaaaccadabbbacdbdcbddcaaddadcdaccaaabbbcacccdaadabcaccbcbccbbdcccdcdbcabacbacacacdbbbdaacdbcbbbcbbbcbcdaddddacdbccdcabcccabbcbbbccdccbabbccaccadbddddcaaaaccddadcacbbdcabddbbaadacacccadbbaaacdaabddbacaaddabcabbbccbbcbcabcbdbbdacadbacaacadbdddabccbbcccdaccbdcdddbdbbdacddaaacdddbdbaacbdccdcaccaadbbdbccbddadaaaabaacbcacbdcccaaccdaadbbabbaaaddbdbcaabdbbcdacccbbdaaddbcaccbccadcacdbdacbdcbaddddbbdcccadabddbabaacbdabbccbbdbcddcdcbccaaadbbcbacdacaababbddddddaabcbccbbdbcaaaadccbbadcccacbadcbabbbbcbcbdaabdcbcbdabaabacaddbaabbaadaabdaadacaaddabadaabbdbcbbaaaabcadcabaccccbbbddabadcccbbdbbacccaaababcaabbbabccddcbcbdaccbdbacdcddbadbccadacacaabcabdabdbacadddbabcdcbddacbbadabdcbacbcccbdbdadabbdcadcbbbdbbbabacdadbbcddaabbaacbbaabbaadbabaabdaaccbabcbaaabccbbddcbdcddcaccdccddadbccdcaddabccadcbbcaaaabacdbdcdcdcbbccddcdbbcabaaabdcdadcacdbbdcdbddbaadddabdddbdbdaccdbcbbaacadbbccacbbcddbccabdcacbccbdadcdbccdcdadddcabbbaacdabdadcbdcdcbdabaccdcbacddadcdcbdbbbcdcbbbbaddbcaacbcabaadbaabacadadbabcdccbbdbcccabcaadccbcbdccdabaaabcabbcdacabbbaacadcbcbdbbcdcbbbcbbbabdabbccddccacccccbccdacadcbbbdccccdccdcdcdbadbcbabbacbabcacaadddbbcadddcabcdbaddcbaabbaaddcabdbcbabaccabdbdbcddabccacbcacbddcddbcadaccccababcdddadbccbcbbaccdcdbacdbbdbcdbcababddbddcabadbaaaaabdacacadcbdaaabddaaadbdbbcbacbcaabbcdaabcbacabdadbbccdacbbcccdcacbbbaacdcabddcdadadcacbbbdcdaacdaabadcaaccdccdaaaaacbcddacaccacbacabbccaabaaaacbabbbabcadabcbdaaacdabdbbccbdbcdabcdbbbccadcccabcdaaaddbccbccbddacbbadadcbcaaccaacabbcbccbdcdddbcbcbacccbacdaccaccaabaabbbddccddccacbacadcbdcabbaacacddddbaccdbcbadacaaaabcdabbaccbcaddcacabaccdbacabcdacacbbaaddcbbababaacadddaddaddcdcbcdcbdcccccaddbaadccdcccadbbcdccaaacaddbccaccbbcabcbdcddbcccbdbcaadadcabcabdcbddabadddbdbdcbbababacbbababbdabdcacbbbdbcdaabbdadbdadddabbbcdaacddadadcdccbddaaacaacdabddbaaabbdabaabbddaaccdcdbbcdcbcbdacdacbdaacbcdacbcdddcdddbcdcbdcdaaabadcbbabadaadddccbdcabcbabbaacaadbccddacbaacbbaaacabbacccbabacaccbddbbdbabbcacdadcadaaabdbbaaccccaaaaaadacbaadddddddabbdbddcddadadcccbabadbddbbbcdaacabacabdbdcabdbbabcaccaabcadcbcbaabbdbdcdcacccacbabdbdbdadbdcacddbbddcdacdddacabbccbdaaaccbbaccbacbadccbaaadaaaabcbaacababadbdbddcadddbcdbbdcbdbdaaaccbcacbcdbbaabbdccabacbddacaacadbacababaaaccbccbdbcaaddadaabcdcaddbccbbccabdbbdabbbcaaccbccccabbdbbacbdcbbabcdbcbbabadccddcbcbadbdcbbdddcaddbcbbabcdacbdbaccdbaaabddacdbabacadbaacbcaccddaccdcbabbbbcbbaacddacadabadbdddadacadcdcddbabaaacaabaaddbdadaddacdbdaddbccdcbbdaadadcadbadababdbaddbdcbabcbadaacaacacadbdaccdaadabaabbaabccbcdcbcbcaccbdcacdcaddddaabacabccccccbdddcbbbdaaabdccadcdbddbaadbdadacbcdbcacddbbabcbcbadabadabdcdccdaaccacbabaccbccdaddadddadddbbabbdddacacdcdddaaacbdcbabbdcdadbadcccddddacabbcdcddadbaaddadcadbdacccaadbadbdddacadddbcacbccabccbacdacbdabdbbbcacdacbddbbccaaaccddadaddcaaddadaddbdcadabcaaabbcadcddcdbbcbbcabbbdddbaacacbdaabdbdbcbdbbdbcbbdacdaabcdcccbadbabcadadabbbbacbbdbbcabadbadbadcbbcdbaabbdddadccbddbacdbbaabaddbbaccacbbacabadacdddadcdccdccdcbacaacdcaacbccabddccbcadbacadacdadcccdadcdddbbdbabbdccdddbcdddaacddbbcbccbbaaaacbabcbadbbbadcbcbddacdccdccddcdddcdbddbcaacaddaadbbaadcbdcabcadadcacabaacacddababacaacacdcccaccabccbbdbbccacddccbabcdbbcabbbdbacdcbcbabaabaabacbaabcadbadcabbacdbcdcbdbbcbccdabaccccaaacddbabcdbcbcabacabdcacbbcbabdcdbaddbdcccaaaccdbdaccbbcccaccdbcccaddabcbbccabacabdbacccaadbccadabaaaacadbacddddadcbaacbcdbbcdadabaccdcdaacbcacbbdcccadaadcabbddcdbbbdddaaddccacdcdddccaccabdaaadddbdacdabcdccdaccadaacbdcdcdaacadbbabadcaaabbaaacdbccddbcdccbdaaaccbaccdccbdcbcbcaaaacbbbaddadbadabaccbcacabbccbcccbbadcbcbccccbccaaccbabbdabbbdbbadaddbacbcbbabdcdccabdccadbadddbaaaaacbabdacaaabacccaacaaaabcadcccbbbdbdcddbcbbbdaabcbbcbbbddacaaaaccbdabaadcbcabbacaacdbaadaadcadcdcaccadaccbabbccaddddabdbcbbcaaacdcddadbdacbddadcaabbddcabcccccadbabbabcddcaacdbcabdabdbcbacddcccdbadacccbcaacdcbadcbccddcdacbccbabcdababcdbbaaddcadbbcaccaabcabddaabcdabbbdacdcbcaddcbabaabdbbaadadcdaabdacbdbaddacdcbdcbdabbabbdddbaaaccacbbadadcdbdcabbabccbcdcababbbbddbacbbbbbcccaccdacbbdbddbcaaacabcdcbbbcacbbcdccbccacddcbcddabbacbadbcdaabbadadbaccbcbadddcddcbacdcccadadbadddbbaaacbbdbdbadccbbadbcddbadccddabacbacddaacabacbabbcccbccbbacbabddbddaacdabbdbaddacbdbcccabbdabdbabcdcbcbcdbcbdacdcddcaadcabbccdbbadbdccbdcbdaadbcbccdbcbcaadbdacacabbccdaadbbaacdbdadddbbdbcccbbbacddaaaadcbaacabadacccaabbcbcaccababadcbaacdaabdabccdbacbdccdcdcbaccabaabbdcdccddddaddaadcabaaccaccacadcaaabaacccbcacadcacbcdbdbadacdacbbddbbccaccccabacbcabbccaabdcadbbcccddccadadacaaadcbdcabcbbdbbdaadabdacbbaddbadddbbdcdadcbadacacbaadacaaaaabaacacbbddaaacbbcdcbcdddbcabdaccbddbbaccaaccbdaaaacaabdcdacbaabaacbbcacdadbcbddaabcbabdabbadbadcdcdccabdddddcccaccbddbcbaddacabddabaabaadbadacadbdabbbabaabdacabbccdbaaddabaccdbcabbcbbcdcccbaccaacdaccbbcbaddcdaadcacdbddbcdcbadbcbcdaadaccabcdcddbddaacdddcbcacabbacaadcdbaddbbadcbcdbbbcabcccddbbddccdaabdddaacabbaacaaaaadccddddddddbabdbcabbbdabdddccbddbaddbbabaadbbbcadbddcbcacddaacadccacacdcaadcdcccbbcbdcbdddabdbdbcdcccadccdbddbcdcbbdccbcdabdadaaaabbabccddadacdabcdcccccdacacccabcdaabbbbbdcdcacabbcccaddaabcabbbddcdbabccbbddcdcbaadacadcdccabcaaccbccddbcabdcbaaaacbabadcdbabaaacddaaadbbcddbcddbcacdddaacddaaabcddbdabdddcbbdbcaacdddaccadcdaabdddbbaaadbcbbdcadbdcacbabdcabcaccabcccdccdaadbcaabadbacbdcddbddcddaabadbbadadabccbadcdaaabdcdaaccdbbdcdccadbbbdddadabbbbddaddbbdbddaacbdbcbbccaddabcbacbaadaacbcbcbcbbadacddacdadbcddadbcadbbbadadaccbddbacbddcbdbcaabddcbadabaddadbdadbbbbcdacabdaccaacacdbddddbdadddaabcbdbabbbcccbddadacbcdccccabdddcccadcabcbdadaaaddbadaddaabbbdcbaadaacacbacbcdadaaccbababcdadddabadcdbabddabbbdcbbcbacbdaabcddaccccddddadccaadcadaddbcccadbaacccdcbbbbbcbbaccbcddaccccbbbcdaacbbcdcddabccbbdadacbcaccbcbbbdbbacdcdcbbbcacddababdbdcdcdbadaabccabdaccdbcacbdcbcddcaadbdaababaadbcddbdbabcadcaddabdaacbdcbbbdaadcaadcdccaacbcbaaabcacdbadbbbdcbadcbdcdabdcddbcbcddbccbadccddcdacdbbdcadaadcbacacadbcbabdbbdaadddacbbababaccacdddcdcdaadcacabddcacccbddcdcddbcbcbdcbaadcbcbcdcadddbadddacddcabbacbbaadddbdbaaadacbbdaccbcaabcaaabcabcbccdccdacbdbdbbdbcdccbdccadbccccacdbccccadabdbbddacabbadbdddaadcdadababdbaddaabdbdbddbcaddbbacbbbbddbcbacdcbaaaddaaaddddbababbdcdbbaacbbdccbbbcdaadcbababbbabcadddccbccacabdbdbbaddabcabdcacdcdbbbabbbaabacdcabdacbcdcbbcddbbababdcbacabcdadabbdddbccbddbdabcdbddbddcacabcabcbabddcddddbcccdcdccaadbacbbbaccadcdabbaddbacabbcabdacdadcbbbbcbccddadccddcddcaddbcabcccddbcbbdbbbacccdcdcbdddcbbbaacdbcbcdbadcdadbcbdbddbdccdadcdccbdcdbbbdaddaccaadbcaccbcacadcadabaadaccdadaabdacadabdbbdcaabdadcbdbccbdbaccddaccacacdcaaacbdcbddabacbabcbcbddabddadcbbdddadbacddcbabadaaddabddddabccbddaccdcadacaaabdaadbbbabddadcaaabddbdbdacbdccdbddddbcadaddaabbcdaabcdcbacdbbddabdbccacadcdcdbacacddadacacaababccbcabdbcbabbbbcdbcbcdbacdcdbdbbbabbaacabbdddaadbaadddabbbaddcdaacdaccdbbbacbcbdacbdaccdcadadaacccdbcdbadccbaacabcdcccdadcbabaadcdcabbdadccbcacbdbcbcaabdadcbaddbdabbacbbbdbdccdbcbcbdbbbcababadadadbcbcbdabdaddaaadbbadbabbcacdccdbdbcccdccabdbadadaaccbaddcabdbabaaadccdcaccabccdbbacdabbacccacddacbbaddddaacbddbbdaddbbdbacddbcdddaadcdabaccdadabbdabaaacaabdaabbabdddbbacbbdaddaaabbbaaaadaddacdbacdcbbacadbaabdbbcaccdaaababccdcacbacbbbaaccbdbacddcbacbacbbbdacabaddcddcdcaabcddddcdbabdbddcbabbcbcbaaadaadcbcddcaabdcacdabdbacaddaacdabbaacbbbcbdcabbbcdadaabdddaabccbdddbdcddcacddaacddcaccacbabcaaabdcadadaaaabdadcaddcaabbbbbbdbccdaabddaddcbabaadadacdaccbdaabbbbcbbdcdbcbaccdaaabbddbacabcdbcadcdacacbddacbbcaabacacacadacbccccbbdcdccbdbdcbaddadbbaddccababbccdbcddbbccddbbabaccdaacbdcacaacdacdbaddabacbabbdbcbacdadddcdbbabaacccbbdddbdcbdbccbcbabddbcbdcbcbcabbaddbacacdaabbbcbaabcdabcbbaabcbaaabddcbbaaadddacbdcbbbcbbdccacaadaaccadabbaaacacbbdbdbacaadabcaacaadbbabddcdcacbcdadcaccbdacadbbaabaaabadacdaaadccacacbdcaadcdaaaabcaccbddcbcabbdaacddcdddacaadbbbacccaacabaaaaadcdbadacadabcbbbccdddccbddbbddbcbbabdcbddadbcbdbbdabdacabbddaaddcabdcabaadcaddbccbaabcabacdcbdccaabdbbddccadbdaccabbbdbcadacaddcaacabbdabcdcacaacacdabdddaadabdddaaddccbbddbdadbadaddcddadacccacdbabaaaaadbacdacbbbcbcbcadabcdcdcabdbaadcadddcacbbcdddcbcccdacadbdaabcbabdacccbcdaaaaaaabcacdcbcacdcdcbbcddccbbbaabcddcccacdcbbbdcbcbbcdddaaaddbdbadccbdaabbacbabdccdbbccabacaaabcdadbdaacabccdacaadcbabcbdadccddbbaacdacaabacccbcbbdbdaaadbadabdbccadddbaabcdcaadadcabcdccacdbdabbcabdbccbdccddabdacbbaacdcdcdcbbdcadcadbcddabbacbcbddabdacaaaaddaaabcbbbdcdacbdcbbcbbababadabbbdcbcbbcbcbacbbdddacbbaacbbdadbcadcabaddabbbcabcbddabbaccdbcbabbdcbbcaddadbcadcbbbbdbacdddbbdcbbaadabdddcacbbcbbdbcbdbaaccccaddbaaaddadcddcdcadaccacacddbbcdabbdccdcdbaacdcbbcccaddbdacdadadbabbccdccadcacbaaabcdbacbdcaacbbabbbacaddbdadbcadabcdbccaaddbdabbacccbbbbdcbcbcdcbdbbcaddbaddbddadabadabcadccaadabdbcbcacbccbdcdcdccacabcccaadcacddadaacabbbdcdaaaababdcacdbbcdabdabaacbcccdacdbbbbaddbcdcdcabccaccddabaadbbcddcacaadccbbabbbdcbcabcdcccdacbabaacaacadbcdbdcbcdcdbbbdccdbccdadcbbbdbcbcdcabccddbbdbdbcbdcddddcadcadbacdabdcbbabddcdabdcbbaddbcadcbccdadabdcccbbbcbcaadbdbddacabadcdadcbbcbacadbabcaadbbcaaccddacaacabdbcaabdbdddacccadcdcacbdbbbcddbbbdbbccdacdadbcadabbdbdacdaadcbbccbdadddcbbcbbdbaccbbcaacbddabcdbaadadccadbaadcbadbddadbdaaaaadbababbccdcdacbdbcbdbbaddaabcbaccdbcaaddbccbccbbddaddcdcacdaddaddcaccccabbacbdbdcdbaaccdccaddaaaabcdcdbabcbcdcdbdaccbbdaccdcaabcbbddddcaadbbcccadddccaabbabcbdbccadccadacbcccaacdaaacbddddbdccddcaadbbbbddbdcbdccbdcddadbdaababababdbcbdbcbddbbccbdacaabbcbdaadcacddbcdbaccaadcccabcabbdabcbbbaabadabccbabdabcabadacaddccaaadcaaccadbaacdbbcbbdbacacdcdaabdbdbddccbbddcabaadcdabacbdcbbadbdcacaaabddddbadbcdabbbacddcaddbddbabbabcbaaababdcaabddbcbcbdbcabddcbacddcbcabdcbbbcaacddbdbaaccdabcdadacacadcccbabdddabbdccbbdacccddccdabcadbaaacbbcbdcdbdadaddbbcbcacbcccbabbbcadbdccdcbaacacadcbababbbabdacaddbccdaddccadadaddbcbbcbabbadacbccbcdaadbbddddaacbdaccbcbcddbcbcdbbcbacaddaaddbdcdbcbcbaacacddaacaaccbdcaadcabbaadddbcdacabdbdbdbccdcaababcbdccaacdadddadcdbabcaadadbacbdaacbbaabaaaadddaacddccbdcbadbaadcacadadabbadabccbaddbdcddcbcdaabbcbcdadcdddcddabbbabcacbbcbddabdbabcbaadbcacbbbbbdcbabccacdbbacdaccbbabbcaaaadbbaddbadadbcbaccdabcddbaabddccdaaadcaabdbcbcaddacdbddcbabadbadaabbacabcddbaccbbdacbbbddddcbdcdccccbbdbcdbadacbbdbacdbcbbdaaccbcaabbadbadcbbcdacdaddaaaabaaadbcbabbbdcbbaaaaaccdaddbdbbaaaaabddbdddbcbbccaadbcbcadabacacbdadccdcccdbccbbaddbacdcaadcbbcaaddbbaadcacbbdcddbadadcacabacbacbadbdcdaacabbdbddadbbccccabadaccbdbbccaabcbaaadcbcabdbaadacdbdabdddddcaadaabbddcdaddbdcabaabbaddbdbbdcbccdabbccbcbcbdbdaccdcbadddcddcdaadadcbbcdcdbadcdacabbcdddaaaabddbcaabcdddbcccdaacdcadbcdbdbadbabaaabbdbcbacddcccbabaccbbaddcdbdbbcbbcdbcacdcbbbbadbdcdbcdccbacbddcaccdabcbcdcbbaccaddacdcdbddadddccdababaaccccdbdbaadbaacaddbdaccbbabdaaddbaddbcbabdbdbccadbbabbdcccbaaaddccdcbabaacccaacbadcbcddbbabbaddcbcbdbcaddbddbcbdccccdbdcdcadbdcbaddcbcbcadcdbcdaccbaddddbdbdccaddacbbcbabbadbcacbddabdbccaccdacdcbdaacdcdcbcbbccabbbadabaaccbccbbbddadbbbbdcdbcdcadbbbcbbcbabddbdccbadbbbccdbcdcacccdcacadbbbccdbabcbcdccddddccaababadadaabcacddaaadabaadbcbcddcddccbadcbadbdacabadacddabdaddbdbbdcbabacbcbddbaddcbccccbddcacdcbadccdaacabdacacdcacbaccacacaabaddbbdbbdadcccddddaadaaddadcccbbbbcdccccacbdcbadaacaabaaacdcacdaccbbcdbaccbccdbbcbabacbddddaadcbbdbcdbbddcacbcccbbdbbddcccddcccbdaabaabbabadccbadbbcddcdababcaacddcdbccaaacacdcbabacddacbcddadaccbcdccabcabadcbcbdcbdccacddbaaacbcccaaaccdacaadabbdddddacdcaccaaacabbdacbabdcabdbcacdcbbbcbddddbabdacbaadccdbddcccdacbbbccadccccbddcddbabdcbaccbcaaaabbacdcccdabdbccdddbadddcbaabccbcdbbbdcadacbcadbaacccdaaadbbdcbadbccbabbabaabdcdbaacdbaabcddcabadddcdcaabadddcacccccbbcccaacbaacacdbdadcbdbcbccbbbacccaaacdabbdadcccbbbdcbaccccbdcbbbdcddacccdbcddcadbacdacbccbadbadaccccbdddddbdadaaabbacbdbbdcdabcdcdbbabcbbcbdddbadcaccadaddccdddaaccaacaacbaddbbabaadabbbcbcaabddabadcddddcaccadbacdcdadabddcabadbaaaccaabcacbcaadcbcdadabbcacabbabcdabcabdbcccaabaaaccccaadcacdcdabdabbabdadcabcabccacbbabbcabbbbabdbadacaccbcbcdcaddbaccbcababddabbbcdabcadcbcbdcadbbbccbdcabbbccbbcbaccdaadcbcbbcdbbcaaddcccddcbbcdbcdbbabbccdbcdacaccbdacbcaccddddaccbdaaaccadbabcaaddddabcabcabbcacadbacaccadddcacbacddabacabbbabcddbdcbaaddcabcbabcbaddadddacbbbcdbabddbbbcbcbddacacadbdaaccccaddbaabbabbaacabccbbcdbcdaaaadccdacdddcdaabdcdbaabbaaabcabccabddaaccdbcccbadcaddbacabbbdcbaaccdaacabbcddcccccabadabdaabcccbcbbdccbabbbdcdaccadaacdadcdccaddcdbabaddbcccbdbbbdbbbdadadabadaadccacbbdaddcacccdcabcccadadacdbcdccbbcbcaaacadcdbadadadcbccdddccdccbdadadcdbaddaadcbbacddddcacdbdcaddaaccdacbddcadddaabbdabcdbbcadbccbcdcdbaadbdcbabccdccbbccbbaacbaabddbdbdccdababccababbbbcbbccbdccadaaddbdabaaabcbdddaaddbbbaddbbdbddbbdaadbacbadbacdbacdaabbccaadbdbbabbcdbdcdccddddbacbadaabadabbcccdaaddcdddacabcbdbadbdbadbadcbadcadcacbdcddbbaaddddddbcdcbcbabdadddabdcbbcdccbbaacdbdddacbbdbccdcdaadcddccdaddbbcbdddcbbabdabcdcdbdbdaadcdddaccccacdcdddbccddbdcaddaaccdbcaabcbabaacadaacbddbcdaabdcdacacabddbbdddadbcbcbddbdcdcadcdbdcbdddabbbcddaacbdbdadcdaddddcdcbcbbdaddcbdcaddcdccbcdaaadcdaabacbabacbdacaabadcabdcbdbaaabcddbccbacbcabdadddcdccaaccdbabccabaabcadbabbdbdcacccdbbdabccddccabcaaaaadcbbabcdcdbdbcabbcccbdcbcabcdccdcbbcdcabcdbbdbcdcbbdcaaabdbcaadcbaddcbbbcdbabbbbbddabcdbdbabbcccdbbbbacccdbbcadccadbaddddcdcdbadbacbdcaabbbccdbcdabacbcaabbbcbbdbaaabcdbabaadcbcbccadbdcccddbabbdbbbacbaabbbbbdbbcaddcbabdcbddadcadaacaadcdacaaabdababaacdccadcbbbccaabaabdadbdcdbaaaabcdbacdcbabcadbbdadbcaacdadbcbcbbcbbbaacccdaabcdcdbcaadbcbacdccbbdccdabcbabbacbadbcacbdaadbbddbacaabbbacaaddadcbacdbcadcabacaacabcccabbcaaaabdacdbddddcdaccadaddabacacbbabdccdbdacbdacacabababdbadcabadcddbdbbccdabdabbaaadcaccdcbccdbbbddbdabcacbbbbdcdabbbcacadacdcdbdcaacbbcdadbcdcdddcbbcbbaaaccbacbbadacdabadbabdaabbddcbccdcccbdbbaabcaacabcdbdccbdbdbbbdbbdbcbdbccbcbaddaccbbacbbbdabacdaabacdbdabbcdadaadcddaddccabdccbccbbcbdbdccaaddcdbadbbcdbadaaaacadaabdcbaddbabbdbdcbadbcadcdaaabbaabddccaaabcbdddcdbdddcbaddadbaabdbaaccdcdabbddadaabbadbaaabbbaabccbccbcdabdcdcabaddddbcdcdbdddcaacdcdabbbbdadcababdaacdbcbbdaabcbabbcdcbbcabdaccdbbcddabbacbabacdddbaaabcaabcacaaacaaabbcbbadacdbcabbaaaadccdbddbdcddcabbbdbddaccabbccdbccbdadabbadaabddaababbdcccadaddbdcadbcdcdaccbdbdddaccdbcdadddbbaddbbcbbdacdaabacccacadbccdcbaabdcbcacdbabcadddbbbbbccbacddaaadcaaadccabccdccbccbcdddadccbdadddcbbddabbbcacddbbbaccdbdbcbbbbadadacaabcdbbbadbddaadddbcbbbcdaccadcaabccdbccdbdbbcbbcaddacdcabdbbaacbcdbcbbbcadbddadbcbdccabbcccacbbbdbddcdcaaaabdcacabaadccdbaacdcacbaddaacdddcdcddbabbcadbccadacbdacbccdcbacbacdbcbcddaddbcbdaadbdbbacaabbbdbddbbbdcbbdbcbdabddaacdadbdbacbcbbdcbbddaabaccdddaadaccdccbcbbcbccbbddbadbcdaadbdccaabadbaaddbddccbddadbabbadadbbdadbcdabdddacccbaccacadaaaddddaabbdbaabacbdaddcccbdadaddbaaadbadddcdbdabbdbdcaabbadcdcacddddcabadbbaaabadcbdacabbdddcbabcacdcacacddcddbadcaaddbaddcdbbaaadaacadbddaccadbddbcbbddabcccdcbcdcccaadcbddbdadcaadaccdcadddaadcabcbacaabbcbabdbbbaacbbdadabcdcbabbadddddcbcdbbcddbabacaaadaccbdbbcbdadccbcabbccdcdaccdbbbccdcdabbcbcbaaabbcacdcaccccaacdbdcbbadbdabbaabdccaddddaddcdbccbaaacaaccbddbabdbabbdcbbdacbdccadbdddbddadbababcddcabbdbabddccaabbdaccdbbdbcdcbddddaaddddabcbbaaccdbadadbccbdcbdbaddbdbbdaccddacdcacdcabcbbaaacabaccbcdccbabdaabcdbcaaadaabaddacabdcdbcadacbabababbcdaccaaadcdaddcaddccacacddbbdddcabcddbddbbbdbcdcdbdcaacbccbaacacacadddcaababccacbdcaddbcdbcdabbbcccdddcdcbacbddcdcdbdadcdbcbacdcdddcdabbbbdbbcbaddcbadcacbcddbabccadaabbcaccbccdbaaabacddaacbdcacbdccacdcbdcbdacdbdaccacacdaaccabbaddaaaacdcdabcabbccacdadbbdcccbbbbcbbcbdcbaabadbabcaaadbacbddcdbdadbacadcaaccbacbdbcccdddbbdcbabadcbddaccdcbdadcbaddbabdbbdabbcbdbcadbdabdcadcccddacbdccbccbdbbcaabbacdbbbcbdddbcbcbccbcdbdcbdaacacdcddcdddbdcbcbabcacddabbdcbcdaddcbacadabbaacddaccccbccdcdcdadbbddaacbcdbacdddacadcbadcacbbadbcacbccccbddabdbbccaaabddacccbaddddcbddabdbaccaddccddbbaacacadddcabacacaacbacacacaacbabbaacaacadbaacdccbdcbcbcbddcaabcbbbabbcaadbcdbbabcdbdcaacdabaaadabcbbdadcbdbbcbbbabbccadbdcdbbadcaccdadadabcccbcbdcadcdcccbcccbdadbddbdabadddbdbbacdaaabdcabddaaacbaaadacabcdddbadacccddcbabaccacadcabcdbbadbcdadaaddbabbabaacbadacbdccdcddbdadbcdccddddabdbaadaacacabbacdcabcdcaaabdacccdbddbaabccccaacaccaddacdbbbcdaadaccadabbcddbbdabcdbbaddadadbdcadbcddccdbbdabdadaabccabcbcadaaddbdcadbccdcdcaaccaaabadaabcbbdabaacbbadcdddcccaccdbdcddaacdbcadbbabddabdbccbdcdaccdbdddddacadbaadddbaadcabadbcacacacccddcbaaaadabcadaabbdcaabdadbacbcbadbabcacbdddcacaccdbdabdbbacacbbbcaadcccdcddcaacbdbacdbadabbcacbcdbbaacacbdcdbacbabbbcabdaaaabccabdaaddbdcbddababddacaddbcdabdbcbaddbcabcabdbaadadaacaacbbdbcdccbbcddcbdddccbcbaabbdcbbddbabccdbccccbbdaaadbbbacbddaabbddcdcdbcdcdbabcdbbacdbbcdbddabbcbdcadcccddbdcdbaadabbccbccdcabaaddcadababcdcdcbbcbccabadcbccbacbcbdccbcaaabbbdabbbdacdbbaaaabcdbbdaadbccdddbcadaadabbcbcadabaadbccbacaabadddacaddbccccdddabbddcbbbacabdcbcabddabcbabbbbdbbddbababcabadccdcaccccdacdadbdbadaabbaddbcadbaabaccddadacaccddbaaaddcddccabdabddadcdcabdccadddadbdadababadbdadbdcdadaaaabbbadbaabddbabccacacadcadddcbcaacaccbbbbbacbacbbadabaccddccacadccbbbbbcdbabdbbccbdbabadaadbcbadbcbdbbbcccaacacdcabbabcccadbcdddaddcaddddccababacdacdbcbbdcbbabbacbcbbbbdbccdcdbabbbcbccbbdcdddbccdbcbdcdbcabbbbbcbcbcdbbbdcddcbbdabdabaddbbccbdaddcdbcbbcbdccbbbadbbababcaddabbbbdbdcbbabbcbddacbbcbcdbdcbbbadacccbdcddbabddbdcaccacbaababcbbdaaacaabaacaaacacccdbabaaababcbcbbcdacbbabcbcadbbbcbacdcdbdbadcaccbbcdacdcacbaacbdacadcadddbbbdbbabaccdacdadbabccadccbcdbbbacccddcdacdaaaacaaabaaacadaacbbbbbddddcccabbabdbbbcdadbcdadabcdcdbcbcddabbbacbabaddcaabbadadbcddadcbaaccdcdcaabaadaadcdcbadcaadcdbcccabacaacabbbdadddccabadbbbddbadaadacdaaddacbababcdcdcbbcacacdcacaabacdbaacbaccbadabdabdddcadcbbbdbdbdadaddabbdddbabababddaddcdaabbbabdacdcadbcbbacddcdaaabdbabddaabdbbbacdaabbdbcaccacddcbabcbcbcaaabbbadcadbbdbddccbbacbbabccdccaaaabccabbbaddddbadbbbaadadadcbadbcacabdbcacdcdadbbdcbcbacbbcdcacadbdccdcbbadcbdccdaadbcaacbcddbbbbccddbbccddacbacacabbbdbcadccbadacaadadcaaadbbaadbdadadabcbdcaadabbbbcdbbdccdaabaadabbadcccaaabbbdcdcdcaacbdbcbbcaddbcadabbdbcbcddadbdbbbbdcabcabcdcaaaddbcbbbdcdacbabdbdccbcadbbbddabcdbbaabdabbabbabbbdddabdcabbabddbdbaddbaaddbdddaadabcacaabcbdacbbacacdcbabcdaaaccabddccabdcdccbbaadbabdbbabccdbbdcbbdacbaddcddabccacbbacbccbddcbcabbaaaabaddccdcdbabdddbdbcdbcbbbbbdcbbcbabcdbbcccdaabcddddaabddbbacbbdabacdcacccbbcbdaaadcccbaccbbbabacbcbadbaaddbcaccaccdcacbbbaaaaabadcdaaacddcbaddbcaccbaadddbbbadbdadbdcddcbacbccbcbabbddbadcbdbcdcacaaadaddabbdabcadbaaababdccccbbbabbabadbabaadbcaaccccbaabdcacccaadaabdbdcbcacdcbaccaddabcddbaacbcdbadacababcaacabcddbcbcdcbaacadabbacccbbbaaadacbdcbdaccaddbcbbaccaaccbaabbdcbcadaabcacbdbbbacbbcacabcdcaccaacdcadbddaaaadbdcdddacbbadbabdabacacbacdbbadccdbdcbdbacddadbbbabdcdbbbccdcdbabddcbdbabbbccaadddcdcaddabcbbccdcabbabddadcbcbbbbccccdddbadaaaabddbadcbbcdcacdabbdbaaccacbdacccccbddcaabdbabdbcccbadbcdbcdcdcdbbadbabdcdcbbcdacadccacadcdacbdbbdbaaacaddcccbdbbbbaabbdacbbccddddbdbbaddcbdbacddcadcbcdabddbbdbaccbdbccbdaadbadbacacdaacdabbccdccbcaabdbbaadcabacbbbaaccddabbdbcddbbcbcabaabdcaababcacbadbdbacdbdcabaadcdbbbddbadcbcbddbcbbdbbbcaaabbbbbdaccbcaaaddcbbdcbadbabbdbcbbdbabacacbcdaccccddbaccdcaccbcddddbddadbacddcdacbaaadcaacdcbbbbdbddcbdcdcaddabcacdababbcbaacbacaadcaddabcbccdcbbacbbaadbaabcaccaabaaccdaaaccbbbbddbdcaaccbddcbbadbcdcbbcbbbddbbabbdcbdcacabcbdbddacbdaccbbcbaaaaabcbcccbaaddbdbcddcccadaabbbbcdbaacadbbaacbcdadcbdbbabcaabdbcccbdbcbdbdadaccadcabacbdcdbabbaaddadddccbadacccbbbdcbcbbccaacababdbabcbadcabddcaabacaaacaaaabdddccbabccacdacdbcaadcdbccacacaadcbaddcddddccbaaadcacdbbbdccbdadababaadccbdbdacbccdacaccaaadbabadcaddadadbdadababcbcdaaddbbaacbaccbdaadbbdccdbcabcbdcbbbccacbaddaadcaadccadbaaaabbdddaacbaccdcddababaaadaaddaddaddaabadddaddabaaadbddcbbdbbbdcbcbbdadacbcabdddbcdcdadbdbcdaaaacbcbdbbaccbdaaddcddabbacdacbdbdabcabddcabbaacdabcdaddcbbbabacdacaabcabcaadccbbabaacbdacbddaacbcbbaadccbdaaaddbbbbdbddcaaadcdcaaddbddbdbdaaadaccbbdbdacaddbcbbdcbcdddccabdbaabaaacbbdaadbdbdaacbcdcccddacaadaabdabbdbadabadacdbdcdcadacbbdaddbcbccddaccadcacdaadcbaabbdddccdadadcacccdbcabbbbcbadbacbcbadbbadabbdbbbcbcaddacbcdcbacbbacaabddbdcdadaabdabcabcaaaabddacaaadccbbdaddbbcdbdcbaadccccddccbcbdaaaadcccdbcabaddcdabbbbddbbddcbbdccaccabcbbbacdaabcaaccbbdabdbddadaccabcaccadbadbdaaddaddaacccddddcdabbdcbabbabdacbdacddcadabcbaaaabaccbbadbadcdbbadbcaaacbcdacaabdaccacabcbbbcbbbcbbbcacacaadbccadabbbbdccbdbbcbdddcabddcbbbcbcabbdaabccacddacabbbccbcaadddaabacacbacadabaacbcbbabadccbbdccaaadcbbcaacdbbbacaadbabadddadccaddbdbdbcdbabcdcbdddaaaaacacdbdbcbbbbdddadbcbdadcbdccbbcdbdaababbddadcabcdacddbcdbaaaabcbcdbabdabbbbaccaabaccdbabdaacdbbacacacdccccbccaaaacbcacdddddadbddaaaabdbabbcdadaaccadabadddcaaabacadcdcbddddccbbbcadcdccbbdbbdabacddbbacbbbabbdcdacddccdbaccbcabcabddadaabadbdbcdadbbccdbddbdbbaddcadabccdbabbccbdbbbccdcaaaacbbacadaacdabdaacbbbacbdccbdbdddaabddcadcbdabaddadbccccccaabdcbaabcccdbadabcaccddccbbabbcaadcdadcaacbddbdabadcbcbcababbccbdabbaaabaaccccabdaaacaddaacacbdacaacbcccabbbadbbddddbcbbcadabccabbadbcadbbbbacbcadcbbcabccdabddbabbaadacabddbccbccbdabcaabdbcbabbddccadbaddcdbbbaaddcbdabbbadadbadbcdcbcacdbdcaaacbaacbcdbddbcbcccbbacbdbdababdaccdcbbdaadcabddbaaccadabbabbdacabcdcbabcaacddddbddaddbbadbdbaccaadaccabdbcacbbaccccbdcdbbabcbcdbbdaaadcddbbbaddbdbcadacbcdacadbdcabddaaacbdcbbdbacadaabdcbabbcddbdcccdacdacabbbddbbbdbdccbdddcadaadabcaaadcbdbdaddccbadcbdbabdaaabacdbacaabbddbacbbcdadadcdbddcacbdcdcbdbadaccabcbcbccababdaabcabcdaabbaccadacdacabaadcbbddadbdaaccaccabdaaacabbaccdabbccdabbabaaadddccbbacdcdbcaccaabcbcadcaddcaabbdcaabdbbabdaaacbabacbaacccdcaaacadccbbdcddbdaaacdabcadbcbbabacdcadabcabdccabbaaaccdacaaacdbdcbbbccdccabbacdccaacababcdbdddabccaddddaadddacdbdbabdbcdbacbdcbdbbccacbbdcaaaaabcbbbdbcccbbcaaadbbbdacacddcdaccbccbacdddadcabcbaabddabbdacbbabdbbababcbaabdcbcccdaacbcabcbabbcbddbbbbacbdabcaabcdbcadcccacdddadadbccbdaccbdccabbdccaabbabaadbcaddbbdbccdaadbcbbdaccbbcdaccdddccaddccdbbaabcbccbbaddbcaccbbdaccdcccdcabcbdaaabdcaaabbaaaacaddaccadbddccabbdadadabdaaabccacdcbabbdcaccaaacbccccadcaaacbaaccdddcaacdcdcdcdcbdcacdcacacaabaccbbdabcddadbcadabdbacacabadbdcccadadccdbdaaacdcbbccaccbacbbdbabaaccbcadacdcddaccbaacdcaadaddacddaacccabdbdddcdbbacdaaddbacaaababaabcaccccaccadabdaacaaabbdccdcbdbcdaaaacadbdcaabcbdccaabdbdbacdbadcbcbadbbcddcbdbbcbccccbdccbdccaadbaacadcaadcdbabbadccabdbadadaddbdaaabaccccadadccbdcaaaabbacbababbdbbcdbacbddbaaddbaaadbabacbddbbcdacbbbcdbdacbacdcacccccadaabbadbbdabcccddcaacbbaadcaccbcadccddbbddcdaacdddddcdddacbccabcbbbaabdddadddbabbabaaacbddbddcccccbbdabaddbabcbbdccbadcdcabccddbbbacabbccdabcdacccbbabadaacacaddbbbcbcdadddcbbccadbcccacbddadcdbcbddaacccbdaddacdcacdabbababdacdccdaaaacbdccbdaadacaabcbdaccbbbcccbcabbbabddabcbcbccabbacaadaccbabbaabaaccaccdcacadcccdacbbdcbccdddccbccabbadcbcbbaaaddcadbcabccbcbadadaddbdddcdcdbcbddadaddaabbbaaaaadacbbcdabbbcdaacbaddadbdaadcdddabdaccadcbacbbdbbdddccbcbbcbccdaadabcccddadcdddadccddbccccdbccabdacdcddcaadacacdccaaddcbbdadddcdccdbadadbbcaacdbdbbdcabbabcbbbdbccaacadabddbbaaabccaaabcddbcbccdbbdadccbbcbdbbdabbcccddcbabcbaaccaaadaddcaacabcbccddccdbdcccbbbdadbdbcddcaacbaabdacaaadbdccacbdcadbcccabbbbabbbdbcabddcdabdbbdbddccacadcaddababdddcacbcaacdbacccbacbaaccabcdbddaacddcccdbbaddbaabdacbaadcdddabacbccbacdccdbccccdbddadbdacddbacacaddddcaccdcbbddddbabababccdcadccaaaacddddabbddcdaaddaccdcdbaccaddaaadacabbbcaddbcbdbadbcbacbdaaddadadcbacaacadbadaaccdccdcabbcccdbbcadacdadbbdbbadadabdacbddccdbdcabddacdacbcdbdcaabdabbabbadbbabcbadbbbdbbcbdddbbabcaaaacbcaadbadabdbdbbaadbcaaababacadaaaacbbabdddbaccddcaabdbbabdbddcacadbaacdbaaadabdbddbbcbbbdcdcabbbcbaaddcabacdaccdadbcbbcaabcdddcabdbdaccbdbbdaccabadbbcaaaddbbccbcadcdbdbaabcadccabaaadbbbdbdcdbdbabbbabadaaabcbbadaabcabccaabaabbbbbddbabcdacaadbbbbdadccaccdddbbbddcbbccbddcabbccbcbcdaddcdacdadbdddcbcbcbddccacdddbbaaacadbdcbcddcbdbacbdacbbaabdccbdccccbccbcdadadacacbbcadbadbcaadddbccbacaabddbdabccdccbdbcbcaabcbabbcabbacacaadabdbabdadccbadddcbdbbbddbacabcacaacadccaabdabbddbcacaccccaabbbcaabaacdcbaadbccdbbcbccbbccbdaabddabcbbaaabdcbdadacaabadadbbaccdbacbaccbddbcddcdbaaadbaaadacbbccbcdcbdcabacbcadaccddbadabbcdbcbbdbdcdddacbdbbaaaddadabadbaadadbbacaacdccdacbdaccbbddcbbadddaddccaacaaccaabcaadaaadcccacbadadbadadcbcbadcaaaacaacbcacbbdccabdaaaabaacadbbccccaabdbaabaabbaaabdccdabbbbcdcccbacbabbbaabbcabdddcddcaacbbddbdabdaabadacdbbbcdbbabdbacbbdcccbacbcadbadadcddbdcbdddcbdbcaddbbbdaacccbdbbaadbbabaaabbcadabddadccddddcbcacbdbbacdbddbdabbdcbcabdcdbcbdccbaacddbdcadabcaaccbddbdccdbcabbdacdccbdbcbbaddcbabacdaabcbaaddacbcacdcadbcbbcdbccccbccdcdcdbddabadacbbaaddbcdbaaaacdadbccabdacacbcbbccdddabbcaddadcabbdbcdcaabadadbccbdbdbdcccbbbdbdcaddddbdcdbcccaabccabaadccccdddcddddabcbadadbbdcddbbaacadddddbdcdacbccdaaaaaabccabdcdaacbdcabbbcbdaadcadcdddacacdddadaacdcbbbccaccabdcadcabddcaadbaaccaabadbdcdcbcbcaaaddabccddbdaadcbacbaaccbabdaddbaccccddcbacdcaacbdabaaddcbdadbbacbbcacadcbabdbabbbddcbbabcbaaaacccddbddbcbbadaadcdccdccabbdccdbbbccbddbbdaccaddcbbcbacadccdcabaaabbdccdccccccdbcacdbaccbcbaaccddbbdcdacacbbdbaccbbbbcbcbcbdcacccbcacadaadbdcdbdadbddcaaabbbccbbcbaccddcaaaabcccaabbbbabbcdcddcabaadccbaddcacacbbbdabacddacbcababdbaccccdbbcdbadccbdcbabbbaddaccbcabbcdacdbbcaabcacbdcbdadccbbabbabaadadaccbcadbdacccaaddbcabcaccdaddcbaaaccadbddbadaccabcbccdbbccaccbbcdcddabbbdabcdbcbcddddaadccabdabccdadbdbdbccbbcbdabdccbaccbaababaabdccdcbbacdbadcadcddcdcbdddddbbbbdadccdabacdabcbabdbacaabacadddaaaaaddcdacbabddbddcbcbbdcaddbbdbadadbdbdcdcdcaabcbaaaddadcddabddccdbabbbaacadbcddccadbcaacdcccdcbabbcddbccacdabdbbbcaddaadccddbabbcabcdcbadcabcdbbdacbdaaccbadadbcddadacaccdadcabdbcddaaddacdcdbbdcdddbddcdbaddddcbaabaaddabdccdccadcacdabccbcdbbaacdcbdddcdaabacdbacdcbcaccbabddacdbdbddcaccbbbcacbcabcaddcdaddbcdcabbddaacccaccdbacbcaacacddadadadabdbbddcbcccdbcdbdbccdaacdddcbcbdaccacacdccdabacaaccbaadbddcaaadadacbdabbbcdcaabaccbbaddaaaddddbdbbaaacaccaacabbdcabbacdabccbdccbaacbbbbdbcbdbcbbcdcbaccccdbcccbcacbaccccbdbbccbbabadbdbbcadaacbcbcadbdbbdabacccadbbbaadadabccbadabbbaddbacaadcabbdbdcdbdddbdbaaddbaccabbcccbcddccdddbbadcacdcacacdaabbadacdccabaaacdaadadbddbcccadaaadadbbcdddcadbbabcdbbcbbcbabcaaccdcddcdcddccacdcbbbdbdcbadbddddbcadaddccbcdcbcdcccbaaaaacdabacccacdcaccaabbdbdacbdbdcabccddabbdbaabddcddddbcccccdacabdadcbbddacbdaadaabbadaccbcaccadddabdacadcbcbabcacdbacddababdacadddcabccbdacbcabbbddbbacccbccbacbcdadcbabbdbbcdbcbaacdaacbbaddbdcadccbccaacbdbbacdcdcbcbdbabcacacdddbbabdaaccddaddabccabbcbbcdbbacbccbbdaabccdaaabcccddcdcdaaabccbdcbbdddbcaccacccbcaccdcbdcdbdcadbdccabadbaddadadbdbddbdacdbcbdacdcaacdccdccadacaaccddcdaccdcbbaddbbaabdccadcbabdbccdddaaababbbdccdabdcaaabbbaabbddacbcbcbdadaaddbbaddacabdbcdaacabaacdbbdccbbaadbdaadaccbcaaabcbddadabbdaccbadaacdbaaddcaccbcaccbbbaccdddacbcdbccdcabadaaddabacdcddccdbbbaddcbdcaccdbccbbdacdabddbcacabddcaacbbacbcccbadbcabaabadacadbadcdaaabdabddcdbaacacbabccadcabcabbacaaacbacbbaccdabcadbbaaabbbcbdadbabbacabcbcacbcabdcdccbccccccabccddabcacdadbbdbbdcabbaaabdbdbbccabadaadbbcdcabbbbcadbbdabcacccddabccbcacacacbbccddcdbadbcdcacccbaabcaadabacccbddcaacdbaccbbbddddaaddaaccdabccbdbaacaddadcdabadcdbdacdabbabdacbaddaabddbbbbbaaadaacbccbdacdadacdadccabbccbdbdadcbadbbcababdcccbdacaadbbccacbdbdbcdacdabadccdaadcdbbbdaddacbccaacbaadaddbcddddcabbaaaadcdbddcbadcbaddcccdaabdcdaabdbcdbcdcbaacacddabbabdddabdacdbbbacacadbcacbcadabdcbdcbdbbbabacbaddbcadadabbacaadacbcdddbbadddaaddbdccbdacbbcdabdbdbcbadadbbccbaddcbbcaacbdabdcabadddcccbbadbdbdbcbccccbadcbbddadaacbcbccdaacdcdccdadadccdbabdadddabcbbccbbcbaddaababdcddaabcddbacacacbddcbbdbdbccadbdbbbacabcbaadacabbcccdbabadadaacddccbcacdcdacccdacadbbdcacccdadcdadbcbcccbdcaadcbddccaccddbbaabcbaaabacdcccbabcaddbababbcbadbabaabcccdabdcbbdccaccddaabbcbacdbdddacaddcaaccdbcbbacbddcddabbdaddabaabbcbbccaadaabbabbdaccacbcaccbdcbadbdcdcbaaacccbdaacdcbaaccdaadbbdaadaaddabaaaadccddadacdbadbcacbcaacadcaacdaabdcaaddbbccddcbbaadaccacaacdbadcddcabdbccccadddabcbccbcdccaddcddacdbdadbcbddadccdadaacbabcddcdbbdacbaaabcacbaabdddbaadcbdccddbcbcadbbdbaddbdabbabddaabcdcddbbbaaddbccdcccbcadaacaacbddcbbbddcbaddcbbcaabbbbdccadabdbbacabbaddddcbaccccacbbbbcbbbcbdcdbcdcadcabaabaadacbcdddbcbbcbabdaadaaddabdcdddbbdadadaaabdcacdacdadcabbdcddccdadaddacbdacbababdcbbcacbdbcaccbcdaddcdddbabbabaabccdbadddaacacbdccbbdbdcddccccccddaababacabcdbaadadcdbdcabadabbaababdbdacbcdaacacaccccacdadbabdcbabccabbccccdbbbdcdbdddddbbbbcacdaabdbacbacccadababdadacbdcdddbddbcbbacccabccccbbbcbbbbaaddaddaddadbdcabdccdcadbddcaccdbbdadddcbcacababbcdddbdcbcaacacddaaacdaddddadbbddbcdccadcabaadcbbadcbdadaccbbcabbabcbaadbdadbdbaabdacccdabcbdbccdcacadacdbacdccbbaccccdbbacdcdaacddababbacbcdbcdbbadbdccddaacdabdbdcacbaaccaacdbcbbdbadcbdbccacbcaddbbbabbabbaaabdbccbcdcadacbcdcbdddcbdaaaadbcbdabbcdddadcaacaabccabbdbbcdbadbcbbabcdcbdddabccbcdbabbbdabbacacddccddadbadcdaaadddacaadccbaadcaacdacbacabbadadbbbcccccddbaadaaabbdbdcddabccacdaddbddbbddbcbacaccbddbbdbddaddacdddcabbdbadcbabdbadbddbaccbdaccdbadbddaabaacacdacddbcacccbbdbbcddbabacddbacbdcdbccabdacbbbbbbadccbadcbaadddcbbcbbcbadcacdacaccadbadbbdbdacadbddccbabcaadadccaaccbcbbdaadbbbcbbbdaaadbabbabcacbcdaabcdaabaccdbccadddbcbacdccbacddababbdcbadbaabadaaddbadcbdabbcbacacbdbbbbbcdadcbddbcdadadadddddcccdbacacbbddbccbbadabdcdbcddbbdaddabbbdcdacdadadcbcadbabbdbbbcaaddabaabdbdacaababaaadbaaaaaacbdcbdbddbcaccbddabcdbdcdaddabaccbacdcbabcacbbabbcacdbdbadabbacaadcdacdabcbacbaaaadbddcdcdacccbbcbdcadbadbcbccabbdacbadccdbcdcdccbdaaccdccbcdccbdddabadbbbcbbcccadcbdabbddbcdbdcdacaaadadbdaccdcccdcddcbacdcadbadbaddbccbaccdbacaadbbdbcbbabbccaacaccacbabaabdbdcadbddccddacbaccbbcbcbabdcabddccccbcdacbcdbdcacbcabbcdccbadcdbddcaacbdccababccdbdbbbbcdbdcbdabaaaaadbcadaabddbdcabcaaccbbdbdbdabbbbcaccdcdbdbbaacabdbabdbcacbddbcddacdadbdbaddbbacabdbabadabdbababaadbbcbbdacdddaddccccaaabadbbcabaabadacdccbaccddcaaaaddbbbcdbddbdaccbaddadcbddbacabdacdbcdbdbcaababcddccabacbdbbbabdcdcbbabbdaadccbcacccbbccabbcbddbbdddbcacdbacdaddadbcacddaaddadcccbdbcaddcbbabbdbbbaacdcabddbacbcdbabcaacbaadcdcbcdadadbbcccbbccbddbdadacabcbbcaabcbadcdbaddccaccaddcccadcadacaadccadbacbdbadccbddacddbabadabcbddddccbcbddccaaadbdadbccbaabaaabaacabcaaaabdcadcdbbacddcccdbdbadcbcdbbaccbbbabcdabbcaadcccbbaccdbbdcdbdcaabdadbdacddbaddddaaccdccaadccaccdababdcabbdcaadbbccabbbdabdacbbbddcdcacbdbcdbdccacbdddbdabdbccccaacdcadddadcbbabaabdbccbaaccdcabdddabcabadbdcccbaabbdcabddbdbbadabacdccdabccaaaabcbddcbbbcabccdbacaacbcdcdabcbbcacbdcbdcaaaadcbbdcaddbcccbbdddbddacdabcbaacbbadccaaaabbcddcabcbabbcddabdcaaacaaabcdbbbccccbadcdccbbbbacbdadcccdcaddcacabccacdcbadddaccbddddcbdabdcdcbcaddcacaaabbadbcbccdcddddccccbbdaccdabcdbbcbcabddbdadadbdbdaabaddcdadbdabcbbddccddabcaadcccababdabcdacdddadbdcdcccbbacbabdcbbabbbddacdaadabacaddcbaccbdabbccbdbdbabbdababcdddcbabbdcabdcdacdcccdadcdbacbdaddacdbbadbccccacadccccddcaddaabdaccaaadadacdabcdabbaabcbbdddcaacadccbacdbbcccabbabcbacdacccacaabdbbbabacabcdddcdbbbdaddaccbcadbdbdacdbddccdaaabbcaadbdccaaddacddcaacddcbadcbaaccbcdacdcdddccdcdcbdadadcdcbaaaaabcabacacbdcaddbcabdbbaddbdabdbbdcdcbbadbacddabcddccacbcccbacbcbadbdbbadbdadcdccabbcdbdbddacacbccaaccbbddaaccadacbccaadbddabbadbcdaddccaabdbcdcadbcccaaddaccddcaccaaacaaddbbccabbcdcadbadbbbdaacdbbaddacdaadcabdcaabcbbaaccdabbadcdbdccbdccdadddccabddbcbdbcadbcbdcacbbdddbbcddcaaaadbdbaccdbaacbccbbbbdbdacccbabcdcccbadcccdbcbadabcacddcdadbccaacdbddcbabbcadbbaddadbbadbbcccaaabbcccbcccbdbdcbbbcdaaaccdaddbbadbacbadacdddadbcadcbbcbaabacaaacdaacabbcbadbdcbcbcdabccbcbcbaddbcdcbcaadbbdddcccadccbbaacabbacdcddaabcdcabbddbadbcaddaaadaadbabadcbcdaabbdaacdcacdcdcbcdcccddbcbbaabaccdcaadaadcddacaacbcaaddacdcddcdacaacaacdbcbbbcabdccacdddcbdbcbacabacbdcdadcaaaabdbcbaccbbbcbdccbdccbcdaabcbabdddabccdddbcdccabddccddbcaabcddabbbcdbcdaccbdaaadadbaacabcbcbdcdcdcdaaadbadbbbbcccababbbaadaabbcacccdadadcbbbccdcadacbbadcccdabbadbaddccbdcadcdabcccdcaccacdccccbcaaddabaacbddaaadbbbbbbdccbbdacbababbdcddadbdabdaaacadccbbbcdbcdbccabcacdddbabbdcbacdbbccaddbabccbcbbdbbcaabaaccddbacabcdacabcbdbbcccabcacdbddaddccdccbbbbcbcccabccdcbdbbcddbabbcbcbabdbccddacadbdadabddaadcbbaabcdddbbaddbcaacbacdacbdddaadacbddcbdbcdabcbcddacaaddcadcbadccaaaddbcacddbcccdabccbcbbacdcddccabadabcbadbacddaaccbdaddbddcddcadddabdabcbdbccbaaacbdccdabaaabdcdadbdaaadcabccacccadbddaddcddbdcdabadcbacdbbcbaaacdddcddcbccddddcadbadcbadbdcdaabacbabaacdbcdbddcabdaabaaadcbdbadabbbbbbcbabcdcbdbdaddbdcabbdcccccbcdddadccdacacbcdbbbaddacabcacbbadabcbadabcabccdbaabcbaabcbcdaaccbbcddddcdbdcbadccbabdabbbcdbbbdaabbcadacaccabaacdaadcdbaddccbabcbaaacbabaccacaabadccdaddccbadbaabbcacbbdbdbcdccdccbaacdddbdbbccdcbbbdbdbbacbabdbbdcababcbddddcbdaabaaddaaaaaaaadcdccbbadcbbbdbcdbcacbaabcadababdbbdbcaccaabaababdabdbbacacbcdcccacbdccacdbddaabdcadaacbcbacabadbbdddbbadbbccccbddbbbcdcadbdacdddccabcbbddbcdaaaaababaadbacccdacdaadaacbbcbbaccbadbbccdadadddccdbccdacaabbbdbdcdabcdaacdbdcddaadaddbcccdddabadcdbbccabcdccacabdabaabdbdaaccbccadbbaddcaaccbaddabddaaddccdbadcadcbacdabcadddbbdcabcdacccabdddbbdccaadddcccdacaacbcaaadaacaadadacaabcccbdbaccbcdcaacbcbcabbaabbbaabcdadbbbcabdbaabdabaddcbbdddcabdcdbcadabcbaabbadabdbcdacabbdabbdabdcdaaabbaadabbadbaddbdaccbadadcdacddddbcaacaaccdbbccbbcccdcbdcbcdadcdbbabddcccbcacbaaabacccdbcbdccccadadadcdcbaabbbbdbdcabbacdadcbccabcccabbadddcbabbaddadbacacbbcbacbdadbbabccdcdbcacbcddccbbdacaabcdadacacdadddbaabddbbadccaddbababbcbcabcbcddcbbdbabdcabcabbcbacabdbaccddbabbcddbaaddbdaaddcbcbbbcbaabadddcdacdadcdccddadccbdacaaaaaabcddcdbdccaddbcbddccdcaadabbaacabcabcaccdccccdcddbcdcdaddadadaddccdaabcababaacadbdacdabdddddcdadbababdbbaaadbdddddcdbbaadcbabbcccbadbbcabddbddbbbbaacaabccdcbbaccccadacaabadaccddbddabdaccdcbcaaccdadccadbdcbbdcbabaccdcbcccdbaadddcadddbbddccabadcacccccdbcaaabcbadaaabdbdabbaaacddccbbbaabbdaaacccbbaaacdaadadcdaccdbacbdbadddadacbaaacaacbaadbddadabcbbcdcaaacadaadacacadbdbaddcdbbacadbbbbacccbdadbbccbbdaaddddcddacbaadccdcdcaaaaaddaacbbddcddaaccbcbaaccdbccbccdddacdbacaadddaacdccbdbbacdcddbacabaccaaadbbbcacddcbccdbdcacddcdccccadadcacdbbcaabaaabacaddcadaddcdccbbbdbaccccdddcbaababbddabbdddbbbcbdbaaabcddbdadbbccbddcaddddadbdccdbacbadaadcbccabbdcabcdbbaccadaddbadcbdadbddabcdccdcaabbddbbddbbdccdaabbbcccbcccabdadcbbcdcdbdcabcbadcadcdaacbacddaccdcdbdadbbcdaaabbbdddcdadcbabacbdacddccaaccdaacdbbdbccbcdcdcbacdbadddbdabaaabbacabbcaccdccdcddbbcbbadbdbbddbcddcabdaaabcddddaacabbacbbbbcbcaabddbccbbcbccadaabcbdaacacdabcabcbbcdcdbdbacddccbdcdbabcacddaccbcdaccaccdbbcdacacbdbdddbcbacdddbccdcccccbadbbbbbadabadccbcabaadaaadcdbdbabccabcdaaaacabcaaccbddcddadaccdacddbcadaabdcdacdcdbdbcdacdadabbbbbaabdbaacacbbcaabbcadccacbaacadaadbbaacdccbdadbdbbacacbbdbdcbaccbabadbdddacbbddcbcbcdcdddddcdddbaabdcbacadaababdbccbbbcdcabbdddccbcacdcacdcbbadcbdbdbbdbadacdcbbcbcdcaaddbbdacbdbcdbdbbacbbccbadadbdabdbdbabbcacabdbddcacacaacadcccbdbadcbadbcacccacadadacbddbdcadaabcccbcbabbdababaaacaccbaaddbdccbdccacbbcabcccdaacbbddabdbabbadaaacabdbbaacdbbddcdcacccbbbcaaaddadbcdabadcdbcbaddcdaccaccbadadbcaaababcadaadacddbbdbbccabbddabbbacbabbbadddaaccbcabddcadbdbadabbabdcbaaaaadbdddbbcbcdaaddaabddcbbbbcadddbdbdbcbabbbbdbcccccacddbbccdaddcbbcbaaadcbabbddacdcccccbadcdddcabcabbdbcabddccaccaddbccaacaabaddcddcdabbaadbbdcdaaabbdcbaacdbcdbbbacdcabddccabbcbbdcbddbabdacdacddbdaadacccabddacdcaaaccaaabdadccacbacbbddcaaddccbccbababbbabbddcddacbbbbbbadaccccdadadacbacddbababbdabbcbbbbcaddccacbaccbbcbdccbadcbcaacbdcdcdddacdcccbabbaaaabaabbbbdddbdabccbbaddcdcaaccadadddacaddcbbbddabaadcdabbaddbbcbbccccbabbbbbbdcbcaddbccbdabbcabccdcccadaddcbdccdcbbbadcacbcbaddaacbcbdbbbcdddbbdbdbacccbaacbacbcdcbcabadbcdbbadcabddaadacbaccbcccadcdaabaccddbaabbcddaaacbcddaaadddacacdcdddcabbbbaaaddacddbdddcbbadaabccbdcaddcabcabcaaaacadddacbbbcdabaaabbdbddbbbcdccdacabbccdcdbaabcbcdbcbababddbcbcacddddddcaadbaabbcbbaadcaddadabdbabadcaadabaacacccdaaccccccdacbdaaccddccadadbacccbdaaacaadcdadbbdbbcbabdcddcdbccdcadaddadacbcbacccadbcacabbabccaaccaabcbccccbadbccccccaddccaadcdbadabaabbcadaaadddccccabcddadbdbbbcacbbcdcbdabdabbabbdcdccaccdadcbdbdcccbddaddaacbbcabdcdbcaadbdbdacacdbbabcdcaabbaddbcdbdbcbbadbddcddbbcccadbcabaddadcbdcdcddcacddbacbbbdbcbaadbbaacacaaabdbcccdabdadbddcacdddcacbdddaccbcbdabbacccbcdbbbcadddcccdbcddcccbcddbdccabcaaddaabbdbbcbacdbddbccbdadbcbdbdcbddabbcadaadaacaddbbcdbddaacccbadcdcaccbabaddbabccdcaccddcadcbbbcdaddaccbacccbbdabbdbcdbcabdbccaaddaaaccbcadacaddddaadbdaddbaaadcdddabadbabaccbbcaabbcbacbbdbdddadbddcccadbcaadcaaaaccccbacbbbdcdbaacccadbcadabccadaccdadcdaadbbdbdcdbaadccaaaaddbdccacbabaadaaadbbabbbddbcdcaadadabbcdbbccbcadababdbcaadddaabadcbcabdaabacaacabdaaadcaaabbddcdcbabdbbbbabcccdadaabcdabcadddadabcadccaccacabaabbddcadcccbcabddaaadaadaaccbbbdaabcccdbdddcdccbddbbadcccccdbbadbbaacbdbcbdcccdcbbdacdcbcbbdbaabadadddbcaddababaaaadabdbddacdbdbabadcacabccadbcabdabdbdccbbccbcdbbaccdacdcccbcdacbcbbdaacdadcbcbcbdcacabaaacaaaadacbbbcdbaacbccddacbcaadaabdbcdadbcbaacccdcdbdcaddadabbadabbacdccdbabdddcdbbabbaccbabdaaabacaabcdbdcdcdbdbbccbadabbccdddabccdbbcdcccbdcddbaddcdcadbcacabadbbdbbabdbcaadadddbcddaddacdbbcaddddbdacccadbdcaabcbbdcbdaaabbdaabadcdabbbdabbbbdbbcbdbbdcdbbbcabdbadbddbaaddbbdbbccbadcdaddbbbdbbbadcdbcaadccbbdaadcbbbbdcbddbaacdadbcdaabccbcdcaccbbaabccdbdbdbacabbaccccdaadcbacacaacacacbacadabcadcbcadabaddabdbadaccbaadabcaabdddddadddddacdabcdcdbaacdadbacbacadbaccdbccdbbdaadddcdbbdcbdbbbbbcbabbdaabcabbbcadbccbaacbddbdcabdcaabcabbadccaaabdbbbcccaacacadbbadccbccdaacbcbcddbcdcbcdccadadddbdcdbbbcbbcacdcdbbdcbbbbabccbcaaccccddddabcadddbcadcadccabaacbcadbccaabbcdbacaaadbdcaacdbbdaaabcddccabcbdabdbdadbacdcdadcbacadacbcaccadadaadcddbabddbbdaaacccaddbdcddbabadcaddaaabcbadccbbdbaccabaabdbcaacbbabbcaacadbccdbcdcbdbadcdacacaadbcbbdccdcaccccdcdbdbdbabcbccbdbbaabcbddbcccccaadbadbbbcadacbbcdbcadccacbdcbacaccdbadbccaccabcacabadabdacdaabbcabdcbbbbbbbccdbbdbbcdacdabcaabcabccadcadacbabbbbbdbaaaacabcdabcacbcddbbdcbaaabdbadcdcaadbcacbcacaacadaccddcdcadacdbbcabbbcbbcdcacccabcbcdccaabbaaccdcdcbdacacbaddcabbbadaccdcbdbdadcdadadbcccaadcbdcbaccabbacbbdadbdbaadbcdaddcccadbdbdccaacdddbdadcaacaacdbccddcbcbcdcdbdacaabdabadadbaddddcaacbdcbdbccdcacaccdbabbadbcadaddcddcdcbbcdcdbbcaadacaadacabadcbcdddbbabacdcbbcddbccbdacdaabacccaccbdcaddddcddbbcabbbcddccdacadcadaadbbbdcbbbaabdadaccabbddabbbccbdacdcdbaabdddbdbadcdccbcadaaaccdabcccccbabbccababddcabacccbbbcaadcbcdcacacdabbdbdadbbcccbdccbaaaadcacdccdbadbadaadddcabbccbddddbbdccadaacabbbbccabccbcdcdccaaadbbcaaacabadbcacbdacccadbadbbbcccabdaacbbcbabbbaaadadcccdbdcdbccdacdccbcdbcadbbaadcacacadacbdbdaaddcdacdaaccdcdbbbadcbbbbdddcbbaadabddbdcabaddbadccbcaaddbcadbdcaaacacbabddacccbabacacdbcaadabacddaabccdaddbbdcbbdcadcacaadaabbabdcabbdaadcabcbddcacbdddbacdcaabaadbbdbacdcbaddbcdbcccbdcadbdcddcbcdadddbccabddbabadcbcacdbdaadbdacabdbbcaacbcbcaccaddcabbacbccaacddbdbdbcacaaabdacdcbaadddbcdcdcddbdcdbcadcbbbaadadbcdadbabddbbbcbdcdadbdcbaccbcbddbbdacbdcbaccbbccbccadcbacbcdbcaaadcbcddacaabbdabbbdabcdadbbaabccdaabddadcbcbcbaaadbddabdddccadddcbcdcaddddbaadcabdabadbabcdccbcadddabacdcaddbacabccacbacbcddddddacdcbabdacdddbdbcaadbcbcccccdacdcddcabcabdccbdcacacccaadbcbcacccdbbabcbcdadacaaddddcadccacdaccacabccddcddbccdbbcdababbdbbcdcdadccccdacddcaadababcdbdabccacbbaacccabdcabdbbabbbbdcdcdccddbdabccddcacacdcacdccbbdcbadabbcaacdcbbbdadabbabbbdccddabbabdcadbdcbbaabcaccdabcbdadbdaacdcdccbacdadcbaaaabcbccbcdabdbdbdbbabbadccabbdbcaaacaadadcabdaccddbddcddacaddaaddccabcbcaacdabbdbdbdcabbadbdbcabccaadcaccacbadddababcaaccddaacacbbabadddbbbdacadacdcbcadabdbcabbacdadbcbbbdccbcadccabacacddaaaaacdbccdbacccbdaaddcbdbbbbdbcdbcbccdadaaacdcabdbadbbbbcaabbdaabdbcdccabdbacccaadbbcadaacbccbbbdbccbbbbcdaadaccdaaacacccddacdbbadcddbdbcbcbcbaccdaababcccbddadccbbcacacabdddbcbbbcadddcbbdcabcddbbcbdcabbccdaabddbbdacadbccdadbbccdddacdbbddddcabcdacdccbbadddbcabdbacbddbdbcaadccbabbcddaadcdbabdbbcccdaacdbcacddcbdbadccdbbbddadbbbaaaccccddaacdbbbdddaccdbbdddcbacabadcacccdcadcbcdbdbdbccdcbacdaddcaadbaacdadababbdbbadccbabbdaacadbdccdbacbcabcaccbbcdabbdaccadaaacbdbbcabdcaccdbdbbcdcbdcacbacaaababcbcbcccdabccbbbcdbdccbbbbabdbcabddbbdddbbbdddaccbdabbaabdcbdccaccacdccdcdcbdabaabbdadaaddaaadbaadcaddbbabadbabaadcccdbaddbdcaacdccdadccdadcdcdbbaddbccadabdbaaccabcdbbadcdacdbbdcbaaadcbadacdbbcdbdbdcaccbadbdbdaacbbccdacdbbadbcacacaabcabadcccdabbcdbcbdddbdcbbcdaaaaabcaacadbaadcdbacbabdbcdcddcbdbbbcaacbbabddcbdbcabacacbcbbccdbbcddddcddbbddaccddacabaaaddbbdadabdcaddbdaddbdddcaadcbaaddadddaaabcaadadaaabbbbbadcacdbccaabdcaabcacdcacdadbabaaadbaacadcdabbbbcbccabdbccdbbdcbabbddbcabcbabcdbcdbbcadbbaccccbbcbdcaacaddabbabbaabdccdbdccbbbcabddadacbacddacbddbadcdabcbbdaabacbabaccabbaddcdbcccccadbabacdacbcaaacdaddbdaadcbcbabccdcacddbbcccadaaacaabcbcdaaabbbbcccdddcbcdcdaaaadccaaaacccaaaccabdbbbacbbdddcdddbabbbcdabaadccbdcbaddadcbbdcbcaaddcaddadbbcabdcddbbdcbaaaacdbaddbbabbcdcacbabacacaabaabcaccababacadbaacaccddaccabcdbbcccadacbddcabccabadbddccdddcabdddddbbaadbbbddaddbbbdbcbcbcadbaddbbaacdccabadadabcbabbabbbcbbbbcacbbdcdacccdbaddcaacacacaddccdbccdaaddbcccccbaacbdaacbdbbcaccddadbcdbcbabcabdcabcbcddabaddcdaadabddbbaabcdabcdbccbcacbbacbcbbdacbbbbdccdcdbacaaddabdbbcddadabbadcbdaccbdccdbdcdddcccbbadaaaaaacdaccbdcbdcabdbccccadbccddcdddbbcbbcaacbdababcaddaddbaaadadddcbbcabdadcacaaccaddaddcadbacbcbacdccabbaddbaaadbdddccacdbbcaabbcacbbdcdadadadaaadbcccdbababdbbcaaadcaaacddcaddacbbbbcbbacbcadcdddcdbdbbbdbbccacdddcadaacccbcabcbbdcbabbbcbccaaadcddbcbabdcaacdadaadbabcdbcbddccbacddbbbdaadbccaaddaaaadbacdbdddbdabbcabdccbdacdbabccdacabcdaddaacccaadbcdbabbdabadccbcddcaadccbbdacaaaaadcabbdacdccbcbcabbcadadadcddcdbccdacbdbccbabacaabbbdcdcddabcddaadcbdacacbacdabbacbabbabcadaddccabadcbbbadadcbddbadadacabbdbadbcbdbadacbadcdddbdabdcabcbabbdcddadaddacbcdcdcddccdcacacabcabbbaddbddcbaadbcaccadcdabdbaabcdbbcdcacccacbcbadccdaaacbbacbacdbdabcbadaababcabcddcdacbaabbdabaddadbadddbcabbbdcadadbabaddbdcadbbcbbcaccacaadddddcabdababddacdccdbaccbdcbbadcbdabaddadbcabddcabadccdbacacaadddaaaddadbaabcaccbcaddbbbdacaccccdbdcbaaddadcdaaaadaabbbcdadcdbcdadcabcabadbdabdbdbcdacadbddbbdcdcababcddacddabdbccaaccadcdaaaacccaacbacbddccdaccdbdcddabbadaacdadcdbbbcdaaaadcdcdddacddddbabccaacbbcbbacdcdcbaaccbcdbccacdaabaccbccbbcccbdcdaddaacbdcdbcddcabccdabaaacbbaabdbcaabddbabbbddbabdbdcdaacbbbbbdabddbdabbaababccddcbacdadbdabcacdbdabbcdbadcbcddcddbbdbdbbabbdcacbdcdcdddabccbdcbabaadbadacdddcddcdddcbcdccddcdbdaaccbdcaacbaaadddcbdaabaacaaadcaaccddddbaaabbcddbcaadbbcddcbcddbaabcabcddbdbcacbacaccdcbacaabcacdabdabaadcadbaccabbaacbababcddbbccbbacddbbcdddccabbcdcdbabbddcdacabddbaabaaddccbadbcbddacbbcdabadcddbabbbcabacaabbdcaccadabbcbcccbdddcbadcaccbadacbacdbcaabaaaadccbcabacaabcdacaadcbbaaaaaababacdbdbbdaaadbacbbdabbabadddccdabcaddbdbbcddbabdcddabbacbcdbcbdadabbdbbdbcabadddbaacbbacacddccaadddaacbddbcdabbcbcadbdadacdaaacdbdabbdcbdcdbdaccbddacdaaabdbbadacbaadcaabbddcbcaaabbdacabbaacdabcdbabcadbdaaabcbcabcabbcbdccdabdcdcbababccdccccbccaccbcdbdacaacbbcaaacbdacbabaddabcadaddabacababacbbcabaaabcbaabcbcdddaddddaabdaacdddabcabdabccababddadbccbcacbabcaaccdddcbbcbbadddabbbababdabbbaccbaabacbbddbbabdacdcbcbcdbbdbadbcddbadbcdccddddbaadccadbacdcdbbcbdbacdadddabaddaadaabdbcbbdcaaccdadddbcacaabdcdaadbcadabdbdddacadccdcaacddcdbcbdabccacdcbcadddaddacacddccbbbdcccabdcdbccadbbbabccbcaaaadbcbacaccbbaabaadddaabddcdadbdddaccaddacbcdaaabadbbaadbcdbcbaadcadacabcdccdcbbbdacbdabccccbacdcdaaacdaccacaccacddccacdbbddacbcdaabaaddcdcdacacbbddadbcccbcaabcdbbabdcbcddcabaaabccdcacdbdadbdacbaabcdaababcaccdabaccbdaadaddacbcacdcbababadddcaadcaccdcbbaadbaaacacdbbcdabadddbadccbbaaacbdcdbbdabcacacbabdcccadccdbaddbcbddabddcdadbaabcbbcadbcddaaadcdbdbddbacdddcacbcbbaadcbcabdcddccabdddccacdbabdcaccabccabdadcdcabadbabccabaccdbbcddabacbdaacdddacabaaddcdddaaadaddcdbababcbcdbdbcdadbacdabdbdcabdcacbdddadbdacdbaddbccbabadabdaaadacdacbdaabdacbcddacbabdbccbaddbdbaacabcddbdaacaabbaccabbbbcaadbbbaaabdbbcdacdbcdddcbadbbdcacbcbaaaddbabdddaddbbdddccdcabaaadbdddacdccaabdcadacbbaccbcdbbacbabaacbbbdbabbbbadaddcaabdaabcccaaddabcbdccdaaacabadbacacacdbcdadaccddbccaddbaccbbbccdcbdbdaccdbabacbddcccadddccbbdcccacaababdadcdccddcacdbaaaccaddacccdaacbdbbdacdbdbccddabbbdcdcddbcdcdadcacbbacddadbadbdbcacbcaaacdddabbbbaadacddadddbccdabbbccbcdccabcdccbabcccaacaaacbcddbdddadbbaadddbaadadcdbbcdcaacbabbdcddbadbdcabbbdcbcacddadcaccdaaaaadadcccabbcaddabbadadcbcbbbbccddabbaadddabdcdbcdbaddaaadadccdacaadaacdddbbdcadcbbccccdddccaddabcdcdbdddccbcdbdbdddbdaddcbcdabacababcaadbdccdbabcacdadabaaacdddcaaaadddabbdccbdcdabdcddacadccddbabaddbcbbdbcbcadaacccadbaccbaddbacbcaccdabcbdddacdadcdbdaaadabadcdbdabdcbcbdaacacdbbbbdcdadadcdcccddaabccbbcacaacbdcadcdcddaabcabadcbbadbdbacdadbbcccdbaaadbbdbccdcdcddcddbcabcadacadadbbbbdaccdcdccdcacddcdcccabacaabbcdabbcadbcdcabacdcdbdadbdcbaaaaabbdcaacbbcabbcddadcddbcdacdcabbbabcbdabcadbabbbccbdbadabdbdbbcbccdbbbdabbcddbadacbcdcccdabbbbdbbaabbbbbdbacabacbdbdcdccdccababdddaaaaaadaccbcbdaacabdacadcacdbdcbdcddddddbcdacccbabbbdbaabbbbaadbabdcbdbaacccbdacbbcaccdcdbbaacbbbbccccabbaacadbacbcddaaaddcbddccabbcbcdcdadaaabbdaabadaadbdabbcbcacabdbcbbcadccaabcbdddadabdcaabbbccacababcdacadbbcdabcbadcdbbdbcbbcbcbcaccbaaaabaabadabdaacacadbdcdbbcccddcdadbbaadcddbddaddbcccadbddabcddacabdcdcdaadaddcbbdddbaaccdaaddaabddcccbccabaacadbdacdcdbdadbcbaabbaabacbbabbccbadbdbacbcbbdbaacaaabacbcddddcbbcccccbccbacaccbcbccdddcadbdbcccaccabdaabacdddaadabdddaddcbbcdcdbdcbdccdddbacbbcddacbcaabddababdcbdacbcacdbdababbdccdbcdadaabdcbcdbbdcbaddddbccaacabbdcbccdadbabbcbaabdbbbaaaddaaacdbbbabcdbbcaccdcaccdadddbccbdccccdccbadabcacadddbdbdaadaacbabbcccadabbaabdbbdcabdcbabbddabacdabdabdaadcbdbdbdacddbbdbaccabdbdbacdaabadacbacccbdcbbdbcccbbccddccbbddacccdaaaabdabdcddbaccadadccdbbbcdddcdccaacbabdbbdaadddacdaabcacbdadacdacbcbacaddcbcacadccabbbcacbaaadbbbdccbcddacdbbdcddbcbadcbbbdabbbbaaacbcdcabcdbbcbccdbcdbbbcbccbaaacdcadbacdacabccbbadddbdaacadacdcbabddadbbaaadcbbdabadaadbbbadcadbddbcbbcbbdaabcbbccdcbbabbdccdbbacaadabddbababbcdcaaaaddadbabcacbaaadabbccbabdcbcdcddbadbabbbddcbbccbbabdcaadacdcdaacacbbaddddbcdcadcdcabdbdbbcddcacbbbcbabdddadcbdddccabbddbadcacadcaccaabbcbddcacadcaadcbcacababadaaacbcccaddbcadbbbcaacbdcdccacbabdbaddadbcbbdbdcdbdccdbbccddcddacbcbcddcaabaaacbaadbaacbacbbcadbabadbdcdacbadaabbbbacacdccabcadbdcabdddadddcaaddcbaabbbaadcdbcbcbadabaacdcaaddbdaccccbdcaaacdabacbbbacacbbbabaccddbccdbcbcdbaaadcdcddaacdacbadcdbcabbbcabdbaadacccddabbaacdbdcabadacacbabcbbadabdaadbbbbcccbdaaacdcbccdccddccadacddaccdbccaadddcbdbcccabcabdabbdacdcbbdcdabccdccdbcbaadbbdbbcacbdbcdbbabccaabbccddcaadabbbbbcabdbdcaabbcdcdddcddabcababddcacadbdbddddcbbbcbdddccabcabddccdaabcbcbcdbcdabcbcddddccaabbdabdacdbbaddbadaaddabccccaddcaabaadabacdcadaadabcdabdbcbadddbdbabadbcbbcdddcddacdbdaaabdbaacbdbdaadccccccdcaabbbadddcddcddbbdddbcdcddddacccddbcddddbbccccddaacdbccbdabdddacbaddbabaabdcbbadcaabbaabbbdbdbadbbcbabdbbabadbbabbddbccbcdbcdddbacdadcbccdbbcbaccbdabbddaababdacddaabdcadbbabacadbcdcdbbbaddcdacdbcccbbdcbaddcabdbcdccddccdcdbcabddcacaaddcbababaadabdbccddddccadbdddadcdbaabdbbacdcacbccdabdadbbdbbcbbbabaddddadbaddbdadccbcbcbbbacbccccbabdbcbabbbbbabbaadaabcddbcccadbcaaccacdcdbbbdcbbdbabddbcacaababcdabcadaaaaddcdaabbbbdcbadbacbdbacbacabcadccbadabdbcbacbcdbbddbbdabcadbbabdbdbbbbdacdcbbcbcadaadacbcbdddcaaabdaacacbcaaadbbdcbbababcccdbccccbacbacddadabaaabacacbcdcaacbbdcaaaaabaaccbcaacaaabbacbababcddbcaddaacabcbbacccccccdcdcdbbbabbacdadadbdbcdabcddcbdacccbabbccbdacbddcabbaadcbdabdbccdcaababbbdadcabacacddacacdbaacdadcadabcabcbcaacadbbbcdacadadadcacabcacacaddbcadabcdabcacbbcbcacbaccbcadadbaabcdaddddbbaacaabacabbddacddbbcabcabadcbdddadbdbbbcdabbaacbbbbbcaabacddcbcddccdcdabcacbacdbcddbaccbcccbaabadbabdadbaabdcdaaccacdccccabbddddadddddaaaadaadddaabbaddcdabbdbdbabcadabbbabcdcbdbdbadccdddaccbdddcbbddaaaacbbdcbbdadadacbccaacadddaccddaaacdccbdcadbdbbadccbabaacacdbbbbaddcdbdacacacdbaddbccaacbbbbcdcdddcdbdbcaadbacbdacdbabccbccacadadabadacccadadddbbcdaccbcabdacbadaddaccdcdcddabcdbbbabacdbacddccadbabdbbaadddbadbdbadbddacbddaccdaaddcbdcdbbccddbacbcbbdabcccbdaabbdcbcabcaaddbacdcdadbababdaccbccdcbacadbbacaababdcdaababcccbddbdadbccaaddcbbcaadbccdddaccdbbbdaadaaccadabcdabadcaacaaabaabadcbdbddddddcbcdabcabaadbbdbaacacdadadbdbdcbcddacddaabbabdabddcbcaabddbaacabddcbabadccadcccdaaddcbcdbcdacbbccadbbabcccbdbabbbbdabbabdcdcbbacbbcdadbabbbccbaabcdaadcccbcbccadbdccdaaccdbcdabcbcbdaddcdcabcabddabacacddcbcadddadcacabaabcbabccbbcbbbbbdbdbabdcdadcdcacadabcacccdbdbccccdcccdcabdaccadadadccbcaadcdcdaadbacabcadcbddddcbaccbdccccaaaacacdcbaadacccddbdaacdcaddcaccabdabcacadcccdccbbbdadbbdcbcaadbdbbaacbdaadbcddbbbccbbcdcdddddaaaddbbacdccbbbacaaadaadddadcaaacaabaddddbcabbcdcbbbcbacacdbcaaadcbacaddccdddcdacadabdbaacaadcadadbdddcddabdbaccdaacabdaadabcdccbcdcdddccabddbdbaadcaacabcdcccadabdabcaaaaccdcddcbcabaaaccdcacadadccccaddaadccdccbbbdacdcbbaadaadadabcaccccaddbddbddcddccdaabccddcabccadabdbbbdbcddaddacadadbacabbbccdaabcabadcdcbbbcbbddbbbbdabddccbddcabbacbaddbbabbdcbcbcbdcdacdbdbcbbdbadcdcdcdaaadddbdbdcccdcdbabbbcacbcabcdaaaadbddabcbabbabadcbccabaccbdcdddbbabacccaccdadcddadabbcdbccccadbaddbbaaacacbabbabaaabdabcddccbccdcbdcbaccacbabbccadbcbcbbcbbddbbabbcacbadbdcaaccbdaadccabbabbaddbbcbbbabbbcbdabdadbaabddcadabccadbcdcaddccacaabaccdcbcbbdbbcdadcddabcdccddcadacbcbbcacdbadcaadbccacbccabbbddaadacadacbbaaacbdbdcbacdcdababadcabbddabddcaacbccccdddcadbaaacaaaacddacdbdbbacadaddbcdcdabcbdabcabcccaaaadacbadccbdbcaddbcbbdcbdcacadbccbabdaadaaadbcaadcdcbadaaaddbcaccbccabcbcddbbddcbcbddcaadccdbbcdcaadacbcabcbdddabbaccadccaadccadbacdcabcbcaaccccbdddcddcdacdacddaddaabcbabdbbdcdcddbaaaddddbbcdccdabdabddcbdbdbdabdbadadcdcdcbacccacadbbccadbccdcabdcccddcacddcaacddabddaaccdabbddcdabbbbaabdbaacccdacbaccdbbbadcbbdddcacbdaccaaccaccaababaacdadcadbcadcbcbaadaacccadcaddadaddbabbadbdcbcadabadcdbcbddcaacbcaaacabbbbacddcbadcdaccbbbdddbdbbbddabcbacdcbccbccbcabdcaadcbcbbbcdccbbcaabbabbadadccdcddbccaccbdabdbaacaacdbbaadddddcbdabcbddbcdadacbabdcbbdbbccdcdddcdbccbdcbccaacbdccbcdaaddbadaddbbcdbabcacaadcbadabdbbaacdddadcdbcbcdadcddaaadcacdadcbaaccdbaabbadabdcbbbabddaacaadbabddbcbdccbbbcbaaaaacccaabccdcbadacdbdcdbbbbddababbdabcdadaabdbbaaacaadddacbacabddcadbaaccababaddbbaccdcddccbbccbcbabbbccdcbccccdcadabccbcdbbaadbccbcbdacbdcdacabbbaddadadbcbcdacbabcbaabddabdaabcdbbbbcdaaadabbccbabbbddccdddccbadbbbccdbbabcdbddbabbaadbdaddcbdacadabbcddccdcbcabcbabcbccacaacbaabbabbdbadddacadaabbdbbbbcaabdadadcccbdadbabbcddbcdbdbdcbdcaccbccaadbadcacbacaddadbcbccbaaaaabccadaadcaaccbbdacaaabdcdcddaddbadccbacabbbbdabaacbddcbbdbbbbadcadacdccbdadcddbadcbdaacdbabbacbcdcdcadbbcacccdacdbcbbbdbddbbcaddccbdcbbdabadcabcdadcdaadaabddbbabaddcbbcdddabaadcdddadabdaabcdaddbdabbdbcadddbccbaddbbcddcaccdacdbcacbbadbdcbacacaadbacbabacdacdccdaabcaaaaaadabcbddccdcbbbcdacddbbadcdabcacaacdcbccbdddaaadddcddbaccbdbcadacdaacbbacbacabbcaadbcabcdcbcdcbcadbccdddababaadbcbdddbbaccaabcdcaaadadddbcddcdaabbbbdbabdcdccdaadabdaacaaccdcbdcdbbaadacacdcabbabcbadccccababbcbbabddacadcdcdddaddddababbaaaabadaabdcdcbdbcbaddcbbcaacdbcccabbcbcabdcaadbbddacbbcbdabadaadbaaddadbdccdaaabdcbdcdbbacbabcdcccbadabcbcbbbbdaadbcccbbdcabcbbcdcabccbdddcbabbdcaacdcacbdbdddcdbaddbbcadcbdbcaddadbdadcdbcbddadbbdabbcbacccadbbdabccdccdbacddcbbdcccabdaadbcbdcbcbbdbccadbbdacccadbcaacdcccddcdcbccbbbbbddccdddbaacddccbbacccaadabacbdbbaacbcdccbcddddcbbbaacdbbadccadbccaacccacaaadabaacbadaaadcbcddabcbaabdddbbbbadbcdabbdbdaddbddcbbccdddcbbcadbbcabacaaaaddcbaaabbccadccdbdbddcbacdcacbcabbcaaddddcbacdbbbcbcacdbbbddccbdadcdbabdbdcaacbbccbcacacbacbdabcddddcbcbddcacacaadbddbbcccccbbdcbcabcccdcaabdcdabbccadddccaabdbbddbdaabaabaadbcbcaabdddcdcdadccddcacbccbbdabccdbcbbbacbaadaaaabddccdbcdbdbdbbadaaabccbbbcccdbaddddacbdbbcbbbcbaadbdaaccbdabbdbacdbaabcbdbdbdaadbacdabbadccbaadddcbccdabccdaaaaabbacdddbcacdabbcabcaabccccbaacddbabcbcaadbadadbdcababddcbdabddccbccdbbcabacdaccccacdbbcccbbdcbdcbdddabadcccdcccacbcdddddaadccbaadcdabdadaccaacdbdabbcaadadbadddabcbaadcaccaaabdccbbabaabbcbdcdcaabbcbcadccccacdcdccdbbdbddccdcbacabdbadbcabddacbacabddcdaaabbaacabdbbbaaabbbcddddcaadaadabdabcadacaddbdccbbcdcadbbadcbbcacccbbabadbacddbcdbcbabdbabacbbdcdcacaaabaaaabcbcdcddaccddacdabcacdabadbbcbbadbbbcaaabdacbddabadaddbdbbdbdcddaadcbcbdcbaacbccdabbacbdbdbdbbdcdddcbccbbbbbdbadaddbadadccbadbdcadcbdbbcbaabcddcdaacddddccaacaababbbdccacbcbcbddcaadcddadbdaccacdbbacdaacccbbabadadaacbddddcacbaaadcdbbaddcbacbdabcbcddcccdadbcdbccbdbdbdcbdbacacaccbdacdcdcaccbccaabbbbdbcbdcadccbccbcacdcdaaadaddcdcbccddbdaaaacadcdcacbaccdabdaabcbcbccbacddbbccadbaccbdcbadaaccadcaaddccbdbdbabdaaccbbbbacacaadacbcdbddaabbbabaaabdcbdacccbaccaabccaaacdbaacdbddcabbaacdaaaacdcaccdacabbddbccabbdbbcaacabcaabdbcdbcbcabddcbdabbbccdaacdbbaddcbcdcddbdbcddddacacacacddacdabdbbcacbcaabdcadcbcaddabbdaddaaabddbdcbaaadbdbcbbcbddadcdcabdbacdcdaddcbbbcbdcdabcadcbddcdaaddbcbdcabddacdadcdaaacbbcdcababdcabdcdbcbabbaaccbdcacdacbddcdadacacddddaaddaaccaadbdcdbabcbdcaaacdaadacababaccdadcabbbccbbbdbadabbacacbbbddaabbccbbddcccaabbdacaadaacaccabadaccacbbdbdbcbdcbddbacdaaaacccaacdcacbaddadcdabbadddabaacbbdcacddcaacabdadcdbcddcbcdbbcddbaddbaccdbaadddbacdbacbaadabacbdbbcbbddcbbcadaaaddddcbcccbcddbabdcaccbbbccddbdaabadcbcaaddbaccadacababcdbbcadaddcabcaacbbadacacdabbabacbabcbabcbbcddadddaccacccbcadaaabcddbcccbbdcaaaaaacacaccdcdaccaabccdddcbbbbdacabbddbacbbddbacdaccbbbcccccacacccddabbbdacccbdacdabdcddaccbcdcbabcdcacdacaabbccdbdcacaccaccccabbdaaadcbbbbcbcaacbabdaccdbbdbdddaaaaabddaacacdcaababadccadaddccaadaccabbbccaadbabccddacabababcadcdcaddaadcaddacdcbbacdcbaabbabacbcabbdbacbdadddccbcdcbdddbcacbadacdabddacdcabaacacdccbcbddbbbdcbbddbcdadbddababdabdadcacdaaabdcdabaccdbadccbbccdccdadbabdbcdacabccaaccbabdcbbbccccccbcaadcaaaabdcdadcdccbbbdbddabadccbdacaddbdbbddacbdadabccaddadbdbcadabcbcacccdaacabddccabcddccbbdbdaccdccbbdcbbcbaaddabdbadaaabadbdbacaabdcdbcacabbbddcaddbbbabdbccbacabcaddcccbdbcabdabbadcddbacdadadbdddacdacabbccbcadacbcbacdbdccdbdaaaaacadbacdccdbbdccabcbccaacdbdcdaccccabcbacbbbdcacbdcacbddaddadcababdcdcdbbcbcdbaaaabcbdcbcbdadaddddbbcbadcaddcdbdacdddbdbcadccdcbbababbadccbbadadabbdadcbcbdbdbdccdadbcadcccdccdcbccddcbcbdbaadaaaaacddcaccddcbcccabddcabcbaadccccabcbaaccdaabbabdaadcaddcadbacdabcadaacbaabdbccdcbabdaadaccbddaddbabccdbcacbddbbdadcbbaccdbaadadbcadadcbbddcbddaaabddadbdbccdbadccdcabcbadccbddcadbadabaccdbadaacdbabccdabaadccaaaabaccadbcbbbcadbbdabadabddbddacddbdddcdbadddbdccacdbbdadbcbacaccdacacdcbbadcbbdadbddaddacbbcdbdcbdbacabcacbdadabcbbcbacbbacdacbbabcdbaccbadcaacaaaabdcaddadcdddacabddcddbcdcdcbddabadcabcbbacabbdbacadddaadcdaabbddccbcbcddcdccbdcabddaadcdbdccdaacbaadcadccbdbbddcbcadcdbdacdcbbdbcdabdacaadaaddbaadbdbdbacaadddcbcddbcadbbcdacaacacbcabdcadaaacaccdcbbcccaabaaabccaccacabbbdcbadbabbccbabbbbadcbbcdcccacdcddadcaadddadbadddbbdcadcccabaaadcbccbcdacdbaadddacadbddaaabdddaabbadabbbbbcccdbadbbdbcacddacdcaadaabcacaadabdabaaaccddcbcbacadcdabcacbacaadddbbbcccbacacbaadcbcbdabcbccbadcbbadbbbdccdccdddcdbcdabddabbbdabbdcdaabcbbbdcbadbdaaabbcbadcadbddbadcbbcbdcbbdbbdbbbdabccabcdabdaaabddbdbdabcaabddcbacacbbcacacbdabadccdcacdcadcacbadddbbbabdbbcbbcbdbaacbdccaabdcabcbaccdccbccbabdcddcdcbbadcdaacbaddcabcdddabacdccacbabbaddaaddbcccbbccbbbbacccddbacbbcccdabadddacacbdacdbcdcbaccbadddccddabdaadbdaaadcabddacaddcbabaddddbaddcdacacadcccddddaabaabadbababaaabbdddacddcdcbccabccbcbccabcdddbabbbccdccbbdbcadccbacdacaacdaddbccacabbaabdbaaaaacacaccddaddcdbddaaadcacbdcccbbadaaacbcabcacdddabbcbdddacddbcabdbadbdcdddbcdadadccbcaccbcbcbddacbbabddcdccacabbabddddbbbbcdbabacacbcdabcdcaaddddddccbbcadbbbaabcdccdbbadbadcddcccbcdbcbaabbaccdabccaaddadbcbbcbbbcbdadcdaacabcaadbdccbcadbcccccbbcababccbdaccdcabbbdbbcddaaabadcccddbdcdacccaddacacdbbaccdaabadacbcaaaabaaccabbddbbccdadbddbbaabaccbdddcdccadddadcbaabccddbdddadbdaccddacaccbbccbbaabdababcaabbbbdcdbaaccabdadddbbcddadbcdadcadbbbcdacadddaabbbbbadcaadbbcbbacbdbdabcabacabdaabbaadbbaddbddadcccacadddbcbdabcdacdbbdbbbadbacaacaadcbdadacaddddbabdbddbdcccaaaddaccaadabdcbdacadbbdbdbaaddbcadabdcccbbbaaaabcadaaacdabaaccbacdbdcdabccbcadbbcdbbabdadcbcccbbdbcaaddccacaabddbaaabcbdadaabbcadbcacbcbddbacdabcaccabdcbcdacddbcccdcbcaadadcccdbcdcaaacddcccbaddcaddbaadadbbcadbacdabbbacabaadadddaadadadbdaabbdadcdcacabcdccacbdcbbcbbcbaaddbaaaadbcaabbacbddbcadbcdbaaacaacbbaaadacbccccaadbdaabadddcaccbabbacbbaabcdddccdabaabcaddcdaddadccccacaacbaccbacddbccbcaadbdacaccdbcaaadbacdbbcaacabcbcbcaddbcbcbdadbaddcdbacdcbadaabddbabcbddcdacbbddddddbdbcacccdbcbdcaddbdcbbcaababddbdcaccbccacbccabcabacdcdcaccdcbaacacddcbddbccbabccdacaabcbdbbccbdbbbabcdbbaaadcccccabbddcabacddbdcacdccacbdbbaccbaabbdaabadacabadabdaaacccabcbdaddcdacbaabaaacddcbbbabbbdcbdcdbacbdcdabdbccbdbbcdbcaacbacdccaccdbbcccbbcccbbcbccccbbabbddbacaddcdddbddbbcabddaaadbdcdbabababbbadcdabacabacabaadcdbaadddaaacadbcdbdacdcdabdbbdbcaaddadacbabddbdbdcacbabbcbcccaaaaabcdacbdcbddaddaabbbacdcdbdbabbdaabcdddcdddbbacbcbbcddcbdbcdccabcdadaaccabbcaadbdbcbbdcaddbbbbccbdcccdaabcccbdcdbddccadadaddbcabcbdbabbbcdbaddbadcdacdadbaacccabdbabaabcabcaddabaabcbabcbbcbddabacddbabacabcaadaabdcccabbadcabbabacbdcdddbcddccbdcadcdbaabdcbaccaadadbcdddcabaacabbdabcbadbadddaaaccdaccccaabddbbadcbbadddadaddddbbacbbadaaaadaabcbbccbbccaaddbdccdbbdcdbdddabdaaacaddbdddaccddcbacbdccacabdabcbbadaabaabdaddbbacaabddcdbacadabbdcdbbdcabadcbcdcbcdaccaddadabdccadaadacababcccbbcddaddbbbdbbdababbbcababbdcadcddddbacccbcdcacbcdabaccbacccdbdbccbbdbdaaadaddbcbadacbccabdddcaddcadccbcbababdadddcbbcaaabcacdccdbdbbadccbcccbcdaabacddcabddcdbbdacaabcaadadccabcadcbadbcbdcacdcddddaabbadabaddbbcddcbdccccbcccdacdaaaadbddaabcbcaacccbdccaabacddaccabbbbdabadcadabcdbaadbdabbcaddabcdccddadabdcbbdbccddcaccdadccaaacbacadacbaddcbaacaaaddcabdbbccaacddacccdadaaadcdbdcddbaddccbacbbaababddbdbacddccdcdcdacbbacbacdbbadddaadaaaadbacdaabbdabdcdddaaccadaabddacdabdcacaccccbdcbbddbcbdbbbbdbabadcadaaddcddadbbdddacbadaaacdddbdbbbbbbdacaacdbcacabcdcddcdddccadcaddbdccbddaadcdcacddaccbccdbacadbbdadbbabaaadcddbaccdcddcddbabcabbbcbbacdaddaaaddbacccaaddbcdcabcdbbcbbddacaabbdbcdbdcbcadacabccabadccabdaadcbdcadbbccbabccdbdcddcdadacabaabddacddcbdbcbccdacdbbbbcbcbcbcbcdbddddcaddacdabbdadcabbdcbbdcdabaddbbabaaddacdaacdddacdbbcdccaddbdbcdcabadaabcbcadaababcddacacadaddbcccddcdadcdccacddbadaabcbbcbcdddcacaabbcccbabadccdbadcdbdccddabbcdbcacaabdaddddddaaadacdaddadcbdaaaccdacdccaccabbaacacbdbccadbaaddadabdacadbdadbdccacbbbaccabacbddaaadbabddcbcdacdacacacccaabadbabccdaddddbbcbbbaacdbabcacacaaaaddbdbadcadcdadbaabbbbddbcbcccccbbadcdaadaabbdabaabbbbbcddbbcdbdbbddcadaacdcdbdaaddcabbddaaadccccaddbdadabdaadadbcbbcdaaccadadddaadbbcbbbccbbbcabddcbbbcbdcaabbbadcbcbdacbbcbbabcccacdadcccdabdddccdabcbaadadcbcacadccdcdbddccbbbabbacddaadddbcbdaadaddadcccacdddadddaacbcbaacccbdcdabcbaacbdcbbbbabdddacaccddccdabdbccbccabbabbbaabdacbadacbcacddaadbabdcdcaacaddbbccacddadbacacbacbddabbdbbadaacccbaacdbbcbbdaacbccabbaacacacabbbdadcdccbbdcabcdcdacbcdacabdcacdadccdaaabbcdadacbabbabdcbdadccaddbdbdaadbdcccbbbdcdbaabbdbabaccabbdbddcbadddbcdbddadbbcdcccbaddcababdcababdabbcbcadaadcdadabbcdaabdbabcaacdacbaaccadcacdccdadddbddacdadcbddabdbacaadcacbabdbcbaccbbdbcaaadacbccacdaabdddbcdcccaccbbaaaacdcdbbbdbabdacdcdacdbdccdacbdddddbcdbadabbdcbcccbbadacadddaacbacadddcdaabdacadbbddbcbcdbbdbdabbcdcaaccbaabdcadadcbabcbaacdbaaacdaaccbaaaddaaaabbbaacdabdabcaababcaabbdbddabaddaaacccbbcabddbbadccacabdbabbbcbbbccadacadbccbacbabdaaabbddcbbdacabadbbcacccbcccdccccdcbadaddddaaaaadcbdadcbbccdbccbdaccadaacbbbbabcbcbacabcbccbadddddbdaadcddaacddcdcabbbcbdbbabbadbabbddcbdcccbbdacbbbdccabacbcdbbccbacababcdddcbcdcbccdcbbaadbccddadabbdbcddccbdcbcbdadbbccdcdacdbdcdcbbdcaccaabcbdcbbdabadcbadbadbdccbcaabdaabbabbababdaadbadbaaaacaddbaddbdccbaccabcabcabdbacbdbbaaccabdccaaadabcdacbdbdccdabdbcabcccbaccbdbdddddbcccdabdbcdacccccaaabaadacabcbdcdbbdabbdadbccbabadcdccacdacaddcdbabbdcbbaacdcbdbbaadbbcdcbacaddddabcacaadddaabcbbdbddbddadbadcbccccbbaaddcbacbadddadcdccbbbbaddbdcddddcacddabcabdadbcbcbddaacdbabdbadabdcdbaaadcaccdbbacdcabaaadababbdabbdcccbaacaaddcbdcacabbbdcababbdccbabdbdaccbbddbbaabcdcbccabbdbbbbacacbabbddbbcdcdcaacdbbdabaaadbbddcbdcaacbcaddacaabbbbdcdcabdddddbacccbabbdbdbabcdcdabcbbaaaccbbbbababbcdcbbddccaaddddbcdcacdacababadcdadbbaaddcacccabbbadabdcdaaabcdcdcaabcbbdacddcbddbadcaacdcabadaddbadbcbdbaddbdcabdacdaacaacddbccabcbadaaccbbbbdddbbaccbddaabbaccdadabdcbccdcbcaabccbcddbacabccbadddcbbbdacddcdbddbcdccdbbcdaabbbcdcabadcddadabccdacadaabdabbdcbaccacdbbaadccdbccbbdccbdbcadcabaddddcdcdddcabbadcbbbbcaadabbacaacdadcaaacbaccbcbaabbadadcbbbddaaaacbccabdaabccbdadbccbbdbbdbbcccccccddcdcabaabbacbddbabcdacbadadbabcabddadcccabadbdabddcddaadbabbbaacaccbdddcdcdbacbaccbdcccabbadcbddbbdabababbdacbbdbadbdacddbbdcbbddaabaccdccbadadadadbdcbaacbcadaadcdaaccbcdbaaccbbacdaadcbdbaabbcbdcbccdcaabaccdacaddbaaabcdbabaadcbdbbaaacddacbccdbacabccdbbdaacdcdadcacdababbcbcbdbddbacddbacbadcabddaabadacaaabacaccdbbacbcacadbbcccdaabbbbcdbaaadddcccbacbabacaacaccbdbdabcbbcadabdadadaddcadcbcbdaadbccaadbdbbcccbcbabcdacdacdddbcabbdbbcaabcbccddcbbddbacbcbcbacddbaccadccbcabaddcdbdbacdbccacadcadbdbdbdcbacccbddccbcddccdbbdcdddcaadabcdbcaadbcdcbaccaaaacabcaddbcaccadbdadcdbbbbbcdbcbaaacdbcacbcdcbdaccdbbbadbbddcaadddbddcbabddaadbaccbdaaacaabccaacacacaccbbbdcccababcabbddbdacabcbaccbbcddccaaddcacaccddbadaccacaaccbdbbdbbbdaacdadcaadccabcaacdabaddcabaaabbdcaabcdcddbbccaacabbbddcdacaaabbbdadacbbddbdcccccdabdddbbcababbccbddabaaaabcbbaaaaccaccdcdddcdaccbdbddabbbadcaadaaadbdacdbadabcdbccbbaccbcadadcdbdabdccbbacacbaadccdaddadaaccabdbacbcbbbdbbadbdbbbdbdbcdcabdcadaaadbcdacbdabcbdbcccbacbabdbccbdbdbabdbbdacbddcbdbdcdaabbdbabbdbdababdabbaacadaacdbdcbaacddcbbdbdcbaddccdcdadabaababbdacabcbbaaaaadcdaacbabbabccdddabbacbbbdbdaddccaccacabdbadbaabcbccdcaabcdadcbbcabbcbbabcddcdddddaabbdcbcadccadaacabcaddabdcbdbaccacbccabbdadcabacdabddacbabdcbdabbddccbcaadaddcaabbcaadabddbdbdbacbccaadcaddccbaaaacacbbabbacbacddcddcaddcacbbaacdacbacbcbcbcdcddacbddbacdcdcbbbccaaaddadddccacbdbdbadcdddbccadacabbcdcdcccdabccbadaddcacacdabaadbbbcadbddccacbdbaaaabddadbaccbcdcdcabddabcbcdcdbbabbbaccbdbccbddadcbbddaaaadcbbabdbacbbababdcddcaddbccabaabdcdcdcddaddababddcacdbdbaaadcabbbdbaddcbadcabaacccdadbcadbbcabaddbbabdcbbdaccacbabaddbbcbbdbcaaaddcddadabbaabcadbaadcaacbdbadddccbbadccdabcaaaccbacacdbdddccbacdcdbbaacbabaaaccbbbddbacbaccccbbaabdcadccaaaabacccbccdacbacddcadcbcbbabdcabcdaaaddbbbbbaddbcdaabdcdcbdcdcabcaccabddacaddddccccdbdacadadbcbacbdacaacbddbddbcdbbccbdccddaadaabadadccdbdbbcbcdddddddcadacacbbdcdbcddddacbaaabcdbdcccabbcdadbdcdbbcdbbdcabbbabbcaabbbcbcbbcbdabcbbddaadbacaddcbacbccddbbdacddcaaddbcdbaccabbbadcadcdaaaaadcdabacdaabacabbcadacbddbdaabbbadaaabcabdccbabdacdacaabbbdddcdbcbabdcbcbdcaccabdcabbcbdabdadbbcdccacabdadaaadaacabcaacadbadaddaadbbacdabbbbdadcadaddabccbcbabbadcdbacccdabcabadcdacadccaaaddbcbaaabdcabbdbadaacdbdcdbccdccdbcaabbbabbdaabcbbccadbaacbaabacadddbbbadabacdbdcddcaadcdbbbabadbbbcbdbbaabadbaadababcbbdbbbdadaaadddaaacacacbabbcacaddcbbcacbdaabaadbccccbbabcbcdbdabacacbcccaabdabbcbdbbdbdacaccacccbbdabbabbccacabbaaadccccdcdbadabacbbaaabcddbdcacbcdddbbdabbdadbcaaddbddddbbddaadbaddbcdcacbadabdbccabcacabacdbbcaddaadaabbdcaabccbbdcdbdcbadcdbbdbabbcdddccaabbbcbbcdcbabcbabbbbbddbacccdbbbbaacddbbadbaddbcabbbbdcdbcacdbbcbabbcabdabdbddcacccdddadbcabccaaaccabbdcbdbbdccddbaaaacbbcbbbbdbabbbdcbbdccdbacdccccaacccbaddacdbdccaacbdbdbbddaaadacdbdbdbdbdaacabacadaabadbadadbcbbcadadacdccdbabccacdbabcbcaddcdccbacddcccbabbccbacddbbcabaaaadcdcadcdddaaaccbbcbdcadcbbadbcababcadddbabaacdbbdcbcbacaaaccccaaccdbabccdadbcdccdcaccbdaddbccbcaabcbabacaabdddbaaadcdaabbcabbbaababbddcbcdabbcbccadbcacddcabdcccdbadacabdcbcbbcabdcaadaabdcbddbdccdbcdacbaaababddcbdadbaccddaddabccabbdbdacbcbcbadabccdccabaccabaaadbbbdbcbaacabaabddbbcdadbaaddbaccacdccddaaccddbccdbddcdddaadbabcacaadacbbadccaacbababbdadbaddbaabbbcacdddacccdbcbadbabadccbabddadddcbcbddacdbdbaacddcccdbaaaabcbbdcaacbaddbabddacdcddccdaaabaadbdbbcbddccacdddcadaadaccbcadbaaabccacabaadcddacccccdadbacbacbcdbbcdbcbcddcdbdcdbadababaccbbdabbbbdbbcbabdbbccaacbdcdbabddddbdddcbacddcbdbadcdbbdcdddcdaaccaacbbddacaaaaccbaadcdcbaacbcddbcbbdbdabdaadabbadcbcadadcdbadaadbddddccbcdbccabadbdddcbbcdbaadcaacbbbaccdabcdddddabccccaccacadbdbdbaaccdacbaddaaadacbcbbbbdccacacacbdbddbbddcdddcdbaacbcddcccdabbccacbccbdbdcaaaadadabbddcdcccdbadbbcaadbacbaabbacacadaabbdadbabadaacabbdadbbddbcbbbcdbcacbacbcddbbbbcbaacbabbadbdccbddddbdcabbacdaccdcdbadbdcccacbddbbddadbbddaddcbcabdacadcdadbbdcbacbbbbabdadcccdbdddcbadcbccbcdabbcaadababcadccdadcadaacacaaacbdcdacbbcbccbbaabdcddabccabaacbcdbcdadaccbbddddbddaddddccbdbddbdcbdbbdbbadddcaddccacbdcbbdbadcbddaaadaddcbbbabdcdcdbbaddbdadaaabccdddabdbdadccbdcdcbccdbabdabccaaccbadabadccbabbadababbbcbbaacdbdaaaccdbbcbbaccbcbcbcbbcbaabbbcbbacbbacdbabddbdabababcbbabbabadccccdacddaabbbcaacdcdacbbdbdadadaaccaababbdacbacdacdbdbaacddabaacdcaddadddbcdaacadabdacacdbdaacdaabaaabdabadbaabdcacdaadccddcdbcadbbbcaddbbcbbcbcdbccbccabacbacdacabdbbbcacbccaddbcbaabaacccbdabccbbccbbaabaccdccdcdbaaddcbcacbacabaaacdbabbaabdcdcaadabcbbbbbdbabbddaabcadbddbcaccdddbbcbcccadcbaacaadcdcbddcbbccdabadcdabdbdbbbbbcbcbadcbaaddadcdaacddcacbaddadabaccabbbacdaabdacacadbacdbacdbbcabaaacbabdacbbbdcbbbabdbbabbaadbaaadddcccddcaabacabbdcaddddcabcadacbcbdcdddcdbadaccdabcccacaaabdabaddbbddacdaabaabbaaabdacbabcbbdccdbaadcddbbcbbcdcdcbdcbbddabadcbbbaadabbbdabccbadbcabdcdcdbbcbcccbabcdbacacbaaabdbacaacbbcacddacbabbdccdbcbbccddbcacbcbbaddcdcacacaaadddcabbbdccbdddddabcccdababdaaaaacacdcdaaabcbcabaaaaabdbbaadcdabbdcddaababaaacdbbdbaaccdcbdabbccccccdbbadbaacddaadadcddccdccddddcabcbcbaddbccbddbaddcbbddbacbbacddaccbbbbadcbabacbaaddbbacadcbaddbcbacdbbccabbdadcbcababdbacabcbdadacbaabbadacbdabbbadddaacdddbdaabcdbdacadbaadbdbdddaacdcbcbabccdacdbddbcccbdcaaaabcadbbbbcadbdddcacddbcdbcbccadbcbdabbcbccdbcbbadaadcacdddaaddccddcabdcbbcbbcaddcabccbacdddccbacbcddacadcdcaadbcbabbbdadbdabddbadcabbdadcbbcdaacadbccddaadcaabdbaaccaacbbaabbabdccdbdcabddbcdbacdbcbabdcaccbccdccbccdaccaaadbcadbdabcdbbabaddaabdddddbbacacadbabdbdbabaabaaddaadcdbccaaaabcaadcddaaccacacbdbabbcaddacbacccabcccccdbcabdbbcdabccababdbaaabdccbccaadcdccdabcdddaacdabcbdbacaccacabcadcaacabdacdaadbaacaccaccddcbbdcdbddbbcacdccddadabccbabadcabccbcbbddbaddadacdccbdadddcadabdbcccbbcaadccdcbbcbdccaddbddcbdacbacccdbcababdbcdbabdaadaaabbdacbbcabbcabaabddbaabaadcbcdcaacacdcacacacdbdabbcabadbbbcddbabcabcdacaadacccadbbccccddcaabbbbdbcadaacacdcabaaccaaacdbddbabcdcbcccbdbcbbaaadbaaaccabcbcbdadacdadbbdabcbaacdccbcddadbdcdadcbcbcdacdccaaadcbdcadcbcdccddddabadacbbaaabbcaadaacddddcbcbdbddccdbddbbcdccadbcddddddabddbcdcbadddcccbdaddccacadcabcaacddccaddadacccabbadcdbdcaddabcaacabcccdbacbccaabdacaaabcbcdacbdbbcdbdabccacdbbcaddadcdcdbaaaaaaaadbaaacbcacaadccabddcbdaddddcddcacdbbbdccbbbadcbddaaddacbbddacdddcacccdccadbbdbbddaaddcadabbdaadbbaaaacccaacccabbdbbbadbccadcdbcacacaadadbdbabcbddcaacbdbbaababddaabacaabbccacaacccbacbdbcadbbdcbbbbaadcdbcdcbcccbbaacbbaddacdacabbaaaacdacdcdcadadbbcdcadcdcbbbbccbbcdcdccdbcddccabcccdcbbababababbdaccbadcaddbdcbccacccbdcbccbbcadddabbbcdbcbadadbadbdcdcbdbaddcbaacdaabcabcbccaccdccdcdaddcdcddcbbcdaaadccdbdbacacdccdbbbabadcacdcaaaadbbcdddadbacabdadddbbcbaabbbcaaacbcaaabaccaccacbdddddadddcacbccbcbdadbbcbcbaddacbacabddccccadcaccacacbcbbaddaddcaaccddaabdcaacdaadcbdcccccbbddbbccacbbacbdbddabadbcadbccbacdbbcbadbddbbcbabcbacdcaabdbcaacbadbccdddbbbcbbababbdcabcbccadacbbbcbadbbacdcaaaaaabbbddacdcdcbdcddbdbbaccbbdbccbbadcdbdacaaddccbaadbccbaaaabbbdcadaccbccbaabaddbaacbcbdcbddbbcaddbcbdbbabdbaddacdadadddcaccaaddcbdaccdddadcdacdabcadcabbdcbcaccdcddbbdcadadbdcbbaababdcbbbbcccdbcaaaadadcacddcbcbdabdbbdbbbadaddacadbdcdccabadabacdaadacabccabcbaaadcadbdbdcaddabdcdccabcabdcaddcdbbdccaaaccdaccbbabbbabaccaabbdbddadaddbbdcbbbbdbdabbcacdaaddadcbadbbdcbabdcaacacbbbccbdaaababcdbdbddababccdaacacdbcdbbccbdddabbaddcdbdccddabbbddbcabdcbaccbccbcdbabdddcacccaddadadacbdaddbbbaddbaddadacadacbadcababacadbdacdbcabcaccabacdacbabcabcdbcadaaacaaddaaaaaaddadcbaddacbcddcdbbaddaabbddbaddaddabacbbaadcdacadcabcbaacdcbcaaacbdcbbdcdcbaccabbcbcbadbdcbdcbdaacadbccccaabadcbcbbbccabcccaddbadcdcbadabbadbdbbcdccddaddcadcbdddacbabccdccbcbdcaabacdcdbdcddcdbbbadbbddccabadcdcbbbcaabacbaabdbdbcbabbcaabbdcbbcbddddcabcbccadaaddaacdbcbcdaadababbccabdcacdbcbadaddccacadcdcdcddddadbcdbadbaadaaaddccacaacbbabdbdccbccabccadacbbdccddadadadbbbadababdbabdbaaaacddbdccbdddbbbbadcbdbdbcddaacdddcbbcddccbaabddbcbacaadcdaddaadcbabdcadbbbbacdccacbdcccbdcbacbbcdccbaabbbadbaadcbdcbdcbccbbdddbddbbcdcbcdabcaccdbcbcadbbdaabddaddcddbddadaabaadbbcacccbddbcbacaabbdcabdbddcdcadaacabbbbdbcadcaccbaaacbdddbdcacacccaddcacddccdbaaabdabbbcdbbccbacdadbacdbacbccadacdabccbbbabdadbcdbdbbbccbabcabbcbbdcbcddddccbccbcaccadcbbaabddbcaaadbdacdccdcbbbabdabbccdbbaaadbcddccccbcacadbdcdbdacbcbcdabacbdbcbcaadacdcbccdbdacabdbdcdbbcdbcdcdbbccbdbcdddabdacccddaaddddbdbddbdbdbadbbdbdbacdcbcaccdbacacadbdbbccaddcbccdbbbdbadbbddccdbdcabdcadbacbdadadbabcaaacadccdabbdabadddcaabaacccaccaaabaaaddccdaddddcdbccdbccadcdbcadbbdddbdbbbbcaaacabcdccdcdcaaabcacdabddbbbcddbadccddbbacbbbbabdaabccadaaaaddaadcdbcabaccaaaadcbddcbbaaadcacabccbbcdaadbbcddadccadbadacdcbcdbaaccdbaacdadaaacaabadbabbabacccdbccbccaacdddbacdcdadbcbcacbbcbdbdccccbacadcbbabcbcccdcadcadcdcbbcbaccbabddaadddaaababbdbbadbdbdabbadbbdcbdaaaadcbcdbadbabbccdbaccabdadbabcbbcbddcaaccdacadadbcbdbdddbcdbbbbbcabddabbdcbaabaaccabaaaaaaacbacbdacacbbdbcccaaadcddccabddabcacdcdabacaccaaaadcdaccdaabbbaabbacadcdaabdaadbddcdcccbdbbddbabbdadbbaadcbbadcadaadcccdbdbdadadaadbccddaababcddabcbbbbabbbcdbcababdaabacdcbbbbdcdabcbdddddbbacdacddbdcbdacadacaacddabbbacccbdcccbbabddcaacaccabdacbcccbbccabbdbdcbaaddadaaacddcbcbcdcccdcaaddbaaaadbadadbbddaacbbabcdcdbaaabddbbdbdcbdcacbaabdaadcbcaddcccccbbdbbccdaadcddacdcbaccaacdcdbdcddacaacaddcadcdaaabdbacbadcaacdcccdabbddbddaddccddadccaddabaadbbbddadbdcccbbabaabababcbaaacaacacbaadcbcdcbbaacbbbcbacadbddcddcbacdaccbabaaabacccaadcbccbdadcbbbccababcdbccaabdabacbbbbdbdbcadcddbdadcdcbdddcaacbbdcbdadddbaaadccdbddcbacbcabbaaabdaadbccaadabaddbdaacbcddaacdddbbaacabaddbcbadcdacbbabbaababbacdaabdbbbadbbcabcbcbdcaaaabaaabdaabdcccdaabcdcaaacdbccbdbcacabadcccbaadbdababbcddbadbddccdcacabcbaabdbabbcbdadccbccddcccbcdbccacbacadcbcbbadcadadbcacdadcccdaaacdcbcdcdbaadcbccadcbdbcaddbccbbdadbcccacaacabddacdbbdddddddaddbadadbcacccaaddabbbdadccaaaabccbacbcbcbbccddbcdadccbcbadbddbdbadbcbacbbabbabcdbbdcbbaabbabcbaaddbcccdabdadbbbdadaacbddbcdcaccdaacaabbabcbdcdacbadbcadcbaabcaaadcbccabbaaccabbdaababcdbadddddbbdcacaccacaddcbaccaabbacabdcdcccabdccbcccbdcdbbbaaacbcbabbaddacddcccdcbddaacadadbaadacbdabcabccaabbcbbadadbddbdddaadbcabbbdcdadaadbaccbcacdcaadcadabdabbaadcadbbaccbaddccaaababbacbabbbbacdbabcbaabdddbaacdbbdababcaadbaacddcbaabddcbcdbdabddccbbbadabbadcbdacaadcacbbddcbcbcdbaadaabcaacacbcaacaaaadcddcdcacbbccddbbddaabacaaaacaadabaabadbccddadddccbbcddcadaccdadbbaadcbaacbddddccddacaabbdbacaababcccdacaccbcacacacbdbcaccaaadcdacbddcadbbbbbcadbacabdacdabbdcddbabdbbdddaabbdabacdcaccbcbdadadbccdcdcdabcbcbabbabdacbbccabbbabbbcddcabbcadaaaacbdadbcdbbbbcddcccdbbcdbddbbbacabcbcdabddbabaadaadaabbcaaccababaaaacccdddaacbcbdcaacdbcacaaadddaabbdaababacacdcdadcccbcbccbdbcccdbbcacbbabaadaabcdbdddcbdcdcccddababddaaabaaacadaaccbbbdaddbcdbddcacdccadacbdcdccbcadbbaadcdabdcacacaddaaccbdcbacadadbdcdbbddaacacccbbbccacaccdccbdaddcdcdbabcbbddcdbdcbddadbddacbdbbdacddcdccaaccaadacddbadcababacacbacaaccbaadabcdaadbacaabcddcabccadbbabbaadabcbcddabccdadaaaacbbadbcdbaaaccbcdbdabdbacaddbccbbacccadcdbabcdcdcbcbbabdbdabacbcbacccbcdcbcadaadbbaccdadcbccbdcdaadbdccdddcabbbbdcbacabcbadcabcbbacccbdabcaabcbccacbbcbdcdddbbbcabdccbaaacbbdbdcbdaccbcaddacdcccacdabbbacbaaabcaabdddcccbdbaadcccbdcbbbdacbdbabadaaddcacdacdabbdadbabbdbccdcbdaacccdcccabbbbabdcbdcdadadcaadadbddbddacdddcaabddcacbdacaaccdabcddaabadcbbabacdbbbbabddcbcdacddbadaaaabbabbcddacadcdaacacddccaaabaddcabadddaaddcaabbdadaccacbbbacbcdaaccdcbcadbcadababbdddbddacdbaaaabaddcabddcccaaddbbbcaacdaccbccddddaadcccdbbbcadcacaaddaadddaddcacdadabcddcccbbcccdbadcbabbbacbabadaacbcbdcadbdbabcaadbcccbacaadabdbbddddaacababdcbbcbadaddddbaaccbdddacaacbadbcdbddbcdbdaabcadcdbadaacabdbcbbdcacaddaccaaacbbabadbcacdacdcadabaaaabbadcccbcadababdbbabacadbcadaccbaadabaddccbadadabdcbadccbcddbbdaacdaadccdcbadccdbdcbccaaddaccacaacbdbdbcdcbaaddbcdccbcaabdcbcacacddcbcdabbbddcbdaaabcbacadbadbadaaddabddcdbaccabadcbbccbdabbabacbaaccccbacddbcdcaaacbaccacabddcbbbacaabdbbaddbbbdcdbcdcbdcdcbbabdbcdacbbdccdccdaaacdadabcccaddbaacdcddbaccccbcbcbcdbddbdaccadabdadbabbcaaccccbcdccadaadaadccdcaaabcdbcdddacaaccdbbabcbacbbacabcbdbdbcacabccbdcaabdabadbcacaaaddbacccaabdcabccddbdabbdcaabaabdbdcadbccdccaccbaaaacccbcadaadbbdbdddbbcbabbbbccaccdaaaabbbabbbdcadabdcbabbaacdcaabdabbcbabbcaddcdadbabdbcccddddcdbcbdbdbccdbdcccbbcabddacbbabbadbcccbdbcdaadcaddadbdcaaaaccbcbcddccdbdddabbcacdccbbacbbabbdcaddcbcacdddabadbacbdaadaaabbbaabbabdccdbcbdabcbbaacbbacbccacaadaccddabdcbdadddcbdabbdaccbdaadbcaddcbbdacdbdbbbadcaacdcabadaabacbdacddaccdabbccdaaacbccaaaccddbddadbbdadbacdadbadbddbbbcdbaccccdacccbcabdddccbccabbbccbdbbbcdbcccaadcaacdbbbddaabcbdacbacbaddbdaadcaacaaaacbdadddcdcddcbadbcaaddabbcaacccdbbcccbbdcacaddaabcacbdadddcbbbccbabdccdcccbbbbdbbbcdaaccabadadcbaaaadccdcddbadcccaadbcddcaaabbaadcadbabdbacbdacdddbbacdaacadbdbadbdaabccabaddaccbbadbaccbbabbcadddbcaaabcbbcbbbbbcababcbbabacdcaabbccbacabddcbcbdadbabdccdddddbdddbaddbbbacddcbccddcbcdbdbbaaaabdcdbdcadbaabdbccdbaadabdddabbcbbbddacabbcbcbbbabaadbacdcabbbbdcbbcacaaabaaadacbbccadcabdcbbcccbdcabdbbddcdbdbabadaaabdbdabcaacadbabcddacbbdccbdaadcabbdbacbbbcddbccdcbaadccadcccadddcdbaaabdcabbccbbbddccaacbcddbabcbbbababdddccaaccdacccbbcddadaadbdabbbdcccdcbbbcbcbcbccccbabcdacdbbbabdadaaababcdbcccaaccababaaadccddadccbdcababadcacaacbcbccaddbbcdddadabcdcbddddccabcacaccaababadddbbdcaacacbcddcdadccddbdcbabcdcccaabcbcdaccbccdacbaccbdadaccabdbbbcadbcdbbcbcdbdddbbcaabadcdccbabacabbddabdbaabaddcadacbcccaddbbadcdacabbabbacaacccadacccadbdcdcadbaddaaddadaadbadddbababdcaccbaabddcdacbdaccddacdaacbddbbdabbbdaacbaccabbdbbdbacbcdcadcdcabaaccbccabcdadbddbdbcbbcbccbbbabdaaacbdaabbaacabcbdcbcdbdaddcbcddcbcccacdccbdcdcbbbaabccdbcdaaaccaacbaccdbcdcaadcadbdadbdaccdcaddaabdaddcbdccccdabccaacbaadadbbdbaadcadacbdcdbcdbabbcaacbbabbbabbabbcacbaccddadddbadaabdcbdaaadbcadbddabbbaccabdbaabdcccbdcadaaccddadccddbbdbbbccddcadcddbbbcbdacaacccaabaccacdcabcbddacbdddddbacacadcbdcbacaacabdadacabcbdbaaabccbcbacaccbadbbaadcabadaabcbddbacdcdadcaccdaaddacdabdbcdbbaabcabdcbabbbdcbacdddcacaccabdbcdbdacdcddabbcbbbcbabdcbaadcbdaadcabcdddcdddacacdacbccdbbadbbbcbaaccdddbcbddcbbbbdcdaabadabbcbddaadccacdbdccddddaacbdcabbcbdababadadaaababdbbaacadbabcacccbddaabbcccadbbccabdccbdacbbbdccabcdbdbdcdcacacbcbadbacbacaddaddaddcaaaddbabbaccbbbcdcaaabddaddcabddabbbbdddcbbadaccddbdcbcbabccacdcbcdcbbbabcabaccdcaadaacddadaabcbddadccadabcaadbbadaacadbabbbbddbbcdadddcbdbbabbdacbbbabbcadbbcddbbcdacacdbadaabbadbcbaaadbddcccddcbdcccaacacdcdaadabaaaacddabdacbbdacbacdbabaacbbbababcdbdbcdaccdbabbadccbdcadbbbcaaccddbbcacbdbdbcdcabbdabbabdcdbddacacdcdcbdcdadcbbabdbaacbbcabbddbacababaaddbadadddcddcdddcabdddacddabaaccdabdbadaddcccbadbdcbdaaaaabdbacaaaaadcbcaccacdabbaaaadacbbccadcdaabaacbcdccdcddcbcacbbbbbcbdddcdbcbdcacdccbbbbabdbdacdbcbabdaabcdacdbdbadbcdaddbabdaabacbcacdcacbbcdaacddacaaaaaaccbcccadcaabaadbcbaaaddbbcaadbbbaaccbbbddbcadadacacbdabcdbdadcbadbcaabdaddaaacaabbacbbccabdabddcadabacaadccbaaddbccdabdccaabbbbbcbadaccdaacbbdadcabacaacbacbbcdaadaabcadaabbcccccdbabdbdbaaaacbbadddbcadbdddbcbcacdbdabacadbacdaccdadacabdcaacbccbdbcacccddcbbabcaacdccacdbacabdcaabaddacaaaccdbcbabbacddcbdddcaabaadbbadcaacbcabdaacadaabdaadcdbbbdcacacdccccadbabcccbccdbcabddbaaacdbcdcddbabaccacbbdaabadcddddddbacdccdccbbaabadcccabacdbcbdbadbdcabababdddbcbdbdcbdbdabadabacddbdababbbabbccbcabbbbdcdacbcdbbdcadcdbddaccbbbdacbacadddbaaabbcbbaabbdcadacccdbbccddcacacdaaccadcbbcaabdbbabcbdcacddbbbcacbdddbdbddbaddadbcadaaaacdbbbcdccaabdbbddddadddcaacdaddaacbbdcabccbadbdcdccdbbaacddbccdbbbbdbbddcccbcbcbbdddbbdaadacbaacccaabbddbbccdbdcbbbdbcddacbaabcbdaabaddcccbbdcdaacdbdcccccabbdaadbcdbcaccadadabddbbacdcbdabacdddbcdddcdcccabbbdadcabbdacbcabdbdbdacdcacacdccdcbdbccabdaddddcbccdbdadcbdbccdabdcbddacdcbaabbaadcccbaddabcadcbdcacacccbdbbaacacddcaabdbbdadabdbcbbcaabdbabbddacbdccabbcccacdbccdadbddabcaccbdabbbaadcabbaabadbddaadadbabbbdccdbaacdcbbbdbbadadacbdbadbbccaddbddadacbaaaadbccbbbadcdbbdabcabbdacdbabdbddabcbdbcbbadacdbccdddaaabccbdbaaadadacaabbaabaaacdccdcdccdcaccbcbabbdcdadcbbbdcdcadbaddadcccadabbbcbbabaccadccacadbbacaaababdccabdbcdacdbdbdcbdccbdddaddcbddcaccdcbdabcdbcbddaccddaaacaadbdcdabadbbadadaacbaaaccadbdddccbbddcdacdadcacccbdabddacaabbcabadacaccbddccdabaaddbbaaabddbcbabaddacddababcbdbcbbadbcaccabccdcbdcccdcddacaadccbbbbaaddbdbaddbdcbbdcddcdabcbdbcbcabbabccacacaadcaadcdabbaabaddbbcbcbcdbbbcccccbaccbbcababadaacbdadbcdadccadbbcbabdcdcdcdcbddbddbbdcccacbcabbbdcabaabccbaaddabccabbdbbdccbaaaadcbccadadcababdcabccbcbcacdaccbdaaddadaadabadcaadaacbbccbdbbdaabcbbaddccabcbacaaabadccacdddcbcacbccdcbdadacaddaddbccaccccacbacadcbcacdddacdaaaddbdbadbaaabdbaccdcbcacaddadaadbbabcacbdcaaaadcadccbdaabccdcdbaaccdbdcbbbbccdbddddccdcbbdadcdcabbdcadcdabbbcbdcaadccaacbbabdcccdbacbabcbcbaadbdaccbacbabaccbadddccdddcbabaaadadcdacaacdabccbcddaabbbbddbaabdcccdcdadcadddaadbdadbddddbabcddcacaabdddacabbddaaabdcbacdaabacadcccbddacdbddadddbbdcbcdbaaabdccadcbaadbcaadcacaaabcbcccdcdaacacdaadabdbbaadccbaabbaabbccadcaabdcaaacdaccbcbabccabdcccbcbbbaaacddaacdbcadabdcdddcbddaadbcadccddabddadbcdabcdcaabaabacdccadabadbaccadccdccbadbacaacbcdbcdbdabcbacabadcddcdcabbacbcddbbabbbccabacbbbbbacacacbdacdbdcddcddddbbaddcbdabccaaabccddcdcdbdbdbbdacddbabbaccbadacddbdddcabdaadcadbcaadbacddbdbbacadbbbbccadbadaadcababbccdbadcccbccbdbadcaacdbdaadbadbddcbbbabacaccccaacaaccbadcdcbbaababbbbcbaacaaaadccccbbccdcadbbccacdbbcddccdbbaababddadacdababaadaadbbabdbcacbccdccbddbcdabcccadbbcacbcccabbcabaadbbcabbadaddaccbbabdbbadddcbbddbdcadbaddadcbccacbbacbdbcacdbbbdcbdddcddbabaabdbddccabcbcbdbccabddaaccababbabbccbbdbababdbcbabbaddbdbabbbcbddacbaaaaaddadbbbadbccbaabcabacddbaccabbccccabaabbcbadacbdbaccccdadcbbdcbccbababaccadcdcbdbcbbbacaacababddbdbcddcbcdccbcbcbbcccddbbccccdbbbbcbcbcbcdaacacbdcbabdcbcdbbacbacaccadcbcacddbbbbbcaadcbcdddbabccbdcdadbddbbcaabdcabbaabbcacddccbdbdbcadbdddcdbddaadcaacdbaabdbbaaddabcdbbcbbbbaabccbddbbdbbadcddbcdaddacdcdbadaabdbbcbccbbadcdcdaccacacddadddabdcdababddddbdbbbbcdddcddbabbbacabddcadccbdcdcddabcccadcabdaccdcbdddabbccadcddadabbddbdccdadbbccdbcabbbdbadbcabcaabcaaaaacadadcbccddaddacbccabcbbdcabaddcdadbdbcacdbadccccadcdcdcddadccddccadbbaadbbcaacdbacdbcbcbdaaccdaaddadccadacabadcccadbbbcbcdbcacbaccbdddcbdabbdaaacabccaacbbabdacbcbacccddcadbcadbbdbacabcacbcdddbcabbbabccdaabacddccbbabbadbcabbaadccdacbbbdabcbadbabddccbdcaccadccccbabbabacadcbaaddaaacdcdaadadccaddcdbdaadaabbcccabdcdbabbadadaddaadaccbdcdcbdbdcdaccdbcbdccdabcbcbdcccaadbbccdaddbacadabaaddbbddadccabddddcbbddadddaacbbbaadaccdbbbcbbbbdbabcaacaddbcabadbaddaddbaaabbcdcacbaccadaacadbbabbbadbbdadaadadddbbbccabbabddbbdbcabcabdcbaadaabddbdadcdbddadabddbcadccbaacbadbcacbbddbdccbbadabbcadcabbbddbbcdcabbcabbccdbdadaadacbaacdadbbcbdaaacccbdcbcddbcbbabcbbbacbdbcbddcbaabbabacabccdaadbcdadddbcacabcbcdddbbbcdcdbcbddabbdcdaccdabaaacdccddbddbbbdbdcdbadadcabbdbbdcbccadbdbccbbccaaccdabcddacbcaadbcccadddbddcaaddbdacabcaaabadbcabadaccbbbbccdbdabcdcaaacdaccddbdcdcddccbdccaadcbcbcddadbabaabdccccccdbbccbddccabbdbcbdcbcaaadbdbbacbdccaddbabadbbadaabcdbaddbadaccacddbcacbbbbdcbdbdcbacdddadaabdaccccbbcadbcdccccddaabcbccabbcccdabddabdccbdcdccdbbccdcbadbbbcaccaaaadcaddbbbddddbdbcccbcbacbcbaaddadbbadadbaacddaddddbdaaaddddbacbdcdcbcccbccbadaadbababbdacccabccccbdacabbddabcdccaabdaabcbaadadbabbccbbcccabccddaddcdbbccdcbdbddadbcbdddcadbdaabadddbcaadccbadcaabcaaaababddacbaadddcbdaacdddadddaadcdcdccacdbddbacaabdcabaadaabccdccdadddaaaccadccaabacdcacadddbcabbcbdabdcbaaddacacdcdbdbaabdadaabdddbdabcacdcbbbadbbcabbbddbbdaabadccadadcdacccbbaadbacacbbcabdadbdcdbdabdbcdcdaabdacbaaccacaadaaaaaadcdccbcccacaadddaadadabdddcacbaaddddccdcacbbdbcccabcdddddddccdbdbaacddddabaddaacadddadacbdabbcccbbbbcacddccdbbdddcaacdbabdabbcaacbabbbccddccbbaccccddbbcbcddbbacdaddbdccaddccacbcabcdabbacbbaccacabdbabcbcaadbbdccccbdadcdbbbdcacaadcbdbcbadbddbbabaabbabdbbbcdbabccbcbaababcdbcbcddddccbadaadcdbacabaabbcbdcbaaaddccbcabbbdbbdddbaccdabccbdddcdbddccaccbacaabacabbdcacbabbdababaddcbaabbbdabbcdaccadadddabdbbccaaaaadcdadbaddbcacdcbdbcdadbbbccdacacbacdddcbcbdadaccbadacabbbcbacdbadbccbcbbbddacdacacaddabdabacdbddbbabadacbbaaacdbbdccbbbdcdbbbcabdbcdcbabaaccdcdddaccabbbaadabadbdddbdbdbaacaccacbbccacaaddbcacdcddacdacaddbaabaddcddbbdbcddaabdddabdbbbddccbdbadbaabcdbcbacdcabacdacccbbcbcbbadabacddabdbdcddbabccccdbddcbabadccddcbccbdbacdcdccbbbcacbccbbadcbdacccadddaccacacdacadccddabbccdaabbbabcaddadcddbcbddbdbdcddcabbcdcadcdbadccbaadcbbdcdddbabdddcbabacccdbadcbabbcdadaddacdabdddcbcacadacddbaaabdaadcacdbbbdcccccccbdcabcbadabcbcdbbddcdabdbdcdcdbaaaccadbbbbbbdbbcbccdccadccdcbabdbbddcbcccaddacccdbbdacddbabcdabdbdbcdaadbdcbcbccdbddbcacbadbbadaadaadbaadddbddbaddacdddaadcabccddbdbbdbcccbbbdabddcbbcbccdadcddbdcddcbacbbbbbdbacbbaaacddcaaacbdddcdcbdbaababddacbdcbacacddbbbcccacdbacccbdcbcbabcccdacadcabaccababaddcaaadbdbabbdcddcacaaabcdcdacbaaaacaabcddbcadcdaadcbadcbadadcdbaabdccbaddacdcccddbcdbdacbcddbddccacaccbadadadcdaacabadcddbbbadabbbbaaccdddaaaddaccacbcbdadcccbaddbdadbbbacbddbddaaadbacbcddcdccbbdbbdadcacabcdadabcadccacbbaddbaacacbcadbaabcdbdabdcabccbbdcbadabadabcaddddadcddaabccadddadcbabdbacbdbacadcadddaacbbccbabaadcbbdcbcbaabbccadaaccdaccbcccbbaaaabcbbbacadcdbcdccadbdcccdadccdbcbaddadddaccacdbddbcbcbdbbddbaabbccabccacabcbbdadccabaddbabdbbcdacbabddcacbcaabbaadbdadacdddabbcdacadbdadbadcbbabddbcbcacabbbddcddaadadbcbcbbdadcdddabadcaccdccdabaaacdbcddadbcdddbcddbaabbadcbccaccbbdbbdabbbaccbbcbbbcbdaabddbdcbabaacbcacdcddbbaadccadaacccddddaacccdaaabcaccacbbccdcbddddcbdabcdcdabdcadccbcbaabdddaadaacadaadbacccdbddcbbbdadbcabcdbdddcdcccbabbcacbaadbadacacbdcbaddbcbbccbacbacbabddccbbdbdbcaddcdcbabdccadbbcbbaadabadbacdbbadbcdaccbdacdbacbaddabcbddbdbdcddbcacacadaadacdbcacdcdbaccadbcbdccbbbcabcaadccadbcabcbccacadaccccddcabbadcddaddaabdccdacdadddacadcdababbcaccdaaaabccaabaabdbdadabbadcadbadbdbcdcdbdcaacadaccbccdbcacccbdbdcaacbbccddcacabcacbdbbcdbcdabbccacbdbacadbacdacdaddbbbdcddadbbdddcabadbbbbbacaaababadbdbcbdbcabddaccdcbbbbdcaaadaadcccadcdbcadcccddcbdcbbcaaccadcccabcbaccabbbbdbaaddbccdbdadcbadcccbaddcbaddccbadbbccdcaccadcabbbabdadadbcbbbdcddddddbdbbacadaadbbdcaaabccadaadaddabcddaabdcddaabbdabcaacadbbabdccdbbdbaccddaabbcdcbccabcdcccabcadbdbcccaaadacaacddcdbbadadadbddbcabbdacbdcdabbbdaaacbaccdbadbcccdbabbababccdbdcaddbdadbcaccccaabdabacaacccbcacbddbbaccbcadaaadccaccdcddadbddbbcababbbbbdcdadcacdbcbabacbbbdddcdcdddbcdcaababddcbdadbaaacdccbabcacbcaadbbabdcbcbcbbdaaccdddaaaaaaaacaddbbccaddddbbbbbbdbcdaaccddbcccccdcdaddcaacaaaaadaabbcbdccbcbcdcdadacbbaddaaaaacdcdaadabbdaaaccdacbdbadddaadaaaaaaadbadcbbbbadddcbbbcbcacbabadccbdaacadbdaabadcadbbabccbbbccbddcbbdbbabdcadcdbbadcbbcbbccbaabdbccccdccbcbccdabbcdadadbdbdcdaacdcdcadbabbaabdadacbaddacabbcabdaccbdabadabadddadddaadbbcbddaaacbbadbbcbcbccdacaacabcaddbbdacbcacbdaadbcdccaddaabbbaacabbaccdaddabddcadacbccadcbbbbcdcdddacbcccbdbabaacbbcdcdcbbcbcacdbaabcbcccacbacacaccbbaabaadccbcadcbaacdcbbdccbbbadddbccabbadbdbaccbcdcabbdaaaccdcdcbaddaaaddabbbaabdcddabaddcdcaaddbbcddcaccddcdcdbdaaaadbddadbdabbcadccaaaddccdbdbbaadaaabccbcbddcaabacdacdabbbdbddcdaabcdddcbcaccdbcddccdbadcbbcbddcdbdbbbabcbabadbddacaadcbacdacddbccbcddcdacccccbbcadccbccbcddabdccbcdbdcbbcddcdbaacaadbdaadcdabdbccdccacdccbdaccddcbabcddcabcbcbcbadacaacadbcdacdacccbbdabdbabcdaacbbaccbcbaabacadaacdcacccccbcadadadcadabbbaabbadbbcbdccdaaadaddaaaabacacdcdddbabcdaabdcbdbddaabcdadaaaabacadccaacbccaaaccabbbadcbcdcbbdccacbacabdbbcdbdbbadcabcdababdbaddacbdcdbdbbaddbadaddacbdcddbbacdbadbbddcdccabcadbdcabccbbacbacadaacaaacdbadcadbadcbbbcbdadccddcbbdbbadccddadcbaaddbbddadbbababadcbbbcdbdacaaaabbdaadcadabdbcdddcddcadbddccbcbabaccddcbbbdbdabaadddccdddbcbdcbadbcdcaabbadbbdadbbdbbddbccdcabdddbbdaaadabaabbccccacdcdbbaaacdbdccbdccbcdbbdddaaabadccaccaabcbcadddcdcdaccbbdadabddcbaaccdcccdddaadcccbbcdddbdbbbddaaacccadcdbbdddcabddadccbbcaaadabcadcaadbcaacbabdbcbccbdcdaadbbbccdddcacdaababaaccaabcdddcaacadbacdbcdadbbdacbcdcabacddabcaacbcbdcaacbddddcbadbddccadabcccbcddcccaabbadddccddbbccabdaccbaccadddacdaddabbdbbcbaabcbacbaccccbdccbaadddbcacbcabdabdbcacddbdbbacaddacbaddbbbddabadabcbddaaabdbccacacdbbcabddcabbddcbdacdaadaadcbcdddbbcaaddacccdaaccabcadcbbccdbbcdbcbabdbaabcdcdbacbccbdccacbddbbcdcaaabccdacbcdbdccdbbadadbdcdacacbcabaabcbcbcbdcbdbaccdbddadadbddddbbddcaaacddacdcadbcccdcbdccdbdabddcbaacabccabccbbbaadbbabcdbbaacabcbcccdadacbdddddbcdbcaabccaccbdcbccddbdccaaaabdabaacddbdacacdaccbdadbadddcdbbdadcdddccbabadbbabccaaacddbbbdaddcacabbabcaaadcccdbbcddbadbcbdbadcdaacccbdcccddcaaadadccbabacadacdadccaabbdbcbabbadcdadadcaddacbcdacccacaabaaabbddddccdccbcddbbdcaabbccccdadabbaacbbacbcacbdbcacabaaadcccddabacccdbcddacbcbccdddbbacbaaaddbdbdabdbddcccccbadadbdcabbdacdadbcbbbccaacdbccdbdbadbbbbdabbddcccbcadaccdbcccbdbbbcabdabcdbabdbaaabbacacabcbbcaccbcdbbdbbaacadbcccbdabddcbacbbbabccbddadbccdcabbdbacccaaabacbdcbccabbdbdbcabacdaacadbdbbdaddbbbbbacacccdccbbcabadaadddadaabbadcbbdbdadbcaaacdaabbdbddcdcbdcaabccdabdbbcdddbcabdcaabdbdbbcbdccaabbcbbcdacaacbaccbddbdabacbbbacbbabbcdbbdcdcbbdadaaabdcccababdcacbbabacadbbacabbddbabcdcdaabdbbaacacabcdbbbbbcbacabbcbdbcccdccbddbbbbdbcbaaaaccdadddbbadccaddcabaabccacacbcabacbccdadabdcbaaddbbdbcddbbcbaddbbccacacbdbdbddbddadbbcbbcabcacccddcddccccacddbbabddcddaacbbaadddbcbddaadadddaaabcabdaadbddccbbaacadbdccbacacccaccaaabdbaacbbcadacabcddcbbbadadbaacadcaddbcdbdbacdccbaacaadbbdbbcbbdcdcbbbdbbaaabaadbbbcdbacbbdbcaccbaddbcddacdddcbdacbcaccddaacbccacbcbbccadcacbaaccacadabcbddacaaadadabcdbabaacbccbcdcabcccdbdacacaaddaaacbdddacccbbbdbaddaccacaabcbdbabddacacdadcdcdbadaaaccdccccbdaddcdbcdbdbaddcacbcaabcaddbdadbdaacaacbcbabcaaaabcdddbbddbcbaddaadbaabadbabdddaadddbadcbdcdbbadbdbbbcaaccdcadbbccdbbcaaaaddcbdaabcabcaadcbabcbaaddacaddacbabdcbabcdcdbadabddcabbaccbacbaaaadddcdabbcdccabbbddbcbabccabcaaaddccbaadcdacaddcdddadabddcccadcabdcbbacadabcdccaabdbdadacdbccbcccdaaaddcddbbcddbadcbccacabdcbddadcaadbacbaacbdbaacdcbbaabbcbabcbdbadbacdbbdaaddbadcbcbbddadaccabadbccbcbcddaacaacccacaacabddccdcddcaabdbbdcdcccabaadcdbdccadcbbdadbdbbcbdddaccabbabbdbcaddbbbbddcbacbaadbcbacbbcdbbbaaacbadbddbbdadbdddacddadabbddcbcddcbacddbaaccabcdbdacddadbbdaaaabcdddbabbcbaccbbcbcaccddccdcbbcaabbbddbcbdddbaccaacacbcbabdbddabcddbabddccdabdadccabddadddbcccbacbbbddcdaacbaadccaacbadaadacdbdcdccdcccbcbcadbbadbcdcdcbabbbccacddcdcbadcaaacdaaadadcbcdbabcccdcdacbabcbacbcbacbdaabcacbcdccdabcbcdadaccaaddaccaccbddbbacdabdbdadcbdcdbcbddbbcbdaabcabcacbbccdaabddabdaacdbbbacbbddccabcacaccddadbdbdadddbcccacacdbbaccaaccaccbbdcadabdabdbcbbaccdbcbcaddcaabbbadbabadacabcaccbcdbdabaabcccaacbabbacabbaacbdbdbbbbaddacdacddbddaddcbbbcbbbcdccccaaaabbcbddaacdbdbabccbddadcccdcbdbcccdaccddbbccdbbcabddacdcdaacdcacbaccbcadaadcacdbacaddbbdbbadcbddaadadabbbcadcbdbdcbbbbabbadaddccaddbbccbabbcccdbdaaaacbbdcbaacbacdcdadddbdaacabbccddcbcbbbbbdbcbdcdaccbdcaadcbaccbdadcddabdabcabbbcbcbdbddbccbdcbcdddbdccdabbcacccdddbccbdcbcdddbadcddbaadaddabcbaadddaabcbdcdabdabbdbdaadadddcaddadbcbcdaabdbbbdcacacdbdbcacdbabadbdcacbcdcbcadadcdabdaadababadddbdaadaaaadddbacadccdbcbdcbadcbadabddbbacbbdccaabbcdadcdccbbcdcabccaddadbacdcabbcdccccaccbcccbdadcbbcbdddcabccbbcabaaadbcaddcbbbacdddccabbddacbbadabcabbabbdbabddbdadaccbdabbcadaaaaacbcabddcdadacdbadadccdcdbbdbddbbacdabadacbdadacdaabbddadbaccacaaddbddddaabddcdabdcccdaaabbbddabaacacbdacccdbdabdaadccddadacbbdccbccabcbbbcdccabbcbcdbaabcdabbcdadccdaacbcadccbcbbcccaadaaaaccbbaaaaaabadcdbbabdcadccdbabaadcabcabaddddbaaddcdadaaaccbabdbbbbabdcaaaaababbddbaaddddcbdaacbcacbdcbadabccccdcacddbcadabcddabbdbacbadddbcbcbdcbcdbcbcddbbbbacbdddabcadacccbddccbdbaccdabdcbaadbdabcccbbccbcabaabcaccbccadaacbcacaadadadccaaddccdadaccbcababadaacaaddbdddccadbacacdcbcdabccaaadbddcdcacbcbddaaaaabbbcbabcdccacabdababdbbdddbdbdadcacbabbdbabbaccbbbadccaccccaaddbdcbbaababcaadcaadacbdcbabcbcabbadbcccabbaaadadbbcbdcbddbdbbbdbbaddcbddacbbaacbcddaadcabdbdbdcccbdbadbdcddabaccaaddbbbaccdccdabbacbcacdddcdbaaacdbcabcbccaabdccdbadcddccbbbccdcddcdadbbdcabbbdbdbabbbdadccbadbbbdabdcbdaddcbcdddcbcdbdcaabdbabbbcbcdbbbbbcadcaccdcabacabbcbcabdbacaddbcbcddcddbacabadbcddcbbbcdbcbbacdbbcaadcbdbdacaaaddcadbcacbbbcacbddcacccddadadacdbdbccbdddacdbdbabadbabcdbdaaabadcbbcbbbdcdddcadbbcdbccdbcdabdadadbbcbbaadaacbbccbdabaaabaddcbdcaaccaddbabdccdcdbddddcdabbbdddbcdcdcbcbdaaabdccdcddbbcccaccdcdacbcabdacdacdcabcbaaddcbaccdacabdcccacdddbbccaaadcabdcddabddbacaddbcbccddbbccacddabbccaaadcddabcdbacbccaacbddbddbdcddcccddbdcabccbadbcacdadcccdabbdbdbdcadccdcdacbadcbbcbbcdadccddbbbadcabacccaddcbbbaccbdccdddbdbbbcdcddbcabbaacbaabaabbaadbbcdbaacbacccabcdbdabbcbcbbdadbbcbdbbdcdddcadcddccabdbbbcdaaddbdbcbcdddbbbadddbabbdababcdbddadabdadcaddacbbccdacccbbaccadcddadacabcadcbcccacdcdbccdcadcbdbaccabdaaddcdbabaabbcabcaadadbabcccadcdbdbcbcccddccaabbcdaadcddbbbbcacdcdbcbcdacdbbbcccbcbdcdabdbcaccdddcaababbbdddadbcacbbdacddcabcbaaccdcbddadcdabbbcdadccbbadccccdcbccabbdacbccbdbadabdabaddbbcddddbabdacccdddbdccbabccbdccccbacacdaabccddcdbbbdcddabbbbaddcdcbaaadbacabdbccabdaddabbaababcaadbbcaabbbccababbbcadbaaccadaccdbbbbabddaadcbaadcddacabbdcacdacdaabadbcbbdadabbcccbbccccbbddaaabbddabcbbbadccabaadbdcabaccccbdacdbcdbbaddadbadbcadbdacabbdacbaabcbcbabbcadccbcbdacdaaabdcdaccadddabdaaccaddcbcaabccaaabcccaacbbddddcaddacbdbbdbccbdbaaacaccbbabcabcababddcdadbcbdcdbcbcbaadcdaacbbaacadbadacddcdcabccdbcbadcbbabbabadacabcbabddabbcdaddababbdaddbddaaccacccbbaadaccdcdadccdddccddcacaadbbaccddcdbbbdaabbbddcdccbacacaaaaabccdcccbddbbcdabbaccbddddacdabcdcacbdcbbacbbdccccdbbcaaacbbccbbbdccccbacbaabbcacdabadadddbcbbcbacddabdcdbabdbcbbbacadcbdcbdcacacccdccacaccadcacccadcabddacaacbbaabdbbccdddacbacdadadbdddcdcbabbcdccacacddcbdddbcbaddbaaadabadaddcacaccdbdcbddddbdcdadbdbcabbbadbdbacbacddacbdcaabbccdccbcbadbaddadcdbdcabcccbaacbccbabdbdcdcbabbbacacbbaadcdccbcaabcbabddccccbbabadacdbdcbbaabbdccaabdcabaaacddadbbdaacbdcbdbaccdabcddaaddcdaadddadaccacadbcabbbcdcddbcadbbcddbddcbbbbdadacbaaadaccabdbddabdcacbdbacbbdacbdadacdccdcbbdbaddbcbdbbccaacbbbcacdcdaaadcbacddccadcdcdacddbcccbcbddadadbcacaccadadcbcbaddcbcbdbaaaadbcbcccdbbaadddccbbcadcdacbddcabcaabbbbbbbbdcdddcababbacdabbaaccadcdbddbbacabaacdbaccbcdacbcabbccdacdcaabababaadddbcabddbdcbacadcddbdaadddbaccccbdddbcaabacbcdccbbaccbcabcaacaacccbbabcccacdaabcccccadccadcbdbbbcdbbadccaaccbcabbbdbbacabcbdbdcbdcddbccdcbaacaacdbabccdbaabbbdaddcadbaadcadbbcdbcadbbaccdaddbbacbdbdaccbbbbabdaacbcdabaadabcaabdbcdcacddbabcabbbcccbcdadcbaaacadcbbbdccbbcabdbacddbcbbacbaadaddacaaddccaddadabaaddcbccccabdbbadabaaddddabdcabbbbadcbccacbdabcdcdcbbcbdddbaaacbcdddbdbcabaccacccbdccabcddaacacbabdbdcadacddbdabaabbccbcddadbccbbcabacddbbadcccaccdccdccadbcabaaaacdbabbaadbabcddcbadcccbaabdaccacccccbaadcdbbcdcaabcbdcbaccaaaacddbbbbccdaacbbcbbcdcbcbddabadddddbbcdabdabddacbbbddaabbcdbcaccdcbbabddccccabdabbdbaadcccddddabacbdacacadccaaabdbcbcbbcdabdaaacccdbbdccbbadbbacddaabdbddadacabcaadbdacddcbbcccbabadaaabcccbdadddccabaaacdcdaadadccaadbcaadbbdcbdbcacccdaaddcdbcaccdccbbbdbabbcabdacabaddddcccaccabacadbcbcabcccabacddcaaaadbcdbcaaabdbcbbdcdccddadcdcbbabcbdcdbcbcacbdcaddccbdccccaabcbadddadcbccdaacabdccdbbabbcccaadcdbabbabbddcbadbaacbcdbadadcdccbaaadaacdcbcdadababbcdadbadcbdbbcacdabdcddababdaaabccbadbccabddcbdaccdcddcbdaddadaccadccdcabbbbdddadbdcdaabbcabcdbcacdbdacadcdaaabbbbccbbccabbcdaadbabaccbacccdcddbbadcaddccaabcbbacbbbaccbbbcacabddbcbcbcbabbabddaadadbaaadcdaadabccadbadbcbcdaaadcbdcbaabcacdccaccbdbcbbbbdbdbbdbbbadbbadaddccbcabbadcdbcccbdacabadabbdcabbbbaddadbadbbdbaaaccdabbacdcbbbbbdadaccadcacbcddcbcabddbbaaaadcadcbabdcbbabcdcdaacbcddacddcbddcadbbccaaaacddacdacbdddcdaddcabbdcabbddbdddadbabbccabcacadbbdbbadacaadaabbbbcccbadbccccaddcbddcbbdbddbccbddbcaccaccddccaacbbcbcabcbddbacbdcdbbaacacabbbbcaddccaacbcdabaaabccccbabcacdbabbaaabaadbaccdccbdcbddccdcadbaabdbadabababdcbcabcddaccbddcdbccadabbcdacabbcccabbabdcddaaaabddaacacbbabcdbbbdbbabdcddacadabdcdcbaabccdbadcddcaabdcdaaddacbdbdbccddbbacacbdccbdcacbbcaaabdbbaadcacbccddbcbcddccddcaddaaacdddcbaadadbddcdbbddcbbbddacddccadcbbadddbdddbdbbddccbcaaddadaacbadbbdbcacdccccdbaabdcbabbcbbddaddabbdbabacadddabadaacbcdcaacdbcbdadbdbacdbabcdccabdcddaaccbbdacdcdcdcadbcdbbabccadbaacadabcaccacaccaddcdbadbdcbcbbbbbbbccdbadcdbcdddbcbabcabcbcaabdcabadbbdaabbadcddbcdcbcccdbbcccbcddbddccaadaabaabaaadccaadcdddbcbbbbdcababacdadccccccdcddbbbdccdbddbadcbbabdcdbcbdbabccdabddbdcbccadcccbccaabaaadacdcacaaddadcbddabcbdcbbcbcabbbbcddacdbcbccccdbcacccacdcaabbbdcbababccabacaadcbabbcbdbacdcddcbaaccabdbaaddbbddbbbaddcdabccccddadadbbbdabdcacdbdbbcccdddccdbbacccadcdcadabdcbbcaadbadbadacbddbdcaabaddadacadcabaccdbdbaabccbbdbcabdcdbdccaadadabdbddcdcabbbddbbbccabccacbaaaaaaaadbdcdcdbdcabadbcabbdbdccaacddcdaadadbdabbbadcccabaaabdaddcabddccbcabddbcaacabdaacbbbdcbbdbaabacaaadabbadddcdaadbaabbdcccaadccaadcbbdbbcbcdababbacacaaabbbddddddacabdcddcdcdbdadbaaaababbabbccbbcdbdbbcacdcadbabbaddcbbbadbcbcccddbbabbbcadbcccbdbcadcbcbcbcaadcbcbaaddabbdaabbdcdcdacadabadbccaddaabccccdccacaacacdbabbcbbcddcdcbbcbabddbdccbdaddaaaabccccccbdcbacdbaaddabbbccaaaacbaccdcaacbcddccacddcacaddacbadabcdcbaddaddcbdccbadbbdbcdaabcbabddcadbcdbbccdabbcdcbcaccccccbbbaaadacabcbabcbdaadcaacdccbbcabcabbcbddadbadadadababbcbaaabcacacbbabcddcaaabdbcccaccabacaccddddddbcbdaadacadaacaaaaabbabdcadbcbbbbdacbbbcddcdcaddbcbcccadaabcbcacddcddacaccbaaccdcddbdccacbabddbddbdacabcdbbcaacbbdccdddbcacccccccaabdcbaaabacacbddbdaddaccdcdddbcbcccdadbdabbbdbddaadcbbddadcadacddccaaddaaccbccdcbbdcaabbaddccbbbbcddbddbaaddadbcbacdbdccdacdccbbadcaddcaacaacbbddbdaabcabcdbbbcbabbcabaaaddbaacaacbcbbbbcadadcacaabcabdcaadbbbdacbcabcacacabdbaccabccbdaacadcbadddbcbcaddaabaddddacbaadcbcbcdacdaddcbcabbaaadaabdbcdbbbcaaaacccbdadbbabdcccaabbacdccadbaaadacaaabcabaabcddcddacbcbddccdbadabbdbdccdbbabcdabadaacacabbdabdcaacabbdddcbaacacbbbaabddacaaddbbccdcdaabbadacbabadcdbbabcdacaddaacddbbcdcccadcbbbadaababbacccdaaabcacbbadbbbbcdbccbbaaccdbbacdcdddaaddcacdcbacaddbbcdadcacdcbddcdbaacbddabcadbdaabadabbadbabddbcbadbdbcbcadcdbabbcbdcaacbdaacabbdbcdbcdbbbadbdcbdcdaddaaacdbbddaaadacddbcccadaaccdacdacaadbcddbaabaddbbaaadbbacbacaccbdbadccaacdbbbcbdaabababdcdaddacadacadadcaddacabdabaaccdcddadcdbcaacdcbbbbddaddabccbcababacccbbbabbcbdccabcdbbaabdbdcbcbccbdadddcbaaddcdcdbadbcaaacaddadbcddbdcaadadacbadbbbddbdbacdcabbdadababccdccaadbbccbadaadbabbdccbbaccbbdddddaabbccddccaccccdaadcaabdccdacbbcbdcdacdaddabacdcdbbacdccbbbddacacbabaadbadddadadbdaaabcdcaccbdbcdbbbdbbaddadbabaadaacabacccccacccbdccacdcbcdbabbcbabbbdabdbdddcddccbbdddbdccbabdbcbccdcbaccaabddbdbbbaadbadcddbbcbcbabaadbadcdbcdbbaadcacacacbccdaabcababacbbaaababaccbbbbbadabbcdccaacadadbbbaddbddcbdcbabdaccacdbaacdabbccddaaddaadadadadcacdbacacbdcdaddabdaaabadcbcdbcdbabddaccaaccddbcbbcbabddbbdaddaaddabbbbcabdbacdbaacdbadbcbaadbcccdbcadbadccadabadabcddaacbcdbdccabcdbccadcbdcacadadcddddbcbcdbcaccbadaddbddcbcdcbdcdcdabbbcdbabcbbcdccaacbabcbabbdbdaddccdcddcbdaddcaacccbcbaabcaaaaadbcbcddbdbdaadcabdcbaaadadaadadbacdbcabbbcdaabcbbdacbdabcdbddbbddbabbdccdcbccdaaadbccddccccdbadacbbdbcaadbbdacddbddacbcacdabdaaaabadccbcaccacabaddacddbddaaabcaccbbcdaccaccddddcdbcadabcaaacabaccabacaddccabcbdccaadddcbbbcacbdcabdaadbdcdbbacbccbabccbabbccdbacbbbbbbcccaccdabcaacbbacdcdcccddccdbbadaadadddcaddcaacdccdaccadcdbdabcdbaaacadbadcbccbacdbdddcdddcdcbaadbcdadddddbabdddadbabcdacdabdaadcdddcddcbbbbabcbcdcdadbbacadcbddabbacddaccdabccadcddadacadbcaaaadaadabcacddaccbacccdaccbcdaddcdcbaacbdbbadaccbacbababbabdcdadccacadabbcdbcddacccbbddadddabdbcadbbdabbbcddbcbbbcbdbcbbcabaacbbcbcdadadcbcabdcaababaacdcaddcdcbaadacabbccabdadacdccbcacddbbaaacbaadbddccdaacacbbddacbaabaacaabdabcbcaabbcbabbbddddaccbaacccdbdbddcacaccbcdabdccdbcdabbbddcdcabacaabcccdccdbddbabaabbdbadaccaabdbbbdcaabadaccccacbaccbabbdacbbdbaadccaccbdbaabadddabadbcbddadddcbadaccacddcdcdaccabcdddcdddccdadcdacbdcdcabacabbaacababaacbaacdcdddbbdbaaccadcccccdccbdcaabbcbaacbbdaabaaaacbbccccbccbcbaadcbdabdcbdccbbabcdbddcbdbccabdbcbbbaaabcdbdbdabadabbcabcbabcccbdddcccabaaaddddddbdcaccabdabaacdacacbdacdaaadabcbacbbcbadbcbdbaaddcdaadbddcabbabbacbaacabadcdcdbcabcdbbabdbbaabaaddccbadabdbcdabadcdccdddcadaaddddabdcaabcadbbbdbddabaaabacccbaabdaaabdcbcaaaddcabcddaddbbccacadccaddcaadccbddbaadcadabddbaacccdabbdbcacaccbabdccbcadbcabbbadbbdbcbcddbcacdbddcbcdcababccbaadadaddcbccbabacadaddcbdacdbcdbacddcdaaaccdaddbbacbbbccadcbadcadccbbcdbacdccddbcdbdbddaccababbcccccadddbbaccdcbaaddbcabadadddadadaaaabdaadbbcccaaddddcaadabdadcdcaabccadaadbcbaccbaddabaadcdabcadbacdbacacddadcdabaacdaadbadcabdaccacacbddcaadcbccbadcbbdabcdbdadbdbbcbcccbbddcbbdbbcbcdbbacaadabddbcdbdbdccababbdcacdbccbcdcbcadadabaaddcacdacaddabbdaddbbbdabdcbbcaddabbbbdabaaddbaadaaabdaccbdcababacdbcbdaaaabadabcdcdbddddbdbbbbdbbbacbbcaaabcdcccbbacccbdcadddadaaabadbbdbbaaadaddbdccbcbbdaacccdaacdcdcbcbaddbccbadbaaadaaacdcbabadbabbddcccaddbbbbadabaadcacaabadcdddcaacacbaabaddaccbcdacacddaacdbbcddaaabddadcddccdddbdaddbbadcabcaadcaaaacbcabdcbdbabbddcaabccccdcddccaccddddcbbaaccdabdbcacdaacbaddddcdaabcaaacbdacaccdcdcdabdbdbcdadcabcccbbabdcdcbaccccadcbcadbacabddcdadbbdbaacbcdbccaaaccbbccbddadccddcbacacbadcbaabaaddbaddadadbadacdddccddbabdcadddabababbbbddacbdbaacbdababbccbcacddcdacadcbdadccbbdbaacddddbccacccdbaddbdcdbcdbaaadaadcdbdaddccdbbbdbdcdbbdaaabacdcdaaacdacadbbbbbdabaddbcdcddddacabbbccbddccbcbbacadabdbacddaadaccadadadbabdccbbdddddccccbbdddaabcccacaabddaaccccaddbacbbcdcccabcaaabcadbbacbbcdacabcaccbaacbbcdccdbdddbbddbbcacccbdcacabbbcdbdcbcacbbdadbdadadbaddadadabacbadbcdcabcdbbdcbbcddddbababbbadacccdddddbadbadddbcadabdadbcbccaabddcddbabcddddaccdbabacaadcbabacbdcbccccadcbbbadabcabcaaabbccabcbbadccaacdadaaaaaacbdadcccdbbaddcddacbcbdcbdbddcaadddcbbccadbddabdababdabadbcbbbacaccbdbbbbbbdbaccbdccadadaadaacdcaacadacaacdcbadbdccabcddcdadacdcbaacadabcbdbdabbacbdcaabadbabdbdacabcdccdcbdcbbdbcbccbcacacaaccdbddaddccadbbddaadabccbccdcddddabddbbccdddbabdbbdadbbcdbadcdccdcaccaddadccbdabdbcaaadcdddaaacdbdbccbabcaabbdcdabadaabcbdbcdbaccaabdadadccabddaaaaaaabbdacaabddadabbbbcacaaaaabdddabbbbacbabdccdddbdcbaddaccbbcbbbcbcaaaddbdbbddddbabbcabdbddbbdacccabdadadbcaacbccccbacdddcdbcaccccaccabdbbbdbabddcdcbdccaddabaccacacadabbdcbbdbbbdbbdcabbdbddacdadcccdbbbbabcadbbdbbbdcdbadaaaccdabcdcdbccdababdaabdbddabddbdbaabcaddddaaacabcbaccaccddbbdccadbdccccbbbcdabcdabadbadccaadcbcdbddcdccbbdacbacdaaccccdbbabcbcdadbbbadabbbddadcacbbbbcdacbcdcdbcbcdcbbabcddbbddcacccbcacbbabacbbdddcdcddcbabbbbcbbaddbdcaccacadacddcaabadaddbdabdacdaadbacbacabbbcddbddbdabccbddccdcddccddababbcbcdaadcbbcacdaccbabababbbdbbbddadaddbabbdddcacbcbcdcadabccbdcbdbbcacacadbdddcdcdcbabddcdcdbabdcadabcdaaaaaccccdadcacddbcbcacacaadbcbbcadbbcabacdacbcbbcddacababccacdddacdcddacbcbaccacaacbccbcaabddaadbcdcaacddcdaabacccbabcbbbaaddbccdcbaabcbababbcbdaaadbccbddcdabaadacababbdbbcdcbcbdabdbdcdbdbbbcbdaccdadaabaaacddcdaacabacdcbbacdcadccacbcababdbadbabccbdbcadbabdbdcdcbaaddcdbbdadabcdacabcbbbcdabaadbbccdacabbcdcacacbcaadddbacbbddbbbccdcbbbddcbbdcbacdadcadbadbbcdbaabaaabdbdacbddbabacaadcdabdccacccddbbdcabdcdbccdcbabdbdaddaabadbdcddcdaabdcbcccbaadcaccadddcacacacbddacbdbdaddcabbababbbbcbbabcabdcacaacadccccdccbddddbccdccbdbadaadcbcbcbdacdbdbcbddcabbbbbbbcabdcabcbcdaddddcbbddccaaaccccbbddacadbcccdbddcddccccabdabbccacaacacacbadbddcabdcabbaaaadbacdbaabddbaadcaccbccdaabdcdbddaabcbddbabdccaabbddcbabaaaacccadcbbbbbcdbdaacabcdbbdddcbdbbbbcbbddbbdaaccccccabccbaababcccdaaccacaddbacdbabddddccbbcbbbbaacccadbdaaccacaacddcaccbddddddddddbcabbaaaabbadcdddbcdcdcdaadabcccbdbbbddabcdcddacbbacdbaaddcdddadbadaacdbcacddcdbdbdcaaabdcacbddaadcaccbccbaabbabcbaacdcddccdbadbbbdadbaccdbdacdbacbdcabcacbcaaddbddcbcbdaadabcadcdbcdacaabdadcadbdadaaccdddbbacbbbcdcbbbccddaadcaaabcadbaacdbbbddcacbababbadaaddccaabcadcdbaacaabaabaabadddbcbcabaccbbdbddbabcabcbdbdbddbcddaabdaaccdbbbcccccadcdbbcccaaaddccbadabddcdccdbddddcdacbadacbbbcbabcaaaadbdcbddaabbbcacdacbcbbcbcaaccbbbbbcaaabdbdaadaabcdaabbbcdacdbbbdbbbbbbbacdbcccdacdbddcacdbddaaddabcddcdcbadadadaacddbcabdccaaddcbbbaababbcacaddabbcaccadddbadcccaddbddaabacacddcadcbdcbbdaddaddccbddccbbabcbbdabdbbdbdaaaacbdaddcddbdcbbbbaabcdddabddacbdabddaaaabccacbcabbbcddaddacbddbccbbcacdadacadcccbaccabdcbcbddcaddbcdacdbdbccacabbabcacaabdadabacaabdaaaccbbcdddaabbbdbbcccacdcdbddcbacaddadcaddcaababcdacacadadbbadcdbcacaaabdccbbacdabccbcbaddbbbadccbdcccababdcaacbccaaddcdabcadbdcbaabaadbbaacccbccbcdcccadccbabcbcaacdabdbbaddcddbcadbacbaacabbcdcadbcbbcaabadddbccadbbdcbcbcbccdcaadcbccaacdbcddcccdacddbdbcbbdcdcbcbbbddbcdbccbccacbcbaadbddcadaaacdcccddaadccbcdbdacabdcbbbcacbdcbaaabdddbabdddacddacdbabbaadccdbbcbbdbdcddbcabbbbddacacacddbdaaadcdbbddccadbbdadcccbcbcbadbbdcaddcaccbcbbdccacddabadabcdaacbcbacddbcbddbdbbddccbcdbbdadaaadccdacdcdabdbabdccdaacaaccdadccdccabdcacbbdabdaddddbbcbbcbdbccbabacccbdcdcccccbddcaccbdcbabbcbdadadbbbcccbbbcadbdacadbccdbacdbccbbaaabcaccadcaaaabcbdaacdacdccabbccbcaccddababdcdbacacadddcbccddddaddcaacdbdbcbdcdacdbaaaaacddbaddddbccdabbdbbcaaadadcdbbcbbabaabbcdbbdaadcaaaababcddadbcabaccccbbbdcdacacdccacabdcddccdbbddddcbaaddcbddabcdccbbcbdbacdbbcdcbbaacdabdaacadaccdaadbdaadbaddbcabcabddcbdaacddacdbacdcdaacdababadabdaabadcabcdaccadbadbbbcbdaabbabdaddadaaccaabadadacabcacdaadbcccbbacccadcdcbabccbcbdddabcbccaccbbcdabadcddadaddcdddbddddccdabbbcbdbacdaadddbcbdddccaaaadabbcddccdadaccbdccabbacacadcabcbcccccddbbbcbccbaacacbbbaddbadbacccdcdcabababbdbbabdacdadcabbbdacaacbdbaadccdcdbaadccdbccddabbaabacbcbcdbcdcbcaaacdbaaddbdacddaccdcadadaccdbaaabcbbadbacdcdbaddabcbbdacccbbabdccbcbdabaaaababdabdbadbbacaadbddacaabdbbcdbbbcadabccbadccbbbadddddbaadbccbbbdcdbbbcbbbcbcbdbccdcbacdbcacdabdcbbcabddbacdcccdbccabdcacdabcbcdcaacadbddcaaaaacdddddcdcacdbddbbdcbcbbbccbcddadaaccdbddbbdddbcabaadbabbacbbaabbababdcccbbbcbcacbbdcdbaaccacbbaabbdcdcdaadcacababdbdabccdcabcadcdddcbcbadcccadadcbbabddaccdddbdbdddbdbcbaddaacccdbcddaabcadadbabadcabbdaacbaddcdadcbccdbdbdacbdacddcbcaddbddccbbaccbcdaccbdcbdbddacabbdacdbabdddabdadaaabdddaabdcdbdbbcaddccaacbbcacccdddabacbdadccdaababdabcdddadcbcddabddcdbdcccadddcbbcbdccabadbdcbdbccccbbaacabdacddabcaaaadaddacaccddbcdaccccaaaddacabaaddbababdadbcadbcaccdaddcacacacaabadccadadadbccddaaacddcdaddadbdbbcbbaddbbaacaabbddcabddccbcbaabbabbccbbbacbccaabbabbabcaadcccbaaaadbbddcdbdcbbbcbbbaaabbdbacbdbadcdccccccacbdcdadaddbcbdcbcccdddddddbcadbcdaabddcbabccaabaabaccaddbabbdbdabcdcbadbdacbbacabcdadccbccaddaddddadcbcbbccaacccaaccdaadaabdbbbadaaacadcbdccdcbcdcbbcbaaaabaadbbabdbcbaacdaddbccddacbadacbbdaddaacaaabcbccbdccadabbabdcccaccbbabcbbcdcdbabccbcdabbcdddbbdbaccacddcacadadbaadbadbcdcddbbcaaacacabbdadccdddbabdadbdbbbcdadccababcdaaacdaabbddcabbcdccadbabdcabcbdbabacdbdcddbdbcdadbcbbccbbbcdabbaacacdbacbbcabbdcbdccdddbccadaaaacdcdddccdddbabcdddbbbccdbcdbbdcbddbccbbbbadcaaacbdabbaaddbabbdbaacccaabaaabbdbbcbcabacaaaaccaccaadddccdabdacbbadcbcbdddcbcccaddddcdadbddacdacdbbbbcadababcbcbacaccadadbaadcdcddcabbdccacadbcaaabdbcabcdcbaadddaccbdacbbbdadabccbabbcbbccbbcbadbdaccdadcadaaaacaccdddbaddbdabbcacbacaaccaaabdddbaacbbbadcbdcaadabbdcdddaaddcbbacabdbaabcaddcdccacacaaaddaaaadbbbacdddadacdddbdbaaaddacbdacccaadadddddbdcbacaabaabbdbbcbbcddbbaaaadddabaddacbdabdadadbadcccacaacabdbccbaabcdddccbcddcbbbbcbdaccdbcbabbccdcccbdabcdcccabaadcaadcbccaaadccabcbddcbadddcadbbabbdbcdabcdadbbcbdacaaaadcdbbbaacbddcbadaabccdbbdccddbabbacccadcdcbddabccddadbbccdacbcbbbdcadbbdabbcadcddbbcddcbabcaabaddddacdbdbddacacbcdadabdbdcaacdcdcccacbddabdcacabdbdcbbcadcdcadaacbbcababdbcabdbbcdbcdbccdbbadbbaddaaabddbbddcbbbcdbbddccabadcbdcdcbdacbdbbdbabcbbadadaaaddccbaabbbaddccacdabbbdcbbbcccaddadbcaabcaaabbcdcdbbadbddaabaaddbbbbcdccddbdbbbddbcdccdaacddbabaadabaabdcddbadbcdcbdcbaabacdcadaabdbbdbbaabaacdbdddadaabdccdbaccdcbbcbbcdaacabccbccabdbbbccddbddaacbdcbaabdaadaaadaccdcadabdccacaabdbbdabbccdcdbdddbdabcccbbbbccadccbdddddccaacbaddbabdbdaddabadabccbbacdabddaabddbadbcdcbdababdcabaaadaadcadbbacaaccababacabcdcbbaccadbaddddbddcdccdacdddbddabbbcbbdcbbddbcbacdcaadabdbabdccdbdaabaccdbdbcccbbacacabcdacabcccbbbdbacbdabdbddaaadcabccdaabdbbadbdcbcacadccddacdddcadbcacbcdbcdcddbcccddbbaadcdccacbbaacabbdcaaadbacababdcbcbdcbdbcacbdcccbabddacbbcaaabaabadccbdacbcbddabbdbcdbabccdacbaadbbabbddbabccbccbcdccacaadbddcdcccdbcdadcabbbbacdddcaabaabbbbbabbdccdacddddddcbabccccdbadddbadbbddbabaadddbdbdcdccbdbaabadcdbdaabdccbccaaadbadcaabdbbdcdabcadccddbbbadcbcdbacdbabacdcdbbccabcdcabdbccadbcbccbbbdccabcacaddcdbdcccadccbacbacabcbbccdabcdbdcdbbdcabadbdbcaaadcbcabacaadbdbddbaacccccdbabbcacdcbbabdcadaabbdbcadbbbbbcbabaaaadbbdcacdaadbbbdbcadbcbcddaabbbcdbcdcabbacaaabadaccabcabacbcdccbbbacaabbdbccdabbaabaadbaccacdaadcaccbaadaaacdbbbabadbabadcdabccccacbcabacaadcabbdcaaabbbccadcdcabddccadcbdbcbaccdbbdcbadcddabcdabbcacbcddaadbbddcbbbcadbacadcacccdabcaaddcbacccbbdcabdddccdcbbdcdacaabbdaadcbbcbacadbaadbaadbabbaccdadcbccccdabacbddbdadaddccddaadddbbadaaaaaacddaaabacbcadacdcbbabcccbdaddcbdabdacadcbcddbaacaccccaabcadaabcaddbdbccdcbbabaadbbbbdcaaaacbccadcbdabdbaadbccbbbcbdcadaaddcdaabbddbdbcbbdbcaccccacdcddddbdaacadcbddcbcdccbdbcadbcacdcadbcccacbccdcbbdcccdbddadccaaccdbdcddccaaaabdaaddabdddbcdccaccdaddbcbabcadacddaadbdcdaccabdaaacaaaadbddcddbddbdbadbaddbcdddbcbcccadcdbddbaadadabcbaabddaadbaadddddccddcbdbbbaaaacbcbcbcdcacdcddcbcdbddcbcdcdcaacbcdabdcacbdbcaaacaabddaadaacadadcbbabbddaaddcbbaccccabaaaabcdbbabdbcdbbccccbccbadbddcdddccbddddacdaabcbaacbadbacabccbabdaabdadcdadaacadbaaddddbcdadabadabbabbcaaaaabaadcaabacaddaadbabdcbbccaaaaabdcaabdcbbadbdbccddbaacabdccacbcdcacdbddaddaacdddabbbadcabbcddbdcddabcddaaddbadbccdaacbaacccaaacbcdadbbaaabcbcdadbaaccbcabbcddbbdcbbacdadadddabdbdcbcddcddbadcdababdadcdccadadcbcbbdacbddbabccabccddcccbcadabddabbdaacaacccabddcbaacaaccddddbbcdaccaaaaaaddaaacdccbbadbdbcbccaaccadbacddddcdaabcbcadcdbaaadcaacddcabaacbdcbababbdcabadabcdbacbddcbaacbaaddababcabbcbaaaccdaaabbdcabcabcdadaaabbdbaaddccbabdababdbcdbdcadabdadcdacbacabbccddcbbbaaabccdadbdcacabccbcccccdcdddadbddabddbdbdadcacbabdaabccbcabacccddbaabcdcdcaccdcbacdadccccdddcbcbadbcbdcccdbdcabbcdbaacabdccdbaaaccddaabadbcacaaccdbdbcbbcaabaacdacdaaccbaccabbbbaccccddbddadbabbcdcaadacabccdbbddbcabcbbdaddacbdbcdcabaadcbacbbcacccbcdbdccbdbbdddbdcdbbbaabbddacdadcccacdacadaddabbabadcaaadbddbbdaddbbbbcbcdcddadabdcccaaabddaadbbdadbcdcacaadaaabcbdcdbacaaccbaaadadbcaabadabbbcccbacbbccdacdadaaadadcbbcdcbbdbcbaaabacdcddaacadadddaccdbdabaaadbabdacbdddccbcbddcaccababbcdbadadccdddcaccdbbdbdddcbdacbdabbadacaccddbdbccbadbcbadbbbcccbdbadaaaccdcdccbccaabcbabcdbabdaaccadcaccdbdbdcaacabdbddcbaacbdaaacbdcbdbddbcddbbcbdcbddacddadaadbddcdccdabdbbacbdaacdadddabcddcaaaacabcbadcdcbccbbbcacaccaacacbbbacccbbdbabaaacbcdcdbbccaddbadadcbcabcbbccbbbbaaabbaaccadadbccdcbabcccdbbdbbbaccacaaddcdcbbaccdbabdabdcdbdaccdbcaccaabccdcbcbaabdbbdbddcddbabccacaacdacabddbacccbcdabbacaacaadcdadaabbabbdaccdaccaabccccbabcdcbdbacacdbccddaaaddcadcdaacbbcbdbcaabababbcbbbbcbcccbdcddbddbbbabcbaaccaacdcbddadccaaaaaadbabbddbdabbcdcddddddcdaddcadbadcbddbabbddaaaccbdbacbbcdaadcddcaabbbddcbdccddcacbbacdadbcdbdcccccdbabdbabdcdbdabcbdabaaddacbacabbccabcaadcdbbdcbbcccdcbcacddcccdbdbaabadbdccabdbbacbabcbacaddabdcabddbadbabdcabcccbaaadcaadadbaadbcbacabdbabdcaaadabdcdabdabacdabbbdaabcbddddbdadbdcbbcdaadadbbbdccdabcbdcaaadbbbdacabdbdaadddabcaaadddddbcddbbdcbdabcddbcababaacbcbbdaadabcaccdaaadaabdcbccaaaabacddcbccbdadbccbddbcaadabbcbdbdbaacdbbdacbbabdacbcabcccbddacbcacabacbaacbaabbbcddadabadacdbcbdbbddabadacdadddbddbacdcccccabadcdbacacbbabdcdcdbbabdddbabdadcaabcbcddbacdbbbcaadcdcbcddcbbcdaadabcbcddabdaddbbccbcdbbababdccbaabcbdadacaccbdbcdddbccdbaccccccaccdbbdacbbadabbdaabbcdbbdbbdcddccbdddacdabbdcdbbbacacacabbdcbabdcbadcaadcaddccddcdddbdcbaadcaccdbcdcdaadbcdbddcddaacccbccdbccbbadcbadaadacbacddddadcbaaacadcdaccccbabdbaaccdddbdaabdcbcdabaaabdbbdadcdbcdbbcadcabdaaabbccbbdccddacbcddaddacbbdbadbdbdaccadccdcdbcbdcccacbabdbaddbdcbbcbbcacdbccacdddaadbcbbbdcabaacacbcacdcdbdcddabdabcaaadbdbdcabdbbbabdcbabbcbbabcababbaccbbdbabcaaabaabcdabbadabbcabdbbbdcaacaddbdccbcdddcbbdbcbadbcddcdcacaaababaacddcccbaabddbdccddaadddabccddaacccccdcbcaacdacdcdcbbdbbdbbadbdaaddaacbcaabddbbbbbadbacbcbddbabaaacbdbabdacadddcbcbbcaaaccbbabcadaaaacbbadabcccdbbaaacdbccbaabcdaaaddabaccadbaabbdaadcbaabbdcaacaacabbcabaabddadaaadcaabbbaccddccacabdabdaccdadabaadaaddbbabcbdbccbcadbbabbcbadcdaaabaadccbdacdbdccccbaacccdcdabccdbabaacaadaddbabbbcbcccbdbbaadcbddcbcaacbbbccadbcbdccccaabcbcddcccbcaccddacccadbdcddccbdcbdbdcbcbbbcccddbcdadbadccddcacabaddccbbcdbdbddddaadccbaaadbcadaacaaaabdcacbacdccbddddccbadcbbcdaadbbadbdddbdbbaddbdcacbdddddbadbccaadcdaddbcadadbbbaacbcdbabbbcabcacaccaaadabaaadcbaababbdccdbcccdbccdcdabccadabcbabdccdcdaaabdcbdbcdbcaaddbadbccbddbdaacbcbacdbdacacccddbdadbcbcdabdbadabccdbcbbcdabbccddabbcbccabadccbadbdbcadbabbbcaadbcbbdabddaadcdbcbdbbcddabaddbcdaacccccbaaaabccbdcbababddcbcddbcbacadddcaadabdcadddabccbccdcabbddbbbdcbccabdbacaccccdacbcdaddbdcbbbdbccbcabbbbcbbbbdacdcadbbcdcacaabccbacbbdaddacacccbcbaabbbbdbdbabbdbdcbacdaccbdcdddacbbadbddbaaacdbaddcabcabcbdccbdbadaacabdacbdbcbbdadccabccacaabbcbadcacbcbcbbaabcbcbadbdadadbdbadddacdbbbdcacaaabbabdaaadbdbacbcbbdcabcbdccacaaacabbdabcbabdbbdabccaadcaaabcabcdbcbdadbdaacbbbbcdbdbbdababdcbbcadbbabdadabcbbaaacacabdadcbcddaddbcbcadbbcbbccbcdcadbdacbcccdbbaaddcbbaaabbacdddbcdccddadddbaaaacaccdcdaccccbbccacdbbdcccadbbdbdaaccbadbdbbdbbcbccacdcccacbbcccabbdcdbdadadcaaadabcdacbdcbababdcaababbbcbbddbddddbdbccabccdbaaaccdbbbdbdcddbdbccddcbaabadbadadcbaadadadddddcdadaabdadcadcabcccbaabbadcccacabbdbbccbaaababdcbaabaacbdcacccdcabcccbacacdbbcbacbcaaacbadaabbabddacbbbaabcbbddaaabddacdcacabadacccbbabbaaacbacaddababaadcbdbadaaaabbddbdababacdaccbdadadabaadbdbcbbbdcccacdbdbbdadbbdcbbadadacbdcbbcdaabdbbbacacabdcbcabcddbcbabbbacbddbcabddbacbcccbaaadddddbccbcdcddbacbddcdaaabacacabbcbabcaacbdbaaadbadbdadbbbdbddddadadbcdddbddbdbcacadaabccbbadadbacbcadadbaddddcbaabddacbcacdabccdcbdcddcadabcbacdddcaaabbcbbabdcbdcdcbbbdbabdadbcaddabdcbdcabcabdccddadccacaaccababdbbaadcabdaddbddabccccacbcadbacaddaccbdccbcdadaacaddbaadddccbccaadbcbbbaacddcaaccdbadabcbdcaaccbdcdabdcbaacdbdcbbcabdddaabcdabddacccdadcdbacadacccdabcbddaaadadaaacdcabaadcacbdcccccdbdbdbdaaaaabdcdcbddcaccaddaaaabbcadbaccccabddcadaddbcbbcdddabadbbadbaccaccabcccccbdccabbcacacddabaabbccadbbabcbcbccbacadbdcbbbcddabcdbbccbabbcccadbacbcdaacacdabdbdbdbddadbcbcccdbaabbaddccbccbbacdbacaacbbddbdaddcbcabbcbdabccdadccbcddbdadadacaddbadaccddbcaacbcabbadacaddccbdabdccadcdaacdcdabcdbccbcccaabcbbccadadbabdaaaadacbbbaacbdbaddaccaaccbbdadbcbaacbdcbbcdcdcacaacbdccdcccbcabaccccbdbbaacabbaabdbabbbadcaaddbbdacacddbbcbaacdcbbabccdbbacadadadccdaddaaadcabcaaadcadddcdacbdbddabcbabbbcacaccacccdadadcbdbbacaaaddbcbdaabcaacdabbbacbaacacdcbabdbaaacbccdbcdacbadcdcbaabaabacabbdabbbcbcaadccdbaacacdcbdddcccbcbaddccdabbccbaccadccbdddcccbcdaabbdbdacdbbabbcaddbcbcdbcaadccdddbdcbcbadbccdabcbaadbacdddaccadbddbabdaabcaccbadcdbbbbcccddbcccaadcbcbaabbaadadbdbddbacddbccbdbbdacbcabdccbbaacbbadabcadaccdabcaccdabbadcbcbbabbbbacbdcbaccacadcbcbaacdadcacadaddccbaabbbcdcdaabccbdacaddccadbbdbcdadcbdccbcabddaacdccaddbdcbbaacccbdbdcdbadaacdbacbdaabccababddddadcdbdbbcaacabbabdccbaadbdcadbaccbbaabdadbdcbaccacbcbaacabdbcacbddcddcadcbacccdbdabaaccbaccadcbbdddbbaabcdbbbbabdccaddadbcadddadaabdcdccaabbcaadbaaabaababcbddcaadbbdacddddbdcaaccbaddbddddccaadbcdacbdbcaadacababbbabdadbdabbcbbcadcbbadcabacacaaacabbbbccdcacaaaabbabbdbcdddacadbbbbcaaaaaacbdbcaddcbbbddccdbadbdcdbaccccabcccaadacbbcdacbcabdcdcaabcdbbcbdbdacaddaabdadcadccbaddccbabaabcbbabdcbcaaaccaaabbcdbbdcdcadaaaabbaabbbadabcbacdabacbbdabacaaacdacaaadbacdacbcdddddaccdadbdadaadaaadaadcbdbcdacdbdbcbabaccdbccbaacadacabddcddcaddcbddbddbadbaccdcbbdbbcdddcacdadbbcbababbbddacdbacbabcdaaddcacabaddbaabddadadbbdbdaaaabbbaabbbdcbbccbaabbcaccaabbcadbccbdcbdabdcddcaccbbbcccaacbadabddbaacccdaaaacacccdcdabacddcbcabccadaaacacccbbbadddcabbbcccaddaacadcadcdaaccbcddccdcccbcacdcccadcacbaddddbbcdccadcacdadaaaabaacdddbccadcbdddbabbadcccbcdbbaabbbdbbcaddcacbccbcadbdbddcdcccbdbdbbababcaccdcbdbbabdbcaddbdabbccdcdcbbacbcbdbddaaccdcdcbbcaadaccdaadcdbadacccccbccbdaddddcbccdbcbdcdbddbbccbcbaaccddabadadbabaccbbaaadcaddadcbadcaacaaadaaaccbabdbbcbbabbcccdbcabbaacacacbcddadddbcccdccbbdabccdabbdddaddadaabcddbdddacbabaaacdacacdadddcbdccbcdbacadcaddbbddaadbbaabdbcccdadcdddaaacacdaacacabbbbacabbbcdccaadbaabddbbbcdccaaccbdcddcacacddddbbccccdbbdacbcbdcbcacdddcccbcddddabbdaaadaacbbbcadbdbbacbbabbcacabcdbacabaabdbddaacbcbacbccbbcaadadcaaaacbbccaabdbcddbadcdadbbbcccacdadabadaaabacbaacbddadaccbababcddcbaaddddcbdccbcbbadbcadcdbadbadcaaddbacddddcaadcbbaddccadbbdaaadabdadbbcdddcccaadcbddcabaaadbabbbaacbbcbbbacaadcadcdbdbbbcbdadcbddbaaaccdddbaadcadbdccccadaabddbbdbdabbbcacdcdbdbdcadcdbcddacddccdbbddbcdbdacacbcbadacccababbcdcacabcaabcccddacadcbdccdadaaadcdbcdbbdaddcdacdabdaaccdaacdccdabbdcabdcaccbdcadbacdcabbdaadcadbadabaadddbbdbbacadbacdabdbbbcdcdacbabbdcdbaabddabdbccbdcbcbcaadacdabbdbbdbcbcbdbdbccdaddadcdcabdccacccacaaddbbbdcaabdcbbbaddbcabbdbaadbddaaddacccbdbcbccbccbcdbaaabdbbacdadccabcbaaccbdabbbababccdbadaadcbbbccdbbbcacbcdadcbadbcadbdadccbdcacbadaaadcacbadddbcbcddaaabdbbccdddcddccccadacdcccbacaabbcddababddddbacbacdccbbaccbdabbbbcacccdabbcdcbcdaabddaaadaababaadacbdccccbcddbdaddadaacdacbdcbbdbdaccbddbbdaabbacadcdcbbdcbdabdbbbcddddacacdbddcddabcdadddccbcbabddbaddcbdcdcbbccbaccdaacbbbbaccdbcdcdbcbbaccbacbadbacbdabdababacdcbccdbbaadccbaadbcbbbadcdcdbcdacccbaacddbcbdaaadbdcbdaacaabbcacdadcaddbcacaccadcbdddadadaccbbdddbacaacbdcaadcaccdabaadbbdcabbcbadacaacaadabbccdcddbacbbdbacdddbdacbcabbbbaabcdbbbccdbbbdbabbdabacdccdababdabccdcdccdcdbcbcbdcabacaacdccabadcdbaddddbcbbbddacbcbbdbccadddadadcacaddddbaaabcabbdcdcbcbdcbcccaabdcccbdcadacadbbbbbcddaacdccbcacbaabbdcadbacbcbaaacaaacabbdccaccdadbbdabcbdabcbddabccadbbdccdddaddccdbcdccbbccbbcaccbccaadaadacbabacccbcddccbccbbdaacacccaabcdcbaaccabacabbcddddbacdcabaadddcadcdbddddbbbdbdbcddbbcbcbdbbddbdbacdcbbdabdddbbabcacacccdcaccadddaddbdccaabccdaabccbdaaacdabddccaacbdccddccbcabcadabbbdbbbaddcaadcbadbabbbabbbbdcbbcdaabdbcdacadcbdcdabccaacdcaddddabddcccaadadcbdbdcbbdddcadadacdaabacacdcbccacbdbbdcdcddbaadcbaaabbdbacababcddcbdccccbacabdddbcacbbcbbdabaaddacaddbdabbccbaabccbbaddbccabcaabdcaccbccbccaabbabcaddcacaabacaccabaaacabcabdcadccbacccddbcabcabdddbdbcdcdaccbdbaabaabccdbbacaaadcbccdcadcdadbdcdbbccbadadacaccabdbcdabcbaacaabdaacabdaabbcbcbccccdbcbabddbbaccbaddcbdadabbbbadcbbabbabdabadabbbabaaacbbbaaababdaacaaaddcdcadabcbddcaabbbcccbccbccbbdbddcbddacaaabccccacdaccdacbdbbbccdbddcbabdacbbdbaacdadaaddddcccdaccdccbcdbbcddcbddadbcbddacccaccbdadbbabbcbbddaccacaaabbbabaadbcababadacbdabaaacbddbbadaacadabdadacacdcadbddaaacacabdaddccaccaadbdccbadbdddbcccdcdccdacbadcbddcddbaabdbcbddbddacabbbcbcbacaaddcaaabbddbdadbbccaacadaccaaddcdbddacbcaaddcaddcacaaccbcdaddaadcabacbcdaabcbbabbcaccddbbadbcaaccbacacbdcaabbbaabdbaadbdbcddcbcadbbadababbdccbaddacaabcbddbcbbdbaaccbbdacddcddbccdadbbccbddcdadbccbbadddadcdbdccabcddaabcdbabdcbbabadadaccddaaabdddadcbdcdcddacdadcddabdcbccbacaacaccdacbccacadbccaadbbcbbbaddadaadbcbcbdddbadcbcddaaccbadbaaccccbdabbaabbcbddcdbaacaadccabbccdaddaabbadabdbbdbbdacaabbbbbacacabcdadccdbdbccccacbbadbaacbddcacadbcbdcdbcbbbdaaccbdcaddbbaaabadaabacdcdddcccbabcbbacbaadcadddaddbacdbddabcbacbacaaacbbabaaddcbbcccdddabacdadababcbaacacbcbabcabaacdddaaccaadcdcaadabcadaddabbdacabdddcbbbbacddcaacdaaddaccaabbdbaaddaaadabccdcbaccdbaabdcbcddaaadcbbaddcbdacbddaaadddaccbcbcadadddbbdbaddacbcacbddacbbaaddcadaacdddcaaadcaaddcbacbabddaadacacbcbddbcddacbdaddcccbadcccdbbaacbbcbdbcabadbcabbdaddbbcdccaddbdbcdccbbaacbcbbbcbbcbccabdadabcbbcddbbbbaabaccabcacbcbbcaacbcacaaaabbdcabbdacdbbdcabacbdacbdbdcdcddbccdbaddcccacbacbcadccddbacdbddbccccabcccabbaacdbdcbabbaacbdabbaaabdadbacdcccbddbadbcabcbcbcdcacdacbbbcabddadacacbbdaacbdcaaccdaddaacdadbbaacacbbcdbbacbcabdaaaacacababcbbdccbdbcdbdcabadadbbccdbcbdddcacdacadbccdacdcbbbcadcbccdadabadaadaccbaccbbccbbdcdcdaccbddabbbbbbacbcbdcdccccbcdaaccbcbdcacabcccaadbbdaadccddcacdbcddcadbaaabaaddcbdbbbdbddcccbdcbaabcdccccbcaabcdddbcdccbcccadcbbacbbbdaabddaadcdacbbdaccdbbdbbdbaabddbbacdadcccdaabcbbbbaacabbaddbaccbddbacdbbbdbdcacccccaaacdbbcdbdacbcdcccdcaababccbbccabaddbbacaabaabbbcbbdbaddadbdcaddcabccdcccccabdbccddcccbbbbbbabbccccdccbcddcdcdbbccacbbaacccdacddbdcbbdacdadcbddccbadcbcccdadadbbdcaddcacbadcadcbaccbdccbbddcabcbdaacccbacdadbaabddcadaabacabbaddcbcdccdccabdabacdbbbddaacddcbcabcdadadcccdacbdbbdbaccddbddbabcabdabdcdadabbccaaccaacabdcdddadbcdbddcabaabcaaaabddddddcccadabaadabccacbbddcaccaacdbcaaccdbccdbcccdcdddbccbadcbcaccabaccbdcbadacbadcdbadabcdabdcddbadaacbaaccbccacabacbdddbbadabcdabbbacacbdabbbbaddcaabcabbbadcaacbadcdcbcbaddbddaabbcbbdbddaccbaacbdaaacddcabaabbabaadaacbbbccbdacdbbddabccbbdcaccbdaacbaadbdbdbdabcdbcdbabcdacbbccacdcddaadcbcdadcaddaadbcbbabbbacccbdbccacccdaccdddadaccdbddabddbbdadbddccccdbaabdababcccaadbcbdddaaadbbcbdaadccdadbdbccbdadddadbacdacbacdcccddaadaadcaddaacdacbaabdabcbdcccddbcacaccadaccabcdcdbababdcabbcbbcdbaaccaccbddacdabbccbbdbdbbaabccbddaaabcdccadbdcddcbddbadacacaddacddbbacbcaacabadbaddcddcdcaadbadcbcbdbbdcdcdabbaccdcadacbdaadaadcbaadddddcaaccaccbbcccdbcdbacbdbadaccaddccbadadbcacacdbcdbaaddcabcbdcdbcbcadbacadabccbddaadcadcbccbcdacbcddbbddaadbdcadcacbbddbcdbcacadbdcccdacdabcddbbcddbacadbbdbabcdcdcabadabdcbbdbabddbacbccdabacddcaaaaddacbdccdacaabbdaabbdaabacccaddbbadbcbcbbbdabdddcabbdacdcaccaabbaacbbccccccbdbabbcddddadbcaacccadaaadcaadcccacbbcdaabbcacdbbddcdacbdbcdddabcdcdddabdaaabaccdcabaadabdcabbdcdbcddcccdddbdddaaaaacabdacbabdbacaadbccbdbdcbaddddcabbcbbbdbddcabdccabcbcbccdabdcccaddaadcdbaddbdbdbdbacbdaddbacacbadcbacbddcaccbaabaadbdcabcbdadbdacdbcddcbacaadbcbaccdcbbccbbbdaaccccdbdbcdadacccdddaabdbaacbbcadbcdadcbcdcbadadbdabcdabddbdadccbbbcddcacddcaabbaccdbdccdcccdcbbbdabcaddbaddacaaccaaaadcdbaabcdbaabaabbadcadacbcadcaaabcacbdccbadabddabcbccdbdadaddacdddddadbaadaacddabbadaabcddcacbabbbcbacbdbdcccbcccabadbbcccdcdcacdbaccddacccdbadccbbbadcaadadaacccccbdbabaabccdcdaaadddbcdbccaddcdcacaddbadbbcdabbdbcbcbbacbdbbabdadcddcdddcdaacdaddcbcdcaadaabaccbbdbabbbcaabaacabbcbaabbccbbbaacbbcdadaaccacddadbcdacdbcbdcdcddbbadddaddbddbdccaabccbdaaacaccdcdcddbcbccbcddbccadabbbdbbaaadaddaaaacaabcadaacabbcdbdadaaacabddabbdcabdbdcabaccdddbcabadaacbdbacccdcbacbacaccbbccdcbccbcaacbccaaabbdadcadacaabcbdcabcbbbdddbaddcbdacdadbbbcdbacdacabcbdcbcdabdcdddabbcbbbdbbacbcadbadcbdadadcaacabbdaaabaabbbdbbdcadacbbcddbbacaaabddbdabbbacaababbbbcbdabaacddbbdcaabcdcbdabbdcdddbdbadadbcdbabadddacdcadccdccddacabbaaadcdcbacadccadbaddcbbdbcdbadadcbdadbcaacbbdbdaabdacdcbdaccbcdcbacbdbdacbcadbbdaaaddbcdcbcabdaacaacbddbaabbbddadcbbcbbdacdbbbaaadccbacadacaaaabdaaccaaddcaacaaddbdacbbdaccdbdaaddcccdabddcbddcaadcdacaacdcaacdcaddadacacddbcccacbabbdacdcbbccbdabacaaccaccaabadadccbbbbabdadddcbabacbbbdacaabcadccdadacadccbacbcdcbdddaccbbadacacccdcbcaddbabdddcdaddccdbcbcccabaabbbbcabadddacabcabdcbaabdabdbddadadcbddabcadbbdcacbdcddcbcadadbcdcdbadabaccbddcabbdcaaddacadcccccbcbdcaabbccacadcbdcdacddaacdadcddbadcbbaccbbcbdbbbaaddbaababcdbdbdabdadaddadcabdcbbcdbaacbaccbcddaddaacacbbcaacddadbabcbabbabbccbbacdaadacdbdcccdbcabccaacacaaaddaddcdcddbcdcdcdbaccddaccabcbcabdbcacadcdadcacbabccccbbbabdbcbddbdcacadbadcbddbdaaabdddacbbbddbccbbddddbbabbcaaccabadbbadacaadaabcdabdcadcaaaddbcbbadacadcbaaaabacbbdcbbadcdabdbdbdddbddcbbcdadaddadcbcbddbbadcbddaacaacacbbbadbdaddddadcdacacdadcbaddcbaaabdabcdbbccdbadabcbdabcccaccabcaacccdddccdccdbaabacadcabbacbdaccbcdacddabdbbdaababcbdbbcbcbcababbdbdabcbabccbadcacacdccaabcaadcdadabaabcbdcccccccbbaabbbdabbaaacadacbaabaccdabadcaadaadcbcbdcdaddabaabadcbcaaabaadbabaabdacadcaacdbbbddaaaaaabcbaaccbcbabadababcaaaadaaddadbbddcdbdcaaddabaccabbcbdbbbccbadaccccabcacaadacaadccaabbdabdabaccdbdddbdccccaccadbaaccbbabcbabcbcaccdcbaccacbacbdbbbaccddbdcccbbaabdbcdddadbaadaccabdcaaaaddcabaddabbcabbbabbddcddadaabcbbdbbdaccbcbdbcddbbdabcacbdbcbdbabdbbbbcccacaadaacaacaddabaddddabacdabaacdcbbdbcbbcdbccccbbadccdabdadaadbaccaaaddddbdbaddaacbddaccdccbaabcbbbdabcccbbcbbcacccbbbababdccaabbcdbcdadadbdbdcbbddccbbcbcababcaddbddbbccbccacdcadabacbbadbacdcddbddabbcddaacabbabbaacacaaacacdcacbdaabddbacccdbbadccaacddcbacbbdbcbbacccdaacdccbbdddddcacdcadcadacdadbccddaadadacbaaddbabddbcbadbacaabdcddaddadcbaabcccddcbcbcacadddbabaabacbdcacdbadadcbcdbbdabcaaccdbccabaacbccdcadaaabbdddbbccdbbcdddacdcbddbabcbdaacbccbddbcbbbdadaddacbcbddccddccabdccdcccbccbddcadbcddbccdbaccaaccdcbdbcbbcdcacadacbabbcbcaacbbddbcdbdccdcdaadbccbbabaddcdabdacabcbcadccccccabccdacbcccdbbbdcbbbdaacaadadaddcccbaabbbacccddcbddabaddbccaaddccdadcbcaabbdbcaaadacbddaabbccaacbbdadaacdcbbadcacccdabcadcdbaccabaabbdbbabbcdbdabdcbbbcbddcdabccdddbcdbabaadbddcacaacbaadccdccbbcbdaccdddacdddaaabdccdddddbdacaaccbdacdaccbacacbadcdacbcaccdabaaacbbcbbaaddadbbbabdadbcaaabbdbbcadbdacddbcaacabaccddcdcccbadabaaadbcabdccddcdbbdadcbbdaaddcaaaadbdbbbdbbcdadcbbddacbdababadbdddbacbaddadcbbcdbcabdaabcbadaabadccbbaccbcabccdbdbbdcbabaaadcdbbbdddcddbdddbbcbabcdaccabadddabbdaddaadbbaddaacdddaabacdbcddbbaccaccccbaccdacbaaddcbbaccbcbbdcdbddaabacbaaaaaaadcdaddacaaddcbadcdbbbcdcadaadcadcabdddddccacbbabbbcadbdbaddaddacddabccdaacbdbbdbdddddbbaabbdbcaaadbdbbbadcdcadaabccddcbbdbaccbcdcdccbccdaacabaabbcbbcccbddccabadabbcaccaadaddacabbcbbadbbbcacdccbbabbcbcaadcdacdaccdbdcaddaabcabcdacbbcadccbacbbdcadacdaacbddbdccdaacaabbbcabccddbdcaaccdbccabbcdddbcdcabdaccaacbcacbaaaaaddddaaddbccaaccbbaddacdccddbbabaddbddaacddbbbcacddbddabadadbaddcddcacacdcdbbaccaaacddcbaacbdddacbdcaacbaddabdadbbbacbbbaadaadcbdcadbcbbbcdcdcabbbdbacaaababbbcbbdbacbcaabdbbcdbcbbbddcdcbcddbcdadbadbabcaaccdbbaccbbcddddcdcbbbadabdcbacddcbbabacbccabccdadcbbddaddddccddaccaaddbbadbbcddccccdbdabcbbcaccdbccccbdacdadccbddabcbacadbbdccdcbdccdddcbcaacaabaaabbddbccdbdacadaababdccadcccbdcbcbcacbdddcbbacddcabdaadbcbcbbbcadcaacdcaacabdbcdcadabbaabdabbcddcbcdbcdacdbdcdcdcaaaaabacdbcdbbdacbdddcaaacdddacdaaaacdbddadababacadbdbdadabaddbaaddaaaabbcdbaddadbbaadbbbdcacbdbbbbdacadbcdcdadcaddadadbcbdcaabadbdaaaccbdddcdcbaccbdccaaacdcadcabacbdacabdccddcbdbccddcadaccbdbbadbadbcabaabdcaccadbbbbdbbdddbadccadbabaddcbddaadacdcbabdbaccbbaccbbddaadbccdcbcabdbdccbbbbcbcbdaddddaabccccbdacabbbdbccacbdbcdacaacbbcdaaaaacaccccabbacacbdcbddbccdbdcbabdbddbadadccbcbddbacadccacdadaccbcbbdbbbadcabdbbbadabdadbddaccdbcbddabcdaccddadcdaddccddacbcdaadbdcaccbcddaadaadcaaadaaddcabdbdcccaaccbdaadcbcdbbaccdabaacaddcadacdcccbbdbbbcadddaadbcbdaccaadcacacacdcdacdcbabbabbcdacbbcddcaddbdbadcdaabdddbaabdadbdbcbbabaccacacdddadccdbcbdabaaacbabcccdcabcdabdabcacdaaddcacdcbccbbdbabababbdcdabcaadbcaadabbaccaccabbacababdacacdccdaaacdbcdbadbbabcccddcdbdaadbbbbccacbdaabbcdcdcabaddabcbbbdcbdccababdabbcbdbadcbaddbcdcbcbddacddccddddbbddcaadcdccddcdcbdadbabdcbbbbbadddaabdaaadabbcbcbcaccaabccabdbdccbbdaaccddcbbadbbbcabcccbbcdcccbbcccddddbcabccbbccbadddcbccbddaddcdbababcddbbabdaabadbaadcdcbdbcaabcbbbcccbdcbcddbcacccbacbbabdcbddccaacdaabcdbdbdbddadbdabadcadbdccbabcaaaacccaaacaddddcdadcadddbadcbbbcdbcabbcdcdcddaaadcacaabccdbdcdbbcbbcbcabbbbaaaddbdbcabacdadabacccdaabdbdcdcacdbabccbdcbdadbadddbccadaddbcbcbbcccabaccbdbaaacbaabaaabababbaddaadddcbacdbcbbccdcdcbbdbdcacbacbbccabaadaadacbaaccababbccadabddadaaddabbcadbadbacdacbacdcbaddbaacacaabaabcaddbddaddccaccabdaccdcdbacdabbdaacdabacabaabcdcacdaabdddcddcddbacbcbbaacadccaddabadaadbcbccadbdaddaccdabddcbdaabcadddbbcabbaadbdcddaaadbbcbcaddacdaacbdbdabaabacdbabccbbbdbdbccadbdccdcbabcdbdbcbcacbcabadacadddcaadbaabbcddadaddcadbdddcaccaddbcaaccbadaccbbcababcbbdaccdbbaddacbcccbcbabcacbabcacbbccaaadaaabaddcbdbbddbccddcabaacdbbbcdccadaaabcbbccdbbcdcbddacbdabdcdbabcbbcabbcbadbbcbcacbaacadcbddcaababccaabbdcadbabaadcbaabbccbaddaadacaadabbcadbbdbbdbccbbadabccbcbdcddcbacdddabdcbbdcbabcdaadcdcddbdbbddaaddddbbdaddddaacbdbdbbdcbcbbbcbcacdcabbaddbcdacddcbddacccbcaaccbacaadbbddbbadccaabacccaddababadaccbacddadcbcdcdbadccadddbbbcacbbacccdcacadaaddbddcbdbabccabcadbaadccbaaacbbdbdcaacaacdccccbcadacabdccdcdbcbccdacdcaabaccbddcdbadbbbabadcdccdddabcbbdabbdacadaaddddbabdbccbdbdcbdacdacddddcdacdadbcdcababbdcddbccbbdbbcccbdbdcaacbadbccdcaccaadacadcbdacbcdadcbbbcdbbdacadaccdcacdadbccadbcbcdacbdcdbbbbbdaabcbdcdbcaddccaddcbbbcdcbccdcdcdddcbbaadadbcccdcaaaaacacbcacabdddcadcccdbabbdcdddccacccbacdabccccaaccddbdabbabbaddbaddbcbabcccaacdabaadbddacbdbaacbcbbcdccbadacbcbcdacbadaadbaaabbdcaccabbdadbdaddbbbbaddabdbbcccbcdbaaaabbaccaadbddaacdcbdababccdaadbaddacadaacdbccdabbcbdcdcabbbbcacdccdcaccacdcbccdddadbbadadcdcdabdabbdaacdbbdcdccbaaacbdaddadcaabbdbaabdbaccdbcacacdadabddcabdabcccbbbcacadbadbbabbddcaddcadaabccdaccdcaacadcbbdacbcdcacacbcdacaccbddaaaaddcaaaccaabcbacbdaabcbbdbbbcaacaacbacabdddadaaaaaccddbcccacadaddbabcddacdcccdcacbaaccdcccaccbcdddaadbbdbddddccddbdcbdbbbbdbaabdaaadcccaccbbdadadcdbbcbdcaabdddbabcaddcbaacbddabcabbaacaababddcabaadddddaabaadddbcddbbcdbaaacbbddbcdccbdadacaadddcccadddcbbddabcaacadccdcbdbcdbdbcccaabdcadbaadabbacbddccbabccbacbbdcbccbabccddaccdcddabcdddccddacadaadaaacbbdabbdadabddcbcdcbcddaaacdbcdaddadadcacdcdcbdaadbabbcbdaaddabacadcbdbbddbbdcadbdadcabaacbcbdbaaccbcbdadcdbdaabbbdaaacabdcbabbcaabaccbabcbbddcbdbacbaddddcbdccbcbdabccdcbdddbcbccaccabccaadcbcdaacadcccdbcaddbadbcacacbccaacbdbddddaddbbbcccdabacacdcadaddcadcaddccdcccaacddbdabaccadaaadcacabcacdcdcddccbcbacdacabacacacdbacccabdacabadadbcdcaccddbdbdcbbbccaabccbccdbcbaadcbcaacabacbbdbbbaacacabcaaacbcddccccddbccdacbddadbbbaacbaadccbbccabadcbadbbbacdccdcdddacbdddaabbaacaadcbcaacdabcdbbdaadcadbaabdaacdbababcdbadabadcbaacccdbbdabbdbabdbbcbaddddcddcbbbbacaadadbdadaabadaadacbcadabbbabddadbbdbcbabaaaddaadbdcbcdbabbdaaaadccddbbdbdaacdaadaddcbcaddaabdbcbccbcbaadabbcaccccbcccbabcacaabdcacdddbbbacdbbbcaababdacbabbbaddccddcccbbacbabacbaacacdccadddadbadcdacaacdcacadbbdcacbaabcdccacbbacabbdbcacbadabdcdabcbbaccacabcbbcbabadbadadcccdcbdaaddcdbccbaddaccbcdbddbccbbdddcdcccaaaacdccbaccbdabcbddbadababcaabdbbcdccdacabcddcccdbcaddcbababcbadcbbdaaddddadcccdadaaadabcaddaaadacdccdcbccaaddccccbcbaaabadabbcdddccaaaaddaacdabdcbcbacdcaddabccacacdcdddaaaabcbccdcacdbdbcbbaaccaaababdacbcccccbaccbdacdbcdccdbccddbdacbaabacaababbbccbababcabcccdcabbbbbcdbdabaacacbdbbbccbbddaabddabccddcaadddccaddabbacdbaacaadabdacabccbdbbcadaacaacbbbdbaacbdabbdadcaccaaddcdcdabaacccbdcbdddcabcadadbddaabddbdbaacadcaaabadbaadadbddcadadcdddaadddbbbaaccaaaccaddbccabdcdccbaabbbbdadbdcbbbdbdbccbbaddcdccbacbadacddccadacacdbcbabcaabdaacabacbaaccdcbadaccdbacddcddccbdabdcacdacabdaccaccaaaaababcbcdadbbbbaaaddcdcbbbabcddbbbaaaabbacbcbababdaacbcbdaccaabddaadaccabcbacdbdcdcccbacdbadadddcbcacabbadcbaccacccdacadaacdbbbaaccbcbcdaddbdcbbbaacbcacbabdcddabaaaddabaabdccdbadacddbdcccaadbbbdbadccbcdcbbdbaabcabcbbcacdacbbdcbdbcabaaaddbcadabccddadddabbbcccddadbadadcdcbaccaacccaadbabccbcbbaaaadcbcccadbddbaadcccbccdbbaaddabadcaacbdccdcabdcaadcabdcbaabddaabbcddaacaacbbadcbdbacbaacbadaccabbabaadaccbacdadcabdcbcaabcccdcccaccbbcabbcadaabbccbacacaacaaccacdbbbcdbaabacbbabcdbcbbcabbabadaacbcbbdbddacaabcdbbaddcdaddcbadccddabcadccbbcdccdbbccbabcaaccdcddcadacaddcdcbdbdbcdbabaadcacdacbdbbbcacbdbadabcadcabccabdacddccacababcaddcbddaddacadbcabbcaacabbdcbccdddabdcabbbaabbaabadcbdbbaddcdadcbdbcccddbabbbbddbacadadcadbcacaaaabbdabadabbbadbbbdacaccdcbbabadbcbbdaadbabcadbddccacbadbabcacdaddaddcdaabdddaadddddddcddadbcdccbdcdcabcadbcbaaddccccccdbabccabdadadadbbabbbcadacddabddccabacddbcdcdcdaabbbcabdadcadcbdbcabbcccdbbdaacbcbddbdcccbaaacabdadadbddabdccddcccbdbaaccdbbccbdddbdbacdabdabddcddaacccdccbdbaddadabdacdbdbcadbbdabdacdbbcbbbbadcdbbabaabaccaaddbaaccccddcddbacadacaabbadabcddacbadbbcbaaababbbccdabdcadcabbabacaaacdbabbbcdcbdcbbdbccbdaacdbdcccabadbcaddcaadabdccaccbadadccbcdddabdaaabcaaabdcbdccbdbbdabbdcabdcbccdaabcacbddcccbcadbdcccdabdacccdddcacbdcdabbbbaddaaddadcbcbadccbdcdbbcbddadacdcbddcabddccbbbdcbcbacabdcaaddaadcbadaadbddabbbcababdcbdbadbccadbbcccaabbdabbbcadaddbdabcdaabcbadaadccbaccdbbcdacccbcbdaacccccdccaacaaddccadabcdcdcdbabbabdbbdcdcccbccbbaddcbccbdddbaaaabbacacaabadadcccbbbacacbdadcbdbcdbaaaadcccddadadbcdbddadcbcbaddcdbcbbcabdacacacabbbaddbcaaddbdaddcadbacaababbdadcbbdadddaaadcdaaccbbacaccdcbcddcaabdddccccbcadbbdcbcdddababaaccadbccdcddccadbbbbadadcbccaacadcbbaaabbbabbddaccdabdcaacbdabdbcabaccdabcccabbcbcbbdabcabbdbacddbdcdcadbbbdcbcadbabbddbdbadacdbdaabbdaababbadcbbabadbaabbdccbccadbbdbbbbcaacdccadcdacdababbaabdcbadabdbdbbcadcbacdbbbcabcdccadcbcdaaccccabadbbdaaccacccbcadcbbdabbcdabaaaaddcbdddbbaccbcddddabbcacacbcacbbaadabcaaddccacabcdbadcbcadccbaddbacbbabcbddcbcdbadcbcdabbddbaaabacacbaabdaacccbbdabbdcbbbabaccdbbdadcabdcdcacbdaaacaaaddaccbddccbacbacddcacdadbccccdcbdabaddacabadbdcbddcbbcdbacdacdaccdaadacbaccbdaccccdbcdddabbaddaadbbbdcbdcccadadaababddbbdbcbdbbcbdcddaabcddcddcbbabdbcadcaaadbbadaadcbaabbabdcbcadccdcddcccbdddcddbbbbccaacabddabaccdcbbaacadcaaccbdbaccbbcbccaacbabccbadbacddaadadaaaddbbbbdadcadaaddcaddbbcbcdacbdbaadbdbcbabdbadccbacbccdddadbddbbabcbdcaccbaccdcbbdcdccabbccbadcbbdcbdadddbdcbdcdbcdbcaadadcaacdbadbaabdbabbbbaadacadaabcddadadabaabcbbcbabcbbdddcdcbbcbcddcbbbcdccbabaabdddbdbdacadbdcddcdbbddbddbbbdddacdccbcabdaabdbcbaddcaaccaacbacabddcdabbcbdbdddadbdbccabcdccdcbbdbaabdabcbdccbbadacbdaaabaabdacdcabbdcdcaaabdbabadcdabcacbbaababdbbbccccbbbdcdcccccacadbdadbaaccddccbbaabbbcdaddabbadccaaddcabddcbadcddbbcbccddcbacdaccbbabadacccdaaadadddacbdbacbcbadcdbccbdbdbaabacdcbcbdadbdcbadaacbaaccabdcaddbcadaaabcdacbdccdadaccaccadccdcdbcaacdbbbaabdbccbabcaabbcbcbbadacbdadcbccdcacaaddcdbaacabdcadbdabdacadabdbdbbbabcdbacbcbcdbabaddddbadbbcbdbcbccbcbbddabaddabdbdcdbdcdbdabddabcaddcabaacbbcbcaadadaaaaacacbbccbadadbdccbcabddaddcbbdabaacabdaadabccaddaadcbdacbbcddbdbcbacbcbcdcadaabdabbdcdaccdbdcaaabaadacbbcacabbaacdaccbdadddabbbcbaabaddbbcaacdccbdddcabbaaccdbaadbabcbbbadbdbadcaacaaddadbaaccdbdcbccacdcaaccdadcaccbacabbccdcaacdaaacdadaaccabbdcddbcbdccabcddbbdcacdcccbcadddbdbdbdacddcaaadbdbaabcabbacbcaccacdacadcaabdcccdcabbdbbdbdaccadabdadccbbbddcacdaadabcabaaddbcabbdcccabcddbbbbbdbcdcddcdbdcbbcbcdadcdbdcdcbcbcdaaddcccddcaadddacaacbddbcaabccccdcadddddddacacadadaccdbbabbccacbccaadcaddbadbbbbdadbdabcbdcccbadbbabbaaadbabadbacadabdaacadbdddbabadbaaddaacccddaadaabddacbdcbdbddbbdbddadbbbdbabdbadcdcdaaccddabccbdccdbbdbbcabacaacbcbbaaabcbdcbbacadccbdcbbbcbabcabbdcaadbbcbacdddabddddabbadaddadcdcbdabbcdacaddbaacbaacabbbcbcdbcbcbccaddbdacdcdbdacabbccdadcdacaccbbdbdaabbacabadacacdbdcbdbdcbabacdcbaccbcbabcabaabaccadcadadbbadabacaacabaadabcdcaadcabbcbdcbdaadccccccbccbcaccaccadaaddbaccbbababdcadbcdaaacbbddddccabddaaccdbabccbcbdadacbdccddddccbcdcaadabaccccacbababaaabdacabbbcdcdcbcabddadababaadabcdababdaddcbddcbdddbacabdadaaccbcaabbbdbaadbaacdacbccbcccdacaadcddccdbdddcdababaaacacdddcabdccddbcbcacadadbcdcbdccdaccbcabdbadacdabddacaaaabdacaacdbbbcddbbaacbcaacddcbcdcccdbaacdbacdadbddcbabbaadaccbcacacbbdbadbddcbbdbcbacaddacbacccababccbaabadabcabaaccdcccdddbdcabcdcbcdbcaabaabcbcccccdbcabcbcbdadbbcbbcbaacdadababddaadddcaabdddabbbdcddaaadabbbbbdddbbaddcbbcbbcbcdcdbcbddccbabbbdbdbdabdbadbabbaabcdaadaabadbadddbcdddcdaadaaddadabcdcbdaddddbacdacaddbaabbbaabddabcabaacdddbcddcaacddbbbbcddcbcdabdabbdaacdbbcbdcacccdacccbacaaabbbcbdabdcdcbbaadaccbacdacbcccdcbbabdbbabbdcdcdccddcdccdaaabaaabdbcaabaddcbbcaabcdccaaccabbccbbcbbbcbcdcbaabccaaababbcbbadbccdabdaaaaabbbdabcbbcccdcacbbcababcccbaddadddaabbdcdacbcdbaabbcacbabadadadddaccccccccddbcacacbcdbddaacbbcbadadcadccadccbdbbadabadacaabbdcaaccbcadddacaacbbbddbcbcbcdbbaaccccdbaadcaccaabbdccbdacbddbcbcdbbcabbcdbdbadbdacaabccbacdaaadbcdadbbcddbcbcadbdabbbdadddccbccdacdcccccddbcdbdbacadbacaddddacbddabbdbbddbbcdacdabccbcbadcabaabddcdadbcaaaccbbddbbdcbabddcddcdbcccdbcdddcdbcacbcbbdbdbddbdaaddcdccccacccbadaddcbbaccbcdccbacdacdbaadabbdbadbabdbbccaabacdbddcbbacababccbbbabcdddbdabdadddbbdcbadacbacacbaaadcbcbcdbdadcddddcacbabcadcacbdbdddcbddadccccaccadadabbdbbbadabcababcacbdcbcbabbaaacccadaddcadcaadccddbbcdaabcadcbcaabddadaacabdccdccdbdcdcdacbaccadbbadabacddcbdaadadabdaacadcddccadbbaaaddbdaddbcbddcbbdaddcddddbbccaadacdcdcbacdaadbdddbadccccdacdcaaccbdbcbaccbddcacabdaccccaadddbbdccacabbacddabbdbcacadddadaaccbcbbabbbbcbacdcdabdbbbaccbabdadabbdaddabcaabbdabbccacddcabbacadaaabbaddbdbdaaaaddaddcabcacacbadbdbbaaaacaadddcddcddadaadabcbabcdbdbccbbddcaccbbbcdbabbdbbaaababbdcbddcdaacccbbccaaddadaaaddadddbcaaaadbcbddbabbddbddacbaaaacbaadccabccdacbccdddcdcbacadacaddbcdcacdbbcadcdbbaabcbbaccddabbabcbcddaaabbdacbdbadcbddcbadcdbabdcbcdaccadcbcbdddbdbddbccdcbccbdccddbaaadddacdabbdabbbaccbcacacbbbcdddcdacaabccccbabbdcacdadcdcddcadabdddccbcddaaaabdbbcdbaaadbbbdcacbccdaccbbdacdaccdaddaccdbdbcabcdbaaddddcbacccdbcabcdcdcdccddbddccdacbbdbabbcaadbcbbbbccbcbdacabcacadbcdacaadcdaddabdddabcbbdcbcdcdbdbcacbdccbbabcaacbaabcdccdcacbbadcbcbcbdbcdbddbbabbcdbccbbabbdbcdbabaabcabaccbccaaabcccdbbbbdcccdadcbdbbadbdbbbcacacacbcbcadacacaccacbbdcdbbacccbdcaacbaadbccbdabadbdbddccdaadcbbcbaddcdbacbcbbcbdaccaddaabcbdccddabadbadbccacdddabbdccadaacbcbbabcaadccbbbadbaaacadbcbcbdcdbbdadabdcdabcbdaadbcbdaaacbaaaadabbaaccbaccaacbdabcccdabaabbabcbbbbdadccbdaaadadbcabbcaddaaddddabadcbadccccdcddaadddcacccadcacdabcabbdbbdbaaaddabdcdaadadbbacdcadacbccbccccaacdacaccdacbccbabdaaadcbcaacdbbbababadbccbbbaddddcacdcdacdbcaddddbbcabdbdbdaaadaddbcbcaacaadddabcacdbcacbabcbbacddccbacbdacaadcddbaacabcdadcbccbaadaacabbcdbccbcccdbaddacaadcbcdabdadbcaddbaaaaabbcaccdccdccdbbcdddaddddbdbbaadabbdbcccbcacbadbbcacdbadaddddbccdcdccbacdcaddccbcdbcbdadcdbddaccdbacddadbbcbdbaacadcbbadcbddbcaccdccbbabdaabaddabcddaadcaadcabcdacadbbdccbdacccbccaacdbbadcaccbccdccadbacbcbdbabcaaadbcaacaaabdabddcbdcabddcddabbdbcdbbbcabaddbddcbcdacbaccbdbdddddbdbbacccbababbaabcabaadbbbabaddbbbacdcbcdabbdbdbbaadaddcbbabaaddcdaacaadbbabbaacbddcdbdbbbbbcbaababbdcbbbaabccdbbdcaaadacadaaadbabcdaccbaaabbcccdbbdacbcccddbabcdbdccbcbbaaacaddbddcacadcddddcdbddddcccbbcabaaaccbbdabdadabcaddbccccaadaaccdacbababbbbadbacbabcbddbbcccbddcacdcbbccbacdcddbbcabbccbcdbacdcbbbdbbcbbbccdbddabcadcacdadbcacddcbbabdcbcacbddaaaacaabdbcbdbcdcaabdcacbbcbdadbadbbcbbdabcadbdddcacdaadadaaaabcdabdacdadacdadccbcbdcaadacdddcbbbadacdbdabcbaddbcdcaaadaadcdbcabbccaccaacdbbaacccaadddccdccdcdbbbcdbaacdadbdbdbaaacdbcccbadbbadabccbdacbcdaaadbbddadcbadbaaaddacbbbcadbacddadbadcbbaadbccaaabdabdaadbcadcbdadcacaabadbbaddbcdbcacaaaaaadababacddaacdcdcabadabadcacacbaabdadaddcdccbbddbbcbcdcbcccabdbddaacabdbcdbbdbcdbccabbddccbabdbddaaddccdabbaccbacaddbccbdabadbaaaacdadabcbcadcddaddcdccaacbdbaaadbbbabadabdabcccaccaccacbbcabcabbcbbabccacdbdddbdcbaddccbaaaabdcbbacdbbcbddbcbaaabababbadcaaadaddbaddcbadbacaabbabdbdadacadcdcdcdcbcdcdddaddddaaacdddbaacbcbcdccccddadaabbabdababaadbccabcdbbccbddddbccddadbccadcbaabdcbcadcbcaabdcdcddcbcabacbbbbbdccdaaaabbdaaadbbddbcdcccbdddaacadacbadbdcbdcdcbccbccaaabacdbaadcdabcbcbcbacddbdbaabdbcdbcbcaadabccbccdacacdcdbaacbadbaacabaacacbadddabaabccbbcdbccdbcbabdcccbaabaccbbdcadbdccdaacccdccbbaaddbbdcbbcaadccaabbbdacabcbadbadbaccbcbcdcabacdcabbccbcbacabadbaaadbabbbcccdcdbdcdadbccacdccbbbaaccbbacbaaadaaabdccddcccccaaaacaaacccbadbccbadddabbcbccbdabccacabdbdabcaddbcadbbdbdbabadcaacbbcadbcbdbdacdaabddabcadcabbcabcaaabacbdcddddcbccddccaabcbaadabdaababcdddccbaacbbabacddbbcababcadadbdbdababbadcabcabbadadcaddadcbbacdccddccdbbcdddbdcdcabddccdcadaddaddcbccccccdbdbaacbabbbdddccababadbdaadcccbcaabbdddcdbabadbcbadababbcadbaaddacdbbabadaadbddbcacdcbbddbcbdccbddbbddcabdcacddcacaaccbbcddddcbbbbbbcbbccbbbbcbdcabbddaccddbbdcdccbdcabcdbacbcddbbcabdaaddddddacbaaaddbabcaddcaddbababaabdaadbcbccdbcabbccbbdcacaaabcacdccaaaaaadcaabcccaaaaadaabbabbdaccacaabddbdddcbaaadabaabaaccbacbacadccdccdbcccdccdddbcbacccaabadbcbbdbdddcdbcbdcdaddcbddcabbccacbdccaaaccabdadbdcbdabcabadddbaadbbcaababbbcccccdcbbbccbcbdbccaadccbbaaaabbaddbacdccabaabacdcdbaadcbdddcbabdcadaabbdcdbbbcdcbbbadabcaaccabcaaccadaacacbddacbaabdacbdadbdacccbdadacacaaaadcadaabdbdabccacbadcacaaabcacdabcaadbcaaabadbdcbdacddbdabbcadbacbddcbbcacaabddacbacbbdbddbdcbdadbaaaacbaccbbabbccdacaccaddadadcdccbcaabdbbdbdaacdbcabadcdabbaaadbaddadccbaadcadbbabbdabccdddacdaddccdcabaaddabccbaaacdaccadbadddadaddabddbdcbabbbaadcbbddadcbcbcbaccddabadcdcbdbbbdcdcccccbddadaadccbdacbddbaadaccccdcbbbcacddacaaccdbcbcaccbdcdcadabaaccbbabbbbcdabacdbdbdcccdccacaadadbdbaadbbcbcdaabbacabcbccbdcdaabccacdaacbcaccbabbaddababbabbcabbaadadbcdcacaaddacdbdcaabdaabacbabacdccadbdddccbadcdcadbdcadcabbdbbdbadaacdcdbacacccddbcccbcaacbddadacbdacddccccacbcbdcbabbdcaccccdbcdcaccaabcbbbdbbbdcdddacaababdbbbacaadcddcadbaaabdaaabbaadddacbccdcaadcacdcbdbaccdcdcdbadacbdaaabddddcabcdcdbacbcdbadcdcdbdcadabbbdbaadcabdbacaaacbbaadbcaaacbdbdcccdacbabcacadddcbacdbaddbbcacbdcbbbacddadccccdbdccddddbdccbaddaabbdabaaacccdbccadadccccdbbaccdacabccbbbcbadcaddaaabbaddaaacbccacaadbadccbbcbbbcccbcbccdbaddddcabcddbdacbabacdcddbacddacaaccdadadddcbcbaaabdcabbccdaadbabcdcabbaaccdbcaabadbbcbddaddabddccacdaaddccaaaadbcccdaaaaadaacdbdddbbabadbcaacacdcadaddadbbcbcabbcacdacaaacbbccdddbbbbbabcbcbbaaadcbbdbcdbdccbdcbacadbbdbdcccccaabbdcdacacdcdcddaddcbccabacbbdbbcddbcdddabbcddbacbacbdbbbcdbcabddadbcbdcdddcccabadcbabadcaadacaadadbcbcbabacbbbbbccbcadacddccbdabddddacbcddcacddcbddaccbcabbbcadcbdadbcbaccbcbaccbaadbccbdddcadacbddbacddbcbccdcaababdccdbdcbacbcdadadbacdddddabcadabcddcdaaddadcbccaccddbbcbacabddadbbbacbbaaadbbbbbbbdbbdcacbbccbabdcaccbddbcdaadbcaccddabbbabaabdddcbaabbcabcadcbcbbccabcdcdcbbacbaaabadcdabbdbbaaadadabbbabcddbccadacbbcbabccabcbacbabbdabcbcacdabcbdccbbdcbababdabcdbaabccabccacabcadbbaaacababdabddbcbadccccdacdbbabbaacadabbdddddaccabaddacddacadcdbbcacdcbdcbaacdbddcdaaabaabdcdccabbcdbdaabcabbdbaddacabddbcadccdbbaaccadcdcbdbddccbcadabcabbbbadcddbdadaddbcccbcbcbcbacaacadbccdbccaddbcddadbdbbbaccddabccbbdddaccdbbaddaddbcbabbccdcadbbdcabdcddbcbbcabcdacabbbdcadaaddbcdbbcaacacdddabdddddcbacbaacdcdbbbaaddaddbdbcbcdcaabdbbdbaddabdaadbdbcadbbcacccacaadddbbabcaadaaaacdbaddbadccccadcabbaadbddddccbadcadbaabdcacdcabbdcaaabbaaacddbbcadcabaacbcdbcdddaddcbbcbcadcdccadcdaaaabcadaacbdddbbaaadbdbbdacdbbcbddbacababddbbcbdaaadadbcaaadaabcdddbcbacdaaccaaabcccdcdddbdddccccabbbbbaadbbcbbcbbbddaabdbbbdbacacbaabaadddccbddbddbcbbacdabcaadaabddcadbdaaaccbcddbcbacddaccabbaaccdacddacdaddcacddcacbbadacaabdbabbaadcdcacbabcaccdacacdaadbadaddacdbcbbbadddcacccabdddddcacaaabdbbdacdbabacacdccddcaacdabbcbdbbdaaaacbdabcdcdcbcaddbbaaaababaddacdaadaaaaaadbcdcdcacdddcbbcbdaaccaacdbdaadaabdbdcdaccbbaaadabaabbbdcaaaaadcbaacaacdadacaaccbbccadbdcadaacdabbdddabddacdbbcadddabaaacabadcbcacaccbbdcbbcdacbccdadbababdabcccacbbaadcabdcbccdadccbdbdacabbbdbbcdbcabadbcdbbabbcdccbcdcabbbdbacdbccbbbdcbdddccbcccadcbbcadbbcbbdacdbbbaddcadaadbcdbbbbbdaadccccbccbbccabccbcdcadacddcbbdaaccdcdaaddbabdabdbdaadcccdbbdcbbacdacdbadbcacbdbdbaaacabacbbcbddcbcdcdccdcbadacadbbdcacbbbabacdbddcbbbabbaddbdbcccccacdbabcccdccccbbdadbcabccdcbaaddcabadcccdabaddbcaabcddddddacaadaccacbccabdcabbadcabbdcddcbaabaccadccddaabcdbddabcbcbccbddcbccabccabbadbaaccdadddacdaadcdbadcdcdadaacdccbcddaaaadcabcadccbaabcbabbbbbcbcbacabdbacacbcdadcbcabdcbbbadbcbcdbabcdbdccbabbdaccddddababdbcbbdddcaaaaccdbadcdbcdadadddcdccacddbccbbdccdadabbbababbadbbcabaadbbcdcbbadcacadcddbaccbabbdaadababbdabcccbcbadbbdbbdaabdacabdcddabacdadcbddccbcacaaadabccdbdccddbcaadacacabdbacbdbcdccacaddddcdabacdbdbcccdbdaaadaaccbadcdbdadadaaaaacddabbdccbaddbbcbbcacacacdabadcbccabbdaabbbadadadbdababdbbaccdacdacaccccccdccddabcbccacabdcabacabccabcdcabdcdacddddbdadbbcccdcdacbdddbccbddabdcbaaaabcadbdcdcbadbacdcaadbcdcdadcdaadddaabcdcadbabcadddacdbadcbdaaacddccdadaaabdbdadcbdaacbacdcabcaaabcdbbcdcddaadbddbcdbabbbdaaabcabaabcabcbcbaacbabadacdddadabcabaabcacdbcccdbacdabbddbbdddcaadcdccbdcdcbbcbbcdadccaddcadbcaabdaddddbcbddbbbccddadaabbadbaabccbcdcbdccbcabcbccaabdbaaccaadcddddbbccdbbddcdbbaaadbccbcdbacbdcdbddcbcbcdddcabbabbacbbabccdbbbaaaadabdcddcccaadabdbcbbaacbbccddbbbcdcdcabaabcabbdabacbbbbaacabdbabbaddcddaabcdbacaabacbcaacabbcdaacaadaacdbabbdbdaaddaaccaddbdbcaadbaaaccdccdcdbdaccccaaccabaccaadcbbadbadcdbbbabcbcbddcdadbddabbacbaabbccadccdabadbabaaacccccdddaddbdbcaabcaabddbcccbccbcadacbadacaccddcdbccddcdaacccaaccacbbdadbccbbabdcacabacdaccbbccaadcbcadbccdbacddbbbddcdbacaaddcaaaaccbabdabcadabdbcdddbdbbbbbdadcaddbbdcdaddabccbbcabbacacadaccccabcaaaadbbdaababbddcdbdadbbacddcbbbdddabbcdaacdcadbdbddbbaaabbcabbacbbbccaadaccccccbadccbaccdbdcacdcdbcdadadcacdcbddbddbdcacbaccccdccbabacdccdadcaacbaccadbacaacaadadaacacdbadabdbcddabbbcddbbddcadaabcacbcaadccbaabdcbadaaccacacccbcbdcdadcddbddabdadbcdbdcdbcbadbcabbcaaabdaabdccbaacdcbaacbdabdadaadcbcaacdabaddbbaaddbdaadaaadabdcbbdcdcddacbbdcddadadbadadcbbcadbcbcbcabadcddddddcbadadbdcdbbacbabbcdcdcacccbdcdacddcbcbbdbdcbcbdcbcbccddacddbcdcbbbbddbcddbdcaccbdcbbcdbabbcbcaddcdadbbabbcddbaaaabadabddadbbaacacadabcdcacddcccabbddaabbcacbddabdbcbabbcdbddaabdaccbbbdcaddcbdcaccacaccbcbdcdaadcccacbabdacbbaddbabacbddbadabdabbcaaaadabadbcbbddcdbbcacdddcadbbadcbcaacbadabdaadadaadbbaabbccadbdaabddcabdbddcbbabadbccadcdbdbbaaaacdcbadadcccaacabddacadabaaadcdcbdcabbbddcdcbcccacdabdabbccabbdacbbcbbaacaababcdabdddabddbcbdacaaabbcacadaaaaddbacbbccdcdabaaacdbbdaaabdadcbbacbddcdbbbaddabdbbcbaccdbdaddbbdbbabbacbbdacaaacdccbaddacadbbdcdcbbdbccdccacacaabdccaaaaccdabccbcccdccdcaadbcaabbdddbcbdbabbddacabcbabdccbcbdbdcccbacdbccbbddbddbdbaabcadbbacacbaddbaacdcaaccacdaabdcdccdbcdaccacbcacabbddcccbbdccaabcddbabddcabdbcbabaccabaacbdcdaacbdaddddaccdaccaaddaacbcbaddbdbcaacbcaaababdaacdbbdacbbdaccaddcccbabbbddddcdbdabbdcacadcbcdcbadbbabcccdacbaacaacbcacabdddcaabdabacdddabadaabaaaaadabaccbbaacadccaadaadaababbdaabddcbbcacbbbabbbcddcaadacabbaacbbbbbadbbacccbbccddddbbabddadddcdcdbbbddcbaaaaddbcdcadcdccdadbcacddcadabadacbdddcadcbdccdaaabbddbddabdadaaaccdccbcccbbcdaabdabccdacabadcbbdaabbaacbbbddccbddabddbcdadbabcdaaabaddadcdcdbbdddbdccbabadbcbbaaaaaccdccbcadcbbddcaadabbbcbcdbaccbbaaadadbbccdccadacccdadadcbdbdabddbbcdddbaccaaadabbcbadabcdbbcdbcdadccaddcbcabdcbdbcabbcddbdadcbdbdaaaadbacbcdbaddbcdbaddacbadbcacacdcacaadbcdacaabbcbddccdbdbccbddaadddcddbcaabbcbabcbbacddddbcdddbbbcdbbddddddddccacbddcccbddbabaddcbacccabbdbcabbdaddddacdbbbcacddcdbdadddcaacdbaddbdbcaacdbdbabcaababddbcddabccbccbcdbbbbbbaabaaddccddaabbaddcacacaaccbcabdcdbabbbdddabaabdbcbaabcbabcbbbdcccbdbdcabdadacacbccdccacccbddcdbbcbbcabbcaababcdbdcddcccbabcadbadbddcaabddbadadaabaaadacdbacaddcbdbaabdbbabbdbdccbcbccdbcbbdacadbadbcaabbccdbbacdbbcacaadaabcbdabddcdcababcaacbabbdabbcbdbdcbbbbabcaababdccbdddcdabcdabcbabbbabbcddcbaaaabbabcdaddabacdbddbadaccddbdbbcacbbaaabaabaacbbbadabcbddaddbbaddcaabcccccaccdbbcdadbccdacccbbbddcdbdbcccdadababccbdaaaccdaacdacaacdbddbddbbbacaaabacbdbadaddcdddaadadaaddbcbccdddbbcaaacbdcaabadbaccaacbcbcdbcdcaadcdaaabdcbadaddddbbcdacdcbdbbabbadadaddaaadbacabdadaacbcdbdacdbddbadbbadcbcaccbacadaabcacbcdabaaabbcbaccabaccbadbadbbabcadbbcacacbbcbcadbaddbddccacbbdcddabadcdabdcdaabbddbbbbcddddccdaddadccabddddbbcbabcabacbdcdcabcccadbbdbbabcdadddbacacacdabddbcdddcacaacaaaaccccacabddcabbababccbcdbcabdbddadadbabdbdbbdbabbdacccbccaaccddccacbdabbbcacbcaabddccbcaccaccdadabcdadbbccadabadadaccdbccacdbdbdccaababbaaccbaaccbbacbcddacabdacabdddaaaadcacbdaaaadbbdaabccbdcabbdccddcbbcbcbcbbadccbdcddbbcbdacbbcdbdadcdcdbaaadaaadaaadbddcacdcabaaaacadbdcbaacacdcbababaacdbcbcdcbcaddbdcccbbbcbcacacacdbdcacdbcbdaadcbcaadcdbcbdbcdaddbbbccabccabcbabaadddaddcbaacacabaadcbdddaaaaabbdabdbbddcbdacdbbaadbddcdcdadbdbabdbacabcdaadcdacaadbcbccdabbbccbcdabbdcacbcabbbcdcbdbbcbaddbacbbcdbaccbcdadbdcadbdbacbdccaaaadbaaaabdccbcabcbbbdbaadbbdaddadcabcdbbbbbcadcdababcdcbdccbbcbcabddbaddaacdaaabbcbbdbccbbaabacbbddaccdadabbcaaacbacbccbbbccccbacacadcbdcaaacacadbcadadbbdcdddadbbcdddaadcccabacdbdcbdcccbdaaccbabbabdadabdbccdcaabdcadbdabcbaaacdcddbbcbbcaadddcbacccccabbbaabbcdacaadaddadbacccacbccbddacddbbbcaaccadbcddbadbaaabddcbadbcbdcabdadcdabadbbbcdcadcccbbcdacddbadcacbacbabdbadbabdcaccdabbccacaddcabbabbabcabcccacdcaaadadaabcbcbadabcccbaabdacbcccabcabcdcaadbcbbdacabdccdbdadbddcadbaddbaaddcddbdadbaccdbabbdbbbddacdbdcadbcdcbdadadcbbadbdddaaccbbbbbacbaabdddcccaacccbabadbdbdaacaadabdadccadaaaaadbaadcbcbdabdaacabbabbabaabdcccdabcdabaabbbdddabbcdddbbbabcbbacbdabdcaddcbcdcadcddbdaabadbbbdabdbccdcdddacbbcbccbaaddacabbdcaccacdcaadcbcbccbaacadddacbcababacbbdbcbabdabadbcccdaddbdcbcbbbcaabacbaccbbdcbaccabdaaaccdccddaaadaaaaacbadcdcabcababbaacbcbbdcaddadcacabcdddcdabdbdddbdabadddabadadbacdadcdabdbcbaddcbbccbccbbacabdddbdcadbabbdaaadcdacabcbddddadabdaaadaddbabaccdacaadacdddbcacaadcadacaadbdcaacbbabacbcbdadaabbccdbbcabdbbbcdbccbddaccabcdcadbbbdadcadddddabcaacabacbacccaccbdccbabcdcdcdcaababbacabddaaccccbcdcaaabcdbcdbaddcbccbddacddbbacccdcbcadbcdbbcdbddacbcbbabdaccdbdbadacbbaadabbdcdabbbcaabbcbcacdcacdcddcbaaccdabddccbddbbcaabbabbdaababdadadbcaaadaccbbadcbddaddcadabbdcdacabbccccdaddbdaabbcdaadbadacccabdcccadcaccbcccaddacdcdccdbdadabcdbacabdcbcadccabcdccadcdbcbcbbaabbacbcaccaccadaacccacaabbbcddddddbcbcbdcdaaabcbadabbcdabddcddddacbbaaccacababbdccbadbdabdcbdddabdbdbbccdccadcbacabadddbcbcacaabccddcdbcdbaacccbbbdadddabdbdbaccdcbbacccdcbdbacabcacbcdabcccdcddbdcccbcbccaccadcbbbcdbbcccddbdcbabcbcccdcaadcaaaacddaaaddadbcbacabbddddaccddcbbcaaaaaacdccdcadbadabdcabababddbadaadaaabbaacbdcdddbbaacaadcbaddabbaaabacdcbdbacacbbccadcdcbdcbdcadcdbbbadbabbacccbdadcddddaddbadaabcbabddcbbcdabaadacbbcaaaacabadaacbbaddccdbbcdbacdadcdaabbdbaccbaacccdccccbbcdbdaadccbacddcacdadcddbbcacbccdaaabadacdaaabbaabbabcdbaddabacdcaadcdacccdcbbcdacabbdbdcaaddacccababbcbbcddcbacdaacacbdabbbbaadcbcbbcadadbddbccddddcbdccadbddaaabbbcacbabbaacccaccaaadccacbaccaaccabcdabddcacdaacbdbccadaaaadddbacdbaadabdabadcbabdadaadcabbbaacaddcacacccbccdbcdadcbdbacdbbdcaabbababbabcddbdaaabcbdbdadbbdcaadbdddddcbcbcbdcadbadacaddbbbdbcbbbbadbadcabbabcaacaddbcbbbdbdddbaabbcadcaabbccdadacddbcddbbabccddbdcaabbcbadccdcadddbdabaabcbbbdcaaaaccdbbcbcaabbbddadaaabadddabccbacacacdcdcbdddccdbddcdccacdbdcbcadcbccacdcccadcddbacdaadbdacaaccacdaabdccaacaccdcddcbcddaababcdcabddddacaacbcccbcadbabdaddcdbabddcbcadbccdbccaaacbbbccaabcaaaaddbacbaaabccbadacdbddcbaddddccbadddaaadbdcccbccbaadaadbdbacaadabcdbbdcdaaaaaabddbaddcccbabdabcaadbcddabdccddddacacdabccbabdabbddcbddcabcbddcbaaaaaddcdccbcbdddbadbcacbadcaadbabbababdccbdbacbcdacbbccbabcbddbcacdadaadbadbabccadbdaacdacbcabcbaaaccdcdbbacbabbcadaccdcdbcbddcddcacacadbacddbcdbcaadbabacdcadbbccaabbcbdaccdadbddcbbcaacddbdcddabddadbadcbaabcbddbbcaccccacdddbacbdbddddbdadbadaccdbdbbbcadbcccadccbdabbcadbcadcdaaddbbdcadbaccbcddcabdcadaacacbcdbbcadddddaabdacacaacbcaabcbacbbddadcdadcbcbbccbdbbdcdabdbdaaabbcbbbacdaadabdcadabdaacaacccdcdbaadbaccbcdcbdbddaadcdbdadaddcbbddddacbadadcbadbdadcbaddbddbcabbabaababbbbdbbdacdcadcabdcdcacdcabaaddccbaccacccbdddaddddcdcadabbaddddddbdabdcbdccdabdddaccbadadbddddbdbbcbcdadaccacbbabbdabadaacabdbaddddbdbdabcccddabbacbaacddbcdaaadddaadcdadaacbbccadccaadadcbbdaabbacdbbbbadbadacabadacaaddcadcdacccadccdabdbcddbbaababdadacbcdcdcaddbdacaaababcddabcdcdaabaccbbbbbabddddcbbdadccaaadcbbcddbadbdbabbacbabccaaccaabbbcbcdaaacdbcddbdddbadadacbaabaaadcdcaadcdcdcabcabdbaaabaabaacddaddbacdbaccadcadbadcacdbaacddcdadadccdddbdbcbbccccdabbaacabbdbbccdddadccdacdcbbadbadcbccabacdcdacbbaddccccdcddabdbcbacddcaccdbdbbadbcbcbaabbddbdbccdcabadacbdddcbabdcadbabdcdddcabccbcbabacdcacbdbaabdacccacbbbaaaaddbbdccdccabdbbbacbbbabdcddcadcbbadbcacbdddaaacacdcdccbdabcadbadbaabcbddaadabacbbcbbabcddabbddcdcbddbdcdabdbbcdcbcbacacdbcdbcdccdcdccdbccdcbcaabdacbbbbdddcbbaaddadccddabccdbdbdbddaadbaaacddccdabddaadadabacbdccdaccbbdcdadcaaabdaabcdaddbcbbadadabcbccaaddacbacdbadcadcdddacdabcdaadcadcddcabdbcdcbcbbdbddaabbacddcbadbaaccdbdbdcdcdbadcccaadccdccddbdadaaaaaccdcbcbaadadaddcaaaacccbcbdbdbacbbdadbbcbdacbbddaadacaaadabcdacdccadbbdaddadddcbbddcaacacacdabbaddabdcdaadcaadaddadadabcadaababdabcabdbbdccdcbbdbccabdaacbbabddddbbcdddcadcdccbdcbbdbcbbdbacbdcdddcdadadabaddccadabdcabbabcdbcacbcccbabbdcacbdbadddaabcbcadbcbcdbdaddbacabcddabcdbdccabdcbdaccadcaadbcccdcdccabddcdbaddcdabcddaccdbbdbaaddbabbdabcadaadbadaadadaddaabdccbbccdacabcbacbdbcccbbcddadadbbcadbacdbbdcdaabcacdbdcaabbabdbabcdcbcbbbbabdabbbaaddaacddabdddababcddccacdcbddcadabdabcacbbcddbadaacbbbbcaacadacaddacaddbdcdbaccdbcddaacaabacadccabbbcabdadbdaaaaaaaaadacdbcdcbbcdbdaabaaccdbbdbdbabbdcbbcaaabbcdaaabdcbcbabddadbbaaadbbcdaddddabaaadbbbccddbcadcdcbadbbcbcadcaabcbccabbaccdbbdacbbbbabdbadcadabddcbaaadaaaaadadcccaabcacaabccbaabccddacaaddbbabadbddcbdbdddacdacbdabbabacbddbaadaaccbabbbcbacbcbabcaacdbbdaccdbcaccbbccccdcabddaacccbccdacacacbaddbccdaacacacccacbdacbacbdbdaaaaddadddacccdabadbcdcdaadddbcaadaabcdccdcbbdcbbbbbbbabadadadbccddcabcccadbdadaccdddbdccbbcabdccbddddabacaddbaadacbabdbccbcddbbdbabdaaddddcdcbcbdacadbabdabbaadcdacaddaccdcdccbcadbdbdaccbcdddabdabbdbaadddbdccdccbcadaabcabbcdababcdbbccddaddaaacbadaaddadccdabacabcccbabbdabccaaccdacdaddabbcabbbaddadbbdbbdddcbbabcbcbaddddcadacbbdcacaabddaddcacdacbbabbdcbbcadadabbbbbcdcdaadddbcbbaacbbaadbbcbbbdcdadcdadabacdcbdbbdcacabadbccadbbbbadabaaadacdbcaadaababbbdacbcabdbbadaabcbccdcddcaabbacdadddbbbcdbabaabbdbabcdddabbbdadbbdcddacababccaddaaddadddcccdddbdbddccdbbbddbdacdaaddcdabbadadbaaaabadcbcccdadbacdccabcadaddcabdbcdcddabcbacbdbcadbbccdaaaacbadccdabdddaaaadbcdbcdbbddadddaaaddcabadaabddbddbbcdbbdbbbaaadabbbbddbcdbbddbcccadbbacdccdbcacdcdcbabcbacccaddbcbdabdccddbadbcccabccddcbcbcddacaacacabdcdcdaadbdadcbdabcbbddbddabdddddbcccaccdadaadbdaddacbcbacabaacdcddbacabadbcbabbcbacccdcdabbdaadddbdbadabccdabdbdcdbdddcacacbdacabdacbbadbaccacaadabcdbaddddbcabdadbddaaddabdcaaaaacabaadbaadaccbdbccadcdcdbdadaadabcbcacbadcbdbbadbdacdcdcbcdbdbabaabdcadcdddddcbdacbcddaacbcccbadcdddaadabbdadadbdbddbacbcbddabddbacaabcabbcbabbcdcdcadcbacaacdcdbacbbbcdbadabadccaccaccbdcbaacccbacbaccdaacdacbadbbdddaabbcddcdaabdcdddcbdcdacbcabcdcdccbadaaaacaaaaaaacdcbbdacbcdddaaacbbadaadbccbcadbaaadbbbccdbacbabccddcaacaabaddbdccbcddcaacdcacccbbbdcbdbadbaaaaddababbdccbdccadcacdcccbabdbccddccddbdddbdbdaccdccccdcbbabdbaaccadaaddadaaccadbcdacdadbbccbcdacbccadcbadccbdaccbcacaacdddaddbaaaaadccadcdbbccbccaddbcbbbbbaaadbbddadacdaadbcbcdbababbaabddaaacdccccdacdccbdbdaaadaabadbbddbdaccaababdcbcbccbdbbccbbdcdbccdabbddccdbccdbddcdbadcccabbdcccdbbcabacadbcabbacdbacbbdadccbadacbacdaaacbacbbabbbbbdacbdbcbadbbdcdccddbacacdcadabccdccdacdcddbbdaacbabcacbdbcdbcdbcdaddbdcccbdddbbbcacdccdcdddacbbdaacccdbbcbcabcdabdbabbbaaaadcdcadadaaabaabbadddbbbcabdabdabbabdbdbdbdabadddaaddcabdbaddbbcaacaccdbabccdaabcadcddcadbadddcdcacddacabbdddadcddadcdddddccdcacbdbacdcababccdbbdabbaacaacdbbdcabcaaacbbbabdabbcabadcddbcaabddaaaacdbdddacbcdabaadbcbbaccbcdddadbdcacdccabbabdbddcddccbacbdaaacacdadcbadbdbaddcccbcdcbaccacbaaabdacdbbdcbddcadaccdaabcbabcaaaaaccbcabbacccbabadbdcddabdabdbccccbdaaddbdabccdcdcbbccaccdabaabababccbdbdbcaaccabdcbbcbbadbdcdaaccaabcadcacbabdaabbcaabcdcccadddadbdccddadbcbdacddcaabcbabcbccddaabdbdcdcaadcdabdcbcdcdacdaaddabaadacadbacabcadacdccccdbacacacaadbaacddbcbacbadcadbccbcaaacccdcbbacbbcaddcaddaaaabbdbaccacccadaadddcdddcdccbdabdabdaccbdabbabdaccabdcdcacddbaccaccbabbcddccbbaddbdacdbaabdccdcabdddbabbcdacbccbdcbbccdbcabdbbabbcbcdbdaadbcdcdcbdbcccbacddbdbdacbbaddcbdadcdcaaaaadacddaacbabdbdadacacbdcaabcdcbbdadbdcaacdbdcabdcabccaaadbcccabdccdccbbccaaccddaaadadaadbdcccbdbbbaadbcabaacbbbdacaddbbbdbcdbaabddaaacbacbdbbbdcddcaacdbacbccacabbddadbaacdbbddcbdcababdcbdababdbaccddcddcdddbdaaacabdcbdcaddbcbaddddabbccabcaabaacacbddcccabaabacadcaacacaddbdbbcdaccccaaaddacacdaabacdbcdcbaaaaacdaddacddbdccbbbaaabcadcdadddcbccdcdaaabcdcadabababbbbcdcdbacdbbbaadcbabccddcbcbcdabcbbadbdbbdcbadadbdabcadddadaacbbacbaadcaccbbbdddadbacbbddacbbaccadbdddcddcaddaabbcaccbdcaadddcaddacbcabdadaaddababddccabbbccdbbcddbcdbbdcdbcddccbdcacacbbdbbbccabbababcbaadabbdabacddbcdbabbcdcbaabbdbbccccbabdababcccbbbdaadaabdbccccdaaaaccdddcabbdbbdabbabaaabcbdadadcdbaaaccccbbbabacaadbdbbadbadcbcabbdbccbbddbabaaccabaadabbcabdbbcaabbbdcbbddacaddcdaacbddbddabacddbdaaacbbacccdbabaacbcbdccabaaddbbabddbdaddadcdbddabbbbddaacccdcabdbabdbaccbcdbbcaacbdbcbbacaccaddbdcabbdabaadcacbcdccbcdddaabbbdaabadadcdbcbbdccbabbbcdccbadcacdbcacacbcbddbddcabbdcadcaccbbabcaadcdbabbacbbdbcccccbcacaabadacbcccbabbbbcccbcabcbaabbabccbabdbadcbdbdbabcababbcbabaadddadadbaaacdbddcdbcdacdcccadaabaaabadbbcbdacacabdddbdcaddccacaccdaaabdaadabcbadcdadcaddbdaddcbdcacdbacddcddcaaddaccccbcbdbcdcbbadacbddaccbabdcbdcaccadddcbcdcaddaacacbcddaddbdacbbbcbbdcaabdacdcaabacdcddaccaddcdababddaadcccdddccbdddbaacbdbcccacaacdbcbbbaddcccddbddabcdbdcacdcabdbccaabdcacdbbdbdcadabccbbbdddcccdcdaaccabcadacaacbdccaacbbbdccccbdbcbdabcaadbbdaccabbdbccacbbdccabadacaaacaadcdbcbbdccbbabadacccdbccaaaddbbcbbcdbbdcabcdbdbbacdadcabdbaddbcdcadbcbababdcddacacbddcbbcdadcbaadabbaddbabacdccaddaadbbbaadababdbacbccbcdacddcbabcbdadadccaaabacddbabcdacaabcaacdacadddcbbbdbabaacabcacdaccdddbbbbddcbacbdadcdcbadcbdcddbcdbadccabccaabcbbabdccaddabdddadadacbdcabadabbbaaccdadcaadadcabbccbdcdaadcbadacdddabdcaddcbddbccdcddbbadaacbbdddbccaaddbcbdbccdbdadcdccbabacbcbbacbcdccadcacadcccccbddabacdadbddddcbaaacdbdbddabdcbcbacabdadcbbcddddccaadbbbdacabbacadcadbbacdacccdcababadaadacccadaddadcdbdacdbccddcaccddbaadcbddaabadbaddbbaccacbbdcbcadadbcaadcdacbdcacbdbabccabbdcdbbaadadaadccdadbbcbcabcdcdcdbbcadaddadcdccbadbacbcccdcccdbdcbccbadbbcddacdcdbaabbbadbdbbadcbcaababbbcabdbadcaadcaabaddaccaddacacaadcddbcdddadababcdacdcbbcadaddbcdbbbaadcdddccbbccddbaddaacbcdaaacddbabdadcaddadcabbabdcbcacdddaabadbbcbacbbdbbabaadadbabddacacddddbcccbbdcbbabacacadcdcbccbaabbdacaabbbdcbdababcdabbccbacabadbbbacbbccaacacadbabadaaaaabdbbccacbddbdddcadcaaaddabbacdaadbadbdaaadabccabdadddbacdcdcdadccaacaccbabdcbbaaabbbddcabcbabcadddcabdadcacbccabaaabbbdabcacaabdaadddcaacbacdacbbcaaacddcbbcabdbbccaacbbddabbbbbbddadbddacbddbbcadcabbddbcbbddcabccabaadbabadcdcacdddbdcbdaadcadaddacaadcabddbacadcdcddacddddcbabdbbdaaadbdadcbdbaadbcaddcddbdaabdbcabcadbbaaccaadcabcaddbddaaccbcdabadaccdddaabaccabbcdddcadaaaaadccddbcadcddadbddcadbdaabcadaaadcaacbadbacbdabaccbcddaddcbacbbbcadbcddbcdccdcccbbadcddbadbbbcaaaabcadbdccbdcbcbabdbaabbccdbcabcababbacacbbacdbbdacbcdaadccdccabdaccbbdcdddadcaabcacdcccccaccbcdaabcbabadbaaaadcdaaacacaacbddbbaddaccacabdcacbadcadabcabbdbcdcdbbabddbcbdccbccddadabdacbcdbbbaabbaddbaacbcabaddddcabbddbdbcacdadababbcabcabbbabcdbdbcccdacdbcbbdcdccdcdcacbdaacabaddcdcaababdcccaaddbaaadacddacccdaaadacbacababbbaaadcdbdccabcbdcdbdcdababdbadddbaacbdadacadbdabdbcabcbadbabbcbdbcdcbdbaadcddcadbbcddacbdcddadcbaddabbcbddadcbdadadadcaadcacbbbcaadabcbccccbdddcccacbaaaddbbcdbccadcdddbbbdcacdbabcbbacbaaabadaaadbbaabcddcadcccbaaacbcadbcabccbbbccbabbdcccdbaccababdddabdabbddbabbccacdbddbababccaabaabddcbcdddbccacacadabdabddbadabaaadccdbdbdaaadcdcacbccbadabbbbddaadbdcbcdaabdaccabddbdcbccdadaabadbcadddabcabbddcaccccbdcdcbbdccdaaaaccbcdbdacbdacbcadcbbabddcccbbadcdccabcaaccdcbbbdadbcaccdcbdbbddbcdabadbbaaacdadcbadcbbabcbdadadccdcabdbbaaabdacabaacddabdaccbcbdbdacbbcdccdaadbaaabaddabbbadabdbccdcccacaccabadbbdcadbcccabbbaaabbabbbbbaabdbdbbdcbcbbbdaabcabcdbadcdbcacdbcacadcdddbbbccddacaaabddcadbbdbbcdcdcadbabddcdbbdacbbdabacbccacabacccdcdadbdbddcdbddcccdaacabdcadbbbaddabccbcdccbcdcbadaabcdadbaabbcdcdaddcbaaaccaabddaabbbbcddccbaabdcdbbcdcaaaabbdadabbadacbcbbcaadbdbdccabcaabdddbacacbddaacdadadaabbdbbaadaccbdaccbbdccccbcdbbbaabcaaadccaadcbadcccadbaaaabcbdbabaabccbbbaddadbdddadbbabbaabcbdacdcdcacbbdbddcaababdcbbcccddadaabadcdacdcddbbadddbabddadbdcababacddabbcdabdbddccadadccbddccdcdadbdcabbcdcaaaacccadcdaaaacbcbddcdcbdadbdaacbbcdccbcdabcaabcccdbdcdaacdaacbcbbcddbabbdaabbdcbbcdbdbcabcbccdddbabcabdcbacccdbacacdbaacdbdbdddaddabccbbbcbdddcbdcacbaacaaabbadcbababcbcdacbabbacdbcacbbcdccdaaabbbbaddbdabbaadababcacadcabbbbccddaaddccbdccaaaaaadacdbaabbdbabadcccdcaaabdccacdccaddcaddabbabddbacbbcdcabcabcbdbdbaaaacadcbdbcbbbbbbdaacacabaabaabcaaacbdbcacbaaccccacabcddbadcbcbaaaaccadabccdbadbcadbdacacbbcddabcabbddbbcdbcaddbdddacdbdacdcaccadaaddcacadcdbccaabaddabadddaddbbaadcadccadabdcbbbaaadadcaabcadabdcbacbccadcbaacbcaccccacbdbcdacdabcccabdbaacaadccbadaaaadbaabdcbcdbaaaddbbabbddcdcacbbacbbdabbcdabcaaaadacdaddcabbacbdacbdbbdcdaabbddaaababbbdbacabacbcbaaaaaabdcbadbbbdcbccaccdadcddcdbbbadbccbddbbbacdcdbbdbcaacddacdbabcacdcdaccdaacddbcdbaabbcbaacbcdbdbacdbccbdbbacbdcddacbcdddadcddbabdbaaaacbcacdcddacadcdaddcdbdacadddacdccaaccbddaacdbcacbcbcbbdcbbcccaddbadacbdbddccdccaaddcdddbadabaacadcccdaaacababcccbacbbddbaaacbbccaacdccadadbcccdadbddbcdabcadbcdacdcccddacddadaddbaacdbccddbddacbddbcadcaaacaaacbccddaccbbbccdbacdbcccaaccdcaadaaabaadcbcdaddcbccdcadcccbdababcadabdcbbcbcbadaccdbaaaaddadabbcdcbdcabdbdaabcacbcdadbcbdaccbbbdbbcdcaacbdbdbdbcadbaddadadcdbbbbcccaccddacccaacddbcdddccbbdacbaddddbbbccabbaadcbbdcdaaaaddbbbbcabcbcbcdaaadbcacdccdabbcbccbdabbacddcbbcdaaaabdbaccbbbdddbbcacdcabaaccbabbaabbbaacaabcccacdcccccccddaccbcacadacdadbaaabbbcddaaddabbdcdbdbabbbbbabacabcabacdcbcbcaabaaabdbcbdadaddbdaddddbcdccbadbdabbacbddbdcccababbadcbddcacacacddcdcbccabcbcbcabcaccaaaccadccbaddcbaccdcbddbcccdcadddaccabddbdcaaaabacbccddbdddbcdbcbaddaaaddadcacdaaddccbbbcaccddacbbddcaadcddccddacccacbddaccccdbccbcdbbbaabbadccddacabdbaaacaaaadabbbacaacccbadbacacaacdadbbcadcaaacabdccabcbacbadbdccadacaddaacbbdbbddbabbddcacddbdbadccbcdcdbbcbbccbbadbdbbabdbbcdaaccbcbbbdcadcbdcddbccdcaabdddccdbcbacbdbddadbabbbdabcdbdbdbdabbcbdadabbccbdbdabadcabcbcdaacabdacccddababbcdbcccacaccddaaabdbbddbccbcbacbdacdaacdcdabdabdadaaaddbcdabdcacdcdaaabbbddccbdcdabbaabcababdbcabadcccdcbbcbabaadaabadbdbbcbdcaacdbdaddaccbdccbbdbadabbbabbaabbacddcbcbaddadcbcccbbabbbaadbcdddacdadaccbbbaacbdbdccaaadbdbcbbbdccbcdcdcababdbaaacabbbacacabcdaddbdcdbaababcccbadaaddcdbdcaadcdcdabaaccdbbdbcbcdbabcdbccdbdacbcadaacdcbccabdddbcbcbdabdcbcbbcdbabadcbaccdbcbcdcbcbbcadcccadcbcccdaddccadbcabcaaaaddcacccdabbcbcbdbaacdbabbabaccdcdbbacddddcccdadcbccbbadadccaacddcddadbadcdaacbcccabcbdbddccbbdbaacbdcddbccbdccbaabaabaadbdaabccbdbaacabacdbadcbbbbacbabcbacddacadcabdcbbcabbbadbcdcaabccacccbbdaccacaaaabcacddddababcdbdbbbddbbabdccdbbcdbdababdcadabacdcdbaadaccdaabbacacdcacbbbabcddbcddcabaaddddaaadcbacccbaaabcbbcacdaabbaccddbbbcadddabbbabcddbddacbdbbadbbbaddccbccbcadacacababbdbdcbabbccabcdbccccdddbabbdcdcddbdccacbbdcbbdabdcbcaccaacaabbbbbaadccaccbbdccbabcdcaddabddcaddbccaabdcdbbbcabdcdbcdcccabcadadaccacdabcaaacddbbbbaaaacadcdbccbbccdccbaaccbcabdbbdadbbcdddcbcdcddbbccdbbbbbddbccaabdcdcabcaddddcadacdadbabaaacdcbadccdddbaaaaadadbbbdccdbdcbddbdadddacacdadcabddccacdbacaaaababcdcddbbacaacdadcabdaaadbbaccadabccdcdccdccaccbdddbbadaabbdbabccacabddbbcbdacddbcdabdadadabcbdaddcbdaaacbaabcabbacccacdaadccccbdcbbbbabccababbaccdaabdbabbbcaacdccacddccdccbcabdddbbdccbaabacbababcbdbcdcbbadcbdaacdbbabccbaabcccaddaacdabacbcacbacbaaabdadacddcdbcbcdccccddcddbbcbdbbdacdbdcbbdbdbacdcdbaccbcbdadbbddacddbcdadabbdcdbccbdcbbbababaadaaaabbcdacdacacabbcbddbdcdccabcdcbcabbadaabcbcccbabccddaacabaadddcdadddbcddabdcdbdbbbacbdddbcbbbdbacbbbbdbbdaacaacaaacdcdaaccaabbcdddcbddaccbbcbdcbbbcbaaadccacbbcbbdccbcdbadccdbdadbcdbddbcdcdcbabdddddddcdcbadccbbddccbddabcdaadaacacddcbccddbcdadcccbcdcabdcbbdbbbbdbddcdbdcdcbcddabaaddddbcadaacaacaccdbdcacdbdadcacdadabaabcaccbdadbcccbbccbadcdcddbbabdbbddbdadcbcdcccbbddbadbabadaabcaaababaccdadbbdccbbbddaacdcbbadddabacbabcdcdbabbcbcccabbdbacccdcaccadbcbbbcadbadcabaabbabadbbbaadcadbbcbbbbdccdadbbccacdccbabacabbdbdccccbdbdcbcccaadaccbbdccbbadbdcdacaadaccbdaddcacbdcddadddcbbccbcddaaacaddcddaababbabddadcddbdacdbbdccdcdccbbbacabacdaacbdaabcbccddcdcdcccadcbbcbbbaddbbaabcaacbbcdbadbddcddbbabccacaddccbabaaadcdababbddbdcbbdaacbdbaadbcbdcabddaddaadcaaaabbbbbaadcbabdbcabddadcbdcacabaacdcdbdabbbdbddabbaccdacdbddcadaabddbbcdcccbbacdcbaaaabbbbbcdbbbbbcdcadcabacddcacbbcddccccbbaccbdabaacadbccdadbdcaadbbadbabcaaddccaddadccbaccacaddadaacaacccbbcccbbdbdcccadabadacabbbabbabcaabaadbbccddcdcacdbdbcadcdaabdcccbdbbbdcadabdbadbaddcdcdcdaccaabdbdcdbabacadbbcdabaadcabddccbadcabacabbbdcdbcacdddcccaddcbbacbcadbdcdacdcbcddcccabdcdcbdaccacabadbacccadbadbbcbccdaaababaadcbcacbcbbabcbddcbadbbbcbcdbdddcaaabaadadddbbaccadbaababbacdadaddcbdbaccbbdacbaccacdabcdbdddabdcccadcbdbcccddbccdbdccacddccdcaaccbdcabaaccdcadcadddbdbddbcdcccabbbaaddacbadcdbdadbdcbaddabccbcacbcbacbbddcdbbbadbabcdabadcdbbbbacdbbdcbdddbdbcdbaabddbcddaccbbdaabdabadbacdddabdbcacdbdbdcbaadcbddcbdbcccabcadcbaddcbaccbcadbabbbabdccbdaaabbacdccbddbdcababadaccacbcaadadbccabdcaccdbcabcbcddcccabbaccadaaadbaccacacbddbdbcdddadbccccbacbbccbcabdacdbabddadcdadacdaaabbdadddddabcddcaddcaacbbcadabadcdccaadbdcbcaaadbbacabdcacaaccdbadacddbcbbaaccaaaadbcabdcbbdacaaacaadbabbabddbadbbbcabccbbcbbabccdbabdbcabacdacaadcdaacacdcabbbacbdaaddbaccbdcbacbaddcbcabdcbbdacbdbadbaaddcdbacbacdadcbaabbaabcbcaccddddbaddcaaaddccdadbcbccabbddccccccdcbdaccccbcaabcbabddbbbccacacbaacdddddaaacccdbcbdcdccbabdcadccccbbddbadbababbbaddadabdddcaccadcabbcacddcacdadabdbdcaccbcbdddaaddabccdacbdbcccbcdbbdcbcaccbbccbabdadcbdcbccdbbbadbddcdaaaaccddcccaabbddbcababbadbcddccadabdbccadcacddccbccabdaacccaaabcbccdbbdbccabbbbdcabccdccdabbaaaccbadddbaabcdbccdccdbcacbaaacbccdbadaccabdbacacabcdcddbbccadcabbcaaccdcbdbacbddaddcbacadacaaacccaaabadddcddcdddcdcbadcbaaabbaacacddbbbcddbbbaaabadabaccdbbaccdbcdddabdbbcaadacaacbaadaddbdadcdccdddacdbaaadbbcabbbbabcdddccadacddcacbcccaaadbabcaddbababdcadbbccbaaccaccaacabcacacabbccdaabbddbdadbdaacdadadadcbddcbddabbacddaccdcaaadcdddddbadbacbabddbbaaaadbaadcadccdccdcbbcabddbbabbddbcdbbbcbbbadabaccbbbccbbaddcdcbbcccbacabddaddbbbadbacadcdabcbccaddbbaadcbaadbcccbadaabaacddaacccaaabacdccbcacaabbcabcacddbaaddaddbbcdbdccadadcbdcacabcbcbacdcdbcccccddabbbaaabbbcbdbddccabbbaccddacdbccacbdaadcacaadbcabddaabcbaaaccccccabbbcdacdbbbdddbdbbbacaaaacdddababcaadacdcddaaabacddbccbdcbaacdadadbabbcdabbdaaabbbcdbccdadcaabbddccdddcdcabbbdbbccbaacdaddbbcbdcbcaaabbcabacdcabcbbccdcdbabbcbcddcbdbacdcbbcadbdabcacbabdbbdcdccbcdababbdbdbaaddcbaadcabbacdaadddcaaabbddabcaadbaccbbbcbbaabddbdcddbcbcdabdcdbcdacccadbdbaadbccdcbbccddabddcabddbabbbaadcbbdcacabdacbbaaaacabcccaabdcbcdadabacdcdcaddbdbcbacbbaaacabddbddaaccbbccbadcccabcbadcdbcadbcacacacbaabbadccaccdcabcabbdcacdabcbabbacabdcddcbdcacdbdbddbacdcbcbbccddcabdcaccbbacaabbadbdbddbbdbcabbdababcbbcdbdabddddadaddbacacccddcbabbaabaccacbccccdcccdbbaabdbdadddaaadcabbcbcbcbdacacadbacccbadccdbddbacbadbbdccbdbcbccadadcddbcdccaccaccdabdacddaacabcacbddccbbabccdbbdcaaabdbddacaacacaddcadabddbacdbbaacdbbaaadbbaabdcbcdbadbcacdbaadacbbdabacddabdbbdbccbaddbdadbbadabdbabaaaabdcaccdddcbbdccaaccaabdaacddddbaacbdabbabbdacbbadbabccaadbaccbdccdbdaddaabacdacddccbbbaccbcadbccacadbdabcacddcdaddabccacbbabddbcabbbcdacbbcadabbcbdcabcbbadadbcbcdccbddcddcdddaaabbbdbcbccbcddbbcbadaccabcacadabdbcdaabddccdccadabcdbcbdcaaccccabcaccbadcdbbbcbaddddadabcbbcacdcacdcbddbcccababcdacbdbdcddaadcbdaddbbdabaacbaaccdbcbbbcbbacdbdbdaaacdacdbadaadabbdaddaccadcabdbdadbabaababbacadddbaddacccdddaacdcbaadcdbddccdbcdadcddcdccacaacadcbdccdcddccadaccaccccabbdabbbbdccbadababbaddbadacababacaccbaabbbcbaaccdbdabcbccbaadbcbaddccacdddddbddcaacbbaabacaccddbbccdbdcdcbadbbaacaddaabacdbbaccdbdbcbbdadbddddabdccdcbbaabdbbbadbcbbccdaabcccbcbaccbaaccbacbbadadadcdcbcabaabcddacbaccabcdcabdabcdadaddcbbcdabdabbdaabcdbccddacbcbadaacaabadbbcbabcccddbcaadaddaccadaabacdabdcdcbcdcbabddbadbacbbacdbcacaddbadcadbbbabdbaaabaddcdbcaabcdadbcaacddcbbdddaddaddcbaaaccdbddbbbbccddadacabdcbaaabdaadabdbdaaabbbacdaddabbcacaabdbcdcbbacbddcdcdbcdabbdcabaaccaacaadccdcbcdbcccddddbabddbbddcaddccdcbaddbaddbbdbdbabdcaaaadccdbabadacbdbbcbbcabbbdadbbcdcacdcbbdcdaaadbcbcdccdbbdcacccbdcbbcddbbddccbdbbdbccabbddcccadcbcbbcbaaddaccbcaacbcbadccccabacbcaaccbdaadacbcadcbadbcaacccadcbccdddabadbdacaacbaabbddbdabcabbccbabcbdccaabdddcabcadbabcdcbcdbadbcabccccbbbbbddcabacadabbbbbccacbcbdbbcddabaddcdbacbbdacdbcbdaadbbbadaccbccccaccbdbaddddbaadbdbabcdcadbcacbdbdadcacdaadcccddbbccadddaddabdbdaaabadbddcbacdacabadcabcaadddacbcdbccacbdcddabacdabcdcbaabddcccabdcbacaaadacdabddbbbdacdbbabbcadcabcbdcadcbbbbddaacccdabacddabadbdcdccccabbbcdabdbabcbdccbdddbdbbccacaaaabdbacaacacddcccbacbcbaddcdadadcbbabccacbadccaddccadbbbcbcadbadbaadbcacdbadaabacaaddaaccbbaacddbddbdbccabddacaacbccdbaaacbcabdaaaacdddcaaacaaaabadacccdbdddbabddccddcbacdbaccddcbacbddcdbabadbdbcdcbbdcddaacdaacadcacadbbcccadcaabdccadadcdccaadddcabdcbbacddbcaacccdcdaababadcbdbdadcbacabcbccddbdccbabdbcbbdcdbcbccbdbabbbaadabccdcbaccdbcccabbaadaaddabcbaacaaccaccbcadbcbcbabacdbbaacabbaccacdbddacbbcabddcbdddcaadbbabcddbddcacbdaacccaacbdaddaababaacbcbacabcabcadbcaddccdcddacacdccbdbcaddabadbaabbdbcdbddaaacdaacacdcbdadddbbabcccdacacbcaabdaabadcbdbcdccaddadaabaddbdbbccddbbdbdccccbdccabdcacdaccbbcaddccaadadbabccbccddcdcadaabbbbbacbadcbabcdccdbcbbdddddccadacbbabaaababbcaacccbabddbdadadbacacdaccadccacccdbaaacadddacdacbcddcbdddddbccdabdabaadccdaddabcbacbacbdddccddaabdbdcadbacbdcdaccadadbccadadbadadaacdcbabdaabcbcbdbdaccbcdcadccdcbaabdcbdbbcaddbbabadcdcccbbcbaacddbdcbcbbbabccbaabcbcdddccaabbbcaacadbdbcdacbdddcddccdbbcaaabcadbdccacaadcabdbcbaaadadabdacdbddbdddbcbaaabdaddbdbdbdcbcdaaccddadcdccabdcdabaccdcdcccaadccbbdcbadacbcddbddcdbccaadcbabbbddaabccccaabadcbdbccddddacbcddbcbddcddcddcdddcacdaacddbdadccdacbcbcadddbcddaccdaddbcdbbcdacabddbadadabdcddcadddbababcccaabbddadbaaccccbddbdcadddaccaddcdbbabcccdbcccbbcaaaacbbbbbaddbadcdbcddbdadddccdbabcdcccdbaaadcdcdbbccccdcabccddcadcddbcddcdacbdacdddbbcbbddddcdddddcdcccdccdbcdabcacadbccbdaadabbadaccbcbabcbcddabdbbdddcccccddadcdabccdbcaabccbddcacbbcbbadacadddcadacddabcdabbcbabdabcbaaacaddcddadaaaabdcbcdabbbbaccbddadbbcbaadbbbcdbdbaaaadaaaababcdbbcddccdddddcbdddcdddcdcdabdaaacccddaaaadbbbcdadbacdbaccbacdcabdcbacdddaddaddcbdcdbaacccdddaadddcddabbcbddaaabcaabdbbbaabbcccadcbdbdbbcacbcaddddadaaadcabbdababaabaadcccaaddcaaaddbbcdaaadcadbccdaddbbabbbcdbcadcabbcbcbbbdcdabbacbdbdbddbbcbcddcbabbbdabcabbddadcaacccaacbbabddbcabadababbdbcbcabcadbcbadaacaccbbaddadbacabbadcdbabdadbcaddacdcabacbddcdabaacadbdacdabcdccbdadadbadbddbbadaaddaccdadcbbddacdddbbdccdacdadbabaadbdadaabbbdcccaacdabbbabacddadbdbdbddaadcbdbbaacdacdabdccaaacabbacccaacdddaccccbadbabdbabaaacdddbbcdaadaaddbabaccbaddddcbadddaabaccaacdacacccbabdbcddaaabdccbbcbddcbdabcdcababccbbbabcbacadadadddbbccbdbbaabaaadabbbccacdcccccdaccdaabbdabadcdbcddaaddadadbddddddacbbdaabcddbdbcbdaacdbccabdccbbbaddacdadcccabaaadcbcacbaddbabcccbbbabbdccbdacbcabbcdbcadcdaacaacccddbbadacbabbdccbdaddcbdabadadccdadacadaadcacdbcdbdbbaaadaccbdaacbbabbbabbcdabadccddbaaccacdaddbcccbbdbadcccaddaacdabbcddccacdcadacacabcadaabaabdbcbddcacbbbcbaacadcddcdddadbcdbccaccabaabccdaabcddaadbdacbdadbbdacbbdccddbbdbddbdcaacdbddbaccbcccdabbbbcacccabcdadbcadbbdcaccdddddcacbcadcbbdbdccabbdbccbcbadbaacbacdbbaababdcbbaaadbccabdddbbcccbccaccdcdcbcaddbddbaacacabdcadbcacddbccdacddcdbbbdadbbbadcbbdbcbdabbdcabdaccabbcadbccbacabcaccdbbbaadbbbccaaddcddcbbdbabddbcdbaaadcadadbdddaaacbdcbdabbccdbbcdcaadbcdcbaccddaddabdadbdadaccbdacacdbabddcdddabbadbcbdcadadacbabbcadcacaadbdddcaccdbaabbdaccccaadcbaadaabdaadcabacdcbcbdbaddacddbcbbadbaddadabbdbbdccabaaddbccbabacacacaadcbcabcdaacddcbdaddcacccddaacddabcdadadddbdadacdaadababddadbdadcddcdbdcccdbadbdcdcdbdcabccdabbdbbbcdbcaacdaacdbbaaccadcccddccacdbbcbbbcdbaaacbadaabccccaabacadcdccbcabdbbddccccaadbacadacddbcadbdddddcddcadbcbaadbbdcdbadbadbaacbdaccdcaaaadbbabdddbadccacccacbabbdcdabdcbddabdcabacbcbddbacabcabcabbabdcacaaaaadbcdabdddcdcabacbcdabdabbcdcdbcadabcdbbdbbaccbbcbcaacbdacddaccbadbcddbabcaacbbbdadccddbcccbddcacaacddbdaaabcbccdaaacddbcbaabcadddaccdadcbaabacdcddbbdbbccbdddabcbdcabddadcbcadaadbbcbaadcdabaaacdacbdbcadbbacabcbbcabcdacadaabdbadbadccdaddcaccabdabcbcdbccbdaadccaacbdbbbdaccabbdcaaddadbbacdadddcbdaccaddbcbdccadbdbcdbaacdbbbdaaabaccadcddccbccbdccbacbbbadbdbccddaacadabacdbbbbbaadbcbdccadcadcccdbbcbcabbcdcddbddbadbadacbbbbddbbcacaacbbadacdccaabadddbcbbdbdadcadaacdaddadadcaddbabddbacbbcbcacccadaadaccdacddcddccaaadabcdcdaaaaacaccaadddcbbabaaababdcbccdabcbabacddababdbbabcdaaaaddcdbbdabcccbbacccddcacbcbbabddcbcddaccdcbacaacbcadbdbbbaaddcdddabdaadbcccbbcdcbcacbbcdbdbaacbbbbddaabaaccbabcccbddbcbdbacbaaaddbdadaaadcbddcabadcbcaadacabdccdbdaddddaabbbdbbdcbbcbbcabaabacaccddbbddbdabacdccbacdddbbadbcaadababdbadcddbaccabdcbddcbdacbcbadaacdabaaaccbdadbddcccbdbbdadcdcdbbdbadddbdabccdbbababdacacabcbdbcdbdccadcbdabdbcaccaaadabaabcdbbdadcdbadaacdbaccbbddbbbbbabbbbbcaccabcbbabcaccdaaccdabbaddccbdadbabcccabcabbdaacbddacddbdadcababaddbdcccdcdbadcdbacbaacdacdacaabacabbadabcddcccccccabcabccaccaabbddbcdbbbadbaaacddcbbaadbdbaabbdbbbacdddbcddaccdaaddbbaddcbaccaccaadbddabbabdaacdadcdcdcddcdacdaacddcbcdcbdadddcdbcaddabbdadddabccbadbcbdbdbcaababbadbccabbaabaccaadcbabdbacddccbabddbcbdbcccadbbbdbcbbbdcbdaadcabbadbacabbacddcccbcccbababcbdcdccbdacbcabaccddcadddadcacacaabbabaaababddaacccbadacdbabcacddcddcbaccbccaccbdcabbbabcabbbaacbbcaccdbacabbabacbacbdacbdacaababbcbacdbcadadbbcdddbcacdddcbdaabbcbadbabababaddadadcaaadbaaadbaababcaaadcaccdcdcbadabccddaddccadbcbbacadcabbabadcdacbabdcbdbcbabbdcbdbcdcbabaccbdcabbcadcddaacccbaaacbabdadbccddddcaabcdadcddccdaabdadcababcdaaadbbddcbdddcdaccdccabdbcccdbdcadaacaaddbacabaabacbdaabcabbdaacccddaaccaabadbaccbcbbdcacaccddcdcbbddabdbccbdacbcbbaaabbacddccbcbbdcacabbbababdabadadccabcaaabacaddcabbbaabadadbdababbccacacadacadabaabdccadacbccbbcaacdccbdbbccbcbccacaabbdbacabbccaccabacabccccdadcbcacbdaabaccbbadbbcbcabbcadaccbbaadddaabbbbcdbbbadcabacbadabdadadbcdbcbdacbbbdaddbbabbbabbbddaabaacacbadbcbdcccdadccdacdcacabadcaccccabbbcdbdabbaadcdaadadcaaabbadbbccbdcdbdbbbcabdbdbddbbdabdbdabbcadccbbdcbdcdccbaabddbbbddacadddbdddadcdadaccacccbdadcdbacaacbaaddcacabdcaaddadacabdbcdbacadbadcbbcddcbabdbaadadbabdacbdcbddbdcdccdcaadcbcadddddbacdcbdaaddabdccdddcaacaadddbabdcbadcabdbccdacccdcccacdbcbccdccdccadcbdaadddbdbcacdbddacdbdbcddbdccadccdaccacbdccbcababdbbdaadbacddbcacaabcdbaaadaabadadcddbacccabcbdbbbcdddddcdbdcdaaddbabacacadacbabcccbbbcbdcddabdccacdcbbccbdbabdbcddaabdbacbccbaabaaabbcaadbabdcabbdbbcabddcbbddccaaaabcbcabbcddccabbddacaacddddddccdabbadccaaddadddbdbdcaacdcbcbcbbbddcbccbaddcbadacacbacadbabaddcddaabdbddbaddcbddababbddcbbaacaadcaaddccaadcdacabacbdbbabcbcbbcacaabadbbdddccaacbbbcbccacbdbdacbcacacaabddbccbdaddadbbabcaccddcaaccbcbddadbbabbaacbacaacaccddcbabdadbccbdacbdabbbbddadbbbdabbddbddcbdacdacdabcadbaabcddcbbcaabddddcabacbddaadccbaadacbcaacdbbddacacabcbdccdbbacdcaaccccacbcddacbdbadabcdddbabbdbbbaabddaddcccbbccbaabdccacbcdddcdadaabccabcccbaddaccbbcaaddbbddbdbadacbbdbaabdcadaccddcdcdabcadddcdcdcbbadccaddccacbbabdccdaacddccdbbadbccddcbdbacbdbcdbcdadddadabaccdcdddabcbcdbbacdccbbacabacabacbadcddcdbaaadbbaaccccacbbbaaccddcbdbdabbdbdaabcbacbbabdcdcabccddbcdbbddacacdcccacdcacdcadccdcaaddcdbbbbacbabcbaccbdbacbbbaadbabddaaacdaaccdccacccccbabbdcacddcdadbbabacadbadbcbbacddacadbbcbadaacdadacaaacbbbbdadabacccbcbbadcccaacadbdabdaddcaadbbddcbadacbaddbbbbaddcbacbcbadbccdabacbcbbcbabdcddbdbcddccbdbdbaccdbaabccaacacabcdadbddabbcdaacdbcdcdccccddcdabddbbcbbdbaadddbdddbabbdaacababbdbccdbccdddbaaaccbbbcaccbabaabacbcacabadcdcccadddbabcadcbdbccccdcbcddccadccbdabdcdabdcacdacabcabbdcdbdcbbadcdabbcacaccdacababcaccacdbbacaaccdddacddacadddcbccbcbbbbddbcacbddbbdccaadcbadddabaabdaadacdadbbdadccadcddccabbabdcbcbcadaccbcdcbdacacaabbcccbbaccbbbbbcbccdcacbbbadcbadacaacbcdbaabddaabbdbbdababbcadbbabacbccaabdcacddccbcdbdcddacacbcbababbbcddccbcacccaabdbcaaaddcdbcabdbaccadcbcacabddbacadcadcadadbbbdabcccbbcccdcacdbcabadbdddcccdccabcacbdbcabbdbccccbcabaddcccbaaadccbaabdbacdbdddabbdbbcccccbdcccacbdcdcccbaddbbabcadbadcadabacadacdbdcaababccaddacabcdccbbcbadcbdacbaacbccbcaddaabbbbdddcbbcdcaadbaddbbcaadababdabdbacbbbddcdddabdbcbccaaacdbcaaccaddcdccdbbcdbdbdbcdbabcaabadbcaaadbbcbadcadbadcdcddcaacdcdbdacbddaabdadacdbdaccbaabadcaababcacacbcadaacbbcbabcbbdbabcabdbccaddaadbbbcdaabababbbbbdddccdcddcadbdcaaacabadaddbcadaabbbbbddabcccaadabccbcacaccdbccbbacbccddaabbabcadcabddcbbbdbbacaaacdadaaadbacdacddbadaabbaacbabbadabcdcdcabcbacabbadaaccddacbcadbaababccbaabbcbcbadcbcbdcbdbdccdbcaccacdbbcbcadcccbcbccbaaabdaacdcadbdbdaadbbaabccccaadbbacabbccdacdbbdcdabdbbcbcbacccbaabbcbadadaaccdadbdadacddcabdccdbaaabbbaabbdcbcddbcacdaddacdbcbdccbccccbccbddacdcdddbbdbdddddbbdacadccdcdbbdcdbddbabbbaacdacddddbadcbcaabdddcddbcacdbaabaddaccacdbabdcdabddcbaadacbddbbdbbcbbabbbcbcaaadddbddaaaccbccddacaaaaabcdcacbaaaabadbcccddccbbabcabbcdaddcabddccbaacbaababaddcdcdcaaaadcdbddbcdacabcbbdadcbaabccadcaaabcbbbcaaccbdcbabcabcacccbdbadbaddcbbbdadcbccaddcabbbcbaadcacaaacdbddcccaabddcddccbacdcbddbbcdccdcbabaccddccbcbbccdcbdacacaddcdcdbcaaacddccddbcdddbabbccbdccdddbacbdcdaaabadcdbbaaccaddcadccbaacabdcaccbdabdadadcdaaadcbdacdbacbbbcbcaccacbdacdabbcaabdaabcaccdcccaaabacbacdbdbbadbddcabbcdbacdcabcadcccdabdccbddabadcadbbcbabddabbadacdbbbabaabddbcdcacddbdcaacacdcddcabdadbcddcdbbcbccabdbcbbdcdabaccaaabaadbbadadbbdbbcaacccccccbccbbdccdbabcbabbdabbadacadbbcdbcbdadaacadccabacbbdbaabdcabcbcdbcdbabdddadbcabbdbabadccbaadbdbbabdbdabbccdcacdcbaadbaadddddbaabdacdcccabdbaacccdaadcadbddcbcbcabddaacadadbcbaaaacdcaccbdbcbddaccabcbdbbcdbabbabbacdbabcacabdbbddcbcdbcbdcbccdddcaaadbddaadadcbdddccbdcacbabcacadbdacdcdddddcbbdccccabcaadbdcabaadbdbaddbdddbabcdaabddcccbdcacdaddaaabcdadbbbdbbbacaddbcaabcbdadbdcacaaccdaccbdaccacaacaabdcdbabbacbbacbaccaababbbcbcbbcddcbdadcbccbaacbadcabdbcdadbaddaaacaabcabbababccabbccacdbabcaddccdadcabcaaadaaccaddaddabdbbbcabbcdbbadabccbaccdbbdbcdcadbcabddcdbdcdcbbaabdacbbabaacbdddacacccbcdbdbbabbbacababddcdbdacbbdddabdaaddbadcaaaacaaaadcdaacabbadcacbbbccacddaccdcddbbbbdbbccccbcddbdcbcbcdbcaccaabbccccdbddbabdbbcacdcabddbcddabacabaddabadacacddbadadadbadacddaaaccdcbcadaabdbcaccdadcbaddcadcbcaabbacdaacbacadddcabcddbbdcbccadccaddbcaaadbbdbbdcbacbabbabbdbbbdcabddcddcdcdabdcbcbbacdccddaadcbbadaacdbaaddaccdbbdaddcdaabaabbcabdaabacbaacccadcbcbbcddaabbdcdbdbdcdabacccbbaabbabdbadcdddacdcaaadddccdbdbcdbbcbaacabdccaacacbadbcdcabaddbbcacccdaccdccbacbddccbbbccdadbaccadbcbbcbadbacdabacbccbacddcddcdbbdabbddcbbbcbcaaabddbaaadcaacdbdddcadbbdbbbacdbcdbadcbcaaabbbabdbaaccbabcabdcdbdabaacbdcddcdbdadabccacdbcdbaddbabddcbbddbddabcabdccbababcdaadbddbdbcadaabbbdcbdbadaadcddbcbdccbbbdbccbabdabbaddddcabbaaccbaadcdcdcadbaaadbdabbdadbdcdcdcaacdbcaddcdcbddabbcdbdcaadaccadbdbacadcacbcccccdbaddcaacdbbdddcbadacbddcbbbbabcccdacdbdbcdccbbbabdcdcbbbaddcacaaaacdadbdbdccdcabccdcdbabcbdcabdcabcdabdbbccbacbbcacabbcbbbbcdacbcbbaabdabaccdddcbdaacdacaccddaacdacdaacdcbacddbabaaaccbccaccadcdacbabbbbcddcabadcbbbddcadccdaadbcdbbdddddacbcdbdcaaaccbacdccdadabdbddcddcaddbbbcbabbbaabdcbcadaddbdddcdccacaccddcdbbccdaadccbabcbccadbadbddbcadcbddcacdcdacbbdcacaadbaabcbdbdddbbbbdbbbadaacdabbcacdabacdbbbbddccbcbaaadddbbbddbaabacbaadaacbddacacccdcbdbbdbddacdddcccdaadcacbabbbdbacdcabccbcccabcbcacaabcdacabacdabcadddcddcaabbbcbacccbcdccabdcabcaddbcaaacadccdcbcadbddacacdbcbdacbcbdcbbbacdadccbbaadcdaaaccbccdcbbabccdcdbaccbaabcdddccabbdbacadadabaabcaccbdacaacbdbaabcbbbbdcabdbbcbcacdbacbdcbdadcdcbacdbdacdccbacddddadcabacbddccdcddcabcbcacccaaddcbabbccdbcbdcbdcadbbdaababbaaabccacaccadccccaabbbdddbcccabadaadccacccbdaacacaaabacaabdcbdddbdcbaccddcaadcadaaacaaabcadbddbbaabadccdcdabdacbbddaadbcdabdbbccdddddccbdcdbaadaccccabcaadbacaccacdbbbaaccdbbaddcdcdbbaccdbbbacaddbbbcdddbcacaaadcbbcbccdcbadbadbdccbcbddaadccaabcdbadcdabaaacaadcdcbacadcbabcaaacddcaabbbdddcbbdcbcddabaadcbbcbbacdddcbdabcaccdcaccbaaabddbddcbdccbcbabddbcaddacabddbcabdaadbbddbccdcacdabbbabcaadccabcaabdaacaacadcddaabddacdcddddcacdbcaccdbabcacdcaccddabddbbbdabccbddbbacdcadbdcccdccccbbcaddadaddcdabcdadbdbacabccacbaaaabbdbcabcddcadbabaaddcccaabbcdbbaacdcdddcbcccaddcacbcabcbccbbcbbbaabaddcccccddbcacbabaccaaabbaddcdadcabbbcbdabaacdbaacaccaddcadccbacbadacddcddbbabbcbddbaaacdbabddabbadabcabaaabdbdbacccdbddbabaaaaabdbdddcbbadcbcaaaadabccdbaabadabcdacaaddacacddbbacddcbacccbcccbadacccdcccbbabdcabcaccccaddacbabdccdbbbcccbadbabcdbabdbbdbccbbacacddaadadbbabbacbbddcdccdbcacabdccbdabbadadcadacacbcaddcddcadadcdcbcbaadbdccbbaaaadaaabaddabcddccabcddbdbccbcadbdddcabccccabcdcbadcbbadadcbacaacadacbbcbaaacbadccdaccacadbbdaacbbbddccabcdddaabdaacaccdadcaddabcbacbcbcccbaccacdddaccbacddddbdabcbabcaaabbaddbabbbcaacaadbdadcdbaaaddbbbbabacddccabcbccbdababacaddabdbdccaacadbdbdbcbdddaaaadbdadacdabdbcaacdbcbacdcacccbdadbbddaabdabbddbcddbacdcddbcbcddbdcdcabcacdaadaddabcadbcccacccdcacbbacadbbaaccbacdccdacbcbaabcacdabccabdddaabdaacbdaccdaaacabcbbcbbadccaacdbabdbdbccbdccabbcccdbbaaadacbacadadddcadbbbbbadbddcbbddcbbdabbbabcabcbacadbcdcadadbbcccbccdbbddcbaaaabdaacbacdbdddcbdbbadadadcdbbbbcbdaccbbbaddcabcdaacadcacaccdabbdacbbdcbdadadbcdabacacacdbdacbdbdbdbdcabbabddcdacadbdaaacaaabbddcbcbdaaadbacacaddaaaabdaadbabcdacdccccddccacbdcaaabbbdcdbccbcbabddadcbcdaabaaddaacabcbbddddddccdbcbbdbbcbcdccbbbacabddddaabbdbdadadddabdaccddddaaacdddbdacaaacccdcdabbcdbabbacacbdadaddcbabaddddbcbaacadaaacbdbaabcadabccaadddadccdabcddcccbbbadccbabadcdbbdcccabcbbcaabaaabaccbcaccbaadbcdcccdddbccdcdddadcdadacddaadcddcbdadacdbccccbcdbaacbcdcaabccdcbbddadabcaababcdccacaccadcbcadcdbdacaadbcccabacabdbdbbabbddcacadcacccdcabadcaccaacabdbcaaaaacdbdcbbbabadaabbdddbadaccbbdcabdabdbdbbdbabaaabcccdbbdcbbddbcdcacadcdcaaaadadbbbccadbbdcabaabcbabcdbaacaadadaaadcbdbbbcbadadccdddcbcdaddaabaaabbdbbddbcacdcdbbcbbbbacdbaaabbcbabdcadbabbcbcdccaaacaacddbdcaadadbdadaddcdadccadddbaddaaccdbdbbcbbccbdddacaacccccabbddaadabdddbcdbcddcdbcdabdadaaddbadcadcbbaacbaaccbdacbdccaaaaacabababddbacdadcbccbbbcddcddaccdccdaaadbcacbccdddccdcbadcbddcdbdbcbdbdaadacbabddcabccbcaacbdbdacadbcaddcbadccbccaadcdbcdbadabbabcccaddcbacddadaabccccbaabdabcbbbaaddbdadddadabdbddaddbaaccbcaccdcadcdabadbcbdaadcbcacadaddabcabddbabbdbbcbcdcbbcdcddcbbdabddacdbaddcadaabcddddacacbcbaacdcccbddcbccaaaaabbccddaccabdbbdbdbdbaadaaaadbacdaddddbcdccbaabdbdddbcdacdcadabcadbbaabbaccbacdcacccdddbbcbbccdbaaadadddbbcdcdabcdbbabddcacbcbbdabdaacbdbadbcbbaababcbcaababbddbcbacdcccccabcdaaaaadabcdabdbbacadcbbdaabbdbbcaacccddacaacdcdbaaccdaabcabaacaabcccbacdababacadbdbacdccbcccbbdbcbddddaacacbcbcdcbdddcadcbddadbbdddddcdaaaacdabababcadbbbcddddbadbcccbcdbacaaccbdabbdaddcdabbdbdacdccdbabdcbcbbbcbcbccaacbbabbdaaacddbbbadbccbdaaddbbbccdacaaabcbdaadaadccabaacdbaccddbcbdaadcdbaddbdcdbdabacbaacdaabccccaacaddccdabcaacbddccbcdcddcbaabddddbdccbbabcbcacddddbaccbcaadccddbdadccccbbbdbccdabbabcbbdadaaadacdacadaadaccdaaccbabcaaccdacddbabccbdbbbcdacabddaccdcaddcbcaaabcbcadcaacadaccadbddcacabdbadcbadcacdabacccdcbcccdabaaacbcdbabbbcbdabccadaddbcbaaabaabcaccbbbbbcdaabbdcdcdcccadabccaadcbcbcaaccbcbbddaaccbacbccaabbcadcadccbddbdbaddcaadabcbcdabbdaccabbbddaccbdcdcacbbbbaacaddbbbacbddabddbaadbadbbcdcaabadbadddbddabbdcdcaaddcabbbbcbdaccbdbddbaccacbdabaacbdadbacdadacbadbbbdbbbacabddaacbabdbdddcdbdcaddbbdcbaccdcdbdaddddbccdbdbabbaacdddbabbddddbabdcbabccdcbcdcadabaaaacbcbadaabdcacccaacccbdaacaccbabcdcababbaacadcdcdacacddbdabbbdacabdbcbaccabdbcabbbdbbbbccddabbcabdcdaabaaaadcddabbdbabbaacbcadddabcbddddbbdbccadabccdadccdcdbaacadaabacbdbddcdcdbcdabbacbbdbadaddccccabbbacadcdbbbbadadcbcacaadaccacdaadadadacdbadabdcbdaddababdaaaaaaadbdbdaddcdcdcdaaccdbdabdbbbcccdbbaadccdcabdabcccadcccbdaddaaddabbbddadddaaabacdadbbbaabbcdcbdcaaddaaaaabbbbbdccddcdccddccddcbaaabdbdadbaabdbdccbaabbdbbbdcbbcddbdcbabacbdabddccdbcccdbbcbabcbadcdbbcccdabadabadddbaaaabcdbbcdaabacccbdacdbbcddbddaaaaaccbadabdcacbbdbcbaadccbbcacaababbbbdcabdadadcccaabbddcaaadddbcadbadcbcacbdbcbbaccccccabbbdddbddcccbacbbcdcddadadacccddaaacdabdddacadbdccdbbbbdbbbbbbdbcccbcbcdbcadadddcbbcdadccbcaacaadcabadabdadadcbacdaabcaaadabcabdddcdcadcabbaddbdbcdbacaadbbdadacbcdcbdacadaacdbaccbbdbccdbacccbbaddddabadbdbddbbbddbabcbddcddaaccaddcabddaaddaccdbddbbbcadbbccababaacdbdacdaadaddccddbdbbdbaadcaccbdbaccdbcdbdcacdabcadddabbcddbbbadbdddccddaabaaabcadbbabbbbbdcbdbacbccbdbadbbcbcabccacbcccdccbcaaccbccaaacbadcdcaccabbdbaabbcacdcccdbbdadcdccbbdddbbcabcacddacbcbaddaaadbbdadabcdddccddacccdcabcdcbaddaabbcacbcacaacbadbdcdbbaadaadccaaadbcdcdbbcbdcdbcdbadabdadbbcacaadbbcdcacdbaabdcccdbddaccbddcccbbcbcdbaabbdcabbaabdcdbbbcdaddbcaabbccaaaadbddabbbacabcabbbabdcbbbdbcbcaaccadbcaddabbcdddcaadbcbbddbdbcbaaaccbcbaabdbbccaacdcadcdbdadabdcbcaddabdbbabadbacbbdbddbabaabacdbaabaadcbddaaabbdbdabbbaabcdcabddcbddbadccbdcbdcdcaaddccddcdcbadcccdaabccbdccbcabbddadcdccbddccbaadccdbcadccaacccbddadaadcddccbddacccdaadddddbbcdacaaddadbddadbcadbaaddddbadaaddccbacacbbdcddacdbbcdbcabddbabbaabacbaccabbcbbadaabdabaaadcdaaadababadaabbcccbbaccddbdddbccadadcccaabdcacbacddcacccbacacbbcbcabcddddadcadbaaababddbdcdbbddbaaddbddcddbdaadbbdaacabbdbbdbcaabdaddabadbbcbdcbdacabcaddbcaddbaddddcdaacbcdbbbacdccbcbddccbadaccdbcbaabdbdbbdaadcdddddbbaabdbbdadccdcbbdadadabaabdddbdcaadaabbbdcdabcabdbabadccdaddcbaabacacdccddaaadcacbbcdacadbaccddcccddabbcabddbbbbbbcccdbbbababadcbaddcdbadbadabbbdaaabddcdcdcaaaddcbdbcdaccaacacbdbaadbcaccbaddaddddbabdbccbcdaddcdcdcaabcddcbabaadabababcbdbbbaacdbdbadcabdbbbbaadaaddabbccdddcdbcdcacadaddaaaddcbcaddcbddcadadaabbbddbbbacaaacddababbccdbcabacaaadcbcbbddbcdbbabcaababcabcacadcbcbddbddbacbccacbddadadcdbadbcbbbabacaccdacccbbdadbcdababcadacddccaaaccdbacdbacabdcdddadddbdbadbcccdbccbadccccbdcdabdccdbbdacbabbdaccbbcaabaaacaabbcdacbdacabbaaddcdcadbcbdaaabcbddbcbdbdabdcbbabdddaddbaacabdbcaddadcddcaababaccadacdaabcddcdabababdbaadcbddadddaabcdbdbcddbadcadcbcddcdbcdbaccabacaddabaddbcacdbcbbacccbcbbbddbdacaccddbcdaddcccdbdcadbdccddcbbadbccdccbacdcaaaccbbbadbaaaadaddacaabddbacbcadacadbbabaabcccabbadbdbbcdbbabadcbddcdacdbcbaccbabdaccbccdabbdaabccabaccabaabcbccdcccdbdbdaccaddbdbdddaacbcccccbdddcdabbacdbdacacdbbdbdbccccbbdbcdcbbbaddcbbbaaacbabacabccdcabbcdadabbbacdabaadccddccccdccbdabbccbcddbadccdcbbaddbcaadbaadbcaccdcdbbcccbbbbdabcdcabaccdbaacddcbbabcbaaadcbbbddacbbabcababcdabcbdcddcabaddbcbcbaaabcccadbddbdacdbabadbaadbaacdaabdccbcacacadbdcbcbcdccadbaabdbbbbbddcabadddaaadcaababbaadcabdadbaacabcadbbaadacabcaadaddabcbdddadbcccdcccddbcabbcdbbaccaabcbbaadbaaabdddacaabbcaabddcccddcbdbbacaabddbccdbdddbbbcbdabbabaddbdbdabdcdadbbabcbccbbdbbbabdbdadacacddddadabcaddcccaabdadabdcbcbcbcbddabadaabbcdcddddadabaacdabbddacdbcaaababaddababbdbabacaacdbdcbcbdadddbbadabbbcdcabacbdaabbbdbddcabdccddddccdbcccdbaacdddaddbacccaabaadbaabbddbdaacbccbadbadabdcabacaddbdbbddabcccabcdacbdaabdbccaddbdabacacdcbadbbcaddccbadddcbccbddbcabdbdbbdbddacdaddbbdcbcdaccabbaaacdccacbcbdacacccbcbbadadcbbbaabdbddabbbdabcdbbacabdcdcadbdaacabbaccaacdcaadabcdddbbccdcbbacbdbdacabccbdbaacadccbaaabbacbcaccddcbdbcabbdbdacadbaabbabbcadddbbaddddddcccadbcddcddcbdaaccbdcbcaddcdacdabcbbabbaccbcbdbcbbcbbbadbcaccadcadbbabaadabdbdcdcabaccaddddcabaddaddcbdaabbadbbbcddcadbbbabdbbbccaabddacbdbccababccdbcaccbabaadcabdacdcacaadacaddcadbbabcbdddddbdacbdcccadbbccaadbaaddccbacbbcccdbdaadaacbbbabaaacdbcabadddaacbcabaadbadacbdabbcccbbdadaaaddcccbaabbbaaabacabbbabdabbdcbcddcdaadbbbcbaccbbcbdcbbbcdcbabdabbdadbdabaddacbaddddddcdadacbcccaaaabcddccdacdaddcacadbdbcbadbdbccddccbbcdababdcabadbdaaccbdddbbcdbaadacbbcadcadbacbaddbbddccadcdacabcdddcddadcbccbbabdcabcddaabdbccbbbccabccdccbddacadcbababbaacdadbbdbaaacccbcddbaadbccdcbdcadccbdcdbbdcbaaddabddbabbdcbbbacadadbbdbbdaadcbcdacbdababbbacabcdadbcbcabdbacacdcaacbdbabaacdbacbcdcccdadccdcabbbdbcbddccaaaaaaddaabbcaacadacbbabdcababaddccccbddcbdaaadcadcdbacbabbacbdddaabddccccabdbdbbdccccadcbdddcadadcdbcabccabcacbbaabdbcddccadbaabbbdbbcababdccaaacadabcadcdbccabddaabdbabbddbdcadbdabcabcadcabbaabcbcddbadaddaddbbaadcdbcbcadbbabdacdcdbcbcbbcdabcddaccccadbaaddbaadadddbaacbacdbcbbdccbbaacaaddbbcdddbaccbcaaddbbdadaaddcaadbcccbdbbbbdcbbbcbcaddddadabacccdadbbaadaccccbabadaddadccabcbbadadccdbddddbcaacabbdbdddcbbacbcabdccdbcababdbbadabcbbddcacccbaadcccddbccbcdbbbabadaadcbdddbbbdcbdaabdcbbbbcdbdcddacbcadddccdacbcddcbacabaaadcabdabdcbaccbaddacdbbaabdbdbdbcbadcabaabddacdccacccbcaccbcccaaccdcddaccacbbcaabaadbbdcdcdbbabaaacaccdaacaacbddcbbcaaadabadadcabaadacacdccdcbcdcbadddbddaddaaaccabdacccbdccdcacaadbccdcdddabbcccbadabacddcadaccacdaadcbabcacbbbacacadbbbdcdddbdadaddbbbccdaabbcccbbabadaaccdabaddadabbbbdabdcdcbdcadcccddbdbddbcadcdcababdabadccadddbadcdcdbbbbbacccabbcbbddbccabccadcacddaabbdbabddadccddaadbaaaaccadbcacdcdbbaacdacdcdaadbccadcbacaacbadadaccccbdbadbcbcbdaaabdcdabbacbcbaabcbccacaadaadabadbaccaccaabbaadacddaabcbccbdbdbdccdbabdbcbbbcacddcbddaaabacbdcacaacdacbadabacccbddbbbbddcbcaadcddaadcaaadacbddacdbcaccdbcccbabaabcddbaadcbabdbcbbbccdbcbdbccbdccaaccacdacdadcadbcbcbdccdabcddddaccbdbbcdbadababcbcdbcadbbdbbaacbcdcdccaaaabadddbcddbaaccbbddcbdcacaabdabbdaabdcbcddaaabacabadbdbbaabbaadcbbcabbcdaacddadbccbcccaadacbddbccddbbaacdcaacabccdcdabbabccaabbdabcaaaadaadcbcbbcddbddabdccccbbddacdccbacddbcdcbcbacbdadadabdacaabcddaaadcabccbdabbabcdbaddababbcbdaaacdbabbdcccabcbccccaadbdbaabadadbbabccbaccaadaddadabadcbddcaccabadcdcbbcaababbabbacbdbbbacdcbdcadaacacbbcaddbabdcdcadbaacbaddababcaabacdbddbcbcbcdbdcbadbdbdcccddcbcaabdcacbddccbdaccdaadbcadaacdadadccccaaababdcdabbdcddcaacaddbddbacbaacadccdacabbcacdbabaabbadabcabccbdabcaababccdaaccdbaadadcbdccdddbcaaadadccbabddbcabbabadbdbcdbaabbacccdbdbdabbccbabbaadacdbdbcaacabbbdbdcaacbdbbbbcbcddcaadcbdaaaacbaadaadccdcabadddddcbcccdcdcbabbcabdbbabbbbccabbccbadbbddbabbdacadcbbdadbdcbacbbcacccddcccddbaadcacacbbddaddaacbdbbaaaccccacddcbaaaddcddacbdabbcdaccbdbdbbdcbaacadccdcaccdcacdcbdcdabacbabdcccddacbbaacdcadcabbcdacbaacdadbdbcddbdcbddbbcadaccabbdcdadcdaaadacddaccdbbbcccbcbcddbcdbcbaacccbadabbdabddacabdcbbbdbddbacbcbbacbbacdbdccbddccadbcddcadbccdabcbcbcdaacdadcbcdbbacbdadcdbbcdadccbdddabacabcadbbcabbcbbcaacbcbbdaabbbcbdbddbcaacacadcbbabbdbacaccbdcacaccbccaccccadcadbdcbaadbcbdddbadccacbcdcabbdcdaddccadcacbbbcddaadbbbcadcababdabbccabccaaabadbabaccdabadbbadbaabcacdbbabaadbcadacabdabbcdccacbacadcbccbaddcbcbdcdddbdbdbcaabddbcbadcbccdcdbddabbcdccdadbbbcbcbbddabcdcdaadadaabadadbccadadacbcbaaabaaccbdabcbdcdaacbbccabaaabdcaccddcabcddacdabdcabcaddabbaabddbccccdcdddcabdbdabaaadaddabbbbbabbddabacdbaddcaadbadacccabccddbcdccaaacbbacabacdbbddacdccbddcaabcacbadcbaabdacdaaacbcbcdcbaccbcaccbccdaccddaaddbbcddbbabaabdbaadccdddcccabaabbaacbbcccababddbacaaaddcddddaaddbcbcdcbcdcababddbbbabbcdccddccbcabbbdddbcdbcbababacbbdadbcaadcdbccdcbdabdbcabcddddadaaacaacddddaababcaddbdbaadbcdcdacccdadcbdaadcadadbdaadabaadddbdabbdcbddbcdbacadbcbcbbcddabaababccdaaddcabcdaaacbddcdabdabdbaddbabcdbddccbbdcbbcadbabbdcdddaabddcbcabcdaaabdccacdaabcadbcdccccbcabdbaccbaaacaacacaddcbbccdbcabaddbbaccddcacacabbbdbdcadbadcabaccbdccbbdcadcbbbaaabbbdacbbcbadabccacbaaaacddabbbdaddbbbaacdacbcaddcdaadabbcdadaccddcbbcdadaddbbacaaaadcccbcadcbababddddbccdaacacbbdababacdaccddcdcbddbcdaccbacadbcbbccadacbbadcdcddadcddadabaccacdddcbddaccddcccabcddbdadadbbcabbabcdadaacbddaaacaabacdbbcdcacadbdcbdcabccabaccdbabbccddacdcbddacbdadcbacccbdbdccccddbbdadcacaddcdbddbbabacbcaddaabbcaccaacdbddbcccdabbdbabbccccaccacccdbacaddbaddcaabcadddadcdbabccbdaadccbbddccbdbbdadcccdcdaadadccddbdbabcaadcccbdcdaaddbcbcbdbcabdcdcbabcbcdcbcacdddaabdcbdacabdcaddcaabacdcdbcbdbcdcbcaddcacbdabbbbdabccaccabbbadaddbbdcddcbacdbbaaccabbccccbaaaccabbccbabdcbddacbadbbadbabdbbcccaabdcbdbbbaaaccadbbddacdccddacdacbdcccddbcacbddbddbbabddcdbadddadadcbcbdaaadbadccbabdcccdcdbbdbdabbaaaddbdbbbdbddddcabbbdddddcbcacabaaaddcbccaaaccadaacbaaccbcccadcbdbbabbdddadbacddadaacdcaccdaaadcdcbcdddbcbddcbdddcbddbbdabacbacbacbcbbdabcddbdaadcbaccbabdbdbcabdbdcabdbaaaabcacacdbaabbabcbdabdaabdbabcdbabbcbdcabaaddbdcdaadbadbaacacbcacacddcbaccaadddcadddbaadaadcaccddacaacbcabcdccbaacadbadccddcbdaadaccacbddadcdcddaaabdbabcdadcdbbaabcbacddabaadbdadaccaddaddbacddddbccbbccbddbddccdcabadcdbbdcbbabcacbbcacdbadabdbadcbdaadadbabcbdcacaaabadaadbdbaacddacddccddaccacbaaaccaccdbcbccaacdaccdbccbcdbbdbbaaccaabdcdaadaacdbcbccaacacaacaaaabdaccbdbaaacabccdbadaaadaccadbdbccdbdaabcddcdbddbbbbbbbdcccccddaadaabcbaabadadcccdccdccdbdbcccadcbaabbaadababccccdabbcbbdacadabcbaccadaddbddcbbaacdacaabdbbbcadcddbbaaaaadddbddccaddaabdadaddacdacbadcccaddadbaacabadbaaacaabcaaccdcbdcbcdabababbacbcdaaacbdbabbbcddacaabaaaabbccacacadabadccacacbaddcbbcabddcdcbacacdabbbbdcacddbacdccbdcccadbbccaacaadbbbacbbccbbcadbbbabaadcdbdbabbcbadddccbaddaabadccabcacdaddabdbadbbbacbddadaaadcdcbbbbdbbcdabdababcccadccbdcdcccdcacbbbacddddababccdbcddbdcdacabbdadbcddcababacbdaaddccdcdadbadbcbbbbbbccbdacbacbdbaaaadcabcbddbaacbcdacacddcbcbdabcaabcddabadbbbabcabaabdadcacdabbbabcabdabddccbbbdcadacdccbbbcabddddccdbcdccadbabbdbdbaadaabcdabcdcabcaddddcabcacacccddcdaaaacabaddbdaabaabcdbabcbbccdcddadbbaccaabcbdcabccabcadabcacabcdacddcaaddaabcaabddcddcbcadbdbaacbdabddadbaccaddccddcbadbdbabddccdbaababcdcbbdcbbdaaaddcdbbcbacbdbabddbdbaadabacadbdbccbabbddaaacbadbdcaababacdcabdcaadbcddbaadccdacddddaaccacaddaccaaddcaddbbdabaaaaacddccbdacaabbacacddbabdbabaadbdbbdccabbdcbdcbdcbdcddddaabbdaccddccadbdccbbdcbbbdaaabacbccdadabbacbbbbdadaabaacccbcdddddbddccadcddacbdbabadcbbccdddbccaddccbadabbdabcbddaadbccabcdcdccdadadacdcdbaabbdcbcdcabaadaddcbdaccbcddcacdabdddcabbddcadccacdadabcadaddbbcaababcbcbacdaaaddddcbbcbcddaacbcdaaaccacddacbdbcaddcacaacdccaababdcacdccbbbccdaadaddcacbaacdccbcacbbbaaabbbdcacabacdaacccdcacaddbcacaadaabcbbcbaacddcaabcacccbbbcaccbcabbdacadcaccbcccabbbbdacaddcbdbaacacadbdacabddabccdcdbdacbbcbbabdddbbddcdccadcdcbdbbcbcdaaddcbbbbbbdacdabaaabbacabcbcdacacddbcddcaddcbcbdcccbbabbbdbdddbbcbcccdbddacacbaccaacadabdadbabcdadbbacbcacdddbccdaaddcabacadbccbbbbcabdaccbcbbdbcccadadacaddbdcddabababddcacdabcbaacbacddccbbcbacbdddbabcbbddcdcbbcdbbacdabccaaddcacbcddadbbabbbcdabccbabcaaadbabbbdadaddddbcbddcbbcddddaadddabadccdaacbdaccdabaaaabdccabcadaabcbadcdbddadacaddacbddbabbbacacbdadbbbbadcbbaacbcaccbbcdbdcdbcddbddccbacaabadcddabbccdbddadadadbabdbcaaabadacddabbcadbdccddbdbbacadddcbaccadcaadcbacbbbbbdcdcbacaadcbcccdcbbdaadccaaccbdbdabccbcdddbbbcaabcaabdbbbdbbbbdcaddbccaddbbaaaabcadbacdccdddababbcdaaabbcaabcbdabcbcabcbacdacddcbbacbcdbcbcaadababddaabdccccbdadabdbadbddddcdabbdcacbabdbddcdcadbccccdacddbcabdcddaacbbbcdcdbcbbadcabdbadbadabbaaaacbdddbcbbddcbadcaadaacdadbaabbdadcbbacabcbcdcbadabccadadbddcadddcccbccabbaadbccccaadbddbabcdddcabdcbdaccccaaddcdbcddcbcacabbadbdbacbadadabcdacdccdaabccdbbbbacdddddbabbdaddcbabcdadaadcdaadcbdaccbddaddddacbdcdbcccaadcbbbcdbaacccdcadcdbbddbacdcccdacadbabdcaadbcbbdcccbaabaabbdadacadadabdbaccdbbdbcabacbcbcdbdbabdadbddcadaddaaacddababccdbaccadccdddbdaacbdbacdddcdddabbcabaabcdddacaacddddbdbbddabbabdacaaccbadccbbcaadabcddbacdadabaacddbaaabbcbcbbbcbacbacaaadbaadbbcaadacbcaabadbdcdaacdcadcbddabacaadbbddcccbdddadabdcacaabdadcbabdabacddccaddaaabddaccbcbbdddbdbbcbdddcddcbbccddcaacdaaddabbbbabbcbcaadddacbadcadbcacdcddbaaacbcbdbaadcadddcccdbcdcdbaabcdcbddccdbdbbcbdcbbadcddddaadacbcddadbbcbdacaabdcbcadbbccabdabcbcdababbcbbcbbdcaccdabdcbcaacabbbdbcbddccadcbcbddcbdbcdaccaadaaaaddbbcccddbddcacdadadbdbccbbaaacacdcbdacddadcacccabbbcdbbcccbbcdacdddabaaadacbbadbddcabcabaacbdcbdddcacbdadacadbbcadadbcacbcccddcbcbcaccbbbddbaadcbbcaaaddddcbcbaccdcdbdaccbdaddcdaaadbdcccbdbadadbbbdccabdaabbbcbacbbbbccbdbcabcacacabcdadcacbcbaadcdcbaccbcadaabcdddbbcdccbbdaabdbadbdcbbdbddbaadddbacddddabaadadbbcbbcbacaaabbadcdcbdddaddacdbbccabbbccdadbbabbdbadabbddbaccdababaaaccbcdbddabdbdcccbcacbccaabbbcbcccdddadddacbdccadbdabddbcaaacbabdbbcbccdbabdabbcdbdcbdcacddaacccdacabdddcbbcdbbbbdbaddccdcacabbbaaacccbbbbcacacdbbcbaabdaadacadbcccacdbddccbdccdaaadabaabcccdcddbaaadcabbbbadbdbdcbdcbccbbcdcbcbdabacbacdabcaddcacdaaaabccbdadaccadabcdbaabcdccabbbadcadacdbbdbbcdaabbacdadbdcacaddbdaabaabbbbcabacadcbdcbadcacccbdccaccadccacbcbcbaccccabddcabbbdddadddbccaccdbddcccdbddacbbcbcbddcabacacbccccadcddbacaacaaccdbaddaaccdbadbdddbcccbdbddaaccddabbccaacdbccddcbdddcbcabbdaacbcbacadbbbcadcbdbcdddbbaaddccbcbccacacabacbdaababacccdbdaadcbcacdacddbcbddddccdbbaabcdcbabdadacadcacdbaddaabbcccbcacaabdcbbdaadacdccadbbcbdddadaadbaccccdccdabcdcabadccbcadccbcbbccbcdacdabccdcdabdcbdcdaabdbabacacbcbddabdadbbccdcdcaabbaadaadccbabacbdcadaabcdacddbabaacbabdaaaacdcbabdbabdcbdcdaaacdcaddcddadcabbbbcdaccadbcacdcdacdabccdabbaaddcabcabbcbbdddbdabbbadddadcddbdcbabcbdbcdcabbdddbddcccbbdacdbcbaadcabbdaaabacaddaadbbbcbdbbadbbdcbbdcdbbbccdadddcbdbcddbddababaaccbaddadcabcdacacdcaaccacddbdabdbcbccbacdcdaaccdbcbadbddbccdadbbabcacabddaddadacaccdccbdddaddbbdacccddacbdbbabbcdccbaabadcbcdaaaaaabcbbdbccdbbbdbabaddcdbbccdbbdabaccabadcaccacdddcaccabcbbbdccaadadaccacbcdbabcdabaabaadddcaaddabbbbaaacdacbbabccabaabccddcccdccccdcdddaabbbccccdbadcacbaccddccddcbacabcbdaadccbdddddbbbadcdacbbbbabccbadaabdaabddcbabbacbdcdadddbdcbcccaccbadadbcdbaddbacbbbcdaaddacdbbcaccbabcdadabdaacabdacdccbababbacdabddabdcbcaccbbadccbbcdcbcbcacbcbacabcdaccaacaadaababddcadcabadbaabaaacbbdbaccdbdaaddbcbcdcbcbddbcdbddbbdabdabcbcbbaccbbacdbdcbcdaddacdaccddddddacdbccacbbbbabbbddaaabdcbddaacdbbbbdbabbabcdbcbbccaccdcddbdaaccacdaadbabaababcccbccbadabbdccbdacaaaccadadbbcbdcacccbaabcdcdadbcccaabbdabddaadbdbbaddaccbacdcbdcdabdaacaaaaabacccccbdbdccddcccdacbbaccacbcdbcdbacdcacbbdacabccddccbbabcbbbacbccdacbcabccbcadbbddabacbbacadccbbbcddbccdcadcabcdddcddacddbaacbbcbdbcabccdbdddccdddccdabcacdcacbdcccbaccddcdbaddbbddadbcadaccdbdaddcaddcabcaaadbbaababbdbaddcabbcdbdaadabdbacdbbdcbdaacbddbbdabbadaaadcaccbdcbaaddabcbdcdbdcabdcddccaaabbacacccaccbbaadbbbbaababcbdabdcccabaaaccbaddbcbdddabbcbbdddaadadabcacbdbbcbcadabdadcdacbdacdcdbbcddccaaacddcbdbabcbdaccadcbaadbaadbcaccacadcdddaddababdadddcdbbbdbadcccbbacccaddcbbdaddcdbabbbcacadaddcdbbacdccabaaabadcbbaacaabcabacddbdbdcdbbadddbabddcabbccaccadbbabaaaaaacdcbbabadbadbabcdcdabbcaacbcbbdbbacbcabcbacbbbccccbbdcacddacadbdbadacbadcaddbcacbabcadabdccdbdabacaccbcddaddbacccabdadbacaadbdcccabbcbbadcdcbbdabaaddaadbbaccdcbaacddbbbbcabadcadabadcdbbaddccbaaadadcaaddcadacddabdabacaabcbaaadbdbbcbcdbbcccacdacaddcacaabccacbaadcbadbabbddbdbadcabbadaabcddccacddcbcdadcbcdbacdcacabdbaaabcababcdabbcdbadcabbdccbbaacdccdcdabbaabcbbbdccccabbbdacdadaaadacabacbaabdccacaddbbdbbcdadbbadcbccccccabacabcbcddcbccdcaabcdcddbbbaaacacbcacabccdbdcabbbbbddcdbaccdaabbbddcdcdcddccadcdadbadbbcaacdbaabaabcbabdbabacacbbdbccdbccacdccbcbaabbaddbacdcbadcbcdacbbcbbadbaaccbccadabaccabdccbcbadbaccadaddcbccdbbcdadcdacbbbbbbadcdddbcbcabcbdaabcbcdbdbacddaccadcbabdadaaababddadadccddadbcadbadbbcabcbdbbacddbcdadacbcbaacaacddabacbcbaaccccadbbdcbcbcbbdddbdadabdcdddcbbababccddcadaadabcbcdccdbddadaaabbddddddbbdcbbcdaadcadccaadbbacadadcbcaadbcdbddcdccabacbcaabcbcbdddcddcaccaddadbbdbdaaacddaaaaabddaadcdacbbcaacbdbabbbcddaaadbbcdddbddacdadbccbbdcaadacbadabcaabadcadadbcdcdaaadcbccdcbacabddbdaccabaaabaacadcaaddcadaadbcdbadaaaaaaabcdcbbbccdaccaacbcdcaccccddabbddaccbbdddabaddcacbcbddaccbccbaddcdccadcacabbacaaadaadcbddcbddddacdcabdbddcbadbbdcaccacaccddcbaccbcddcdaaabdabcbbcdbbcbbcdcbcccabdcaaaadccbaacaacaadbdccddccbadddddbaaddacacbdcaaccdccacdabadaadcbdcdcdaabdbdbdcddcbccabdbdabdbccbcbcadcbbabacaddbbccdccaacccaddaaacbdbcbbdbaadbadbadababbcbabadabcacabdbdcdbaacbadbcddbadbbaacdabadbdabbcabdcdaccadbbdcdbbbaccdcbdbbaacdaccdadbbddaccdbdadcbacdadccabbabadcabababddadabadbaaabbadacdaadbcbdcbccbacdcdcacaabdccbabccacddcbccbaadbcdccaabadccabadccdadbdadacdabadcbddabbbddaaddadccbdcbccccabdaadacddbadbddaccdcbccaaabbbccaaaacabdaccbbddbaddbddbbcaccdbddaabdcbccaabccddbacababbdadacddddbcdddabddbbbdadaddcdcaacdadbddbccdddcaadbccdaabbdcadbcddaddbcdbcdabbbaccabdccaadbdbacdabdbdddbabdacbbadbaadadbcbbcdcdbcadbdcbabaaaaacaddcaacbdcdbbbdcadabaabdcdbdaccaaccabbbdcbaddcaccddbdbcdadddbbcbcdbbbdbacacaacaadcdacaacddccacbbdcabbbcdddddbccadbcddcdbcbbbbdbadacadcbcbdaabcabcbbdabdbbdaabbcaccaababababdaccabacdbcdaccacdcbadabbddbadcacdacdababdbccbaddcccadbdcabddaabcddaddbacdcdbdbbccaacaaacbccaabbbacaaddadbdaccdbabaaaaabcbbadbccabadadbcbcccabdbbcadbbabbabbbcbcbacbccdcbccaddabdbcdbcabbbdcdabaaacadaccccccaacdbbaaadcdacbbbababbdaccaccbdbabbdbdddcbcbabcacbcdabccaacdbbbdaaacdadcdaadbdacaddbcbcbacaadabaddaabdccbbdcdcaccaaddddbcccbddabcdaccddcdcdadaaadbadbddcbdbdddbbaacdbbadbcadbdbcdaadaabdaddcbbcaabacbdcccbdccbccdbbaabdabbaadabbaabacdabddacdcbabbccabdccbbadaccababdabadccabdaabcdccbbcaddaacbcbdcbabdaccbabbbcbdbdddcadcbcbacbbabacabdaaabcadcccccbcabdbdbaabdcbaabddaabbcaaaabdcbcaaaaaaaaddbcadaadcbbbacdbcaadbcdcdccdcdaabbbaabbaccbbdbbcabbcddbdaacdaacbacbdaccacaabcdbcdbdbcbdbddbaadababdbbcbdacbbcdabdbbabacddacaaddddddddbdcdbddbaadaacccdadcbcbcaccaaccddabccbaabcaabcaddbccdcaccbdbabacabccacacbacbdcbcdaaccdccdbdadaaabbbccbddaaacccbdccccccaabccdcdbcbdbaadbbdbadbbabadbdbdbaaadaaacbdddbcadbaabbacdbaaacccdacccddbbcadcabdacdbbdbaadbaccabbbdbcadcbbcbcbdcaddbabdaaaddabacddcdbddbcbabccaabbcaabbcdbcbccdabdaddbabddcbcbddadcaaacabcbabbcaaacbbbddbcacbcdbabbcbccddbbdcdaabdbcabcadadaadabacbcacbcccabaacbcdbdabdcddbddacdcbcbbcbccbdbbcadadaadabbbaccccabbbbdcaccacdabdbaccabdcdaddbbbcacccddbacdbbaaadbcbadbddbdcbccccbcbbdddbdbaacbcbcabbbcdacbdadacbcadaadbcbbdcabddddadbccdcbcbacccdccdabadcacbdcbbaabacdbadcbbadadddcdcbaaaabdddddcaababddddaabbacdcccadadcccaacccdbaababbacccbcbadbdabddccbacbdabdddababbcacaaaadbcbbcabdcbdddaaaccbcadcaadccdbadbdcaaaaaaabcbdbabbbaccabcabcadbbcbbadbacbdccdabcbadbbadbdaacaabbacbcbcbadaccccadabcabdcdbdbcddbcbacdbbccbbdcdacabcdcdcbadadacadacddbcbdcaadbaccaccddabcaaadddaaaadcabcbddaaccbccdcacdcccaaacdddadcddbdabbaaabaccdbdbcbdaddbdccbcdadbdcacdaddbacbcabcdbaabcdbabbaccaccccdbbcbabccbddcdbbcddbdadcacbbccdbdbdbcdaabbacbabbdbbbccccabbdcbccababacadbcbbabcaddcaaddcddbccccdbdacdcdbaadccddbddacdcdcbcaabbacbdaccacbbdbdddbaccbdcddcdbbabbbcbcabddaddbabdaaaccbbadbbcbdcadaadccabcbbadcbcbdbbccbcbdbaaccdacbcdcddcdaabaabdbcaddabcdabbdacbbdcbdccabcacbdcabadbddcccadbbdcbdabdcdaaacadcbaaacbbcbbacdbbbcabdcdccabcaddadaadcbdaaacabcbbcbdbcbaaababcbcaabaacdcbaddddbbcbbacbcbccbbadbddbaaacbaaddbcaaabddcccacbbbcbdccabccabddcbbaaadbbcbabbddcbabacdacaadddaabcdbcacaacababdcddcdddbcbddaaaadccabddccaccdcabbddccacbbcccbbbdaabadccbadbbadadaaaadccbddcbccbacdcabdaadbbbabbbddbbdaccccaabcbbddcbcdaaddbbddbccadbaadbdabbcbccacdacdacdcddddcbdccddbbcaccbabbccdbbacbcccdabdddbcdcbaadaacaacaacbccbacacbacdbddbdbacdddcacacbabbdbdbcbbabaccaabbbcdcabdabbdbcdcddadbddbacacdaacabaacadbcadccdcbbddadbbdbddabcddbaadbbdcddbcdabaacbbccbabcaddacdbdccbadcccaabdcdcccbabdbccbabaadbaaaabacccdabbbcdbabbcbacbbaacdabcdbbaabddbbaaadccdddacbadacbaddbdadcaababcdcabbdabcccbabdaaaacbbadcdbbddaacbabddcbaddcbccabdbcdcadbcddbbbbadacadbbcacccaadcbcdbadaaadabccacbadcdacaddacacbccccbcdadcaadccbcaaaacdbdcdaaadbaabbcdbaadbcaabdbdbabcddcbdbdbcaddcdcabbccbbcaaacabdcbabbabacbdacdacdcbaaabddacdbadccabcdccacccababcddacccbcbadbcdbccbddcaccdacdaabbcdbabcddaabddcaacdbcddabbdadcddbdcdacadacacdaacdcbccccccbdbbbddcabccdbddcdbdabcbdccbdddddbbaccddbaabddabacdbadbcabddbcdbcaccbddbddbcbdaaacabddcdcbacddbdbabddcbddddcccdacaadbbbcdcbabaddabcdabbddddcacddbdaabbdccbabcaadaacdaccbdccbbcccccbabcbcbdabddaddbdadadcccbbdaddaadcacdccdddddcddacbbccdaccacdbabbddcaaaccacdcadbaabcbacbabcdadddacadbbcaaaabadadadaadacaadaaadbbaccaaadaddcdccdabcbccabadccacabdacdabbdcccddbbdbaabdabbddcbacbacababccacbabdccdadccbaaaddacbabcbcbccbbbdddaccacdcbddaaddccddbdcaccbacbdadaaddbdcbbdbdccacdbdcadacccdbcabcdcccdbdadccccbdaadabbaadbdddbbbcbbbddbabddccccbdaacabdddabbddcbbdcacacbacdddaacbaabdbaddcababcaacbbcbdcbbbcccdddbcccabbddbcdbddaabdbdcdadbadcaacbbcbcacabbcbadcacbdddaddaacabaccaabbbbaaccaacbddcbdcbcbbdcbaddbdaaaddccccbdbacdcaaaabcccddbbbbccdbbadbadcdadcbaaadcbaacdacabdbabddccdabbbadddccbddcaabccaabbabccbbdbbcddacadccbdbbcbcadccbccdcababbddadcabcbcbbcacadcdcddbcdabddacacdbadabcadbddcabaabcaabdbaacdadcbabdabdacbadcdcaddabdaabdbaababdbabcacaabcdbabaadcbadbbddaaddcabcbddccabdcbcaaadccabdabcdcdbdcbdadcbcbbdccccbcbdaadbbbdaccbacdacaddacaaaddbaabbdcabcdbcbacccccdccddadcababbbaabdaaacacacbcbacacdcaabcdacbaccdacacbbdbaddbadccbadacadaaabdcbdccadcadccbccaddcbbaadccdaddcbdaaadddcdcbddcaaabadcaaddccbacccdddabbbaddccadaccccbccdbaadaacaccdacddacbbacddcdddbcbccdaaddbaacdcddaacbdcaaaabbccdbdacbbcadbdcbdbaaabbbaadbbccaccbddabaacdddcddabdddacddddaabccdabbbcdaccbbbcbdcbbccacabaddacbddabbccabdddddbccdcbcaadcddcdcbabadbaaacabccabcabcdbdbcdcdaabcccbacabacaaddcabaddbbbcbcddcbaabcaaaddaddbabbdaabadaddbcdbcdabcaddcacbcaadbcdccbcdbadddbdaabaaacdddbbcacdaadbcccbdccdadabbcddbddcdadacdcccdadcddbcaacdbbbdabcbcabaabbdbadccabdacacbccdccdbcbaadaddaccccdaddbbcbddacaaacbbcbbdadacbdabbadabcddbddbacccccaabbdcadcdcaabaddccdcababddabbccdbdbdddaddbbcaddddcbdabacbdadaacdcddabddbdbaacabdcbbdaacacaadcdabbadacababaacabcacaccadcccbaaabbdabbaadaddaacdacdbdadababaccbaabcadadccabdaacccabdcabbaccbdbdcdadbcbddadccbabdbdacadbcdccbabaadddcbacadddddddccababdcdaaaadbaacbcadbabcbcacaadbcdddaaaaadaaccdcdcbddabbacbcadbdddadbacbcbbabcbdddccaaaacccdacbbbddaadbbacdacbabdaacdccbaacddcbbdbbcbadbbaabccdaabdcabdbbadddadabddcadbddbcbcdcadddddccabaacccdaababdbcabacdaabbcccaabacddacddcbadcababcbcdaabdbbaacccacdcdcbddcacaabaabddbadabbcacaabbccabddcdbcccbbbaccdccddccacbcacdcdbdccddbadacabdabddddcaabcbbbacdaacacbadcccccdcabcddaccbbacabcdccabaadabbbcbbcadcbbacccbcdbadbbdbdcdaaacdbdcaddbcdbbbdadadbbbbccdddbcbdbbdbaadcdbbcbcacddddcabacccbdadabcabbbcacbdbbabcabbbdbabbadbcbddacbabcccdcdaaaacdcabcbcdbcadbbcadcaacabdcddcddbabddcadadbbcccdacdaadacdadacddaccabcacbcbaccbbcdadaacbddccaabbddabbcbbabbacdaddcdabacccadcccabddabcdcaadaadccbcaacddddcdbadcdbbcaabcddccddacaadbaccbddaddaccdcdcdabccbcccbaddcbdabdaabcdbabdaadddaaddacacdabdcccdbaabbcaaacddcccbbdbcdcbdcdcbdaacdbbbadbcacbdcbaabdacbdadcadbaaaddccbcadcdccaabdbbdbbbccddbaaaabcabcbaacbabbbaacadaaddcdccdabcbacbbbdddabbaddbbaaabdbdcbbbdaacccaddbadaddbadddcbdadbabbdccacdddcdbaabbadbdaaaddcdbaadcbbcdbcaacdbdbdbbbbadaacabbdbcbbcaccadccbbbccdcbadabddcdcbdadadbcccadaddabdcdacbbabadcaaaadddaaddccccbccabaadaccbdcbbaaaadcacdaaaaaabcbbcacabcaabcccdabdbbacddbbdbcccbccccadccababcddddabacdbdababbaccdadaddcbdbbbcbbcadccdabbbdbacbdacaddadbcabccdacbcaabadbdcccccdabcbbaccbadbbbababddacddadbbddacaabcaabcbdbcabdabbbaddbacbaacbaaaaaaabbadbdbacbdbdcbdbdbbacdbabcbbacbbcbbbadcdbbadbbabacbbabbabbdabaccdadcccadbddaababbaaddaaaabcaaadddcdacbbccbabcabbcbcabddddcadbccdcababaabccacdcdcbdadccccbcbcabadacddcdbcdcdadbbcbbadaacaaababdccddcdcdabcbbadbbcbdbaddbcdcbabcccabadadccdadcaccaabdbadacccbabacbcbccbcbddadcbaadabbdabacadbbcdbcbaacdadbdcdcbccadbdcbddbdcacdddbddcccbbbcdaaadcaadbbdcccddcdbbacdcdacdcccccddabcdaaacdaddbcbdabcddbbdcaaddbbcbbdbacabbaacaaccabacbddbbaaaddbaccbcbbbabcdcadabdabcdccbbdbbbbbacadbbdcdadbbacaacadddadcdcdbbdcbdbabcaddcaacacbdacadabacbabbacdbabcbdabbdbddbdabdddaabaacbdbdbcdbacdcdaabbacdcbcbbdadabdcdbaddbaaaccdbcadcadbdcbdbabdcabcabaababdcbccdcdcaddbdbddaccabbdbcddcaabdcdbbdbdaccdababddddbabdcdddcdabcacbccbccccdadaddcbcbbddbccaadabbbaacdcccdaaabcabdddcbaabdcbdabcabbaababccabadadabcacbdddbcaccdcbadcadadbdacadbabdcacadaadabbdbaacbaadadcaabdabbabdcabdcaddcabcdcaabcbdcbaddddcaabbddaacbdaaaaaaaabacdadadadabccaaaabdbbcdbbbdaadbcccaadadacdccdbaaadbbbcbdbbbbccdcaccdcbbccbdcadddddbddbcaabcddaaaccdbbcaaadbbdccbbadcccbaababdbaaabddabaaccacaaaddcdcbdbbdccadaddccdcdcbdabbcabdccaccabcacbabbccadbcbdbccccddbabdbcaacdadcbacabbaadcdabcacbdabccddabbabbbbdacdabdbbbaaacabddccddccaacabdcbadddabcbaababccadabddabdaabbddbccbbcadadaadaccdbddcbccadcaccbaabdbadbdbbadbcaacddbcadbaabcdcaabdadcbddcccacbbbadabcdabdccbbcaacccbacabaccacbbbacaabdbccccbbccabcabcabbbabcaadacccaaddabccabcdccbbdadbccbaaaadbdaabbcadbdbcdacbdcddacaabadaaccbcacadbbdcadaadcadcaddccbbabbcccbddcdacbabbcccaccbdbbcabdbdadaaaccbcbdacdddadcabbaddadbddbdbacbaccbcdbcccdbdbbbbcbbccbdccdcbdbdbcacddaddbcdbdaaccadddcbcbaaabbdcdadaacbacbccbaddddabddabacbabdcacadaabcdccdbdcaccbccabbdccaddabaababbadabcdddddbcbcdcdcddaacdadacbadacbbadbbbacdcdcdabcacccccdbbadcbcdaaddbaccbbaddcccaccccdccdccbcdcdaadaaccbdcbbadbbbcdbddadcdddbcbdbacbdccadaccddbbadbdddcddabcbabcccaadcbdcbcbacbbbbacbdbaccaaddacccabbaacbbbbccddbccddbbbddccbcccaabdaaddaccdbaabccddcdcdabaaacddcbacdddbcadaabdbcdcbcbcbcbbaabdbcacaaccddccbddcdbbbacdcdaaccdcacaddabbdbbddbbbbcbbddccbcaaabcabbadbccbabcbbdcbdcbdabbdabaaabbacbdbbcbbcaccccdbaacdbcdcacccddbcaccadddaccdbbddabbbdaacaaacdddabacbbacddcaaddadbbabcdadddcccbabbadaccdcdbacdddbcabbdbabdcabcabbacabccacaaaaabdbdcadcacbcdaacbaacdadacdbadcbcdbddccbcdaaaddccaababadaccbabbcccaaacbccccabbbbbabdbbdadbdbbddbbabadcabadbdcccbbcbbcbaadadcdccdacbddddbbbaababccacbdcadaaacdbcdbaaadacbbadcccbdcacadbdbadbaacbdbaabcbabaddbdbdccacdbbbaabcbcadaadaacbdccabddcbcdbdadacddaabadcdddacaabbdabbbdcdcacdaddabbddabdacdabdaddabddadcdabaacbdbbacbabbadbdbdccbdabdabdaacccdbcbdcdbaacbccbcdbcabbdacdacbcbabccaadaadbccadaabadcadaddcbcbcbcdaccddddbaadaabcbcabccacdcaadbbbcaadacbbdacddddccbdbbcbcddcacccdbddddaccbabdcdcabadddadacbbdacdbadddddbbccbcbaaacccdcdcdcaaacbabbdaaddbbacbbcaadbcbaaadbddcdddcddbaadccaaddcbddbaabcccabdcbbccaccadccbcddaabbbcaddaacbacabdaabdbbacbacccaaccacbbddcabbbaabbaababddbacbddbadbbbdcbdbbcdbadadaadbacacbacbcbdccddcccbcdbddbcdbdcbbcbcadbbbbdbcaddaadcbdaaadacbaabcadcdbdaaaaabbdabadbdcaadcaddadaabbacbabbabdccddacbcabadbdddcbdbaadbaacdaabbcbbbccaccdbbcabbbcbbbabdacdddcccaadcbacbaacbbbcbdccdabaccccbadcacacddcaaddddbbbaabcdababbcddcaadcabcbcdbcddbdddaaabadddccdcbddbddadcacdbdbdbbbbaacabaaacddadadbaadddcbcacacbdbcaddacdbdbddabaadaaababbccacdbcdabcbbdcdcdcccdaddbddbdbddbdadcccbddaaabdbddcabccbbdcacbaadcdbcbbbabaaccadcdcaaddbdbbacdacdddabcdcdadddbcbacaadbbadcdadaaabcdbdbadadacbabacdbdbabbbcbdcbcbdcdaaddcaacbaaabddaacbbacbdadddccacddacaddcbdbadbbdbdbbabbbcbccdddacbcbcddabccadbdbdbdbdbdcbdcdbdbaadaadadcdcbbcadaaccbbbcccacbbacabcddccccacddbdbbdbaabbabccccaccdcbbdcadabaabccabccaacbdacdaddbddbddcabcbbaaddadcddbcacacbcdbbccbdcbccbaabaadbbbdbcababaddaccbdadcbcaaabbcbcaddddacdaadaaaddbdabbcdbabcaccbdbbdacaaacdbaccdadadbccaadddaaaaaacdcbdbdccbbabcdaccadadbbcdadacbbacaaacdbabbdddcbbdbddcbbcdcccdbbcdcdaadacccaddcbbcbddbdbbdccdbbaaacdcbbbbadbbbbbdadaacccddbdcbccacaacbaaaacaccababacddcacbadabcbaddbadbcdadddcdbbdaaaccadcbbbcbbdcdadaabcddccdccdabdddddadbbcbdbdcabacabbadabddbdbaabccdcadcccdccadccdbaaddaadddbddadadbbbabbcaadbdbbcbbdcbdbccacaddbbbaaacbacabdbaccbcddabbbdccccbbabdbcbcdccddcdacbcbdddcdcdcdbcdcddabdccaddcddcacadacbccddcbdcddaddbddcabadbcdbdddccddcdcdbdadbcacccaaacacdaccbaddbddbbcdacabbbbcdddddccaddcacdddadbbcccbcddcadaaaacdcbbcaacabadbabaddacadaddbcaddbbbbcbbcadddcddabbbaacdccbcbbdcddbbcccaadccbcabbcdcbbdbbdacabbbbaababcacacbbccbaccaccccbdaabacccbddddaccabcabaaabbdbddaabdadbbbccacabbbddbabdbcccbcacabcdbbddccacbacbacdcccdcabcccbcabbaccddbddccadcadcddbdccabadbadcacdccadabaabbbbccddabcabbaaaaaabdbcbbaaadbccbbddccbcdacabbacbdbccbaccadcccaadadbcaccadaaabbdacddbaaadbcacddccccdcaddcabbacdaabbbaadbacacddcdbbdbcadccadbcdabacbbadcdcadbcdbaddcbbbdabbdcbbbcdccabcbdaadaaaadbdabcbabadaacacdcdcdacaccdabbbdbaaabaabccaaababbbcaabccdabababccbbcbacaddcdcadddaaababdcabddbcaddccbdddbbddcdcabccbcddacadabcdcbccdcabdbadaccbacaacdaccccabaaabaaccddccbbcbbdbacabadbbbcbaacbbaddaccacbaacbbabaadbaaaaacbbcbcdbacbcdacacbcaacbbbadadcdbcdbcddaaddcaaddbbbbdddbdbccccddcbadcccdaddbbaccaacacbbccabdaadcadaabbdbabbdabbababbaaccdbacdadaadadddddacbcbabcabdaacadcacabdaadbcbcbdbabaaabbcdcbdaabbdacbbadaccbdbdcddcabdbaccabcdccaaaccbcadbcaabcddbdcaacdbbbdaccddbbddaddadcdbaadbcaadaadcbaaadbaabccccccddabbdcdadadbaaccabbadddabcadcacabacdbdbadbcbacabbdaccbaaaabbcdcbcaabaacddbccccacdbaddaaacbbbacdcbacbaddaabadbbdbcbabccbddccabbabcaaaadadcaddadbdcaddcddbcdcbbaddadadaaabbddddcccbadddcbdbaaadbdbccbcdadcdbcacdcaabcddaddacddacadbdddbdddcdbdaabccabccabcacbccdbbabdbacccbbcabcdabcbcabcadabdbccdcacdadbbbbadabdbccadaccacbccbdcccdcaddaacdaabadcadbabaccdbdbccccabdadaacdabbddbbabaddcdbacadadacababdcdadadcbcaabdabccbbdadaabbbaabdbaabdcbdbdaadccccbaaccdbbcbbcabdacddcbaccabcbabdcbaaaaadddcbdbbcbdcbdddcacdbcccbbaaccbbcbabdababccaaaddcaacbbbbcbccbbdbdcabbbcdbddbabcadaaabacacbbbbccbcbabaadbdbaabbadbaccbcdbbabdccbddacbccbaccdddbdbaabdabdddbadcbbdccddaacacbabbbcdabcaadcacbacaadacadbbdabcaddbaaccdbcbdbbbbdddddbbdcdccbbaadaadabaaaddacbbdddbddccdacaaccaccbbcdbbabcadbddbaabbcacddbdacdaddcdcbadaccaaddcbdaabbccacdcccccdbdbcaacbcaddaaaddacadabccdbddadcacddcdbcaccaaaccdbcddddadbadbadcbacccabaddcadacbdcddbcabdbcbaabccabbbdaddaddabaaacdcddcacbaccbaddbdadbacacdcdbccabcbdabcabaccaabdbacccbbadabbccbaddcadbbadbcbbbbacbcbacddbcaccdacbacdcadaadcabbaddddddddbccbcddaaddcdcccaccdcaccbddcddbadadbcabbadbabcdcbdcaaccaddbcbaaadcbdcdbbabadddabbddacddddcbdababadaddcdbbcdaacbbbcbadcbbbdcaadaacaddcbbcdacdbbdabbbddcacbbbdccbdbbaadaadccacdcccbadbdccaaabdddabadbdbbccbdcaacaccbaaadaadabcbdbbbabcbcbddcadccaacbbbdddbcbbddbadabacbbabdbbaabdcbccddccabcdcdcdbcbdbdbabcbdbdccdcacbcacdacddbbbdcdbbaaadcbbbbccdbaccabdbbdaaaabccdbdcabbacdbabccbdcdcccdbabadddaaccbbcbacabbddacbbbbcabdddabdcdbbddbccbaadcccddccadccbabcdabcdaababacbbabaacdacabbbbbdabddacdccddaccdbbdabdcbddbadbbcbdadcbbbcadcccddbbdabbcccbbcbccbbbddcbabcaaaaacacbdacaabaacadbbcbbddddbadcdacabacbbbcdbdcccdaccdbbcdabaabadabaabbddadacdbdaccbbcbdcacabddabccdcabaadcbdcacdbabbcbacbbdbbbddacbadcaccaaddbbaabaaaaddaaadcaaabaaaaabddaadbbbbaadabdcbcdbdbabdabdbdcdababbcaacdadbbcdbabbddbdcdcbbcdabccccdaadbcbcabcabcbbdcbbdaccccdbddcbdadacdadabdacdbdcbdccbbdcaabacacbaddcdbbaadccbcbadaabbdcacbddcacdaaddbdcbddaccdadddaccaccdaaccbaaaabcbaccddccbaabadbdaaaccbddadaadaaacdbdcdccccbbbdcdadaddbcaadcccbbabaddadbddbbadbcacacddbcadcddcaadcbdaddbabadcdbaddadaadacdacababddbbaacaddbdbaabdbccbdcadaddcbccddcccabdbbccbabbccbdbcbcddbddbabadddbccbdacdbcccadadbabbadabdccbaaddcaaabdbaadaaaccbdbddcaabaabcdcddccbbdbcccbabcadddcabbcdcdbdbaabbadadbccababdcbbacbdddbcaddabcbbccacdadaaddbcbaacbccacdbdadababdcbacdabccadbaabdccbcbdcbcdcdaadcbaddbdaacabaaaacdcdabbdacdbaadacadadcaabcbbddcacdadbbdadbbcdbcabccdbadcacabcbdaccbcddcbaaddaadbbcbaaabbbbddbdbbbddaddbacdcbaabdbddaccdbbacdbdccbdbdadcccacabbbdacdcaabadcbbbdabaccbccbaaaacabcccdddbabcdbdaabdbcddaaaccdddcadacbaabddabcbcacdcadabddcdadbccbacddabdcadcadbbcdbdbaababcaddacacdcbddbddbcaacddacbcadcacdccbdbcabddcabccddcddacccdbdcbcaacabbdbddcccbdbaaccccacbccbcdbbddadcddbcbdbbbcdcdcddcbddbbdabdcbdcddddbabcacddbabadaabdccddaaacdbacdabbaddcccccadaaabbccbcabbbcaadccacaacbbbdcbbabcbddcdbccabcadbddacdbacadccbcaadcbcabdcbcdaadccdbccaaadddddcbdbdbaadccbddbbdddcbabdacacabdcbcaddacaacaacadccddbadccdcbdddacadbdccbaadaaadcccbcdaddacddccaadaacdaddccaaabbaadcbdacbaacbddbbabcbabdbbacadacaacddcacdaccdcdcacdadcdcabcbdabaadaabcaaddabacbdcdddadcccacdcdaccdcdaaccacbcaabbabcbbbdbbacdcaabcbbbdbdddddbadaddabdbdbcccabadcababadcccbcdabdaccabbacadcaabadbcddaadadcbbbdccdaabcaadbddaddbdabcdacdaacbaccbcbbcaaacbcabcbccbaabcddabccaddcadabdcddcdcabcbbcbcbaccabcdddbdaccbaaacddcbcbacddcaabdddbabccabcdababadbcccccccbbcbdbcaababdbdbaaaacbdcbbdddccaddbbbddacabdbcbcddbabbccddcccbdcdcbdbccbbabcaabcacadcacdbbcadacdbddaadaccbdcccabbdbacbdaabbcdadacdddcdcbaddacbbbdbdbcaabcabbddaaccbabcacbdaaacddddcbdbbcbccacbdbcddddcbbabaccbdccbacbcaccdcacbbcddccdddddcacaabdbdcdbdadccccdacbddcacadbdcbacdadbdcadddcababbabbbccaacabdababbcaaabcaababbcdccbdabddddbabddaabdaaddcccbdbaddbabcadbdaaccbadccbcccbdbcaabcdcbaccdcbbcadadacdbdccadababcddacabdcabcbadcbdcbdcbabadbbbdabcdaadabaabaccabbcaaaaabddddddabdbdaadccbccccdcabdcddbdabbacbcbdbddbadddbdaabcabbacaababcaacadcccdcaabdaabababaacdcddabdcdbadbdcadcbdbbdbadabccbadbbaadbccdadabdddaabbcdbabcbdcabccadacbdbacadcabcbdbbcddbbbddcddbdbdbbddddbbdbbaacbbcbccdcbaccaabccadbbdbcabddcbadcdcabaacdcddccbdddbbcadcaddbbcbcadabcadacbbdcdaadcdbcddbbdccbbabbbbacaccadbcddbbdaadabdabdbdaccabcccdcaabbbbcddbaccbcdbadbdadadbccddbacccadcdaacadabdadabbdcbacdaadbcdbaadcbdaaddccaaaabcdabdaccabccbabaccabcbcdadcdbccbcddcadbcbaddbbaddbaccccbdbccbadbdcccbbcddbbcabdabcabdbadbabcdcddbacdcdccbaaccabddbcdcdcbbcccdbbbdacbaccdddbadcacadbaadbbcaaddabbcdacbddbaddcddaacdcabbabdcddbbcdcbddddbdaccdbddbbcdbcbbdaacbaddadbbbbcbbdbaacacccdbbbdbbcaadcbabaacbababaabdaccdaabcccbadbdbcabdbcbdbdacbbddbbccccdaddcaabcccabbbcacdcdacdddcabdbbbcabacaaddbaddadcdbbdccdbbcaaacaddabdbcbdbabbdcabdccccbdbdaacdacaaaadababaabaacbbbadacdaacbcaabddcbccdcdbbdabcddbcccadbcdcabbbdbdacbdaccbccaabccadadcacaaadadaddcdbadbdabaacbcabdadbdbdacdbdabaddcdcbdbccbdcbabbcbcdcbddcbddccabdabddbcdadacddadccaccabbabacdbcaccaadcacdbbddcbbabdbccddcabcbdccbdcdaddaaddcbabacacbcddcddbcadcbccbbbabbaaccdaadbbcbacabaaddcdbddbacdadbbdaaadbbcbbddcccbadcacbdcadcdadbbbbadccccdcccacbcdccacadbcddcaacccacbbbbcadabdabbaaaddccacbdbdcbbbbbdaccbaaabaccdbcddbbcbbbbcbbdbddccbccbdadcbaabcbcddabaadccccbcbdddbaabaacacacccdcdaccacadbbbbbcbdaddacbcbbbdaabaabcddbdbccabbdcdbaadbbaaacbbcadabacdcdacaccaabcbbdcddbaccbbbbbbdccdbbbabbaddccabbcbbddbabccbaacbdddbbaaabbabaccaaacccadbaacdccbdddbbbaaaaabadaccaddadacadabbbadbbbccbbadcbababbbaacbdbbabbdbabcccaacadccdbaaacdcbadaaabadccabbdacddadadbdbbbdccdbcaddacbcdabbbbbaabddcacddaaaabdcccdddadddddabbbdadabacbdaacbadcbaaddadcacddddbcbadababbdcacabdbdabadadaaddaabbdcdaabccaaccdcdcacabdaadcdaaadbddbcbdababdadaccabacaacababaadadcdcbbaaabcbaadabbdbaddbcbbabbbadadcabcbacaabbdacacccddbdbabbcadccadddccdbdadaddccbdccdbbdacbbddcdbacdaaaacaccababbdbccbdcdadadbbbccaaabbbbbadaabcdabcdbaaaacbdcccabddbdbbbdccdccabccbbbbcaacbaaabbcbaadabccdabdbbacabadababacbdbdcccbdcdaaabbadcbdbbbbacbdaccdbaccadcbbbacbabaabdbccaaaababdbbdabaddddcdbbccbaaddcbaddbdbbadaaadbaabaabcaddcdddcdcccbdbdcbdbacccbcacbbbbbcdabcdaabcbdadbbddaacacbbcccbcaddaccdacacaaddbbabdccadcaddcdaddddbdcaddccbbdabaadcaddacdaabbadcdddbabcbdacdabadaadbbaccaabcdaabdbdabdadbabdccdcbaabbbcdaadaacddabcaabaacbbaddaadbdacdbacaabbabbbabcbcbababadbbcadcadabdcaaaabcdccaabdaabaabaaddbbdcbacbbcaaddbbccabcccbabdbabadcacaadcadccadddbccdaccbcadabcbccbdababddbdadadcbdabadcdaacccdcbaaabbaaababcdbbaccacccaaaaddacbdcbcdddadadddbbdbbbcdcbcabcbacadbcdbcaacacadcabddbbddaccbbdbaaacacbbcddcacdacccddddcacdbccbdadacaadadcbcbdcadabbcbbcdbbddbadcabcbabcabaccdaaadbdbcdaacdcbbabdbbdcbadbbbbbbbacaaddbdddbadddcadcaddcabdadaddcacdababaacdbcaabbabadaddaabcadbbdbdbccadbbccdbaabcbabadbadacacdcbadcbbaabcbdbbdbaacdbaddbaaccccaacccddbcaaaadddcbabcbcdbdcbacdaacbdbcdbccacbdbadbabaddcdacbabaabcbbdcbabadababadadccccbcddaccccaadcaddcacabdbcaabadcadadacdacddcdaddadbdbbbaccaadbaabdbccdabddbcbcabdacbdaadbabbcdccbdcdacdbdadcbacdddabaddaccdbabbbabaaccaaaccbaddbbcdcdbddddbbdcbacbcccbacdbbaabbaccbccaaadbccabbbccbdbacdacaaaccdbcacbacbabbccbbdcddcaadcddbcddaddbbaaddcccabcacbcacddcdddcbddbdaababcbcbbcbcaacddcadbcacccdaaccbcdcacabbcdddbabcbbbcdadadacbabdacbddbdddabbbbaddcdccbcddcccbbdabbababcaabaadbdcbaccacacbaaccddaccbbadbcdbabbbdabdcdbcbddccbcbbbabccdcaacaacadbdcdcaacbbcbbbcadbcabadbbdaacdadaaccdaddccadccccbcaacaccdbadcdaadaadbacadccdbdcacccdcdaaccbcbbbdcdaaddcacbccacaccbcdadcacaabddacbbbbccacacabccbbcdbdddcccdabbababbbdbcbddadabdccababaddabcbdaddcbbbccaadcacdbcbbdcabdcaabccdccdbacdbaddacaddbcccaadcadcbbbacbcccbadbcacaacacacabcdabbccdcabdddcdabaabbaacbbbbbbdacddcabdbdccaaabbcddadaabaabcbdccbcdbdaabccbdcabadbddbbbbacdbccaaddbbaadaaaabadbcdddbabddacccbacbbdaaabdabbbacbcbdcdddbcbcabadddcabddcbbbcddccdbdaaaddcaadbadadcbcaacdcdbaaccaaaaaddabdbcccdacadcacddbbcabcbbdcabaaaabadbaccbbcdcabbdbcaadabbdcdbcacdcbccddaaacadabcbbbdbdccbbcbddaccbccdaccadcdbcddddcbabaddbabdbcbbacbacdaccaabdcccddadcabddaaabacbbdbcaaadccbadadbccadbdcdcbbbcdcccbbdabdccbbccccccbbcbadabddbbaaddddcbcbcdddbbaacaacccacbccaabaddddcacbdbbddbcddaabdcbbbadcdcbbdaabdadaddadcabbcdbcadbdbdbcadadbbabbabcaadabbddccbccbcabddabccbcdacbdbbaacaabbaabbbdcdccbcacaacccddbcdbbddabddbddccabaabacaccbaccadddacbcbaabbbbacabdbaabccdccccbdddcdcaaabbddcbabcbddaaadcbabbadaddccdbbdbcadcdcdbdbcbbdbbcacddbcdbbcdabdcbddadccbcdacacdbbaacbaccddbddbdcbaabadddbcbabadddbdabaaccabacbcccabbdabcacdcbdcaccbbdcdccbcadacaacbabcdcabcdaabacddababcaaabbadcbccadbbadcdcbcbbacbdccbbaabbcadcabdcadabcdabadabaaccabcddbcddcbcddcbcbdcababdadbbbdcbaccabdbaaaaacccbccdcabccacdcddbdadccdabcbcbcdcbdccbbddcdaaadcdcbbcbdcaccababbacabcababddbaddaabbdcacaaabdabbccdcdabbbddcdadcaddacabbadcbaacbbccadadbcddacdbbbbdcccadaccadccbaacdbbadadcdbdbcbccdbcaaaacbacdbaccbccdbbbdccaaccadacabdaddacdddccabdccacddaccbbbabbccbdaabaacccbabadbacabacbcbdabaccadbddaadbadacdacabadbbdbcdbcaabcdaabdbccbabdacdaadbdadacabcbdabaccadaaadcabadbadaacbbacbaccddcdddcaadcddcbcdbdbbdbdaaaddddcabaaccdaddccaabbbabcacdccdaddadbdaabaadccbadaadadccbccbabdababbddbabadbcdcbdccddbabacaaaaababddcaabdabbbdaaacbcdbaadddacdbbbdcadbcadddbabacabcbdbaccddddabdcabddacabbcdcccadddcabbbadbaaaacdddbdccbadaacbbdbbbaabbddaaaaadacdccbaabcbacababbbdadadddababdccccbcdbbadccaacdbcbddaddaaccddcaaddacbbcbbccdcdcadaddcdacddccdaaaccdacaabdccaddbadbcdabcbcbcdccabbddbddccbacdcdabdabdccdaabdabccdbcbaddbaabbccadacacdacbcaaaaddbacaabaddaacbaadadccdcccbcdcbbabcdcadcbabbcacdaccdbcccbdadddbddddbcdbddbdaacdcadcddcbcdaacbacbdbcabbdbabcccbbddbccddbdbcbdccdadbdcdbcbbaacccdccaaabddbcbdcbabcbacbbbbcbaababadcccccadbcddccabaadaadbbdbbadbadcacadbbccbacccabcbbbdaaadbdddcbccaccbcacabccaadbbcaacadabaddabaacbdbcdbbccdbacdadccdbaacadcbccbcccbbcbbccdcbcdccddacbbcabdcdcbbcdccdbcbaccccbcdcdddcdababdbcadcdcdbaaddadbacababbcacddbaaaacaccabbdacdbdbacddcdcababacbbbbadbcbadbbddaccccdbcdcaaadacbbcacacaacbaaccaaacbcdbbbbdbacbddbddabccdcacbbaccbbaacccacbaadabdbadcbabddacbcaacacacadcabdbabcdaaaacbabaacacbbbacbbbccbbcdcaccdadbbacdbcaaaccbcdcbbadacabaccbbabbbcacacbbbbcddababacacadcddcbbccdbcadbbaacddaabaabdaccdddccadbbabdccadcddacadaccbbcacbcbcaacababaacdcdbdadaddadddccbabdcaddaccadabbbbdaccadabdccccddaabcdaaaacacabcabbcdacaaddaaabbbdcccadcdadaadadcbbbdddbaaadddbabbbbdcbcbddddbaaabadcccacabbacbacbbcbdcccbcbacddadcaaccabdcdcadaaaacccaabaabbbccabcbbaacaccadcdddabdabacbbbbdccaddabdbbbabdcbdaabbdbbcdccbbbacddcddcbddcacdddbdbcbbdcdbddcbbbcdccbabbbabbabadacdaabccbcaccacccdababdabbaacbacbcacaacccdcbadbdcbbdbccabdacbbadabcabaacbaabbbbabbccabbacaacbaadaacaacbdcbdadcaacbdaadbabbddaabbadbddcacbdcbbabbcacdccadacadcabaadabbbbcdcadcdcdaabdcccacbbacaaabcdcababdbaabbcdabccabacbabbacacdcbdddbddbbaaccbddbacccdddbdccbddcadcdacbcdaacacbadbbdbaccdadaaaaddddaaacbacacddcacdbcdcbdcdbbdcabaccbdddaddbddacbcaddbbacbaabcadcdccbbddcaadcbbbbbdcbbcaccbdaaacdccddbaaabcbaadcdcacbcdcbbbdcdcbccdacacaddccaaddcacacbcaabbccdadbccbcababddabacdacaabccbccaaaadbbdcbbdbcbcabddccbdabaaccabcabcbdcbadbccabcaddddbcdcdbbbdcddbacaacaadbcdabcbdbddcdadcbbcadcbabbdabcccadaaabcdcabcadbdbcbdbcaccbaddaacababbbddabaccaaadcbddbcabadcadbdbbdbacbccbaacddbbabaacadaaaabdacdadcbdcacdabdacdaadabbabcddcabbdacabcbdacabbacadccdbbacababacabcbbdcbddcdbcbbdcdcbacacaadccdaacddddacdbacddbbbbdaabcacdacbdccdcbcadbdbbbaacaadbcbcbcddcacdacbaaadcaabccccbacabaacccabcaadaccdbacbbadbccdabaabdcdabcdadbbcaddddcacadcbbccbbcbbcdadbccaccdbacbbabcadbddbabbbbbbbcdcaabbacdcdbcdbacacaadbcadcbcbbadccaddabdbbddadcbacbcaddacbbdaacccccaaccccaabadaadbddcdccdcbcdcdaacddbcdbddddcbcadbddcdcadbaacbddbcdcccbabddaadcbaadbddaaccacbcddaaaabdccdcbbcabbadbddcdcbdaaaaadcbbabaddcccbacababadbcbdbbadcbadddddddacacbbcbacdcabbbcdaacdbacaabddadcdabbdbdcadbdacdaaaadcbcddbababdbccdbbbbaacbdcbbddabaaaaaddccbcdcadabacbdbcbdbabdcdacaadaddbcbbcacbcbbcbbdccbddadbcbbcbbbadbddcdcbdcdcbacbdbccbaddabaadbabaccbbadbcabddcbaaadbabbaacadacdcaaaccdabbbdbdbcadabbcacbcabaacbaaadadccaddabadcddcccccdbdcabbadbacdbbaacacdbbcddadbbbccbbcabcbcbcbdaadacddbbdabcbdacbaadcbdccbcbcaddaacbdadbdbabbbcaabbcbacbabdcccccdacbdbbbaababbadcdaccdbbccdabdcddccbcabaaacddaddcdcdaacabcbcbdcadddbadacadcdcbacbcdccccacdabcdaaaabbdcdbabadcdccbadcabdadcdabcbddccdadbbcaaadbaabadbbaababdcabdaabdaddcbaccbcadcdccdbcabcbbabbbacdbcacbaadddddcabacabbdaadbacdbabdaacdcbcadacdbbacaadddacdabcdcbaabdabccabcacababdacdbbdbbbbacddbbcbcabcbcccccddbdacbdcabdbccaaacbabdbdcdbbadcddddbbdcabcdaddaaaabccdcccdcbdbababaddcabbdacacadcbbdadaacbbcbbcabcbdbadbdbdabbadbcbbbddcacdcbcbdabccabcabdaacdddadbabbadaccbcbabacacababdacdacccbdaabdabadbcaaaddacbaaccbbbdbcabbccbbdbddccddadbdddacdbaccbacabbbaadccbdcaaccacdcdcbaaacddbacccbdddddabddaaadacbabdddcdcccdaacaddaacaadcaadacddddaaaaabbaccbbdbbbadcdbddadcbdccbaacaacbccbdbabdcacbcacdcbcccdddaccbcacddbbdcaabbabbcaacbabbbaabbbdaddbddbbbdbdabddbcdacacbcadbcccbcacbddaabaabbdaadcccaaabbadbaacddcadccdddbadabbacdddcdddaabcdbddcaadbbcdcdadcdbbcbaaabddbbcaaccabccdabcbcddcdbaadccacdbabbbdcbdabdddcdaddbddbbbbcabaadbadacbaabdbbccdaacddcdcbbdbaacaaccacdadbbabaccadbdbdcccdcbabababbaacadbccbdccbcbddbcbbdabdabbdccccdccbaccababbbdaccddccbdbdbbbbbbccadcbcbbbcabadbadbbdcacdbdbdadcdcccabdcaabcdbaaaadcdaaaaddadaaacdcddadbcbdabacdacbcbdabbcabddbbadacccdddcdaaaaadbdccadcadadbdacaabaaadcdcbcdbcdbbaddbdbcbbaddbdbadcbdbabdcddbbddaaaddddcdbdaccabdacbbbacdbaadadbccdaaabadbcdacccdabddbbbdcdcabaaabcddadbbbcbaabacacbbbacaabbaabadccdcdcaadaacadabbbdaadddadbbcadbbdaccdccacaacddcdbcacbbabaadabbbabcbdbadccdbbdacabbcdbddacbbadbaadabcbaccbbbadacacaacbaccddcbdccacacaacbccdbaabccdbbbacbddacdabdabcbccdbdaadbadaaadaaabccadcabbbdacadbabadacdccdabbaaaacbadcbacbaacdaaaddaacababddcaddccdabacdacadcaccbcabbcdbccbbcbabaaaddacbdadbbbdcccbbdcbcccbabcdbdbaacdabbaabbbbaccbcadddcdbacbbbdcdbbcbabcaaabdcaccbbabaacbcbaaadacbcbdbdaaaaabcdcdadbadccadddddbddadbaaaddbacaccbaaddccbdbbcdcbcbbbbccbaacbcadabacabaaabacdabcbbbccadcbadaacccaacaddbcbdcdbdcddababbadcbdddccccdadcbccdcdbaacdadbddbaddbccbdaabcabbabdcddadbbdcdaaddacaddaaddcdcbbddaccbcbdabdddacdddcaacbddabadddccbbccbdcdcaabcababadddccbbdaacddadddccabddddbaadbbddcaaccaccbacaacbbcbddddaabadcacacddbdbdacacbbaabccbadaadbcbccadbbcddbadabdabcaacdcbdcadbbaddcaacddbddacccbdaacdccbdbcadaccadcdadcaaabbdbcbbbdaabbabbaaadcbadacdbcacdaaadcbdbbdcbcbbcbadddbaaadaaddacdccbcdcbdaccaababcacadcaaabaabbdbdadbbaccddddbaccdcaabcadaacabdcbacccdbddbcdbdcacdaddaacadbccaccdbcdbdcdbbbcacdabcdcdcaabcdccdbadccccbcccadbdddaabbccccacabdcdacaaadbccadadcdabbcddcaccbdcbabbdaddadcabaddddadacaadddbcacdccbbabbcbbdcabcbdcaabccdabaaaddbacaabaabacbddcbcdcaddacacccbbdcdabcbddbcdadcdccddabccddcccaabbcccdbabcbdbaaccbbcbcdddbaacabbacdbbabacbbbddddccadabdcdbabdaddacdacacacccbdbaadbddaddccbcccccdccbbdbacacaacdbdddcaddacabacdcdbbaaaccaaacacdbddccdcdcdcabaadacccaaacbacbdcbdabbddccaacddacaaacadcabddadbbcabacbacaddbdbabbcdaccbdaccbdddcdbbddabbbacccddadbccbddbabdabbcdbbdcdcaaacdcccadcdbbcbdbccccbcdabdccabdabccadbbdacdbbaacdbdcaddadcbcadcbdcbaacbdabbdddbccbabddcaccaabdabdadbbdaddcaccbbabdddadcaaabcabcdbcabbbaaacccbbaabdaabcacdcbccabbbbdbabccaabadbddbbbcdcddcccbbbddbbcccabccdcbbbbcbcadaccbbadacaacbbcbcaddcccaddadbcaccaabbcdbacccadaadbddcadaddbcaadadabccadbdaaaddcbdbcabaabdbbdbbcccdccaaabbcbcccdddacccaadcbcdddadabdddddbacbbacddcabaadbbccdcbdddabadcaaddbdcccbacaddcbccdadddbbbccacbbaccabacacbacccabdcabbaacbcbcbdbdadcddbbacabccbddbccaacadccabdddcadbcccabadcbbccdadccccbabbcadaaabcbabbcaccbacddcacabccdcbbbddcdaadadacdabccddcbccccbdcddbccaababdabbddabbacbddddddadbbbbbdddbcccdcaaddabbcdaabbacdcccdaabcbcdbcbbcdbaccdcbacaabcdcacddabbbcababbcdaabbcdccacdbdcaacabbccccaabdbdccacabccdcdbbcaacddacbaccaabacddadbdcbbbcbbbccbacbddacadbbcccbcabaaabacacddcccaadaacdcdcdcbaadddbddccdbccbcbaaddcbbdaacddaccbdbcadbcaaddcaadaddcddcbccdccbbdabcaaaacbcdbbabcdbaabccaddcdcbaadadccbcaddabcabdaacddddbbbdcaaddacbcbbbacdbbbdcbaddaaabdbbbadbabbbbdcdddbbbaddcdadcadccbdccacddcbaabdabacdbdccdcaaadbcdbadaadbdbcabaaaacdacaacdcaabcccdddcaacbaaacddbbbaccdacbcdbddbabdcbcabdbbcabddbdccaacbdabadbdbbdacbdcdbabddbcccaddbbbbdcdbddbdcbdacadbdcbadababadddbabacbacbcadccbdcbaddbcabbcbcddcdacdcdddaadacddacdabdbcddbcddbcddaaabaaadddbdcdaccbbdcadaddbabacbbbadddacbcddccbdcacadbadbbdaccdacacdbdbbbbbdadadddcbdbbbabcbcbbadcadcccadacaacbdadbacccdaaaabbdcacddcdaccbbadcacdcdbadabccbbcababcadadbdaacbcbdaabdcbcabbacbdcccbbcacbdcdddbbbdddabcacccbbbabacbbaaaabcacacbdbcccbdcdbbcbaaadbbdcacdbbccdaaacaaccabbcbddacbcddcaaababacdadabcadcbbcdcbaaddbbbccdbbbabaaddbdddbdbbaaddabbbababdadbadbaccddacacccbdcdbbdbaabdbdabaadabcdcbddabdbcbdaabbdaabcdbcccdddcaccadbdbbbacddcdbbdabacccbcddbdaabbbcccbcbdbcccdcacaaaabcdcbbbabdbcdbcbbdcaccdbbbddbabacbcbddcaadccdbaabadabccdcbcacdacaadaaccbdbcabadaaacbcdabbccdabcadaaaadddaaabdadcdaddcdbbdbabcbdbcadbdcabdcaabbaddccdaadbaabbccabdabcccdcbbbddbabadddcccbdbbddcdcdbcccdccbbcbbdabdddbbbcbccbbbbabbaacaabaddaddddbcbcbbcccbbbbbdaabddddbcbbadcdbdbcbcbdadcbbcadbacbdcbbadababddbcbbccbbcdcbcaaadbbcdabcbbbddabacaaaaaabddcdaaaaabcadccabcbccddababddabababadbabdbcbbaaadbbccdcabbcdaacccadbccadbdcbdbdbbdacacacbdbcacbbcacddbcacaccaaabcdbcbdaddbcacacddaddabdcbcbbcdbccbcdbbbcbadbddbccacdbcbaabddbbccaddccdbbcddaaccbaabadacddccccdabcccdcdcbaddadaccadadddacaacbdbcabcaaacbdbaaddccbbccddccabbbdcabbcdcbaaaacdcdbabbacbaacaabdaadacccbbbdcdbadaacdaaddcdcbaddbabcbdacaccdbccdcbcaaacddccbcabbdbadcabdaccdbcacddcbaacaddccddbbbabbbbddacddcdbaddaaabbaaccbabdacbabdcaabacccdcdcddcdacbddbcddbddbbdcaabcbcbcadadbdbbcbbbcdbabccaadaabbdadacaabcadbddcbaaadddbbacbaadabadbabbdacbaababaacdaaadcbbbbcbbadbcabbbcdddbabddaddccadbdacacacbddabbbcbcccbdddbbaacdaccaaaaadaccdaadccccacbacdcddccaaadcdbabdabdaddbaadabbdcdbbaadabdaaccdacdabdbddcabddbcbabccccdcbbdbabaacaabdbcaadcbddaacbcbbbbddcacbbdbacadaccbabddcbdbaacdcaaddbddadcdbcdccdcaccccddcccdcddddccaaabdcdacdcdbaaacbdababadbcccdcbacdccdabdcdbaabcbbdcdcbbbddcadaacaaabcbddbcdcacaaccdcbabcaabdaccddadddacadbcbaaaddcdcccadbbdcadbbabcadbdbcdcdaaaabcaccabcabbcbbcbcadddcddbabbbadddbbaadcabdabacbbabcbabcccbccccbdddabaaadaadcbcdbbdadaacaacccdbbcbabbaaddbaacdabaadaccbaccdabbdadcbcbdbaddacbcdcccbaabcdbcbadaddbccbaadaabaaadbcadccabdbdccbbbaabddabbdbbbacbbabbcdbbddbacbdbcbadadababacabdbdddcabddddbccaccccaabbdbccacbbaadccdabdcbdbabbbdbcbbabcbbcdabddacbddcbcddbbadcacbbccbbcddbddcdadcdabbdcccdbdabdaacdadbcbdcdbadacbbcddbbdcbadcbacbcccbbccacbcdcacbbaaabcbdcaccddcddbbdcabdcdddccadcccccdbaaaacbadbaccdcabbadbbadbdabddabbdbbccdadabcabbcadcabdbdaaccacabcbddcddcaadbacddcbdddddbabbbdcbbcacdcacacbaddacbbcccbdcdcaacacdbbdcaaabccbaaabbaddbddbcbdcbaadbadcacaacdbcacbdaccdbaabacbcdacbabcddbbbdadcbcabacbddbcadcaddabadbacbdbddbabbbcbcbcdaaaaccabbdbbdbddddaacddbabdccaaadccdcdcdacadbbaaddbcbabacbbaabbdddaacabbaccdaccdbdadccddcdbaaddcaccddcdbdcacbcbcdcabbdddcbbaddbadcdcbcbddbdcdadbcbcbdaccbcaddacccdabaccabaabbbcccaaabacadddbdbdcbaddddacdccbabcacdbbadacaadaabbbaacacadaadddcbadbddaabddaddbddbcbbbcccccdaaaadbddacbadbacacbbccdbbcbccccdcbcdbdabddbcadaaadaaaddbbcbacdccddadadabcddbccabaaabdbbcabcccbbdbbdcbdbdccabdbdcbdbcabcdabadcdcabaadcaabccddaddacbbcdacbaccacdbdbdbdadabcbaccaacbdbddccadbaaadbbdaddddbadbababbcaaaddabdaacdddcddcdabdadcacbaaccddabcdcdacdbbcbbbdccdcdacabcbdcabdcdcccacaaabcbacdbabbccadcabcbcbdcdbabdabbabddcadadabddcabdaddadbcdaacbccddccbadbdbaadcccccaddcbbabababadbbaddacbbcabdcbaaadcccccbbcadabdbddcdabbdddcdadaaccbaddccdbbbacaaaaaacacdbccbacbabaddaccbdbadbdbbadddaaccdadabdadbcddcdadcaacaacbbccdcccdacdddccdaabaddbacccaabcbbdddbaadabdaabdbdbdabbaccaadbcdbaddadaadaadaddcabddbababcdaadcadadacadadadadabaccdbbaccaadbcabcadbabddcaabbbddabdbbaccdbcdabbbcccbcbcaaaddccabcbcdbabdbaabcbcacbabbccaaccbadcdddadddadacdbcdbbadbbbacacbddacbbaadadbcbabdadaaaddcccbdcbdbabbcbdcddccccbbdbdbadaddbbddccccbccbdacacdbdaabacbbdacdccbcccbcbdabbcacddcaacadabccabbacddcbbddbcacdcbdddcadcaccbcbaaaadcbbbbcaacdabddddbbcaadcdcbadcbbdacddbbaddbabdbbbbddcaadbdaabacadbcdddaddcdcbcbcbbabadadccbdcbdccdaaaaaabbbcacbcdbcbdbccddbadbcdcbcdbcdacccdbbbdaadccdbcbcbacaaacaddccdcacadcacbacadbbdbbbcccacdbcabbbcbdcbcbacaadbaccbdccbaaadacacbcccbaddddcdccdbdabdcaadbbabdabbdccdbdccdbdbddbacaadabdaaddaddbcbaaabcbdcbdabccadabcbccaadaddbbdddbcbaabaadaadaadbaaadcbabdbcdddbcadccadaacdaacaccbbabbdcaccddcdabdddacabdccdbccaaccdadddbccbdbcbdcddbbcbabddbaddababcaabccbbabdaabdbcaaaabacbddcacdbccbccaddadaabdbdbcdccbbbcbbccdaabdadbccaccbdccdcbcacaddbbaaadccaabccabaacdaaddbbdbacdaaababccbbbcdaccbadcbaacbdaaaabcacaacbdbccdaddbacbdacaddbdbdaabbbabbcacaaacdaacadbcaaccaabcdaaaccaaabaddcaadbbcbbabdadcddbaacbcdaaabddacadabadcdaccccacadcdbbdccbcaccacadaccdcaaccdaddbabcacccabacaaabccbabadcdbbcbaabbadbbbadcdcbcacadbadcbccdcbacddadbbbbdadacdacdcabdcacaccdbabbaddbccdccacbdabcabdcbddbbcbdcdacacbbadbabdadaabdabccacdbddcdbadddaadcaaacbdaccbadbdaaddaddabbacbbaccdbadbcdaccadbcdadabdacbadadacadacbddbcccbabdadbbcadddadbdbcbcaddcacdcddddadabcddbaddadbbcabddababacbbddddaabaabcdbcddbcbbbabaaadcbcabccdbcacbcdaabcbcaadbdabacccddcadbadbbdbcdcdbaaadbddbbcadddbdcdacdbdacaacbacdcbbbacbdbbabacadaacaddcbabadaccaccbacabcbcacdcdcbdddcbdcdbddcddacbcddcacbdbcbadbccbbcccdcbbcacccababaaadbaddacdabcdbcaddaacbaccadaaabdcadbdbcddbdcdddcaadbdcbdbdcacbabddaaacbacccbadddbadbabadddabbcadabcaaddabcccacacdadaacabadbbacadbdbaacbbccdaaadcbaccaddcdacccaacaaadbbbadababadbdabadcaacdccbcdbbabcbcadaddbabcacbcccdbacaacbabcacbbdcbadaccaccaaaccbccdbbbccbdaacdbdbacbabbabacacbdbabbabbccacbbcdddbddbbaadadabcbddcddddccdacbcacdcccddbabbdbbcdcddcddabbbacddaaccbbaccbabdcaddbabbcaddbbabcccdbbdcdcbacbccdbdccdaaacacaaadaaadbdacddcbdbdacbccabcbadbdaddabaabdccdabadacbccbcbcccaacdadaaadccdcdbdbcbbadddcdadcbddaaddacacbdcbbddaadbbcadbbbbbdcaaaddcbaaccdbcbbccdcabababcbabdbdabaacccadaadddcdaaadbccabcbcccadbcdccddbdbddcbabcdcbbdbbbdbaaabccdbdcabcbcbadaadaddbbabdcddbcdabaaaaaccccdddbbddbcdbbaddddcddaddcbddccddcdaccccaaadcdaddccacccbaabadaaddbcbdddadcabbabaaabdcbacdbabcaababcdcdbbcbcddbacadccdaaadcbcacaaccadbcbccbcccdcaabdaadbccadaabbcdbaaddcacbddacbdbbabbdbbcadbbcbcaadadadabbaabaaaabdbdadbcbbdcdadbdccddcbabccbbbbaccbadcccadbbabdcbabbdccacaadaccdbabdabdcbbdadbababdcbbdbbbbcbbbbaabadcadcadabcddbbcaaabcdbccbbcabcdbcbaacbcbdcdbcccbcadcadccccbdcbbbbdaaaddbcbdbbcadabccabdcabdcddadacdcabdccbdcaacdabdaadbdbbcdbbbbadbcacaddcccdbcdcdaacbdadcabdacdddbdacbddbbddbbacadccccdadcdccdadacacbaddbdaabbbdcccdcbdcdbaaacabaaadcddccbbcdbcadbadcdaadddacdabbabdbaabacbcadaabdcbccddadbaccaaabdcccbacbcbddadadbdacdabaabacacadbccddbdabdbdcdaabdaaadabbdbdcdccddaabaabdcbadbccdaddcdcbdabaacaddbcbdbacbdaacccaaaabdcdbabbabdcbccddcdccbdcdcabaadcccababbaddabdcacacadabddbbdadccbcacacdabccacbacbaaccddbcbdbbdbbdbbddabddbbdddddbbcabbccccaadddaabccbabbcbabdbccaaacdaacaacaccaaadccaddcbaddcccccddadaccbcccdcadbadabaacbcbcbaaacdbdcccccaddccbcadbabdbbcbbacbcacbdaddcbddddbababdabdbaaabbcdccdbdbcbacaccaaddddcabcabbbacadbaadcaaabcbdcaadddabddcbdccabddaacdabaaacaddcbccdadbdaccaabddddbabbabbbdabaddbbaddbcdabbabbccdbabaaddbddddcabdaacddcaaabbacacdbccabacabdabcbadadbaabccadbcbccbabcabaddbbaacacccccaaddacdbdbcbcbccbcaadcbaacccacaddccdcaddcdccaaddaadbcbdaddcbcbabaaadccabccadabbbdbcaadddabbaaaccaadadbadbbcacdacbabadadbbabbdbdacdbbabcbcccccdaacbdcaadcdbbbbcaadcadcbcbaacbaddbdbbdbababccabbabbddbdadbdacdbadbaccacbccbbabdbddbadaddadcabbbbacddadaaddbccdcabaaabaadbacccddabbcabdbbccaadcabbadabddabbbdbcbccbcbbacacbacbcaaacbdcdcabdacdbddcaabcbbcdcbabcaacbbdaddabdcddbabbbbcadbadaccadccabacbdacbcaddaadddcaaabccbdacaadbadbaaddadddcdcdababbcdcbbbacdadcaccbdccabbcdaabdbbaddaabaaadcddabbcdbdacabdaadbccaddadddcccabcaacbdcaacacadbdacbcddccdcbadacbaadcababadcdddbaddcddbadbadaabccbdbbabccccdcdabdddaaccbddaaacdacbbddcbadddbcbdbbdabcaacddcabbaaccacaddbdddddbccdcacabdbcabbcbcdbdaccaccdbddbcbbaddbbadcabccadddacabcadbbcdbbbccabcdaaabcbadaccdacbcaddcbcbcdbdaacadaadcdcaabaccdbacddabacdcdcacabaccadbbbcaacdaabbbcccdabcbabcdabbdddcbacabbdcaadcbacdddcdaddaddddacccbbccabaabbcacadcddcabbccadadddacabadccdccddaddcbcaddbbabddcaabbabaaadbdccccddbaaacbaccdaadaddbacadcdcdaddbdcabdbccddbcacdaccbadaacbdacbddddbacbcbdcacbbcddddbaacbcdaabcadaadcdcdcacaabdcdaacdccadaaddddbbdbcdddbbacccddbdaccbdcbbabcacddcdbadddbbbaacdcbbdcdcabcdbbacadcdbbabccacaabdbaadcaadaccdcdccccbaadacbbdbabcbaacdbccadbcdaabacabbdabbbdaabbddcbcdccaacddbcbbdbcdcccabbdaadcdcabaabddaddddbabcbbbcabbdadcbbcbbaabdbadbdaabdbbdaaddcbacbbdabcadbaddccbbbadacccbccbaccabaacaadcddddbacddaddddbbbdaaccddbcabbbaacccbbddaacadaacdcaccdbcbbbaabddaccdddabacdaaadaaaccaccdccbcbcabdaddbcbbbdbdccaaababacabcdacaaccbcdcddadccbcdadbccbabbadabcaccccabcadcacadbcdcadcaabbbdbccbdbdaaddaaabbbbdabcccdcdbdcbbdcdabdadcbccbadbccdbbaddacaaacbcddddbacbdbcbdcaadacddababcbcccadadcacbddacacdcbccabbbcbacaddaaaddcdabcccddccdbacdcabbddaadbbdbadddaaccdaccbadadbdcdccbcdacdbcdccbddcbaaccdaaaababababdabbdadcbdaadadbadaaaacddbaccbbadbccabacbacbbacaacacabbadcbbdabcdccccabbabbaccdcbdadaabcccabdcdddaddbbabdcacabdadddcbbadadcccbccbaddbabdddaccdbbadbbccaacbdcbaccabbcddadddcdbdcbdaccabaabbbaaadcdcbcadbababbdbbaaabcdcdacaaabacbcccbabcabdcadbcabcacbdadcdbcbabdcdbddcbaacabdbbcbbdbcbbcbddcdddabcbccdaabcdbbaabddabacbdcbcadaddcdaadaaddacdcccaacbadabcbadacbdccabaabbbcdcdcdddbbbbccbbccbacbbbdaabbbbacdcaacbdcdadaccbcaacbdcdabbbddccadadddcbbdacbaacabddbaccdabcaadacdbbabccdcaddaadbbbaccbdccdacabaadddadadcdabbbcdcccabcadcbdccdcdacbccdbaacadccbbcdbdabddbcdacccadccbdaccdccddbcbaabcdabbabbcaadcbcdcdbdabadbbabdbdacddccadcbbcdbcacabcccdacbacabccacdabbcacaaaaadbbcbadbdcccdaacccadcddbabaaabacaddbbacdadcbbabdcbcdbbbbcdbadcacdadddddbaccaacacacbaadbdbddacaadcbcbcdacbbccaaccccaaaccadddbdddbbabcbcacabdcbabaabdbbdddcabcaccbdddccabbdbdbcdcacabcdcdaccbddcbcdacbcdbacddbdcbadbcccdbcdbbabdbdbbddccdabbccaacbaadbadbcadbbcccbdabdcbacbaacabcdcddaacbbbaaccdadaabcbcccdabddcadccddbababacabdacddcabaccabdddbcbacadcdabdbbcabdaccdabaaddabbdccacccabcdacbdbddcbadbcdcdcdbaaacdadaabcdabddababaabaadabaaddcaacababdcaaaacbbcdcababbacdcbbccdabcdbccccdacbabdbadcaaddcbcdbdcababaddcbbdacddcbccabddbbaddcccdabaccabccaadcbdadcdabbdddaabcadaadbcadcbdaccacacbacaabbbbbaddabdbcbcbddcdbdacabbdbddcdbddbcacadcadbaababbbcaaabdbcdadbbcbddcdabcdcaacbbbaddcbbdbddbdadddadbcabdbddddccbadbcdcabbbdcbcaadcbdabcbbadccddccaadbacdbdcccbacaabddabdadaaaacabdaacdccdcdcdcbcdabbadccbbdcdddcaabcdababccaaaacdcabbdcaaaabcacaadbbccdabcbccbbcbdcacaadbbadabdabcbcbcabcddabaaaaddbcdabccddddbbadbbbaaaaaccadbdadadbbabcdbcabbcdddbdbddcbadcdadccabdababdabcdbbdcbbdccaaaabbcbadbbacbbacacacbdcaacacddccabcaccacccacbddabaddddcdccaaacdddcddbcabbdbababdccadcdcbdcddcdabaabbcdcaccdbcdabbbcadbadaccaadbcdbcabbbccdadcdccbdbddabbdbaacdccddddacdbbcabccbbbdcdbacdacbcbdccdaddcadbacbcbcaccaaaaccbbbacddcabadbcadaddcbdbddbacaabaaccbdaabadbdadabcbaacdcbdcddadbdccddccccaacdddbddddaacbcdcbbcadbcbcacddbcdabbadacdabaadccddadcccaacddcbddcdcbdbdccddccaccddccbdadaadcaadbcbbdaaccbccbaadbdbabbcdcbcaacaaacabdccdaaacdbdadcddbdadbdadbddabcbabaabcdcddbcccbbddbcacdacbabcbcacdbddadaacaccccbdcbcaddbbdcdbbcbddbbbcdbcdabbddcdbbcdbbccdbcbdababaacabdbacaddaaaaaaadaacdcdbcdbbdabacaaddacbaaddcaaccaddcbcadcbcaabacdaadadacdddaccdccdadadaacdcadabcdaddababacacbbacddcbdaabbbdabbbbcdaacabdacddcdbcbbabbbccbcbcbbdbccadcaacaadaccbdaccadcabddaaaadbaabbcbbddbaaccbaaaadbdcdbcabbddcdcdddacbdddcaabcddcdaccdadadcbdaababaacabdbdcbbacbadbbadaabddacbadbaccaabbbbabdacddcacbcddccbdcbbacdadbcacdcbdaddddaacbccdcaaacddcbadaccdbbabacbddbcbaaabbbaabcdbaacabcddcacdcbadadadacccbcbbddcccbcdcbcccdcdcdabcbbdbbaaddbcdccbbdcdaaadcbacbdbcdbaabdbbabbaacacddccaadadabcbbdddacbddccdccaabccdbbaadaccdcdbdbcdadbdbdcadbccbdddacdcdaddccacbdcabbbbccccacaadccccbbcddabcadcbcdcbbccaadadcbcaaddabddaccabaabbadcaadcbdcddaacbcacdaaabbcdadcdaaabadbdbbadadbcbcbbbdbddddcdaaacdabbddadbdcdcdcaaaddcacdaadadbdbabbdbccacbdacbbbaacbcabddbdbdabbaccaadbaadcbadcbcbcdcbdaacdcddbaaaccdbcccdccdabdbbbdcdaacbacdaaabdcabdadbcccccaabbbbdbaccbdccdaacddcdcacacadacddbccbcabdcccacccdcacaaaccddbcabbabcbbccadddddcacdcccbdccbbabccdddbbdadbabbaddaaadbccdcaaddbbdbcccbacbccacbdbddddbcdcdddbdabaacabcdbdcbabaadcacccbcaccabadcaabbbbaabdcdddabccccacbabdabccacccadaaaccbaadbddcaaaabbbcbdabdcadbaabccdcaabdbadadddbbdbaadddcabbdcdddcdbcbaddaabcdbbcbdbbcccdacbcaccbdbdacbbdcdcbdaacdaddbccbdabcddcbbbaddbcbccbddadaabaaabadaadaacddadccbadcddbadadadbdddbdbbbcbcdacacabaaacaabcdcbddbdbcaacdddddcddcbabbdbadbbabadbbdccaaddaaaadcadabadabccbdbdaaddacdcbdbaddbacdcabddccbcddbabbadbaabbcbabbaccdbbbdccbabcdadcbdaadcacbccaddcbaabcadaaabdaabadbaddabaaaadabcdbaaadbccbaaaacdcdcdbaddabbccadbcccacbcdccaadabdbdaababdacadacccdacacbcbaddaaacddabcabbdcbdcabcbdcbbbbbacdbbdcbdcdbdcaabcbbadcccdcdbcaadbbccbaabdbdaabbcddccdbaabddbabaccbdbaadbccaabcdbdbddaabdabbcccdbabaaccacbbabbaadbdddbccbaccaddacbdcabbabbabaddbdaacbbdaaadddababdaddbbbaacbadbbaaabacddadddcddcbccaaaadcbcaddadaddbacbbabadbadbccbbbccabcabadddccaaddcccbcbdddbbbdaccacadbacddcaaabaacadcbdaddcccdbbabaabadccabcaacccdabcbbdcacdbbbdaabaadcaaadcdbaaadadddbbacccaabddbcccacbabdaadcdcbbabdcbcbaccdadcbcdcbccbadbdbdbabbdaaabdbcabccdbbabcabccbccbdbaaacdaabdcdcdbddbabbabadccbdbcbdacddbddaacdadcbcdaabcaacbddcbbcdbcdcbddcadcbadcdacdaaddbbbabadcccaaacdbaddbacdccbdbccddaabbacbbbdddbcbadcddbaacadaadccbdbdccacdccddcadccadaccdbbbaacbcbbabcdccdbdbcbcbdbaddaacbaadccdaddbcddccdbdbdabbbabccccbdbadbccbcbababbbcdcbbcbaadbdadccbbaccbababdaaabcccbdacdaccbdccdbbadbccccadbcdaadccacaccadabcdcdacacdbdcabcacbcbabbcbaddddabdacadcdcdbccbcbbaaadcccbddbccbaacdcbdccbbabcbbaaaccbabdaacdbadaccacdbcabbcaacacbdbbaabdcbdaacccaabdacbabccaadbadaccdabbbdccddccdccaadccdccadabadbcdabcbcbbbcdcdbaddabccccbdbbdbbdddaaaaaabaccabdbbccdaabcccbdddbdbbddaddabcaccddacaabbbbdbbbccbbacadabcbbdaccbdbbacccbdcacbbcddbaaabacacdcacbbdbbabbcbabbcddacaacdadbccdcbbbcbcdadacabbbccbbacccabdbcdccccdacbddbcdadbbcdaacadaacabdbacaaccaacbcbddbbddadacabbdadcbbaaadbddccaaaddacaadcacadccddaacdcabaaccbdcacccccdaddcbbacdabcbbbbddbddbabadddbbaccdddcaacacdadacbdbdaacbcacaadbbdcbacabbaccadbdccaabadadbabdbdcbdcbddbacbabcdadcbcdbcbacbdccaadabbcdcdaccaccdcbaacbcaaddaabcbaddbaacccdbbdddbdaccdbaccdbdacdbcbabaabaaaabbccbaaadbaabdaaddbbdbbcdddcdcbcdbcdaabaccabdcccaabacbaadbddccacdbbddccbccbadbcaccaacdacaacbadcccbddacccddcabcbdddabbbaadbacbdcacdacadddacddcdcdacbcdbcddacdccaddcdbdbbabbdcabcdbaaddaaabcccdcadbcdbcddadbcbdbacabababbdcbcadabbacddccdbaacbcccaccbdbadacaccacbccaaccccdbadbaacddabbbaacdddcbbdcbadbddcabdaabbdacbbddccbbcbaddcbdbbcbbbcacdacaddbcddcbbcaacccddbaabdbacabacbbdaddbdddbacaacccddbcacccadadadaadccdcdaccaababcdacbdbbbbabcadcadbccbdddbadbbbbcbaacadbdbabcbcbddccbcdbcdadbdaabddabccdbabbddbbcaadbababdacbbcdadbcacdccacdbbdddcaaabbcdaccaccabadaaddcaadadddddacadcaccdbdbbbddacdaacbaccbaadbbaddadcbcabcabbcddbdcbbbdcbbbbacbaaaccdaaabbbabddcabdbcdaadbbbbbdbdcccacbccaadbddddcaddcacdacbaabccacbbcaccadaaaaaabbbabbdddaaccccbbaaddadbcbdbbdabbabcbcdbdcdbcaaabdaddbdbbcbdacbabbcacdcababcdcbaddbabcabbcacdaacbdddcabbacdddcdcccdcdbbcddcaadaadcdcadacaddadddcbccddbbbdbbabcdbbccccdcabccbacdcaaabccbabacdccadcbaaabadcdadccbbcaacaabbbabcdbaddcacaddcadcbbbaddbadbbbcbaccdbddccdacbaddbcdacbbadbcbbacddabddacbdadacacaddccdcaabadbbbbdcbbbdbaccccaadabbbbcbdcdddcdbdcdaacacdabadcadbacadccabdcbbcbabcccaccccadbcacdcdaddcccbaaddccbccccbacbcdcbcbaaccdbdacddaccabcadbaababaadaacdaddaadbaddbddddcdbabdaacccddaadccababadcaddaadcabaddccacdcdbbdbbaccbcbddbdcaddabdababbccababdcacadcdddccdabadaccbbabdddadcbcbadcacdcabdabdbcdadaccadbaacdbdbcacbdaacaadadbdbccadcabdabacddcadaaacaabcdcbbcacdccaddcdaaaaadacbacaccdcadaadcabcdbbabadadccaabbadcdadddaabbbdabadbcdcacbcadccbabaddddadcadbcaacdcccbbccaaaddcccaabababcdabddaaccdcdadcbcdbbdaaccbccddccbacabdcabdddcaaccbabadcbccccdcaabdccaaaadacaabbdcbabaaddacadcdbccaabbcccabdadbdbbcdabaccbcbddcaacdddacbbaddbaabdbcdcabdabcbcbbadacdcbcdbcdcbabcbbbcdbbaadacadadccdbabacabcadacdaaabdacbdbdcaabababbcabdbbcdcdddbaaaccbddccbadaaddcbbcacacaabccdadacbacaabbdacabcbbccbbcbcacacbcccdccbadabbacabbbbcdaacbaadababddacabbabdcbbcbaccdbcccdabadddabbbccabbbbcddabbadabdcdddcbddabbcbbadddccbacdabacdacdccccbbabddacbddbdacaacacdadbcaaaadabadcdabddabaccabbcbacdbadaaccbcddadabadcdddadccdbcdbcdbbbcacbbdbdbcddcddaabdbdaabbddbdcdacadabacaababbcbccdcaccabadacbdaaaabbcacbaddbcbbbcdaddadcdabdbaddbcbbccacacaddbdcabdaddcdabdbbddcacdcbddbddbbcdbdbdaaadcccbdadaabcbcbadcbacaddacdbacacbbccddcbcbdbaadadcddddccdcddcadadcbadabdbaabddbdbcaccacdabdbadccbbdbaadacbbbcdcdabcbccddcadabadccdababcbccdcbdbadbacccabcadbccbbddabbccaacbddbabcbdcadbadacdbbbcccacdbabbcbdacbdbbbdbbbccaaadabaaddccadcadaddbdabadcbbcbaddbddbbdbdaccaaadbcadddbbdcbdccbbbbacacbcbcbcdacdadbaaaddbcccadbcbdbccadcbcaacbccddbaabcdbdcadcddcdcdccbdddaadccacdddaabdddbcaaacccbdcdacddbcbbbcdadaaccdcadaddbaddabbdacaadbcbbbaababcbacddbcdababbcabbadabcbccbbccddcbbaaaaccadbcaccddaddccccabbcbdbbbadbaaddcbccdcbadccdaccbdabdccbaccdbbcadaccbcddcaaccdacddcdbbacdbaadddaddcccbcabadcdbabdaaccbaaccbaddddbdcdbaacbccacabbcadcbaabcccacbcbcdbacbbdcdaacbbdadbbcbdcccdaaabdaaccacbcaaacdababdbadacaacdabddcbcbaaacccddbadabbabdbacbdabacabacdabdbabcccdcbcbabccadddabdabdcabbcacadbdbbbdcaccbbcddcbbdccadcaccaccaadcdaabcabccdbcdcdcdccbbccaaacddbbbcbbddcdcdadaddddacbdbabdbcbdcdaaccbcbcbbabdcabdacbcadbcadabbddbadcbacdcdbdaaccacbbdbbcddbbadbbaccaaabdcddadbbcadadcabdbadbbabacabaddaddaaddaadabcdaacddaabbcbaabbdabdcbdadbcdbdababbcadbcdcadbcbdddcbbcbbdddcaacbbadbccccabbcdbbaadbccdbcddaaabcdcbbbdccdcaadcdbdcdbcbabacbbcbcacbbccdddbcabbbbccdddaaaddabaaababddddabbccddabdbdbccddadbcdcacdacdcacadccbbccbaddadabdcacdcaccdbbdaccababccdbddcdddaaabddddccaaaaccdaadaadcdcdbbcddcabbcbbbdcdacbddbacdcacdccdddbaabbbcdcbcdcabcddabdbdccbcbccbaaadaddadbaaacdcbbbbbdaabcdbaadbdbadcdaaabbdccbacddccacbbdcbdbbccddadacbdcbbdbcbbcbbadcbcadadacbbdabacbcaddaddcabddabbcbbbddacaaadddccabbccbdaccacaddbbcbadcbabbdbcbdacaaadccdcadcdbbdaccbaabadadcdabbbbdcdcbdcadacbccddddcdabbdcadbbbcbccbdbbbbddcbbaabdbcbaacabadaddbcadbdbbdbcbaccacbbbbabadabbaddcdbcadcbddcadaaabdbbaaacaccbdbadaadcadaddcbacdaacbdbabaaacdbbbcacccbabbdbbbacbbddbbabaaccacaacbbcabdaaaadcbaaacbacdcdbbdbaaabcbcacaadaccccbbaaccabcbcdadbcadbacbbdabbabbababbcbaabccaabccbccaabdaadabcdcabdaddbccacbdbbddaddbddbcabcbdaacdacccbbcadbcbbaccbddabbcccdbdacbdbcadcadabdcccdcaaacbccbabccdabcdcbcccdcdddbcbbdcdccddddcbcdcbaabacadaadcaababcdcdbcdbabdadbaddbdbacccadadabcdccbaddbcbccdbcdcbccccbdadaccbbdadccaaccacacdbbacadcabbadcaaddbcbabcccbcddcddcdaabaccabdbaacbdbcccdbbbcacabdbddcabdbccacaadbddcdbbcbadbccacdabaabaaaabdbcbbcadddccccdadbbcdcbdaccbddaabddcddcdbdabcacbdbdbcbbdbacadbadbaacdaddcdbdcbbaaabdaccdababbbccbdadacabbcdabccaddacadbaccbdabdbbdaddabbdddbaacbbcccabbadadbbcbabdabcddcbdccadadacdddccabbddbddbcabdbabbbbcbadcbabbaddabdcaaabccdacabababcbbbbdbaacdcadccacbaacbbcbccdcdaacadbdbbccaabadcbbdddcccccadbaababbbcbdccdbddcdbacbcacccbbbadbbbccabadccbaaddbbbcaaacabccbbccbcaddbdbdccbaabcdccbbacbdcbaaacadaadbcdddbaddcacbbcababadccddcabbaddaadabababbbcdadbdddaaadbaccacdacbdcdbadbcbbbbaddbbbdaddbdbaacadbadbdbdadbaadbcdcddddaccbbcccbcadaabadbaccbcdaabaddbaacbcccccdadaccbcabbdcddcabbdbaacbbbcabbbbcdaacdbbcbbbccadbdcbcdbaabadcabbadcabbdbdccabbbdabddaaccccbbdbdcaabbccdadacacddbbbdbdbbaaabcbbddcdabdcabcdaaabbadcdaddadadbabbaababdbcbabcadabbbacbbcabdbacdddcbadbaaaaaccbbcddbccbbadcaaabbcadcbccddaadbbbdbdaaccaadaacbacadbcbbdbdbcdcbbcbbbabbcdbcbbbdcabaccadadaadbadbddadacbbbcdcddaddbadbdcdbbaabcdccbcbcdbccddbdbddadccdbdcdddcabddbbaddcaadbacbddbbcbdbbcadbbabddddcadcababadbabbadbcadabddbdbcdaacbbacbddbdacadbbababcbabdddcabbabcccdaabaddccbdcbaadbcdcbaddbbcdccacaabcbdcadbbdddabbcdbdcddbbdbdbaaadabbacdbcdbbadddbdcccdbbbcdcbcacbdcbacbcbbdcdbdcbcabbcbbabbcdcbabbbbcacabccabbaabaacbdbbdbccabcdbbaaaaddddabdbcabbdabccbdabcbcbdbbcbacbbbdbaddccdbddaababadaadcbcadcabcdcacabdbaccacaccaaddbdcbcabcdbbccbcbcdacbaabddbdcacdadcdaddcbcdccddccbbbadaaadadaaccabcabacbdbabcbbdbcbaccbacabcabcbacccdbabdaabcdabbbdcdcbcdcdcbdcdacdaaacaddcabaccbcddadbcddbbdcbcabdbdcabcdddccdabbcbacbaccaacbaccbbcbccbbaddccbabbcddcdcdbdadbcacbcaadcbddaacbadabccbcbbbbdaaadbaadadbabacbbaaacacbbbaadbcabbdbddaaccbaacccbaadadbbbdacdcadcbbbaacbccaaacabddaaacccbcdbbbcdaaabbbbbbdbacacdbaabcbcacacaadabdddcbccaabbaddadbbdbcaadabaaacbabbbabbcdacaaccbbcdacddbabbcbcdbddacdadddabdbbddcbcccaccbcbabaaabdccddbaadbbaccccdcdcbcadabaadaccbccbcbdddbcbbbdaaadcbcadcacaadcdaadaadcdadcdbcacbabbcbddccacbdcbabcacaaaacabdabcaaddaacabddaaacaaddcdccddccaaaabcacdcdacdcbaabacdbccbcbaabaacbcddabdadcdaabdccaacadaaacbdacbaccbdbbdadbbdcdcccccabcdbdcbccbabacbddbdbacdcbbdaacbcbadaabbcdaaacbdbddcddccaacddabbabbdccbbbdaccdcbcbddbacccccaddcdbddaacaadcdacaaaaacdcadbcdcaaccdccadcbdbbbcdbddcabdddacccadcdbabaddcbbabbcddbacabdddaabbacbcccbbbaabadaaaababaaadbbaadccaaccbccbcbcdccbccbcdcbaabdbbcaaabdcdddaaddcabbccccaaaacaddcacdcdabcdccddadddabcbdabacaccddcddadaacddbcacbdbaddcabdbdbcccbdcadddcbdbbbccdccdadcbcaccaadbccadcdcbaaaacabddcddbacdccbbabcacccddcbbddabdbabaadddabbbaaaacdcbcdcdcdcaabdccabdaccadabddadacadababbacddddddadcbaadcbdbadabbcbbdaacabdcbcdbbabcdaddcbbbcacdbabdaaadabccbdddaddbbbaabdbdccaaddcaaddcbbcabcabccdbcdcdaaadbdccadacccaaacdabbaccabaabbdcbbdbccbdbcdbacddabdcbacaccdbabdacddabacbddddbcacababdccbbddabbaabaabbadbbcdbbbdcaabaadcbaddbbcabbccabaabacabccccddbdacbadcdbdbcccdcabacbacbdacdbbbadccadaaacadbaacbcbcbabbbacabdcbbbbabcbbbcdbbbcabbcdbabcdcaccbbddbadcdaddcadcababbbabaacaccbbbbccaadcbadbbcbbcbcacacdbaadbabacdbadabccabdaddbcbcacacdddaaacaaabaccbbdbacbcadabbdbcdbaccadddabbdccadbabcaaabbbcdbbcaacabddcaaddbcbdbccbcbddddbaabacacacbcbbbbbdcbcbbaccbbcddcadcabbdbbcacdaddcabadbbbbddbbbdadbccababbacdadabaaaadacbbcbabddbbabaacacccabcbcbdcaacaabbdbcacbbdcbbcadddadacbdaabcdcdcaaacddbacdbbadbdacaaacbdadcbddbdababccabdbbabaababdbcdcabdcaddccaddcabbcacabddddaddbbacdcbdcdbdcaabbadabaacadcdbbbdabacccababbcadcccababddbcacdadabbbadcbbcddbdbabaaccdcbbbcddaacdbdbdaacbcbdbaddddcbdddadcdaddcbbaaacdbaaacaacbdacacdcaaacdbdadaddcbacbccccddbddbbaaabcaaacdbabddcadbccadbbdbdaddddaabcccadddccdabbddbcbddaccabaccaccbbcddddcaacdbcdbabcaadccbdbaacccddadccbbaaacdccadaaddaddcaccdcabcadaacdbddccdbdbddbdabcaabcdbcdcabaddcbbbbdbaaadabddaacccdddcabccdababadacbdacdbbbcabbddadcbacbabccaadadadadbccdbacdcbadcacaadbcbcddaccdacdaacddacabddaddaadddbabaaccdaabddaddbaabbddddacadddabcbdbacabbcaddcbbbddbdbdabdcdbcbccbaadcadbdbacaadddbcbdbacacaabacaddbcaacacdaacdadaddcdaaddaabdadbcccddcdddcdadabacccabccdaacbdabbdccabbdadcabaadcdbcbabdbaaadadcabbcccabccabdbcacdbdcadbcbcddbcbaaabcaddddcccaadcccbdcccdcbddabadbabcbcdadddcddabbcbbdbabbcbddabddcdcabadbcdccddddbbdcbddbdacabcadaadaadacccbbdabdcdccaaabdbabbbdcabccbcbabcbccdddcabcccdcaabdbbbdabbacadaccbcbbcdaaddbdbabbcdcabbdcdacdbccbabbdbacacbddadbccccddcbadababadbbbddcacbcdcddcddbcacbcbbabcaaacdbaacaddababadabacabbdddcbcdadcddddcdcccadcdabaabcbabbdabacbaadcadcbbbcaddbcaadaaababadcdcabcdadadcbddbbcbadbcccadcacbcdacacddcbbccdabdcbcbbcbdddcbddaaccdadbdccaccadadccabbcbadbcdcddbabdbbadcaddcccdbddbadbcccdbcdabaccabdbcbbbcbcbbddddcadbbcbcddbbacbbcabcdbabadacbaacadcadddcaaddacdaaacaadaaddbccdbcbcddaacdabcdcacdbcdcadbbadbbcabdcdaabaaaabbddcadabcacaacbacbaabcbdccabacbaaaccddaccadbccdadcdabbbdacacdaaacdccbabacaaabaadadbdccddcccdcaaabdcabcddaaacbccabcabcadccbbccadcabddddddaddabcabdadaaccbcdbbbbccaccaddbbacbcadaddddcaddaabdccbdbbcbbcdabccaabbabdabaadadbbacbdacddccabaacbbddbbacdccbbcaddcdacccbadbccddaadbaaaacdabcddbccabbdbdabddabdaaddcadcbaddcabbddadccbcaababaddcdddddabcddabcdcbbabddadccabbabcaadbbbbcbddabbcddcbdccbbbaacaaccdcacddddcaadacddddadddbbbcaccbbbdcdbcbdbadadcabbcccdbadcccadddcdbaacacbdadbdcbccdddaadbacddbaabccdbadabbccaadcabddbdbcdbadcbaabacdcddcbbdccaadaacbdabdcbcdabbcdbcabacadcbdabbaaaadcaacbbaadccccbabddcdccdccdabcbabcabaaadadcbdbddbdbdacbadadacddcdcaddcddbbdbdbbbbabbabbdbbbccdaddaaadccadacdacbcdadbadbccdcccccbbddadbddbbacbdbabcadcacbddbcbacbadbbbcdbadcbcacbadcddbbadcabbbaacbdaddbddbcaacbbbabdcaaaabdcbababcdaadcdabcadddcdcacabcdcbdbdbaccbbdcddaadaaacbddabaabdcabccdcdabbcadacacdabdaabbccbdabdbaabacbaadcbddaccbabbdaaabbbbdaddbdbbcbddaccddcbcccbbddcdbdbbccdcdbaccdcbccabbddbdcbdddbddbadcdbddbaaaacdbcdaabcdbbdccddccabbdaabdbcdbddabdaabadabcaadbccaacacbbadbbbdbccacbdccccbbacaddacdccbdcbbbdcddacadacabddbcdbcacbdaadbdcaddadcaccdaddbbbadbbdaadacdcdacaaadcdacbdacabbabadbdbdbaadaddabdbdbdccabddadccddcdacbdbacbddadbcadacbbcbbdbadabdccddbbbccdbbbbbbaabdbcbacdccddacbbdcaacababaaabcadacbdadaccddadaddabaadacdbadccbdccabbbbcbbcbddccdbbbddbdcddabadbddbcbbacdcbcaadbccbbddaddbcddcdccadcccbaabbbcdbadadbaabddbbddcdbddcabcbababdacaaccbdddcdbdbddddcccdcbbadacbadddcccacdccccacbbcacbcacacdbcbccdbbbcbbcbddbddbbdcdbddcabcacaadacaaadbbbbbbddbbddaddccdabbcbaddcbbddbdbdcbaadbbcbbdcaddcacadbdaadbbbaabbdbadbbacdbaddabcbcdbcacaabaabbbabdbbacaabbdbdbbabbcdabcccabbcdcbaaccabdaaadbbbddaddcdbcaccdaaaadabaadbccadaaaabaabaaadbbbcccddadcbdbcbdabacabbaccccaabdbaacbdccdacdbcbbacbdaccdbbcaabbcbcbcdabbbcdbdaaabbaaacabbccbadaabacabbcabbddcbdadbdbbaccbdaccddcacbbdcabacdbcaacddddcdbabcaddabaacdbadacbbaaadcadbadcdcbcaccaddddabcbccdadaaaccaabcbabdcabbabddcddcdbadabbdaddacbdacbcbdcbdacabdaadbaadbccadbdadbadaaddcabbbbbbcbcbbddbbbdcadbabaccabadccbdddcdaccbbadbcdbaaabadaddbbaabcaccbcddabaaabdadccbcabbbaddcccdaccbdcbdcaccbcbcacdcdbbccabdadddcbccbbaadbaaddbdadcdabbbbbcaabdabadcbaddcabbdddbabcbadcbcadcaaabaabdcccabaacaacbcadbaaacabddcdbaaaaaddcadccddaacadaccdbddddccddbcbabdbbacbddcadbddddbdaabadaadcbadbcbdbbcdaaccbaacccdaacbbbcbabbdbaabdbaacbadabadacdadbcbaabadccbcbbcdbdbbcabcdddababdddadcccaabbdbcbcacbdaddcbbabdaaabdbabaaccddcdcbbbbddddbcadcaabcdbacbddbddddccbbdcacccddcddbdcbbbabdcbbcaabcbbcdddacabbaaddccacacddccdcaacbaacaaabcbccdcbdacdcbdcadddabbddccbdccabadadcdbbcbcbcbccdbabdbadaadbdacddddabbadbaaaccaddbdcdcccbdadcbaccdaacaabcccddababaadbcbcccabbbccdcbadddcdbdabdcbaccdacdbdddccbabadbcacdaaacadcdaadcadadabccadcbbcbbdaabbbdcdcbcccccbdadabcdadcdcacbcbacbbaddbccabcbcdbacccdabbdcaddcacaabcdadacddcbbcabdcdbccbcbdcaabbbdbaaaddacbccabcaabbbadbbdbaccddcccbcbbdcbbbadaaacabaaccdaabccdbcbdddcadbdccdcdabdbacbcbbbabbabdbbdcdbadaaaadaadcbdccdcbbaadcacbbcccdbaadbbcddbaccddcbcdccacdbadcdcdcabcddbbaccdcbacbabcbdcdadcabacabbdacbcdaabaccddabcaabdbcbabacddcdbdbdcddbbdacaadbdddaddcbacbdbacdbaabaddbbbabadbdbcacbbabaacdbacdbabccdabccbccdacdaaaabcbbbdbcbcbcccbbbacdbbdddcdbbacbcdabbddbacaadadaccdcbaabdddcabadcbaacccbdadcddadabcbccdbbccabbbacdbbcbdbdcacadccbbadbcddbabddcabcbadddcbdbdccaddcaabbddddaadcdcdacbaadaaadabdaccacaabccbaacbcbdbccacbcaaacadcbbbababcbacdabcccbddbccddbaacdbaadacccadbadccdbacabdaabcdacbcbcdbdddacdcbacbbbddcaaacaacbbcacbadbaabbcadacddccaaccabbaabacbbaabbddcadbbddacbbccdccacbcccbcbcbcaccccaaadbaaaacbadddcdbddbacaccbcbaadbbacabbdcdbadbbcdbdacdcbdbbdcbdddaacadababbbddcbaaccbcabdbccbcababacdabbaaaddadccddccdddbacbdcbaacccdbddbaddbbdbbcbdcabbdbadccccaabadacacdcaadbbdabaabdcdbbddcbaccabccabaaaddcbacabddcabdbadcacccaababaccdbacddcbbbbccadbbbddaababbddbaaaababcccacaacdbbacbdacbcadccabbccbbbaaddbbcbdbdbbdabbbdddcdaacdcdadcdaabddcadbccbcbdcaddbabddcbadddbcbaaadabbbdcbaccbdaaccdbccccdcddcbbbdcbabaadacabdccbcaabaabcbbbcbcccddcdbbbddccdcdaabbbaacdadbbdadbaadaccbccaaadcabcaabddbaccbbbbbabaaddaaddddccccdbcaddbbbbcdbaccbccbcbcdbabbdbacacbbdccbcacbdacdbcdaadacbdcdbccdcdddcaaacabcaccddccccddcaacdbacbabbadadbcabdabadcadcadccadccadbdaddbdcdacabcaaddccbadbcddcdadbdbcbcacbbdacbaddbdbbcbbcadabcadacccacdaddddaadcbccaacbacbbccbbcbbcaacaacdbdcbaaddbbddddaccadadbbdadabaacacccabcabaddbcadacaaacddaddbabbdbcdcdbbbbdadbcbcbbacaaadbbcadbbbabccdadcadacbbdaccbaadccbccbcbbcdabcccacbaadddbaabcddabababcdbcdaadcccaaccdbabbbadcadacaacccbcabdccbcddccbbccbbdaadbbcdbccdcdcaaabaccbbbddabaddbbcdcaacddaddcacbacbcaadbbdbdbabdbbdbdadabbbbacdaabacddbbbcbaddbcbcbdbdaacbbdbdbadbbbabaaccddbbcddabdbdabadcbccadcbadaaaccadbbaddbbccaaaabcaabbdcbbacaabadacbacdddcdbabaaadcbabbdcbdbdbbacdccbbacabdcdbdacddbddcbadaadddcabcbddcdccdbccdaddacdcbaddcddacdcbabcbcdbddbaabbcbacbabbbcdcdcbdabdcbcbaddbddbcddcadcbacadcbcdcabacbcabaadbcbdbabddcddbadbbcbbbbcacabdcbcbcadaddcaadcdcdbacbcdbabddddcadbaabbddcadcdabbbccccaacaadaabbdbcaadadccacdbabcddddacdbbabadacdcdacdaccabdbdcbcacdddaccacadcccabdcbddaacbcbacacabcabcccccdbcacccbbbccabbaabdaccbadabadcbdbddaaacabbbdbdbbabaadcdbadbbbdbcbccbbdadbcbdccbccacbabdababacdaadabbaadddbdcadbcbddccadbdcbaccadbccaacdadbbdbdcaccabacaaacddcacdaadcaddaccbaacddaaddcaabcbdcbcbbadccdcdcccbbabccccdddddcccacaaababbadaacbbdcbddbbabddabcdbbcadcabbacacacccddacaccababacddaacdbbbbcabbbdddcacadabaadabbbbadadbbdaabcdbcdddbccadadaaccaacbabbcdabbadabdccbcbadddbdbdcabcadbdccdbbabacacbbddcdaaaaccccaabacdbbdacbbadcabadabbdcdbcabacadcdbababdccbbabacbcdacccccbdbcdbddbcabbcbdccadbaddaabcbbaacdadbbcdaadbbbcbbdacbbcadbdadcbdcacbadadcbcddcbcabdccbbbdadaddadbaddcccadcabcaaaddbdbcdadadccbacbaddcadaddbaacbbcdababbaaacdccbaadcacdddbdcacadbabadaabacddacbacabbbdcadbbaaabdcbcaacddaaaaadbbcdcbdbabcadacdbaaddcdcaadadddaaaddbddbbabbadcdbbcbbbbdcbaadcbdacdddbddabadbbddcdbbccadadaccadccbdddcadbbddacdcdaaddcbcbcbaacdaddcdbcabaaccdcbadabdbcbdbbddadaccdcbadbdbdcabadabaadbdcababbdabaddbadadbcdacbdcabcdacaabaccdaaacbabcdacccabbbbacdddbabaadadadddacbcbdbbabdacdccddbcabcbdddbcccddcadacbcabcbadabddadcdcddbdbababddcdbdcbbdddbcaccbabdaccbdbbacabbbcaacaaddabcdabccbbccbcdbadcaabbbaccddddcacddbbaddabddacdabbadbbddbdaadbabdbddadcbcccbaadbbccabbcbccdcaddaccdbbbbbdaccadccadabacaaabcbcacbdcbcdaaacbddccddcddabaccbccbbacadacbaabdcaddbbbbbaadccdbacdacbbaacaccaabdbddcbdabdadbadcbccbddadcdbabbdcadaadbcddcbdacddcccbdabcadababbcadaabdcccaaacbcabcdcabbcaabadbabbcbcccaabcbadaaaaaaccbabccabadabbaadcbdbcdaabddadbccbdacabaabcadddadbcbadcaddabdabadcbcaaabbbcaaacdaacbabaaddacbabaacddadcbdabbcadcacddcacddbdadbbacadadabdadcdcbccadaabdbdccbbbabdddbdccaaddccddbbdddccacdbcaddbcaddcbccdbaccbbbddcabddbdddcdcbdcdbdcdbdccbcdbbdcacdbddddcdcaaacbcdadaccadaccbbadcbccaabdcbcadcdbcaccacbcacbbdaaacddcdcacbdddbcdbbdadadcbaddadabcddadadddcbacadccbadbdcbaccdcbbdbcadcaabacdbbbddbdcbaddaabcddccddbcdabdccdbdadcbdaaabbaddbdbaccdabadadbdadddcaacbbccabcabadbcdaddbbcbadbdabddddbcbcbdabbdaabbdacdacaacaacdbbcbaabbabbdbbbaacbdadacddcbccdacdacdcbcdbdcbaadbbcbdbcdcdcadcdbcbdbdbddaccddddccaccacbabddaddcaccbbdccbccbabadbadcbbcdadabcdcbbbbcdcdbbccadbbbaababcbbcaabcababadbbbaababbcddcdcdcdadacaadbddbdbcadbbcaacbbdccbbcdaaadcddadcabcbbbccddaaabbadbcdddbcbacddbcdccabaddbdbcabddcddbcbdcabbddaadabcdbaacdcccddbacbaadccbacbddcdbdddabcaddbbdcaadacaccdacbdcacaacadddcbaccdcdbdddcaddbddddccdcdadcacbbaadccdcacaddccbcccabaddcbacbcaacccbaadcddcdabbbcbcbbddabbaddadaabcdbccdbddaabcacccabbdbdcbbcccaacdaddcbaadbbbaadbcaaddbadddcbaccbcabadcbaacccbbbcacdbdcababcabbacdbaaccbcbdbdbaadbcccaaabdbadcbaccbaccaaabbcbbabaacbcdbdbbdcdabaddcadcddcbcbddddcdaacaababaaaabbbdbccdbdcbcdcbdbbabbaccccbaddcbabaabbcaadaaccdbcaaaabbaadbbdcaadddcdcbbabdcbcabddcdbadaccbcabbbbbdacadbbddadadbbadcdcbcbbcddabddacaccdadaccdbadbdababdcdbacabaccbbadcbdbabbdaddacaddccdcaacccdcadcdcdcbadbccdbcccbacbadcbacdcbcdcbaddbccdaccddbbcccccbdbbacbabbdbbdacababdadbcbcabcccdbacaadaaccdaacacdbdadacdbadbabddbbababcdcadacbadadbbcaacccbdacbbcdcbdddcbbbaaacacbdddcddddbacdcaabdbbbddcbcdbaacbdbacddbccdccabbcbbbabaccbcacdcbbaadcbddadccaccdabdccbbcdaddcbbbbcbcdaddccdbbaadbbaadcbbccdaddcbabbcdcbcabdccadabcdbcdbcbbcabcaaaaadcbdadaabbaaabdacaacabcbdcacbbcbdacbbbcacbddbbdbabdcaadabdcbbadaccacdcaddcdbccdcaaaacaaaddbddacccaadcaacacdacbcdcdabbbacaadbdbaccabcabbacdaadddbcdbddaacbcdbdacbdcaaddcdaadcbcacdcccccddbacdadcdccdcdddbaccdacacddbdbdbabccaaccdaabbbadadaccdcdbaddaccadbcabdcbbbabaadabcaacccdbdbdacbaabdcbddcdcbbddbbccbbcdcddacbdbcbccabbacdadbabcddbdbbbdbcdcacbdcccdbcabdcbcbbadcdadbdccdcabbdacadadaabbdcbccababaaadcbddcbacdddbddadbbaaaadcbdddacdaddababcadccbcccadaddadcaaddacbbdbaaddadbdadaddddbcdbbdbddccbdbcaccdbadadcdcdcccbbdcbcdbcbdccccadbbdcdbddbcbdbacadbbadbcacbbbddacaacdadbdcaabccadccbadcaabcdcaaddbbadbcdabbcdbdcdabdcddabacacdbaccdcaccdcabbccdcabcccdbcdbadcddddbdaccabcbadcabbcaacadcaacdcbcadbbcbbaacbcccdabddaddbabbdabdccdbacbdabacacccddcddabdacaacbdbbabaddaaabdcaddcadaccbaaadacadccdbbbbcdbadccdbbccccbadcdcabcbcbcdccdabaabbacbdbcaccaabcdbbabcdadcdbcccddadcbccbbccbbacddabdabbcdcabdbbcdbaddbdadbddaccdcbbdbdadcdddcddbccaabdcaaadbccdbacaabdcdcbdbcbdbcccbbadcddbcdddaacbbbccccabddddacacbdbababbbdcaacbadbddaabcadbabacdbdabcccdccdcdcaccabaccacdabbbbdaaaaacabbacbcccdbaccdadcbdcbcbabccddababbcbaddbbcdbccbcabaabaacbadbdabbacabdbadcacddbdadabcbbbcbdbabccabaaaaaacccaabbabadcdbacdaaaaacacbccbccbcaaacabccabddbbccdccdbcaaacadbadaaaccbadbbacdcdbcdcaacddadbdcdaabdaababdcaddcbddcabacccdddddadacbdadbbbcadcdacdacdcaaccbddcbcdaacabbbababdadcbdabcbcdcccdddcaaacdbdabcdabdbadadccadbacbaddacdaccdadcbbcadcdcaabcccbaadddbcbabdbbcbccdaccbacbbdacddcdcacddbcabcdabdbabbbbaaabcabbcbacacccdbdcddcaaccddcbadbbcbbacadccdbbabbccdddbccbdddcbbbacbacbbcaaabbccbadbadcdbcaddbabdabcbacbabbcbabbdbdabacacadacdcccbcaabdddcbbbcbcbabcabaccadadddabdccaaccbdbccbccdacadcabcaaadbcaabbbcbacddabcacdbddcccbaddbccbcbdbbdadacadadadbcacbaaabdadccaabbbddbccaabadbdbadacccccaaabadbcabbababdcbacaaadadbababbbbbaacbdaddcbddcabcbbddbdcbbcbdbdbbbbadcabccdbdacbbaddbcdbacdacbabacbbccdcbdbcdccbddbabcdccacbddcdaccdbdbabdddcaddabcacbcdaabaccaaabdccdbcccdcccdbbacaabdbaacddacbbaaaaacaddabcddccbabaaabcddcdccdaadbcddadbadcbcaaadcaaabdddccdabacaadbcadacccbdcdcbcccccdcadcbbdcabcddaaccbacacaddabcbccddcaabcadacddadbbacdbaacdbddccccdbbdddbbbddabdaccdcbbaaaaccbdbcbcbaccbbadaacaccddccdddbdddbaccbddabaaccacbbcaddcbaddbccddacdbdaabcaababaaccacacacdcadccbdddacdcbadcddcbdbbbcdcaacddbaabccddddcdcbddbdaaadddbdbbcbdbabcbdbdaadcacbabbbabaccbcbbdaaacadccbccbdcddabbcaadbdacbcdabababcdbdcbdbaadbaacadbcbcacbdbcadccbbcdbccadddcbbacdbdabadcdaaddbcccabcababcdbabbdbbadbaaaccbdbcaacabddbaccbdacddadcbacadcbdadcdddbbaaabacbdbdabcaadabbbdcdcbdcbaaccacadcbadbcbadbcbbddcabcccbdcabadadacbdcadcdacdcdacacddadabacaabbbbdaacbcdabaddcbdddcacbbdbbdcacddaaddbbadbaadabdadddddccdccbcaaccaadadddbdddcaccdcaccaacaaaabdbabcabcadabddaabaddabbdddaabdaadcabdaaccccbbcbccacbdbbabcaaddbabaaddcdcdaccdadcdbdccadcadadaadacdabcdcadbaabddabaaaccbdcbbdadbcbdaadbdccaadcbbbcaabbdabdddaccacdcddcdbcbdacddaaadacdaaabddcddbbbcbcacddcddacdbacbcaadcbbdbdcddcddcbcdcdaaabdacddcbacdadbddaccbacaadaddcdaddbcdbabacdbcdbdadccdabcbddbdbdcbcabddcabdccdcaaaddacbbbcabcbbdbacdbdbbdbddcaccbccdbcdabdbdabbcdbcccdbddabbabccddabdbabcdccdbddbabccbdcdbdcaacaadcbbdbadaadacadbbbdcbdadadbcccdcbcbdbaadbabdddcddbadccaaadadadbadabcaacbdcacddcadabbacaacaacadcdbbccacdddadcaabdddcbccababbcbbbcadbadbaddcacadbcddccbaacdcbcbaabaaabddaccbcbcdbadcbdcdddadcdddbcadbbbcaabcddbababbddcaaddbaddcbdacbdbdadcbaabbbbcdadadacdbdacbbbcbcaadcababddbbcbaacacacbbcbbabdbaaacabdbccaabcabaacabdbbcacbadccddcadbdbabaaaabdadcbbacaacccdbdbcaaccdbcdcabbcbcaadddbcbbacdbdadbdbdcdacdbcccddbddbcacbcabaaaccddaddbdabdbacbabddddbdbdcadbaddbbcddbccdaaaaabacdbbbcadacdbbbbbccdbacaddddbbdacadbaadcbaaccaacbcaaaacacaccaabbdbaddcaaabdddaaddbcdbbcaaaadacbddbbdcbaacbbdcbbbaacacdbdcaaababccbddbabccdbbdaababbbadbbbdabadcbabadccbbabcbbcbbcadcbdccbbcdbdcdbdcdbcccdabdadcbbbcccaaabcabdcdcccbdbbccabbbabaadabcbbccbcddccabadbacbdbbabdaaccdbddbdaabbbdacbdcbbbccbddcacbadcadbbccdbdcadcdaccaddcbcbbbcccabdacaacabdcbcccdbdcadabcabccbaadcdcadacaddaddadcccacdacccbcadacccdbcbddbdbbddbcacccbdccdadaacbcaccbcbdbabcacacdbcbaabbdcabcbcdacbaddcccabcbcadddbcdbaccdddbccdacadbaddcbacccacccadbacccdbdddbdbbadabbcadaadcbcdddbabdbdabaccacabbdccbbaadbbabaacadccbcdbbbbabddacbadbdbcdbaaaacbadddadcddcbbdcccbdcdcdddaddbabacacbaabaadddaabcddcbbbccabbbddbdabbdcccccbacbdbcaabadcbcaabbbabacabbcbcbabbaadcbcdcdcadaabbcabdcbbcbdddccccdcbdaabcaaddaacddcdbaccababbaacbcbcbbadadbbbbbcbaaccaaabdbcbdcbdcaacacbacdcdcaabdadbbbabdcccdccbbaacbaadccddabddcaaabdcddddbdadbcccdadcaccabccdabcdccdbadcbcbcabcabcacbaabcaabcccbbdcbbabdbcbbadccddbcdadbcadaadccaaddbacbddbcaabcdcdbdacadbadcbcbddacdbdddcaadaadccdcbcbcaaabcbdcdbbbaccbacbdbcbaadaadadcadccbdbcabdbacdbcabcddcbabdbacaadacdcaccbcababcacdbbcdcdcaaaddcdacdcddbbbccddaaccdaccbcbccaadabbbacdaadbcbacdcbbdbbcbaccbdabbdcbabbdbccabcbabcaaaaacdcdbccaaddcdbddbaadbbcbbccbbdaacdcbccdcbcaacadbaddaabaadabbcbdaadcaadaacbccabcaabcaddbdbcbabcddaccdcbbccdaddbdcabdddddacaabdbdbcddcbdadcccabbbbdcbdbdcdbddcbccacabbcbaddcdababadcbcbcbdccbbcddcbabcbacabbaddcaccdbabddabaccadcdadcdbccaccaccbdbacdcaacdaabdacdcdcbccbdabddbbdbdbddbaccbdbdadaabdbabdcdccadadabbbbabbbaaacddabbdccdbbdccbdbaccbadcdbcbdbdadabcdcbadccabccbddacabdabcbbdcbadbdddccbbcddccdbacddaddbccbddababcbbddccbdaccdacccdbcbcccddaabdccddddddcbbcccdcdccbaaadbdbddaaacadabddbcbaddbcbbcbbabadabadccbadacdbddbaaddddcdcbaadbaabcabbccaadbbcabadcccacdabbdccaabacbbcddaacdcaadcbadaaaadadcaabdcdacbdbdbababdaababbadcabadbdccaddbaacdaadcacbdadccbbadddcaddccdbdbadbddbaddabaccbbdccddcdccabbdadcbdabcbbccdadcdabddbcdbaabdbcdbdcdcdcddcdabadaddadbbcbabddbdbbdcdbcabdacbbbbddbbcbbcddbcacbdacddbbdccbbbcabdadbbbdabdadbcbbadbacabdcdacbbbbabccdcdddbabcdadbcdddacbaadcdbbbadaaadbaccbcacdccbcdaccabcdbaacacbacdaabadbaadcababcbdbacadbadccbdbdabcdbadbaabdbdacccdcaaadbddbdddaaaadccbddbcdbdbdabddacbdbbbddadccadaacaaabdcdbcaccddbdacbcddabbdcbdcaaadaadddcaccbcbdbdbdadcdaaccacddaabdbacdddaadbcccaaacdbaccdacbcaddbbcaadbddcabaacaabdabdaccabbddccdcdbddddacbdaddcbdcbbbabaaabdacacaaadbabddcccaadbccbdacbcccadcdababddcccdcdbdcabcbacadcadddbbcbbcbacdabaacbdcbbbacbcccbdcdbcbdcaadcacacabcbaddcddaaadddbbadbadddcbdbcbddcbdacdbbdccbcadbcbabcccdbbcdbbbcbbdcacbdaabadccbaaabddddcabbccdaabacbabaadadcdacdacdacbabbabadbadcacbddabcabbbdabcacddbcadccbccaddbcbcacacaabccacdcadccddcbbdbbdaaaaadabdcacaaaddcdcdcaaccbddbdacdabbcbbabbbaabbdcdbdacccbbcaaccdbcbdacbccaababdbadbdccdaaabacdccbaccdddadbdccdddcaaccddcacbccdcdcccacabbadbbbbccbcbddadaddbbdbdcdddccaddbaadbcaaccdcacaabbcbcdccdbcccacbbcddadcdccdbbbacbbaccacddddbbcbdbcabccdcbbbdcdbabaacadbbcaababdddaccaccdacdabdbbadcccccacaadaccacaacabbccadbaaddadabdacddcaadcdbaaaaabcbbcdbbadabbcbdcdbcdcccbadcdbbccddcdadbbacdabadcdbcccbadddaaddddddbaadadbbbaacabcbbbdbbabcdbbdabbcabcbcddbacdbcaabaccaccccacdddacdabcdcdcbaacdbadcdcbdbabcbccdccabbcbcaaccdacbadbbbbbcbbaaadaaaadcabcbbdadbdabdabbccdacacbbdccadbdbaabcbdadbadadabbdbccabdddbaccbbabdbcabbadbbddcabbcccacabaabaabadadaadbaaaadcdadbbddccbbcbcccaacdaabadadaadccaaadbbacddbdbdbacdbabccddaacdabdbdbcddbaadbbddaacdadaabdbabdcccdcddccbcdbbadabaccbdbbcbcabddccbdabacadabdbdddbccacabbccaadddcadcaabacdaccbdabcacddbcdbaacbbbcabacdaddcdbbabadddbcbaadaacaabaacccbadcbddaccbacadacacddcbbabacddcbddcdbdddddcaaacdaabbdbddbbbaadbddabbcbbcbccdacdcdcaadbddacbcabbdaccbcbbcbdccccacbaaadacdbdabdbbacbdbaccdbcdbdccbbddbcbcbdcdacbdaccbcddbabdbabbcbbdbadcddabbdbadcaacdbabdbcbccccddcaccbbdbacccccbabcbacccddbddacdaccdccdadccababbdadddcbdcdbbcbdacbaaddcdddcdcbbadcddabdcbccddbbbbbcacadcbbcadcdbadcdcdaabcbabdacbbbbcbbaacddaccccadadadcaadbabbddcddcabbcaabcdaaabacaacaaacbdacacbbcbaaadcacbabbcddcbaacaccdccaacdcdbcbaddcdbadcbbacabccabbcabbccdcaabbacaadabbbbdbcdcbaaabbacbcbccbbbdcbaabacccdcbdbabcadcaabadbbbbdbddcabdbcbbddaabcdadcadabcdddcacdbbaabbdccdbbdbdcbabccaccdbabdbbbccdccabccbbbbcddaadadadddbbbaabcddaaacadbdbadabcabdaacabaacdccdcddcbbcbcdddadbccabdbbccbbaadbbbbddbadabaaabdabdaadcaaddbbccacabcbbcaadcabcdadacdaabcbcbcddcbbddadabaadaaccabddddaaacccccbcbadcbacbaaadcbcddaddabcbbbbcadcacabbacabcacdcabdddaaddbbbbbcddcaccdcdacadabcbbbbbabbadcbcadacaaaaacbacbacbcdcaaaaaabccbbadabdbbcbdbbcbbdcbdaaccddadccdddacaddcbabbbacccadbaaaacacdbbdadbabdbaddacdaaccddabddcccabbabbabdcadacddccdabadabdbcbbbbbcddbbbbbcbaddccccacdcdaabcabddacbdaacaacabdbadbbbacdacaadcacdcacbadacddcbddcabaccabcbcdbccaaaacbdbcadbbaaddcddaadaaadccbddaacbadbcaabababbbadcccdaaddadaabcbdbaabbbbabcadabddddbcadacddaaccdadbddacadbbdcbadbdacaacdcacacbdaacdcabcdcddccdccbbcdaacbbdddaabdadadddacaabdadabdcaaaabdacddaddaabdbadacdaabacadcdddbabbabcdddbddcbcbbbcadccbdddbabddbcbccdadaacaacbaaddcbdcdbccbabbccacabaabadcddcdbcabacdbacabacbbdbcaddcbccbabbaabacdcbddbababcbdddadcaadbcdcacacaddcddddcbddcdbbadbaddadababcccaadaddbacbddbdbbbbdaadbccccaadcbdcaacdbbaccccabcbdbdccaacdbaacdaadbbbbcaaabbaddcacdbaacddbddaccdcddbbadbdbaacbadabbaadbddcdcbdbbdccabcbbbcbbaccccacbcbdcdcbcbaccbcccdcaddcdacddacabbcccbdcdacacbaadacacbcdcbbacbbcdcbababbabadbdbcdabbbadcbadbbbacbbdaaaaccbcdccdddaacbcccbccacbcbcaacbbbacddcabbaabbdbdcacbbcbacbbbbcbdbaabcbbaaabbabbcbdcddcdaadabcaadcbdabbbdccbddadbbacacdcabcdabcddacabdcbddbddbdddcbcaacacbcdbddddbcdaacababdbdbaababdcccccbdbdccbacbaacdadaccddcadcbddaabdaaabbdcacdcbabccddcadbcbbdcadbabbcacbaccbbaaccdbbdbdddcacadbbadabdcdccbacdbabdadaddacdacdbaccdcbadaadddabdcbbdbcbdabcacdaabdbdaaacccbbbacbcaddbcbddbadbadadbdaddbdbbcbaccaddaaabdbdbbbbabcbbcaadbaabddabcaaabccbacadadccccbadcbacdddaabbbdbcddadcdaccccbbbcbabdaaddbcacccbcddbadcbdbdbdaacadcdadbcbdaaadaabcdbaddbddadbabddbddbabddbcbaaacaacdaadbdbcccddaababcbacdbdcacdcaaddacbbdbbddabaaabdccadccabadccdbdcbbdbcaaaddadbccdbbccccbbccaadccccdcdcadaddccacacdcccbbbadddcddbaadabaacacacbaddbdbabdddddbdbddbdbbacacdbaccddabaccbddacddabbaddacddaccacadaacdbbacdcaadcadbacabdcaadcbdcbccbbaacbaaaaccdbdacbbcbdccddcbbcadddbdababbcbdcacaddadcbbadbccbaaabacabcbabcddddcaaacbaadacaaccccbbcbbcaccaabdbcaccddccabddcdccbcdababacddbabddccccdadbacbcbdabdcbddbdcacaddcbcbcbdcdbcdcbbcdbbddcdddaccaaadaadcbadadccabddcccdaaaaaddcbaddbdadcbdacdaaabcdbadbccbbbdbbbcacdbdbbbbcdabcbaabdbcdcdabdccbdcaaabacdaadccbcaabdaddcdaacdaacdaacbbcabdcbaaaddbcdacaaabcbbacdbbccbcaaadbbcdadadbaacdbabbbacbbbabbcdcbabcabcadcaacdacbccddccdddcacdabcacadcdabbbdaddcaaaababdccaabacbcdbbbbabcadadadbdacaacbacdcadddbdacadcbadcbbbddadcacadabaaabbbccacddbcadadaaaadabadcccbdcbddaccabccddabccdaccccbccccbccadbaddbcccaccacdadbbabadadbcddabbcdaacbccccbbaabacddbdabcddbdabaadbacbbaccacdacddcddcbccddbbdabadcccaaaabacbacacbacbdbacdaaccaaaaabccdcadcacadbaabbacdddbdaaabbacdcdbcbbbdacbcbaaaadbbbcbabbbabcdcbaacacabcdacabadcdacbcbccbcdbbccbcccaadcbacaccdabbbabbacacdbdaabddbadaacbcaadbaaaadcbacacdcbcdcdbaaabbaccbcdcddcbdabbdcddbcdccabbbbdcddbdbdccbaadcadcdddcbdadacccdbbcbbacbbbdccdbacddcbabcbabdbcccccbdbcbbadbdcabccbbaaadcdaaddddccbdadcbbdddcbccaabdbdaddaacbcdadcddbdadbccbadcbccdccbbabccbacccacbdbabbabaddbcccccbdccbddacacbdbbabcdccbadabcbbdacbabcddbccababdbdaadcdaaabcddccddbaadaaabddaadddbadacdcddbadbdbacdabdbbaaadaddadcdccddbbddbbcdcbbbadcacacbcabbcdcdacdddcbadccabcaabacadddcabdccacbddddcbaadddabbacadccdddadddacdadbcdbacabababacdcdacccdbbbddbcbbcddcddbaabbcadccdbabbdbdaccbababdcaaadaacbaabccdaadcdccadccbbbabcbaaaadcbaccabaadacdcabddcadddabaacdbdbcbbbdcadbaabaabccdadadadadbdaaaadcdaabdbdcccdbabccbacbbaaccaadbbdacddaddccbdddcbdbbbadbabcbddddaaadabcacccbaaccaaadbcbddbabddcdcdcbcdadcaddaacdaaabaddbaaddadcdacccbacaadaadacbbbbdbbddbadcddddcdbcabbbacdcacbbbacccdacacbbcdabbdcababcaabdabbdbbaaacdcabbdddbcdcdddabdabbdbabbcdbdaababbdbdcaaacbcdaadadcbdcbdbdbbbddcbbbabdbaddabddccbbcdadacbdaccbaadabcacbdaaddbddcbcaaddcabcddbadabddcabbbcbaacddababcbcabdacbbaaadcacadcdcaddaddcdacccdcbbbcbcbcdbcadcdabacababccbaaaadcbdcbbbaddbabbcadbbbdbcdadacdaaabaabcdababddcaddcccdaaccbadbcadbdbddabbadabcabcdadabdbcdbddaadddaacbdaddbbbadcbdadbabbdcbabbcabdccabcdbcbbdbdbcaadadccadbdaacbabababcccbabdcdbaaaadbacbddbcbddacbccabadacbcbdcdcdddbbbdccadaabbaccddcaacddbccddabadcbbccdccdbbcbdddcdadacbbdcdbabbaacbbdbddacacaaccbbcdaaabcdbaadbbdbccaabcccbcabbdcbbdddbdbaccadcdccabbacdddbaaccabcbcacdcbbacdbbdccabcdadbcdbacdaddccddacaacaddbcbdacdbcbacbddddcbbaddccbcdddbccaabcadaabbbcdcacabddbdadcbccccbcaabccabdbdbdacdbbcbbadcbdcdaccccdacdcdccabdcccabadbdaabaaddcdcaaddbdccbdddcccabbdcaabccdcabcddcbbbbbdbaddabbcdcbddaaaccdddadacdbaccadadcaabbabbbccabccdbcbbbccccaaabcaadbabbaacbbbbbdacaddbcddaabaaaddbbadcccabcbcacdabbdddddbbbabcaaadabadbdbccbcdacddbbbcccbadccdbaacaddbdabddacaacacdddabcbbaccbdadbdabbdcbcaadacccdbbbcadabcbcaadacdbbdaacaaabdcaddcdcccccbcbbadcccdcdcdbacaadcddabddabbabaccaaadadabadacacaacabcadbddbacbaccabccabaaacdabcaddcbaaacdabbcdacdabadbccddbabcdcacddcaacddcbaddbcadbddbbbcbadbccbdbacdbadbacabbaadcdccadbadcadccbacaddaddabdddaaadcbbaaaddbabddcbbbbdcdbdccbdabacacaccbcccccbaabddbdaabbadcccbacdbabacccaccbbcbaddcbadbdaccadbcdcbbccadbccabbbabadadbcacbaaddcbadcdabdbdbabbbaddcadbcddabdcdaaddaacbbabdbcaababcacbddcddabbcaaaaddbcbcbabbbbbdbbabdcabbcaddadaabcbcbcabdccbaadbdddbadbcdadbadcbbccdaaccaaaddbbbabdbbbdbbdcdccbbcbadadbdbdcbbccadbccdadbddcdcddbbadddababdbacdddacadcbbcddcacbccaadcadddcdabcabaccbddddbbcccbbcaccaaaddbdadbcaadbabbcbdacbacbbabdcdcccdbbcbdbaccadacbdddbbbdbdccbacccabdbcbaadaadadaaadaabdbaaccdcbdcacccaabcdbbddbdbdbdddcdcdbbaaadaddacddccbdcdbdbdcadaddabadaaddabdcadabbddbbbabbaaacbdaddbabbcdacaadadbccabddbdaaacdbccadbccdcdaacdbdacdbcadacbbaddccbbdccbbdcddabcacdddcbbddbcacabddadacbddcccbdbabcddcaabacdaddddacdbbabaccbccbbaddbcdaacdabaadabaadadabddacccbbccbcacadbbbabbcccaddacbbdbdccacdccadbdcbbacdbcdbbcaadabcbacccccdacddbccbabaabaababbaccacbbbcaabbadaacbdadcddaadcabadbaaabddbdbdbadbaddbdbccababbdcdcabcadadbdabcbcdabcbdbcdcaabcbcddcadcbaacdabaacaadabacdabcdcabddaccdacadababdaaabbccbbadaadcacaacbbaaaabdcbdaaababaadcbcdbdbbbccbadbdadddcdbbabadbaaccabdaccdddddcaaadcdcaacdcbadaaacddbabaadcbccdabdadbcadccaabdddbbaabbbdcdbaaddcdddcdddcdccadcbcaaaadacadcccacdaadcbabadbddaabcdabbdbaddddcdaaaabababdcdacaabbabdabadccbbcdacbcadbadbcccbcdadcadaaadbdddbdcbccaacabdcbacdcbdababbbbdbbacbaccaacddbbdcbadbbbcccdcacddbdabccaaddadaacaadadaadddddacbdabadabbbbbaadabbbdbaccbcdccccdababccccdacbaadaadabacdabcbcabaadddbadadbdbbadaadbdabcbbddbddcccbbdabacbaaccaabcdccdcccbabcbbdcdcaddcccdcddacccdbbbbbbcbccaabddcdbbdbbbcacdadbbbcdcacccddaacadcbbdbbddbddbdbccabdadcbbbdaacbbaabdbbddcddabaddcacaadaccacabdacdadbdcbbcdccbcddaadcbdbaabcbcaaaabcbabcbaadadcacadcccabcabbbccbdcccccbbddaddacdbabbdadbacccdddabcccabadcbdccaacdcdcdbcacbcdddabbcccddbabbddcaaabaccbdcdbadbddcaaacbcbbabdbacabddddbdbdcaddbbbcdaabcdddbcccbadcbbcbcabdddcaddaadcabbbbacddbaacddaaccdbcdcdbcbdcacdcabbbadbdddacdadcdbdbcdaacdcaccdadabbccccdcadbcbccdccbcccddddabcacacbbcbbabcdbababacabbcdbaadcadadcaaccabbddbacdbccbadbbccdccdabbdbdccdababcaaccccdabcdcadcabddddbddadaadadbcdbaacaabddbaacbbbdaaccacdbdbbcdacddaaadddcdadaaaabdcbbcaaacbadcaabddccdbccdcbddbbbacbacbddcdccabdcabcbdaccbdadcdbaadcbaddbcdadbcaadcadbcbddbacbabacdabcbbbdabcabbdaddadcdcdcaadacbcdabddcabdacabaccbdacbbdacbacdbdaaaccbdcdbbdccbabcadbaabdddbdbacacbbabaacbdbcacdcabccdbcccdcbadddccdccdaacadaaabcddabadaddccddcaaadbaadaaaaaadcacccaabbdbcdbadaabbabdbadabcacdbcdabdbadcbccccbabdddbdcbdcccdadbdcbabdadaddbabdddabbcccadddbaddbaadcbddaddabbcbdddacabacdcdcddbcbbddabcaabacddccdddbbdbddbccbbabbaddccababddcccbabadcacabadccacacadcddcdabccaaadcabbddbcabdbbacdaabbabbaddbcdacdcbbadcacaaadcddaaadbabddadbacaaadccddbddddaadbaabcbabaadbaddddccdacdccbccabbdadbbabbbccbacdadaacdadcddcbacccacdadbddcbadddcdcdadccddaaccddbccbddadbbddaaadcacdbaabaacbcbdcbbbccaaddabbddddaacbabcaddddaddcdbcddcacdacabcabcabaccabddbbbabcddaaacbaabdaaccabdcbdbaccabcaabaadbdcdbbbcadacaabcadbbbdacddaadbcdcbbaababbacdcaabcdacdcaccdbdabacdaaabbcabcdccbcbcacdbdccaabdbcccbadadadbddadcdaabbbbbdcdcdcacdcdcdbcbabddadabacadcadcdbbbdcdabddcdbcbdacacaddacbdaabddbcabdaadbaabdddbabdcbccbcaaacacdddddadbcbcddadbbcaadddbadcbaabbcdacdddbbbacddbacccadcdcaacbcccdcccbbbbcbbbacbbdcbcabbddaaaaaabbcdabadddabadccdbbbbbbddccabbcbcccccdddcbcdccddbccaaddadbcabcaaaabdcbcbcdcaaadbadbcbbcddadbbadbddaabbbddccacadaabccabacacabcdbbbcccbadddbbbacbadbdcdbacacdcbaaddaccbbcbdadcbcacdcadabcddbbdbaadcbdbbcddddcdabbccaddddababaadacbdcdddddbacaacbbdadbbdaddaadcdcaccabddaddcdccbaacddabacccbcaabcaadacdcabddabbdbbaaccaaaddbcaabbaadccccdaaddaacaaacdadaabccadcacaddcbcadbccbbcccbdcdcddbddbcdadbbbcdbcdccbdbababcbddacbadaabdaadabcddccbdabaabdabdcccdcaaadabdbcddaadacabaddcabacdcabaccadcacbdaacbbcbacdcdbbbdcdadaddbbcbcdcacbaaaccbbcbcbcbdbdccacacbbadadcbaacccacdacbbdbcacdabbcdbdbbadcdddaaaabaacdbbaccbbcdabbabbacacdabcdccabcddabddcacccadcbcbbacbdbbaaddccabaadbadbcddcbddacabbcacabdbaabdbccddccddcdcacbacccaddcbdbacaacbbbcdcdcdcacacbcadaccddcadacbbdbbcbdaabbcdbdddbacccbbcacbdabdaaadbcbcaadbadacbbbcbabdcaacdddacdcbdbadabddbdadadbbcaababcdcccadadcccabdcbdcdaacbccbdbbbcabccacbdbbbddbdcdbcababdbbaacaaacccadabbcbbbaadddcadcbbcbcadadbbacdabccbbadccdaccadbacdbcbbdccdaadbccdbadbadbdcbdcbccbdcadbdaaabcadcbddadadadbdbdccdcdacaddaaaadddbdbcbaabcdcdcccbcbdcdccacdadabaadddcacaabdcaadaacbbbbbbabbddcadbcbbcbcbcabbddcbbaadadccaabddcabadacddcdcdcbccbdacdadacbdcbccdcdbbcbacbbbdddacbcbacddaabdcccbabbdbcdcdbabddbaabbbdbddcadcababbadaacbbbaccbacaadacaddbbddcdcacabbdaccbaccbbaadbbbcaccabbaabadcaaadbacbcccccabadcdcdaadccdcccabcdcbaaadabadabbbbdaacaaddabccdabdbbdaabcbaddbabbbcbdbbdcadccdcadcbbbcabdadbbbabbbdbdbacacaaaabbadbccddbabbdbdcbadabbbbddcbcbbddaccbccdbbccdbcbdacdbdcbbadcbcddcdbbbbcaddcddbdcdaabdccbddddcaacaaadcacbdbaaacdbccbbcdbbdbaaabbbcbdcbbddccddcbcacbcddcccdcdbbacddabdccacccdbcacddbbbadbddcbddbbacaaababaccddbcbaaccabaacccdcbdbdabcdacbcacdaacbacadaaacbbabbadbcaddabbcdabcdddbcbdbbbccbaddcacabdddabaadbdadacbbcbdbacdbbaddcdbcdacaccbcddbdcdcdabbccaabdaaacaadcdcdabbbdcbbbabdcabbdbbbbcbaaddbadbccccdbcabccdabbadbccdbbaadadbbcdaabdcddaaabbdbcbadbabdcdbcdcbdddbdcdbdcaacdddbacaaddbcdbddabbcdbacbdabdcbccdabdcaaddbcccacabaaddbabbbadacdddbcbddacbaccbbbcbbddbbbcdbdbaaddddabcbbccaabbccbdcacbdaabbcacabddccabdbccccdacdabcaaaaccdabcabcddbbddbacacadddcddaadaacadddbdbbaacababbaabbdbbddbdadacbdcddacdaaadbaababcdabbdddccdcacadbddcbdbaabacadddabbbcbacbbaabcccdddcaddcbdaaddaddbdaddcdbaacadddaadcdcbacbadcacabdcdacdacddbdbabbbacadbdbbccccbbccbcdaaacbadddaababacddbbbdabcddadaacccabcccbcccbdaaadadbaaddcbdabbcaddacbaccdaaacadacbdbabcdbccbdbdabbdcdbaadbabdaccccbdabbbaaddbaaccaadcddbabdbbcacdcbadbddbdcccaadbddaaabcbbcbbbacccdbadabbdcccbaaabbbacaddcaaddcabaadbacccabbdcabbbbcdbabbdcadccddbabacaaabddbcabacbcdaadbcbbdaacdabdbbbdadbbcaaccaccdabaccdcbbbadbaccbadababbcadaacababcccacccdacdccccaadccbddddddcdadaddcaacabbcbcdabadadbadddcccddbdccbdccbdcaddabdcbbbabdbbadccabccaabcdabbcddccddbcaaabcbbaddcbdccbaadcbbddaddabacdbcdcacbbbcbcbbbaddaccddbcacdccbabaccdcbaabdabcccbdbddabadabdcbaaacbcabbbbdcddbdbabbabdbddddcdbacbccacbadcacdaaadcdbccacbcbddcccbacdaddaabccababaadacbdadaccdadadbabbbcaccaadbcdacbaccddcdbcdcbbcabaddcbdadcadacbdcdbccdacbdcadacdacbaddbbdccabbcadddddccbbacbcacbbabcdccddccbdbddbdcadcaabddbbcdbbabadbcbbcddaabbdacabcdabaadbccbbbacbcadadbabcbdabddbbdcbcbddcdacbcbdcbbbcddccbdcbbacccbaaabcabacadcadabbbdbaacaadbabbaabaccbdcbbdddadacdbdaccbcaabcbabadbcdddcdbcdaccdccbdccbcbbddaabbadddddacbbccbaacdbbaaabcdcccddbcdaadabccccdcdcaabccdaaaacbadbdbbdcdaadbbdddabadbadcbcdacbdabcbddcabccaacabbdcaabcbcdabccadbcddaacbccbcddccdbaaabcbbdbabcdbcadbcbbbdddcaabaacacccaccbcbcabdcbbbcbadbbcbabcdbdbadacddddbcbbadcdbbbbdddbacacbbcccaccdcaadccadbaaabcdbbcacaabaddbbdbabcdabbcdcaacbbccdcdcdbadadaddacacbccabccbabdcbbddcbcbccdabcbaacbbdadacdaabaddcdbdbaadabddabacdcddbcdcbdaabdacbbcdbcaaddabcabdbddadbbbaaccdaddaabbccabaaaaadabababacbcccbcababbdaabdadddbcbcbdcadddbcbcbdabadbddabdbabcdbbadbbbdddbcadabadddcbdbcabdababccccdddcccdcdaddacdaaadddadbbdadccbcbcdbbcdbdcbbabcadcabbccbdbbccabababadcbacdaabdddbccaabadccdbaabbcaccdaabbacbdbdaacdacdabdaddbcccbbdcacbdcdaccdbaabcacbadcacbaabaaddadcddbcdcbdbcacabcbbaddbdddbcbdcbcddccdadaaddddbaaaaaacccaabbdccbadcacbbdddbaadddcacdbcdbdcddccbabcdcaaaaddadcdccaccabacdcbbacaccbaddcbbdbbacdcbddcadcdbcbbaabbadadaabdbdbdaacbbbcbbbaabacbdbaaaaaddbaaadaaacaddcddbdcadcdcccdaadccadccddabcbccdbcdcacbcbdcccbabdcabaddabdaaddaddababdacccadcacabccddccbcdcaaaadadaadcabbacdacaabacaadbdacdacccdcccadbacabccbabdbaccbcccccbddabadbccbdbddbdacaaddcbbadacbbbddacdddbcbbaabddbdaabdbdaaaabbdbddabcadcacbccbbabcbbaabdbbcaaadcdbadbadcabdccbcadcdadbaddcaabcdcdcadcbbbbbaabbcadbbabbcbbcdbabddbccabcccacacdcabcabcdbcbdbdabbdcddaacadcbabdddabddbbccccbabbaadddddddcdbcaabaaabbacaabdddaddbaaabddaccaddadbdddacbdcaaccaddaacdcdabaccabcbbcbabaacabcaccaddbbdbccdddccadcaaacaddbbbcbabcbaccababcdccbcccdccdcadabbbdacdaabcdbbdacbaaabcbbcbcddcabccadababddaababbcbacadbacaadbbcdabdbbabaacbccbddabbacdadadadcdcdbcaabbdcadaacddcbdbabaadddbaadbaaaabddabcabcacabcdadbacbdbdcdaccbcbcaccccdadadccadbcdcbcacdcdbcbdccdcdcbbdbbbccadaababacdccdcaadadcabaacbbacacbbccdddbbccaadccaddbdacbbcddcaabaabcccbbddcdbbcdcdabbdbdbaddbbddcacaddcababdaccbcbcadcaaaccbddabcacbcaadcdcbbadcadcbbcbcbcadbabbccbdcdddbbabddbbdbacbdccbdbcaadcbbaabcdbaaaccccbbbaacbadbaabdaaabcdcaacabcaacdabbbacacbdcacbccbbabddaccbacdabbabbccbcacdccddbcacdbbdcbccdabbbccbccbbaabcdcddddcbcddadcbcbbccbcaabccbcdbaabccdadccbbbbdccbddbcbcaabbcccaabdacdcccbabdbbbabdcccdddbadccdaccdadcccbdaddcabbcbcbcadddddaccddcddaddaaddddbdcdccbacdaccbdddbcbcaddbbaacccdcdcdbbdbdacbacdcccddcdccaadbcdddababcdacbcacbdbdccbacbcababbdaaaaadddccdcaaddabcbdaababdddacccbcbbdacbddcacccbcdadaacccadbbaaccddaabbaddaabaabdadddbdaaaadbccbcdbbdbdbcbcddcddbdcbcdbdcacdbbdacbaabcaabbadccdbbbaabbacaccabcbddbcddabdbdbcaadcabaacdaadacaabcddaacaccbbcdaabcddcdcccdabcbacddddaccdadccbcdcabbdcbdadbbbaddddcaacabccabcdacdaaacabbbbaaaaddadcabcbdabcdcbcaacadcccbbcccddcdbbdcaddbdbcbdcdbaabaadabdcbccadbdcccdcabaacccbbdddabbccbdcbaacbdcdccbdcacbaacbdadbacabcdbaabacadabbbcacaddacdcbcaaadabddcbccddabcabdacdadababbbccbabcbbcdccbbdababdaadbbaaacbbdbddcaabdccbcaaadbbbdadbbbbbbabccacadcaacaadacadbbccddacccabddbbadbbdddcdadadbbcbbdcbdcaaccdbcdbacabdaccdacbacdbcbabacaacbdcddcbbabaccaadaabcccacdacccdaabcabbccddadbabcabcbbbaaddaaddaadcbbdccbdbaacdbdbadaabcdadacddabbbdbdbddcbaadabcacbbbcddbbabbdacbdaabadcaadaabdccdbcadbdcaaacbdadbcabacddbdabdacadabbacdbbccdbdccdaaddaacaddcacdaadcaaddbbacaddcdddadbbbbabaabbababccbaadbcbadbacabcdccddcabdacbaacbdaabadacbdcdbbacadddaccddddadbdbcabddbdddcbcaabccbbaacaabddcaabaaccdbdbbdbbbacadaaddcabadadabdbcbbadccbdcbdaacbbcdbcddaccdbacacbdadcdbadbcbacbaccbaabcbbbdcabdabdbcbddaccddcadaccbcaadbacccacabbabdadaaaacbcbabbbdcdbdacdaadbdccacbccbabbcbbbcbadddbbbcdaccdddaaccdadbbabdaccbadccacbbcbcbcadadadaacbbaaddbbadcaabddbcbdbcbaacbaddbbdbbcdaddababdaddbadccacdbabddcaabdbaaabccabcacabccabdcbcbcdddaabdbadddcabdbbbddccabbcbccbbdbaadabccbccccadbdbabcbdbbbcdccdcaacbdbaadcacaddcbdaaccdcaddabaccaabaacddbbdaabbdbbcabbadbbadbdbbdacdabccbdcbabacdcaacadadbbdbcadcbcddabdadccbaddcbabcdbdbcdadaacdadbccbadcddbcabcdcdbadccaaddabdaabdbbbbdadbdabbcddaadbaaabbacdaabdbcdabdcbddaccbcaaabcdbddadaabcdcbdcbadbbbdaccbbdacbbdbbcdddacddbbccdabaadacbacbabdaadddadcccbbcacbbadcaabcbdcbdababacbaacbdcddaddadbcadbcddadbadcbbbbbbccdaadcbcbdaadccaabbdcacaabdbbcabcbdcbdbddbcddadcddacddaddabddbbddbdadddddcbcddbdddabbdcdccdacdddbbdabacdcdbbdcdbddcaddbdcaabdabdcaadaadaabadbbdcaabddbbacaabcaabaacccabccddcdabdabbadcccbddbbccccadbcbcababddacaadcbbccacabbccabbaacbbccabacbaabbdbccdbdbadccccdaaacdddacccddadadadcacbbbacacbbcacdcabaadadccbabadcabdacdbbcddbacabcababbddcbbccacdaccacbdacbacdaaccdccdabbcadcadcacbcaccdcabcabdbdbdbdbddcbdaabbdababbdabbdbdaaabbddcdddabdbacbcacabcdabbbcdcaccaabdcaabcabacdcadabcacdacbcaccacdccbbbabdacadbdaabadadbdacbcbdbddbdcaadbdcabaabbcaaccccadcbcdcbcbbdacdcbdccdaccdddaababdbdccdbbccbccccabccdbddaaadacddaabdacdbcaababbdccccbcbddadcbbbdcdccddaadaacbddbdbccaabadccbbadbaacdbccccdcdaddddcddbddbcbdcbbcdaadbaddddababccaddddcbabbbaddbaaccccdcbdabdcbdbbbabcdbbdacaaabbabbdcbcbddbbbbbcbcabbabdbdcaccbadccaccccccaadcdcdcaabdcdccdddbddcaaacbcbbbdcdccadbdacdcddadaaacdaacabccabaccabdddbadaaccacbbabbbbaaabdcdabdbdbcbaaaacdabcddccdddadaabdbcdbbbcddabdacbbdaaaabcaacaadbbdddcccbcdcdcbccaddadcdbaadbccbdddddaacadbabcddabcbddcdbbcacdbdacbddaadcaddbcaadadcccddacabdacaabbabdcbdaddddccbcdabaddddcdbabdddabbdbcbadcdcadabddddcccdacabbacaacabccbbbbdaacacdbbbaadcbabaacbbaaccbdaddcbadadddadabbbcbbccdcbaabddabddcaccbadcaaadbdcabbcbbadaaaaaddbacacdbaadccccabcdcaddacdcbdccbcaacccadbbddccbddcdcbaacddcbdcbadbbbbdbbdcbcaccdaacbacdbccddddbcdcaabacdcdaaaddccaccacdbdaaccabdccabcacaaacabdabbbdacbacbcbaccaaaadacdabadcabdcbdcadbdabdaacbbbdabdbdddadbacbdaccdaaaaabdbcbadbbbbababcbaababbcbbbbdcbbbaabadddccabdcbadbcdaabcbbcbddcddbdaaaadbbcaddddcdadadbcddbbddaabcdccbccabdadcdabbbdcddadbcdcaaddbdcdcbbaaadacdcabdcbabddcddabbbdbdcdbddadcccaabacdaacacbaadabdaacdcaccacadbcdddacaddaaddbdaacdabdaddabbdacabadcccacddacbcddcabacabbcddcdaabdacccccbcdadadbabbbbbdacccddaddbcdbcdadcdcccadacddbdbbabbdcbdbabcaaaaccacadcddaabcccbccdccbbadccbcbdacbaddaacbdbacbdaabbdacbbadcdcabdaaaabcddacaddbbbaacabbbbcccabdababcbcbdabbaccbccdccaaddbdbbbbcbbccddbaaaddbdcbbaddcdbbddadbccdcdbcdaccadbbaaaaacdcacadbdbdaaacbacbddddcdbdaddbbcaabddcdcacddaccabbbbacbaadcbdcdabbbcaabbaaadddcbbcbcdabacaabdbdbbdbcbadccbbabcccadabaccbcbbacacbbcaaacaadbbacdabbccdabcdabbbbadcadddcbccbbdbbadbdaabdacdcaddccbbbcdcdcdadbadadababccadbacbbdcbdadabdabcadbaadbccccddbaaaabdcdbbacdbbdccabbabddcdcccdcbacaaadbcaabdbcdaccacbbbccdcabdbdcbaaaddddccddcdbdddcdaccdaabbaabacddbcaddddaacbccdcbdbdaaabccddcdababdcdadabcbcdacaacdadcbbbadccadcdbdcaddbbbaaadbdbacaabacabbbcaaaaabccabcccdbbdabcbadadacddabaaddbcbaacbcaadaacabbbddbdbcddccccdcbaabdadbbcaddcdcbbbdadacaddccbdcbabdadbcacbcacddbcddcdaabdbdacbcddaacacbbcacaaacacbdaacabaababdabddcbccdbadacdcddbbaaabacddbcccbbadcbddbcbccaddacdaddcbaaaccabcdaaaadbdbabdcdbbababbcaddcccddaccdddaadabbbcdccbaccaaacccbcdcdacaddabdddacaddbdcbbcbddaacdcdcdcdadddcccddcbcbbacbcddabaccddcdcabbabbdccbcadbdcdbdacabcaccdbacadbadbacdabacdcccbdbbaddbdaadcadbbadacbabbbdabddccdbacadcddbadabcadabdbcbbddabaaaacadccbcabdcdbdbcddcddcddcddddabbaccddcbddabccbccbddbcabdbadaccabaddbccbdaabdbccdaacabbcddcdbbabaaaabaccdbccdacbaaccbbadbcbbcacdbcbbddbcadaaccdbbadbdbbdaabcbbdcbccadccabdaabdcccdddccabcbdababbbababacaacacacdaadcabdbdaadcbdccbcabbbadcbaddbcadbaddcaacadbdabdcdbdbbdccabcacadccdbbbbabbbbdccbaddbbbbdbbcbccbddbbddddaccddddacdacdbaabacaccbbbabcccbbdbbbdddcbcadcaacaabbbabbbbadbbcabbdcadacadaacbbbadabbdcacdbcacaabddcacbbbaabdbcbaddbdabdddaaddccccadbddbddbddcaaacdaaaaacdaacbddaaabbdbbaadaadaddccbbccdabbbbdddbabcccdacbcbddcadcacccaabcdaccbcadcbbbdbbadcbcacbbbacadbbbbbdcddbcabdcaccbadbdbaabdddbaababaacdcdababadabcabaabbccbdcaacdcbdccbadddbcdccddabbdcdbacaababdcccacbdcccdddadccaaaddaabbdbbaccccadcccbcdadacaacaccdbbdbacbabbadcacbcddccadbdbaccccadddabccddabaddbdbbcacdbdcaccaaaadadaddcddabdbaabbbdadcdbaaaadcabccbabbaccdaaaddddcabddcbbcdcbacddaccddadbcaaadbbaaacbbccccbcdbbcbdadaabbddcdbcadaabcbabdcbccddddacdcbcabcdcacbadcdaddaabdbbddbadabdabddababbccdbbdaaadbdcacccbcbabadabdcacbcdddbcadcdcbdbccbadbbbcdacacbcbababcdcccdcccbadadaabbcccadcbbdacaaacdabcaaaadcabcabdcbacadbcdcdaadcadddcbadaccdadaaaaddbbbcddaaabddbabdbccbbdbbdcbabdddbbabbdadcdbbabddbbbcaadaacbddadaacbccacbacbbbbcbabbaacbadccdababcbdabdddadddadaacdaaaaddcacbdabcbdbadbabdabbdbabbdbcdadcbcbddabbbaababcabaadccdacdcaddcbdcccbdcacbcbbdcacdaaaaaabccdadabacadcababbcbddcaccddaadaccabbaaacbdccddbcbcbcacdbddaaabaabaaacbcaabaacadddcaddbdcaaacaadcbddbdddcbaacacddaaaababacdacbadbcdaadcadcdacadcddcbbccddbcbcbdbabcdccbadababdddbaaacaddadabdbcbacaddbcaaaaadcaaacbaadbdbbddcdddbdbbadccdbaccaadcddcddbcacdcbaccccacbcaabccddccdccadbaccdbbbdbacbacccacaddcdbaabdbdbbdcbbbadccacdcacdaddbccbdcdccbbbdbcbcbdcaccbabdcddcbbbdbcaddbbbcabdcdddcbbcdbabaccbbdadaadcbddcaadcbaadacaadcdbcabadbbbdaabcaabaaadabdadccbcabadccdddddbcadacbbacacbcbaddcbdcbabacbdccdbbdddadbcacbbcbacaabddabbcabbabcaadaabbbccaaacabbaddbcdadaccddadddbcbacdddbccdcdbdcabccacdddddcdcadbbbcabbcdaacadacbdbacacdadcccaacddbabbabadddabbabbdacbaaacabcccccbcabacbccddaaabacaacbccddacbadabdbbacaaaadcbacbabbacccaddbcacbccdddbaddbbcdbbabbdcabaadcccadacacadaaddccdcccdbdddbdbcaabdadddbabaadabcbccbcddcbabbabdccccbccbddbadcbdadaabdbdccaddacbddccdbacbbcbdcaadbcccdbdbaabbcdcaacdbadbbdcaddddbaabbadaacdbccddabccdbbccabcbbddabaaddbcabbddcaabbddadcdcaaaccdaccdcbacaddcacacaabbddccaddcccdbdcdaabaadcdcccacbbdcaacacbddbdbddabaaddbdbabcaababcdbdbdcaacbabccbcabadabbcdcdccadcddacdaaacbdaacaadddabacdcdbcdabdddcddcbabdaacadacbcbaaaabdcdbabddccadacccdccdcdbaccdbdcbdaaccdbbaabcacbbcabcbbcbabdbcdbccbcadaaaabdcbdcadcdbaabbadbbabbdbddbbcacdacbaaacdbccdcadaacdcdbccbcbccddcbbccccbbdbdbdbadcccaadbdaadbbdadbaccadbaaadadddabddaaddaacacccbabcdbdaabbadbbdcdbbbabbddddaadcdbcdccbbcbaccadbccbccdbcdadcaaaacbaaddacdbbdbbbbbaabcbacbcddaddabbdadadababdbdacabddcadbddbadaacddbdbbaadbbdccddbdacdcbaacabdcaccbdcaadcbdacbaaabdbbbbcdddddacadcbccbccdabbbdbdcacacaddaccbbcdcbdababdddcccaccdcdccdbaadbdacdbddcabcdbcabcccbdacbdbadcabcbcbddacadddccccdbbadadbabccdaddcabcdddccadacbdbbadbdaccccccbbcdcddccddbcdbbaadbcabdabccdddcbbcabbdcbcbbadcccbccbdcdaaddaccdbbaaacabadbadaaacadcbaacaaddadadcaacacadbadaadccbccddaddaaadcdabbddabbcbcdabdbcbacdbbadaabbadbccbcaaabcccaacbcaacaacdbdcabdabbcdccbddddbcbcbabdacdbcabcbadaccdcbaabbbdabcbcbcbbaadcadadbbcdabcacddabddcacdcdabcdddbddbbbaacccddabdadcddcccdbcabdcccdabbcadcbbbbddcddcacacccbdcbdcacdcdbbabacdbdddcccbcbacddbdcdaabdbccddcbdaababcaccdccdaccbcadadaddbcabaadaccbbadcbdbbccdadbddaaacdcddbdcbccacdcacbcdbbbdadbdaabacdccdbcbcdabcbdcbbccdacabddaaabcabbbbabbddadabddabdcaacacdadaddcddadbabaadadddcdbdbcdddcccadaaccabdbaaddcbaccadbcbacbcacabccbcbbbcdaabdadadcbbbcdadccbadccdcabcaadbdbcdccbddaabbdccdcddbcacddbbcaacccbdcdccbbaabccdbbccadbaadabdccaddbbabdaabacdadbaababccdbdccbbbbdbaccbdcbadbbcdabccbcaaabccbbddbaadadbdadaacdabbcacacaacaaabdcbabcadaadbdaadddbacadacdacbbbabdabbdcbccadacbdcdbdcabcccadabcbbbbbaccbbaabcacbcacaadababbaaadbbbbbdbdccbdaaadbbcddabdacdbbdabadadcbacdddbddbadabcabddbbacdddbcaacaaaacaccbcccacabccacbbccacdcaaddbbcbdbcdcccddbabcabcbdcabbcaaaadbabcccddcbbaadaacadadcbbcbaacaaabddbcbaddaccbcbccabaaacacadadbddccbdddaddabcbdbcabbccbaddcabddacddcdcbbabbddcbddbdbbcabdcbadbbbcdadccddcacbabbbbdcbccacbcdabaabccdaadcaccabaccdbccdbdbccadaaadcbccacbbcbbbbbdacbacdbbdcddbbaabacaadabadccdcddccaababccccaddcbabdbbbdadabcddadccdddbddcbabcadcdcdaacacddbbddbbacdcdcdadcdadbdbbaacabcbddacacbabacbdcbdbacbcaddbaccddcdacabbacdbacaddcddaddbbacdccaabccbbadddcccbcabddddacacaadabcccabdcdcbadcadabaaaabbdabdabbcdabacdaaddaddabbcdcbbcdcccdddbdacabdbdadddcaccddaaccdbcddcabcaaabbaacbadaaaacddcacddaadabaadaabcbbdcdaacacccccbcccaddbccacdcbbaaddabcacadccbcbdcdaabbdaaddcaabcbccbabaabaabacacbaacbadddacaaccddbbcaaddcccabdbdbabbdabadcbadcbbdbcccccadccbccdcdbcdababbbdadcbdbabbbccabccdbbcadcacdbbbdccaacbcbddccbcbbbccacdccdccadcddcccdbbbcdadaaacdaababdadcccadcdadcabccdcbdbabacbabdbaacacbdcdccacdabcbdadcabdccdcacdabbbdabdabbcbbcbddccddbaabbdbccbbcddbbbaadaabbdbabadbccbcddbabbbbdcdbadbbacaccabaddaaaadcabdaaacdbaaccabdcdadbdccacbddccadcbbdadcdacaddbabddadbacdbababdbdddbdcdbaccbaaadabcdbacccccbcabccdcdccaacbadcbbbcabccdcbababcdcaadcaaaacbaddbabcbbbbcdacbcbcbddcccdcccbabaadbbdadababcacadcdbddbbababbdacabdcaccbdbdcddbcdbdbcbcbabcdbdddacdbdcdbaddabcbdbcaacdacbcadbdabdbcacbcdbddaccadddaabbcadbbddcddcbcbcbcbdcdddddddadcaacdbcdcddadaabcbaaacdccbcabdbddbdbacbadabccbdcbbbcdadddcaccdababcaccdabadcaaccbcbbccdccdaacbcabdababdbabccbbaddaccdcddbacdddcccdcddabdcddcccddbdbabcadcbcdcddbabaabbdabdddadcccbbbcabddbaaccbbbdcacbdaaccacaaabcbdcdbaddcadbaaadccbadddcdaccacdcbaccccabcabcbbaadcabcbddccaacaadcdcbcdacbcccddacccacaccdaccadcddddacbbcbaddbaacbdabbcabaccabcacbbcdcaccdcacbcdabacaaddadbcbbaacdcbaacbbdccdbaabcabaadcdbdbbabbdacbdccccdbcaaaaccdcdddbcbdcbbcdbbbcdadaaaaadbddaadbabbaacabccdddbccaaabbcabbacbddbbadbcaccaaccbbadadbbcbccabacadcaccdacbdabbdbbdaaadabcddccddadbcdbcdbaacbaacacacbcacadbcaddcdcccdcabbadcacddcbdbcdabccbbdacadbbcdbcacbbaacdcbacdbbdcdccadbcaaabaaaccdcaabbbabdbdaabbadbcadaccccdadadbacccadbcadcdcacadbaaacbacdbccadacdcddbdbbccbddbbdacbddabaadddbcbcacbbbaabdabacdddaacbdddcadadcccdaccacaddbbaadbbdaaabccacbddaabbcaddddadabdaabbaacdbcddbdababbdbacbbbacadabcbcddccbaaadaabcccdbbabcacbcdcbcdcdbbbabdccccdddbadddacdacbbbdaacccdcaddddcdcbdaddcaacddabcaacbabdacccabbbbcbadcbcaaaaddbcdcaaaaccbdcdadcaabcbcbdbcccccabbadbdcbabdaadbbcdddabddabccaccdccbbdbdadbccbabdbccccbcdbbadaaddcdbcdcdccbaaaddddcdcadbaaaadaacdbbaacacabdbbbcdcbccabacacbacbbdbcbcdcdaaccdaacaaddcabdcdbcaaacbddaacdbdbbccdacdcaacbaacdbdbbcacbdddcababddcaaadbbcbdbaabdaadcdcacbbbaabbabbccdbbcbcdccacddbdddccbbccabccabbcbbdbdabddddcdcdcdcdbbdcbdccdbaccdddbaaaccabddabccabbbcdbbcbcbcbbbcbadaabddbcdbbdaaccdabbcabaddbaabbacdaaabbcdaacbcbbdaabcdabaacdaacdcadcaabadabdbbbcabcdaaadddcbbcdccbbcbccddccbcadbdababddccbcbdbcaacdcaacbbaacadabdccadbacbcdbdbcbbcddbbbbacdbacbdcabcbdcabcacacbacccaadadcccbaaccaddcdbcbdddbdcbdbbcbacdaabaddddadbddcadcbabccaadddcbbbcdddadcddbaddbabccccbbdcbdbcbbdbabbaabcdaaaacdabdccdaaccccabbcddabdbdbaddacacbdbacbdddbdcdcdbcbcbaabbbbdacbbbcaddaaadadbcdbdcdbbdacdaacbbbdbbbabcbbabacdaddadcdcdaaabacaddddbabdcaccacabdadbacabbacbcdaccdcbabdbdabbbcdbdbddcbcabdbbccabdcdbaababaccadbbaccbadbcdabddccacacdddbbcdacddcdcaddadcbbcdadddddabacbaaccbdbcdcadcbcbbdbbbcbcccdcdadcdcaccaddcadacacdbbdcabdcaacbbdbbdcaacdcaaaaadacabdcaddcddadbaadcaaaacdcabdbdacdbcbabcbdadaacbcdccbddbdbbcacdbacdabbbbdaabddaadcdadaaaccbcddaabcbbaacabacacaccdaabacbacaccbbdccdcddabdcddbabbbbadabaaabdaaddabacadbdbcbbaacddacbcaaddbccbbdcbcabdcdbbbbcdbdcdbbbccadbdccaddddacbaccabcccadbbcbcdadbaabacbbccddcdcddbdcdaacbabdaddabcabbcdbcdbaaccbcbdabbaacdbdcdbcddbdbdbcbaabadccabccbbdcaaddcddadaddcaaadbcdbaadbccbabbdbbadadabcdabcccdcdcddaadcbbbcaccaadbacbdabdccabbccbccacdbaadbacdbabbaacacccdcbadbabccadccdabcbcadbdccdbdbdccccbbbccacbcbcbcbacabdddbdcbdbaddacddbabadaddacbdcdadddbacadbcbddabddbcaabadbaaabdcdacaddaaccbbaddbbdddbbbddcbaadcadddaacbddbbdcdccbbbbbcbcbdcdddadaddbabccdcdaadaacaaccbcacacdccccacabdddccabcbbbacbcdaadbcbabbcbaadaabaccaaabaacaabadbcdcadbabcdbdaddbcabadabbbbaabcbbbabbbaabbcccccbdadcbbcbadbcadabdcbbdbdcdaccccccabcdaccccdbcadadcbabbabddacddccbabbcbaadabacdadaddabcdacbcdcadcaabbbccdbadacddcbdaaacaadddcdcccbdccdbdcbccdbcadbcdacbdacacccdbcaddacbbacabbcaccaabcccbcdacbdbbbbcaddacddcabdabaacbbcdcbdcdadddbbcddacdccdbaacadabdbacbaaadbbaacdbdcdaaaabdcbbdbddcababdaadddadccabbbdbbcccdcabbccdacbbacbdddaacdcddcbbbaccacdacddbacdabccddcadbbaadddbdddbdabadddbcabcbbabadbdacdddcbbdacaaaddbaadadcdbcbaabdcdcdbdbcbbaddacabbddcbbdbccdacadbcaccbaddcddabbbccdbcbdbcdaaadaabccabaacacbacccabdaddddaabbccabbbdcbabbbcacaabaccaaaadcabcabbcbcbaadbbababdbaadaadbdccabbbabbdbaaaabcbdabbabaccaddccbcddabdabdcacccdbdddbbcadaccadabaccbaccdcdbccccdcdccddddccbadcdbbbadbbbcabdcabdcbbccacbcddaadbabccaacadccdcccdbdddbadbaaccdcacdcabddaacbbddbdabaabcdbbbcacccaddbcacbcaaabcaabcdcbcdcbdccbbaccdccddacdabddaaacaabdaaacabccadadbbdddbadabdaadcdcbdcdbdbcbaaccaaacbdacdadcbabcdccbbcaaabcbccbaadbbcabadadbbadbbacdccbbdbcddadcbdadddcabbdddccdcbbcdcddadbbdacbbbcbacdcabdcacbcbabbbddddadbbbdbdacbbbdcacacdbbaaaddddbadbddbcadbaadcbbbdbbccadcdcadbacdddadacbdbacdabaddccdcbccbbddccbccaccbcbdbadaadcdbcaaabaacbaabdaacbccaddcaacccdcbaddaadcaadacddbcbbccbbcbdbcdcbadccaadcbacbacddccbbbbabbddcbcdaacdcabacaaaabbcdaccbccbdabcdaddbdbaaaacabdccbddccbaddbbcbdddacacdacccccddccccbbacacdccabbbaccccdcbbcbacddbadcbababdbaddccacdbcbccbcddccabbcabaadbdbdcddaddcbabccddbcacddbcdbaccbdbcdbddcbbaaccbbdccccdcabdccbbabcbbbdcbcdbdaababaacbbadcacababaaadbaabdddcdcacccaabbddcabccdbacccaaccaacbabcaadabcdbacbbaaabacabbbdabbdcbbbbccbbaabccaacddbaddacdadccaadabdbccaccddbbbdcbacdbaaacdbacaaacbdaadaccabdcdccaaacaddcdbcdcaaddabcdbddddacbdccccdcdccdbbcbaaaacbabbbbabadbadbdacccdaaabbddcbdaddadccabadacdbcaddddddddcdbcaacddccbbcdcbbabbcdbbdcacdaaccdbaccddcbcaaaabadacbcadbadbdcacdbabaccbcdabdcccbdbbdcbcdddaadabaccadccdacbcbbacdbacdaccadaccdbdadcbcaadaccbadcdcdbcbabdbcabbcbdaacdcbbacbbbcaacacbadbabdadaaaabdabbbdbdbaadbdbcabaabaabdbcbadddddddaabdbcbbdcdaacdbcdabddbcdcdcdadcbbadcabaccdacbbcababdabcbabbcccdccccacdbbcbdadcbcbcadcddcacbbcaaaddbcccdadcbdaadcbbaaabacdcddaababbbadbdacbbccbcbdcaabdabbcaabbabcccbacabccdddadaadbcaadaaaacaadddabdbadcdddcacabbbaabaddacabbddbabddadadbaccdaaaddaababdaabcbddcbadccbcdaaacaccccdbbccdbbcacaadcccaadbadbbcdabcadcaadbacdbacadbcbcdbdbbbddaadaabadccbbcdacdcadbdacddabaabcaaacacbcbbcaabccabacbcccdcacdbcdcccbacbbacbddaabddcacaaccadbcdcaacaaccdaadacbdcdaaadacbbdadabcdccacadcbdaaaabcdacdabbdaabdddcdbcbcdaccbdcdcdaacdadcaddddadcdccdaccbcdcabddadbabbdbbddcdcaddacdaaaaadcabbbbaaadbcaacbcacdadaccdadadbdcaaaddabacbaaacadcddbdcabacacbababcdabddbaadcbddbcccdcdcccccccdbaddaaaabccccadbcbdddacdbbddaadadcdabadaaaacbbbbabcabbabdcbacaacdbadabaacccbdbadcddbcacccccbcdddcdbadbccdddddddbadddabacbabbbbbcdbcdbcaddbcbdcababbabdbbcbccdddabbddbacbcdbccdacbccdabdcadbcaadbcddabcabcbbbbbcdaaacdccdbbbdcdbdbddcdacababbbcdadbbadbbdbddadbabdbaacacbbcaabbbbccaadadadcbaccabbabcaaccbcbaaddaabacadccabbaccccdcaadcacaddbbdcbbcdaabdbbbddbbdcacbccddbacddcbddcaabcbbaaaaacabdaaadabcaaaabdbcaddabbcdddcbcdcbcccbccbbabbbbaabbcdaadbcdabccccbdaaaabdccbccbacaaacdaadcbdcadcaabcdaaadadabbdbbabddbbbdbaddaccbbaabbcccbdaabbadbcacbbbbacadaabdcdabbaaddcbadbccbbdbaaabcbaaadbdbdccbcacdbdcddcaccdbccdabccabacdcbbbadccdacadacbdcbcadabdbdbdabcaabccabcccbdbcdcbdbccdccbacbcbabbaacaadcddcdabddadaaaabdcddccbaadbddcdaabadcddcdbbcdccdaddddbdacaabcbadaabdcdabdddacddabbadabddcdddcbcbbbadcdddbdcbacaaaccccccadbdcdddccdcbcbbbbaabbbaaccacbdbbabddcbbdcbcccdcccdcdacbbbcbbcacdacccbcaabcdcaaccccdaaacbcbcccacbbcdbbaccadaccbcadaabdadbaadcbacaabcbcbadbadcbbaaadcdacbbdcabdbddcbdbdccaaadbbdbbcacccaadabcabccacbbddcbdbbcbdbaabaaacbabacbbbbdcadbdcbadbdacdbabdcadbbdddbbccdadbdacaccdbccddcdcdaaabdbcabdcdbdbcdcbcdcaaaacbcccabdccddbbacbcbcaadcbbadadacacbaadaabbbcdbaabcddccaccbaabbdaabdbbbaaacdcccbacbbccbcbdbdaaddcdccbbacbdacbaccbbdcddccabaacddabddbbdcbbdabcabaaaacbcdccdccabbaaaccbdcccdaaadbaabcbcdbcccdbaacacabaccbcacaadabbcbddabbdbdbdcddcabccabddcabdcbccbaccaccbcbaacddcbddddabbcccabdcacdabdbabdddcaccbabdccbdadcadbccdcddccbdcbcddababbaaccdbbabcdabcabadaadadcddbbddccdbadbcccbcbdabaddbbcbbdcccacbbcccbadabdcbdacbdcdbadababaabccdcbcbccaacbacdcaaaabaacbabcdcbaabdccbcbdbcdaaccbbbcbcdbdbdacccddbbbacadbbaacddccbcddadddabdcadcabdacbababcabaabdddddadbddadbdadbacddaaadbdcddadcdbbbaacdcddcddccbdacbdbdcabcacaccccadcabbdaddbcdaddabccbccdddadcbaacbddbcdbdabccacacbdbaddadacacadabaddacccacacbbbaaccacabaadccadbdbadaddbdbdbaddbcccbdaaabacdccbacacbdcbabddabddadababdacabbbdcdabbabccbccdbdaccbcbcddaabbbddcaddcdddbcbbbcbbacdcdbcdddcdcaaadabcdacdaddbcabacddabbaacacddbbcbcaacdbcacaadbcdbdcdbdddbaccdbcbbbcaddbdcbbdadddddcbadbbdaddbdbbcdcaddbcbadaccaddbbbdaccdbadddadbcabccdabbdaaacaddaccdbdddbbbccbcacdcbabccbacdcbcbaccccbaccbbbbbcbddbadbaabbcddcdcdabbcbaccabdadbdcdddddbaaddbcccdbabdcaaacabcabcdbcdacdadacddabbcbdbcaacbccccdcadcadbccdcadcddaaacddacbdcbcadbbdcadccbaaaccabcaabddbdacadddbdbdcaddaacbdcbadccdaadcbaccdadbbcaddacadcaaaacbacaddccdabcacabcddbccbaacbbbbbaabdaababbbcbbbddcccddaabdaacabcaadadbaaaddddbcdbccdccddacaadcbacccbdbbcaddababddadcccadacaccbbddadcbbbcacaaacabddbbabcdcaabdcddaadcdbcbddcbbcacaddbccdcddcdbbacabdadddabaadcaddaabadddbcaababcdadddabaccddaddcbcdbcbcacbcdadcbabacbbabcacaaaabcadaadcaaddcbccdbadbddcaddbaddccbdcbaccdcdbcabdbcacbcdccbabbcabcbbddadaccccacbccadaadddccaadbcbbaadbabadabdcbbcbdbaadcdcbdddddccbbbbaaaaaaaadbbcdcaccaaaacaacbdcaaacccdcbacaaddccbbdbacaabbdcacbbcbacabacadadbdcdaacdbbdabcbddaadbacccbcbdbcdcccbcadaadbddacdaacaaabbdccbabdcdcccdccbdbbcbcdabbbaadbbccadabdacadcbdcbddcabcbccbaccabbadcdcbdbdaaabcbcbdcdbbcccbabdacacdcadabacbbdcaccabaddcbcddabddabbabccaccdbabbddbcacdcbbabcaaccbadacaadabaaddadcbcacaaadbaaddbaadbdcddaaddaaaccddcdbbbddbbdadcabcbbbddbaadacbdcaabdbaadbdaabadbdaabacaadbddaabdcdddadabbdabcbcabacddbbadbadadcbdcdbdadabcadabacdcbddaddbbabddbabbabcccbadbaddbdcacdcabccabadadcdacbcaabcbbabcacbbbdbdaccbcaaddadcacbabdbdbdcddbcccddadbbbdabbbaabacdbabbacadbccbdacbadddcdadbababcaacddbabddbabbacaaaadcddabdbabaddbbddbacbbdbbdadcbbaacdabcdccacdcaacaacccbdaacdccbaddbcabdacdbcbadabadaccabbaaadbddcacacccddbbcaacddbdaaabbbcdabcbbadaabbcbdcbcbabcccddddcbccabccacabbbaabcadbdaddcdacbbadbccaabdaacabbadddddcacdacccddcaacdacbdabddcddcccddbdbdccadbadababddddccccdccbdaaadddbbbabccbcbcbcaabbabaaddacaaacbadabbaabbcadccbbaddcabbdcdbbaddcadadababcbbbdaabdcdacdbbbbddaddbaaadacddddabbcccdcaadcddaacddcdbcabbdccacabcaddcacddcbbbbcbbadacdcbbbaacadadcbbacdcbacabdbabbbbcbccbcaaccdabacdacabcbcbbcbadddcccbbbddddbdaccbbbaddaaaabacaccdabbaadcbacbddacccbccabcadbdccdbacadddccabaccacabaabaabdaacdadabcbcbabdadbadbdbddbcacddcaadcbdcacdcababbbdbacdddbcbbacbacbbbbbcbaabdbbdadbcacabdabccbcdbccdadacbaabcabddbadbbdcdacddccddbbaaaacddccbcdcdcaabadbbabbbabbdcaabbddaaaaaddbcdbbdbddcbadacdacdbcdaabaccdaaacaccbcbabcaacadcacabcbdddcabdbacabcaadcaadcacdccbccbdacaabccadddbacbdaccbadcdcdbcddcbbadcdacbdacdcdbbadaddcacddbbbdcddccdbccacbccdaccacacbabbbbbbcadbbcbcbcbdcaccaacacccaccaddcbbcdccbabbcbdadaccddadbddcdaadcbccacaaacdbddcbdadbcdadcdbbaccdcbcacdbcbbcdabccaddcbacdaabbacaabdadcdbaadcbcaddbdbacaabcbcddbacabdccbccbaaabdddccbacdbdbcabbbbbaaacacabccccbaacbdddabcdbbbaaccbacdcacacddcbcddbabddcbaaabddbaadbadbcacddddacccbdcababcccbcbdadcdddddbcdcacbccdcbcccbacdaacccddbdaadbcaabbaabbbadcbdcacdcbcbacadddcbdabbcbcdbcabcbcbbcbcaacbdbdbdbdbbdcaadcbbdbccacbbcdddbabaabcddacbcacabdbcdbdcaccadbbcbabcdbcbdcbaccabbccbaacbdbdbcdadddcbccaabaadcddbbccacbbacccdadbccbddbaaacddcbdbdbdaabccdddcbdaabcdcacbbcacbccbdccccdcdbbbdbadbacdabccadadadccbdcacdcbacbbbccbadadcdaadbbcbcbcacdbdaaccdbcabbcbccbadcaadccbadacdcbcbcdbdddacacdcdabbdcbadcaccbdddbbcacccdbaaabdbcbbbbcddddddacddaaddcacddaaddbcbdbbddcbccccccdcddabcdbcbccdcdaaccdbbdbcdbcdccaaccbccbccbaabcbacbadabcdcccbbcccbacbaccdcdccbddadcbadaccabacccbdcccaacaaddbdccacdbadddbccbbbabdabadcaabddcccbccaadbaaacdbabbdcababcbcdacbcddcacdabbacbcdabacbdbcacadcadaccacbbbddbbdadbcabbbaadddadbcddddbadbccbccbbacaacacabdcbbadabdcbabacadacbbaccdabbaddadcacdaaaabbdabaacacbbaaabddddccbdbabacbbabbcacabacaacccddcaddbaaadacabdcdabcadcbdcbdadcbbcdcdaccaacdaabbccdabcbdcdaadabcdaacccbbdbdcadcaccddbbccaadbaacddcadaccccdcadccaddbcbabbacdcaaabbbadabbbbdaaaadaadaabbdabcbdddddaabdcbcadbcaacddcaacbbdccaaaacacbaabcbbdcbcbbaccadadcbbdddccbabdbaddbacadaacbbccbdabcadbbaacadcccbaadcbdbbdbcbacdccaadcdcdcdbbdadbabbbddbaaaadcacdcddcdbaaaacadbcdaabbcdadabbbddacaacaabccdbddadcbabaddcdadcbcaabcbcccbbabacbadbbadaacdbcabccdbbbbbcbdaaacdaddddcccdaaabdcdaacbbaabccabdadabbcbbdadadcdabdbcadcccacadbcccacbacabbddcdcbacbbdadbddaabddbbbccadadcccacdcdbaabdcbccbdbaaaabbddcadbcbcdddcadccadbbcddabbcbddbaadaccccbbbbdbcbdacbcbcddcabbdcabddacaaddadacccccccaabcdccaddcbacdccadadabdddcddabacccbcabcddadbabdbcdcccdccdaddcadbbdabcdcabaccabacbaaabaccdcdccdccababbcdcaaababadbacbddabacabaccacadcabbdaabdcbbdbacaaaaddccacbacaddabbbaaddbbbdcacaacabcdbbdcccbdbcddadcbccdddcdddcacccccbcddacbdadaacadcbadccacbdcccacbddadbbdcadbbdabdbacaaaddccdabdbddcccaabadabdacaacdcdbccbadacbbdaababaadbccdccddadabbbcbdaabbcadbdabdbcdabbbbdbdaaadbdbdbddcbdbdacbdbddcadbacccdccdcbbbbaddbddadbaadcdababddabcbccbcdcbdbdccacbcbddadcdaddcbcbababdacdcaabbcdddabbdcdbbccbbabdbbcbbaaaadcccdabbcaaaacdbddcadbaacccccabbbdddcddcbbccdadddadcbcabdacaacdbdadcccdcaaddaccbccaacdcbccabbddcabcababadadababcdadabbdcccdacacabbddcbcdcbdcccdbcbaaccbbbbbbbcaccadbccbdcabbdcacbbbbbaabcacbdbbadddabcacababcccdcccbcadbbcabadcabdbdcadcdaccbcbadcdccccccaaadcbddbdbccbcabcbdbbcacdbacaaccdcbcacbdcdddccbacdcdccdadddbdacacbddabaaabccadaccabddbacdbbabcbbbacdabcacaadabaccacbcccdbcbdbcadaabbcabacbbdadbcdbbddbabaddbdcdbcbdcdbacbdbcdcadbcabacdccdaddcbaaacdcddcabccabaaabaaaadadbdacabdccbbabacaabacbcaaddcddcbacdacaaccbdacabcdbdacdddcabadcdadadcbccaadcdcdcdddbdbcccacbabdadddadcdddaccaccdddabaabdcdcdcbadbdcadaaabbddcccabbcbdccdbadacaccabdabdcdbdccccddccaabacdcbccccdbddcaccaacbdacaadcabdcbaaababbdddbcbacbbbcbaddbcaccbdcdcdbdadbabadbddbbdddcdcaadcaacaadcdbdacbddbcdaabdcbaddcbbdbccbdacbbcbddababaabaadbdddabccaaabbcdbddcccbabadcbcddbddadcdbcddadbaacabaabacdabdcacdbdccacaaacbacdbacdcaadbdcddbcaaaccdddbbccdcbccdababcaccaccabaadcbbbddbcbdbacbabaaaacdbacaaacabcdbbbdaadbdbbacccdbabbbabcaacabdbccbcabaaadcddcdbabbbabddbaddaacbddbbcdddbaacdcaabbbabcbbcbcccaccdddaaadcdcbbbdaaacbcdcabdbaabbcdcbaacacbdcadbbbcaaabaaadcddbbccbabdbcbbdaaacaacccabbddbadadcabbbcbaabbadabbdbcbcbbbcadadccbbdabdbbbabcadadacabacccaddababddbacacabbcddbddcccdddaacccccbbddbddbbdbcccabbadcdbddadaadbdaaaadbbaadbabddabdbbccbbdbcccbbdcccbdadcadaabcacadacadbcdccbbdbadcbdbcdbccbadbdaaaadbcaaacabdbabcadbdbcadddbabdcabdcbcaaccadccbcccdbccdadbaaaadcbccbdcaddababcddbcbbccbbdcddbdddabcdbaababbbcbdddcdcbaccadcbdadcbcdacabcbcbcdcbcbbdcdadbdabadcaaccbcbcdcababddadbbddcaaabcdacbacbdcaddccaccabdbddbdcddabbbabbbcdcddbcccbddaadbbabbddabdcbdadbababddbccdcacadcacdacaadbaacddacaddaaaababcababaabacaddddcbaccccbccbadcddbaaacdcbdcdbbbdbdbdcaddccacaaddbcbdccbddacaadddcdaddcbbbddddaccdcbdcbdcbaacdabbdaaccdacdbbcccccbdcddbdacadbbdcdcadaacdcbdccadddaacccbdddbdbacdcddabccaaccbaddbabadadcdacacbbddbdabadaddddbadccbccccdbbaadcdbabcbcbdbdbbbcabdacddaacdcddacacdbaaacbacbbbbdadbccbdbccaccdaabbbbcdabdcacbdbbabacbccbaccadcbcbaabcabbcabaadaccddcdbacdacbabacbcddddccadcbdaadcdcddcddcdcadccabcbdbcaaadcddacdbddbcdacddbcadbbdcacdbcabcadadbcadcadbcdbddbccddcbccacdbabdcbdadbcacdbdbbdcadbdccbbabdbdccababbcbdacbaacabcbbbbadcccabccdaccadbdcdcddabdccdbcadbbdcbaacaddacddbddccbdbbabbccacbddbccabddcdadddabccbdbdabdacddaddaaccdbdcbcddbacbddddcacdabcdddbbdcdaaaccbaaddddaaaccaaadcacabbbacbacabdacadaddabacabbcbbaccadbccbcddcaacbcbbdddbcaddbdbbaadcdbbcbadbccccdadaabdccaadcaaabbcdabccaadacccbbbcacbbcaababddccbcddcabadabcdccdacbabdcbbcaadadcbcdabaadcddadbbcdbadbdccdbddddbbbdadabdbbcdbcbabbbbcabddbbddbaddbcbccabdcdcadcbbbbddbacadccdbaacdbabbaddbdbbcbbdacccadcaddddbabbabbabacdbbccbdcccdabbdacccbcbcbccbbabbbdbbadcbaabbacddddaccbaaacbcbbaabbdacccbbacbbaaabadcddbabcadcacdaabbdbacbdacaabaddcdadbaabdbacabddabadbaaaacaddccdbbbdbcaacddcabaabccdabdaaadabbdbacbdbdbabaddcbdbbbdbacbbbcaacacacaddddbadcbababcaccddcabcbccbaabddcbbbbccbdbddaaccddccbcacbccabdcadcaabcacdabbcdaddddaacccacaacccaaccddaadcbabbdaccdbacdbbccccddbcdabbbcaaccabbdaaadccdaccdbaccbdababaaccbacbcbabadbbacbcdacddcdadbcdbabaddadabccadccabcdbbccddcbddcbbbbbdcaccadccdaaabbdbcbbdcccdcddacddadcadbcddccddcbaaccabaccbdddccadaddacddbbdbbccddcdaaacbdcacbdcbaadaccadbcdddaddaccabddddcdbbabcccaaadccdaccbcbabaaccdabcbbabbaccdcaadcabaddaccccddbdadaddccadccddadabbccdbadbdaadbabcbaabcabbdbbabdcabaabcccccabbacdcaadccbcadcbabacaaadbbbdbbbacdadbabcacadddcbdbacccaccbaacccbbcbcdaacacdbdcdaddacbaabbdaabacdcbcaacaacdddbbadbbbcdcccccaaccbccbbdbadaaacadbddcaaabdacccddccadbbdabbacbccbbdcaaaacdcbddcddbbddcbbdcbddccdcdcddacdcdacdbbcaddbcccccaabadbaadcadccadacacddaddadbbabadbbcccdcabbcaadaabadbaacacddaabcbdcdabaadadbddaaadccddcdbccabdcadcccdcbadaabaddbdabbdbbcdcbaccbabacabccdddcbdddcdcbdcbabacddcdbcaacbccddabbdbbddcdcdcccddbacbdacddbcdbadcaadbccbccbccdaaacaccdcccbbcccdddcaacdbdadaacbadbadbbbbbcdadcdacdbcdbcaadaaacdabcccddcadbcdadbacdccdbbabacacbdabacdbacabbbbabbabdcdbdbbcddcbbdbcbbddaaddcdcdcccabadbdabcbbcbdbcdaccadaaaddadacadccbcacccddbccadcccabdcbcbdadcbabacdcbabdcbbdbdadcacbcdadcbcdccbcaccabcdbdaabdccadcdbadcdcbbbcaacaaddddcacdccdcdcaacbcbdcdacccaacccdcdbddddacccbbddcabacccbcccbadaabccacbbdaacdbccdcaccdbadbabaddacdbbcabcccbccacdcbbabbdaacacdadaccbdbcddcdccbcabcbdbbdbbccadbbcbcbabdccabaacaabdcdccacdabddbbaaabbccacabacddcdbabdbabbddcdacbacccabaadcccdadacaadbcbaaddabdabddabdcbcabdbbbaaccabcdcbadccdbdbbbbdcaacbcddddbddacbaccacacbcdcbdccacaabbcbdbbcdcccbdccddcddbcccbaacacbdacccccbadddaadadcddbaadbbcaaccdccbccccbdddbacccccdbbbcabadabbdadddcacddcacadddcbbaccddbbbcbdbaacbabdbccbacbdbcabcccdddabcaabbacbabaadaacaaabbddbacbacbaccbabbddccbdadacadbbbdbcacbdaaabbdcccddaccaaaaadaccdacabcdcbbbbcbcbabbababbcaadbbacabababcdbcdbbdcdadcccdcbdcadbccaccabbaadbdababcbbabcaaabcdcacbbaddcdadbbcaddadbbdbaaadaccddbdbdcddcbbcdbabaabdaddacacdaddacbcbacdcbbabaadddbddaaaaddbdccdabddacaaaacdbaaadddadbdddbccdabbdadacbbbddadaacabbbcbbdacacbcccbacacbccbbbbdbbadcccacacddccbddbbacbdabdabbccccdbdbcbcddbacdcacbaabababbbdadddcccddccaadcaacacdacdaaabdcacdcbddccdcabaaacbaddccccbdadadbcbaddbababdcdadcaaddccadbbaadbdaaacbccbacaccadbddbcbaaabbdcbdbdddbbddaaacaaadbaacabbbaccbccccdbbcaacaacbdddbaaaabcbdadbbddcbbcdcdacbcdddbaabcdaadbddddbabbcdaaacbdcbaaadadacdbbdcdbdbdcbdbdbbddadccbcddccbccdcdcccddacacdaccaddbaadbabbbcdcadbbdbcbbdbbabcbbaccaaaacbacddcdccddcabacddccbacbdcbcccbbadaddbddacbcdddacdbdccabcccdadabccddacaddabadcdccbdabdccaaadbcabccbdbcabcccaaadaababaadcbdabddacddaadacadbcddbbdaaabdadaadbccbadddcddbbddadcabbcadabdaacddddddddccddabbcbdacbdccddadcabcbabcdddccabacbabdaccabdbcadabdbbdadacbacbacddacdabadbaddcdcbbccbabbdcaddabbdcbaaaccbccacbddbdadcbaccdaabbbbbdcdccdbbacbdcdcbaacdacbcbcbcccacabaacbddcdaddcabdabbddbabbcbaaccadbbbaadacacadbccddadcbbdbccdaccabbbabcaabddcaacaaabccbabccdcdaaccabdddadbddbdcdaadcbcccaaabcbbdbcaccabbadbadabdcabcbacdcdabdbdbcaaccbaccbdcbbbabdcdaaddccaaaddbbbcdbaddacaaaadaabcabbacccbcdcadcbbccadcaacdcbdbabbcbdadadaccdccabcdadbddabadbddbbaabacdcbbddcabdccadbcbcaccbacdcbcadddddaccbadadcbaadbdadabcdbaaabacbddcacbddbdbcbcccbbcbddbabbbbdddaabbbbadbbdabbabccadcccaccaacabbcbbcbcbadacaddbbddaaabccdaddaddaddabbddccbadcddcbcbadbcdcdbbccaddbbdcbcdcabbcbbdbcaddcdcadbaddbadcbbbbadbadacbdcdbbabdbaccbbbbadabddccacbbbcacaaacdadddbcadcdaaacbadacaaddccaccccaacdcadcbdaddbcbdcbabddcccddddabccbccabbbbbcbccdbbadacdabacabcbacacdcdbbdaababbcbcbbbabdacacaaccabaaddcbadbadcdcdadbcbbdaacabcdbdaaddcccaacbdcddbcbbadabdbbbdabbbbccabbbcbdaaabcccbbcdacadbdbbccadabbccbbabdbbddbdaaddcdcbdaaaacdabcdbcabbdbdbccddbcaaccbbccdcbdcccadbddacdbdbadcddcdcacaabacdaabadacdcbcddbdaaacdcccacdbdacabadabaabbdaacbdccddcddaadbabacbbabcaabbccdbadabddcdcbadabcbccdabbabcdccbddbaadaadbacadcacccbaddddcbbadbcbdbabacbbdccbcbcccaacccdadcdabbddbbacbabbbbcadbacabaccdcdcdbaabababcddabbbcbbdcbdacdbaababcccbcaccdccbdaacccabcabacdabbabadcabadaabbccacbdcbacdaccbdacccaddadbdcdcbccddbacacbdbaadbbcdcbcdacaacaaccdcbcaaabddbdbbcdbacaabccdaadddbbacdbaacdcdcbdaaacdbacacbbbddcadbdbababdaddddbcdbbddbdadcbcbaacbdcabcacbcabdcdaabdbdccacacdddaabaacadbcbbabcdbadadadbacdacddbacbdadabcbabdadbbdadcdddbaacabadcdddabddbdbbdaaaaababdbadcdbdbdbbdacabbacdbadbcbbadcdbcadcbccbaccdcdaccdabadcaacccabdcdcbadabccabaacaddadcacddcdbdbddbcabbdaabbdbdcdccdbaccddbaaddcbbbbaddcaaabbdcacabdbcbcabbadcabcabddcdacdbcccaccbacbbbbcdbcbdbcbcdbacdaaaaabcdcbbdaababdbccdacabcbcbdbcaadbdcbdabbaccccbddaabcadcbdccadcbcadcccbccababdccdcbacdbbccaaccbdcaabddcbdbcbcabdbbcaaabdddbbdaabdbbbbcbddccadaddcaccdcaacbbbaccccadabcaabbcdcabaadcacbaacdaabbdccdbdaccddbacddaadddddcdaabbbbacaabddacacbadbadddabccbcdccdbbaadccaabbcddaaabbabccbcdccaababaacbbdacacdccbdadcbdbabcbcabcdcdadcbcbabccaaaaddbbbddacdaddabbdaacddaaddacaaddabcbdcddbddccddadaacddddaccabbadadaadcdbaadaadaadcbadaccabcdbdadddbcdaacdbdbcdcdbcdbbddadddadcbaddaabddcbacbbdadddbadbdbdbbaacbbacabbcaccddadcdadcbabbcdccacacaacaadcaddbadbdacddbcacadaabbcdabbdadabdaccdbccbaaadcaddabddacbadddacdaacdadbbdbcbabdabbdaaabcccabadcaadcdcdaadcaabbacacdabccabdbbcdddaaddbacacacbdbcddadcadabbaccbcdbcbabaabdaaadaabbbcabddbbcdacabaadacadacdddabaacacbadbdbcbdaaccdccdaccdbcbbacccabadddccbcdbdbcdabccbadabcacbdbdabbdbddbadcddcbbdcbcdbcaaddbccbcabaabbaacdabacbbbaabaaccdcbddbdabdbbabaaacbbbcdcaccdcadabddadaadacdcccdbbdaabccabaaddbcbaccadbbaaaacbddbbcdddcabdadbacabbdccaacdbdacbccbcbcddbabbabdcbcbbaccdcbbaccaddcaaabbcbaddcadbbcdddcbaccbdcdcbbaacacbddbcacdaaabbdadcdbbbcaabcbcabaaaabaddcdddccaababbbbbddbcdcbcacadbddbdbcbccbbbbdaaadbddcabdddbaadbcabadbdaacddbbdacbbbdbaadddbdccdcdcbdcdbabcdcdacdbcddabddabcbbabbbaadaaadcdcdbacbdcbbcbdbbacbcadcddaacdabccdabdabdadcbacbdbdbcccadccbbdadaccdcdcbcbcccbacdadabbcbacdcddadbabcacbdaddbaabcdcdcdadacdddddbbbacabcbddabdaacddcccaccccbdabcbdcbbddaadaacddbdbdabdababcbdaaaaabadabbccbcbbdacacbaccbabbdcdddaadbbaabbbdcadaccddcccdddbdcbcbddbaadaaabbbdabaccdbacbdacaadcbbaababcbddacdbddabadabdcbcdddbcadaacbcaabcadccdbabddaccdcadaaabcadbbddbacababcbcdbaaddbbdbaddbcdddbababcdcabbbcdacaaabcdaaabdcbcbcbdabcabddbdcddbcbccdcabbadbdddbbcabcadbddcadcacbcdbdabddadddaaadaccdccddccdcaacccdddcdaddcacdadaddadcdacdadacdbbcdcbddbccccabdcbccbacabcbbddbbdcaccbbdaadcbcddbabccbabbabcbbbadcbdaadbbdadccbaadccbbaddbccdccdaadcbbaacddbcbdaababddadcbdcddadcdddcbcdcdccacbbdbccdacbbcbcbcabadaaccbabcbccdddabccacadaccadcddcdbaaacbadccaddcdbdbbdabdaadcaaacccdbbbabbdbccbdddacdcaadccacdaabbaddcabcbdcbbcabcbbdabdbabdddbbdcbcaabbcbbbcadacdcabbcdadaabcbadadaccddadcabbaabadbdbdddbadcbaaaaaccadbadbbdcabddaccdbdbcbaaacadaadacacccbccdcbcdabbddcbcddbcdcbbadcdcacbaabaccddcaddccadabccabcbabddcadadbccabdbcbadbcacccddaacccdcbabbacacbcaacbcbcddcdccddcaabadcbcccbcacddaabbcadbbcaacccdabcbaddddcaaacddddacaaabababdddbbbdbcacbcdbcbcbacddbdbacacabaaacbaabbacbdcadddcbdccdcbdbcaabdcccdadcddcbadbbaacbcdadaadcbbacbdcdccabbddaacdbdbddcdbdcdcaddddbcaddccccccddbddbdcabbbabcabcddbabddcaacabcaacbdacbbbdbbcccacddccaababbcbcbacdbcabdaabbaaccbdbcbcdbbdabcababbdbabdbdbbaddddcdbbcdbbddcaacdbaaaaddacbdaacacbabcdaabaccaaabdacdcdbcddcccabcadbaddabdbcddbdbccddccacacbdabddbddaabbaadbbaabbcacadaddcbbbdbaccdadadcabbcdcbabadbadbbbdabbdadabdacddcdcddcdcddababccbcccbdaabbadbcbbadaccadabbcdadacdbdbadbcccccdcaaacdaadcbddbbccbbdddcabdcdabcbadbddbdcacbbaabcabcccccdcbcadcadacaddbdbbcadaababaabdccdabbacbcbadadbadddccbcabbcaaabacaaadbdacccaaabddbcdabddcbcbcbdcdabbbbbbcacacbdcdccccccdbaaaacbdadabaabbdcdcbadcdccbdacccbddcbbcdcdaabddccacbdabcbdcbaaacabcccbbccadbdbbccabcabdcbcbbccdbabaddabbcdabbcbcadcadcdcabdadaddababadadabccaccaaaaccaacbacdcdbbababbadddbacdccbbcddbacbdcbdcdaacaabbbddaabaccbacbadcbcddbdcbcddaddbaacacbadbcddaaacbbcbdbbcaccaccbacccdbbaccbcaadcabccbcbabbaaaabdcddaacddbcacbabdcbcdcdbdaacadbadaacaabbadaadddabcaaacdbbaacbadadaddbcadaccbbbcddcbcdccbaaabbddbddcdadcbacdbbdcaddadacbadaaabdcdcaadbbbcacdbaddbbadbcdaabdcacbbdcdcdadbaccacbbbaadccbcabdbcbbccdbbbacaacdcadbcdcdbdbccbabbdddabbddddcdaadaddadaadcbcaaadcdacdcaddccccadddbbccbdadacbbbdbabaccbbabcacaaddddbaadaaabacddcaadadcccdcacccbbaacbcccadbadaacacbdcdcaacdbcbdccabaacdacaaaddbdbccaaabadaadddabbbbbccabbabdbccadbcbabbabcdabcbcbcbcbbcdbdcbdcadadcbdbadbabdadcacacbcddbbcadabdbdacabddccdccbccbbaadabbadccaabbcabbaadaadcdbbcacaadcbcaacbdcaadcbbdcbbbdbdadbdcdabbadcbadcabcddccdbaaccbaabaaaccbcbdabbabcbbdcdbcacbbaabdccdddbaabcdbdcaaccacadcdcadadddbcdcdacdaaddddcbadaacaddbaadbcacbddadddadbcdddadbddbbcbdbcccdbaacbadccdbdddcdcdccdbabacdabadabadabddbdbdcdbacccbbbdabacbcbbdccbcddadbaddaadcbbbcddcddabcdbcabaabbccdddcbdccbddcacdcbaacdaaaabddcacdacdadaaaaaabddbadaddbbadacaddcccdacbbcadcccbcdbacaacabdabcbbbdcccabddddcbbabcccaacdbadddabaadcdacaccccbabcccdbcbcadacaabacbabcbcdbddbdcaabbbcbbbdbaacccddaddbababcbbabcddbcacbbcdabdbcaaaaacaaadcaddbaaaddcdacacbccdabcaadacadbaaadbadaccbbbadbddaccbbdbbaacccbbbaaaaccdcdbaaabbabaabaddadbaaaaaadbccadbbdbadaacccdccdcdcdddbbcccdddbcbcccbbabcdcbcddccbddcdabcaadddcbbbcdcddddbaacbacaaaddbacbcabacacbdabbcbbbcabcacacbabdcbcaaabddbabacacbacabadabbacacbbdbcdddbcaddddcabbbccaaadccbdbaccddadbccdcdcddbcdacbcaccbcdaddaccabdbdaccbcdaabdddbdaddbacaadcdabbbdccbcadddcaaccdccadcbcbbcaabbcdbcadaddadbdacadcdcaadcadbccacbadaacacaddddbaccbccacacabaccabaccbdcddcbdbbbbbdcdcacadbaabbacdbabdbdbbcbcdadacbdbddbdcbdbbbadcdabacdcbaacabdccadcdcabaadcdccddacdccdcdcccdbbdddaddbbbadbcbbcaaaaabdbabbdbbdddbdccbcdaabcbcbddabdbcbadcbabbdadaabcdcbddbabbccabcbcbaaaacdaabddbcbacbdcbdbdcbaadbadadabcdddcbdbabdaaccbdacdcbbabcccabcdadcaddbaaaadbcdcddbadcdaccaccddaccccbddadccacaccbacbabbacabcdbcaaaadcdcbdbadddacdbadabccccbaacbacdadbdbadacbbcdadadacccdcdbabcaabdaadbdcbdbbdbdaaaccddccbadcccbaabcadbcbdabbdbddcddcdbadcbabdabbabaabbdbcbbbdbaacdcbacbbbcdcdacddcbaaabbdacdacaabadaaaabaabaccadaccccbbcdcaacaaabbbccbadcddabbaabbbbdcaabdcabddcababacddaabdbaaaaabdacdacdbbcddcbdbadaaccddabacdbdabadbbadcdcccdabccbbdacdadddbcccabdcdbdbbcbadaabdbcacaccbcbbdabccddddbbcbcbadacdccabbadadcbcbdcadbcaccdddabbcbcdbddcbaddcaaadbdbddacbbcacdddcbaccbddbaacaabddcccdcaaccadcddaaacbcbadaddcabadacacaadabbbcbdcdbaaacbdddccadabdabaccdcaabaacccdaadbabddcacddaaadaaccadaddcddcadbaccbcadbdcaddcdaddbcadcdddbbcbcdcbcbacaccdbabbcbcdddbccdcccdbbdbdbccabbacbbacacabcbabddccbdcacdacdbabbddaaaaabdabacaacadabcbadddbbdabaaadbabdadbadbddbbabbdccbbababcddcbddddbbacbbcaabddbcddcdcbdbbdccaaccdddcbccaacbadacdabdbbcacddbdcdcdbacaaadbdddabddcbbacbcccaacccabcbcdcbccddcabdaabcbbacccaadaaabddbbadcccbaabaddcbcbcbcbcccdbabdbabbbdcddccccadadcaccaccbcdaccbdaabbadcadbdabacaabcabbbcdabdddcbcadbcdddacbddbcaababaacbbabbcacbccdcadbacbdaaddcadbbdbbdadaccdbabacbddbaddbaadcdbadddaacdcaadbcbacdbcdbcbbccaaaccdabaaccbdcbcababcadbbcdabcbddcaaaacbdbbdbdccdbbcddbbaababcaabdabcbbbcbcadbaababcdddadcabccaddbbbcdcdbbbdcbbddcbccccbaadbdddaadbacacdbcacccbbbdccbddddaadaacddabbcdcccbadaccdcdabcbdddbaddaccdcbabadbcaaadaccccbdccbadaacacbbbaaabdccdbddaddcdbbaacadaaccaccdbadcaabccccadbbbdbacbadbaadacbadcbaaabaaacbddaabadbbcbdacdbdbddcbbbadccaddcaaccaabbbcdaacadcabbdcbddadaabbdbbbbdadddcdbccabddbcdccbcbdbbadccdccbdcbcccacdddaaddbcaacdacaadbddccdbacdbbdbcdadaaccaccdbbcdabccbbdbabdabdbadcbdcbcabbdaaccaacbbacdbadccdaccddbdaadbcdcadbbdcaacaaadbdbcdcdbcbbbacbdddadabcadadabdbcadcbcbcdadabdabcdcacddcbbbcadccddadcbbbcdcccacbcabbdadcbabbcdcacacacbbdbbbadccbddcabcbadcbcbcdbacbbcdbbbcabdababacacdacdddcccacdabdcacdbbaaabcddbddccddbaccdabdbccbcdadacbcccccdddcbbddcbddaaaacbdcbdaccbdbabbcdbcbdcacaacbbdcabcacacdaaccadbbdbddaabddbdcaaccadbbccbabcdccbbabaacdcddadcacdcaabbaabadabbccbcaadcbbadbadcdddaccbdcbaaabaccbbdbcbcaadacdaabdbccacacbdcbacbdaabcacbaacadcacbcadddcbcdaadcbccbadddcabaccbabaccbcbcdbdbbdccbadcdabbccaaaaadbacbcadccbdddadaadabcccdaccbdbaaaacbdcacaadcbbcadbacddbddcabbaaabdaabadadbdacdcdcacbcaaabbdddadccbadadbbcdacbbcdabccbacbabbbcdadaaabddddacdbbccbbbacbacccabbdcbbabdadccddadacbabadacabcdaabcaacaabcbcbcbabcdbcdaddcadcdcdccbcacadcbcddcdabbadbdbdadbbaadabdadcacbddcdacdcbbabcbbdccdbbddcddbcabdbabddadcddabddcadddbdaddcbdccadabbcdbdbdcaabbabddabbbacdcdadcdbddaaddbabcdccbcccbbddbcdbdaddccaaacbcbcbadbbbcdaaddccaddaccdcccdbbbacbdccbccdcddadddccdabdcdcbdcbbbbcbbaaccdcdcadabddaabcacdaaabcacbdcacadaabbdccbdaccadbbbbddcaaaddddbbcccccadcbccadbcaccdaccacdacdadbaaccddacaadbcccbacbbbbaddccbccaaddaddbdccdcddddcdbabcacdababccabababbaaddddacccbbadbdbbbacddcabacaccbbbdcbadcabbbabaccbdbbacdcbcabacbdddcaacaacddbbbbccccbdcabcadaacccabdbcbaaaccdaddabbcbcbbdcdbdbcddaabbdbabaddbccbbcbacaacaababcadccbddaabbbaadbbdacbccddbabdabaaccdcbadabaaadabdabdadabadcdddbbddbcdacdcbddadabacdddadabbcdbbdcdaaaabbcdacddadcadadaaaaccdabdbdcadcddcddccadbccddbcbaaaacddadbcdbcabbdddacadcdbbbdbcdadacddbcbaaccaaabcadadbacdcbcbbaddcddcbdbdcbcbaacccbadddcbdcbcabccbcaddbbdadabdabcadccabcdddabdababbacadadcbadbccbdbaddbcadbacbcacbccacdaacadadbaacbbdddcbdabcacddbbaccdaabdddbdbadbcbbaddcbbbcbbdcbdabaddccddcdbbbdbbbbadcabbcbccadbcdcbbdabddcbddbacdabbbaccdbcdbcdaaacabaaaccbadcbcccddacbdcacbccadabbdbadaadcdbcccabcbcccbaabcdaaddccdbcddbdaddbdcabcccdbacdddaaacaaaaabbddcbcadaadacdabaaaddcbccddcaddaadbaaaabbddabdabdbaabbbacaaddbddcddcdbcaabbccddcdcadabbcabcdcbcddddcbdccdddaaccdbddaccdcdddaddcdacddbaabbabbccacccbaddadbdbaadbdbbdadadbccacbbbabaccdadbcbcabbcddcaabbdadcdcacdaacaaacdcbbdcdbadcaabdadccbdcdccacccabbccdaacdadbdccbcddbacccdaabaabdcacababbcaaabacbdabbddcbcbcbcbbcdadbddbaaaddabdbbaddcdbabcaccccaacaaacddbdacccbdccbaaccbbdbbddabccdaadccbbcacddcdabdacdaadadcabacbadacabdacaadbcadbccbabdcdabcbdbcabbaddbdaadaadadbaaaddaadcdabaddbdaabcabadbcbcaccbbbadacabcdbdaacabcadddabdcbdbacbabddaaacaabcdacdaddbaacccdcadaaccdcdacacdcdcdbaacdaccdcaaaadcbadabbacabaabaddacbdaccadccadccbcabbccccaadbacdcdbccbaacbbddabbdbdddbaadbacddacdacadbcdcabbbccbacdcccabdabbddbcddddaadbcabcadcdabbcababcadccccbcddddcadaaacbdbbabcdbadbabbbcbddbadbdddbdadaadbdadadbdccddcaccadacbbcdbcddaaaabccadbdcdcbcbbbdbabcbadaadcdababbcdcccdcabdcbabadaaccaaadddddcddaabaabdacabbbdbdbddbcdcbddcddcbdcaaadabccabbbcbaaddabcaccbcdbcbbdcdabddddbcbcdbcbcaaaccadcbdcdadabbbcbbdbcbdabdccabcadcabbcadcbbabaacbacbdcacbcabbaddacacddbdadabbcadddcabcabaccdbcdcbccbbddacdcccbacbaaaddcabdbadcdabcddcaaaccbdadcbcdcbdaaaddbbadabadccbacbbdbccadaaaacddccbabdcbbababbbabccadcdabcbabbcdaccddbaccbbdacdddddbdacbcabbddbadacbdcacdddbbcaaaadbbadbcdcadcbaadbbddbdadcabcaabcbadcbdbbccccadbbaaccadcdbabacaacaabaacbccaccdcabcaddbdaababdacaddcdbdcbdbaabdbbadbabdbdccadbbbbccababcbcdbccbcbbcdbcababbbdbbccbbdbcbbabbddadaadbaabdabaaaacaaccbbaddbdbbbbdbacccacaadbcbadcdcbdbbdbdcdbaadcaabaacbbadaadabcbccdccdacbcbababdbdcbbbababacaaddbccdcadadcbbbbacbbcacddababaddcacbcadadaacabdccaabbdadcddcaaddcaadcbaddbbadbbdccdccbddbcccbdbdcabdcdcadbcdcbcbdbdadbdbddbcdacddcbdbadccbbbdadcddccbdaabaacbadcbddacaadaaaaabacbdabddacbdccacddcccbcdababccdbaacccbbdacbababbabdaaadadcbcdcdacbddbdacbcbaacdabaaaaaadccabccbcbabcaddabbddcadadadadcddbdbbadbdabdacbaddcbdbaabbabbbacaadbbddaccbaacddcddacbbcbdcaaadbcbbddbbbdadcdaabaaaabdbbcadccdadccacaddcaaaccbcccaaadccabadcbddabbbaaccadabdacbaaadcddcbbbcbcccbbaabccdaccababcbbdadbaadabcabdcdaacabcacabcbddaadbcbbcbccabbadcbbdbcaabcdaadbbacccccabccbbbadddcbcbbcdddaaadbddcbcdcacdcbbbcbacbdadcbdadccdadacabadaabbbbcbcdbbadbcdbdbadcdcaccdccccaccddddbabdaccbdbacdbcddbddaadaddbacdbcbcbdabddadcbcddaadacaccadabddadaaadcdcdbdbbbbcacabdadddadaddbbbdaaddcacaddbcacdadbdbdaaccdbdbdaabaaaaadbbabbbaaacadcbbaacaddacdcdbbdbbbddbdababbacbbcaddbcabcdbaaaadadaadaacdaddadcadddacbabbcdbbdaaadddacbbbdaaccbcddcbbcaaaabcacbacbbdabdbbdbdddddcdbabcdcbaacbaccaabdcaaaacacabbaadcaacbcdbbadacdcdbcdbbaabcdaddbddabbccdcddcbdabbccaccadbccaadbccdaddbaccbcdcacdcabadbbadbbdabbadccddadabdccdcdcdccadccccaacbadcccccadbcdacaabdccbdcbabddcdbdcbbbbcdccdbaacdbbabbacabccadbcddcccbbcbacbaddcccdcdaaabcdbcccbcdabacdbbddadcdbbcdaaaadabbdcabcccabbdbbbaabcaaabcbcacaaabbbcccdbcaddcccdbcccdbaccdbccdcddbccadccdcabbaadccbbdcadaadcdcdcbdbbcddbadcddacdcbaabdadcbddccdaacddbbdddcadbcdadbaacaacddcddacdcbbadbdaaaccbaaababadccabcadcbaacacbdcaadabbadbcbccbcbdbdccdbbdbadddcdbcdaabbcbccbcbaadcccabbcadadcaadabdbcbbbbaaadcbddaaaaccaaacababcbddccaaaccdbdccddddddccabbdbcccbbbdcbdbdccbdabaacdbcdbdbbbdbcbbbccdbdabbcccabacddddabacbaaaddaadcbdadbdaadacdbccdacbbbddacadaaabdbccdddbaaccbabbcdacbddbbdbbbaacbabbbcdcadcbbbabdcbccccdaddacadbaaaaddacdaccbdddadcdbcddbbcadbbacdabcacbdaadaabadcbdbcbbdbaadbcbccadabcbdcaacdbcbadbaabdbaddcccdcccdbdbadcccbbdcdaaaadadacbadbdcdadbdddcadcdbdbcacdcbcdacbcbabcdcabbbbcccbbdabcbababbddadbcbacdccdbddbacaddaaabdcbaaadddddacddaadbcbbdbdbacdcddbddabdbbdabaccddbcbdccdbbdcabdacbcdaaadbdcbcddaccdaabbcabccddaaddddcacbddcddbbbccbbacdbdcbabdbaaacbcaabbbabbcacbbcaaacbaaabccdcdabaaacdacaaaaacbcdaadacabbcbcdbaaabaabbbbcdbaccaacbadacbbdcbbbcacadadcabbacdabaaccbadcadcccbabcaddcbcacdacbddaddbbaddacdcdbadcbbabdadbbcabcadbaadcbdcbacddddbaaadcbdacacbaaaddcddccabccbcccddadacaadbdbdcbaabddcabdcbbdaaddddadbdcaaaaaaccabddaabcbbbcacaacccabdababbdcbabddccbcdccabdaddcacadcaccbacbbbbcccdaddadddadadbadcbdacbaddbbccccddccbacabadacdbacabbadabbbaadbacaccaacadcbadabdcbddabcbaacbddbcbaaacccacddaccbbcaacbdaabbdbaaabaacacdaabbdbabacddbabacddcabcbacccddaacacdacbababcdbdaadbcbbaadacbddadabdbcbbaabcbabbaadbacabdbcacddabbdcbdbdbbaccaaabadbabacacbbbcacdaccabbaaddbdcaddbccdbccadddaaacadddabbddadaccbcccaadabbdcccaacdddccdaddaacbacdadcbaadadaacbbaadcbaabdbabdcdadcddaadaccbdadababaddaadbcbadbdaadbcbdacadaccccabdabcbbbddabbcabbdaabcdcaabbbaddacabbcacbcddcdadbdbcbcacdcbbbdadaddadbdabbbbcadccacbacddcbccbbacbcdddddacccadbdabdbdacbcdcaadbaadbcaaabccdcabaadccabadbccadbcbdbdbacdadccaabbbaaccbccbccaadacdaabbbababcacdbcbbabcbbcbcaacabcdacdccdbbbcdaacdbcbadbacbdbddbbadbdccadbaacccbdbaacaacdbccdcdbdcacdacbbabcabdbdcaddaabbbbdbdbbddbccbddbdcacdbbcdcaccaaccccbdaddbcaabaacbcaccadcdbddaadabadbbacadbcadaccacdbadacdbdbbcbcadcacbacabaaadaacadaabaabddadcdbcaadcdaaabdaabbbbcacbddbdccbddbcabbdccdcdccaddbccbccbdacadaadddddcaabbdbccbdcacbdadddbadddcdbbacccdbdcbaacbdbcdbddbdaabbdaaddabcbcadddaddacdbaacaacadaddcdbaadadcddcbbbcdadbbdcadbcbbbbbdddaaadbcdbdbddbcccbdbbaabdadcacbdddadcbdaabccacdbdbbccaddccdaadccbdccbcbabbddbcdcbcdcdcaacdaaabaabdddaadcadbdbddbdadabdaddcdabbbdcdcdccdabcbabccbacacccbcbbadbcdbbcdbaaccddbcdacadbdcadabbdcbdadaababbbcbcddcadbbacddadbbcbbdbacacbdbcabcbddcdadabdbddcbaccbbcddddaacbcddcacacccbcbabcacdaaacbdddbadaaaddbdccaacdbdacbabdaacdcaabdbbdbccddbbdcbacbdcacbbdadaaaaadabaddcbadaacdbcaccaadbdddbadabbadcdaacacdbbccbcbaadaadacccaabbdaddabcacccbbaaabddbdbbacbbcdaabccbdadcdccdbbbabcbdaadbbdbccacdbdbdaadbaaaccdcbbdaabacccacabdbcdabbcbcdcddddcccadcbbdacbdccacbbadadddbdacadccbcdcdacdacadcdcdbcdabbdbdcadbcbbbcaddddababbddcbdcbacbadbbaadadbabbcadaadccddbabbdcdccdacbcacabcbbcadcaacdbaddbcaacacadaccdcacaacaaacccabbddaaccbcdacdccaabdaddddbbbaadbbbbabbdbdbcccdacdacbbdaadadaadbbdcccbbabbdcccdacdadcbbbcdddaadadadccaabbbaabdbbcbdcddbccbdcbdbbcddadbddbbcabcbabcccbbdbcccbcdddcdbbaadadadacdbdaddadcbdbaddaccccbdbdccddbccdbbdccdcaaddacbbcdcbbaadcdaaccbdaddadccdadcacccadadbaacbacdbdbbccccdadbadcdabbdbcdcbcbaacbdcdcccdcbadddcdacaddaddbdbdacaabcdaccabadacbccbdcaabcaabcbacadbaabbcbbbdcdbababbcadaaddcaaaabacadbbbaccddbcbcddbdcddacdddaccdacccddacacadddcccbdaaccbdbdbbddcacddbbaddacdcdacaddacbabbddddaaacabaadcccbbbdcddacdcaaabaabaabdcccacbdaddddaddcccaadabdcbccbbadaddcbcccbbcdbbaaacdcbcdcddadbacaaddddccaadbdadaabbbaaddbadccbccabbadaccbdcccbaacabaaddcdccbcdcccaadadddcdbabbcdccdbcadcbdcbdcbddadbcbbcbbddadbdcabddadadabbacacdcdbacdaaaaadbcbaabbaadcccdbabbdaabaabbbcacdbbbdabbbabdbaacdcddadcaddcdaaacaccacbddccaabacddbcddbbdbcbcabccdababbdcbbccacbadcdadababbaaaddcdcbbaaddacdcccababcabaacbcabdbdcaaaaaacdcbbdacabbcbdddcdcbbabcdcabdadccbcabaddbbaaadaddbddcbddadbbdcbdccdcbddcdbabcbccdcdaaaadcddcddabbccacddbbdbdcabaaacaabbbbcabaccbdbbbcbcabbaccdcdcddcbcadcacdcbadcaabbdbccdccdbdcbdbdccaaccacacabcacdbddcbabcbbdcabadcaccdcaabdcbbcabbaccbcabbaddaabdcbcccaccbaddbbcdccbdccabcdbcaccdbcbaadbcddaabcddbbdcbddcbdaabdbbbcbdcacabbbcaccccbbadccabaddaccddbdcacccabbaccabcbbcdcaababcaabbdaacaadaddbbcccccaaaadcabadacdbddbacacdbcdaacbcdccdbbbcdcabaaccbbbaddcacadddbbcacbccccddbbaacdabbcadbcbdcdcdcdcdcabbcbbaabccccbbcacbdcdcacbdcccdababdbcddccbbcdbcaccacbcdbdddbbcbabcacddabcaabdadbddbcbdcadbdddacdcaadabcbbcabbabbaddcddccdaccbaaacacbcccabbdbaddbcabdabcadaccdaccaacadacbbccbcacaaadbcbcddabdcaadbbddcdbdabcacbbacdcccabdcbccacaaaabdbdcbabcdbccccccdcdbbbdabadcccbbacbabbddacabbbbcbdbcbaadacbaddacabbdbadabbcdabbcaaccdbbbdadddaaaacacabcbaacdadcdaccadadadabccaaadaaadcbaabadaaabacddcacddadbbdacacabcddddbadacbacaaabdbacacbddbadcbcdacaaadbddddccacdcbadcdbadbbdbcdbaccadcacbcbbdadcddaadbbbdadbacdcdcdbaddccbaabdbdbbdabaddcccadaaacdddcbcddbaddaabcddbddcddcaddadddaabbbaccbbdcbdbdccdadcadbcaabccddbdbaaabdccaadaddbbcbdaadcabacbbdbbbdbcacabadbbcbacdbdaddbcabdcdadabcbcbabcaadbddbbabbabaababcdcaadbaaddbddcdcacdbcadccbbbcaadccaacbddcdaddccccbcccacdbadbabcbcdbcdbcacadabbdacdcccbaccdcaddaabdbcabcccdabcbdbabccbccddbcdddbaacddbcddbcbabcdbcaaaadaabaccabdaadccdddbdabbcacbcadcdaabaaacaadbcbabbcddbdbbaacdbdcbbaccccadbcbcabacbadcbddbccdabcccccbddbdcaddadbcdaacacbbabccddcabaadccbadcdaacadbadcaacccdaccdadbabdabcdaddccdaaadcddbdccddaccdddbacabbcdaacdbcdcaabccaaaddadacbdcbdcbdbabddacadbddcddbadddddaacdabdacdcabdbabbbccabadddccbaddcbbcacdbddcadaccaabcccbcbdbbadbbbaccaccddddcdaaabbcaddcbbbcbdbcbbbaacabaacaabdacdacdacdacaacdbdbbbbcbcccadbaacdbdbaaddbbacaccccadbdacbcbbdacdddbcaccbbbabbcabccbdccbbddccacdcadcbcaaaccaaadadcdabaadbbacdbbbacddacadacbccdcbcbdbcacbbcbdccbbbdadaddaaddbbccdbdaacaadaabaabcabccdbdacbaadbacacbcdadcdddaddadadcdaabdcbbdcabdcbcccbcccdacbddadbccabdadbdddbccccaacddacdadaaabadccbbbbaacbdccdaaaddaacdacdcbbdccdaccdbabcbcccccaccbbcbcaddcbbadaadbbabbddbadbcccdaabbdccdbacacdadbdbabdadcbdbacacdcbbdcddbddaccbdadcabdcadabbcabbacaaaccdbbaadbaddaabcaacabddcbbddacbcabacadcccbaddbbcadabcacaddcacacbdadbcddbbacabcbbdcacdbaacabaddddbbdddbbbbdbbbcbcdabdcbacdbcbbdbdccdbcadcbabdadadccddbbbadbbbabbddcdbbcdcdccbaadcdbddbadbbadcdddaddcadbddcadbcdcbdacbbcbbabdbcbcccaddddcacbaddbccbcddccbcbabbdccdbbabcbccaddccddcadbddabbbbdbdbbcbcbdaaabdabcbaadcbbbcdadacbddaccdcdbbadbabacdbdbcabbaacddcabdcdddccdadabbdbbcbbcabdaacaabacbcaabacbcdacbabdbdbccbbabbbcadddcdbcacabaccaccbabcdacddadabddcbccdccdabcaadabcbccdadacdaccdcdbbabacaddbcbbdbcdddbadcdcccccadddabdababdcbccdabccadcaaaacaabcbabdbabaacbadabbcadcbbcbbbdbcbcddaaddcbdbbdbacacdccbbaacdbabbbcbdcbabaabbbbacdcbcaabdddbbdccbcdaacaccdacdcabdcabbccccadddcbbdaddbdaaacacbaccacdaaabcbadccdbccbaccbdbdcaabdcdcadbddaaaadaccbcadcbcadacbacbbdcbdbccdbaacdcbcdcdbacccdbbdccddaddaddccaaabdadbcacbbadcbcaadadcaccbaacddcaaadbcaaccacbbcaadaadaccaadadbcccbaadbadccaccaccbdbcdddcdccbcaabcbcccdcacbbaddaccabccccbbaaadccbcdcbcabbdcdabbadababbcddbacbbacbbabdcddcbabcdbdddabbacaddabddbacadddaaaadccccaccaddbabddcbddbaabcacbdabccccadbdcaadbadadbabaacbdbaabaacbcddcaaaaaabddbabbcbcddabddcdcccdaabbbdcbddcddaaddbcabccdbadcdddbabcddbcbbadcabbdabdcbbacccabaccdabdbdadabbdcbcbaaddcdbacbddddbcbbdcbacbccdcbbaaabbabaabbdbbbcdbdaadabaccabccbdddddcdcdacccdabdbacbdaaaddaadbacaadcaddcaddbcccadddaabbbcdaadbbbaacaacbaddccccadbbddcdcddadbddcadcbddadabbdbcbacdbdcaaccdadcccdcbcbdbcabcabcbcdcaacaacbcacdbdcbbdbabdbadabbddcacbdbcdbdcdcaddaaccdcbbcaadaababcacbababbcacabadbabbcbcbdbcbbddbbbbaababcdbdadaccdcaadcdaaaccbadadcddadbadbccdabcadcabcbbcddccbbbddbbdddadbdcbdaacbaccbbadddcdbaadbacdddcdbccacdaacacdcdcacadadccdbbcbcdddacaaaaacbcdcccdccdccbccbbbbbccbdddbbdbadcabbddcdacbccccdcccddababbbcdacddbcbaadacbcbdacdddacaacaacddbcaacbaccabccaacdbcbccabcbadcbcdbbbabddbacbaccacbabacadcabbbbbbabdbddbaabacababcbdbbcdddccbbabccddabddcdcdadaadaacdbbabadccccdbbbabbcbabaccaadbcacddaaabdddadaddddbaacbddbcaacababcaacabbaaccabbdbacadddcbadbdbddbadaacbcdddbdcacdbbadaccadaadcadbacdcbcdcdcbccaadcabddddcbdcaadadadcabdaccaabadbabbcabdbbadbbadbdacddbdbaccddcbcadccbbabdbaadcdbbcbddacdadddaabadadcacbdbbdcbabddaaacacbbdcddcbababcbbdcbbacdccdbaaacacbdcdaacccbbbccccacacaaabdaaabcbaddcbabacccccccdabccdacccbddddabbbbdccccdccdabaabbbddcdbbdcccaaaabbddabaacaadacaaaddddbbdbbadabcddbbbbcaacbcabbacbddcacddaabdcbdbcccdacdddcbaccaccacaaacaccdcbbabbcdaaddabbadbdbbdabdaccddaaacdabaaacbbdadcbbaaabacbadccdabbbdbabacbaadadbbcbaccbabccbdabdbcdabcdaddacabcabacadacddcaaabacabddccdbdbbaabcbdbcdddbdbdbbdcabddbabbddcacdcdcacadbbcccadbbdbdcabcdaccaccdccbadabbdabaddbdddccbacbabdccdddddacacaabaabdcabcdcaabccddadddabbddddadbdbaabcadbaabccbacbdbbccbcbcacabcabdcabbdaabaacadbbdccbcbbacdaaacdbdaddddbcadccaaabaccddbddadabbbcdddccaacdddbaaadaddadcdddcbaccddbaadbdabdabacdddbcabdbcdcdaaababaddbadabbaabcdaaaaadaadcbddccbabcbccbbacdabcbbcddabdccbbbaddaabacadcadbdacaabacdbababcddbabdacddaddcdccaacbcbabcadabaaadbbbdcaaacbddbcadbdabdccdcbabdbcbbbbbccadaabbabbcccaaadcabcdbaacccbcdaccbddddabcdcdabbabcbaabcccaabbabccbdaddcbddddbadbabbdcdcdaacccbcdbcaccccdaccdbadabbdbaabdddbdcaacbdaaabaadbaccacabddaccadddbbabbdbdacabcdadbaadaccdabdababddcccccccabcccbbdccbbacaaccddabbbbbaaadbbcddddcbdbdbddaddaccdccbdbbaadabbdbadcbcdabcaaabdbdcdbbcaaaddbbdcacacbccdcdadacacaababcccabbbdbccabbbdddcbdaacdccabccccdccccbbbdddadbddaccdbbbcbdbbcbaacddadbacabdbbbcdbdabccabdbccbbcdaababdbcaaaabbadcdccaaddcaaccacdddcabdbabddcbddbaaabdacbcbcbabaaaddabdbdacbbaccbbcbadccdbadcdccabbdadbcdbadacbbdaabcdcabcddbbbddacbbcbcccdbcdabdaaacbbcadabcbddaaadcbddbcaadbbcabababadbcccdddacbabaadabbccbbdcbdacdcdabddacabcbbccacbcbdabccabdddbcdcbddbbccddadabdcbbaddabdaadadaaddaccaccbcdbdbdbbcdcddacddaddadadccababdccdcdcbadbdaaaadbbdcddbacabacdcbccdccbcbbddbbddbdadcaadddccaccbccbabdddabbdddbdccdbbdacbdcdcdaabccbbacdddacccddccaccddacbaabbadddabdcbbabbccdabcadbabddccccdcdabdabbbdbcbbcbbabddabcacaccaadbdadabddcbadcabbccdbdcabbabbadcacdbccbbdccdcabacdabbdbdaacaadddaddabbccaccacaddcadddcddccacbbbdadbcacacdcdcaacdcbcddccbadccbbbdbdaaacddddccadbaadaababccccddcacdccdacbccbbbdbabddbccdaddbadbcdcccdaccaccaccbacdcdbbcccccadacdcdbcdccadadacdbdbcaabdbdaadbbdbddadbcaadbbaccbadcbdabbabbadbbdddbdccacaaddcbdacabcdcdcabbdccddabcdbdccaabdabccdcdbbbbdcacacdacdbdbdaddaaacbccaaacbcbccbcbdaaabcbaccbdbcccddcbaadbcdcddacddcbdcbaadccdccdcabbbdbadbadddaddcbcbbaadadbaadbabdbdabaaadbdddcbbaacbdccdaaacbbddddbddcbaabbcbcbdcbaaadbabbdbcccddccdadacdcabdaddcbdbbbbcdbcdcaadcadacdabdbdacaabbadaabaacdcacbcbbbcdbccddabbbccbacdbcacccaccaadadcdcdccdbbbccbcbdcdbbcabacaacdcdcadbbcaacaaabaaabbaaaadcaddaddaddcacabdabcaaacbcdddabbbaddcaacbdbbcdbdaacdddddadabdccdadbddababdcaabadcccaacbdddccddbccbdcdadcababcbccadabcdacbaaaaaacbcddaacdccabbcacbbaacbbbdacabadadaddbbdcddaccbbcdacbddccbabbdacdbcadbddccbcacccddcaabcbcbdabdaacdcdddbbbdcadacabbbadadcbbccbabccbcabaccddadadccdccbddbbadcabacdccccadbcaabddcbaaabbbabbdcbbbbbddcababccbddddcdaaacdbccbbdbccbdcdbbbcdddbbacaddbccaaddcddbdaccdcaabaddcbadaaccbddcdbbcbbdabbbacbcadaaddadaacaabbbdaaadcadaaabcdaccbccbabcdddadabdbcabdacabccdcbbcacadaddcaaabacbcabdcdccbdcbadddbaddbbdbcadccabdaadabdbddcacbbcdcccdcbcadaadbccbbadbdadadccdacdcacbcbcddabbcccbddbcaabccbacbccbdcbabadbababdacacbaadcbbddccbbadbdaacbdadbdcabcadaaadadaadbcbabdaccacaadbcbcbdbdbbbbaaadcdaccdacdbacdcdacdaaadaadaabccbaaccacadcbdcaddbaaaaccdbddadacbcccaddbbabbbcddbccbcbcdbbbdacbbacbdcbadacdbccddabdddbbadaccacbdaccccabccacddddcacdddaabbcabdaadbcaaabbcdabbbbbbbdccabdcabbbdadabddbcadaccadcdcababdbbdcdccacbbbcadaacadacdcbabcabcdabcbccddbaccdcccaadcdacabdbdcddcdbbadaacabbbbcdcbaacdccbbaadacddacbbdbcabaabbdabbacdcbbcaabdddacdabcacacaacdcbdcccccddcdcdadbbaadbdddcbcdddbcabcccccadbbaacacdbabcadbaabcbabaddbbddcdbdcbddcbbbccbadadaccdddabcaacccdcddaaddcccdadbbcbabadabaaccbcdbaadacbbaaabcadbbadaaaadbadaadabadacbbbadddacadbaddbabacadcbabbbccbaddbccbdadbdbbacdcbadaadcdadcbacaddbbbabdadbbabbbbdbcacddabdcbaccabbbaddbddccbdccaadddbdabcbdadccbcbabcdbdccbdcaddabbcbdadacaddbddacacbaacdcbdcdaddabbddcddbbcdccccdbdbdcbdabcacdcccaddcdbbbcbddcacddbcbdbccbcbddaaccdbddccacdadcadcbbccabcddbccccdabbbadabdbdaddbccadcadbbcabcbdbcadcbdcaaacbadaabddbddcaccaaadabbaabaaabbbcaacbbcbaaadcccdcabdbabbbacdcbbccaaddabddcabbdcacabaaaaccbdaaaccbdccadbbaccbcaccddacddccdddcadabcbacbcccadaacddadacbbadbaacbdddaccacbaaaaddbcbacdacbabcbbbcabadcbaabadbbdbdccabbddbcacabbadbcabcdcaacbbadcabbbcccadccbdbaaacbdbbdbdcbdaaacacbbcdabaccacabacaddcacdcbcbbcdddaddaabcbdcbdabdbadbcaaacccbaabbdbcdbbbcddadaacdcbdaddadcbbcaabaabbdaacababdbdabccdbbbabbddcbddcdcdbabbcbacdcaaaacaddbbdcbddbdaaacbbdbbdbddacbdbcbdcdbdabcbadaadcdddcdabdaccbacbbdababbddcccbbbbdcadbbdcbcbbccdadddbbcbbcadddcbadabbadadbbaddbbacbbdacccdcaaccdbcbcbdaacdacbbddcccbacaacabbcadaadbabbcbbbdcbcbdaacadddacbccadcdbcaacadbdaacadbcdbaccadabbccbcbababaaacaadcdddaddcccadccddccdbddbaacabaabdbdddddcdabcccaacaaccacbaacacaacddcaacddbddbacbdabbaddbdccddcbbccaaacbccbabadddcbcdcacbdcdbbbbdabdccabbaddcabbbdcbabbbdcadcaaadcaadbdacdaabaccacbccddddcdcdacdbacccadcddaccdcdacaddbbadacaacaacdbcddaabdabcbdbdcbcdbdbadcccabcaddaddbcbcbdabbbcdbdcdbcbbcdcaaadaaccabcaaddcddddddbcaaadaccacdddabaaabbbdbcaddbbadccdddcddacbdccccddadbbcccccdcbabaddaacbccdcbddcadabbdcbccdaccbdbcbbdcadccabacccabdccbdcdccbacaccbbccdccbabbadabbccbbaabacbaaadaaacdadcdaaababdddacccbabdcabcdbdbbbbbdacdbdaaabbabaadabccddadddabbbbbcbbdbbdbdddddcaaddaadadbcdddacadabdadbccabcdbbacacaccdadaddbdbabdcccbdcaccacdabcbacbccbdbcdacbbadadccbbacabbdbdacdbdacbcabdbcabbdbadddacdcacdbacaadbbddadbadacbacbbbcbaaadacbdddccbccdddcccabaddabcadcadabbbddadbadbbcddcaaddccdbdcdbdcccbccddbcdabccabcdacddacbcadbdaabccdccbdcadcdbacacbbbbdbcdcacdaacdcbcabcbaccbdbbbcccbbdaadcbcdaaaaacdbbdabcbabcddddddbaabbcabbadaadddbdcbbbddddddbdaabdcdbcaccabcadbaacaadaddbdbddbccbbdbbbaabdcaaabbbbdbcabadbacdbabaaacdbacddbbaadaacdddcbbbcbaacdadccaaabddbbaaadccbcccdccccbccabcdacaaccadbbccbbbabbacdaabddbbbbadccbabcdbcddccccaccabcabdcaaccbabdbccbcdcababadcadbdbabccabdabaadabdddbccbcacdaaacdcbaabcabdcdcdbdcaddbccdbbddcdcaaabdbbadcabdcdbcacaacabcbcdaaddcacdcacbaccddcbbbaccddddbdbaddcdcddbabdddbddabdcdaacabadbcbcbcddcccaccddcbcbbacaadadbbbaaadaadabbaadbcdaccabccaabbdabcbccdccbcbccdddcabbbaaababdcbdacbaccbbabdcccacddddbbcdabadcbbcdcadacabdacdccaddbacbddcaabcdbcadccacbbcadabadcddacccbdbddaacdadacddbcdbbcbdadbbdcdddcdabadbaabbddcaccdaaadaadabdbcdabddbabbadcddbacdddacbccbabcdabacddbbdadbaccbaadcdcabcaacdccaccddabadbaddbaaaccaadbabaccaadaddaabbdaadbbacdcaadcdbbdbdabaabdcccddaacaaaadacabbbdbdbabcdbacdabbbbbdaacdaaabcbddccbbaccdccdddbcaaccbbaaccababcaddaadabaabcaacbacddccbdabccbaadcbcdaaadbbddacaddccccacaacbdaabccddcccadcbacddcaccaaacbcdcbaabccdacbdddcdcbdcabcadacddbacaddabdadadaabaddaccddddacccbbacbbccaddcacdcabcadbbdbcddbacaacdaccbbddbbbdbcaccbaaabbacbddabdabadcdcdadccdbbbdaccbccdbacbddcccadddbacaccddbdcadbbdbaadbccbdcdcbbacdccabaddbcdbadcbabaacbdcaccdaddbdacbcabbaccaddbbbbbcaddabbbdabcbbcdbaabbbcddacbbaaddaaaabadbddadaaabcabcdcdbdbbdbddaadbcdbdcdcbbbccaddbbbbbaddddcabaddbbcdbaccadbcccbbbcababaadbdbccdaccadddabddcdbcbcbacdabacdbcaacbbbcdccabcdbcbaacacddbbbaddcdacaadbdcaddbabcbcacacadcadabbacaacaccbaabdcdabddadbddabaadccdaccdadabaccbbaaacdabbaabdcbaabbbaadbbadaacbbcaccdaccdbbabbbdbdabacbcbdcccbcbddddcacccdbabdbaccdaccbbdbbaabcbbddaadabcddaabcdbdbabcdcccbbacbaddbabcaabdbabcabbbbaddcabdcbcabbcbcbddbacadaadbddbbdbbbccbbbabdcdacbddccbaddcaabbacdbdaadadaccdbdababacaccdaadbdbabdabdcbddacccbccdabdcabbcccbdcabdbcdcaaadcdcccdcadacaddacdcbdcbbbbdbdcaadbacdcccdcadcbdbcccacbaadbbcddaaabbdcabcdaabdabddbaacbccadacaacccddbcbaccbaacdabbcbdaccdbbbccacaaabacaabcdddcbcaddcabddaabdcbdccaabbabbdddbbabdbcadacbddbabadcbcadacacdbadbbdbcbbdaddcbbcbdddaddaabcaaacdabcdbabaadbbcbbcbbcacdcbcdcddaadaabdcbacdadaccdaadadaabbacdbcadadcacbcdabdaabbbbacbdaaddaaadcbbcaaacbbdaaaaabbbcccdbcaacddcbdaadbcaacabcbbdcdcddadadbdbdccdabadcbacbdcddccaacdadabadaccbaaccadaccddbcaddbdbbadacdcaabddaacdccacaddbcddddaadaccbdaddccbdacbbcbdbcaccaacddbaaadddccbcbbabdbacccaddbdbcbcaabdacdaccabcdbcacbbbdaadbcbbddcbaacdddaaacadadcdbcddcbcdcaacdcccccabaddbbbbbdbcbcbabbcdcbcbcddcadaddbddbbcdddcdbcabbdddaacdbaaaacbddaabaddadcbadbcccdcbcdaaabdcbdbccbdacccdbcddbcbdaabbcbdbdcdaddddbadbabaddaabbabaacbacdcdcdabdadbdcbbabbdbddaccdcadcdaacdddadbdacdbbadbcaadbcacbacccdcbdbbdbaabddbaccdddbdbaadcbccaaaadccabcbcdddaacadabdbaabdcbacaadccdcbbddabaabacdaacadcbadbccdcbccbcbacabdacdbcdcaccbcacaccdbadbaddabdbdacdaccaddbaaddbcabbbdbcabcbacbadccdaaacbacddcbcbccbddbbccbbdcddddbcacccbbdcbdabcddcacabcbacaddcccadddabdcababbbbaabcaccbadbdbddabcadcaaacdaabcadcdcadccaccdbcbaccaaadcddcaccccaaaabacbabbabdddbddcacdbdabcaaabaccbbaacccaaaaaaabaaddbbcdcddccacbdbabdabbddccdccddadaadcaabbabccacdccbacbccccbdacbbaacbcbaddadcdccabdccdddbaacdcddaadbcaabdddbabbbdadbccbadcdbdbdaaaddbbcddadaadacbbddbcbabaccbcbbdcdddbccbadabaccdbcbbdcddbbdcdcddcccabbaaccdcbbdddbbcadbdabdccddaddaacdaadadcccbcbbbdcdacdacaabdddcaaaabdbdddacbcdcbabbabddabaaccddbacccadcbcdcaadbdacccdacadcaadcdaaabbbdcdcadcadadbbbccbbaaadcdadccbdbadbcdaabcdcbdbabdbcdadaaaaddabccccdbaaaaabdbbcaacababbacbbbdbdabcbbddcabbdcabdbcadbbbaabbacbcdbcabbcddccaaddcbbbdabcbbdcacdadbdcdaaddabadaccbbcdaadbbbadcacaccdcddadababadccaabbccbdcbcadcdccaadbaacccadabbdaccbbcbbdbdbaabddcbcbacddbbdbadbabdabccaaccabbbdadcadcddadbcabcabdddcabdbcdbacabbdbacacdaacbbcddabadaddcbbdbcacaccbadaaddadaccbabaacabaaaaadacbdabbbdacdabaacbcaaaadbbacaacaacdbadddddbbbbdcacddcbbababdddacaabccdbadbbacdacbccadcbcddbaddacdbacadabbcacaccaacabcbcbaacadbcadccbbbdbbbccdcbacdaadddddcabbbbcadccaaacdbbdccbcbbcccadbbcaabdcbbadcdbbbcdacabbdddddbccdacdcacccaccbcbcadbddbbbcabbabdcaccbbdabaaddcbbadadadbdaccbaccbdcacdbcdbcdaabadaacdaccdccccdbcbacdddadccddcdcccbaabcddcbcacbcbddcbcdababacbbaababdcdcbbbacbdbddacaadacadaaabdbbbdadacacdddbacddabbcbdcabddddbcccbaadcbadacdddcbcaacbbcaccbbdabacadbdadaabbabddaaaccaaaddddabacbccdbbacdbbbbdbbcabbdcbaccbbbdddcabbbbbdcdadcbdbbdaacbbcbccacdaabdcdaacdabdbcddbaaaaaddabaccdbadcdddbaaaaaccabdbadabbbacaccbcbbdbabacdcddcbbcadddcabdcabbdbccdcdabadbbdbbaddabacddbacbadaabacadbdccdcaabcadacccdddbbabbdadbcdcccdacadacccccddcbbbabbbaaddccaddcddaabdccbbccaaccbdcdbacbcabccdbaabcabacababccdbdcaadaacddbdcdabdaaddbaaacdbdadaddbdcaacbcacaabcabbadacdcbcbbdabbcadaabbadcaddbadaaacddccddaadccacbccbcdadabbcababcaadaccdababdbaadbdacabaddcdadadaadbbcaacccaaccbcdabdabdbdbbadabddcddbbcaabbabbbbacbcbcacacdadbccccbbdaabadacdbdbccdbcbcccdabdccacddcaddadabcbcdddbddccdadccbdcdcbaadddcbbdbacddddacbbaaaadabbadddbadabbbdabbaabcbaacbcaadadcaaabbdaabadcabdbdcadbbdcddabbcdcabdaabaaabacbbdcdcabccdcbbbbbdaadbabddccdccabbaddababccbcbaabbbcbdadbcacbcdcdabaacabbaddaabcbcadabdadddacadccacadcccdabbcabcccbadcbdddbdacbbcccbccabcdaaadbdcaacaaabbdacdddbdddddcacccabbaddcacbcbdbddadabbdcddddabacaccaabdadcbbcbaccbaaadbddcbbcbadcdcbcdabbadacbaccbcdbaddcadbdabccaddbdbcabaaccacddadaaddbacdddaadccbbccbadabadadbadbbbacbdaadddcdbdddaadcaacacacbbdbdabbcdabcadaddcbabadcacadaccdbdddaaaccbdabdbbdcdacbbacabdadbadddaccdbacbcadbbabdaacdaddbbcaccbacaccbcdbcdcbcbbccdacbbbadadbaabdbdddcddcabcdbbdacccbdccabbcdabcdcccbddcdbacbcabcabbdbbbdbdbbdabbbcaaadaadabbaabcaddaddbbbcdabdbddacadabdddbcbbdbadbbbcdbccabacaacbbccbdbacadaaadcdbaaacddaaaccddbbaddbaccbacddbbcacbddabaabccdbadabccbcaddcdabbcbdabbaccadbadbdaacacacaccaaddbdbcdcdbbbdcacbcbbcbaadcabddccacacdbabcabcbdbdcdacbddabaacbdaabcbacbacbdcdcdacaabaddacbbbcccddddccbacbbcacbdabdabcdccaaaddbbdbdbcbadcbabbcbabaccdbaaadbbcbbbcabadddddacadbdccbdabaabdbacccddabcbdddbbdccbdbdcdccddcdbddadadcdbbdbccbcacbbaabadbabdcaacbdaacdbdbcbacacabddaddababcaddabcabaccbdcbcccdacbbaababacdaaacadcbddabbddcadbdcacaccbddabaabcacbacbabbbadacadddacbabcbaadbadcbddcbacaddadbabaaadbbaabbddabdddcbdbacbacbdabcabaddcbbcddadcdcbcdcdbbdccbbbbaccadaacddddadcbbadbbacadbaacbacddcabddbabcadadadbaccbdbcdcccbdabbdaabdabbcaabdcbbcaaabbbabacdbcaadcacbdcaaadbaacaabaadaabbdbacddaababddcddcdbdabdddccdcabdbbcbccadbcbcdbcbacadbcdcaddbbccdbbababcaddabdcbaaacddddabbcbdbdbddccbdadbcbcbddbcdabdbabcddddaddaabbbbddadbadbccdbadbcbddcbaccacdaadaadbaaccbdccbdbbddcbbcbbbdadbbdaacbccadcdcddcddadabacbdcddbdcbddaababbbdcabcabcaacaadbadcdacacadddcdbabdbcccaabdcccdbbdaabddbabcaddbbaccbdbcadccbbddabacbbccbabbadccdbbdcabcdabdcdacabbbbcbbadaadcabaccdacbcdbadaabbadddcddcbaccbbadadaaddaccbbcacccdacccaacbbdcdbdadabbdadadaddaaacbbcaddacbbadcbaddacdabaaabadbbbabaacabacabbddaccdcccbdbadcbdbbdccbabaddaccdababbbdadbdadcbdaaccdbcacdcababadbbbaacadcdbbcbaddadddddccdbcacbbcbdcabbaaabdcbbbbaddacaadaaddcccbaacdcdabccdcbbadaccbaacbcbdddbdcbdcccaaabdddccadcbbcbbadacdcdbbbbbacdaaccdacbacbdcddbcdadbccabadacacbcddabcdbcabbdcaccbacdabcdddcabadabadbddacabcaaddbdbacbadbacaadbdbdcbadabcabaaddcbadabcdaabbcdcabdababbcccbdddacdacdadcabdbbaaddbccdadccddbbdbabbcdacdaadbccbbbbacdccccabbddaddbadabbaaadabdccccbaadbbcbaadabbbcbbacccbcddbaadabdaabaaacbaaccaaccdadbababdbbdcdcbdadbdbaddacbababccabcbccadcadcbbbbacdadaadacdcdbbaaaabacdcaddcddcdddcbbdbaadbcddacacbcacbbbbdcddaadaaccaaadabacdddabbccbcdbcddcaacdcbcbccaacdcccadacadcaabdbddccabccdcdacccbdcccdbdbbdbadacdccacdabaddaabcdbaccbaccdbbabcdccaabadbbcbdddbdcacbdbcccaaddadbcccbbdcdaadbacdcdcbabacbbbcbcabaadbacacbcddabcccdcabcbdaaaaaaaacccadaccbdcdaabaabbadabddcbacbdcbdddcdabacaaccddcacadccabcaccdbbadbaccdddccadddcdbbbcdaccbacdaabbbabacdbadcbbdbbacbdbdddcaabbccbbabacbabaaddbadcacacbdbbcbdbdddcacbcdbdbbcdccacbcdbbbcadddbddbddbdbabbcdbaadbcadbaadbccaabbacbacdadadaaddddccaddbccbbcddcbaadaddddcddbcbcaaaccdcccdbbabbabacdcbdccabccacabdddbcddabaaaaadaabbccdaabacddadcbabbcdcacbabdbcdbddadddbcbbdaabddabadbabbdaddaddaadcbcaddddacbbdbbdaccababbbdbbcbadcabcadccbbcdaabdacbaacdcdcdcbdbaacddcccadbcdcdcacacbbcaaccbccacdcdbadbdbccaacacbbdbabccbdabcadcccddaadbcdcaaadabdaddcbddcaccbaddacbdccdbbbccabcbaacbdadbaadaabdbcaabaccbbdabdcdacdbabccccdbcccbadaddbbdaadaabaadbadbccbaaaacadcaacbabaaccbacaabcdbdaabacabcbbdacbadbbbacacdacbbaccccbdcaccbbbadcbdbbcccacabcdbdcaaccabdaaacdcbaabcbcdcccacbdabdccaccccbbcdcbdcdddabdbcbdbcaccbaabcdadbccbacdccbcbaacacdaddcabccdbdabbdaaabcbdabbabdadddcddccdaabacabddbaadbbbdbdadbbbadaacacccdcadcacbacccadbcbdddacbcabbdbbdbddabbddbdbbaabdaadccabaaadbdcbccacddacadacbaacbaacbbdcabbcabdcbbcdaabcacddcbdcdcddcdadcabaacadbcbcdbaabbacadcbddcddadaaddaacbbbddcccbdadcdbdbaadacacacaaaacacadcdbbbabbdadacddbabcdabbdccabddacdbbaddadbdbcdabdbbdaccbcdcbdcddcccdcbccdddbcdddaabcddadabacdadbbadbcbbdccbabbdadabccaccaccaaaaaaaaccbdacccacdcdbaabbdadccbbdbdbacadbbcbbabdcdcdabcabcbbcdaabdbadaababcabbcabdbdaabdddbbcbbdcdcbcdaabcaaddcdaaaabcbdbabcddcaaaaaaccbabbdcaddaddcddbcacbddbbdacdcaaadddbbbcdbbbbaabdbbbbbadaacdcadbacaddcdcdcbcbaacaabddcbcdaabdadadbbdbaaaabbbdbcddbcccdabdbacccbdbacabbabacddabaabadaaccacdadbabbbdacabcdcddbbaacdbcabdbbddcbacdaabbcaddabbabcccccaaacacbcdbbcbcbdaccdabdbabaadcacbccbcbaccaaacaaaaaacabbdadcdccdcbdadbacdabcacbbdcdbbacddcacaacdadccbaddbabadbdadcdaadadbdccdcbcbbadbcadaabadacdcbccbdabcdccddaacaaacaccaccddbbcdaadadabaccdbcacbdddbddbadcbbcccbcdbdabbcdbdbbcacbcdcabaabaadbddacaadcbabaccdcadabddbbaacabaddacaaabcccbbbbdabdabadddbcbcdaadbdbdaadcacbbaacbadcabaaddcbacacdbddcbdbaabdddbaadddbadaadbbbcdbbcccabdbdbdcdbbcccccbbaacdbdbdddcdddbaabcadcaabaccbdcbcbbabbadcdbcbbbdbdccdcbcabbdbaadbadbbbcdbaaabcccdaaaddcdbddbcddcbbacddadddacccacdbbddcbcdcbdbadabccbddcacbaaccdabadbdabbdabbbdadbcdbacbaaccccbdbabcbabacbabbccabadcaadbcdcabcacdccdacdcddadbbcbdabaaccbccbbaddcccddcacbabdacccccbdadccdccadcccacaacabdbdbcadcbaaabacacbddadbcdbaaacbdcabdcdadcabcacbdadbcabdbdcabdccbaaaadcccdbdbbadaaacdaddcccbdddbcbdcdabdababddddaaaaabacdcdabdacbadacaddbdcdcccdadbaaaadaadbdcaaaddddcadaddddaaccccbcbabcbdaccccccbdccadbaaaadbacdcbcaacdcdddbcbacbdbccbabbbccbbdaaacdcacabccbdacdcbadddcddbaacbbdbbbacaaadaaddbdccbcdbadddadababcadbbaccadddcbdabcbaccddcacaacdabdabdcabbbbcdcabbdabbadbddabcddbbddbcdcabbdbbbcacbccbbdddcbccaddccdbaaacbbbacbadbdcbcacdbabadadbccadcbcbbcacdbdaccbdbcbbcabddbdddbddadbbbbabcbccaabdbaccddacddbabacdccdabdcbdadaabdacdcbdbcdaadadccbdacbddddcddacccdbddcddcbdbcdacbabdcbdbbacaacdddbbdccddbcbabcadbdbcbbacbbaabcdddcaaadbddbbbacdacaabdbcaabdcbcbacabaddcdaddcabbdcccadcaabbabbddbadbcdcccbcdddcbabbdddaacdcbbdaaadddaacdcdcbccadcddcacbdbddbcadadacacaaccdacdcbadabcadcccaadacdaaadaaaccbdaabdabcddabdbadaccbaadaddccdcbcadaabacadacdcbcaababadcdccdbcbdbbccaccacaddabbcaaaabaddadcdbbaaccbccccbbbbddcabddabcdcbacaacdaabacadabaacadcccbcbadacaccbbdddaddbddbbcbabcbdabbaccdaaaddabbbdadcdbdcdabcbdcadcdacadcbcadcccddddccdddccdbabccabcdaacdbccaabaacbacbadadbcbabdbdabcdbdabbadacdabacbcadaabdacbbbbdbbccccdabdccbadadaabcbdbdcabcbcccbadbddbcbbdadacbbacbdacbbddbcabccbddaaacdddaabcccdcbabdabcbdacacdbadcccaabcacbabadcddccbcbcbcbaccbbcbbabdcdcddacbaaadabaaabcddcbadcbabddcccacbccadbbabbaaadcabbdbbacaadcccddacbbbbcbaddbdacbabcccbdabacbbbdaacddddbcbbdddabdbacbbaababbabcdbaaddbbcbcdcdbababadcadbaadbddabbdcbcdadcacadcdcadbdabcabbcaccdaadbdccaddbddddaadbbdabaaacacbcaddbbccbcdaaccbdacbadbbdaddaddbbdacbaabdcdbdbcccdcacbbbaaddcbdaaadbdbadcabbbadcaccadacabdbdcbcacdbcbacaabbbbbbadcadbcdbdacbbcdbdbbbccbdbaccbddabddccbbacdcbdbaacbcbcccadcacdaddbadddabbddcbadaacddbdcdbbcaaaddcbdaddccadcabbccaadaadbbbbdabbbbbabdbcaaadacdbbcdcadbbcbacdcadadccbbacaababcddcbccdbbaacabbdccadcbbccabaaacaacbddbaadbcdddacaabbbccaddbbbdabcdbddacaaaddbbdbdbccccbbbcabbbdbdbbddbdcbaddaccbddacbbadaadaccbbaddbbbaaddacdacbdaccbcddaabcdbacccdaacadbcbbbdadbbcddbbaacbdaabbdabbdbcdbcabcaacadccccbcbbdbcacabcadabacacbcaaabbbdacaaabbbdcdbbbcdddbdcdbabbbccddcddbcacbdaacbbbadbdbcdadcbbdcbcabdacdabaddbdbdccadadbcabbcbcccccddcdcdcbbabbdbdadddbcbcaaabbcddaadabcddbdddacccbcbadcddaaabdbabdcabadbadbcddbcaddccbcddcdcbdbcaadcbbaddcdabdbadbdcaccdbdaabccdcccdbbadaddccdadbacdcadbbdddbcaaccdbbaaacdbabccbcacddbbdacdcdaadacabdaabadddcaacbabdcbbddccbacdccadaabcdabbcbccdadccbadcdcaabccbcdddbdbaacacdcbccbdaacacaabdbdbbaacbccaddddcbdcbaadbccbcbccbcdabbaaabcdaddcacbbacdabbcacbbbdbcbdbcbbbbcbbcbcabcadcadbcdacbcdccbbdacaacbcddabdddcacaadaabddddbddcdbbdcbdbacadcdaaaccaaccbdbababcdaddcaabbdaacdcaddcbbcabbdbcccdccccdccaaddabdbcbddccaabcdbdcdabdadbacaaacbadbdddccbabcccdcbddbaabdabdadcddcabdbdddbccdabddcdbddddaccbdddbdddadbdabcbaadbaaabccaacacaaadcaadbcdbdbcdccddaaadcdaadcdcdcdcddccaaabbadadcacdbccabdbdcdaadcaababdcbbcadaabcdabdbbdbbccaaddcadcbbdcadbccbacbbcccdddaadadbadcccbaccaabdadbbccbbabaadbacdcabdacadaddcbcbdaaadbdaabbddddabddcbdabbbaabdcbdbbadccbcbcaccdcbcdbddccaaabbbddadcdbbbbbbcbcbacabbaccaccdbdcdababdacbdccbddcccdabccccbcadbabacdbaabbddaccdcdbcbcdbacdadcacbbabcaadcccacbdbbdbdbadbabdcbbddbbcdccbdcaabdbccdbbbbaaddcbbbbccbddddaacccdbbcabbbcaabbcbdccdbaddbbdbcabdbddbacbdbbacdcabcabdbdaaacbabdaadbcaccdddccbbbaaadbccdbdbccdabaadccddccbcdcccabcdbdaaddbadaadbdccabaaacbbcadabaacacdaadddadbaccaccbddbcadaaddcdcaaaadcbbbcbccaacbbbcabddcdcadabcccaabcdacaaddbcaaacdacccdcdacabbbbcbbbdbcccbbbacdccacbccaaadddaacadbbcbcaabbdcadbdaadcabdbdbcaadcccaabbbcdbbdabcdbdcbaadcdcccbcdcdcabadddbddaabdcbbdbddbbdccdcdbcccabcbaccdcbddbcacaabcdccacdcbcabacbdcdcaddddbacddbdaaccadddbdaccccaddaaaacbdaaaddbbdbdadacdddddacacbcdcdbdbdadbcdaaaabddccbadbabdaabcabbabbbbdbcacacaddccdcbdccadbdcddadcdadcbbbdacaacbcacbbdbdbbdaaadacdbdbccbdacdbbadbacbbaccdbccaaaadacccbabdcbcaaaacacadcddbcdbadaaacacdbaabdacacacdacccdbcadabbabaddbdbabadacddcbadbdcabcbbcbcabddbabbabaddcbabdabaddaddcabbcdccdaabdacaddbbbababbccacdcbccdcdaadcabcdabcbaddaabcabbcacbccabbcdbdcccaddcccbbaabbdabddbadabdcabbbcdcadccccadcaaacdcddaacaacacaabddbdbcddccddcdbdbdacccdbabccbccdabaacbcccdcdaadaddacacabbccbacdbabcaddbacbbccddabbaaacddcbaacbbddddbaaadbdcabdcbddaadcdcdbacddddcdbacdacdbbdcccddaddbabdbdacdadcaababcadbccdcccbacdbdaabcaddbbbcdccccacdaabdcddccaacbdaddbcaaadbabbddbcbdaaacddaaccdabccdbabddabacdddbbabbdbbbabcddcdcbaaacbabcdcddbaabacddccadaaacbaddabdcacdcdacdadcdbdcabdbdadbabbcdddabbddbaccbdbaaccadccdbcbdddbccbdbaadbbdccbabbdddaacdcadbaadddbcccdadacaccdbccdcbcdadcdaaadaabacbabddcdbccbdcdcaaaacbdbabaacdbddacccaaaddaaadcdadaabaababaccccccdcdcbabbcbcdcddbcdcbdadccabddbbdcaaadcddbacbabdcccadcccbcaabaccccdbdbdaddbcccacaaadccacacacbbbaccaddbdbaccdcdaddbadccdcdbadbcddbbdddcdcabadcddccdbcbddcaaccabacaacbcbbdabacdcacbdbdabbdcadbdaacbbddcdaddddcaaabbadbddbbaccddcacdcbcdbcbccdacacbdadddcdabbccadcdabcababaadbdcacdbdadcdabdcdbcdbdbbcacddaccbcddbdccdbaabcbcaadddbbcdaccabdbacbccbabcaaaccaccdacccadbddabbadbabdabcdcccadbbbccababcccaddcdabdabcbcdaabcbabcaabaabcccbcdcdcbdaadddccacbaabadcbccbcccbbddcbcbcadcdbbacbbdbdbddcdbcdccaadbacadadddcabbaddbdcadcddbadbdbacccccacaaddaadbdcbaabbaccdddcddccabbddcbdcdabadbdbdabccadcbdbdcddddbbcbccdccccabdbbbcdcacbbbacaabacddadcabdddbddbaccbbadcadaccaadddacccdddaaaddddbccadcbbabacdbdcbdccdcccdaccbdaabbdadaaccdbbbbbbabbadacdbbbdcbbcabcbacccbaddadaacbdddbcdaddbaddbdaaaabdbddbcdcdbaacbacdbaadbadadababbcdbacdcbacabacacdbcbdbcccabcdcdcabdbbcabbcdbcdadbbcbccbddcdacabacbcbdaaadaaddadcdbbcaaadddcddbcbabdabbabcdbaacbaaddccdaabdadbadabdcadbcbabacabaabaacdbcacdaddbdadcbbbdbdacdbbbdbbccaaaabcbcbbdacdcaabddabbdddcbcababccdcacddacdbcbdadaddbbabaacbbbccdaadcbabbaaadabcdcaccabdbdaddbbccbabacbacccaacbaadcaaadcaaacdacccacbddcdcccadabcdadbaaaccaabccddabcbcdaaaabdcdadccabdcdddcbadbddcadadacbacadbcacabacdcbaacabadccdacccddbbcadcccabaadbcaabcabbcbddaccdcbbabaaabcbbcdbbccdaaaccdbbbbddcbadaccdcbacdacaccabcaccbddcbbabbacabcdcacddbcbcdbcdcdbacbacbddbbaabcdccddbcaaddbbdacadcacdaaddcdbdccdbdcccdcbadcadaaaaabadcacddadccdbddbbbccdbaadadacdddbadcaddcabcaabbadbdccabaacaacbabdadcbcccaaaaadabcdcbdcabbdacaabccdcdbabacadaadddbbcadacbbddcdaccbbbdcbbbcccaaadcdcbbadccbddbdbbcbadbddadbdcdddcbaddbcdbadbbacacbabdcdadaddcbccaacdbdbbcaabaacbcccbdddcacdbdadbdddaddcdcaacbdbbacdadbdadbbdcbadcadcdbdccdbcbdadcbcaacdcaddbdcaccccbcabccccadbbbdcaabcbdacbdaccdbbbbccabcabdbddcaabbdabbcdccbcaaabbcbadcdcbdcabadbadccabbcaddadcdbadadbbacbacdbaabadaaacdcddddacbcddabdbbaddbaabacbcaacaabbbddbaacabadcbcccaadbbccaddadcabccbaddaabbadcbcdbcbdbdaadbbcccadaacadcbadadcbbaddccbbddabacbadcadcadddbbddccacadbcaaacdabcbdddbcccadcaadbbcbdbdbcbcdcadadccbbbcdbdbbcbabcdcbbbcdabcdabcadbadbddbdccabacadddcdccaabddcbbdcbdabcacabbdbcaccdaadabddcbbddcbcbbadcdadadacbdabcbccadbbacadcacdbbbaddbacacddabdbbbbcbdcbadababdbcaabbadcdcbcbccbdddbdcbdccdbabadcbdbbbdacbddccdcccadcadddcacddadcddddccbbdacbdcbcdbdbacccdccaddddbcbcbcacccbdbcbcdbcbddbabddcbdabddbacabdbaccdccddadccbcdacbbdcabcdbbdddbcddccdddbdbabaddadadbddbdbcdcabacbbcbcbcadccdbacddabdcbccdbdbdacadbccddbaaaccadbacccdbbbdabccbdabaaaabaabbccaacbbdcdcbdcbbbacdadaccbdddadcbaddccdcadbaccdccacbcbcadcdcadcbacacccbacccbbabcbabbaabdbcbdbbcacbcdaccddcbbcddddbdcbadbbbaadcabbddccdbcdccdcbcdbdabcaddcbcababcddcccddccddcaabcccbabbcdaacbbaccbccaabbaddcdbcadbaadccdcbcadadbbdcbaaaaabababdaadcbcbbdadcccbccaddbbdabbbcbdbcdcbcabbbabacbdbabbbddadbacaccabaadabacddbabadcbbcabdcbbbcaabcdbdbadacbacbccdbbaccaacdabcbdcbccabcddadcbbdccacabbbcbbcdbbcbabbddabcdcccaaccadadbcacddcdbadadbccbbabddbababcbbaacaabccdbabacdbcaccddcbbcdaddbdccabdadaaccbabbacaaacdbbabccbbbaabbcdcacccdbaaaddadbdadccddbacccaaacacabaaaaacbdcbadaabccacdbcccbbccbcbadacaaacadcbcaddcbcdbbbacbbabcbdcdcabdcbdabcbccaabcbbcdcccbdbcbbcbcbbcdcdcadccbaaabbcccbbadccbbcaccbdacadadadaadcbabccdcadcadbbbdddcaaaccddbabbcbaacacbdabadaaccacacacaddaacadabcbaaaccacbbbcbbdcbdaccdbabbadbcddddcddddbcbcaddbbadcdcadbcdbddcdccdaddbbaaadaddaaabbcdbbbaaabccdcdbbcaccabcaadabdabdabacabaadcdbdcbababbccaabbccaacaccdddbbaccbaddbbdccbbbcbdbcdacccddbccacdabdbaadbdbcabcbdbbcacbdcacdddaabbbdcbacabdcadabdbbddbcbddbdbadacaabacabdddddabbaaccbcaabacaabcbcdabacbaabdbddcbccbdaabaddabbcdccccabcdadcabdaccbacddcbbaddabcabbbaddaacdadacaadcabbadabaccaaacdcbaddaaadbbadddddaddbabadddcacbabbadcddaaaacaabcbbaadcbbdaadcdaccccaadcdbdcddcdacdadcbcbdcbabdcdcddcbdbabaabaaaabcdcdccdadbabbcccbdbaccdcddbaabbabbcaccdcaabaacbbdccbbaaacaadabdaccaddbdabbbdbbbdadcdccadddcbbaacacdabcbcababddcccdbabdadacaddcbaacbccbbccbddbcbdcdccabdaadcdaadbdccdbbdaadcaaacdabdabbdaadbbbbcbdacddababdabcdcdcbcaddccbabcdcdbdbabbabaacdddcddaaddbdaccdaddcddddadbbdbddabcacdcadabbbdbaddaabbcbdaddaabcaaacdacbacdaccbbadcaddcbdbacdddcadccadcabcbcccdcdddbbabbbcccbdcaaabaaadbbcbcabaadacdcaabcacdbacbdcddcdbcdbabcbdaaacadabadcacddaaabacbbbbbcaacbdcacdacdadcbbccccdbacbbbcdaaacbbcdacbcaaacdbadddccbabbbbdcbcbcbdabbababbacddbabdbddbadbaccabdcbabadccaaaccbddbcddaaacaabdcbbcbddcbdbcdbaabacadbabdddaaabbccdcabddbaaddbddbdcaaccddbbbabdcbcacdcadaaacccdbbcbdccccaccaabcacccccbcbaabbcdacbdbccdbabadcacdadbcadbdddcabdaadabbcddbbaaaabacbaaccccbcadcccdaccdbadcdccabbdbadaaccccbcacbbcbcddbdacaccdabbcbcdbdcaaabadcddcdbbbaccdddddccadabbcabbccdbcddacbbacdbabccdadbdcabbdadbbdbabbbbbcbdcacdaacbdabccabbbdddccbdbccdcdaabccadcbbaaabaaadadcbbcbddbbbabbcbbccdbcdccdcbcdcbaabbdcddbcdaabccdddbcddaadbcbadbabbbbcbbabccbdcdccacdcdcacacccbbddacddddcdbbaddabaacdbcbbddbadbcbaadcdccdcbbcadadaddadbabdcdcbcbdabcddaaddaccbbbcbcadcbbdddddaccbaabcdaadbbbdcbcbbbdaabcdacadcdbaadcbaccaabbcabcbdacbcaaaccddbadacbadcabbbaadcbcaacdcabbbaacccaaabcbdccdbddcdbbbdbacbbcdabacdacdddbddcadacbbbbcbbcddaadbdadbbdccdaacaaabbadbdbbcdddddddaccbccabaaaaaaadacaabdaccccbbbacdbadabdbdbddcaadcaacddddbdbbddaacbdacaababbaabcbdbaaabbbbddccaaaabcbcbdcacbacbdcdbdbdbcbdadbdadbacdaacaadcbaabbdacdcdddbdbaddbbbabccacaabdccbdddbabbbcacddddbccabbaccabcbdbbacdccddbdcadbaadaacdcdcdadccccabddbbadabcbbacccbaacacacddabdadbddbcddadaacadadacdacabaabbcdbcdccdabcdabbbacddcacacdccbcccccdcdbccdbbacbcaccbcaaccbdabdddaabddbaddbacdcbabcbcbbaabadbcbcbaadcadbcadbbddabbcccabcbcbacadbdbdbaabdbcdadbdaacdadbbbacdaaacbbddbddbccdcbbadbbabbdddbcbadddcadcccdddaadcbbcbdbaacbbadbcccdbcbbacaccddcaacababadbbadaacddcccababddbabbacabdadbddacdbbbbcddbddaabbbdbdbaadcbbdacbbacddbbaccabaabadabbbbccbabcadcdcbcbcbdadcbcaadbdbabcacbadcddcdadddbcdacabbbdabccabddaacadcccbdccabaabbdabddbadbcccddbccbccdaaababaacdbcbbacaddaabddabdbbbaddcbccadcccbdddddaadcbcaabcdbcddbddddbcdbdabaaaacbbadaaadabbcdbdbcbdabcdbcbdbaddaccbbbcdbdbcbdbcdaababaabacdbdaabbdbbcddddcbcccccddabaddcabbdaaccbacddbbacdcbcdccacdbabdcadcdcbcaaaabadcbdadbadadcdbdcbcddbddcbdaccccaccccbaadacdacdcdbabcbdcbddccddcaddaddcaabbdccbaadacbdcccbdaabbbaaaabacdccbbcbabcccbbbabdcdcacbbbbbdcdcbbabbcdbcdddddbbcdccabbdcbdbaacbdaddbacdbbbdcbbbccbbbbdbcbcacaddcacaaadaadddddbababcccdcbaaccabcccbcbabccbdcddaacaadbbacddccabdcbbddbdabaaadbacdbdaddbadcaacbaadcdddcababcbcdbddabbdadcbddbcbdddcdaadccdbbdbcbdcdbdbccdbcadaadcdccbdcaddcdcdbcbdadabcddbcdadbcccbdacaaadcacabaaddbbbbddabbdcccabcbadbccaacacacacbacbdcaccccbdbdbaacabadbdaadddbcbcccbdacbdbcdbddcdbaadbabbbdbabddccdbadcbcdababbaaddcbbdaaddbdbdcadcbacacdaaabddddabcadccdcacadacaccbcbaaacdcdcbbdaaacbdcadaacadbaaadadbdadadbabbcadccaaabbabcdcbdbbadddcdcacdccbcccbadcbbbcbaacdaddaadcccacbabdbaccddaadddbaaacabccdaaacbbbbcabdbaabdccbbaddcddcdcccacccdcbccccaaabdcbacbcddccddbcbacacdcdbcaabcadabcdccbaaaaadacbdaacdbbcbdbcbbabdcdabdadbadcaaadacdadcbccaaadddbbddbbcadbdbccaadadcaabcccacccbdbbddbdcbacbaccabddbabaadadcdddbccaadbcbcbbbccbaadbbaadcdbcabaadcabbdabcbacbccacacabccabbcbacdaabcbbbbadbadcdbaabadbabbadabcbccdbdcabcbacbaddababbcccadbdacdbbbabcabcbbdbadaccbcaaaadbcddbbbddbaadbaddbabadbcadbacddbddcbddbcadbccbddaaddbacacadddbdcdbdabdaddacaaaabdbadaacaddccbadcbbcaddabdccaccacadbbdacbabbbdbcdbdadccababddcaaabddacadcdcaacaaccabaccaacdcaddcdbdaccbbddbbbacdddacbbbcaadcabdaddbddbcccbbcdbdbdddacbcabbadabdacdcdaccaccacbbcaccddaddbbcddccbcccddbcabcdabcaaadcacaaddbdaabbaaabaabdbbddcddbbbacdacaadacdabdcadabdbabbdaabccbabaabaaaaabbdabadcbabcbbbddabccbddddbdbdcddadbbcdbddaabccbabbdccbddccbabdaadbbdcccbdbaccdacdaccbbbbaaaadccccbbbaddbdddcbbabddabadacabdcdbdbddbbbacdabaacdddbaacabdcaccbbbcabccbbbdcaabcababadbbdddcabdcccbacbccdcaabaacbcbbcbbcdbbdacbccdcddbdbaaadababacbcaaddccadabbadcdbcbbbbdcbbdccccddccdddabcbbbccaaabaddbdbccadcbcaacaddbdacbacabcccdbcbdaadbcbdcbdbbabadabcddccabdcddcbbbcdabadbcadbcdbbcdddaddcbdadccbcdcbaabcccbdbaddcccddbadcacbbdcdabbdcadabcbbadbcbadcbbcdcdabcbdaddbcaadabadcccacadbbbcbddbadbccdbcbdccddabbcdaabbbabbbdbadcdcadabbdabddcadcbdcbbaaddabbdadbdbdcdacdcabbbcaaabdcabdddabbbccbadcbdbacdbdcabadbdcbacabccabbbdaddaaaaaadbdabcabdbaacdbdabdbbccbacbbbdbacdabbddabbdccddbacbbdbbbcdcbdcaccdbabdbdaabddbcbdaaabcbaaaccdbbbccadaacaaabdddbdbdacabbcaabcacdbaccaadddcbbbbcbdddaaddbacdaccdcbdbbdcccccaaaadbadbcbcadbcbadaaabbddcbbcaacbadbaadaacaddaddaabdcbdbcccccaadbdabbbdcbbccbccdcbadacccabadddaaabbaaaadabdaddcbdacadacdbaacacbbdadbdbbabcabdacaddadccdcdabdcadabcabaadbaabdaabdcdddabbabdaccadbbaccdbbdbaddaccccbbbdcbcdcbdadbdabcbdccdadccadabcdcbdbbaaccacabadbbacadabdadcdaacdabdddbabbbbaddbdbdacdcbabccaabcdabcbdcdccdcdcdbbdbbbbbbccadaadaabdaccbdacadbcaaabdccdbababcddacdbdacabbcddccbabdddbdbcdbbbbaaacdcbcbdbbaaddaccadaccdddbdccaccddbbbccdbcbcacbcbbcadcaddabacbabdcbdabbddbdcdbbdcaccacdaabaaaadddddbaccbcbcaacacbdbadbdbccaccaccbdabdacbcbbdbbabdcddacdbaadcbdcdcccaacccadcdcdadadcabbaabadabaddadcddacbddadbbbbdacbcbaadbadacbbcbdacdbcbcbbcdbdaacbcbcacabdadbadadcddccbcdcabccadcdadadbcdaccccbadbbbdadadadaaccbabbaddccdaccddacaaabbbccccccbabcbabbaabbddbabcbbacbdbcaabadccccbcacaaddbcacbdaccddcaacabaaccbdbcdbdbcdcbdcaacbbacbddbacbcbcdbbdacbcbcdbcbcbbabcbdbbacaddcbbaacbabcbcbbccaaadbbbddcadaaabcacabdabaaabbdbbcbddadbddddddbabdaadbdcdaddabaabbdddcadddcbddacdccdadaccbddadabdacaabbabdcddccabcababdbacbcadabdadcbbcaadabbdaddacabcaccbaabbddadccccadbbcbcbccacbdbdcccaaacacaddcddacabdbdbacddbbbcbbdcccacbadabdbabcacccacddcdabaabadbcaccabaddbbdbdbdaaabdaaadabcdaaccccbcddcabdadccadbdabddcdbbdcabdcbdabcbbcbcbaacaccaaddaadacaacdadacadcacbdaccbbababbaabdaacabbacdcdacdcccacbbabdcabacbcccdccabcbaacbcbdcacddbddddcababdcbbcbbaababbdcdddabbccadcbabbdbbbcdbbbbaadcaacaccbbadabbccaadcbadbacacdaabcaaaabdcdabaabbcccaadabcccdacbccdcacaabdaacddaadbcddbbcbadbdbadbbbbdccbbcdaddddcbbcaabcacaddbdcacbbdabadcadcdcbcbcadaabbdbdadbabacdcbbdbdabadbaadcbaddcbcabcabdbdcbaacabbabdbbbaacabacbbacadcbddacbaccdddddaacddbacdabbadccbdacacbdcaadcacbdbadccabdddcaaabcdaaaddcdaadbadddaaadccbadddabcbdacbabcacbadccabbcaddbaacacdbccaadcbdcdabccaadadabccccdccbcdadabcdddacdaccbccddbbbcbbdacdbaccadabbacbbbbadbbdcbdcccdcaabbddcbdddbdddbdaadadddcacacbccddbbbbbaddbbabdabbbcdacaacbbbbdaddbbbdacbbdaccdcbcbdcccaccbdddacdcbdcdbcdbcddabdaaddcdaacabbcccabcddcdccbaaacccbbabaddacdaadaacdcbbddbcdadabcabbcacccccbbccdcdcddccdaaacbbaabdabaabadcbdcccbbbbcacbcdcabaddaadcacddadbcbacadbbbbdbabdbdbacbcadcabbdbaddbcbdbbddadbcbbbdaabcadddcbbdaadcddcaaabdccadddabdcbcbdcaadabacdcdbcaacbdabdacabacdbacadacccbdccbaaabadcdaccadcaadbcabdcacbacdbdcabcabdcbbacabbbdcdcaabacadcaabcbdabcdbdcbccdaacdaadbbacacaaabbbbadcccaadbbbbabaacaaccdbbacbcdcddadddaadbddbddccabdacddcadbcaddddcacaaaabadcddcbbdbbbdabdbaaacdacaccbaaabcddcababbdcbacbddccbbbccbbcaaaadaaccdaddaacbddbaabacbacbcbbbabddcddddadbbabaadbcbcdbcbcdbcdbcbcbabdcdbbaabcdccacbbaaaacaadabcadcddbbbcddcbacddcbacaadbaabcaaddadcddccbdadcbbbcacbcaababbcacbdcddcaabdbbbabdcadbbadbdcaccbdaccbcabdaaddbbccbaaadabbacdccabbcaaddcccddaacdcbccaaaadbbbcbccdbdccbdddabbccdabbbcbcabcbbbdadcdabbccdbdacdddabdcdadaabbbcbbcdadccabdccbadbbbcabddbbbdbaaabbaacadadacdabddbbbccadbdcbdcbaaaaacbadcdbaadabbbabaaacbdddcccdadadcaaddbdcdbdabcdbbaabcdcdabbcbcbcbbcddaabacccbbdbcddaccdabccbbadbbccdccaaaddcddaccabdadaadccddbaaabcabaaddddcaacdccbdcabdadbbccdddddbacdbcbdcbaacdccacaabcdbbaccdaaddbbcbdcacdcbdcdcdbcacccdcbdacaaaddadacabcddcaabcadbadcabbdabcccbaccccacabdababaaadbaddabbccdbdbcaacbbdbcbcaacdabbcaaacadcccbcbcbcadbbcddadbbbdcbacccabbbabdbbbdacccbddbcdbadbbcbcbdabcadbbbbabbaaaababdbcdaacdcaabbdabbddbdcaaddcdacdaabbdacbacdcdbbaadcdcdccacadbdbdaddcaacadddbcaddbaccccbdbaabaccdcbadacaccbaacaacbddcbaddacbbbbccadabbacbaccbabdccdcadacaddbccbbcccabbbbbacdaddccacbddbcbcdcbbdcbcbdcadcddccaaddbaadadaddabbbadbbccdcdbaaaaadddadcdbcdadccbaacabbdaccddabbdabbadcaaddcddcdbcddabbacdbbacaaccdcabcbaadadbcdabdaadcdcbbdbacdadaaddacadddbbaacdcacbbaabddadabbbadaacdbaadddbddbdadaadcbaadbccabaccddbaabdbabdcaddbdcadcabbddcbbcacdadcbdddbacbabcbabcddbaabcadbaddcadbcaaabdbbbcdacdbcdcbaabccccaabadabcdbbbabcddbababcddbbdcbdbddbcccabbaacbcbccbcbdccdcdcdcbbbdccacccdcdddadbabdadbdbcdcccaabbbaaddcdbaaaacaabbbaccadbdbdbcdbbacddabcabbdadccbddccacbcbdabddcdddcbddabdaddbdbbabbaccdbbbaaddcabbddccddcdccbbcaaacdcddcabdbdccdcaaabdcaaaaaccdabadbadcaaacccaddcdcdaabcddadcbabbbbbcdbbaabbddadcaadcbdcadbadcacccbdadcddaddcdbaacacacbbbadcdccdcaaabcdcaacbcabacccacddbdbcdcdacbacacaadccaabcbcaaaccccacdadccdcaabdddaccccbbacacaabaadddabacbddbcbabbddcabbcdcabbbcbacbcccbaddacbabaaaabaadbabcddcbbdccbcdaacdcdacbdabbbdbcbdcdacccdddaaabbbbcdddcbcdcadaccbdcbcddaddadabaccccaaadbacadcadbccdddbdbcaabcdbbbabaadbcaaabbacaacdcaadaadbddddbbbdddacddcbcbacbbbbccaadccdbbbadbdacbdabbccaccdddbdddbddccbabdbdadaddbcdccadcdccdbcddbbcdaccadbbaadacdddcddabcdbcbbdccddaadadcbddddaabdaacadcadcdabccacdbbaacbcaabbdcccddbbabaacaabdcacbdbdddddcadbacccabbccbbcdccbadcaccbcacacdaddcbacdcacddadcacabbcbdaadcbbabbdacddadaaaaddbcbaddddbbcccadcbcbccddadaddcadaadcddcaaaacdcbbcacbccbadcbacacdcadcaddbcbadabbddbdcccabaabdcbdccbaabbcadadcacabdaacbaccdabdcdddcaadbabacdcbdbdbcacdcbbabcaadaabaaaaddaddbdbdcdbcaccccbbcbccaabacccadbaadbccabaddbbaacbbcabcbdadcabcaadcbbbddabaccdbddaaadabcbcbdacdbbdcdcdcdcbbccdabddbddcaacaababbdcaacccbabdcbaccbccabdcbaaaddacbaadccdabcdabcdacadadaadbabbcccccbaddcacdcdcaacccabbdaadcdcdaaaaccdcccaddcdcbadbadddbdabcccdcdcbdbdcabdabddcaccadbbdcbddbccaacaccacaaaabbbbcbcadccdbccdaadddbccbcdcdbadcacdbcdbccbdbaddabcddbdadcdbbcdcbabddcbcdcaddacddacbacdabddbadaccdaadbcbdbcccdbaaddaacdddccacdbcccdadddbdadaccacdaaaddcaadbaabacadcdbdddadaddabdbdbcdcacddcdbbcccdaacdacbbdcabbadacddbcadcbbcdbbbcddadbccdbbabacbaddcbccaccdaaabcabacccaadbbbdddccbccbdaccdabcdcdcdddcbcddcdcabbbdabacdbabaabbacbacadaccdccdbcabccbcddbcadbcdbacabcdddaddbbadbacbcdbabccdacaddaadabcccbbcdaacaaabccdcabdaadccdbdaaacbcdaabbbdcccddabdadabbabddbcbacdddcddbdadcddcacbbcbbcacddcbacacbdcbccdbcadcccbcbbacaadcccbdccbdadacdaacbacbacabdcdbbadddcdbdbdcdcbdadbddbbbdcdcdbabdbdcdbdbdcacbccdabcadacbddcabbdcccaacadbdacdbccbbddcababadbcdabbcaabccdbadaccacadbbddcdbcabbddbadbaaababcdabbabbbcadddcbbaadabbdcccccbdddaddccacbddbcddabcccaaddbdcabbbbacbcbdcacdcdbababdccabbabdcdabbdaaabccdadbbabbcaabbdbcacdaaddbdbdcbcbbdbcddadaadcbbdcacabbcabcdccccccbadcddcbcbccddbdcbdaabaacacaacacaadcdbdbaaabbadabcbbdbcacbbaddccdaadbdacdbacccdadaadbbbdcadddacaacbbccdcadddaabdcadacadbccacccdbdabdddaabcaaaaddbbcaacaaddbcacbdaaccdaccaaadbdcddbccdcbbdaabdacdbbcaaaacabdcddbbdaccbbbddcdddbadbbdddbadbcaddabddcbbaaadcbccadbaabbbcabdacaccddddddbbbabadcbacaabcdcbadbcbbccaadcdbdccabddcaabcaadbabddbbcacdaadacdbabbabbcdbddcdaddbabaddcccbdabbdaadccabbdddacdbbadbcacaccbcbbbcaaddbdabccabaabaabbacadabbbcbbcbccddddccccdbaaacabddadccdbccadadcdbdacdcdcbbabadadbabdbdaadcdccaabbdaabdbdbacdabbcdbbcbcadaddcbddbcdbdbcbadcbaadadcbcadccaacbcccdabdddccbacdaddadbdcddcbcababdcadaacbddbddddcaddabccbbbdddcdbbdccbabcdccaadacaccadddbabbabaabcbbadacaacacdaaabaaacbdccdcccacadbaabbaacddaacabccdababbabbcdccbcbdaddcbdcadddabdcddcdddbbcdddcacccbdcacaddbadadcdcddccbdabacdcbaddcddadcbcbdbcaaaaddbdbabddadddbbcadbccbbcdbadddcdbdbcbbadcaccaababacdbbadaaddcbbddcadaacbaddaabbadcbdbadcdbbbcdacbcbaaabbdbadcccbadcbdadcdbadcdddabdbccccbdbaabdcacbdaadbccbcdaddbccbdbbdbdcdccbcacddbbcdbabbadbdbcbdccdcbbcaaddacdcdcaddbbbccdbaabdabddbcaaacdbbabdadbdaacbacbabdcabadbddcbadcbbabccccdccddcbdbbdaabcbacddacdccddcdbacbabcdcbadcdbddcaccdbcacdbadccacbdccddadccbbdcbabcbabbaaddadacbbcababaadbdbbcbcddacbaabdccccbbcbdddbcacdcacbbbcadcaddacdddbbdcbdbccdcbbaccacbccadaccccbdcddaabccbcdbabdacaacdbabdbdccdaabbbabddbaadddbddabadddddcabaacbaacdbcdbbcabcdcbcaccdddbcaaadaaacdbabcbcdaaddbcaabdbadabaacbaaacccdcbbbbbbddbdadcdcdcaddcdabcdaabaacbbbbdbbabcdacddacccccabbaaadacdbddbdcdcaddccaabcbaaaabcccbdbdbdaabaaaacbccbccbbbabbdbcbccaccacbdaacbcaabbbdadaaabbdcabaccabcbdcadabadbccabaddcbcbddccdadabccdcbbdcacabadddacbabadbdabdabacdcccabcaccdccaabccaabbaadaddabcdbbadbdabbcdddacbbcdcabbadbaddcaddcbacbbdbbdcccccddaacaddacabcbbadbbddaddabaacadbcabbcdbdbdadcdcdcbccadccaccdcdcddacbcdbcdcdbcbaadaddcddccbddbbddbcbbcbbccdcacaaabbbabbddccccccdccdcbbacbbcdbbccbcbdcccddcdadadbaaccdadadcacacbbddacadacddbddadddabbddaabcabcacaacdbddcdaddbdadaabcdabbdddbbbdcccadcdadaaddacdccdccbcccbadbcccdacaaadbbdcccdbdbacbbdcbdcbcabccabadbcbaddabddcbbcbdbbacabaabdacdbdddbdbacbcddbccdbdddbcacadbdbccaadddddcadacaddbacdbacacaaabcacbdcdccdadcabaabcddccadccbbbdcdbbdcabbdcdadcddddcabddbcacbbbaddcbbbaacbbbbcadabcadccbaddbcaabbcdbabcabacbddbbdddccabcacdaaacbbadbdbabdaddcbcaacddaacbccdcacdcbcaadbaddcdccbadadaaaabbadcbbbdbdddbdaacbcbabcacacbbbcbccbccbdcacbaddacabbcdacddbadccddbadaaddcabcdbdaaadadacbcaccbbadadadabbdcdbaacbcbabcabcababdddddbcccdabdbabdddbbaddbcabcabdadaacdabdabdccdadbbcadcadbcadcdbdadcbbaddcadcbcdacdacacbccacbdadcdcbccdabdbbdcdcacdabdbcbdaccdccdbcbdcbcdcdcccbdadcadabadaababdbdccdbaddcaaddddbaabdaadcdabbbbbacdaacbaadcdbdadbbbdaccacddabaaddaacbbaacddcabbdbcdaaadbdacacbcacbbadacbddcbbacdcbaaabcdbdcbdcaabdcccddccaaadbaadccdbbabcbdabbacdbbdcadcdddbccbcabccacacdacbbaacbcbcdbbbdcddaccdbbcddbcacadcdbdacbadbddccddacbbdddccdabbbcbadcdcaccdaddbcdcababacbbacddcbddaabaadbcbdcadcbbbdbcdddcabbcdcbccddcbdaddcbdbbaacadbdbcacaaaaaaccdcabddacdbdbdacbdadcbbacbbcabccbdadddcabbcaccdbdadcdbaddbdccdabcbbddadbccddacabddcddccbbcacbdddacabadaabddcbdbccdbdbadcbaaadaabdbababcdbacaaacbaaadcccdccbbacbcbadbcaaaacaaabdabcabbadbcacaaaaaccbbcccbabdcacddccabccdacbabbccaabbbbacaabbcadddcadcadabcdadcbabdabbaaccababcacdabbcbbdaabddcdbdaccdddaaabcaccdcdadaccdabcbbabdaabdddbcccddabbcddbddddbddccbcccbdbadcdcbbdcdbaccbcadccbabdaabbbdcadcacbabcdaddaccaaadccbddddaccbadcbccbddaacbbbcbdadaabbddcddccbdcacccabaccacabccdcbbdbcddbbaabbdddbbdbcdcbbcadbdccdaaddacbbbddcddccbaacddabcbcbcaadadcaacbbccaccdaaadadaddbccdbbbaadaaccbbdcdcacbbccacbbccadbccbaacaddbacbbacaccbdacacdacddcacdaabcadcaabbcdddbaaddadddaddccbdccdcbaabccabbacddabbddabacddbcdcbcadaadddaadaacdcbddcacddbbccabbacdacbcdbbdbdababbcabbcdbadacbcbbaaabdcadbbdbcabcddcbdccdccdcdbadababbbdcdccdbcadcbccddbaabdadcdbddddcccbadcababaadaccdcbbcbdcabacdbdababcbcddbdabaadbcbadbadbdbdccbbbcaddadcbdcdbadacddacbdccaacddbcccaddbbcbbabdddcaabccbbdcadbbcacadbdbbddacbdbdaacbabdabbbcbccdbcbbcbcccdbadaaaabbddddbcbbabbcacabdccadcbccabdcdcccdccaacacdbabbccbddababddddcdddbbdaadabbdbbaddabcdadcbccbdadaadbcbcabcaaadbddacccaaabdbdccbbbdabdcdaaacbaddabbcdbadacacababbadccbbaadcdcadadaadcddddbadbbbcbaabbabdabaaddaaabbdadddcdbccbbbbacaddabcccdcbdcababadcacacadbcdcadccadaaaacabcacbbaaaadcddbcddbdaaabdaaaabdccdbaacaadabcdacbcabadaabacddaaaddcbdabaddbcacccddbabbdabddddbcbaccaaddacdbbadaccacabbdcddabbacbcbbdcdbcaddbaabcabdbbacdbbdacaadcdbdbbbbccbaaddbcbbabdbdaadddbaabcdaacdabdadcbdbdccdaadbdaddadcabcabcccabbabcbcccddbddabbaddcbbaacabbcbbaddcdbbbbbadcdcbcdddbcccacacadadaaabbaadaaabacdaccacdacacdaaccadcbdaabcdaaccdaaaacdcabcdcccadbbdcdadadaacbdbabcadbadbbddbdacdabadcddabaabdbaacdbdaacdcadbaacbbccbdccdabcabcbaababacdbbbdacbdccbacdcdacccabdaaacccdacdddcdacddbbcbcdbdccbbddcbccabbdaacbdbcdadbddbabcdbccbccaacddbcbadcdabcbccabbcaabdcaccbbaadcdabacabacbacbbdadbcccbbdcbdddddabccdcadbcbddaabdadccaddcaccaccbbabdbabccccadaacdabdcdcdbbcacccbbbccbbdcdddbcacaddcaabacccbbbcddbdadddaaacddaabbcaaddbaccccaddacbaccaaaaabcbdadadddcbcbacdbbcccacaabcddbacdadabddacbddacabadabdaddcbaaabbadbdabacbabcacababaacbacaacaaccbcbbccabddadbbabddabacbdbbadccdcadbcddbbacccaabdacccbbccbbbadbabcacaddbabbdbdaccdcbbbcadabbdaabbcbccbcbbdcbbaccbcbbdcbdddacccbddadccababdccabaadcddbdbdbdaaaddccaccaabdabbcaacbbcaadbddcaacddcababddabcadcbdddcdcbccbcbbcbcddcaaacbdcdadbaabdbcbbabdaaabdbbddaabbaabdabbadbaccaaddadbddcdcbaabaabcddcbcdccdbdcbcddccabbdcadccccccdbbccdadacdbbdaacdbcbabccacdbdbdaabbbdbabbabbdcdccdabbbadbaacbdadbdbabacdaadaaccbaadcdcdccadaadbacdbddaaddbddacbdbbbcdbdbacbbbbbbbaabccbcbccabdcccddccbdcacccbdaadbaadaabbbabacbbcbdbdbdababcacacacdbdbabaababcdaadabdbdbcbadbccddabbcdddbbdcbabcbaabadababdaabdddabbcdddcadacacccdcbdaccacaddbcbcdccaabaccdcbbbacbaddbabcbcabdcaacaddccdbdaddbcbbddbaaaaaabbbcdabacbaadaaadbbdddaadaacbbdbaacdadccdcbdcddcdbdbaccdbadccbdadadcddccaabbcdaccbcabaaadccdcdadbccabadcabcabbaadbcacacaddbbadacdbdddbcbdbcadbbaccbdcbbcaccdbbbbaaadaccdbbddacdbdbcdabcadbcbacabdacdcbccccdacddabbdadddaccdbadabdacaccbcbbbccdcdcadbdbdaadaaabccaccdbbaaacadadacabdccccccddabdbdadabdabcabdccbacbabddcddaadcbcdbabbacdcccdabdadccbaacddcaddbdabdbabdcaacccbdadbddabdbbbddacccdabacdcbdacbbacdccadaddbaacdbdbdacbcccbbadacbdbadccdabdbbddadabdcaabbbaaabcaacdbcbaabcddbaccacccccaaadaacbbbbdaabbcbaccdcdaccddaaadaabcdacaabccabbacdbadadddacdaddaccbabcdcaddcabcabdaaacbcbabcabcbbbbabcacabcbbcddbbdadacbccdcdcbcdddbbcccbdcabccaaaadaddabdacabadcadcbdcddbdcbaaccbbbacbaaabdccccdaddccddaaddcbdbcaccadbcabbdabdaaacbabdbcddcbadaacccbcdccdddcbcaccaadadbcddbcdbbbccddaccdbcabaddabdaacdcdcbcdacbdaadaccadcaacdddabdbbaacadddbcbddabccdcdcbdccdccdcbbcbbdacacccccbbacccddabdcdabbbaacccdabacbbcdcbdaabdaabcbcdabbacadbdbcbdabddbbdcbaabddcdbaaccbaadbcbdbbaccabccdbadaabdbcbdaccaccccacccdaaabadddbbbabacadcbaabbddadaabdacbacaadbbdbdbddacbddbcbdbaadcccbcabbdccdacbbabdbcbabacadadacaaadaacccbdbbbcababbdcbbbdabdacdacbaaabbaadccdaadadccaabccddddcdccdbdaabdababdcdadbbdbdcbbccdbbdbacaababcddccdbdbbccdaacdccccdbbaabbbbddcbabacaaacacdaabbdaacaddbaccacabbccddccdcbcbcbacdbaadcbbabddbcaadcabacdacdaaabaabcbdcbdaabbdabdadcdcbccbaccbabdbbdbbcbdababbdcdddbbbacbbdbcdbbadbbaccccaacbcaabacddcbddacddcabbcacdcbbdbbdbacddbbcaaacbdbccbdbbbcaabacbdddcbcaddddadddcbabcbdacbbbcdadabdcaabdddbcabbccdcadcddcbabaaaaccbcaadddddbadcadcadcbadabcddabbbacaabacaaacbaabcacbbcbbdbbcadcdcbbbdadddbdbaaabddcbcadaacacbdaacbdbdabddcccbaaadbbdbdabbbbdbdbacbdcbcdadbcbbcdaacaadaacbdcbcabbbbbcabdcbdccdcaddbccacccbbcaabdddadccaddbbdababaadbabaabcadbddacbdcbdaddcbbcdaddccddbcaaddcccbbacdcacacadccbdbcdcacbcddbcacabcdadcabcdabdcdabaadcdaddbdcbaadbcbcdcccdddcccadbcacdcadcabbadacbcccaabcddbadacbddcbbadddabadadcaacaccaccbbabbaadddccbaaabcccdabdbcdcbadadadddccbbdbabaccabcdcbdcdcadaadadabcccabdaabbdcaadabccdccbcadbbbdddacddcdadbabacdabbbdadcaddaabcacccadbcbdbbbcbcbaadbaccdbdcbbacdcadbcbccbbbbdcbdbdccadcbdbabaabcccdbcdcdadadaddacdcbdcaaddddabbbbbccdacabcaddbaadbacddaaaccbaaacabbbbbcdbbbcaadaaacadcddbadccbbbdcabbbccdaaabadcbbbdbabbbbcaddcadddcbacccbcddccbabaabcadaccdacbbcccadbdcbcbbbdabbdabbbacdcdbbddbbdaddbcabbbadcababcaadcacddcbbbdbcbdbdacbbaadcaaddddaabaacdbccabbaccabbdcacbddbbacdccccddacdbcccbacaabddcdccadbcdbabcbdccbbbbdaaadcddcabbbdaacabbcbdcddabddcdcbdadcbccdcaddcaaaccbcccdadaadcbacaacdcccdaabddbbbccaaacaccaaccbdaaccbabaadcadbcdcadbdbcddcacdbdcbaccacbcbbcaddbaaddddbdbbacdabbacabdaccdcdbaabdbabacbccbcacdbdcdbdaacaddabbdacadddbbddbcdbdcadbbdaccabaadaabddbadababbacbddbbcddaadabccbaacbdccdbacabacabaacbdcbdabbaddabbddbaabdaaaaddddbbddaccaaccbdacdccabaadaddddcdadcaccbabdcbacbadccaaacdbbadcacaadddcdcdcaacbdcdcddddacdcbccabdadabcbcacbbaacbbcdadaddacddcdaacdbabddcadccaaddaddbddbdcabbdaaccaacddbcdbacbbdadcdccabaaaaddbddcbaaabdaaddaccbbbddacbbbabadbcbcbccacddabbbcaaccadcdcbaacddacbcddadcccaccddbdaaababcbadbbdbbacadccbabddabaabbadbccbaabaaacbdabbaccbbcabdbbacacacabdaadccabcadbbabbbdcbdbccabccdaadbabaaccddccbadbcdbbcbcccdbcabadbcadcdbddbbddddbbacabbbdabbcaacdabdacacddddbadccbddbccdbdcaaadcaabbaaaacabcabdabdcacbcbaddcdcabdcadbadabcdbbdacbcabccadcbcddcbbbdddbbdabdbbccadadaaaaabaacaaddaaaddccadbdbcbbaaccdbbbbacabdbbaaabbbccacbacbcadbcacbbdcdaaacadaacbdcaadddbccbadcdcbcabbdbcbabbabdabadcbccddbaadcadccdddababbadbacccdcbbddabadcbdddbabddaddcadccdabaacaaacbaabbccacdbccbcbcdacddbaacbbbcdcaaacaacadbcabacaaacdaaddbdddaabbdbcccbadacbcbbdcbdcdcdbbccdccadadbadaacdbdcbaaabddabbcdbdbbcbacabaabcabdccacdbadbabdbbadbbdbaaaabdbdcbbcbddbcddccaccadbbabdcbcacacccacbccdcabbacdddaddbcaddcccbbdcacbcdcababaabbdcdddcbdcbddcccbaddbdddaabcadbdaacacbccbdabbcbdadcaaacbababbababdcdaaddacdcdbdbbbdccddcdabddbacbadddcdbbbaacaadcbddaacdbdbabcdbcddcdccacdcbabccadbaddbcdcdabbbcbdaddcdbbaadbdaacdcbacccbcdbadadaccadcdddadcbbacadadadcbcdabbbadcdbdbbbabaccdcbabbdcdbadcadbbcbbadbbabdbdcccbddbbbdcaccdbadcbaaacabdbabdadcbaacccbbccddbaaccbbcccdbdddcaaaadacabbcbdcbcacdddbaaaadaacabcddaddddcbaacdbbaadbabcadbbdacbaacadacacdccbaddbaacbbacbcccdcbbadcbbabdbcabccccacbabcbaadbbcbcbbacdcdaaccccaddcaccbdabbcadbabbdbaaaadaaabcadbdcccabbdabacaabdcdadaccaaccaaccdbcaaaadddcdacccbcddaacbcdabbbaddbcdbdadccdbaaddccacbabdaadcacaaccdbccbdbadcacdbbaabcbcbbcadaaccccbabbcccdaadbbdacbabcdddbbddcddbdbbabaababcadbacbddcadacdddadcaacdbbbabcccbadcdaadaacaaadccadbcbcdcbbccadaaabaaccbdbcbacdadbcbddacbdaadcbcababdcaccccadcbbccddbabcabacdbbbcbabdadacacbccabaddbcdbaaadaccdcccaddcadbcbbbdbdbdddcabcdbbacaaadbbcdcbdaccabbbdbcccbddcabdbdbbbadbbabcdcbcaacbaaaddabdcddadbabcdcaddabbccbdddbabdbbbbdddbcdcbccdbbdbdabcbddabcdbcbadabbadabaacbbcdddadccdccdadcadcadbddaadacadbcdbcdbcacbbbcdbaabaccbddcddccdccbbbabddddaabbabdccabadcdcbcdbdcdddbacddacdbdacacdcbdbbdcabcbbddcddadbbabdcabddbcdbabbddababcadcdbdccdaacccacdcadabddbacbdaadcaabadbaaccbaccbbbaddcddabdaccbcbcabdbbdbaddababdbaadaabcdccabdbaadacacbdcadcdcdbdadbcaaaabcccbbdbadddabccabbccdcdcadadbbdccbdaabbdadaaaddddcdcbcbbddbcbbccccccbcdbcbabdbbdaaadabdccdcddcdaacadccdacacacdcdbdbbcddbaaacadcbdbbcbdadabcbcdddbbaaadacbbdabcbddacbdbabccdbabbddbdcabdabdbacbadadaaccaaddbddddcbcabdbcdbddbacbaccdddbabdbabbadcbbadddaaaddccbccdbaacdccacadadcbcdbbacabcbcbddabadddcddddaabbcdccababdaabaadbadbdbdbddbcacabcddbcbccbbdcbacabcacadcabbddbacbadbcaaadcbbacbcdcbbbbcbabaabbabbdccbbadcbbbbbdccdbdcdacbdbcccbcaacbcdaaabbddbdbcaccabccacaacacbbbacbaaabccdcbaabdadccdadaaadacbcdacaccccbadbbbaacdbbabbdbbcdbdddbccdaccadbdcaabcbabddbcbbabccbdaadbbcdcdadbbabcaccaddacdccbdccddbdaaacbbabbcdddacbcbbbdaabbadabdbaadddcddabbaddacbaadadccddbcdaddacaaabadacbcccddbcdbddcadcdbcbbdbacdaaccbcacbcdacaaaaabcddabcaacbdadbcccacdbddccacbcacbbaaaddcdbddbdcdcbcbabacacbadbdbbbdbcbcdcbadbacbdabbccddcbdbcccbddccacdaabcdbdbdccdcaadbcdaaacddbcbaabccbdbcabdcbddabaadddcbcdddabadadcbccadabbdbcaababbbbacbcbabdababbcabababdcddcbbcddadbbddcdbaaadcbccdbbbbcbcdacdbcbbdbacdbdbaabbbdbccdaadabbdcdbbbbcdbbabcccdccbdddacbbcbdabcddacbacdccddcdaaccddbdcddadaddacdbcadcbdbbbddadddbabcadbaaabbdabbbdbbbccdcabacabbacccbaabccccababbcacbadaacdccabddddcddbbaacabbcbdbbacaadacdcbacdadadcdbbbabbdcacaadcaddbdaacccaadbaccbabaacbbabdcadbcbaacabccacdaadccaddccaaadcccccdcbaadcaacbadddcbcbabcabcbdabdcdccacdcbdcddcbabadcaadcdddbdaddbbdadcbcdddaacaacacbdbbdabaabbdbadccadabddbbccbabbcbcbcbdcbcbaabbdccbdccbaddcbbbccdcacdcabcdadcaabadcbcbbcddadbdddcaaccbdabcbcadcbcccbabaaabbcabaadbdcaabcbbadbabbdabddbcddcdbacddbdaaaaadbacdcadccdccdcdacacadacdaababcdabdddccbbcdbabdaabccbddbdbbbcbccaabdacdaddacbcdccdbdadddaaabbcdacaabacbacdadadcbadbabbdacbbddbcdbddcdcdabdacdadadcdacaabbdcdcbabacabaabacaaadbdddadcbaabcadadccccdbadabaaaadbdaadddbcadcddcdbacbcdbccaaadbddbdadbbadcadacdcbdabdbdacbbdddabcddcacbcadbcacaaabcdaddabdcdbbcdccdcbababaacbbcadcbdcabccababddccdbcaabbcccdbddbdbabcddadbcadbacbcccabdbacbcbdcbccabdbccbadbabbbdaacbddbacbbdadbcabcacacccccdcadbbccccddcbacdaccbacaababdaabbcbbaddacdcaacddcbacabacadcccccaadaadbdacaaaaddcdacbbdcddcadcbdaaabbcabdcaaabbdadaaacabdcbcdbcaccdccdbabdbbadababdacbccabbbacbdcaacbdbabcccbbddaddabddcdbacabdbacbcbcdadacaaacacdcbbcdacdaccbdadddbccbdbcdadabaaabadccddcdcaccdaddddcddbbdadbcaacbbdacdacaabdcbdcbadcbdbdadaccbcccaddbcccddddabadcdbabbbadaccaaddbdaaddabadddcbcaabdabbacdacbcddccdbbcabdacbabdbdabdacadcacbdbbccdbababcdcdadccabcdbbdddadcdcdacaabcccbbbcbbddaacababcabaacacdcdbabcaabcbabacbdcdbbcdaaacacdddaccbbdcddcdababaccdadccabdcaddcbabaabbbadacddabaacbdaaadcaabacdcccbadaaadacbcaacbbcdbdbdbdddbadcbdbddbbcababddbacddddbcaddbcabdaccdccabccbcdadccdbbcaababcddcacbcaccdbcdcddbbabdbadaaabcbbbcdbaaadbddcbdddbbcbdddbcccdadbabcabacdadbcddadcbcccdbcdbcbccddadabababcdbaadcaccdcabdaadaabadbccbabdcdbdbbdcdbadcadabbaadabcaabdaaaadcabbbcacdbaddbbadcbbdadcacbabdbcccdddcbbddccacaccbdcddbdacacdbcccaccdcdabdaadddccacbcdbaaacbdaddababcaaddaddddcbdcbcdcdacaddbdbdbbdbdddcabdddbbacacccbbcadaddaaacadcdbdccbabdcbbcdccbddddababadddabbbdacadadacdbdabcbcacbbdacdbabadacabcdadcadbaadcbcbadabbcacaaddaaabdcbaaccaabbbadddcbdcbbcdaccdccdddbcbbcbddcccddabacbdbbdcabcaacaadaabaacdbadbbdbcaaadccaddcaccdccdacdcabddcababadaacbbddcacdacadacbdbdddcbccdababccaadbcddacbaddaacdccbdbcbbccbbdabdaadbaabbddaadaadcabbbcacadddbdcccbaacacbdccabdadabcdbcacbdcbccbdaabcabccbadbbaabdabdaaddaaacccccabbbcccccaddaacdbbaddddccacdadcadadbaaccaaccbcaaaabcabbcbdaaabdbaadcbbaaaadcdababaaadcbbdcccbbbbbdddbcadbbacddbaccacadcdacdacccddcbdcabbdddaabdbaacccabdacacccbcadadcadaadbdcbcccababcdbacbadbcbdccdadbbbaadbddccdadbbbacadcaadaabcccdcacacddddadaccbdaaccbdaaacbdabbabadbbdbbaabccbddddaacdbcbdabdabadcdcdadacdcddacdbcbcacbccaddcdcaaabcaaccbcddddddbacacdcaadabbaaaabaaddbbadbddadadbcdcacdddaccabcadccdbacbcdababbbacacccddccbcbadddbadbadabacaccdcbbbcdabbbbaacbbdbbcaadccabddbdcbcdacddcdcddcaabccdadbaddadaaacbdbcddbcdddacccaccadbabadcdaddadcabcabbbacdddddacacbddbcbcddbcacccbadacccbbdcdcddcbbcbcccbbcbbdaaabcbaaddcbddacaaabaddbbdbabccbdcbcdbbcdacdabcabbbdbbacadabdbccdacabbcbcbbddbaacdcacaccbcdaaabaddbabacadbcdcaababbcbbdadcbbacbbbcdbadcbcaaababddbbcddccddadbbbaccbbdbdbdbdcabbbcbbcaccdadbbcadbbbbbbdbdadccdbaadcdccdcdbadabacaccbabddacbcdaccbdbccbadccaacbdaccabadccbabddbabaddccacaccaaddaddaacadadcacbaacbddcaddddbbbdabddcbdaaccabdbcddbccccccbaacbbaababddcaccadbbbadbbccbbaddcaddcddabdabcdcdadaddbddbbddadddbadaabccacdcbcccacadbbbbaddcabaacacbacccbabdcdcdcccdddabbdadacccccadddbcabbddaabbadbbadcbbdcddbcccdabbacdadbadbbdcdadcbbbdaccbdbdcdbdcaabaddbaccadbdcccccddcbcacbabcacaaaccdbacdbabbdddacbdddadbdbdbcbbaaadacbababdabcbadccdbbbbadbbaccddbbdacbbccabacddadbdcaadaccacddbccadabacccbabbabadbcdddbcbbadbcdbddaabbdcabbcabbadbdbbdbaacbdacddacdccbdbcabcbbdcdcabaaabcaacdbaccbbdcadcbbbabadadcdbdcddbdbadccaddcdcbcccacbccdabdaaabdadbdddddccbbabccddbbaacddddbcacbacccccccbdabcaacbcbabbcacdbdbbbbbdcbdbcccbdccadabdddccdddbcaaacbdbdacdaadccdddaddcdbcccaadcababbbacbacddacbcdddccdbcbdbaddcbacdcccbaabbababdaabaadaacbbacbddcbaabacdccdcaaabcddcbbccddcbaabcccdbcaabbadaacbbbdcbadaccdadabaddbabdcaacaabddcdaadabcbbacbcacabaabcccbbadabcdbddccbdddbaaadcccbbcdbaacbaddbaaadaabcabaccbbaabccccddbabadaddadbddacbacccadbbcdcbbcdcccabcdacdbaabdaadababbcddcbddbcacdbacabcdaadcbcbbaabbbdaacbdbbbcaacbbbabddbadcbbbbdddbbcdcddbdcacadcbbbbbbbacdabccdcccabcddbbacdcdddbcbbcadbadcbdbbcaaacbaaaabbdbbbcaadbcaccabcadacbacdbcdcabbbadcabcdbadaabbacddddbdaabcdbddcdcaadadbcaacabadacaacbcddaddaadbabbcbdcaadbadcbadbcaabcaccbcccaadaccadcbbbcddacbdbbadadbcdcadabbbcbddbbabaddbabbaabadcabcbadddbaccbcbddbccdbaabbcccbcdccbbddbddabcbbcbbdabaccbadcdadcdbbcabbcabbdcbabadabbbcdacadcbdddcbcddadccccaccabacccccdacaaaccdaadbcabccccaacdccadbbadcaccdbbcbadbadadbaacbdcbbbdadcabdbdbdcbbbddacdbbbdccaaadcdaaaadbabdbcdbaacaadbbccbcccbadcbbdddabbabadccccabcdcddbcbabdcacdcbabdbdddacaccdbbbdcaaacbabdddcbacdbbcdcacccadbbbadbaaaadbbacddcbadccdababdbdacddcbdcbbabaccccdacbbbdcbbbdbbcdcabdbbbbbbbbcacddbcdcabcdbbadccbdcbcacaaddcdcccadaabcbbdaccddcdcaccbcddbabcacbcccaabadaccbbcdadcbccdcbaaadabadaabdadddacdacaababbcdddadcccdbacccdabcbbddacdcacdbbbdcddabccaddbbbcbabbbbccbbbdaaabcaabbbcaabccdaacbccaadbdcdddbdbccbadcbbddbbaacddcddaddaabbcaabdbacaddadcbbacddaacabccbdbcacabdcbdabbddbddbdccbdcabaacdcadacacaaccdbbbadddaabcddddbccbcccdaccbaadcdabbaddddabdbadaacdbddaddbcccccbccadcbcabddcdddccadbbccabdbabcbbdaccbadcbcdcdbabbaaaccabbcbdacbaabbadacdddbbcbdbaacacbcadccdacaadaddacaddbbadcddcadcacdbcbcbacbbacdbbaaacbdaddbccadbababcdcdaaaabdddaadbadbddcbbccacabaaaacbcdcccaaabcbdaccccdccbadcbbddababbadabcdbdcdbdbdbdbcdcdcbdacadddbddabddbdabdcaadbcdcbddccdbabccacaccabbcaaabadcbddcdbacabaadbddacbbaadddcabcadbcdbdddcdaddddabdddbddcbccacbcddadbaabddddabaaabcddcaacdbbabccbbabbbadcbbcdabbcdccabddabbbacbacbcadcbcdccdbadccababadabacacdaacddadcbdaadadbbbdabccdabdbbdcbccaabbacbacbccaddbddbbbcbddbaabbdabbabbdabbccabcbadbdabcdbddabacbdbbdbbacbddbcdddcbcbbbbbddddcddbabbbaddcdcdadadddcadbbbcbbcbabadbcaaccccacbbadaabdddcaaaacbdbcccdcaabcdbcabadddcbcbcbaabcadbaabbdaaaadbdadacdddacdadacabdddcdccddbccdbdbddcbdabaabcaaabdcdcdcbacbdadacacbdcbdaadaababdcadaaddadabbabbabddddccbdddcddddcdacabcbcdbbbdcbcdccddacccdacbcdabaadbdccbcdabaaccdbccdabacbaccacabdacdacbdbddcbdcdaccbbbdacddbbdaabbbdbabbcbcbabcbddbdbdacccccacdccbddbdbdcadcbaacdbddabaddccbabcdaacbdbbcaacbcbbaaadcdbaadabbdcccdcbcacddaddabaaadabcbcdddaabaadbabcadadccdcbdcabababdcdccadaadbccaadabcddcbddbadacaccadbabadcccccaacbdadacccacabcccdbbbbaabdbbdaacaccbdaaccacddbccbdcbbadbcbaccdaabcababaacddadaabcdbdcbbbdaabccbdabbbdadcccdbdbbdabacccdabcbbbbbdcccadabbabcccddcddbdbcababaaabacddccbbdcdcbdcacdccddccddccdbacbababbbdaccadbacbccdadadbbbbbbcdbcbabbdccdcacccacbacaacbbcddbcbddbcbdcdbbabddcacbcadccbccdbbcbbddabdbaabbbcdccdcbbcbbabbacaabdccbaaddcbccacbaabcdaadbdadbadcaaadbcdcccbccbdaacdbaaadbdbbdaaccabacadbaacacdbbacbcdaabdadabdbbadacbbbdaccaabcdacddacbaccabbbcbabddccdcdddacdbacbdbccddcbcccaaccbacdbcbcbccbcdcbccbdacbadcccbbcddcabdcccaccddbdacbaacbbadaacbaaacbcaadccdcacdbdbccccaacbbaadcdbacbdabaabadcabcabbadbcbdddcdbbcbbdbadacddcbacbdddbbcadbdacbdcacbaccccacbbdcacbcbcacaabcdcdaabbcdaadcbdcbaaccddaabcdcccacbccdcabbdbacadbbdddcbababccaddbbbccaabdccccdcccaabccabaadddbcdbabcadbbccdbddcacaaabdbabcbabbdcaccacdacabdbaadcadcabcaacdcccdbdbcddbbccddcccdabacaadbbbdbdbbaaadacbcdbaabbdaaacbcbccaadcabdbcbccacaaacdcabdaadddbaaddadadbcbddcaacaacabcdabdccbbdacccdbdaddabadccbdbacbcadbccddadabbbdcdcabaabbcdcbadcdabbadacdcccdbaadabcdddddcaccbdaaabbcbdbccdcacdbdabbcbdbccadccdcdcacdadacacdbbcdcaaaccbdacbdacabdddaccbcbdddabaabcccccadabadadbdadccdcaabacbcaadccdbdbdbcbbabdcdbadabadaabcbbddbdcadcddcbaadbaacbaadcdbbdccdbcdcbdbbbabbbbcbbcadbdadcadaadaddbdcaaccaacddabaddbcddaacdaddbdcadbdbdddacdabbbbdcbdbabccbdababcaddabcbbbdddcabcabadaadbdbdabbbdabdcadabdaaaabaccbcbacdbdabdbcabbcbbcddcacbcbcdddaaabbcacbadaccbcdacdadacdbccbbacabdabdddbbabcbbdbdadbdbaabdccaabbbdaccddaaacdbdcadbaccadacbcbdccdccaadabcbcabddacccdbacaaaadbbcabbcaadaabbcabbdcaacdcdcbcacbbbbddbabcbcbdbbcbaddcacdadadbdbbaacdddadcbddbbccbdabcbbbbcabaccadbaadacbcaadcaaadbbdbdabadcddcbbdcbabbbbbbadbbdcabababcbdcbbcabcbbbbcccbbcacacbdbdaabddbaacccddadcdbbbcadddaaacaacbbaccdccaaabbcbcdbaacadbcdbbcddbcdbadbcbccbabacdbbacadbbbbdcbabddccdacacacdabaaadabbddcbdbadcabcdaaccacbaaacbcbbcdcdabdccbbbadacbdcdcbbadbabdaacddcdbabaaaccaddcccacaabccdbddadbcabbaadcabdbdcddbbbcddddbacaabcbccdadababbbccabbbbcacbabcdbccbadabcccbddddcaccabcbacbabcdcabcbbbaabbcdbdbabacdbdcdcacccbdccabccabcddcadccabbcdbabadbbdccbadbaadbcbddbcdddcbacbdadbcbcdbbabadaddabbcddbadcddaddbaabbcbbcbdabcbcbabbcbabababcdccbcabdbcbbcccddcadcdadbbbdcdcadabbaddabdaccadddccaababbaacbbddbadaccbbdccbbcadcbabbcaaddcbcdbdccaddbcdcddadcaabdaacdddcbaadadacabddcdcaccbdbcbacdabbabcdbbdccbbadcdaccccddddbcdbcdabaaaccbcdbbdbdadcaadcbadbcabcaabacdbdddaddabbdbaccbcddbaacadbcbaccdacbddadbbcbdacdcacacbbbabcbdbddcaaddaacbbbabdcbbcaaddbbccdbabdbcbacadaccdbcabbadabadbbbbbadabacabddbacbaadcbadbdbbaabbddbcbadcadbacbdcdcdaaddcdcbbaacccbcbabbdaddbcadabaaadccdccbdcbbaacbdbbadadddbddccddbbcddddbaadbdadadcdaaabbdacdddcdbacbbcbcdbccabbbdbadabcaaccdabaccbccdaadccddbadacdcdbbdabbbdaabbdbbabbdacaacbbbcddcccddbdccbcdcdbcdccdcaadccbdadaddcbcbdcadbaacddadbacddddcbdabaddbadbbbbdabcdbadcbddabdbddbddaacccbcdbdbddbbcbbbbaabacacbaabdcdbbdcdbddbdcabdcabdcdcddbabcccbcabccdadbdddbdadaabddadcbcbadbdcbddbddcacbbcbbbaddbdabdacabbbbbbcabcacaacdabcacbbddccdbcbadaabcabaabbdbdabadadcdcbddaadcbbaccbcbcbbdbaaabdabbaccaccbdbadcbccbccbbddcccacdcabdddadddabcbddbbadabdaaaccadbddcdcdaddcaaddaccaaababaaaabcbdbcadabbabbadcdaababcbaccabddccaadcbcabbdcabddbbccabbbbdaaccbdbaadccdadcdacabbabadddcbbddadaacdacccddabcbaadcaabdbdaccbaaaaddbcaabcbcdacbbddabacabccbcdabdacdcdcdbcddcbbaaaaddcdcdbdacadccabcbbdcaabcacddccaabcbcbacdacacccbcccbbabbcccccdcbcdcdadcddacdbbddaacadbcbcddaacddcdcaabbcacbbaddaaaddbbbdbbcccccbabcdbbabcaadabcabbcbbddccbcddcdbaaacdbcbcacdddadcadddbbbadbcbcbaddaadcbccbadcdddbddaaacdaaacaccbadbdbcdcaabddccdbdadacddcadbbcaaabbadccbbbaaadbaadcacbaacaadcacdddaadcdbacdcabdbbbdbbaacdaabcabaadbcabcadcbbbbdaaabccdaabdadccadabacdacdbcaaddaaacdbbcbaaaaccdcbacbcbddbabbbdcacababccddadaddddaadaabcdbacdccaabcdababdbccbccabaabacbdabbddbddccbcbddbcaaddaabacabbaaccdacbbacddcbcbcbdaddcacdcbdcaaaaddcbdacabbdcdbadcdccbcadabbcbadcaccdacbbddbdcbaabdcdcddaccaadbdaaccacbcbaccacdddaaadbbcbccdcaaadbacdbaacdabbadaaaddacdbdbacacdcddadbabccdcdabcbdaacdcdbdcbbcbadaacacbadaabaaabcdadacdbcbaddccadddcbbdcaddacddcbdbbbddabcdcdcbdacaaacbaddcbbadcdcadccdabbadcbbddbbabdaabaddbcbcaaddbddcccbcccdbacadddccbddacdddcdadbbcbbddbcddbcbbabdacadaaddabaadccdddccbacbbacbcabcdbabcdbcabbbadaaabcbddcbcbdcaacdcbaadbbcbcdbacbbbdcdcbcbaaaddaddccdcbbbcbddbcdddccdcbdabaacdaddaaaccadcbaccddacbdbddbbdacbabcddbaddbadadadcaacbdbaaccddbdcdcdddaacdccdcdaacabbaacadcbaaccadaabddbabbbcbbbdcadbaacaccdbccaaadccdbcddccaccddbccdaacdabdbadacbdaaddaddcaccabcbaddacabdabbdddcdccaddadcacadacbcbdbddaaadacdaadccacdcdddcdbdddcddcaabacaadadabcaadadbbadcadacdbcddabccccbcaaaccacacdcacdaaabacdcabcdcccacccbdaccbacdcbcccaadaddddcccbadbccaaddcbcbbcddcddbcbbcdddaccaacadabadbdcbacaaaaccabdbdbacdbccddbcaabcbcdddccbddddddcaaaabddbabbdbaacbbdacbababaddcaabbabdbbbcdbccbbaaacbbcaddbdccddbcdccccdccacbbccadcdddacbaabcdbbddbddaaaadadcdcdabdcaabbdcadabbcdcbadbacdcbbabcbccdbdbccadaabacaabddbbcdacdbcbabdccccbacadcdbcadcaabacccacddcdcddcbbddabbaccdbaadccbbcbdccabddadbdadccccaacbcbdacbbabdadbbdcacbdcccccbcdbdbcbbcdddbdcacabacadbdcbdbdcddaaadbdbbdadddcbdcadaabbababacdacddacacabdbadccacaaabadaababadadadbdcdccacabdcaccbcbcccabcbcddbbaabacbddbbcacddddadbabcacaadabdbdcbabddbcdabdacccbbddbaddcccddacdaaaacaddbdadbbccdddaacccbddacdababbccbcaaaddabdadbccdcbccdbbddcadccabbccadcdccaababbcbabbccbcccbaaaadccbaabbbbdbdbcddcaadacbbcaacdacacbbbadabbddddaadccdadacdccaacababbdccaabdcbbdbdbcaabdcbacabbbdbbbdadcaacacdcdaacccbcbccbddddcdcacbcbcabacdacdbdaccaabbbcabbbcbdbdaacbabadacaaadbcdbbbcaaaabaabbbcbaaabddcdccaabccbbadcbbdcdababccdbcaaaacbbbccdaadbdccbdcacddbcbdbdbcddddcabdbcbcacdbcdbddcaaddddacadbdbcbddaaacccabdcacbabccdcdadbcdccacababaccabaacdaacccbbacabdcbabcaaacbdbbcdcddccdbbdaabbbdacabdbcbdbabadcdabccaabcbaaadacaacdcdcbbdbbcaadacddcbdbbbbbbaaddbdcbaadcbbbcbabdadbaaddbbbbabaacbaacccdcbbdcadcdcdbacbdcbaacbaaabbabadcccccacdcbcbaddcbddacaaacacbcbacbbbcaadcabdbbdadacadcaabcccccbaacbccabdbadcbabdbcddbcbcacacaccbdddadabbbdbdbdbdaddadbbccbaabbadcacaabdadcbdadbabccbbbbaddbddbccddccaaaddaabdcaadcbacbcaadaaccbdcacdbdcacbbcabdcbcddaddddbcbbcbddadaacdbbacabaddddcadcdadcccdbbabcdccbcdabdddbacabcbcaaccabdcddaccabccabcadcddabadaabbcccccadbcadccccadcdddbccdbbaacabbddaaaadbdabccbdcdacadddbbcddaaddacdbccbdcdccabcabdbababbbcddbacdcbdddcadcbcdcabbaacadcbdbaaadddcdacdacaadcabddbcaacadbabbbcdbcdacbcdacaaddcdddaabbbcacacbbdccacdcabacdcbacdcdbadbcabddcccabcdcddabbcaddadccccadbdcbdacddaababbaabaaaadabdbbbadbaacdbacccccdaddbbaadadbbddcdbbbcadbabcdacacbdaddbdadcccddbcaadcacbacaddbcabaadabcdacbddbcbaaadbbccdabacabbbcbddcdbbaaaaacbadadbaaacdcddddccbddaccdcacbababaccbcabcdabcccbcbcbccaacdacacbdadbbaacddddcbdbbcbadddabbcbdcdddbdcdcbbcdabbabcdaaaacbacbddaadaacbdcacbcddabbadabcabaaaabaccbbaabaaacdcdcaccbdabccbdacacacadcccbdaadabbbddacaabccdcbcccacdddccddcdcbdbdbadccabddddbabbbdddcbbbcccaaacbcbcbabbbcccbbbabccbcdcacbdddbdbdddddbaaacccadbcdbcaaddcddddaabdbddadcddddacaacabcaccacabacadbabcbcacbaccdacadabdcbbaabcccaacaadccaadbdddddbcbacaaadcdcbcbabbbbccabbdccbdcbabcddcbaabcdcacdabdabbbaacbbbcacaabababbbcbbacdcdcadcdccbabcdbaabcdcdbccbddbcabbcabccbcaaacdddcacdcbadadadbaccacdddbdbbadbbdabbbcccdbbadbbdaddcbcaaadcbaddbcbabaaadcccdcbabbdccdadbddcdcbacdbcabadccbccbdddabaaadacbcdaadccabbbbbbdadbcadaacdccaadddacdbcaabbcdddaccddcbddbbaaccddadcbbbdddbaaabcdcaaadacbdddbcaabaaddddcabaccdbbcbccbdadbadccbbabbbdadabbdabaaaddcdbccbababaccabccdccbabcdcaabaabbacbaacdacbcabcaccbcbbdbcddddccdabbdcbbbbabbcccccccbaabbddacbabcaabcbbdadddaabacadddabcdddbbadbdabadbbbbbbacddbddcbcacdcacddbdbcadbcdccbbdcbdcbadccbdbdcaddaacaabcdcbcaddabbaddbdacacdbcbdcccddccdcccacbbdcabdbacadcadacbadddcbbcabbcdbdaacaddcaddabdadccdabcbcbbcbdddabbdbdbbcaddbbcadabbadaabbbabccbbcddbddabbcaacabacbccccadbcdcbbbcbbdcdddabdcaaabadbadcddbbcbacadcdaccdaabdaccbdddcaddabcacbadccdcdbcbccbdcbddcaaddcdbbcbcbbbddaacdacdacbdabccccddabcbbdabdcaccbdbcbdccdcaddcbdcadbbcdbadcbaddbadabcaddddbbbddcddbdbdacbbccdaabaaabdaaaadbacbacdcadadadbcdddbbdbbaabccbbabbabaadbdbbaadcdddddbdbadbadbbcacbdcacbaacdddddddacdcbcdccbccddbbabbbbccbbbcbcbcbabbdccaabccbcabcccdccbbcdabdbabcabdddbbbbcdcbbadbcbbbadaacccccabcddbddbbcadbcdcbdababbdcbbdabcbdcbaccacbaaacabdddadddccdadcabdadcccabdacbabbcbacbbdccaaacabbddbbbbdadbbdabbcddbbaccbcccccbbcbbddbacddbdcaabdbbcadbdddbcccadcdacccddacddadaccdbdbccdddaaacacdaabddaaccccbddcccabcddcbcadbddabcabadabaddbcbccaabdbcccccccaadccdbbbbddddbacbbbcdacbabbbacbabbdddaacdaaacbcdbbaacaaababacadabaddbbbcbcbdaacbdbdaadcdcbdbccaaadadbaddbbdadaabcbbdcdadbaacdcacccbdbdabcdacacddddccbdbdddcabcacdcdbcacbacbcccbdaacbaacccabaabdbaadacbdcbbbdbddaacbabcdddbdcbbdbbacdabbbcadbddbbabdaadabbcbbdbaddddbcdcaccbbacbaaccbbadaabaadbbbdcdbccbdbbbbacdadcbdaddbbccccadbaddbaacbacaaaabcabaabbadaaacbdabbbaacbbcdbaddcaabdcddcdaddbbcbdcbcadacacdcbcccabbbbddbacddabaadabbcbccdaadbbccabcabcdbaadbaaadacdcbdabddabacaaacccabcdacaccbbaaadabdcadcbbbbdcbabccccdabbdbcdbbdabcbdcdaaaadcbcdadddbbccaacacacdbdbcbdbabbbbbabacbddbbbdccdadacdbacdcaabbddcdbddddbdddddccdbdbaacdaabbdccbdbacdcaadbaadbdcdbbacbaacbaccdadacbdcabbadbbaaabddccabbbdababdbbbbdcdcabaacdcbcbbabdbacadabcbbbdcacccbbddcbdcbacbdcbaabaadbacbbccccaababdcadbbcbcbcdcaaabcdabddddacdbccddabcabbaabaaaddbdbbdbaddcacdcbadaadbdbcdcddccdaacbdddabadcbdbbdacdccbbddaaadbacddccacbbacbacbdbbaaabacacddaaadbccbdbdbbcccddbcdcbbdbcbccadbbacbdccbdadbaaaccabdccacadabacccbacbcadbcbaccbdbabddacaddadaaaccadaddcaadadaadbddbdddadddbcabbaadbdddcadadcdccabbcdcaaddccbaacbaaccbdcabbdbadcdbdbbcbccadbbbcaddbdcbbbdbacbcabbcbbbadadaaaabacbbabacdacbaccccccbacccdddaabdbbbccababbbcbadabdacaaaccbbbacbaadbbcdbddbcbdaaccbcbbcdcacddabacbddcbabbaccbcddaabacbbcaaaccadacbcbcbdacbccddaabbcbdacadbacbcddcdbadcdbaaddccdbaacdcbaababcaaaaadabadabadbbdcccdaabbbbabcadaaababbcddaddaacacaccbbdbdabdacccbacadbbdbcaabacdbdcadcabccddbabddbbddddbdacbcaacaacbbcdbadcbcdccdcaadccccccdabdccdabbcccddaadcdbdbabddddbabadccddadddabcaaacccddddccbbcaadcdbddcdacbdbbbdddbdabcaacbcccbbabbdbabbbaddababdbadbdcdbdbcadcaadbdcdcbcbbccaadadcacdcabbdacaadadbabbdcaacbcbabdccbaddaaadbcaddbbbcdcacabaddbcbcdabdddcdaacdbdabbcbdaabcdcddacdddbcadbbbcbbcbddacccbbddacabdcbdcbbbddacbacddccaaabcccadddcdabaadcdaccbcaabbdccbdabbdcaadbcddbcddcdacddbcccbaddcbddabcbabddacbbcaabcbacaaacbacacaadaaddaabddbbcdabbbcdbccbcccacbbabababbccccadcbcaabcbbadcbbbbddaabdcaccabbdbcabacabdbcabbcaabcaadadddcbdadcdcdcbabccbbbdacdaccbbbcdbdbbccbadccddbaabbaaadcadddcadaccddccdbccdabccddcbdadabdbdcdbadbcbbabdccbccabdadccddaaadcbccdaacdbdcaacbcbdacdcccacbaddadbadacdbcbbacccddccbcbcacbbaccabaacabbaabcdcacbacbcddbdbcacbdddbccbcdbddbbdccbdbabbdbcaaadddcdbcabdcbcdadbbcbbadacabadbbccdabbadabdadbbbcaddbbcaddcdacbabcccdcbaaacdaacdbabcbbadcdaaacccddacadbcbcaccbcbbbddacbacbdadddbaabcbbbbadddbbcaadcbdbaaabaacdbcbcaaabddbdbccdacdabbabdacbdaccbcaabdbbcaddcccadaabddbbbbccdbbaabbcaddbbaccbcdbbbadbbcbdacdcdcbddccababbcbacabcbdbadcbcbabbcacddacabbcbcbcbdbcbcccbcacaabdccbdcbaddbadbdadcdacaccaccddaddcbcbcbdaddccdacbadddcdccccccdaadbddbacdcadbbacaaddcadbacbdbcbcdcbacdbcbaccbadaabaccacabccabbbdcbbbdaccdcbadbbdbacbbddcbaabcbaddddcbbcccdccabdadcbbdcbbabbcdbabdcbdcdcbccaabcddbabbabbcbddbbcdccbbbcdbadccccbdccdacdbccdbdabdbbcdcbdccaabcdddadaabacbaaaddccccabdadbbacddaacccdbddabcaaadabadbaadcbcbccdcdbccdcacbaacddccbadbaddddbcabaabdcacddcdaccdaabcaaaccbdddccdacdccdddbcbbaccbcdabdbaccadbcdabaddadcddcadcdbdcbaaadbdcbdcbccccddbdbcbdcdbbcbbabaacdcccdacdaccbadaabbcdbcccdbdabcbaccccbbdcbbdbbbddbddacbcdadccabacdbbbbcbcaacaaabacaddccdadbcddcbccbcccccaccaacbaadabddbdaccbbaaaaacdbbaccdcaccdcadcdbccaadbcdccdccdcbacaacbbbaaddaddddabaabcbbaccdbdbdabcdaadcbdbacdabbabbcddbcdadacbabbdcdbacdbcbdbcbaccdaccabcbcbdcbdadadcbddbdabccdcddaadcbddcadadcbacdcbbccbdddccabaacaddbdddaacbdacdacddccbdbddaadbcdadabaaabccccbdcadabdaabdabdbaaddcbcdbbcbabbdbaaccdbbcabcdadddabcbcabadcbbcacdcaabaacdcadadbdccbcccaddbdbaacaaaabdacdabcbcadcdcbddcbacbdcabaddccadcbaaddcbacadabcdcacaddbcccbbbddbbdbbadacbbabdccdcbcacacaabacacadbddbabbbccdcaababdddaadbbdcdbcaddcdbbaabbddcccaccdaabdcacadcccdbbabacddbbcbccbbcddddbdadcbbaadbccdadadbadddbdbbccbaabcacdbcdaabbabbbddabcccdcdcdddacddabbaddbdadddbcdbabcdcbdcbbdddbbdcbdbacaacaaabccdcccacaadadbdccbbacdaabaaabacdcaccddadbcdaddbbbcdaaccaccdcdcaabaadddaabdcbcbcdccdddbbaccaccabdadbdbdbdbcaabaccdacbdccacadacbcbaddadaacbdabaaccbcdcddddbabdbdaabdbddcadbbadbbddbbaccdbcdaccccbbdadddbdbdbaacddabdbccddddcbcbcccadaaaacbbacbddbcdbbdddbddcdaaadcddddadcbacacdacadbadabdcdadbbadbbdbcccaddbccbcdcdabdcbdcccadccbdddbbbabdaabacccadaddbcccdabdccbcbbdbdadcddbabdcddbdcaaadcadacdcabbbbdabdcbaddbbccbbcbaadcccbbddaacbccabacdcddadadbbdbdbcbacaaacaccccddcddacbdbdaabbbbdbcaacacdbbaaabbcdaabbdcbadcddcbdccabbacdcaabcabadcbdcdccacbbdccbdabadaddcacadabaccacdbbddbccbbadaacacaadcbaacdbbdcaaadbaacadaaaadcdbadcdbcadcbbdacccccdaaabddccbdccdaddadabcdbdcdaccdaabcbbbddabadaabdbbdbcbcadbbcadcdabbcbdccbbaddddacdbbddcbabacaadacadcdcbddaaacdbaaaccdacdadccbcdbbbdddaabdbbdddddbbdcaaadaacbcddddcddccacdbbaacbabccdacdadbcdcccdcaadcbabbabcaaabababdbbaddaaaccadcbcacbcbcabdbbadcaabcabcccdbadadbdcbabacddbbabbaaadcbcbdcbaaaaabdbadccbabcbbbadcbaacccbddbaabdabbabbbabcdcadbcbdcccdddbacadabbdacaddcdbddbadadcbaabadddbadbbacaccabacdabcccacaaabcabdbbbacbcdbbdbdadbddbddadacadadcbddbddddacbacadcccbaaacbbadccaadaacdbcadccbaabdcbbadacbcbdbdaddcdcddcdcabbcbccbdccdadcdddadcdabbdccbabdacadcbddddcacdacadbaccbaddadbacbadbdccccccdbdbaacdccccbbddcdaaaccdacdbdaadbdcadcacbdcdcddabdaaacdacdadccbcabcabaddcbccaacadbcddbadaccaaaaccbdadbbbdaabddcabcaccacdaccabbdababcbbdbbcccadadacacdddcacddcbdadadbdccbdbbdabdacdbcadbddcbbbcdcbcdabbbddcabbccdbaaaaaddaababbdcaddccabbddcbdabdadacbabdbaabddcdaccddaacdbacabdcabbabcbdadaaabcdadabcadacbbcdcbcaddaccaadcbdabbcdcaaadbbdcdbcdcbbdacdbccbdabbdcaabdccbabacaababaaaccabadcbbcacadaccbbcccbdddadcccdadcdbaccccacbbcbdddcdaacdcaacacddacccacdcddccddadadcbdbabcadadccbaabcddccbddcbadacbabcaaabcdadcdabdbccbcdbcddcaadcdddbddbadccacbdddbbacdbccbdcddbbbadcabbadddccacaabacaaaabcbcbacadabcadabbdccadaddcdccaaddbdacadccbaaccccbbabcabddcdcbbdcbbbcacacdadaaacabddcccaabbdddaacdaaababbcbccaacdaccadadccdadaacbddcaacabccdcdcabdcbacdbbacacacdccdaddabdabbdccabbacaaacbccacadcdcdaddacdcbbdbababbbbbbddcbcdbcbbcddcabcbdbacccdcbddcabcdadcccbdbaddacdbbdbbbdbdcbdbaabbadddcdacbaacbbdadaacccbcabcbccadbccdaadbbcabdcabdbadbcbcaccdbadbbaddddbdbcabccbdbadcddbccabababaabaacbbaddaacadcdddccbcbcbcadaadbbdabdcabbcbaacdaccabcbbbdadcabbbabbdbbbbcddccbcabcdacbcabbdcabcdbdddaaabbbccbdaabaaddbbddcdccdadbddcddbcbbbdacacbacadbdcdccbddbabdddaacbbbbcbdbaccabddadacdadbbbabbbaccbbbbabadddaacbdbddbbaabbbaacbbdabcbbbbcaddcdbbcbadddbdbbaddbabbdcadbcaaabbdbdbaaacdbcdbaabbcbcddddabdaccdccdaabbccbcbbabdaaacdcaddbabbccdadbcdcbcbcdcddcacacddaaaadadbdaaaadcddbdcbcababbcacabdccbddaadbbaccdaabadccbadcbccdacbcbaaababcacddccdcbaadcbcddbaabbbdabbbdadacbdaccdcabbbabdbcbadbcbbcbddaacabbcaccabcdcacdbadadadadcdbcaacbbbbbbabadcbdcdbadbbaadccabcbadcadabddaccacbbabdbbaadcabcaabacddcbbababddddcabcbacacbadcbbacaabdcbababbbdbdbddbdadaaddabcacbbbdaaacccbbdcccdcacbdcdbbdbcbddccabcacbcdddcbdcccddddabccbccbbccbacccddcabcbcabbdacccdcaabaccccacbbbcbbbbabccddabcacdaacaabcccdbadccbbddbbbcaacbdacbadddddbbbdcddaccddaaaddacacbcdbdcaccbaaacdbcddabbcccddcbdccbaddbcbcdaccadcacddcaddaadacddcdbacaddacbbbadcdcbadcddbdadddcbbbcabbadbbbacabdabbaabcabdadcccddbadbddacbccddbdacadbbdbcdacdddbacccbccbaccabcbaccaadccdacdbaccdcdacdcbcbdaacaaabcabdccacdddacbbbbbaddadbdabdccaaadddddbaaccdadabbbbbcadcdbbdddcbacdbbcdbcdabbcabbbddbcbabcbadcabadacabddaacdbcadcdbbddbccadccabbabdaadacbdbbcbccadcdadccadbdadbbdaadcbddadbacbbacadccdcddaabacbcdccdccbcbaacdacaddddabdabaaddbdacdccacdaccdcaabbaadcabdaacdbbdcaddcdadbcbcbbcdbbdaabddbdacdcbddabdcccbbbccaadabacacbabcdabbacddaabaaaacdcacadcaabbabcccacddcddcdbdabbcdaddbaccacaadcadabadbdbcdbcacacbacaccabbcaacdabbcabcddcccaacbcbbbcccccabbccbabdcdcccddbabdbbdcdcddcbdbdabbcddccdccaadabcadabaccababddaababcbabcdbcdacadcbabbaabdaddabdcddbcacdbacdabbadadbcabdddacdabcbcddcabdaccccaacbdbcdbbadacccaadacbbcbdcbdbbdcccdbbcaddcbacbabcdacdaccbccabdcadcbbbcdacbddbdadbbbbcddcdacdddadbcbacdbbdbbcadcddacaabccdbcdbdbbbbddccbcabddccbdddcccddcdadbddadbdcdbdccddadccabbdcdcabbcababdabdccacdbabddaaaabdbabbabcbcacadcdbabaabacaaadbbbccddbaabadbabbdbbcaddbcaddddabcabdabbccacccaadbacbdcbcdaadddaadbdbcdabbdcccddcbacddbbadcdbbcbbbccdcccdaabddcbcacdccbccbabbcbdccbcabdadbbabddcbbbacdadadabadbccaacdbcdaadacbcaccbdbbbaaadbcdabdbbacbacbacbababbcacadcbadacbacaadacaaadabbabacbcbdbacbcdcdbdcabdcbccacccbdcadbbaabddcaadaacdccbacacacdadabbbbdcacabcdadabcccccccbcbabaadbabbcaddaadaccdbcbbdaccaddbccacaacdbbcadcaddccadcbddadaaddabcadcbcbabbcdbddabdbdccdbbcbdddbabaccddabdbcccbddcbdcaaddabcadbdaacacdbbcabbccacddcabbcadddabdaabbbbdccdddbacacdadabcdbaadbbcdaaabadddddccccbbaccbcccdbdbaacccdaacdcbbdddabdbdacccbaccdbcbadbcbabdbdbdbcbbadccdabaacbcddcbdcbccccdabcdacccbbcdbdadabddcccddbbadcacdaddddcaadcaaccdccacaaccdbccdddcbacbddcccadbcabddcbdccddccbdcbcccbbccaacacdbadabcdccccbcdcabaacbbadccaccdbbcbbdabccbcbdacccdcabaabadabcadaaaddbccadcabddadbdbadaaccacddbbcccccaaadbabaabbddaabacdddabbadbabdccadacbdacabdacacddcbcdacdadbbcbcbaadaddccccbabdacdaacabadcaadcdcdbbabdbbbbaadaadccbccbdababddcddccdaadcdbdbadbbbbdcbdadcacdabdadddddbabacdaabaddbbbaccaaababdddacaddabdcbdcadbadbccdddacacbcbcdccadbdbcaccccbadddbddbdbbabccbddaabccacbcadbcaddaabdbaddcdbdcaccdcabbdbbbcbbbcbcaddbcacacdcdaabdccccbbcbccdddbcacddaadaccbbdacdbbaddcdcbcbbbbdcadbcbadcdcccdbbadbaddbbbaccbbbdaaaacdabbabbaddbdaaddccbabaadcbcdbbdccabccabcbaccacdbccacaddddbdddcccdcabcaddbcbbddabbdadaacbdddcbbdcaaccbbbdacabbbacadbacadaddcbbcbbaccdabccdacacddbddcbbbaabdbbbcdcccbdccaccbacdccaaccdbacbbaddddbaaaabaddabcdcdabcdadacbbccddbdbddaabddbcdbabbdbcbbbccddadcbcdabcababcacbddadbcddacadbababdcbcddcdacddacabdadabcdbbddadabbdbadaabbdddbddadcddcabcbcbaadacdaadccaddbadaadadaaaaaabbbdbabbbcbdccadcbdcbadcdabbcdcdcdbbcddddcccddabdaaaddbadcbcbbaccdaadcadccbcababaabbcbabbadcbaabdcdcdddbccbcdacbaccaabcdaadaacddbaaacabcaadadcacacddbddacbcabaabdddcabddadcaabadadbdcdcaddaddacbaaaacdbdbdcbcbbddddbcddcdccdbacdaabccbdabcdcdabcccacdbdbaacccabbbcbadccdcacabbcddbadcacadccaacdacddbcdcabccaaccaccaacdcbcdcdddbbbcaddacaccbcbdbbcbddcbdddddaaabadcdabaadbacadcbcaabbaaadbacaacababccabbddcaccabbaabbbababbbdacadadcbdadbdbbccbbccadbbdbbbbbacaadcddabdcddbcdbdaaabcabacaadccadbbdbbcbcbabbaccdabcaaccaddbcbcccabdddbcdcabbbaccacbccbccdbdacbbddaccbddbcaccaacdbbaadbabbadccbdbacdbddadaadbdccbbaaabaccdbbddadcdcdbdcbbbabdaacdcdcaddddcadddbdccdddacdacadcdbacaaddcddcdcaccabccabdcddadbbddbacaabcdabddbbdbdacdaddbbdaddabcddcddbadbcddcbcdbcabaabbacdcaaacacaccdcdbabdabbabbcbadbddcbdddcdabbbbacdbaddabadababcbaaccaadcacccabbddabaacabdadaaaddccbbddccbadbddbbbcdbbbddbdcbaddbdabbbaaaabcdabdbadbabcdddcdcdabccaaacbaccbacddcacbdadcaabcdaccbbcadaadacbccccadacdcbddccccbdccdbdcdbbccdaccacdbaacacacadcbcbdbaacdadddccbbaadadbbdadaccacbcbdbddcacbaacaadadadbbaddbcccbdbbdccaccbdccdddcbcbdcbbcddcbcdbddbdadaaaadccacbbdcdaaacdcddbccdacbabbbaababcccacdcacdaaadbaaaccbadbbbdccbaccdabbccbbadadbcdacbccbbcbaacdaacbccbaabbcbbabdccddbddcacdddcdadbacbacadcdbbaabbcbaadbdacacaaccdccacbdbcadabcabcbabbddaadccacdddabddabaaadbdcaddbbccbcbabcdaabcccabccbbdbbaadcbadbcddacddbdbddbcacccdababbbdaccabbcabbacabababaccacabaabbccadccddcaaaaacacaabcbacdbadddcdbbbcbcccbbdcacddaadaacaaaccbacaabcbdbcbbddadaddbdccacccbdcabdaddcbbddababbabcddaddddaaabdcbdcbcbcdcdccdacdabbbcdbcbddbccbadccaddbabcdcbddaccbdbbcacbdabdcbaaacbadbabadadcdabaaacdadcdbcabdbddddaadadacaccbbbdacbbdbdacdadcacddadadabadbbcdaacddbdbcabdbdbacddddadaababacdcbdbdaaabcccacdacdbadadadbdaacbacbdbaddcbadccaadaacccacdbadcddbbcbbcaacccaababbaaadbbbaabbdcabdaccbdacddadaaaaccbdccbdbdbabaaadbabdbacccdcbacbabbcaccddcbdbaddbadcccbacdbbbbbdbabdacbaccccdbbdbbaabacdaadbbadcadddbdabddbabaadbadddbcdcdccabdbddddabdcbaabcdcaaadcbccccdbadcdddcbbbaacbbbdbaaabbaacbdbadcabcdbdcdaaaaaaacadadcbdcabbacabdcbcabcaacdbcdbdaadccbbdddbaddcbabdccdaaadbbdadbcddcdabacbaaddadbbadaccbcdbddbbbabbdcdbcbccaddcbdabadcbdcbdbdcdbddaaacdcabdbcaacdbacabccbccacdbacbaadbbaccbbadccbbcbdaaaaccdddcaccaabadbcddcdacdccadccbbabccbcbbcabdbccdaacdabcacdaadacaabbddbaacdabccdbbabaccabddaccacabadddacdddbbbaaaddcaaccbbcdddaaccadddadcaacabbcbbddbabdbccdccaabbcddbdccadcbbadccbcadcbacabccabbddabaabccbabcaadbbbadaadacbdaaddcbcbdddcdacdcddbdbcadabbaaadddcbcdbbabcbddbcbbaaaacbcdcbacdbccabcbcbdbacadcdbadaccacaaadcdddaccccacbabbccdcdbcdbadbdcaccddbacddbcadbddcaccdcccaddbbabcaccaddabdcacacdccaccabacbddaccbcdccaadcadbdaddacccdaabbcbdadbcacdbabdcacaccabcdbcbcdacdabbddbcccaaccacdbddccbbaaccbbdcdcbbbbbbbacddadbcbaddbbcdbdacdcacbacddccaccddbbbababdacbdbbaccddaccbbcbaabbdbddcdaddacccdbbadbcbabddbcaadddbbbadbbccabdabbadabbababdadbabcdbdabddbacabcbbbcaaddbaaadddbddbccccdaddaacbccacdcaddcddbbdaaccadddcbdcddccdabdcbaadccccbaddcdacaaadcbcdcdbcbdccbcbcacacdaddbcaadbcdbcbdcacabcaabbaccddbccdacdabdcddbababdcbcbaabbadbddcbacdbdadacbdadcdadadbbaaaccaaaabbdbcccabddabdccacacbcdaddcccccdacddbddaadaaaccdadabbdcbcddcadcaadadcddbcadbabcdcadcbdbbbdaaacaadcddcaacbcdaacbaddbcbdbcbaaabbcdbbcccdaabdcdadbddccabdbbabccacaddcacabaacddbbaacadcdabdbabbddbdacdccacadddcbdccadcbccbdddabbcdbbbbdbcadaacabcacacbbacbbcbddcbbdaabccddaacaaddcbbccbbcaddaabbbcadcabbcccddaaabdcaccdddcbccadbbaacdadcbcbbdcbabacdcaabdbdcdbbdbadaacddaaaaccdbbabccbcbcdcdbaabdaacabacdaababbdbbaacababbadbadccaadcaacabdccbdccaaadbcbabbaccbbdabbaabcbcccbccacababadbddccbcabdbccadcbddadaddbcccbcdccbcbbcdcddcbbbccacdcadabaadccbacbddbbcadcbbabdcacbbdbccddcabdaabdccbabaccddaccccbbbbcacabbdddaddccaacdbccdacbcbcbcbaddcbbdbdcbcdbaaccccddcdaadadacbcabbbcdaadadddaddbbbaddcccdacbadbbdcccabcbbbcbdbcccbaacdddbbbaccacaaabbddaaaccdbbcbadbadabacccbbcabadbdbacbbacddacccdcbccbbbaabbbddcccdcaccbbccacbaaddbdbbcaadaabaacdadcbdbcdbdabaaaaaacddcaabcbadcadabbbadbabaaaddabbbcddccdbdbdcdddddacbabcaaccbacaacccccacddbacaabdacbcdbdaabaaaabadbcdcdbdacddbbdcaadcbbbcabbdaadbdcaadddbbdabdbccbdbabcbaccbaddcdbbbaadabaabdccdbadbacaccacddddabaccaddbbaabbbcbababdcdacaccbbbabccabbaccdaacddddadcdacbbbadddcbdaabdbacccddbbdccbbddcccdddcbbbacacdcddddbcbabbcacacaacbaccdccbcbabcadabcacbacadcadbabadcdcaacccbcbbbbaccbbaabbaaccdbdadaaddabadabddbacabbdcbbbccabdcbaccaaaadddbdcacadddccacabbbacdcbdcabdcdcdabcbdacbbdaddbdacdcbccabcbddcdbbdbdbcbaccbbccdacdbbdddbbabdbaaadabbcdadcbcdbdddcbbcdcdbdccddcaaacdaccddaccbdcccaacbccdadcbdbdcbbccadbcaccbaabcdcdaabacdcababadddadccaacaabdbbdbccbddaaadddbadacbbcababaccccdabddbdbbbbacbcabddcabbbbcdbdddbaabadbdcbdcaddbdbadabbdddadadaacacdaabddaacbbabaacacdabcddadbbaaaccbaabbdcdacbabcabbbcadbcbaddcdcdbdddddcccadbdcbccdcdacaabadcbdbdaddbcdddcdcdacaababcbaddcaaaccbdaaadaccddadcabcccdaaaacbcaacdaadcaddbadbaaacadadcbbcbdbcadacdddccadddddabcacdabccaabaadbbbbbacdccbbabbccdaadccabdbaabacdddcbaacdadacabaccacacbbdadddaddacbcddaabbcdacaababcaddabacaddcdbbbbacbcacccbbcbbbbccadabdbdbaabcaabaccbaaccccacdacaadadcbcdadbbcdaabadabbdabcbcabaabccaadbadcbcdbabdbacbccacabdcbcbaabddcdccabddbbdaacdcaacaaabcdabacdddccdbdcaacbdbabacabbcabdabccaddcaacabcdbabcccddaaddccbaacbaabbbddcbadadcdcabacbcaabadbcbadcbbdbcbcacdabcaaaadabdaabcccadabddcdbdcdcadbbdbbccbbaaddadcdcdddcdaaddddccaaacbccddbaabadadddbdcbbadbacdabcbbcdacaddccbcbbcddadadcbdadddcddcddcccadadaccaaabdadacadadccbabcccbaacddacdcdadcacbddaabacdcdccaccdacaddcdbdbcbdbccdbbddccbbbbaaadacadbbabcbadcdbddbacaaddbcaddbaccbabdbddaabdddbbdbaadabbbadaadbabbcdcccbcbabcddbacaabcdcaaccdcaddbbadcababadbbacdbbbdbacabadacccaccdbdbdacacbbadacccdadcacbaadadbbaacaaccdcabbadbbbdbdcaacaaccbccdacaaacacbddcdbcbccacccaadbaacdcabccbbdcacbbbcdbcbbabcacadcdaddabbadcbccbddccbcddaaddcacbbadcdababbdaabcdaccadbccacdbdddcbacabbcddccdbbacbcdbbbdadaaccdbdaabbacabdbcbadaddccaddbbdcabadadddadacdbacabdcbddacbaccddbcdbbbbdcbabbabacdcccacdcccdbdcccddddadbcabdbcddddddcbcbbdbaacadccddadbdbccdaddccddbddbcdbcaaacacbcbbcadcabbcdaccdaabbbcccadcaaaabdabdcbcdbaabdbbbadbbbacddaadcbbcbcdabaaaaadddccddcaabdbbdabdbabdcdbbaacacadddcbdbbabdbbbaaddcaccccdbbaccddcbcbabbddaaadbadcaccccacbcbccabccaabaabcbabbdaccbacccbacbbdcdbcaaaadcaccccacadadaabcbabababbacddaabbdadcaddadccaacbcccdbbadcdaaaadbadbadacbaddbccdbcbccbbccbccdcddccdbdbacbdabccacaadcadacdddcbcdacbbcaabcdadcbddbaabbbbababccdbbcdbcbdbdbbcadbcbbccadadbddcccbabcabdaaadcabcbbabcdbcddababdcdcdbbccddcbabccdcbdcccddcdbccbacdaaaddcaddbcaaacabbadcdbbaaacabccddcadcdccacadcacccabbdbdadbccacabccbaddacbccccaaddcbaaaacbcaddaddbbcabaabaccdcbbcadcaabacabcadbcbacacaadddbddbdabdbbbadbcadcccdadadbcbabbdccaaabcbadbaacdcbdcdbabddbcaddcadbacbaacdabccacdaccdcacdccaddabcbdcddababbbdccadbabcbbcbdccdbccaaccccacbabddbadbcccbcaabbacaacbcadadbcdaddbabacbcadbcaaddcddcdddaadcdbacddabccaacdbccabcaacaccdaaadadddcddbcbdbbdbaaccdacdcdacddcbdacccdadabdadbcaaaaddddcabcbcaacbcccbbbdddadccbbdbaadcdadabcddcdcdcaabadabddacabbacddcbdcccaabadbcbdccbbbdbcaababdacaacdaaccdbbbcdcdaadaadccadccadbaadbbabbbcdadaacbddbdadaabccadcdcdbbdbccabaddddbddadddcbaccdbaadbbcabcaaaadcddcbbdbacaddcbcbccdcaacbdaccdbadbcddcdcbbbbbccbbdabcbcdcdcadcaaddbccbbacdaccbcbdccacddadababaadbddddacbadabadaacaccbaaababbbcacbbccdcdcdaccaadbbcabcdcbdbaccaabaadaadbbccddaccabbdcddbdbcaddaccdbacbbbbdddabccaacdaabaccaddacbcbcaccccbbadadcbaacdaababcdabaabaacdcbccabccaadbdbabadacbbccdacbbabdcccdcddaaacdccdcabbabcbccaaddbbabdbadcdbbadbccaabadabcaccacbbddcbcccbabddaababcbccdaaacdbbddbddabdabddbbadbdabbdcccdacdcaccbdaccbccaccbdcbbbacdacccaaddbcdccddbdcdcccaacbaabadacadadddbadccaaabbaabdcdabcaddcabcddabdcadabbabcdacdcdcbacdcadcbcaddddadadadcdcbdbdcdcbbbbabadbccaccbbadbbcbaaddaabacbadbdcaabdbcbbdcabcacabaccaaccccadbbddbbbbacabcbaabcacbbabdabbbbdcbbdcdaaccbddcacccaaddccdcbdcabbdbdbaddcbddbcddcdaadababcbccdcdcddcabaccccbcaabaabbacadaccabadacccbbdcaaadaaabadadbdddbcababadaadaaababadbdddddabbbccabcddcabccdbcdbcaddcdddcdcdcddbdbaddddaabbbcdcdcbacccdddaabacdadcbbaccabbadadbaaacbbdbdddaddacaccdaaadcbdadcaabcdacbdcdcbcabbddcccacdcdadadbccbbcbbccdccbccbabdabcbadaddcbaddaccadbcddcdacabdbacadbddccaacaacccbbddbacbdbcabbdabbbddcddddbbdabbbbccbcdacdddcdcdbcaaaadbdcbdcaaadcbdccbbbbddadbdadbcbdabaaacbaaadadabddbddbadacadbacdcacdbadaabbcadbabccdaabcabacddbcddadacbbbbcbaadcdaadbddcabccbabddbadaabbcdacccabdcccdbbcbddaadaddbaabdadadadbdbdaabaddcbbdcaaddbbcddcbbdcabdcdbabdabbbbacdbbadabbbcaaaaacdbdbdbddaabcabbdadcdbcabcdabacaddadccbccdbdbdacdbcbbbadcbbdcdabacaaaadaabcddcdbcbabccccddcdaaadabadbabbbacbbcccbdccccaddcabaacbcaaaaacacadddccddcbcabdbaccadcdabcddbcbbcababdadccaaaadcbbaaabbadddddadadaacbccccbbcccabaaccabccabcbaaccdaacccdcdabbdabbadcbcdcbcdccbbabcccadcadbbdcbbbcabdcddbabdcbcbdacaaaccbcbbccbaaccbdabcdcdbbaabaaaddccadcaabbddddabdadabcbdccbadacbabaabcbadcdadbcdcdbbddcbbdaccbbcdaddccbacbdcbbaaabdcaabddbcbcdccaaddbdcbbbaabcdcccbdabcabbabbdbadccbbbdbbbacbaabdadcacdcdadccacbccbaabaddbbdcaabbdaadcacbcadbbaadcacaaddcbaabadadccadcdbcbcacacaddbaaccccbcadddaaabacdcdcdbabbaadddbdacbabdcbacbdcdbaacccaddbabdabdcaaabddcdaadacadadddccdadbaaabcacacbbcdcaabcabdcabdbcdbbaadbacccbcaccdcbbdcadaabbaddbbcadbdbccabcabdbbdacbbcaddcbcdcadaddcacadbdccdacdadbadbcdbabbbdcdbdcaabcbbaccdabddabddacaaaddbabacabcddaddaabbadcbabcdadcdcbbcdbaccdcaacbdccbcaddabaddcbbbacbbcabcddddacaccadbbdbbbbcdbbbabcbbbdaacdcaacdbdbbabbcdddacabcabdccdbcbddadcdaaadbdcadbbbcabbbbabaadbcdbccddadddcddbcaaaacaadbbcaabccccddaccaccdacbaaaabbacbcbccbaacbcbddbcbdaaccdcdcaccadacbababdcbaccbacbddcaddabdcbdacdcbbaadddadcbdbaadccababaaddabcdbbcbbaacdbdabccabdccacabcbccbadcdcbaacaacdbadcaaabdbbcbdcbabdaadbcddacdcbdbcdadccdccaadacabdacacbddaacaabcaadbaadcbccdccbcaabcbbacbbcbdcbacadbaddcbaabdaaacdbcabbdbaacaadbcbdbcbacbdaacbcbaddbbddcccccdbcdabcddcbcabaaaabdbdcadbadaabcccbbaabcdddcbbcaacddadaabddbadadcbbadbcbdaddbacbdbdbadcdadaadcbdaaccbcdccbbbbbbaacdcdbbcacabcbbabbaddbaaacbccdbdaaacbabaddacabadbcbcbdbcadcaddabcccdddcdcaaaddcccbbbdabdddbdaabcdabbaabdadbcacccbccbbabdcddacbdcbdbccddcabcacaaababdbdbbbdacacddbccbbdbdabbacaccdbbcbbcdbbbcbbdbdbcbccbabbcdacdbdccdabaadbcbbdbbadaabdadcadcbcccadabbadbcadcabcdadddaccaaabacbacacbdcbcbbbbdbacdbdbadaabdbbadcbabcaaacdcdbacadbbdaaaaaccaabcbaddbabcdaddcbdbbdcadaccccbbbdbabdadddadbdadddabdadbdcdcdaddacadacdababddddaccbdadaddbacacbdcbdabadcbcabdadbaccbccbbdadbddcabdbbdaccdbdccaacaadacddaaddcadcbcacaaacdcccbdbdcbbbdbbbcdcaddacbbcbbabddbcbbcaacaccccdbacdddcbbadccddccdbabbbabbdbdaadddddacbccdddcdbbdbcccdcadcdabadabdcabbbbbadaccadbdadaacaaadddabcddddcdaabbbcbabadabbcbaabcdcbcbcbbbbcdaabbbbbcdbdccaccbcabbbcbadbbacaaddcacddbaacbdcababdaacddccdcbcccbddaddaabdbccbdcddcdbcaaddcabaaaabbcaacddddabaddcddacdbcbbbcbdbbcbdadbbdaddccaaacdbbadbbcacacbdabcbddadaadadbddddbdbbddbdbcbccdccdadabcdbbabadbaacdccbbaacacacbaddcaadddbbcdbdcaaadaddbccbcdbdddccdabbdabaacdadbaaddcbcaddadaaddabccaaccdaddcaccbbdadcbbabdccccbcbabbaadcdcabacbcabcdbadacdbcbabbcaccccdacacbcacbcadccacdbaacdbbacdddcdbcabdbaadbbcbcdcabadbbcbcbdaaccdadbcbdbbadbcacaaccdacbbacabbbdbaabccccccdcaaaddacabbcaddcdcbaabbdbadcccbdcdabcbaabacdbadacabddaadadbbbcccbcadaababbcadcbbbadabbcacbabbddbccdcccccdabddaacaaddabccbdaabdcbccdcaadaaabdbbdcaabbcbbadadbacdbabbdcddaddbcdcaabababbbaccbcacccdbccdccabbdacbbbbbbcaddcddbccccbbddbbbcccdccbdbcdccaadaabadbaccbbdbaabcdbbbccbaaccaaaabddbdaaabcaddcdbddbbdadadbbabbdbbdcdcddcaddbddbacdbcbcbccdcaaddbaacabdcdcbabbaaacacaacaacccaddcbcdccddcdaddcbbdabdaacdcadbdbaaaddccbdcbbdccabbacbcbbdaaaacbcddccbaaabdbdbcabcadcdaabbadbdcabcccbcbbbabcddacadbbdbdcbbdcdcaccbdbccddbddbcddcdbbdadcbccadddabcdbddaddadbcaabbbbdbccbcacaddbacbacdcaccbdadaccdcadacacddddbcdadddacbadaadccdcababcccbadacdacdbbccbaccbbbcadbadcbbaabacadcabdcacadadbdabbcbabdacacbdbcadcaabdacbcbcacdadacbcddadcbaddddcaabbddbaccbbbaabbadccbbdbbadbcddbdacacdcbbbdaacaaabdccacdcccdaaabccbaddaacaddbbbccbbbcbcdbaadbbdabddacaddadcaaddbabdabbcddcbcdbdacbbaabbacdcbcbbadbadababbdcdbbbaccbbbdbaabccabccbacacbabaaabbcaaccddccdbdbdaadaddaccbbbccaccddaabbdddadabbbcdbacbddbbadbacadabdaadcadbccccbacdaacbcdbbbbdaacbdcdddabacaabdbcabcddacdcdbbaaadabdbddcadcddbaabbdbaccbbcadadbbbddcdcaadbbcdbbcddbcbdaccbacaddcccaaacabcacdddddccbccdabadaaccabccadbcbcabbddcbaaddaccadbcabdcdbaccaacbacccaadbdadbcabbdbdcbbdddcdcccadadababbdabddabcbccdadaadbdcbcadbbdaaccdbdabccabcadbdccbbdadccdbccabbadcacdbbbdbdcaacacadddcccdddabcadbcbddddccbdcbaccbddbdcbaacdcbdbbbcadbcbcbcddbaacbcdcdbcabdbbccbbadbabbabbbbdacbbbcadccddabacdababacddcdbaaabbbddbbdadcadcdcbbccdbcbdcbdcbdbabbccccaddacacdaddacbbbaccbadbbbddbcccdcdacabddcbddddcdaddbaaadcbbbbabbbacdcbaacbcdadbcbbdcdbdaacaddbcacddccbaabcadbabcdabdbadcccdcccbcdccaacacbaaacddbabcdbcaacaaacaadabdbabdcdccbcbacbcbdbddaadcbabcbbdbbdbbbdbabdadbcdadddbbaacbcdbdccabddccaccaccbbcadddadbcababdccdadcaabddadcaaccadaddcbdcaddabadbabadadbbaddbbacabddbaccbbbdddadbbcbaaaabbcdcaadacbcaabadcabbabcacdcddbadbddccdcabbdbdcbaababbdccbbbddbacbcbbbbdbcdcaabbdcacddcaacbbcbacdcbcaabbbdaabdcabcdddababbccabbdacbcbaaddaacbbcacbadbadaaababaacdcabddabadbdcacbaadcccaddbbdbbcbdddabddadbcabbbdacddaadcdbcddadbacaaccdcbaaacdaddacaaddaabddacbaaacdbdbbccdcaddbcacddcadaabcaacccabbbacddbcddacdaddbbdacccabadbabcaacacdcdbaacabdcdcdbbddadaddcabbbdaccacdccbbcbcbaabdadbadbdcdbccdbdcdcdddbcdcddaddbbcbdbccbcdddbcabdcdcccbbddbbcbaaaababcbaaadcddbbdaccacbccacccdabbbaccaccbcbdccbdcdcadadcbcdcdcbacaabdbbdcaadacbbadbccddcdbadccdabaadbcddacdbdbcabaadcadaaadbabdaadcbddccdcdccccaaacbdddbcccdcccdccbdcaddadccadaadababddddbcdcbabbdddacbadbbaadabbcbccdbdabcaaddcddbbacbcabacaabbbcddbcbacbcbadbacabbcabcabbabcdcccbdbddcdbbcdddadabadacbaccacbcdacccabbbabbaadabcbcbdbcbddbacddcbaddcbdcddcabcdbddcabbabcabdbabcaacaaddccdadbbaabcdbaacddbbabbabdbdabcbbdbcbddaccabaccdcabbdbabbbcdcaadcbbabdadccbcbaabbcbbacddcddddbbaabadbacabccbdcbdabdadcbccccdbcabbdaacbddabbcdacbbcbabccbabacaabcaacaccddcddbcccacdcacbadaacbaddbdbcbdbdabacbacddbccaaccacccdccbdacacbabbbdcdbdbdbdbbdbdccbcbdadbdbbdccacaadacccaaaacabbcdbadaacacdccdbbaccccbacbdadbbaddddadacaaaddaabbcbcbdccdccabdbbbdacbcbbbabbcdabddcddcccbdabccdadddcabacacabbadcbababdbabbcacbbcbcabbddcbadacdccbabbbcbcabacbcbacdcdabcdbbcadaaadcdbcbbacabadddcdcdabaaaddbacaccdbbdddbdbbcabdabbbaacabdcbaddababacbabbacdcdddbbdabadadaaddccabbaaccadabdcaccbcbacbdbdcadbdbcdaabbabccacbbdcbaaddacabbbadcdccdcbbaabbabdadaddbaadaddacbbbadbacdabbdbdbddbcbcacbcbbdbdbdacbaddacbbaabcbdadabbcccdaacadadcacdaccacdcaadcbadabaaabcabccabcadadbcddbcdcbcdbdcacbccaccdadadadcabacaddcadbadabbccbacdcdaabadabbcbcdccdcabccbdabaacbbcdcdddcdaaabcbabaaadcabbdbdcaabcdaddcccbadaadcacadabacdacddadcbbdcaacdbcaabddabccdacbcabcbcaddbaaccddabdadaaccbabddaaddcbdaddbdbbaaaaccbabaacabdbbcdcdacdbbcbbabacbcdbdbaabdcabadcbacaaaababbcacbdbbabdacdabccdbadabaaacdadbabdddacbdbdcaaddcaadbcabbacbcbbddaaabcbabddadacadcbadbccacababaddbdacddcdabdbdaaadabdbdcabadbadbcadbdcddbdbddddbabaaaacbdadcccaaacaddcacbcbcbaadddcbbddcadddaddcbcdadccbcbabbccacdcdbcdcdcdbaddbcbbbbbddacddadaabbddcacbbdabbabccbaddcbbcabbcabaaccbaacacdaaddcababcadcbbbadcddcadbacddbccbbcddcabbdcbbcdacccdcccacacaddcddcccbdbbabcdaadcadcabadcdddaddabbcbacabcaadcacbbabdaaadbbabacbacddaacbdddcbdbdaaccddcdbdddbabbdcbcccaaaddadbcdaacabadcbdddbadbbbdcbddacbbdcddddacaddaaadadbacadddddaaabdbdbaccdcbdaddcbadaabadadaadacdabadbbaabbadacdabbddbbadabcdabcbdccaaabccadcccbdcdacabbabcdabcacabdadabdaddbdbccdacbaadabbdbaccddcbcbcbbbbdcabcbabacdcbbbdaacbaadbccddacdbbbcaccbcddccdaaddcbccdadbcadcccbbcccdbdcbcdabbbabcaccadddccbbbddcbcbdaacbbabcbbcddddbcbaacbbcadcabbcdaacadcacbdbdcaabababbaadbbaabcddcddcacddcccbaaccbdcccccabbdcbcccdccdababbbcdbbdbbabcccbddadbcbccbabddddacdbdbabacdacbacadaaddcabadcbabaadccbccbadbdccdccccdddcdddccaaddbdaccddaacbbcacdcbadcbdabbaaadbbbdabacbdaadcaabbcccdccdcacaddadddacacdbabababcdbbaccbadabcabddaccdabbbcababcdaddddacdcaaddccbabcddbabcdacbabbacbbaacacbdadcdbaabbbbadacadbabdbadcccabbaacbcdcdbdaccbacbacbddadcdbdacaadbdbdcdcdbdddccadbadcadbcdabcacbaadadcbbcdddaabddaadadbcacbdccdaadabbcacdbdabdaaddadadaddbbaddddbcdcadbacadacddccdbbdddcbbaababccddabddadaabdcbdccbbcadcadbcbdacacccabbdaadabdbccaadaadabbbcdbcbadcbcaaacadcbacccabdadcaadbcddacbdabddbdddddbcaaddcccbcbacaabdaccadbbcbaddccbacbccddbaaddaadcbbdbcdadadcaadccdbbaadcdddcdaadcdaacbddbadaacacacdbddabaccdcccdaaacdbcbbbbcbaddbdaddbadcdcbbbddcbbaabadacdbbdaccdccccdaddccabbabccdaacdcdddaccdbdadaacbacabcbdabbcbcbddaccabdddabcaadbcababacbbbdaaddadabcadddbabbdbcabccababbccbcdcddcababcaccccadbbbdddbdcbaadaddddcdbbcdbbaaadbadbbcdbabcbcbacbdbbdbbbdbccaccbdbaddccacddddccbcccbdcacbabaccadbcabccdbcbdcbcbcadbdcdcaadccdcbdbbbacacbaaabadddccabbbddbcdbccddcbcbbaabdabcbccdcccbabaaddbbddaccdbadcdacabddbbdcbaabddddbcdaadadaddbdbdaacbaadaaaadccdaccbacabcbdbcacbbcbaacdbddaacadabaabadaaddcdcaddccccccbbcbcbcbcadaccadcdcabdadcabcbaaaadbacdbdbccbdbbcbadadcaaccccabbbdbdadcbaccdabbcdadacccadccbcadaabdbbbbbccddccbbdaccbbaabadadbaacbbbabdaaddabdcacbdcbcbdcaabadcabacababaadacdaaacaabcacbacabdcaaacbaadaddbaabdabbcbdabadbacbabbbdbbddadccadbcaabcaddcbbdcadacadbdbbdcdddddacccacbbcacbddccbcdddcdcacbdabcbdcaadbcddaaabbbacaabcddcbccaaabcbccddcdbbaddccabcbcbddabddcabcacacdbcccbacbaccaacabbcbcbcaaaaabdcaaaabddabbbabcbdabbcabdbdacdaaddcdcabccbdbcccbcddcbddabddccbbdccdaadbcacadcbcabcadcabddbccbbacdaaacccaabbacdadacacdcabaccadcaadccacacbabaddabadccabddcacdadabbadcdbdbadaacaddcbbbaaaccdccabcdbdaacdbdbcadccdddbaaabbabaacadadaacacdccadaaaacbabadaaaacdabccbdcabbddcbabbccdbbacaaacccdbdbdadcaabbcbbdcbabbccbcbdababccabdddcdaacbcbcccdccdcbccaaaaccbdacdacdcaddddcadaadbbbddbcbccdbdcbcdcacacdcacdbbbbddabddbddcbaddcacabacbcccbacaccabbdbaadcddabaadddbbcbacddbddaadbcbbbdcbaddcbdcddddabadacdccacdccbdddaaadcbbbddcdbacccdabbdcdddabbdcbaadbcbcabcdbdccbdddccbcabacbdacdcdccbbabcdcbdaccbcbdcabdbcbcbdcacdacddcabcbadcacbcbaaadabbdaccbaddaccdcbacbadbcadcdcadcdcccbaaaadbbddbdcbabbaccabccddabcbadcababdaabbddaacadbcadbbcbabbcaabdabacbbcababacccabbcbbbaaaadbbbbdcacccaddacdbaacadbbcbacddadbabbacaabccbdacdbabcaccabaababaacdaadcccbbcbdbccadadbaddacabddbaddccbdbadddcadabcccbdcdaaabccaababdbdaaabadcacbdabacdccbbcdbaaacaaccbddcdbdbdbcacadaacbdbcccabcdccbabdcccbadacbccdbaadcddcadbdbbaadcdaaccddbbdcbbdcbbcbcabcabdcbccbddabccdccccddacccdbbbacabbdccbabacadccbdadbabbdbcdaacaacbaddadccdbcccdccaccbcbddcddadccdacaacabcdbcccbbcbabdaccaccdddcddabacbacbaabccadbbbdaabddcddacdaaacbbcbddccbdadacbbbccabbdbdddbaaddacbdcaaabcddaaaaaacbacabccbadbabdcaabcdcbcaacbdccccdaaaacdcbabdaddbaacdbddcabddccabdaabdcbcbbbdddbcacbdbbbcaadbbacccadccdccbddabcbcdaaabdabbcaadbbadddacdccbdbabcbadaaadaadaadcacddcdcdacdbbcadbdcaddccbdcbadcaaadcddbadcacbcdddadcddadcbcbacbcbbbacbcbcccbcacabcccccbabbcdcaadaadacdbdcdabdbbadddbbddaaaaddcbacacbccabdaadaddbadbbacddbadadbddcaabcdccbadccadcaabcdccabcddabadaddaaadbacacbdbaddabadadaadbaaccbdabccbcababccacbbcdbacabddccacadccddaabbdaccddadcacbabbdcbaadbcdadcacbadddbcccbdacadbdaadccbacacabbdababacacbadbaadaabcddadccddccbaacdbccddcaddaaabcadccdbbcbdddbbcaabbacdcddbcccddccddcdbddccababacaaccbdabbbcdaaaabcddddacadaacadadadcdaaccbdadaddbcbddbacbaababbdddcbdcbcacbbacdaaadbbaddcbacbacabbacadadccccccacabbdbbabcdbcccbcddacacbabacdabcadbccbdddbcdbdbabaaadacddccbddaccdcddabcbdbccdcabbbdadabbbabbbcbcbccacdcbabbbabbdcbbcbacddcbbdcacdadcbbcdbabadbdbcdadabdaacaabbadadaaacaaaddccadbdddadbcdcdbbabbdbdacddaabcaabcccbacbdbadadbcabddadadabaccdbbcdddcaaddbcbdccdcdcbaaddaaabaccccbbaaaddbccdccccaabcdaabcbdaabccdcaddaccbcabdbdaadacbdbdbadcaaccddbcacbacaabaacaccbcdacdabddbbaaadbaccbdbbcdbbdbbddadcacbbdacacbadaaacccacddccdadcddcdaddcccbdabcaccbacbaacbcbbdccacbcdccaddaabbabcbcadadadccaacabadccadddbacbddbcbacbdbaadaadacccabdcbdadaacbaacccabdcacbdcddddacacaaacaabdbacbacbdbbbdbdbcaadadccbbadaccabdccaabacabcdccaabdabbbcaabcbbabaddcbaacccababdbbcccbdcaabccdbdbcddbccddcbaadbcddcdcaaadcbaddaacdcdbaabccbadabdcbcddcbbbacddcacddacbbcbcadaacbcaddcdbdaddaabacdddcacaddcddbdddcdcdcacabddccddcbdbbaabddbdaadaccdbbdbbdbdbabbbacccdbcbcbbdbccdbbcccddbdbbadbbdbbacadccbdaddbbdccddaaacababdadbbcdcacbcaccaadbcdbdbccabdaabbdbbbccabccdabcccccccaabaaccbbaabcbccdddcdbbdabcbddbaddcabdcdbaddaddddbabacbbdbaacaddadbabbbcabdbcccdddcbaacbcdbbccabcbcccabcbbbdadddbaababbbabbaccbadbacabbcdaaabcccabbcdaddcdbbbcbabcdbcabdddcbcbdaccbadaacabaddbccadbdcdbcbbabaabaaaacccadbcdcbadbbbdddcbcddcbddcaddaadcddccbdcddccbadaacaacbaacdbaddacdadbabddababdbcadabcaddbadadbdccccbbccdcbcddbaadccbcabbbdcbcbdcabdabcdcbbbdbabbdbadadccdcbdcbcdaccddcadbbdcbaabdbacdddcccacabaccaddbcdcccacabcacacdadcbadbddbcadbcccdadcdbcacccdbbacacdabcbddbaaddbcbbaccbadcacdadcbbdcdabbccdbcdbcddaadbdcccbddabacccbdddaadadacbbcccdaadcacabbcccbddcabadcaddbbcdbddccbbdbbddbcaadbdcbbabdbbcbcbddbccbadadccaacaadbbadbbaaadaaddabcbadacbbdbcacdbacbacaacdacccbcddddcabcacccabaddabacbdbccbdadabdbdcccdadbaadadacabdccacaaaddacccbdaabcabaaabadccddcccbcaddcaabcbbbdccbdbacaacadaaabbcacdcadcccbbbbdadbcaddaadabdaabcbdadacadcadcbacbcdddccbbcdacbaabdcbcaabdacbdbddabbdaddadbbdadabccdadccaaccdccccbcbadbcdcabbaaacdbadcadbbacdacbcaccdccacbabccadcdcdaddcaccabaddbcddbabcaadaadacddbbddcaaadaaaabaacbaaadaaabbadacddacdbbbdabbccbcacaadcbacbacdcacbdbbdccdabcbbcdaacbabddaacaadbaaacbcdcacdcaabadcdcaddcbdbdbbacccbaabbbbcbdabbbcdaadbbdbccbdcbcbbbaaaddbcccccbdaaaabcdddccdaabdcbdccdaccbabdbccccacacdaaddabbcdbcccbaabcbcdcbcbbcbaacdaabaabacdbcdbdbcabbcccdaabbddadbbddadcabdcccdaacadbbcddcdacacbcadbaabbcbadadabbdcdabbdacdacabacdbbbbdccaaaadcddadccbdcaabcabbbdcdaddcadddbcbbbcadccdbbbcbcdaadacaccdaacdaacadccdcbbabadabbdcbbcccaaddcdddddabbcdbdbadaaaadacadbabcdcaacdcdcaabcaadacdbadcaacccbdcbbddbbaabbbcadbcdacddaddbbbdbccbcccbacbbcddcbabccacdccdabdabcacacbdcbbccccaabdccbcbadaacdcdbccbcddabbbcbdcdbccaadcaccbdbbcaababbabdcdcacdbdaacbddbacdaccbcdddbbabcbaaddddddcdadccdbabdbbbddaccdcdabdcbdadacaccbbcdbdccbbbabdbabcddacbacadbdccacaaadcadcbcdddccdaabdaacddcccdcdbcdcbbaaaacbbbbdaaabdbcacccaaacaddbbdddbdcadbbbcdcdcaaacabbcbbaddbcababbcabbcddaddbbdccdcbdbcddadbcbdcdbaabaadcadabdabccdadabdbbbbbadcbcbbabccabbadabdbdbcbcbcdcbccbccddbbabbbacacbcdcbcbdccbbaabaaaddcbdddbbdccddaaaccbcbabccbbdbacbbcaaacdadcabccbbbddbbdaadcdcccabddcbbccabbdcddbdbcdbacaacdcabcbbadbddadcbadbadcdcdcbbccaaadcdadadbacbbdddbcdcacdbbcddbbdcdbcddadbcadadabdcddcbcbbbacccabacddacbbcbcbdddabaabbaabdacdbddcdadbdcbccdaadbbdbbadbbdaadbcccdbdcaaacdccbccadbcbdbadabbbbcccaabccabaddadcddcbdddaddbbbaabdabbbaddbdbccacabbdcdddabcbbdadacdaadbddcbbcdbaddcbaccddccabaaacaabaccccadaddbdbcdbaaccbabdddbcdbbababddbdabdddbbabddddcbdcbdaacdbcaaddabcaacdcdcbbbdcbcadbcdcacdbbdcaddbbddcabcbaacccdaaaddccbcbacbdcdcccccdaccdcddacdbaababcaddddddcdbcadabdaddcadcadabbadbdacaddbadacacaccadacccbacaaabdaadcdcadcacdcadcbacdabdbadabbaccabcbbbbcbbacacdaacacacabbcbdbccdcaabbcaacabdadbacbaabbccdbcddabcdcdcaacdbaabddddabdadccbcbccbdacdbcbdcccccadabbbdbadcbcadcabbdbcadbdcddcabadbdbadddddbaaddcdcccbdbdcbbbacbadabcdababcbadaaddbccdaaccacbcddaccccdaddcdadccdbaabccdccadbdaabdccaddcbbdcdddacdcdcdabbccadbbcadabdabaabdbadababbdabaddabddababadadadccabdcacccbdccadcbadcacdcaadcaccbbadbbaadcbdbadddbbaabddabdbcbcbaabacdbcbcdbaacacccdccdbacacdbacadcbdacacbbbbbbdbbddbcbbdacadabdcbdcbcabdccbcaababbdabbababcbbbbaaabacddaddbdcacabcbbbaaaddadddaabacbbbddcccdcdcdddccbbddcdcdcabbcccbbbdacaaccbccccdccddddddcaddddabbcdbbcaaddcbddcbcaabdcbdbcaccbcdbddaacacadbcaccdcbbadcbaacbdaabddccccddbcacbbacaacabbbbcadaccacaaadbbddccbbbcdadaacacbdcacbcbddcdcbaacbdacacdbcdadbabbadaacadcbcbbdbbaadccaccbaababbdbcbaabddabbcbcdaaadacbccbdddcbaaaadaaccbbdbacbabddadaaadcbddababdadbdcdcddaaddcaaaacaabbbabbcbdcadbcdcacddbddadbbccdbccacbbbacabbaabccacdcadcdccaabcbbdabbacddcdcbdbbbdbdbccbadbacaddaaddccacbbcaddddbbadacbbabdabaaddabacdddaddbbbadcabaaaaaabdbdbdbcddbabacbabbdabdbdddaddadccdcacaaddbddbddbcbaadbbcccaaccbbccdabadccdbaadacbadbdbacbdbbadbdbababcaadadadcacadcdcdadabdbdbcccbddccbcaabcbabcabddaddbccdaaaaacbdcddbddadccccbddcbcaccacbddcdabdacccaacccabbadbdbcccadcddbcbaadcdaaabcdabcbcdbcabdbbbbdbddddcbbcdcccadcacdadaccbdccadccaacddbcbcadcdccdbdcabbadadbabcbbdcdaacbadadaaaadcbdabdbbaaadadbdbbaccaadadbbcbaabbabadadcddbccddddbdaadbbbbabadbbabddaaabbaddacdadcbdadcdbbbbbddcbbdabcbbdcbbcdcacdaccdaaadacbacdbaadaccbcacddcabbccaadcdaaadbcabaabbdcaacabcbcddbcbbaaaaaacdcdcbddbcbabaddcccadaddadadccdddccdcddaadcbdcccddacacddacccdccdadbabccbcbdddbcdcabdddccbbcbcdbaddcbdbcbbcddddbbbbccbaaadbdcdabadcaadcbdccddaabaaddbcbbbadccadbcbccdbdabddccbaadbddbbdabacdddbcabcbdcbacadbcdcbbadabcbbdcbbbaadaccabbccababacabbacdcdadaaaabcbdabacbbcaabcbbadbcdbcbcbdabbcddbadaabaadcbabdbcaaacaddbdbcacadacddccdcddddbbcbcddaabcdaabaddaddbdabadbacbabbdbcacdddccbbdbdadbcbcccabaaabcabdcbaaaabbbbddcdbcbbbacbdcbaccacbbbcbbcccdbbdbccbcbbabbbcaaabccdacadbbdccadcdbccbcdbabbcbbabacabacbcaddcbaccdabdadbbdaabddabbababbbcdadcaadbbaaadbcaaabacdcadcacaacaddacddadbbcadbddbbddacaddbcbbcbcdccdaacadcddbbaababbbcbbcbbdcabcbabbadbcbbdddcabddbbacabcbabbdbcacdcbddcbbcadaaddbdddcccbcdcdcacbbdccbabcbcccabbcbdacbabddbadabacaaabbbcbdacacdbdddbbcdacccbcbaabadadabaddbcdbadccddadbaddcddabbccbddbbbcccdccabdabdaddbbbbdbcccdccddaddabddbbabadabdcacbaaadacdbccaddaccbcdabddddcdcdbdddcaccccddccaacbdababacbdcdddbdbadbdbdddcddbacdcbabbacbdcdbddaabdabcccbcdcdabbddcbddaabbabacabbddabdacacaaccdcdacccbaccbdbadbababbbbdbcbcbcccbcabaabbbacbcdacaacbbdcabbbadaabddccbddaadccababddccbcbcaabcccaadccddadccaddaccaaabacbdddaaddcdcccccaaccabbdabbccabbaaacbdadcbdbacabbcbdcccdcbcdacccaabddaabbabbcccaadcaddabcacacabbccadcaddbddbcbcadaaaccdccacddbcabcabdbdbadabaabddcaaddacdcaaddddddcbbdbdaaacacbbaccadcbaaccbcaddbabadddbdbabdbbbcaaccdccbcaaadaaabbadbbabdacddbbcccdccdbbdbdcccaacbbcacdadbccbaaadacaaabdddcbddbbddabdbdabacbcdcccaccbccabbbbbbbdaaacbccdbacacaaaaaccdddbccacbbaadddbababbbdccbbabbcdacdabdccdaabcbdcbddabacaaccddaadcccadcccaaddbccabbbbcbdabccdadabdaadacadbdbcdcacabaccbdbbacdacabddacadbbbdaaacbcbbbcaccdcbacbcdbbdabcdabdccbaddcaabcbcdbadcaadcccabdcbddcbcddddcadcbdcacabcaaacccbabccddbbbacdaaccaaacbbcaadbbaadbcbdbbbaaadaaaaabdbbcacadabbcdaaacbcdadcdccdcdcddaabbdbcdbcadadcacabdbcbddbdbcabbcbcdabddbdadddabccaccccdadabcccadaccdadccdcbacbbcbaccaadacccbcbbdcbdcdaabbccdbbbaaaadcddbcbaadaabcdbbaaacadacbcdbaaacbacadccbccdcacdcbdabaccacbcccccbaddcbbdcdabbcbaaadadddaccdadbcccbbdadcacbccaaaaaccaabddcbbaadbbcabacabdcadbadbcabcabacdbaccbadddddaacddabddbddadabdcaadddabacdccabccdbbddabdacaadaadbbcdcbabbcaadddcbcdbdbadcbbadaddddabdbcdbcdcdcabcbbdcbbdbcaaadddabdbbbccabbcbbcdcdbbcbcacbabcaadacadacabccdaabdacbbdaddabccbbacadaddddbbdbccabccbdccdaccdcccdcdcbccadcadbaddadbdcddacbbdddddbbcaccbbccbacdadbddbddbcdddcadcaadbbbbacbddabbbdadbbbbbabccbbaabdbcbcbcbddcbbdbcadccccabcbabdbbabddbccdbaddcddcabaaddddaaadabccdadbcdbdcadcdaacdadddcccbcbdcdbcccbdccaabdcbcdacaadcbaabdcdccdccdccaddcaddacbcbaabdddcdbbabbaadcdbcbdadbcabbcacccaacacacdabdddaaabbdbadadcaabdcccabdbcdaaccddadccdbcadccbcbdbbbabcbbbcdbdadadacbbbaaaababdaabbdaabdcccabddaabdcdbbadddaccdabbddcaabaabbaaaddcbacdbcddacccaadcaacbbccbcdaccabbcbddbdbcbcadccccaabdcdcbcbdbaabddcdccddcdbbadcdcaacadacdbdabbacbcbaccdbccbdccadcacababdcabdbbdadbaaaccdbcaadcbdbbbbddcbcbaadbcacbcbbdcabdabacdddcbabcdddaaddcdaccddacccbdbdadaacbbbddbcdacdddbdaaaadadbbdddcbdbcddacdbccaacaddabcdcaacbddacaccdbcccaaacdbacadbcbcabdbadbbbadbcadbcdddccadbdaaddcbdadabcbaccdddacbaacccdcababddccbcaabcbdcccdbadcabccbacdaacddbaacbdddcaaddbdcdacbbaacacadbbcbcdbdbacbbadadbcccbcbadbbddbdbcbdccbbcdbcdabcbacbcacbdadbcaadcbabddbcbbcccdcabbadaddbadcabbddbcdaaaabdacdddbcaacacdbdddbabaaacbdbcbdadbabdccaaaaabaaccadcdaabaadcddccadbacabddcddddddddabaddcdabcabbdcaddbcdcadadaabcbddacdbdccbabcdaaaaaddbbabaaabbcbaabababbcbbdddcbdcccdaacdcbabcdbaabddadabcbbbbbdddbadadcdbcaccbbacdabbabbcbbdbcbcaacacccacabbbabbaccdcbbdccbdbaaabcccddcadabcacdcacaaadbdcccdbbccdbabbcccacacddaccdddadacabbabaabdbdacbcdcccacacdacaccbdaddadcbcbdbaddcdaabdcdcdbcbdcdbbadbcdbaccddcabaccdabcbabbdcaabaaabdddcdcdadbacdcddcbdddaccbccbccbddbababbbdddabcbabccddabcbdacaccbcaccacbdbddcccaabadbdbdbdaaabbcdadccababcaacbddbaaaccadaccbbdaabbccaadddbaddcabcbcabbacacaabcdccdacbcbbcadbcbdabcdbcddadcdcdbbcbdbcacbabbbadaaddcdadbdcbdaaabaddcdacddccaadbcaacbccdadbcaadaacdcadbdcaacbdbaaaaddddbdaadcabcbacbcaadbacbbbdacdcccdaccacdabcccdbdabcaddacbbcbbabaacdcbdacccccacaddccbccdcbbbbcabaacdbbbbacdaabadbdadbcbdaaaccaddaccbddadcdcdcababdaacdcaaaaaaadbdbabdabacbcbbaddabbacdadbbcdcccccdcddbabaddcbadddaacacaaaddddcbdabacaaadccbcbabbcbbabbdcdcbbdadbcadbcbacbbcbbabcddacccacccadccacadcdbdccbacdaadadbdccdccccabbcbccbbacbabbddabaaabbdbaabbcbddcbacdaadcaacaddbbadccccbcaaabdbcbccccbddcdbaccacddccdddbabdbadcabbbcccacddbbcaddbcabcacabadbcacaddbcbdddcbabadddbdcaabdcaadbcaabaacdcbbcdbacdcbbabbbbdbdbcdbbaaddcbcacbadaaaabaababcdcabbcacccababbbddaccacbcdccdbdababddddccbbabadaadabdcaccbdacbadadabcccccbdbcbdccaabdacdbadcddadbbdcacadcbbbbbacaddcdbaaaabbddcbbaabddcacccccaaaadadcacdccaaadbcccdabcaddaadbcbbbbbbaaddbaabddadccbcbbaaabaddcbacbcdccdbcccbcacabdbccbdcbbdbdddabcaadadbdbaccccabcbabacbcaabdbcddaabcbbbadbcbbaacbdbabcdaadcdaadcdddcadbccaabbddccdbbcabccdadcadddaaabbcccdcddabadcdabcaabdadbdcddcbbaabdbacdddbcaabcaacaabddadbcaababdbddaddaaddbabdbbbdbccbcddbccddcacbaacbdccabdbdaccbdabddbabdcdabbacacabbadcdadbabbaaaabdbacbdadbaacaacdbdbbbcabaaddcbbddcbaacdbabcbbcaccbbdbccccbcadcacbcaaacadbaabcadbabddbcbdaacdcccbbbdcdadcacddabccdadbcbdbcbcadbbbaaabbadabccaddbdbcaaddbbcdcaaaabbbccadbbabaabcdcacabcaabccbbccabdaadccdccddacbbaabaabdcacbccbcdcadddcacbdcdcabbabbadbdbdbbbacccddbbddbbadaaacdccbadbcaabaabaddbccbddcddddbdacbbcccdadbabadddbbdbaadddbdcdcdadacbbbbadccddccaddaddcbbbbadbbbdccdbabcbdbdbdbcdcabccbacaadaaccadcdbcaabbbdccaddddcdcdacabadaadadbdcbbadacbbcbacbcaaacabcbabcdcdcbaccadbabccbccbddddccddacbddcbdcccddbbcaaddcdbcbdaabcbabdcdbbaccbacaddaaddbbbabdadbbaaddcadacadabbcbdbbacbdcdbbbbccadabddbaacdbdbcbcacdabbaadadaabababbcbcabacbadccccaabbbdacdcaddccaddcabcbbcbaabaaaddadcdbcbccadcbcdbdbaccabadaababadcccddbbdbdaabddbddbbcbdcbabcaacabdbdabbddbcbcaacbdaadcacbaaacbdcacdcbabdddadaacbdcbdacdccbaabbaadbdcbbcbccdabdbccbddcaadddcbdaaacbbcbaccbdaabbcacadabcdcdcccbacabbcbaaaacdddbacdacdcabbdcdacccadbdcadabccdbcbadaddacadabcbaccbdacbccdbbddddddabbddbbaabaacbbcccaaccbaddddbdabddacabccddcbbcccdcadadbbdcddcdcbcdbdbdadbbccbadaabcdadaabaaaadacbbbcaabbacbdbddacbabbacbcbccaaacaccdddacdaabccdbaddcccdaccaaaaacaaddbabaddbaaacbcabccabbcddbaadccdbaadddabdbccbdbbbbadbaaaddabdcabbcdbddcdccbcacddcacabbcdbcdadbcdaaaababdcccbbadacccbcdadabdbbdacbadbcadadddcdcccbbdbaacadbbbcbdcbcdcbcacbbacdccadbacdddbbdbaabadaaaabacbbbbcdabdadaadcabdcdaaadadcacabadadaaadcabaaadaacddcbbbbbdcbabcdadbcdcdbcbadacbdddcaadcccdacadcbcbcdbdaadbbbbdddaacbbddcbddcbdaddddacdaacbacdccbbdcadddacdddcdcccaaccaddbcaacbcbacaacdbbcddaabdcbdbacaaadcadbdbbcdaaccacdbbbaccaccddcacadcddabadacbdddccbacabbddabbcbbaccbadaaabadbdcdbadcbdaababaacadcdadabccdcdcbacdcbbacaadbabbaaabcbadaabbabcddbdabdbacdbacacbcaadacbbcacaccbbddacbcbbabaccbddcaabadcbaddddaadbcaddcadddacccbdadcbcbcacddbcbbdabcdbcdcabddbdaabddcccacaadbdadadadddacdccabdcbbadcdadaaaddaacaadcdcdbbbdadbacddabbcaabacacbdcbbbbcaccbcbbcadbabbdabbdabccbcadbaacccaabcdaacabcbbdacdabcbcdcadbbddccddbdcbdccacdbcdabdcbaaabdcbcdbcdabadadacdaaaccadddcbccccadcdcbadbaabcbcdaabddabbadaabaacddcbddcbbbabcdadbdcbdcdbbdacddaaadbbcacccdacacccbaaadadbaaaaccbcdcadbcccccbacabcaadaaddbadbbdacbbacbbccbbcbdbbcccddcacaaabdcdcccbabaccccdbbddbcbbbdbbcbadccacbddbbcdbdabacccaacadcadcaaabbbdadababbdbcbbadaadcbcdaabdddbacababcdcbbabbcbddbadaaddcdcdaadcacbdcaaacacdbcbcadbabcccabcdadcabbcbdcbddcdcbccbcdaabbdcbbbcdcbbcacdacdbbbacaabcdbaabaabaadbdcbbacbdbaaacbaaccdbbcbcccdaaadabdaddcacdccddaaaaaadabdadbaaaadaaddbdcadbdcbdaadbbaabcabbbcdcdbabbdbddadcccadbdbdabbaddbcdbbdbdadbccbbabcdbcaccdcaabcbcabdccaaaabaaddadddccadddcbbcdaaabadcadababbcdccbacdaabdabddabddbaaaacbcbcbdabddcbdadbbbbbabcacbbccddbddddcbcdbbbdbbadcbcbbdbdbcbcaababbdcbcbdbbacddcbcbbabbdadcdadabcbdddbaaaacccdcddabdcaccddcabdccacddaacddbacaccddadabacbaddbbdcccccbbccddadadbaccdcbacbabdabbcbacbbdbacadaacdcbcabcacdacddacbacbddadcdcbcbcdcaaaddcbbbabbbdabdbcabbdccacdbbabbacaaacdccbbaccacdacbccbdbcdbadcddabbaaaabcdaddacdadaacaaaabcbbacdaabbccccbbdcaddcccaaabbccbcadacbdccccddbcadaadccccaddcdbaabdabcbabccacbadabaacacbcbadbbbadbabadcdcbbcabcbbbbacabbdaaaabdbbcadacacabdbcbabcabbbcddcaacdccdaabaacddccaaacbdbcdabacbadbbccdcaaabacbbaccaabaaadabdcccadbdabcbaccaccdadabaacdabadadbdabcdcdccaacdbdbcddddddcababbbdbacabadbcadadcdcbabacdccdabcbadcdbaccbbdaaabaacbdbccbdcadbaacccacadddddbbabadddcdcbcaccaadcbaddadbbdaadccabdaabcaacdbaccdaabcbbdabbdadbabbddcccbabcacaccdabcabcacbcaacdabadcbccbbcadacaabdbdaaaccbadddccbcbacdccaadcbabcaadbcabbbcadacdcdbbdaadbaadddcacddbcbcbbabadaccdadbcddabdbdddccdbadcdcddcddaacdbdcacdcbcbccdabbcadadabbbdbaabaabaadcddcabaabccbcabbdabdcbaddbaacdccdccbadaacbaacdddbdacaadddbdbbabcdaaddabcdadddbcdaaabbacbddbaabccadbddbcdbbacabddcddabbbabbddadbbacdaabccbbaaaadadcabcbacacdbbaadbdbcaccaaaaddaabcbacdbbcdaadadbccabddcccdcdbacadccbcbcaaddccacbdababacabaaccbbbbbacdacacdaaaadcaacddbddcccbaacbbccbcdbcabdcccadaabccbacadcdbdbdbcbabcaacacdbaadabadcadcdcbdadbcdcdccdddbcbcbcacbcbbccabbddcdadcdacbabaabadbdacbabdabbbbcdbaaadbdbbbdcaddccbbbdbdcdbadbcdaaabcacbcaabdddbdbddbbaacabcddacdaccaaabacccadccaababbdaccabddbaadacccddbdaaddacbddbacdcacadbadadabbbbcddcaddaacdadabdcbcadbcbcbdadbbdbbbbcdddbcbdaababaaaadaadcbddabbdbcabdcdbbbadaabdbbcccccbbbdabbccacabbacbbbdcaabaadbcccacdadcabdcbdcbdcbcdbbcccabaddcbbbdcbdaabbdadabcbccaababdbcdaaaaccabbcdbbaaccdccdbcdcbabaacbbbddabbbcdbbdbdbaaccbbcacdddddbdbbacdacadccbdbdddaaacbdbacdbadaddccbdbccaacddbdbcdababddbdccccdacbaacaacdcdaddadabbccbbdcacaacabdbcaacdabdbdabdcdbbbabdacbcbbbdcbdadcadabcaabcaacbacbdcbadccadccddddbdcbcdcaddcdacadadaccdbcdddbdabbbbacabdddbccacccacbccbdbcbddcaabcacabcbdcaadbabcaadabadadabcadbbbcdccbcbbdbcbcdcadbccabddddadacccaaabbdccacaacdcddcaabbbaabbadbdcadbaaaaadbcddbdbccadbcacaabbcbbbdcccadcaddbddaddcaccabcaccbcbccdbcddadcdacdabababcbabdbdaccdacbbdbdaacaaabcbcbdabaddddacccabbcbbadaacbcdbaadddcdccbadbbdcabcacbbacddbcbcaddcdcbaadabbbdbadbacbbadddbdbddcdccbbdcbcacaaccdbacacdbadcabcbccdbccbdbaccabcbbdcadbccabdbbcbcaabcccdbbcbdbdaadccaaadadbadabacbbcddcaccaacdbdabaabddabdcaaabbbaddddddbcbbaccdcacdbbdbaddcadacbbddbcccdaadccbcaccacdaabcacdacbaddabcbbccdaabacabdaabddccabbaadabadcdadddbcdaddabdcdcddbaacabbbddbbbcaaacbbcaabbcadcdcbcbbcdbdcbbaddcdacbbcccbdbbcbbbbcdbcbdcccdacdaddddddaacccdbabccdcacdaddbbdbccaaabadccbadcadaddbaadddcdacacadbccbdccbbaccdcddbcdacaaabcabcaacdbcbcaacabcaacdcbbcbddabcdaddddaabdbadccaaabddbbcadaacdbacdaabccbbcddbadcacbcddddbbdcadcdcccaccaacbacaacdcabcdacabccadaaaaacccbdaabdabbaaabcdabbacdcaababcbcbaccbccabbdcbdccabbcbbddccaddababbccbdadbacbcdcdcbbcacacabacdccabbcaacdbbccbdacbccadbdaccaaddbaaaccdacbcbdaacbccdcabbdaaaadbadbddaaddabcaabdcbcbdadbbdddbbdadabdccdbccaddcdcdbdcbbabdaaddcaadccbbacddcaddbaccbcbdbdbdcbbccadbabcccccdccbabcabaacbacccbdbbdccbcdcabaadacbcccdbadbbdcbbbccaddbcaabadbdadacbbbdbbdadbbcddabadcacabbcabdbaddaabccaddbcddccdcbddaabaacabaaadbdcaccadaacbcdcbadbdcbdcdababbcbcccccdcdaabdbdccaddacbbbcabaaacabaddadcadcbadbbbacabbcaadabaccbaccabcadcddbdcabcddddbcdcbaaccacdadadcabcdcddddbbcbbdababbdabaadcdacbbdaacccbccabdbcbabbaacdbabcdddbcdcabcabbcdbdbbaababaadcdbbbbaccdacbadccaaaabcadcaaadacabacdababccabbabababddbbbacddbcbdcaacaacdddbdbcbbbdcbccadcaabcaccbddbcadcdbdcccdbbbbdabacbaacadcdaaabdaccbbdbcdcacaacacdacdaadcaaadbbcaccdcdddcacbcbbbdaaabdabcbcbaaccababbdaadadcacabbcddadddccdaaacaadcddcbbbcdbabacbaadadccbdcaabbccdacadcacaabbddadaddccdcabdbbcacbcccdcdccbaccaadadcaadcdabacddbddbbdcdbacbbddcccdcbccacacaaddbcabaabccdccbcdabbdaacdccbcdaaaaabbcacdcdcbdabdccbdacaaacbacaaccdcaccdaccdbbcacdddcdaabdacadabbcadddcbabbbdbadababacccbabccbcbadcccbacacbadbaabacddccbbcacaaadadaccdccdbbaadbcddbddbbbccbadbaaddbdbcbddbadbadcdbccacbdacdaabbcdcadddabdbdcdcbcdacbababcbacaabacbddbaabadddddbdaacbbabdbbdbddbcddcbddabacadadaddbddcabcddbddbcadbddccbacabdaabcbbbdaddcbcbdaddbcdbaadaaacadbbacabaaccbddbbbdcabcdcdddbdcbddaabaacdbdcddabcacbcadbbaaacacbccdaaddacacadcccacbbbccaacdabbccbcadddaccdcaccadcdadcccddcdcdacbcaaabbabdbcdbcddaabaaadbdaacdbababccdbbdadabdadadadaacadacccdbacccdcddcdbdcdcdbbacaabcddbbcacaaacaccccddbcddccbacadbacddbdbdbcadcbdaddacaabccdadccaaccbbdabbcbaacbdcbcbabbabaadbdcddcabacaaddccabcbacdbbccddacbccaddccadaabddcbbbdccacaccccbccadcdddbaabaccbdabcaccdcadcaabadcbccccbbcaadccdcaabacbdcadaccbcdbcacccbabaaccbcbdabdaaaccdbdaacacddacabcaadacddbadadbabbcadaadddbcadbcdddddbcbabbaaaddcbaddcbdabccbacbdbdcacccbcbbcdccbbcccbbccbcdcccadacbbcabcadbccaaccbcbdddacbbcbacbcacababcbccbcbacdcdbcaaabbbaacccbdcbcccbdcbadadcdcbbbabcabbbacadabbcabbdcbadbbdbcbdcdbabcdaddddcdcbacaadacddbdbaacacdcddaddccdccacabdbcabbadaadbcabbbddbdaabbacabaaacdcbddccbcbdacdbdacdcdcdcbdbcbbbdbdcbcbcddcbacdaacdbbccbabddadaabbdbdabcccccdabbaacadabbdaccdaacccadabadbccccdaaddbcadaaabbbbcdcbadcaaddaaacdbccacdcbdcbaddcdabaabcaabababbdcbbcdcdbdbababdcdaaacaddaccaabbbccacabdccdbaabcbdbddcbccddddaaadbdaabdccbdadcacacdbadabcddbcbabaabadbadcdbccdacccacbcddcadadbdbdacabccdabcddcddbbbcbbbddcbaddadcbbccdcdadcccabdcacbdcddcddcaaacbbdddccaadacdbbddbcbbcdbcbcbbabadbbbdcdabbddadaacccddcaabcdcadddcdbdbdbaccabdccbaabdbccdddbcbdcdbaadbdcbccdaaabdbbbaaddddaddccadcaaabdabbadddcabbaaaacdcbbaacbdbdabbbbdacccbbbddcacabddbabcbbdacddbdccbcaabdcdbbddabbbabadababcbadbbbcdadcddbbcbaaadadcbadaadcccdadaabdadbdbccacabdadbdaadcaccbdcccdcacbdcbcbbbaabcadaadcbdcabbdbbcabdbabbdaccaccddacaaacdabbdbccccacbbbbaabaddbdddddbdcadcddcadcbadcddcbbbbadcdcacdadcddbddbdcccddaaaadaacdcbccbcdacddacdaabaadcabbdababacbdcbcacaddcbdbddaacbdbcaabdcbcccdbbaaddccbadaadaccdbddddbccbcbbcbbdaababdbaaadaabdadbdddaaccdacbacbaddacdbdabaabacddbbcbbadaaccddbbdbcbdcadcaccbbcdaabcddbcbdaaabacdabdaabdadbaababacddadbbbbbaadaabbcdbaabdcadbabbcdbbcaddaccaaddabbbbababaddbbdcbbdcdbabadbadcddacbbdaadbbbacdcbdadaaaacdbccacababdcbcbcbbdccaaaddacccababcbcdddddacaddbcdababdcdccbdacbcabababdacbbdabdbddcbbcacbdbaadaaacdbdcaddaccdcdadbbcccababcacddcaabcadaadccdabbabdcdaabdbacccbccdbacacdaaddaddddccacdcdadbbcabccabdbacbdbbbaabdccdddcbbbdcacacabacadbbccdadccdbadbccdcabcdbaacbcddbddbbadaaabbdadaacbdcdbcbaabdbcdbdacbbccabdbbadcabaacdbccadccddcbbaadbddaddaacdcadabdaddcaabdddbbdcacdccacadddacddbbbbdcdcabadcdadaccbddbcdcbacabbaddacdbcdbcacbbddaacbcdaabcdbcbdcbbbbaddaabcbcddccdacdbdbaccbdaacdccaddcaacdbdadadcbaccbbdcbcbccadcaacddaddcababaccbcaaccdcaabbbdbbaaabaaccabbcdbcbdaaccccdaaaabccadbcccacdcdcabbbcdaddaaaddacdaabbadcbccdaaabdbcbcccdddbcabccabdcdccdcadaaacdcdadcacbcbbabaddaccdcadbcbaddcbcacbdacdddbdacacbbdbddbaadababaddcbaccdcbcccccadcdaaccddaddaabbbadcbbbbcacadcbdbaadddacbadadccabdcdccbcccbdacbcabbdbadacdaaccbbcabcbdcddcabadabdabbaddcbddcbddadcadcbadddbbdadacdbbcaabbbaccbcddbcbabadadadabcaaaccdbbdbaddcdadddbbdcadcaadcadbcdcabbaccccdacbacbcbddcabaaabdaabddacddccbbdaaccbbbcaabbaaaabbcbbccadcbdacdcddaccdaadbcdabddcabccbbaaaaaccaacbdbbddabadacbdbaddbdbbbabdcabbabdabadbbbdabbdcdcadbcddabbddaaaccdaacdbcbbabcccdbcaddaccdbcbdccabaabdaadcabcaccdbadcccdbcadababcaddacaccdbaadbbbbabdabcbadbbaabbbbcacabbacccdaccdaaddadbacabccccddccabdabbaaddddbdcbcaacbdbdacaddaacddcdacdacdbdbaacdbdbcacbadccabadadbbbacdcdccacdcabbcdbadbccccbbaccdcdbbcacbdaddcccdadbaadaabacccbcdddcdaacdcddacdbcacbabccdcaabccacbdbadcbcbdbcaddbcbddbaaccabadddbabbabddddadbbacdcddacbadbcbacbddaacdbdccbdccacccbcdacdadadbdcadccacdacacadcbabbcddcdabaadcaaaadbdabbccbdcbcadaabbacbababaccdcbbdbbdccbaadcadabbbddbabdcbddcabddaabbaabcccccbbaccacccbdaacccddccdacdbdbdadaddbdadcaddcdadabdddcabdbbcddcdaadbabaddaadccddbbbbabccaacbbabdaaaaadcaddadddbdbcbbcbdddbcaaddccacbcbcbabacccccabbacddaaabdcbdaacccddddbbadddcaabcdccdccabccababccaaaadaccbaabbbadddbdaaabddadcdbdbabddbdcaddbcbdbdacaadadaadbbdacdcdbaccdcbabcbcdbadacdabdbdcddbcbacdbddddbcadcccbacbbdaacccdbbabbcccaaabccbbbddbddbbbdacccbdbbbdcccabaaddbcccaccabdbbcacadccdcbcabcbaddcddbcddcabcdaccdbbaaadcdaaadcbddbacdbdcddabaadccdbaaabbbbddcbcbbbabcbccacbbdbbbbddcabcddbbdbdcbcbdcdbddaaaadcacabcababdaaadcadbdcdccdccdbacbadbdbdabcccaadbbddcdbcbccaacdacdcdbdbaacdbbbcdddcaddcbbdbbaadbbcaccbaddddacadabcaadabadddacadbbbbcdadbbcdbadbccddaadcccbccabbddadcacbcdbccbabdcbdbdccadddccccaacdbbacccdcdadbadcbadadbaccabcdadbcdbddbababcdcaabcbbdabdcaadddcbacccbcbaaddccabbdbddbbacbbaacbbdabdbbcaccaaccbccacbbbccdaaddbbbacacdaaddbbaadccbdbaacdccddcdddbaababcabaadcdbddcdaacbcaabcbdabbbbacacabbbadcabccaacdcbbaadccbbbbdbccbbbbddbbcbddddaaabbccacabaadbbdacbdaabcbcdaacdddddcaadddbbabaddccaadbdbbdadbccdcabdacaacacbadbadbddaaaadbddaaadabbbbbaaaabaadcacccdbdbccdcbdbcbaabaabbbddaacbcbddabcbdbdbacdcdcdbdbcaaabdbbabcdbdbacbabcbcbddcbbadaccdadbcbbcccbbbbbbdccbabdababadcacbcaddcacdbddcabbcbaaaaabbcccbcccdcbbababaadaabbdaaddadccccddccccacbdaccbbaccdccdcaaabdabdacdddaddbbabcdccaacdddbdadaaadcdabdbbbcdacaccdcdacbcbaddacdcadccdcaddacbabbadbbddbadaadaccbbbcabdddcdbaccbbbbccdbdccbddaaccbbdcabacbbabddbbdacccacadcadcdccabacaddcccabacddaaabdcbcddadbabaaddbbdbcabcacdcdcabadbdddcdcbaacdcacaabaacddbdccbadccdcacccdaccdcbbbddabadaacbdccccbacbdcbdddccdadccccdbbccaabdadabcbcdcbabddcdababdbddccacbbdcccbccbbbabdbcdddbcccaaddcaccdbdadbaadabdbdbccabbdcddcccddadcadccadacbacaaccbaaaacdcbcbdadbcacdbdcabaddcbddccbbabaaacddbdcddbbccccddaddddadadcddcadadccccbaadcccaaacbbabbbcacddcbdccabcbcacdbdccaaddbabdbdbabdbabdcdcadaaadbbbacbcabadabcacaddccaccccaaaaccdbbdbbddbcbdbbdbcccdadcddcdbbabbabadbcbdaddcbdcdabdbccccbcbaabcbcccaacaccbdbbbbcbbaaccacdabcdabaccacbdcdcabbbaaccadbccbabcbcbbabddcaaaacacbbcdbdbdcaddcbcbbbdcccdadbbccdcacbbddcaabdcccadbaadddcaddcdcabbbcbdacbbdcbcaabacaaaaddcacccdacaabbadadaaaadabdcaacbadbbacccccbcdaaddbcabcbaaadadcbbadacadaccccbbababdcaaddbcabacdbbacbaccdcbccbabdcaacbbdcbdaaacabaacdaddbcabaddcdabdddbbbdbccddbbcaabdcbcababbdbbcbdabcbbdbbdccabbcdbccababaddddccdbbaaddabaaddabacabacbcbabbaaadaabbcddddabcaadaacbbccbccbdbcdcaadadaaaccdcccaadcaabbaabcaddbaccdccbbdbaaccccadacddbddadabcdccacbacbacdbcdaacdaccdaabacccdababdcddbbbbdadaadcbdaddbdaaaabcaadabbdbcaddabccdccdddaaddabbabddccadabdadcdbcdbacbbccbabdbaddadabaccabddccbdacadcbdbcaadcbdabdaabbcdbdcdadbbdccadbaabdcdbadbdddbdccbabaddbbbcaadcbcadcacdccccaadadbccababacbdbbbcbcddabcddaabdddcddcddacdadacbcdddbcbbbdadbbcbccaaddcbbbbbaddcdccdbaccdcbdcdccacccbaabbbaccbdccdcbbdbabcbacbbbacbddacbcdccccabcccdaabcbdcdcbcdbcbcaacbbbdcddbcdabddcacbccbdbbdadabcdabcbbacabdaabccabbcadadcabcadcbcbccadddcdcaacacdcbbbbabbcbcbddbcdcbbcdddbccdbaaabbbbbdbbdababccbcccabccbcdbacdccdcaaadbccccaccdadbacdabdabcdabbacaddddcbbabacbbacabbbaadbcddbadcbdcaddbaacdcabddaccbbcaabdabaacbbcbaabadadaadddcacbdcacaaabdcdadccdccbabdaaaaaccbddbdccddbbabcaadaaadbcdbbdbacbbdaccdbadbbdcdbcaadabacadbcaabaadddcbdbbbbbddddcbdcacbabcdbbbbaddbdbbcacbbabbcbddacabbcdbdcccbcbcbcacbccabdabdcaadaddadadbaddccdbcbbababbcaadcddacabcaddacadcbdabcccdcbabdaacaccbcbadaccdcdaabcbaabccbcbdbddcbadabdddbddacbacaaaadacbaadbddbdcdbdabbaacdababdadbbaccbabacdcdbdcddbccdaddccaaccdcddbcdaccbbcbbddaacabccbbaddbccadcbaadccccdddccbbbccadccccdbaadbbabdacdcabacccadbbcdadbbbdabcdcabaacdbccbbbcdbcdcbddbdabdcbdbbdaadddaddabdacaabadcccbabaddabcadbaaabbcddbcddbccbbdbcddcadcbdbacaadadddaabaddcbddcccadadbdddcbbcdcdaabddccbdbacbacccbbbacacacadccddbcdbcdadabdaaccdcaacbacddddbbbcaabdcddbcdbdbdbcbacccbadcadbdcddabbbdddcabdccdcabacccccaaaddaadabbcacadddbbdcbcaadaddbacacbccdcdbbcbdccdcbcbccaccbcbabababcccadabbcacdaccbdbbdaddddabdcbbaccaddcdadddabccddcdcbbacabcaadcbbcdcaddcbbdabcaaccaabbadddcddcacddcacdcaacbadbcaababcdacdadbabaacbcaacbcbaccacabddbcaadbaddaacdbdaccdddcdbbdcbabbdadaadcbacdccbaadadddadaccababcbbbbadcdbaccbcaadbaabbbccdcdacbbbddccbcbaccdadcccdadcadddbaadabcbcabccadcdbbcbbacdabaddacbadaabacbadbcadbadcbdccacaabccdbcabaabcacbcdaddacccbcdbcccadcbdbcdcdacdcacdbacaaabbcbbcdbdbbcbbabaacdbacaadbbabbbbcabdbdcdbcdbbbbdacbaabbbbaaaaadcbdbabcbdcbdadcbdcadcdbcadcdccbccbccdaaabdbdbbdbdbadddbccdaddaabddaddadcdaacbcabacdddaabaccaadadcadacaaaddcaacabbdadbcdbbdcbadbadbadacadbbacddaabbdcdcabbbaabbcaadbbaaaaabacdbaabbbaadababcdabbbbacacacccacdcdcabdadbddbbbccabadbccddbcaaabbabddabaadcacacbcdaddcbccaddaaaaadcddbaacbaacabbaaadaddadabaadbaccdaccbdacbaddbdaacdaaabbacbdddadadbdbaaccbddbcdadbaacbdcbddabddcddcccbdcdbbaadcbcbaddacddacacdccbdbacdccddcadbcaacaaddbddaddaaadaddaabcdbbbdcabbcdddacaaaaabdcdaaadccbcdddabcbbdccccadbdbbaaccaaabdaabdcddacaaaddaacdacbdaddccdddacdabbbcabadcaadbaacaadddbaaaadcabdacbaabccaccdbdcccacabddcadbdadbbaadbbcabcccbcacacaccacbaacbbabbdcdcbdccabccabdadbbbbabddbddabbadabbdadbdadaaccdabacacacdaaaabbababccdacbbbabcadaadcaabdccbaadbcaddcaadacdadcbcddacacaddabdbcbabcdbbadcaccadacdaaaacacbcacddaacbcadcdbaabdcdbadbdcbdbdddcaddbcdabbbccabcccbbcadcdbbadadbdbbdcbdddaccbacaabbdbadcbcadcbcdbabbdbbbaaddbdbbbbcddbddbdacbabaccbadccdababadddbbdccdadbccdcddbdcbcbbddbbbcbbdadaddcbddaaadcacddccbcaadabaaaadabdccaccdcbbccdabadbbccbacbbccdaadbabaabbbbddbcbcbcdbdccaccccbacdccddbadbabcbbdbccdddacdbabcaabaacbbaccccabcccbddcadcbbabbcabcacddbaaabdbbbccabdddbaccacaacacabcabdadadcbabacadbaabcacaadbbcaccdbadbcdcbcadbcacccddcdcabbabbccacdccabaacabcacccbdcdbdaabccdbcccbdacbaaadacddacabdcbbdaadcabbbdcacdccbcacccbacbbbbdbccbabbcbabddcbdcbacbcbbbacbcbbcadaccdcaaabbcbcdcbdbcbddbbbaccbaaaabdccbccbbcbdaadacbcacbcdccdadcabdddcadccbaadcdcbddccbdbaabdcbcdbdccaddbaaacbbabadaddcbdbabbddcbbbdbcabdbbaccdaabddaabacadacaacacacaabcdcbbbdddbaddadcabbbbcccdacaccddadbdbcdabbdaccadaccacddddcbddbbbbcdabdadbdcbacbacccddbbcdbdbabcdddccacbbabdaaaabdabacbdcbdabaaccddbaadcbadbdccdbdbdacbbbbdcbddccccbdacbbdbbdccabbabbbbdcbcaabbcdacccadddbcaccbcbaaadbccdacccabdbbdbbcaccadadbdcaacdbaadadbcabdadabaadcaccbabdabdcdaabaddaacbdcdccaabdccacacaababbcdcddabdaacdddbbcaacdbacaacbcaddaadbbdbdacadbdcdcaacbccccddcdacddabcdaccccdddbcdcccabdbbbdaadbcbccbadaddbbcbccdbdaadadcdbddacabcdaabcadbcdccdaccdddcbabcbbacbabdcacdbbbcccacaabdbdcacadadcccccadbdabdaddaabdcccabbccccddbabcdaccbbdcadddddbbdcabacdbccbbcabcbcdacbaddcaaddabcbcaccbcabacdcccbdbbcabbbbaabaccdbabbccbacdacbcaadbbbcbaddbacbccbbcaddddbadacdbddddbbabacddcdbdcccaacdcbaddcbdaaadaaadddddddbdaddacddabaabccbdacaacdbdaaccddbcacaacaaddcaaddadcddcabbdaddcacddcaabdadbabcbdbaaaccbcbcadcbdcacdcbacaaabadbacdaadcbadaddacbbbccbbdcaddcaadcbbaaacdcdabccbbabbbcdbabdaddadcbbadaccaacaabaabadcbddcbcdacdccadbaaabcdccacdabbbadcdabcadabccabacbaaababdbccabbccdddbaccaaacacdbaabcbaccbbcbcdcbccdaacdcdbabcdcbddacbbcdacbaddadcdbbbcacabbcabdddbcbccdbdbbadbbddbadbabcdcbcdbbcdcbabbdccabdcadababcbaccccaabcadcbabacacaabadccdbddbaabbcaabbdbdacadcdbdbcbbbcdbbdaadcbadcdbaaadcccdaddabbdabddacbaadbbbdbcbbaaacabbdbabbdbbaabcadbacbabdacccaddbccbadbbbdbcbcbcdbdadbdccbdadcdbaadbcadabaccbbddcbdabbaccdbbacdcdcaaabccabccccbadaccddbbdcbccccadcccbbcbcbcdbabaadcaacabcbdcbcbdacaaaaadadacdadcbabacacdcaddddbacbacbdcbbdabacaabcaacacaddabaccbbdcbdabcbdccdbaaababcbadccdbbbaadacccdbcacddbbbbddbdbccdacacdbaadababacbaaaacdcbbaacacaccddcbadbbbcacadbdbddadbcbcccaacdabdaaccbadadcdcaaaddcbdbaddbbaaadcbabdbabbbcdaabcbbdddadbbdbaabbbdbccdcadcdadbdbbbbaadcccababdbbbdcadddbdacdaaddadcbadacadadccdbdbbbdcddbbdcbcabcacccacaccddcabbaccbabcadbcbaaadcdddbbdaabcbabddadcaddddcbbbbaccccacbaacdaccddddcadbbaacdaabdbacddbcbaccadcbcbabdadacbcdabbcdddbbacddcdbdbadbcdcaacdddaccdcbbbababdbacbaccbaaccdcabaddcacccdbdbbabbaccbccdbaddacbcbdbdcdddbadbcdacbcdacbacbccaaaccadacdbcdadadccbacccbcaaabbdbcccbbbababadbabaccaaabbdcabdcabccadabbbadabdbbbcbaddacdddddcacccababcccdacdbdbcadcbadaccdcdbaaaaacdcdddddccaabbababbadbbaccbbaaaddababccacbdcccddbacddacabcbbdcadddddacacabdabcdbdccccdcaacccabaaadacacaaadadbdcddcbcbcaaaaababaacdccdcdabaaadbcadddcbdbcdbbcacdbcaaaacdbcbdccbddbcdddbdaabcbdadacdadcdadacacbbdcdaccaaabccaaacbccaaaacdbddbddcaacbccddbcccaabbbcaccdaccdbbdadbdbcdbdccccaaaaaaacdcbdcbadbdcbbbcbcdcdbbcaaacbcacbadadaacbdcbddcabcddbabcadcaabddaadccdcbdcbbabdabbbdbcddaabcabccbddaadbacbabaadadccdcbdacaadaccbbbdadcdcbaabdbcdadbddbacacbdacddabbacccbabcdccaadbdddabcbbcbcdccbbcdccacdddbbbddabbaaadcaacabdcadcdbddaabaacccaaaddbbcdbaccadcbdcdacaadcdabbcccddcbcdbacbbdaaacacdadadbaaccbdadbabbabbdbccbcadabdaddbddabacaaddaddccccbabdbdabbdabdcacabcbbccbaabddaadcccacaccbccaddcabaddadbbbbbbabaabbbaabdbbddcadacbadaccadcddcbcdaacdaabcdadcbccbadaadcdcbdacabbcbbbcddacbabddccccabcdbaabdcaabccabaabacaaadbdaddccaccdbadbbcaaccacabaaaaddcaccbcbdabbbaddbdaabbdacddbdbaccbabbabbdddaacbddbbdcbbbabbdbbbcbbdbaaaccdbcbbaababaacbcdacbdcacaacabbbdcdbadaaabccdaabdabbcbbdbaacdcddabdbdadaaadcbacccaabbbaaabaaddaabbadcdcacacacbaddcbdadcdbdccacabadbdbdabaabccdcbcacdbccabccbaabaabbddcddaddddcdddcdbdcadddaadacaaaadbbcaaacdadadbcdaccaddaabbdcbdabbabdddaddcddccadabdabddcbccddccadaabaccabbaaabdbbabddabcbdadddbcabdcbdbdcabdbbbdabcabbcdbaaaabaddcadbcbcbacbbdddccbbbcbdbdcbdbbaacbaadccadccdadbdbbdbdacadcccacbaaadbcddaadadbccbcabdcbbddcddbcbbccdbddcbabdcacacadddddaadbcdacdacbbdaccacabdaabaacccccbacbcbbaccaddadacbabbbdcbacbbaacbcbabcdcaddcadcabdccbbaacaacaabcbbdadbcddabdcabbdaccbcbddccaabddcdcdcdabdddaaaacccadcaadcdaaacabcdbabdcddbaababcbbbbdadbaddabccaabdbcbcccaccdbbcbaadcbaadbaddcdcadbcbcbcddaaaacbacbacacabdbbcbcdcacdaabcdcbcdacbdabbdbccddbbddbbccdddcdccdbbddaddaccccdbbaacdccdbbdcccaddddcaacccabbdcaccdcdbddacccadcacaaccaccaacccbbababdaabcdddabcababbbbbaadbcadcdbdaddcabaccacdaababcbacbccdcdaccddacaccaccdbacbbbcbbcbaadabdbddacddddddddcaaabddbaabcaadbdacbdbdbaccbccaabcbddbdaabbdbadbcbdbcdadcadbbadcbbdbddaaaaccbaacbdcaadadcccbbdabdbaabbdbccddbcbcbdcdaabaaadacbdcbbcccbccdcdbdcdbbcdcddccbbcbbcdcbadcadcbabcaabdbcabacddaaddbcdcdbbadccbccacdbbdadbcdbdccccddabcacbaacdaadddbdcdddbbadaddacccabdacacdccacaadcadadddbaadccadaccbdccabdacbabddddaacaccbdcbbadabbbcacaccbcbbdcccacdcdddddacbdddcdcaadcaabaacbacadabbcbcabbddabbabdcbcacbcaadcdddcacdacccaaccbcccabdbaadbdddbbaaacacadcccbdcaaadbdadcdbabcabcbbbcddadbddcabbbddabdcacabbbacdcbddcaaddddabadcdbcabcbddbbbdbbbcaaddcabaaddacacdabbabaaddcddaababbbabcbcbbdbaaaadadacdaddaddcbdcdcabaacddaaddcdbbabbbdadacdbccbccdacbcbcbcbacddccaaddbabdddaddbadcdadbadbdaaabdbbbcdadcadbcaddaaaaaccababcbccabcbaccbbaccaadcaabdccddcdddccaaacdddacaccdbdbaadaaababcdbdcacddcbbdbdcbbaacbbadacadcacbcaaacaacdddaacddabdababcdaaddbabdcdabccaddbcdbcdddcddabbadaccddddadddaadccdccbcdbddbdbcaabadbcbcacdddabcacbccabbddbbadbdccdcbbcabbbccccdbbaabcadbaaaccdbbbdadabcccaadbabbcbaacbddbddcbcacbcadbcdbcbbadaabccaccdcacaccbddddcabcabcaccbacdadcddcbadbababdbcbcdbabcbcbbccadcdbcdcbaacaadddcbbdcbbbcaabdabaddcadabbddccddabadbddcdcabbccaacdbaddbacabbcadddccaccbaadcbdcddaadaccbdcdcdcbdbbcdbbdbbaacdccccddaacdbccbbaddbbbcbddbbabaaabdbdaacacdabbcdbdbccddbacaddbbaaabdadabdbccdbbabdbdddadabbadbaadbaacdcbdccaddacbadccdabdbdcaaabcdbaddbdcbcddbadbcbdadcdcddaadcdcaacdabbaccdbbaaabddabbccbabdbbadcdbbabbacbbbabbadcaadcddadcbabdbddcaccababcbcacdcddcdcbdbbcbcabbbaaddaadabaadbaabcbdccaadddcacaccabccabaaaccddaddbbcdbaaddcccdaddadcacccabdcdddcbccdbcbcbbccadbaddadadcbdaaccdcbaaaabdaabbbcbcbbdccdccddcaadabacbbabaacddaabdccacdaabbaddcddaababbcabacaccdddbaabddbccacdababdcddbccdbddcbacddaddaadabbbdcddacbbbbcbdccaabbddacbbdbcadbdddbdcdacdaaccbccddacddcccbbbcadbbcacaadbdbbcadbdcbdcaccadccabbdaacabcccabbbcccbacddbcdaaccbccacabcbbcaddcbcbcabdbcadcdadbbcadbbbbdcabbbbabcbdcbcbddbacabdbbabccdbaadcbbbbbbdcdaaacccadccbacbadcaaccddcccbabdcadcbaaddddaadabcddbbdbdbbababbbabaacaddcdaabdaaacbbcbcbbadacbacbdbadddabcbabdbdbabdbdbaabdbaddccccaccbbcdccacdbbcaddcdbcbadbcbbdbadaabcbbcccdcdcddadcbabadbbaabcadcbcbaadcadcbbddcdbbddabccbdbdabcccbacccdcdddcaaccbcadbabcdbcddadcacccadccbcaccbabcddccaaadddbcbcaaacddbacbddbcbcaacbabdcccaacbcdcabbdbcacacbbbddddcdccddbcdbccddbdcccbcabcaabadbdccbddddddaabdaaddbcadbbdcacdbbdacbdcabccaadbadbccdcdcbcbbdacaaaccababcadbdaabacbaababadcbcdbdccdbdbdbdcbccabadbdacdbbddbdcabbacadbdcbababddbddcbdcbbccdbdabcbbbddcaccdbbbbbaaadcbccdacabdcdccadccbcdbddaabbdbabdcbbabaccdbaaadbcdbcabbcdccdbbbdbdccacdcccbdcacdcdabdbadccbdbdcbdbcccaadabbbccaacdccdbcbbabbadbadddbadaaddadccaadccabdbacbccccdbbacbaadbbdcdbddbdbbbabbcaddacaccdadbabdaddcdaabcdbcbccbdddddabcdccbddbcddbdabacbcacbaaaadcaaccacacbbcaababdbaaacdabaabaadcaccdababdddcaabddcdcdabcbddbbcdccccccaabdcabbcdbbcdaaddcccbdccabdaacadcaacaababcbacbbcaabdacbcdaaaaaabaaabddacbacdbccddabcddbcddbccbddbcbacbaccaaccdbaadbadcbdbddacabacdccaaacbcdbcccacdaccabbcbaaaabbcbcbacbbcaacbcdcaadacadcbcbcaadbdbdccadbbbdacaaddabbaadbbdcadccbbaddbcdaddcaaabaddcdbbbdcdbbbdccbbbbbcdcaaddccdaaacdbccbacccabaaacadaddaababaadccdbdaacbcccddabdadcccbcacbbcbcdacbaccabadccddabbacbddcbbdcdcdabcddacdcbbcadccaacccabbbcbadadbcabcacdbdacadbabaababaaadbdbdbccbdadccdabbbcbdcdaccdabbccdaddccaadcabacccbcddbbaaacaccbcbbcaddbaaaaadcdcbadacabbadaddccbabacabbabccadcccbcdcadbabcbabdbbbaabdbabbdcabcbababacdcacbbabbccdacbdadbdcaddbbdcdbdbccacabcabcacbddcccbacbbdcddccccdbbdcaaabdadacacbabcadcbadadabacccacacdccbbacabbbdbcabdcdcaadccdaaaaddddbabaabaaadacbdbcacbbabdcbacbdbaadbbadbbdadbacabaadddaacaabbbadbadcddccaaacabcaadccdbaaaadcadbdabcaabcaaaacbabdcadbbaabccdcababbccbbbbddabadadacdbbdaadbdddbbbaddacbabbacdbcbdbacbcbcbdadbaddabddcaabdabbabdccdabccaabbdacbccadbcacabaaadcddcdddccadcbbcaabacbadadddcbdbbdaccbaaacccbbdaadddbbcbbbaabadbdbacccccacddcccacccdddbdcaadaccccbabdbdbcccccddcbdbbdacabdbadaaabcdadcdbcadabccaddddccacbaabdcccddbcdaaccacacaaddadccdacadaabdacdababdabccadacccccccbbdbbcdcbbacdbacacbddcaabbadbcdddaabadaababdaacaaadcadcddabbdcdccaacbcacbddabdabbdcdacabcdcbacdddcdacdbcbccbcacaadbcbcbcbccdacbbacbaacbdbaacbccbaabbbbcccbbbaaadadadccadabbdaacdddadaacdabbaadbbdbdacacdccadabcaddadbdcaacddadbddcacabcbcabacdabbdcddbcadaaaabaaadaabccacaabbbccdacbbcbbdcbadaccbadadbadddbcbbaaacdcaddcbbadabddbcaddcdcbccdabdbbbbcddabbccdcddbbcbbbcbdaddbcbcaddccdbbbcbccacbddaccccbbabddabbdccabdccdcbcdccacabcddaaddaddacaaaaacddcaabbbcbabdbcbccbbdcaacccddcddccabdaccabcadacdbdbcaccdbcbdcaabadcbabaccbbcbdbcacaabbababbcccacbddaadbabbbcaddaadabdcccacbacaabcababdccbdbccdadbbccbdadccddcddbbaadcbccbdccbadbaaddaabcbdaddcddddcccccadcabccdcbdaacbdbcabbcabcdcbaccaaadcaccacdcddbbbbcbacdaddadbdbbbcaaabbcdcdbccaccdcbddcdcbbbabdcdadcbddadadcdcabdccbdcddccddddadddaccacdbdccadcacbcabcdcadadcbadbbbbcadbbcacccbdcddbbacbdccaadccddbddddbcddcabcaaaccbacabbbccbcdbaaadbaaacdcaaaabcabadcdcbbcbacacdcdcdbbcdcaddcccadbacadaddbdabddadbbbccddaabaddaaddcbaaccbcddacdddbccddcaaacacdbaddabcabddbbdcbbccbbbdacdabcddbacddacbbdbdadbcdcabddbbbddacbacacdadacdababcdcabcacadaddbdccabccdddcdacdcddccbaadaddcccddbcdbacdacddcacbcdbdadacadbdacbacbabadbbacbccdcbabaaabaddbdbddabacacbacdccadaaabbdbcaadabcaacddbabadadcccbacadbcccaaabdcccddddbadbacdcddacccdcbdcabdacaadabcbccdabaddcbaccadccdbdbaacdcdadbbaccbbcacdcbdbcaccbaacadacbddddadbaadbcbabbbcacbbcdaabbbbaacbccacaaadcbaccdcbbaadbdddcbcdbcaadddadacabcbbbbdaacacbdacdadaababbdabaabcbaddbddbdaaaadbcbdccbcbcbaadabbaadacbcbdabbdadddcbaddcacacddaccdbbbcdbdcdbcacabaaadaddbdabddabacddabcdbddbbbcdaadcaccdacabababdacbbdcacdcbdbdbaacadbdbaccbdaadddcbdcaaaddbdbcdbbbabbdcdbbdabcbaabcaadacaabbadabbcdcbbbadcccddddbabddcadadccbabaaaaaaaabaabaddadaabdcaccbbdbbbaccbbacbdccabdacbcbbbdaddacbdccabbdcdacbbccaaadadbdabbdacbbcaababcbadacbabcccdacabcbabaccbadbaabddbbdadcabdbccdbccbdcadcabcabdbdabacaddbaadbbcbcccbccacdbcdadacdbdacbccdcadcadccbdddcbcacdcadcbbccbcccabdbacccdcddbabbbcdcbbbacdacbaaadbcbadbdbcbccdccaabccaacdaaaabcccacddaccaaadbacdadaddbdadcabbacbdddabbcaacccbcaabaabbacdbbaabbaccadcdaadbcdadcdacabacbacacaaababccbacabdaddabcdabdbdbabdacddcdaabaaadbdddcddbdbcbdccbbcbbdddddbcacaabadbacadbabdbbccabcaabadaadabdcbcbccabbcbacddccacdabaaaddaddcbdbbadbbccabacabbdabaddadbaadbaccabdabdcbdabbdaadcdabacbbadcbddbcdcaadddddcbbdbbbdccaabbabdbacdddcdbddbcccadcdccabdbbddcccdccaadacaadbaaabccabdbddbaaaaabaabcbabdddadaddbabdaabddcbcbccabbacaaddbdcdabcabbdcadccccbbcacdadddaaabcdbbdacdbcddbcbadcdbccadbdcdcadbabaadaacabddcbdbcacabcbdcdabacccadcbcdbbbadaaadcccbdccaacaacdbccddacababbdddcabccacddacdccabadacdbbdbdbaabbcacadbdcbbbdacbadddacdcabdcaabbacdabbdcbcdcdbddbadacddaddacdddcabdcdccdcadabadbbccbccbbbdcdbdbbdbbdaccabbddbdacdcddbdcaabbacaabaababdadabdbcacadbadbbabdbdaccadbbccddccdadbdbccabbbdacbbbcacdcdbddabcbabccbcdddddabddcbcacdcbaddcdcdcadbdaaacaaccabcdbbccdcdccccabbadbbbdacbdcadbabbcbcdadabbbbbaababadbcadbabcacddbdacbbbbacacdcacacbabacbdbbbbbcaddaadcaaacadbdbcdcdacbcbabacddadbccaaccbbcccaccbdddddccaccbdddcdcacadadaaddddabdcbddcddcdcbbbcdcdddcdcbadcbacccbacccdcbddbaddacbbbdcbddcbbbdbbadbbabdddbbdbadaddadccaacaaaabdbabcdcdcabcbbdcbdaacddcbcbcaaaadbbcdccadbbaddddbdbccddcdccbdbaadaddacdccbaaaccababdcbbdacaccabaddbcaabdaacdabdbcbadccaddcadcbdcaaccbddddadcdaaabcdcdaadaabcacbbbcdcdacadddaaddcdbddabaaabbbcbbbdcdacabaacaddbbbddbacccababbbbbcbddbacdbdaccaadbcdbccbbaaacdcaaabbbcbbcacaadbadaacabbdbaabbdccdcbbcdddaacbbcbdbbcadccabbdddcabcacadacaaddaccabbbccdbaabbbaadcabbccccbacbbccddcdcbcbaacabdcdcaacdccbdcddbcccbdcadbbbcbaabdcaabcdcbdbbdaadddbaddcdccddcbcdbaadcdcadbbadddbbddcdcccccddbabbccbddcdbabccdbcabcaaddccbdabcabcdacadacaadccbdbccbbbdabaadbcdbdddccbaaabdbcacbdccbabdcdddccadcdbdbbadcdbbabbcdbccccccababccbaadadbbdccbdaacdaabacaccabcbdcdcdbabcbabaadcbacdcaaacdcddaccbccaddbbdbcccaadbcaadaaabcdababdaaababbcbdcdbcdcacdabaaadadaaccbaacbdbadbcdadcccdbccacadbccdcbdddabdabcbddabdcdccadcdaaadddcdcdbbaacbabdaadccaccbddadbbcabccacadddccabdbcccdcacccbaccbdabbacdaccabccbbaacababcbdabcbbdbbcaccabbbabcababddacaccacdcddcadcdbdbdaacadcbadcbbabcddbbbdaaccdbbdabdddddbcaddccbbaacccddbbdabbaabbbbdaddbbabbbcbcaadddcbbacccacdcddcdbbcabcdcdbdaacdbbbbaccadcabdbcabcddaadbcdaddbcdbadbcbddbcaaccbcbaddbbddadcbbdcbbaadddbcaddbbcddccdacacddbabbcccaabcbdacbacdccadcbcddddaaaddbdccdabbcccacccbbaacdcadaaccbbdcbbacadcbdacdbacdaaadcbbbacbbccccaccaadbacadddcdcabbabcbdaacbbbbcddbaacbacbbcbabbdccbccacdcddcbabadcbcdbddbaabaadcbccabddcdbbcadcdaaccacaaddbdbbccccbcdbabcdadbdcdaaccadaadaccbacadbdbdaaacadbcdaacbbdbbdcdbddbbbdcacadadcccadaaaacdaccacabcdddbcadcbccaaccaacacdbcbaabbdbcadaaadcacacaadcdcbbcdacdccdbdadaaaabdaabadcbadaddcddbdcccdbdbababbdcaaccbddadbddcdabdbabadabddcabcbacbcdddbbcbddcccbcdbccddccdacccbdabbcacbddcdbdccbcddbcacddcdbccabbcdbbaadccbadcbbdcaccdbbabccaaaccddadccddbdbcadaccaadcbbbbcdadacddcacccabcacbcccadacbadbacbdcaabbbdcdaaaddddbaabbdaddaadccdbbbaadbadccbdcacbacdbcaabbbabdacddadddcabbaddbcaccaaabcdccaddcdaddbdadadcadbcbdaccbccbadddddabbcbcadcbdaacbccbbdabaaddbcdadabdadaacadadcdcccbcbdbbbcabdbcacabacacbadabdadcaadaccdddaaadcdcaccabdbbdccbbddddbcdcbadaacdaddababbcabadbbcdaccaabdcddadcabadcbcacacaadbbbdabbaaccbadbbaadabacacddccdbdccbbcccacdbadaaaaacbcddabbccadaaabddcabadccbaababcddcbbbcdabadadbaddbdddacacbddadbacdcddaccddabdadcbadbdabbdcaaabddacdaaccccacbddcbdaadcaabdcacdadbbddddbabbdbaadcaaadcdddbccdcbcaccdddcbaadcdbbdddbbdaaddcdbccddaabacdbcdcdaccdcccdccaddbabcbaccacaddcccabddcaddbcdcccbbcdddcdcdcdaaabdcacadaaddbccdbccdabbdaddadbaaaaaacdddcddcdbbcdcccbcaacabcdadcaccdbcbccbabbaabaccdbdbacaccadddddadaacacbddbcbdbbadccddbaadabababdbcabccccbadbdddbcbcadaaaccbbdbdddcdccbbcbddcbbdadadabccccbaaaccacadcddbbadcbabaaccddccbcaccdabdbccdbadadbbcbacbbbcdbcdcadcccbabcbcacacddaddaccaacabbbcdcbddccacdabdaacddabcccbbbadbadbcdbabccaddacbadbccbbbcbbdbcddbcacddcdddaabbddbcadaddabadbabcdcbaddbdabaadaccbdbdcdcddccbcdbdaddbcadcbcbbaddaabcacadcbdaacdbcddcdabdcabaacbdcdbbadcbacabccbdaacaaacbaabddabdaadacabbdacbadabdbbdccddccbcbaabaacddbdbadabcbcbdacdacadadcabcdcccbabcaadddddaabacadbbabacdadadddbdbddbabaccabdadabacbcdaddaabadcabcacadcacdbbccaacbbbddccacabdcabdaabdcbbaccbbccddcdbaddbcbcddcbadccdcaddcadcdccbbbdacbbddbcccacacbccdddbcdbadaccdcccabadccddbcbcaaadbacdbddaacdadadbcdccaacdbbccbbcdcadbabbcacabcacdcaacbcabdcbdbdddccbadbbbdddcaaadbdbdccdaadcdbadbcdaddbbdbdcdcbacacbcddaaacbabddaaacacbdaaaddccaaabbcdabbadcdbcdddaabdbcdcbbbacbbaadcaadacbbddbcccabdbcddcbacdadddabbbdcccbdcaaccbbabaccdcdacbcdabaabbcdcadacacddbcaaaaabcabdbccdcadaadcdccadacbcbdabbaaddbbbbcdabaddaacbdaccbdbdcdcadbabbdddbbbdbbdaaacdacbcacbacbbcbbbaaacaddaabcbbcdcdcdadacabcbdaabcbaccaacadddcacccdacddccbccadbdbdcaacbcbcbacacbbccacdddadcbabdcabcacabccaaddcbbbbbcaccbdabcdcabcbdbcdddacadbbdcdabaccdcbddadbacbaadcbbcabbdadcddbbaaabbcbaddbbdbaccbdbbbccabddaacdcaaacadbccdbbcdcbdaacbcdacdaadccbaadcdaadaacccdaddcbbccbbccabdacdbbcbdabcbabadadabdbddbcdaadbadbcaccabdbaccbabcdbbdbabbcabbbdbdbddaacdbcaddbcaaadcacaccabacbcddcdddabcdccbcbbaabcbcccddcbddddbcddabddcadaabbbdacbcabcbbaacacaddbddacdaadbddcadabcacbcabcacddbdcdbdcbbbdbaaddbbbddbbccbbabbcaabaabcccbcccbcdaddccdcdbdbabaabababaaabbcccbcacacdcdabbdcccacdacbcacadcbdddccdbddcddcbcaccaddadcccacaaadadcabdcabbaccccabadcadbbcbdcddcccbbcbaabdbbcdcccbbdccbdbacacbdbbadccaadcddddbadabacbddaaaddabcaadabaabcccadacdaabcdacaddbdaaddccaadbdcddabdabcccbddbbccdbddcabaddbbcabacbbddbcbaddcccbdbbbddbdabbbdbcacbdacaacacbadbabbcddcdbbdabbacaacabcbbaacbadacaacbaabcbabbbdacdbbaacbaabdcacbbabccddbacdcbdbcaccabadabadccbcbdbaacaaddabdadcbbbcdbdbbdcddadaadddbdabbcdaddcbdbbcacdddcddcacccdaacdaadccdcadcadbbdcbdbaccabaaddbddbabdcdbdcdddddcdaccddadabcccdcabcacddcccdbaabcadacbcdabdddbcddadadcabbbbdcbbbccacacdaaaaccdcbddbaacbcdaadcbabaadbcdbccbbaaadccbcdbcdbdacaccabcdbbdabbddbcbdaabbdbaacddcddcbaacbcaaddcbddccdbbbccaccaabcabcdbdcbbbadacbbbdbaadaabcdccadaacacdadddcbcccadbbdcbdabcbbdccadabcbbbdcabdddbcaaadcaabbaddaaaadbdbacddcbaaacbdccbccbcaaadacdbccaddccacbaddbcdbddbdcddacaddccdcdcccbbadacdcbcbcbcbdddccaddacbabbbdcbcacdbbdbdabaaabbbdbcaccbccddcabdbcccadcbcaddbbbcbbacbadcdccccbcbdcaadbcbcaddaaddadcddadcaaabbbbccaaabbccddcbabbadaabddaabdabbccddaddddacdadddabcdabbbddaaacdbdcacdadabbbdbacbbcadadcddccbacccdaaabbbddcbccbccccdadadcabbcccdbaaaccdbcabdbdbacadddaacbbaabdbcabcbacdcbcacaddbddbdcdccabcbbbcadddbcccbcbabccabbccdcadcabddacabaccaabddcdcccccbdbaddbbdcbdbdcbbbccdcbbbcaaddddcccdbbbcccbaadbdabbdadddcbdbccddddabdcdcbdccccddcbbddbacdbcabdcaadbaacacacccdcddddaaaaddbaaacbddddcaaddaaabdabcbaadcdbcbabbcbabcbcaaaacaddacbbcbcadcababcadadaacddddaadadaabcaaadcaadababdbbbabdccdddbbacabcaccccabcbccdbadaccdcaaaacdbddadcccabababdabdcbbbbcbddadaaddacccddadbcddcdbbdbaddcabccdbbaaaddcadaddcabbbcdbbbabbdbbccbbaddaabcbbabdcacbadbcababbacdaabdabdcdddddaccddbbcddacabbaaccccdabccabcccdabaabcccdbbaccdbcdccddccbadadbabbdaccddcacdadbcccccdaadbacdabcadbaababadbbbbbaccdbadcabbdcabcaadcdbaacdbbaccdacaccbabdabbabdacabddcdddadddcaadaadccdbccbbdabadcaacadacadadadabdacdccaaaaccdaadbdccabccdbccaaabccacadacabccaadccaaacbabbbdbcbacddbadddaddcbdabcbcccdcacdccdabcbdbbcaaabbaadbbabccbdacabcbacbacdbbabccdcacdcabbcaacccbcaabcdadadddbbcbddcadbbcaabbbabcbdbbaadcccadbcddbaddbdbdabdcbabbadbdbddacbcacbbdbbabacccbdbbcbbcbdcbccbabaaccabcdabbbdcadddcbadaaabcdbccbdaaadbdddddcacdcbcccdbadbbcacdccccacabcdaaaacddabbabddabbcaaacbdcabaaccbabddbcdcaabddaabdbaaddbdaddcdcdadacdbcaadcaaddbdcdbcbbcbcadbabcdcbabdbdbabbcbcadccabaaacbadbdcbccacaccbcbdbbaccbbcbbbddabcdabccdaaddcbdaabdbbdbcbcacaacddbbbdcabcaadcbdadcdcdcabdccbadbcbbdcdddacacbacadbcbcadcdbaadbcbabadcbaccdadbbaddcbdabdacbdabdcaadcdaddddbaaadcbcdababcbacbabdcdbdbcaaddabdddcccdbdddbacddcbbbadcccbbdaadaccbbcdbccabadcaacaadcbbabadaaacaadbbccbcbdcacacadccddadbdddcbdccbbbdbaaccaaddaaddbbcdacadcabbccbcbcababbdbadbabdcdcccbdbcbbbbadbdcdccbdbcbdbbdcccccbddccacabddaababbbbbccabbddacaccaacbdaadcadaadccbcbacbaabcbbacbbdbccaaddaaccdbaacdbadcabcbdcdbcbdacbcdcbbbadacbcadccbcddaacabbbaacacacdbdaaaccccddaadadcbdbcabbbddbaacdbccaaaabbcaabaadbcdcabacbbbabdabccabcddaccdcaccbccaaccacdbdbacbdbacdadaabbdbadcccadcddbcbddaabcdcadacdaddacabbdbdadccdbdddaddbbdabcacbdacaccbaadacccbaacddcddddabdbbdcddcadcdccadbaaccabccbbdbcdcbaddbdbaadbbababcccaccaacbbccadbcacbdccdabaabdccacbbdaaabcbcdbadadadbccbccdcaccddbcbdbaddcbbcdccabbaabcbccdbbdcdbabbabaadbaaaddbababcaadcbaacaaaababdadadbdbdcadbaddadbdcdadcddbdbadddbbabaacdbbaddadbbcdbdbcdddabbcddcabdbdaaabbabdbcadcbbdcccdddcacbddcdabdbabdcabbddddacddbdabdbcdbdcacaadbabddcbcdbddcdbdcdbbcdbdbcdcbdacacadacadccddadddabcacbcabaaadcbadbbcbcadadcdcadbbadadcdbbbbcdcadbcddbddaaadbccdccdbcbbadcadacdcddabbbdaacbddcbabdddabddcbbbbbcbbcbdbaacadbbbadcdbccbaaadbddcdcbdcdcdbddbdbdbbaddacddbcbbacdaaadcabbbabcbcccdcaabcdcdcaadcddabdccdcdadbcdaaadcdcddcdabbdcaaaacccaacccdabbaadcabcaacccadccbbcabddcccbbcbbddbcbbdacddcabaacdccadcbbbccccdcacbbbacbbbadddcdcdcbbaaddccabbbabacadaabcbcaabddbdabcbadaadbcdcbbaacccddabccbbabdddadbcdaabdbbbadbccdbaaaabddddacbcabbbcddcaadacbdcdaadbaabdcddccacbdbaacdddddbdabadaadcdcddbcbdcdbbcdbcdacdbccbddbaddbadaacdabacacdcbcdbcdddbbacbccdaccaacdaabbdccdacadbabbdbcccabcbcadacdbaadbdaaabcbaacbbcdbaccacdabbdaacccdabbbdacdbcbbcccbababcaacaacdbbdaddcdcddddacabdbbbbabdcccdabbabbbdadbaaadcadabbcacacbaacbdaaadadccaadabdcadabbdbabcdaacbcdaaabdcccbabdbbdbadabaddccdccaabdcbbcbbaadaccbcaaaadbcbdadadaaabaccbbdadbbbbdadbcdaacccdbdabdccdccdddadbcddbbacdadaadadbdaadbccabcbbcdacdcddaabacdbcaadbdadaaabdabbcbcdcdaabdbdbbbbaadbddacaccdaddabdcaaabddbdbbdbacdcbabbcbcdccadadaacdacbcbcbabbcccdbacabdacabdacddcbabacaddccbaccaadbaababbcbdaaccdadacbaaddbaccddcaddcacaddcdcbddddadddbdcbcdccadcbccdabdcbdddbbccccddaccabdcdcbddadcdbcdaaccdbdbdadbacdabdabddcabadccadaddcbbaadabacbbcdcbacadddcddbdcbacbbabddcdbcadbdcddccbbdcbcbaaabacddabdbaadcdbcccccdadcbcbdbabaadbcddaadabacbbcbcbdacacccdccbbbcccbdbbbaacbdbddcbdddddbccdbdaacbdbaccbaccbccadbddbadcdbdababccdbadbbacaddadaccaacbdcacbddbcccbabdbbcbccaaabccddddcdbaaacbcaccbacdaddbdcbadadadcdbdaacddbaadccbbbbcaaacabbddbabadbdccbdadbbcdaddddabcccadccdbccccbbcbabaadcdabdbadcaadcbaccccbbadbdbabbbccbdbccaccbaccdbccddbabbbcbacbcddabcbddddddddacaccddcacddcdbabbaabcbdbacadbaaadcdbbdacbbabacbbddcdaccbaadcaabaacdbaaadccdcadcabacaaddcccbddbdccdbcbddabbdccaccadcbadbcbdaccbbbdbcbdbbadcdbbddcabdcbacddcbabccbbbcacadcabccacbabbacdcacacdbdbcddccbacabdabadcbbcdcddbcbdbcaaaaaaaccaabacdbadacccdcabdacdbdadcdaccabaabcabbccdcbacbcdcbdbbcbbadddbddabdcddababbcbcdcdbbacdddbabccbbdababacabccddbccbaadadadbbdcadcaaaaccdaadcabcdcbdcadbabbcbaacbdcbbcdabbbbaaacccdadbddaadddaacbabaadddaccdbcdbbbbdcaabaccabcbcddaacabbcdbdcbaadbaaaddcabbcbccdcdbcaccaaaaaddaadccddbaaabcbcccbabcbabddaabcccbbccbaddcccaacdbbdccdabdcddbcdccbcdddadcbddcadddccaaadababacbabbcaaddbbdccbddbcabbdabdadccaddacdbbccccacdbdcaadbbcaaddbaccddccbbaabaacacdaccddccacaddaabcaacadacadaabbccdcddabdaabcdbcbbcdbbbddcbcdbbdbbbaadababdabdbabdcaccdcccbdbdcbcbaabdaadaccacbddccdddabcdcadabbbacdbbbbbabcbdabdbcdbabacdaabdbabcacddaadcbbcdcbabdabbacacababaddadacaabbabcbddcdbcbbbbdbdcbccbadbbccacbdcadaaaaaaadabbccabcbddacabcaddbbdccaaadabdbccabbdbcccabbdcdcaddbccdbdbbccbaabbcbcdaacbbddbcbbadccccdabdcabacbbaabdacdcadbcbbbddcdcddadaacdaadbccbbbcadbbcacdddcababcbbcdccdbddddabbdcdbdacddabaddabbaabdbbaacddcadabbddaddadddadaadacbddaadaccbabdddaaabacacaacbcabadcabacdbcddabdbcbacbcdbadbdabdaadbdaddbdaacdaaddadddddadacbddddaaacdcdccdccaabcaabacacdcbbaaaabcdbcbccdabcdcbcbbbcabddadacdbaaabbaacabddcaacdbcccdcaaadbddbbababaaaaccaddcabddcddaaabdbdbaabbcdddadbcacbcdacadcabbbabaccbdbbadcdbcabcbacababccabbcdbcbcdcbbaababcbddcadccacdbbbbcabaacadabcddcccbcccdbdccdcdbadddcddaaaaddcdcccdcdbbbabacdacdcddcbadcdbcdabaaadcaadcadcbbdbdaacabbcbbbdbdacdccbbbcbdcbddcdddcabbbdcbaaacabaccaacabadcbbbddbaacbbbbadcbbbcbdddcbaadddccbacdbdccccbddaccdadaddbcdbabbbcccaadaabaadaddccddbbaaaddbbccdaccbccdbcdccacbdaccbccdcaccddbbbccaccaabdcabdcbadbdaadcacddbabdcabddccdbaccacaaccaabcdadcbccbcbadcbccaabcaabcdcdacabdacbbbcaabccccbcabccacdddbaddaabdbcdacbcbaaddcdacbddddbbcbaaddaccccdadcacaabcacbdbbabbbcbbdbddbddaaccdadbdbcbcdbaddcdcddabcadbbacabbbaccdbddadddcdccaacdbcccccdddbcaabdaabddbbdcabddbddbbcccdcdaaccbddadddcacbccddcaddbdbadcaccccbbbddccbcbbdddddddaccbdbbcbdcccdcabbcbdcbcaacdbcdcddbcaadaccdddabacccddbacbbdddbcadcbdbccddccaabcdbacacbdccbbcbbdcacabaabcbacaabbcbcccacddbbccaabccabbadaabdbdbbadccdaaabaaddddbdcbbbabdbcdbadaabcccdcdcadcddabaddaaccbcccdcbaaccdabccdbbbdacddbdcdcbdddabdaacbbbcaadbaddbacdcaddbdaadacdbccddbbbbdcaccccaccccccbaabcdbdaccdddbcbbbccabdaabaacadcdbbcbcbdcccdcdbcdccdcddddbcadcdacdaaacdcaacdbadddddcdababbdacabacdabdacdccbabcdcbaabaacaddbcaaabbbadbbbadaccbcdddcaababccdbcabdcddcbbbacccabaacadccbadcbdccbddabbadacdbabbcbbcaacbaabaccbdbdbacdabdadbabcaaddccccddacbbbbdccbcdacbdacbcdaddbabdaaaccadcadddcaccabdacdcdcbcaccbddcddcaddadbcdaabccbdacbcbddacababdadcbddddacbabbaaaaddacaabaccdddddabccbaaaccbcabcdadbbdadcabadccadbbaabbbddadcbbadcbabaadaddcaacaacadcbdbccbccccddbbaccaddbddaaaabbbbdaaadadbadaadbcbcddcdbcbacbdcccadccbcdaccbdddadbbbbacabdcbbccaadccaacbbabacabaadbdabdadacbccacbdddcdcccadbbabbcccadcbddcabddddbcccaadbcdbbcbaddbcdcadbbccadadaacccaaccbcddddaabbacdabaaabbdabbbbdcbaccbadcdcdcacbcaacddbdabdabddaabdcbbacababadabcdabccbccdcdccaaacbcdcdbdbbdddcaabbdcbdacabcadaadbbbadbcbaacdbadbaaddbabccbcaaccbccdbbccaddbaaabbbabaadabddcdbccbcaadbacccdddbbcbcbbbbbdcaccccdddcbbaacabaccbbbbbaaddcbdacaababaacaacbcdbbaddcadccbbdbcddabadddcaccddadcbbdddabababdcdacadcccabccbcdcbcaddcdbbdbadbcbddaacddbcdccaaadadcbbcdbddddabcacbddddddcabcbccbdddbdbcabacadacbcbcbcbcadccddbbdcdddcdababcaaddcaaaaccccbcccaabbbdaaacccdbdbaaacacbcbbcccdcaaacdabcdbcbbdcdaccdbabcbaaacbacbacdacbaddddaaabbdabacabddcdaddadccdbdccdaaaccccddacdcaaabbabccdbbcdaadbcabccbcdccabccaacadcadbbdbbdccbcbdbcbbabdcbacbbcdcadbaaddbdbdacdcbccbbabdcdabaaacabaddbbaddccbcbbdcdabddcbbcadaddacdbbbbbbcabbdcdcaadcbabccdcccaadcbbdcbbadcbdbddaddaaabbcdbbbbdabdbabcbcccbbcccacccdaaabddbcacaddbccdaaabdcadbddacbddbbbcadaddcbddacabddddcaddaaabdaaabaaddcbadabccdadabacbddaadbddbddbccacbaabbddcdcbccbcbdbabaaacbbcbdbddbdbaccbbbaacbadddbbbacaabdcdcabdbdcdbdccbdcdcadbcbcbbcdaaadcdcaacbcaccbaadbcaccaaabbcbdccdaccabcbabcaccddcbdcccddcaadbabaadacbbdbcdcbaaddbabbdbbbbdbcdabddbbdadaacbcbbabdacababcccbdccccbbdaabcaddabdacbbbdcadacbaacdcdbaadcbccccdacacddacdacbadbbcbaaacbdcadddcacbddbddcaadbaadaccdcbcbabdbcabccddbaddbbddccaddbdbbbcdbacdbbdbbdacaccaaaaadddddaadcdcbabdacbdbbbadcbbaaaababbcbdcdccabcbddccdcccacbadadacbddbcacdbadddacaaadaccccddadbababaadacaaabdbbcabcbddbaddcccbbcdcdbcbabcdadabdaabcbddaabadaabcccbadcbcdacccbadcbbcddadadddabadddabddadaacaddadcabcddbabbdabdccbacabacadbdcadcbbabbdbbacddcbdcbbabcbcacbcaaacdadadabaaadbacbdccdbdaabadaacccdababbddddadbccddacccccabbcadaabdcbabdcacccdabbcabccaddadcbbbadaabbbcbddbcdddbbdbabdcadbaacbbcddbdcddcacaaaddccdddbbcabdabaaccbbdcabddccccccdabbcadadbdbacdcdccacdccddcabbdcddabacdbcbacbaaabbbcabbaccbddcddabcccbacabbcbcbbdaabddabcadbbbddadccbbaabccacacaccdcbbadddbdcdacadccaaadbbbaccadbcdddbaccdaaccbaccddccbbbcbabcaddadabadcdccdcdabdaaddcdcccbcbccadaabbdccbaabcabbbcaabbbbdbadbcbdbacbdccdaddbbaddbbbcbabcccbabbcbaaadcbbbbcdcdddcdadcbcbddcccbacdbaaabdcbadcbcacabbbbcccbacdccddbccbabacadadaabcddabccadabaddabddddacdcccbaddcbdaabababcbdaaabcbdadddcadcccabcdaaaaabdadbcccbcbdcdccadbcadacdbabcbbdbdbaacbdbbcdacadadacbbadcdbbbabaacaacdcabadcdbdcacdbcdcaadbaaaadcabbdcaaabbaaacdcadcdabccddccbccabababddadcabbdbaacacbcabadadaacccdbcbdbadabccdbcdbcadcdbdaabadadcadcaacccaacbbbbdccacaacbccdabcadcbdaaddddadbabbbaaadccaabcddbbacbbdcdbdabadcdadcccdabcdaabbbbcacbcbaaabbbdcadbbbaaadadbccdaaddbdaabdbccabdddbbcabbabbcdbdcacddbdcdbccbacbbcdcdcbdababbbcddaabdbdddadbcdccaacbddaddccbcdcbbbbabaddddbdacadbddbdacccbbbbdcdcbcaaabcddaabbdbddadcadddacbbcdbbcaabadbbcdcdbcbddcddcbdcbdbddcbccdbadcadcabdbdbcbbdbbcbcadcdbcbcadbbbaccaaadbdbcbcdbcabacddabbbabbdcbaaabdcdabadacbdbaaaddcbacdcbcdbbcaddaacadcddacbcaccaaabcadcbcdbcdaabacaaccaaacbddddadaadcdbbdddbccabaabcccdddbddbcaaacaaccaaddaabaddbaddadadacadcddabbdcbbdbbcdcbadaccdddcbbbcabbadbabbcbccdadccbabbdbcacdbcbcdbbbccdcccdacbdcbdaacdaacddabaddcaabbadadcaccdbabcbdbbcbbbabaccccbcbcacbdabadacbbcdadcdcdcddccadddbaddbacdcdbdaaaaadcbbcadbabacabaacccbbacddbcbdcbabdbddabdddcccdbbccddcaaadbdbbdacadddbabcaccdbbdcadccbadaadaacbcddcddabcdccdadacccdabddbbadcdacbbcaccddccacbddadcaccbabdddbabbdbdaadabdacdddbadbbadacccbadacabbcacdaaddcbbcdacbabbcacdabddccbbbcaadccbdcacaadbcaaabdcccbcdcaacdcdbcaacbaadcbccbdbcccacdcbcddacdbccbbbbabcaabaaaaaabadcaaccdcdaddbdccabbbdbdbcdabacdccbcbbacddabadccadcbcbdbbabbbdbabbcadbbcabcacadbaacaccacbcbcacdabadabcaabadaccbccdaaabcdcdcbdbbbdcbcccadccbaddcabbcaccadbaccacdabbbbcaaddcdcdcbadcaabdaddccadcaaccbaadabbbdbbbdabcddcbaddaccdaaabcbaccabcddaccbbdccbccdabddcbdabadadaaabbbaaccababdbdaccaaabdcccbabcdaadaabbcbdccdbbadcccabdadadddbcabbcdaaddbddcaaddaddcadcabadbbaadbccbacbaabddbddcbbddadbbdddabbcbacdcbccbdbcbdccdcdbbcabcbcdddacdaadcdbaaacbacbadaaccbdcbadabcbbbbacadacacadbdadbacdaadaadcdbcdddbdcddbbdabbddaabbdccdccbbdbbadaadaacbbcdcbdddbccaccccdbcbadabbaccadccdabbabaabaacaacddadadbbdaabdcbacdcaadbccbccccbcdabcccaddcbbaccbdaccbacdcddcbbccacdacaddbbdcbbbaccdcbcadccdbadcddcbadacddddccccdadbadaaaaababdcaaccdbdddbdacabaccdbbdcacbbdacccbdbbdccbddcaadcadcbddccaadbbdabddddbabbbabcdacaacbbddcbdabdbdbddaaaccadadbabdaadcccadabadbcdbdddcabddddaddadbbdbddcacdaaadbcbcccadacadcdbccdcccbbddbacbcccabacaadbdcdcbdddccbcddababddcbabdcdddcbbdcbbbdacbbbcabaaabdcddbaddbaabbaacaccbdbadacccaaabbcaadcccdbcdcaadcaaabacddcbccdaacbcaadcbaccdbbabccaabbbdbcbbbcbcccbaddcdcabcbbdbaadabcaddbccdabdbbbbdbcabcaadadacccbaacdaabdcaacbccccbaccdbbadcdadcadbbddadbaaaddcdadcaacddccccbdddabcbdaccdaababaadbbddcbcbbbaacbabccacbcdabbbddbcdbdbddadddcdcbcadbbbacbabcdbbdcacddcdaadcdbdaabbadbcdcccabcdaabbbddadddacbabcbbcababcdaaaccbdccdabcaaacdbddaadaaddacbbacbbbdddbdaaaadaaabdbcadcaccdccabadcababbddcaabcbbadaddbccacbaacdaaadddccccddccccabdbbcadbdbcddaabdabcddacadcaaabbbbaaabdcbbbcdcccadbccbbcacaaabdabcbccbacaaddabacaabddcbbcddbaadcdcbacddcaaadbdadbddbabaadbabcbbddbbdbdcaacbdddbbaadddaabddddcadddabcacbcbcaabcacadcddddddbacadbbcccbbdbadbadccbdcbbaddbcbcccdadacdaaccbbccacdcdbaaaaddaadcadcbccdbdcccbdcdbbcadaadddbbacdcdbbbcccadcabaddacadbccccdbddabaababbdbdccadadbcbdabcbacadabbabcbaabccdcccbaddbadbcbcddcacadddabaaabdabbcbcbbccbcbcacbbcabdbbabccabaccdcadabcaadcbacdddccaabdcabbcacadaadddcbcadbbaacbcabbdbaccbcdcdbbcdbddcccaddabbbcbdbabaabdccbcdbcbddcabdcbdccdbcacadadadbddadbaddbdbdaaacacbabbcbcbdadcaddbdbcdbaacccbbbbdacaaadadccdccdadaaadabcaaacaddabdcadaabddcbbadbaabccbabdbadddadccacbbdbadcdaccddaacbbccaccccbaddaadbccaaadcddbdddabbccabadbaccbadbdadbdcdabcbadbccdbddacdaccbadbdddadccccccabbdbcdcdbcccacaccabbcbdbcbcbddddbacbbcaadcbdcdaccdacabdadcabaadcdadcbdbbdbdbaadccbbbccacbcabcdbbbdbacacdadcdaccdbbbcabcddabbabcdcbbcbbcccbcbbdbccabccabbbadcacaadccbbbcdcbacabcdaabacdbaabccbdcacbdbdbbbccaddabacdbaccbdcadccaabbacbaabdbbbababddcbcbababaddddcbcbbcbbbdacbcacdadcaccabcdccbdbcbbbbaaabcdcddadbdcbacbcbddadbbdcdbbbbccdcbbacabbbaddacbbbcddcabaacabadbbcaaacbaaabbccbcbabbadcbbcdabccddcbcbcdcabadddcbabcdcabbbddcaadbbbcaabaccabbbddcbbbbddcbdcdaacbaadbbdcaccbbcddaccbdbadbccdcbdcbbdbdbabddcbacacbbadccbaadaadcbdbcadddcadbbdacbacdcaddbbaddaaddccaddcdbcabddaaacdbbdcddaaadaddaadbabbbbdadcdbdbbbadddbbbabaaaccbdbdcdcadcacbccdabbbbadbddadaddaacddcabacbbdadbbdcacadbbcdcabcdcbcbbcbabdccaccdbddaccacbbdcdadadbdacdacadaaddcddacbdaacbdbbaacbbaddcbdcbbdadbabaabbaadbbdbbbddadacadccaadcbbdadabcbbbdbbabcbbccdcbdbdbdbbdaadcbbdccccdbdaddcabbacbcaaacacacbdbbbaaaddbaacbacbbbdbcababaccccabddbddbdbbaaaaccaaaaaaadadbdddacdbbadcaccdadaddccaaaabcdcbdabdaabcaaaacddccbdcacdddcacadaccadbaddacacadbabaaabdbbcbdbbbdcbabcaacaddaccccdcaaaccddbddccbbddbcccadbdccbdacacabcbcadbacbbbabcbdbdddadddcaccaaadcbababddacccbbacaaabccdcccdbcbdaabdaabdabdabbdccbccabaabdccddacdbcbcabbbdbcaacdbbddcbbccbcdabcaaadbacddcacdccddcbcdbcdcabddccaddacbdddbadbadbdbdacbbbcccdbddccdbacdaabcacadabccdcdcdacdbcdcdaadbbccdddbbdbdabddcadacbbaacaccaacccabbabadcaccdacddadddaabbcaadcddcaadccacaccabcbbbbbcaccdacdbdbcabbbccaaadbdddadcaabadccabdcabadacbcaabccacadabcdcacbbdbddaabdddbbadcacbbbcbccbbaaaaccbabbbabbcccdacddccdbbcccdccbcdddcacaabbbdadbcaaccabcdccbcddddccdbddbcabbcdbcddccdcdcaaababcababbbcbccacccbccadcccbbcbaabbaaaccacbbccdbcccddccabdbbdbbaddabdbddacdbcbccacdcacbacdbbcacdcdbdaccadabccdbdcbcdabbadcadddddcdddaabcbdacbddcddadbbaccbbbccbdddaacdbcadabbabcbdddadbdacbccddacaaadbacccaaabbdadcabaddbbaccdcbbccdbdcadccacaacddbddaadbcbbcdbcddcadbbaddadddbcbccaddcbbaadbbadcbcbcbcbcaaccccadbcdcdabadaddbabbddbbbbbabdcabbadcdbdcaaacbdbbdbadaaddbabcababcddaadbdddccabccdbdcbdbcdccaacdcabdcccccacaccadbcccbabdcbcbaacccbbacccaddbbcdcdadcbddccbdddcdacadaacccaccbdbcbccdacbaaccdbbdccddccddaddcaddbbdaacbacdbbaaccdbdcbddacabacabbcdcbbcddccadbbabcdcccccdddcbbccddbaabcaadbcbbcdabaadccaabaddcaabdcbacdbddbabbcdddbbdcaacadccbacbdbbcdbcdbdccbcdccdcbddaabaabacaaccbccdcacbbbbcddaddcdcbbabcababddbbbddabbaaaadcdaacabbbbbabdacaacbadacadddadcbcdcddacbdaddbacaccddaabdacdcabacccadabdbdccacbadbcddbbcdbbbbadadddaddbccbbccbdbdadcddccbbcbbbdadaaddcaaaacbabacbdabbcbbacacbbabbdcdbbbcbabccaaadbacbbdabadddbcacccdddcdacbbcdadccdbdbdbdaadbacbaccbdcdbbbcbbcbacbdcbadbddbdbccddacdcccadaabdadaacccaacbbbcddcdccccccacaacaadcddcbacaadaabbbbbdaddbbddccacdabbcaccbccddddcbbcdadaadbdabbcbaccadaddcdabcdcdbbaccbddcbbcabaddadbcbadbbacccbbbdcaaacccbacacdddabdbdabddaaccccacbdadaddbcdadbbaccbcbdaabcbacdbbddabcbbabcdabacbaaacaaaadcadacdbabcbabcbaadbdaccaabdaacababbdaaaacabbcaadacccadbccbddabcaaccbacbaadbdbbbcabaaadcbccadacccddbadbcddacdcdcadcaccbaaccbadadbbaccbdabcacccdccbabdbaddabdbddcbaaddcbaabddaccbbbdbbbbbaacadadaaacadadccbcacdacdaacadddccacaabbaacabaaabcdbbccdbcbaddcaacabbcbacbdbddcdbababbbcbaadbbdbdadabbbbabbdadcdadcaabbabaddabacbdbcbbccaccacdccccdbacaacbcbbbacbccbbbcbadddddaabcddcdccdaabbacadbabdbaaadaacadcdcbaadbaaacaadcabaccbdbacbbaddbccbddcccdcdadacbddbccdcddaabbdbaaaacdcddcbbddbccdaddabdcdaacadccacdabdbbccdbbbbbbcbddcccabaddbdcbdaddabbaadcdcdbcadaaacaccabdddabdbaabbccddaaddadbabbbabdadaabcabcdbcacbbccacbbcddcbaadabcdaacacccccdcbcaacaddacaababccbdaabacbbbbddbdbabcbdacdbcccccdaddcdcdaaaccaddbdaaaaaadaaccadacaddccccdacabcbaacdcadadcabbdddbacdbabaddccaadcdccdbbaccacdadbadacbdcdcbaabcdbbdabcbcdcdbaddbbabbbcccddabcaacbcadadbbbcdabbdbadbadbcaddbcabcaacdcbabbadbcbbdbaabdccacdccccadddbaadbdadccddbddbdacdaadbaaaacdddcdcddbcbbcbaccacdccdcdcbabbbcdcdbbaaccdcaaccddcdcabacbbbbcdccdcababbacbcbcacdacaabbcadadbcddacccaccdaccddababdababbbaccbdaddaddaddacdbadbcaccdbdacdbdddccaadddcdccacbbaaaabcdddbabbacbcdbdbcbaaccacccccbddddaaccabddcbcdcaccacdccbdbcaadbaacdcbccccbacbcdabbdabbcdbcbcdbaddcacabdcabddacdaaadabaccdbadddadaabcabaadbcdbaddcaadddaccbaadcaddbdbbaaadbcdcdccbadabbdbadaaaaabcabdbdcaaaccddbdbdbbbbabbcbdbcaadcacbcdbdbcaabbcbabccccacddbbdccdaaccaccadddddabddbcbdaabaacabcbdacacbdacdcbddbcdcbaabbdddbccaddcbbacbddacdbaaaddcadbdaddccbbdcccbdacadccababbccbbabbccdbcadaacbcadbbabdbadcaccdbbdaabbdcdbdbccbcddccbbdaabdcdcaddabcabaddcbabcbdcbaddbdcbbacdadacbababdacbcdcbdcadddccbcdacddcddddcabcbdcabbacdbcdadaaddbadbbcddaacadacbccbadbccddbadbbbbcabdccaddcdddcdccaaacabccacccbdcdabaccbaddbdcadadbadbbbabdbdcadccaabcaabdabaababbccddccbacbccbccacbbbcbdccdabcaaccacacacacabbbccdaaddccbdcbbccdcdbbdcdacdcaabcbbbdaaccdddaaacccdaaaccdabacabaddcabcbcdbdbbbdbbbdbaccccaaaaadddddcdbcbcaaabaccdcdbcabaacdbccacbcbaadcaacdcbbdbbadabbcaddbcbbdaddaccbbcbdacadaccbbddabdadabccbdbcabbaddbccabdcbaaccccbadcccbddbadbddaddcaadbcdbdcaadbabadbacacbdbbccadaaaaccdacabdbccbacaadbadccabbddddcccddbccbbabbadcdacbcdadacccddccadadadabdaadacdbabbdbabbddacbabbacbacccbbcabbcbaaaaacccddddcaaaddbddbacbcbbaaaaccaaacadcbacbddbdcddcddcbddacbddbbdacdacacbcaccbcbbacaaabccbabbcbbdcdcaccbddbddacdbabbadbadbadbddaaaadcabbacbdbcccabddcddbbadbcddadcbddcbbabdddcdacabddbbccdbbbdacbadcdacdabdabdbdcbbbdacbbbaaddcbcccbdcbdbaabadaccbbbdabddbdcbddacdcbccddbcadbcdaaabbabdaddbdabcacbdbdddccbcdddadddaaadddddadbcaacadbababcbcccddbacdbcabddbdccbacacbaacabacbcbaadabdadbcbdbadbbddcdbccbadbcaabaacaacbdcabdbdbcabcdaacadcccbaadcdbbdbbcadaaaddbbaacadbcaadccbcabdddbccddcbccbdcdbccbbbccdaaddabbcbaacbdadbcddcadcbaadbbaaadddacbbadabaccacdcbcaddcbcddabbdbacbbaccbbccbdaacdccbddccbbddaccdacbaaadacdcdbcdbdadacacbccdcaaabdababaaaabddbacdcdaaadbadccdbbabaccdccdacddbdddddddadacaabcdccbadcbcbcdbcadaaddaabdcdccbdcbccdccaaaddbbcbbaacadcdcbcbbdbbccadbdbcabdcbbacabcccabacaccaaaaadacacdaaacadccdcabcaaddbdaccabcccbaabbdcdbbdcbacdbadbccbacdbdbcadbbcdbbdcbabbbacdcbbcbdadbcabdcdbdadabbcdcbcbdbccababbbcddcddcacaacdbddaddbacaabadcabadcddddcdddccbccbbccbcabddaddabbaaccbddadbcdbacbccbacacdbaadbcbbcabcccabcaabdadccbdbddadaaaddccbcaaadcdaaabdacbdcabacacdadcacdddcdadacababcbddbcdcddacdabcdddcdcbbdbccbdcabbdaabdbdddaccbaaddcaadbbcddcbdddaaabdaccbdcbccddcccdccbbabbcadadaddddadabdbadbccddabbcdaddddcacbcccdbccaababcddbcdabdabdbdbcaadcdaddadccaabcddbcccbdbbbdccbcdabbcdcaabcdbbdacacbbbcdbaadcdbbdaadccddadcccdbdadcbcabacadaacbdccaaccabdccadcbdabcdcabdcbcdccabcadccbbdacdacaabddadbdbcaabbdabaaabcbbdadadadabaacabccbbabadbdddbaabaaacaaacbcbbadcadcdcdcabbbddaaabbcbddaaacddbcddbaddabbbcbccdcdacdccdacadadaaddcadbabdaccaccabcbcbdcabdcadacbdccbabdddccdbdbaccdbbcabccacbbdbddcabddbccdcdcddbbdabdaabbddadbddbaabacbabbbaadcbacaadacdabbbdadbbbacbbcbddbacbaadbcbcbdddbcaadbbaabadcdbddabcabbccacbcaaabcacadadcaacddbaccbabdbaccddcaddcdcadaccbbacdbcaabacdcbcaadccdcbdacddcdbadcbddcaadccdaddbababaaaaccdabbacbcbbcdaacddddbbdcddccbacadddacacbbdbbabdadacbbdbbcacdabbabbbcaabaabdccdcdadaaddabbcabbcbabdbdabccccbbcddcaccdbaccabccccdcaadabacdbbacaaadbcaddcbbbcdbdbbbcacdadcabbbbdcdcaabaaaddaddacdbccdcacdbbbccadccdcbcbcbdaabaabbdbabadaddadbcdaccacdddcddbabdbbcabbaaaccbdcbbdbaaccbacbadcccddcbcbcdbbccccaadbcdddcbabcaddbcccdadbddadcbbcbcdbcddccbbdbbcbcbbaaddcbbddcbabbbaddababaacabacbacbddadacabdbdbbcdbadcbbabccccddcacdcadccccdadbcaccbaccdabbdcbccdbcdbdbaadbcadcabbbcbdcaacbbbbcadaaddbaaabbdbbddadccdcbcacdddaaacdaabccdabacbcbccabdddbdcdcdcaacdccabaaccaabbcccbaddcbdbcaabbdacccaddbdbbccbcaaacbabbbacbcbddaddbcddcddabaadbdaacddbdbddbdbbdaddaabdbadaababdddcaaacaabcbacddbddadaaaabcadbbbcabbddbbaabbcdcacacbdabcaabdaabbbddcccdbcdcddcaadaccbdababdccbbcddbaccacacabcbadccdccbbcddbbabccddabdcbaaadddcbaaacbdbcaaacbaacaaddacacbcdbcdbbbdbcccadbdcbacbbbcaddbaaaabcdababddadbdddbcdcbcbbdaaddaddbcdddababdbcdccbccbbcbdabbdbadcabcdbadadcbbcbadcddbacddaadcacbabbbdccbdddcbcbaababccdbaabaccdcddaccaabccccacbcbdbcaccabbaccabcbcbdaadadaabbdbdaccdcaacccbacbbacdbdadbcbbbbcabcccdddadddaccaddbcbadccbcbabbbcbbcccddcbcbdbbaaaddaadbdccdddadbaabdaddcbccaddabbabacbdcdaaaccdcbdcbcaccaaddabdaaadcadacdccccbbdddacbcabdbddcccbcddadcbbcbdaaadcbcdcbaaacdbbdadcdaccbbcdcadcccacbbdbbccabbdaadaccccbacaaadababbccadbcdccaaaacaacdaccddcbcbaddccabcdadaddbbbcbbddbcbdbdbbcbbbadddcbcabdcaadccacaaddccbcaaadbddbbdbaaadcbccabaadcbdbaadbbaabacbacbbdadccdcaaaadbbbccbbdcdbdccbbccaabdbdaaaaacdcaadddbcdccbbcbacdcbadbcbbbbbcccaaccdbbcaaacabadbbcccdacccbbcdccdbbcbcbbdbdcdabcababbbaaacbccbaccddccddaacaddabaadcadcabbdccacdbbabcaaabbbbbbcadaccbbabbccabcddbaabacbaabccaadcddbccddcccdaabdbcdbcdabddbadacadbddcaccdcadaddcdcadacdacdbcbdabbbaacaabdbbaadcddbddabbdcaddaaddadaccccbabbdbbcbdddcababaadbadcbbbaaabcdcbdbbdbbcbbaddadaabacbddbdcbbabddadbddddbaabbcaacbcccbccaacdbacccdcabbbdabcddcbacdcadabadcbadcadadcbcdcadbabcdbdddbaacacddcadbaddbcdcaaaadaaabbdaabaaddcdbdccccbcacdadaccabbbcbcaacbcabbcccbdbabcaccbdcdcabdddacacdabcddccdadabdadaabbcbddccabdcababbbabcabbaacaacbdbccbdbdcaabdcabcdaccdbcadccbcacaadbadcccacbcdadcadacabbcaccdbcaaccbcaacdbbabccdbcdcadaadaaccabcadbbaadbddbdccdddabbcbaaccbadcdbdcbaadbbddccbbbcadddbadcdbcabbdbcadcbabcabdbcaabdcccacdcabdbcadbdbccababccddbddcdaacdbdbbdccabcddcccdabdcdccaacccdddbcadbadadccbabcdbbabdbdcdcbcbdaaacdaadddbdbbaaaaadcabdacddddadaddcddcaaccaddbacacaadcbcbcdbdcdcddccddadcbddacddcaadcaadcccbbcdaddcbdaaddcddccadcdddabbccbddabbcabadaaccdaddbcdaacaacbdccdbabbaaabbcddcaabacdbbbdbbcaaddddbddcacaabadccdcbaadcbcdcdcaaddbcabdbbacaacddabcabbacbccaaabaccaadcabbcbadaddaddcddcbbacabbccacbdbdbdacdbcbcadbbaaacaddbcdbcadaabadadccdcabdabbcadaabdddcadabbdaabcdadbdaadcdadccaacabbabcbcdcbbadddaaddbcbadccaccacddacababacbabbcdcbcbdddcabbcacdbddcbabbcaaadcbcbcdbbdddabddadaccbcadcdacdaccbbdacddcbcdabcbdddbabdddaaaaddbabcbbdbdcadcdccbccccbcbcbdadaabdcbdbcbdacddacbbccadddbbacaaacccdbababccadacbcaacaacabddcbddbbbdbcddcbacdcacddbaabccddccbbbadaccaabcabcabccababdbddcdbacabddcddcdbbabcadddbdacbcdcababbaaccdcaaadddcdadcbbcdccbccaaacdcbacadbcccbacbccadcaddbddaaccabaccadccdbdbabccadbddcdcccaaabbdddadbbacbbbcdaaccccacdcadddadbbabccdbddaddbdcbcbbccbdcbbdbcdbbdcaaaacaaaacddcbaaddbaabbccccdbbbaabbbbccccadbdaccabbddccabdacbabccaabbdbbdaccbdddcabddcdacacbccabdadabcaddbcbbdccdabaabcaabcabdaabbbabccbaaaacaadcccbbbcbcbdddddadadaddcacbcdbcaddabbadcadcadbcdbaccdacdcabdbbdaaccabdcdddadabbdbcccdacdbdaacaaccdadbaadadaaabcacaddbdbdbcadaacadccddbcacdccddddddacdaaaabbdddcdcdcdaacdaaccabbbcbdcabdacbdabdcdaddacbbddcabaadbabccdcdccabdbaacbaabdaabbbacdadcbccabcddaadabadbccacddabaccabdaddaabbdbbbcdababbacccabbbbdccaaaccdaabbdabdbcbcbcbbbbcaccbadacccdbcbcccacdddccabdcabcdbbcbdbcadacacbacabddbacbcdcdabcaddbcbbcbbcccddbccdcadbccccdadbbccaaadbbdaabdccdddacabacbbddddcaacdccbaaccccaacdccbaacdaddbddbcccbbdcbdadaccdcbdcdcadddcccccccbbdbadddccdaabdbbdcaabcabbccbdaccddaccddaaaddadacbbdacdabacdcaddabcbaccccacdddcdabbcbbbcadcbdbcabadaccdcadddcabacaacacbccabaabdbabcbdacbcbcbaddcabbabbadabaccccbcdddcdcbdccdbaccaabddaadababbcdabdcadcabbdddbaadddbccdbadaadccccaacacdbcdaadacdbdbddcdaaddaddaabbcdcaacdadacdcdaacbdaadacbbdbcbbbdadaadbbccaacdbbdbbbbbcadbbdcdccadacadbcccddbcdabadbcddddccbccaadccaccdaabdccdbcbbbdccadabccdaabacdbaacbacdabcbaccbcbbdbbaadbdbaccdbbccbddbacadabcccaddddabdaacaabddddadddadbcbaddabadccacbdabadcaddbcccbbbdaddccbadcdcabddbabaacdbddbcadaacbdcbbbcbbbaabcdbdacbdcbcdbdaadaddcbabbacabdddadbbbaadddccaaaabacddcdcababcbaccccdcdabccbabaacaccabaadadbdcdbddaddcddccdcdacacbbcdbbbbbadbdccadbcabcabdaabaabadccbaaaccddbbcbdabcccdccdcbbdbadcbcadacccdcdccdbaabdcadaaabcaabadcbbccccdbabaabaaccdddbaacbccbdcaaacbabbadadbdaaaccddacbccdcacababccaabaddcbcdabbbdcbcbaacbbbaadcbddacddadacbaacbadbbdbbcadaaabcabbdcaccdbcadcdcdbbbdabdadcbcdcadabacddbdbbbbdcccaaadbdbaddacdbabbccdaaccbccaadabdcadddcddacbdacbccaadbdbcddadcaaabdbddacbcdbacdbdabbdbdcdbbaaabacbcdbabadacadcdbdbdcddcbcbdcaaccdbacaabbbcddcbdabbddddbbdcaaacabdcabdccddabdcbcaababbbdaacdcbbddbcdababdbdcccabcdddbdcdcaacccdbaccaadacbbccacabaadcbbdcacdcabaddbbcbacabbbdccaaaddddcddbcabbcaabdacacccbdabcdcdcacccbcdbabaddacdaaaaabaccdaddcaaddcabcdabdaadbcdbbccddcbdbadcdaddddaccbbdabbbdcbbcbdacddabbdddccaddaaaabcbbcaadcadacdadcaaccddcbdbaadbbcddaacddabbabbcaccbabacdcbcbccbacbddbbdadaaacdccbccadacbaadbacaaccbdccccaabbbcacaadadadbcbcbabcdaaaababbcdadbdabdccdaaadccbabbdbdcadddcbddbbaddbbdcdbcbbadddbbdcbacbacdbaabcbddbbcaadaaabbaacabaacbbddadcbbcbdcdacabcacadddcccaddabbbbdcdabbccbcadbbaabaabbcababdbcdabbdbbcadadabdabcabdcabccbadaccabddddadbdcddadcdbcdacaddbdcccddccbabadbacdabbadbbabbaccdbcbddbcbbaadbdcaabdaddcbadddaaccbadcbcdaaabbbbdaacacabacdbbbdbaaaacbbbcdbbdddbcbadddddddbdddddaaaccbdcaacbcbbdaccadcddddacbaacdcadaadbdbadaacabadadbccadbccbbdcbcdabaaccddcbcbbddddacccbbccddbccaadcbacbdbcbbbdddabaaabdcccdacadddccabbddddadbcabdaaddbbbbccabdbbcadbccbcddbcdbbbabbdcacabcdbaaacccddaadaadacbdbaddbddccbaabddbdcbcbacbdbbaabbbbbdcacdcdacaaabbaadbdbcbccdbcacbbaacbcdabdbaaaadbbbabccbbbbdbcaadbdcccbddbbbabbbabddbbbabaacdacdacdbdbcbccadaddbdccddaacaddaadbcddcccdccccbaabdcbcbbdabdcaadcadcaaccdaadcabccbddcbddabdddcdcddaacbcdacaccbddcbabddabaaaacaaddabcaabbaacaacbdacbadbcaddbcdcdcbbdccabaaadbcddbcdbccadabbadcaaddacbcacbbaaddcccaaabdbacdbdcccbcbcbcacbadbbccbccbcaabbcbddbabdbdcbdcabcabdacbdacccbdbbbccccadcdabbbbdcbabdadddbadabadabaacdcddabdadbbcbdabcdaacdcdacadccaaccccaabadadcbddbdadcdbdcaaaddcbcaaacbdbcbcdcdbcbcbbdadcbcddcdcdcdbbdadbbcccdcabcddbbaadacdacadbcdcbccbbcdddbcdbdbacacdbccabbabcadadacabdbccdacdacdbcdcbadcadcbadccbddbbcccbcdcadbacddbcbacdccbbacaccadbacaddadbbbddaaadaaaadadaacbdcccbcbabadcabbbcabccbccabbcaddcabaabccadadaacbaccdcbbaaddbabdbdcadbbddbddabcdcbaccdababbbcddacbbcdcbaadacddbdddcdbaadbaaadbccacdbdccbcbaadabccdcadadccbababdcabbbbadccbdbbbaaaccddbbaadaaabbdaaaadccbdaacacdbbdbabcacabdcddbdaaabdbdabcbdaccdbbbaabadaddccbcdadaddaaccbcdaacbccdbdadddcaccdaaccbcdcdcdcbbaadbbbcbbacbabaccdabccdbcdbacacdddbcbcdbbcbaacbdbddbaccdbdcdaddaabdabdaadddaadaaabcacddabdadccbaaddbdbbbcddbbcdadbdabddddcbcacbbadcdddaadccdccddddaabcbacdcdadabbaadaabbbadbbddddccbbdbbbacbccbaacccbcabdcddadabdcbabccabbaaccddcaaabcbdcbadaddbbababbddccbbccadccbaacbbbdacbcbadddabcbbcddbcdacadacdacccbdcbbacdcadaabdcdbbbddaddabacaaaaddbaccaaabaacdaabdccbdabaacacaaddbacddccadcdcccccbadbcdbccbbaaaccabbadcbdbcdbacacabdcccbcadaacacbacdcabbbbddcacdaacbcaaaabaadacaddbdbbccbbbdabadadbaadbddbcdccaaaaabdcbccaddbdcdaaacabbaacdabadacdccdbadcbcbbccccaabadacbcbddadcbabacadbdccdccababdabacdcacdaddbbadcadcbbdabccabadcbbbbbcbaddbddaddacbabacadbbaacbddbacaadddaccdcccbacbdaaacbabadbbaaabbaaadbbcacabacbdcdaadabacbddcbcbcabddaaaddbdddbcabdbdabadaaccbaadbdcabdbcbaabcacbadcaddbccbbdcaaccbbacddadaaabadccbdaabbbbadcbcbbcabcddbddddbacbbdadcaabcacdabacacccbbcaaabadcdadaadbdadcdabbacabcaadbaaacdcdcccdaaadacbbaaddaaadcdbbdcbdcccbccacdacdbdacdcaacbddbbbcabdcaadbdadbbdacacaacabdacdacaaacdccddbdbdadcbcbadccdccbddccacaacaacaabcaaaabccbccbadaaabbbcdbaabccbcbbbaabacbbccddddaabacaddabbbdcddbacabadaadbaaabaddbdddcaaaddcdbacadddddcbabacaadccccdbcacbcdabdaddbabddbcadddcdbacababdaadadcaaddddbccaacdbdddbcaaabcabcbaccccdadadbdbdacbcdaadbdabbccaddacaccbdbdcdbcbaaaadaaccbddaabcbcddcabccaaaaacbbbabbdabccaabcccbcbcdababdaadcbbcddcaaccdbbcbcbbbaabcccdcbbcdcdddcdbccabcacbbaadabdccbabbbcdcdabaaaccbadcadcabcccbbcbdcaccddbaddcadbabdadabbdcddcbddbcaddbacadadacdccdacadcacdbaaadcdbbabdadaddcdcadcbaacdbbabadbbdcccbbbdcaadccadabcdacdccaadbcabdbabbbdabdaacdaaddccbdbabbbcbbadbbcdcbdacbaaabdcdabcbabdcadaaadcbbdbdcaaacaacbabbdcdbcbaaaccbdbacdbabdcdaaddcdaaabacbbcadbbacbbcbcdbabcabbacabdababcaddcbbbcadcccabcdbadcdaaccabbbcdbdcaabadddbbdcdccaadbcdbcaabbaaacacbccdcabccadadbddbbbdcdcdcabacdbcdccbbacccabadcadacbdabbbbbaadaaadacacbcacbcddccbdbaabddacbccbdbbabadbbacdbacbccddcdcddddcaabbbdaadcbdccbabbcddccbccadbacbbacdaacddcaacacaabaabcdddaacacacdbbcbaacbbcaadcbbacddbdabbbddacdccbdcbdbdcadcbdbcbabcbdbdddaddcddcbcbbbdcddacbdaabacccbbddaacacccdbabaddcabcccabddbcabbddddbcabccdbbcccbccbdababdbcacadbbcadcabbdccdcabbcdabacbbcadcadadcbbbcbcbaaddbccadddadccdacdbaabaacdabacadbcdbdddddccdbdcccabdddcbaddabdaacacdacabbabaabcbbdcabcaabadcdaaacdbcdbcdcdccdbcadcacbcccacabbbbbcddabdacdabcdabdcbadadddbaccbdbabdcbadadcacccabddbdcdbbccbcabacacbaaabdddbdcacadaddccadacbddabccccaababacabbbdadbbabdbdbbdbacbbaabdcbddcdbabbdbadcbcdacbaaadadcdaadddacdbcddbacbbccdcbbdcdccccddbabaacbdbdbbbbdaaabcbbddcdabdccaaddadcbdabdcdbbcbdcdcbadddacabbdbbbddadbdbaabbbaddccbbcadbdbccaccdbcbcdcbdbdcddadbbbcbaaaaccbbbbcccbddabbddaaadccabcadadbbbcadacbcdadbcaadbdcdcdadabbababadadccbacccaadcdbbcacccbbbcadcbcdadbdacddadaaadcacacacadaadabadcabaacbdabcabcbddbbddadbadcdacdbadbbaccacddadbccddaccdabdccabbbbadabcbcbbdcdaadbadcdbddddddacbdbaaadabcadbcbbadadbcbcccdbcacaaabdcbbbccaadcccabdacacaaccabbbdbbcccbcdbaabcadbcddaaacabdadbacaadbcdabdbdbcbcbdcccbcabacacbdcadcbdbacadbcbdbdaabcdbbaddcbdcdbbdcdaabbaabccdadcadabcdacdabaddccdadbbddabcdcabccdacadababadcdccccdbcdabbabbbccaadaaabaccddbbdcbacbddaabaccbdabdbcabdaccdadcbcacaaacaaccadacbdcbdbcdddbacadbddcbdbcabbbcdcabccdbadaccbbabacabcbcaddbacbdbbabcbcacbbcbcbabdcabddccdadcbcbaaabacacdbdababdbbcdbcaaccacdacacddaacccdaacdcaaabbdbbdbbabaccdddcacdaacddacdabdaabcccabcabddbadcabacbadcabcadaccbabcadaaccbabbbbccbcabcbaadccdadabdabaabcdddbbbcbdcdcbbcbbdcddcabcadacaccbdcdabaacddbcddccbcaadcbaccdcbacbbcacbcdcadaabcdbabccccdabcadcdacbdbccdbdddbadadbbcdbcbabbddadbabcabbcbdadbbdcaaabcbbdbbbdabdbbdddaacabdacbcdcdaccddcdddcdbadadbdbaacaddbbcccdbcbdcbbcaddadacbdbddcddaadbadbddbbdaaccabccadcdbbadcdbbdcdcbbcdddcbbbbaaabbaaccaaacbbacbbaddcddbbdcddbdbbadcbbddaaccbabbaccdcddcdadcdacccbbadcdbabacdaccbccabbdbbdcdabaaabdcbacdacaddbbacdccaaddbbbbabababcdccbbdbbbddcccaaddcaccbaacdacdadbaddccdcdbdbdbbbdabbbacbabdacaaccadabccaadbbaddcdabcdaccacddabccbadadaabcdabadabbcbadbdcaaaacbcbdacabcacdccadbbdbcccadacabcdabbddacacbdcdcdddabaaaaaaaacbbbaaddcdbbcbdcccdabdabaaddddbbbbbdbddaadabdadabaccddccacaadababbdaadadbdadccbbcdccbcbbbadbacbbdbcbdbcacbacadcabadbadaababacbbcbddadbbcccaabadadacabdcdcacbddbdddccabdaabdccdacaaddcaabbccbcadcbddcddabcccbbaddabbcdbcacbacbbadddcabdbadacbaccddbcdadaabaccbcbabbabbcbbccdcccddaaadcaccabccdcdbbddbaaaaabacabccdacdabbdcdbabdaaddaaccaacabcbbaaacbbdacacdaccdbabbccccbcbabbaaababdbdccbbccbdcbdaccadccbccdddbccbdbbabcdabbbbddddbaadbdcddbadadccbacdcadcdcaaadbbdcdbbccadacabaadaacdbdbccbccccbaaacdcaacccacdaaacbabbaaccbabbcbdbacaddacacbbddccddabbcbacadcabbbaadbcccbcaadccbdcccddabbcacacbabbdbdbabcccabcbccccbbbaddddabbddcbcbccbccababdbdbbacccdcdabacbbbdcaadcaccbaabcccccddccbbcbccccaccbaccddadbdbbabcddbaacaddbbddacbaddbcdacadcdcbbccabdbbbabbdbdcacdbdcdcdccacccbbcbddbdabcaadcdadbacaccbcbcbbddcbddcacabadccaaabbacdabbcaacdddccbcbadbdddcbddbdcdadaacdadacdbbabaaadcdbdcadabcddbadcddddbbbcdcbcadbaacabadddacccbbcadaacbcdadbaddddaaccbdbdbddbcacbccaabadcccdcbbabbbcbacababacaadabbddacbddabadacbddadbbadaacbdcddddbdcdddbaabcaaadbaabacbbaaccdbbabdcbabdddaddbbaaadbddddbacbcdbaccdaccdbcccccacdadbabaccabacbcdadcdbacbabaabdaadbcbabcacdcbccdbbaabadcccadbabaacccbbcabbbbcdbabcaabbacbabdccdcdddcbaadbcbadccaaccbbcbdcddddbcababdaacacddaacbcababdaabdddcbdbcbbdbdddbcbdaabbadacbcddcdaaccbcddbcdcabdcbcbcadadabcccbdbdcbaccaccbdccdcddadaacdcbcbaacaccccccdbdbdddcddbcababbdddcbaccabbcbdaadbacdcabcbcbddaaadadbacbbabccbbbcbacdadabbabdabcabacbabcccbccdcbadbadaabadcdcbbacdcbcabccadbacbbbdbadddacacbbccbcbbcccabbdaddddaabaaaadcdddcbddddcbdaacccbaccddbcaccdacaaabbcabbddadacdcdabaaabddcbdcddcabcadbaaabbdbbbadaaacdbbddbbadadbbbbacbdadcbbbdccabbbcccabbdddacacbddbbdacddaddddcacbbdcbccdbccadadcadabababaaaaaddcabbdbbacaccddcacadcbbaacacbabcdcacbadcbabadbaabdbadcabacdcdbbadcbbacdddddcbccbcddababbdadcbadbccbdcbbcbadcaacbcbddacbcbcdcbdadabdbdbbaaaddcbbbadcdbacdcababdaddddcbbbdccdbacbdbdcbddbccbabcacdddacdccbaaabbdabbcbcacbaacdddaccbabddbccbcacccbdbbabbbdaaccadabaccdadbbabbcbabddcbaadaacbaadacaabaddabccaccbcbddbdacdcbccbabcabaaabaabbbbdacdaddadbdccadacbccbbccdccacaccbbdbacdabbcdbbcdabbabacbbbccbbabdbabcaddbcabbbadddabbabaddacdcdbcdacdaaabcaaadddaaadaabcbddbaabcadcbacdddddccdcbbacdcabbcbaaaadbcacddadddacbaadccacdabbdacbddccddaacadcdbbcbacbbdcadccbbcdbcaaaddbcdaddaddadcadcbbaaaccabbadcdddbaabacabbbbdadccaaaccdacadbdabacdadacdbbacaabdbdbabddbcbbbcddaddccaababcdddbccacbbbacccbdddbcacdcdcbaadaaadbdcbacacbdaddaabbbdcdabbabbcccadcccadadbdaddcbdadadacbdabaccdbddaddbbbcccdddbdbccdcbcccdcbbbdacbddbcaadbdbdcddabcaacdbdabbdcaadbabcbabdadcbcbaaadccdbbaabbccccadbcbbcccdddcbabcdcbaddadbadaddcbdbdbbcbbccdbddaacaadbdcbacdcabdaabbbdbbdaadacaaacccabcbdbdcbadddbadcccbacabadcccdccdaadacddcaaccbddbababbadbdacadaaacddabdbdaaddcbbdadaabbcbcdcacccccabadddacbcacadcdbadcbbdbddcddbaaaacbcdaccdcdbccdddddccccacbbabccbdcdddbcadddabbcbdddaadddbbababacdabcdaacbddcddbbdadbbabaccaaaabbcddcbccdaccdcdabacacccadadacbddcdcabcccccadddaacddbabccacaaddaababbdaddcbddaccaccbdaccdabacbccbccbddaacccdaabcadadccbddccdbbdadbcbcdbdbcccdaadbbcdcacbabcadacbaacadacccadbdbdcccdcaaaabdbdbcbbbccbbabcccddbabccbbcbabddcaabbcbcbadaabcadcbbacacdccddbbccdabacdccbcbbcacccdacbaacdbdbdabcdddbcdaccdbdcaababbadaddadadaaacadacadadadbdcccccdccdbcacbcbadbcbbbcacdacdbacddacccddcbccbacbcddccbcadadababcdbbcbcadbdcaadbabdcabbaacbcdbaddadcacabdcdabccdcbcadcdcdccbaadacaddccadbaaaacadddbcccbacdcbbbdddbdbcbcaccbbccdbccdbddccddaadadadabddcaccbcaacaadaaaacabddaaadbaccddbddadbbaaaabcbbadcdaabcbbbaaadcbcdabbacdacdbdddbdcdbddacccbddbbcbdcddacbcbcddccdbdddcbddadddcaaacdddbdaddaaacdccbdddadbcadadabacabcdbbbcbdbabadcadbdbcbacdddbbbcaaccaabddaddbcddcadbcddcbcdacaabacabddcbcaadbbdacbabdddaaaaacadbdccabbaadaddadcddbbadbcdbaadabadccddbccacadbacdccbcabbcbdbdcabbabdbabbcadacdaccdadbaddbcabdcaddcbacdacdbdcbcbadbbbbbaa
cadaaacadb