acbccdccbaabdaabcbadbcdcdbaacccbbdcccdbcbddbabcbdcbcbadaadadbdabddbcabdcccabccadbdccddabcacababaaabaadbaacbacdadddccabbabacdbccaddbcbddcbdbbddabbbbcabdabaddbbabacdcaacadacbbbbdbcbbbdccbbdabcdbcbdabdccdaaadcacbcdcaabdadacacbddcadabbadcabaabcdddabbdabbccdcbadcabbcddaddabcadddcadbacacdcbdadbaccaccbbbdbbdbadcbcbcdcdbbdcdbabddbbcbaddbddaadbaaacdcabddcdcbabbbabdacdbccdcabbddacbabadcdddadccaadacacdddccaaccdcbdddaacbadccdcaaacdadcdbccadbdabcbadcaccddbbaaabbbbaccacdacdbacabdcaacccccdccabbaadaccddabbcacbcbbccdaabaccbcdbcdbbadbcaadbdcbbdaabdadabbbdaaaaaadabacadadabaabcbddadcbdccadacbcdbaaabcdaabccbcbbcdcdcbddddddadacacbbcdaaacdadbabbdddabcccdcddddcdacacdcdbbbadaddadaccdbbaadbaaddabbddccbaaccbdbcbcdccacdbcdcdaabddddcbccbadbdbccadadcdcddcbdcbcaabbacbdaabaccbdcabdbccdddadbcadbcacabaaccbacbaddaaccbdddccdbcacbbbcbcddbdbbcbbbdabcdccbdcccddcddbcdbdcaacbababadccbbabcdbaaacdacbdabaaabdccbbacacaaabdadcacababaddacdcaaabbaaddccdcccdbdddbcbcbacdbcdbbbdcaaabbdabacccbcdaddcbcbbbddccddddcddadccdcdadabcacabbbadaddaaddcaadccdbaadcbadbcccadacbaacbacacabcbadacdadacdcaacacdacaacbdcadaabdaaacdabbcbacacacdbbdaadccacddbdadcdbbbbdccdccdbbcdccabadacdbcdddbcaaddabdabaacbaddaadacbdaadabaddddcacdddcaabcbbbccdaabddbbbdcdcabbaaaccdbccadaacabddcccdbababddddbaaabcbdbbdaabcaaadacbddcdbaacdcdbbacacdccbcbcbaccbdbbccdadacbccddcaaccbdddccdcadaddcbaaaddaadbbaabbdabacbdaddbacaadadbbccdbadcbcddddccbdbacdcbdccbaabbcabacdabcdcbdaaaabcdadcbdaabcbcabaaddabcdcacaaacabcddcdbaaacacaaccdaabbcbcadababcdcadadabbcbdaadbccababdbbcbbdaddaaaaddbbdbbcccbabbcbaccdbbdcabaabbdbbdcacaabcababcbdccdbcbadcbdcadccdaabdabcbcccdabcbadcadaadbaabbccbcbadaadbaaacadbdcaaccabcdddbaddbcaabbadbcabcbcbaabaaabcabbbbddabbcbdadccdddbbabdbaadacccabccdacdbaabcabcbabadcadacddbcacacdabcbbdabdbbbddabacbcbbaacbaadadcddbdacabdabaabdccbcaccaadcdbabaadcbaabdadcbdddadabbdbdbdbdbccadabaadbcbcbaacdaaaadacccaadbacbaaadadaddbacaadabbaaabddaabbcdcbccaddcbdbbbcdcabbbabbdcddabdcdabcbcdaaabdbdbadbaddadacbaabbdbbbaddbabcdbabbbabadccdbccbaadbaddcabbcbadadcddaadbaccccdaacddcbaaadcbccacddccddbbbaadaccbadcdaaccacaddcbbababddcadcccbdccdaacbadabbdaccbdcadabaacbbdabaacaabdddacccaccbbcaaabbcbdbcbcdaabcbdddcaaaddddabdcbbdcaddadbbcddcbdabbabbdcdadbadcccbcacadccadcccbacbacbbcabbdbbbdcdaccadbcabbcdbacbdccdaddccbcaaaadddcaaacaaddcdbabbdbabcdaabdcdbbdabbdaddbcbdcbabddcacdcbbbdbcbccaaacbdbaadcbcadbcbdababaadbddddacaadaccdbbcdadcbdbcabaddcacdabdaaddaaddaccacccccacbbcabdcabcacacadcbabaacbdbbccbcdcadccbcbddabcabdbddbbaacdcadbcdbadcbcdcabbbcdbdacacaaddccacddbacadaabcccddbabcaadacbdadcbbcabaccbdacaacdccbdaacdbabcbdddcaababcccabcddcbddaccdaddcabddddcdcbbbaddadbcdbdcbccbdcdabaabaaaadadcdccbbacbacddbccdcdaaacababcddaadcabacbdadbbbcadcbcddbcbdccbadccccadddcaacdccbbccdabadddcacdaddbabbbcacdaaddadabccddbdcccdacdcdcacabaaddbccbbadbadddacbaacabdbcadbbcbbccabbccadaacaaddadadaabadacbddbccabcdcaabbdbaddcdcbcdddbdbaddaaabacdbbdbadadaddcddbacbbddbdcaaaadbdbbadacaaabdbcccaabcddddadacccabadbdddaacbadaabcdbbcdaaadbcaddddbbdccdddbbcdbdccbadcbbabbbccbacacbbbbbccdacbddcccdbbbcbbbdaabbdaccbabaacdddbcddcbabdbdbbdcabcbcbcdbabdcddcbbdbcababbddbccbccbdbaaaadaadbbcadbcddbcbcddcdadababadcbaccbbaacadcdbabdccdcdbbacbbbabcbccdbbacababbccdbbdadbbadbaaaadabdddbdccaadcddbdcccccdabbdcdcadcdabbbcdcccabcccacdacdcdcdbcddaaacbadbddbddcdccdbaccdadcddcdccbdcccbccbdcbbacbccaacbbdaadcabdbadacdadcacaadbcbdccaadbbabacacccabdbccddbadbbcdabbadbbdbddaddbcbacccadbbbddaadbadcaaabdbccadcdcaaccdbcdabdbbdcbadbacccdcbccccaddcaddddacdbbbdcadbbdccdabcaccdcbaddbdbabadbbbbcdbbabdaccbdcdddbbdcdccbbaacaacdbccbbdcdbaddbdcaaaccabaabbddcdcbccacdbbcccdccaaddbcbabcdcccadcbaaccdbdabcadbdcdcdacbcccdcbbbaaccadacadaaddaaabdababaadccabaadcdcbcdccacbddbbaaccabbabdabbbacaadcddabadadbacccccbaacdcbbdccabcdacdacacacadadbcbcccbcdccdccbdcaaaaabcabbccaddcdddcaaaaaabbaacaabdcbacdaabcdccbbcbaadadacbdddddcccddadaaaddbbdabdaddcdacbadabacddabcddbabdcaccddabbabbacbdcccdcdbabbaacbabccbbcdbadbbcdcaddddcabdcdbcbbcdabaabbdcdbdaaaaaccdaabcdaacabbdbaabdbdccaaaababbacbcdaadcbaccccababdbcabcaaabbcbacbbdbacccdabdddddbacadccbacbbdbbbdbadacbcbbbbdacbdbbbadadbbccadacccdcbaabcddbdabbdabbbbabddbbcabaaddacbcbdbcddbdadcbcdddddcdccdbadbcdbadddbcabddbdabdcbabadabdbcccadcbdababaabdbcccddcdaccacacdabccccadbcccbcbdcdcabcabddbadcbdabadbbadbcbdadbcacaabacadcdaccccbacbacaabccdaccabcbdadbddbbaaaaadbccacdaccccbcacbcbcddaddbcaccbbdbcbbddadddddcbdcababcbdccabccbdababbccdccdbbccdaccdadcabaacbaadcaccdcbcabdddaddbabdddaacaccbbbcabdbacaabbccbbccbadadbbdddcbbbaddaabbcdbdccadacbaddbdcdcaabdaccadadaadbaaabbcddbbbabdcdcacdabaabcdccdbdadcadcadbccdabaabaccdbcabcbacaaacbdccaabacacabaddadbbcaaacaacabacadabcacdbacdaccdddddbbccdccabccadccabdcbcccabccadadabbccccacdabbcaaddbbcaccccbacbccdbbadaccabcdcddcacbaddddcdbdabcdabcbdcbddaccbcadcbaadbbdadaccacadddcaddbccacbaccadcbdbddcdacabdcbabbddadddaabdbaccbcabdbddadcdaadcccdbddbccbbcdddbcbdaddaddcadabdddcbdaddcacacddaaccaadccaddbcdabaccdddaaaccbccddbdbdbddccadcdaacacaabcaccdabbadddadbdbddbdcbcdbaacaaaadaddaacbabbdbdcaccddbcacdacdadcaacbccabddbcaaabcbddadadbcadddcbcbacddbbddcbdacdadabdabacdacaadaadaacbdcadabdabcaacbabcabcbcadbbcbaadccddcbddbccdbdbabaaabdbcdddbbbacdaaadadddbddcccaaabdbdcbdcdccdddaaaacadabbdbbbaaddaadcbbacddabccdcbcdaddbcccacbdbdbcdbcdabdcbadbabcbcdaccabaaaaaddbdbccdbacaadabaccaccaccaababdabadbabacacaccdadbbdcdaacbbcbccabbdcdbbabbdccadcbcabaababbadbdabccccadcdcbabcccbcabcdccadccaabbbadaddbccadbcabababddccbcabdacacabdbdcaaaaadabbcccbbbbddaababddccbddbcacdbcdbbddcbbdacbaccdcbbbabaccbdbdbbadbbcbabccaaddccbabadddbcacbaccbabbcacdcccdaaaddbbadbdaadacccacdddbcdcccbbbbaadcdabddacdcdbaddbdbdabcdcabddcadbcbdccbabbacacaaaacaccaddcbdacbbabbbdadccbaccddcaacacbbbadaabddacaadccdbbdbacbdacbdabbbdcbabcacbcddacdacbaaaccbbabccaadbccdbbaadbcaaaadbcdbaddbbdaccbdacbdbcbccccdccabdbddcbddaaaabbcbbbccaccbdcbccadaabbcabbdbdabdcbdccadaccabcaccccaccabbaaddcbdddcabcbccdcdacbbdbababcccadadbcdbaaaabcaddcaabdaaccbbcbadbacbdddcdbcbcaddbabccabdcccbdabaaacabbabbadcaddcccadaacbadcabaadcacabccbcccdcbbddbdaadbbaaaaadbdbacaaabbcaccddcbcadcdbdcaccbcbdababbbdbcdabbadcadcbcbcaccbbdbdbacdacacbcadccbdcdcbdcdbdaddcbdadcbbcacaddcbddbabdaadaabdbcdadbccdcbdcdabaadacaddbcccabcdbdcdccdadaccbaccccadabdcddbdaccbabbacddabbdadbccddaacbadbbddaacdcccbcadabcaadcccdcbadcccdcbdcabdcbbcabbdbaddcccabbcdaaddadbaccbbdcadaabbabdcdaababddcbcabddbbcbadaaddadddabdbdddddadbbbcdabcacccaabbadadbbcacabadacadcadcacacdbdddcbabccdbbdbdcddbcbdacbddbdbbacdddbbbacdbbdbadccbbcddbbbabdaabaaaabacbdbdbbadabadaddabadaadacbdaddabcdbcdddacdaadcbaddabadcdadbacaaddaccacddcadcadbbbacaccadbbacbcdacdccbdbbaaccbbaacadadacdbccbbaacbccbcadacccccdddbcaccdabccaaccaaacbdbbacccbadbbbbcddabbababcadabdcbccacddacddaabaaccdcccababbddddacbccdaccbcbaadcababddbdaaacdbcadbcacaaccbdabdabacdadaddacdcdbccddaccadaabacabadcdcccadbbacadccccbbbddbddcdcdabdbdbbaacbbddadbbccbabcdadaaaadbcadbbaadaddcbcbaaaababdcadcbccbdcadabacccdccccccabcddbccaacbddabacadcaccbcdcaaaddbbdddcacbabbaccbbbdcddabbdcdccabccdcbadabbbbbdbddbcbdbcacacabccdcddbdabbaccadcdccaccdaacacaadddcbdddddadbcdccccbcbcdcdbdccccbcabcbbcbbbdbbbccabcbaabccbdacaaacbbdcccccbbacddacadabaacdbdddaaadbabacbddadbacbdcbcbdadccbdacdbacbddadadbacdbbdadcabcdcbbdababdbdacdbcaadccababddccdddddbdadbcbdaabaacdaadbbdcacadbbdcdabdddaacaddbdabbadccbbddaddabbacdcadcadbacadcabbaadcbdacdccdbcdacaabcbdadbadcadabcdcbdcacdacadbcadddcccabadaaacdbbacccbacaddbbcbacdaaccbacbcaddbdadbabcbacbdcacaacaddaaacbdbbcdadcadaccbcbbbdccbcaabbddbdaabdbbabdbbccbbdbbddcacdcdcacdcccdcaacabcabababcccdadacaaabbbabdbbcabcaddabbaacddccbcdbbbbacddcbaccabadddadadbdbaaabcccbcbcaacbbdadaabdbbacbddccbabcacbbabababbcacdcdcdcdbdabcdcdadbabbdbcdcaaabbaacadcbdacccaadcaccbbbaacccdaccacdbcbccbadcdbbdabcccddcddcdbbccabcdcddcccbabacabcbabbcdbdacdbdcdcbaadbcdadbdabbbccacababcbbcddbbcbbcdaabdccbbccbacccdbbcdbcccaabcababbadadcacdacabbcacaaaddccaccdaddccaddcbbdccadbdcadbccaabdcbabacccccacabdcaccdcbabcdacadccddaaaccccdccaadbacbdcdbbbccdbdcacacdaabbddabcbbcaccacadcdbdcdbcbbcaddadcdcdcaacdbbdcdcaadddbaacdddcbabcbaaacbdcaabbabdbcabdbdadabdbdcabacbccaccdcaddbdddadccbdbaadccbddcdadbcacdacadacabcdbcdcdddcabbbbabddbbdcaadabadacbccbabcbcadcdaadbdcabdabadabaaabdabadddcccbbacadababcacadcaabbccbdcbcaccdabccabbcadcbcdbadbccadaacabbacbdbaababcdcabbddabdacbadaccadcdbdccccddcacaacbbdbadccbdadbcddddcaccccbdcbbdcabcaacdaddccaacdcdaaacdccccdccbbcdbcadccdcdbdddcbddddaddcddbdcddcdcadcddbaccdadcacaddcdbbcddbcdcdcabcccccbbabbdccdaabdddcdbcdbdbbdabaaaaccadccccbcdccdccabcbdcdccbbaabcdcdbdabbbddbacbadbccacdddbaaacacdbcadbdbabdcdbbdbacdaadaacccbbaacdddaacdbdbabadbadaaacbccadcbdddbdbabbdacdcbbabbcdabaadcdacbdabcdabacacdbbbcdadacdadccbdaccccbdcdbdaabbbaddacddddaccacacbacdcdcaddacddaadbbbaacadaccdaddcaacdcbaabdababaacdbbaddccdadadbccbabbaaadabbdbddbbcdadcccbcacacbdabbabcdcccbacccadaacddbcdabbadccbdbccbacddbccdbabcadcddbacbacaabcddcacabcddccaabcaabdadbcddabacbbdaacbbcabcababdaaaacbbdbdbcabdbbbaaabcacccaadcbdabddbcbbddbacddcbddacbbbddbdbbbdcbcbcdcccadcdbabbdcdaabcccacdaacddddcbbadcbbcccacbbddcddabaadacddbdaacccccacbbaaaccbbbbbcdcacbcbacccdbadcbabcbbddaddccdddddacdbdaadcbddcaccdbdccaddcdcacbdcbdbcbaabcbbdbcdcacadcdbcbabaabdabbadbadaaaacabbadcaadadcddbcdbdaacaacaccaccaaacabcacdcdabcadcabcbdabcbbcbabbaddddbddbcbaabdcdcddbbabacdacdcacbaadaddcadccccddcbbcdcbabdcbdbbbdddbdbbadbcddbacaaadaaacdccaaaaabddddddaccacaacadbbbddbdcaccbcbbacbbcabbbdbbdcdcbbbaababaaaddbbcbccdadcbabbaacddcaacbaadcccbadcdacbabcbccbdaaadddbaadbbdabcdcbacdaddcdbcbdbabbddddaaadaccabddbddccdccaadcbdcbbcdaaaaababadbbbbadcbcdbbdcccabbdbaadcadabaadccddbbbccbadadadacdacdaadcccdddaadbcbbbbdaaaaabdcabccbabcaaabdacbddddbdbdacbbadcccabdcdaabcacacacdbaccacaaadbdcddadabcddbcbaabdaddddbacaacdddabbcabcadccaabbbbdadabbcdabbcbbcbbaccddcbabaaddaabaabcbdbadaadbdbcaacccddcadaacdacccbcbbbbbbadcbcbddbaabdabcabdacbddcdcaaacabbdcbbddacdbcddbdcabaabdddcacbcaccacdcaacbacacbbaabaacdabdcdbbdccacdaccbbbdcdcdcccccbdbbacadadacdabbaadcaaccbdbadacdbcccadcdaddcccdadcbdbdcccbdcaadddccbabdacbcadadcdbacaacdcadcbacaadacaaddacdabbcbcbdccbddbbabacddbdcbbaaadcacaabacadaaacccddcdaddccdabdbcadaabdcbadbbaadbcddcaddbbbcbbbcbcaabadcdbbbdddddcbadcbddaddcadcddababbacbdbaccbbbdcaabcdcbaabbdbdacdcbbbbbcdcbacbbbbdaccaacabdddadbbdbcbadaaadddddcccabcddbdccbbccbabacbbdcddcaaaaadbcdcadbbdaaddbccdcbababdddcbccadccbccbbdbdddcbabdcadaaaaddadcbdcaadddaacdadadabbabcdadabddddacaacacbacbaabaddabbcccdaabdbacbbbcaddbbabcbcbdaccbdacbcdbbbdbaaccabcbdcdcbdccabbddaadbacabccddabcaabdbbcddbaabccbabccccbaddcabcddbadaaccccbcaacdcabdbabdbdabbaadccabcdcaadbdbadacaccccdbaabaccbccaaaaddddbbaccabcbdcabbdcacbaadcbdcbcdddccdccbcaacabadcdcccaadcbacadddddacbccaaaacbdabbdcbdaaddbbcdbacbbdcbdadacbbbbcaccdabdcbabdaaaaddcbaccdabaabcdcacdabdcdaccadbcdbdbabdccbbdcbbaacdabdddddabdbdccaacdbbdbbdbbdacccdcdbdabacbcabbcdddbdccdcaadbbcbdcbbbbbddcccacddbdaaabdbacdcbbcabdabadabddabaaabcaaddacbdacacbbaccbdcacaccbacadbaabacbbacacaddbdabbaaaadbdcdaabaabcaaddaacddcddddacbdadcdaadddcbddcbbbdbcbadbbdcabacbcabdddabbaddbdcbbacccabcccbdaacaacadbdbdcbddbbddbaadbbcbbccbddababadcaadaccdcbadddaddbacccbbbdbaccbdaaddbacacbbcbdbdddbadbbccabacbaddccddbbacdcbcdbcbddcaadccaadaccacdcacaddccbdbbccbadcbbabccdcbacdbabbbddbcddbadccbbdddcddcddcccaacaaddaabcabcbaddaccccdacbcbcddbcdaddabccbaacdcbcbdbadaababdbcadccbaddababcabbdddabacbbdbcbbacdcbbcdadabddbdccbbacacdcaadadaabdddbcbdacabdbbabdccccbbbccbbbdbcadbbcacabaadababadbcbbbdacbadaacbdbddcccbccadabbabcabddcdbbacadcddcadcbcbcdacdacdaabdbbddccbdcdcdbdbababbcbbcbcbbdbbaaccacabdaabbdaacabdacccdcbbaccbbdacdcdccaadbddbcacbbcdcdbdadbcabaccadcdcbabacabccabcbcbdcdabaadbdaddcaabdbcadbdaacbcbadbbbddbaacabadbaacabbbcbabcdbadbaaaacabcdacddbbbcabcbddcbabcdccadbaaccbdbdcddcaabdbdcadbcbcdbcbbdcabccabdbddaddcaabddadcbbcddcadccbbadabcabdaccbacbcdbbadcbdacbabdcdabccabdbdadbbcdcdddcdcccaaadabdbbcdbbaabdabcacabcccbabbdadaabcdcdcbcdbbbcddbccbbabaccabccabaddcadbcdaabbaabccacbdcbcbbcacdddccbaacddcabbcdadbbabadcdbbbbcaadbbdabdaaccaaddaaccddddabbcdabacbddbcbaccdaaccdadbcacabbcdaacadbacdbacdabdbdbccbddbaadbcbabbddcabcacbaccbaccadcdbcbbcadcaacadbcbbddddbbbdcbadcabbdaddcdbacaaabbadbdadadbcdadcaccdbbccccdcabdddcaaaccaadcdacddcdcaabbadddcbcaccdbdcbaaabbaddcbcbadccacabcccacadaddcbcacdbbcccddbaacbcaadcdcdcbdbcccacaadbabbcabcbdabcacddbdbbdcdbbaccbdcdabacbabbdcdddbbbbcddcadcdcbdadcdbbcababdabcbdaaccccaadcbacbbabbacbdbcddcaddadbaadabccdaccdcddcccbbccdccaccccbabbabdbcbcdabcbabaddddcabbbbdcbcdcadddcaddbbadabdacdbccbbdadabaccddbdbdbdacadcdaadcbaabcadadccbaadbcabcabcccbddadbabcdbdbabcaabdcdabddaacdbdccdacdcabbdccadaaddacdacbccbbaaabbdacaaadbabcacddbccacbddddbbdabcdadaddbbdbbcdabcbdbbcbacbcdcdbccbdaccddabdbbbccabbbacbadbbaadddbabdcccaddbbdcbacbabbbbdbbbddbbbabdaacadbcadbacdbcbbcaaccacadbcdbddbaadaacdccbdbbaaaaacbccaddbdacaacbbcaacbcbacbbadbbcdddcdcacacccbaaccbcdbcccadddaadbbabaccacdadabbccddaccdbdddbaacacaabacbcadcbaccdbabcbcdacddabcdacadcaccbdbdacbaabdccbdacddadccbddacdacdbacbcbaccbcccaaddadbbbbbbcadbaccdabbcdaccabcddabcdcbaacccccbaadcbdaacbdcbabaddbdbddadbdbababbddbdbccacadcccbdcdcabbcdbdbdccadcbcacbdddacadcdabcdabddabdabbbacccbcbdcddcccbddaccbbdbaadcaddcbabbbbcccbacbabdcbbbdcaaadcabccdccaadcdcbacbbbbbbbcbdbdadbcaabccbdcddbddadccdcabcaaddaaacbbbcabdacddcbccbacdaddacbbcdcccbadddacadcccbaccaccbdcdbcaabbcadcbcbbaddcadaaadcdcaaadacddddacdccaccbbcbcbbababbbacdcccdcbbcbacaaabacdacdbadcdaadacdcdbabaccdbbcdbaddbbcdbabddacdcbdbdabadaaabccbaadadaaacbbcaccbbcbddabdcdcdbbcbccdbbabcdcdabbbbcddacbacbcbbaadaacccdbacdbccdbdcccacabcbaddbdacdbabccaaabbddbcbddcccbadcdbdbadbcdcabbabbadbbbbacbccbcbcbbddcddbcdbcdbddbaaaadccacaccadbbcbcabadabddcdbbdddccbcaacdacbcababcbdccadbacdbddaacdbbadcacadaacbcbddababcccadaadaddacdddacadbbbabbdbcaabccbccbabddcdbabaddacbadcbdabcabdabccdabddbcdadcdbdacccbabbbbcdbddcbcccdbaabdbaacbababbbdcddaaacbaacaacddbbdaabddcbbddcccdaaacdcccacaddbdddccaaacdcbcbaccbcbdbdbbcccdcdaadbcdcabcaaadbccbbddbabbdbbacabbcddaaadcddbcdcddcdbacdaddabaadaccbcbdccdabaaacdababbbbbadaddcabbaddbbbbcbbcdbabddcbaddcaadcbdaaadddbbdaddddddaaabaacbabacacdcbbddcdbdacbcbaccaaddcbdbbddbaaaccadbbdacadadbbabbbabcdacaababbabdcbaccdbbdddaacabccddaaaacbbcdcbcbacdccccadcacdabcaababcbcbdacbbccbbbddcdcdccdbcbbbcaacdaddbaaacbbbcdadddcdcbaaddcccbcddbccbdccdcbacaddddccbdaaabbdadbbabacdddabbccddbacbaddabaccacadbaadadcadaadcaacdcaadcacddccbcacddbccdbbbabbaabcbcadacbabdbcdccdccbccaacbadabbacdbdacadddcadcdccdcaacccbdbbccadbccbaabddcbadbadbbcdccabcabddbacabbbdcdcacaadccdabbdddbbdbadddadddbbadcabcddabaddbcbbabdbdadcbcbcbccaabcadcdaabdbaaaccaaaabcdbdccaaccbdabcbaaddaddddbcaaaccccaadddcddcaddabdccdcdbccbbcbdcccbacccaabbbcdabbadbdccadccdbabadcddddddbcbbdddcaacdcadcbccbbcadacacbbaaabdbbccacaddbbaabbabdabacabbcdcdbcaabbbdabdbbacaccaaabdbbcacddcbbdbdaddbbabcadabbcaccddbcbaabaadaacabcbdbcaccbbccbcadaddcacccbcdcbccaadccabbcadcbccbbdcbbaacdbaddcccdcddcabbcaccbbcddbccadcbccbbcabcaccbdcbbccacdabbdbaacbadccadcbadddadadaadaacbddbaacbaadbdbbababbbcacdaddcacbbcadddaddcaaacdcdaabdcdcaadaadcbcccbdbcbaadcdcbcadcdbbcbbacbadacddcadbbbbccabadcbacdadccaccaaadcbaddabccadbbabdbbcadbabbbccdaccbccadbaddccaccdbdbcddcbdbbcdbacaaddacacdbcbaabdacccbddbadbbabdbacabcbccddbbddcbdbdabcacbccddcbadbdccddcdcbabccbbccbabbcbacaddbdbddadadbccbdbddccdcddaccacccbbcbaddabbcacdbaccabbacbcaacaaadadcaddbccdaccabccbadaaacbaaccaddadbdcdcdabbcaabdccaadccdbbcadcacdbdabdbdbaaccdbaddbbcaadbbaaabdacbbddddcbbbaccdddcadaaabcacbccbadbdcabbcbccdcbbbcbcdcbacabbdcccccbaddcccbdbccbbcbccacacbadabbdbaaaccbcacdbdcddadbbddbccacbaaaababcddcbabacacabddbdccaadacbddacaabbbcadbdddcadbabbdcabccbdbcbbacaadbcdadbbcbabacaabcccdaaccbddcadabddacadaaadcccaadacccbbababdcbbaccddbdcccbcabdbcabbccdaaadcadcbccbbdcdbaabacaaddcbbbbcbbcddbbabadbddbdabadadaacbccadddadbcacacbdcbdddcccaccacbaadabbcdbdccdbcadbbbbbdacacdcabcaaabbabacbcbbdbcccbcbcbbabdccdadacabadcdccaaccbdddaaaabdaadcbadcdbdacbdcccbdddabccdacdcabbabcbadaddcbccdcdaccddcbaacbcacaacacdcabdbbcabbccdbcbdabdbddbdabccccaabbcbbbbabadabdaaadbcabdacbbdcbcbcaccbdbbababbadbcdcaaaccbacbbcbdcdbcbdacdaabaadddacdabdbcdcdbdbcbbcadabdccdbdadccabaadadcbcbbadbcbcaddacaadddbddaccbaddbdaadbccdcdaabaaacacaadcacddbcadaddbaccacdcdaadbddbcdacdacbababddbbdadcbbdccddcdcbdbaaddacdcaacddabadbccbacbdabcaddacabcddbbbdddddcbdacabacaaabddbccccbbcbdbbcadaaacdcadbcddcbaabcbaabccbaabdacdabcaaacbaaabacdaacaddbcccaabddcabcbddabacbdbbdadcdbdaccabdbdcadacbdbabacbabbabdbaaaccdaccdbaaacacbcadabcbbdadcdbadabcccdbcabdadbbacbacbbdaccbdbadbcdadabcddbaaababccdddabadacbbddddaaaabacccbadabccacacbbbbbcbabbbdcdddbdabcaacadbcddbbdcabdbbddcbacadaccdcaabcabaddbadcdadabcddaadbbacbdadcaccdaaaddabbcbbaddcbccdbadcabcaccddccdacaabdbccbbddcbaadacbacabcccdcaadcccabacadddbbaaadccbaacdcbcbddbbdbbbcadbdbdacdaddabdbdbbababbaddbacdaadddcabddaabcabbdaacabbbcbddabcbbabcabbcddcbadadabaaaacddbaddacbabcddcabcadaccbbbdabdbbacbdaabcabdbaadcadbcddadcdaabdbcdcaadbbabdbddcccaabcaddbccddcaacdbadddbbdbdddcabaddbddaaacdcdabcddacabdbbcdbcddadcddcacbdbdcacaacbdabdbdbdcdaddcaddcdccbcbcbdcbdbbccbdddcaabdbdadccbbdbaaccadcbdccdccbaadadbccdcbbadcacbcbccccbbacbabdadcaccbdccabbacdaaaaddaccbbdccbddabccdabbabdcabacbbdbdaddadcaabcabdddbbbabaadbcddddaacaaaaacdbbddbcbacbcbbbbddaacdadbcaaacdabdcddbbdbccdbdddbabcaaaaccdadccbdcadbcbbdacbcbcdcacaddabcdbccaaccbccccddddaccabcacccacccbbbcbdddbaccbddaaaaddadcabadcadcacadaccbadbaddbacbdcbbdabcadccddacdaaddddacdcddbbaacbcbabadcdcadcacabcddabacbaaccdbcaabcacabdcbddbabdaabdaabdaadbdadcdddacdcadbaacbdbcdaaccccadcbbcadacdcabcccbadbaacdaccadabddcdaabdddbaddcaddbddadaabcbbdabacccadcbbcbbcaabbaccccdcdddcddcbbacbadbdddddabddddccbcaaadddbacbacbaabbcdadcbadaabdbaaabcdcbcbadcbcacacbccdccbaaddabacbdaddddcdadcdbdaaddbbbcdddccaadabbacbbdcddbdcdbcdabbbdcbddcabbddadbadaddaabaddbcdacbbdbcddbaaadcaabbdccdbdacadbbdcbadcaaaccbcaadddbbbdaadabacdbdbcbbbccbbddccaadcbdacadbdaaabcddcdbcdbdbcccbdcbaaacbbdcdccbbdccdcbbcbdaabdadbacabdcaaabcabaabcdbddcbcaacbdbbdcdbadcbddcbccdccdadaddadbaabdbbdbabdcadbaacbdcabbbccacaaaadbbadcdacaddacbabaddabbdcdcaabcabbdbbbdabcaaadaaadaddcacabddaabdbdacacdbbabdddbbdccbabdabddcbbadadccdcbbdddccbacccbbcbbcbaababcbdbcabcdccacadacaddccabdadbcdbccdccccddbbacbabdbbbbaccaacdadccabdbabacbddbdbdbdabadabdddaaaccaacbddaddaaddccaadabdcdcbadbadaaddcabdcdacababbdcccaadcbadadacaddccaccccadbcddcdadbaacdbbdbdacadcdadbbdcabadccdbdcabdaabbccccdaacabadaacbacbbbadcabcadaaaabbdacdbacbbcabdbcbddadacbadcbbcdcabababddccbdccaabdcbcdcabbadbabbadaccaaadddccdaccdcabcaadbcdbaabdbbbacdcddbacbaccbbdcbcdbcdcccdbbadbaabbabadcbadacaacccccabbdddabddadddbacdbdbdbcbddbcabacdddccddbaaccdcbbacbacdccbbacbddadcddcacbcbdcbabdbdcdcacbccccddddbabcadbadbcadccabadadccaddcdbbcbcbcaaabbcabdbadccabbcdbaaddacbbaadccbacacbbaccacaacdbbbbaccaaacddaadabcaaadabbcabddadabacbcddcdbdcdcdbccabddcadaddabdacbdaddcabaacbcadbdcddaddcaabcbaddbaadbcbcdddcbacdcbcaabbdcacbbcadbaccbbabbbdbcdcbacbacdbccabacbcabcccbdbcdbccbdbbdabccdccdbdbbdddcbaadbaacacadbdbcdcdcbadcaabbacadacdcbcdaccaabdbbadcbbababbcaacdadbabaaaabacdcaaddadbabacccddcabdbcddabdabaacacbcbaacbababbcdccbddbdaabbddcdadcddbcabdbdcdacdddabccdbacaabccbaddbcbdbcaacdbbbbcdacdcabbdccddabaddbdaccabaaadabbbcbdddcdabbadbcdcbddabacdaaabdcbcacaadabaababdcabaacdbdbdccbbbaacdbcbacddabcdbdabbdcdbbdbadccbbadbbbdadbddcdddcdcaaaabaabbabbaadaccddbdcbbdadcabdbcbddbdddccbbbbcdccbdcaadcbaaaccdaabcdcbbcbbaccbccabdcbbdcdbdbcccddcadaacbdacbddbbcddacabacbbacbdadaadabdbdabbadcdbddcbccbdaadbacdadabbbbdacdbbacaccaddbabdcccddccbcaabadaddababaaadaabcacbabcdcbbadadcdababacacbadcdbcaaacabdcccdacbccaaabcadcdccbbcaaadcbdcadbcaccbbcbaaabbcadcadccdccacddbabcdddcdaaabbbdbdcdccbcbacbdaadddbbbacccccdddcbbbbabaaadacdabaabccdbaaabbdcabcaadbcbccccabcbcbcccacaacdbdaccbbbdcddbbbaaacacbcbcdaddcabadcdcacabababcdadccadcdbcdbadcccadcbbddacdbcdbccbddaccaabccccacddccccbbadcbacdcdcacbcdabbcdcccbdbdabccbdccbbacbdbdddbcdbcbacbbdaacbabdadabadabddabbdabbacbdcbbacabbcbbcbaccdadaacbcdcdccacacbbbabdabbdbacdcdaddadbacbacddbcacddaccaddbcbabdcaaaabcadbdcdacddcabcbbcbdaadbcbbddaabbdaccadccaabcddaaabcbaadcbccbcacacbddccacdddabbbabbaabadcbaabbddbdbbccbababdddcddacbbbccbbdcbaddaabcdbadacdcdcaabadbabcabcaadbbacccbadbabbbcdbcaabdcbcdbbcdcbcbdcbdcadbabddaabdccacbbacabbaccccbdabaccdcdddbdbdbccbcdcbbcccdccbbcdbbdddacdbbbcddcabdccccbccdccaddbcbadbabdbbbbbaaccadbdcdcdbddadacbbaadbcbbbcbbdbaaadbdcdabcabbccacabbdbcdaaadadaddbacdcadddcaccabdbbadbbabadacdaccdadcdbacccdcdcadbcbdbdcabcdcaadadbcbdbbadadcdadbcadbdddadaacbacbccdadabddccdcbcbdadadaaddbcacbcbadbadcaadddbccaddacbcddadbcabdabbdccdadbbcddabbacccddbccbbbdbcdcccabdcaadbddbcbcacbccaaacaddabbcccdcbadbcdbdccaaaabbbabdcbaaaccaaadbcdcbccabdaadcaaccccaddababcacbbcadbdcbbbbdacdcbbccbacdaaddbdccabcbccdcddabbdadcccabdcadbacabcbccabbbccaadacaddcdbdbbdaaabcbccbdaaabcddbdbdbdbcabdacabcabaaaccadacacabbadcaabcdcacdcddccdbcdacaadbcbbccccbdddcbcdbccccdbbcaabdbbcabbaccddbccddcbbccccadaadbadddccbdcdabadaabcaaaabdbcbcbdbbcadbcbbbdcbaccaabbcddcbadaabddcdabadadcbdcababbdcabadbbcbbbadadabcaadbcacdcadddcccaaabbdcbadcdcaccabbcccaddcacddbcbddaacadaddbcabbcbbcbdcbbcbaaccbbcaccdadddccaaacdbcbcacdbbdcbdbaadccdbbdbbddbdabbdabaaaacbabaccdaaaadbaddbddbcccbacdadbaacddcbcaabbabcbbabdcbbdabbbcbacdabbadaabaaabbbabcdaaddcbcbadddbbdbdbdbcdabbbbbccaccbacdaddbcccbbcdccaadbadbccccbcdabdaddabddbcbdddbdbcdcbbdadabadadbbccdcdbbbdcadbbdabcdbdcccbdddcacddacbdddacdacaaccdabcaadaddbaddacabbabccddcaccbccdabcaaabddacadbdaaccdadabdbdaacdddacddbabaadccdaddddaaddaacdbadacccbaabaabdaddabdacabdadccbadbccddccbbcdbcddbabccddbabaddbaaddadbcbcaaddbbcdcbcacddbdcadbcdbbcdcdacdabbdbaabbadddcabdbccbdacddbacdccabdaabcbadbcbccbabadbbbdcbbbddaaadbbcbabddabacdcaabbbacacbcaacdcbbcbaacaddbbdbaacaaddaccccadccaddddbadbabcddcaddabaacadbbdacccaccbacaabadbaabcdacaacacacbbdcbdbcaccddabcbddabaacdbbcbbdacddccbdaadcdaddadbacddaaadbcdbbbdaaacacccddabaabbcbbbcbdbcbbcadbacaccadabadcbbbbdcdadabcddcaccdbddcccdaacbcddbbcbdaaccdaaaccadcaaabacbdbcbbacdddcbcddcdabacdcbdbdccabcbbbcdabdacddbbabcdabcbaddcbddcddddbbbcacbdcbdcacdcaaaaacacbbddbabcacacbaaabccadbddaadbaddbacbacbccbbcbdbabdbddadcdabbdbdddbaacdbccbdddbadcdcccaaacccbbabdcadcadcdcbdbacdcddddadccbaaccacbbcdacbaccdbbaddadacabdaadacbaadcdccbabdcacaddaabcbabcbdbcbcdabaccabbccccbbaabaadcadbaddccdcccaabdaadabccbacdcaccbdcaaaaabbacacccacdccdabcdadbaaddcacabdbcddcaacbcdccdabbbadccbadadbdbdbacdbdacddcaabbcbbdbcccdccadccdcbaaccbbddabbadaddacdadcddaaaabdaaccbddaaaabaacdabbddbddaccadcbdddadcbbaaabdccddadbcbaadbdbccbcdcdbacbbccababadaaaacadcddcabdaaaddacbbbcdbbcbccbcbabdccabdddcadaabccadbabcdacbdcbabcbbcbbbdadacadcddaaacbbcbbbadabaaabcdabbadaddbcacaacdcbccaaacdcdaaacdcdabcccddbaadcacbadbcdaadabbaddadabcbdbaabaaadbcdadccbdbccadbcbbdaabcbdabadbbdcdcbdbbbdbaabaacaaadacbcddddbdcbcabdacdabbaaccaddccbcadddbadcabbacbacbadcdcaacdaacaaabbbcaadcbdbdbbabaacdbcbbcdbdababdbdaadcdbcbabccdabbbcdadbbbabbdaccabbcbbbabcabcbbcaddacacdbcbaddbacabcbbaaacadcadcdccdbdddadbbbcbcbacabbbccddbbdbbaadaaccbbaacadcabcbbcbbbbadcdabcaaadadbbcbddddcccdbbdcacbdadbcdbbbbcaddbaccdbddcdbaabdbaaccddcaccadbcaddabcdbacacbcbdddabbdcaccdbadaabbdbbcdaaaaabcadbddbdcddaaaabdbbcbbcaccbccbdbcbdcaaadbacccbbadbdbaaaaaddacccdbabbbadaabcdbadaaaaadabadccadddbcdddcabcbddaaacbdcddbdcddadbacdcbccdaadbdaccccaaabbbcdcbccaaacdbdbccbccbbdaacacbbdcadaabccbcbccbbbcdacadabbddcdacbdcbbaacdbadbadbbacbacdcadcbaacdcdbabbadddacbbababbaacdaabdbccabdaadddaddcbaddaaabcabbdccdadabccaccdcbbcabadabadbbacddcabcacbcadcccabcababbccccadcbadbdcdbbddaabaaaccaacdcbbaabcdbcadbadccbcdaadddbabbdddcdbaabcddcabccacabacbadaddbaadaccbddbdcbccacbadbdbcbcdbcabdcaccbbddbdaadbbaaddaabbcccadccdcdddabccdaabbcabdbbbaccddccacadbdbdcdaaccdbacccbdcacadcacdaacccaaacbabdcbbcdabbcddcdcdbaabcddcacddabdabbcacadddcadadaadbabbabbbaacdbcaddbcbdabcbdbcbdbdadaccbacbbacacabcaddbaddcddbaabccbbbcdacacbdaadbcacdbcaabddcabbacdbcdbadbbdbcbddaccddbbacabbbaccdabaacdaabbcccabcdbabdbdaadcaadadbddddabadbbbadcdcbdbdbadddbddbdcbccbabdacdaccabbbddbdbcdbacbabcccccbbcdabbacbaddbcabcbadcdaddacabbbccbbaabcbbbaadaddccabbaccbbaccccacdcbaccdbbcbbbbbcbacdccbbdabdcaccaccbdbcaadbcaaccaabbdcbabddbdcaacadbccbddddcbbaadbbddabdabdadabcbcaaaacdbbdcccbbabdcccdabaccbddbcbdbadadacddabbbacbcaddccadddbbabcbadcbabdbdadbcadaccbdcacddabdbcabddccbcbddbcccbbbcccabbaddaabdddaccaccacbbbadbcddddcadbbdbacbdcccdbccbdcabbdabcaadbaddbbddbbbddbbddaacbddbabdcbababcddcadcbbddccadbddddcdcbadcdabcbbcaabaaccaabaccddcacadaccccabccddaddcadadaaccbaabadbbdbcdbbabbddaccdbaabadcadcddcbcbdbcdddbccbbacdbccccacacbbcccdddbdddbaccdcadbdadcdaccaaccabccdacdaaaacdabadcddcbcbbccccabbddadddccbbaccbaaccbdaacdacbcbdcaadbdadbabcabaababcddcdcccabbbdadcdcacccaadaccbcaddacdaabccacbaadccbbacbccddabadbccacabcaccadcdcbdcbdabdbcbddaabadcdcbdbacaaadaddbbaccbcbdcdbacdacababdbadbcdadcdbbdaadabdbbadbcdaccccddaadabbdaaccccbbbcddbbdaaddddcccbcabcaddccbbaddcaccbbacacabbadaacbadabadcbbcaaadccbddddbbddcacbabddbddaccddbcdddcabbdaacaadacdaaaddbdbcdabdbbbaccadcbcabbbdcdcdddabcbbccadddcdacdccaddabdacdbccadaacadabdbcabaddbdbdbabbdcbcdaaadabaadcddbbccabacbccbddbbaaddcbccdcacbccabbdbdabdccbbdcdbbcbdacdaddccbcbcadaadaddacacbdadabbcbcbddbbdabcddaacbbccabbbccbdcddadbddabcddbcdacdacacaaabbccdbbdcdccaaadacdcaabdcbabdbcadccacdbccacaccaaddaaadbbcacabacddcbbdbbdbdbbccacddacddddaaddcdaddadccccacbcbbdbdcaabcdcaadcadcdcccdabdddbdabdacacbbaabcadcbcddadadaccbddadbdccddabdddcdacaddbdadaaccbbaadbbcdccbabadbbabbdbdabdaccdbdcaaaabcdccabacabbaccddabcbbdabdaccbdbbcacdaccdbdcccdcaccbcbdbbbdaccdaaccaaddadbbaccacdbdabacaabbbbdbdcbadcdbbcaccbdaaadbbabaaaaadddbddcdabbaddcbddbdbdbbcacdacbbbcbcacbcbdabaccaaadcadadddaabaaaaadabacccdcbcbaccaadbabdaadcdababcbbcbcaccaacdbccbadcdccacacdcacddcddbacddbdcddabbaddbaccadcbdbcbbabaaabbdbbaaacabaacddaabcbcbbbccbdcbccabaaabddcaabaaabccaadbacdbbcbbabdaddddbdbbdbdddddcdbdbaacdcacccdcdcaabaacdacdacbdbacbabdcacaccbbdbabadbadcddaaccdcbdcdccaabdcaaabcbbcccdcccddcbddacdbaadccdbabccacbacdbdbcdccbcdaabddcbabdacabccdcdccbacdbccbaabbbdadcccababbccbbaccaddcaacaadddcbcadabdabdacdbaaddcbbbbabacddbbabbdcddbdbbbddcbbcacbdcbbccabbdcabbbcdcbdbdbadbaabcdadadadaccabdbcdcbddbdbbbadbdcccddabbadcaadbabdccdcbadbbaaabddaadbddbcdbabbadaacdbbccdbbdcbabccaadcdddddbbbaccddadbccddaccdccddcdcbbccdaccddcdcdaccddbdddccbcbcbcddbcbbcbaddaaccbcacabbcaabbdcaccbbcdaacddbcabadadbcdddcccccbddcdabcabccdaaddbadabcacbaccbcadacbcdbcaaabdaccddcadaaabbcdadaabbaacacdabaacccdbbcdcabadacbadcdcdacdbcdccdaacbccddbdcbadccccbbbacbcdccbcaaaabbddbccdbcacbcdccdbadbdbdabcbaadcddbdcdccadaababcbacaadcdadddccbabdabcdbadabcacbaaaabbdbccdaaadadaddaabbdbccaddadaccadcbcbaaccdbdaaaccadaabbcabaaaacbcbaadadbacabbcacbddacdcddbdbabbccccbdbbbcaaccabcbaaccaadcbdbabcbdcadcabdbabacaabbdbadccdabaddabdccdadacaaaadbbbdbdcadcdadbbbcbadcbbdbadaaccbacdacabbddabbdbbaaddbaaccdcadbaaadbdbaadbbdaddbcbbbaaddadbabacdcabbacbcbcdddadcbdccdbcdabccdcdcddccaadbaabcdcbdacbacadcadbdbcdaabbcabdaacabdccaadbcadabdbcbcdcabcadaddbaaaaaabddbccdabbcdcdbdcdcbcadbcadacdbbacdaabababdcadadabaabcacdcccbddbbbcaabadaadcadbbacbdbdabdaacddaadadbaaadbcaacdcabccacacdcddbbdbddbaabdadbcbdcaccadccdcaaadccbacadbdcbbccbcbbbdcbcbbddcacdacbabccbccbdaddcaadadccbdcdbccaddcdadbabbaacaaabcbaacadbabaaddccbdbcdaccdcdcdbbadcaddcbadbcbcacdcddddaabbbbaacadadabcacbbbababdabaaddccbbaaccbbaaaaadbdcaadcaadbcdbbadcadbdacaccaaabbcdaccdcdddccaccdcbcddcaacaabdaacabaaadbdcababcaacdacadacbbacbbbbddbbcabcbaddddcccdabacdcbaabadbcadddbacadbdddccdbddccddbaddbadbdadabbadaddbcbbaaddadcdcaacadcaadcdadbbcabdbabaadccbccabbbabdbcaacddccdbcdbddbacabdbbccccbbdbddbbcadbdaaccdcdbdadbadacddccabdbaababbbbbdabbddcbcaccacbccaccbaaaadbddbcbdcabcbcbdbbdcbbdbaabbcccadcccdbaacdccbbdaabcabdccccccdadcbcccadbaccadabbcdabcbbcbbbabbcccbcbdbcdadbbadacccbacaacbacdababbcabcddbdbdbdbaabdbcbcbbbaadcbabdccdcacbabdcbbdabdcddccbcddbccaaadcbcccccbbaccbbbddbadcdbccccbbcaabdbbdbbcbbddcbdcdacbbdbadaddbabddbddacbdcccacddcbcdaabcdcabdacbbaaddccdaddacddbbcacdbcbaacdacbdcbcdbddaaadacabccbacdaddbcbacccdaddabcdbddbbcacdbdcadccacdaacdaabcdbaabaacacbbadadcaddbacdadcbabdabdaacdbcaddcbcdaabcdaddcabcacdcccccabccdaddcaaacdaddadacaabccbacccaccddccaccabaaadbbbccddacbcbccadcbdacdcbaddacdabcbccccabaaacdcacbdccdabcadcbadccddddccdaddaaaddccbabacabbabcaabbaaabacdadccbbbddcbcccbdcaaacaabdccdcadcaaddbbdbabbcacbaadcdcadbccbdabdcdddbddabdcdcbacdacddaaddabbdcdcccdbbcaadbaaadbcddbddcdcacacadbdaadcaddaaccababddcbccabaabacaacabbabaccdaaacaabcdabddadbabbbaddcbdcbaabbacbccdbdcddbbbcbbbdbcdacbdaaadccbcaabbadaaacdadccddbdbbdbbcbcbbbaccbddcaababccabcadaadccddddadddbcabcccccccdcabbbcddddbdbbbbcbdbadcadacddcddadddcadbdbbabdbcabddddddcacbabababbadcdbcddabddbccbccaddcdacdddbbaacdbccbacacbdcaabaaccbabbadddbcacaacacbddccaaacccbbaddbcbadaabbcddadbbbbdaccdcbcbbddbdcddbacbccbcdbdcbbdcabccbcaacdcacddcadbccbaaddbbcbdabbcdbcaaaaccdacadddcbcbdaaacbabadbcbbcbddadddbbbbbcdbbcdcccaaccdbaaaadadaacdbdbcbbcdbcaaddaabcdacadccccaaccabcaababbbdabdcddadbadbcbadbaaabaadadacacabcabcdacdaabadadacabdbbcccababbcdbdcdbabdcbbcbbbccbcabddcdbbdccdbbccdbbacdbcbcacbacbdbacbbcddbbacbbcbdbdddcaccabcbcadcacdabbdabbadcabaccadcabcaacbaacaccbbbcaccaabaaccdcbbcbdcadcbbabcddccddbcbaadbacbaaabbdddcddcccdcddbabdbdbcdadaadcbccabcabdcaccccddbabaaaddccdddbbdaadbcbcacccccdaadbdcadcdadccddcadaabccdcbdbcbddadaaaccdcccdacabdacacddadacbccdbdccccdbccbcdacacbddbcdbadcbadcacacddbbbcacababdcaabcabcbbaaabacacabcaacadcddaaadcbabdadcdbcdbddcdcdcdadaabcaccabbaabbcacccaacdbccbbdaddccbccdddadcacacaaadccbddcdbdbaaddcbcdcdabcaadaacaadacccccbaacaadbadddadcbddaddcbcabbabbcbdcdabadcddacbbadabcaadbcbaababdcadbdbaddddaccdbddbbadcabbdaabbbbdadacbdcacdadbcccbbcdbddacddaaadbcbdcababcbddcbbbaccbbdcadddccaabbbdbddbaccabbdaadbbbbacbacbcadbdcaabbbcaaabbcccdbaaababcbccaddadccbccaaacdddcbbcdcdbccbddacdbadacaacbbbbaddddcdaadbcdaaabacadbbcdbbcdbcbcabdcbbbcbaadcbcdbccacaaddddccdacddddbdcbddcacdccbbbcaadabbcdbaabcbadcddbbbddabcdbacdaaaadccabaaccdcdcadabbbbcacbcaadabcadabbcbdcbdbabbadcaaadcccccbabadaaaadbabbdaddaccbdbadadaccddccdbbcbdcbddbaabdbbcdcaccddaabddaccbcbacdacdccabbbacdbdabbccabaadbddacbdbadcbbaddcaabdcddadbdadccbbacccddacbdbaaacdbdbddbcacacdadaaddddddbbdadaabbbdccddaddacddaaadbbacadaaadcdbabdbaccabbccaddcdbbbaaabcbadacbbabcccccbdddcabbdbdbaddcbcbbcbbacbbddbdbdccdccaadccadaaddbdcaadbddaddcacbadbcadadcdddbbcccadababdbacbbbadbdbdcabadbddccddacdddcdcabccdcdbcadabbadbbdbdbbbdddddbaabacaaacababadadbbcdcaabddcdadccacddadcdadcadcaadccbadcdcccdcbdbdddbbaadcdadabbbcdacbddcadbccbdccddbadbdaddbdaaccbaccadadabacbbadcaadbcbabbbacbdbcabdbaababbddacbdccbaabbbdaadbbbccdbabccbcabdcbabacabbcbcbbabdaaaabbaadbdbcddbcdbdcdacaacccbccabddccdccacadcbabbcbcdbabcdaadacccddaaaabcbababddbcdacdddbcadddcaaacbdbcbacadccdaddcccabdcaaddaaaaddadddddcadbacadcbadabcdcbbdbbcbdcdcbbacaadbbdbdbccbdadbdbaaacdabadaacbdaddbccdabadcbbdccacdbcdcbbdaabdaddabdcdaabbbabdccaadabdcdcabcbcaaacdbcddcbcaddcccadbcdcabbadbbcccddbabdbdddddacbbdadadaddabbaacbacadadcbddddcbadbbcdcdaabacbdbdbaacdbdcdaacadcacacbbbbdbdaadabacccbbbdbbcdabdcbdcbbdcbdacdabaccdadbcbcddcaaabdcabacbbaccaaadbcadabcbdacadcdbbbbbccadbdcdbdcbabbcddbbbcddcabacddadaaacbadbbbccdabbcaaddaabcbcadacdabdbdbaabcbbdbdadcaccdbaabcbcabddbcaccdaddaacdbacbbbdcabcaaccdbdcbbdcacddddbdcbdabccbcccbbdcabccdababccdcbcdcdaaaabcdbcbaccbadbaabcaacbacccdbbadacdcdddabdaabdcaabdaacabcadbaaabbaccbbcabdddccddcdaadbaccaaabbccacbcaddcbddcccbabbdddbdcccbdbcddbabbdddaddcbdbbcccccbcaddccacddbccabcabdacaaadbaacbcdbacbcccbacadcabbbacacdcaddbcadbcdacdccabaabadbddcabccabacabbbcdcdcaabacbddddadabcddcddbaadcadbbaacbabaaadaddccaccbcbbddccddbdcaaccbbabbbaacdaccaabcaccaaccabcaabbbccabdcbdbdbbaabdcaacddaadadbdbccdddadcdbbcabaddcbbbcdccbababcddbccdbbbaccbdabadadacaacbaddacacaadccadcdbddbaacabcbcdddccbdcbacaccdabaacdcacbbaabdcbbbbdcccadbaabbdacdaaacaddcaacabbcaabcaaadaaacddcddadddbabcbdbacadaababdbcaaccddbdcaddbaddbcaaccbbdcadacadabacdbabacdbcacdbbbcdbbbaabcddddccbbbcddbcccdbdbcaccaddbdcaaadabbbabdccdccbdbbbbbcadabbccbddbbaacbddaadcdaddcacbacadcbcacdacacbdbdbdddbbbbadaabccaccddabcaaaccddabccdadbabaadcdacccacbbaabdcbccdcaaabdaababddbbbacacccabbadcadbbbbacbabcdccbbcbdababdddabcdbacccdcadcabccaddcccdcbababbacbcbbcbcacbcbbbdcccaaaccdaddcbbabdacbbbdabbcabbddcbdcddaabdcbbbbccdcbbccdbdacdccadadbbacbbdcbbbcaabcdbcbdbbdbacccbbdbabdaccccabaacccacaaddaaabdbdccccbddbdbbccbcaaabdacdcaadcbbdddacbdadaaabcabdcbabddcadabbdbccadcbccaaabcabaacdbdbdbbcddcabcacadbccbaddabbaccbbacbbcbaadabddbddabdcbdcdcddcbbbcbbbdbbbaadcaaabbcaacdbdccbcdcacdadcababbbbdbaaddcdcdddddacdbcccdcbcbaadcbcdbabbbcbddadadcbaccddcdbaddabdcdbacdcdaccbabbabcccabdbcbdbaddabdadccdcdbdddbadbcbbbcbccabaccdddddcadacdaaaadadcabdcccdabbbdbabbacacbcdbbbcdddbdadddbbcbdbacdbadacdcabadbbbacadcdacbddcbcccdcbbdaccbccbdcddacdbbbbbbccdcdddabcbbbaccbcbbdbdcdbcdcabbbaacdbbbbbabddbcccdadbcccdabcbdbbdababacbdaaccbbddbcdccbddcbaaaddbaabacbddcddacdbdabbbbbbdaadbcbbccdbdddbacbbcabccacddcbdbdabcaabcdaccbbadbdbcabadddadbdcdcddbcaadacdccdaacdacddbbbdabdaaccdcbbbabdbdabadaaddbacadbbcdbadcadbddbbcacdaadcbbbacbdbbddaaacddabdbdccccddcddbcabcdbcbdddacabacdabacaadaadbcbccdababddaccbbddcdcdaadbdbcabbbbdddadbaddcccbccdaadddacbbcbccdaacccdacabadcccdcbccbdcaabdbbacdadbadcaddcacbbcbcdbbaacadadacbbbcdbdcdbbaaadcdbaadbacdbaabacacddbaacccadcbddcdabbdbcbbaddaadabdbcbdddbdbbbbbbaacadbcdaaddcbdaddcdacddccaabdcadbcacaccdacadaabcbddacdcbcbdcccaabacadaaddcabccccbaaadbdcbcadddccaaccbbcdbbcddabacbbddddbccdddbcaabbbdbddbaabbdbbcadaddbbadbbcbbdcacacabdaaaacdbbbddcabdbadbbcdddacdcbdbdcbcdaacabcbddcdbabdacacbdccbdcadbcbabdabaacacbacacbdacddaadbbcdbbacaacbcbbcddcaacdbacdddccaaccbcabcddcacacccaccccbacbadbbccdbdcabdabbccdbbcbcdcbbacbacbddcabadcbacaddcaaccdbddcccdbdadbddacdccbaabddbdccdacdbaaadaabddbcaacadabdbcdbcdcaaddadbbacadbabacbdbbdccabbadbaabadabbbbcdbdaacbbbdacddabccbaadcbdbbdadbadaabbdbabbbdaabaddcabcadaadcbcdbcbbccdaaacbccdaccdccbbcbaadcbcbabbccbdabbbcbddacaccadccaacbdbdbcbbbbdcdcdcdcabdbcacdcddbdadbddaddccbadbdcccbbadccdcdaacdbbbcddbdbddadbaaddaddcccccccbaabbdcaddabccccdccabcabaddaabdadcdcaaadacbcaddaccdbbabcbaacbbddabcbccabbdddaccacddcccbaabccbbbdabcabccbdbbabdcbcbdddcbbbbbbcbadbdbbddacbbcbcbaadbbdcabddabbbcaadbbdcbbdcdacbbaaacdbacbbabbadacadcdcadccddcdcaacdbcccddcabbadddadbaadbbcaaaabbcdccaabaadadcacdacbbbbbcdabdccadddccbdcacdcbcabacbaadbdaddbbdccabdcaabbdcaacbbcbcbbcbcbdddacbdbbcdbddaabacacccbcdcababddcddbaccbaabbadbccdddcddcdaaadadddcbcdcdccbbadddacbcaadacdcccbdbbbadcacaabbbccccdacdadbcdcbccdbddbcdcaabbdcdacccbdcadbacbdabcbddadadababacabdccabbabccbaadddbddaaddadbaaccbddcdaaaadbaadaaaddccddacbdbcadcdcadbddcaccbccacdcadbacbcdddadcccbabbbdaaaccdaadcbcbaaaddcaacddddaccabacabbacccdddcdaacaacbbcbbcbadbcadcdaaadccbbadcdadacacdbcabaadabbacadacadcbdccdbdbacadabccbacdbcaadcbcacabbaacdabbdacbabddcdcbbcaadccccccdbdddddadcddbdacacaacadcdbdccabdbbdcdbabaadddcbcacdccccbccdcacdcccbbdbcacdbdccdadcbbbcbcabaaddabbbbbbadadbadcaacababddcddaabaccaabdabcabadcdacacaabbbdcaabccbbaddabacdcabdccdbacaaabbadaddbbcdccbbbabbcbaadbcadaadbadaaccbacabbdbcbbcbbcdbabcdacacaadabbdacdabcdcbdcdbbcabdacbcddaacbdcbdcadacaccaacbabbdbcdbbdccccacdcbddadaccdddbdbcbcabdacbccabdacdddcbdbcabccabbacccdbcbaacadaabacdababbbbabbccbdbdabaacadacddabcdcaccbaaabadbdbcdbadadddbadcbcabcbbbcdbcbdbdccccbbabdbdbdcacccaaccaadccaddaabdccdacdacdabdadbbbdcacbcaabdbccacccbdcbbddcbabadbaabcaccbcadbcdddbdcdccbaaadabccaabbcabdcaabcbccabdcdcdacacadbaacbdabacbaddbcdcddccdcaaacdaabbbdadbdddcadbbdbcbbaccdccdcbbdaccaabaacdcbddaabbdcaccbccabaaccbacbbbdacbdbbccbbcdccccadaddddabbdccddacadcbcdaccbadaddadacabaccbabbccbbbabdbdcaacccbddbccdcadddbdcddaddccabbcdccbbcdccacbaacbabaaccaddcdbaacacdddbddcddcdadcbbbddbdbaabbcdbddbccaaadacacabcaccdcbddcbadacccbdadccddacadbcacdacddaddadbaddcccddcbdcdaaddbcdbabdbbbadbccbdcddcddabbabbcdccaabbbbcdacaacddbdbadabcbacbcdaddccccaabdcbacaabbacdbaacdcbbcacbdbdaadcbcaaacbdcdcbbdbdabdbddddbcdcadbabbdddcdbdccabaabdbbbaddbbcdbcacbbbdddccbaabdabcadabaaaaddcddaccdacbbbdacdcbbabccdbcdbbbddbdcbbdcdccaaabddcaccbbccdaccaabbabdaabaadddbabbadadccbcaadbcbacdccabcbddcbbddcbbdbacdaaddaadacdbcdadddcbbccaaadaccabadddbddadbbdcdbddcccddcccaddcdcbdbcacccabbdbabcdddcbbcbabbaddcbacbbccccadbabaccbabbaadcccacbacacabcbdabacddcbcbaadbdccbbbacddcadabdbbcbaabdbdbabcbcdadddaababdbcbcdcabbdcaddabcbdaabbdccdbadcdcadbdcbadcbaadddbacdddaabbbccbccaaddcdcbbbaadcaaccdaaabbcbccbbcaaccacbcccbdabbdbddaaaadccbbccaadccbbaadacdcdcaccbcddcacaaaabbdaaadbadaaadddcadaaaadbabddddcaddabdcbaccdbccccacbdbddbdddacbaacdacbcacddacdabacbabdcacbcacddcbbcaadddccbdadbcbbcbcaabbdbddbbcdcdadabcdbddaadadcaacddabcbdbabbddcddcbadadcaabcbdaacbdabbcadcccdcadabddadcbcbbcccdcbdbaadbbbaddcacdddbcdbdcdcdbacddabdaaacdabcdbabacdcdbbdaadcadcacbdbacbccacdabcbbdabdcdccdcdbdbaaddbbcddddacbbcdcccadbbcccabcadbcbccacddcadcacdcadccddadbdcdadbcadbccddddcabdadbccbacbcbabcaacccbbbbadbabccddcdcdaacbcccaabadcdacdadaabdabdabcaaababaadacbbdccbcbbaaccbadcddbabaadaabbcbadcadaabbcbcbcaaacbccacadbadcdacdbdacaddadabddbbccdbccabcadbbbadcbbdddcbbccbabbacadaacacbaabcaabbbcddcbcaccacbcabadcbadadbcbbbccccbdacdacdcbbadbcdbbbccdbbcddccbbcdaabadacdddbdbcdbbbaacbccdacbdabbdccbaaabbbdcaaccbddddbabdacdccabccbcadbcccdcbcbbdccccabbdaddacbbaadabacbbbdcbaccaccbabacccbcbdcabbbaaabbddbadcaacbcbcaadcacaddcbbabcbdcccbbcbbcdcdbccccbccbdbbcddddacaccaccaadbcaccabdbdcaabaababddbbddabdaacddcdabcccdddcddacdddbdadcdcbdbaaadcbcaadaccddddbbbcbbccaabdadacdbcdbcbdabaddbccaddcbbabcacbbbbbcbddddbbdbdbcbbacdcdaacbddadaabaadbcdabdabbabcbbbadadaaaadacabbdbacbacbbcbdbdcaacabccddbdbcddacccdcacddbccbaadbadccaabdaddcddbadacdcbadbaccdcbacdccacbacacddccdbdbbadaaaabbccbadcdcdcdadcbacaaccabbbdacccbcaadabbdbcadcdcddcacababcbcdbccbcadccddacccacabbdabbdbcbaadcdbddccbdcccdddccbcdbbbabcbaaaaabddcacbdaddbabbcddaaabdbcbbdcbdbdddaaabddbcccbadadcacbacbdcdbcdbbababcdaccaacbdddbbdbacbcaddbbadbdccababaadbacdbaacdbcdccaabdcbcdccabddcbabdddabdbbccaccaaadbddcbbdabcbddbaacbdaaaaccccbcdabcabcbbccdcddbdadacabdaabdcdddaaccbdcccdbcbaaabdaddbaacacabcccbbbaaacabbbccaababcacccbcccdabcdcccbadbbdcacacabccacadbdbbadbdcadadbdadbdbbdccbacdaddbbccaababdadbcccdbccaadadbadacccbadbaabccbdcdbcdcbbcdacbbdbbdcbdbdccbbcbaccdaabdabacabbcbabbacdbadaaccbdaacacdcbdadadbbbcaaabbadddadddccdbbcccdcbddabdcabdcadcbaccadddddabaacabdaddaadcaabdbcaddcbddcdbcaacbdddabbdbcdadacaaaddaaacbadbcadabcdbddbcacababdcddddcaccadccaadcbdbdcbccbcbddbacbdabadadaadcbdddcaadadaddbcbddadabdcdbdbbabdcbacaaacbdcdbbaabaabaccdbdaddccdcacdcaacabadbcacbdadbdcaabcbabcbbcbaadbdcddddadbbbdbaaaaadddcddadaddabddcdbcacbbddbaacabdcacdaddcbccbcddabbcddcdabbddcdbbaabaccdbaabbdcbacbcabbaaadccccbbaabdbbcdadaadadddcacbbabccccbcadacbcaacbdacbcaccbacddbacbdbddbcbaadbccabdcacbccbacbbcabbdabcacacdaabdbdadbadccabbcabcdbcabcbabbbdcbadbadacbcaccabbacdbddbdcdbbcaccddabcabcbabadbaacdabcaabcdccddcbbcbbabadddbaacdcadabddbbbcddcdacbcabcbdbbaaaacaabcbdcacacacbcccaadaccdbddcdadcabddcaabcddbcccdcbdaddcabddabbabdcdddcbbaabbcdacccaacbdaaaabddcaaaacadabcddbabddadbacabddaccaacbadacbdccadcdbdcbdaaaaadbabccbbaccabbcbcbddcbdabcdaacadddcbccbaacbbbdccbbbaadbdbdbcbabbbbdadbdbccbdbbbccdabcdabdacbaccdbacbcaccdccaaddcbdcbcdddbabbbccdddadbbadcbcabdcbcbaadccadbdbcbcabaccabacbadacdbcbadddcabdbcdbbcaabcbacbcdabcaabbcbddcaadaddcddbaddcaaaadbcccdcdccbbbdcabdacaddbbdaccbcccbabbbcdadcbdaaaddbabcdccdabaddcaaaabdaddbbbdbaadcbddaadbdaddbbddbcbbacbdcddaaccbccaccbbadbaaabcdbddcdadbacdbcddccadaabcacddbcbbacbcdbbdccbcbadbddaaadabccccdabacbcaaacbaabdccdaccbaaccbbdbddcdcbaacaddbbbcadadbddbbbdabcadcdabcbaaacdacdabbbcbcdcdadaddabdddcbaccdadbccdbabbbabcaaaabcbdddabcccaadbbdddbcdadacaccaccadbdbcdabaacbdcddbddbabdcaddcbcbacaabdbbcdbbaaccbaaadabadacbbadaabbccddadbdbcaaaadbbdabddbccbbbdcccbcaacbcacbdcddbdddddcbdbbaababcbcdaaabcbdbaccddbcdcabcdddcabbdbdcccdccbdbccadcdcbcaddbdaabddbdacdccdcaabacaddbdbabbcadcabbaaadaacdadaacddbcddbaabdbcbdadbbbdcadadcbdacabcbbbdccbaacbdcccbdcdddcabadadcacaacdadcdadacbdcdbbdadddcabcdcabccdddbcdadacaacccdcdbaaddaabbbcacbcabbccdcaccbbadbadbacdccdcabcbcaadddaaacacccbbccaabbabbbbccbcdcaddbadbadcacacccabbdbbaccdbaabdccbbaaddcabbdcadbaccbddabaaccaabcabcadcaabdabdddbaddabaabaccbbcddbdadccadabcbcccbabbcbbdadccbcdccbabccdcdbcbbcaccdbaacaadadacbaccacacbcadbcbaabdccbaacadacaaaadadcdcbdadcdcbbbcdcacacbbadaabdcdadcaaaacccdabccabbccbbbddcddcdabadcdbaccacdcddbbcaabddcdbbababbdbcdaccdaacacbdaaaacdbbcabbcadcdcbdacbcdcaadccbbcbabbdadadccddccccabaddbbbdbadbccddcadaccbabcbddabcddbdacccbddbdaabbbccddbaccccbddaaababbcabbaacdabcabdbdcbcbcddacbcdcdbbbabacaaddccaacadabdcbbdaccbdbabcdcacadbaabdcaaaadddadacaababbbccbaabbdadaabdccadbbddadaddbbccadddaacaacbbccdccdddbddbdcbcccddddacdbbacdcbadbcdddcbcacaddacdccacabadbcdbddbdcaacabdadcbbdbcbdcbabbacbabadcbdadcdddaaccddddbcbdbccbbbaddcdbcddddbdbcbcdbabbdbbbbcadbaacbdaaacacbbcaabbdaacbacbdadcdbaaaddcbabaabcdccdcdbadcadddcdbbbcccabbabacddacaabacbcdbbbcdccdabbdcdccdacaadddbabcabcbdabbdacccdcbcbaacbacabccabbadccbcdbbabbcbcdcdadcadcddbcabcbbdabbcdaadcacdccaaacbabbbcddaacaabdabccdbbdbdddbbabccdcdbdbcdbadcbbcdcbbbbcbacdacabadaacbbcbcbabdddbddbdaabccaaabadccdadddacaddbbdacbbdabcadabdabccbdccdbbdadbdcbcaddaaddaaabaacaabbaabccccdaabbbddabdcbadcdabbdcdddabdddcbbcadbccdadbbbbbacaacbdacdcbcdcbcdbcaabbdcccacaaddadbbaaabddbcbcacdbdbcbcdcbddaacbbbccaaadbcbcdccccbaccbcaabcdbabcbbbdaabbcdbdbaccddaccbcdabdddbcacbbaddcbbaccdaddabddddaacacdaabbcaadbbcbdadacbdcbcaccbcbbbddaaabcdcddccdcaddbdcbacaacdadaadcbaaabdbbcadbcadbbdccacbaaadcdabaacdcccbdbaadbcbbbacbcdbcdcdbbcabcaaacdccdddcbcccdcdabbccacbbdabbdadbcabaccdccdacadcabdbbaaddbbaddcbcdcaddddaacacccbbdccaadbccddbdcdbacdbcbbcbcccdbdcddccaababbcbdaabcdcdbddbbbacddbaabbaadcacdaacddaccaccabcbbcbcccadcdabddbbcbacdbacdacbaacabcddccaccaacbacbddcaddcacabadbbcbccbacdccabdbadddccbabccccdaaadabbdcaccccacadccdddbddabcaabbacbaacbbacdcacbbbacddbaabbbdaabbabcccdbdbdbbaccbcbcbaabaaccbcddcbcbbcdcacbabdabadccdacdabddcabaccdccabaddcbcacbcabbdcdccdabdacacdccbdbaabaadabdbcdccaabbadbccccaacacdbcaccaddbacabbddddcaababacaacdccbdccddbbbcdbdcdadcdbbcccdaacbaabbbadbdacadcbaadacabbadaccabcdbcbacbbbadbaaacbaaabcacdbdbddcbcbdaabbbbbbacddddacdbbdbbcdaddaabbaaaadaaaadbbbbdbcdcadbbddbbbadbcdacacdbabdbadddddcadcdabaaababdccbbdbaddcaadabacbaccbabcdcddbabccbbbcacdcdabbbacddbdbadbcacdcdacbacddcaabcdbaadaaccabdabaccadcaadbcdcbbaadbcacbaadbcaaddaadcdcdbddadabcabccbbadabcddbbbddbcabdbbcdacdddbbbbadcaaadddddcdcabbdbacdbdbdacdddcdaaadccabbbbdbbbbcaaaabcaaabbcaaabbabdacaadccdccbddabdacbaddccadbcbbdaddccbdabcacaccdadccadaaddbcdccbbccdabbbacacbbddddbadbabbdadbcccabdbbaacdccbdadaacbbacddbdcbadbdcabcabbcddddbaabdaaabcbddbcbbdacbcbdbbdbdaddaddcadbcdbcadadbaddacdadadacbccbdccdbcddbddbacbbccaccbacbaddadbbccbaadacadaacdadbbaabcbcbdacccadadddaaaabacbddcbdccccbacdcdddbacbdcdabcdadcdcddabbdddbaacdabcbbaaadadaaacbbbacbbdcbdcacccadcadadbbbabbabaddcacadbcbbcdbbbdbccccadddbadcbbbdabaaacbdbcabcddcaadbbbcddcdddcbcbacabcdabbbdcaabdcbbabccaadaddbbbbbcbbcbcccbbbcdcdaabbbdcbdaabdbcaacadccbbaddccbdabbdadcadbdbadcddccacaaccddbdacabadabccbbcbdbcaababacacbbacdcbadcababcbdbbabcdcbdbaddabadbbdcbbbdbbdaddabdbdaccaacddaabadbaaabdcccddcdacdbabbdcacdbdcccdbbbcaabaaccacaabbdcbdbdcbcccadbbbacdcdddaddaaccdcbdbccbbdddbdcaaadacddaadccadadbcdcdbbbbbabcbbbdcaaadcaabcbcbccddcaaaadacbacadbdaacbdccbdddabaabacdbdcaadbddcaaddbccacbcbcaadbbddcdbdcdccbbaabcdbaabccdaaadcabccbbbcddbcbdbabccdaaacadacddbddccbaaabbbbaccbcbacbbcbccdcaaabbcbccbbabacbbbbdabcbcccadadacadadcccaaadbbcdcddacdacacbddbadbdccadcdaaddabdcdcbdaadcbbdcabbdadbaacacbbbadadccbccabcaccabbbdbccbccbaadaaccacacbacacadacdcccdbcaaabcbbabbddbdbcaaadacabaadcdcabdccacdbbdcacdaddbccddcbbbdccdbaabbcbcbccbbcacccdcbbdbbbcccbdbcaaaabddacbdccdadcbaadddcddbaaacdbbddadacccbbcadadbdbabaacaadcaabccbbbaadbbabdaaddbbbbdcaabbdddbacaacaadbdabbcacbabacbbdabddcbcbcbadbaadacbdacaacbddddbdbacabddaccacdadbcaaccbdadcccbccdddbbdadbcdbcbdccaadcdacdaaccabaccbbcadbadabbacbbbdcdddacbcdcdcadaacddbabddcaaaddadcdbccadddcababacacbacbbdaddadabcaddcbcabbaabcccbcdbdaccbccacadacacdabdaaaabaaccbdadddbcbaadaabcacabcdcbbbacddcaddadaddccbbbaabbaadaccbddcdbacbdcbdadaccbabcadbdaabbaaacabcdadcbdabcbbccdaabbadcadccbdbdaabacbdabdcadbabadbbcaadadbcabaaccadacdcaabccbdacdbabbdbadbacbddcdbaaacbbcdcbccacccbcccadbcddbdbdbadbbcabaacdcadccdcbdbdddcdcabaabcddacbdcccdcacbacbbdbdacacacdbcbdcdcbdccbccccbbccddccbdcadbaaabadaccdacbbaabcbcccbaacadbadcdcbbddaaadbbadbdbaaadabdcbcbdcdcadcdbdbbacabaacadacadaccdacdcbcdbbbbadadddbadccdbcccddbbbacbbadbacadaadbbadcbcacccddcddaaacdaccddacdddbcbbaccddbbcdbcbddccdcbbbddadcabbdbacdcdcbdbdccaccaccccaacbbbbcbddaaadcdcabdadbcaaadacbcaaacddbcbcabcbcdccbcccaadbdacbaccadababcdcccbdbacdaacdddccbdbbccdcadbdcadacadadbbabdccbacabddaadddccabdcdcbbbdbbdabadbdabdabaaadbdccaaaabbdddabadcbdbbbabccadccabacabdbacbdaaadbcbadbbccabbcddddaccdbccbdbbbbaddbccbbbbbbaddabcadbaaacdadbbdccbcbbaabdcdbcbdccdcdaaccaaabadddbcdabcaacacbbdbdccacdbdbbaccdbbbccbdcabbaabacbabbdbdbbddadadcdaadacabbccdbcdbadbdcbdabbabacaadbacdbadbcdacdcbcabaadacbdaaccbabdbacdcacbcdaccbcccacbabdadcbcabaaddaaccbcbddcadbbadbbddcabddadbcccabcbdadbabdbbbdacdabbdbcbddbdbadcbdabccdccbacadacadbcbdabdaabdbddaadcbdaadaaadccdbbbbddbdadaacbbdbcdacacdabbccaabaccbddcaabbacdbccbcdddcbdcbdcbdccabbbbbccabbbacbabadcbbcccccbdcccbacbbaddbcabbcabacbcbbccccdcbbdbdbdabdcccccbcabddbcabbbabbabcdbdcacbcccaabccdaacadcccbbbbadccdccaabaccdabdbdcbdccbbcbbbacddcdabcbcbaaccacaadaddadcabbdddbdcacabbcdbacdcbcbaadaddcbaabcadacabcbbbcccacbabcaaddabbbbbdbdccbcdabaddcaddcabcabadcbbcaddccbcbcabcddaabdbbcabadcacbcbbcbbcaadabcdcbddaccdacdbbdcbabbacddbabcadaaccbaccbdcbadbbbbacbcccadacacbbbdcbbbccaabdbccdcdcbbadaabddbcddcccbabccacddcddcddbbbcabdcbccbbdcbabbddabacdbaadccababbccddcbddaccccdcdaaaccbbaabcbdaddabcabdbbbdccaacbacaaabcbddbbbbbcdddacddbadccbabcaaaacabcadbcacabbdddaaacdacaadaccacbdccacdcbbbaccccaaddbddbccdacbadadbccddbbdbaaddccdcdbccdbadacdbcbacdcccacbcabdcddccadaacbbddcdbddcabaacbcacbccabdaddbcccdddcadcdadabbacbddccbccbcacbccccbdacdadbdadcadcbcbbddcdcabcabbddaadcabdadaccbbaddaacbbdadcbcaabccdbbdcccbcbbbbcbbcbcccddaccacacbcddacacdabbbdcbaaadcccdcaadcbcaaabccccbdbdbcbcbdacdbadcaccbdcdbdaaacbcbbddcbddcdbadabccbcadcdbcbbaacdcadcbcbaaadcbbbbbaccaccdccdaaadcdbcdbadddcddbdbccdaadabcaccdcbdccdbdabadccacccddbadaccbcdadbaacabcddacaaaddbdcbaccddddcbadacabddbbacdacbcbdbcabadddddbddcdaadabdcbdaabaaaabddbacacbdcbabaabbbccdddccdbdbacbacbabbdbbbdacbccbaccddbddcaacacccacdbdcbadcbbcadcbcdabdbccccbbbdbdaacdbdbabdbddaacbbaccaaaadacaddcddaccaabdbdaadbdbdacadddddaddbabaddbcdabbadbbccaadbbcbbcabbcaacbcadcdbbbcbdacccbdddabcaabdbabcbbbdacacddabdbbdcaacabbacaacdaddbcaaabbdaacbbdbbdaadabdcbdcbcdbacbbcbcdadbccdaacabdbacdaddcdbabbaccbaaddaddbcdbcababacaaadbbdacccaadadccdbbdbccbdcccdcaacdddbabdbcdbcaadcbbccddbabccaabcbbaddbdddcddbccbcabdbbddcbdccaadbdccbadcbdabcdcdaaadabaabcbaccdbdabacacbcbacdcdaddcdcabdcbcbcccaaccbadbdddcbabccabbabadbabbacddabcbacbddaaddacbbdcddcdddccccbbabbaccaadabacacbbbcaccdacbbbbdadaacdaabacdcbcbdbbdacdcbddbcdddbdccddcddbcbbdcbbbdabcabbdaabbacabcdbdadabadccabcdbbaacaaaadadabbdbdccdbdcbdbcdaaadabcaaaaccdababbbadccacbadcccacbdbbaadbddbabbacabadaaddadcbbabdddddababdbadbdbaaccdbcadddabaabacdddbbdbdabcadbaaddbcabadcadbccddacdcdacdbcbccdabacacddccabcdaaadadaacacccaaabbdbdacbbbacaabbcabccdbcadaababcdcbcccdbddcddbdccdaddcbcadcdcbcdadacdaacbbabdbdaabacbcbabdcbddaccbbdbbcbcadccbcdddbccdacbaabcbbcdaabccdcbdbbcaacbddadbacbbcbabcbcabaacdbaacbadcbabcbcdbcadbdcaddccadcbbacbcabcdacaabbbcadbdbbacacbcbddabbdbcadacbcddbcbcadcdcbbdaaaadbbbcddcbbcaadababcbaddcaddcbaddccbdaaaacababacdbdbdbbbddddcbabdccbdbddcdbcdbccaccbccdcadadddaabdaaaaaaadddbabdadaadccababbcbdaacaacaddcbbaaabcabbccbcbabcbbcdcdabaacbdccdbcbcbcaacdddbcadbddbaaacbadbcdcadbcddcbbadccbdccdcccddaacccbacbbdacddadabcbdcddbccbadbaddccdbbdabbcdcbabacabaabdacdbdacadccbbdccaddccbbcbdccccdbaacaccaddabbcaaacacaaaaadaccbbabadccddddbcdccdcaaaccddcbaccbccadabcbcccabbcdcaaaaaadabbcacdbaddcbbdddbdbcabdbdccccddccdbddccabdbbdabcabbdadacbdacddcdcbcccadcadaccbbdacaadddbaaabcacdbdabcaabcbbdadbabbbddabaaadbddcaddadabaccdbccccbbbabcbabbcbbbaaaabacbaadacccbcabbdddcbcdaddcaabbdcaadbbcbcabaabcbbacbbdababbdaacdacdaaabdadaabdccbabccbabcdccacbcaacaaabcacaacacaaddddcaddcabbdcadddbcaacdbaccbbccdaabbbdbabacddbccacdbbbcaaacddaacbbcbcbdbbcbaddbcddbbdbcadbdcddaaadabcbccdbccacbdcddcbbdbbaabbaddcbbdbdbdbdbbaccbadacbabccdaabdcbbbcbdaadcbbcaacbbdaacbbbddbadcbddbaaddacbbddabbcdcbabcaaabbcaaaccdaaadccccdccccabcbabaabacacbccaaadddadbdbaaccbdaabbadccadbdcdcadbaaadaaabbbccccdacdccadccaadccdabdadcdbccbdcddababbaaddcabacbddbbcabcdddbbbddbdbcbabbaadbccddbcacbbadaabddbddbcacddbddacbdcbcdaacdbcacbdbdcbacabbcbaaddababdccbdbddcbcbbacdbbcaaacacdadbdadacbadbbdcccbcbbcbcbcaccbdaabadbbacbaaacbccbbbcbacbbcdbcacdbdbcdbdddabddaaaaabdddbddacaacdcbccddbcbaacdbdcbbdbdbcbcabcddbaaabcaacccdaccdaaadaabdcbccbcaabdcdbdbadbcacbbbadccbacacbababdbdccababbbcaddaddbdaaaaacdbabdbbdadadacaadabcbbdbdbdddcdddcddbdccadcbbbdbdaddbbacdddbbcaccbddabcaccdddababccbdcaaccdcccddaccdcccdbcbcacabcdcbcaadacddddabbbabdbdcddadaaccbbdddbaccbdddbddadbdcabacbdabbcadbdbdaacadbcacaaadaccdcabdbcbbcdabbcadadadcbddcaacdbaccddcbaddacdbbdccaabdbdcbcdddcddaaadbbaacbdbbdbcccddabbbdcdaaacbbcbbadccdcdcaaacabbbcabbdbbcddccccccaadaababccbacaddcbbdcaccacaaabaaccbcabdbdcbadbabddddbcabaccbdabbacdabcbcbcccbdabbabbabdbbbdcdcabadcddddbdccbaacabcbbbbaaadaccbbbdadabdcdcbccabdddbccaaabcabbbcddddcbadccbdabdcbdcacadaadcbbdccdbcddcbcdbacbabccabdacddaaadcbdaddccbbdbdadaaacbcbbbcbabddbcdaaabddcdbabbbcbbcdbaccdabaaaadaaacbdcdcddccdcbbbaddbbddaaddaabccbbcbbccbbcdadaacdcddbccabbbacdbadbbbbaacddabcdadaaaabbbabbdccdccbdacccbbddaadddabdcbbccdcbaadbbbcdcbddabbcdccbccdccabbaaddcbbacdaccdbaccddaacbcdbbacadadddaddcddcdcbaccacdcbbaccbbdbccbdcbabdaacabadcdaacadbacaabcdaabcdbdbcabdaacacacddddbbbcbbdcbbdbaccbacddaacdbdadaaaacbcbcdbdbdbadacadbacaabbaacccbddacccdcbdacbadccbbbacaaccaacdacccdbadbaabcdaccabaaaccaadacacdbbbdcbcdbdbadddcdcdcdbdbabdaadabcdddbdddbbbccaadbaabadbccdbdaadcccbbbcbacddbbdaaacacdcdcadbabdbbbbccbdaddcaacdcbbaacccabbacbcabbbcdddcbddbcccaccbacacbcbcabdbaabdbdcaccaddacbbadccccbbccbbddbcdcdcbcbaaacaabdacbcccadddcaabadbabbdaadcbbddbbabbadcddcaaccabbdadbbdbaacbadcbaaaddbbadaccadbcbbbdbdacaabcabaabaabadbcadbbcccdabaccdbadbcdbbbbcbdcbdbcccbcccbadddababdbbcacdbacabaabdcdcbdaabbccabdacbbbbacdbadbcdcdccdddccabcddcbdbdabbcdccbdaacbbadcbbcbaaaaccabaddaddccbbcbbadcbcabacbaaaadadaadcadccccdaacbacdcbbabcabdadadaabdabdcbccaaccbbdacabccdabbadcbadbababcdbaadcbcdadcbccdacbaadccadddaccbcbcdcbbddaaddcbaacbdacdcdcabcbabdbadbcacdadcdcdaccddbcbbbdaddbadbaccbbbbbaadbbbccbdacdddccdaddaaabdccccbccacabccdabacbccdaadacdcdccaaadaadaacbdabcdcddbddccadcddaadaccdcdadbdcaaaabcabccbbcdbbcaddabcaccadddbacbabbaacaadaabaadcaacbccabbcabadccabdbdadcbacaadbabaccaddddbdacaacdcdbbababbdbdcaccddcccabdabbbcbddabbdbdacbacbccadbbcacdcbabdadbcdbaccbacddbccadacadacbaddcdbaabbdaddcadbcdcaacdaacdacdaccbcdcbbaaddbdbbddbddcddbbcdabccbacdaddaaabdcacbccabcabcaddaabadacdcccbabbbbaaacdcadbaadbdbbaddbccababbacccbbdaadaaadbddcbbdabbaaccbabadadcbaadabaddcabcbbcdcdcbabbcaabadaaaadbacbabdbcaabbabcccdbdddbaaccbdddbbdcdcdcdbccaacabbdbbbcddacddbcaadacbadcdadbcdabadddbaaccddcdaadcccbcdcaadcddabaacaabddacabcdcdbadbadaacdccdcbdaddcabdcacbaaccbadcccccdddadacbaabdacccbcdbabddbdddbdcbaaddacbaddddcbbacbddaabccbadcaddcadbaccbdcbcbbdcadcabccdacacdaccddbdacaddacdcabcacdbbcbcaabcdabddcdcacdbadcadbcdcababdcddacaadddbadccdaadddcadddbabaacdcacccddaabcbcdbcbaaddbddadcaadcabbbbaddcdcdbbbdabbcabcbdbbcccbdaccabcbaacccdcabababaaccbcddddbcddcadbdcbacbddbdcdbcbcadccbdaabcbdcabbacacccdbbaaddbccddbcdcbaccbaccbcaabdbdcddaadbbbdbadccabadbdbccbabcbacbbacbbacccddddddacbbcabcbacaaadbbbbdcccaccddabbdadadaccdcdcddcdbaacdcbacbbddaddccacbcccbbdabdababbabdbcddaabbdcbcbddcdcaabdabacbcadadbbdbacadbbaaabaacaacaaaacdccdadcdcaaaadbdbddabcdadcbbbddaaddbabdddddbdcdaabcaaddcacdbabddabababccacddcaccacccbdacdaadbaccaccbdcbbacbacdcbdcddcdbdbbdaabddcadaddaaccadaaabcbbaacbbbddaacbdcbcbbcdabcacabdbdbbbcabcdcabcadbbadadddaabaaacbdbbbcdbdccadddaaccdcdcbdbdcbbdaddbccbcadddbcdcdcdbbdcbdcabcdadaadaabaddcacdabcaadbcdbabccaabbbdcccdacabbdacdbbcabbadaabcbcccddccddbccaccddabadcabdddcbdaadccbccbbbdadabcbaabccccbbaccbababbdccbcadacdbbbacbabcbbdbdbbdababbabdacbdddaabcabbacacbdcbaabbbabcdcabbbaaaabbadcaabadccccddccaaabccbcadaacdbddacdccdddbabdacddacccabbcacccdbaadddbbcadabcdddbbdcabbddbddbcbadddcadabccbdbabcaaccacbddcddacdabdcddabaccbcbabacbcbbccddcdaccabaacdabddcccabcbcaacdcbcbdbabddcadbaaddcabbcabddabadcacbadacabbcbdaccaccabacdadaaabbdbcadaccacaabdabdacdadaccbbdcbacbcbbddbacbbcbadcbdadadbbbbddadaddccdcbcdabadaccddcbcaaaccabdabdabcccddbcadbbbbcadcddbbcccacadbbaadbacddacacccbdcdbcabacdbcacdccddbaadcababaaddabbcaadbbacdbaddddccaaaabcddcdbcccabddbcacbdbaaddcaadacbbbcbbbbddcbadacdbaadbcaddcadddcbcbcccdbadbaddcddacddddcdbaaadddccacaddbbcbcddabccdabcbaacdababdabadaadaacddbcbddcaaddbbcbdbbbbbbabcadadaabacadcbbbabdcaddadacacccbbcbdbbdaccdccbdbdadaacbaccddabcdcdbabcacbabdbbbbbaababcddabcabbadcbaabacddcacdabbaadbbcadbcbddcdcacaaadabcaaabacdccbbdadccdadabdadcbdabbcdacdbbbccbcdbbbbacaccaaabcaaaaaaddbcdadbbabcbbadddccabbabddddcbccabdbdcbbcaaccabcaabadbdacbbaccccabadbbccbdccbcdbdddcbcbdaccdbbddcdcccaacddcadbdacbbacaaaadbaaddcbbcbcacbadcadcaaaddadccbdacdacdadbadbdcbbbaccacddbcbbbbbcaccddcbaadacdbdddbbdccacaabbbababbdaaddddccddccacbabdaacbbccddbcddcabbaabbcdaaddadcbbdaaababcddcccdbacacccabdbcbacabdadacbdbbbcdabbddbabcabadccdcbabdcbcacbabadaccadbdaddabdcbdacdbdccbdbbacdaaddabbbcababaacdaaaacdbcdcbbdbdcadbbbabccadccbdddbdccdbbddccccaacdaaddccbbabdadbacdbbdbddcbbcadbbdabbaababddbacabdbbadbadccdadcadaabaabcbddbabbbdccaaadbddaaaacbddbcdadbdacbabbbcccbcacddbababccdcbabacacdbcbaccdcadbddbabcabdddacccbaccbcbdbbdbdabddababbcdabbcdadaccbccbbddbdddacbddbccccaddbcdbddcbddbccbbbabbcdbcaaadbddabcdacdaaddacadbccdadcccdcbacadbcdbdbdcbddcddbbcbbdccabaddbdbdacddbdccddbbbbbcabdaaadaacaddbbbadbabbbdbbbddbcbcdcddcabbbbaadacbaadcaddaabdcccaaccdaadcbdddbabcdacdbdacabccdcaccbacdbcbbadcbcabcdaacaccababaacacabdbbcdcdddddabcabccdaaccaadabaababcbbdbdaccdddbdadcaddadadbdababbddabcbabcbdbbdcbaacdbaabbcabadcbaccbabbcbcbdcabcabbbbbdbdcbaaddaddbddacbabdbaabbdbbddbcbdbdbacbcbadcddddbddabdaacdbbbdbccacbcaccadddcccbababcaabcdcdbbcbcadbbcbbbabddcdbccdccdcabacacababdadddbabbccbacdbcaccbbccdcddbbcdcabbcdacadccdbbbbadcabbdbcaabcccdbdccaaacccdcacbcddacaccdccdbcbaacbcaacbadbbccbdcbbbccbbbabdccdbcdbabaadacbdcdccbbcacdbbbaabcdabbaabbddccccacdccadcccadbabbbadabaaddabbcdabbdbdbcbccccaddacdccaababcdaadcbcccddcbcabdccdaaaadddbccaaaadababaabddbbdababcadbccbdccadcabadbbcbabbadcaaaababccdddcbccacbcbcdcacdcddadabbabdcbdadbacdbaaabdcbbcdccddcdbdadcbcbcbccddcacdcdacccadbadddcdbdbadbcccaacdddaccacdddccddacbdcadcbcccdaadabbbdbcbdbaadaaaccbabcaacdbdcbbbbdbacdacaddccdddbbccbddbbabdcddbbcdaccbadbcdddabcccddbcddcdccddbdbaadcddddcbcadcbacabaccdddbbbdbcbacabdbdacaadcdcadacadaadaabcaaddccbaacbccccbccbbcadaabbcccaacadddcacdacaabdcadbbcadcbcccabddbabcacdcccdcacccacbbbaadccabdddbdddbcbbccdbacccdabcbaaacbddbadbbaaabcbcbdabcdcbcabdbccbdabbbcbdadddabbcacacbcbcdcaacbcbbadacdbcbcbacacabdcacddccbaaabacdcddbacaccbddbdaacbadbaabcacaccdcabdbcdaacabcbcdcabdcbaccdcabdcdabdcdcacabbccdbbccbbcbbdabcacdcbbaccbbdcdcbbdccdbadbbccacddaacaddabdabdcdcaacaaaaddbbbdbcbcdbcaadcddcdcccaddbcdccdbdbaadbccccabadbbaadcccddaaacaddacbbadadbbacbaccdadbbbaadbcaaadaadcaacccababbcbbcddabbcabaaaaaabbadbabbaacdaddbccbbcdbdcabadcaaacdaddbbcdcbadaccbbdbcbcacdbcbacbadddbbcacacaaddddcdabaacabccbddadcccddbabcdbbccdacbadabccbaadccddacaddcaaccdcddbadcbdbababcdcaaacbbdbbabadddacdcaabdcbdcadddbaddadddcacacaddbbdacddbaacacadbbabacbccabcdcadccaabccaddcbccbacaacdcdccccbabcaaadbaacddadabdabdbbdcbdbcaabdadbdcbdcaaaabcadadaddacdabbbbcaacdccdbbaaccaaadcbcbdaacdabdbcbcdaaddbdcbdcdcdcabaadcddadbcaddcbcbaccbccdbdccbccaabcacbacdbdccdcbdcaacbdccbccbdadbcaaddaccbbbbababbbdcaacaacdcbccbbaacdcddaabdcabddcdbcacbaddcbbcbacacacbcabdbbcbddcbcaddadaddbdbbdcbdadcdbacbcacdbaaccacddbdbccbbbccbcbdcbdadddaddcacbdbaadbcbdcdaddabbabbcadbcdaccaabbadbcdccccbbddbdbbddaadbcabdbdbdadaaabacdccddacacdddadbcacadcdadadcbacbadbaabddcbdbcbbbbdbbbaacdadddaadabacabaabdaadbcacdbdcadbccabdcaddccddcbbcbcbbdcacdabcbcddadccdcadaacaccbaaaddddddcdbaccbbccbdbddacdaaadcbddbdcadabbbdbcabcadbcbdaabbabcdbbadcbbbcaaaacaaabbabbdcbcbccccdbdbdcdacdcbabdcddaaccbcdcdbdbdbcbbbdabbbcdddaaacabdbacbcddbcaaabcdbdcacaadcacccddbccbdabdcddccdadcaaababcdbddacbaddaaabdacbaabbabdbccccbddaadcaddbacbdbacbbadadbdcccdbdaacacdccbbcbadddbcacddcaadbaddbbbcaabacbccdcdbcdacaaddacabdddbdbaaaacccddddaaabaccbabccdccacbddacdabaabbcadacaddcdbcabdbcbcdbbbdcdddadabaccccbacdaadbabdcbbdadbbbcddbbdcccaddacabbbacbcacaaddbddbcbbcdbaabcbbcacacbabaaadcdaadcbddacddadaccbcdcabbcdadacbacdcacdcdcbaacacbbaddccbabdbccabadadaddccadcacccacdbddbaacddcbdcabaabcdaacaddcbccabccaacbaacadccaacaacaaddabddbdcbbbacdbdcdaabcabdcadbcdcbaccaddacdddddcaacccabdadbcbacbccacabcccacdaadcbdcabcaddddabaabdcdadacbbbdbdaccbcdaadcbabdddaacadcaacbdbadacaacdbbacadcdcbccaaddaadddcdaccddcacdbacdaddbdcadcccccddcadddcdadcbadbdbacbbbbddbdcccaadadddddbdbcdacbdcbcbdcbbbbbbbbdbcabdbdbbdaaadbbadbcabcddbbaacadbabacacdcacdddccdcbaddcddddcddcccbbdcaacccddcdbacbccdcccaacddaacbcbababcdacbadabbacabcbacabbacbacaadcdabbbdacddaccccccdaccadbdadabddccadbadaccbbbdabdacdbbdabbdcdbcdcbabbccdacdcacadabdbbcdddddbbddcddadcbdcacbbadacbdccdaadbaaccdcdbbbbddbcaccdabadcbbcdcdbbadbddbbbdbbdccdbcbdbaddacaadbbcadabcdbdbaaddbabcbbdaccbdcabaaacdbcadadcadcacccadadccccccbbbaccdddbdbdbbadccbbcaadbadcbbbdacbaabdcdddcdbccacaddbacdbadcbbabcdaaaaddcbccccdddbadcaccacbaabbdcaabdcccdacdacabbcbdacdbbcbcabddcabcccadcadabacbdadbbdacbabcdbabbcccabaadcbbaaccbccdacbcbadccdbdadbadbaaadccbbcbccadaabcdbaaacbdcbcdbdbadabacbdddcdbcadcbcabdacddbacdaaadbabcdcbaaaaaacbaddbbacdcadadabadadbadcacbaadaccadacbcdccdbbacddbbaaadcabbcbbccdbbbaccbddaacaccbcdbdccbdcddbcdccacbbbbabcdcaddbaddddcbadbbacbbbddabcddcbcabababdddbdabbadbccadcdcdbdcbddadcdcddabddadaaacbbccccbbdabddccaddddbcddaacdbcdcddcbbacadabccbbbcbabaaabdcccdcccbdbbadadbccaddbcaacdaccabcddabdddbdccdcdaacabdbbbaddddaacbdaddddadababcbdccacaccacdabacdccacaacdabbddccdcbdaabdaadddbcdacbddbadcabdddccabdcabbbabbbdabdacdcaaccbcabdaababbdbbabaccacdbbbdabbbacaadbdcccabdddaaccaaddcaddbcddddbbbcdbdabadcbdaccbcbbbacccdacacacaaaadcacbdaddcbcbddcdbbcadbcbcaaddbbbdcbdaaccbccbcbabcaacccddcbdcaacabcddddcadaacbcbbddccbcadbacbabbdacabdabdacbbabdbdcddadccadaccdbabdaaaddabacacdacddaaabddbdaacddbbbadcccdcccaadacaccdabbbcbcbdbacccaddbbdcccbbddacbdbcdbcdcbdccbbbddcdbdddcccbaacdabadbdcbbabdaccadbabbaaabacbcddcbcabacdaabcbbdcdbdcdbdaabcbbdbbcdccbcdcbbdddccababcbcbccbbaaabadbddbbabacdcabdbdcbdbcbcabdbbcdacdaacccbcaabdbddcbdbbbcdbcbaaddbaaabbbbddbcaadadaacdbddaaddbacadbbbcabcbacacbddcbccabdbdbbcdcddaddaaaacdabdcaddcdddbbbadacdccbcabbbabaacdddbbbccacacdbacdacbcabbaacdcbccaabcbbdaacbaabaddbaaabbdadacbcaadbabddddabdcdddcccabdacaacdaacabcdbbaabacacdcccddcadbdbcadadcbbccaadccabaddbcbbbacbdbbbdbcadbabdcbbbadcbbacbdbcccdaadcbcacdbbbcddabbbccaacababacbabbdcdaaaabcaabaddbacdcabdaacbaaaddaaccacabaaabbadcddbbcaadaadaccbbdadbcccbacdbbbbdccbabcdadacacaaadacbaaabcadccddbcdabadcaabdbcadddddccbddbdcdababcaaaddaabadcbadaddddcacbbdbadccacdccabccaadbaadabccbaabbabbbbdccbaabdbcadddaadbcdacbccaabbbcaddaabcdcaccbaadaacaaadcccabddcbdbaaabadddadadadbddaabcdabbdccbbbbadbdadcbbddccccadbdbbbcddcccaaababcbaccdddcaacadccccabdabacabbbcaccdacacbaacabadddbaaadabcbadacddcbccddaccddcdbccacccdddbbbbaaabbdbbbadcccdbbddbaaadbbcccaacdcdacddcadaacbbcabcbdcddbaaaccacdbdbcabdaaaababcdababbbbdbaacaaaaddaabccadacdbdcbddbdccdbbdaddcbdbddcbcdbbcdccacbbdaabbccdbcbcdaccabbddcccaabbdcdbbcbcaccbdddbdbdaadcdcbdbddadacddadaabbdccabcdcccdacddbabdbcbdcbccadccddabcbdababdaadcaccabcabdbadccacbdbccbddcacddbdddbbdcdcaabddabcabaadcbddcabcabadddaabbcaadaabdbcbaadddccbdcddaccabdaabdadcdaccbacdaaabdaacccbdcddbdcbabbdbdcbadcccbcbcccccaddcdcaabadddcaccddddcdcaabbabdbdbcbbaadabcbbbcaacbaacdacddcabdcbccbcccdadddbaccbcadccdaabdccdbbddaaaddbcdcaadcdcbadddbbbdccaababbcabbdbcdbdbacdaddccbbcccddbcdcdacdbbbdbcddacdaddccadbdcacacbddcdacbccaddbadbacabbbabcadccbccabbcbcbdccbdabaaaadbcbabadaabdddbddbbaacdabbbccdadcaccbdadccbdaaccdaacadbddbcdcaabacddaadadbaabbcdaadcacbdaadcbdbbabbdabbcbbdaabcdadbcdbabcadbbabaaabccbbcdcdbabaaabbaddadababdbcabacbddaccbbcbbcacbbcacdcaddaacdadddbdabdcdbbdacaaadbabbacacddcabbacccaddacaccadacbcccaadcccaaaadccbbaadbdbaaddaacdccccbacadaccdbbadbbbbdcacbcdadaaacaaabaaddabdaadddbbcbcaacaacbbccdadadaddabacbcddcaadbbdbabdadacdcdbdddddcbcdcbaaacbabcbbddbdbcccdbcacacdabcbccdacabadbcdddbccdcaddbcbbacabacadbcabcddccddbcbbcbdaadbdacadaacccbacdbccbcbaacbabcbbddcdbbdddaadaaadbcbabbbabddbbbdaaaaaddccaacbabdadbccddcddabbbbacdcabdcbacdabbacaddbcddadbddddbddddaaaaacdbbabbacdacbcdabbaddaadcbabdadaddddaddbbdadddacbcccbdcaaaaaddccaccccdcbcbddacdcdaabacbcddccaaaaabaccdcabdbbbabbbcdaacddcccddcdcadbbcdcadabcbcbabaaaaddcdccabcbdbadbadbbcbacbabcdddddcdbabcdbdcbccdddacddbaacadbdddbddbdaacacdaaadcccaacbaddbabcacbadccabbbcadaadcbdbcacabddaaaaacdcdcccadbbbbccbbacacbdccadbadbccbddcbcbbadbdaddbddbdbdabcadadbdbaacbcaaccdbadbaaacddaadaabbacbaadcadaccbabaacdacdccacacabdacbbcabdcdcbabbaadcadbcdcddaacdbdabbdcdaabdbccbccabdbbdcdbdbcbccbadcadcbcadbbacabbdbdbbbcccbbabbccdcbddbbbabdacbbbacabcbcccdcbdcddcdcccacdacaadbccdaadaadbabbdcbadbadcddbddaabcaccbcadabdababdcbadbcdadbdcbcccaacabadcabcbcaacbcdbbddcbadcccacacdcabbcabaadbbcbdbdaacdabbcbaadcbcdbcbcbbcdbbabddbcdacaadcdcbdcbbcabdaaabcbbdcbbdcaccbdcbcddacccbbddabdacbdaaaccbddadccabdaddcaadcdccdddcbdabbadbbabdddaabacabcbbbdbccbdcdbbbbdccdbccddacbcbaaddcbdcbbbbbdaaaadbadcabdcaaacdabcccdbacddddadacadddbcbaacabdbdaaabccdaaaabbaadcbbabccabddaaddbdacddccdacdcbbabbddcdbaabdcadbaabaddacabdbbaadaacddadbdccbcddaadcdbbdcaaaacbdbaaadaaabcdabdadcbddbbaccbdadabbbccbacdccbddaddcbcadbbdbaddcabccaacbbdbcbbababaacbcddcdddddaacbdcdcdcdaabbbaadcbcacdadabadacacdaccdddbadcdbaccbbaaaadddbbdacacacadccdadbacabccadbdcbbadbacbcaddcbccbaddbabdddcbabdbdddbbcddddbadccaddaaccbbcddabdbdbaaaadcabbacddcddbccdbddcdacddcaadcbcacdbcdbdbabcccabcdcabcbabaaacdbcccbcdaacbaababdadcdaabcbacbabdcdbcbababccbccbbcbccaddbdaccaaacacabacabadacdcacaddccacbccbaccbacacbccaddcdbacbacddaadaddddabadcabddcacabdcabcbbdcccacdadbbbaacaddcddccccabbcccbbadcdcbbbddcbadddadaabaaaccabbbaaadddabacadbcadbbddabdcdbcadbcdbdccdbdaadadbdadcbdbcdcacdcbadcbbdacccdbdbcdabddbdcbcdbdbbbbbbdccddbcacdcaaccddcbbdadbdbddcdaddabaccbbdccdbcacbbdababdabaacaadbbbaccbdcddbccacddddabbbaadddbdbdccbcdabcaadbbacbdbbaadbcaaadccdbbbcababbcdaaabbdaaabcabbabadbdbbddcccdbcdcadabddcadbbacdbdbdacbbbabdcacdabcbcdaccdadadcccdccccddddccbbaaacacdcbdbcdcaababcbcbbccbdbcbcdddbacaccddabaacaccdadcabbcdaddcdbbacacdacbcadbbbbabbaaccacaabcaadabdacaccdcbcccdbadccbbcdcbcbbacdbbacbbbbdbadcaabcbbcadcaacaddacbdaabbcadbaaababbdcdccdbcaacabcddcbacbdabaaddbabdaddddcdcdaacdadbbddbccbbbcbcbcdabcddaabaccaabddcadadbcaddabbdbcacbbbddacdbbdacbadbaaacacccbdabcdbdabcaadcdbacbcbdabadcddababbabacbcdabbbcdcbdccaccdcdddbdcdadddaddabdadbadbbacbaddacbddbcdcccdbadcbaccbbdaaddaddbdcadddabbbcaabaabaabbbdcdadbcdbcbaccbcacdabccbcbbdcdaabbdcaaadaccabcdabbaadadaddcadbaaaaacbbbcabdbcaadacaccaabddabbccbbbacdccacccdbcbdddbccbacbcaabbbbcbccbbdadcaadacdbdabadcbdccccbadacdccbbcabaadcdbaaccbabdaddcddbcbddbccadcaabdbcdaddbdcabbcaacabacadcdbaaaacbcabbbdddabbdcdbaaadbdadadbcabbdbbccacbcdaaabaabccdbcbadbbabccabaaadbbdcbccbadcdadcdcbddcadaddcccbdadbddccadcccbaccabdcbdbcaaddccacacbdaddcdbbcbdacddaccddbbcdbadbddabaacaccacbbbcaccccabacdbaaadccadcdbdaaadddcbcabbccccccdccdbcaacaaccbddbabdabbacbdacccbddaabacaaabcaaabdcbaabcbdcaddbbdbbaadbabbdabbabdbdbacdbbadbbcabdacdbbabcdadbdcaccbaabdddaabccbadbdcacaacaabdacdacdcccaddbdcdbadcdcbbcdddcbbbddbbaadddcbbdcaaaddadbabddbddabdbcadbabaacddaaacaacccccbcccdaccbccdcddcacdbdadcdbbadbddbdaaddbaacadbdcdccbccbbdaccbadbaacaabbcdacacdacaacbdbccdcbddcabaaabddccaddddbbcabccdbbcbbbadbdaccdcababbadccbcdbbadbadaabbdbdbcbcabcadacdacabaccadbbdacdcccacaadbdcadbcbdbcbcdcabaabaaddbbcccccaaddaabccbadcaddcccdaabcdbccdbdbaaddbacdcbcdccadabdaacddcacccccacbcbcadaabdaccccadcbabbaddddbcbcababcdbaadadcdadbbcdcadccababdbdbaadbcdaaccdccababacddabcbdbbddaadbbcdaabddaabccdbccacbcbbabcccacacccdacadcdbcdbbacddababcdaaabccdbdadbdabaadcbadbcababcbacddccabccbbbbcccbcccbcabdcdbbadacbbdbdabdbabacbcabcaccbaababbcdcdbcccddbcbcadbbcdaaacbbaccccdbadaccbaaadddaaabcabbddddcdbdaabacacbddbbbdbcbadaccaddbabacabccdbaacdaccdaddccdaadcbbdcbdcabbcdbadabbbbabdbccdccddccadcacdcacbcdabaccdbbdccddbdcdcacdaadaacbcaccbadabcccbcdbddcbcaccdcdddadbcbaaddcbccbbacccabcdcdcbbbaabbbbdbaddbdbaabccbbabddddbcdcbaadbbbadaabdcabbbbaccadccbaccacbddbabcabcbcacdddaacbdabaaadadbddaacacdcacabccacdacddcaacccbacdccbcdbaabccdcccdcbdcbbcdacacabbbccdcaaddcadbbaddbdcabdcddbdbcbdadcddbadbabcaabbaaacadcdcaccdabdaaaadaccaacbbcabbcbbadcccdddaaacaaacdccdbddabcdbdabcdabbcbdcbbbaabbddbacacdbcdcaadddacbbacbdbadcaadabaabadcccbbddbdaabbbdabdaabccdcdccbaddadcabddccaabbbbcaaddbdbbccbadbddbdbbcdadbbcbabcbbddccabbdabddabdadcaccbbdbacadacbdaadcbcbacaacdadabcdcdbbcccddbcacdbbccbaaadbabbcddddbcabddabccadcbacccccbcbbabdbbadacaabcccddcdccabbaccbadcbacaadbbbbccaaaaccaadabbdccbcaaaadbdadcabcbbdcddcabbaadaabaabbcdbbbdbdccadbccbcdddbbbacddcddcdadcccadbdcddcbbbdbcbdbadbdaaabbdbddacdbabbaaacaabccbabbcabaabababcbddbcbccdacbacdaaacbdacdcdbcdbcbbbbbdadccdadcdaabbcbaccbcbadcbadaaddddddcababdaabcccddbcabbbbbcdabcbdbcdabdadcdcaacddbbcdbaddacbcacdacacccbddddaaacddbddbcdadbccdcadcddcaabcabcbacdbdccbacadaabaaddcbdaccaaabcddcbcbccdadcdacbcacbbcbccdacacccbdcbabcbcadbdbcadddadbcccacbcbbadabcdccbdadbbddadabababdacdbdcaaaadccbcbbadadbdccbabbdbadaacadabbbaccdcacadaaccadcdddcbacacacdadcacbadbaaaabbddddacadacbdbdbcadbadaacdcbdbdbddbcabbbcbbbbbcaddabbcababdcaadbbabdaddcdcadccdaadbbbaacdbccabbbdcbbaadcccbcbabdabccccacddaaccdcabdabadbaddcabaacbdbddbccbbdadcdcabadcdbacdddcbddacbdcaabbccbccdccbbdaaddaaadcaabdcaadccdacbddbdbcbaabbbcaabcbdcccbbddbcdacbddaadcdaacbcbbcdbccaacdbbdbcccbadaacbdccddabbbaddbaaadabcccdaaabbabbaabaacdccbdcddadacbacbbdadccabdcbacaabccddbabcaadbbcacaabbddcbcadbdaabdcbccbccdacbdaddadddcacabbacdabbaabcdbcadacdbaacdadbcdcbcccbddacdbbccbbccacdabdddcbbbddcdbbccdbcbcbaacdbcadacdcdcaaacdbccdadabdadcbccaabccaacdcdabbaddaadcadaadbcdaddbcdcccbbdbcddbdaabbdbcbbddccdabddbbdbcbccddcbdcddbbddcbbaabdbadaccdcabdbdcddaaabdadcdcadcaccacbadccbdbdacbdbbacbccdcadcdadbdbcbddbabccbdabbaccabddcccadccacbcddccadcdbabcbbabaaaabcadccabbdcdabbdbcbbdadcbadcacacabcdabbdbccadbaadccdbaabacddcadcbdabcabbbdacdabbcccbbddddbcbaabcaaabdbbdcccbaaddbdacaaacdadbbddccabaadadcadadbbccbcbcaacdddaacdacdbdbaabbdccccbdbcacabdccacbcbacabbdcbcdbacdacdbcacabdbcbdbcbcccacbacddaadcccbdccabcccaacdadcacddddadcdcbcbcbaaaadbdaacdcaacdcbdbcabaaabbcabcaaadbcacdaccaabadbbdadbcaccbbdabbbbbadcbbcacccdcabdcdcadcabcaacaaaacbbabacabacabacdcbcbbcabaacaccbddaaaadabdbccbaacbddadadcaaaddcbcdbdccdbaadabdabaccdaddddaddbbccccacbcadcccbbdbcbadcddabcdcbcdddbddacbaacdbbbaddddccdddbccdbbcdadabbccdcdcacabaabbaaaadccbdbccbcbbccdbccdbdcbbccbdbadddababddbbbbbbbdababbadadbdcbdcbdadaadcadcbdaddbdabcddaccbbdbddcdaccdbaccbdaddcabddcdbbdcbbdacacdbaccbbbcabaccdacbacbdbbdcbbbaabcdacccdadcdabacdddbccddaccdaaaaccbcdabadadbccbbcabaacdbaabbbabdacaddaabacbdbbaabcbdcdbdcaacaddaabcbdccbacaccadcadacaadabbdcacbabcdcaacaccbcaabcdbddbbcadccdddababbcbaccdaaabbaacadbbdcacaddadbcbcdbabacdbabccbcdddcdacccabaabbdcaacbaacdadbababacadcabbddaacdadbbccdbddccbbcdcabdaabcbccababcabcacbdbbcbcbdaaabdbbccdaadacaacacadadabdbddcbdaddacdabbdbbcccdbbbccbaacbcabdabcdaaaaabddcccbbddbbabccbcccaacbacdccbccbabddddabdadaccdbdcbaccadcacddcacdccacbaabcccbdabccbbbbdadddacddbadcdddbbbbbadcdbcdcadcdbadaaddaaacacddabbadbddbdbbabaaccdcddbcdccdbbdacdcbcbcabadddbdbbbbacdabdcadabcbbcdcaaddbddcabdbcaadacbccccadabbbbcdabcabbccbcadcdabaddbcbbbbbbacccaddcaccaacdcdaaacbdcacbbdbcaccaaaaacdadcadbdaadbcdcacbcddcbddcbaabddbdacccaddabcdadaccacacdcaaadabddcdddddaccabddbbadadabcddadacccddbabbbdcbdddaabddaaaabaddaaddbdbcbaacddadbbdcddaacdadbaccabbbcdcaacdaddbaadcbdcdabdcdbcbdbbbbdcdbbacadbdcbccabddcbababbabdadcadbccddbdbcdbbacadbbacdacbacacaabdabddcabaacaccbcaacabaabadddccbacdaacbadbdccacabaddccacacccdbcbdcbacaadbcdcdbdcddcddbbaccdddcaabbdadddccbaacbaadbcdbddbdbaaaadaaddacccbcdcabdbaaaccdbbbbbdddaaadabccacacdccdbbbbccbcabbdccacddbddcdbbbdcdcbdaaabbacdacbdcaccbcddbabcbdbbdddadcacbdcbcbbbcaabbbdddabcdbbccbcadabddcdbccddbaaadbdabcbdddbaacdbaaddccbccdcadacdbcdbdabadaacbdcddadcdaaddbcbcdaddbbdcbcaccccabaaaabbddcccacacdcdccdddacddbaddcdbddbdbccbcabcabbbbcdadbdadbddcdadacdbcbcdadcbcccdadabacbcbbcccbbdcbcacbbcbdddbddacabcacaacdabdbcbabcacccbdbdddcdbccadbacdcddbbcadabbcdabbbbddbcdcadddbdddcbcbbdccbbcbcdddcbbabbaadccabaabdbdcbbbbacacdcdcbaabbdcbacaddcdddcdadbbcccbcbccdcbbaaaabcdccccddbadaaacbdbbbcbaccbbaabbdcbbbaabdbbcccabbbcabdcccbacacabcaccaddadbadddbccbaaccbcdcbacdccacdaaddbdbaaddbbbccdcdacadbbcacbccddbacbdbaacdadbcdabcadabadaaaadbdddbbcdcbacacccacaddacbcdddbadbccadbdbcccdbdcbccbcbcccdacacbadcddccacbbdcabcdadaccbddaacbbdacbddababdcddaadbddccdacdddaabccdbcbaadbaabdcacdabdbaddcbcbaaddccaabaadcbdadacdbdccadbcbbdcabcacbabacbdabbbaccaaabccaddaabbaabbcbcaaadcbbddcbdabdbbcddcdacaadacbdddcaabdcabacdcbdbcbcbdcbbcdbcdaaaacccdcbaaadccbddbaddcdacbdbbdcbaccdacabdacdbdaacacbaaaaccdbaacbdbbcdbcbcccbbadabbbcdbdaabbcadccbdcbbaabbdbdbbdaccdbdcddcbdbbdabdccbdbabdbccdadbbacdbcdbdcddbcbabcdbdbdaacaacaadccbbcabccabbcccaadacabcdbcbbbdddddabaadcacddcdadbadccdddacacbccaabdabaaadbdddbddcbdcadbbdbdbbccccbcabdbbbdcbdbcbdabdcbddbacabdababcccdacacdbbddbbcbaccaabbccabaadadadadacbadddaabaccdcddaccdcbdcaaadbaabbbbacabcdbabddcbdcadddcdadbcddbbccadcaccaabcddaaaaaddacdaaaccdcccdcadbcbddddcbcccccadaadcbbcccacdcbaaaacbdacdabcbbabaabadcdcbdabbaaccdddccbddaacbaddbcbcdabdbbcbabcdabacdbadbccccabcadddcbdccdcadccadcccabcccdcbdddbadcddbaaadccadaacdadbbdabddaabdcbbcdabacddaaaacdbcadaaddaddccbbabbabadcbaadacacdccdadacbbcabbbdacbadbdccdcbccbadababbcbccabbbccccadbaaddbccdcabccdabcbccadacdddddbaddcababdbdabcbdabddbbacaccdbacdccacddcbbcadbddcadcaccadddaabbadbcdadcdcbadaadaacaacbdbddcbaccbbcdccddcbddbdddcababcaabaababdcacdabccacabdbaabccacccdbdabdbbabddbaaaabacbadabdcbbaddbdbacbbcbbdcaabcaccbdbcdbccbabdabdbddccbcbcabdbdbccbcccdbbaaacbaaabacadccabaccbaacaaabdcbcdcbbadaabdcddcbaabcbaccbacbccdadbadbcaaabbbcbdbaddabccbbdaaaacabacdadbbddbaadacdaadbbdccabbcabcbababadacbadbadbbbabcabbccdcacdbacddaaadcdbaadcaaccbcdadcaddcddcccccbcccacdabbdbcbdcdadacdbcdbcbdbdcacccbdccbdccdccbcbcaccbdacbbccddcadcccdddababacdbbbcabbdbadaccccccbcddacbbbaacbbbdddadbccabddccdaaaadcabcaccdcbbcbbdabccccbbbcbbcddbccaddbdcddbbaabbddacacbcbbadbdddadbadbdbccabccbaacdacabcdbcddaababcdadcddabaccaabdbddcbacdbaccdccbacdadabcbdbbcadddcaadbdcacccbddbbcdacdbbacabbddaadaddadbddddadddbddbdcdccbcbcccdbddcbaacaacbabcddbacacaacaccaabaababdbbdabdcdcbbbaccdadbabaacbddadcdddbdacdabdcbbddcaadcabbcccbdbaacaadabcbbbdababbdcccacbdbcccbdbcaaccdcccacacddddaadbccacabcbcbbddbdbbadcabaddacaaacddccccccabdcdacdbcbddbbbbbbdacccbbcaacabccbbcdbdcacaaacbabcbbcdaadddcbcbbdaadadacdcbddaaadbaaaacadbaabacbcdcadadcdcacdbaabcbdaacdcbdabcdbbaacaaaacabdcdadaababccdcaacdaaadbccaabdbbcadcaddacabbcacaababdcddbbaddadabccabdabaabbdcddcdbcabcbacaaaabacdccbcdabcdbccabcbdddbacabbbcccbadbcabdbbaabbdcbadacacbdbcddaabcdbacbadaddbacbaabcccdcdabddaacbcdccccccbdcbccacbddbcdddabacbccacdaadcdaaacaccacbbabadbddaccadcadbcaccdcadbcccadcbbabadbbccddbabcdadcbdaddbbbdcdcdacdacaaabbcabbbbbaacbbbadcaccddaabcdcbadcbdcdcaaaccacaddbacccdbdcddbbcabbdacbadbbdddabbdccdbbcddccbdadbcaaaadbddadccbacbacabadaaacbbbaddbbddccadabccbcabccddbddcaadcacccaadddcdcbcabdaaccdbcddcddaccbdccdcaabcadcccaabdddcbaabadacaadbbbacdadabbccccbaaaaccadaadccddbdbcabbbbbcabcbbdccacdaadbacacbccabbdadcbdcccaddbdabaaccdbbcaabdcbbcdbadabdadcadcccabaccbccccdddbbaacacbcddababdbaddddbacdaabbbcabddabaadaacdcaabdabbabbccaababaabccbdcbbaddcddbbdcbccbbdaccabddaadddcdbabdaaadcdbadcdcaabdbccbaaacacdbacbacaadbadcdbabadbdbbbddabcbcbcabcadaacddbbdbabdccadadadadcabadaadbbcdbdbdbbcbbdbbaadcdcaaadcddaacdcdbdabcabacdbdbdacbcdabacdccabccdacacbdcbabadabcaaddbddcdcbbddcadaddccadbbacbdabddabdbccbddbaddccbcbaadabbdcbccadabbdbadccddcbabddacaccdcacbdccbbcbbcccbccbccccbdcbbaaccaabcddcabadadacaacaddddacdcadbbcddcbdbcacbcbbcdcddcdcabcdccdbcacbbabaacbbadddadbaaabdaccccbbbdaacbddbabcacacaabbadccdcbbbcddddadbadccabcadabdcbcdadaccbcacdacdaacbdcdcddbacabaaabcbddccaddcdcbbdaadababdcbdbcccaaaaddcbcbbbbbccbaacbbbccdccdccdccbabcaacadbdbcccabcbdbaadbbaacbbbaccadbabadccabdadddbadacaabcbdbdadbdbdacbddacaaadaadbcabadbcaababdacadadddcbbbbdbabadbbdadbaabdbbbbcbcaaccababbddbcdababdcbddbaddbdacdbddaadcbcdbbdacbbdbabdadcccadaabcaadbbdacaadcdadccaadabbdbadcacabacbabdadacbaccdcdbcdbcabcabdbdcdbbcdddcddcacbaccacccddbdbccdddbcbbddcadadcccbbbbcdbccbbbacacbbbbddcacdbdccdbdbdcabaabbacdcacdbbaaacddbddbcbddaaaaabbdcaaabaabcbaacabcbcdadcabcdabcdbdaacdbadddcdbbacccccaaaccdacadadcdbaddaaddccdabcdccbabbbdbcdadcacbbbdaddbbcbbbabaaacbccbbccbbcaaaabbdbadacbabaaddccbaccaccaacabcabdbacaddabddbccdddadcddbabdcaaacabcaccaacabbcbadcaddbccaddaddadabbbddcdcdabaadacdaddadcabaabdcdadbabcdddbbbbdbdbaacdbdabcbddcbcddaabbbccadaacbbbbcdddabdbcdbdaaaaabdaabacccabbadcbdcbabccaadbccbccccdddbbacaacbcbccabbdcdabbbacbadaacbbcdacdcddadaccddbabddbaadcababacadacaadcaaaccbdabacdcdbdcddcddbccaacccadaaacbbddbcbaaacddcbabcbdaacbdddadccdbdabddacaabcacbbacacdbbbbacdcbabdbdacbccbabbccaccbcadacccbdbdacdaadddadcccacdbadbbcbbababdbdddbbcacdddcdadcacadddbbbddaabcddcdcbbcbbabadbddacbccdbcdbdabcddbacccaddacdcababbdcdcbacadbbcdacbaabadccdbacaddaabcaadbdaadbcccbcdaabdddbcaadbcddaddddbcbaddbdcadcbaddcaacacddacccdcadadbdcdbdadbacbabacbdcbabcbbcadcaadbdbcdaccbddccbcccbacccbbbadadbbdbaccbdadbabacddddcbcacbadbdddacbcddacbbdabbacaadbdbacdaddcddccbaacdbdbaadabaadcdacdcdcddbacccccacadcddcdcdaddbaccaacbabdbbddddcbadcdabcbaddcdabbdcdbdcaccadddcbccdddbabaddacaacbdbbdaacdbcadcabbadbacbbdaccbbccdcbaacbcbbadcbccccddbabccbbabcacbdabbddadabcdcbdcccabddbdccccabcdbdacdacabbacacddcaabaacaaabcbbcadacdbcbbdcadaacacabccddbcadcabddbcabdaccabcdccbddbbdabcdccdabcacbddaadaadbacbbcbdabbdabbbbbadbbacdabacdaabbddadcaddabdadddccaaadacbbbdccdcbacacbabcdbcdbaccdaaddbabdbddbbacadbdaaaaadcdccdaaadaccabdbbabcacaccdaadcabbbaccddccccdabbbdbbcadadcabcbcdbcbadaddbbaaaddcacaadabdadacdaabadaacdddabcbbadaababbdbdacdbbaaaacacdaadcbadcbacccccbbbbadccdaadcdaaaccabcdaadadddbaacbacbcbaacdadbdcadbdcdbbdbdbccccacbcbcdddababaaaadacbdbddbcbbdcaccaaacabcdbacccabccaaaadddbdcacabdcbaccacbcaaacbabdacdbbdcaadbdabbaaabacbbdbdadbacdbdabddcbaacdbbcddcdcadbcaabddacbdadabacabcbcccaacadbabbaaaacabdcbbacaadccdabcbddddddddcccddbdcacbcdddabdcdaaacacddacbcbbacbdcacadcbcdddabdbbdccdaadbdcbcdddcdbdababacbcaccdbbcbbcccdbadcdcabbacbdbccdbcdddbcbbcdbdbddadbcbdbdddccdccbdcadcbadaddccadaccacdadddbdbbdbbaaddcbbadcdbddabdbadbdcbdcabddcccbbaddccbadacccbbaabcbddbabdcadddbadaddbbccbcdaadccdadccbaddcbbbcddcaadcbbcdacadcaacdddbcbbcabbaccdbbabcaccaacdaaababbbbdbdcbcdbcbaacbadbbbbdbbddaddbcbccdadddacdbbadaaacdcdddadbdcbcccbbdbccdccbddbabdccbaaadbacdabbacdccbddacbcdaabcaaaacdccaadcbdbbaacadabdcbbaaacadcaddbdcbbdcadcabaccddbdccabbcdaddbbdcccdbdaddaaddaccddacbbbaddccbbaccadccdcaaddddbbaabadbcdbcababacadcdddbddaadbddddaddaccaddaabbdababbdccaddadddcdacbbcbacbbaccdddbbbbdbdbcbdaabddabbacdcaaabdcabdbbdacabcdbadaccbadacccbcdddadbdadcdcdabaaacdadbbdaacbaacdacaacadbabbaccbacbadcbbdbaacabddddddcacbbccbdbbaabcbdcdccdadccdcdabdbcaaadcaadddabbcdcbdabcdcbbbaddcabaacccabdcddaabcbaadcdadababdbbbcaccccdadadaaddaddbddbdadbbbddbbbcdbcadccabdddddacdcacddababdbcdbccdbccccbbbccaddcdadbbbbbbbacdccabbaddddcaaddbadcbdacacdcdcdcbddcccbbccbacbbcabcdbabccbaababcddaacaacdaccaabbdbaddacabaadcccdbdcdaccdcbacccbddaacadcbbabbaabbddbadbacabdbaaadbdbddcbacdbdccadcbabaabdbdbbdacacbbabdbbcdcdbcdcaaadcdcadbcddcadadaabdbddccacabacbbdadbadbdccbbcbbbbbddaacdcbdbaccdbccdabaadbcddabcaccbacbccacaccadabdbcccdaccabbcbadbcaadabbbcdbdacbdbbcdcacacbbbdcbaccbbaabcaccdcdabadccbddccadabdaaccaddbadcdabcaadcaddadbdaccaaaabdaabcaadaccaadcaabbbabdaddcbbadbdccbadcabacccabacacacbcabaabbbbdcacdbdbcadbcabbaddccaccbccaaabcddbbcddabadabddbbdccadaadadbcaaaacdcaccbaddaddcaacacabaddcddddcbddcbbdccccdacdbadbdcadbbacbbaabadababcbddcbbbbbdcadcccdddccabdbacbcdadaacbbbcdabddcddadbdccacbaaddcadccabdabbdabdbdabdbcadbccbdccdaaabdbdcbadcccbdabacaacdcddcdcbcddbccddbbcdccbcbaddadbadbabcbaabbbdcbdccbbacaddcabcadbdcabcbbbbdccddbbbdaabdbabcdaabbabdabccbbaadccbcdaccbacccabddbcadbacaacbdaacdadcbacdabdbdcaccbaadcbaadacbbcaacabaadacbabcaabddbbcbacabcabbbdaadaccaaccbaaddcdccbaccacdbbcdbccbcaccdcddccaccbbccddcbbdbbbabbdcabdbdbbccaacdacdadadbbdbbbaddabdcdbbbacacacddccbbdbaacbcbcbacaacdcacccbcdbbdbacbadcaabaabcccbcacacddcdabcbaccddcdbabddcbccbccddcaadacabbaabdcbdddbcdbaccaccdbbbadbdbdbdabcadbcabacbbdcddaccaccdbabbaacbbcaddabaaddbaabcbbbccccbbdabcdacadabbccdbaabdbdabdaccaabdbcccadaabbdddbabbddacbdbdccbcdaadbdddabbdcabbbddaabccacccdaaccaacdacdacbcdbaaccbccbabdabbccdbcddbbdaddcabbbbddcdbcacddddabdccabcccbbdabacadbcaabdbcaddbdbdbddccddcbadadaabbcbabccddcdcccbddabccbdaadbcccaaaddcdaabdddbbbdcbbcdcaddddcadcbddcbaaaabdbbadacdcabdccddadbacdaadcbdcbcbccadadaaabcdbcddaabcabbaadbdbabacdaaacbbbcabbaddbacbbcacacbcccbaddbcdbadadababcdddacadddbacccbddbdcadadcabdabbdcbcaadbdacdbaaaaadbbdacbbaccbcdbbddbdbbdbbadddcbdabbaccdbdabadcaddaadbabccdbbbbbddacddddbcaacbdccdbabcadcaddcacacaacacaadbbdbcacbaabaadcbbaaddacdbabcaccdaddddcabcababdbccdaddcdadbdbddbacdbdcabacdcdcbadbcccddaccbdbaaabdbcddaaaacaccaaaaaddacbbbbcbacddcccacccaaadddbacdbaccbbdccccbabbcddddabaadabdbadbaabdddcabcccccdbccadbcabaacdcbdbdcdccaacabcabdacdcadddabbddbaddabcdcaadbabdbcacccadbbddadddcdaccdbcabbdccacaabcbabbcbddaacbcbcccbdcacbcbdbdbccbdbdcbbdcdddccbdabaadabaccabcdadabcbbbddddccaaaabbbcddabacdcaddaccbcdaabbddcdddcbacbcdaaaccddddadcbbaddcdbabaaabbbcdabadcbcbcbbbdbccaacbadbbdacdccadcbacdbaacbbbbdcbbadddcbabcadcddccbacbbabbdadcbcbcdcaaacabbdabccaacabcdcdabddaaacaddabacabbcdcbccadcbabbacccbacccadcaacbdabaaaaacccdcacbcdcaccdcadcdbbdbcaaabaadabcabcacddddbdcccaaabccbccdaabdbdbdbbaddbcdcddcbbbdaccadabcdcdbbbbbcbdcdbdbddcbdcbcbacbcdccababccdcaaacdababcdacaacacbdbadcadddacabcbdcbabaaabbbbabcbcacbdddabdccabdbcbcaaaaadbadbcbaacccadbddbcacdcccdadaacddddbbcddddcaacbddbabaaadbabddadabdadadcdbcaaadaddcadbdadbbababdcbbbcadbcbccbdcdbbcddabccbdccdacbcddbbaccaabcbdcaddaacaccbacabccdaaacadabddabcacdccbdccacbcabcabbddcaccbbddddccbbcdcdccdccadadccdcccdbbbadbbdaccbcbcccaabcabaaaaacdccddcabccdcdbaddcbbddcaacbbddbdacbdbcdabbddbcadacbbcadaacdcacaadcdcabdbddadbadbdaaacadcacaabdcbcacdcacacbaccbabdaaaacbacddaabddacbacdbdbbccddadbacbccccdbbbbcacdccacdcdbbcccbaabbaccdbcdacccdcdbdbddcaaaaadbccbbccadcabdbcdcbbdbcdbaababddaaabbcbadabdaaddacbbcacaddcdcaddcabbaccccabbbadcadbcddccacabcbbaacdddcbadbbbcbdcbbdacadaadcddcdaddacaccbccdababbcabddadabbbdbcddccacaacddbaaacacbdcbddbbbbabccababbddbcbabacabbcbcaabbcdcbcddbdaacbbabccdaaabadaadcbdbcdcbbabcdddddcdbdbbadacdcacbcccdacbdcabbbcacdbadbbacccdcaccccaabaaccdacdccbddbccbabdcdcaacdacacdccadddbccbabacbacccdababcddbbbcdccbcabbaadcaacaadcccddcccaaddbccaabbddbbddababcbcdccbbccacacccadccdccacbbcabdbbaccdbabcdccabdacadbcbacdbacbdabacabcdcdcbdcdbdbbbcbaaacbacacbabcccbabdddabaaccbdbdbddcaacbdabcaaacbabbdcaaaabdcdbcaabbcbdddbcbbbdcaadcccbbbcdabcacdacccbbdddcabdcbdacccddddabccdbdbbdcdbdbddadcbadbbcbcdacddacdbcdcccbcacdbaacdcdcdcbacddaaaacbbddbcabdbccbddaacbdcbdacadacdadccbcbbabddbcdcbacaddadcdbdcdbddbdbbcbbcdbabddbddadcdadcbdadcddbaccdabbababcbaabbbcbaccacbcccddabdcaabccdcbccbaaccdbcdabccbababaadabcccadbabbbabdacadbcbdcccdcbcaacbdadddcacacadcadadbddbacaadadddcabadcbcbbaadbbdadadabcadccddadadcdcabbcbcbacbbbbbbdaabbdbdcaadacdcacaacadcadadbcccdcdbcbbdabcddcccadbcaabacbddcaacbbbbbbaacadcadccdadcdaadcbbbccacddbbdcdcbcaadcdcdcacdabdccddcbccdcbaadbdccbcccdabcaacacbbdbcaddacddbbaddadddacbdccabdcbbdcabbabccbbccbbaddccccdbadadcbcadacccdadabdacdbdadbbadbdaacdcddaaadcaddcbcdabaaacbcdcdcbbdbddadcccddadbdbcbadcdddabdcccdaddddddcbbbccddbdcabaabbadcaaacdabdcadadabacaaadbadbacaaaacdaddbdbcbdbccaababccccabdcdcddadcdaaaacacabbbadbadbdbbcbdcbdababcacbabbdacbdabbacbdaacbdaccaaddccaadbacdadccacdccdbabdaccbcbbacccacbcdabbbbbbddabbacaaabacccabddabcbaaddcbcbbabdbdccbccbcbddcabcdadbdaadcadddadddcbcadbdacbdcadaaabdbaccdddadaabaacdaaabccbbaabacadaaacbacbcbddbacabbcadacdddbcbcccbbabcabdcbdccdccdbdcdbdaadddccacccbbdccbbaaabcdbabdcdaadcaabbcbabcaabcbccdbdbabdccaadbcccbdaabcdbbcbbacbccdccabdaacddddbdbcacabddcbbabbdbdbcddcddcaacacabcbdddbaacacdbacbabbbdbabccacbbabdadcbabddbbdcdcacdcacaacbdacbcacaabcacccdbacbbcabdbacdbcadcaadbabadcbaaacbbdbacddcdabadcdacadaccccaddcdcccdbbdaaaaddbcbdacadabcdbcaaaccdcdabbacddabccbcabddacabaaaaddbdcbaadbdbabcabddcbcbcadadbcddaacbaaadbbcadadcbaacdbbadcdcbbadaaadabbbacdabddcbbcbababdbcdaddadabdbbacacbdbdbabddacbaccccbcabcbbbddabbadaccaabbddaddbdabdddbcdcaabbacdabdcdcddccbaccccbaccdadadbbdccdddaccbbccccaadcccdbbadcaaddabddcaaaccbdcbcabcdabcacdadbccaccaccdaaddbbaabadadbdddaacddcbcaadcdddbdaacadbcbacbaddabdcbdcacadabddbcaccbbaacdbbdcbddccaccdbbbbacadcbabcbacabddcaabdabcdcbdccabbdbdddaacbbcdcdbbabbbddbdddccdabdccdabbadbdcdaaababcbcadaddadaabdccacaddcadabdaddadbbbbddbcdcbdbdbbbbcbacdccdcacaddbaaabdbdbdbdbaacabbbcdcddabcaabdbcacaabdcbbcadbcaaadbcaaccdddbccaaadaddbbdcdbdddcdcbcddcbdaadbcdabdcdbccdcacbbbcdbaacabdadcacbddbcdacdcdccbdbcabbdddcdddbccbbddccddccdbaabcbacaaabccbcdddaccbcbabccdbaccacdcdcdcdbaacbabbdcdacdaadabbcdbbdbaccccaaaccabbddbdcabaacdcaccadcbdbbcdabbcacdcddaaccdbcbdcdcdbbddcdaabadccccaabaddadbcccbcddbadadddbabbbbacccdbadcccbbcbacbacdddbacccbabdcccbbccddadcddbbccabbbcacdbcbbdbcddadbbdaddcaacaaaccccdadbacbcbbddbdbabddddbbabcdccbbcaaabcdbbbcccdcddabadbdabdccadbccbdbabbcbbdbdddacadcbccbbbbaddcdbcdabcadaabcbaddbdcbbacbbacbddabdbaadddddcaadacbacdabccbddaadcbcdcccaadccddcbcddabacbcdaddabbcbabddaccacacbdacdaaabcadbcccbddcabcccbdbdcabbbdcacbddacbadbcbccaadcccdccaccdadadcdadddbcdbdaadcbabdcccaacbccdabadbcbbcacdbdcddcccbdadaddcbdbbbcaccaddbdbbbbcccddbdadaddcadaaabaacccdddccccdcbaabcdccbbddaddcdababcddcabbcbddbbadddcbaddcdbabddadbabbaabcdadbcbccadcabcacccadadadbadcdbaccdcdacddddaddcbcbdbcdbdcdbacaacacacadcdaacdabababdcdcbbbdaacbdcdddbabaabbacadcbcbccbbabdbcdbbacbbaaabcabcacababdbccadbbcdbbabdadaddcbbdaacbbbbaabddacddabdddbdddcadaadbbababdddcbccdcbaabdccadccbcdaccabacabacdddabddaddbdddaccdcacbdaddbbcbabcaadadcddbdbdadcbcbdccaabbccabbccadcbcacdcabdcccdaacacadaacacacdcddbcbdccdcbbadcdadccabccbcadccbdbcdaccdbbcabccccbcdcadbbaabdbdcdacadcdccabcdbabdcdcaaadbcdcddddbdccbbacbdddcbbdadadccbdbbabdaddabbcdabbadddbbcadbddcccacacdbddbaacadcbaadbaacbaacdbbabddcdccddaadcbcbcbcddbcddcbababaaabccdbabccdabcbbcbdabdbadacddabbcacbbbabbdabacaddaabdbbbdbbaaacadbddcadacddcaabbdaabbdbabdbddaabbbbadbdabbbcbcaaabccacbbaabbcdacababbcacadacdbbcaadbabacabdcddbcccaacddaaaabbccdbcbadbaadddbddaadbdcdcabbdbbddbacaccccbcbadbcbbadabaaaddddccdddaccdcaccbadbcacbadabbdcbdadcacadbabbcbcadbdbbaacbadbcbdcbdbdddbdbcaabbdcaababdcdbdcabccadabacddcbbdddacacddbabccdbbbcddbcdbdabacadccdbcccdccacbcdcbbbbacdcddacbccabbdbcdadabdadaaacbacdaacabdbcbabadcdbabcdbdbbdaccbdaddaaadccaacaabdbbdcababbacbdbadbabbcbccdccddbadbccacbbddcbaacdadbaccbacdcbbccdbccdaddaacccaaccadadcacbadbadaccabcaaabddaaddbaccabacddadcaaccabdbccbcacadddaadccbcbbdaddcbcdabbbdbacdddcadbbbdaacabadcabaaccaabbbddaaabdacabacadbcbaadbcddbcbcdcddbbadccbbdadcbacdbcdbbaccadddcbaadbbadcbbbddbdbaccbaacaccaddcccbddadbddaadadcacbacdcdbbddbbdbbcabcaaabcdbabadcaadcccaddadbabcbdbbdbbccccbbcaabbdbcddaaadcdaabdbdcabcaddacaaddbbbaacdcbababbcdddaacbaadccbccabbdcdbcabdddbaddcbcbbdabbdaddabcbbdacbccddbbdbadcabcadddccdcdaccacacaababbdabaddbaaadbdccadacddcadcbcaabadaacbaacabcbdcdbdcaadacbddadcdddccbcdcdcdabdaccddaadabbcccdbdabcdbdbadcccbabddadaaacbaabbbdbdadabcbbdabddcacaabdabcbabdbacbddcabdabcbaaacbadbddadbbcbdaaccbcbdcdbbddacbacbccccddcccdcdcbaabcbaaabbbdcbdbbdaaaadbcaaacbcbbbcaddcdcccddabdbbdddaccadbdddbcbbbaaacbacdcdccddbaddabaabdbbdbacdcdbaadabbdbccbadccaccdabadbbbcbddbdadcccabaaabbdacbcddbaaadddcaabdbaabacaabcbabcadbdccdbccbbbcdbacdcdcbbdccccbdccdbcaadaaaadaddacbbdaacaddaadddbcacdcdababdcddcabcbdbaaaaddbabbaabcadcbcaccadcabdaccaabdcdadcdbadcccddabdadcccabbabdaccddbbadadabacadccabbdacdccccbdcacdcdccccbaccabdaadcddcdccaccbabbabcaadcadbdbcccaaacbabcacabaabcadccdddacabadadbadaaacbdcdabdddaccacddcccccccdbdcdabbbcaacacabdacbcddbbccaaacdccbbdadcdadccdcbaadacaabdccdaabbcccacbdaddcbdcdbdbcdcbddcbbdbbccddbabdcbccadcaaddcbccaaccbdadaaccabdddaabbabaaddcdacbdabadbbbabdbacccacdacaaddcaddaadcdcaccadacbdbaaaacddbccdbbcdcddcacdaaddaabdacdabdcadacdbdaccdaccabbdbdabdbabdcacacabaaabbdcbcaacccbacbdbccdacbbbcdcabbcdcdbabcdaccaddcdbbdababdbcccaababbccdcacbbdacddabacbcbaaaddcdcccabdcdacbdddcbbdbbdbbcbbaaccdacbcbdcacbaacbdccbdaadbddaacadacbcaccccdbdcccdbcadabcabdadbbabcaadabdbcddcdbadadbcabdbcacabdcbacbadbbaccbadbddcddbbaabcbdbadbdabbaacadaadbcabdacdbadadcddaabbcadbddcadbdbccbaaabacbaaddabacaaddaabbdaaddbabaabdaccbdbdbcbcdbaddcacdaacdcaadcbdbabaccdbddbdcaaddbbccadcdbbcadbabddcaadcccbbcbacbacbcbbdcdaddaaacaaabbbbdacbdbcaabdddbdccaacacabdcbadccccaadaabbadcdcdcddcbacbbdbddadcdadbbbcdbbcabbaddabaabaaddccbcbcbddbbccccaacabcdddddbbaacdbccbddacdccdbdabababababcdadaccdcaacbbddabaddcbcacbacacaabdadbaabccbcdbbbaadababccaabbbbccbdbbadabdddabaabaaaabbcddcbcdccdbcbdacccccbabcaabacdbabbcbbdaccbcdcbcccbcddbdbddadbcbcaccbddddcccbcbacdccbcbaccbacabaacbdbbddabbdadbadccdbabacbbdaccacbcaadbdacbdddcdaacdababbadaaabcaadcdbcdadbaabcbbadcadcaabadbbccacbbdaccbbccbddabcdbdcbccabcdbabaaddbbbadcacdadcbbbccbbbdabcacddabbbacbdbcdaaaccbbdbdacccbadabacbbbdcbbdadadddaaabaaaddaabaaabacbaabacbdcccbadbaadbdbcccbabbabbaaadacabcbcddccaabdaabdbbcaadccabdcddcdcadcbabdaabcdbdbdbbabdabaccbcdddcbdbcdcbaccbcabcbddcdcbdbabacddcbcddbdbacabbbaabadccdbcdaddcaaaddbdccddcbacbdbdcadabcadcdbacbbabdbdcdaccbaababdaaacaaddadadccacbaabbbabdcaccabdddadbbacdadddbcacdddacaabadbacbbdbbaccbbcdbdbdacabdcdbcbdaacacacbbbddbcadbcaabaccacdddccabbbcddaacacbbccdbdcbcaaaadadccabbacbaacbddbddbaadacdcbbadaddabbcacbaacbbaddacdadaddbbdccbdadccaccdcbddccbdddbcccbbdbacdcdcccdcbcccccabdbdbccdbbabaacbbabbbacbbbbdbdbcdcbadcdccaaaddcabcdbbdbbdaabcaadbbcaaabaababbdcadcdddacbcbdccdcdaabaaabccddcadcbbdddadbbcacbbabbbdcbaaaaadbddbbdabaadaccbbbcdcbbddbdbcbbdbdaadadddbbbbcccaddbaccbbcccbbaabadbbdbdaaddadacaaacdcbadbaacbcaacbddbaccbcaacbadaaccabaaccbcbacccddbcddaaacbbbacddcdbccadbcdcadcbbaacccaabbddadbbaaadaaaacababaaddcadddbacddbbacdbbacbbcdbddaaabcdcbdcbaabdddcbbaacdddacdadbbcabcbddacbbccdaabddbbbadbbcbbcccddbbddadaabcbdaadcdbcbddbdaaadcdbddddbdddbadacbcaaaabaaddbbccabbbcbbddcbabbcadabcabbaadddaddddddaaadbddaaaacdabccabdbbddccdddabccbbdddabbdacbbbbcddcbbabdcabccabadcbabbbcbabacddbacdcdaccababbbbcdbbdddcbdcbaadcaadbbddbccccbbcbcabcaccadbbbccdabbcabbbbcdcddccbadbcadacbdddadaacbbaaaddaccdacddbacacbabbcaccdcbcbbbbaacbcdbdadacaccacbbcadacbdddcaccdbaadbcccacccdaaaccbbcccbaabbadbbdaaddaacaabccbaaabaadaddcccdaabbcadbddddccbbaddacbcadabcbcdbbaddacababbbdadacaccaccadbaddbcdddcacaaabdaabdcaadbdbbdbbdcabbcadbdababbbcabcabdaddcadcbbacaaacacbbaacdbdbbbdcacbbdbddbabdbdacdbdbacbcbdcbdbdadadbbddabbccdcbbbddaababdacaddbcabcdddcbbabdcaabcdcbdcdcababdddaadbbbacddaadbdcbbcbadaacbcccdadcbdbbbdcaaabbbbbddacccbacdcbaacaddabbacacadaaccabcaddabaacadacdbadaabadddddbdaaabcddacadbabcdaacdbccbbdcbabcdcbabddcdbbdaaccdbdadabcbddbabcbcddaddcbadaadccaaaddcabadddcbabbabbaacadcdaddbdccabcdabbcbbdddbbdbdadbdcccbaccccbcbbbdbdbcbacdaaacdcdcdadcdaaacadcdadcccacdbcdaacaabbacdaabbdadbdbdbdadabcccacbcacdcbbcabcdccadcaddbdadcacacdddacdcbaccbdcbadccdaabacbacacbcbdaaacbaabdcadabdcabbacdbaabccbcbccbdcbbbdacadcacbbbcccaccbacadbcacdbbccabbdcbacaabdbcabbbabbbabaddbcdcacaabdaabdcbadddaadbdddbdcaccabdcbcaccdbaacbdbcadaaabcccabaccbabdabadaaaabdcddcccabcddbadbdcbccbdccadaccababccdcbbadbbccabbbbbbbacaabaaccdaaaccbcdaaddabdabaddcbbbccdcdadbddcbbbacdbcdbabacdbcbccbcaaaacbccabbcacddacabaaaccbcdababaaddaadcadddbdadbbcdbaabcbaacdabbdcaccdccdcddadddababbacababbaadadcbbdcabaddbddbdcccdaacdcdadbcdacadaabcbcabacdaaaadbdadbadcdbdadbbdbaacbdcbdaaacbcbabbadccbdbadcbddaddaabbadcdcabcacadaadbbaddacdbbdbcabcadbbcddbbbdcccccddddbdbababaddbbaddddbadbdabccbdacddbabbdddddaabdacbdddcdcabcbdbacaaaadaabbaddbbbdcacaccbdadbadaccababcdddbacaddbbbcdadabdabcbdbdadadbbabdbccacbbbcddbbdaccaadaacbbadbadcdbabdcbbabcadbdcaabbabddcdbddbbccacbcdbdaaabbbdcadadbaadbdbdcabdcddddcdadcacbccdcddbdbabdcacaccbbddaddccdcadbbacacbadcbdaabbcaccddbadbdacbaabdbabdcaabcdacacaddaddddadabacdcaabdadcadaabcbbccbacdcdaacdccaabccaaccabddbddaccdcdbadbcbdacbcaabacacbbbbdbdccddadaacdadccddbccbccddbbbabcdaadcdbcbdaaabbaaaddcacddbdcaaacdddabacaabcaabcdabaddaababbabcdbbabcaadcabcddcbaccbccadbcccaabdddbdccaaaadbccbbbacbcdcaaddaccabcaacacccaabddadbbcabbcbadacabadccadcdacbdddabbdddbcbddadcaabbdbaacbbdbdaaabbbcdbcaacacbbdccabdddabbcccbcbadadacccaadacddcddcccadbccbdbccddbbdcddbbadccabcbabcddcbdbdaaaaababcdbdaadabdaccbcdbaadaddacbdabcbbdbaddbcadacdadbbaaddcaddbbdadbacdbabbabaacddcbbadcccabacbcaaddadcdcbcdadabadbcccdbdddbacabadddbaaadbaccdcbbdabcdbdaabaccdcbbdadbbcaccdbadadacacbddaaadcdcbcabdbcadbabcbcddbbcbadccbcbbadabcbbbdddccbbbdcbbacccbcccddcadaddcbacccbcbdabdbbaddcddacdbdccdaacdadcbbddaaccadabadcdccbdaaaaaccccaccbddbdcbbabadbbdbbbacbaabddcccdcbdacdacbcacbccbadbbcddbbbadbcbccacadccdcaacdddbbbcabdcdaddacdddaadabcddcbbacbbbaddadbbcdcccaadadddbcadbadccaccddabbaccdadbcadcdcbddcabaaccadbbcadbbdadbdacacbabccacdbddbbdadadbccdabaabddaaddcbbdacbbabbcbddcbccbaababcbcaddacbbcaccdabbbabbabbaaacabcbacaacdccbdaacdddbcaaccdddacbdcbaaccaacabbbadcdccccdcaccbdcbaddabdabaacdcbddbcdadaaaddbacbcbdbdbcdacadadbddadccaddcadbdcabdcbbbbbacaacccbbdbddabcdaaacaddbdbabdddcccbcbbbabddbbbadbbbbaaabbcddbaddbabbbcdbdcddacaadbabbbaaacbbbadcbcdccadddddccdaadbabcabdddabbbcdccdcdaadabcdadbbbbdbbaacdccdbacbcdaadbaccabccbcdaababaccadcdacabdababcabadabdccacadccbddabcdcbacacccaabccbdacadbddbcabbdddbcacaaaaabdabcadadcaadbbcdcaaacccddabddddbcdbdcaddcdabadaddaaacdacbcbbdaaacdccbcdadddcbdbaacbdcdadaabacdabdadbbdaacaabaaacbdccbcbccccdadddabacdbaaddabbabdcabbcaabcdbbabdddddaddbdcccbddbbaacbdbdddacbdcccbaaaccacaabacbcddbdabaccbcadbccbdacdbdcdbcbbcadabbacddaabcbcaadbdccabdcabbcadcbbbaabadaddddcaaacbacddccdccbcaddbdacbadadbbddbbdbbdbdccbbcacacacddbbdcbdcdaddaacbcadbbabaabbaadcddccaacbbbadcdadbdaaaacdacabccbdbccaaacdddabbbbbdbdcdcbcccdbdbaabbcabcdbabcdbabccacaabccabbdcbbaacdcbbcaddacabbcabdabaacadcabdadbbbaacabdaccacdcbacadbdcccbacbcaadbcadacbbaadcbcacdadcbabccadbdbaccaaaadcdbaaadaabbbaddddcaadacbcabbdcbabdcaaadabdbddbaaacdcabaacabbbbcbdaabababdaaabcddddcadabdabaadaabaacaddaccbaaccbddccbadaccdadccabaababbabbcbbbcbcadbdbbddbadbbbcdcdcdcdacaacabccdacddbcaccddbacbccabcbcbcbbcdbaaddbbdcbccdbdccdabcdacadcacbabdbbacddbabccbaddbadcbddaacaaabdbdbabcddbddddbccbaabddacaddadbcabdddcadbbdcabaccabdacaacacabddaabbaaddbabddadcbaddacbbdcdbdabadcdabadcaccacdbccbbdacacbacccdaaddabaaccaabaccdddcdbbcddbdbdccddccbbdcccbdacaaddbbacadcbbbbbbdbcdcbacaadaaaaaabdcdbbacdaaadcbbabacdddbcdbccbddbacccaaadaacdbacdbaabccaabdbccddccddabbcdbbcdcbbbbdbcddcdbaccadccadccaabbacdcdcaccbbdadbcaadaadaccccdaccaccaabcaadcbdcbcdaaacbaacdacadbabdbbddaabadbadbdbdbbdcbddbbcacaaccbdcacdbabcaccdbccccadcbbbacbbaddbabaaabbccbbaddabddbabbcabdbcbdcbccbadcabcbcbcdcddbdddbaadacacbbdadaddbdbcdcbaaddadacccbcdabcabaabccaacaacdbcdccddddabcddbdadddcdacdbcacadcdbabbcbbaddbbbcdcaaadbcdaaccddcbbacabbbbbbcdbddbacbddcbddbabacadbbcccbcdddbcdaabbdccadbbaabadccdcccadabbcaddccdbadcdadaadcdccadcccabdddabcacbccdccccbdcabcbcabdadbcccdbdabccbbcaadbdaccabacdaadadabccccdacbcdbcbacdabcabadddbddadccddacabaaaabbcbcabcadcdbdbdabaadcdcdcdabacdddcbdccdcbdbbbcaababbcadaacaddacbcdcddbabadbabcbaabddbbaadacbaabcdaccacccccaabdbcaacdabadbcaaccbbbdbdabbcadcdddababcabdcbddadadcddaadbbacbacaddacaaadaddcddabcabdcabbddacbaadaccbbabdddbddadaaaaaacccdadbddcbdbbaadbaddaacbddcbbbbcbbbbadbabccbcdaacddbdaacacbaadacbbdcdabadcdddbbdcdbdcabccddddccdaadbbbababadddbaaadbcbcaaadcabacbbbbbcbcddddacdccabccddbcbbcbabcabcbcacaccaadacbadadcdcacdbdcabcbbdcaabccddaadbacdbaadddcabdbbbaaacbacbcacadbbabbcacaacabcdcabcdcdccbbccccbabcbbcacacaabccbcdbbacbbaddadddddadcabcbddacacabdaccabaabbdacddaacabddddacbbbbbbccadacbcddabccdcacdacddbdabaccabcccabbbabbdbaddaaaadcbdbdadcbcdcaacaacaaacdcccccbacdccdbdbadccbbcbbbacdcdccccbcddbbdbacddcdcacdaaddbbbbcdacccacccacbacabaccddaaaabdabacbdaadaaabaadaaacaacbddaaabdcbdaabdddcddbadbdabcbcaddbaccbbbddaddcddddbdbacdcabadadbdadbccddbabdadbbaaddbbbdddddcdcdcaaaccaaaadddbdadcbccccbadbcadbbccdbccbbabddbdaaadcdbaaaadaacdccbadbabbcdddcacadbadbccbbbbbddbdcabccbacadacddddbcbbbcddbdbbbabbabdbbbdddbcadcdabcdaddbbcdacadbdddccbdbdabbbbcdcccccbdabbacdbcabbacbcddaacdabbdbadaaccbddcddabaccbdbdbcbcdccaddaacadcddccbdaacabdbbddbdacdabcdddbbabacbdccccddacdbabcdbaacacacddcaadcacdccdbddbacdbcbbbaacbcddbbabccdabbccdcbccdcabccdaddbbddcdcccadacbbadcccdbccadabddbbbbcacaacccbbabbddcdcadadbcdcccddccaabbdbacaabdaabcaaaadcbacaacbacbbdabdcdadbcdccbccadbdbdbadccdccaacbcdbcdcdaacacbcbbbcbdbdcbbaadbdcccbdccdbbdccabaadccdacddabbbacaddcabcdbccddaacadbbaaaaadbdbddccaaabdaddccabdbccadbccaccbdbdcaabccaaadabccbdbddabadacaddcdddbbbdbbaabdccabddabcdaacdcbcdcbdabccabadbaccbddbccacbacbddbabcbccbdcccbcdcccbaabdbdbdddccbdaaacdddaabbcdccadccacabddbadcbddaaddccadbadcccbddbaaccbcaaadaccabbdcbbabddcdbddbacdadcaabdddadcdaaccbbbdddaaccbccaaaddbbadbcacccbabdcdbdbadabdaadacacdadacddcabbbcdabbaddbaadaadaaaccabbcadacbdcbbcdabbcaabccbddcacccbcdcdcdadbbbaadccbcccbbbaadddabcbccaadbbabccbadcdddababdccacbcddcdabaabdaccadabddaddadabbdaddddacddbccaddcdbcbabdadddcadaabdaddabcbdddbabdcacacabcdbbcaddaaddbbbccbadbaacdcdbcccacacbbacbddcbcabbacdddadabbacdbcddaabcabbadcdddbdbbdadbccadcacaadbbadddcddcaabcbdaadcbaaaabdcadcaddacadcdcdcdacdaadbcadbdbdadaaaccccadbdbcaaabcbdcbcdcdacabbdbbabbadaaadabbbababcbdaddcaccccbaaaccbdabacaaaccddbcddbbababcbbbdcbbabcacdcdaaabbcdddbcbcababaacaaccabbcbdabacddcddcddccbadccbdbdbbadbadcbbcadacbbaccbaabbcccabdbacddcabcbddbbbcbadcdbabbcdbcddbbdaacbdcaaacddbabbcddccacacabbbdbdacccaddbbdcadcbcdbccdaabbddadddcaabccadcbbdabacdbcbddacdcccddbaaddabdcaacbacaaddacadcccbdccabddaaddaaaccbdcabcbbbacbacaacdcbadaddcbacaaadcbcdadaadccbbabcacbcbcadbbbbdadacbcdddbabbdaaabddcbcadaddbaabccdcdcbaabcccbacacbaccdcbcbbdadcabdbbdacbbabadacacabdcbbcdbbdcbaacacaadbcabcccaaddcbdbdddbbaccdbbadacabaccdcbbcacbdcdadbaadabacacbbbcdabaacdaccaabdbbcbdcbacdbabbccbabdcbababbcddcbacbbbdbdbcdadcddbcdbcdbdccbdbdbdcbabccccbcbabbbacccdbcbaabccdbadaacadbddcaddbbbccbdaadbcbcccdabcabcdcccbbccadcdcdbcddcacbbabddcdaddcabddbdccdaddcdadbbabdbcbbdcdacadddbabaabcdddbbcaabbdadbadbcaddbaaacddbbdbdaadbbbdddddacbbbcdbdaddbabcbdcdadcabcdbdddcccbabbdbacddcbdbddbaabacabaadabaaabbbcdaccaadabadacdadcbdcdacdcbaabdabadbaadaabaaaabbbdcbdcdccabbcdccbbccccbbbbbdddacacdcbcbaccdabbcdcddcbcdbabadddcabbadabccdaadaadbccdaadcaadcdbdadbdbadcbcaddbbddbcddcdaddcbadbadddaababccaadcbcdabaacdacbbbaccbacbcabddbdbbccccdcadaabbbaadcddcbbbcddcadcdbabdccbaabbcbbbbdcdddaccdcbbddadcaddbacacacacdcdcbccdaaacccbcdbbdccdccabaacadcaabdddcaaaacbbbaddbbbabaaddcdbadabcacbbcaccbcbcccbdacdbaabcdabddcbbdcdbabacaaddacbcdbdcdaabdcccbadccccaaabadbdcaccbcbbdaabdacccabdccdcbdccdaccddbbbadcbcabcadbadddbddbbcbbcccaabcddbddacbdadaacdccacbbdbdbbbbdcaacdaabcadacdacabddcadbadbbcabccdbdcacabccdaacbddbcdcccbdacccdbbadddacdabbbccaacccbacbdbcddbbcbaddadabccbaacbaaabbcdaadccadddabbddaccadddcabbcdcdbcdaccdbabcddbdacccbdbcbabdcddaaacdbdccbacdacdbaaacbaabccbabcadbdbcbdabdbddcbccbdabdcddadbbccacbbaccdccdbbccacbcccddbccbbacacacaddacbacaddcbbadacaabccdbcdbabdbabdabbabacbdcdcbabccaddbdcabddddcbbaababddbdcadcabbbdbabbbdababdbccbddbacaadcaddcccbcdcbadbbbadccdcbadaacdadcacdacdcdcbbabbdbacbbccdabadaacbabcbcbbadacbaccacbabdcddabbabbbbbdcbcbccdaadababdbcadbcadcadccbaabadbbcabcaccbbbacddbadbdbccddaddbbbabddacadaccaaccdcbcdddbcadaccdbcdcdcbdddbbddcaaadaadddcccdbadbcaabdabababacdaacdaadbaccbdbdccabdaccbbcddbacdabdbbdbcdcdcadbbddccbbbbbbddbbddadadaaacbccaaaaaddabaddadacbacbcaadcacbcbbaaadbbcdccaaacabccdbdbaacacdcbdccdcdbccadaccaccbddabbdabaabdabbbcacbcdbaacbdabdcbaaaacaabaadbddbcadcbdcbdaddccadcacacabddbddccbdbaaccabbacbcbacdbdcbbadadaaddcdaadcbdcdbacaadbcabdccdacdddabcbcabbaacacdbdbcccbdbcdbadaddcbbabaabbbdbdccbaadcaaadacccadbadcbaabdbccadccacadabbdcccbccadcacabcdcdabdcbdbddadcabddabdbcbaacbcbdcdbaaccdccbddbbcdcccaaddcbaccdcbbbbaadcaacbdaccabaddccdbcbdaccbdbccbdbcbcadbccbbbadadddddadccbabaaaccddbdabddabccaadabacadddaaabadbbaacdaacbdaddaadcbdbdbdadaccbabaadacabbcbcddcacdadbbabadcdcbabaacadbdcccdbcadcbaddbabbcaadbabdccccdacdaccdadddbddabbbbabbbdcdcabcaabcdddaacbbcadcbadcbcbdcccabbccdbdabcaadcaacdcadaaddbcdaddbdcbadbbcdbabacaaccacbcbddddbcbccdcdabddcdadcdacbcddacdcaacbdddbbdabaacdddcaaddbabdcbadddddcdcbacdaabbbbabdaaabdcbdcbccdbbcdcddcbccaadaadacddcdddacacabbcdbdadcadbbbaddcabdacccddcdaccdbabacaabbccaaaccacacbccbbbcdadbaaaacdbbabadcacacdaaccadacadadacdadbcbacbadbbdddcdbdbdbdcccccdbadcdcddbbabccbbadbbbaaaaccdabdaadcbdadbcbaddaccdbacabbbcbdbacabacbbbbcabbdcabaabcdcadddacbaacbbbabddbdadadcaddabddaccddbddadddcdbcadbddbdaddbbdaaddbaccbdabdbaddbddbdcdcdcbbbbdcddbacdaadcdaccbdabbcccbccdbdcbaabdabdccdbadbbcdcabdcadbcadbdabccddbbdbddcacccbbcaddbabcdbcbabdbdcddadadcdaadcccbcbaacaaabdccbdbdacaddbcddbcddddcacbccadbcbabdcacdcabcdabaaadbbcbabcaabddcaaaabbcabdcaaaabcaddacdbcbabaadbcccdccbacabcdbbdcabaabccccbbcabbcdcbabbbabbacaaadbdbadbacccdbaddaccbdddadcbacaacdccabdadabbcaaabcaccbadcdacccdbcaaaddbacbcdbbddbcabdbbbbccccabdccbdcbbddaaaadcddadbdbbbabcbabbbbcacacbdaddbdcacdbadccaacacadabbbdcabdccacabbbbcccdcbdcdabdbdcdbaabdccdabdbbdddcadabcdbadcdacbadcdccbbbdaaaaaddccaaabdbaadaabcbcaccadcdccacdadbaddbcaadbdabcacddbcdbabaacabbcabdbcdcdaadbdaccdcabdaabcadbdccbbbcccccacabbddcbaaabddadadaaacbaadacdaacaacdbbdbdbccccadddaacbddbcacabdcbbdcbdaabadacbadacdcabbdacbaacbbaddbdbaddcbaadcdaabdbbdddbacdcaccccddcdccaccbadaccbcbababbbdabaabdcadadaccacdcbabddbcccabadccabbdbdbcacbcbaddacaaadbaccbcbcdbaccabccdadcadbadddcdaaabaacadbadacbadadaacdcdbadbdadddaacdacdbadaccacadbababddbacaadccdbcddaddccbdabacbbddbbdcdbbaccadbcccacacdbbacadabddcadbadbababccadabcdadabaccdbabdcccdbbbcdbdaabdcacccbddcdcdbcbbbadababbddbacdbcdacbdbdbdabcaabdabbaadaddddbbdcbcbaabdcdbcdacccdbacadbadadddcbbddcadddddcddaccacababacbbdcbdbbcbaabbddbbddcbcdcdcacbbaabbcdcaaabbbadbbabbadcbaabbacbdcbacbdcdbccadbacccacdacacaabbbcacbbdaddbdcdddbdaddcbcdbcacaacacbdcbcadcbcccbbbdbddddaddcacdbbabddcdcdcdaabccabdcdbbbbcbaaadadbdbadabdbadbdabbcbdbacbcaaacadbabbbaaddbcabcabdcbbdbcccdacddcabadcdccbaaabacbddddbccccdcbdcddbadbcaabcdbccbacbccbabcaaadcacbacaadaddcddbcaacccbacccbdbbbdccbcdacdbbdbbcccacbdbcbacbaaaccdbcdcbbcbbdbcdabddabcabcbcadccbbdbbccdacbcacadccadbdbbcbdbcdacadcbdccddbbcabacadaaacddcaddcccbcccdadbcaaaccabaaacbcdabcccccababdcdccbcaaacaaabccccabdcbddcbddbbacdbbcbbabdaccdddcccbbaaddbcaccddbdbcbcbccbcdbccdcdcaaaaaaadddbaadaccadabdbbdadabdabdaabdaabcbaaabbdbbcabaacbbdcadbcddbdcbcbbacbcdcabddbacaddacabcccbaccbbcbabcbacdadcdcbdbbacbbaacdddabaddcdbacadaadaacabcbadbbcbacdddaaaaababdbbaddababccccbdcddbbaadcdcdcccbabbdaaacaaadacdbbabbbddbdaccdcbaabccccbacbababdbdacddabbbdbcacacdddbabcaccabbdbcdcbaddbddbcaddbbdacbdddadacdbdbaacdadaacbdabadabbdbadccaacabcbcccaacdbcdbaacbadddddaadddadbcbcbbababcbacbdaadddcbcbaaaccbabbacadccbcdbdddbcaadbabbabdabcbadaadbbcddcccbddcaaadabddcccabcadacadaccddaacdbaadbbdcdaccbdbadbbbacddcddacadcbdaccdaccbbcaddddbbbaddacbddbcadcddcbcaaccdddccbdbaabbbdadbbabcddbcdcdccbccaccdabbcdabacadbaddaccbaaccaaccbaaadbbbdddbbdcacbaccdcadccdacaaddddcbdbcabccdabcbcaadacdddbdcbbbadcdcbcbbdcdddcbabdbcdccaccccdabadadbaadbdadabbddabbaaaaabbbbcdadccbbcbabcddbcaabdbdccdcadcadaddcaaadbbadabacabdbdddbdbdacddbdddbcccadbccbababacabcddadbcabddbdabbbcaadbcaaccbbcabaaacaadcdadaacaccacaccadcbbddaccbdcaaddbddacadbbaabbabbabdaaddcdcbcbaadbcdcaddabacdcdbccbcbabcbdaadcbbcabdcdbbcabdbbcdcbcbcdcbdbcbbcbcabdbbcabbdcdcbacabddccabdacdbbcacadcabdbadaabdabcaddbccacbdbabcbcbbbddccabcbcbaaabbbcbccddcacdcdcabadaacdababcdcabadcdbcbcaaddadccaccabdaaccbabbacabacacbadcbdbbadbbcbaddcbccdbbdcccbdaddccddadbdbbacaadaabbdccbbcbcdddaadbdaabbdbcbdaababcaaaacccbabcbbacdcacbadacdccddcdabbdabdddaccccddcbccdbcbbdaddcbaacacccdcabdcdccaddbccdccdaccbccbccdacaabcccabdcdbddbabcbadadbacbabbbacbdaddcabaacadaccdcdbbaadabcababadddabbddababccabacbaabcadacccbdddacabadbabdbbcdabccbbcbdbcaacbcccdadcbadcabbdabaaacbdacdaaabcbcbcadabdcaaabcbadbaaabbbdddcccbdaccbbacadaaabdabbbdbcbacbbddaddbadabdbabcdbdbcaacacbddadcccbdbcdbbbbbacadadbcacbadccbadacbbadcbdccaacbcadccbdaacabcbadccbbdadccdabcccadbcdcbbacdbacdcacdcccbbdadabbcbaccacbdcbabdcbdbdcadcccaaabddcdbccdcdbbaaddbcacaabdcdcdcabaadbabacbbdbacdacbaccddbbcbbbababcabacdadbccbbcaacccbbdcbbcdbbacbccdcbbdcaddcabcdaccccbbddaddcdcccacddbdbddcdacabcacaccadbabdbacddabadaacdccabcdaccbacbbccbcadbbadbacaaacadbbbdcdbcbbdccababcbcdbcaabcabdbcadabaabdbcaadbcbbbaddcacaadddccaddaccbcbaadddccaaabdadacacadadcdadaacacdaccacacbabbcadbabaaddcdbabbaaccadbaabccbccdcddcadccdacdbdcddbdbaccabdbdbbbcaccbbbaabbbbdadddbdbbacdccaccaabbdcacddaabdcbdadddaacabcccabaccbbadaabbccaaaaaabacbacabddccadbbababcadddddabbccadcbdcccbcbabdbdbbbacbcacbcbacbabdbabddabbbadbadddcacadadbccadadddbdbddbdcdbcbbdbccdcbbdabaadadbdbdbcdcddbcddcaadacdccbbdbddbbbbbccbbcdcabbcbcdddcbcbdcbbbbdddcabbbdcccabbccbbbccbcababacaaaccaaabbbcabdddacaadbadbcbdabcaccddcbcabbcbdcdbacaddddcdcbbbdbaacacbcccddadacbddcdddddccadaddccacabdcdcabbbcabddbdbdcaacccaacbbcdbbdadacaacbbdadbdccbdddbcddadcdcbcdbabcbabcadaaabbabbcdcbdcbacbcadadabacbadbdacdcdbcacdbabbcbadddddacbcbbdbddcbbacaabbaadcbacddbddcbadcaaddbbdcbcabddcccaddacbbdbbddbccbacccddabaaddcabadadccacaadbbbadaacbdabcccadbaaadcdaadbdadbddbbbdadaaaabaddbddbdaddaabbdbcdadcdadbdacbbcdabcccbbcbdbbdaddbbadcbccbbbcdbaacccbababcbbbbcdacdabdbdcadccbccbbdacbcbcbbdaacdbaaddaccdbdcbadcdddbbbaadbacdaabdabacdadcdcbddbbaacbabbdbcabdcdbbcddddbbabacacaaccadbbdaadacdadbdbbaccdcaabadacbcaacaaaacbdaadbaddbbabbbbabababbbacddbdbbdabcaddaacadacdccabdcbbdbdbdcbcaabadacbaccdaaaddbdbaaaabbbdcaaacdcacccdcadadbdccddcabbdbabbbdddabddabcaaddabdccbbbbddaabbabadabcaabcddabccddcccddacababbaababaddaddbbddacacbcdadcdababdccdacddddabdbddaadddcbaccaccdbddbbbddbddcccbabacbccaddacabbabdbcdbaadababcbcabdcddcaaaacdddcccaacadbbacbdaaaccdadbbcbcbdcdbabcacbaadcaccaaabaccccccbdcbdaadbcbbddbaddccccacccdccacacdcbacdadbadccaddbcacbadaabaabcddddbabbbdddcbdddabbbbdaaaabadddcbccbabdcabcbcbcdcdaacdabdccabadacddbccbbcdbdcbcccdcacbbbaadbacaaadadacddcbadcacdccbbbbdadcbabbabcdcddddadddcdaddbdaaadbacccddcdcbaaadcccddbdcadaaabbbdbbddcbadaccdcbbcaaacacabdcbadddbdacdccddcaaabbacbccabdadccddacdbbacdbdcccbbbcacaabdbdbcdcbbbdbcbadbbdcacacadcadcacadccbcaccccaddbabaaccbcdcbbcaddcdadcdcbacbbccdbbdaccbbdacdccbaccacabdcbbabcccdabcbdcbdddcaabdcacbbaccaabdabadbbdaabaabdbabcdbaacddabccadbacccaadaadbdabcadccdadcddcdccadbaddacbdaddbbaacadaabbbbdcccdaabddbbdbabaabcdadcbadabbbbddcccbdcdabadacbbbadcbccdddcdddcbdbadabcaaaabddadcaaabcdbbbacaacddcccdbbdacadaccaabdcbcaabcbcabddbbaccacaaaaaacdbccddddaaddddabddaabdaaccbdccaadbacbadaabcdbaaacbbaaacccdbababdcddadcbabbaccaabcdbddccaacbcbaaaaabcadcbdadadddaabbcdaddbabbaadbbadbbcacabdcaaddaaacbcabccbacddabbdbcbaabcddddcbdcdbabbacbdcaadccacdabcdbccbcdaccddaabbcddaabccddcbccbdbbcdccabadaccadbdcbbdbddcdcbaaacadbcdbaaaadcaadbdddaddccdadaccccbbcbcccaabdadaababcbadadbadccbabcccdcbaaabbbdcbdacdbdbabbbbbcdaacccaadcadbaabcdccbddcbbaadaddcdbacdbcbdcbacbabccdadcdacddcdcdacdbdddadcccdabcbacbbcbcdbcababcbdddcadacacacabbbdbdddccdabcdcdbaddcdabacdcadcbdcddbccbbdcbdbdbddadcddadbdbcdccddacbaccbdcbbbbcdcbccbbcaccdccdddbdadcbdbabdaddcabdbcabcabdaadcbacbdcbaccbaaadddadbbcbabcacbcdcdbaaccbacbdcddbaabbcdbbbadcdaacbbaacabdadaacbbabdbacabcccdbbaabdaaaaaacaadabbbdbbaacdaddcaabadcdccbabdbaacadcdbccdddddbbbaabbcaddacbcbbdbacacaddaddddcccbdacbccddbbdabbbbdbaaaacdbaaaaabdbbaccdbbabcdbbbbdccbbddddadbccbbddabccbdbadacbaabbddbdcacdbdabccbcccbdddcdacaddbdbcdbbbdbacacbacaadcaacacacbbacadacbbbdbcbbbddbdccabcaccadbdddccdcddcbbdbcbdbbcadacbbddcbdadacbcbdbbbdbbcccddcdcbcabbbccdaccbabdabcbabddcbabcddadbbcabcbcaccbacdaddbdaaadcaaaccdcbbaccdbadbbbdacbddbbdccbddbbcbdccbdbbddbabbadbacabbadaabdabadccbdaabddaccdabcabdcbbbadddadddababaacdbcbbcaddacbddbdadbaabcdcbabbdbbcaaccdccccabacadbdcabccdccacdddcbdcdbbdddcbcaacbacbcdcabddaacbcbccaacddbcddbcccdddcdcbcadaabbabdbdbddcdcaababbbddcdddbbaacbcbaacbdcaaddcdbdbacabaaacbcbcdadbbcaacdbdabaacbcbcbdddccdadbbccdcccddaaaabadadbcbccdddbcddcbbbccccccdaccbbadacdbddbadcadccdadbadacbcccbccbdcddabbabbadbccaddccbbccdaacdadcaadddbcabcbccbdbdaacccdabdbbaccbccaabdadccbaddabdadcdccaadadcacaabaaabaabbdaaddbcdacbdcccabacdbcbbdadcaabbcdbababbbbbbbabbccdadbaccccabcacdcaccbabcdabdaccccacbddaaaaabcacabccbdaaaabbbaabaacaccddccadccbabbaccdbdbdcabbbbadadadbbddacddcabacdcabadddbdbcdbadddaacadacbabaddacbddaacababbbdccacddabaabbcbccbabbcbbdcabddbbcaacaabdccabaaccccddcbcabdddcbbbdbbccaaabcaccaadacbbbbccbcdacdcacaccdbbddaccaddbaddccbdcdcdaaabdcaddcacdcdadbacaccddbbcaccbcccdcacdbddcdcaccddbcbadacbbcdadddbbcbddcddddabcabadcbadcbcbaabdbbbbbbbacadacbddcacacbdbdccabddaddadabbcccbaaadacddacdcacdbdccddbcaaccaadccaaaccaadbdaabacdddbbacdbdacbdaadadddcbdbadbacaadddcbcadcbbbcdadadddabbcabddcdadbbbadbbadbdbadddcbcaaacaaadcabcdacadcdcabcdadbcddaccccdaddacacaabcabddcdbcdabacccddcaabbbdaaaadddddcbcccbadcdcddacdbbaaaaaaabbdbadccbdbdddcacddcdbcbdbaccbcabadadcdbaaacccbaaabbadcbaccbdbdacadccbcabdcbadadbaaabcdabbdbdacbbcaabbdadcdcadaaacdcdacbcabcbcaadbaccabdccbbbababacbcbbbbadabbbacacdbccdaacdccbdabaacdbcaabbcbbcadcaabbbdbdccacbccadcabcbbbcdcaddddcbadccdabcbabbbacadaaacacdbbbaddacbcbddccacbbdbadccabbccbbbabddbccdbbacccbabbbcdcdbcacbbdcadcdbcbdcbdbbcabdbcabcbadcdbcdcdcaddddcaabdadccbaabacadddabadcccabbbadbddbbabcacdadcacbdacddcbbaddaacdcdddcbbaddbbcddbabbaadacaacabbbdcdddcdcbaacdcbdadaaddbccacacddabcbbcbddcdcaacdacdbbdaaaccdcdbbddcccbccbdcbbaacdbdcabbccdacbdabcaccaabcbadcbbcadbacabdbcadcabdaaacaabbbbdccbbdcadbccdaadabccdaaddadaccbaabbbcaaacbdadcacdbabbccddbcdbabcacaaadbcacbdcbcadcacbccbbdacdcdbdbbbaaabbcdbacacacdcdacbaabdacbaaacbddddacdbaabcdaabdbdabddddabbdcdadbdbcbdbbacbaddbabbccacbdbdcbbaddbdaaadaccbcdccbcabacbadddaacdddbbdaadabaaaccdaddbccccbddbbdbaacdcadbcaddcacdabbbcdabbacbababcdbcdbdaadaabbdadccdbcddbaaddaadbbacadbdbabbbaccadddacbbbdcadabddccabbcbadaacdaacddcccdcbcaddcaaaddaabcbaccbccbdbbddacbbacadccdcccdaadcaaccbbccadcdbddaddcacbdacbbabcdccccacbcdcdbbdcbdbacbcdbbcbacacbcadcdcacdbcbbdddbcadadacdcdcbadbbaccbdbcaddadacacbbadbbabcdddbbbbcdaccabaabaabdbaccdaccbbbaaabccbbdddbbcdadcbabcddccabcacbaccdbdcdacddcdadaacdabadaaccadccbdcccdbbbadabbdadccabdbdbacaaccccccccddccddcddccdaabdacbcbbdaddcbcbbbddbadbacbdacabbcdbbbdabcbbbbaddbdcdbdbcdcdbdaadcbaddbcbabcabbcbcdaabaddbbccbcbccacadddcacadadbcddabaadccbacadcdaaaaabbdcabdaddcbacdcacdadcaadcbcdcdcdbcbcdbbdaddadbcaacbadcbabddbbbcdadaddaabaabdbbabcccacddacbddaaabbabaadcddbabdcabdbacabcbcdbdccdbdcdcdcbdbacadaccdddbadadbabbabcbcbdcddbdadaaaabbacdabccacdaddcabababbaadbbbcdcdccbaabacbaabbbdcbdcbacaccababbcdccbadcabccabcdcdddbabbcdddadcbdcaababccacdccbbbddbacbcbccbbcbadbbacdabcadcabbabdaddcacbbcbbcccbcbddbdacacdcdcabbcacaabdaacdadcacdcbbcccccbacbcadddcdaddbdcacbddccddddccdbccaccaacdcbbcbadadabcbccaaacbcdadcadacddcbaaccacdddbdabaccdcbbdcbadcbddccbabdadddbccbadcbcbcadacbbadbcbbdddbadbbddbdacddacdbdccacbadccbbdbaddccdbbacabdaadacdbdddbbdacdcadacadabcacbcabbcbdccddbadaabdcdaaddccadacaaabcbcbdbdbdcaccbadcadccabccccaacccacaabbddbdbccdcbbbdadabddddadbdbdbcbddbbbbcdcbbbcbdbbabdcbddaadabbcbdaccbdcbbcbdcdcdccdadbddbcbcccaadadbdadadacdcdbbadddbcbcdbacadddccabdbccdcbabdccbadcaabbcadacabcabacabdbcddbdacbabdaacdcdcdaaabcacdddaadcaccacddacbdbcacbabdcabcdaacdcabccacdcbcddddabadccaabbaabaddaddcdccadadddaccabccacbdbccbbdaccdbdbacbbbaaababaccbcbccbbcddadcbbdcbaaddbaccabadbdcabdbcdbaddababdcbaaaabcbccbbbddcdcacdbcddddbcdaddbcaaccccbcdddabadaadbbcbddbbccbacaccbaccbadbcaabadaccbdcbbbccbacaddacdabcbcbbdccbacaacddadabdcdbddadbcaababdacbdddcabcaabcbcbbcabbbbdccacdbcadcadcaddaacacbacddacccabbcbabccaadddcbcbaadcadadacadbbcdbbdadcdaccdabbcbddbbddccabcdbdddcaadbbaaddcdbbacbbbccdaaaacdabaaacdbdbbdcbddcbcdcddcbdcddbcaaabbccbcdcacbdcabbabcaaddabdcddadcabdabcdddcddbaddbcdbbbcbcaadaadaccdbcbbaccacacaccbdddcdaddcdaabbdaacacdabccaacdddacdcadacbadabcbdacbbbddadbaccabbbdaddbdddaadadccccbdacabadbbadaacddacdabddddccbbdcbcbadadcaabdbbdacadaaacabcbdbbddcccbbdccbdddacadbbacbbccaabaabcbdbadaaaacddbbcdbdabacdcabccbddcbcbdbddcababcdbbcacacddaaddcbcdaccddcdaacabddbdcbbbdccaabaaaabbdcdacbbccacccaaaadbddbbdbadbbcdbcacddbccbdaaabdaadcdcbabbadcbcddbcccddcaaacdbbabccbddbaacccbadccdcdcddaddadcccbccbacbddbdaaccdcbcccbddbdddcaaacadaabbbdbccadbbaacbbcabcbccbdcbbdcaabbdadadadadbbddadcdabbaabbdcaaabbdccdadabbddaccabcbbcacbadaaabadbacbbccaddbcadbdbdaacaabcccbacccbdadabdabbddbacbddcccbabbddbbddcadbdabbabcbbdcaaaaaabadaabddacabccddcccdcabdaabccabcbaacbbdaccaabddcbddbbcdbcbcbdcbcbbcbbddbbbcbaddbdbaadcbabdbbdaadcdabdacbcdcdadaaacabaacdcdacdbcabbbaacacabbccdbbbcaaccbacddbacbddababcccccccdbadadcaddbcbcbabcacdbaddccaddacbdaaaadbcccbcbdbccbdddcadddabccaabcbbdaccbbcccbbccccbbbddbcdbcdbdbbaacbbabdbddcaaddaccbaccadddaccaaaadacdcdcbbdacbbbccdaccadadabadbadccaaaacdcddaabcbbcaabacdbcbaddababcbcacdbccdabcaaacbcadadcdccccdacabadaddbaaabaadcabbabdbbcbbddcdbcbddabbccbbdabdccbcdddcaddaadcbbadbadbbbdbddadbcbdbdcabddcccbbaabdbcdcbaccbabbbaacdddbcaddacaacacdbddbbadabcaaabcacbdcaaccdcdadcbddaddddadcdcddcdbddcdcabdaaddddcdcbbacbacdabdbababaaabdadacbbccdcbaddacaddacbdacbcccbdbdddababadddbaaacbaddacbdbccddaddbccccbccabcdcdcdababbbcacbbcbcdccbaccbcbcbcaacaaadbdadccdcdbcbdcccbddabbdbdbcabacaaacccdbdbabcbabbdddcdbcaacdbdbdabccbdcdadaaccaabdbdcddbbabcbaccdcccacbdacadddaddddbdaddbbdcbbaacbcdcddbdabaaadddaaadbccbcbccbbdacbaabcccaccacabbdddbdabccaaccadcaacdcbabddcdaddbdabbbacbababcbdcaadcadaccbdccccdbcdbabacccaadcbadbaaccddcaadacdadbcabdcbbcbcccbcdcdcddbbcabdadbbddadbddbaaaaadddaddcdcabccaccadaaddccdbbbbabaddaccccacbcdcccbdcccbdcaddddddaaacdaccddadbbccddadbbaadbcdbccbabbaccdccddadabcbbddaaccbaabaadababdbbdccadaacccddaaabddbccacdbbdaccbddbdadacdcddbcaaaadabccdadcdcacaaaaddaabaaaabbaaacaddbcbcdddcaaaaaacbdbbabbbbadcdaddddbcabcaabdcadccabbdddababacbbbabacadadbcbbcddacabacdcdcaaccdaadadcbccddaaaabcbddaacdccabaaaddacadadbdacadcbabcdbcddbacdcbcabaaaadcaacdbcabcadddcdcccccacdaacaccddccbcbccabccadacadbbacaaaabbccdbcbacabbdcdbdadddbccbbbbcbabcdacdaddaabcaaaadbbbdcccbcacbaddbdbcabbccdbccadaadbbcdcdabcccadccbdcaacdadbdcaddcaaacdacbdccbadbddacaccbcdbcaadcbcabcbabdcbbbccdcbdacdcbcbbadbaacbdbacdddadabacccbcaaddbdbadacabcabadbccacabcacbacccddddcdcccacdccbccabacdabbbabcabccccccadbcddaacdbdcddcabcbdbdcbbaabcaaccbccdbbadaabddbcddccbdccbcaabddababcbccdcdadacadaacbcdabcbdccaadadbbcbdabaabcbabdcaaadbbadaadbcbcdacababadccadcaabadbdadbbdaccaadccaccadacabadccabdadbaddcbcacadadaacccbbaccdbdcbdabcbbdaaacbbdbdadbbcbacdacbdaddaabcabbdacddabbacbbdacbabbcabaddcabacbcdccbdbddaaaaacaccaacbcdaabccdcbbbacdcbddabcadbbdbacbdcbbcbddadabcababbabcaacbddacdbacdcaddddbccccaccabdbbcbbbbbaacaaabbdaddcadddccddacaccdacccabbaaacadbcdcdabbbacddcdbabdcababdcbbacdcbcbbbacabbadcbbbbaacdadcbaababddaacadabcccbdcbaccaabddcaddadabbaaaaadacadacabbdacabcaacabdddabdddccabaacbbdbaababcdbbcbccdaccdadbbddbddbdbbcddcdccdaaabbcddabaccbbbadbaaababcbabacdbbbcbbddcbccbdbdbddcccacdabcdadbdbdcbdddacdbbcdbacbadbaadbadadbcbcddbddcdaccadabcabcaccacbadbdbacdbcadaacbaabdccbdbddbbbbcdcccdabbacdcacddcdbdddadbbdbbacbbdcaabbbddadabacdbabaacbdccbbbbacdcbabddcbbbdaabbdcdaaacbddabbabaadbbbdbbaacbddcddadccbacdddcaacdcdcabdbadaadbbaddbaaccbbcdacdaaccdcddcbbadadcabddccccbdcdbbbcabacaccbdcdcadbcbaaacdaadbadbdbbdcbabdbdabbdbabccbbbabdcadcadcdcddcaddcdcadcbcbbaadbbbdcadbdcdbdbcaccabbdaaacbbcdadacddcacddaccdbdbbcbddbcdabacddabdbbccddabdaaacaccdcaccdbadadadaadcdacaaaccbddbabaddbdadddcadcccadacccccdabcbaddddbccbddbbabbacdabbcbcdbbcbcbddcaccbcbababcddcbadddccccadbaabdbbdbdbbcdddccadddaaaacbdacccbbbbbddbbadcdccaacdbcaacddabcacbcadcbddbddbdccddbdbaacbdddbacabddbdbcddaabcadadbbbabdbcccdaababbdcdccccabcabbdddbcabaacdaacdcadcbcdaaabcbbdacbcbcadddcbcdbbcaaaaadbdbbcaabaabcbbcadbabacabccbbabbcdbbbcbbcdaaadcccdbaaadcabbbaacbcbccbbadccdabdbddabcdbbbddacaaadbbbbdcbbacccbddbcdbdbccdbacaddbbcdbbccababaaadbaabdcaddaacdadbdbbadaabdbcabaacbabdbbdadbadaadbbaaacddbccbbacdccdcddcdbdacadccccdcaccdabbbdaacacadcdcadbcdcaabccdcabdbbddadaacbcbdcdaddcaadabbaaaaaddadacbcadcbadcbbcacbbacbcbbabbbacaddbdcccddbdabdbbcbbaccdcacbddcbcabacdcbabcdcadccabadddbabbbababaacaaabccbbacccbdaabaaadbadddddcabdacdcdbdaaaaccbaddcddccadddbcccabcdbdcabaabdabdbcbabccddcaddababcdbabccbcddcdcbbdbbbadbbbdbaccbbacccdbabdaccbbacdbabadcdadcbacdccdbabacddbcadadadbdadcbcdbdcacacdbbcabadbbbbbcdabdaaadaadaabababbaadbcbbaadaaacccdadababddbbcbdacddcabbcaaaaddcdaddcadcccbcddadbbcddbadcadcdcaccccabcddddacaddabddcbcddddccdbabadcbdadbcacbacaabddbbddaaadabdcabdabacbdcdddcadddcacdcaadbddaaaaccbcbbbabbbabcdabdbacacabdbbadddcabbacdacadaaddbdbcaaabbdaaadbababaccaacbabbdcdbbdbdbaddbbaaacdcbaadbbacdabbadacacdcddbccaadbbbbaabcabcdddcadcdabacbdcbbdaadcdabdacacababcbadcabcddddccbaabdaabccdbabbbdbdadbccdbcbbdcaddadcbbaaabddcbccbcaccbaabadcbbccccacdcbbdadcaadbcddacaaccaacaababbaddbcdabccdbdbcdcabbcabbaccddadabacdaddbbccbdbcadabcacabdcbbdcdbaacbbdabbcbbdbccbadbbadadadddbcdccdbdcccdacdaaaababacddcacbcadbaadbdabaccaccaadaaadcbccacabcbddacdadcbbdacdadcaddcbadcacbbddcbdddcdacbbaabdcabbacaaccbcbcbddddcdabdabcbdccadadcbcccdacacacbacdaadbbabdbabcbdccbcdbdadcbdbccbbccadcacacccaadaddbbabbbaddcaaabbbdddcbdadbcaccdbcaccaadbbdddbcbabadbadccbddddacbaabdabacbcbcbaadccdcdcdabcabcbaabbdcbbbcdbbbbdbbbaccddbcbcbbbaabcaabbaadbaddcbbabaaacdbddadabaabbddacbbabddbbdbbaddbadcdddcabbcadcccacdccbacdbddacbbaabbdcabcbcddaadbcbbaadbaddabdbdadabddccadacaadadadbbbabcbcbcadadcdabbbccddcddbacaadccdbdccaccbdbdcaabaccbbabcdbcbaddbcdbccddaabaddcdbccdadbbacbcddbbbbbaddcbdddcaccbaabdbbacdbdcacaacdccbabddccccbbddcbbcabcbddbcaacbcdcccdbabbccbabcdacacbbbbccbbcccacddbbddcaacbcccdaadbdacccbacdcdddaaaabbcacddbcabcdbdbcbbcabbaaddabcddcbcacccdddaccbcbdabcbdbbbdccdacabdadddaaacabccabccaabaddcbbcbcbccbaaddcbdaacdaabcdaadbadcbdbaccdadacaacabaabcabcabadbcbccdbcddcaaabaadddaccdabbcbadadddabdacdcbadadddbaadacadaddaaabaddcbaccdadcbabdddbcccbbddcdbdcadccbccadabbbbbbbbcadcacccbdcbbabbadbbadabdaadbdbcdbbdcddcbccbbcbcbccbbbbaadcbddcbcbabdbcddbcddbdaacacadcadadcaabcaacabbacbabdccadcdadbcbcacbcbbaccbdcbadabbddddcdcdcadccbacaabaabddadacbaabbaabbaddddaadacabcaabbbbaddcddbdbacbbabccddbcdaabdbccccdddaadbbcaddabcaaacdcccbddbcabbbcbaabbbddcaacbbccbbbddbcccddadaadbdcddbcdcadaaaddbdbdaddcabcbbabaabcbacacdbadaabdcbcbddbccccdccacbccbadddccadaabbddddbdbabaaababdabaaddcdadcdaacdcbaaaaadadddddcacbcbacabdcdcdcdaaaaadaccabadadbcddadcadadbbddcdbbbdacddcabacbdaddcaaccaaccbcddabaccdbabadabdbcbcdadcccdcacacdbaddabdddcaccdcaddadccbbbcbbcaaabdcccdacacbdcabdadbbcbacdbdcccbbcbdacbbabccbdabbbdaadbadbdddcacbacbbbabbbbbdbbcbacccdcabcacddbababcabbbcbcdbcdddbccadcaaabbdcbddadcdbbcccbaddcabdaabadacbdddabdbcaacbddbacccccacccdaadaccdcccacdccdddacddbcdbbaacacbdaacabcaaccbcdabdcabcdddabdadabbdbcadaaadcdccbcbccdadccdaacadbcccabbbdbbdcbcdcbdbddbdcbdabbdabcccabbaabddcabababaccbcdabcdcdbdddadaadacbcddddadbcbcdbbabadbcddcbcbcddbdacadcccacacbcdcbbbccaabbdddcbdbcdbaacdcdcaaccddcdacbdcdcdbbbdbbcbdbacbacbcbcaddcdabacaaabbacbbdbccbdcdcacadddbbbdbcddaaabacadcdbbcadcacbdacdbcddaacabacadccaacacbcaddaabaaadcbddcbdbacbdccccbccbcbacdaabcadadcdadccdaaccadbdababbcbbcdcacccabacdbccacbbabcdcbbcadadddbdccaddcbaddbddcaacbdbddbaaaabacdcbdbcccdccaaddddadadbbdcabcbdcddcdadabaaaabbaddacbddaddbabcabbddbdbbaccbacccbaabccbcdcbcdabaabdbcbaccccdcbbaaaadadadaccdcdcbbddcadbaaacbbbacddabbcdadacbbbcbacbadbaddccbaddaaccddabbccddbcbbcbdbcccaabdadabcdbdbbbbaacbacbccbdacdcadabbbccadaccbaadabcaaabdabdaddbadabcbacdbbccdcbbbbcadddabdadcccbadaaabdacdbdaabccadccdcbbacacccadbaabdccadbcabbabccacdbadcaabcdcacbddddadcacccbbcdcdabbbcbdddcacabbcbcabcbababcdcdaccbacacacaddcadaddcccaaadbacddbcacaaacbbadccbaaaabadcdcaabcaacccdcaddbcbabbaabbbaabdcbadccabccacabcdcdddcbadbbabcadbbabadcbcdaccbbcbccbcabadddbacbaaacbacacbcdbdacdaccdddbbbdbcccbabccbabbbacdababdaadcbbcdbcdccbcbacbadcbddbbdddccdddcdccdcaacdcbbdaaaddaabdacbcbcbdccadbdbcccabdadadcbadcdbcaddacdccbadcbabadbccadbbcbdcacbaddbdadacbbcaadcdcadbcacdcbdaacdabcaaadcbadacbcaaccbcccbbbabcaadcaccbadaadcaaaddadbcdbaddabbbdabdadcccbaaddcaddacbbbbabcbabacabddcacbbcdcaacbbacaabdcacadcdacddbddaaaaacdbaadabbbccccbdddcbacaaacddbcbaadbadcadcadacaccbdddddbadadddcdcacccccccdadbbddcbaddcabbcbdcaaadccbaaddcdadaacbdccccbaaccccdbababaabbccbbabbbcaaaccccbccbaadcaaaaadbbbcaaccccbbbacaaabbdddbcdbbdbcabbbbaccbddbbcaccdadacdddcaaacbdcbddbdcdcdbddbddbaadabdcabdbaaaccaccccddddddcddbcdcabdcaaccbbdcbadddbbcbbcbcabcadbcbacadacbcbdadabdcbcbdaacccdcdcbcbcddbbaadadcadbacccabacdbcacacbbabcdbacabcadbddaabcbbbcbcbdcacabcacabadbaacbbdaabdbabaacdcccddcabddddacacabdbaccaacdbdcadcbccddacacabbcddbacdacbbbccbaacbddccbdaabaacbdbcbcabaddacddcdacddbbcbaddddcbabadccdacabbddabadddbabbbdabbbaaabccbadabcaddcccdcacbacaabdbdadccdddbddaabddbcddccacacaababcbdacdaccbbacbccadcadadddddbcadaabadcdcbababbacacdcaacdbabdaddcdbbcabcacababbbddddbdcbdacaaddabdadabdcddcaadbcccdbcdcabbcbcadccaccabdccdbbdadaadbbaddabaadbbdaacdadddacdadbcddbacbbaddcbacdccddbabcdcdbcbaccccddbabbbbbdabccdcccdcccacbcdaaddddccaabadabbbcccacabbbbcdbcbddbbcdcbcccabaccbdaabbcdccabdadbabcbbacbcbadbdabbbacbacabbcaaadccaddddbabbaccabdbaacbddbaadaddcdbadacadcbcbdcabacacdacdcabbbdbdabdcddcabbaaadddacadcbcacdbaccbbbbadbbdacbdcdbbccbaaacddcbacbabdccddbbbcacaaddcbddbdcacbbcbdbcbdbbdaacaadaacddabcbbbadbdcbaddcbcbaadcbacbcdaabccbdccccacadcdddbcdbcabcddccbbbabccddbbadcbadacccacccabcbcddccdddabddadcacdabcbaabadbaabacdabbdbddaaaacdbbbcbcabddaacdccabdaaaabacbbcaaabdccbddabdabcbbcdddddadcadcdbbccbaabdaacadbbcadcbbdccbdacdcbccadaddacbbdaababcddbdabbaacbdabadbdccaababdaddadcabdabaddbbccabbdcacbaddbdbcacaaccbbbaadbadbbdababccacbcdddbddbdcaddbadbcaabdacaadacbbbdcddcbcddccbabaabcbcdddbbaddaddddcdbacdabbdbdddadcccdcadcbadcbabdccadabaacccadbabbbcbaaccacabbbbcabddddaaaabcccadcacbabbbdddbbabbacdadcabadbdcaaacddaabcdbdbcaccbaacaddbadccacadcbaccdbaddcbcbaddcaaacdbdbddcabcddcdacdbcdcddccdcaaccbdcdbacdbbcbadbbcaadccabdabccacabadaadbaaadcababdbdccdabddbaddbcdcbdbadbbacaabdabdcabbcdbdaacbcdadddbdabbccdccbbdcadddaabdccbddddcdaadaabbccccaddadadbbdccbccacbdaddabbabccadbaccbaaadbbbadbdcdcbbbdcccddbdacccbbdddbabdaaccdbcbcdaacdcdacbdcdccbbbdcdccddbddbadacacdbbdbabbbcbdbdcaadbabadbbcdbcdacbacdadacacaddcccdcdabbbbbadadbadbaaacabcccadccbabadabdcaccaaccbdaadbcdcdaadaacbacacaaabaacaccabdccabdbbbbaaababdbddcbdaaacbddcbcdbaadbdbdbcabbacabcdcdbadbdacdddcbcbdbbaccabbaabcbccdcbcbabbdcdaccdbbcbddcaddaaddbbdaacbccccaaabdbbbcdaddabcacababcabaaadbbbdadaaccdcaadabaabdbbbcbadadcdbccddcbdaacdddacacccbaaabadcdadbcdcbdcadcacdabdcdbcabdababccbbabbbcbcacccbacdbbaaaddddacddcacacabbbacdacbbdbaabcbcabdbcadbabadbbdbcbacdbabcdcaaabdaabddbbbdbccdcabbadbaacacbddacabbbbbbcbcdddcbbbcbbcbdbccaabcdcabddbdacbbaddddcaacaacddcbadabdbadabdcabaabdaadbdadccbdabadbbbababcababcabcbdbaaaccdaabccaababbbbdbbbdcdcababadbdcbaaddaacdaadcdcdbcdaaadbadbabaccdddcdadcbcbcdabadcacabcaccbcccdcadbcbbcaabaadbbdbdcacdacddcdcbcdadaaaddcababdababbaabccdadcddcccbbabccdcccbcdcabaadbaaccccadabaabbcaccbaacbddccbcacaddbddadabcbaaccbcbdbaaacbbaabdcbadbdccdcaddbcadbdddcbccadccabdccbcacddabcbaaaadadddadbaaabacacbbabaababadcabadacacabaacaabdbbcbdbcbcacdcbcaaccadcddbacdaadcdcbbdaddcbacdabdaacbcdbbaaaddaabbbcadccaaabbadbcddcbbcccbdccccdabdddaddccadadbcaaadadbccbcbcaabbbddcdbcdacacacaaabbcddbccadcddccdcbdaacbadccabcaacacaddbbbbcbdbdddddddcbabcabbaacdbddacdaccacadbabdadaabbdbadadabbcaddacabcdcadcaaccbaccabaccbadcbacbbbdcdabadddaacdcdacbbcbddbabcacbdccdcccbdbddacdccaccbadabadabccddbbcdcbbddddbabaddaabdadcaadbddabcbcbaaadadbdbccccadcaaacdddbacbaaacdbccaaaacdbacbbbadaabadbbdcbdbadabadcdccaaccbaaccbbccdbbabcbdbddcacbdbddbabbbbdcbcddadabacbcaaacabbcbacdbcabcdcdddddbbabadcccdccaabbaccaddbacdccaabddcaadbadadccbdcddadbaabdccaadccbdccbdadaaabdbaabdccddbcbdbbcaacdcabccccbadcbdcccddbbbdcdabdabbaaaabcccdddcccbcadbcdcacbdcadccdddccadacddadddcdbcabddaaababaadbcaacdabaabaaccbbbcaacaaabadbabdcddbdbdbbccacaaaacccbdaabcddbaccdbabbbccdbcaaccababbddadadccdabdacadcdbcdddaacadaacaabccdccdddcdcbcbbaacddabcadcbbaddaabadbaabaaccabbcdcadbdcdcabaccadbabcbadbbbcbdccaaccaaadaacdaaaabdbabcaacbdabaaccbdaccdabdddcdbddaaaabbdabccacacbcdabbbcdbcacdbdadadbaacbbdbacddbabadddccdbbcccbabacbddbbacbddbababadbbaadadcdbdccbacabaaacbaacccdcbdbbaccbbaabaaddddbbccdbcababcbbcaadbacbddcdacdcccbcdbbdbbdccbdcbdbdcddddbbbcabdadaabbaacddbbcababccacccdabccdddcabaccabbadbacbadabcaacaacacadaddbacbacaddbadbacabbdbdcadaaabccabadcccbcbccacdcbdaddbddbcacdbcadbddacbdbadcaccdcbddbadaaccacbccabbacdaaacaadaaddaccdcadbadacbbcbdddddcbaacbbbcaccadadaccbbbdbbaabdbbbacdbaddbbdbabadaadbbabcbbcbdccbdcbacadbcccdaaacdbcadbbbbbacdabcccbadbcdcbdddbdccdacaccabadbbbabdbbbcacaacbabbaabcaddcdddbacdbdbbdaaacadacbcabbdcdcacabacaadcacccaaadadbdddcbccdbddcdaccaccbadadbdbbcbdbcccbabbbaccdddabacbbcaaaccbbbaabaccdbcccbabdabbacbbdcabaaacaccabaababccdabdcbbaacdcccbdacbdccdadababadacdbcdaabadcbdbcadcbcdbbdbdcabdccbbccacacbbdacdcadbabadbcbaddabcbdabbccdcacaccccadcbcabadcdcddbdbbaadbdbaacdcbabddaccddadbcbbdcadbcacabaabacdddacbbcbdcdbdadaddbbacdbbabccddabacccacadbddadcdbdbcbbccbbacbdcbbbbbabcdcadddccabbcaabdbadcbdaaaabbbacccdcadbababcdcdaabaadbccddbddcccddcddaacaabdabdaaabaadaabdcbdbccdbcccbcbaddbcccbccbbaacdddbbdacddadbcdabddbddabbaabbadcddbbbcccccdacbcdabbacdadabacadaacbaddbdabadabbabaddbaddccabccaadbaddbbcccbcabcbaddddadabadcccbdacdacabbcabddbbbaadbcdadaadcddccbcbcaccaddabaacccdddabacdaababadabbdbcdabaabccbaabadabbbadbcaddddcccbdbccbbdadcbdadcabbdacddcdaddccaabadcaadcabbcaccbccabbcbdcadcdccabadacdaadcacaddccdaaacaaacbadacabbdaabdacccbddbbcdbdabcdababcaabbdccddbdcddcabbcbbbcccbcbadacbadcaaabccaddbbdbcbaadbbbcbaabdbccacabdadbaaabdaadbbacbadbadbaabadbbabbbbaadaabdbcdcdcacaccbcdcdaaaabcadbdccdadbcbcaaccddbbcbaadcacbbcacddbbacbaabcabaadcdbbcbccdbcdabaadbacbabccbdbbabcbaabcbbcdabdbadcaabccccccbcbccadcabdacdbbbbddbacdbccbabbcaabbaaadcabbcaccdadbdadcbcbbbdaaaaaccdcdabadbbdbdacdabccacddbdbaaccabbcdaababbacddccbcabbbcdbcdddbbcdbaaccacaaccdacdcdacdaccdabaacdbaabadcbdbbcbaddaabaddbdbcbddacadcabdcdbbbcccbaadddcacacaacdcdababcacdcccdcadddccadccdabaabaaddaccdbbbcacabbbcbbaabccacadcbbbccbdababaadcbbbddbddccbadbbabbdcbdacbbbdaccbbccaddbbcbcdccbcaabddabddbadabdadadbddcdbdccbbaccaddbbddaabbbacbbcacacbbcdbcbdbdddcacbcabdcbbdbbbcaaccaaadabcdbccccbbcadccabcacabcabaacbcccbbcadabcbbcdadabccbadcbbbaabbcaddbcadababcacdbbdbbcdaadbaddcccbaabdabaccaacccaabacacbcccdbadbdadabcbabddccaacabcbaabbdbaabdaabdbcdbadbdaccacdababdbcdbccccbdddbdddadaacbdcdaddabbadabaabcdcbbbabbbccdabdaaddcddbcaccbcdcdadaabbddabcdbddcaabdacaaddcbaccabbbacdaaddadbdcdbbbcacbdbdaababbbbbabaadbacbbaadbdaaabbaddacacbababaccbbdbaabdcddcccbccadbdddbcccababbbbbdccacadbacbbbcccdadacbddabdccdbcaddbdddcabbdbbcbabcdddcccbdbbcdabcabadbabadddcacbcaaaaacccbadbacbaaccacacbcbdacacddcbccacbbabbaaccdcbacababdadcdddbabcbbdaadadacccdaadabdadcbdacbaaccddbbddbcccbbabcbbbdbcccbdcbbcbcccbcaddcdbdbbdacaacacbbdcadbacbcbaaadbbdddcccbdcabbadbdccbaacdacababaddbbaaaaddcddcdcbadaccadabcadadcbdbabaababcbcaacbaaddbccadbdaaddcbdaaadbaacaadaadadcadbbbbbddbbdabcbbbbadcddadacdbcbacabdabaacaacddbbaddcdabbbabbadabcababbdacddbddbccaacbcccddcbcabcaaaaddacabadbddbbabaabdbcddacabcdcbbacabbacdaacadbacccddcccdcbabdbcaaadbcbdaccabdbdbaadbdcdaddcadcccadbbbadbdddbbbcccbcaaadacdacdcbccdbcbdddadbacbcdaccccdbbadbccababdbadaaabbbabbdbcadabcbdddadcadaaababcccbadcdddbbbbccabdccaddadadbccccccbdcdbbddbcdcdcbcaddaaaaddddcbadddaacdacabddacdbcbdaacbcdbbcdcaabdcbacaaacacbabadcdbdccbacdbcabccbddbdbcaddaccdcadaabbcacadacaabcdacdccbbbcbccbabaddbdabbdcbdabadcacdbabbabbabdbbacabbabacdadcddccaacaaabcaaddcadbdbbdadbbcdbaabbacccabbcadcdadacaadbddcdadaaabbaccbdabcbaadacdaaadbcbbdadaabbcdaccbcddadcdbbdabdadccdaadcddcaaadbaccbaaadbbbdaacbdaacdcadadccdbbcacdcaddbabddccababbacddcddbbcacbdabbbbccacdaccacbbabdcacddbcccdcccadcdccddccaaabdaaabdcdbddbcbbdaaddabdbabbadbddbaabdcccdabdabdddbcbdacddaaddcbdddbbabcadaccdccbabdcaabccbdbbcacbcddaadabdcdaaadccbcbbbbdadadddacbbcadcabccbddbcacbcdabdabddabaacccccddddbabbcdacaaadaacdbbadbaababadaacdcaadbbdacaccbabdbbbbaccdabcdaababcbaccbdbcacbcdadacbacbbbcbaddbbddddadaadcadbadcadaaddaccaadcbddbbbaaacdadabcbdbdbbcdccdbccdcaddcdddbbbabbcbccddacdbbaadbadbcaacccbcabcccbaacaaababcbccddaabdccadbbcbdaaddbacaacdcbddabcbcabdccdaabbddcaaabccddccabddccacababbacddddbbabcdbcadabbcaabcdabbacabdbbdcbaacadaaddbdbbcdbbcccdbddabccdacdabbbaaabaddcbcbacdadabcbbdadacbcbddcacaddacccacccdcddbcbaccbbcdbbdabcabaaddbcddbccbdadbbcdacbacdbccdbcbbadcaaaaadcccabdccaabcdbadcdbdbdbdbddcadccdaacccdcccdbddaabbdddaddddbcadabacbdcdccbadaddbbdaacadaddcabddcdaadbaacdaabddcdacabccbdcbbccdaabbcbadacdbdddbbadbaacbabaacacbbcbbdbcaabcbbdbdabcdacdccabdbddccdcaddddabccbbcadccddacadcacadbcadbddadabaddaacdcadcddbdcacbbabccbaaaadcbcaddcaabbddbadcddbddcacadcddaacdcaabbdbcbabbaddaccdbaaababadaccbbdcaaabbcdbdabbdbbcbdabccbddadbbadddbaabdaddcacdcbdbcbadbcbabadbcbddabdadcbddbbcdbdaabaaadcadbdddccadcdcbdbcacbadababbdcacadadbacdaabdbdbcbbccbdbbbcbbcccbabbadbcaadabddcadbcaccaacbbbbbaabbadbdcbaacbbabadabbcabddadbbbbcbbcdacacaddcabadcdcaadadccbddabdcadcbbbaaabadbcadadddbdccbadcdcdaccbbacdcbcbcbdbaaaabaadaabdabacacddbbcbaaaccbbacdbadadcbbcaacddbbddbccccdbdbaccbdaddbbaddcaaabbdabbaacbccbbcccdbabadbacbdbcdadaadabbddaacdabbaccddbbbbcbddccbbcadbccbcdbdaadbacbcbbccccccbbbcdabddadcadcbddacbccdbbbcabcccddddaaaadbbcabbdcabbbcdccdcdcabcbcbbaadbddcdcadcacccdbddbcdabdbcacddadababcdcababcbbadcdaddbdaaaabcbddbaabcbcddabaadaabacadcabbdacbddbacccccdbadabddbbcdccaabccbddbbaabcbacbabaccdacdbdbcccdaabccbbccdbccadaabbadbaadaccadcccbdbaadbddadcdacddaabcdddcdcacbdbacbbadddcabdadcadadcbacbbdccaabcaadccadaacadcabcaabaddccdbdbcaabbcbdaabaacabdadbdbcacacdddcdbdbcacaadbadddddcacaaadaccacbadcdcbbcbadadbcbcdaadbacaadbabacaddbdbbbabcabbbaaaacaabccacccdacddadbaddddaaabacabbddabdbdddcbccacacdadbadcdddcdcbacbadabbbabbabaadacbbadabdddacacccccdbbdddcaabddbabdbaacddcdcdccbdacbccaadaccdaadbcdaccddbddbabbbabaabbbcacdbabbabbbbbadaabccabdcabbdaadccadadccbabdcdbabbaaabbcdbccbccbbbaddacdabbdacacaaaddcabdbcacabaacdaadcbaddbbaccaacdbbdbbcbccbddcaaadbdbdbcbbddaabddbaacaddacdcababdbcabcdcbdcbcddbcacacaabbbababccacdddabdacbdcccaaccccbcbbabdccbcbcaacdcdcabdacbadccdbdbdbdddacaabcaadccbbbdccadaddacbdcdccddccbbbacadddbbbacbbabadddbccbcdacccabdccbcbabdaddbbcccbbacccbbdaadcbadaaacacdddddddbbcaacdbddccadccaddbaccabccccaaddcbdbdcabdacddadccbcabadaacbddaacdcddddddddaddabcdcbdbccbdacbdbcdabbbdbbbbbbaabbdabccddbdacaaddabaacdaddcacbcdcbbcaaacdaabbdacaacbacbdcacacbbacbdddacdcdddbabaaabcdcbadcbbadabdcdcadabdaadabcabcddbabcbbbcaccdcdbadabcddddcaddcabaddbcdbacccbbadddaacacdbbcacbbbddddaabdbbdbcdddacdbacaacaacccabaacbdbbcabadcacdbcdcadccbbabadccdaacdcdaaaabdddbacbaabdcdbcdcdacbbbaccabbaabaccbcabcdcddcbaacbdcaadcccddcbabcaabccdbbdaacbdbcbddbcabcadaabbddcabadacdccacccadcacbdccdaddadbcdcccacddccbbccdcbddcacdabbadacaaaaacabcadcbdcbbcaddadcccaabcdcdadaaacaabcbabaaacadaabdbcbdacdddaadbdbabdcdccacbabadabdbcdadcbabcbbdbdabdadacdbdbbccdaaaaddacbdacbddbbcbdabadaaadadadcbdadbdcadbaaddcaadcbcbcdcddbbbdaacbbcacabcdacadabcddacbaabcdcacbbccabcbdacaadcbbabadadbabadaabcdacdcaaaacbcddcdcbbbcccbadaccbacaabcdcddacdcaadccdbbbcdabbbcbbcacadcdaaaaddbbcddaccadadacbcaaacdcddcbbbbaccdccbcddcbabdcdabcdcbcbbabbcbdcaabddaddcabadbdaccdcccadaaaccccbaaabadaabccddaaaacddacdaddcdabacbbdbbabbacbaaadcbddcbbbbdababdacbbcbbddccaadccbdaacaaadddcdcddcbcaacdcbcbdabbadcdcaacbdcaacbdcdbdabcdabdaacdcccbcbcdddbbddacdbcadbbccccddcbbddabaaaabbacacabcaddbbabddbaddcaaaddacdacbdcbdbbaddcbdbccacbcdbccdadccdbccbcdabcddbdadadbbdaadddbbccdddbbdabcdaabbababdcdcbabcbaabcddbbacbcbbbdabbacacdcccacdcdcdcaaccccbbaccbdcaadbccbcdaabcdbdadbcccadbacaddbcdcddaacbcbcdaadbdadbbddddabddcabaddaddbbbaccbdbacabccbdadccccadbaddaadbaaabdbdcccccbbacccaadcabbccbaccdccbbcaadabbdabaadabccdaaacaddacbdaddaccccbbbabadccaabbcbbdaacdaabcbacabbbcbdaabacaadcacdbdbdcccbcaacabddabbdbcadcabdaadbaacbacdcdddcdacdcbdbbbccacddbccbbccacbadbcdabacbadaabbabdaccbbcacaabdbbcaabacdbdbcaddbdabdddcacadaaaddacabbccbbaddbcaadbbdabdbdbdccadaaccbbdbcbcdddcdadcabacaacbacddbdddacbbcaabadcbcabdadaadbdbabdcacdaaacaaaaaccabcccdbddbcabaaadaccddadadcddbbdcddabcabbbbcbcdacdcdbccbaababacbabbdadaaccccacdcbbbaaaaacccbddcabbccccbcdbdcaccdaaaadcbbbcdddabbbbccddddaacaacbbdaadadadbbadbdabbcbdcadccacbcbbddbccbacabaabbdadbcdbccdddcbcdcababdbaddcbdccbabaccacdbdddababccaddbcddadbaacbbbdbbdbaccdabbbbacbacbaddbdbaadaccdadcddbacdcbccdddbcaccaccbabcddbbccdbaddcdddcdddaabbdacbcbbdadabcadacabbcbdcbddbdbccbdcbcaccbdcdcdbacddbcdcdbbabcdccbabbbbabacacabaddbdddadbcadcddcbadbccbaabdddbbaaaaabdbdbcaaddacdbabdcdacaabadcbbbdbdcddcdddaabdadddbdcbbcdbbcccbcdabdcbdcababadcbdababacbddcbcddacabcbdddbcdccbbcbcaaaabbbdddccddbdabadaababcbccbddaababddacdcabbcdadddddcbbbaacbccabbccaddbacacbbadbdcbcdaccacadcbdcbcbadbbcbcddaaaacacabdaadbdbbbaddadccbbdaacccabbbddbaddccbdaccdbbaccabddbacabaadabdccabdbacdabddddbbcbbcadccabaacccccbddddbddaaaddcdbabbdcccdddcddaadbbdaabdcccadcaadaaccabccdabdcdcbadcbbadabaabcabcdaaaccdccdabcadcadcaddccacddbddbdabbcaddcddcdddcdbdbacaddcabbbbaddaacbccdccbbacddcabccbdcaaadbaacaacbadcdbbaaaadbdbbacadbacdcbcddbabddabcdaabbcadbdabdcadabbdcdabbbbaaacbbbaccbccbdbddcadacbcbbbdabbdbcbcbcbdcbadccbbccddcdcdbcaababbcbbaabdcbbbacbbadabdccccacbaabdbaabddbcabcdadadcdbbacdbabaccbccbbbcbaaadcbadcddbabaacabdbddacbbaccdacaccbcbcccababdbbbdadbacccaddacdbbcbcaccddaaadbdacbadaadbdbcaabddbadcbdddabbcbdddbabcbbcdbddabddcbdaabccbcdccddbabdbdadcccbddbabbccbbbcdcaacbccabacbbdaccacbbdbcbacccbbcadccbcbbdadacdcccdddbccdbacbbaacddabbbccbbbddadaccccbabdcbbcdabbacaadaccbadcabbddccacbddaaccbbdbcaacaaaaabdccbcbadcaaaacbbdcbbbadcbcbacdbcbacacbadddcbcbbdcbbcdbcaabacccacdcaaaccbddccdabacdacdbcbccdbacabcacdadbccdbccdbdcadabbbbcbacbdcccbabbbabbccaaadbdacbcacddabddbccbccababdcdaadacacbaaabddcbcdbadbcaacbccdbcaaaccdbadbbadcaabdcadadadbddbdbdbcdadcaccaddddbddcbaacacadcccdaaccbdbddbaaaadcabcbacbbbbbdccbbbdbdcbbbbbcacccccdaddcaadbababdcacbbdccaddddbbacbccbddbccccacccbbbbbddbbdacabaabbacdbdbabdadabbcacbcbdcdcdcadbadabaadabbcaddccbbcdccbaabdabcacbabcbdddbadccabcdccadcdccbcbdddacaaacbcdccacadcddccadbbadbaccbcabaabdddabcdcddcdaaddadbdaccbcdbdadacddabbbdcbdabacddbccccaabadcccacbdccaaaadbbcdabccbcbcdbbccbdbddcdbabbbbbdaaadaacdbbcabdcadddddccacaaadbadabdccdbbcacbbcaabdbcbaaccaabbaabacacadbcbdbbbcbbaddadddbcbaabcbbadabdcadcadaccbbbdbaccbabbdbcdccadacabbdddacdbdbdadbbccaaabadaddbbdacbbabcaacaabaccadabcbbacaaacdbbdbdcadddcbdcdaaadcbabcccbacccdacaabaabdadddbdbcdabdbabcccaccabcbccdcbdbcaabddbbcdccbabdbdcdacacbddbacaacbbddbcaacbbccdddaabaadddcbadcdcdaacccdcccbabaccdaaddaddccbaddaddadaaacddbdabdcacbcbdababcbdcaaddaadddadcdbbabcdbaaaabcbcadddacccbcdbdababdbdaabdddcdbaaacbcdbbbdbacbcabadcbdaabbabbabbddbccacbcccbbbaabdaacdcbcbbccbcccadcacccddbddaccccadcabbaabbdabddbcababcbdcdabbadadcccdcdcdbbbbccbdcddadcadabdadbdbdccabaaacdadbddbdcbddcadcdddabcbdabdcccbcdbaaccbdabadbadbcaccbaaacbcdcdcabdddbdacbaaaacadbadabbbcbadadcaccacaddcdaaadbabdcddbcacbcccbcaabbcabdccbccbacdcdcdcdbdbbcabbbcccdcddaaccabaabbabbbcddbcabacdaddaccaabcdcddbcdddccbbdddcabbdcbadabdcaaababcaabacccaaabadaccbddcabdabbbbacdbdbccababbdbabccbbabdbacabaaddbdbbbbbcaadcdbcccccdcaaabdacababacbbcbbabcbadbbcddcbddbdadcdcbadcbdcdaccabcbdacddbaabdbacbdccccaccdabbdcbacaddccbabcbabdcbaddccbbacaaaacdbcadabcaabcadddbcddaaccacdbbddcdbacdbbbbadccacdadcddaaadbcdbcacacabaabcbbabdcdddcdcbbbbcdacbdccbdbdcadaddcccdccbbcaadddbcdbadddccdacadbbbadcabbaddabbcbbacacadbdaddcaabdadcbbcccaccdbccbcdaaddaaaacbdadbbdabdbcddbbdbcdacbbcacddcddcbdacbbdcddccbcddabdbdbbadabdddbcccaadacbcbbbdbdaadddbcdbacdadcddcaacdcdcbcccbabbaacbccccadccbdaabbacbdccbdbbcaadcabaccbbcdbbdabcddabadbbcabcbdaadabdaccbcddacddbcaacacbcbadbdcacbacbdbacaabcddccbbaadaaacbadabbdcccaacbadacbbcdbdbbbabbcacabaabcbbdcdccdadbcdbbddbbaddcccababcbdbabacdcbcbdbcbdcbacaaaadaabccbbddcacbacabdbcccbccbbaaaacbdbabdddccbbcbbcacdccdabaddbaaccdcccaadabdbdacdaabbdaacbdbdbcbccacddbababaccdcbdbabbccccadcdccbbdddbabbaccdddbaccdadadcabaacddbdcddcabadddddcbcbbddabdacbcabdaaabcbbbcaabbadccdbaaaacadadcbbddcdccdaacbabdbbdaadcbbbdacbcdabddabcabdadbddbcccacaabccdbcbbbbbdbbdaddaaadbcccacdbcadcbbdaadabcdcbbbacadaadcbbaaddbaaccbbbacbdcabdabaacadbabacbaacdacadbcdcdbabadbacabdcbadcbbabccacbcacbcbdabcdbbcbaccbbbcdbaabbabcdcddcaabadddcabddbdcbaaabbdddcbacbcbccaaadcdadcdbaccaabbcdadddbbcdacaacbbdcabddbdabaabbbcccddccaddcaaddacddddbdcadbdbcbacabbdcddaccddbdbaaacbcdabaabddaaaccaccadaadddcacdddcadbbdccddbcdacddacdbbddbdcdbdabadcdbcacdbacdcaccbcbcddcdbdabbacddbacbbabadadbcaccdcbdacbdcddabccabbcdbacadcbcbabddbccdcbabadcccbcccaaaaccbbcabcabbcddcdbcbbaadaccbbcbdaabbaacdcddadccbddbcaadaddabcabdcbbcdccbdacddaabbaaadaabaaaddacbacaccacbdbdaacdaccdccbcddadcaddccbccacacbaaddaadbdacadbdadbcacaaccdbabddddaaddaadabcbaaddabcaacaabaccdaccbbaccabbacdbcccadbadccacbadccaaabdcbccaddddaaccaddbbabdaababddcaacbabaabdadacdadabadbbdccadbaccaddbdaaddddcbcadbbcbdcabadaadbdaccbdddaaaadcbdccccdcabcdccadabaaaccbbcbcaabaabbdabdbbbccdddacaabaddbabbdbdbcbcbcccbaccbddccbccbabcaacccdaabacbdddaaadcdbaccdbcbcdcbadacdccbdbdabbacadbdddbaabdaacbbaababddbbaadcbbcbddcbdaadadcbcbcbbbdbcdcdbabbbabadccdccaaadbbbbdaadbcbdbccbbbcbbdcaabbabdbddcdbbcdbaaabdacbcdaabbccbabadccacdccbabddaccabacbbccaadcbbcadaabcccdcbdbbdbbcddadcaddbcabbcbbbddcabdddcccbbaacbbdabdaadbddabcbccacaddadbdbaadadcacbdddcdcbaabbaacbcbdcddaaadbcdaacdbbbcccbadaaccbdcbbbcdcaaadaccbdcdabcbdcdbdcdcdcccdabdcadacbcbaadbdbadcdcddbbacadcdbbbbbcdccdadcbddaddcddbdbbadcadcacbacaddbdbbaccccbcbacdcdaabcacaacbdccdcbcdcbdccdaabacccacbadccdcccaddbbacbccacbbabdadbcacbbbddbbadddacdadcccdabbddcadadcbdcbabdbbdcddcccddcbdbcbaacbbdabacacdbaacaacbcbccccadbbadadbddcccdcacaacacccbbacdcadabbbdcddbccbbdcccbaaaabbbbabcacbdabbacdacbcbadbbdbbcdcaacaacddadccdcdcddbbdabcaabdbbcaddbbcccbbbcbcadcdbddacbbaddadcaadbabbdccabbdabdcbcaaaabaabdddbacdabdabbadcddcdaabbbdbcdabdadbadcabdabaacdabcabcbbbaccccdacacaacdbadaadacbadaccaabcdbdbdacbcbdccccdbccaccdcadcdbabbcccdcdabbaaddccbaaadaacbcadbcbbdabbdadaababbabccabcacbdbccacabcddccadcbabaacbacccccaaddccdbdbbcacdcbccacbbccddabdbbdcbcacbcbdacddbdbacdbbcccaabaadbccdcddcddbcbcbccdbbbcaadcdbdaccdaddbdabcabbdcbabbcbdbbadabbbcaadcddadbbabaddddacdbdaacbbbdbbaadcddbdadcbbabbbdadbbcdbacbacbccdbddaaabcbacabdbdbadaabbddaddbabcadbaabbbcbccdabaacdaacbdcaadbadbbdbdbcddddaadadadacabccccacbdcaabcbadbbccbacacaccbdcccbaaaddbabdadbcadacbacdbdbcaadddaadcdbbdabaaabcccbabcbcccccabbaddddcdbdaccacbcbbdcadabbacacccadbbaadcadabbaadddcbccadbdcddbccbcdcacbcdccbcabcbcbbbcccbbadadcbabbcbacbbdbcbbcdddadbcccbadacbbbdbabdbabdcbbbacbdabbbbbbbcdddcdadaacbbdcadbaddabddaaacaadddcdaccbdacbbadbbbdcddcaadacddcdbbabdbbddadabcaaabbbbbaddbbdaddcadbaccaabcccbaadacbcccccbaabcabbdcbcdadababdaaadbcaacccacbcaccddcadacbcdaaddcddadcbcacbaaacbcaacdaccbaaccacdbddcbabcbbdbdccaabaadbcacadbdcabccbdbcbababbabdaddbcacccccdcaaccbdbcbcacbadcacbbbacdcdccadbdaccdacbcbdbadaadcddbbabbbdbdccddbccbbddbcbbcdadcccacddcacacdaadbacabbbdddbaddbabbbcdddbdcbdbaaacadbcaddaccdadbacccdaccacdcddabbadacbaddcbbadacdccccaacaabcbcbbacccdbbacacdbadaccdddaabcdcbdcbabdabdbcaddcadcbcaaaccdbabddcbbbadbcbdcadabacdbbddaacdbadbadbcbcabcdcccacdccaacdbbcadbabdaabdacbabbadbabaddababbbbadcdbadadccadcccadbacdccbccdbbaadbabbaacaadcccaabbdbbbaaacbdadcaccbdaccdbdcabbcbdbacabaadccbcddbcbabacacaaacaabcdccbcdacabaccdccbdcdcacbdbbbdddccdcbccdaabbadddcccccdacdcbbcbacacddaadbccaabaaadbaaddaacdcbbacbdbdabcbcabcacaabbcabbcadddcccaadbabdbbbccaccadcdaccacbcacdbcadbdadcdcdaadaaacbacdbadbaababbddcdaababbddbcdbbaabdcaddccabacddadcacabcbdbdacdbdddbbccbcddaabcdadabddcaacbdbddbacdacadaddbdaabaccadaddbababaaddcaadaaaabaaacdbccbcdaadccbdddcbcbabadbcbdcdacccdaddaaacbbbdaccbcbbbcaaacdcbaaabcdbbcaadbcaabaabcacdbdccabbaaddcccababadcabbbbadcabddcdadcacbdababcdccababbdcccaabcadaabcaaabdccbbbbbbabdcdbdacdcddcaabadbbbcbaaaddaabdbaccdddccacccdacbccadbaccddbcdaccdaabbaabaabddbacdacdcdbbabcacbcdcbdbdccbcdabdbbcaabdcdabbbcbdacbddcacdcabbacddddddbadaadaddbbabbabaadddacbdddcbdbbdcdaadcabcdbacaddaadddcbdaababcaadaccbcadbcabaababbccccbbadaddbcdbbbdcbcbbabccacaccbdbbdccdddbbcbdccbacddbbddbccdaddbbcaabdbbabaadcbbdccbcabbccdbccdadaabaddcababadddcaabcdaaacdddaabcdbadbcaaacdadddaacaaabacbbbcdaabcdabcbdcdaaccdcddcbdacdbcddcacbbdbdddaadadcbcbbccccdaacddcbacbacdbbcbcbdbbbabaadaabaabcdacadacbdbbcbbbcbbdddbdcabcbdcadabbabdaaaadcdbdbbbcbaadaacbabbcbddadcdddbadddccccdaacaaadcccbbabcccbdbabbdbbabddadacdaacbbccdcaacacdbdabcbcddcbbbacdddaadddcbddcccbaaadacbdcabcdbcaddcbaddabccddcacddbacdddcccbaddddacdaabbbaaddcbacadbccacbbdcadcacadbacbddbcbacaccbcccbbbccccbadcddbbbabcbcadddcdcdadcadcacdcacbadacdbdccacbabcbabdbbbdbdbccaaadbacccbaccbdbacdccccccacadcdbddbcdccbdcdcacacadacbacdaadcbbaabcbdcddcccbababcbccbcbadaccabdaddaacdddadaabcadcbbddbbddacddbcdabddbdabddbcbcbbdbacadacacbcdddbdacadcadacddddaccdcdbdbbababbdaddcabacacccdbaabdccadddbbadbcacbdcadddbaabdcabcbbcddabbaabcdccbbadbcbdadbccadadbcbabbaaccbaddaaaacbdacadbcaccbdcdbdddcdabbacabcbdcccdbdddbcbdcccadabdadcbcadcdcadaaadccadbbaccbdcdacdcddcccdbcaccbbccddadbaaaddaaaaabbcaacaacacacdaabdaccdcbcccababdcddcbabacbaaabaccdbabccbcabdbacacdbcddddbabbadabdaddcddcaabdadabadcabbdabdcccdddbddcccdbdbcabbbdcbcababcdaccdccdadbbbcddaddaaacadbbdcdcaacdbdacddabbcbcabacbdbdccdacbbcdababaadbcdbdccbbcacdaaaadbbaddcbccabaddbdabdbcaccabcdcbaadbbdbabcbacdbbdcabaddccacdabadcbcacaabcbcccdcdddaacbabbaddcbdababccaaddbaaccacbacddcadddccbbabccbadababadbdbdcababaddbdabbcdddacabcbbaddccacadbbbdcabdaaaccdbbdddaadddbaddadaaaaddabcadacabcacddbddddbaacdaccaddbbbcbdbababbbbbbbdcbbbaadabacbcbccabbdcabbcbbbdaaabdbabdabdccdaacaccdcddcbaabcacabcabacabaccabddbbcbaababbddacaddbbdcccccadbbaaacbabddcbcbbabdaaaaacdbbdcadcacabbdddccbaccddbabcccabadbaabccbdbbacccaadbacacbacabcdadddaacbbbaccdbddcabcbbacdbdcacccbdbddaddacbadbdcbaaddddbddbbdaacbbbcddccdddbacdbdbcddbacabcdbcccbcacabbbacbbcacbcdcbbaabbdaaaaaddbbbbaaacaaadaabccdcbacaccaccdbacdbcdcbaadddacdcccaabbabcbbadacadbacacdccdccdcdaabbadaadcccbccacbaaaacdddcdccdcccdbccdbaaaacccaccccbcadbadadadabaccccaacdbbdcbccdacdabcdcdbacddddbcdbdabcbcbdbcddcdbbdacccbaaaddabcdacbdbdcabcddcdaabbabbbdadcadcaadbadadccaccccaabadacbddccabdcabcdaaaccdaccbdaccbdadaaddcbbacddccbccbccaabdaddbbbcadbbdbbccaadcdcadaccdccaddccdaadcbbbccacdaabdcadbcaaabddabbbbdddddcbbabdcbacdcdddcbdcabaadbdbabdacdbbabdddcaddadbacabcdcbaadbabdbccdbccbcbbacbabbcdbcdbaaabaacaacdaaabcacdcbdccaadcaccbbddcbbdcccadabaaaacccdcacabccbddcbcaabbcadcbddbaaccabaaaaaaddadbaaadbacdcdbccababbabadddbbbdbdbbaddbbaadabdcadaadbacbbabaabddccdadbbacabbacabcabaaaaddcdcadcdbaaaaccdacdbaabaabadbacbdcdddacdbacddaddccadcbcadbbcddbcbcbacbbcaccbcaddcaaabbbabaddcbddacaccdacccdcdacabaddbbcbaaacdbcabcaaddbbdaaadacdbdbdcacccabbdcccbcdbdbdaacbbddcbabdabbbcacacbacadccdabacdbbadacbdcbaabaabdaadbadaaccccabbacbbdbabbccacddabbbcccabcdcaacadbcaacbabaddbddaabdaccabcadcdbcaddbadaadbdcbcaddbbaabdbcbbdcadbdadaadcbbbbbcdcbaddadbaabbccabcccaabbbdbabcadbabbccaaacaadcdcacbbdabccadacadcaadcccbcacbddcbcbdabcccbcbdbdadbcdbcbdbcbdaaabbdbacabcdababcccbaccdbdbddacbdbaacccccdaddbcbbadddcbcdddbdabccbdbcdccdcbddbadbaacddbbdcbadadabcbabccdcbaabacdddabcbaaadcadbccbabcbaccdccdbcbdcbddabbaaaccbdbdaacbbddbaaaabddadbcacbccbaadcdacacbddadbdcbddaacbcacbaddcbbabaaacbdcdddbdbdacaaabdabbcbbcbccbccaaabdbdbddcbddcbccbcbacaabaccdcbbddcbdaccdbcdadbcbaacbcdbbbcdcdbadbbaddcdbdcacccaaacbbccdaddbacbadabddbacbdcaacaddbbbcacdaaabccbcadbdccbcbacbdbdcdcadbdddaacbabdbbacdbcabbbccdadaadaadddccacaadbbadcbcdccbdbabddcbdccbcabdcacacaddcdbddcbccccdaaddaabddbadaccbbabdadaccdccbbdbcbccdccdbaaadbababaaccbddabdcdabbccaacbddcadbaacdacddbaccbbbdbacaaabaaaabcbdacadccabdacdbbccbaccaccabdbbaccddaacaccdbbdbdaabddcabdccdcaabbcaccacbbcacbbbcdbcbcabaccacabacccbaacabbcbdddbaadbdabccbaabbdcdbccdabdaabcbcdbdabdbabcdcabadbbcbccacabdcdabbaadbbddabcbbddacacccbadbcccaadcacbadccbcdabcacdddabdccaabcddacaacdaaddddbbacbbcbacdbbacddcdbbcccccaadccadddddddadabdcdabaadcbcaccdadacbdcacbcbccccbcbacadabbcadcbbbbdababadacdbbccbcadadbacdacdadddacacbacbaacbbcdbbadabcaababcdccbcadcdcabbbadcccaabbbcdcacacaaaccccdddcdadbcddbbdacaacdbbddcaabadcbcdcdddccabdcacdaadaadbadcdabdabddaacabaccaabcbacccbbcddaacbacbdbabaacdcbdacbcabbbabbccadbadddcacaaccacaacbcacdaccbbdadcdbacdaadaaaabadbcccbaccadbcbbcdbcbaddcccbcbccaaababdcbddbabddcacccdbbdabbbdababbccbabdcccaacbcabcbcacaabdcadbdbbaabdabcddacaababcadcadbbaddacbdbaadddacaccbdbdbaaadbababdcddaaabddaabdbbbcbddabbcddcbabaaadbbadbbaabacdbdbccabaacddbbbaaaccdadcbabdaddddabdcdacdcddcbacdadacdccdbccbdccaacccabcdabbdddcacaccacbacaaaadcdcacdcddbccbbaaaddcbdddaacabababdccbddadcddcaadccadccbdcabdbacaabaaadabdccbdadacbaacdcccbdbbbcdabacaddbbbcadadbabdadccbaaadcdaacbabddabcbbacacdadaabcbccccabcaccdacbaaccdaaaddddcbccbdacbbcbdcdcacbdbddbbdcacdcaacbddacccdabbddaacdcbcbdadccbbdccbbccdabaaabdbcbccdababacdddaaadbcbabaacaadcbcddccaddbcbbdbbbdabdcacbabbbcdcddccadcbcdbdbcadbcaaddcbbbcbaccdadbbcabacaaccacabbcdbdcaaaacaabcbbbddcdabcaabdbbddababbbadabdbbdccacdbcdbbccaabacbbbcddaadcbabdcdaaccacdbccadacadabbabacabbbaaacbbcbaaccbadcddccaaccbdabbdadababcdbdacaababcbcddadadcbaacbaddbbbddcdcbcaaacddbaddcabdcdbbcacdbacdbabddabdcddcdcbbbbdccbdcabcbdcdaaadcabcbdaabdbdaabdcdbadcabccbadbcdbbdaaabbdccbcadbbcdcadbbcaacbcdbbdcbaccaadcaddbdcbabcdbdbdacaacaddcdbdcdbddcaacdacdcadbabbddadabccacbdacdbdcbcabbccbababddbaabbbccbacaccdcdbdbbcabdbbddaabbbcdbbdaaaddbddacadbaaacaacccabbddcbdcbadaaacccbcdbccbbbbddadbdabdabdaacabdadaaadbadcdaadabbccabbcdabaaccbbbbbdccacbaacdcaabacccbbcdbccabdbbadacbdaccbbbbccaabdcbcbacdcdcccacbdabdbbbdddacdadcadbbdcacccccbbbdcbdbadcbdbcccaddcacaadadabbcbacaaddddaacbabbdacaabaaccbbdcadaabbcabccccddccccadcacdcbdacbccbcdbccddcddbcbacabacbdacccbccabaccdcbcccaabcacdcacacadadcadbccbadaccbbddcddbcdbbbbbddbdadccddabbacaaddbdcbccaacdbddabbddbbcabcdcbdcdcbadccaaaddbcccadbadbbdadbaacaaaaacbbbbbadddbbdabbbadccadcbadaacbabcacdabcdaccdbbbcddaacdbbbaacccddddacddadddbbabdbadadddadbddaddbbbacdcdcbccdbcbadbaabddadbbdbcdcabcbdbdcbcbdcdbacabcddacddcbbbbdabbdbbbcdbbcdcbcdbdacbbdbdaaddbbcaabdadacaadccdddacaacdbcccbacabdcddddbdbaacdddccaacdccdbcbddcddccbbacddababbdadabcdabacdabadcbdbbbaaddadababdaaacbbcbdbbbdadbdbcccdbbdbcccabdddbbbcaaddbcbbbbbbdbbaabaddabacbcdcdcacddbacccdbccbbdacbacaaccbacdcdadaabdaccadccacdaadddcacdbcacccbcccbcddaacdcdaaccdbdcbadcbcbacdbacdcddcbacbcaddbabacbcddbacdcbabcabcdabbcaddbcaacdaccaccaacabaabdcbdacbaccbabcbccaabbbdabbaaabbddaadaaccdaabacaddddcadcdbacbddddbcdddcbcdcccaccdaddcdababcbaddabbcadccbcdbbcacdbcadccbbdcacacbccbcbccabaadaabcdbcacddcdccbbaccaddaaadccbcaaabbadaccbcacddadbbbcdacddcbbaaddadcadbcacdbcdadaaddbabbadabcaccbddcdaccbcdaaddcaddbccabbddbacacaabbbbaccdabbdbddacabbaabdbdcaabdbaacccadaabcdcbaaaaccbdcbbabdaccabddacaaacaaadcccacaadddcccdcdddaabacddacddddbadccabcccacbbcaaddbbdacdbabbcdcddbcbdabdacdcbdaadbdbbdbdbdbcddacdaabaababdbacabacddbcbaadcbbcdbcacbbddcbcabcdabccadcccddddacbbcabcabcccbddbcbaaddccdacabbdbbbdaccbcccbdacdbadcaacccadaaaddabdbbbadbacbdcdbcdbbbbadacaabddcddabddbcabbabadaabdaabcdbdadadbdbacabbddcbbbcccdabaccababcccaaccdbbbaacadadcabcdaaacbcdbadbdbcbbabaacbdcaaddddbdbbadbacbbbabddaaaacabdbdadadbddcaddbcbddcddcacbdaabddabacdbccddcccccccacbcaccbbabcccdadcbbbdbcaaacbdcdadcabdbaaadacddbdcadaacdaccccbccbbccddbcbccbdcaabdcbdbdbcadabcdbdccccdcdbcbadadaacbcadbdacdbaaccddcacadaaddcadaccdcdcabbaccbddcabbcdbaccabdccdabdcbaccadacaacbcbbddabaadcadbddadddbcadaaabbbaababaadaacdcabbbbbcaabbaabdbcaaadbbbdcbdabbdddbacbabdcbbadbbdabdbcadbddcadaaabbadcccbddcbbbbcdbccadccdccdcddaabcdadccbaababcdcdadbccdacbbbbccaaabdaccbdbcbcdccdadcbdcbbbdaabcaddabddbaddddabaccaabacbdaabbaccdddddbbaaadacbddabbccbdbdbdcdbdadabbcabbcabcddcdacbcdbaaacadcbdaaddbbdbbbdcbddbadaaccdbcccddaccbdacabccabcabbdabdbcddcbcbcdbbaacbabaddbcaccddacadadabcccadcddcdabdbbbddccdacbdcbacbacddacabccdaddccbccbbddaadaabdadababcbbadbdadcbaccabdbdababcbddadaacacaddddbcbcababccbbbaacccaabdccddbabccabbddaaaabbddcaadadabbdcdddabddacbcccadabbccabbcacaabadbbaaddcbcddbcaccdbabbcbddaabaddacdabcbbbcbcbcaadcdccdbcacdbccdcccadbdbbdcaacaddccbacacacbcbbdabbbcdcddacdbcdadaddaccdbdbadaadcdddcdababdaddaadbbccbcddbcdcadbcccbadabcbbccabbcabdacbbdcaccdddbaabcbbacaaabbccbacdcdddcadcccbdaddccaadcbcdcccbbbaccbacdcdddbbcadbcacacdcabdbbdaaabaaacdadbdcaacadcbaddcdbbbdadabadaaddadbbdccccbcdabaaacabdbcacdcddacdbbabcbcaccdbcaccaddabdbdacdadcbccaacaababcdbbcdaaadbcbadbbadadabaaaabcbabbdcabdabadcacdaacdccaabdccdaccdddccbdabadcdabbdcdcbcdbaabbbccdbbabbabcdbbcdddcbccbcddcadbdbcdacbbcccbdaccabbdccabdcdcbcaccddbcbcccbccdaccaabaacbbdcaaccdabadacdddabadcbabccbcdaddccbdbabcbcbbcbacadcbbbdaddaaddddbcdaacadacbbbcaaadccdaccccbdbbcdadcbbacabddcddbbcabbbabbcacbabccdbacbaadbccdaddcbdabdadabbdbbdadbbdaaaccacaacabacbcabdbbcabbddcdacdddccbdaccbdbbcdcbcddaacbbcbbccccddbbaabbbcbccdddccdcabdcabcdaddaccdacbdcdcdabbcdddccccbaadbdadacdbacabcaadabcacdaccaadbcbccbbcbdabcdddcaabbacadbbcdccaccbdaddbdabddabbdccdacdcbacbdadacbbdaaccacaccddabbbaccdcadbbbccabbaadaaddcbdadcbbdababdbababbacccdcabccaccdbaccaadcdcacbcbcacaacabdbbdcaaddadddcbbccdcbdbdaddcacacdbabdddcdbbaadadabbbcddbaaadcddddbbcbdaaaccbbcbaabddcbdbbbacdacccbdddbadabcdddacbabdccabdcadcdcadbbaccbadbdcdcabaadaaacbcbaaabcddacaabbacdccbddbbbbccbccccddbadcbdcdabddcbdaabcdaddabbdcdbddbacbdadcdadbcccbabbcdddabbabcabdccccddcdbcaadcbdbcbcbbcadabcddacadbdcdbdbbcbacdcbdcabbbbdbaacddabacddbdbdbccdcadccdbbdabdabddaaadacdcbacbaddcbcbcdcabccabbacdcccbcbcbccdabdbccdbcabbadbadaabacbaccdadccdabddbdaabbcdbcbddadddbabaaacabdbcadcaabbcabbbcadbbaaccdbdbcdcabadaddbcddcacdccacdbddbbcbcadccbcdcdddccccbccaddadadbbdacacdacbcdbcbbaaacccbabadbaaadccacdbbddacdcabdbdbbbadbccccabbcbcbdaaddbccbddacbbccdccbaabadcadabdaacaaacaadaaddbabdaddadabcdbacdbdcaccdcabdabccbbcddabcaaababaaacbcbccaaaccbdbaaaaacadcbbcdbbccbabbadbddaccacddddcbddbdbcccdcccdabbbdbbbadcaadbabbcacdcdbcaadcdbdbbadabcdaacbacacadcdbbdbbcabccbcbddaddababaabdcbaabbcaaabbbddbcbbbcddbdddbbabaccabbccdabdcccbdcaadbcadacdacccaddccbbdacccaccddbbddacdaaadadbcdddcaabbcbdcdcabbcabacbcddcabdcaccbbacdababddcabdacdddadabadccabcdbccdaabaabdcbbabaadabacbcaccdcccdadaadaacaabbbdbcdcaacbddbbbbccdccaabacdadcbbdbbbadbaccbcbcdacdddbcdbaacdabdbddccdbbdbadacabdbdbbcaaadbdbbbabcbdaabddcdbcadabdccbcddabccbddacaaadbccaacbdcadaadabccddacaabcdacbcaabadaacbaacbabacddbabbacbddcbcccbbdbcddbaadbcaacaddbbdcacdaccdcbdddaccacddcabcdcadbadddbaaacaabdadaadadaddabdbcccbacccccabdbcdadacdacbcccdcadaadcdcdaddbdbcbcaacddcabdbdbbabbdbdbdacddaaacacbcbbaaaadabdccbbdcabcdddcabddbbacbbdcddbcdbdddcdcdbdcdabbbdadbcdcadaaaddccacdcbabccddadccaddaaddcccddcdcbdadcacccccdcbddbbdbddbaaccdccbcbadaabaddbadbbcacbaadccaaadbacbcdccbbacacbdcabdadadccccbccbacdcddadbdddadbadbbadbdadcabdaababdaccccadbbaaaabbccbbacacbdcdddddccdaadbcaaabbacabaacbdccacdaabdabdbdbbbcadabcabdbcaaaaadcbadabdcdadcddbbbabddadaccddccaabaacdcdcbccadccabaccbadbddadbaababcacbdaddabcbcaddcddaaacaabbacbbcdbdcddbcbbcaaccdacdcdaddccdbbaaddcadbbabbdacdcbadacddbaacdcabcaccaccabbbaabddcdabbbdababadbbddbcaddaaabcbabdaadbabbadddbadcddacddcacbaddbaaacdcaddaddabbdaaaddddcccbadcacbaddcadadaddbcddbbccddbcabbdadccdcbbdcbdbbabcdcbcbcbbcacbbabbabcbcccdbcdcdbdcdcdaaacabbdbbabbcdbcddddddadcdbcaddbbbaccdbabdcacadcaccacabcbabbdddbdcdcacdbacbadbacdbbbcbbcbadaaaababacaddacdcccdacbacccdbaccacabbaaacddadbbbcbbbcabcbbddddcbddbacabcaaccabaaaaddcbbadbcacdaabbbbdabdcdbbdccbccbddabccacacbcbbdccdbddcdcdbccccbacdbaabadcdbbcbbcadbdbabbdbdcdcbddccabaccbdcdcbbcbaaaacdaabdaccbdddbbdbccbbcdabdccabdcccccdcdbbcaadcacddccaaaccabdcbaababbbdcacdabcacdacbdcdbbdcbdaaacadbbacaadbacbaccddabdbbdbdbacbabaabbabaadaddddaccadcacbcacaabcccbbabdcbdbdbccaacdccbbdacdbdcdddcdbaaacdbabddcdddaaabcdcccbcdaaccccaaabccaadcccbadabdcacccbcdbcbdbabbcbdbdadccadcdbdacddccadabbabbcdbbbabadddbacadacdbadcdacddabaccaaaddbabccadddddbddccdcdadbddcdaabdabbddbdabbdcabaddbdbbcccaccdabaaaaababacbdcbbccddbdddbdaaacdcacdcdbdddccddbaabacbbcdcacabccddbcccdcbdaacacaadccdccbbbabbaacacdcdacddaaccdcbbcdadaacaccdddddcabbcddacbbbdcaadaadcdacaaaaabdddbbccabaacababdcbcbcaaaadcdadabbcbcaadbaadbbcccdadbbbcdcbacbdcccbaddbdcacdbddcbdcccbadacacccacbdbddacbbddbbcaadacacbcadaaddaccacbabcbbaabcadadababdadcdacbcccbdccaadaccaccadadacababbaadacddadbdddcaacabccbdccabacdadcaaddcbabddddbbdcccbaabdbcaabdcdbaabbddadcbabdcbcccaaaaacadacacbaadbcbbbaccbbbddadbaccddcbcbdbcadbabdbabcdcabddbccbcaabdbccccabcabacaabbbbdddacccccdccbcadbabbcbaadadadbdbdacbbbbabcbbdcabdacddbdddabdbcabadcdcbbddbdbcbadcbdaadcdccbccaacdacdadbcaadcacdbadbcacdcbddbddbdbbaabacabaabbccbaacbbdcabdbbcdabddaaccaadcccdddaacacabbccdbcabdcdcbdcdcdadccbbccbccaabaddddadacddbcacddcaadaacdadaaabadaaadaddacdacbddbdaabacddccdddadcccacdaadcaaadacacbbdddbbdcadabdcabadcbcacdbcbbbacaadcbabbccaddacdabdaacbcdbbcddadbcbdbdbabcbaccdcdcababbabccaccabdaccabcdddabbaddabdbdcddcacbabbccdcbbbbbbcbdcbacacbaccdacacaaccbbbcbbbbaababcbcdddddadabaabdcdaabddcbcbaccabbddbbbccdbddacbcdcdbacdababbadbacbadccaadaaaababbaabcbcdccaaaddacbadcacadccdddcddbddadcacbabdacacbabbcdbbdbbbabddbbbacdbdddbbbbccddacddcddcbccddbdcabcdaddcdbacbdacbcbccdaddbcddbcadaddadcdaccddadbaaabbdbabdbdaccadbddbccccddccdddcdbacacbcbaddbcaabdbaadcacccdbdadaddbbbacdbacacdacbdddaaabbccabbbdabbcaabbdabcbdccbcdadcdaccbabdbbcbadbaabcaaccdcbcabdaabdacadadbcbcbdddcbdccacddddbdcbadcdabdbcabbdccccccbabbddcacbdccadabdcccbabdbcaadcbdbbbacdbacaababcdaddacbacbdbadbacaccdcbcbbbccabdabdbabdbdbacaccabcdccacacadacbbaddbdaacbaacaaacbbdbdaaabbcacccccabacacacabaaabdddbbcdabaaadddacbadabccddaadadabbcccccbcdbcdbcccabadbabdbaaaaaacddbaacaccbabbdaaabbddababbadbaaaddbbdaacbccbddcabdccbbadaadbbdcccdcacdcddcadaaddaabaacacdccddcdccababcadcabdacaddbbaddcadabddbcdaadaabdcaacdcbcbbabdbbcdcdcabcccdcbcbbabdcaddacbccaabbbbbcddbdacdacdddcdcccabddbcdcacbadcdbadcadbddccdddbcbddcadcdbacadbbdaadcddadbabccddccdacadbbdcababdbadbcbbadcdcabbabbcbbbabbbacddacbdbdadbbcbabbcdaddbabacbcbbbdadcabacbcabbabdcdbacbbbacddbbcadbddbacacadabdcdbcaddbacabcdddbacddacaacaadbadbdadccbbaadacacdacaadcdbbccdacacbaabdbbaaabdbbbbddcdacdcbabadbbddbdcabaadddbcacccbaddbcacbddaabadddbbcabbbccabbbbdbcacadcaabacaacdbabbacdacccddcbbcddadddaacadbbadbbcbcdccbdcbcbddccbadcabbacaaabadbdcaccbcdcddbcaadbcbbaccdbddaadbacddbdaddadbccaadccababdbddacbdcccbdbbbdbdaaaccaabbbabdcdabbcbccbadaabaccdacaccbbbbbdbcbcbcbbacddacbcddddbdbccadccadaacccbcadacdaccdaaaabacadaaddcddbcacbcccbbcdbdbcbabaccadbaddbaccddcbaaacccdbacdadabaabccacbadbaccbbdabdcacbddcbaaaacdbbcdcbcdcbbadcbbcdddacbdcbccdaaddbdbadaadbcabbdddadbbcbdaacacbdccaacddabaccbccbddcbdbdacdaaabbadacbababdbbdbabddabdbabcaadcabbcbdabcaabcadccdaddcdbdbdccddaddbdbaabdddaccdbcdcbdcbbdbddbbddbcdccdabdabdbdccbabbcbadcccbbddadcdbbcbbbdcadaadcbcddaadaddddddaadbcdbddbabcdbacbbbaadcddccaaddbaadcdbdbacdcadbcbddaaabdadccadbadabcadcccddbcaaabdbaabdddaaccccbdabdcccbdbacbadacaccabdcacdbddaabbaccdddbabddcccbcacaddccadbbbdbccdcdcabbdaabdccddbadcdcbccccddddcddadbbccaabcbdaadbdcdcccaadaddacddaaabbcdccabacdaabdcdbccdcbdcbdcdcaaddabbbadcdcadadcbccbccbcbadbaacdcdcacbddacdbdbcbcbdbacdccdbaccbbaadddadbdbcddaabacdaabdccbcdcbcabdcabadddaddbcbcadadacbcbadcdbdddbaaaabbccacbbbbcacabdbdbbdddacabcbaacacbbbcbbabadabdccbadccbbcbbcadccaabcdbcdbadbddcbcbdbcdddaabbdcdcdadadacaaddbcadaaabdbddcbdddddaabacbaacddacdcbacacabccadadcabadacacbcdddaacacccdaaddbbcaccabdabbbacdadcdaaabccdbccacbaacbdcdaccbabdbccabadcccabcdaadcdaaabcdcdaaccbddcbbddbccdadbcccbadacdbdbbcacddddddaccbbbcddbcdddcadbdcdccbacbcaaaadadacdcacaacabccdbdbdcbaaccadaadccdabbabbdbbdbdbacccbbdabcdcadcacdcabacccabdcdbcbccacddbcbccdccacaabababadddcbcaddacbdacbabbcbddcabaddbcabbcaacacccbdabdddccaccbccaabddcacabdddbdcdacccdacbccccbbbbcbdaaabacdabdbbabcdacbadbccacaacdccabadcbabcacdbcdabdcdcacaacaacacbdcbcddabdccbddabbbbabcdcadcadccccdddcaabbdbaaaacdbaaccbaadbcabdccdbcbbcdbbbcdccbdbbdabdbbbcabccdcccbbbacbbcbabaaaadaacddbdbcbcbccabcabcdadbdaccadaccbbbccaaddaadbdadabccbddcaadbdbdccbabbdcdbdcaddcdccadbbacccbcddbbaccbcaaaacbddbcdddadcdbdbcdbdcbcaabcabbdbaabcacbddbaabcabcdbbcaaadabbdcdabdbdaaadcadcaccbdbcabaacadcbcbdbcaabcddadcabccabbbcbdbbbcdddaabdddbbabbbcbccccbcbcdaacacacdadacbdcbddccadbcadcdbcacaddaaadabdbcacdbccacacbabaddcdacdccdbabcabbcabacacccddacddcddbcccadbdaacbbcadccbdbcccccdabcbdaaddcdbddbdacdbbdcddcccbcacadcdccccbdbccaddbaadadccdbbcacbcacbbcabcdcbcaabacccdbacacdccdbcbbaaaaddddcdabdcddabdabcdadcdaaaaadbbcbaabdaaaabbcddadbacccbbaccbadabacaadcccaaaddcaccaddcacadbcadaabbabcdccdbdaaccbcdccabcdccadcacbdcccadcbcaaabbbdbbccaadccdacbbddacacdaacabbdacdbacdcccccdddabadddbaabacddaaadaaadcdccdcdbabccdaddcdbaaaccaadcdbdcdcabcdbcaabaadaabaaaccdacabaccccdaadddcbaccdcaddbdbaacbabdccddcbcccbbddabccbdabcbadccdbaddacbcdcacabcbacdaccbdaacbacabdcbbcaccadadccbcbbdcadbadabadababcbdbbddabbadccdcadaddacacccacaacbbbbdbbdbdcabcaadacabcdcbbaccbbadbcbcaaaaabaabdabcbaabacadddbabbcbcaabcbbcadbadacadbdbadcadaaaacccdccaddddcaadcaddbcbaaadccadacdaccbaabbdcccbbbcabcdbaacccbccbbbbbaaaccbcaacacaccbbdbdacbbacdcaacdcdaaaadddcddcacaacdcbaaabbcaacabbcdddcbcaaabaccddbabdcacdaacbbadbbcaaddaabbdbbbcbddabdcdadbcbcaaadbccccadbdbcddcbdaccccaadcdbdcbbaacabbcacdcbaababaaddbdcdcdbcbbdaadcadbdddabababcdbbdbbcabaccddabdcccabadbcddcbbcccbcabddacabacbadacddcadccccbaabacdddbcdbcbdbdccbbdadbbaaddcabbbdcadcababadbddbabbadadcbdbdccadadaadbcccacdbcdbaccbcdbcaaacbddaddaabddcdbcacdccaddadbbcdbaaabdaddadaabaaccccaaaddabbcdbcabdbbbabbadccbdccbacacacdcbcadbdcdaadddcadccbcdbaccbadbddcdddbacdaddaacdbcbcdadddccbbccdabacbbcdcacdaabccbbbdbccbbaaababccabdcdbaddbaaacdabbcacbbdcacadcabaabdcbccbdacbbcbccdadcadabdccadccbaaaadcbccacccbddcbabadcbdbddcadddabddadccddcbbbbbdbddbdacadcaabcddababccbddaadbbacbacaccdcabbaaadacaddbcdacacddddcddcaacbddcbaddcadaabacacdbabcbdbddcabdccacaaacbbcdddabbbdadaddabaacdbbbadbdbbddcabccdcccabddabdbaddacaaddcbcbaddbadadbcacbadaadbdcddbadbacdaadcaaddcdcddadacbdddbdcbcdaccbdbaaddcbadddbbaddbacadccdbcbcaacadaadbdcbbbcacdbadcbdcadbcacbdbcbbbaacddbacddadbabdadaddbaacdccbcbcaddcccccabbddacbddbdacabacbaadadcccddcdaddaaadacbaabaadacadddcbcbdcddadbabaddcdbccbbbcadcbdcdbdbacbbdbdbdaccdabbaccacadcbacbbabcbbcddbcbaccbcaaacbcaaddaddbbdbcbdcdcaaccaddbddddccbcadcbdbbddbdacabacabbbacdccbaadabccbccddccadcdcdadaaabcdbacccdaacbdbcdbcabaacbcbcabcaadcacaadcbcbbcdbbaccaabcaacbaadcacadcbddbcbbccacacdbbbabcaabcacddaaababbbacdbddcddacabdcdaccdabcbbdbdbbbddccdabddbcbcccadadcddabbcbdaabddbcbdbabcdddcaabbaddccdbddcaabcabbbccdbbdccbbcbdbbddaccadaaacbdbdbddcbccacdbabdbddcaccdbdcbaadabbbbbabbddcacabdddbaacbaccacbabdbbddaddabdabbdbdbbabdbaabaaadbdbcaabbadcbbbbcabdcccddacaddbbaadbbacbaadabbdbccccccadadbdaacabbcaccdcdabbcabacbbcdbaacaaaccbcbadacaddcaaaaaadddccdbadddacbccaabbdaccaaabbababbcdabcddbdbddcbbdbdcababacbaadabacabbdacbdcdbbcbabaadcabacdabddbbbacbbcadcbadbadbddabbdcbbccaaaacccddaccdcadcddbdcddcdcdcddaadabcddbbddbaddaadbddcbdbbaaabaaaabcddaccddadbacccdcaddacdaccbcbbacdabcbbbaaadbcbbdbbbdbbccaadbbbdbdddacabbccdacddbccbaccdccdbcbbabdacbcbdbadcbbdbddcccddacdcacddaaccababdbcbddbdbcdacccbabbdcddbbcbbabcbdbcacbbbbbacbddddbcaadcbdcdcbbdbbcdddbbaadcadbbbcbbdcbccddaabbaccadbabadacccbdcbdcccdccbadbcbdbddbbccaadbaabcabacccbaccaacaacaabbbccccdbdddcdbdaadddaaacaddbccccccdcacdddaabcccbcbdbadbbaacabbaacdbdcacacbbbaabdbabacbcdccdccaabdccbcababdaaacbbbbaacacaddadaccccaacadadbbcdbcccddadcbdabbcdbcadcbacabbdadbcbbdbaadbcadacbaccbbbdcacaacaadcdddbbbdbacaddcacacdbaaacaddcdcadbbbaabbacdbaddbddabdcbdaaaacdabdcbdbdccacabddbdbdbabaaacddbadadcbadcdcbcddcbbdaacaaddcdccadabdbadaadaaacadcdcdadcacbdbaddbcaabcacbcadcbdbbbaddddbddcdcaddcbaacbdbcaddacbddddbbddcdabcccadcbcaccabadcaccabaddcbbbbdabddbdcabadcacbddababbacadcccbadabbdabcdadbcbbbcaddddddddaddccadccaabbccbdaaacaddddbdbdaacccbbacbcdabbabaccbdabbdddccadcaadabcadccaadccbbcdcbdcdaccbaacbdabcbcacbcbaccddcbaabaccdbdcdaadddbcddcbcdadaaaaddcbcadaabcdbbdabadabcdaacccaddadcadccbdbaaadbcbabbadbaacccacdbdaacbcdccbcbbdccccadcbdaadacaabccbbbaaddcbcdbbcbaabbbdbcbcacadacbdcbbdccdcdaabbadacdcadddbccdcccdcccdbbcdcbbbdadcacbbadcddcadacdcddaccdabcbcdbddbbdcdaadcaadcccbdcdadadccbdcaabdcdbadcddbbddcaacaaababbdcadadbbcbbbdabbacdcdcbaccbdcbbdbdaaadccaddaddadadddbcddaabaaddaaacaccacabdabbdaaaddcbccccdbabcdacbcdcbdbbabcaaaddbdcdbdcccdadcbcdaacacdbaddcadbcadcdddabbabdcaacbbabaadadbbdbabcacdadcdabcbadbaaadadddccabbbcacbaadcdbcaabadbaabaadcbcbbdcacacababbdbbcadbaddabbddadbcdbcadabcbcbdbdbbdccbbabcddcdbaddacdbbbcdabacbbbbabacbddddbddaddcaaccacdbbaaadddbbbacaadbbbddcaccbaaddcbabcccacbcbddcbacdbabadcabcdbdabbbbabbdcbbdacbbdbddadbdabcdaddabbcccbcadcddcbddadbdbadbaadbabdadaadcbdbbadcbadbadadddbbcdbaadaaabbabbbdbaabbdaddbdddadddabdcbbcbaaccabdddccdcbbccccdaabbadbbcbabddaccdabdcaccaababdaabdcbdbacbdccaaddcdbbdcbdcdbbcdbbabaccccdabaacdccdbcadddbbbbdacbdccdcbadbbddcccaaacdbaabccabcccccbccddaacaabcbcbcadbbcbacdaadcdbbbcdaaddcabdbdbbbcdadbbbcdaabbcdbababcdcadaacacbacabbdcdbdcadcdbcdcdddbccdbbbddddddaacabaccdccacbdadacacbcdabcbcccddcdbbabcaacaadacaabccdddbdacdbdacdbcccacbacdcacdacbacaadcaddacdbdcbbcbacddacbbcbaabddadcbadabdbacbcdcdcdddaaaacbacabacbdbddbcdaaaccabaaaadcabbcdacdaaabbdacaaababbbcddcaabaaddadacacbddbcddddbddcbccadcddbdbbcaabbcbbacdbdcccacababaacdcbabacaacabdbaaddbbacbaddcccabaccddbabcacccdcdbaddbacabbaaddcabdabccdaabaaadbacdacacdddabaadccaccdbcbabdbbcbbccdacadcbadbcabdaaaadcbcdaabaadbadbdcbbbdddaabdbccddaadbabcdcbdadbdccdcddcbbbcbbdadcbdbdbcdccdcbccdadbddbaaabbbdbaacdcccbaaaacdccabbdccbbbdcacbbccacbcccdbdbdbbddaacdcaddbbbddacabacbcaacdbdbbbbbcabcbabcbacadbbbacbbdacdbbbdadbacadabbcbbccddcacbaddcbaadaacabbccbadbbadcdabdbdbddacddcddbbaacdbbdadcdcadbbccdcbbddadbdbaaadcddbaccccdacbdbddcbdcbdabcccdbbcaddbdabadaaaacbabadbdcbcdbbccdbbadddbbbaaabdabbaacddaacaacbcdbdaaccadacadcadbdcdacddadcbcabdabadbddbccacdcdccdbdbcdaaabcadcaacbabbcbbbbabaccdcbadcaadabbdddadaaaadacaadddacdadccacdbdbbabdcabbbadcdaabdaadabdbacdccbbcaccbddaacddabacdccaddcbcbdaaccccaacbaacbacbacdacabcbbdbbddabcdcdbbdbbcbccbdcabadbdcabccaababddacbccaddbccdbbcddacdadcbadcadccbaacaaacccbcbdcaabcbccadbbccacacccaccbcccdcdacadacbddbbccaaaacdbcbadddbaaabbccdccadadaadbcadbadcbbcbcdddbbcaccaadcadaacccdcaacabadbcaacbaadaabcacdaacbcbcbbcbdcabbddabbbbaabaadaadadbccdbcdbdabbabbbbadadbbbcbccaabdadcabdcabaadbbaddbbaccabbadcacaadadcdacbbaddacacdcbcbbbcddbbadbddbdacddbcdbadddaaddcbacccdcccbdcdcddbdbcbbcdaddccccaccbabbcdbcddadbdbbdacdcdaabdbbabdabbcccbbdcdacbbacabbbddbadddbcbdaccbaaaaacbdaddbbcccacdbcdcaddcbbcbacbddacbcbdcbcacdddbaddcdcdcccdaabaaaccdabcbddbcbcdbbcdbbdaacdabcbdbcddadabddabdbaabddddadacacdacddabcbdcdccccddbccdccbddbcaaadbddddddcccbadbcaccddacdaccdacbadbaabdcabbdbadadcdcdbbddcdccacadbbdbccdbbcabcaaaaaaabddabbaddcbcabbbcdaaadbcadaaabcaccadcbcdadbadbabbcbddbcdcbbaadccababacaaabcddcbdbdadccadcabcbbaddabddcdbacbbdbddccdadccdaddadbcbadabadddbdaddaddcdcbacaadcccbccaabdacdccdbdadacbddbcdaacabdcbcdbcdddcbbccaaabcacabddabccadcccbdbbbabadcabbbabcdbbadcbdcddcadbbdcddcbdbbbcbabadbccddcdbadaabdccbcbaacbbcddbdbaacbbccddbbbadccdaddbcddccdbccdddaadabddcdccdaccdddcdcbcbaabbcbbcabcbabcabcdaccccdaccdaaaabadadcdcccabdbcbdcaababccadcbdccddacacdbccbdbabdacdacdcddbdbbdccdcaadbccbaabdcbcdabccacdcadbabcacdadabcbbdaabdcadddabcabcaccccbbdcddadabdcabaaaccbadcacdadccbadcbcdabbdaabccabcaaccadbacddbaddbaadbccdcabacddbbddabacbcbbdbbbddabccaacbadbcbadbababdadaabadaabbddaaccabaaacacdccabcabcabdacccaccbdcdddcbdaacaaacdbcbbddddadcdacbaadddabbaacdadbcbabbadcaadcabbbdbcbbabbddbcadbcacdadcdaabcadbadadbbdadcdaccddbbaabdbadbadbbbdcbadaacccadcaddcbbcbacaacbaadcccbdbccddcacdbabbabaaddddcbcdbbadadcddacccbaabbbddaacbcbaaddaabbadabacadcbcbdcccaddbdddabcdddcdbbbcbadbdddaaadcbcccddbcbbcadbababaadccaaacbaacccdccabcdbdcdddbbadabacbcbbcacaadacbdbabcbaacacaabcabdcbabbacbccdadcdcacbccdbccddaaccaacddbcaaddcddadcccdadacbdbacccaaabdaddccbdadddcdadcddcbabcbadcaddbcdadcacaaacdbaaadcbdcdbabaaacaaaaadcbddbcddadbbabbaccadcddccbdddcaccabbbcdcdcdbdbbabdcadabccbddaddddbdacbbcddbbcaaddddcabcaddababcaccdcaadaaaddbcadcadacdcabbbacbbdbccaddadabcaddaadccacbcbbbbaabdabaadacdcdbadbcbdbcdacabdabacdcaacddadacddbcbbaccbccbcccabccdbadaabcdaabbbcdacdccdccdcccbcdbabbaaacbbabccadabbccbcdbcdadcacdcabbcabddaacddcbaccccbdcadabcdacbdcbbbddbacbbddadccdbbaabbbbcccadaacdcbdccadbbbddbcadcdacdadcabddaacddddbbdcdcaadbbbcbdaddacddccbdbccabdaccccdcdddaddbcacabdaacdccabaacbdcbdaaacbcdbdacacddddcdcbcccccabdadacdbaacbacacbccbacaababbdbdccadccdaaabcbbbbbdcbdcddadbcbbbcdcaacbadaaaadaddcaaaabaabaddbbcbdcddcbaacbaadbcccdbdcbbbcababddbdbbdcdabdbccbabbbccbdaaccbacadadcaddddcbbcdacbdcdcccacaadaddabcbcbabdbcbcaabdcddbbcdbbcddaabbaaabdadabdbaddcadacddbacbadaadcbbacbdbbbabcbccccababdbbbdadaddbdbbdddaadcdbacacbdaaadddbcddabcdcccbdccabbddbdbbaadcdccbbadcdcaaadddadaacbbcbdbbdcdacdcccaadbbbcbccbddcdccadbadabcdbdacccbadbcbdcdcbbaabddcbbcbdcddcabdcabbcbdbdabbaddbbddbdcccccccdbdddbaaabbacaadcdbcbdabbabdccabbbdbaccdcccabbbdbabcbacdcacaaaccddbbcbaacdacbbbacadabcaabccbcbdcaaaacdbddbabddabbdcdcbbadaaaacaaaacccbacbdcbbcddbdaaddcdacaabadaccadbbbcadabaaaacacaabbadbdcdbbadcdcaddbbdcdbcaabcdacbdaccdcdbcdcbdacbbaabcdacddaaaacabbadddbadccbbabdddbdbabccbababbcababadbbcbccccbbdcadcabaccccaacddbdbacbdcdbadcdadcaabacddddbcdddcbdcddadacbbadaccadbdccdadbadacacbabbbadbabccdddbabccbbaadddcbabccbcdaddccdabbddaabcaabdcccbcdbdcacbccbcbaddccdcabbacacddcddbddbabddbccabccbabcccbdbcacaccdadccdbcdabacddadacabacccadcabcbdcbcdcaacddccabbdcbcadcdaaaadcdaaadaabbddbdcdaaddcdbdcabbacccddcdcddabbbcdbcddaddcdaabdbaccbdbdddaaacdadbabdaabaabdcdddaaabbbbabaddcccbaddcdccabcabcbabdbcbbbaadaacbdcdcbcabaacdcacbabcbcbcbcddbabbabaddadadcddccccaabdccaaabbcdacbcbcccccaaabcbddbcbccaabdbdbaabccbcbabdcdccddcbacbcacccacaaacaccdcaddddcaadcbbccdcdbcbccaccbdcdcdcddbadbacbdaadacdbdaccabcabdadcdddbacdbbcbacabdbacdcaaacadcdbcaccbcccdabcaabdabcbdcbaaddcabaacdccaaaacadbbdaaacbcdacabbdaccacacbccdaaaabadccddbbbaccccddcdadaaccacbdcddbdccbbdcaadacbbcaaacdddbcaddbdcdccbcaadcaabdbaaadcdbdbdbbbacdbdabbccabdddcbacbcbddaddccbbdcdaacabdcdbddaadbaddaabccaacadcacadabbadddcbbbaabbaddaacbacddaddbdbdcbadbcaddddadaadbcccdbbbdcaabadddcabbaabadacccaddcbbabbcbaabcabbcabbcabcdacdccddbadccabdabccbbbbcbbdaccabddbcccdaacbccdbdacbdaddcacbbbbaaababcdbbdaabaccdbbbadddcdbdbacabdcccccacbdbbdacacccbaabbdbdacdcabcddcacbbdbadbdbbccaabbaabdaadddbaabaaccaabdcaacbccdbcddcabbbacddcdbdabdcddaaddacccaacdbdddcbcdddabdabacddadddbbdabbacccaadcbdaaadddcadbaacbbcabcabdbaddbbbddcbdabadcddbbabbadcabbcbdcdbabcaaabccbaacbbcccbbbbbcccdacbccdaaaccbbcbadadcdabbccbcdbcdccacddaaaabaabdacacdabbbaabddaddcddaacdadaabdbaccdbcdddbcbcaadabacabbdcbbabaadcaabddbdbabaadaaaaabcadddadcacdaddcbbdacadabadbccabadbcaddacdbbcdbccbbaacaadadabbdabcbcdbcacabbcccdccacccbbacbcaaadbcadacbadadbbbadbcabadaaccdabcbadddbcbabadacbcdbbcbaabacbcddaacbddaadbbbadbaccdaccdacaaacaccadadacbdabaabacbbcbbdaaddcbdccbdddbccbadbabdcbdaadbbdbdbbaaccdaaaabbbbbdbcdbcbbcdcccabaacccadbbabdbaccdaccdadccacbaaabcbdadbbdddabccadacaaaacdddaabcaccaabdaaabcdbdbbccdadcdcaccdcadccccaaadcacdcdacdacccdabdcbccddadaddbbccaaaabddadabddcddcbcbbbdacbaabcbccddccccaacacdcadaabbacdacacbcadcddbdbdbdcbcaacdddbbdcdcaacddcabdcdbddbaddadbdbaabacabbdcbdccbbcaccdcccbddabaccdcaabddbcbbdcccadddbadccdcdccbacddacdbdaaddcbdbadbbdbdcdcaadbcbadcbbabccbcdcbbadbccdabcbdbcccbadbaaaadabadaabdbbadcbacdacaadbbacdcbbbbadacaaabdcdaadccbacdcaccabbabccccbbbcacaadcdccaaaabbcadadaadcbbbdbdadadcdaaaabcbcdccbaadaabcbbabadcdcbaabdacdddddcdbbababcccbcabbabcccacddbcdabdaababdabacacdcaadaadadbbcdadbdababadbcdccacdddadcbbbddbcbacddabdbaccccddbdbcdcbabbcadccaadccbababababaacbaaabbbddccbacbbacadbbbaaadddbcbbbcbcbcbdacabbcbdacbddcaacddcaddcadaacaaacabccacacdbacdacaabcdcdcaaccdbaacdccdcbacaddbaaddddacbcaabaaabbaacccddabddccccdadaabcddcbaabababcaadbdbbadccbcdbbcdccdaacabaadcccacaacaabbaaadbcbcdbadcdbbcbcbdccaddaccddabadabdbbbaacbdbcccbbbbdbbddcaddacccdcccdbdcaccbabaccdcbbadcacadaddcadaddaadabcacbcbcbdabaabdbabcbccbbadbbaabdcbbcddcaabccdaddcadaddcbbcbcacadbaddcdcaabddccacbcdadaaababbdcabbccabcabcbcacbbbbcdccdacbcccacdccabbadccadaccaddcbcbccddcbadccbadbacbbdbcbabaaabdcbacbabbadcbacdcacccbcaadbbdddddddabbdbbccbacacaaadcabaddcabbbccdbdcbabcadccddcbbdbcaaacbcbaaabadbcacdccbbaddcbacddbadcdcbacadcdbcaccddadcadddaddbbbcbbdadabcccdcaaadaddbadcddaacabbbbaacadbabbcbddaddcbdcbcccbdcbacbdadabbcadcaaacdbbdbdbbacaabaacbcbcacddbdbcbcbccaccdabbabddbddbddbbacacbacdabbaadcdbbcbddcacbdabbcbaddaaadbcdabcabdbcdaacbadcddbaccacadcbddbbccbdbcdbcaaabddcacaaabdccbcaabcbbaaacddcddbbbcbaabdcddacbbdcbcbdbccbddcaccaabcbdadddabdaaacacabcbbacbadcadcccabdbbacddaabcababacabbcacbbadccdaaddccdabdcdaabbcbbbdbccdbabbcdbcdadacbaccbaddaddadbaadaddccbbadbbdcadddaddbbdabbbdacbaaabdabdcccabbdaabdbdbdaacbcbdbccacbbdadbccbbaaaaaabcabbddbbbbbdadcdcbcccdbdbabbbbcbbcdcabaddccacbddbdbdbcddbbbccbdabdbbcdbbdbdbcbbdaddddcbcbbddacbdddabbddddcdcdcaddabccbcadbcacacaccdbdbcdccabbcacaaadbbaabcbccaabbbbcbcdbbaaabbbbdbabcdbbbbabdbabcbacbbbccbbdcddadbccbdaaddaacccdbbbcccbbdccccdcbcbbbcabbcacddcddbdaaabaadcdabccbaacdbbddacaaaabdabcadadccabbbdcdbadcdbbacccadddbcbddbabbdbcbbbbdbbcdaabccbdbbddbcdcabbddddcdbdcccbdbdcbbdbcdbbacbabdddaccbddcbdcdcbddbdcdcddddacbaababcbddbcbcdbdacdbdccaaccdaabbacccbccdcddcaccabadabadccdbdaaabdbcddcbcbbabadddbdacbbcbacbdccabbdbbdbaaadccddcacdbaadacbbdbbacaadbaaddbcabaabcbcabadcabddbccaabdbbabadcbcabdacdadbbdbdabbdadabbbcbcccbdbabbccadadadacbabbaabddbbaadbbcbccccdbdcacabaabbddadbdccababdaaccaadbcacdbddcbaadcccbbcadccabddbddbdbbbaaccaccacbabcacaacddcbdaaabaddbdaacababadddabbcdcbbdacdaaadbdababaaddcccdcbddcaadaccbadcabdcabcdcdbdadbcccabbdbabbaaccabdbbccccddcbdddacdcbabcbdcbccbcaccacacdcdaabccdacdcbbdbbbbddcdacdcdbbdcbbbdadbdbacdcddbbbdbcbbadaddcbdbabdccdcbacbccacdbcacbaaccbccddcdbdadbdabbdcdcdcaabbbcbadbcaaacbcdcabbccbdadaccabaadabcbdcadabdbbccbcaccbabcbaabdaacbbcaccbbabaadaabbabcddcdbdbddaabacbcaaacbdbcdddaaaacabbbbcbdaddcccdacccacdcccaaddabbaacabdcdcddababdacadddbddddadbccccdabbdacaddcdcdadbaacccbadaacddbccbdcadacdbadabadddcabdbbdcbaddaadbdabcadbdcacdbabdababddadccbbcdbcbdaccabbccbcddccbbabdccccbbcbcddbdcdbabacacbdcbaacadadddcaadbadbcccdbdababacbaaccddcaadcbabdcbcaabcbbadbddcacbdabaccdbaacbdcadcbbdcacadcdcbdcdbaddccdcdbddaaddbdaadcbbaadaccbacbabaacddbcdabaddcacdddccbbdbacacdaabddababbdbabdaacbcbdcdadbbdbaaaadbaccbdbdddaabcadbbdcdccdcccdcbbbcdbcbcaadaaadbabddbcdcbadddbccccaacacabadacacacabacbadddcaacccbbbdbdbdacbddadadabbacbcbaacaaadacaddaccdacaaaaaaccbcdcdcbcdddbbacdabbadbaadadcdaaccddbcacacbabcdbbcdabcdbaadbdcaddaabbaccaacdadbcadbdbcaacbccddabdbcbadcbaabcbddbdcbdbcdcbcddcbcccbaddabadcbcdcbaabccbbbaddaadaddbbbabccbabbdcdadddabcabdacaddaadbbcccccddabbdbcbdbddccbbcccbbacbdcabccabddaadbdcbdbaacbccdddcbdddcababaccbdacbbdaadcccaabbcbdabcdcdbaaddddccabdabcbbcabadbbaabbdbbbccabccddbccddbcdbbdcdbcadbdbabcdabbadbdcbccbbadcbdbdbadababdcbaccaddddddcdabbcdccbdbcccccdccaccbbbacdbdbabadcdbaabdacdccbabcacadbaabdabbacabcdadbbbbaccdaddacbdabcccbdddabcbcbbabbcbbacaddccbbdadaacabdaadabdbcaadaaabbadbcadbcadaacaaacabaddddcaddababbabacacdccbbadcbccccbbaaabcbccdabcaadabbcacdcdbdccdbbbbbbcbbccabbbcacdbbdcaddabbaaaccacaddcdcabacbddabdabcdaddbacdaddadacdaccaabbdccddcacabbacccccddcdbcdcbccbdcdaabadcbacadabcbbaaccbdccbbaaabbdcdcdccabccaaddcbbbabdcddaaadaacccbddcbabbcdcbdbbacddbbacddbcabcadaddacdcdaccdcdaacacdaddccbabcdcbaaccdacdabbadcacadddddacbcabbdacdddcbbdaccddadbcbddcdcbdcdbcdbcbadadddbaabaaaacadcdcbaabcbbccbdadcbdcccccccdbdccacbbabaacabbaacdcaacdbbacadcaaccbabacaccdddbbabdacaddbcdbadaddcbddcaaabbbadbbbbcabdadabadacbdaddadcaaadacbbdddccbcddaabccaaabbadddbbcaccbcbccddcbbcbdcabccacdcdadbcbccabdacdbacbbbdacdacdacabcdcdbbbdacbcddbdbcdccdaababddaabbccbcdddbddbaabacbddadbdcdaccbddbacbabbccaddbbddadacabdcbbadcbbabbdabcdabddacbadbcdcdccdabcbdaaddaaabdcabcacbbbbacadbdcdcaaccbdbddcdbdcaaacbaabbdadbadbabccccdabdcacdaddaddbdcdabdbaccdcabdddbbbbbcbbaaabdacbacdcccacccadbdddcbbddababcdacdcdcddcbcabcabcbccdacabadaccbcbcbbccbdbbbacbaaaacdcaddaaacccaacbbdabddbddbaadabbbccddacbcaadccbbccdacbcdbaccdbbbbcdddabbaaadbcadacacaadabdcdbacabddadcdcdcccadbcbcbabcbaadbcccbdbcabdacaaacabaccadaadbdcdaaabdbbdbdccdccddcadbddabdbcabbacdaabddbabacbadcbcaacaddcabbbbabdbbadbddccacdabccbcbcbcdbcacadacbcabdcdabddbabccababbbbbbadbaccbcaacaacdcdccbcbcbbdbbccbcdaddababbcadadaabdcdabbbacabadaddbcbcbcadbddccbacbabaacabbaabdbdbdddbaaabdadddbdabaabbccdaccadabaacbcdadabdcaadabbadaadaddddbcabbddcbacbaaddbcbdaaabdcaccbbcadbdadbaabcddccddcdbbaddcbbbbbdbbaaadcaaacbadaddaddaabbaacabcbdadaabdccdddacacbdcbabbbbcdbcabbbaaddabbcddacaacbccbabbcadabdddddbadcccaccacbccbcabdcccdbbbddacbcccaacbaddbaadadbaabdcadddacdcbccdbacaacacccbddabaadbabddbddbdaabdcdbbccbbaddcbcadaccbbcdbdcbacbccabcccaaccdaccbbdcbdbcadbbdbcbabbacabccbdccabdccaddcbabcaccacabdabddabbaabcdbacdcbcddabcddaabddcbdbcddbbabbcbdadacadadbbcaddaaabadacbaccdbbabdcddcbabdadbbbddaabaaccdabaabdabbbbbbbdacddaddbcdccbacbacbccbcadabcbadaccbdbadbadbccadccbdcabdbcccdbdacbbcbbcdabbacccbdbbabcbddcbddcacbdadaabadbcdacabbcacabbaddcccbdbcaacbadccbaacddbcbdcdbbaaccdacbacbccbcbdccdcdcdbcbbbcccdaabaabaaccbcdadcbccaadbadcaccbddaadabbdbbdcdbcbadcdaadaadbcddcbabdccbccdbbcdbbcaaddbbddbadcaabdbcdddbbbcbaddbdbddabdaddcabcdbccdabccbddddbbbcaabbbaacacdabaaadcaaaddaadabbdaadbcaaaabddbabaccdddcdbcdaaaacbccbdabdcabbdcdadcbdccabccbcdacddaccadcccbaaabcdaabdaccdacacdacdbcbcacdccdcabaccababbacccdbbdacadadadcbdabddadbddbcbdabacdbbadcbacdccbdddacacaacdbcdccacadccddacbdcddacbcbdccddaadddaddaabacbbdacdcadbaccdcdcadaabcbcbababadcccaddbabdbdcdaddcbcbdaccbdbadacbcabcbcdaacbdbcdcabcaadccadcabadbbaaadccdcbbccbdacbcbcadbdaaccacabcbdaccbddcbcdccbccaaabccbbcbcdbaacbddbcabdbdbdddadbadadadcadccadbdbcaabddcbabddadabadabdcabbddddbdcdaadadbdaccdcbbaddabbcdaacbdcccabccaabcbdaacddaddcabbbcbcddccbcadbacdbcbcbcdbaadddaddcbaddabcbdbacadadbcbaccaaadbcddbddabaacaadaaabcabcdcdbbadabaddbbccbdddbbaadbddcdacbbdabdcbdcbacbbacacacbdccbccbbcbbabdccddddddbbbaadcaaccddacdacdacbaabcdaacbbcdbdcccddbbaddcbbacaaddabacbddaadadacbbddddbdbabadacaccdcbcbcabbccbddcddddbaabdbaccdacccccbddddcabbbdbadddcadcbcdabcdbbcddaabbabbbdcbaacbcbcbbbbabcbadccccbccababcdaddaddbbcacbabaadadcacababddadacabcdacbabdbbddbbaaddcacbbdabacadaacdcccbddbdadaadbabccdacdaaccacdcdbdbabdbcadadcdbcaabcbaddcddabcbacadabbabdddbbbcccddbdcbbcbaabcbdcccbbaccaabdaadbccbddbbdddbbabaccdbacccaaababdcaddcccbbacabcacdacbbadddcdbdbccbcdabadabcdcbbbadccaabcddcbababcbaabccadbcdbddbdccabdbdcdacdbabcbaabacdcbadbbbcbbbbcaadaaacadbdcbccabddcacbccddcdbddacdadaddbaacdbcaaacacaabcacabdbcddcdbbccadddbbdbbcbbabcaabaaaccdbbbbabdcacabadccbaccddcabbbbadbcbdbbbcdbbdacaaddcbcabbdbddbdddcbdbacadccdbdbdaccccacdcdbaccaaccadccabcabdbaddcbbdbadabcdacdbcbababccbadaadbdacddbdabcdabdcdaddbcaabddbddcdcbdcdbdbbbcbcddcdacabacabbabbabaddabdddcbdabadbbbdcbcdcbaaccdddcadbadddacaaadcadbbaacccdacddacbacbdaadaccddacbddabbdddcaccddcdabbbcabbaabcadddddbaccadcbdbcdccbcbcdddadcddbaacadaaadcdacdbcddbbcadbdcbdcaacbddabddaadbccacdacccbcaaacadcccaaaddaadbbdbdbccccddcbdcabaccaadcbcbbabbaaacbcddaaaaabdadacbbaddbddcaacdcbcbccdcabccdbbbdbcbdabdcddcbdbbaababaadaacbababbccaadbaadbbbdaabadbdbaabcabcacbdbbddbcccacccdcaabbdaadacbbadcabccbaacacdcaaadccacdcdadddddbabccacdacbdcbdcdbabccbacadbbdcddaacdcdccacaabdddabbccccadccbccddaddbbaaadbccdbbbddcaaacdcccaaccdabadabbacccaccdbbcbaacbbddaabcdbbddcacbcdaccbabbcdaadbdcbbcbabddbdcdddcbddbdabcaabadddccacdbdbdabbcbdcdddabdcdaabcdcbacaadbccbaddabababdaadccbbaaabbbbbdcbadcbbccbdccdcaabbcabdadcdcaaabcaaadabdcacdbacdcadcdcdcdbbcccaacaacbbbdbcddbdaacbbacacdaadbcaaabaabaadddddcbdddbbdcaabaadabccdbcacbadbbbbbadbbccdddcdcdddadacbbdcdbbcabcabbdabbcbadbaabacddbbbbabbdbbbacbbaccbabddbbadadcabadcdaaadadcbcddcabdabaaadcdaabcbccaabbccbdcbdbbdaccbcabadddcbcccddddbddbdcddddcadccbbddbbacbaaddabddbcddcabcdcadaaddbacacabdddcdcbbcddbabdadbcabbdddccbdbbbadbbcbaabaadbbadbcddacadcbbacdcdbdddbbbdbcdbbaddcbacabcabbdaadabcadcaaabdbcadbdccadcadccdadcbcadbbcbbcadcbbabbbadddbabadbabdabadcdadabcdddbdbbcbbcabcbadbdaddaccdcdcabdadaddbcbcdbaacadbadaabbaacbbbbbcdbcddbdbadadddaaadbaadabaadabcdbacabdacbdbcbacdaaaccacaadbadadcadadacaccbacccadcccacbacbbaadcbccbaacbdabdaabacbadcbbccdbdccbcaccdabccabbbdbdabaddacddadadbcadbbabdcdddccbccdbdbadcbddacdddbdddccbcaacabdaaaaacddadcbbcacabaddbdaadccbcccdbdbacdddcacbdbcccbcdbbaacddacdaaacaabdbbaabccddcaaadcbdbbbacbcbcccbcbcabcaadacdaddbddacbacbdacbcdaaaaacccddacadabaaccdcacdddddcbbadaababbbdccaacbddaadbaddacaadadcccbcddcbabbbbbabcdaacdbcddacacccdddacbbdbdddddcadabbbabddbaabacbadbdcbadadcaabadcdadabaaabbbdbdbbbbccbdbacadcbbcdbadbbaadadbdcdbddbadabbcadaacbadacadcbaabdbbdcbddabaadaccdadbbacaabbaddcbcbbcdcbbaabaaaadcccbcbcaaaacabcadcdaacbdadbdbbbdabbddcaacbccdcbbabababbcddacdabbddcbdcadbaccaacbcdcababbdcdacdadaddacbdbaacbdacdddaccadbbbcddaababadcdccbbbbbdabadacbbcbbbbcababdcabcbaabbbcbcbcddbabadcacaabcbdabbabdcbcaaaaddbdacbcdadaddbacaaddbaadabbbcdcdadaccbbaccbbdcdbdcbdacbcbadddccbdaabbdcacaddbaadbdbcbabcdaacadaabcdacbaababbbcacbbdbabbbaccdbdababacdcaacabddacdadaddacacbcaccaaaadbdabbdbdcadacddcbccbdabcdbbabddcbbcdcdbcbcadcadaaaaabbdcdaabdddbcbddbaabaabdcbbcbddadbcbcbbadcacabddacbcacccbbbcacbaaccdbccccdadaabdbdacbbdccaadbcccbcacbbdbcdcadddcccbacabbdaaccccbdcbaacbdccdcdbacdcdaddaaababdacaaabacbdbcaadacbdcdbacccabbccbbadabaabcabbdabdcacdbbbbbdbcabdddcaabcbddddacaddaadbcacdddddbbcccabcaadabdabdccbddcdcdaacccddcbbacacacdbcacabbaabddaaccadddcabdabdaabdabadaacdbbccadcbdabadabbcdbdadbdddcbbccacdcadbadabbcadbcdbbccbcdcadbbccaabbbcaadaccbacbabccdddcdaccdbdbbacccddabacaacbabbdbcabcacacbbbbbdccadcabdadacaabbadcbbcaddccadcbadadcbdcbadcdcbbdbdabdacacbdcdcabddbbccdbbbdccacdcadbdaabbdbbdddadbcaaacbdadbacbcbcccabacbdabcaaadcaaddbbcbbbccdacbdcbcabcacabdbaddbcdabdacaaaaadbcaaabbddddccbaaddbbdcacdcbdcaccababdbbabacdbaccaadcacabdaccdbbbddccdbcbcaccdddacbbbdaabccbccacbabdaacacdcddacdbcbbdcbcaaaaacbcbbabdbcdcbacbcdddbaacddcccadccccbcacabdbddacbbdaaabdaabcbaabaccdbbccbbbbdacbccbabbcaadbbdbbcbdcddcddbaddcbcccaccaaaabcadacadccbcbabdbcbadbaabcdbcbdddcbbcaadddddbdbdbbcaccdccdbaaabdabddacdabacdbcbccdaadcadccdcdbbacacaaadddacbadacdabcaaabacdabdbccbbbcdacbaccbdabccbcbacdabbdccbbcbcbbccabcbaaddbbbbcbabadbabbccadcbcaadacbdbdbdcbcdcdadcbdbccabccddbcaabddabacbacadddbdaabdccadabadbdccbadbacdcbcbcabacdcccacabcbdaaacbddbcdcbddcdbcdaccccaacdaaaacbbdadcbbabccdaacabdbccbccbacacaccbaacaaaacbaabcccbcbbcdaadacbdaacababdcbbcdcacadddacbccacabaadbacdddbaaaccbccaadbacbcdadcdccacbbbbcbbaaabababcdbcabbdcddbdcbcbbbcdddacbabccccdcdadabdcdcbabadabbbcbaacacababbcabdbcdabaabbdddcbbcbdbcadadbacdabdcdddccbdbdcbbbbdacdadaaaccdbddbbbddbbdccbcddbbacadbaabcbadaaccbddccddaccbcbbcaaacabadbbbabdbdbdbcbaadcccbaabcadddccadaacadcdcacccccdcbbdccbacdddaddcddccbabbdddbdbdadabdacadadbdcbcdbcdaaddadaacbabddbaccabbdadcdabdbacabacbabdaacdccdabddcbbaaabdaaabbbcadbcbcbbddbddcbdabaaadbcbabadbabbcddbdbabdadcdabdabbacddccdbadcbaacaccdaadcbbbadccdcdadbaadbcbabdcbbdccbdacbdcddccbdaccbaadcdacbbdabccdabbadaabbcbcdcdddcdccdddabacadabddddbbabcbbaadcbcabccdabadabcbabcccdbaaaccbbcbaabdadacacbaabbbdccbcdacddaccddbddadcdbaddcdacdbcccbdacacbcadddbcbadccbaabbbbcbdddcbcacabadcbcaddcbbbbcadbaacdadddbabacbccaaacbdcaacbaaccccbacaccbdbcaabdaabbbbbbcbaabaadcadbcddbaccbbbcbdcdbcadbdbcadabcdaadacaacddbcbbdaabcdbabacbdddcbccccbbdadcadcbadabdacbbdcbaddbbcbdaacabbabaaddaccbcccbdbbadcaadcccdacdbdccaaacccbcbdaaddddcadaadcdadcbcbcbbaaccaddcbabcabbdcccbbacdddadacaadbbbbcbaadbdbbadbcbddacdadbcccaacbdbcaddcdbbccacdacbcababbbddddbcacacaadbcddccdbbdcabbabcdbccbdaccadbcaccaacdcddcddcbbcaccdcadcbadaaddbcdcacddcccabcbabaaddbcbddbabadccadbcbbbddcdbddcdaaddbcaadccdbbccdbcdcbcbddabbaccbacbbccdddcaadbacabcabbcabddbbabcabddcbdcaaaccaadadcdbbacdcdbaadabdcccabacdadaccdadabdabdccbacccacbcdcbdbccbdaacbcbacbaabddabdccaabcdbccbaddaaccaaaaccacdcbadbbaaccbbcadddacbabdbcbbbbddadccccadddbabaddddcbabcdccaccaacacbbacbdabaddbbdadbcbdcabcddddbaaacaabdaacbccdcabadacbdaddbbbabcaddcdcdcaddbabdbbbaadacbbcdabbabbccdcdbccdccbbbaacbadbbbcaaabdacccbbcacdacddddadcbbbacacacaabccadbabcddbccbdaaabbdcdddbaaaaaaaadccabadaaccccdbccbacddbdbaaaddabcbbbbccaabaadacdabdacbabdbaddacbdacddbabbcacdcababdcaccbbcbaacbbbbcabdabadbccaaddaaabddcdbbabbdaccbdcabadaadbdaddaaddabdbcaacbbcdbdcbdbbadbbabbcdbbbbbbcdaacdabccccbddbbbdcbaddaccdcddddcbbcadcabbcbddcaabbcbadcacccadacddcaadabddbbcbcbadabcbcccbaddcabacddaabcdbadbcddddaddddbbcbdccbbcdbacdccbcddccdcaadddbadbbdcacacccdddbdbaddccbcbaaddbbbbbbbaabadabbbaacbaabbabbdbccdddcabdccdcabadbcbacbdabdcdcccddcddddacdbdcbbadccadbabcdbbcaabdaddcbcbbccdbbdbdbdbbdaaadcaccacdbcacccddacaddabbbcacadcacbacbdacbdaadbaabbacaaddaaccbadccdcadbdaacaaddabdaabbdbdacbbcaacabcaaaddbccbaabcdacddcccbcadaadbddcaabbdbdbdbcbdbcaaddbacadbbbdbdccdadcdcbbbbcdbcdbcacacadbaaadbcbbabbacddbcddacabdbacdbbbdbabddbcbbdcbdcaddcbddacaccdacabdadbaaaacabbaacccdbcacbaacacdcacccbdaabdddddabbdcaabadacbaaaabbcabbadaddbabcbddabcdcbcadbabacaadcdcbaccabdbaccbccdbadbbcbabbbbcbbacdabbdcddbaacaccbabaddcbacaadadbbadddcabababddccccccdbdaddbcbabdcaabbdbdbcdbabcbddaaaacbbdcbacacbabcabbccbdbdcbdccaaabbbbbcabaccdbadbcdaaabcbccabcdadaccdcdbcbccbaaaadddcadbdbaabcbdcdcabccbaacdcdccdaabcbdcdbdcacdcbdaadccaddbacbdbcacdcdbadadccbbaddacdbabaabbdcbabacabadcdaaacccaccdcadacdbaacadbbdcdbbcabcdccacbbdbdcbaddacddddbbdaacdbddcdbdabcababbdcddddadcaadbdddaaabbbdbdcddcbbbddbaddbddbccdbcbdbddabdaccaccacabadabdbcdbcbacacbadbcbdacbcdbcdcacccdacddcdcdcbdccaabbccccabbbddccadaaacddcddbacaaababbbaacbdcabbaacbccaacbdbcccbcacaabdcbacdabbdcbbcbadaacbddacadcadbcbdcabaadcadaadaabbbbccbbbbaaabbbabadadcbcddbbacabbdcbbdadcdccbcbcccadadaddddcbaacaddabcbabdcaddbdcddbbaabdaaddcadbbcaccdbacaaaababbaacbadddbadcbdabbbdccaddccadbabbbccdaabbbbacbbdccddaacabacbabbdacbbbbbcaabdacccdabaddccacacadcbaccdbbaabdabaccdabdacadcccadcadadddabcaddccdadccdbacbcbaaadddaadabddcbbdbbaaabacbbaaacbcbbccdbdcdcbdbaacababccacdcddaaabadcdaadddccabddcbacacaccadbaabbcbcbccdcccbbbaaaacabcdbbbaddadbcadddadbcbdccdcbaaadbdbdddaadcabaabaabbccdabcbdddacdcbbbcdaacddbadcdbddbcbbdbabbdbbabaadcbcbdabaaaacdaabaaccabbadcbbabadcaacbbbbaaadbbacddcbcbbdcabadbabbdbaddcbdcdbdcddcbcabaccbcbcacbbdacacaaadadabdcbcadadacabdabbbbdccddcbbbdbaaabcddccdbccbbcadddabaddbdabccbcddbcccccbccbbdcdcdbaaaadcaddacdababadcdbccadadddabcdbaccdbbcbbdccbcdccaacdccbdcabcbddaddadabaddaaababbcdbbbbdadbcdcdbcadddacdbabacdddaadabbddcbbccdbdcabdccdcdbcaddadacbcaacabbacdbcdabbcbdaddaabdcddddbdddacdcbcbbbabcabcdaaacdbaccbdccaabcbaaaacabacdacacabdbdcdcadbdcbacbaababdbdccaccdccdbdddccaccdacdbabadbaddbddbabdaabbbbdbdcadbdbcdcaabadaadabccbdccccbacdaacddabccdccdaaccddaabbaaabcaddacdaaccbabcddcacbccdcdddbadacbdbdbcddaccdabbacacdcbcdcadbcbccbcdabccccbdbbbbbadcdaadbaadabbccdbdddcacbcddbbbcccdbdcdbbcbaadbdbdbbccbadcdcddcdbcddbbddcbbbcadbacccdcddacaacdbdcddbddabadddadcadadbadcadcddbcacdcdbdbabcdaacdbcbabbcdccdbabddcddddbdabacbcabacadccddddbccbadadcbdddbbabaabcbdbbadbadaccbdaadbaadbadcdcbabbdbdabdaadcdaabbcdaaaaacadbaccbbbcabadddabaacccacbcccdaccaacbcdcdcadadbdcacbadcddccaadbbaaabacbddcacbcdbbdabddbcacbbaaabcbabcdabcbddbabacbadcbaadccdcdacabcaccaabbbbabccadbdcbcdcbacbaacccacbadbadacbabcbbacadaacbbdacbdcadddbcbadccbcbdbaccbdadcacdcbdabcbabcbbaabbbbdbacccbcbaddcdaaabdbdcddacabaccddcaabacbbcabbdbcdcaabdabbbdddbcbcbdabbdbdbacbbcadacbcbaabcbbadaddabccbdcabdacbbaacdabbdbbaaaadbabdbbdcababccccbcacbcdaabcddddbcddadddabbadaccdbcadcdbbcdcddbcbcbdbaabacadbbcdccddabcbbbdcaabccdabcbbbbcababbacbdccbdabbbbccbddcadcacabcdbcdbbcacadbbdbbdcdbacbacaacadabcaaccaccacddadadaddadaaacaadaadcbcacdacaaacdbccdbcdabbabbccddcccbdaabadbdcdbdcabdbaccddadcdccdccbcaddbbaabbbaaddbbabbddcaabddbaccbdbddbbcacaccdacbdbbdcdcbdbcbaacabababbbbaaadcbdabdaacccbbacbbccbcdbabbabbabbddabcaabaaaabcbadcccddcbcccbddabddabbabadabadacaccaadaddadadacccbaabbcbcdadddddaaaddcbbdcdbbadaaacdbcbbbaadbbbacdbdabdadddcdbdcddcdbccdabacadbdddddadcddadcbbadadbbbcacccbdcabadbbcdbdacccdbbcadaaacabbdabbcacdbcccabbdadcdcaadbcbddbbbccbbddbccaabdacdbddcdbcddcbbccaacdaabcbaacabbccccdcacbabcdddddaaacccdabcaacbdaccabbdcddbdcddaababcbdbacccadcbdaadccdbbccdbbabbcacbaaaaabbaabdcddcdcacaadcdcaaacaddadbbacbbaccbcbbcaaaaaabbdadbadaaabdcdddcadcabccaccccbcbbcddaaadddadbdcaadbbadbccdccdddacdcbcbcabbadbbdddddbbcadddbdaaadadcdadbcddabcabcbadbbbcdbbbbcaacdbcaddbbdcabcdcdadbcdaaddaababdaadadcdadbaabccdcacbddcadbdbdbdbbbadadababadcbabbccccccbccabccabbdbdcbadcbbccbddcdcdacaacacbcbdacdbdbdbcbcaaddaccdadddaccbabcdcbbdccdadcddbdabbccdaacdccabdaabdbdcaacdddbcbdaabbcacaabacbdabaabbbbcdaaaddaccacabacadacaadbaddcdbbccdabbabcbbabddcbaadbaaddacccdcacdabacadacbaccddcaccbdbcccdadbdcccabbabbbbdacbaddadddadbdbddcabcabddccaabbadccdaadcacccddddcacddcababbacaadbabacdbcbddbbcbdabadbaaddadabaaddaaddbcbadbbbbdcbacdbdbbbacdabdadaadcdcdccdbdbddcadbcddddaaadadaacacbdadbaacbaaadbbdacaabbbbcacbccdbacbacdbcbbacbaabacddcacacbabaacbbdadddadcadcdaaacadabbbddaddbcbcccddaaaacacbcdcbbbbbcaccbcbaccbdbdcbaccbacabccbbcddbbacaddcaacdbbcbdbbbdbbcababbdbdbbdbaabddcabacabcdbaadbcabccabbcdababdbadbabbcacdaababddaaacdcddaaccdbbbbdcdccdbcbdbcdacadcbabaacbbbbbaddbaccdbaabaddbcbbddcdcdbaadadadcdacdccaacccdbbbacddddacdbdcadbdbdadbbbbcbdaababbdadccdcabadabadbbbabacaadacbbdabcddabbbbaacdcabcaaaaaccaadcacbacaacddaaabbabbacacaabbbadcaabcbacbcdabbbbccdccbdbbbabdcabdacadcddbcdbbcabcdcacacdaadbddbababdcacdbcdaadbddcdabaacabdddbadacdcbcbbddcbaaddaccbbdbadbbddcbadcadccadcdcaacbcabbdbddcbccbdadddadcdcbbcbdbadbddbacbdbddbdbddabaddbdcdbdbdddbccdccbccabaaabdbbdaadabacdcdbdbbddabaaaccdddcdcdbadbdcadbdccdcdbaccbaabaadbcabadbccdbadbaaaadadcabcdbdbcacddddcccbdadcabcadccddaacbbbddbdcccbabdcadaccbddcadcdcdbcccdaddabbcadacaacacdbddaaaddccdaaaaccbbcccdabcccddbabadbbababdbacaadcabcbbdbcbaaadbbbdbabbaaabcccaacbcacbbadcdcaabdcadabbdcccbbacaddcabacabccacddcbbcdcdbdaddadbdcbcdacccabacbbcdabbddabcbbaadcdabdabdccaabdcaccbdabbadadaacbdabaddddacdbcacaaddbabdaacdcbcaaddaddbbadaddcacccdaadbcdacbccbdcbcadcdbcaaaaabaabddbdbdcaabbcbadabcdaabbbadacacadddaaaadbbaccaabbadccabaacababacadcdbcccdbccbaabbcbbccadddabacaabdbdadbbbbcaddbbbddabbdbadcdaabccbbacbaabcbacbccbbacdbaababcbbbbbbdbacbdbdbaaadccacdddacacbcaadcadaacbabcacabbabcbadbcddcdbabbdacdcbcbcdcdbdabcdaabaddabcdaabddaabcdacddccdcabcbdbdccaadbbdcacbaabadadcaaccbdbdcbddcbbcacdcabdbbbdccccabcccbddacdaacbcbcbcaadadacbbabbcbbdaddbcaddbadddccbdadcabbadbaddbddcbbaaaaccdbccadbdbbcdaacbcabaddcaddcbcabbdbbbaadaaabcbcacaaaccbcddddaddbbabbcbdcbbcaaabcccaccbbcadaaddaddcdcbbadbbbcacadcddcbacddabdadcdbcbbaaaabadaabbbcccbdabddcabacbddbbcaabcbcbadcdabdaddbabbcaadaddbcadcdcbdcbbadccbacaadddcbacbcbcaaabbdcddcabbbbadcacdaabacbbbbbdaccbbaddaabdabddddadccdbcdbbacddbddabadcacbaaaaacdbdccddcaccbcbcbccadabcdbcbbadbabcdcaababbcabbdcbaccdcbbbddadddacdccccbadadbbdbdddddabbacacdaabbdbbcbbddaadbcacbcccccbbddcbacdbbaaaaabaaaccaabdaccdcdbcbddaaaaccbcbccccdaccdcbcdaacabbbdccdacbdadcacacdaddbdacbacdacbaaacddabcdbccbbcacdbdabcacdacdbabbdaaacaabcacabcdaaccbdacdcbbabccadaddaabdbbccabbbabbbacdbbcaddccbcaaccbdbddccccdbcbdbaccaccaadbadcbbcbdccbbdbbbdcbbaddcdacdadcadcdaccdacbdddbcbdadddbbbcaccdabacaaddadacbcadbdddcbdbbbbaccdbdccbbbcddcbbbaabdddabbdcdcabdcdbadcbacacbbbbddaaaaaacbdddaaadbcbadccacdcccdbabcdcacdacacdbbdcddadabdabcbcabdcadbcbcdbbcdccdbddbaaaccaccbabacddbcbcadcbabcbdbcbccbddaccbcbaaacabacdcccabdbdbdbabacbcbabdbacaccbdbbaddcaaddcaacabbbacadababcdbabdcbdcbbdbaadaccdddadbdaddbddabdabddddcdbdbdbdacdabccabddbbaabbbacccbbdbacccbaaabacbaaababbcdabdbdccbdabbccccccbaadadbbbddbcdccaadcdccdcaccdbcbbcbbadaadadaaaacdcbcadcbacacdbaabcdacaccbbbccabddccddcdacbbbddbbcadbdababcadcadcbcdcbdaddcabaaddddabdaccddbbbbdaabbbacacdadbcbbadccaadbadbabbcbccbdbdabdcaaddbdadcbbbbaaabddbdabaaccabdcaacdddcddadaadcbcbdacdcbdbbcadcdaabcbacadaabcbbcbabbcaaccddadbaacabcbbbcbdcaccabcbdcddcacccaabadcbcaaccacabcacbdaccbdddaddcdbadacdadacbdbbdddbcabcacbacababcadcaabdcbdccbadbaacbacaabadddcabaaadcccbdccbbacbbdbddacacaccdcdcccbabaadbaadabcdddaabaccdcdbdddcdbdbaabcbcdbdcddcabccccdaadddcbaddacabcaccbabcdcabcdabcaaabbcdabbdaccacdbdadcbcadacdccaddcdabccaccbdcbcbbcbcbdaacacdacdaacdabccddbdccbbcbadaddabdcbdbccabcddbcddcdddaccbdabaaadbbddccdacdbcdbccdcbddcbbdbdaddddbcaacdadabcdccccbbddacbaadddaaaaccdbdbbacabadbacddbdadccacbddcccabcddabdacddddcbabccbccdacdacaabbaadadbabddbbddbbacddcacadadbbbbccdacbcadbdcdddcacccaabbabbbdcaaaacacddcdaddcccbcadacbcadccadaabdabbbaccaccaadabbacdbccbbcdacdcbaaaccabcadaddcbbcdcddbbcabacaccdccddaabbabaccdcdbcaaccadabadcbbdaaabbcccbaccbcaadddbadcccdacadbcbdcccbabdbdacbddadddbcaaacabbbacdccabababdaabbdccbabcbbccbcadabdcdabcaadcadccadaacbdddadbcdcdcdddcaddccabbdbdacbdbccbbaddadcaadddbbdbbabbddddaccdcaadbaacdaadabcddcacabaaddabddacddabccadbabcdcddaabbadadbcdbdbbbcababadcdbcdbddccdcbcaccccddacdbcbcbbabcddbabdadbbdaaadaadddccdccbcdcbbcacaabcaacccdaabbdaddacddacccbcdcabaddcdccdaabdbaddcdccbaaccacbdccdcabdaddbdddbcaaabaabddbacdacdcacdbbdbacdcabbbdcbaacbbcaaaaacbadbdcaaaaabbcdbddcbcdaabcababcdbbddcddccbdaabbabcacbcbdacabdccabdccbddabcacabacdcbcdbdcdcbcbdbadcbddbabacacbacbbadbaaacbdddacdadbdbccababaacbdbbcaddcdacdbcccacbbdaccaadabbdbcddbbcdcaadbddaaaadaadcbdcdccbbdaadcbccdccdcdbabacdcdcddbacbccccabccdddadbacaaccbdbcaccadbbcbdacbadbaacbcaabdbcadcbaaddcdadbdcaabdaaabadabcbadacddcddcbcbbbbadddadbccdacdadcccabdbacbccbacdcbdcccbaaabdadbacdddbbdabbbbabacccccacdcabbbbddcabccbaaaaaaddbbacccddcdcddbdbadddbcabbdbcadbdadacdbcccdabbdcbcbacdaccbdbddbbabbcccbccbbdcdacbaccaadacabdadcdcbbdddaccbbddaadbbacdccdcbbbbbdbadaabcbadacbbcbbdbbbddaaabccacccaaddbcbbabaaababbdcbcbdabadaaabcadadbdabbaabbcaddbadaababcbcddccdacbdbbaddacdbbcacdadbacbbacbacbccbbabccadbbcdcbaacaadcbbcccbcdacabacbdddbcccdbdbcdcdbaccbbccccaabbbcbaabddbdcdaacacdaccacdababdbdcbadbdbcbddbddddbaddabacccbcdcccdcabbbbcdbbdcbadccdcaddabdcacadaddcbbadaabdbdccbaadcbacaacbddacadbadbbcacababccddbaccaaccdacaabdbbaacddadababacdcbdcdadcbcbaadbbcabbcbbaadbdcdbdaaadadcdccbcdbbabbabcbdbcaacaabccaccbacabddabbcdaadabcbaddcbabdabacdbccbdbcdabbacbdcabcbadbdacccbacaccabbdcabcddcddbbaaddaaaaaddbdbccaacaddbdccacdadbcccbbcdbaadbdadbababdcacbdbcbccaaaccdcacbbacddcaddaccbbcbbcdaddcadcdddbaccbadbdbbbddccbddcbbdabdbacbbbddccccdddabaadcacaaaabcabbabaddddcdcbddabdcbadbbccacccbcbdbbcadcdcdacdbbbdcabaaabdcaabbabcdbcdbcddccdbbdbcadbbbdbbbdcbcbbccadbdccddabacbccbdcbacdaababcdbaacaccbbcacdaacdcdcacdbcbdabcddbbddcdacbdcdacbcaaaccdabaacbdadcababaadbbccdbcbbddacdadaaabcbbdabbbdbdbcdbddbdddcbbbabdbacaadabdbdbbaacdcbddacbdbdbdadcccdbdcdacababacbadbbccdaaddcccaaacddacbbdddaadabbabbdacdbbbbcaacdbbccbddcdabddcbcdadabcbbbbbdbaddacadcbbcbddbddbabbaacaccbcccabdcddbbaadcabbacadcabaadcbdcaccdbcbddabccbcaabdccddbadbaabaabbdcccabbbcbaacbdccbdbaacabdaccadaacdaccbddcdbaadccadcbcdbbcbbbcacdbbdcddbbdabadbdaaadccbabcdccdbcabaccccbbcaadccbadcbcabbcaddbddcbabacbacaabadaacbdbaaabcaccaabdbccaadbdbacbdadcdaabcbccbbbdaabbadaaddadadaaccbbcbcbbaacaccdbaaadbadccabcbddacdbaacdcbbbbaabdbddbdbbcdddcabccdcabccbbacababbbcbbcaaaabdaccdaddcdbabbdcccbcbbcddaabdbbabbababcabacbcdacaacadbcdcadbdbaddbacaccdddcbdccabacdcdadccbbaaacbabdbbadacdacacbaacadbdaacccdadababbcdbaadabdcdcdbbccbbdcccbabadcbaadcbdcccadcaccbaabaaacdcdcdcccacabdadbcacddcdaccddabcbcdcaccbdccddabdbcdacbcbbcbcbbbcdbddbabcaacddddcdbdbdcdbcaabdcaccacbabbcbccbdccccabbacbdddaaabdcacbbacbcdbaccadcbbcdaaaaabccddccbccdaadadbbadcdddbcaddbbbccabdaaccdacbdbcbaabdcbaacacaacdbdadcccdadbdcccdbabbbbcbbbccacacbaccdabddccddbbcbbbaacacbdbbacdabdbbccdbdaccacabcbdbababbaddbccadbabddbadbaccbdbbbbbdcdbdbcaaaccdabdacdcddaaaadbdbbccdbadcacaadbcdacdaaadadbbdcbccbccccabcdcacabddbcbacdaddcddcdccdccacabdbcdadcabdccabaddabacbadcdbcbdacbabdcccdbbabbccdddabdaadbddacbcccbccddcabacadbccaccbcbabbbccdadcadbbaddcdbacacadacadbaacbbbdcdabdadcbacbaaaabbacbabdaadbdabbddcadbdccbccabdcdbddcddbdaddacadacabddababcccaddcbabbacbbccadadccabccbbcabbabbbacabbdccbcbbbabcaadcdddbbcdbcbabbccbbdaaccacccccaddbccadbbacdbcbdbddccbaaddcacccccbcbbadacdccccddbcbccacaccbcdccbccdabbccabaaaacbbaaaaadadddcaababcacdcbaabbdbdbdccbaaccdbbccbbaadccbcbdacdbdcbbbcacbcaaccdcdcadbcaabccbcddaaaabbabddcacbcaaddbbcdccdccababaaccccdccbdbcdacbdbabdbcaaacdddcccdccbabaadcdcbacddacbdccbbbccccbdddcbabcbbdacaabdccdbcdcdddbdbadccadcbcdaabbacbbdabcdbbbcbadbacdddbaabadcdddbabdbabaaadbcbdcbccdabbdababbccaaadddccbddacccdcbdaabccaaaacdabdcadbaadccdcbacdbacdbbbcdcbddbccddaaddbaddccccccacdadaabcbcdaaadcdaadbbdcdabaacddbbbcbcacbdcdaabbcbacdbdacacdabdbadaadaaaadacdacbbcbbcccabaacdccdccaccdaccdadbdcdcadddbbddacbaaddbacccddbcdbbcbdbcbccaabcdcbddccdbabdcdcbcabaadcdcadccdadadadabaaadcbaadbccadaddbdbaddcaacacbbbacadadbacdaabcdcdadcddbcbdcdcbcbddadcbcbbabbdaccadcbddcaadadbbaababadabbcbcdadbcddbcadbcdacdddccddaadcddccccddcdacbadcabcbbcddbbcbaaddadcbdccddcddcdbdbbcdbdcaddccbbcdacbadcbbadabccccdabdbdcccccbdbdcbdcccaadbcdcccdbdcabcdccbbcdcccddddbbadbadabbcbadaabcdabdabcadcdcaddddbcccbcacbbadbbbcbbcadaaaccdbcacadbcddcacacbadadcaadcdddbcabaabbddcbdddaaccaddbadacbcabdaaaadbcaaaaddbbcddbbdbbbdaacaaccccbcabbaacbcabbddbbcacbbdaaadddaaacccdcbccdbddacbdcdbacbdadddadbccaaaccabbccadddbdaccbaacdaccabcaccddcddaabcdadccabcdaaaacabdacdbdbbcbcbddaaacadacbbccbbaaddadcaaaddbdabacacaaddaabbdcbababbbbbcccbbbaccabbaccbbbdcbacadaddabaabddcabdddcdddaabdcaadcbccadccaabacdaacccabbaaadbacbaabcccdadbddbaaacdcccddcbabaabbcbcddaabdcabbacbdbccdbcdcabcbddcdbbdadcbaacdacbcdcddbaccbadcdddadccbdbadcaccaacbbdabdcabcbbcbddddbabbbdbacdcbbddcbbaaaadcaddbaadadbdddbbaccbdacabaaabbdaabbbdaddadcdccbdcdabbcdddbdbbabdbdbcaaadddcacdddcdbbdcdbcbbcddabbcdbacabcdccaabbdcddcdbbadbbddbbcdcdaaddddcabdaddcdcaacacbddbdacbaccdcaadcaccdcccadbddbbbcdddbbccbcacbdaddcbbcdacccbcbadaddadbccaaccccbaacdddacbabddbbbccaaabdadbbbbacadbcdddaddaacacdbabdddbcbdbadaccccadaddbbaaaadcbcabbcabadcdbdcbddcccbbdcddbcaabcadbdbdbaabcccdadaabadacbcdddadadddacddccddbcaaabccdaabadbcbcbaadbaccddcaaabcdcbbdddcadbbbacdccccbacbdccadcdabadaabcccdadcccabdccddbbadbcdcccbbdacadabcaddaabddddcbaacacccbcababbcaaaaadbdbbccadbacacdaaddcdadbbdcdcdacccadbacbbddbcddacbaddabcbaaccabadcaddaadabbbdbbadabacaacdbdaaaaadccabdadbcdcdcccbcaaadabbdacbabbbacbadbadcbaaacdcdbbcaacdccdddabcacdaabbadcdacacbbcbbcbacdbaddcbdcabddcdddcbbabdacccddcbbdbabdccbcabbbbacaddacccddcdadcdcbbbbbabdaabbbacabcabdaccbdcadadcbaabddbcaacccbdacccaaccbcaabacddadaabababaacdcbdabcbdbddcbdbccbbddbabaddcacccaccbdabccddddcbbccdddcccacccacbccbabdcaabcbccccbbbccabccacabbabcbaadddccddcdddbaacbdaccadbabccbdadbccbbbccaaaaccbbacbdbbccadbadabcbddbbdaacbdbbccaacddccbdbdbdaacbdbddcdcaaacbadbabdacdbcabdddccdbdaaadcdccacdbddadcbbbbcdaccacdddcdcccacdabbacdbbbdcacabcabaadbcdcdcdcacbddcabdbacdadcaaacccacbcbbbdaadbacacdbaabcacccdaccdaabbbdbabdcdbcbaadbccadddbdcccdcdbddaabddabddbcdbbcdaadddbaccbcdcbabcdbaddbbabdacddcbcbaccbbdcabddbbbccbabaddbbcacabcacbadbaabbadbaacdbabdbcdcdcbcdbacbabcddbcdacaaacbdaabadbdaadacaddcccccbcbcaabdcdacdbacbabdcbbacdbbadddbdbacbacabdddbbbaccbcbdbccdbccadcbccaccccbcdbcabbdaacdbcbcdbbbacaadccdcdcdcabbadccbddaaaacabcbdbbabbddadccbcbdadacadccbcdbbbbddddccadccacaddccadaddcbdbdadbcadbcadbabbcdacdcbbbadaadaaacbcbdddccbccdcbbbbadcbdbddbddccaacacabccdbabddadddbddccdaadaddaddccbadaaccddddadbbbcabcaacaaadbcadbcdbbdaabbddcbadbbabdcccddaabdadcbadcbdcdadbdaaaadcacbbacacbaababdddbaaddababcabacaadccdcaaadcbdccbcbccababbcbdcddcbabdddaadddcbdbbbadaaaaabbddccccbcddacaddacbcddddcabdcabcdabbcadccccddaadacdbadbcbadacbccdbdbaadccbdadbaababbabcbaacaccaccdcbbcaadaadbcbadbcddbcaccacddaddcbadaacdcdaddcdddbbcdbdcdadacbdcddbccbadaccbbccbddcddbdacdddcdaccabdabdcdbcbdcbbabcabaabaaabacccdddcaccacccdbdbaddbddacacadbdcabddaddbccccaabdadccdbcbccddaabcccdacbbaadccbacdddbbbdbcadabdadbaaddbbcabcacadcdacabcdcabdabaabbbbbabbcdcadabdabbbbabccaddadbdaadacbcbaabaacbbabdaaaaccaaaabdacbaadaccdabcdbcccaaadbacaccdacdcdadaccbdbccaadbdcabdbaabbbbbddbbacdabaabbddabcdcbbaccabdadadcbbacdbddabbdbdabcdadcbcadabcbbccbcbaccddbbcbccdcbabdcaccdbbcadaaaabaaababaacdbbbdbcbbbbadabaddabbddcbbcaababbaccdbaaccdddcbdcdcddcbcbdbdadccbcdbbabdddbdaadbdcbddaadbadddabdacccdcacbbaaddbbacaabcdcabdccbdaccdbadccddadcdbdabcaaccaccdbcbddbbbbbdddcaccddccabbbbbdbbdbcaaddbbddadbcaddbcbcbbdbbbddbdaaaacdaaddccbbaabdaaabbddabdcbaddbcbcddbcbdcdbcaaddcbcaccbbdabcdaccbbaabbccddcbabbcabddadabaccacccdbbddcacacbcccaabdcabbcabbadcacbacddbcbbcccacddbabbccbdacbdcdbadccbacacdabbbcdabdccdcddcaabccbbcdcdddbcaabadabbbddcaabadacccddcbbaacaacdcbacdbcbababbadcadaccabcaddaaccbdacaabacadcdcddbaadcbddbdcdcadaddccabcbaacccddaadbddddcacbcbdbbdbcdddadbbcbdbadcbdabaabcaaaaddbdddbaabcccaaaabaccaababacabbaddbdbaaaddcbccdaacbdcbbddbdaaacbcabbcdddcdddbaaabacbbabdddcdabaaccabdbaabaddbabcbaabbdadaabdbdbbacbdaaabcddcccabbddbbbcabccaccdddcabadacbdccbdbbdddccdbcdbccadacacbbccccbdcbadaaacbcccdbdabdabcdbcaabddbbaaadbbbbdcaabcbbbcacacbdbacddcadacaacadcaaddadabdbcacbcbacdcdbacacaacbcbaabddbccbbcdbcbabbacacabacbbcbadcbaadbabadbabdaacdbcbcdcbbddbaddcccddcddcadaddabdcdaaaccbcbacaacdddaacdbadcdbcdbdcccadbacdbaddaacdcccdacccdabccadbcbdcbbcdcbacdadbdcbdccccaccdbbbbaacaccddbbbabbdcaaadbacdbdddcacabaddcddbababccbaadbcbabcdaccabcabcbaccbababccddbcbdaadcbbabacbbadcbdabcdaddbaabccabdbbcabbacccdaccacaabaccabacaabbdaabcdbaaadadccddccdacbabacdddbbbacbbbbbcccbdbdbabbaacdadbdacbbcabbdddcdcaacbbbcdbaccaddabacdcdcaacdabbdbdcabbcbddaccdabacdddcbdacdcdcddddadcacbcabcbdcbcddbccadcabbadbbddbbbcadbcabbcabcabddcdabbcacdcaaaabaaaaccabadccdcadcacdacdbacacbacdcdbcdddcbcbbcdcacccddbbabbbcacaaccabaadacbdbbbacccadbcacabdccdccaaadcdbbaddcbacbbbddcbbcadacadcabcbabadccdbcddabcbaccdddacdbaadbbcdcaddbbcabaaccccddbabbccdccdadcbcccbacbbacabdbbadcdbddabbcdcccbcdbabbdbacdaccbaaacdbdbcaacdddcddaaadbcbdbbdddaaacbdacbdcacbcbcbbaacddbbcbbdccbbbbcaaddbcaabcbcbbadaacdabdadcbdabdcbddbccdbabbcdacaaaadcbbaaddbdbbbdddbdadcccaabaadddbbcdcadddadcbcdbcddcbbaaabdbabcbbcabbbbbdbaddbbbdadacccdbbdcadcbbdadaacdbadaaaaabbacadadbbdaabbbdababddcdbcbbbcadcbcdbacccbabcacaaadbcbcbaaaddbaabbabccdcaadbacdddaddbcbdbaabacccbacabadaadcbcdaccbcbcaccabcbacdbbadaadaaaadaddccdadaadcbdabcddabdbcdbdcbcbcbdadaaddabaddbdcbaadbcdccbdacddbaabaaadaddacddabcbaddbdcadababbcaabcaddddaccbabadacabadbcdadcadbbabdbdbacccccadbacbccbbbbcbadaacdbabbdcaadbbdcddbdbdccccadaacabadadcdaaadaddbbdcaadcabdacbdababcbacbaddaaabcccaabddcaadbdabccaabdaadbaadaacabacadadbddbbddcaacdaadcbaaccdbabcabdbcbdcbbadaccbcbbabbabababcbdbaacdadcdddcddddbcdabaabbdcacbaaadbbcdabbdadadcabbbdadbbcdabbabdbabbbadcdcddcbbcbbdcdadbcdccbbbddacdddbccdaccbdbcbdadababaddbaabcaaadaaaaaddaccaccbdbccdbadcddccaabbcbcbacdcccacdcddacccacbacaadbcbbdbdcdbbdadabaabcabcbcdabbdddcdbdddddddbacdaaadaabbbadddcdddbdbbaccdacaaccbcbbcdbdababbbbabbdbbbbdcacdbabdccdbccbbccabccbbccdadadcacbdcaaabbcdaababaadbcdbbcddcdacbbcdbbcababdddaabdaddcbdbaacacbaddabcdcccdccdabadbabacbadaccabdcccddababbbbdbbdabbdacbbabacbdadbacaaaaddcaabcdccbaabbadbbcaaaadddbcdbcccaacabdcbaaabcbdbbdaacacccacdbcaccaaabdcacccadacdbaaabdcabdbbccddabaabbbbcacabbdaccaadcbabbadbabbcbaadcbbdaadcddaaccdbcabdcdddabbdbaddbbcbbdaacbbaaaddabcdddbbbbadbdcdaccdcbdbbaabdcacaccbbaaadcbddccbaadccdbdcabbddbabddaddacabdaddbccdcbbacbcdcbcababddbccbcbbbcdcdacbcbdabcdbbcccabacaaaacacdabcaccbdccddacbabdadacdcadbaddaabacbcbbcadcacdacabccaacdcabdadcbcbaadcadbacaddcdbdadcabcbbbaaabbbaaacacaabbbacbaaddbcccddbcabcbcacdbcddcabdbdababbccadcdadcadaddaccbadaaccbabddacdddbaaaddacbdcdbcacddccabccdabbdbbabdcbccddcadcbdacddddadaabcbcccbbabdbdcaccbabdadacdadacabaabdaacbcbacadccaccdabacdccbbcadaccbdcbcdcdddaaaaadcaabbbabccbcbdcccaacaccbbabddacbdbbdccddcaacccaabaadbbccdcbbbbbadcaadaddabbdcccbddccdbdacaacccadacbbbccbccbbdbdddbbdddcbbaabbcadddddadbcbabbcdcbbcdddcdabaccabcbbacdadcacdaacccccbbdcbcaadbbdcacddccbacdcaddbbddbbdbadcdcdbccdaabbcaaaabbbcaacccbacbbadabdcdabcbdacddcacdcbaabaabccdaddbbbbcbbababdbbdcbdbbbabbbbdbbdaacabccddccdaddbadcadcbcbcdccbbbabccdddccdddbdacaabcdaaaaabcddbdbaabbbccadcbdcabbbdcacababbbbddcdcccbcbcbbacadaccabbaadbbdcdbbabcaacbbdcbdaacadabdbaaaacbabddcbdcabbbabcdabbaaadccddbcdcdcbdddcaaddddbacdadbdadddbcaadcaaacadabccbaacbddddcaabbbadbdcccbacabacbaadcbcdddabadddbcdcddbbbcbbccbdcacbbccdbcdccbbdbbadcadaabcddcacbccabbabdadbcbadaaacbbadbbabadbccbccbdadccacdcabcccacbbaabaccdbbbddccdbccbbacbdbcbdccdddbbacbcccaabdbaacdddddcbdccaacdbcaccaaccabccbbcdcbadbadbdcdddcaccdcaddbbadbbcdadcbbadbccaacbaadbcacbadbccacaabbabaacdbdcddcbdbdaaacaabbadcaaaaccbbdbbcdcbaadbadcbdaacabdcddadbaabbdddcdadbcddbadccadbaaabaabacabdadbbbbbccddaddbdacdbcbabcababadbbbaccbabdddaabbcbacabbdddcbaabdcadcbdbdcacdaabaabbacdacbdbbbbcaacacbaabdaacaaccdcabadcaaaccaacbdbadcaadaaacdbadddbcaddbbbbcdbbbcbcacdddabacdbaddbddddaddabddabacdaddbabdababcdadbabbbbdacadbdddabbbdbddcdccccbdcddbcacdddbacdddcaadaacccbcddbddbcbdccababcbdbabbdbadcccbdaacbadabbbacccbbadcccabaadaacacccabbcbaacbdcdcccadccccddddbbcdbbaaacdcadcdccbddcabcdbcaacbbabdcdddcddcacbbccbdbbddbbdabadcbcdcdacbddccdbbbbbcabbdcccaaabcddbcadbcbbbdaabdddcdcabdcaddadbadcccbaddadbaabcdbbbdabbdcdbbddcddbcabacddacdaccbdaabccddcddcdbaccbadadcbcbbcccdabacbdbabddadcccababdadadccbccdccacbbbabbccabdabcacabaaaaacaaaaccbcccaabdcbccccdcbddabaaaadbbbccbbcccdbccbddccdccaacbcdbcababcaadadabbcddadcacaadcabcbbddcdccddcccbacbddddbcaacacdbcddaabbbadcdcbcbcdddbcbcbaabacdccbcbcdcbadbccabbadbcaaabddbdcaaddadccbdcccbdcccccdaddadcaccdadddcbddbcdddcbcdcdbbabbadcaadccabacbcabdbdababaaacccbacdadddcabdddadbbccbbacaacadcacbbccadcbdcdddcabbdadcbdadcadaddddbbbaccbacaacabcbccbdaddcccccdcbcabcbacbaadabcbcbbababbcdbddbdbdbbbcabddadcdadaccbbdbadaaacddacabacacbcddddaaddacbdccbcaddabdacbcadbabcddbbcaddcbcdabacccaaaccdccdaaabcaadacddadddccbbbbcbcdccbbaacadadbcddbbcdcbcdcdcbcaaacccdcadddcbbcdaaadbcbddadbcdccbcccbbaddcdbcdbbddaddcbcddcaaaddcbabdaabcaacdcabbbdcababcbbabcbbadcabbbabadcccabaaddacbadccbbdacabdaaaabacdaabccccccbddacddcbbbbcaddccaaacbbaaadaaddcccdacbbddcdcbaccacbbcbccaacabbccbbaaccbaddddabbdcdabbbbbbcbbdcaadbcdcaaddaaacdbacdabcddddcdacdbddbbccbdcbcccbadddcdabbdcbaabcddbccdacaacddbcacbbbccbdadddbbabdadabadbaaaabacdbaadbdadabcaaadacdcbcabcddcdbabbcdddbbccbccacadaccccabaabdcbabaaccccbcdadabddccdbdcadbdbccabbdbbaaadbbcaaddbdcdcdcbdcddabadabdaddabaccbbbcbaaabadadaababcddcdcbbddbcbacaaccaadcccdadacddcddbadabacabaadcdcbbdbcadaccbadbadbacbaaddabbbccabbacbbcdacaabaaaacbbdbacdaaacacadbccabbdaccddcbbcbddbaddddaabcdaaaabbcadabaccccabbdbaddcbdddadcddbaacaaaadacdcacddabcaacbbaddacbcbcacdacbdcbcdabaaadbbbdcdccadabcabaabcabaccccaabbabdadacdacbccadadadcdcabccbdadcdbbdcaccbaadbacdadbdacccbacdabbddcddaaacaacdbbcdccbdacddbbbddbcaccacccbddccbccdccadbaadaaabbadbbabacaacddbddadcbaaadcdddddbadacacacacdcbacbdbcbabaacdddadbbbdcdcabdddaabdacacdbaacbdbdcbaaddbacdbaabbaaacbdaccdcbcbccabbcddbbdcacabcacbddddcccbcabdccbdbbabccbabddcacddabbbaddccdbcbbbbdbbbbbbcabccadccaabccdbadbbaddbbdcaaddaddaaccaabbccacbbbbdcccaddcdcaccdacbbccbcadbbbdabccdccbcbddccccbabddcddccdacbbdcdcdbddcadabdcacccbaadddddaadcaabacbaacbbcbbddadbdcadaabdbbdbbadccddaaabdcccddcabbdccacccddcbddabdabacbbbacbdddcabbdbbaacadcbbacdddbbbddcbdcadbaccddcccdacbbcddcddaabaaaacadcbdbdbadabcdcdabaddcaccbcdccbacdadaacbcadababaddbdadbabcaaaccdcaaccacbbaabbaabcdbbababdaabaaddddcbdadccdcddddbdbadbbbbabcbdbbdabcdbdabbddbcdccbdbbcbdbbcddadbcadcadaaddaacaaccacbacabccdcbadcbacbaddbcacadbaabbbdcabaccbddbcdddadbcbbabddcbcbadddcccbcbbdbabcaabbdababdabbccabbbdbdadbadbadcbbbbcaacdbcdbaadcbcacabddabbadbabcdbcabcbacaddbadababdbbcdcdccdbabadccdccddcbdddbbbcbdcccbaabccbcbdcdccadcdaabccdbbbdcabbdabcababbacccbabbdbaadbdacbdaddddcbcbccaaabadcdaddbbbddbcddabaaaabdbdbabacdcdaddbaacbacbcadbbdbccdaabcccbcdadbddabbcacaabbdadccdccabdcaacbdcdadbacccdbdabadbccbcddbdacdbadccadbdacdcbbbbadbcbcacbabbddaadcddaacdcabcdcaaaabbbddcdaaddddcbdcdddaddcddcadcbdbbcdababadccdcddccbadcbbdaaabacaaadbabbcbcbccbaccaabaccbdabacaccaabddabcbdcbcbbcabcabbdabcdadadcaccdadbbcadaccacadbcabddabbaadaacbbbcddbdccaccbddabdbbbbdabcdaaaacdacadabbaddbddbcacaabbaddcbabcbcbdbbcaacdcdaddbbcdbbdadcabcdbdbcabbbaaadbcdccadcdbcbdaccbddbacaccdcbdadadddaacacbacbaadabcdbdacacbbddcbbdaadcdcbdaddbaabcacdcbaddaddaddbdadccdcdcbacdcacdcdabacbdddcbaddcbaadbdddbddacaddaddbccbacbbadddabcacabbdbcdcdbdcaacbacccdaacacaabaadabccadcaadddcacccbdacccbcbcbcbcccdcaacddaadaddddadadaddaabcaadcccdcadcddcbdabdcbcbcacabdcccbdadbaddcdddcddcdbcadbcbaaabcaccabaadacdccaccdabdcabdacdcbbdadbddcacbabbddadccabccadbaadcddacacbacddcbdcccaccbdbdccdaaccabbdadacdcdbadaaccdbaabbaadababaacdaacbcbbabbaadadcaacbcbacababcaacbccabbbdbddccacaabacaacaacbbaccdadacadccbdbbddcaacbbdaababcabddababaccaddcbbcaabbcbabbcbcbdbbccccaabbcbbcbcdcbcabaadadbcdcccbacccbdaaddabcccdaabababcbdcbbbaddacabdccbacdacbddcadddddcccaaabacbbbbcdaabbbadbaabdbcdcabddbcbddbadbbbbbdabbdacbdddcddcacababcbbcbadabacabdbbcacaacdbbacddcaababaacbabacddbadabcbaadbcdccdccaaababbdacaaddcdbdadabdabddcabdacaabadabddcdccacacbddbdaabcccbbaddbccaadabccbabcbadacbacbaaabbbcbaadccadcacddbcbcbdadccbccbcbbabccaccdadddaacabcababaacbaaccccdddcddbacadcbbacaccbabaddacabdcdbbbdacdbdcacacdcbaaabaabacadcccacaabddadcddbadbabdddbaacadcaaacaacddbadbacbccdddcdddbcadcacacdbcdadbbbdaabbddacacaadadaaddadadbbccacabbadaacaaadbccadcdaabacabaadbaabdbdbaccbdadddadcacbdbbbcdcbcabddaacbacdbbbaadcbddccaadabcbbcccbbbbbdaadbbbaccdcaddbbddbadcdcbaacacbdcaaccbacaacdacbdbacacbbdbcdcddcdcbdacabddbdcadbbbadabaacaaaabcccbccdddccbcddbcabbabcadaddcdbaaabbadbcdbccacdabacaadbbaddbdbcacdccdadcdaccdbccaddabbaddaccadccacabbacabdcaadbcabccbbdcbcacccbabaadbaababcccbaacccbbbdacdbaaababccccddadbdabccdcbbcacaaccdbabbaaadddbcdbbdcdbcdcaaaadbcbbdadacabaacbdbabcacaddccabdaaddcabaacaccccdcdccdcaaadacaaaddbcadacacabcdcccdcabcadccacbaacbaadadccdadbbbcbdacddccbbaacaaaaacacbaaddaccadaaadcdcaabdbaccadacabcdcbbdadadcbacdccdcddadacadccbbadabbbbaacdcbcdbdcbabddadabaaaddacdaadabbdcadcdcabadcacacbcaaabdcbbaddaccccbdadcbddbddaacaccccdbdcdaadaaababdccbccaadbaabbdaccddcdadcabcbdadcdabcbbaabbcdbbdbaddbcdcdadcadcaadabbaadacaaadbbdcabdcbbcddaaabdccbdabbabbabdcdaacbacbaddbadbbbccaaaddcdcdcbdbcccabcbacccaaabdcddbababacccdcbcbbcdbacabdabcacdbbbcbdcdcacbcbbcabcbabbababddadcddaddccbdaccaddabaaacdacdcdaccaaddcaacaccdbbbbabaaccdbdaccabbcddbadcbbddbcdbdacbcdcabcdadcdacadbbabcdaccaacdcacdbdadbdccddddcdbdcdaabcbddcddbcbcdaabcadcadabcbcadbbccadddccbdaaaaaabacdbbdadbcaaddbcbaaaccdddacdbcccdacadccbcdabcbddbbbadbbbbadbbcdcaabaccadabadcbcddcabdbbdbdadccbccbdbbbadadadddacaadaacbddcddbdadacbbbabcdcaddbcdccdabaacbaababdcdcdabcabcbbbcabbcaabbaabaabcbadcdadbccabdbdacabbabcbbdbaddbcdbcbbaabcaacabdadccabdcddbcdbadbcadbbbacdcabcdddadbccadbbadbdbdcdcaabcdaadbdbababccdbdbcbadbcbaccadbccbdccacbcadbbbdbaacbbaccdaadbabdcabdddadccdaaacbdaabccbcdcbabaaadadbdaaaddbdccbdbcbbdcabbcabccddaadbbcadaadbabbdbacccaadcbbcbcabacdacbacdbccabbcbdacacdbdcccbccacccbddbcbbcccbbcadabaccdcdcdbddddaacdacbbdabaddccccdbaaadbbdcccaaaadbccbacddaaacaaabcccdccacdbcbcbbaabdadcaddcbadacdbcaddcbadabacdbbacbdcbdcdcdbbbbdaaddcbdcdabccadbabadddcababdcadaddccddcaadbcdbbdcccbbdcabdddcdbacbddbadbaddddacdbdcacdccdaaddbbdabbbadbddacabcdbaacaaadbdddadaaacdaaddbbadbdaabccbaaaadcacacdaddccdcaabbbddcbbbbbccacdacabadacdbadadcdaadcdbcccaabdcbdcabcbaaadaaddacaaaaadbababcaabdacccacddcdacddabcdbcaacaadbbcccdcdadcddabdcaccbcaabbdbadcadcadcdaaccccbcddccbacbadaaadacdbcbcdbabaaadadaadcadadcbdaabbdaaccdbaddadcccbbbacaccadcdbdcbabcbddbbaabadcaccabddccdcabbdbadddbbdbadcbbcdbacbdadbcaddccbbdadbddccacdbdaaacaaacccdadccccbaadaccdcbdaaaddacadadbaadbcbaabcdddcdbcdababcbddcdaccdaccdcbcbcdbccdaabdaacbaacdaabcabdccadabcabdbbccdadbdadbadcadabbbaccddddabbcacdaccdbaadbcadacbdcaaddbcadbcaacddaacbddddacbbdccbddddddadadbccabcbbbbcbcccbdcbacbcdacacbdcdacbdacacbbabdbdadbbdddcabcdbaacaadaabacaaabbadcbdbbbadaaacbacabddabbaadbdadadcdabbabbdadccadcbaadbbabccdcbcbbbbdabcbdabdbcbcabddbacccdcbadabccbbacdabddbaaccccabcdcdbbbaaabcabcddcaababdbddcbaccaadacccbdbbdbbbcbbccbdcddbcaaacabccdcccbdadaabdbbddcdbbaacbcadbabcdacddabccbcaaaaccdabdabbbbadabbdcbbddbdcdbcbddcbdddcdaaaaacababddbbcaaadcacbaadcdddbabcccbbccacdcaacccabbcdcbcddcccddbbacbbabdcccbbddcbbbcdddbcacbabacadbcdacccbdbadabdcddddddaccdbcadabcdcbadbdcdbcbdacabaaabdabbcacdbbbaaacbabcdacddabadcacdcbabbcadcadbaaccaccddcaadadabbdcdcaabdbccdabdadddcbabdcbcbcbbdabbcdbddbdbbdcabcabdabcbbdddbacdcddaddaaadcaccacacbbdccacdaddbcbdaccdddaacdbddbccccdccaabcaddaacabaaabdcbaaaaadadccacbcbbcbbbdcbbddaabcdbbccabbdaadacdcbbbabdddbabdcacdcdcdabcdadbbdbcadbcbcccadbdddbaccbabbbabdcadbcbaddadcbabadbdaaaacbbcabcabcdbdbddccdddcbccdabbcbcbadcadbacaccccdcdbdbacbabbabcbaddddacdcdccacbdbbcdcdadcaadcabccabddaccccbbcaddccabbadacbdcadcbadcccccbbabdbdabbabdbabdcdbccddbbbdabbaadaddbbabbdabdabccdccdbdbdbabadcbabccbabcabddccdbaabdbbddadcdcbadadcaaddacabbadcbcbaabdbbababddcbddcdcdbcbcbccbacacbdddcbbcacdaaadbcdabbaadbcdbddaadacaadcbadaccadaacbddcdcbdcbdabbdbbdcacacbabcccddcdacddbdadddacacaacbdcddbbdaaccbcadbcdaaaadccbcdbbabbdccacabcdbdbbaadcbbaddcaacdcccddbbdaabaaaccccddcabccaaadbcacadccbcabbacbbcaddddddcdbdccacdaddabcddcdbcccdaababbcdccbcababdaabbadddbadacdcbcacddbbddabcddddcccaabcdadcdaaabacdbccacbbcbcdcdbcbcdcadadbccbcbbbcdabcbbdabadcdabadaaccbacdccdbdccddcbdaddaddbcabdbbddcadcbdbbaddcddbbccdaacbcacababdcbccdcdbacdcdddcaccdacddaaabbcbabaabdbcbbcacccdabaabbabdbcdcbbbaaabcaaaddccddbabaaddcbcdabdbacabbdcabccbacccdcdbdabadbbddbddbbdcbcacddcdbadcaddbdcbbadacbdbadaaadbcbcdaacbdbdadbacabdacadbddcdcabbbcccccabbbdaabbbccdbbcbdddbbbabdbdcdacaacbdbcdcadcaabdbbbbababcbcaaacaaabcdccaabadbdcccbcdacabdccdbcccbcadacadadbaaccaddabcadbcdbbcaacdbbbabcccaadcdddaccdccabaaacaadcdacccbbaddbcbdabaabcdabaddacbaaabdacbbcdcbbcbcabcddadcbdbcdabcddaddcdaccaccbddaddcaabaddbbaaacbcabdddbaadcaaaccbddcacddbbddddbacbadbdbadcacbbabbdbaadddabdbbcccbabcccdcbcababcadbdcbcbaadaddccaadbdabdbdaddccbccccadcdacccadccaabdddddbcaaddaaacdddcdaacbaaddddcdcdcbbdadaccdcdbdbcacaaadbadccbddccadabddbbbdccdbaadaabadcbdbbbdbdaddacdddddbcacdbaacaadacabdcadbcbdddddacccabbdbddccaddaacddbbdacdabacddbbacacbcdbbabaaaddcbbccbbdbdbcdabaddddcaddbaaaddadabdabacaacdbdcbdacacdbddbcacdbdaabdcbbdbcaaabaaadbaacbbbbcabdbaacddcdcddbbdaacdbbaaccbadaaddbcdbdacdacbdbcddccbcccccdcbcdcccacbadacaccabbbadccacadcaabcdbbbdaacbaaacdbaaccdccddbbacaadabdcbacdcdbbcadbbdabcdcdbbadaacbbccababdacbcaddcddccbbbbcacbbccccbbbcbbadaccbdddcabadbbadbaddddcbabdbddcbadadcbddcbbadccddbcddcccaaaaacddaaacbcdbacbdaabbdcaccdacaaaaddbadcbcdabbcbbbcddcddcdabbddbbaadcccdabddbadaaaacccddcdcdcdcadacccdbaaccbdcccbdcacaadcababccbcdcbcdcddaadbdbccacdbcbaccabadbacdbbdbbcbdbaabbcddbcacccaddccbdacdabdbcbccbbcbdabddcdbaabcbcdccbabbcdcccacabbdcbbbaddabcddbbbaaabdacdccadcbcadacdbbdbbbcbdadbacdaabbcadbbdadadcbbadbdcbdcbadbcdadbaabdcbcbacdcbbbabcbadbdacadbcccbcadadbabddadabaabcbccbbbcabdcbdbbbcadabaccdbbdaadccacccdbcbdbbabaaddcccbdbaaabacdcbacaabacbbbbcdccbadadaaccbcbbddcbaddadaabcdacaacacadbabbbbbcbbcddacadbdabbbbbaaccdccbaddabaacccdacdbcdbbddaabaaacbdccdbcbcaabbbaacabaadbabdbdadcdccdbcbaccdacaacabcdcdddddaabadcbaadbcdbbacccbabbcaabdaaaabbbadadddbcccbdbcacabcccacaadcdcdddccadabcdbdbaddccbadbdcabcbbacdccabababccdadbbdadbacccbccaacbbcdccddbcbbbdcddabdadccabadbaabdcaabcdbddbaadcbcbcbcdbcabbcacadbbbacddcddcdcdbabbacbbbcdccdcdabbaacdbcacccbbdbddbaccabdadadccdcabcdccadcadbbabbcacdbbaaddacdbdcdbcbccabcccdbacbacaaaccccdcdaccbcdababcbaddabcbddcdbdcdddcabbbccaccaabcabdcdcabdddbaaadbacbdbcbccdcaacadddccaabdcdaccbadbddbcadadabddbddbbcbbabaddddbabcacdbaacaaaaababacbcbdccbcacbcbbbbaabdbbbdaaccabdcadabbbdabbabaddcdabcdcbbbaaacbdadcbaccbcdddcbbacaabaabdabadbddaadaadbdbaddcbccabdcbacdbcaaadcbcccccddcbaddbdbbadcbbcbcadcbacdcdcbabdbacadcddbbaabbadbcbaddddbddcdcdacbdbcdabcbdaaacbabbbbabddaadcacbdcccbdbcdaccccaacbddcddbaaaaadbdcbdbaadaabbbadcabdbdbcdbacaabacacaddcbadcadcbbabaccddccbbbbcabdaaabddcdbabaaacccbbaddddbddcbbdddcddacdabbcacbdacababcbdbbccdccbddadcdbbdbccdbadcaddcbdabddaddccbacddadcacabbabcddccddcddbacdabcbbcbbdddacbabdaaabcbbdcddbdacabacadbaaababbdbaccdbacbcabcddccdaacacbbccccdbbabcdccaddcbbdadacccbabbdaaddbadabbdcadacdbaddbdabcaabbcddadcdccaabcdcbddbdadcdbacbbcdcbbadaadbddddcbbaababbaaaddadddcaacdbbbcbdcdccaadcddbdabddbadabaaaaddaaabccbbcbadbbbdbcdaababbbaccbbbdbabccaaddbcacdcadbaccbbbcbbbcccadaacbcbbcccdbaabdbcccbcbdcbdbbdbaadccdabacdccbccdaabcbaacbbadabcaccbbadcabadccbbaaddbbdabcadaaaabcdcccbccbaabaadaaaaaccbccbaadaacbbacbddbcaabdaaaadabccdacdcdcaddaacaadccaabaabdabaacccaadcdcdbdcbcbbcdbbbacdaacdacccdddcdbaacbcbdadbcdbbcbdbdcbbadcdabdbdaadacdabdccaccdcdabdabcdcdbcdabdbddbcdbdbcbdcdcdcdbbadcbbbbacdadccccbabdadbcbdaacadadcababcacbcdccdcdccbcaabcddccbdadadbabadbdcdcddbbabcbabbdaaabccbcdcddccdadcbddddcbdbddaababaddbbdcacccababdcadaadabccadaabbdddbbacaaaabdcccdbcbaacdabccdabdddccdbcbbaabccacaccdadbabacdbdddbccbaadabbbbaddbabbbcadccabccaaaaaaccabacdbcbaddbbddabbcddbcacdbaccadbaccccdccbcdacbcacbabbadddbddddaacacbbbcdaadaddcbacacccbadcaadbacabdddccbdabdccbbbcbcaabcdabdabbcacbbbddbbdddaaddaaccbaaccdaacaabccbdbbaadadbcabbdcabcbddbbbdabcacdacaabacccdabcbaaabddddaddccbbbaccabdcddcbddaaaacbcaabacbdddbadddccdabcaacbaddcabadcaddcbdcacbddbacabdddabbcacdcbabbababacdbbcdbbdbcdccbacbdabcbacddbadbcbbdbbccababcdadabcaadbacacadadcbadaadccbbdccdccddbabcbccaadababbcdbdbcaddddcabccdaacaddbcddbabaabbcdaccdacbcdbccbccbcbddaacdbdadbaacccbaddcdacdccaadbaaaddabaacadcdabbdaccdaacabbccadbadabacabbcabcddbabaabaabdcababcbdcabdbcbddadbabacadbacdcbbaacbbbcddddbabbcbdcaabdbcdaacdaccdadbbbcddacdbbcbadaddaaaacaddddddadbcbaadddbbbbcacbddbdcabacabcbccbcabdddbbddaccbdaabcabccadccdabbcdacbcccbcbadbbccbcdbadbdcbccacccbbbbbdcdcdcbddcbcabdabdbbddaddabdadbdaccaabbdabdbbcaaabdcbdcbbddcdbbaacbbaddadabcdddcbdcdcdbaddbdccdacbbddccbbadaaccadbbbacdbbbabdccbddccddbadbdaddccbbbdddbaadbaadcbdcabddbcaadbabcbcddccadadcbdcccdbcbddbccbcccababbcdcabbabdcacdadcabacbcbdadbacdddcccaabbbdaaabcadddddcdcbcdbabadaaacbdcbdbbbacbadbbdddbcabccbccaccbccabcabcaccabcbccabbdaacaadcccbbddadcbddcaadabadddcadccdbbddbdaacacbaaaaccdaabadbbcacaacbcabbacacadbdacaccbacbdcdaabdcabccbbbbcbdddcaddbbccaddbbbddacdabaddcadacdaddddcdcabacbbdaacadbddcbababbbadcdaaaccadcaadbccdcacbbcbbbbaacdbcabbcdcabbdcbacbcccbbadaddaadcbcdbacadbcdabbccaacababbaaaddbddcacdabbcbbadbcabadacabccadcbdbbdbcabddccaaddcbbcdcdaaccabcadbcdbaddbcdaacdcdcccaddcbacdccacbadadbbbbdbabababdddcdbadccaccdabccdccbacabcaddaadccbccbcccdabcbccbddabddacbbddaaabdaadddadbcaadbaccccaddaaabccbbcccdaaaaaadcccabbadadcacbcadcbddbdcabcdcbacacaabddaadaddcbccbcbdddcdbabdccdadcabdbacbdccdddacbadcddbacdbadddcacaadcdcadbabcdbbcaaccaabdaadaabccccccbaccaadadcbdadbbcaddbdacdaabdddbcbcddbabcccccadcdbcbdddcadaabbdbcbbbcacadadabdbaabbaadccabcaaadaccccddaabcabaaadadbbbdbadcadabadbacddbbccaddbbdddaadadcbacaddaccbacdcbdbabacaabbcddcabadcadaddcaacdaacccaccddacbacbbbaccbacaaaaabacbdddccbbbcdadbddddbdcbcbbdabbdbababcddbaaddbacbcdcdcbbadbcdacaabadbbbbadbbacddcbadbdccddbbbdddbdcbddbaccbbbccbbabbdbacccabadbcbcbdbdcbcbaacbbccacdadbddbddcccaccdccdcbdabcaaaabdcacaaacddbddcbbbcccbccaaacadaddbcbcbabdacbcbdaaacbbccdabccadaabdcccbadbdbdcaddcbdbdcdcbbdcacbccccdcdaacdbccabdbaaacccbbcadcdbbbbdcdacdcadbaabdcadccaacacabcdcbacccdabdadbdbaccabadbddddcbcdccabacadbdcaacbaacacadbbadadddccabadaabbadcbbddbaaababdbadccaabcacacbdbaaaabdbbcccccbbcacccaddcdbcaadccaabbdabcdaaddcccdbbdbccaddbcdcddccdadadbbdbcbdddddbdcdabccacbcbcbdcabcbbdbccdcdadcbdabdcbbccacdabbbbcbdddccadcdcdcaadbadccdcdbbdbdcbbbabcaadaaacccaacaaabadcccddbbabddcdbdadacbdacaaddacdabddacdbddcaaabcbadadcbcdbdcaddbbddcadcdcdcaabbdaacbdbaacbddaddbbcbdbbcaabcbcabacccddcbbaabdbdddbdcacdbdddccdbbaaabadbcddaddcbacbccaddcaabcabaaabbdccbadcacdacbbcccdacbcbabddaddccbbacadbaddacacbbaaabdcbdcdbabdcccdaaadbbdbbbdbdaababdcbbdbcbdcacadadbdcdcbdaaacadddadaacccaaadabddddcaaacbbdcdaaaadddacaddabdadcabbabcabadcddcbcbdbbaccdcdaadacabaaadbcbcacaabbddccadabaaddccbcaccaaabdccccbbdbddacdcacdddbdbdabdcccbabdcdaaaddddbdddaddcccacbbabacbdbababcccdcbdaddacdcbddacdbababadacdddbacaaadcccbbacbdddbabcacbbabbbadddbcbccbcabbcdcbadcdcaccbaacccdcbdbaabacddcbdabbabbddbadcbcdaccdabdbbbcdcdcbdbbbbcdbbaacdbadbbcdcbadacabcadcabacccdddacacaabcdbabdacacbcbdbcabcddacdcddaaacadacbcdaddaadbdaabccdcbabbadcccacbddddbbabaabbbbbbbcdccbbdcaaaadaacbaddbccadacacdbaccbbddbbadbacababccadccbcdccdccabaacabdcadcbcbaadbbbdaaddbdccddcbbcbcdbbcbbadadcaacacddaddccbaadbbdcbbcbdadcbaddbdaacbbbbbbcabaccccbdadbddbaadcaacaacdcbcddcaabddbbdbcddcdddcadadbbbdddbbdcabddacdbcdbdabcabcaabbcdbbdcbcadbbbaabcbabaacacbbaabdccdcaccbbbccbaadcbabaaaabdbdbcddbaccdcbacdbbbdabcbbdaaddacdddbcbadccddadabdcbbbddcdabcdccddababcbbbbaaddddbaadacddadcbccdacaddbaadabcadccbddaadddadbcaddacbbcddcaddbbcbaaabcdadcdbcdbccbaabbaaccbbcbcacdccbdabaadcbddcccdcdabdccaabbbbdbdbaaacacdcdacaacccdaccbabadacbbaaaabbacbbcbaaabdbcacdcccdaadbbadbccbbcdcaacbdabccbbadaddaaacdacbcdbcadcdaaadccbbbbbaaaacdcaabcacddbdabcacbaadadadaccbacbbadcdadaaccdaacabbbdaddbbdcacadbacdadcabdaabbcbcacacccbcbadabdcbdbbaadcacdabacabacabccababacdccbdbbdbdbdbbacababbadacdcdcdbaadbaadbdddbadcdddbaccbccbbcdbcdcbacbabddcaaacddabcaadbcadbadbdccdcbdbccdbbabcabbdaaddbcdccadcdacaddcdabcbcbbbbcdabcccacbddaaddcbacddbcdabcaabaaccbabacdacaabbacbbaacbbdbcadbdbbadbaacabaaddacbcaadabbdaadacabbdcabbabcacbbbabcdaabacbbdcaabcabaabbdcdcaddbbbbaccbcaccadaacbcababaddddddbddcccaacaaaabbaccdbaadcbbdcdcdcbbbabbccadcbbcdccdbbabbadbdabdcbcbaccdcabdaacacacaacdcddabdaccacbbcccccabbcddcaaaadaabbcddbbbbacbaddcbddbdcddabdccabbbcdacbadaaabcbbdabbcdcacaaccbbbcccacdcbddaaacdddcdccacabadbacdabcaabdddcccbbbabddbcaaccbdbbbbaccdcbcbbdcabbdadbacacadcabddacddabbdbbabdaacadbdbadddcbcdbdccbabcabbaaccbabccbbddcdddbabbdccbbccccdbabdaaacbbbadbcdaadddcddcdacbacbcabadaaadddcdbdccdacccddddaaabdcdbdaaaaadadcbdababdbcaaabbdcabdabbbdbabbdadbabbcddcddacdddbabadadbaacacaacddccbddbcaadbacdaddaaccacbdbdbbbbadacabcbadbdbdbababadddbdacccdbcaabcdadaccbadcacbcabaaabbbbdabbbadadabddacbbbbdcbcdababdcdcabaccdcadabdcbaccddbdcaabbcacadddbccbbccdbabccdabaddddcddbbcdadadacbacadbcabaaccbcabbccdbbddcbcbadcbdacbcddbbcababbaaacaacdbcdbbabcbbacaadcbaaccccbabbdcdccdcacadabdadbbdccddbdbcaccabdaadacabbdcdcabccdddaacdcaddaabcdcbbcdbbcbdbaabaddbbbdcdadbcadadabcacdbbcadadcdaacabcddacdbabdaacabdaccaabcbaadccaaaabdcddbdcabdbbacabdbcbaabdbaaaccdbddcbcadacbbdabbacdddcacccbabcdbcadcbdacacbdcbacdbbcdacddacccbddaccbaacabbbaacbcadadbdcbbabdbaaaaccacadbacbcbbbddcdbcacdbbbcababbabdbababbbbcaaccadaadacbcbbcccdddbadddacabccbbaacdbaabdbacbaabdcbaadcbcbcddbacbcbbbddabbbdacdbaddcabbcbcaaabaddddcaadabcadcdabcdbabbbddaabddccaddbbaddcaadacbadcbbdbcdcacbacbcbbdcdbacdadadcbabadcbdbdcdaabddccbbabcbabdcdbaddcbbccaaaddcdcaddbaababbbabdddadaaabbcbcbbbcdabaadddddbdcdcacdcbbbdcdabcbaccbacadccdbabbdbccbaacdcbbddadcdddcadddcacdcdacbadddcbacbcbbadcddbbdacabdcadabcddddccdcbacdcdadabbabdbbbcdcdbbbbbadcbaccaadabbcddccddbbccdabdacdddbcbadcacccbdcdbadcccbbacbccdbabccccddddadaddcdaddbacaaacbdcbddbabdbacbbabbcbbbcbdcbccaaddbccbdcbbdacdadccbaadcbbaccbbcaddcacdccacddbacdacdacdaddbcdddcbbdbbabcdbddbdbaacdcdabaacdbccdbdcadbacdabacccaaadaacacabdadbdccadadbbcaaadbdabcacaccabbabcabdddddbcdddbcdbaacddbdcbbdbaddabbdcdbcbcdacbadbbadaabcdbcbadccdcdbdbacaadaabbaacbbdbdaddadbbcdcdbcbabdcdcaddacdaccdabbdcbcdbcbabbaabadbbcccdacdbccbcbadcdaaccdababcddcbaacadaadacbdbacadabcbdcbacadcbaadbbaaacbacbcdbdaabcabbcdacbabaacdaccdbadcccdbdbdcabbbbddaacdcbcdaabdcccbcdacbababddcbcdcabaaaddcccbaaadccbadddcbccaadaabddaccdabdabbbcbcdddabdccbdcbcddadcdadbccdbcccaadcdaaccbcbaaabcdcaacbaacabcbcbccadddcdcdddbdabbbdccdabbcabbbdbcdbcababbacabbdbcaccbacadcdadaddddabcddbdcdcbabdccccdbadddcdbbcbcabcbcabddcbbbccbdcacacbacbdabbbbadbdccccdbadcdbaabbadadbbcdccddadcadccbdaabbacbbbaacccdbbdacbdadbaabdbbdcacbcbbdaddcddadaccbdcccdccbabadacbbcbbdbccdbbcdcbdbcadaacdaadaaacbcdbacadcddccccaddccccabdacacdbbbbdddcddaabcaaaddbabaabdabbdbbadbddbcaadbabdbdbdccbdbbbddcdcdbbabddaadadddcbcacadccabcddccabaccacababccaabbdcdbcacaacadaaaabdaaacccdcdabadbccdcdcbbcbdcadbdccbdbbabdbbdcabacdbccdcdcacdacdbcdbbacacaadbdcccacacadbdcbbadabbcbdbbadacaccbcacbbabbcddccbaddbcbbacabacccbbccbacccabdbbcbbacadcddabccccccddbbbcadcacdbbcdddbddddbbbbccabbcdddccddccddacabbdacdcbcdaabccbddcdddcacabcddcadbcdcbbaadbccbdcddbcababbabbbcadacbbbcbbdddddabdbcbbbdbbdbbaabdabcbbbccabbcddbdddddbdadcdcdabadadacddcbdaaadccddacadddbabddadbcccdaddbbaabbbbbbbdcddddbccaadddbccadadbbcdbcdaabbacaaabbcabdbaccbcaacaacadbdbcbdaacbcbbcbaabbccbdddccdbbcbbccaaddacbbbcdadacdbcaacaabbddccddccaabbdbaccadabbdbadabcaaabbdacadcccdbbbbbdabcdddaadbcbaaabddbbbabcbcbabbcabdcbdcdbadabddcccddddabcaadcccbdbcacbbbcbccabbdbbcaabbcaadaccbbdcddadcbaabaadaaccadabccbacdbddcbdddbbddcacbcdacdacbbbbacbcccbbcbcccbdaabccbabcabacbbbaccbcaaccaccdbdbadddbbcbcabdacadcbbcabcbcaaaacdadcdcdbccccaacadabbdbbcccacbcbaadbcbbdabbdddacdbbdccbddadbcbcbbabdcadbaabdbaddaaccddddacdaccbadddbcbddbcbdcccaaccdcaadcaadadbbaddadabccdaacdaddcbddbaaaaaaccabccadbcacbdcbaabbbaadcababdbabbddacdcacacbdacadcccdbadbcacddcdacdcbacbbaddbccaddbbadbdddccbbcdbbbabdbabddbdacdcccdcabdccadbdbdbcbcaddaaccaadbddbddadddccbadbdadbbadadabdcdadadbbddbccccccdcbcdbccccbdbddacaabccbabaccbdbdcbbaddaddbccdbbcccabbcbccbddddbbbdadcacdbdabcaadbcbcadabacdcdcacbdaaaacbabadcbddcccabbabcaaccdddaccadabdcdaddbccbdddcadcbbbdaaacdbabdbabdacbacaaccbdbbcaacadaabdadcbdabbaabcaaababbadbacaaabdaaccbbccccbdcdbacccbbdddacabcdcbbccbaaabaacdcdddcbacdddcabcabddbbadccdbbabdadcccbbbbbaaadddbccdabaccaacabbdbdccbabccabdccadbadbcabccbaccadddcddaaadabcdcdcdcbcbcdbbaaaadaadbacbcaaacdabdacbbcdbadcbbdabaabdacbccaabbabcacaabdcdbcadcabdacccdcbccdbbabdbdbccbbdbdbdcbbbadaabdbcccadddbccbbdcdaddadcbdddbcdcdcccaaacccaaaaaccdcddbcdadbcccbbaaaccdbcbcbdadbdbaacbccaccbbcdccbdbbbdbadbabddbadabccbaccbdbaddcdbcdccabdcccabcadbbcacadababcbdadabacddabbdcdbcbcaddbbcbdacbbdbdccacabbdcabddcacacdbbaccaaddcaadaaddacbccbccbcacbaacbbabcbccdbcbdaabaabbaabacadddcaadadaddcaabbcddbadaadbccadbabdbcdddccddbdaabacdbcdadbcdbccbcbdaaabdbaaddbcdcdbdcdaaaadccdabdabbadaababaccaabcdbadacbdacddcbacaacdbcacbbbbdadbcdabdadcaccccbbacccccaddcaddcdbcaccadaaabdccbabdbbababccadbccdaccbbaabcdddccabdddaacdcbddababbcdacddbdaabcadcbdcbadabcccacbaaddbbcacbbabcadddcbbdcabccbdcdbdbcabbcababbdbcdbcaaaaaccdcdbdccbcadcadcbdaadccaddbacccddacddbdddccbbbddccaaccddbaabadcdaccaaabcadabdadddcccbccbbbdddbbbdcacaabcabddcbaddcdbbddbcbbdbabccbcadabddddbcbbdbacbbcccdcdabcabbacabdaaaaabbdadaaccbddbcddcacbdcaadbadbcdabdcabcbdcdcadddbdaaaabbcddaddbcbaccabacacbadddddcdddbdddacabdaaabdacdcbcacdadacaccdaddcadbcaadabdaccbccabbcdabcbdcacdabddccbdddbcccbccbadcdadddbdbdacbcddadbbbdccdbcacdcdacddddbbdbdcdcdbababbcbaabcdabacaddbbbdcacacabcabdddbbccbccdaddbdaacdccacdbccdccdbacddccbacbdddacbdbbaaddcabdabcdcbddbcdcddbacabbdddcdadaabaaddabaadbdcbcdbdbcbddcaabbaacacbddbbacccadccdbcccdccbbaaaabacdbcbdabbcadabbbbcadddadbdbadddbabdcdacaaaddbadcaadbbdabaddbacdabbcabadbcdbcccabdcdabadbbbbcadcddaaadddddbbbcdcdacadccddcbcdaaabcbaacdacaabcdaacabbbcddaababdaadacaabdbccdaaabccdbddadcbbcbadccddbdadcdbbadddbcdadcbababdaacdcdababcbbbbaadbcdaacdbaacabaaacdcdbbddbabbcddcbacdccbaaddadbbcbbadbcacbcddbabbacbbddbdbabdababcdbaddaddadaddbababcacdbbcacbccadcbdcccadaabcdaacdaccccbcadcccdccbdacbbdbbdcadadbbcddaaddbacbacdbccababacadadbdbaacacddbbdaacadddbdbdcaaaddabcaaaacbdcabaaaaabbcbdddababdbcbbddddcdbcbacccbdcdcbaaababbcacabcdaabbcaaabbabbddaadcbbadbbbdcbdcccdbcbccbaacaadcaabcbcadddcbdabdabaccdbbadadcbbbdabacbcdabbbcacbddbccbccaabcbcacabdcbddccbcdccaaccabbccdcacbbbbbaadbaabbbccbadacbcddbcdcdbdabddcadacdccbaabdabdcccdabbdcdadaacbbddbabaddddddbcbdcbdbbbbcababaadaaddaddaacaabdbacadaabdaacadbccaacaccbcdcdddcaacabcaacbabbcbbdbdacadccaddcacbaadaaadccbbbaabbbadcbbbacbdbaabaabaaacccabcbbcdbdacdcccabdccccbbdacccaadaadadcbbacbcdaddaadadbabaaacccbabbbacddcbadbadadcdadbbcbdcbbbabdbddcacdbbbbaccbcaaacaccccbbcddcdaacbbbcabbacadacbcbcdbdbdadbdcddadbdcccabcdcabaddcdcddccbcccdcdbadaaaabddbbbaadbbcdadbcdbacabcbcddbccbdaaaabacddacdcacaccdacadcdbddcccdaabadbbbbcabbdbdabdabaccdabbbabdababddbaadccdddbbdacdabdcdbaabccbdbbbbcbdaccaacabccbbacdbcadaadbaddddbabbbcadcdcacaaabdadacacbabddbbaddbabbbabaaababcbabddabcdcddbbbcdaddbabcacbcabdaadacbdbbbbdacbaadcddddadabcdbcacabadaddaccbddaaaabcababacbbabcbccabbadcadcddbdcaacadcadcbbbbabcadbdacbdcbbaccbaddcbacaadacbccdacbcadbabccdadaacbcdccdadcbabbaccabdccadabdcdcbddcbcbdadcddcbabcdaacdbaabbdbbbcacccbdcabdcdbcdcbabadddbbabacbbabbcadbcbdacbaccbbbabbabbabacbdbbaadcaaaabadbbdadddcbddacddbbbdbabacaddbbdbbcdbbaabccbbbdabbcabdcacdacbacdccbddbdcbacadccbbaadadcbcbbbbdcbadbccdadcbbaabaacbccddddcaabcbadbbbbbbcbccdadccacacacdbbcddcbbbbbcbcbcdacdbdadbbccbacabbacadbadcacaaabcaccdcacbcdddcdcdddddcbcacaababcdaaddacbdaddaabddadbcdcdbdcccdadbbbbaadbabccdaacadbdcbccdbcbdcbccadadabcbddcbcaddcdbbcdbbaddbddbdcabbcdacbdacbdbbdbbcdbdacdacacdaacbdbddcaadbadacbadcaadddabaaaaabaabdcdbadbddbcbcbdddcddacbcbddadaacbdbaabcdaabcacaaacdbabaddcbccadbcaacabcaddbcacdcdacdabccbbcbbcccaacddbadbbdbbdabdcbbaddcbbcdbabcbbbccbcbabdbcbbccbbddbccbbadcbbccadbcbcaaaacbbbacadbaabbdddbbbdabaaaacbcabcaacaccaadcdcddbbcbdccbcaccadccdacacdbacdacadbcaabaadaaccbddddbddcaaacdbacacdcdaabaddaadadaddccbaacdcadacbcdacbdcddcdccbcabcdabdababddacaaaaacccdcabcdbadaaddcddabbaaabaccbadbbaadccabddbbabcdcbaaaabdcbcdabcaaabdccababcbdcccbbcbaadbcddccddddcccbbbabcbcaaadaddbdcabbdbdabcccbabadddacbbaabbacbbabdbccdabbdbcbacbdddcccaadaaaacbcadbbbddbcaccbbbabacbdddcbbabdaadabbacbaabcabbadaccaabdababdbadbcdbdabbcbcdbcadbbbbcacbddcddaabbcabbddabcabccbcbbbcccabbbdbccccadbcdbabadbdbbdbdccccaadcdaaaccddcadcbcbbacbbdadccdbbbbdcbacdbbabdbccbcbbcdddbbdacdbabdaabacbdbcabccbdcabaccabcaaabbcccbcbcdadadbdbbbdabbbdcdcddcbdddbcdddaddcbbaaaabbddadccdbbddacbdadcbcdbbabbaacdccaadabdccbbbcdbadddbaaadbbdbdbdbaacadcacdbdbababcccdbdcbbacdcbbbdcbddaababbaaccddacccacdaacdddbdcbababcbbadccdbccbdcbcbcbdacbddbbadbabccaddacdaacbaabbadaadcdaabacddadadcdaaabadadbaaaaadbcccddaabbdbcddcdabbabcccdbdddaccbadadacbdabddbdaccddbdabcdadcccdbdabdbcabdabbdabcdaaabccdbbdbabaccbbccdadcdbdddbabacaddcddaadccddbadaacbbbabbcacdddbbcadddaaadbbbdcaddddbddbcabaabbdbdbdcdbdddddccbacadbdaccbbbadcacbddadcdbcbdbbddbcddcdacddbcbbcdddbdccbddcaccddadbaacdcaccaccbbdcbbddbbbdcccbaccacaccbcacddcdaaddadddccbaabbcacdadcdcccbbcdadbadcbdcdccbbbccacdccbcbdbcccdcbcbaddbaccabccbacbdadcaacaabaccdabcdcaaabbddacccabcacbcaabccacbdbdbcddacabdadcdcbbbabccbabcbcbdabdabbccdcbbdcdaccbadcbbbbddcaddbadabdabaadaabaccaadabdbdaddddcdbbbbccadccaacdabbcdbddacdddbddbadcabbdbbbaaacddaddaaabccabcdcdcaddbccdcbbcadcdbdcabccababdbbdbbdadcaaccadccadbcdaacbdbacacabbdccabdddadbcaacaabbdbbdcaabbaccccccbadbcbdaaabbdadcddbcbaacadcbbdcadbcbacdacaabbacacddccabacdcdacdbdabcaababacbbcdaaabdccdcdbbbbcdcadbbccbbbdddacacbbaccbccabbbbcbadaaabcbbcbaaabcaacbddcdadabcaadcbaaabcbcabacdbaacadadbcbdbdacdccbdcbcccadacaabccdadcbdbdbabdabbccdbaccccdadbaabccddddcbaccadbdcbbbdddabddcdacdbdbddabddbdbaccabcbcabbcaccaabddadadacbbaababddbddcaaaacadadcddadbcaabccacdbbbdccbcbbccaaddadacbbdcabcaccbcdbcadddcdaccabcdabcbdcdcbbbdcacbbaaaaacccabddddccaccbdbdcbadbcdcababaabbacbddcdbcddcbaccccdbdbcdacccccbbcbacdbddcccaadcabbabaaccbadaabcaddbaaaddaaddcbbdcbacadccbabcdbacddaabbccaabdaacdcdbacaddbbbbcddbccbccdcbbcabcaabcacbbdaacdabbdccbbbbadccbbbacbcdadacccadadacbdaccacdcbccddcabdadbccaabdaabadaccbccababadcdaadaccbdadacbdbaadababbcbccbaacabdadcaccaaabcccbdadcddaccdcddaadbabadabacabccabdbdcadcccddcdacdbbbccccdbccadbabdbaaaadbbbcdddaadbbcdcdadcbbbdaabcaddacbcbbddbcbddddbdcbcbbcaaabadabacdbccacacbcdcccaacdcadbadbaddabcabbcabdaabcbdacdbcdadabdbcaabcdaacbcccadaddbcacddbcbdddadcbbbcddacbbacaccdbcbbdcacadaaacabacaaadacbabdcddaadbdacdbaaabcdcbadbcdbacbdadbcccaacbbcadbddabcdadaaabacbdcbcaacabddcdacbdacdababbdcddaacbdcbcdabdccacbbaacabdcdadadddaabaadcdaabbdcababbaaabacdabddbdbbcdbcccdccbccbabdbdbacdbbacaabdddddaabdcaadcbdcaddbcdccacbdbddbadaacadcaaccbbcacdacacadccadacbadcadbbddcabcacccdcadbdbccabddabbaaadadbbbbaadbaaabbcdabdcacbccacaabdbbdaaaaccaccaabdcdcddbacbabaaabddccbbccbadcdccbdabaccdadacdadabcbacbbbbbdbdaaccdbadbbcdbacbbccbacaabcddacabaddaaabadacdcdbacdcddbdadbabacdaddaccdabccaadbdbbbbdcdbbbdcacacbbcccbdadbaaacaaddbaccbabaaaaddbdbbaabababcbadabdbbbbcdabadcabddaadaddccabddaababcacaacbabcdbadbbcadbbbdddacaaabcaacbadddbaacbbbdaadcaccbdbabcbcadabcbbcdabcdabcccbbdbbdbcaccabcbbbccacadadbdbdcbcddcbddccacbdbcdcbbcdaabdbabbbadaabbacbaabaaacdaadaaacbdaadbadbcacdcaccbbabaaddddbbccdbbddcdacbbdccbcacbabbcabcbcbcbaabcaadcadaddbcbccbdadbddbbddccacbacdaacaabcbabdaadddcacdbcaadbabadadcaacccccbdbcdcbcdddcabbdacadbadabbcdabdbdaabcbbcdadcbaddcdaacdcbddbadcdabdbbcccdbdaaccdbbbcdaabbdaddcbbbaacacabdccdaabbaadadddcbaccdacdacbdddddabbbdacadcaaadacbdbdddbddcabadbdaddbcddbbaadadcaddbcadbcdbccacaaabbdbdadaaabddadbdcbcdcdddddadacdccdcdabaccbdbccdadbccddbcbaaacbdbdbacdabaccbbadbddddcbbccadbcdadddabaadacbacbbdbcdbcdcbaccadacaaadbbcccadacaddabccbdbdadcbdbadcbcaabbaaacdbbadddcbbbdcaddabbddccdccacaaddadaccbadddddbcdbabdcdacabddbaadaaddbcccbadadcddcdbdbccacbcaaacbaacdbbaddadccbabcddcddbdcccadcdacddaccdbcacabbabcdccbdcdcbadcdabaacadaaabcbccadcaadabdabaabbdaababbbbabacadacbcbbbdccbabacadabbabdaadcbacbcdabaddabccdcdbbacacdcdbaaaacdbcbcdcadadccddaabbcaaccddbadababbddddabbcdaddbadacdcccaaadbcdcabdcbddaccbcdaabbbaddbcdcbdabddddcbdcbcabcabbdbacbbccbaabdcbcadcdbcbadcbdbbacdbabbbbcdcdcbdbbbbdcaabdaacdcbccaabdcdbdbcaaaacbbbbaaccdabaadcbbcbcdcddaddbbadcaabcdcadddaaccdbdccacdcacdcadbadabdaccbdcaddcabbcbababaababaaddaabbdcdadbdaccabcaddccadddbaaadacccbdbbdbabdcccccdbddaddbdacddcbacadbccacddacbdddcbcadcabcdbadcaaccbcdbbaaabcacdddbdaddccabdadbcbaacbcbcdcabddaadbacbacbbddadcbbbdddcacdaaccdaadbabacababccccbaaaaddcaaaacddabbcddbbcbdcdbacccbacbbbccccdaddbdddbcacdbdbdbbaddbdbaabdacabaddcdacaacaadcaaacbdacacdbdbaacbaabacdadacdddbabbbddabcbbdabbbdcbbccdcccdbbadbbbcadbdddaacdacdcdbdbccdacccdbdacbdccbbdabdbcabbccdddccabbaabcbcdadbdcbaabccddababbbaaadddbccdabaaadcdbabdcdacdababacabbdccbccdbbcdddabccaadacdbaaacbdcddbdbdccdcbbddbabbbcbdbbccdbdcdcddcdcccadcdcbbacadaccbbdddddcabcccaabcacaacdadbacbcbcbbccccbaaaddcacbadbccbbacacbddcbdabcdccdbcaabddcdbdcddadcccaaccaccbbdaadadddbbccbdbbaddcdbbbbbbbccccaccabccadbbbbcabbbcbdccabccaadbabdadcbddadadbccbdddabbcdcdcdaabcdddabcdbabacddcdabcbbabaaaadccdcbbbcadadcbbbcdbaadccddacbdabcaabcbdbdaabcbbcddacabdccdddddaaccabcaacddabdcbdaddbabddcbcaccdabcbbbdbdcbdcdcbabcabbdbcaaaddbadbadcacbaaadaabcccdcdccaddaadccdcdcabacaccaacabadbcccbacbcaccaaaadaccdadddccdcdcdbbbcdcacdadaddbaabbcdabdcbcdccabcbddbcbddcccacddbabdccdbadaddccdcdacbbdbbabcabadbdbbbccbbadbbadbcdadcaabacadabcaacdddcbbadacadabbabdacbdbdddbdbbcdcabaabcaacadbcbcbbccabddddcaaacccabbccdcddcccaaadbdcabadacabababccbcdbacbdacccdddaddbdccddbdacacadbddbbadccdcdddbdcdbababbdccbbcbabdcaddcdcdddcaaaadbcdddddbababcaabaaacddbdcdddcbadacadbdaccccabacabbacdacbcdbdbadbdabdabbdaadbdcadbcacdcabbabbcbaccaadddacbddadadcabbcdccadccbdbadcabcaacaacbcdabbddcbdbadcabbaadacaabcdcaaaaacadccdacacadacabdbdbabbddccdacadadbddcdcabccbcacbcdddbadbddaddbbbdbbdcadcadccdadcabcacdcabcacdcadbcdbcbccbdccbcccaababcdbdadcaccdaaadcdabdacccbbccdaabaadbdbabadcaccaddddacaccbaddcbabcdcabbbabadaaaaaaccccacdacbdacccbaadaaaabbdabcbadbbccbbbbdbdcdbcaddabddaaadddabddbddcabdbdaddcbaaaabcddadcbcadccacdbcdccaabdabbdbadbaaadbcddbbddadcbaabbcadadbbdaacbdbaddbdadaadaccbabcbacadbbcbaddbdbdaadbdbbdbbaabdcddbddacdacddcbbbaccdbdadddaaddddbbbacabbbacdddaaaccaaacbabcbcacabcbcadaaadcbaddaccddbcadbbcbacbdbcbcbacddbccbbcccbccbcbabdbbcbbcaddaacdbadaddbcdabdcdcaddcabccbddcdbaaacdbdabdddabaddaadcddbbbdaadcdbcaabadabacdabdbcddcbcbdabcaddbccddacbacadbbbabbcaadabdabacadabbabdaabdbcbccbbbbdcdcbbdbbcbbaddccccabdbbadddbbcbacdababcbdcbaababaddaccabbbccbdddccccdcaadbcdbcaabbbaaacdcdabbcccbadcdccdccbccbccddaacbcbcccddaccaaaccddcccbabadbabdddaccaaacbcbdadcdbcdcabccbdbdbcbdbaccdbccbcaadcdbbdcdbdcdbcdabcdacccbbbcabadabdcacadaaadbbcabbadccabcaabccdbabdddddaaadbcaacbacbabdacaaadbddbcbbcdcdaaaababdabbabbbaaacabdabbbcbbcbdadbdaddcbcdaadbaccbddddaadacccacabbcdbdabbcadddbcbbbbdbcbcdbaabdccadabdaadadcabbcbabaadaadabdcaacddbabddaccaccdbccccdabcdcdbbcbcaaccacaabadbabadccddadbbcbbacbacaabddcaacbcdaabaccdacaddaccdcabcabacdadddddacdbdbdcdcddbacdadacaccddbddcadabacadbccbcbbddcadbbacaabaddcbabaccababbbdbaabbddadcaccacbaaddacccacadcadcaabcdcacadbcddcaddbddbbaaddccbacccbbacbabacdbaadccabadcdabbbbcaabbbbbdbccaddbcaabcdadbabdbdbaabcdabaddcabbbddbbdcdabcbbcbdaaacdcbdddbdcddbacdcbadcddaabacdabcbdbdcbcccdaabbaadcaacbbabbaabbcbaadbddcccddbdadabcdbccbbbcacaacccdcadbcbaaadcdabbabddbbcdacadacdbcccbbcdabaaadbddcdabcaadddcdaaccabbbdbcbbbdbbcdaaaacbbccbcdacaabacccdababbcccaabacaabddadbbdddcccdbbcababadbaddacdadcadcdbcbcabaaabddaddacbccdbacddcbdabcacaadadadbbccadcdcdccdaddabadababdcbcdcbdaaccdaccbababddadccbabadaacddadbdbddcccdaacccdbbcccbdbcdcacbcbaddadddbacaabcdbaaadacabddcbdabcdddadcadcdcaccbbccbbdabaaaabbadcaadabadacaaacbababbbbdbacdbcbdbcabdddbddbaccbdcabccbdaccacddbbddcaaddcaaacadccabdcbddbdcdcbacbdbcaabbcadbbbbabbabbbbbbcbdabaaaccacdadaccbdadcaadcdaadbcddbcbccbbdccbbccdbcdddaadaabaddbdbbdcbadabacbdcadabaadcbadccdddcbdcaaaacaaaaccccbccadcbacbbbadccdaadcdbdcdacdacadcccaccdabacbadcccccbacdddacbbaababaaababdccaadbcbcbdadbbcbadadbcbbdadabbadcccabdddccacbcacdabaaddcbcdcbcdbcaaabccacaabbbbbbcdbbcbcadddcdccbbddaddcdbbbbabcbcdcdadcbbbbabcacdcdcdbcdacbbcaabcadaaacadadccaddbcaabacbbbabaacccaadadabdcdabddaddcddddddddabdacaabaaacadccbaabddcaadbcdbdbddabaddcdabdbcaaddccaacaabdbddacddcbdbdcbccbabaaddaabcdddbbbdacccacccddacadbabbcdaddaabddbcdcbcddbdccadddadaacaacdddcaaabadccaccacbcbcbbbdddbcddbbacccdcbddacacdacadaaddadadcbcabcbabaabadbbaaabdabbcaaacaddadcabdccbbcbbbdaacccaacaaaddbddaabbcdbabacbccababcaadddddbcbdcddbcddcaddcdabbcbccbcbdcdddaaaccdabcbdbdcbaadddccadcdaaadccdabdacbbdccacbddaabbcdcbcddcdddabaabcaadaacabacdcdacbabcdaabbdbdbbadacbcbdaaccaacdaacabcdcbabdcddabbcaabbcdcaddbbbdbdcccbbcccabaccadbdbbcabcdadabdddbbcbcaadcdbbaabbccabbccddaadbdcccbaabadaadcbdadabcabdaddbadcdbababcbdadbbabddabbabbdbbbbcbabbbbbabcbccadabaddadcdaddabddccdbbcbaadbdabbacbddabcaacddddbabcdddadccdabcbdcdadabbdaddcdbdaabbcbbdcaccbcccbdccdcbbaadbdaaccaddbdbadbbcddddababdccaacabdaaadaaddbbbaaaadaababdacacacabbbdbcaccbbdbadacbccddcbddaccbddbcbaccabbdcbaddacdccacddbcdaddabbbabaaadcbdddbaaccaddccabbaaaabdadcabaccbdacaadcabadaabdcdddccccdbcbdbbbcbbaccdcbdbcaabaccddacaacddbbdbddbdcccbbacbcdddbcdbabcdbdccabdbdbbdcccbdaabdabbdbcadabaabccccbcacdbdcdbabdcdbdaadbbabbcadddcdcdadcccbcbacbcaadddbabacbabababdadcbccababdbbbabdbaddcbbcdbccbabbcdbbdaaddddabadcabdbbababcdbdbcadaddabcbdaaddaddaccdaccbcdcdaccbdcdbbbadbabacaaaddcbdddbdbcbdccddcacabccaababccbdcbddabbacbddbdcaaddcaccaddcaacacbdbbdbdcdcdadddacccbcbbacbabbdcdababaccbacbbccbcbadcbaddcdaadbacddcaabcacaaaabdbabcdbdcccbdddbcbcaccaccdbaccbddcccaadcaacbcbdcbbbcbcaabdaddabddbbbbaccdcdcdccbbbacabdaddddbbcbbdadaadbccbbcdcbaadbacdbdbddbabcbcdaabbddababddadbcccbacdbbbcbaaaadaabbdbabdcdddccdcbcaddbccbccbddbbacacbdcdbbdcbacadcdcddbababbbddbcdcbacccbdbdccddaabaabcccbbbddcbdaaadbdcdddcbcddababdbcaccbabbdadadaddbbcbcaabdabddacdaccadbcaacbbdbcdbcacbcacbacabacbdacdbcccacbcbbbbbcccccbdbcbadabcdaaddcbbbabcbddabacdbdadaadaaacdbcaadabdcacacadbcbabbbbacbdcadacddcbbbaadbbdbcdacbcbacaacbcbcaacdadccddcdaddaddaddccbdcaacadcababaaccadbbdaaadcdacddcddcbcdaaddddccdbadccabbbaadbcdbbaacbbdbddcdabaadcbbccbddadaddaadbdbccacacabbcabdabdaacbbdddbbacbabbdcdbaddcdcdbcbdbadbcbccccadaaacdbdcbdadcbcbdbbabdbcbcbabbdbcdbccaaacddbbaadaabbacaaacbbdbccdcabccaabbcbabcdbabbddbcabdddbdcccccbdcbbbaadbaaaaaccaadadcaacbdadbacabaababcbbdcbacdaaadddacbdadcaadcaaadaadbdcddddcccbacccabbaccdabacbbbcaaadbbcabbcddbccddcadbadacacadbabaddbabdaadcbbbacdbbdabadaaabdcdacddccbbbddabccbcdbbddcbdbbabdaccdbbbcbcbcdbdcddddcbabdabbccbbbcdccddabbaaaadcbdbbcdddccaabdcbbdacdcdccddccaacadcbabbbcbdbbcccabcaddacbddddabcdacdbddadcabdddbabddcacabbbabbbdbababcbbcdbbcdaaaaababbccbadadbcddcddaccbdbbcdbddcdadbcddacdbddddaacabbbccdbbcaabacbcaaaddcdcacaaddcbaaabcaaaababcdccacddbabaccbddccccbababbccbcccabdacccbcdbdccddbcaccbcabadbadccbaccbabbcabccaddcbadaacccaddcabaddacccaccbabdddbbadcccabcadcddbdbddabdddabddbbdddbddddcdbcdcaccbddbcddbaabaddbcbbbdcbabccdadabababdaccbbcbbbbdbcdcdaccdbddcbdddabdcaddabaabdabaaccbbcabaaabacddaabddddcacbabbbdcabcccbcccccabcabbccdddccbbdabdbcdbccdbccbcdadbaaadcbccddccdbbbbaabdddcdddadcdccccbbabcaaadadadbaabadbdadbbccbacbdbdbccddbbaddcbaaabaccccbaaadacbddcaccacadaaabddadbcddbcacbbdabddcdadaccbaadcbabbaaababbbdacccabbbabdabdacbdaddcdabbcababdccdbdadcccdabcbdbdcabbadbadabacbabddadabcccacddcbaccccaccabcbccaacaabaccbadccbbabdbddbcbbdaddacbbccaddbadbdacbbddcaabccccbcddbddddcbaadadccbddbccbdacddddbdcbadccadabbacbbbcdabbaadbccbdcdbacbccbccadadadcbaabccbbbacbbbbcbcdccdcdabcbbdadcdbbadaccbcaaaaabaccdcccaadbcdccdaccdbcdbbcddbababcccbadacbaacccaddabcccdbcccbcdbbacbadbcabddddacdacaaacdddddbcccbdcaacddddccbabcacccddcabbdbbbadcdacaacdbcddcadccaaaccbdddaccddccabbbacdadaabcbccdcdcccabcdbdbcdbcdbbbddacbbaaabbcbdacaddaabccbbddadaddabbcabcbcadadbddaadababcbbcabdbccdacdaabcdcdaccbadbbbccacbabcaaadbdaaddcbbbdbcaddcbbaadcbdcaadbbddccbcccadabdbbbccbcaacacddcadccaabdcdadadabdbacbcbddcadaccdcacbdccdbccabbbbdcbdcadbcbcbbadcabadacbcdddbbcdbdccabaadbdbdccaddaccbbbdabdbaabadddcbbaadcbbcdddbbddacdbbcacbdbcbbcbaaaadbcdcbcdadadddaaadbabcbadcbdabacdccdcbdbadddbdddaddadaabbdabdadbbaddaccaacbaadaaabcabbcabadbaddccdbcddddbcabdabcaccaadbdcbdadbdbbdabaccbbacdbbabcacadcbbcbaaccdabdbcdbbcccacdbdccbaaaadbbaddaddbcaacbdadcaddacbdcccbbaacabcabbbabaaabcdddabbadbbacaacbcbdbcbcdaddbdacdddacbddcddbbbdcdccdbbbaddcbbbacadcacbccbcabbddabbacbcabacbbbcadcdbbcacbdbababbacacabbbdccbbbabdbcabccddaaaddcdacaabaabcaadaacacdbdddcaadcacacbbabddbcbaacacabcccddbbbacddcbbacacdcbabbdadcbcddabbacbdaadbcdccadaaccbcbacccdabdaccbdaddaadabbbccabdbbababbaadcaccbabbccbccaaadaddacacbbacdcbbacdcadadbadbcbdbaccddbcdcbcbabbbacdbbbacbbbbacaaacdddbbccdbdbdbbcdcacdbacccbcabcaddabaabcaaaabbcddabccacadccbaccccabbaacbcdabadbbacdcbdaabcdbabbddbacaddbccbddaadbdcbdbdccccdbdacadbdddbcabcbdccaaddddbdcaddcbcbbcdacccdacaddcaadaabcdcbcacacadacdbbdadcabaccbdaccddcccdbbadacacbccbdacdccddbdbaaccccbadccddacdccbcacabbdcadacdbcbddccdcabcababbbadaadbbcbcbdbdbadbddccbbdbadbabddcdaaadcdbdadacddcaccbcbccbddadacadbdaddabaaaacbcdacbcbcbabbacccdccdaaccbbdbaacbbddabdcdbdcabaacdbbacadacbdcccdbbcbcdacabccacbcbdcaaacdccdbcbabcccccadaaacddccabdbbcbdcaddbddadbbbddbcdbdbdbcacabadcbbdbcdbbacbdccbcbdaabcaccacccdabaacbbcccabddcddcbadbaadabaddcbbabdbdbcdcbacaabdaddacadbcaaaabcdbacabdbbcdddddaddaabdccccbaccbbdcaaccaaccbbdacadcbdcdabababbacddbbaadcdbcbacbdbbbcdbabcdbbacadaaaddacacdbcbdbcbabcaacbadbbacbdabdcbccbcaadcbcbdaabcacbbccbacbcadabdaadbabbccbdddbbdbcbbddacbaccabbdaddbcdaacbadabaddbbbcbcbaddaadbbddadcbdbcacbbacdaabdcadbacbccbbccaacbbcaabcbddddbccdcdbcaacaacaabdcdabcadadbcbaabdaaddadcbbbdadaaadadaadaabbdbaacbaddcacbaaddaadccccaadcbddaddbaddcdbdadbcbccabdaccabddacabcabcacbabcdadcbabbaaaabaccbaacbaabaaadbacdbddcccbcabdadbdddbdccddbdbbaccdaddbaadadcbcddabdbaccdcdbbdadabddbcdacbcbaabbbacdabbdcdbbabdbdbadabddccdcbabcadbacddacbcaaccdabccdbdbadccccadbddcadbabdcddbdbcacccacdbcdbccccddabdabccccddadbdbadcddddbddaababcbababbcddcdcabbbbadcccdabbadcadddcbbaaccacdcccdccadddccbdadcaadbcbaccbcdbdddcbabcabdbcbddcdccaabacbccabbcaddcabdddbdccaacdbcaabcbabbbadcacdbaabcadcbdabdbcacbdcacdccaaaadbdbddadbcbdbabbbcbcccadabddababccdacdcacacbaccaccaccaacaacadaccacabddcddbdadadcbacbdcdbccdddcabdbabbccbacbbcbcbaacadacdaadbdbacdbabdaabccbbadacdaacdadddcdcbbadcdbcbadcadcdadcbdbddbdacbbbddaccabdabcadaacdcdcbbccabbddcdaacbaabcbbadcbabdaaddadbbbcbcaddddaadbccadaaabdabdcccdacccacbcdcababccaadcdbbbdbabbbacadbadaccadaaaaccdddaacdcdaddbabccbccbbacbadbaaccbaaaccabccbcdbabcaabadbcdaabdacbdaabcabaccbbbbdbcdccdbdabdcabddbbbccaddcbcccaabddbcbaccabbdadbbbababcabbcabbacaaccabbcacdabcbaddcdcacaddabadccdcabacbdbcabbbcddcbdaabbcdacabcadcabacabacddbcbcbdacdbddcabdadbaaadbbdcadccabcddccaadcbabaabbcdcbcabcdbccdbcdabccadacaadbacbbbbccdacadaccaacdcccdaadcabbabaaadbccdbadccaddbcdaababbbaababdcacdadadbaccadbacdacbbabcbcdbbbdbddcbcdbbbcdacabdccccbcbbbccbaddcabdbcccbccdcdcacbaaadadbbbaacacbcaadcbacdabcbadabdbabbbcbabadabbddadadccdbdddccbbabddccddbdaddcdbcddacbacbbdcdcdaddadcdcdaabbcbacbcabacbbbbaabaaadbabacbddccbccadcbccbccdcddccadbdaaddddbadbbacccdbadcacacdbcdabbdadacabbcacababacbdbaaaaccbbdacddddaacbbabcabacccddacabccadacccabadccbcaacbccdcbbddbbaccdbdbbcccbabbcbacbababbdcaacdcabaacbbbdaaccddbbcdbbcbcccbadbadcaacacaacdbacdcdddbcacdcbdccdcbdaddcaadbdcdbcaacaddacbadadcdddadacaaddcbcbdadbcdbbcbadabdcabddcddccbdbcddcabdbcbaccacccbdddbbcdaabbaaacbbcbcbcbdcccdccbbacdadaadbdcbabdcbbcaadaadccabcbaabddcbbacdacbdcddddabaacccadbcaabccddbcbaddcbababbcdcdbabdbabddcbcdcbcbcbddadcbddbdddaaaaacabbbababbcacbdaabbddbdbaacbabdccddadddddcadbdddcbdaaccaadcadabcadcddcbdcdcadabcbddbaabbaaccddddaccacdabadcccaacbdabbadbaccdabdcccbadadbbacdacbcabcadccbdabcabbadacbbddddcdccbdccddcdddbdcaaccdccdbddbcdacabbacccbdadaababacdbadcbdcdcaadbdcccddcabcdbbccbadbddadbdadbabbababdaacdcdbcdddcaacdcdacdcdbacdbcbabddaaddddbcbcaaadcbcacddbacdbaacbcbbbacadabacabbaccddbddabcdddbbabdbbabbacabbccbcccaadcacbdadadbabccdbbdacdcacbdddddbcaabcbdbbddcabdccddccdaaadbaaacabadbadaabddccbdcaacaabacbcacaddcdcdbacccacbbbdaaccaddcbdcabbbbaccdbabbdbdaaadaddbbbcadbadbadadadccdadcaacbdbbdadbdcacdacadabccacdbabcbadbbaddcdadbdabbacdbbabbdcadcdbdbcdcbadbdabbcbdcdaddacbacacccabdacbadadaacaaccadabadacdccabbbdddaaaaabacbccdabbbdddbabbaccaddaddcccbdcaccabbabdadbaabbddccdbbdadddaabdcdabbccbcbbddbcbabbcdadabdaddbccacddcbbcaadbbccacbcbdcaadcdbcbcdabdabddbcbbabdbcadaacdbcdacbbacabdddcbcbcbadddbbabbbabdbdbbaacbbcdcdacbbdadccddcbbcddacbdccadcabaadccacabdccaadacdbddddbbaaaccbaababcddababacdaacdbadcbabddbbbabdbbdbaccaaadaabaaaadbcaabdccdacaaacbadbdbaabaadcbbaddbaadddaadaacdbacabccabaaadbbddbddabcaadbdcdacbcbbadcabcbdbcddcadcbcadabcbbacadbdcbcddcbaadcbdbbdddbaadcdabdcccdbaabcacbccaaddbacbcbdbaadabacddabdadcadabbdccddbccccacadcaddabdcbdbaccabddcbddddadcbdbdcbdcadacbbcaccabbadaacbaddabbbdbccacdcdbcaaacdaadbbdacadacaadadadaadabcccbcccbbdcbdabbccacaccdddbacbbcadaccbaabcddcdaadaacaadccbcbbaabbbbbbabcdbcdbddaabcbbcdbcdacccdcaccdbcacdabddbbbbcbaabacaaabadbbbcdacdcccddbbbddcdcdbdcbaadcaabdbbddcbacccbbccbabadbaccccbaadbbdcacbdccabbcbabbbadcaaacbcadbdbdbadcdbdcaadacbabddbdacdbadabddaaabdbbddddcdabcbacbbbbaccabbdaacdbcaabdabdacacccdcdbaaaadccbdbdabacdbbdbaabcdaadcabdabcddaacadddbbdadcbaacdbabcbcdbdccdbaaddbdacccabcaadcaccabbbbadbdbbbbdacdbdbbadbbbdbdccadbbcabbcdcadcababacccacaaaacccdddddbbbbbdacabadcbdcaccaacacccddaabbcdcdaaccaabadcdbbcdddadbabdadaaaabbbcbaadacccadbcbabadcbaccbbbdbbdbbccdabadccdcaadbdacaabdaabdbacadbcadcdadcdbacadabadbbbcaddadadabdbbdbabadbcbcbaaacbcbaabaababadabbaabbbddbdbbbcccddcbbdabdbbdacabbacccbddbaadccdaaaadbdcadabaaadccbaadadcacadacbcbbbabbccdbbbabacbbabababbbdabadbaadbbbabbdadacbabdbbcababcaacbcabaccdbbbbbcdddcdadcdabcccacdbdcdcbabdbbbdcbdaaddcbdabcbdcbdabcbbcbabbdaaaabcbbbbdcbaddabbdcacdbaadccddadccccadbaabacdaccacaacdcabddaabcaadcbabbaadccadbcccdccacabcaabbbbdcbaabccabacacbdaccabbbabdaaabadbadcbbbddbacdcadbdbbadbbddbccbabdddcaccabdccabbacdacdbbdadddcaddcacdabbabcbddabcabbcaaddcdaddddcbabaadbdbccccbbdbadcbcccbcbdcbdbdbdccadbadbdcccbadaabdbcaaacacbccddddbdbdcdadabdcbaaddbbacaadcdccbdacdcaaabdcbabdcbbdaadcdccddcaccbabdcaabbbacacacdacdccbaaabbdbdbdcdabddadcbdaadcccddabbbddcdbddaaddccbacadacdcddcdbdbcdbccdbacbcbddabccdbcadabaadabdcbabbbccddadaaaacaadcaddbbbabcaabaccdccbacadbccbbaaddadcbbdacdddabdacdbabdbdcaccbcddcdadbbbbccdbdadaacaabaaccdacbcddcacdabbbacdaaddcaaadcdacdbcbbabbbddbabdbbbbabbcaccadcbadbdbdadcaaadbdadacabaaacabbaaaddbabdbcacbbdbcacddacdadaadacbbaddabdacbcdddbababddadcdddabccadcdcbbddbaaabdbbdadadaadadddbadadddcdadccccaaabacaddabbcacdcdaddddccaadcdbdbdabdcbabdddddccdcdcacaaababdadacbadbccabbbbabddcdbdcbbacbbbabdccabdccabcbcbbabbaaaaaaaadaccddbdbcdbcdbbabadbcbbbbcdbdbdbdbbdbbbdbbdbaabbcddccdadcbccdacbbacabdcaddbbaabcddcacaaddddbaadabbcdddddcdbacbdcbcdbcccbccbbbdccacccdcbbdcbbcdaadcdcbddcacbcbbddadcdaacbdbaaabaccbcacbdbbddbabcdcddacadabbaacdaaaccbabdadadcabaadacdbddaacdbbdaacbcbaacccdacccaacacadbdbacbbcdbbbcbbcacadadcbbacbbaacaddbadcadbcabdadbcadbdcacacddbcdaadabcdbacdbdbbcaddcbbdccbdccbaaaaababbccddacbacbaccdccdbaaaccacabdbcdbcdbaaadbabbaccaadacadcdacbaaacacbcbbcdcbbbddddaadaacacabadacddccabacdbcbaccbbbabaabcbbcbccaccccadadbcabbdcdbaacbdbddddbababaccdddcdabababbcbbbdadabbbddcdbaabbdbcddbddcacccdcdaccdcadccbbcdbbdbccbcacbdbabbbbcabbdccbacbdbccbadababaabbdcadbaadaaaaacbdacadaabacbbaacdaadbacdaabcaabaabdcbcadcdbbabbacbbacdcbcbbcbdcaadcdccaaadddcbcbaacadcdabbccddacdccdcdaccddcdbcabbbbdcaabdcaaabacdacacdaddbaddabdacccbcababbddbdcbcccbaaccbbabddccdcabaacbddaabdccabccbdbcbdcadbccabcccacbddadacbccdbcadadbcbaddcddccdddbbcbabdcbccaadaddadcccabcaaaddccbbdccaacaabbaadcabbcddaabbaddbcbaaaabbbbbbbbcdbcaddccdbdddaaddbdcbadcadcbcadabddbbdadddadabbdabbadbaaccadccbaddacdcdbcccbacdabaddddcdcdcbbcbbdacddddcbcadadcadbdcdccaadddabaababbdaabbaccbbcacddbdddacaaabaaccddabdabcbcdddaaddacdabddbccaddcccdcabdacadcaaadacdcdbddccbbaacaccbaccdadcbacccbadbcabdacdacbbdcaabbcdddacdacadbaccdabccbddacdbccabcdcdacbbbadabdbcbbbadbdaaddccabbddacdcaabdbdacdddaacaabcccbacddaadbadccbbbdaaddacabdbbcbddacddcabccbccccacdacdabdcddbababbadcdcbddcaabcccbacccbadcacddabadaccacbcdaddbccbdbabdbdcccabcdacbbdbbadddddbdccdbdddcaaadbdcbbcbcddacabbddaacaacdbaddaabccdcadbdcaacbdbcbacabacadabadabacbbccbcccaaadaabaddcbddbccbdbababbdacbdaabdbdbabcabacadccbcddaadabbcaccaccbbadcccbacdcdabddaaccabbcbcadbdccacdccaccadbcccbdadddadacbcbbacbdbbbbbacddacacacbcbccdccbcbbcccdbcadaacaddaaadbabdaabacdabbdddadacadabcbdbcdddacdccddbdddddbbaabccabbcabbadacbcaaccadcbbaacbcadaadbbacdccdcadbbcaaacbcdcacdadcacdccacddacaacdaaaadaadddddcadbbbbbbbdbacddcdadbcbabadbcdbabadccddbbdddbcbdaccddbdbdbcdcbbbdcadbcbbdcdadcddcaaacdabcadcabcadcaddabbacdcadbdccdddbbaaabdadacccacacadadccdaddabbdcdbcadcacabbbadddbbaddbdcbddabcabddaccccbbdabcbcdacdcdbccadbcdcbaacaacaacdacccccccaddbccccbadbacabdccdbcddbadbdadbcbbabadcbdbcddacbbadcbadbcabdbdaaacdadbdbbbdcacbcbaababadbcdddbaadadaabcadabcaaaccbcddaddcacbddbbbbcdbccbdbcdcddacccacaacccddbddaddccabaadadaacaddaddaacbdddbdaaabddcdbcadcccbaabdadcdcaaabbccaaccccabacccbdbdbddcbadbbaccabdcdbdabddbbbccaaadaaabbccdadadbbdaaabbdbaddadbacdbcdcbabdbcbccaaabcadabdadaaaadbbbcbcabdbccdcbadadbdcabcdbacdbacccccbacccadbbddbdcbbddbadbadcdadccaabbbcbdcadaaddaabbdbcbdbdcadbaaadadabcdbccdcbbadcccbddcabbadadcbccdbaababcbaaaabacdbbdddcddacadcddbbdcaaaabccdabadcdbdabbadcdacadddaddddcbadaddbcaccabdbacdaaadcaccdbccddadcbacdbddbdabbabcdabccbadccbbcdacdccabdbdadacbabddccabbcbbbbccccbbbdacbacbacccddcbbdcbbacbcdabacdacbdaabbabbcbbaacdadbadcbbddacbccbacbcabdbcdbcacdabaaacabddadabacdcdadacdbcacbbcbbacadabdcacaabddccdbabcadcccaabcddccbbacacdccbdddabddabbbcacdcacacdbdcbccbccabdadcbadabddcbcdccacdaadcbdcbbddadddadbcdacaacaaaacacaaddaacccccdcacddbddbddacdbcbcbccaadddbbaacaccdacccccaabdcaabcaaadbccdaadbdbdccdcabbabdddbdaaddcdcbbaadaaaaabacbcaccddccbcbddabcdabaaabdbbbccbabaaadcdcbccbccadaabadbadaaaddbadcdcbbdaccdbdacbbaccaadabbbbdccbbacdacdabacbcadddbcdbbaacababbcbaddccdccadaaccbdbadcadcdbbbcadccbbddbabbacccdacbbbccbdcaccaaaaababaaacbaaacddbcbdcabcbacdadcacabccaabdabaababcdbddddccabbbccdbbddabcdacadbdaabcabbddbadacabdcacbbbadcbbcadbbabbcddcaaccccdcadacdacbabadaccaccdbbcbabcbdccabbdddabdbcaccccacdbaaabbcadcbddabccacacdaacdaadbacbdacbbaaacbbabcdcacdccccdaaddbdbbacabcccdabcbbcbcbbcbcdbbaddaacdabbbdaccccaacaaadbccbbbbadaabbbaaaaaadcccabcbadcdaacdddacadcddcbddadadcbcdbabbbbdccddbacbbddbdbccadbdadcccdbacdcacdddabadddbbdbdccdabbbddcadacabbcddddadcdbabccccaabdadbccccacabcccdcadabdccaddbbbbdbdcdbcdadcccbccabbddcdbdbbcacaacbddabcddacbdddbacbaaddbccccdaddacdabdbcbbcbdabdcccbacdacbacdadaaddbbbddadbdcbdacaaddcdccadccbbacdbcbacbbbacdbcdcbdccacaabbddbdaabbbacddaccbcabdbaabddccbdcadabaddabaccacbaabcbdaddbdadabcdcbacabaaaadbbabaddcbccccbbdbbdcccbcaddccbdddabcabacbaaabdabbaaabdddbabcccadbcbaddbabaadabbbcabaabbaacbccddcccacadbaabccddbddcabcadcdbadaccdcbdbcabccaddcadbcaacccabcaaabbcdaddadbccbdcccbdddddcaaaadadaacacbcbccbacdddddaabdcadabbdddddacdbdbbddacdddbcdcdccaacadabdaaaaaadbccbaadabdbaabbbcdbabbbbaaddadaddaacbadbbabdaababdaaaadbbaabcbbbdabccabaacbbbbdddbbdcbbcabababdabbdbabcdbdcaddbbcadabbaddbbaccacdbddbbaccddaaacacccdbcabcbbcaccacdbddaacdcabcaddddcddbdcbdcbbadadcadcaaadbbbabdcbdaccdbacdccbbbcacabdbbcaccbbddacadabacdacdacbdccccaaabcacadcdabdcddbbbbdbaccbadcaaaccccacdbbdccbdaaddbdbcdcaabdadccaadadadbbbcddabcbddbababccbcbaabacdbcccbabcdcdddbbdccccdbababcdccdabbcbabbccdadcbadbaddcbdbcbadcccdbbdbdadbcdcdadabbbccadbabcaacadadbadacbcbbbddababdacacabddaaabbbcdabbbdadcdcacbdbcbcddcdaaddbdacdbaddbbbdddabcdddcbcbdccbaaaaddcbacbadddabcddbbcbcddaabcdbdbddcdccdddadcabbaccbccddaaabaadaadabaabdaadbdcacacabddaccddaaddbadccbcbdbdadabdbbcddadccbacbcdbbbabccadacacbcacaaaabbaabcbcccbcabadbbdabcdcadbccbbccadbabadacbdbdbbbbdaaaaacbaacadbcadbaaddddcdacacacbcacaadcdcbbbdaddaddbaadddcabbcaaddcbcdbdcdddddaaacbdbcaddabddadaaaccbdddccbddaacaaacdbcaabcbccdbddcaabacbcabbdbbaadaabdbbabacdaccabacabcdbddcbbddddbddcabbcaaacbbdbcbbdcbcbbbcdbbbdcddbdbcbcadcaccbbbbddbcdccabaddadaccbdcabdbcaadaccdadabaaacbcccabbdacbaddccdcbbccccdbddcabccdcdcbbaaaddacbdcccbdbbacbadcccccccbddbaaadbbaabcbaacabdcbcddbaccdcccadcdccbacccaddbadbdabbdbadacabcbddadabdcdbcabdbcccaaadabbbcccabcdabdbabdbdccacbcbcaccdadbacdbacdacbccddcacdabcaaacbcddbbccbbcbbdddadbbbdacdcbcbdbcdacabdcbbdcbabadcbbdcaddbacddabdcdacabcdbbbbdbcbdbdbcdcabbbddcabcdaabdcccbdacccddaaabbdccccacdcaadbabdccacabccbdcaacadbdcdcdcccbcbadcabccacddbdcadbbcbacccccacbbcadccaabbacacabacbcaaddbdbcccccbbdcbdbadbcbcdbbbbbdcbddbbcadbdbabbcdadaaadaccccbddbbabbaaaaddbadbdcadbacbbdcdcbbcaccbbcdcadaadcabddbdbccdbcadcdaaaacacadbccabddddacadbddadcaadcbbababaddbacbdacdcaddcbcdccaabbaaccdbccbdcbcaddcadccaaabdddcccdbaabdaccdabdbbccdcbdcdcddcacbccadccbadacacccbaabcaabacacbcdcbaddbcaadcbcdbddccbddccbbdcadcaaccabbccbdccadabdccbbbaacbccbcaadadbadaacdaadccaaddacbabddaaaacbcdaaacbbddddcbdaacbbaddbdcbdbbbbdbbbdddbaadbdcbaddddabadbbdaabdbabdbbaadcdadaddaddbcddbbccccadacccabbbcaaadaabcdbacaabbababdddbbbddcdabbbadcaabddccacccdcdbcdbccbadaaabbbbcdcbaaaacbbdbcbbaddbcdcbbccbbaabaabbbbcbdcdcdcadaccaadacdbccdbcbcbbadcacbcbaddbdbbccdacbcbdabbddaaacaddbbadaaacaaccbbdccadbabbabcaadbaabbabccbabbddbaddcbccacccdddbbdbcabadacbababdbadcccddadadcdcbcbdcbbcabacbcbdbdddcdbcdcddacbbcdbdbaccbcddcdcdabcadcadabcacbaccaaadaadaaabdadadbbbcbacdddbababadadcaddbcacdadccdccbdadabadaabbcccddbaddccbababcdbcacbbbcacbacdaadabbccddddababadbcadabcbaabacdbdbdbaaaabababdabccbbbdababaaacacdcdcdbbbbbdacabcaadcacbbabbbdddcbcacacaddbdbadccadbcabdcabdacbabbadaabcdabcdcddbadacddacdcbcbbaadbbcabbabbcdacacddddabbdbdcdbbbacabdbdacacdabbaabcbbadaccabaacadbbdcaadbcdaabcaaccdbdacdcaaacabdadabccddbdbdbacddaddbdbcabdcacbdcbaccdbaccaddccbbaadddbabbbbdaddcdbbcacbaddcbbdcbcdabdbdbbbacbccdbaccaccabbbcbbbbdadddbdccddaadabdccdcbdccbddabbadcaccddbdcdcacdababcddccadbadacddaccdaadbacaccdbdbdbdccdababacdcbdabbadbbbcdbbbdacddbacccbaabaaabbcdddddcbbabaddadadabbabbddccdbbbcdccaaadcaddcdabaacbccaccdabdbadcacacadadadcdacacaabbcdbdcdcdcccbadaabdadaacadcdbbbaabccbbabadddaacbdadadaabdddbdadcaabaadacacbddacbcddabdbcbacddacbbadbacadabcdacaabcbcbacadbaccbdabccddbdbabbdaddcabccbbcbbbcbdddadbdabadaaddbaadbcbbccadabdbdacdaddabbaccbbdadbacccacabadbadccaadcbbdcabbaadbcadcbdabbdabbabacabbbdbdaddccbdbdccdcacbcababcadaabbdbcdabcddddaddccadabcabbbaadaabababacaccadddcdbcadcacddbcadabdbcdaacbcadabbbcaaddadbbaaddaddaaaaadabababdcdacbcadbbccdbacbaddadcacacbdbbbcccdcdcbcbaaddbdaaacccbbcbcdcbcdcdbaadacadbbbbdacbdbabbcacbbacccbcbccacdcbcccaadbddaaacbcdccbabcccacccadccbabddbdccacbaccbdabbdbadacdcccabbdcdbaaccadbaccaddacabcbcbcdbcaddbadcdbbdbbabdaabdddbbabcbabbcdddbabccaabdcaabadcdbccbcbdcbaabdacdbddbbbbccbbdbaacdbbdbdbdbadaabdbdadbcddcbdcdacbdbccccbbaabaadacabbdbabbcccbadbcaacbdbdcbaaabdaaaadacddcdbdbcdbccabbbabdcacdabcdabdaabbbbbccbbcbccacbcbdaaddcdadbcbdaabbacbcbccacaaabacddbaacbcdccddbcabcabcdbaccdccbdbabacbdbdbddadddcbdcaccdcccbcbbcbbadcacadacdddbdcbdacabbdbccdccdacacabdbadacbbdcbcacdaacaddacaaccaddabadccaddddccdcddbcddadadcdacdcdbaadaccdcabbdbccacbccaacacadadcaccaaacacdbbdaaddcaadbadddabccddcaddcdddabdcddaaaddabcddbcaaddbbcddcddbdcddbadadccbccbdbbcdbaadcbaacdbccdbbddcdbcddacbacddaaddaacdbddaaddddabbccdaaabbadbddcaaddcbbdcbdcdcabdabcccdababaabddacbdbaacaacdcaddbaddacacdbdbbbcdbcdcacadadcbacaacaacaacabcdbabdbabbdddcbbdcbcacbbccacdabacadbdbadbbddcbaddadbdabdabccdaccbddcaababcccbccbccdadbdabaaaaaadbaccdadadabbddbdacbbbdcbbcdbcaacacacacabacddcbaacabcdcbacaacccccdbcccccaaadddcbdcbcdccacbdcabdbddaddbddbcbcadbccaadcddadaacacababcddbdbadaabcbddcaadaaacbcaabdccddbbbadddcaadabcbbcdcdcccbcdadddbbabdbabddbadcdadbadbcbbcaccdddbbbaaabaabcaccccbbdbddabbdacbbdccbbaadbdbcaadaddcadacbcdabbccdcdadbacdbacabacdacccbddcabcbddbcdcdbdaaaababccadaadabcbaadcccbbbdabacccbdcdbcbcacbccbccccbbbbbcdddcbcdcadacdddbbbdbbaadcdcbcacacbddcddacbdbcadcdbcdbdcaccacabaadbacdadababcddcbdcbabdbcaabbccaaccabcdcdbdacabcbbdacabbdbabdbdbacdbbbddcccbacabcbaadcccaabadcacaadbbddabcdaabbbdbabaadddbbbcacbdcddbccdbacdbdcacabcdddbcdcdddaccbddcabaabbaabbdabbbccccbadaaddaadcbddacadbbdaaadabcddbccdaaabcdccbabacccbbcddbacabbcaccbdddcbdaabcaadbdbacbbccdaadabcadaadbadacccbdabbdbacadadadbbbabadbaccbacaadcacdcbccaaaccdddaadacabcdcdbdbccbbbdadcaaadcadcadadccdbacbcddabbcbcdacdddadbdaddbabacddacdbadcadccbbcbddbaabcdaddaadaababadddccdabaaaddccdabaaadbbbdabbddcabdadbabdcdcbddaabcadcdbccccacdcbaaaacabdbadadbcbbbccaccbdabccababbccdcbdcabacddbaadbdaccbbaddabddcbcbaacabacdadcaaabaddddcddbabcbdbbddbccbadcddbbdccddaddcbcdbcddacabcbbdbcabcbddbabddadabcbdabdddbbccdadaadbaddbbadbbdbbbdcbcbccdbabadcccdbcbababdccbcdaaddbcacabbcdddbadacbdabcbbbdcdbcbccaacddbcabcacbbdddcadccaddccadabdadabccdabaccbaaabbdbbadbdbddbdadbccaccddcdcddbcbcbdbadbdabbcbaaabaddabdbdcabcabcccbacaabbcdbaaadabbabccbbbdcdbcdbaddcbbdcacbdbcabccdbacddaccadacdabbabdbcbddcdbbcbbccdaabdcacadcddaaaadaddbaacbaddadcddccacdbbdbccdcacdddbdaadbdccaadcadcbabacadcacbabcbbdaccddabaacddbcadbaaaddaadacdaddabbbadddbadbbbdcaccabbcbbabaaacabacdbdcddccacbbbdcccdcadcbdbaabbababbccbabbacaccaaaacbddaaadacdaaabccbaddaabddaddadaddbcddbcccaddcdacbbacabadaabbabaddbabbccbdaaaacdcccddddcbabaccddcdccdcdcacbcaacbaaabdddcacddaadddabcaddbbabdbaccdbaaccbaaabadbbdcdddbaaacdcaadcaacaacbcaacddbbdcaaabbccbcbdbbdacacbadbccbbcbadcbddabaaadccacaacaabbdcbdbbdababbbbcbababdbabcccccaacbacaaaddacdbddaabccabcbbdbbddcdcbbaababddcbbdacdaaabbbbcbcaaccbbcdddcdbadabccdddccdacbacdaaabaaddbbdddbbdddbacbdcbabbdbabdadacaadccbdbbdbdbddacacaacadaaacbacbaabcbccdadcacbcdabaaddccddbbccbbacddabddbbbabbbbabcaacddcdddcdddbddadcdcacccaabadbbdaaabcbbdcccbbacabddcbdcbbccccdcaacacbcdcccdabbddbaadcbdbbdbadcbacbbbaddcdaadaccdcaadbcdadcbdadcbbbdcccdbdbccabbcbdbaaadadcbabcadbbddadbdbdabcbbddccadbcbcadbbabcaaacdababcadbddccbaaccbdabbadadaabcdbcdcbbcccbaabdacaddddcccbddcbcacadaaaddbddcbdcadaadbdbbabaabaabcccdcbbbcabcbcbbcddbbbccccbadcbcccacbbbcdbccccbdacbccdcbaabacbadaddaadbbbdcccacdcdcacbacacbabbdccbdadacbccbccabdbbdcdcabcbbaacbabacdababdabcabacadaaccaddbbccdbabbcdbddcadcaddcaaadbcadbbacaacdcacacaadcccdcbdcbacccbbbddaddbbdadcddaabcbdddbbdbcbdaacdbcaaabaaacbcccddadbacdabbbadcbcadccabaacdbbadcbdddbdccbaaacdabdbcdaaadccddddddcbbccddaabdbdbabbaccbbadabdcbbdbcacdbbaacdabbaacdabccadbaacacacaacdcbaaadbaddaccaabbccdccccaacdabacdabacaaaccdccbaacdbaccbacdbddbcbaddcbacbccaccdaacbaaacdcdccaddddddbbbdcbdaabbdaaccbccdcbdccddbdacbabbdbcbdcacddbabbbddaccadcccbbbdccbbaddddccdaababccbabdbdbbddbdbbaccaadcdbbacaabbadcaccaadcbaaccbbdcbabdcdbabddbaabbddcbbbbcbdaaaccabacbcbcdcaaabdbcdcdcbadbadbdbbdacaabacdccdaacbcacccbcadbdaabbbbcccccbadcddaccbcdabaaadbcddabacbbddbcccbccbcddbacdddcdddccdadbddaddbcacabaabbdacadadcdcbbadcacbdbbacdbbddbbcacdcaccabdbcccbdbcdbabcccabddabcccaccacddabcabaaaadbdabadabdbdbbadaabbbadcdabadacbcaddcddccbacbbdbbbcaadcacbacadbbbaacbbabacaccdbaacdbbbdcaddaaccbcdcdaaabcdbaaddaadbabcbabadcdddbdcabcddaacddbdabccbadbcbadcddaddadaaaccbbbacdcabddbdddcaacacadddbdbcbdddcdacbbccbdccbdbbbcbdababbabababababacacbaabdaaaabcdbdddabdacbbdacacdbcaaddccbaaabccbcacdaddabbbaddddddcdaabcdbbdcdccbbacaddcdcaacbaaccaaccbaddbbbacdcdbbaccddabbbcacaaacddabbccdbdcaccdaabaaccabdadabbbaddccdbaacdcdddbaccdcbddcbdaaabacdbdaabbdcddababcbaacdddcdcbaddcacccdaaabbdbacaabdddddaadddcbdbcacddadadbcbcccccddbcdbcbbacbcadccbbcbbabdccbcaacdcbdbbddbbabbababcbbcbbaaaaacdbcabcbbcdcdcdbaccddbbcbdbdbaacbcbdadccddccbdcdadbbaabbbcddccdbcacbcbdacdcccdbcdaadbccddabcadabdacadccabcbdaaddbabdacacaddabadabacbccddcdbcbbddbadaabddababacabdabbbddabcccdbaddbabacbddabdcbacaaddbbcaadbcaabbbaabdddbcbabddadadcdcdbdcaabbacdbccdaddcddddbcadcddcaadcabccdadcdcbbaaaacddabddbaaccacaadccbbcaaccbccdcacdabcbdcbaadaaddacabddbaabbbcdaadbbcbdccdbabdcbccccdbdaddcaadcdbacaaccccddcadddcdbdaccdcdcbbccbcbaccddcacbbdabbcbcbabbddadaacaacaddbdbdcbccdcadcabdbdaabbbcbaabcbabacdacdbadbbabbaabacdbccdccbdbadabaccdabacdcdcdcbdbcbdcdbacaacdcdbadbccbbbabaadadddbabaddcccdbadaadbadacbcaadacaabddbcbddcacbcdacdbbbbcaddddccbcdadbdaccacdaacbcddabccccabadabdaaadcccbabacbbbbaccabdddabacccbcdabbadcabaacbaacbccddaacbbcdabcadccbcacddabbcacccdaacadcdaadbcbbaaacbbcddbacdaacacdaadbbcccacdacdbdcaddcbabddcbdacdaacddcbbbcacccdccdcbaadbacccadbbdcdadbababadddbdcdcdbaacdbdbadabaddcdaacdcddbcbddbdbccbaaddaaabbbadaaacbccdcdcbddaadacbaadabccdbabbcaaadbcacaabdcbdcdbdadaaacbacdabacbcacdddbcbdbbbcacbcccadbdcacccadcabbbaccdaaabddcaabacacbaddbcdadcaccabacbbdabbbbaacdccdccddccdddbccbbdddddbadbaaadcdcbdbdacdcbdcabdbadabbababdccbdadadcbcbdbcacbbaddcbcadddbcbcbdccacddddadbacdacbccddccbaccaadbaadcbaccaddaadcaddcadbadaddbcaabdaadddccbdcbbcdadbacddacddccdacdcdaccdaacccccddabdbbbdbbcdaabaddbcddacbdbbabcbadbbccaaddccdcdbdbaddccddcabdbcbdbbabbdcdcbadbcadbdbbadadadbadbccabdbbdcdbbabcdcdcbbabbdbcdbcadbaacaadbddbcdcabaddbaccddaccbbbdbdddbddcddcbabbbbccdacbbddbaabcddcdacbccbbcabccbaadcaadbaaabaabbbbcabdbbadbcabbcdcadcaacabbbcdddddbaaabbbcdacdabdcaacdbaaaaccbdaacabacdbdbaccddddadbacabbabdbdcbbcbadbcdacddbcdddbdacbbbaaabdcacccbcddbbcbbcbcdacbcacadcdbccddcbdaacaabacdbddabdbddacaaaddcddaaacbdabcdbbacbcabababbddbdcacbdddccabdddccbcadbaddbacaaacabbbcdbaddaababcbacacdbbabdbddbbbbbdccbaddcdbbbacdbdcaacaaccdabdddbcddbbbcdabbbdcddcababbadabacabbbccaccabcccdcdcddbdcdcaaccbcbbdddccbdaadbcacdbdcabcdbcacccbadadbcdaabacabcabbdcbcabacbbdccadccaaacaaaacbacaabccddcbbaacacaabcddcdbcaaddbdabadddcaabcbccdddccdbcbcccbddadcccaabbabddddbdaacdcaabbaaccdbcadadbddcbcccadacccdabcacbdccaabccdcacaabbcdbbadbdcbcccacacbacbddbbccbbdabddaaddbbaccccbccabcbddccddacbdbadbdbbddcdbacbcdabbbaabaaabcdddcdddcdaacaacdcacabacbbcabdbbaccddcccaaddbcaabdcddbcbacabcdaddbacccdcdcaaabddbcbdabaddddcbdaddaabbdbbbabdacabcabccbabaabdbdddaadcbaaaabdbabacddaabcbbddbcbabbacccddbbabbbddcbbacbbaadaabdcabbabbcbdadbcaabaadbacaadbdbbdacadbcdbddcacddaabddbcdbbcaadaadbbccabbbcabbdcdbcdcaddccccdcdbabaabbaacdbdadaaabadcbcaaccbaddbaccabaccdadaddcccadabbbaddaddbdcbaadbbbcaacaddadccbbbabcdbbdbadacccabadbdddcdbbdbaccddbbbbdbaadacbbcaadabaccbdcccdbadadcaaadbbadaddabbcaabdcdcabdbcbcadabbcacacbbdcdbbadcaccdcddbccdaccccdbcbabdaccaadcbdbcabdcdbbdbddcabccddddddddabbadccdbcabadcabdccdcaacbdbdcabbbbbcddbdbbcabadcccdcacaaddcbdcbbabbcacbdddabaaaccabdacadaddacccdccbbbbaacacdbaaadacaddbddcdbadbbcddbbaabaddacbcbcccddcbbacdaadabcbcdcadaddcdaccabbaacccacdccbacdbcdbbaddaddddcbacdbcdccdcbddbbadaccbccbcdadadbadbabcadccbddbdaddaccbaddaaddcccbdcbccbdbacdccdbbddabbdbabaadcadcaadcdaddabbdcbabdabddddcdcbaaccbccadabaabbbbcaddabbddbdddbbbabcabaaddcccdbbdbddcdcccbcaccccbdddcdcbccabcdbbcacddbdabaaacabcacacbcabddcaddaacddcaaabadbdbccbcccccdddccbbaaacdddcacacabdbabddacbacddcbddaddcbddbcbbbbaddcdacbcababdddddbcaacdcddbcbbdabadcddbcabadcdbadacccdddcbdccaacbdaaadccaaaaaccbabcddbdabbacabdbcbdabdaaaaaababaaccccadbcbbaabcdcddcabdacbbdacddbddaaadccbbbaddbdccccbadddbadabdbdbdacdbcddabdbdddcbabdabddbadabdbcbaabacadaabcbcdcbadacddbaaddcdadcaaccddbdcbacaaddddbccadadddaabbadbbbabadcabadbdadbdaadbadccccdcdcdcddbbabcadbdaabcaaadabaadaadadaaccbcbdabaacabcddbbdbabbabdccbcdddcbbbcaccdaaaddddabaacbcdbbcbbddcdbcddcacddddbccabbacbcbcaaaaaacdcadaccbcacaaaadbdbbcbcdcaccccbadcbdbdccadbccacbadcacbdaacccacbacbabaaaccdaabcbcabbdbdddbbdbabadadaacbcadcbdabcbacccbcabbcdabadbaaccacdadbabaadbbbadcaabbcaaddadadbabdbbcbdccadbccbdbdbbdddbbddbbdbddbbcbcbcdaadbcbacabcddaccbaadaadabcbbbcadbbcbbcdcadacaadaaaddbcbabbbcdbccdbbaaccbdbbabaadbbaaabaadbcdaddadabbdaaaabdddbdcadbcbccadbdacdadacdacddcbcabacbbabcabbddccbabdacbbdccaacbbdbaacbbadbdbacbcbbbdbbcadcbdaaaabbaccbbdcdcdccabbbcbabbbbaadbccdbbbbddbcdbabacdddccaabdddcacdbaabdddcbcaccdacbbaabdbcaddccdaabccbdadcdaaabbddbcdacbcdaddbdadabbcbbadacbcadbcbcabbdaacacbacabddcdddaadadcddbcbbbaccbabddccdcabbdbbbbaaadcccaacabbacadadabdcbaadcbcbbadacabacbcdbcdaccdbdbcabbbbbcbdcadadcdabcbbcbbcdcacabadaccaadcaddacddbadcdcdbdabdcdbbcccddcddabadadaaaabbdbadddacbcacdbbdbdbadbbaccddacbbddcbdabdacacddadbaaddbbdaddbdbabaccdbddbaabcabaadaabbbbacdbddccbbcacdacbdaddcbaccacacbcdabcaaabdbbddcabadbaddacdbcaabbdccdadcdbadaddbdccdbabdaccdabdbcccbcbabacbddddbddacbdcaabbaabaacbbaddbdaddbccddcabacddbccbcdcadcdbbcbcaccacaabcdabcbbdbbbabccbcdcdcdacdbcaddddcddaaacadadddbccddabcdbabbaaddcdabbdbdbdbdaddcdbddddacaadbabbbabababbbdddaadcbbdbbcbaacdaaaacacbdcddacbabdbbaaaadaaabddbbaaccddadccddbdbcaccadaacdadbacdaddbabbcbdcaabddabcdccbcdcaadccddbbadaadbadabbacadcdadabcaaddaaccaadadccccacacadabdbbcbaaacbdcdacbbabbacbabcbdcabcbdacbaddabbcaccaadcaadbadcdcbabcdaddcdaaacacbcbcadbdbbababcdbcbbbdaabbdabacaaddccbcdcbddcdbdbdaaaacbdbbddbddbacbbbbbcbbbbccbbaaccaccaadacadcbabdadcabdbcbabcbaadacdbbdbcbddcdbccccddadbbacacadddccddccaaadbddacacbcbbbaccdaaacddbcaadbababbaaacadccdccdadbdbcbcaabbbacacadbbbcddbdabddbddcdaccadbadacbaccabbacbaaaaddbdcbdbdcbbbbcacbacdbdbdcdadddbccadccddacccbacacaabaddbcdbcaccdbcbabdaccccdadbcbbacddaabbccdbbdbbdcbccaadbcdcabcacdbabdbaddcbaccddbdbbcdccaccadccdbcddbbcaadaddcadaccdbccbdadcbccdcadaacadcccbdbbddbabdaddabbadcccdcbaabdabdbdccccddaaaaddabdbcabdbadadbcbbdaabbacbdccbdbadcadcbcbddbabcbacdbdbdcadcddaacaaacdbbbacccbacabdcccdbbbaccbadcdcdadcbaabaaaabbbabdddbcdcbdbabbdbabadbbabcddcbaccbbbbaadddcbabdbcadbcaababadaabaacbbbaaacabbaccdadbbddccccadcdbaacababccbcadabcacbccbcdabbcbabcbcacacddcacacbaabcaababcbbbdcadbdbcaadccdaaccbcccbcdadbddbbccdcdbcdcdbbacdccbbcbcadaabdbabcdcbabdaaacabcacdbbbaddabdadbaaaacccdaadadcadddbddbacdaadbbbaadbabcddbdacbcbaddbaccacaadaabbbcbbcbdcacdaccbddbcadbbdbdcadbdcdbcbbdbbbbaadbdacaacadbabaacddacdbcadadadbacdacbbbbadcaadbcaaaadddcdaaacabddccbabcdacbdcbdcccaadcababdbbcabaabbbbbdabddcbbcdbbdddcaccdccadabdabcbdbabcaaadcaaabddaabbbacbcdcdbddccbbcbbdcacbccbcaacddbabcaaaaabadcacbbabddaccbabbabdcbccbbbcacbcabcbacaaadbbabcdadadcddbbabdabcadbabcccdcdcbacaabdbddbcacbadbcaabbacdabcbadacbbaccdddaaabccccdcbdddaccacabdbadaadcdcccddcddbbbaddbdbadabadacbdadbdacccaadaaaacbadcbcaaddabdccaccdbccabcbcccdcbccaccabcdcadcddabcaccdabdcbdbcaadcccdaaccdbdcddaaabcacaadadcabdbdbcdbbaacbadaacdbaaddcdbdabbddccdcbddaadcccdaccacacbcbdccacabcacacaaaaddcdcbdabddcbadacbbbadacaaabbcacdbdbdbcaaadcdcbbaadadacabdabbcccaccdaaacbcdaccacddddacbabccdddcbaccbcacbbbbabaabacbabdddbdbaddcdcdbbbacbbdabaabbcdcbbcbcabbbbaddaadccbbcdbdcbddcdcadbacddabcadbdaaccadbbcdadcdcdbddbddbabbcdbbcabbcbbdababacdddddaabcbddbabcaadccaadddccdbccacadbabdddbcccccdbdacccbdacbabcbcabacadcdbaabaadcccbbcabbaabdbdbdaaabddabaabaabacddbcacbdadbddbaabbcccccdacadadbbcabcaadcdddcbbbcadaddbbdbcdccaadadadacbdccabdaaadacccbacbdaabdcbcacabbcbbaaabbdddaaccabbbbadadabcaddbbbbcbbadadacbdbbbcdddbbacbbadcbddccbadcccbccadbddbddaabcbddadbdabbbabccddaccdcaabcabcdddbddbaaabaadaacbbadaacaabbbbadaccdaacaddcbcbcabcacbbbbbbdcdbaaccbdcabbaddacddaadbabbbcabbbaabbaaadbddccacbbacccbacdbbbbbbdbaaacabdcddcccbdcccabdcbadaacadadcdccbbaadaaababdadcbaddcccbccabaaabccdbadaababadabddabacacbddadababdddccabddccacddcccdcddababccbbdacbacdbacdcdcabccacddbbbbbbcccddbaaaacbbbdccabdacdcaadccbcbdddcdaaccacddbdaaadbcbcacbbddadadbcbabcddababdacbddbddbcbcbbcbdbbaabacdbbddddbcddabddcacbdbbcadabcbdbbcbdcaabcaabcbaccaacbcdacdaabcbabcdddcdcdcccbbbddddaaadcaddcabbbabcccdbaaabdcbcaabdbabbbddddbcabbbdcbabcddadaacacacbcdcaddddcbdddaaaddcababbaddbdbcacacbbcdcbdbdaadacaaabdccdbbcdbdabaaddbddaaaacbbdbcababcbabcaaadbccbdaddabcbbcddbbbadbcdcdcbbabbdcdaabdaacbcdcdabcdcdadbcaadbadadadbcdabbddbddcaddabdddcaaadabdcaaaaabbaabdacdddaadccaddbbbccacadacdcbddcdccddcccbbdaccadbaaccdcabdbabddaddccbdbbbdabadacdcaaccbaccbcbbbbaddcabccdaaddccaadadcbcaacdbbbdacbbadacbadcaddccbbbbcbadbadddadbbdaccacbcdcaddaacbbcdaaccdcdcdddacaddacbcbdbcbdbbcccaadacdaaadbcadabbdcbccbdccabcccadbcaababdaadaddcdadababdacbacdbabcadcadaaabbaaabacbddabacdbbaacccaacbdabbdddcadaacbdadbdaccccacbbacbcaaadccbacdddbbcdcdabacbdabcdcddbdccbdddbdbbdbdbcacccccddaabcdbddadaaddcbaadbbdbcddcbdadbaccbcadcaacddacbcbcabadcbaabaaaddbbdbaaabdaacdddababcddaddcbaccaccdbcdacccbbadbcdddacdcdbdaadbccabcdabadaadaadddbdadbbdaadcbcdbabdbbbbdcbbadabcadadaaacdcdaabdaddbddcaaadaaadcacdbddcaaadadcddcdbcaabcdacaccdaccdcccdacbbdddadaaaaddddacadaccdabcbaacabbaddaadcabbddcbbabaaccdbcdcbbadcadacacbdabccbcdcdbcadadcbaabdacaabaacbadbbbccdaccadbdbcddcacdcacdcaccacdadabbcabcaacacdabddaacbdccddcaddddaabddccbccadaadbcbcaaadbdbbbadabdccdaaacaccdbcdddcdbcddccccabdddaacbdcbddcaabbcacadacadbcbabcdddcadccbdabbaabddcdacdbcaccdbdddacdcacccacdacbacabdbaaddabadacbcaabcabcbcbabacdcaaddccbaabdcbabdcdbdababacacdbcdccbdcbbbdaaadddbcaadccbbadbabdbbbabaabbbdcacccadacbcbadcdccccccadaaccbabcaddddababacaadbcdbcabdabadcbacabaddbdacbacacaadbaddabbdcbcbdcacacbaabdddbcbdcadaaacccbccabdcccabccaddbaabdacadcabbcabbdcacadccddcdacbddbcbddbbadabbadbdadadddbdadaaabccccbccbdccaddabccbddcccacccabacddcaacacaaabddcbdcccdabdbddcaddadabcbabbcabbcbccccadacbcbbcdaacaaadccbcadadbcdbbabbacdbdabccaacdccaacaadbdcbacbbcbbacbcdbccccadcadccdacdaddbacacdcdbaadadacbbbabdbcaabccdbabbdcddabdddbcabbaddbbdaacadbbabdcccaccddddccccdcbdccabcbbbadabdccbadaccccbaabadcabcdabdaaaccbdadbbbdbbbbbddabdbdabbdbadcacddbccbabaadcdbdaabaddaacddcabaaabbccaabbabdddccdccaabcaaadcabaacbdcabbbcbdbccddadbdcbccbabadcccbaddccdacccbbabbdcddbbcbabdacdadcaaaabccababdbbadbdcacaabacbaacaaabddbaaabbcdcbbddcccdbaddbbbbccbcbabbaaacdcadcbdabdcdabbdcddbbdcaacdbcdddbcddbbcbcacacbdbbbaadbaccabdabadcccaadbbcacdabdabbddbabdccadbdcccddbccbabbbbdcbbaadadcddacdadddcddabbbdcabbacabbcabcdcbcdddacbdabccacbbabaadbcaacabbccbadcdbbbbbcaabbcdcbacadcabbcdbabbddbaccabdbcdacdaadcdcdddabbdacabdacbdcdcbbdadacadaabdcbbddacaddcaadbacdadacbababbddcccabaccbadadbcdcabacdadcdbdcbdaccacbdbbabcbabbddbadabcbbbcccaadabbbccbddcacbadbbbabdcacbbababbbacdabcacbcbcdcdababddaccacaddcbaaacddaadbddabcbbabccbbdacbabbcbcabcbbdbddcddcdcdadabdddaaadcddcacdcdaabdbbacabccaccacbdaccadabdcbdcbcdaadaddcadbdbcddccccabbbadcacaadaadaabaadaabddbbbbbddbcddcabdadabbdbbbdadccaabbbaaccaacbaddbabcdddcadbcdababbbadaacddaaddcacabbdbbddabcacddcabdcdbacbaccbdcbacadcddddcbbabdcbdcdbacdbcabaccddbadddcbacabbbdcaaaabdcdbcbcaadccdcabadbcdccadbdbcdbdaacbdcdccbcdcdbcdcddbadbdadacccaaabcadaaaaadbbacdbdcacbacbaaaddcacdcdddbbdddddbdadbbcdabcaadaadccbdadbaaaabbacbdddacdccdacdddbdddbbbdababaaacccabdcbbbdaaadcdbacddcbddcaacdaabcbccadabdacbdaccacadbadadddddcacccbcbdccadcdadbdcabaaabcabcdcaaabcbcdaddacaacbbaacdcbdbbacdadabccbbbbacbbbddabcbabcdbdbbbdccacaabbbcbbadacadaababcdcbbbaadbbaaabcbdbcacccbbbcdcadadbcdaaccadabdadacdccccdcdccbcdaacbcddaadadccddccdcadcdacdcadddcabadbabbaacaacadbabacbcdcacccabaaacbdddcdaccacccdaacbacccaddbbccacdaadcdadddbabddcdbacccaabbdbddbcccbbdcaaddbaddadddadabcccbbdccbdbbbdaaaaddddacacacabcaabddbbdbccdbcbcdcbabcbbbabccacdbaddbbcbaacdbcacbdbcbdcddadbcabdbbbabdcbcdaaacbccbdadaabbcabbabcbcbcccdbdcdccbcbacdbcacbaaacdaabccddddcdcadcdacabcadcaddbbcdbadcaacbabdcdacbdccbdadbdcdcdcddccdaadadaadcddcbbcbddcbadddabbaabcbdabcabcccbcacdbabaddcccccaccdaddaddbaaaadbcccdbdbdaacabcadacababcaacaaacbabdbbcdcadbacbaadcbbbcabbdcdbcbadcbadcbaacdcbddddcabccbddcabacdcbcadddcadcadaadddaabdacabdbcddbdcdbbccadaccbcdaadbbdbbdbdadbbbddcbddbdacdbcdcbdcabcadcadbcbdadbadcbcacccabadcabcdbaaddbaaadadacabdaadbbbcbdbdbbbbbacbabaabccdcbcbbbaaddadaccdaccdcbddadbdbbccbbbddccabbdbcdddddbadbacccddbcdbdadbccdbddadbbbdbadacdbcadcabccbdacbccabdaabbaaabacccbcccccbaaabcaadccbabaaaadbcbddacccdcbdbaaaacbabdadaaaacddbcabdddbdcdabcdccccbbbbcaabdabddbbddddbaddadaaacbbdbabccbabbabddddacabadbbdadaabddabcbababddcdbadaacddbddbcdcaaccddcccaaddcbbcbddaaccdcdbbddacbbccbcadadddaddccdabbaccadccdacabdcdcaabdbdbccaaccadbbabbdbcdbcdbddabdcddbddaabdadbdbdbcadadbcddaddadabbbacacdaabacbcdcbcdcdcbcdddabbaaccacddaddbccaadbaddccdcbaccababcdbcccabaabcacbdbccdadcbcdaddbdbabcbcdccbbaabbdacabcbaabbdbcbdacdddccdbaabcbabdccaccdadadacbbbbabcabdcbcabbabadbddbcacbabccadbdbdcdbaaacdcbcbabbaddccacbbacdbcbadbbcdbccbddcaabbcbddbcadadaacdcdcbcadababccdbaabadbccddddbcbcbacccbaccccaccbadabacdcbadbabcadababdbcdccbdbadccababdcbddacadddccbcacbcccccbacbaacabddacadcbbcdbcaadadddbcadcdbbdddddabcacbadcababdbbbccbacccdabdcddddaacbdcabacaccbadacbcabdbcdddcdbbcbcdcadddbadccbdbccdadaaacdbbbcacccbcaaaccabababbcbabbdcdbbcabbdaccdaccbabccaaddddcbaaacabbdcaddcdcdacaaccacdaadbddddcbadbcddcacacbabbbcaadbabcabbbcacacacdcdacbddaabbbabdaccbbcddcdcacccabaadcdcbadbadcddbdbcaaacdbdadbddabdacadabbbddcadbdabbaddcaadcbbbadcbdbabbdaaaccbdadcaddcbbcbdadddddbdcbbcbadaaadddadaabcaabbbcbbdaacbdcaccadaaacaadddbcabcdbaabbdbbadbabadcabccdabdbdabbadaabdcdcacbddcaccacdabbaddccbccccacbcdcbacddbdcababbccdaddccbddbdacaabcdacdaadcacbddcabdbbcbababdcbbcbdccbcdbbabcbcddbddbdbcbaaccbaaccabaabccbdcddbcbbaadcdbbdddcaaaaacccadcaacddbaabacacacadbbcbadbdabbdbbacbaddabdaadbbbbbdcabdcbbddbdcdbaaabcbccadddaabcccadcdccbddcaccaabbadcbdbcaddaabcddbacabcaaddaaccdbbcdcdadbddbacaddbbddbadcaccdcabbaccccaacbbaddaadaccbdaaaaccdacbdbbacbdaabbcddddadbbbbadbadadcaddcdbbcadccabbccbcbaaacccbdbabdadcbbdccdbbcbdddcbbdcdcbcacbdbcbccbabadaabcdddbaaadcacbacccacdaadbdabccadbaacbddbaddcacddcbcaaaabdcbabacabbbbdccdcccacabdbbccacaaaccdabaadbdaabcbdbdbbcddbcddbcbdabadadacacbbdcabbcdccdbcadacdddbbdbbbbdabdbcbcddddbdbacbcacdddddddbdbabadabaccbbcbabbaccadbdbabdacdaaaadbabacbddadcdbcbbaacadadaabbbcddccaaccabadaddcaccddcdabdcccbbcbddadaaddaaabcbaaabcddbcaaabccacabbacbbccaacbbdcbacbddcacaddbbcbacdcddddccdcaccccdcaadcbaccaacabbbcbcbadcabaccdbccacdcaddcccaaabbcdbaaccbbaabbbccdcccbdddabdddbbdaddacdadbbcddaadcdababbbdbcbadddbcbccdccbaccdacdbbbdaaaccadbaaaccbbbadcabcaaadcbdcdacbddadcccabcaaacdadccbdacaabbddbdcbcbdbbbaaaaccbbabdddbddbbdaccddbbbbaaadccbdadddcbdadccdaccccabbadbdababbbbabcdcaaacbdcccbaabbccadcbaddcbdbbbbdaccccaccdbddabccacdbbcdbbacdbbaddbbbdabccbadccbadcbacdbdcbbdcdcadaaabddcddabdaabcdbbbbdacbbcdbaadababadbdabbccbcbdaddbbddbaaddaccdbbbbadbbddacbcbabdccaabdaadbbabacbadaaaddcbbaacdbccacacccccadbaabacbdbdbdbaadbabaabccdbabbcaaaadcbbabbbdcdbddadcabdccbaabaabbbbcddccdbaddacbbaaabcaccadadccdddccbbdcdcbccbbdbbdbbadbdddbdcbaccacbbdadddababdccbcbdbaadaabadbabddbbcaabcdbabbaaaadbbacacbacaabbbcdbdcdcbadcdbbcccbbcddcdacabcbdddabdaaddcbabbabddccaacbcbdddabddbdbddcdaabbaaabadadadbddacddccbbaddbbbbaaacbadbdccddaabaaaaabccbbbcaccbdcadacdccbbaccacccabdaabbbbbcadddcadabbcbcbacaadbaadbcaccdadbdccdbbaddbbacdbdccbcacccaadcadbaaddacdbadbbdadaddccbdccdabcaddbadccdacaabadccabbbddbbbbdbcdbabaaaaddacddbcaccbccbabaddcbacbccccbdbccdadbccbcacacddacddcdbacbabccdcddadbccccadbdaadabadbbaaabacccdcdadbaabdcbcabadbaaaccaacdabbcccdccaddadadbcddccbccdcaadbcdababbdbbbaaabdbbadccbcbdccabadabbcccdcbadaadadaadaababcabbbddbbdbcddbdbdbdacddcbabdbcbccbdccbcdbcddcccbdabdcccbcbbdbdbcccaccbbcdcaacccbaabbdacdaadbdadadcbcbbcabbddbdaadaddbaccddccdbccddcadcddcdccacabcbbaabcbadcdddcdbdaacdaabdbadccacbdbcbddcaacbdabdddcbadaddbbddcdcbdacaccaabcdbdbdcdcddacccdaabbaddbbbadddddabdaacbacdbdccdadadaccccadabccdbbacddaddbdccbcbabbdbbabbbdaabdddcdabbadddaadabcabaabbbacadbcccdabcccddbddccbbcbaabbabcbccbabdabccbaabacdaabcadaccbbdbdcbcccdabdaacbbcbdbcbabdbbacbbabbaaabcddbaabadbbaaabaabbbcccbcbbbaabdbdadbdabcdadaccabbbcabdcadbcddcccdabcddbddacdcacccadcaacbccaababbdcaaacbabdaabdddbaccbbacadbbbdbdcabbcaccbacdccdbacbcdadabbaabacdbcabbbbadadcabaccadadbcdabdacdbcbbbbabcccbadbbbcaddcccbadddcdabadbdbdcadacbababcbaaccdbbadabbdabdbbbdadcabbccaacbbcadbbbccbbbbccbdacddadbadabcdacaaaaabcabcabdcbbbcbaadaddbcbcabbdaaccaacdaaadacdbcadccbaccdbadbbadddcbbbacccdaabbbabcbaddcdbacabbcbddacddabaccbaabcaacdbaaddcbaadacbbbcabdddabdbcbcdcbbaccaaaddcdcbddbdbcaddbdcabccdbccbcddcabacadaadcbcbbcdbdaccdabadddacdbdbccbdddbbbaccdaadbbcdcdabccadbccdcdaaabaccbadbbdcbbcacdbabccabacbccdacccbcbaababcbcbdccccadbbbadddadbdccdbcaadcbddcbbbaaabccaabbbcaaadbdadbbbddacbaccccaaadbcdabcbddddbdbdcadaaddabbbcaabacbdbdccccdacdbbbdbbbdddbcadccbcacbcadacbdbddbccbcacdadbddcccbbbadddddbbadacaddbbdaabccabadcaccaaddbcbadbabccaabdaaabcdbabcddcddbbcbbadadcacdcbcacbccbdcdbcbcbcddabaddbcccbababbdcdbbbcdaacadccdbbdcbcacbadcbbbbddaddbcbcdbbcaabcadacadbdaccbaabbdaaaacbacdcabddbdbaabbdadccbcdbddccbacacaaacababbbdbdbddbbaadddcddbbaadccbacabdacccabbcacbdbcaaddadabbbcadcdcdacddcbdabcabcacddbbdbcacacaccadddcbdcabbabdcbbccbaccabcdbabcbbaabaccdcabbbbabddcbdcabdaaaabdcccdcbacccbaacdcaadcbcdccacdaacddbdcdadadabbcbcdaddcdcbccbcaddcbdabcbddababaddbbdacdaabbcaadcabbccaacaaadbcaddddaaacbacbbaadacabdcabcababcbadbacabddabbbacadcbcaaaadbcdcaadccabaacbaabadaaaabbdbaadbcbdccbacbbccccabdaaadbaddddaaacabdacacbdcdccccddcccabdacaacbdcabcabbbdbcddbdaddaaccddbcdbcbddbcbdbcdaaadcbcbcdbcbbaddadaacbdcbaaabbaabaadacbaddadbbcddcdddbcdbdcdaacccbcccadadadbcacabdccbaabdccdcdddbcaccdddacdadbabbdbdcdbaadadddcaabccabddbdbbbdaacbacdcccddadaccdcbddddbaaccccccacacaccdbdbcbcbdadbdabcaadddddadbccbbdcdaabdbabbcbbddcbabacddcbbdbcabccaacddccbcccabdcbbcccbabdcdabaccddbbdcbbbcdadbdbbdbacacdabcdabcbdabbdbcacdcddcbadcaadadcabddcbadbcbbadccacdbdbaabdbcbccbbccbcaddcacbaaccddaaccbdddcadbcdcccabadcdaabcbbcbccadabcbbabaabcaaaadbcadbadaacbaacadcaadbbcabbaadbbbccbadabcccdbadbaddaccdbcbaabbdaddcbcdddbbbbabcacbacddabccbccabcbbcaccdbbcabbddbcbadaccdcabcdddcdaccbdddaccabbdbdbacdbbdcacdcadcacdadbccddbacaddbabcbbdcdddcadbdcaddbbabacdcbddabcddbbadbddcccbbbddcabadcdcaabbcdcddabcaccddcbbbcacadaadaaaadadaccddaadacbccdaabdbbdbdcaddbcdddabcccdcabbacdddabdcddadccdbdbcbcdccacaabdadadbbbadabdbdbadccccbccadbabcaadcbabbabdbacaaadcdadddcbacbaadcacddddcacbadabaccbcdddbabcbdbcbbbbaacabaacbaacddcdddcacbdcdbadbdbcddcbabbaaaccabdbbdaacbdacaadadcaabccccabbdacaaabaccddaccbbcdcbdcddbbcdbacaacacaabcaccbdabcadcaadbdaacdccbaaddaddcccabacabbbbacadaacbcadbbcdcddcaccbdbbcbbbcabbacddcabcdaccabdcbacbbbbabddaccbdcbcbbcabdccacbbcacadacddcccabbbcdbacddbcaacdcbdbbbccbacbaaacaaccacaacaacacabdacabddabbcdcaabdcdcdbadddbddaadadcbcbabdcddbbaddbacddbcaaadddabbcccbdddacbdabccddcadbddbabbbacbbabbcdcaccbcccbdcdddbacacdcccdcaaacbbbbbdacadcadadcddcaacdaacabaacbccbcdabdcbcaddabbdaadcddcbadcadddbabbaddbacbdaacacddabaacaaddaddabbbcddadcdacbaaaaacaabbdaadaacadcdbadbdbaaddcbbbabaaadccbdbacacccaababaacbcaaabbadadddbaaadbbcbadddddbadadacbdcbabbdcbcabbcaccacccdbdbdaaaaccbcbbbbbbbbccdcdaadabaaddaabacdbabadcbabaabdbacaadbaccadcadbdbbddcdbabacdacdcadbbddaadddaadabaaabdccccdabcabdbcbcaaabaaadcddabddddccadbddaabdadbddbcabbdcaaaacbacccbaabacbbccdbcdabcccbbcabaaabaddddbbabdbadbbbdccaacadcbdccdabbdcccdbdbcddbcacccdbccbbabacdaccddbbbddaabcbcdbbbbbdacacdbdaadcadabbbdcadddbcdcaabcaadddbccdddcddbbacdbadbacbbccbcbdacdbbadabbbcbddacacdaaabadddbacbdadcdabcacabdaaabdacadcccdcbcbdcdadccbdababbbacbddcddbcdaabddbdbccbdadcbaadadacaaadcaacbbddbccbcbdcaadcabdcbddbacbbcddcdcbadcbaccdadadabdbdaacdddbbdccaabbabaabbdcdddaccbbddaddacaddacadbbadbcdacdadacadccacabccacbcadadcccdcbddabdcdabbcdbcdcacbcabdcdcacddbacdacdccddbbbbbbabcddbcaaccacabccbaaacaaabaacaaadabdcccbbdcccbbbcadbbadcadcbcdcbcbcbdccaccaccababbbadddcbcadbbbabcbdcbadcddbcccaadcbbcddbcdbdbcdabbbddbbacaababacaadbaabcbbaaaabddddbdabdaabbbdddbabdcaccbdcbbcbadaabdcaaddaacaaccbccdbcdbaddbcabdcdadbbbaabbbbdbcdbdbdbdcddadbcbaabbadacaccdcccbdcccccddacddabbaddcaddccabbdcaabbbaaccdcddaabaddbddcbcbbaacdbbccadaddbaadbabadbcbaabdcaabddabacdcdbbddabdcdaabcbdbccadcbdcdadbacdabaabbaabcbbbcadbbcadabacacbdaababcbdaccddcbdbabaacbacabbccacabccdcbabcdcabdcbcbbaabbadcdbbbcabcbccadbadadbadbabaddcabdbdccaabaddadbdbdbccbcccadadaabadadacddabcddadacbcdbdbdcbccddccaccdaabdccabbdcccadbdcbbcccabbcccccbddbabcaaaabcaddbacadacbcbbabbddbadcdcadacabdcddbcdbcdaddccacbdabccaccbdacadcabdcdccadcbcbcddbbcabbbaaacacacabdcbaadcaabacaabbccadcabdbbbcdcdbcdaaadbbbaacdcbcddcbcbabcbcdaaaacaacbdbbaddadabbdcbbabbccbadcdabadbcddddaadcccddabbcbbdcbcadacdacadbdbccabacdbbdcbbbbcadbdbabcaaadbbcaabcbdadbcacdbbbbbcdddbadbccdacabacaddbdaddcbdbaaccaabdccadaacabbdbaabddbcabcadadccbdcbcadaadaddbbdabaaaabcdbabaadaadddcdbdaaabaaabbdaabdbbcbabdbcddcbdcccacaaaaaacaaabcacdbdadbabbaccbdddbddcbbcddcbddaadddbbcacbbdcbaaddcdadadbcadcdcacabcbdcbdaccadcbcccccdabcbaabcbacacadcbdcaacaacbacdcaadaaddcdcbacccadabcccaaabbdcbabdbadccdcbcbcaabbbacabaddababbddbbdcadbbcccdbcbbbaadacdbbbbaaacddbccbabbbdaaccbccabccbddaddcbaccadcacccdacbabdbbdddbcbadadbabbccdddcadddcacaddaddddbcadcccdaacbaadccdbbcbdbcbbdcdbbdbbdcacbbaaabddddcbadcaaaddddbbbcadabbacbccbbdcaaaadcdbbbdacbddadadbbcddddabcbbdddabaacacdcbccbbaadddbbddcaadccbbdbddcbbabdadcdacaabbbdabbbadcbabbbcdbaacdabcadabdbaccbcbbbddddcbbabdaaddbaabcabbadacabddcaccbbbaaaabcbcacddaccacdacccaabddadbcbacabdabcdddbabdcbbddcaddbdcdaaabbbacddadbcaadbdddbaaabdaabbcacdadcbdcdbdcadadcdddccbdbaadaadddcacddccadaadbdcdaddadcbdaadadcbdcccddabaccacbcadacdadcabcdcbaaccbbbbbdbdbabbbacadbabbcaacabbbccdcbdbdacbdcadbbaabdbdbcdaaabdadcabdbbcccbdbabddbdbcddaaddbbdcdcbcacbcabcdabdbddaccbcaabdacccccbcadadcabccdbddcadabcbacbaddccbaaaccbaddcccaddcdcaaabbaddacdbbccabcaacbdadabbbadaabccaadcadabbdddcaccdcddcaabadadacbdcddbbcdadbadacabadadadbabcdbccadcabcdcbdcabbaababcbbddaadccacabababbabbbadccbcbcbdcacabacdbadaaddbdcbbcbdcccbcbadbcadabbccadabbbdbacbacbacbbacabcbaadacdcdbccbbcddccbaababcbdcdcdaaccabbacdbaddcbacdadcdacdddcadbababbdccdccaccbacbbdccabddaacdaabaabdacdacadcdcaaaccabdcdbcadcbcccacadadbadbdacdbdcadcdbadacadabbaaddccddddbdbcbadbadcbbacaddbcbbadaddaaddbdbcbcabbdddbbcbcaccbbdddbccacacabaacbddbcaddcdcbbaacdaadbadbdcdcbdcabacbcbccdaaccbdaabcdcdabdbcaadddcdbadbbdbdccbbbbaaaaacabacaaccadadcbabdacacabdccccbddbaacaaccccaadcadbadaabaabccdaabcabdcbadcabcadcdcbbdacdbdadddabbccdcbcccdababdbbbdbdadcacbcdbaddabbaabddbdaddabdbaccabdbdbaabdaabdadbdacacacaabdabbabadabadbbdddccabaaaadddcabbbacbdacdccabddacdadcbccacabacdabdcdacbbcddcbdaaadaccabcbadcbadcdaddbadabadbcdcadcadbaaadbcaaabcdadbcdabdadccdbdcdaaaddbcdccaaaadbbddcdcdbabcaaacbbabacdaaaacadddcbaccbcacacbbadadacdbabadababcabadcbdadbcbadccbccaaacaaaacdbacacadbaadddabdcbcdbaadcadabcccbbddbdbddbaabdadcbbbcddacacadbdbbcacabbdbbabdcdbbbbdbccdbadbacddbaddbccbcbbacbcccabcbcdbabcabcbbcdcdcacbdddccdccdccdbdbabdccaabddaabcbcabadbaacdcdacdccabbcabdcccdbbaaacaccddcdbdabaabdabadabcacbcabdacdbbcdacddabbcddddddbcadadabaaacbbabcbbbcbdcbcacbcbddcbcbabaadbadccccdadbcaabddcbbbabacdcddcdbbcccdbcacabaddcbadaccacabbccbbaddadacaabdaaaccccccdacbcabdababdaacdbbdbbcacdabddcbdabdadbdbdbcccadbcadcdcccbccbdacdbacdabdcadabbbbdcdcdcddcdcdaddbaacabacbbbdacaadddbcbccbcdbbbcbbdaddddabcbcddadaacbcaabcacdbadccbbcbcaacadcddbbdbadcddbcabbcdbcdaabbbdadacbcdcbbbdbabdbbcaccccbabaccdddcccdabbdabdcbdacabdcacaddbbbcacdcdaaaccbccabcddbaacaaacacaaddccaacadabaabcbacbbabbbbbbaadcbabaaaabdcaddaacbdadbcadadbbbababcaadccabccbacdabddcbadbdccadbdddcbcadcbcccbbabbdaaddbcaadcbcdadbbcaddcbcaadadaabcbaccaaccabababdbcacaddadabaccdadaaccaccdccbdacccbdddddcaabbadcabacdcccdacdcdbcbbbdcbbdddbbcacaacbaacbdbcbbadbabbcbcaaaaaacdcaadccbcabadddcadbbacbddbdbbddbcbacdbdbdcdbcaaacbadccbdbadcaadbdbbcaacdacbcbdabdcaddcdbbdccabdccccdadcdbdccbabdcdbaddbbddbbdccbdacccbcbcdbbbcdadcadccddcacacdcccbdabaacbadddbababcdcbdabdbdabcbabcdbbddacccaabddbdbbadabdaacbcdcdadbbbbdacdaaadcdbdcadbbcadbadcacacbdcaddcaacbbcabaaaadcddbcabbbabaadccdbbccbbbacccbbdddbbccacccccaacbbbbaccadadcdbdaddbbcdaacdbcaaadacbabdddbaccbccbbacacbdbddadcdaccdcbcaabbbdaaccbbccbbadccdadbabddcbdcbbcbdbcadbccddaabcacbdbcabcdbcdddcbdcaacbadaacdaccdadddcdacabaddccdccabaadbabbdccacccacadaacbadbcaabadbbabbaaadcaddcddbaaddcdcdbbbdccdddabcaddadddbdddadbcddbaaccdbacdcadadbcbcdbababaaadbcdcacacbabddcacdbcbdadbcdacccbaadbbbccaaabbbadcabdbcdccababdabdccaaaddadacbcbbcadcadabbbaaacddcdbccaccbdcbccadacabbcbcddcddabbbddcdddccddbcdabbabcddbcdcabbabcbbccbdbcadadacdcddbadddccadcccbbccdccbbaadaadcddbadbadbabbcadcdcccaccbbabadbbbdbdcabdaaabccbaccacccbdbdbdcabadadcbcabcacacdcbbbcdacdbacbccdbddcdadabbdddccaacbadcadbdbdcdcddbcacbbaddcdabbddbccaabaddabbcaddbabdccddcdbacbbcdbcddbaccbddaaddbcdddaabaacdcbcaddbbcdddcdcaacbacaabbcdcdcdcabaadcbbaadbbcdbddcdbbccbccddbaadbacacdababdbbddddcabcddadcbcccbccadacabacdddddbbcbcbbbdbbbdbdcbccacadbddbaabbaaadcccbcabbdaacdabaacdcaaabdcabbcbcddcdbcccbcbbcacbcdbdcddaaaaacbbbbddadaddcdcbdbabccbdabadbaddabbdcdbcccddaacccacabaacdabacbcddaaccbbccabdcbacadccacbbddcabcaabaadabcbbcadcabbaacdacbdbbacbdcbdbcdddddbcddcbbccdbcacbbdcbbadddaacbdacdbbdcbbcaacdccaadadbddbbcbabcbdbbaaabcbacbbadbbcdcadbbbccacbaaccacbbdcdabcaddbbcbdadaddbbaddbbcabbbcdadaaaadacababbdddbabadadcaadbdabbbdcdbaacacddbbadccaadabbababdccbcabababddcddbbdbccbbbadabcdadbcbbdbaacbaacdbacabbbaaacbaddbbacabdbcbaadacacccccccddabdbbabbdabdbaacaaaabcaddbaccccdbaadddacbdacbdabdccccdaacddbddaaadddccabbabbbdddaadbabdcbbadbbdbccaadcadcddbdacbadbaddcdbcbddbddabbdcaaadcdbacabadadaddaadccddbaacbbdbbcabdadadcdccdccddadaddacdcbabcdacadcbcabaccbaaadacabdbcaacddcaaaadcddcaacdccdcdccbbdcbaccacaddaadbdcdaddcdddddbadddbccbaabdaaddbbadbadacdabddacacbdbdbacccdacdbacbcbadcaccdcadbdcabddccabcdcabdacaadaacdcdbbdaacaadaacbcdcbdaaccdccadbadacbbaaabddbbbdccadbbcbacbcbbabccddababddbaacbaabcbbdbddadbabbaddabaacabcbbcabbdcdcbcaabaabbdbabbdaadccbdcccaaabbddcccbdadadbbabaacaccacacbadadddbbccbbdcbaabdabdbbcbcbacbaddbdddaabccbdddcbdcdcbbbacdadbcaaccccddabaabcadddabbbdcdccddbdcdccddcbccacabcddcbbadababbdadacbcccddcabcadcdccddabbccdbaabaacddbcbcbdbddcabcbacdddaabacdccbcabddcbbacacddaabcbadabadadbacaadddabccaddcdacbcddaabcccccbbaaccaaccdcbcddbadddccabcdcbabcbabbbddbbcabccbbaccabdbaccbbcadbacaacccbabaadccbbdaabadbcdabcddbdbbdbcddbabadcacbddabbbbacdddbabddccacdddccccaadaabbbbbbccbbacbdabdcdcdbcacdbbbaaccbbdbabaccbdcadcbaabcbdbdbadbccccdcaaaddcbddaabdccbbbbaaabdcdbacdcdadabcdccddbdcdabbabcaccadcbcdaaadacbdccadbcabbacdddcbbdcbdacbbbcdbbacdbaadaadaaddadaabaadbcdacccbcbadbdcdaccddaabdbcadbbcabbdddadddabcdcccacacbccccdaaadbbdcbdcabcaaaaadbdddbbbacaabbcbcaabbdadaacaadaabacdddbbbcbaddcbdacbdcdadbaabddbddddcadbaabbdbddbdcbcaabcdbdacdacbbcccbdbbbbddbbadacabcddbaacacaddccadbbdbbbabbbbbaddccaaacdbdacbacbccdcdddbdaddcaddbbbacbacdbaaadcdcdccbaaabdbddcdbcccabbdbcdbbcabcacacbcddabaddbbcaaddbdccddbdcdabbccddccbabcadabdbdacdacccccaababbdcccacdbbcbaacdababbcbbabcadddbbaabbcdcbdaadddacadacaabcdcdcbaddaccbaccdbccdcdccbadbabdaabbaddcdddbdbaccacdbcbcbdaccdaddaccbcbccccbcaddcadaacddabbccbddbbcbddbcdbdbbabcbbbbaccaacdadbadadddcbcbdcabbdcddabcdcbabbbbccbdbccccdadbabddcbcadaacabbbaccddddbaadadacdcccbcbddacddabaddacdcdcaddadaadddcacddbbdccababdacbabdccbdcddaddabcddcabaacdcdadacbbaadcacbdcddadcddaccabaabbdcddacadacaacadbcbabadbcdbcaddccdacdbddcbccbabbcdbcabdccbcdbcacaacaadcadcaacdcbdbbabddccddcccdcccbbdcccaacbdcbdddcdddaadbdddbcbadbbcdbdbcabaacabdbcdcdbadbacddbaaddaabcdddadbaadcbbacdabbcbbcadadddbcccbaabddbdcbaabcbbbbadaaabbdacccaacaaaabcbcadddadbaadcbadcdbcbaadacbcbddcddaddaacaacbcdcddbbddadbddadaacddcdcdabdcadcabdbbcbbdbadbbbbbdbacdacababdaabcccdccdbadacbaaddddddccaabbabccabadcbbbbacacbaccdabcbaacbabdbababcddacdbbddcacbaadbaddbacbdcaaadbcbbbaacdabaaaccbadaaacbcbaddcdabcadbcdcddcdaccbbdaddddaaccccdbcaacdcdadddabcaddabbdabdcdcdabbdaaccbccdcccaccbabcdccdabdbacabcbabccdbabbabadbcbdddadbaadbbbdbaabdbbbdbbbbbcaddccbddaabbcddcdacaccbdaadddadaabbcabadddbcbdacdcdbbabacbddcdabdaaadcadcdbacaddbacbcbcbbaacabbdababcdacacbdbdbabadaddbccaadcccbbaaaacbbbbabadcaddccaddddddbaacdbdccdcdbbaabccbddddbcaacbcbcdbccdbcbadbddbcbcdddbdcbbadbcadaaacdbdabdbbcddacdbaadbadccdcdabbbdabcddacacbbdaadcdbdbbdcbbabaddbdabcccaddabbdcacdaacaacabdabddccbbcccacdcbdcbbaddcabbacbbdbbdddbbdddcacddadcccdcbbbacadadcbcccabddaaccccdbcbbccbcbcdbadcdddcbbabcccccddbaacaaddddadbddddaddddadcdadcaddabddbbdcacaddcbddacaadcdccddcddadabbbacccddddadaaddbbcdcdbddcdcddcacbdcadcdadaadcdcacadddcabdaddbbbccddacdbdcbbbbcbbcdbabadabaabaaaaabacbacbcababadbddaadcbaabcbcbbbbabccadcbabdadaacdddacaacaababaabccbabccbcacaaaccbbdbadcdcdbacabbcdbaaddcadccbdcaabddbbdcdbccdadccadacacccbddbccdabaadcddcdcdaddadabbbcbdcacbdcbabbbcaaadbdcbbbbdbbbdccdbcbaccaaabadbaacaddbcddaccadddadddccbdcbbdaabbbbabbdabdbcabbacdabaccdabbacbabcbbcddccccbadbbbbcadaaabdcadccaaddcdabbcacababdddbdbcdbbcddbbdcdbccabbdcbddcadaaccaadddaabddbcdadccdcbdabcdbcabcabacbccaacaccdbadbaaadabacacaadcddcccaccccbdbddacdcabbbbabadabdcbadbdbdabddcabbdacccadbbacbaddababcdadccdcacccbbcbadaddbdbaaaadbadabbcaaddcccdbcbadbadddaccadcbcccabcddccbdbbcaadacbdbdacbdabbdbddddcdbcddcddbabdccdaabcabcacacbaabbddacbdcadbdaaccdbdcabacdbcdcbcbdbcaccbdbbcbddacbadcdbcdadcbcbdabdcddcacdcccccaccdcabbbbbcdcbdbcbdbcdbbbcdabdcabaabbbcadcdadcdbdbadacdacdbcdddaccdccbddddccbdbbdcbcaccdacdbbcdbaaccddbcbbadbcdcbaabbbdcccdbcdaccdddbbbacdacaacdadccdabbcbcdddbaadddcaadaddacbaaabcccbdaaabdbbdbbddcdacccccdabcdddcdbacdabccaacbacbaabccaadbadaaccadbaabcbbbdccdddaaacccdadacadddcccbdcccdbccddbbcbbdcdaacdddbcaccdaddddbddbbaadcbbbcaacdcaabdcbcadaccbbdadcabcccbbcbdcdbdccbdadbbcbccadbddadcacdaccbbccbcadcbddaccababcbcbabdbacdbdbbbcdbadcddbacbaadadcbcbdddaaccdacccbcdaabaddcccbdabacacbacdddbdacbbccabbdbaaaaccadcababdbaccabbbaaccbbcabbcdcabbccccaacdcaddcbbccccbcabbbdacdcbadccaaccbccbdaabbaddcbadaccacbbbddcadabbbaddbccbadcbbabdddbbdadcdcbbbdddcbaacbbcdcdacadddcdbadbdbcadadcccbdacdcbaadcdbbdcabddbadbdccbbdbabdbacdbdbbcdbaccdccbcabccdabaccddbcacaddccabccdacdadbbbaddaaadcaddddbadbdbabddcccddddaabdbbacdadcabccdddbddaacccadbaccacbbdbdbdabccadaadabacbacbabbbbbaaddbcdabcaaacdabbbcaaabcdaabdbaaabcdacbcbaccdcddabdabacabacbabbccdabcabdcddadcaddcbcdddadcadabbaaacbadacdbcbccadbdcdabacbaabccdaccbbbcbdcdaabdaaadadabbccbabbbdcdabdbdadbdbacdcccadcbbabcdcbdaacadbabcaddddbdadbcbcbbbcdacdacbccdadcacbbcdabcadcdcdbbadcababddbcabacabbaaccddbdcdbabaccddadccbcdbdaddcadbdcaaacbbdaabdaabcacddbcbdbbabdddadbdccdadcabbabcbdbcdbcbccadbbadbadababdaddddcadadcbaadcaabbdcdaaadcadbdbdccccacdacbbdbaadadccbdaccdcbbadcdddccacbbabadcbcacbadcddbdcadaddccdaddcbabacdadbabbdbbcabdaadadbbbcddadbbdddbccdcbbaccbadadbddadcdddbdddbaabddaacaacdcdbcaddabddbababddbbabadabbbdadddbbdbaccbbccddbbbbabcdbaaaacdddabbdabbddacbcbdbccccacdacbdaacbaabbbababbcacdcdaabdadcdabbadbbddcccdacddcbcaabcbbddaaaacbdddccddaacdaccabaccdccabdaacbdccccdadabbdadbaadcabddcdacddaaaaacbccbabddcacdcadaaaaaccacbbbaabbabcbbcddddbabcbccbdabdabdddbaabbcdcbbaaccccacaadbbbbabcddcacbdbaccabadabbccbdacbcdcbcbbacdcccdadaaacccadccdbaccacbbcdbdadbaadbdcacbdbbdaabbbadcdbbdcdbdcddabcacdbbbbccdddcbdcbcbaddaccdcddacdadbcdddadccdcccacbbcdbdbdcbaccbbaaadbbacdcddbdcccadcccaaadaaaddbcbbdbbdcacdcbaaccbccddcdcadcbdaacaadaabdbcbabbcbabbdaaababbcacccacccacacbcddcbccdcdcabcddabdbccabbdbcdbbcccadcdbbaddcaaadbaaaccacacdbcaabbcbbdbcbbbcbadaadcbcdbaddabadcaddbbcaacbaabdacdcbadbdcdbbdccdadabadadbddcdcbcaaccdbabacababdbdbabccdadccbcbbddccacdcbadcdabdcbdbadbaddbaabdddbcbbadcddcdbcabdddadcbdacabdaadcabbddbdaaabcbcbaabadaccdbbcadbbacbcccaccbbcbababcbccbdcdcdcccbcccdcbaadabaacbabdbbdbaacbbcbcaaccdabaaabdbadbadccccbaddddccddcabcccabdbadabccdbacaaaddabdabbdacdcaddbcacdbbcbbcbbbddbbdabbabaacbacbdddaddcbbdcbcbdddaccdbdccbadbbdbcbdbacdbbaaccdbbcbddddbbdcadacbdadbccdddccbddcabbbcaccabcdcbdcbcadddcdbdbdbbbadabaaacadbcadbbcbaccacaabaccbcbaacbdbdcdcdaabbccdbccaaaababbaccabcbaaabacabaacaccccddbcbcbddbdcabbddabbbcabdbadabbbbccdaddccccadcbcdddbbcbbccddbbbdcacbcbccbcbdcbddcaadabdddbccddacaddccddbccddcaabccccacabddcdbbcbdbdbccdabcacbcbbabdbbbabaddddaadadccbbcbaddcbbdaaaabdbdbcdaadcaaaaabddacaccbabadcdcdaadbbcdacdcacadcbacbbbdacdaddcacdadddbdcdadbbbdcacaccbaaccabbcdbcddbbbabddabdaabcaddbdbbddcbaddbbbcdbdcdbaddacbdabcdccaaddcdccbccaabcdbddccbbdbbadcabdbbdbdadbbbaadcacaababbaddabdaadbacddbdbbcaaabdbbacccdccaadacbbdadccccdbaabadaadbbabdadbdbbcdbdabccdaadccdcdbcdcaddbaacadccdaabdccadcdadcabdaabaccdbcccbdbdabadcabadaaaddaddabbadbddcadddacacbbbdcabcaaadcdbacdcdbacdbcaddddcddaabbaccbacbdcdcdcabcdddbacadbabcddcacbdbdcdcbdacccbdcabcdabdcccddbccaddbccdaccbbabccbbadaaddccabacdbdaddabcbccdbbaabbbadadaabadbcdaaacabcbadddaddcbbcddccacbbbcddbdcccacdddadcdbbdcbcbbddddbdacacdddcdabcacadcdbaabdabdcacdbddbccacdbcacbcdacadaabcbbbcadaaadcadbabbabbacbbcbcddbdbbcabbdddbcccdbddbdcbdaaaacdcbaccdcdcccdcdaddbbaabcaadbadcbaccddcbaacbbcaaadbbcacddbcacddbcadaaaadacdadaabdbacbabbbacdaccaaadccddcdadcbdaadaddaacaacaabbbdaccbacbdadbddacbbddabbbcccbddbbddccbdbbadbaccaaaacdadabcbbbcdbbbbadbcbbbabdacdbdadcdbdbadbcabdaccababacadcabaaadaddabcabdcbbdcddabdbcdcdbbddababaabccbcbbccbdaddcabdddadacdcadbdbcddbbacdbcbcbcdaaddddcbabcadcdadbddadddcaaabbddabaacdababbddbaddbbddbdacabcdaababacbccccbabcaabcabaaacdaddbaacabcaaccacadabababbaabccbcbbabadadabbbacdbadccababcdbcabdccacbabbacdddbcdccdbacddbbcbabbddbaddaccaddccadaccdacbcadcdbbadbbdbabbdbdcbddadbabdacdadacadccccaadbbcadcbdcacaccccabcdadddccbdaaddabbbacdcbaaccdbcccccccaaabcabcbabdabbaadaccdbcdaaabdcbacdaacbcbbdabadcbccdcdccbcdbabacccababcbdadabddbccdbbacdadccbbbdacbdbdcdadbbdcbcdcddbbdababaabdadccccaadcaddbcbbbdaccbdddabbbabdcdcdaacccacaadabbbdbadabddddacaaadcddcbaadbbbcacadbdcacdbdcbdcadaadaabcbdcabbdaabccbbddbbcbacabbdbabadbdacbdcbddbccbcabbabcdcdcbddbcbaddbaaacbbcadbadbbdccaabaccccdcdcbacccbbdcccbddacddabbaadabbaabcdbdbaacbbabccccbacdcbdbcabcabbacddadbadbcbcbbccbcaddacbaabccacabcabddbcdccaddcacbbabccabcaabdcdbacbccadacddabbcddcadddbcdaacaaadadbadaaaaccbacddadbadaaadaabbdaabaaccdaacbacdbcdbdbcbadaabbbbabccacabcccaadccdcbacddbaaccbaabdbbcbbbdcccdabbcaadababddbcdccbcbbaabadadaddbaabcbbccbbcdcdbdbaaadacabdbbddbaabcadadcdacabadddbcbbcbcaccabdcbcbcddbbcadabaabcbbddbdababaabaaabbdababdbdbbdabcdcdabbadcccdcadacadbdcdcbcbccaacbcbcbddccccdbadbbddbbbcccddadaadaaababbbbbdacdddcadcddadcacabdabccdcdbcdddcbabacadbcdabddbbbbabbbdbbdddcbbbdbbccbdbacccbabbbbcbcbcbbbcaaabbddacadddaadcbdaaaaddcbbcdcbbcacdcbbaddcadbacadddccabbacccadcadcaccdaadcaddccdadbdaaddadbdccddabdabacbcacbabbadadbcdbdcdabbdbbcddbcbbcacbdccbcccbaadcbcabddcaacaacdccbcbcabaaccdbbadabdcbbbabaabdcccdcbbdadaccbccbbaaabdbdccaabdbccadadbaccbdbbcccbcaacbdcbbcbdccbdabbcccdaaddbbbdadbdbddbdcbcacdbcdbdcbcccbbcdadbcdacbbabdacaacbbdaaabbbaddadcbcdcdbccacdbcdccdbdccabcdbbddaabacbabccacbbdccadadcbadbddbcbccbddcbddaddcbbbaaacabaccdabaaaaabccaccaccaccabdcbddcbbbbcccbdbcaadbbbabcbaacabdbdaadcaaabacaababbdbacbbccbcbaadacacdddbbcacaacacbcdcdcaacaaabbababadddbbdaaacbdbbdccaaabdbdcdcbaaaddbadbdbcccdaaddcbcadcaaabdddddaaacbdaadbaccadddbaddddbcccabcacdcacccdcbdbddadacdcccdbabbaddcdcdaaabccabcbabbbbddddbbcdbcdcdbdccbabdabaadaacaadacdbaaddadadccabccbababccbbdbaacdcacabaaaaacbabbdbccdadacabdabddaddbdccbaccbcdabadbddcbbbddabdcbccddadbadabbbdabcdbabadabccabaddcdbbbdbdaabcabcabccbadcdadcbcddcacbbbacaababbccadbbaddbbabcddadcbcdacaacbccdccdaaacdcbabcdbbddbbbdbcbbddbddbdbcbadadbcddaababdbaacabcccbdbacacbcadabcaadbaddcddcdabdcadbbacaabcbabadbabcbbdaaaddaadbacddbcabdbcdccdddcccccdbbdaacbdbbddabadaabacdcbdadcbaaaacaabbddbcbccaaaabbbbbaadcccccadbacbdccaadbabaadaddbbcaddbbdddddddbaaabaabdbcbdbcaabbccdbbddcacdcaacabadcdbcbdcbcddbbbababcacdabcdabdbddcacccaadadbbcdacaddcdccacbdaadbdccaabbdbaaddaadaccdabcdbadccbbabbbaaaababcacbcaaabcaababbdbddacbaaaadccbaddcbcccacbcabbbcacdbdccbababcbdacdbcdcaccaadcbdabcdcbabbacddacdcbdacbcabbbabdaaaadddabcbadbdbdbccbdaccdababcdbcabbdabbabdbcdcaccaadbdaacdcdaccaacbcbcbbbdcbdcaadbcacadbaabdabbbacbddacbbcccaaddddaddcdcaadabbdabcdcacabcacccabddccdcdbacddbcddcbddabadabaccaddcddaabcdbbbbcbadbbcccdbbcbbbadcbdcbaadcdbccddcdaaccddadaddaaaddcadbabdcdccabddadbacaabdbabbdbbccbabdadaccdbcabcbadbdbdbbbacbdcabdbababddccaccaacabcdacaaaccaddcacdbbbaabbadcbbabaacbcbdaabdccacbbbbabbabccbddbabdbdadcbbcabbadaaaddabdbabcacdcbdbadaaaaacaaacbbbddabadaacacccbdddadcadbaccdcadaccaddcdadcdcaadacacaccacabdbcdbbdbdddcabaabdacaaaadddadabbbcbdaaabadccbcccaddabdaccbccdaacaccbbdbcabdcabbddaddaccabcbcabadccbcbcdddcccdcbddcaacdddddbcabbdadcabacaddbbdbaadacabdacdcdddbadbadcbbcacbcdddcbcbccdabcaacdbcacddbabddbdcadbdacaacabddddcbacdbcbcbbbddaabadadbacacbbdcdcdddabdbccbaacadadbacdaaadcaccbbadadabdcccdcbbdccdbdaccbaadcddccdcbdbcbccddddbcacabcabcadbacbdcccabcccdcbdabbaaacdddbbdababbbacbbdaaaccacabcddbcdbddcadcbabbbcbabadbdacccddbbacaddcddbaabdadccaabccbddacababbcddbcccbcacccbbdbbcdbaaabbdcaccbbccccaddacbddbcdcaadcddcdabadbbdadcbadddcadccddbaacdbcbdaabbccbabcabbbbbdbdacccaddbacacdacccccabbbabcbcabdadbbdcccdcaaccabcccddbccddddccdccacabdbbaddcdbacadcbdcbdcabbddabaddbcbbbabdbbaccccbdacadabcacccacbcbccaccadddcabcbabadacccabdbdcdadacaccccdaddbcabdbbddccaccbdacabccabbbcadcbccacaabdccacabdbdbdbbaacbabdcbabbaaaadbbaaacdabcdacadbabbabdbdbbddcbaadaaadccadabacacddccbdddabcdabbadabaacdcaddcbdbdbcbddbdabbcdabdcdddaccaccdaacacacddacbdbabbdabcbbdbbadbbabcdbdadcccbaabbdbabdaddadbaacbaacbccabbcdcbbcadbbacbbdccbccbcadbcdccaacabcaccaacdbbbabcbcacacbcabbaacdbdabadcdadbbaabbadddcdcbddbdccdbdabccbbdbdbbdcbdcbdbddbbbdbdcdacdcdccbadacbbcbabcbbbccdadacbddcaaaaddcbccaadccdbbbddddacbcbbcabaadaaddcbdbcabbcabadcdbdbddcbadcdaccddcdcaabdcccabdbaacabbcbbcbdbbbdbcbbaddcbdbbaaaacabaddaacacadadbaaddaabdaabaccacabdcddcddabddccccbbddcacbcbbbaacccbcdcbddcaabbbcbbbbcdadabbadcacdddcccbbadcddbbadacbdbdcabbcdbdbdbdbddbbbcadcbaccbcdbaabddbadbbcdcdacaccaaaadbdbcbbbaaccbccbaadddaadbddcbddbbacbbaccabaaaadacadcbdbbccbddcbacbdadbcbabdccbacdcdcbdcbaddacbddbdbadccbadadababbdaacadbdccdcacdacbdcacbbbabaaccaaaaaaadbdaababddcabdaadccaabcbdbdcdbbbddaaacbcddddaababbcbdbbaddddccdadcaacbdcddbcabacdabacbcacbdbabcbcccdcdcadddbadccccccdaacbbdcbbaaacdabdddbcdbdbcdadadcaabaadacdccaacccbccabbbbbcbdacbdbcdabbcadcbcbabaaddbddccabcabacaddcccbbddadccddcabdcccdaadcdaabcacbcbcbbcbccabbbdadbdacccddcdbddbbcababbaabbbbaabbdccabccbcdabaacbdcabbaddcadddabdaddbacacabdcdacdbadcccdddbabbacdcabbadacbdaadbaaaddcdbccbdabcacdbbdcdbccabadcaadabdabdcddbacadccbddcbadcddbcdabbadaaacbbacaddddbcdacaabcadccabbddaaabdaddacbcadaacdcdacdcaddaccacacbbacbabbccdacbcbadcabcbddbdbbddbbcbbaaaadcbbadabdabbdadaabcabaaddbacdacbbbcccabadccddccdbcdadacbadcbcadcbcabbcadaddacbccacccbabaaccdbaabdaadcaddadcbbdbcbcbbdadbdcddbadddacabdbaaabddaaddaacbccbdcadbababcdbbcdccbcdabadadacdbcabccbdcdabcacdbcaabbaaadbbbbbbcbdddccdcacbdcbbcdcabbabbbcdaabddcbbabbddadcdccbbcdadacbbacbdcdcdbddbddcbdddcabbbcccdaabcabbdbbbccccdbbaadadbbaddcabcbcababacbaacdcabccdddbacacdbcadcdcbcccbbdbbabdacddcaddcbcabcddabadbdbdbdbcbbdabadbdbdacaddcabbccabddbcccdcacdcdbacbdabcdcaadabaabdabdbaaabdccaccddcdaacdacaabcdbcdccadcbabbacbcdcabbcbdccadadcdcdccdddcadddaacbbadcacabdabbdadcabbdaccdcacaddbadaacaaddcaaabbcddaddaaccbabbccadbbabbadabccaabcddbdccbcbdbbacaaabcccddadcabadcddaccbbddddccdbcdacadddcbbaddbccbcdbcbddbadcabcbaaddadbacbbabadacdaddddbadccbbbddbbdacbaddacdcaddbbbbcababdbdbcddcccccabcacbacacdbacbcacbbdaacaacbbcbccccacdbccbabbabbaadaccdbccaaaacdbbcbcabcdcbdcbcbcbcddcabddadbabbdccbbcdbaccbbbabdaacddaccccbcaacdcdbcdabcbcabbcaacadddddadabacaccbddadbcbbaadcdccabdaabacadcabbdaacddcbadbcccaadcbdcabbbdcacbcccbdbccaaaaadcaabacdbaacacbcdacabcaccbbcadbcadaccbbbbacbadaaabbccaadccadddcbdbbaaabcaddbcbccaadbdcbadcadbcaccdaadaacdaaaacaddddcabbbabdacadbadbccbdacdddbaadcbaddaddccaabdddbcaaadcaaccddcdcdabdaddacddbcddcabacdbaaddcbddcdcdcaadbacccbbbdadabddbacaddbcdbaddcdcddbcbcbddbdaccddbabdccddadadaadbcadccccdbabaabdcdacbacaadabcbcaccddcbaaddbadcbbadcadbbdccdaaddbddbabcbcabaccbbbacabcccaacbacddbcaaaabccbddddbbbaaacaaccbabdbdaaadcbabcdaccddbdbbaddbbcbbdcccaacdbbccaabbdddabbabcccdcbbababacaacdaaadacbcccadbbaacadcdcacabddbacdcacdbbccbaddbdabdbcbabaacdcdcabcabaaadbcbacdacbbbbcdcccdabcdacdadbbabbcddddaccbadbabbacbadaccacddadcaddbbcdbabadbacaccccbddbbbbaabcddabdbbcbcbadadabbbcbdbbddbabbbdbcdccbbacbcacaaadaaadcdcbaabdacaacbccbdbcabdadaadddacabdddcadaccccbdcbadbbcdabcdccbadccddbcdbddcdcdbcbcaacabdccbdaaacabcbbdbdcccccbabdccdbcabbababaabddacbadcbcbbddddcabcadbadccbbbabddcdcbabdacacadaaaadcacacababcabbdbbdcacabccdcdbccadccabcdccbbdccdcdbcacdddccdacaaaadacbbabdcccabacbdaabbddbdbcdacdcbacbbdbbdaaddbaabccbadbadaacaaccdccabdbcabdddcababcdbccacbcbbbdcbdcdaadcbcdbbcdddcaabbcbabaadbadddcacbbcdbdcdacccbcababdddabccdbddaadcccbbaaadcbbabbcdaadadcdadbbabccdcabbcddacbccdccccadcdabddaaabbdbcdcddbdadbddcabacabdadcddbcbbcdbddbdbccbacdddbbcadbdadddcddbbbbaacddddcadacaaddcaabbabbbccacbdcdbacbccbaadbcdbaaddaacddcbdbcdcdaabcabdcbdadadcacbbbccbdcadddbbcaacdbdccacdbcddbabdcdabdabadabaaabbcccaaccaacdbbacbcdabbaabbaddcddbbdbcbcbabcabdbaabbcbabbddcadcbcbdddbbdbadbcadbcabaabdddbcddacaabcbdddbabaacdcddbdbabdcbcccacddadacaaacacadcbbacddddbdbbdcddcababbdcbbabcbccbaaabcdadacaddbbbbcaddbdbcaadddccccbdccbdbcddbababddbdcbaaadddddaaacadabcabacddababdbacaacddaabcdbbddaabaaaabbdcbadabcdcdabbabbdccabdadaacdaaccdbdabcdbbacddcabcdbacddcbaabddbccaacdcdabcabcbcdbaacbcacbbdabbccaccaacbabcbabdbdacaddccaddadacbaacacacabacdabbacbdbdbdcccdcddaabdadcbbacaccccaccccdbaabacaaaaccdabddbaaccdabdadbcdddbaadcadadcdcacdbdbcbccbdcdbbadcdacccadaacacacbdccabbcddabcaacdccbdbcadcbbbadcddacaabababdccbbbdddaccdbababbbabcdccddaddcccddaacbbadabddddaaaabdcbcadcbadddddcccbadbbadaadbcccbdadcbdaddabbbcbdabacadcaacdbbcdcdaccabcbbdccadcddccddbabdcbbbaddbccadbabbcaaddbdadaaadcdbbdbbabacdcbbdcdacbbdbccacadadddcbcdcdbcabaaacaaccccddcbaaaaaddacdbaaacbdbcdbadcdcbacbbacaaaacadadcbdbdadbbcdaaacddbbbbabdbcacaacadbdddaabaccbbdbbbbaccbdbbddcacaccdadababddaaccbdbbddadbbaddbbdbadddbcbddbbddaddddacdbbbcabcdcbdadddbbcbdddbbdcdbaadbaaadbdcdbadcaacacabdbaaacaaccbaadaabbbdcdbbdbbaadadaccdccbdbabdbbacaadadbbdbcdddbcbddacbaabdbbcbdacbacccbbccbbbcabdcadcdbbbccbdabacbcdbabccaadbadddbbcbadacabdacbadadacabbbaddccabbbadcddcbdcacaadaadbdccdddcdbacccaacbdccbbbdbdbbbadcddadabcbabbbcaabaccdbacbbbcbbdaaccadadcbadddacabaacabcbbadcaddbdaaccbdcdddbbcbaadaccbccadcccbbbaaddabddadddbcdbadbdcbccddcaacccaaacaadadbbdbbcacaabcccabadcabcbbadcdcbddbcbbcdadcbdbdbdbcacacddcccacdbccaddacbdbdcbdbdacbaaabdadbdcccdcaabbbdbadbbdacdcccbddbbcaaabbcbcabcdbdacbbbbaddabdcdacddcbdcddbccdbdaccdccaababcbaabcddaabcdabbcccbdbcadbacddddcccdabdddacdcbcbacbccbbbbcccaacbddccccdbbdacddaccaabbadbaadadbcddcabdcbbbcaadbcaacbcccacbacddbcdcaaadabdccbbddadaaddbdabbcabdaaababaacabcabaaabadabdbacbbcbcddacdbdcbacbacdcbbabcdbccbbdcdacdaabadcdaadacdcabbbdadaabbdabcadaaaccbadddbbaaabdbbdbddabccbbbdcacbaccbdacaaaaddcaaccddbcdcbdcacdbcbaccdaccadaddcddbaabcbdcccccabacddcbacddbdddaadacccdbcacddbdbbaacddcbcbbaaadcdadaacadbbdabcabacbcbcacadddcaddddcbcbdccadbcdaddddacbbdbbacbacacbcaaababacadcabaacdcbbdddaaddadccacbbcadcaababbccdcdbdcaccabcbddacbbcaaddddbadcacdabdcacbdcaacaacaddccdbccdddbadbaabadaadacacdaadcdcdadccbcaacbcaaccccbccacadcbccaddabaacbaabbaaaabcbdabdcabdabadbccbbdacccadadbdaacabbdbacdaaddddddbaddacdbbadbcacddbdacddaaaaaabdaabcddccccdbccbbdabbcccbcbdcdcbccabaadcbbcddbccbcbcaaacbddbbaccbbccccdacdbaaacadcdcabbcddbacadadaccaababbaccacacaaddaacabdcddacbdcdcabadbbddadcabacdadbbbdbbbcabbdccdcbbccddadaddaadabbdcadccbcaaccbdcaaadcdaabbccdbabacdbcabcdacbcabbadbabbddbacacccdabcdbacddcabbcbbbdbabcbbccbcaaaacbbdcddcadbdadbddbbadcdbcdabababbccadbbbbacacccaddccabbaadcaccbabbdccbcbbccaccdcdbcababcbbbaabaadaaadaacdaabccaacdcdbccdacaacbbdabbaccbdbcdccbacbbbcbdbcacdcbcbdacabddbacbccdbcbdccaabbbacdadacdaccaadbaabddbbdacddcbaadcbcbcbddcdbaddabacacdbdbdbcabdcadadcacbcabaccccdcabddddcdcadcacbbcbbccdadadccaccbccdaccdaababcbacabadbbbcabadcaddcdbbacbbaadbacaddbdcbbbbbdaacbdbacddbdacdabdaddbdaddadbdccdabbbcbddacacdccbdcbbbaadbbcbaacccadaaaaabaccbcdaccdccbbbcabccbddbcdacdbaddacccddccaccdccdacbccdbdabacababbcbcbdbbbacdaccabbdacadcccdacbbddbcdbcacccdaabcbcdacbbbddccaddcdadbaacbdabcccacdcddccccbdacadccadacaccdbdadddccdabcbaadbdcccadaabcabccbbbbcbcddbdcababccdbaaabbaaddcbbadacabdbbbdccbadbcaacbbcdbddcdabcbcdbdadddcdaaacddcbdabaacdcdabbbcdccdacbdcdcbcbbbbbabaababbdcbdaadccabccadbacddcbaaadabccbcbdbbbcadcbabcabaddacabadabccdaddacbdcaadacaccdcdacabdacdcbdbdaaacadabbcddbdacacddcdbddbdacdccdaaabacaddabbbaaaccbdadcadbccabadccccccadddaadabddcbdcadcdbccabbddbdddabcccbdbacbbbbbccaaabcdaabccadcbdcaabdabbbdcbdbbdcdcadabdcabdbbbcddcdabdbdddacccadabdcdddbdbadcaaccbdbdccabcbdacadccdbaacdadcbdbdcaaabdccabbdcbdccacdbbababacccdacadbcddbcbacccaacbccabaaaddcaccbcdddbbdbbcaabaccddacdbbcabcbddbcdcdbcaaabddbbadcadbdaccbdcbccabaadbaddbcacaaabbbdabcdccccdccccdadddacccbdccdccdcbdcbdaadadcdabccadbbcbaababdaddbccbcbaaccbddacdabbbddcaccbbdcadabcdbabcdbccadbdabdabcdabccdccdaaadbabaccdbddaadbadcddbabcddbcadbadacbacacdccddabcddcbccccbccabcbbaaccaccdbadcacaabacbaababbbaaadaabdabbabdccabcbaadacccccdddcacdadbbabdcbbaccdccdbcabbaabbcbcddabbbcdbbbaacbccbaccbcbaadcbcaddaccdbdbdbccbbcbadabdbbcdbabdabbaabbbaddcacadaaadadacdcaabcbbbaabbaaaddddaddadcddcddbcdbdddadccacdcdaacbbabbcadcddadacdaddbdaacababbbcbbdcaccbbddbbbccbdccdacabadbbabaadcdddbcbbbddcabdadaacddbabaccadabdcccbbbacdcbabdaddacbbcdccbbacbaadcccdacbccbadbaabdddacbabddcdccabcadadcddbcccaabcbabaddbaadbadcacaadbddbbdcccdabbaabbdbdddcbbbacdcbbbbababbcddbdbcbcbbdcbcdcdddabdaccccaabdaccadbbacdccdbaadddbcbcabbaaccaadacddabbaabdbbcdacbadaacdabddabbbddbdaadccbbcccbcdcdcabcdacbdcbadaaaccddabbdaababbdcbdcccbaddccdaccbcdccaadccadcaaadcbaacdbacdcdaaadcddbdabdddabcbcbdbdccaacadbcacdadcbccbcddccadcbdbabdcbaaddcabcdcdaaabdacddddcababcddcdbcbcadabadcdaabcaccbcaccadbacbbcadabbbdbdbbaddbbaaddbadadddccbbbbadcdbbdbadcbdbdabacabadadcdbacbaacbcbcbcabaadbbabcddcbdbdbbbdcbbdbcadcadaaddddcbcdaddadcdcacaddacbccadcdbadccbdcdbadddaaaacbbcaaccbddbcdcbbbadcdbddbcccbdccbadbbddaabacdbbdadcdaabcaccdbbccbcbadcddaaddabcdabcbdcdccacbdcdabdaddbbddcbdcadcaaabbdbcbcdacabbdbdbabdcdbccbaadacddcbaadccbcdabacaaaddbcadcaaabccaaadcdcbdbadccaaacaccbcadaabcdbabbddcdbdaaaaacbdcabdbbbacdddcdbccdbabccadcacabccbabbcabdabbbabacbadacaddcdcddcaaadcbaddbdcaabbabbdbccdaadacbaccbcacaadccddbcabcbdbdddbcdbaccdccdddcacdccdacbaacddadadadcadaccddabdbdbabacabccbaccbababbbbddaadddcaabcbdbacbddbbdaccdaabcbbcbabaadacdcbabadaddabbbabddbbbdbccddaacacbabdbcbbaccabaabbacdbaabcbddcacdddccbbddbdcbdccdccccccdccbcbdbccacddccacdaddabbadbacdadbbddbbaacdccdadccadddcbdcbcccaccaacbdbdaadaccdccccdcdcdabacddcddcaabcddddbabbcdbbcabaccbbbbbbbbdabdcaccaabbcbdbbaadbdaaadbcbaabbdddbddbbccddadadaaabaaabcdacabacdddabdcdabbababaaacdbdbcdadadbbaadaccacbbdaddbbbdcdacccacbdcdcabccdbdbbcdbaaabccacabdccbdbdcdabcdacabdaddaadabbccdcbbbcabddbbdaccddbbdbbdabaacdbadbadadaaaddaaabdbdaddcdddbaccdaacccbbdcddcbbcbacbbcaaadccaacadbaddbaddabcadabddbbacbddddbadbdadaaacbaabdddbcbbbccddcbbccccdddbcdddccdacbcbccdacdbcaaaadaddcbccacdbdddadcdabbadaabaaaaaadbabcabdadbcbbaaddabaddddadccaabdacbbabdacdadcbccadadbabdcdcbdbbcdddbdddbddbbaacbdccaaddbaadabaddabcaacbcbacadccccbcadadbadacccadcddddadbbbaaadbbbbbddcbaadddcaacddaaacdccdacbcbdcabdcaddaddbacadddcbcbadddccdaacbdadcbadccbadabcabbdcbdbabbaaaddddddcaaacccccbcdacbbabaadabcbcbaaadbbabacbbdddbcccabdbbcbdcacabaaddbadbbaadbbcadaaadaccbaadccadbbacbdddbbcbaabdccdaabbdcabcacbbadbacaaadacddccdcbbaacdabbbaadadbdcbcaacdbaaacbacabababbadabbcaaacbbcaddbaaaacbabbdbcadddcdabddaddabacaadcccabbbdadadcbddbbbbcbacaacbcbaacabddbabaabccdbdcddcdbbccbbcacdbddcdbbadcbcbccdccccadcdbbcacaddcdacabaccbdbadadcccdaaabcccdaabccbccbbccdcbaabccbddacdddbdbcacbaabdbdbcadaadcacadabcabaaaaccccaacdbbaabbabdbddaaacaaaaaccddbcabcdbbadbdcbdccddcbaaaabbbddbddbddccdcdaccbadcbacacabddbacbcacdbdabbcccaccdcadccbdccbbcaacccbbbbbcbdbacacdabaddabadbbbddbdcaaacdadcbddcbddcccbbaacccccabdbaccaddcbaadaddcacadbbdabbacadbcbccbdddbcdacaaccbcdbaababddacaacddabdadccdcdbabacabccbdbacadcddabddbcaacddcaddadcdbabbacdabaccdacadacabdcabcccacaabbcdbcccdabbcbaccaddcbbadacbcbdbbcbbababccbbbadacbbdadcdcaadaabdbccddbaddbcbdabdbbdcdaabdadbdcbdccabcbcaacbaddacddbdcaadcabccbccadadadaabadccbaddcabbdcdcdbbcbbaaacaadccdcabcdaadbccdcaacadaddccacbbaaaadcdbacdacabbcacdcdbcbcbdaadcddcacbdaacadcbcbdaabcbdcdbccacaacbbbcbcbbbdcddbadacdbccbadbcdbacaaddddabccdbcadccccadaadbdcddacdaacbdabdbdacbdcabcddacaddcccccbbadcbbdcadcddaaadaddbdadddbaaadadddcdcbaaadbbbadcaacbdcaabdbdbcbddcaddacbbcdbbbcdadabdacbaadbcaabdadcddaabbabbbcbbadbdbbbcaaddacbdcdabcacadcbdbaadbccdcdcadccbbcacccdcdbbbadcbcdcddddbccdbdbabccbddddcbbdaaacbdbacbbabdbabdddaadacccdabbcabbbcaadbabccabadaddabcccdbabacacccabbdbdbbcdabcccacddccdbacbbbaadbacdabdcbbbcccddbbbcaacdacaabcbadbdbabbaaccccdcadcbdbdaadbaaadbadccbbbddcdabdcdabbddcbccabaccbaccdacacdcabdbacadcbccdbbaadccaaadabdacdcbcbbaabcdacbdadcbaabcaabbcadbbbdababcccdabdcdcbcbbbdddcbddccbbccadbbaadaaddddcdcaacabdbaabbbacdaadddbcabcdcababbcbdcadaaabccbabcabbaaacdcddbaadbbdcccabacaabcacdcbdabaccdcdabaadcbdcddacccdbdbaaabcddbdcbdbdbbdddbdddcccdbdaadbadcdcdbdcabccdbadadbbdacdbcdabdadbaddbdcacabdadbbaddcdabbbbabdcdbabadcbcbabcbaabbccacccbcadaadbabbbcccddcdbdbaddabbadcdccbaadabdacdcbdcdbbdbcdaacbddddbaabdcbaaaccbccacbbcbaacddcbbabacbdbdbdcbdccccbcdaccccbabcaaacaabbbbacaacadcdaccacbabacacacabcbbcccaabbacbdbcddcacbbcbdacdcbdabddcbdbddbcdbbbccacbccaadbabbdbadacbcbbdadcbbaaacadccacbadcdacdcbbbbcabdbcdcaacdbdacdbcaabaaddbaaaacbbaccabdbadcaaabbdbccaadbbbcdbbdcdcadcdbabcccaacdabcacbaaadadbaccbbddbdcaadddcbbbdccabbabdaadabaacadaddbcaccaddbadaddbcdbadbadcddcddbaadbbcaddbdcdaababbdaccadaabacbddaccadbcbcdddaadbcdcadadccdcdbbdbcbbacbabaadcccdbdccbcddcaddccdbaccabacdccbcabadbacbcdbabababddcdbdbadcbadaddccdbabcdaabdbdddcbadddacbcdacadcdcabdcbbdaaccacbdbabdcaacdabccacaaddcdccdbbacdcccabbcdbabccbadddbdbbbcdaabbbbdddbabddbacbcdababcdbbccadaaadbbdbbadaabbcbbadbcccbaddcaabacbabdcbcdaadcbbbaddccacdcbbbccccabcdaacadbdadcbcacabadccbdabddabbbdcccdcbbbaadacddaddabddddabaaadacccbbdabcccdccbcdddacdabbadbddbbaadcaacaabadddccddbbaccdacaacdaddaccdacdbbcdcaabbcdccdcadaddcdacddbcadcdaacacbdcddcaabbcdcaccbbabbaccabbaabaabdbdbdbdcbdcadcdbdbdcabacbbdddbbccddbccbbddccadbbabaaabadbbbdbdadddbddcdddadabbddcbcccdbcbabcbbbccadadbaccbcbcdabbbddddcddbdbdddddbabaacdaddcabcabbbbcaabbcabbaadacbdacddbdbadbabbbaacadadaabdcdbdccbdaadaccaccbacbaabadcdbadbacccbdaadaabbacdccdabacbbcabcacddcacabadcbccccdbbbddbadabcaaacbabcabacdccadbacacddbdaaacababdadbaadadcdccacbdcadbdddcaccbacdaabdacbbaabdbacbdcdbbabaddbbccadbadadcdadcdbddabbdacdabdaaaadadaabcdcbccdaccbadbabadccaabbcddccbddadcbabccadbbbcaadcacadacaccdbcbdadbabdaabbddadabdcabdbbcbcbaccdbdbccaaaddbacaaccbcbbcdcdbdddddaddcbbcccbdbdbbcdacaddddcbcadbacdcbdbdbcdaabbdbbbbabcbcacbcbcabcbddddacabccadbbabddcaacbdbacdcbdbcbbbdadbcccddaaddbccdddcccdbdcdbdaabbbcddcdacaaaccddbcbccabbbaddddbabcbbbcbdabccdcbbaddddddaccdacacdbdcbaabdaaccdbcbaadccadadadcaabdbbbabcbbcdcabdabddbcadbbcdadaaaadbdabdcaccdacbdacdddaadadccadcddaadbcadabccdadaddbdbaaacddccbbdddcccdbaaccbbdbcddacbaaadbbaacbccaddcdcdccddacaaccabbcbccdcabcadadacdadbbcbdbbccabbdcbcbbdbcacccababcccccacbdcdadaabcaabbcdcaabdcddccacdbdbbcbcdddadadaddabdadacdacdccccabdbbccadabacbdbaccbdcbacbbdaaadadcbabdadbaacaabbdadcddcccddbcabbcddcacddbdababdaaacacabccbdbcdbcdddcbccbdcdbcbaddbadaabbdbddaacbcacbbcccdaaaacbbadbdbabcabaccbdcbbdaccbbddacdadcdacbbbbcccbcddaccaabadcabbdadacacbbdbdcdabdcdbbaacddbacabdcbacabcadcddccdaccabdadccdbaabdccacdcbbcbbccdcadcbaacdaccbdbcdcccdabdbdcaddccbaaacddcbdbbddacbbcabbcbdcdbababbcbddacbcbdbbadbcadbbdcddbdbbaacdcaabaabadaababdbdabcbbcdbdbabbaaccccbbaccdacdcdbaacbddacbaadbdbdadcbddaabdabaabdabdbcadaccdddbabdddbdaabccacccddadbcdcaabadbbcabdaccddadbbbcddaadbcccdaacadddccadccdaadaccacbbccadbdbbbcddcbdcdcadcbaaccaaadcadaadcccdcadcbacaacacbddacdbdbcdbddaccbbbcacccacbdcacbbcbdcddacaaabdabbacddcccacbacabbaabbcddbdbcaadacababddbacaacdcbcccdcadccdadbccdbdddbbcdbbddaccbcadbcbcaacdccdccdcdacacbadcbaaacbdcbcdbbacdddccadbadacbabbaaddaacbbcdddbadbddbdcacdbbddbaabcccccacdabdaacdddccbbcdaabcbcaddcdacccbbcacccddabddbadacaacbdacddcbbbcbdbcdcabbbcacccddbbcaccbcadcbbbcabcadbbcadddbbacdcdaabbadcacdcadadbccadadadaaccbadacbdacbbcbbbbaaacdbadcdcbdaabbacbaccacbbaaacbcbdbaddcdcdccdabdabccbddddaaabdaadcbbcdddacdbbccddadbadcadddbbaacbadcccccdaabddccabdcadabccbacbaabbbddcbdbbccdcbabadaddaccabbaccbccacdaccdbbdadbbdcacbccabcddbcababbaaabacaacbabdadadbdaccddcaabdacacddddabdddddbabbddbdbabababdadcdbdacacabadbabbcdadddddbbadddabdcabadddcadabcaccccbccccbdcccbbbabbaddabacbdbdcbccbcadbbcbbacdcbdbbabbbadaababaacbccbcabdcaacddbcdbbbbdabcbbcbacaabbadcbaacccaaaccadbaabdcbbbadacaddcaabbdcbacccacbccddcbbddaadabcdaaabbcbcdccbccaadddbaddccbddcbcaaaaadcbbdaadbbcadbbababcaadaddcccaaabcdcbbbdbbdbaacabaaadbbdadccaaaddbccaaacccaacbcccccaabaacdcdcdbccaacadcacabcddbdacdbbabddcdcccccdddaaaccaacaddbccdcbadaaccabbddaddaabdddbbcbbdacbbabcbadcadcbabdbcdbbdbadaadbaabccccddcdbdacbcccbcabacabcbbcddccdbddaacacadbcbbabdbacacbddcccdadbabddabcbccabbacabacbcdbbccdbaadcdababdacbbddbcbcccbbddbbccdaadcdcadadbabadbcaacdadbaabdcdcdaaacdbaabacadabdcbcbabdcccbdcbcccdbbddbadbcbdcddccbadbbababadacddacddaadadbabdbdbaacbbbcdcaccdaacdbcaabbddbdaaddbdccdabbcdbdbddbabbdcacbbcccbadbacccabaaadcdaaccbbbbcadbcdcdbbbdbbabcddcdacbccddcacbadcbddaaacbaabacaabcbdaccdbaadbaccaaaadacacbbdcccdbcaaaabbbaaacdabaaacaccdcbbbaabbcbbdabbaabcbabcababadddbdbaddabcdcdbcbdbbdbacddcbadcacddbcdbcbadaccbdacccadddccabbcbacaaccbacbccdadabcbbbdcbdbdcbbabbcacbdddaadccdbccdbcccddaccbdbaddacacacccacddcdccdacbdcaadbabdacaddccabbbaccdddcabbccccdabdacacbcaadadabbbbaacccdcabdcccbcacbbabdccddabbabbcbaabddbbcadccdccdbaaccdaaddbdcbbbdadbdbaadadbdcaabbcbacbbababbbbabdcbdabbbcdabccdccaabcabdbdabcadbbbbaabdcacabdddbdbccdddcdaadcaaacacadddbbdcdddacbbbaaadbbddbbcddabdadcccbcddbdadbdbbacaabddbddcbaaadcababacbcabababddbdbdabbbddaaccbaabcaadadbcdaddaaddcdaaaccccaadcdddaaaaccbdcdadbbdcccacbbcaaccbbaadcdaddbacccdbadcbbaccdcbabdaadabdbcbaadabbcbacacadcdabbbbdbbccdcaadbadbacabdadddcaacbaaccacdccbaaabcacdadcbcbcacabccbdccddbbbbabcddccbcaddbbbdcaddcdadbaaaaabbdbadbababbadbbdbadaadccadcaacdadccbddbbdaaccacdaaabbdabcbdbbbabaccaacbdbbcbbaabbacbcbbacacdcbdbddadbdbbbddcdbbcbccdddccabacbaabbbdaacadbcbaadaccccddacaacacbbcaabdabaaaabdcdadcccaabddabccdacbcdaaabdadcbdbbdabbccbcbadadcbdcaaadccbddacacbddabbdcabccdbabababcdddaaccdcacccabbdadcbccdcddccadbcadaabbdbddadadadaaabdbabcdacdadbaadbdaddcbacadcccbdabdadcdbbadddcaaaaaccabbdcbdadaddddcbbabddbccbcaacaacdcdacbadacdabdbaaaaacabaaabccdcbaddbbbcbdbbdababdccadcbbaaadaadcaccbcdccdbbbaaadcbbacabbddacaadbbcaaadcadcdaaddadacbbabbaaababcacbdbacdbccbbadbdccbbbacddaabcbbacbdbdcccccccdbaadcbabcabbcbbbcdbdaddadaadabddcbccdabadbaccaaacdccccdaadbbcbaabccaaacaaadbdcdacdcdbcdbcccbbdbadabdaacccbbbcbbbbaccdaaabbaacacdbccdabcccbbcbcccbccbddaaabbabdabdaaaacdaacddcccccaccacdaadccbabaaaaaccdaadbcdcbdaddbdcbdcbbbdacbdabcbacbabacdaacacaaababadcbbbaadcbcacacdbbcabbbaabccdadadabacbbbdaadbbdaddadcddbddbcaaddcbbdbbbcccccbddbbacacbccacdccdbcbdbbcaccbbdbbbbacbdaaacddaababbbdbdbcdbdbddadbdbbbcdadccbaacbdaaaaabdabcbbcdacacbadcccbcacaacbdabcbabbcbabadccdadbcccbbdcdbcbbdabcdcdadaacadbdbacccdddbacaadacacaddaaacadbdbdcbaddcddacadcbadbcdbcdadcdddcaabbcdbdabcdcbdccdcdcdbdbaccccdbbcacdadbdadcadddbdcabcccaaaaaddabcbcccdbcbaadbbbbbcdbdbdccbabbcababdcdcaababdccbbabbdaccaabbabdbaddcdacbaccbcdcdcadbacdbacbcadcdabaddccaccdbaccbdbcaadcbbbcacaacdccabcdabdcaacbacabcbccbbaaaccbcacdabcaacbabdcbccbdaaadabcbcdbcdbbaaaadcccbdbcbbcbbabbccacdbbaddadcbacadabbaddcdaacdacdadcabdacaaacadbacddaabbcdddbcccacdcdabbbcdcbdaabccaabbbddbbabbbcdbbdcbacababcabaacbcdbaaadadabbcacaacdddcbbdadbaabbadbbcddbdbacbdbbcaddcdbacababbcdadbccadabcbddbcabdabdccdaabbbaabadddadcaaabcddadaddddaadacdbbaaaacadddacdccadbccdcdccbccaddbcdaccbaaddabcddaadcddbccdbcaabcbdaddcaddbaaababcbcabadccabbcdccabcbcabcbadcddcbcacbddadabbabcacabcaddaabbccdabdadadbccddcdbdacdaaaabbcdbcbbdcadbdbccdcdcccbacdbbacccdcdaadbabccbadbdbdabdbdddabdbccccabdcaacbbacbcdacabcbabacaabcddbcccdacbabacdaddaddbabbbadcacbdcbbdbacbcacbcadaacdabcddacbababcacdacacabcddbcdddbbbbbcabbaadaaaaaccccadccaddaabdcacccbbddccaaabdcccabdbdcccaabdbabbabbdddadddbbcaaaddabaabadabbdcabbdaddccbbdccdddbaadcbdacdcabbbbdbaabbdcadbcddcbccbddbddbddccabcbcbaccbdadddbdddbadaacdcdbddcbbdabbbbaabccaabaacdbddacdbabbaddbaaacccbcdcbdbaadcdbcbbbcbcdaddbcbddbdcdcdaddadbccabcdacdcadccdadcbacaddbabdbbcbabaacadbbaadbdadcdaccbddcddcdadbdcabbbbcdabacbdcdabbabccaddaccadddbbcabbdbcdacdbdddbbbbabadcdabadddcaabdabcabdbdadaaccabccccbababdabbbcbccaaacadcabcbadcadcbcdadbbbdbaadccaacdabcdadcbbadddcdcdcaabcdadbdccdadabbaabaaabcdaccbababbdbbbcdcbbccbcdaccbbcdcbbaaaabccdadbaaabcbbbbacbcddccdbcdabbccdaddcacababbcaddaabdaacdbdcdddccbdabcccabbccadbacdaaccdcbbacbadabbbcabbbbdaaddbacbbdbcbaaccbbaccccbadbadccabbbbacbbdadcdacdddbaddcbacbcdddadaaccadbddbdbbcbcdaacdcccbaabaddaadbaaaacbdacdabcadbdbaaaaacadcdccbbacbbbaababcabbddacadacadcabdccccaddcdcdcbdcddcbbaabacdddcadcdbcbcdacbaaddcbbdbddbcddcbbdddaddcaadbcbbdcadddabdabadaadaabcaacbdbaaddbdbddcddbadadbddaaacdacbadadaaccbacdcaccbdadbbabbcddbdcaaabddabaadababcadcdddadabcddcbbdcbabddaadbbcadcdaddbdcbbaadabadabbabddcbddcabbdcaddcddbadddcddcbcdccadacabdacbcbcabbadccbababacaadbabadacdabdbadbcacaccccbcbbacaaacccadadbcdcacaaabbbdbdcddadaabccdabaabdcbdbadabdddbddaadccbddbaacbcbbbcacdaddcdaccbaccbccdcbdbaabdabcaddbaddabcdadcaadadcdadabccadccabbdabdadcdbdccbdaddcccaaaddabbadcbbaabbddcddcbbbccdabbccdcccbcacbcbdbcdbdbbddbcabddbddddbcdcbdadadbacabdbabddcbaaaaadbdcdacdadacadaacbaadbddacacdddbbdabddabaaaaaabbddbabaaabbccdcadccdcccdaabcdccaacabdaacdcbbbaadddcbdbcbabdbdcbadcbdbccbadabbddcdcaddbcdbdacdbabbdadcabadcbbaacbbdaccdcaabdddabbbbbadbadaabcbbcaccdcadbbabcaacaddabdbcabaabccdbdbbdadcbaadaabbbcabdbdbbcaaabbababcaacadbacdacbcadbbacdabddcaadcaaccaababdcbbbccdcdaabcbdabbdbdbdccddcbacbcadbdacabadcbcdbcddcadddaaddcbcbaacadcdccbadacabbadcabdcacbcccaddbbddbdacdbbdacadbcaccdddadccbcbcaadcdaadabacbdadcacbccdaddccbacaadabdcbbabbdcdcdabbaaabacdcdcaabcccaaccbadbacbdcddabbadcccadcabbdbdbdbbbadbdaaabcddbcbcdaacacdbbdcadacababdadccdddbbadcaddccdccadabbdcadbbaacdccabbbadcadcdabbddcabddddbdbbcacdbbacbabddcddbcaadabdaadaacbbcdbdbabaaabaaddaccacabcdbbbbacbdcbaacbcaabaacabcacaddcacaacacddcabdbacabddcbacacddcadadbbbbccbdbbbcbdaccccbcaddddabdbcddcddcdccccaabccbcdcdacbcddabcaaacdaaabbadaaaaccdccdcbadbbbdbaaacddccbbddbacccabcaccacabccdacdccbdacbbacccbdcbcbdbaaadbcccdabcbcbdbcdadcbdccaccbddaccbaacbdddaccaaaadabbcbadbcdbccccabaabcbccbcbcacacdcdcccdcaddabbdcdbbcccbdcbbbaccacdbddaadaccddddccdbbacccaddbcbbacbbbccdadcdccbaddcabdbbdddaaaaccbccddcbbcadadacbddddbdadadbbccabbbdddbcccaddccccdabddccbbcdabaadcdacbcbccdbdccdacbdccdbcccabbcdcddadaabacdbdcabcdadbbbdbdadbacacbaaddcdbabbcdadcaacccaddbadbaddccabccaabcbdcdcdbbccdcdaddbbcddddacdaacdcdaccaadacabdaacbabbcbbcbbbcbbbcbbdbbccadddacdabccbcddbacabddadbaacccbbdddabbbdaddbdacdbcbccbbcbcccdbcaccabcbcbbaaaddacacddabcaacddaabdaccbadcaadbdbaaaacbbaaddcbbdccadbaadbbdbcbccdcdbaaadadcacdcdbdbbdacaacacbadccabbbacdaddbabddccdcbddbdddabaadbccdcccabcaacbbbdbddabcabdbadbbadbbbdcadbaccbcdcbdbbbcadbcdbddadaabaadabadbbadbcdcabadddbdaccadabacccdcbdadbdbcdcbcaaaacbdabaaddcdaababcbaddccbabbbcddbdbcdbbcdacaddccdbdcccabcaabcabdadddcbcdcbdaabdacbadcddadcccddacabbbccbaaddabaabddcccdaadccaddaababcaabdcdcacdabccaaacaaabdcbbdbdbdbbbbdbcaddadbaabaacabcacdbacdcdccbddbdaaadadddadaaacdcddddbccdcccbdaaccadddaacbbadcccccadbcbbdbcadbcdcacacccabbddbddaacbbacdbbcaabaacbdccdcbadabcaababdbbdddabccdaccdddcdcccbdcbccddbcacaabadcddbcabdcdcdbbbaddddddabaddaccddaccbadcadccdacbcbcbcaaadbddccaccbacabaaaabbacadaacadbdddaacdcabdaabcdbabbdcbbbbddaadcddacadcddcaddddaabcbcadbcbbadabababacbdadbdcdaaadadadbdbbcabcaccacbbdbacdddbabdbacbcaacabdbdccdbcccddaacbaaabaddbaccbadbbbbbccaabbcbdabdbcdacacddccaadaaaadbbaadaabcadbaaadcacddadcaaacdbdcaacdbaadbbccacabaacbdaccdcbdaabdaabcbcbcadcdbbbccccbacdadcdaccaccdadddcdbaaacdddccdbccadddcbbabaccbbcdcabdbdabdaddcddcaabaccdcacdbcbadbcbcadcccdabaccdddbaabaaccaaaddbdadabcbcadabdacbbcbccccabcbdbbccbdbaadcbadbdadbadbaabbccdaccbabbbabcccaacbadddcbbbbdcabcacdbcdadabcadabcbccbdcaabbcdcabcdbdcaaacbbbadccbbcadbbcbbbadcaaddaaacaccaaaaccadacdacdabadbadddbadcdcaabbbccacaaababdbadcddbcdbaccdacaabbdbdcbdbadbcdbddddbabbbbdcdacadcddadcbddddabaddcacadabacdbbccbaacacbbbcdaabaddccadacaadcccbcccbaccabdccadddadccacbaacdadcccacaadbbbaaccaabccadaccaadcbaccdcaaabbdbdbbddadbdacbcbabbbbdacdbddaddccbdddbdddbaaadddcbbcddbdadbbabbacaccbaccbcddcaabdacbaadcacdbacacdbbbddbbcadbadaaadadcddccabbdbbabdbaabdbabcadccbcdbadabcaddbcbbcaabddaaadcbcdbddaadbbababcbcbbbbbbdbdadbaaccdbaadbcadddcdadcdbaaaccaccbdbbacbdbbacbcacddbccacabcadccccdccccbddbbbdbcdcbdccccccacadcbbadaadbdacdccdcddddbcccddcacbcdadddbdbdabcababbdcdcdabccdbbbbbadcbccbbaacbdabdbdadcdbcadbdadddccabccdddbcddbcccdbbdbabdaaadabbdabbbaaabbdccdcbadbabacdaadbabcddaadbbcdcdaadaaddbdbcbbbdddcdaaaabcabbbdddbcbbadacacabcadbacbabbdcbbbbcdacdcabacbadccdabbbcdcccccccdcdbbbbccdccacadcdbcdaddaacbdccabdacabcbbdbddcddcaaccbddddadbbcacdbbbbdaacddccacabcbaabdcacdaacacbbbcadbadacaadcbcdccabcdbaccdabaaacddacabccbadbddadddddbcbbcdabbaadbbcbaaaaddbaaabbacbbaacccdacbdbccbdcddaaabbbbbccbdbbddcbbdacdabcbacaaaccddadbccbbcdaadcccbdddabdccadbbaacbcdcaacddbddbccacabdcbdcddcbaddccadbacbdbaddcadbcddcacddaccadcaccccddacdbbcddbcacaccdddbcadddcacdadccdbadcdadabdbdddddacaabbdcabbcdbacaddbaacaacdbadccbdccdbbccdbcdaabbdbcccadbaaaaccbadbbbdbbdacdaabacabcadbdaacaacabaabcaaadababaacbbabdcdabddccbacbdabbabdadbaabddddbbaddbbcbbabbbdaacdbcbbacacacbcbbdadbbbdbacddbbccaaddbddcbabaabdbbccbcbcbadcdccdacaabcdcbbbbccccccccddaddaddbadcaddccacabbadadbdaadadacbababccdacabbddaaaabbabbddabadcbdaccacbbdbbbbcdcdbaaabbbabaaadccabbdababadabccacbabdcdddacdcdbdccadcdbdddabdccabcbcaaaddaacccbccbccbccdbabadbccaddbadbdddbdbbdbcdcdabcabccdddbaaaaacbbbcccddbaabdacacaabacadddbbcdcacabacdaddcabccdcdbbbcadcabddccbbdbccadcdbabadcdccdcbadadbaccaabadbbaacbcaccdbcbadbddaacdbccacaaaadbcabbbaabcddbabdabcddbcdbdbdbbadadbbbdcdcacaaaadcbcbdabbcadcacdacddcbcbcdcddbbccdbbacbaacbbabcddddabbaddcbbadbbddbacbbdcbbcdcccbdbccbaddbbcdbcdaacadbcbcbccacdbbbaadacbbbadabcaaddbbcddbcdcadcdbbbbadaaddbaaccdbbdbabbbabbadccabdbcadcccdcbcbbbbbbbcccdcdabaccabbcccccdadccccbbcadbaadabdbdacdbbdcbcbabddbbababcadcadccdbbcbcbdbddbabadabdbcbccbacdcbaacddcababadacabadbbdbbbabacabcdaabccdaaaabbadcdbadabadacbcbdaddadaababbccacbbaabcaaacdbddbdccddaddddadbaaaddbdccccbdcbabcddcaaddcabcbcdcbdbcbabccacccdbcbdbadabcccaaaabcccabaccddaacdccadcdcadadabdcacacabcdbcccabbaccbcccccbabdbbadddcdaabdcbaacddacbbdddbdaadbadbabadcdcdbbddbaaaccbddbcdccbcddacadbcaadaccdcbdcbdcbcddcccbcbbbddadcdccbcbabcadbdcddbdadcacaaccbdbbabbdabdcbdcbdbacaaaddbbdaacccdbcdbaddddadbcbcadaabcbaabaaadccacdbaaddcbdcaaabcccdabcbbdbcddcaadadcbdaadcdcadacdaacbcbbddccabcdbdcbabadccadbbababcbdadaacbddddadadbbdcdcbcdacddcdbccaccdadcbcbdbccbbacdcdccbdddacacbdccbadcadcbccacbdccdccccddadcbbcdaacaccdbbbbccddaabcacabcabdadacbadbabccbdbcacdbabcdcbcddacbdcccdddaccddbadccdabaadbaabacbbdadddcbddbddcadacadccbdddaaaabbbbabacbbbddccbbdacccdacacbbabadadbbacbbdcdaababddadddccaacacaadaabddababacddbdaccbbbcccabaacadcabddccadbacbbccaaacddbccbaabbbcddcbcccccccdbaaaaaadcdbcbdbcabadbbacdadcbddddbbcadacaddabbbdddddcaaacbaaacbadbbaacaadcdabbdcbdaadabbabdbccdcaabbcccccbbbacbbadcdccacaadbaaacccacdddcdcadcaababbaacdbaaacaaacbbadccdbcdccbdbcdccaababcadaaaccabdbbccddbcbcabadabbbacaabbccacdacbacbadbddabccccaabcdbbdccaadaaaacdabbadbddaccbcbcccbcddbaddbaacdbcacdcabccdbcccdababdcdabddddacdaaababdadcbcaadcaaccccacabadaadabcbcdbcaababaccddccbbdacaabcdbdbabcdcddbabdcbacdcbabcbbdadaadcbaabdbcaaaadaabbabdbdbaabcaaaacbbcbbddddccbaadbdcacdbcbbccbacdbddcdbcdbdcbdcdbdaccccbcdbacabacdcbddddbacddbacacdbdaababcabbcccaddccdbcddbbdbabadbbcdbaccaabacabadbdbbaabcaddccaccabbbbdabbcbddbbdcabadcaddaabdcaacbaadbbbcadcbccbcabcdccbcdcadbccbdabcbccbacbaacbacdbbbddccacbaacdbdbbcbcaaacdaddcdcbcdcccbdaaacadabbdcabbbccbddbbdcacbccbbbaacddaaaaabddaaaadadbddabddccaadcdbdbdcdcdbbacaddacbdadccabaabdbaccbbcbbbdcabbadbdabbcadbaadcbdbbbaabcdddbccdcbbacdcbcdcbddabcccdabaadbadbcaaadccbaaabbcdbacacdbbbbadadababdabaaabbaadcdacaccbcaaaabcdaadbbcbbbbaccbbdccdbcbacaddabcadbcdaadbcddcbabbbabaacaabadbadddcbdaaccadabbbcbadbcacbdacbccdaaccbdbbabdcaaadcbbdaabbcbdccddaadcbaacabcacaaacbbbcadbcbcadbdccdddddbacddccacdaccadcccddbdbcddbdcdbbbcdcbbacbcdcacbabcaabaccccdbbbbcdddddaddaccbbaddccaabdaabdbcacdddbacbcacdcaccdbabacaadcdbbdaadbbcdcdcdaaaabdbcaaddbdbdcddacdcbadcdaaadadbccdcbaddccabbdcdbadbaaccdbbccadcaacacabddddbabcbcdcccacbbadaacabddabbdbcabcaabadcccbcdcddbccbccbcddcacdddbabbaaddbdaacacbcbbbbbbbdbbdbcadcbacbcdaabcdcdcbbccbdbbcaacdbccccdcdabcbdaadddcdccdddcadaacdadbadcacdddbdabcccdbaacacadabdcbdababdcbdbbbacacadabbbdadcdccaadbaadcdadadccbdccacddadabccdbaccdacabbdadddabcdcbdcacdadacaaaabbdccbabbabddcdcabbbbcadbddbdccbdbaaacbcbccbdbcbbadaaabbaadbacdbccccdbdddaddbbcdcdddaccbddaaccacaccccbdcbaddcdbdbbddadbcdbbdcbbadbccdcacbbaabaaadadddaacabbdccbaaadacdbbcbbbabddcaacadcbdcbaccaabdaccccacddaccbacbdddcdcdabbaaadbccaacacdcaaaadddcdbdcbbcddbcddcdbdbdcdaabbccadadacbcabcacbbddbdbbabddddcdaabbcbaabbdadccbcddbaaacbaacdbaadabbccccbccbbabbbaaaabbacbdbdabadaccbdabbddacbbdabdaccbacdbddbaadbdbadababcadadcddaadccddbacccdcbcddcdcbcadcbaaadbdcaddccdbbbacbddbbddcddacbcadbbbdcacaaccdcadbcccabccbcbcdcdbbdbdbcadabbcddbcccbbcbbbdabadcdddbaadcaddcabcababcbadddbbbbbacaacbcbbdbacddbcabcbabcbadbabacbabdcdbdbabdbcdddbbbccbdddbdcabddaadbadaddadbabdbcadcdddcccbbdcacccccbadadbaccbdbcdcacbbbbddddbcdcaacaddbbdbbcbadcdcdcaadaaabbdaccaadbaaddaadaaadcabaddbddaaadbdabdcadbcdabcbaddddcdbcdadccbccaaacdbadacdddccddddcaabcbcdadbadcbdcbcaccaadcdaccccdcdacbbdbcdccadddcbabcdddaaaabbacbbdcccacadcaaddcabbcacddcadaabdbccabcbabbbcbbddaabcdbccadcaadabaacaadabbdacbbccbbababcaddbbabddccdabacbdddbbacdbcaccacbccdbccbaababbbdaaccacccaaaadcbdbddaccccddcbbdcccadcbabbacccccbcdacdaccbaabddacccacccacdccbadabaddcdbbdaadcdddcdddbdcaadcdbdbcadcbadbcaaaccccaaddbddcdcaabbbdbdcadbbdccdaadacadddadcddcadcccdbddbbcbaaddbadbcdccbccddabcdccbaadbccaabaabacbcbdbaadacaadcccddacdbcaacbcaaabdcaaabdbdbaadadadddabcbdbdaaccdacaacbadbcdbdcdbbdbcbbacbadbdaddbadabdbacbbcbddddcdaacdcdaccacbcdcacdbabcabaabcbaccbdabcdddcbdbdbcdcccadaccbbcbbbdbbbadaacacbcdcbcbbbbdcbabcbdbdbbdbbadaacaaacbdbdacdcadbbbadbaaacddcdadddcdbacbdcbadbacbbddcaacbddcdcbddacaadacdccbdcdcadaadcbbdbaababbddcdbabccbccbbcabcabddbbaabcdabbacaacbacabbadcbdbddcabddcaaddcccdddcbadcbcbcdcbddadbddcabcbcbdcbaccabbbadcdcbcbdadcabaaacbabaabbbdbabdbaadcbcbccdcccadbccdbaaababbbcdabccadcbdbbdcbadbbaadcbabbaaaddacddcabcdbdccccccbcdddbacadcbcadaaadaacacbbddbaccdcaccacaccbbcadddbacbcdcbacaabbadcabdbcabcbbcbdaacaacbbadadbdbaaaaddddadcdbbdadbbcaacababcaacbbcddbccbcbdbabdbbbacbcdacbabbdadbdbcbbbcbadbbabadbdcdccdabbccacbbbadddcbbdbcdbccabcddbbabddddccdcaaacdacacdabbaccbbdcddbdaccbcdbcbbacbbaddadaaaabddaacabbbdacbdcbbcbdbbbdddccadacccadacbdcdcacdbcdcbdbdccbcbacccbbcaacabaccbbdacadcdaddbcccddbdcbacbdacadadcaaddaaddbdcabbaadbcdbbaabaabbcccacacdcccbdabdacddbcbabcbbabadadbdbcaadcdaabdcccbdbcccbcaabdacbabbdcbdddbbaabbccbcbadadacaccbabccaabadccbccbbabbcccbcccdabababadaddbbbacadbcacbdddcbbcdccbbcacccdcabcbbaababddbabddddbdbddbcbaadadabacdcdbdbaaadbcbabccbcaabbcbabaacddddababaaaabbbdbbaacdbbbbbccabdcacdabdbccbdbdcbcdadcbbbbbcaacdbcadcdddabadddbddabbadabdbdaaadcccdaaddbccaaaddadabcadadccadbacabdcbadbadabdccaacdbdbbddacbdddccccdaadabcbccdbadcccbdddbdadcabbdcddabbbbdacbabdccbabcdaadbbcacbadcbadcccdbdddaadddbdabdccadbcacddaadbcdbdadbcaababaddccbbabddbbbbacbdbaadbcddbdcdbcacabcccbccadacbaabbdcbadcccabbdccbbcadcbcbacbdaaccbccabadadcbbacccaccdcccaaabbdbbdcadddddabdadcaabcccdbaddddbccbadbdbadcbdacacdabddcbcccdacbadbcbbddadacdbdcaabccadcdadaaddaaabadabcdbcdccbdcddcaaabbdbdddcdbcacddcacdcdcddccdadcabbcabccbbdacbcadcbaaadaccacdacdcbbdaabbcdbbabddcbbdbaabdaaaccdddcbbaaabacadccbacbdacaacbbccacacdaccdddddcacdbccdaddadcacaccdccdccbbbdccdbbcdcdbcadbadadcdbcdddddcaaaccbcadadbacdbdddacbdadbdccabadaaaabbacacacaacacaaadcacdccddbdadccdadcddbbbcadabdabcabcddcdccddaddaacaaacbdacadaabcdcbcdadbabdbbbcaacddddbdaccbcbcbcbbdacdcccdbcabacacddaddaabdadcbdcbacccbcbcacdbabcacdbcadadaabdddacdaccacaccdbabbdbbbddbbbababbabcdbccccadbdbcdcacbbaddbadaacdadbcabbadcbbdcddddbacbbdacbadbaddcaadabaaddbdcabaaccabccbadbbbbcadbdccacaabbddbacdcaaacdbdacdccdacdbaaaababcdbdaccbbabaadbaabcabaaadbbcdaccccbbccadabadcabccddbdcbdcdbddccabddadabbcbabbbcbcabbbcdbbbbbdbdcadbbdccbaabbabcdadddbdbcaccbcdbccdcddcbaccbcbccdbadccaccdcadadacdaaaaaadcdaaabcdcdbacdcbdbddcbbcccaacdabbbddadcbdbadacaacbcccdaadbcaacbcaaccbbddcccdacdbcbbccdadbcdaabbacaddacbcddcdcbcbdadacccdcacdabaddcacacbddcbbabaabadabadbcabdccdacaddbbccccccbababaddabadcaabccdbdbbddccdbdccbccbcdbaddacdaaababcccabbaadacdcdbadcdddbbccddbcbbdccaabcabcaaaaaccabbccbccbcdcacbcbaaddbdbbbbacdcbbcbabddacaddaaabdddbbcbdcaadbcbacbabbacacddcbcdbcadddaddabadaaddddaccbabcbdabbcbbbaaacbdbbdcbabbbbacdacddbadacddabdbdbaaaddacbdddddcddcdcaadabbaaaadcdcababbdaaadaddddbbbaccdaddadadacdcacabcdbdbdbcdcbdadcbaadcadcaddabcbbccbcbbdcadacccbdcabcabbddbdcbdabccabacbacdcccdcbbbaccadaacbbdddcccdbdbdacbadcbbddacbbbbabbdbbcaccddaaaadbcbaddadbaadcbbddbcbdaabdaddbacacacdddcabdbabadcacbaaccccbaaabcbbdbaacbcbdbadccccacaccadcbcbcdaccadabacbdabadabbbaccadcbbddccabacddbcbcbaaaaddcccbadbcabbbbcbadbdcdaaddcbdccbcbddadabbcabdcaaadbadcbcdacccaaadbbdbabddaddcabcbcdbdddcaaaaabcacaacbcbbcbbbcdbcccbcddbadbcdabbabcbabacabcadbbdccadaabddaacbadbbcbaabbbcbccdacddbabbbabdbcdbabddcccdaddcbabcaaddbcadbacccdaddaddabcbcacccdddbcdddaadbbcadbdaaccddcdbdcbbabdabbbaaabdadcdaaccabacacabaddbbacabbdcbbaddbccdcaabadbadddacbbdadcabbbcccbccbccaacbdbdaacabdcccbdbbbaabddcbcbccaaacababdcaaccadacccbdabbaadbdabbaaabbbcdabbabccaacdcaddcabcdcabcdcbbdabcbbbccaadcdaddacaabadbbaddaabccdcadbbbadacdadbcaaccaadbbccaccbaadacbbaacbbbbadccdcaadadbaaaddacdabddbdccdadcdcacaabcadacbadadbacaabbacaccbbdcadcdcaccdbaadadbaacaabdbcaccaddcddbddccddddcccbbbccddcddbbbdcbdacbcacacbdaaaadcbddcaccbaccbcdaccdaaaaacacabdcaddccaaccddcabaccddbabcaadbddbcdcadcacacdcbbbccdbccbbbdcabbddbbababbcbacdccacbdbacaccadbbdbacadcbdcdaabbacdaaaadbcbccbcdbaddacdbbabbddaadbdbaaacaddbadbcadadcacaaccbaddadbbdabccbccacaddaadcdcccaaaacaddbccbaddbdaacbccbcbabbbbadaadddddcbcadaaccbadccddadcdbccdccaacdccccadbcbacdaaabcbcbddcdacacabadabbcdcddbddcbadaadaaacaddbcbbdccbdbadccabcbdbacdccdccbdbccdccaddddaccbbabdacbbcdaaabbdbdccabcbaacbccadbdcadcbaabdaacbdddccddbdbbccbcdaacadacbddbdbbbdcaabcaadddbdddbabddddabaaadccbabbbacddddccacbddddbcaccbcccddcddcaddaccdcbaccbacbbdbadbadbaabcdbdaccbaccdacbdcadccccdcbcbcbaaaddcddbcaacacdacdaaacbbabdcababbbdcbdcbabcbcacbadcbdaddabbdaddacdddbcccdbcccbaaacddbdcbacbbabbcabdbbacccabbbacddbcacdabbbdcdbccaaabbddbaaccacdacaaadcdcaaddbacdbaabadbcbbacccbccadcdcbbbbaacaaadabbbacbdddbdabdbbbadcdbcbabcccabddbaabadbaddbbdabdbdaabddcacadbcadbbbcdaacbadccdbcdcccdcdaaddabdccbadbdcbbdbccadabacaddcdcaacbbdaccbcadbcbbcdbcbdcccacbdadddbccabcbcdbdbccdbccbacbaacadaabbacbdaacdbacccacdcacbaccdacdaaadabaddaddbdcdccbcdaacacaadbaccbadcacccbcbadcbbbabbbaadaccbcdcbbddcaacabadbcacbdabbddaddcdcbababbacdabaadacdbcacbadccbdbcddcddcaccbcccdacdbbacababcbcdddabdbdcccaabcddcbabcdbaccbbcbabdcbbcbbbcbabbaccaccacdbcdbcbabbbadaadbddcbcbbcbbdbaabadbadbadcabadbdddbbcdddaaacdcddaabcbacddcdccbcbcdbabcaadcadbcaaaadcabbbdabbacacabbbdcacbadcbdabcaaabcdbcdadbaddbaabcadcddadbadaacbdbdacdababbdaacbaccddacabcdcaadcaacbacadccaadbbbccadbcddaccbbdcccbabcdbabcbdcadadcacaaaddcbaddcbcdbdabcbaacbcaddbdbbcccbccbdbcddcccadcdabbabaabbccbbcabacbbdbccdacabaaddaadcddabdbbccdcdcbdbcacbdcdaaaaadbddccaaccbdaacadbbdcbbcabcccabbdadbdaaddaddbbcdadbaaaddbbccabaccaabddcadccdbbccaabdbcdacccaadaccdaccdbdabacdcdacaaabddacccddbcddddbddacbbacdadabdbcbacaaddadbddbccdddabccbcbbbbcbcbacabbacacacdabaddaaddbbbdabdbcadaabbddcddccddcadadcadcdacacaddbdbdacbacbadbbbdacbadbcdccddaccacbbccdbdbbcddacdddbcbbccddddcddccaadabbdabbdcbbcbcacaaaccabcbcbbacadddaddaabadccddcdddcddabaababbcbdbbcbbdddbcdabbdccdcbcbbaadbcbbddbbcbcccddbbcadcdbcddbbcaddbcadaccaaaadbcaaabacdbdaaccdabbdaacdcdadbdbadccadccacdddadacccacadabaacbdbadaddaadbcdccbddcabddddbababadcabcdacaaacdbbacaadccaacaabdddcaabccbaccaccbcacbacabbdaaaacccaccdddadcddaacdccabcdacddbcdacccbacbdbadabbdaddccdcbdddacbddbddacadbccdcdbbcdbaaadbcdbcccbddcbcadddabadccbddcbaaabbaccbadbcddbcddcaadacadbcbcabbccdccddcdcaddcbcbcbadbaadaccadcddbbcbcbaaaabdadcaccdbdbaadccadcaccacdcbaaaabdadaaaddcbdddcbabaacbaaabdcaaaaaaadcacbacdcabbdcbddcdaccbaadccbddcdbcdadccbdacbcabcbaaabbbbdadacbdcbdaddababbabcaddddbdbcbacbccabdccbdbcbddbcdccdabdcaddddbcaacabcdbdbaabbcdddabbdccbcdacccabdcbdbdabcabdaabbbddddbcddbaabdbbbcdcabacbbcabcccababbcdacbdbcdcacbbddacdbcdaaadcccbcccbcaccadbabccadadcbaadccdcddccabbdbcacaabcaccdadadbacbadabcccbdacbdcdabcabbbdbbdbcaacadabadaaaccdabcadadadaadaabdabdaaccddaddccaababddabbccadcaacbbabbcbdcbddababccbacaaadcacbcaddadcbdccaacdcdabccaaccacabbadcabddabaccbddcbdacdcdddddbaadcbbdccddaddddbcdcddccaddbaadcdcbdcdddcbdccbccbdabbadaadcbdbbabbadbdbcdbcddbcdbadbbbaccdcbbacccbbdbccdcbacbdbacbbbbbabdcdaccbaabcabbabacccccabdcdddbaacdbddabcdcddcbcabadadbcadcdacacbacccaaccbadcdddbbbcccaacaddabdbbbdababaddbdaaacadbbacbbbacaacbdcbacaccaccddcaacccbcdbcdabcbabbadcddcdaccdccbabacbcaabadacccbcccddbbaacdddbbdadadcaabcbddbadacabdbcabcaadacaaacbbcaccacdccabccadbcdacabbcadbcbcabcaacacbcbdaccacdabbdacdadbdbbdcdcdddbcbabccbacaabbcdabbacdbcbacbdacbdaacbdddccbccaaacacbcbabbdacbbaabbccbbadcccdbbabcddbabaacabadcaaccbbcbdbdbcadadabadcddaabbbdbdcdcdabaacbddbacbcdbbadcaabbbabbdcadbacbcbaaddbadcdcbadbdcaacdbcccdddabaaabddcccccacaadaaccdccddcbbccdbcabbdbabbddbaabbaccdbbbcaccaccbbdaadbddbbcdddabddccccdbadcdddbdbabdbbcbacddbacbaabaaddaddacdbccbaacabbbcdcabddabdbbcadcabbccdbcbdadaaddacdadbdddaadbaccaaabddcbaaaaadcacdcdaaacdcdaccdbbdbbcabaacdbccabbbcaaabacaacbcbdaacdddcbadccbccababcababaccaadacdcbdaabcccbaccdaddbddcdddcdbabbdbbabbdbccdbdbdadaccbdaacbddbdcdaccaaaccbacbabadddbabdadaabcdccdcddddcdcbdcabbcbaadabdbadcdbddbbcbcddcadbcabcacccabadcbbaddabcaacdcabbaddcacdbdacbdcdcdbbaabbadabaadcbcbbbabcabaaababddbbcaadaddcacddcaddbabacdbcdcccacaabcbbabcbbbbdbaccaaacbcbdabaccddacadcacaabcadaaccdcabbaadbacbcccdcdcdadaadcadacacccaadbbccdbaabcdababdbdacdaaadbccccdddacbdacdaaaadaddabaabbbdadccbcbbdddddabdbabbacdccdcdbddabcccbccbdbddabadbacdbcdbdbbbbcbbaaccaadbdddcbdccababdcccbccabcdbaacacaadcaacdbbaacddcadcdccccbbcbabddcaccabbcccbbcccdaaadabdbcbddabbcddcbcbddcadacccaddcccbddcddbbdababbddbababdbdccadbaddbacddaddaaadbbdcbaddaccbccbcdbbaaadabdaddbdbbccbadbcddadadacbddacbadccacadcdcabbccdbcbbbbcddacacbccdbcbbcdababdccbabdacddaacdabbaaabadbdccdcabadcdcaabddddcacaddcddcdccaacbbcbcddbcccabdcdbcbacccbdcbdbcacaabdabdbdbdbabbbaaacbcbdabcabbbcadddccacacbbbdbcbdddccbcddcdcddbbbaccbaabbccbcadbaaacbbaadddacddcaadbaaddacdccbcaaacbcbaabdcbcddbdacbdbbdbabbcbbcbcaadcbccdcbabddbdabaacdaabcccacccadcbcdbbdbcccddbbddccdcabaccadcbabddccaadbccacbbbcbdcdabbbbcacddabcbbaccccaaccbabcbdaabdadbbdcdaabcdcadbdbccaccdadbcbccbdabdccbddcdbcbaaacadcaaabdacbadcdbbadccbaaaddbbcabbcbabbbdcdaacacbcdcaabddbaacbadbbabbbaccabcacbabbcadcadbdcddaccbaabbcbdbbddacdcbabdcdbccdacdbccacacbccdbacdadbdbbbcacabbcaadccbadbadadbbcdcabbcdacdcabccaabacbcdcdbdbdacbacdaddbaaacadbdcadaadaddbddcbbaddccccdccbabddacbdaadbadcdbcbdcadccddabbdccbcbdcbbaccccdbcaaccdbbbabcaaddbaadbdcabbbdabcbcadbddcdaabcdccbbacaaabbabcdcdbadcaddabadcdcabdbddddcbaaaadcacbaababdbaddcdddcadbddbaabbbcbadababacbacbbcbaccaccabbbadadaccaacbccaadadacdaaaaccbdbccbadaddabaacaadbabcbdcadcaccdcdbcdbcdbacdabddbcacccaadabbbcbaccddacdddacdbdccbabdbabbbdbbacbcbacbcbdaccbdbbbbbbbddacaacababaacacdccccddbdabbcccbddabbcacddbdcaddacddcdabcdcadcdbcbbbcddacbbdcaaabbbcaaadbabbcbdabbbdabbdaddabdcabbcaaabbdbdacbdbbdaddcdddcdabbdacacaadaccacbdbaadabdabdccaaabbababddadcbccdbbddacdacdacddcabdabbdbddbcdaacadcbbaaaaaaadacdbadbcbdbbbcadddddcddcddcbdddabadcbabbbabadbcccdddacdbbdbabacbdcbacbcbcabcadbcaccdbbaabbcccccbbdcbabccdadbdbbdddbcaaacacabccdbdbddccaddaacbccbcddaacababacaccbccddcaccdbbaabdaddadadacdcbaababcaaaddddbbcbdadcbabbabdddcbaccabaaabdcdacdabbaddaaddccadbbbdaadcbaaabbacdaaadbbaddcdcdcdcabccaacdcbbdbadacdbccdccaabcaccbdcddaccbdcdabdcdbbbcaaccccbabacaaaabdacdcbacbbbacddcbabaacccdacdabaddddcaddbadcaddcabbdabcbacbdbbcccdabadbaddbbccabcabbaacddcdcbbaadaaadaddbdcbacdbddabbdabbddbabdabcadaccdaaabccadacadccccbdcbbcbdccbdbdbaadcadbabbbbdadbdcabcabacbaacddbdbacccadbbccdccbcacbdbdcabdcddacdadddbddcacbbcbbbdccdacdaacaddccbaccabcdadacdbdccdbbabbaddaccacdddcdbcbbbbbcababcddddaacccdbdcacbaddcbababdbacbdcccbbcbbbadaadbdcdccaaaaadaaadcbbddababaccdadcdabdcccddbaccacabadbaaacdcadbbdddcccabcdcacdbcbcccdcabbcbcbaacdcdbbdaddcdbdacabbbdbcbdddacbacadbbaacacbaadbacbbbdadbbccdbccbabbbadacbbcbbbcbbcbbcddabcbcbcabbdccabddadbcbdadcddcdcccabbaaddacbcacbcbbddaaacbcdaabacddabdcbdaaaccaabcabccacdcaaaaaabdbbaaddacacbcdbdaacbddbddabacdccbcbabdabcddcadccabaccdaadadbccddbcaabbbcbaaaacbadddbcdddcbdddbbcdabdaadcbcadcadabcbbbcdcadcbcccdddccdddddddcdadbcdbbabbcadabbbccbabddadaddaccdbdbdbabadccbcbcbdbcccbdcbdbbdcadadcbdcaabbacdbccaddaabddbbcdbcaccbddcaddcdbcbcccbabcbdcdbabbacddaababaadbccabbacdcbddcdcdcababddabaddacadadbbcddddcccdbcbcaabcadcdabdabbdabbbddbcddbcbaccdcaaaddbaddddbbaaaaaddbdadbaabbccdcaadcdadccadbcccbdbdbbdbccacbdadacbccbcdddacdddcbdbaacaccabdddaadbdadcdcdcbabcadcaacbabdbbbdbcbccdaabccbaabbabbaccccbaddcbddcbbaaacdadadbbbbabdaadaaabbcbaadcabccdcdbadccdcabaccbccddbddbccbbdbababcdcddcdabbadcdcbddcaabaadbbacbcacbcaaaabbccdaddbaacbabbacccbbbcabbcdcdbddbddcbcabdaddccdaadcbdacbbbdddaddbdacbbbaabaabdccbcdadcbddddbbddadaccabacdddbbcbcbdacdcdccbdaadadcddbdcacbabbcacbccdacbcacbbdcabaadacdaadcbbaddddbaadcbddcccaaaadcacabbcbdccabdabababdcabaddbdbbbcbdbdacdccccadcbacbcbdbdaabdbdcccbbbabcdcaabddadcbccaadaccbbadacabcbaddbcadcdaddcbaacddccacdaaaabdaacbcbdbaabcbccbcccbabccdaccaadadddcdaccddaaaccdddcaaabdabcddbdacaadcbdbadbaaccdddbaddacdbdbbabdadadcdbdcdcbdaaccbacadcaacbdbacabbacabadbcaccadaaabccaaaaccddacbdddcdbccadbaddbdcabbbbaaaddacdaababbcabbcdadbbbdddacdbaccaccbaddcacaaccdaddbabbdaacabcdbcddccdcbbddddcbbaddcddcacabaaacbcdbdcbabcbadccadabcdbababddbacdcadaabdbcbbdcbcbaabdacacdbdcbddaadaabadaddccbddaacabbdbbbdccabaaccbaacaccdbdabdaaabacdcdcacacadbcbdcbdacacabbbdbabbbaaaabbaaddcaaddabaccccbacacacbacacdbbccdcacbccaaacddccbdcaaabcaacabcccbcdbabcbdccccdbdccbaabcdcdcdadbaacbacbdacccccabddadbcbdaddabdadbdadcaaccbaaddaddcddacacdaaadacccaadcbaadabcdbdadacadbdacdbcadcdbccbcaddababdcadcadcdddcbdcbadcabdddddacdbdbadbadacdaaccccadbadbcbbbdcacccbcdacdcbbcbddcccacadbbcaccacbdabbaadbacaabadbaccacaaaacdaccacbaccbdbadbaaacabddbbddbbbbddadcdbdcaadcaadadaacbccddddaaabadabccddcbddbbccbbdccbbbcbbdacbdcddaaabbbcadadcbdabbbbbbcaadcabcccaaabadcaadccbdadadbabaaacbbabbaacadabdddaadcbaddaaadcddbdcaabbcbccaaaabdbbaccdaccbcdbbcbcccbbddabaddbdddbcbacbadbacdbcabcabadcbdabaddbcccadacaadccadcbaadbdaacdbcdacbddaabccabdbcdaaddabbbaccbbdabbabcbdbdbcbacacacabbaaaabddbbdbdcdbdcbdbaddcbdababdadcbdabccdccadcbdddbbdccbdcdcaddadaacdcabacbabdbdabdacabacccbbdadaacddaacaddacdbccbdacbdbabacbacbdccccdbaacbddcbaacbdcbadccaccaccadbcbddcbacabbcacbaddcdccdcbdbdddcccbbcdacbdcbbccaddcccaddcacdaadcbdcbaaaadccadbdddbdbabdcdccdaccacabcaabddcabbbbbbddbbdabbcdaaabaccacdcdcdcbbcabcddcabdacdcabccadcacdbbccdcadccddcacaabcbcaddcaddbddacccaaadbbcccdbbdaaacbcbbbbacbcabcaaacabdacadbaddabacbacadccbddacccabdddabacddacdbddbdcddabcbbbccabdbddabaccacccaabcacdcdbbcabcdbdccdddabcbabcadbcdbccadbbaaddadaadddcccbbbdbccbdabcadbbdcbcdbbcacbcbccdbdbdccccaccacadacdcddbdddadbbddbdbdddaaddcdccbbbcbdbadbccbddcbcaaccccbabbabaababdadcaccadddaaacddacdcdbbdacadddcdbbaccdbabcccddbcdcbabadccdcdccbcdddcbdbcaaabcdbbdcdabcdbdaaaabdadacabcbbbadcadcacdbbabbabcdbbbaaabbaccbcbdaacaaaaadbabcbdccadbddacdbdaaddbdabaddaabaddbddbbddbcabbaababbdbacdbdcdbacbdcaccadccbaabbdbabaddddcdbdcddcbdcabbccabcdcdddbdbddaccdccddaabacaccdbbcaddbaddcccdabdabbadcbdaaabbbccdbcdaaccaccddcddbdbcddcdcbddcacdaddbcabaddbaddbbbaadaabababcddcaaacacabaabaaddcbdbbacadbdbccacaddccabbccbcbaccdbaaccbcdbdcbaaaabcacaabbacaabcaccbdadacdddaddcbdcdbcaabaadbccabaaabcabbaabcdaaacddabcdccdcadaabbdabbbcbaaaddccbcdbdaaacddbbddbdccaabccbbaababacbbbcbbdabaadccbacbdbacbbbcdabbbbdaddcacdabdbcaabdbbbadddaacabbcbdddabcbcaccbbaaaccadddadddbbcbbdbcdcaccbbcbccbdaaddcaadbbbababddbccdbabcdbbbbbacaaaacadcccdbdcaadccdcabdbcccacaabadbdbcddabcccdbdcadcbbcaadabcacdbcaccabccbaccbadabcbbacbadccaaccdbdcdccaadbdbdbdcdcdaaaccabbcddccbcccacabcbcbaacccaadbddabacaaabdccbbbbdcddbddbababdcbcbdcbbbbdddacdaccbbcaaaadcdbdbbbcaaccabbcbdbdcdcdcabbdbcbddcbacdddbcbadbdbcadbaccaadacaaadddcaaabcddccaccaddcccacdabbcaabddccccbbaadccabdbbcdccdaacdaccadddbdabdbcbddcddbcbdbbccbcbcacdaddacabbdbadbdbabcbccadbcccabbccddccadbbbcabcaabdabcbbccccbbacbdaabadcacbbcdbdcbdddbaaddabaddcaacaccacbbdaabdcbbbdcacddcdbbddbcaabddccaddcbcbccbbabacccdacaccbbdcacdbdccbabcbdccbdccaabddcbabbcdadddbbdaacdaaddbbdabaccaddacaabacdbbadbcaccdcaadbaacdbcdcbbccccbcccbbcdbaabcbcccbadcabdbcdaadbbddacbbcdadaadccbbabcdbbcbbdaaccdadbacacdbaaaddbbccbbdbbabcacabcadaacacdadcdbbacacaadabdccdabbdbbcbabbcacabdddcdcdbabbadccccabbbddaccdacdbdcbbbbbdaccabcdcbccaaacaddbbcdacacbabbbacbcdddddaaccaaacbdadcaaaabccbdacabddaacbcddcbdbadaaabbaddddacbbcbadbabccbabacbadadaadacdddccbbbacccaabaccbcabababbaabdacbabcbabadbbcbbdcdbcbccdbbcbcddbbcccbdaabdccaadacbcabcdabdcbcaadcddbdddbcddcdacdacddaddbabcacdacdddcddadbbbaacdbbdddbcadcbbcddcbbadbadddaadaaddbdbcbcbdddcddcadbdacdadbdacabdacbccccdcbbcdbbcdbdaddbaaccadacdcddaabacbdaadbccaddccbacdddbdcdbbadabdcbaaaccbbbcabdbccdbccabbbadbbaccbbcaadadbdbaaabcbcbbcdddbcbabcccddddbbbdaccabccbcadaabaadabbdbadcadcaabcaabacddbbbbdccaddccbacbcbbaaabbdcabaccabbcbababdbbddcadadbcabadbbabdbcadaabcaadcabaddcbccabbbccaabaaabacdacdbdbbcccdcacaaaabaaddcbcadbdcdcacbddcaaadcadcbaacbadbcbbccbaccbddcadbadcadccdcccabbdacddbddddccdaacbacacacbbccdadacccdddcdbcbbcbcbbbbdaadcaddccbccbbcdcadcadcdbcdababddabacadcbdbaaccaddabaadabacadbccddcdcaadbabcbabcdcbbcddacddbdabbcdbbbadccbbcccbadbcccccacccddcbaccbbcacbabbbcacaadbccddccbaddacbcbaabdddddbacdcdaccddbdcabdabbdbcadbcdacaaccdabcbcbdabdcdcbabdbdabadacdbdabdccaabccbcddacbbbdcccccadcacddaaaaacaddbcadaccaccbbaabbbcadccbbdadacacbaaabcacddadcdbcadbccadbddbbdcdcdadcbbcbbccdbcdbaddbacaadcbabacadbcdbbcaaabdbaaabdbaddbaddcaccdcccaccbcccdccadcaacdacbcbbdaaacbbcdddbaabccaccbabbbdbbabbccdbbbbdaddbdbdcbdcdbaaccbbcdcddcbdcaacccdadccacdcadaccccdcdbdcbbcabdccddcbbaddbddddbbbddbdbcdacdaaddbbbbadcbdbaddbbbbcbdcacbcdaaccacdccddcbdbbacdbdbacccabbccaadacadbbbbacdabbadadbcbbddbccdbaaaddcddcabcadbabacaccdabaccabcababbcbbbdcbbdbbcbbbcbabccadcbbabddbabbaabacdacdddaadbcccbbdacccdabdbacaaadbdcadcdcddccbaadcacaacccbccbbacdddaaabdbaccbdbbbcaaabddbaacabadddbbaadbbadbdbabcbddcbddddbdbaadcbcaacdcadabbbdbadaccccaaabacddabcacaccacbbbaadbbadcacbdcdadbbbacddaaadddbaabbaadbbdadbcbacaadaacbccaccddbddadacbccbddbcdcaabbcddbabbcadadcbbbbddbabbadcdabaacadcbdadcaabbabddcbdcddacccdcabadbbcbcddabcccccdccdddabbccbdaddbdaaacbdcabcacadaaabdccabcccaaabbdacbcaaaadccccbdccdbaddcaadaaccacabcbddddcbaacdbdadbdcbacabcaccbacacbddadccbcdabaadbbacadbdcabbdcaabcaabddbbbdddddcaaaacddacdabcabadcadbdcbdcdaadadaabdbaabadcccbaabdbdccadbcdcadbbcbbbbddabcadccadaabcaaacdbcccbcdbdbcddbcdcdadccbbbcbadadcdadddbdcddaddbacbbacbacbdaabbccaacaddddddbddaababcccacdaacacabaacbdbddacdbaabbcdacbbaddabccdcbcaabbbacacbacbdcbbcdaccccabbbacbacacbbdccaacadbbbaadaadccaccbcaaddadbaacbdccccbbbdaccacdbadbdbacbcaaabcacddbacdcdcadcddbccbddbdbbcccaacadcddccaddcdacaaabdddbaadcbbabcdbdcbccacadcdbcadbbabbabdaccaababbbdddaccbbdccbcdddbbacadcdabdbbdbabadacabccaacaabdbbacacdccbdcbacbdcacbdcdabaadbdacbcaabbcbddcddcbbbdbcbcbbadabbadcdbbcaddadcccbbdcbcccddaddcbadccdacbdbdbbabbbabdaabdbcabcadbabcabbbcdabcccabadbccdcadccddbaadbbccadbcbddababbcadccdbabacddbcabaccdbccbdaddddabcaddbcddaaacacdbacbbccdcccdddbabbbdbccaaccaddbdbadddcadbcadbcababdcbcbbcbccdbddbbdbbdacacabccbdbdaabdaabdbdbcbabcccbadabacdcadbbbbaacddbacaacdcabddddbddcadbabdbdcdbbcacbbdddcabadccdaadbccbbadddacacbccbcbcbbaabcbcdddddbcbbccdbdcadddaaacdbcababddbabaaddbadacabcdbcaabdacdcddababaadcbcddbadadadbbbcddcdbadcbcaabcdbdcbdbcbcdadaddccaaacdabcaaaddbbaaddcbbccddbccdcaaaccabcaadaddbbaacaabacbccdbcbbbaaadccbddcdacdaabbcdbdbccddabcccdaaaddacccaabacccdaabcbdbaacccbadbaadbdcbbbacbaacccbabacacdcabcabbbcabdaaaaacacbcacabbdbbadcbcacabcbdbaababdbabdaaabcbdbcdabdbcccaccadabbddcccbdcdccdaabbaccabddccaabacabdddcabadaaccacbbbbbdaddbdbbdaddaddcccadbdadcbccdadacbabcddaccdcdcaddbaaabadaaacbdacacdbcbbdadcbbcdbcddbccabdbdabbcbdaadbadadbdcbabbcdbccdadaaadbbcdbaacaaaaaacaacdaacdccbccadbdbccbccccbaddbaccbccbabdbdbdadbaddaccacdcdbcdbaabcabdabdcddabcbccabaccabaccbccbadcddbcbdccdddbcddaaabbdbcddddaaaadccbcadbcabdbabaccadabaabcdcdbacbdaacdadbddcbdcdbcacabaccaddaddacacdbcbbbcdaaddbabccbdccbccbdabccaacbaddbdcdacadbbbdacbddddacdacdcdddbdcbccddcdaccacabdaaadcbdacdcdcdbacccbbabbaacaacdaaacdcddaaabbbdcabaccbcccdccbbcaaaaabcadaddddaaddcdadbadaddacdabbddcadccdabadadaaddbabcbadbbbaaaccddcbbadccdccabadaddaaaaddbcaabacbcbdaaabbbccbadcadacacdabbbdbbccbddbadcaacbccbaddbbacabaacdbbdcbbabdacdcacbcdccddcbbcabbcdacdcadcadddbddcdbdbbcabdcacddcbdaacdcaddcbcbbcbaddbcdcdbccccadbcabaabdbbdabcdadbbbbdccbcaaabcbcaaddcbcaddabdcadcddaabcbadacaddbcdcacccadabcbcaaaccccaadabdacadbbcbddbababbcadadbbcaadabccddaaaccdbabcaccbbacdcaadbcddaacaaaaddcdcdbdbcdcabadbddbcbbacdabaddbadabbababacdcabccccdbdbbcbcacdcdcaccadbdbadacbdabbdcabdbbadadbbbcbcdbcbcabbbaaccbdcdbdaadbddcabbdddbbbdaabddaaacdaaabbbcbabcaabdabdbcbacbcbbaaaabaacbaadcdddaabdbbbbbdacddcbdbcacbddacbbaaddbccdbdbccbbdadbdccabbcccdddcdbdddacccacadddbccbacaccbcacccccbcddcbacddddbdbadaacbdabdbabbbdbabdbbbbccccdccacddcdbbddddacdcaacaccbdddbdcdcdaddddcbacadbbbbccabcdbcaacddcdbbbdcdaccddbdaddbbaaaccbcbdabdaddbaaabadcacdabadcdbbbccbcdbacdaaabbcdbbddccdcbbbcbbbcaaddcdadabdadcdccddccbdcdcaacbccdcbbbabddadccbacbcbbbcadccbcddccdadbbdaddbdddbbbdcdadbbddcaddadcdaddddddccadcabbdbcbccdbababccddaadbdabbccbaacdcdbdbabdaaadcbccddcbcadccbdbccddcacbadcaddaadcaaddabdcdaaabdccbaaaadbadbccbccbdabccbbadcbabdabbcccbdcccacabbcdcbcdbbdbcadcbbcbddaaacdcbabcdbcdbbbdabdabddacccdbccabadddaaabbadbdabddccacdbcdcaccbcdaabddbddbbacbbcbbacdcdabbacccacdaccabcacadcdcdbcdbcddcddbbddbcbcbdddadcacacabbbbcbdcbcacdaacacbdbbbbccdcadddccaaadccbdcacdbcddccdbbdaddcacaccaabcacbcaabbcadcbaabbabdbcbcbbcaadbcacddbddcdabccdcadddcbccdadbcddabccdacdccdddabdbddbbdcddacbdbadaadbabacadadabdabccdacbcbabccaacabdddbcbcadbcaccbdbaadccbbbacbaabcabbadbdbcbacaabbddaccabbbcacbbdcddaabbbbacdbccccbacbcacaacdbaddbcbcacbbaddddbdadcbcbcbaddaacbbcaababbaaccdadacacbbbcdcbbabbcaabddaacbdcccccabdbbababbddcccbddbabbdbaccddcbdbaaccdbdaadbacacccdabdcaacacbbcadbccbccdcddadcdcaacadacaadbbcdcdaabdbdacbadbdccbdcccdbbccdabcaaacadcabdbdccaabdcddaccbdccacbcacbcbcccbdbcdbbcdcbbbccdbbbcaaaadbbbdbdccacababaccddadcbbdcacbdbcadbacacabdcbcbbbabcabbababcddacaccaaccddcadddbdadbcabddccdcaddbdddccadabbcbbdddaacbabdddbccdaaacbadbaadddbcadabbadbbdcdaadcdbcbdcbcdbcdbdacddabdabcbbcbaccdbbcabbaacdcaddaccccdaabddbaaadacabadcccadaddbdccabdcbbabbdccaacaadaccdddbaadddacdcbbbacaddbcddcdabddbaadbbbcabbacbacaddddaacddbcabdacdddbcaaacbbdddbcccccaacbadbbdacdbdadcbbcdaaabdddbdadcaabbbccdcbdbddcdbbcbaabacdaabbbddaaacbbbadcbdcddcababbdcbaabbcccdbaccaaacacdaadcbbbbddbbcbccbbdaacacbbabaadcaadadbcacdadcbbddabcccccadadbccdaaacbadbbbdabaaccdaaddbdadcbdaccbadaccddaaacbdabbdbdacccdaadbaacddcdcdbbcbacbccbdbddcabadcbaacccdcbcdbbaabbbadacdbccabbbbaccdcdcdaaaaddbccddcddaddadbcabaaddccaabbaadbdddbadccbcabcccbcddddbabcbaaaaccabbbacdbbcddaacbcbddcbdababccbaddccbadbaadbdabccacacbadddbabacdaaaabcddccaacccccacaaadaccacccdccbcaaabcdbdcacabbacabdacdaccbbbaacaddbdcccbbdabcbcbaabdbcbdcacabdabbcddcdadbdbacdccabbaaabddccdcdbccaaadaddacacaaacbcadaadddbcddddabdccbcabbbbccbaabdadbccadabcdbacdbacaddbcabddadabcbbaacacbbaddbdbabadbcbddcdccbdbccdcbaaddaaccddddcdcdacbaaadbdbdbaccaacddacccbdcaccacdcdccbdaacbacdbddbbdbabcbccbbcdbcacabddaaacabaacccdccadacadacbbdcbddccbcccbacaaacddbcabadbacbadbbacadaacaadcdadaacbccaadaabaabaaddacabcabbbbdadcaccbbccdaddacdddcdbcbdabcccbbabcaacccdcaababbdccaaabbdaadbabdcccddcccbbddcacbbbbabbdbcacaddcdbbcddadaaaabaabdcdadcabdbaadbbdbaacdbaaabacbcccbacbacbdcacadcbbdcdddacbdbcabaadbbaaabbbadabbbddabdbdabcbdadccdacaddadbbadbccbadddcaddcbadbbddcddccabdadbdadbcaddbcdabbbacadbcdbbaabacdbaaccdababbbdccdcbddaccacabcaddddaadddadcddcbbcacdbdbbccccbbbbaddcaaacdbddcddabdbccddadbbccaacdcdcdcabbadbbaaaabdbbdddbbddacadadcaccadbcccbbaddcbbdccdaadbadcaacbacdacdcbbaadabbcbaadcdbdaabacacacbdcbbabccddadbbdbbbcdacbbdabacdacaaabdcccaaccdacaccbdbcdbcdccabadcacadcdbbdcbddcbcdadddccccabbdddadadbcbabadadbbcdccdddcddabadbaadaabccdabdccdaaddaacbadabbabbbcacabcaccdcdbcccbbbbcbbdccbdabcadaabdcacdadaadaaddaaaddddbbdacddabbccbbddbccbbdbdbbdacadcaacacdcdabacabababbccbacccbbcccdbabddddcbadcacbcbacccdaaccbabccbcaacbbaaacdccdcaabdddbdddcbcbcaaabddbdccdabdccbabbbdbbbdccddcadcabaadaaaadacdbbabbbddcadbdacdcadcaaabbdaabdcaccbbaacbabaacbbccabadccbdcbabacaaccbdbccbdbaccacbdbccadaaabdadadcabdccbaadcdcccdbbabbdadcacddbcababaaacbacddcabaaaadcdcaaaaabaaadaccadbdcbabcdcdddbbdcccbaabcdbcadcbbddddddaccaabdbaadbdbdcacdcbdcbdaaaaadcdbdbbcbcadadabcbacdbdaddbbbdaccadbcdddaaccbadbcbbddcbababaaabcaaccdaddacadadcaddcbaccabbabbcadabbcbcbcdaadacbbccddabacddbddcbaaacdcccddacabcabcbbbcbcccddbbbaabdaabadbbdabaaabcbbbbaadacccbdddcabbbddcbccdbddbdcadbcdcbabcdbdaabccbccdcdbdddcccbadadbcadacdcccbdcbcbbcbcdccaabdbaabaaaddbbadbcadbcdddbcdcbcbdddbdddddbaabdcddabaadbabcaababdcacacdadbcbabbacbdadbcbbdddcbaadcdccaadcccacccabbabbdacaacbcdddbbdddabdddcacbcbacdbdcdbbaddbcbccdacadccadbddcabcbbcbaacccdadadabbaaaaaaadaadacdbbdcaacddadaacbacaaddadddcbdcaadaabaabbbbdbcbadbdcbcdabdbbdbdcddcbdabacadccdcacacbbcaaaddabdbacdaaaccaacabcbdbcdcbacccbdabbccacbdddbdadccbcccdbadbbccbddaabcbcabcccdbaddcbbccbacbcbbbbccaabcacdcdcbcdbdcccacdaabaddbcbaadcadcaacbbbdcdbbccdcbdcdccababcacdbddbacbaacdbcacbdaaccabaaaaaabadbcdcdabbadbacbbacdbcadbcacbccbcdabaccccaccdbbdcddbaccadbbdbcddaadddccbbadaacbbddbcaccbcbabcbaccbbbccccddbcdddabaaddcadbddacabccdcadaacabdadcabdbbbbdaccadcdacdcadacccdddbdadaddbadcbccaadaaacdcdbdcdcadaadddbdccdadcaaabddbdaaccccbbcbacdcdbbbdbbbaaadcaddcccbcbbdacdcdaabaccadccbddbbbacaaadaccabdaccaccccdcdddddbbaadddbdcdcbaababbdadaadbbbbadcabddcbcbacabddacaabaabdddcabccadbaccccccdccbcccacbabddbadcdcbadcaaabbccdadbdbbacacabbdabbdcadbabccabaacdaacdacdddbdddadccbbadbdbaaacdbacdcaaddbdcdbdacadadababccaacbcabaabddbdbadadadcabddadbccbdadcccccdadcaddbdcaadcabccbcbaadbdcbbcaadbbdabdccddabddcbcbabbcdadcbbbdbcdcadbdbbbddbadabdccccabadbbaccdddbacddbcadabaabacaabadbbbcdcdcdbcbaacddcacccabbbbcdbcadcacdcbbbbaaabbdbbbabdbcccadcdacbbbbbaaaccbbbcdbcaadcbabdbdddbbbacdaacdbdbcddaadacddddbdbccbdcccdbaabdccbcdbbccabaaaadcabcabbccacbdaabdccccdadbccddbabcdacccdaaaccdcaadcdaddacaaadaabababddadcddaaaababcbcdbbcaaadadcbcaabacdaaaacbcacddcddcacacbbadbdaaddcbccbbddabcbcdbdadacdbaadcbddbbcdcaacddccbddadabccaabadccddabbdcddbcdcbaddabbcabdcbaccacccabbbabcccaacdbdaccbcdcbdbbddaddbcdcdbddabbdddadabaccbbdbcbabdcaacdbbdbabaddcddbbbaabcccbdcccaabbdbcabcadbcaadbccbbbdadabbbbbdddcbbcbccccdadcdcccdaabadbcbbdcccbabaacbccbaabcccacabbccbbaabdabcdaaaccadcdabcdddddbbbdbbbabccadbdbacabdbdbdcbbdcbbdbdcbcdcabcdccaccdbdccbcaabadddacbabcbaadbccdcddbccdadbabcabcacaccccacddbcdbaccbadadcdcaaccbcabaaacaccdbdbccadbdbdcbbabaaccdbabcabcdbdbbcccbacbdbbbcdabacdcccaadbbabdcbdcadaacccdbbccadcbaddbabcdbbdbdbbdddadacbaabdbbcadbddcbccaddcaddbadbdacddccaadabbabacdbdbdbadcabcdaacbbdaaabaddbacbcddbaaadbdccdadabbaaabcccaaacacdadcbdaccbabbbdcbccabbbbccdcddabacccdddbcbcbdbdbdabcabdbacddbcbdcdcbcabdccbbdadcdadbbcadbabbbdbdaccabadbdabbdcbddcbcabcdcdbbbadaccbbcdcbcabababdaddbaacdccbccaacaddddaaccbbaacbbdaaaadadbbbbdabbcaddbbcbbdbcbbadaccbcdabccaadaacbdcdbcdbadacbbdcaadbdbcdbaacbbcdbdbacccdcdbbdadaaadbbbccadccdabccccdbaacaabcdbadcacbdcaaaccbcdaababaadabbbdacdcdbbdccadcbcbbaabddcbaaadbdaaacabdabbaadbcdddbcabbcbbcaddbabdddcadacdccdbdbabacdccadadbccdadccabbdcaaddbabcaacaacaccdccbacaabbccbbcadacabccacabbbdbacdacbbabbbbbbdcacaccdbcbdabbbadbdacdbbadcdbcbbbabdabdddbccdabbbadbdbbbacbdcbadacdadbdaddbbddddaddaacadbccaccdbadbadaddddbdbbaabbccdaacbadaaaddcccbaabddcdaadcaddbcbcdbadbaddcddbdabddccbcdbcbcddcdcdbdbcdddbdccdaabdcdcaaddbdaaddcccaadbacddaadaacbcdbadcdadddbaabadcbbcacbcdddabcaacdadacbbdaacadbaccbcadddcbaacdcbccbddbccbadcdcddaccccbabadacccdcbdaccabaadbdcbdaaccdacbdbdcdadacbcaabdccdcbddbddcbbcbabddcccacabccbcdabdcccdbbacbdddccdbbdcccddabbaabadcddcddddbdadbbdadbaacddbabbcaddbabdddbcdaddcbbacbbccabbbbbdaddcbabacbaadbbcbbddbbabdbdcbadcbddaabbdbdbbacbcbbcdadaadbddbcccabbdbaacadbadaaaaccbaddabdababcbdaadaacabcbcdbcdaadcdbdacddcbbdcadadccdbdddbabbcadcbcdddbccccadacbcccbddccabbbacddadbcbccdbbccccaadbdccbabcbacbcdbccbcbbdbbbdddbddcbbccccbdcabadbcacbcdccbaaaddaabccbccdacabdaddbdaabccadcacdbaccddbbbdaaddcddbcbdcaccbbbcccaadcdbccabdbcacccbbbaccaccbccadcbcaacdabccddcbaddcadbbbdcadbccaddddcddbcdcdcdaaccbaccbbaabdacdcacdbcdcaddcbabbbbadbacbddbacbaabcdddadcdadccacbaddabbddcbbcddccaacdacaadbbdcccbdcdcbdcadacbbaabaaacbcccabdbaaacbbabaabaadacdaaaabdaacdaaaccbacaadcbdacadddacdacaacdbcdbcdacbbbcdccbabbcabcdbdcbaababcadadcdbabababddbcadacdadcdcaddbdbccdddadbcccbdbaacacbbaabccbcdaadcaadbcccabadbbcdabcbbabdadcbcddadacaddcdabcacbdadcaacacbdddcddcdcababdcdbdcddbbcbaacbadddacdbabbdaadabdabcdbddbccbbcbbbadacdadaabdaabbcababcbddabaaabccabacbcaacdbaccacdabbbccaadadabdbddbaddcbbccaddbbaabcabdcaddbdccbacbccccaaaaabbbdcbcaabdbbdccabbdaccaadacbadbbdbbbdbdbbbddbcdadcddacdddccdcdbbbdbbaaaababbbadacaaaaccdcdaccbabbdbdbbbcbcadaacbbbadabcdbbdddbdbbdaacccadbaacabbdabbcdddbdbbdcccaccddddddabccbbcddddaadccdbaaabbadbbbddcdbddbdbabcbdcdcadacbdaacddccddadcbcadbcdbbdaaaaddbddbbababbbacbbddbacdbbbcbcddbbdcacbcbdcdcabbdadbcdaabdddbbbbbaccbbccabbddccadcadaccdaaaaddaddadaddcddbbdbdcaaabcbabcaddabaabcddaacdacdddcbbdabbdabaddcaddaaaccdbbbccbdaccdcaacbcdcacbcbaaabdaaabbddddadbbddccbbadbcabcdbdabaadddccdbbccbcacddbbbbaabcbbdaabcbacbccbddbbbbccbdabddbbbadcaddcbccbdbcbadbbbbdddacbcaabdbbbbcabaaddbdcaabcacbddaddccdcccbbcaadcdbbbdbdadcbbacbadbdcacadacbcbcbdadbaaacccddbdbcacadbabacbcbbabbcdbadabdcabbabcbdbadaabbbaaacdacddddadccdddddaabcddbaccacbacaccacddcabbababccbdaaaacdbdacbcaadbaadbcbbddddbcdaaabdddadcddaaadaccdaaadcaaddbaacbbabbbabcabcddbddbbaaccabbbddcabccadbcbadbcbabdadbacbbacdabddddbbaadcddcabbbadccbcccddbdbdbcdcbdbdccbcbbccadcaabcaaacbcaadaccddcaaddaccbadacbbbbcaccbbddabcdcadddbabcbcaadbbdaacdbdddccbcabccadcaabcabccdcbbbabadcdcdabbbcadaaaaaacadaddcdaccccccdacdabbbcbbbcbdbacbddaaddcacdbdcddbaaddcbcbabccbdddcbdadcbddcbaaacccaaadabaaadcabdadcdadbaddbadacabbcabaabdabcbbabdbccbdbcaadaddbadbcbcdbbbbdabadbcdbcdbddbbbbcddcabaabadddbdacaabdaccabbcadcdddaadaabadaccbcabddacbbbbddbdddcbdabaaabbdacadccacadcbbbdbbcbbbbdcdbadcbabddacdbddbdbcbdddddabbcacbbcbdabbaadbcddaabadadacbacbccdabccdcbbbddbdccacaaaaabbdbdcdbccbcabccdcbbadbcaccbbbcbaddabaddaaccbcdbaabacbbcccbdabdacbccdacdbaccbbdbadbbaacbabaabdbbbcbbaaaaaadbdacaacadadccaaccacacdbaddcdcaacdbddddccabcbbaabbcdddcddbcbbcabacbadadaccbcadbddbdbdccbccbbccbdbdcbddbcbbadcaaaabcbaccaaccaacdabdcdbcabcabbaaddcdaabdcbcbccbcddcbbcdaaccddbcddabaaccccadddaaddccabbacbcbcccaabbdbacdddccccdcdbbcbdbbaadccacadcadadcdacabddbddacdacaabacaacadacabbaaabccbdbcaddcbabbcccbbbabdbdcccddbbddbcbbcbcdaaacadbdbaddaaaacaaacbbacdcdddaadcdbaacaccddcddbaabcbccaadadaaaacaacadbcadcdcccadddcaaabadbcbbcbdcbcccacbacdccdddbacacbaddbbdbdbcabcbcbcddcaccddccddbbdbabcbbbbbcccaddacbbabaaddcdbadbaaadabcaccadaddcdbbcdacbabdbbabcdcdbababdbdddddacaadadbdcddadabdcdadccabdbbbcdacdbbbbddcdcadbdaabdbcbabcddbcbbabacccaabaacbdbaadbcacdaacbcdadaddabbdcbcdadbdcddcbbacaccbbbddcbbcaccccbbbccaccccabadcdcbbacbdabbdcccbbcabbddbdadbaabcddacddcabbaacdcaaaacbccacbdaabbcabbacbbbaacbdadcbbddccbbdcadabdcbbdccbdddbcbbcbddcaaacaccaddddcbdabdaccacddcbbbbcbaaabbacabaacaddddadcbacbbcbcbdbbbabcdadcacabdacbaaacdabacbadcdbcadbacdbcbbcdddbccdccaabbaddddbcabaddbacbbddbcbcddbdcbbdadbdbcacadaccacabdadddbbaaddddddbbbddddaaacdbaaddacbabaddaaccdadaccacadbbdabdbcabdbcccbcaadcaacbdaaadddddccaadabcbcdbbadbcadbcbbcbaddbaabdbcbaacbcacdaacbaabadccdcabdbccdcacaacdbbdbcacbcbdbddbdbcbdcbdabdaabdbbbbdcdcccabcbbdbddbddbacdacdcabbadcdcaddbabbcadcdbabadacbcdddababcdaacbacddadadcadbcacdddbdacdcaddbacbcacbacbbddaddbdcbddddcccccbadaaabaacaccdbbcbadbaaaaabdbbcaacabacabbccadbdcbbdbbdcbcabdabbddbacdddaadaaaaccddbbccabbcdaacbacdabaaabddddddbdcdaabcdadddbcacdccdcddaadacaccddbacaccaaccabccbcacbcabaaddbcaccbadccabbddadbcbdcdbddacbaaadbbdacdbdaccabadbcaccbaadcbcbbbcabbdbbdacdbdcaccdabbddbdcbdabbddabbcdcaaabcdcddacdadcdccabbccaddcbdcbcdcccabacbcdaabddbdaccabcbbacbbbadcccdbbddcacabcaadbacccbcadcabdcabddabbbaacbcbdcccdaacccbdbcbadaabbdbcdbdbcbbbbbdadddcabbbdddbdbbaddccdaacbbabbdcbcdcadccbabdadadbbdababccdcadacadddaabcabcababdccadadcabcbbdbcaddbaabcddbcabcdccdabccddbdbdcdaaadbcbdbbbccdabadbdbdddcccbadbbdbaccdbbdccabdbcddbdcadbdcdaadbdacbaaaabddaadaadadacdadbacabbdcbcbbadbabbaddbbcaadadcacadbbbcddcdacccacbbcaddaddacdcdcccbbdcacbaaabacbdaadddcdbacbcbdcbbdcabbcccabcadabbaaabcadadadabadabcbbcddddcbacbcbaaadabbcdcccbacccdabbbcacccabcddbcbadccbdaabccacddccdbdddbcbacdcbbadcdacbaadbadccababcbcdbcdddbaaddacbbbbdbdadbccadacccbcdaddbabddcabdacccdcdcdcbabbababccccbbdbabcadabdbcadaabbaaabbdbbdadcdaddacdbcdacbdbdccbbbccbaabaacdaabcbccbdcdbddaacbdacbbdcdadabcbcdbdbdbadbcbabdabdcaacbdbbbcbaccbcbbcbbbbcacaddbbcbdcdcdacaddbccbbcdcaccababcabaaadabbddbbbcbbdabbdccaadacacabbcadcaabacddbdcabbcbcbadbcacdcbdabaaacbbbacadcbdbcbaaacdaadabbdcacddcadabcbababaabdabdbabdcbdcbdcccbcadacaabaabccdadadcbdaacccacacdacccadbdaddababcadacdbaacccddbbddccdbdcdaaacdbbccdccabcdaaaadddacaccbcdbdabcdcaabcbdbbcdadaadadbddddccdabaadbcaddcbbcbaacadbbbdcdccacbcacbabcbbaabbaccccbbadbadadcddaadbcabadabdabcbbcdbbabbabcacccaacaacbcdabbdacacdcbacabccdadbbaaddabaacdabcbbbdcbabbabddddbccaaacddbbcacabcdbcbbacbccababaaaabaddbdcdbcaadcacadccaacbcddadaabdabcbbadbcaacdabcabdabdcddbcababacbbdabdacadcbacaaabbdbacbdaaabdbadccaddbcaadcbbcacbbabbacbcdbacddbdccbcaacababccddbacdbbbcbcbadbdcbacbaaacdaababbbdaddbbbddbccdcdbcaabbabcddababacacaaabbbddcbdaddbaacabbccbdddcdcdaaccbbcbbaabcdddaacdbbddcaddccabcbbabcaabddbcbbdaccbbcdbbadcababcabccabcbdcadcabcccddaacbccddaabaddadacdabbcaaccddcbcbddbcbddacdbbbdbbdabbbbbcbbcbbbbabdddabbdaadcaadaabdcbcbcdcaadccdaacbdcabaabdadaccdcbbbccbacdaacdacaacbdbacabaddcaabddccdbaaaaddbababadddbdbacabbdbddbaaccdcdcadbddbbcaccdccdcdbcccaccbbcddcacbabbabdbcabaabaacadddababdcabaabadbdccabdccdaabcadacdbbaaaaaabbbdaaabaddaadacadbaadcbcdbbbcbdaaadccbddbdbbbcadbbadcaddadcbaccdbbcbaddabbbddccaacbbaddbbbbbddcaccdbcbcaddabaadcadbcdccdbaaacaaabbbaaddcdddbacbdcbcabaacabcdcbdadadbbccaddbdaabadcbabdbdbdbaddbcbdadddacbadccbaadbaabcaccacbcabbdccabdccbbbccbdaadabbcabdbcdaaaaddabcaaaccbcdcadcddacadcacbdaaccbddddddbcccdcbaccbcbdbababadddaadaaddcbbbaaadbddddaacbdbdabcabbaaccbcacaccabccdcdddcbcadadadbaadcbccacdbdbcaabbaadadabdbccbdbbdccdadbddcabdbdbaacbcbcdcbbabdacbbccaddcacaaddaadadbadbdcaaddaadaaddcaddadadadcdadadcbbcbaccdccacadabbcacaabdbdcbddcadaabadadbccbbcbdbacacdddabbbcbcadcbcdbdaabcdcbcacdadbbcbdcbacbddbbacdcaacbabbacdadabadbacacbaddccbbcbacbcdbcaabaabbdacbddabacaddadddddadbaabddcabadcabaabaacccbdbbadcbcabacbdbcdcbaddabdadbdbaddadadccaacdddacddabbaaccbddacabbdbcabdabddbddcdcaabacaadccccbabbaacbbaddbccddccabdcacbaccbaabbcdddbbcdddccdacbbdcbadbbbacabbbabbdcaaabbaaccdbbabaaadaddabdbbdadccabadbccddcacbbdbadacddcadcdbdbbddaddabbcdcbbbdcccdcdbddaddccbcdcbcabaadcbdadbabbcccdbabdaddaaadaabacddcadcccccbcaaacbaaabaacadcaccbdbdaadaddbabbcabdbccddddbababbccabacaadcaacddbcadacacaaaddadcbbcdaabcabbaccdcdddaabdaddadbdabadccaadbcbdadaaacbdcdacdaacabcdabccbadcbccbcacaadcbadbdacdcbacbaddccdbaabaaddcdbbabcbcdddbacbdbcaaaccabacaaaaccbcdabbbbdcacbdaddadaaaaabccacdccbcbcaaccdbbbdabdcbbdaacbabbcadccdbabaaccadadabbdbcabdcccbabcccdacadbadddbcccbccdbdcababadccdadcbaaabbbbbcdcdcabbcdabddbbacaabdbcdddccdcddbcdbddddcdadcccbbbcbadcbaccdadcdddbcbcadbcdabcddcbccdacdcdcdadcdbbacccddddbcddbbacccbcaabdcbdaabadabadddccabaadbccccdabcdadaddddbaabaadcadaaaaccbbdaabccbcbdbbbdbccbcdaacdabbbbacdbdabbcdcbcdbbcabdcbbcdcdbbaaabbcadadcabccaaaaaaaabbdcbbbcdbaccabdbdbcdaabbabbccbababbcabccacbdbbacbdacdbdcccaccacbacdaddadaaaddaabaddbcbdcbbccbccabccddaacdbdcdabccaaccdbbccbccdabcbacdacdbcdccbddabdbdadbcbadabccccccdcbccaaddbbaccddbcadbbdadcbadaccdccbdbacacdbdccdbcdcbabddabcdadaabbbaadcdbacddcabcacddadccdacdaccaaadbbcabcdcaddcabcacbaaadbbcbbcbcabddcbcdbcbbcddabbdbcbbddacbbcabdabbbbbdcaddaaabcdcdaadcddaddcdbacddcbbadaabdbacadddbcbcbdbdcadcccdbcccaabdbcbcddbdcaaababdbbddbacbddabaadcacbddcabcbcadadadbbccddabaabbdbadababcbcbbccbbcabddcdbdddaabbacaabbaaddaddadacaacdbabbbaaacdadaadabadbaccddacbbdaabacbcccdbcaccabcaaccdddbadbcabcddbdbdaabaacddaabdaabcadababcddaaacdddbcddbabcddaacbbbbcccdddcccbadaccaadbcccbaacbaacdadcbcadbadbbaaabaccbabdadcaadbacaccacadbccaadaccaaaddcdcaacdddadbbacaabdabdacdacabbccaacadcadaccbacdcaacabccbdaaadaadaadcacdbddacddbbdbbcbcddbbcdabcaacbbaacddbddabbbdbabdcbaaddbbaddacacdbbbbaddaaacadadcbdacdabaaabdadbbbcbcdbbabbdaccacdacacccbcdbcbaaadbdbbaabadbdcbdbdbbcbadacbabcabadccadadccbbddacdddccdddacbabcbccbdbaddbcbccbcaacacabdaccaccadbbcddadcdcddcdcabbaaabcccabcaaacddcbabbbbddbacacdcadbaddcabacacbbddbdcabbadccbdcbcbadcbbcbaccdbbbdcbccccbacbbacbbdadbccaadbcbbbddbbcdabbdbcaabdcdbacdaccdadcbbacdbaacacbbdbbdadbccaddcbadcabbacabbaadbbdddbdbbbbadbabaadacaacccbbcccccbacdcccbabbbacbcbabadaaacaccbadddcbadacbacaadbdbdaaddaacdbabcbbcdaabcbabcacccabbbddcbcbbbdcddadddbdbbccdbdabbacbbdccbbbbcbaccbbbbccdacddcbddcacaddccabaacaccbdcaadadddbababbcbdacdbcbbdcbabbaaabcadbcdbcddcddacddaccbacbccacadcbdcacdcbbbbbadbcaacadcacdcbbcadccdbacdbbccabbaacbddcbdbcacabcdabcccdadabbacaccbdcbddbccadcababccddcdddacddbccdcbaaaddcadbcaaaaccbbcbbaabcbadabdbbbdbadaddabbbdccbaacbaaacaadbadcbaaccabcbbbdccadccacdddbcdcdabbcaccccadaaddbdbaaccdddcaabbbdcbadaaaaadcdcaaadccaccccaacdacdbabaabbcadabaadcdcdcbbbbbbdbabbccbaadbbaabcacaddcdbdacddacbbcdcdbccddbbadcaaccacccccbccabaadcacabdcddaabbdbacbddcdddcaccbaabbbddddbacdddbddabdccdcbbcbbdabbbbbbabaddccccabbbcaabcbddbcddcbcdcaccabbbcbddadbbdccdbabdcbdccacaadadabdbdabbbbcdccdadbdabbdccdbcbadbbabcbbacccbcdbbdbbcddcacabbaacacbaacdacbcabdcbcacacdcddbcddacabdacaaddbcacdacbbdcbddbadbdabdddacccbcbdbdadacdcdbdaadaadcdddaaadaddbcdcbbdbdabbdbdabacacbcaaacacddbdbdccbccbacadccaccbaaaccbabaddbdbcccaccbababccbaadcaddcdbabcddcaaccbbacbdabbbdcdbdaaddbcbaaabcdcbaabbaaaaaccdbdcbadaabbdccaacabdabaabacabbdababdabbdccdacbabcacdaaaabbadbacaccadabbaabdadadbcaabcdcdbcbcbaaacabbcbbaadaabbadaabcabddcbadbbadbabaaccacbbcbddaaadddabcadccbdaaacacdcbaaddcddabaacdbabcbcddcddadacccdcaddbabdbcaacbcaaccadcbdcbbdaaccaaaaabaaaddcdddbdcabbbdcbccbaabccabaadbbbaacacdcbdddbdccaccbabbbaabbcbacdccabadcadbddbbdccccabbabbcdddaddaacdaacdccaddabcdcdcbbacbbabbcbdbacbcdddaabcaccddcbcdbbdbbbcaccdaacabbabdacbcadaccbdaabccbadacdbbbbddcbabcbcdccaadccdddcaabbddccccccadbacccbddababdccaaccdcbaacdbabaabbdcdcdabccdbaaccdccbddaadbcadcdadddcbcbcbadcdbbbdaccdadbdacdaaddcddacddcdcadbadcdbdbbabdbbbcabbdadddcdcabcdbadcacacbdcbcbdaadcaabacdaaaddabbabccbdadbdcbadcaacccbbcacadababdcadbabddcccbbcbcccbcdcbdcddaaddddcddaddababcbbdadbcbbaccdababcabbbdaababacaaaccbbacddccdcbacbacddcbbacbdaaabaccadcdcbaabbacddacccbbdadbacadcaddaccdcdbcbcbabbbdaaadcbbdbdcadbadbdbaadcaaacddaaddcddacddcdbabacdddcbbabacacbccddcdddacbaaabddccdcdcaadcddbbabbbbcbcdadbcdbcbdccdaadbdbaaddadccbdbdcdabcacaccdababaabcaddabbdaacbdcdbaddcbdadcbabdbbddddddaadbcbbaddcacadcdadbbcadcacadadcbdbbdadacabcbddcdcaadcccdbbcdddddaddbabdcdcdcacabbaacdacdcabdcddcaadbbcdddbaaaaccacdadbbaccabadbadacabbddccdadadbddcbcdabbbababaccadddbdbdcadadaaadddbbbcddbccacaaccbaabbdbbbbdbbbbcdbddbdbcabdbbadacdaacbcbcbdcbdddcaaaabdacbbbcadcdcaadabccdcbdaabcbabbbbabaabdbbacacdacdbaaddcabdaabcdbaddaaddacbdcbadaaabcabcdcdabdbbddacbdbcbcacdbadcdcacbabcdcaacadbcdbbdabacccbdbbbcbcccbaabbccbcadadddbbcbbddadccadcdbcbdccbbbbdaadbaabcbbdcdbdbddcbbabbbacbbbcddcbdddabbacadbbbcaadcbaadcbddaacbbadcccbcdbcbbdaadbbbddacadbadcddabadbbdaadbddcdbcdbbcbcabaabacddddccadaadcacacbacacddcbdbdbdacabdbcabbbbdbddaaadbbdadcacccdaadabdbcabbccdbaacdbbadddddacaccbcabaababbdbaacabccaadbcbcadbaadddadabcbcccabcadbacddcddddaaaddddccddcadabaabbccdaacbcaacaddcaabddcdccdbbccabdbbabdaabddcadddbbccddbccacdcbdcbcaadbdbbddbaaddabcdccacdccddacdaadbaabdcabbabbbbacaaacadadcadaccacdabbbdbacadcbbaabacdcbbbcbdcbacdbbdacdacaaaccacddcacbaadcbcadacaadccccaaaaacddcabaddaaaddbddddaadaaaaaaaadacccdaccdcdcbddaabbdacddccbbcccddbdbcddaaacbbadacadcbddcaaacacbcdbdbddcbbdcbddacdbbaaadabbddddcdbcacaddcbddcddcadbaabcabbcaccacddaadadddbcacdadadaaabaabccdadbcbacabcacaabadcccdbcaccbbdaabcdaccdaccbdbbdabccccadaadbdbaaaabbcbacbcdcbdddbdbdaddbbdbcbdddbbabbbaaacdddadaaaaacdaadbbadaaddbbabbbdabcccaddacdbbccbaabcbddddadcaccbaabbbbcbbcdddabddcbdddbadbabbddbbbdcaddcaabcbcddbdbcdbaccbababcbaccccbdcdcbcbabcbababbdddbcddcdacbddbbadcdaadbabacbcdcdacbddbddcadcdadbacbdaadbadaabccababaddbbabcacdadacadddbbbdbdbbbbbcabcaadbdcbdddbbbcacbbabdbbdcbccdbadcbacabbabcdbbadacaddaccbcddabcbdbadcaadabbadbdbaaabddcabcabcbabadbadaaabdacbdabdbdccdbadcbcdddbdddbcaaacbbccdbaacadbcabaabbdaddabdbaaabdabbaadddbbcabbadcaabbcabaddcddacadbbcadcbdaadddbdcdddbcdbcacbbdabaacadbdddbaddbdabdbdbcabcccccaacbbddbcabbddbdcaacdcaaabcddccdcdbaaddddccabddabbadbdddbbdacbadddccaabccacacdcccbbccabcbcadcbdcdbacaccdbcbcdcaccbcabddbbbccdaaccbcaababccabacdddacdcaccacbadcacadcabcbbcabddbcbcaccadcacdadabccdbabccaabaddabdbcaacaabbcdbacddddbdccdddbaadddbdcaadaddbdbdcdbaaaacadbcaabdbbbddacbabaccddacdacdbdaacdabdacdbcabccacacabdbadbcdcaccaadaabcbdbadadcadaabbcbbabccdaadabcdadabbbbbbdbcdbcbddcbdbbadcaddadbcaadcbbadbbacbbcdcbddcadadadaaaababacdcbdabccbcccccadacdcabcdcbbbdaadbdaaccddcabdcbbadcdaacccbcbabddccabdbaadcccdccdddbddaddbaddbdbcdbdcbadaaaaaabaaadaaccbdcddadaabcccbddabddbabbbccdcadbcddbdabcccddcadbaabcdadaccdbcbcbdcbcacdabdaabddddbbacbdddddadccccbaddbbcbdddcccaaddcddbbddbbddbcababdacacdcbbbcdacdcbccacdbbcaccacdbbbacbccbddddbccdcdccccbcbaabaabddbaacdabaccdadcdccabdaaccbddadaaddacaaadcaacbdcabadbccaacdbadbbdbdbcbbcbdaadddabbbadddbcdabdadacddbabadccddaadddccadcccacdcabddadacbbddddbddadacacdadcacaadccdacbcaadaaadaacccbbaacddabcbadacacdcddcdcdddacadababbaabcdcbbbcbdbddbddbbbddbcccdbcaabdcaababacbaaadaccbdacbbcaccdcaaccdadbbbddacbabccccbcbdcdadbbdcdabcbbcabbdcacaaccddcbdcdadbabbcacadcdcbdcadbdcadbcbbddcbcaaabcccdbbbddadbbdbbdcbbdaddaabbdadbccbcbcddcddbdaabdacdbcbbcacbbacdbabbdbacdcccbcbddaabaccdaacadbbcacdbbdcdcacdaadaaaacadbcdcbabdcaadddacdacdabbbcaaabadcaacacbbbabdddccddbdccbcbcdbadbbaadabbcbbdcdcbbbbacccabdaacdccddcdbdbcadacacaadcccdddaaccacdbbcadcdaccaacdaabaadcddccdbdbabbaabbaaaaaabbbacabacbcbaaccddccaaddcbcdabdcdcbcddbacabbbcbbcddabdcbcbbaccddbcdacdbdbcdbbbbaadbbaddaadcdbaccaccdcaddbadbdbcadcaaabbdbdacbbbacacddbddcccbdddbbbaacccabccadcabadcadbbcadadaddcaaddcdcdaddcbbbbaaddbcbdddccabdacddddbacdbdddccaccbdbdbaacbcdcddcdcbcacbdccdacbbdbcabccdcbbcbaddccbbddaccdaaccbbbaacdadcbcacabbabdbbdbbbdababcbdbbcdddbaabcbcdbdacacabbacdbcaabbbbbabdaddbabddcccbbabadcaddaadcbabdabcdccccabaaaccbadaaadbadbcdaacccbbadddcacdbbcaddbbddcabcbabbabaddbddcddccdddacabdbbbccaadacadbcddcddbadabdcddddbdddadbbabdcaabcbdabdbbddddcdbaddcabdbccbadbadacacdabaacdbcbdcddbcbccddccbdbccdbccbabcbdaaaadabbbaabacabcbdadcccaadadcbdcdbdadbccaaabdaabaaccaccbdbddbcdcabdcdabcbcbbcbbbdbccdbcababcbdddcadabbdbcdcabbcdcbdcbdadcadacdbaaaabbddbaccabacadbdabadcaadcacdbccadccdccabbcaabddcbdcaaaccbbcbcadbdbbccdcdbacbcddcaaacabaccdbbcadccaadcacbddbccbcccdacacabccaacddadcaaddaadadbaabadddcaddcabacaaaddbcaadbdadbaabacbdbcdaabadddcadabadbadaaaddabcdbbcbbcadcdcaaddaaccabaabbbcbbadccacadbabdbdccbadbbcaabcdaadbbaccbdcaabbcdaabbbcabacdadccccbacdbbcbbbccadddccdcdbbdaccbdbdbbdcdbcacabbbbcdddbbcbbaacdbbacbdcccdcdcacacccccddbbcddabdbdbcaabcbbbdcbbdaaabdaddcdacaccddcbdacbdccdccaabcbbbdcdcadbdcddbdadcadcaababcdadddbbbadcdbaadcbcdcdabcadaaacccabbbcbdadacdaadcdaccacbbabdccccabbbbdcbaddccddaacabcdcddcabbccddabbadbcdcacdacdaccaaabdbaaacaaadcdaaddaabaddababcdabaaaaaaabaabccabdccabddbdabcacdacaaabbddccbbacabdadadcbadbdaaacdadbbbcccabadbdadbbbbcadaadbbacccdbbcadacababcaadbdcbcaaccababbcdbacdadddcdcbcdbddccdccdbccbbcacacabbcacddabadbdaadadccbddbaaabaadacbbdcbddaabdbccbcabdddbbcaadbccccbcdabcccbdabddbcdbccdbbadddcadadadcaabbabcabcdcbbbcdaaabbaadbdbccdcdacddaabbadcbaabcbacbabbccccbccbdccabbabddabdbcbcbaaababdaaaacbcaaacaadabbbdcbaadccdbbcaaabadcccdccdadadbdcbdaacddbcdbcbcaccccbabbcaadbbaddaadbdaddbcaacbdcbaacdacdbcddabacabdbaacddacbcdaabdcbacddabccaaccadabdbabaabddccadadaaacaacacbbabdadddbbdcacbcbcdadcdcdaaddddbcaacbdadbbbdbcdabbbdcbadbbddcabbdaadcbddbbaaadcdabcdcdddbbdabcdaababacbdcddcbbabbdcbbcbddcddaddbbadadbddddcddacccacbcbcdaababbdbdbacacbadccdaaccddcdabbaacbbdabacabbbcbdadadcbaccbcbcacccccbdadcaacabacabdcaabadbcaaccdbbbdbabbdccabccdddbbccbdcadcdddaddcbbbdbbbdbcacdbabaacbadbcacabbbdddaadbacdbdcabcdcbdbdcaddccdadcdbcabddbbaddabdccccacababbbccccdacdbccdcacdcaabcbadddcdddaadddccdaacacbadadbdbbaaadabbbccccabaacbdabbbaacabddcadbdabbbcccaccadabbabddaadcbdcaaacdbccdddcdcbbdccbdddbcdabddcbaaadccbabdcacdcacadbadcdaacbdbdddbabbbdddcadcdbcbacababbbcccdacdcddbbdacbddccaaddaadaaaccdddcaaccddcbcabbacbccdddccbdcaabbabcbacdadccdcbbacbbdabdbbbcbbdcabbbdbbdcbcdbcbcdabbacabacdbbcdccbbadcbcbbbdbaadbadaabdbaccadbadccdaacaddcaaddcabdbbacddddbadcdcabadadccdcbcabaddbbabdbabcdcbbbcdcbdbccbbcababccbcddbbabaddaadcddbbaacbcdbabadbbcddcababdaaaddbdbccbacdadcddabbabddbbdcbbdbbdadaaacbccabdcbacddbdacccbaabbabccdaddbbbaacbadacbabdacdccaabaccbcbdabbcccabcadaadacdcdaabcddaacbdbcbddcabdbcbabacbabbccdbaccadbcaaacaababbdaabdabcadcccbcacbaacdbdddddcccabbddddccccabbddbccacbadcaddcbaadbbbaddbbdbacdbbbaadbbddbacdbbccbbdaaccdbdabcbcacadccccaaaabdabbbabccbbcadacdadaabccbccdacddddddbcbcddcddbccdbdbbacadabbabbbcbadbaacbbbabccdbaabbdacbacddadddbcdabcaacbbdcbcbbacacdddabadacbdcababdbdabcaabcaaabcabcadabccabaabbacacbcadcdccbbbcdacbcbccdcbbdabdbacaacbdbdacabdaaaccccccdbcbbbdacdaaacabccabadccabdccdcadbaacadcbccabacabbccabadcaddbccaabbddadbbbadbcbbadaccbaacdbcacccbdacbdabaabddcaadbcbdbbddddbdddcaccdbddabddcccdbdbacccbaacacbddbcbbcdddbdbbdacbccdcccdbdaacbcacbbddcdcaddcadbdcbcbdadcbbdacdbddabababdcdbbacacbdbdadbbcdbcabbddadbcdbcdbadadbbaacbddcbcdcdabbacdddbbcbcdabccbdadaaaabdaaadcdcccaddbbdbabbdbcacaddcaabaddcddccbbaccbcbdadcacadccbdaaabadddbbacacaccdbadbccbadbaababcacdbcdaddaabaabcadaaddbcacccacccdcabbacbbaaccbbccddcdacacbbcaabbaccdbbcddcdbbbdabcdbdabdadbccadbdbbbcaccbcddcaddcaadbacddcbbddaabadbaabbccadaaddcbdcbddacadbcabcabddbadbadabcdadaccdaadadbdacbdbcdabdcbcdabcacdccdabdccdcdcadbcdaabccacacbcaddabcdadccadbdbcbabdacbdcdbcdcdababbaddcdaccbbabaadbbaccbccdbbddabadcabbcbbdddadabadccdddabdabdadbacacbbacadadbadcdabacbddbbdccbcdccadbadddaabcdabdccdbadbaaddabdacbcacccaaccacdacccabcaaaabacaabcadbabcddabdbcdcaacdadacdacddcaacadddccbbdcdbdcacbccaabdaaddbcbbbddaaadabcbadbdbddaabaddabaccabacaaaaccdcbadbcdaaabcabaabcbaadbbbbaaaaaccddadccdcacbccacdbcaaadcacccdaadbbbadaacddaadadbcbbadcdbabdcbabbbccccadbaccbcbbcdcacacadcaadcbabaadcbdcabddccbbdcdadcdaddccbaaccdbbdbadddcbdccdaccadcdddcccbcbdacdbaddbadcadaaacbdcbbbdabddcaddcabbadcbaaacbdaacdbdaccaabaacadcdbbabccbbacabbacaddadcccaabdcddabcbaaacdcdcbbdcaaccacdcaaadccaabaaaccdaccbbcdbadcbdcdaccacbdaaacdcdbbccaabcdddbcaddbaddbdbcbacdabddcbcbcaabdbdadaaabcaccacaaabcddcbbdabaacbbdaabaaadbbbdacbddbbbbacdbbdbdddaaabccdccbcabaaadcdaacdcacbbadbdbadaccdcaadddcddadbddbcaadadcaabddddddcbabcadcbccacaccbabcacccabacbcccccbbbddcaaabbdaabbaabcbdbdccacdadaaabadbdbaaccddbdaaacbdadaaadddddbaacbdbcdbacbbcdbcadaabcdbdacadcadbcabbbaddaccbacccadacddddcaddccadbcbcbacbccbdcabaaccbbcbaabdcbabcccbbbcdbcacddcaabdaabadaaaabaacaabbdddcadbbbbabcacbacddbbadadabcbbcccbcabbcccbbbcabaaaabadcadcbadcacdcabadabccccdcbadddddaadcdbadcaabdaadcddccdcbcacabdcbcaccaddaabbdccaddbabaccddbdaacddcbbacabddddadaaadbdcbadbcdbdcaacdbddbbbcbabddcacabdbccadacbaacbdbadddabbdbdcdbcadcabdccdcaaaccabdcddaadcbcdaabdbabdbdabccbbacbaabbbabccddacbbbbdaadbdbadcadacccbbdcabdbbacccdaaacacadcddacdacaddcbcdbadbbcabccccbdcbaabbdcacdccdbbdcbbbcacccccabdddadabccacbcadaddabaabcdabcdcddbddcadabdbbbddbccacdddcccbabdaddadbbcabbabdbaccdbddbbddcbabbbabdcdadacbdccadacadaacbbcabaadddddbbbcacabcdaadabaddbadbdccaabccccbdbcaadaaaccddababcbabbbcabadbcbacacacdacacacddbadddcdacadbdabccddcbabbadccddddbabacdabbbacbbbcbababcacbdacbccdcaddbbddbcacdbbacdddcaccccdbdddbdccddcbdabdadbdbddabdabaadadcbaaddaadabacdcaadaacccaacbabcadbdaaacacbbcbcdbbbbdcbadccdddbdcbccddccccaacaaaacddbdadbdddbddcddacabddcadcbbdacbcbbadabaacdadadabaacccbccabddddccdabcaddcdddbcdcbadddcaabdcdbccbdadbcadbaabbadccadabbdabaccaccdbccbabdcbbdbabbbadaccabacdcacdbcaddbadbdcabdabccadccacccacacabaacabadbcbbadcbacaacbbbbacabbccbddcdbacdcabdbadaccbcdbcbbdccddbbcbbbacbdaabbcbcadbbdabbbbabacabdbbbaccbdccccbddadbaabdbcaddccaabdabcdcabbaccbbbdcccabcbddcadaabcaabccaaacaccaccbaaaabacdacaacbbadcbdccdabbbcddbccdbdcbcaacacacbcdbcaddccacacdbbbadcdddcbadccddccddabaddddcbdacadcdaadddcbbabbddcbcddcbccbacbcaadacdbadaacbbccbcabcabdadcddcccbcbdbcccbbdbbcbadbacdadacbdcaddbcdcbbddddabcbbddbbcadddbbcbbbccdcaacaabbcdddddccbdbbccdcaacbccabdddbbbdcdcaacccabcccbdcaaaacdbccdabbddaadabcddabbdcdabdabddddadcabccabadabdadcabbadcdcaabcdccababdbbbbddbdbccccbbdddaadccbdccaacccbdcdddcadbbbdbdbcaaccadaaaaacadabddcadaaccdccccadbadcadbbddaadddacacacacbaaddccacccbaccabbaaaacbcbcccbcaabccdcbcdabbdbbbbabbddbcdcbbcdbdbcbcbbacdadbbcbdcdaabcbcddaadcaaddcdbccdccbdccaabacabcaababcdbbdbacacdbdbbddccbacaabdabbcbcabdbdacdabcbcadbbcdbcaccbdbcbabcbbcdcbdaddbacbacdddabdcccccdaddbdbddabdcdabddcddcbabadadacdadcddabaabacdaabbabbdbabdbabbaabcddcadbcdcdaaadccdbdddaddccdcdbdddcdcbbccbbbcccbacbaddbabdacdaccbabcdadbbdcccdccadabadbbdaadaadacacddacccdcaababcabbddbdcbcbccaaacbabccbacacadaddcddbcadbacbbaadadbdaacaccdbccbbdbaacabacbbcacdbcdbacaabadbcacbabbdacddadddddaabbbdbbbdcaddbbbcadcdcacdabdabccabdbbcbababaddadabdccaccbdcdcccbcbbcaddabacbbbdbacabacccbdddbbaccbdbcccadadbdabbbbdcdababcbdccdadbaacccadabdbabbcbbadbbddaacaddabcbbadbabaccdcabcdcdabdbaccadadcaadcaadcbccddcaadccbbdabdbcbddbccdbdbcacadccadddbbacbaacdacbaacbccbdbbdacdcadbdabbddcbcbbcadcdcaadccbcbccccdccaccacabdbdaabcbccababbcdddcbcacbdcacbbaddcdaccddbdbcadbbcbbcdcacdddabbbcbcdabbdcdbabdadbcbddcbbdabcaaccbcdcaddabdbbddbabcbbcddbdcdbbdadccabaadabcccaadddcddcbcbbabadccbdcbacdbdbdcbccbdcdbbcabcdbaacbbacacdabdbccaaacbdcdcccadbbabadbadbbdbbdcaddbcbdddbbbaabddacbcdcacbcaccbbccbbdddcabdadacbdbdbccaaccadadadbbddacdabcbbaccadbbdbdcbccdabcacadddabaadcdabbabdcabdddcaabababbdbbcabbdbadcddadbaabcaccddacaabbbcdadcbddbdbccaadbcbbdbacadbbbaacadccabcbbdaaaccbacbbabaabdccbcabcadcddbddcacaaadabddbccbadbbdbcadcadabcabbadbadcadcdaacbbbabbacdbbcdbdccaabccadcbdbcbdadbdadabdaadbbdcdacaaaddccccaadadacccacabacdadddacbadbacbdcccabdbdcbddcdbdcacbcdaacacbccdddcadbbdaddbaabbabcadcdcdbdcbcddccbccbacabadaaaaacbaaddabcadbaacacdccccdccadbababbabdbbbcabbdccdcbbcdcccaaadabdbbbacbcadabdbdccbbbdbdbbaccdcdbbbbbddadbbbbbacdbadaddbacaabdbadcddccbadddcbaabbdcdcbbbdadcddacbacaccccabbadadadcadbddddcaccdcbaddcbddbadaadbcbcacacbbdbccbaabdcccbcdbdadabdcadadbacabddcaddbcbbaaaaaaacbbcbccdbdacdbbdabadacbadbaaaabbcacacddbddabdcaccbbcbacdcdbdbcccbddcccdbddbbdbbcdcacaccddadbaccdcddaaacbdcbbbdbbdbbbcadbacbcbbacccacacbbdddacdadbabcadcbabdbbdcbdcbadbacdcbdbcccdcdbddcdabdaccbcdcbabccbcabbddddbaddccbdbaadbcaaccddccdabccaababbacdbbdabbaadbdbddabcbcbabddcbbcbdbadaaaccbaadcaaacdbcbbbcaabbabdbdadbcaaccddcabdcadcacadbabcaaaddbdabddcbdbadcabbaaacbabbbbabddbdbbacdbaaacddabcccbdadbbdbcbabaccdbcacaddabcacacacdcaacccdcababbaaabbdaadcdacbcbaaaddccbdbbbcdbdcbaccaadbaabcaccadcbdadcbabaaacbabadacdbdbaacbcaaddddaaccdaaabbcaddabccdcddadddccbbbadadacaccdbdccbaaacbabaadaddcacacddbbabddbbccabdbdccdcddccdaadbddbaddbcdcacbbadbaaabdccabdaabbabbdbdddacacabaccadbaacbbcaccdbcdcaacadccacddbdacbcccbdcdadbbbbddcaaadbbcdbbdcaaabaaccadddadcccdacabacadbbdaadabcbacdcabbdaacddadccacdddddccacadcddccacabddccdcddadaccacccbcacbdabaabddbcdbabdbaabdbbcdababbccacacddaccbccadcbccbcaadcbcdacaddbadcbbbbdabccdbbbadbcaadaddbbcccddbccbdbbbaabcadadacdddadddbacdcbcdaacbcdabcdddaccbcdacadbabbcbbccddabdcbbccdcaddbbabbbbdaddbcbddacdccccddbabcbbaaadccdcdaddacaabbadbaddcaddbcabadcdabadadccdaddaadddcddabcbbccddcccbdbbdbccaaaccdabcaadbcadccccdcbcccbdbacabbbacacdcacaadaccabbaacbabdaaadbaacbabcbcdcbdadaddabcbcdcbdbaadccaaaacbdcbdaadbdcabbdabbccaccbabaddbdcacbcdbdacbcccdddcbcadbbccdbabaddcccbabbdcbacccacdcbbbdaacdccbdbbcccadccbccbcddacbacdbdddcbabacccdbdbaabdabbbaccddbabdddadbcabdabdddbbccadbdbcacadbccdabbccaaaddadabbcdaaabcddccdbdbbbdbccdbacbcbdacbddddbaaacbabcbcbadabaaacdabcabbcbaddacbbcacbdccabcbcadcdccdbccbcccbadaadabbddcbadbbccccacadbddbddabdcdacdbdcabbdddbcaddcdacccdcbcaccdabbbdbadbacccdabbadabbadbdcadacdcbdacbcdcbcadccdabbdcaadaabcbcbcdbabbbbcaccbabcbdadcbaabcbccddbbbdcccddcccadaabadcdbdbdcbaadcccccadbbaacabbaaccbadabaabdbaaaadaaaccbdabbbbbdddddbcadbdccabcabbaadacaaccbddacacbbacccbabbbabcddcbabacbacdbcdcbbbdbcdadaaacacdbdcadcbddbdbadaadbcbddbddcbbbacdcddcaabddadbbbaadbddddbcaddaacadcdcacbabdbabcaaaaddccabbcdbbabaaadbbccdbadddaddaccbcccaaababbbacddbcdbdcdcdddaaddbcadddcccdcaaabdaaabbbcabbdaccaddaaaccacaaddbdbaccababccacdccadcbadaabdacdddbaddcccaaccbaccbbdacaaccdcaccdcbabdaaaabcdcadbcacabdabddddadabbdccbdaaccbbdcabcaaaabcdbbbadbbbbbcdaddccccaabdacdccdbcacaabacddccbcdcdcabcadcaacccbddabdcbdadcdbdcabaaadaccdcbabacbaabccaabcaaaddabbacdcddbcdcbdbdcdabdccbcabddccbbaadcadbbcccaacbacbcabbabbadacbbdbdacddacbbabcbbabccbcadbaaabbdcbcccacabacdbdcccdbcabddddddcdcbcdbbdadcccdddccdddcdddccccacbaacbcbdddccaaadacdaadbdbabbdddaabbdadadbccdacbdcbdaddddbacabddbaaadbdcadddccdcdaaabcadcadddddccddadcaddbcadbbddcbbaaccccaaabcaaddcaddbaacbacccddcabaabcdcbcccabaacaddbbabbdbdbcadadccdababbcbcdbddbddccbccadabaabbcbcbcccddabbbadbccdabbdcbbdbaaababccccddacbcbdcacdbdcdcbcbaaaacadbcbabcdbcdbdacdddbabcbccdaccdcadcdaabdcdadbdbaccaddabcbbaacabcddadcbaccbdabccdcbcbdbdbabababccccadabacddbbcdcdadadacdabcbdbcdabdddcabadddddbddcbcbbaabdbaacbcadccadadbaabdbbbadccdccbcbbccbabdcccdbbdbaccdcccadcdcbdbadbababdddcaabcbbadbabbddbbaddccdbbbdadadabcacbdadcdcdbdbcdcdadbcddbaccbcacacabbadabddcdddbbaadcbcbaaadbaccdbdabdbddbdcadbcadadbcbdadbacdacaadcadcddaaddcaacdbbbadddcbbdbddcbddaacadabccdbddcbdabcbcadaaabbdaabddbcdccbaaccdcbadcbcbacdbaddccababbbaacbdadbbdcdaadcbaadcdccbaadbcbabdcdcdadababdacccbdaabaacbbabbdbddbdbcaaccbcdbccadcabdcddccdbaaccbdabdccacbcababcccdddcdcabaaabcaccaaccdcdccabacbcaaddcbcdabbdbbddbdbbaaccacdaccaabdadbbacadddbbbabcdaacabbddaabdbdcadbdbdbbaabbaabcaaaabaabbabadaaaddccacdbcbcdaadbcbadbcbcdacbddadabaccacddddbacbbccdadddbdcdddbaccccabbccccbcbccbdcddcbcddabacbcbdccbaababdbcbbdbdacbcdccdcdddccdaadbbbdcaabbccdbbbbcbcbcbcbadbdacbccacbabaaacdabdcddbcbdcbadcccdbdddddadbdcbcacaabddcbaaaaccdcbdabaabccddcdddacdbacbbabdddaabccabaddacbdbdcbbdadcacdccdcbadbbdbdbcdbdaacadbddbccacadaccccbbbccabcdcdddcdcbdbabddbcccaaaaabdaddbaccdddaacaadbbbbaacaadccaccbcdbcccdbacdcdbbccacccdcdabbcaacbdbadbccdaddcbdbbbabbdacacdcaadcadbddddbbddccdcabccaddbadaaabccbabaadccaabccbabcdcbabbaaccbdcdccdabcaacbddbcdcdbbbcbaaccbabcbadabbcbacacbdbaccdcbbdcdbccdaaddddcbacaaccddcbbddddcbcbbddbbdadbbbdcdbcdbcbddbbcacbacbbabcdbdbbacabddcdcadcccbacbdcbcdcabbdbdcaabbccdccabcdacbcdddcdcbcccdbcaabdcbdabdcdaaddbabbbcbbcbaccadcdbbabbabbaccdbdaaadcbdbacccacdacadaddacdbaaddcddabdcbdbadbdabbcddcbacdacbbaacadaadbaddcbbbdadaaacddcbbabccbcbcdbcbcadbccbccccdcadabcaccdbdcaabbcdccadcadaddbccaddabcbbddbccbcbdaacccabdaddbccadaccadbdddbcacbcaaabccddbaaacbcdadbcddadbadabbdaacbabccbcddccabcdaddcabddabccbdbdcdbcdccaaaddbdbdabacbcddaaabcaacbdbdcadbbccccacacbadaadcabdbbdbcdddbdbadabaddbdbdcdcbaaaabcbcbccabbdbbcdccdacdabbddbabcdbcaaacbbaaccbadadadacacdcbabcadcdcdbbbcabdbdadbcdddbaaaccbbaacaadbdbabcbbadccabccbcadcdcadaadbacddabcbdddbddadbbaadcbaaccbdbacbbbbbadccdcbabbccbdcccbbbdccacddcdacabccdbbbbadaadccbcdcadbbbbaddbcdaacccbacdbdaccacabcbdcabbdaacaacddbcaacaddbcabbdcdbddacdcdbabbadbbddcbddbdcbdbcdddccdadcccbadddddcdbdbbacbcabbcaacdbcbadbbbdbdcdaaaccbabbabcacdabaaadadacbdddddbddbaacbbbcaadcaacdbbababcbbdbdadbcdbbadcabdbcbcabdbcdbbddddaaddabcbbadcacadbcdbcbabddcbaadabcccdbdcbdbdbdabdacbdaadcaaaadbdbbdbdbadbbdccaddcbbbdaddbacdcadcdbaddbdadabbddccccdbbbbacadbadadbdababadbcdbbbcddddbdaccadcbbdcddacdccbdcaddccacdddbbcdbcaaccbabababcbbaaabdadccbacbbdbddddbdddabdabadcaababdccaabababbdbcbbbcbdcdcbdcbdacddddcdadcccbdbcbaccbdbcbbdcbacbbcabaddcdbbbbaabacdbbcdaddcddadbdbaaacbdadccdbcacbdcccdacbabaddbdadcbdabaaaddcddcdcdbdbabcaccdaaabdbbbdcdcbdbdddabcbcddabdbcbacddbcadbacbbdcadadddadcbbdaaacadbbcadbdcabddcadbccbaadbacbbdbccdbaccccccbbabddacbdbbbcddacdbbcdbddacaacabccccbcaaacabcbaaabbabaacbcbaaaabbdddacddadbdcbcbbacbaccbcadadcaabbcbbdccbcddcacaaccbacaabdaadcadadcaacdcbdadabcadaaacbcdcbccdbadddacddbdbcdbbcadcbcdabacaaddcabdaabcbabbacacbdcdcdbaccddbadccaabdadcaaaacadbbddcddccdbadccddadbbdaccbdaadaadaccdaabcdbbcddbccbabcbbcabdccacaaabbabddcdbbbcdbcacdaabdbaacbaaacccbcdcdcdabcaadcbacbbaccacdbbbbabaacabbabababdbabaaaadbcabddcbbdabdababcdaaaaccacccbadddaaabdacccdabaaddcabbbdabaacdbacdbbadcadbdcddabccacdaaabbdcbaaabaacddacdcdbaaadbacabcdbbadaccdcdbdacabbadcbdccdcbcbabbadadaadcdbdabaabdbbabbbcabcdbadbdabaaacadcbdccdacacccdacbdcbdaaaacdbacaabbabcdcaadbccabbdddccccbbbacbbcbbabcdddaddbcdcbdbaaddacadbdccabccacdbabdadbbbaccbdacbbbdabcbbdbaaabbdcddacadbcbacbabddccddadbdcbdcadbcdabddabdcadcaaccababbbaccabadacabadcbbcababdcdadccdcabdcbadacdbbbdbbbbaccbcacdaabccbcbbbdbdcadaccabaccccaacbcabbbbaaadaddbdadddabddaacabdcccbabdcdcabaddbbdabaadacbcadaabaddacaabdcdbbddcbaabbcdaabbbaaccdddadccabdababcbddbcbdcbdbcaaabdcbdbcbcdbbbcdcacddcdaadbdcccbbbacbaadbcbdadbdddcabaaccbcbdbddccccaadcbcacddcbadcdabbbabaddbddabbdbababdcacbbbabdcdcbddcadcababddbddcdcacaabbbdaaccdaabdcddcaababacbdbbbaaaaaadcdcdaaaddcbcbcaddaddccdcdacacaaccaadacdaaabcdbdddcbbdacacacadbaaadadbdbcabacbdbadabdbdcbcabddddadadbdaadadaddcbcabacccbbabdaaaaaddbcdcbcdbbbcbbbadcabcacabaaadaccacddddcccccddbacabacaadaccbbcacbddccbbacabcbaaddabadadcccdcaabcaccabddacdadbabccbacabccbdaaccadbddbcbcacabddabccabdadcdcbcacadabacdcbbaabdacccadaacdbdacacacacdcccbcbaaabbdcdcbbdbdcadcdbabcabacdcadabbaabcccadbcbbdbaabcbacacdabcbdcdcaadbbcbcaabdacaacbdadababbddcbdcbbdcdaaddcbdadaddcbcddadcbbbcbaaaacbbcbbdddcbbccdcdbdcdcbcbbcdddcaacddbbdccabcbcbbcbddbdbcbbacbdccddcbbbddbbbacbaababaacdabbadaadaadabbdcdcccbcadcddddccdbaabbbcabbaccbaaaaabdddbcdabaddcaabdbcddadddbccccdcacbabccdcaccaccdcdbccaabcdcbdcbbadcbaadbdcdcdddbdcdaadcbabcdcadbcbacbdccacdccbbccbaabcbdbabbcccddaaaadcabdbcdcdcacbdcbbcadcacadacdadcaadcccdababdaaaacabcddbababaaddcdabdcabdcddbbdabbdbdcccabaaacaacddbaccddcdbccddadabcdcaabdcbcbadcbdcacddcabbbcbbadbbababbcdbdddbbcdcadcadadcabcbbbccaddaabaccbdbbdadcadabcdbbaadcbaaddaddcbacacbccbbcccadccddacbadcdabbdbbbabdddaccbdcacabcbcdbdbaccdcabcdbbbbacacdcaadcdabbbaddcabdbabdadccdccdadcdcddadccbacdbbbaccdbdadbaacbddbdcddbcbccdcdaacbacacdcaacddbdcdbbdbbacbdbcbdcacbbdcbddacdddcddabbaabcdacaabdabbababacdbcaacacadcabaccbddbbccababccbddcdbaddbccdacdbacbdbdcdbdcbddbcbcdaacbaabccbababdababadcddbbcdabaabbbbbbdaccbddaadcbbddbccacdaddadccaabacaddaadabaddaccdabcaadccdccbdcbdcbdbacbdcbacbbbbaddcacbdcaabcdcbccbcbcbdcbbaadbadacdddbaacacabccaabaddaadcaddababcddbacbcbdbdcbdbbdcdcacadabaccccdccaadcbbbdcdbdaabddbaaccabadbbaabcdbcdcdccdbbbdadcaabadbaadaccabaabdbdbcdbccbbcccbcaaccbbabccdbaddaacbdacaddacadacdcbaabdadabacdddaaadaddcbbccbabbcbcbcccaccbadabacddbbaadbaaabbcbadbabbbdccdcadbdcbacbabbcadbdacaccadccdcbddbadbcbbdadbdbccaabaacdbaddddcbdcbcabdabdcbcdbccbdaaaccadcdcaaabcdadbcdbbcdcaaaacbbdbddbaacadccaacbcaccdddadcdbcdcdccaacbcbdacbbcbbdbdbbbbacbcddbaccbcccbdbadbaaadbdcdabdbcbabddbbacddcdbcdcdaabdccabbcdbaaaacddaacdbabdadaabbccdccdbddcdddbadcbcbddbbbadccbbcdcbacbabccabbbadadabdcbddcacdacacdbbdbaddbdaacdacbdabdcbabadcbccbdabaaacdcbdcdbbbcbaabbccadcbcaabcdcaacbbddabccabdcbbcdaaaccdaaccadcaaaadddcbbcccccbdcaccbbacdbabddbccbdcdabaabdacabbdcabcdacadddcccbddbcccacdddcacaddbbbcdcdbdaabbdbddddbcbbdcbbcdbddbaabdaacbaccbbadccbdbbcabcdbcdadcbdcaddacaccbbbdacdccbdabdccdbaccdaaaadadccdcabaddcddcbbccdbdcadcccaaccabdbdcdcddbccdabacbaadacbdaaabbcbdcccadadbcdbcbcdacbaddbccbdbcdadcdbbdbbccaabadcaabccdbdddbcccdabdbdcabbcabadabcbcbbccddcabdbaacbbcdbbabcbdbdbbbdddaaabbdcbadacabbcdbabcadccabbaaaaadabbdabadbdbaaadccbdaabdddbbdbadaacaccccbabdadbdabaabdbdcbdddcbdcbbadddcbdaaaabdaaccddaaaabdcdcbadcbadaaacdabdbdddaaabbacbaabccdbbbdbcbadaadcbcdadbdcaadbccccbdcadbcabddcabcaccccdbbbdbbcaabdbabdacdacdbdbdbabdbdcbadadadabbccbbbbdaabcdddbbbbaacbacadadbcccbbdabdaaccccbbaaaaadcbdcacbadcdaabdccacbbdcbaabdcbabcbaadbbbdacdccabccdbadbcdaccbdcabadcdbbbbbdabaaabbbdccccacaccbbddbbbdaaddaaadcdbcaddacaaabcdabcbbdbacbaadacdaabaacdcbcbabadbdabaacdbbddcdaadbcacdabccaadbbadcbacbddcddccdbbddcacbcbcabbcbccccbbbccacdbaaaabbbaadacbccdbcbadccbcbdbaccacdbdbdbaccbabcadddccadcdabccdcbcdccbcdcacdcdbaababababbccdcabbaaddbaacdaaadbbbbbdcbdbcccdaaadadabdbaccbcddbddbabdbdbdbbbadabdcabdcccdbdcbdaaaabbdccdbabacaccbdccabadadadbadabbbddacacacaddcdbdabbccbbcccddaccbbbbbacddccddcabcbccbaccdccbdabdbaddabadcabddcccdcdbdddacdbdccbcadabbadabcbadaaaabaddcddcbcaddaaddaacdcdacbbaacdccaddcbacbbccdaacdbdccbdabddcdabcbbbdcbadaddaabbcacdddaaccaccacabaabdbdcabcadbaadaadbdcbbacbbadabbdbcadbcadacacadadcdbbbacbabbbaacdaaaccbdcbcbbabdacbdbdccdbabacbddabdbbdaadbddcbddddcaadabbdbdbabbcbbddbaadabbbccddabbdcccdacbbcbcabcaccbabcbdcbbacacbcacaccbdcdddccacbcdbcabccaccccbbbbadaaaadbccdaadadabbdddacaabdccdddbdacdccbcbadbbccdcdccddbccbdbdabcadcabcabbbcdcccacababcadbcbbbbaddadaacadbdcaaccdbaaadbbdaabcdacbbdccdcdcadcaccdbdcaadaaccaabbdbadcdacbcbbcdaaacaddaaddcddcbbbbaccbcabacbbccbadbbdcdcaabdccddbcabcacadbadbdddabcbababadabcbabbcdbddbbdbccacacaaccdbcbaabdabcccadbacdbbdbbadcabbcdaccacaaddcacabddadbbcbbddccaaabbcbabaaadbdbdddadbaabaaadbbcdccaadacaacaacaacdadcccacbddbbacaddbadbdcaadcacabcbbcacdddadadddabdacdbddbbbdcdbadadbcdbdacbcbaadccbcdbccbbbabdbcdbdbccdaadbacbddcaccbdcacabcdabbacabdaabdadadaaaadcabbcacbdacababcaaadbadddbddabdacccdbcacaacaabdddacdadcaaaddabcaddcbbbcbbacbccabcbcdddcddcbddbbbddccddbbcbdcaddbcaabbaaccdcdbccbcdbcdbbdadbcbcbdabbbadaabdabcdcbcadadcbaaacabadbbdcacbccadcdddcbacdbbacdacdbadddaadcbadccbbacaacbccaadaacbdcbccabcbdabcaadbcabacddcaddccaccababbcbcbbaacaaccbccacbdaaadcbdaadcccdbbbaaaddcbacbdddbbcbbdcbcdbbacdbbaacaddbaaaacaddcbddbbcdacddacdcdbaaabcbdacdccaabcdcdbacbddbccdcbcbaccbdaadbcbcaccbadbdacaddbdadcddadcdddbddbbddcddaadcdacddaccdbacdcddbccadacccbdddacdbdcbbdbbccadbaadaddbccbdddcdcaddcabadabccaadaabdccddabcbdccddaccccaddabadcdbbacccaddadbddbbccacacbbcdbccadacccbaadcacdbaddccadabbbdbbcaaabcbaabbcdbdbcbdccbdbcbadbadadacabbcadbaadadcabdbdadbabcdbbababbaadcaaabbacbbbacddcdcacbbaaddabcccdcbbaaaddacdaababcbacbbaaaddccbbccbaccbaddcbadddccddcdccabcdcbcbadcbabcbdddcbbaabaacbcbcbbdcdcbdaddcadacbddbcddbadcbdccaaadcdbdcccaadbcddbacadbacaccdcccbabccaddcaaddadcabcadabcbaddcaaadccbdbdcabbdbbacbdbcbdcadbdccddbbbbccbccddcabbacdddddcaddbdadbdaaccbdcbdcbccabcbddadadccbbacbbbdaaddcbcabaacabbaabaacaccbcaacdccbcaddbbccacacbbaccabdcbddbcacdcaccabddcdcdabbcabcbccabacdaadcaabccdcacacbdacccdbddcdacccacdccbccbaacbacdabccdbcbadcaddaabdbcbdcbddbcdcbcaacccadddaadacbbddabcbabcaaaabdbcbdcacbcdaaaacbdadccbdbccdbdcaabbbbcccacdcddcbcaddcdaddaabaaabacbddabccbdccdccadacdabddaacdacacdcaacabbddddaaccdccdcdbdaaababdbbaabbddacdadbbbbbcdabccbbbdccabbdcabcadbdacadcbbaabbdacdddcbdbdaabbbdbbbdcdbdaacccdcccccddcdcbaacaaadccbdabcdacbbbcacbcaadcaaddabaaaacaddbcddabcacbacdcbdcccacaacbdbcdbbbdabcbccaaaccadbacdaadadbcbdbcbdbacadcaaccadabdaaacbaccabaccdddcabcdacbbaadccdcdbccbaddaaaadbcdcadbdddcdbbccbdaaaabaabadacbccdbabbbadddccabdabbababdbcccabccbbdddabbcbbdadbbabcbcacabacbaaadabcaabcbdaaaccdbcbbdbcaccbaadcbbdaadabddccbaccbbbadbcbadbdaddabacadbbaabddadcbbaabdbbcdbdadcbcdbddbbcbdcabcabcddabbcbadbccbdddccbdccacadcdcdbcaacabddabdbbacadaddbdddbaddcadcdcbdabbdbbbacbcacabdbdcbbcbccaadbdddaaccaabdcdacbdddacddcddbcbcabcdddbacbbdcbbccdabbddbbdcbdbaccdcdcccdcabcabadddddabacbcbbcaadaadddadbcccdddbabccbaaadbabaaaddcacddbcdaadccaacccdcbbabddbacbbddbaccdabcccadbbcbabababbaaccbaaacacdccdbcaaadcdccbddcccaabdacdadcbccddcdccadbaabaacadadddcabbbacaacbaccdbddcbaaadacaadddaadabbdcdbbdadaadacaacdadbcbccbdcccabdddcdaaadcbaadcdbbbdbcddbcbbcabdacaadabacddaaaabccddabbdcddcdabbdccddccccbcdcabdbaabbdaddbabdbacaaccdccddbabacbbaabbdabaadaaaabbabacbadddcccacdcaadddaaccdacacadcacbabdccabbaaddbccbaaccdadcadbddcabcbabadbbacdbdcabcacadbcaadccabdddbcdaaaacaaaaaacbcbbdaaaccabcbcbcdbabddabccaadabcbddbcbaaabdabcacaabbdcaccabbddbbabdbbbcadcccbdcaacdcbabcaacdadbbcbbdcddadbdabbadccbcbcadadddabababaabbdcaacadddacadaaabcdabdbdbbdacddcdccccddcdccdbcbadcacdcabbaacdabbbdbcbacaaadabbdddbbadaccbcdbaaacddbccbcccbcbbcdddbcadaadacdaaccadbcddaadcdaccbbccaacdcabbbddacdddcbbdabdcabdacadbcdaacdddcbbdacccdddbcdacccbdbdacbcacdadcaaaccddbadbbbabbcaddcadcbbacaabdddacadadbdcacdcdaaacbcaabcdaabdcbdbdaccadadacbbabccaaddccddbdcbacaaacbaccdbbbaaabddcbbcdacdcbcdcdbddbbddabacacadddcdbaadabccaccbabcbbddcbddddadcbbcdbacdaadddcbcddcdcbcdbbdabdababdaacddaaddccbadadbcbccccbaaabddbbddbbccccababddccbaaccccbabdbdbbdacaccabddacdacdacaaddaddccbbabcdcbccdccdccadbccabcddbdbaaacdacbabddbdbdcdacabcabbcddddbdbddbcdbcacaadcbbbbcdadccbdabccddcbaddacaaddacabdabdbccdbcabbddadccabacdaacaaddabcabdcdbabaabbbbbddbddcbbaccbabcacdbdbddbbababcbcabdabdbcacdcbcabaaccbdbabcdcacccccccabaaaacddbabadabacbdcdaadadbddccdccaacaddacbccdbcaacdcaabbacabccacbcbdbcbdbbcacccbbaaddbbaadbbabccbcaadcddbadbdaddbbbabadcbdadaabcddaaabddabbdbcbbadcdcadcddaadacadbaccddabbabbcabcccaaacbddccbbddbbbbdcdbadacdacabbccccbabdaaabdbabbdbccdbcadbccacaabdbaabadadadcccabccddddbcdbcddbddddcbbabdcddcdaddbdbdcdadddbcdccacbcaccbdcdbdbdbbdccccabdacdcbabacacbaaddcbcbdbcadcbcdbcbccdabcbbabcabdcdccdcaabacdcbbbcdacabcadaabbdbaabddabdaaccddbacbddacaddabbdccacddabbbcbbabbcaaaacddbacdccadadaaddbbbaacdadbacdbcdddcacacccaaaccbddadbdbbaadcdddbbbacdacbccdacadbaabacadabcaaaacddabcbaabcaadccdbbabbcadddacdcdabcaddacdacbdaacbacdabcdbdddddddccdcdccccdcaaddcdbbabdcabbcbcaaddcdaabbbcdbcddbddcdbdcbdbadabbdaabbdadaaaabcdcadbacccbcbdbddddcdadbcbbddaabaccbddabbbdabcdabddcccbdabdddadcdaadabcbbcdcacaddadcabcbbdddbadcccadcbbabdbcbddcbcdccadaccaadbdccbacaaaddcdaaabcbdcadcddababdcaddddbcddbabbcdcddbadaabadbcddbdbcbcbacccdcaaaadccacdbccaacbcaaabbaabcdaacbdadbcadddbcddacdcacddacbaccccdaadcaccabacbccdcccdbcaadbcddcabcdcdddbbbacddacbbdbaccadbdaadccdadbadccbbaddacaaaaabadddaaccddbcaaacaddccabaccdaddbcdcddccdddabcbdaddabbadaddbddccbcadcabaadaabcacaaadccbbdbcbadcdaabddaccbdacbcbddcbdacdbbcccbddbbacaacbddbbddadcbdddddddcdddcdbabaccdacdcaadbbdaaaccdcbdbbbccbdbdbbbadcdaabacababadcdcbdabdacddaadbbbabbbcbdadbddbbabacdddadabdadcacaaaccbbdcdccbadacbadaaaddbccababcababbaacbdbcabcbcaabbabddcbabcadcacadbcdaaccabdcdacbbdadaaacbcbbbdbababccacacdaabccaacacbaabcbcbabdacacaccdadcacadabdbaccbaabaadccadacbbadbbbaaddbddbcbcabcdaabbbdbaacbbaabbcdbbbdccabcabbcbbddacddcadabdabadbacaccddbddcbbbbddbabdbcddcdcbcadbbdbbcbbadcabadacdadddbdacbcbaabbddaccdbaabbacacbaabddbbabccacbacccdbcbcbdadcbbdcbcadcbddbcbdcacdcaacabcbbdddcbbdabbaddcccdbabcacdbbaadcbcbcdbabbdbddaacbdbccadaaaababbabddcbdddddacdadacbacccbbddaacbdddadabdaccdaadabcbcaddbdcbabbabcaacacbcacddbcadbddcbbddcabacbddaccbaddabdcdcdcccbcccbdbdacbadcadcdababcdbcacbcabdddbaddabbdaddbccbcdbdcaaabbadbbaaccdbbcdaaddacdbcacccbaabaacadddadbaabcdddabdcdadddcbdcaccaaccddbbaccdddbcbccddbdbcabcabdcdbdcaccdcdabaabccaadadbbdcacacadacdabcbcdaadbdbdbcddccbdcacdabdacacbcbcbacdcadabccaabbccaddccaddacdabacbbbadadddbaacddcacddbbcabcacdcdaaabaacadbbbcbcabbbcaaadcdadaadabdcdbcadadbcdcbbadaabbccadaabdcdadabddbcbabcbdddbbdcdaabdcabadcabadddcdaaccbdadddacccbbaadabdccacbdababbbacddccdabccdbbbcbcaacdaddaacddacbbbaabcdbbacdcdaacbdcddcbaacdbddaaaacbddabddcdabbcacbbcdcadacadddcadcdccacccadbaaaccdbccdbcccaacdacddabdacacccdddbadaccbcadccbddbbcdcdbdcccbcccabadcaddaadacdcdbbcdbcdbccdcbdcdadcdabbcabcddcbacbdcdbbcdcccbcacdbaacbddbdcbadcddacbbcbbcadcbdbcccdcaabacaddcaaccadacbaaadcbbcddbdcbdddacddbdccddcabababddccbcdcadadacdaacbbcdddbdbdcbdaaaaccbdbabbadcdcacdcadaaaddabbbdcaaaadcccbcaaabbbaaaaabdbabbcdbbcbaabadadaddcbcdbcbdbbadaddddadbccadbabcddbcdcdbabadcdacaacadcbdbabbaadbcbaadaccddccaadbcadabcbabbabdbcaacadaadabcdbcbccdcdadaccdcaddacbbcdacddacbbcbdacbddddbacadabcbdaddccccbcbcdbaaabdcdbcbbdadbbbacddbbccdbdbcdabcbcabdcddcdbddbcccccbabcadccbdbacdcccccbaddabbbadcdddcccdbdcbdabcaccbdcabdacdadbbdaaabaabdadaddbabcbdabdabcaaccbcbdacdcdbbbdcaaadbbcadadccbccadcdacdbdddadcabbccdcddacadbbbbbcdbdcaacdcdbdabaacbadbbadbadccbcbcabcababdbabddcbbbaadccbcbadddcaaadbabdadcaabcdbcbcbcacbdcbddbbbccdbcdcbabbbcbcdccaddbbbacabcddccbdabdddaddbdcacbbbdbadacaccabbdaababacdadabcdbadbbcdacabacdabccdcdabcccbbbdabdcacbdbcacddbaaddabaddabbbaaadddaadcaabaaabcacbaaabadbcbdcdbbccdadcaaccacdbcaaaabaaaacdcddcddadaacaaddbcbaaacbbbdccddcdaadcacbacacbddbdacabdcdaacbdbbcdacbaccbadacacadaadbadbdbddaabbbbbaacbbbaadacaccbbaabdcdbbabcadbcdaaddcdadddddaacaccbcaacaacdcbbabbdcaaacbbcdcaddbbbddbccaaadccbbaadacbcbdbdadbadacacabdaadaadbbcaaadcdadcadddbbaabdacbccdddcbdbcccbaccbdaccbcdbbccbcbadacabaadaccdbcbcdcaccdcdacdbabdabbcbcdddadbcabaccdaaaaacbdabbbaadcbcacbdaadcdcabcccaaacabacdabbcbdaabadbcddcdabcdbaadadaacdbcbaccddbdbcbbdbadacabbcccaaddbdadbdabcacddabbbdbbacdadbbccdbabcabdbaccdcacadaabaadcbaccdabbbdacbbcbcdccabbdcbbcccccbbbcdadabdbddccbbadbdcaddcabcbbadadddaaacbdddccbdcdbcaccdbaaabacaaddadaadbcaadadbccbbbbccacdbadcaaabbbcbbccadbdcddbbcbbaaaadbadabcacbdddbaabcdccddcacacadaabcdcadbbdccdbaaccabccbbacbbacacddddabbcadabcbaabbabcccabcdbbacbbabaddcccaaadacacbddaaabdbdabdbbaabaacabcdacdbddcacdbbdbaadadabbbcbccbcacdccbbbbacaddddbbbababaccbababaadddacbcdccdcbdbbacaaccaacdabdadaaadbdabbcccdaabbddbaabaccadababaacaaddccaaabddadcddccaddbbdbadaabbcabbbbdddcbabbaadbdddbbdbabccbabbadabbdbbdcabddbacbacaaacbcddcbbacbbdabbddbdbacbccadbaabbaddbbadbbaabbbdadddbddbcddddbbcbbbbbaccbcbbdabcaacbabddbbbcadcbdcadbbbbabcbdcadcbdadaabacaddaadacabbddcbddbcacdccaccaacbaccaacacacbdbbbbddabddcdccdaccaacadbbddddbcbbbcdbbaabaddbabdabbcbbdbacacacabdabbddbabdbcdacabcabdccbacbdadcdcaadcdcbadaaaaaddcabdbcddaaccabcdadadbdbcbdcdaabcbbbcdbabddcbcdabcabbacabcdcacbdcdbbdbcdcdbbbcdbacbbbcadacdcdabacdaabbdbdddaccbacdabcbbaddacddbddddbaacdacaaaabbddaadcddccddbbbbbbadcdccabbdddadcbcbcccddddddbccddbbbcdbccdbacacabaadddacdabadabcbcadcadcdbbdcbcbdabaaababbabbbdddccbcbbdcadbcbcdaabbbadcaaacbdaaabadadbcacbccbddadbcbbbcdbcdbcdbabdabaddcddacaddabbbdbacccddabaddabbaddcdaaccbbdadcddcdcbccaaccdcdacababcbaabcbcaccbcbbcabcbadaabccdbccccbbbcdbbccddcdccddddbbdcdbddcdaaddcbbcaacdccbdcbadddbdabbbadcddcabacdaaccbcdbccdabbcacccdbdcdbcabdcbbddcccdbdbacddbbacccdccdddbdbcabcacccdbadaaccbbcbbdcbccaabacabdccdaddcddabcaddadcdccaccdcbcbcaaacacbbaadbabcbddcdbadcacddaaacccbadcadbaadbbcbdccbbcaacadbccdabdaaabcadadacdadadbadbdacddcdcabaccccadbadaacdaddcdcabbcbadaabbbbddaccddbdaadabcbbadbdababbccbbbabcdaacadbabacdbdabbaadddcdabddabaadbbdbdcdaaaabdcccdbbdbddbccdcdddbadacacaccbbadadadcdbbbbcbbaccccccdcadbcbcaacbdcdadddcdbddcdabbdacadacdacdaababcacbdcdabaabbadcadbababbcdaadacdcbdcbbacbbbbadddcbadcbbaccbdadbcbcabbcaccccbacacddaaaacbbdacbabdbccdbcacdcbababcaadcbdcacdccadcbaadbcadbaabcddbaadacbddbbadacadbaabbdccbddacdbcdddbbcbaaaacabcbcaaacdddadacaadcadccaadcadadaacddabaaaaabddaabaaaacbababbcbbbdccbacabdadcddaabaabadcbbddddcbbbccccdccdcccdcdbbcacbbcadbbbacbadcacdacccccbbacddccdccadabccdcbdbadaaccbacccaacccddbcbdcddbbbdccbaaadabadacabdbbbcabbbbdbcbbddacdccadcdddcbbacccbaddaacdbbdaacdcadcdaadcbaacabaacbabdacbbcabcccbdadacddbcadadacdbabcdcbdbaccdadaccccdbbaadccccddccacbcadaaddbccddbadcbaadccadcbbdcaacdadbcbdadbbabdabaabddbdccbbdddcbbdbccabcbdcdbdadbccccdcdbcbbacdaaabcbcaacacdaddddcacadcdbdbccaadcaaacbacddbccacbddbaacdabbbbdbbadaccaccccddbdcccbcabdaaabbbadcdddadadcaabaaabbbdabcbbbbcdbdcbccdaaccdbdcbbcadddbcddaaabcbbbdabcbababacaaccdbcbcacbbbadcadabaabdcaacdacddadbbddadcdacbcacdbbdbbababcbbddcabbbbdcbcdabadddbdcbdabdbbaadcbabadcbadabcbdaccdcdbbdbacbcddbcabacdcdbddacbbdccbdcccdccdaaddccdbbacbbccdabbbabdcbccdcaaccbaddcaabcdcaadaaddcaaccccbbcbddbddcabbcbcdbdcacdbdabbccdababdbdadbccdcddcbbacdaaddabadbdbcbdbacdbadccdbabdcdabbbadbcbadacddbadabaadcbdadbbacbdbcaaaccaabdbdacbbabdaddbacbdadaabdcdcbbddababacadbabdcccaabacacbbdccabdaaddcbadaabdadcadbdddabcabccbababcddaaaccdccabbccbcbbdacbbadcdbabcbababcadcccddcabdadcdcccbcccaabbcabbbabdadaacabcccaaddcadadbdabdcccaabcaadbbcddabcababdccdababdadcaccbacadbadaaddacccdbbcdbdbcaccdabbcdcaccbbdcabacbdaaddbcbbdbcbdddccdccdcbabadadcbccadadbcdaaaccdcccdbacbacadccdaaccdbbadcdcaddbbcabacbcdadacbacdbdbabcdbdbbadaacabdcacabbaddbaabcbbaddaddcdabcdabcdacabadcdbdacaddbcdbcadcacabcdbcaccbbbabbdbccbbbbdaacbdbddcbccbabcbcbdddbcbddbacadaccdccbcabcbacacdadcdbadabdbddadcddacbcddadddbbbaaabdbbcbdbcdabbcbdcabbabcbcaccaaadddddcaaababaaadddaaabbcbbbacdcccbbabccbbaaadcacbdcdcbdbcabbbdbdaddcddabaaaaacaaadccacacbdaddacdcbbdcbabbdadcbbbdbbbdcdbbbdabcdcabaccbdddddcacddbbaadcdcbbaaadbabdababbccabcacdbbcdcdccacccdcacdacbdbcdabdabadbdccddadabdcdbcdcbccacbccccdaadabccdcdacbbcacdaabccaddcbbdcadcdbdaddacbddbdccdadbbbaadbcaacbadcacdcdcbcbabcbdaadcabadbdabcddcdbdcabaaaccbccdccdabcdaadcbadadadcdbacabbcdcccbdbaabccbcccbacadaabbdacdaccdcadaddcdbbacbaabaddcdcbcbbbdaaabdaddcddaacbccdcacddddbdbcdccbcbbdcdbabdadabaabaadbdbbddcbddbdccbdaaccdccdbbdbdcbbcddddcbccadabadbcdbdbaccabdcdaccadaddbadaaabbcbdcccbccbbbcbcddddbcbdcbabbcabadcabddbbdcbbdddbcacaaaabdacdbbdcdbdcadabdabbaabdcbdddbddaaacbbdacdddbdbacbcbddabaacbadcbcdabaaadbadbccdccddccadadcabdabdbdcadaddcaabdbdacddbacccddbabcaabcadbbdbbcbabdcccbcabddaabbddabbdaddacbbcbbdcbcabcbdbadcadcbdabbbbdbcbcaaccdcccacccaabddcadbabcdbdcbdabccadcabddabdbdcaddcaabbbacacbbabbbcdabddcbddbbaaaababdaadbbccbcabaddcdcdbdddccbadccddcadaccbdbbbaacdccbabaddabccccacbdacddadbccacbbcccdaddddcddabbabdadaacbaccdadcacbbbaadadacbbcbcbcccdbaabddcdabbacccadbbabdacdababcabbdbdbbaccbaaabcdabbadaccddcdcdbdbddadcacccbbacddbcddaaaaabbaddadbbbdbdccbcbbcbbacadcacbcdaadadcacdbbbcaaccdcadbcabcabbcdbcdcadbbadbdddcbdadabcbcbcabcdabcbbcaadddcaadcbadbabdcaaccacabacbbcdcdacddcddacccacacddcaccdaaadaccaccddbabaaacaabddaaccdacabdbadcbcbbbadcbbbdcdadbbbdacbcdaacbadcbccadcaabaaadddcbcbddbacaacbdcccdacccccdaabcddbcccacbccbabcacdbcdddcbaabbcccddbabacdcbcadddccabbdcbbdaddcaabacabdadccaadaaacbacacbacdcbabaaaacccabbadbbcbabdbddacaacbacacaacdcacddacbcacabdcbaaccdbaddcdacbddadacbadddbdcdbcadbddbcacddbacdcccdaaddabbbadaabaadbdbadbaacabadadadcccdcaadadbcabcabdbbbcaccadcacddcccadabbcbcaaabadddcdadacdcbdcdbcbdaadddcadabbbadcbdddabddbddacddbdbbcbbcdcdabaddcbccbdcbbdaaddacacabdcdccdbacccaaaaaadcadbdbcdbddacaaccdcacadbdddccaacbbccbbbdaaacdbdccacdbcdcddacadccbcdcbbdacbcddbdbdcabbdbcdbdcdcaadcaddacbbdbbbcaacdaadcbcdabbbcadadcddcababbbdccabbbacdabaccbddcbaadbdbdcaabacbbdbaadddccbcabcdacccdbcbcdadbcacaacccadcaabadcdbbdcbbabbbbcadcdbcbaabdbcbbaccadbdaadcbdaddbdbdcaddacddaabbccaddbaadbbbaccbcbbbdaacddddbcbaddadaabbdccbadcdabdacdadaccaccddbbadbadddbdcacdbdbcccacacdcbdddccaadcabababaabbdccbbcacadcbbbcabbcdccdaabdbdacbcddbcddbadabcbadcbdbaccbadaacddababdcaaddcddbabbdacacddcbdaacbcddadcaddbbccbbdbcdbcbcdcdadacdaaaaabdccbdccbadccaccaadaabdbddbacbaadbaabbabbabaddcadbbdbdcdacddbaabbaaadabadcabdababbcddbaabbdbacdaadcaaacaccdababdacadbbabcdddcdadbaaaccdbadaccbdaddcdadddabcabbabaddadbadddcaabdddadaccadadcbcbbabbccdcaccbcbdccdbdcadabbbbbcaaddddabaabbcddddcdccccdacabcddaaacadaaddbcbdcdbcdbdadaccbcbddbdcbabcdccbdaaabdccbacccabcacaddbaaaccabadbdbcbbcdcbaddadcabbcbaaaabdccbddbdadadcccccadaaabddaadaabdbdbdcbcdcdbdddcaadcdcdcdbbababbdaabdcadaaaddddccbabbcbadbacccacbddccbcbabbadddaadaaddaddcaaacccaabdacddabaaccdcacddbccabdccbcbaacccbaaddbdcdbdcaacbaaaaacbbccabbbbdbbdadbdaabcdbcccdabbcbabdaddbcdabcaddadddabbcaccadcbbabbbcadabccadabbbddbcbcbadbdddaccdbccbcaccdcdcddcbcdadccbcdcbcabbcddbabaaadddadcbcdddaccabcabcbcdcabbcbcabcbbccdacbcaacabcdcbdcacdbacdcbaabcbbddaccdbaacbbcbbadcaddbacacaadcbdbdccdadbcaaaacaadcbcddbbcccbbddddcdabcaddcdbdacbbcccdcdabacacbcbaaddccabaabbaaacabbbaaaaccdaccdadadcbacccdcacdacaabdaaddcbbccadbcacdaccadaccccdababccddcadccdbbcdccabdbdaccbdaaaacdccaadddbdacccbadcdcdacdaadadbcbacdcddcdaddbdaaddbacccaaaaabcacddcdcabdddaccdcbdccaadbbcbbdddcdababddcdddadabdacdadaaadabdccdadddbadccacbcddabadbcbbcdcdabdcbdddcadbbaadbbddccbabadabcabcbbbcdaddcaacaddcbbacdaddddbbdbbaabdaadadadcbcacbdbadadcbaabbcaaabbbbddbbacbddabccadcadbdcbdbadddbaaccbaaadccbbcaadbcccdcdddabbdcacacabbbdcdbbdadbaddcdbaadbbadbddadabdcbccdcbabbadbdbbccaddaccbcaccaacacabdabaabbdaaadcdcdabbdaabbbacdcaccaadbdbccccadcdacbbcbbcbdccdccabbdcbdaadbdbaddbdcbbbcabcabccbabacdcabaacabaaabaaccadbabcccbcdabccabccabcdbabcacacaacdbbacaabaaabbdaaadbbaccadbbbbbdcbdbdabcddbcddadadbddaacdcacdccadadddacdcccabdcccdabbbcbcddbdbbaabcbadacdbbdcadbaddbdacbbbaddcbbbadacdcdddddabcaadcacdcabaccdabcabccadbbccabdabadbccddaabbcdadddbacbdadbaccadadbabaaabacacddadaddaadcccbddbdabcbabcbccddddcbcddadabbdbcadcaabbccbdcdcaacabcbddcabbcccbdbdcababbadbdcaaaadbdbadcdbaacbbdcbccbcccdcccbdabcdcdcbbdcbacdcbaacdbdcbaaaacadacbcadabbcacbbdbbaddbccdbcdacabaacabbcbdbcdbcbbdcbcdacbccdcdbcabccbbabaccdadabddbacbbccdbcdccadabbcabbadbccaacdbabdccddaaadcdcacbccbbcbadbcbcccadccaaccbbcdddacadbabddbcdabccbcaddbbccaabacbbcbadcccbdbcaaadaadaadcdbbccddbbdbdbaaadcbddbaddcbcbcddaaadcaaaabaadadddcddbdccbdcdddcaddccdabddcaaccdaaadadccabcdacbbaddddabbccbcdcdccbbbccccabcabdbadcbbbccbdddacaccaccbcdcbccadabcdcbdaacbbbbababdcaaacbaccddabcbdbadccabcbacabcadcbdadbdabaabaccbabbaadbabaababaabbaaccdaaccccbcaabbacadbdcabdaabcadcdbadbdaccbbdbdbbaddacdbcddbcbdacbcacbacdddcdadccdcadbbcdcccdaacadaacbdbcbaababbddcddbadccbcacccacbbdccdbdbaababdcacadcaadaadabacaacabdccdadcddaabadaacabbbcaabbbbdacbcbcabbdbdabadabbadabababccdbddbbdcccbacaabdcabaaaabccccadcabcddbaaacddbcabbdcdbdcaaddddbccdcbabaacacbdcdaabbddbcbbababbbaadadcbcdacdaabbbdaccadbcacdadbcbbacbccdccdbcaddddccccbcbcaddbdcaadbbcddbbbcbaacdacdabdccccdbabdddbddbadabdabacddbdcbbbcbadcdbcdbbcbcababdaadababcbacacdadccbcbaaaabcdbaaccbbadcbbabbbabdbadbbabdcccacabbaaadacdcbaaacdccaddbcdabbadddcbdabbcadcbcbcbcbbbbbdaadaacabcadbccabbabdbdbbcccabddacaadccbdadccdcdcadcddbbcdcbddabbccdcbbcaacdbaddaddddbbddccdadccacbaccaabbcdaadaabdcdababacbabcbcaaadcbdcccbadaababbaadbdcdabccacbdabaaccbababccdbcccbaacdbbaccaabdbbbabaaadacaabbbbcaacdbbbdcaababdddabcadcdacbccbcdbcadbdbdacdaaacbdaababcacdaddbcacaaaddcbddcbcccdcdcacaabdbcbdcdbdccadddbccbcddadddabadddccaadbbdbbcbbdbadaabdaabdbbadadbaddcbddabcaacabdccccaadabddbbaadabcbbbddaadacbbaccdbabcdbddbbaadbcadaabddadcdacaccadbabdcdcaddbcbadbbbccccccdbbcddcccbadbdbbbbcababcbaaaabcbdbaadacaccabacbbddcdbbbddcdadaadbbccdcaaacdddcbdaddcbadadaccccbaccabaaaabbdddabdcdbabddaabdddccadacdbabcbdcacccabccbadaddbabbbdbdbccabacdcbcaaabaacaadcadbbcbbacdcbddbcddcadccadbcdbcbbcaabacbdcdcbdbdcabdcaaaabdccbacdcbacdcadbbbadadcddcddbaadcccbddbdcdabdabaabcddcaabbdcccacbdcaddacbcaddbabdccdaaaadccbdbbdacbbccccadaadbdcbacdddcaaaadbdccacccccacbaadcacdaaddacadadcbdaabdabcbcbbcddabbdcababcbcadacccbbbaaaadadcbbdccaacbbbacabaadcddcddddaccbbddcbdbdbbcccdacdbcbaccacaccdddaadababccaabbcdcdccabdbbcbbaadcdadbbbcdccccbcbdcddccbaabdcacacdaaaabdaadccdcccadacacacbbbaaddccbacbbcdddaababdabdcaccaacacaabdbdabccaddccaccacdcdabcdbccdccdacdcddbdabbaabcaaacdcdbbadbbdbddacdacbadddccbdbbcaacadbbabdbdadbdbdbcbaabccabcaaaaaacadbcdbbbdacabacacdacacccdcaabcadbbaccadaaccadaddddacaadcadbdbcddddbcaaaaabacccbdadaaabcdcaabcccaabccccdbacccabaaaccaaaccccccbdbbacdaabbcccdddbcbcabddbaaddadddacddacdaaadcbbcdbadddbbdadbcddcdccbbcccbaccbaddaaaacbaddabacbacdabcccaaddadcabcbaaaddddabaaccbcaccacdccccdaaaabbadbddaadbbccbaacadadaccbbddccdbbbbccbcbbcdadcbadaccabaacbdddaccdacaabaaacbcacddaaacbdcbbcbdbdbbdabcaacacababbcccdabddbaacbdacdcdaaddddcbddacdbddbaacbaccbaacadadcbbbdacadacdbdcdaadadabdabdbdabdaaadadbbdddbcacdaacbaadcdbcacbbbabaccbacbaadbbdabbbbbcdcabdbbabcccacadcadbccbabaaccaccaccbcaacbbcbccdaaaddbabbbbbdabbacacdabbcdbddaddbbdabcdbbadccccbbcacddbdcbbcbccadcbbbaadaddabbcbacbdbabbabcbddabccbbcccbbdcacdcdcddacccdbababdadcccabbdacdbdaacbabcbdcdbcadadaaaaaddadbbcdbccaaabaaacdadcbbdababccbdcdacbdbdddacddccabbbcbaacadcdabbadccdcddacbcbccbabccbdbbcacbadcdabbcdcbcbabdcbacbadaaadcdbccaddcbddbcdbbdadadddcadcaddccdbdabacdadabddbbcccdabadacbbddbabccbddbacccaadaacbacacacddbaacbbdbbadabbbbaddcbdababaaaacabbbbbabdcdabadaddccadcdbcacbbbbbbcbcddbaccacbcbbdabbaabdddbdcbbdcddadcabbadcbcbbbaccadddcddbdbaddbcbacbbccdcdacbddbacbcbdacddcbadccbccbadbddcbbcacbbbbbcaaaddaadaaddccaccbcaaabaadcacaaddaaabaaacacdddacddaadcdaddaaadabaddbcbdddaaacabdbbddaabcaadadbacdaaaaadcaddcbdcadadcbdacdabcadaadcaadccbbdbcdddacbbabbbacdbdcaaabbcbddacadbcadcccdabacddcdbcbdadccdaacabacadbddcddcbddadacbddbbabdbdaddcbccadabdbbababddbdabbdcabccbaaccdcddbddcbdccbddbbcdacabddababcddacdbacbdcabdacacbccccabdcdbbbbaacadbcccdbdcdbacacbaabdaddcabaadaccababdbccddcbcadbccaadbdddddadddbcabdcabddbbcdcdadcbbccaadcaaddaccaabccccdcbccdcccabdccbcdaacdbadbaaacabcbcdacaaccdcddbbbdddcbbacbbbdbbadcdbccddcbcdadccbcacbabdbdccbbccdddccbbccbaaccdbabcaababadbadbcdadbcdcbbcbbcbdbabdbabdbdcbabdbbcababbbbacadcbacabcbccbddbacdccabdcabddadddadccccbbcbbddcaacacbdccdadadbadaadbbdabdcdbbdabdbbbdbbbaaacbbccdcbaadcabbddaacacadbaaddddacbdccdaadccacdccaccdbbbdabbdcdbacdcddcdccbadbadbaaaadadccccadbbcbcdabcbabacdabaabdddbdabbbadbdcdbdccccddaacaaddcacbbdbdadbacdcabbadbcbcbdbbdbbcbdddbdbcadaccbccdabcdcbabdcaccabbccccacadabdbddbcbccaaabdbbbbbabaaabbdcacdadbdcbcabbbadbbbdcbacdbacacaaaddcacbcbcaacbabbabccaadcaaabddcaadaccbdcaababcaacbdcbbaaddbdacdcdbabcbcaacbccaadddbdcbcaadbcbacdddcddacccdbcbccbbaccdcabdaadcdddbaabbcbcadcddbabcabadbcabdbabcbcdcbbcdcdcbddbadbadcaacadddaacbaaddabbcbcdaabaadcddaccaabcbdbdcdbcdacdacccbaadcbdddccaacaaacdccbacadcacaaadbcbadcdacddddcdbaddbbabaacabdadcabccaabcdccdabcdcccabbabbaacbcdabbdadcdddbddddcbcbdcdaacacdaacccaaabbacadaadcdcaaaaabccdaccdcdcdbcccbabadddbaadbabaadbdbbbbbddadbdcdbaccacddbadacdcbacbabbabacbbacddddcdcaccbdaaaaaaaadbbbabcaabadbcbabbdaccbcaaaabbdabccabdcbddabdadddcbcdbcdbdbdcdcdadbbddcdcdaadadbbbcccbabbcabdcbbbdadcbadbcccccabdccdbdbbcaadadcbdbaacdbcccadcccacdccbbabadddcbaabcdadcbabcbdaaabbbbdacaadaaaccbdbcbacdcddabadbbdccdbdabaddbaabbaabbbbbcdcbdbbbaacbccbbcaddccbbdcbdbcabdcbdcddbcbbdbbaddabcabacabdacadddbbdbdadccabbdabadaaaabcbcddcaddcbaabdcbdabdddacadaacdddcabacbcccaddcdadcdbbdbadadcabcbcdcbacaadbddabcbccbaadcacaababdddabbcaacdcbacabddcbacdccaaaabcadabbaddcdbcacacdcccbddaacbadbbddbbcbaacdbcadcdabadbbacadbaabddaaadbadacaaabbaabaddcdbaabdbabcbabbcbdcaadcddcbccacbbacdacacdcbccbbbcdcdbadcbdbccaccadacacbdaadcbddbdbcaadddbccaaddbaaabcdcdddbdbbbbdcbbaacabdaaaccbaabbadddcdbcacadbcddaaaadadbcbdcbddacdacbcdbdadddaaababccdababaaadbcbbabbbbddddacdbddbdbcacdddddaabdaacdaacacddbbadccdacabccdadabddadbbdaaaacacaaccabdddcbcddcacbbddccdbdababdbabbccaacaadaaccbbbbddbccddbaaaabdcabdcddcbbbacccbdabcdbcadbdcdcddcaabaabcdabcdccadcddbbbddbdacdaaabddccbdabccdcdabadaddbdccaaacaadabbabbadcdacdabbaddacdccaaabbcaabadbbccbccddbbddcabccabaddabccaddcbcbabbdbccddbddcbadbcddbccacaddcbbddcdbbcabdadbacccdbaadcccddcdcbbbcdbbacdcdcbaabddddcbaaacddddbadcbdbbbdcabdaabddaababbaabcddbaddbbcdbbcddddcbbbacbbabbcaccaadcddbcdcbbacaadcaaacadddcdbdbbbbaaccdabcdabbabccbbdbcccdbbdccbcccddadababbbacadcdcbdadcbbbddaadacabddacdababccbabdadbbcbcdaddbdcacaccadacbbdbbbaadddacacddccacdbbaabcccddcbbbcabdcadcaccdccccccddbaddabacbabcddcbadacbbdacbadabbdcbcaaccdbbbdddbadadcadaadbabdddbbdbabadbcbbaadaddaacdadcdcabaabadaddacbaabaccbdddbdcabcddbabbacbbdadbddbbaaacddbdcbccdcdcaacdcdbcdbaccdddcbabcbdbcaccacdacaabcadccdcbacddabbdcccbaddddcabccdabcdcabcadcaadabdcaadaadcababcbacaaaadbcbdadbcaaadccddddbcabdacabbdaddbbbbdbcdadccbdadddabcbcdcbaddaaabbcacbcbdbcacbdcbaabcacabdcccaabdbabcdacbaacacababbdcbadbdbcbdaccccbbcbdbbdbdbbbaaadbcbccdbaddccaabddbcbbdbaddabcbcdaadcbadbcaccbbcccadbababadacddbdcddadaddacaabbcbbaadcabdbaddbabacdbbccadcdcabdbdaaabacbdbacdcaddacacacbcbdcbcbdbcdbbbdabdbabdddbccdacbbbdbdbbdabaadabbadcdabdcaabdcbacdcbcdbdbdabbaadcaaadbdaadbaccdbbcdcdddadadadcbaadccdcccbcacdccdbbcdcaabcbdddadccbbacdaaaccccdcdcaadcacabaaadbbdadaddaccadaaaaddbadacccabaddcabcdccccacadccacaaddaabcdbadbddddabbdcaccdbbadcdbcbbdadbdacdccaaaaaadbbccacbacbbbbdcaccabadadaacbacdbaadcadcacaddbdccaabaaadddcdbadbbabbdbabbdbcabbacdccaccabcdcdddbbbcccddddacccabbbbaacccadcbaacabbcccddbaabdddbbdbaccbbdddbbdcbcccddabbbbcdbcddcddbbabdcacdacadaacbaaccddbdaaacbbdababdaaaaaaacabbdbadccabaacddaacbcabbacbaadcabcdccdccbbacacabdacdbdcdbaaabdadbbddaabdbcccbddaccbccacccadcacacbdcabddadadcccadbcdabadbaaaddddacbddadaabadddddbbbbdbbbcacbbabacbcbadbadcdabbabbdccdcdadadbdaaadbbdaaacabbcabadbadbbddbaaccddcccddabbaccadadaabadacddbdcabbdaacdbdbcabcccadcddabdcbcaaacdbaabccadccccdcdaddaccbdbcdabbcdadabbcbdaacddbaacdacbcccbdbdbbaccabaccbccbdddcbbdcbdbcdaabbbcabaadaabcbbcadcdccbddbbbabcaaddabaaadbdcbcdaaddbccabbccabbbbbcdddaabbabadabdccbadacaccacbddcdaaccacdadccacdbcddcabcbadaccaacccadbbcaacbdcccbcaadaaccabbdcbadbdcaadabcccccdadcddcadccadadabddbcddbacabaaabdddacdbbcaccddaadadbbbcbbccabcdbdccaadbcddacbaaccbbaadacbdadadbabbdadbcbbdaadabbbddadcbbacdbabababdbcbbabcaacbcadacdddcaccadbdcadabbcbdabcddbcdcbacdbbbbbccdcbdaaacaacabbcdcbdbcbabbcbbaacddbcaababacdbabacadddcabcdbcababbaddaabbdaaadccaddbdddddabdcacbddabdcaadaadccdcdacadbaaccabccabcdadcdabaacaaaddbcabcdaaccadaadcdadadbdcbaaddbdbbbbddaabdbcccbcbaacbbcbbacddccaddbdbbdbbcdccccadddbcaaddacaacccbcdbacdbdcacbbcbcdddbabdbbabbdccbbdcababcacddabcdaadadbadbcbcaaaabbddbacbabaaddccdbcaddadbdccddabbadcbbdaddbbaadaababcaddabaccdacaaadccadcdbccbaabbccdabcbabbdabdbcccbdaacccaabdbabcbbaacaccbcaacbcadddccabcabcbddbcbdbccddcdcadabbaccbabadcbbcaabadadcbbccdcddadbcccbabbccabadcadabbadbdcbacaadabaaddbccadadcddddcbdccdbbbbcaddcacdcdbddabbadcdcddaccadacbbcbdcbabddacdbdccacbadcdbaddbbdababdcbbccadbcccaadcdaccddcacbcbdbdcdcababbabdbdcbbbacdbcdbaacccdbabcacdbacdbbacdcdabdddabbabdbadacbadbaacbdccccaacccdcbcddccadcaaddabdbbcadcadaadbadcccabcddccaaccccacccadadabaaabacdbabadcaabbabdcbbdccacdadcaadacdbdbaabdccdbbaaccabcdddbacdcbadaccbcabbcbcdcacddacaacdbdcaababadcdbbddccdcdbbcbadaadbaadbbccacbdaaaadaabcaaaaadcabcbcddbaddbdcdddcbabaacadbabdcdddbaddcddbbbdadacbadcbadcdddbbbbddcbcddbbdcccbbbdaadaacadbacbdcababddbdcaccadbbadbcbbcbcdbddadcabcdcdaaccbaccaccbdacdbcdbbcbaabbdacbacbbbbbdbadcdbcdabbdcdcdcdddacdbaccdbbdaadddcdaccdabdbaaabcdddbddbbddcbcadbbaadcbbbdcaadadbadcbbccbbcbbdbcdddbdadccbcbababacbbadbdcbbbccdaddccaacdbdbbdacdaddbdcddcdcdbbcbadddadadcddbccabbddcbaaaacbbacbabaaacaaabbdcbcdbbbaaaacbcdbccadcbdbbcccdbdaabcdbaacdcbadcbdbbdcbdbdaddacbddcadccccbaabbdbdaccddcbdcdcaadbacaaacabadbcbbcabcddaddabadbaadaacdbcbcdddabbbdcddaaadabcccabbdcdcaabdbaadbcdbabbbdcadccbbcadbaaadcccccaacbbddaaccdcaadddccdbbbabbcabdabaaaabdbbdaaacbddbadbacbdaccdcbbdbbbdbacaddcabcbcbddddbcbadbdbadccbadabcabaccaddbaacabdaabbddacccbdacaabbdabacbcbacabddbbdbccacdabaacdbccbccddcdcaabacdabacbccbdcacbbdddcdddbdbdbcdbdbdcdcabbccaadbbacccdbdbcaccdccdccbabbbcccbbaadacdddadccaaddcdcaccdcbaabcadcadaabdbbcadacdbddadbbddadddcbdbbbcdcaaddbcbcabbccddcdabacadaaadcacbcaababbbbcbcddbddcacaadcbcadbcaaadadbadccccabbcddcdacacabbbbbcbbddcbbddcacacbdcbcdccababbdaabacabdbcdaaadaadcbaaccbccccbdacababbdccccbcccdbaacaacdddbccbbaacbdabbcbacdbcaddddaacbadcdaaacdcbbcdbdbaaadcacddacccbcdcaccdaccbabdccaacddabadcdcdaaddaabcadaacdbaadbbcaaccabbccdcdccdbbcacabaaccccddbbababdabcaccbcacccabaacadbdabbcbbdccdcbbcabacabaacddaadbcabcaabbdcbdcbdbcccbbabbacbdcacbaccabbcccbdbabdbbbadcbcdddbbdbcbcaccddadddadbabbbddabdcbbccdadacddbdaabcabdabcadcaabccacbddaabdcdccabbcaccacbbadacabbaadcaaccbbacbbddcccbdcbabaaddbaddbcbcdadbcdcddacbcadbccbbbbbabaccaabbaadbcddccdbcccbddcbbdbbbdcabddcdbbccadbcbccacdcbdccaccaacdbdaadcaddbbdbaccdddcaadddabbdbbdacdaaabddcbaadbdabaddacbdadacbabdaadcbcaadadddbcaabcadbcabdcadbdcddbaadbbddaccacacdadbbddacbbbddaccdccaddccbdcdacdccbcdadabdddacccbcdcccddbcdbdcbdcddccadbacdbacdbbacdbadcbcaabccabbddaaaddabbbbcabbccaccddcdddccdcdddbcbbcabddcdaadcddbddcaacccdadbaccaaadbaccadacbcdcccdabacbbbcabbdbcacdaacbbacaddcbdcbbbaadcdaaabcadcbccadbbaaaacbcdbbacabdddbabdaccadabaddcdabccaadcaacaddbbacaabcbcbbbdcdbdacabcbacdddbbddddaacadbdacdbadcdacacaddbbcdccbaddacbcdabccbdbbadcccacabaadcddbcddcadacaccaaadcaababcbaabdbbdcdbcbccbcdcabcccacbacdcabdbaaccbaabbbcbbbdbcadbdadcdcbdbddaadddaaccbddccabacdacaccaadcdabbaaaadbdcbbbaacadbabbdcaccbbabcbccaaabaabbaccdabdcbacdbbcbdbbdcdcadccaaadddbadcababcdccbbcdbcaaaabddccddcbcdcbbbaacdbabbabddbbdccaabadadabdaaabccbbbcdcbcaabccdccdcdadbbdcacdccbbaadbaacdaccbcbacaababacaccacbbcadacdddadcbadaaabbaadcaddbcadcbcdcaddcadacbbcbdbdbddbacbcdbbaacbbdabccaaccacabaaccadbcdcdcbbbdbccbbbdbbadcddcabbadaadddbcabbadcdaaacccacaaddbadadbbabdcddcbadaddbdabbaccaaacccaaadcadbbbabcccbdcabcdcccbbcddaddaaaacdbdbdbdccacacbadaadaddcdcbbcbdaadccacadbcbdadcacbccaaccdcacbcbbcbcadbccddbcbcbcbcdaccccabbabccaccdcbcdbacbdaccdbaacadaabaabcacbadadddaddadcbdabdaaadacbdbacbdaadbdadccdbccbaacdababbbcbaddcccbbdccdccbbdacadccbbabcbdcbccaacdaddbaddcaacdbcddcddacbbbdccaabccaabbdaddcdddbadcdcdabddcaaacadccddacaadaacbbacdcdaccbbccacdacdcabadbcdcabbcdaddbbadcddbabbbcdbccdddcddddacacddacdbcdcbbddadcccdacdbcbdbabcbdcbadddbdadbabbdcccccacaaaadcaddaacacccaaadcccccccaabccdcddadacbaddcabdaaadadcacabdddbcbddbbbcccccadbaacbaccacdaabcaaccccbbadccbdbbbadacbacbabaabdbbbcabccdbadbadbbddccbacbbbacbbbbaadaabbdbabdbabbbcdcdaacabddcaabacddbaabbbdbdacbdaddcacbcdbadbbabaaaadbabadcbbcbdbdcdcbdbcdccddcadabdacdbbcadbbaccbbbbbbaadbcbabbacdcbcdcdbdbdcbcadbdbbccccddbbaabcbdccdcdbcabdaabcdbdbbdbaddbacbdcadadacdbcbcaaaddcadaddccdbbbdccbdabaaadaadbdacbbadabaccaadbdbcabaacccbdcbddcbccabdccccadacdbdadaccdcadbadbbdaabdccbacbbbcdabaccadddbbaabbcbcddbabacdbdadddbbdaddbcdbbabcbcdbacddaacaaacdbccbaabadccaddacbaaaadcbbcaaaccdacaaddbcbcdbdcaaddccdbcccbdccdcdcadcaddddbabbabcbbcbddaaadabdbbddcbabbddcddaddccbbaaaacbdaaaaaaccbdbbbccaacbcabaacdaacabaddaaabadabacabcddbbadbaaacddbacddcdacbdcbabcddbcbdadddaaabaaaddaaabccdbadbbbdaacaabdcccbdbcbadaaaadbcadbbbbddacbdccccccabcbcbdabaccbacdcaabacabbbcacaccccdccdbcbccdcaaacaccdaadcadaacddacbdbcdccddcddddabbbcdacbabcbaabccddbbadcbdaddcbabbbadcbccdbdbbdbdabcdbacacaaddbdacdcadddbdcdadabccccbbabaaabdcddbccbaadbbdabdbbaadbbccdcbbaacbdcccdcbaaccbbcababbcbddaabcbaabcabbbcaddcabcbdcdadadcddddaaaaababbabbcadbdbdccacbdcddabaddadbbaddbcdbabcddbcaabbcabaccaddcdacbccdaaaddacbadcdaddddcbdbccadacbbadcbbcbbdbaaadabaaccbdabbcbccadcdaacbcdcabadabdaabdcdcbdcbbbacbabbcbddacdacdccadbdacbbbcabcabdccddadbccdbddddddccaddcbacaaabcbddccbabcacaccddbcbdacadabdaacdcabcbddbaabadabbddcbcbccddbcdcdbddaddadcddcadcbadddcacccabcaddddbdaadbabaacccabcbabdacbbbaaabbacaabbccccaacdaddccadbbccdbaaabccdcdbccdcddcdacbcaacccdddddbccaaadbccdccccbabacbacabadacbdddbdabcaacabaddbccccdaabdbbacbdaacacdcaddcccbbbaadcddccbdaaddaabdaaccadacddcacdcacbabbcabbacdaddaddcdbbbcccabaacdddbdcabccdabbcddcbadabdadccabccbdbcbbbcdddacadababbdbabbaabccbacdacaaacbacdcdddcbcabcaccbbdaccbcaddaadccacddccabaacabcbdbdbcabddbdbdcdbcdcddcdaacacccdcbbabbadbadccabdccacdaccdcbadcadcbaabcdcacbccaacaacdaddcbadadacaadadadddbdbccbdcddcdcbbcbadbddbadbaabbcddbcbadcbcbaadbdccbcddbbabaacdddcbbdbcccdabbbadacaabccbbddbcdacbcadcdcadccdbbccaccddbadbbcbaacbadbaaccbaaadcabbacbdcaccdabbdcabcabdddcdadabbbcaadabcccccaddbbaadababccabbbccdbdaabddaaddcdbaabdabcccccccddcddbaadccdbcaccacbdbddddbcccbcdababaacbcaaaaabaddbcbcdddbadbabbcaadabdbcdcadccacabdbcccbbaacddacbdaddcdabcabccbdabddbbcadbccaabbabaaccadbabbcaacbaacdbaacdcddcbbacbcaaaabbccdcdccdbdadbbcdcbaabaaadadabddbdbbcbdacdadbcbbcacabdcabaabbbcddcbabcbdabdaabadaabbbabdacccdcadbbbbbdcbcdcdcaabbdaacdacacdbadabcacbdadacdddccdbabadbaccdacabacaacbdababcaabaabcbdddadaadbdabcdbbaaccabcbbcdddcaaaadbcabbbcabbbbcabdcaddbbbdcbccbcdcbcaacaabdcdadbddbbdbddbcabcabcdcabbdbacdadbcbdcddddcaaaacddcbdbccaaaacbcccddcbdbddcbbcdddcbabacabdbbcdbcaaadaccbcddbcbababbcdccbbcbddcabaadaaccaccdabababddacbccbcadccbcdbddbbbbaaaacddaabdbcbbbcdbbacbcdacabdcaacbdccccdadadcccddabacdaddadcaabdbbccbacccacdbdcdaacabacddacacbccadcdbdcbdacbaaabbcaaabaadaccadbbdabadbbdadddbbcaaaadcdaddabaddbccaddadacddadbabcbbbacaccdcbcdababbccabdacccabdbacbaddcabaccadbcbabcacddaaaaadbccaadcbdcbcdcbbadbdbcbdbbbbbcdbbabcbabcbdaabddadacdcbacdadccdcacdcdbcabaddddaaaaaddbddcaccdadbaddddaddadbdbbcdbbdbbcdbbabaacbdaacaccabcbcddbbbaacbbaddcdbddcaccbbdacabcacccddccacddcacdacadbdbaaaabcaccabbdbaaacaadcccdcdabacbcdccadbdbbddaadabbaccbcadbddabdddbaddadcabbcdbbbbbddbacaaddacbabacadcabcdaaaacdddbacadcbdcdaabdcaccbbacabaaabcaacdcddbacdbdddbbbdabacdbaaaaccbadbaacadcacbcbabdbddcbccddbcbabcccdccbddbcdbacaaaaaadabcadcddbaaaadddddcabbabccbcbbddaddcacdcbadcddaccbbdbbbbcaadbcdccacadbbaacdbcdbbddcdabcdacbcaabadaadadcabcdddbcbddaabddcddcabdacbabdcbcbcabacacddccdaabbcddacabdbddddacdcccbabdccdaddbdcabcddaddcbdcaadccaacbddcccdbdccbddbaadadbbddbcbcaabdcbccbcdaabdbbaccdddaaccaaaadacddbaabcbddcddbadaabcddacaadbdccbacbcbaddacccacdccbbbbddabccabbccdccbaccdabcbdacddabcbcabaddcddccdabdbdcbaddcaacbdcbbbdbadbdbcdaaaddcdabccbcbbacbbadaacbbbdbdcccabaaaaacbbccbcdbcbdcbbcdddccabdbbdddcadbdbbddaadbabddaabbcbbbcbbbbccaababbabaadcbdaaadcdbdbcbdbcaadacabdbadadccbdbcacaacdccccacacaabaddbbaddacbcccacadaacaadabcbababbbaadcbdddadabadcbcdcdddabdadbcbabbdbaccbaccdaadaccbbdbacbabaacddbcdddbdacddcccdabdabacabcbcaadccddcadbacbbddcbbddabdcdbbbbdbdaadadaacdadadccddcdbbabdcdbabcbadaabaddcaddabbaabdadababdaacddcbababdadddccccaaddbcdbaacaaaacababdaacdbdccadabbbbabadbccdaabbcdbccbaabccabccbaacaddccddadcdcdcdadabdbadccaaddcbaababcbdddcbadadacbdadbdbdbcdbddcddacbabbbbbdcbadadacdddbbaddcccadddbabaddddcddabaddcddcdbcaaccaccdbcdaddaaaadacddcddcbddcddcdccacdccbdbbdddccaacdbdacdadcddbabdccabbbbdbcddcdddbdcadbbacaacddcbdcaabbcccbdbdccacccadabbbacdaacccadbaddccabddaacdddcaaacdddaddcaacaacdaadbdddbacabccbbdccbbbcbbcdaccbdbaadcddcadcacaadbbdbcadaccdccdcbadaacbaccdcbdabdbcdaccbdacbdddbcbadadacbbacccddcaccbddcccaaccaaabdcbabcdacbdcadadcbcaaccdcddbddbbaddcddddaadcddbcacbddabacabbcabcbccdbcaacccdcadaaacabbddabcbbadaddbbbcaddadaccaabcaddcabbdcbccbbbcbbdacbbdabacbaacbacbcdacbbbadcbdbdaaadbcdbbbbcabddbaacbadaaadcdddddcccdbbdcacadcddbacbcabcdcacdcbacccbddcbccbdbcadcbcbcacadaababbbabbbbadcdadcdacdabcadadaacdaadaacdcbdbbddcacccadbaadaabdadadccbdaacbacbbdabbaaddaabcbaacdcccaccbcdadbadcdacabddbbcaabaabcdadddcaccddbcbdbccddaaabacbccbbaadbcaddbbcdcdadcdcdaccbddabbcdccdddaccaaddacbcbcbdccadcdbcbdadacabbbacacaacdcacbbcbcaadbcabccdbdbaddcdabdddcbbaabddcabbaadabadcadabacbaacdabbbcabdcaaaadbbaddabbbbccacdabccaaddadadbdbcbacdbaaabaaabacaaadabbccdcadaccdadcadcdccaabacdddabdacabcababaabcdbcdccabdbdbbcdcabbccaccadddabbdabbbcccdcdbcbcdcaaaabcaccaadbabbabbdbadcaacbcabdcdbbacdbabaacabdcccddcddbacbcacabbcadabdadbbccccbadadbadbccbcabddddbbcabacaadcacdbbbcccbaaadaabbdbbdbaabadaccddcacdcccbaaccddcbbcbbaccbbcdcaabbbbadccdaabbbdcacdddcdacdcadacbdabccdcbaccadccbaadacaadadbbbbabcdaddbbbcacaccabadaddcbbcdbadabbbbbadcdbbdaacbcbcdbaaaadbdbbabddbccdbbccaddaacaadbbbcddbcadbcbdccaadddabcabcdcbcbddaaadadbaaacdacbddbaaaaaddaabdbcccabcacdcbaddcccacdcacbdaabbadacccdaadddabaddcccbddbbbabadcdabcabababddbacdbbadadddcdacabcbbacdbcbcbdcddbdcdbcbddbacdadbccdcbcbdcdaabbccccbacacacaaddbacbcadabddcaccadbbcaaaaaabccdccabddcabcbbccbaacddddbbccaccadaabbccacdacbbcacbbcdcababdbacaadabcacdccadacadabcabdcadacbdbccdcbbdaccacadcacacdabcdaddbbcdaaabbdbadcabdbadbaabccddbbdabddcbcbcccdddcbbcacdbbdcdaadacbdbabbacbccbbcaacdcccdcbabdcccdaddaddaddccdaaccabdadccbcbdbcaddaddbadccaacccbbcdccbcbcccabcbbddbbcbcadadccabaacddbaacbbbabddccccaaddbabbddddcaacabbbabdcaacaacaddaadbddbddbaacbbbbbbbbcdadadcbadacabadcddabaddabccdcbcacbabcabaadcdddbabdcadadcbcbddacbdaadbdadbdbccaacbbdccdbdbdbdaabccbbccdacbcdacbdbcbbabacadbcdabddbbacadcddbbccadaaabcbcddaddacbabcdcdaabcbcabbadadaadabdcbdbadbbaaadcaaddbaddcacdcdddbcbcdbdcbcbbdcbbbadbccddaaadcbadbcbdaacaddbcdbcbdababcbcccddaabddabbbdcaabddddcdbdabcdaabcbccaccaaaccbcdaddccbddaddbcdabacabbdaccacdaacbcbdabbdacabdaaddccadcbbaadbbdaadacdaaacababacbdacaaabaddaaddddbacbdbddbdccacccddaccbcbddaaacbdbbacddcabadaaabababaaabcccbcbdaadbabdaddcabcdcabddcbaabdaddbccdbdcaaaccdbcbbabdbacbdaccccdbcddabdbccdccdcdbccdbccccabbdaacdaddacdcadcbadbbcbbacbbaccaaabbbbbdcdddbbcabddaccbcddddccbcdbbccaabbacdcaaaadbacbbadabccbbcdcbdcbbbcacaccbacdbbabcaaccbbaddcacacdcbcbcabaccdcdbddacaddcbcbccbdadbacaaccbdaccdcbaabadcddabadadacdcacdccdcaddcbcadabadcbaddcbcacdbcabddddadaacbdacbcbbdadcaaacdbcbadbcddbaadcdbaccbbcabdcccaaccdddaaddcbdcddccddcbbddcbbdbbbaacdaadbcccbbccdaabdaacdadcbdadbbcbdadbacdbadcacbcaddadccdbabdcbbccadbaacbaddadbcadadababdddbdbabddcababbbbcaaadaabaaaccaadadcddcdabcbabaabbdcddbbbaccbcbdbaccaacdaababcbadbbcabcbccbbcacbaddcdcbdcddadabddcacdcddaacbbaddabcbaabcabaaddabdbbbcabcdcdcdadddadabcaccaddcbcccbbabdbacaccddbbbcbbaadabbcabcdacadccaabccbbdbcdbcdadcbcbbcaaacddcdcadbcddbcabcdadbbdcdcbdadcacbddbdddcddcbabbccbacbcbdcdbdbcbaccbadbcbbbadacacdaabbdbaaacccbbddacbbbaabacdbcbcaadcacbadaacbaacaabdbcccbbbbdbacbbbbaaaddacaccaddbdaabcccbbbcbcbbaddadbdbbcbdacaddbbacabdccacbddcbdabdadabbdbdcaddcbaabbbdcbbbdaabbdddbdcdcaaadbdcbbcbbabbdbcbdcdaabcdadcacdbdddabadaddadddacbdcbdadaaccddddddbbddccdbcacaacdccbdbbaaabdcddbcacabbccccdbbcbdbbaaaddaaadcadacabddcbbcaadcbcdcdcaaabacdcdacbdacaacabbdcbbddbacacbcbaabdabcccadbadbabadacabdaaadddacbbcbdbcaaabdbbdbbadacbcbbdadcadbccdccaaaadaadaadadcdcaacbcdbcbadacdbbdabdbccabaaacadbdcadabbdcbdbdcbdaddaadaddcdaaccacbbdbbddcdcadbddcdcdcabbddbdddadbcdcbcbbbcbcbbdcacbdabcbcccddbadadacaacdaabbcacbacaacbbddbadbbdaaadccccdacbaddcbacdbdbabdaaaadabbbccddbacabcccdddadadcbaaababcdccaaadcddbbbbdcacbccacbddaacbabbaadcacbabaadacbcaabbacacddbdacdadcaccadbbccacbbacddaddcddcadbcadcabbbbcdccccbaacbbaabbacbdcdcbdbcabbddbcddddcaaddacaabacbcbcbabdaaadbbbaccaccbcabacdadbccbdbdabcabcbaddcdbcacbccbcbcbdcccdbddbdabacddbabccbdabcbccdaaddbddcddcbcdbbcaaccbdacccaacadddcddbdcdcacdddbcaabcaccdcababcabaaaccbcacacbdbabacacadbddabdbbdadcccbaccaaccabadbacbcbdbdccccbcccccccadbdddadaccccabcaabdcdcaadadbadccaabcaddabddbaddadaaaccccbddbacaadcbadcdddbbdbabdcabbbdaaddcabdddbdbcdbbaadbcdcdaccbaabdbbabbdbdbdbcdbaabcbbacaabbcadacdabbcacdcccdccbabbddddabcdcbccbcddbdbbbcbccdcddcababaccccddacdbcdbbcccbbddcccbcbbbdaddcabcaaaacbdaabcbadacdcccaaaabacaacbaabbccddbddaccbaadccabbddcbcdaaadcabaaccccbcbabaadcadbbcbccdddbdbdbbcdcdbcdbacddddabccadbdabdbdcbccdacdbccacabdbbccbbddbbdddcabcddbbdacddbbbaaacdaadbacdaaadadcacccdaddcdcaadbbaacdbcbdbcbcadcddcbaadddadbbdddcabcbbcbbbbcacdadbdbabbabdadccbdaadcccabbabbbcaabbcdadbbddcddcbadacdacdcaacbdcdbaddbccacbbbabccdcbbaaabbbbaadcabaccbdcdcdddabbaabbbdaaacddbbcdddcbdabaddcbdbcddddbbbdacbbadccbcbcbbabaaccdbbbadbbdbaaaccccbdaccaacbdccdcadabbadcdccaccaabcbacabacbaadcaaaccdacdcbddcbbbbdbbcbaaaaacbbbacdaddbadbadbdcabbdcaaaddbcdcdacdbcbddccaabbcdbdcbcbcdaabadccadaadcddbddcbaccabdddbacdcbadbadccddbdacbadbaacdcccdddcadcbbacbbbcaaddaacbaacbbccdabcbacddadccdadabcacadbacbdadbcacbababdabbcdaaabdccdcadcaacabdddbddabdccbabdccaacbcaabadaccadadbcbdbacacbcacadcdacddbccbdbdaccbcdbaaacdabdabacdcbdacdabbcdbdacbaabaaadbcabbbcaacbbddcdcaabcbdabdaccddbdbabdcbbdbcbaacbbcbdbabcccadbacdbbccddccabcacbcacadabbcacbadaacbddcbbbccbccdbccbbcbbddbccadadbbacdddddabcdddbaaaacdddbabbdcdaaabbbaccddcacabbbbadbdbddbabaacabbcdbbbbdbbdcbbacbabbdcbabccccadccabdcddaacacdbabcbdadbdcabcabdbcacadabdacbdadcdadbdddbaaabdaccbabbdbababdaabdbababdbdbdadbbaabdbcdaadbadbcdbabbacabbcbaccdbccaacbacbbbadbdcdaaabbcadbabcbcddcbacdbaaabdddcacddaddbaacccbbdbbaadcdddcbcdbaababbcccdabccadbbabdaccdabdbddbaadadcacbadcbccaabdabcacdacabdacbadcadddbccbcdadcacddaaccabbbdadcdbdbdadcbadccbccbdacdabdccbacbaabbbdbdababbcbcdbdcbcdcacdcabdbcccadaacabcddddccdccccaddadababbdcddbadbccdccbbabccaabcacbbccbbacdccbcacbbaadabbdbbdabdcbccacbbaadcdabccdbbcdcdddbdcaadcbdbccaccccbdcaddcaadcccabbdaacdabcdabbcaadcccdcdbbdcbdcabacddadbabcacdcadbacbbcaabbaabddaddbbdccdddcbddbcadddbbbaadadcbcabbcaadbbbdacbbcaaaabcadbbcaabbbabdabddcccccdbbcccaccdbbbdbdcabcbcbbbbbcdccdcdbabdcdcdbbbdcdbcbdbdbcdbcaccdababcabbaaaccbddbadbdcbadacbabbbdadcdbdcdddbdbdbbabdabbbdcbbccbacaabdacccddbdcabbaccbbdcbbaddcbbccdbdadaaaddbbabacbdacbcdabcacadbabaadbcbcbadaaabcbdacbbdaddbacacbdaabdaacbcdaadbadaddadbdddbcbbbbdabdbdbaadddacabcccccabbcbaaadabddadbdccbdabcbdcddddcadabbccdabbaccbbaaddcdabcaaaadaadddcbbcbbdacadadbdcddbdcaaccacbbabdbbcacdaadacdbddccbaccaccabdbadccbbdaaadbbddaadcbdccaacdacbccacbdabcdbbaadbaddccdadadaaccadabdcdbbcdaaabdcadaadbcbaaaccaadadbabbbbddaaccbbcbabbdbcdddcaadcadbcccbbacdadabbdcdacbcbbcadcacadacbccdcdcacabadcaddcbacccbdbcadaccbbaccddabccdbdacdbaabbcdadcbaacababccdabbaaaccccdbdcdabaccbcccdadaccadbccddacaaabbddcbccddacaaabdccacbbbdccadcaaadcbccaaaadaacaacddcbcbccdccaaddabadacdcdacbabababaaccddcccdddbbdcdbaaddacadbbdabbbabdbdadacbddbcdbdbcdddacbaddddcbbcddbcaddccddababdbdbbaaabbccaacaddcbadabcdccaccbbabcaadddadccbacadacddbdabcddbbaddccacdadcbccacddaabaacaadabbabbbbbaaacdcdcccabccadbdaddaadadcbdcddaddaaaccbddcbbbdacccadbdaadccccaabaacbbaccbaddaabaccbaaacadacddbcdbacddacaaaddccaddcabacbacbcdacddbacdaccaddadcdaadadacbaacadccddbcaadddbcacdcddababdbcdcdabdbcbaacbdddbdaaccdbadcbcadbcadbcaaabcdbcddbaabbdcabcdddccbdadbcadaacaabaccabbcbccacadcabaccadcaadbbbbadbccdcadadabadcbacccdaccbccacababbdcbbbbadadbdddabddbbbacbcdaaccdbcadccaccbbcdbcbdbbbbabbbcdbbdcbcabdcdccbbcccaadcbbdcadbcdadddcbabbdbcacabdabadccaabbcdcaddabbbbcaddaaacabddbbcaabaaaabbaadcabdcddaabcaadbbadabadadaacdaacccbdccccdcaaaacbbbcdacdbbccdabcbdcbacdcdcadabdddadadcabbbadbcabbbcaabababaccdcaadaadaadaddacadcdabbadadcadbdddcabdcdaaccbcadcadbdcccadcbdbcccccbbdcdaabdbdaadacaacbbbcbadccddddcdcdddcddcaacdacabadadddadccadaabbdcbababdbaabaabdabadbabbdabbbcaccbbaddaadabddddcdcdcaaacaaadccacaaaccadaacaaddaadaacdcaddaaaddadbbbbdabbdddbddacbdbbbcccdcdcdbaadbadabacbcdabddbaabacaccaaacbcbaccdcaaadbdbcadaabaabbdddcbaadbbbcbcadcacadbaacbbbcbbbdcccbacaccbcbbcdddbcbddcdacbbdacdbadabdbdbabcdaacaaacdaaabcadcaadaccababcaacbaacdcdcbaccbaaadddacaacacababaadddbcdbbcabcccbbbdcbbcbaccdbbbddbbbbbdabdcbadbbbcadbabcaccdbacbcdacacdacbacabbaababdbcdbcaccccbdbbcbdddcacbaccbddbddbddcddcdacabdcabaacabcaacdcdaccadcaaadbabcacbdabbbcdbabadcdbaabacbcbaccdcacababbaadadbadcaddbccddbdaaddcdbcdacaccdcbdcbccaabccacabbbdcbcbcbabdcacbdbbbbbbbabdddabbdbdcacbccdcdcaaddaabaabbcaddaabbaaccacabcadadcabdaaacdabbcaadbcbcdadacccdabacaabcaadaadaadbdbcbddccbadbabcdcbbadbbdccdbccbdaaaddaacdbcbbcbcadabbcacaacdcacbaaaabdacccccacdcbbcccbddaadadcdddabcbaddabacdbaccbbabadacacddccdbcdccdbbaacccdcadbbcbdbcbdacdacddbaccccbcbaddaaccadabadbcbbdccbdaaaaddbdaacabdbbbbcccbaddbadbbabcdacbaacbdcaacabcbccdadbdddbacdbdbcbdaddaadddcdbabbcccccbcabacbcabcdbaaabcadabadcccbbabcbcdcbbdbbbcacadababdbaccdbcacbbbdcaadcabcbbaacacbadbdcbdcaaabbddbacacdbbacaddabddbbaddbcbbacabdcacaabacdcabadadbcdbadabddadcadaddabdaccaacbcbbabdadccbccbbbbdcbcaacaaccacccadbcddbddabdcbdbbbbcccbccaabcaabbadbaaddcacbdadbdaccabaaabbbddaaddbcbbdababadbccbdbdcbcbaddbabdbbdcaccbdacacdbcadcdcdddddacdddbbbbcdbacaadbbbacccaaabbdbbaadaaccacaacadccbbaadaaadddcbbaaadcddddddacddddbbbdcdbddddabddcdabcdadabaabbabcbbacdaacabcbbaddaaacbddcabbcbbdbaacabdbcacdcbaddbbddcdadacdabcbbcdaabcccbcaaddcabadcbacdccadbbccdcccdbaacddbcaddbadbababdabbcbcabaccacbbdacdbcabcbabaaaddddcaaccbcbcccdcdcccddbbbbcbdbcddbcbdcccdcdccbcacbcdbbdbdbaddbbcdccbddccbabdbbdbdbaabaacabcbbccdcadaddccaadabdcbbadabaddcbccdcdcbcacddbcdddcbccacccabaabdcbabcabacbaacdbdaadaababbbbabcaaaaabadbccddcaccaccdddbaabcdbaccadcbadadadbaadaddacadddddaacabadcdbddaacaaabbacccbcdddbdcabdbdcddacdddcdcadddddbacdbadccbdacabdbaccbcdacacbbccdbcddaaacdcabdccdacacdbacbddaadbcdcdbbbdaabababcaadcbadaaddcacbacbcbdcbadabbacbdacbbcddadbbdadacbabbddacbddbcdbbbcdddcdadcdbadbcaccbbcdcabdadcacbddcddaaadaaaccdacabbbbbcccbbacadbabcbdacbadddcaccdddbcdccabbbcbbadaababbcbbccbdbddbdbcabddacabbdbabdaccccdccdaddcdaaadabccbdcdccdbacddbdcbcaacadcdcabcaabcdbbabccabcbaacabaabccaabddbbbdccbbaabbacdbcdbabddcabddbcacccdabdadbddcbcbcbbccaabadbddbbddabbdaacbabbbaacadcaaacdabbbcbcbbabbdbcaaaddacaccacdbacacbacacccbbdddbbdbccaddcabccbdbaddbaccddcdcdddbbcbcdbccadbcbcacabccbbcbcdbcbccbbacbccbddcbdbcddcdabcdccdbcccbddcdabdcccdadadbddadddadaccdbbacdccdbadaadccdcdacddaddabcddcaadcdcabaaadbcabbccccccabcdaabaadcbdbacabcabbdbbbcdadddbbddddacaabdcddccbbddbdaddbdacaadaccdaabdaaccbdbacaabbadadcdadacbaddcadadadaddddbcdabddcacaddaddadddbdcaabddddcdababcdadacdbcdabdbdddaacbacdbbdcabcbababcbababbcdcbdacbcbabbabcdcabcccddcdccbddbcacdddadadcbbcbbaaadbaaaaaadcbabdbcddacbdadbaacbcccbdbcbaacddbcdadacabbcdbbddbcccabbadccaaaabaaddccabacbadaadddcdbddaacabdbbdbabdcbdbbbacdbaabcdddadcdcdbdbdddaadcdadcbaddccaddaabdbccccabdcadbdbdbbacabddcbcbdbaadaddacacabdaacaaadbbcaaaccdaaabbdcbbcaabccadaabbacdaabdaaacccdbcbbacabbdabcabbbcddaadcbdcdbccdabaabccaddcbddcadadcabccabdddccdccadbbdcacbbbadbbcbabcadddcadbaabcbcdddcbadabcbabbbdadcabbbbabddaaacdacdababababdcddbdaaadaccbacabacaaabacbcdaaddaadbadbcbcacbaccdabddcbaaabddcdcabccaaacdacdaabacbadcbadbcaaaabccacbdadabbdabaabddaaccbabbaaccadababbcabdddcbccbbabbadcddbaabaadbbddbcaaabbbddccdaddaaabdabcbdacddbdccbdbccbdaccacccadcaabacaccdbdbbbdaaabcddcbdccdabbddbbbacaabbccdddbddbcaadaacdccccbdddcbccbbdbcbddaacadbdcccabaadaabcbccaddcbbaaaadabdaabaabcabdcddbcbbabcbbaabbdbadbbdadbacddcbacaddcdbbbddcadcdbccbacaabcbbdbabbabdbbababbcdcdaabbbcdbabdabcdddcbccdddccdcbdcdddbaaababdaccacdcadaaccbdbdadbdcabadadaddccacabcaddcadbdaaddbddabbbddbdcacaaadacbabcdcbdaaaabacbadccbccaddbdcaacadddbacabbaacdcdbbabdadadbbbadcccdaaaaccaccdbbadcddbbcadcccdbdabdaadbbcaabcdbdcccbdbacbccaccccaaabddacdbaabaddaddccbbcaccdcdaaccbcbaaacddbdbaabcbcdbbabadcbcbabcaccbbcadadababcadbadcccbcddbccabccbbaccdabcabadddcbdddaaddbddaccbacbdcadacdabbbbdabcbacbcbbbcdcacccccbdaccdbdababbcdbbdbacbbdbacdcabdabbdadabacbcbdcbccdddbaabacbdcdadcaddaaabaadcdabdbcbbaccbcdacbcddbabaaaaccddddcdacacdaabbbaababcbaaabaacaddaaddbaaacacacabacadddddbcccbaacbbcbdbdbdddcabdbddddaddbbcbddaddcdadcccddbccdcabbdabcacccdacabcddacdacddbaaaadbdbaddcaaacbcbdabbaaaabcacbcacdbccdcdbcdacdcabbcccaccbcacadabcdcbdcacbabbadacabccdccdbbddbbdaccadaaaacaacdcaccaaabdbabbbabbbcbddcaadbbbbdbccdcabbbabdadbdbcaabcadcbdccbccbacdbbbccdaabccccdbbdbabcabbcbbbbddddddaacccdccbdcaacacccbabadccabccdaabbccadacdbadbcaccccbdbacabbabdccbacdabddbaadbaaddddaddcbbacbccbadabacdbdddacbbacdcbbabaaccdcccddabcbcaacdcaadbbdacbbacbbbcaddbccbbdcbadabdacccbbacadacdaccdacdbcdcbbcdadbbbbacccccbdabcccabbcabbadbadadaabcaddddbadacccabdbdcacbadbbbbbdcdadbdaadaacdacbcdbcaaaaacadbdcbcbddccadabcbdadccaacadadccbbaddbcaaaddcabbbcbccabddcbbadbdccdbdabadaaacbabdcacddabdbbaaddacbdbbadbcccacaadcddbdcadbdaccdbbbdbdacbcccaaaadcbccadcadbcaccbacacddbccdbcbbadadadbbaccaccbadcaaabccbcbdcbddcaccdaddaaacbaaddbdbbbabadbadacccccccaddbabddacabcddddbbcbdcdbaccbbcdcbbacbacdacabbddccdbabcbbacbaadbcbbdcaaacbddcbadcbaccaabcaacabcbbadccdbbcabbcbadcacaadaccddacddbbbcdbdcbccbbbaaacbcbdcabbdbdaaacbdbbabaabbabbaabcddacabbaadaddddbadacacbbcaacdbdacbbccbacdaadddccbdaabddbadabdbcacaaabdbabbdbddaddacdcacacdacbcbddbbdadcdacccacbdcbddbbccbabbdbbcacbdbaabaddbdcabaacadaabdadaabdacaadcdbddbbbbaaacbdbddacdcbdcccbbbcbdbcdccaadcddcdacccbddcabdaadaaaddadbdbdcacaabcbacccdcabaddcbcaaddcdabccabcdddddcdbbbabadadcccaccddbbaacbdcabdbccdbdbddbdbcdbbaaabcbaabadcbdbabccdcddcaaaaaacadcaabdaadcbdbbccbcaccbaccbcddaacbaaaacacdbaaddccddbdadacdcccacddddbadbccacbccdcdddaacccbcccadbccddaddadadaccbdaccdaddaabcdcdbbbbdcbdbbadcccdaddadbcbaccaaabddadccdbbddbbadddbbcabcddbaabacaddbdccaddaacdbbbaddbaacabcccbcbdadccdbccbdccacaccabdaabdbcbcacaccadadddbddacabadccdaacaaacbbcadbbdaaacbbcdcbbdbccadacabbcbaabaadaabadcbbcabdbcdccbcdaaacbdbdbcdccdbcdbcbadccbddaadcdcbcbbbddcdaccbbdbadadadabbadadbdbdbdabbcdbddbdbcbdcddddaabcabbcddddcaddabbacadcbbbcacaaadddccddbbbbbddcacddaadcbdcbadcbdcaabcbcbadaddbadbacbcccddbaacaabdadadacdbdaacbaddaaabaadbcbbaadaacddccbbbccbdacabababcbcadccccacdcbddaddababcaabbacaacaacdbdcbdbdbdcdccbdabaadabababdacbcbdbabbccaccbcddadbdccdcddaabcdcaaacccdbdcbabbbacbbaacabaaccddcccddbabdacacddcabccdddbddabcbccddaddbdccbabaaaadcdddbccadbbadcdabddcbbbabdbcdadbddbaddaccdcdacddbdbdaccbdcbabcccddcdcbccbccabcaabcdddcdbdadcbaadaabbaddabaaddbcaadadcaaccccdcacddacacaccddacbcbdbccaccadccbdbbdbacdcbddadbadbcdcaaabdbbadbccabbdabdddccdcbcccabdadacdacaadbcbccdccacbdddcacccadaadcaaccdbdcbddbbdcadbdcacbcdbbdcdaadbccacdcadcbdbbdabacdccabbbddccdadacabbbdaddcbadbdccacadcdacbbacccbbddbaadcdbaacbdaabcaaabaaaadacaddcbddccaccdcbcaabdadbadaacddadbacccbdbbaaadcdadcdbbbabaabadaccbbbbcacaccbaaaaddcbbabcadadcaacbababbabdcbbabadbddbbdbbccbbdccaccacbaacadbddbcbcccaacadabbaacdcadaabcccbabbdcbdbbbdcbdabaaaacacccabbbccbbbbbcdbbcccbbacdabdbcabdbbabdbbdccdbabccbdabcdbdccdcdcdacadcbddbaabdcaadcabdcabcadcbbddccabccddaacabbacacbcbdcbcbaccdbcbddbbddaddddccbbaabdcddddbccbbadddcababddccbbabadbcabbcabcaccdadbbdaddadabbadddccbdbacbddccdbadcdbdadcccbdbdcdcdddccbcabdddbbcdbcdbbbbaaabdbdacdabadbdcadbbbadbcacdbdbaddddcbabdcdadbcadccaacaaaccdddbbaccadabbbbbccdccdbaaadadddbcddbbccbabccabbadadbbacacbabcdacbbdccccdbabdbbabccbcacdccbbdadbcacacabababdacaadcaabbaaaddadbbcdbdcbdccbdaadaacabbaabcbcdabacbacccdbbbccacbabaddaddddcadbdcbbbcbbbcabcdbbcccbdddadbdbccccdccdcbccbcacadbbdcbaaccdccacadbdcbadabcbabcdacbadaddabaacacbdbaddbdcacdddaccbcbdcbdcdbcccbaaacdddaacbadcbcacbbcbaddbadadbbcdadbbaccdbcbcdccbaaccdcdcbdcbddaadacccdccacbbdacbdcdccabcbdbdbbcabbdcdbadacbccccabdcdcbdcbdcbbaaabbbbdaabdacacadacbbaacdddbdbdcbaccccabbcccaccdcbcbadcabccddbdddcaaabcbbcbadaabaccabcbdabcaabccaadbdddddaadacdcddbcdabdabadbacaaddabbcdddabaddababbcdbdbbacdaaabcdcbcaccbacbcabbdcabbaabbabdbbccddcbcaabcaabbadaaaaabcadabdbcaacccbbbdadcaaccbdbbcacadabbadcadcabbdcbcaddbdababbcdddbbbdabaadaaaacbaabbcbcdcaadccdacccadbddaaacbdcddabbdaccadabcbcacacccbbacbbcadcadcdaaccccbcbbbabacaaacaaddcdddcdcbabcacadddccacadcbccbccaadbcbdbdcbaabcbcaccdcbacaadbabbcbacbbbbababbcdbbdbbbaaaaddacaabbcaacabbbddbdabbccbbcdddbdcacbddaabdbdaadbbdcdcdadadadcdbabcadbdbddbdbdbaccbcdbcdcabdacbcdbacdbddddbdbbcdacdcdbabcadbdcbdbddcbdcdaccccadcbbdccdcdddaaaaaabbdacadacdacccabcaaaccdddddbcbcaacdbacacabadbbbacbdadccccddabcbccdbbddbadccaaccbacbaacbbbbdcdddaabaaddcacdbbbaccadbaccaadbbcbccaacbaddbdabdaaacabdcbbdbdadabaaccdababdaaadadddbaaddaaaacdabbbadadccacbdadccddacbabbbcbdcabacddbdbabbbddcbcbcccabbcdbbdcdccaadbaccababbbcacabddaabbcababdbadaadbdaadbbdbdbbacddcbbcadacbbbcadacbaaadbcdccbdcddddbcdacdabcdddcdbadddbcbababaccdacccbbaabcacddcacbbcbcbccdbaddbaacacccddbbaacdcdabadcdbccaacdccadbbcadaacbccccbbcaccbbbdaaabbcbddcdbaabbccddcabadacdddccdadbbaacaadacabacadaccadadddabcbabbabdabbdacddcbabcddbcccaabadddcacdcaaddbadcbdcdadbddbcabddbbcadbbabcadbababadabbbccdcddabbdcdcdabdcadabbccabdcaaababaccdcdaccbcadccbadbdbaaccbacbddbbbdbbbdbccaaccabdcbdacbaddbcccabaacdcdabdccbdbbbdbabaccdaacbadbaddcacbbacaabcdadabdaabdcbabbddbaaaaccdcacaabdccbdddcaccbadccdccbaddacbdabdbbaddaccbcabcbaabbaacdbbcabadababbacabdadbbbabbdcdbcdbbbcdbdbbdcbbbacddaddcabababcdadabbabbbbdaaccbcaccdadbcccdacbaddaadaaabcdccddbbaaacddabdbbbaaddabaaddbadbdbbbacdacabacaaaacacbbabcddddacbbcbbaacdadabdbcdcbddbcdbcbcabbbcbacadcdcbddbdbbbabccbaccaddadbbcbcdcbbbdaaccbddbbbabccacdaddadccbdaccbbacddacdbcaacbacddcbbdcccbbccadadaabccbccccdabdbbaaaabadbdbbbbbbddddabcddcccadbbbbccadcdcadbdadbacddcdcbadbbdacdccaddabbcaacccdbcbbcbbcbdbabdcbddbbcbbaacbdcdccbdcababdddbbdbcacbaddddddbaadabaaacccadbdccacbbbcdbbbbbacabcacababcddaacaabdaccacdcaadbdcdddbadbccacbaabbdbccdbcadddcccabccdcabacddaddcbbdbbabdddbdbddccdbddbbbdddbddacccbcdccbcdbbddcdbababadadcacbaccbdacbbdcdcadaabbdcddbadbaadaadabbabddbbaddbdbbabdabdddccdcaabccaacddbbbbbdcadddbcdddccdababdadddccbabbcacbabccdabcacccbbbabbcdcccdddabadadddabcdccdadbaaadbdcadcbbcacadcdabcaaaabcbacdcacccbbadbdccbdadbacbbdbaababcbdbdcabbccadbcdbcdbcbccbaddddcbabdaccaadcdbbddaaabcacbabbbbadbcbdcacacadaaccbdcaacabcadccdbaddbddcabcacdbbcaacccbcbbdacdadacacdcbaabbcbaaaabaacdccadabaccbcadcbbcadcdabacadaccbdccaaaddccbcbadacddbadbacbccbcdbcabaadabddddbcbacbcbdabcbddbaadbcdadacaccbdacbdcddccbcdbbadbbbcbccbcddbadddbdcbadbccdcccdbddcccbaabcdbcdacabbccdcaacbbcdcdabbaaadbccbabbadaddbccccacacadacccdcacdcbbaddbccccccacdaadaccdaabcaabaaaccaaacacaabaadcccbcdacadcabacbbddbbadbcbaccbccaabbcbadddbdcbdcadddbbddcbcdbdaadaabddbaabbbaccdccddcdcabdbcccabcbaaacccbbdbcbcaadcacababcacbdacddcbdbbacdbbbaccdbbccbaaacddcabdabbcaabdadbbbaddcabdddcdaabdadbcacdacdaabcbdabacdbbcabdcdcddabccbbabdbaaadcdcbaadaababdbcbaacaaacdbcbbabddbaacbbdaadabcbacdbdabbdbdaccdbaccadababccccdaadcbbcbcabaccddcbaaaabbbcccbbbbbddccdadccbababbdccdadaddccaacbcbdbbdabccabadbaadcadbdaddbaadabdcbacabcbbdbbcaccdbacbbaaaadaadcbaadcbadcdaddacabadddacdaddcaddbbcacaddaddabddddabcadbcabbdbbcabbabaadadbdabbcbcbabaccbbcdbacbcaaaddbadbbcdadccabcbdbcaabbbaabddaabcbbccbcbaabdbaadacbacccdbcdddbaabdbacbbbdacbddccdadbdabcdbdcacdcbddcdcdbbdaddbccbcbcdabcdcbbccadadbccacaadcdbacaccccbcaccbdabdddaaabadabcacadaacaaadbbdcdddaddbcabbdadbabadaabdcaacaabcdcabaadcbddbdababacbbbcbcdcaaaadbabddbacbdacdcbcbdddcacdcddcdddcbcaabcdbdbdcdaddacbcadadccabaaabcbdbcdadadcbbadddbcbdcbadccbdbdcacbbddabacbcabcbadcadbdabaadaccdbcbcccdaddccacccdbaaddaacdbbdababacabbccccdbdbdbaddbccaadbdabbbdcdcdaabbadaaaaddadabbcdccaaccbcbabcacdccddabdadbbcddaaacbabdcbcaabcbdbadbbcdbddbdacbbbbbbacccabddbbcacdbaddbbbacacbadcbadadadaddcadcdbdacbdbcccacacdbddcdcbccabdcaccdadcccbacdbcbdccddaaaadbcdabbbcabaacbcaccdadbdcadcdcdcdbbcbaccdbabdabbdbadbccadbdbcddabdaadccdcbdcbaaaacacacabbbbccaacbdddaacdddbbdcaccacdcdddbaacdbdddbcdddbbbcdddbdadccdbaadbddacaccdcabcdccacccccbcbdabadcddcbbcbdcacaaccaacbadcabadaaabccabadbbbdcbdcbcbbadbacabcbcaadacbcccdbbcdacbddddcabccaccadccbcbcbcbbacdacaaaccdaccdcdbcadcdcbadbaadabdaadbbdbabadcccdbddcbbbdaaaddcadcdadbacadbddabaddddbacbbdbdcabbccccbbbbaaaabaaaaacccbdddcbdadbdabbabdadccdbcaadddabcbdbcdcccaabbdacccdccdbadcababcccbacacaacbcbdcdacaccbabbdcccbcbabadaacabaadbbbcbcabdcbcabaddacdbdddaaaadadacdcacbbcdabcabddcbdacdcaacdbbdaaaaddbadccdabbdbbdadabaccbddaacadabdcdccdbdcdacddbbdcbdacdbdbdaadabaaaacaacdcbbbbacbdcabdacdbaccaaaadcbcdbbdcbbccaabbabdabbaaabccccdccdcbddabacbaaacacccaacadddbcbbcadbdddcadbcdcadbbdadbacabbdaddcdcacdbdcabaabdacdcbdbddacdbadcabdabcccdaaabacccbbcadcdaabdcadcdbdaacabbdbbabbdbdcacccdaccacbabdbabcbaddcbddbadddaaadcdabdcaabacbabddadddbcccbcaddbcbcdbccbdabcadbbaaadbbaccadaccaaabccbbbbbaccdadccbaaacabcaaacdbcabaacdbcbcbdcbabdbcbdccdaccdbbddbcadaccaacbddaabcbdbbabddcbbbcaaddabbdbdbcadddcbbcbabbacaccdbdcbacdbadaddbccaadaadabababdcaaabcccbddbabbcdbbdadbcdbbcbccdabbabcacacabdddbbadbcbbabbbcbbabadbdcbbcacabaadbbdbdbdbabcdaadacdaccadbbadadcccaaabdcbbddbdcacacabddacdcabbbcbacabaadccbabccaccbcbbbdbbcaacbbdbcaadabcbcdabcddcacabccabcbbdaabdbadbddbcadbcacbccdddbbabbbdbcdbcdcdcaadbbcbdbbacddabcdcdbaaddbadcacbabcccaaababcbbdcbcaccbabdcbabdbcbcbbbcbcdcccbdcdccdcbcacccbddcabdbcadbdddbacbaddcdcbdcbabbdcabaaaadadddbcaaabcddbcbabbddccdadcabcdadbdabcabccbbbcbdbdadbcdcdbaadaddccbcbcdbbdbcacacdabcdacacadabdaddcaddbcccacbccbaccdbdadbaccabdababddbabcdbababcadabaabddcddaadadaacddbdcbadcacababcccdcdcbcaaadadadadadbddacbbacdbabdaccaabaadddaccbaddbbaaddbcbcbcabcccaddadbadbadccadccdbbdddbdcddbbbacdadcbdbbbcbcadcadbcddddcdabcccbcabaabadabbaccbcdbbdbbccdaddcbddbdbaaacdccbaccaddadbbbacbcdcbbdadbdbbdbbcaacbdcccbbdcddcabbcddaccaaacbdcabdadabcbbcbacbadcbcdbdbccaabbccdaadaaabaadbbdcbcbdaaabccaabdaccbccbbbcccbcddbdadbbdcacdddbcacdbddbccabcccbaabdcbaddaddabccbccbbadcbcdcddbdadcbcdcbdadabccadaccbcbdaadddadbbbbbadcaccdaccaadbddabcbbccabacddbabbcbaaaabaddbcdddacdcdcdddadcbbcbdccccbbcaaabadcbddcbbdabadddbcdbacbabbbabaadcccadcbbddcbdbccdcccabbabdaacbbacbddbacbcbdcaadacdcccacbbcbdcadbbddabbcbbabdbdcbcccaddbbdbbddbacbccacdbcbbdcdadabbdbdcacdccdcabcbaddaddaacdcadccbabaccbaccacddcddadccddaaaadacbdcbaabcdbddcccacccbdbdbbddcacacbabdbcacbdbcbdddadbdcdacdaaabcccdadcaabcbdbbdbdacadacadcddaddacadcababadadaacaacdbcbbbcabdcbadadaccdddbbadbcacdbdaddcbcacbaccbdbbacdabccdcbbacdccabcccdaaddadccaaaddcaadccdccacbcdbbdcbdbcbadabccabbaaaaddbdcdcaccdacbbdbadbacdcdabaccacccbdabcabaabdcbbcbdcddcbacbdcacadacababdadcabdcbadcddcadabbcabccddbdcabbcacacbcacbcabdadabdaaccdbcbbcaccccdadacabcabacdaacbccadccacabdbcbddabaadddabcbadaddbcaaabddbbacdacddccdacdcccdbbcdddccaccddcdbcaabddabdcaaddddbbbbcbabcdccadaddacaaaddaddddbccaaccbcabadacdbdccbaacaacdbdbbacadbccabcadddabddccadcdcbadddddccdbbcadcaabcaabcddcdcbccbadcccbdbdccdddabbbcbdddbcabdaadbcdbbbaddbbccadbdacbdbdbbaababcdcbcbcaccdcaccacabddcdaabdbdbbbbacddbbddaaacdddcadaadacdcddacdaadbadccbbbbbbccdcaababbdabbabbdacadabdaadccaabaacabdbdcbbccaddbdbbaddacdbddbbdcbbadabcdadcdaabbcddbdbacbcdcddbdcbcdddcbcddbccabbbbaacbdcbbbbdbdcccbbbaabbcddcccdbbbccbddaddadbababcabcccddbbdcaccdbbacccbccabcdcaccdbaababbdcbdcbbcbcadbbdabcabbdababbddbabdcbaccabbdaacccaabcbbcddcaaacabbabbdabbbabbdaaaadddababdcddcccabddbddddbbdbcbbcccbabcddbcbadddcbaabcbbacbdcabcbbbccddcadcdbcacdbabbbbcddccacdbcdcaccadcbcaddbdbdccdbdcaadcabdbadbcaadbdccaaccbddbbacabdddcccdbcabaabddabbbaddbcdbbaacacccccdcbdacdacccadbabddadcbcdbcaaabbbbccdbadccbddaaacaccdcdcddbbdbadbacacbccaabbcdacabcdabcdadcbacabccdcbaaccddbdadaababdadabcbdbcdcbdcabdbbdbdddbcbdddcaacacccbadbdabbadbbbacacbaabcbcdbccdababcaadcaddadcccbcadbbbccaddcacddcbbcdbabdddcbcadbbdcccbcbcccaabaacdbdacacbbabdddadcbababdccbcbacbabbbdacdbbcabcaddaaccabdccbcdcabbbdccadbbccbbccddbcadbacdbdadacbbadaacbaadcbbcbdaccbdddcadbbabbbddcadcdabbacabaaccaadbbaaddadcddaacaccbadaabbacbbccddaadcaaccdaaccaccbacbdcbdddbbccbaaacbcaaaabbcaadacaccddadadaddababaaddaddccabbcbbdaadadcaadabbbccabaabbdccbdcadaaadcdbbaccaccbcbcbaddccbcccddcbccaabacadaacdbdccaadccaddcadadadcccdaaabcccbccbcabbcbddbcdaabadcbaaddaacbacbadddabcdbbdbcacaaaddbabaaddacdcdcabaccaacbccccdddaddbcabccdddbbbabccccbcbaabababbcdacbdbdbacbbaabcdcdabbacaaabcaddabadddbdddcdddcbdacddbccadaaaacabbbbadccdbadbdcbbdbdbdcadbdbdbdaabcaadcbabcdcccbcaaacddabdcbabdbddddcddadabdadcabbccabbbbabbdaaccbcbcacadcbacbbcadcdadcbdbdddabbcbcbdbbdccbaacbddbbcbacddacdbdcdbbdabcddcbcbcbbaddababddbbbcccdadaadacdadadaaccddadbadadddadbbbbaaddcacbdcbddaadbdbdacabcddacdcdbdbcdaccbabbbccdddcdadbabdbaaacbcdbacacdbbabccbaddadaabdbbdccdddbacddcbdbbdcccaabdbbbdcadcadacdcdacdccacabacbaabcadcdabaccbabddbccabaadaccccbbbabbbcdaaddbccaacdbbccdcddccccacdaabdcaaacabbbdacdddacbbcdacbbbbcadbaabdbbbbbdddcddcbbdccaabcdcccbabcbcddadbcadabdddbadbacbaddacdcdbdadccadbcddbdcbacdcbcaabbccdbaaccaaaacabacbbdcdcacabccddaacbbbdcaaabcacbbcbdddbaadcdcacbbcbdbaddbccddccdcdbabbddddabadadadccbaadcbcbbcbcadbabdbacaacccaacbadadbacdabaacdaacaadddcbccbdbbbdadacdbdbcdcbcbbcbbdbabdcbbacbbbbdcdbaaccdaacddddcccbbadbbdcdbdcdaccbdacdccdabdaacdbbbbcabbdbaaadaddcdcbbdabdcddbccccccbcbdaabcbbcbbccdadbaacdbccdbbaccdddccbccdccdcbabccbbcabbdacdaabdcaccbcabbbaadacbacdbdcaccddaddbadbabcadcccbacadddadcbdbacacbcaabddaacabdacabaaddadadcbadbaaddcadcaabacbabaaabacadadddacaabacdaaabbbcadabddacbadbababaddddadadddcaccacdababaacabdaabcccabdcdbcbcbdbbbadddaabcdcaacadccccdacaaacacadadabdcaacabcccbadcbdcaccdaccdccdabbcabcdabbbdbadbabbaacacdcabdcdabddaadbabacccbbddabacbaaabdcdcdcbbcdcaadbacbadacacbcbbdcdacdacbadbddbaabdcbdcbcdcccadaabaadbadbdadcddbdbaabbdbdcaaddccaccaabccdcdacbdcdadbbcdadbddbbccbcadbaaddcddbdddaaaccbacdccdbbcddacaddadbdbbbccdddaaaabbbbcddcaccaadcccdbbadccbddcaacddccccbadcddacbacbaacacddabbcdabbdadcbcadbdabbdbdbdaaddbbcbbdadcbdcddacdcbbccdadbcddabcdbadabddcabdbbcdabcbabbdbadaaaddccabcdabbddbbcdadbdaaacdadddcadcacdacbddaccacccaadcabaccddaddaacddaccbaccdcdcdddcddcdcabddddbcbcddacbbcdabbaaaccbbddbdabbbabaaaddccbcbbbdccccadbcccdcbcaacadbcdadbaddadadbbacadbddbbbdcddddcababadacdcaccbbddaacccababdbabcabcdacccbbdbbdbdbacacddbdddcaccaacdacddcdbbdcdbdbcdcdcbdacbdadacdbadbbacdbaccddbbcccabbccdaacdcbbaacdcbacdcbaadabdbabbbdaabaabbacbccabacdbdbaabadabbabcbcbbbadabadbbcbdaaacaddadcabadabbadcbcbccacdbadcbdadcdabcadbbbbdddbccdaacbcaaddadcbbbabaccaabacbcdabdadcaabcddbdcbdbbdbcacabcbabadcdabdadcaacdbdcbdabccabcdacbadcbabadccdcccadadbabadadcdccbabacbdabdaaaaddbdcdadababbadbabdadbbcbbccbbbababacabbadadadaacddbcbacadbbddcbccbcaaadaabaadcddcabbccdcdadabcdaaaabdccddabcadcbddbdbccbddacbabaabdabbcadacdcabbbcadaadaaddbbcaddccdadbcbdbaaaccbbdcaccdbcaddcdbcbdcdbbcacbcacbaabbdbadacdbcdadbddadabbaccdcaacbcccabcdaccadadbabdbbdadadbdbbccbbacacacaaaabcbcabacbbaadacbaadadcdacdbbcddabcdabccacbaadccccbbaabababdbdcaccaddddccdababadaddcdcacbbccaabadbaccadaadacbbcaaddacbccadacbcbddcbcdbadbacabdabbbddbadcdbbddabccdacbbddbcbbabbbacbbabccdaabcdccdbaabdabdbcccadabdcadacbabdbdbabadbabcdccddcaddbdddbcadcaabdcbbbdbccacbcdcbabdabbaccccdcbbaaaaabccccacdcdabbacdddbdaccabcaccbacddddcbbdaaadbddacaabadadacdddbccadddbccaaacaadadbaadaaaddcadbbabbdbcddbadcccddcabddcbadadabddaddccddaadcdbacbaaadbaddabdbbababbbadccddaaaaacccbbcaaabacdbbacabdbadcaaaaaabbaadcbacbdcadaababcbadbdddabcbdbdbcadabaccacabaaadbcbcbaadbacbaaacabdcbaaaccdbbccbbdcacbbddadcbbdabbdbdcabdcbadabcabdcdabdccbdacddbdbaaadcabdadbdbcbdadacdccbdbaaccddcddcbbdcadcbdacbcbdacbccbcbddbdabbccbcacaaddcddccdddddbbdddcddaadadabbabcabacadacaaabcacabdbbababddbdabdabaccacbabbacdbaddabdddcddcccbaddaddaabbdadbbbaadbddcdddcddcdaacdadbcccdbabbccacccaabacabaaddbcbaaccccdabdbbbdbbbacaddddbbccabbaaaabacddaabccabcdbbccabcdcbbdacdadbcadbbbbdcaadcdabadbdabadccbcabbbbdbdadcbdcdcbcbcbdcdcdcbbdbaaabdcdbacbacccbcabdddcdaabcdabbadbcbaabddcdcaabbadcabcbbcabcdadabcdbaabbcabbbaabcccacbddbdcbdcdbdccbdcdaadddaaccccaaaabbdaabcbabcdcdadbdabbcadbbcabcdbbbdccdadcdcbadcacdabbcdbdccdaacccbdbaaabbbcdcccdbbcaaadacdbdbdadadaabacbbabbdaccbbdacaabddbbdbaadbaadadbccdaccacbbbbbbadabbdccdaddaccdccdddcabddabcacaaadbdbdcaaacdcbbcbdaccdaacdddcddbdacbbbcdddabadbdbccbadddbcbdcacddabdbcbcabbadcbccbdabcaacaaadacbcadbadacbabbbaabcccbaadccbcacadaddadcaccbabcbcbdbcbbdcdacaadabadbaadccbdcdbabcbadcbabbbabbccbcddcdcbccbbccdadccabbbacddbabccdaadcabaaccbbbcacddababdaababadddbbccbccbbcbcabcbdbcbadddddacabcabcdaaabcabbdddaabacbcbcccbdbcdbabacaddbcdcdcccaccabbbbdddbbbdccbcacbacdbacddbcbdcbdddcbbbddccaabdbccaaacbccaaabddaaabcdbbcbcabaabbbdabababbababdadabdcaccddabbbaddddadbdccddcacaacdbcccabdcaddacaaccbbccdddcdabbabcbdbccdcccdbddcccccdccbcaddbddddcaddccaaababaadcaabdbbcccbabaacaccbaccaddbaaabbddbdcdddbbccaaadcbdcddcbbaabcdbdddbcbabcdccaaddcbccccbaacdadbcbacdabcccdcadcbabbdbcccdbabbbdddccadbbdcdacccbabcacadaccddddcbbbabbadccbadadcaadcbcdcaccbcdcbabdbdbabcaaaacdcadadcbbcbababdcdbbaddccbdcadbdabdbcbcdcabadbbdbcddbcdbabdbbabbbccbaaacbdddddcdbdbbddddaacdcbdcabbacabdbacaabcdcaadcadcaacadadcdccbbdabdaacdabaacdabaadacabcdbdbbaacadadccbdadbccbbddbdcccabcacdadbbbbacbbbaabcbcdadbacbcbbcbcbcddddcaabcdccaaaabaacaaaadcdbacbddacbdacabcabcadbccbcbaadbaacbdcdcaddaadaddabcccbcdbdcdbcdabcbbddaaddcabbbaabbcdadaabadbddcabadbadbbdaddacddcdccdccdadbbaabbbccdbbbddbbcbdbbacddababdabddccbcbbbdcacccddadabccbbabccbacadadadacdcbcdbabadddbddabbccadcddabbcadcacdbcaddaadabddbdbbaadbaabababdbcadbbbaddababbbcadcbdbdbddddcbadbcbaabdbdacdccbcbbacdbddcbdcbbabdddabdaadcacdbacbbdcabaadabbdccadccddbabdbcbcbbbcacbcbabcabababdbabdcacbadbacaaddcbcbdbdaaaccabbcdddcdcbbcddaabacbadaabdbccddcadbdddbaabbabdcacccadcdccdccbccabaadadacbcdacdcabbcabddadabdbcbdbcdbcbdaaacdbbaaadbcdbaaccabaabbacbacbbddaccdacdadbdcdccbcbdacadaacaadcdaaccaaddbdbdccdadaacddcdbddcddbcadcacbaabdbccacabbdcdcaacadaacbaadcdcddbcdcaaddcacdbdcabdccbcabacaddcabdabdcddbbcdaaddacdbabaccccdddddaaababddcddcbabbdababadcdbabcaddcaaaaaaaabbcdaacdadbadcdcbdbbacdbadbacabdccaaaaabadccddabaabdbbbbbadccccdcbbacccccdbcadbacbdcdbbadcaabcbadadddbabaddbdcbadbdabdbbbabccdddcaaacdddadadcddcddbccaadbadabdbccabcbcaaaabaabbcadbdbdcccbbcdacdcddcbdbbcacddacadadadbaaadaadadbabbdcacaabbcbddbbabbbbadddadbcbcaaaddbabcdcdddbcdabdbcacccbdaacddbdcdbcbcbccdcbcbdccddbdadcaddbaddabbdcdbddbdccddddbbbcabbdacbcabdabcbbabacbadacdddcbbabcddaaacdbdcbcccdbbaccacadcccadcdccbdbcacddadbcbdcabdabdcdaaccaddabacdddccbcadccabdbdbbbbbcdcbcdaaaccacddcaadcbadcacddccdbbcacbadbcbbccacabcbbbaacdaaccbdaacdcdbabdccddbacbbadacaaaddcccbdbcaadddabbdbbdcaacbacacbdcbbccbabdacaabacbaccbbbcbcdddbbbbcabdbcaccaccabbddcbcbdbbbaadcdcccddacbdcddccbdaddaddadbabbbabbbdbdccbaabccdabcbdadcacbbaadbbaacdbabaabbccabdadabdccbacaddbcbcbabcbccdbcdddbbbdcabacdaacabddacdaadcbdccdacaadaddaaaccaddbabaacdcbcbbdaddcbbbbabadcacadbbbaddacbbabadacbbcccccdddbcbbbdbbbbdbcdddcbdbbacddcbbaadcbabcdddacbadaccbdcdddddbdbdbbddcbdabdcdddcadacbabcccbcbbbbbcaacbcbcdcdacbcdbdcbcadcdbbcadcadaabdccabcbbcaaccdaddacdbadacddbdcacbdcdbbdaabcddaacabdbdcbacdbbbaacacdcdccbccbaadcaaabbcabcdbdabaacacbccccbbcacabacadddaaaaaddcccadddacacddcbddaabaabdddddacccddbaaacdccbccdadaaadabaaadcdcbdbdacbddccccaabddccdadcadcbcdaabaccdadcccabcadcadbbcdbdacccbcacbaaaadabbccabcdaacbcadbdccabcccdadcbacaddccbcabbacbcaaddabbbcdaadcbcddcdadbbcdbbbddabacbaabbbadbabcbcbacbadaddabdbdaaadbbaaaaacddcbddbacdcaddcdaabbddbdabdacdddacbbbaabbdbccdaabdaadabadadbdbbabaddcdcdcbbcbdcccdbbcdaacbbcabacabcabdbddbdbdaabacbdaadaaccdcdcacdabdbbbdcbcabbddcabbbaadbdbabcaaaaccbdbdadccabcacbaddbacbadaabaacbcdddccababcdacddacdadbabccabababaaaabdcabdcdaacabcacdbdbcbaadabaadcdccdcdacabaabbdadacadbdcaadcabbadbddcddadadaddbbbdddacdabcddbabccbbcbdcddddbacaacdcabccbbbbcdcdcbddaccacdbdcdcdbaddacdacbdccbcbaccdabbccaccaddabacdcdbbbdcaaaddcbdcccbcbcbdcacbbaaccdddaaabddaaacbcdacbbccaacbacacdaadccdcccaacadcdcccddcdaccdacaddccdddcccabdadbdcdabbbccdccdcaaddaabdacbaaadcdcbacaabdcddcdbcadacddcdadbdabababcdacdddddbcaabcaababadaaddcacbabdaaadcacbaadcbbbbaaacaaddacbbcccdcbdaccdadabbcdacbccaadcbbcddcbaccdcbcaaddccaaabdcdbbadddaccadbabaaabbbcdbcccabddbaddccabbdaadacabdbaddaccdbbbdaadabcddddabdbbcaddddccdddadbdcbddbadddadaccdcabbccbbbbbbaababdcbccdbccbdbaccddaacdbddcbcccacbacccbcbcaabcababdabcadcbdabdbcbabbadcdbabbbccacdabbadddccdacdcbbabaadbcdbbdbcabacbbbaddcaacdacbbddbadbdadbbbcbbddcccacdcbdccdddbbcbcddabbaddabaadddadbdbcbcbcabbdbdabbdbbabdbbaabdbbcdbbaaaabbaddbbccacaacddaccabbbacccbbaccaccddbabdbdcdbacbcdbacdbccbdccdbcaacccccacdbbbcabdccccdadcadadbadbdbcdbbdcddabadcbdddcccbabcdaddbbdacdbabacddccddabbbbbccadabddabbdddcababbbcdbcdbccccdbacaaddabbaccbabbdcbdabbcbaccacdcaadbaaccdddccabadcbdaadbadbbcdcdbabdbbbcccbdbadacbbabbcadcbcccdaacdbdddacdbccbbdacacbccaadcccbbdcbcbacbcbaaddaaccdacbbdccaadadbdccaaccaadddcccbdbbbbcdcbdbcccdcbcccddabdcbcccabdcdbabcaacbbbbcaaacdbcdcdaaabdbdbddacdbddacbaaadcadcdabdbccccdaaaddcbcbcbbbcbabdcbbbbdbdcbbcbdacbaccaabbdcacacbaaabadcccdaccbcbadcbabdbbabbacdccbdbbdaccadbadcadccbcdbbdcddadcdbcadcacaadccdabddaccbbcacacbabdcbaddabcdadcbcccdcdcadabbadcccadabddacbcdbbbbdbddcddbccdadcdcbbbaabaabbbacbdddaaadcccbbadcbccdaddbabbbccadcdcbbacbadcbbadacbcaaaabcbdbbbdbdbcaacabbdcbdbbcbcbddbaddbbaaaddcaccdbaccbbbcabbbddcacdcdcabccdaddbbaacbccccadaaccdcdbbcddaccabbaccacabcbbbabbcddddbbcdbabddbcbccdbcccbdcabbdbcdbbcaaacaaaabbbdddadaccbcddaadabadbccbacbaabdcccdabbdcdaacbadcdbbbccabbbaaacadbbbadcdcbdbcddadbcaacddabcaabdaadaccdacacdcabadabcdcaacccbbbacdadbdbccbbdbbbcbabbccaadacccddbdccbccaabccabcadbdbadcdaadcdabcbdcccbcbbdbabcadcaacadcccbdbccacddccdbaaaddadcbaddccacaaaccddbccdddcabccdcbddcbbaadbcdddabbdaabaabcdddcaabcdcacbacacbcdabdadcadbddbdabbcbaccbbcbacabcdcacbdadbcbaabcbbadadaacbbcdbcadaacadccabccadcbaabbcdcabacccdaddabadabccabbddcddddcaabdbaadbbaabbdcbdcccdaaccddcaaccbbdcbddaddbbccdddbbacdcacacbacdbbcabddcdaddbbddbdacababbbdbaddbaaccbbddaddcdddcbbcaabddabcbdcdabacababbbdbbababccbcbddcacccbbdbabddddbaaccdccaaacadcadccdbbadddccdcadbbbdaabbcacdabaacdbaabdcabadcbaaadbacccbdaccdaaaabbaabbdccdcadacbcdccbdbbbadaaacdcbaccadadddbddcdcaaaaccdcdaabddadcadcbadbcdabdddabbbbacbacbcdbbdadcdccccdddbddacdaaddaddcdbbbbcbaccbbaccdabbdcbdcbaccbadadadabcabdaaaddcabbbbdbacbcdbcdbaaabddcabcccdadacdbdbbdbbccddbdbbbaacddbbadbbaddaaacbbcacacaccabddcddcdbcbcabbcdaddcccbabbacaabcabddbadbddadbbdacaabaaaccddbcbccaddbdcdddaaccbcabbcadadabdabbddcbdbbbbabdabaacabcccbddcbdccddbdbcccadabababdabccccbabcadabcbbdcbbaacadddbdcacdddcacbddacacccbdcadbbdcbcaddcccddcaabdabbbaccdcbccdcdcbcababdbbddccbbcabdadcdabdcabbcaccdadacccdccbdddaacccbabadcabbcdacdcaabdcbdddbdacccaadababccbabcaccbcbaddaabbcacdaabadaabadbccdaaacbbabbccbbaadcddcbbabadaabdbdbcadaabcaddbacbabccdabdbacdddbdadbadbcdddcbacabbbcdabacddbcdcadcabddaacbccddbabbddcabaaaadcbcacbdabdabdcbabbadcdaccacdcbabdababcbcbdbbcabdbdcbcbacdcddadbacbdccdcbaacaaccacaccbcbaabadcaaadaddcdaddbdabddbdbdddbdbbbadbdbddaabdcdddbdbadbcdbdaaabdcdbbbbbbcaccbbcddddbddbbaaadcabbbadbddcdcdccbadcabcbaaabbdbaacaaababadadbbccccbddcdbadabcbbdbccbbaadabcaaacabcabbbbaabdddbddadabadaacabbdabaddbbbbcaaaadabdddabbacacbcabbbcaadbbccadbcdbcbcdcaabcbbbadcabaabdaabaaaddcbdcaaabcbbccdbdcdacdadccdddadacddcddadcbdbdbadabdccacdbdbddabbcbacdaaddbacbaabccbbddcccddbdbbddcccdcdadcbaccbbacacdcdaccddcbdcdbcabbccababbdbbbbbdcbdacacddcaabcbbccbccbccaadbacabcbccdbcdbdddacabbdbbcadaaabcddcdcaaadabbcabbbddbccccbadcddabbbacbccadadccdccdcdddaaddddcbcbdcbcacddaaccadccdcdbddcabdcacbaccdbacccbdcacbddbdacdbdaddbcadbdcdaacadcbdcccaadbccdadbaabcaadaabcabbbdbcbdaaabdcaabaaddbccacdcadaacbcbdbcacacddabcdadacaabaabaaaddccddbccadcaccddabcdbddcccdbbbdacaadaaaddbdbcabdacdbbccadcbaabaacaaddcbcababbbbbdadacaaddcaccdaaacdbbaaddcdaaadcacbbbbbdcbdcaaacdacbbccdbdcdaaadabacbdabbcdadbbbdcaccbdaabdbdadbddccccbbcdccdabdbbacbdadabbddbbddccdaaccbadbbcbdaadbcdddccacddddcbacbbbbbbadcacacacbcdacadcdcbdccdbcacbdcabcbabbdbcacccbdbdccbcbbdaadbacaaacbacdcbbbbcadaccadccdcccabddacdcbacdddbcacdcdcadadcccbdcdbabaddbbbdcddccdacddbbbdcdbbdddbccacadbdcbadabccbbccdaaccaaadbacabbdadddbdbaaadcdaadcacdaddacdddadbabddabbbdccccdaacbcaadacdcbdabbdddcbaababadaddaacacabdadaccbcbacadbaccadddadbaadccacddccdcdbbcdbaacdcdbaccabcdbbaaaababcddddbaabcabcccadbcccabcdcdbbdadbdddadccaabcaabcbcbdbbabdccddaadadbcdddadbaccbccddaadadbbacddddbbadaaaaaddbaabacababdcbbadacbdcaadadacdbcbbccdbcdbacdcdcacbabaccdddbccdbbbbbcbbaccdaccacaaabdddcabbabccdaabbbbddaaccadcdddcddcaddaacdcdcabbddadadcbcbdadbdddcbbacdbccddabcccdbabacacbcbbcbdaddabdadadcbddaccbdccddaddccbcbcacaccdcdbabdcdbbccccbcdcccdcaabddbcdcdcaddccbdbccbabcbacdddccacaaabdaadcadadbadabdadcdcaadacdbdabcdacabbcaddbadbdacbdcbbaaddadaacdcdaaaadbdbaacadaabbdadaabbdddaadbcdcbdabccbbbccdddbdaabbdbaaabccadbccbbcbbcdbbcccdccddbddcacbcccaddbdcccbbdcbdaababcababacbddbaabbcbdbaadddbbdacabddbdadbabbaaddbccddbdbbaacdbbaadacbddbdcdbcbcaacccbacbdacdbbddbcbadccaddcdcadbaaabcddcadbccaacdcccbabaaacccbbccabbabbdabbcbbddabdcaacbdaaaaadaddcaacbdcdcbcabadbddbdbcbbcdaacaacacccdbadabbccdccacabbdccbcacaacdcabadbcbbcddbaabadaaabcbdddcaacadbabddbbcbdbccbbcdcdddcccaccbdaaacbbbacccabbdbccdbbcbcccdddbccdbbcaddbbdccbaddcabdaddcccdaabcbdcbdaaadbccbdbdccbbcdaadcdccdabbbdcdbababdabcbbbbbbcbcdbcdccbbdbabcaaadccdbabcbddcbabbccbcddcdacccdcbcdccdcbdbdcaaccbdbbdcccdbbddaddccbbccacabdccbddadddbaddbbaaccdbaacdbdbcaccdbaddcddabaacdacadbabbccaacadccaddcdcbcdbcabdcdacaaabcaaacbbcccaccdbbcababdbbddbbabbcccdcccdcdcdbbaabdaaccdacbbdbcaaaddccbacbcddbbcabbaccbcbcadbddacdcabbaacbcabacdacacadbdcdcdaacbdaddcbbbacdcaaccabadcddcabdcbdabaccbbcdaabbcaccbcddbacbcdccdbacdbcbbdcbadaccdccadaabbcbcbdccbcabcddacbacbcdcdadcbabdacdbcadababaaddcaabbcabbabadbcbbcdccbcbbccdbdcbdbbaaaaccabaddbabdbbdaaaacadacbcbbacadddacdaccaabdaaaadbcdbbbcdcacdccccbababbdbbbdadcccabacbaacbdcaccadbbabbdcacddcdcbabcdbcaaabbdbcdabbdbbabbdcbaddccbaadcacbbdacaadbaccdacadbdccddadcbccacaaccbccabbcdcdbbbbbaddcbcdabadabadadcccbcaacbccdbbcdccacbbadbdacccccddbbccaabaadbddccababaacccccdbdbbbdaaddaabdcbbacaddbccbabbcdddcbbabbcdddbdaaaaaccbbbbbdaccaddccbabaacbadadbacbbbabbacdaaddbbddddbbcacadccdabccddbcccdacddadddbabaaacaaabadcbcdadbabcbaabcbdddaccaddcaacaaadcdadbdcbbacccadbababbdbcacbbbcabdddadaaabbccdcccdcbacaaaaaabaabcabbbdbcbcaaccacbacbacadbbdadbbdcccdbcdbbdacbabbbadcdaabbdcccabaccacbaaabdbdaddcddbcbdacddcabcdccbbcddccbdbcadddaaaccbbcdaddddbdbbbdbabaabcabcabcbcddabdbabbbabdacadcdccadcbdbbabbaabbdbddcdadcadaddaddddaacdccabaacbcdbdacdddccabaacdcbdccdcacdcacaababddbcadaadaddadcbcbdacddbcadaaaacccdbacaccbacccbbccbdbddbdcabcadcabadbdcbcbaabbbbcadbabcdacdbdddcddadddbbddddcaacbbabdddcbadcbdcbcacdacccacdadbdbacbbadadbdaccbababccbcadcbadaadcdbdadadddadbbbabcaddbdbdbbbaddadadcdbbbaaccacddaddcdbaccdbcadcadcddacccacabadbacbbcdaaabcbdabaaaabdabbbbcaddbbbacbddbabaaacdcdcbcddacbdbaaccadcdddcbaaddcddccabacdacbacabdacbdcbdbacaddabbaacabdbbdbbaaadcaaacbccabddcdadbbdadaabbdabcdbdaaadbabbddbcbacbdccdcacbddadbaaaaddcaaadccdbdbaaaaadbbdbcdcbdcddabddbadbbbcbbacaccacdcbcbadbdababddccaabdabdbcaddbbbdbddcdadadaccccbbbaddaccbabccdccdcdabdaabcdcdacccacdbadacabbddadbddbbcdaadcabbabbbadbdddbbcbccbcdcccbdcdbdcaabcabaddaaccbaabcdcbdcdbdccaacadacabacdcdbcaadacabadcadcacbaadddcbbcdcdddababdccbdbdccbcccdbcdadbadcddcaddcdbbbbddaaaacbcabcaddcdccacbcdcacacacaccdbdddacccdabcbdbaddcdbddcddbcbcbbbadcbaacbdccacadabbcabddbabacbdbddacdbacacdbaaacabddcbbbdaccabcbbacdcabcababbdcadbddbcbbbaabbbcdabbdcccccccdcabbabdcbcdddabadddcacadddbcbcccbdccbbdabbcaddabacccdaddddbadbcbacaddbadddcddcabbbccddcdbcadcacbddadaaaddaddddbccabdaaabacbdbacddbcbadbabcbdacbdbcbbacbdccdcdbccdbcacbddcaaccbdddadccdbbdadabacdbabbaacbabbabdbcbdcdcdbbdbacbbbbdabaddbcdaacaaacadbddadddbbcaadaccdadacddadcdadbbabdddabbabcadbaabbbcbbccbccadcccacdbddccdcadcdaacaccbdacccbadabcddccaacbbbccaaaaababcdccbdcabcddcdaadbdcbccbdadcdbaddaddaaddaacbbdaccdacaddcdabcbdaaaacdaddddcdbbabcbaddbbbbabdccbaaaaadcddaadaabddcaddacacbddaacabbbacaddbaabcadbbacbbadcbabbdcccbbabacaccabcacaabbadabddadadaddbbabaaddcbadddbcadcdbbcbadbddbaacbccdaadbacaadbbaaddacabaddcbaaadcacbaccdaddbcccacbdcbabbadabbbdcbdbdaacbacdabdcbccdbdbccdacdbcdcdddbdbbcaaabbccacbbccadbccbbbdacaadabcdaaccddccbdadcacadcdddadcaadddcabcbabddddbbadccbdadcadaccacbababbaadcacacaabaabcdabbdcacdabdbcabcbdaaaddbdaccacbabcdddadabdadacadddcbbcbbcacadcdcbcabcbbadccdbbbddabbcccbcbabccccadccdcacabcdabbcbadcbcdcddadbdcdacabbcaccddadacabaabcabcdbdaabdcabbaacabadbaaaccbbcbccbaddcddbdcbdadcbbdbbbbadabcabcdadaabcdbdbaabbccaccbdcdaacadabcbddbadccbddccbbdcbdababacadcdcbcdbccadccaadddcddbbbccddaaaddbdbcbddaabcbaaadbaccaddcddccddccbcbddbbccaacabddacbabdccbbcbaaddcddaddaaccaaadbbaccdcbcccaadbcabcccddcadacddacccacdaddcaaaccbbcdccdadbcadccacbdbbbcdbbdaaadcaacababdaddbacabaabbbadbdcadaaaaadbdcacdcacaaabbdadbadbbabccdbdaaddbdbbccabbdbaccdbdacdbcdddaacdbdaaccdcccabdcaacdbdbabccaaccabbdbacdcdbddbabbcbacaccbcacdadadbbaddbcccbbcdabbdadacbcdaddbacacaaaabcbbbbabaaccbadbcadbbacadccbccddaadbcbaaaadbadccaacbabdaacacaaaadbbbbaadbbabcdbacadbaacbdacbddcaabbcddaccbddaadbddddcbdbdaccdcdaacdcddacbaabccdbcdccbaaccabcadabbddacccbbacbccadabbaacbbdbcadababdabdbbdddcbabccbbbadaddbdcdbdcccabbbaabaccbadcdabadccdccaddddcaaabdaacaddbabadddddadcbccadbcacdbabdcbcaacbdcdbcadbdddddcaabbdcadacacbaadcbababbcacbbadcdbdcccbdadddcdaccabdbccbdbdaadacdcacbddadaaaadacbdacdbcbcaadbacaddddbcacaaabaccdbabdcaddcacacacbbbbbbcdbaddcddabaaadcbbdabadabcdabdcbdaccccbaddcaddbbbbbbadccddbacbdcdcdacadbaddbdcdbadabbaddddacbbbcabbcdcbccdbadbccabbcdbbdbbcabdbcbcbbbcbddddbbbaabbaabdaaaacabdbcdadacdadcccbcdcdbccbbcdcddcddbcccaacdcdbbdaaabbcdabdbdddcacbbadcddcdccbabadcbabbdcdcdcdddabbacabcdcadaaddcaccdacbdadbadbaaccdbbcaaacbcabadbabcbbacbdaaddddbaacdaadabddacdddccdcabbddbdcdbddabcdbbbbadbbbbaaadabcacccabbcadbccaaaaccbddcddadaaabbaddbaacabbdccacadacbbbdddbcacbabdcbdaacdcdadabcbccbabbbaaababbcabcaaaddcccbbbcacddbcdbbcbbdbadcccadacdcdaaccaccbcabbacccdbcdadbbbdabddbccbadcccbdbdbdcdddbbacdddcbacdabacddcaddbadaaadadcabbccabdabacadbcdbcbccabbaccacdcdbdbcbbabbcacaddaaddddadbbbbdddcbaccdcdcbaacdacdccbacccacdcdacdabcbbcadadcbddadbababcccdaadbbdbdbdaddaadbbbaaddaadbbaaddbabdbbbdbabdcdccaddbbbaaaacacadbbbccbbbbcabddaabcabdddccccacaddbdabaddbbcadbcbdbdbdcccbdccacbbdaacabdcdbcaadcccdbcbdbbcbcdcaadcdcbabcaccaccadbbbdadccbdcbcddcdacbddbcaccadccdadcdaaacbbbaaddbccabdcbbcadadbdaccddaaabccbcacdcddccbacabdbbaabddaccdadbbbdbbacbbdbaabdcdbbaababaadbcbbbcdcbdcccdcbccddcabcbcbbbccbbacacaabadddabcacdaddcadabacbdcbaacdbcbbdaadaccadbbdbbcccdaabbbcccabcacabcdcddacbcbaaabdbbcdcdabaaadaaadddadabacabbbcbaadabccbbdddaaddbccdbabbbcdbbcdbbddccdbaccacdcabbcabadabcdbaaabbbcabcdaaadcdabdbbdaacbccabdcbdaddddcaacadbdabadadaadddaabdbabbbccddcbcbcabacbcbccdddcddabadcaacdbabbadcbdabccabbbdadddbbbbbbbaccbadcbbcacadcdadacbadcbbcacddbdcdbdcaaddccccaacdcbdccbabcbadaabacdaababdbabadaabdccdbadcadacadbddddadacbacaaadabbcbbddadcacdcdbccccaadbdbbcdabaaadbcddbbdcccccdbbabdbaacddcdaaacddcccabaaadadbacbcdaabdabdccbbdccbbdbababcabccbdbbdbabdcadabbdbdcbbabbcbabccababcaccbbbcabcadcaadaabdaacacbabacbadbcdacddbbdcaddaccbdccbcdccbdbacacbdaaacaaddbadcbaccabdbbabcdbdbddbaaaddcabdabdbbadcbcbbbbcacdbdbacdcadcabcdaacbdadacdbcdcabbccbbdccacdbddcaacbcdbbaadaacadbdcdaabccbccdabdcbaddbbacddbbbaacbcbcadcacbbaacbbcadacddbcddccbacacacadbacbcbdccbabbdbbadbcbcbaacdbcacbbdadbdadbbbdddababdaadcaabadcacdcbabadcaacdaaabbbadadbdacabdcccabadbaddbbabaaaccaadcacdadaccabcbddbacdbcbbacaccdbdbdcadcacdcccdcabcbaaddcaddaabccbcadcbaccabbdbbbacdcdadbcccdcdbbcdbaaabcbbccadbbdcaabddcbdbdbadadabddacdacdcabbaaadbbaaddadcdabbaadadadccaddcdbddbbaaccdadacccdcdcbaacbdddaacaabcacdbbaabbdadddcadadccacababaadabbdbabdbdabbcabcdacbadccbdcdcbaabdcbcdbbcdcabcdaddacababdabccccdbcdbcdcbacbabddacdccbacdddbcbccdcdbaacddccccdccdbbccaaacdcbbcaadccbacaadcbcbcbddbbdbdaacdacdbbadbcbaaccddaadccbdaadbccdccdaccdcddbacaccbaaabccaccddbbadbcbaddbbbdcaaabccaaccbcacdcbabbbbddbdacdabbbbcbabdbdabbcdccadaaaadcdbcbaacacddbddddcabcbbccabbaabbcbbdddababdaaaacbccdaaaaadcdaccadccdacbbbadcbbdbccadcaaaddacacacabcdcddcccaabbacbcdcabddabbddaddbaaaaaacbbaaccabdaacbcdbddccbcbcabcdcdcdcaaddcadcabcdadbcdcaaacccbbdbdccbaabadadabdddaaacdabbaddadaabaacacdadaadbddbccbacdbcbcbcbbbaddaadabdbcdaadbbcccddbcaacaadabdbbbdcbcadcbcadaabdcbcbdaacaaadadcbbcddddcbcaaccbbbbdbbdbdaaacbaccbbddcbbcdadcbccdbcababaabacbadbbcdddbbbadabaadbadcadbdacbddbdabdbcbcbacbbcadadbdbabaddbbcddccdcdcdcbbcbcbdbacaaabbbbbbddbcadaccddabbabccbbccdbbbbbbcccdbcdaddbcaddbbbadbcccdbcadadabdddccdcdbcaacabacaadacbacbbbbadbdaddcdbaadaccbcbbbcbcdcababdcdbabdccccabbbdccbcdbbadaacabcdbbdcdcbcbacdbadcaadcaaaadbbbabcdcbcdbaacacaadcbabddccbddaaabcdcdcdadcbdacbbaacdabbaaccababdcadadddacdacdccbdbbccabadddccabacbddaddcabbbadbdbcddbbccbcdaaadbcbbaabcdbcacacacacbbcacbdbbabcddbacadacdccadacdadbacbdccaabcbccddbaabdbbadacbdcbbacdbdadaadcacadaacdabbaaddddadccdcdaabacabcbacdbddddcbddccacabdbcacdbbababadcbcddcabbadcdaaaddccdbabacaddddcbcdbacbccdcbdbaaabdbbcdbbaccbbdbcbdaccadcacddcdcddcdbbcbabaaddabacddbbbdbcdcbccbaadcbdadbaddcddaaaadcbbcdaaacccbaaccdabdabaaaddaccabcdcccbbdadbdbccdabddaacabcadadbdcdccccddbdbadbdcdbadcdbabdaabcdbccddcabaaacacabcaacabadcbdcbdbdcbbdbdbcbdcaacacdbdbcadbaabacaabddbddbdcbbddbdacdcddbcbadcaabcacbabdaadaadbcadbaacbbcaccbadbbbacdbdaaaaacdcbbcdbdaacacdddcbdabadbcaabacbcbacbbbabddbdcbdbcbbacabcbbbddaacbcadadadabbaadbdadaacdcdcacdbcabdbacdccbdaacbdbccdadbabcdcacdbadcadcaacababbabdccadabbbcdcdbcacadbcbddbdadabbbacbddbbdaccdcabbacbcdbccbadcdcbbadadcbbabcccdaacdbdcdaccababbaaddbbccabccabbcabbddaacabbbddaaccdcdcbdbcdbcddccdadacabbcbccdadcdcaaaabcddcbabaaaaacbcbabbddcdadbaaadbdcabbbdbdcaacccddabddcdaadbbabdcbdaaadacdacdbcddacdccabbdbacdbabccddaacacbadbdaaacdbaacdbacdcacaddcdcbacbccdacccdbbdcbcdadcdbdddbdbadcccccccabcaddbdabcccdcdacbccbabdbccdcbaabcbaaabbccabdaddbdddaacdbbbcccdbabaabccaddcdbcdbaccbbccacdbdabccdbddcbbcabaabacadbabcaaacdcabccdacdcbacdadacabaccadbbbbabbdbcddadabddcbabdcbdaddadadbdccadaadcddbcbdcaacbadbbadcacbcbdcaaaaccdbcaccbdaabccddcacdccddccdacddbcdcabcaacaccacddbdaaaaababdabccbabaaabacddcacdcbabdbcabddcabaacbadcbacbbaacbdbaacacabdaabaacbbdbddabcbaccdcdadcddbcccdccbbbddcabacacdddcdbbdcadacaaaaccbabbacccdaddcabdbcdddccddaccdcaccadbdbcbacccaabdaccbdcacdadcbdccdccbbadadaabbcddbcccbccbcaaddcbdbddbaadcdcdacacbabdcaabdcaccadcbcabbdaaccacacbaabbadbaaccdcbdaccacdcdbcbcadbaaaddbcbcaacbcabcdbcabbdbdacbbcbdacdaaadbdacbdaccddddcddbcbbdcbdddacdbdcbbdaabcccbccbbbdaacaaccbbadcaabccbbdadcacbbddcbbbdccbbbcbcabcddbbdadddccdadabbcddddabdbdacaaaccaddadbcabcaaabdcdcbaadaacdcacdccaabcabdcacdacadddbcbbdbdcbadbcdbbccbdcddadadbdbcaabaccdcdbcddcaccaddcaadddabbbccccddcbbabbcaadccdcadbdcbbbabcdbaaaacaccdbccbdcbdcdcacbacdaacdbddcdbbbbbbdabbbbcdbdddcacddabdacccacccaacbbcbadaabccbabadaddaddbccbcbdbdadcdbacbbdaccdbcddaadcabcdddcabcacdabdbacadbaddaabccbaabcbadcbccadbddacbdabbddaadddabadbbdcdbbdbddccdaddbdabbaaaaaccbcabaabbddcbdbbccadcbbabcbcdbbcaaaccadddadcaadabcbdddabbcabdbcabaddbabccacaccadbaddacaddbbbcbccccdbadbcbdbcbdaadcabacbcadaddaccbcdbddcaccdacbbaaccddcdabdcdacddaaaabababdbcccabdbcdcbcadddbaabaddcaccdadbccddccddbcdbdcbcbabdacbdbaacbcaaddcddcbabacdbddbadbbcddccccbadbccaccccdcdabacbbbdccaacccbbaacccdbbbaccabbaaddadaacbadddcaacdadbcbbabbadccbcaaabbbdcaacdbbdabccacdddbcacbadbdccddabcbabaaadcaddcbaaadbcbdddccdaccbaddbabbcdcabbdabaacbdcbdccbabbabbdbadbbbdadacadabdccbcdddabbaaacadcabadcdbccabccacabaaaccaabdcddabbabcaddbccdbdcccddbadcdcbababccddcddbcbddddbdbaabbccaccabbdacdddccbdcbadbacacabaccadbddbaaccbccdccbdacdabdccdbddbcadadddcdaacddbbbbcbadbdaabccddbadacbbacccacccbcccbcbdbcbdaccbcbdabcdbadcddcdbaacdabcccaabbadddcbacdcddcbbbcbadcabbbdaccadadcabadbbdcddbbcbdcabdcccdccdcdabdbdaadccdacdcdbdddcdddcacbcbadacbdbdbccaaabdcccdddddddabacbdadabdbabcdcabddaaccaaaddaaddbacdbadbdcaaacdabbcbaaddaabcddbdbcbaddcbacaaadacaaddbcbddcccdbbaccadcccbacccbbaccacddbbcbcaddcdcbabbbacbccccdbdcbcdbaabbacaccbdadcacaabaacbcacbbdcaaabbbbdcdbccabdcaabddbccbdcaaaaaacaaaabcccdaddddbabadadcabacdbadddcaaabcccbccbabbbcadcabadcdbcbaddbbcddbbbbabaaacdabadbcbbbbaaaadabbbcaadcacacbbaacbcbbbbbdbccdadcdadaaadcbbabdbadccddddbaacaddddcaddadddbabbdbacddbabbdcdcbdabbdbdabdbabdcbbbbadbbdbadaacbbabaadcdaabacdabbadbcbbdcadcaabbddbabcabbabcbadacabaaabddbaadcccbbcbbdadccccadddcdcbabdcaaadbdadcaababcbbddbbabdaaadbabdaaacbbdbabccaacbddcbdadbdabcbcdacacbdcabbabdaaacbacdbbddadcbaacddddccdabacbacaacadbbcccbbabcccdcbaccdbccbaccdbbcbabcbdbbabacbccbbdddabaddccbcbdaaddabbababcddbaddbbcbcbcdaaaacbaddbdcddbcaabdaabacbbdaadcacbcddbcbbbbdbcdcadcbabdbdbabdcacaaaadbcbbadaaabdababaaabcacdccbdbdbdcabadbcbbbaddbcccddcbdcdacbbaccdbbabbcadabacbadadbbbcabdcdabbacacbdddadbaaaacbaaaaadbadcaabdaddbdcdcaadadddacdddabcdbdcabcaaadcbabaacbccaccacbddbccbaadaacddcaaddabcabcbbcccdaabbaacadaaccbdaaabbabacccaabcdcadabcadbadccadbbdaadabcbddabbcdcdacdbcabccbabddcbadbaadabdbadcdabacccccdbbababdbccbcdcabcccdadacaddbbaccbacaaaaaaacabcaddbdbdbbadacddcdcaabadaccaaaabbdbddcaccbbbaaabacddddacddcabaaacccbcabdbcdbdcbcddaadbdbbaacbbbbbcdcddaabaddbbdaacdabddbbcacabbbadbddcbaccadcabababcccaddcccccbccadaadbacaabaadadbaccaaaabbadaadbbccdddadcbdadcdbdabacabaddcbdbcabcbabdcacdaabbccbaadbdadddadabbccdbadbcddaabbccaacbcbdcdabbdbccabaddcddcdddaabddcdacaabaacabacbddbacadcbcdaadcccbddbdcaacdccdbdadadadadbdaabcdcaaacacddddacdadadbdddcbadacaadaaaadabccaaccaaccaccaccacacbabadbabbcabdababbbadbabbcdbddcdbbdbbbdaadbcccbdccdaabbbbabcbbaccdbaadbbccbdabdccaadbaadacdcaacdaddbbdadadbadaccabdadabcbdabccccdcccadcbcdccaacbddacacccbbcdaabbdccccbbdbbcacacbdcbaadcbcdcacbdcbbdbccdcbbddddcadbaccbabdabddabbcadbbdbcadccbbadcbaabdccccaddacbbdddaddaabbddccabcaabababccddbcacaaabcbacabdddbbbaaccdcddcaaaaccccbbbaaddcacbccbdbacadaababbbcdaadaadbaadadddcaacaddabbcbacddccdcdbabadddbabddcdbabdcdbbcddaabdbbbcbabcadbcacdadbbdcacdbaccbcdaddcdbdbcdccbcbbaabdcbdadcadddbdbadcdbccccadddcacaacaccaaabcbcacdcbdaddccdccbbcacbbabaabcbaaddbadcdbbdaddccbdaccddaabdcdaccdaccabadcddacdaddcdaddbcddbddabbdbabadcadbbbdbaadacdaadadabdccccacaacabadbdcccbbbbbdbdcbbddaaaabbabacccbddcadaacbcbcbaaaabbdbccddcdbbdcbabaaaccccaddbabbdcabbaabcddaacadacdaadaadadaaabcdadabadcbbddcdcdccdaacaccbccaadddbdbadccaaacbbdbacbcbbdcddabccbdababacbdbcbcaaabdcdbdccdddcbcdacaacccadbcdacaadbacddabbcdacdabcbbbccbbbbddbcaabdbaabcaacbbbddccacdbccbccdccdbdcaccbaabadacccbdbbcbdcbbccdabdaaaaccddaadccbacabdbbababcdaacbcbbaabccdbaacadccbaabbdabbbcdabaddbcdddcbbadabcdbabddbcbdddbdbbbcdccaaccdcddcadaacbdcccabdacdbdaaadcbbcccabaadbabdaadcbddcbdadaadcaaadaabccbaacbddcdcdbbdddaddddbdbaaaddabaddbabcdccbabadadbdcabbbacbaccdcdbbabddbbabccddbddbcbddbdbdabbdcaaccbdbcaabacacbadacdbabbcadacadccbbadaccdabcdcbcabcbdcdddcbddccacbaddacbbccbadcccdddcbcdccbcdbbbbabaaaacccbabddbacccbbbbbbbdabddacacaabacacabadbbdccdacddccaadaabdcaccaaadbdbbcbccbcddbdccbddbccdabacacacbbcabadbccbcddabaaddcabcdcccbaaabbabccbbdadbbbdadbabccabdddbbbdcbddcbacabacdadbcdadcaccdcbadbdcabcddaccddccdcbcdabdbcdcbaddcadcdbacdccccabcbdadaddcdcacdbaaddbcacddbcaacacdbdbdbbbbbbcccdcadcdcdaccdbaccddacaacbcaabcacacaaadaadbbcaaadcabdbdcbdcbbddaaadbabdbabcccdcdaabdbacdcbbdbdcabcbdadccccdaadcddbcdbbcbdcddaadbabadaaaababccccdbaddabdabdbdccbbbaabbaaddbccadbabdbdaaaabdadadbaddcabcdbcbadccdccaaccbabbcadaaababddbdabcabaaadccdcbdabddacdbbacdbbcbdddcacbdccaddcbcccabbaaabbbcadbabaacabadbccddcdbcabccaabbcddbacadcbcddaaaacdbcaccccaadbdcddbcacdcccaaddccbaddccbbadccaabacbadddbdbddbcaadbcabbacdccbbdbaacccdacddbbdbdbdbdddccdddaaaddacdaaccacddbcccaaacdcbdcdcbcabaabccaabdcacabddcbcadbabcdaccbaddbacdcddcbdcaddccaaddcdbadbddddaaadaddcbbacdcbbadababdadcbbabacdbabdacaadaccdaadbaaabdacbcbdabcabcadbbcacbbbbabbacddcbbbdabbbcdbaadbbabccbbdacabdddccdcdbbadbdcbaacbbaaaabacbbdcdbabbacbbcbdcbabacddacacbaacacdacdccdcadbddddcaddadacdddbdbdabbddbcabddbcbdadbcdcbacdbcbaaacbdcadbbaddccbabbdbdcbddbacbcacaacbdaacacaabbbcaadaabbcddacdcbbaacbaccdbbccadcabddcacbbdaccdaadbcccabcbbbcdbcddccdabcbddbabcacdbaccdacbdadabdbbcccdcdaadadbbdcdbdaadabbbabaaaccabbccddaccccbabcacdabacbcdbadccaadcbddbaddabbdacdbbcabaccbdcdcbdcdbdbbbbbacbcacdabacaddabadaddcbcdbdcaccabaacdabdbcdaccbcccabdacbadadbbdcbbbbdabbacdcdbbcdbbdbbaacabcbcbbddbbbabccbdbadbabaacdbdcdcaaadacbbcbddcdddcbadbbabdccccccaabddbadbccccadabccaabccddbdaadabcbcabbddaccadaacbbbbbcccddccaaccacbbcadbbdcabdaccadabdcbdccccabbbbacbcbaacbcbdbbddcdbdbcbababdcccbdbaccaadaadccdbcabbabcdbaccbcdcbbbdbdcbbcabdbaccbdbcdbdbaacdadbdccbbccdbbcdbbcacbabccdbadbbdcbcaabdaabbddccdbccccbaabbcaaaccccdaadbbcabaacdaadabccabdcdcdbdcaccaaddaabcdabdbaadcdcacbdbadcdccbbdcabddcaddccbcdbabbcdbbdacdbdbabcabdcabbaaabcacbbadbbcbddcbcadababadbcadabccbbcabacaadaabdcacbdbabcadadacabdbcdddaccbdcadbbcaadcbacdbbcbaadcdcbbaadcdbbaaabbdabbabbdaccdadbbdaaaacbdabacdabdacdbabbdbadabcdaaccaccadbbdbddddaabadcadcabbbdbdbdadbccddcacbabdabaabbdbaddadbcaadccabdaadacbcdddcbcbdddbbcccbdddbdccdbaacdddbcdcddcdbccbbcabaaadacbddbdaacccbdcdadadbbacbbaaaabbdbcadcaaabaadadbaacdccbbcbacbbaacaabbadaddadbcbccbcadcbbdacbbcadbcbbbcbcbdacdaaaccdbaaacddcccdacccdcdadddccccabdbdaddddbcbaadbadcdcabdcadcbdbbbcccbcbaacbcbbbcdabadcdbbacadddbbaaadcbbaabcdadcbbbcddbdbcccabbcdbabddbbcdcbbabaabcbccdbbdcadccbddcbcdbbdbbbcdcacdaabdddaadbcddacacaddcdcbadddbbbbbabdbddbbdabcdaabddacbcadddbcdcbbbccadbbdcbdccbccdcdcdbbadbbccbaabdccdaabcbcbddaaddabdacdabccabcdaccabbacbbbacdbabdcaaddddcbddabcaaddddbabaacddcadcbacaabdbddccbccdabdbdbdaacddacdaddccadadcadccddcbdbcdbabcdcdabbcaabdcddaaddabcacdcbbdbdbbcdabbbdbabcddbccaadcaacddcdccbbbdaadabbbacadaccbadddbcccdcabbbbcdcccbdbacabcbcacbbccacabcacdcbdaaaaabbbbccddcdaddbdddcccdddcaccbdabbbddbbabcbacbdbccddadbdbacaccacdbcdcbdcdcbdadabbccdadaabbddcaadaacacbbdaadcbdbdcabcddccabcaabcdadcddabcdbacaabbccdadaaaaaccddddddbdaadbcacdccddbaddcdbdbccccdcdbccabbcbbdccacaaabacdbbdaccaadcdadaadddccacbcccddadbccdaccdaabbabababddbccdbdbcabdbcbdccabcacdbadaddbdabcabdaaadbbaaadbadcbdbaacccdadcbcdabbdadccabcbdccaaccbaadbcacbadcbcaaddbdccacaabdadbaabacdbccbddcbacbcadabbadbabadadbaccaddccacaabbdddbdcbbdabdcacdabadbdcaccdbadcbccaacccbbbdbbdcdaacabcdccbbcccdbcaaabadababaacacacccaaddcadbaddcbabaacdacbdcbdaaabcabbdddbdddcdbbddddccabaddbdcacdbabaaaddbdddddcacddccdddcbdaaabddccacaabadddacbddcbaabcbcbcbcabdacbdbdbdbdbcdaccadbacbcacdcbdbaabdbabddabadabbbacbabcbcccdbbdabbabdcbbbdabcdcaccacbdbbbddbdbcdcaaabaadbcabbccbdaaaaaddaabdaaadddbabbdddccbdddaaacbbaccbdaaaccdcddbbcccbabadacbbcdaccadcdcabbdbacaaaabbaacdaabddcabcddcdcbcdbcabcddbbaacccabdddaabddababddbdaadcacdaaddccbadbcddcdcddaaacccccbdbddcdbbaacbaadabaabccbacbbbaddcbdcbaddbbccdbacbbbbcaaaccaadbabccbbccdbcadddddbdbcbcadbcbdbbdbbcdbdddcaabccdbdcaddcccdbbcbcdbbddbdbbdabdacaddabccdbbbaabdadcacbddbdcbbcaddddacbcaaddbdbddbdbcddbbbdadbbdcadaddbdadabbcbdaabbdaabddccababbabddcbdccdabbdcdbbabccbdcdaabadaaabbdccbcddabacdabbcbacaaccbccdcbccbccaacabdacbdcdbbcacbabadbcdcbadddbbdbaabacdccdabddaacaadcbacdabaaabcaacadaadabcaaaccaabacbdccdbcabbaccbbddcacbaaccddbcddcbddcbddaccbabbacadabcababbaabddcaacdbbbdccdcdaadddcadcbacdcdacbcdbdbdabaccabdcccdbaadcbbdccaccdacddacbdadaaaadcdcbadaccbaaacdcbddddbacaacabcabdbdbbcddabadcdaacacbbaaacbaabccdaabcaadbdddbddbdbddbdabbbccbcabbdbbbcacbabadddabcdaaaddaaaaabbcbcbddcdcaaadbdabbadadbdcdaccbaabadcbdbbdbbbaaabaaacbaadbbddcbcdabccccdbbbbcddbcbacdddbdbadcdccacbbdbdbadbddaadcbdaaadbcbdcbaacaaabbbcdacbadbccaabdabcaadbbdaacbaadadcdbdbdbdadbcddaabdccabcccbacacaaddbbacbaddacaacdabdacabddadddbbdbaabdcdaaacccdabdddadcbbabdbbaddadbdcacbbccabdacaddcbaddcbccbaabdbcbbbbcaadcbbaccaccccdacdbaccdbadcbcdaaabdababcbbcbcbbacacbaacbbbabccccddcabcddcbadccaaddabcabcbcccacbcacacbdadddadbcccdbcbbcbcbbcaabadabcbbdcdbccaaadabcaddadbddabaddcbbabddaaabdbbdcbbdacacbcadddbaaacbacabadbabbdaddadcadbabdcdaadddcddaababcbadcbbbdddcdccbaacbcadbcbccaadccdadccddacabcccabcbabbdaaaccabccbaabcddaadadcccdcbaadccacdacbdaaabccdcacbdbdbbdabcababbcdacddcadacccbaadacdcbccdbcaababdcdcbcbbdaadaccccabacababbdcaaccbbdaadaabdbcadbdbaadcccdaddbccacabdbacbcdddadddaccadddbdccccccdabaacddaabcadbdddbcdbdaddadaddabbdcaaccddbcbbdcabccdadaadbcadccbdacabbadbcdacdcbadbdabcdcbacababadcbdcccacdddcbabadbdcbbdbcaabdbcdccddabcbdbabdbaacdbcbacbbccacdacdabaccbbdabdbcacccbbadbbabbacdadabddadabaaabbdbbdddcddaccaaccbdccccadbbaaacabcaacbddbddbcdadaabbbdcdcbddaacccaadacbdbabdaaaaadcadbaddcdbbcbbcdcdcdbacacdabdcbcddbcdddbddbbacacbadcddcbcbdbcccdbdbcbdcddabdccccabbbdcdadccacbabbaadbdaaadccbadaadcadababaaaaacbdcbabddadbaddadcaababcabbabadbddbbccdadadadbdcdbccbbdacbdaaddbbddbbdacabddcbdccdbdcdbcaddbdaddaccaadaaadccdabacddabccbdbbccadcbccadbcabddcaadcbddaacacdaaccdaadadbdaaadbcccabcbddcbbcdbabdbcadaddabbadacbacbcaabcdbaddabbcaadbbdbcccdddddadacabbadcddcaaaabcbbcdbddcbcdccabaccccccabcdaadabcccadbbcbbadbdacdcbdcbabbcbcddabbadddcbdbabbbaacdcaccdbdbcccdcabcddbdaacaaacdbbccaabbcccdabababccbadadcdbdbcccdcbabcabaacdbcacabacbbbdbccaccbcaaccbadcdabdbdcccdaabbdaddcbbdaccdadcccddaacbbbdbddbacbdacaacbbaaadacbaabcddabbcdadcdcaddabdacdabddddbdadddaccabcadddadaaacbdcbccccbdbabadacbbbaccdddaccbdcbaabdcaabbabadcbbbbacbaabdabcdbcadcacbcdbadacdddaaadcbddbbaacabaccdcbacaabddcbdddaaabccdbaabbddaaccdccbabacdddbbcabaaaaccbbdadcbacdaddadbabbdbbcdbbcaccbddabccadaccabadcacbaacaaccadcdabaddadbbacbbcabacdcaacacbddacddbbcaccbddaabbbaaaddcdbaadaadcdadbcbdbbdcbdcbaccaddbacbbddcbcadcbdbaadcbabbccbcabcddbbbcdbdbbdcbcbbabbcdabdbabcbbbabbddccdbdcadcadcaacacbadccbbacabbbcacccddcdbdbdbcbcaccccaadcabcddddddcbbdacddadacacacdbdbaaabdadcdbcacdbbddbbdcbdbcccaabcbdcbcbdbcbacbcdddbaadcbdddadbbdbbcaacaacdbbcddbdbaadbcdbdcbaccccabaccbaddacbdbaaadbbbcadadacccadcdcccaacbddbabcbbadabacabddcadddcccacdacdaabddcccccbacaacababdcadaddcbdbcbcaaabcbbbbcbcdadababadbdbbbddaadcdccdbdadadccdaaaccbbdbcbdaadbbdbccabbdbdcaddabddbdcacccdcbbcdbadbddaacbdbdddcbcbbacdbdacbaddddaaccbdbbcbbbbacacdbdcdccaddcbdadaddacbbdddaacadabcbbacdccabbadcccbcbacaaabddbccbdbdbbdcbbbaaddadbbaddcabbbcabbcbcbdacbabcbdaddcacadaccbcbbccdaabcdcbddcbcdacacaabbcdccddacadccacbcacdadcdbbacdddaabdbbdbcddcaabdcbcdbababbcaaabacbcbccdcdbccccaacacaabcddddadcdaadacadcccaacdcbbbbbbaddbbbaaacdbbdddaaaabddaaccdadbbbbaadaacbcdcabbdcbabababcabcddbccdbacaadbbdacdaaabbaaacdadbbacdabaacdbcdbcdcacdbbabdccdbddccdbbbdddcbbdabacbcccadddcadaacbacddcdadcbcbbabbdcadddbcbdcdbbdbabdccdcdcddcddbcdabbcbcbacaaacaacadddbacccaaabdadadcdddbcaadddcbbabbacdcbdbdbcadabcdcbbddbbacbbcadbaabdaabaaaabbbdddacaacdcaacadcdddbacabcdbccbcbabddabbdbccbbacdbaabbadacbbcadbbdadcbbdbadcbcbccbabcdccbcccddbdbdddbacccccbcdbbccaabaacbdacaaddcdcabbbbacbdabbdaabbdccccaacddccddcadcccadadaabacdababbcbabaabbbccadaabbbabaacabdccbabdaacabcaacdadbcddcbaaacbaacdcacaacbcccbbabaccabcaddcaabddbaadcacdababbabadabacadaccdbbccbcaababdbadddacbddbacbcddcbdadccbdaababcbabbbcdcadddcddbdabddbbdaaaddadaddbbaacbbadadbbcdacccaddbdbaaaacaacacddcbbdcbcccdcaababbcbcdcaccbbadbbcbabaddababaababddbcaccddcacbbccabcdcabcaaacababdcaccbbbaabddcabdabcabbddcacabaacddcdccdbacaacabaabccabcbbdbbaaaddcbddbaccaaadaaabddcdbddacdbbbdaddbbdbdddbcdcaacccaddcdbcccdddadacababddacdcdcaaaddddbaaacccccdcaabcadaacbdabbbbcbbacbbdbbcbdbdbcccbbcaddcdbcabbcacacccdcbdadaccbdaccabcccabcaccdacbddccbbaaccacccabcadaaacdcadbdacbcbdbdcabccddcaadbbbbcacacacbcbacbaadabcadcdadcbacbadcdccaaaddcdcddbbacdbdbacbccaddaaccdaddddbbbdbacdadacabdcadadcbbabbddbcbcbadcdbcaadacacbbdbcdaadcbbababbcaabbbbacacddadcdaabdabdababbbbacaacbcbaacbabdccccdddbcbdabaabddacdaabbadacadabbdaabcabbdcaaadbddadcabbdcbacddcbcacadabdcabdddaaaccadaadadcbccdabcacddabaddcadaacdbdabaaaddbaccababaabdabcabbacccacdadcdadcaadbdcdbadadaaabdcdbbaabcbdbaaaabdcaabdbacbabdddbdcbbbdacadcdaabdddacdcdbbcbbabadcaaaabcbcddccabbdddabbaabbadacbddadaacbbbbdbbdccbcaabadbadbdabbadccaaadaddcbcadcdacabbbdcadbdbddababbdbccbaaddaccaaccadabdbcbbbcbbcbbacacdbddccbcdbcdccddaaabacabdaacacbdbbacdbabadcdaabccaccddaacbcadbacdadbbbaadccbbbcbcabdbabbcddcdabadaddcbdaabcabcabadaaabdcdcacdacdbcdcbaaccbacacbdcdbdccbccbbadabcdcddacdacccdccbdddcddabbbbcbacacccbaadcbdddaaaccbabbbacaccddacdbbaacdaddbdcacdbbddadcccacaccbccccaabccdccbabbbbdbddcbccbcabacadaadccbabcbdbbadbaacbacddddabcddabcccbcaaadcbdaddaccaabcaadcbadadcdbcaccbbccacaaccddbdaddcccddccbacadbddcddabbccdcbbabddacdccbabbddcdcdccbabbdadacaccdddadcdbdbacdcbdcddadbccdabacdbbabdaaadabbaaadcdcccabacaaadccaacccdbcdbcaccbcabacddccabcbbbaacbbcccdbbbbbcddaccdabcccdcdabcabbdcccbcccdcbcabbbddcabbcacadbcbbabdddddadcdcacabcdacbccdcabaaabcacabcdadcbabadacdacacccccaaaddbbbcccddaacbcdbcbbdadcdbbbccbcadddbadddbdddaddbbacdbdbdacabbbaabbbdbdbcbdccbcaadcddddbcadbdcaacbdaabbbcdcccacbcbcaccddaccaabccbdcabcdbabccdbaccadcdacccdbbccbbdbcddaddbacabcbcadbcadbacddcdcdbbccbacacdcadcbbbcdaaccddbdddbaccaabcdcddabdbacbadababadcbddadccbacccbdaabbdbacddcaababcdddbddbcaccbbdaddbbabadbdcdacbbcbbddbbdaddabcddccadabbddbcddcadbdaaadbdaddcbacdcbccbbccbdddbcddcdccaaaaccaadbbcaacdddcacaccddbccbcdbcadbdccbbbbaabacaadabbadabdacbbbdcbbbccbcbdcbacdaacccddbbdcaabddbdbcbcdddbcadbbbccdcadaabddacdadabaadcdabccdcacdaaadddadbaadcaaddddabacddbbcbcdaaabbddcbaacbddbbacdbacbbacaddddccdadcdbbdddbdccaccacbbcabbabdaddaadddbadbcbacdccbaadaadbbabdbbbaaccabcdbdcaacadadadbccadcbdccbacbcacdcabacbcdccccabadabccbccaaadcabaddacdbddbbaaccbbddcbcbcacbbdabaacadcdacdabccabcadcdcdccbddcbdbdbcdbabbabadcacbacaadddaaabdadbbabdbbcccabadcabdcaccdccbadcbdbdaddcacabadbbabdbdadccdbccdaccabccdddcdabbbcadcaddddbdacbacbbaccbdbcacabdadbadbacccaadccbdadbaccdbddadaaadbacdacaddbacdadcaaaaddabddadaaaaaadddaacdbaccdaddcaadcbcdcaaacdabccdcabbccddbdcdbdbdbccdbadacbabcdaacbadcccabccbcdbaabcaabcdabbbcbbbcbdcbcdbababbabddddbdcadbbbcdcbaddacdcadacdccdadcbdbdbbddccbbbccbddabccababdbacdcddacbbbcbacbbccbaddcaabdadabbcdaabdbdcdcaacaabcaaabccabbbaaadccacbddccaadcaccbbdbcbcbbbcadccddacbbccbbadcbacdaddabdbaddccadacdbddbdabcbdcabdcaaacadbabadbdabaacbabadcacbdbacacabcabccdddaacaddbcbabddccdabcaddbcabdccaaadccabddbdbbddbdaabacddaaaacdcccaacbaddaadccaccddbcdbcdcbdcabacbdbbdaabdacddacdccccacbdcbdadbddaabbdbbcacadcbdcdaacdcabbabbadcbaadbadbbdbaddcaaadcbdbbddcbdbcaacaaaaaaddbaabdccccaaddaadbbcbcbdcdadbcccdcbcbbcdbbcdbddacccadacbbddacdaddcacacaaaccdbabbccadcccddabbaaaddbcbbbdaaddaaacccbcdaacccdcadaadbdbcbbaabbddbcbaacbbacbccdababcdacaccacadaaacdadcccdbbaadcadbacbcbacbddccdbddbbaacacabdbabadaddcbaddbbbbbbbcaabccbadcdccababbbdabcbaabaabccbcddbaaaddaacccbcdcbaacccdccccbcdadcbbdcbbccdbbcadabaabcddbcbccbbabcbcbddbacdccbbbccdcddcdabdbaaaabcddaddbbaccabbaadbadaddbbcdaddadababcbdcccdbaaaababbccacddbdbbabcacdbcbddbbdbdccadcddbaacbaacbcbbbababbbcdcdacacdaabbdddbadaadbadcbbaaaadbdbbdacddbcddddbabcbdddcdcccabdcdadcdcaacdddcbdaddddccddcccdadbbdbddacdbbddcdaacadcddaacdcdaacdcddbdddcdbcaadaccbabbaabbbadbccdccdacddacbdbccabdcaabbcdbacddabaaaddbadcaabddbddacdcbddadddddacbcacadbbcbadacbabbddddabbbbbcdaacccbacacadbcddbacacadaacddaaadbbcaacddacbccaddaaabbbdaaccabbdcccdcbbcdcbbcadcdabccbdbaacdbbdaddddbbabcbaacaaadacbccacdddbcaabcddcdbdcaddcdaddccacccdcadacadbaccbcbbcacdaaacaccacbadacdcbabbdbbcadbaccdccbdccccdbaaadbcaabadadcdcbcddacaaadcababdcdacbbbcadcaadabacaddcdcdddbcdcadcdcbbcaaadbabcadabbccaaadaddbcaacacbdddcbcaddbddacbccdbcaccddadbcdbbadaaadbaaacdbbdddcaabbbadccaadbadacdcbdacdbccbcdadddccbbdcccbbdcdcaaccadcdbadbccdbdbbabaddddddacdcbaaaadcddcddbadccdbacdbcacbccbcccacdabadacdacdcdbcbbcbbdabbbcccbbcacbddccadccaaacdddacccbaacdadcddbccdccbcaabdcadbbbabdbaaabbbdcadcbabadaadbadbccabdabcaadabaddbabdccdbcababcbadacdacbdbabdccdccdaacbaaaacbabbcccddbdbbdacbbbabdadbaddadadcbcdcbadabbcdddaadacabcbadcddcadcbddbcbbabbdbcddbadacadddbabccaabbcdcccbbcdacddabccbbaddbcdccaaddddadcdbdbacbaddaaccaddbaabbbdcbbcacbbcdccaaadacadbccddabbdccbbbddcbbdadabcbcbaabbaadbabdaccaabdabbcdcacacdccbdbcaadcccbbbcbcabdbcabacaaccccadccdcacccddbdbddaccddbbacbacacadcaddbdddbbcbdbbacbbbdcdcabdbddddbdbdaddacdccccdcdcadbcadbbbdaddcbcdbbbbaaaabdaaacadcbdadbcdcacbcddbdaaccbdbbaadbcdddcdccddbcbbdaacaaccccacccdabcbdacadadabccddcbacaabacacabadbcccbcaadaccbbbdaadccdbdbcadcacadbbaaabdcaccdaaadcccaccbbbadbbcbdcbbcccbacbbbaaaaacabadccacabacddcaabdbabbcabdbdddddbabdcbbaadbcddcbdacbabbdddbabccccbcabaccbcdbcbbbcdbacbbacdadaabddcbbdacaddaadabaddabbddadcaddadcbcbadcdcdbadbdadcdabadcdcbdcbccbabddbbacabcddddaddaaddbabababdacbdacabbaddacbabdbbcaacbbadacddbcbbddbdbacdacbbccadcbccacdccbbaabbcdabccdacddddcaacccdadacddaddcdabdcddbcaabbacbbcacddcccdddaabbbaabcaccaadcaaddcddbbadbdcbdacaabadacaababbdddaaccacdbbbacccbbbacccaaaadbdbcdcbacbbacdcbaacdabbccdbbacbcbaabdabbbabdabcaabdddcacababddacbcbbcadcdbcccddddbabdadbbbbcdbaadccddbddbdaccddabcbdbccbbbacabbbdcbcabbdbbccdaacdbbcdcabaaaccbbbccbaddbbbbdacdcaaccdaabbdccabbddcdbdbdcbcdcdbcddbabbcadabaddbcddbdbcacddcddabdccbddadddaacbbcdabaccbbccbdcacaadacbdadddbbadcccdbcdadacbacadcdcbdabcbdadadbdbdcbaadcabbacdabdddbdccdabcabadbabdbccbbdcbaadadadddabcacacdcbbdacdadccbcbbabbabacdbbbbdccadcccaccadaaadbadbdcadadddacdbcadacbabadbcabdddcaadbddaaaaddccbcabdabddbacbcacbbccaddddabccdcacddccabbbcaacdaacadcdbcdcacbdbddcbdbacdbbbbdddcaddccacbbcadbcbdccbaccbbddaaacacdabbdddbcabdbbdabacdbcdbdadbdbbcdbdabababcdcbaacdaabacbacabdadcbcacddaabdaddababcacbaabaccbbbdcbbaacbdccadbddbddadbbcaddcabdbbbdbbddccadbcacaaaaddbdcbcbddadcdbaddccacaaccadadbddcbcbbcdadbddbcbdbacaadbdacbbcbbdacdccbdaadccacbbabadbbabdbbcadaaabdacbcbbdcbadbdbcdcacadcdbcaccabcbddabadddadbaababbcdadcdbbacabcbdcdbacdbcbbcdcddcacdccbadaabcbbbbcdbbdabaaacbcdcadadbdbdcbdcdcacbdbdbdbacdbcdbcccdcbdbdadbcdbabaccabdababaddbadbbbbdbbbbbaccbdadbcdbadcdaaddbdbabaacccbacbcbbcdddcaaaadcbbccbcaacddabdccddabbcbcddababbadbdacddadbcbabaddacabbcdbbbdbbbdadbddbbbccbdaddcdaddbbcdccaacbbcbdaccdccdbbaacccdbdabbdcadbaddcccdcabacdbdacdbabbdddbabdbcdbddacdcadbbccbabacaddcddaadbbbcabccadddaddbccdbcaaccabdcbcdbddccdbcbbacdcaddabbaccdbaacaabdabbacbbbdabdadcabdbdddabdccddbdbbcaadbcdbccadcbbaacbdcdbcbbdbabbcadcbbcccabcdbbcdcdaabdbccacdacaabcbabaabddaacbaddacabbbbdddbdccbcbbcbaadcdddbddccdaaddaacccdcbcdcdbcdddcabcbcbadcbaadaaabdcddcadbdabacccddaaacbccccbcdbbdbbaabcaaabdbacabccddacdcadbbcdabcbdbccccdcabdbaadabcdacaadcbbdabcbcccbbbcdbcbdbbddbabcdddadccccddcdcbadcbcbcaccaaccaaccaddaacdddaabdacbcabdacdcbaadadabacddcddbcacacdbadccccbabdcbdaccacabdaadadddbcadbdccccccacacdaadaadadcdcabdcadbcbcdacadaadbdcbdcdcdcdaddcdddaddbcacbbcacbadddbacacbcabddadbdaddadbcaddacbaccaacbbcbbabcdcbdcccdaadbadddbbcdcbcccdcaabaccbbcdabdababdcacdabacbcdbbcacdccabbaabccaacdccacbbdcccbdadbabdbacacbdcacabcdcdcabdbcaabaccbdbdbbdaabbbaadbdcdbdadccbbbabbdacccbdadabbdddbdaddccbbaabaadbcabcbdcccbcbacdabbddaddcbcbcbaccccaddcdbddbdaadbbbaaaacbdbbdaabcbbcbaabcaaaccabdaacddccccddcbdcccbcadcbabdcddadcdbcbdbcdcaadbaabdcdbbddcadbabcabbbdaaccadadccccdabdadadaaddbccddadabaaddbcddbbdaacdcdadddaaccaacbcddcbcaadcddcdbdddcaabbccaaabbccababdcdddccbacdabbbdaabbdccacdccacacdbcbdadabcbaadbddcbddaabcdcbabcacdacdbacdddccadaadaadabbbabbdaaccacdabdbcdbdcbccaaabdacddadbbddbbbbaacdabdacabdcbdbaaadacbbcdacadabcdbcbdabdccadbbcddbbaccbcbbabcbcbabddaaaddcdcadbcbcaaaaaaaaaabdccddacbbcbabcacbbbddaacbadacbadcaabbaaadbdddddcdabdbcbcbcbdccddabccacdababbbaddcaddddcdcbbdaadadacbbbdbcdaadacbbcabdccadaacacbcaddacdcaadcbbbabddadcabbbbcbdcaabbbdbbcdaadcababacdadbcccbbbbbacdbbdddcaaccbcbaccabdbbdaaabdddbcdbcbbabacdaacacccbdbbdbadddbaddbddcacdbbcbbacbdddadaaabcaccccbcdcdcaaacaddddddabcccdbcabdddbbaacbcbcacabdbabdbababdbbbcddacbdcbbabcbdcacddcaabaddadacbddacbddabbcccbddaabcbdcbacdddddabbabcaacaadbdbdcdbadbdbadabcddcbaacbaaadadccccbcdcbacaadbdcbbdacbaddaacbdcacadcddbbbaacadcdaaabcdadcbbacacdacbcadbccccdaccdbdcdbadbabadcacbdbadacbccabbacddccdbbcaacacaabadabbbacbbaabbabdacdbabbacddabaabacccdddcbcbaabbdbdccdadacdbbccdddcbddcabcbbdbccbccdbcdddbdacadcbaacacbdbdbaabdbbccdcadccdbadbcbbdbdbaddbdcabbadbadcbbaacabdbccbbdbdabdcaaadaddaaacaddbdcdbccbcdaccbdbaccdccbcdcbdccbaacbbcbadcabbdbaabcdbcdadccddcddcbdcacddabbacdbddcbcacbbcaddbcdaacaccdbabaccbdabadbbbadaaccccbbbbadcbbabcdcccbccacbdcddcbacccbdcbacddabacabaacddcbddbaabbababaadccaaabbbadaddabdddbacaaabadabdadaabdddcbbccdcaacddbaabbaaadddbbcddcbddbaccbbddcdaccccbcdccbadbaaabdcaccbabcbdbdbddaabdbccadbaacacbdaccbacdddccacadddacccbcbbaadaddcacdacdacbcdcdcadacdbdcbcdcacbaccbadbdccdadabcccbcccacadbdcdacacddbbababbdaaadadabbdabadabccddabbbbcdccacaabcbabddaacaccbdadcacdbaaabcbcbbccaabbcadabbabbcadabcdcbbaaacaaaccababddadbbbcbddccdabccaabcbbccacbadbbbbcdacbbcabadcbabdcaabbdccabbbccaccababccadabdcacdbbadadccccbdbacdbbdaccbdcdaddcacbbabdbcdadabdaccbbbdbcdabcaaabacddbbadddadaadadadbadbcdbabcbabaddbcccdccdacbacbcbbcbbbddbadabbabdbdccdbdbbddcacbcdcdcdcdbdbcabbbcdbbcaaadbcadabdabddcaabacdadcbdcaadadccccddbcaaabacdcccaabdbbadbcbbccacbbbdaddccaddccbaacddbcdabbdabbbcbcadbccdbcccbbaccaaddabadcbaaadbacbbdddcdbaadbbcbbcbcabdbdcbadcbbdbddbacdacaabbbdddadabbdaacabcaaadaacacaabdcdbcbccbccdaacdbcccaaccacbbbbadcabdccbcdccacacdbdbdcacaabcbdbcaabbbaacbbdddcbdbbccddacaaababaccbcdbaabdcbbcadcddcaccbdddadccbacaacbdbcbacccdbacdaddbbcabbbcdaabdadccddabbdaacbadbaadddadacbcdcdabdbcbddcccadcaacacbacaabcbbbadcbcabdccbaddbdbbccbbbadcdcababaabcbbdcccacdbbbacdaddabbdbbacbddbacbcdbcddbbdabcccddbbaabcabacdabbacdabcccaccaabcdcacabbacbacbbacdadcdacbccacbabbbcdbadbcacaabbcdcdcddcddabadbadbaaacdddcbbcbbbcdabdcdcabbdbabdbaabccaacbbccbbdccaddacacabccadddcbbdbdcacbccbddabbdccccabbabbcddaabcaacccbbdbdddbacbccadababbdacbccabdccadcbadbbcaabcaddcbabaaccbcdaabdcbdcdbdababcdcbddddddcbcbddbbbaaaaaaddcaadcbbdaabbbccdbdacbddaabbcacbabacddacabcabcadaaadbaadcbbbdcbdccdddaadcccadcbbbbadaaccbbcbbaaabcaadaadbdccbdacaddccaabadccdcdcdcbbadbbaacbacbdddbdaabdadcbcbacdddbbbdabacdacaccaaddabacbdacbbddabbcabdcadccacbabdbacddcdababbaaaacbdababbbcbaadbdbaaabaacccbcbcbabdadbdddbbbabdaccccccbadddcdadababcdaacacabbcdccbbaaadcbbadbbaaddaacdbdaccbbcccddddbbacbdccbdaabbdbccdaacabccadbadaacaaddbbdbdddbbdadcdcbaccdcacacccdbccdbaddddbdcbbbbdaacbaacdbdadbdaaacaaadbbcddccbccbaadcdcddacdaaabcbaccbddbbbacbadababdacdcdadddcbabcacdbcbcaabcabbacdabaacbccadbbdcdacdcbbabbccbcdbccbcdddacdbcbdadbdcdcbdcccbddbccbddccdbbccbbaacbdbdddaaababbccdbaacddbbccacbadaccdcdbcacbdddbaaaddaacaacccdbbabaaadaadacbdddbdabcbcbaacbcdacdccaaaaccbbaadcbbdbccdbcbbbbcbbaadacbaadcbddaddbcbbbbcbdaccacbbdccdbabccccdbdcbdbcdacdbbcbcacdabacbbdddbbabbaddbbccaaadccaadcacccdadcdcadadaadaacdbaabddbddcaddaaddaacbddccbbddbdacadabbcaadddbcdcbaddbbccccaccdcbdacdaaadbbcacccbbccacdccbcadaacbbdbbdcbcaadcbcddbcbabdcbcadbccddbdbbccdbddacdcbbcaddccccbddbbbcbcbdcddadbbddccadbacbdbaabdabbdcbabcccbaccaacbcabcdaccdcbcabdbcdbdabbbcaabdaccbcadacbbbacbdcbddddadcbadbbddcccabdbbdbbdbbbaaababdccdccaacbbbdcaacccbaabcacbaaaacbdadcbdbcbccdacacbddcbbabcddcbdbababbbdcbbcdbcccdabaabbbdcdbaadbadcaccbcbcadddcaccccdcaaabcacbaaabcdbdcccdbdbbcaadabdcbdbccabcbbcaadcacaaacbbbcbaacacadbbcabdddddaccddaccdcbdcdbcadaddadcbbbccbdccbbbcdacdccddbdadaaabddccabbddbccddabcbcdbbdbbadbaabaabdaabcababacccdddaababcbaaababbbccccaabbddbdcdcdccaddababccddabdcaaabbdbdacbddbddabacaadadcabbaababdadbdcdbacabdaddcdaabaabdaacaddcdacbaadbdccaabccccbabacdbabbddbdcccabccaadadabbbabddccbabcbcacbbcdcdcbbcdaabbacbdacbacdcdddbbbbdcdcbbbbcaadbcbdbcdadcacccddacbcaaddbaaddcdbadbdacbcbdacccbddacdbbdbccaacabdcaaccbcdaddcbabddcadaccddaddcbcdbcbddacbddaaaadacdadccacdcbadcdddcccadbcbbbacaabdcdbabcccaacbabccdbdddcaaabdaaaabbaabcaabddbbaaadbccdcadbcbdbcbbbaacbabbcabbdabadbcbaaababaccaacabdbcababbbbdcdbcbbacaddddaabdcacddcabdbdddcdbadaddcdbaabdbccdbaadbbbdbdabdaacccdcaadcdcacbcacbcdbcbcdcdcdccbcdaaddaadcbdcccadcddaccddcdbbbdadddcadaacdccbbbadcbadaaadccabdcbaccdcbcaabbabbdddbdccaccdbddbaaaddaddadcbcdcaaaccbbdbaacbadbbdbaddddddaaabcdccbbdccdcbcdccdbbaaabaabcaccadaaacbbacbcbbcacaabadabacdcacabcdcddccabdcaaacacaabbbbdacabcdccdbccabbabdbadbabcabdbccdbacbcabccaabacabadcddacabddcabaccadbbcaadaaabbdcbaabddccaccdbdccbbadabbbacaaabdaaadacdcbabdbdbdcbadadccbdaaaabaaadacaacbbaaadacddaadbbdaabaabbccadddbdccdaabbacbababcdbbdcacbcadacacabddbdccabacdaaacdbdbabbbccacacaabbcaadabadacabbcadacbcdcdcdccbabdddccabacbcdbdcdbcdaddcddcbbbcdcadbcddbaababbabdbbcbbdcddddcccbdcabdcbacbdcbdddaabbbacacdbbbaaccadaadaabbcdaaabcabbbabdbddbcbabcbdbaadbdcbbddbbaacdadddcdbcdcaaaaaaadcabadacacbcbbbbdcacbaaabbdcbadcbaabadcddaabbadcdbcdbacabbbdbdcbadddaabccdabbbbbacbdabadcaddcbbbdddcdaaacbbdcaadbdadadacdddddbcbcdcbabacbccdcddadadbbaabbdccbbddadbddabcaddcaccaaaacdccbabbdbccdbdadcaaadcabbbdababdacadaddbdaacadcbccaadcbccdadaaabbabbaaabcddcadccababbacbcaccbcacabccaccaddddbddadbccbbcbbcacbdbdaaacbabadbdbcccccacbaccbdcbbabddbaccaabdacacdbbdbacbddababbaaabbbccdcdbabccbbcccbdcaacbbccbdbacbdbcbadddbdddadaadbbacdbadddacbdaacbddaaabbdbbcbcbbaaacacddccbbdcccadbbddacdadbbaacbcdbdacaddccdccdcdddbcbcabadcaacbaddcdacbabacbbcbdadbadccbcbbbbcbbdcccadcadcddbdaccacaacdccbbabbdccaaaadabacadccdaabbbadcbbcadccaabadacbacdccaccaacaaacaacbccbacdbaddccddcddbdabcdbbcabcdbbbcbadabcbbdbbabadabbcacccdaccdaccdaccbcabccabbadbbadcdacbbcabbbddcaadbdaabadbcadbcbbacbbabbbbdcdabbaccbbbaaacddbcddccbcdcdadabbaaacaadcdccdaabdabadadcdcabcabdccadadaccddacdbddcbdacaaddadccabacbdacbccbbcdcaacdcdbdadddddbcddddcabdbcdbcacbaadbaccadbbcddabcdabcbdaabcdbdcadaddbbdbccaababdbabbdcabacccddcdbbdcabaaddcdaddbbcdbdddbcacdadbacdaabdabdbbbbabadcacddbcaacabbdbcdbcbcbbaaacadabdacddaccacbbbcbdbcddbbdabadbacddbcadbaddbbdbdbcaddcbddabadaabbccdbcbabbccccdabacaabbacbadbabddaacaccdabbbcbaabbddcbdacabcccbdaccabbadbaabcbbcddbdcdbbddaadbbbdcadbbcbbacbdbdbbacbdcaaacdcaddaaabcdccbacdbdbbccdcdbbdadacbbddddcbcaacbbccddcbddabdaacacaacdddbbaddbddcacdacdacaabcdcabbdbdabaaacbdccccdadbdabbdbbcbbacacddabdccadacbccdbdabbcbcadacddaccbcdbcbbbaaddbcbbbaacdbcdcabaadcacdadcaaccbadadccbaabdbcdbacabadcddbdaddcdadbdccbddaaabbdbbbccdbdbdababcadcdbadddbdabbcdbddabbddbaacccdaadddddddabadaacababbabaccbcaacbbbcbaadbcdbcddaddbaadbbbadadcbbaccbabccbbbbabddcacadcaaddaddddbabdabaadacaaadadccbdcaaaccbacaabbbacbdadbadacabbacbbbbadbdbacdbcdbbdcbacbdbcacacddbaaabadadcdacaddccababddbdccdbabdbabccdaabaccbdccadadbcbcaaaacacddaabdcdabcbbacdccbabaddabccabccdaadbaaaadbaabaacccbbdcacdcbdadcdabaccdaabdacabccaddbbaddcabdbcbbdaaaabbcabaaaddaadbbcaadbacaabcaddcaddadaadbcbcdbabdaadcdcadaddcbbbdcabcaddbacbabcdbcacbdaccaaabbadadaacbddcddabadbabdbcbabdccbacdaaadabccbccddbdcbcabddbbcbcdaddddcaabdcbbbbdbdadccddbabcdcbccaadaabbdbadbdadddcbbdaadbadcacaaaaadadbddcddbbaddbacdcacaccbdabcacbcaaabcacbacbbbadbcaabbbccabccbcbbbcdaddccbcaacabbabbdadccabdaadbdbcdaadaaaaddbccdbbdacababcddabcdbbdcdbddcdbbbbccccbabacbbcbdddabadadaccbabaabdbbcbdbcaabbccaccdbbaadaddbdbbccadacaabbbadbcabdbadbccbaccadbdbccadbbbacdccccadaddbdbbdaccabcddcadbdccadbbdacadadcaabbbdbcacddbdcdaaacbadacddbcbddcbababccdbaadabdadbbdbcdaddccdabbabcddbadcdadaaaddccaccbababaddacccaaacdcdddacdcadddcccadaaacdcacacccbdbbbbaadacaadcdaadcdabbadabdadbbbdbbabdbcddccacacaabdbcacadaadcbdbabdacddbbddcdaacadacaccaaabdcdbacaacbaacacddddddcbbadbbbcadbdabdbdabdcdbaaaaadcdadabbddccbbcbddddddbbacabccacbacadccdcdccccaacbbacbcbdbdcbbdbbaadddbdadaccccaaacbdbcdbccddcaddcddbabcadbdcbcccabcbacdacccadddacbbaccdbadcbaabbababcdcaaaadcddbdbbaadccbabcababdbdaacaacddcacdbcaacbadccabacaadcbbcddabdabdbadbccbadcaddabadcbdbaddaadddcdddaacdbbdcbdbbababcadcadbcdcdbcacbdbdadbabdaabadcdbdaadababaaccaddaaaabdaaddaaaadacdbbdcaadcabadcbbbbbcdaabdadddcdcaddadbcbababacaccdbabcbcbadcababbbcaddacaadbbcaccccddccdbcaacbbdacdbadbbacacbbccadcabaadccdadbddddaccdbacbadabbcbcbaaacddbbbbbacbcbccaacaccdcaddacccdccaccdccdabcabacaabababdbabbdadddabbadccdacccaccaddabbdccabdbbccabdbbcaaccadddcdaadddddabaccbdabdbbbddcccdcdbcdddaaddcadcbddbabcdbbcbcdbcccbdbaddabbabcbcadbabbdabcadccadcacaddbabbcabbbbaabdbabbadcaaabdcdbcabadbacccbacdcdbdcbaadbdaacccabaaacabbdabdbbccbcaaccccdbaadcbddaadccbddbccbdbcdcacdaaadbadbabbdaacadbcbcbcdbbaaddacabbccbbabdbadbaacaaaacbddbadaabcdcbcdbdadcbcacdabdbbcbddbccdaacbdcbaacaaadcadbcdbabbcdcbdcadbcdcacacbdbdbbcbccaaddccbbbabbccaabdbdcbbbbbdcdcbbacbaccbaabbacaabddbbdcdbcbaccccdbcddabcddccdaabbcadbdabbdbadcacacdcdccbddaaccbdaaadbcbccaaccdadcdbdcbcacbdacdaadcdbbbdaddddabbbcadcbdcaccbadbaccccccbbdcadbcadbaadccabdcddbbbaddccabcacabadcbcbdabdbcdbbadccbddaddabdacdbdbadaabcacdadbcacddcbcbbbdcdbddcbababbdcddabdddbbdcbabaabdacdbdbdcccbdcdaaddbbabbbccbcdcbcbabbaaaadcadcadbcbcdcbbdacbadbcbabcddcddccabbdaaadbcbbccdcdcdacbddcabdcbabaabbcdadcdaacbccaaabbcabcadccbdcaccddbaddbcccdddbbcdbbccbdcbdbdcaccbcdacaaababdbaacddacdaddbcbdcaabbaaaacdbbabccabadddbabbbbabbacacbdddbcccdbabcdacbaacaacadabcbbdabbbbbaaccbaabdbcbaadabdacbdccbacdbdbdcbbadabcaabbadcdcbdbacdcadacdcdaabaccacccbbdacaacbaaabccbddaccdcdccbadacacadbabaaddbabccbbbabbcdbccbccddabdbdbcacabbdcbdbcbbcaccabdabdaabacdcacccadcccadadabcdbcbabdcdababcbdcaccaababbbbbacbcddbabbcdcdaccdbccdabcbddcbbdbcadccadcbddcadbcaaaaabdbdadbcdcdcdccdccdaabdaabcccdbccdaddbbddacbbbacadbadcaaccccbcbabcdacabacdaccaacbbabdbbdcbcbbabccbdccdaccbddbccdcacbdcaabaaccabcdbabdcbbbdbbabbdcaacbcadbabcacbccbbaadabccdcccadacdddadccdacccaabdbbddacccdddabdadcabacacabcdacdcadadbbccbdcbabddbbaaabcbddaabdbbcbccbbcdbbccacababbddccadbdcbbdddcddddaddddcbdddbccdddbdbabdabaacccdabacdddcdabbabdbadbcddadbdcdccbaadbcaaacaabcdcbaadcdaddcaabbaddccdbcbacddbcccccacdabccaaccbdabbbddbaaacadcdddcacbbddabaaabbcdbdbcdbdcbabcbaabcadbdababdaacdcdccacdbabbbaddcbcbdcabdddddcacacbccaacabbacdbcaadadcbbdcadcbddbdabcccdbcdbcccabbbccdadbbdbbacdcdaacabdbbcacddcacbbbbdbabaadddddacddbbadacadadcdcdcdcdaccbcdbadccbdbdddcbddbacbcdbbbcadddbaacbabbcaaacdaddddacbacdababdcdababaccddddcbadbbabccadbdbacaddbbddcddccbbcdaccbbdbbddaacaaaacbcdbadcbdcdcaaaadcbbaacbabdaabdaabdbcbcdcbcddaddbbccbaadcccaabbacbbaccacbddbbbbccdccddadacdbbcacbabbdcdccabdaabdbbaabddadadacbcadcddabdcaaccdbacdacacabcacbbccaacccdbbbaaaaabadadabbdbacabaccaaccdacbbadbdaabcabcdccadddccbbbcbaccacbabccdbbbaacacdbaabbbaabaaccbaaaacabbaccbdcbbbbddaabadcddddcdaaacbcccabaaccabbdbbdaddadcaabdbbadbacabbdccbbcacdbcbdadaadacdaabcbdbcccdbcabcbcadbdccaccbbbbddcddbbbcabdccbcbbdadaaabdacdababddaddbaaadbbdcabbdcdccaadcaababbbddbdbcadcdcdadcababdcdbbbdddbaababdcbcdbbbdccdcbabbcbbcccddacdddaaaaaabbcdccdcdbadcdcaaabdddbcacabddadcbdbacbadbddbbbacbbadacdcbcccbcadcdddadbaadcbbaacbdabdbbcbdcdbddadcbacbdbaaabdcdabbcdbcdcddccddababcababdddddcbadbdaddcbbccbadbccbbccacbacbccbdadcdbcaacbcbcdadbaaacccdbdcabbacacdaacacccaacbbddbbbdcdaacaaaaccaccbbbdaccdacddbdcaacadadcbbdcbcdabaacbcdabbabccbadccadbdaaabaaadadbdccabaacccbcbaabdacbacbaccbddddadacadcdddddcacadbcbaaacadbbcddcdbcabcbbddcbbaacdabadcacbcccdaaacdabaabdddcdbbaddabbabccdaaccbabddaadbbccdbbacbdbdcbdcbbcdbbccbaabdacadaabacdabaccbdabdaabddbaddaaacbccbbacbcccdbccadccddbbcbbbcccadcdbabbaccdabcbaccbdababcdbddbddccbabbabcdddcadabcdaddbaadbacabddbdbdccbbcaddadcddacadcaddddbdbbabcbadaabacbbbdbbabbdcaddbabcaabcbbdbcbbcabadccababacbacaacdbcaccbcbdbbcbbdaddddbaccdccbacbbcabaddacbddcacbdddddcababaababadaccbccddbdcabbdacccacdcccbbadddcdccdaacabbcbddddababddbaaadcacaacccddaacbcddadbaccdaabdbbdbdccccbabbacbbcadcbdbdccddcbcbcbbbbccbcaccddccabadadbcaaabddadcdcdddbcccbadabbadcadaabdddcbdbccdcaabaddabccabdddabcbaddcddcdbbabdbbbdbbdccbdbaaadccdbadbccaccbcacaaaaabcccabdacbcdcdbcdccccdcdbbdbaabcbaacdcabcbacbaaadacdcccddabacacdbabccbddbdcddbdadcdbababbdaaacabdbbbbbcaddbbbdacaaddacbdddaddbbbbbcdbdbdcacbdacbbdddaabcacadcbadabddcdcbabccaabdbbccccdbdbbcbbdddbbbccdaaaadbdcdaccdcdcdccbcbbaaaabbccbaabcbcccddcdaaaccbadabbdcbaccdacaabaaaaadddccdbaaadbadcacabdaaacbadadcccbdbbbdcbdaacdcbbcdcabaccbcdbdccbdabdacdbadadbcaaadbaacbabcdcacdbabdacddbbbdbbbccacbdcddaadbddcadcdbbccdbcacdacadbbdcacdcdcadadbccbdccaaaabddadacbccccacddcccccccadacacbbbbccbbcddbbdcbaabadacccaabadadadbddadbabbadacdcbaddcbacbdacccaabcdacaddbbaccadcbbacacadbdbdbadaabdabbcdaddbbacdccacbadaccdaabcbbabcdcdadaabbbcbacacaddcdbcbadabbbcadddcbcacccbdbcadbcbcccdcadbbdbbbcdbddcdcddcbdccdadcbdbbaadbcbbacddadadadccabacbacaccbcbdbdaaccbbbcbdbabaaaddcaddacabccdbbaddbbaacdbbadbdddbadcdbcaadccaddcbcaccadbccbdbddabbbcdcbddbbbbbadacccaadcadcdbcabccababbdbcdccbcbaabddccbdddcbcabcdaacbabadcaacabdcadbdcbdcabbababddaddbcbdccbcaaadaaadbbccdbcbdcaacaaccabdcacadbbaacdadbabcacadddbdbbaacbbdacaabbacdddbdbddbbdacdbcdcccdcbcccabdbccaabbdaadbacccacbadadaacaadccdbbcabcbdbcaccadcdcadbdcdbbccaaccdaadaaaccbcadcdbddcaabdabacccccaadcaddbabacbdcaacdcdbbcdbcadbdcbcbacbcadbcbaacdcdbcaccdacddadcbccbbabacacdcbbabdabcdcddbaaaacccbabbcdadcbdccdccbddcbcbcaaccccacbdccdcacbccbdbcbcbaacacabacaacdbadbdcacbcbcaaaabbbdadbbbdaddddcdcdccbaaacdbaaddcdbbaaddcbabaaaacabbadccddbababcaacbbbdbbbbbabdcdbacdadddbbdcadbbdddaaabdbaacddacdbaabaddcbcabddabcbdcbcbacdbbabcbcbdcdbaccaabaaacdcdcaacabddcddadcbaaccccadadbdbbbcdbcbbadddaadbadbdaddcabdcccbbdbbbbbadcddbddcbaadbabbbbaadbcabbcabdccdbddcccbddccdababcbcababbcaaacdcacbbcdbbddbbdadbdbcbbbbabbcdaaddbabcbcbbdccabcdbcdccdcbdbbbbdcaccaddcbdddbddcaaaadcacbdabbdbdbaabdaaadabbdbbddbcaaddcbabccdbadabbcadacbaacaacabacbcdacdbadbcdcaccddadccaadddbadaccccabadbdcbdbddaadcbadaddcdbbabdddccbbacbddcbdbcddcaabbbcaadbabdbbadbdcbbdacbabccabdbabdbbbaacbcabbbaabaaaaaccbdbaabdabacdbbcdbccdbbbdbaabdbaccbcabacacbcbdcadbacaaccacacabbdcdcdccbabdbdadadcaaddaddbabaadbbddccbccbbbdacaaadcccadddabbdcbdacddbdaacbcdcbdddbbdbaaadccdaabdccccabcdcbbabcaaadbdadddabdbbcababddbabadbbdabaccbcadbaddabbbccaadcdadbddababdaabbdbbacadcabdbdcdcacdacaaaaaabacabbbbdadcacaaddaacabbcadbbdabcbaccabbcbbdacabbdadcdacccdabadcadcbccaacdcbabbbbacbabbdddcdaaddaabdbacdccdadcdddbbbdcbddaddbdadccddbbbdadbabaacbbdababbbdabbccacdaddbcbccdbadadbabbbdbccbdaaddabcbdadcbbdcdcbaddbccdcdbbdabccabdadcdcdddaadaabacabdcdccbcdcdbdcdacbbcdbabcdbbaccbdddddcdbdcadaaacdcaaadddadcabaadacbcdcbbdbaabdabbcbdcbddccadcddddaacadaaaacbacabcaccaaadccdadaddccbbcdccabcaabbcdaabbaadcacaacccbcdbdabaadaaacbbcbdddacacacbdcdadddcbdadaaabdaacdbcdabacaddddcbdcdcdaddadabbaddbcabcbcbaabbcacbbddcadbaaabbbaabbdabdabcdababadaddacddaacacababbcacbcbaabbaaddaabbaababbbaccdadbbddbcadddacccddbabadbbaccdabbbdadccabcdabacddacbdcbbadabcdabaaccdbcccbababaabaabcbcbdbdadbabdabcbbabaaddcdccddbacdbcabdacdcbbabbccbcadbcccdadbadcbdbdcbdcdaccdabaabaadbdbbccaadacbabdaacaccadbcdbccbcdbaccbbaddadaadcbcbbdbdcaccbbbdbbccaacdbdbbcccdacbcbdbddbacccdbbdcbbccbcbcdadacaddddcacccaaadaddadddcbabcbdaaaddcabaabbbccacabcddbcdacdccccdbcacbababbdadabbdbdadcdbddcddcdbaabdaacbbcacbbbcacacaabcadaddbcbaddccdbcbdbcdbaaacbdcdbaaadcabdccababababccacabcddddbccbdccaadcbddaaadbdcdabdbbdabbddddcbdaacdabbcbaaabacaccdbbddacbdcccaccccacadbdaccaccbabbdaaddadacbacdadababccccddcbaddbcadacbdccbcbdccdbaccccadbdaababbddadccadaccbadcdaacccdbcdbdacddccabadaadcbbddaddcbadcacccadcaadbadbaabdcaabbddcddbbccaadbcabaadbabccdbaaacbdcaaddbbbdcabdabbbaadacbdbaacbdaadcaaccddabdbdbbbadacadbdbadabddadddbbdcdbcbbaccbabcccbcaaddaabdabdbdbcccbbbabdbbdacbbccbccaabdccbcdcbccddaaacdbdbcbabbcacdbcabdbdbacbabacbdbabcbbcccbcbbbaaccaaabbbacbbaadacacddbddcaabacbdbaccaabcdcdbcbdcbcbacdcadadcabcdbdbadbcadbcabbcbcbdaddbcdcdbbccccbbcccccbcdddbdcacaadccbbacabccbabbdcddcbcaabdddcdacbdcdccdcacbcabadccbbcddabcbbacaccabacdddcddaaababdacdaddcaacbbdccccbddbbcacaddaacccddcbcdbccdbdddcbdbddbdbcacbcdcabdbacdacdcdbacacdadcadabcbacbaacbdbbadbbacbdabcabdbdaabbddcbbdcbdbdabdcabaacaccccccbbdacddddcbbcaccdcabcddddaabbdcaaddacdaadcbcbcbcaaadabddbaabcbcaaaccbccddcdabcaaadaacacdcddaadddadbbbdacbabcdcbcddcbdbdccbacacabaabbcdcadadccabacbacdbcdbbcabaabdcddddcbbbbcccbbbadacbbacbccbadacbbabbbdabbdacdacacacdbdaaabdaabaadabbabbbccacabbbcabcbdcadabccadabacabacdbcaddabadcacadadcbaacdcbbcbabcaaaccbacbccddccabcadddbbaabbdbacddacddacadbcdbadccbbbacdbabbcadaaaabacdbbaacdabacddbaabcdbcdddbdbdaadcbddbacbbccadbbccacccdcadcbcadbcbdcdaadbdbbbadaadbbacbcbadbbbabccacccacbaacacddbacccbbcabcdbcabbbcadbccdabaccdbdccaadbdacacdddddacbdababaabbcacacbccaacadbadcdbccbacabccacbbadbdabacdcbbcbacdadbcbbcbabbdcbaddaddbdccbdacbccbdccadbccbbcdccbbaaccbcdbccdddcccccaccdddcdbbcacdabaabddcbccdbdccabdadbaacdccbbbcdbcbbbabbdbbcacadbbaccccbaddddbcccadcbadabbddaaccaaabbcaacacbaabdcbbacabbbddbdbbcdcdcdacabdcdbaacbdcddbdccbcbabaccabbcdaaacdddccacccbdccacdcadcddbddcdadabdcaadcdddbbddddcbcccbbdbcbcbadcdbbbdcbbdddccadaacbcabcdbdddccdcdbdcdbaddbbaddcacbbcabccbcbddcdccdcdcaccbccccbdaaacdabdccabcbbadbbdabaacbcbacabacaaadababbbdcacbcacabdccabccdbadccadbcdcadacbbcdccababdbbabbddacbccbaacdbdaababcbadbdcbbaddddacadabcdacaccadacdcddcdbcabbabbcadcbdbdcbdcccdacbdbaacbbbaaacacdbcadcabadcbddcacbccccccbbcbbdabddcdbcdacddcccaabdcbddababddabaaaddbaacbdcdbaddacaaddcaaabdcbdcabbcaccdaacabbabcbcdbaccccbddcccacccabaacbcbbaaaadddcdabadabddcdbcadbbabddcccacdbadcacbdaaacbbcdaccbbdcddadcaddcbbdaadaabdacbcbacbbaaaaabacddbcbdbdadacadbccccbcbdbaccccdaabdaabdddddaacbbbaaacdabbdcbbbaaacdaccbbbadbaabbccdaaabbdabadcadbdabbddccacacccabacaddcdbaaabbdabacbbdbabcbacdabbbccbcbcacaddcaaadaacaadddddacdccbcddaaadcadaaddacbcdbcdddcdccddcbbabdaddcadcdccdccdddcdbdaababdacdccbbcacdcdbaaacdbadcddbadddbcdcbadcbdcbaacbccccaccacbdcbbbabbbcaccbcbbbcddbbdadbdabdbdcdaadcccbbadbcbaddbdaddadcbdcccbbcbccdbdacabadbdcbabdbccbcabbcbaaaacccababbcadcccbbbacbcacaabbaaccdadacabdabbaadaabbddddddbdacdbbdbabdacabadaadcbcbcccacdcbadcdcbbbbbcdadddcbababddbacaccaabcbbddbacbbadbdbdababcdabbccbcdbdddccdadcccaaabbacbabbacdbdaadbcbdabcbacdbbbadaacacddcccbbdacdcddbcbddbacccbcbdcdddbbbbddcdcbdbbcbbabddaadcdcabcdbdcbadcbdcbdbbdccdccbcdcbcaddbbdcbabddabbbcaababcdbdbdbbacacadabdbabcbdabcbaabcdbdbbccbddcbbbabddcbaaaddcbccddbaacdcbdccaadaacddaabcdbaacbadcbbbddadddadadacadcccbbbdcbbdbddabadcbabccdbdcdabaabcabbdddbcbbaaadbccddbddabbcbabdaaddbbcaaccdbdccbbdccbabdcccdaddccdcdbbcdccbddabbacbcdbcaddbcaccdabcbccacabbdbaaaaadddbaadadbbdbcbbbdcbadacaabaabbbdbbdabdccdaccbdabbbacbccaddccbdddabccbcdcadbaaddabcacaaccabbddccdcddbbcdbbaacabadadabcaaacdadbdadddcdacdadbacdaddcbbacdddbbbdbcabbdadcbdbccacdaadabbbabcaddbaabddbdcbacabacddbacccadabddbdcadbddcabbaccdabdbabbdcddbaadbddccabbacababbcdabcdcccacbdbaccccdbbabaadaddccbaccddddcbadcdaccbdcccbccabdccabadbdcccbcaabcccddbacbbdbccdabadbccbaaadccababdcaaadbacccdcbcaabddcdadbabbccbccdcaaadbabbbcccacaaaaacadcccdbaaabdadbdabdcbdcdabbcadbdacabcaadcbdccaacdccdcdacaddadacabdccabadcddbdccbdcccabbdaadbccbcacdbdbccbaccabbcdaadccdbccddbddadabcdaabbacdcaaadccbacdbcccabddadabcaacdcbcddbcbbbdaddaaddcadbadabbaadaddccddabdbdccacdbccadddbdbbbdccdddacaccdabacccbbbadacdbacbaacacaadbaddacabcabacaccadacbcddadcccaaccbcbbbbcaccdbacddbdbacaccaabbcabbdbcdacaaaaadbddbbdcaacbbacccbddbbdbcdaacbbbccacdabbdbbcdcccadbdbdddbabcacaacbdbccacaaabdbaadaacbcdbdcbdccbaabcbdabaaadddcbdadbddacbbddadbabcdbdccccbcbbaabbdddbbddbaccbcadcdddddccbdaacccccddadcbbddcddcababbcadadacacbcdacdadccbadbcadaadcabacaabbccddbacabcddacabdadddbbbabacdbcbcbbbbdcabadbddbddccdaccaaacccadddddadbbaacabcadaabcccdbdacdccdbbbabcbabacbdabdbabcdccadbbdbcddccbddbdddbbdddbaaddaabcddbaadcdadcbbdacacbaadddaccadddbabaadcbcaaadacbacbcaaccbdcbccdbababccdbadbcbcadaddccacddbabdcbadaddabbdcccddddaacadcaabcabaaadbcadaaacaaacbdadbdbaacbbaabddaccabbdbdcbabdbbdcccbbcbbbddcdadbcaddabbccadcbccbdaabbdddadadaabccbbabaaaccaacabacabdbcabdccdcdcbccccdcbdccaddcbcaccbccbdcadbdaadcacabacdbcacadbdbcdabdbcdcbacaccbdcabbadacddaacabbacacbbbaacbccaababaaddbcdcaccdadbabbcaadccdccdabbdcbccbbaabbdaaccdaccddddccbcdbbddccbacaacddabcadbabdcbcbacbddaabbaabcabbbbaccbdabccddadbaaaabdddcaaaaacddbddcbdbbacaccacddbdabbcdacbdbabcccdccbaabdddacdcbddddabdcaccdcbbcdacabaaacddcbcadbbdadcabcdbbabcaacbdbcbdbaccddddbcbabbbbaaaccdbbbdabccbdcbdaaccaabcccaaddbacacaaccbbbdddcaacdccddcdabddbaacaaccaabdabbbcacddadcddccbcabccacaabdbadabcbadbdabcacbacadacdadadcddadaacbaadccbccbbcbaaaddcaacbcbcddddabaccabbaadbbdcbabcadcdadaadacdcacaccdbabddcaadabbdacacabdccddbdbadddabdccaddbbdbcadcbbaabdbcaaacccddbbbbbdacaaadabcbbabcbaadbadcdaaddbdaccaacdadbddbabbbcaacadabbccbadadaddcdccbababcbdadcddcadddcacdcdbbbacbdcaddbbbacaadbcdddbdacabddcabbcadbdddcacbbbaacdbaddccbbdcbabbdacddcccbdcbadcddcaaccababbbcbccacbbdbaacaccaadccacdcddbddcaadbcacbbdcbcbcccdabcbadcbbcdbcddcdcdcccbbbaccdaccbcbbbdcbcabbcaabaadbabdacddcacdacacbbcbdbdbaddcbdccbbbadbbaabbdaacdbacdddacadbddaadbacbaccddaabdddcaddcabcacadacccbbabbcdbadcadbacbadaddcbdabbbccdcabadbadacbbdcaccadabddabbadcbbddadaadacdbdbccbbaaccbdabcabbabaabddaacdddbdacabdbabadbcddabcacaabcbbacadccbccabccdbadbaddaacdbadbdccdbacaabbcabddaaaadcabaaabcacaccdccacdcbbdaaaacbbcbadabdacdcdbbdabbdbdaaabaadcbdbacdcaccbadacacbcdbadaddababbdcacaaabccbdcdaabacaccaaadcadcaaddccadbbcaccdbdcbbddacdbbbcddaccccccddcdbdccaccccdddddcaddcabcbaabaaaaccaaadcdccaadcccadaabbccbbcdaacccdcccdbbbadbbbbdabaabcdcbdabccabcdddccdcdabcccbbbbabbcbabcacaaadbdcdbaaacabbdadcccacbbacddaabbdacdbaaabdcdcccadccacacbcbbbaaddaaabdabcbcaccabadbbbcccbabbcaacaacdabcbddcabaaccadbcbbdccddcbaddcdbbdddbacbdcaaccadadbcbbdbaaacbdadabddcdbbbccababadabbcbccbccadbdaccbaddddcbdadaaccbbcbcadabdddcbaadacddabcdddadcddbbdadcadacccdbbcaabbdaadccbdbccacdcdccaddcdaaaaadbaccbcbabbdddabcdacccacacbcacccbdbcdbabbcddcdbcbcacaddaccadddcaadccbdcacbcbccdcbdddcddcdbdabcbacacbdbcccbbccdcdddadbdbbbaadadcdcdcdbddadbcbdcadbaaddddcbdacbdadadbdbaddcbbbcacaaacabbbcadbcdbcccabcaaacdcbbabdcbccadbbdaddbcadcabadcbddbcabababdacdcdadaabadacababacdaacbbdacbababbacccddaaddadababcdbaddaccbbabdacddbcddbcbaadbabacddddadadbcddbbbddcbbdbdbdacbdbcbacaabacaabbcbcdcaaaabccadcdbbbabbcaccbbccaccacabbdcccbaaddddaaabbdccadaccddabbbcadcdbbdbddacaacbacaabacbdcacaddbaaacbdccbccadbbbcdadbbbbabaadcdbdacddabddadcabccdcdaacbaabbcccabdbcdbdccbadcbbdabbbccbaabcadbaddaccbbbcddadaaaaddcbcacaddccbdbccbccadccadadbbbddccdabddcbadacccdaacbabddbbadaadaccaccdbdcadddcbadcabdddcdadcbbadccddbcdaccbcabcadbccbaaddbbcdadbcabacccdcacbadddccbcccddadbcbdcbadbddcbbccbacddcbbcabbbdacbcbdcacdcadbccbbcabbaadbcdbaadacbdbcaaaadddabcdcdddbbaacadbbbabcbcaabcdacdcabdadaccaabaaccbabdddaadacabddcdcbbcbaacdbddcdbbbabbcdabbcaddadbacbaacddbcabbcbbadabcaacaccbacbddbdacccabdaaabddbcacdaaccbaacdbabababbddbcaadcaabcdbbbdaabcdccdbbdcacbbbcbcbddcdcaaaadacbbbaddbabcbdccbaabbaaacabddcacbacbaadbddbdcbcdbaddadadccbccaddadabaaccddccbbacadabbadadcbcbaacbbcdbaddacbbdcdacdbacdbbaabcdbdcbaabdcccdbbabdcdbcabbcabbacbbabdddddbabaacacbdaddccdaaacaccbaacdadcdbccabbbbdccbcbabacbbdbbaddacaadcaddbcaaaabaddbadcdcbdcdbbadcadddbbcdacdbbaaacdadccdbacabcbbdcddddbbdddacdbcbabdbdadcadabcbcdcaaababddcbdddbdbbacaddcccdddcbdababbccdaabccdabbbaadcabadbcddabcccccbbcbbbbcbdbcbaaaacaaccddccdaaacbcbddaddaccccbcdaddddbadbbacdacdcbadcbdbbabaaacbdccbadaccdadadcabdbaccacccdbababdbbaacadcbddcdddccbbbaabcddaddbbdbcdabbbaadccbddcbdabdabcbdcadbbcdaaabbbccdbabcacbcdddadbcdbcbdaaddcabbdbbcbcddbacbabccbbdabaabcccbcaabdcbcacbaccaabbcccdcacdbccbaacabcabdaacdbdbbdadcaadddacbcccaddabaccadaddbabdaabbdbcdabbabaacdaaaddcccbdccabbcdaacbcacdddbabcabbbcaaccabcdbdaacdcbacabacaabdbbdaadcaaaaabcbccdddacbadbcabdacbcccbadddddaddcbcaadcbcacddbdcaabdcadaddcbcbccddabcbbbccaaabdaddaacdbbdbadbdddddbabdbddbabcabaacbdcdbcdabdbcaabbabddbacacbcbdcbacdbdbacccbcadddbbaadabccdcdadbbabaaacbdcbdbabcdcabdcbcdccadddcddbdcbbbaababbcddcbbccabdbbdcdaccdddcdcdacbddcbccbdbcdddcbbccdccbaacdcdaaadbcccaadcbabaddbccdcbbdbbbcadcbabcdacbbabccccabbaccbbdcaaddbaacdaddacbcaaacadddccaccadcddcdcbcacaaabcbccbbdddccabdcddbcadcdadccdcdbabbaccaaadcddcccdacaadddcacdacbbdccbacbbbbcbbdccbacbcdddccdaddbcaccdcaadacacbccaaccccccbcbcbadabbadabdaaabdabaaacdccbbccaddcadadaaddcdbdcbbdddaadbccbcbcbbadbbaacddbcacbbccddcdcbdadaacaccabbadcabdcbdbbddbcdadadaacbddbdacabacbcabbababcaabcbaddcbbbcccacbdbbabccabcacdbdaddcdbcccdcaabdbccddabdcddccdbdbaaabdccbdbacdaabbcdddcacdbcacaccdaaabaadcbddaadadcaaaabaacbacadbcaccdadbdbcccdcbaddabcabadbddaaabdbcabaccccbcdbacdbadcaccccadcaaadaaddcabaaadbcaabacadaabccbaabcbdccacbccabbbbcdccccbcdbdccabadbdabbabdcbbcdddbadadcdcbbbabdbbddddccbccaccaacadaadaddbaaccccbbcdbaccbdabbddaaababcaccdbaaadadcadabbbdcbdcdaddccbcdbaabacaacadcbddaacdbbbdabddaddbdcbbacbacbcaccddcdaaaacdabccabababdcdabcaaacabadccaabcdbabcbaadabbcabbacddbbaccdcabdadbcbbaaaadccdcbababbcdcdcdcbbaddbacdaaccbccdaddddbcdccddcacdaccccbabbcadaabbbbdbbdbcdddbbbcbbdddababdcdcaddaccadcbabddbaccbddbdadbbdcddabbbccbdaaacdabddabddaaadcaadcbaddcaaccbcabbdcdcdaddbbaadabbaaccddcbdaadaacddaddcacaabddbddaccabbdaaccdddadcbddcccaabdbdabbbacdcdacabbcbbdaddabdccdacbcacbaddadccbcdbbdaacadddcbcaabcdcbacacddabdadcaababbddcdddadddadabbbcdcbbcdcacdbbcbadcdacacdcadddbcbadbaaabbadccdbcccacbdbdbadcaadacdcddbbcbabbcadddabaadcddbdbaddbcddcadbcdacdccaaadacccacaccbadabbdddaddddbbcccbabbbadddbbbbaddadbbbbbadcbdcacacdddaaddbdabbdbbbdbddbcbacaacbdbbccddbbdcddccbdcabcbacddbcdbbaaddbcacdcaacbdbcbbbbbbbbcdcccadbaabbabcdadcbaddbaadacccddcdbccdadaabcbccdcdcababddaaaacbdcbaaaadcbabddcccdacacddbcbcdbcadcbdabcbbddcabaadaacbdbbccaddbbadcdbcbdbdbabdaccdbbdddbddccdddabcdbcdbcdaadbccbddabbacbddcdcddcbacbcaacaddbdcbbdbdccddcccbaccbbddccdccacdbcdddadcdbbaccaccbadacdbcbdaccaacbbaccccadcaddbdcccdbdccbdddbcddacacacbadbbadacdcdcbbabaaaacbbacadacaddaddabcddcabaccbaadbbadccabbacddddddbbbacbbccdacbaccdaddaadcbcabdddcbdacbdacdadcabcbbdaacbbcacabbdcabbdbbaababbbdbcacbbdacabbdaaabaccacaaadcbdaccabdabcbddcccbbddcaaaaddacbadadcdadcadccdbccbdabadddcacdcabaaddadbbbcbbaaddadbcdcdbcbdacabbbcdbadaaddaccaabdaabdbdcbbcdacccaddbaddcdbbcdadcdabbbddcaadccccccdddccaabacdabcbbcddbadddbddaadaaccdbcddaadbbddddbccbadcbdbacbdbcacacbaaabbccabdbbcdbdbcaddbcbbcbcccccbbdccbbcbbbaacadcacbcaadbbcdcadacbabbdbdaadbadcbadabbdaddbdbdcbdbbbbbcdadcdbdcadccdaccababcdabddbccdcbdbcaaabbdbabccccaaddaddddaabbcdaabccbdaccabdacbaacdacbbbacbcdbcbdcccababbcbcbbdddaccddcdddbbcdbaaadcadcabcbbaadbdcdccdbadbbbbdcabcbdbcaacaaacabdbcabbdbbaacbacacadcddccbcbaabbbabacccdcaaabcdcadbdcddbddaacdacddabcababcaadbbddaccacabcbbaadcdccaaccabaddcbbdddadbbdacdadcdbaaadabbcdacbbabcaadccaabbbccdbaabbdbabdadccbbdadcabaabddddabdcbcacbdaddabddcaaadcbdbcaabdccabcdcbcdabdabdcacbdcbbabcdaadbcadcbcaaccadbbaabdcccbdacccdcaccdbadacdacbddbababaadadccddddbbcaaaaabbdccbbdcbaccdaaadbccaaabcbccdddaacbccacbaccdacccabdbbbddcccbdbdbccbddaaadaadbbcabbcdcadbccddcbacbbcaabdcaaddbddabdaaaddbaaacacccacbbbabccddbabcababbcccccddbabdcbbacdbaacacdaaacbadcdaadddadbaabbaacbbabbdabdbcdbddaadaabcbacaabcbaaddadcbddbdadaacacbaccbaaadbbdcccaddcddadbaaabdacbdaccdcacaddbccdbdcdddbadcdcbcdbcdcaabbcadcaddcdaacdbadcdcdbbababdccdabadbdcddaacdbccdbbdcddcdbcdbdbcacbcbaadbbccadabbdbdbbcaccdbdbacaaadabbbdcaaadabccdddbbcbbdbdabdcbaaacaacbdacadbcbbdadaddddbdcaaacbcdcabcbbadbadddabcddaacadcbdbdababbddbccdcbccbcaacdadcbbdadcdabdcbababbbadbcdcdddcadcacababdcddddcbddcccdddbabbacbcddcdbaacdaaabbdcdbaddbaabbcdbcbdcacdccbbbbbcdbbadbbbddcdddcbccabcaadccdcabadacadcadddddacbccddacdcbaacddddbabcbbddbadcabcaddccbcdaaaaaaaababbddababadcdaacbdbdababcbcdaadcadaccabdbccccdabadcbdbbcdcacdbddbaacbcbddacbcbabbbdcbcaabaaacdcaaaabdadaaccaadbbdcddadcdabbcbbaabbcdaaccccabaacdcadbdbcaabaaababaccbaaccbcacdcaabbcdabbdbcbbcdddbadcccaccbdcabddbacaacacacaabbccdabadcbcddbdcadaadcacddccbbcabdcbdbcadacadabbbcddcbaabcdbbadaaaabbaddbbcdabacababadbaadaadbdcdbadbcbdabbddadbabdcddcddbdbcbcacaabbcbdbcccabaacdbdccdadbabdcbabacdacbccdaddbabdabaabbdcadaacbdccbababdbacbdccdacccaddbcaddadddcdbacbdadccbdccaabdbbccccbabcccbdcdbdcbbacdcaaabcdcbbabbdcacacaadadbaacdbbaddbadccbacabdbbddbbdcdbdbabccdbadddbbcacccbccadadbcdbbabccdcadcabbddddbaaadaacddadcbabdbaacdbcbcdbddbcbccdddbacccccdaacccdccbcdadbcacbacbdcaabcbdadbddddbbbcabcccbbcbdccadcdcdddaabbadaacdcaabcdcdcaddccdddcbdcbbaaccbbabdbbaacdadbbddbcaabdaccdaabbdabacdcccdaccdcbbcddbbabdddbdbabbddacaddbcccdacabcbaddddbdbdbaccdcababbddbbdccabaddabdacdbbcacdbdaaabcdacdddbcdccdbdcdcdacbbdbddbbcbbcaadcaaaddaccbadddddcdddddaacabacadcdabacaaacdbddcdbcbcaacdbdccccbbddcbbcaccbdbcaddaabdacaadcbaaddbdaabccbbadcaaaabbacdcbbddadcdacbaccabbabaacbdccbaaddbddcddcbcbcbaaddbbcdacdccbadcbcddcbddadbdacbaaddbbbbabacadcaadaaacaabdcbdccbbcdbaacadbdcccacbbcccabbbccddaaddacaabadbdcccbdacddbdbadccabdacaccaababbcabdaaacddaccbcdccadadacbbaaddbbdbccdddbcaacdbdcbcabbbdcccdcbdcdcbdadcaacabccbabcdadbaacacaaabccabcaacbbabddacdadddccabadcbabccbacadbbdbacbbabcbaaadcacbdbaaadddacdcbbdbccabdabbbbdbacbcbaccbbadaddddadaaaaacabbcddccdcaccbacccadcabdcdaccdcacaadcaaaaaaabdbaaacbaacbadcacbbccbccccdbacbacdcadbdcbbdaadcdbbdcddcccaddaaadaaaddcccbbddabbcabcdbcadbcddcbadaabccddabcaadabdcddbaacaabcacadbbcbbadaacbddbcacbdbbdcbacbaccbdcbabdcbcbacabdadacaaabaacdbaaabcbcdaccbbbcdbdbadbaacaccbdaadbacaacdbaacdaaccabadcbdabcadccaccdaddbbccadcdbdcbcbacddbabbaaacdadbcbabdcbbaaadadcadadbdadbccadabdbcdadaadcbcabdbdbdacddcdbddcbdaddcbdaadcdbdccbaaaddbccddcbaabadacbbbddbccdcbddadbdacbadbabcbcdbbddadbaaabbbadabbbbaaabcbcaccbdcbdbadcccabcdbbcbcabcbdcadccdbcbdaaadddcabcddcadbaddccaddddcbdaaaddbdcbdcbdcdcdccbdbbbbcdbdadbbabaaddbbddaacddacdadcdcbcbacbdbaadbaaabdbdbbcaddabbbbbcbdadadaadbddbdbbabddbaabdcbdcaccbcbcabcacaadbcbdddbadaddccdbdcacadbbacdbbaadadadcdadaddcadddadadcacdacacabbdadcbacdadbdbddaabddbaaabdcbadcbadcbacaddbccdddbddaccccaabaabddaadbdacbdccbbcdbdddbabadbccccabacccaabccccccaadacaaaadbbdbcbbaadddbddcbcabdcaaadaacacabdbbbdbaaaaacbacccdadcccabbbbcdcadcbaddddabaddbdadccdabbcabbdcdadcddacbccccaccdacbbbccacbaadcbbdbbaacdbcdcbbaacdbdbcdbacbbacbdcababbabdbcdadccaadcdbaddbabaadbaccabbaadaddcbbbacbbddcacaacdcabbaacbaacccccacdcbbccbcdccadaadccbabaabdddaadcabbbcacdcbadbdcbbddaaabaadbcbaccdcbaababadccdaacdbddcdadadacabdadbbcdddadbcccbaccacbddabcacccaaabbccdbadbccccbbccbdacaacdaacbadbaacdabdaccaabababbcdddcbcccaacadbbcdcdabbadaccabaccacdccadbababdaccbdcddccbbcabcdbddcccaddbaabdcacabdaaabaadcdcaabdabdabddaabddbaabcdcacddbdaacbccbdaabbadaccdbcaccbcdacaaadcbcbdaabaacaaddabccadaabcacabcddbcbdbbdcddbadcdbaddbcadacdadbaddbdaddbadbdddbabaccdacaadbdaabbbbddbdbdaacdcabddcccdcbaddabcacadaccbbbdadbcabdccabdacabbbdbbcacdbccdcddabccabbdaacdbdcbcbcacabbcacaacdccddddabdbdabaadcdbbdcabdadbacbabbcabcbbdcdacacbabbbabbbcdbbcdaddbdccacacddadabbbbdcbdadbdddcdcdddadbadbcbdccbbbbddcdbdddbbddabbaaccdaacbcdcdcbcbaacabadcdababaccbdddcabdadabbadbcdbdaaabbbbbbdcbcbcbdcdcadabdcbaadccbdabbbaccbbbbbadaadddbbccdbdbdacdbacdddcccdacddbcaabdbcdccdbdddddcabbcaccabcdabdcbccdadddcdaadcababcdcaaacccdbcbcccdbcbcbaabcaddcabcaccccbacdadbaabaaccadcdccbddcdbbcdbbcdcaaccacbacccddabbadacbbbddccccbbcaabddabdcbcdcbcaccaadcacaabadccbbadabdcbdccdacddcacbdaddbabaabccdcbdbacbaacccdcdbbbbabadbbadacdcbabbccdadbbaabdbbcdbdbbbcbcbdcdcdcdaaaacadddcddbcdcbbbbdcddabdcbdcacbacabacaabddacbcbdabdbddbdbbbdbbaacbadbdbdabaabbabbdbacbdbbacbbdccccaddccdbbcbbacdbbdcaccdbcaabcbcbcbcbbdbadcccbdbbddbcaacccbcdcdaadbcdaacbdbdadcbaccaacdbcbbacabbcbcbabbabcadcbaddbdcbacbcdbcadcbcccaacdcddbccbdacadacbabbcddadcabdcacaaaacaadbbbbddbddcdadabbadbdaabbdddaaabbcbcddbcdabcacdcddbaaabbbaadbaaaddaccbddaaacbbdbdadabaadadcbadbdbcacbacdacdddcacdbcacabcdaddcdccdbacdbdcbbccaaaddbbaaccdbcdadcbaabcdddcdaadacadbdbdaccbdadccbddaadabbcdcccbbbbccdcadcccbbdcacabdaacccdcadbddbbccdaaaacbbdabdaadcbddaabdbbbcbbccccbcbdbcdbccdcdccabadbbddcdaadcacbbbaaaababbdbcdbaabddaddabdadbddbbadcccabbbcbbbbcbbaadbdaaddabdabddcabadbcbdbcaaadccbadaacdbdddcdcbcddccabbabdbcbbcdcacbbdbacbdbbacddbcabcaabccaddbabcabcdacdcddccabcbaadcadcdaddcdaadcaddccbccadccbacddccaabbbaddaddddcbdcadaacbddabddaacbccbacccadaacbbddbddaadaddbdaccdbaaacabdaaadaacbdadbddbaadbddccaacbacbaacdcbcbaaaadcadadbccddccbdbacabadbbdbdbadbacdbddbaddcccddbaabcdaacccdabababbbbbdacdcbcbdbdcaccddabcaabbdbcbdbdbbbcdcaadcbacddabdacbcacabaadcbccdbcabddcbbadcddccdccbddbbdccdbbbacddddadbccdcddccdbcaaaacdbbdcccaddabdccabbdbcbcabcbbdcaaddddaccbbddbadbcdcbdbcaddbdbccdabbdccdbcbbcbbadcbcdbdacabadabccdccdcaacbabbaaaccbdbcabddcddaabbabdadadbbbbadbdabadabbaddaabacadbdcdbacadcbdcadddcddadaddbadddababdcabadaabccccdccbbdcbbcdbaaccabbcdabbbdbaacacbddddacbbcacddbdbbdcadcbabcbdaadbbdbaacbabbbdccadcddddbababbcbdbdbcadadbdbbabddcbbdcddabaaddaddbcaccadadaabbcaacccbadbbbbaabcabacdacccdbadabadddddcacddcbbccbcbbbcbbddbbcabcadbcdbbbcddacccbbcbddccaabbbcaababaadbcaacacbcacabacdddcbbabbbdacdccbcacacbacdaacabaacaddacddbcdabcdabaabaacbdcaadbdcabdabcdacabbcbccccbdbbbbacddcdbdadccbbcaaaddaacacdccdabcabdaddabbaddcbcaccdbcddabbaabbdbacadcdcaacacaccaadabdbbbcdcbbdccccbdadbbbbcaadcdaddddbadbcaabbbcbdbbbcaddacbcdcdabbcbbcdacdabdbbbcbcabcabccdccbcbdcbccaaaaabcdccdcaaadabddccdbadcbddbddccbbcdbdcacaacaacdddaccadaaccaddbcdadcabbaaacababdaddaaddbabcbdbbabbddcbabdacccadbcdcdcdcddbadcaabbcdbbbabcddddbadaaddbcbacbcdcabdacbbcbbcbacacaddccacaaabdcdcbbbcbccabbdacddbcbbbbaabdacdccdcdbcbccbaabacdabbaddbabacdcabadbabaccbabdbcdcddbdccacdcbdbbbcacaacacbcbdbcdcaddbdaccaddcbcaadabbbdccbdbdaaccbadbcdbbabadcbdcdababdacdbbbadbbdbacacbabbbbbacacbbaccbbcddcabdccaacdcbdcddbccbabbdbaccccbbcadbdaaddaadaaacddcdbaddddabbdbccaccabaabddabbbabcdcdbcdacddabcdccbcdcabbcbccbabcccaccdbdcdddabbbdcbddbadddacaaddaabcbdaddacddaabdaadacbcadbacdbadcbbccbdacccdaacacadaccbabaccddababdabccaabdbbdadbdbbbcacaadbadaadcacbcbbbaabaabddbdcadacbdcbdabacabdccbdcadcbcdcddbcddcbabbcdccacdcbcabccbccbcbcddaccacaadcbcacccbdbcdccdaabbdcaccccaaaccdcdacabddbbdccbbbbcabcccccadacabdaacbcbabcacbbdcdcaabcbcdcbbdcdaaaadadabcdcdbbacabddacabbbcbdccacbbbbccbcdbdddcbcadcddbbbdcdcbdaacdacdbaaabbbbacddccbcaadacccbcadcdcbdbabcbdcdbcaadbddccbcbcdddbcdaabdbbacccdaabdaabcdbcbbdccbccccaaaacbacdbdcabddacaccbadccbcbdcabddbcdbaddbbaddddcadcaacbbcdcaadbbdacabaddcdaaadbcbaabdcbdaabcbbcdadcbccdddcacbadaabdacdacbacbcaabbccdcccbbdccdbcdcadbdabbbabaaadbbaaaaadbdbcbaddccdcbdbacaadbcacdcbbbabadbbaaccbcbccadaabdcdabdcbacadbcdcdbaaabaabdbabcacdcadddcbccdbbdacbaadbdbbcbbaaacdcaddbcdacdabacbcaddbbdcbccddbbbbcdddadbcbdcdccdabaaaacdcbccdccbdcccbddbacbcadcbddbdaadddaddbadadacacddbbbadaaaabadcbdcdcbadcbaaabadbaaccabcddabbaccabaaabddaaadcbddbacbdbaacabaccbaadccabbcbddbbcbddaadbbaaadbcaabbdbabbbcadccdbbddccdbbddbbaccadbbcbdacbaacbaaaaaabcdadbabdddadddacadcdadaababacaddcbdcddddabadbccbaadcddbabdabcdcabcdbaacdccbbcacadabbdbddbbbadbcccbacdaddcaccdcadcccccaccaadcdcbbccbdbddaacbdabbdabdaaaabaaabbccbcaaccababdabccdadbdbacaccacddddadaacddbcbbbdbadaddcadcccdbbbccdabbabccbcbcdabdcacbbacbdadbadbcddadbddcdcbccbdddaacccdaaaabaabbbdbbbdabddbbcddbabbcaaaadbaddbdaaacdcdabbabcadbadcbaaddcbdcccdcdcbcaaddacacbbccdabbcddbbcdcbcdaaddacccbbbcdccbcdbadaabbaccdabdabdbccabdcbbadaddbbcdbcccdcabbaadbcbbaaabbccdbaabcaccdacaabddddcaaababcaaddabaddbbbbdccccbddadaaaabaaacaccacbdbdaccbdbddcbacdccdbbbbdbaccccaabbcddacbbdaddbbacbcbabaaabbccacacadcacabacababccdcdcacbadaddddcbabccbcbcbcaddccabadabccdadabddadbddbdaacbadcbcbabaddbaaccbccbdaadcbccdccacdbbbccbcbcdddbcbcbddbaddbcacaadbddddbdbacbbcaaacaaadbaaadacacabbccadcdbcbdcdccbddabddacbcbdacdbabbdbdbadabcbbbccbbdbdbdcdaccabcdccccabdcbadbdabbddaddcbdbbdcbcdbdaddcaacdadccacdbcabbcacbdbccdbacbaabaccddaaccadbcdccbddbbdadbcdaadaabacadbcabbbacbbadcddabacbccddadccadbcbabaccaacccbbdaabadaaadacbcaababbbaccdbcccdbcacddddacacaadddbcbabddbacdadcaddaddbcdacaccccabbccdcbdbacabaadcabddbdbbcdbcdcbdddccbdaadcdbacdbdadbccaadcbcbcbbccdcccbcacabacbdbdadbdadaacbdadaacbbdcdbbcbcdadcabbddbdaaacbaadbcbdbdcddacddabacdcdaaacbddcbcddbacaadaddbcdacdcdbddbcdcddcccbdbdacbaadddaaadccadbcdccbcaddcacacbcaaaadbacbcbbcdaaabcbccadccbaacccadacbbcdabaaadccacbbacaddddcbdcdbadbaadbcccbacdcbabacccdbddbadcbbaddbccdbaacbadbbcabaabbbbcbbacbcddaaacabcaaccadbadcbbcaacdbbbcbacaadacddbdcacdcaccbcbabacbddadacdadaacabcddcccbcbdbdabddadadbccbdaacacbabbabdcccaaccdccaccbaaacabdacaabaacbaddbbcdcdabcbdcbcdcbadbcdbbbdbbbabdadcbcacabcabddaacddcccaabadbcccabbcaabdbbbdcbcaccbdbacbddccadaacbdabbaccaaccdccddbcdddbddccddbbcbbacdaabaacbacdcacababdcdaacabcdabaaccbaacaabaadbdabbbcddadbcdccdcaddcabbdabdccccdccdbcdcbcbdcbbbbbccbbdbcccbcaabdabdaabcdbaaabbcdacaddadaaaddcdcddabbbddbdadaaadbccddddcababdcdacdabbbbbddccdcabcddacdcabbaaaaabbcaaadccabddcaccabdbdabcdddaccaacbcaddbcaaaabdbbccbcbdcbdcaddadacaccdabaddbcdaacaacdbdcbbbcbabbdcbcbdacccbcccabacacaccbbacdadcccbabcddcdbbbacbddcccbcabbabbddcdbbaacbdbaaabbadbdddbbaabacdaccddccdabcaacdabbcadadcbcdcdbdaadbaacdadbaadcaacdcadbabbbcccabccddcdadccaacdadbcbbccaddcaddabdddcdbaadbcdccbbcaaabbdddcdbbcbdaabbbaaddbbdbdcddabcdbaddacbaaabcbddcdabdaacddbcaadaadbddbacaaaccbcaccdcbacbadbddbaaacdddbcacbcbdaaaacbcacadbbbcbbddaadcbdcaddbacdbabcddbdbbadbadaaacdccbdddcbaacccacdbcccdbcbadaabcdbcacbaddaddadbbadabbabbabcdbccbcbbccbacdaddaaaccdddccaacbddababcbcabdcddbbbccddbcbbacbcacdcdccddaabbaabcabaadadbacdbaccacdcddaddddcdbccdddcdabadbdbadccdccbadbbdcbbacccbcdbbdababbddbcbddcdcbabcadbbacbaadbcdaaabacdbdaabbaaaaabbbbaddbadbaacabcdcdaabcdbdccabbabbbdcbbcdbaaaddabcababababcacabcbcadccdbcadcdbbbbcbccabacdbdaaabacbcbcbaaddcbddcdbcddaabbdaaaaabdabcbdabaadcabcbdbcbbcbbddcabdabcdcddacbbbdcabcddcabbbaaadddbabadaccbcabdbaccaccbbbdddbbddddacadaccbbdaaccaabbcbdcdcbddcaddcdabdccbcbadaddbcbaaccaaadadcabddaddcbdcdcabadcdaabadccbbcbbdcbaaccbdbacbcccddcaadbbacabcaaabbbddbddaabdabbccbdcbcbbbcbadcadbcadbbbbdbbbdbabbacabccbbdabaddbdbbdcabcbbaaadcacdabadbacdbaadcaadddcbaaccbdbcabaacccbdcbbbbaaaadbcbdcccdcbcdabcbbbdbbddaacdbacbdbbcabdbcbccbdddcabcabadcbbdcbdcbbbbbddbdbbbcdbcdadacbbdccbcacbbdcdccbcdcbbadcbcdaaaabccbbcacbbddcdbaadcaaddaabbadbdadcbaadabbcdaacdaabcbcaaccabbcbddcddbbaaccbdddacacbcbdcaaaadbabcdbcadddddbccdccccbbaddabdcbcaaabcdcdaabdbbabadbadcbaddddcdcaacacbbddbbccaacdbabcdbcbddbbddabdbbaccadabdcadccdacbdddcaaadcdddbaddddccdaacbdacbabcdcabaacbaabaccabacacdaaaaadaccacbaddcbadbdbdddacaaaabcccaccbdbbdccbabcabacbabaadddbaddabaadabacadcabcbcbaababdcbdcadadbdadacddacddaaddaaccadccbaadaddacacacabcbccccdbbddbabbcadababbbbbdbbdbcaadcaabbdbbdacdcbbcddcdcccdacbcacdbbabdbddcbdbdbcdbbbcabccccabadaabadbdabdbccdaaaaddccbbbcbcbcbdbacbbcdbbbbcbddcbcdddbdbdbcbbadbaabdcbbabcaaddcbbbaaaaaadcadddadabbacbbbcddababaabaccdbcabdbdbdbddbcacbcbdcbbbabaccabbddbdcbdbbabcbbdabdcdadbccacadccaacbbcdacbacbacddcddddcbcdaacbcaacdaccbcbcbbbbbacabcdacaabbdadbbdadbbaddcdcabbacddabcacadaddacbbcbdaccaaacbcdadbcbaddcbdbaaddddaabaabcbbbdaabbbaacaccddacbcadbdadadbddabbcdbdaaacbdcbcccdbaccaddbadaaacbccbacabacacacaabadddccccddbadaddacacabbbadcbcdcaabcbcadcdbcbcddaaaccadbccaccaacbabadccacabbdabbcdcdcccbbdbddccbbacccdbdccabaccdcacdbbbdabaacadddbcdcaacdccaadaccbbadddabbbadbbccbbdcbdabcbabddaadccbbccabbbadcddddcdcbacabdddcdbadadccaacaccddbaddacbcdbbcbbddbbaababddbabaabcdcdcbabaaacdcbadbbabcdacccbdbccabcacacccddcaddccdddabdddcbbacaccbcbdbcbbacabddcdbabbbbddadccdcbadbbabdddbbadddbcadbbdbcbbdbcacdaabbbcaaaadaabdbcadabacbcadadcbccaddcdadbcdbbabcaaaadabdabccacddaaabbbdadcdcdcdcdbaacdddaccbcabbdcbaccbabadbbbabdcccdbacccbbdcbcdbcdcaddababdcdbcaddcbcbdaabaaaddcbdddaabcdcdcdccbcbdaadaaaaddadccdddbcbccacbbcbadabdbdaadaabbcccdcbdbdbcdbdbaabdbcacadabddbdcbaacddcdaacddcdcddadbbbdacabcdbbbddbdbdacaccbacdcbbbbadabbdbbcdbcabbdacddaddcdcbdabadcaaababbbdacadcabdaadcbbdbddcddacbddbcabcaaadacaacbbabaadbbddbdabcdbccdcabcbbbddccaccbcbbbddbbdaacadcabcadcbaabbbadcccabcaabcbcbbcdabbcadcadbcadcdbdbdbccbbccacaddabccdbbacbdbbdababdccbaabbabdbccbcddcabdabbaddddbdcbcbcdccbcdcabdaaddbaacbccdcddccabdaaadbdbdadbbacbaaabaadabacbdcdabdbabbcaabcbbbabcbdabadadcbbaabcccbbdccdcbabcccdacabcdcabdadbbcdacabbdadbaacccddcbccddacdabdddadbdaacdbbddbbabbdadbbccaaddaaddcccbcddcdbaabacbcdacdaaaaaabadaabdabbaadbcbbcdccdacabaaacdcacbbdbdaadbdddbaaaccdabdccccbdcdbbbdbcabccabbabbaadbadcadbdaccdcdccccdbaadacaadabcddbdcadbbcdabdcdcdadaccdbadacadddccadcbcacbacbbaaacdacabccdaaabbdaabbdddbadabdadbabddbdacaccddccddcacdcaadbbbcdacaacdadaabbdacadcddadcacbadcccbaccbcaaadaaccadcdaadbaaddbdbddbaadcbcacccdbbdaabaacdcbacbaadcbbadaccacdcbbdabadcddbbbcabbbdabccadadabcacbcbdadbbdadaadaadbbbcabcaacdacbddadbaadcdabaacdddddabadaaacccdbaaabadacbcabcccdaaddacdbbdbccaddcacbaadbbbaccdddbcdbdbdddddcccaaabaabdbdbcbbdbcccbbadbacdaacccbabadadbadccbddaabdabbbdbbbcbcbdccabaccccabdacbbcabcddacdcccdddbdabaacadcbabbbadbbbbbabcdcbdcbcdcbdabaacdccacbcdacbdcaaaacdacbddccbbdcdbaccdcdbbdccaddddcddcaabacdbbbabbddcbccbbbddcccbabcdbcabcbddccddccddacdcbddddcbabcdcabccbcbcddabcabbddbbdcbbbdacbbbcabdccaabcbacdcddbadccadcbadbddcaddbababaacaaddadccadacadbcdbaadcbbdbdcbbbabbacddcacdacabcdaacdaaadadbccbbcacbbbbabadbccbabdacdbdbdaabcbcbdcdabadcddcaadbdcbaddcdbcbdcacdddcdbdadbadabbdbabbddcacdddcbbccbcbdacadddacaaaaacadababbccbdbcdbacbcbbcddcbbbcabbcbbbacaacbabbbdcabbcdacbacbddbcbbcabcaddaddbcccccdaacbdbacbdbcdbaadcadddbdcdacbcddacaccddcbdcdacbdcdadadcbbdcdabcaadacccbbabadcdacaaddabbcacdcbdbaabccaadcacdabcdbaabadacbbddabbddadbcbbbdbcabddaabddaccabcadcabdadbadbbbcadbbaddbbdadacbaabaadbdbaabaaadbdcdacadbcabaddcdcacbbdbadcdcccdccabdadcccbdbbdbcbcccdcbdcdbbccacacbacaabdcdcdadabacbbddabddbadbbdbcddaabbacbdcddacacabaddbcbccbddbdbddabacdbcbcbdcaacccbbdccaaccbbbcdadbbacddbaaaaacccdbbddacbccacbadbddcabccddccdbadbabdcaadcdbbbbcacccbbdbcbdadccbdadbbaacdcacdadaabbccabcccbcbabababcadbbaabacbdcdcbccbbcbddcacccdbcddacabbcbbcdbcdadacdcdcdbbdcbbdbdaabcaccadbdbcbcaacbdcdcbbcbccadadabadabdadbdddbbcdcdabadadadbdabbaadccbabdbaacbbabddbacbdbadbacdcdabdaabdcbabaacdacdcacacbccbadcadacadaaaccbacacadadbdccdbbccdbbcaabbbcdadbddbadddddcbacdbcbbcbbacbcbbccbccacddccadcbaababdccaccccdbdbacbcacadbbbcbcccacdadddccbddbdbbbdbbdbdacacabddbbddbabbadacaadabdbcbaaccabacadcabdbdcbccacaacdbaadbbcdadcbacdcadcaacbbdbbbcaddcbaacabacdddacddbbacaaccadcbbdaabddcccdbcacaadcbdadcaadaddadcacddaadaddbddadabadaacbcabbdbccbadbaddbdbdcabcbdaaacbacabddaaccacacbdcbbbcacddcbbbcbcccbaaddcbacbbbaabcaacabdcabcbbbcdaacbbbdcdaabacbcdbabaadcbccbbcccdcaacadaabddbbaacdcaadabacbbbdbdacbaadcdcdbcddcbdcacdaabccbadcabaadcabcdccbbabadcaddbacbdbcdbddbaacdcdcddbadbcbbadaacaacdabacccccaaaaacadabbaabcbbdcaabccccbbaccbcaadbcdcabdaccdabadccdbdbcdaaadcdbdaaccbdbdcbcbabdccaddaccabacdbdcdbdbcabccdddbdabaaddbdbcdbdbdaccdaaacbdaadacabacbdccbddccdabbadadccaaaacaabbaaabccbdaadcaababaaddbaddddacaaaddacdccaddacccccdcbcdcdbadbaacaaadbcdbdccadadabcbcdcccbdacacbbabcbdbacdcaaabcabbbcacbbddccccbcaccadbcbcdbcccddbbdadabbdcbbddadbbcababddaabdcdcbcacbddccccabaaddccbcabbdacdcdbdaacbdaacdbbccddbbbbacadabbccbccbbacdcdbbdbdadcbccbccdaddcaabbddbcbcbcabcaccdcbdbbccacadaacabaddabbacabbdaabdabbdbdbacacaccbdcdacbccbababbabbbdbdacdcaccdbbabdabcdbcbabcdbddddadadcccbdbdacbcaabadabbcdcaaccdcdcbbdbacadbabdbbdcddadbcadaacbdbdcaadaaabcccccdbdbbaabcabcddcddcbbddcaacddbadbccdcbdcbabacbabdddddcaadacdcaaccabbbbdcbdcbcbcddbaccababccddcaaccdcababdbdcddadbacdbbcacacabbbbdcbbdaaadadbabbadabddddddccbabacadcdacaaccccbcccddadaadbbabbdbddacabbbcadccacdbcddabbaccdaddbdcccccbdbbcbaadacbdaacbcbaacabdbdcaadaabacddbaddadbcabaabbacabdabdddbcdbdddbcccbdbcacdccbaaababddcccbdcdacdbdaadccdbcccbcbacbcdbacadabcbbccbdccbbdabddcccbacdcdadccbadbcacabdccabddccaddababcacddbdacabccdbcddabdadbbdabcdcdcdddbdaabaadbacaccdadacbcdbcddbbcdbabadbdcdcbbbdaccdcbccdbdcbdaccbbddacccdccabccadbcaacaaccbdcbbddabbcdcbcbbcbcabdabdadaadbabddacdcbbbcbacbaacbbaacabddbdacaddcdcddacbcddcaddbaabbddcdcccbbbcacddddcdbdbbdbcdbdcddacacbbdbdcdcddbbbccbddacdaabbacbccdaccbdbddccaaaddcbbaacbabdabcdacdcdccdbadbcbcccdccabbddbaaabdcdcacbcbcabdccdccacbcccddadbbcdbcabbaadbacadbbaaabbabbbbacdadbdbddcbddbddadddbacbdcdbdcdaadbdabdaaabcadbbbbbdabdabbbbbcaadbdabddcbcaabdbdbbcdaabddacadcbabccdaaabcdccccdabdbaabbaacabcbbabaccddaaaddcbdccbdabdbcbabccbabbbcdbdddadbcaccbdbcccadccdddabbbcabbdcaccbbabcabaacdcccabbabbabdddcbbacacbddccbcddddbdbddabdacccbdcabadbcadadddcdcddcbbcddccadcbdcdbadbabcadcaabcbdaaacacabcddbbbcbcaccdbcbcdccbcdabaabcbdbbadccabdcccdbbadacbcbccabacdabadcdcddababddacbbcaadabbbbbaacbbcbddcbcbcdcbdbabcbaccbbabcacbbacadccabcaccacbacaacbbdbbbaaacdbacadacdabbdbdbabdadaadbaaababbcdacbbcaadcbddaacabcddbcadabcddadaccdabcbaacabccadcbcbabbcbadcbbdddbadbdbcbacacacdabdbacacabdbacbacdbcdcccabdbacbbbcbdaaabcbcadabbabcbacbbdadcaaaaaddcbcacdbacaabbcbbbabcabcdadadccbbcdacdacdbcdaabdabacbdddccaddcccacdbddabaaccdddcdaccbddadcacbddaadbdaddcbdbdacabcdcaaadbbbbdaabbcdbabbadaabdddadccddcdbadbddabbcaabaddbbbadcbddbcabccaacaddbcaabaadadcddcbbbdbacdadaddcbdacbbabbacdbcbbccbaccddccddbbdbadbadacbcdcddacdbaacadbbbabcbabcaccbbcdaacbdddcdabbadcdbcbadccadddcbadbcdbabbdbdadadbaadddcdbdbbcdcddabbdbbbadcacacaabcdcbadcdbadccbdcadbcddaabdcaabadcdacbcbcbacbbbaaabbbcabdcbaaadcbaababadacdbdcbdcacdbcdadbacacbabbaaaadcaaddcadcddddbcacadaabacaaccadcbabccbbdaabccabcdcdbcddcaaacbbbbaddbaccdddcccaabcaabddaabdcbacdabacdcdcddacacddadacacdadbcaddababccaabcbdcadadcacadadbadaddcbbccbbddddacabadbdbddcdbbbcdcbaabcbdbccacdcacacbabadacddcacdaacdcaabdbccbbbdccccadbddabbccdddbcdabbaaaacdcdadbcbacdcdcbbcacbddcdddcabacddadbdbccbddbaddbabaabcddcbcadbcbaadaddddcacbcdabaaadabcdbdabdcbaacbdaccbcddaaaaabbdbacddcdacdcddacacadabcbbacbadaaddaccbbaacbbbaaabcbccacbacdcbddbbaccbccdababcdbccabbdacabdcdababaacccacabadbbdaccadaabbbccaadbbbadbccaabacdcdccdbcabddcccbabacdadadcdbbbddabbabacdbacbbbbbbabdcbabbbaabddaaabcbbacdccabcdddccbbdcdbcdbabbaacdcdbbbabccccdbbdcdccdbcdccccdbabacdcdbbaaacccdccaacddadbcaacbacbbdbcabbadaaaddbcabdcdcbcaabccdadaabbdcacabccbdbdcababcdbdccbbacbddadbbadccacddbbdbccddcddddacaabaadddadbcdcaaaadcbacbaadbbcdbcdcbcdbdcbacbcaaacacddaabbadbaadcaadbddbaadddddcdadddcdbcaaacadccddadabcbadcdcbddddbbcbddddccdcdbaacdbaacababdbbcdadaabbcaccdcaaabacacbcbbcbababadcbbccdbdaddadcdabadddbbbdaaddcdddcabaabaddbcdbaccbabccaaddbbdcabababaddcbbccccccccbcbbabddddbddbbccccccddbacdbccddddacbcdabcabcccbcbaaaaddbdccbccabddacdbbbdcccbbaaccddbdbacbadcdbabbcdbbdbbdbacabcbcaadbbbdabdbcddababddadbdadddbcccdaabcaabbabadaddadbadbbddcdcddcdbdabacdacbcdddbbddadcccbbcddbaddacdbadddddabadbabcdbacbabaadababcbabdddbddacacccdcddccaabacabbbaccccdabdbcbadcbbdbdbccddccbdbdaadbdbadacccbdaddaabbbcdbddacadcadaabcbabdaadbababcdabdcdcbaabadabdcabbcddccdabcdbcddabadbbcbdabccadbaaacacaddbaacbcdbbdccdcdacaaabbbdcbcbdbdccacacacbabcdcccabdababccbadbadcbddacadaabcaacdabbddcdabaaaccdbacdbbddbdcdaabcdcabddbbcababcdabcdabdadcacaacdccbbccdaaabdaabddabbaaddbdbdbaaccacddabbdabadccbaacacdbaabccbabbbccbdacbbbdcdcbabcaacbddbbcbdcdcbdbdabbcdcbdbdccabdcaadcaabdbccaabddadacaaaddbdbccddbbaacbaacbcaabdbbaddbcbdbabdbdabbbcbcacbadaddcabdadbbadbabcbdaaddbabdbadbaaadbccddbbdacaadacdaadbdbcbbbaacbbbaabbbdbddabdadbbccddddabbcadacbbcbdbcbcbdcacddadbcaadadbadcdbcbbaccdcbcdadabbbbcadbdbcddaaccaaababdbdbbdcdbcbaacdabcbabbddaacdccdabcaaaabbaacadddccdddbcaacddbbbdcadadcdcddddbaabaddadacbabcababdddadabcadabdadacbadddbacbdddaaabcabcddbccbabbbbabcbacadadabbdbcbdbbbbdadccaddbdddbaabbdabaaaadcbadcaccaadddccdbdcbdabcbdcbacddddbcbaccdcbacadabcbbccaacddbcabbaadcbdddadccbaddcaabbbaadcaaacbcdbccccdbadcccdabccbcbaaccbdbbcdacddacbbccbcccbacacacbacacabbaccbddacdbdcacbacdbabbaacaddacbbdadabcccdcaabbabacbacdcbcaacbbbbdcaccbdddbccbccdbbcbadcaaabbdaccdccbdbdbbabbbdcbcccdabbabaccdacdcdcddccdcbcbbdddabdccbcaddcdbaddabbacacbccbbbbbdcbaabdbbaccabbdcaddcccaddaaddbcaccbccddaaabbccdadcbdaababacbcbcddcbbacaababaaadbdbbcbaabcdcbdacdcdbabbcabadaaaccbcdacdbaccddbccaacaacbabacbbdbcaccbbbddbaadbccaddddcbbbdcbdcabdaaacccaddacdaccdcbadcaacaacddabaddacdbbdccaabaaaaccdbabadbbddbbcdacbbbbcddcccacbcbadcdacbcbadadaccdaaadbdabbddccddbbbcbbcbbdabaacbccdbcbbcdddaabddcbbcbdabcdadadacbbcdccdbcbddbbddabcbdacdddbbcdcdbbbbdaccbcabcdcdbabcbadabcabbcccacccdbcbabaabdacdcbbacbdcdaddaddcdccccddbdbdccaaabbbbabaacaadaadbbadcdddadccadcbaccddbcababdacbcdcbdbabaabcaddaabaccddcbbcdcdddacacadbbdbdaaabddcabbabccccdbabcacddbbdbbcabddcbddadaacddbddcdbaccacbdbaadcdbbaaaccaddadabcdcdacdaddadcbadbbdbdccdbdcacbaadccacbdbcdbaabadabcaadaaacbbbddcdbcabbbcbaaccddcdbcbaaabbcbadadcddbcbbdabbccbdaccbabcaaadccbdbadcdccadaabdbaabadbcdaaddbcaddbddcdcabaabccccdabadcdccdacbbcbdcdadccadbacbaaaccbdcdddacbdbaabdabdcdaccdaabcadcbadddcaadcadabaabacbcdacaacdddbdccadadbdcdaabbdabccbdacccabbaccbdabaccaccbabaadcdadcddbcdddddbddcbbacadcbdacdcadcabaabcbcacdcdbdcbcadccdbdcbcaaabdcdababbdbdcddbdbacddadbccbdbbaaadbcbbddaabccdacdbacabaabdddddaddcaaaacdcaabddcacacbbadcdcdbacdcadbbdabbcdcdadbbddaaddaaacbaadaadadccddacdcdadbccadadacadaadcaacacabadcdaaaaabbdacdbacbbcaacbbcbaaacbcdbccccbbbabacddadbabdadcddabbbaadbdcddcdadbccbcadddcaacabdaabaccbaacdaaabcdddaabcddbcdbaaadbdccabdbdbddacaabccccddbbcdbbdcbddacdcbccbcacdccbcaaabbcabababacadcdcabbdbcccdababbdcdaaadaacccddaaaddadacddcdadcdbababcacacacdccddabadccddaabdbdaddcbbcaabcbdabbccadaadcccddbcabdcabbbabdccbadbccadbccdcabdacdcddcacccdadcdcdbaacaadbbbdcbbbdbbcbabbbdaabacaabdddcabacabccbabddbcdcabaccaacdccdbdaabbdccdabaaacacbdcabaadbcabdabcbcbabbdccacbacaccaabababacbaadaabbcdbcaddbaabcbdacadaacccccdddccadabdcaccbadcdbccdabddcdbbbbabdcababadadcdaddacaadbaccdcccccadbaabbcbbcbcacacbadbbadbabaadadddddddbacdbabdbadbdabccaaaddccdbccaaabbccbccbdbbcbbbcacbdadaadcccbdadbaddabadaaccddaabcbacabaaddddccdbacbddddcbdbbcabbbabcdbaddccaaaacadcccdbbdadcdacbbaccdcdbaadaddcccbcdacddcbaacababddadcdcbccbccaadcadbacdacdcaddcdccbcadddbcbadcaadddbbdcddcadccaadcdcdadcbacdcaddcbabaddacbccabbaabdccaabcbbbbddbdbdaadbabddbbcaacbadbcdbccbdaccdacbdabcadcddbabbabcabbccdacddacbcaccdcdbdadcaacccabaaadbcdbdddcdcdbabbabcbcaccadddaadcbddddaabccdbcbbbaacabdacacdacdcbaabbdbadcbdcdabddbdabccabadbcbbcbdbcbdabdcdccbcadababdbdcdacdcabacdbcdcaccacaaddbcaaaadaadbababddcbbbacdcbcbcabccaaddbbaadbacadddddaabdbccdaddbbddbdcaadbbddcabdddacddadcabaacddbbcacdaddbcabccaabccdacaddccdabbdddcdacaaadbabdcdcdbdbcdaacacdcbacdddddaadccdccabcdddbdadabdcdbaabdbdbcdbbcccacadacbacbacccdadccccadcadbbdcabbcccbdcadacbabcbccacacddbdcaaaadadddbcabccbabccdaacdbaabacbdcbcbaadaaccddacbcdadbdacadcadabadabbbdacbbdadaacadacbadbdddbcddbaccddabdcdababdccaaabbcbcbdcbbadcbbabbbdadbaccabcdacaacabbadadbcdbbbdcaaabbcbdcdcdabdadcddcdbaaadcdcccdacbcdbcbacbdddbacddacdddcaaddcacbddabcbaabcbbbcbbacdbcdbaadaccdbaadbcaaaddaaacabccacabdcaaaddbabcdcccaaaaadadccaabdaabccacbdcacbacaddcdadcddaacdcadcbabdaacaccbcaabdabadacaacabaaddabcdccdadabdcddccbadcabdbaacdadcccccbdbdbadbaacccdbcddbbbaaddcaccbdcabcdcacdbcdccddbdccbcbbccdacdcbcbccabbddbddccacccddbbccbcabacbdcbbdacccabdaddccbaccbaadaaddcdcdaaccaccdadadaabccaddaaacbbdcacbdbdcccdbbbbbdcbbaadadcbadccddbdadddbbbdddabcadddbaaddbaaddbbbcaaccbaddaaadaabdcbbacbbbadabaaadabcacbcbdacdbbcdabbdadadbaddccdabddccabcaccdcbcddbdbbaabcaddcaddbddccadddaadcbcdddcacbbbbbccbddabaadaccdabddadaadddbddcdadadabdabccbadaacccddbcdddabadbaddaabbbbaddaababcadabbdacdbbdadbbbabdabcacdbaccbcaadbaabcdbbdaabbdbbbccdbccbcaaccabacbbcdacbbccacadbcadacbaacccdadcbddbcacaaaaadcaadccabbbbcbcadaddacbaacdcadacdbcaccddbcabbdbdcdbaadaaacbbbcbcddccabdccdccbaadcadbcbdcadcbcbcaabacbcccdbacbddcccbbbadcaacbdabbccbababbaddcccabccabcabdbbcbdcbbddabccdcccccbccbbdbbcbdaccdcdcbdbaccdcdadbadbdadabdddaacacdadbacbbbabaadadbbdaddddcdabbbaaaabdaaaabbbddacaccbdcdcadaadbcaddaacbcababadbdaabcbcdcabadbbccabaddddbbaccbacbdcabbcbacbaadbbbdabbbbaccddaacbdcbccdaadccbbddbbbbbaaacaccadccccbbcbdbabdadbbdababccadadabbcacbaaccbacbddadcdcddccacddabcddcabcabbdcbbcdbbddccbdbbbddbbdbbbaacaaddaddadcbddbcacaaaabadaacbdabbabcaadcdabadadddbcdabacabbccdbaacaabccacdbacacabcbcababaaadabbddbbcbaadbcbbbcacbccdbdadbddcbabadddcbaacaaaacaccddbabbabcabcdddabdcaaccbdcdababbdabbacbccdcabcbdbdccbabbccaaacdcbcabcdbbccbbcabdbdcadabdccbbadbadddcadccdbcbbbcabbbadcccbcdcdcccbbccdaddabcdadccdbbbadcbcbacacbadbaacbcbcdacccbdbbbacaddacabadacadccdcdaccadaadcaaabdcbaabcacabbbacbbacdbdabbacdcbcbbdabbddcabaaacdcabdcdcdbbdbbcbccbbbddbdcabdbbcbdabbcabaaddddbaaddabbdbdcddabccdcadcaccbbcacaccdcadbabbaddaadabbdadcacdcbabbbbadcdbdacdabdaaaddacdcaddcadcdcbaccbdbdbcdccaadcccabdcdbcbdbdbadccddaabcdcbdcadcaaadadbcaddbcabcbabcabaaacbdcababababcccdddcacdbdcadcbbcabdddccbbbcbdbdccaadadcdcdccaacccbcbdabbacdccdbabccddcadcaaccbbddbcaadccabcaaaccccadaacadabbadcddbaddbdccdcbdcacdcbaaabddddcdacdbcabdcdbbdaaaadcdacbdacccccdadccacadadccdcabdbccaaddccddcbaaabcadddacaacacbdaabcbbbcbdcbbadcabddbdcabaccdbccdcaadaabacbadccbddacaabdcbcbcbbacaabbbaddcccabcdcdcdbcabcbabadabbacadabcacaabbccdccabbabcaadccbccccbcaacadddcdcaacbcbdbdacccabadcbadadabdaabbdccdbabccbddcbaaacddbacddacccabdaddaacadcbcbbddacdadbddcdbbcaccdacaccbbddadcbcccadaccaadabdbadcbcccbcadbdabcbcdddddcbbcbbcbdbcdbaabdcbddacdcbbacbabdcaddcdaaaacddcacccabbcdadccdabbbddbdcdcddccbccbcbdcabcdcabaddbcbcbbbbababbbbdcacaadaacdbdcddcabbacaabacabbbcbaaabdcaaddbbcabdbabdddccbcbbbbcabaacddbadccdcaaccbcbacdbaccaadcbbbbddcabbabcdacddcbdababdbdbabbddddcbcbddddaaaccdadabcbdacdcdbbcaaccdbccdbcdcccddbabcbdcbccacbababdbdcccbbddaadbbcddcaccabcdcdacbadbcbdbbacdbbadccacbdbbdbbccbcdabbcbaacdaacbcdadaddabbcbaaaabaacabaaacaabcccbddcadbcbcdbdcbbcaaddbadbbbcbcacbdcdddacdaaadcbdadabbabdbcdacacdbcadaacccababbcbdbdadbcdcbccabbdacdbbbcaaadaaaacababcdccccccaacccbaacdbdadaadbbcacacbcacbacaccadbdbbccaaabaddbddbcacccbbbbcabbddcabbcbbbbaccdacabaccadcaabcacadbacbdaccadbbabbdcbbaaccbdccdaadbddcabdbadbdabcbcccbacbabaababcabcbcacdbdabbadaddacabcdcaacaacaacbcadddcadaaddcbbacadaaccaccdcaaadcadbbddbabacddaaddbbcadacbddccadabcacaccbccdabdabababcbbbdbacaabcacbdbdaaaabacbdadacaacaabbccbccdbbbbaaaccdbcddabdbaacabbdbbabcdaaabccbccaddaaabbdddddccdabbabadbcdbcaacbacdacbadbbacbaaacbbddabaddbabbcccbdadcbccacadbccdcbcdacdcddccaddbdaabaadccdbadadbddccadcbbbaaacbddbaddaddccbddaadbddcdadbbaacbaabdbddadddddcbcbcdacdbadcaabcbcaadacccbddaacacaadabdcddcadacbccdbaaaccabbdccccacaacaaadccabcadbcbccdccccbccaccacbcdcdbccababdcbcdbbcaabbcdbcadadabcdbaccbadaacabaaaddccdadabddacdaaaaaadbdbaadaaacbbabdbdcabacbbbddcabcbbbaadcacdabbdcaccabbabccabadbadbcbbbdbcadaababadbadccaddabbdddbaddcabccacdccdccbcccbaacbbbcdbcdbadcbadabcbdbcdbdadabbcdbbdacdabbadabdaddbdbaaaaccdbbdaccaabbdaaabbbdccdcbabcbabdbcaacbacdcdbcdbabadcaadbccaaaccdacdccddadbaddbbdddcabcddddadbdcdacdcbaccbdbcdaaacbddbcbcdabaddbcbbdcdacbbaaddabcaaddddaadbdadbcacdbcdccbaacbaaabccbccabcadbbbdbdbbbacacbaccadcbbccaaccdcabdcaabbcdcdbdacdacccadabbdacbdccbbacadbbcaddbdcdbcdaaccbcdcabadababaadacbdabdbbcaaabaaadbabcbdcabbdbbadbdbdcabdacbaccbabdabaabdcddaddcbdbaaadaadadadcbbdacddbccaabaabadcdacbcabccdbadbbadccbbdcbbdcacbddacbdbaabbcbddddacaccddcdbabbbbbbbcdccaaccccdcaaccccccbdcdccbdccbcaadbddcdacdcbcabbdabcbcabbadccbcdcccaaccdbbdaadadaadbcdccbbaabaaccacabaaccbabdabcacdbadbccbabccbcbcccbbaaadacbccadabccadcddcddcdddcddacbbbbcabbabbdccbbddbadbdaabddcdacdcccbacbbbdbcbbccddbbdcbddccbaabcaacdcdbdbcabbadcccdadaccdcbcbcbccbccddcdbdccdbabdacbaabcdabbcaaabbbcadaabdabcdbbdadcdbcbabbaabbdcbddaabaccaddacddcbdbdbdbdcdbbdacadcabaddbbbbdddbdabdacbadabbdabbdaabbabdcddddacbddadbcaddbddaadbbcdbdbcbadcbddbdbbcccdaccbbdabbcdddcdbddcadacabaccdbacdbddbaaaaadbbacbaacccaacdbacbcdbbbdacccbddacccacbcdcdaddbbdcadcadbddbbaadadcbabaacadcbabbdbbdddcabcddbcbbcaaaadddcdaacdcccabababaccbcccdcabddccaadddcaabddbcabddcdcdaacddcddcbdbdbaddcabcdbdaaabdcacdcddacbccbacdcbdcbacbcbdccbbbdcddacdacbaabbadaacdddaacddaabbbaccbdcdcccbbabadbdbcbccbbbbaadabddcbbacaadcdbaadddaabdcdbaadddddbdcabdabcbbbbacacbdadabdddacdbaabcdcbaaadaddddacbaaccacdacbadacdadbacabddcacbbcbdbabacbcbbadcbdacabbbbacdadadbcbdbdadacbbaccbaabcbdcaababcbcaddbcdcdbaabbdcdabcabaaacaacacdbdcbcdddbcbadbcadbdcbdcadaabadacbacdacccdbdcacadddbaddcbdcbdacbccbadbccbacbcaacaccbcaadacbadbaadaadcdbbabbaaaadacbbbadbcdabacdacbbabaddacddbdcaaababbcaaaccadcdacabcdddcddccbcaaaddbaabadababacbadcadcabcaaddbcaaadbbacddbcabcbbacdbcdadabddbadabadcabdbbbbabbdbdbadadbbccdcdacdacaaaabddbbdcadadcabbaaaadbdddcbaabdbdbbdcbcaadcbcdadabacbbcdcbdccbcccaaadbdbcbaaacaaababcbccbdaaadbdbcbbbaaccdbdbccdaccbaaabadbabcadadcddbdabacbdcbdccddaabbcabddcddbabbccdbaadcadacdcdaabaaccbbbacabbadcaacbbaccdcabcadcbcdabdcacbacbacdbdadddcaccacddbcbcaaccdaadddccbacccdbacadaaabddadbabccaabbadaacaaadaddadcbbadccbbcddaadcdbccbdcacaabddbcdbaacbcddacdbbbabbcdbdccbdbabdabcbcbacbdabccacdcdaaacdbaddcdbdcdbcacabdbdbcabbcccdbccccbbcaacbbdbccdcdabdbcbbdbbaaddbadcaccbabddbdaddcccddabcbdadbccdcacdccbccbcdaddadcdbbabbcacdcbbdbddcdadadacbcbdccaaaccbabbdcabdbcabcbbdcabcdabadcacbcdbcdaacbcbddcbbdbddabbccddacabccababdcddbabddcbabacdbdcbbbaabdbcdccdddddbbaaadacdbcdcbcdababdbdbdcbcbccdaddccaccbbdacacabcdacabdadbccbadbccacdbcddbabbbcddcbbbbbadbddcdbdcacbbacdacabcabdcacdcbcbbbcaaabdacbdabdcbcddcdaaadddcccdabbdccaaaadbabcccbddadcdbbdbabbdbcbbadbbcccabaaccbcccadcacabccccbbdadddbdaadadbbbcccbcababdbcabccacbbacbdbbabbbdadbcdccccaadbadbbdbdcdcddcbcdcbcbbabcbcadabbdacbabbddabcdddbcdbddbabddabbbbdbcacbbdbabbcabccccacbaaacbacbdcddddcddccdcccccabcadbccdacadcddddaaaaadddbcccdcabacbdbacbcdabcacdaaaaccacdcdbcdaccdaaaddddbdcaabcbdccdccbbbdcbaacbdbcdccaaadaaadcabdcdabcaccbddbdbbbcbbacddaccbcabadcddddabacdabbcbcddddadacccbdbacaabcdbdcbaadbacbaacaaaabbdcabcbdcabdcbdcdcbacacbdccbaddaabbbbbdadbcbddacbdabadcbcacacdcbbccdaadabdacaabbbbaddcabcccaddaccdbbddadabddbadabaacddbcddcccdcbddcbddddcababcccdccbccadcbbabbbbbadccbcdccccacbccddbadcadbcadaadacbbababcbcabcbaabbbcadbdcdaaccadccbbdddbaaddadcbaddccaadccddaccccbdddbdabbbdabbabdcdcbdbaababacadcbdabacaddaaccababaacdbdcdcbbcabaccbacddbabbacaaddcaadaacbabdacdaccbadacdacdddbccdbdbabadbddbdabdcacddcadcccdacabccaaaddbbccbbaaccdbcadaccbccbdcccbdbdaabdabdddcddcccbddabbdcdcbdbdcdabcbdababdabaadbbdcdbbdadccdcaddbcdddabbadcdadcaababaaacbbcbdccddbaadbcdadcbbbdacbdccbbbbdbbdbbdbcbccbaacdadbdddcaccccabbbbbabcdbbdcabdcbadcbaadadaabbddccadabacbdcadbdbabadcdbdacbddcdacbdbdadbabcdadbcacbddbdbddccaccacdcdbadcaabbadadcacaccbdcbbcccabdcacdbaccddaabcdbcdcddddddbcdaaacadbcdcbdddcbdcdabbcacbcdcabcbadccacabdcbcaabbdaaacdaaadcabacaabccbaacccadcbdadcdccbdacbccabcdadcddacdabbaccbaadbdaadddcabdabbacdbddddaabdaadddbcccbbccdbdccbbbcbaccaabcddaaddcdaaccbdaddddabbdcaabbadadadbbbdadbcdddcddabbbacbdbbbcddbadbdccbaddadbadcbdbbadcaaadcbcaacdcdadadcabbcdbbbaabdaaaabdcbbdbaacdbcbaaddaddcaccdaabdcacaddcbddddacbcacbccadbdadaacadababaacbcccdcdccbccccaaacbbaabadcbadadbcbbccdccdddbdcaccdadacbdbaddcaadcadbbcccbddabdabaccbccdcaccbacbadadacdbcbaddbabcacdbccbaabacabdbcbbdaaccbcadbacaddabcdbaccababdcaacdbddacbaccccaddaaaaaaaccacdcdccbbbcbdcbdccbbdbdbdaaddbccdbcabcbddadbccbcabccbabdacbadcadcdddcadcdbbccadbacbababbdbabbbbbaaccaabbccabcaaaccdbbdddacdbcadbaadbbcbadcdbbbdbbdbcddbbacdbbacddccbaadbcaaababbabdccaadabbdadbaccbdcacabcadddbccbdabaddbbbaccdcbdcdbdbccaaddaacdbadcdaacdcabddababadcbbcdbacaaaddadcbdacabbcbdccbabacddcadadbcaacacdcadccaaddbaaccacdbddbdccddabdccadcdcbaabdadcaadcdbbdcabdadcaababbaaadcaaadbbccbbdbdabbabcbddcbbbaddcddbbccdddcdcccabcbddacdcbcddbcbbaccdbacbabdddaacdcdcdccbbbbcdbcddcdddcbbdacdacbaadcadccdbccccaadacdcdcbddabacabdbdbabccddcbdbacbdbddbbabacbaabbcabcdbcbdbcbdaacdbcddbcdcccdbbabcdbabbbadccdbcbdddbabbaadbacccabdcdbcddbbadaddbbcacbddbbdbccacabacacaadbabdadbadbacccbcbbcbbcdbcdbddcbadbcdadcaaabdcabacdbadaacaccaddbaabcaacdbcabbbbcbdbddccccadbabdcdbbaabdabcddbabcbcaaababdbdcbabccbbddcddbcbbdbccccabaaadcdcddbcadcabcabbdddccccadabaccbcadabcbcbbbdaadbaabadaabacdddbccadabaddbcadcdacaadbacddddddabbcacccddbcbcdcbdbdacdbbbaadacdbbccbdabdddcccdddcaddbddcbdbdacacccbdadbbbbacbcbaaddcdadaaacccdcdabadcbbadabbbcabdabccaccbaccadcbdababdabdbdccabdcabdadbdddcdcbacbdccbabdddbcabadcadbddcdbdbbbacdacaadaddccdcbcdddbcdcddcadddbbbdaaaaddaabddabcadcddabbbaccbcabdbbbdacabdaccadabccbacccaabaaacbadcdbcccdbabbdcbcacaddcdadbacadbdadaaabdbbbdcacbcbbddaadccaaacdaddcabbdaabadcdcadcadcbbccbcbabbcaddaaabdbbbacadadcdddcbadcadbdccccbddbccccdbaccddadbabbbbacccadcabadbccbcacccdbaaddacaddddbbbbdcdbacbcccbccaacacbddaacccbdbcdbaaaacacdbdbdddccabdadccadddddabdcbdabaacaababcadccbdacaadbcacbcbcdaddcaabcbdadbdcbbcbcdaadbbbcbbcbcacadbabbbcbdcadcccbcdacbdbcabcddabaaabcbadcbdccaabccacbcccbcccbdbccbaaabbdadddcacdbbdbcadcdcdbcbdadccccaddcddbdabbbadaccadaabdaccbdbcdbccbdcdbbadacddcdabccbcacadbbdbdaabddacabcaddabdbaccbccacacdcacaabddddccbbbccabacaadbbcdddcbbabcdcdacbcddbcdbbacbdbbbcabbabbbbcddabbdbccdaccdabccdbdbbbbccacaadcabacbacdcdbdaadabcccccccdddbbdcdcaddccddabccdababcbccbcacbbdbdabdaddddcddacddabddcdbbccacbaddddcdcbcbdcbadcacbdbbaabaadddcacbbcaddbcbbacabacccddcdabcdcdbadbadbbcadbddddbbbcabbcadbddbcabcabdddccdccddbacbaccbbdadbacabcadbaaaddabbbbbcdcadbbbaddadccabcabdccdcabdcdbbbbbbdcbbabbdbdacdcbaddbcdacdbcbdabbbbdbbdabddbcdccbbbcbdbbbacbabbbadcdbbabdbbabccadcacccbcbccdddcdadcabadddccdcdaadbdabcadcdbadcdaadcaadcdbcdbaacaabbdcaddadaaccdacbabcaaddddcbcadbaaaabbadbcccacddbdacabddccbbdbdbcaaccadcaaadbcbaddabcddddbccaccabdaabccbaaabacbbddbaaacbddbcaccacdacdbdbaacbaaddcbbdaddaabbdbbacabccbbaccccabcdbddacdaacdcadaddcadbabbbcbbdbcdcabccbaaddacaaaaacabddcdaabcdcbdbdabdbbbcdaabcbdbdccbccadcbbbbbdaabadccbaadcdabadadddcaddaadccababdcddcccabaabcbacbbaadddbbabcaadcdaadbcbddcbacaacdacbddccdbacdcabbaaddddcddcbaacbbadabdadadbbbbabdccababbbddabdccdbcdaaccbcdbdabdadbcbdcdbadabaaccbdbdadaaccdbabdbccdcdddaaccbcabaddbccaadbcdcbaabbddccddcbbbcdbdadddcccbcaccddaccbcbdbccabacbcbbdccabbcacdccaaabadbacdcaaaabacdbdacbdcabcabbdddbadbbacaaddaabbacbdbdabdaccababbabcdbbbcacdaabcaacccaacdbbcddcbcabcbbbaabadddddcdcdcdbcbcabacaadadacddddbacdcbaccacddccacbbdabbaacabcdbcaaabadbddbdcccdbabcbdcbcbbcdababddbbdacdabdadbddcadccadbdcdaccacccbcabddbaabcaadcadddcaddbdbcbdaddabddbaabcaacbbbbcdacdadaadcbdcaadadacaabbdabadabbabcbbdbabccdcdccbcdacdddbdaacaadccdbbbbccbddcaacdcbaaaadabbbbcbaccabdadaadadcbaacdcdcdbddddbbdcbcbddbddbdadccbdcbacdddbacbaddddacdcbbdacbbdbbabdabaccbbdcbbddcbdbcbbbcbadaacaacccbdaaccaaabaddbcdccdbdbacccbdcccacdbbcbdabcaacdababaabdaabbdddccddcdaddbcbbabcdabbabadadbdaaddbcdaadbcaccdbabbdddabcdccacacdbbdcbdbbcaddbdaacbacbaadacacddcabaababbacdbdddbbaadbcabbbcddbcddcdcdddacdcbdcbadacaaadbadcadbdbbbadbaddadcccacabdbbbcababcccdcbaaaddadbccbaccbbcabbbcdbacbdcbacadbbadbcbbaaabacbadccccabbcabcacaaadddbcdddcbaaccddcdbbcbacbbbadacacbacdbdaabbdadcdccabaadcddaaacacdadbcaabcddcdbdadbbcdbdcdbcbcacadddcdacdddcababcbbbadccdcbccabcbdccaacdcbaacddaabdacccbadbadaabbcbbdabcdbbddaabbbcbabdbcadaabbadbabbdcdaababcaaacccacdbdcbbcbbbbcccccacbcabaddbdbccabcabdddccccbacbacdacbcbdbacbbdcdacbacbacdbdcacddaacaccbadacccaabdcbacbabdaabdacbdaaaacbdacaacbcabadaddacacccdadcddcbddcabbaccdaabbabcdddababaabddacabbcbacbcbdddddddababbccdcaadadcdcacbaacdabadcbbbcbdacbbaddbbbbbccbdcbcddbcdabbcabbdabbbccddcaddbababbdbbbacbdbcadcdabaccbdbdaacdacbddbddaadbabbbbcacbcaabcbaaaabcbccabacabbbdbbabbacacabadabdbbbbbbbdadabddcbdabdcbacdaddddbacbdcacddacdcbcbbababcaaadcdadbdbbddccdbdaabbddacbacbaccbdbacaccabbbbbbddbdcaddabacaaddddddaaabddbcaabaabbccaaaacabcbdcdddbbdbbbcdbaadbcdbdcdbcdbbdbbbbcbbbdcaaddcddbbcaccaaccddcdbdcdbcaccaabacbaddddbbdbdcdcaacdbdbcbcadbabbbbacdcddcccabbabaccddacdccbabbdcadaaddbabdbcabadadcdabddccadaddbcbddcdacbacddbcadccabadcbcdccdacddacabdadbdbadccbddcaddcbccadbdddbaccaaaccbaacaaacacbddbccdddacbadcdbdcadcbcabacdcddbadbdcdccbacdbaaaaabaacacdbddabadccadddbbbbdabbbbdccaaadaabcaaaacdddcaaccbbaddabdccbcbbdbadaabcbacbaaabcdcbbbbadcbbddbaaddcacbbadddbcacbdbdadacbacacdddbbcaabdcadbadbcdcacbdccaaadabccbccabccaddabddababccdbabacacbabcaccdcaadabcbddcacababaabdacabdbbcdadbaabbaddcbadadbbbbdddbaccbdbdcadcaccabbaacabbadcdcbaddbbacbbcddaababddcccdabdbbcabdbdbabcdbcbaccacbbadcbaacbbbcaaacbdbddcccadabdbacbbccacdddcacccbacbcddcaacdddbbcaaaddabbdaccabbdcdadccaccadacaaadcccdbbddacaaabaddccdabcbdccddaccdddabccdbcbbcbadbbbcbbddbadbdadddaaddbacbccbdbaadbdcacacccacbaaaadbddabbaacccdaaaadbcacdcbbdcbdcacaacdcdbdbbcbccbdabddbbdcaccbadabacbddabddbccbbccdcadadaddcbcaadbdabcdadaccbabbaddacdbcdabdcbcdccdccccaaccababddabbcbdcaacbcddaccadbaddbdddacabbdbcbbdadbabbbbcaabdbcbbadbcacdccdcbdabadacabbcbccbbdbbdabbaadacbaccadbadabbdbccbbcdcdadabaacddbdabbbacbacbadadddccdcbdaabbcbccdacdaaaacbcbcacdbcabbcdabccabbcbbbbdcbcddbcabdaccbcaadbcbdcacaaddcbdbacaaaabcbdcdabbbbdbacadabbaacaddcdaccdcddcbbcbbdbadcdaabbbbdaddddcdcacbbbacbbcccbdcccccbccbdbbdadddacdabccdadcaaacbadbbbabdcbabaabdadabccccabaacdbdbccdbbcbcccdacbdcbadcaadddccdddacdadabddbacaadbccdabbadabddbacbbdcdcadaccbbbacbcbaddbcacbadcbbccdcbadbbccacadddaadadabbaccdcababcbcccddbcbbaacdbbadadbbcdbaccabbccacdddababbdddcbbcacaccdbdcbdcdbddbdcddddacacabbcdcbbbddabcbdbdbdcbaabbcddadcdaccccbaccccbcdbababccacbcaabbcccdcddadabdaaaccccccbbcbaaacccdaccaaabdbaacacbdabcdabadcccdacdcdacabdaabacbaaabbdbadbbabbcbabdaaabbdacabdacddaccdddabaccdaccbaccdddddabccdddcbacbcabdddbccccaccaddadaddaadbdacbadcabbddcabdabbdcdccdbcdacbddccaaaddcbcccadacccbcccbabdacddacacccdddacbabddcbcaddbddacaddcdbbbacabcbcabcdcbaaacddaaccddacaabaacabadbddccdccbbddbdaaacddddbbbbaadbdbaacbccdcbccbbbaccabbddaaccbddcadcdbdddcaacaddacbbdbbdadddbddbdbcbababccccaaacabadbbbddbbcaddddabddadacabdadbdadbcdcabddccacdcbbdaddabdbdccaadbbbddccbbcbaadccaaabdbbcbddcbccabbbddacadcccbddcdcbbaccbdcbdaaacadcccccabadaadaaacaabcdaaaacaccbdcabdabcbaaddbbacccabaabdddcccbbbabbbababbbadccbddaadddbbddcbacaabdbcddcddcddaccacddaabdaccdcacabdbaacaddccbaacdababcccbaadbabbbdaaddcacdcbbdadbccddadaddbadccddadcdddbdbadcaaddbcabcbabbbcdaccddcccaabdbdbbcdcacddbabadddaaddbdbabccbcbdacccbcddcddaaabbddbbcddbadadbcbcaaabcdbacacadabdcdbadbaccddbacdccdbbccdddaaccdacacddadbcdcbdadacbadaccacbacdcabbcdbadabdacbdacaccdcaccddbacddbbcadccccddacbcaaadcbddabcbbcbccabbddbddbbbccddcbbabbbbccdbdbabdcbcccbdcbaabcadccbaabadabacaacabcbdbacbbddccdcdccbcdbddabdcdadaabdbbacdabbdadcacdcbbcbcccbbbabddbdcbdadbdacdddabadcaccadbcdacbcdbaddbdbcbdcbadabaaabdabcbcdbadcddbddbbdccadbdbbbabacbbbdcdbaadddbbacabaacacabbcbbdaacaddbcabcadcbcadcdcdacddccdbbcccccbcadddccbddcbdbabababcdadccbdaddddccbddaccbdababbcaccddbdcaddbcaaddabbacabdbdbcbaacddcbccbaccaabaacbdaccdadcbbcabdccacaaabbdcadbcccbbbbbcbbbbcdccccaacccddddadcdcdbcbcddbadcaabcabcdcbbaccccabacddbbcaababadcaaabaddaadbbbaabdacdddccdcbdcaaddbaccccdbcddcbcdaccbbbbacbcdbabdaaaaaaddddcddabcdabccacccdabacadcddcabacbdadbbdadbddbbcbcbbbbdccdcbddddcdacccbabdbdcdcbadaadbacdaabaacccabbaddddccadddcdbbcacaacadcddddcacdbcdadcbccdbdadcbadbdabdadbdadddadbddbaadddbcbaaadbccddbbbbbdddbaaccddaadcccbabaabbbbdccdcbaaaabacacbbadcddbcdcbbbdbcbdabbbabdadccdcdabddbaacdbdbdddaccdbabddabaddbdbabcababcdbddbdadccbcddbccddacccbddaacdbadbbdbdbddaabbaaddbcbcdaddbcbbbdbacacccddcddcaccabbaaccbbabbdadbadaccacdbddacdaaaccadaacbadacabdabbaddbaabbaacaaddabadaccbdabbdccddabdbdbcdbaadbbcbcccbadbacccbcacdbbccdadabbacdcdcbabcbddbbababaaaaabdbcabbbbdbddbaadbcabbaadbcdccdbadadcddabaaadcddcdccacaddaccbdbcdbbcddaccbbaadcacaadcbbbbccbddcabbcabddddcabababdcdbdccbaaccadcccdacbccacdadababbcbbddaaacbbcadadbbddabdddbaaccbbabcaaaccaadbcbbaabdccdcbbbcddaacbdcbaaabbdadbabbccdaaaddccbbccbadbcabadaacbbccdddbddcddacdccaabddcabbbadabccdbbbdacbbbbdadbbcbbabacadaddaddadacbdabadbdaacadbacbadbacdcaaababdbccdccabcbddbcadbcdacdbacaacddcadbccacacdccabddbaabbaadcbddbbbbccddaddcaaadddcaacdddddadbddbdabbdccdabcacbababdbddcacbbaababcabccbdbccdcadcbccccadcdadbacccbccdbcadcabcadddbabaccbccbdbcbdbdabacddacdbbdbdaababaabcaaddcabdacadcbdadddcbcdbcddcddaadcacaacccbdbbbaaabacaacdcadcadaaadaccbacdccbcbadcdaabdcdabadbbcddcbbccbbcbdacdbbbbbcdbaabaaadcabaadcbcababddbcacbacaddcbbcbdadcccacbadbaacbccbbcdbaaabccaccdaabcbadbdaadaddbabadbaacdbadabcdbcbabacdaddacabbcbcaabdcaabdaabbcbadbbddadcbbbbcdbdbdcdccbdcbaabbcbabcbadcdadbcacacbdcadcdcccadadadcdabaddbcbbaaaadcadccbacbdccacdcdccdabcabaacabdbabccbbcbbabbcabdacabaacddccddbaadabbdbbdbacbadcbbbdcbdaabacaacbcbccadbdaccdcdbcbabcbdccccbbcbaadacbadcbbbcaadbaabaabddbdddcbabaabadacacdddabcdcdbddbbbcdbbbabdbddcabcddacbdccadcddbcaabaddddbccdcacdccbdacabadcdcbbbcbacccabddcbbdcabbdadadbabddbcbbcababcdcdbabcbcadccaacaaacbcbdbdbbccbbcbbadbcdbdcaaaabdbdaabcadbcbddcddcddaadaddbaabcbdabdaaabdbbcccccbcddaaccbddcbddbdbcbbbdaababcdbaadcdbbaccdbabddbbcbcccddcbddbbcdddccccbdadcdacdaddddcbadaacacacdbddccababbcbbddabcdbccacdbabbdadbdcbddbadacbadcbbdbacbababbdbdadcdbddbcdcbcbadbcabdabadddcbaacadcddbcdababbbbacbccbcbdddaabdadadcabcbddccdcbcaaabbaccaaccaddaddccdbdcdcadbbbaaaddbabdccbccccbdcbdddabadcccadaabbbcbbccadbaddadadaabdbcdabdabcdbcbdacadcabdabcdddcdbadacdddcbbcdacbbaadbbadacbadbdcabdddccdacddbadcbacadcbdddadbccdabcacdcbabccdddbdcddadbbdcbcdccdaacdbcaabcabdaadaddcdacddcdccdadbaccadbbbbcddddbbbadacdbbcacabaadcbbccbdcbadaccbbbddbadcccbaadabdccaadbcdaadabaacbacadadddbacdbbaaabaaaddbdcaadbbcdddaaabdcbbbbcaabddbacadabbbcadccdbcadacabbbcdadabcdadcdcadddabdbbacbbdabbcbdbccadcdbcccaadddddbcaabcbdadbdcaadacdddcbbbcaccbbcddcbacdcbbcbdabacbbaacbdbddcbbddacddbdaacacccacbcbabdbdddcdcbcdddabaaddabcdadaacdbcacbaadbddbddbbdbdadccadbcbcbbcbbbbdcdaabcabdaadccbbacbadcdccdaaadaacdbaaabdcadadcbddabaadaaccaaaaaadbadcccabdbaadddcbacaabdacdcdacccbddbdddbdbdcbabaccddaabdbadacaadcdcdaccbbbccbddaccdcbcdccbdcabdddcbabddaccdacddbdbdbdbaaacdcabdabbdbccbbdcdaaacaacbbcbccddacabbacaacdabdbabbdccaadabbbdaabcdbbaadacaadccabdcbcbdbbddbddabbdbaabdadbdcdadcadaaacaddaaaccbcabacbddadcacbaaaabacabdcbbbbdacabdaaccdabcabbddcaccbcdbbabadacccacdddccbcbbacbdabaddcaacdbacaabbcadaabadacaaabbcbdcbcdddbadcbabbdbbbddabdbdddcabdaaadbcabcccbbbcbabadbcdcabacaabdaadbdbcaadcbbbdaadacabdaddacbabcddabadbaacaacaddcbabdadbdccbaaacdabaccbcccadbbbbaadaddcdddaaacddccaddccdabcccadbbdbcaacabcacbaaabbdcdcdbcdbadabbddddaddadaaddbabcbcadadcdbdccdbbbbdcddddbbbbddabbccdaaddbccadbbcacaadabadccddadababbddcbcbcabcaaccbbcacdacdbaabcdbbaaccadcdcabddaadabddbcccbdabdbbadadcaacacbacaadbbccdbadaacbddaddcaadcddaaabaababbbcdccdcdabbbadbbababccdaacacbbddbbcdbbabaaacbddbcbdbaaaabaaabdaaacddcacdddddbbccaacacadbbacbdadbcaaaccbdcaadcadbaaabcccdccbaacdaddcbabacabcbdcacccacaabdcbdaaaacadbdcdcdbdadaaaacabaaadbcbcaaaacdcacddccabbdcdabccdbdacdcaacccaabcaababbdcbcaddddddcdaaaaacbbcaaabdabbcdaccbcacbccddddadacadbdddbdacbcbcdcaddcbbbccbbdbabcbaaabbadadcdcacbdcbcadacadddaabbdaddaaabcabdadddbacbcabddbddcdaabbdadbbbadbbacdacbbcbcdaaabadcbaccacbcbdcaadbabcdcaddacccccdccccccccdcccdabcbdbaabaabcbdbdbcdddbaddaaabaaadcbadbbbbbdcdcbdccccaccdbdaaacbadddbcdddcabdbabbdccabbdbdbcaacabbbaccddbccdccbacadadacbbdcdccddadbcddaccdcddadccadcadcaabcbaccacddbbadcaabbbddbabdbbdbcbdcabdadacacbcccaaadcabdaaabbbcabbcadaacbdcbacdcbdccacddaacbbddbdabaabacccadaddcccccdcbbddaabadcbaabdbbddaaabddaccacdbdbaabdbcdcbcaccbbaadaaabbaccdbbdaabbbdaddaccacbaadccbddacbbcbcbdbcaabbaddcbcaadaacddaaaadadbadacbbcaddacdbccbdaabdabbdacacabddacabdaaabadaadaaaccdadccadaabcacaadabdbbbbcdbadcbadcddbcbdcbacbddddcdaababacdcdbbdaccababcbcbadcacdabdcdcbabaddadcaaddacccaacacacabadaacbddadcbcbccadddbbcbbaadddcaadbbbccbaaacdcadbbcddddbdaadcacaccdbcbddccacccbbbaccbcaaccdabdbacccbddddbdcacaaadabbcccbacadaacabbdcadccbbccbbbbaccaccacacacbbaabcdddcaacbcaacddcdcaadbacccbcbbacacabdbdadbdcbddccbbbcdcbdbdccdaacadbdbdbbacccaccccdcaabaaabddcdbaadadcbdaabdbbaabaccdbadcddcbaadabbcdacbbdbaccbddbbadacbdbbbcadbbadadcaaaaaddabbbcbccdccaaaadbabccacdbccadcacdcacbccadccddbbdbbcadacacddcbdaabadcdcdabdabcbacddcaccbacbcbbabaddaacbbdbdcadcbcabcbbacbbbdbcbcabcadccbabbabbcddacbbbcaadcaddbdcaadcdcdcbcddbacdccbdabdcabccccdcadaadaacacadddbabadddacdbadaccbbddcccadabdabddccbcddbdbabcdabaccdcbccaddbbacadbcaadbbcdbcdddaccbddbdddcddbbbaaabbdadcdaaaddddcdcaaccbdaddcbdaaaccbabaadcccdbdaacbcdbcbdcacdbbdadcababcbbabcaabbcbdcacbabadbbbbcdcaaacacddbaacbadbabbbcddabcbcabbdccdbddbbdcabcbcbbcddcaccbcdbbabbdaaddacddccdabaccaddbdacadcabcbddccabbdaacdddcaadcdcbaacdddaabdbaaaaaddadbcaacacbcadbcaaccddcbdbbaabddcbabbddccbdbdcdddbabacbdacbbddddbabbbddaaaadddddddaaacbbbbabbccbddcbbcdbacacbcdbcbcbcdaabababaccdaabadbacbadbcdcddacbbcdbddababbbacbabdbadddbccbdccbacddbdccbcddddacbbacacbadcbaaacacbdbcaadbbbbbbbdcdcddbbdbadddbbaabbaacaaabcdadddbaabaccabcdbadbcdddccbbdcdddababadacbacaacdacbddcaaadacddcabdcdaccbbabbbcdddbcddbbcdbdcdabcacaadbcaabdcccacdbcdababccddbbcbbadcbdbbadadcbcdcdbdbcaccdbcbcacddaabadadbacaadaadaabdcbaaaccacdcdbbcdccddbbcabaaaacbdbccddccbcdaadbdbbbbbcccababacaaaaabaccccaabdaccdcbdaadaaacabcbbabababbbaaaaabbbdddbccabcddacaddbbaddabcdbcdaadaaadcbccddaaddcdcccaadddccdaccadabdddadaacababadcbdacdbadbdcaadbbaaccaccaccaccadcdbdbccbddbcccdcdabcbdcdcbcbdccbcbaaacabdaaacbadcbddddcddabcdcdcdcbcdabcdbdaadbaaaaabcaaddcbcdbacbcabcccdaabbbcdbdddaacaddbbdcdcadddbcacabcbddacddbdcadccbadbdabbcdbbaccdabbacabbabddabaccaaccaaccbaabbcbdccbccdccbacaacbccacbdbacddbbbcdddabcccbbadcacbbaccdcccbcddccacbacbddbdddaaabdbdadcdbdabccabcdcdadcbadcdddadbaaddadddadaccdabdabbcccbbcccddcacacbdaadababadddacbdcbcbadbaabcbcbacbcaccccacacbabbabcacddbbbcbcdbbccdcccddcdbcbbcdbabaadaccabbaababacbbdbaabacaccddaccdbccbdccacdababddbabddcbabdabcdabacbcdadbabdcdbdcbbdccdbabacabdddbdcabbbccdbcdbbbcabdbbccdcdadccdbcaacbbbcbdcadbbadbdcddccbdabccddacddcbbcccbbaabbcaccbadacdabaaacbddabbdcabbbbcbdabaccbcccbcbbbadacbdcbadacadcdababbdacbadbbcadbbabbcccdbbcadcdcbdccbcdbbcdcaaccdaacabccbdcbadcddccbbcccabacdbadcddbbaacdccacddabaabababcdccbbdcacbbddbacbaabbabcabbacbcddacbccaaccbcaabbcdbbbaddddcccdaaddcbcbbdaacdcddabbdddbcbbaadaacbaacbddcdbddaaaadccacacbadcbccbbcaddaddabaabcaaadcacaaaddbdcacddaaadcdbcbbcacbbdcaadbcaddaadbddbddadbacbddcdcdcbbacccbcbbdbcbdababcdadddcdadbdcdaabbbdadcacbccbbabcdbdbadacbbdabadadabbabccccdcadcabddcadbccbbbabbbdaaadbbadccadaaddbcccdaaccbcdadaabdaaacdbcaddcdcdcaccdacdabcddcaadbbadbacbdcaacccacdcbddcaacbdbbdccdbbbbdadbcaabccccdbdcdbacaadadcbacdacbdcaacdbbdabaccdbaaccbddcbabddddcbbabcccdadcbcacacdaaadadbadbbbadccdcccdccbaabcaacdbbacbcdbacaadbbcbadbdadcccacaddbbdcddbcadaccacddaccaabdbaabdcbcdccaaabbccdddcdcbbbabcdcdacaabddaabaccbabdccdbaacdddbabacacdacddacdddbacbacdcaaccbacbdcbcabcccdbbadaabbabbbcdabdbaabbcbdccbcacaacaaccbcbbdbabcbcdcdaddcdddaaadccbadbbbacaacdbddcaaacccadcacbabbbaacccbcdcbcbbbccbaaabaacdcbaacdcdabcddaadadcacabcccbaacbcaddcdadbdabdcccdbadaaacaaadcaabbdcbdccaaccccabdccdadbcccccbddacccdaadaabcabbabbbacccabacdbccdbabdaadbccacdcbcbaadabbccbdcdbdadabbcdddcbccaabcbddcaadddacaddabcbdcccbcbbdccbcdaacddcadbdbabcbabbbdbbaaacdcbdbadbcdbacbabaabdddccadcadaaadbcbbbbcbbaddccdadadcbabbddabbddccbcdaacbdcddbcabacbcabcaaadaacddcacdcabbdbbcaadbdcabaaddcacbcddcdcadddbdabccccdbabcbcaccdabadbdbaadcbbbddabdddbbadaddabbbcacdbacccddddaadbaccbbcccbcdcdddaacbcaccbcdcdcaababdbcddddbbbacdacdcabbacdabcdaddbdbbadcdcdadbacbaaadcbcadcdddcdddbdbadbbcdcbddbcdcdbdbdbdddcbdbddabddadabacaaaaddcdadacdccdcbcaaaacadacdaccacdbddadaabaabaabccbcbcdabcbbddcacdacccccddbaddaabbbdcccbadcaccbcdcabbbadadcbcdbbbcdbdbdaabcbbbdccabbdbacbaaddcdcccabbddbccdcbadabacddadbbddccdbccbbcbbbbdabbadcdcbabaaabaccbacdddbcccccbdbcaccdccadcaccabdbcdbbbdbcbbadbccdccbbccccacccbacbcdbbbccdcdcbcadaaabdbcdcabacdbabdcbcadcddcdcadbdacdddaaccabdbbbbdccdccbbcccabaabccbaddbabdcadbabddccbdbaccdaabbbdcddddcacabdcadbcddbcbddbbacdcbacaacadcadbadddcdaabbbccbdacdadcaccbdbabccbcddbccbaccbbcbcddbacabbadbbcccddadcacdadcacbcbaadcdcdbadccdcdccacdabaabbbbbaabcccbabbabcdddcbbddadadaababaccbdddaccccbbcaacdbcdbaccaaccbdacabcadadbcbacdcadbbaabacbdaacdddcbdbacbadabaddbaacabdbbbdccbbbadadbabddacaccadbdddcbbcdacbdddcccbcaadbacabcdcbadcabdabbbacdcaacbbccbcdcdaaabdaccaaaddabddcacddcbbadccdbabaacbcabcadcbaabaaabccbcaadaabcacadbaadbbcdcdaccddbaccccaddacdccdabcdcaaaccbcbccbbacaaddadbbabddbbdaabdbcdadcabbbbaadaaddbddcbbdbcdbbccbccbdacbdacbdbdaabddbbcadbbbcacbbaaddcadacddabdaadcaacdccadccaadddddccccabcbdaabdcddbbcbcdcbdadbbbbccabbcdaabdacbbadcacdacacccdacbdddbbbcddcdcddcddbbbbdacdbdbbbddabcddabbaddcabbbcccacaaadcabbdccadbddcbcdcdacdcdccabddaadbcbbbcdbcbbbdabcdbcaaacddcaccadddcbbbdabdbcadcaaaabcccaadccaddbdabccdbbbddbccbadcdddcddddbaacccccdbaabcdbabbbbcbdcbcacccdddcbbcddabbbbabadbaadadadabccdbdacaadbdcabcbadaddcbaccabcdcdbacbaddbaabdcdbdaccbcbbbabcbbbadcddaaddcbbbcbbbcabdaabbbbdbccbaadddaacbdbbcbcdbcdabcccabdbadbaacacbcaabbbbacdbdacbbaaadcddabbbddbbcdacdaadbdabcaaccabbdbdadbbcbbaaccbdbdcdcbdadcddaddcbacadbdddaabbccdcacdbadccdcaadcabcdbddaaabadccadcbaccacccdddadbcacbadcdacadddbcdccdaacbbcdbcbcaaddbbdbdcdaaabbadcaadaccbaacbbbbacabacaadbbdbabcaaaccdccbcababbbacaccdabaacaacbdadcdccdabbacaaddbcccbbaddccdaabdcaddbbadcabacbcddddbbbcbcbcbbadbcccdcbdccadcbcdbcbbcadcaaadcddadacbbcaabdbbcdbabdacdaadbacdabbdcbcbdccabbdabaaccacadddaccbbabaaccddcdddbbddccadcddccddcbdcddbaaabdadabcabbccccddbdbcdbabcdbaabbdabcdbadbacdabacdabbbbbcbdadddbabddabcbadbddabdccbacabacdbccdabcbaddddbbbdbddbabccbcbdbabbddcdddccdbcbbaacdcdbcdccacbacaadddabbdbbabbcabcdacaacbcdcbddadacdacddadbdacbccccadbcacbabbccadaddbdabcdaaaacacdbadbcdcabcbdcdcdacddbbaadbbdcdbdacbcaaabbdbbccdaaddbdcdddbbacadcdaabcabccdaccbdbbaddbdbabccaadbababbcccddbbbbadddadcbaadcbdcdcadcadbcddddccdacadbcabaabccdbcbaabdcbacbccabbbdbdcbdccadccccbbaacacbbcccddbbcbccaadcdbbdbaaadaaabddcdbcbccdddccadcbbadaadbadcbdcdcdaddcddcdcadbadadddcbbaddddbcdcaaccabdbacacbcbcbcababcbcdcbacbaaaacacacccdbdddbbcaadcacbbcabbcdbbbbadccabacbcdadccdbcabbcbadbcacdbdbacaabbcdccaabddbaaaabcaadbaadccadbadcccadbccddddbdcdbcccccccdacddbdadcddcbcdcadaabdabadccdddbbccbabbacdadadadcbdcbbbabcadcbdcccccdddcadbdbddadaddaabcbaddcdccabdccdabdddadaaccbcacbdbbdddbcdddbbdccddcdbacacdccbbdaabcdaadddcacaddddbdcbbaacacccacbddcbabcdbdbcadadcbcaacbabbdccdbdcbdaadbabcabbbaabcbdbddbdbbcddbbcabbdccabbabbbbabddaaaacadcacaadbcacdddbbdaadadcbadbaacadaaacadaddbccbdadabdaabacaddbbdbbcabdcadaddacacaddbddacddbdabbcacacbbacabadcacaabbdcdcbacdbbbcacdacaaddbddadaaddbcddddacbdddbdbdbabcbbcbadadbbdcbabdcbccdabccbabbbacabcbcbabcdbaadcddbcbabdbcbcccacabcacdaacbadddaabacbccacbabcaccdcddabccddabdbbbadbdabbcaacacccddbcdcddbcadbdbdcdbbddbbcbbdbcbaadadabccbcbabcddadddccacbdabaacdababdbbbaaabadcdcdababcaabcbbccbdaaacbabacbbaacdcddbbdacdcdabcabccdabaaddcbadbaabbcdaacabdcdbcdacaddabacccdacbabbdbbadddcbcbbddcdabbdbaadadcbcacacacdcacbdabdbdcdbcbbcabacccbdaabaadcddcdabadbdabbdacadbddaddbabbbddadcbadccacabcdcdadacbbcdccaddcbdbabaaaabdcbdcaddbaccadbabddadabbadaadbddcddacdcbdbababbaaadbbddddbbbadacdcbbbdcddbddddccbdbaabdccbbdbbddacdababadbacbbdacacabdaddccabbcdbcbaccccdadccaaccbcccaabbbbccabdabbbadcdbbcdbacabddcbacdcdbaacacadddabadbabababdbbdbddadcacbdccdcdabbabbcdcbbdbdbababccccabaabddadbbbcbcdaccbbbbdaadcdbdacdbabddaccdbcaccdcdcaaddadbbaccdbadbdcccaacccdbbccdadbdaaaacabcbbacbcbddcabbbabdcdacccacadcabcdddcbdabacacbbddcaabdcdcccbcdbacbbdaaddcbdbcaabbdacadddacbaaddaddbdbdbbdacbcabacbabdddbbccabcbdbccadccdbadcdddaadaaabcbadcccaabdbddcaaaabcbddcbccddcadccadcacadacccdcabcadccaadcbabddadacccdadacbcdbbbaaabcbaadbddadccdbcdaadcdaabccadcbbabababbbcddbbcdccaacaabaaabcacaccaacbcadccddbbadbcbacacaabbacadabadaadcbbdacadadaaddbaaacdbbcadaccbbaacbdbddddbaabaaddadcadabaabcadbbddacaabbbdbadbdadacacadcacbdaabadcaabadaadbcbbdcccbaacaccabaabcdadcadadadbdaaadcaadcbbdcddccbbaddddcaddbdccacdcabaaacabdcbddcccdddabcdcbbdabacbbdbacbdcbcadbcaadcabbadbbdbbbacbddcacbbbcbbdaaadcdadbacbbddddbddbbddbbdccbbbdccdddabdaaabaabbacabdcaabbccdcbdabadabcdcacdcdbaaccbabcbddddabaddaacbbbccadbcbccadbcbcacbabddaadbccdddadcccacbbabdadddddcccccdcdcdbbddbdcdbdbacbbcaadbabaaccddccdaaaadbdccdbbddddbdaabbaaaaabdbcacbbcccaacbcbbbbdcaaadcbdcbcbbbcabdccacaabdccaabbbabdcaabaadbbabaaabaccaabbdcdbcbcdbbdbbadcdbadabacdddcdabcccabbcadcdaccbccddcadbdbacccbcabbbabdbdbcaadbdacddabaddcccbbcabacbdcacbdaaddbacbdaccdcbcaadadbbbbacbadcdabaadaccbcbbbadaacacbccccdaacbaabbddacbdbdcaacdccccdabbcccaaccbdddbaadccaddbccdcaccbbabdbacbdddaaaccbbcaccacaaccdadaccdbcccabbcaacacccabdddccdbaccddbdccddbbbbadabadcbcdcbddccddddbdddbdcaccddabadadbccabcdaacbddddcdaaaaacbccbbbcadbacdccabbccdabacaacadcdaccbababbaaabdacbbdbccddaacdbcbadabbdcdccaabcdbabccbcbcddaacddabbcdaadadcbccbaabcbcaddadcaacadcadbaaacccbbcababccbaacabcaaaabdcdcbdcccdaadcdcbbbcdbadbbddcbcdbaabbbcbcbbcaabacbccdcdaacbbacbbddccdcdbcbadccbdbaadcdbbbdbaacbbbcaacdbcbacacdadcdbbcaadadabdabaaadabacdbdcdbdcdbbbcbdbccabbbcbadaccaaaaadbabdcdcacdbaadcdaddddcaddbbcadaccddcccacabbbdabcadaabbacccbbdbcdcabbdbccdcbddaaadddbbdabdbbdcddbdbaaccddadadadbdadddbcadbacbabdabcaadccddddccacabddabaacbbbdabacbbbbbbbabdabdabdaaaddddbbbcdbbbcddddbcccdabadcdacadbbbadbdbaabbcadadcddacccdbacabadbbdadcbbabbdadbcdbbadcddccddcdbbcacdccdcccccddbccbbcdddaacdcdabbbaadbdbcbbcccdabdbdadcaaaacbacaadadcbddbbbabbcbcbcdaaaabdccaccdacdcbdccadadddadcbbdccacbdbcdccdbbacbbdcbbcbccbbcaddaacaccacdbccbabbcccbbcdbdaaabbbabddabdcdcbbcdbccaabddadbbdccbcbbbdcbbdacdaadacbcaaaddabaadadbbadaacdacaabdacdcabcdbabbccaababdcdcacaaaccbddbabadaaabcbbaccbacddccddacabdbddaadacbbbcdcbbacdcdbacdddadaacbbbccacaadcdcbcbddccaaaacccdcbabaabccbabbabadbaaadcdadccbbdaccddadbbaabcbdabdbaabddaabcaacdccdaccdbaccbddccabcaacaabacdbddccadcbbadbaaacaadcadcabcbcccbdcbbcdcdcbccdbabbabbacdacbaddcbadbcbbccbbaddacbbbcbdddbacdcbdadcccdbdbcdcbaddddaddbcdcbdbaaaddcbccdcdccbadcaadcababbcdaabcaaddbbabbddcbcabbbcadaacccbcdcadcddbdddcdcbaaadccdaccdcabddcababccdcbcadaaccdbccbdcdacdbcbadabdadaaccdddadacadcaccaaadbddcadbcbccadcdbaabbccbcabccbabbbabadbcbdbbdacdaabdcdcddbdaacabcadabccbcabbbbcccbdbdabacddccdbcdbaadabdddcacbadcbacaddcaadcdcacacdccdaacbabdddbbcbddbaacbccdbdbbdbdaccbbbbcaaccabcddcbccbcdcadddbdbbcdbdacdbdcbacdcdbdcbbabdbccdaacbaddaacccacabccccaabaddbbaaddabccaaccadadbacddcccbbcadbcbbdabbcccdadaccdccbdacaaccdabacbbdddddccdacadaddddacbbbdabaaccbdddbbbcccacbaaababbbaccacddccccdabcbbaaccaaccaadbbccbdcddcbbdaccaaaadabdddacccbadbbdadbaababbdbcdaadbccbabcdbdcbaaddcdaaadadddbcbacbaaacdbddbcddabddbbdabdccdbdabccdbbacdbccdcacdbbdcdaadabadccdbcdcacabdadcacbdddaacdaccacbcbbccbdacbcbccadabbcccabbdcacccbddbcdccbadddbaaacdbccbdccaacaccbccababacbabbccaaddbbbddbabcbcccbaaacacdbbaadabcadaccbcbccccccabcddcdbcbcbdbabdbbcdadaddaaadcabbcabbbcaacccacccdcaccbabbdaadcdddacbddccbbaaddbcdcbcabdcbddccabdddbdcbdddcdbddcdcddccaabcabdbacbaddbaaaaccdbaddcbdaabdddaddabddbddbcbbbccbaabdbbacbdbdbadbadcabcdcbcaccdcabaaacbabcdcbbcccbcbabdadacdccdbbcbadbcbcaaccdaccabcdabbbdcaccdbcbdaaabdcddbaacdbacbabbddacdddaabbccbcadccddcccdcadbcddcbacabacaadaaccdaaababdadbddaccbdbbbacaabadabacbacaabbdbccdcdaaacbabcddcadacbdddbddddabbdbcaddaddabababcbacbbbcabbcdccacacdccdacbdaabdcddcddbbbbcadccacbacdcbbacbcbdcdddbaacaacabcbcbbbbcabbadbbcccabaccaccbddbdbcbdcddbcccdaabbcdbccbbcdbadcadddbbccaaadddbbabadabcabcbcdaaadacdabcdbbdcbdcbdadcaaabdabcabbcccbcbabcaccacaaabbcbbabccbdbbacddbbbadccacbacdadaaccdababbdadcdaaddbcdaccadbdadccdaddaaababdbdbcacbdcbdbddaaddddcbdacbacbbabcacbcddaadccbdabbabdddaadcbacddbacddcdccbabccbcadbddcdadcdcbaabcdbbacccddbcabdddbaadcdaaadcbaabccbdacbccbaabcacacbdcbcddbacabbcabacbbdabdaadcaadaddbcacdaddcacdbaadaacdbadcddaaabbcddbdcdbacbbaccabaaaaabccdcdaaaddbacadbcddbcacdabccbbaccddbcabaadcabcadcdbdbdcbacbbbbabbadcbbbbcdcbabaaaaddccaacabacdcadcddbdbdddabbbbabccbdbaaccbaaacacaddcbdcadbcabbaadcbbcdbdcbadababdabaacaccbddcabcbdccabbabbbdacaaaabaddcdcaadbadacbcaadcddddaacbbdadbbbcdbbddbdaddbbccddabdbacdaaccacdbdccddcdababbacdcdcaddbdbcccaabaaadaabbdddbaacdbccdcaabdbbaadadbbbdbdaacbacdcbbaddbcaddcbddcabcaccdabdbdbdcbabbaaddbabddddcbcdbabaddbcbbdadbbcddcadbaccccbcccbdcadcbbdbadbbdadbddcbaabcbacdadaacabaaabcbaaabbbcdaacbcdddacccdbbdcacbbdabddbbbbcacdaadcbcdadabddacaacddaadacccacdcaddacadbbbccaabddbbdaddddddababdbbbaddaddaacbadbbdccdbadbacbcdccbddcdcdbaadddaddccacbbcabdbcaaaadacacdcbdaaaccdacaddddcdbbcaacabbcccadbcdbcbdcbcbbacbbddcdcabddbdaaadbbdadcabadcaaabdcdbbcaddaabbadabdddbdcdbbcbdabcadaddcbbacbdcddcabaddaacdbabbccbbdbbbccbaacdcbbacacdcccabdcbbdbcddbabacdcdbccdaaababdbccdbdcddabcbdbbcdacdaaacabbacdbabdabacdabdaacaabcbcadcbabdaddadbdbcbdccdbacdddcdddbaabcbbdbbabccbbcbabcbbdbddaddddaaadcbdaacdadbbbacbbbcdbdbccdcadcdcdbccabbdbabcbbbdcdbacacdbaacbcbdbacdccbaaaadaccacdaaddbdcbccdbabdadbaacbdbdaaccddcddbcbcacdbbddacbaddcdcadaabcccbdbcbbacaddbabaacdadddcadcbaaccdcacccabbdddaadbdaabcdcbaabdcadabccdbabcacaabbdcbddcacddbcbadddadcdbcbcbdbddabcabdddbacdbdaacdacabbcaabcbababacbdcddcdadbccbcbcdbbccbcbaaadcaccdcccabddbdcddbbbabaddcbbdbbadbdbcaccaadcaababcacacbadbdcbcadacdbbddbdaabbdcbddcdbabcdbcdabcbcdbacaddacdcbbdbcdbccadbabdbcdbdabaabcabdcbddaabdccaadbbcbbbccdbdbbaacadabdcbbacdcbccddbaadadacdbcdddcaccbbbaccaabaddbbcbabbaccadabcbdcbbdacbddcbdcaabdcacbadcbdbaddcbdcbbbabaabbdaacbabdbccdbbcacccadccdbdbabaacabbdddabdbabdabcdcbbcadaaaacdcbcadbdbbaddbdbcacdaccacddbccbdddbaabdbdccdcbcbddcddcabbdbbabcbdacaabbdccccccbcabbaabdbdbbdbddaccdaddbdbadcdbbabcadacabccacccbbbaabdbbddcadddccccdaabcabccdcdacddbcddaacdcabaadbcbbaabcdbcbadcbabdcadabddbdbdcbacdbaabcaccbbddbdacaaaacccbbdadacdcaaaacdbaabadccdadcadbbccbcccccaddaabaadcaadccbcbdaddabcabbccbaaabdbbaaacbdcdbabbadabbcdadadacdbbdcccabdababccccbacdbaadbaabcaacbcdbbcadbbacbbaccbddaadccadddbbaacccacabbaccabcccbbbacddcbacccadbcadcacdabdacabdcbdbacadacbbdadbadabaaabdddabadcbabbbcdbaccddabcddaacbdadbbdddcadccaabcbbadacacbcdcccacadcdccbcbcbcbbccdaddabcadcbdadcabcbbccbccbdacccddbcdacbacacddbaaddcbccabbadadaddadbabbcddaddadbbddacbdcaacdcacbdcabddbcdabbdcbddccbacababbdadbaccccaabcdaabdaabbcdcabbcadacabadcabbcbaadbdadccbacbddbbabadabbcadbaccbaadcaacabacdcabbbcccaadadcbbcaddaacadccdaacaaaabdddcbdbaaddcdbbccccbabaadbaadcbccdadbcbcbbadbadbbaacbbaabcdcbaccbabbbbdababdbbdcbdaadbabcdbabbaabdacdacaacbadbaccbbabdbccabdbcacacacddddbbbccaaaaacbbbdacaaacaaaabbabbadadaaacdbcdccadacaddcbccbcbcbcabcacacbcbcadbdabaddadbadabdbcaaccaadccdcddcaddddcbdabdcbacdbccdaddbbcbaacccaabbdbbbdccdbccbdaaadbbcdcddddadccabdbcadddbdcbbcdbdbbbdacccdabccbdddbbdcaabddbcbadcbabdadbbccbaaaddbbbadccddbccbbbcadabaccbabdcccbbdaaddcccadaccbdadbcabadadcacdabbbcdadadbcbddcbcbacbddcdcbdbdbcdbdcacbdacdaadbdbbddcadabadaacacbdbabadcabababbabaccadcbacccbcbbadcabaddbcdcccdbdccabaddcbbacddabcbababcdbdbabbcdacbbdbcadacccdbccaacbbabacbacbddbabdacaaddaaabbcdaddcaddcabdbdbcccbcbbabbacaccddcdbbddbacabdddcbdbdacdaacdcdcabdbdabacccbadccbcacdbaddbdccabacaaaabccacdccddccbcadcddcbaacbddbcbacaaaaadcbcbabdbdbbbaaddcaacabcaaabbcbcccdacbccacadbabdacbdabddbdccaadbaccbaabaadaccaccbddabbdddbbcaadcaaadbdcdabbaaaabbdaccadabbcabdbdbcaacbcddacbbadbccbcdacbbbcbadabdaadcbdddbddbadaadddddbcddbabbdcacdadaadbcaacbdadccdaddddddcdabdccbbcacccacccbddccababdabdbccaaabcbdbbcbacaddbabcbaabcbcdabddbdccabccacbcaabcababbbbdcccacbbcdbaadadbabbdabadddbdacdcbcdccdcdacacabccbcddbacabdccdcaacbcaabbbcbdacbcadbdcdbcbbcdccdcddccdadcbbbcdcadddadbbbdbddcadbaddbdbcccabbbaccaddccddcbccbbdaacdabdcbcacccdcbadccacadcaabdbaddacacbccbbdcaaadbdbcbabdccaadacbbabcbcadabcbabdccbdcabcbadadbadcdcbaabbacadacdbcbdadcddacabcaacddddaddccbaabdaababbcbbcbadaacdcbdcdbbadaadbdccacbbbacdaadbcccbbcbbcdcdbcbbcbaabbcaabdcbaccadcdbbadacddadcbcbcddbabadcbacbbccccbbbcaaddacadcabddbaccdacdadaaaaacccbdbbababacdacdccadacdaddddaacdcbbccbbcaaddcabbbacccbdbccbaadaaaabcddabdbadcacaccdddcacccbbbcbdacdbabdcccbbaabadcbabbbbccacadbdccbacdbbdbbdddadcaacddcbbacbcaaaabddaacbccbdbbbbdbaadccabbcdacaacddddcddbbdbdbadaccccdaaccbcbdaccdddcacbcdddbcbbaaacdaaabbbdcdbaacccacbdabdadcdaabdbbbacadcbaaadbcadbacbacbbdbddcbaaaabddcdcaadadcbbaddcacdaccaadacdbcbbcbddbdbbdbbcddbbcbcdbacadcadddadccdbcdadcdaaccdaacdbcbdbccdcaadccabbcdaabcdccacdbadaacabbadcbaadacbadccddccbdaddddccdbbaaacbccbadbcadddcaccacbaaccbdcdcbdcdbcaadcbadaacabdcadaadbaabdbbbcaadaabdccaccdbddbcdadabdaacabccdbdccdaacabdbdcbcdcdcbbbbcadcbbbcacddbbdacbbcccaaadbabcbbbbbdbdbdbbbbaadabcddacbabbbaaabadcccabcadbbaacbbcaadbdadddcacccaaaabcdabbabddcbadcababdddbdbaaaccdaddcaadacbcbcccbbbdacadbdbccdcbcdcabdadcbbbdcabcbdadabccbcaddddbcabcccbabbbdccdacccdabdcbbdbdcdbccaddbacadaaabbabaaadabcccbcabaacddabbdadbccacdaacabadacdbcbbcdcddadbbddbddccccbcdccddbcdadababcdaaadcbcdcbbabdcacdaccbbcdcbcabbbbcdbabbaaabadcbbdbdddbadbdbcdbbaaacbaccabcbbcaacabcdcaadcaddcdadcabccabbddabcacbcccabbdcabdadddabadbaacbaadbcbcbcadbcdbcdaacbcbcddaccaadcaaadbdaccacdbadadbaababbbcaddacacbdbdabdaadbbcadadabaaabbcccbccdbdaccdcaaddcdbadaaaadcaccacacdabaabacdaadcccabcbcdcddadcbcbddadbcacbaccddbbcdbbbcacdcaabcaacbabaadcabbdbccbbadadcdaadcdbdddadacaaacccbcbaaddcdcaccadbdaaaabdcaaabaacabbbbaddbbbacbbaaabbcaaccabccdabdcddbdbccbbaacdadbbdbdbbbaaddbbcaaacbdbdccbbbdcdbaccbadaabdcacbbbcdaaaccabccbdcdbcacabdcaacbdcacabdcdbbdcdcdccabbadbacbacccbacbdabbaddbbdadddccbaadcabdcccbccadadaadbccbdcaaaababcaadddccbccaddabcbacdadccbbcdaaacabadcdbcbbbbbbbddddbacccdbbddacadbbacbdbbacbaddbadbcbacbadbcbcbacdbabccbdbddbdcdcbbcbcddaccacdbaaadaacaccbddcbdaaaaaccaddbaaccabcdcacddabcadaaddaabcbbdbadaabbaabcccbbacdbaacabbbdbdbdbcdaadcbcbaabbaaabbddcbcdccabababaacdcabbadbddacaddcdbcbacbdacdaadbabaaddbcddddbadabbbbccccbdcdbcbaacccbaadabababdcbbcbcaadabcdbabbdadbbabaabbbcadaadbcaacddbdbdcddccbdcbccadddbbcbddacbbbacadbcdacdbcbadcabaaadaaaddbaabaaccbdacdcbbbbccbbcdcccdaaaaddaadadcbcababbdbbbdbbddaaddbabcdbbcacbaaaddcdbaadadcbcbaacccbadbcaabcaaacbcdbcaabaddaaabaadabddadaaaccbdcbccadddbbddcbabdcbababccaaadabbdcbbacbccabccaadcaaacbdddacdaabadcdaaaddbdbacaddaaccccaabababbbbcbaccdcadcdcabcbabbcaacadbbaaccdaabddbaddbcbdccdadbaccbacadacdaaadadcadddbbacbdabbbacaaaadbbbaabbacdcbadbaccbaaaaabdbcbddccccbaabaabadcddccbbaabddddcbcadabbcaabcbacbcadbccbabdcbdadcdbddcbccdcbdaabbbddaaacdbbaadadbdbcdbdbdacacaabccacccaddacabcdbdcddbcadcbddbcabcbacddbdccbcbabbcaabddcddcacdbcdabdaaccaddacccacdcdccacbddddbdadcccdccbaadbadabbbabdaacbacbdcddcaaaccbadccddcbbcdbbdadbcddcbcbddcccbbaadbbbbaaacaaddccbcdcddacbbbcccbcaaadaabdbbcccdaacdadbbacbdadddccadcddbbadbbaadcbdbdccdbdbdbbadaddcdabacadbbcbbabacdbcdbdccaabcacdddbdccdaaacabaaacbdaadccabdcdcdabcbcdbbaaccabdcddcdaacababaabdbaadaaccbbcaadbbbaccadabbcaddbacbabbadbbaaaadaabbddabddbcacbaccbbcbabcddadabbbdcacdcbcbcadbddbbcbacbaccabdbdacbddbbddacabaccdccacaaaababadcddbabdccccddaaaddcabbdbbbabcaadcdbcddacdccbdbdbcaaccdbbbbababddcbdbadbccadcadcbdaaddccbddbabcddcbaacbdbdccacdacddddaacdddbdbdbdbdbbdcbcddcbcbaadaacacbcbdbaaaadacbbbdbbaccbaddacadcabcacabddaaabbaccdbddaaccaccaaaadcadacdbbcddabcdbbdadbcbdcdacabadddbbdadcccaaaaddddccddaaddbbccbdaaccdadadddcbbdabbdadddacbbccaaddbddaddbcbbdbacddacdbdddcdcbdcbcaacbccaaacdddcacbcadbaacabcdcbbdbccddcaaddccbdbbddbbbdaabcabdaadcdbbcabbbcaabcdababbbabcacbabddbdddbabddacdcddbcbcacaddcccdbbcacbadbcdbbdbddcccbbbbdbaabcdbcccccabdadcddbddabdbddaaccbaadcbdddccbdccdccbdaacbbacccadbcacbccabcbabaabbdaddddaccabcbdddaadcdacccdcddabcdabcdbaaababbddcacccaacccbbdaccabbdcabadcdbbdbbbacaaadcdcdcadbacbacccacbccabaababcacabbdccbbacdccdbcdbdcadbbccdcaabadacacabbbcbdbaaacdbacabdadcbadbabbddaabcadcacaadddbdbccaddadbcabbaddccdbcbaccaaacbcaddcccccbdadbaaacbcbadaaddbbddacdbadcacdabbdbabbdadbdcabadccdcacbbbddbcaaacccaadcbdccdbdaddabddaaacbbccbcbccdcbbcacccbcdbccbddcdadcddddaaadabdccccacbadaacdbcacdcccacacaaacaaadddbaaabbadaaccdbacddddacbdcadbcbacbdcccaadbdbcbcddcdddabcddccbdcdbccbdcaacacaadabdaccdddbaabacabcacbcaccacbaccdcabbcbbbbaacbcdbbbaccddbbbaaaabcdabdcbbbbddabacdcabacdddddabbcbaadddbbcdcaabdacacbdbddbabbddacbbcabadcddaaabbcbdcbbadacbdcddbbccabaccddabbdbacdbcccbcdcdadcdacacbaaacbababbcbcbdaddcadbadbdbadaddbaccdaabbacdcbcabaccabacbaaddbacdacddbcdbbdcbcddbdbccbcddbcbcccaddaadaababdbdbbbabbaadbbdbbaaaadbccabcabbdaabdbacacccdbabacbdbbaccdbcbadacaccdabacacaadbbcadabbcacdbdbddabcaaabbddddbbadbbaadbddbdbccaddbabbdabbdabaabdcacccdadbdbbcbdbadaacbacaadccadbacacdadccdabcadbddaaadcadbcddccacdaadbbccbadabcdabdbdbddcdacccaadccbacccdcdabacdcaddbbadbbbacbdcbcdbcdddbbdacdcdcdbdccbbcdaaccadbaababbdacbbdabcacccacadcaddcabccaaaaccddabbdbacdadcbddccabbcbbcdacabbacbbbacdccdbddcacadcdacdddcdbbdddcabcbbdcbabadaabbbcdbdcbbcdbbabdbdbcbbcccacbaddcccbbbcacadacdccdbbcaccacbdaabbddaddddcddccaabacaacbbabacacabbdabdbbaaaccaabddaddbccacaadcabbdadaadcacacbdabbdddbbabbccbdabdbdcaccdbbcacaadbdbddcbcdbdbddcdbddcbcdabcdbbbadcbcccaabcbacbddcbbdbcbcbdcdacbbadabcdaaccbddccdacacacbaddccbbdabcaccacaccbddbbabaabacbccccbdaacaddddcbddacdbbbdbbccdddbdcbcddbaacdbaddaacbdbaddaccbcadccccabbbbacaacaddcbabababbbddacbaadbbabacccadbddbcacaccbadcdcbaddcbdabbbdbbbaccdbdcdaabaacbddcacbbddcccbddcaaccbaadbdcddddadaadcabaddcaccadcdddbbbbbbbabccbcaddcccaacaaddbdbabbdbacdbdabbbaadabcbbaaabdcbbaabdaabaacdcdacbdabacaadaaaababcbbdbbcbbdabbaccbbdcbddbbdddddcbaaccdcbdbacabadadccbabdadadacadcccdaacdcacaabdcbddadbbdbdaadbcabaabadadddcbbccccccbdbddbaaadbbdadbcdddcbabcccdaccbdabbadbddddabccdababbbcbbabbacaddacdbdaabacacbddababadabbacaadbcaabbdbdbdacccacdbacadbdcddadcdaacddcadcbbdaccacbccdaadacdabbcdbdcccbbdaccacbccaacdaccaacbbadabcaacdcbdbcbdcdcdbcbcbcccbbaabbbdddacdbaabcbdadacdcdaabbdbacdadccacacddbcbabbdcbaacccccbdabcacadcaabbdccadaacccbcdaabccddbdcadbbdbbacbdaacabddcabdcdacacdabbbcddbdbadcbbccbdbbccaabdcaabaddcbdbaabaccdbbacdcabcdcbcacacdcaaabdaadbbcabbcccaccadccdcbbadaddbaabaddabacbdddccbdbbcacadcdadadddbcdcadcadadcadbaccccacaaacbbcbcbadbdbbccdccdcbaaccbdcbadcdbbbdbcbadbbddbbddbdbccdbbdccdcccabaaadcdbcddacbacadabccdcbdcaccbcbaabbbbcabdcdcdbcdddcbaacacacccddacabbcadcdcbdbcbcbcbbabcdbcbabaadadbcddccdacbbddaddabdaccbbbbdababddaacdadbbbcdbbcbbacadccbaccdcdcaaadbaadddcbdbcacdcbcacaabcbdabdbddacdadacaadbbcbddbddababddaddbdcdabcdbdadadaabbdbdcadabcdcbabddabbdadccdababadcbcacccabbcdcabbcabcaccaabcdcbabbdaccabddbbcadcdccacaabcbadabbbbaaacadadccdacbdabbcaccacbcdcabacddcbdcdadadcbcdcbdbadacddcdaaadabdcdcdddbcccabddadcbaabababbdbdcdbccbcccbddaacabbbaabbaddbacaacaaaaacddccaabdcaccbccaabcacbdadddaccaacaddbacdabdbbdccbadbdbdaddcddcbcbddadadaddddaccbdbdddacdcdbdddcacacccaaacacaddaacbddbbacadbcdcdcbbbdaaccbbbcdcbaadacabbdcdcadcabdbdbdabbbbcccddcbdbcbdbaaddbcdbbdddacabbaddabaddcaabbdbcbdacacbbbbdbbdcdbabddcccbdabcadbdaabbdccbaadabdacabbcbcbcbcccdddbddddbccbbdbbdcbdcdaddbcabcacdacacbacadbcdcaabcbadaaddbaaacbaccdccbdacdbaacddcddaacdababbccbddadcacaabdcddabcaaaacdaabbbdabbcdcbdadcbdcbaabcaabaaadadbdbdbbcbbbbbadcddcdcaccbddcdcaccadcbcbccbdbccdddddabdbcccbdbaacdbacadbbbcbdaaacddbddadcadcacaaabadddbdaabadcdbaabbcccbcbacacabdcacdbdaaddadbdadcadcaccadcccacbacaabbdddcadbbaddcabadaacadacaadacacddcdaccadddadddcdddcaadbcdadbdcdaaaccbabbcdcdbccdbbcacddddbcadcdbdaadccaaacbacddacbadabbdbdcdcdbacbbcbddacabbacaadaadbaabdbbdbcbddbaccdbdabababadababaaacabccdabbcddbdbbcdcdabbbacbacddddacbacddcaccaccccbbabcaabababbcdabcdbdaaddcaaadaaaccddcdcbbbdbaabcdabbabcccdaadacbdccbbdccbbdbacdbadcbddadcdbbbcdbcdbadcaccdbabcaacaccccbbbccdabdaaabbbbdcdcbbdcbcddbcaccbdaccbddcccdbbcacacbbcaaccacadcdbbbbcbbddbcccabaccbcadcaacbdcaadbdbdbcdbcbaadabdaccabcddccddbbbbcbbadacbacdcbccbcaacdabbbacdccbabdabcccdbacbacdccbabdcbdcdcbcadcdcacccaabbbccadbdaacaabdcbcabdbbcbbdbdccaccdcadacddbaccdbbdbbacadccccbbdcabcbaacdbddcbdcdddabcaabdcbaacbcadcbcddbdcbcbbddadabdabbcbddbcadbbddcabccbbcccaccbdbccbdbabccbddddccabbaddaaccdbadbbbadcbaaabbbccacabdacdbbabaccdbabcbcdacabbabcadbcacaabaddcaacddbccdbdaabddcdcdadbbabdcaabdddcdddabbaabcaaaccdccdacacccabaddcbccbaddacdbadbdbadbbdbdbdddddabdbdcadbcbcdcdbabbdcacbcbccbbbaadbdbaaddddcbaccbbabbaccaacbdbbadcdcaacbdbaabccbdaabccddcdadacddcccaadaddccddaadbcbbdbdaccbabcdaccccadadbcbdadadbcabcdaaababcbccaccbbcaddaadadcaacadbcbaccacabdbaccccbbbccbbdcbcbaabbcaacdcdaccbacdddaabccaadddcbcbbaccbbddddcaabcbadcaccaadccbccaaddddadaababcbdabaabccbcabbcaabaacdbcccdbbcdcbbadcabdabcadbcdccabcdbadacdadabacbaadbdabcbbcaaabdaccdbabcbabbcbadbcbbdadaadbabccdcabadabbbabaaabbcddcacdaddbdabaacabdbdadaddcbbbbadddcbaabaaadbadcadbbdbdbcacbbcaccbdacddcbbbcbdcbacbdbbdadbaacddbaabaaaabcabbbbdaabbcccbccdccacbacdbbadaccbddbdcacdddbbcbacdcbdabadbcbdcccadddaabbdcadccadbdbbbbaacbbdcadaddcabcccdacbbaacdcdbbbbdaaacbcdcbdbcdcbbaccdddbcacadbcacaddaccdcbadabdaddcddaccacccaaddacdcbdbdbccddddbdbccdabcadbcccdbacdbdacddbbdccddbbdbdbccbacdcddaabaccccbccddacbbadbdddbbacbabdaacabddadacacdbcaacaccddcddbbaaadbbbcbbcdddadaadbdcabddcaadbddbcabddaabddddcddaddbabadaaacdbcabaaadaacdbddcdcaadbcbadcaccbbbdbcadbbabcacadaccaadcdccaabbdaadacacccccdaacdbcdcddbbccbaabcbaabdacbbcbaacacadcacbaacaacadabaabacddadbdaaaadbacbbbddbddccbbbaaacdaccccbdddccaacacdbaaadcdbbddcdbbdcddbcacaadbdabddbdbacccccaacbabbccabaddccbaabacdcabbbdbbaddbaccdcdbddccacddbbabcbdbbcbaaaadbdababdbbdcdbbcddabbadacabcdbcbbaaabcaaccddbcdcaacbcadbdbdbcccacbbbbadbdabadadbdbadbbabacbcaaccdbddbbbcacccacaaabdbbdcaabbdbaacddacddbdadbacddadbadbbacbccabcddbcbbabaadadbcadabdcccadbadadadbadbddbdccdbcdcaaadadbddbbadddbaacacbbacddbbadcccccaccccadccacbdcabaddbcbbcadbadabacdccdddadbbbbdbdaabadbdbaccdbbccccbddadccdabdbbbadaaccdbcaaabbdcacccdcabcbbbccdadcdcccbccddabcabcbdbdbadcadccdcdcdbbcbadacdaddddbacabddbdadabcddcddaaaadbacabbddcaaccbdccbddbaabcadcdbdacdbabddcbddaabaabcccacacbbacacabcdbddabddcdccddccbadabcadbddddbdabadcbacaccddddcadddcbbcddaddbbaaabdbbcdbdaaccbbabbbdaadcbabbbbccbcacadbdcadcbbaccdaacdddbbddddcbaadadbabdaaddcbabccdbcdccaaaccacbaccbdbcbaccbdcdcadddbcbabcdaabadaadadcdaccdbdcbccdcbacbbdbcbdddacbdbdbaaaccdcbdcddaadbbabcdcabdbabdbdcbaacbdccadccadadccccabcddbbaddbbbdbcabdccdccacdbaacbcdcbdacabcbcadcdabcccaabaccccabadcccbadccadacddadbadbdacddbcbdbdcbbdccdacbabbcdcaaddaaacbcbaddabcccbbcdadccbcacabbacbaaddbaaacadccbadaccbdadcaababbadbbcccddbdbadabbdbdabdcabddcbaabbadababccaddbcbccadabadacbcacccaadbddccaacbdacdbcbaadadbbdabcbdcdcccdacaccdadbdcdadbdcbabddcaacbbbaabbaadbbdacdbcbadacbbcbbdadccaabdacadbcdbdabddcdadccbdbddaaddbddcddcbdbbcdbdbcdaadbaabaabdbcbdccbdabbcadababcbdaacdcbbabcabadaaabbaaaccdacaaacbdbdcbcabadddbcbdcbdbbccdadbccacdcbddbbcaccacdadadabddcdddcdccabbcdbdbddcddcadcdcaacabaddcbccbbabcdaacbddadcaadcdcdbdbbacaadbbbaabacdaacbdddddacccadcccaccbccbbdbcbddbcadcdcbbcbddbbcccbadcadbcdcddabdbacbaabacacccbbdbbdabdadddbacaadcbbadcbcdcdaddbcccdbdaaabbbadbcacdccaaccbabccaaddccaaddabaaddbcbdbdbbbbaaacbabaabccdbdabcbacccdcddcbccdbddbbadbacbbccdbddcdbbadaacbdbcacccccbcaccdcbdccaabcabcdabacddabdcccddcaccacdbbddbdbabbbdddabcddcaccabddbbcdccabdababdabcadbdcdcadacbabdaadbabcabacdbadabbbccdcddcaabbcaadcbadaacbdacbabdbcddccdbdbbdbcaddbcbdddabacbccaadabcbbbbbdbaadaaacbacccabbddcddcccdacaabcdaaabbbacabcbadddccbdbcdaddddacdbccccbbaadadccabacbdadacbddbcddbbdbbaaaaabdcbcdadcdccadccbbdbabbacccbdabdadaccadbcdcdccbccdcbdaaabbaadbdbbcbacacddabbabdbacbbaabbabbdaaddddbddaaacdcdbbbadbcaccbdcdcadddddaabbccacbaabcbdadaadcbabdaccadaccbcdbbdccacddaacbaabbabbcdbcdcbccaadbbabcbbdcacddbdbbdabbabcdaccbbcbdaaacaccddbabcbcbaaaacdcdccbaddbaddaacaabcdbbcbbabcdbcddbbcbcccbbbacbbacccbadcdbbcaadacccdababdbdcccccadddacdbcbcadaadddacbadababdabdcabbabbaddbcbdcbacacccbcdabbcaddcacbdcabadaccabaabccbbacadbbbbacbbdcdcbabbbbcbbaabbbacdadcdbbacdbdadccccbbaccccabbadbbddaaaaacdaabbcbdcacccaccccdbadcaddddbbaadabcadbddabdcbbaacccadadcdbacdbbddbbaabcdcbaddbcccdbbdbdbaccaaddbdabddcacccadacdbadcacbdbbccbdbddcdbabadaaacccdacbddcdbcbdacbcbcdbaaaccacdaaabcdcacdadbcdcbaabbcdcacdbbbcadbcddbbccdcdcaabaacabdaadacaddadadccbaccbcdbcbdccabcbdddaddacddadaccdcdacdaabbdcacacdcbcbcdaacabcdddddcdadbcbcbddbadcabbabddcabcdbacabaadcbcbaddbbdcdaddcaaadbaabdabdbcacbcadbdcbbbbdddcaacbcbbdbdaabbddbcbdcdabcacddabbacdbcacbadaabbbddcaddcaababcdbaabdabdbcdbcabcbabccabddbabadbdaccbccacdbdbbabcbcabcbdcdcaccdaababbabdadbbddddddcbabccacadbccaddcdbcabbbccbacddadababacddaaaccdbdabdadbabacbbbdacbcabcccabbcacddacdaaaacdccbcbbbadbacdcbaddbadbdaabacddcbbddbdaabcbcaadaccbaacdcdbbbaacacadaaabcbacababdcddbbaaabaccddbdbcbcabcdddbadbaabacdcadbaaccbcbbbbadcdadbaacbbbcaabddbdbbacabdabacacdcccdbbdaababcbbaaacacabcddbaccdcbcccccbdcabccadbcbbadbccaddabcacabccabbcbacdcbcbcadbdcbdaccbabddadabddcdcddccadbcacdbdbdcdccbacaadbbaccadcabacdbcadcdacddbaadccccdcabadbbacdbccdcdbbddaacbacadccdddbcbdbddcaccaddacddbacbaacaacaacdbdcdcaaccdaacdbbbbcddaadadcdacdcccaddcabbddaadccaabcaddbaabbbcbbbbaacdbaacbaccaaaadaacbadcadaaabbdaabdbbdbbabadbdabbcdbdadcadcaabbdadaaadadadbabadcdadaacdcaabbadccabacccababddbbcbbbcdbaddaccbdccaabbbbadcadbbdaadbdcddadbaddcabccabadddcabbbacaacdddddcbdddaabbccddddbddbbdbdcdcdcacaaabdaacacbabdaabcaabbdabababbabbacbddcccadbadbadaabbcbcaacbdaddaabbbcdacdcaadadadcdbbbddbabadcbdccbcddcbdcbdbbcbcacaccacccabdaddcabaacadaacaccadcdcbcaacccdbbbbabdbabccaddacbcdababcacbbccacaadcdadddddaadaddcadbabccaabadbdcbdabacccacbdcaabadcbccaacbadcbdcdcabbccbcdbcbdcabacbbcbccaacdcbaabccddcbbaacdccdbaccddacbadbbcdbacccccdbcadbcacbbbdacdcdcbacddbbddbbcabcbcbcdbbadbbabaaccabcdccbcaaadddabcdaadbcdcbdaaadcaddbcaaaacdacdbbaaabacbdacbabddaaabdabdddcdbcddcabddabdccbbacdddaacababadbcacbcabcadcaaddbcadbabcaccdbcbaddadaccacbbccaaadcdadababdabaacadaaccbcbadacadabcccbabccdccdbdacccbcdabbacdacccdaabcdccacdbddbddbbccdcdddadcddbcbadacbbbacdbddbdacbbcaaaadcaccccdadcbadcdbabcaddabbaadccdadcabdbacddbbacbcbbbbaabdccabddbcdcdbbaaddcbdbdaabacabaccdbaabdbdaccbcbadbdbaaaaabbbadaaccbcccdcdbdcaccabcdaabadcabdbdaaaadcdabbbadbacadbcabcaddcdcbcdbbddacbdbbddacdbbbbbdbcdddddbccabcbcddbcddabababcabcbddbbcbbdcccdddccadaaccbaccbacadcaacdbaaaadcdcdcdbbcadadbbdaabbacdbcbddcaddbabaabbcdabacdadbcbccbdbdbccdbbadabcbdbcdddcdddcdddcdabbbabcabdbcababcbbcbbcdbbdadddaabdbbaacccbaadacbbdbdcdabccdbcacabdbbccaacaaadbabccbccbcbdccccbabcabcadcccadbcbcbccacddbabadcadacbadcdaddaccdbacddcaddcbdaccdaaaaccdbcaadbcaaccddbdbbbcdabadadcccbbdacbbbcacbbaccdcbcddcccacaadbdbcddbcaddaadadacbacccaacdabbadcbadbacbcaacdaccbbdaacaaccabcddaacaddabbcaddbbbacbaddaacccdaaabbcaabcaaaaabaccadcaddbcdabbddbbaddcdcabdcbadbdddcabbcbbacbcadcabbbdcdbaacacdadcdbcddcbbaaabdacaadcbbdbdaabdccdbccadabbdaddbdcbccabdbbccbdddbbdcaddadacbaccbadcdaddaccbcacbadaacdcbcddaddddaadbcbbcbbdddabaccbccadabdbccacbdbcccbccdccbbdbacddbdcdacdccbcabadbdddbbdaaabdbbcddcdccabbddacddbbddcabdbccbbbcacadcbabdbcccccbadbccbaaadcddcddbbcbbababdaddabdccccbbaadcdcdaccaabaabccddaabacbaaddbcaccaccdcdcdccbcaaddbcbcdadadbcacaddaaabdabcbcdaadadcbbadbbcbdccbabddbacdcbbcbadcccdbbadbacbdaddbababbdabbdadabacdcadcdcdaacdaaddaaaddaadcbbbdacadbbbbbabdcdabccdbdbbdccbbacdaacbbacdaabbddcdaabddbcddcdbdbbbcbaadaaccdcbadcdcaddabaccbcbbaccddccabbcabddcbdcddbabcdbbbddbacdccbbdcaccaaaadaddcbcbdbaddbabdadcaaaaddbcdcdcbccdacdcbadcaadbccabadbbcbcabbbaaabcabcadbcdcdddbcaadaaccdacbaabdaddcbcadddbbdbdbbbcddaabababbbbdddaadcabddbddbaddccbcbdddacbcdddabcaddccbcbcddbabcdadcdabbcaabdcdddbcdccddbbbbadcbcbcaccbdddbcdbddadcdacadbdcbbdcbdabaddbccabccdbccdbcbbaddccdaacdcbbabadacdbabcaddcdccccbadadbdbabbdccacabbbcddacaabcaacbddbabdcddcbbcddacdaacccddbadbbabbadaacabdcbadbaccbdcaccbcdacbadabcbcacabccbaddcbcacddcaabdcbaaacbadcdcccdaabcbccadbcbcbdabbbbaaccbdacabbaabbcaabdbbabcacccabccaaaddbadcddcabcdcdcbdcbccdaaaadadcabdaabaccbbbcbcbbdbcdacbacdcccccdcbcdcbcdacccddabcdddccababaccccccdbcbabcdaddbcdbdccdddbabddabdcaacddbbcddbdbcbbbabaabadadadccddcadcabbbddbbaadbdadaabbddabdddaaaabdacdcbbdcbdbdabcccdacabacdccbdacbbaabbdabbdbbacbbcdabaccbcacddbcacbabbccbdddccbcddbcadbcdbcababbdddddcaddbcccdcaddcccdbbaabbaaccdbadabadccadadcbdabbbbcacdabcaaacaccccccdbabadcdaaacccbbcddadbabdccadabcaccdbabcacacbabcacddcbabccadaaaaaabcababdabaacddcbbdadddccdddddaaadbdccaacdbdacbabbdaaaaabcabaccbbcadbdadadadabdacdbcacccdadbcbbbdbabddbccabcdbcbdbcdcbbddcabcaaaaccddacbbdbcdbadbdbbcbbabbddadbbbccbcdacaaabaaccacbdadddcaddccbbacbacacadabccabcaacdacabdacdcaccccbbabcdacdbcccbacdcbdacbccbbccbabccbcbdccbbabadbddaaabbbdbbccdadabcacdaccbbcbccadddaaaaadcccddbdbccaababcaaaadddcabccdddadadabcdacacabaaaaadaabdadbcbacadcddcaccdddcdacdcbaddcccddaaaddbcddaccacadaacdcadacdabaccdcbaddbcbbdaadabaaadbacdcbdbabdcadcabbabcbcccabacdbddcddaacccbdbccdccddddacabcdadddcdcaaaccdabaabcaacabbbababcddbddccddabbabdaabdbdccdddbbbbbabddbddcadccabbdaddaadddacdcaadddbcdaccdaaadccbdcdbbadbbcdcaaabbdcbdacccddabdaababdaadbabaccabadbddaaacbddcbdbbdadbbcddbbdaccbadccbcdaddcbdadccddbbccaabcdddcadcccabbccbdccaaccabacdbaabbbcadccabddbdcbbaaadcaccabbacdcaacaadcaadbbcadaaaacbccabcadcadadbcabaaadacbbaadbddacdbadddbcdadabbcccabaadacddcdaabdacaccdacaabccbaaacabbaabacbcdcdacbabaacabbbbdabcadbbddaccddbadbcddddabcabacddadcccdaabbcbcacddbadcbdbcabcdcddbccdadaccabbabbbdccbacbdbbbbddaccbccccbaccadcabcabcdcdcbcbdcaaaabadccddaadcdbcbcbbdbabbcabbbbccdaaaadabcbcdaabcaddadcddddcdacadccccbabdbdcdaacbccbaccaccddbccacdcbdaacbcddadccccadbbabadbbdacdabdaacbbcbbdcacdaddabacabbdcbbccbdddccadbbccdcbcabdddcdcdabbcdaacaadaccccdcabcabbdbcbccbcaacbabbbaadbdbadddcaabcacdbcaaaadbbddaabacadabcdcdbadcddbacdaabccccbbcaaabbdbbbaaadbcbcabbdcddcdcabdddabdcddbacacbdabbdcbdccaddacadbbcabcbdddabcbddacdcbdbddcbbddcdabdddaadbcaabdbbddddbbacdacbbbabddcabdbdcccccbcdbbaacbacacbbdbbccdabadcadcabbaabcdaabbcadcabdabbdddccdadcdcbdbdccbacccbabadcaadaabdaddbabbacccbdcdbbabbdbcbdcbcddcaabddacdddabcbbccdddaaabacbcabbcbdacbabadadaccadccdbaaabcdccabadbabdcaadbcacdcbbbacdbaaaddccababcabcdabdcdbccddadaabcbcdcadbccdaadaddbacccddaddadbbccaaadbdddcaacabaaccbbdacdcccbbaabcccdcdddcacabdcdbbdabddabbabadddcccdacaddadcdbdbccacbacbbcbcadacadcacadacadcbaacbcbcdaaaddcbdbbdcbadabbbaabdcdbbabccbdacbacdaaabdbcdbbbacdcddcbadbcdbcddadccdadbccccbbdbacadacbdcdbcdddbdabdbdcbbdcbdaccacdcccadcbbaabaccadcbcaaadccadcaccdddccbddbdccadcdbdcdaaabdbabcbbbabadcacacbdcadbccdcabaacadbabccbdbaabcbcabaccabcbbbdbcddbdbacdcdddccccdadbcaddabcdaacadbacbdddabbacbccdbcbdbbcbcbcabdddcddcdddacdbcbddcaacccddaabacbcbbcaaddcdbdccccabdacaaabbddaabbddddbdbbabcddacaaacaaccdddbacdbcaabdbdcdbdbdaddbdadcccdbdacaddcbcbdbabcdbcdbdabcbddcacbdaccccbdbaabaccabcaccbcadcaaddbcbbadbadccabdcddbbbcdbcacdbbadbbcddbdddcaacdbbadbdacdbdaadaddbbbbadbbbdbdacadcbbddabaadabdbabbcacdcdbdacbdddbbdcbdcdacbaabcbccbcbdaaccbbbdcbcabbbcbbbdbcdddccdbcccccbaadadabbaccbdaabcdcdddabadbcabbadbacbacaaddbcacdcbbdcbddbbdbcdacdadadcbacacdbabcadcbaccbdbcccdddbbddcbdacdadcdaabbcbdabbbcdcdadcdbddacbdbccdcdadadaccacbabcbcdbdbbddaabdadddadbcaadddababbcbbadcdccddbdcaddccdaaaaddbacdbbabbdcbddbbdcaddddcbdbcdadcccdbbadadaddbaccabccbddbababdaabbbdaadadcccbcbdbbbcbcadbbbcddacaacacdbbadbdcaabcdccddbbdbabbaddcabcbbbbcbacabbbcddbaabbacaadabadbbaddbccacaadbbbdabcbccacaaacdccadbababaadacaaaacdccccdbdccbdccccdccacaddbacddaacccbccacbddaadbdacbbcdaaccaacbdabdabaacabbbbcbabadccbaaccadaadccadddcbcddabbcacddcaacadbaaddbbdabcabdcbbbacddbaacdcbbacaaddddaaaaacdccddacbdcbabcccccccddcddaddccdddbacacadddcdacddcaaaaaaadcaacdaabbbcbadbccabdccdbbdaddbdabcbadabcacdbcaabadaaadbacadbddaadbabdcacaaddddddbccdbbcacddcddbbcdbacccadaddbdbdbdabdbadbaccaabddbabbacacdbdddbaaddddadcaacbcadbadaaaacbdbcbcbcdcdddccdbadadbddcaababaabccaddabdbadabdcbcabbcacddabaabbdcaccacadcdbcbdccdcbccccbbacaccdbddddbdcabdadabdaaddbabdcbaabacbddbbbddaacabaacdcdadaabaccbccabcabbdcdadaaabdacdaaddadccdcbdbabdbddbbdcababdcdabdadacbbbdcbcbcbbdcadbdccdcdccacdacbdabccacbabacbbbddbccacdccbadcdaaaacabacbcbabbacbaaaacdddccabbdabbbcbacbdcbabdddddbaddcabacccabcadaccabdbcdadacaabadcbbbccdbbdadcaabbcdcaddcbbbccccdbbabccdccbdcdbbdacccacbccbcdcccaccdcbbbaadcdadabaadccaaddcdccdbddbdabddadabdcacbbdcaccbaabacccddaddbbcbbacdcbdccaccdcaaabaabcddcaddccddddaaddacdacbbbaacbabdabdabcbbcbdadcbddccbcaadaddcbababbcddbbbdbaabbbabdacaabaaaadbcdbaccccccbdbbccccbcccaadddddaddaaaacccddbbdbbbdccbbbdaddbbddbabcaacccdacddaaabcadcbacdcacdcdbaabacdbbccabbdbcdbbdddcdbbcbbcacbadaabbdddbdbdabcacbcacdadcababdabcbdbccaccabbbaacacacbdcddbbdbadbdadadbdddabcacbdbadbbcaccaabdbcaddbcdddabdcacaccaaabdccbccbcdddcbddcabcaabdbdddadcbdddbccddbdcddabbcbcbcacacabcbcbaccbabdcbcdadacdddacadcbdbddcdbbcbbbcdbcddcabbcddcdcadaaddbcacbbdabdcabbdadcccddabcaddcadbccaacaabaddcccccbaccdbbabaabaccabcaddcbbaabcbadbdbdbcdbccbccdaaabcdcbbdaaadbcacabcaddbacacbbccbabddcdbadcabccdbdcadddaadccacbcdbabababdabdacbabadcddccadabaccacddadababbbcbbabbbcacddcbbbdbdbabcdddacbacacabbcccadbacaccbacbabcacbbddbbbcabdaadccbdcaaabddcdcccddcaddbcccdaccbabbbaabbcaadaaadabdbdabadaccabcadbaaadccccbacadccaabccdbdbbcbbccabbacdbdaaababccacabdccabdbbacbbcbadcacdaacadbdcbbdbabadcbabcddddcddabbbccdcbdaaaccdacccdddbdccddcaaacdaacdbadabcaddcbcdddbccbabacdcbabddcbdbdbadddbddbbdbcadccadbcdcbcddbcbcdaadbcddaacacdcdcbdcadaabdbacacccbaddccdadbbbdcdadcaccbdadbbcabbbcdcababcdcabbaaacdabbccdcdbbbcbdadcdabbbcccdcacbdcabbbbadcbcaaacabdcacccacacbcdcaacddacdccabbaadccaddcabcadbaccacaccddabbabaabacdcbabddcccbdacbbdcabcaabdbadabacdccddaddbabcdddbddddcdbdcaccbaddacbcbdccdcabbcbbcaadacbabdaaaabbbcbddcccabdcacbabbddcddbabbdcbdabaddcbacbccbddcabaaaddbcbacbbadcdbaddadabacadabbdadcacdbabdbaabbaccdbbcccddadadabbdcdaabbabaaccbcdcadcbcbdbbcbaacadccccbdbdbcadbbcdcabaabcdbdbaacbdaadbdaddbbadaabaabddcddbbdadadcaddadbcdcdcdbcdcdbadacabaacbadbabaadadcdcabddcdcccbcbdacddcbddbccdccabcabcbaaacbaddddbcdbdabdbbdbcaaabcccdabbaadddcccaddaccdabccbaddcabddbbbbbbadcbdddbcbacbacddbadbadbcdccdbbbabacddabccbccabaacccdaaacadccbaaabbdbcaaadabbdbcaddabdabbaacbcbaccadbdcdcaacadabbcbaccadccccbaadbcbaaddbaddbddbadccbbabacaccaaabbadaabddbcbabcadbcbadbdaacadbacabadacdbbabaacdbdbccddcbcabacbdcaabcccdccdbbccaadcabacabdcdabcaadddcadbbcbdddddccaccbbbbbacadcaabbbbabbcbbcddacabcabbdbbbadbbacdaaaaabababbadacdcaccbacdddaabadaaaabbabddcbccaacccbdccdabbbbcabdaccdacccacacbadadcbbcdadadbdcccabbcacaccaabdacaaacbbdababacadbadaccccdddbcaabdabcbbbdcdbdbbbbbbbbddbcaaadddadcdbabdcbbbcddabcdbcbdccdbbbdcdbacacddcbabacacaacaabdcabadaccbddbacdbbcbcbddbdcaaadddcbbabcdaccabcbdddbbbdadabcacaadcacccbdbaddacbdabbdacccdacabccdbcbbbaddacddbcbbcdddbabacabbcbbadaddbbaacdacbccccdaabbddccbdbdabaabdacacbdaaabbcadadbcdcbdabbbbadcccdcacccdcabccbcbccdacdcddbbbdbaadabcbbaaccbbcbbacabbbdcaadacaaacbabddccaaddccaccdcdbcbaacaabcabdaddbcbbbabcdadaaaccccdbbabbdbabccddcbdccdaacddbbabdadabaccbdbcacabbaccddbcdddccbbdabcbdabbadddcaaaacaddabbdcdcddbaddcadaccbaacadddbaddbdbcddbddcaabdacbdbbbabcdabaadaaddaaaadbbcdccbbaadacbdbcccacccabdadccabbcbcbaaabbcadcbccbbadbaadaddabaaaddbdbcdcddabaabbabccaccbddddbdaddaabbbdccbabbaadbabaaccdbdaabcccdaacacbccdbdbbdcbaaabdabdbaabdabddbbbabbdaabcababbaacddcbabbabadbdcdbabbdacbbabcccdcbcdabdbdadbcdbadbdabdacdaacbccbddadaddbabcbcbbcbabccbcbcacabcbadabadbbdbbaadaddadddcabcccdccaddbdbadcccbccadbcccccbdccbdcdbcccaabdbbcaabbdbaabdcddabaaaabdcabdcbcbccbdbcddadcdddcacdadbbcaadbbcacbccaaccdbdccadbacabbcbbbbdcbbcddbcbdacdcdaaddbdbcaabdacaabbddaaaddddbcdaaccadabdbcacbbabdbcdccacacbbcdabdbabbdadabdbdcdcbddcaacddccbcbaccbccdcdcdbdcadaadbbcdcdcbcacbbbbacdadacabcccbabcbbcbcbddbdbddaacdadcdcbbadbdaaaabbadccabaccdcbadbaabddacbdbbcdbabbabadccdbbaaabaaaaddaddcccdcbdabbbbaaccbcaacacabbccbcbbcdadbbcccacadcbdbccbbdbdbadddcbabacccabdbaacbdadbabbcccdaadbabaaabcabbbbcdcadccdcadbbbbdabcbbddccbdcbacadbcbcadcbddbddadccbbaddbcdcbcacdacbaabbacccaabbbcabbdbcdcadbbcddcddaccbcaadacddabadbadbdcbacddcdddcaabdcdadbbccacdcaaabcadabbdcabbcdcaabcbdddbcdccbacaccabcdcaaadbdaacddbdcddbdcacdabadbbddbdbcbcdaccbabcbbbbdbdcaddaaaacbcbabcabbdacacbccabdbbbabcdcbcbadacdccabbabcdddbadcdacbdadddcbbcadcabcabdcdaacddacbdcdadbabbaccddbaabddcdbbbdcbcaaddacdbbbbadbcbbcacabcbacaabbbcacaabaadddcadccbacbcdbdcdccbcddbbcbbbccccbacbacbaadccaabbdadbbabacabdcabbabcdacbcdcbccadabdaabbbabbdcdbbdcdcccddcdbcbbaaccbcddbcbabacccccabdbacdabcdcbcddabddcdbdbacaccdbcddadbcdcbabdadcacaadaccabccbcabbbcdcacdacddadcacaaacaaccbcbbdadcdabdddccdbcddadadddaaadaccaddcdacbdadaaddbcbddacddcacbdbbccbdbdddbddabbaacaabbcbbadbcdabdbabbdabaacdbcdcaabcacdcccadccccdaaccadcdbcabbbbdbacbbacdacccdcbcbbcddbaaacdbdadbdcbdccbddccbbaabddacdbbaadbcccbbbdaadcbddaadacbcdcccbcabbcabbaacdabcaacbaddcdbcbbdccdcdbccdbaaaaaabbbacaddbbaccdcbdcdcbcbdbbdaadddaccadadbbaaccadaaadcaddbbbbabbbbcdccbccdcaccdddcdbaaabbdbcbddbcbabbaabdbccbdcdbcccbcdbddacabcadccbcacdbdddddcccddbabdabacbdcdcdcadbccbcbaaccccdddcdbcdccbcccddacabaaddbacdbccbbcbbdabbabccabbbccbdcbaabbaccbdbabbcdccdbccdadcbcaaadddbcacadbacbbbbbcaacabbcaacccccddbcddddddaccbadcdbbaaddacbaddacbcddabdbabcabccdabadbabdcbadabddabbaacddacabdbbdadddccbcabccbdaccbddcacddccbccdccaddcccdbabcbadbaddddbaaddbaaabacdbacdabcbcbabaadadabccbcacacdcccbadbddabcdbbddabbbdadcbdbddcbdabcbbcddbccbbbccccaacdaabdbabdcdbacbcdbbaabdbddcabacaabcbdddddacabcbbacddccccdbcabcacbacbdcaaddcaaabacbbaaaccdacdaacbcaacbdbabcccccdbdadbcdbcbcbbaabadbcccbbdbdcddaadccadbdaabdabccbccbbbdaaccccddccbadcdddabddbbabdbbaabadbbcaccdabbaccaddcdbcdbacdacccaddbbbcbdaddacdcbdacabbddcbbcaddacbbbbccaabaddaaaacbbdcbcabdcbbbbcbcbaadbdaacddbadccdbdcbdcaaaacdadadacdabbdacbabaaacacdababadaabcdcdccadabcadbcaaccdbbcdadaabcbacdbbdbbaabdbdccdabbabacdccdbcccddcadacbccdcadcbbbcabacbbacdadbccbbcdbbaaccbdacadbcccbbccdcbaabcacdcabcbcccddaabbcccccaaabcababaddbbbdbcdcbddbcccbadadbcddabacdcbccbbbbbdcacbacadddbcbdccabdabadaaddbccbdbbbcddbacabcccbbaccdcacddbbadcbbcbaacbacccadacbbacbcddbbbdabddbccadcbacddbcbbcdbabaaacabaadcabbcabbaaddbbadbbacddadadcdcbacadcdbcbbbbbbbcaabdbccbdbaabdccbdcbbddabbdbbcbaacaadaddabddaadccdcddcdaaaaddaaddddccbdccdbdddbaacaaacadccbbacdcdccbdcdacacddcdddaadccacdbcbacbcdaddaabaadcdcaadaddbcbcabcbcdaddccbbbddcaacabdacbacacacddccabdaacbadabaacdbdcaaccbcbbaccdcaadacaadcccbcbbaccacaacbbbbdadbbcdccdbccdabbcbbdccddcaabbdcdbbdbdabadcccbaccabdbdccdacdbbbacbaccdcbabbcabdaadbaddbccbccccbdcdbbbcdbdddcdbbcabcbaacbddcabadacbccaddbcdaddbcadccadbcacdcddccdddbaccadbcbcdaaccbcaccacbbbaccbaadabdadccbcabbacdbdbcaaacadddabadbccdbbcdcdbdcdcabcddcccdddbaaccaadacbbbaacdcdbdcddaaabaaaaccbcaacdaaabccccbbcdbcabcbbcbccbcbcbdddddbcadbbacdbdbacabdddabadbcadabcbbcadbacdbbdaaadabcbbacaddadddbdacbabbabcabdddbacbdbaaadbbbbbbdcbbaabbaccadbcbddaddadcbdcdbddbbaadbcbabdcdbadadbddcdbdbddbdbccadcbacbaddacaaccdadbadadaabdddabcdccadcdcdcaaccbdbbabacccbbadcccddccdbacacabdabbbcaccdbddbdcaabddcdbbbbbbaabdccaabcdbbdddbdbddabdabaaaaadcbdadbcbccacccbaaaacbadddcbddcdddcadbcabacdcadacacacdcbaabcbdcaaddadbdaabacadbbcddbdbacbcbcacbaddcabddbbbcdcaaaddacdadcaabbbabaacbdaccdbdbacabbcbcddcaadbdccdcbcccccabbacdcabbddcddaccaacdacaccbcbcbccadabacdcacabdcaaaadacaaadbcbbccdbdbacacccdabadddbcdadbbadbdccacdbacbadddadcacadbdcdbbbdbdbabcbcdccbcdadadbcbadaabcaddbbaacadcabdcdbadaddacddaabddaaccabcadadcbbdabcacaadabcdadcbbacccdbdbacbbbdbabbaacddcaaacddabbacadaddddcdcbcadaacdacdbdcddbdabdbbcbcdbcddaabcbdcdadcacccacacdddcbabccacabbcccabddbbcaaaaacaabbbbddabbbbdcddbcaaccaacacdcaadcdcadacbdaddccbcbadcabcbbdacddaddccdaadcdcabdabccdbbcbbbcdcadcabdcbacabcaadbcbaddcdbadcabbbdaacbdbddadcbcbdcdacbddbabddabccdccbabccdcaabcbcccadbdaabcabacbbcbabbdbaacbcbdbbcccacdbddddddcdcaddcddcbdacbbdccbdabadbccbbdcaddbdcbdcbcadabaaabababadacaabccbbdbddabacaaacaddccbdcacabcacbdabbbccbacbdddabaaabbdcbdaadabdcccaddbadbacdcacdbbdccadcaaaaadaaabcdcdcbdcdbdbccadaabdbdadcbaaaddbcadbaadcadabbdcadcdbcdcdbcaddbddccbbaddbdabcbbcbdccbbcaacbccbabbaacdadddbaacdcdcbbcdbdabcbcbbbddcabccccddaaabcbbddbadbcabdcabbaaaddbbdabbbbbdbbaccacbbdadababcbbdaadbbcdbddbaccdbabbccddddcacbdaabaacbbaccbbbcbccbdccbdccdabdcdbabcacccbacbabdccdccacbaaddacbcdcdcdacaadabcdcbcaacdbbdadbadcdbccdcbccdbdcdbdcdbacdccacbdadaacbbaaacccbbaacbcbcaacdcacdabbbddbdcabbddbcbcbdadcaacbabcbcdcdacddadcaabcbccddbbadccdabdcdabdbcbbcbcccddbbbddccbbdaacdabdddbccdddaccabbbdbccacaaacaacbabccbaccadbbbdcbadbabdaadcbcabdbaadbabcbdadccaaacdaacacddbddddaadadaaabbaddbcbadaadcaadcddcdbdbcacdbacccddbadcbcbadccbdbbcccdacddbbabcbacbacaccdadbbadccdcaaccdabbadcdaabccaacdaaabdddcdddacacaadcdbcdbcacabcdddaaddcddacadcbbabcbdbabaccbbacbbaccaabccaabbcdadaccccddbbbdadadbbaccbbdacbcccdbcddadbaaacbabbcacbbdbdbabcdacacaaacaabcbcababdccbbdbbbddaaaaadbddadbcacbacbbabaccaccaddcbddbdbccbbcbaccaacdaaaabacacbddccbbccdbdbbbaadacaddbbbdbbabbcdcdcbacbbddcdbdcabcbbbadbabbacabdbdacdcaaccaabdaccddaddcdcdaadaaabcbbbdbdadacddcabddacbbabbddcbadcbbcbacdcadddbbcbaccdabbcdccdaddcbcccdddcbadbbadcacccabddabdbccacddcddcaaaaccbbdccdcdabaaddccdabbaacdbdabcccbadbaaaacadcdccacdbbbdbbcbacdcabacdadddcdcdacdacbcabdcdaddbdbcacccddabccaaddacbcbbbcabaacaabcbacbcbabddadaadccbdbbaccccddaccbcbadcaacddacaadbbcadddbaddcccdbbdbcabdbacbaacdbcdbccabddaddacaabddbbddbaccadbbbabdddbbbdcbdccdbcadcbabadaadcdaabccbbcdaddddcbdbdbbaaabadaddabcbaaaddadbcddddddaabbbdbbaddbaddccddbaddbbdbcbacacadbdacdbabdbdddbcaddabdbdcdbcbccabddaccdbdbcbabcdabbaaabdbbcbcdbbcdcabaabbadcccdabdbccaabcabbdabbdadaadcdbaadbcabcaaaadbacbbdbbacbcccbbbaddcaaaaaabadbdcacaddadacddcdcadccbddcbaaabadaabddbddcbcbccadabbcdadaccbbcaccdccddccabbbcdbbadcadcdcbcbbaccaabcdbbbacbbcabadcbcbcabacbbddddbbbaaccbacbcdccddcbadcccbcbdcdbccbddbcbaabbadcbbdcacacdcaaddccbcadadadcacadbacbadbcabcdbdacbadaacbabcbaddbdcddabbddacbdadbaccbdbaaddbcadcbbdadcbbbbabaabbdccbadaaaabdbbdbadabbbddbacbcdbcbcababbdaadcdccbbddaacacccdcbaabcccadabbdcbcdcbabcddbcdbddbbaddcddcacccbbbcdbbbcbcabddccddcacaaadcdbadadcbadbdbcabdddddbcdacdcbbabadbacddbcdcbabdcacdbcbabcbdbccdcdacaccabbababdbcdcbcadadbdbaddcbcddaaaacaabddbbdadcdcbcdddcbcdbabddaccacddabdddbbaabaabbcabcbdcbbbcdccbbddccbaacaacdcbbcdbacdcbcbdbaabbabccacbcdccdaaabccbdbcbdcacabdcbbdaaadaabcddbdabccbccccccdaddcbccadccdcdbddacccddbaaabdaccadbbbbaabcbaabcbbdaaabbbadddcddcbcbaaccbadbacacaadcbcaabaddbbdbadddbddaadabdadcaaddacbbdbcdabbbdcbadcaabcdacbcbbddbbaccccbbdbcbddcbacddadacbcdaccdbbdcbbcacaaccaacadbbdbdcbdcdccccbaddaddaaadbbabdbcaadccbabcccaaaaaacccbacddbddccccdcbccaadbdbadaccaacbbcaacdbddbbbaacbdbcccaabbacabcbadcdbbabaaadbdcbacadcaacaadbbadacddcbbaaccaaadacacabccacccbaaccdaadbbbbabbbbbdbaabdaababbacccabdcbdddbbdcbcabbcaaadcbabbacdcccacbbbadadcbacbacbadddbbabdaaababdadabaaddddbdccbbccccdcaddcaccdacbcaabacdabdaaccbcabdbbccbbdbdacbdaabdaaadcccaaacaaccdbbdbbbdbcbdbaaccdabdacadcababdbddabbabdaaddbdbddabacbcbdbccdaacdcdabdcadcaddaaaacbdaaacdbbccaabdabcdccbacbaccaabddbabdddbbbccdacbbbaddcaaccaadcaadccbbdbccdbcdcbdaddabccddddcdddadadabdbddaacdcbcbcadabccbcbcbdcaadddabacbbbcdbccdaadcbcbdaabdcbaccabbabcadcccccddababdabadcbdddbbaadbadaddbcdbdccdadaaaacdbdcbbdcacaaacccacacbaaccddcbbdbbddddcdaabdbcbdaacccbcddacdbdcbbddcbacbaabcabacabbacbbccabbcaabbbadcbcadacddbbcaacddddaabccbadbbadbcbadcccababcbccdcaacbaacdadcccbbacdcdadadadcbddabcbbcacbaccaabdcacbaaadbcddbdddadbadcdcabcccabaabcbccccabbdacbdccacbaacddddbdbbbbdaacbdcacbabbabcddbaadcaaaaabbabbddcacbadaaadccdadacbcccbdabbccdbbcaddcdcbcaccacdbbbddbbaddbcdcbbdddcbbcdadaaaddbcbcabdacaacbddaabcbbdbccaaabdbaadabccddbabacdccdcbbcaadcdcacdacddabcbcdaddcdccdddacacacddbabdcadbdcaccacddbbadcddddcacaaaccadcdbbdbcbabbccdabdcbdbbdadddccccabcbaddcbcdbcbdbdddcbbdddcdbdbbbcdbcacccbcbaddaabadcacdcccdccdabaabbcababcdbabaaaccabccdbbcabacdbbcabcddbdbcbbdaadbbadababdbccbaadaddbcbbbdcabadcbcacbabbcbbbbacdcdcdacbcbbcdadcddacdaacababaddcabccbdabbdbbcbbdbbbcadcbccdccbcdaaccccbbbcbbbccdaccbbbcbdccbdabcbddccbddccbaaddbdbacdacdcbddacdabcadddaadcbcdbccbbdbcddcaccaadcbdadacbacddcdaccbddcbaadcddbcddcadcaacddbbabbbbcabccdbdbcbbcbddadaaadcdcaacbbccdadbddbbbdccbadbabaaadabcaddaabcddbabadcccbdabcbdaadbdacabbbdbadccbbddcbabababccacdabaabdcbadadbabaacaddcddcacbcdaccbcacbadcadddbbabddbddacddaadcbabdacbcdddacdadadbabddbaadaaaccaadbadabbdabaabcdadcbdccacccadcbcabbcabdbbbaaacaacbddbbdabaadddaaddbdaaddadbdddbdddacadcaccbacdcbcdaacdbbabcbaaadabbbbbadccdadabbabbddaddaadbaacbdaaddbcabcbbbacbaabdbddcdadadadbdbdccbabcadcbbdabcdbcbaacabdabadbdabbccbaacdacaadccbcbcdaaaaaabddccbdccccacbbabcbaabddbddcaacbddbbccbddacadbdacbaacdcabdddabbacabddcaabdbdbabbbbcbccabbabbabdcaadaddbbdcadddbdcdcacaaddbccabdacaadbdcabddcbdacabcdcababdcdbacabacacdccdcaddddbcdbdcaccacdbbcbcccacbcabbbadacdaaabbcddadbbcddccdbcbaabddbbabdccbbdbaabbcddbababbdaddbcadaccbbadcbbbcdcbacbadbbbacbbcbcbcabcbdaccdbbcdabbadbcdbabbaacbccdadbcccacddbccddbabcdbdaabcbbcccdddcadcdcbccddddcbadaaaadabccbcbdabdbddadbdbbdcdadbcacadbccdaccdcdaaaaccbdddaadacadddbdbbbaddbcddabbccbbdacacbbabcdbdbbbabcbaaaddbcbdaccdacadddcddbdbdcadbbbabadcbcabdabbcdabdbbdbdacaacdacddccaabcdaddbddadcabcbacbdbddbacbdcbacbccdadcddbbdabcdabadaababcaddcccccddcdabdccabdccbaacccbbbbabbacccaddaccbdbdcddbaabcbbaaacddbaaddbbacccacaaacbaaaabacdaccdbdcaaaabbabddadbbdcdcbbcdbcbbbdccadabacadadddddbabbccbcccadbdaddbddaccdcabadbaaacdaddaaddadcbddbbdadbabaaadaabcdabacccaadaccbbbcbbcddddbacddbdacaabbaaacdcacdadcdcbacaddbdacddbbccbbcacbcabcadcbcadbadddcbcccdbabcdcccaccbbbcaccdcacaccbdbccdabcdddbdbbaabcacbbbdbcaacddbaaabdcdcbbbbabaabaadcacdbcdadabcbbcddddabddcadbbbcbcadcdccabbacdbbccaaaccaaaccbbcbabbcdacacdbaccbacdcdbddbdbbccacbdccbacbacacdbbbcaababddbaacbbbcaaaaaccbdbadcabdbbbcddbcdbcbaaddbddbdcbbbababcbcdaddcdbbddbbbcabdabacccbbdddbbcacbaacbcbddbbdddddaabaadcccdadabbdacaddabaccadabdacacbbcdcabcbabbdaababddcbbcaabdcdaadccdbaadddcbabcbbadbbdabdcbcbcccacdbdbdaddaabccdaaadbadbabdcdcbccbbcccdabcdbcbccabbdbaadcdddcabaddddcbdcbbbaaacacccaccaadbabacbabdbbbbdbcdbadaddaaaccdddaacadacdcbbbdacccbccddcdbababbbddbdcaabbccdddabcaccbcddbdbdcaadadddbddacbcbbdbbbdbbacbbdabcbbbdddadacaacdcaaadcbabbcdbdadaddaabbabbdcbadccadccbaaaccababacaaaadabbacabbbabddccbbaaccdabcccaadbdaaccdabbccbccaaadcddbccaddbcabcaddabbabcdaadbbdccdbccbdaadccaaccaddbbaadacacdddcdbdbcacbbdbaddbcbacbdaaddadbdadcbcdacbbcabacbadbaabbdbbbcabccbdccdcbacbdccbcaddcbacaccabcbcbccadacadbbbbcdaddbddcdabcaccabdcdcdaccbbdabdaabdabacadddcbbcabcadddbccddbabaabbacdacdbcaccdbbbccbddacdadbddaddadadaadacadcbacacccadcbbbcaaaadadaacbbbbbadbaaaadaabcbbabcdcddaadbdcddcbbdbbaabdbbacbcadbcdbabadbccbbcbacccabbbaacdddbddcacaadccbdccbbddabaadcddcacbaacadbccbbacddadcdbbcdbcbbaccaadcdbbccdacdcdbaccdadbcadcbcdaadbabcbacbcbddcacabaaaacddbcacbbbdabcdddddbcabcaddaddacbcccddcdcbbabccbaacbccddbaadbdbaaaabadaadbcacccdbbccabacadcbbcdcdbccdbadddcdbabcabccdbcddcbaabcdccdbccbcccbbccbaccacddabccbbbcccdbacdaccbabdbdcbacbabbcbadddbcdccdabbcdcacbbcaddccbadbbabbcbbcaabddadadbbcbcbbacdbadbababbbdbcddcccabaccbdadcaabcbabccbacbccadaaabacacacccadacadcbdabbacaabacdbacbbababcdddabdcacbacbacbdbadbddddbdadbbadbadbcbdddabbbbacacdabccbcbaacdbcbdbcdaccdbadccadcbbcdabdcaadcccaacdccaabcbdbdddccabdadbcbddaaddccdaadacdbdcacaadcaabddbcdcddaaadaccbbbbddbbadbdabbadcabdcacbbbabbcabbbcacbddadacacddaadbcbcadbcdcbdcaababccdcbaddcdbdddbdaadcbddbccaacdadcaaadadbddddcdcdaacacbdcdadcbcadcccdcaaccacabbabbddadadbcbdadadcdacabbbddbdcbcdcdcacdbabadbdaccdbcacaacaadbdababdaaaadadcccacdabdabcbabaaaccadcacadcacddcccddcabcbcdddbacbcccbdaabbdaabadcabbdbadbcccdacdabadddaacbdacaadbbcadddabdcadbdcaddabddcbadabbcbddacdcaadcddcaabadccdbadddcbbaadbcbdbcaaaabdcbaacdbcdbabddcdddcbabdaaaddcdbcdaacbddcbcadabbddcacaabbcbabbbbacaddcaadcbcabacadcddbcabcbacabddbcababaccdbdcdcdabacdccabcadaabbcacdccadcdacdbdbaabccdccdcdccccdbaccbbddcbaacdacabaddacbcadcbdbbcdadcddbccdcaccccbaaddbbccbabdabbdcccdbcbadbdccaccdcbaacdbdbabccbaadaaacadacdcdbdbdbcdccadcaacbdbccadcbdcbbbabaacadbdcbdacbacadcbacbacaccbbacababdcabdcdbdaccbabbddacbcaddbcddbddaacbacaadbbabdcaacbddcbbabacaabbbaaaaccccbcbcbdcbdbdbdbbabdaaddaddaccdbacdacbdadacbdbaaabcadbadadcabacbbbaccadacdadddbdaddddbbaaaaaacbbaababadbbabbccaddcbcbbdcdadcddbcabaccdbbdcabcccdcdcdadcbddacddbabbdabbaadabcbcdccbddddbdddcdbdbbdbcababbdbccbadddaabcbdbdcccdaaacdcbaaadaabaacadccdcbaadbaccaacadbddccdaaccdabdbabbbcabcddbdcccacabcadcbaddadcbbabdcddcbacbadbcbaaabdabbcabbcbdbbdaccbaaddcddbcbdcaddcadbdbadbbacdccbbcbddcadbbbbacbdadabcbdcaaabbacadccbcdabacaacbaddaddaddbaadcbaaaccdddcddbccddbacaddccdbcbcddaacbcababbbbcdaabcaacaaddcaaaddcdabcdcbdbababdddcdaaddbddbaaacaacccbaadccbcabcabaaadadcdcadaccdcacdbbaccbaaaabbcaadbbddabbacddabbbbcadaadabbcdbdccbdddbabdddadbbbdddaaccbcdccccdabcddcadaacbaabacbadcadcddcdbcbbdbdcacaabbdbdcdbaaaabadaccdddabcbddbacdaacddddabcdcbbdccdcdaaaddaaddccabdcccadadaddacbdbccdddbbcabacbdbdadbccacddaddbbcabccdcbabdacaabdbaabaccaddaacccbbaaddacdccdddcddaacabbdcadcccbcdaaaadadabbaccbadbadcbdbccacdaaabddbccbaabdadbbdabdccbaaaddadcddcdccadcdabdbaacccdcdbddabacbcadaccaabbbacdacaccabcabbbacbacacdcddacbbcdacddadcaaabadabdbdacbaabbadcdbccdabbccbaaccbcadaadacdacacaddbcbbccaddacddbcdbbbcbaacddddbcadbadacccbabdaabcbddadacabbabdcbabcdbbadddcbdcdbaacbddcbdaccabbaccbdbcabdaabdaaddcbbbaabddaabcdddadbccabbcdbdbbcaddcacdcadaadbdbdcaaacdcdcaabdaaccacccaabccbbbcbcbbcccbacbbadbacdcbcccbcbdbbdacdbcaacbbadaaaabbbabbacbacdbacdbddaacbdacaccbdccdadbbababaadadababdcbcccaacdbbbccaccbabbdbbdccbdbbabdaaaaaccbccbcdcdcbbdbbdcddaddaadcaddcadbaaccdcccdcdbacdaacdbbdadacdcadadadadcbbdccbbddcbccababcccadcdbdcaaaacdcbcbcdddadcdbccdacbadcabcbbdacdcbcdbbaabbadabdcbcddaddccacaadcdaabbddbbdddacdcdaccacdbbddcdccabdcacaadccdcbdccaddacdbaddaccbdbcadabbcabdccccacddacbaddaaddaccdbbbcbbbdddddccbabbbbaccaababbacabababbbdabacbdbabadccbbdadaabbdaccabdcaabbbcdccddddbdbdacbaadddcadbccdacbcdcbccbcacbdaacabaaadbccadbbdaadabdccaabaacadcabacabdccaadaacadcdbabbadaabcdccbaacdcbdbbadadddbcadcbbdddddbbddbcaccdcacbdbadacadbddbabcddbacbdaacdabaaaaaccbaddbaabaabddddcccddbaabaddcbccacbbbdcbadaabdcbddadbddaccbbabdddaddcccbdcbdccadddaacbdbadbbbcccabdadabbdabcbaacbcdccbacbccbacaabddbbcbcbcbddcacccadbbccdbbccbdcadacbbaaddadcbddbdaadbcabdcaaddbabdadadbaaddcbcabccaaddbabbdcddadabcbabaaababacaabddacacbbacdcabaabaddddddaccdbababdcddcbcddaabbbbaadccbbadbadaaaccbcccdbdbbbabaaabacbbbdabababbccbbdcdacadbbdcdadacaddabacddbcccbabbaddbdcaadbbcccbddbaccadbbcdddcaadabcbbcacaabdccdcabcacbbabacadbababdcccbbadaabccbcadaddcadcdcbcbbabcbbbacbcaacbdcaaabdaacabdccadbbaccbddaabdcdaaccdaddadbbccbcacaabdabbbacacdcccdcbcababbdcbcadacabadbccbbaaddbdbdbabdbcbacbaababdddaabbacdccccbadbdacacccacadacbdbbbccadacccabacdaadccdacbcbcdbccbbabdacbdabacbdcbcddacadabacadbabaaccabbddbbcbcaaabcabbddaaddddbadcabddaaaaccbbbbaaccdbdabdbcdacbcdadabaadacdaccaccccbdbdadbbaabbbccbddcbabaacaddcddadccdcbbabddbbbadcdaaacdddcbcaaaabcccacdacacaabcbbddbbddbddcaddbddcbabdabbdbdadbcbdabadaacabcbaacdadddccadcdbcdccaadcccdaabcbbdbcccdbadccdcabccadabacdaabaccaccbbaabadbbadbdcbcddddbcadcadbcdadbdccadacbcaaacdbdaddccadcadabbdccdadadcdaabbccbbabcbdaaabcbbacdbbdcddcbbadbbdddcdcbacbbddbdcdabdabdbadcdacabdbccdcbaabcdadaaacdbadcdcdbbbcbdbabaabbabdddcccbdbddabbbcccccdaaabaabdcbdcccaaddbabcddabdaaacacdbdabaabbddbdccbdacbbbdaacbdbbbbacddbbdcadcccdaabcabcaabcdcbcddacabcbcbdaabadbbbcbbbdccddbadadbbcbabaacdcdccadddbbdddccbddbbdacabaadbccdbbdbcccabaabccdcbcdabbdbbdbcdaccacdabacddcccababdadbdacdbcddbadcabaccccbbcacbcaaccdaabdbdcabdacdcdaacbbddbcdcaccccdcccabccdddcbadcbbacbdcdbcdcdccacdcabaaadbbbcaadddbddaaadbcbdcbcbbbaabddabddaadcbabddabdddadddcdbccbcdcbbbddbcadbdcddaaaddccddbcbcdaddcadbcbbddcdbddccdddbcddbbcbbcdcdddbcdcbddcbcbaabbddcbcdbbcaadbdacacaadacadcbbbacdddabcdbccadddadacccaadadbabdabcacadcbbccbbaacbdaacbacdcbcddcbcacbbddcbaabdbbdaadbcbaaddbaaacaadaaccdbadbbbcbaaaaaacbadbcbacccadaddabddbcadababccbacaacbcdacaacccccbddcabcdbaacacbcbdabdbcabcbabbbcbcddddcadaabadcbadadcaabcdbabbbabbdddcbdbaaccdaabddbccadcadddcdadbacabacabaabdbadcdbcdcbdbbcaddbcbcbacadabacdccccbaddbdbdbdbcddaaadabaaabbccabbdacababcccdabacacbdbabdccbdaaccaaaaccadadabbaddbadddacaadabddddbdaaccabadcacabdacdbdbccdcbddccdabdabaccabaddcbaacabbcdbbbddcdacccddaacccdadccbbdcaadaabaabcdcadccdddacbdacadccdadbddbadacacdaccbddadbdbbbbaacddddcbbdbbdbaccbbbbbaaacbcaddddacdbcdadcdaabcaddddcbbacbdcaadaacdadcbcccdbbbbcacccddcadcacaccabacccbaadbaaccaccadbdccbadbaabbdcacbaacbbbaadacbacbddaaadaacdbabccdcbdbdaaacdbacddbdcbbdaccdbbdcbbaadbadccbdacdcdaccacccdcccadbbabacaadaabbabcbaddaacbadadcdabbdcabbaabbdcacadddabdccaabbbdacdadabadddbdacbabcccdbcddacdaadacabbacdabdcadcacdcaddcddcacddaddbacccbbdbaadabdbbabcaddaacbdbcbcbabcdaadbbbcbadbbabdddbcbacbdbddcccbdacdbabdbbcdbaaaaaccadbccaabbbbccaaaaadccdaaacbdadbbbacbbcaaccccaddabbddacccddabdbcbaabdaadbbcbcbaabbccbbcdbbbddadababbdababcabcbdabbadcacdccadcccdcadaddddbbcdacdcccbbcdcdbcdcaccabcccadadbccdbcbbadaccbbbddbabbbccdacabaccdbabbaacbdaacdcaaadddccdcbdddaabacabdcadddccbcccccbdadacdadbbaddddbddcaaabbbdaacadadccacbcbbadbcdcbacddbbabddddabdcbabadbaadbaabcddaddccbdcdddbcadbbaddbbacccccabacabbddaccbdbbdddbddabcdcdaabcdacaaddacddccdacdcdddcaabadbddbbdbdabcbdbbbdbdabdbcddacbadbbacdaddcaabacdacdddbdcabadacacddbdcaababadccdbcbbccdababdbdadabcdacaabdbbbddcdcacadbabdaabacbccddbdbbbcbaccdcdabbaaccadcaaadadbaacbadbddbcbbcbdadcbcabbdbdddbbdccdcdccdcacaaccaabcadbbadadaaddaabddbadbaaaacbbbcadcdbdbdcddcdbacacaccdcddcccbcddacdbcbbccccbcdbbbcbbacacacdddcbdcddaccdddcbabcadbddacaaabcdcadcbdcccddbbdaadadbbdbcbabbccbccbbcccabdbccabddcdbbdcacbaccaabbbcaccddcacbbbbaadbbbbadcbbadbdaabcbbbaaccccbacaaabdcdbaadcdbbbdcaadbdaabdaddabcbdcbaacbcbdabbccabbbcbbcbdaabcddaaaadcbcbcdbbbdbaababcdddbdcbdbaaddbbccaaddcbbdaadbdacbbdadabdccacdaababaddbababbdcddabacccdbbdabccdadbadabdddabcccddaccdcbdbdbcaaadddccbbbadabbaaddcbcaacaadadcabaccdddbadcacddcdbcbbdbacdbadbdbadddccabdacddcabdcbbcccbaacabacdacdddddbccbbdbdcccccacbccbacbddcadccaddcdcadbaabbdacdbacbcacbbaacadabaaacbbacacbbdbbdbbbbcbbdbdbcaddcbddaabbdbcabadbccddbcdbccacadcbaddcbbaaacccbbdacbadbccdaadddabcdcbcdccbacccdadbcdacbcacadbdcddbdaddcacaabbabadbacdaaadbccdacdadcccaaabdcbdcbbccbbabcccbdaaabbabdababbaddadabcabccbcbdacbaadccadcaacdcbcdccbddcddccbcabcdaaaddbaabddadbddcadabbdcadbacbcccbbacabcbccbdcbbccadcbadbddaabdaabdcdcadcaccaabaaccacbacbadddcbdbaccabadabadbcdddcdabdccccbddaabbbabaacdcbcdaccaadbcbaaabbddddcdcbcabbdbdbdaabbcaaadcbbdcbadcbbcddacacccccccbbacaddcdaacaddbbaaccbbaccdabbccdaadbcbbabacbbadaccbbdababaabcabcaccbdbddcadbbdbdcbacaaccaddaadadbbdcaadadccbbbacabdcbabbbcaacabcbbcbcbbbbcaddaaadddbdabcccbcadcacdcbdbbbbabbdaabccccacabddddcbbbccddaccaddddbdddbbdddbbacccadcacbcdcabdbdbbabccdaabbdbcdbacdbaccaaaccbccadcdaaadbdacddcbdacbcdbacbcbbdcdcbdaacdacbbacdbabcccbdacabbbaaacbbabcccccabcddcbcaaabcccddacaabdbcbcacdadacccaddcacbdddddbdbadbdcaaabcbbabdaadcaaddcdbccabacdcbabbcbacadabcacabddcbcbdcbddcbaaddaaaababaaccbabcccdcabdbbabdadbcdcbccbbbaaccdacdddbdcccccdbbdadccdbadabaddccddbdacbdddbcbabddadadbbcacabcbcccccabcbcaddbcddbbaccbaacbdddddcacbddcbabbbbcbcdccabcacababdadccddaabbaabbbcccabbcbbdcacaaacacaabbcdbdcdaaaaddddcbacccdbdbbccdcddccbbbbcddabbbdaababbdbaaddbabcdcbabadbcadcdbaacadbacccacddaaabddacbadbbcabddabacddcddbaabccbdbbbabaacbcdcbdbacadaddaadbbdcabaaacdbbaaaccdbcadbdbdacabbaabdbbcbdbdbbbcccbadaddaaaaddaccabcabbababcabbbbcccabccbadacdbabcbdadcbdbcdcbdaccbbadbadabacbcbabddcddcaacbdaaadbbdaabbdaaacdddccccccacddadccdddcabdcabbcccadadbabadabbddddadbdbbabdcacddcdbadcabccacaabaabaddbcddaadabbcbdabdcbabdcdacacbddcacddbdcbbacccddccadcaaacabcacdbbcdababdcbbadcaaaabbadcabcacabcccbcabdaaaaaadbcbcdbcdbaadacdddbdadbabcbabbcbdadcdbdcbddadcccccbaabcbbddaccbdbcbdaddbabadcdcdaacaaabcbcabdbbccbcdbbdcdbabcddccdbabadcbcdaacbcabdbcacadcdbadddbcbbbbbbddbdbbdbbaddabbabcdbbdccbbdbbbcdaacacbddaddbcbccbdbccbcabbabdbcdbdbaabbccadbbaacddadacdbacaaaabaabaccbdbadbaaabbacabccddaacaadabccbacaacdcdacbacdaddbaababcccdbbadabbcccabaccacdbcdbbbdbcaaaabbadcabbcaabddabbdcbdbadbdbbabadacccaacbdbbdbccddcbcdaddbabccdcdbdccadaabcdbcadaccbbbbadadccbdcccbdccccaddddccbbcbbcaddbcddbaababcdccdcacbbccdbcdbaadabcdaabcbacbaccbaabddcaacaccdbdabcdbaddddcadcbcccdccbaaaacbccacbadbaddcddacbadabccacabcbabcaacbbdcabacaabbadccbddcaaacbadaccdabcccdbabadbcddcdbdbcdbdacacccccbabcbdcbdbbbdacccbbdcabcaaadcbccbaadaadbabacaccbbdddbcabdacbabbbbabbbbdbccbadbcaccabdccabaccbacabcdabcbdadcdcbbccacddcadcbbbcacabadccaadddaabddaacdcccbaacdbaaaddabcabdcbccdbcdcdaccdacdaabdaadccddcacabbbcabddccbaadaccdcbdcddcacdcbadbccddabbbacbddbddcbcccdbcbdabaabbbbcccbaaadbccdbdaacaaabbbcbcdcbaabdbbdbcbbcdbcdbdaadccbacaabcadcdaacaaaaddcddbaccabacbacddcadadadacccdcadbbbdccaaadbdadbabadaccccbbbbdaadabbdcbcacdbaadabaabdbadccbcbccbadaadaaccacdbcbccbbdacdbbccdbaddcdcbaabcdaccccdbcddadabbbdbcbabcdbcdddccbdabcddbcddbcbbaaadbcddcdccccbaacbcccddddcdbdbdadcbabbaacdbdacaaaabdaccadaabdbabddadbdbabadbdbcdddadacdbcccccdaacdccdcbcbdcbbcdddadabcadcdbbaacccadcdbaabaccbbaaacbddddaaadacdaaaabaaccbadbbdcdbaadacdbbcbcbaacadaabccbcbddbccccbdcacbbccaaabbbaacbdaacdbbcdcbdaccdbcadaccccacabadbacdcddcdcddddcbbadbddaddbdcadbdbdaaadcdacabccbacddaccaabdcbccbaccabdaddabbbbadbdacdacdbacbccaabcabcbdbaccadccbdababdadbbaaccbddbdabbbcbbabbcdbdbcbcadbacbbbadaddaaccddbcdabbbaabbabbcaacdcccdcccbbccacabcdcbadadaacaaaabdcdddbbcbdccbbbabbcdacdaadaccdbbcddbccaddcbdacbcaaccbccadbcabacdddcccdccbacbdacacbbcbadaacdabbabcdacccddccadabdaacadcbcababaddbddcdbdaddbcbabdcdcaadcbacdbdabdbcadcbbbdcccaddababcbcddabaadbabbbaacbbadcccacacccccbdccaccdccbcaaabaadcbaabcdacbccccacaaaabbbcbabdbbddcabaaabcdcdaabdacbabcabbcacaaacbaaaddaaadcdcbbbdcbdcabcdcdbdacabcdbaccccccadccaabdaaccacabbcbcccadacddaaacdbddacbcabcdabbbcdcbbcdcaacbaddbdabcadcdbbbbcdddbbbcaadbdcdbccbdadabccbbcaacacaacaddadbabdddaddcddbbaadbabcbbdacccdaaaccdbbacddbdcdbaabacacaadbcacbabaccbbbadababbcbdadacbcbcdcbabbbadabadccdbaddbdbdcddbcdccbcdbddbcacbccdbddcaccacadcdabcdbcdabcaddbcacbaccdcdabdbccbdabaddaaabdbcacdcdabaabdcbaacbcabaddaacbcccdabaabadbaddcccbccbddaaabdaacbdcaabdaccbcccdcadacabbacbbdbcabacdcbdaaaaabdababbbaddaacdadaabcabaddbdbccaabbcbabdabbbbbaabcabaaadcbacdacadadabdbcaabaabcbbbdabbbbccdbdddcbdaaabbabcacaadbcbdbbcccaabadcabcbbaadabbdaabddabccacbbcbbbadadadcadabbaabcaabcdabbabaabcabdacccbdcabdcdcbccdabdbbcbccbcbadbcaaaadabcdabcabcacbaddbdcacdbdbdacdaaabcbbcccabdaabbbaabdabcbbccaddabddabbdadcdabdaaadabacdbcbbcccdaaabbabacdbdadacaccaaccaaaddccbbadbccdbcacbdababcddcaccaaabaaabbcadadddcdbcccccabccccbcdacbadbccbabdaacdccdcaacdacadbddcccdcdaacbbbacaabadabbcbacaaaabadacdaddcbdababbadddbcadddcdbbbdadcbabcaddacbbbcbcdbbcbcddccdcbcdadbacbabaabcbaddabaabdbcabdadabccadcacacbdaacddcbbddddcabdbbdccdbdacbddababadaccaabccaabdbaccdbabbabbbcaaabcbdcbdaaacbcadcacabddcbadccdcacdadaabcdcadbdabcababcaacbcbababaccbbaabdaabacbbaaabaaabaababbbadccabdacbbacadbcacddddaaccbdddcacdbaddacadddaabaaabcbaadadcbdccaaacddddbbcbaccdcbcbbdadaddddcdabcccccbbbaabcaacbccaaabbadcbaaadaaddcbdcdcccbaacbdcbdabbdcdbaaccdbddbdacbdbacbccbaccbbdcabbabadabccbaababbdaaaacaacccaddbaaaabacabdacbdbddddadcbdddadddbbbddcabdcbbaddbcbcacbbcbdabaddabddcabbaccbacbdbcabaacaddacdbadbadcbacdbdaacabbbdbcbddbadcaccbaadacbdaadbbdcbbdadbcbdbbdbdaadadbdaacacacdacdbddcbcdaabdbddbbaaacaddcddaacbaabddcbcbbaccddbabdbbbabbdbdacdacdabbabcdbbbbcdcbdacacabcbacdbacaaabdbbdbbcabdbabdddcadaddcaabbabaaaddccdadccbacdabdddbcddaabdaababcaacbcdbdbdbaaababcccdddcbaddbccadacccbdddcdaddacdbddacadadcbdbadadbdbcbbcdbccbccbdcdabaccdbdcacdbaadadcaddbdbbaabbdccddcdbddcccacaaacababbcdcacbadbcddaccdbdadabdaccdcdbcdcacdbcbbbcbcbadcbcbabddcabadadbcaccddbadabacabcbacaaabbdabcddaabbbbadddcacbabcdacdddcdcacdbdbbaabbdabdccddcdbaadbcdcabdabcabbcdaddccabbccbdcaaddbdabacddcababdbbbbaaabaacccdadccacdaddaddbcdccaabbacabaabbadbdccbdbadcdabaadbbbaaddcbcacbcaaaccbaadbcdbbbbbccccccabdbadaccddcabddacbcdccdddacdbaaacdcaaacbdbbcccbcabccadabadcacacabbdbcdabcadbbcccbbadccabdbacabddbbcbdbacdbcbcbabbcacaacacdcddadadaaccadddabdccaaccbbbbcbadadbbdacbacabbabdbdcdaaabddadcababccdadbaccdbcacabbccddadaaddcaddcbdcbcacddabbbbdbbdaadbabdbcaacdddabbbccbaddabcddbccdcbbbabaacadaabacbdbbdadcbbabcdbaddccbdddaabaacabbdcbbabbccaccbacbabaaacdbcdadabbbcdcdbbccbdbaabcdcbcbbddcbaabdbaabdcddbbbbcaabbdcdbdbdbaadcdbaacdbbdababcabdcadcdbcaacabcdacbbcdabccccbbcbdbacbccbbbcdccbaaaadcdacadacbacddaddbbbcddacaccbcdbcdccdbdcbababacacdcbdaaacbcbdacabacaabdadcbabdcacddaddacaccadbdccbcadbbcdbbddbcccadcaddbaadaccdcabdadacacbcbdbdbcccbcaababcacacabaaccdbdcdbadbbcbaaadabaaaabadbbaddbcddcbaadcdbcabdaccdbcddccdababbbadcacdadccbbbbcaccdbbdcdbaaacdcdbcaddaccacaddbdbaabcbcacaddbcdccbbcbaababbcdacdaaadaddbcbcababccdbdddccadcbdddcbbaabbaccbcaaacbddaacacbabcdacacbddadaddbcabcaddabbbabaadbddacdbaaadbacbaaddddcabbababdaabdbdcaadaccccabcaaabbdddadcadabcddcbaabdbdbacaabdcdbdaadacacdccabddcdbdbbcddccaacdcdaaabdbccddacbabdcababbccbbdcabccdaacbccbacaabdaabaccdaddacdbdbbbadcabacbaabccdcccabcdabddaabcdaacabcddcbdcacdbcbbcdddbaaaabdccdacaaaddaabbabddbbcbaabbaacbbccbbaccdadaddcabbaadddbdaaddbdbdbbcaabbabcbbdababbdaaaaddabbbacacbcbdddaadacdcdddbdbddabcbdabddacccddddbbbbdbadadaacbabdbddbdbdacbcdcccbadadbbbbcdddaabdcbbdabbbdbddcaddadbccbcabcacddaabdddbdbdbadbdadcaabcbabdbcbaacbbcbcaabbdbacbdadbcacdcbbcabddccdcbddbddbdcabdcabacdbdacbcdaabcadddddddcccccbabaacbbccaadaaabbccdabaadadbaddbcaaadcddbccadbdadbcbabaabbcabadabbbcdccaabdabccdcaaaabcdccaaccacbdbabdabbddbacbdadabadcdbdcabbcbcdbcbcaacdadbcddcadccadbdacaacabdcddabccadbdaabccacdcddcdbddcbbddcaadaabbcaadcdaaabdbdabccaabbcaaabcaadabbcdaabacbacbdcbbbcdcadaabacabdccbccdbadbdddaacacbacccadadbbbdcadcdaaccbaaddbbcdddccbccbdcbbbaadbabcabdcbbbdaabaccbdcbdadccdbbbabacaddcdcbbbccbaccacaabdcddabaccdcdccaacabdbacababcadccbccdcdaddbcdccbaccbbdcaabcdabbcbcaacdbccbdbddbbdcbdadbcaddbdabdccbcdcabaacadcddbabdabdaaaddbadccddacccdaacdabbdbacdcaacdacabadbddbbccddbcdaaacadccacbaccccadabacacadcdacbbbacdadbaaccdbcddcddcdddcddcdddcacbccdadacdbdadbabcdbbdbbdcbaaadbacacadbcdcccdcadacbaaaddcccbdacccacbcdaddaddacacccdbacabddbddcadaaddacacddabaadbcdaadddadccbdcdadbcdddcdbdbdcbdcbbdabdcdbaabdbcdaaadbaaadbdcaccaabcbcdcacbadcccdcdaaaaddbcccdabbacdbcbdccbbddbdacaabbabcdcacdcbbbabcccbdbbcacbadcdddbdbbadabdaacdbdddccbddcaadbcdcddbbabcbadddcdbcbcacacbddddacbaccacbbadcbbbdbcbbdacccddcdccdcaabbddacaaaaabaadaadcccbbddcaddcadccdccdcaacbcbabdabdbccccdadddabcdcdbabbcbbccadabbdbadaadacadcbaccadbaacbabcdccddaacbdcabdaddcdabdcdadacdccdcbcabbdaaaabccdbdccaabacaabdbbdbaccdaabdaadbaaabadbadcdcdcddacadbaccbcbcaadaacdddcaacbbcddddbcacabbcddddbadadbdcccdacabcbbbababadcdbadbccddccaddbadbdcbbadcbbbddbcbbbbaccccbbaddbbbdadcddccaddbdbabdadcddababcacbbddddcdabcdabdadcdcddbcbdabbcadacbcbaacdbaddbcacaaddcdacabddbabcbcccacbabbdcdaddbbdabacaccaabadbccbacbccdbcdccbaacdcbdbcabdaccdadadadbdbdcdacdcbddabaabdcbcbbabcaabcadaadcccddcddcdaaaabbbddbdbabbcbcbacadddbbaaabbabdacdacdbcbcdcadcbbadcccbdddbcdccbbdcdcccaabddddbabdddbaabcabddbaaccaaaccdcaaaadcabbcaddcdaddccdbcabbcaddcdcbcaaacadddbaaabacbbcdacadcaadaddcbaaababddbdacccacbbadccaaccbdcdabcdcbcdbdbccddcbbaabbbdccdbdacadabcaadacddcbadaadababdabaadbbdaaaaacbadcacdadaccdacbccbcbbbbcccccdcabcbcdaacbddcccdcdccbcccbddcaaccaabababacddccbddabacdacbddbcbdbbcabbadaccdbacbbccbcadbcdbbdcdadacadddcadaccccdaddbdbcddbcdbcdaacdacbaccaddaaddcdcdaadccddaddaaabdadabbcdbadadbbaddbadacadcccddbddcbcadddddcdcaddbdaddcbdcdbcdcbdcadcdaccdabadbdbbdaabddccdbbbbbcaadabbbdaadbcbdbcddbcddcbcddabddbdbdbaabacaccbbbbaddccddabacaaadbabadacabacdabdddaacccdaaaadacacbbabbccdcadacbddcbbdbbbbcabbccdaadccbcbabcdbdbabbbdadbdbbddcbdbccaaacbdcabacbbcccaadabccababddbbbbcbacddaddbdabcdabcddaacaabccbaacbbaadaaaccaaacbbdccbcbdcdcdcabdbaddbcaddbaadabbdddaaccdbdbbabbbddbabcabcccbcdaaadbdadcbbbaddcbbdddcbccbdacadbcdbbdbdcadaccbacbbbcbcdcdbbdbbadaadcacdccbaacccabcdbadbdddbdccdcdcadbacbdcbccddababcbaddadbabcbcaadbbcccbcbdccdcdcdcdbbaadadddadbabdbbdbcbabbcdabccbddbcddcbbccabccaddabbcdadcdbcdcbbdaacaacbbabaaacbaabddcbccccadaaadacadabcbdcaabdcdcbbdbbcdabbadaaacbcbcdddacdddbaabacdbdccbddddbbbdacaaccabadaacbcdddccdbdaaadddccbcaaddcaddadcbaccadbbdaacadababcadbbddcabcbaccccbaadcddbdcdcaadccacddccabcacbdbbacdbbbdbbcdadabacbdbadbcddbaacbacdcbdcaabbcbdaaccbdcccbdabbbaccbaacdacabbcbcdcccaacabdaabababcbaddabcadcbdaaabcbccccddcdbbadbcbadccacdaaccccabbccbdbbbaadbbbbacadccadadcdacccdadbbcadccdcadcaacbaddacadbcbacbdbdacdcdbcbabacdbddbbdccdbcccaccddaaabaacadcdcdbbdbbbaacaadbbddbaccdccacaaacabbdbccdcacbbaabadcdacaccabcbaabacaacdcadbbdbbbdbaacdaccadbaadbbccacccbacdadccacbddbcccdbacbabdccdaddcbbaacaabdcbcdabdcdbbddcddbacbdcbcbabdbbcacacbcddccbadaadddacdcdabdacbddabdacacdcacccbdbbadbabdacdaaabaacbdabbaacdcbaabbbbbaddccacdaacaabbbaccbccbcddbbcaaadcddbaaddddaaacadacbcbdcdbdbbcbbccbcdcabddbdbbdcddccdacddddadabbaabadabddbadddcbbbddcdcbcccbbbccccdabbdccdbdbbbdbadcddddadbcdaaddcdbdbbcbdabbdbaaaabdbdbaabbddabbddbdcaaabccaaacaadcbaccbbcdcaabdbbaadccccbdcdbcdcdbaabccdbdbccddbbaaacddccbdbbbaaddabbdccbadbabcbddbcbabacbccacccaadaacccdaaddcbcdccacadbbbaabbcadccdadbdaacbcbdadcaaaabcdabbbdcaacbddaadabbbcabcddaadccbadabddbdabdaddcababccaaacacddbcbaabdadacbcdbdbcbcaaacbbadcaddbcbdcbaabdcabadbaacbcddaaabacdcdcaaccbdaccadddadbbdcdbdadcbcbcccbddaaccaaddacdacaaccadadbbdcabdcabadbdadacabdcabbdbbbadccddbabcccadadddcddbcacbcdcacdbdccccdaccddadaaadbdacbdaacdccdabdcdddcbbdabddbcbcdcacabccccabdbabcacabaccdabacdddcddaaaaaccacbdaaccbdacdadbdaadcabddadaacddaacacacdcccadbaddcddcbcaccbbbdcbcadbccacbadabdbbdcbbccbdadcabbcbcbdbbbaacdcbacaccbbcdcdbbdcaaddadcbbaabccababbbdccdcdbbdabbacccbdcaccdbcdacdbdadbdbaabbbdcdcbcbdcccdacabdcaadbbacaaccdddacdcbdaacddcabdddccaabadcbbbbdbddaadcccaccbdcaaccacabcdbbcddcbdbaddcdbbcaacdaccabbbcacddbccccbddbcdabacbbdaddabacddcdabbbabaababcdbbaabbddbbcbcdaddddcdcdddcaabacdacbddbddaabbabbacdacbcacacbcdbcaacabbbdabaddabdcababddcbbdbacacbadbabbccddbbbccbdacbdcdbbabdcbcadabddddcdbbddcabaababdacccdbccdcbbccbaddbbdbdaccdcbddcacdacccbdbacdcabbcaaadbbcaaacccbadadbbadabcadacacacddcaccdbbcdaacdbbccdadbbbcbbdbcbdbcbcadadddcdadbbdbaacdcbbdbaaaacaadbcabbbdcabdcdbbaaacaadcbbdbdbbbcabacccbbddaaddaaccdbdcdaccbccbbbccbccddbabbaddcaaaababdababbdddcdadbcadbdabadacbaaaaaacdcbbdabcdbdaadbdbdbabbaacaaaccbdbbacbcdddddbbbdaacabacbdcbcbabddaadcabadcdbbdbdccdadabaccbacadadcbacbbddcdbacdbabcacbbbadbbdbdccdcabacbcbdaaccdacdbdddbadbbbdcaabaabbadcdcaddcacaabaadbddbcbacdadaaabbbcadabddadccdabbccadddddbcbdbabccdccbbbabbcbbcadddcdbbbcddccacbbbacacdcddcbaadccbacabcbdbcbcabdcddcccddbdabbcbcbdaccbbdccaacacabddacaddaccadbcaaccabadddaccccaabbbaccadcadbaccbaccccbccdbcababdcaddacacabbcabdccccddcadaddbcdbcdbbadabdcaadcadddabbabbcdaabcbbcdcdabdbdaccdbbadccacccaabccadcbaabdcddbaadddabbcddcbbdcdbbaacddacbdbbdcdccdbcddacbcbcbdbdbdccdaabacacabcccaadcadcadacdcddabaddcdaddadccdacdbcdcdbdabdbbaaababcdcdacdccadcdaaabcaccbcccccbaacdacbdadaaadcababbdbdccdcbaabbabbddadbcddbacdddcabacdaaaabadaabbbaccdcaacaccacacacbbcccddadadcbdcbaabdbbdbcadbddabcdcdbaaabbabadbcddccababbaccbaabaaacbdabdcaacdbcdbbbbdacbdcbcaaaaaacbbadbcdcddbdbccdcabbdcbadddddbabcbdbacdbdccaaabdccadbdbdabddcdcccbdadabdcdbbcadcdddbccbbcdddcbdcdbbcbaabaaabacaaddaabbbaaaacaabcacdbccdddbaaacbaccddadcaadbabddbdcabdddaadcdacdbcdaadaadbbbbbddbccbcaaccacbbdacbbdacbcabdbaaadddccadcbacadbbdcdaabbcbdbaddbcbcaddcbcbddcbbbbdadaaaddadbbdaacdbacaadaddbaaacdbdbdcddcacbcddccbaaadaacbdabbaacbdabddcddbcdabdcbddbcbccbdacdaadbcbadbadccdbdababdacdbdbbdccbdaacaccbbdbdcbdbdcdabaccdcabdccbadcbccaabcddbadbdcbbaaaddccabadcdbaabaaacabcacaddbcddadbbbcaadccaadaacdbbbacbacbacdcddaabcbaddbddddbcbbbdddcbbdaccbaaadcdcbaadbabadddddaddcbcaadccdbcbbcbcaacbcbddabdacdccbadccdcdbbaaadaccddadcdacbbbabadadaddcbddaacabbcdbacccaadbbbdaadbbddacabaccdabdbcdabdddbbbbdbbbbcbcbcdddccabdadacbbbadacaadcbbdaaacccdbaaadbdaaacddcadbccdbbdcaabdbddcbcbccaddddbaabddcaabadbccdccdacdadaddaacbdbdbbbddbabbcdcccbacbbbbddbcbccadcabddcadacddbdcdccddbacbdddaddacdabbaccacbcbbbaaacabbbbdddcbccdbaccbbcbdbacdcadadccbccabddbcdaababccadcddbccdabdddabbddddbaadacccdbadccbadcdaaacabdcdabccddadcacbadcbabaabcddbacabbbcbdaaaaccbbcbacaababaccabcbdadcccbadaabcaccbadbdaccbccdadacdddbccacbdcdabdacddbbaacddbaadabdbbcddbcccdbadaaadbcdbdaacddaddddcadbccbdaabbbcacdbaabacaddbcdadadcbcdcabdbacdbadadcaabcadcccbadbdaddbbbccccddbdcccbbaddcbcbadcdcccbbcadddadcbcddabdcbcbcabdbacccacbddabbdaaacdcbcbddaaaadabbddaabbabbbaccbaadacdbbbdcbcdcbcadcccaacaddccbddcaacadcbbdbbdcbacccdcbbadacadddacbbddcddbbbabcddbdadbbcbdcdadbccacacbadaabadccbbcbdbcddbadbacbbadbdaaabcbdbcbdbababdbdddcbbdbcacaaccdcdcbcaccabcdacbdcadddaabcdbcbbabcdaacdaabdacdacaddbcdabdcabaacdbcbdccbbdaacbcaaaaddddbdaddcddcdddcabbcdcaccbbcdbbcddabdcadbbdaabbcaabcaaaccdcdbacdbdababbddababbaddabaaacabaaccbdcbdbdcbbadccbdcaaaadbcddaacdcbccddbabadcaaaabddadbadbabdcddcbbcddabccabaddacaabadabbacacddaabbdbbccdbcdcbacccbcadbbbddbdabbbbdcbdbbdcbbbbadbadbdcdbcdbabdcbddccdcddabbdbccacdbabcdbdcbdcadadadcacbaaddbbdabddcadaababdbcabbdccbcbccaccbddddbdabbcaddcbbbdcdccddddadbcabdccbbcdcdaadcdaacbbdbabdbbcadbdcaccdcddccbdbcdbcddccadaddadbcddcbccdbcdddaabcbbbbcddaccdddaaccdaccbaddcbcbdcbccadbbcaabbcddacccabadabcdcacadaccdcdbbdbbddabadaddbabbdcdaabdddbcccddbdacaacbddcaaaaccdbbcbdcbbcabaabaaaccaccbdbbdcabbbbabadbacacdcbdccdbcbbdadcdbdabbaddcdcacbdbdbbddddabbcbcbcdabababacdcbcbddbcadadabdccbabbccdbdabaabaddbacdddaaaacdbabadadbdaddddbcddcbcadacdabdcaacccdbcccadddbaabacddcbcccbababbcdbccbadcbbbbdcacbdadbbddbbbacabdccbccaddaadbdaabdbbcbcabaacdbcdacbacdddabcdbbdadcbdadaadaadbdbdaddbaaabcadbbcaaabcddcbabbcdddabdcaddcaccddaabbbbdbcdcccdbcacacdbaacacababbbddbcdabaacbdaaaaaabbacdcbcccadaaadcabccdcdcabccbbbaacbbbaccadbcccbcddabdbdaadcbadbadbbcbddbccbcccbbddaaaddbbadadcbbccddbacdadadacacdbdabcacbcdaddadcacddabcccaacccdbcaabacaddbbbbabbaccbaddbcbccbacddbaaabbabcacacacdbbcbaacabdbddbcbabddbcdbdbadaaacbdacbdbcbbdaadabdaddbcbdbdccccacbdacbddcdcdbccadcdcdcddbcbcacaccddabbcdbbdbcdbddacccabbdcbbcbdbcdcbccdcdacaaadddabaddcbaccbdabddddcadabcadbccdbcbaccbadadaacddadadaabdcdcbabcdaacabdbcbaccbcbcddabdbdbbaaabadcdbbbddabcdcaccaaadabdbcbcbcdcbbaabdbaccaabcccbbacbabdbbccacbddcaabdccaddccadcdbdacbacacddadbbadacbbdababdaabcdcdabddcababbabcccacaadaaabcdaadadcbaaddabccbcbcacbddaadcbccbbaaabcddacddbbbdbcaabbccbccbacaaadaaddbccbdacddbdbddddcadddabaacdaabbbbabddacdcababbdcabacacddabccdbadcdabcdacacbcdbdcaccbaabbcbbaddbbddcdddcabccdbaccadddcadbccdbdbdacbbcddccdbbbcdcaadacaddabaaaaabcdddcdbadbaccadabdccbadabaaacbdcddcabccccaaddabcaccacbabdadabcbaccbcbcaaaddcdbcdabaabacbccabdbacbaddbcbdddadbdaddbdccabaacbcdbccaaaadadcdbcdbabbaaabbcdbdccccaccbacddccdcbaddccabcbcbaabbbdcaaabdabadcdabdabbbabcbccbaabbabadabdccddaaaacbccacbcadbbdddbdcdcaaacaccbbbcabadaacddbdacdbcbacdccaddbbcbbbaabadbdbacbcaabbcaadaadaabddccdcbbcbcbabdbadddcbcaaddacccaaacbacdcdcbaabbabcaaabaadaaabcbabccbaadadaccbccbbadddaddbadacbdcdbdbcbbabcddbbdadabbdccbddacbdbadadaabadbbbbbdbdbbbcbdaabbcdcacbdbadcccdccaacdcacaadcadaadcdadadcdbbdcaddacdcaabdddcabcbbdbbadcdbbccddbabccbcadaacaabbcadcadadadbbcaccdbdcbdbaccacaacdbacdcbaadacadcdaddddccccddbababdddbcdbaacabbdddbcdaacccdddcababacdcabcbdbcabacaaddacbdbccbabaccdddcdcdbdddcacddadaabdcdacbdadcdbcbdbdacdccbbcbbcbdcccccabdadddabacdadcbcdadbdddbacbddbdbaccabaddacaadddacbaddbcabbdcaddcacacadabbdbbdbdbcddaadcdcaccbaccdbabbabddadccacdddccdadbacddaacdaddaddcaabbabbdabcdadccacbadcaaaadbcaccbcbabdacaabdabdccddddcdaababbdcddcacbacdabdcddbadcbbcdbbcaaddaaddbcbbddddcadbaaadcabdabbbdccabdbbbadabcbddcdbccdcaabdabadbadbaccccdbbadbbbdabdbdabaccbbbaadabdbbbaccabdddcddaabababcaddadbcdbacbdbbaacbccbbdcbbcdddbaabacccaadacaaddccbcbbbccaaacddabcdddadbdacdaabcbddcddddacabddcdbdbccadcddaddaabbcadcdbdabcdccadaccabcadbbcdbdabdabdcdadbcdcbaaddddbddddadcabadcadbacdbddbadaddcbadcbbdcbacbabdccabcbaacdcbccbdacdcadbdaddbcadaacdddabcbaccbaacacddaddcdabcbcdbadbadbbcbdddddbdbcabbbcdbcccbbacdcabadadabcdadabccabbaabdaaacbadcacbbdbcadabbcdcacadbaacbaddaabccbdaabcabababadbacaddccaddcacadabddcbcbcddcadccddcbcacdcdcadddadcdddccbdbaacdabbcddaacadbaaaadbacaadcbbcbddccabaccbdccdabbcddabbcccddcdcddccbdbcacbaaacdabcbaccddbaccbdbdbabccaddcbbcccdabacdadabcabbaaaacccdcbbbaccccddabdbabdbbcddcabcaddbbaabadabbcacadddcabddcdbcadadaabccacdadddccdcdadccdadbcabdabbdcddbabdbccadccbdcabdddcacdbcbbdcbcddddddbababddcaaccaabdcccbddabbcdbccaccdaccbcbaadadaaccdbdcbcbbaddabaadbbccbcabaabdbbbccdbddccacdbccbcdccdbacacbccabadaadbbcabdbabdabddaabdbaaccbbbdcccdcddcdbcdbaaaddddcccadcddabcaabaabccbbadaadaccaabbdcddddcadacbccaabadbdaaddcccccbccbbccccbbbcdcbcbacbcdabdabdcacbacdcccddbbbabdaccdaabadaabdddabaaaaaddaaadaacdbddadbcaaacadbbacacdaacccadbcacbbbdaaacdcbabdbdcdadaabdacacabcdcabcaabaacddacacdcbbacddaaccbacbbcbacabdcddbbdbdabdabddcdcacaabbbddcdbaabaaadacacdacabdbaabaddcdadcdbbcadcacdcdddabddbdabccbcacdcbdbbabdbcbdbacdbaadcbccacccabddaabbadbacdbdadadabcadbbbddccdbbaadccbbcaadacbacbacaddcbdaccbdaaaccacbcccbbcabbdbbbcabcbdacbcdccbcadcdaccacacbabaadabaccacaacabddbdbacabcbdccdababbdcccbcacdbbcbaadcdadbbccccacbccbdadbdacdbdbbccaadbacdbcddbaacababcdbadddabdddccacddcbcbacadaabbddcccdbdddabbdbadadcdadbdcaccdcabccdcdbbcbccbbbdbdadadbdcdabdcaacbbbdadbaaaadbdaaaccdddbddadbddbcbaaddcbdacdbddaacadbbcbacbccaaabadddcabaaacbcaaaabdbaddadabbccbdcdbcbbcbabdcabadcbabadbdaacaaddcabcdcdbadbbaacaccaacbbbdbccaabddddcdadbaabcbcdbcdaaadddbaddddbaccaadadddaadccbddacccadbbccbcbdacbcccbcdcadbbbacacdadadbacaabbdacbcacccddbccdabcaacdbadcdbcadcdcabcbdadbdcbaabbadcccaadddcbdcabdbbcbbccbcabdacadccaacaacbdabbbbcddadcbcaadacacaacaddbcaababbdabbabdcabbbdabbbcadabbaaadbcccddbadaabcbabbbdcacbdbcadabacadbcabdccccbbcaaadbbdddccbaccbdddcccbcdaccdacaadacdcacbaccbddabdacbabacdaabccacccccadbaaaaabbabbadacdbcbbabddaabdbcccbcbabdabaddcbadbdcaccdadadbbdbdcadbbdbbadddabcbaaddcbbdbadcaddcabcbaccacdbccbaabdbbdccadddccddacdbabcccacacacbcdbdaadccbadcadaaaadbcbdadcbacaacdabccacbbdacbaaabbbbbadbcdbcacaacddabcdbaacdbdcbabdabacbdabaccdcaddabcaddaabdccbbaabaaddaacadcacdbbcccbcbbcbbbcbcadcaddaabcbcaddbdddabaaccaaddcdbdbcbdcdccbaadaaaaadaaccaccbbaaabadcccacbddcaabbcabcabdcbdcacccbdadacdccddddbaaaadacabacdcabcdcacdcccbaacbcdcaadcdcaaabcdabaacbaabcacaccdaccacababcbaacdcadcccbdddaacabdbdbcbcdbdabbbdacdaacdcadaadbbcdddaccccdbdccaaddcbbbddadcdaccbdcdcadbabcbaccbdaadacdcaabaaaabacdbadabdcbbdadabddddbacbccbabbbbacadbacdbdaddbabddaadaabaaadbbbaddbabddbaddbabddbcdddcbabbcdcbddcdbaddccdadcbbcbddbacbbaadadccdbcaadaddaacddbdaabcbccacdcacaddbadbadcacabcbcbcbaddcbacdbddbabdaaabbacdccddadbabcaaacdbcbbbbcdbccdcbcccbcaacbdacacabaacddabbadcadcaddbaababcbddcbbcbaadcdccbdbbbcdcbbdaababcbacaaacacaddbdddabbddbabccdbddcacccdacdccbbcbccbdbddbdcdcadddccccadaaadcaadcaccddaddcbdaabcaadcaacdcabbcbccdcbddbcdccccdaadabdbbdbacacaaddabdadbdbabcbadbcbabcacccdbcadcddddbaaacbbbaacbbcbacbddcbddabacdaadadabbbbbdcbdccbcbccaacbcbaddaacbbcaddbcacabbbaaacdbcddbcabdaaacbcdcccddbcaacaacddbddabbadabccbcbccbddbbabddbdcdbacbabadcccaccaadbdcdbacadcddacacdbbcdbaabdaabcbbacacdccdadbbbdcbcaaddcdaabcbbbdabdcbcdcaddacabacbbdacbdbaabbddbbbadbbabbdbbddabdcadcbcadbbccdacdcbbaddaabadabacadbbacbcabddbdacadbcaddacddcbdabddadabbadbdbcdddbcaccdbdbdbdaccabaacccdacadcbcbcbbabbccdddadacabaddaacccacbbcaaccabaccbdabcdadbcabacbcadcddcbabcbddddabdbdaabdbdaaaadccdddbbdbcacdbdbbbbcccddbcbddcaccbaddddaddaadbbdaababcddccdccacabacdccbdacdddadcadccbcbaaccbcbababbbdcddcadbadcbdacbbcacdcadbbabcbdbcbdacdddbbaabcbdcbacaacbaaadcaadcadadcdaabcbbcadccccddacbcaadbddbcbacdaddbcdbccabcadbcacdaaaddaacbcccaabdcdcabababdaacddaccccbccccbbdccccacccbddacdaaacaadcbaadadcbccaddccaabbaccdabccaaccbbbdadababcdbcddbabcdbacbabdcabddccbdddabbbdabaccbabaaccaddadabcdaaadccdaadddaadcacaaddcbcddbcabbbbdcaadadccddcdbcaacdcbccabbadaadadadddabdbcaadacbbdaadcdddaaabdaccadaadcadcbcdcacddbdbaccbbcbacbbddabdccaacadadcaddccacbcdabdcbabcbcabbabdccbaadbcbadddcbaadacbdbdabccbdadabaaaadbdbcbcdcbbcccadcaabddbcaaadaccdaccdbadbdbbcbbccbbdcdcdacbbdabadbcaabaacbdcbababcbdbcbbddacddccddddbbabcacacdaadcccaababcbabddcdddddcadcadcdccbbcabccaaacbccabcadbccbcdacbccbacaabacdbabcbacdcadbccbcabcadacbcdbabdaadacdbbdabbcaadcacaddcddadbcbbcccacbdaccbbcbcddbaacbdcbccabbabbcbbccbabcdcdbcdadccbbdadabdbcbbbbbccbdbdbbdadabbdbddddcdccdbbacabcbcabcbaabcbadccdbabcadccccdbdbaabacccdaddbccbadddaccdbcbcbacddbdcacdaabcababdaaaadccbbdcacbccabddbcbaacdccaadbdbacbacadcbcabbacaadcccbcbdaccdcbdcbbcabddbcddcbabdbacdcbabaacbccdaacdcbbabdbabbcabbbccdcccddddbccdbcadcbdaabadadbaadddcddacdababbcdddaababddabbdbdaabadddbbaacabdbbcbbaacccbacaadbbdbadbcdabcccabacccabbdcdabbaccdbdccdddadbdbacdaaadbcabddcaaccadadaaabddabcdbabbcdbabaacaddccabddadcaaccccacbaddcbabacabbddbbbcabdaadaddacdcabdabbddabbdcabdcbbbdcdabddadccccaadddaccbcbaccccbccbadbcdaaacadbdaacbbcddacbdddddadcabbbcdabdaddaaaacddaadcdbccbbbbccdadccdaccccbaaacaccabddabbcadcbabbbbdaddadbadbdcbaddddbdbdbaabdaccddaaccabcbabacdcacccdabccbabcdacddbcbabadbcabcddcdcdbacddbbbbcabbddbbdccbacaadbaadcccacaccdcdacbcbdbabcbbcccbbdcbdddbcaacadcdaddaadcbcdddbcabccbcbdacbccbabdddcbcaacdacbabbdbccbadacbdaacdbccabddaccaadcadabcadccadaaadadcbdbabdddbddbbbccdacabdaaabcdcbdadaddaaadaccbdcdcbbcbbdabdcaaddcacbdcbaccddabbdbadcacbcdbcaaabbcdaddbcaaabcbcdbbdcccbadbbbcbabdbbdbcaacacaadbdaaabcdbadcbdcbacacaacaacdcacdbcacccccadaabcbdcccbcbdabbdddabacacdcddbbbabbbabbccabdccdbbbdbbbbbdbdbdcccbadcbdccaccdaacbacbadcdbcdbccadaccacaabccddbbdacbacadaabdcaddddbddabdabdbcddbabbbcadbaabccbdcacbadcdabdbcbacbaacddcbadccaadddbdaaccbbbddddaaaadcabbabaaaccddbcbaabacddacdcaddccbddaccababdbdadbdbcdbbcccdbbaccaacaacbddaaccbdadbaaadbbcbcbbbabcaddbcdadabcbddccadbdcbdcdcbcacbabbcddabacdacdaddbdadaadcdcaadbdadddcaccdacccabdcdabbabbaddababdbdadaccadbcbdcddacaddddaddccbbbacccbadabdaacccadbabbabcaacbaaabddbacadbacacbaacddacdbabbbcdbbbcdaadcacdcdddbabdbbdacabcabdbacdadbbdcabdbcacccaaddbabcabcaccdabcddcdbddbadbbbdaacdbaaaaddcabbaccbcdadbdcdcacabcdaacbcbbbbdabcbddcabadddadacbcdccacbabbbcbccababddbacdcdcacabbbabdcacdcbcacdaabdcacbbbadbacabddaccddddbadcdadcbaacabcdcdcaacddcabadbabdbdacadcbccbdbbcdaccbbaaabdbbcbdcddcbdbbacbacbdcdcbaaccaacbcbdacdccdcccdabccbaacccaabcabcacccbaabcbdbddcbccaaabdcbcaacacbcdcdddcdcacbddcabddacdbaaaddabcddbbbabccddadcccdcdadcadabbabadbbacacbddccabdcaadbbddbcadbaadccadbdaaccbdaababdbdcababbcbbbadcbcbbdabaabaddddbdcccddbaadbcdabdbbdbcacddccbcbadcdabacccaaaddacacbdbabbbbbcaccccacdccaabbcbdaababcbccaaccadcdbcbcaaacbbbdaadaaddddbbadadadaadaacbaaaccddbcbdccabcbcccbdcdabacbdbcdccbddbbbccacddcbbbaccdacccbdcbabaaabacbddcdcaabbbbcabdbbbddbcaddddacccabccdbdadbbcdbaccddadbacbccdccddbaddadbbdabcdacdaacbaacdadccddbaccddccdaabadbcbbdcabaaadbccbadddabdabacbdddbccaddcdaccbaaaaaadcbccdabacdddaacaddacccbaabaacbcbabcaaaaaabbcdadcaddbdbcdacccccbabbcdbabcaccabbcbcdadcaaacccbcabbdccccdcbcaaabbdaadbdbaccdcdadaadcddbdcbadbcccbbaaacddaadaadcbdcdaaadbbdbbdcbdcabdbbdcdbddccdbcdacacbdadaddacbacabddaadaccbbbacccbddabbbcdbddacdbaccdaaacadcbbddcadabbbacbacaabbcbcdadaadcbbbaaabbbcddbbbbabacdacdbcdddcdbdabccdaacaddacdccdadbbdcbddccdabbaaddbdccdbabdcadcadddbdcabcaccabbdcdbdaaccacbdcaabcdbbadacdcacacaabbbaacbdccadbacbbdcaadbbcacddadbcaacadcdabdddadddbadaddaacbdaabccadbcadbcaccaddaddadacbbcccbaadcbdcabdabdbddbadbcbaadcbadbbbacbdbcbaccccadacdababaddacaaadcaaabacdbcabcaabaaacacdbabcbcaadbdaadadcccdacdacadbacaadddabbaddcaccdbaaacacddbbabadccdbcabaacdcbaabbbdcddcaccaadabcdcccccbccdcccbcbbbbbdbbabaaacacaabbacaccbdbdddccacbbbabbbdaaadabacdbdcacabddbaadadbbabacbcbccdcaadbdddabcabbbbddaadacdbcaaddbaddcccddbcdbdbabdaddacbbdbdaabbaabcbaccdadbabccbcbcbcbdcdcddbcccbdbcdabbbbaccbcbdcababacaddacbddbcddcddaaaadcabdcdbadbdddaccddaaacdaccbbbacacdabbbabccbaabdadcbddbbcdbbdcdbdcbbcdbabacbaacddaababbadddaaabcbaaadbbdbdbbbdbcdadacdcbaadabadcdabacacadddcddaabaddaabbddccadcaadcccbbaadacbaccabdcbabcbccdbbcdadacdbdbbbaacdbadababcbaabccbcdcdcdbabdcabcdddcbddcaadadabbadcbbbbadadcddbbbdccadadacbdaddbbabdbcbccababcabdabcdacbbcbababacbccbdccdbbbdacababaabdbabcdbcdaccbacacbcdcbddddabcaacadcacdbbccabddacbddcddcccccddacdcbdcbdbbaabadbddbacaddabbddbbbdcbdacbadaacbaadbbdcaadacbcabcdbddadbcaacaacabdbdbcbdcbaddccbdccdddbcddcbbccccacbcaaacbcaadabbcaadacacdcbdcabadbddcbcddaaacadbdbddcacccaacaababdbaabaaaddaadcbbbbabacbaaaaccdddaadabddbcdadabdaaddbcbbdaaadbdabdaaaddcabdccdadbacbaaacccbdcbbbcabcbdbdbbcdabddbdacddbbadacbdadbbaaacdbbcbaabbdabbccadcdabcabbdcacabccacacacaaaddcbdadbabbbbcbccacddbcaadadbadbccbccbbdbccdbabaaccaaaadacdaacabbacdadcdcbbadacdccabaadccaccdbdbcddaaaccddacaadddccbdddbadcacdaadcbacbddbbbdacaaaabdadbccddcbccdcaabdbaabdbddaaaddcddddcbcbcadcbdbabccaaccbdcbcbcdddcbbcaaddbdbdaaaacdcdbaacadadadccacbaaccdcccdbbbdacbcabcbddbacacbcddaadbaccdabbaabbabcadaaccdaacdbaccacdadbbdbaaccdaaabbaaabbbddadabacabdabaabbbdaabdaaabccbbadacdcbdbaddbdbdcaddcadcdbcccbcdbdacadabdaabaacadbcbdaddbacaacbbdbaccadcdcbbdaddaacbbdbdddacddbadddbdcaabbccbadabbbbcbbaaaddadadbbaadbabdbbadaabaaccacccaacbcacbdadbbddabbbaabbbccdadbacdababaabcbcdacacdcabaabaccdbcacbcdbccdcaabdaaacccaabddbbddacbbcbdcacabbdcabaddcaadcaacddcddcddaacdcbbacbbadbddaacdddbbddbdbaddddacdabbaccbccbdcbbddddddacdaaadaaaadbaccababdadbcbcbcaddaacadadccbcbbdaabaaaaaccbdabccaccadabcacddcabaabbbcbdddcdabbcaaacbdaacbbbddcdbcababcbbccdbdbdcdcbcdaabaadcdcccaccccdbbcaaccbccbdbdddbbcccdbdbdcbcbbabaacacdabbddcbbcdcbbaaccabacdabdcdccbdbcbbcacdccdbdadccbaaabbdbdcdbbabbbaaadbaabbabbcbbdccdcdaaddcccccdadbddbacdadadbbabddabbadaaaccdccbddbbccadacbcdbacbabdbacdddccacccbbdaddcccdccaddbbaabdcaaadcaabbabbbdadddaaacbadccccaddadabdbbdcaddadbdddabbadaccbaabaddcababcacbaabdcbbcbdcccabccccbbbabcadaddcacbbdddabbcdcbbbccbbabdacaacabaabbbdcdbbbadcbcddcddcaddbdaddccbbcbbaccacccbaddcccdccdaddddcadaccaaabbcccdcdbccccacbbbdbaaaccaddcacaabbdcdccaaadccddccbbabcddcccacccbdcccccaabccddbacdbcaccbabcdccbbccbcacbbacdbdcddbacabdaacdcabbadcbbcacdadbaacdaabcdbdccdddaacccbdaacbacabaadcacadbddcadcaadccaacabdbcabcdbacccdddbddcdadabdcddcdccdcacbccbaadcadbdaccadacdbdcddbcdbabcbdbdacdbbdbbddcadaccddbaabdbbdacacabaaadbabbddbbcaaaabbddcadacabbabcabaacdbdbcdaaaaabaadbcbbaaadcdaccabdbaddcdbbccbaaaababcbabcddcabdbadbaaacbadcdaabbadcbbbabcaadccdacadbcadbacddadacbdccbacacddcadcbbcabbadadaadbcddbadcdbcadbbdcbacbabbacadbcbaacacabdbbdcaacacbbdcdbbcacbccdddaabaddbccdbdcbaacbddacbcbdabccadcdbdbabdaaccbcbbacdbacbcaddcdacbdadabdddacbdbbabacabcdabbcaccbddaadaccaadabbbcdccadcccaadbcddbccbbcbaadcacbbbbaccccaddddccdcdadabbdacdcbcccadbcacbbadbbbdbdacbbbaddcaaaccccacccdbcabccdcacabacbdcbcaadcbbbabadabcacbdbccbaaabcababbcbbacdaaaddcadbbcbcaabdbbbdbababaddcdbaacdcdcdabccdaaddabbdbbbdddacbbbdbddabdaacbdabccbddaaaabbcbdaaccadbbcdbdabdbbaccadadabccaaaadcbaacddddddaabccbbdccbccbaabbabdcbaabacabcbbbdabdbbbbbdbdbcacadacbbcbabacaaccdacdbbaddabbbdcccbbaabccbacbcacbdcdacbddbcdcaadaacadbbbaccacdcbbccccdadcdaaccbdaabddcbadaacbccdcddaaaadcaacdddccadaaaababadcabdccbbbacbaccadcddcbcadcdbbbddbbadcaccbbaacaadbdbaadabcdddcbabbdacaaabddaccddadbaccabbddbcadcbcccddcdaaaccdadaddbadabbcbabbadcbccacdccadcdcccacbdaddaabbbbdcadcdacababaaabcbcbdddacbbdcbbdaaababadaaabbbaababacddaaabdaadabccbbddddbccbadcabbdbabcdbcdcbbdccbddbdbbbcdadccbbcbddbccdacaabdabccdcbcccabdadbcdbdbbcbacbcccbbdacbadbbcbbddddcbdabbbbbabdddcccaadcacabbbbdcbacdcbcdbbbcbcadddaccdacaccdddbabdbbabbabaddddbbadddbdadbaadcdbadaadbcccacaccddcbaacddadcdbcacdaabdabddbbdbbdbadddacaaaabbacdabcaabacbaabdadcaddbcdbbbadcaacabcdcdcdcccaccdbccbdacaaabcbabbcdcbabdaabcabbcbcdddcdcabbcabdbaaccccddbdcababcdcccccadadcbabddcbcaacbcacadbacdcadcddcddcdcbbccabbbaaaadcaddbdccadadbddddacbcdbddddbadccbaacdbccddccdacadabaddaaddbdcadaddddaccbdaabcdcababbcdbddbbcdbcdadcddcdbccaaccdbbdbdbcddcabdcdcdcdbbbabcababdadbbdbadbdbadaccdbdabcddacdbdbacdcacabddbbcadcacbaccbbadcabadaaddddadbbcbdbacacabddadadbbcbbdadbabdaabaccbccbcbcabdbddaaabbcabbcdadcdcacdaabcbdcadabadddcbbbaddccbbbccccaaabbbcdabdacbaaccaabcddbbacadddbcaddaccbbbdbcabccbcddbacadaaadbabdcbabcdbabcbcbccabdaabbadbcbbaccdbdbbbaababbcbcddaadacbddbbadbcabdaddbacaaddccaadadadbcacdbdaaccaabdadacbcdacadaaaacccadcddbbbcdddababdcbbbaaddaabdabcaddadaccbdcbdadaacdcdaaddccbdcaacdbccaadccbdcdbcbcabdabbbbdddabbbbdaabcbccbacbdbccbaddabdabddabaccdbcccadacccbcddcabbcbbcdbcdcddccdbbbddbcaddabccadbdabacadaabddadaabbdacdcbbabdbacadcabdbabdbbcbaccdacbbccadacdcaabcbababdddabcdadadbcacdbadbaacddacbdbcccaacaccdccbcdddaaddadddcaccccbdddcccacacdabcbcaccdbcdcbcdaabdcaabcabbddbdcbcabbacadccbbcdbcbccbaaaccdaddaaacaccbaddaccbbdbbccaacbccbcbdacabbaabaccdacdddbbdcaaaabacbbdcbdcdcaabbcaaddbddacccbdadcbbaaccddbdbadbaddadddcbadccdadbadbcbababbacbabaaacbabdabdcdadcdcccbaacabcdcacdbccbdacdcdacbddabddacaaccbbbbacbcadbadbaacaadcdbccdabdbacbaccacccdcdcbbcaadacdccbbccbdbbdccdcddbabcbadcadbcbbaaacbdddcbbabdadbcddbabbabaaaddaacdcadbbbacddacdccabdddccdddbdbdaacabaacbdadbbccbabacbbcbcdadabcdababbbdcdbbdadcaaaddbacadabaacaabbccbbbaacccaaccdbddcbbbdbadbcdbdaababddcdbcbcdabadaccdadabdcbdbaaabbbbabcdaddacdcadaaacdabcacbbdadaacacaabbdcbbbaacbadcccdbcbcccbabbbdadbbacdcaacbbdacdacaccdcdcaadbdaaccbcadabdbdbacdbddcdddabbaaaadacbddbbdbabbcdacbbbbaddcbabdcbbddacdccbbbcbcddbbabaadcdbdbbaacbbbbccbddcbbddacbaccaddbcacacabaabdccdbbcdbdcddabbcdccccdcaddbaadcccbcbaadabbccadadcbdbcabdacdcdabbcdbbdcababcbddcddacbabcbdcccdacccadbabbbbdddaccaaaaccdadbaaaaaadbdacccdacbddcbadadcabbccdcccbadcdbacbcccbcacababcbcbdbacdbdbbadbcdabaacbdacccdbaccbdcacbdaddbacacadccdccadaaabaacacddbdabcacdcddabccbcbddacbccaccdccccccccaabcdccacabcdbdabaacbcababbabdccdaddadcccbabaababbdabacadcdbcaccdacaaddadadddbbabbcbaccababccdacbdbcbaadabdbdddbadadadcdacaccbabdcadadabcdabadbcbbddcaaadbccddbadbbcbccdbcbbabdcbdbbabccdcacbcbadcbcbcdccbdbbdacdddbcdadcaaacadddbddccbccaaacadbdccdcaccaabcbbbbdbabbcddcbcccabcacddcdccbbdaccbbbadccdabbdcadddbdabaadbaccbccbcdababadcdbdcadbadaddcbadcadcdcbabbbacdbdbcbcddbccdbdccdcbcadcccbacdacdacdccdcacdccdccdbbbacdbdbaabdddbdaddabcdacacdbdaddbabccaccaaccaadacdccacbacbacacbcabbcbddbddbadaabaaaddcbbdadacdaabdcbdbcabadddbcacbddacdcddbdaadaababbababddaaacdbcaabbdcbdcbbaadbaabdaddadcccaccdcaaaabccccccdcbddcbdcbbcccbacbbdbbaddbcdbacccddddbbbddabbddbaababbbaacbaccbddbdcdbaccaaddcdacdaadacbbdacabbbcdbcdacddccababbbaabbdcdadbccbaabbcabdaaccaccbddddbdccbadccdbcaacadbadbcdcbaadbccacddbdadbaabdcaabcccbadcdaddacaddcdcbcdcbabacbadbaacdabacbadcbcbbbccaaacccabbdbddcbaddbdacaaacbcbddbbcdbccdbdddbdbacddbbbcdcadcacaaadbababbbccdcdccacccbabbbdccccdcdbcabdbadcabdcbaababcdcaaabadcbdbdddaddbbdccaaaacdbddccaaaadaabbadbdbacbabdcccacabdabcdbbccdcbccaaadcbcdcabcddcdbabacbdddabcbbabadadbbdbbccbddcbacacacbdcabccdacdbbadaddcacbdbbaacbdbabbdbcdacaccaaacacddbadacdbdacdadbdbdcbccdcbacabaddbdabadaacdaaccaccadcbdbdadbbbddbbbabbdbdcddabdaabbabbddabcdadccabcccbcadbcdadccaabaccdbddbdbdbcbbbbbdbcadcbcccbdabacbdbcaaaabddddabccddbddbcdbbdbdbccdababcdadaaaadddbabacbdacbaacacddaadaaadcabbaadabcbabadabbaabcadbabccdabacdcdcbacacdcdcaadbdbdaaabcabbbabdbacbddaacdaaabbadcbabdcaacacaacbddaaddaadaacddacbadadcbdacaabbcabcddabadabcbcadbabcddaccbbdabcbbabdddbbbdacadadcabacbddacdaadaccdadadbaaabbcdadaacabaccdbadbacdddcbbcbacbcdcabccabbabadbdbbcaacadddbcbabacacbabaaacdbaaabddcdbdbcbdabbbcabdbbdaadaaddcbcdccaadccabbdadabddccadbdbbbcbbdabaddddcaccabacbbbabadbdbdddcddaadccaabdabddddbadbbdbdcccbbaaaddcaadbcdcdcdbaadacddbdaababbcaaacacaaadcdddaaaadbcbdcdcdbcddcbcdcadbadcacacadcbdabcaadcdcbccadcdbaadbbddadccaaccaadacacdabdcdcccddaaaaadaacacbadacaddcdacdbaddaadbcdbcbcdadbcdbbdcbbaaacaddcbadbacdabcabaddabddbdcdbdbddadddddbbdbdbdadcadbddccbabbcbdadacddbcbacddbcabddbadcdababdaacbacaaabadadccaaccddaddabcabcbcbdcbacbddbcbaaadacdbdcccbcbdaddcbaaddccbaadabaccbaababcdaaaaccdadbbdcacbbacadaccaddaaddddcbabbbcbbbccdbcbdbbcbcacbaabbbdabaabdacbabaccaaddaccbcbcdbddccccaaccadbcbbddbaaccdcbcdaccccacdbbcbcaacddbabddacdcaacdcbdccabbbbaccdbccbacdbbdbcdcaadddaacddddbccbdaaadaaddccdacacaddcabaadbbdcdaacdbcadccdbabbcddbaadcbdccbcdbccaccddcbcbddbdbdaadccacdbbdcdcbbcccaadcacdbcccdbbdbacaccaabbbacacccbbbcbcadcbcbdbabacacddbcbcacaabdacaacadddbbacaadcddacadcbdbbcaacbddbabdcbbbaccbabadbccbbccdabbacadacbbdccbdbacccabdbadcdadbcbccdabdbcccbbdabdadcbabdaddbbdcdbdccbbbcbacadabadaddbdccadbcdcdabbdbbacabdaadacbadbdccaccabdaadabadadbabacbaaacdbcbbbacdcaddcbccaaadbcccababdcccbcddabbbdbdccdcbbbcdcbaccdaccaaaacdabaadaccccbbddcaababbacbddccdcbcadcacdbdbcbcbdacbbabaaacbbcdcdbabdbacdaacaaacdabcccdddbcaacdccabdbadcdaaadccddbcdaacddccccdbbddbbbcdcdcaddaaaadaadcdbbdbdbbbccbacabbbcbccaadddcadabdccdbbcbbcbcadcdadaddbbdaadcdaacaddcabdaadaaababdcbbdacccdcadcdbbabbcddacbcdbbdbacddcbadccccaaabddadcdbaadabcbdbccbbadaabbadacbbaccdccddccbbabccabacddcdcdbcbbabbcdabcadbcbacbacadbcaabadcadbbacaadbdcdaaddaabbbdbbccbbcadbcacbaacccddabacbacbbcdacbbdcdbdccbaccbbaddbbdbadadcadbccacdabdaddbcbddabddbdddbbdbbbccbbbbcccdcaabadddddaadbccccacddcdbaacdccacdcccaccadacacabaaacaadddaccbdcddbbddacaacdddbabaababdaaacccdcbaaabccadbddaabbcabdbbddaacbadbabadbbbdcbdbaccabadbcccadadbdbcdacdabcdbacddaccdddbdbadbcdacbaadbbdcbcddcbbcbcdacbdaababaccbdbcbbadcbdbbdcacdccbadcdacbaadbabaaaddaccdccdcbcbccdaaacadaaaddbbcbbcdaabaddadccaaacbabcaabcbcbcbddabbabbadcdbaadaabcdadbbacdcdcbabbcdbcacbaacdbbcccccadddbcabdcadaccaacdcadaccbabccaccdbdadacabddbabbbdabccababacbcabcadabcdccacabddbbdcababbbcbcdbbbcabccdadbdcdaaacbdddcccbdbcdddcdcaacbcbbcbbbbadcdbaadddaabdcaaacbdbaaccbbdcdcbabdcadcbcadcdbbbbaddcacddbdddcbbadbbaababbaadcdacaaabdccadcaaadcdcdddbadacaaadaaacbbdcaadadbbbabdacdddcdccccacbbdccbccdcadcdcaadbcabadbbbbbbabdaabcbabbaacbbbbbbdadaaccddbdacaaabdbdcaccbdaddbccadcdcddbcbbcbacdccbaadddbbbdddacdcdaaadbdbdddadbcaadcddaaabaccddacbbdccabcbcaaacaddcbcdbabcaacbcbcabaaacdabcddbbdcdcbadcdcdbcdcbccbccdcdcaaacdddcdacaaccbdbcbccabdabdbbaadaacbdbcbcddddcadbabbbdbcbddcbddcdddccdcaddddbbdbdaccbbdbbddddaadbadcacddbadabbaadccdbdabacdaacbaabdabddaadaadbbdaaccbbaabbbbcddccddbcbccdabcccdacaadabbcbcdbdcdaadbcdcbbcadcabdabdbdaccadcaccdadaddaadacbadaccabacbacdaacbdddadbbabbcbdbbadbdabadddaaddbdacadcabcddbbccacaaadbbdbadddacbcccdcbcddcddcabadbdcbcccbdcbddacacaccdbaaddbcdbdabbaccaaaaaccbaccaccaabccacbdbbbbdcdbddcdcaabbdbbaccdcdbaabaaddabcbbdadcbcbacbbdccccdbcdccbadbcbbccbbaaabaacbccbadbcddcabaaacdcaddcaaabbaddaaacadbdcdaaadbddabddbbddcddddbcbabbddcbdccdcccbcdcadbdccaabaccbddbdccaccbdcdabbadbcddcbabbccbcccaabbbdddccdccccccdaadaacdcddbacdaddcbdddddcacdbcbdcdaaadccccbddbadbdaccacadccdbcadcbdcbbcaddbaacabcbcbaadbacbacbcaabaacdabcacaaaabbbacabcddccbdadacabdadabaddbbdbdcacbabcddcdbdcbaaacccaaaabbcdccbbbaadccdccddbbadbcdcccacbbbddadccdcbcdddddbacddaccbdadabccddccdbbcaacabdadcabddadadcbcbdbbbacdcadcdddccdaadbbdbdddadadbcccdabdabdacdddbaadcdbaddadcdabbbcdaabcaabdcbddbacacccddacdbadbbcddcababcdadcacdabdbdbabbbbadabddadadabbabadcbccbdddbbabcddacbcdbcdacacaabdcaddcddcdbbbddaaaabbbaddbbbdccbaababbcbdadbcccaaadccaaddbcdddddabdadddaabaaaabcbacdcaabbbdcbbbcacbbbcdcdadadbabbabbdbacdabdaaabcadbccbcdadcadcbbdbbaccadcbabacacbddddadbdddbbaabbcdaccaacdaadaccbacadbcacbabacadbcddabdbdddcaaabcdbcdbccddbddaadaccaadccdccbcbddbdcccbccdbbaaccaacbdbdbcadcdaaaaaaabcacddadbbaddccaacaaadbaddcdcacbcdddddddbcbdbcbbdacbdbddddadbddccadccddaadbaaaadccbdbacbcbcbbdcaddccbaaccdcddbbdccbdacabcccabbdacddbabcdadaccabadadcabccadccadbbcbadbadcbabdcbdddcabdbdcddacdbadababccbccdbbbbcbdcacadcbbaabbcdabbcdbbadcddadbbbccadcdacbdbbabacccbacdacdcaabaacaaacbabaddcacdbcbadddbbcabababdbdabbaddddcabcdbaaaaacddcdabaccbdaaabdaacaaacaccdbacccbadacbdaadcdcabbdbdaabaaababdcaadabcacdbaacdcbdcabcdadcbabcaacababbabdaabacadddddcccadababdccdaaccbccdadbbcddcbdbcbbcacbdbacabbbdcdadadadabcbabbadcddbbcaaaaccbcbcaaaabcccabdcddbcdacdccbcdccaabcbdbcbcbcadbbdaddcbbbddddbbacbcadbbccdbadcbbcdaaaccbbdddcdbdaabccbddadaacdbbcdaadbaabacaccbbdcdbabbccccbbababadbbdcbdbbdacbbdccdcaccadddccbaddabdcbbdbdbdbbabdaadcbaddcbaabaacdcacadbcdaabaccdcbdbdaaacbbaabccccaacbbcacbbbdacdcacdcbccddcddddbbaaabbdbaadcdabcaabadbabdddbabccdbbaacaadcababdacaacabbdddacbdcadadbbdcbabddcdcbbcacccddbadabdbbaabbcddcbcbdcacdbacccacbccddcaaaabcbacbdaadaabdacaaadccacababdcbaaccacabccaabbaddccdbcdbbddbbacacbaaabaddabdccbbacbcbaaccdadcbbbaaabaadacabcccdabbddacaacabddaaabddacdabbbbbcdbbaadaaddabccaabbadbbcadbccbbbaccaaddcdcacbcbcbdbdacacbdabdddccacbdbadcaabaabaacadbddbbbcabdcdcadccddbbbbcccbbdcbaaadaddadaabcdbcbdacabccbabdabaaccbdabccdddcacbcacdabcdadcddddddbccdcdcbaddaadcdadcdaddbbbbbbbabccccdbcabcabcaabdbbadaaabbdcaccccbccbabdddabccbddaddccdaccdadacdbbbaadabcddcbdabbcbbbdbdcbddcdaddaddabcddbbbcccbcdadadaadadaacbcaacdcbbdadbbcbbcaabbaadbbbccaaaacacaabcacbdbacddccdbddadcbccdcbcccdcadbcddcbadbcadacccabcbbbadcdbcbdbdcaacbbdcacacadbcddbabaaabaccbccdbaacaccbcdabaadbcbbcbdcbacddabdbcdbdddbacdcbabcbcbbabcbbcccdbacacbbccbacadadbabdadbcaccaacacbdbcdcccbbbbdcacacbcacabcabdababaacbbabcbdabdddcbdddabdadbcaaacadbbbcbdabadbdbcbcdacbbddbdbcdcdcddbadcddccdcabaccdddcacabbddbabbbbcdacbaaadbacbbabcccdcdadbccdaaacbccabbacacdccdbdcadaaacbbbdacdacddabdaddadcbbccbdcbbbcadbbdcabbccacdbcbcdddcbbcabcbbacabcbccdcadbcaacdddacbaaabcadcddaccccccdcabbcaaabdbabbbaddaadbaabcdccbdbabbacddcbabdddbaacbdaabbbcdaddcdbcbcccbcbaaddbcbcaabccbdcdaadddddbbdddbbadddabcdccbbdaacdcbbbbaacdbbbdcbbddcdbaaaababaddcccadacdaacccabcaddaaacadbccabcdaccccbcadbdddacbcccacbaddaadbdaccbababcbdbbbdcdddbadddaabcacaadbdacabcaabbcadcdacabddbdddbaddcddaabaaadaabdbabbabcbbdddccabacdbabcbcdaadbccaaabdadadacdccdccaccbbcbadcaadaadaddbadabccbcbdcdadccbcccbbbcacbcacdbdccabbcacbbbbbbdacaababdbbcbbcabcbcbbcaabacadddaddccddabcabccbaabcacacadcababcddccbcccbccdaccaabbdcdccddbbbbabddadaacbbbbcdccbdcbabdacccbaddbdcbbbbddbbcdaacaabbccdcabbdbdcbbbbdbacdcbdaacaddccbdbcccdcbbbbdcadadaabbadbabaaabadcbcdbcababadbdddccdbcacbbbadcbbccadabacdccdcbdadbaabddaddbbacdabaabaaacacdbbddacdcbaabdabdcdcdaadccbaddbddcbdbbaaccaddacbbdaabdaabbbadcbacbacdbbccbcadcacabcccbbcdbccbcadacbacadccbbcdbbaadccadccbdabcacbcbbacadabbdabbccbadbbbbabadadbdacdccbbbdabadbbbcccadbcdaadabdaabdcbbbcabadaaaccadcccccacbabaccabaacabacbbdaccabdacccddccaabcaccdababdbdaacdaadbcbaccdddbdabcadbddddddadaddcbbbbcaccbaabbaaccaacabcaadcdaabaccdaabbcdaaccacadbcdaddabbdaadbccbbabbaabdabcbacbacbccddcbaadbdbbdabcdcbcabbbdadddbbacdbabcacaacddaddcadacdcbccbadbababbaaacbbcdaaaccdacbdccbbaaaccdbcbabdccabddaadcacbdaacbaacdcacbacbabddbbaddadaddbacbaadaacdcadbdaacdaacbaabadadacacdaabddbcaccbddbdaacdbbdcbbddaaaaabbcdbbadaacbccbdcbdbdddcdbacdadbcdbbcbddddabbbbcbcdddcbbccbacdcaccbcdcbbccaabbccaadbbabbcadadcaaaddaccaadcbddabdcdcddcabdadcbdbbcdabdcccdaaacccabbbacdbcccdaddbacbcacdaaacdccdabcacddaabdcbdddcbddcbcabdacbcbcbadcdbacacaacbcbbcbdbbaaddacddccbcddadaccdcdddabbbcdadbdddcdbbdcbdbbdbbbaddacadadcbcddbccbbcaccbaabdbdadbacacccbccccdcadbabadabaadcddcacbccdccddaadbcbdaddbaddbdcabddadadbacbabcbdacabcbccdadbbdabbdaddcbcdbbcdbdccabdadcdbabdcdcdbccccbacdadcdaadbcdccabaaacbbaacdbcdbdbbcbaaccccdbcbcadbbadbadcabbbbcdcdabacbcdbdbbaccbcacbadbddcdadadbbaddcddabadaddbcdacdccbdacdbabacaddacdbbdcbbaabbbcdcddaacabacdbbacbadabdaabbabbdcdabaaadddcadadacadccbcaccccbcabadbdaacadbaadbacdbaccddaccdabbcdbcbbdcbdbddadbccdddadccddcbccdbbabbdacdbdbdcabacadbabbbbaababaacaabbdadacabdabbcddcdabbddcbbbcdcdacbcdabddccacbacdccdaabaccbbccbabcbccbdcddcdbbbaabbcbaaccbcabdbabaabcdbbccdddccdbbcbadbdbdcdbcaaccadbadaaddcacccaaacccbcacaddbcbcdbddcaddaccdadddacbcabbcbbcbdbcdbddcccccdbcbacddcaaccaacadaaaabaadcadadddcbaabdcdacadcdbcbbdadabdbbabcdcabdacdacbadbbdbabdddccadbbbdadacdadccdddbacdaaabdbbcadbccaccccbccadbbccacaaabcbaaaddccbbbbacccdbdbdcbbdaabbddbcdacaacddabacccdddbaabcdcdaadbbbacbccbdddccdabcdbcaadccdbcdbacbbcbdddaddbdacabbccdbdccadaabcddacdadcabdcccacdcccaccdbcbddddbdaaddddadacbbccdddabcabadcbcdaacdbdcabacddadabdadbdccbcbbdbaabaabdcdcdbbcbcdcdabcccdbcccdcdbcdabccadbdacdaacbbadaaccbbcadcbabdaddbccbddbbacbadccdcabddaccdbbcbdccabddabcddcddddadbbaaadacbbccdbacdaabcabdddadaaaccadccdcddddbcbcacddaabbbcdadabdcdcdcbbddcacdcdacddcccbabcbbbddabdaddcdacdacbdbaadbdbacacacdccadcbdddcadaadabadcbbbddabdcbaacbacaabbbbacddabdcdbcdccadacdaaaaddcabdaadcacddbcaaccbabcbadddaaddaddadbadaccbddcababaaddadbddddaadacbacccbbacabbbccdccbdcdbccccbabcbcabdbdaccaaaadbcdaaaaddadadcbcdbacbdbbaaaadabacdcbcddcdadaacbbdcdbacadcaadacdaabcbddcabacbcabdbadbaacbddaadacbcbabbbbaaadbdaadccbcabaddaccbbdadbbcdcdaabdbacbcdaaddbcdcaadbabdcddaadadcdbbdadcbccddcdadbaacdaccbccacdadbacbdddcaaacbcbdaabadadaadcdcdcbbdbcbaacacdaadbbcbbaacadbcddbbdbbdaaacdcbdddccabbbccdbcccaadcbbccadcdcccadadbcdcbbbdbbcaadcadbcccccadccbddcbbabaaabdccccabbbbbacaababacbdcabccdcbdcdbbbdabadabababcbcccddbbdadccbbdacadbcdbadcdcccabbaacbcbbbaaabcdaaadabbbbabcbcbcdbaaacaaccdccaaacaacababdccbcaabcccbccdaabdcddbccbdacdcbaabdaaddabcdbbaaadcccbabaaccdddcccbbbaaadddcccacabddacadcdcaababbbbbcbdacdbbcbcaadcddbacbbdbcccdaaabdaabbaacdacaacbaddabbccdcddcbcdddddbbbacaaababacbdacdcccccdacadcdacacbbbcccbcaddabadcbacbdacabcddbadaaaabbdccccbcabababbabdadccdacbbddcddaabbcadbaaababbaddbdbadbdcaccbabddacdacbcbacaacbddddacadbcbbcacdaabcddacaabdbcddabadcbddabdaadaadbdcbccabadbabcbadcbacaadbdccabddbaaaadaababdbdcabadcbddadddbbabcaabcdcbaabaaddcdaaddbccaadaaadaabdabccaabaccccbbbdabbbaddababdccdbbbcbaacacaacacccaaacdbbdbccabacbaaaddbadcbcddcccbabaddbabbabccdababccdabbcabacaddabadcabbbdaacbdcacdcabccddaaacdcabadcdabdcdbbcbdadccdabadabdcccdcbcddbbccabcbbdcdaacaaddbacacdccbdcccbdbbdbacbbcabbadbcadbcdcbcdbacdcbcbdccdbbcdbcddbcddbdabddcdcbaaadbacdaaddaddaccddccaabcabaacaacbbbbabdcaddcbdbaadbcadccaabaabccddbaabdbccbdccacbabacddabdadddbadbbdadbaaccaddbaddcccbbddbcdaaaadbcbdcbdcdaaddbdbdaabdddcccbdcacbcaaacbbbdaaddcbcadbaaccccabbdddaaacccbabbdcbcddccbacbacabddcdccaaabaadbaaccbdbdcabdcbbbbcabadbdadcdadbabbcbddbbddbdddaadbbcaaabbbbacbaccabdbbcdddababbccbaacacdbaadaaaaacadbcbdcccabbbcaccaabadccabbdbcacdcdaaabbbcabdbcadcabcdddaabdbcbcacddbcdcbaccaaddadddcbdabccabdbcacaacdbabadaacdabcdadacdccbdbbdbabaccabbbabbbcaccdbccbadacdcddcdbcccdcbcccaccbcbdcaccdbcabacadabbcbdcbdbbdabaccdbacacdccbccadaccbbadabcbbbdccddbabdadabddcddcabdcbcbdcdcdcadcbccdacbadacabaaaaacbabaadbdcaaccdaaacbaccccdaddbcdacccddcdbdccddadacacbdcdbddcbcacddddcadbdbccdccbbdbadbabbbacbccdacacdacaaddadabdcbbdccdcdbddabadbcdaadaacababcdcdcdcbadcbadbaabbccbcadabcacdacaacabcbaadabdcbacdbacabbcaaacdcddbadcaddccbdacaccaccbabbbcbacccdcaaddddaacacaddacacacdbbbadbbaaddbbadcbbcaadbaaccdbdddbbbcadcdcacdaddcdcbcddbaabaaccbcaabdaaadadcbdbbbdbdbccbccbbabacabbdacbdcaabdaadccbcdaccdbacccacbadabbbbcabaacbcadacdcddbdacdacadaddbbaccacddaaabbadabcacbdbdcadaacdddbbacddbcabcaabbadadabcbaaddbcbacbbcdcddaaadccdcaabccabdbcbacdbabdbcbdabdcbbadbbcabcdabdcdbadacabcaccaabaaaabaccbcadbabacccbabccdabcaccbadcbcdbdbcacccacddbbbdbaadcccbbadbddaadbacbccadabbacccbccdaddcddcaabddadaccbccbabcaabdccdcadbbbaabdcdbcbbabdacdbbccbadcbbcaaaabdacabbacdadbbcacbbdcbcadacadcbbcbcbbdcccccbdbacdbbdacadabaacdaaddbacbccccabdcbbadadcbabcbaadcbcadcadcbcaabaccaabddbdbbdcdddacdcdddadbdbcddadcaadcdcdaccaccddcdcaaccdbadbcbbccbbdabcadabbccddcbbdabbdbbdcbbdcdabddddabbcadcbcabdaddcbcddbdcdccbccddadcddbabacacdcdcccacdbadaccccabbaaacccabdadccdaddcccbddcbaadcdccadcdccaaccaccddccbbcdcacbdcaabddcabbadaacbdadaaaaadccdbaaabdbbcdcddbbacddccbbacddcaccabbcadaacadabbcbcaccaaacbcbacaabbddbcabcaaadbcaabcabbadaadabddcdcccaccddacbdcddcbbaccdadbacccbbcbaabdbdcbdbcbcdaaccabacdabcbabdabaccbdbdccacbacccdbabdacbdabbbacbdddcaccccacadbdbcadccbacbadcddcdbadccadbcdbdbbbddbcddbbacdaaadcddabbddadabaccddabaaddcabdbabccddabccaabdacabadcacdbdcddddcdbddcaacaacdccbdbaacbdddcbdbaaabacdaacdacaabcacaacaddcddadcddcadcdaacaacdbdccbabbdaddcbcbcdcabbcacbbcdaaaabcdacccbdbbdaabcbcddbabaabadaabdbddcdccbbbaadacbadddbabddcadccacaadbbbbbbadccdaabdacacacadadacddaabbabaababbbacbacaaccacccdcdbabbbbdbaddaaddcbdbbcdcbbbbdcbdcacacbadbcababcdbdcbbbbacacdcdabdaacdabcdcdbdbccbaadbccbcaadbcabcdcdcabcaabdacbdddddabcacbadcacbcbcdbcdbbbbcdcbccaccdcbbacbcbdadbcccdcbcbbccaddddadcdcaaaaadbcadcaccacccaddccdbddbbddaccddccdbbcbbcdbbadddbcbbcddccadabbccdbcaaadaadcddabdcbaaaacccccacddaccaaccdbcadacccccdaadddcadbcbacdcacdbaddaaccbcbcbdadbdbacadddbadbbdadacadbcaaaacccdddbbbbdcdbabbddcaddbcbbbbcaadacccbabbddcbcabbbbbbbdaaabcdcdcbddbdbadcacbdadbbcbadadcbbaacdcbcaddbcccbddcabdcacadcbbdbcaacacaadcdcdbcacbadcdcdacdbdbbabccbabccbbbaaddaadcbadbcaaddaaaabddbcbdadabcadcddccacddadcacbbacdcaaddabadbdcddaaaabcbadccccdacabcadabbacabbdddcaacbadbcaacdabccdacbabcbdccdcbdcacadcdbcacdabbabcdbadacadabbbbdcbdddaddddbacccdcbbdbaacadccdaacbcbcacdccadbccbccbdcccaaaabdcbcdababbbddabadbcbbaabbcdcabbbbddbaadacddaadcdbabbbddbbacbcacabcdbbdddababdcbccccadbcacaadbcbacbddcabdbadcddbdbdcbabaccacaaddcbbcadbccdacaabadbcdcddccbbbdaaadadddbaabaadbbcbcdbaaaddcdddadcaddddbacdbabcddcbcbbaabadbdddddddcdbbbccbaacccdcdacbdcbaddbbdabcdabaaabbaaabadbcddadddcbcdbccbcdabdcbdddbcbdcbdacbcdaccadbcdcabddbadbabbddabbbaddcccaddabdaccbdbdcccacacacdabcbbcdadbbbdacbaaaadbccdbbdadcacccddddbcdcbabcbbcbbbbcbbbaabadacdcdbaaadacbcabdbccbaabdbacaadadcbcddcaaadcccbbadcabbabdbababdbbcbdcbbadccddcdccccbccadccacbdbdacccbddcabccbdabaadcacadbabbdccbcacdaaadbbbcbdcadbbcdcadabbadcdcabbbaccacbdabdaacbbbdbdbabbacddadbdabdbdacbcbacabcaaaacdcccddbbdacddacabdaabccadbdbadddcdbaadacdcdbcdcccdbdbdcdcbcdcdddcdbdacaacdaacbcccacccabcdadcacdbbcdbaababbbbbcacbcabdccaddabcaccbbbbacdddccdacdcdadccacdcddbdcdbcbbbddcacaacbbbadbabbbabcababaddbabbaacccbacabbbcddccddbababdcddbdbabdbcaabacbbadaabcbdcbabdbbcbddbdaabdbbcabdaccababacadaccabaddbbabdbacdbcadbbabacadbacddbcadaaddbaacadddbdcbbbabbadcdbbbacbdabbcadbcdcacabcccddadaabaccbcaaabbadddcbcccbaadaacabbbcccaacddacaabadaacdbcdcbdbabdbacadaddacadbacdadddbbaccadcbbdbacaaaabbdbaacdbbacccadbddcaddbaababdbaaaabbaccddcbaaaaccdabaccdcaacdcbbcbabdcdcbadbddcddccacbabbdbaadacdccbccbbdcddbbaadcbdcbddcdcdacddaccbdacadcdbbaaabbbcbdbabbbaabcacddbdabbbbcadbcbcbddcdbabcccbaadabacdaabaaabccaaaddbabddddadaccdcaabbcdbcdbabcdadacbbcbcdadbdbbccaaadbdccacdbdadbadbbbbabadbcdcdcaabaaacaddaccccccccbadccbcbdbdbaccddbcdccdcacdadcbcbaadcbccdcadbbacbcbdabaaabaaddcccdbaccbcddabdabcacdbdccbaabcabddddbcdaaaadcccdadadccdbdadbdbdcaabbcaacbdcacbbcabdadbcddcbdbadacadcbbcaccabcaddcaacaccbdcbcccdaacdbbdcdcdddacddaaababdaabaadaaaaabaaddbaacaccdcbbbabccbccaaabbcdbdabacaaabaacddaacbdccdbaddadcadacdccbbcabdaabbbcccababdbaddabbcbacdcbbcbbcdabbcbbbacabbabbabddabcdcaacbaadcabdbaddbbabdddccbdccbadabadcdcabdbbdcddcabaaaddcbbbcabcdcbdadccdbdabccbdbacdacddbaabcaabdadcbccababbabdbbbccbacbbacdaddbbbaccabbdbdcbaacbbccdbdbdcacabdaaddbbcdcbdacaaacaadbacabacbbadbbcabaaabadaacccbaddcccababbcabdbdaabadadacbcbcababcabcbcadccbdbbbcabbdcbddbcbbdadaacaaabadcacdabaaaccacbdabcbdadadbdcdcdadccdaccdcdbbcdcacbcccaddbbbcdadaacdcbbbadbaaaabcdaaadddbbaddcbbaadacbccddaadcccadbadccccdbacddcbacbcdbacacbcadbdbdbccbbdbacdddbbabbcdcdcdbacbdcacadbddadcdbdbddbddadadbcdabcbbccbadcddcdbcdbcbacbbdaccaadbbdaadcbabcbdbbddcabcddaccaabdadddbbccbbaccbbbbddbbdacdaacddababbbcdcadcabaabcacaccddbdddcccccbcddcbbbbbdcacadbacbabdbdbbccbccbdddacccacadabaaaddabdddaacbdbdcabadbddbdddcdbdbaadcbababbbbbaaddaaaabcacbdbaccdcababccdbadbacaaadacbcacccbdbdcbabcccdaddbdbcadcaddcddbccbbdddbacadacbccdbcaadbabbacbcdaddacbbcabdbcbbdaadadbcbabdcbbbbacabaccdcbbbcbabbbcacdcbdbbbabccabbdccaaddddaaddbcaddaddabccadbacddcabaccdadddccccddcadbacdbacccdccaaabcbddbccccaaddbcbcccbbbcaabbaccdcaacbdaadcddcdcadcdccdcdaabcabcdddabccaddbdaaaadbaabaacdaabadcbccdbbbadaacabbccbdacbcddbcacbbcadbddcddaaadcaacdbdcbbacbdadbbdbdbdacbcbdbcadbacabbcbdacddbcaddbcbadbcdaadadacdbddabbaaabdcacababdbbdbacbddabdccabacdcdaaabdbaacaccdabacaaabcbadabddbacabdbcbdbacdcbbaabdcbccdbaaddbcdbdcbbdbdbcacdbcddbdbdccdbabdbddabbccbdabdbdadbbbdaacadcbbbcbadadddbabbdcdbdbaddbdbcabdadcbbdcdbcadaddabbdabcaccbccdabdcdbacccaadbdcacabaadbcbddcbacbccdabddccbddadbacbdbbdcbcaaccccdddccbdddacaccdacdbcaadddcaddbabacccddccddadaddbbadcbcbdaabccbacdadadbcdbccbccdbcbdabcbcacadaaaadaabdbdaadaddbdcdbbabaddbcccbaaaddbbcdbdbdabbaacbdbcabbcdaaccccaabaccdaaabadccddadbcabdbdbacccdcabcababbcddbcdbddcccabddccaccdbddbcddcacbccbbababdacaaadcdacbbbdbbdbbdaabbdaaabddabddabcaacdddbcacccccdcdcdcdcbacabadcbdcdcaabdcabccbbdccdbabcdbcbbabbbdbbbcdcadddccdddaddbbdcbaacdacbbdacaaadcccbbccdbcbbdbbbbdddcbbccddcdabdabddadabbcacddcbdbdccaaaaadbbcaacadcacaacbaaacbddcddabdddddbbabbbbdbaaaaadacbaddccbcdbdddaabababdabbddbdccaadccbdbcaaabadccaaaadbcdaaddcbcccdddccddaccdcacacadbacdaccbdbcdabcdacdbbbbaadadaddacbccbadccdcadccbdbbccdbaccdbabbbbaddbbbbdddacdbbacdacbbaadabaccacaacdadccccdbddbbdcbdacadaabbbbabbadbbabddacabdcacbbcdbbdaaacbbacdaabbbbaabddbdacbbdbcbcddbccbcbddbdcaccbdbdbcdcdcbdabcaaaadcbdbddccbdbbcbdacbbadddabadbdcbaaadcdddacaddcaccaccacabadaabdbcaaaabdcaaaabcbcbcadaaccbbdcdddbdadcabacbaabccadadaaabdcbaaacacbbbbaddccccacacadaaacbbaccddbababccbbaabcddcbbaababcbdccbcacaadbccdbdbdcadcdaccccadbaddabdddcadaddcccdccbabddadccdadcdbcdbddbadbddabcbdadaddacdbbbadacadcccddbdbdcdcccadaddddbdcccbaacbacdddabcdddbabccccdbcaaccdcadbcabcdadaabbbbabdcbbbabcdcaadcbacaacaaadcadbbaacbbbdaacccdcadbacaacccaaccccbbaabbaddabbcabdabcbcaadbaacabbccbcabdadabdadcabdbbacadbabadaaabdbdcdbdccadbbbbddddbbadbddcadacdadcccdadbabdcadccadbabdbdadaaacaaccbcacadcdcccaaacabbdaccdbbabaabcbcacbbbccaaccdadabccdbbadddaaccaccabbdbdabaccabdcbdacdcaaacabbaadcbadcdcadadbbbccdacaabcbabcdbcdabcdcddabdbacbacbdcbdabcadacadcbadcbccbdadddcccbbaddcabbdccabccdcacdacbbbdbdcccdbbaaacaccccbddcbdbbbdbaccdacdccaaaccaaabbbbbdbdaabacccbbbddbcbcbddabbbcaacadcdbddccbcbabbabaaabbabdddbdacacbdbbbbccddccbbcbccaccbbdbcdaaabdbdbbbdaaaaadcdbaaacbdabdcbbadcbcdbadabdcccadcbadbcccdcbcabbdcbcdbadabadcdabaacbbcbaacaccaddcbbddbccacbcbdcaacaabdbcbdcaccadbdacacacccdddbddbcadcbcbcbcdacacccbccccbcadddaaaccaaabccaccacdbbcccaaabbcdaaabbabaccacbbcbdddddcbdcdddadccadccdbddbbdabdccbaaaadcadccdbacbacababdbddccadcbbdcdcaaccbbadddddcdcddabcdadabcdacdabcdaabacdbbacbaadddabacaccacaccbcdcdcbdbdcaaadcadbbbdddcacbcabdacdcbabbccddadbdcacadcbdbddcbaddccadacbadcabdbbabccbdbbcadabbbdbbbccdaccabbcddabcdbdabcbbccbbbaacdbdaddbddadbdaacdacacdbcbadddcbccdddabbcdabcacdaacddabcaddcccbcbabcdbdbadbdbbbbaaacdcdbbbbacbaabadcdadcaadcdcccbbdbacbcdaccbaddbdbcbddbadcbbadcacacacbbdccdabccabbaababddcbaabcabdccdcaddbbcddddbadccddacaccaacbabaababdadccaabdaabacccccdadcccdacbccbbdabcbbdabadbdddccbbabadcdaaaaddaacacdacddaddbdcbabababaaddcabcaaabddbcddbaadbdbacaadbcbadacdccdccdcacbbaabbcdbdccdccdadbacbddbdacdccccbdcbcdbabddaaacaabddbbacbacaccddbbcabbcacddcbdbbdddcaddbccdcdbadcbdabbbbdcbddbdcccbcbbadcddbaabcbbcbbdddddacbdbaabbadcbcbdabddababcccddcbabddbadbbcdacbcddcdddacbccbbabcdcbbabcbdcdcdcccaadabdbcadcabbdacbbdcbbaaddaadcbcdcacabcbdcaddcbcbcdbacbabddccbcdcadcddabcbadccadbaaadccbdadaaaccbcbbacadabcbbddbdabaabbaccbaaacaabacdbaaccaacadcbaddcdbdbdcaacddbccbdaabdddbdadccadcdcaadbbdacacccaacdccdbbdcbbcdddbccacbcabddadadcdbccdbcbdcdbbdbcbbdcbcccdbdbbbdabadcacbbccbbadacccaccabddddbdcdcaccaddcdddcbbdabcacaacdaababdbdadacbddcabdccadcdbcccbacabadabcbadcadddbbccbbbababaaddddbcbdddddcaabbbdbadbbccadaddccdaababaaaccbaddaadcaadbbacdaddabaabbbcdbbadcbcdabddcdabdabddcaacaabbabcaadcdcaacdddccbadaccabdabccdadccadaababcdababccccdbbbadccdaddbdccdcdacbbbcdbaaccbdaacacdbcabcabbdabdcdbbacbabbdaddccadbadccaadbabadbbcdbacdddbadccbbadcbcddacaacccacabababccdcdccbdbbddcdbcdbcbcdbccabbcdabcacabdbaadddbaddababbdacaacddaacdaacbccbacbbadddbacaababbbabbbcdbbbbdbdcadabbdbbcbcbbcccdddccbdbdbbadcbcaaabcdddbaddbccabdacbdadbbdcbcbbcdbbdcbcdccccaababbbbabbdddaddccbabdbadcddabdcdaddddabbdaccdcadbbcdcdccddbddaabadccbaddbcbacdbdbbabddadbcbcdcbddadcbdcabbdabdadcdddccbbaadddccadcccdcdddbccbdbccddbdccaabaabaccadabddcbaaabdacacdcabbadbdcbccacccababcbcddabbcdbaccbcbcdacdbddbaaadadadbdbabdccbadddcabacadadadbbdadbcadcdddbbcbbccddbcaadbbbbadbdaacabbbcdbccaddbacdcadbcadbbcccacadabbddadccbcbacaabbbbdadbadbabcdddcbcdaaccdccbacccbddbdbacbdddcddcddddbaddccbacdcadbbabbabbcadbbbbacbdaccdbdbbccccbaabcdadadadbacdcbadbacbaabcbcdcccbcdaccdddbdcacacacabbabaccadababadddcbaddbabccdaabadbddcccbcccddbdccbaddbbacddccbaddcdadbdcccbcbadadcaabbcbddbcddccdbcabbacdddcbacccddadcaadbbdddddcabccacbcdccaacacdbbbcabacadabdcaacbbbacabacbbaddbdccccbccaaaacdcbdbdcccbcddccdabccaaccdaacaaccbadccbacaccaddccbddbbacdbcbccccabddbccddacdddbcdbcbbcbaabcccbbacccdbacdcaacacdbacddadcccdabacdacacdcddcdcacdbdbcbaaaaaaccbaddbabdbaccabcbcdacaacddddcbccbaabcbdcdbbbdabbacbacbbbccdccaabaddcabccabcabdadbdbdbacacddabaabccdcacbdbbddbcccbaadabcababadcabdaacbadbabddddcabcacbbbdaaccaaccadcaacbbcbaccdabadbcbcdbaddccddbcadbbdabcdbacdcbdcdcaacbcccbbdcddccddbdccaddbdbbabdacdccbacbcacdacdacaccaaacdadcdbacbbbddcccccbcddcdcabacbadcddcaadcabcababccccddbbddddbaacacaabaaccacaabcdbbcccdcccdaaccbbddbadcbcdadcbadbdaccbcbcabdbbadccddcdaaaacacbdbdccdcaaccbbaababddcbbddaacbaabbbbcbdcacddaddcbadddddbbaaddaacdbcdccdacbabbacccaabadcdcdbbbbaabcabbbabacadbdcbdbdabcbdbdcadacccdcccccdcbbcdcbcbccabdcdbbdcccdacbbbabadbcabcadbddcabadbabbaabdccbcbdabbdbccbdadabddbddbacbbdccdaccbdbabadcbbaddbbaabbcccaaccccabaaccdbdabbbdbbdbadbcacbcdcbadcbacbbddcabdbadbcacbadaaacbadccdbacdcdcbabbccdcaadcbcbbcdddadcaadcddccbdbbccbaadacacdcaadbaddcbcacaddabadbcaabcacaccccabcbdcdbddaaabbcbcccdacdccaccccabdcaaaadbadaaaaccabbaaaaadadbabdbbacabcabcbbcbddccccdcddbdccddbcbbabdcaaabadcbdcadcdcacabbdcbbdaaabccbbabbcacacadabaddcbcaccdcabcabcadbccdadbbbbaccabacbaaccddabacaacbcdccadbddbcbccbdbcaacbdadcdccabbcbabadbaccaddbdabdadbbcadadcbdacccbdbdcbacdbdccddcdadaabcdacbbaccddadccbbdbbaadbddcbbddbadcbccadaacccdddcddbcaacaccaacccabbbaabadadcbbabbdcabddddbbaaabbbdccadacddbababbabcdbdabadddacaaababacaaaadcccbadaadaadcbaddcdddddaddababbdbbbdacbcababcdbcddbdbacadaccbaabddbaacaabddaaccbdcacaddaadcacdabcdddadbaabaadbbdcaaababdcacbdacbccacadabdcacbcdbddabacaccacdaaacdccacdbdbabadbdcbbadbbcabbccadccdadbadddabcadabcadacdbbbabbbbaccdabcadacccbbbbdbccdbcacadcdcacacbbccaddaddbcccdbacbcdcabdddaabaadacadacadddcccccbacbcccbbaabcaaacaacdcabccaacccbacabbcbbcccaddbaccbcadbcacdbabbccbbccdcadcbbaccddabaaccadcccbbbdbbcbcbacbaabcccbadbadaadcdcadabdadaabdabaddbddbcacddddadbbcadacdabccbbdddbdabaddddcaddcdabcbdaaddbcdacdaaabdaccaabbadccdcbdabcccdcbaddaacabcbacdcaccadbdddabacadcbbdbddcccdacaccdadcacdbdcdbdacbbdbacccdaccabadacbbddaccdbddaccabcccbcbcacbcabbcbabdcccbcbbcadcdabcbcbcbddcaddadbcbaabcdbcacdccddababdbddadabbdbcddbcaccbcbcbcaccbdcadccadcdacbbdcabbbaadabcbdbbaddabaccbababcabdbdddabbcbdadadbdcaabbbabcaabadcadbdddcdddcdbcbaaadabbddaabbabddbbccbabdacadaadaacbaabdaadabbbdcdcdaccabcacabcadddaacbddcbbdddbadaaadbcbddbbcccbbdabaaabddccddbadcdcdaaddbcaacdddbbcdcdabccacbddacadbbbcbdcbbccbddaadbcabcabbdcadaccdbccbababbdcddddaaadcacdabcadcbbaabaaabddabbccacacbacabbdbbbdbdcddcdcdbdbdcadbbbbbdcbbdbabccbbcabcaabdbdcbcdbcddbbccccbbaaccdadbcdbcdcdbbdccdcbbbabdaadcdbbcdddcabcbaccbcdcddcacaccbaaaaddbaccddbbddbaacabbcbccadddadddadbacbccabbbacaadbbdbcbcdddabadcacbbbdcbccdbbcadcbacabbdbbcdadacccdcabaacddbadbdcbdbcdadabcaccccddabbbbcdcddaadbdaacddbaccdacbdcabdccadaaccdaaadabbaddabaacbbcdababacdbbccabaaddbcbbbbbdaddcaabccadacabdaadcbabdbacbdccbcbddbbdccbcdacabdbcadbcdaccaabbcdababaacbdaaccdbcbcaddaabcaddabbbcdddbadbcdcddbcaacccabcaababdbbcbdddcaadaaadcbcdbdcadaccabbbccabcdbdabbdbdddcaaddaaccbcddcacbddadbbcadadbbbcbcbbaadcbdbcdbddcaccadbbdcdcaabdabbabbbbcdccacaddbacdcdcadcabdcddbccbadacbbcbbbcbbacaadadadccaabcdcdbdcbadbcbaaacccccdaaccdcdcdabcddaaabcbcccccccddcbcdcaaaacbcbcadacbdbacddbdbccbabddcadbddbdaabbcaabbabbcabdcdabdccaacadacdbddcabacdaabdabdbdbdbddaacabdbcccdcdbdcadacdcaddbdbbdbbbccabcbcdadadcbbcbbdddaccaaaabccccccdacdbcaddbacddaabbddcabacadcaabcbbbddbbbcccdacaaabdbcadbcbdacbadacbdabacddcbbadcabccccabacdbbccbcbbacddccddadddcdadcbdbacadcaabcdbacacdccccbacdacdcaabcbbbadcbbbbbababbcbaacdbabcbbcbddcacbbdacddbdbabdabacabcddcbbbdbbbaacacabdbadadcbabdcdbcbcadacbaaadbbdbbcbdadadbbcccdacadcdccacadcacacccdddacaadcbbccdcbaadddbcdcbbbdcddabbdddadaaacaccbcadbdbddbdbadcaddbcadccbdaddbcdadcaabddcaacabcaacadabbdcbaaadaccaadddcacdabbdadbadbcccbabdbadacdcbbaacaabbbbdaaddcaaaccccdcaccacaadaacdddbddcbddacdaadbbbdabacdddcaacddadabcabaccdcbbcaadacaddacbccdbaddcddbcddadbccbbaaabcbcdabcdddccdabdddadcaaacbbdadbacdaaaabbcdbdbbbbadadaddbdcdbdcdcdcbbdccdbccdbdbbaaacaccabbddbabcdabadabcbaccbbbdbcdbccbaadadbccdacadbaaddcadcddcacaccbaacddcdbdbdbcdcbbaadaabaabbdabadcddcbbddcbddddaabbacbccbaacdbcbaaabbbbcacccbcbabccdadacaddcbdcacbabbbbbaacbcdacbbdbbdcadbdadbbcaaadbdaaabbabaadddcccddbbabbaadccdcaaabadbdcddabadbbddbbdddabcdcbddbbbcbbcadaadbbbddbcbbbbaaadbbcabdacacdcccccdacbacadcbdaadabdbadbccbdddbbdaacdaccdbccacdbabddadbadabcccaabccaaadcaacadccaadcddcbdcccccbdbaaadabacdabdaccccbbbacbcaaccddacdbadccdcabbdcaccbadcbaabdaddaaaccbbccccddaacddddaacaadacbcbbdccdbdccbdbcddbaaccabaacbcababaadaabcddbbaccaacbdcbcddcacbbcbcbcaddaacddacdbbccbbbcadadcaacdacddadccabdddcbdadccbddacaadddabddddbaaacdaccacbcbacdddddbcbdbdbdabcccbcbcdaaddbdcbbadbddbdabaddbcccdacbdccccbdcbbcbabbddbaccccdabddcccdddddadbaaccacadbcbcbbcdcabbbbbddadbbdddbcacadcadacadadccdcadddaadcbbaaddbdbdbaacbdcabcdcbcdbdaadbdacbdbbaaadccdbcddcbdddcdbbcccbbcabccbccccbcbaabcdcbdcccdcbcbdbbabbaabbaaddcadacbdddbcacdadacadbbdbbabccacdaabdabadbbacbbcddbbccdbcbaddbbbadcaabdbbbcbcbdababadbddaacbddcdcddcabdbbdccbcbcbccabacbcacdbcdbcdacccdbccddcdddcddbbdaacdbbaaadadcddccdcdbcaabcadbccdcbbabbbadddcbabbccacdabbbbbdbbbaadabacbbdccdbddcacacdcdccdaacddaacdbdbbaaddadbdddbbdaaccdcaadbabaadaacbdabacccaaabadddcbdddbdbdadacaabbcbcdbdcdacaadcdbdaccbccbcaccbbbcbdabdccccddadddcdbdabdabdadaaddcbaaacaacadbbcbcaabdacadacaabbaabbcdcadcdabcdcabdacadbaccaabccbbabbdbabacbdabdbbbdcadcbbbabadcdcbacddaccadacadbddbacdabbcacdcdaccbacbcbadccdabadcbdddabbdddcaddadbddaddacaacdbadbbabadadaccababbcccbbbadbddbcddddcdcdccdbbaccbbbdaabbbbadaaaadaaadddcccdaaabbacbacaccabbdccdcadbabadbdcddcadbcddacabbaacdadbbccbdbcdaadbdbaabdcdcbcbacdccbabdacbddbdbdcbccdbbacccadaddaadbcddbacddabcdcccadcddcadacacadadccaadcccaddcdacbdbcddbabdcabdcdbaacdbdabdcabaaddaadbbbbdccdbdabcdaccabacaaccbaddcaabcaacdcdcbaababbbbabacaacccadddacabdbdaacdacbbcbccbdbdaacbcdaaaddbbbbdacaabbcadadaccbdcbcddaddbdcdbabadddacabbabbaabdddacadbccbdacdcbcdacabbcdbaacdbadadbbbcbbddaacbccabacdbacbaadddabbaaaddadcbdbdccbbccadcddaabacbcbbaacadcabdbabdbdcbbadbaadadcadccacabdccadadddbccacdccabdcddaccabbbbcbdaacbdbcabdcddbcbcbdbacacabaaadacacbcbbcdbbaaccbbdbcdacbabdacbcaaabcbbbbddccbbcabbbcaaadabcddbadcdadaacacdcaddaddbcdaddccdacddadbaddddbbbdbcabbdcccaadbdbbccbdbbcddbbcbcbbdbcddcddddcdccbcbbbdadbbdcdccccdabcddbabbbdadacabccadbdcbdcabbdbddbacabccbbacbdbbabdbcbdcdbabccdabdccbccaadaabacacabcbddbabdbccbcadbadddacdccddbacdbaccaadccaaddcdcbaaaacbccdddbcbbcbccadcdcdbadbddbdbbadcadddcbdacbcbcdaabcaaabcadaaaddddaccacddadacbbccbdabdbddcbbcaabccddccabadccdbaadbadcacbabdabaccbcaddbabcadababdacabcbbbabaadaddbbdcdcadcbdcabdcccaddaacabbbddbcbaaaaabbaabaabaaadbbdbabaaacabbdcdabdbbdadbcbbacdbadcababdaddaaabccaadabddcaacddcacbccaccbadadaccacbdbabcbcadbccdbabbacaabdddbbdbacbbabbaacacaabdbbdaaccdbdcbcddadcacbaabbcdbbdadcaacaddcacdabbaababdcbdbcdadcadcdcaaaccbbcabbadcdcaacbdbabadabbabcdbcacccdadcadacadbbbabcbdbbbdcddccaacdababccdbdababbbdbbaadbbcabdcdcabadbdabddcddccddcddbcdabbadcabbabbdcacadadbddbacdcaacdccccacdcabacacaaadbddbddadcdbbccbdcadbcdcacdbccdcadaabbacadbaaccdbdbbccadaabddbadbaaaaaacaadcdcaadaabbddbdbcbaddaddaacbaaccadcacabdbaabbacdacdcdbccacddbbbcdbddbdcccccdbcddbcbaccbbbccbaccbcdaaabcccbbdabbdbdccdcbdcdcddbdbbcbcbbdbbabadbbbdaabdcbaacccacaaacdaaabbcdacbbddbbaccdaaaaabacdccacadacdcddbaabacacdadcdadcbadddcdcaabcacdabbdcadbbbabaabdcdcbabbbdcbaacaccbcbbbcaaaadabaaddccdbaadadbccdbdaacacdbaccdbacbcdbadacaadddbdacdbbccbcdbddadddbaddccdddcabcaaaaccbdacbbdcbdccbdaacdbbdadcbdddbcbccaaccbaaadcdcdadbddccdbdbbbabccddbacddccaadcddacadddcbaabbadabbdcbbabcdcabcbaacbacdbdbbccddccabcadcccdccbddddaaadabddddcbdcdaacdabcddbacbdddcbacabcccbacbdbddbbcacacddbcbabbbdcdbbccadcbdbbbccacccaacbbdcbdaabdadabbabdbacdbcbabccdcdcbbbabbabacdbaaaddccbabcaacaacddaabdcbcdadcdcacacacbababadcbdbbdbbcaaaacadbdcacccaacdcdbbdacadddcbcadadbdabaabcdbcabbbbbcadcdabbcbaccddaacbcdcbddbcadbddcbbcdbdbdabccabbbbbdbaacadccccbaababcdaadbadabaabbdaddbbadbacdccbacadccbabcbcadaabadcbdbccdabaaddddadccdcacddaccdbdccbababbbbaadcccbcbdadbcabbbcaccdabccbadadcdbaccdaaddbccdaaadcdbbdacccdcdbcbcdccbbcbcaababbbccaababcabadcdccdbbdacbdbbdaacaabdbcaadabdbddddddcbadcadbbdacbcddbbdaaaaababdddadbddadbcbcbccaddabaacabcbacdaaddbbacbbbbcbddbccaaadddbdbabbcdcaacddaabdbaabdcbdcbcbcbaadabcdbcdcabdcddccbcdabcaadbdaabcaaabcaccbcdddbbabaddddbdccdbacbcdddbacbcaaabbbdccaadaccbbcdacbaaadbaddacbcdcdaaaddabaadcadbddaccdcbccdcdbcddadbaacaddabbadabacbccdacdbbaababddcbccaabaabadbabbcbbdbaddccccabcdbcccdddbccccdcacbbbdcdbabbbaaabdcabdabdddbcdbdcbddcadbdbadbcaddccbbbbadbbacacabdbcbaadcaccdbbcabacadccabcbcbcddbbacadacaccabdabcaccdbcbddabcbbcbcbbdacdcdaccbddabcdccbcaccbbddaaacbcbbadbddaabcbaadaddbbbdbdacbcbbdadbbabacadcccdacadcbbddbbdbacdaacabdcacdacdbabcbdbacabdbdbadbccbbccadcddcdbdaddcdbabcabcadacabacdbdadcdadccadabbdcbaccbcccadddbdabbdcdbcabdddbdcdbdccccbacccbbaabaddcbbdaaacbbccccdadadadaabacbacdcaadabacacdcacccbdbcbbbadbaabdcdccdbcdddabbdabcbdaabacddabcbdcdddaaaddbacdcbcabadaaadcccdbbbacdddacbbbabccbadaddadbaaddcacdaacaaadcbcbadbabbdabcbdabcccbbcadcdacbbcadcbccadcccddbbabdccbddaabbdaaaadadcdcaabcadadcdabbaabbdbdadacadbbdcababcadacdcbdcacccbbdbccdccabbcbcaacabdbcdcccadcdbdbbabbdccddacadadabbcdcbdcdaadddbabdcbcbdcaccdabaadbadaddcccdabcbdddddabdbaddcadacddcccadacadbdabadbbcacddccadbadbdddddcccacaabdddbbaadacdadaabadbcbcacdbbbbbdcadbbabcaddbadbdbcdaacbadadddbacbddccadcdcddddcacacbdbdcdcbdaaadcddccbaddaacbbdaddddaacabdccadcaadcaabaabbcabbcabaaacaddbcbddcbbdddcbbadbcdcbaadaccaaabcbaadbadaabaabbdccaaaddbcdcdbacaaabbcadaaccccababdddaccaaccdccbdaaaccbbdcabbdccccaabaccbccdbaddaacaaadcddbdbacadbbaabdacdbadcaacbdadbdbcdbcbadaacacaadbbcbdbccabddcabddacadcccddddabbccabdababdbccdadaddcadbbbbababbdbddbaaacabbcabbcdbbdabdcacdadbcadccabdabbcbbdcbdaabcacbbdacacaccaddddcabdbcacbccddcdabacaaaacdbadccabddbdcbdbdabbbbbbcabccabbdbdddbbacdbccbdddbcadaddbdbbcaadacddcdacacadccaddbcbccdcdddcabacabdcccabbccbcadadbdadacbacccbcdcccaabdbadccccccbaaaacbabaacdccdcbaaabbaddaccbbddbabccaddabaccaddaccabbccbcbdccbbcbbcdcdbbccbcdaabdabccdbcccccddbccadaccdddadababbcbcadbadcabbbdaabcddabcdaabaddbaabbbadbbcbabcdcacadccdbbabdadaabcdabbdccccbccacdcbdddcaccdbdabdacdddbdbabcbdbdbdbcdcdcadddcdcbcbdadacaacabaddacddaacaacaabbccdabdddddaababcdcccadababbccabaaccdddcbdccbbacadbdbaabcdcdaabcbdaddadbcbdbcbddccabcbbcccbbdccdbbdacadddbcadabcdbbdbcbdccdaaadccccbccaccccaadabbdcacccaaaddaddcddcbccaabaabbcbcbcbacddbadadbaadcbbbdadacdbadadbbabcdbbabcbacbaccbcccbddccddcadbdcbcbccbccadcaadccadddcbccabccaccdadbcccbcbbcbcbcabccaabbbdbdaddccddccddbabaadcbcbddcdcaacbcacaadbadcacccdbcbabcbaababbdcddaaccabcbbadddbadcbbbcdcbdbbcbddbddacdaadacddbabacdabababaadcdccadddddbbbbacaadcabcadbadcdcbcccdabbdbbccdcccdcadcdacbcbbaccccaadadcdcdcbbdcbdabbdcabbcdbbdaabadaabbcdbddcdcbccbcdcbacaabdadcadadcbdcdcaaacdcadddaabbacbcaabcaadaaacbbaccbdbdbbbacccaaabbbbdcdbdcccbaccaadadddcccbdbcdacabbdcbbccbaccdbcbbbdbaddcdbccdccaabdbdbcbadddcaabbcdbcadcdbbacddadcbdbadadccabbdcddcbcccbcbccbcbbacaccdcdbcdccaabaddddcbbcbbacdccddbbbabddbdcdcbababbdcdccabccccccdabcbdbbdcdabddbbbddbaccacbcdbcacbdcdbdcbdadbcabcbcabbacbcbaacdbbaaadbbbabdbcdadabbadbacccbbccbcbdbcddddabcccddbdcacabddcbabddaacadbdabbbbadaccdacddccaddbcbdaccbddabccacccadadaabdaccbddbaaaacbcabbdcbcaaadaaadaddbcbddbbdcbdbabbcddccaaddcdadabcadbddaadccdbdacdacaacdcadcbcabbddccccbdaaabdabacaddcadcbbbacdbabaddabadccccbdacbadccadaadbcbdccdbcabadcabcadcadbdabcaddbabcccadbdbbcbbbdaaacadbabdaccbccccdababccabaddbddabdacbbdccdaccbadabbccddbdcadaccddadcacdccbbddcaccdadababbadbbdbbdbcaccaabcdacaccddccdbadbddabaaaddbcbdbadbabababbbdcacbaccbccccaaacbddacadabaadbbadcbdcaaaaabbadabcaadbccdacddcdbcddabcabcdcdcbdcabbaababdbdcbddcabbabdbcbcccaccbccdcacdabaddaaaabadbdbcaadcdbdcadccccddcabbbbaabbcbcacacaaddbdbdddaabbadbccddcddaddadcdabaabacbababbadbbbccbaadbdaddbbddbabbccddbdaaadddabaddacacdcadacdcddbaccabababaadbdddddcacabdadcbdcbbbbdddacbabcddbdbadbbdcddbcabbcbdcabcdddbcdcccabaadcbccdcbccdacacaaadbcccbbadbcbcbddbdcbdbbadabdabdccaddaddddcdaabbdabaaababbbdaccbaccdddabdbdabccbcbcdcabbddcddaabaacbbccccbbdcaccddaaabaaabcaccbadcbdaabbddcbccdcacbbacbadcddaaddbbdabbcbbdcdccbdcddcadbddadccddadcdabcbaccbabbdbaadccdabddddaccbaabdaacaacddbdaaccbbabbadbbdbbbdbcbbcddddcbdcababcadacabdacdccbbdacbdcdddcdccdcdddcaaacbccaabcadccddbbcbdbccdccadabcdcdaaadaaacdbcbacbbdaccaaccdadbabdbbdaabbdbccadbcbbabcabcddbbdbdccdadcdbcadccdbbdcdccbddcaabcacabcabbcdacaaccbadccabddadbdaaabbcdbcabccadacdacbcdadbcdddaccdbddcbaacaadacbbaacacddddbcdacdbadcabccdcccbacbdadadbbdbbcaacaacbdaadbaaddbccbddbabbddbbaccdbdaddcadaadddbdccbaaccccacdabcaabccdacbdabdcdbbcabaaaadaccbbccacdcdbbcaabdadcdcadbdccdcaaddbdaaadaadcbacaaaabaabdbcdbcaaaddcdcdbabaacadacbbddcdbadbabcbcdcabbacacacbadaccdbabcdddcddcdacdacabbdacbbdbbbcaccbdaacbdcbadddabcbdabccabccdbadacaacaaccdabcbdacdbaaddbdbcadcdbbcdbcbababdddabdddbdccdbacbdbadcbabadcaaccdcaaccdcdcabcbcbbadcbbddbbcbdbdcdbbabdddccaadbaddcabbaadccaacccbdaadaaaadcdaaaddcbabbdbdabcccdaacddcbbadbdbbadccddcbbcabaacbabbdbdbddbcdaddaadbbabdcdcacdcdabbbbddcccdacbdabbabcdbdbbcadbbdabcadccbdacabbacababaabbbccadcbbbdddbdbcbabacadbbbdbcdaadbcaccaadcaadbbbdcdabbdbdcdadcbacbadacbdbaccbaaabdcacacaabcdbcdbbbccdbccdacacdbbbdacdaccdadbaccbccdcaabbaacdacbbdcaacbcbdbacabcadccaddaacccaacbadbaccacbbacddbcdddddcccbacdbbcbbadabcdcdddaacddcdcbbadbadaacbcadcaacbadabdacbcbbbbcdaaabdabbadabacddcabcdbdcbbcdbadbdbcadacbabbaccbaddbcdbacdddbdccccdcbadadcddddbdcdbccaabdbcadccabcacccccdacbbacccdacabbcacccdacbbacbdcdcbdcdbccabdaacbcbdcabbcccabbcdbaccadcbdcbdacbaacbddbdbdddbdbacaaaadcacbdacadaaddaacaaddcbadcabbccadddcdcdaccccaabadccadaabdabdbabdccbabaadcbdddaacbacaadccabbcbddadddacbcabccbbddacabbcaddbacaabdcaddbcadccaddcbacccbdbbdabbdbaddacbcadbccdcbdddbcddbccaacbbbdbdbcddbdbdcddaabbddddcacabbbbbadbacdadcadcccaddabcccbcddcdddaabcdadababacddaaccacbbcdacbbbabbbcaaddaacaadbbbcdcbbbddabadbbdbbbcbaaddbbaddcdaccbaadbcdbdabaacdacbbbabbbbbcbbaaadaabadddcabadaddcdbbbaaaddcdddbdccbbdbbcabcadbadcacabdcdaadaadaccdabdadbaabdbaddcbbbbccbabbdaccadbdcbccbcddacddbbbdabbcaaaaaccccadbdacacbadccbddabcacdacdabccdadbbcddabaaaaddbdbdaadbcddabdbadddbcbcabddabcbdbbbdccbdbbaabbcbbbdabbbaacbadcbabcbdbdcababbcddaddcbcbbbbbddababdadacdabacdccccdbbddbbcddddbdbbbddcbaaabdbbddbdcbbcabacdbdcbdbbbcbbbbaddcdaadadcabbdacccdadbdacdddcaaabdaadddbbcccdabaccddddbbadcadddddbdaadabccaabcccaababacbddccadcaabdbccccabddabadcbdbcddabadcabcdabccadcaadbdbadccadadbbbadbaddaaacdcccabcccdaabdddcadddbccaaccdabbcbddaaccddccbbaaacbbaababddcdbdbcabddbcaddabdbbdacdaddbadbccddcaccaddcabbcbacadbabcddacdcdadddbddbdabbdbccbabaaabcdcbdcadddcaccdaccbcdcdbcdccabddaacddcbcdbbabadabaccabccccacadacaadabcdcccdacddabadaabcdcbcdbbddbadbaddaacaabbadadadabadbbbdaabadcabbaccbcbacaddbaccccdcbdacbbcddcdcaaaaaaccbabcbddbaaadbabddcddccaaabdcabadaaacddbdbaabdcbbddcbcaddddcaaacdaccdccddbddcabbcbbdacdddbbbcdccddaacabccdadcccddaabcacbabccddaadccbccaabbcdbadadcaccbdbdadccbdcbcacdababdcbbbdacddabddccacdbadddaaccbccdbbbaccdbdabcccdabaaabdcadbdcadabbbcbbdcadddddcdbcabacbaabaddbcdbdcabdbcdbadddccdbcabbdbcdadcbbbbcabdacbadcabbdcabbbdcbbadadadbacdcdcddcbbcadbdbcdabcbcdcbabaacbbdbcadaaddcdbacabdbbddbdbcabbdccdacaaccadacaddacacaabbbbcabccbaddcddbacbdccbbacaababdcccbcdbbccdccbcabadcdcdabbcbdccdcccbccbbbabcdbabcabccadcbaabcabbbabdbddacdabacdaddccaacbbdbacdbadcdcbbadaabaabdabdbbdbcdbddccaddabdbbabbcddbcadbbcbcaadbbbaaaacbbcdccadadcbacaabcaadaddccdccadcccdbdcabadadccbddacadbaccaacbccdbbcdadccbacacabdacaacddabbbadaabaddbbcbaacabdacbdbacbdbbcddbddaddbcbcbcdcbcdbdccadcadabbdadbbadcbacdbccbdcbbcdbaabbdcdcadabbadbcccbacababadbbddacdabddcccdbdcddcdccadabdabdadacddbcdbcbcbbadcbdaddddacadddccdaccbbaaaaacaadbacccaccacaddbdcbdcdcaadabaacddaabdbabacbacdaccddcbadaababdabbbbdcdcbccccacadaababadcabdadccdbcabcacdbdbadcdbccbdabdbdcdcabaccabdcccbadbdacaaababcbbddaacdbdacacaabdbcabbcbbcdbddcbdcdacdcbabdcacaacdbdccdccdccdbdbbbcbbabbdddacdabdbcdccbabbadcaaacccbbbadbccddcbbddbdcdadbdbadbbbbccbdbaadcccaacbaaddcabcabcaccdddccdbbccbbadadadcdcccccdbbbbbbbccdacaabbdbbcbcaddbcabdbbaacccacdabdaabcabbddaacddcbddcbaabbaacbdbddcbbabaccbbbcacadbcdadccbadddaabdddbcbcaacaacdddcbadcdcadadddccaccdcaadacaccdaccccbdcbbbcbccdaccdccaabcbccdccabcccbdbbdacbbdddbdacbbccdbbcaadbddcaaddcbababaccadbbbcbadcdbcdcdcbcccdabbacccacbabdacdabbbabdbccdcaccaccdcdabaaaadacabccabccaabcadbdcbdbaddaaaaaacdccadcdadbadacddaddcacbaaadbcaabccbdbdacdcddcbbbbdbacdadacbddcaaabacbbbdabdacdcbdadcbccabdcbdccadcbdccdccdaaaaacbbcbcabbdbcadbdcacabaddbddbbbbdaadabdcbbcacdccdcdaccdaacdadcbcdaccabadbcdaacadcabaacaacbbcbbddabcdbaacaadacadbccadcbbcccaabbdcbbaddabbabccaddbccbacaadaddbcbbbdacacadccdddcdbbdabadddcccbdcbbccabacddabbbdadbbbbadaabbabbdacadcbcdaddcbabcddabccaccccccaaddccdddadbbaababdcaddccddbdaadacadcdbcaddabbabacabcbadcabacdcacbaabdcdddccacdadbcbcdbdabbbacbacbadccacddadddbabacbdbccccacbbaadbabbbbddbbbbbbbcbcbbababaaabddacaabbdbadddbcbadbddbdcbaadcddcacdaadccadaabbbdbaadadcacddbbdacdcaabbacbdaabddcdbdcaaabcbbcbacaccabdadbacaaabdcacbbcaaddabcddaccacacbcadbcabaddcacabbdcaaddabbdbbabbccdcddbdbdbbccbaadabaaddddbbdcaadaabacdaccdcdadcdabcabbdbbbdddcdddddbbbaabbadbaddcbabbacbabcadcdadabddaabdadbcaabdbadbaadabdcbbabdccdddadccdaadbadadcaabadabaacdcdbcdcbddacddabccdbbaccabbcdcacdbcdaccdadacabbaddddccdbbadaddaaaadbacbdcbdabaacbccddcbbabcdbaacdaabcdbdcbabadbabbbcbdbaabadacbdbcdaaadcbcccdcbcbacacbbacbcaabcabdadddacdacbcccccaaaddcbabadddaabbdaabdaddcaadadcbbddabbddaacdbcaddddabbdbcaacbadcbcbdbcaabacbdddbbbdbbbdacbcababbacbbabcbcbdcbccddcbacabdbadbbcdbdddccdddcbbbaddbbabbcddabcabbbabcdcbbbcadabcaabbdbabdbdadcbdadbbaaddabcabdaaccdbaccbadaddaddabaddcaccaccccbcaddaddadbdacbcbdcdddccdadbdabdaccccbaccbdcaddacadbdcdddcdbabcbcdbccadddcccbaacaabbbdccbdadcdddabacdbdcbabccbcdccacaabbddcbbddccadbbabababcbcbdbcdadbcccbacabcddcbadcbaaabbdccbabcbcbcdbdcbcaabbabbaabdbbaacbdbadcbdcdbacbbcbcaacdacbccaacdbdbdbdaababcabadcddabbdabcbbddcbbddbbdbdcbdaccdcbaababcbcbabdabcbbddaaabbbbdddcabbababbabadaaacacdadacbdbacdabababaccdbbabbadacddcbbabdcddbabbbbaaddbaccacbaddddccdabdaabacdaccddddbdbbdbdddcddacacdaaccacdcbbaccacbcabbdbadaaacccbdbdbbdaddcacdbcbaabdccabbccbbaaadbbcbbcbbabdcbabdbcadddbddbcbcbbbdddacdbbbbbddbdabbdbdcbcabdccdbcbcdbbdcabbccccdcbcdcbdbdaaacabadccadbdccacaaccddccddcbbdbbaaabdacccdbbdbbdacbcbcddbbcacbddcbdbdbcabbcbbdcbbabaddcbbaaabbbbdabccbadcabddbabdabadabacbdaadbdabbcdadcacaddabadacacdbcbbdacccabcbcadaabaaccaaacccdcabdabccbcdaabdbbaadacdbcdcbaaabdadcccbaccdcacccdacabddbbbabdaaccadbaccabdcabbacadbcbcaababbbddadbdaabcabbcdcbdaacccadcadcbdddcbcdbacabcabbdbacbdcddbcbddbccdbbabddbdabdcbbaddcbdcaaddbddbcaadabbbccbcaabdbabaaaabdabbddbddcdbbbabcdaaaaacdccdcaadbbbbcdaaddbaccccccdccddcbadbddddbbbaabbccdacccabaacbcbacbbacbdbdabadddbbabacabbddcaacbdabaacacdadccdaadbccabcacabdbcdadbaddbadabaabbcadbcdbbdaccdcddcacbacddcbccbccbadaaccdbaabcccdbcdaababcbcddbddabdbcbbdcadacdaaadbacabdbabadbddadbddacbddadbbbccababcdcdbbccbcacdcacbccbdddbbbbabdcaabadcdbbccabcbadddababddabbcaacabbbddbdacdbdcbbadcdadddcdcddbadbbadaacbbbbdbbbdddbcbaddabcdabdddbdbacaaccdbbacaababddaabdbdbababbaacbcaacacabdacccdccdbbbaacaababbacadbaccababadabccabddbcbacdacdadddbbadcabdcbaaccbdcadcbabdcccacdcbbcbbccdabccdcddbddcdacaacccccddbadacaddacbbbcacbdbdcbaaacdaccabababacadadbccddbdbcbcbdbbccbcbcbcdbaaddbbcbaaacdbbcaadcbbaddbdabccacabddbbdbbdcababaacbdaabacaadcccabdaccbbabcddacbacccbbacadabbaadadddaccdcdcdddacddadccbacdadacadacaccadbdaddbadddadabaadbdadddbccaacbadddaccabacacdadbcdacdcdbadbdbacaadbcadabcbaabcdcabbdccddcdcddbaaddcbbabdadacbaaacbdcdaccbacacbdbcbccacdcbdbcddcdddbbddbbdbaaacbbacacddacdbcdcaacbabccbccdbcbcdadadbbcaadacdbddcdadbdcbcbabdcacaddadacdbbcadaaddbdcbaaccddaaddddbdbaaacaadacdcacadaddbbccbdcbcacacaabadcdabbabbbccccdbbaabcbdccbcccddaaddbbcdcbbcdddccdbdcdcabbcacdbdcaabcaabbcccbbdaadaadccddbaacccacbdbccaacdcbabadcdaadacbaadacddaaaadacbadcabbbdadcbacadabaadbddcaacaccbdaacaaaabccbcbacbbccaccaaadcacadacbcadccadccadbbbbaccaadaaaaaacbcbaabddcbacddbbddbcdddbddaaaacbbccbbabdbbbcbacaacbcdbbccddcdcbcbcaddadaadccdaacccbaacbbbdcdabccaddbdccacbcacaabadbbbaaddcbcaddccbdcbcbbdbacbbcabdaabcadabddbbcabcbaaabaacbdccccbdbadbbadbbcccdacdcbcdaddcbbcdaaccdcccbcaccacbbbbdcccababccccdbcaaccaabdccddacddadcacabcdbaabbacdabcaadcbcccabddbdcbcccbaccbacaaadacddbbdbabbbddbdaccbabdbadcdbdbaddbddbbdbbcddcbccabbbbabacabbcdbbdacbdcbcbbbdcdababdabaabadabdadccaddabdcbacdbdcbbaddccabbddcdcacccdacddbddccbacbdadcadcbdccaacaadccbdadcddacaaadddbbccdcadccbdbdcbbadcbbcbbdaaaadadcccccadaadbaacdacacdadabaacababbcaacdcabadaadbdacabdccdacabbddadddbcbccbbabcacccdacbdcbccaccbbbdadadabbdccbbcacabbaacbbabdacbdccbcdbabdbdacaadbdbcacdacddbaccacdddaaacddacbabadcbbdaadcdbdabadbbdadbbcdcbcdbcbbaaddddabdddcbaadacdabbdadbcbbdbcaadbcbcabccbacdcacbadbdaaadbcccbdddadddcacabadaadaddadaaaaadbaddacdcdacabaadcdbdcbbadadbabaccbcbcddaaccbddacaadccdadcbbadbbddbbdcadbacbacadaaaadccabdbdaddacddbcbbcaacdddddbbccbcdadaacaddbccaaaccabcaacbbbcdddcaabdaadcaacdccbddbcddcbaddddabdddcccddbabbbccdabbbadabdbadcaabbabbdcdadccaacadaadddddccdcbaccaddaddacbadcccbaacadadaccabbdbaababdcbadaacbccdaadddcddbccadbcdbaabdadadbdbcbbccddcaaaaaccdbadbbbbdbaaadddccbdaddadbaddacacbacddbcdcccacbcccbdbcdcacdcbcdbcabcdbbcaaacaadbdbabddadaabdbcbbaaabccadbbddadcdccbabddaccdacabdbaadbdaadcddaaabcbdbacabdcbbcbaddbbdbcccdcdabdabcdbabccdbcdaabaababbbdcbadccaccdcaddddacddaacbdddbaddbddabaabcaadadcdcddccacadbbccadddcdbccddccbdcddddbddddbbababddcabbdccaddbdccadadbdccaabbaaadbaadcbabdcbdbacaacacaadddabbcabadbcdaddaaabbbcdabbcbbdcccbcabbbacabbbbcabbccbdddcaaccccbdaccccbcbabbdbabcdbbaacbdddcadcbcdbdcdcaacdaaabcacacddaabdcdadaaaacccbcdcdaabbdbaccddcbcddccbcbadcddaaccaaaacdcbdddcbdabccddcccdbdcaabdbbacbcaadcadcdacdbbacdacaacbdaabbbadbbdcacbcaabdbcaaccacdcbbdabcaccddcdadddaabacbdabdabcacbbadabdbdccdbdaacaadaccabccadddaadbdcddbadbdaaddccadaacbbaaabcdbbcddcacbbddabccaccbdcbcccdadcbddacbbacbabdadcbbbdbcdddaadcaacadadcadaabbbdccbcdccbbccddadbbbddcabcbadaaadccbcdaaabacbbcbcddbcbbbdacdddadcadcadaaabbcaacdbbbbadabcbabbacdbdcaddabdbcbccbcdcbbdddcbadabbbabdbcabacbddacbcbbdcaabddbacdbcababbdcdadadbcddbbaababacdabddcdcdcabdccbaaccbaababacaccadcaaacdbdaaddbdababdccabbaccacdbdcdaacccbddbccaccadddbadccdbdbbdcdcdddcbaccdbccddacdbbaabbbdccaacaaaabdabdcadcddcbbbcbbdadbdddddbbcdbccccdbbacdacacdbaaadbccdcddcbacaaadbdcbcdabdcaabdacbddaadbdbdbbddbdcdcababdbcbdabcbaabdbaacbdbddbaacbaabcacaadddbadccdaacacaaabbdabaadaabaccadbadbcbddbabdbdbbdbddddbcdbababacbadbacccdcacbcdbbbbccbacbdbacbbbaaabadccbbacbdcdadbdbabdcbcadacbbccaaabbbdccdaacdcbdcaaadaaccadcdbbadcabaaacacbbdccccdadaabdcabbdcdbcdabaacbcadcabaddbadbddbdbaadbbdbbbddbdcddaaddcaacdaaadacbbadadcacacbdaaabbdaabcbbbcdccbddadadcccbcbdadabcbccbbacdccdacddacdbcdbadcadcccabbcabbbbdbdbbabcaccbcaabcacbbcabadcdbabbababdddaadabdcabdadacddcacabdddabacababdbcdcbdcdbcacddaabadaabccabbbdbdbacabadbcdbcbbbdbccbcacbbcacddbcaabaaadbadbaaaacbcdbbcacbdcadabdbcccbdcaaaccddbbcddbbdabbdacbadbabbcdddbbcccaacdbbdcdaaaabcabbbddbcbbdbadabdbabdbbdbbdcadacacbbbaacdbbbdacdabdacccbdbddcabbbbbbcdacdddbccaaaaddadadacccdbaaccbbddcbdcbadaaaacabbcadaacdbdbdaacccbdcbdcbbdcabddadacbcbadaabdddbdcaabadbddadaabdcbabddccdaabacbcababbbdadaabbcbaacacaddbaacdbddbccacdcbadcbbbadabacdcbbbabdbbccddcbbbcaaababddcddadbaabaaabcbcbdcaaacaaacbbacdbabcaacadacbacaaaabdaacabcacdacadaabcdbadadaaacdbdadcbabddcacabadcdbbacadbcdcdaadbcabcacbaadbccddcdddddaadacbbabccaddaacbbbcccaccaacaacbaadbdaaaddcbccdbbbbddddadcccddbdcccaabdadccbacccdcdcbaacaaaabcdbdbcaaababaaccdbadbbabcdadcdaccccaaccdabdbbbabaddaabadabdbabaacadabbaacbbbccbabcccdbadcadadbcadbdcbdddaccbccbcdbcbccbcaadcbcccabdadbdbdabbdcccdddaddcbbbccdccddbacaaddacdddcabdcadaacdcacabbcdaabbaccbccabcabadaadccbbadcdcddbbccbcbadddcaccaacdcdbddbccaaddcbaabbbbcbdddbbccabaabbdacccdaaaabbccbdbaddbcbacdadcbbabbbbaaabcbadbaccbdbabddcddbbbaadbaadcdacdddcbcbbacbddcbcbadabdcdbcdcddbadcdcdadcddccacdbdbcbaabbbbcbcdccabbddcddaccccaaccdbaccbabccbbdadbbdabccddadcdcaabddcaaaabaddbcbabaddcdabbbacadbabacadcadaaabcddacabaccdbaaccabdbbaddcaadbcabddbcbdbccdcbaacbddbcbbdbcddcbadaacccdabadcdddbabdacbdcddaadbbadabdbcdcabdabcadabdadcdbcbcbbaaaabacdbcaadcbaaaccaddbdcbddbbcbbabcaadccdbbdaabbaccaabdbbdcbcbdbbcabbcacaccdddbccdbcdcdddbcaaaabddaaabbcbbcccbabbdbddabbbbbbaabcdabacabaccbdbaabcbbdaabdcdaadcaabdddccaaabcdcbdbbdbaccbdccdccadcddaccacdacbdcbcabbcadabaaacdbcdddbadbdcdbbbdbdccaaddbbddcbdcbbadacbacbdddbaabbabcbddbdabccbdbdbdbcbabbabddddcabccaaacdbbadcccddccbbabccbbdbdacbccbacddcccbbbcdabbccabcbcbabbbbacdacdaabcbdaadbdbcadbabaddbbabaabcbbbacbaadcdcadcadababcdabdcbbcbcdcdbbbdbdbbabbcbbccaacbcbcbabaaaccbcbcabdaccddbcdcccabdbbccbcabdbabdbabbcbbbdccaaaabddbcbbdddaddcdbddddaadaadddccbddbcabbdbdbdddcddbcacabadaddaabdcdddcbbcabbccbadcbaccbbdbdcccddcaccdddaddccacccccacbacddbbccdccbcbdcbabadcbcdbcbbcdaddabdccbabcadaacbaccacbacaddbdadbcccadbbddacbcacadbababcdadbbcbdbacacaacdbbbdaadbabdcaacdddddadacadbddbbdccbbbcadcddcbaabaccbdbccbddcdbdccadbbabbdbdbbadbdddadcdbcabcaddacddcaacdcdaacbabaaaacbacddacdbacdaacaacbdadbdabbccadbdcadbdaababcdabaadadbbcabacacccababccadaadddcacbaaadacbaacaaadbabadaddbdabaabbcabdadbdbccacdcddbbddbdcdcacdcdccbbbbdccadcabcdcbddcddabbcdadbcabacacbdcacaadbacddbaacbccabbbcdbbadcccdbcdbdddaadaabaadbddcdacbaaacadbccbabdadcaddaccbdaabcdcdbaaabbdabaccdcbcdbcacaabbcaaccdbabddbcbdacadbadcdabaccdccaadacbcaabadbdabdccaadaddccbcdbcdcbdbacbcababbccdcdcadcbdbacacdbcddcccbcacaabddccdbcddddabaadabaddbdcbabccbddccdbbccacbaabaaddcbdcabbbbadcaabbddaabababdbaacdabdabcbaabbcbbdbaaddbcbccdcdcbdbbbaddadccaabadcbbcbaabdddccbbdaabbacaccadacacaaacccadacbbadcadddcbbccbcddabbabbcbddbacbadddbbbacadcbccdbbcabaabcadbbcbdddddbdbccacbadacbcbaabbcbddcaccbaadcdbadbdabcdcddbbacacccbaabdbaaaaaacabaaccacbaaadadbacabbcbacbabbcbacbcababddcbcdabadcdccdaaddcdacbbdbadabbcabcdbccbadcabbbbcdacbacacbabbbcacababcddcbcaabdbddbdbdddcdcdacbccddcbccbbbbddbbadbabbaacbacbabacbdbdcdbcbddacdcbdaddaddbbcaaadcccaddabcdaacbcddbbcadadabddadcbcbadadbacdbcccacacaacdccdaacccbbbacdaacacabbcdcdccdbbaacccabdcadacbcabbbcbcccbaaddabdddcacabaccabcaabaadacccbdacacdaadcddabbcadbaccbbbbcdcdcdaaaabddcdccbbddcadbbbadbcdcdcaabddcbabdcadddbdcaaacbcdacaddabbcadcccbabdddcbccbccbaccbbaacccdaccdcddcbadccacabcaccdcbacccccdccabbbcbcdcbbcdcabddbccccdddcbacabaacdaccbacbdbcbccadadbaabccbcacdccbadadcdacccabaadcdddabcaadcbabaaddbbddbbdcdbcabddbccccaaaddaddabdccdddadacaadcdbbadacaaaabcdbabbcdcddcbbbdbcaabbaabbdaddddbbdbddddcccbbacabaadbbddccbabbbbbadbadccdaadbdddddddabbaccbdabacdbbaccdddbddbddaaddabbadabcdbcbbcabbadbbbddacbaccddacdcbbdbbadddacbbbbccbbbccddbdbdbdadaaccddadaacdcbcaaadbdcbddddacacdccbccdcaacccacadcbacdadbaddaaabccdbbcdcaddabcabbddcabbdadcbcccdaccbcdbcbdbdadacbabcaaadbabadadacdaadbccaadabdcbbbdcdccbddacbbcacdcdbbaabddbcaddddcaabdbadbacdbaaaabdcccbbdbcbcccbacaddadbcccdbbdadadcbbcaaddabcddabcbbbaabbbddcaabdadbcdacbdacaccdadbbcbdcdcbaacbcddabcaddabcbbbcbddaccacbcaacbadbadaaaabccdaaaabccbbaaddbacacabdddaadaabdcadddbbcdcdbcdbaacbabdcaccacbdabbdcaddcaaaacadcccadccbaacbdcaccdbbaaaddabddccabadddadcabdbacbdbcbadbadaaaaacbccdcddcccbdbbccacabbcddbdcdacdbbccacdacdaaccaacdbacbbddacbaaddadbabdbbbdaadbbbcdcacaacadaaacdcbababbdaacaddcbccdcdcdbddcdcdbdcdcbacacbdaacababdccdabdabcbdbdbdbbcddccabbababacccccaddbdbdcdbdccbdadbbadabdcbadcbbcbdabcccbacdddcaadbdccbacbaaadadacabbcabbbddcdcaaccabbddaaccdcbdbdbcaddcaabddbcabadbcabcdbcacddaadbbbbbdccdbdabccddcaddddbcaadbabcccaddbcbadcadbbddccaaaabdcadaddbbddbbccbcddbdbabaadbaccdbbbcbcaadcbaaadbbdcadbcbcacbcdbdbbbbdacbcabadabcbbaacbcbbabaabccbabdacaadaaadaaadabdddbbdcbbabdccdabbacbcaabddcbcdccdddacaadcbdcccacbbababadbcddabbbbdbadcbbdbacaccbbcdcaccbaabddddbdbbdadcddbddbacdaccbdadbddddcdadcabcdddaccbdbbbcbdacbdaadcdabccbdacccbcadddbaddcaaabdbdbcbdababdabcacabcabaacacaaacaaccccbbbaccdbbadcdddaadbbbaadabaacabccdccbcccbbddcdbbbabacdbcdcdccbabccdbbbdaabdadcadcdbbbbadacadcdddaabdaadaaaabcdcbacdadcdaabcbcdcddbdcbccbabcabdacdabddccddaabccadcbdcabbbacaadbdabccdadbdabbaaadbcdaaccdbbbabdaabcdaaccbbcabacaccddbdacadbacccbbbdbcbddabbcccbdabdcdadacbddbaacbbccdbccdbbccbdbadbbbdacbdcdcdccccccdadbbaccddadccacbdcccadadbbdbbdcbadbcddcdbbbbbbdbbbbcbaadcacbbbccddadbbdcddabaddaaaabadacbbcdddcbcadbbcdaaaacdabddbdbccdbdcdcddbccdcbbccddbbdcccbaddccbddcbbacadbbbdddccdabdcddcacaadccdcddbcdcabadacadbdabcaaacadcacacbbbdaadbcacbacabdddadddccaacdacaacacdbdccdbbbadbccabccddcccdacddaaacbaabadcadbdcaaadcabacabcadacaacbbbbbdacdbadbbbbdabaccdcaabaacddbadbbcaddcbccddbcadaabadcbaaaaccbdbdadbdaaddbadcbdbadccaabadbcacdcdccacacacbaabddcacdcdbcdbaacacdddbdbaccbccacabaddcabbdbddbdbcdacbaacbdbbbcdbbacabcaacaadbdabaaabbcabbbaabccdabadadadddadbbcdbaaaaddbdbcdabcdbcddbcaaabdcadadcbcdcccabbdacddadcdbbcbabdaddcdcbbaaccabccabcdbadbcdabdcabdcbbdbdbbadabcbaddacccbacadbdbccbababdbcccaabdbadabccacddaddccaabcdaadcdbbabcbbcbbdccaddcbbdcccbccbdbbbdaaabddbcbbcbcddabdbbbdddcdacbaacddadaadbaacbccbcdbbdccabbccdbaabaaddddccbdaaacddaacbacbaadabbcabaadbddbcbcccabaacbdcddccbddaacabcadbacaccccabbbcdcbbccbdbbcccaddcdbcbacddbcbbcbdbcacaabbcdbaaaadbadbdaaabcdcbaabaddbaddaadccdbcadddbabbcdcdbadacdacabbabccacdcbadcbcccacddcdabdaabcbbacdbcbdcccabbcbcbdabacdddccbddbabbdabcbbaccbdcbcbdadccddcdbacbcdddcababaacdaabcdbdbdcabdadaddbbdddcbdaabdbccccdcacccccaadcabbaabcadadddccccaaccadbdaadbbbdcdcaacaadccabcbaaacbbdcccccdcaccbacadbadcbbbcdabbbbbaaacdaddadddcccbccbdaadbaccddccdacabbcbcbabbcddbbcbdaabddcbdcdaabcbacbcdaabbbbbbacccabcdddadcbacbdbadabdbbbcabdbddaacbdcddaaaacbaadbabbcbdddbbacbbacbcdddbabdadaacdcacadcdaacccdcaacdaddddaacccbbdcacdcdaddbadcabddcbccbcbcdcccddacdddaaddabbbcdcaadcbbbcddbdddddddddddcbbaadaaadcaddcaacddcdcaaabbbaabccaaaccadcbccbdccadadcdacddabddacaaacbdaaccaacbaadbddbcccbabcdbadcacddbccbabbbcddadccbccdaccdcddbdaddcadbaaadabcdcbddcdddcccbdacddbddbcbdcbcacdbacaaccbcccabdcabcbbbcdadaabbddaddbbbbcddddaabbdbccbacbbcdadbabdabcccacbabcdacdbdacddadcabaadccadbbcdddddcdbcacaabddbaadcbcaacddcddccbabcbccccabbccddccabacdcdaadcbcadddddcbbabcbcbaaadcbdaddbbbdbbccccdbbcccdabdaddcdabdbadcabcabdcabacdccccadacabcbbddbadaddbbaaaccccaaaacbabaacddbadcdabdadccccdbbcdbdbaaddcababbbbdaabdbdbbbcccacdadabadadddccbcacbacdbcccadadabaaaacbcdbdabacbdbcdddccccabdabdbacdaacacdabacbbdadbdcaaabcdabdccaabbdadbccbdcacbdcddccbdcdabadcddbdbaddadbcbdbbacaadbabbaacacacccaaadbcacdbbbcaaaaabbabdacdbdcbcdabcacadaadbacbaacccdcdcdddacbbacacdaccaadbdbbaacdacbddcbbbddbcdcbbdddcbadcbbdcccdccaccdbbccbaccbabcbbacbccbddbbaaaacbccaaadadadddddcdcbddbdabcbbbbbcdbddbadccbcccddbcadaaabcdddabccacaadcdaccdddbabdabcbacbacbccddbbaaccbddbddcdcbcdccabbbdcacbccbdcdacdccbcdccdaadcadacdbcdbcbdaddaccdcddbbadbadacdacccdbdbdaacbabddaabcdbbbddbdadbcccacadaaabbbaadccaaccbaaaaccbccacbabcabcadcbddbaddaddbcadacaccaaccdcdbaddbbdcbdbcddcdaabbbdbbacbdadccbbdadaccbaaaacadddcdbbbdcdbdcdadcdadcbaddaadcbacbaacadabddcaabacbabdbbdcbbccdabcccddcdabdaabdccaaccdaabaaadbdcacbacdbdadcbdbaddbbabcbdabbacacbccaccdababcacbaacdacabcddabcacbcdcbbacdabdddcbaadcbaadadcbbcdddaaabbcadacdababaaabacaaabdaabdbcbbdcbdbcaaabdbbddcabdadbccbcdadbabdadaddcddcadddbaadccdabcaacddcdadaabcdcbaacacacaaadbbcadbdacacccacbcabcbdabbadadbcbcaabbcbccdadbcadbabdabbbbbccaccdccdaababbccacacccbcccdaabdccbadbdbbcaccbddcabcabccabaaadcabadacbabdabaadccdbddccbcdaaabacaaacabababdadaadbdbddbaadabcaaacaadbabdcbbabcaccccddcdcdaadcbbbbdadadcbdbdaddacddaccababcdccaabdabdaaacdbdddadccdbdccbcbdaaccbacdbcadbcdbadcbcdacdbabdddabbbbcbadbbddcbbabcddcccbddccaabadcabccbcbdddcdbbdcacaddbacaaadcbacabbccddabdbbacdccbdacbccbbaaccdbabbaabcbacbcdadbdddbcadbcadcdabccccdddcdccacddbdabaadadddabcdbccaddbadbddadcabdbdcdcddcdbbdcaababcacbccabbaccccbcadabbcbcadbbcadddbcdcacdcdaaaacbcabbcbadddbbdaadbddbcaadacddabbdaabaddcdaadbbabdaacdaaaadccddddadbddcdbbcdadadbccabdbcadadccdbdbbdbbbaaacaacdbcacabbdccdbdabbddcadcabacabdcdaaabcacccbabccddddbbacccbcdbdbcbbcbcacccaacdcbbcbbbabbdadaccbbbaadbdacbcdcdcdbbcbcdcbbcaccbccadaaaabbabcbbacacacbabdadcdabacaabdcabaccdbdbdbabcddbabaccbdabaccacabaabddababcdccaccccdadcbccbabcbdbdacacbaacbccdddcdbdccbdadcadabaabccdbaddcbdbdbcbbcbaaaddcadaadcbaccccddccdccddcabcadcaacaacacaacdaaabbcaabcccaadcbccbdccadacadbabcbaaacabdadadcbdcacabbdadbaabbbacdbcabccbdacaadcddcdbddddddaacbdaabcddbaaadbdcbdababcbabcdabbdcbcaacccccbbcaddccdababdcdcbacdcacbcacabccbcaabcbbdcadcadabcdbdcbdcadcacbaccbaacddabcddddcdaadaacdbdccbbdcabcbdbdcddaacdaadcddbadbbcdbcbacaadcbaaccabdcdbbabdaabcbccbbcccabdcaddadbaddbcaddbbcacaabdcbabbbbbacbcddacddaaccdadabdadcdaadbdcbddbdacdddababccadacabcccdddadccaacacbddaaddbbbcbacdcaacabbcdabcbadbaadbbaccccaadccddbbdadaaccbcaabacdaacaaabdcbbabbcdccddaccbbddcaccacbcccccbbbadaccaacaccdcaaabcabdadbdacadbcaccaabccdaccbcabacacbcdbadadbaaacccadddccdbdcddacabaabdcbbccacbcbdcddbaabadbaacbddadcbcbcbddcaabccbdcabaaaccbbddcdbacdbcdccbabdbbabdacdbadcadcdcbbacdccbbadacbaabdbdaaccabdbcdbddccabbddccdadcbbadbbadbcadcababddcddbcadcadcacbcabbdccacbddacdadcbdbaddaacbdabcddbcadbdaababcabdcbddcbcdaadadcadacdcbdddbbbdacbcbabaabadbbcbbaabcadcadbbbabdcacabbadbbcbddcdbabaaaddcbbbcbacaabacbcbbdadcbdbadaddccbbadcbbabccdacdacadbcacacbaccadbdbcdccdddbaccbbcbcbcbdbadaccccbddbdcaacdccdbdbacccdccddacbddacaacbbcdbabadbcbdcadbabccaaccdcddacaddadbbdaccbdcbbdcabdccdcccbbddcdbdadadcbcbdaddabbcbabbdbadaccbbbaccddadabdcbdabcbacacaccbdcdbaaabbacbcdacaadbdcddbcbaacddabccbdaccbabcdcdcbdbcaaadbddbbaadbdbacbcccdbcbadcacabcbccbbabadbcbbcbccddaccadacaccaaacaaaccccaabbcbccdabaccadadabcbbbcdddccacdcbaabbacacccbbddccdbcccbabdbdbbabaabaccadacdbdcbbcadbdaaccaaddbdcabbcbaadddbddcacdbdabbdbdcaabcabbcbdababbbcadaddcdaacbccadbcbdccdabbdbcdbacccccacabcadcbccddbddbcaccdbdbdcbcadcdadabadaaaccbbdabccbbcbcdaacdabbadddddcdbcdacaddabacbcaccbdabcacabbcccabacddcadcaccabaacdbadbbdcbbccbbbcbcbdbddabcccbababdabddcacaccabaabcdbdacccaadabbacbadcdccbbcabbacadcccaadbaddadaabcadccaccbdbbaaaabaabadadabaaccdbcbbabdbabadddbcccdaaaacbcbcbabacdabbccccaaddbdaddbdaccbddddbadbcbbbcbabbbbdabdaabdacaadcbacbbbaaaacbdbdddadbbaaccbacccbccbacdaccadbcddabcddccdcddcabadaaacbaaabdcbbbaccdcddbcdacabaabdddadbcbcbcdbbcaaccadaadaabbacbaaadcbcbcddcbddbcdbbbcbccddadbdbacbbbdcacaacbcaddbbcbcccabddaaadcaabcacbccddacbbcbbccccabcdcdaabccbccbccbadbbcccddcdbbaadbdddcdccbbcdbcbdbbdaddacdcdccdbdcadbcccccaaaddbacacaadcabbdddbdadbcbdbbdcbdacddaaadddbcdcabbcdccbdbcbddbbddabbbaacaaaaddbabdbccaaaccdccbabadbbbbcdcbbbdbaacabcbdaabbbbabbaddcadcdccdcbbddcacadabddacbaddcbdbabaabaaccbbccaabdcdaacbaddbabababbacabdabcbacbacabdacddbccdbdcdcddacbdcababaccdbbdaacaadbdcbdbdcdbdbccbdbdaddadcbbbdaddadbdbaabacdbabdabcdcacabbdbbdabbcdbabbdddadaccbccdadacdacacaadbbbdabadbccbcdbaacbbbbcddbccaadcaaccdbacdcadbcccbcbcbcdcdacbacdbbdcbbdadaddddaaccdbbdaadbaabdccccaacbacdcccaacabcdadcbbdcacccdabcbabbacbabacbddaaadabdcacdababadbdbabacabdccdaadcdbdbaabcaabacbdbcbbbcbdbabcaacccbaacdcacdddbddddbcabbcbbcacdccdcdaaccdaccddcabcbbddcbbdaccaaaadcdaacbcbbabcdadddbcdbbabacabbbcacaaddadbacdaaabcccbaabaadbdbaaaaaaaabcdcbcbdbcaabdccdcdaabbccbbdaaddaaccdbbcadaadadddcbcaaaabcbcacbbcdcdddaadbcabbcabcbbcddbababddccdadcacbcacbcdbdddcccdcababaaccbdaccacdddcdcccdbabdadcccbcacccdcccaadbadcabacddbcccdcdccbccdcdbccbddbbdbbdabcbaabddacccaacbadabdbbaadaccdddddcdddbdbacdccccbddbaaacdcaaaaacaaadbcadbcdcbddadabbababccbacbdccaaaabdbddabdcdcacdbadadabbdabcdbdacbcbacacabbbbcaadcadcdbdbcddabaaaadaabdaadacbaacbcbbcbdcddcacddcbdcbbabcbddddaabdcdaadaddacbcabbdddabbbdbcdabaaacccddcacdadbaacbaccdcbacacadadcccadbabccaaccbdbcdcabdbcbbadbcabcbdcadbdccbddbcdadddbaaadabaabcabbccbbadbdbcdbabdabddcbcabaccadbbadddaddacbaccabadcbddbccbdddddacbcbbdacddcddddcdccabbcdccbabccccbbddcabbdbcdcdaacddbbbcdddadcdabcdacccacdabccbcdccdbbdaddccdabbadbaacbacaaabccbddaccdaaddbbdccacacbcbcbabdadcaddcacbbbddaccbdadcdadbadddabddaaacddbcacaddaacbccdbadcdbdbddcccbadadbacbccabdbabaaaaaddcddcbbadabdbabcbaaacbcdaaacbccdabdccdbabdbbdbdadcbcccabccdabcacdcdaccccddbcbbdaabdcacdabdaabddabaccadcacdccaacbcbcbbadddccbadddddddccdbadcaabccdcbcabcbbcbbdadcbdddbdbcdaabdbbcabdbcdadabdcdcddbbbdccabbabaadadabbbddcaccbabcacaccccaccbcdbbcababcabbcdbdddcadaddddccaccabbbcdbabaaabbbbaddcbbccddccbcadbbaadcbdddcdacddcaadabbaacbabccbcddcaadacacddabcbaaadbabaccccbaaaaccdbbcbdddaaacbbcacadbaaaaabcabdbdddabbaacbbcccacadbbbbdcdddadaacdcaaccccbcdbadadbbabcaacadcaddbcddadaaccaadcaabbcbbccabacbdacbcbbabddcbcabdcbadbadbccddddacdcddbdbbbbdbadbaddbcbccddcdacacabdbbaacacbaaabdaacdbbdccddbddabaaccdacdbbdddadccbbbbaddcccbacccdddcccaadbaddcbadccaccbbcdcbbdcaabdbbabbcacddaaaabdbbadcbbbcaddbcaacbacaabdadccadcccbddbbdbbaabacaccbbdddcdbcdbdcdcccdbdbacdbbacaddadbddbbcddbdcbbcddadabbcdaddacabdadbccaabbcdbcdaddabcbaaabcdcbabadadddaaacbcccccacbdacdabbacacabbbcadaaadbacbddabaddcbbaaadadcbccdadaacadcadbcaaabbbdcccadccbddcabaabcadbbbbacbcccdbdacaacdbdacdbbbacbaaabaacdbbadbbacaaacbdddbbbbadbcbcaccdddacbdacaabcadbcddbbcbdcbddabcdbcdbdacabadddbabccdbadaaccbcbbbcbdccaacbbbcdcbcddbdaabbdacbbcbabaacccdacbcaacabaccdcbabadccababdcbadaabcdadcccbacbdbdbacdbcabaabdbdbcaddabccadcdbcbabddbcbabcdcbcacbdddcadddbbcabbdccbabdaddaaacadacdcddcdabdbbaaaaddddccaccdaacaaaacdbacacbcbdbdbddbbaadcadbaccaabddadcabacbbbcaddcaddbcccacdccbccdbcddbdbbacbbbcddcadaccaaaabcbdbbacccddbbaadbdbacbbcbdacadddddcdcccbddaacaabdbdbbdddbadbdbbbbacadcdcabcdadbbcacacaabbdacbbcdcbacbbdddbbdaddbccbabbdbdcdbaaddcdaabdcacacaaddabbbaacacbadbaabcadccdaaccbcbbbbdcadcbbdccabdadcbabdbdaccdcdcbbdcabaccacaabdcdcadddcdccbbbbacadaccccccdadadabbaddcabdbbddddadbbddbbdaccaabaadacdacdbccadcbabdcdadaababbcbdbddddbbdbdcbcdbaaabadccaabbcbabdababaaabcbcdcbcadbacabaabadbddaabcadbddaadbbcbbbcaaaddcaaababcacbcdbadddbbcbccbbcccdababcabbcbbbbdbbbcdabaabaabcccadbdddbcacdabaaacbacadaddddadaababadbbbabbacdaaaddaccbbcabaaacdbcabdadabaddbcdabddbdccabcddccadcaccacdddbdbdbbdaddbaccadadcdbdaabacbcdbccaaccabcbbcbdcaaddddbdbbbadbcadcbbbdaddabbdcacdbcdccbddbddaadcabbbabdbcbaabdcdaccdccababdcddadabaabbacbdcabcaccbdbcdaabadbacccdcbaadabbddcccdcacdaccdaabcabccabdcdadddddaccadcbbbcccacbdbbababdacdbadadddbababbaccaccadaccdccbcddbcaaddccadadcddabcdacbcbabbbabbbbcababacacdaaadbddcbabbaaddbaccdacacbddcdbaaaddcaaabdddacccacacdcddddadcbdbdbbcdcacbaccdccccdabcbadaabbbbcbadcaccaacdadaabcbdabdcadadcaaadbabbbcddbdccaabbcbbcbbacbcadaadbbcbccabdcbdbcadcadaadcdbcdcdcbabddbbaaacaccccbddaccacbdaccccaddcccaacabbbbbbcbbccdcdcadbddbcdddadabcadbacdcbbdbdbbddbbddacdaadbdaccadcadcbcdcadadbaadccddcdcabdbbabbbdccdacadcadbdbaccbdcbcbbbdbbdacacdbbcabcbcbdacccdbbbbcbbbccaaccbddaaaadcbdacbcbcbcbbbcbbdcbcbacacdbdabcbbdbddcacacbddbbdbdcddcbbdcbadbccacbcddccccacdcdbaaabdbabcacdddbadbcbaabdbddacddaddacadaacacdabadccbbabbbadbbaabcbdaaddcabadbcaadcaddcbdababaaaaaaaaabccbcadddddadcdbdddacbcbdcdccacbadaddbaccacaddccdccddabbadccccddcbdcddddcadacdababaabaacccccbbadadcdbbaaabddbabbcaabbdcddaddbcaabdabdcdcbbdaadcbbcdddccadbabbaccbacadbbaaddbbabbaaadddcaaacbcbaddcdcaabcbdbdbadadcaadcbbabcabccdbadcabcbbbdcdbcdadacbbcaabcccdacbbaacbcdcdcbdbbcbccadacdcaaddcabcbcbcbacdcddddbcdcabcbbcadcdddcbdcdbbccdbcabbcdcdbadacdababdbdaaaacadbabcacabbcddbbcccbbcbbacdbdaddabaddddbdcbccdbbdbaabbcddddcbcdacadabdcdaacbdabbabbdbbbaccacdabbcadbcccbbaacdabadcbbdaddbdaabcdadacbabdadbacdaacbcacaacdbdaddbcbaabdccaadadcdadbcdbabdabadbcbaadacbbbbaaaadbdcbccdaaacadabbbaabddbcaadabdadbadbccacacbcacacddcdddbdabaddcabdbaccbbcdddaabbaabbccbdccabbcbcbccabdacdadadbcdacbdbccbddacaabbbccbaabadcaacdbdcbcdabbcdcaacbdadcbcdbdbaaccdabdababcadddabacbccddadaaddbdddddaabdbcbbdadbcacbabadbbdcddddbbccccacadccabababaaabaacaccdbadabaddddaaacbadbbadcacacdaaacdccdcddbbdbdcabadcaacbccbbaadcbbaabbdcddbdbcdabbdcdccababccbbcabdaacaccbbacbddcabacdabaccabdacdacbbdcccdadbaddbabcbacadabbdbddbcbcdaacdbcdbacdbccacdbbabbbabdbacddcccadccbbbddabaccdbccabddbcbadacdcbccaddcabdcdcdaaaccbdcadabbbdbcabaadddbaccaddaabbbddacabbdcccadbdcdbdaccadbadcaadcbccbbdccdbdcdbddacbbdbbdbdacbbcadcbccbccdbaadcbaabdabccccdadcdbdadcbdbdcbcccdacbcdbaddddabacbddbbdaaddbaaacadadcbbbbcbbbccdcdbdcbbaaaadbdbdcadaacdcdcbccaacadbcbcaddcddbddbcbbababaacbabacacaaabcaccbbddcbbcbacacccabadaacdbbabdadadabbbbbcdddacbabcabacbabaabbcadbbbcbddcacaccaaacaacacdcccdcccccacaadccddaadaaadadcacddabbddddddadbddbaddbdaadcbccacababcbbbdabaaabacdbdacacdbdbabbbadcabdcbddccdabaddabdaabddabcabaaddcaddbdcaadccbdadbacbabddbccbabcbddabbcaccbbaaacdddabdcadccabcacbddcbcbcbacbabadabcaaccbacacbbbbbadddbacbacadccadaddcadadbdbddacddbcbabddbbaadabbccacbddccbdbcdadddcadcbdacddbcbaccdccbacbbcadbacdccbcccdcaabcbbabbadacabcaddbddbbbdbdcbbabbaccdabcadabadbcacbcabbbdbabadacccdcdadcbdadbccbdbdaaabadccbbbdcbdadcaadbdbdcdbdacccbaacdcbdbbadaabdbbcdbadaacababdbbcbabbacdbcdcdcaadcaadbcddbccbddcbcaccdbccdacdadbaaacccabbccbabdacdadacbacadddabcdbdbcaaababaadcadddcadabbbbaddcacbcdccbadabdaadcacdbdabadacbdaacbccdccbbdcdcccdaaacdccdbdbcbdaaddaaccbcadabcdcbabccbcacddcccbbbbbdacabdcbbaacacbcacaaddabccdbacadbcdcaacbbabbcabbcbcabdcabddbaddddbbdcdaaddddcccacdbcdcdbbccbbbcabcbbdbaaaccdaadbadadbdbccbccbdbdadaaadadadbabcbdcdbccccbcaadacbbdacadaddccabadbdadacddabdbcbabaaaccadacacabdcacabdabccbaaccaaccbcaccabcabdcbdaacbdcbbdcbabbbaabccbbbbdaaabdbdccbccccbbaaaacaabdccbabadabbaabaccbbdcbaacabddbccabcaddbbabddcddbbacbbddccbabbcccacbdcaadbcbdabdddccdbcabddaaadbccadaccccbcdcddccbcbcabbdabadabccbcbdabdccbadddabbadcbdbcaacabcbacbabbcacdabbdabbadbddbdabbdaacccaaaaaccdbdbabadbbccaacaacbcdbbdcbbccdbbbabaadaaabacadacbaaaccdaadcdcccbcdbbbddabdbbbabbdcaddbdabccbdcbdacadabdcaadaccddddaaccdaccbcacbbacdbaabacdbaaddbcdbdcabcadaadbcbbcbbbaddabcabddcdacaccdaacbdbdaadbdccaaadbdbcadccaabdbbccbdbaabcbabbcbcbdbcbbbbacbbdddacdcadbabaadddabbadbbdaacccddacdbbacadbcdccdabdddbccccbcdbbcaadadacdccbcadddcdacbdccdcdabccbbbdbcbbabccbbccdbaccddbadbaacaadcccbcbbabcdacbcbdcdaccabccdddabbabacaddcabbacdbccbcdbbbddddaccbdddcaccdabddcaaadbbbcdbdaccbacbbbcabccbcbcdccababbbddbbbbbaababdbabadbbcbbdaabcaddccddacabcbbcbdbaaccbdbdaacccaadbbcccbdcbdcbccabacbdcdacbbdcaadddcacdbdddccadddacadccbcdbbdbadaaacddabadcadcbaabdbbddccabccbdbbadaddbcbbbaabcccdbcadabbadcddaacacdbbbbdabcdcbdacbccbddbcbbdcaaccadacddadabbdacbaddcbbababcccdcdbbbbcdcdbabcdabaacdacdccadaabaabdacbdacaadddccccccbdbcbaccdbdcadbbbadcddacaaabdaddbbccbcbabccababdbdcdacdacbbbbbcbbababdabddcadbbbdaacbbbcadbccbbdcccdaabdddcacbadaacccbbdaccadadaccbadacbaaabcbdabbbaabdabdcbbaaacbacdcdacdacddbbddcbbacdaaaacadaccacbaccbbcbacdbbdbaddaaddadabacadcbdacacaacadabcbdadaabbadbbbccbcdaabbcbcdadcdadaaadbdcdcbddcacabadabcbcbcabddaaabddbdbdcbcbbbbabbaabdcdbcabbbaddddbdbadbdddccdbadcdbadcadcabcdddbcabbacccacdbbacabdcaacbacddacadbcddacdcaddaddadacddbccdaddbdbabaadcaacbbbbdddcccacabaacdabacabbaadaccccaccadbbabacbabaccdcaddcdbdddddcabdcccdaaddaabbdcbdcbcabdabbdcbcdddddcdbcbcdccaddaaaaabcdcabcddcbacdddacdccddcccccabccababdbadacccadcbbddcbcccbabbadabccabcbdcccbddbaaddcbcdaccacacbcdacccbbdbddccbacabdbdcdbcdccdbcbcddabacddabdccadbcdaccbaabbabcbcaaacaacddabacbabbbdddcdbddcbaaddadaaadcdddabccbbdcadbacbbcbccdbbabacdabddaddcdbbddcddaccdbbcaddbbcbabbabcccacbbcabdcbbdaadbbcddddcdbdccacadcbdbcbacdadbacdbbbadbbbcbdcdacdccdbcdbcdcdcacbdbccbcdbbacdadcdbbacbadbbacacdcaccdbacacddadabcdcabccdacaddcddacacbadcdccdbbddadccccdcdcaccbaabcadcacbadbbcddaabbaaaacdccdbbcdcbacdcdcaaaaccacdbbdbaacddbbcccddbdabcabaabbdcaacbbdaaabaddcaacababcbccddcccadbabbddbcbcddaacbccbddaccdabdaacbbddbbababaccbdabbbbcccbcaabbbbbdaacabbaabdddcbcaccddcbadbbacadabbcaaaadaaababbbdadaadabdbccbdbbaaddbbcabadaccabbcbbbdaddccaccbcbabdaddcccabacccbdacdbccdbcabddaadcbacdbcaadbabdcaacddddabdbdbddacacdadbccdaddbdcaaaaddaababcacdccabadaaabbaddacbccbccbcdddbdbdaaadaaaabcbacacbcacdabccccabbbbbddabbdbdbcbdbbddacacbdccdcdddcdaaddaddbbcacdccacadaaacaddddccbabcdccaaacbaaaacddadcacdbdabadcdadcabcaddabbbcaadbacadbdacbdacddadbccadbdbabdcccdccaacabababdbdddabbbcabdabacbdccbbacdbacbacabdaabdaadaddddddaacbccdbacbdbaadbcbadcacacadcadbcaacdbbcdccaaddbdaaacdcbddcacdddddacabcabaccbadcacadbcccdcddbdacbcdaacaaadbccbadaddbcccdcccadbabaacabbacbcabadbddacabcbadaabaddbdadccdcccbdcccabaaddadcccdcbbcbbcdcddbaccacaabdcbacdbacbdcaaadcdaacdacdcbbdccaaabbcddabdccbaccacdddaaabcbdbdcacaabbaadadabccbcdcddbcacbdacbdddaaddbdccabdddabddadabdddaccadbbadcddabdcadaddcaacdbadcabaccccacccccaccaabaaabaabcdbdbacddaacbadaacbccbbcabdccadadcaaaaddadabdbbbbbdccddadbaadadbcccbddcccbcdabdbcddbbabacbbacdcdaadaddadabddcbbcddbacbccadbdabccbadbabbcccadbbdbbacbbcbabbdccddbdccdacabacaccdbdccbacdaadddadddcdbaddaabaacbabddddcdabacacdbadbdcbdccdcdbcabcdbbbaccacaddacabbdacdcdbaacdbbcadcbddbdbaaacdacadabdbcbabcbdadccddcddcdcbcdcdaaacbdcacdbcbdacbabcdcbacbbcdaacaccdddaddbbaadbdbdcbbdacdcbbdadccbcdbcabbbbddabbdaabcccccdcbadcdaabddcddbdbbbdadccdcdacddaadbdbccbaddaacaabdddacbaabaddacaacbadcabcbadbdbcdaccdcaabbddbcdddcdbbbcdaabaaddaabcdaccbadcbdaabbaccbdbcccdcdbcbdcddaacdaacbdbcdccabadcddcbccaadcbdbaabadcaabdccabccbcbaadabbdabcbbbabaadaaaccbddacadabcddcacbdddaadcdaddadddbcccbcacbbcdbbcdccdbdbbadaacccbddbacadcabaababddbdcbdaacdddaacdbaadadccdcacdbbccabacacbddcaaddcccdccdacaaababbdbdddbaacbacdbcabcaadbccdcdbbdbabdcabbccdbbccbabbbabbcbcbaccaddbdcdcdaadcccbbdabadcdbcccdaccbacdccdbdaaabbaccdabbaacababaaabdadcdcdadcbcdabdaadcacbccdabbcadcababccbdbccadccababbaddbbcdbbdcabbabbabbbdddabdcccccbacabaadcbacdaccbadbcccabdccabbccadacddaccbaaaacaadccbddcddddddcbbbddcdaadbcaccdbbacbdcbabaababbdadbdcccbcdcabaccbadadbdccbbcccccddaacbcbcacbabbacaababacdacbcdccbbcbdcdbadadccabdcdddcdccbcaabcddaacbcccaaccadbabaaabacadadabccadcabcdccccacbcbbccacdcaacdcdccbdadcdddbbaabadaadccabcddaddbcddcdddbbcdaddccaddbbddcbccbbcaddbadabaaccacbbaadbaddcdbdaddabbbccccbddbadbbababccdbbccbdbdcbbabaadccacaaabacdacacbdddbadddcccdabaadbcccddcdaccaaaacdaacdadccbdddbccdcdbabbbcaddcbaaccbacaddddcdabccaaddbdbcacdbdbdcbbdabcdabcdbdddabccbcbcabaccbddabcccccaadacbddaccbadadcdaddbbdbabbcbccaaddcabbbddccddccccacccbcabddbdcbccbdcbabddcaacdabddcacaadaddabacdbdacbdcbabdcccdcdabcbbaaadcdddcacacdbddacaccbdbdbdbdaddaaccaacdbccbccbcbcdcaadddccdbdbaadbbdacdcbabbcddddbcaaabbdaabaddbabccadaaacdbaaacdaccdcccdabcbdacaccbbcbbcbbcaccccaadadbcdddabdbccdacdbadcdacdbabcbccacbbbcdaadccbdadbdaaacabaaddbaabadaddacddadbadddcbbbcaabcadccdbddbbbcccbccbcdcdbacbbcabcbdaddbcaadbabbabbdbccdcdccabdaabbccdadccabdabbbdcacbbddddbbaabbcdbdbaadbaaccdcadccbbaabdaccdbdabdbcdcdbcaadacdbbdcbccbcabadcccdddccdacddcbddcdaddaaaaddbaacbabcabcbbdabbcdcbacbdabbaacdbcddcbcbaabadddabcbdbcdbabdbbacacadcbdcbadcccddbacddcbbccbaadadbadcaddccccbddccabaccdccbcbdadadbaaabaaddababcaabbacddbdabbaccaaacadbbaacaaaabdbdcabadadaadbaadadcdaddcbabdcbaaccbabdcbcbdccdaacacaccbccbdabcaaddabdabdcdbcadbdbaabbcbdddcdabcabdababaabcdbbdaadabbcadbbdabddaaccddacdadacbdbadbadddbabdbabacadccdaabcbbacccccdbcdacdbddacadadbaabaadbdcbbddbaadcccbccacbbbabbcbacbdcbddbbbbbcdaaaadaabbdccbddbccddddadbcadabccaaaabaaddbcdaabdaaadddbcbccbadabaddaadbcddccbcbacbdaadbcdcbcbbbcabadacacdaabdbbbcdcabcaaaddbdcdadcadcaccdbdabdcdcbbcbcacbbddcbcbcbdcacccdcabcbdddbcabdacbaadddaddcabadacddbdccbcacabcdadbcddbccdbccdaabcbbacaccddcbacdcadaaccadbdacbcdabcbaaadbacabdaddadcabcadcbbcbadaaaaaaadadadcbabcbbcccacbaaadabacabcbbcabbbababbadcbdadbaccddbadcbbcbcadcabcccdddcccdcadbcdabdbcccacdbadddcbccacbdaddbcbcddabbadddbcbabadcaccabcdacbdadabadaabdaddbabaacdaadbbdaaaccadcabdcddabcccacdacccbdbcbcbadaadddcdabdbadbddcdddbddcdadbdbbccacdcbcbcaaacaaaccddcaaaccabbbcbbcadbcbcddaadbcaaabcdbcbcdbbdbdbaddbbbcabbdddcddccdbbbbcadaaabbdcacaaddddcaaccdadcbcccdbdbacaabccccadcabdbdbdabdcadbcddaabdaaaacaacbdbdccbcdbabcdbbbdcdbcdbbdadacbcbcddbbcdcbccacbbbaacddabdbcdddadcaabbbdbbbbaabdadcadadbbaacbdcbdddbddcabbdacadcacdddddcbbbcabacbbaddccbaacabbcbdabadaacadddcbccdadbaaacdcbdcdaadccccbccbddbcbdcacaabcabcadadacabcaccbaddccbdcbbadcadbccddadccaabadbaddbdddcacaabbbccddbaaccadcdababbacdcdaaddabbaccdabbbcccbbccacbbcbbdabaddadcbcadcdcadcbababdcacdbbdbdbdccaacdcccadcbbdabbccabcaacaadddaacdbacbbaadbcddaaaabbaddabbcadcbdbddccaababbdcdbdccbdbcdbccaaccbaadcaabcbbababaabcadcdabaddddaacccccddddbdbbbadbbabbadcccddcdacccbbbbbbcdacdbbddbdacacaabbdbccdbbacbabdadababdadacabbdabbccdcdbbbbababbacbdacabdbcbacacdddcdcdbbcddcdabcbcbacadccdbbbbbbdbabaaacdcaccadaaabdbdbcabdddabbaabbaacbdadacddaadbacdaabdbbbccaababacdddaacaadcaadcddaaddddaadbcabadaadbcadaddcdbdcdadcabbacadccbcbcadcddcaaadbcababdddadacaadcbbaabdadcddabbdbdaadaadddbadcaacddcbabcdaccadcddacbdcdbaabbdcccbcbdaacdacdbcbbdbadcdbdacccabddaaadcabcdadbddcabdaacddddbcacccbccaadcdbbcaacdccdadbcccaddcbbabbdaadbcabcadadacacccaadddddbacaadcdbbbcabdcadaaacabdadcddbaabdcaadaddabbddddbaaddabbaacabbcddddcabacacbbbcdcbadbadcdabaabdddbccbbadccaaddadaccdddbccccadaddcbdaacbabbcbacbbcbdcbbacdcbcdbbacbdbadcbabbaccbddbadbbadadccddcccbbbccdddbdcbdcdbbddddaddaadcbcdbaaabbcbdadcbcdabbacaabacbdabcabbbbcdcbbbbdadaaccdbccbbabbbabaabdacdcbccaabddbabdcdaaccbddbadabbdcdbcccdbaddbbdaababcdababdbbadabcbbcbacbbcdddcccdacbdaaacbdcbddcaabccbaccddccabbcabddacaacccdaabaddcbcaccbaddcbdcdbacbbacaaacadadbbccdccaaabaaadaaccddcdaadbbdcbccaadbaadbaaadaacddbcbdbbabbaddbdbdccdbabaaccaaccbcbaacbcbbdadddadcabbdbddbaccadcccdacabcdccccacdbddaacddcdaabbcdddbaaadcbaacacccabdbccbaacdadddcadcdddcaccacbaadbdaacababadcabcdccdbadcbbaacadcaadabbbccccddcadabdddccccaabccbbbccacacbdcdccadbadbccbbacbaddaaabbacdbcaddcbccaddbbacbbcaccdadaadabbcbbbacdcbddaaddbccabaddbbccccdaddaacbdbaacacaabccacddabcdccbbbbddabbbcdbbbddccaacbacbdbbaaaddbcccadaadcbbdaacdcbbcdcdcddcdadcdabcadaabadccddcdccabbdcdaddaacddabbbbcadbdcbadcadccdccbbddbdacaaacdddbbddddcaaccdcaddabdadbcddaccdacabbdbccbccddcadbddddbcabdcdcbdaddbaaaabbadcdddbcadbdabcccdcdddbdbababbccbabbcddccabddacabacbcaababcdbaadabcbbdcccdaddbbcbabdcdccccccdbddacabaaadccdabbcabbaadaadcdcaaaccbcbaccdadbbbaccddbbcddaccbbcacdaacdabadbbdbdddaddadabbcdcadbccdabcdbddbaaaadcaadabcddbcbbbddbadabccaaadbacadbbbcdaaadbccbabdbdcbbacbcacaacccaabaaacdddcbcbabadabbccdcdcbabcaacbdaabacdbdabaadacbcdacacbddcdbbcabbacbabdcadbcbdbbdcacabccacacacbabcbccdbcaabcddacbabcccabaccadcbbddbdcaaddbbbdaacbcbbadaccbbadadccacbbdbcbadadcddbbaaabbcaacccccacabcdcdcdaadaacbabdacacdabddacaaacbcdabbadbaddcddabacacbbdbabdacadadadcbcbcbddbdacccbccabacdabadbdcadbacacaacadcabbaadadbdbcbabcbcdaaabbcabbcbbbabacdcdaddddaaabcadacccaadbddccbdbadbaabdbcddccccdcadcdbadcdbdccdabbaaadbcdbccbdacdcbcabdaadbddcdabbdbaadccdaacdcaadccbdbaaaabbcccaadbccccbcbbbcddacccccbdbbabddbaacbdccdadcdbcabddbcbabcbbacaaadcaacaacaabacdacdbdaddccbcbddacddbdcdcccdbabaaadacbbdadabdaaabdadbcaacbaadbabaccaccdaacacdaaabdcbaaddcadabdcacddcddbadadcaadbbccabadbaccdcaabbadbaaaaaaadabcddbaaabccdcaacaacacdcbacaaadbbcccbdbcccccdbbabbdbddcadacbcbbacbdcadbcdbcbccdbbbbcbbabcbdcdddcdccdbacdccacddabcdacdacabdccaacbcdaacccbbbbadbdadbdaaccbcbbcbaabbcdbabbbcadcabddcdddaaabddbdbdaadbdbaccdacbbcdbcaddadacbdadabcbcadbcbadcccbddbabdbbadbdcdcdcadddbadcdacbcdbcccaabccbdbbadcbbbabcbcabcaadcdbaaccbcaadbddbcdbaccbcccccbabdaaabddbddadadabbadcbdbbdbcacccbdcbacacaaadbbaddabacabbcdcaddabcbdcbacbacbddbadbbaddccbdaaddbbccdbcdbadddddbccddbddcabddcadbcdacbbbcccdbdacadadaabacdababbcdcadaabcdabbadabcadcdcbbacbbcccbbdcdcdcabaadababdbcbddadbbbbdbabdbdadccbddabcbabdbadbcdacddcbbbbbbabcbdcbacbbbdbacaccdadaacabaccabbdcacadcdaaabbcabdddbcbaaacdacddaaabcdccbcbabbbdabadabccbacaccbcaaccbbbcdbdacbcccdbddcdcabbbcbbbbddabcdacccdcbcbdbaadadccacadcbbdadddcccbacdbcdabbbdbdadddabaacccaabdbadcaabdddbbcdcabdbbbaccbcacbcaadcabddaadaacbadaacdbddbccbddbbbcaaaababcbbdbbbcbbbcbaacbcaabbcdabbcbaadbabbaadacacbcccaaddaabbbcbdbbcbadabacaadabbabbddbcabcbddcdbbdcbdcbdbdddbdacddbddcaaaccbbacaadbaabddaaddadccdadddcdaadbdccdaaacaacccdababbdacaddbddbccbbbcbcbbcaccacaaaaddbcbddbadbcbdcadaabadddcdbbbcbbabccaabccbabdcaadbbbacddabbaadacbcbccdccbaaabbddaddabcbbbcbbdddadaccbccaddbaadbababdbcdbdcdddbcaadcdaaacadaaddaccaabbadabcdbabacdbcddcdcbaccbcbbdbabbbdccddcccdcddbdaacdbdabadbacdabaaaaacaadcddbcacbdccaddcbccdcaadbaccaccbccccbccbabcaaabadddbababcbcadbdaccacaddbbdabbcdabdabdaddbaaabdcdbdbacaaadddaaaadcccbdbcbdccbdcdbbdabaaccacdaccbdbababacdacbadadbaacccbdbcacddbcaacddcabcacbdbbcaababbddbaccbccadcddbbaabbcbcabaacaaacdcaabddbcccbccdabddcbacbcdddbaaddbdccbadaaaaddcbcdbcbababbcaaddabbbdaadbdcbacacddbccbdcaabdcddbbadbddadbaaabdaccdbcadccaabbbadadbbccbcbcadaaabbddbbdcbaadcdbabbbacddbccdaacdadcbbcbabcdbdccbcaccadadccccdddacdcdcaadbddddcaacdccbdabcabdbbdccbccdbbdcbacbdacdaabbbbaadccbabbbdacbcbabaccbbdbdcaabaaaaddcbbcadabbdbaaaacbaaaaccddabddbddbcbbcdcdcadbabadddbdbcbbbaadbcdcbdadadbaabbbaadbbbdcacabadcbbdaaadcabadcbdcdbdbdbcddadbaabcabcaddaadcbabdccaadcddbcdbbddcdabcacbdbabccdbcdbdabbdcdcaddabcaaddcbbccccadbbadbbccaccbaaaccaadaccabaabcbaadabaddbddcdbcdcbdcaaddabdadaddcadcadbbcdddaadadbbbccccbdaddcbabacbabbadaddcbcccabcbabadabdbcaaaabdabcaacdcadddcdbbacdadcdbccbadcdaadbacbdbdaacababaaddccdcababcdbddbabdccddabcbdaaccbcbacbbdbcdbcbcababaddaabbbccddbccabcccdacacbcdabdaadbcdacdabdbbbbbacadcacbccdcacccbaacbbdddbacccbcaaccddbbbaadbaccbbdcaabaccaaddccccaaadccdadadbdbadaabdbdabababdddbbdddacbdccddccaccbcbacdbadcdbdadbcdbbddbbbbbcaccdcbccadabdcdcddabdabcacbddcdadccabbddbcddcaccbabbdabddacddadacaccccddbaddcdbbddbdabdbabaaabcdacaccbacddbbdcbaddbbddddcddaccabddcddbdddaadcdadbabbdbddbcdddccdcbdadcbccbbbbcdaadaadacddccbbccdcdcdababcaaadcdcbbdbdcbaadaddddcccbcabccdbdaacbbacccddbbdcbcbaccaccdbadbaddbdcbbdbcbdabacacdbcabdddcdbdbbdaddaadbdddabdbacbbbabddabbacbbccdbddddbaddaababcdcccadcaccdbcabcbbcaabaacdcbbbaabbdaabadcbdbcbccdaaaccbabdcbcabbadbadcbadaaddddcbdbbdbcddbbaadddaaabdbbcadcbccdbbcdbbdcbdddadbbacccdbdbcaccacbdcbadcbdacbbcadabadcdcbabacbadccdcabcacbcbacccdabddcacddacdacdbcdaabcddcababddbccaddcbaccabcaadbbbacbbbddaccbbadbacacabbbbacbabcaccaccbdcdddbbbcacdacdccdaaacbbabddbbadadcdcbbbaddabbdcabbdcdbbabdcddbbcbbadacadaadbcccdbccdcacddadbacaaadcabbdbbadcaccaaaadbccccbbdbbbabbdccbacbabadaccbaacbcabcdcacccbbcacbcaddcaccbdbddaadbbadcccaabaccbcbdaccaccdccdccbdbdcdaccbabdbabcadaccdcabdadddabdbacddbcabadcdbcbdabaabdbccdaadbddaccdadabacacddbdbddabbdcbcaacdcaddabaccacadbbbcdbbdabbddacddacacdbacaaadbbcaacddacdbddbbcbabcaabdbccdbcadcddbaddcbbcaacbbdccabcbccabadbccdcdbadcccacdbadbbbcccccdcbcdaccdabcdcbbcbdbdbdcdcccadbabbbbccddbdbbdacbddcadbcdacdbbbccbbabbadddcbadddbbcdccabcbdabdbabbccbccadabbdbdddbcaddabbacbbabcacbabbddddbcbaabaaaadccabbcbbabdababbbccbbbbccdccdbbcbdcdaddccadadbdbbbacbcdddbbacacddabccabccbccbccdbbaddbbabbaddcdabdcccacdbbcbbaacdccbdcdcadcaccbbccadabbbbcbbcddcdbabbbccdabbbcdbaccbbbbbbccdacdddacaddaccacddddbddcabbddbdadbdccbcabaaccbbdbadcbbcdcaccbadbbcddbcdbbcadbbadcbccdaaaacdbabbcbcbbcbcdacabbbaadddccaadcbaabbcbbdaaabadbdbccaaacbbacbbabbbbcdadbbcaadbccdabccbdbabcaacdbbbaaacadcdcccbaddaabbcabadbaadbaabbddadadbccdcabdabdaaccdcadcdbacdacbaabcdcacbaddcdcdabacdbbaddacdabcdcbaaccbcccbddbdacbcdbbccbabbdaadddcbdbdcbbcadccadbdacaabdcbaaadddbdbdddbccbaaaadddddaacaadcbddacbdadacbcccbabacbdbdacccdadbbaacbaaacccabdadcabdccadabbabbccaacaacbaaaadacaacaccddddcabdabbbabdaadacccaccdcbacdcbdadcabcbbdccbcadbdddbcdadaaadbcaacbbdbbabcdbdcbdcccaadcaacdcbdcbbcaacddaadabadacababcaaabaacbbadaaccdcdbcbbdbcbabaabccabbbddbccbcdccdabbccdccdadacadaadaadbadccbbacacccbcadbabbcdccdabaadcbbcddaabadcbacbbdbbbcaaabcdaacccacdcccacdacddbdaadacdcbabbddacaacabdbdcdbbabacbabadbdbabccabadacbdadbdbdbccbbbbdabdacbadbbddddcdaacddddccbcadccaccdaaadddacbaacadcabbddacbbbaddcbbaabbbdcbabaccbcacaadbacbaadacdcaaaddbcbdaccdabcbdacaaabbbccdbcabddacababdabcaabbcbccbdabbbbcccbabaaddddcbaddbcabdbcbadaddbccdcabcaacaddbcbaabbabcbaaacccbadccbaabbdaddcabccdadacbbadcdddbaaddcbddbcbcbacccaaccdbddbdbdcbdcbbddabaaaccaaddcbcaccbbaaacbcacabbbabbcaadddccdadbdadccabbaaadacdbccdacacadbdcadbcabccacaabddacdbdbbbabcdbacdccccacbabdbbccdaadadcdabcccdbaddadbabddabddccaaddcdddabcaacaccaddaaadcbdccdcbcccbcccccdadcdbcaabddbccadabcdbddabccdccbbbdcadbadddcabcabcdacaabadcdbbcdbdbbcddddbddadbdabddaadaaaddbcccbacbacbcacbccdbadadbcdaccdacdccccaaabcbcdabcdababbcaccaaadbdbcdacdaacacdadccdcbcccbaadccaddcdcabacbcaaaddabcaabcdcaaadcdcbabbddccbdbacaadbadacbaabbbbabbadccbddbbcbcbacbdabdacadcbdcabcacacabbddbdaddddadddacadcacddbddccbaccbdbdabbddcabdbacadbccdddabbbbadaadbbcbbbbcbaadddbbcdbddccabcddddaabcdbcccdccccbcbcccdbadabbbdbdadcabdabcacbdcdbbdccdcdcdcdbbadacbadabaadccacabaabababcabadddcaabbadbddbbdabadbabaababbcdadbaabbabadbcacbabccdbdadcddccaacbadaaccdadadbdbdbbcbdcacbdacdbbbdabbddccbbcbdddacdccaddbaaabbbcaccbbdaacdadbbbdababdcddadaccaaadbabdaaacbcadbbdabaabbabbaadddacbcbddaaddddcdcaaaadcdbbdbdaaacdadcbdbadbbdbbaccbcadbcdbbadcccbaaccccaabbdcabbbacaccbbdcdccdddcdbbcaabbdcccdbcabdbdabdcaabadddbacaadccddcacadaddcbcddbaaacdcbdaacbdaabcccbbdacddacdcbbbabcddcbbcbbcbacbabcddaccddcadcacbccbcbcccddacaaccbcbbdccacdbdcaddbcdabbadabcdabcbccaaddbcabcdaddbaaadcbddabcbcddadcdcbcaccbdaaaadddaabbbbdaaaabcdacaacdabbbaadaccadacbcacbaadcdabaddcbdaccacbacadabcabcabbdbdbabddabbacabacdbccbcabdacbaabaabbddddcaabddcbdaccbdbbdcaabdaacdcdaacbbadcbcbccccddabbadcdcacabccdcdbacccabdbacbabdbdaabcbbacbabcbddadababddbdbcabadbcdaaababadabcacccddadcacbaddbbdbaadacbccabbcdbdcadcccbcaadaacbdccbaaccddaaaddbddabcacabadbbdbccacabbbccadccaddcbcccccdbbdcbaddcdcbcbdbdacaaddbacacdbbabacbdcdddcaccccabdbcdcadbbadadacdbacccadcddaccbddacadbcaabdbdcaaabccbcccbdbbbccdbdbbdbdabcbdacacacbadcaaaccdacadadabbdaabdaaddadacbbdadaccabbdaaadcaadaddccaadddbbddbaccdbdcacadbabcdbbbdbbaacbcdbbbdbbdacdccbdcdcdacddbadaacbbabcdcadbbaccbdacbadddbbbdcabdacdacadbabdcdddaadddacbcdadbdddbaabdcbdaacddbdcbcaabddaacdbabdacaabbacdaccabcbdddddaaaacbbbcbddbbddccdabbdccccaacdbccdbcddddcaaddadababddcbdcdbbbdbdbabadaabddaacabcdaccdbcbdccbcabcacbabdbdddcbdaddcadcdddbdcdcbbdaacaabcadcaabaaacccbbcabbcaabdccabadcbbdcbcdcccccdcabcdadcdaacdadbbdabaaabccbccaddbdcbbdbbdbbabbdcaadbdbabbaccaccbdbacacdbcbaddbadbaabcbccddbdcddddacbbaddabccddbcccabaabbcababcbacabbadccddcdbcdbdcdbbdbcdcaddcbadcadccdccacdcbbabbcbdccbdccbbccbcddbbcdadbbbaaddbacdcabcacadcdcbddadcdcdbbaabdacccacddcddcbdbdbccbdbaaabadaacaaabdacdaacdbbaddcaaccbbccddbddaaadbdcbbabcddcabccdcacddddccacbabbdaaacbccdacdacdaccccdadacbccdcdbbddababdaaadddacbbdbcaabdccdacccdabcbdabdbaaaaacddaaaddabcccdabbbbbbcddaccbcdbbbdbccddcdcbbdabadbddbbcbbbcdbbbbbbbbcdbccaadaadbccacccccdbbbcadcaabbcbadcacbbcacbdccbccbccdbdbbdacdbdbccabbabddaccbbbbdbaddcbbdccbdadacadaddabaadbcbacbbdcbaddddcdbbdcaccdbcacbbbdaaaccbcbbadaabacbaddaccadbcbadbcdcdccbcbaaaddacbccbdaddbdbbdcaabbdcddcddbaaabcaadaadbddddccdcdbadddbddbabcbcaaabbdbacbacdbbbcdcbabdabbabbcdcacbbbccdaacccabcdbabdcdaabbdbcaadacabcabcdddaadabcdcbbadadaaccbddcadcccccbccbdcdccbcaadcbcadbbbdcdbbdbbabaabbaacaddbcaabcbabadcaaccabbbbcadaccddccbbcbcdcdbadbcdadcdcbbddbdacccacdcaabdabcbccabdcdbabbcdbbabbdbaddbccbddacacdcaabaaddcdcaabcabacabdcbadddddaddadbbdbdcabccbadcabaccdaddcabadbccababdcbcdcddaadcbddcaadbaacdcacdbaadbadddadababbaabcccbcdacdadccbdbcadabdbbcadcaccaccddabbccadcccdcbbccadcbcdbacdbcaacaabcdddabadddddcabdacdcbcdcdbcbcbcccaddcbcbaabacbbbbbcacddcaccaaabaddcaaddccbadbcdadadcaacbdcabaccadaacacadddcaabdaacbcbcbbbcdccbabcddaddccaccaddbcbcaabdaadabbadadbcddccbcccdacabdcdaacccaddbdcdacbbbabbabbbbabcbdcabbdabcdcbcaabcaabdcdadadbdbbdcbacccdadbcccdbaabadcbaaacaacabbddadadcaabbaaccbdbbcbbbbddcdccadcabadaccbdbdcdcbacabcddabdccdaddbcbaadcabbcccdbcccbdcabbabdabaddadcbbadccdaddadbcccbbdbbccabacdadcbaaaabcabbccbacacacbdbccaacbbcbaccbabbcaacabdbdacaddddbabacccabcaddbcaababdbddcddcdcbcabdbabaadbbaaaaddaacbdccadcbdddadbabbcbbddbbcdadbddbcbbdccbbcbadbbccaaccadbabbbdbdcbddddcdbcdaddbcdcdbbbbaccbadcdbdbdabcadddddaccbcbdababadcdbababbdbddbbdccbdbddccbacdacaacaccaaaddccddbdcaababddaccbcadaddbbaaadbdbbdabdcaabababccdadbdbbcddcadaabbaaddccccbccddcbbdaacdcbabdcddbaabbaabbcddbcabadddcdcbcdcadbdcbbbbcbbccaddbacacdddbbbadddbaaadbaabddadbbaabbddaaabdaaaacadaddbbdbbbdcbbacbbaddbaddcdabddbaadcbcadcadabbbddaccaaadcbbbcccdccadddccdabdcadbacbdadbbdbdcbdbabbdbabccbadcaabdabacddbdcbcccccaabdcdacddbbbbcdcadcadbacccbcdddcbccacdccacbddacccdacabcadadabbaadddcaaacdccbaadadacadbbadddccadccbdaaacddbdbdddacdcadbdddabdaaadccadcabababdbaaccbcabcdbadbacddabbdbabcababababccbcaaddddcdcdaddadaabaacbdcbcdbcbdcddbccadbadabcddbabdabbcdadddccbdbcbccdabcdddadbbaabccdaaadaacddbcbaadacdbdbccdcbccdccabbadcbccccadbaddadabbccdbabcabaabaaccbdcdadccbacaacdccaadadadbccaccabdcdaccbbdadaaaddaaaacdccbacbcdabdddabbaaacbaddbbbbacdcbdcccacacbbddbccbaaaadacbccdcaabbcababadbcccbbaadbdbdbdddbaacdcdaaaabcacdddcbdbccacabdcbcdadadbbdccaaaabcbbbaaaadacbabcacacdbbdddcbcadaacbbbcbbbabbdbccbabbaaaaccdccdadaaacacbddcdddbaaddbdbadbbcacddacddbacbacbbbcbacdccbcabaacaacaadcdcdbbcbadbbbbaacbaaaaabbbaaddaccddbabdccccdbaadddbbdbadabddbcbdcccaddbccccaaaadbabddbaddcddacabbccddddaaacaadbacbbddaddaccdcddcadbcddaccbabbcbabaaabcdcacababcbdacdadbbaccccacbcaddabccbacabaabdabadcbadbaacddadadbddbadadbcbdabdaabdbccadbbbacacabaccbddaaabcddbabdcdbcacccaaaccabacacdcbbddcbcadddbcddddacdaacccdcccbcbdacaaccaacbbabbcddbbbbccabbdbdaabbddadaccabcbbadacabcbcbbbbbbdabbdbdbbadbbbcbbbccdabbabdbbcdcadbaadccabcdddccbacddabcbadabdcbcabaccabaadbabddcbdddacbadbcbcadcbdcbadabbdccaacddadddbbacbddaddcacbabbbdccbcaccccdbcbabdccdacdccbcdabccdcadccaadadababadbcdabbbabccdddcaadcacdbcccadacdbaaacabdbbaabacadaabbbdccbabccacdadabdaabadabdcbcabbbbcdddbbdbdcbcbdbbcaabbcdbdbadabdcadadadabcbdcabddacdcabacabbbbacadbadabcdabdccddbabcbcadbaacccbbcbdbaabccabbdccadbcbcddddbddbbacdcdbababccddccbbacdbddabaddddcbccddacaadbdcdddccabddaccabcbcacccdccabcccbdadcaabaddacabadacacaaaabdcaaacbaabddbcbbcddacabdddacbcbacbdbcadcddcdbadbabcbdbddcabccbdabddabaaccbbbabbdbbcabdcadbcddcaacadcbbccbddcbdbdcbdacaabdaccbacddacccdabdddbdddcccdbccbdcdbcadbadddcaacdadacbbacbdbdbcacabdccbbaacacdbbadaadaabdbbcdddcbbdddaaababdacbbababdbbbdcacadcabccbaccdbccdbdadacbbdbdcbdbabbacccbaccdbccdcbbcacacddbdabbdaadacbdcdadacbcdcbdaccadccbabbddddcaccccabcaccdbbbbccbdccacbabcbbcdbdaccbaabbadcabcabbacadbaddbaaabcaadadbdbdbcbbdadcbccadccbbccdcbbbddbbabbdabcbccdddbbddddbbbdbdbcbccdcdbdbbaacdbdadbcababadaabbdcdddabbbcddcadadabdbdcabbadddcdcbcadccccbcbbddcbdbdbabbaabbacccbcbdaaaabdabdbacccbacabbdbbcdaacdcbcacdbdabcaaccdaccaabacacacccbbcdaddbadaddcbdaaaacbddabdadddddbbddddabbddbdaccccabdbbbbadadbbdccabbbcabbcbccbabbbcbbbcdcdabbaddcdabbdcadbccabdbdadbbdccbddcaadacbaabccdddccacbddbbcdcdbddbccdbddcadababddcdbdcdaabaccddbbcaaabddbddbaddacdddabacbdcdbbcbacdbddbddddbaccccccbcddadbbcaaabadacccccabddbaabdabcaaddadbabbccadcdbbccddccbdbaabbddaddbdbcdacdaabbadcbadcadbdcdcbccaabaabbbdbbdcdaacabcbccdbcdabcdddacdbcbbadddcddcadccbaabacbcddcabccdbbddbcbbabbcccbdbccdbdbacbcbcabbbbcabaaaaacbacbbbddbbccccadcadaacbaadacbabcdbcbbbcbdddaaabaccdcdcdaaaabcbaddcabbabddbacbaabbddddaadbdabaadbadcbbbabbdbdccbcdbababdcbddbadbaabbcdaabdbddcccbccacabbbdbbaacccddaabdcabcadbaaccbcbbdbccdbcccbbacbddbadaaacacacdaacaabbdcacbbcdcacbbadcdcdddcbbdcdabbbadbbcadddabbadbadcccacabcddccaabacbaabbddaadbbcababcadbdbaccacbdacabbabadabadabdacdabacbbddbbacabddcccabdddcdaaccbabbcacbbcddadabacbcccababaabcacdddaacabbddcbcadbdcacbbaaabcbbbcdaaaddadabaadbccbababbcbadddcaccbdbacaabbcdbaccacbadcdcddabcccdabbcacddbddcdcabdacbdbaaacbadccabcaadabcdaaabcbcaacbbaacbdbdccaccdcaacbdbaddadbacdddcbdaccdabccbdbbaacbbaddcabaddacbcccbddacacdbcbcdcbdddaabcbdabccdabcabbdddaadbbcacdabaaacbccccaabdaadbbdddacbbcdcdbdaabbcaabddaccccbdcaccbdadcccbabacbbddaaabadccbbabaabcdbacaabadabdddddbbacbcacacbdcdbcaaccdaababccbbdacccaddbcccadbbccadaacacacbcbddcdaccddccabbbacddaccddaacbabadcabbacabbcdbddddabaaacdbcdbacbbaabbcacdbccdbddccaaddbaacdbcaaaddacccaabdcdabaaadbcbbddacabcdacacdcbcdbbccbbcaabbaacdcbcbccdcdccdadcdadabcbaaaddbddbcbdbdbbcdacdbacdbacaacddbbaacacdcdacccccaccbadcacdaadcdbbcadaccadbdbdcdabcaacacddadbcdacdcadcabccbabbdaabccaddddacaaacdccbbbccdabbddccbdbdcbaccaacadddddabadcaadbdddddccaaadaadcdacbbbcccccbadbdacdbdcdbaddbbabaccababbbdcbdddbbbbcbdcbbddcaaccccdcacdbddadcccdabcbacddcbdccccdcdcccdaccbbcdbbabdcccbdadadbadbbbcbdabcdccccbacbcbdbbddbccbcbdbabbddadaddabddbaaacadbdabbcaacadccadcdbaccdcccacdbbbddbabdcacdbacbadaddccbadabcbbdcdbbacdcbdcbaaaaacaaddaccbbdaddcdbdaaccbccccbacbcacbdcddacdaacbbbdbabbdbaaccbcdaacbcddbbcaccadaaaccdaaadaaadadadcdadacaccbbabbdbdcdacacdcacaadddaadacbabbdcddacacdbabbdddccddcbcddcdadbdcaccabacddaccddabacadaaacdbbdcbaacdcddabcdadcddbbcddbbcdabaccbbbdccbcdcbcdbacbbdaacddbddddabcbccddcacaaddcbcddacacaaaadddabcdcbbdabccbbccacdbabaacccbbabdcbcccdcbcbbcbbddaccbacdaddccaddcadbbdbcabbcaacccacbabccacbbaaabdcbccabddcadaddccdacddddabdaabbdcdabbbcdabababaaacbabbdcaabcaabddbcaabbaccacdacdcdaddcbbdbccdbdcaabddbdccdbcdbccacbacbcacdcadbaaabcdcddbaccdacbddcdaaacadaaaabdadcaadbdabdbbbccacdacccabcdddaccccbcddadcababcadbdabdccbcccdcadabcbcabdcddbaacccabcabddadacacbabcbdccddcbcccabbcdcaabadadbcbabacbcadbcddadbabdadcacaabdbcccbdcbddbaadabcdddbcbbbaabbcddcbbcddbbcdbbdccbccaaadcaacdbcdaabddacaabcdbddbbbbadbddbdbcbccdbbbbaaaabcdcbccdcddcadcbdbcbccadbbcbaccbadadbcaadaaaddcbdcbaadcdddacbababcdaaacaaadaacccaacdbbcabbdbacabacdcdadcdcbaccdacdcaddcddbbdaacdcdabaadcaccbcbdddcccaccdabbadbddbdcadccdcccadcbcaabbcbbbdbcabbcdbcabadcaaaddbaaaabaadbcdcbadcdcadbdaadabdbccdabadbcbbaaddaddcdbdcddadbdcdaccaabcabadbbbacaadaadaadbabbbbabcbbdbbbbaabcdbabbaacddcaaddcbccaaacbddddaccaabbcbaddbcdcbabdacbbcdcbbdadcaccabbcabdcbccbcbaaabcabdcdcadcdcacacddaaaabddaccdcdcaaacdddadccbdaccbaccdbdccdddcbcaacaadabcddaddbddbddbbddaaddcbacdccbdbcddaabbcdbcdcadddbdbbbbccdbccdbdccbbadbcddddadabcaacbcadaccdaaabacccbabcbcbbbadcbddcdcbcbbcbccadcbdddbdbaadcadbddbbbccbdcdbacdaaaddbbdabcbbbbdaaabbbbabccacddbdababddabaaaccdaadaccdacacaaabcaadcaadabcaccdadabaccbdaddcbccbbdbdcbbdaddababccbdbbbcdcddccadacbacbcdbdbaadabdabdbcdacbbddbbbcbabbdacdddacdbacbbddcbcbdababbdbdddbababbbbabddaaadadaadbaccdbacbdbbbddbcaaddadbdcbdcbbdbdccadacbddcabababaaddabaadaabcbdcddbcdbaccccacbbccacbcaababaadcdbdabdbabcbcadbcaaadcdbbcbbdbcaacbcccbcbcbdaaadabddaddbcabdcddaabbdddbdaddbdddbcacbbdaaccbaaacbacaddaaabcbcbaadacaddcdbcdcdcddabaabcadabdccbbbabdccdbaacddbdadadacccbbbcbdadcdcbaaddbbadccbadddaccadbadccdbdaccbcdabbcaababacbaaaccbacbbadccabcbaacabccdcccbabaddbdacddcbdddadcccacbcacbadcaabbdbdbaacdcacbacbdbbbdbdbadacddddcbdcbbdbbcbacdbabbdcbabbacaccdcaacaccdcbbcaaccbcaaabdabccdaccccadbddabaaddccbcdccbcddbbbcaddacabcddbacdaabddccadaccdccbdbacdddabaaabaccdccaccdcdbbbddadaaccacbaaddbddcacbcddcddaaccaccbdcccdcaacbaccabdcdcdbbbccddacabacbaabddabcccdbcddbdbadacdbbacaaadabacbdadbbbaaaddccdddbbaddabbdbababccdabdccddbcdbcabbbaccdadbbcdbdcbcbcaacdaadacaccdbababdaabaaaaaadabbababaddcacbaadcaacaabbabcaaabcdcacababacdbcbabacdabddddadbabbacabadcbcbcdadadbddacddcdbccbbcbaddccdadcccaabcadabdabacbbdcaacdbabddcbacadaaaccddccacbaccbdccbdbbcbababaacddddcadbadbdbdccbabdcbacdcddcdaaababcbcbacbdccadaaddaddcccbdddaabacabaaccabbacdaabdddccbcbaaacadaadcddbdbabaadbdbaabdcdcacdcdcdadabbcddadcbacbccacbddabaabacbcbaddcdacbabdcdbadabadccaabbbdbdcdaaacadddbbabacddadadacaaabbcddabababbdbcacadccaacbcbcccdabaddcdacaacacbddbdddbabaacbcddbabbacbbbdaccccbdbdbbadcbdbdbaabcbcddbbcbaddcdacdadaccddccaaaabdabbbaddacbaaacddbcbcbdccabdaccadcbcdbcabdaaabbccaaddaababccdbdddadadbbdcabccaabbbdddaadcaccccbdacadaccbbdccabccdaacdbacaacadcabbdaaddabdccbccaacddbaacccaadbbdbdadcababbcdbabaabdaadbddcccacddbabcccbabcbaaadacbabbacbacbbbabbdaadccbcbadbdadaaccbcbaaddddcadcadcbdddddbacdaabcacbcabadbbccccaddabacaadcabdbbaddddadaaddbdbbbabcbaadccaaabdabcdbbdaccabdcccaabccbcdcdcdcadbcdbdbcaabcdbbbdcbbdbaaabaaabbaabcddbaacbcbacacbbcbbccaacdaddbbbbadcadbbdbbcaaaadabadabbacbbbabcabdddbbabbcbccaaabadaccdddcacdbcadbdcaccdaababdcbbcbabcbdcccdcbbccdccddaaaabbbaddbcadacbacbcacacddcdcaaabacdbccbdabdcacadadbacddcbbdbdcaaadcadbddbbacbcacdcbbaaaadabddbaacdccbddbbbadbbbddbdbbdddacccaababaaccdbbacbccdddcbdcdaddcaadbcbabdbcaadacbbbcdccadbcbabbdbadbbdacdabbdbcddbccbbddbaacbccabbabdcdabcaadbcbccdccccdbcddadcdbddcdbdcbacbaabaccaabaaccddddbbacabaccbcbdcabaccddddaddcacbacabadbdcdadbbccdcccdadcddbadaccccdccabdcacbadcdcdbaaaacbdadbdcababbaaadbdcdcdabdacbbaadacbdabcaacdcbcccadadadaccccccabdbccadbacdbdbbbcabbabbbdcdbabbbabdaccaddacbadcaabbccaaaadcccbadbcaddccccbadbccdbcddcdcbadddddadbccccdbabdbcbbdcddbcabbdcdcadbadcbddaaabccbbabbdddabdcbccdbaaccbcabdbadccbcacdcdbbcdcddbcbaaacbdabdadacadbccaaaacccbbbddcacdcdbdacbdabdabccdddacbdabdddadddccdbaadaaacabdaabaacdbdaadbbcadbcbaccbdddacadabaadcbccabbbdaddacdabacdcdccdcbcdcaccbbbcbadcbccacaabbcacababcdabccbddcbcbabcccbcccacdadcbaacddaddbbddaaacdbbbbaacbabcbbacbdbdccbadbabdccdddccbbbccadabddddacdabbbbcacdcdbdccccdadacabcabbaabadabaabdcbccabccdddcbdaddcabbaccacddbdbbdacdbbaccbbcaabcbaccdbdacbbdacbdcacbbcccaccdaddbabcdcdabaabbaaabacdbdadcbcabccbbbcbddabcdbdcaaaddccdddbadbbcbcdbcddcdcdadcabdadbdbbcadabbbdabccacaaacbaddcabbdbcccbddbbdddbcaccaccadcbdcacddacbcbbadddccbaababbcbbddbadacbadabccdbddbbaccddbbdbaddddaadcdaabbbadccbdbdbadbbdabcdcdcccaabbaacccadcdbccdbdccccababdddbabbababbbadddcbddadaadaabbaaaaccacbabacaccdacdbddcbaddaabbcdaccadbcabbaccccadaadbacadcacbabdbacbabbcdbddcdbddbcdbcdaacdddadcdcbacbdddddadbbcbacdbbbcadacccdcbccbdbcbcdcabdcbdabaddacacabaccadababbccadcccabdbcacabdbbbaabbbccaccbbadaacdcbdcbbaacccddcbcbaabbcababcbccdccbccdcbdddbabddccabaddacbabccbaddbccbddabbbdcdcadaddbbccabbcbbddbccbbaacadabdbccadbabddccadccbbdbdbbbdbacbcaabbbbacdcccccccddbcaadcdddcbccbcdacdddabcdbcadbcddcbaddbccdcdcadcccaaacdaabbdcbbbabcdabcabbcdbbcdbbdababdcbaadbccbaaddabdbccdaaaccddbabcdadddadbbcbadabdadcccdaabaddccadccabdbccdcdbbbbabbdbbdabadaabcaaaaacdcccbdccbcaabdcdbdacbadccaaabddbcacaccdadbbdadbbbcadbaaaacdccdcabbaaddcabadcbbdaddbaaabaccbaadcdcbacaadcdcbddbdaddacdbccacbcadcbbbcbaadbcaccdadccaabaabccbcbcabacddbbaadadbbabcaacddcaaccdacddaabccadadcbddabadabbacbadcddcbadcaccddbbadacaaaadacadcdbcdabdbacacccdddadcbddbacbcddaaddcdaabadbcacaaccbadcacbcdaaacdabbcdbacbdaddaddbddbcddcbdccbcbbaddcccdccdbbdaddbcaadbaaccdbadcabbcacddaabbcdcbcdbadabbdbbadbdbdccbabbccadacbcdcbdbcbcbbaccdbccababdacccbadcbcbadadcdcbacdddbabbcaacdaddadbadcdbdbbcaaddcaacbbdddadcdbdbbadadbabcddbcddbdcdaccbcadaadcaccbadddbcbdbccbcdcacabcccbdcabccdbdabbcbbdaababccaccbaabacacddcaadcbacbacabcadbcaacaddacabdbbcdadcddddbaacbbdbccaaccbababbbccdadbadcadbaadaccacabbcbadaaabbdccbcdcabcbaccbdadddbaadaacbdabbdcdaadcbabdcbbbabbbbcdcaccddccddcaacccdcdadbabadcdcddcbdbabbadabaacbdcbcccdcdadcdbdabbacadcbdcadbababcaadbcaaddbbaaccbbcdcdccdbbbdddaabdbabcaddacadcbacccacbbbdcbadcdabcdcdbaccacacabccddbbadaaadcbbcdcabdcbadcaabbdddbcbbbdcbbdaadaaacddbcbacbadaddccbdcccccddbbcbadabbaccddadadcaabbbbcdcdcabccadbddcabababbbbabdadaccadcacdaacbdababcababadbccdddbabbabcaadcddbdbcccddadabccccabbcabdbdacaddccbbccbdbdbbddbacdaccbbaaddcaccacdbcaccabbaddacaddddbdcaddabacccaaccdaabcccbdddaabbabbcbddcacdacdcbcabbadacdcdacbacbcaadbcccdaadcdcdadaabbdbadbbdccdadbacaababdbdaaabddccadcbabbaadaccaaccdacdbdaadababccdcbbabcdadbbcaaadccdcbabdcdacaaadccbddaaaabadacdccdacbbcbdcdcdcdcaddcbbadabbbdbabcaaaadabbcccbdadbdabccddbdcaacbbddadadcabddadbdccdadcbdadcbcdabdbadcbdbbcacacccbccaccdbacacadbdcdccbbcdccccbdacbdaadcdaacdddcbbcababcbddbcaaddcbcbabdbaddaaddacdbdbbbcbcdaadbdbbdccbdadcccdabadaabbabcacdcacbaaccdddbaacdadacccddbdbbccbccdcabcbaadaddcaaaadccdbdacdabaaacddccbbdddaddcccabcaadcacadcdbadddaacbbcabdcdabadacdbcbbbcabaccdcbbababacbbddddbbadddabbccdccdbbadbcaddccbabcbbadbdbbdddccddcccbcdcbdbcbdcaddddcccbdbdcdabccdcccbcadccbbadadaccccddccddaddbdcbcdcdcbbbbababdbbdcdccabbbcadbbacbdadccccadbabbcbdabccbdcadddadadacdacacbadbdcbbdcdbaccbabccacccdbcdbccbdddbbbdaacbcbcdcbcdbaadadcbbadaddabbcaadcbcbadcaadccabddcbddacbbbcbdcacbaaacbdcbdbdbabbcbacadbbdbdbaddbabaacbabbbccddbdaadadbdbaddadadddcbaaddacdadadcddabbabbcbcbcabcaddcacadccbacdabdcaadccddbbdbbcaabcabbdddbaadabbcabddacaddcacdacddbcdcababcaddcadaacbbabcbdddcddbadccdaadcadddadbddcacacbcbdcdddaacabbccddccbddccdbadaaccdcdbbdaacbdddddadaabcacaabaddbccdcbacccddabdbccdcaabbadcdcbdcadababbbbbcadcbddbbdcccaccdcaccbddcbbddccdcdbabdddcdcacdbcbaadbabaadddadbadbbbbdbbaddbcabdaacbaaadddbcaadaaccdbbbbbdbdbbacdaabbdcbcbcbdcbcacaccaacaddcbcacacaccaaaaccbcdacacddcdbabcccdcbbbdacbbadbdadbabdccdaaccacdcdacbcccaccdbcdcddcaacaacabdcdccbbbdacccddcdaddcadaadacbccdbacadbddbbddacdbccdababccdccbbccaadbadbabaabaababadbabdacdcbcbdbdbcddcbabdaabbdcbddaddbccbdcabccbaabaddacacababaabaabbbbabadbaabbdbddbabbbacadbbaaaaaabdbacdbdbdbadabadabdcaadbbddcbccdcccdadbdabacbddcdbdbdcdbdaaaaaddddcadcbcdaaaacaddcccabaddcddcbcbbaaacadbaddabadabdaccacdbdabbddaacdbadadcdcdbdbacdaadaddadccddbccbcadacbbbccdbcabaccddababadcadbdccddbdbdaadaaacaaaccdccdccdaccadaabbcbdcdaacabddaaddbcababadbddabccadbcdddddcbdbdcbbdbadbadbddbdabdcbdbaccdabcacabbddccdccabacadaccccbcbbbbbabcaaaaddadcdbabbbbcbdacdcbcdbcccccdadbbbbbacdbcdbcdacbccacccbbcbacdddacbcdcdbccadaaadcccabbcdbddccccdacbacbcddadaaadadddacdbbdcbadccddcdcabbdccbbbabbaccabadbbdccbdcccbdacbbacccbbbccbbcddabdacdbabdbacaaabbaacbcaacadcbdbabccddacaacacabadadbcbaaacdadaccbdcdaaaacddbadabbbcabccdabccccaaabadbbcbccdcbdaaabbcacacdaabcacccbdacbccbdddacdccadaacaadaacddbbdbbcaadbccadcbbadabdadbbaaabaccbdabbddcdccabcdbcddaccabbadddcbaccccbdddbbdbadcaccdbdcbaabadaabbadcccbbbcdacbbbaadbdabaaacadacadbabcabbbdacdacddbbdcbdbddddbccbaccbbcaaaddbbdcdabadaaaddbdbcaababacaaadaaaacabacacbabcddcbadacbbbdacabaddbdbdbccaddcacdbdbdddaddbbddaabdcdadccacdcadbdbcaaddcabbbdabdcacadbadabdbbbaabacbcddcdbddabbcdbbddaddadabdcdddddddccdddbbbcbdcbbdbbddacbcaddbadabcadaacacccdcbcbccdbbaddcdacbccccabbdaabcbbadabdccddaabaabaaaccbdcccaaccabdcbaacbccbadcbadddcaabddcaddbdcdabaaddaaddaaccbdacdbcabcadcbcbcdccddbccdddcaaddddccadbbdadababdddcdddacadcdcccbddaaaabbabccdaadcaadaddddabcaddadcbabccdabaccabdddcccdbbccaadacddaabadcaaaaabbadaddadbdcacdcccdaddcbaabcbbcbdbabdddcddacdcdcdbcacdddcbdcddcbbbdcccbadacaabaadddddacbbacabaaaacaaccaaacdabdacbcbbaacdbbdadccbcbdcbcbdcccdddcacbdbdaabadccaadcbaccccacacbcccbcdcaaacbbadcdccadaabbcbdbdacbbbaddbbaadccddbdbcbcdddaabdabcaaddabbdcdcaddcdcdccdbcdadcabdbdbdbbbbccdbdcacbacbaacbbbddbaabbcbbbdccbccddbbaccbdaddcabbabbabdbcdcdadccdccdbcbbdadcddacadddacbbcbddacadaddddadbbaaddacaccbabcadabacaaaadadddadddcbcbdbaabbbaadabbccdbaadbbbddadbdccbaacaaaadabaacaababaadacddddcabbddcbabddbabdbbacdacacadddbccaccbcadcddcadbcacdadabbdbddadabaddbcdddcccddcacbcdcbadcdcdcbbaabdbdcadcccdbcdccbcdaaccaaaadadbbacdaabdcdbbcbbcbdbaadbdcbcadbddcbddbdccdacccdccbaadbdbcaaaabccaaabbbdddcdacbabdbcbbdaaacaccbccdabcabadaaabacbbbbdbdccadccbccbcbccdbdcacacaabddbddbaccaadbacbdadbaddcccaabbcbccacbcadbdabddadadabbbbcdbbbdabdbbdcaadddaccbdadbbcdabbbbcddaaabcbdddaadcbdaadcbddcddbacbaabcaadbbddbcacdcabbdcdacbcddbadcccbcdbdcbacdaadcccaddbbabddaadbaacaddbabbbabdbaadcbbcdcbabbcccbdbccdacccccadbdbbcbdabbbaaabddaaccbdaccbacacbaabbacdbcadcbcddcabcabbcadbaaadbddcccadccabdbabddbababcbbdaabadaaabadbdccbdccdadaccbaccaacdabccdcaacabccddddcadaaabcbabacccccdaacdaacbcccdbbbddabcdccacacdcaadbccabbcadadabdcaccccbbbbbdaaddddacabaaadcaddcbbccdccdcbadcbacdaabdbcaadadabdbdacdcdbdcaabcdcdbccddcddbccabbaacdbccdcdaadbcaccbdcdcbaacdbbbabbbcaacdaccadcbdbdccaddaddccabcdbbdbbacdacbcbdcdbddccdccbbcabcdaaaadcadccddcaaabdccdabacdccbdaaadcbacdacbddddcabddccdcbdcacbbaabdacdbbcadbcacadbcadcccabdcdaabaadbaccbbdbcddaaaabdcccbdaccaacbadadcadcaabcdbbacddcbcabcbcbdabcbbadbbaaabacdddbdcbabdbcaabdccbcdcaabadaacabcdddaaabadbcbdcbacbbbbbadddbaaaccdaccacbbdaadddabcbccaaabcaababdabbabcaacbddcbcbbaaddddcccadadbdcadadadddaadaaadabdcabcaadcccaabbcaccdaabbababdadabdbcdcacaccabcadabbccccacbddaddbaaaccbcccaaacbaccabbbbddbaaaccdacaaddcdcddbdddddacacccbbacaccbabdbbbdadcddbacccbbbcdcbbacabbdbadccbdcdabbacbabaababaadddccdbbbbaaccaccbacbbcbabcabdbddadcdccdacdcdbcddacccdcccdcdbbbcadadbbbbbbdbbbbbdcdbaccdbddddcbdcbbbddbbaadccccdbbbcbdbdaddbcbacdbdbdaacbbcaabbdacddbdabbadaadcdcadcabbcacdddacdadbcddbbabccaddcabcbcdadbaabcbadbcabbacaaacbcdcbdcdbcaacacdccdccccbacaacccacdcdbdacaabacccbdabccbccbbddcdbabdadadadddaaacdccacadacdbcadaacaddccdcbdadababacccaabcdddbdaaacddaadccdbddcdcbabdadcddadadcdbaccdcdabdabbcabccdbdbccacaadcddbdcbcccccdcacaacdbbdbcadaadcdddcbbcdbdbccdcbaaabcaaacbbdcacbaadbbdacdadaaaacabcddbbabbcaacbbbbdbbadccbddbcbbbbcbddaddacaabacbdbcbdddcbaacbaccbacdbdbcdadcabcbbbabbcadbddabacacadabbcdacdcbadabbcbccbcdbddcaadbdbbcbcbadadddaacdbaabacbbdcabdadddbcabdcdaacacadadcbaadbbadccbdcccbaaaabbdbccadaadabddbcbaddcddadcbbdabddccacdbbdccdabbacaaaabadcabccbdbabcaaddaacaddbdabddbcadddbdcacbbdcaacbcdccacbaacdcabaabcdcbcadbabbadaacddaaaacabbacdcabbddbbbbdcadccacbbaddcaababdacadacccbcbdaddcbaddbabbadabcadaadccbaddbbdbdaddbddbbadccdadcdabcdaccacbccacdacbdcadccabcacbbbdbbbbccabacbdcaaaacdcaaccdddbdcbcdabcdcadccdccaabdabcccbdddcdaaaddaabcbdccbabcccbcbabcaaaccbabdcaddccdcdbcabbdccacbcdcacbdcdcaccabccdcacdccbccccbabaabbdbaaccabdbcbabdacaaabcbaabadccdcdddcdabccdddcaabbcdadaacadcdccddddcaddbcaddbcbbbbcbaadaccaabbbdbbababaccbbddaabcdcaddccddadaaaccbcaddabbdbdddccdbcccdcadabaacdddcbddbcdbaabbabaddcbdbabcadbbcdacacdddbddaaddcaadcdbbbdadbbcbccbccadacbbdcdacdddaddcdcccacdcdcdbdbaccccacbdaadbcbdbcaddbdbcacdcdbbdcddabdcbacadcbadcdadcadbbcccaccaddadbbbdcccaccdacbacadcccbccdaccbaabdcbddbcbbcbcababcabcdcadabacbacdbcccacdccbdbabdcbcadcaddbddbdabadaadacabddbcdbccbccadcacbcaabaddcbccdbbdbcabcccdbbbbaddbbdbaadddbbddadddbacbaddbccddccbabacabcaaabcbbcabdaabccddbbacadddbddccacbbaddcbaccacdcbacadaccaddaadbccdadbdbbacbadbdabdcaadaabbdbcbbbdcabcacdbaadcddddcbcadbbaddbdcaaddccadaadaabddacccbadbcdadadadcadaaabcbbdadbabdbbbddbcaadccdadbaacddddaacbbabdbaaadbacdddccaacdcbaddcdbbccacbcbaadbdcdacdacadddbbcdcaacdaaabbbdbdcbaacabdcbbdacacdadbbbabaaaddcadbbcbcaadacdcaadddddcabcabdcacbbbdcbabcadaadabbadcabaabbcdddbbbaaccaddadbddbdcbacabdcbaccabdbcdbdaadddbacbaaaddbbcbcadcadadbcabadcacccabaacbccaababcddcbbcdcaaddaadbcbabbcbadbbdacdcbaabbccaacbdcdcbdabbcbcdcacaddadbdaddabadbddcadccbabcdbdadcccdbcbcdcaabdccccacabccdcdaadaacbdbcdbcaacddcbbaadbbcdbcbdbdabbdcdcabbcdacddbbcababadabdaaababcbaabaddbdccacadadcbaacabbaaacabccabddbabdbadcbabbbbbaadacaadadcbaddccacbddcaaaaccaccacbcacdaccddabbacdadbaabbcadbababbcbdcbcabbdacabdadccccaaddcbcabccbacccdabddaaadababadcdacdddaacacabddddbdacacccdbddcbdacccaadacbaacbbaabbdcbaaadcabddaccbcdddabbdcbaacddadcbaaaccdaadbabbcbacdaababcdbaadadbdcaaadacbabbbccbcaccbabdccabaabbdbdbaadcbcacbcbbccbcbacbdbdbbbacbcdcbbbdddbbbcdaddbdcbadbabbbdbbbaddbcdadcacbbabcbdcddbddddbdddccbddbacbcacbabbcaaadcbcccbbbcbdaadadacbcbdadcdaadcbccdabcbcddbcdddcccadcadbcdcabdcccbbabbcccadbdcbdacadcadddaccbaccdbbbccdbddbbadccddccdbacdbbbaddaccbbcbbbcbaaadccccdddabaabdccccadccbcadcbbbcdaababbbaacadaabdbbbababddbbbbbccaaccbcccbcbddcdcbbcdaadccdadaccbbcdabadbadbccdadabddccababdbdabcbbbabccdacaaccdcdcbcabdcdccdbdbccabbdbcdcbcdcbbbdbccaaacbcdddccaddbcdcacadbcabbcbbacacadcccbbbbccdbbadadbcacbcbddabbcbbddacbdccbdaacbaccbdcaaacdbabdcbcbadcddcdbddccaadbdcbaabadbdcabdccaabacbddcbdbabcbabcbbdcddadcbdcbdbabccdccbbabddaddbccaabbcadbbaabcdbdadbccbcadcacabdbcbcacbbacccbabaadabcdbcdbcddcccdbcbbacaddadccbddaabdbbddcacbdadbbacaddbddcbdcaadacddaddcbbadccdcaadabbbccdcbaddcabbbacdcbcdbbbbdcacbcdacacdddbcdddadaccacdbdccccbdbbcaaabccbbacdaaadcdadbcacbcabcdccbcaaddccabdaadcaabcddddadaccbccbbbdabaaabcdcccdaaacabadcacddaaccdbcdbcbccbbcbbbbbbbddcbbcacbdcdbccbcbdbbccdbcbbbdbccdcdadddbacabcbdcdbbadcacbbbbdacaccbdcbbbccddbbadaadcabdabcbadbabaacbcbbdabcbbcbbdcadcdacaccaddcddccbcbadcdbbbdbcbdbacbcdaacdadcdcddcacbdbcadcaabccacdbadbbbdcdabbcbaaaaaccdcdcccbddbdcbdddacbdcbcacdbbccacbacbbdacabdcccacaaabdaaaccbbccccabdcacbdcadcddbacdbabcbdaaaabbbbdcdadaaabdcddacadcbabbdbccadccaddaccaaddbccadbdbcdabdcdacbdccbbabcdcbaabbacacdbccdabbdbdccdacbdacababbabaadadbbabdbcacaabdddbdccdabdbcddabcacabaccbccbdbaacaddacbbcdcdbadccbbbbbbacabaacacbdcabdaaddbacabcaadacdbbbaacacdcaadcbdbdcaabddbccaadadbdacdacdcbbccadbaaddcaddcbbdadbdacbdacbdccbaddbbdbdacbbcbcaccccbbdcaccabddcabdddabcdbacdcadcdcbbbdbdaaddbbabbddbaddddddbdcbdbbdbdbbcbaccabdbdcbcccbaddbdacbcdcbaadcbaabbcabcdddaadcdacabcccdcbbdddbccbdcdddcbdacaabaaccccccabbbcdadcbcdadadaacbbdcaabadabacaabbcababdacadcddcccabaccddcbbdbdbdbbccbbbaabdcdabacbaddddbcaccdaaccdbadbbcdabcadddcbdcabaaaacbccacddcbdabbcdccabbcdacbbbdcbccccabbaaadbaaadddcdddabadcdaccdbcaaaaacdcabdaaaddaacaaacbbdbccacbcabcdbbaccddbbabadcdbadaadaddacdcddcabdcbbbaaccdaaaaabdaccdcdcaababcbabcdcacbaacdbdcddabddaaadbbcbcbbadacddcbdaaacdbdaacabdbaccdadbbccadccbdbcbbaaccaacbdcccbccccbbcacbaccbbdbbbabcdccaaaaadbbbbcabdcacccbbaacadcddbcbbacbcddbcbabdbbbcbcdaacdcaaadddcdddddddcdddddcabcacccaaddbbdaaddacdbcdacdacbbaabcacabbddbcacbabdcbdcdbaaccbcdadbbabbabbbbacdcbccdcccccbcbdddbaadcaddddddbcdcbbcccbddaccacbcdcdaadbdcdcaddcbcdbcacdbcddbbbcdaadbaabdcdcadbcaccbddcdaabbddabdbaaabddabddccddbbdddabccbababdabadbbacddbdbaddbaacccbddbccbadbccabbdccaacbdcbbbcacbabdbcabbbadccdcacccdbbabababbddcabddabdbcadddabaacccbcaabadcbacabcddadddcacbddbcdcacaaddcccaabccadcaccaaababacdbdcdaddccccdbaaabcdbcacaacdacddbbaabcbdbcaddbbbdacaaddadaddadabdcbbacbdccabcadcdacaccdcbcaadaacbddbadbbbddacbcbddadbcddcdcdcbadcdabccccadbaddddabdababcacccabcdcbacbbccdbaabbadcacbaddbbabcbadbbaaaccddccbaccccbbcabdcbbcccbdcbdcddacbbcbbaacbccacabbdaccadbdcacadbdbcbbadacbddccdccdbcbcabddcaccbdbbdcccddccbccaadcbddaaabcccadaddadccbaccbabbcaddbcaaadcbcacbdbbcdadcdbbcbabcaaddcabacbcababcccccaddaddadaddababaaabddaaabccabcddadbaacaacbcdbaddbacbdbaccbbcbabaacabacdbcdabadcaaacaddcabcaacdcacdaaaabbccdcaddcbbdaabcdbcadabbccdadcddbbaccbcadddacadbcadcabbddbaadbacdbbbadcbcbaccaccaaadabacbbdbbccadcddbcbddbcaabcaddddcdbabdbdabbdbbbbddacbccbacacddddadbccacccadcaacadabddadcabcdcacbcabddbddaaccabddcdacccbbcacbadddcdcaadacdbabbcbbcbcabcdcdddbdacaaaaddabdcccdbddaaddcababaacbcbccbaacabaddddbcdcabaccbbbacaddacddcccdaaddcbcbbadacacbadbaabcabcbdbbadcadbdddbccdbcdbaaadbbdbdaabddcbbaacbbabaacaadbaaaccbcbcbacbbdbdbcdacaacadacdccdcdbdbaddbaabadbcaacbdddabcbcdcccdabbcacbaccabdcdbacaaaabdcbaabcbacdacdbddbdcccccddcbababbcadbcbaccdcccaddbccaabdbdbdddcadacabcacddacbdbadbcacadbcdcbacacadccbaaadcdaccacbccddbdabbbcdaacacaccdadcabcadcdaadcbbbddddcddbacbccaaaaaacddbdcbcdadbdcabaddbdbcaacacaabdbadbbcdcaacccacbdbdadcaaaacaaabcdbddbacbcaabcabcdbbacacbadadbddbbabbdbbddbdabcaaaaaacdcdbcbbdbdadccddcaacabcdbdacddaaaddaddbbcbaaaccdbdbbcaacdaabbddbbbcbabcbbabbdbbddacbddadbaadabcdddadbbabbccbaaddbdbabdabbbdbcbbcbdbdcaddbbabddbcdbcabbbaddccbbcbbbbcdddbbdbbbabadbaaddadaadddaaadccacdcdbabcddccbdcbdadaacaddbcddcccacdaabdabdccaabddcabcbabdccbcbcbcdabdbabdccacddacacbbabbbbdbdccacdaadcdbbcababbdaddadcddccbdddacdbddcbaacdddaadddccabacbadddabdddacdbdadcddbcddbadcbbabdabacdbbbbccddcaaaddcbccaaadbaaadbbacacbdbadbbbdcabdadacabcddadbacadcabbacccccdbaaabbcaabaddbdcddbbbcacaaaddccbcdcdddacbcbdacbcdddcacccdacdbdcbdbacabcaabddbbcbcdccbadbdbabdcddddcbcbdbccdcbdbacddabadbacaaccbadaccabbdcaccabdacbaabdbbbcaaddbdccdaabcacaacdcaadcccabdbadacbbacbcabbdbcadabdbacccdabbbcdbdcbdadcccdacddddbadbcdbbddaccacbaaddcdcadabbdaaabbdacdacbbbcdcdbdadbdabdcbbbaaacdcbcbadddbbcbbabaadacbcabdcccdbbdaabbbabbcacabbbaaaabdabccbaaacbabbcadddaabcbaaddcbacdadcccabcdabaaaacabdcbbccdcacdacabaaaccabcadddcaddabdcbcdbdcadacaaabcaaabaadaccdcaabcbbaaccbcaabdcccaccbcbbdaaccbdcccaddbbcdaacddbcbdbdadbdddcbbddbcbddabbbbdcdccccaacbddddaccddbadabdacbdaaabaddcbdaaabaddcdbddddabdbbbcbddcbcbbdcdbcddbdcbccbbcbabcbadadcaabccbbbdbaadaababcbcaacccacabbbdbdbaabcccddbcbbaabbcccdabcddbcadcaabbabdaccacbaabddcaadabbdddcadbbdbbdddbddddaabacdaacccddbdbdccbbabbdbcadaddbcbbacbaacdccbaddbccababadbdacbcabcdaabdddcdccadccdbbbbaaabdccaacbcbbabcdbdcdbdcbdabbddccdcdcbacbabccadacbacdcabaadacbbcdcddaabdaacbbcdbaadbbadddaababbbbacdccdbbddddcbdbabbabdcbbabacbbdbbcccbdadbdbdcadcadcdaddaddcaddbdcccdbbcddbaabdaadacdbcaadaadcbdcbddbdaaaadbbbbaddadaddcbbcadaacaacacdcdaccacddccddbbcdccdbdddccdcaacccadacadacbddbaaaaadacaaddcdaadaacdaabcaaddadcabacdddbdbcaacaaadcbabcacbbccaaacabcdbbbccbbacdbcdbcbbcbaacbabcadbccbababcbbbacdbddccbbddadddbbccabbbcbbcccddbbdabbdaadbcaccabbccddaaccccddddcdccdababcbbcdcbdccadbdcdcdbcbccddccabbddbbcacaddddbccacdbbcabdaabbcacbcacadcbcdaccbadcbcaadbadbcbbdabaddadcabbaaabccbdcdccaababbbadbdddcbcddbbddbcccbaacdbcbdbcaddccabddaaaddaabaccbcbaccdcccdbdbdbdddbbcdaadbcacbdabcacaabbbcacaaadbbcdbcadcabbbcaabcabcabdbdbadccbbcaccaccdabdcdbacadbdbdacaadcdacbdbdccabcbbbdcbbaacdcccbabbdaccdbcdbdcbddacbaaadaddaaaabcbdbabdbabcccbdbcabcdaccbdbdbccbdbcaccddccacbaaadaabaadcdaabccccadbabdbbdddadadbccdcdabdacacabcdacabcacdabccaabcbadaacdccabbaddddabcabccbcbbadddcccccbcadcbbbcbccddccabacaabadbdacbcaccddbcbbbcaddccdbaaccaaddcaccbbdcdbcaaddcabcabdcbbcbbdbcdccbadcaadacabddadbddcbdcccaddaadbcbaddbcdbcacaccdddbcbadaacbdbbdbcbbcccabaabdcbadbadcdbddbbccdcbdacbbcbcbabddaaddcddadabdcbcadbcddaadbdadcacabbaaccadbdddbbacaddcbdaacddccabadabdcdaddcaccddcacdadacacdbbadbaadcdbddbdaabccbdcccbbdaaaaddccdccaaaadbbdbbcdcddbbdcbcbbbabcacdaabddabacddcabddbcadadaabdaccdcbacbcbbccdacccaddbdbbdcabaaaccbabbdbadbcbcdcaddccdccbaccaadacbbcbddacdbbcbddabdccddbaadbdcbdbdadcdcadbacabdbdcccdaabcdacaabaccbbdcbaabcddbbacccaacbbdbccadcdcaabbdaadbbbdaabdaadddbdbdacacddbacbabddcbcadcbaabccacdaddddcbabbccbabddcadbcbcdddcdbaaabcbcdbacdcbdbcadaacddacbbddaacbcacdbbcddcacaccbacdbcddbcdbdccabdaadcadddcbbaabddddaadadbadbcccdccaddcdabccbdbbbbbddbacadaabcddaccdcccddcabadaaabcdabccddabcccbbacaaaabdbbcddddddbddddcccddcbaddaccabccaccbbccbbbdadbacadccdcddcccbabdccaddcaccaddcdaabaddcacbcccbbccdaaadabacbbdcdbabbacdacaacaacadcadacdccaddcdbbdbacddbaadacdabdbdcbbccabadcdaadbacadccccbdcbaddddacdacbdddcadcdcaccdabadcddaccbaadadcabdadaddbcddccbcdbacbacbaadcbcccbdaddcacdabccddbadddaaadacaadadbccbaadabcacaabadcadacccaabbaddabcadadaddcaaabccbadcddbcdacaadadaccabacbcbccaadaacccbbbdabdccacaabdbdaaaabaabddacbcddaaabcbbdabbcbcdaaccbacacccadabbcdcbbdabdbadaaabddacacdbdaacbccbbccadcccddbbdbdcadccadbabbcccbdbaddabacbacbdadcbbadccaadababdbdabccccdcaabbbacadbbcdbcbbabdbabccadcaaabdbdaadbccaadbabbcbcabcbddcbbadddcccadddadaacaccbbbcadccdccbbdbdacddcaadbbbddcabddcbdbababadbbabaadbaccdccbadabdbaadcdcbaddaadddbcbbdcccdadaddcabacdbbacacdabaccccdaaacdaaaddcbcdbcbaddbbbbdadadbacaacaabdbbcdbbdbcdaccdaddadcccbbaabcdaddabaccbbadcaacdacadcdcbcbacbaadddaddacbbcbabcbcdcbdcbbccbaacccacdbcddbbcddcbabbbbbdddbccbbadaaacacddbdacbdccddbbbbdcbabaccabcdbbdbadbccbcacaacbbbdbadbdbbcddddbaccbaccbbaadaddbddadabacbabcdbaadaddcbbdbcbdccbcbbdcacdaccbcacdaabbcbbcadadbadadbaaacdcccbdabdabbdcddcdbbdacdcbacbabccddaddbdacbadbbdccaadbbadcacccbbbdcdaadbbcbaccadbdacdababbaddddbcdadcbbdabadbaacdabaccaaacbabcddbddbdbadddcacbbcbdddabcdcaacbccbcbadcbdbacbbbbcaababdcbccacadcabdadbdcccbbacdcdddadaddcabaabbcacdacccdcaadbacaddcccdadbbacacbddababadadacdbabdccbdbdddbddbacaabadabbddbbbaadddcdabcddabcddcdddbcbcbccccadaadcdabaddcbdbbcdbcbadabbddcaacbcabcdcbcbdaaddabddadadaccdbdbddbacdcbbcabccdcbbadadddcdacdbbdbdbaccbdacbadcbadbaadbbcbdbabcccbcdcdbccaabadacbdbdacacacabcbccdbdabddddabcbcdabdccdbdacdbdadbcdacbccddabbdcbcbacabdbadcabcabaccddbddbcddaaddcbabbaaaabbcbdbbcdbbadababcdcadccddcccadabaaadbdbbcbdaddabdddcaaccbacbadbbcdabaabbdbaababbaadbadddaaccdbdcaacdcadbddbddddaddbcbacabcabcaabaacdadccddcbacadcadadaaabccacbadbbbdcdcbbdbbbaddaabbdbabdabcabbbaddcbbbaaadbbaddcbabddbabddaaccbcaccbcdaccdddbcacbcdbcacdabddabaddbabbdbdaccddbcacbaabcbddddcdcadaadcbbabacdacdddabadbacacdcadacdbbccadacbbaacdccadddbcbbacaadbdcdcdadbbdaaabaccadbdbddaacdbcdbdcbcbadbcadaadcbadacbdaccdcbadacbcbbbcabdabdaabbcadcbdbcbcaabcbaacddcccbdaaabddbbcdcabbacddadbccdcccbaddcbddcbabbddbdaabaacbdbdccdcaacccdaaadbabbaaaabbbcdaacdcdddcabacaddccbabacbacdaaccbabadadccbcaacaddbcadacdcaddbccccddcbdcdddbcbddbaadcddbaccdabbcbabbcabbcddbcbdbddcaadbbbcccbcabcdbadbbbabccbcacadbdbdacacabbddbcccaddbccdcacdcabbbcacbdadccacdbbaacaaddbcbbbaadacdaccbbbdbbbcdbaaccddacbbbbabbcacbdbddbacbbdcbaadbcdaddbbbdcacbaabcbddbbdbabdddcdaaaddddcccdaccaaccddaddbdaaddcdcdcaaacacaabaaaddcbbcabcaaaabdaadcaabababababddbabcdcdbdaabbbdaccdbdbdbbabdadddcbabacdaaadabdbcacabacdcbdcdcbaddbddadcddcacdabccaccaaacbbabcaadbdbccbbcbbcbababcbadadcdaccbbccabaadbddcadcbcabdbddccdaadbcabcccbbbacbbdcdadabcadbcbabadbcadbacdbcddacaaaaacbcddacbdcabbbccdcbaddacddcdaabcddbcbcbbbdbaabdcacaadcbbcccadaaccbabdaddbacdbccaababddbcccdacbcacdbcbccccdcdccdcabcddccccbdccbccaddcdcddabdbcaddbcdabbdbcaccdaaddabbdcbbadccddbaccdcdccacbdbdacadbbbdacbcababbbdaaaddddcbaaadadbadbbbcdbddbcbbcddbcdaccbbacaadcbacccacbbaaaddcccbabdabbadbddacdabcddbcadabbaddddacbdbcdbddcbdabcdaccbddbbcbdddabcbdbdcbbbacbdbdbbaaccaddabbbdddaabddabbdbdbbadacdddabcbdadaaaaaaabbaddddaaadccacbadcadcabbbcbdaacbaddbaaccdbddcacaabcadcadadcdaabaacddbabbdbacbdbbaaadbbbbdabcddccbcbdcccbdcddabbdbbbadcdaddbbbdadcacacaddcaadaaaabccbbbcdcabadcddaaccccaadaadbbaaccbabbcdcadadcaabbddabcaabacdbdbdcbaacbbbcddbccccaaaacadbbacccbbbdccbcdbaaacddacdbdacadcdbdddadcbbabacdaaaadcdbddbcacdbccbdddcdbcbdcdddcbcaacaaddccbaadacaddcbbdabdcdabcbcaddcbadbbaddbccdccaccdbcbcabcbdcbddcabaadcabbbdbabbbdcdccaadadccdcaacbbccacabaadbdbbaddbbaccbabcdaccdbbbcbcacdcccdbabaaaaaaadccacbcbcddbababaacdacbcbbabcdbbdcadbbcdbbcaddacbbdbdaaddcadcbadddaabaaabddbcacadaaaccdacadbdbcaccaccabdcaabbdbbcddbbbcaccdbbbcddcaaabccabbdbbcbdbdadaaaaccbabcbaaaaabaadabcbbddccdaadddabbddbccddcbccacdbbdadcbcbcbbcaadadbbbabdcccacbdbccdbbddccbbbaadcdbccbcabbcabdaaccbdacccaaddaabbdacabadbcdccaacbbaaaddcabcbaccdabdcbdccbaaaaabbcbbdbcddddccbbddacdcbcddcacddbbbbdccadccddbbcbdcacbbcddddacabcbdcccabbbadcacbdbccbcbcbacddccbccbccbccadacdaaacdabdaacabbbdbdaadccbdcbdaadcabbaacbbcdcbdbdaccaacbdacdacbdacbacddcacdbcbcdaabbbaabaacdbdaaddcaaacdbadbdbcadcccaadaacbccbaadbbacbbcbaddcccbadbaadadddcaadbbcadaaacbdcbdcbdbcacdccddcacddcbcdddaadcdcddcbacdbbaacddddacddccaaaddbbcbbcabcbddbddbabdcdacdacbccdcadbcabaaacccaaabbbaacdddabccbdbbadbcabbbbbcbaacacddbcabaadcdbaabccadabcaadcdabaacaadaaddacccbbbcaacdbdaddccdccaadddbddddbcabcbabababccadbdadabcaddbdbacddabcaaadcaaaacbbabdcbacaabaccabaaaacdccbacbdacbcadccdaddddbbddddabbcdaccabbcdabbcbcdaaddccdcacaaabccabcaaccbaaccdcdcaabcddbdccdabbababbcbdabbdbcbbadabddacbadabaddbbbdcaddaadabbabdbbbddbcadcacdbbdccdcbddcbdbcdccdaaccacbcaadcbcbdcccbbabcdddddcddcaccddcdcacbcdcabbcabcbcbbcccaaaddcacadbbcbcdbcabdddaabacdbaccaaaacbcbacdacbdcacbacccadcdabaaabbcddabaaddadaccdbcdbdbcacaacadacabddcabaccaabdaaacddcaacadbadcddabdddddacddcdacbbbcaacccaccabdcababddaddbabcbcdbcdcddaabadbccdbdcdacdbdbcbdcadbaaddbaccbdabaacdbaccdcadaacbccdbbbadbddcbdcacbabacdacbbadabdbaccddccddaacabbcdcabadcaddaaabadbaaadcccbdbcadbbaadabaacdbcabbbaaabbadbaadcbcccdddcbabaacccabacacdaababdaaacacbdaaabdccdaadbddbcccbddcdbababbabdaacddccabdbcccbbcdccadacbbdabdcbcccddcbdbaadcdaadccaadcdcabdcdbacaabcbbbcabbbdbcddcdbbcdadadabacbabcacccadbbdcddbcaabacadccddcbdcdbacdbbcdddbcbcaaadaccadbcadddcccbaadddcabcdaaaabcbdbabacdadadbbaddacbabdaadaabadacbdbdccaddddbdbccbbcbdcbdccdbdbdabadbaadcdadbabddadaccabbdcccaabcbdadbcacaccbabbbbcaaccbcbaaadcabaaddaccababcbdaadacdabdcbbdadbbadcbcaacbdabbcacaaccaaabadbdbdaccbdacdbcdccaadbddabcdbbdcccacdcbbadcdddaddbdccabcbbbbbabddcbdddbbdcbacccbcdacdcdccddddbaadcdadccbcbbbdbcbdaadbbdbdabdccdacbdbaadacbcabdadbdaaccbbadbbbcdcdccdbdcbdcadacdbdcadadccaccccbddbcadccdcabcbadcbacdbaadccaabddcddbabcbccddcaaabadbdccbbdddacbaabbbcaccddaccbbcdbcdabadbacbdccabaccadcbdcaadcaccadbdacdbdacabcabdbdadcdbbccdccccaabbcacbaadcddaddddcaacdaaabbacadabbbcdbacdcccdbcabababdcbbdaabbdcacbbdbcccbcdcdbbdbabdcbcbbbcadcdcbbccaabadbdcdccabdadacdcaddcaccbcadcbaddcbacabdabbdcddcddacadbbbcaacbbabdaacbacbcbdcadacbbdacdcbdcbaacdacadcadabcbdcbdadaabbdbdccdbbcdaddcddababaabbddbcadabdadccdbcaccbcabcabddaccaadaccadaddcbccbdbacaaaadccddddcdbcdaacbadcaddadbddbdadcbccbbadcdcacbcdcbbcbccbbcabddadcdcabcabbccddbcadcdbcdadcbccaaabccccacbddaccdcadacdcbcbacbdbdadbcacdccdabcdacbdbccdbcadabccaabdbbcaadbbdaacadccaaaccddbbcdaabddbcdccbbcaddaabdbcacacccdddbdabbadbadabcabcaddbdbdbcabbabdcbbdabadbbabdaccbdabdadcabcdcaaaaaaaadddcbbccdddadbabaccbcddccbbccdbcaccabbdcaacdaacaabbcbcccccaababaacabbbcddbdbbbdaddaaddcdbbdbbadabacacbabcbdcbbaaaaaadcbadbccbdbacdacacbcdbcdacccbdabbbdadcaadadabcadcccdacdacdccdcccbbddbdccbbaccbdccaadcccacbbcdadbbbdbcbdcadbcaccbbdcdcbadbdaadababbccadacddadaaabdbadddadbaabdbabadcabddaadcdaacacdbacccdcbadddbadcbadabbaaacbbbcaccbdcaadbccbccaadaaacbcbbcbcddaabbbbbbdaadcdaccabcbdadcaacabccaacbbcaaccacadcddccbbccacadaddbdacdaaccdadaaaddbdbdbbddbdacbdaadcaabcbaaacbcdabdabbbaccbdaaabacbacdaccadddcaadaddbbcdbacbbbabdadcbcbccabbbcdcccdacaddcdccdcbadbbacbcdccaccacbbcabdaabacdbbabdaddaabbcbbbabcbddadadbcccbbdbdadbdcdbcbabbcacbcdbbbdcbdbdcbaaaddbbaddbcbddbbbbdabcddbbbbaaddaadadaccddcacddcbbcbdcccbbaacdabaadcbbdbccddcadcaccbdbbcbcbdacdacbcdbadbaadddabcacbbdccbddbaacdbcbdbdacdbcddbcdddcdcbcabbcccbdbccbbadacaabcccddbccdcbbcbccdaadabadbbbcbbdccbdadcabddababcdcaabadbcbaaddabbbbaaccbbaddbbbccadabadbddabdbdbacaabccabacadcadadbcccbabaaddddadcbbbadabdccdaaabdcbabbcdaadbaddcddccbaaacbadcacdadcdccacacbcdcaccaaadddacbadaaaddcbdadccccdbcbdbbcababdadbcabbdbcdcbddcbaadadcaddacaccbdcaaccbcaabacdaddaabcadbadbbcdbdacabccadcbaacaddccbabcdccdbcabddbdadaaabbcadbccdcacbdbdadbbdccbbbccdbaccbddaddacadbdbcccaddbaccabdabbcacdacaabbcbcadadbbacabaadbadadddbadbccbcbbaadccacabdabdadbacdadcabcadcbcbbcabaaacadaacbacbbcddadabdcaaccdbaaddbcaccddbdcacaccadadadbbdbadbccaacaccdabccdcaaaaacdaccaacacdcdacbccbccaaaabcddadddcdcbdbdccabdcdbbccadbdbabbccabacbcddbaabddbcacbdbcdacacabdccdbcbacddbaddabcdcaacbcdccaccbadaacaacbbaaaabdccadbddaabcdbccdcddabbabcacddccbdbbacbacbccddaadaaddadaadddabbcdabacaddaaaddbddacbabcdbddbacadcbddbddccabaacccbdbcaddccaccdcbadbadadddbcacaddcaccaacbaaaaadabcddadacccddabdacbcdbdbdccbbaaacbdacdbbcdbdbddacabbcbaadddcdbacddabdadccccabcacdcdbbaacbaccbdaaabbcbbadabacbddadbcadcbbaaabababddddabddbddbcdaddbdabbdbcacdccaacdabcdcddadabcdaaabaacaaccacaddccdbbdddbdcdddaccadaabaacabcdacbcbacdababaadaccdabbddbdabdbbbcaaadbacbbabbcdbdaccddadcbbccdbabdccdbbcccaadcdcccbadcbdbddbadacaabacbbdbdbcdbaabccccdbbcbbbaccdadbdcbacaaadddbabcbdabdadbcddadaadbccabdacdaacdccccababacbdcdabbacbdaaadaaaaacdcdadcdccaababcdccbbcdbcaacdcbbcaabadbbadbddcbbbbaadabddacacdcccdcccaadccbbaddabccddaaccacaacddbcdcbdcddbbaddcabbadcdaccbacdadacdaadcddadbadbbbcabdccdbdacaddbdaaddcacdadcbcbdbdcdadacacbbcaddccabbdacbdadddaaababdaaddbadbbaaacdaaadbdcdadcdbdabacacadacbdcbdcccaadacdccbadadadbacdbcbcabccddabaaaccbabdddcabbbdbcbaaacacbdddbacddcdadbdbbdddabdaaccbddbaacbacaddcddadbcaddabbdabcbbdddcdbdbdbdcdbcdbadbcdcabcdccbabcbbcaddaccdaccaadddadabdbbabbdcbbdcddcdcbddaadbacbcabbacacbaacbaaacdccacbcadddcbdbbbcacadcdadbaccbacdbcbbdbcdaadddabaadcaddacacdbdbcbcbabddcaadcaacadacbbdcbbdabdccabcaadbcacbcbdcbccabddcaabbcaabacccaaadccabddcbdccdacadcddcdcaabbaddbcdaddddadccbacbcdaaabbbadcbbaabcadbdadbbacadaabaadcadbaaacbcbacbadccdcbbbdbbdcdddbbbdddbcccbaabcdcdbcbbabadbbdcdbdbacadbabbddaddcddbcbabcdbcccdbdcccdaccabaacdbadddbcabacbdaadcdbdaccccddcaabbccbabbaabdcddacbdacbccddccccadacbbbbdbcaaabddbbccabcbcacdbcacbabcbbbbcdaadbdaacdcdddadabdabdacabbcaabbadbddabaabddabadaadaabdabadcbbcaccadbccabcacbababcbcddbabcaabcbdddadacacabcababbddcdccccbaacbaccbadcbaadbbadcbadacacbcddbbaaacbdcbcadcabbcabaadaddadaabcddddabbbbcddbaccaadaadcbbbcccdbdabbbdbaccdbcdcdbaccbaddababdaccdbddabdcdbcdbdaadccabcbdccccbabbdabdbaccdabbdddcbabddbdcadcccbacdadbbcbdcdbcaddcadcaccdcbcdbddaaadcababdbabbcbdcbadcacdacbbacdcaaabbadabcbcdbaddadacadadadbcbddcdbdbacbddabadadcdbaadcbbbcdcdbcaaacaadaaadabadcdddaabaccbbdcbaaaadcbcabbcadcdccdcbddcccabbcdadabbddcadbaddadbbcdaddcbbbdadddcdbacdaadcaadcadabaccbadbbaccbddcbccdcbbcccbadbbaacaddbdbbcbcaaccabdddcbbccddcbdbcaadbaccccdabcbbddbdddbdcabbbdaabbdabdaddaccbabdabbbaddbdabddccabcddbddcadbbbdcdaababcbaccdbbbbaabddbbcaabdabbbcdabdaccaddcbaacbccbcaaabbbadaaaadcaaacbcdacdbbdacdcabbccdacdcaacaccdcbbadabdacddbccabdbbaacbcdacdbbbacdbdbdaacaacdacbbbdbcbdbbadbdbaddaccdaabcbddaacabdacadaddcdacbccaccabbacdcbcaacdbdccbccdadcddcbbccdacddcddbcbacadabacddabdbcbdccabcdbbcaaabdcadcabccdccbacbbadbdcdadbdccdbaaaccdccccbbbcabdbadabacabccdcbacbbbcccbddadbacaadbdcdcaadcaaabdaccdcadacbabaacbbacabaabaabbcbcaadabcbdccdcddcbbdbaaccbcddadadbbacdacadcdadcadcbbaaadaddddcacdaadbccabbabadbabadbbabccccbcbcaabaacacdccaacbabdaddcacaccbaccbabbbdadcdbdabaaaacccdccbcaaddabddbbbbcaadcdaacdcbcaacaadcdddadcbbbabbacbdbdcbbaabcddacccabdcccaabbbbdabcaadbbcbdddbdcadbaabcdaacddbbbcbdaccbbdacdbadabccdbbabdbadcdbbcbcdcdabdabacbbaaacaadbdabbadadabbdcacdbcbadccacbbacbdcbcddacbacbbdccbdadacbadbdbdbbcddaabdcddcaddcadcbcbaabdacdcbdbbaccbcabcaccbcaadadcbaacdddaacddabbccccadaaaabddaddddcbdcdabadadacbccabdbbbbcbdbcacdadbdaccbcddbabaabcadcacddbbdcbddacbadbadccdcdbaacbcaabacababdbabcccccccbbcdacaaadaacdcccbababaccbacabdcbccccbbcadcabaabccdccbbdbcdcbaadbacddbdccdddabcdbdbaccddcbbbdabbcbadabaddacabcdcbadbaabcacadcdcbacdacacdddbdacdbbcdacabaacddbbcacbaddbdabbcdcdcbdcbbccaacabdcacaaddbcccbdcbccdbbbcacccccddcbdbacddbcabcaccabdbbadbaabcddcdacabdabcdaaddcbadabdacbaaabcdbdcdcdccdbaaacbbacdccbdddddcbdcbbbabaadaddbcbdbddbddcbcbdbadaaabacaccbaadcbdcbabdcdcaaaacbcccacbbddadadbbbaabbdbbcacadacdcbbaabbdbcdbdcbcdcadabdbacaaaadbcccacbbbdabddcbacdbdacbadbdcbccbdddaabbaabbdddbcdabdbabbcbbccdabdcacadbdcababbbaccbabacbcbadccababccdcbcbcbcbdaadbbbdcbcbaabcdcdadbbddbbaacdcdabbcddcdbcbcddcbcaabaabcdcdabbdacaabddbdccdbadaabbdaabcbbaaaaabaccdbbccaadbdcabdabaaabccbaabdbcdccbddcbcabbbacabaacaaadcddbbcbccdcbcadbcdbdabcadadddbadbdbbddbaacbcabbcaaddabbcbabbbddbcccacaadadacabbababcadcadccdabcbadcadcadabccbacdaacbcdacddddacabaadacdaddbbbaddccdddbcccbadcddddaddcbcccbaacbdaaabbaacabcdcdaccbaadababddcdadacdbabadbbbbdacbbbbbacdcacabdbadbcccaaddcbdabbadadccadbcccbcccaccadaacdddccbdbccaabbcccdbadbcadcddcdadacbdabbcbbccaabbaabbddcdbababacadbdbabbddbcbbdcaacaaabdbaccdababadaaaadaababdbcaadcbcdbcdcaaadcacacbbdcacbdabcdacacddcacdbbbaccddcbccabbbbbaccdadcdccacbccbacbbdcaadcdbdbcdcadcdcabdbccbddabdcadbcaabccacabaabbbdcbdbcbbdadccbbababadaacddddcdacbadcdccdabbddabccbccccadacccaabcbabadaccddaaccccbdabaddbcbbadacdaccdcdbccacdaaacbdbdbcbaddabaccdacdbdccadbaadbdbaccccadadabbcbcdadbdbdcdadcababaabccbcbabaddddacacaacadcaacabddabccabcdabaccbdccccddacbabadbadbccdcaadcdcdbdaccdadbddbbcccccacaddbcdcdacadcddaacdbccddaadccbabacdbdbaadbddadcbcbcdcdacabadcaaacadcdcadbdabcbdbbabdabdacbadabacbbccdcbbdbbbdddabdccacdaaccbadcbbdbbbbdbcdccbabcdccaacbccbacacccaaacaadacddaacdbddacaacbadaacddccddcdcdaadbddcaabdbcdadaccaabaabccdbdadabbcabaaddadccdacdbaadadcddbbbdccdcddbbdabddacbdddbbaabadccdabdccaddbccdaadaaacdacacdccbaaabdcaccaaccadabaabaaaabbdbabdaaaadabdaaaacccbdbdaabcacddadcdaabbcddacbbdbcbbbbdacdcaccccdabdabbbacdbacadbdcccbcccbdadbacdacbdbdbcaaaadadabcdccacadbcdcabadddbacddaccadaadccddcdabaabbabdbdacbbbbdcbcaaaabccdddaaccbcabcacabbaabbabccbcddcbacddcdddabdccdbabbbbaadcdbdadbddadcbdbbaaacdbcddcddbcacdbbdbddddadddcccaddabdbaacaaddcdcdcbbbbaccdacdaddcccccdcddbbcabcaddbcbdbdacbbbcadaddcdcdcdaabcaaacadabdbbadadccdaacbbadadaaadbcadcbcabccccadcbadabbcbbcbdcbbacdbcbdcdddddcaacacacadabadadccdddabcdbddaddacddcaaccdcacabcacbadbdadbbacdbcacabcadbdcbadbbdcabcdccdaddacbdcbabbacdccdcdacddcbbbbacbdacbcddaabacadcbbcbccbdabbaaccdbcaacbacbadbadabcbabbbaadbcbbadcaddbadacdbadcbbcddabacdacbaabbbadbdcbaaccadbdbcbaacdcbabbadbabcbaadaacdcdbabaaddaacadcabbbdbdbbddbbcbcdacddabbbdccdbdcbabdcbaaabccdbbccdbdbdbdcdacdcbcaabbaddcbdbaacbbcbbdbbabaadadaabbbabaaabbaccccccabbcdbbacbcbdaaccbabcbbcbcabbbdcadccbbabdbdcaabaadadabccaddacddbbabdddbbadbaabcabbdbaaabbabcdbabdbabbcdaacbbccddddbbaacbcbdbbadcbbabbaacbcddaabbbcddcdbbdbaabcadddaaddcbcbdcaacddadaacbaacadbaccbadddcddadbbbbdcbaabbadcbbabcbbcddbbaddccbbddcdcabadabccbccbcdbcbccadacabbdcccabcddacbcdbbaccbccccbabddbcdadaaadbdbacbcdbddccdacbccdbccdddcadaccccccbaccdaabcabdbadddbbcacaabdccaacadccbdcccbdbaaaababcbbcadcadcabbddbddacaddabdccaabbdabdbdcccabcbdbcdaabdbbdbcaacdaabbcbcdaccdbadbcbcabcaddbbbbbadacddbadddcadcccddbdddaadcaddccdaccdbbcdbaabaabbbabbaccddcabcacdcdbabadbcbabdbdbbdddbbdbcdbdcabbccaddcbbbbccddacbcaabcbdccaadcccbacdcdcdddddaabacddaddadccddcdcacdbcdaadddcdbbacdbcadcdabcddcaaacddadbdcaabbbcbbabbdcadacbbccbcbacdddccadabbabbdbaddbdacdbddccccbdccdbbbadcdabbdcccbabacacaccacaaaccdcaabcdccdcddcdbccdccccaadaddbacabcdcddacddbcdbdbcdcbbdbbcbaccdcbdcdcaacbccdbddbccdcadcacaabbcccdbaccdaaadcdbcadbbaadddbddcbbbbdacdddcaadabdbbdcbaabdbdcddddcdacbdcadddaccccdcccaaccddbcdddcddccbaaadcdbaadaaaabadabbdaababdbddbacccbdbdbbccaddaaadddbbadacdbacabcdbbaadbcbdddacbadaddaabbdbddacccdccdddcdbacdbbacabaacccddcbcbddadadcbbccbaddbbacaddccbadcddddccccaabadbbbbbdadbbadcdbdcacbaddababdbbddaabccabaaddccdbdbacaabdacdcbccbcdbcddcacacaabaabacbddbadadcbcbabcbccadbbabbddcbbcddacddcbaadadacbdcaacacdcdbccacddddaacbabbdacabacbadcbdbbcbdbdbdbbadacbcaadcddadadcbaddcdaaccdaaacadcacdbddbcdcbbaddaaadddcdbbacddcdbbadaccddabcddcbdcbcbaacacddbcbdbdbcbdaabbaddaaabcdaaddcdcbabbaacbcbccaccadbacbabcaabdddbdbabccbdadcddccaacacbadbbcddabbbdccaddbdcbcaadcbdbcaadcadcbdcdbaacdbcaaddadcdacaaaccdabaacababadccaccaabaabcccdcdccdbacccbaaccabadbcddcaabdadbdddcaccbadcbbdcdaddcaccadccacdaaabcabbcbbdacabdaaddbddaddacbabaccbcacabadbbdabdcdbddcabbbbbcbdcaadbccbacdcddbabcbbbdbadcbddabcbbbabacbcccbcdddbbcaaacacddcccabcadccaddabcccdccbaabaaaadbdcdabbcdddaddcbddbabdbcccbbcddacabccacadcdcdabcaaabdaccdbbcabdabcdbdbaabcdaabdbcbbdaaccddcabcaacdaaadcabdcbdcababbddbbcbaadccdcacaacbadcadbcbadaacbcadcdaaabbbdccbacadcbdcbccacadcacbbababacabdbacbbdadaaabccbcdddabcadbcdddbdcbbabcbcdacdcbbdbacccbabadbccbbbbdacbbadccdbcbbaccdccccbcdacddccddcbaccdcbdbbadaccddcbadcdbcdacbaacacbcccacaadbdcacbdcdabbacacddabddabbbbaaddaaaddacddbbcbcdbcdcbdcbcbdacbcbccaddaccadcdddcacdccbbbddcbabaccadbcbbbacbabbbdcddcadbbbdcacabcaadabadcacccdcadcacbcbcabbbaaadccdccacabddcabbbaacbadadcbdaadccacaaacbacaaadccbbdbcccdcbdcaacccdcdbddcbaaccdbbdbaabbdacdaccadbbbbaaacadcaabdcbcbbbdbaadbcabbdcddcacdaccadcbbaadcbdaabccbabcaadacbcccacbcadaaccaccbbadabacbbdbccdadcbcaddcaddcdadcdcddccddbddddacbbacdcbadacddcdbabbcacbbdbcddcccaadabdaddaccadbcadabdadbbdbdddcccdbcaccdaaacbccabaccdccabcaccacddbcbaccdbbcbbbddddbdadbbbadbdacaddacdddaaabadbbdbbbdcbdbddcbdcbbdaacaadcdccdbdcbaaaabbcccdaabcbccbbadabdbdccabdbcbabbccaaacccbcbcdbccbcddbcdcacbaccbbadcadabbbbbabccccaaababcdabcbadadbbbaabadbcdddcbccdacccbcaddbadbcccababbbdcadabddbdcdcbcbdbbcbcaddcbbcdacddbcbccdbacacbdbddaacdccaccacdbadcdcbdcabbddacdaccbcbabdccbdcdcabcdcbabbcadaacaacdbcbcdbbcaabbcabcbdaccdaadcdbcaabbccabbbdacbadbcbcaaaddbbabadaddccdddaccacbccacdcbaadbddddccabdcabbcbcdccadbbdacadaadbcadddacdbcbdcabcaccbabaccbdbcbdabbbdacacbaadabbbcccccbccdbcbbbdddaaabadbdddcccababcbaabccdccdddcddccbbccdadbbacdabccbdbcbcaaddaacadbcdabdccdaabbababcdddcdcaabbaabcbdcdcaadddcdacadcdadcddbdbdbdddcaaacaadbbdaaccdbcbdbcbccacabaaddcbbcabdaadccbdabbdbdbbcdacbcbadbcdcadbbdcdcdaccbdcccbccdbddaadadcbbbcabcaddcacaddaaddbdcabcdcdabccaccbbcccbaddadbbaaabbacabaacdcacbacdaabdbcdadcbabaacacaddcccaccccacabbdcbdcbabadacdbcaccababbbbdcccaaadcdaddadabadabdbbdbdaacdbaddbccabbbbbbbbabbbdaaadcddcacabbaddababddcacadcababbbbadbcaaadcdcacacbcbbcbbdcadadaaacbdcdcccadbbadaccabbdcdddcabaccccbbcadabadadcbdbcddddabaccaaacaadabbabdddaaacddaabbbadacbaabacbdacacccacababcddbcaacdcccbadbadaabdadaacaadcbcdbaacabbddcddcacbdcbccccbbbcadcbdbbccddbccdbadbcadbbdbbcccaacdbbaaadcdaaabdcaadcbaabcbacdcbbdbcbcddbaaababaddbddbaddccddaaaabbdaccbdaabdbbdacbbccbdccbcaccccdbbacbcccdbaabdcadcccdaabcacbcdcdcbacaddadabbcbdcbcdababdacaaacbdbbacdcddcbdbdabddcddccbdcdddaacbaaccccbcadcdbcdaddcbcccdbaaaddaadadcaddbcdaddcdddbaaaabbabccbcdadcacccaabaadbbccbaacdaabadbcbadbdcdadabcabbbdadcbcccadddabcdbdcdcddbbaaddbbabbbabcccccbabbabdddbdcdacbabbdbcbacdccccacbaadbbbdabadcbdccbccadaddbcacdcddbddcacadacacdcbcdadacbcdbcadadaaaddbdbbacabcbbcbcbbdcdbaddbbbaaccbcadbccbccaaadbcadbacadacaacdccbacccbccbdaccddacbdccdacbabadadcccdbaccbabbadacbacdbaccdbcbdbaacbddaaacaddcdcbaacbcbaaaddabaadaabcbabcabaababadaacbbdcddddbcdbaddabcbbaadcccaddbbaaadbcabddbbadbbbcaaaacacbaadcabbadacdddbbcbdccbadabdbcbdbcbcdcbcadabcbdcccdaabdababdbbaddbbaadababdddcbbdbaddcdadaaacaccbaddbcdcdbaddadcccdbbcbadbbaadadbbdaabbadaabbbdcbbbbcdcbcbdbdaabcdbbddddddbbdaadbaccdcbcaccacdcbacbcddcdadaacdaabbccdcbcbaababbaccbaaaccbcdddccdcbacabdacbcbaacdbbacbdccabaccbbddcbcabbabcdcacdbdbaacdbbbaaacbdacaccdcdcbbcdcabaabdbbccbbccbccbacbdbcabbdbcbbaddcadaaccaaccdbcbbcaabadbaaddbcdbdacadcbddaadbdaccacbacdccdcdcaabcdbbdcbdcccccddbbcccddaacbbbabcdddbadadaacbdacdacbaccbbaaddbabbbacadcdabaadacacbabdaaaadddcccbaabaccccdcdacdcbcdddbadccaadbacaddbcccdacbdaabaacbdbdbaaacaddbcddabccacbdccadccdaaacbbcadabaddbbcdbdcbabbddbcccaabdcccbdbcbcaadcdbcdddcbccccddaabcbbbaaabbdaabdadacccdbdcdabdcacadbabbdcdddbcdbcaccdbaabcdccdddcdcbabcbcaacddadbbbbcadcbadadbbdbaaccbadbaaccdabacadbabaabcbbdbdcccbabbadaaaaaabbbccbdcbcaadbabaddcbabbddbddaadacabdcdcbcbacbbcdccbbddbacbccccbdbccdaaabbcaacacbdbdcadcbbbadbdaddbbdcbcdaabbddbcadcddccdadbdcbcaacabccbbcabcababbbdaabdababccdbcacadaddacacaacaabdaabdbbcdbcabdbbadbcacddcadbdbdbccbcbbdadbbcdacbcbababcbbadddcacbcadcdbcdaabbacbadaabcdcaaacbabaaaacdbadccdccbdbccdacaccabcabcbaacdababcdbbcdbdacdcbbcbcaaccccacabadcbcadaacbbbbcdaaabaddccabdababdadbaaaabbbcccdabaccbdcacabbbddcccabbadadbdadabddaaaadcdcabadcdcbcbdcdbbddcddaccadbdacadabbbbaabbdbcdabcaccbbadbcbcdacaaadacbadbadabbbabcbbdccdabcabddddaabaaddbabaaabdaccadcbdacdaaccdabaddbdbcbccdbbdccacbbddbcbbdcbccdccacadcdadbbbbbbbbbaabcacdcddccbdbddaabbcddabddaadaccdadbbcaacadcadaadcdcbdbacccbabddaabbcdbdbacabbcbbacadabddbaadaacdaaadabbcadcbddccbddacbccddababcaabbbddabdcbdadddddabbabcbdcbcddaddbcbccbddbddbccbabddddadcccbcdcdadacbabbacaaddddbbaddaaaacccacbdbddbaccbaccdbdbcdcbcababbdadaadcadaddddcbdaadabddbcccbaaccaacddaddacbcbdbcdcacbcdddacbccccabbcccaaadacbadadaaacbaccdbcadbdcabdcdbadbdbaabadaddcdddcababcdadddcaabcdbbbbcbccadaaaaaddaccbddbcabacabbdbcaabbcdaccddaddddcabdbbbdbbcdbdcdbbdccbddbdaadaabaccaccadadbbcdbdbdbbcccdbbddcbadadacddbdcdaaaabbaddaacccabddcaddbdaacbdabcabadbddccaaccabbcccdbbabcccdccacbbacbcbcdbcbcccadbabccdcbccccbcbcacccbbdadcabbbacbaacabdaddabdbbdbdadccbbadcdacaaacacdbaccbdbadaccaadcbdcadbbbbcccaaccbadcdddcccbcdbacdddbbbcdcddbbcbdacbaabddcdcbbadacbcdbcacbbcdabadbcdaddbdabccdcccdddacbcaaadbcbbdccbaacdddbbacbbbccaccbbcaadabacbbccddbccdcdcbcabbbdcaccadabacccdadbbcbdccdcacabcbcdcbabcccdccddcbdcbccccdaababddaacccddbabcbcdcdaccdaacbccddcaabdaadbabcdddddcbcdcbcacbadacbdcdbddaaacbcacdbbacbccabaccabdadbdcddbbaccbdcadcdcbdadaabcdcbcdcdcabbcdbadddcaacdcadbbcdbcabbbdbbaabbcbaaaacbcbbabcbabcbcdddacdbbacbbbddabbaadcbacadaccdbcacaccbcbacbbcaaadcbdbcdaadbdcabcabcdcdaabddbaaccdddcddcbbadbacaaacaacbcbcaddbaddccbaabbabbbdaacacccdacbcbbdbbabbdcadcadbcacaaabcadcbaccaccaddbddaddcddcdbaaadbadcdcdbdccbadadcbdababbbadabdacdacabccbacbaaabadcbdabdbbaadababcabadbbcabaacaabbacbbadabbdbdccacbdddbddabcadbccbadbdcbaaccccaccdbccbbabbaacdcacdaddddbbcdbddaddbbadcbaabaccddbaddadcddabacbbcadddaccbbdbabcbdbddcbdcadcabaadaccdbddbcacacdabbccdbcdacadaabaacddacdaabcadabaabbbaabddcabccbbabdcadccbababdcbbccdddccddaaaaddcabadbbdaccbaabdaadbdcbdaddbcacddaaacbcabbabcdaaccaabdbcbaabccddcbbdbcbdcdabaaabbcdacbdccdbcbacbcbcbabbacaabaddbbabbabcccbdbdadcbccabdbababdcdcddaacdbcbbaabcdddaccdbdbccadcbddbcabcbbadcabbbdcddcaadcacbdbddcacbcdbbadadcddbdaadbaaabdcdacdccadcdbcadbcdbaaabcbcacadddbcbacadbdbbdbcbbcdbbadacdabcbccadbdacdaccdbdcdbacdabdcaaacbadcabcadccccbbaaadbbdcddbabcaaaaacbdcabccbbbcaccbbdababbabaaaaadbdbccaddcddaacbdbdccabdacbacbbbabdbcdaccccabbbaadcbbbdcabbaabbdcbdbabcabbdddbabcaddddddddaabbcdbdadbdbbccdaaaaacccbbadcbddcaacaaabcddbddacdbbaadbdcbdddbcadbbaabdcdabdaacdaddcbcacdcadbabaadaccbabbddaadaabacbcbcaadcccbcacdaabadabdcbacadbbbacdbbcbbbbccdbbacddbbcbcbcaddccacabbacbddcababdccbccbcabdbdcacccadcdcdacbddbbabdbbdcbbcccbdbbddabcccbcbbbbaccbcbbaabaccadcbccbbbbdbabbaadbdccbdcaddddcdcbaacbbdacdadbbdccccabddbbadccaacbdaadadaadacdacacadbbbbbadbcbbdaacddcabdcaadbcdcdcbdaddbbdcbadaddcbdbabbacdcbbbbdcdcbcbadacaaccdcbbcbbbababdabbadccbbcdcdcccadcaabbabcbabdbcacddcdddaddbcadaccbddacdbaddbacaccbabdbdcccbabdcbaaddbdcaacbbaabdadbcdbbabbdcccbbacbadbadbbcdaccacdccdadbaccdbccbdccdbcbcccaaacaddacaccacbabcbddbddcbadaaacbaabdcadbbbdacbcadbbccbaacdacdcbacccacdbbcbccddbbbdbcaabbcbabcdbdcaadccbddaddddcdadddccdccacdbccddccbbcbcbcbbbacddcbbacbbdbbabadcdaabdbbabdabbaddcdadabacbbdddabacbbabbadcbacbcbccbbcdbacadabbbdaccdcdcdbcbaddabbbdcacabdbbdbddbbaadccadbdccbbcdddbdaaadccdcadcbdbcdbbbacbbbcbbbbabaabdccddcdcdcbabccdaabdbddcaabcabdbdabdaadcbacccbdaadacdbddacbadcccbabccdabccbabcdbdabcaabdadadadaabbccbbaccadcbbdbaddbbccbadbcdcaaaabdcdcadbaadcccacabaaaacdddccdaaddbcaaadbcbbbcdadadbbaacbbaaacaadaddabaaaabcababbcdccbbcacddacaabbcbababadabbbcbccccdbcbcdcdabcababcbcbcbcdbbbcbbbdcaadcbdbcbadbacbabcccddadacbacbbaadbabdcdbbadcacdaadcaaadbbacacdbcadaccbccbdcbaacbcddddcbabacdddadccdadbdbacdcbbadacdbbccaacdbbbbbdacbdaadbdabaddccccdbccdddcaadcbdbdbdddcaaabaadacbababcabadcaaccaacdbaacacbccacccdcaddcddadaccadcbdabddbddaadbababacbddcccccdaabccbadabbbdbbddacdabaaabcadddcbdcdacbacdcbacdabcbbcadaacddcacbcddcacaabddcadacacabbcabdabaabababcdaacacbdaadaaaccddbaaaddbbbabdbacdcaabbbdcaaaddcaabacbdaaaaddbcbbdcbbcacbbdbadcdcacbadbdccabcdbbdcabbacbabcaddddcbadacabbacbcbbdaabcccdaadbadaabcdcaddcaacbdddcbcdbcdbccddbdcdbbdcadacadabcdabdcaadbabbdacadbaacabcadddbcaccaadadddbccaacddcadabbdbbbaccabacdbacaabcacbbbacddcbabbaadbbbcbbbccadbcbdaadabbbbccbbdbcbbdccdadbccbdabbbaccdcdbbbbbcaddaccccdcabdcdbcdbdbdddaacccbacabbbcdcaadbaadccadcacabaddccaacdabcdcdadccaadbbdddbdcdcabdbccaaaacaccdadacdbcdaadbdaddabacddbcaacdcccddbddbbacdccddacddabaaaabdddaddbdbbbadbacdabbcacdbbdbcaabdccdabcdcbbcacbcadaadacbcdddbadbbbadadabaaaaadadcdabaabaaabbddcaddbaacacddbabadaddddcccdbdbdaaabbacaddcdacdcaaacdbdadbabdaaabbbdcadbadbdacaadccdcaadddacacdadbcadccdacaddcccbcbacddbdadcadbbcaadcadcbddaddddcabddbcbbdbabddccdcabaaddccadcccdcabcdbcadddccccacbbcdadcdadadbcaabddbaccdcabcbacacacbbcbcabbdddcdbcbccbabbcbcbbbbbddddcdadbbdcbcccbddaddccccdacdcbaacdadacacddbaccdccabbcccdabbcdaacdbddddbccbabcbdcbdaadccaadcaabcacbccbabdcddbbdbcbbddabdcaabaabddbabaccbbbbabcbcbacccaaccbddccbcbbcdcbddacbacacbacadddaddccadbcbbcbcdacccbadcbbabcdcacdbdbbbaabcadbcacaadabcbbbdbdbccacbdbdddccaddcdacaaaacbdcdcbcdccddddabdbcbbcadbdbccdaabaadbbadadabdabbdbbabdcabaacbbddcbcdcdaddccdcbbcccdbbdcaddcbdbaaaaacbbbbbacbbcbccbdaacbbdbbadcccbcaacdccdadbdabcdabaaccbaacabadcdaabbbcbddbbbbdaccddaddccddcdccdccbaddbddaaadcaabaacbcadaccadbbbbdddcbaaabddbdabbcacdadcdbcbcddcaadddacacacaabbcbdcddaadacdabcabdcaaadddabacabddbdcdbcdcdacabbbcbbdddcdbccdbdbbcdbabbbdddcbcccdcbbcccbcdbcbcaabaabadcdccdcadcaabddabbaabaabcccbbbcccbddaccbddbccabcadadbbabccdaddcdaadbdcdbcaddcddbababdcdccabcccdcbabddbcaaccdcdaaabaadabbaaddadbbadadadbcaddbaadbdbbbddbddddcbdaacacdbadcbdaadaaadcaabddbabdcabcbbbabbdacacbabadbaddccbacadcdbacddbadbbdaddaabadabcbcadbcddbdcacbabdbacddbabbbcbdacdaddbddbdddbbddaabbbbdbbabccaaadaaddbcddcccbbddbbcacdbaccddbabadadbaadbdccbdbabbbbabbcbadcadaabbccdcddbcbdbdabbadcaccdcabacadbdbbbcdaaddbdcbacdccbadbaccdabdcbddcdcdbddbadcbcddcbbcaccbabdbbdcbcabdadbdbaabbbbdacabcadcccbadbaadccdaabddbcccacaaddbaaaadbcccccaddbdbaacadbddababbaccaabddacdcacbdadbcbabcadbbbcbcadbbcbdbdcdacbbddcdadacabbdbccddcdaadcadbacdbddddccdddcccccdbdbbbbdacdadbdaddbdbabbadbccccbbbabcacbbbdcdccbaacadccccbbccbbcdcdadccacdcbacdaaabcabdaabbabcbbbccbccaadcbbddbdddcacccccabdcabcccdbacacacbddbcbacaadaddbdbcbacabdcbbacdcbbccbababddcbdbabdcbbacadcdacbddbbcbadcabacbabbdabaadbaacdacadaabadbbbcbdbdaadbbdaabacaacbadaadddddcdbcaaccbaacbdaabcaadcbadaccbcacdacccbdcdccbdbcbdbccadadbbdcdcccbcaaccdbbbdddaabcbddadcccddbadbbccbbbaddbcdcddccdcdaccbdaddcdadaddddabcddbdaaacdaaacdaaabdaccabcddddcaadbdbbbcbbbacccbcabdcbaddadcddcacbddcabaacabcbadcccddbadcabcccbcabbabdbcacabbcbccabcacdddccdabadabcbdccdcdbbdaadccbcaddcdaaacacbacbbdbaaaadacbcdaddcccccbaadddbbaccaccccbbccaccbacabbaadbccaacdddbccdccdddcdabbdbccdadcdbaabcccddcaccabbdcacadcccaabdadddccbbdbbcdbbcccbbabdadabaacabdaacaacabcdbacdcdadbbdbdbbacbbabdcdaccabbbcddcbaadadcaacbcacbccaaabdcdbacaaaccaadaaccbaccbcadcabbcbccddaacabbaddacbdcddcbdaabdaddcbaacccacadacaccbcbdcacadbbabcaadbcbcabcdbcadcacdcaabaaddadbbbaaddcdbdadbbaabadcdcaaacddabbcdbaabbdabbbdbdacdabacbddbdbdaabbaccbccddaaacbaaacdadccccaadbaddadabcdcbddabdbcaccdbbdcbdcadcdddaacdaccbbbdbabbadddbadadddcadadaaddbdddddbdbcdadacaaadbdabbbdadddddadcaabcddcdabdddbdbcbbdacdbadbbbabddaaddcdcdbddaadcbaadcbadacababcbbbbaacdaaaaaabacdccaddcccabddadbbdaaaaadabcbccbbdaacbbcadccdbbaccdacdbacbacdbcdbbddcbdbdbbdcccbadccbaddaabddcacacacadccacbdadbddccdbabdaaddccabadbdccdcaadbbcdbbadbdaaccbabcdbbaadccccaaadcddbcabdbcbcbacbccdabacadcaabdcbadddcaddaadcddadcabccdbaddbabadbcbdcccaadcabddcaadbbdbadddbccdbbbdbacbabcabdaaaadcdaccdddabcddaacbdcaabdadbaaadadccdaccdaccdbdacbbaadbaabbbdbdcbdcdbbddbcdcbbdccbbcaccbbddcdacccabcdaaadaacbabbdabbcccdaccaccdadcdbdbcbddccacddcccbcacbccbacdcdaadaaccddcaabcbcdddbaddbbaababdaccadcabadcccacccbaacbbddcbbbbcaaacbabdadbcdbcbdbbdcddacbbccdcacacbaacccccbbbaddcdabaabdbcdabaacabbdbcacdbccdbcaaccadabcbbaaaababababbabdbccdbddbcbdbabbabbaccadaacbdcdcccadbbabaccabdcabdcadbddbadbcdaddbbcdcdaacbbbbcabaaddaadcdaccdbccccddcabddcbcbadbbcdbdaaacbcdcaddbababcabcaaacdabbbccbadbbaacacccbdadccdaaacbbccdbbdbacddbdbaddbaabaacdbbcdbcbacbdcbddcbdcbbddcdaaaccacdddbccabcaddcccbaaabcbbcacdbbdaabbaadacccadcdbcaabbcdccaadbcdbdcccbbbcdcbbbccccbbabdcddcbcabbdcdddbbcbbbcdabdcaababcccbcdcbacabaaabbaabababaacabcbabadcdabdadbdabababdaddcbccadabccdcdabaaaaaaccbcbcdcddadddcaccdcdcbbcbcadabadddcadcbbdaadccdabbcdabdbdcccbbabcabdcbabdcbbdbccbaaadbdddadacabccbdddadbcbbabdccbadcacbadaaaadbbbadacbdbabccccbbcdbcabbcbbcddbbcabababbbddcccdcddbacbcddaacaacdbbbbbaddaabccbbcaccbbbdbbcdacacbbdaadbcaadddbcbacdabdddbcdbbadbdcadabaacaccaacbadbbbacbdaaccbbcbbdbbbccaabdaadcdabcacbcddacbbcbdbaabdccabaabaaccabaacbaccdcdcdcdadcbbbacbdcbcabccbdbbccaabbcdbcddcdcbcacadacdbacdcadcbabccdaadcccbacacbdbdaabddcacdaccbdacabdbbacddcddcddcdbdbacabcbbbadbbdccdcacabcaabadacaabbaaacccacadbcdcbacdabdcabdccabadbbcaaddabbbcddacbacdbcaadcdbccadbdccbaccddabbadbbabbacaacdbabbaabcadabcbbcdaccaddbdaabadbaadbcbdccbddbddbabcbaabccbcccadcaacbbdcdbdcadcadcaacbcdabbabbcacdbadbcaddadabcdbaadcccbcdcabbcccbdccdbbcdaddadccacabbcaddbbccabdadbbbbbdcaacdcbdbbabccacdabadbcbbddbccabdbcdccabdcdcccbaaacbcacccbdbbaaccacdcbcbdddcadbdacadbddaaddcbaaacddcbbdbddadbcacadddcdcbabdcccdccbbbccbcddccbccdcacbcbccabbbbdbbbcbdcdbbdbbabdcddcabbacbddaacbadbaaabddaadcccdddaaadcbdabbbcbadcdbaaabdcbcdacaadddaabdbbdbcaabcdccbcccabdadcbcabcbabadbccdcdcccbdccbcdbadabbabbaadbbabdbbcadadadcaccdcaadbadcbadcdadaaabadbcbcdbbaaaaabcacabdcacbcdbcbccabccadabcdcdbcdcdbdccbddbdcccccadabcabaabdacbbdbbaabdaabbabdacadadbcdcabbcbcadbbcddacdbcadbbdcbadadbdbcdcddcababbbcadddabcdaabbdccaadcbbdcdddabddadbdaacadbdccabddcbabbdcbadacaabbdcbaacbcabcabdccdabcaccdacccaadbdbdadabcddbbbdabdbadcaacbadaabbababdccddbdcaaacccacaacddacadbbbaaaacbdcdbabbccdabbacdbacabadbdcbccdcabadddccbccddddbdabcbdacaadacabcacacbcaddbadcacdbcdbcadcbbdbabcababddaaaacaacdbabdccbccacaddaacadbadccddbbccadaddbdacdaadadcdbababbabbabaaddddddcdddbaddabaabcabccdacbacabddbddabacadbdabaadabdddaaaadcdbdddbdacbdabdadcdcabbadcbbdbaddbbadbaaadddccdabddccbcbcaabbabccadbccbcdadacddaadccbbcaaddcbbdadbdcddabaadbccbdcccdbbcaddcccbacdbaacaccaadaacacaadccdcadbbcaabdbdaacaddcaaabcbaaadccbccbcdcaacccabdadbccdbadaaabadabdddddbbdcaabcabddddacbbbdadcaabaabcbbadbdaccabcccdbacbdaccbbbbadaadaaabaaabdbbaaaaadbcacdaddbaabdcbcabbcdbdcddadcbaddcdacdcbddddaadddcdccbbcabcbbabcdddcdadaaaccbbbdaaadadccdbabadcadabbbccccaabaccbbdbaacbccddadaadbbbcdaacdadaacddaabcdaaddddacdbccdacacadadabacbbcbbcadaddadacdabdcbaabaadabbccccbcbdaddcbbbdbbadadadadcabddcbabbcbbbdbaccdacbbbddacccccddcccabcadcbccadcbdbabbbbdbcccdbcacabaccdddadccdabdbccaacdbbbabbcdbddabccaacacbadabccbcbbbdbaabbccddabaaccbcccdbbbdbbcaddadacdbbbbcdcaddabdbaccdabacbccaccdbccdbdcdbddbdbbddbdbdbadbdaabdcdbacdbbbaaccdddbdacabddcadabcaaaaccdaccacadadcaaacbbcdbacabcdbdcaadbddcbcacbcabbbadcdcdcbcccbacabaaadcdccdbbbbbdcbcabacacacbcddbccacddbcdcbaaddacbddaabbbdcbdabbcdbddddadbbbdacdcdbdbadbcdcbabbacdaabdacbbaacbacadaaddadbddacaddacbcdbaddabdaacaadcacbdacbdbcbcdbaddcddadadbacacbdccaccbacbacddbcdcdadcbadcacdbdaabdcaabbbadaccdbcbbdcdcccbcdacdcacccbddccccddaabadacbccababccdcbbdbdcbccbdadcdbcabbcccdadcccadbcdacccdacaddaabdcdbbcbbddadaacaccaddabccdbbdcbbbbbddabcaacaccacdbaadabbcbcdacaadaabcbbaababaccdacdcacdbabdcdccacdacdadddddbdaabbadbbddbaacabdaabdddddcdbaddadbcbbcbddddbcddabbcacacbdcdddbadcdcabadcacccccaabadadbabcdaccbcabbdcabbddacbdcaaddaabadddadcbaddcabdacdbbbabdbaabdbdbbbbbbaadacaacaccdbddccdcaccbdacbacbcabbcdbbaccdbcdabaccdcbbabaaadddadcbdaabdddbdbbacbbbbcbdabbbcadddbdcdccbdccabadbdaccadaabaadcdcbdbbdbacbddccbbabdcddabcaddcdbacaddbbbcbcdcbadcbddbcacabccccddbbbabaadbcbacdcbaccaacacaccdaadbcabcabcdbadaacdaaabacbbacdbaababbbabdcaaaddccabbcacabdbabacbbbdadadadadbadccdadacbdddabadbcddacccdcdbaabcdaabbccacabdbbbbdcdadadcbdaabdbdbbdbdcdcaaaaadabaabadacbcababcddcbbcdbddacccbdbddbbaabcddabccdbbcacbacbbaabbbcdcccaacacdbccbcbaddcbbccdbdbbaccdabcdbcdbacbbaabbbcacbbcadbbbdcacabccacbccdbbccddbbddcbcdccddbaaacccdddcccdacbabaaadbadbcbbcaaacaaccacabccddadcddcaacccadaadacddddbcdccadcdcbadaaaaaadacdbdadadddcdbabadbdbacbcbbabbcdbdcddadcaaadcbacccbcaadbabbccacabddaadddddabbddbdcbcddbaacadabddccbbbabccdcadcdcdacabdacaaacdabdadcaddcdbbcdadaacddddaadddccabdadbcdcdabbbcdadbbbaccdadbbccabadcadadadddaddcdacccaadbdccdabcaacccdabcaccbddabaddcbcadbdadbbbacacaaddddcdaacccdabdabdcccccadaacbdcddaaddbcdcbadcdcbcaacdbbdcaddddbccababbacbdcdbcdccadbdddbccabadcdacabbcabccadddcbcdddaaadcdbbccbdbcbcabaadbdbdbacacbbddcacadddcababdacadadacbacbacbbbccadddcacaadaadadabcdcddccaccabbcdacddacdbcdbcbdddcbcddacccddabccabcddbbaaacdcddbbbdaabbbbdacdcadccbdcdcbadacdadacadaacbabcabaddcbbadabdaacbdaadacdbcbaaabaabaccdcccdddadabccbdbcbddabdddbbbacdaadbaaacbccccdccdacabdacdddbcdcaaadccacbabbbdabaaaddccdcddbddcaabcaadaccdaaabdbddcbccddadddbcaddacdcbdaccddcbadcbdaabaddbacbaadcabaccbaccacdcbdaddacbccbcdabacabcadadcbddadcadccbdddcbabbdbbddacdccabcdddcaaadacbdbdacbbbcdbdbbcdcaabbbabdbadddcacbdbcbcbbbbbdbcbdcabccbddcadcbbdbdcbcdadcbdacddaadcdbbcdccabcdcacababaacaddaacaadaadcbaacdabadbabcddbdbdacabaddddccdabdacddbcdaabaabdaccabdddadcdbabdbcacdcddddadabcbdccbadcdbadbbdbadbcdacdddaabcbcccaadabdddbadbcabdcdccaaabcddbabdabdcbabcbcadbaacdccdcaccaddbccadddbcadcbbddbacdbdacadddadccdadaccbbbcacdacbabadcdbadcaccccaacbcacbbcbcbadbbacbadbabbbdbcbcbbbbdddcaacaabcaccbcccdddbaaccbdddbbaaacabdcdcdbcabaaaacbacccccdaaddddcabdcbaaadacbcabbbdcadcacdcbcdcbdcacdaaaabdadadbdbcbcdacacadcbdbcaddbcdbdacbbccadbddabaabdddcddbacccabbdccbbbbbccbdcbcacdadbdaababdbbdbcdbddbaadcadbbcbbdadacdbadcccdaddcacbdcbabcddcdbdadacdcacaaaccddcbaddbcbdcbcccbabccbbdbaadcadabdbcddcddacdabcdabddaadcbbabbcbdaaaabcabacccbcccdcdddbbbcbddbcbbbcdbccddadadccabcdbcbababbcccdcacddccbcddcacbdabbcaabaadbbccadbcbbbcadabbacaabdbbbacabbdbcbabddcdcbbbacccddacdbbbddcbaddbbacbdcdcacbdacdddcbdcbbabcddaadccbadadbcddcbbbaddcabcabaacadadbcbacaddaacccbdbcbabbdabbdaacbdabcccabdbdacccadccadabaaadadcbcaaccaddaccadacbbcdbccdaddaabbadbdabdaaabacacbcdbcdaaddbddddadcdcbdbcddbddddcadbababccdccadbbddddddaadabcdbdbdbdbdabaacdadcadccdabcabcbcbcacdabddbccddadbdcdaababcbbcaadbbabbbabbcccaadccddbcccdddcbcbcdaddbdbbdccbbacddcaabcbbbbabdbdbadabadbaadbbcaadbcdcabaddbcbbdcbbdabdcaaacdacdddabaaacbcdcababddccbcabbccaaaddddaacbcdbdbadbacbbdbddaacabbdddcadbaaddcaaadadccbdcadbaddbcbacacdbbabadbbdccdabdcbdcdaacddccacdadbbddddabadcaadbaaabbcbaacddddccabbdaababbbdaabdbddbdbababdcbadbbcdddbdadacbbadcabbadbbcadabccaabdadcbabcbbcbdbaddbccacccabcbccddbabcbddbbdbbaddcacbbdcbbbdbcadcadaadcbadcacbdcbcaaccbbdaddbdbddaccdcaddbbdbdaacabacbcbccbcdcbccddbdabdcddbcbbdbacdcddadbaadbabacacdbdcabcbabadcbdcacadcdbabccbbabbbdcabddabbaabdcbaadbbdaaabccdbdcbaadccbcdcaacabbbacaabcbdbcdabbadaaaaabbdbdacdaacbabcabadaaccbcbcdacdcbcbaabdbbccdbcaadaccbbadacddbacacabdaacdabcbdadabbcbacbbdcbdacddcdccdabaddaccdbccaaabcabaccdcdabacbabbbcccccadcdcccbbbcbaaaccbbadccbcdbbbbbbaacacbabbcbddbaabccbabdabdadcbcbcacbadcbabbdcbbddaccbcbcbadcdddaacadbacdacdabcbcbcccbcdcaccdaabbcdbbabdddcbcaacbbcbcddcdabdccddcadcddcacbdbababbabbaddaccbacbddbacbcccaabdcbaccccdbadcdbabaacdabbadcbcdadcbdccdcdbabaccbbbaccdcbdbabdadcbdbbdabababcdacacabddddaabbadabcaccdccaadabcbbaadacabdbabdadcbcbbcbcdbbbcddacbbbdbcddbdbdbcbdabbdadcccccbdaabbbbbcdbabcaabaabbbdccddbacacbcdbaacbdcdabccbddbdcaabddbadabbbcdaadccdbccaccacacabbabcbbbbdbddbaacabcdaadabdacaadccdacabadaaccbdcacbabdccbccbcdbdabdcdccdaccaccbcddcdcbdadaaacbdcbbacbcbabcdddbadbcddbbcbdaaccdbabdbcadcadcadbdaddcdbddddabbcbdaaabccdccdaaacdbddaabdcdbbccaadbcdaccabdcdbbcccdbcbbaacaadcbaaccddcaddcabdcbacaaabaabbbbcbdccddbdabbdccbccbadaabdbbcdacdbdcacaadcacdddabbddcbdbbdadbabbbbcbbaddabddcddcadcadabcdacabddddacddbaddcaabdadccaddccdbbcccabbdcbdaccddaddacdcacdccccdccbbbbdaadbbbdacdaaadaccabddbacdabadcdbdabdbbbdacadbacdcaadbcaddaacbaadcadcbdbcdbabbdaddcbddbcadaddbdcddcabdadababbcbbcdddcbacccdbdaccbcaababbabdddccdcadacdbdacdccbbbbdaaccbbcbbcadbdadccdabaaaaadccbdbbdddacdabcaaadcbbcaccccaabcbcddddabdbdacdabccdcdcccaadababbdacbbbbccaaaaabcbcdcdccddbacbdddbddcbcadcbcbcdbdbbcccdbbabaacaacbbbbbbaacabdacdabdadbacaccabacccdadbbacdbdacddacbddcdddbcbbdacaadccccbcdddabdaabbacdaababcdbcadbbdcabaccdcbbcdbadaadcddccbdaacdcdccdbccbcdccdccabdbcbcdddcbccaddcaadaabdcccdddccbbacbdcdcdaddcdabcdaddccabababaacbcccbdccacddadbbadbdbbdcabcbaaaccdabadcbccbbbadbddbbccdbcadadccababcacddbaaccdbdacdddbbccdabbaccdbdcacbdbdbcbcabdbcaadccaadaacadabbcbabbadcddacaccbbdcaabaddcccdbcadaccabddbdcdbccabbaccdbaaacdcbaaacdadaabdccbcdddcabcdbcadddccdabbadcccddbaabbdabadbcddcbcbdaaaddccdbcbcabdcbdbaabacbbcdccadcddccdddacaaaaadbbddaddaababbbcbaaacbcddbbabcddabbabdacccdccbdbacdaadadadabaccbdaacadacbbbcabbadcabaddbacdccacacbddcaaddbcaaadbdcbcbccbcdcbcbdadbdabddbbbdbadcaaadaacdcaaddadcdaacaadbbbddcabdbdcdaddacdbddbacabcbcaaccbbbcccddaccbaabbcacddbcbbcadbdcdbbadbbddcbabaabbddcddcdaabbaacaaacddccbaccaabcbacbdbcdcaaaddddabdccdaacbbdadbdcacbccddadacbddbbdbacbcaddccbcbcacbddcaabababcbcdadabdaddcadbbdbddbcdcababbaacddaccdcdccaddacbabddbcaacdcbabcbcbcadddbbacbababccadbabacdcdacbbbddbacaadaccbaddaaadadddaccccbbadbabcdadccbcadccadbacbdcccdddddbaacbbcacccdbccbdbdbbdbaadddbdbdcdcbaacdaabdcccccddbdbcdddbdccbcccdbbadaaadcbdadcdcbcdadcabdcababbdadadddcbddbadbcaacddacaadacccaaddbcacaaacaabbbccdaacacadbdacadbcdcadbcabaaabbaacaabdaccddccacacabbbccaabbdcddcbbbbbdccbdbabddaddbdadcdadcadcbbcbbdbbcbcbbdbbdbaccdcabddcadccaaadccbcaaccdbaabcddcddbdcbbbacbaaaabacbdadcbdbbacbbdcbbccabacddbcacccdbcaaaddccdbaacadcdbccdcdaaadcadbdbbddbdbbbccccabdcaabccaabcbadacdabccbacbdbdddddacdbacaadabbdbadcbabbaadbddcacaabbcadacadbdcadddcbcdacddcaaccbbcdadaaaddbbdcaabcacadbcbabbadccaddbdabdbbbdccbdbacdbcaddbdaadaacabddcbadabcdbbbbccccbadbdcacbddadbccdcdcabccbaabdcddbabcacabcbdcdddacaadddadcbabcdacbbddbbbacdddbbbdddbabdbcaccdbabdbacacdddbacdadbbcdccbdabadcccbcaabdaddcdbdadccddacaddddaadbccbccabcdcdbaccbbddadddcacbbccaabbbdbcbcabaaabdddcdcdcaadcbadbabdacacccbabaaaacccdacbbdbbbbbbcdbbaccbabcacbcdabababbaaadddacabdbbcdababccaadccdddddaacbbcdaabcaacdacddbccddbcdadddcdccdbdaccbcbcbaccbddccbdddadddaacabbcbadaacdbdacdbdabcdcbacccdcddcbcddbccabaadcdbdccdababdbdcbabbaddbcbdbdcdadcaaaabaadbdadabcbdadcaaabdaabcbccacccddbdcbccacdcccbddbaacddabbbdcdccaadbccabadddddacbccbbabbbbabaaaaabccccdbadcabdbcabdccbdcaddadcdbcdccdcbbbbbcacbdddcbcbdddddbcbbadbacccddacbaaadccdbddbbdbadcbccbdbdbdcadcabdaacadcccbddbdaddbdabcdccdcbddbdbddacbbdadddbdbabcaacdcaddddcdcbadbcbddaadaddbdbddccadbdabddacabcccddabcacdcdcbccaddaddbabbcbdbcbcbccccbddcdddaadabaccbadadcbabdbbabcbdbbdbcddacacadbacacabdadbccbcbdccdbaabaccddbbddadabbddccbdababaaadbdaaddcbcccbdabbaadadbdabbbdaadcabacdacbbdbdbbbabcbbbbbcaddcbbadbbdbccabbbadccdcadcacdbbdabbbcccdcdaacdbbcbbadbaacbbbabcbbababbadaadbcacdcbcadbcaddcbcbdadddddbcacacdcaabacbbdbaabaddbcadddaccbdbaabcabbadbabcadbadcaaadddddaddbddaacacdcaabaaddbabaaacabaaabccbdabaabdabccbaabdcbaabddccbadccbddadcadcccbacbcdbddcadbcbadbdcdcadaaabbccdaccbaaddccbadbaacadddabcaacbcdcbccccccaaacdaaccdbbadadbdbacdbccbdddbabacaaadbabdccababcdbdcacdbadcabaccbcaaccbccbccabdcccaaadbccddadbbcbccaccbddacddddacbadacdbcbcddccbbcccbddacadbbbdbaccdbccdbdbcbddbdacccccccaaccdaaababddcadbcdbcacdbabdcadbdaabdbcddbbbdbdadcbdbbddabcaaccacaacadccbddadcbcaacdaaddadcdbdababdccbbddaaddbbaddcbdacbdddbbbaabadbdcbcdcdccabbbcbdbdbaccbadccaacdabadaccbccdcddabbdaaddacdcccddbababdabcbbdaaadbdccbbbddddcdddcccbabcddabdaddcabcdbddbcddaccacadbaddbabbddcbddcdacadbccbdbbbccdabbcddbddcbcdcdddbdcacbbbcbacaaaadcabddcabdcababdabcdadabbcbadcddcdbacaaabbcdabbdadddddcacadabdddbcaaccdcbcbcbcabbcbbaddabaabaaacabdabcbcadbddcacaddbddaabcdbabcdbaaacbccddcadccadbacbcbabccaacbacacbdabdcddcdbabacaadaddbdccbbdbccbcbcacbcdbcacabbacdccbbddcbaddaaabccbbddaddbbaccccadaaabacdbcbcaaccabdbdddabbccddbadbbdaccbdacaddaabcacadacaacaaccbddcbcbadabbaacabacbbbabbcacddbccbcaadbcdaadccadbabcdccdbccabbccdccbbccbdaabbddaccbbbaccadcbbbbccccbcdacbcacbdabdadbaaccbdcdaadcbaabbcaadbbddcbddabacdcdaadbdbddbdcaaadaadaacbdbdccdadabddabddacabaccbadbbdcbcdaabadadbabdaadcbcdbbbccadadaacdabaaddddddccdaabdaccbbaacddccbdabddcdcddbaccdacacddabadcbbacbdcddadcbbcaabbaccdacabcabcaaadbacdddbcaddbacbacacddaccabbabbaadccadbcddadcadaabaaccabcdcaddbdbdbadaabdadacaccdabdadcbcdbcaccaccdbadaddacdbacaabdcccdddaaaacaaadbababbcdbddacdccbdaddcdbabdbbcbdbbbccbbccbacdbabbcbcaddacdddcaabccadbadbacabcbaaddcdddcccdcdcadbdbcbaddbbbdadbdcccacdadaacbcbcdcdcdcdddaccadcaadbdbccaadddbaabcbbcbccdcbbabcbddaabacddcaabaacddbcaacdacbabbbbbadcdbbcbcacabcccbcaaacacacbdacabbbdabacdaadcaabcbcbddcaccbabaddaadcddbdcaccbadcaaaddcbcdcddcbcabbdcacccccabdadbdccdaddbdcaabaabddbdbcccaacddcccdbadaddacdcbcdabdcdcadbccaccdcabaccadbcbcdccbbaabbbddcacdbcabdbbacbcccdcbbcbbcaddbdbadbddccdcbcccdcdabdbddadcaabddcdbccdbdbcdccdddcadadcabadbcaaacbbdccdadbaccacadcdadbddbbdcccdddcccabbadcccdbccbdcbcbbaccbdbcbaadcbbccddcadcdbddcbcaacbbabccaacadcdaaaabaddcdddcacdccbbbabadccddaadccabbbcdbdaabccbdcbbdbcbbdacddcacbaacbaccbdadabcccdabccccdacbcdbcbabbdddacdacadccdcbadcdbaccbcbbaddcaacbdcddaaacbbccbaabdbbaabdbbbbbbdbabccacbcabbbabbccaaaccadabbbadcabccbdbdcdbabdaddddbbbdaadcbbbbacccadacdcddcbdcabaadcbbaacacccbccaabbabcadaabbdbbbaadcaabccaccacdcdbadbcadcddbabbbcccbcabdadccadaacacdbcaaadaabcacbbdcbbbadbcccabcacbaacabccddcadacacccbbbdadaabdbbadccaacadabadcbbaadcdaccabddacdacaccdcadacddbbacaaadcadbdbdbacbdcaabcccdabcddcacaddbdacdabadbcbdadddaaabbddaadaacdcbcdcabcbcbccbbbdbaaadbcbaaabcbaadbdddaddbddcacacddababdcaacccdcadcbdddadddbcabbabcdacadabbdcdcdccbbbadaabbdadacbcbddccadacccdbdaabcdcabcdadcbbcbddcbbdcbdddccdddcdccaadbaaabbdbbbadacdabcdcbaaadcccdcbdbdbabaabcaadaaaacdcaaabbdacbabbcbacaabdcbbcdabcaacbbccaacadbdaacddcdaadbcccaccacabcbcadabdacadcdcbaccabccacbacddacddabdbcbbcdbabacabbcbbcabbcdabcbacdbcbbddcdcccbaadccdaddabcddccbcadcbdaaddbbbddbdbbaddbddcacdbbccddddbbcdcabcdddbdbbdcadcdcadbaadcbbddadadbabbdcaaddbbddabbaacdadadaddabccadbddaacbdaccaddabcdaaacdbddddabbbdadacccdbbaabcababaaaaaabbdcadbdaccabbdddadcabdaaaabbbaababcccdacbcccbadaadcdddddbbbcaccddcdcbdcdbdacacacacdbbdbcaadddbcdcbdccadbacdcbcaaccdcaaabbddcabaddccdbbadabcadacdcbcdcbcdccdddcbdbdcccbcbacabbbaadadbabaaacbccdacbaabaadbdbcaaacbcadcaabdbcdbcacdddacbbddccadbadbcccddbddbbabdadaaaaadbadbdcbdbcadcabadacdaccbbddbdbcaacbdcabcbabbcadbaccbaaadaacdadbcbaabbcdadcbccbbddbcacccdbbcdcddcacaacabbdabaadcacabacdaccbdbbbbcdcdbbbbaaacdbdbacabcbacdbaadbaccadaaadcbccbaadbcdccacadcdadcadddadbdbccdcbbdbababdcaaaccadabaabcaaddcdcabbacdaacbdadcbbbaacdccddbcccdcbbbbdccdcccccdccbbccacadccbdcdabbcccabbdcabaaabcbaaccccadabdacddcbdabbdbbccadcdbcaddbbcabcccacadbabcbcaaababbadcdccbdbadbcacaddadaacdbabbbbbcaadabdaaccbdcbabdbdcdcdcbcbdcdbcdcaabccaddaabdcbbaacbaabdddadbaccdcbaddbaabbcdadcabbddaabddabacabbcbcaaccbaaaaacdaabdacbcadbaaacaadaaddbbabbadbacaabdddadadaddaccababaddcadadaabbdbcddcacddbdcdadadbddabcabcabcbbadccabccaabcaddcbdddccdbdcadacdaaadccdbbdbbcbbabaaadbcbccbcdbcbaaabbbacbabbccadcbdcaabbdaadbbaccccdbadcccbcdaddccaaddbccaaccabbcddddaadbcccaababdabccacdabbaaacdaadbdcdcdbaccdaacdbcadaaaddbabadabbdcbbccacabcddddaacdddabdbccacbcddbbbbccccaadabbcbdaaccbbbcbbdcdbbbccbaaccccbddcbddbacddcdacdaadbbddcadcbdbcbbbbdaddabbdabdcbbcaaabbabdcdbdddbdcababbcccbbcbacbacccacbcbaadbccadbcdcbbdbadbcaadcbdbadbccdaadbbcbddcabbbcaddccaadddadbcacbcdcbbcbacccbbdcadaaaaacdacbdadbdabdaacbcbccdbbbcabddbcddadcdbbcbdaccdaabbbaddbcbbbcabccbacadccaccbdcddcaddbadbbddcaabacabcacdddacadbdbbdbcabcbcdaccdaadcadacbcdaaabdbcbcabcadbdbcdbacabdcbccdbacbcdaacabbaaadbacbcdaadababbcaccabbacdbaabababbcddbbaabbccccadbcbaacacacccacbdacaddccbcdacccdaaadacbdadcbbdaddabaabadcbcabacadaabbbdcdbabaabbcbcbdcbbbbdabcbdbadacbccabacbaadacabaaaddbaadaddccdabbabbaccbddcaddbcbdbbdbbccdacbdbdcdcbbabddabcbbcccbdcddddacdbacdabacbbcddcbdcaddbdcdbddacbdccadabddcacdaabcabccaabcabcbcdbdddaaacccdcaddbaabccaaadcccdcbbcccbbbcddcddabcdbaabbbcaccabdbacdddccbddddcbaacabcacaddabdaccdbaabbbccdddabbbdbdabcaaacbbbcddbcddcaadbabdcdbbdadcdbdcaabdbcdabdadcadbadddbbaaddbcaacaabddcbbacadcdacdabcbdccaaddbbcaccdddacbabadadcdcdacbdabbacacccbaacadbcbaadccbcbbabdcaadddaccddbabaddbbcdddabbdcbddadadbdcbccdcbbabaadddbcddddbcadcaacdabbcbbbdaabddbbccbddddadcdbbbdbdbcdbdbccbccbbbcbbbcdabadbaaabbaccbcbccbaccdddcbdcdbcacaabaaccabdaacaacdbbcbaccdadccbddddcbdbdddbcdcacbbcaaccdaadacaabbadccdbbacbdadcabaddaabcaaabadbdddbadccabccdbdbcbbaaabdcabcaabcdcbcbbddbadaaccdcddacadbdddbcbdabaabccdddcdbddaacddccbdcacccdbddadbcdbaddddaadbaddacbbcbcdabaabbabddbababbdddcbbcacaaddbdccbdaddddadcdbdcaaddcdcbcddccdacaaadabdaddbdddccdbcaabaacdcaacaadacdadbbbbcdbaaccbabcdcacbcdbdcacdccbaccbdbdaabbddccbddccabccbddabccadccadddddaddadaccadacdccaddbadcbaaadcaaacccbaaddaaabddbdabaaacccaddccccbbcbcdccbbbdbcdcbcabacbadcacddcdcdadaccccdcdabcdaddbcbcccaddaccccdbddaaaadabbaddaabcbcdaadcadbbcacdbabbadcaaaacbcbddabbabbdddddbccbbaddcbadcacdabddccdcbdcababacacbadddaaadbaaadbdbcbbdaadababbbbadddddbdccdbbddbcbaababdddcdcddadbbcbbdcaaabddbccbcaddacaaccbdbcaabbacbacdacacdccbbcdabbcdbbdbaccabdacdbaaadadabacbcaabddabdbdadcdcadcaaadaadbdacbbbdddbbbcbadcbcddbcbcccdadcbbbddaacababdbccdabdabcdaaacadabbacbcaaadaadadabacccbbdbddcdabddacddcabdabcbcbdbccbdbcabbdbbaccadacbcaaaabdaaddccaddacbcbabdbbdccacadbabcadddcccbadcaaadcdacbcacdaabddaacdddbdbddaabdcacbcdacdadbdcaabaabcddbaaaadccaadbbabaacccaccaaccaddcbcddddbbccdcbbcbbabdabccbadbbaacccaccdccdaddacdaadcbadddbbbdcccaadadbddcbbcdccacaacccabdcbddbcaadcbdaaadbdaccdbcbcdbbddbdbcbbabbdcdabddbbcdabcbcbdabbbadddaaabdddccbbdaddcbadbddbbbdadcddcabbcabdabaacbdccacaaacadacdacadccaddbbcbbdddadacbabdacdccaaadacacacacbabaaadaaadbabcccacadacdccbddbacabdcacbdcccadcaaacabdaadcbbcccddcadabddcababcdccdbacacdbcbcbbbcddabcbddcddcacccddadaaadddcdccdadbcddadccbddbabadbdbacbdddbdabacaadbcaabcacadaabbaabcbcccbababaabcbdbadcabcdddcccbaabccbddcddacdaccdadbdddacdabbccdbbbbcacbadadbcbadabdcacbddacbdbcaddcabcdbbabcdabccbcdaccdcbcbbadddbdcbbdcbbaaaaabaadcbcabdabbdbbdbbdbbdcccdbdacaccbdcdbddcdddadcbabdcdbabcbadcdddcaadabcabbdcbddcadcdddbadbaccbbcbabbcbabaacbdbcdcddcacdbadbdddaddbbadaadbaacdccbacbbdadbbadacacbbbbcacbdbbbcdddccdbabddaddbbcbddbcbacaaacaaccabcdacbbdadbaccbcaadcddddaaaaccbcaabcabddddacacdbcbcbbabdbbacdbcdadccccbddcbcacaaacabcdaaccdabcbccbaaaccddaddbbdbbdcadccdcbcbdcabbbcbccbccaaacdcbcaccadadbdbdcacccadaadadcacaabacdaddbccbccacbccdacddcddbabacddcadaaabbbdbddacbacddbcbdccadbbcdccabbbacacaabddcbcaaabddccdbdddbacccccaddadcadaaccccdacaadbcdccaacdbbaddbcdcdaadbbcadaddbabbcacccaaacdacaccbdddabcdadccabdccbcdbcabbdababbaacacbbdcdcaddabbdbbbaccdcbadbdbbcadccbdcddaabdbbbacacaaddccccbbdbdadbcababbabccbddcacbbbbbcbbaadacdaacccccbdcabcbcaaadcdbdabcacdbbadaccadddccacdacabacaabaadbaddbbdcaabbdbaddcddbbaaacbcdcdaadbbbbcddcbabbbbcadcdddcbbbacdddaaccccbbdbbcaabbddbccdbbcaccbccdadcabccababbdadbdacacaaaaabddacdbabadcddacdcabcabbdbccdbadacbdbadaacbccbdcbcbccabacaaabdccacddcadcccacbaccdacbddcaddddcacdbdadaccbcbbbcacbccadadbdbadcabcdacddbdcdccdcacddcbaacdacbabdabbbccbcaaaabbbaaadbabacaaaaaadddcccdacbdcdcdacaaaaaddbabbccdbdbdbdbbdcdcddcbdbccdcacdbaabcdccaccbbbddbaaadababaaaaddcbbcdbbccdabcbabacaaacacbccdabcdcdbdbbbdadaadcdbbccaabcdacaaabbabcbdcbbbbcaaddccbdddcacbcaddaabdcacdabababdadacdbbbdaaabbabbdaddddacbbbcdadbdcddbcbcdabcbaaacdabcbdbdabddccadbbcddcabcbbabdcccddcbbdddbbcbadacbdccbccccabadadcaaddaabacddbcbccacdadbdcdcbbdbbccabcabcddbbdacdbdcdacbbcccddcbdbbdabadbcbdcbaadbcccaabdcdcdbacddbcdcacdccdcdbabdbbcababcbdcdddbadbabaaabccbbcacadabcdaccdbbcbcbbbcabdcbcbcbccabdacabacbcdcdcabccdbdddbbaddbddadbbaadbccddccbbaabcccbabccddacaadcadbccadbabcadcdbcaadcbbdcbbbbdabbbbdcbdbcddddcadcacacccdddadbaddbbdabbdbccbdccddbadcbcadbbcbccdccdacdcccabbccadaddddbdddccdccddabdcbacbdddcaadddcbdaabddabcadddcabadbcdbbcadbcadbcddcccbbbbcdbdbcdbadddbaccbcccdddcdcbbbdbbacacacbacdadadcbcacdccccbbbbcaacbcdcbccbdadcbabadbdadbccdbaccccaddabcbacabcabdbbddacdbdcbbbbdabbccccadacdcccdadaacbacdcacdacccccadbcaacbcbacaababadcabbacbbcabbcbccbaabdbbdabcabdccddcbdbccacdccdaabbaaabcaaaabbcdbdddabbacaaccdcdbcaabbddaaabdcdaccdacaabbbdbcaacdcccccbcaaadbcdbaacdaddccdadccdabaaabcadddacbadadddbcdaabadcbbaaccdbbcbdbbaaddbadaaabbdcdbcbbdabbbcbbcadbbbccabcacddcdadcddbbcacbcccaaacddddcbcbcccabcdcdccaaaacadbdbdbbddabcbaaddbbabaacdaaaccbcaacaabaacacabcccbaccaadaaacbcbddcdaadbbdadcabadaabcddabcddbaaabdbabdaccbcbdbabcdcadaabddddbbdbbbbcababdbcacabdcdaabcdadadcaaabccaacbcabdabdcaadbccacccdabadadbbbacadadaaacbcabaddacdcbadcdddcbaccbbdbcbddaaccbbdcacdcacacacdacbbacbcdabbcbabaadaccaadbcbbcbabbdbbcbabcdcadbddcadbcdbadccbaacbdbbddbdabcbabccbcdcacdbdcccdbaaacccdaababadabbbdcccacdbaddaabaddbddbaacbdadddcaabcbdaddbcabdabaccdccdacbacabaadababddcacbdbcdbaaabbcbcaadbadcdcddccabcbdadbbbcbabbdddbcaaccaddbabaccacbbdadaaccacbcdadabdacadbdddbadcbcccddddcbddbdbdcabaaddccbacddbdbdaabacccbcaadcddbaaadadbdbcdabcddbaadccbaacdcaacbddcaacdcacabcabdddbcbbdacabccbbaabdabadbabdbddddbdcbaddddcbdccaacdaacaadbabcaabcacaacbadcbbaaacdacdbdcbaaabcdcdcdbccdabcdadaabcbbbbacadcbbcdccddccbcbbbdaaaabcacbcabdbccccaadabaadccacbbddcddacbdcdadcbdcaacadddbbcdabcdbaccdabcddabaacaddaaaabdbcccadcccbaadcddacbabcdbcdcdddbbcbddbadbdcddbcdabaacdadbbaabbdddcbaadbcdcbdbccbcabdbbbaaabcabbcbdbbdbdcacbcdacbdaadcabdcadbbadaaabdadddacdabbddbdcadcdcccbddcacdcacdbbbbddcccdbcbababaaababdcbadabccccbdddacbdaaacbdcdadaaddbdcbdadcbbadcaabcbbcbacbdcdcbadcbcbacbabaadcccbdabcbcbdadbadccbbdbbcbbaaabccbccabbabbcdbdbdadccbdbbdcbabbbaabacbaaaaacaccbbadbcccabccdbbbdbacaccbdbcbabbbcdcacbdddabcaaaccbaabcaacdacbababaadcccabdbcadabdbcadacddbcccbbbccbbcaacccacbdbdbbbcbccdbdcbdcbbdcadcabddaccbadaccabcddaddbadaabcabaaabcbaccacadcddbdcddcdcbdadcabbbbccbacacbbbbacbababacdbdadcccdbcdccbbddbaadcacbcdcdcbdccbbabcbacdcacccdcddaacbcabdcabaddddbdbdbdbcabdcdbbddacbdccaabbacdbbbabcddcdccacabdcbaabbdbcacaabbabdcdbdccdccbbadaaddcdadcdddddcaabcdcbcabbaabbddcbadabdacbcdddabaadcadcacaabbbacbbdcbdbddaaadcadcbdbcdccbaddaaaccccdcdaddcabcbbaddadbbdbaaadbdaabdbabdadcdddbdbaabbcddaabcbcaabdadcabaacdccadbdabcbabdbdcabccacabbccacdbbdadaadbdddbbaabcddddacdabdbdbcbabcacaccdcbbacbadbadadabdadbadabcdbbcacbbccbdcacabadcbbdacabcbabcaaaccdccddccdabbddcabdccbbcaaadcbbacadacbabcaabbbaacbbbbbdcbdbcdddcdacbddddaadabcdabdacdaabccdcdacbbccdbccccddaabdbcdaaddbbdbdcccbbadcbbbdabdaccbbdbdccddbbddcbacbcccadaddabcbadaacbcadcbbdcadaadbcabbbcacdbdcbadbbdcaaabcadaaaabdcabdbdcaaaabddcabbaadccdcaccddadbddadadaaabbaacacaddadaddbacdcdacbcddbacccaddabbbcbaaaabccaaaaccabdabadacbdadaaaabbaccaadbaacdcabacbaacdabadcaaddaccdbacbdbdaacdccadcdcabcdbdbbbabdcdccdaabcdbddbbadccabcdacdacadcbcbdbbaababcccabccaacbaaddcacdddabaddaaabadbddbaabddcdbbdbccdabaacbbdbccddbdaaddcddddbdabddaaccaabdcdadaddcacacabbbdbbdbbdbcabcdcccbbccacacbcdadacddbbaccacbcadbbddbaabbaabcdcaaaccdaaabadcbcbcdbabaadcbadddbbacadcaddcdbbccbccbcaabacabbaaacbadbdccbcadaabaaadddaaadcbbaadbdaacbabdbddaddbadbdabcbabbbaacddabaadadcacaabdcaacdcadccdbbdddbbccadaadbccbbdcdcdbbccbaddacdacabdacbdcbbbccdabbacdddddddabbbcaccbcddbdbcaacbdaadcddbcaadddbbbadbbcccdbbddbbdbddaabbadbcbbdddddbbdaadabcbbaddaaaddcbcaabcbaaabaacadadbcaadcadabddabbacbaccbdccaabbcaacdabcdaddccbaaddddbaddbaadabcbccdbabdacdcabddabcadbddbbadcbaabccacddddcacccdabcbbdabadddcacddabcdbbdbdddbbacddbbdcbbcaacbadcbdbcccdaaaadbddcbadbbddcdbabbdabbcbccbdacdcdacdbdabbbbcddbcadbddcdcbaadacbaadbdaadbccbbadcddddabdcdcbdbdbbcbadbcdcadaddabadbcababacdcbbcdbadcccacacabddbaabddbcabddabcdcbdadabbccbbcaddacdbaabcdcdbccbdcaabbaddbddbbdbbcbcbbbbdbccaccaccbbaddaccccbbbdcbbbcccbbdbacdcaccdacadaabcddddadbadabccddbcaccbcadcbbabdccdcadbdddcccacccdbbadcabbbbababadbabdddbbdaccddbaaccbabbbccabcdbcaabadcbaadaabcbacddbcccbadbcbabccdcdccdbacdbddadcdbacacbabaccccbcdcacbacababcadcacbcaaaadbcaccbadabbbddcdddbaacccbddbaacbcbbddbaadbaabbdaddcabbddddbbdddcdcbdcbbcdccdbcbcbdbdacbdacacbdcadacaddcdacbaabdacadabdccaddabcbddacaabcacccacbbacddaccaacdddcabbdbdcdbaabddbbcacadccdabdbbaaccdbabdbbcdaccbacdcbdadadbdabdabcadcbddbdbbddababcaabbaacbcddacbdbbadcdcabcbaaccdaadcdabbbbcdcdbcacdcddcbabddabdabbbcccdcdbdaadaadddccabdbcddcbddacccacaacccbbaddacbcddadadaaabcaddcccbdbdacabccdccadbdddbbacbdcabbcdacbaabddbadddaabbbbdbbbbdadabcbcaaccacdcacbdaccbddadbddbdcddbddaabaaadababcdddcbaadabcdccbcbbacadbdccacaaabdaadbbabbcadbddbdadcbbcaaaaccaaaabbcaaabaddacddabdacabcdaacdcbabbcbbdababcdcddcaadadacaaacccdacdcaabdacbdaacdbbaaaadaabaabdccabdcbdbcdadccaabdadbaacdbabddcbbdbacacadcbcaaddcadbabcbabaccbbcddbdbaacacbbdbccbdcabbdcdadacccdcbacdadbcbcddccbacacdaacbcdaabdccdabbcbdbabccdaacdbcbabccddadbccdabcbdbdabddcdcccaabbdbadcbcdaccbdbdacaabaccadadddbaccdcccccdcdacbccbacdaacbddabdcdaadcdabbbbabcaabbccdcbcbcbbcdbabdcaabddadababacdbbbdcccaadcddaddcbdabaabbcdcaddbabdbaccccdbbcddcbddbcbcbbaccdbcaccbccbdbdcbdbabdcdbdddcbddbdbdaabdaccbaccaacbbbdabcbadcddbabcccccdcdbcdbdacccaabbbbdcacbadbacadbacbbcdddcddbcacaaacccabacbcacabcacacbbbaabcccabdccaccadddadcbdacbdddbcdcacbaddaabccdabcabcbdaaacbcdbdbbabcbcbaadbcbaaabaabdcbcadadadbacccbbcdbcdccbbacdbadcbbbbcabcabbdbbdddaddbaccbaaadcccacccdabcbabaaabdbabdbcbcaadcbbccbccadabdcaccabacbbbcdbdbdcbadcbddbdbbdbbbacaadbaaabadbdabcadbbbaabdcdbcbbdbdcdcdabcbbbdaadacababcdbccaababccacdcbddccbddcdcdadaddddccbdddcccdbcdabbadbaaabbddbdcbdadcccadaadacacadcdcaacdddcbaacdabbdbbabbdcacabaacaaaddcdccdcbbcdcaabbdddabdddcaabbcdabdadcdbbadabbaaaaacacbdacbbaccadadaddcbdcccabddcbcdccacbbbabbabbdcdbaabccbabdaaadadcdbdbcabacbdddaaccdddccddcadcadaabaccdcabdddddccdccbcadadbdbddadcabdadcabacddcbacdbadaabcdbdddabcdcdadbbadcbcabcdadccbbbcadaaabacadbcdccaabbcdccbcabdaccdcdddcacadbcdbbaacbbcbbdbddbbacbbaaacbdccddccddcccabbbadbabadbddabaddbdcaacacbcbaababcbcbccbaadbbddaddbcdbaacdbaabcbcbbbddcbddbaaababacdbbdbccdaabddbaddcbbaccdcbbadacdadaabcabcbbadbabbadbdcbdaacbadcdaaaadbcacddcbbcacbbbbcdaaaadacdbdcbaabccbcabdbcbcdaaccbdbbdcccbabdcbdbcadaccadcadaabcdbcdbdcdabdbadadddaccbaadadcabbcbccdadbcdcaaacbdcacacddbcadccbbadaccdbabbaaabdcbdbaacbdcacacacccdbbcdaadddaadccbbcabbcadadadddddbbacabdcbdcddbdbdcdbcacdddbbbbdcbcdccbdcdcbdbcbbbcbaddccadbcdacadbacdacbcbabbcbacaddacbbaadabacbdcabaadbaacdbccababbddcbabbdbbccbcccabbbcbabbcabadadbbdaacdbdddbcdadbcabcdddaaabccacbbbaababcdacddcbcabcdbccbbccbbcbbbdbcabadccbadacdcaddcddabcdbcbdaddddddccbcadbccdcabcdaadbabaddacdccabdcbcaaabadbabcaadcadcbbdababdccbbddbcabbadabacdcababacbdbaababaddaccacadcadbdcabbccdabaabdddbdddcbbdbdbdcddddccdaaaadbdbcadcbdaabcaababbcdaadddaccdcbccaccdadadbddcaccacddcbaabcbbdccbacdacbcacadcbcbdaabacaccbccbdaaaaabcaaadbcaccdcadbbacbabdddacbdbabccbaacccdbbdcaaacdbbbaabababdaacddddabaccadcbdbcdaddcbaccadadcdabbbdbcdbbadacbdddaaccadcbbcbddcbbdccdddcbdddcbbaadbcdadcccbbcacabcdcddddbadcacccdcdacbaaabdbaadbcbadcacabbaacacbdabcbdbccdaaadbbdabcbcdabbbaccdcacbaaadcdddbcadbabdaddbbbcbdccaabdcccdcdccdabdbdadbaaccccbbbadbdbacbaccaacbbddbdbcacdddbbddcdaabddbacabadbaddaddbacabdacddbabbacacdbacccacbabcbbcbbbaabcbdaddababcdcbddaabadbbcbadbdadaccbdcdadccaacbbaccdccaabddddaaadcbddcbbdbddabdcdaadbbccdcadaabbddcbdcadbadccaabdadabcdbdbaccadcbdabaccacdbdbbbcdaccddbaaacaccacadbabbdabcdcdddcbddacccdcdaddcccdccccdaccdddbcbbbbdccdbcaccddabddadbdabddbdcdaaccacdccbcddbdbdaccdcdacdbbdbaacbdaccaccaddbbbdcbbdbdcdcabcbdcbdbabacbccbddcbaccdddcacdccbcdbdddddbcbdbaadcaadaddbdaadccadbdaaadbbacabbaabbdadaacabdcbbcddddcacbbadcccaddaaddbaadabbdcccdcdcddbdaabdbcdcbddabbcaadcdccabaacddcacdacbabaabcddbbdacadcdcbadbbadaacdbadccbbdcacaddbbbaddcadcbdaabbaabbacddbdcdcbdaccdcdcccddabdacbcbcdadabadaddbabdacaccbdacacccbbaabcdbccdddaaacddabaddcababacddaadbabcbbcaccaacadbadbbcbcadacabcbabdbbcbdbcacacdbaaddbacccbabcaddbddddadbdcbadbaaddaccabcccbcacaccbadcadbcddcbbabdacbbbacdbdbdcababcccbbbdcbbcbdcabcbdcdcccbdaacbaaabcbddcaacbcabbdacadcddbcbbbbdcaabcaaabadbdcadbcbdbababdcacbbacbdbcaabcdcaabcddadbadbabbbcaddabccaccadabbdaacacadaddddcdaddbadcaabbddcabbbcccccbaacbbbbcbdabdbacdcbdadbbadddabdcdddabaabcbbdadbddabdabdccccacbabcbbdcacaddcddcbcdbdabcdbaadbbadcadddbdcbcccddabaabaacabbddabbbbccdccccccddaaddadaccaacbaddcadabadbabccdabcbbbaacdbaaadbaddbccbbdcbdadbabacdadbacbabddbdcbccdbddcdadabbcacabaccccdbcbbbccddbaccbacaacabcacabcacaadbdbcddabaabbbabbcdbaacabcadacccbaddcbdddabcddadddddbdaccbcdabbbddcdabaaccdbabacdcaccbbbdaabcdadabbaabdbbcbcbbbbaddbacaabcaccdcddacbbbdcbccdadadcaccccdaabbcbbbbcabbdbddabdbbbcddbbdcbccadbcddbcababcaaabcbadbdacbcddddddacbcddbccccdbdcbdbbdccdcaccabcbaaabddadbabadbcdccccabcdbacdbcddcccaadacdacddcaccddcadadbaaacdbaadacabbdbdcbaddbabbddccdccbccbacdcddacaabcbddbbacdcacbccacdabcacacdcbcdacbcdaccbaccdabdddcaacbbcadabbcbbdccaacbdbbbddacbbdaadddabaddaccbbcdaaddbdacdbaabbcbabaacccdddddbddbdbcdaaadbcdbdcbdbcbcbccacbcaddddcadddadcdbcadabccacdccbadcbbbbcacacaadbcddabdabdcbabababadbcadaabcaadcdaadbaacbddaaacddbabcdcbdadcbbbaaddccddabbccabcdddbdbcadabacdcaabbacddddbabdcdbacabbabcdbababacbdaaacdddcdaaabaddcdcdaccdbabaddaddddcdabdacacacddcdddddddcdbcabbdbcddbbaacabacadbcbddccdccbcbaddcccabdbadddbbaddaabddbacbadcaaccdbdcaddaadadcbccbcccbcabacccadcdbcccbccaddcddbabdcbabddcbaadcabdbdcbcbacaacdcadcccbaccabbadabdbccaadaaadbbccacbabcacdbaacaadcbdbcdaaddabaddccdaabcccacddadbdbddccdcacbbacaaabccbaadbddbbcccdacdaadccccbbaddcdbbbdccbcaddcddcaadadadbdbabadaabcadadadbacabacaacccbcbbbabbdbaccbbaadbdbadcabaababdbbdcabbbbcccdcadbbbccaabacbacadabdaaacabcabdbbddcdddabdaacabdcdbbaccddcbcadabbaccadaddababddabdaaccbdacacbaaccbbdadcdbbaaccbabbaccccbcbbccbaacdacaddddbddaadabcbaacddddcdcbabccbadbcddabadbcabacdddcbdacbccbababaadddbdaabbdcdcdccaadacdddcddaabacbcbccdddabdbcacacaacacdaccacbbbadadacaaccbbdabbbdcdaabaacdabacbbbdbcabcaadadcbcacbdbcbbbbcdadcbdbdabbbbabbacaabadaacdcacdcadaacadcbbdbabbddddcacbbaacbadcabbbccdaddbadacdacabcdadcacadaadcdaaccbcbdaaabccbaaacacbddbbdbddbcccddadbcbbbcddcabdbdacbccbbbbbcbcacdddabaadccbabbdbbdabdccddcadddbabbbdadaccbbaaadcaaccabadaddccaddacddaabacdaccabccccadcdaaacccabbcbdcbbdccdbadabdaacdbbcdaaacbbcadcdadddccaabbacbbcdcdcacdbaaaabbcbcbdbbcabdaaacabdcabccbdcddbdbcbbaaddbdabadbdbcdccdbcdacacacaddbddaacdaaadddcbaddccccbcaadbbddcabbcddcacddbcbaaddaddcdaddacadbcacaabdadbdadbbabbdbabdadcbbdaadddabdaacaacbcadaacddadacddcdbaabdbdcabccadbcbaddcdbabcddacbddccdababcacaccacdaadbacdddcbdbbddaaaabccabaaccdbcaadbdbdcdbcbabcdddaadccbbabdaadaccbbdcaaaabdddacbcbdbcabaabdcdbddcacbbdddcbbdcccdcdaabaabbaabccddbcdccdbddcacbbcdbaaddbadabdabbacacaabdcbbbddabccaccddadcabccacdacbccadadbacaaddbbacdaddcddadacabbdddaaadadadadbbcbddbadbdbdbdcdcbbcacdcaabadabacddaabaadccbbabccbacbbcdadddcadbdbbdaaaccdaabaccccbaaacbdbbabbdabcdcdcacdabdaaaddbabaacaabbbcadddadddcccdaabcbadddcddcdddacaaddaddddacaccdcdcdadababcdacaaccdadbbcdccaccadbdbcdddbbababccddaaabdcdccdccacdbbabbcdbbbddbabddbcdaacdaaaccccdcdbaabbbaddbadcacaacacccbaadaacccaadbcccddadccbaabbccbbadbdcbdaabddcbbddcdbdbabccdaadabdaccbadddacaaacbddcdbbccddddacacbdcacdcbcbabaaadcbbbacdbdcbadabbababbbccbdddbbacadddcabbaaccbbccadcbdcbdcbcaccacabbdcdaabdddcbcacdcbabcaccccaddaddaabacaddcbcdcddcbdbbcbdcbccadadddbaacadacaddcbcbcbccbadabbdccdbcbccccdbddbdddaabccbccdabddadbadacdcbacbdcacacbbcbdbcdabcbbcdaddadababbdcbccdbacddddbccaabdcdaadbacbdbbabdbbadadddcdcddccacccdbcbbbacadbbdddbdbdaaccdbdbddddabbaadacbbbabcbacdcbcdaddcaacdabaacdbbbbbadbbcacbcccdbcbbdccdabaccbbdcddcccdacabdaaadbaadbdcdcbbddcddbbbcbddaaadbbdadadbcbbacdbbbcbdbcdabddcbacbaadadcbbabcdaddadabcbbdccbcbaccbacbabadbbaddbcddbdccabbdbcaddaccdbccabbcddbcccaddbabccbdbaaacbadcaacbadcccddabcbdddacbbbbcadbdbbbbaddabbdacadddbaaddadbdcccbbddbcddacdcbdddaccbdaaabdbdccababbcadddbbabddcbdcacbcdcdbbccbbcbcacabacbccdbcabccadbacacddcccdcdbdbbcbbbdaddbcbcacbdadbbdcabaabdaddbcbbaaacbaddbadcbdbbdcddbabbacacccbdacaaadddbdccabbadbcbdcdacacbacadddcbabddcaabaddaacccaadadacbabbbccdadddaacdbbbdbcdcddbbdbbaabbbcdbddacbdbacdcabbdabdabacbddabcaccccbcdcbcacaddbcbcadbabacadbdbbdadbaacabbdcdbcacddcccdcdcbbdcadbddaaccdadabbbddcdbccdbccdcadcbacaabcddaccddaaadddcacbdadbdcbaabcaadacdcbbaaabacbbdaabcdaabcccabaccdabdbdccbbdccbcdbbaacccdcdbcccbbbcbbabddbadaaabddcabbbcababcccaccddabccacdcaaabccccbbdcdabdbbabbdbbaacdadaddddabccadbcaccdabbccddbbcbabccabbbababababccbbacabdcbdcddadbabaadcadadbadbcaadbdabaaaacadcdcacbbcbdcabbcbddabdbacbabbddddbddcdcaddbccdbddbcbdbcaccdbdaccdbbccaaccbbaddbbacbbdabccadabcabadabccdcacdbbdcbbdbbadccddddddcdbaaadcbcccdbdbacabcdababdbcadcaddacdbcbaacdaaacbddbdbaddcdddcbacbcacbcbccbccdcccacddaabbcbbcddbbabdadbabdccdcdcccadbccddcabddcadcabcbbcbdaaacacababadbbabbabbabcbdcbbadccdcdbdabbadcbcbcbadbddcbacbdccdbcccdbaaccaaacccbbdaaacdcccbcdbdbaddcadaabbbccbabaaacbddddcbbbccdcaccabcbdcdacacdbcaaacadbcbaabadbbdccaaacbbdadbbccdbbadaadbadbbcbccbcaabcdddddabbdcaaabbbccbadadabadaadcacbbaddbdcdcddabbcbccdbacbabacbcaacdabadcccbcbbdaddcdadcbdabdadcaaacbcdcbcbdcdcbabccbcbcbdbacdaddabccaacccdcacdcddccacbbdadcbccdbddcadcadbcadaadddbcddadabaaadacdbdcbbcbbcbbddcacadaaabbdcaacadabcadbcbdddcbddadbaabdddddcaadacdbbdaadbccaaabadcdadbbbbdccbabacadbabdcdabccccbacbdaddaccacdacbbaccbacccdadadcbadadacbbbabacadbdbdaacdbadcbacbacababccddaacdcbdaddcddadaaadcbbbcddcadabcccbcbabccdcbcbadcacabadccaadadcdbbbbaacbabcbddddddccdddcccaaccaabcccadbcaccaddacabdcaacaaacdbdbabaadbbddbdddabcaabdcaaabbcdadcddbabdcbcccbbadccbcacbbabcbacadacbdcababcbbdadacaabadabdbadbbdadadcabcbaacaddbaabccdcddcdbccadcccdadbccddadabcaccacacaadadccdccbbacbaddadaaddabadbcaacabbdccddacacccddcccdadccdaccbcdcddddcbbcbcabbccbabbbabcbbddadcddcaabcdcdacacaaacccdaabbcacbaabdacbabbbdacacadbbdaaabbdcacbaaddbdaabdbddbdbbadaaddcbadbbbaaccadabaadbbccdbddcaaadbdaabccccdabdbdcdbbccdabdbbcccdcbaddccdbdabbcbcdacadbbbccbcdcadbbbdacacdccdbdabcdbcabdcaaddaabcdaabcdabcabcaabaabcddbbbcbcbaacadcabcbabdcbbbadcdcdcccbdbaabcaaaaacbbbabcbabcbddbaabddcccbbaaabbdaacddcbbbccbacacdcaaddacacbbcdaabadadccbcdcdbaacbcbabdbbcacacdcdaabaaccbbbcabbabdbabcbcddbdbdcdcaabdcbcbdabcadcbaddbbdccdadcdbdaaacbbcadabacaacbcdbbabbdbddaadddcadcaacabbacdbddabddaacadcaadccbbabbddcccacbdadbdabcdbacbacacdcdbdacaccabbcbadadbacdcdadcaddcdbcdadbaadadaaadbabdddbbcbdbcbabacbaaddadddadbbdbcbdccabbccbdaddcccdaaaacdabaddcbabbcdbcbcabcdacacdcaccdbdcadacdcacdbbadaddbababaabdbbaddbabdabdacacacdbccccabcacdbddbdccbbccbabcdabcbdcbababbccdacbacaadcbbcccadccbdbcbdcbcddadaaddcbcddbbbcaadaaccabccbdbadabbdacabcdadccbcbcbddccccdaddaadadbdbdadbbbbddacdabcdbaababdadbaacaaccbcbbcabddbaabcbdcddbadcccbccadbddacccdcadaddbacacdbbddcdbcbacbadacbcbadacadcdcdbcaabadcccbadbadccccdcdcaadacccacdbbdadcabbbcacabbdabbcabdbccbcdcccadcdabcddcddaacbbddccccddadaccdcbaaacacadcbddccbdcddddabbbddcdbdaaabdcbbcbdcbaacacbcbbabcadcdbcbacdbbcdbaabcdbddcbacadabcaacdcacacdbdcbddacdcaacbdadddabdbadbadbaabcdccddbdcdbacbabcaacdbbbbadaaccbabdabcdacbbbbdcdcabdcccbdccdccdaabcdbbdaddaadabddcbccdbbacdccaddcdcabacadddadabdbcbdbaccadcdcaabccaabdaabcdcaccdccabcdbaddaaadcbaadabbabcbdbadcdacadaddaacbcddacbdbbacdaddcdcbbacbacbcdcddbdbbcdbbbbcddbdcaabbdddcdcddacdcdddbbbdccacdccdbbbddcccccbbcbccaaaddbddccdbbbddbdcddbdacbbdaadbaabadcdbddaddaabbbabbbadbdaacbaadcccbcdabaacaabdddadbddbcbbcacbddcabdcdbddbbbbaacbddbbcccbadbacabaabdddcddbaaacaccbdbdcbbbadddbadbcaabddcbdaccccdcabdcdbcbccbdbacbacaaaaacbcccdbdbdbabbdddcbdbddcabccccbabadaddbcdccaccdccbaabddaabbdbcabcabacbcbdbddcaaccabddccaddcacaccccdcbbcdadcbdbbabdadcdcbdaddddbcdcadaabbadbcaddadccbbddbcadcdbadbddacbacdadcbcaaacdbccaacdcadaaaaddadacdadddbcaacacbabcdbcbbaddadddcbdadcaaacacbbbaacdcacbcdcbadcaabcadbbdcdabdacdcaadbdcddaddccdabbbbadcdcdccadaddbcababcddaaccababaddcadbbbbdcbbddadddbadacdabdcdcdabacccdcadbdcaccdcdacdcadacbcaddadabdcbdbadcabacdbbbbdcbadcbdbabbbdcacbdcbaacaaaaadcaddaabacadabbdbaadabcdcdbacdcacdabdbddcadcbabdbcbbaccacbdccadbbddcaddcadababaccaabbcabcadbbbcdbdadadaaddaccaadabdbabbaadaddbdadcdcaaabdcbaacdddbcabcbbbabbcbccdcabaccababbadbadadbadbddcadbbbdcdddcbcbdcbcddbaccaddcddabddabbbdaaccaddbccbbbababcacddaabbbbadbcdabbcbbaccdbaaddccddaddaaccadcdccbadcbaadbacbaddbdcdabcadcdbbacacbddbbabaaabaddbdbcaabbccdbabaabacdadcadcccbcacbcaacbbdbaddbbaacaabdbbabcbcbaacdaccbcbbcdadcbdabdddcbabbaabbbadabdcbccbbcbdbbcbbcccdcaabaaddbdabccacbabcdcbbcdcaabdcddbabcbdbccadbdcccaadddcbddbbddbaccbccbabbcccbadcdacaabacadabbbdbdaadcdbbdadcabccbccbcacbadbaaabadcdccbbbdbbdbbddbcccdddddadcbdcbbbbacdcabbcdaddbadaacdabdbbacaaacbadaadcabbabdccdabbbcccaccbaccaddcabbccabbaaadaccddabdccbaddcdbdadbcacaaadcadcdccbabbabddbdcbabadcbcccdadacdbbbccdbccbbdccdcccacdabccbbdcdccbbdababccbcbcbaccabcdaadcabacaadccdccbbdaabcdbbabcbdcacdadcdabbaacbccccadaaacdadaddacadcbcbddcdbbdcdbaaabbbdbbcadbaccdddacaccaaadaaabbabaabdbccdaaaabcabaaacabbdbbcdccdbcbbdcddbcbddadacdcdcaccbbbbacdddaccdbbadbbabaccbddaacaccabbcaccddcbadabbdcdbbddacbbbabaddcacdcddcdbcbacbabcaddcbabbcddabdabaadbbbacbcdacddadcadbbdcdbcdaabbccddcbbccddcddadaaabdccdacdbbcccbcbddacdabcbcdccababacbdcabdadadacdadccaacabbbcacdbbaaaacccacdaadcacbacdcbdddaccbdbdcacdcdbdbdcacbcabcdcbcbdbbaacdabdbabadccbdbccbaabaadbaddaaaccacaacbcaabadcabaaacabcbddcbdcdbbddcdcdbadcabddcbcbababccdcacbcccadadddbcdacbabacaabbcccdddcbbbbbbbbaacdcaadacdbcbbcbcddbddbcdddacacabcabbdbdbcabcccbbddcbcadcccbddbdbabbdcbaacdcdbdbbcdabcbdbbcdadabdbcadbccabaadbdabbadcdbbadbababcbbcccadcbcbbabbacaabcdbbddaaddaaabbdabcacccaabcaadaccbddddbcbcdddcabbbababdabcbaadbdaccbbaccaabacbbadbcdcdbaadccadbddbdcddcdacabdddcbcdddabaaaaabdcadbaaabbdabdbdccabacbccbdbbbaccacbcbbdbabadcbdcacccacdddcabbdddccddabadbcddccaaadddcbdcdaccdbaccbbbbbbdabcadcadbaadbbcdabdbbbdcddaaaccdcdbdabacabcaabdacaabcbcbaddabcbcdaaabcabbccadbcacbaadacdddcabdbadbcdadadbaabaabacadacbbbadaaccbdabbddbcbcdacbacbbbdacaccadccbadbdcbadadaccaccbadbacbddabdacaccccbdacddcddbaaabbdddbbbadbbccbddccbdbaadbabaadcbcdbbdbbcccaabcaccbaadacbdcbabbdaaacccdcaaddddbdabacdabcdbccaabbcddcbddadcdcbbadcbbddbccbcdccddbabadcadcbaacddabaadbbdbaaacabaaccddcdaadaabcadabababaadbdcbbbabcdcacddcbdaccacacbacacacacabcbbabaaddaccacaaacadabccddbacabdcbbbdadccacdadabaadbbadccbacdaabcdbcccdaaadcadbcddddccaccacdbaddbdacbabbbaadcbaacaccaabddbdbdacbcacdaabdddcccddabadcdabbcdaccababdbaaddcabdacaabaabdbcdabcbaadbcbdadbdccddcbdddaccbdcccbaacbdcdcbdcacbdcccddcacdcaaaddadbddbcdadddccaaaadabdbbdabacbaabbcdacaaddcbbaabcaacdababbdaadaddccaacaaacbcaadddcaaacdacdabcbcccbcccdcccbccabdddaadbcddacdbdcbbacddbcbdacadadcaccbacddadcbcadbdccddbabacdccddacccddbdbbbdacabdbaccbcdddaadaddbddcbdbbabacabdacccddcaaadbddabaabcdaadccbabdddaddcbddadbdacccacadddcbdddbcbbbddcdabbaddcdcbdddbbdbbaaabdaabcabbbacbbbaaaaddbdbddccdcdcddcdacbaaccacabcdbabdabcdddbababdcdadbbbadbbbbddbbacdaabaaadaddbdbbbdbdcadcbbdbacbcccbdddcbdbaaacddcbcabcadadbdaabadcaacdbcbbccaadcdddcacbdddbcbdcbcbcacacaddadadbbbbacdcadbadbbcabccdbbbdaabbabddaabcdbcbaadadcbddbdadabbcbbcbcdacdacbcdacbdddbbbccadddcbccdddbaadabacacacbacadaaadbdacabcdbcbbdaaccabbdaacdcbdcbbddccbdbadddcdacbcdbbadabdcbaacdcaadaabccccdcddcbbbcbadbcbcabcdaaddaaacbcadbcadcaddbcbdbbbdcdbadcaaaddbbdcbbdbcccaacbbaaabdccdcdabadaabbcdcbacacdabcabacdddcbbdbcbcaacdcdadbdccbcaadbcaaadabcdcbbcabcccabccadabdacabacadbbbcbacddcdadbacccdacbddabbdbabcbdabadbadcbdbbbcbaccbaabdcdbbddaadbcccbdbbdbadacdbcbddcccaadbabccddbadcdcdcccdddcddbddabcdabbcdcaabdabdbcdaacaadcadaadbdcdcabbcbcbddacbabcbadadaadccadbbdabbbaccdbbbddaccdbdacccbdcaaddaaacbcdccadabccbcccdbbbacdcbddcdbaacbccbcdcbbddaddabbbccacaccdaadabccabadaabdbababbcabbbabaccdbbdccbccadabbbcbccbaddabbbaadabcdbbbccccccbddddabbadccdbacdadddaabadddbabdbdbbabcabbdcadababdbbabcbaacdbddcaacbadbbaacabdacaadccadadcbdadcdbbabbaccbbccbbacadacabbcdcbbaccbcaaabaaddcbbaadcdbdcadddacddbaddcbaddbabadbdccdbabccddaacacdbacacccaddddaaaabcccddbabbaadcddccbbbaccbbbacbcbbbabbcaccdbbaadaadadaccdbbabccaacabaacacabaabcaabbcdcabdbdcccacdbababaddcaadabcbbaddbcdcbbbaccbcbcbdbdbdabaacbcdcdcacacdddbbddabcabbcadadbdccddbbbbdadaadaaddaddbdcbcddccdcbccabcbcdccbbbaabcaaacbdadbcdaaadbacdddaaacdccacddabbabaacaadbabddccdacbcdadacbdabacdbdccbabaabcadaadccbcbacaadbddadbbdabcdacbbdcaddcbadcaaaccccaadabcbcddabddbcbaabaabcbabbbbaccbdbcbaacadcabcccbdddbabadabbdcdbbbbdbdcdcdacbdadcaacdaccbacaacabdcdaaaadcaabbbabdadbbbabcbbaddaaccaadcbacaccdbcbdcaacdcddbcbbbabaddacbcbacdbaacbbbbccbbcaaaddababbadcdcdcddbaadcdadbdddaddbdaddcdaccadaaabcbdcaaddddaddacccbcbcdaacdaaaacbaccddabdbccaccaaadadccdbdaabccabbdcaacdcbaccbcaccbbdadbaacdabdbddbbbdcbabcbdcccbaaaccdbddaddaadacdddbadabacccbbddcccacbdddaccccddcadacaacdacbdbcbddbabbdbadcaccccacaadaaaadbdcadabbccbdcdcbacaccdbddadbadbbacbcdbaabcdabbbdacdacacdadabdbcadadaabccbcbdcdaacbaabbadddbcbbaccdcaacbdaacabadacbaabbcdaacbbadabccdbbaaacbbdddddbcabaaacbdcbadabbaccacbcacacabbbcadadcccaadbddcdddbcbbbaccbacdbcbcdaabccddaddaaacdaacaaccbcbaaaadaabcdbaacbcdaacbcbbaccbcabaccbcdccddaabdbdddbcdddacaddddbcdbbddbabbcaadcbbbcccdacbddadcbabbdadbcbacdbcccdccabadcabbcccddbbbdddadadacdccabbdbdcaabcdccbcbabbdbbdadccccadadcaacadbcadabbdcaddcdbacdbbbcacadccaaddcdaaacccaacacacaadccaacaaaadddbcdcbaadddababcbdaacdabccdccbbbdbbbabdccbddabdcbbcacbadddcdbdacbaddcbaccbacdbbcddbadcbccdabccccaadddaadaccdbdbaacabbaccbbaabdccbabdabbabbdcbddbdaccccbbaaadbdbaaddbadbdcbacacacdabbadccddbcaddbaabdbdadccbadcdbbcacdcbdccbbbaabcbadbdcdaaaaaaaaaadadcdbabbdbbabddabbdddbbcdcacdbbacacdccdcadaccdbdaabcaddddadbdadaccacddbabadabdbcdaddbdcbdaccdddcadcadbaddccabbbbcddbadabadcdaaabddcadcbadcbddbabccabbdadbdacbabdabddadaccbbdbabbcbaadadcbdbbbbdbacaccdacdabcaadddbcddcadbbcdbabcbcabaacacaacdcddbcbaabbdbcccbddacbbbbdcbccdcbbdcdaaaccbbccadcdcacdbbdbabddddcbddbccbabcbcaccadbdaddbdaabacdccbbacaacdbbacadbdacbbcabcbcadadbbdcabddcaabbaccdcddbbcbbacbdbcdbbacbbbcbcabacbbacaccdbcacdcdbdbcdcbadcdbabcdacbadacadcadcaaaaccbdcadadbbccbdddbcddaaccdbbcbbdddcbbcbcbabcbabccbaadaddddaaddcddbdaddcdccabbbccaacaabcbbcccbbadabdcddaccbbdcabbbccbccdaabbbbddabbdbaacbcbacbbdaabcdaddcdcabccadddcacbddbdcdcaaaaaccbcbbdacacccdcbdacbcbddbbabdcadccbbcdcbcdcabcbdbbacadacbcdabbcbbcbccccccbbadcdacaabaddadcdaaccabbccddddbbcbabaabadccabbabbcaacdcabbdbcddcdaaddaccacdbdbaadbababaabaddaaddcbdacdabbadbccdaaaaddacacbcdaabbccbbcaccbcbbaaaddcbacbacbdcbdcbdccabacddaaacbadaccaabaabcbabcbaccadddbdbaabbbabbdbaddabccccbabbdddacacbdaddabcdccbbbcbcaddbabcbcddbbbbdcdddcdcdbcdabacbbdbabbbbcddddcdcabdabbcacdacacdbadadbccacdcaadbcacddbdbbccbbbbcadbcadacbdacaabcddaaadcddadacadcabbdcccaacbccdadadabcabdcdcdcabdacbadaaccbbbabacbddbddbaccbcbdddbccaaacdcbbacabadccacbcdddaabdabbccddddcdccabacdbadaabcddcbdaabcdaacccaabcdbbcdbaacabdbcaaaccbbbaccaadabdaccbdbcbdbccabbabbbdaadadccaabddbadbadbbcdbdcdcadcabcaabbdccccbdcdcbbabcaddbbbcbaaabbaaaddbcdcccbdcccabadcabdbbdababaabacbdbadbbcaabbaabcbabaadcbcbacbbcbdbccbaddbaddcddbcaddbcadbdaadacdccbbcbcaabbabbbddbcbbcbdadaabdbcbaddabdbbddbdbbaadadbbdaababccdcbacacacdbdbadccabdcdbcddcbcdddbdaacbdcdbddbccaadbdccbdacbbbbcadaabdcdacabdadcdaadaccccddddcbcbdcabcdccaadddccabbbddbaccdbbdddddabdadcabcbadbbbdbdcabadccaadbddcddaacbbaaabdcccaaabccaaabacabdacbacddbdcaccbdababdcccacadcbacddaadbdacbbdaadabdccacbdadcbdadbacccddddadbbbcbccbdcdccbdbaddbddbdabbdbddbdbabbbdabbcbaccddadacbbcdcddcabadbbabbbcadcaabdcaacadbaabbccdbdbbaacbbacbdccaccccbccbacadabdddbddddbddabdcabbccdbcccddccccbbdcacddabddbcdcbbdaaacacbabadcababaabaabaaabccdbbaacdabbcdcdababdacbaddccccadcdcaacbcabcdaccacbdacaccbbcacadcbdbdbaddddacaccaccdbadbbbbcadbcdadaccccdacbacdbdcacabbdddcddcadbccbbabcdaaabbdaacbcbacdaacadbbbacbccbcbccccdbbcbdbdbadaaadbccdabbdbdccdabccdccccbdacaaaddccacaacadcacaccadaabdacaaaaccdbdaccbddcddddcaabaccbabcaabbbaaacbbbacabddabbadbdbbacbcbcacdddddbbaddbdacdbbcccabccbacdcbaacbbbacdbaabbbcdcaacbdddbbdbcaabdbbcbddcccaabcdadddaadadacaddddaabdbddabaaadcdaaaddbdcddacbdaddaaccbdadcbacbbaaaabddadacbdddcbdbadcbdbcdacdaaabcaddddddcaabddcacaaccbbadccbcdcbcbaababdcbcbbcacaacabcabccabadadbddaccabacbabcbcbdbbbcdccccbaaabbbcadcacbabdbadddaacddacddbdcdbbdadaadabcdaddabadddcacdbbdbbbaaadabcacdbadbacdbdbcbabcddaaccacaaaddaadccbacaacaccdcabcacabbbabcdcaaccbcdabddcbdddddcbaabadcaaacaabacdaadbccbcadacbabbcbdbacbbcdabcbbacdadacaaaddbabddcdabdcadaadbdcdbccbbaaccaabdaabaadcdbdcdbccccdbdadcbabadcccabcddbaacacacccadcdcdaabaddbabddacddbdddbaabaddabcacabbdcddaacddcddddabbddadbdabcdacbddcdaaabdbdaabbdbacacbdadcadcababbbccdacbacdbcdddcabacaccadbbccdcabdbdddcadbdcbaacadacaaacccacdbbccbdacbdccabcccccaddcdbabcdbbbcbddacdbbdabdbbbdddddddadadcdabcddacabdacbbbbbcdbabccddadddbabaadccdcbdcbdcbdabddcbaaaddddbdcaaaccdcbabaaacbaccdaddaabddccdbbcdcaadabbdddaaccbcccbbdcbbaabbcacccbcaacadaabcbbcbadcdacabbbcbcaccdcddaaddcabcccadbabaadacabcdaacadaacbdbcccdacbcacbdccabcbdcbbaaccdcccabddccdadbbaaccddbbdbdadbdadbaaabdbcaaccadacddbbccabdbcdbddccdddbdbccdddaabbccdabdcdbcdbccdbbaadaccacbdddadbbbdbddabcbdadcbcbdcadabadadcccabccabbadcadabcbccadccbcddabddccbdacbadcbaabdcbdddccacbccbbdbcccacbccabbaccbbcdcbdcdbbacddbccdbdabdacbccbbcacbdcbacbccbbcadadccccaaacbacabcbaadcbbcbdcbddccdcadcdabdcdcbcbbddbadbabcddcaadacdcbdddadadaddacbdadccbbcddbdbadaccccddbdadaccdddbbcdabccadcbccadabbdcbbcdcddbbcbccdadbdadbbcbcbccbcabacaaadcabddbdcaccadcbbadccdcadcbcdaadaddbaabaadaaccaacddbccaaddddcdcdccadaaabaaccadaddcddaadccbbdacabbcdcabdcdbaaadaccddcccdddbbcbbdcbbbbbddcbccacacbdccaadbaaaadcdcadabaddbdaaccbbadbdbbdcbadabdbdbbcbdcaabdaaabcdccccabdccacdbaadbaadacacacbbcdbabbbcddddacabbcacaadcaacbbccacacbbadaaaaddaabddadcadadcdacddbdbbcdcbabbbbbdddabbbcdccdbbdbdaccdaabbaccbbaccaabbbbdabccbbddaaadadbdddbcbddcbbcdbccdadbbcbbadcdadcbbbccccabcaacbbcacabbbadbbaadaabacabdcddcbaaaddbccadabbaabbacaddccdadbcdcabbbdbccdacbcdacaacabdcbcaadaabcdcbcacdbcccaadaaccccbdddbaabdcbccddaacacbbcdbcbaccbacdbcaacdaadcbdaadcbdcbaabadcccdaaabaaacacbbddacddbcccbabbdddcdcbcadbdacbdbdcbacbcddbccacbbadddccccacddbbcacccaacbccacddacabdbcabddcbddcdaddbbbcdbbacdcbddbcbbcbbddadcdcdcdcadbdbabbbaabdabccdbbdaaadabbcdcbbbcdabaadbbcdcbdbbdddaaacaaaccdcbdccdddddddaaabcdadcabcadbadaabdcdaabdbdbbcdbcbcbbbdcbcddbacbdddacdcdabcacccabadabbcaadacddadbcddccbabdbbacccbccdaddddcaccbaccacdcddcbcadcadaddcdbacbcdbdbcaccbcbbbbaddbcadbdbcabccddacadabaddabacbdbddcadbdcbbbccacdbbdacababcbdaddacadaaaccbccdcbacdadcddbadacadbddababbcdbdbdcaadddbacadabcccbadabddaabadaccbbdcddabdacddbcbabcbcbcbcddbcbacabaadcabcdccddaccbababbaadbbadcaaabddccccadbdddcbbcbdbacdbcdbbbdacdcbbbbdcdbbbccddcbabbdbbccdbabcadccdbdbdcdcabdaabcdbccbcbdbccccbbbbcabdbbcbccdabbbcabdadabbababaacddcdbdbabbccbadbddadcdccbdcabbccaaccacbcdabcdbbdcbdaabcdacdbaaccddabccbacdcaadaccddabbacbabbbbdadbadbcdcbabaabdcacabcdaaccbadddbabcccdbcbdbdadaddadbdadcbbaadbaacdcaaabcaaaaadcadccbccddabbcbddcbcbbdbacbdddbbdbadccdbcaadabadbacbccdbddcdcdcacdddcadabbbcbabcddbcabcddbbbcabddbdbbddaabcdbcdabdadbcaccaddadbccaadaabacbbbbcdbbbdddbcbddbbabdbbcdbdbbcdcccdcbdccdcbcabdbcdacadaacacdaddcddcdbbbddcbababcbbaababbacccbcccbccaccdddbaaaddbbdccbbbdcbabdabdcdcdbabdcbdbcdaaabccababdadccbcdcdabddabcdabcaddccbbcdcbdbdbcadadacabdbcdccbbdabaadbbbaaddcbcddcdaadadbcbbdacbabddccdacbbbdadaddbaabbcccbcdaddaacbbbcacccdcbbdaaccabbddcccbbbcadacacacdbaacbcabbdcadbcbacbcbabaccacdcaddbcadcbababdaabdcacaddcadcbbdccadbacadbbdcaacbbacddaaaddcbbdbcadaabbbbbabcddcdbadbdaccdcdbcbaaababcacadacadadcddcbdaabaccbccbdddddbbcdcdddcddadddaccdabcadbabbcdadbbddaccdccdadcdacadacdbbccdddcbcbccabbdcdbacdcaccccaaaccdbdcdababcdaabbdcbcaaaaacacbddcdaddacbcbbcddbacbcabcbdadbdaccdccbcdadaaadbdcdbabddccaadddcdbccdbaaacbacbabaccdbddcaddcadabddbbccbdccdbddaddccdcdcdddcadddcaccaccdbdabdbbcbbadbbbbadbaccbdcddbdbdccbabbcacbbbbbcacbbbcdbdaabaccdacdcccdadcaaacdbbdcbaababacdcdbbcdabbcacaccdcdddaaadbdbcaaddadcdbaaddaacccbcccacbcaadbacbbdbddddcddbabbadcaacddbccbdcaacdccabdbbdcbbddacabcbaaaabdcaddcbbacdaddacbdbadddcdbdbabacaabcbbdbbbbcdcdbbaccadbababbabdcdcddabbaacdcadcaddbaabbaacbdbbcaaabcaccddcbcddcabcaabcbcacbabddcbbcbbbbdcdbcadcabacbbcdccabbdccdabbdbaddaacddaaaaaacbacccbbbbacdbddaadcacaacbddabbccdbdbcabdbddcbcddabbaaadadccbdacbbcddadbbdcaccbcbadbadbbbbacddbdadbbaacdadbbddabbdcbacbbbccbbcadcdabcccdcbdaaabcbbdaabdbdbcaadddcaacbabcdccdabccaabadcaddcadbcacbadcacdcbcacbddaccadacbcdbbdcccaaddcabbcdbbabdaaaaabbadbbcbbbacdccbbdbdacabadaadddbacdbbbdbdcdddacaccabcacccbcdaaccbddcbdbaabddcbcbaddcbabccacbcbcdbcbabdcbdcabddcdbcdadddbdadcabacbbcadcbdddcbacdbadcbbddbbcadabdcbcabacaccccaddbcacdcaadcdbacadacbccccaccdddaacbacdbaaddcdadbcabdaccadbdddcadaccbaacdabcbbdcaaadbbdbbccbddadbaadbdbacadcdacabbcaacbddddacccdaadccadcaccbbdaddcdabdabdbdacdbbbacdbcacddbcaddaacbadcaadadacbacdbbaadddcccddcbadbddddaabcbacddbaccaddbbbbdcabcdddbbabcdabbdcdadadcbbdbcbcdbcbbcccadbabccaccdcccadaaccaaabaabddbbababbaccaacdabcbdadacbdabadcccbddbbbbabadbbacdacddbccacacaaddcaaababdcbddacdcdacddbcdbddcabcabbcccdacacddddacdaacdcbcbdbabdaddacbbbbbccadddcadcbadbaacaddbacccbcbddaaddbcdcaabcccbadadcbddbdbcacacdacbacacdbcbcdccddcadddccaccdaaddadcbdbacdbaadbddcdbdcbcbcdaadbbaaaababbaccdbbbadbdaccacccabaaddbdbbabbdbacdcadcdcaadaadabaabddcadabdcabacdbccbaccdcbabaddacaabcbdbcdcadbbbacbadbcabdaddcbbdabacbacbbbbdcaddbdccdacdbdaadcabcbdbbdbcccbdbcabbddcaadbdcaaccbdddcaadababccababdcaaddaccdcbadbbcaccaaadaadaaaccbddbdbbabdbbacddbcdcaabbbabcadbcadcaacbaddcabadbdacaccdaaacccdbdbdaacdcbbbcbccaccccbbabddacbdbcbaacbdcbcdcdddbdcdadccbccdcabdccbbddbcdaccccccbdaaddccccbcbcdcadccbacadcaddbdbbbbbbadcdbbbacbacddcabacbdccdabdbbbdaccaccdbadcbddaccbdbabcbcbcaaaaabbbddddbddaadaaccacbaaccbcaddcabcacaadcaccacdbabcaababadbbbbbdbbccdaaaadbaddccbdccdbdaadacdcdcabadcccaacbdccbdaaccdbddabcadcddcbcacbdcbbdaabbaabdcdabddccabadddbabacddabbbbaaacacbcdbbcaabddbadacdddddcbbadcbdbbddaaccdadbdbadacddbcbabbccadcdabdadbaccbddbcbacdaccddcdddaabcabbdccaabbdacbccbadcbabaabbdccdcdabdacacddcbdcccabcaaadcddaadbbbdcdbdcabbdccacadbdddaadcbabcaccdabdbdbccbdddaaaddaadcbacdaaccdabadbbdadbbabadccbddcdcaaabdadbabcccdbdccbdcbaaaacbcbbacbdacaccbaddbdaaacdacaabcdbcdbcacddcabbbdbddacbacaabadcbacdccdacdcbddaadbabbccbbbbcadcaaacacabadaaabdadcaacbddcdadabcdbddabbcadacbcbacbabdcbbbccbcbaddcdabbbabbcddcbcbaccdbccdbcdccbbacbcadcadcadcdacccbbbabdaabccdacaddacaadbdaacbbabaaabadadcaaacbdbacacacbbacdbbbbcbdcbdbdcdaabcddadbadacbdcbdbcbcadcddcbdcdbcdccddabdccbdabbddbbbdabadadaccbccbdabacdbcbdbcbcbbcdbbcddabccacdadabcdcccbbdbbaaaacadbbbbbbbdbdbdbbadbdccaaddbbdcddbabcadcdbdaadbbbcccddcccccbbbcacbbcdbcbddccdacaaaaabdacabbaddbacdaccabaaacacbdcdcadabddadbbadbcbaaaaacacdabdcbacacccbacddcdccbaabbdacacbaccbabdbbbbdbbcdddacddacddbcddcdcddacdacaaaccbabbbabbbcddcadcaddbaadddacbdabbdbdddbbcbbdbdcdbdbacdbdbddacdccadcacabdbdccbdcddbbdaadacabbcacacaabbdaabbdcacddddcabadddaddbcbbcbdbabcdcaddadcccadcacbbccbbcadaaabcbbabdcabcbadbdccdddaaaaaadbadcaaabbaddaadddbcabccddccdabdccacdbacdbbdbbddadabcddbaaabdddadbbdddbaabacddaabddadbddbddbbaddaddadabbdcabcaacdcbcbcaabbdacaccdbdaacabbbadaadcaabacdaaaadaabcdbbaabbdcdbcadcddcdcdbdccacdbbabdbbacaaccbbbaadbdbbacdadacacbbadbabbcdaaaacccdbcdbbbaddbccbcbacdcbccccdbdbdbdddcdddadcabbddcbcddcdadcacacdbacbbbabbbadabddabdcddbcbabbbbdccbabbaaadcbcdacbbdbbbcbbaccdacdddbccccbddccdcccaacdcdbbccdbdbddadaccaccbccbbbabbbbbbacdaccbdccdcccccdbbacbacbdadbdabdcccbdccaccadabbdacabddbbdccabcdaaddadbaccbaacbaaadccddcbcadacdabadcdbaccdbabcdadcadcccacddadddcbcbacacbddccbddacccdabdcbbbdbdbbdacdcccdaccacbacccdadcadbbdaaccaaabccbbaabdcbddabbbbbabccdbcbaabcacdabdacabbcdadbbbcdcaabaddbcbbbbcbcddddcbacbcdbcadaaddcaccaaccdadccddbcacbdbcdbddacddcbcddaddbdabcbdaadaadccccbdbbcdacccdaacdcbbbcbbcdcaccbccabaabcdbacdcbbcdabddacdaacccbabaadadababdcddcccbddddbccdabdadabcddcadbababdacbccdabbdcccbaaaddcadaabccbcacaddabaccbbcadbbccccadccacdcdabddadaaddadaaccdaccbbdcaacbacdaaadadaadcacbddbcddadcaccdabcaabaddcbccaddcadaaaabadadbcacdabddbbddcadccaadacadaaaabdccccdcabdcbccbcaadddbcdcbcccadcacbaacaccaccacbbcbbdbdacccccdcddacaadbdcdcaadbadadccdbdbcdaccdbadddcadccdbcbabddacbcaaddaabdbabcccadbccdaccaabcdcdbbaaccbbdabbacdaccacacdbbdcccbbcbccabaaadaabaddcadbccddadbdaadbddaaacadddbbbbaddbbcaddccaccdcdbbcabaaaccbccabcabccbbaadaabcbccbbadcccaadaadaadddcdadacaccdbbcdadcbaccbdbbdcaddcacbdbbbbcadcccbdcbddaacbcddddaabcdbdbdaccadcccbdcdcccacdcacabaccadadbbbcabdabbcccabcabcbcaaadaabdadcbbbaaacbbcaaaccabdcdaddabadabbdbcbccdcbbddacdacbbaaaaccdcbbabbddabadabbdbddbdcdbdcbdbadbdcdcbaabdccccbdabacbdcaaacbbddcdaabaccaacbacdacabcbccddadcdbbbaddcdbbadcccdbacdbabbbacabadbabaccbabdddbbbabccdaabdaddcdbbbcdbbbcbcddbcbccbbcacbbbbbdcbbcbabbbaaacddddadcaaccaadcdbbadaddcdcddcbbabcbcabdcdaadccabcbccbbacacdaadcddcdbabdbaabcccdcbbdabddcadcbbcdadbdbbdbbadadcbbbbcbbacdbbdaddbcdadbcaaabbdccaacbddcbdcadbaaabcdabacacdacdbaddbbcaabdbdbdbbacadacabdaaaabaccbdbcdddacdddabaccbbcbadcabbbaccadaddbadaadcbadcccbddddadadcacdacaabadcbbccdadacdbcbbacccccdcabcadbbbaabacbadbacbdbccbdbdadcbdaabddbdbadbbbabbbcdbccacdaadaccaaccbbccbddccbaacacdbaadacaaaddcabcdadaababcbdadaacbacbaababaaacabdccaddaaabcddbdccdbdadcaabddbadccaadabaacdddabcbaadcdbbcabadddbaabcacbbdbdddbdadcbdcbabbadcacccabdbadbcdbdabbabdbcaadbbddcabaaabdcaabadcddbcbbacaabbaabbdbaddddbddbaccdcdbacbadcbbbdbaaaaccdcabdcdbdabdadcdcaaccdcbbacccdcbadbbbccdbbbcaacbbbcbdcbdbcdcbdacbddddccacacccccbbcdaabacadcdcdbdacdcbbcadaaccccbaacdccdbabbcbacdbdccdbabbbbddbadabbacbaabcdaccadababdabbbcddacccbdbbbcacbdacabccabcdabdcacdbacaccbdcbacbddbbbacadcbdbcabdccbccbbcbcdaaacaaccdcbadcddcbabdcbdcabbacadddddbadddbbddaabdcddcbbddddabbabccdbccbcccacaacddcbbcdbddbabbacddcdaadaacdbbddddabaccaccaddaabbaaacdabcbdddacdcaaaacdaaccccbbddadbaccaacdcdcbcbcbddcdbcaabdcbdacbcacabdaddabddabacdcbbddbadcddaaccdabbaccabbcddbddadacacddbdbddbdadbbbbcacdadabdcbcbbbbcdaddacaccdaddcdcbcbbbcbddadaccbbdbabcccbbcbdbabbcdabaabbbacbacdbbcbbbabcbaaabaddabbdcdadbcabcaccadacaabdcabbbadbbaddbaaddcbccbccaacacccdcbdbcccdddcaccddddbabadaaacdabdbcaababdacadbadbbaacdcabddadbbacddbbaaabdbabcbcddacaccaadccbacbcaddcaacaabbdcadbcddadccccdaccddbaabcdbddabdcbbaaadddccacaaaccacabcbdcaacacdbaacaccdcdbbdbdccddcbbdaccdabaaddbcaaccdcbaddbddcadbababacadadacbbbdcbdbadbdcdbbbaaababcddaccabbadcbcbcbcadcdaabddcbdbadcddaabbdacbdddbdaadbdbbccadcbcdbcbbbddadaccbcaccdaccaddacccbdbbcaaabbcbadcccbbcccaabbdacacabdbaacaccbbcdaaaccabcccbbbadddddbbdaacaccccbccdadcccadbddabcccababcadaccbbcccaabbcaabcbdcbbcdcbabcacadcbcddbabddbaabdaddddacacbbabcaabbbacaccbcadbccdccadcccccacbdbddadbddbdbacaaacbdcdbbbbdcacabcbdccababacacbccaadbcabbcdaccccbcacaccbadacbbdbbdadbbadcddcdcdbbaacbaccadacbbdbbbdbcadaccacccadabadaddacbcacacdcadcacbbdbbbccaaadcbdaccbbdbadaccaddbcccabacbcdbcccddbbaddbadbbbadacdcbaaadbdcccabbadcdaadbaccdbdddcddabcddbaaadcdccaddddbdabaadddbabaccdabddbabcdbcadacdbccabdaddaddccccbdbdccbcccadcbaacdbdabdcbdbbcdbccccabdbbbbddbabccdbcccdabdbaaacccabcdabacacabdcccdbcacbbcabcdddbaababdcacbbbddbaabbcdbbccccdbdadacdcddbacddbbcbcccbadcbdabbdbdcdccbdacaaddcdcdacdabcbcacbcaaaaccacacabcbddccdbacacaababbbadcbdcccacadcabbddbaacaadaabcbcdcdbabccaccdaddccbddcbcbbcadddccadcdbbbdacaddccccbbbdaaaaabccdbacbbcdccccdbaaacaabcccadadaaaacbaadacbbbdbdcdccbcbbbcddcaccadcbccbabdcbdcdacacaddcacacddaacdacdacaadcdbbbdaacdccbbdadadcbaccdcddcadabdcabbaabdababbcbcbacbbbdbcaaacbacbcbbcbbbdacbaabdbadccbadbdcbbbcddcaadacbababcdbbbdadbddbaaccbaabbbbccdbdbcacdccbbbbdbdccaddcdabacccaddddbbccabdbdbaddcacddcaadcbdacbbacdacbacbdaddcddadbaddabcbcbdbdddcdaddddbcccbbdadbbddaadbbdcabdbacbdbadadaadaabbcdcbbbcaaaaccdaadcdbdbadcbaabacdcbdbcccccabacadcaabbcaddbcdccddaddaaaadbbdddcbcabadbbdbdababacdbbbacddaacccddccdddcdddaadaabcaacabcbaacdcacbbcccccbbcdcbcddbadbaabbbdbbdddccbcdbccaddcabbaddbccbadccbcdcccdaacccdabdcaaddcaaabcddabbaaabcddbadbddbcbaacbddddaaaaadbadbdcbbbdbbdacabbcdacbbcdbbcacadbcaacdccaaaaaabccccabbacabcbcccbccdaacbccddcaaddbcaacdddcbddbcadccddbcaacdcbbaaacddaadaadcdaaaababddacbbabdcdabbbaadacdbbcadcddbdbbacbccbbdcdbcdcaadbbddcabcacbbbcaabbcdbadcbccaaadbccbacdcadcdaaabbcdbaacdabcadcadabdadabbcdcaaaaccddbddaabbaaaaaaabddbcadaaccdcabccdcdccbccccabdcdbdbbdbddaaabbddbcbddabdadcacaaddacccbdbacaabadcdaccdcaddabcdccbabadaddcadbdcadadcbbbbccbdcbdcbabcbaaacaccddcbadcbcddccbcabcaddccbadadccaaddccbdbaccbbdbcbbacbdaddbadababbaccaddddadbbcbaabbbddbbaaaddddabcacbbcbcaabddacbddbdacabcbaddddbbbcaaddcdcacbbdbbcadbcbabdcdacabbacbddacaddcaabbdccdcdbccbbaadbabcddddcbabcacdcbdacaacbcacabbbccbdbdbbabdaadddbbaccbcadaaaacabbbcaaddbbcbacbbacacdddabdcccabbdbcadccddbcddabdcdaacadbabcdddcccdcaababdccccabdcbdcdcabbbccccdcabcdddaadacdcaccbababddccdcdbbdcaadcbdaaaaacbddbdbadbccdbbccbcbbcdcbaaacbdcddababcadcccabbddcbdabbbbdddcbdbaabddbdbddbccdbacabbdadbacbbbbcbdcddbdccddbbaabacdbabcbdcddbcbabcccbbccbbbbadcbaadcdaacbbcbaadbdbccdbbadabadabcacbaaddacabcaabaacadaabcbdcbacaadcaabbbacdacabcadccdacccababaddadcbabbcabddacccaaadbdccddbadaabaaacacccbdabdbcbdcadcdacaaabcaccabcacacddadcbbabacdbadbbdcddbdccdadbccccaadddacdabdcdbcbaccdcdbdabdcadddadbdbacaccadbdbcddbadbddddcbbacacbdadcdcbccdcbbbcdbbbadacdabbddcccacbcaacbabadadcddbbabdddbddcbacaaacabcddddacadbbdcbdababbaacbcadbdabaccbacadacaccdadabcdcdcdbbdcabbabadddbdcbccddcbddddbbadcbddcdabbbcbaadaccbabbcabdabacadaadbabccccbcabbcddbddababacabbabcacdabcddcaacbdcdabdabcbbaacacaccddcadccbdbdaccabdccddddccdcadacbabbcbaacbbccadbbababcbababaaddcdcacddabbbadbabddadbaabdcbaccaacdddaabbddadacdcaaadcaccbaaacbacdaabdcaababcabaacacbbddadbdabccacdabaccdababdbcccadacdcccadddadbbcccbdccaabbaacadbcacddbcaacdbbcbdcdbadddabcacbcbcdcdaaabcdadacaaddbdddbdcddcacdabbcdcdcdcddcbadaaddccdcddabacbdacbadbaadbcbdcbbbcdacccccbbbabaaccabdbcacccaaacacbdabbaaaabcbbaddcdaccdccaabbdbddcdcadbdcbdacadbbbababccbaddbcbadaacbbdabcaaadcccdbddcbdccddbabccdcccaaccaaccdabcccdacacacacabadcddcabaabdbbbbaabacdcbaaddcccbcacbaaacbbdcbcbcadcabbccdabdbdababddbdabcdcacdbbcdccdcbdaaddccccbbdcbadcaababccddbdddcacabcdadbaacabacdbabababbabcaaaababdbaabdccbcdbadddddbadaababcbbaabcdbbacaddaccbacaccabdbbabdbddcadddadcbcdabbdbdbcdbcbacbccccccacbdaccbcbbadcbdcbcadbbcbccbcbdbaadabddbcdacabaaaabdbaccdddbacbcddacadbcdcbcdbacadabbbbbcdbbdcbbacaaababbbbaddcbbabdaadddaabdaadbdbadddccdaccbbdbabbadaabddaddabacadddaadadacbcaaabcddddaadbababddbbbdbbababdbaadadccabbbbaddaaddcaabaadbddabddcdbdbabadbaccadadcbcdcbdcbdaadacdcccbdcbdbdadacdbccdabdadcddbcdadadabccbdacdbcdcabbbcbcddbbacababaccbaacccddaaddaadaabdbdaaacabcdccabdaadbccaddccaacbaacccbaacdcabadbdbbaaacacacddbdbaabbbaaabcadbcadabcbbdbbdccaabadddbcaddabbcdccadccdcadcdcbcabacdbdaadcabdadbdcadabdaaadacbcacabacadcbcddcacaccdcadabbdaacccadabadcbbbcbabcabdabaddacadcdcacddbbcbdbbdccbcdabacabbccccdbcbccbbccaddcbdacabbdddbbcdbcdbbcdbaaddaacbbcabddcdccacdadcbadddbcaabbdbdcabdcccbbdaacaadaaddbadddbbbbcdcddacbcbcadbabddbdddbcabdcbccbddbaccbddbbcadabbcadbcadaccaaaccbacaddcadbbbccacacaaaadaabdadbdcaccbadbcabdddcbaddaacdccbdccbcbadacabcccbbdbabcbcaaacacccdcbdaabcbbcbacccdbdbdccdcdcbaaadccdcdaaaccaababbdbdabcdbbbbdbdcaabacccdddcbcaababbdbbbdcbbdbdcbcbabbbacbdcdbdddcdabdacababddcbdaabcccaabacacdadacaccaaaaccadbbbddbcddbaaddcaadcbabdadaacddabcbbacdacbabacaaaacbddcdaaccabbaabddacbacbcadabbdcbbbbacadcaddbdacbddcccaaccdbacabcdaadadddacabbdbaaadaaddacbcaccadabccbcddacbccbccabbcbbacabadbcadbcbdcadcbcbbcbaccdaabbcdcdbacaccddaacdcabdaabbdbadbacddddaabcdcbdabababadddbbdcbccbdbcadddabadaababddadbcbbdcdcadcabcabcbacbbbcbaabcacaacacbbccccdddabcddbdadbbcddddabdbbdccddddcaabcddabbadcbdcacbbdcdccccdbddcddbbacddbddccacaddabddcabbddacdcabcadddbddcaabababcccdbbbaabdcaacdaddccdabbcaadcbbddcbcaccbdbdccddccbdbabddaacddacbbdcaccbcdaaccaadabbcdaddabacadaacbbddcacacaabdcddadbbabdacbdaccdddbbbbcbacbcbcdaccaadcdaacadacacacabbddcadbabcdbcabdcbdcdbcadddabcaccdbbbcbdbdbbaacacccaccbcbdcbaabdbcabbcbcdbcbbdccaaddddddddbcccdabcbbaababbcdccdbdadbbbabaabbdbabdcdadbddbabbcdbbdaccacdbdddbccbddbacabcabadccaacccacacdaccdddabcdccabcaaccbbacbddaaccccaccbaabcabcabdbabacdbadbcbaacdbdabbdaacdcbdbcbbbaddabcdcababcddadcacaaccacdbcbdcdabcdbcacccdaabbdadddcbaaccdcdadbdaaddabbaabccddbcbdacddaccbccbcaaccdaabbbbddbccbbddacaddbddaabbccbdbcbbaaabdbbdacbbbbbccbccccbabbaabcaccbaaddbcdbcaddcbcbaadbdcacdaaabdcbddcaadcbcddbdabdadbcdcdaabccccacbcababddacdbdbadbcbbcdccbabdbcbbabbbacdadabbddcdacdadcdbabddccaaadaccdbabbbadadaacbacaccabddddcdbbddddccbcbddbadbbcbbdbdcbddacbcbcacccaccdabbdbbddbcbdccddddbaaacdbcdadbbabcbaadddccbdadbdccbdbbddcdbcdddbdabdcbcaaabbddbccaddabaddbacbbbaccacdacaabbbbbacabadbcbbbbcabddbdccbddcacddbadadaddacabcddccaccdcabbcdddbcdbaadcaccabcbacccbbcabbdbcddcadaadbddccaadbbabcaccddbabcdcdacccabbbaaccacbbcdddbabdabcbdbbabadbacdcacddaaaddccbdadacddcdcabacababcbdaddbdabcbadadababddbccdddadbaabcabddadaadcdacdbadccccacbabcccddacbbcdabcaaddbbcccbcdbdbbddadcdadddaddaaababcdbcbaddabaacdccbabcddacdcbadbacaadbabaabdcbadbbadbbbbbaabbdcccdbccddcacabacbcddbdacabaaabddaabaaaacadddaacbcdcbdadbbdcbdabcdbbbbcbcbccaabdaaacdacbcbdacadbdaacaaddbdacbbdbbdbdcbdbbcbddcbcadababdadcccaabcdcbabbdddcdcdddbcbbbbbcaaaacdbacabbcaccddcaabaddbabdccdddccbbbdbdbaddbbadcabdcddbbdbbcdabdaccddacaddcacbccabdbbacabadababcaccadcddbbbabbaadacbbddacabaccaacdbabacccdbadabbabdccccccbbaddcdabdddadcabdbdcccbaccbdddcacbcddbdbaaaaabadadddacbaadcbadbccbbadbbcabcdcddabbacbdbbaddbbbcdbdbcdbbdcaddaadacbabbccdcdccabdbcbccacdcdabaccacbabdbccbaddadddbaadccdcaddcccdadbabdcacddcdcbdccadccdabcabbbaabaccbdcabaabbbabdbdbccddcaaaabcaadccbcadcacaadaabbcbcdacadbdcbacabbdbddacbcdaabcadbbcbcbbdcbdaddadbdddbabdcccaacbccbdbabdaddccaaabbabcabbaacbbdcacddcbadbbdcbbadbdbddbaddbdcacabbdcaccabbadaacbcadbdadbbcbbbcdabdbbaacbbcabaadbbaaaacdaaabbcdaddbcbcbbcacabacaccdbdcdabcadbcddbddcbccbdbdacbccaaacdccdabdacddcdbccaccbdbcaabbdaadddacbcbbbcdcaabbacbaacadcabccbadcaacadbacabdaadabbccccdccbdcdcabacaadcccdbacacabbacddbacbbdcbaddcdccbdddbcbadbacadcaaaabbadaababcdbcbaaaaaddcdbcabddaccabadbddaccdbaabbcaccdddbbbccdbdcdbbdbcbdcbbcbaccabcacbbcbaabbccddcaacadadcddbdcdbacdddddddcdcbcabcbcdaadbccdccdccdcbdbcdaaddbbdacccaababccbacbbcadbdbadbddccbbadcccacdbbccddabbaadbcaaaddcbdaacacabdbdaacdbbbbbccdcddbaabbcabbcbdbbbcaaccbcccdcbbdbdbcccccadbadcbbcbabacdbccaccdbdccaddddcdabbdaaaabcacabaacdbcddbacbbccadccbbcbccbdbacdacccdbccdbdbcbbdaabdcbbcacbabcdcadcddccaaccadcbcabacddadabcdbccabaabbabbddabbbdaccadbadcbcdbbbaadccddacadadabcaaacbccadcbcbccdbabcaacaabacaddbbabbddbcbabcdbbadbadcdbbaaacacbdbcdcabacdacacbdddbbbdddaadbbbcdcddbbcddddbcbccaaddbadcbacddacddacdaacacabdbaabccbbcbacaddbbaaaaaddaabaabcbaadbbbdaacacddbbbbdabcddccabbbbbbdcabcabacadaacaadbaacaabdacacacdbbbacdcddbbacbaddacaccdaadbbbccdadcdcdaaccbcabbddaaabddaacdbcaccdbdaddcbadccbccdbddcbbaadbccabadaaabcdccccdbbbcdbdacaddbdaadaacdcbbaaabcbadbdccdadbbabdbcccacacddccdadcbabdbbcbacdcaadcadbaccdbcbdcadddccdabaddbaaaabccbdcabcccadcccaddddcdbacbaaccaabbbcdadcccbdbcccacaccacbbcaaddbcdadbdbabdcacadcdccbbbacabdcdddbadbcdcbbcbaddacbdbabdacaadbbacabbbbdadcddbabdaaccdcaadcbaaadbaaadbbdbacbddbcdbbbdaaddccccddaaabddccadbacccabdababcbbdddccccbcbcbababcbbbbdbbdddaadaaccaadbddcdadcadcbbccbbbabcdbccacadcbaadbcabbdcccbbdbaddbcdbbbccdcdbbdadbbacbacbbbdbccccdaadcaccbcdaaaccadcbddadcbcdddaccbcdaaccbaccdaadaaadbdbcabdaddacdbbabaabaddaabaccadccacaaacaaaddbcacbacddbdbacbbcdbaacaacbcdddacdaadcadcacbcbacbdcdacaabddbbcaabccddcbbddababbbdcbcacdbdbababdaaabdaddabcbdabacddbcbadcaccbbaccbccccaabacaaccacccddbbbaacabbaddccdbabdbdadbdccaaccdbadddabbdaabdabdadadabbcddbcbaadcbdaabaddbccccdcccbabcbbdbbcacabbdddcdbabcbadddccabddcccbcccdcbcbdbbcbdccdbbdcbbacbdbbadaaccdbbbcabddadbdddaddadcddcdbadbccdddbdcabbbdaadadcbbaabbbbadcbbaddbcbdcacabbbadccbcdaaccdaabcadccadcdcacaabaaddbdabbabbadcadacbdbabdccabbdccbcdcdbaabcabbbbbbabcdcbbcbcabcbddbbaddbacccbcadbbccdbbbbadcccaabdcabdccbbdcbaababdacacccddcabcccbbdccaaadbadcabbdbacbaadcabcbddabdbcdbbbaddabcadcdaacabbbbbccbaababaddabdcbbadabdbaabcabcaccabddccacabbbccdbdaddaadbabbcbcdcddbacbccacbbbadddbbcacdbdabbdccbdbbcadabadaaabaacaaabddcbadddabcabddabbadcdaabdbccaccbbbddabcdcdcdccdabdcbccdcabbbcdcaccddabaacbbcbcdaddcaaccbbbacaabdaaabbbdbccddacdcbbaaaddbcbcdcbdcdadabbaccabcacdaaabdbadcccdccccbbadbdbcbadbacbdaadabbcccdabcdbaabdbddcdbddacbcbaccdbdcabcdabbbbadacddccbaaadaacacacadbadcbddcddacdacddbcbbbbdacbbddbbcbaadcadaacaadabcbbaaadbabbcbcccdbaddccaddcdccdcbdbabbacdbadcbdadcadcaadcaacddcbdbdadddbddbcbcbadcdcdbbdbadbadddadcaddaadddbbcacdbcacdbbdadcddcdbaabaaaadcccaadccdbbabbdbcdacdbddcacaabacccbacddccbbbdddababdddadacaaccccdbbaabdacadadbdddaaabbdccbabbbcbcacbcadcacabcadadbcadadadbbdadcdcacbbcdadbaacabacaaadcbaddacccdbbddadcaaddddadcbdbadadacbbcbcbaaacacbbbadccadcabaabddaccbcbacdbadcaabdaacbccbbadcdabddcdaabccbddaabbdacccbddcbaabbcbaaaaadcddcbcabddbabdabaaddaacaaaacddbdabcbaabbbcdcbcabbdabcadcaacddaadcaaacacbcdddaccadadaddccadaccdcdccddbbdbccbbddcaacacbcaabdcdcacbdaccddcbccabbdcadcadbdcbcaadabadcbdddccbcbaddcacadccdbabacacbdddbbcacbbccbdbacacabccabccdcaabadbcdcacacaddabadabaacaccbacdcacabaddaddcbaccdababbcdababcacbadcbaacdcbdbbdddddacdbbadbcdcdadddccddadcdabcacdbdccbbdcbaccaadaccbaacdbbcbdbadbcbaaaabaadbdabccaacbcaadacbccddbccaccdbaadccbadddbcdddaacabdbabbbadcbdabbdabdabcddcaabbddbabcaacdaadaacccbcbbabbbadcdccabbadbcbbadaabcabcabcbbacdaaddccdbddacdabccaddbaaacbcbbaaaccacbcdaccaddcbbcccaacbbcdaaaadbcdcdbcaaddacaaddbaabdcadbcdcaddadbbcabbccdabcbccacaddcdabadbdcacaadcacabbddbdbdbbbdccdbabdbaaddddcbaaadaaadabdbaddccbbbbaacdabbcaccdcabadbccdbdcadcbdbbddcbcdddaaccbbdabdadabddbaabcadaacbbcddcbccbdaabbabbdaccdccccbdadbdccddbbaabcbbdcbadcadcacadcaccdbbaaabacbbabcdaaaaabacdcbccdcbaacccccbdaaaabccabddcacbcdccbacdabaadcbcbbdbdbcddcadbbabbccbcabacacdbaacddabbdbcdddbabbabccdbbcbaddcbcbadbdcbdbdccddabbdcdcdbbccdacbcaaabdbbdbdbcbacddbddbabbbcdaddbcccbbdddbddbdacdbbdaccbcccbbcdcccaddadcbdcccacdcdadcbdddadddbaabacabdbddcacaabdcccccabaadccddddcaaccabbaccaabcdcccdcaaaccdbabbdcbbdddcaaaccbacddddbbbabbdaccdcdcabbccbcbccadbcadcadcddbccccdbcbcdbbaacdbbddacbbaaaaabbddcbcbadcdbdcbbcacbbcccaaabcbbadddabbbdabaddbcabbcbbcdddacaadabcddaccbbcdaababacabaaadaaaabccabdbaacdcddccddacacdcbcdacdaccdaadcaaccbadacccbbaaccbbddbcadadcbbaccaaaadadbcdddadbcdccbadbaabaddbabadacdabaaccabadbcccdddbdbaaaaacdcbddbbdcdaddbabddacbbdabbcaddcdabadcabacabcdbcbbbabcabddacaacacdcacbbbadcddbbacadbaacbabbbdcbbddbbbadbabcacddbaaaacdaaccbdacdcdbbcdddbbaaadadbaabccdacaacbdcbcacbddccddaacdcacdaaaaacabcaddadbaadbcbcdcdaccbbadcbddbdbabccacbacaacbaabcdcdbdadbdabcacadccdbbcabbadcacbbbcaccaadaccabbddbcbbbcddabcadbabbccbbcccbadcabbdcbbbccacddcbaacbdcbdabaadacacdcbbbcbbbabcaadddadddcaaaccadabdcbbddbadcddabcdbbbbdacdcbcdabaaddabdbaaaabbdbbcbacdbbdcdabdacbdcbcbdddacacdcbcdabbccdcdccbddcacaabcacaaadbbcaacccbcbaddbcabdaacbbdaccbbcaadccddabddcbbccacbbcddbdbbdaaabcddcacdcdadbcbddbcdcbbdcdbdbdbccbabcadddbdabccbadaccabacddbabdcbaadddcdbbabdccbaccbacdaaabbbbddcdadcdcbbcbabddaaabdbabbcbdadbdadbcaacdabbabacacdcbcaccddbcdddbbcbaadaabcaddacbdcdbbdbbabcdccbbdacdacdcdbdbdcdacddadccacacddaadadbcaaccddbaccdaaabdcbbddcaadbcbabcabadbbcacddcacdaabcbbdacbbccbbababcbcbaaddadcbddadcbabcbadbbcbdaadcdacdccbcaacdbbdbbabacbbcbccdbbbddddbbddbcddcdbcdbbacdbbbadcbaabacaabdcbcaaadcadcadbabbdcadcdadaccbadcacbaadcdadcdabcdacaaddadcbbdcbcaddaacbddcbcbbddcbcbdddabdbbbbacbcbcdabbdcdadacacbccabcdcddbabbaadaadaaddabacdcccaccaaadcbbadddcaddacaddadacbbbcdabcccacadcdbccbdbcaacacdaccbacbbdbaccccacdbbbcacadaadbababdabacacabacbaabbaccadbdacaabcbdadadabccaaabbbdcbdbbaabaadabcccbcccdcbaaacdcacbdbccccbbbabbbadcdcaaacdcbbaadcdadaccdbddaccabcabcdcaabaadabdddcdaaaadcbbbbcadcdbcdccacacbbbdddabacdbcbdbddaaddcdaadacdaadbbbbcccdadcadcacdcaacbabdbadccdcdbaabcacdbdcdbbabbaccaddcdbcaaadcdacadbcdcdddbcaddadbabcaacdabddcbacdabddaababacabcdbcbbdcaaccbbbbcadcccadcabaaacdcdacbacbcdadbadbddaaacdbcccbabdacbccdbaacddddbdddbbcdbacbccddaaadaadcddcbbbcbdccddcaabdcbccddcadccdaabdbbcdcdbcaddbdcacaababbdbdaddadbdbcadcbdcbbaacbddbccbdcbcaaccdaabcccdccaabdacacdddbbbabbcbabacaabcaccccddbabbaacdaacabcbdaaddbbddacaacbcadcacaabdbbcbcbcbaabcdccddcdbbccbbccacaaadddbcaddbccbdaacaddadbaacdddbbdcbacbcdcbccccadabdbbdddaddacdbbbcdddadbcdbcddccdcadacdadbbcccbddbbcabaacbabcbdadcbcaadbbdaadcbdcbcabdbcddacddddbbabadbcacaddacdddabcaacdbdbccdbcbccbcbaabaabadabaadbaabbdabcccddacbbadcbccbacdaacbcdbcccacdabaabbaabddddcaadbdcaddbcdcdcbaabdcaadcbaadbacadcdacdabacddbcdbbbbddbacccdcbbcccacdddccdcbacadcabcdbcbcdaadaddaacdbabacddbccddbaaadacdddddadaddcdcdadaddbbdaabccaabcbdbdbdddadcdbdbaabcdcddcaddcdbddbccbdbdbcdaabbbbccabaaadddadcdcbbccadaacbdccbdaacdcccdacaadacbdbcbcbdcbabcbbbcdcbccbdbabacbdcabdcbcccbbbaadabdbcddccccbccbababccbcbcabccdcadbddcaaadabbbbaaabcbcabdcdcaadbadcacdcabdcacccbdddcdacbddaabcbdaacdddcaccacdbbabadcdbccbddcdddcddcabbacabdcbdbbbdadcddbaccdbbddcddaaaccbcaaccbabaadbccdbcacddddaccddacdacbcdcaaadbcdadaccdababdaacbccabccbdcbbbcddcaccbcabdbdcbcddaddccccbdabdbbbacddddacdcdccdaddbcacbadaddddadcbbdbcbccacccccbabbddaccdbbccdadaaccbcaacdbbbabcdaaabaacaddaadcaadadccdddccaaccdcabcdbbbbcadccbddcdcdaacaabadbbadddbcbcbdaaacbccdaacbcdbaabdcdbcadbdabcbcbddcbcccddabdadabbbadcdbcbbdadcdddbcaddcacabddcbaabdccaaabdbcccadaadabdbadbabcbbcbbbadbcabcdddabbccacbbcccadabaacddaaabdbaabcacbccacdbbddbbddbaacadaaddacabbacdbaacdcbababbccabcddbcaadaddddccbdbadcbbacdddbbababacdcaacbbacddbcbdcbccddccbbabbbbdddcdcdabbddbaabbdabaabbdcdbccbadddabccbdcdcaabdadddbdcddcbdabcddbdcaaacadbdbbdcbccaccdbddbddbacacacbdcacbcbdcabcddcbccdddcaddbbcdbdacdccbdabdadcbbdadaaccbddacdbbdaccdabcddddddddabcaccbdcccbbbcdcdccacdbaacdbaddcabbabdcbbdbddccbcbadcbcccbdadcabdcdbbcccbcccbcaadabacbcdcbdbcdbdccacaaaabacbdacccbcaaaccbaaddaabbacadbcdaaaabbaddbbcaaddadaacacbddcdcbbadacdbdadcbaabdcaabaaaaaabbbdaaacaadbcbdcbdbcccdcadcdadcdbaadbbcdbcdbdcdadbcbccddcbbccdadcadaaddababaacbabdccdabbaddbabbbabcccbdcccdcddcdddaddadbbcdbcccaabcbbaaabcdbadabbbacdccddbdcdbccbbcddddddbabdddcdadbcdbaaccdbdaacdbdbbbdaadccbbacdddadddcbcdbababacdccbbaaaccccbcbdaddddccddbcabacdbdbcbcdbdcacdbacccdbbcbbdacccaaaddaaaacbacddaadaaacbabcbacdbcdaabaabcccbbaacadcdbabaaacacdaadaadcbbddacaddadbbdaddbadbdcaadbbbcaacaaabdcdcbcccadbddbbdcaaacdcbbadddbddcdbacdadbaadbbccbacbcaccdbbccadacbcdbaaadbdbbacddbbdaabaaadadacaadcbbbcddcacaaddacbbcbaabacaacbaabadacaadcbbacbdbaadcbbbadcadabbaccadabcadabcbddcaaadaacdbaadccaacbadcacacbcdbbadabaaabacdddbbcddcccdaadbadcdbdbdadcbcdabcbbdabbddaaddbadaaabbaacbcbdadacabcadabccddcabaadaabacddcacbadcbbbbbbdbdadcdddbadcbabbabacbabaabdabbbbddbacdbaabdbabddacdcabaccbdbdcdbcadbaabdcbdcaaaababdaadcdbcbddbdddbdccbabbbabcdcdccbcdbdaacaddcaaddcdcdaabacacbccaccaadddbbcdbabdbdadcbbdcbcbadacccaddcadcdcbdacccacddddacbcccbadaccdbcbccabbaadcdaccbaaabaacdddcdbccabcaadcbacadbddcbbabbdaaaaacadbcddcabdccdcddcdbbdacbdcbbdbdbdacaaacbdcdabbddcaabcbcdcabcdcdbabacddacacaadabccdddddabdbabdcdbccbbcabbcacaacddaaddbcccbcbbcaacaadacadccbcbdabacdaddaaadbbbcacbabbdabcccbbaacbcacddacccbddadbbcdcabacbaacbbcdddacdbcbcadbbdcbdaacccbcddccbdbdcbddbbdcbbdccddbacabbbbcdcdbdbdabccbdaabbcdababbbddcbacbacdacbbcbbdaccbcaabbdddcbbaacadcdcdddadbcddcdadcaacdadcaaacabaacbaadbdbddccdabaaacbbcaddbacbcdcdadadbccaaaadbbcaddcacabddbbbdcbcccaabbdabbcdabaadaacadadcbacbadaadbdbbbccabbbcdbcaccbdbaabcbcdabcabbdaaaddddccaaacbbddcbdaaaabbbddaadabdcbbaadccbddccccbabcdbcaabbcdabddbdadbbdcbbadbddbadadabdccdadbbcbbddbdaaccbdaabdcadbbbcbbddbadcdccacbccabcaddddadbcaaacdbbdddadadaabccbdcbccaccddbacacaabacbbccadbadacababadbbbcbcabdbbbcdbbccadaabbdbbcbcbdbabcdbaabaccddccbaabaaaadabdbcaacbccdbaadcccddcbacccdadabacbbcddbcbabaaccaaacaadcddbcabaaaadaadcbadcdacbccccdcaacaacabdacaaacbcccadbcccbacbcbbdcbbcaddddcddcadcadcabdadcacddadadccaabcddbadbcbbaddddddcdbcbdddadddbabbacbbddcdcabaddababcadadccdbdcbaacbdbbdddbcdcddcddbdbcbadddcacabbbdabadabcdcdadcbadcbbdcabcadbdcaccdccccdcabbdddabdcacbdbbbdabadcdaabcdcbcddcddbbcbddcccaaadbdcdddbdacabddcdbcbdabcaadaadaccdcdbaccdabbdcddaaccbdaadaaadbadbcdaadacaaadccdaaabaaaadacbbbbbdcbadddbbcabdaacbccddacbdcbcdacacaabadabcccaabadddacdabaaabdabdcbaaacabddcccbaabbdccabdaddadbcdbdcacabdaacadbbbccbdbaddbddadcbbbdbbbaccaadbccaadabaaddbbcdacacbbbddbbccabbcbaccadaadadbdccdbdcccbbaadbbcabcbabcbbbbbadcdcccdbccccbaaaddbaacacbbdadbdacddbbbacabaaabbcbdbdbaaaadddbcabbbcbddcdbadacbadbacabdbacdabcacaacdacdaabacacbbdbbcdaddcaaacdaccbcaaabcaabadbcbdcadbbaadcabdbdbaadcaaadbcddcbcaccaadcddbbdcabadaddcaadbdabaddbbdaccbbddcddddbbdccbbcbbccdbdbaccbdaacdcbbdbabbddbaaababdcdabdaacbdabcbccddbcddaccaadccbcbcbcdbabbbccdccabbddcadababccbaaabddccdccbcdaabdcbaaacbdabcdcbaccdbabdaadbcbabcbacbbbabccdcdbdcdcdbaadbabacbcaaaddaaacddacbbcdcbbcbccabbabadbdccbbbaaacdbdddcdcbbbaaaccabacddbabbddabadaccaadcdcbababcbdabaacacdcabdcbaccbaabcccbddccacadabbdbbbabdabcbccccdcbabdacabcababadacbcdabccddbaccbacbabcdcbabacaacdbbbcbbadbdbbdcdcddaccccbbdbbaaabaabaaabcabababdbccaaacdbbaabbdaadbccbdbdcacbbccdbbadacddaadcacaddcaddaacaadbcbabaaaaddbbdddbabbdbaacddaddbaccdbcaacabbdcabbdabdcbcbddacabcccbdbdddbbabacaacbcaccacabddcaaccbaddcabcdbbcccdcacdbdddbbcaacbbcbdcbbabadbddcaaabcadcbcbbabcacbbadaddbccaddaccadbdcacbbcbdcccbadbabbbccddaccccdbdbaaaabbbdaabdddbcbcdbcdcadbcabadbdaddddabcbcadcbddacdcbdacdacbbcdcdcddbacbcbaaacdabbacbdddaddbbacbacdcacdadbabcadabbddabcaabbdadcdcbddbabcadbacaccacbccdddcddddbdacabbccddacaadcccdccadbadcdcaccddcdaacdbdcdbcacabccaabddcbbbbbccacabbcdcacacabacbbdacddbbaadbddaaccbaabccdcdacdddcbcbcbabcdccbabadbccccdacaddcaadcaaadbdbdcadbcbbccbccadbddbcbdcddbabcabccaaadccbbcdddccacdabbbabcbaadcddaaaddaddbbddcddadaaaccbbaabddbdbdcdaadacbbcbbdbbbbbbaddcdcbdbcbabdbbdcaaaddcdadacbbbcbdccabcbddcbcacdcadddaaddcdcdabcbbbdbaaaabcddddccdcdabddcbdbaddbacbbbaaaacdacaddcabacdcdccaddadbdbbbccbbacbcccdbbdccccbcacbadabadacbacadababdacdcadabbaabcdcbddcbabdaddbabbbcbbcabbacaaaadaddaccacabdbdaacdcbaacbdadbcdccabacbccddcdbadacbbbbdbaacbcbcacabdccacbdacccbbdadadaaabbccddbdcbcdddbabcdabddaddadbbbcaaccbaccacacbbcddbbcadccaaaacadadccddbcacabdcbddcaaacbcdbbcbabccbdcacbcdcadadabadabcbbdbccabcabadacbdaddbcabcadbcacddcdbbccccbaacabbcbbbdcbcdcaadccbcbbbdabccacaaaabadddcbbaccbadccbbbbcbcaddadcbbdcabbdddcaabaccbcbdcabcbccabdbcddbbbccbdcadbdccdbcdcbcdcaddbbddabdaccbaabddddbbcaccacccbabccbbbccccbcadcdadbdabadcbcdaabdbddbacbcaddddadcddbcdcdadddbbacbdbaabccdaabaaacbbdcddcbacaacccaabbbadbcddccdddccabdbccacccaddddbbbbdbbbcbcbdcbddbabadcbcaccdacbbabbddcaacaababccabbadcdabadddabdddcaddccbaabaababcdcddabccaaaadaabcaacddcbbccadaadcaaacbcdddabadcdcadaaacdbcbbbccababccabcadcabaccccadcbddbacbccdbddcdbdccbaccdacbaaabdaacabccbabcdacdcccbacbddacacabbcbdccbdaaadadccadcdcbcaacdddcbbaacbabbbbbcacdcabdabddbbcdddcccbdbaababbcaddcaccbdabdadbcdabbcaadbbdaacabddabbcbaacbcacdddbaadbbbbcaddcddcdadccbbcdbdbdbabbcbdddaabbaabbcadcdaaaaddcbcccacdccdddccbcaccbcadccbddacbbdadcdcbaaacdcccaaacbddcbbcbadbcdbcdbdaddcabacdbbaaabcbcbdbddcbbdadabcccadbbdcbdcddcacbdabdacadddabdadaadbddbbbcabadbdadadbdcdcaaadcbadadaacbdcdabdbcdccccddbdcbbbbacccdcbcccadcbcbbadaccabccabbacadccdccbcccabdabaabdcdddaccbcdccbdbcaaadbbbbbabbcccaaaddbdaabcabcdcbadcaadacdbcdccddbbdabcaadacdbbcbcccabdbcabacdbcbdabcdcaacaaaacdcadaadddcbacbddcdaaddbacccbbaacbdcdbddddcdcabaabaadddbcdddbccbacdccccdbbddbcddbccccbaaccbccdddaddddcbabbaaadbabbccacbdbbdbbdbdadbccaabcbacadacbddbdbcdbbaccbacbdccacadddddacbbbdabccdbccbcabdbabcaacaccaaabcddbddddbdacabbcbbaccaddbdcdcbcaccaabdbbcabcbbcbbcaadcacbcdcaccaaacbdcadbadcdcbaddadbaacacbddaabbcccbabcbbdaabdaaabacbddcdcdcadddddbcbaacdcdadaddbcbabcbbbadbcdadadcdabdbbdabaacbcaaabbbbacbbabcbbdaaadadcbaadbdcababcdcabcabbdccadcdbdadbdabcbbbabbdbcadcaacacddacabdbbdadacdcbbabcdccddcddaabaacbddcdddbcbabaccccbbabccacddacccdbacddccdacbdabcbcabbcbdbbcadcbddabdcdcbababdabbcddbdbbccccdcacbaccacbdaacadacaccdbaacdaabdbddaaaadadcadcabcddcadcbbbdaadacbcbbdbabbdcabcbabbbcabbabacdaaadadaccdbaaddbcdcbdcccdadcabdaccbacaacadddddcaadcaaaadbaaaacbccbaccccdbdcaabcaccbbcbaacabbdbaacacbcaadcbadbcdaabbdccdababababadcbaddcacdbdbabbdcdcddaaccdcbdbddbacaaadbabbaddbbbdbbbbacadbabbdddadccbdcdbcadbaadbcbbaabaabacbaaccdaaaaaccccdddccaaccbdccdbdcccdcbcccddacaddbaacdadbdaaddcaacccddcccddaacbabcbaccdbabdbaddaaccbbbbadcdbddcaabbbadccdbabbdabcddbaccccdabcababaaadbaccbbaddacbccaddcddbddcaabddadcbbbbcbdaacdcabbcddcbccacbbbaddccabcddccbaabdcacaadcbbacbcacdddaaaabdbadbbcbcbbadcdadbdabbcbdddaccacddbbabcabbcbdabdbaddbbadacabcaaabaaddddcbdcaaadbaadccdadcbaabddcbdabaccddddadaacbdcabbbcadaccccbcdcadcdaadaadbcbccddabbbccacdaccbddcccbcbddddcbbdcadccbdbaddaadbbacbbdbddbccaddaabddaccdaadbbaaaadaabcdcabbacacbdcdbbddaaccdadbbddcdbbcbbbbbdddcabddcdabaaaabbbabcddddbdbdbbbdbcbbcddcadcaaabbababddccaabcccaaccdcdadccadccdaaddcdaabbbbccacbcbccddddcdabacddbbdaadddabcbdbbdbbbdccbcddadadbddbcbdbbdddcdbcbdabdbccbadbcbcaccaacdccaccbcbbbaccdabdccacdcdccbaaaabcdbacdbdadacdcaaadcabadaaaacdadacdbdaabbdacdbbcbacdbbacccaadcaddcbdbdcdccbabdacddbadadccabcbbbbaccacdbcdcbbbbacabbabbcadccdaababddacbbbbcabdccddacadddaaabccddaabcbdbbacacbbcccccbdacabcbacabdabdbbcbcbcabccbcacbaabdcdbccdacbaadbcadbcacccdacdcbbcaacaabcccbccddccbbacbbcdacacbcbbcbdbabdcacddccccaadaababdabacadbddaadbcaabcdddbdbaacbabddbbcccbaaaadbacdaacacdbbcaddbaadbbaabcdcabdbbbcadadcdabddbcaadaadabdaacbdbcbdaddcabadbcdbccacbabaadcbbdbdccbbcabddbbcddcdbaccabbbbaacadaabddbbaacbcabccacbabacdbacadcaaaddbaadbdaddddacbdbaaddddadbbbcbcbcdcdcaabbccbddcbcaddbabdcbbccdacaacddcbadcbacadccacbbdbdbcbabacbcdbadcdcdcccdaabdacbaadddddabadabadcdaaadaddbdbaccabcdbddacbadbaaddbdccddabbaabbcacadaccdbacdcdcbbacbacdadcbadacddbccbdacadcbdcbadcdddbbcbadccdacbbbbddbaddbcdbaccccbadadbcaaabbacdcbddcbcaaaabdbabaaccbdacdcbdbdaaddbddcaaaabbbabccdadbabbcbdbcadbbaccacdcbdbdaadcdbabcbddaccdcdddddcbbdbaabdcddddbbbdcbbabdddcbcabcdabdaaadadaacbbabcbddbacdaaaacdddbdbbaaababcbbbacadddcdbddbadbacbbbabdacbadcbbaabbcabbbcbbbaacbbcdaaaacdcaccadbabbcdddbbaddaacacdcdbaccadccbbbdbacccdbccbbadcdbbacbdcdbdbadabbcbacbdcbccabdbdddaccabbbadcbbccbacdcabbcbdabbdabbdccabbaacdadabcacadaddbbabdccbccabaacbdacbcbaaabababbcddabccbaddabacbcabdcdbcbbabbdccccbbaccaccdacbccdadccbbddabaadacbabaddbdbbdcdacdcdcbbbdddaadbcccbddabbbcbcccacaddbcdddccdddbdddacadabacbdddbdadabaabdbbcadaacabbcbccaabccbccdaccdacddcddbcaaccaabcbcbbcdddcdabcaadcdcdadadbddbdcacaadbacbcddbcbbdddcdabcbdcdbcaccbccdcdadddaaabbbbaaccbbbcadaadbadadaaacbcbdcbabcccbdbbcdabddcbababbbcbcaacccaacaacddbcccdcaadaadcaacccdcddcbdcbdcdadadcbdacaacdababdbaaaccccdbddbccacbdbdaacbdcbcdbddbbadcadcaaacbbdcbbbbcaddabcdbaaccdcdcbddaaacdddcbbcaadacabccbadddacabbacddbcbbbbbcbadabcbdabdbdabaacbadaaadadbbcdbdcdabadcdbcdbbdcdccbdabcbdbccacacbaaddcdadadcabbddbacbdbcccbdacdccdadcacddbbaacddbdaabbccbbdcdcdbbbbcdacdbccabaabadaaacacaadcbacbccdacdccdaabcadcdddacddabdabdddcccdadcdaccadbcdccbccbbdcaddbdadddccdbbddddbdcdaabccabbccbccadadcdabbccddcbcccbdabbdcbaabbaadacbddacdbbdaddaadbccbcdbdccdbbcbbbcbbadccabbdcccbcabaadcbadaaaabdbccabadcdcbbdbaddadaabccacddbbbcacadabccdcabadacdcaacccbddadbdbcbbbaabacbbabddadcccbdddcbdadaadccdaadcdcbcccdbbdcdddcdbcddbdbdaaddaddcdcdcbdbbdbbccddcdaabbcaabaccbadabcdbdcabdabccbbcaabcddbbdbaaaaadddbcadbaacadbccbbabbacddadaccbcadcabadbdaccaadacbbdbabdaaccccccaadbcccccddabbbdcbaadcaccccaaacdddacdddbadacbdaaacacaccaacabdaabdacacadaacdacabdddacacaabcaaabbdaadccaadadbdbbdaabbbddaaabcdbcccadaddcccaabbbdddcbabbbdccbadccaaadcbdadbcabbdcbaddcaaccccbdcbacbaacabddcdabcaaabaadbdbddccdaaabcdbbaaaacbbbccdacdcaddbdbbcdbccbdacbacdddadccaabcccdbbcbcddccbbdcbcdadcbaadbaddbbdccdbdccccdbabcacdbbdabaddadcbacdabbbacddccbcbddbabccdbbcabcbaaaaadcdbdcdddbabcaaddbacbbbacbcaadbcaadbdbbbaaddacdbdaccdcbdacbaacabaaccbaabdaaaaacbbbcbcadccbaaccaaddbddbcaaaacdccbcaabcadaacbddaaadaacccadddbcccbadabbbcdcbbacdabdcbcdbcdddcdabddcdcbadcbbbdcaacdcdbcbbcdbaaaccdbaaabdccbbbadbcdcdaadbbcdcddcddabadadcccaddddcbbbbbcbabaaaddacabddbacddbbaaddddaccabcdddbbbcaccbbaaacadcbdaaacdbacababdabddbaccbdaabbdacaaccdbdcaddaddbacdddabbabbadaabadacbdbdabcdcaccdcaddccdbcaacccacddddbdbdccabdbdbbddbdbbdcdcbdbabdabcbbdcddcadddcaacaacccaaadbcbbadbddbacbaababbaadbbbaabadbbacbcbcbdcabacdcbbccbdcbaddbcbbadacdbadbbadcaaadcdbacdbbcacaacdbbaadbbdddbbdacbbbbbbbaabddaacbabdccadbaababcacaaabacbabadcaccccdddbcabdbadccbaaadcbadadacdcacbddbcbacdcbaddbcdadcabddabbdaadacacdbbadcbccacadcbaddacbbbdcdadcbaccbbddddcbbdabadbbdabdcabdddbcdccacdbbddcabccbaadbdcbccdbddcacacdccbaabdcbddccbddbdccdddbdbccbcdaccacccdbcabccabdccbbdacaddcbbbaaddbaacadabaaddbabcdccadbcbaacaaaccacbccdcdcaabaadaacbbabbdacaadcdbbbcbbddbbacaaaacbccadccccbbbaacbdcbbaaddaccadccdabcdbbcacbabdabcacaaccccbcbddbbbddaddbacacbccdbcbbacdcbaddbabadbbaccbcbdbddbaddadbccbabaabbadaabdccbddbbcccacccdacdbddbdbcdbcdbbcaddabcccdcdadcdabccdabdcabaddccaccabdcdabccacbaacabdddbdbabaadbadbbdcbcacbbbbccbababaacbcabaadccaaaddccaddcbaccdadcbadabacadbdbbadbdabddacacbbabbbbaccbcadadbcbbcbbaddbdbcdaaccdcaddcaaccbbabaabbddadabaadcbaabdcdddbbbdabaabcccccbcbadcbaaccaadacacdbabddcbacbdacbdbcaddbbbdddcaadbbdbbbcdadacbcbcaccdccbbadddccccabddcdbdcaaaaaccdbcababacddadbbdbbdbcbcacadcaaaccdbbaaabcbcdbbbdacadabadbabbbccccacccdbcbcdabbccdadcadbbbdddcacbabadaadcdabaabdbccdabcdbbabacbdcbadcddbbcbcccbbbdadbdcdbbbddbdbabacbbcbcdccabaaadbacbacbcbccbbdadcbcddbdbabcacccdcbcabacbccbbbbccddcdcbdadbccdccdcbbbacacdadcddabbdcbdabadcbccccbdaccddaabdccadcbdbbdbcddcbbbddcccaccdaabcddcccccacbadcbddbababddaabcbdcdbbbcdbdcaadabddacddadccccbdddadaabbdbbaddcaddcbaaccacbaabadcacabcaaabaabbcccdabbddcabdbbcbabbccabdddcdbabbaddbcddcdddadcbbbabdbdbdcbababbcbcaadaadaabaccacbbcccbacbbadadaabdbbcddbcbaddbccbbccccabddcabbcabbbaaadbdbdbcbbbaacacbabddacbaaccdbddccbcbabbdcacbddacbaaccaddcaadcbadadacaccbccccdbddbdbdabbcabbbcabbbaddcbdddcbbaaacbbacdacddddacdacbbdbabacadbdccaadbcbbdcdbacbbccbccadaaaaddbddcbcadaaabcabdcaddbadabbcaadcccbccdabdabcdcdabbbcccbdbccacbddbcbcdaddcbaddadcccdcabcacddddbbadccdcdbdcababccadcaacadcacddababcbccbcadcddbcdadcbbcacddccdaacbcabacdbaaccbcbbdaacbaaaaccbcdddccaadaaabcddddbbbaadaacacccaddaadbabcabbbbaabdcadcdccdcddcdaaabbddcadcaaddaddabdabddbccbdacbabcdcdacadbbbdabacabbadabcbbabdbcccdbdbdbdddcbcaabdbcbdccbaacdbbcbddacbbaaacbaaabdbccbabdbccbbdddadaccaacbbdccabdabadabcdcaacdadadaaccdcdabdbddacaadbcdcbdbdddcbcdbbbbbdacdacadbacddccddabbdcdbbccbabacbcdcacddcaaddcacdbcbaadabdbccdaadaadabccaddcbdcaadacbbcddcaabadbabdbbbdbaddbbacccdcbbcddadcbbadccbacdbccabadcadcccdbdbbbdcdbaadbaabbbbdcbcccabdbcdcaccabddbcaccadacabbaddbdddabadcccaddacbdacbaaabbccbdbaacabddadcaacabdcccccabaddaabccaabdcbdbdbdcdbaadbddbcbabdabadddabcacbcdacacbcdcdcdaabbadcdacacdabcbbdcddaddbdbdadaadcbadbaccdbcdccaccdaddcccbbcbdaabcddacdccbbaadacddbcbaaddbbbaddbdabdabcbaabbbdabaabaaadcadadacdbadbbbcaadadbbaabbaacccddbdcccdbddaacbbccaadaccadcbaaabcdaadcabcbbaacaccdaddbbbbadcbacddcdddbaccddabcbabcaabadbcdcacdbbdcddbbbcaccccbbcaabaabcdabaabcbbccddaabacdbdbcdadccccdaacddddbabdddbcbbdbddbcaccdbdbbddcbbabaaccbbbbadadbbdbcabdaaacbdcdabbbcaabcaabcaccdbdcbdbdbcdcdbcccbdbcdadbccacbabddabbcccdabbdbcaddcacacadccacbaabbbdacabcaccccaddbbbaabdcccbbabdddcaccacbcdacadbadbccddddaaccbbbddbddbcccbcadabacbbdcbabadcbbbabccdbbcbcccbbcaccdbbdccbcbdcdbbadcccdcabccbccccccadcdaaccaabbbabaccccddcadaadbaddcabcdcbbcaddbcbadabcbbbdbbbbbdcbcacabdcccdabaaabdbddcdacbcbbbcabdbcddddccadcdbbadaacbabbbbbbbccdbacdbdabdcbdddadbdbdccaccbbbcddbbbacbcacbbddadcaddbaddbbddacccbbccccaaadcadcdcdbcabacdddbaaadacdddcabcabbaadabbbdaaaaddacdadbcacbccbaaddbcadaabddabcbaddcdcaabddabaacacccbddccdcbdbbbbdacabaddbcddddcbccddccadbccadcccbcdcbcbbbcddcdcabaccaacaddacbcddcddbcbccbcbbbbbcbbddadacaadcbcaaaaaaaacccccbabacadcddccbcbcbdccbcaabbccababbccaadcddbcdaadbabdccbaabbcdcbcbcbdcacbabcabbddadcdabdbccbbacdbdcdbbabcccbcadcadcbbdcbabdaabbbdbbdbcbacdddcadadcbcaacbbbcaabbadbbcdbadaacadaacabbdbcabbbacabbcbbcaaadbacccbacbdbacabdacccaccddcbddbadbabdbbbdcbcddbadddabacbbbcdbaccdddbcccbcacbbbacbbbaacddcbbcadcadbdcdaadcbaadbaaaadaadcdadcdddaacbadadbcbbbbacdaacadaaaabcccbbccaccaaacbdcdcdcdabddcaacdaabcadcdcabaaabdbdcdadcddbdcdbbdccbbaaabacbbbbdbadbbdbdbadbdabddadddcbbddbbcdadbcbaddadaaacdabdacccbacaccbabcadaabdcabcccbadacbcbacdcccccccaaacdbcbabbcbbbdbaccddcdabbcbdcdcddbcbabdbababbaaccbdaadbbaaaacaccdbccdcbcbddcbaaadadbcdddcbacbbcadacdacbbabaabaddcbaadbbbabcacdcccdacaabadbabdadaacbcabcbcbcacdadcbaccbbdccbadccabcbabcbaacadababccbdcdbcababbbcdcadddaccabbcbddabcaacdbadcadaaaacdbbcbbbaccaaabaddbbbdbacbcadcacaddbbcbaacdadaccbccbaccbdabcbbabdcddcdabccabcaddddbbadadaddcaccbdbccdbcdbcccaacddbcddbdcccabdbdacbcdaddabddabbadddddcbbcddacbcdcccaaaabcbbabbdaccccacbababbaddddbbcbbcdacabcbabbbadacbabbddaaaabbaaacddbabdadcddccacdbbaaacddabddaadcbbdbaabddcdbbbbbcdbbbabcadbbacdcdabcbdbbadcdbcddcdabcdbadabaddcdbbdcbcbaccddadbbabdabccdcbcdbdcbacbabdcdabdcabbcaadcddccbccadcaabddabbdadaadaccdcbbcbdaccacbcdcddbcbbdbdaadcadbbdaddbabcdbdcdacdadbdacbdcbdcdadbccdcdbacbcccbdadcdabaabcabaccccbbdccbdbcbbbbaabdcddabccaadcdbdcacdbdcabddacaddddabdbbabaacdcbdcdbcabbdcbabbbdaaaccdbdabbbbbadabaaddaabcccdcdaabbdadcccabcadccabddcbcaaccdcbcddbdcbcaaddabddcdddabaaabbbbdddccdcaccdacadcadcddcbcadbbdbdbaddabcadbcdbaabaccdbbbbbdbacbcadbbbdddcdacbdacdbbbccbdaddcdacbdbabadabbbdbacadaaabcbcbdbaababdaaadaabddcdadbbdbacccabbdbdddccccbcbccdcbaaaccaaabcabbbbdbddcdcaadbcccabdbcbbacddbaaabadbdaacaaabcbbdadcdcdcdaaababbdaabcabccaadabcdbdccddcccbcadbbcbcdbdccdbcbdacadbcdacdaacbccddccdcddaaabbddbbabccdacbdcabbccddcacaabccddcdbccaccdabaccdbdcabcccdbcbdcbabccabdadaadbabababddadbbddcccacddbbbaabdaccabaacccaadcdbbcddbadabcbcbddbbdddcccbacccbbcbbbcabbabcdbccadcacbabaddcddaacbbaaddbdaacdaddaacdcdcacddbddadbaabbabbcbddaadaabbdcbccaabbdddbababccdabbaddabdabaddcbbbcadaacbbababcdbacccaaabbadadbabcbdcaddcdddcbddaadabbbaacdcdacacadbdbacadccddadabdacddadbacabbdcbdcddcbccbbbcbdbdbcdcbacacbabcbabbdadabaaccbcddcacbdbbbddcbcbcbaabdbcacccdcccddcddbdacdcacbaaaabdbabbdaacccccccbcadddcbcaaccbccdcccbdbdbcababdabcdaaddbbcabbabbadbabddaddcbccbbdcbcdccccbbabbbcbacccbddadbdbdaddbdcbbaddabbbbdbdbaabcbdacbcdcdbbbccdbdabdbbbbcddbaaacdcaacdccbadadcaddccbcaabaaaaaacdddcbcccdbcabbcababaddaaaaaaaaaddacabddcdcabccbdcdacabdcaddabdcdbabacababbbbbbcddbbdabbaaccddababddcbbbdaaacabccbabadacdbaadacbcabcdbaabbcbccdcbbcbcbcdddbbddbbacabcdbaaccacdbcacdcdbacccbdcbdbcdaaddbaccadbbacddcddbacdccaccacadcdaaacbdcdcdcadddcccbccabcddbcccabdabbbbbcacbcddabcaabddcbdabbbadbcbabbccdcacbdadbacabbbddcbaaadadabddabdcdbadccababccbddcbdbcaccbcbacbdabaaddbabbccddbcbbabdddabaccadabcbdcdcadbababcaacabbcdcddccbccbabdbddddabcdcadabcbacdacacddadadbdbbddbdbcddcbaadaadddbcccaaabcddaacbacbcaadaacbadababacddaccdaaddccbaccdbbdccabddbdabdcdddaccaaccbabbcbcaadaabbdaacbcdcdccbdadccdadabcdccbbbdcacbcbccaccbcdaadadcbabbcadbaddaddadcbcaadbdddacadbadcabdabadddabbcdabaadaccddbadadadbdbbbdbdbacdcaacdadbcdabdbaadbaacbbbccdaaaaaadcaccdacaaccbadcdcccbbbccbaddbaddbcbddbdbacdbdbbaabbdbbbdadaacadcaacaacbbdccadacbddadaddcacdaacbcddcadcbbddccccaabcdcdbabaabaaabdcddcbddbcbdbbccdacdaaadcaccdbadacdaaacbcdbcaaddadacccdabacbcddccadadcddacdddbbbccbcabcbbbabddcacbdbdbbabdbbdadcaacbaccabddaccdacbdaccaacabbcbccbcddbbddadcbabddbdcaacdacbadbdbdbadddadcbacdcacbadaaddcddacddbdbcbbdccbdcbcbcbdcddbcdacadcdcbacabbbdaaaabdbaddaaadcadabdcbabdcddbcbddaaaabccdcdaadddbccaaddbbbacbbccdaaaabccdccbacabdabdcdcbdbaccbbddbbbcddcbdaccdbbcccbdbcbcadbbcaddbabbccbadddabbdccadccdaabacbccacbaabdcaddbcaabdbddadcadacbbaabbdaadadbaaacaaccaabdabdbbabaabcdacbbbdbcbadadcadaaadcacabaaadacadddadacaaaabbbdbcaaccadadcbadaaccbcdbdbacabbacdddbdcaacdccbdcddaacccddddcbabdccaaacccadcbabbacadbaadadacbcddccadaadbabbbbaadadacdbdbdababddacabddadaddddbaaacbdccdcaadaacbdbcadbaccaccbadbccbacccbdadacaccaadcdabdccbcdcadbdbbcacbddabccdacbcabbbccaabadcccadddddccbbbdbadbbcbabdacbadbbbccbddbacaccabccbcddccbbcccaadbbadcacbdaadabbbaddabcddadaadabbabbcdbbadaadccdcdcaddbcdadbbdbaddbdcbbccdcacbaabcddbdcaddcccbaccaabbaabaadbcabddacacaaccddaaccbacbbdbdcdddbbccacccbbadbcdcacaccddbbcacdccabbdbdbddcaacaddbabbbbbccddcddbdcdbdabdbbccbacdbdbcbbaaddaaaacbacdabbdadadaadadcdbaabbbbabdaccbcdacbcdabbbddcbbbbdadaabaabbaccdbacabcadbbaabcbbbacacbbbbacbcbcbacbbcbbabcaaccdcabcacdddaabdcdcddbbcadbcabcdbcdbbaaabdacaccaabacaccbababbadcccdaabbadbabbcdaabcbcaccaddabbcdbdcbcdadccababcdbaadbdccdadbccbdaacdabbccabcdddddcbdacbadbbcabacdaddaabcddcbdcbbbcbcaacabbcdbbacadabddabdcbcabcbcabcbcddccaaccbcbbadadabccdcaacccbabdbdbcdcdbacdbabbadddcdcdadbbacbbcabacadabcacccdadcdabbadddcadbdbcbaabdbbccdcbbbcbbcabdadacaddaaabacdadacdaabbbaaaddcaccaabbbaddcbdbcadcbbcacdababbadcddacbdcbcdcdacaccaaaddabdddbaacacdaddbbdbcbabdcaccdacbdbcbbcdaddaadcdadcdabcbdddddddaadcbbabcdccacadddaadacbcaccccacaaccacacddcdcccdbcabddaacddcdbbdbacddaaadacbadbddbbbddaaaaadbdcbadbddcaadabdbbbdacdbaabdbbccbddaadacadacbaacbbccdacbbbddacdcdcdaccadbbdbcccdcdcabdcdbccdddcadaacdacdabddbcbcdcadabdcdacbdbddbbdbddccbcdadaabbcadabdddabcccccccccaaabcdcccdbdcbacdccaccccdadaddddbdbccdcbaadccaddaddcdbacddadcbdabcaaabadccdbddabdbbbaabdadbdcdcabccabcbbbcccddacccbaaaccbbbccaaacabbaabacbbddcddaabdaaddabbacbaacbdbdbcdcbbcbacdcacdddbccbbccaddcbbaabdaaabadbdccdbadccbaddaaacbbdddcddddaaaccabdbacbbbdbdaadcbacddbadccbdaccdcccbcacdbdbdaabbbccccaaccaaaaabbaddbbddabcbcacaccccbacadcadabcbabdbdacaddddbbcdccccacadaccbcdccccdbccabaccdcccbaacadbaabdbdadcaccabcbddadcbbabbddacaccbdabbbadbdbaabdcbbdadccdccbdcadacbcbcbcbdbdbcadacbadbcdbbaaccaacaddbddbdbacdbcabbbbdbcadadbdcadabaabddaababbbaabdbcaabcbcaccccddbdadbaabdcdbbccbcdbbbcabccabadaaccdaccacbdbbdaccabcbdbadbcbbddaadabbabbdccdaabcdbdadcdccbdccdabdcccccaddbbcaabdcdcabdbdbaaccbcddbddcbacabbabbcbabcacbabbcdbdadcacacbdaddcbddccbdabcbadbcbcbcddaccddbdbdaddddddbbdbdadbcddbaabddaccbbccacccdcaaacbdbadbccbbddddadddbbcaabccdabccbbbccbaacdcbbabdadcadadbadddbcabbdbcdacbbcddccacdaddcdabcdcdcbadbccdcdaabccbccbdabbbcaadacccacaaaadabbbbbaccbdbccdcdbccdbdabcbdaccbadbdacdcaddaccadaccccbadacadcaddbcbdbddbbbcccddbccaccbbddcbdbdcacaaccdcbdccacbcbabcacacdcbcadaddabcbdadacaadcbadaabbabdddbcbcccbbbabacbbcdaacadacbcccbdadbacbddcaaabbdbacbaaccabbadcbdaabacbdcbbaaaddbdcbabaccbdaaabcdcdcdbdadaddaadbbaddaaccaaacacacadcabcbcaaccdcdabccccddadcdaadaaabdabbcddbabdbcdbacccdbcdaacacdcccddabdccacbbdcddcacadabbdacddcdaacdccbabdbcccddadcdcaaacbcadbaaacadabbdcadccbacadacdccddbcaaabdaaaaacaadabcaabadbacaadadcdcdccbaaadadbaaddadcbcdbbbcadcddbdbbbdcdcddcacdadbdbdbbadabcbcbdaabdcccbcbddbdadbababbbcddccbaddbacacaacdabcdcdbcbbadcdbdcaadbadbcaaccaabbcdcdabccbabcacadaaabbcadbcdcdccbcaadcbdacdcbaadcccdcdbdcddcabdaddadcdcccdcbaadaccdcddbdccadcacddbaababccadbdcdabcdacbabbcbbdcbcacddccbccbcbccababdabdaacdaabcccaabdcdaaaccadccbddccdababbdcaababdcaabdaddbcbbabdadacbbacacddbcabddacbbadcbcdcccddbddadaadcbadbdabcccdddbdabcbdcacaddababdbabcddcbcbaddccbaccdadddbaacbacbaccccccbaabcdcbbbddbddddaababaddadbcaacacadddbddcccbcccadbdbabbbcbbdbddddcadabbdbdabdaddaaadccdddbaacabdcadbccdddcddbddbdbcacdaaaaacdcddababcdcabaddaaadacaabbbbdaccacadacbaddbbcdbaabbcdddcccdabaabbabaccddacabbbccdbdbdddcadcadcbccdcdcdbcbabcbbdaadbcadcacbadbbcddbdadaddcadcaaabcdcdcbcddbacccaabdccdabbbbacdbbadccccacaddbdbbabbddbabcddcadcabddaccdadcbdcadaddadbdaccbbbddbacdcdbaccadacbccddababbdccdbdcccdcbdcdbcbdcdbcadcbdacadcddaaacadaadacdddbcccbabadcdbcaabbbdbadacdaacdaaacbbabddaddcbcbdcdbbcadcbdddaccbdadabaaccdbdcdccacccdcabdcbcaacbbbcababcadcaadbddbcccacacddadadbcdbbddcdbbbbcbcdabcdabaabbdaabdddbabaababbcbbccadddcbdcaddcdbcbcaccbadddbddddbcadacbbcaabbadddbbcbcbadcabbacccdcbaadadcbdbdddbdcdddbbdcdaabcdbadacbbbabcbcbbdbcdcdccddaacddcaaddaaacbadbdcccdabadbabcacdcbbbbbbdbadbccdbaadccaaaaacdcbddcccdcaadcadbadddbdbdbbbbbccdabdcdbdbbbbcadbccdbcbacbccbbcabadcdbaadababbbbacddcabcbacbdacdaadacddadaccdbbbacaccacababccadcbcdbbdbcbbacadbadbaddabddbddbacadcdcbbddbcbabbccddbbcdcccdcbdabdadbdbccadddcbdcdcccdbbcbbaccdddacbdcccbddaabdabdbaacbcaacbbadbdaaacddcbcabdbaadacdbdacbbddcdbbcaabbbbbbdbaaabdaaacabaccddcbddbaaacddcdaaccbdacdcbdbbcbbdcbdbdcaccbaacbaddbccabbccbbabcdbddabbcbdbbccbbadadaaacdadcbcdaccbdaddccdabbadccbbcabbcdcddbdbdbcdcddcadbbbcbadcabdcbcbbabbcadcabaacccbdcadbaacacaaabcbcdbdcddbabcbaadddbdbdabcbacadbbdbcaddbdadbcbaacabbbbccbccbcacabadbaddaaadbccbcdddddbaddaaadddccccaabbaabbccaccdacccaccbbdbbadcbacdbbaddcdaaddbbabacddbbdbaadabacabdbdbabbacaadcbcaabccdcdacadbabbaaadabbdcdaabcbaaaabcbccbcacadaddbccdbdcabbbdcbddbbbcaabdacddddcabaacccbbadccddcddacabbdddaaadcbdadddaaaccdcadcadcaddcdaaadaabddcbbabbaacdabbabcdbbcdbdadabdacbbaddcacaabdbdbbdbaaadbaccccddababdccbabbdaacddbacccbbcbcdaacdadbbdbdbdcdddccbadadddcdbaccbacaacdbdacdbccddbdbdbdacdacbbdbdbccdccabcddccdabcabcaacdbcbccdbbcdddcabbaabbcdcdcddadcdbbdddcbdcbddcddccbacddbbbdbaacddbbddcbbdbbbbacdacbddcacddccddcbbdcccaaccadcdcbacbbddcccbdabbababcbccabbddbbabcbbdbadacdddaaaccdcdacadabccabdcbddcbaddbcaabddbabdadddacbdaadcaaabbddacbbbbcadbdadcbcbaaaddacdadcbccaadccabacabbddcbadbacbdbcdcbbdbdcacbdacacabbbacaabccabdbacbadccdcdbbccbbdacabdccacaddbababdabaaddcacbadaadccbaaaababbaacdbdacacccbdaaacdcdacbaaacdcbbadbabbcbadacccacbcacbacdbcbaabbbcccdacaabcacdaccbddbaabdbaaabbcaacabccbdddcddbcdbddddccbdbbcabaaabbaadcdaacabaabbdbcdcdaadbdbccdbccdbbdcbdbbbbaccbcbcbadaadccddbdccbbcdcccddbddadddacacbbcddbdabbbbdddbcddabcabbbccaacbadcaddabacbdabcccaadabcadaaddbccbbbcccccddacddcaacbaabdadadcabccdaaabcdacbcdcaaddbdaacadbbbbacccaadaabbccbccacccaccdacbbabbccababccccacddbccbcabcddccbcaabdcaabbcadcabdbcaddccddbcdaddcbbabdaabcccdccaaddcdacccdccbbcccbaadcdcdcabcaababdcabaddbccacdbddcccdcdbbadabddbaadcdababcbaadcabbdcdaddbabadbbaacaacacabbaaddcbaadddcbcdddabadbbadacbdcbddbddbaabbdddddbadbcadbbccbaabdaabdcdcadcbdcdccaccbababbbaaaadddbccaacbdadbadaaaaabadabdcccbaaabbbbbdbcdaababbaabbdccbcddcbbccdbacadbbbacaacbbadcbdabaccadcccbcbcdcbcbabcccdbcdaacbdcadbabdacacdbbbcccbcaccdcadccbbccbbbacbdcccdacacdaaddccaacddaadabdbccddaabbcccbbbdacdacacdccddcdbdcdcddacbcdcaaababbdacbccacbcdbaccdbdabadcbababbdddbabdcbbaaabcaaabddbdadaacddbaadabbabadacbbadaadbacdcccddbbbdbddbabcbbadcdcdddaabaacddbbdccdcacbacbddbadabcdacdabbcbacddbdccdaccacccdcbabcccbbaadabbadbabbcaccbddddbabcbaaaacdbbdaddbcacbacdbdacbdabbbcbdcbcacbabddadacbcbabcbcccaacdccdcdabbcaccadcaadccaacaabbbbdddccdadcabcddaccadbbbccccaccdccbbaccadcadcdaddacdaabcaddacddccccadbbbbbdcabbcbcbdccdcabcbcbbaacbdacbbcdcabdaaabcaabbcdcacbcdccdaacadbddcdadcddacdcdababbababcabdcccadddbabdddbbcdbbaacddcadcdcaabbddbbacddcaaccbdacdcbcacbbbbcbaacaddbabdcdddabcdccacacdccabdbdcaaaadbddadccadcacaabbabaabcbdbcadadcbaacbddcddaaabacdddcbcdaadacadcdbabbdbaaadcacdccddbcaccbdcddbdcdacaabcdbabdcddbadccacccdbadbdbcadaacadcdadbccabdccbbaccbddddddcadcdbbbdbadbcbcdbaababdccbbabdadcdcdadbacdaddbbddbdbaaaabadbaddbdadcabcddbbdddddacabcdaabaccdaaddcacaccbbdaacbabdbabccbbbcacdaddacadadaadbbcaaadaadccdaabacbcbbdccdbcbbbaddbdaaababcabbdcbabccbaacabdbadabcbdadbdbcccdddbcdaadcbcccadbbacbdcdcbddddaccdabbadbccddabbbcbbcddbaacdcccbcccdbdcabcbcbabbdccbcddbaaaaaadadaaccaadccaacbdccdcbbdcdcbcdcdbdcccdbacacababacdbdadcabbcbdaddcaaccbaacbbdddabbdcdbdabdbbcdcadaaaacaaccbdaadcbadaddccadbbbbcccbaabaaaabccbbcddbacbcbaccccabbbbdccdaacddbccddbcbbaaccabdaaaabdddcddcabcddcbbdaddacdabaacadaaacaadabdbbacbaacddcddcaaacbaadcaddadaaccbadabdadcacbbdcdccaabdddadadbccacbddbccadccadacaabaaacccadcacbbadcbccdabcbcabaacccabccabcdbddbcbcdbbcaacbbdabcdabdaacacdbcccacdadaccccacccadddbddcbddcadcdbacbcabcddbccccccabbbdaabbdbbbccbbcabdccaaaaacdcaacabbcacccbddaadabcadbbbcccdbbbbbabbdcdbbcabdcabbaabaccbaddbbcbbdbabdabbbcbdbdccbbdcccacdbacacacddcacababbdddaabadabaaacdaabbacbcddcbadddcdaccdcbdaccaaccbcdbdbbacbcdbdcabbbddadbcbaacabaacbdacbacbbaabcbdcbcacbcddaabcdbdddaaaacbadabbdddcbbccbabcdddcacbcacacdddacccaadbdcdcadbdaadadaaddbababacbaccacdcccdacbbaaddcdbbadcdcaabbadcbddcdaaaaadccadbcdabaadabdbbcbcdddcdcdbacdacadbdbdcadcdcdaabdbaadabbddddbcdbddbbbbbbabaddaccdabaccddcbaabbbbbbbabdacbbaddcddbcbadaadbbcbdbbbbadcdabdaddddabdaaababcccaacddcadaacbbbacdcadbbdbdabdccdaacadddaabdbaddabdddddbbbcdadccbbdabccdacdadadcbaaccbadbbabddddbacbcdbaccbcdccacdbdccbdaccbaccbdabcacaacbbdddcacbabcdbdaaaaadaaccdcbbccccaaaadaddaabaabdcdaaadcbbdadabdccaacbbbaaadbdbbdbcccddabbbacaadacdbbaddbcabaccacdbdbcddbcddaaabccabdadcddcddaaddcaddbdabadaaddcdabcbdadaaddddbbdddbcbdaacacadaddacbbadbaaddabbdabbbabbdabbdadcccaddcdacdbadddaddaaacacaaabcdcbaccdcacbbadccacaadccbcbcabbaddcbccdaccacacbabccadbabbccddabcbcacdcbcddaccdbcbaacaacbcdaaddaacbbcadcbdadcbcbcaaccacacdabbbdadbbcdbccaaddadbbadabdddccdadbcaccddccccbdaaababbbcdaacccdcdddddbbbaacadadbcbaabccbbcccacdbddbccaabcadcbddccbbbcacccbbddccacaddddcacabbdbcbddbdddabbabccdbcddaacadbdaccbccbbdbccdcacacabccabccdabdbcddbabddbdccdacccbaaddcdbdbbbadbdcccbabacccbaacabdbaddaaadabcbadbbcbcdbbddbacdcccababcbaabbdaddbbcbbaabbcbacabbdacbdddacacaabbdabacbcbccbdabddccacaadcadadbdcbdabaccbbabbcacaadcbaabbcdccbbdabbbbaacbbccbdbacabccaadbacabddbdcdbcdbbaacabdbabadccbacbbacdababbbdadcccbcddddccaaabbdaaadabdccbcddabbdcccddacddcddbcadcadabddbcbdaccdbcbaacdaaacbcdcbdccbccddacdaaabacdcdabacddbcabacdbbbcbddaddbcccabaaaacbbcbdbccddcbdbccaabadaaccdacdacbdcacbdadcadaccbdadccdbaddddababcbbadaacdabdddadbbdcbddacbbabbddcacdbdcdcccacbcdbcddadccbcaccaaaaabcbccdadddcbadbbadacbaddcaabdaaddbcbbcadcbdbbadccadbcdadcacaabccbadaccabcccbddcccddbbcababdddcbbdabbdddaddcabdcbccdcacbabacbddbacbdbdcdcdbcdaaaabdcadbdbcddddddaaababdaaaddcdcbadadbbcdccabcbabbdbbdccdabcdbadbccaadbabdccacbcbaaaddbbadabbbcabdaabbcdcadacbcddadacdbdbacdddaaccbabaddcdbaaadabacbcabacbcbaaabccddcbcbbcbddbbdaaacaaabaaabcdabadcddddddccccdabadadaabadbdbbcbaabcdbcbadacabacdbbcadadbabdbbbaadccbbadcabbcbadcaaddbbccbdbaccbaacbcdacbcdcdbcbaaadbdaadacabbadbbdadcdaccbdbbccaccddcabdcaacbccdaccdaaddbdabcbccdccdccacddbdabaccbbdddbcbacaacdbadcdccabbabcdcdbddbabbbdadcaaadbdaaaaabcabcdccbbcbacadbadbcdbdcdcbbabdddbdcbdbadcddcacbabdcbdcdbccbadbcccddcdddbcbccaaaddabaacadcbaadddbacbbbdbddcabbcacdbcdaccaccbbaacdcbbaaccbcaacaacdcbcdbcbdbacababacabdbbdcacdadaadbbccbbadbdbbbcdbcaacbddcdaccddbaacccbabbaadcdbabccccbbcdbdadcaaaabdbadbacacbcccbabaaddcdacaacbddbbbbbbcbbcadbbabaccaaadccabdbdbccdabbdbbcbabbbccbbbbccbdabbdaabbaabdaababcacdcbaddbcccabbddddacdadaaaabbdaaddccdcdbababacdadddaababadaddababbaabdbbbbcdcddcdccbdbccdcdaddddcbbaaaccdacbbaabcacddbbcbacacaaccdbbddaabbdabdaaadbbabdabcdacdabdcbccdbcdbcdbacbcbcdbbacbbcdcaabaababbacdccccbbcccdccadadcacbbbabbacbcadcdaadadaaadddabdcdbbdcbaacacadbddadbccbddaacacbcacdcbadaaaccbabacbaaacdbabaaaaabbabacbcdabbdadcdadcddcddadaadcabbbbdbbcddaaddadcddbddadcadcbbcdabccaacbbbbdadcdbbdccaadcccbaacbacacdaddccaddacbccbacabaaacdacbcdabccdbddbbdaabacdddbaacbccbaaacddbbabbbccaccccdacaabbacbabaccbcdcccbadbbadadabaaadcbadbacadabdadccbdcbdaccabbbcdaaaaddadadcdcbdcccbccdcdbbcbbabcbcdbdbabdaccbbbbdbabdbabdcddbacacdbdddcdbabdddbdcbbaddcdbdabdcacbccdbdacbacdbbccbacacabdbacbaadbcadcddaccbaddbadcabdaddbaccbadadcbdbdccdccdaacbacbbacccacbddaadcabdcddcaabcdabcadddcdcacabddcbcbcccbabdbbabbbbbcbdcdcacaacbacccbaabcbbbccbdddabbcaacbbbadcddaadcdcbdcadcbcaaddcbcbabcbbaadcbccdadbbcbaadcaaabdabdbbacbabbbcaabadcdaadadddcbcadaabcbbcacbbbbabbbaabcbbddcacbbacccabaadcabbdcbddbbaabadaccbdacacbbcdabbbaccabcdcabbbcbadbbdbbddccaccdcabddbbccaabdbdcacacaccbacccccddcaabcccdbdacadacadcccabbbdbcbcaddabaddddbbcaaaaacabbbbcbdacbddbbbcccccddadcccccbbccbdccabbdbdabdbbcaabcabcbdcbdccddbbacbacbbcadbabcacbbcadbcacdbbadbdcbaaacddcaaababbcbccdacccccdaacaacabdccabcdbcadaabbaccbaadadadbaaddcccbdcdbbacdccdabababdccccbbcbacdacbbcaddaaadadcdadaacaddbddabbbcbacddbabcbabdbadcaddabbcaabbdaaccdaacbcccbcbbcccadadbbadbbdccaacaababbcadadddcddbcbcaccbabcdcbdcabadbdccbbbadabbbbdbdaadacacdddadabdcaacdbdcbacdbcddbaaadcccdcabbcbadddbcadaaabcbadddbcddcadbbccadbabbbdabaababbbababccaaadbccadbdcbcdadbddbaadadabbcbaaacaababbbdaabcadcdddccccbbadbbccadcaaccdddccdddcdcbbcdcbbddaacbdcaadddaaccdddbcddaadbacdbdbbbaabdacddacdbdabaabcdcbdcaccabbadcadaddbadbdabcbadacccdbccdadadddbaddcabcccdabbacaddaacadddddbbaccdcaaabdbadbbcccbadacbcdddacbabadbdbabcabcdcbaccdacbbcaacccddabcdbcbdbbadcbaacbccbbdaaaacaabbbbdbddbdcdddbbcdbbdcabcadcadbacbadcbdbdddcccbcacddcdabdcbaaabcdacaddbdcccddaccbacdacbadddbaabbbabdaccaccccabbbcbdaccbacaadddbcbacabdbaaacdadbacbbdacbbcabbabddcdacbabcacdbbbacdacdcadbbcaabbdadacdaccbcaabbaadbddbdcdcbacaabdcadcdabbbbcdaadcabdbbbdbbabbbaadaacbbdcdaddbdaacddadbbdddbddddbdbacddbabcdddcdcbcbaddddcbbcdcddccbcddbccbcbbbbdbaabcbaddccbbddddbcadbcbbadcbabdababbccabbaddbbdcbdccccbbdbaccdadbccddccdbaacacbaacbcdbcacdbdcabccacbababaacabcbcabbbbbdcbddadaaaaccdaadddddbcabdbdbbccdadcbbdabadcdcabdaaddbbdcdddabdabcdccadaabdcccacdbbabdcdacbddcaabcababdabcaddccccaaabcddabbccdadccbaaabcdaccbdcdaadcaacbddccbcbabcaaacdbaacddbacdcbdcbbabbddbccdbcbddcacabacbaccabdacdddacbbcbdaaabadcccdcddcacbbcaaabbdddccaccdacdaaabddbddcaacbabbcdacdcbbbddbbcabcabbaabcccbdcacdadccacaacbccbdadaaadacadacdbaabbdabcbbabddaabaddacbbbdabacbaaddcaacbaaacaaddcabcacccaaabcccdaccdcaacaaadbdccdcadcadcadcaadcdaaccbccdabaacdbbbdaaccccbdcacababaaadbcaabdbbddddbccabbacaadbaabcdbdbcbbccbaacdbbdcadbbcacdabcddccdcaaabacbadacccaddaaccbaabdaddccbdddabddccddacbcbcabcabdcbbddaccacabababcbaabcdcacadddbccddcbbddacabcdaddaaddaaaaccddaaddbcaacdadacbbbcddbacdbdaccccbaaadbcddcbbbacaccdacacbdaacacacbbdcbbcbbabcaabdadbdcddabcbdbcbdbdacaccaccddaabbdacdcbbaccbacdcacdcdddbcdddbdbcccbbddbdbdcadadccaacdbdbaddbadcadcdccadcccbbadbbbadaabccddbddbdadbddcaacbacaadbdadaccaacdabbbbcbadcbcaacaacbcdbdaadabacddabdaadacbbccaddabdbadcdbccdbcdcdbbbbbdacddbaccadcadccadccdbdaabccbaacaadbbbcdcccbdaadbdddbaadbccabccdccaadbbbcdabbbdddbddadacaddcbbabccadadccaacdcccdadbcdcbbbdacdcdbbcaaaaaaccaadcbdcbdcbdcbdddadcabbccdbcbaaaabbadcacacbddbaacdabadaaddcaadaabdcbccabcbbabbddabacdaacbabbbdbbbddccddbbddacabaccadabcbcdaadccdcbacabbbccbcbdcaabdcabcccdcabdbccccccbaccbadddbdbbbaabcdcaaaabbcaddaddbddacdacdcdbaaadbbbacbacaadacaabddccadccdddcaaccbabcaadbccaaabcabbadaaacbaaaacaabdaadbaadbbbadccddadbbdbcdccbcadadccbddabdcbdddbbdababcadcbdcabadaddbcbbaadcdaaccdadcabcaacaadadccdcdcdccdbadccabdcdabaccabcdabdbdaadbcabdcacccadadbaccbbccaaaacdacddcbcdccadbdcbbdddabacbddadaabdddbdcbacbaccaadabcacbdbccbdbcacbaaaacabbccbdadcadccabbcccbdaccadcdcbcdbddcdcdcacccccbaaddabdadccbadbaddadcdadbccccadcadaababbcadcbbbdbbdbbcccddacbdcbacdaccccbbdacdaccaaababdcdcddacccbdadcccdcbbabbbcdadcbbacacdabcdddddcbcacccbcbaaabdabaabcbaabbcddbdbbccddabadaccdcacddadddcadcbabbcaacdcddbbdbcbddbcbcccdbbdadcbdbdbccdccbbdbbccabdbbcbdadcbbabbdcababbbbaabbdbcdbabddbbddcadbabbbccbccccbddabccbbbbababbcdabcdcbdbbcaadcbcdbccccddadacdacbacadbdbbcadbcababdacbbaddcacddcddbcaaadadabdbccaabbbbadbabddccdaabddadcdcdaaadcdacbcadcdccadacaadacaccddacbadbcdcbcbadaaddcababbbaaccacdbcaddabacdcdadabbaaddbcacaccddabdabbddabaadcadcbadcdaabdbcddadbcbdadbbccbabbcbcadbdcbcbacbbbaabaabcbccabcdbabadcbcacdbccdcbacccbcccabacbcbdcaacdcbbbdddcdddbbadbadcadbbbadcbcdbcaabadbddbadaccbdaadbababcdbdaccdbabbabcbabaaaaccbcddcbcbdcdadabdabbbabcbaacbcaaacdbacaabdbaaaccbdcdbcabdaabbddccacbcdddbcddaabbbaabdbabbaccccacdbcbbbddcbaadcacaadbdcbbbccbcabdccccaaccaccaddbadacbdcdbbddabacbcdcacbbbadbadaacadbbbdcbbccdaddccccbcaddbbdbddccaddcddbbddddabdcabdabcbdcadbbbdacbbccabbcdbdcbbbcaaaddadbadddbdddddbcacacadbdcacdbdbaacddbcdadaababccdddddbbcbccdddacdbadddcaaccbddadcbddcdcbdaadbbbdaadaccadaababadaddaccccbdacbbcadbbbccbbcaccabdacccbbdabbdbbbdbadbdbcbcddbadaaaaabbbcdddaaacbbcbacddcaacddbdbbbcaaadbdacacccabdbbbbdaabbdadbdcdbaadadadbcbabcabbbadadbcdbcbaabadbaccaadababddaaadddcccaabbacdcbcbbbabbdbdcaccddabaddbcaaddbdbdcbabbadccdaddccaadacacabbaadaabddadbaadaaacababcbdccaacdddbdcadbacadccccccabccccabddbaddadbbadadaaccadbadadcddbaadbadbccdbdcabccbaacabbcbdcaabacccabdcababdbababbaadbddccdabbcbcdaddacbdbcbaddabacccbdcadbbcccdbcddaccadbdccaccaadacddaddbadbbbdadddddcccadbaaabdcbcbcaababbabcadddcbdabdacadbbacabbcbccdabbcbaabcaacdacdbcbcacbcbdddaccdabddbbbdbcdcbdbcacacabdbdadddabcdaaacccbbbccbdbccdcaacabacbcdcbbbcdaaabbabbbaaccdabccdcbcbcdbbabadacadbcabbcdddbacdbbccbcacbbcddccdcbbacdddccbcacabacaaacdaacacdcaabcabbadbadccdccbcdbddcaabaabbadabbaabcddbabacbabddaadcadabadccbadcadccadbccbadbdbcbbccdabaaccabcbbdbdaadabbdbcaacbbdadbbdabacbddacbbbbcabbbadadccbdcbdbddcbdabadabdcaacabbabdacbbdccddbdcddddddccbcbbcdbdcdbabbdbadbdddbdacdcdcdccaabddcdbbddbcdcaddcaabdbcbcbaaadbddbbbdbbabccdacbddadddaaabccbbdbddbacccccdbbbbbdcacdddcdbdddbcdcdcbdcdccbdbcccaabdabbdadbccdbdcbdabaabbbbbccadbddcbcccbddbaaabcbacccadcdbccabbaaaddaccdbbbbbbbdbcbcdbabcdccbdbadcdbacddadcbddcadcaabcdbcdcbaadbaaaacaabdcdbbccacbabdccadddcdabccaccaddbdbacbbdccbddbccddbbadaddaddacaacddbcbcbdadababaaadabacdbdbaaccadcbbbddacbbdaaccbbdacccbabdbacaacbdcdcbabbcbbbdbdcbbcdbdcddbdabacdbdaddcdbbbbcabbbadadddbdcbbdadaacdbbdabaabcacacbabccbccbacacaadbbdbccbaaacaaadcadcdbbabdabbdcdcbdcbcaadabcabccadbcdbaacbacdcaadcaaaaddaabdcadcdaaaaadbabbcbdcabacdbbddabdadcadbcbbcdbbdddccaadbacacaccbbdcdacbbdcdbabdbbadbacdabdcddbaadcbcbbdbbcaccdbccaaaadbdacdaaacabbdbadbbcbcddcdddacababbdccbcbdcbcbaacbcacabdccdbccadcabacacacaabadbdbbdddadaabaccbcbcaadcdadccacbdadadbbacbadcacbdbacccadcadbaadabbbbbdadbcdcbdadbcaabbacadaabdaadaaaccdbdacbdaabdbbdcdbbdaaadacacdcdabbabcacbbcdbcaacadcabbabbcdcdcdadbccddbabcddbcaadcadbccacccdbbadaccddaaadacbbbddacdddcdccdcdbbdddbaddabcdcbdddaadddbaaabaccbcbccbdcccdbdcbbbddbddaadccacbaaadccbacdcbbabbbcbcddccadcbabbdccadcacdbdaddaddabaccbddcbaacccdaababbadabcdcddaadddcbacbdbcdcaddabbcabcdabacdadacdbadcaddaccaabdcdcdaaddaddccdacaacdcaddbbadabadaaabcdbddbcbdaabddbbacbadcddaaccacdcbcabddbccbddccabccdcdcbbcdbddbcddcabdacdbccacbadbbbbdbbbaccabbdccbadcaaacadabadbbddcdddcabbccbaacadbbdabdababaadacdbbcddbdaaccbdbaaaabaadddabacdabdaaacbdbcbcdcbcadacdcddadbcacccdbbccaccdbaadcbbdcdddbdcbaabbabdbdccacdcdabcccdcdcaccbbdbdcbadcbcdcaddacdbccddcccbbccdadacbbddcacdadbcbdccacacbcdcccaadabaabaaabcdbddbbaabbbacadccbcbadccacbbdabdbbadcbabcabdbcabdaacccabbdbabcacccdcaabcbcdbcbbaadbcabccdbcababbddacacbbcbcacdcababbdcdcaabbcbbbddcdabbbcccdabacabdcbadabcacabbaccbcaacbbadcdcdabdaaadbabadabcacdaaabaccbbdcaaddadcbabaacadadcadaaaabbdadbaadbccbcbcbbbcadddcdbbddacdacaaabaadcaccdbbdbbbcabccacddbcaccdbbdbcbbcabaaccbabbabaabaabbadcadbbabaacdbaccddabbddbdadbcadcdaddcbbbaadcbdaddbcbdbccbbaaabdbcdacbbbbccdcdcddbdcdddddadddaddddcbcaaababdbaabcadadcbcbaadbccdcddcdcdacbbbbadddcdbccabbcadaddddbddcaddcddcdccdddacbdbddcacabdcacdbcaddcbaacbdaaacbbadacabbdaaacddbdaaadadbccbbaadaaccbddbabbdadcdabcdcaabcadddcdabaabaddaacbacddbcbdddbddcbbdcdbdcadacdcaddaacaacdaaddcaaccaaccbaabcadaadbddbbbdcddacdcdaddadadcdbdcbbbdbabcddcdcbbbdcbccaabaababacadddccbbdbdbbdadcacdcbaadcdbdaaadcadbaaddddcbbcccbadbdaccdcdacdddcbcccbdbdabbddcaaaacacdddccbddaccdadadcccadabdbbbbddbacdaacbddccccbcccddabbcbbcbaacdcdaaaccadaadacddabaccabbabbabbcccccbaaaaabddaadddbccbabadcaaacbdbdcddaabaabacaccbbbbcabdcbbabcadacdcbabbbdddddbdccccdbbcdadaaacaabbbdacddaabcadcbbddcddddbbdddbcddbbcdaadadbacbdcbbbdabdcacbbadbdcbcdbbbbcabdaacbabbdcdcdabaaddaaacbcadbdbbdcdcdccbdaabcccdbadcbdbddbddaaadabccaabdbcaaadaabdccaddcdccdabbabccbbcadadcdbddbddadabadcbdccddbddbacadaaccdbdabcaaddddbadcabaabbcbdcbcbaabcbddccdddcddddbccacaabcbdbacdbbddbadbdcadadacbdcbdabccdbdababbabdcccaacccdbbdcacdcdcbdbcbcccabdaadbdcdadadabaadaaccadacdadbdbabcbcdcdcbacdbabbaacbadddadcabaccdcdadabccccaacbcacdbcccbdacddcbccccaadbdbbcabdbddabdbddcccdaddbdcacccbadcdcbdadcbdbacbdcdccaccabdaabbcdbbcbbaadccbbdcdbdccbbdddbcbcdaacbdabcdcbdcdddaddcbbcaaddbcdacddaddbaccdbccccbbadbcbdaaaddccdacaccadcbbaccbddccbdcadbdcbbdcadcdddcaccbbdccddcccdbbccbadaddcbccdadadbadaadacaaccbacbbbdadaadddccbcbdddbaccadacaddadacacaadbcadddaabcdcccdbbdccccbaababdaddabbaadcabddabdabbbbbdcabcdcabaacabbaccaabbaaacbdcacddbcbabbcdcadcabcdcacacaaddacbbaabcbaddccdbacabbdabbaacbbbdcdcddbcbccadbdaacbadbbcadadaddcccdcaadbdbcdacbcdcdccadbaddbcaccaaddacdcdcadadbbaddbdccbdaddddadbaadadbdcbcbacdcbadbbddddddacabccaccbddaabccbcdacbcabbbcadaadcdccbcbcbcbdbadcaccbdbbcacbcacbadacbdcdcdccbdbaadbddabdabaacbdcbdbccdadcbaaacdcacdacdabbcbdacbadcacdbcdcccbccbddcaabacbbbaaacadbabadccbbabadadacbccdaddcbaddcacccdcdcdbcbbabccccbdaddcadaaacbbbadabaadaabccddcaaccbcccadabbbcbdbcbcddcdabbdcaddbaabacdddacbdcddaaaababcabddabbcbabdccbbbdbdddacdcaadbbabddcadcbdbcbbcbcbbdcdbddadabddaccccbbacdaddbdbbaadbccddcbaadadcbbdbbadbbcdadabcbcbccaababdddaabddddaadbccdcbbccaacbcbbbaadcbadddcaabcddbbccbacbcdbabdbccddcaabdbdbcbccdbaaadadcbdcdaabdbbccdddadbabdbbdcddcddabdaaccbcbdcabccacaadddcaaccaccccabbcdbcdbcdbcbcaccaacbcdbbcbbbccabaadccabdcddbbabdddbaaaacdbadaabdcbcadbbbabccadabacaaaccdccbadbbbccbdcdbcacbdddddddccbddadbbdcdbccadbcbabacccbaadbcabacdabaabddacacdbdcddabcabcbcbabbbdccbaddcbbccbbbcbbdbbbcbaaccaaccddabbbbaadabcabdcdcaaacdadcdcaccbbdcdbacdcbcbdcacdddbaabcabcbdbccdcdbacbbaaddbdddabacaadabcacbabcbdcaaacadcddbccbddbaabccdaccddbdcdddcacaadbcacbbaacccbbbcccdbdbadbcacbadbdbbdddccacdabcbacaabdbabbabdbbacbdaaabdcbadcdbabbdaabddddabdbbbccbdcdabdbbbabbaabcdacbbcabaccccaadbddbbaabdcdabcbbabacbcabdbadacdcddcbcbcdccbdcbaaddabbdcbdacadbcbcadbbadaabbbcbbabdcbacddadcbdbbbbccbbcdbbdddadddaddcdbdaacbbddacbbcdadadcabcdddccadbcbdabdadddcdadccaabbaddbcbbddbdacabcddabbcbccdadacacaabacbaaccccaacdbabaabaddbaaadbdbdadcbbbadcabaaddcddbcdbdccdabadcdabaaabbaddcacddabbadaadbdbdcbaccbababadcdadbddadabcaaccdbdaaccadaabbbdcccbaaacddddabaacddabadbbbdacbddbadcddcbcacabcbadaadbcbdbcdbaaddacadcacdabbaccbbaaccdbabdcabacdcbdbcbbbcdacbacadcaacdccbdcabbcdaababdbdababbbbccadcbcdbcdcadcbdccabbdccddbdbdaddadbcbbdcbabcddbcbccdbadbcbacddaaccddddbbbdddbddaddbaddddddabdbcbcbbabbdabccadbcbaadbabbbadcdadacbccbccdcaccbbbbbdcadddbdadadcaaccbcdbddbabadcbbcdabcaaccaaaccdacbbbddbdbabbdccdbcadbbbdbbbbbcaddccdbdabddcdaaaaaabdcabdccadcabccddaadabddbcdcbdcbcdaaaaccdacbccbcdbdbcabdadcbcacbccaacdddcbabbabacadadcddabdacaabdcbdacdccbcabacabddbdadccaaddbdddcccaacaaadcdbabdcacdbabdcdabdccbddbbcdbaadbdaccacdadbdbaccacbcaacadbcadcbadbacccdcaaaadddbbcabdabcdbdcccdbbcbbdbbbbddcaadcdbccdaddddcadababadbdcbdadddbacdbcdabaadacdbacbcdbabbcdbadddadbcbddbcdaddbbcabbbabdbddbbcdcbadbbccbccaacaabdaaddccabbacbaabcccdddacccbccbbbcccddbbabdbdcdbacdababdacbcbaddcddbcbccbaaacdadbbbccbcbbcbdabdcdcabddcaacabbdccccabcaccacccaacdabdcbcddacdadcdacbabbbcbcbbbddcbbdabddbdcbadbacbcbcdbddbdcabaaabcbdcdbddddacbcbbbddbdccbbbbdcaddacccccbacdadabcbbcdcbacbcbddacbcdbabaaccbbbdbabddcadddaacbbabbcccbbcbdacadbcdacccbddbbcabcddcadccaccbbbcacbaddddbcdbacbcacacadabcddbddadbcbaccdaaddddcdbadccabbdacdcaacdcabdccaadbbbccddcaabdabbaddaddcbbaaaddbbbcdabaaadbcdadadabccdbcbaddaadcdccadbbbbadaccbacacdaabcdabcacbbcdccacbacaddcbadbccbbdbdaacacbdacccccbbbbdacccdbccbcbddbbcabcbadadbcbbbccbbbbccaaacacadcbbccdccbbddbdcdcadbdddddcccbadbacacbaaacddbacbbcccadddcdbbdccbcbdacbdcddddabbacccbdbbbaddcacddacabbbdbdbdddccaddaaddbddaababcddbcaaacdcaacadbbcbacbdabdacbbcccaacaacddcabbddacccbdacbabcbbbcdddcbdaadaaccbddcdccbacdbabcccdaccacdddddcbacddaaabdaaabcdacbdcbbbbabdacbcacdbdbbdcddadddadcdcccccbccacccbbcbabacabcabbadcabbcdacaabacadbcdaabdddbdbaddbacbcadcddcadbcdbbbdbbdcccddadbacbcdcdbacbbbbbdbbcddacbcddccbdbddcdcabadcdccdccacdccdbbcbdaabbdcaccabbdabbccaacccdbabcbdacccdcbdcdbccddbbcbacabddcccbaddccadcbccddcabbaadcdcacbdaddabcbbdccddabbbaacaabdacbbbdabbcbdccdbdabaadaabdbbbbaddaadcdaccbdacacbcbadacbaabbcdccccbdcdbabacaaddcbcdddbbdddcddddaaccbbbdddcaabbaddccbcccadacdbcadacdaadcadcacdcbcadbddcaddaddaadddddcabdccdcdcddccbbcdccadcbacbcbdabdcdbcbdbccaabaddbaaacdddcaaadaabbacdcdbabbdcadaaacdcdbdaabcabcddaadccabbaaaddcbbbbdbdcabdbddacbddabdaaaaacddaaabbcabaababcbaabbcbabcccbdcadbaadcdcdccbcbbdacbccaacacddcaaccbbcacdbdcbbccdbaacbacdabadaccccadbcdddacbdbabbaacbacddacbcdabbabadcddadacabdabaccdadbcccbddadacdbacbbddcaadbdbdabbcdddaacccddbbbccdcaccdccddaadbaadcbbbdaccbdabdadcbabdaddbdaabddddccaaddabdadddbdabcccdadabadbbccddacabbddcdcdabbdcddbcbabdbdacccbbbbddccadbbacaccbbbcadaadcdcccdcabddbacadacbbddcbdabcdddbaabcdaadabddaabadabbdcbdccabbbdbbdccbbacdaacbddcbbacbcaccacadbdacbabdbacacddacaddcaaacbdaaabdcbdcbcbabdaacdcdccbcacdcadcacddcdcaadaadddddbadbcbcbbdcbabacaacbdaabbcacbddbdabbbdcdaccbbaccdccabdcbdcabbacabadddbdcccbbdadabdabcabaddcbbddbddbcbdcddbbbaacddcbabadbddbabdbdabbbcbcadbdddddddcadcbccacddbabccbdcaddddcdbcabdaabcccdaabdddadcdcdbbaccbadbbdbadadcabcbcbabbdadaaddcabaaddcbbcbbabcbdadcadacaacdacbabddbaccccdddcacdabccaccabbccaacaabbaaaadcdbcccdacaabbccdbbabdaabbccddccbbddabbadaadcdaacabdaddddbdaacbcababacbdcdbaaaaccdbaabaaccccbddbbdbcddbaaadbabddcabcacabbbdabdccaacaacbacbbcbabbdbcdddabaabbabccaaabacbcbabadaaddabbbdcbccadcdcbacaaccdbbccdaddacbbdaadaabacdbbdadbcbcdbbbcacbbddaccddddbbabaccbdcabcbaabacdbbddaacacacccbbacdcaabaadcddbdcabaabbdcddccdcddbacdcacaabdccbbbdabbcabdadcdabdabcddbdaadacadccbdcdaccaadcdcacbddcbbacadabaddcbadadabaddcdaaccadbdddbdcddbbddbbcccdaaadcadddacacbcbdddccacdbbdacdadcdbbcbacbcccddabdadabccdcaddbccbdcdbdcabadcacabbabbdaccccccaaddbccacabdbbdcaabdbaabadcccbabbddbcdbaabddcddbacbdbacdbdccdcdcacbccbbcccbcdcaaccdaaaabdbacccbcbdcbdbbccbddcbbbdcadbaabbcaacdabcdccdbbaaddadccaacdabcdaacaccaabcaccccdbccbdabdadddcaccadcdbdcdbbbadbaaaacccaaccbbcacdbacaddcadcaaadbbbaabdcdbbcdddabcdccbadaadccbccddaabdbddaabdcabcccdcdacdcdaaddadbcabdadbbddcaaababbabdbddcbaddacbbdbdcadcaaadacabcddadaccbcacadaacdcabdcdcadddcdbbbbdbbddabadbdcaaaaaabdcddcaaccdddcacabdbadbbbddcbbadcaadcddcabbbbbaabdcaaddbabbbaadadcbdcccbdcdabdbccadacdddbbcaddcddbbcaabdbddcddbdcbccbdcccdddabcdacbababccddbbaddcbdaddcbbcabacacdccbbababdbbbcacddaddaabbaddbbcdaddcaabbacdcdcbbdcccacdcaacbdcbccaadabcbdaddacbddcdcddbcdbcbabdbcacbdbbcdacddcaddbbccbcdacbacdddbbaaccddabbcdbdcbcbdbccdcddaadbdbbcaccaadddadbaddbaabbbaaccdbcbccdbccabdbcddbccddbcaabbbaadaaadbbcaadddbadbdabacbccaccddddabdcdcbbcbbcbdbbbdbdbbbbdaadbabbcbadadddbdbbcabbabcacddcdcadccabccccccbbacdbaadbacabadcdadccdabaadabccabacdcbddcabadaabdddaabcabacbaabcacdaadbdbcaddaaacaccabacacbdbdaababadacbbacbcbcdadcaacdcbbbadcbcdcbcdbcbddbbacacdacbacdacddbcdddbdaaabaabbacadabbbbcbddbdcdcacccaadcccdbdaaacacdbdcddadccdacdddbddadacdccdabbbcadbabdbcdadbcbbabcddaadbaddaadaadbccdbdaddbbadddcdbccababbbcacdbdcbccadbcadabcbbdababaaaccbadacdccdaababdadacbadccdadadaddbbbbcddbbbbccbdabbadadbbcdcacabadaddbdbbbabbdbbbdbadbddacbbdbacbbaadbaaaddabbdcababddadaddabdbacdcdbdcbadbcbbacccbcbccdcdbabcdbabbdbcbdababccbadddbbcdaacadaddaadccaacabacbdadbadaddcbddcdababddcaabdaaddcdddadbcadaddbbbdbbcdbddddbabcddacacdaaadcabbbdcbadbbabaccbadbaaabdbaaaadabdbaaabddadaaacdbdabbbbdcbadbdbbdbdcbbaaaccbbbcbcbabcaaccbbcabbdbaabdcdadccdcbbcdbadbdaababcddcbaacdabadabcbbdbbddbaaacddccbbbbaccddbcaaccadbbccbabaaaccdcabbcbdacbccbdbabddbdbcacaaccdcddddacaabbcbdcdbddbbabddcbcaacabbbccabbbabbdcdddbdcbccdcbdccadbdcacbbaadbbacbddbcabccbbcbbadddbbddaddbaddaaddcddacbdadaaaaaddcaaadbaacccccddacbadbaadbddabacbaaccbbbcbbaacaabbcbadccbcbdcbbcddccbcbbbaacccdaacdabdcdbaccaaaddbaddcaccddcbbbbadaccadcadcadbcbcdcdcbbdcbccbabccadacdbdcadabbcbcddcaddacabbdbbdcaddbddaaddaddabdcdcbabacddabdcbccdcabaaccbccbbabadcabbbdbaaddadcabccddcccbadbcaabadaabddaadccdbdccbdbdbbdaacbdadbccbabdcaaddacccadcdcaddddccaaaacbadacabdddccdbdcdbabddbadcddcbbabdaaacdcbadaaacbdacacbdcacaccbbdcbcaddcbdabcddbbdccdacadddbaaabcdcdbcbdabbaccdadcdadacdcadabcbcbdaabacabbdddbbadddbbaabcbaaacbbdcadbadbbbbbdbdcaabcbbcdbbacdabadcadcaaaaccadccaaaccccacccdadaccdbdcbaadaaccbbcbabacabccadabcbdbdadcdbbbabbbadacbcadbadddcddbbdcdbaddccbdcdcbdabbabcaaaccbdbcaaabdbaaddbbddcabcbccbbbababdbbaacaabcbbbacbcbddbbcddcdccbadddcadacdbaaabdccddbdcddaaacddbccbcdcabddccbccadbdbbccbabddddbabccacdbaabdacadbdaccbdddacddbcadcdcabcbddbaddadcdbbacdcabccddcbbbbddaccbddcabcccbaadcacaadbbdbbbbaabacbbcdcdbaccadacdaddbbcdacbbabdaabcbcabaadaadcacabaabcccadabbdddcddcbcccababaddcacaaadbcddcbdccdaabdcbacabdcdbbcdccbbbdbdbdcccbdbddccdaaaddabcdcdccacadccdacdbccadaaccdbdcddbdbccaaaabbddabdccddacabcdccddaadcddcbbbabacabbbdddcdcdadabbddaaccbddbacbabaddbdcacbcccaddcccdccddadadcccabcbdadacdbdcdbbadcdcbadbdcaaabacbddbcdcbcadbaabccbbddcddbbaabdbadbbbcdddcbbadcccbbabdcdcccdcabbccbbacddcacabccaadaaabcddbccbdcdbcbadcaccdbdbcbbccdbbbcdbbabdccabacdacacacbadaccbcaabdaccdbdbccccddacdcdadbdabcdcbddaadddabcadabdaadadacabaabaabdabbbbaaccadddbbbbcadcdbbdadbddbccdaadbadbabbddadcbbadabcaddacbbabbbdcaabaabcaccabaaaccbababaddbbcddaacaccbcbccddacddcbacadacbbacabdaaadbccdaabdbdcbddcacbdaabacbcbbadaaaacccbdacdcaddcaaacdaaabaccbcabddcbcadaacdbcddcabadcddccbbcddbdcacdcdadbcbacbcdcaacbbcdaabbbcdbbdaadbcdbbabadbbbbaaacbabadbccdbbddbcbdbcccacbbdcbcdaaacdcddacbacbaaabcccdadbdbdbbddbcbcbaddbbabcbaaccbaaacabcddcaacbaaddcbccbbdbcdaacccbcdcdaaccbbacdbdacbaaaadccbdccaadaabdcddbcbcadadadaabaaabdaaccbbdbdbbbadbcddbbbbdbabadbdbddcccccddcadcdacbcdaaabaabdcbbcaabcabdbdbbdbbbdbdbdbadadaddabbabcbdddcdbabcdbaabcabacaadaaadbababcabcaacdadddcbdaccdaddddabbbcaacacbbdddabadbaadcacbabcbaadcccbabcdcaadbdbbcbcdaacaccdbaacbbbbbbbbdacacabbcaddcdcabbdbcbdaacdbcadbbcbbdbaccabdbadbddadacbdadbaabcdbdbccccacabbbbdccddccdcbbbddbcccadcdabadbbcbddddcdcabbaaccabdcdaadabacbbddbadcadbabddbbcccddcdbbcdaaddadadbdddaaacdbcdcbaddbacbbdbcdcbcdbccbcabaadacdacabbbbdddddbdbabdcacabacbcdccabdacaabaccabdbadbbcbccdabcaabbcbbdddbdadcabcdcdcdbdbbaaaadcbdabccdadbaaadccbadbbaaccdabbabbadbaabcdddabcacdcadbccabdadadcddbacbccccccdcbcbaddcbaaaadbcacdbccbddaddacddccabcacdcbbdacbbaccaddbcbabdbadbadadddbdbcbaccbbababaacabcaacccadcaddbcccadddddadccbdbbcdbdbddabcbadcddbccddbdbdcbbdcccaadacddacbdacbaabcbbbcbbabbcabaddbadaaccacbadbcbbabbacbbaadcbbbbababcbdcbcdbaadcbdbdabdddddccadaccddcbdacacadddcbdbbcbbacdbddbcbcbcdbaabadbcaacabbdbdbaccadaacbbdddcdcabcdacbbdcbcccdbaaaaadbabbbcdccbacaddacdcaadadddbdcacbdadcbdacdaacbbadbdcbcdbaccdccbbbcdaacbbbccbdcabbddacacaccaaddbdbdbacdabddbadcdcacdadbdddababddcbabbadbcadadbcddabccbbdcdabacaacbcccbccdbbcaadcbccbbccdcbacccdbaccacadabdcdbcbbbddccbbadababcacbcdcaadabdcccadccadbdbccbbacdbacadcdbdaccdbbcdcbaacdadddbdcdcabbcdaabadccdabaadadcdcdacbacabaabbadaddbbbdadacdacddcabcadbacccadbcddbdcdbcdaaccbcdbccaacdcacbdddcbddabadabcccaccddccbadbbaabcbdabcabbbcdacacddcadacbcbadabadbdadabddacbcabbabacdccabcbbabdaacbadcdaabadaacaaadbbabcddbdbaadddbcaacbabbaddabdbabaaababababbabdbddadaacbcbcbcccbdddcbdacabbcdbcccbdbbcbcacdadccbddccacacddcbdcaddbccdbbabadbdabccdcbbdbcbdbdbaacccdbaddaaacbcacadcaaddcaccdddbccadabcacbdbacbccbbadbadaccaabcaccdccdaabddacaddaddbacdacdbaadbabadabdbbadacdbbcdbacabbddcdbdccbbdbdbcaccdbcbccbcbbdacdcddbbdcccdbaddbdcddcdaaabbddccacddaadabdaabdaacacccccddadcccbdbcbacbadbdbcddadbadbbaccbdbddddacbaaacabdcabddadabbcdcabaaadaacbddabdbbbdcccbbbcabcbdbbbacbaaadcccbabcacddabaadbddadcbbaacbbcbbbbddbdbcaacbbdcbbacddbabadcdabdcddcacabdabcabacbabdcddadabbdbacadadbaadbacadcdcdcaabcccdadcdddacbdbbbbabadaabdaddacacccacabbcabbaabccbbbabacdbaccadabddadaaddacddadcdcddcbbbacacccdccadcccabdcdabdddcacabccacbbdcadcddbcbcbccacddcbdbdacbbbcbacdbccdabaddcacacdcdcddadabbcddbdaadadcdadcaabdaddacbbddacbbaddbdbdadcacdabcddbabdccdddccdbcdaaaccbcacdcdcaccacaacdabbacabdabdcdabaabdacabbbbdbdaddaddacdbddaddcabacbdcddcaccdcccccddcdbdbbabbbaabbdcdbabaaaccbaacaaadbdaaacacdbbaabcabadddcccbbadcddbaaccdddccacddabbdcbbddcabbdcbdcaaacabadcccaabaacdcbdacaddcdbccddbcabdddddddddadbacbbccdaaddcdbdbdcbaaacbaacdcaabcccdcddacdbaadabcccadbdbbabcdccdcdddbadbcacbcabccbaacdcbcbacaaabdbdcadccabbbaccdadbdcbacadccadcaddcaabdbccabbcaadadccccdcccdbcbbddaadcbccdccccaccadbabacabdcaabddadaabababccbaadcdcbaadbbaaaaacbadbbcdaaccadcdcabaccbadcbbadcccabaacdbcaaaaddcdacacbbcbbccdacbabdccccbaddcdddbdbdcabdccbcdababbabdbaacdaddaddbbbaaabbababccdabbcadabbacabadbdadbaaadcccccdaddaaccddcdbdccddbbbbbdbccbaaddbbdcbdbcddddbadcdcbdbbcccdddbbdcddbaabdbcababbdcabbcddccdbadbbddbbbccdccbbaddabbcbbacaabcbaaaddccdcaabaddcacacdcadbcdbddddcaacadddbaabadcdacaacaaabbbdbdabdbbdcadbdcbcacabbddbcabbdcbccaabbbaccadabbdaacdbdbacaddbabaccacaacacdddbddbbccbbaabaaddbaddddcbadacdddbdbcbcadbdabadcbcabdcacacaadacddadbcdadabdccccdaacbdbdcaacbdccaccbabccbcbbdabbacdccddcccbbcaddddbbddabadcabaacadadcaccbaaddcbbbdcaddbdaadbddddbbaacbbbccddcbdddbbdaaadbbbbddaaaaadbccdacdcabcdbdaadbaabbbbdcdbdadbccbaacaaadccdbbbaaaadbdbbaadbbcdddbbcdcabbcbdbddbbddbccbabdabbbcdcaabcbcdabbcbbdadacbdbdbcdccdcbabbcabaccbabcbcaddbcccbccbaabbaacbdcdacbdadcadbbdcbbbabbdabccbaaaccaaabbdbdcaaabcbcdccbadacdbcdacbbdbcbbbdadcabacdcbabbdcddababcdadacccbababcaaaabdbcccbabbcaccacccccbadbccccdbccbbbacddbbaccdaabdbbabbadadcbacbbdcbdbacccdccaddbadacccadcacccacbabcdabbdccdcadbbaabdbdbbccdcdbadacbdccbbddadbcbdabcccbddbdcbaddaabcadbdcddbbddaadaabadabcdbbadccdacbaadabcaccdacababcbcacddcbcaccaddbbcddbabcdbcbdbbadcadcddccdaacaaaacccbbadccdbcdbbbbcbbbdabcbbaadacccacbcaccdbcdddbdaccadddacbbcbaccabcbabadbaccacadcbdbcadcadcddaadabdabccacbcdbdcddabdaccbbbdddaccaadcccaacdccddaacbdcccacabcabdbcdcccbdccaddabbdbaddcbadadbbdaacdbdcbcaccdadadbbccabcabcbdbccacdccdbbcccbadacabdddcbcdacabccaddbbcddcabdbdcaadbabddacbdbbbacddaaabcdcadabccbbbdbcdcbcdcabcadcabadcaaabcdbcdcadddabdbcbdcbcbbcbdaaaddbbbcddbbbdacbabbdcbbabddbadbaccbbcddcabdababdacbcdbcaccdddadbbacbbdbbcdddadcdcbbabadadbdaaaccadbccbbbdbbcccdccdcaccaabbbdbcabbdaaabbdcbcbbdabbaddbdcdcaadaccbbcbaccdcddadbbbaabaadbcabadcbaadabdcdcacdccbbcddcbabdddccddbbbdbcabdabacdddbbaacbbddcbbcbcdcbcbdbaacccaabdddcbaacdcaaabdccaadadddbbbadbaabbcabcdaccdcabcabcadadbdaddaadaacbdaddadbaadbcbccddbcabdacabbcbdabcdddbcbcacbcacccbadccdcacccbddcbdcddbbcaddcccdacdbacaacbaaaacdddbddddabbbabcbdcaadbbbbbbacdbbcbdbabaaadbbbabddcbaddbcbcbabadbabcbccbabdacabcdbcbbabccdadadabccbdcadcddbabaabbcccabadababbcbccbdcaaaabccdacccbcdaabbdbcacbbbcbcbcabcadddbbaccacccdddacabbdadbbdcadcddccddbbaaacbdbabbcaacabaabdcccdbaadcbcdbdbacddbdadcadbccdaaabadddadabadcdccbcadbccadbaccbabdcacaadcbcccddabdbdbbdcdccbabdcabddbccbbdccbbadcddabddcabadadbdbaccadacbddcdacbbdbacadbbbddddadbcbdddcbabacadabacacaadbdddabccbaadcbcdbcacadcbccdabdcdcaabadbdbdaccddaaaacbdddddaadbbabacbbbcbccbbcacacacdadcacbcacbdbcdadabdacbdcbdbccaadacdadbadddaddbbbcdabbcbabcaaadcaadcbbacddbcdccabaadbabbadcabdcaddaabbdabdcddcdbddddabbacddcdbbcaadaacabdbadabbdbccbbabcccddcbcccbabaadacacbaddbcaadcbadcaaddcdcabccacdccabcdcccacbdcadbcabbcaabbbdaddcbdddbbcbbdababaccdccccdabddddcbabbcbbbdabcacddbdccddcccdbcddddaddbbdcddddaaccbcabddcbdcbbbadbcadbacddadcbccadcdcccadcbddcdabccadabdadbcadbdaadaccadcbccbbdadbccadddccbacaabcdbdaabcbabcadadcabbaaabbacbcbddccbdbdcaadcccbccbbcccbbbbddadbcdacaacdbdbabcdcdabbcabccbbbddccdbbcabccbdacacbdbbbcddcbddbdaacbabdbdccbccabbaabaabdacddccdaddcdadadcdcbacaadaabaacacccadadcbdcadaaccccdddbaadbbadacbccbcbcdbadadadddccbbbdbbccbcbacdcdbbcaccdddbaacabdaacdabdddbdddabbcacdcaddaababacdcbcbdbcddcaaddcaacdcaccadcadcdabaccdccadaddbcabccddaddaaabcacacaabddbbabaabbbdbdaabccaadabbcdcadaabbabadabaccaabdaadbabdbadcbcabacccbbbcccdabdbdcaccdcbbbabacdcddadadbdbdbbddbcdaddbacbaacdbdacaacbaabadaaacbadcaddbbdddbbddacdddcccacaaababbaddbabbbbdbbddbabaaabbdadcabaabdddbcbcccaadcbdbdcbbcddbbccddadbcaadadaddcdbcbbdaddaabbbccdccdacdabdbbaacddcddbbcccddbbdaddccbddcabcbbcabbdaccadbccbdacbdcccdbabcadbbbbdddabbbacdbacdabbbdddbadaaddbabcaabcdabcbdddaabbcaaaacdadadacaacabbcccbacacbccacdbbdbcbbabacbddcaaddcdbaacdbaddaaadbdaacabcddddddcacccaccabdadabadbddabaacaacbbbbadbdadbacacaccccccdbdaacbcbbdbbacadaaadbccbbbccccccaaaacacdddcdaaadddddcbcbbdaabbcddabbcacacaaababcdcaaababaccabdbabbccbadccaadbcacacadcbdadbbacdcaadabbbbacadcdadbaaadcccbccaacbaccdaaccdddbcddbdabbddbbddbbbccccaadcbbcbcbbabcacaaccdcdbacddaaacabdaccbbabbadbdbdbaaacccdadcdbaadbcdddcbdcadcccabbbbcdbdcccdadcabaccabbbdcbdaacdacaadaacaaddbcadbbdaddbcbdbbabcbccacccbddbdaadbabacaaaaaacddbbdccabacbcacbccdadbaddbddbaaadacbccbbadbdbcacccbbbcbabcccaaccacbdddcacacabaaaccdcccdbacccdabbdcacdaadadbaccbadbbccaccdcaabadaaacadddddaddaccdddaabccacddcacadcbaccdcaaacacaababbdbdbbcaaacbbabcdddcddccaddadcaacbaadbaaabdbacaabacabcdabaaaddddbbbbbaccbddbbbcbbcdcbdddcbbcbddcacbabcdaadbabbcdbdccdcaddabbdabddcddbacddbdbddccbdbdbdcbdcdbcacaadccddcbaabcdccbbcbdbbbaddcbabaabbbacbacccacdccaabccbcadaacbcdaddccbccbddbdabdbcdcccbcbacacbbdabbbddcbccdbddddbadacabcbbabbaaaaddccaccccdbdbacdcbbdbdccadcccdbdcabbaaaabaacbbdcadcdbaabddbbcccdacdaadaaccdccbbcdabccbdbaabdabbcddbcadcdbccdddadddcccbdbaadbbcddbccaccbabddcbcaabdcdaaccbdcdbacccddddcbbbcabcaabdabbbbadcacacbdaaacdabddcacdbaaddacacdddcdccbcaddbcddcbdcdbcaababcbdcbcbabadacaaccbcbddcccbcabaaabcbdbdaaacaabaaaadabbcbdcaacbbbbaabbcaaddabaabdcddccdcdbcdbaccdbccbcbbccbcaaadcdcbdaaaacdbbbdbdabbadddcddcbcdbcdcacbabdcbadabdacaadcbbcacadcbadacddbaabcaadacbaaabccdbcbacbbabadbbddbdbaaadaaabaccddccbbcdbdacdccdadcccbcdbcbcbbcdccbdcacbdcccdcaddccddbadbbabbcacabadcdabbacdabaacbbbabaaadbcccdccaadbccbcadbaabadbcaddbacbabdcccbbdadbdbbadabacabcccddcbabcdccaadbbbdaabcbabdbcacdaabdaabbdbbcabcababaccbdcdadbdabacbabacbbacdbaacdbbdccadcdaddcbabdacbabdababacbbcabbacbcdbabbbaddbccdaadabcbcbbbdbadaadacdcabbadcdaacddddcaadbcbcbbadbbdbaccdbccbccdaddcbbbadadbdbdcdcdbccddadbbaccbcdcbbdbadacbabaabcddaabccabbccdacccaaadacccaaacdcbadaddbccbaabdccbcbbbdacabadbacadcabdaaddbcbabadaddddaccbddbccadcacadbbcaabbcdacaabdccaddcddbbbddddddbdbddbabcdaacdbcdccaabdcacdadccddabdbbcaccbccdbdcdcaccbaaabbacaacaaadbabccddbcbdabdcbbdccccbdbbdcdaccccdddabaacabcababaddaadddbabbdbcdbbbbdadcbadcacdbbdacbdcdccaabcaadbdbabdaabbddbadcdddbbcddbcbcdacccadaccdbabcdbcdbaadacaadcabaddababaadcddcacabbcbdbbbacaacaccbaadccdcacadbbddccbabcbbadadbaadbcbcccdbccbcccdadbcbdcadbaaccccabdcbdbaabdcacacdcdccadaabbcbaacaadbdbcacdbacccccdaabcbbbcadacaddabdbbccdbdbaccbdbcacaacaaccdabdccadcadcbcbcbdbaddaaccabcdadadbbdccdacadddadddadddabcbdbcaaccaddbdacdccacabdaabbaaabbcddbcdbaddbdbadcabbaadbbbcdbadbbadabbacadccdadcdbccdddcdbdddcdcadcdabdadcbcdbacdcdbdbdaabbbcaababdcaaaacacdcabaddacbdbdacbdddaddbdcdcaccccbadadbcbaacabbcadcadccaacdbdbbdcaadacaadaabaccdaabdbabcccacbbabcdcdadadadadccdbbabdbacdddcacabcabdbdbbbabadbabdaacddabaadbbdcbabdcdbdcbdacbcdcccbadabcaddaababcadcccdabcdadbdbbbbdbcaaaabdbcdbbdabcbcabbcdbdadcdbbccbdabcbcdaddbcaacaadadbddccdbaacccdbabbcbcadabbcbcbabcdbcbdadcbbddacdaccbccacadccbbbdcdbccbabdcbdaaaacccbacdbaccbacddacbbcdcbabddabccaddbadddbcdadbacaadbbddabbcbbddcbbccbadadbaaaabddaddccbabbbdbababdbacbacddbcbcdccdcabbdbbbbbbcbccdbbcddddddbdadacccbbacbddddaabccdbcdcaadccbacbbbbcadddbbbbbdaddcaadadadbcbccbadcacaacdddcdbcdbdabdddadaaabadcadbdadcbcdccbbaadbcbddbbdbbadbabdbabaabdbcabdaabbdaddbacabaadcbbadaacbdddbdcbcacbcacdbdbddbaddbbbadbcbcbacacccaadddccacddbddccdadbadccdadcaacbddaadacdbdcbdbbcaacbdabbcbcabbdbadadadbdabdaacdbcbcbddadddddadbbcdbadacbccaadacabbdccddaadacaaadadadcabccbcdccaaaccddbbaabdcdaacadcadcddbaacbdadccadddbaabbddbbacdcccbabcaadcdbbcddccbbdccdbaaccddaabbadbcbcababbcdcabdddacbdcdbccadbddadcbbadadadaacdcbdcadddacdabbbdaaaabbacaacbadaaadccbdadacacadadbcaabdbcbcdaddababbddbaaddbbdcbabdbbcdcdcadbbbdcabaaabccbadcdcdbdbadbbbccacbcdabdaaddcabacdabcabbaaabcbcaaacaaaddddbcacbacbaadcacbbbabccdbbbaadaaccadcbbdaacaabddbabcbabccdcdbacbabcaababccbccadbadcacaccadbaaabcbcddccccdaadcbcaccbbcabbbddcdbdddbcdabacadbbcbacadcdcbaccdbdcdbaacbcabddccdcbbcbadabbacaaaadbddbbbacbcdddbcdcacddacdbcadcaccdcdbadbbcddbaadbdccdccdccadcbbcdcdddbddcccbbdbccbcbcdcbbadbacddcdadbbbdbdcacababddcbdbdcdbbccbadaacadcadbbadaacdaaddddddbdaaabdccdadbbbaacdadbcacbdcdddbbddccacdccadbddcbabdcbdbacdcaaddabbabddcbdccacdddccbabadddbacdbdcbcdcabdacdcabdadbddccabddcaddaacbdaddcdcccbadacbdddababbadabbdcacddacdccbcdacaaaccdaabdbbaddbdcddccccadacaaabcbcdddbdbdbaadacadcaccbadbadbacaabacbcacabcacbacaaadcdabccbcbbaaadbcbbcccccddcbdccdddaaababcbaabbbbbddadbdbcabcabdaadddabcddbcbddaacdcaddcdacaaaadddccdbabbadcddbbababaabadbdcabadacbcbadddaadadbbbcddacaabcbbddadcacbbabbcdccaddadcbadabcbcaccbcaabaadcbdcbdbcdaabdcabbccbadcddbabccabccbadacdbdcbdaddbbcaabbccddabbbbdcdccbbddaadacbdddaabbbbdcbcbcbccdbcccdbcabacddcddbcccdbcdbbbcacacdbadacbcdcccdabdddcddcbbacacaaadbbdddcbbaaaacdbdbcbcababbcccddacdaabddbdaabacdbacdabcaaaaddbdbaccbbabbadaccdbcaaaababbbbccbbbcaddcdbdcadbbcdaabbcbbccbccaadcccbbddbdcacadacbbbbcbdcdbdcbdadacddaccabbcccadbdcbdaabcbdcbadaddabccdcccbdcbadbddcaacabadbcdbdccddbaaabdabbccdcadccdcdcbaacaccbadbaddcddcdacabddadcdadbcabadadacadaccacbbdcabbcbdcbccddcbdbccacaaacbddabdcbcabbcabbdbbddbdcabcdcbcacbbbadaaadccacbbbdbdadccdacbbcadbbccacadcadcbcbbdbbdcbbcaadccadacaccaacadbaccabbaaccbaddcdadbcabbaccabbaadddbabbcbbaccdddbbadbdbbbaaaabcbbbbbdddcddbcadadbcacbbbcccbabaccbdcaaccabbbdddbaadcbcdbdbddcabbadbcadaabbbbdacbdbabbccbdbdbbdddaaddddbcacbbdddbbabaaccbbbaaabdcdadacdccadccdbbdcdcbbbdccccdbbabaabbddbbccacaddacbcacacddaabcabdddcabbacbdadbabbbaccdadabdaaccdbadcadcabaacddbbdcadadbacbaccddccdddcdaadacaabbdbaaddaadaccbaccdcbbcddbcaaaaabcbbbadbaabcddcbdaddacdabbababbcbaccbbadccbccddbadcadbaabaabacccaaabaaaacacdbaddacdacdaaacbccacabcdaadbacacbcbcbcaaadbabaccadcdbbdbaaacbcbdacbbacddadaabcddcadbbbcbbddaadaacbddddbacddadaacacdcdaacdbbdccacbcdbddabbbbadddaabcbbadcbcacbbbbaddcbcdcdccdcabbcbdbccacddbdbbcdbbcdbbbadbddbccbcdcbadcdabdccbcaabbbaddbddcabcbbacdbcaacabbccacbbdbbddbadbbaababdbcbbdaaacbcaabacaadadacddcaccdccbcbdbadccdddcbbaddacdbbcadacdacccbdaabcbdcdcaaaaabbdcabdbdbdcbbabcdacdcbacccdbaabdaacbdbccbaccbddcadbacadcbbbbaddcacabbcbcacacbadbaaababccadababddbbcddcdabacbccacbbdccbdddccccaaadaaadbbcbdaaddcaacccbaabbbcaabbbddadcaaadccbcdabaadcacacdcdbabcdbaaddacaacbaabcdcabdbdabcaabdadddcddcdcccdbcdcdcdcaddcdcdccbdddccadbbabaaadcbabaddccdddbddabcabcbcadbacbababdaaadbbcaddcdbcdcacabcbdcccdaccdbabdddcaaadbcabaacdbdacdbcbbadabbacbbbccbbcaaadbcbbcdadbadbdcbbadddcdbbdcbbccbdccddabaccbadcadbabccabcaaabadbbcddbacdacaaccadabcaabccdddaadbbbadcccdbddcbaaabdadccbbcabcabcabdbbbabbccdccabbbddaaaabbacbdbcbbadcddcadcdabbcabdadbdccaddddcbdabbddddbddbcacccbcadcdddbbbbbdbccaccddaadcacbcbaddbddabbacaccabbddbccadbadaaddcdbbcdadbdbbbbbaadbcbdddabcbcbbbbabcdccccdbccacbaabaaccacdcbaccaabadbbcbabdccbdabbcdcdbacaccccbdadcccabccbcccddbcaabbdacdcbcbadaacbccacbabacabdabcabbaacdaccbacddabcccdbbbbabbcbbbcddcccbbbcdbddddbdacccddcccccabbbcdcaaddbbacbdbdadbcadaaadbcddcaccdbdbdbbbaadccbabadcbcdcadbbbdbbabdaaabbabbcdbccadddbaaccccaccadaabaddcdbacccbaadbbbbdbdacaacdbccdcacccbdcbbaabcabbaabdadaabbdadbaadaaddbacdabcbddacaccbbbaaddbdcbcacccdadbddacdabbddbbcccccdccabaddbcadddcbcddbabcaccdcbcabdbbcddcdcddbbcaadcaaacddbbadabbbdbdcddccdbabadcbbcbcadcdccdbdadaddaabdddabdbdbabaccadccaccaaddbadccccbaaabcccbbcbdddddcbdcaaaacdabaacaddabacddcbbbcbcdbdcccacaccaadcbaadacdabacbbcdccabbcabadccbcdbbdcbcbdaaadccbcbacdadcccdabdcbbbcdbdabaadddcbbbadbabddbcadbdadacddbbaaacdcbadabcadbdcddcbdccbaabbdcaccbcbadbccaddddaddbabcccdabcdcbaadaabdcbadcddcaaddbcbcacaccddbaadcbadcacbcccacdaccdccbdaacdabdbcaaadddcaddbaddbdacaddbbbbdaacaadbaaabaadacabbbdadbadabaabdcadbbbaadcccbbbddbbdcbbdcdddabbcadaabaabdaddabcbbdddbcbbbccdcaccdbddabccdccabaabbccbaddbcbdacacacabccdddbdcdcadabbbcabddaaabddbbdcbbadcbdbdbaaacccbccdcdbbddccbcacacdabbdbdacacbbabdccdbbabbcdcbccdaabadcccccdccbbccbaccbcbccaaadcabdccddddadcbcabcdaadcbbdccaabadcdccaccadcdbbbccdddacbbbcbaddababbbccaadcbcbcdbdccdbaadadabdbddadbbdaadadddadbaaabbbddadabdaaaadabcbcdcaadcbaadccdbaabddcdaaaddbcdcdbadcbbbccccacdcacbbdaccdabbadabababadcbcbdcccdbbbdcdbdcbddddbccbddbaadaaacccdbcadaaabddaadbcdbadaaaacbaaacabaccadbcbbabdacbdcdacdccdbcabdcbabacbbcbadccadbdbbcadbbcdaccbbcaadadabdabdbbbcdcdccbaccbcdabcaddccccdadbcadbcbdccacacddbcdbaadadaadcbddcbbdbcabcccdcddccdcdadcadbdacabaacdadbacbddcadcdcddbbccabcaabdbcabbcbccccbabdbacdadbbadbbcbababdabcaaaabccaaaddbdcccdccacbabdddbdbbbdbaadbbdcdcadacbbaddcbdaddbbbcdbcdbacadcccddbcaacaababdddaadaadccdaadddbbdbbcccbcbaadaacdbcbacbdbddddbbcccaccacccbacacaacacdcbccaaccaababcbbcbcccabdbaaccdcdbbbaabccabddbaaaddbbdcdcbcddbadbbbaabccacddabaadbaadcbdadacdacbadadcccdcabbcbacbbcadcdcbddadcddcccdabccdbbbacbacbadacaaacaabbacbbaccbcaadabacbcdcabdccaadadaddcbcaccbcddcdcdcbaabaddadcddcacaddcadbbdcbabdaacaaacddaccbcddaadaccaddabbabddbabbaaabdadaaddbdcddccccddbdbaaabadbcccabacddbccaaddaccbbdcbccdddddaddcccbcadbacdcdcdddcbdcdbcdbbacbbdcaadcadbcabacaacddabbdcdbbcdbbccbbccddddbaaddccdadabdadcdaabdbadbdbaabdbdadacccccacbcdacadbcdbbacddbbdacbdaacadbdccadcbdbbdbbbbadbcdaabbdcbdccaaacdadcdacbaccbddccbaadadbacddcacbcabdacbaaddaaadcbdcbdbbddbadddbbadbdcdccaadbacbddcaccabcdcdcddadbcbdadcadaaadcbaabcdddadaaabbddabcccbdabbdbcddbbddaacadbacbdabbabadacaaaadccbcabddadaccdcddbabdbccbdccbcbbdbcaababccaddcbbbbdcadadbacabbbdcaddbcdbbcbbdddacacdacccaabdacbcbccadbcccaaadccdadccbadcbbcccadddbdcaaadabbdcbadcbadccacbcdacddaddccccdacbcdcadbbbcdbdcadbadbcbbadcbbdbcaacccdbddabcdddcdcccbdddbbacacbacbdcbcbdcdbadcbdcaacdaddcbbadcadaddbaadcaccabdbbbbcdcccdbacdcbcababadacbbdabaabdacdbaddaccccdbdcabcbdddcddabacacbaccdcdbaacacabdbcbcdcadacbbaddbdbadbbcccbdcccbaccadcdcbbcddbbccdccddddcadbdaababcacaaacbdcbcadabbbdadcdcbaddcbbaadaabacbcbcbdbdcaacdbdbabbcaaaccccdacddddadcaccdbaacdcaaaacdaacbddcdaccadcacdbadcdabdbacaacaabcdbdbbddadbdccbbaaaabcbbcdbcacabaddcabcabaddbddbdabddbdbacbccdcddacdbadcccccbbbbbcccbdabbbcdbdbdbaddcdbcaaacbdacadcacdbddabdabbcacacdddcdbdbdbabcacdbcdbbcdadbdcbccbabacacacdaabcccccdcdcdcaaabdabbacdbdbcabdabdddacadbbbaadbabbaddaaccacdbccaddacabcdbcacbdabaadcadcdabdddbbbcbdbbacccabcddcdcdbaacbcbacacbbacdbdccadabcbcacdbbadbaddbdcbbaddcbdaabddabbcbddaccacaabababbcddacdadcbdcabacbabbacbdacabdbdbdcdcaddadbbacddddaaabcccddccccdaccabcbbdcdaadbbcdbabaadddccdabbbbbabbcccbdabbdccdcdbdaadcdabaddbbdabbdcdcdadddaccbdabbdcabcdbabccacdadbbdaadddccbdccdcbbdbddbcbabdddcddaacdabcdaccabbcbbbbcaccbabdcccdddaadcaacbabcaacaabdbdcdbdcddcbaadccababccccbaccbccdcaabaddaabcaaaacccddddabdabcddcddadbddabccccddbbacdaddabcdbdbdadcadcadacadddbcaaaaaacdbccddccbcbaddddcbaadaaadddcbabdcabcaadbddccadbadcaaaaabdbaabacbbccdccddcbcbabcccabaddbbcddbabaaabacbcdabcaadddbaddbbcdaadbddbbcabaacdbdbbdcaccacddddcbddadaacbabcdddbcadbccdabcddbdbddddcaddcbcbcddddaabacacbdccbddacdbbcdabcddbcbccbaacbcabdbbdbadcdcbcbccccbcabccbaddddbdaaaaabdddddbacdddcdcabbcdcccacddbbccbbcaccadcbaabcbbdddcbbabbbcadbdddbbdacdccadabaadcbdadcdaabddabaddababdabaaaaddcdaacacdadbdbbbcacabbbbacacdbcdacdcdbadbcacdbdbbcdaacbdcaabdddbddcaccbacdccaabdabbcbdbdbaacdccbacccdcdbdcabdacdddbcdcdcddcbbccdabababbacbaadbacaadbdaacbcccadcadaabdbcccbaadabcccbcbccdbbbaccddcacbabdaacbadadbaadbccdcdaadbddcacaccbcdbabbacaadbddbddbdddaaadddabccccaacbacbbcbccaaadbbdcadcaddbcacbcdcdaadbacdbcacadbbcdcddcacbadcdacadadbbacdcdcbccdbadcadabadcdddddcacbdabaabcacdadadabaaabaadcbdacbaadddcbbccdbabaaaacaacdaccdcdcabddcaacacbcdcabbcdbabdbabbaabbbcccaabadabcbdccbccdababdbaddadcadbccadbcdddabbcccdbbcbabbdddbdcddcdbbcbdabcdbbaadaabbcdcbdcbcdccdcbbcadbadcdbbdacacbdbbbbabbccdabcddbaacdaccbbdcadadadbbabababbacbacbbbacabdcdcddcbaacbcdbccacdadaabdabacbaabcbcbdaadbbccbbcacbcdcddbdacbabdaaadcaadddaddacbcbbcdabbdcdcddbacccbbdbcbcbddababcaacccdcdbdccacbbbcdbaabbdbdcababbcaaccabccddbcdacdcccdddabbbdcaddccdcccddcbaacbbabddcccadbbbcccdcdaddccbddcccbbadbbdcbacbccccbcbabadcbdabcdbaddaddbabccbdddcccdbdaaabadbbcccdcccdbcbbcaabdcbbddcdaaaddcbdcccdcabbadddbdcddbaabcadcaccbabddaccdadddabdcdbabcadbbbcddddcbbdadabbdddccbdbaaadcbbdcaadccdcccbddccddcddbaddbcdddacbbacadbdacccdcbcacdaadacddbdbaabbbbcacddddbbcadbbaadaadddadbbcbbbdaaaaddbadddbaabddcabbbcaaadcabaabdbcabadbddbaddababaacbabaaddacaddaabddcbddcbdccbcdcccccdbdbbdacbbdcabcbdddbacabacadabbbbacaabdcabbcddbabcdbaccbbbcdcbbccdabbaddccdcdbacccdbcdbaabdabddacccdccdddcbccdbcdcbcbbdbdacacaddcadcdabbacdbadbcadddadbbddbacccdccabddcaadddddbdccaacaaadccbdbbacbddbbbabaadddacbcdbcdaadbcbdcacddccddaddbcadbbbadcdadacdbbaaaaaaccbbdadcaddccacdbbbddabcadbbbdacddccccbdbcddddbcacaaaacbadaababbdddbbcababdcddcbccbbcacbbaaabbcbabbcbdddcddcddbacdddadadacdadcdddbdadaddaabdccbddacdcccdadbdbcdcbbdbcccbacbbdbcbcbbbadbdcacddacdccbdcaccabcbabdcadccddbdbdbababcbcbabadbaccbccbbcdccccbabcabdaaabbdbccdbbacaacaddcdcdaaccbdcbbcdcbaadbbddaadabbaacacacbdaacbbbcaddbcddadaccdcdcdcadcbcbddaaccdaabadccabccbdddbcbcccbcbddadcaacbacabdccddcaacbdbdbacdacaddddaabccabbbabddcabcbcbaacbddcacdcdbdaaaacccaddbcbadbdbaaabdbbccdbcaccaadaabdcbcccacaaadadbdabdccbabadacdbcdbcacbddacddabaabadbaaabcaaacccdccdbbadccbcbdacaaabcabdbbadacdbabcabdacadbacbddacccddbbbbadbddcdbcbabcccaabdabacbdddaacbdbbaaadcdaacdacadacccddbcbdbcbacadbdabacbbadbacaaacaccdcbdbacbaacabdbbbdaccadcaaaccdbdccdcdbadabbabcdddcabaaddcacdbbcbcaabcbadccbdbabcadaacaccadddaacacddcbacaadbcddacbabbdcbcaabcdcbadcccbabddabbbcbbcbdabacdccbdcddbacdbbdccbaaddbabababdcaaadbccabaddccdacdbdbabbcbcadddbdadacaaccdccbaaacdcaddadbdaaadabaadcabbadacccdbcdcbddccdacacbbddbbaabdcabbbacdddabaccbbdbbccddcbacdabdcccaadcdcbdcbcdcbdaaddaadbcabdcbbcbdacbabbcdbadddbbcdbdddcbbdbbabbdcaabcaddcbadcbaddbacbadbbddcaabbcadcdaddadabbdaaadddabbcdbdbddbdccccaacacacdcacdcdcaabbabdbdbbdadcdcbcabbcaaadaadaabcaabdcbbaabdaadacbadadadbacbdbcacbbcabdaadcbbccbbccbcdabdcabaddccbdbcaaadbcdbbacddbbacdacbbcccaadaadaabaaddabbddccabccbababcbcbbcbddbabbcdccbdbbcbcacbaacddcbaaacbddaabadcbbddbcccabdcdbabdccabdadddbacbcaddcaccdacbcddaaccdbaabdbbbbddcbdcadacbabcabcadabdaddccabddddcbddcbccabacabcbbdbbbbaaacdacadcbbccdbcdddddbacdcadbcdaaccbdbcbaacaabaabcccbbcbcdabdbaddddcbdccabdcbcacbbdbcbcdcbbadbdadadcbbcddbdccbabdaaccdbddadddcccadddacbddcacdbddaadadadcdacccdadbcdabcdcbdccadbadbcacccadbbabaacaabbdacbbdcdbddbddbadcacaadaddcacbbcbccddcbddcacbdbadbdcbabbbaaadbdccdaabdacdcdbdccacbdbaaaabdccabdaadacbabdadaabaaabacacaaadbdddbdbdcbddaacddadcccddbabbcaaadcaaccbdaabccccbacbabacabbbdaacabbccaadcbdcdcbdbbddaabdabbcaacccbacdcdcaadbcabbadcbddbabccdbcdcdbbbacaccdbdadbbdcbdcabaadabaabbdccccdabbddccabcacdbacbccddaabbbabcbabaaaaccacdbdbdbdddcdcbaaadbbccbdcacddcbdcdcdcdabbdbddddbbcacdadababaabdaddbadaccdbbadccbdbdcabcbbbadaadcbbaacbcdabdaddbcaccaaababccbacbdabaccaabcdcdbbbbbbcdbbbdbcaadbbadddbccdaadcdbbcccaadacaacbddbdbacbddaaddbcbabdbbbcddddccdababbcdddddbcadcccdacabcccbdacbbdcaacdadddabdaadddcdcdadacaaadaabcbcdcabdbbacbdadabcbdbcbddbcbdabaababadcacbcccbbcdadbbcaadbaacadbbdcabbdddaaaddcbbbbbdbcdbbbbbdcdcccccbbabacbbbabcbccacabcbddccccbcbabbacbaccaddddcccdbddbcbaaccbbaddacbbdbaadaccaccbcddccdabbcdbacdaddbcbccaddddababadddddddddadbbdabddabcdadcacaabdabcddccbabadbddbdcdddbcbbbcdbcdabdbbdbcdabdddabaccccccbcabddaddcaaadcddcdbbbcadcabcdbdabdccbccdddabccbaaaaaaabccaabcbbacaddcccacbbcdcbcbacabcbbadccdbcabcbdbdcbabacdabcaddbaaaadcdbbdbcaadaabdaabcbcadccacaabaaadccdcacbdddddacccadadcabaddddbadbabcbbccadccdabccdcadcacccabbaadbabbdbddccccdaccdbcbdcdbdababcabbdccadbadabbaaacaacaddcbbadbaabbbaaabcccacabddcdcdbcaccaccddccaadcddaadaaccaabccdcacadcdadabccbaaababbbcbadcbbdbacbdbcaabbababcabbbbdcdcdcaddcbcbcaacddccadbbaaddcdbbaacbbdbaabcbbacccbdbdddcacdbdcaaccabcbadccbacaccccbcdddddbddbbdcbaccdaccccccdbcaaabcbacdbccaadbcbaaabdbaaccbcacdbabdbcdabcaaccdddadbccbdcbccbbabbbbbadaadaadadddbdaadcccdccdcaddbbdcddcccbacabcdbdaabacdbbbacdddbcaaadbbbddcbabcdadaacabbacadbbccdbdcabbbdbbbabccadbbcabacbdbbcdaaddccbcddacdcbccbbabcbacddbccaabdcadbaddcaddddddaccddbbcdadabacdabbcbddcacabbbdbccddccdccdbaabcaaddbbccdabcbbddcccdabdddacbaacccddbbddaddcdcddacbcbbadddddcdcdbdaaadacdaadbcdcbcbcdadbcbacbbbdcdabbaccacbaabbcaabdbaabbbcddcbccbdbdbabbddbcbadaacdbaddcddcdcdccdabccaaacdcaccbabbbadcaddbaccbbcdbcdabbdcadbdbdbbccababdbaabaacbcbcbdacbacdbbbaddacccddadbacbadbdbcccaacdadbddcbbbbdaaadbbdbdaccdacaaddcdadaaddddbbbdcdaddaddcadcacdcddcdcccdbcadcbcccdcabbdcccdbabadcdacaabdbcdacdcbabbbbacdbcccdcdaaadabdbabbbdaddbacbaccccccaadacadacabadccdbbdcccbdbbcaabbcbddacadcccadabbcbdacdabbcddabbdbcccbbcbacdcbbcddaadaccbcccdabcacbaadabaccbadddddbcaccaaddabaabdcadaddabcccdbcbccdacacdbabcaabbaacdabdbbbddbddaddbbbdddbcabacbaccdddabcdacddbabadddbcdddabbbcdccabacbbabbbdbddccbcacdddcbaaacbacaccccbdccaddaddbcdabddacdcdcaaaacddbccdbdaacabdddbcadaddaaddbcccaacbbbbddbaccbdbccaccaacdbcccbbdadcdcbbaadddbdbadaabaaadbadabacbcbbbcdaccbbacdbacdbaddbdcaacdcaabbaaacdacaaadcbbacddbccccbcbaccdcacbcbdcddcadbdbdacdbccbcbdcbdcdaababccdacaabbccbddbacabbdaaddbcbaccbdcdbdcccbacbcdcdaaaccbccabdddccbbdccccddbcadaddcdcdaabccbbaccdbdbcacbaccccdcbdbbdbaadabccddaaacbbbcacabddcacaaccdbdabbdaddbcbbbcdddcdcaadaadaabcbdbdccddabaccbbbcddcbdcdcdddbcccddcbbabaccbdadddacaacbacbaacbdabcdabaaaddbccbbdcadaaaacbbaabaaaacbdcaabcdcbdbaddcacbbdbdcccdcbdbdddccdabdcbddbcdbbdccccbcbdccbacddbddadbbbcdacdacbbacbdacdddbcccadbccbaabbcdacabcbadabacacaaddddcacbdabccabadcaacbabbcacddcbcadddabcacadacadbdbcdabdadcacdcaadbbdaacddbacccbddcddbdbccbadbaaacaadcccbbcdddadbbdcccaadcdcbdbbbccaabddcdddabbdcaacdbbcbcacddabbccbccaabaabbdcbcbbcabbbbbbdccdcdacdbbdacdcdacacbcccdcadcddcdaccddddcddaaabcccacdbddddcdaabadbaabcddabcbbbdbbcabcadccddcdbbcacaadcdcddbcdcdcabdcaaddbcaaadddbcaacbbcadbcbaddccbdcacabadcccccaabcdcbcccabdbcbbdcdaaaaacdcbdbbbcaaacadabcdbdaacbaaacbcbdcbbaaccaaaaaaddcadabbcababbccccaacccdcbdbbdacaaddaccadbcdbdcbaacbadbbdbcdacbdbbbbccbcddbadcaaacacacdcddccbaddbcbacddbddbbcaccaaaaddccadcdbabdbaccaabdaaabacadddbddbaacddbabacddadbbcacbdababccccdbdabccccbacdaacacdababacbbbdabbcbcbbcccacaaacccbcbdbadbcabcddcdcddacbcbdcdaddabbdbacacdbcbcbdabdaaabacdcdacdabbdccccbdddbcbabdaaccbabbdcdacdaadaccadbdaababcbbcbbabbbacdabbdcacaaddcadcbdcdbaddccddcccabdaccbcbccbcbcbdacddacababcabbacabbcbcaddcbabadccbdbdabaccbcdbddaadcdaaaaabbaaaaadbabaddccdbddbcadcacdadbdcbccddddccaccdccdaaddcacbbbdcdaaacdcbbadacdcadaacdcdaddbabdadbaaaaaaacdbccbcbbdcddcabcbddbcdcaacacbbcbadacacabadbaddaacbcadddccbcdcbcdadcddbbccbbabcabcbbdbcddaccccbbadcdbcccaaadcdddacdcabaadbdddbdbcdbadbdddbadaaaaddabddabacaddcbdddacbccadcdcbccacccbabbddcbaccdbbdcbdcbdbdcbdcacadadbabbbdcadababbcabcccccbdbabdddcdcbacddcddcaacbccddcadcadbcdbdcdaddccbcabbdccdddcaccdaadacddccdcbccbcbbcbadabcbabbababddbdbcacdbbaddbabcdccbbccaccdadbbcddcbacbdbcdbdbaacadabcccabacdaadadbccdbccdcadcbabddbddcdcbbabababcaadbbdbacbccaddbdcdcbadbbddcccaaaaaddbbcbaccdabbdbddddabadbdabbabacddacbdaacbbbdcdccbaaaaacbacddbabbbcbbdaabccadadbcbdbacbadacbbbabaaaadacdbbcbcabbddaadbbddbbadcbbbaaddccbcdacdbadabcdabcddabbaccbabcbcdcbacbbbccbccbabddddcbabbdacabdbdabbcdaaddbbdcaddadabcadcdbbabbcadbbacbccbcadacadadbcdcbbaaadaacdbabdddcdbbaacbbbbbdccadaabcccbdbddacaaddaaaadbcbccbabbabacaaacadcadbdbdbbdddcacadabccddababbbbdcbddadbcaacacacbcdbcbabaddaccdbbaddbcaaaacdcbbbdbabdddccccabaaccbaccdbcbdcbdbddbdddcbabaddbdcadbcbdaacacbdacccccbabdccacbbabbbaacbdabbddaaacabbbaaaabadacaabdbcbbdbcaaddcbcabcaaddbdadddabcdcbddbcaccbbaabdacccbddcbacaacdcddbdbcdbcbdccadcabcddbcbadcbcddbcdccbcabbcdbcadbbddcdbabadbabbabcdacdbbcdcbbacbaccbbcdaccbadcadbbbbbccdaccbdacdbcbadabcbdcbcbabcabbaabdbdbacaaccbcbccadcbcaccbabcddacbacabcbcddbbcbdccabccbbcccbcacbccbdddbbbccacbbbdddabcaccbccabaadaccdbddbdabbddaadccdbcdbbbdddbbdaacbadcdddbbbbadadabbbcddddcbddbaadaaddadbadbcbddbcbbccbadcacadbaccddababbcddacababbbadcdccdbdcbababddcdcdadcababacacacdbacabcdaacbcdabdaadbdcaacacdcdbacdbaacbcdddabdcccdcdcddbbbcadbcbadddbdccbaadcacccbabbcdccccadbcabdbaabbcdacbdbbddbbdbbdaacccbacacacddcbdbcadbcaacbbdbccbccaacaddccaaabdadadaacaccbdbbbcacbadcddcddbbbcdcccbdabbbbdabadadbddbbcacdabaadcccdacaabaccbbcbdcadccdcccbdccbbcddcdbdbbbadcabcdbaacadcabadcadbaadabcbadccbbcbbccddbdddaabcccaabccdddbddacdbabaabacbdbdaabbacdaddddacbabacdabcadddbcddcadcaadcadaabdbbcbadabbaabbbcbbbadbbcdbbbabdbcbcaacbacdabbbcadaadbabcbbabdacdaabcadacccaddabacbccdaccbcdbcbdbcdbbcbacacaddccdbdccdddadcbaccbbdadcdacdbdbcbaaddbdacbbbddbbcaabbaccbadddbbcbbcabbaccdcdabdbbdacaccbcbcdabdddcbadcdacabcdccabdbdacbcabcadcdabacdccccacabbbaccbabaaaadbbbcdbdacbbbcdbccbddddadabccdbaacabcababdacdbbddaccbbcabddabbbbdadcabcdcadddabdabaddcaabbadbdaddcacdcdaaabaadcccdbadaadbadabbdddaacadccacbbcbccbddaababccdbdbdcaabccbabccdcdcbcbadbddcdaccbcddaddacdaacaacdbdaacabcbadadadbccadabbbcbbccdbabdbadabdbabacabdaadadabaaaaaacbbdbdadabaadbabbccdddcabaaaacacbabadbadcbbcdabbbcabbdccdbbcacbaabacdcdababcccccadbbdbdaaddccdbdbdbcbababccabacadbbcbbdaadcbddaaccbacccbdcabcdbbcdbdbdbbdcbaddabaddddcbaccbcaccabbbabbdacadcaabbcabbccdbacdabbabcaccdadaadabbdccaadcdbacdacbbbdbcaaacacbcddbbbaccbcdadbcbaadbdaccbcdcdcdbdcaadcccbacabbaaacdbacddaacccababdadcbadbddcdbaacadabdbabcbcaaccacccccdaddcdcbddadbcddbccdadacadaabaaaaaddbcccbbabacdddadccbabacdcabcaacdddadcabccccdaaadbcdbbbdcdadacddaaaaacbacaabddcbdaabacdadcdabddaabaabcaccdddbbdacccccbdaadddcbdabcaaaaaaddcddacbddddcabddcabaabccbaabacadbdabbaaddbbbddccdaabcdabdbaddadbcdadabcbaacdcbcddadbdbdcaabadaccdaccbcdbccbbdccdcbbccdacacbaabacccccdccabacbddbdaccacbccdbdbbdbcdacbdddbdbacdcacbdcaaabbadbaddcbcbddcabdadbcaacadbababacdcbabadcddbbcabacdacbabddabcccaddabbddacccaacbadaacdddacdcdacbcbcbddabdcabcdbccabdbaccdbadacddaccaabcddaadcdcbbacaadaccdacaabbdadbdbbcbbabbbdcdcbdabccdbdbaadbcdbdadcddaacdcacbcbbbaaaccaabadcdbbcccadabdccbdadaabccbddabccbbdcdbabdbbcdabcbbadddddddcbcccddaaadbabcbaadbcbbcccacccacacdcadbbbbabaaaacaabccccdaddadaccccbbcaaacdabaccbacdabddbbaccbbddcaaccddcacdbaaddbdcaccbdbcadbcaacddcdbacbadbcbdcbaaacaccccaadbcabbcbbcdbabacbcdabcccdbcbdacbccdacbbabbbdabcdcdcdbadaddabcacbcddbbdddcbbdddcbcaaaaaababcbaaabbdcdccacdacdabbbddddadbaaddcaadadadccccdcacadbdbcccddbcacadddacdbcbaccacacaddcabcadacdacbcdaadbcdcadbbabdcdabddacaaacdcdacaabbddcbdcbccbbabababddbccaddbcbbdbcddadbbbccccbdbddacbaadcdddcdadcccdbccbcdadbbcbbdbbaadbbacdcacdddbabcacbbadccbcdbccacdcbcacacccbcdacbcdcaadacdcdaabdccdaadddbbddcccbaaabbbdccdaddbbcadadddcabdbadbdacdbdbbbcbacbdcbddccaccbcdddbbacbbacacdcbabadccbbdaccdcbcbaaacccdcdbddcbcabaabcbcdcbdacdddacbccadbcddaddabcbcbcdbadbdbddacdbddbbddbdacadacaccbccccacddbacadbdaccdcaddddbaacbbccbbabdddcbbdddacacdcabbddccacaacbdbcdabbdccdabbbcbdcbbaaddddabcaaabccbbddacdacbabbbaccadcbcdcbbcdccccdbadcbbaabaacddbabdaaabcbdcbccbadabbdacaabababcbaacabaaabbadaababaaadbccdbdddccbcdddcadbabcdcbdccaacdbbbadadacdddababbddabccabcaabdacacdbadadabcbbcddcdaadcabcabcdbadadadcdadbcdacdabaccccddbdcdbddbacdabbcbcccaaadbcdaddccbbdcabacdbababcdbadbddbdccccabbbdbcbcdddbcdadacbbddbccddddaddaaadadbdaddcaabdbdbdbdbbbadadabdcacbcbcaadacacbbbbacdddaccccadcdadcdbdcdbbbadddbdbbbdabcbdaddaadaddacdadbccdbadacdbaaaabbdccdcbbbadabcdbdacdbadcadcacccdbbacddbbbadcbcccdcdcddbdccadcdcbbadddcddadddbddcdccdcadcaaddaaabaabbaccaccdbcbcdadbabcdcdabaaddddccaabddbdbcacbdacddcadcbdbddbbcbcbbbcbdabcbbcbaaddbcacddabcbdbbccaddcaaddaccacdddacabbdaadacaacddbdabcccabcbdbbdddbbccbaadbbcbdddcdacbbcbcadcdacadcabbaacaabbdabddabbbcdbbadbbbccbdbadaadcdcbbaadadaaadcbcddacdbddbbadccdbadcdaabcdacabbdbacdddaddcddaaccadaabcbbaddbbdaddacacabdaacadabcdacabcddadcdabcbbbaaabbcbcdbdcbcddbbbadcdcbcbcaddbbbddbabcbbdbdaaddaccdcbcbbcddbbabddccdcbacdacbaacaadaacbdbaabdacbdddcdbdabdbdacbccadccdbbbcacacbbdaabdacbadcdbaaadabccddacbbddbacacaddacccdddbdccbacadbcdccdbbdbbcbbcdabbdddbcbbcdbdaababddadbbcbbbabacdddbacbaabccadbcbdcbaadddbdacdcdaabcdcccaadbddadbbdabacaadadcbbbbbbdbdbbddbcaaccabcccdccdcabadcbdbaddbdadbddbaaaabbdbcbaadbadacadbcbccdddadadcadaabcbaaabaddbabdabbcaacabcaccdacdbcccdccbbbaabdbaccbadbdadddddcaabbcadbbcddbbcddaccdacbaddbcaddddbcabdbaaacaabbcbacdbbbbdaccadbcabacdcaadbabbdbadadbbbbcccbddbabdccdaadbdcdbacadaccbcbacccaabaacbbcccbaccabcdcbacbdbdbdcbdaaaabcdabbabcddcdcdbcdccbcddacaacdccbdbbdbccccdaaaaddbddabcaaabcdababadbbcbaadcccdbbadcdbdaabddddcccbdbccaccbdadaadccdbccbdabccbbabdadcbddbaacacaadbbcaacaddaccbcbadababcadddcadbcdbcbbaccdaccdabcbbcddddabdadcdbdaadcdaccacdcbcaacababccaccaabbcdaacccddbdabbddbacbcbcbddaddcaaaacabcdddbbababcaabacdcdcaddabbbbdcacbacddadadbcdcbdbbddccdddbcdcdccccbacdcacddaaddbaccbdbcdadbddbbcadccbbbdbddcbdaaaadccbcbcbadaaacbbcdabccbacabddbaaaababbdcaabbbdcdaaabdbcbccdcddcddcdadaadadccaddaaabacbccbddddcdddaddcbaacaddbbcacadaabccddaaccbabcdabbdcbdabdabbbddadcbcddbbbbdaadcabadacdadbbbadddabadacacbddcbcbddcccdbabadbaccdcdbdabadcdcdcaaacbbacacdcdcbcdbcbbcbdbaadbdcaacccbdcacdccaabbddcbdccdcadadaddaaccdbddbdadcbacccbcbcaacccacdbbacdcbddbacdbcaaaaacdabdabcdddcdcccccdbddacaddddccdbddbdbccbbaddaacbabbabacccadbdccbdabbdbcdbbdccddccbacccdacbcddabcacaabbdcadbccabbcbcdbcdbaabccddcdddddbcabddddbccacdaabcbbdbcabbcbaccccccbbbabbdabbdaabcdcccabcabaabcaabbadabdbcbdbcddcccbcdbbcabbbdddbacccccaabbaddddccaadcacddadabaccabcbdaddbacdbadaadcbcdbddcbccdccbdddbdbbddccbcbababbdbcadccadcccbabbcaccbdabbbbbdacbadddabdacbdcbcdccabdcddcaabbdbabdabbccbdccddaccabccaddbdaaaadccaaabcccbcabacdaabaaddcccbcdbabdbacdbacbbddddadabadcddacdaacccbadabcccaccaaabaaadaadaccdadacaddccacacaddbdbbcdaadcdddaabdcdccbcddddddcadcabdaaaaacadbbcdbbcabbdbbdbdacbabcaacabbbaaadbddabbdaadacdcccdadbbdcccdbbaddbcadbcaacbabcbabcaaabbdbbbaaaccaaddaacacdaacadaccadcdbddadcaddabdcbabaadbddcbcdabaddabcbdadbdadbddcbaabdcacddccdcdcabdbccbcbbdbddaacddbbbdaccbdadaabdbdbaabaaabcbabaabccbcacdaccdabcbaacddacadaccacdccbacaacdbbdcabbdbcaabcbbabcaacadcdccdcdadadacdadacbbbcacbddadcaaacdbcbbdcbdaacbdcaaadcaadabbdbacdcdadaadcbaccaaaccbadcdcaaadaacccbbaabcacaaadbaccccbabcbacaadbdbaacaadccccbbdddadddacababbcadacddabdcacaaddbdadbdcccbdabdcdcacdcdbcdbaccdcbabaacacbadcbdbdbbbcbccacccdbbddcbcabcdaddcaaccaccadabaabbdaaabaadadabcbccbdabacbdaabbbcadbdbcdacddbacbcdddddddaaabaaacbcadcbbadadaabacdbdaaacaddabbabdcacbbcbcdbdbbadcdcdcacbcdaabaaccaccbadadbcaccdbdacdabdcabdcdabcaabacdbdcdbcbdacddbdabccaacdbbaadadbbcbdbbdcdabdcbcacbaccacbadccbabcbbbcaccddcbcdcbbaccabcbadddbdcaaabdbdacdbaadacadcacadcccaccdbbabccadbcccdcdaabcddbbbaaccdadcdabbcaadcbbdbdbaaacacdbdaabacdacbccccaabcaddcadcabdabccbcbbdbcbcccdbbdcdabbabcaccdbadbacddccdbdccbcbdcaaaabdccdcbccdcbdcbcdccdacbacdccacdbaccaaaaabcdccbaaddbdaabddddcdbbbbbdbddccadcacbaacdabcacbaaadddbcdaacadccbccdacbccaaccbddacdaabcdbacdaddbcccbaaccdacdbbdcbbcbcbbcdacaadbccadbbdaadaadbddcacddbcbadabbaacbbcaadbabadbcaaccbdcdabcdcaaccddabcacbaaaddbbcabcdadadbbdbaacddcdcabddbdddbbcbcacbadabadcaaaaacaddbaddbaaccdaaacccdbcdbcdadabcbbddddbcaddddbdbcbdbaadaabdbbaadcdccbcdaaadcacbcaabaacacdaabaccaabbbdccacbacbccbcdbadbaccacabbbacbcdddcaadbccdaccacdadccdcacdccadcdbddddadbcabbccbbcaabcddaadddddcbbbdbbadbdddbbddacccbbdabaabdbbccaadbddccbddbcdddabdacacaaddcccacbccbcbcaacbbabcdbacdacbbbaaddadcbddaddbdcbcbbdabbadcbdbaccbacdbadabdddbbdbdbbbbddabdccbddaaccccddcacdbbdacabdcaaadccadcddbbbcddbbacccbbadbbcacadccbacdcabadbdadbacbcbbbcbbdacabadbaadcdbdbddccdddadaaddcbadbdbddddbcacbcbbcadaababcdddbdaddcaabccddaacdbababaddbabacbabddaaaddbdacbcabbbacccaabbabcbcbaadcbabacadacaaabddccbaaabbabdcdbbacbddccabbcadcdcdabcacacbbacaaabbcbaacddacaabddadcabcdccdcddddcdddbcaacabadbaadcaadbacbdcdbaccddbcccbbbbacdbacccdadcbabababbbbacbbbdcbcdbbddddcbbcaabcccaabdcbadccacacdbacbacccbabddbbadabbccabbbcbbddabcdadbdbaaccdacadddaabaabcdddcacadcaaddaccddabdaabbcdcddccbcacabcabccccbcdccbbccacdacdadacccdbcbcabcbcdcccbbcdaacdaabbcbcbccdaacbddadccbcbabcdbadddcbabdcdaaaabbdcabbcacababdabaacadcdbbacbabbdabbbdcadacddaccbbadadbacaabddcadcdccddcbccbcbadbdbaacdcacddbdaabdbccabaaccccabdbcaadaadcbdbccbbbddcdaadaabbacdaaaadddabbadcaadcbdbbadcabdbbbbdddcacbacdbbbbcdbddbdbcbbcadddcdaacdbcbdbcaddacaaccdabbbddaacabbcdccbccbbdacdcbadadaabcacacbdcddbabdadcaccadbbaabaddcbdaadbaccbdbbbdaabccadaddaccbccdcccbababccdaacabbdcaabbacccdcadcadddddbccbbbadbadddbddaaddbababdadabcaddbcccddccdbaccbbddabcbcdabdcacbdaaaacbadbababcdbbdcbdbbdccdcabacddcdbbcddcaddbabdcbababacddddaabbbabdcccdcbcddabdbabdaaabaabbabcadbcbbbadbabbbdabcddabbcaccdaacdaacbbcdcbcadbdcccdacacdddaacdddaaadbbaabcbcdaaadabcbddaccbdcaadbbcddddaccbaddacacbcdacbcdabbcaaabccbbcbabdbcabbddcacacbbbdccddcbdddbacccdbcbbccbddbdaadcababadbddcbdbbddabdadcabdbbddacdcdbdbadcacbadddcdabbbdcbdadaabbcbaaaccbdadcdbaadbabbbabccdbabcbdccbcabadbbdacddbccdcddacdadadabbbcababadbdbcaaddcccbbabbaaddbcbddcddbddadabdadbaccdaddcacacccccacddcbbbcdbdcaadadddbdbccadbcccccbadddbabbdababccddacdbdbddbdaaadbcdbbdcadbacbdbabbcbdaadabcbadccabccadaaddabddaacdacdddbcbccaddcdbbbbdbddadacbbbcbdaacccadcbcacbcdbaacaabaadacbccbbcaaccaabcbcccdcbabcabdcadaadaacabcbbccdadadbbccdcbcbcacbbdddcbddacccbcbcdbbbcbcbadccbcbbdacbbdcaaacccaacccacbcbaabddabacdcbaadbcbabcaaadabacadabdbdcadaccababdcccdccddbcadaddbadbadddccadbcdabbcaccadddcdcaaddacdabacbdcdddaacbbcaccccbbcadcdcdcbbcacdcccbaacdbbdbcbbaacbadcadcbbcadbdbcabaadabbcccbaccbccccbbddbaadbabdacdbdbdabbddcccaaabdadbdbccbddadbdbddcdbbcccdddaabdbbddcbbcddbcddcaadcbbaadcdbacddbadddbacabbacaacacabbbcadccccabbadabaddcbccbdadbbbbddadaddaadbdbcddbcabcbcadabbbadcbbcdcaddacdcddadcbdaaadcbcaabdbaccabcabbddbabbdaddbcccdddccadcddabcddbaabadbcdddbbdbabbddccdccbbdacdbcdcdccccddcacacdabbadbaaadbaabbabcadccbaaaaacaaadcaaddbdadabcdcddaaaabbabcabadccdaaabcdbbacacbbbddbdbaacbbdcdcbacdbbccccbccbbcdcadbcdcabbbdabcdcbabcaadaddabcadbcaaadabbdbdbddccccdcdddaaaabbbdccaaadaadadaaaddbcdbdbcddabaaaaddaabcadabdccbdbdbdaadbbdacaaabbcbcbaddddcbbdcbddcbdddaaccdddbcabaddacaaddadbbbbacdddaabdccbccdbcbcbbbdacabaddbbdccabdbddcaaadacaacddcbdccdaadbddcccbdadcbddbacccddcdcadaabdbcaadcaccdcdcbddadbdbdbcabbdcddcaaaaccbcbcadaddbcdbaaccaadaadcdbccacdabbcdcdcbdbaabacbaccbdddddabbadbcccddbcbcdbbabbcabaacdbcdcdcdcbdcbccdcbdddcdbcddcbacbcdcddcccdbccabccdacaaccbacbdaadaacbccbdcabbaabddcddbaaadcddccccbcbbdccdbddcdcdabbacccaacbddadaddddadaabbcacacabadaaddcdccadbaadcaaababacadbacadabbcbcbcacdcadbcddacacdbdbddbddcbbacacaadbbacbccbcccaccadaddddbbcdadcadaaabdcdacbddaaaacbcbaabdaccdcadddcaacaabadbdacdbacbdbbdbdddaddaaddbdadcdcaaabbabdbacdabdaabbbdabaddabbbdcabdddcacdbadacdabccaacbbdbbbbaacccbabaabddbcddbcaccbdcddccdcaddaabbdbdccbdcdaccdccbbcdaddbcddacaacbacaddbddbacaabcdbacbbcdacbbacacadaccbdcbabddbbbaadbdccbbcbdbddadaccbdaaabaadbdddbdbadadaaacccadaadbdbbaacdcbcadcdccbaaaababcadddbaddddbacbaccaddabacadaddbcaaccabdaaabdcdbbcddacccaaaaaadcdcaccdaddbdcbbaccccaacdcabcdcdacbddbdccbbbddccaacbccbbbabccaccabacccacabbddccddbdadcbbcbdadccdcadbcaadbabbcbaacaacbcdadabcabbdaaadcdbcabcbdcccaacdddadcaaddabcdbdddaddcadaabbbaccaadabadcdaabddddcccbacadbdbdcbacbcbaaaddbbadddddbcadacadaadaddadbbadaaadbbddccdcdadbdbbdadcaaababcacadacadaadacacaddabbdacdabbdcabbdbbaacabddcbdbdbcaaacdcabcdbcbcdbcbabcabcbdcdbccadcbaababdabcddbcbddcacbbabcbccaacbddadbdddaccacabcdbcaddaaacaaccaccaccbbcdabacdabcbdacabdadaabbbdabbacaaddbddaddcacdcdaacdbdccdaaccadbcccbbdacdcdccbadbdcdbcbabbbbacadbcdcbaccbccadddbcddbcdcacbdbaaaddcaaddcbdbaaaadbcccdacdadbaadcabadabcbbabddaaadaaadbddbccccccdccadaaccdcdadabccbdbaddcdbcdbccccbbadadddcccbadddddabaababcabdbbbdacbadcccbacbbbbcabbabbaadddddcdbababacbdabdcabdbdbbdddabaacaabadacacdabdbdccaabcabcaacbbabaabadbdcaadaabaaddaacbabaccdbcccacdbcdccaaacdaccdbcbabbcbadadbddccdcdabdcccdbcabdabadcbadbccdccccaaadbddbbbcadacabdcacbddcbbbbbdbadcadbaccdcdbabddcbcdccccaabaaabcacddddbcaddbcddbcccdcdcdddbbabadddbaccdaccbddaddbcbcddcbabbabacabbbdddcbcabbdbcdabdabbabcaacaadbccdcdbdcccbbbacbaddbadcdcadcabcabdbdbbacaabcacdbdddbdbaabbabacadabacdacbcbcaccdccbcadacdacbbddbadcbddcdbadbdbdacdcaabbabacaabcccccaabdaaacdcddaddcbdbbdaddaadcabbacbacadcbbbbbcdcacbaacccccabaaabbcadababdacdbdadadadaaabdcdaabaddbcbcadddbddacadaddcbccbabaabbcabadbaddabcbcaccaaccbbcaccaaababdadccabdcacdbcadadcdbcdbdbaadcaacbaddddcadcadbbccaacacacdadddcadbcadaacbcddadabbbabbbbaaabdcacaddbbabaccaddadcbadbcbdcbbbccbacdcdddbdcaacbdcbaacbccaaadcacbbdbbaabcccacddabacbcbdcccdcbccbcdcbdbdbaccdbbbbabdbccadcbdddacaacaaccadaadadaacbadcbbabbdbabbaacbbcacacdccbdabcbcbddccabdbbccbcababcacbaaabacdbadccbcdaadbcbcaabadbccaababacbcbdcbdcbdcabbaaadcbcaabdbddcadbdadaddadbcaacccccdddadbccaaacabaacbbcabbdabdaacddddbbdcbbaadbdbdbbdbccbcacabcacaddbbcaabccabadbcbdacacbdabddcbbbaabdacbcadabdcdaadcdcccdcbabddaccdadcdadadccdccdadaddcdbbcabaabbccbcbbccbccaccbaaddddaabbabbddacdbcddbaaabccbcbaacdbbdcccaaacdbbbbaddcacabbbcdabaaaadadadbbdbababbacdbacadddbddcaccddacbcaddbabddacbadddcaabbabbdbadcdbddcbccadcabbbbaccadaccbdaadaabbacbcdddcadbdaddabbbcaabababbcdbdadbcaddadacabaddacbbcdcdacadbbcccbdaaacacbdcacbdbdcccccdcccbddcbbdbdcbbdcdcbbddacbbababccbabaadadbadbdddcbbcddbdbacbddcaaddcacbcdbbbbdcaaabcdbdadabacbccdabddbcccbadddacacccbdccaacbadccabababddcccddaddadabcacabdcbababdacbaadbbcdcaaaccdadcaccdaccbccddadadabbdabacbbbadaacacdcacaabdacbadaadcacddadaacaaabdabadcbddddcddcccbaadacabaaabaaabacbcddbdacbaabdbacbadabbcabcddbdcccadcaadcbbdcbdbaaddbddbadcacacbdacbaabbaaadcbadaacbdcababdcaadbbcabbcacbaccdddaaaaaaccadcdabdcddbddbddcbdbdadadbaaddddabbadcdcacdcbdacdbbcaacbbdcbbcdbddccbaacddcaabaaabcdadcacbccdbddbcdbdaaabaabacabcccaacacdbcbabcccdcddbbacbdbbbccdcbaabdddddababcbaacbcabdccbbccaadacaddacabcdbdddbbdbdaaaddadadacbbacbdbaadcbcbaddbaccabcdbccbbdbaacbbaddddcdabadcccaaabbbabacabcccdacdbcbabbbabbbacabdabdddabbdddacdbdbacbbcacaadacddadadbccdadacbabbdabbadaddddbbcbaadccabcacbaabbbbcadcacddddabababdcaabbbdcbadcdcabaaadadcdacbadcbddaaddddcbacbbcadbacabcbccadbddcdbdcacdadacdabbccbddabbcbcbdbcadaaadccdcaadadacaabbaadbcbcadcdabcdcacadcaadbacdbbbdcccbbacabababbbdadbabdacaccabcdbdabdddaaccdcbadabcdbcbdcaaacccdcadbdaadadaccbadcbccbbdcdbbdbcbdbbdacabdcabbccbacacdacbdddccadcacbbcccbddadcbcaccbadbbcbaaaadcadabadddacddccdaacabbdbbbbbdbaadcdbabddbdbbdadbcddbdddabaadaddcabccbddcbdddcacbbcaaaadddbbabbbdcbabcbdadabccaccaccdcddbdababcdbcaabbbbacdbadabccadaabdbaacdbccabbbdabcccdacadbacadbadcabacbbbdcddabaacbabbacdaccbcdbbaadcbdcaaadccacccacadddaddccccbbcdaddaacadcabcadabaaaacdcdabaacbabaabdbcbdbbcbdbddcaaabccccababdbcacccbaadbcccddabbbbcabadcdbcabacbdbdcbdbcbbbdaaabbbbdacdadadbdbbcddbbcdbabccabbbcaddddbdbbaabbaaccacdcdbbcdccccdcbbaccddadadcbbbbcbbaabccdbaacccdbbbcabbbadbbdabddddbaddbadcdacdccccaadadcabdbabadcacacdccbabcaaaddcbcddacbbbcdaadcdaacbdabacdaaccbbcccbaaacabccddcacccdcaddcbccbaddcbbcbabbbaadddbdadabcbbbccdddaacadaaabcbcdbbdadbaaacbcabdbcaadcdcddddbbbdbdcddbbbdbbdbbcbbabcccbddcabcadadabdabacadbcbdddcbbcddabcbcdddcababbbcccbcaddacbdacccbcaaaadbddaaabcabcbbcbccdccdaabdbdddbaddddbcdcbbaccbbbcaddaaacaaacdbbbcacddddbcbbcdacadcbcdcddbdabacabdadccaadcbbddddcacacdbdcabdaadcbdadbbdcdcdadcdabccadcabdbaacdcabdbcbdacdcbdcdbbbbaadacadadcbacdbbdaaddcbcabddccccabbaadcaadcbcaadcdaacdabadbacaadcadcacaacdcadbcbacadbaddbddabddadbcdacdbbcddaabbccdabbbccddaddadbcbbdbdbaaaabcaccbbddaaadbcbbdadbcadbccddcbbdbaaccbabadcbdcccccdbbbbabacacccbbbacdcaaadbbdbcaacbbbbcdbbcbcdaddddbbdcbbdbccdcddaadcccdadcdbbbdccdbbcaaacdcdbbcaddcdbdccacbbcdcacaadcdbdaccccbdacbbddacaaababccddcacdadbcaaaaabcbdbcdbbdccbbcddccbdddddcabadccbadcbcbccaccbcccdbdcccbbcacdbccdbbbdbdacbacdbbaaadadcabdcdabbccaaddacddbacbdabcbbcbbaccbcbbcdadddcadbababdbdbbccccbacdbdcdbdccdccbadbaccabbbddcaaddabdcdcccdaabdbbdcdbdabdcbbbaabdccdbbdaaddcbcaacbaadcccbccdaabbccbaddadaccacbddccbaabbcbbaaaabbdaccabbdabbacccbccddddbddabacbbcacdbbcbdbaabcacccdadcbaaaacaddcaccdcbdbbdddbcbababccaadbabacbdcacdcdcbacdaacdabbabaabcaaaccdcacdaadaddbddcddbdabcadbdcadcddacacaadbddababcbaccbbdaabaabdbabbbbbcabbbbbcbbbdcacdbadadbcaaccccbdccdbacbbdccacddbbcbddcbbaabcdddbaccaabcccdccbbdccbbdccdababacbaacaacaadabbbacdaaddbbbdabcdbdadbdbddcccaacccabacacdbccbbbacabaadaadbddcbaacdbabdcbaccdbaabdbadaddbaadcbabbbacabbadccdcddcdbccaccaaddaadbacdbbdbdaacbacccbcbadabaddcdcbacccaabaddabcdaaadbcdccdcadadbbaccdbacaadacdbbadbaabcdbbadaadaacadbbdddcacdaccddbadcbdcaddcccdabbccdbbcaccacabdbbcbccadadadcdddaaacccabbbdaabaaaabcccdcaacbcbacabdaaadcbadccadadaadcbacdacccabbcacddabbdccdcdaadadccdccdacccaddaadaaabaabbcdbdabacacccbdadcbacdabbbbbcdacacdacdbcacdabdccaaddbdccddbbccdcddcacacbbddabaddbdbdcddbcdbdacbcbadabcadcdcacacdbcbdaaaacaddcabdaacadccaadcaccddadcacccdddacaacbaaccadbbbbcacdacacdaccbdcabccbbdddcabaacbcabacaddacacbcdbdacdbddcbcbbcbcbdbcddaabbacccaacabdacdddadbabccdacdbaddbbdddadccdcadabbddaccbdcbdadddacadcacbbbcbcbbdbcbacdaacbbaabcbcdbaaadacdcbacccdadbabdccdcddbbcbaadacdcabddaadadbcbbdaddcddaacbdbbcdcdcbcaddaabbbddcdcbacaadccaaaddaaaacadcaabdcbbaadaaadadddaddccaacaaddbbcbdbdccccabcdcbbcbbbcaababaccabbbbbccabaaddcbaabddcbbbcbbdbdaccdbbdddbaccacbadcbbdcbadaccbdaccccadbbbbcdccdadacdaabdabadabdcdcaabaaabbcbccbdaccdcbdbaaabdabadcbbbdadbaadcbccadaaddabacddbbbbccdbbdcbbccddbbccccabbabcaabdddabaacbdcaabbcbdccaccaabbcbccbcabbccbaaabbdbcaadbbdbcdbbddabdcdbabdabddcbacdbbadadacbbadaadabbcbaccadabbadcdcccdccbacadccdcdabdadcadbbcbbcadccbbadccbdacdaddbcbaddabccbccbbbdacddacdcddbcddacadababbaaaabdccdcacdcdcbbabbdaabadadabbdcbcbbbacccadbcbaddcaadccddddddccaccbcabcbbdabddadcddddaadcacdccbaacaaabbddcdcaaabccbcdaacadbcabcdbbadbcdacbdcacbabdbbdddcaadcdbbcdcadcdbadcbdadbaddddadcbccadbbcccbdcccccabaaadadacbabdaacdbabcdccaaddcacadcabdadadaddbccabcdccabcdbdacbaddbcbbdbadcbbddabbbcdcdaaadbdbabcccbbddbabdabdacccddddbccbdcdbaabbdcdcaddbaacdbbabcdadbaddddcaabacbbbaabcbdadddababcdccdbccdacdddddddaaaaabdabbacdbadacadcbbadaccdaadcbacdbbacbaadababadbcabadbcbdaacadaccdabcddbdcabbdcddcbccdbbbbcbbbabccbccbdbaabbddbabbbcddcdcddbbdddbaadaadacbdabcaddcacbccbcabbbadbbbbdcddbcaabbdabdbbbbabbbbdbcdacdaabaadadadccaccddbcababacdaadabdaddbcddbbbccdbcbaaababaadadadaadbdbadcddaacdbbcdacadcdcdcddbacdabaababbababccacdacbdbabdaccbaabacbababccacadabbbddadcaddacbbccabcadacdaddcacadaccdbdccaabbaacbdacdcdaadbbabaaacaadbcbbccbcabbdadcadccdaabacdbcbabdcabcccaaaabccbbabadbdaaacccbaabccbcacdbaacbccdbaaaacbdaadbdbbcbabdddbddbbdacbbadabbbcddacdacdcddddccccdaddddbbbbddaddbdccbcaababbdcbbdccaacccddddcadaaddcdaccababcbbdddcdabcbdacdaacddcbddbdddcddabbbcccacbdaaccabddbcabdaabdcbadccbaaddaadcbdcccdbcdcbbadabcdddababdccbdaaabdabddcdabcdacbdacdacdbbcadcbacabbbcdbabbdbcdacbabadadddbaddcbacadbdccbdddadcdcbccccdcdabdcbbabdcdaaddacaacadabdbaabbdbcbdccbcccbbdcabcdccbbbdbccccbbdacbcdbbdbbdabddbdbabdaddcadccdaddadcaadbccabbbaacddbbbbaacaabbbaacbddbbaacdacadbdacaddababbadadadacdcacacacddcbbcdbdabcbcbabadcbcbacbbbacabbbcdcadacccdabadbcabcdbdadadbcbcbdacdaddcbaaabbcabddbcbcbcadccbbdccbccdccabaaabadaddbbbacaabccaacadccbcdcddacaaabcddcaccdcabccdaacadccaadbcdbddbbcadadabccdcdabcaadaabcccdacdbbcabbccdababaaddbbbacccbcbdbbbbbacdbbcbddbbddcaaabadabdddabaadabbdaccaccdcaccbccbcacadcccdbaacdacbadcbddcdacaabbcbccaaaddbabaacaaacbadaccddbbccdabaaaadadccbcbdbcadbcacccbbdbcbcdbcbccbcacabdadbbcdcbdbdbcbdcabbdacacddabadadadbcacdbddcbbccabdbbcaaabccbccddccccaddabdbadaaacbbaadadbcabbbbccbdbbdabdbbcccbcbadcaaadcaaadbccdcadcdcbbaaaabdadcccabdbdacdcddbabacccdadaaaadbcadcdbcdcdabbcddadcdbbcababaccabdcadacbdabddacdccbcabddddabaacbdbadacabcabdddbdbcbdabddadbbadaddbcbccdcacadaabdccdbaacacaaabbbccdcdcbcdcaddaadadaaaacddabbcbdbccaccbbabcdccbdddcccdaacbddbdddcddcdaccbbcbcbccadbcbbdbbdabcadcabaabaabbcacbcdcabbddbbababcabbdbcddadbadbdcaccccadaacbaddbcdbcdbabbbbbaaacaacbaaddcabbdbdabdbdbdcacabdbbacddacdcdcdddcaadcbadacddcbbbaabaabcbacccdaabbdbbaccbaccbbbddcccdcbccadabdbccbdcccbddcacdacbbabacadabbabdaddbaddbbcdcbdcbcdbcaaadbbccdbbabadcabbcbbabbbddaccaadbdbcccaabacadcdacdbbcadbdaababbaadacddaccdddabcaabbbbcadadccbaaddcdcabbbdccadacabdadbbbcbdbcbdccaddbbadbdacaddccbbdcbddccadbbbbaacabbbaaadabdbaddabccabcbadddaadbdcbaccaacdbdbbcdadcbccabbbbdcccbdadacbadaabdccbabbdcccbcddcabcdcbadadbaddbddcbbcbacdbabbcaacdddadccdbbdbbcdcacdcbabdcacbbabdcacdacacabdcabcddbbdccaaccadcdddadcacaaddddacaabcbaacadaddabdccdbbaddcccdbcbddbcbdadaabcbaaaabdabbbdadabacddbdcccadddadddbdcbacacdcacacddacddbaddbabacdabcacbddcbbdacbbbadadbaacdbbcdbcddddccabbdcdbccdbccbcdabcadcbdcddbdaabddbcdbbbaacbcbdacbddadadacbbbbbbdcdaacdddaabbddbdcacbcdaddcaccaddcabcbcddaacaaacdddabcaabdbdbabaacbdbcdaabbbbacdcaaccbaacacbdccdbbbcccdabdcdbbdabdaadcaaddcacbababbabaaaabbdadabdbadaccbacadcaabcdbdbdddcbabdbcabadbacbacbacbcccaaccacbabbccbbddbadddadbaadbbabddabdaddadabaabbddcbaddbbabccadabcddcaadaadbaccbccbbcddcdcdcaabcbdcdaaadabbaacacdccbddabacdddccacbdabccaddadacddabddbdccdbbbbbddbdbcacabbabdaabdabadbdbbacabdbddbbdbacdacaaabbccbcbdcccbadadcdcbdddbcacadcbbdcabaccbddaacdbbdaccccbcbbbcabbccdbbacabcaccaaaababdcaaabcdaabacabacbdbdadcbbdcabadbacbbbaacabcaddcddcddaddaaabcdcdbbaadbccbbccccbdcddbcabcddbbcccaaadcbbbdcbadaabaabbbdbbcdabbccccabdbadcdacdaacdcdcaacbdcadddacbcbcbbdadaaadabcdcbdacddabaaccacabaacddbaccaabdddddddddadcdbcccdaacbddbcbabdacdaacbbcaabbcababdacddbcccbcbacbccbcdcdabddbaadddaaccbcdbcbbcabdccdbcaadbccdbbcbadbadbbaaadacddbbabccdcabacdbcbcbdcaaaaadbbbbbcbccadcdaaacbbddcbabababccbadbdbaaabdcbadabcddabddbdbbccdacaadcabaadcccadbcdaabdadbcaddcabcaacbaabdcabaddbddcdcaccaadbacbbcacbdcddbdbabcdaddbccabdddcaaadaaccabcacaccdcccaddabdcbbacaaabbbbabbadcdcccadbcaaacadccccdccdaacddaadabddbbabcaddabbacbdcccabcabaaaaabababdcadaacbdbdccbbdacdcbcabcacbcccaabbdadddcbbcbcccdcacabdccbbacabdccdccacbbcdcbdbdcddadaadaabcbaaadabbdabcaabaabacbabbddcbbcaabbdcacadbabaddaadadadccdbcaaaddbdcbabbbbdddcbbbcddacaabdacbbabbadcbbbaabbcddacccabcddcadbcababdaababdadaaababcdadaabccccdddcddcabaccdbadbdbdddaadcbcdcabbcacacbdcbaabbcbcbadcabdcccabddcdbadddccadcdcdbbbcbbacdcccdcadadbdaddacdaacdbbaadcdddaaaacdcbaddaabbabbcccdddabbbbcdabdcbbbdbbddadcaddcaacaadaadcdabdddabbddacbdbdbdbadcaabddcdabdcdcaababbcdcbcbbadccdbbbcacbbbbbbabbcaacbbcbaaaacaddccbcdacccacaabbdddabbbaadcdcbcaaccdbcbaccababbbcdbadbdabbcaabdbaabaadbdcaadcdbcccccdcdaaacadadbbbbbbdcacadcbdbbddcbddcadbbcbdbbaacddbcdaabaadbadbccdddcbbbbdacadbcbabcbcacaddbdabaaccadacaabbabbcdcbddaaaadbacdcdbdbcacdcdbadbbbccbbabaacdaadbbdcbdcdcbcddcddbbbbcadcbabaaddacdcdcdddaabcdbddbdbbbcddbdddaddcdabbacacdbadbdabcdbaddbabbbbadcccadddcdaaddaddbabaacddbdbadaacdacbdbbaaddbbcdcddbcadaaabccdbbdbcabbabcacdadcbddcdddabacaaacdbddcdbacdbdcaaadbadbcddbdbdccbbdaadcdadcbabbabdcaacbacbabcaaaadadaddcdcdacacbcaabdcadabbcdbdaabddaacadbdbabdbdaaaadccdcddaccdcabdbaabbdcaabdddbbcddabaacadddccabcbdbcabbcdbccbadbdbbcaaccbadacaacccdcddabdcadbabcdbabbcacbdbcdcccccacbacccdcbbbbdbddbdcbcaadbcccdcbcaadaadccbcaadcdababadadddaacbadbcababbbaddddbcdddccbabcacbcbbbcbabcbaaabbbdcacbaccdadcddbcddadadbddcaadcbbccaadcccbaddcbdccaadabcadddcdadccbcbccacdccbbbabbbcacdbcadcbcdcbdccdaddaadddbdcaddcdacadbdaadbdbccdcbdbbabbcaabcdbaddbdccdcdddcbdcaabcaadaacaaaacdbadcaccbdabacbbacbacbddcaacbdcccbabbaadaccbaadccbaabdaaaccbbbcdadbbbbacaaacdccadbdbbacbcccaabdacdbdddacbbdcbaadccdcdbaddcdaaadcbdbcbcacbbadababddddbabdaccccaddddabbbbcdcbbbcbdbbadcddacddabaddbcbaabdadacddbacdacabcbbaabcbaddcdbbaabaadbcadcaccacabcdddaddddbbddabadadcacabdcbacbbdacbbdccbbdccbdbccccacbccadbccadbbcacabccdbbcbdbbacbbbddddcbdbdaabacbacdcadddbaccccaadcabdcccabdacbbcddcacdbbcdadbbadaabcbbbacbbacdabbbdabbdcdaaddcdadabdcbbbbbaaababbdcbccadbbaacccdbbabcddcbbbaabccadccdbaccbbdbbcbbbdcaddbbacbdbccaadcaddaaddddddbdcbbbdddcaabbaccacabbdcbdacaccdcdabdcadbddcbbbbdbadbabccccbddadabcbccccddabcdacccdbabdddccabdbdabccdcaadcdcdccbacabbacaddbbbdbaccbbacacaaababcccadcaddadddaacacdbacdbcadbcdccdcbdabdccbcbaaccdaccbdcdaadcbcaddcbccdddcadababbbcccdbbccabaabaddacbbabbcacbdcdbbccbdcadcdacbccbadcbaccbaabaadbbcbdccccccddbccabdaccdccddbacadabdcaabbbdbbdcbaadbacabcddbdacbdbdaabaadbdccbadccaabbbcbadbccddaaadbcbadbdcabcabbccccabacdabdcdabdbdbddbddcdcabcbacdbbcdcdcaadadbcdadccbdcaacddcdadacababbccdbccbbbbdcbdaacacababacddddbadbbcbcaccbcbdccaadbcadbbcbcccdacaccdaabcbbccacbaaccccbbcbaccaaaaaacabaaccdcadbdbddbddbcddcbaaaacbabaaddddababdbdaacbbdcabcbdabadcdccccbadabddbcbdcbbadddadcdadccabbdbbdabaadbcccdabcdacdbddacababbccccaaaaccddbcaaaadcdbbdbaabbadabcbcbbbabcbacccadaaacacaaccbccabbbbabdaccdbddbdbcadbcdcdaaddbbcacaacbaaadbbabbdadaacabacddbdbbddcbbadbdcbdbcacdacdabdcaacadddabdcdbdcacabdddabdbdacbdaacdadbacbaaacdcbccaddaabdcdbcbbabbdddaacbbcdddbccbbcdaccbabdaccacabccddccbbabcabadbccdcbcdadbcaabacdaabaaadaddabaccdaccdcbcbaddcbaacdadcadaddbdaacdcccbbdbdabdddddcdaaaddbdacdbccccbbddadbccadbcbdbbdccaabdccbcacdacdbbacbacddcdbbbcddabccadbaaaadcdbdbdcbdcbbacccddaabbbadccccbaaacdbccacbcbacccdbddbbccabacccbdbcacaaddbacbdadaacbcbcbadddadbdacbacadddbdaacddabaddadbdbbcbcccdbadabdabcbbbddbaddbcdccacdadadcbbbcbcdddaaabcdccbcdacaacaaddabbacababbdcabadbbcbcbbabcccacbcddabddcdaaabcbdaacdabcaadcddbdbbddadccdaadcdbadcbaddbcdcacaadacadbcaaadddabdcbbcbcabbaadabbdbbdbcabdaaddadcadabaccaddcccdbdbdbbbbcacaadacbcabaadbddabdcaabbbabddbbbdbccccadbdabbaadbadabcbcccabaabccdcccadbdbcbabbcccabcabacabbcacccbdbcbdcbacabdcdaadcdaaaacdacaddbbaaddcdacbcbbddddaccadddcbbaddabacaadcaddcbdaabdcdabbcbddddcbdadadbdccbbbadadabdcbddcdbdadddaacabacabdcabcbaaabcbdaacbdbbcdaaacbaaddabadacdcaadadbaabbdaaccbaccddcadbbacddbbdacabcbcacaddcaddbddddbdbdbcbcccdddcbddbcbbaabbdaaddddacadccbcabdddbbdacaaabcaabcaaccdabddcbccddbbabcbdbdbabaadcbacaadddddacbccacbbdccacddadaccdbaaadcdaadabaaaabadaccdaadbcadaacbbbabdadabbabdabccddcbdbbabddcbbabdbacdbcddcadbaaddbcabbdddbdbcbbcdddaaccbddcbcdcabbadcaddddabbcdccbddbddddddbbdbcadcabdabccabcbbccdababadaacacbbbcbabadcbbcbcdbabbbdbddaddddbbaacbcaddabddabbacdcbdddacbabdddcdbbaddcabcccbbbaaccdbaadbbddddaabcccddacdbdaabbadbccccdcadddadaaddddcdcccbaddcacddaadcacdcaadaaacbaaddadbdbdbaaccccdacbcbbadbbdabbbcaccbaaaaaadcdbbdcadbccadbdcbdaabccdbdbbaaadbccdbccacdcbaaacdabcbadbabaacbaacccabaabacdddddabddbcbacacdcdcabddacbbdbaddadcaabbaabcbdcccaacaddadbadcdcddbdddccdacdbccccddbaabcbbdcababcdbabdcdcdaaadbccbadadddcbdbddbdbcbccbaaacddbbcdabbccdcabcbcaaaacbacdacbdbaabdbdadcaddcaadabcbccdadbdbacdaaccbbcbcbabbdacdccabbbddcdbbabacbaddbadcdccdbcbbdabaccdaacdcdcadacabdaddddcdacacccbddcbbbadbdbdbaacaaddbaaadcbaccbdccbbbccadabccdadacccbbaabcaabadddcaaadadcdcddcbdabddaccbacacabdbcadaddcbabcdbacaccbbabaabdbcbadcdccddacabccccabdabbccdbaaddcbbddcddaabcbdcabdbcadacbdcddcbdcdbabcddbbdcdcbacbbabddddbaaabaddaaabaaabcdacabcacadabddbaacadbcdcdabaadbbcbadaacbacadabcddccbdaddccccdbbcbcbcabcccdcaabbdabadcdcabdbcaabacbaddbbcbdbccbddcdbcdaadccabcaabcaaacbcdcacddbaddacccbccacdbaadbaddbacbcddbbdaabacbcadcbaaddcbbcacbbbbbddcbbabcabcbcabbdbcdacdbbdcbdabacbaabcabdbdbcbcdbdbacccccbbbcbadbddabbbacccdabbccddddaacddabbbcaaaccbcbdacbbdccdcdadcabaadddaabcdbaaaaadbaabddbddbabbdcbabbabacabccacccadaaccbbadcccddadbabcdcdddddbbcadbbbdccacdacabdcbcdaacbaacadbacccdaddbdadddaacccaaddaccdccdbbdbbababdaadabbdaddccaddacbcbacbbcdbcbbbddcbcadcabcbbddbdabcabccdbbdbbdbdbcccabddbbdbbcacdccccdcdadcbbacbbabbadbadaadbdabbdcbcaccbadbadaaddbbcbcbadbadaabccbabdcddadcddbabdabaddddcbcbcacabbcdaadabdaabbbbaacaacbbaabdabccadacadbbaacbbcdbddbabcdbcbcaaabbcacbdaacdbdbdabbccbdcddcadcbbbadbdbdbdbaacaddabacbdabbaaabbbddadbdbbcddacdbccbacbdbcbddbbbdabbbaddadbdaaadaabaacaacdbbbaacacddddbbdcdcdabddbacacdcdbdaddabccababcdacbdcdddaaddbcbcaaabcabdcdddbabdcadbabcabcabcaccabbbcccaacccdcdbbbdcdadaadccbbdbdabbdbdcabcaaabbbbccaacabcaacdadaaacdcdbcadccbdadddbcbbdbdbaabdaddcaddccaacaaaaddaddcdbdcbadcaaacdaaacbdaacbaddaccbbbabdccadabddbadaccbddcbbadaadabdbaccabdcabbdbadbbdacabccbbbbaaaabdbcadaccccdccaabccbcbbacaabbbaabcdaacdcbcaaabdbdadbbbccabdcbaccdadacadccaacdcccbdbcbbacdaacccacbbdbddbaddacaccbcdabaddcdbddbddcadbcbddcdbbdddccbdbddbcccddcaabddcaaacaddbdcbadccabdadbbdbbbdbadcccddbaabcdcdcaaaccbdccaacbdabbddadcacdcbcaccccdadbadbcbcdcdbaccdcdbaccdacdadcacbdbdbcadbadbcdddcadccdbabdccbbdacbbcadbabdcccdacccabadcaabbabbcacadbbdbbacbdccbdacabbbacbbbabcbbcacccdadadbbadccdadcabbddccbcaacbbadadddaddcbdcaabacdaccbdbdcbaabdbbcadaacddddbaabcbcdbbbbaccbbdabcdcdaaadbdadbbaabdccabbadcdbdbbbbccdbbcbadcddddcdcccbddddccdcbbdbddbadcccbcaadbabaaddbaaabdabccdcdbadbcdddababccbcccddcaaadcabbdadcadcbbbaccabbadaadbbabdbddabdababdcaacbbaaaadaabdabccabaacbcdbadddcccbabbabdcbdaabdccdccadbdccbcdbcbacccbcbadbcabdbbacaadadadbcbccbcddbccbdadbcbcbbdcdcaddbccacbcccdbbbdcdddbbcdcdcdadacbdbbbdbdbdbbabcdaaaaaabdaaacacbdcdadcbcdcacdabaacadcacdbaccacdbadddbbacbaccddaadbcaacadcdadddddadabdabcbddbbccabbdcdcccdacbbabbbbcbaddddccdbdaadbbcadcaaaacbbadabdddacdcacdcddccabacbacabcccdbcaccbbdccabcaaaaadaadddacaadaccacbacbbadbcadaaadbcbccbaabadaadccabbdbabbbaacaadddcbdabdaadbcaccaccbcbcbaccddacabcbdcdaacbbccbaadcbabcabdcbcabbacddbbbdcdabbcccccdbbbcacdccbabccbbcdcbdcdadacabacdabaacabdaaabdcbaadcadcaddbcbdbdbbbbadabbbbdbaaadaccdadccaaaadbcbaadbbbbbccbaadcbbcaddbdddcdccccdcadbdbbcccabacadabcdcdcadadabcbdababdacaaabbbddbdbdaadccddddadaadbdbaadabaabcaadbaaaddcdcccbdcabacdaabacabcdbdcdddcbbccdbdabcabbbaacaabbbbabadaaccdaddbbccbdbdbadbaddcbcadcaadcddbbbbdddbdcaaababcbbbcacdbccacbaddaaddbcaadacacabdcdbcbbcbbbcbadacaadcbbadaaccbdabcdaabdadcdcbdaaadadbacddcddcbdabddbcdbbdcdadcababcbccdcacabaaabadcacbdaadbcaaabdbaaaaabcddbabbcdbddacaaaddaacbccdabddbaabacaaaaababbaacabbbababbccccbacdaddcadaaadbbcbaadbadcabaaabddddcccdbacbcddcabbabadcbaacddbddcdacadcbdbbacbbbacbaaaaadcbdddbaccddadccdccdaccbdcbddadcccbcdcbdadbcbbadcbbbcaabbabbbdccdbdadbdcbcbcaacadbcabddcdbdccdcdbaaaaadbccddaabbbcadabcdcbdcdadaccbaabcdabcdbccbbdadccbbcabdaabcbdbcacccdcdbcdcadabcbcdbaacdadacddcdccbdaccccdbccdcabadcccbddbadccbdbdcacbbbcabccddddabbdadbccabaccbcabbcccddbcdbcaaaabacabcbbbbccdbabccdddabaaabcbacdcbacbdadaabddabccbacaccadbdbbbbdbccaacbbcdbcddbddcbadbbdcddbbadcbaaccbbbaddbdacaabcacccbaabdbcdcbabbcccabbdadabcabaadaadbacdbbcdccaaadcccdbcbcccbbbddbcabdcdcaadccdbdbdcaccaaaabdadcadcdabdaddaabccdadcaabaadadddcbbccdaddccbbdabcbacbabdaddccadaabcaccbccaccbccdbcddadaccbabaabdabdbcdddbdaaabccddcabbdcadbbddabdcdbbabdadccaacbaaacbbbbddcbcbabcdcddbaabbbaccdbddadabccccbbbbcdbacdabcbdbbacaabdbdbddddbabdcbbbdabddadabbbccbadadbccdabcbddddaacdadbcbbccadacdbdadbaabbacbbdbcdbdbcadacdddccddbbdccbbdabacbcdbbddabadcbdbacacdccadddbbdacccbbdadbcbadcaacddaaaccbdcdcbbdbaccbcdaaccacacaacbcdcbdadbadadcaabcababcdddddcddccadcbadcacaadbdabdccbdadcdbdbaaabacccdbdbcbabadbddcddcabaadadcaadcaabacbdddaabdadcccdaddacaddcbbbabbaaddbdccbabbbcbabbadcccdaccdbbacabacaaaababcddbbbbbbaaabbbacddcdbbdbcdcacaabbbdcbbbbdccbaddbbaaacdddbaadddbccabccccabcdcacbadbabbabadccbddbbbdbbaaacddbbcadcdbabadbbcbbccbdddbddabaccdbaadcddbadcdbcdacabbcddddcbccacdcdcacaabbccaccabddabbbcaddbcdcddcbdabaaddabddddcdddbdaacccadbabdaadaaacdadccbcacaaabdaaccbbbdabacbadbcdbaccddcbbbbbbcaababdcbddddaadddddcaabdcaaacaddbdbbddadbbbabdbbacacabbddddabdadadbcbdabdccdaaddbaddcbbababacbcbbaddcccacbacdbbdacdccbbaaaadaaaddcdacbadbbbcdcbddcbddcccdbdacabcaabbcdacddadcbaaadddbdddcdddccbdddcbbacbddccbcababdccdaddccacddacddbbbcbadbbbcacababbbacbdddabdbdbccdacddabdacdbddabacacdcbcccabddabbbdcbdbbabdcbaaadddacaaabbdbcccbcbcdbbdccadddbacacbbadddcacdbbccbbbaabbcadaadaaddddbaaaaaaaddaacdbabbadbdcdaddcbcccdcadbbaddabdadccacdaacaccaccdddcbdcbcaadcbbdbbcbbacdadaacdcaddbcbdccacabbabdacccbbdabaacccadaabccabaaddadaabdcbcdadbbaccbbbdcdbdacdacdddbcdbdcddbcdbdacdaabacabbccacbdbbcdddabaaddabdcabbbdcddbcadadbaccaaddcdadcbacbbdccacbdcdcabbbdbbbdccdaaccaddddbababcaabdddcacddcabdabcbddcbbabcabccdcbddbbbcacccbaccdabacabdcbacbdcccbdddcdbbbcdadcbdaaddcbaacbcccadbcbcbdaadcbdacdcabccabbbaddcabbdcabbaacdbbdabbbbcabbcbbcccacbabdcacabacddbbbddbaaaadcbdbdcdbbaddacddcadadacbbdcdbbbcdcdccabddbbbcdabcaacabadacbccdccccbbabdaadacabdccaabdbaabddccddddbdabdccbdbccbddcdbddaaabdaacdcccdacdadddcddacaddbababbdadabcdbbabcccdaccddbbccbdccdaabbadbdbbaacabbdabbbacabbcbcccdacddcdbbbcdcabaabddbcdadcaccadacdcdcaccdaacbabcdccaaadcbcdcbabcddadcdcdbbcacbbabcbcabaadbadbccdbcccdcacbcabacdbbbbdcaadadabbacddbcaaccddaddcddbababacdbbdbdbcbcdbbacdcccbbdbbccabbdccbacbcadabdcbdcacadccadbbcacdaccdcbacbddadcbdcaabcccadbdaccacabbbbcddbcdbcabbbaddbdbdddcddabacaadaadbbabbdcdabdaabcaccccadbadaacadcadbaccdcdaaaabbddbabdcddbabdacdbaaddaddacbadbbdbbcddbcbddbddbdadabcccdcbdbcbdaccdaddcdadbcbcdbdbbaabadcdabaacbaaddcbcdaadcbababcaccdabbacdbddbdbddabcccbbacdadcabbcbbdcadbadaabbabbcacaccacbbabdbdbdbadbcabadbaacabbabddbdbcaadbbbababbddcbabdddbadccbccdaaccacbdcccabbabcdabacccaddcdbcadcbbdcababccdcabbdbaacacbcdddbdddaaadaaddbababdacbbbadacdaccbdbbbbdbcbcabcccbcbcadcbddaababbccbdbacdadadbadbabcbdcdccbadaccddbbadccdbbbccbdccaccbccbaacbbabcdbdcdcabcdadcbdbbbcbacdbbdbddacaacbbcbddbbcccbaadbacbdcdbdcbcdccddadadadaadadbbcadadddadbcccdaddbcaddadcbbdcbcdccdadbacbdccadbaccacccddbaadadbddcccadbdddbadbbccbadacdcbdabbccdcbcaabdccdbadcbdbcdddbcbcbcdcbddcdcdcbdbaabdccaaacadcadcbcacbbcccddadcdbddaddbadbdbdcddcbdbaaddabdbdadccbbacbabcaaddadddaabbdcbcdcccdcbabcbccbdadcadacacccbadadbdbcaaacadbadabdabddaddcddbbbddcdbaaabddddaaaabdadcaccacabcadbbaaabbaabbcbcdcabbacabccbbaacbcadbbabcdbddbdaccccbcddccddccdacccddbadbadcccccddccdaabcdbdbcdaadabbcbadaabaaddadbcbbbcbadcababcdbdadbdabcacddbaabdabcacbdbacabbbdbcccadaddddcbbbccdddddaabcadadbaaddcdacdacadadaacddcdbcbadccadbbaddbadccacaacaddddabccdacdcdbdcdabbaadccdaacdddbbabbcbdcabccddabacbcbabdabcaccddabdacbbaccbabadcbdcbdcbcadadabcbdcbdcdddcbdbbccaaacdcccccdbaddbcaddcadabbccccccdcdbbdacbaabaddaadbaabacbbaacbdbcdddbccaacabcbdccdacbaabadbdbcdbcbadbccadabcbddbcacaddcdcbbabcadbabbdaadabadbadaadcadadacdababdccccadadbccbbbabcaacadcdcacdcbdadaacbacdcbcacdccddabccbcddcdbcdcdbdccddbaaacbaabcadbcadacdacabcbbbcbbcbcbdbadadcabbcccaabcdccccbacadabdbbbbdbcacabddbdaccbcbbcdbdbbabacddbdcdccbccdadbbacbdadabcbadacdaaddacdddbdacadddbdababacabcbccddbadacdcbacbacacbaddcbadbddcdaabbcbdbacdcabbdaaabdcdbbbbaaadcbaaadaacbabbdbccadaaabbdcaaaacccabcacadcbbbdbccddadababcccbdbabdccaddaacdbdbdbabddccbbaabdbaadaadbaaacacaccbccbbbbbbabcccacaccaccddddababccadaaaacdcbbbdbddbbabaccaaaacbbccdbcadbddadacadbccddcacadacdccaccbdbabbbaaccabbbbcadacdbdcdbdbbdaaaabdccbcaadbdbcbcbaccccadacaccabcabbddccbdacabacbbdcdbbcbadcacdadadacccccdccaadcdcddcbbdbcdcacdccdbdbdcdccccdddddabdbaccbbbdccbcabcdbcdababbccbaaaadbcbabbaaddcdacbcdbdddbdaaacdcddddadaacaaacccddacbbccbaddbbacaabadbbcbcdaacdddcdacabcbddccbcbbadadbcabdcadbcbacdcdbaaabdcadbcbdbdbcabadcdcdddabcaaacddbabdcbacbabaadaabcdbbbbcdcccddadcbcadcdaccbcdbcaccdccbbdcadcbadadabbcdddaccaadacabdccadbbddbdcaaabccaaaacaadddcaabaacdbccabbdddbdcbaccadaccabdcccadaccdacabdcdbababbddccbbacdacadbcbdbcbbcdbacccdcbcbcddaadadcccbcbabcadabcabbaaabbcabcadaaadbaccbccdaaaddcddcbacddababbcacacccacacaddddbdcaaacaaaccdacaacadaaddcadadcabacacaacadabdccaabababdabbbdbbdccdcbcbbaacdabcaaaadbdcdabcdbcccbaacabbbaadadaadbcccccaddaccdddadbbcccbdcdbbbccadbbbbbbacddbbdbccdabaabddbcabbbbcbbdadacccbdbbdabcddadcbabaccbcdddcaabacabdbbadacbbbcadaabdbabaadddaacaacabbbdaddcccbaabddcbbacbccabcbdbbcabbccdcaacdcbadadbdbddbadcabcadbcdbdbbaabdbcbbadcadcccbcaccadbdacdaccccdcdaaabababccbbacabdcddcbcdabcadcdddcbbdbdcdabbaaaadcdcccbbbcbcdbadadcadccabbdcacddacbabadcccabccbdcdabbbdccddbbcccabbbacbdbdbacbddddbcadcdaddcddaaaacaacbdcdaadcabacbaddddcaabaccaccbbcadcdddcadaacbacdcbbdacbbbddcabcdcbdaaddccbdddacddbadddcbcacccadbababcadbaddadcbabcaacdaabdcdcbaddbddcdbaadbabddbbcbcddbbbcddadcbaccbcbbacadadbbacdcbabaaadbbbdaabaacbbbdccadbcccbcabddaccddcaabbdbdbdacdaddbbddcbadddcddaacdcacbbdcadbcccdbdbdbdcccdbddbabaaacadccdbabcacdbbbaaaabdddabbccdbacacadcbaaabcdacbccbbcabdccccbbdadadbcacaccddcdadcbacbbbcdcbcaddbdddccdcacddabdadabcdadbdbdbbccadccbcddccaadbbccaccabbabbaadcaccdcbbbddaacdbcdbbdacacdadadcacbcaccccbbacccbbaadbdaacbdcddadbbabbdcccadcdabcccccabbcabdbabadcbbdbddabbccdacabddaabcbdbbbdaaddcabbacababcddddddabdbaacddcadccbbbcabadabcccbbaadddbaddcdcabbdbccbdadbbaddddccadddcaadcdbcabadbbdcccdabbabdbccbccacbdadbcbdaddbbcdbbbdcdbcbbcadacbcccbddbdaacaccbcabadbadbbdcbbdddbbdbadaccbcdbcbadbdccdddbdabdadabbddacadbcddabccdcbccbbadcbccdacbcbbcadbadddadddcccadaccadddcbbabdcdaaccdcaaaacaacabbbcccbcdacdcaacdcabdbbcbacbbacdacacdbddccbccccddadcaadbbcdcdbdcdddadbddcddabbaddccccdccbbcbbabbbacddaddadabbbabcdcddaadabcaabadacdabaccdabdbcbcccaddbcdcabddccacbbbccbadcbdabbaccbccddcdcdbdcacbbbcbcdaabbaabdacbbacdbdacacbdddddcbccdbdccbcbbcabbaddabdcacaddadcadacabbcbbdaaabaacddbcacacbbbaaaadaabbbadbbdbbcaadccccacccdddccdacbbbddcdddbbdcbddcadcddadcadacabaccdcbaccbcacadacddccbbbbabbccabcddcbadbccbbbbcadabadcabbaddbcdccccbdaddddaacbddcabcaddbcadcbbacbbadaddacacbbaaaabcccdbddcbdaadcdabacdcdccccdbccabbbddbddacbbabbdcabddaaadcacacdcbacbcaabadbbadbcbdabcddabacbcdbdcadccdccbacddcdcaabbcaacccbccaabbabdadcdabccaccddbaddbdccddcabcbbdcbdcbdbddcaccdbcacccadacdcadacdbacdaacdbadbccdbcacbabbcbbbbbdcddccacdcacdbdaaccdccadbdabaacdccbdacdcaddcacbddaadaadbbddbaadbbccbacdaaacaacbccacbaaaddbbcdddddabcbacbabdcdabbbabbbaabbbcaadcacadbddbdaadbddddcccbbaaaadddabdddbddddbdcdddbacadbcdabddcdbbbddcdacddadabcdcdbbdaaaaadcaadcddddbdcdccbbcbcbbbbcbdbdcbcdbbcdacbaaacdcbaaaacaaadaddccadcbabaddabdcadbacaadaaaabaccbadddcddbbcdcbaadadabacacbaaababdcadacdacababbddcdababdadacbaababadcdbbbcbadbcaaaacadadccabdcccdccdbdabdabdbbdcabacacadcdacaabccadadaacdadbcabbdaabcaacddcdcadcdbadddbbccadcccbaccbcddddcadbacadacdcccbdddacdbaacdcddadaccdabccbaababbcacabaadcdcaacaadcbdbdcadddcdbbbdcaadddbaddbdbbcbbcccbbbacadbaccddadbbdbcdcccddcddddbbbadcbbcdaadabbabbabbbbaccdccdadcbbcbcdcbcbdaabcbbdacdcabccdabdbadcdbccdaaabaabbbcbaacdadcdaabcadbdcdadccadbcbbcbddbabcbdadbbdcdcabaacccacabdcbbbdcccacbddadbdabdbaadadbaccbcdcdabbbcabacaabcbbbcccbcccbdcdcdbabaacbbbcadcddcdbdcacbcbccadbddaaddadcaccdbdccbcddbccbcbacbdbaadcdbdabbbdcbdbdadcddaaadccbbdcdbabadbbbabbaaabdbabddddabcbbadbdaacabbbbadcdcdacbcdcaccdabcbabddcadcbbcadbccacddcbbbcabdaadbaadbcbbcdddbaccccbadbddbbcbcbacadbdddbcbaadcdabdbdbbabbbbcabdaccacbbbddaacbadbbbadcdcbbbddddadccdddbdadaaabccbdcbcddcdddcaddcbabddccdaddcacababdabcabadccabccbaccbcbacbbcabccacdadcabcdcccbbdcdcacaaaaadcdccbbbbabadcbccadbadabdbbbabccddbcdaaadbabbbbdadbbbcbcdcaddcdbddcddcacccbadbbaddccbadddabcddbacaccaaccdbdabbddccabaacbdbcdadbdcdbbbbcbcdddcddcacaddcabababcacadbaaaddbbbadaabbccccdaaddccaddadcacacbacdadbadcacaddbcdbadadbcbcbcaddbaadbaabccbacbdadcbbabddaabbcdcadbbcacbaccbddaddbaadaadcdbadcdbbaadcbbcdaaaacddadddcdbdacbcabbbabbcaabdcddabbacdbdddbcbbbcbbabaabdaaadadcaabbdbcbccabcabcdcddadadbaaabbdbadbcdaaabacbbcdadbcabcbdbbddabcbbccaaacbcccbcdaaacdaacbaccbbdbcdcbbcacadcdacacdbdcddccdddbababaabddbacacbbbbdcacacdbbdcddaaaaadaccadacccbbcabcbadadbadcabdaddbaabccbdcbaddacccbbcaaddadcaadbdcddbccbaddcbadbccabbaccccacaaaddcbdaacdbbacbbaaacbbadacbcaadcdadccccbbbccbbdadaddabdcdccaadabcacabadddacbabaaaadabbcbacdbcabaadbcabbbddccbbdacddadaabaccbcdcdbabdcabdadbdccbdddcbddbabbbcadbadadccaaacddbdbcadddcdabdadaacbdaacbdaddcbbdcaaabdacdcdbacbcccdcdacdbbdaaadaaddbdcbdabadcccdadbaabbddbcaaddadadcbadccbdbbbbccadccabdadbbabdcddabdabbadbcbbdcadbccadaacdbabaadbdcccacacaadcdaaabacbbdabdbbccabcdcdcbcaabcbcaccdcdcdadddbcccaacccabacaacdbbddbdcbbcccbbdbcacccbdaccccbbbbdabbabaacccbcdcbbddabbccacbdaacbaddbbdcdbcbabbddbdbaabadddbabdbbaadadacbadbddacbadcaabbbdbaccddccbaccabdadaaabccbddcccbdabdcabcbacbbcaadbcccbbcabaadbccaaaccadddcabcadabdcaadabaccbcdaccbabaadbacccdcbadabcabdcbdabcabbbcbbcabcbadbcadacccccccdacdcacddcdbbbaccabdabbdbcbbbbbcdababaddbaabbadadcaacabbadadadcbbbddbdbddccacdacbcdaadadcbaaadabacbabacbbbdcabadcddcccdbaacbabddacdbaccbadbccaabbabadcadbcdcdbadcdbccdbcbbbbddadcbababcdbccbdbcacbcbbcaadbcacddddcbbcbddabdddabaddbbadabaccabcccbdbdbbccbacddccacbdcbbaadbbaacabbaccdcccdadddcaaddaddaaaabcdbbccaaabccbabaabcaabcbccddcbaddbbbdbababddbdbabcbdabaaadcaadbbbddcdabdadcddbbcdcabbbabdbdbbaaabdcddbcdacabcbdcbbdcbaadddabbcccdccabdddcacddaaddcaaccdbaddbdaacacbaadddadcdcdadbadcdcccdbabbbcdadbaaabdbbdbacdbadacaddccdacccbddabcbadccbcbbdbddcaaacbccccbccdbdbcadcbbaaabdcbbacbdbacadddcdadccbdccadabccdcdadacdabccacaaddbddacbabddcdddcaddadddbcdcaadacbcccdaadadbdacbbbbdbbddaccbdcdaabdcdccbbcadbadcdbcdbcaaccdcdcbddcdaababbcdcbddaacddbaccddcccdbcabababadcbadabccbbacdcbccccdaddbcacbdbccdcccccddcbabcbadbddaccbdcccdaacadabaacdadabdaaacdadacbcaaaaddcbadcbcbbaabcbcddbacbaacbaadbadabacdaaabadcdadabadcbadcaaaabdabdaabcbaaadadbaccdcbadacccadccabdddcbdbcaddacbdcdaadbaadababbddaacacbbaacacccacdacbdbdcccdbcccdbddadacdcdbbcbacbdcdccadacdcdbadcccdcbaaaadacbccbbccdbbbaadcbadcaaabcccdbdababacacccccaccadcbdcbbbcdddbbcdcbcdddbccabbddbbbdbbcccaccdccbabcaabcdaccdcdddbdadacadddcdbbdcccdadbddbbcacacdaddcaaadbbcdcacdadacdaddbddacdccbcaabcacaabbbbacbdcababbccacbbdbbbcdaadaddddcacaabcbccdbdaaddbddbabdcabcaacbbbccdabccdadcdcdaacbddadabddbbbcbdadbbbbbdcbddaadbababdaadaacdbdabccbbcdabcdacadcdcdbdbacdbadaaccddadadbcddbccbacabcbbdcdacdbbdcbcbadcddaaabbbbadadcdbdbdcaccdbccddaaacaaddbdbacaadddbcabdaacbabcccaabcbccadabbaabacadbbbaddcbcaccdcbdbbbccbbdaaadbdaacbbadbdcdcbcbbadacdccddcddaccbaaabacddbdcbbabccaaacbdbcacccbacccbabcbababacdddcdcbdadcddaddbcbabcdbdadccdacacbbdacbdccbdacdbbbababacdaabbdababccbabcacadccccacbbccccacadddbabdcdcadcdbcbacadaacbacdccadcbddddacabbcbaadcbdabdbbdbaadbddbbddaabcbbcacabddcabbabcbbacaabcaacdcacddbbaddaacabdbbccbcadcdbbbcbcddbaacabbbccccaccabbdcabddacccdbdcdbcabadabccababbbaaacdbdcdbdbccbadcbddaacccaacaaddacccdcbdbbacaadcbdcdbbbbccdbabccddbddcddcbcabcabdbbadcbacdadabcdbbaaabcaddcabcadacabbcabdaacdabbbacacabbdaadbcdcdaccbbbcacdcdadbccdaabcbcdbcabaadadabacccdbadadccdadcaabcdacdddacbbddbddacbdddcaabbccdddacbcdbcdcccbbabbdbbabacadbdadbdbcbdcabddddbbbaacdcbdddddbbaadcacabcadbdcdcdcabadbccddbbddacbdbababcabcdbcabaabaacbcbdcdaacbdbabcbaccadbdcaaabdacabadbbdcdaddababddcadcdbccccbdadaabbdccdacdabaacdaccacdcbbccddacdbddbdacbdcbadbbacaabbbdcbcdabbbadbdcbaabbdadaaabdabccdcaabcdcccdcbacbdbabadbcddcadbabcdbdbdcdaabcbccadcdcaaaddddaabdccaabcddabbddbcccddacaddbdcbdcadacadddbaabcadbbacccbababdbadbcccdabcccdccaaaaadabcabdbdbdbbdbabaabcacadbdcdccdaacaabacadcbbaddaccdcddcbcddbbdbcabcdbcaddbabcdbdaddabbdadadccbbcdadbabaddaacbaaccccbbcbabbccbcaadddcaabddadabadcbaaabbadacbbbcbcdbbadcadbbbadacdddddccdcadddaaacbbacacbcddcbddaaaccdbddbacbccddcbcdabccbbbbcaabbbcacadbbcccaccbdabbbbcbddbbbccdadddddbbbdcaabdaaabacbcdcadccaaddbdcdbbbcbaaabcadbacccdddbbbbbcbdcccbacdcdcbbdacddaccccbabbacbaabdbdbadcdbcbdbdabbbccbcadaddddacdaccddaadaccbddbdbadbabbcddacabdcbdbbdcdcbabdcdbabcacabddbbacaaadadbcdcbdcbabadabccaaaccccbaccdcdaccbaadacacabcaddddcaccaabbcadbdccbbdcacaccbccaaccadbcabbdaacaaccccaccadadabbbcabddaacaadacdbbcacadccbcccacccbcdbcbbddaadcbbccaadbacdabaacccdddcddcaddcddcaacadaacdbcacbddcbdbaaaabadcbadcadccdcdabdaccdcbaadaabaadbcabdaabcbdbbaacaacbacdacdbbbaaccbcacbbddbcbccdacbdabbbbcdbbbabacbddaacdcbdcabdbcabadcadbcccdddbcbadadccbbbcddbabccbacdaadacccaccdcbdbdaadddaadddcabbbdbacdbcbbdabacbdbcbbbbccbaabcaadbcabacbcdddacaadadadabbdbbcabdcacbabaadcdbdaccbddbbdbcbbdccbbcbcadbccbcbbdaaabdabcbbcadccdbdbccdccdaacdbacbbbddbccabbaadbbcccbdbbaacbcbbcdbcddabbddccdddaccbacbdcabcdaaadbccadbbdaacacbcdbaaadabaacdaccabdbcddacbabadddabbbcddcdddbaabdddcaabcbacbcdbcacdbdccbbcdbadcbcbbcbcddcdcddbddcddaddacabccacadcdadbdbadaacaabaacdcdadcdabddddccccdabbbcdaccbbdaccbdbdddbdacabdbcbbdaccbabacaccbaaaddcabaacabadbadadadddcbdbaaadaaaabbbbbacddbcadabbcbabdccdaadddbdcdbcdaddaccbabbabcacbcbabcbdcabcaaacbdaadcbdcacddacdacccbbddacbcaabaccdaaacdbbcdcabbadaddaacaaadacabbbaddccdadddcdaababbbabdabccadbadcccccbbaccdcabddccabdabcaadbaaabaccaadccbacacdbccdcdcdbbbcddbddbdabababbcaabbcdaaddbcadcdbcbbadcacdbbacabccadaccccbaddcbcddbaacabdccdbbadcccadcaacccccbbbdadaacccbcbadccbbdbcabbcccabccdabbddccbadcbbddbccacdcadbdbdabbadadbcbbbcbadacbcccadabdbbbddaaacdbcdbcdbbdcbcdddadabbddbabdacababcbaaccaabdccbbadbbabbabaacabcacaacbdabccacadaddccdcbaabcabccaacbddbbacbbbbddccadcddcaabbbadadbadabddcbbbadcdbcaaacdaaadacabcdcaabcdbacccdbbacbbcccbdcabdccaaccadbcbbabcaaabcccdababdbddadbcddbaabadcddaaccdcdaabdaabdcdcaacccadcacddbccacbcabbccddbcabcddcaabddadbdccddbbdcbccaddbadddcddbbcaaccabbaaccabbcaabbcbbccabddcddbccccbcdddaaccdadbadcdacaadbcccbddadddcdbbacbabbbbbdcdbccdddbbbbdccdbbaabaabccaabbbdacccdbbbddccbcdccdbbccacdbbbcadabdbbbdbdcbbbcddaacadddccbabcabcdbddadcbccbbbccdaaccaaccbdbbdbbabbacadddbaccacabaddbacadbcdbbbdabdadadccadbbdbaddacdacbaadbdaaacddddcdbddddbccbabddbabbadbbdcadccacbccbbbbccccddaabdadaacabccbcbcbddcaabacccbabdbddaabdddadbbbcaacdbbbdbdaadddbbbdbcbccadadcdbcdcbdcacabbbbbbaaccbabbcccccccaddaccbbdabcbdccccbbdadabdcacaadddbdbccccbcacccdacacdadcddbaacbbbdbaaabdaddcaccddbdddbcabcadbaadddbdbccdbcdbdadccdcbdccdbccbadcbaaacddbadbbcbacdabbccaddacdaccbbbbadabdaadaddcbdabdcbccbccaabbcdadaadccabaddcadbdcdbdcacdcaaaaabbbadbcaddddcaddadddbbabaccaddcdbbcbbcccbdcbcbdcbddbaacbadbcbaaabbdbbbacaadbdbbabdbcbdacadbbbaacdcbbaccabcdadccccddddccddcdbbdddbcdaabadbbdaaccbbdadcacbabbbcadcdbadbcdabcabccbdccdccdddccabcbabddcdccdcbdbdaadadccccabcdabbbdaaddbcccbcddccaababaabbddbabbdcdcdaaccdacdcbbcbbbbdbbabaacbddccaaddacadaccbcabbadabbcddaaacbaadadaddbaacbdcdadababbbcbbcbacdabccdabaabdacbdbccbcbaacbbcadccacabcdadbbbbbbdbbbcadcbacddacbcbcccccbcaadacdddbdddbaacaacdbaaabccdcccddbdbacaaadaaaabbccbcbcdabddbcccabbccdbaacdaccbabdbdcadcddadcbccccacbcaacccbdadddbdbccdbccdcacddabdcbbdcbbddbbdbdbdbdcdcdcbcadadbbdcddddddcadabcbdaaabadaabadbbdabbbcdcbcbccdaacbcdabcbcbaadcdabbbbbcabcacdabbacbbaadbbbbbaadbadadcccdcaccddacaddcaaadacdccbcdcabbccbbacadaccdcbdaacddadcbcdadbbdbaacbdbdadccdbcaddbdcddddadbdadbdcbcddcdabbbadabccaaacbbbdcdbacdbdcddddcadccdcdbdcbcaddbadcdacadaddccaacbcbbbbadbcadbdbbabacadaaacbcdccdacdcbccadaabdababcadcddbbdbbcdcbacbddbcacdddcbbbaaaddabcbdcabaaadbacacccbccddbdcdadadbddaadcacbbbccdcaaaccbcaadbabaacbadbcddcbbcbbddcadcabcbbbacbaddaabbddcddaddbbddcbcddbaccabddddddbabbbcdbbdcccbcccabcdbccabaabcabdabdabbaddbacaadaacdddbdbbcdabadccccbddcacdbcccbbbbbddbaadcaddabbbcbdadbcabdccbbdbadababcdccbdcbcbacbdddddcbdbddabbccccabaaddcabcccdcdacabdacdbbadabbddccaaaddcabdbadddcdbccaaddcadbddcbadcdbcacadadbddcaadabadbbdcdbcdbdabbaddbccadbabdddbaacbbadcdddbcbabcccbbcdcbbacbadccabdabcddccdaaabadccdcbddbaaabbcadccbdccbbcbabdcbbccdbaabacadbaaacbcddcddcacaacbbccbbcdbccbcdaccbccbdccaaaddaddaccccdbaabdaabcdcaccccdbbddcbcbdaaddabbbbcbaabbcabccbddacbdcbbdddcbcacdbdabbdcabaadbaaabbbccdabaaccddcdaddcddbdbbacdbcdaaccddbacadabcdadbadaacbcbdbcbdacadcbdacdadccabaddcbbbddbbbbdaacbcbcadddaccbcbddabaabcbdabacbccdbccddaddcddacadacbbcadcbbbccbdcddccbcbcdbaaccbbadaddaaaccdaaccddbacadbbcdcacbbbcbdabccbbbcccbacdcccadcadacbdaaacdbcbcdcbabadaacdcaaadcaadbbdcddaadcaacbaadaaadaadaddcddcbcdcbbcbccbdccaadbcddcdaaacbddaadaaddacbaadabbbbaadadabcdcdddaddcdbdcadcadbbbbcdcacaaccbbbaacbdcbaacacbcbdadbcdbcdbbdccabdbcbddbbdcadddbaacdbcdbbbcdbcbcbabbadbadcddcacddccbcbdcbdddcdbbbbdaabacbdabbcdddbadbbcacdcabaacdddbaadbdbacccddaadabcacaccdcbcddbbcccdbcdabaddbbcdbacdbcdcadbbbdcdacdbbbcdaadcaddaccbcbaacbbaadaddbbddbaaabbaddaaacbdaacacaadcadcaadbadddcbabcabbbaccaaadcdcbcccadbbdabcbaaadadbccbccadaaabbddaabbbcdacdcdabdcabcccccdbbdbbababbcdcdbabbbdbbbbabaacbacbcabccbabdaacaaccdadbbdbdbcdddacadccbacbcbcdcddddddcddaccbaabddabcdadcbacbdcdabababccaabdadbdcaacdadbbadcaacacbcbbdaadcabaaabacaadabdbadadaccccdbcaddbcdbddadbbdcabdcddabbadabcabcbddcddcbbababddcbacaaaabccbbcbcbdbcdcdddbdbbacbadccbcddcacacdabaabadabcadbddbdaabbbadddbcbadbbabacdaacdabccbcdbdddabbcbdadccbcccaccadbbdbdbbaabddccacdccaaadcccbcadccaaddbadbaabbbabcbcbcaadacdcdddbaaadbabcbccbaabccadbaababbccacbaccaadccbbaacdbdccbcddadadccccdcbbcbbccacbbcdddcddcdcccdacbdbdbaacddacaabdaacaddccabdcaacacaabccaccdccddccacddddbddcdccbdcacbdaacaddccadcacdbabbbbbaccdaacaacdbdaddbbacbdcdabaccbaacdadcaabdaadabcbdccdccdabdadbbbdbaccbcbbcacaacdbadcabddccdbaccddacacdaabcaccabdcbdccdbcaccacdacbaabcbaaadccaacaabbdcbcbbaddadacbcaabdbcbdbcdaadbdacacdddbabadcadbabcbbbaaadaabdbccddbbdcacaadcdbdddbdddcacaaabaddacaacbdcdacadaddddddccddbcdaacddbadcdbbcbccbddacaccbaabacdddaabbcdaccdddcabbdbbcadaaabbdbdaacbabdcbbaccacbdabadbbabddabbbaddcccabaacddaabacdcbcbddbbbabcdbdcdadbbdcbadcccaddacadbcdcbbbdbcbcdbbcdadbabaacadcbbccbabdbcadbcabbdcddbdbdbbadaddcccdcddcdccdbabbbdbdabdbdccbccbbadadcbcccbddddabdaadbdadabccabbadbcdcddbdbddadbdbacdacadacadcaddcbcdbccbcdaaccacaadacdddcccaadcadacdbbcdabddbacbdbbbddadbbaacabcacdbdddbdccbcabababcaccbdcddcdaaddaddacdbadcbdbdcddccacdddcdbbadbcddaddccbcbbbdcbbdaadcaddbdcbdbddbbadcccddcbdddcaabcaccdadbccdaadcccbabcdacccdcccabbbddbdcdaccdcdadddacbddbdacbccbcaadccdbcabdabcbadaccbbcbcaaaacaadbcabcacaccadbcadabcacabbcabbdaddbdabcddcadccaadcbacadcbccddbddcbbcabbccddacbddadbbdadcbddbddcaddaabbcccbdcbadaabbccdbadaaddcacdcbbbdbdaadabccaaaccdbacadcadbbdacadcbdccbddcaddbdcdbadcdbbadaadcadbdadbdbcbbcbbadcbbdadcbdaccaabcacbabcdcdbcbcdcbcaddadbaadbbcddddaacddacdcbccbcdbcddbadbcdcaadaccdbccaadbbadbdbcdbaabbbdcddbdddaadbbbabbcbdccadacdacdcabdaacdaddbdcabbdadcbaaddccddccddbbacddddbaadaadcbdabbbbccbdaabdccaacdbddabaddddcaabadaadbcaccaaadabcdacddbababbdbacabbabccbbcdbcccbdbbacbabbadcbcbacddbccabcccddbaddcdadbdcdbddaaabccbacdcbbdbdbccbdbdacdddadaabbbabbbdbcaaccadbcaddacaccacbddaadbcdaccbcabaaabcadbbaadddbccddbbaccacabdcacbcbdbddbcbbdbdbabaabcadcdbcddddddababdcbbacbbcddcabdacaaacbdccaccbccdbccdddadabbcaacddbbdccddaadbcabcccbcbdbbaabacdaabacdbbabbdaccaabdaabcbabbdadcddbbcbbacbaccacdcdcdaaabcbaabcbabbdaadcaaabddbcdaacaddccbdabdcddadabacddbaababdbabaadabbadccbdcccccadcdcddccccdcbcdccbddbdaacbbbdbddcdddbaaadcbcdcaaadaaddddacdacccdacabdabcbcccadccbadaabbadbbbcacbcddacadabaacbdccbabbcbcaddccacdcdcdcbddbacdcabbbadccddbbacdaccacdcdddbbabbabbbbbdacdabbbdaccbcbbbaadabcbadaabbdacbcdccadbaaadcdbaadcddadabdcdaacabbdaaccabcdacbbddcdbadddcdcaabbadaabbbcccdadbbdcbdbadaabdcabccbcccdadddbdbabcbcbaadddbcdcdcddddadbbbaacbcacdddaaacaacbdbdbbccbabddbdbaadaabbabdccacaadbdcaaabcbdadcbdbbbbbddcacabccdacdbdbacaaabbacbbbcccacadbaddaddbacdcbbbaaddcadabccdadaaddaaabbdbabbdaddcdbdccaadacabddbcbdbbddcadaaabababddabbddaadbdddacbdadcadabddcddcdbcdadcacaabaddabcdcdbdcbcdccbbcdababdddaacbbabbdbdddacaacddddabbdbcddbbdcbdcbcdbddddbdbcdccadabbadcabcbbdcccaccadddbbdbcbcdcdbcccbbcccdabdcbaabaaaddbbcacaabacbddddbdbddbdbadadcbccadddabadaddadddcaacdacaccabdcbaadbdbbbbbbabddaacccbcdbddbdcbbcccdabbcdabdbacdcbaaaadadadadabcdabaddccdbcadcadccddddaaadbadcdabdbcbaddaaccddbaabcccbdbcdaddcbbabddbdbabccadcddcdbddacadcccdcbabbadacabadbcbbbabcdcbdaccccaadddddcbacdacbbacabaaacddcccabcbacbbabcdcbbdcdaaadbabbacaadcacacccdbabbdbcaabbbcbdaabddacdcdabadccaaadbacbcbdcbcadaacacccbbdddaaccadbbabcaaacdbcbcabdaaccdacbacaabcddbddabacaabccbbdabbacacaccadcbddbdadcbbbacccacccacdcbbbabdcbcbacaadbdddcdcaaacabbdcaaacdbddadcdabdcdcababacbadcacaddabddbcacbbdcacabaaabadddbacbbdcbbcdbacbabdbcbdcddbdbccbdaaabadaacaaaabbccbaaaadbcaadaaabbadabcbdbacaccaccdabbccddbacacbaacccbbccabdccadddcbcddbaaabcbdbddaadcdaccbcbaadccadadabaabadaccdcadcbdccbddccccddbbdbdcbbadabdbabbccaccdbaaadbaaccbbcadddcababcabdcabadcacacacbcbdbbcdbccdddabaccccaddcdcbacbccaddcbcddbabddcacdccdbbcbbbababaabcdcbdddbbcccccccccbabbacbadadbbcbbdcdddacbabbabbcacddbdbbcaaacdbaccbbbbdbddcadcdbdbbdccbaddbcdaadabcacccadaadccadccbcddadaacacbbdadbabaaaaaacccdbbacbabdcadadadcdbddcadbdacabbabbcabdddabbacbacbdccaacbcadacaabaccaddacbdabbaddcbaddbcadcabadddddadcaaadcaadbdbbbadbdcdcbaabbabddacaaadcddabacccbddcabcabbbcabcddbacaabacdacdbaabbbbcbbaaacdbabccdbcccababbcbbacdbbdcadbdddaacdcbbbbaacddbdcbcaabaabaadaaacccbbcbdbcddbadaddadcdbadacbdaabdaaaadcbabbbacadbbdcccccdaacabbbdbacdbccabaccbbcdcdacabbaabaaaacacdbcaabcddcbacabdddabaacdcaaaccbcbcbbcdbbbddaddcddcbaddbbbabdccbaadaadcccdaabdbcdbbccddcaaadbdababccacbdccbabdaabbbcabcaddcdadbccaababacdbbbaaccababccdbdcadbdbdbabdacacbcbdbbcbacbbdddbacadbdbcccdacdacbdabcddbbdacbdabadbcbdccaadbcbadddabacadaacdcdbadcdccdacbaabdacccabbcadcdcddaddaccddbcdbbbbbabddbbcacccabcaaaccbacbdbdbcddbacaddbdbbbdaaddcadaaaccbdbdbacbbdacddbdcbbdbbabaaccbdbadcadcadbcbcbbadcdddbbadaaddddbcaaadadcccadacdacbbacadbdbaacdcddbacacdaacabdccadbcbbbbbbcaccbdadbaadbdbacdbacbaabbbbbadbbdcdddcbaaaddadbaccbaaacdbcbcbdabdadcaccacdadabbcbbadcbcbbbdbdbbacdccadbbcddadcdbbaabbdaccbbdbcabbdcaabcadbacbddbddaabbcaaacdcaddddcacbaaadbcbcbcacbaadadbdbdcddccabddddbacadbbdbacabcbbdacbbcadbadcccabcdaaababcbcbccdabaaddacdabbabbcbcabddccdaddabccabdbcbbbdaddbcacababccbabcccbbaadccadbbbaddcbaadcbbbadbcbbadbdddccbbabbccdbacbabcdbaadcadbabcccbbccabaacaaaabdbbdbcaadbcdadccbccbddaaaabbbccdadaacbdcabdbbabaadcaccbcacdabdcbacaabccbcdacdbcbdcbbbdcddbdbbdbbcabcaadcdabbdddadadabcaaddccbdabaccbbaccbcccbaacddcabdaacbbadadaccbbdaacadbddcdbdacabbdcdbaadbbbddbbaabbcaaadccabbcddbdbbadbadbbccdbdcaaacddcbbdbccaacdbbabbddacbadadbabcbabbbaacdcadcddcbaaadabbdbcbababaddccdbacabbbbccadbdabdcddbddbdcaacdbdbbdbbcdacdccddabcbacbbadacacabcdcdcacababbccaddbccaacadccddaccabdaabbdbbddaabbdbbaaadcdcddababbbdaddbdddcabdcdbaabdbccdaaacaacaabcbddcacabbcdbdcbacccabacdabacbacdadbcbbbbadccbbdddbbcdbabbaccbcabbcbcbdbaddbbaadaaaaccbdddadbacccbdacadcbdbaabdcababdabdcdbbcbadddabaccaddacdabdccdbdddabcddbbdcdccbcbdddabaabccbaaaccacbabdddbddcabdddacddaddacdacbcadbadacacacddabcdbaccdbdcccdcbdbbcabaaccbbaaddccbdcdacccacaaddacbaabbbcacddbbcadbbadadbdaabcadbdbbdcbdbacacaadcdcccdbdbbbcbbdcaabacdaabbcccaccccdbcbadcadccbcbdbaaaaabacdddaaaadddbbbbdbddcdbcbdcbaabdabbbbbcbaacccdbcdcaadabdaddabdadbaaaadccdacaacbaacbddcbbdbcdbdccbadacdcbabbcdcbacdcaaaabadabddcadcbabcdbaacccbcddbcadcdaddcdbacabcdccdcdcdbccadbabcabcbbccdbcbbabbbcadcaccddacdcbddcdccabdcaaabdaabdbbaaadabbdbaaacbbdcbbcbdccdbccbdccdbaccbccbcdcccdbdddddbcaccbbdbbacdcccddaacbddacddbbdadadddabbdcbadddbcaacdcaacadcdacbcbdcbccaccdccccbaabacabadadacdbdacbbbbdddcababacbddabacccdccaaacabcdaaddbdaacdabcacddddddacdbdacadcbbbdcbaadbdaaccdbbcdcbacddabdcbacabaccaccacacaadbcdbacdccbcccbaddadbaddaabbaaddcacbaaabadbbcdcaddaaaadcadbdbbcaddcaadabaaabaacbddddaddcabcccaadbbbacdbbacaabcdaabccdadbddcaddadccabdccadadbcddbdbcbbdcaadaddbacabbdbbadbaddabbccbcdccbacdcdccbddddaaadcbdbbbbabaddddbcdcddbddcdddaccacdaaadcdbdccabdaacaacddcdaacccdbdabbdddddcbcdcbbdabacadaccbdddaacdadbaddbccbddddbaadbacabdabacbcdbdaaacaacccbbaccadddaacadacccdbbcadbbacccabdbccabcabdbbdcacddcbdbdbdaadbbdbaddbbdcaccaddcacdccbbadcbacddabadcaaccacdbbdbdaacdaadcabdcadbabcdddcacdbdcbbbaccaaacdccbccbdcabbabdcabdbddcdcdacdcaadbcbdbbccbabaacdaaddadabadddbcbbdacbacacacccadaaccabbaacaaaadcadcbaaadbaadcbbbbcbcabdabdcadacabbbcbdbabadadcbadddaccbcacbaaccabddaaccabddbddaaaddbaacbacaadcbcaacdcdcbdacacddbcabddbaabaccddadbcaadccbcdcdddbdcbddacdadddabbbccbcccdccccdbcabaaaaaacdbdccaaadcbcacdabbdbcadadcdadbbdbcdbbaaadccadddbdbbcabbcbcbddcdbcdcdbcccbbdabbdbdabbcaadadacbacbcdbbbbacadaddbacabcaacaccdcdbddbcdccaaccbdbdbcdcaddcdcddadadadbaaabcabcdcabdcabcadbddbaaabddacacbddbabdabcacbccdcbaaadbdababadcaacbadbbadbabdccbbaadccbdbcbdbdbdcabddacdddddbabbaddcdbcbaadbdccbdcdadbcbdbadcbdcddbdbbacabacacaabddaacbbcdcbbaddbbcbcbdbbcaaadaadabbccccdcbaaaddababcdcbbbabcadadcacaaddacdacdabcadcdabacacccbddbadbdaacabaaddadaaacdaccdddcccdcbdaccbdddddbccababdcaabbbccabacccbbabdadbdbbbdcbbcacbaabaadcacdcbabdacaadbcbbccdacacacbcdcbccbcdcadccadcdbdbabdcdccadcbbddcbbadadcddcddcbcabddbbbacdbccdadaabcadcbbbbbbdabbdbdcacabbdaaacacccaaccbdbcadddaddcabcbdcddddacbbadadcdaaaabbaaddaaaabacacabbadcbbdadaddccdadacbbbdcbdcaaaccaadbacdddbdcadcadccdcaccacbadbccdcaaaadcbaaadbaabdabcbaabbabdbbbdbaaabcaaccaddcdddcbdaddaddcbaacdbbdcdcabcbddcaddaacbdaabcacacacadcaccdcaaabbdcacdacdbcdadaabdcabcabbdcbbddcabdaabbbbcbddacddcbbcbbdcbbacadacbdcdbaddbddadaadbaccbbbcbaccdccdbbbcbcddcabcabaabbcccaccacdadcdccdbbcccaadadcadacbcbabcbbaaaabbddbdbababbcdcbcaccacddddbbacddcbcbdccacdabdaddbcbddddcdbdbacdaaaababbdabbcbacaabdbbaaababdbbbcadadcdbdcaccaddacacddcaddccaacdcccdbdabcbcccdcbbdaabbabcacadbddababbdacbabaaadabaadddacbccaddadcaccdabababacdbaaacdbbccaccdacabadabdcadadcaabcaacccacabcddddaadbacdbbbbdcbacacacdbdbabbcbccdadcdadaacdcdaccaabcbcaabdadbddbbbabbcccbababcadbbdadbdddbcdbadaacccacaabacdcdbcadadddccbcddacadaacaacbcccabadacdcadabdddbbacdccabbccccdbcdddbaaabadaabcbaddacdbbcbaddccdcddacadcaadacdaabcccaabcdbdababdacccbadaaccccdabcbbaaadccdbbbbaadbacbcccacbccadbbbdbdaaacbcdddcaccbdddabbacdabcaababacadcadbbbbcaccccbabcaaadcaddacadabcbaadbabababaabaabaaabccbaadaddbabbbabdcdddbdcccbcdabcbbdbbcdaaabacacbacdacbbdcbcacddacbcdddccccddbdddaaababccbbabbcbddbdcadccabbdabbaabcdbacccabcddcbbbdbadacbcacdaabbadacadabdbdcdbccaabcccbdabaccadddadbbbacadbabccdababdbabdcaabccdbcaddabccacdacdcbcdaddbdbcbbaaddcabbacbadaacdabcbcbcabaabcbbcdcacabbbdcdbbaadbccacddccddccddaacddcabccbacbdaadbaddaacbabbbcaadabcddcdbdcbbdccadadaacdbcadaccaababcbdcacdbbcccbbddbbdaacdcbcdbadbcdcddadccaabcccabcdbadadcdcdbbcdaadcadccacdcddbbcdbcacccaccbcabdbdacaccbaabacbbcabaaaacaacadabbabacdcbdcddbaacddcadccaaaccadadadbadacbcaccacbdacddcabcdbcbcdaddbddabaddaacdbadcaaacbcbabadadbdbbddbbdbcdadacccccabccaadcdacdbddbaddbcabcabadbdbddbccbaaddadcddbdacbdccacdadaabccdaabaaaadbaaaaabddcdababadccacbcccaaaccdbabcbdbcaacdbddaacbcbcdadcaccccdacdcdddaccacadabbaccdabddcabacccbacaacdbbaadbacabbabcdddadccccbdbaaccabadbdbacbbaddbadbcbdcabaccbbcacdcdbcaadacbaadaaaacabbbaadbabdabaaacacddcbcccdcbdddbadddbdcabdcdaadcccacaabadacdddabcbdbbbaadcaaccaaababbddacdadadaabbccbadcabdbccbcaabcadcababacbbaaddcaddaabacdbcbdabaaacdacbaddabadbadcbcbcdbaaaaabcddbdddadacbdacdddbcccdadabbbabdadddacbbbddaacccaddadaccdccbdadbdababddaababbabcbbadbaacccbbdcbaadccdbaccbabdbacbbccabcccbbbacdbaaaabcaccadabbccdabdcaddcbbdadccbdbcaabaddbcddaacadbabacddcdadbcaadbbacdaddbbaaababccbadccbbbcdbbacaabdbbacdcadbdcbaacccdaabbbccacaabdaababccadccddabacdacbdbddaacacdaddaadcdabccbbadccdcccacdcadbbcbaababbdbbdbcaaaddcccbbccdbddbbddabbcbcdcbcdbccaaacbbdccadaacbbdddbccddcccaadbacadacccddbcdadabcbbaccabaaabcabaabcddadbccdbdacacadcbcddcbdccbaacbdbbabdbacdddddcacaddaccacdacbdadbcbcdbbcbcbdadadccbccbbdbadabbacbaccccacbbbcadcdaaabadcaabccdbaacbdaabccddadbbdabcbcaabcaabdaacbddacdbbabbaaccaaccccbabdcacdaadcacdcdaacddcdabcacdddccbabaadcdcacbadccddbcbaadacaabcaadcdbabcccdcdbbccdbddbbddcbbbaabbbbcbbbbbddbcbaaaaccdcbccdcaadccccccabacdbbadaaacddacbcabcdbdccdbcdcbcddbdbdadccabccabadabaacacbaabcaaabccbdacaacabbcbcdacabddcdadadccdbaccbddcbdacaddcdccdadabcabbbdaaadcdadcacbabdbccaadaacdcabdbdcbdbbdbabacccdcbcdacccdbcaddacbbddcbbbdaaacbdbdbbcdccbacccaaacadbccaadcbbaddddcacdddabbdccbbcbabcacdcbaabdcddbadcdabdcccbcdbddbabdadbdaadcbccacbababaabdadbdcbabbaccdccbdcbcaacdaaadbadbadbcabdcdaacacaaacadabdcbdbacdaadddcdcadacaadddccdcbadabacaabcacbcabdbdbaabaadbaaababddddaabdcadccbacabdbdaacdbdbadcccdaaadcddccdcabdacbbbbcabdbbaddbadbbadaddbbdaadbcbbcdcdabdbbccdbcbcbcbabbaddbcbdbddbadddbbcdadddddcbddddbdacddddddaadbcaabdaaddbbcabddcdbcbccdcbabdadacdbbdccdbabaabdddabcabdbcadccbdcbbcddcaadbaccadbdabbdddcccabcaabbdbdcdccacadcbcdbacbcdaccbaaacadbdbccccbddbbdddcbcbcddacacbacdcdaccbcacdabacabdbaddaddddaaddadbbccdbccdbaddbadcbaccabcbdabddcddbbacacbabaccdadccdbdbbdadcccbbdbcababaacbaadcbadcdbcccddacababdbabadbcbaabbbacaadadccbadcbdddabcbccdabaadcacabddaacbbbccacbbcbcaacddbacbcabccbacddadcdbdbbabdcbdccadaacaacccaaababddaadbabdbddbdddabbcdcaacdaaccbbdccaaaccadbadabbacdcbbabdacdbccbcdcaacdcaaaabadcdbaabcdcbabacbaababaddabacdbcbcccddacdacadbcbadccababaacdbdbcbacacbdadcddbcccccbbdbbaccddaacabcaddadcadcacacddadbdbaaaddccabadbdcacdccaacabcccdaaacabbdacdccadcacbbdbbddccadddadbadcbbccaaacdcdaababdcaccbaadaaccacabaaabbbaacddaacacaccbddbbbccddaaaddadccdaaaaddaccdbadcbcbdbddacbbbccababdcdbdabcbcdbdbbaadaaabbacaddaadbbddccddbcadaaabbadbcbacababdbcbbcdddaddcbbdacccbcabaddcddcbcdccabdacacbbbddbccdaccbadaadcacadcacddaadaabbddbdcaddcabbcddccaacacadcbccbacacdbcbbcdaabbcacbcadadbbaacaadcaabacacddadcbbabaacbdbcabacbddbcabcdcaccbabbadcdabcdaaabcabdddddcccdddbdbcdddaababdbbababdcdcbbbdadbdcbcbdabdacbacadbadbacbdcbcbaddcbdaaacbdcbcdcaddcadcabdcbcadaabbbbbdbabdbdaaccabcaddbdbccddadbdbccbbcacadbccadabbdabcadaadabdbcdcdaaddabdadbdacabccbcbabacdbcdaaadbccadbbaccabdacaacdaabbdadbdbbbdcbdcddcacdadadbdcbcababdbdbdaaaaacaadddcddadcdcbaacdbbbdaacaadbddbacddadcdabacddaaacdacbdcadacaaacbcacbddabbbadbaddcaadcbbdabcbadcdbabdcbbbddcccdabcccbcacacdcbcbbaabdbbbdbaccbbbcacaabdaccccbacdaccaacdaabbdcbdbaddcbdcabcbdbcbcbadbcbbddbdabcbababcdbddabcabaabbddcddcbdccaaddddbcbbcbccadbcbcbbccbcccabccbdaddadcbddaaacadcaaddcbadbbaacccabcdcbbbcbbdcabaddddabaddccbaabbacbdaaadbaccabacbbbdacdbdbdcdcabaaacbabbddacdacdbadbbdccbacbdccdabadadccabcccccbaabdabcbaddaddbddaccdadbddcccdcdbdbadaacbadbbdaddaacbadddcaabdaabbbaccdcbadccdbabcaacbacaccbacdacbddabcdbbcabbccccdbdbdabbbcbadbacacacbcdbddccccabadcdccaccbabcbadbdabbdcbdcbbbaacbbbccabcaaddaaaddaddcaadabdaacdaddabcccaadcbcddcaadbcdbccbbbdcdbdabbaacccadcddddabdcddacdadbaacacaaacdcdcbdbdbcacdcdcbbcdcbcaabccabdcaaaacbdcccccbdaabaaaddacdbcdbcbadbccbbddbadadddaddbccacdbddccddaddbddaabdbdadacabcdadccaccbacbdcdcbacccbabbdbcccbacdddaadadddcbacdbdbbcbacdacdaadadbaaadccdaccbbcdbbcadcdbcbacdcddaababaadabbcccadacbcacbcbdbcbacdabbddbcbadabbadbadcdcabbaddacccacbbbcaadbdbbdcadaabbccdacdaadbbcaccbbdcccccdccccadaaccacaddbcaaccadcdadddddbbcbddcacbaddaccccabcabbdcbbccdcddbdbcabacbaaccbdbbdbdbacabdccaccabababcacadcbdaddaddddbbdbaacdbaaaddadcbdacaadbadabbaabbbabdbbadacdbccaddadaddcaabdabaadbabdcbbddbcdbacabccbbdddbccabdcddddddabadacdcdccbddadbbcbdbbbcbbacddcbdaacdbcbdbcabcdddbacaaabdabacdccbaaabdcacadacbddbdbdbdadbbdadbbadadacdbdbadbcaabbccbcbccbbaccbadddcacccaddabbccabdadddadbbbcacabaadcabbbaacbdcbcbccbdcdaacaacbdccbaaacbbddacbcadadaaccbdbbdbccdcabbaccdcdcbcabdcddcaddaaadbacaadcccbbdbbcaccdddbbddbaaaaadacddcdcdccbbddccdaaabccdcdabbaaabacccccbbcbaccccbdbbadbdbddbabdbaabccadadcbdabadbcaaacdcdbdadbcddcdddcaddbcbcabdcbdadcbbaaaccbccadcdcaaabcdcabadbbcddbccadddccbcccbbccdcddabdbabcbcacbcacbdadbbbbaadbdabacbdddadcdddadbadaaaccdbdcbbbdcdbacbcbbacaadcbbcacbdadccddaacdddaddacbdccaddacadcaacadbcbdaccadcccdadccbdbbabcbcdabcbbabbaccdbaaacbabcbdaaaacdcddadcbddbcddbadacbdabcbbabcdcdadcbdcdbcbddbbaababccacdccaacbbcccacacbcbcacadabcadcaaaaacbcacdcbaacaabddabbadccdcdbbdccdcbdabdccbcdbaaacbacdcdbdcddccbaabdabdccadbbdbddbbbdbbcbaddcbdddabcdcdcbdcaadbbbbcadabcbcabcadaaaccbbbccbdcbbbacddbdcaabccaaccabaadbcaccccabbbacbcbacacbabcbacbabcccdacdbccadcdbdcbaadcdcacabadbaabdddbadadbadddaabcccdaaabcdaacabcbbacddadbbcbaccdcabaacdaddddcdcacbdccdcddadbbbcdddbbbcabdbababdbdadacabdbbadbabbdaaaaaadabbcbacbabdcabdababadabccdcdcdbbbabadadacbaddababaabccbbaaabbdbddbcacdccaaddddcbdabccdcaadaabadaccacbbaababdcabbdcbbabbccdbadbcdbcbdbabcbcdbcdaddbbdabcbaadbaadaabcbdaababcdadacbdbdabdaacbcdadbcbdacddadabbadadbbbccaaccacacbbaccabdcbcaccdabcbdadcdcaacaddddacbaadcbbdaacdcbdcaddbccbcbbbdccddaadbcdaacdddbaaabbbbcaadcbdaaccaababccdddbaccadababaccdbdbadddaddcddcdaccdacabcbabbbaddbccbabdaabcadabdabdbcaacaacababacbbdadcaacdccbbdabcaddacaaddacdaaccacccbdcbcbbcbbdaabccbabdabdbbcdcadbbaaaadddcabcabaaccabbddaacddacbaccbacbccdcbcbadddacbcbadcdcdaacacaadacdcbcbadaacdbabdbdcbacadbaabcdccdcddbacbbacbddbdddbbcddbcadadcdaabbbcabbdacacccccaccabbdaabcdacacdadcabaadcccaaaaaaacdaacacccbddcdbcdcbcadabdcadbdaaddabdbaacaaccacccdbddacaadcbbcdacaccdbcaccadaccddaccdddcbbdbdabcccdbbcbbcdbbcdddccacdcacbdcbbdcbbdcbdacaaabdbaaadcbacccbacddbdbbdbaccdcacbbdbcbcbaadcdcbdcaabcaacddaccacccccdbdbdbdcbbcbbdaadabbdaccaddbcbcbabdbabddbdbcadbbdadadbcbdaadbcaccbdcaddcaadadadaadaaabbccbbcadccadabbaacdddadcbdbddadaaacacadbdbaadcdcbbdabaadbadcddbdbcccbdcdcbbbdabdaaaaaabbbcbaacdbcbbaaacaccbbabbbbdddbdaadcabcadabdcadbaadbabcdbabadcddcddbdddddccbcadcbbabbcdabbddbbcaacbdcdbadbdcbccbbdcccdcdaadbbacaacacacdbbcdabadcabbaadcacdcaacabcdbcdcaaaabcbdadbdcbcabaaaadcbbadccacbdabacbcccbccdbacdcadcacbbbbdcbdddacccbcddabbbaacbbcccdbadcdbbcbacbadabdddacacdcaacacaaccacbcddaacdcbaabcbcbcabbdbcbaddbaacabcadabddaabadbddbcbbdbcdcadaacccbdbcabcbbcdcaccbcadaccdcbcabbcbdbbbbdbccbbdbbddbababaddadbccaaccdcdacaaaacbdbaddabadcdbcbcdbdcddaccbbdbcbbadbdcddabcacaddbbbadbbacbbcbcacaabcadcaaaadabacbdbabadcbcaadcccbdcccbbcadabddabbdbabbbdddacddabbaddcbcacadcbcdadccccdaabcdbbadbaadccccabbaddbcaaababaabbdadadcadbcacdbdcaaccaddbdcbbdbcabdbabcadbcbddabbbaccdaadcacbadbbacadabdabddadcbdcbaccbdcbccbabccabcbcdbcdadbbcdbdccaaaddddaabcbcbdcdbcaabaccbcaabaddcdbaaaabdcadaabadacabdcaddcacbaadbabadcbcacaddabcdadaaabdaaabcbadbccaccbabcbdaacbabbcbdddaadbdadcbcdbcdabaaadcbabdcdccbccddbcddbdcbccaadcddaddaccacdcaaaabdabaadccadddabbcabbbbbcbdcccaccdddcadddabaaacbbaacdbaadbcbacdacdbdbaaabdbcbaccdaccaabbccbcbadccacacadaaacadadbdaaacdbdabcdbcbacaaabcaadbccccaabcbbbbdacbdbaccdbcbdcaddcadcbaaccccabccddabdadaadccacaccbacbdbacdcaddabcacabdbbbbdababcadbaaabcbdbcacdcadcabcdadbdabcbdddacdccdacbdaadcaaadcbccbbdbddaddbbbcadadcccdbadcaddccabdbdcbddccbbdddaacbdbbcacacadacddbcccbadadaacddadacbcbbbdcdcbabcbbbdccdbbadcabddaddbacbabadcbccbbddccdbbcacccaaacabddcccdacdcaaaccbaddcdacabbddcdcdcabdbbcdacaacbcbcbdbcccccccaccdcdbdcadddcabbacbbaccbbcaadcbcaadbbdaabaabdddbaaddcdbbcbdaacbcddaadcacbcbcacbaabadcdadbbdbbccdddaadcababcaaabdbbddbdabbbddabcbacdcdcacbdccbcaddcdcdcdccabbadcaccabaadbaadbacccdadbbadcbcabbbdbdcacdacdcbdacbbcbcaabadbabababbcdbabbaabdcdbbabbcdaadaadbbbbbdcccbbdadbacdbbbcddbabdadddabdccddbbccbbacddcabacabcddbaacdcbbdaaabdccbadabcdcdacadbabababbbbbbccccabaaccdcdbbdcaaaaccdaacbcabdcccadaacabcaabbdaddcbabbbaddcdacdbcaabccddcaccbbbbabbbdabdaddcdbddbacdbbcdbdddcdaadacdaccadcdcdcbcdcbaccbdccacddcdcddabaadabdbbdbabcacbdcaccccbdbbabaabccabbbabacadddcdcaadcbcbbdacbbadbdbcdaabbbcdcabcbabababacdbccacacccbbabccdacaddccaabbadbcbcbdbdddbaacbbcadccdcbdbcdccbabcbcbccdbadbbaadaaddcdbbdabbdbcbdaacdbdccabdbbddbcdadcaadbabbdabdadaacdcccaddabdbbdcdadabdadadaadadcaadabccdccadcbcbadbddbcbcacdcabaaacbcaccbacddbbbbcbdcaaadddacbdabcccbccabacdcddcbcaaaaabcbdadbcbabcdbbcbbdddbcacdcbdaacdbaccabcadcadbcbccddabcadccbcbdbcbddadddbbcadabbcdcdbbddddddbcbabbdcbacbdacbcdabcbbcbabaddaaccdbbbbaccbbcbbacbdabbbbbcadbbadbcacccccdacbacbccdddccbaaaccadbdcaddccabccabdbcccbdddccbbcbdacbadcdcdccadbbbdbdbcacbacbadddbcbccbdabcccdbdacdbdcbaccbadbadaddaabcabdcbbbabbacabbddbddadaaddbaacbbbbabcabcdbbdbcacbbcbddcdaaabaccbbaabbabbbdddabacaacabbdabccadbddadcccabacccddabcaadcdadbccccadadaddbbacacdaadbdbbcccdaccbcccbbddcdcaaacbcaacabacbcacaccadaaddacacbbcbbddddbdccccdbadddadcabdcbdabcbdaaabbadbadbbbbdabdaddddddcbdcaccdccdbadacbbabaddbcabbacccdddabcacabbabcdddaddddddaaabcbacddabcbadaabdabbdcaacacacdbbabcdbcdddbddbabcccdabbdddbdbddccccdcdbbabbbcadabddbdacaddabcdacabcbbbaadadaccaadaadbabacddcbcccacddcdcbbbdbdcbcadccbaadadddadaccadcaacbdcaabbcbdadbdcbbaababdbdbbdcbbbdcaccccbbbabbbbbbcdcbdbaaddabdccbcbbbabdbbbdcbdbaadcdbcddcddccdbdbdaddddcdadbcdadaccbbdacccdbdcaabbcdadcabacabcabbcbdcbbcddccabbcbacacddbbbacbdbbdbccbcaadbcacdbaaadbacbcabcabcabbaccbbaccbccdddabcdbcadabdcdadbbdbadccabdbadcbbdbaadacacabdaabccbcbaccbdcdbcbbdabaacdacabcbadadcbdbddbccbbdcdbcdaadccdddcdbbbddaabaacabadcaaabcbcabacbaabbcabdcbdbdcdcddddbddccbdcdacadbaddbcbcaadbbbcbcddddbbcbbacdcdcdabddcbcdaaddbcccdacbadbbabbadcbbcccaccabadbadbadbbcbcacdcbdacdadaabacbcaadcbbacacbccaccacdcbacaacdaacabadadadacbbcccbaccbababcbcbdaacaddacbbdcdbcdabacbdabdaddbacacadbaccbccccdcaabadbadccbdaacabdadcdaaadcacccbcacbdcbbbcacbaccacaccacadcabbccbcbcccdcaaacaaabccaadcbdbbbabaddbbbaaccaccabbcddbdbdcdcaadccabadabbcbcbcdccccbcaaadaacbbabddbdddbcbccdcdbcaabcaccadcdcdbddadcabbcaadcabbbadcdcaccdbadddacddcbcbccccaaacddcabddbccdccccbbacdcabdcccaddadccaadcabcdcbddbabdbcdaadbabaaabcdcbdcbdbdaacababcacccacbabcaddbbbccbabcaaadcccacdddcaaaabbbacdacadbbabccdcacbdcdddbbbbcbadadccdbdccccdccaabdbcadabbacdbadaacccaacdacbdabbbabaaabccacbcaaacadbdbdbccdcbbadcddadddbaddbccabccadaccdacddabcaccdcadbcbadbdaaabcbbccbdbbdbdbcdaacdaadabdddbbcbcdcadccacbdbabdadcbddabccadbccccbcdbdbdddbdcdbabbdcddadbbadbababacaadbddcacaacddcabbdadcaacdbcbcabdcaadbabadcccadaddaccadbbccdbbdabcabbacadabacbbbdcbbbbcbdbaccacdaababbaddbcdadaadabdddacccdbbacdadcdccddcdddaabaaacdcacdccddacdbbabdcdcddddddddbcdcccaaccaaadddcdaaaddbbbdbbacaddbaabdcaacddcbacaaddbaadbabbadcadddcccdaddcddacadbacabbdaacbbcbdadcdddadcaddcadadcbcadddbabacdbdbcbaddbbacddbbabaaadacacdbcbdcbccdcacdbdccccbaccccacdcbbaadacbcddcaabadbcccadbcccaccbacdcdadaadccbcadbaaabbdbcababaacbadbbaaabbcaabaadadbaadaccccddddbdbbbddaaabddbabcacaaadcccaaabbaccdbccdddccbabaddadddabdccabdddabdbdcdabcdabcaadaccccaadcbadcaccdbcccadcccccddaacaaaccdacdacbcccaaaaabccdcaaabdadacbcdabccbdcbdbaaabbcbddaababbadbdddcbddbbaaabcbbaaaabbabbdababcbbccaaaaccbbcaddbdabcdbcaaccbabbcddcdabbcacadddbabcbbdcbbaabdaadacbadabcbadddcdcabaaaacabbdcabbaacbdcccddbdbbaddccdcdaaaacacaabaddbccddbbbadbcddabdddcdccbcbcccdcacbabbcddaadbddabbcdbacccddbacdacdcadbaacccdcbaaaaacbcadcdabdaccccdbbddcabcccdaaacacddacadccbccbaddccdbbacadabadbccadcaabdcbaaadaccaddcddadaccddadabbdbadbaaddcdbcccbdcddddbdabacbddabdaadcdcadbadbaaacbbdcccccadbbbdcdadabadacbacbcdbcbdbabcbaaccbaddbacbdacbdacbdcdaccdcbbbabdcabcaaaabbbccbbccdbcccbdbaccbaccbbbabadbbdbdacbbbcbccdddcabbbccdddbdcaadcdcbdbbcaaacddcabacadccddccbaabacdddacadccbcccbaadcdabcaddabbbbcbadcbaabdbaadabbccabbdcdacaddbdbabaaabbcaacdadbdaaabddadcaddbcaccaddbbccabcbccdccbabacaaccdccbabdcccaadacdacababbcbdcbdddccadccccddaabcacbbcdbcbbdadabdbabadaadbacddacdbbbadddddacaacacabcccdbdcdadcddcaabcadccdadbdabaaaaadddddabcabaddcdaabdddccdbcaabacacbdacddbcccbbdcccdbaaaaaadadabdccccdccdacaccdbdaddccaaacdccccdbccbccabcdbabccddaaccdbcdaadcccbbaaddcbabacdaaccddddcacadcacdcddabbbccaacddbccadabacdcdbadbbdcdcccbbadbbddccaacadaabacacddbbdbccaccabbcabddacbcaabbacdbdaaddcdbbcdcccabaddbbcbabaadbadaaccaacdccdbbdbdddbacbbdcbbcdabdbacdbdddcdcbaccdbabcdcbdbabadcddcaaaaaaaacccbdcaddbabaadadbcaccadbbcdbabdcdcdaddbadbcbdaccccbcccacacacbabcdcdadbcacbabdccdabaabaccddcdbbabcccdbbacbddbdcbcadbbbdadacccacddcbadbcdababaddcacdbdabcadcbacabaadacdacabdaadadccdacbbcacbdbbaacadaaabddcacdacadadabababdabbcdabbcdbdabcadbabdcbabdcbdbadacdccbacdddcbccabcaacaabacdbccbaddabdbdadbcaaacbdcdccdcbcacbdcbababdadabaabdbbcbdacadacdacadcddacbddacdaccadbaadbabcbbbccbcbbadbbabcbddcdadbccbdcccaabdcadddbaadcadccaacbbaccdddaacadbbbaaadddddddabbdbbddbcdaaadabbdcdadcbcbadaddbadacbabadddadaaccbbaddbacbdbbbadddabadbdccdbdaaccbdccddcbbbdcbdbcccdabbabcdddcdcdbbbcbdaacbaddbcbbadcaccdcbbcbadbccabbbcbabcbbccaadbbbabbaaddcacddbddcabbcbabbdcadadaadcabdccddcdcbbabdcbdbbccadbdcccbdccaddadacaacbdcbcbbadadadaadbcaadcdabcbbaabddaabccbbbaaddbdbbccdaadadcdaddcaccadbccccbcbbdaddaddddbdacdcddbccbbbbaaaabdbabddccccccbcaacdbbaadaccaccbdbbcadacdbacabaacddddcaadddbaccdabbdddbadbdcbaaabadbbdbcbabdcacbabacdddcdaaadbbdcbbaacccbccddccbbdabbcdbcabadabbadcdcdaadcacbabadacccdccbbcbacacdcbabdccbddcaaaabdcbdabccaccccdbbcdadbadabcdcdadbcdbadbcbcdaccbaabdddcdbadcacbcdacacbabddcdcdccbdddadaccdcbabbcddcbdabaacdcddaabaacbdadcdbdaaabbccbadccccabccbaddddcbcbdbcadcbbdacdabadaaaabdbcbbaaacdacccdadcabbaaabcacbdadbbacbaacabccbabbdcdbaabaddcddbacadccaabaabcccdcabbbbdccacbbbbbaadcdccdcdabaadcdabbdbbbdbbcddbaadbaaadddbbadacbdbdddbbcbaaddaaccabcadbdccdcdbcadcaabdadcabccdcacdcdbbcdcacabadbdccddadcaddbabbcdbdadbbcadbddbccbbdbadcabcbbaacbdbabdacbadbccbdcbccdccdbadbadabaccccaddbcccdddbdadabcacbaccaaadacdcdcadadbabbdbbbdbabadccbdbaccccbcbddaacabcabbddccabcaaccddddddadbbdcdcdccbdbbbcaaabbabacbddccdcabcdbacbdccabadcdaacaacbdcaaaccdcdcbbbcacabcdcbdaddddddbccbbdbddbbddcbadcabbbddacabcdcddacccabbbccaaaacdddddacbabccdbcdcaabdbbacddadacaadddcaaaccddbdcaadbdbdabccdbdcabaccdcddaaddcccbcddbabbbabcccabcdacaccdcdaacbbbabdccbdccbccbdacadcccddbcaacdcacdbaaadabbbdbaccdddaaacaaaadadaddabccddaacadababdcdbcdcdcbdacabbbdbcbbccababaaacaadcdcddccbccbaddbcbadaacaccddaabcaabadabbccbbacbbdacdaabddcacbaadacbddabacbbcdaabbaddabacbbbacaddcaddbbbadadaadbdaaccbabcabbdbcdbbbbcbdcdddabbadaadabddddacbacccaadbcbaccabaddcddcddbbacaccccddabbbaddcadaacdcbbccaddbcccbbcbabdbadaccacabdccbbbcbcbbccdcbababacdabaccaaccaaaccddbdaadbdbdbbbdbbdccaadcbcbaccbcacddccddbdbdadcbbbdaaaacbbbbaddcbccbdbbadbdaadaccddccbddbbaacbcdacadabddbdacadcadadcbccccbbdaaabababaacacacdadaaaacbaabdacccabcbcddaadddbbddadcccdadcccaacacbdbabcddbbaabccbaadacdaacccbdbacababccdbbcaabaaaadccbaadbdaababacdabcdcaacdcbbbdaccaccbbccadabbaaabcdcabdaadbcdbaccaabcbdcdaabccdbbcabaccdacbdccaabbdbdcddcdaaddcbbbbcabcacaadccccdaaabdbcbacdddbcbdcaddbdbbbbbddbdacdadcacbdaccbabdadbdababbaddcaccbaddbbbdbbbdadbcacbaccbccbdbcbcacccdbbccdddadbbbacaaddcbbcbbcabaacdddccbbbdadaaadcaabacaddbacacdcdaaadbadddccbabadccbcbabaddbbdbbabbbdcccadcacbacdccbccdcdccdaadaddcccbaaddcddccacabddbcbbbadbabcabacddadcacdacaaabbccabadaadbbccbabddbadbabbabbcbaddbcacddcbdadbbcddacdadacddacacadbacccaacbabcdcbbbadaccaddabdaacabbbdabcbbabccccbbbccbccdcaacadbdcbbdaaccdbccbccccbacdcdabadbcbbbccaabadaccbbcadbdabbdcbccddccbddbdbdcccbdbbcbcadcdbdaddccadacbaadbaadaadbabdaadabbddabbdabbadabddddabcadddabcbcdaaacabdaadddcdcabdbdbbcaabccabbabcabdccabbcddccbdabbddcbcbbbbddaaaacccaabbadadcacbadccdddbdcaabccbddcadaadcdcdcabcaaacdddadaabcaddabbcbaaacaabcaccbdbbacdbcdcbbbcadbbcddbdadccbbcdacbcaabcbdacaaadbbcabacdbcbacabbbbcbcabcacaabbbccadaacbaaccbabcaaabbccdabaacadcbdbcaadbbbcbbccdbaabbbbaaaddcdcacbccadcdadaaabdadabacbdcdadcdccdccbbacbddadaaaaccabbadabaccdddcddaccdcabdaaddaacddaabcdabcdbaaccccaacbbbcabcdacbddbccdabdaabcaacbaccccbccbcccbacbbcddbdbbadacccdbbbddadbddaadddbadadbcccbddbbcacaaabacabaabbaacccaadddbbbacbaddcddcababbacddddaacdbddccaabcbccbdaadcdbaaacbacaadbacdbbcdcabaabcbabbdbaddbbabbddbabcbaacaabacbdcbddcaddaadbccbdadbdabaddccdbbcbaddccaabaacadbcbadaaaadaddcaacdcaabbdbdaadabbdabddaabbbcbaadbdbccdbbacadadddacaddacadcabaccaabbccdbcbcbbbdcbcabcbaacbaabcccaddbaacbdbadcaccdbbccaddbaaaaddcdacbbdcddbaddbdababaadadbdaadaddccbabdbaddcccdddaabadbddcbdbcdacaddaaadcacbdcdcdddbcbdabdcccccabbdaaadbbbcadddbdbddcddadbdcbcbbdbacababdadccaaddbcbbcbabbbcbbbccbdbccdacacdcdcdbacdbbdadbcbcababddccbcabccbacbadbcdccdbacccbddcdddcdcdcbbdddcabbdbaabcbbbaabdcdbdaacadcdabcbcdcdabadbdcdacccabbcdcbabbcdcbccbadadcdbdcdcdbabaadacdbdddddabaaaccbccbdcabbbcbbdcddccdaaccaaabaabdbadaccacabbccbdbdbaacaabaabcdbabcbdbcddbccacacacaacabdcdddcaddcbddbcbaadccdbccccbdadacbdacbabacdbbaabadbbabbbcdbccddcbddbbbbbcaabccbcbcdbabddbcadacdbbbabbbbaabdcdaadbbcdacddaaaacbccbacadbddcacdcbdababdcdbadabbcbbabaabdadaccaddcbbdddaabaadabdbabcbccaadcdabcaaacabbcacbabcacbadddcacccbbbacaacabdabcdcbdbdaadacaaadbccbdcbcbdbdcbcbacbdcdcddcadacdabdabdaadbacbddcccdbcccbaaaabdacddacaabadbdabdbbcaadcaaadccccabcdddbcdbacdddabdbcacbaabdcdaaddabcacacccabdccbbcbaadbaadccccbaccccbcadbcbdccaccadabaabddadaccdabbcbcacbdaccddbccabdbcdbccbdcdcddbdabcccddcddaaacdcbcbbccaadddaabbccacaacdbbabcbcbaacdcbaddcbcbdbaaabcdcadccdacbdbddbccadcadccdddcbbdbccbdbabcbcddbdabbcacaaddcdbbcdbcbaaadbcadcddcccbccaabcbbaccadaacccccaadcabbcdbabcbadbabcaaaddaacaaabcbacaccbbbbdcabbccaadccdbaabdabccaaccabdbbaadabcbabdbbdacabacbaaadbcdddcdbcbdccdcdbbbbbdbdbbbacccccacdbbaaaccacdbadcaaadcabdcdcdabcaaddaaddbaddbdcbcbdddcadbaaadaaacdaddccbbdaaddadcacccccadbcdabddacdbcaababadaddabdaacabcbcdadacbabbccddbadbadbadcaadbdbcaadabbadcdccbcbdbbcbdbcddbdccadbddbccbcdddcbccbbdadbaacabaddacbbcacadaadddcbacbdccabcdcabbdcbbbadbaccddacbdabcacbdbaaadadabaccdaaaccbdbacacddbbacdcbdccbacdabcadbbbcbbabacaddccadacdbbbbbbaccdcbbbbbaadcabdbaccddacdaaacdcdaabdbcdacbdabbbcdddaadacdbbcbdbcaccadbcbddadcacdcadaaacbbbcaccbbcbbacacbccbdcddcdddabccbbabccbcabaddaaccddadccbdcacabcbacaacaccbcabdbdbdbdbbacddbdaddadbccccdabbcdcdbddcaccddcbbbcbbcbdaaacddbbaddbbdbbabcaabdcbdadbdcadcaabbcbacadbaaacabcabbdcbcdddbabcadabddcabcddccccdaabbccacddccddbbaaccabadbcbcdbaddccddbdcbbcdcaaabaaabdacbdbdacbdcdccdcccabddddaaccaaacbdadaddddadadaaabbbabcbccbbcbdadccdbcadbdababaabdaaccbccacacbcccadddaabdcdacddddbadccbbbbacdcdbdccaadaadcdacadcaddccbdabdadbdbdbdbcaabbaaacccdcdddbaacdcbddcdccbcdbccdcbcabbcddaaadbccadbcbdadaacbabaaadacdcbbdaddbaadadcaddbbaddccccdddaaacbabccbcacbcdbccbcbaaccdcabccaccbdbddbcbacbccdccacbcbbbbaabccddadbbccccbdcbdbbabadccdbddcbddbcbccdcbaccaccdccdcdcababaaacbcdaaaaaccdbdcbdcdabdcdbdddaabbbddacbbbbccbdbcbddcbbdccbcdbabdcadccdbaaacaadaaabbbbdcaacbccdbddacaccdbddcccdbdcadcbbdbcccdcbaaddcabccadacbbacccaccdbacbdbdacdadbbdcbdbbcacabbbcdcaabbcccccbcbadcabdaddbbbadbdaabdadabaddabddababbbadccaddcddbadcdcbbbbcbdcbcacbddbdcbdbdcaccaaccaaabdcdbcdbccdbaddcbcdcacaabcbddaddbcdccdcccbcddabadbcccddacdcbbcbccbbdbadcabccaaaaababcbdbaadbabdbcdaadbacaccdbdcdaabccbaadcdabccdaaddcdcaddadbdadaababcabcaabddbabddabbadbdccbbbdbcbdddacadcabccadaabaabcdcabdbcccabccbaddccbbcabbcddccadbdcbcadbcdadacacaddbbbbdadcddcbbbbbbdabbdadcbbabddddcbcadbcbdabcdbacdababccbdbadcdbbaccadddbbddccacaacdabdbabbddacbbddbacdcaacbdcbdbdbcdcbdbcbdbdcbccdccacdabbdbaccbcccdcbcaacaccccadadbcbddbcbabdccccccaddcbbacdcbdccaadbbccccdacdaacccaabaadacbdbadbddbdcbbddcabdcbbdbadbbdabddbaccdddcbccbdddcbabbcdbbaadcaadcadbdabaabadadcabaadbcddbcccdcadddaabdddaaaabcadcdccacdbaccaadddcbddcbcacbccddddbbbbbcdddbcdbdcaddcdbcddacdcacadcbdcbcbddcaaaacdbccccdcbdaaadcbbbabdbaacbdddbdacccaabbadccdcbaddadbdbcdcabbcdbacddbdaabcddcdbdbdaadaddaabbcaaacbbcddccddbcddbbccccbdcdbcbabdcbaacdccaacdddcddbdbaaacbbabccdabaaabdcdaddadadbacdbdbddbbccaacbbbcabccabcbddbccaadddcdaddadcbcdbccbaaddbbcdcdcaabdaccbcaabcadcdcdadcadccaaaccdccadababbdbdacbaabadccbdaccdacbcccbdaabccdcccccabbddcacbddbcdcdadaadcadcaacddbcacabbbbacbadadacdddcdbcccabaacdbadbadbababdccabbddbcaaccccdabbbabddbdccdbddcdaccbcbdabbcccbbaccadabccabaddcbddbcccbcdcccadbdabdabcbaaacbadbcaddbbbacddaaabbbbdcbbdbadddbbbbcbcacbdcccaccbcddacdabbbddbcdccadbbdcdacadbabbaacabaabcbacbbcdcbbbdcbbbbbbaabddcccadcbdbdabdcdbcacddcddbccdaaaccbcacccddbccccaddbadbbdababcdaccbadcdbddccddcbbdbdcdddcacdccbdacbacccbbcacaccbacaaabaddddaabcbcdaaaacdbbcaacbdaaadadcbccdbcddacacbcdaaaadbbbcbbdbdcaacbdbcdacddabacabbdcdddbdbcaccbdbddcacdacadbdbcbcdbccbaddcdccbddbdacdabadbcacacccbbaddabddccdacbacdcbbccabcccdcaacddababababccbddbdbbccbbdbbcaaccbdcababdacdcbdbcadadccbdcbbcbbddbaabaccaaddddbdcdcbadaadccacdbdcdabdcacccdacbaaabacacaddbbbbaacddcdacdbbabbbdaadaddaacacdcbdddcddabdccacbdacbddbcaccbabddbdbccbddcbcdadbddacdbbbdcdacabdaacdbdabdbbdccbdcbbcbdabcaddabcddcabacaaddabaabbdaadabcbbdadcdccaabdcbcdadcdccadbaddbdbdaabacccacdcdaadccabadbacaccabaabbdbbdacdcbdacdbbbddacbaaababcaddcaaaadddbdbbdbdabbadcdbbcacadbadcadadddacbcbaacaddcccdaaaadcddcdbacbabadadadaacccdbddccabadbdcccbaadcdaabdccccdccdabddcdbadddcaccadaddcacbdaddcbacbabaddddbbbaadbaacbccbcddbcaccddaadbacbabdbcacbdcddddcdbacbccadadadcdabccaddcadcccdbaabbacdddcabbdadbdbabbbcadacccbacbdbcbcbdabbcadbcdbbadadcddddbbdcdcdaaadccabdcaabdddbdaaddcdbaadbdbcdcbcccccddddccdcaacadcaabdcccbbcbaaaccbcbdbaccadadaddbdbaaddcbdaaaacaadacdcdbaddbcacabaaaaaabaabacdbbbbbbcdbdbcdadbcabbbabbcadddaabbddcbdcbbdbbbabdaadabaabccdbccaacaaaabbbacaacddcabaabdcabbdbaddabaadabdaacbbddddbbabadbbcbabcdbabaaabadadadcbdccbdbbbaaacbcbdbcacdbccabcdcadcacbcaadcbccbdaaddcbdbddcccabcadbccbbbbacacadbaacbaabcabdadabcdadaadddbbbacbbabdcdbcadacccadbcdacbcbcacdcbbaabbcabbcaddbadadbccbdcddccbaacdcdabdacccbddbdabcbbbdbbddcabdbdcbcbcadadbbdbaaddacdccdabdccbacabbcadcbdabdddbbdcdadbabaccddbadaddacbcdacdabccdbddababcdcbdcbbcbcddadcbdbbbddadcbddcbadbdbabbabdaadddbdadaccbdcddddcdaaccccdbacbcddcdbaabdbaadbadcbdccaccdaccabadabcdbaddabddbccbbcababbdcaccabdabbdcdbccdbcccbcddcbbaccacbcddcacaadcbccbcbadcaccdbacddbabcbdbddccadbbddddabbabdbdacddbaaaabadccddacacdddaacabcaabbbddcdbcaacaccbbacadcdbdaaacbcbaaddcbaadbaabaadcaaddbdcacadcdcabdbaddaabbbaabdccdbbcdbcdcbcbddaccdcdcabcddcbbdbbdcdcaddddcddabddccddadbbddabbbdcbdbbbadccbacddabbdcaaabbbdbdaadabddccbdacdabcddbbdcbbadcdbaaadccbbccdbbcdcdadababdbdcdddccbbcabaabbcaaacaadacabaccdccbdaccdacabdcaccbccddddaadcbadadcdcdccacacdbbbdadddccbdbddaaaccabcbadcdbcaddbdddacbbddbbdabcaddcbcbcbdacbddddadcadcaabaadcabddabbcdcddabcbababdcdacbadcdbaddadcdbcadaccabbbdbabaccdcdbbbabccacbaabcadcbaddcbddaaacdabdbacabadaadbadaddbaacaacbacbcadabcdccdddbcbcdbbdaaadadccaddabdcbcbcddbdccadbaaadcdddabcdaaabddaacdbdcaacadaaabbbcbbcbccbcddbcdbbbdcaacddbacacdaabcbbbbdadabbdaaacbcbcdccccbcddcbddadcacccbdbabadcbbacbabcabcacddaadbcacdaabbdbdbdddbddcacbdccbcbdaabbdbbadaaadcbcaadabbccbadacbabacabacaacdcdcdcdccbababdbddadbbcccaadadaddabcaabdddcbcdddbbabbbbaabcabbdcbdbabdddadaaadcbbcdbccbcbbcbcabcaacabaaabbcaccaacabdbaaaadbdbacbbcdccbaacdbdaaaccacbbaccdadacbcccccadcdaacbdbabdbdcddacaccbbdcbacadcdbadbbdcacaddbddddbbccadbbaabbccccbbbbbacbadbbcccadcbbaadacbdccaaaadcdcaabcbddabbdbaccddcdacabaccccbbdcbdcbbcacadacdbcbbcbbcccbabbcbbdaaacdcaadacaddbbdcbadbababaabccbbcaccdddabdcdddacaddbcdbabacdadbcbaabddcdcdbbcdaaccccacabdaaabadcabcddbabddbbcadbcdaadbdaadacdbdcaabccbccbdacbbaadadbabacadacddddcacdabbcbdcdabdbdaaadabaddcdabbdacbaabcbbdcdcbdcddadacbaddbabddabcbbdddacdbadabadcbababdcabcbbbbbaabbddbdcbbbbadbdbdbbdcdcadcabbcbccaadbaaaaaccadabcbcacacddaddcccadbccdacabadcbbccbccaccacccabdaacddccabadbcdbcaabdaadabcbaccacadccabdabdaccadbbbdcbdcbcabdbdadcadaaadacacabcbdddbdddcdcaccaddabdabcabababccdcdadaccabcabaabaadcdbddcaacadddbadaddbaccbaabccbdcdadbaddabacddabbdaabacbdbbdcaccabbbadbbaaaabcaaacccabbdbbcaddcbacacbbbcaccbbbcbdabacbcbdddaabadabddaabadadaacaaccbccdccbadcbcdaacbaacaccbabbaadbcccbbbaddbaacababcabbbbabccbdcdbbddddadbdbadcbcccddbbdacaaaabccadbdbccccbacadbcbbcbbdcabbcadaadadddbaaccaacdddbacabbbcadcacadbbcadddcdadaabcdadddacbddbacaddbbccdacdcdccadbbacbdaadabbdccadcaaababcdcddbaadbdaadadddaccbddabcbccdaddccdccabdddbacadbdcbdbccdcbcbddadbbdadcacbdcabbddadbbabdbaddbcbbddbcbadcabbbbbadbccdbcacbcdcabacaacddcddacadcdabcbdbdccadcdacdbcdacbcacbabdbddcdcddadbbaccbaadaabacdaaaccacbdbccbaccdbcbadccddccbdaabdbadbcaabdaaabadcbddcaabadcccdcbdaabadaddaacbdddadabacaddcdbdbddcacabcbcdaddcccaadcccadcbddbaabdcdbaaadbadcaadadadacdbbdbaadacaadadbbcbcaddbadbadaddbdcadbbdacdcaacbaacabbbcccaccadbddbcbddabaaaaadaadaaccbaaabbaabadcddaccdaabaddbcbdaadcbccdbcdabdbddaabcbbaacaddcbabbbbbacbbdbcbbdaaddcdbbaccadbabbddbccdababbbddcbccbadcdddadbbbaacabddacdddcdcdaacdacccddbccacadcbdbdcbddcadaaddcadddbbdaccbaaadbaddcdcdddbbbcdadcddccbddbdbcaaddcbaaccaadcaacbaccddddcdccccbcaaddadcbabcdabbdacbbcdaccccbaacacabbbccdddacbccbaababcccdadabaddacddccadabaacddcbdcbcabddaddcdbaaabddcbbddaababdccdcdaaaddcbdbdcccbaabbddacaddaaabcddabbddbdcdbaccdbbacbddbdbdbbaaabaccbcdcabbcdcdbbcccadaccadabccccacbaaacdcadacabcbdbacdcdcadccabaccdacdbddaabdddbcaaabbadaaacbcacabdccbbcdcadccdabcdadacbacdccaaccabbaccccacdbcbacccddcaabcddcbaacbbaddddabaacacdcbadbbcbcacacdadaabbaadbbddcacbbcbcdccaaacddddbdacdbacaadbabddaaddadbbaaddddbccaacabbcacbadbbabdbbdacdbdddbbdbacbbcbbcdbdadcdadddddbcbdbddabacdbacdddbcddbddaaacdcacccbdddbcaaccbadddcacdcbccbadbddabacccdccddbdccccbdccbcdbbabadbbbcdcaacbbccdaaacdaacbbbcbddbcaddccbddbbcbdbdbccbdcbbacdacccdaacabdcbacacbabcdccacbcdabdcbbadcbdcacacbccabdcccaacbdccbcaadbbabbddbadbcbcaddbbacaccabdadbaacaabaccbadcdcadaabdddcadbcaacacabcabbccbbacdccbabddddbdbcadcdaddacacddcdaaacccdbbbcdccaacbdccbdcbcaadcbbcdccccaacbcdcdccdbddcdccadddcbbccacacdacadbadcbadcaccdbbdbdbddaccabaaddbdbadddabbbacddbcbcadddcdbcbaabbbaddaaaaccacbbdbcccdbbcaddddbddcccbbbcbcddaaccdadcbabdadcdcdcaadbbddcdcaccdcbdcdabbaaadcbbadcacabdaabdbdabdaadacbabbaadaddcabcbbbbcdbacbabcdacdddddbabadacacbdbaacdbbdacbcadadaaccbaccdacbcdccddabdaadbadbaababaddbddaababdadabcbacbababaaacbdcbaddccddadddacacccdacbacabddaabadcbbcadadddccbdcddcbaadcadbddbcdbcdddaaacacdbadcdadaacbdcbdbbdcdcddababadbbaddbacdacdbaaabaaabacdcdcdbdcabcddcddbacababdacbbbcabbcccdacdbabcacbbbabddacbbadbcabadcddbdddacadcdaadbbdababacdbadcccbaaccbcbccddadbcdaabbcdcadaacbbcbadbddcbacdadbaaccaadddcabadcbacccaacaccbbdccdcdcbdabbcadccabadadcabccdcbbbbdcbbddcadccadcacdaacdcdabcaacdcccacabadcdabadccbdacabdddbbdbacdabdcdcaacaaacdbbddddbdcacabdbbaadabcbdccaacabdddbbadbdbcddbbdcbdcdabaaababbbacdabbdbcaacabaadacabddcacdcbabdabdaaaacacabcddcabddbddccdacccabcbdcbccabdcdbacacaadbabaaadcdbddcccdcbbacbbbcbbcaabbbbccbaacbdcdaabcaddcabbbaacddcadddbdbacccaaaddcababcccbcdcdabcaddabbaaacdcaadabdbcdbabbccbcaaabbbbdccccdcddbbabccadbdcabbadbcababbdbadbbaacacbabdaddcaabbcbbcbaadabccbbcddabbbcddbdcabbddbabadbadcddbccacddabcbcacdacdacadcbbadaaacbabdcdabadbddbdbdadabaadadbcdcaccadcddcdbdddacddcaabbbcbdcdaabcaacabbcdcdcdbdcddbbdbdaaaacbaaacccdcdabacdcabbbcdcbbdddddccbaaabaacdbdbdbcabcdbcbaddabcbbbddacadbaaaababdbbdcbbcddbcdbaabdbaddbbdbdabcbabacadaddadcdcccdacdcaccadbbdcbbdcbcadabcdabcabcccabcbccdabbccdbcddcbbaabdbcddcdbbddbacbddaddccbaacbbdbaaadabdcbccbacbcbaddddbdaacacdcbcbcdbacdcaddbabdadabddaccabacabcaccdcbdcadcdccbbbdaadddcbccbcaddbcdbdccdcbdabcbaccadbacbbacadcacacaacadbcbccbbbcadddbabadcbaacddbbddddbbdddbadacaaabdadaacbbabccaaabdadbacadbbbdbdbbbbaaadcdaaddddccddcbddadcdbbbddddccdaccdcbccdaaacdacbadcabadddddbbaaaabcaaacadabcddcdbcdccdadcdcbbdbbdbddadacadbbbaabbcabacccdbcbbdcbbbdbbbccdbbcdadadcbadaaadcacddadaacdadddcadccdaacdccccdbdcbbdbdbbbadacbccdbababdaabcadaccdbbabaacadabbaaaadddbbadbcaadacabaaccbbbccbababcaacbabdccbaddbaccbdbddccdddadbddbdbbdaabbabaacdaacbcddabcdddbbabcbbbcbbbbabaccbaadaacaddccccabadbacbcdabcccabcbbddacaaddccadbcdbbddcadabbbdbcaddadbdbdccbbabacdaacbbcacadbcdbcbddabaadccadbadcdaabdccaacbbaaaadbdbcaddbcdabdaccaabcbdcddbabacaddccdbbdcaddacddbbcacccadcdccdcabdabbdacbcccbcdbaacbadabadddbbdcabdddabccbbaacacabacabadaabadcdcddacaccccaddddabaccacdbdcbddbcadccdabcdcbacbbbccdaaddadbdaadcdbddbccccadcbddcbbabbdbbacccabdabbbbdcdcbcbaadbdcbadcabbdbaaacdccccddacbccadbcddbdddbaacabcaaadacacddadabaadbcbaacbbdbabcabcaacdbbcbacbbdbdadcbaccdcbcdbbbacbaabbabaccbbabaaadadacbccbcaadadcbdadccabddbaddcccbcdcacdccdbbdbdddcaabacbabacbbbaabccacbbbdccbacbdbbaadabaadbdbbabbddcdaabbcccdbcabcaccbbdcdbbacbccdabacdbdcdcdaddcbbdabadbcaddcbbccdbbaacbacbddabaccbabccbabdadcbddadacdadcaabcbbbccdbcdcbcaacaaacbabbdacabdcbdbbdadbaaacdcdbbbaccdcabbdcdcbacaabcbaaddabdbacbbabcadcaccaabaabbbdccdbcdbbaabacbccbbadbbcaaabdbdaaccadbacdbdbbbbbbbadabcdcccaccbababaacdcadcbacbccdbdddabdaadbdcaabaccabacbbccbdaadcbbdddabbcbaaadabbbdbcbacacabdacdcaadbabaddddbacccbaabbcccbbdbcbabbaaacdcbaadbdccbdabdcbaadcbddabcbadadcddcdcacbcdacadbdbaacabaccbcddadbdcbacadbbcacabacbbbdccddbdabbbbaadaddbbbdddadacabaaaaddddbbabbabaacdbdbbccdabacccdaaadabdddacccccddccaacccdcddccddbdccaabcccdabcdcdccaabdddbdbbddcbbdbbabcbdababdacdccddcadaabbabccccacdcbdadcdcbaadbadcbadbaaabcaccddabacaaaaddcbcbdbdadcbcccbdbbbabdbaddbcdbacdbddbadbbadacddcdbdbddbbaccddcddaddadcdccacddabbdaaadacccdcbabadabcbabaaabbcdacbaadcdcbddabdadabdcdddabaccdaacbdacdcbcccdadbadabdbabbbdbadcabbbabbadbadadcddabdbaccabaabbadabbbbbacdbdacaacababcbbabbbbacbacaacdcccddcbdaccddaabcabaaacbacbaccdbadacbcbdaddbcbddbcdbddccbadaabdacbdadaccadabdcbadcaacbbacdcbcaddccadacbbdcdcdacdaddbadcdbbadccddcddddbcccbdbacdcaabcacdbbcaccbaddbcbacccaacbbbbabcabacababacdabbddbdddadbbddabaccbcaaacbbbbacdcdbddbacbbcabdbaaccbccbdccdbadbbdbbdaddccdccbdabadccccdabcacdbbbacdccbdccdbadbddabdbaacaadabcbacccdbbcaaadcbdacdbadacbdacadbdccacbccaddddccdcabbacaacacadaaabbcddbcddacdabacacccccccabcddccabddddaccadbadcadacdbcdababbaddbbccccbbadbabdcddbcbaacddadaccdacdadaadbbddaaadadccbbcbbadacadddabbbbdcbcbcddbcadbdadcabbdbacbabdacbcdbdcbdaaddcdadbcdcbccdbabdaccbdaaddacdcbacadababddccddcdcbcdcdabbaadbdbbccbaaaadacaddbddabbdddddacbdcdbddcadddababbaddcbadccabbadccbccdcccbbdddddacaacddbdabcbddcacabbadabcaaddddaaaaadabbccddccabdcacccdcccaaadcdbaadbbccbbdbadbcdaabdadacabcbccbbcaddbaaadcbdcbcbcadabddaacbcdcbadaaacddacbabbacabcbccddabdbabadababcabbaaccbaaacabcccdcddcaaaaaacdcdacabdddaabdacbbdcabadadabcaabdccdcdcbbbaabdcacddcbbdcaadbcbddcadccabbbcbbdaabcaddabdbcacbaccbadcdddcaacdbbbabaaccbbbcdbcdbbadbcbcbccabcaacbcadacbcbbdcdaccdcbbacbccbddccbacdadcacddbdacaacccdacaddadbcabddcbbabccdabbbcbabacdaabcdbcadddcacbcdadacaacaaaaadcbaddabcabcbbbccddbbbbadabbdcdbacccbdbbbdadcdccacbaacdbdbbacacaacdcddadbcdacdaadabcdadbcaacabcbadabbbaabcacccdcddbcbaaacaccbdaaabdcdacabbbcbdbcadbabbddbdabcbdbcbadcaabaabcbdacadbbddcaccdbacdbbaacdddcbaccdbdcdacadbdabddabdacdbaaaadadccaddcdaaabbddbbabccdbddddbbdcbbddbdbcbbbadcbaddddccaacdbbbddcccbabcbadbddccadcbdacaacccccbdcbbdbbcdbbdbbcaadbaadbcadbbadccbabdddbcadbacadbabbbbddaadbbbbbcdacdaaabbdbbadadabdbabaaaddaddaadbaabdadbadadcabbdbcbdadbccaadccabcbbdccaacbdcdabdbcdadbcbbaddaacaacddcbcacacabddabcbcbbdcbbadccaaacadddabcadcbcacadccdddbccdcbddbbbdabcbcdbdbbccdddbdcacacdccccddcbdaddddcccabacddaaadcbbbaccadcbcdccacadcacddcdcdadbabadacbaabbdabdcdabbbdaabccbbbcbdaadabcbabdacbbdaddadabaddcacdbdcabadabbaddbdacccccaacbbacbaadddcdbaadbcbdcbccbbdccccbabacdcdccbddcdddaaaaabadbababcdddccacbaadddabdcdadbbdcabdbcaaadcabcababbccaadccbcabcaccbbbdcacbcbcbbcabbbdaadacddabcddddbccdabdbbcabdcccdcabacadcbdccbdbcdbdcbcbdddacadddadbdccdcdbccacccabadaddabaacccdbbcdabcacaaaacdccddabcdbcbccbcbbbccdbcacdbcabdaccaddcbcdabbdcaddbcbdadbadadcbcadadcddbbddcacddcbadaacabbbabaabadbcaacbaabaaacacbdcccaabbadcbdcbaddaddaccddddcaabbabdcabcccaaaabccbabbcbcaccddbdacccadbacdcaacdbbddacddccbaabddaacbbacacaacbbacbcbddcdcddddbadcbbccdabcdaadaaadbdabadcadaaaaacbcbaabcabdabcacacaacbbbaaccbcaabbddabbdadadadaccbcbccdaaccbaabbddacadbdbbcaaadaddbcabadcdbcaddbbdadaddcbaccdaacdbadacdbbbbaaacdcbcbacbcaccdccdacadacacccbddaacbcbabdcabdaabbdccbbbdacdaabdcdbcbdbacbbaccdcdbcbccacdbbcaccaddccdbdadccccacbbcbdbbabddbbdccaababddabdbcdabdbccbaadcaabadbbacbcacaddcccdcbccadbbabacbbaddbbdbadaddacdcbacaadbabbcbcbcacabcacbabcbbdbaddcbbcadcddadbddbcbbabddacccdabcddbbbcccacbddbbbcaddacccaaccbdadadcaabadbaabbcdadccbcddacbbcdbdcadbcddddacbcbbbadcbbbcdcdddaccadbdacaabdcbcbdccaabbdbdbdababaabddddcdcdcdadccdabddbdbddaaabdaadabadadaddbaacbbddbbccdcdacdbbddadcbdbccaddbcadaadcbdbacbdddaaacabadccdadadccbbcacabdbdbbdbadbbbbdadcdbbdadcbbabaaddbdbdcbcabddadcbcadbdcdbaaadaccdabdcdcdccccdcacbdcbbdcdbcbdbadcaabbddaacbbdbdabdacbdcbcacbacabaadcddaaacdcccdbdcdddbaaddacdbcaaadacbaccacdbdcaaaccccbddabbbdabbdbacaaccccbdacdbdadbbaddbaacdacdddabacabcadcbabdddbabdcacadccaabdbbacbcbdbaacdbdaccccaacdcbddccbcbaddacbadbdaddcacbcaddaaddaabdbddaadbcacccdcbbdcdcddddddacdddabcbcabccbcaccadbddadabcbbcdddccdccabacaaddbacbbadbdadbdacbccdbdbdbabaadbcdbccdadbacbadababbdbcbbadbcaddbbbcaacbcababcbbdabbbccabcacdabdbbcdadcbdbadcccccdddbbbdbcdcdcbcbbdcbbcaaddadacbcccbbdbacccbdbcbdcccabcdbdaccdcbacadadbbadcacdbcdbadcbdbcaaabcdbaddaaaccddcaadbaccddacdddacddbadbaddaaddadaabbabbbaddabdadcccbacbbccbbaabddcadcbbdbbadcbdcbdabaacbbdacbdacbcdbaaadbbdcccdaccbcbddcbadaadadacdcaacbabaadddadcccacccaddaddadaddbcbddcdacdacbdccadbcbcadacbbacccabadacabaccabcbacbdbcbabcdcacbabdbbbcbabababbdddacadcbaabbdcacbbabcabbaaabcbadbbcacdbcbcdcddbbaabaabbbbdcabddcaabcacbddacdcdacdcbbdcadabadacdccdcbacbabbdddadddddcbcabbcdddcaaddbcbccdcabdbbddababbdadbcbddaaadcaadaacbccabcadcbcddcbabcaadaccbaaadbbbbababbddbadbcadcbbcababbcdddccdadcadddbdabadcbddddacdbdabcadaadbbbbdbacbdcaabbbcaacbbaadbacdaaaacabacaacbccbbdacdcaccdcdccadcbdbcdddadaaabbbbdaaddbdbdacbaddbdbdadaacdabccbbadadcdddadaaddddbcbbacdbaaabacdcbcddcaaccccacaabdbccccdccdcadacaacbcbbcccbbcaaababdbdbcacababddaddabdbabcbccdacdaacaabddcacacbdaacbcbdcacdddacdaadddcadbdbcabdadcacddcbcdbacdacbdbdbbdddaddbccccdbbcccbadcdabbbccbbbbdaadcbcdccddcadaacbdbdaabbdbddaacccbadcadaaabbbabadacabbaccaaaaaabbcacccbacbdaabdcaddcbddbbabaabbcccdadbcddabadbbdcaadddcdccbdabadbcadccadacabbdbaddcdcbcdcabccabbddbaacddddaaccabcccbdbbdadaaacbddcaabbbcbcddcaaccbadacbacbabdcccadbbcbbcbcbbcabacaacbbadaadabdbdadbabbaccccbdccdbacbbbadabaccbddcbdccbaaadcacdddbadcccdbbdacbcacaccbdcbbdcdadaccaacbbdddabdcbdbccbaccbacbcacbdddadadcaadadacacdcaaaababddbcbaadadadacadacdadbaadcaacacbbacaccaddacadaacddaabbcabaaadbccbbabcbbcabacdddbbcdccbaaacbacdaccaddcacdaadcbcdcdbcadbadcbdbadabdabdbbcbbbdacdcdccddcadbddcbaadbdcacdcbabbbdcdcdcabbbdabaddcacabcacaaaadadbbbddaddbadbccdbddbcdddacdaccaacbbcadcacaccabddadcaaacabcbcdaaadcccdddbbaccbbcdcdbaddddaccbbdcbbdaacaaddadcbdaddbbcdbcbcbcbdddcaababddaccbacbcbbcacacdcdcbbdacdccababbcaabdccdbadabacdbcdabadbbadccccbbcbccbbddddaacaaaacdbabadadccdcadbabadacbdabbbabacbccdbabdaaddbddbaabddbbadbdbdccdddddccccddbbccbdbbcddbacbdadabbdbabacdbdcaabbdcccabdbddabccdbbabddddaaddbccadcbbbdbabcbbdcbdcaaaacbacdddcdbdaabaaddddccaabddcbccaacbadacbacbaddcbacadbccabcaabbdbcbbbacadbbccbcbdcdcabddabaccacadccbcdbbbddabbacbdcddabaabacbcccaaccbbadccbbbdbcbcbaddbbdbbdbbdbcacdbdcddbbcbdcabcddadddbbdcdadcdacbdbdabaddbabccdbaacbdccccaaadcccdcddaadcdaadacbcadbddddbcaaccccccacdbdaacbbdbbbaadbbaddbdabacabbacabcdcadbabcabdccbabddadabddabadccbcabbcdddcabcbabccddddcababcddcdbbacddcdbddcbbcccdbacacbbdcdaacdabbccadbacbacadabdcccadbdabadadccabdcaaaddbcdcdddacacabdbbacabaccdccbbbcbbcdbaccacccbbdabdabddbaabcadbadbcdaadcabddaddacbbcdcbbccaaaddcacbdadbadabdabdcbddbdccbcbacbdddaddaddcdaccdcdaddbbcbddcbacbaaababaaabdbabadccdababcbbcabdccaddacacbcdbdbabdaadcddcadbacdbadbbacddabcddaccdcbbaadcaddcadaabcddcbababdccbdaccdacbbadbcadabaabdbccdabcddcbadcbddcbaddbbcaddddaacbcddbddcdacbaddcdbcaaacbcbacaaaaaacbadbcabdddcaacadaadbaccddacbabcaccdbdadadaddbccdaccbcbddaaadadcccbdcbcbcbdccbbbaaaadabaacccbaabaaabcababbddbacccccbdcdadddbacbbdacacacccadddaaaaacbaccdaacacdbbabacaaaccbcaaacdaadbbcddcdadcbcddbcabdbccacdbdadacabaabcbdcadcdaaddddacabccbabddcddbcaddcddabbbcddbbbabaadadcddddbcccadbcacaacccbdaabaddbcddababcbdbcbdadddcdbaabcadddcbbccbdcdacdabbaacadbcadcbbcadcabbcbbcbadacdadccacdadbccdbcbbdcaaaacadacaaaddccbdbdbacbbddabdcabaaccbacbcabcabbdcaddccbbabcbdddcdacddbcbaadbdbaabddbaacddcbacbcbbcabadccaadbdcaadddababcddcacacccdbcbabacccbbabcccbbcbcbaacaddbbbdbdbcbccadbadcbbaddbbdbbbcbcaaaaaacacddbaadbdbadbaaaacbbaabbcbbcbdbcadaabdcbcaacadbbbadcccbdbadccdccddcabbbdaabbcdaabcdbcddbdbcdcbcbaadcadacbaabdcdacbadbccabcbcbabbdbdbdaabadccbabaaccccacacbadbaaddccccabbcddcddbbbbbcdacbadadbdddbdaccdbdabdbcdbbbbdbdaaccabbaadcdddaddcacaacadcbabdabdddcaddadabbdaabadbbccdbacdbcacabdaaabaccaacbcbabdbdabbdbddadabddaadccacccbbddcdccbcccbbcdaabbabddcaadddabcaabbabbbbcbadabaabadabdaddccbcacabbcbdaaaddcbdbabbcbacbacacccadbdaaaadbaaadddbdcaadddcbacbdadcddcabbcbadccbccbaddbbcacdccbdbddacaacadcdbdccdbadccabdcbdcccbcaaccbdcddcbacbbabadabbabbbadabbaddaabdaadccadccabdbcccbacdbaaaadabbcdbadcdcbdbccababacddcbadbaaaddaadabaacdbcbbcdadbaddabcdadadbbabbdbcbddadaaccbcdbdbcddbcaccabbcddaccdbccbbdbdbcbdabbbaaabcddabadbbcdcbabadaacabcdbcddcbabaadbcddbaacdbbaaddbbddaabbdacbbaacbcbadcdcbcdccbacbaabadddccdaadcbabbbdcaabdaadbdbacbaabbaabadadbbdaccaabbbbcddbacabcddababcabcaacbcbbcbcabdbabababcdaccbaccabdbadaddcbddbbccabddccaddbbcccabcabdbabbbbaadbcbaddabbdacbddbaddacdccccabbcdaadbabcdbbbdcdbccbcdacdccbadcaacbacbcbbcaddbbacaabbbbbbaaabaddbddddaaaccabcccacccadaaacabcaacadabcdadcababcdbcdbaacadadbabccacdacacbdadcdcacddbbdacdabcadacdadcdacadbaddbcabcdbadddbcadcabbbadcbcccabcbdcbcddddaaadcddcbbdaccbaaddacbcbbabadbadabdaccccdddccdabacbccabcddaccccbabbdbbadccbddbcdcbdccddcbcdbacdbdbcbddcbcadbadcdcdcadacacccadbccbcccbdcdbaacdcbccdbbddbcdcddaacdacaacddcdbccacdacdcdabcbaaccdacadbdabaabbacdbbdabaaadabaccbbababcbcdbaacaadcabdcaddbcccabdccacccadabacdcadcdacddabbbcdcdbaaaadbbcdbdbcbacaaadbaabbddcbdadbdbbbaccbddddacacacbabcccaaaccdcababbdcbdcdbddbbbcccdbddcaccbaabcbcdddbadaabaabbbcbbacaadacbddadddacadcaacbaabdbcddbbddbadbaddbcacdcddbbdcbbbdaacccdcbcacbabdddcddbdabaabaacdbbccdaaccccdbdacddaacaabbcaadadacaabcdacddadbbbaccbbddaddcbcbbdbbcdbdccdcbcccbadaacaaaacaadbcdcdddcbbdabdbcaaaadaacbdbdaccaaabaccadbddadbbaacacaccbbddcdcbcdbdaccbaacbbbbadcabbdcbadaccccbccbaaacbbcbcddabadadcadaddccdbdcbdaddbdbaabdcddccdcaccdabbaaddddbdacabbdaddbdbbbacabadccbabccdddaaaabcbbbbacdaccadbaaadadcaadcdabcbdccaaaddababbacbddbaddcbbcdbdcbcabbdaccdbdaacddcabbdcddbbdccdaacadcdcbdacbdccadbdacdddcadcdbbbcdccbcbbddcbbaccaacacacddadacabcdacddcabcbadaabadbdcdcaaaacadbacbabacabbaddbabccddabbbadbbaccbccabdcbcdadaaccbdbbdaababdcdabdacdcbcddbcbcbaaaddbcddbcadbcbaddbdbbbcccadadaccccccbabccdcabdabdbbacdabcdbcbcaadacadadcacccdabdcddacbabdccabbbcdccabdddcbdaccabdaddadcaabbddbaacdcaaddaacddadccbaddabacbadccdaddddcacbaaaacabcbccacbabcbdbcbcbcadacdcadabbddacacadbdbbaddacbcaccdbadcadadbcbdbdcbbcacbbdccacbddabdbbbdcdbcacbdddcddbdabddddabbbdaccabddddbadaabdbaccbdaaabddcbccbaaadabddaaadcabdabbbcaddbdbdbbbdcdbadccdbabcdadbaadbcadcabbcdbdaddbbbccdddaaddbbdbcccdbacdabcadbbbbbbbadbcababcbcabdccacacaccacbaaccadddacdacadcabcbacbdbaaaacdcadbaaaadcabacdccbcdaadacadaaaaddbbbaddbcbaaaccabcdbaddadbabbacbcddbabaddddddaaadbabddcbaadbcaacadbabbcbdabddcdaddaddadacaaaccbbbcabcbabcdbbdacbcccaabacdcacadbdbcdabdadbadcadabdcbabddbbaabdbcbddccacbcbabbcdbabbbcdbaaadddcabcacdcabacadcddddadaddcbdabbbddbabcacbbdbbbdacabcaabdbacddaacbdaaabcaaddacaacbbaaabdcdcaddbdacbadcbbdbaadaadbdbdcacdbdbabacaacdbbbbdbabaacbcbdcacabbcaadcbbaddbbbcdcbbaddddaaacddaccaacddddbbacbccddddaaabddbcadbbadcbacdcadddbbdacadccdabacccdcaacabcbdbdadadacaadadcadaaaaadccbdbddccbacaaacaddcbccbaddbdacdccabdccccdbadccdbccddaddaacadbbabccdbaaabbacdddabaacdbdacccdabdcddcdcaadaddbaacdabbdbbbbaccacaadadbadaabadddbaacdacdacbbbddddddbbabcaccbcabacaccdaaddccdaacabcbadbbcdccaadadcacbaaccabdddcccabacacaacdabaccddbdbadbcbdacdacbabcaababaccabcbddddbdadaddacdcdaddbdccabaaadaabbacbdadaacbaadbcbccabcccaadcdaacacbdcbadddbaabbcaabddcacdcdadcbcadcbddcbccaacbdbddcbdcadadcacddccddbdaaabaadbcacabdbcdccbccdbadcbacbddcaadddabcaccbbdaaaddccddbbbbcdabdddbbcdccaababccacabbccdbbddabcdadddacbacdbbdcccabccacccabddcaabbddabbcdcadccabccbddcadbddbbacadacdbbaaababadcbbbdddddddabdcdccaddbaacbdbbddccbdbdccabbaacdbbdcbcdbccaabdabcaabcbdaddcaddbcdbccbddddabbaadadbbcbccacdcddcdbdddbbbaabbacbcddacbbbbdcbcbacccbacdbdadadcbccdacbbabbdaadbdbdbcdaccddccadaaabbbccdabdddcbcadcddadaabaaadcdbbbacaaacdbcddcaccddcacdabcdcbcabdbbcdddbddcbabdcdabcbdccaddbbccddadcdaadbddaaababbbadbbddadaacdaddbadbacddadadbcdacdadaadbbaababdacaccbadcccbcabbbcbcddaadabdbabdbbbdabbbdcbdaacbcaacacbabdcddadcccbcbcbbbacabbaccddadacbccbcaadbdbadcadbcccbacbaaadbcddcdabbcbbbabadacdbdbbabbbcbcbaabbadabccaaacaadbccddcbcbcddbbacdaccbbdcdbdaccbbdcbbcdccbacbccbbddacbbddaabdcbaacacdcbaddbabcbadabcddcdaaccdddbadadbcdbabbaddbacbdbaccbaaddabdbadacdcbcabdacbabbbcdaabcdbddccdabadcaddbbdacabaddcbbacaaddcccddadabbcdcadcaddbaabaacbcdcdccaabbbddacaadbdacccabaccaacacaadaacbdabbcaaccdddbcdccbdcaabbcdbcacabadbcdddbbccbcacddbdaacbcccaddccbaddbbabbadabdaaddcabbcdbbbcbcbbcdcccacdcacccddadddbbddddbcddddacbdbabadcbdcadbddcbccbaaadbdbbabdccbdcbccacdbdaddaaacbacccddcdadaccbbcddbddbbcdbcaabacbbddbcbbdccbacacabcdbcdaaaaaccbacabbcccbdccbabbdcdbbdabddbcdbbdccddaccadcccbbadabcacadccabcdbbdadbdbcadddbbcdcbacbbdcbbcdddcabdcaccddabaadbbaacdbcdddbccaddacaabbabdcdcbbcacadddabdcadbaadaaaadadcbabaacabbacaadaacdbcabacaccddbdcbbdcabaddcdbdbadbbaabbbbcbdacbccbadacbdcaacbdcddbcdbdbcccdbdbdcbcccbadddbdcbdabdaadadabbdccbadccbadcdcbabcddbcbcdacdaadcadbdccaddadaacccdbbabdcccdcbbcbcdadbaaccdddadcbccbcacbbcaacacddbbacdabdadbacdbdabbcdcbcbabdbdabddcbccbcaabcabcaacdbbcbaabcddcdbbccacadaaaddabcddabcaddababdcacddbbcbcabacadcccbcbdadadcaaacadaddbcccdbdcbcddcaacadbcbadabcccacaaccdaaadcccaacddbbabbdbacdbabaaacccbbacccdcbccddaccbccbbddbbbbcddbaaddaccdbcddbcddbdbcbdbdacbaddbadacacdbbcccbcdccbdbdbdbadaadacdcdbbbaabadabdadabccbacddcdcbcabacaadbadbcaabdbdbdaaaabdaadddabadcdbacadbbbdcbdcbdcabcadbcbbcdbbccbcccdcdcaccccaaacddbbbbcaaaacddbbddcdacbcaacbdbaddcaaacbccdbccbbcbcccdacccbaacadaadacacadaacccacddbabdbbdcdcccdacdbaaadbbabbcdaabdadcaddbcbddddcccccabcbcdaadabacccbaabcbbdaccdddabdddccdddcbaabbcdcbcabbcbaaabbaadbcddcdcaccbdbdaccbabbabbcadcadddbbdbcbdaacddbaaadccbcaaddaaacdacdaadcddbdacacdbdbadbbabcbcbbbbbbcdacdbdbabddddbaabddcdbacccdddcabbcdbcabaaddacbabbadbadccbcadddadbcdacdbdaaaababdbcbaddbabcabcdbcbdabbadaaddadcadbaaabcbbbaaaccdcadcdbcbbaddacbcabbdddaaddbccbbdcadcaaadbbddbdcaccdcdacdacabdcccbaccdbdbdcaddcdadaddddbbdbbababbbbdbcddccbbcdacccdcadbabcaddcaabacdccdbdcbcdcddaabbadadccbbdaddcccadabcbddabaddbbbcadddcacbddbcddbbcdadbadcaccbdcdbabcdddbadcaddccadababacdcddbcbdabdaddbbcbdbccaaacaabcccbcadaabddadcdabdaaadbcaccdadbabbcccdbccdccdbbcabdcccdabdacddadcaadccabdcbdaaabbbdacbadadbbcaccbadbdbbbaddbdcadaccdcacbadabbcbaadacbbbbddacaababddbdbbdbababacbadcacabacacaadbbdccbddbbbdcdadabbadcccdabacbcabbdcacaddddbdddacbbbabadcccddbbbabaabaaacccaadbdcdaaaddcadabbaccbccbadcabdddbccdcccabbcdacdadabbabcacbdadcaaabbccdacbadcabddacdcbbcadbdbdccdcbadaaaadbcacbaacdbbacaacbdbdaccccbdabbacdccbdddabcccdcbbacccdabccdabaadabdbaadacacbdbdcddcbaacbbacdaabbabbaaadaacbacdddbbdaacbcbcaadcdaadccddcbbaaddabcbccddbddccbbbabddcdbbcdcacdaaccdcabdccbcaabaadbacabcdacddcaaccdabcadacbdadadacaaccdcbaacdcabcabdcabadbbcbcacabccabcdcacddbcaadbdaababbcbccabdbaddddacaabbbccddcbbbccdacccdbdbbbbbdadcbabdcbaabacbdcdbbdababaadaaabbcbbdaacadbaaaabbabcadddaadbadcdaddbaadcddccddcbcdbadccadabdadbcbbcbcbbbdabbbcbbcddbacaacccbbdaccdbbccaddccbacccbadacabdaaaadbddbcadadddbbdcbadcbaccacdbcbbbcccdacbbbbcdddaaddcbacddccbacdbbcababcdaccdaaccbdbdddcbdbcaddcbacdcaddcdcccabbcdbdccddacddddcdbabacddcdacbabbcbdcbbddacbdccaaaacadbddddcaadcbaddcccbbaaadbdddcaddcbbbdababadaddacbdabacabbdabcbdbaaabccaaaaccaabbbbccbbdbbdcccadbbcdabcdacabcadbcbabddbbaccacdbddcddddcdbaaacccbaadbbdcbcdaaccbcdbdadaaddcccadcabddbaddbcbabbdcccabcbddacbbdbacaccbdbcabdaabbcdaabddcddcabadaddacacadbadbddccdbddbdcbbaacdbdadadadaabcbadccdbdaabdbadbcddbbcdcbacccadbaccdabdbbcaacdacdbbcdddabdcaddadccacbcbddbacbdaaacccbdadbdabababdcbdcadbdbaaadbdbdabcbbdaaababdddddccdbbbdcbcdcadadacabdabbbdaadaacbdbcbacbcacdabcbaaacbdaccbbdbdcbdbcdacabdabdccdbadcacccaadbcaaddcadcbddadacdbcbbacdccbcaadccccbabdcbbbdacbabcdbcaddccabdabbddacbabbdcdadccbcdbbddcbacacdcdbbcaacdcadcaaacddcdaccbaabacccabbcaacdaacabbacbdadddabbbccddbbddcadbbaaccbcbccaccbaacdbcaabbcbcccbbcdddddcbcbaabaddadbababddcabaccccddadbdbbccaacdbdaaabacdcdabdbbbdbdcdaccadacaaaadcabadaadcdaccabbbddcdbcadaccdccdacddbbbadadababadbdacdaacdabbbabbccdabdabbcbaabccacabdbbcababaaaaacdbaabdabccacacccabcdddcbcabaadcbbdaabdadddcbbcbbabbddacdbdabbadccccbdbdbdcbdccabdbaccdbabdadacddbdaadbddbabbacbbbcdcbaabcdaaddadbadbaadddabbaaabdabcdabbcabddabcbbdccddbdbaadcdadbbbacdcbadacaddacabaacdabdbbbcdcababacaababdcdcdbdbbbadbddbdaddabbdbcaaaabbcabdabddbadadabcdbcccadaccddddabddcaaaadadacabbccabbcbcabcacbdcdcddbaadbadbcbbdcdbabcabadddadcdcdadacaccdbbbdcdaaabbbdaabdabdcbadacddbbcbccdaccdcbdacdaaadbccdbbcbbdbbabcdabcacacdbbcdbbdbccabbdbabdddcbabdcadcaaccadabadbdcdddbcdcbabdccddbacbbdbbbdbadddbdcddcaccdbbdddaacadddadadaacbadacbabddbbababadbdddcbbacbcccddcbddcaaccddcbacabdcaccdbdbdbaaddabcbcdcaaabdbccabbdabbcbaaaaddadbaccadddabcbcdcbdbdddadccbcbadbbcbacbbcdaadbbadaddbaaddbbabdccadabddaaaacdbcabcabbdcaddadadadadbabbddadcdaccbadccdcdaaadaadbcbbaaaddbddacdcbbddadbcacbcddbaccbabdadccdadbbaaacabccacadbcabddacccdcabacdbdbacdbbbdcbbcaadddddadcbbbdbdbcdbcdccadabcbdadcacbdbaadaacabcbcdcaadbcacbcdcdaadcbabbadddcdbddbadbcccbcbcabbaadaabdacdabcadcddddcaabaaccbbbadccabbcdcaaddacbbddddaaddbabbdcccadbcdbbccacbbbbdcaabddbcdadbcabddddacddcadbbcdabaccbaddbbccddbaadadadbcbddcbcbbccacddcbbcadababcdbcddbdadbbccdbaccbcdbbdabadcdadcccbccccaacdbbbcbabbdbacbbdacbbaacddabadaabbbaddcccddbcbabbabbbcabadcccacbaccdaaccbccaccbcaabbbcbcbddaaabcabaccbdbbdbdacccbccaddadddcbbccdbbcbbbddaddcbdacacbdbddacbaabbcaaacbddadbbcdabacbaddaaccdaddcbcdccbabdccdcbdcbddbccadbcbadacbbcaacccbdcadbbaabbcdabbdbbbddbbaabbdaccadcacabcbacddadcabbbbabacdcbcadadbaaaaddbdbcacaacbdaaabbdddadabcbaabdabbbbddbbcddddccdaabcbacaaddabaddccddcdcadbdbadabccbbcbbdacddbcdabacacccabbcbadacacccbbaccbccbaddcdbdddddcbaacabaaddabacdaabbbabacbacbddccccbbbbbcbbacacdabbdcbcabdcbcdcdbbbddabbbabbbddcbcabcbbbcabaadddabaadadbacdcdccaabdcdddabcbddaabbcaabacdcaabdadbbbbaaccbdcccadaaabaacccadabbaadbbcadbcacbdcabacaaddaaccacbbaaaaabcacddaaadddcadcbdbacdbacacabcacaacdaaadadddcbaccadddbabadbbdcabdcabadaaaabdbcdbacdcdbcaccacacddbcdabbbbcddcaccdabdddcbbaadbadccbbcacbcddcdddaabddcaddbbbbaadcdadbacadccdbbdabdbcbcabbadbddcbbdbcddcddbbbdbcbcbccaaadbcbacdadcdcbccdabcdabdabbbaaacaddbadaddcabacbdbbbcbaaabdcdaabdcaaaaaadcabcabdaddbbbdcadcddaadbdaddbcabbbcaacaaccaddabdcbbcdcccdcacdcabcbcdbadcdccadbddcbdddddbbddcbabdaccbbabcaddcbbcaddabaabaadaabbcabdacdabdcdcbacbbbdddccababdaaccddccaddaabadbdcbacdbbaddbccabadbabaabdcadbbccaddadaabcadacbbcbcbabaabddbadcdadbdabcdccdcaabbbcabbddbbacdcbcdcdcbbbdcdbacdcacaaddacbccabdddacbababcabcdbbdccbccdadaddbadcbbbdadbdabbdbddddddbdbbcbadbdbcccaacdcaccaabdbdcbaaabccacdbdaaabababcdbabcdccdbccaacacacbbacddabdcbadabdbbdcddbbaadccaabaabbcaacdcdbcbabcadabcaccaabadbccddcddbccdbcccaddbcadaccdcbbbdbdcbccabadcdbbbddbabccadddbaccddadaadbcbbbccbddbcccaadcbddbacaaadccababbacdacabcccaabcaccbdabcddbdbadadbabdcbbdbcdccdbcaaccbcaadbcbddabaddbcbcbbbcbbababbbdaabbbbcddbababddcccabbbbbbdcbaccacdbaaaaabaddcabbbdabdbdadcabacaaaccbcbccbcbaaabbcdcadacdcdbbbbccdbdcabbdbadbdacdbadaacabbdbadcacabccdcccacabcdabaddbbccdcdbdddabdbcbabbbcdaabbcdcbcdbdcbbabbbcadadacbcdcbadaacbdbacbcacaccacadccbdbbdaddbdadaabcbbaaacdcadbbacacccadaadbabbdcacaccdaacbadaaaacbbcaccbacddbdddddccbddcbdddcaacdcbbbcabbdccddbbccacacdacbcbaddbadbbabddbadbaaadcdbdacbaddaadcaaabbadcdbbaacdacddaaacabadbccbbdbbabddbdaacadbbbddbcabadcbcccadacbcdddaadcbdbabcbbcbdccadcacabdbdbdbdadccadcdbdbcbdaaccaaacbcdcdcbcbaacaacdcbdacacbaaccbddabbadbccbcbddcbbaabbacdbcacbdacaacdbabdaacbdccaacdbadaadcadadddabcddacaaaddaacbbacbbabbdcadcdbacbdadbabaabcdbbcadaaacaacbbabaccdbdcbaaaabbcccaaddbdcdcabacacaabbdcadaccbaacccdbbbabbdcaaaddcdbdccbcdddbabcbdadaacdbdaaacabadacbddddacacadacdadbabdcdbccaaddbaaadbdcacddaddabcaabcbbdcaaacccdbcbdacbcdbcbcaadcdbaccbababbcbbcddaddddaccbaccaabbcadcddabacccdaaacddacaabbbbdccababdccbaadbddaccbbdaabababacccbcddcbcaddcbcadcccaabbcbcacbcdbdadcccabbbccadcbbbacbadadacabdaaabcacabcdabcdcabbabdcadddbcabdbbbccbcacabcbcbccccadbcddbdabcacdabaaacbaaadaabdcbbdccdcdadcddbabadabcdccabaadbdabddadaacddddbbabababcdcaaddbbdcacbabbabdadcaacabcdbbdcbacdabaccbaadbddccacacbdddacdcadbbbbaadadabaccdadbbaddbdaadddcaaaaddabbddbbbbccddaabbcbcdccadacadaaddabbcdcabbdddcdadddcacdcbdbacadcabbbdbdbaccbddacccaabdaacaacdcdaacacbbacdabdbabacaabbabaaabbabdcdbccabcccdcccacbddbdbdacbddcabcabcadabacabdcabcbacabbbaacacbcbabadcbcdadcdddcacacaadcdcbccdddcccbaddadcaacdbbadcbcbccbbcbdcdccabddaaadbcdcdbbcddbcabaacdabddadcabbdacbcaaaacccadbadadcabaaccccdadabdbaabbaabbcbcbddcbbaacabddbdddcbdddddcbabcaabccccaabbaadaabbdbdccbdacdbabdcbccbcbcabbddcbaacddddddccbaabddaddddbaccbbccbcdabadcbcbaaddcadbbdcbababcaaddbdadacbaaadccddbcaccdbdacddcbbcdaaabbbdbadcacadbadcabaaccbbdbddcdcdbbdacbdbdbcccdcaddcbabacdbcbbabdcbdaacdcadddabadbaccadbaccbabddbbbdbcaaabdbaaaacaaabcabbdbdacdababbcbdbdddbcbcaadcccadbdbcacdbaddddbcbababadadbcdddabdccbdbcdccbacdabbaabaacccccbacacdccabddcaabadcaaaaaccabbbbbcbdddcaacccdbaddbcacbcdcaadbbbaccaaabbbabddddadddcbcbdabcbadabbbbdbddcacdcaacabdaaadcdcbdccbbbacbabcbbaccdacddaaaaadcaabdababddddbbccdddbabcbaddacdabaadcadcaadddbaddacdadcbcbcbabadaadbbbbddbccbabdbccdacbdcbaabbadcbcddcdcccabdcbcbdbdbccaccdccdcdacdcaabdabaacdacbaaccdadadcabbbbdacbacbdbdbabbaadcacaacabbdabbcdbadcaaccbbbccbbacabbbcdbdaacdbabcabcbabaccbbbbabccdbcadacabbdacbabbcbbdbbbddacbcaaddbabccddccbdabacadbacabbcaddacbcabacadbadcaabdacccaadccaabbdbbdcacacbacaaabcbbcbddaadccbbbcacacddabdbcbdccbabccdccaacabccacddadabbacbbccddaacadbddacbaabdbcdccdbbacbdbccbcaabcadbcadcbdaccdbccaaaaacbbbddcaccdddddddaaccaaacdaccdabdadabacbcbdcaabcddddbabbdabdcaccbbdbcbbccacadabbadaadddaabccbbccdcdaabbabdbaadbddacbbadcdbdcdaddacbcdccdbaddcbaccabcddcabcbddcbdcababaacdaccacddadaadbbaddbccadbcbadbbdbccabbbcaddddcbadbddcdaabdbdabddacaacaccacdbbcdcccbaccbdcacbcddddaabcccabaccddccdbcabcbdadddcabcdddddcccadcdbdbadcabcabddbbaccadcdabacddabbcbbccbabddcdbccaaccdbdadcabadbddbbcbacaababaddacaabadaadbdcccabddabbaddacabcaaacccdaacbddbdaabbabdcbdabadacacaaababddbbccccbbddbbcddabaacbcabddabbdabbcbbddcabbdccacccbdbdbdccdacbcdddadabcabcdcbdccdaacaddcdbdbaadcdaabddcbbbdbaccdadbacadcaccadbbdbcbaddbbaacbdaaadccdacccadbbbadbdbabddbccadcdbcdccdaaddaddbaadcaacdccabaadccdbaaddacdabbbddcccbcbaddadadaccdcaacbaacddbccbbddcdcaacdcbbcdbcacddaadbcbacbaaccdbaaddacbbcdcadaabcaaadcbabaadabccbdcadabcdbbcbbdbcbcccbcadcbcccadcbbdaaaccbccdaacccdaaabbbbadcdccbbbcaabacbdabbbcdddacbcbadbcbbdcdccbbddbcaaaabcadcbaddcddbacbdbdaccdddabdbabdacccbaaadddbaacdcbbaaddcddbdacdbbddcccadaadbbdddbcddddcccaaaaabbbbdcdaabacaddbcadccdddacadcaadcdaacdaddbadcbdcdcacccdbaaacabbcdcbdabdaadabddddaccbcbbcccbbcddcacdbbaaabbcccdcacbbdbbaaddddcccdbabccddcbaddaabdbdccbbabddacacaacdaaabaaaddbcbacdcccbacadcaacdadccacabbbcdcdaaddcbadcaabbddabccbdaaacadadabbcdaccbcdabacaaadaaabbbaccaacbcbaadccdcddcaacbbddbcaaacacbdaabcdcdbddcdbbcbbbadccdaccacadbcbddcdbbdcbccdaadaacbbabadcdcdbbacadabcbdccacabbcdccbacbbbbacdabbbbbdcddaadadccdcddaadcdcccbacadacdcdacaccddabcaddbcdaadcbdcacddaccbabbdbdbbbccabcccacbbcdddccdccbbccadadbccdddaadaddbadbdbdbbdadcaddbbdababaccababdbddcdbacadbddacadabcdbbcbdddddbccaccbaccbddaccdabdacabacbbcbccbabdadbcaabcdadbcbdbacbacaabcdabbbaddaccaacbcdcbaddabdcadbccccdadbdaddadacacacdabbdcabdadddccdbddcbaaacbdbdaabdddbabddbcbbcdabaaaadbdccdcdccaaadaabdccbdcdddabccadadddbaadacdcabacbdcabdddaaadcacbbdbabdaadaccbdabdbbaadbdbdddcbabcbbdaccbdacaaacccdabcadaabcddcdbabaccdadbdaababdbdccddacadbdcdcbdbadcacccabdaaacdadcbadacabcbdbdcbdddbbaabaaabcbadbaaccacbaaadccabbbacbdccdcaacbcaadccbccaabcddabbdcbbbababccadbcadaacbdccbaaaddabadaabababcdacaaddcbcbbaaacbcdcadacdbcabbcacbbbaaaacbcccbbbdadabcbcbabbaaaddcadbcdcdaddcacbabcadbdcbbdaddcadbdbdaaadbdacdcdbaccbdbcddcccaadaadabadbdbadbcdadcaaccccbdcbacaaacacdddddbdddaabbaacbbdbccaaaaadbdaccddcbbdbaabdaaacdadddccbabcbdddcaddbcccdcadadacbdaaccdaaabbbccdcdbcbcaaaacddbadbcadacbdccdabbaabdacaaacaadcdbcdbcbadcadabbbdccadaddddcbbacacbdccdddaabcbbbcaaadbaacacacccaadcadcdaaacadacdadbacbbddbdbbbacbabaccbccbaaccdabacbdabbcdbbbaaaaadcbacccacbabcddddacdccadaaadabdadbacaabadbadadcccdcdcdcbcccabbdcbdbaccdccbdcacbbdaadbdbcccddcadbadbccdbddcdcbaabbcdabddacbddbaaabcaabbdacccabbbbdbbacaccabdbcaabdccdcadccaadcbaccdccadbaacdcdaaabddcdadcdcbcbbbcdcaacdccbcdadbabccbbabccadcbdadbaddbdbcdbabbbcbdaacabdcaccdbbddbccadbaddbbcaacddccadddacddcdbabaddcabaddcdadbddabbababddacccabbbcaaddacdaaccabbccbcabadbbbacadcccbabbabbcbabadcbbdaaccabddcaccdbbbbbbaacbacbabbddcdbdccdaaddcccbdaddddbcaabcbacdacdaaaaaaadbbbddbcacadaddcdbcdadabbaccbaabdcbcabadacacbdcdaadbbbadbaadadcdcdcdccbbaaacadccaacdddaabcbbabbbbdddbabbdbcaccccacccbdcaddbcbacbadadadbbbaabccacbcdbadcddabdcbcbdcbddcdccccdbdbdcbacaccadccacdababacaabddcbadccbdbacadadabbaadddcababdbdddacdbaccbbccbadddbbcdbdcbccaacccbabbcbcdddadcacaaabdaacdcbabcbdcdbaabcdddbbadaacaadddcbaddababcaacbcbcdbcdbbdcaadcbadcdacdcbcaacdbdbaccadbacddacaccddaabcabaaccdccabccdcdaacdccadbcadbdaccdcdcaabacadaccdccbcaabbacbaadbbbaddbacbcacdccbcabaaaadabcabcbaabbcbacdbcdbcbccbbbadcaaddcdcbbbcbacbcdddbaccbdbaabddabcdcabccabbbacdbbbdcddbdcabccbcaabaaadcddacdcabbdabdadaadcddcdbabdabddaadaddaaacbbdadaabaddcadbcaabbbdacbabcabbccdccaaaaacabdaccabcbbadbddcdbaacbbcdacddcbaacadbcbddbdccaabbbcdabbbabddaaaabcdbcbcaddbbbababddacdcabbababccdacddcaacbbcadbbbaddcdddaaabaabaacdccbacbbcdbacbbacdcdbbccbdccabccdbabbbccdccaabbbaaddbdcbbdbcbacacacabaaacbdcdcbcdccadcacbcbbdaccbabbdcabbbdaacddddacbacabacccabbbabacdcbcbcddbbbbdbdccdcdbbcbdcadacdabacadcabcbaaabaddcbbabaccaaacdbaddbabadcbacddcbcbcaddddbddbcbbdcaddacbbdccbdabaacaccddcccbccabaddbbdbaadcddcbacdccadaaccbbadbddbccbbcadadaccbbdbdddcdbbbcaddaacdadcaaaadadadcbcabdcadccdcccdcacccaabdbdccdadabcacbbadddddbaabcdbbdcbaaabdcacdcbbdbcbbabdccabdccdcbabddbdacacdbbccdbdcaabdbcacbbadadcdadccccbbabadcbabcbcabdcdcadcabccdabcaaaabdaaaccbbadaaaabdabddbcacdcabccbbaadddddadbbabdadbaadaadabacadddaabbdabacbdcdabacaacdccbaaddccbccbbbdbddddcbddccbdacabdbccbdcbacbcbbbabcbbccbbddcddaadacabdbddddbadbadacbaaaaacdbbacbbdcdddcbabddbbbcdbaadbacdcdbacccdbcdcdcacadddbacbaadabbdacddcbcbbcbdbbaacdcbdacdcacdcacacabdbdbacccbcdabbababdaaccaabbcabcadddddbabdcdcbdaadcabcdddabaabbdccbbaacbaccbbddcababddadcbabbbadabcadacaccbadcaccddddabaccbccbbccdccadababcbadddbbdcdbddad