0
1
mirror of https://git.sb/baoshuo/OI-codes.git synced 2024-12-25 16:11:58 +00:00
OI-codes/S2OJ/639/data/string11.in

2 lines
977 KiB (Stored with Git LFS)
Plaintext

dbccadbbacddbaadadabbdddcbadacabcbbabbdacbadddcabcccdacbbddcbbaadccdbddadcaadbdbcccbcbddadcbbcaabaddcdababbaabbaaababcbcbdaaacadddddddbadaaccdaaddccaabccccddccaadcbacdcdcabccaacbbbcbccbddacbdaaaaccbddbcababcbccabcdabcddaadabcbccbccbacbbacbdbdcdaabbdbabbbdcbacadddabcabdbaccabdabcacccabccdbcaddaabadcbbdaacbdaadbabcdbbbbaccdacadaabccbbbdbdbaadcccdcdbcbbacbddcadbcccdcadcddcabbcabbbdbdacddababacdbdaabdbbbcdbaccddcadadbbdababdaabcbdcddcabcabbbcadccdbabbbcadcadbaacadcdddcbbbabacddacdcbbdbabbbcadadaaabbadcadddbadbbbcaddbbbbaddcaddcbdadcdabcccbaabbdbadabcdabdaaabbccaadadadcdbbdadaabcbbbaccadcdbcbbcbcbdabdbbdccdbabcbbdcabbbacaaccaaacddcbcadbdababcacdbacacddabdbbdbaddddbdddbacbddcbaddcddbabddbdbaaadcbaddcdbdacadaddcaabbbbdbabddcbaabaabdcbabbadaccdccbcabdcadcaadadadbbaaaccddddacccbdbdcbbbabcbdbcbacdddddabdbcaaabbbdbddabdbcbbbcadabaddcbccaadcddcbabadbadaaddacaadaddadbdddcbacccbbcdccbcccbdbbdcadabaddcaaacbaddbcaacdcdabccddacbdbdbccbdbbcadaddaccdadddaabcdbcbabcacddccabacababbaccdbaadacdcdcabdbcacaaddaddbcddbcadcbcddcbcaadccbdcbbddcbdcddcbcdaaaadbabbbbcccddcddbbbaabbdcdbcdcccdcaabacaaabcacddacdbbcddccaadbccbcbcbdcbdcbbdcabacbccbabadccbadaaabcabcdccabacccdadbcaddadaccaacdbdccaaabbbbdbccbbaccdbdccabdccbaaaddccddacdcddccacbbbcbcdacaadbdbccdacbcdacbccbaaadddcbadbcdbcddcaaaabcbbbcacbdacccddddaddbddcddbbbadcaacbcddbbaccdbcddcaacdaaadcdddcbccbaddcbbabcaadbaddabbcadbbacabddaddcbdbdcabbcacdcbdcdddcdcdaadbaadbdddcdcbddabdaabaaacbdbabddacbaabdcdbdcccbddcaccccdbdcdadbabbcccdadaccccbdccaababcdadbbcbccadcbcdbbdddadccdddacdddddcbdddadbaaabdbacdbbddcbcddaaadccadadcddccbbdcacabcddcdacbaacadbcbccbadaabbbdcbaadcbadccccdadabdccdcbabbadbcacdaabbbcddccdcbaabdacabacdcddccbbddddbdadcddcdadccdcdbbbccbdacbbbacbcababdcbbdaabbbadaaccabddbcaacddbcadcdcaaadaccbdbcadaaadbdcddabbabbccdcbcdccdcdbdbcbcdbbbacbdbbbdcddaacdcdbbbcccbddaadacaadcdbaaddbaabbbbbdcddabcbcadddabbcdabbcadbbdbbacbbdbabdacddbdccaaadbababaaddbbaddacadbaadadbbaddcbaadccdababbcdbaaabcacdbacbcdbaddccacdcbdaacbabcaacdcacdbcdcacaaccabbdcddaddbcbaadcabbbbcbaacadccdaccbcdbbbccddadcbaacabbabdaddcdbaacabcdadcadbdddbccccbbbbdadccabbcbadabbbbaabacdcdabbcbdbcdbdaddcbdccbaaaddbdbbaaacadaadbaaddcbccbdbdddddcdadcabcdaaccdaadabbcbccddbbcabbdaaaccddaaccaadbcdddabddbddbdbdadaadbccbbcccbddddbbcabbdcdbdbadabadaadbaddddaccbacaadcdcdbaabbcdbdddccbdcbbdbdabdaaaddddacaaccdaacadcbacabdcadcdacadbddbcbabdbbbbbbdaccdaacaddddadbccdabbbaacacdcbacbabdbdcbdbdbcdaadcaaaadcdcadbabdccbdaaaaadbaacdaaabbdcbcbdacaaddabbadcdbdcccaccbcaaadacaddbbddcaabdbbbadabdcdbdbdcdcbddccadbdddbcdcdcaacaadaacdddbdbbbccaddcbcdbdaabddccabdcbabcbacbbadacbababddcdcbccacbdcaaabcabbdadbaacabccbacbadccbdcdacbbaabddddbcccadaaccaaccabdbcbcaddaddbbbcddbacaaddcbdbbbcbddabbcccccdccacadccdbbaccabaadabdbcadbcadbbaccabddcbbbadbccbbcabdbbcbdaadcaccbaabdcdaabadadbcdbaddabccdcbdbcdcbdcabbddacbdaabbaacdadadcabdcdcaabaaabacbaadbadbbddabaaaacbdddcacaaaabcbdcadabcbcabcaabdccbbdbbdbbdaaacbccaccdacbbdadbcbbbbcbbabdbcbaddaaadabbacababbdbdbdcdbdabdaccaaabcccddacddacbbaacdccbbcdbadcddbbdaabcadddadbbddadcaddabcaaacabbbaabcbaaccdbabbbbcaaaccaaaadbbcbbbcccacbaadbbbcabaccadabccccccccddddacbdaadbcaddaaddbdcaccadbdddaabdcbccbbcccbdcacdbadbadbbdacdbbabcdbdcbcadcabadbadadcdbddcbccabddabcaadcbcaccbadbaabacdbcabacccdcabbaacbccbabadbabbbdabacadbdbbcdabccdbdbdabcabcdcdcaadcdcbbccddccabcddcbdddbcbbdacaacbdcddcadccbcbcadcabbdaadadbcdcbcccbcaadadacdbaaaaddacbabadbadccadbcaddccdbbadaacbbbcabbccdbbbbdcaabbbcddcbbbcaccadcddadbaaaacaacdacdbcbddbbaabdbcbdcbcbbcdbadbddbbcbbcccdcbcaaaddabbaaaabadaadcdacdadcdbbdbddabcbdcadbadabdaabdaadbbdbabdaaaacabcbadccbdacbbdcccccddcbccdadddbcabacdbaaaacdacabbbbccaacadbaabadcdaabbaccbccaddbbabbaccaabbddadbddcbdcaccadbdaaacbaddbcccbcdcabdaccdbdaacadbcccbbcdaadddadbadbadcdddaacaadabbdbcddddddbcdcabddaadbdccabcbdcdaacbdacbdbcbcdbccacabdcadaddcdcdabbbcbabcdaddddbbbdbadbbdaccdbbbdbdbdadaacabcadccacccaacddbdbbcbbccddacdbaaacadbacdbcdbadcadbcaccddbaaacbdcccbbdcbbdaaabdbcdbcdcacadbddbdcbcdddbddccdbaccdbdbbdddcbbbadcadaaccddcccabddcdcdcbdadadbcababbbbacddddcbcccacdadcdbabcdaadabdabdadccabacdabbbbcbdaaddbbabcbdcacadbaadbbddcbcdacabacbbccccdbdcddbaaddaddccabbadabbccbacdacaacaaaaadddacacdbbcbadbaabaaaccacdccadbdddbcdabbdacdccdbbabbdcbcacdadaddcadcdbacaddcaabdbdbabdcbbaddcbcccdaadbccaacbbbddddbccddddaaaacccbbbccdacabcdbcadccbabcdbddcdaccabbbaccdccbdcbdaddbbddbadcacdabacabcdcbdadcccadbcddaabddcbcdccbbdcaacbdbbdadadcbcbbaccbbbdbcacadcaddddbbcbabcbdcdddddccdaaaabdadcdcbbdccacdbcbdabbccaacdccaaaadadbdacbbdaabcbacbdcabbbdbdaddbaddbdbbbdcdbdadbcacacdacaccbaaddcbadababadadcaacadccabbabacbcdcadcdbbacdbcdbaabdddcbddcadbbbcbacadddbdbbddabcbbdaddcadabaabbbcbcacacadaccbcbbdaabcababcbbadcaddbacbdacbccdcaaadccaccabbcddbdacbbccbdbacdcabdababbacbcdcadbdcbcdbaaadbbaadcdcdaddcccbcddccbbabddadacacbabbdbbadcaabcbbaabccdaabdcaacccdacddddddbbddaabbcddbacdabbaabcddbaaaacbcaacccabddbcabbccdadbdaabbddddbdddcadddbdbbdbacdbcaaadbadcaabdbdbdddacaabbdababdaacccabdddcdbdbacbabacdccbbbbcdcccccbbbacccadbcbadbdddaaaabccabcadcabcaddbcccaaaddbcbcbabababcbabaaaccbdbcbbdcabdcddcdcaadbdccaaacdddacbacdbaacaabdacdbdbcabbabccdccddcadbbaaacbdaadadaccacbbcdbcadbdaadadbccbcaabddbbdbddcadccaddaacccccbbbccdbddcccdddddbaaaccdbabadcdbaddabbbdbcaadcbddcbbcadcdaabcccaaaadbcabccbaacdbadbcaacbbbdbccaabcbaaccbabdcdaccbdaadaadadaaaddadcadbcbdcbadddcdccbdccbbcdccbcbdbcbaabacabacadcccadaabbddacbbdcbbccbbaabccdaddddbaacbcdddadccbaaaccacdaccccbcdcbddbdcbcccaaabadddabacbcdcbbadcdcaddbddbbaadcaadccacdcbabdcbcabacbdbdbaaaddcddabbbbbcdbdbabbbcbcccbdadcababccbdaaaddbacbdaccdbdcaccdddcddcccdadbaacabdacbbaaaadcabdabcbdbbdbaaababbaadbadcbddcccacbcdbcabadabbddacdcdacdaadacdadcbabddddcbcabcdadcdacadadadccbaabbcdbbdcaacdcbdcbdbaaabacdbddbaccbbaddbcdcadcbcddbacacdaacddbddadbbddbaccdddacbabdaacbbbcacbddbccbbcbcabdcaddbdbcbbaccdbbcbdabacacdcabcaadddddabbddbbadcbdbdcbdabddcdcbadadbcbdabacbbcbcdacaadcbcdcdbddaababacbbddaadcaaaddbbddadcaddaccaadadccaabbbcadcdacaacadcddccdcbababcddbdccbccdcdbcdcacdbabbbabacccddccdaaacdbbbbbbdcacabdbbccabcbbcaacaacadcdbabddaaadaccdddbadbbcadaddbccbcabcabdcaaaccdcdbbcbbccabbbaadaccddacdbcdbaabccbaadddcaaaaabaadbcccaacacccabaddbccaaaacabdbcddadddbacdbaaaaabdcbccaaacccbbbdbcdcadcabaabbacbaaddcabacbaacdcbabacdabbbbcbcadddbaacabddcdcdcaadaddcaacddaccbbbccdddabaacdbaabaaaabcbacbaaaaabbcabdcbdcaababcaaabbddccbabccbabacccabcadadcadaaabcacaaaddddbcaaddcabdddddcbdddaccbdcabdacaacbcdbaabbcbaaaabbddabcbdaaaccaaccdcbbcabcddacccccbdcadabbccdddabcccdcacbdabbaddaaaacacabdaabbdbaddbccccdbabaacadcdcdbbbdccbacccdddaadadcaddaaadadcddabcadbabcdccadabcdcbabdbcdbbaabbadddbcccdbccdddbdaabddabbddcddbdbdaddcbbcbbcddadcbcbcbcdcadcacdadbccbbdccdabbabbaacdcacbcccadcababbadaaababbbddabdabacadcdcbdbbcdacbacdccacdaccaaaaccaaaadbbddbddadaccadbaaadbdbaacacbbdcbbcaccabbbbccacbddbcadccdaddabccaddbcccccbabbdadbbacccdacabbcddabadcdaaccdabbdcdaadadcbdbadacbbdcdbaabdcccaaabdababaddadcdccaddbbbabadcccdbaaacdcaccbbabaddcbbaddababdacdccdbddbcdbdabccbcdddcadccacacccadadcdbbbbdadabbabbcbabdbaddccacbcbdbdcddaccbaddcdcadbacbaddabaadadccbaaddbcdbabcbdabddbbbaacbbcdbacdcddccdcdadbcbbadaadbbacbdacbdcbcaccbdbbbdbcddcbbcabcccccacbaaaacaddcdcabdbbbdbacbbbbccabdbbbbdadacdddddcbcdadabccbcbadccdcbbadddddddbdcdaadacababcbadaacaadcdabbbcacbaadcabdadcdacbadcadbadcddbbbdbddccdaddcbbdccaabdbdddababcbdaacbbccdadcdcbbbabbdddcdcdbcbbbdddcbbdbcbddbabbbbcbaacdcbccaccabaabadaacddcdcdcddbbdccdcbdabdccbcdcbdbccbdbcaacacdcbabbdbaacabbbbbbabaddabdddbccdabbbadbbcbdbccacccdcbddcddcddbdbaddbbaaaadbdcdaacadadabbbabdaabddbcdbcbddbcbdacddadbcdddadaacbabdbadabdaccdacaacaaadbbdbabbdadbdacddadbcbabadddcdacddddbacaabdcdaaddbdcadaddcdaaadbbdcdbddcabdacaacaaaccdabbdadcbdcbccbdbbcadaadaccaddcccbcdcdcaddadccaddbccbbccddabbaabbaadddccddbcbdccaddcbaccaddccbadaadcdcaabdcbcdacbbccddaccabaadbbcabaaaacdbdcbabdaaddbdddabcddacbbadcabccccbbcacddcadbcbbcacddadbdacbbbcdbadbdacaaccdddbcbcddacaaabbaaabaddccddbdacccdcbcdacaadbdcdaccdddddcbdcccdddbbdacaadcacabbaabdbcbcdabcaccdccaaaaacdcabbdbbdbcddbdcababccddccaacadaddababddcbacddcbabcddbbbdadadcdbabbdddacbbdabbdbbbddaaccdabccdcaaccdbcabdcaddaabcdadbddabcdbbdcccccbaacbacbdbddddcbbccdbdabacdaddccdaacbdadabcabddabbdbdbcabbddcddbbcdbbcacdacbcbcbcbbdabdacadccdadbcbabbbcbcaaabadcbccdabaccdabbcbdbbdbcadcadaddaddabbbcddddacacaccadccbadaaaddabbcddacaacbdbcbdbcbcddadbccdadcaddaaababdbdcccdbcadabdbddbaaacdbdbacbdaaaddabcaaaccbaaadbaccabbdbabcbdabdbabcabcaababccaccadacabcabcabcdbcdccbccccacbabbcabdaadbcdaddddbddbdccccbdaadddcdddbdacaacddcabaddcdacbbababbccaabbcdaabdbbcddaccabacccbcabccbdaadacadbcbaacdbdbbcdadbcacacdbaacbcdabdaaabcadbdbbacbdcdcabccbbacaddabbdaabccacccbccdddbacdabacddacacdcbadadbadadbcadccabbcbdbbbbdddaaabadadbbaabaabcadbbcbdddbbdcdbdbcabcabcdcdadddcdadbdbcadcacabdaadacadccdcacabccbbaccaabdddbdadbdbdcadbbcbccdddaabbdaddbbbcddcccdaacdadbcbdbdccdacabadbcaadcaadbacbbdcbbcabcddbcdcdaacadcabbabadbcadddadbcdbdbbbababcdbadabcccaabbabdacdccccbaacacdbaabacdaaadbbabdbdadadbbdcabbdcbbaababbccbdcccdaababddccbaccbdbbbddcdcaadaccddbdbabbabcbccdddbabddcdaadbaddaaaadcbdbadbddbbbcbbbacbbaadddcabcbbdaaccaadbddbddbcbcaadcbdcdacdcbbcaddaaacdddbbabaaddadbbbadbaacdbdcaabcbbaacadbddabaaddcaddbccadcdbdccccbddcdbacdddaccbdbbcaaadddddcdaddcbcbbaacbddaaacdcbaaadddbcbddcbbacdcddbbabcadbbacaabdabcdddbabbaccddacbbdaabadbbcaaacdbabaaadcacbdbbadddbbcbdaabcbdbaabddacaddcdbadcdabdbabdaddcbcddadaccddaaaccdbaccbdccdbbdbbdccaccaacabbbcaddcabcdaadcacacdccbcdbadacaaadabbddaaddcbcddcdbdcaaccddddcaaccbbdbbdbcdddddddbbaacddcdaddabcbddbadabacbabdbdcbddbbbbbbcdccacbcdcaaccaabdcdcdabaacdcbdcabddadddcdbbbaacdcccbcabcadbaccdbcdadddcdbcccacdabaabaddcddccbcaacbbcbdaaabccacaaddcacdaaacccbcbbdabbcdbabaabdbbcdbcdbdcbadcbdabccadcbdabcaabcdbdaadbabcbaadaacccaccddddacbbdbbdabadabccdcdbccbccadbbccbbdbaaabdacddccaadbacddbcdcbaaacaaadbcdadcdbacadaacadaccbbccbbbaddcacacdaadaddbdabacbadaaddaabcdbabcabbcadcbcacdbacdacbaaadccdcadbbcdbabbacdcabcddaabddcbdbdaaddbccadcabdccbdcabdadcabbcddccbaacdaaabdcbaccabdacdaddcbddacbddaadcbbdaddabcdddcbbabddcadaaaddabdababcbdadbccddbcdbbabacddbcdccdcbbaacdbcbddadcacaadbbbaabcbacabadaabadabadbcdcaddbcacdacccdbcccacdcbdadbccaadcbccbcccabcbddbbabcccbababcdcdadadaacdacdcdabadacbaadaadadcaddbbaddddabdcabddccdddaabdaabddaddbbbccaaaaaaaacccabddcdcdbdbadcbbacacddbbccacbbdbbbdabbbaaaadcbcbabdbadbaadddcacbaadddbaccacbacabacdcacaabdbabaddccddaaacacacccbbcdbdcbcbdcadbaacaddabdbcbabdaadbcacdbbbabdbbabcdcccadbcddcbdcbadbddabbacbbbbacabbdcaccdabbbbccabcccadaabbcabddddcbbcddddcacdccdbddacdbdbbbdddcbdabdccddcccadbacaaddddaabdbccbdcbacabaddcacbaadbabcbadadbdbadabadbbcdbdcaddbcabdadabdacdbaadbcddcdaadbdcdddaaaaabdaccdbbdabccddbdcacbdbdbaaddadcddacbadcababbcbdbababbadaddccbdbcdbacabcccdacabbcbaccadadcccbaaadcbadbbdbddcdcabcadddbabacabaaabadcacdabdbdadddcacadadabadabccbaaddccccdcddaaacdbcccbcabdbbaadbcadabccdccacdabbbdddcdbadccacabbaabcbcdbcaacaabcbcaddabdadbaabaddcbdaccdaacccbdbbbaadcaadacbabcacdddcbaaddcaacdabadadcccdaccdabbddddbdcbddaaabdacadbbcdcbdbbacdbaddabdcacadcaddbdcababddddbbdaadcbcabaaabaacaaadabdaaacdcbacbabdaccadaccccdcdacdbacaccadbabadababaccdbccbaaabaadabdcccbcdbbbabdcaacbdaacbbddbbadabdcbcadbadacbbdbddcdcddccbacccddaaadabdcdddbbddbabbbbbbaabccbbdbcababcdabacccdcacdbddacbbacdabdcdcaaacbabadbcbbccbbbbbdbddbbdbbdcbaadacdbcbadaacdabcaadcddbacabcdbbdadcdaacbcbacbabdadbdadcbbcaaaacacdabacbcbaaabdacddccccadaabdabbbadcbcccabbdbcabcbbbacadabbcdbbdbbbbaadcbbadaccbdbaacdaaddbcdadbbaadaaaaaaccacadcacdcdcdccccbdacbacdbacccbcbcacccacabdbcdadcbabaaadaadacbaaabdcdababbacbcddbddbcacccccbaadbddcdcdabcacadcddacadbccdbdcdccaadaaaadabadabacdccbdbabbccccbaadcacaddcdbcddbdabaacadadaadacbdbcddccdcbcdadbcdcacbabacbccdbcbdcbddbdaaacbcddddacdcdacdbdcccbbbbbdbbabacaabbcbbadcddacbacabcbccbaccbacaccbaabcddbdbbaaddcbdbadcddcdadbddbccdcacabcdbbbadccaddcadacdccaadbbadbcaccdadbbbddacabdbddcdcaddacbbabccbabdaddcaaccccadbaacabdcbdccadbbccbcdabdbacdcbddcdbcdbcdcacdaddbdacbcacaadbacaaadbcdbadadbdabccaccabcacbababcaddaaabbaaabdabbbbaacadacbddaacdadaccdcdddbbbdacdddcadcdacaccadbcbbbddacabdcabbaacbcabccbccbdbacaabdcdaddbdadbacaccbbdcbcaacbddabcdbadbccccbabaacabcdcadcbbbbbdcaaaadacbdacbddbcadcabccbddabbcddbbcccadbcbbddbdbbcacdbbdcdaddabaadbcbcbcdaddcddccbbcdbaaaaabdddbbdcdcdccdbdcababacadabababaacdaabbaddcdbdcbdbdcbabbadbbcacaaabbdcaddbdbbdbacdcdbcbbdbaacccccdbaccbbbddababcbcdccdaabbcdddadcadccdcaadadadbcbcbcddadacabdbbcddcacacbbbdbdaacbbabdbcccccadcadaccbcbcdabcaabaadabdacbbbbbdaadbddbdbcaaacccdadcacdbaaadddbdcddacacadbabbbadbdbcddacbdcacadacdcbdaacbbddacbcabdbcaddaccddddcdbcbaacddaaaaabbcadbbdcbbbddddadbdbcacabadacccccbabdcdbbbbdcdbdbaaadcdbcbddaacdabccdaacbabccbddccddccbadcddbdabcbbdbdacdddabcbcdccccadbabdbbaabaaacababdbbabccdcddabbaaabcbccddcccdcdcbbbdccdabbcbabcdadcaaadcabcbbbdddcdcccdabbbddbbcdbbdcbcabbacbaaabddaaacbadcddbdbdacadccdcdbdabaaacabdadbaddacaddbbcccbabddabababcdcababbcabbbbdcabbccbbbbacbcccaccdddbcbccdabababaaaadbddbdcdbbaabcccaacddcabdcddadadcaccabbddbdadbcbbccadccdcadbdcbadbdcdbdadcbcaddabcacccadcdcbacccdcbbcbaddbbccbdcdbaddcadabdddddcddddcbbbaabbbbcaacbbaaddbccadcabdaacaacacdbaacadaaadcccddaddbcdcdbbdbcaacabaacacdbdaccbdbbcbddcdcdacbaacadcdacabcacbbcdddcaadcadaaabcbcdbbaadbbadaaadaadabdabdbccbabddbdbaccddabdcaabddbcacabdaadacdbdadabdbccadddbacbcddabcdaadcaaaddabaddcadaaadbacaabcabcdbaccacadbcabccdddcddabadbdbcdaaaaabaadbbcabddcdaaccccdabcdadbcaaaabcddcacbbcbbbcaaacbbacabcdcadddcabbcacdbabdbcbcccdcaacacdcacacccbabdddbdacbbbbdadcacddbccdbcaccddcabbdccbbaadaabbdccbacbcccbdbcdacdadccbbdacbddcbcadaadcadcddddbadcdaacabbabccdabbabccaaadcdbddbadadbbbdacbcdadcdbcddbcbdcdcbaccadabaaadccadabbbdadbdaabbcdacbaadcabcbdddcacbbbbbbbaabddcdccaabdacaccdacbcdcdcabaacdbadbbdabbddcdddadaaacdddabacadddcdaccddbaadbcdbbdddadbadddbdcbabdaaadcdcccbbdabacbdbbccdaccdababcaccbdaabbaaabcabbbbbdddbddbddbcbbbcdcacdcddacbccaadabcbbaacaadaabdcadabcbcbdcaabcbcaaaddbabbbaccabccacbaaacdaaacdccdbadccbdbdbccbddcbcacbcbdbcddaaaaadbccccaabbbacacaddcbdbccbdbcdbcbcdcddddadaaddbaaccdcbacabadbdbaaaddadcdcddbdbacdbcaadbbccdababccacadcddaccdaadadaaadcddccabcadbadaccdaabaddaaacbcbbabaacbcbabcbdcabdaadacdcbcacadccbcadbbbadbcdacdabbbcdaaabaaadbaaddcdadbaabdccbadcdacdddabbddddacbcacbddabbbaabbcbbdbcbbbaadaadbcdccdbccacbcbdabcbabdaacbaaabadaccccbcdcacbcccbdbacadbcbbdadcbbdaccbdbcdccdccdaadaaddbbbcdbdcdaacabbabaddcbcabbcdbaacabadbcdbabcccabacdddacacaccacdcaccbacaabddadadbabbccdcabbbacbacdccabacaabcadbbccccdcdddddcadacadbdddacaacbddadcabbcbabcdcacbbccaabbccddbdddaddbabadddbabdbddbbdcbadcbadbcccbbdbadccbbcdaacbcbdbadaabdddbdbabadccdaccbbbddbbcdbbacabdbdaacdadccdadbabddbabdcbddbaaacabdbddbbbbcbdadbaabadabcbacdaadcbcdbbdaacadbcddadaadddbacbcddaacaacdbdddcacbbcaccadcaabbcaacdaddaaaadbbcdcddabaaccdcabdbbccdcbaddbcddccaccaacbaddbbcdabacccaaadadbbacbdbbbacddaacbaadacaddabababdabbcadcbbddbaadccdcdadababcdbdbaddbccaaadcbbdddacbddcddcdacaaabacccbdbaabcdbadaabaccbdbcdcaadcbaccccdadbaddadbacabccaccaabdacabdadcbacbdadcdcbacdbccdacbcbcaadbaacdacccddcccdcaacdcbabdabababdbddddaabdcdccdbccdbbcaddaccadbccabdcaabcbacabcccdaaccadccbcdadadacacdbdbaabadddbacaaaabadcddddddbcdcdbddcababdaaccdaabacbaabbcacdadbcacbcbabcbbbbcddaccddbbbdddccccddcbcbcbbdbcdbcddabbbcdbbbdccabbccdcacdcabdacaacdacdccbaddccbcdacdcacbabdadbabcdbaddadacbbbaccbdcdadcbdadcacbbbbaabbddbaacbcbcbcaddaacacbbccadabcdcccbbdaaaaadcdaddabbcccacacbadcddcbaddabcccbcdddddcaacdbdcdadbcdbccbdaadbaaadbddacbdcbaabaadbbbdcdbbdbdbbaaacbbbcbbdddcdabbdcaccdbddbbccbaadbabbdadcdaccdcacdcbabcaddbadaaabddacbcbdcdbcaccabcdbbacbddcdddbcbccccccabaababdbdbaacdacabbdadabccaacbbadaadadadcaddcddbbdacddbddcbcbddcbadbdddbdabbbbccbaadbbdaabbddbdaacbdbcdcdcdbbcdacdcbbddcabaadddacdbdacaabddbabcbbbbcbadaacbccbdccaaddacadcaacdcadbbdcdabadbacbdbaadbcdaabbaabcadabdbddcacbdacbaccddabdababdccaddbaccbdcccacddccdabbcdabbbcbacdbaaadbadddbdabaddbbcdbccccccadacadcbbacacabaddbbaccabbadbacbbbdaadaaadcabdbcaaaddccbdcaadbdabacacdaaacdbcbadcbddddccbcbbbdbdbadbbbbaadbbbcccccdbccdcdbcaddabcdaadadaadabdadbadbbadabacdbcbbbaacbbcbacbddbcccbdbcddddacddbdbacdadadbdbaccadbccabaadbbccdccddbcddddcacdbbbacbdbbccdcacbddddadddabdbdbbacbababaadbccacddcadacccdbcdbabbccbcccabcccaacababaadacdaccdcbdcdbcadbddabbacbdcddadbcbddadbaabccdccaaaaccbbccbacdcbdbdbbacbddcccddcdddcbabccdccbdaaaddddddcbcdbdabdacabbcaaaaccdbabadcbcccbdcabdcbacdbbdcadcdcacdbddacddbacdabdcaddcbdcaddccdbdcccaabccbccacbbadddadcdcbadacadaabcbbdaabbccbacddacdcdbabccaccaaabdcccbacabbcdbdabdaacbbccdccdacabadacdbadabddcdbccaabaabadabbabdbbdcbdacdabaabadbcdabaacdbddcdcdbdcabacacabbacdacdaacadcdabdadbbaaabcddacbaacaacbddaabaddadcdcaacdccaccaccdabaccddbbdabddbcbbdbddaccdccdabdadccbacdbdccdadbadcccbcdddbabcadadcbcbbbddcbdaddccdddbcbcccabbbdccacbdcdddcaddaccbabbadacadacbbdbdaacccaabcbbcdadbbbccacdcdbbbccbcddaabcaccbcaacaadbabcbccdddbdbaccaabcbcdbbdbcddbcabdbbdcabcbaaabacdaadbdccdcbdddaabdcaddaabddbdabacabaddcabadbddddabcabdcadcbccabdbcccaaabdcaccdccacdddbdbabbbcabddcbadcbcdcdbbababddaabacbbbabddccccbdcabdbcbcccbcdcacbcbacabadaadbaccbdaddcbbbcbabbcbaacacddbdaadbcdcbccdcbdacdbdcbacbaadcdacacdcabbdbadbadacdccbacbadaccbcdbdacbaaadcccbbbdcddddddbbdcaadabdbbbdaddacadcbbacadaadbcdbbcbddabbaddcaabaccacbdcdabbddbccdbccaccbbadaddbcddabccacbbbadbdacaddbaabdbcdbaaddacabbcddadaddadabbcacbdcaabccddccdadcbccbcccaabaadccccbbdcdbbdcbdaadbcbacbabadaadaaadbaacbdbadaddcccaddacccddaccbbcacadbacbcdbbdabbbadaababdcdbcdadccdbdaadbcbbdaaacdbaabbcaacdcbaaddadcbbcabddabcbddbbbcccdabccbdadacacadadbabdcbabadbdaddcbddaabaadcaddcacbacaaddabbccdddaadbccddcccbddcbadabbcccddbbbdbacdcababcbdbabdccadcaabacaaadddccbcbcccacbdacbdccdabbcdadacabbddddddcccabcdcaadbaaaccbadaaaaacacbbcccccdbbadcdacccddccbbbbdbbcdbddddadbadbabdbcabaaaddccacbccabdbadadaccddddbaacdbaaddadacbdabcdbacaaacbbbdacbccdcadbcdacdcdccacdcddacbacccaccbcdcbadadbcdbddbadcacbadcddbcacdcbcdccdddbdbaddcbdabcbbaddaccacdaccaabdadcadadbbcdaaaaaddaabbaaacdbbcaaddabcbddddbdbbabcccbbcdcdcccdbacbadbbbaabbdacbcdacaaddbbdddcbabdcccaadbcbccababccbacaadacdbbdadcaadbacdbacdbcdcdcaacbababcbaccabdabbbbdabbcddaaccbbababcddcaddaabdacdabcbabdaabdabccabbddaacaccdcaddabcbbbadacbadcbcbbbddbaccaccddadbdaadbdcaabadabccaaabbcacbbddabbcbbcdaddcbdbcbdbcdbbbbcacbcbccdaadbbabbbcaaaaabbdbacbdadcaadbcabdbcadaaabddaaaddadadadbadbcdcdacdadaddabdabbdadaabdabbdaddcabacdbbdbccabbdbadacdcbbcbcbdbdbbbddaccdacabaabacdddacaaaaabddcbcccbaccaddbccadddccbbdadbbdadaddcddaccaddadbaadadacbdcacbccdddbbcbbaacacdcbbccbbbddaaddbcbcccbbdaadcbadbaabcbbdabbadadcccbbbbddcacadbdcaccccaabccdcdaacccabccadbcbacddcaacacddcccabbcdcbbddbcccacbbcbddbcdbcaaaabdadccccddcaabdbbccbcaabddbcccacacaacbdbadcbbacbccbcdddbacacbccdddabccdbbcdbbbdcbaccabaacdabddcdadbdbabcdcdbbddaacbaddaddbbdbccbccdbbbaddcccdcdddbdabddcdcbcababadacdaabbbcddddcadcbbccaacdacddbdbbcbbdabaccbdcbbbabdcbccbbdbddcddacdcaccabccbacaddccaadcbbadacbdbbbdabdadbdcbbbaaccaccbacaabaddbccbbdddcdbcaaabdaadbaccabcccbdaaadbcadccdacbbcccaadaacabacaddcabaacaddccbccacccbcbdaaddbbbabacdcbdddcbdccdcbdaabaddcacccdcdcdbadbbadcabcdcccabccbccddcbacbbabdadabaadccbdcdcbbcbcdbaadcdacdabccccbcaaabbbadbcbcdbdcabcbabddbcdcbabdcacbabbbabcaacabdbcabcacdcbbdacccccaabadccbbaccddcbdbcbabcadcaadbaaacbadbcbacbbdbacadbbddcdcbddaadabbbccabbcdcdbbcdbccbaadaabbaabdaabdbdadbdacaaabdddbacbcabbccccbcabacbbbddbbacdbdcccabcccabbacadcbbbccdddaacbbdbabddcddbaccbabcdaddbdccbddddcaadccbacabdcbdbcacdabcddccbbacaddbccdbbabcdbcddadcadacdabbbcdcadbacbbacbdbdaadbadddbabbbacccdcbccbdcabddaddadabdccbdcacdbcaaadbdddabaaaddcbcaadbbdbadadddadaaddbbbdbbbbbcbbacbacddbddabbdbdabdcccbdabacbadbdaddcddcdbcbacdcabbaaaacabdcdcadbbcdbcccddcacacbdadaabcadddacdababbbcccdbdbbacacdbadbdbbcbacabbcacdacaddabbdacadcccddaccaacbddbacadbdccbddbacbaaacaacdbabbbacaadcdcddcbcacadddddcbdcabaccbddbdbcdacabaabaadccdbabaacdbbcbccdbbcbcabcbdcacdbadcdddcbaacbbbdbbbabbddcbdaabacacabaacdacbadcdcabadcaacdddacddccacbbadadccdbbacacbaccdccadcbcdaabcdcbadbdbdbcdcbcadacdbdcabcbcdbbdbadaccdbaddabdabbcddddddaaabaacdabbddadbacaaddbcadadccccacbcdbbdaddbbbcdaacdbdbdadbcdbabbccdbddcbddcabdacabdbcbbbbcccbbdbdddbcbaddbaabbbdababccccdadadcdccbbcbccaddbadddcdcddacabadacbbccaadbddbbcbdbcbcadcbbbcacdbdbcbbbdadaacacacdcccbdbaacabaddadcdcbaacadadcaacbccbcadaccdcdbbcadbcbddadbadbccdadbcbdcdbbdacbcddbdabccbbbccdbabcccacaaaabacdaaadaaacdabcaadabbbcbdbdccdabccbbbacdcbaabacccdbbdcccdcabcccdaacdcbaadadadabdbcbbdcbbadcbaabaaaaccbaaaccdaaaadacbadaadcdcbcaaccdacdddacddabcdaacaaadaaacadbdddccdddabcdacbbcdbdbcaacacdabadabadaaddadacadbcdbbaadbdbdbcbcaacaadcaaddaaaaadbdbccaadcbcbbdddbbbcadccadccccabbdbcaddadbdddacddadcabbdccbdcccccbcdbaaccccabbdbaabcbdacbbadcdccdbacbabbdcdaacbaaacabdaacbcdbadaaacaaddaabadcadccddaaddbddaaaabbbbdabbadcdbbdbbccacbabbacadbadbacbadadadddadcacbaadbaaadcbdbaacabdcdcdbcccdcccdaaabbcdcaacccbacadccaabcacaabdcbaddbadadacdbaacabbcacbdacacabdcbacaaacdbbaaaccbbbdbbbdddddbcbaacccabbaadabbbcbbdbabbcadbbbbadcbbadbbddbbbbcadbcdcdaccdaaaccbbcbddbcddadbaacaccbbccbadcabbbacbcbcdadadbddacdcddacbdcddacddcccbcbbbbbccaaccadcbccbddcbddaaadbaabaaaabbabcbddacabddbdaacdaddbdaaacdbacdbcddadbadabcdcbadbadbcddbcdbabccdddaadcaaddbbbabdbdcbaabbabbbdbbcddddcadbbabbbaaaaabdaaaacdacbbacbbccaabbaadbddabddbbbabbccacdadabcaaabbaaaaaaaaccbbbcbdbcbcbdadaccaabddadabddcdaabaccdbbaaadbdcdbdcccdcdbaacdadbacbcbaccaabcadbdbddaaabddacddccbcdabccabcdabcdadadacaadbbbcaadcabaadcbccdddccbbdbbacbccbcdaccccdddaaddbdbbdacbaccacbdbdaacabdbcbbbbccdcccccabaaabbbdaccbcadbbcdccbacdcaaddbbcbbabcdaccbcbbbbdcaabbdcadbbaadbbdcbdddbbbabdbdadbaaddbaabcdcabbdaccbdaaabaadcadaddbbacdcaaccbccabbaadbacbdaddadcdcccacdcdaadbcabccacdcacdabddbdabacbbdccacdccaaadacbbcbddadacbbcbdcabcccbbabcabadddbadddbbaacbbdbbabbcabcdaddcbbcdacaccdbccadbadbddbabdbcdbbbddbadadddddbacbabaabcadbcdbaabcbadbcccbbbaadcbdcbdbbdbdaadbcabdddcdcbbdabdcaccccaabcdcbbcbddbcacaadabcaddcbdbccbcbddbbbcbcccaacdbbabadacacbbbbbaabadadddaacdbcabbdadcabcdcbdabdccbaccadbaccdacbbabdcadcabbaaacbcaaadaadbdcdddccbacccadabcbaddbccbaacaaadacddbadabadadccdadcaacadacdcadcbaaadabbdabdddabcdcdbcaadddaaabcbbbcbaacbccaabcbcabaddcabbdbbbbbadaddcdcdadcaabbcbcddccdaccbaadbdcdabbcadcbaabcdcbdaabbbaddbadbdcbbaaadbbdbaaddabaadcdaccbadcdacbadccbbdbdcdbdabccaabdbcaadccdbbcacdddcbabdcdcdccacbccabacabccaccaabdbccbbdbdcadabdacbabcacdddabcadcdcacbcadcaaadacacbbccbbbbddbadcadbbaacbcdbdabdccdabbcbaabcacdacabadcbdacccbcadddadcaccaacbcaacacddabcdccbddadaadbddccbdabdbbbdadaadbdcdbbdadbcbddcacdacdbaadcdabdcadcdcccbccabddddaabcaacadadaccdbbbcdaaddaddddbaabbbddbbcacaaccbcddccdbaccbdaccccabcabaaccaddccccdbcaaabccbccddbbbadbcacddddcbddbaabdaababbbaacacacadcbccaaccccddabcdbcccbbcbbccbacacdbbdcdaacbcddccdcdcdadaacacdabbccbbacbbaccadacccdadabccbdbadbacbbdaacacacabcdccadbccdabcddddadcdaccddcbdbbbdbbbccddcdcaaccbbadcdabaddadaacbddabcdabacbddadcdacdaddccdabbaabacbcbabacbabaaaccadaabaccbcaabddbbdbdddbddabcbdbdbbadbcdadbcdcabbdaaadadbccdcaccbddcbababdbcacddaacaaaccaaddacbbaddcbbbabcdababcaacacdaaccabdbbddaccbbaddaadbbddbcdaaadbbaacaabdcdccbdaddbaddbadabbbaddbcdbbddbdbdabbcadaaacadbbccbddbabcccdbadadddbdcdbcdbadabbabdcaccddccaddbdccaabaabdcaccdccabddddcddacacdbaadbbcdcbbbadcddaabcbaccdcdbaadabcbcabdbbcabbacbccbbccccadbbadbadbddcbacbcdcdbacdccbdabdbccdaacacbdbbbcdcdabadabdbaaddaabbaabaaccdccadcdbdcccdaccbdaabdaabcdadaccbcbdaaacabdbcaaaabaccdccdbdcbdcbccabdbaadcdbcbabbadbdbdbabcaabbcbddacaaaadaddbcbbabadcabddadabcaddcdadccbcdbbacdaaacdcacddbddddbbbbcacbacbdbbbaaacbddddbdbbbabddcdddababbadcddaacdccdcabacadbdcccdcddbcbadcbdddddbadaaabccbdabbdaccababcbbdbcabbddcbcbbabbcbacddcdaccbbcbadbbcbacbddbaadabadbdabcccacdbdccbabacaadbadbbccddabbbddddaabbbdbabdcddcddcdaadabacadbdbcdaddadccccbdbccccacabddaacccabaddccdbadacccadbbbdcacbacdcaccacccbddbcccaaacaacaddbabccaabdcbaacccacdbdbcdddcddbaccacccddcccaaadccdaacbacdabaabdcacbdaaadbbacdadbccaabdcadbddbdabbdcbbaaabadacbbacdbddddccccaadcdadbdaacaadccbcbcadacadbabdccabccacabcaadbcdccddaadbabaaadbbccadbbbadbdacddbcbcdcbdcdabcdbcddcacdbdadabdbbdbcccacdadaccadcbdbdcccbbccbcdbaccdaadacbdcdbbccbadbbaaababbdaacdcaadbabaaddbddddacdbddbddcbcadbaabaaacbcbddccabdaacacddddaabbccbdacbbdcbdacdbbbaccbadbbcdcddacadacdbadcdbbdbacdbccacdcadabaddcddacddbdaddacadbabddcbdbddbdbcbacaddbbabcbcbbaabaadabbdbacadbcbaacadcbbbaddbcbdcaccadaadbadbdbdaccccccbddabaccbabcdbabcccdbcdbbdbbaacbbbaddcbdaabdabbdcddddcddbbbabccadcabddcadaababcbaaddbdaaaadcbdcdaacbdcbaccaaccbdcdacaabdadccadaabdddcabbaddacdccbadaadcdcadbbdbdaaadcdcadbdcbaccdcbcaacbccdabdabccccdcdcddbbbbbdbcbcdbaadbadaaccbdbcdaaccbdbbdabbdabbaacbcbabbabcacdacdddcbcbcbaaccbcbcdcbcdccaabbddcaadcbaabdbaabdcdabbbddbddcbcbdcbdccacbbbbcccbbbdcaaccacccbbbabcbdadccabbadadbdcbddcaccaddbbacddbcbacabdbdbcbadadddbacabddcaddabdbcbabddcaabbdacabbddcdabccaababbbbdaabdcdbbbbcbadbabdcddacadadcdabdbbdbcbccddbccdccbaadcaadccddacddaaaabcbadbbadaadbdddcccdbaadacdbaccccddaadbcdbccdacdbccdddddabadccccbadabdadabccbaccdadbdcdbdbcbdabbcbaaccccdcabdcdadbabcdcaaaabccbacbabdabccaadbbaccdabccdbbcdcaaadcbcdbcddacbdbccddcbbbcbbbbbbcdbbcbacdbcbcbaddaaccbbadcbdcccdcdabaaabbcaaddbcddcadcccbddbdcbdabddaddccdaaddddccbbcdababdbdaadbddbddbacadadaddddabaaddaccadaadaabcbcbbcaacdadddcacbcccacccdbaccccbdcaabbacdbcdbbbcbdbdbbbbcddbaddadabcdbcdbbdabddadacabbbacdabadcbcabddabccdbcadbadbcbdbdbcbaadbadddaabdcaacadcadbadbaaacdaaccbbbacdabcdcadccbbaddbbdddbaadabbaddcabcdddacbdaabaadbabdcacdbcdabdaccdbcdbadaacdcbbdbbccaabcaaccadbdddbbaddddbdadbbdaacbacccbababbadcaababacbcbbadcbbdbbbcdabbbaadbcbcacddcbcbdbcbcaaaaccbcdcbcdccdbbddcacaaacdbbdaabcdbbcddcdbcaaddadcdacbbdcabaacbdddbdcadcbaccacaccbaccacbccadcccdcaaacabbccaaadadaacbadddccaddbcdcbaaccabcaadaccbcbbdaababacdbaaccdacadacdcaabcdcbdcabbaabdccaaabdcbbcaaaacdacddddcccbcabbbbdcdddbabbbccdcddcbacaadbacabddbddcaddaccbcbadadddaddacdbcadacdaaccbddadbabcdabdcbaaccbdbbadacacabcbcbacbddaadcadcbaabaabcdbdccbdcdacbaacbbaabbdbdcadbbcadcddddcaadcbdcbbacbcbcdaccaadddabaddccbbcbdcbddaadbcdabcbacdcaaddcabaacdadcdabcbbadaacdccddbccbbcdaacdccadaccddabccabbdbdddccdbaddabdadababbdabaacabbbdcadcadcbadaacbddbacbadbcddaabacbaabdccbdadbdcaabbddabbbcaaddabbdacbdcacccdabbbdaacbdacccbbbcdaddccbdbccdbcdacacacbbddcacdcbaabcdadbcaaaddbaccbbbbcdcadcddcdbbbbccacbcbdcbcbdcccacabddaaccabaacaaadabababbaacbdaadcbdccacaddcdbabdcbbdbabddcbbcacbaddcccacbdbbbaabadacaccdcacddabbabcdadaadcdadabbabdddccbcbdaddbdacadcaadccaaabaaacabdcddabdadbadcdddbbbbdcdccabbcabbdccdaaabcbcbaacddcadaaabcbadaadcbdcadddbadcbbdacacbabbacdcbcdcdcbbbdbdccbbdbacbcbaabdbccdbbbdbdbdbadbbdcbbdbbbdbcbbbdddbbbbdbdbddadddaddbadcddaccacbccaccccbbbbbcbbdddcdaddcbcadacbaddcbbcbaaadccccdaccbaadacacbbcacdccbdabdacdadbdcdccdaccbddddadaacacabccbbbbdcddaccddcaacbdaaadacbccaaaabcdbccadabcadacbddbddadaadcaadadadccbdaaacdccdccaabcccdcacbadaccbdcdaacaddaadabaccbbdcacdcacbacaaccdabbdcbdccddcdccabadcbacbcbcdcbcbcccadacdcddbdadabbaccabcdbbdabccabddacdcccbabdddaddccdbacbbbcdbccdabaccacddabbcdddcaaabaddddcabbdaacadadbbdccdabddcbabbbdadadbddcbbcadbbdadbacdaadcdbcdbbddadcaadadadbcbdbcdbdcbbacbcadbdacaaddbacbbabdadccbbbaddcdacdbbbbabccbaaccaaacdbacdccbbbdbdbbcdcacdbdcbdaaaabbdcdaddabdddbdcabbcabcdccdaabdaaaccbbaabbabdbcdcdddadadddabcbacccddcccddbbbaccbdddacbabddaabdcabcaacccbacdcdbbccbbbdaaddcacbbbabbbcbadabaacbbbdadbbcabbacccbaacdaadddbbacbadabadabaccdbcdacbabddbacadcbdbcacbcbaadccaddcbbcaaddcbcacdccbdbbbabaadbacbadccacbbdacbcaccabaaabddaddcdbcbdacdabaadadcdcaacabdacdcbacbbcdbbdcadccdaccdbadddbcdccbdccccbcdadccbbacbccaabbbbbbdababdcccddddbdcdadcbdabdcdaaabbcdacdabbdcbcdbdddacbbacbccaacbaaccccbbccbccdacaabcccabdbcddbaccacabacbdcacccbcbdbadbccccbbabdacadcbdaaabcbcadcabcbdbaddbcdbbccddbcaddcacbdcccdddacdaaabdbcdcaccbabbaadddacdddbbdaccababacbdbadcdaaaadababaccdbbccbbddccbddcdbddadadbaaaabccdddacacbbadaaacabcbadbdcaddbdbcdcaccdaababbabcdbbdaaacbaabbbdbddcbccbdcbaccdbbcaddabdbccbbbadbbccbbcbbaaabaddaddccadcdadbdcbbbacdbaadaddbbdbcabacbdadaacccbccbdcbaaddbdbabddbddcabcadcdacbbccdacaadcaaadbaddbddcbbdcbcdacccdbacbbcccbdaadcbccbdddacacbbadcdbcaabdcaaadbacccbadbddcdbbcbbcbdbbaacccaadbabadbabbadddccaaddccbaacbdccaddcccddcbbddaddadcabababcdcbaacbdcbbabcdadbaddadddadbcdbbaadbbdaaaabaccaaaabdaccdbdadbaadadbbdcadcddddbaaacddbaabcddaaaaaadababcabbaabddcabacdcddbcdabdddacaaccbdbdbdababbdcaccbaaaaaadcaadbbccdbbdbbaadaabcaccdacbbadbdcaababdacbdbadcdaabdabababacddcabcdddcabcbcbbdaddabcccbcadbcaaddcacbbcadbcbbdaacdcddcabaabbdbdcbdabccbdbacaacbbadbbccbdddabccbcdcadaaddcddbcbabcdacccaaccdabaccbacaadbbdcaacdcddabacdbbbcbabcadabacaaabdbbddabbcbbdbbbbbdaacbcbadcbbbdbabdcdadadbddacbacdabbacaaabcaadadadcccdbdcacaadcbdabcacbdaccdadcdbadabcdcdbdddbacaaabdadabddaaabdbcbbadbddabbcdacbbdddaccdaaacaacbcbacabbbcbdbaaaadbbddcababacabccadddabdddbadaabadccadcaabbccccacdaadcdcacccddabaaddaaaacbbbabbddbdadcddddadadbcdddaccdccdccadbdcbaaabddcababcccddcaadddbdaabaaabdbddbabddadcddcdbaacddddbcdcbbaccbccbadaacbadcbbdabdbcadcabdadbddcdddbdccaccccbcdabbdcdacabaabbaabdccccadaadbbdadcdaccadcdacdacbbcbbdccacdbcdbbdbcdbddccadabdcccdcbcdadccacccdbbaccdabccccaabacbabbbccaadabbaaddddbcdbaddabdcaacdcaddbdcbbdaddcbaabccdabaabbdbbadcaabcbbdccaabcbdbacbbccdbccdabdaccbdbaabcdacaddaccaacdacaaddcadcacbdacdadcaacbbdddbbdadcaabdcbccbddbaacddcdbacddcbdddddabcdbacbadddbcdcababcbadbccdcbdbcadadbdcbddcbcbdbaaabcbcaaccacbcbaddaadabdcbbadabcbcdbdabdcccbbbdbbcacbcddbadadacadcdaabcabcccaaaccdabbcbdcbadcaaacccdbaabdadbcccdccdddaccbdcdbbbcdbbaabbcdaacacccddbbbbcccddaddaaabbabccbdcacbbbabbdcbabddcbbbbbbabbaadadabaacbadccabacaaabddcbdbacdbdbccbacabdbdbdcadcdccbcbaacacabcccbdccbddcbbdabddadbddadbbaacadbcdacadcadbbcbabbdacabdbadbbadacbddddccdaccccadcbdbbddadaadbdaaaaaaddbabbcdcddbacddcddccaccbbaacdbadbcddcacaabaaadbbadadbdcccaaaacaacadbcdbcacdaadadcdcbdcdadcaaccbccabbddbdbdddadcbdbbdaabdcdaabbaddcddacbaaaaaddbbbabdbdbaacbabacdcbdbabbbcabdadbccdcdbaabcdbacbdccbbdcabaccddcbdaccacdcdbaaaddddbbaccbdcbdcbbdbcbdbaadbbaccacadcbbbbdcabaddcaddcaaabcadbaddbdbdbbbcaccddcdaccbdacbdbdbdaaabaaaacddabacbadcbdddabbccbcbdddbdbdabcccccaadbadbcbbcdbccbdbcacacaddddacbacabcbdbcaccdbdabdacdbddcddcacddabdbdddccbcbdcacaccabadbbaadcddbbddbdcdcdbbbddacdddaccbbddabddcdbdbbcccaccadaabcccdcaccdddaaabddbddadbbcacccdbcdbdcabaacdcabbcbabbbacabcdbbcabcbdadcacbaaacadbaaacbbadaccdcbabadccbbdbdbacadbbddbadbadabbadcadbdabccadbadcbabdccacadcdbdbdacababbcdabbdbddbdcbbdddbbcccaddcdadcdaddcbbbccbaadbadcbccacbadadcbccbbaabaabcabdbcdadaacccaaccdbbbddcbccbadcabbbdbbddcdbdbbdcbaacacdccccabdaddaacbbcbcbaaadaadccadddaccabbdacbacdbcbadcdaacbdadbdbcbbbbbbbddbaaddabadcabcdcabbaabdbdbddccadccaaacdcabbddadabcaaccdabdacdcbdbdccccaadccaaccbaabbdbabddabacabcddcdcbaaadaadcacdccdbdbbbbbbdabbdbdbacbbdcdcabacacbacdaddbdcadbdacbadccbccaadaaaacaddaabbdcdccacbcdcdcadaccddcbccdcbccacbdcbbcbbddbcbcaadbdcbcdcbdbbdbbaccccbdbaccbaadacadcbcdaaadaabadddcadcdcbcaacbabcadddbdcaadaaccbdaddbaddaacccccccadcaadcdcdbdccabaddabcdcbbdacdbbaaabbbdaabcadbaaadadabcaabbdcadbaccbdabccbbdacaacaaadbcbacadbaacaddbdbdcccbaabaaabdacddabbdaccdcbccbabdbbcddcdbdddddcbdcbbbababbbabaccacabaddcadadcccacddaaaadbacccbdaadbdaabdcadcacaacadaaacadaccbaccdbbaccaadabdcbcdadaaddcdbabcdcabbaaaaccccbcabbdbbddcdcbabcbcbcbccdccaddcccadddacacadccbaabbcadcacabccbcbacbdaccbdddbdacabdaadcdcbdddababcbbaddaddadabcdccdcbadbdcadabddbbaadabdcbdcdcdbcddbaadabdbcbdbdadbcbabadaddabbbabbcacbbaabcdcacbdaadcdaaaddbdadcabbbcdddbccdbbcabcacdcccdbcbcbbbbcbadbcabbcbdacadaaccdbbaccabbcdadbbccaddadbabacccacaaadbdadababbaabbcdbadadacacddbabcdbdbaadcabaadacddcdcdaaddbcdbccbbcadaaabadbccadaadabbbbbcbcabbdbbdaaccbabbbcaabbbdbbccdbdbbbddaddabdabdcabbddbcacdbacccbadaaaacbbdabbdbdcddddddadcdcbacbacdbbadbdbbccddaaadabaabaadccdabbbacdaacbbccbdcaabcbdcadbabdacabdcaaabdbaacbbbbabadcdabccbbcbbbcdbbbbdcdcbdacdaaaccabcbcbdacacbadbadcaabdbcbbdbccdaabdacaabccdcaadadadcdbccacdaadaabddccbcdadcbacabdadcccddcacdacbccaabdaabbacbddcbcddbadbcaadabddddababddadcadbbadbdaccacbaaabaccadadacbdcdabcbcabdccacdcbdbadccbbacbbdaccbaabbcdcddabababadbdbdbaccbbaaabbdcadddbbacabdbaddcbbadaadcbcabaacadbdbbbcdccdcdbdadccaaddccaacdbcabbcaaddaaadddbcdbdadcadbbbdbaccbcbbbadbaabacdbacacdadcaadbbccccaccaaabcbaaacabcddcccadcddaaacadaddddcbaccacacddccabaddbdbdcbbccbbdbcdcaacdadbcdcdccadcbbdbcabdcccccbcaccbacacaaadcbcddbddbddbacbcbaadcdabaacdabaadccbbccabdadaaabdadcbbdabacaccdbbaccbbdcadbcdbbcbaddbadbccacadcbdababdabdddaabdddaaaacddcdddaabadaccaccdbddddadccccdaacacadbbabcabbddbcbaabbcaacbaccabaadaadadabcbddbaaabbadbccccbdaddbbdcbcaddcadabcdcbddccbcaaaacbcabbbccaacaddbbaccadaacdcdabbabadbbddbdbcbcbccccdccadcdaddbcacbcacabadcdadaaacddccbadbadcaabcccabdcddcadcdcdbbcddcbbcdbccabccacbcdbbcdbdcaadddccadaaddbdccdbbadbbccdacddccbbdbabccaaadabbcddbdbaccdbcbcccbbdaddcbdabcbcddbdabbadddaacdadcadcdaacbdddcabdacbddcbcdbabaccadbacabaaaddccabacbcdbaabccdbdaabcbdacacbaaabbacbadabdcacccbacbcacccdbbcbccccdacdbcdcccbbadbadaaccacabcaaabcdacbbccbaabaabdadacdaddbbabacdcddcbbbadbddacdabdcdcabbadcacdbcacabdabddccacdcabcbadbadbdcaaccaaddcddccacadbadaddbbaacdbcbcdaabadbcacbcbdbbdcaacbbbadcadddcdddacbacbbadbcadcacddcccccdbabbaccabbdddabcbddaadcbdbbdbddaddadcdddacabcbabbcbadcdccacbadcaabcbacddcdbdaaddcadcadcabcacacabdbabcdcbdbbbdabbabadbbbcccdaaccdbdcacdacdadbcbcbdbddbddccdaddaabdabaadbbccdaabbbacdbdbababcbacddbcbadcccbdbdccdccabcaddabdaaadbbadcdadacaacddaddaccadcddaddaaaacaccbcaabadcdddcddcabbacdbbdadacbccdaadadbdabbdbabdddddcdabdcccccbcabccadbabccddaccdabccbaddaccddaddddcabbccbcccdacbcdcdadbbddbbdbddbdaabbabbacaabadaaadabccddaaaddbdbbbaadbbabadabbdaaadacbcbdaacccadddcdacdbcbadddaacadbdbdbbaabddababcabacddcbddbbbcdbaaabdaaddbdbabccdccdbbdbcccaaacdbdcdbbcadcdadaacaabdccccabadddadcabaadcdccdabdcbbdbcbcdabdaaaaacaaabcccdcdabbcadaacacdddbbdbdbdbdaacccccdbcbccbabbcbddddccbaddaccdbbccbdccddaddbbabdbbbcacdbcaaaddaadadbacdadbadcdabdcbacacdadccdbacdabbdbddacaddadbdbdbddccddbadaadbbdddabdcdaacbdcabbbbdcdbbbddbdbbccbddbbaaabaabdcaaaabcccabdbcbdbddacdccaacadbadcadddcadadacdccbadbabbdaddcacadbabcabdddababddbbbbabcbabddcdcbadcbddadacdacbbcacacbaaacbbbddacdaabbadcadadacbaccadaddbaaabcaadcacabccdaacdbacccdccdbbbdbbbabcaaabaacddbcdbbdcdddbdacdcdabdaaaccaccddbabcaccdbaabbbcbdddaddcabbdabcdbbadadbbcabbaadcaccadbbbcddbcdacdacabbacadadaaabbcadddcaadbaabacdbcdcddacddccadbddaabccbacaccaaccabacadddbdbaadcddcbcdcdbadbbdbbcadaacbababbdcddbcadcdabaaaababbadabacbdbabbdaaddabcddaadcbbdabccbdbaccaddabdabbbdddcbbabdadabaddbdcaadbcadcddacaabdabddcadcacdadabcbaadcdccccbaddbcaaadcddcddaccbdccaabdabcabdaadadacabbcbbaacddadacaacbbcacddbbadbdbbdcbbacabcaadcabcdaddabdadddabbdbdcadbadddcbbbcbcababddaccccdddcdddabbbacdbadadadcbdddcccdbcccccaaacbdbcccdcbacaddbcbdbbdccadccdddbddccbdddbccbdbdabccaacbabacbabbdabdabccddcddcbdabdbaccacbbadcababbcbccbbbddbcbbbcccbdcbbccbabaacbccbbbcbbdcddbddbbbbaadaddbaababcbdbcdadccbcabdaaddadcbcccabadbaddbbbcbdbcadaabcadccdaabaccbdbaaccbadbdbbaaadccccadabcdcddaaabdcbdadabdacbabcabdadbbdbadbacbdadaddabcbdadcbbacdaddadccaadaacccbcbdcaaddacdbddbbabdbdccaccbcadaaccbdadabdccdddbdabdcaaadaaaaacbaabcbccacaaaabacbbbcdbabbcbdadcaabacacbbdbcaddbcabacabdbadbacbddccbbbbacdacbdabdbdcacbabaacabaccbdabccabccaddcdbddaddccbbbbabbdccbadbbbdcbaadccdccabaadcccbabdcccddacbbadcacabcdddbdcbaabadadabbdacbcbcddcbdbcbdbdbacbddabbbbccbbcacccbccbadddaaabbbadcbbdaabdbbdbaadcbcaccabbabdccdcdbdcabdcabcdddacabdcadbdacaaddbbbbcddcbddabdacdcabbccbbbadcdabacdcbdaabcdcadaddbbcccbbcdddbddcbbabcddacdacdcadbcdcdddcbbbbabdbcdcdcaadccdbdcbccdcabbbabcdadadbbbadcbdabbdbbabbadaabcddbddcbaccabdadaacbaccaacbdabacdddbcabcadbbcacbadcdaaacabdccccbccadadccbbdacddcabbbbcdcdabccaaaaccacdcdbbddaddbdccddaaabccdccbdccbddbbbabbaadccbddddbbadbaaaacdbdaaaaccbbdadaadadabdabdbcacdcacabbdabcdaddbbccadadbbadbdcacdabcbbcadcacdacadddbacbcbcccdacaaaabdccddddcacbbdcacbdccabdbaadbcbaadadbbacdccccbcabbcbccdcbbbddaaadcbcbddbcabbbcbcbddccacbbdadadbbdbccdabcadbbaacbbdcbbabddbddcbabccaabaadccdbbccdcdbabcbcabaaaabdbcdddadcbdbbdabacbdcdccdcdddccdabbcbbacbacccdacdbddbbadbbdbbbbdcadcbbdbcabaaccbddbaabcadcacdabadabaaaddadaadddddcbdaddabdbcddbdccadbbdcacdcbddaababdaccababddcbabaacacbcbdcbdddacbadcacaadcdbcbdddcbcabacacabaacdadcaddaabadaaaadbabccacbdaddddcbaacdccaadcccbcdbbcbcbacaacadabaccbdcacaaddbcaacadbbacacacbacbdbccacbabbabdcdccdadbdddbcbacbababababdbcbcbdacdbacadabbaababbaabcbacaccacabbbbdcdacbcbadbaabcbcbccbcaacdaaacdcbaaabdcbcbdbdbadadbbdcacbdaccaaadcbbbddbccddacbdcacbddadccabbacddcbddcaaccbcbacccccdcbaabdaddbcacdcadcaaacdbbbccddbacabdccdcacaadcadbcaadcbdbcdcbdbcaaaababadcaacdbdddadbabddbdbdbdcbccdcabdbbbadddacdddbaabcaadadbbcaddcdabbacaaaddacbbbcdbdacdbcaaabaadacdccdcbdbbcacdddddccccdbdbcbaabbcbaacdaccbcdccddabcababddccabbbdbaccabacdbadcbbdbcdccbacbccbdaccacbdaadcbdbdabccaddaccaddaddbcccbddadadadddadadddddabccbaabdbcaccdabdababcaccabbccadbdbbbaabbccccdbcbbadacccdcdddcacbdaccabdcbbaabacbdaacaabaabbacdcdcaabccdabbbdababbbbdaadaabcbcbbddccbcbcbcbbbbccaadabddcdccdaacbbccdddabdcadadddbdaaaaccbddbadacbdabdbbadbadccdaacbcacabcccbcdbdccaaaabdddaadbbcadccadbbaacabdadbdbbabbbbaacddcccbdacbbcccdcbbccadaadbacdaabcaacdbacacaacdbcdbdddadcbadddcdcbdbdcacdbbacddaadbddbdacdcdddbdddabdccbbcacbacccdccbbcddcacabbbcddabcdadbcadacccdacbabdaccdbadadcbdddccbdbdcbccadddbddddaddbdcbaabbdcdccadbdddccbaaccbcbbcaadaabcbcdacbdabdacdbdbdbdbbcabaddcbdddbccccbbcdbbddaaadbccbbccdcbadadaadcdadaaccacacaacaadbcbcdbdcddcdabddddcddadbcabcbadaaabbdbabbabccbadbabbadbbccaaaacbccaadadcbdcdcbcdadbbdbdadccadcaaabdbdcaaabcabdddbbddadbaaaaacdcdcccdacdbadcbcaabcccbaddbcbbdbadadddddbbdacabcacdbacbacdbbbbbaaabbcdabbcdccdcabcddcbcdcadcbcbaacaaabcdbcbbbcacdcbabcdaadbcdbacbaacbccbcdbadcddabcaaadcbbcbcddcdbbcbacccdcdadcadcbddacabdbacbaccabcabacbbdadccbcdcabdbbcccbddacbdcbabacadbddbbdaaddccaabdacaacbbbabbaaaadcdbdbaadaadcbcbccbabacacadbacaabcbaadabcdaaddbcbcdacbbabcabbbccbbbddadbbbacbdddddddadcacccaaaabaadacdaaadbdbcbbcdddcdcdaddaccdadbcccbdacacdabcdbdddaacbaadabccdddcaddaccdcbbbbbacdadbdbbacccdaddbdbabbddddccccbabcabbcdaacbdaaacbcdcddddbcadbbcbbaaadaaaacaabbcdbbaacdcadbccdbbaccbcbaaaaadbaabacddbbddaddbababdccdbbccdacbbcddcbaaaaacdccacbadddadbddbabacbcaaadccddcaaaddcccdaccbdbdabdcabaabaccdddcaddacdddcabaacbdcaccaabccaacaacaccbbacdcabbcdbdadcbddcdbbcbbbacdbadbccccbbaaaaaadadcccddbbcdabccacdadcbcddddaadbcdcdcddcdaabcccbcbdadbabaadccbddbccdccdcbcccbdddaddbbaacccbcabccabdababbabccaccbdbbccbcccabaaaabadbadcaaabdaabdaaaaabcbbdacadbbabcdddddcaaaaabdbdadddbcbacabdbccadaddddcdcabbddcdcbcccccbccabdcbbabbcacccdcddabbadaacdadbabcadcdbcccababbbccaccdbcbbcbccbccadacadaaadaacacbcacaacbdbaacdaccdacdbabaacadcbaadabaacbadbbdaacbbddabccbdbdddaabdabadbdcbaccaaccbccdacbcddadddacacacccddcaacadbabbbbdabbdabcaddbbcdcabcacbcccccabcbacbcbdbdadbddbdbcabbbddbadbddcbdacabdddbcaddbddccbcbcdddabcaaddbcaadbdcbaaddadcaacbbcadbcbdddbcdcdadbbcaddabadacaacdaabdaccacdcdabcdbadcccabdaaadcacacadcabadaaddcbadbadabcccbccaabaacaadbacdcaaacdbbbbdbbbbadccccacbbbababcccacbcbddcadccccbcaadcccdaaabaadddaacabbcbddadbbbadabcdbdccdbdbaaaacbcbabccadbccdbcdcbdccccbaadaabdccabcdddacaabbdcbcbadacbdbacdadabadcccddabcaadaaacbbdaaaadabbcacdbabddccdadcbdddcdbdaaaccaadaabaacdadbddcbdaddbaabadacbcbaddbacbcbdddabbdacbdbacdaabbbdbaccaaccdbdabcbbabadcdbcbdabcccbccaababbccacbbbdbadccadbaadabbcadaccbacabbaaccdbabccdabbcaccccbddacbccbcababdbcddacbbccbdcccddcaaddcabcdbaadcaabdddabbbbadcbcbbdcbabdcdaabbcddcbdbcabacbdddbdacddaacbddcbbbadddababcacdddacdcdbcbbbcbaddaaaaccccccdccacbbdaaacaacacadbbccadabcdcbbcabbadcdbbcababdcbbbbdcaadbbcddccbdabcaaadabdddabddadbbaaaddbddbbdccacbdadabddcaccbadbdababcbcdbaaddddcbdaabcdbacdccabbadaababacdcacccaccdcdcbddcadcaccccbbbaccddaaaaabdcadcaabdccbbcaabccbaacadbccaddcacbdbbddccdcadbdacabbacccbabbaddacabaaccccadccaaaccdcddabbcbbbbadcbdbadacddbdcabccaaacadbbbbccdadbbbddbccdabddaaaddddacdacbcddbbccabbbdbbcdbdaabbcbcdcacdaabaabdaddaddccbddadabdbacdccaddadabcaadcaacadcaddddbbddbaccbbcbccbdbdbdbdbcadbddccdbacccdacccccacdcdaadcaddacdadabbaaabcaaaacacdbbaadadcbadbbdccdadacdcdcddbdabdadbaadbcdccacddbdddadccadcbacbbcddcdccbdacdbdbbcbccddadaacddbdccabbddcbcbacdbdacddadbddccbbacddbddbbbadccbbcbadcadbcdccdacbbcdcccadaddccccaacabcabacacdddbdcbdbdcbbbabaacaaaadcbacababccccbcabaddbbcdcdaddacddddcdadddccbaddaaaacaadbcacbdcacccbadbacccaacbacdcabbbcdcdabdaabbdadbcbccbddabbdbbdccadbaccaabccbabdacdcdaadabcbcaabccbccbbcbddddcbbbcabbcdbabcadccdadddaacbbccaabcadcdbccaccbdccadbbcbacbccbbabbddbddadccabadbabdacacabbdaadbbcddcdbdadaabdbdacbddaddadbdbbaadbcabaacdcaddacbcaabbdccdcbbacaaadcadddbacccbddabacbbababaccbcccdcacaccddcbdaccbdccdbaabacccdbbcbcbdaaabddaabacadcbdcdbbcbadddddaacabbbdcdcdcbbdbbddccdbadbaabcddadbaacbdaccbdccddbbaadadacabdabdbacbbbadababbcbcacbbcdabddacbababcbacdcbcbcacadadacaadddcacddbdbbbadcbbbadadbadabbdaddabadcaccccaacadaaccbdbcabcadbddccacbdbdadadbcbbcbabbbcdbcddbbddabaabacabcbabccacdddcdbacadbcabccdabacbbabacbdabddadabddcdcdddddbdcbadcbddddbcbdcddcdcbdbcbadaacacbcdacbacccacadcabbbbccdcbdcdddcacadddbdcbbbbdadabadacccadbdababacaadbbccbadbaaacdaddcabccadbabcbcbaaddacadbabaadacbbcaabcddcdddbadcaacbbdccdcdcaaabacbdddabddacdcdbdbabdcbbdccbcdddaabbdddacdbacaddddaaddadcbabddcddddadbbacccadcbbcaacdbbadcccbbaddbdbbbaadbccccbddaaadabdcaccbdbabddabadacdaaccaaddcacbadcdbcaaddcaddacbddadadbcacdbcddcabcddcdbddacdbaaacddddddcbbbcbccbabcbdccabbbbdcbddbbdbcadacbbcacbaaccdccbabbbbdcdccddadbaddaacabbbbabdaadabcacbcccbdacbabbbaacdcccdccdcaabcbbdcadcacbbdbdccbbbdbdcacbcdddacabadbaacbaadbdbccdcaaadcccdbacabacacbcccabbdccdcdbddaabdaaadaabcdcbcdabcdcdccadbcdbbccccacdaaaadbaadccbabcadcabdaabadcabcacdabddddcddccabcbcdcbacbbbadcadbdcaabdcabdbbaaabddbdcdbdcdacccdaabaccdcbbbccbabbbbaccaabaabcabcbbddbbadacaacbacacbabcdacddcccadbacadbacabbadaacacddddccbacdbccacbdcadcadcdbaacbdadaaacccccadbcccbacacbcdccddbbdaaacbddbaddcadadaaadccadbddcbabcbcbbcdddbacdccacbcdbcdbaadbbaddadaccccdbdacbdbcbdbbacabccccabbcbbdabdaacbabacaabadccbacabddaaaddaaacdaddaaacbaabcdabbbdccacbcdaaaaadbadcccbcbcccabcaaadcbbcadbddddccabddcccaddddbdaaaaabcdbddcdaadaadaccabbbbdbbdccdabcabbbccccabdcbacddbdcabdccdadddbbadcddbddbcdcabaaccadddbacdbaabddcabddbbbbbbaabcabaddbdacdaabadaccdcdaabbbbabaadaacbaddbdcbacaccbaacbccaaddbbaddacabdccbcaaacabcddcbbcbdcdcdacddbdcbccabaaadabcbdbbcaccabdcbabbaccdacaaacdcccccbdacacdbcbcbccbdbddaddaaacabadccacabdabccbdddbccbcdaadcaabbbdbaaddcccbabcccbbaacbabdbabddacbcbcaadddbccaccadbdcacbbddacbbcbcbadadbcaacdcbabaadbacbdcbcdabbbbbadddabdccbaadccbcdadbbcabcccbdbcddaaddcbabcabaabdabaddbbdbbcccaacadabbcbaaddbdcacbdabbaccbaadcdbdadadcddbbaabddcccbacaadcbcacdddadabdacadbbbbabbdcdbcacbaabaabcbcacbcddcdadcadadaadabcaccaccabbdacddcdadbadcbcdcbcabcbbdacacaccdddbacbcadcbcdbbdaddcbddaccbcaadcbbacdddbadadbadaccabccbbcdbdabbbddcbddadcaccbcbccdaaaacaccdcddccdbbadbbdcadcadadcbcaabaabdacaacbcbadcddddcaababcddcabdcdbbcaabdbdddbaaabcdabddbacbbacbbcdabcddbaabcdababccddcbdbdcaadcadccbabbdcabcaddcdcabdcccccbdcdbcabdcbadcbbdacbbcdddcbbddcacbacddbaccabbabcbccbccdcdaddaaabacbaaccccdcadaadadbaabbcdbcccccaccaaaadbcccddbcaabdbaabcbbdbaabaccdbbaabbbccdadbdacbcacccbccdcdadbbddcdaadadbbcababcddbdabcddddddaacaacadcccadbdadcbdcbbddadccbabadabdbcdccabcddbaacbddbbcbcccddcbbccadddaaccadcccabcdabdbcdccbabdaddbabbbbabdbdadacbbcdaaadcbbddbadccccddaccadbcbcaabcbbcbbbcdaacbdbcdbbbaccacacaddbcdbbcddcadbbbcadccaaaddbacacddbacbadbdbbaddaacabacdcbdccdccbcaadacbacaaadbcadcacadaacababcabddbdcbdabbdbacacaabbcbacdbdccbcaccaadcccccdaabdcdcbaccdcdddacbaaabdaabacabcccdacaaabdbcdbaddcdcaaadadbacbdbcdbbdcdbabbbcacbaabdddadabbbbdcaccbacbccdabdabdbdccdacdbbdadadacabbbadddcacbbdacbdcbaccbcadcbbaccbddaabccbbabbdbcdadaaadcccdcbbbacdbdccabdcdbccabdacddabcbbbaddaaccccdcbabcdacbcaddcddddbabbbcadddcabcbcadaacbddbabcacdbacddabbbbabababcdcbccdbbcbcdbdacbddbddccccbbbcdbcaddabdcadadccbbcadcdabaababaddccabcdccbcdcabaaaabcdddbdadacdbcdacbbcccccbadcaadcaabaacaacdacaadcdacddaddcabcdbcddacaabddcdbdabcbacbaacdbbaddbbabbbabddacbccccadabbbcadaccaccaaadcdabaaabcaddacaddabdaccdadbdcdbddadaccbacbdccdacacadbcdadbbddadabaabccdbbabbdbdadacadbabbaddadcddaacdbddbdbcdbdccbbcbacdcdccdadbdbcadbdbcbbbdccabaadadcbbdbabaadcdcbbcadbabbbadbabdbaabbaabcbaabadabbbdbdaabdcaadbbccadbbabbcccdbddbddddcacaaacbbddbaadccbbbbdcbdabaddabadadcbbbddbdccdccbdcbaacccacbacdcacbbdddcddaadaccaccaadddbacdadbcccaabacbcbadcdcadcabdbacddcbdbdaacacabdadbabbddadacbabdbcdbadadccabdacadbbdbbaccaddbdabacdcabbccdbbcacdddadaadaccbaabbcdaccbcabcbdddbbbbabbcdccbcbccbcdcdbbddcdadcdcdacdddcaadbaacabcddcadadacaddacababcbcaddbaaaccbabcacccdbdbabadcbcdcdbcdbcbccbddaccddbbdbbabadccccdcccdbcbcaadddadbbcacdbcccdbabacabcbccabdcdcbcbadcddadaadddcbaaccdcbcbdcacaadcbcdacaabbcdccddbabacddbdbadbddaddcaabaccaaddbccddcaadcacabdcbbcdbcbcaadddccdcacdbbddbadddbabbbdbabadbadcccbdbadaddccdcbbbaaddacbcadaddcacacacdbcdaaddcdbabbdaadadadaddcaaacbadaabcdbaccbcdbdcacdbbdbcbdbdbccacdbaddaddacaaacbbbbdccaccdacdacdacdbcdbdcdcccddcbdbabaccbcabbcbcdcdaddaccdccbddbccdadbcbadcbbdababcaddaddaaccaabdbdcbbdbacabadbbcbdacacbbcadcdabadbdaccbbdacdbabdaccdddbcddbbccaaaaacdcdaababbbdddbbadacbdabdcaaabacaaacdaaacaccdbacdbbaaccaabdcbdbbadbdccadacbcbaaababaaccabacabcacbdbcbaabcdadbdacdaabdddbaabdddcbabdabacbcdbbacbadacdcacccddcbaacaaaaadccdcccbcabdbbabadcbddadddcacaaaabaccbddacbcddaccbcbacadbdccadacaabddcdbcabccdbbabccbadccbaadcaadaaddbcddacaadccadabcdacccccbcbcaddbcdbcacdbcabccccacbdaabdacbcddcadcaacddabcbadcdcbccbdccbacababacbbbdbcddbaacabdbccbdacdadddddccbaadcadbabdccdddbcddadaddaddcdccabcdababcbdbccdcaccdbdabdbaaabacacdccddabbcbddddbadbacbdbddcdbcbbccadabadcdadbddaababcbcddccbdaaddbcabacbacabadbcdbdcaadbbaddadbdccadcddaacadacadccdbccacaaaabaadbdbdbbcbccccaccbcbcdbbbdbabdcbcbdcccdcabadcbcacbdcbaacbacddcadcdddbadcddbccdcbadbabddabdddbacbadcccbcccdbbabcacdcbbdbdacbddaaddaaaaccacdacdccabbbacbcdbcacccdbdcaacabbbbadacdbcbcdaccacacadabadddccaccbddccaddcbbbbbaaadbbaabbbcddcdbbdcbaccdaadddbcbdbbbabaaadbadcadbabbccadcbcaacdcaddaabadcbcccacdaaaaccacaccaaaadccbcccdacdbdcdaaadcbdccadcdcbcbdddabababbbbcbbdcabdbaaddbddbbaaacbdbccbbcccdccacaadbbcacdbabaabbacbacddbcaccbcdadccacbcdaddcccbbbaabcbbcbcdcdacaabdaadadccaddcbabbddacaddcdbbbbacbbbbadbcdaadbbcaddadbaaabcbdbabccdcbdcddcaccdabaaaccccbccccacddcadadacdbddbdaaaadbcbbdaccaaccccaabcdcdadbacbdcaccaacbbbaccdaacccacadbbdaaacddacdcbbdddbadabdcbbddacddbbbcadbaccacbabdcbaaaaaacdccdcccdddddbcbacbdbbdbcbbdbcdddbabcbccdccacdaabddcbddbcdbcaaacabdcdcdcadcdaaaacbbcbbbacdcbbabddddbdaaadcddcdcddddbddcdcaaabcdbbdbcdadcdbaadddbccaadbccbabcccbcdbaaccbbcbbbbddbdbddcabdabbadddddbadaccabdcbdddacbcbbcaacddacbcddbadbdcbbddbcbaaccaddabbabbbbacdcaacbccbabacbcbbacacdbbdcaaddcccbbbcacdcbacccbdacaccbddbaabbadaaddabbadbaddabadddabbaababccacbccdabcdccbacddcbabdbbaddbdcabcdbdbbcbbcdcbdccabcbacbcbbbabcbddbbccacbbcccbbaddacdcbaccdbcbacaccaddbdccacbbddcddccbaacaccbddccabdbdadbbddadaddcddcabdcdcdaaadcadaabbaccabbccdadabadadcdbabaacbabbdcbcdacbbcbbdcbbabdddcbdbcdcbbdddbbbbdcbccdaddacacaacbbcbabadddbadbababccbacacdbdbddcacbcaddcdbdaacabddaaaaaacdbdacbaadabdbbcaadaccdcaacdadbccddbacacabdbacacdcbbacabdbbbccadcccbacacbadbbbcdaacbbdddbbcabdadcaacbbcccadaccdaabcdcdabbbddddabdcacabdddaabcbbcccaddaabacaaddbdcdadbccbdadbaacdcdcbbcdddcaddaacbbbacddabbcbaaadaabdcbabccbcabdddbadabbdbcdbbddcbacccddcbaabcbacaacbadcddadbccabaccccaaadcabadbadccdbcdcabdabcdcbadcccbaddcaadbbadbbcabdbbaadacbcdbabcaabcdacbbdbdcaaaaccdddabddbbdbcddcdcdadcbcadcbccbbcbcdbcbbddbadadcdababcdcdbbbccacddbbdadacccdbcadcbaddcbbcaacbbacaadbabbdccaccaacdddbabdbdbcabbcdddcabbbdddaaddcabdbccdcaaddadcddcaccdadaabbbddbbdcbaccdabbbadacacdbdadbbdcabbaabddcaabcdccddcaadbaaadbaacdcbabdcbbbabdbccaccbcbbcbdbabcaccaddbbacbcacbdcbbbbcdcaccaaadaadcdadabddbcaacdabdacccddddcdadaaacacbcbbcaaddbabacccabababbbcacadcabcacaccacccaddccacdaaadccdcdddabbdbbbccbdacdbaacdbbbdcaccdccbcbbdcdbdbcdbdbcccabdbadbdbcdccdbacaddddccadacaadccbbdcdcdbabcabcbbdbdcabbbdbadddaacccdbcadccabbdaaddaadcaddaacbbccbcddbcbcaabddcacbbdddcccdcddacdadcbcbcacdbbaadbddbccbccabbbaadcbddcaaabcabbdababdacadddaccaaabccabbdddddadcdadabcadcdabdddbaabdbddbccdcbaacdaaadbadddbbabbadddbababccaacabdaacbcbbbcbaaccadbdcdbcdcbbbdbabccdcbbcbbcdadcddbddbdccccdcabcdaddacadadbaaadcaadcadaadcdcdcbacbadccddcaaaadacaababaacabddadaacccddcdddabdadaaccdacbbbdccbdddcaaaacdacadcdbbdcabdcaadadaaacabbcbaaddbadbcddaadbcbaabaadbadcabbaadcaaacacbbaaadcaccbcbbcadccccbdbcabaadcdcbbdbccacabdabbcbbbacdcccadccadcaaddddccbbbcaccaadddacccdcdacacacbccacdbdddddcbadadcdadbbabbcbdbabcdbcadcdadaddccdaadcaddbbacabdcddaccbbbabaaabccdcbddaaacccbcaabaacbcdababddcccbaaaddbacdccabcbadcabdccdcdcbcbcdbbdcabaaddddaadccababbbaaddadbbbbaaabdbbdbdaabadcbccabddcabbddcabaddccacbcdaabbacdbacbaacbccdabdadcccaddabcddbddcccbcadbccbbccdcdbdadbaabdcddcabddacbacbccaddababccbcdaaacbcbcbcabadbcdcbbadccdbdbabdaadbdbcddadcabddcbddcccdacdccadcbaabaacbbdcbdbbbbbdacbabacddcccdcdadcbaabcdacadaddcbcabbbcddaababbbadbaccbabbcdcbdcccbbdbdbdcaabcdaddbbbaddddcadccddaccaacdddcabacdabbbbddacaaccbdacdbbaaacdbbadcdccdadaddcadbdbbacdcccdadbdbcdadaacadddbcbdbbababdcaaaccacaacdbacbacabbbdbadbbdababbaccbbabdadddbabccacddadacadbbdbcacddaabdababbbcbabcdcbdabcdbcddacadccbdcacdbdddbcaaabbdbccabdddbddcdcdcbdddabbcbdbdbbaddcabdbccddbbbdbbbdadaddcccaddcbcbbdababdbcdbdcddbcbbbdbcaadcabcaabcabbccdddccdabbbabcabacbdbbbcbdcbddacdbbdabcdccdbdbbacbdabadacabcdabbbddbbccbcabcccadbaaaaaaaddbbbabacddccdcbcadacacbbcbaadcbdcdcabbaadcccaaaacacababacadbdcdbdbdabdcabdbcbadcdcbdbddcaacdcaadaabbccacaaaddddcccadacadccbadddabdbdaaccbdaaaabddcbcadcacadddbaacbaadaccdcbdddcdccaaaacabaadabaabcdabdbbabbccbacabbdbbaaaddaccdbbbbdcbccccbdcccbabccbadcbdbccbdbdbddaccbcbdcabccbcccacccdbadcbcababbabacabdcbcbdddabadbcbccbaacbbacaddcdccbdcbabddcbccaccadaddbbadbabddbacdbcdaccdaaadcdbaaacabdcadabbdcdadacbaaaaacddbcbabaacacdcbadadcbadacaababcbdacbcdaccacdaaaabcdbbaaacbddacbabcdaacaccccdcaddaddddacbaddccdbadabacbacaddbcbdbcbddacadbaccbcbdbdbcabdcabdadcbacabbbabccbdddabdaccdbcccaddcdbcddabadcdaccabacaadabbdbaadcabdcabadcddaddbddddacaaabbcbadccdcbdbdacadacdcccbcabdbcbdaddbbdacccacccbdcddbbdbdaacacbccbdbdcdcacbddbcdbcddbcabbcacdddbdbdbdcbcccdaaabcaacbccbcbcbcacaacbdcbccbaabcddadccdddcdbaabbadacbbbacdbdacdaadbcdddbcadbacbdaabaddcdccbddcabccbdbdbabdcdabbcadaabbbcacaaccbddcbdcccacddadabbaacddbdbaccbbdabcdbabbddacbadaacdacbadacbaadaabacddacaaadbcccbdbdadcacacbbcabcdadbbbbbcdbcbbadcccbdaddddcdcdaaccacddcacabddcbcbbdbdccadbabcdaccaaddccbbdbdbbaccbcbdbcabcbbccdcbcdbdcabbabaaacbaadaaddcadacbbbbccdcdcddcaccbabbddabaacddbbdcccadddddbdaabbadaacabbaddddaaabdabddcacbbddcbaadccdbbabadaabbcaaaacbcadabdccaccdbbbcadbcbdddddbbbbcdbbaabccbbbdaabbbcaacdcdacdbcbbbdcbdccdbabaddacddccbacacbdbcccabaddcdbacbddccdcdbbbaacacbadabbbcbcabaadabbbacdaabddbdbdbdcabcdabcbaaaadcadbdaabdabacacbdcadaabbddacbcbdcbabadadabbcaabcbdbdbacbcdcbaaddddadaadddbcbbcabbaadbddbbbadbdacdaadbcbddaccadadbbbcbbcaccddddaabdcadaadacdacabdcadcdcbdcacdacacdbbaccbbbdadcdbaaccddbacbcbdaadabccdbdadacbacadbaaccbbbbbbacbdbcdbcdabbcbddaaacdcddddcaadccdbbacdccdabcbdcbbddbccbdaadcdcadacabbdaccbdaccbbcbcacadaabdaabaadcbcddabdcbcadadbadbaaacdcaabacbccabbcadabdcbdcaacbddcccccbadcaacddacbbdaddccbbdddbbdcbacddcccddbbdcbaabaccccbcddbbccccbbabbbabacaadabcdcccdbbabcdcabcaccdccbbcbddcbacdcbaabacdcccccadaaacbbaabbcbadccdbbcdcadbdbbbcabaddbabccccaacdcccdbbaccbdbbcaabddccddbccbaccbcadddabdcbbcddacbabddccbaabbdbdaababacbbcbaaacdddbcdbabaacdacdddacadddcacccbddbdcaaaacccdcabbacaccbcacbbbaadbaccabadadcbbbdaddbdacaccbccbcbaddbcbcbacbbabcbbcccabbcabdcbcbcadbccbcaabcdaddcbccaabccabbcdaadcddcdcdcabbbcddccddbcdacdbcabaadbbbddbcabaddccbdddbbbdcddacbbacadbbdbdddccbabbadcbcaabcdbaadcabbcacbabbcabcaadacbccbcaddabccbdaddacbdbbcbbbcdcbdabbaddcaadabadddadbbccdacdcadcabccbacbccabcacaabbdccdcdbaaaaccabdccbabbaccccabcbbcbabbdaabcbaadcddaacdbdddababaacbcbabdbdaccdaacbabdaacaadcabcdaaddaadccbdcbbbbcacdbbddddcbabccddabaccabddbaabdbacdabbcadbdabddbcabbaacbbccaccddabbacdbcbdcccbbdcaabbddbcaaccadacddccbbabbccdbdcbbaddaaacbdcbcabbbdcabcbcddcbcabdadcdadbcacadddaababacdddcbdddcbdcabbaaabdbbdadcbdbacbccdbbcccdaadcddbdcaacddbbaaadbcdbdbddcbbbdddbbaaacbadddbbddbabdbdacdadbdccddbcbcbbcdddcbcbbaddcabccaccbadaccbabaddacaccadbbbaddacbbbdbbdcbdbadcdaabbadccdadabadaabcbdcbbaadcccccacacbaadaaacabccacdadccbcabbbaadcaadcccbcaabacccccddcddadbadcbdaaabbbcaadacacabacbdabddadcdcbaacaabbacbdabdbabdaccdbadabbaaacbdcaddbdccdaaaaabadbccbcccabbbbcbcababddcbadddabbbbbdacbbccaacbddcdacabbbbabbbddababaaccbabdadadabbbbaaccaaadbabdacddcaccacdbbbddcdcdacdcabbaabbbdcbbbbddbaadbddacaddacdcdbabdbaccddaabadabccaacabacbbbcbadbcbbaadaaadabbdabbcaabcbcbabbabccbbacdaccdbbacaaadbdaaaaacdbdccadddcbdaadddbaccbbaddbcbbdbacccaccbdbcdaadcdbbabbabcabbaabcaaaccdcaccdddbcbbcccbcddcccbbcdacbabbddadcddbcbbdaadacbccbddacbaccdbbbbcadcbadbbacacacdccdaaddacddcdacbbdbbdbbdabbaadabcaacccddacbddacbcbccacaadcabcccbbacbcddbcbacabaaccaacaaaddaaadadcabcbabdcdbcdcaccbcdcaddacbabaacbbcdbbcccbadbccbddbacddbcdabbacdbddaabcdccabaaacaadaaaaabbabdcccdccdbadacbdcbcdbcbdcbcabaaacadacabdddbacbcdacccbaddaabbddcdcacdbcadbabcaccdbcbdcdaadcdabdabcadbaaadcacaddbacdacdacaaadcaaaddbbaddbbcccdcdbdabdddcbcdbcacdaaadddacaccbdbccadbbaabbcbcdadaadcdacdccdbcddadcddaadddcccddbdbdcacdbbccaaaabdbcbaacccdacacbabcacdbbcaddbcdcaabdccaccdacbdcbaaccaccbcbabcbdcaaaaaccddbdcbbcccbddabccccbbcbbbdbdbaabdaccbaabaaccbacdcabaccbdaccbcdacaddccddbbdabbbcabbcdcacbbadaabadcdbbcdadbdababaabdbccdcdaddccddccccacadcababcdddcbaacbddabbabdbbdbcabbaadbbddbbccadadaadaabdbabbadabacccbbdddcbdcdabbabcadcccaaadbbbabadcdacbdbdacaddacbabbacbacbddddbababbbdaaccaaaabacadcadbddabddccbdcdcccadccaadbdbdcdbdbaddaabcbddcdddcadcdcbcccbacbdaadabbbbcbdddbaddbdcbcacbbcbcdbdaaacdcaadbbaaaacbabbdcccbddccaacadaacbadaaaacbcddcbdabacaaacbcbbbdbacacbccaccccccccdcdccabbcbcbcdbaaaadcdaabdcdbabccbdabcddddabbbccccadacabcbadbbcdbbbdaadabacabadccdcccbcadccdcabcabbadbcbcbdbbcbaccddadccbdbcbcbddacbbbbdcbcdccbaacdddbcbabddcaacdbcdcbbcccddcdcdddbabdbddccaabbddaabddcbdcbaadcdddcbaabdcdcacaabaddddbcaadcbabbcadbddaadcbcdbcaddacdcabdabbaaadcdbdbdcbadbbcaddcdcbabaccbccddbbcabdbaddaadcdddaccdccddaccbbbaddddbdbcccccaadccdacadcccddccddbaacdbdabacddadcccacdaccbbcadabdacdbaddbccaccccbaaddadccabadbdcabccacdbddcbbbcdbbdabacacbddbaddccddcdbcababacddacbbadabcbaabbadcacaacbccaaacbdabcddddadaaddabdbddbdcddbdddcabaacdcaacddbcddbcbdadabcdccadcaadadabacddabddbbdccdaaddbbcdaddccbdaccbcdadabddadcadddacddbdbcbdbdcababaadbbcccacdbcbdccbaddcaccbaaadabcdacadddbdadaacdaabaaccbdadbaabbabcbaaabcbbcbcadbbbbabcadabcadcdacbdabccbaabbbcdacacdccacdccddddaacbacdcbcbcadbccbddaddcbddddbbabddbbbaacbadbdddcdcbacddbabadbaabcbbdcdbbabcbaaddbbbbacdcabadbdcbddddbbbcbbbbabdadcdcabbdbdbdabbacbdacccaccdbbaccdcdcbdcbbdbdbcdccdcadacddcbccaddcacdcdbbbdcadcdbbadbccdcddcbbaabcddbcdbabcdcaabddbcddacbcccdbddabcabacccadabdcbbbdcdccbaaabacbdadadacdadcdbaabaddabadbbdcadcdccdaaadbdcbcbbbadcbddcabdabddbbacddcbacbccddbaaacbdacbaccabdbddaacbcdcccbdadcabcaabdbdbdaaccbbdbaaacbcbaaabbbbaabbabddbbdccbdcdacdcaccbdddbbbbbbcdcdddaadbaabaabaddcbbbabdcbadcacaadcabbcdbacbcbabcbcadacbabdcacacbbdbabdaaddaaabcbbcaabddadbccdadbcdadabcbccbaabcadacbcdddcbaacbacbbaaadabccdbaaddbacbcdaabdcdddbbccaaddbdacccacacddacccabcddccdabacabdaaabbcbcbdabdccbaddbacccacbbabcaadccbbddbdacbcabcbbbdcbdccbbcbdccdbdaddcadddcbcacbaabcbcbaabbdcabcbddddddbdbbaccbbcbccdbbacdbaccccbdbddadaaddabdacacaddcbabbdadaacddccbccbcaadccadddabadadbabcaabcaacdacdccabccccdcadddccacddbdaddaacaccacbacadddcdaacbacbdddcdbdcdbcbbadcdbababdbbacaccabcabdbdbdacbdadaddcbdcbbaddbcbacaadacdaaabacadacdbbdcdabdadcccdacaddadcccdcdbdadbcbcbaacdadbddadbbdadcddccdaccaadadbbcbabdaaadcbbdcdcabbbabbdbcabddbaabbbbdbccdbabcdaaadcdcaadbddccadcccadaccbdaacadbbcbbddcdbaaccacbddddddddcbccdcbabcccbcacacdcdcbdabdccbcbbaabbbdddacbdabbaadbcdabddacdacdabacaabcccddddcacbbaaaddbbcbcdabdcbdbccbbdbdacdcdbdaacbbaacdbcdacdcabaaacbddcaacdcbbcccbccdbcabaacdcdadbdabbcbadcdcabbadcadcadbdcabcdbadcbcbaddbddbdcbbcadcccbabbadcdbccdcbaaabbdaabaacbabdadbbdbbcdbabccbdccccbbdcddccbadbcaddcdcdacdbbcadddcbbaaaabdbbddbaddaaccdcdbbcdbcdadccdaadcaddccaabbbadbabbbbcdadaababccbdccaacdabccacbaaabbadcdadcbabacdbdcccaacdddddcadbabadbdccbdcbbaadcaabadccbcddaddbccddccdcdbbadbbbbdbddaadcbdcaadcbcaaabdabbcddddcdaadcbacdacdacbdaddcccaaddcadcdccdacacdaddabbdcbadabcdcbcaadbababcbbbbdccbbaccdadbcccabcaaadcbcdcabdcdcacaddaadcbcbbaacaddbaadcadbadabcbcaaaaabddcdbcdaabbaacadcbcabdaddcccccbdbddcbbdadbaccdbbbadccaaaabaccbadccbdadaaddabddadbcbdbcddcdabadbdbbaadabbbcaaabbacabcabbcbdcadaabbbacbacdbbcbbbcbdaadcbcbaccdcdaacadadddbbdaabaadacbcaabcdaddcabdaccdccddbaccbbdbbcddbcabdddddccdadbbddbdbdccbbbbacccccaababadacdbbbcacdccdddcbccddbbbccbcbdbdbbdbcdbbbddabdddcdccdbabbbbdbdbbbccdddaaacadacbdaaacadcddcdbcaaacdadbbbdbcbadbbdbbaaccdbddccbdbadadddacbaabbcabdbcabccadbaaddddabbbcccdbcadadbcdacabdaddaccbadabaaacdcabdacddcdccacbbbbabbdccbacddadbcccdcdddcbbcdbacddccccccccdaacdcbdbaaccdddcddadcbdcbbaacdacbddcccdbbaaddbcbbbacbcadbbdaadaabbdcaadcacddbdbcaccbbdabdbcbdaabaaaadcbaaabcbdbcddaccdcdadbdadcccbbaddbccaacdaabcdddcbabcdabbdbdaaabcbbdcbaadcaadbbcccbdadaaabbdcaccabcbadcadbcabbcddbcabadbdaabcbaabbadccaaccbcccbdccdbdcdbcdcadabdcdbcbbacccdcccccbacaadabccbcbaabbcdccbcadabacbdbabacbabcaaabcbbabdcdcbababacabddbbbabbbddbddddcccadcdabcbaaadbddbccccdcbbcbdcddcbbbacdabbbddcacacaadccbbddaacbbcbbcdcdcaaccbdaabddcccabddcdcacadcddcaacbacdccbaddccadbdcaccdcabbdabbcaccbadacdccadcbaadbbabbbccdacaabdbdbdabdbdcbdbccbbddbcabcdadadaccdcdcacdddacbbabaddcdaadabcdaddcbcbcbddbdcdcaaccdddbaadbbcbcdddccbdadaaacdbbdacadcabcdbddccdcdddcdaaabddaadbdabacbddbacbcdaacbccddbbdbcbdcbbadaacdcaaabbcdbbbcbaaddcbbdbaabdcaaddaacbcdcadbdabadbdbddaddbdbaddbddaacdabbddcacddddaddbdcadbaabcbcdcabbaaacdbdcccadabcadaadccbdbaaabaacbcaabbccacbbaccbddbbcdcaddcbddccacdabbccdcbcbaaddbbcacccbbdcdcaadadcbbbbdabcddbbcdcbdcabaddccdadcbaddcaabadcccddcddcabdcbbcabcddbcdbcdcbcccdcdddcdbcadabbdbcbbdddbbdacbaaddbacababaacdbdbcbdaddccdcdcdaabbcacdccaaccaadcddaddcdaacccbababbabadaaddbcbadbdcbbabbaabbcacbcaadbcabcdbbbdbbdcdcacabdadcddddacddcdddcacbbdadcdbbcdabbaddbacdcabbcddabdcbbcdacdbddbbcbacccdbbdbbddbbbaadccccdaabdbdcdabdbdcdcdadabcaadccdbcabcabdbccbcaaccbdaabbdcacddcadbcddbcaadcacbdcdccbadddadbcacabbaaddbcccbbcabcdacabcacddbcbdbdaccdbbdbdcddadbcaddcaabddbbadccadddcdadbccbacdcccbbdccadcbbbaabbdabcdaadccadcbccbabbadabccbdbadbcbdbbabadadbdcdbcdcacbaacbdabddccbcddccbcdaddcbddcbdbdbdbdcbadacababbddaadccbcabddddbdadbdacabdbddccdaabdacbdccddbcdbdadbcdccccdcaaaabbbabbcdbbabbaabdddbcccdddababcbddaaabcabbdcbbcaacdcbdddaacadbdcdddababbcdbbcbaababbaaacadcadcdaaabcabdbcdcbbacbbdbaccccabdbabccababbccccbbacaabcdbbbbabbaadbadcacacddcdcbdbabbacaaadcbbcccadddbcaabdbbdcacbbbdbbbcdbdcadcddcadcdcdbbcbcbabccaccaddddddabbaaadcbcbdaabddbbccacccabacaadaaccbcddbaabbdcddddbcdcbbcadcbdbcccaadacdaaabbdbccacacbadabbdadcdcbbdbbccddbadbadccbdadbbcccccadcbbcdcdddbddaccdaddcdbaacdbcaccdcababdacbbaaaaddddddbbdcadcccbccadcdbbcdadbbccddcddadcadddcacacdacccddbbddbdcbbddbcbdadddabbcdbdbbccbcdbcbcacaccbaaacccbdadbbacbaacacadaabccbbadabbccdacbdccadbacdddbbbdbcabdcbaccbcdcdbbcdbcbcadadabcadbddcabcbaddadddcacbcbbabdccdbcdcbaacadbddaddaabacbdabbbbddbadababcbaabbabaabbaddddaaababbbdcaaabdbadcddbcbabaddadddbadacbabaaabaacadadacdaddbdaddcacddaccacdcaadbcaaadabbdbdbadcaacacdbcbdacbbbdadaddddaacddbdaddacbbdcbcbaaabdbbdbbbdbdbabcddcabaabbaadbcaadcdbbdbadaaadcadcdabbaddbddadddccccddbbaaaaabdbbcbcabbcacacbdaaaadbdabcacacadbbbcdaaabbabbccdbccaadcdcddabdcddabcdbbcdaaabcadccbdbcbacadcddccdacddbdbadcbdacbbacaddcaabcdacdcbcdccdbdcddbdbcbaacbadcbccbbbacaabaddcdccdbbabdbbcdddcdcdbcbbabcbcbddbbddbdaabddadaabddbccbddcbacccdadccdbccdbaccacbdbcadbbcdbabdcabcbddabbbadcacdadadabdbbdcddcabcabcbbbccadcacdaadcbdddaaaaaaacdadbccacbabdcddadabcadacdcacdadbaddbaabcdddadabbddaaabacbddcaddbdccdadccdccdddacaaadcbbbacddcddababaabaadbadaacdbadcabdacdbdcacdcabcbbccdbdbbadcdbaaccdbabaacdbddabadcaadbcacdcbabdbbccabcdccddcabdbdbcadbcbaccabdbdacabbadbdaacbacdddadacdaddcabaadddabdabccdacdcccaaabbbabdabadabbdaaadbabaddbdcccdbbaacbacdabadbbcbacadadddacdbbaaacaabbdccbcadbdccdddbbccabcdabaadbdbbbcadbaccdacccbdbbcdcadcabbadbdbcbdcabdabadaadbbabdacbbdcbadbbbbdbdcdadbcabccdbcaadbabaadbaaabbddadcbacabacabdccdcbcdcdabbbbddcdbdcdcdbcbabacdcbacaccdddcabdacabdddccbdddbadbdbbcddcbaccddbccbdbcddbbdcbadacbadbbdddcdaaabdbadcaadccccdccccacababbcabccdcacdcaaadbbadcabbddabccbaaabbdaacacdbcbbcadbdcbadbdaaddcdbcccaaccabbcabcaccdcddbaacbcddabbdcbbaccbdaaddaadadbdddbdcddbdbcbdaacadbaaadaabbadadbcbbabbbcdcdadaabdcdddbdddbcbbbacbbddcdddcaaccdacadbdddadacccacbdbbbcdabbddcbcdadbccdbdadbbbabacbbccaaccacaddacdabcabcabbddacaddbcdccdcddcbcccbdcbdaaacdbbabbbbadbaccbdaaccdddadcbdbdcadddbabadbdadddacbadaadcdacddcddacacdadbcacdcdbdcdcdadabdabdcdaabadbaaaadcbcdadbdacbadbcdbcadbdcacbadddaccccbacdaadbbbacddcddbdabbbabbadddddcaaccaadbcaaddabcbccaadcdcdaaabdabbbacbddccacbadcbdabcbbdbcaadcbacaaccdcabbadbadbdbbaabcddbabbccabdbcdbcaddccdcabcaadcdadddbddaddbcbbbacccddbdadcacbcdcaaadacdbbbdcdabbbccdacbbabdbccacadaaabddcabbadbcdbbaacbcacbcdbcdaaabddcadbabcdabdcccacaaabdddcbabbabdacbcaaabddddbabadcbcdbdcbbdabdbdabdaddbdbbbcdbcddcbcddaadabccacadbdbcabcbbbacaadbcbdccdbdbadaacadcabbcdbdcbaccbdbaccbabdabaaccabcbdcaacbbbabaabaaaadbdcabacabccbcaabddddacadcbbcdbdbbbbcccacbbdadabddddcacbbbacbbbcacdbaabbdbcddacdadcddccbdaabaddadccbcaaaccbccdaddadbdabdcddbabccddacdcbcccccacababadabccddbbdabdacadbcacddadbabcbdacaaccdddadbdcdbcaadadaabbbdadccccdabcbccddcdcbaabbbbdbdadcdabdacbddaabcccaabcabddbdcbcbabbabdbdbbabbcbdbacaadabcdaccccaaaacacccbadcbcacdbbccaacdbaabdaddabbdaccccbbbdbcbbbbaadcabbaadacdabccbcdaaaccccbbbdcadbaaaaadcaabccbaccdadbbbddbbcddaccaaccbcadcadbdbadbbcaccaddcbabbdccbbabbdbbbdabcabdbbbabaaddadbbbabcbabdbcdccccddcdbdacadcdcaabaadabcdaadbbdacddbdbdaabccbdbbccbdbbabbbabcabacdadccacaddabbaabbcacbdabbcdbdbabaccacbbdbabbbacbcadcdabdbaccdacdabdabdaacddcddbddcdbbcbddabcdcabaabadbcdabadcabdadcadadccdddcbaacabaaddaddcaacadcddacadccbcadbcabbdbdbaacdacbbcabdcddbcacdacdcccddddbccdacbcaaacacbcdcdaadbbbbdaccbcbdabcdcbbbbddcabadcbdabdbadccaddbaacdcbccddaddacdbaabdcdcacabaddabcdabdabddabadadbabbadcdcacdcbbbdbcaaadcbbabadacccaddabdbacbacbcabcdabbbcddacbcbbcacdbbbbbdabadbadbabaabcdbdbadbccbacaadbaddabccacbdcaaabbabcdcadbcdbddcbaaccccdadbaccacbabacaaabbaaccdcddcacaabdbcadcdddccccdccaacaadccaaadabcabccadbcdbbcadddbadcccdbaddcdaaaacbcdccccbcacbabdbdaaadcdabbcdbabaababaaccbbddcccadabccbccdacabadadaadccbdbbddcccbacaacacbccdcdacddbcddddccacdacacdbdcbcccbbdabaabbbdcdabbacbdcbbaaddcbcdbbdbcacabaacbdbbbcdbdabbaabbbddddbbdabcdddbabaabbcabddcbaabdcbcaaccbaddbbdddccdbbcbddcaacaabdcbaacbcdcadcdccabccaccaabbccdabdbbacdccdcbaabdababcbbaaaacdcabcabcadcbcbcddcdcbaabdccbbddddbcbbbdabbadaddadacccadbcccbbbcabaaaaaddabdacbabdaccabdbdbddbcaccbccccdbaaaadabbbbcabdbbcbdccadcacbddddadadaccabcdadbcbdabbcabdadadcbbbcbaacbbcdadbababcdacabdbcccddbcbaadaabccaacacddcbadbcbcadacbbcddcbdacbbccdcaacdcacabdccbbccbcbdbdaccdccdcbbdbcbaadabdbcbddbdabbbbbbddacdccddbacbdbcaacabbaaabbdbdccbdabcccdabbdbacaccccdcbaaddabacbcdddbabdcccdbccbcdbbcbacbabdacaadcadcbdccbcabacadcbaabbbdadcbdaddcaddadbbcbaaccdbcdaabdbcbcddccdcbcaaaabbccbbdbbbbaababbacbaaddcdbbbcbbabadaadcaaaaddbadbdbabdadbbcdcbabcdacadbacacadbcddcccdccdcaadacbcaacdcdddccdddabcaacbacbcbadbbacaccbbdcddcabcaddcbdacaaddabcddbbdcabcabbbdbcdddadbabcdbbdbbaabaccdccaababddcaaccdbcadccadaaddccaacdbbbadcdbdacbbdbbabbccdbbcaaabdddcbbcdacbaadaaabbdcbcaddabdbcadcbdddabbdbbacabccbbdadbacddcadbbbcdcdbbdbdbaaddcccdcbaadccbcccdacbdaddcbbdbcdacbcaabcabbbbbcbaddaccacdcccacaddbbadacbcadacbbacabacccdaabbcacaddacdadacaacabdcacbcddbdccdbdbabbdaaccbbabbaccdddadbbdaaacdadcddaaaccacbcbacabdbcbaddaabcbccbcbcbcdcadcccddabbaccacdccbbcbccdddadbddabbdcdcadcddccadadbaddcbaaababaadcbdbbccaadadccaccbcdccbcbdabdaacbdaacabaaacdbcbcddacdacdabaaacdbcccdabbcddcdcbccaadddccbdabddcbccacadcdccacbaacdbcdbacadbbcadbcdbbcccbbbadddbacdcdaccbcbadcbabdaacbdadaacbcbaacdcdacccaacdbdcddddcbaddadcdbaadbdcdbdbdaabbbdbbadcaabcbcaaaaacbcacacadaaaddbabddbabdcadbcbdbabcbbddbacbadbccbbaadcabdcbacdcabbabaabcacdbbbaadbcbcacacabacaaacaabcdacadbacddddcbcabbddaacadcbddbcbbdddbcadadadbacccbbaccbaddbcdbbccbccdcabaacbcabccdbaaabdacabdddddcdddcdbadcaababcabdbbaadacadcadddbadbdaddbdadccbbababbbddbccabbbbcbdabddcbddccadabbbddacccccaabadccabaaacccbacaaddaacaabacbbcdbdcaaacaccbbbbcacddccddadaabbcacccaddcdcddbabdcbaccbaaacdadbbbbcbcdbdabcccaadbbcdcdcbddadacbbbcccadcbddbdbbcdcacbaacccadbaadacacbbbbbdcbabcdccbddadcdbaabbcdabdbcbdcddabdcdcadbaacdbdacbbacaababbcabdbdbacbbacbaccacdbbdadbbddcbacbaabbdbbcabcbddaddccccabbccdccdabdbbdacdddacddcbcddbccaacdbadcadbcabababcccabcbcccbbcdddacccbdabcdcbccbabaaccaaccdbcddcabdbacdababbbcddcdbbbdabaddbdccbddaccbacaaccdcbdbdcdcbaabbcbadadbabcbdbcbaabacabdcbccdbbcaabbccbadadabdcddcbdbbdacdbccdabcbcccbdccbbabaaadaccbcbddbabdadbbcbcdacaddccacbcdcccbacabdcdcddbabdcbadcdcbcddbadaabbacdbdaaabcaacbcdbabdbdaccdbdbaccaabacdbcadababbcdcbccadabdbdddabccbcaccabdcdbbacaccbdccdcdcbdbabbabbdaddadbbbbbadadcaacabbdccddacbaddbddbabbcadbcccadbdabaabcddadbbdabaabcacccddccaadadcbcccbadabddbcbaabcdbcccabdadcaabdbcbaacbbbdabcdcbdbaacbabacbddcdcabdacabaabcddbcdaacadbdcddccbdadcaaadaddbdadbbabaddaacdcddabddddaacbdaddbcdaabcdabccdcbddbbcdcdcadccaccbaccdaddbcdcaddbbbbbcabbdaccaaccacdbdbaacdbbdbadaacaccbabccdbccacccbcbdddaadddccadbbaabdcccaacbdccdbbdccbaacbbadabcdadabbddaabcadccbcaadbdacabadbaabdbbccdbbabddabdbacadadaccbabdacadcbabaacdcdcccbbabcdbbcabdadccabbaadbccadccbccadbbbddcacadaccadcbdddadaabbcccbbdcbbabdcddbacdbcbcabdbcdbaadcababadbdabdbaababbcccbdabcabbabadadaddbdbcaadbbbdbbadaddbacabbcbbdcbdaccddabbabdbdcbacaababdaddccdccaccbbddacbbaccdaaccbcacdcbdadabbbaaaaabdbcdadbadccdcabbdabdabdbbcddbacbacddabdadcdddcbccbcadccbcbacddacddabbbacdadadbcdaaadaaddaacadacbaaaacdacbacbabbabdaacdcdcdcabadbdabbbaabcdbdcdacdaaabbbabcbcdcacadcabdacbbcabdadbdbaabbddaadbbababadcabbaadbddbcddbbbdadcbbacdadadaadbddddabccddbbccbadabbaacdabdaadbbbdacacbaabcacdcaacabbaaabddddcddcabcdcdcabaabdbbacbbaadcbdcdbcbdaabcdddddcdacbcaccdcdbadbddbbbacbcdabdadadaadbcabbdcddbbdcaccdbdadadabbabcacddabbddddddaaabaddbdacaaacadaacddbdcadddaaabcdcaddbdbdbbbddcadbaadbbcbccdaddcacaacbddccbdabcacccabddadcbbabbbcaaddabcaccdbadcbbdddcbcdcbbbbbbcddbddbaabaaabadddbccaabaaadcacdddbcbdcacaccabbdadcbddddbccaccbbcbadccbbcaabbabacaacdbccdbdacddcccbacacdbabbbbcbccaccbaccccdccdccdabbdcabcdcbcbcbabbdbbaabadbaacdbdccdbbddaadabadccbdcdbbacdbccdaaccbdcdcbcabddbdacbdcaddccdccacccadadbdabaaabbcaadcddaaaababcdddbadbdcaabaacdbdcdddcdabaddcbcdbacadcbbdddddcbcdddbaacdadcbbcadabdccaccdaabcadbcbaddcaabccddccdaccaadadbccadaabcdbbadabaddcabadcbaaabcaaaaddbcaddadcaccddaababbcbbddddbbaaddbbdabccbdaabacbccdcabaadbdaddcdabcddbabbcbcccaabcabccdbbccdcabcaabaadaccabbbccbadacabdbddaaacacadddbbccdacabdbcabbbbacdabcabddbcdbadcacadcdaabddcdcaaccdcbdbdabddcbdaadcdbcaccdbbbcabbabaacbcaabdbccdddddaaadcdaabccabacadacbccdbaaccddbacaaccbaccbccbdbcddddddaaadbbdadddacbdaabacbbcbadbddddcddcdcbbbcacbbdaaadccdaaabcdcaabbabcadddddaddbacddabdabbcdacbbcdcaccdbcbbcbbdbdddaadcddacddadadaaabdbbbbabcdcacbbaaccacdabdddcbbdaadccdddbcbccdbbbcabddbcaaaacaacaacdaddbdacdcabababadcdabdccdbabdbccccaaaccacbddabccdddcacbacbdccbdbbdddabadacbaddacbddbccccbddcbcddcacdccbdbaddbbdbdacbdbbdbdbadcbbdacdadbccbcbbbdcddabaaddabcaaadadaddcaaacbbcdcdddabaadaaadbbabdabbbcbbdcddabaccddbdacbaaddabddcdbdbdbdcaddbdcdcccbbbcdbdadaaabccdabcdaaaacdbdbddbbdcaddbdcdbbdbacbabaababadcabdaabcddcadbbdcaacbbbdacadbcdbddbcbbdcabcadbadcbccacaadbbbcdbcbbcbbdbbbabddccaaabbbbddccbccbdddacbdadacbcabbaadcdacddaadbdabccacdadabbbcdbaddbccaadbacdbcadabadcdbdaabbddcabdccacadbabdaabcdadddcdaddddddaadcaccdbcbddcadbdacbdbbcbccbcaadddbccacdcddcdcbcdbaccdccaabdabbbabcbdcccadaabcdbadbcdbdabcdcaacaacacbbcbcdbdbbbacccabdbccbaddbdadbdddcadbcdcbbbbbccacbbadccadddaccabcbdccaacaccdaddacbdcdddcdaccaadbcbdccbcddcaaccbaaadccccacccbbabcddcbaddcacbcacbadaddddbcadbcdabbcacacbbbaaaabbcadaddbaaddbdbbbaadcdbddaaddcbdacdbcaddbbadddbbcaacacbcdbacbbbbdbacaadddbcccbdbcadaacdacdbccacbdcaaaadacddabcaacbbcdccbbdcbaabbddbabbbadbaaaacadbbddddbabcccaaccacbcaccabadaaabdbabdaacbbdcaccdacacacdcddcbddbbacaddcdacbbaabadccdcacbabdcbadcbdaabdcaabbcaacdbbabacccbcdbacbdddadcadaacddbccbabbcbbaadaadcdbabcabdcbdbadcdbbcccabbbcdbaabdbdabdcadccbddbadcdacdabdaaddbdbdbccdaadaadadacabcbabbbaabcdbbaacdccbdbbcddbcbbdbcdbdcabbddcbccabdaaccdbdddcababddcccababcbbadabdcdcbcdcbbdbaaaadbdaaddabbcbabbbccbacbcadcabbdaabbbadccdcbadbcbaaaabaabdbcccbcbbddbbbbbbbbccbbcbddbbaccccdcacdbcbbbcbaacdaabaaddbacadadccdcaddccacdaacccbbdcbacccbcdccdddccdadddddadcccaccddaabaacbbcdcdacbdadcaaddabaabacbbcddbdbcbdabbbdccbababacabbbdadcacaddbcdabddbacddccdcdadbdacababadacdcadccbcccdacaddcaababaccdcbdbaddaadbcabadbadddccdaddbddcccacdbdbadddbbcaadaabaaacddadccbaaacccbbacadbabbbbbbcbddccbbbdaddccddaacacdbadddcddaaccdbbdabbdddacbcdddabdcadbcbbacabccbddcbacbacdbccaaddadacaaabbbadbdcdcbdbacbbdacadacababcdadcdadbbbbbacbbcbbadabdbcbbcbdbdcdacadabddadccccacabcacadcdcbaaadbccbbcbaaacbbdbccababbcddabddcabbcacbabaabbbbcbbadbaadcddcccacacdcaaccaadddcbcccdabcdbcbdbaaaaacbcaadaaddbadcdcccdadbdbcdbddccdbccdadaddbdacdadcdbcaacddcaccacdbbcdddaaadaacdccabacbddcaddccbadccdaabcaacccbbcdcbaaabaaadadccdabdbcbdccbbadbbbcdabdbbcdadacabddccabcbddcdcbcdddcabaddacbbbdaacbbccbddaadbbccbdbacbcacaacabdacbcbaacccbdbacabcdccbddbbdddbbddcaaccdbcdddabadabdbcaadbbddbacaabdcdaadccaadaacababdabccabbbdbbddcdadcabcdccccaabababdbaddaadadcdbadbbbccadbdbbacddddabbccaaabdcaacbabccbdabbaabcbbbbcddaabbaabccddbccadbabbdadcadbabcddadababcaddabbaaabdaccdbaacbcdbbdaaaadddccacaadbdcdaabbadacbbdadbdbcabababcaabacadcdbabdbbbabbcbddacadccacadacbaddadcbdacacbcddbcdcdabbddbcdbacdcdbbdbcccabcdbacbdcddccbbdadbadcbdcbdbbbccbbaadaadacaacacdaccbbabbbacbbcacbaaaccdcddbbacaadbdddaaadaddaccacdadbaaddcccbdbbddcddcbadaaabddcbdcdaadcacdbdbdcccdaddbdaccbacadaabdbdcacaacbcacaddacbcccaabcabddacbdbaccabccacccbacdaaccdbccdcdbacadbbcddabdbaabdcdadddbbbccaacbbaacadbcccbbabcabcdabaccacbabbadcaaacbbbcccaabdcaccbcddcadaabbabdacdccaaadcbdacbbadbccccacaadbaddaacdabbddccddacacaccccaabcabdcddbaabaddccabdbadddcbbdadabbddddbabdcacccaccdccadaadcbaddbacdbacbddbdcbdbadcdbcabaaccbacdabdbdcddddbbabbbaacccddccaacbaaadbccbbdcdcddcddddbadbbbbccdabdbcdabbbcbcdbbdbaddddcacbabccddaabdcbdaadaccdbcbabcdcadbaacadcdacddcdbacdbccabcbcdbcadbabacabaccccdcabbdabdbddaabcddadbdaacaabcbbabbacbabcaddbacddcdbbbdcdbabddcaaadaddbabaadaababdddaaddcdacababadbbcaddccccddbccacabaaacdaccccdaddddbbacaadddddcdcdcbbbbdbaddcdccdcacabadbcaccacdadabcccbdcdbdbbdcadacaddcbdcdcdacddddbdaabdcbdccaaaaaadcabaaacdbdabbaacdbccbbdccbddbccbbdacdaacdaccdcccccbbbbaccaabdbdccddacaaadcdcabdbbdbbaadcdaddacbbaccbbcadddcbdadcadcadddaccdaadbccdcabbdbbbbaccccbdadbcacaccdabaadccbcbccbbcdbaddcdbabbaacaccdaaaccacddcdcdaacccbabdccddacaadaabadacccaadadadaddbdccbbadbadccbcacdcaaccaddcbbadbaccacccdbbcbddabdacdaabdbbcbbcbaadccdccadcabadabaadbbdcaacbbbacbdcddcacbacbccccababadcaadabaccaaacccbdbddacaababdabbbcbcdacbcbadbaabbbbaaddabcbcdabdbaabddccaccadcabddbabddacdbbacddadcccdccbadbddddabbcdaadbabbdccabbccaadabccabadbcdbadacbabcdcccdbabdaadddbaacdbaddcbaacdadbbabcbbbadacbccdcccabbdbdacbbabaaabbdbcacdaadbddbacdaaabaabbdbdcdaaddbdaacaaccddcadadbcacaadaddcdaadbcbcbdcbaacbaaddaaaccdbabdbcabbbbbabdbaccdabbbaaadcacddadcabccbcbcadbabbbcccbcaaabacbdbacdcbcccbdbdabbbcadbabdbbcadbacbddaacdbbccbdcbdbdcacccaacaddadbbbcbddbddacabbbabbbdaacdbabbadccdddabcbabdcaaccdadcdadccbbcdaccddbbaccaddbcdccabdababbbdbddadabdbdabdbdabcccbadcdbacadcaaaabcdccccbaaaaabbcddccdabccacbdadbacbadddbabbcabbdaacbdabcccadbdabacbacabcbdbddaabcbaacacbdaddbabddcbddddcaadbabdadbcacbdbcccdbacaaddcdbabacacdbdacbaadbcbabbbacddcaddaaaccaabcccbaadcddbcbdcdcdacacaadcbddabcacaacadadbbdcadabdddaaabcbdacaabadddaddabddcadbddacdcbabbcdbbabbbadacadbacdadcdcacaccbaadbacbddccacccadccbcddcbbdcadadccbbbadbdcdcdbbdbaddcbcdbababbccdcbdccdbccbbbdabaaacadbdccdbdabbbaaaadadbbbcbacaacbadbdccbabadcaccdacabcdadbbdbdcbbadbcacddaccdcbcbbbbcadcadcbdcbdbbbabacadbacbbdaaadaadbbddadbabdddaacddddccbacacbcbccadbcacacbcbcdcadbcbcbaddcabbbbaaaacbaccccdaccacbbccbdcabdccddacddbaabddcaddadbbcddacdcbdcacbacbdabbbcbccbbcaadaadacabaccaccdadabcadcdddabcbccdbababcdacdccbacbabcaddbabbabcadddbabcadcaaababacdcdadcbcacbdcddbadaababdacadcbdcccadbbdadadaacccbdbaacccdcacddcacdbdbdabbcaccbddacddaaadcacdaaaacbbcdaaccacbdbdacbcabacccabbdcdbbaccabdbcbdcabbdddcbcbdbcaabbaabcbcadbcabcbabdacddddabacbabbbdabdcdbaaaaadbddcabdcbbcbbbccdcbcbabacdcbacbacacbdacdddccdbcbbadacbbcbaaddcbdcbbabdbbbdbcaabcdadbaddaddbbddacdbbaabbbdaddbbbbcdddaccdcbacbacdccaccdacddcadadcbddbcdaccdcccabcdadbcababcdcabcccddbbbdbcbcdbcdbcaaabbacddadbacadabdacabdaaaccdcacbbbabcdcaabcddabcaddbdaccaacadbaaacbaaaccbdcacacccaadcbcabccbabcdabbbbddbdaabbabcacacaabdccdbbbddddcabcabbdadabacdaddacbcabdcaacdcdcacaccacdaabcdbdddbddbcabbaccbccaddcaadabccdadbccadbacadbcbbabbcdadcaccabbababacbcdadadbbddacbaadcdbbbdadcbaddcbcacbdcbcdbcbcbdaaaaacbbbdbcbdaaadccacaaddddccbcdcbbbbaaddbcabdcbdbacdabdcdbcddddcabadcacbadadcdcadcaacdbbbcccbdaaacbdcaabadbcdddbcabdcbadcbaccadaccdbcbdaaacaaabddaadcaccbcbacdcbcdcbdaacbbcbddacdbcaabbacaaaaddbdbbbdadabadbcababdacdcdbcbcbbcbbccbabddcaddccdababacdbcbaacabdacacaddccaaaacbcdaacdcddcbbccbadddddbacbadcddacbbcaccbbbdacabcabbccadccbbdbcdbccbbdacdcbababcccaacbcddddcacadcccdcddcdbbdcbcabdaadabdbaccaadaadddbdbbdcdacdcbabbadccbbcbddaabbbabcabdcadcbdcdacabdbaccddbdacccaaaabbbacaddbaaccbcadcacadbbcadacbdadacdbdbadadadcaccdbbabaacbccbcccbdbbacabdbdaaacbccabdadaacdcdcacaddbacccbadacbcdcbcbaccbdcadbbccbdccbbabadaddacdddacccadcbadcadacbbccbabbbbaaadbcbdaaddccbcabcabdbcaabcbcccdccdccbddbaabbbcddabccdcdcbbadaccbcbcddcbddddbdbabbdbcdaccdbaabacbcbcdbaacdbbcaddccdddabbdadbcccdcdccbbcbbbddbdbabbdabaadaaadbdacbdaaabbbcbddababbaaadbaddccdddcaadcacacbccacadddcdbdcadcbaabdacaddbcdbabbadbbdbabadbdadbdabdbbccbccbcbaadbdbabccaccdbdbacabbbdabdbdbdcaddddadcbbbbbbbadcbcdabadcacdbbacdddabcacaddcdccbabcdbcaabbbacdacbbbcbbabcccbdbbdadadabcccacccaabbcbabaddbdcccddbabacbddcbadcacabbbdddcaadacccbcdaccccdbadcccbcaaddbccbababacdaadadbbbdadbbdaaddbacabccccbcccdaccdbdbdaadbbdcacdddbabddcbaacdcabacccaacdcaccbaaddacbbcdaabcddcdabbcadcadccadaacbbcaccbcaaaaadcdaadcbcdcddbcadcdcccbcabcabbadccaabbddccdbaccabcdbbabdbabbacdcdabbddbddbdcdccbbadddcbccaccadabacabaacddddcddbcabdcddddadaadbcdbcdbbaabacacadacbacdabdcbccdacccacadcbaaabcbabacbcbcdaadbbaacacdddbaabaccdcdbcaaadaabcbbcdccbbabdbaaadddbdbdbccdbbdbccadadabddabaaacdcabacbccaaccbbdabddadddcaabcbbbccbabbaabdacdcbabbccdbbbcdabccaaadcddbcaaabbcddcbacccbddddbaabaabbdcdcbcdcdcddaacabddbddabccdbcbddcdddbabaadbabadadcdaaddcdccabbaadccababccbcddabcaddacdaadadcacbcbcddcddcdbacaaaabccdbdcbabdadbdadbacccdcbacbccbbcaaacbdadabbddcdccbcbcabbddbbbdacaaabdacbddcbaddcbdbbadacbaadadddcbcbaaaadacdbbaaacabdaddcbbdbdabccdbadbbbbbbbaccccddccbaccbabdbdabbbddbababcabbcddccbddcdaacbdccdbccddbcaaacbadcddbdcbacddcbddcdccdcaddbdcabadadbbdaddddaabacbaddbccdbbbdbcadabcacdbaddcbbcabdddcccccacaaaddacbbdcadcbdacdaadcbdcbcbdbdbdadbdcaacdacaababaabbddbdcacddaaccacddcacbacbcdccadbcccbddcdcbbccbaadbcadbadadcddcdcdbdaacaddcbcbaaadbaaacccbcddabcaabcadcbaacaddcaaacbadbbbbaaacbabdbcbdbcaabaaacabacbbbcbbccdabddcacbcdabdddcdaccdcbbddabbcadcbabdddcddadcddaadbbacaddddbaadadccdaccccbcadaacabdcbbbddcaacccccbbdddcbdccddccabbadcaadbcddbccddaadcbcdcaabccdccacdcdccdcdaacddacddbcddcaabddadabbbbaaaaabacccbaadddbcaaaadbbadcdababcdbddacbabcbbdccadcdcabccadcdadbdccabadcbbcacdddaccbbbbbdabacdbaabaaccabccdadacbccaccbdbcdacabdddcbadcdcaddadaacdcdbccddacdcaabacccdbddbbcbaabcaacaaabcbccbabaadcdddaddcadcdbbcbbcbcddbdcdabaddadbabdacabbccbdabbbaacbdccbbdacdbbbbbddbdbcacdacdcbcbbdcdddbacbbabbbadddaacbcbcacbabcaacbadbaacdcdbbababbdddcabcdcdddcccbaddadbacbbacbbbbcdadadbacacadbdbacabaccabbdbccccbadcbdadcacbcdcccccdbdbcadccbbcdcbcaadacdaacdbcaadcaddcdbdabbdcdaccaadbaabbbdbbadccdccbbbababbabcdadbddddcdbdbbcdaddccdcbbddddcacccccadabadbbbcbadbbaddcccabbadaddbdbbadcddbabddcbacbaaadcabdadbaaccbaacbbcacacdaabcbddddacbddddaacdaacaccadcbbcccddaccbabdcccbaadcdccacbacccdcacbbbddaacdbdcabcdacaddcabacbacdcbcaaaabcadbccadccdadcdbcadbabaacacdbacaadcbcabbccbacaacaabdbabbbddcaabdddbbdccabaacccdbacabcccdbdacadaaabdadcabbccaabccdbabbaacabbacadcdadaddbccdcaabcacbbaabcbadcabbbdcdcbbabbdccbbdbbcacacabccbbdabdadddadddbbdbadcdacacabddaccadddaaacabbaaadadbcdcdbddbddabcadbccbadccacccacacdabcabbbdcddddcbbcbbaccbbdbcadcaabdaddacabcdbbdccacdcacbabcdcddaccbbbdadacbcdbbaabbabadabbdddcacdabcdccbabbcbbcbcdcacbbcbbbbcaacbacbadabdbbdddcacdadadbadcaddddcbdbbaabccacbddcdacabcbcabadaddcaaadbadddaacabdbaabdacaaacdddcddccabdcabbbbadcdcabbdddcccdcadccdcdccbdbabccbadccaddabacdabcdbacaabcabdccddcdcbbcddbcccabbcdbbcbbabcabadbcabbaadacbbcddccaacbcccaccbaacdbcdaaadccbbadcdbacbaadbcbcddcdcccabababbbbacabcdccaddaabaadadddadbccdcadcbccaabcdcabbbbcabdbcabbbbdcabaacbdddbcababdaaaabbacbddbcacbdabaacdabbdacaacadbbcabdcbdcbcdcabccaaadddcaadaaaaacbcacbaabcdcdcddbcbddaababaddbbaacbaabcdabdcbbbdcdcdcdbbaaaabaaddccdbdaaacdacadddbabdacaccadcccccadcabababbbabcdbadddbdbcdbdccbcbcdcaadddadaacbaddacdccadcdaadadbbcbacdccbbdcbabadbdadcadbddacabcbbcaccaaacccbbbcbacbdcabcdbdcddccacacadbbabdcaaadbdcbcaabacdaabcbbcacddbadddabadcadbcadabababcccbdbaaabcdcdddcbbacacbbcdccbbccbdcbccbdadbabcdabdcdacccacbbbcbccabaacddabcdddabdabdcdbcbdabdcadbbbcacdabaddaacaddcdccbaadaccdbabbacbddaaabaabccbbbddbacdbacbbbabdcdbacbdccbbadabbdabbdcbdcdacbcbbcadbbbddbdccababbbacbacbbdbdcccadcdddcdbbacbcdcbdaaddccbaaabbababddbabcbddaadbbcdccabdcbdcbbbdabcdbcadbcdcbbabccacbbdacdadcccbdaccacdabddbdbcbbbaacbbaccbddccbdadcdabaaaabbccabdbdbdbadbdbaabbbbbddbabdbbbdddaabddababbddbabdcdcdccbbacbabadbabcdddcabdcdcdbacaacbcbacbcacccdccadccadacacbaddcbdccdabcabbcccdadcdbbacacbcdacbccdabbadcbadbdbdcdccccbbdcdbadddbcbccbcbddbbbcdabbccccbdcbbaabdcabcdcabdbbcbcbddbdaadcbdccbcdaadbdacdccbcdbadbacadcdcbdccccbbbbbdcaacddaabaaaadaccabdbcbabbbbbdbbdabbacbdbcccadbdaaaacbddbacbbddbdbbdbaddabcaddcbdbbbaadababdcbccbcacdadccabdcccddbbbdacbbadadabbacdbbadaaccbbadcbadcccbcbdbdcbdaabadcddbbccddbdbacaabcdaacdabcaabbacbbccacbaadaddbadbabddbdbcaaadccaadbacbabdbbcdbbcdbccadbbaaaaacbccdbdaccaaadbacbdcdacacbacbacbbddacdccbbdbadbbbcaadbbbdbabbacadccaadabdddacbabadbadcbbaadabaacacadcaacaccbaabbbabccacbbdabccbdcbacddddaadbccbbadbacbacacbdadbcddbaaabdbccbaabcbabaacdacddddadcccaadddccacbbacdabadcadaccdccccacabbdccdddcbdadddadaddbdcacabcbdbcbbcddabbcbdaacbdbacdadabacdcbccdddbcdcdbdcdbaadbddbbcdaacacdcadcbbddcbcdbddacabbaaabcbabbbbcadbadbdddaabdcddddcbadbccdaaabcbbabddbbdcbbdddababccbdcdaadacabdbdaddabaacbddbabcdbccdcabaabccdccdcddadabaddaccbbbcdaacbcbbbcdacbabdcbdaadadabcccabcbacdcdcdbcadddcaacbabcddbcdaacbaaabcacbadcdbbdcaacccaccdaaacbccaabbdbdabdaddcdcadddadaabaabbbbaacdacdabacabdbadaaacbaacbdcdbaaaddddbbcbbabbababcdccddacbdbdcddcccdccccbbcbdadbcbdcccdaabcaccaaaaaddbdadaaaabbddabddbddddadbaacbadadaabaddddabacdcdbddcdbbdacdaaabcccbbadbcbbcbbdabddcdcdcdddcbdddbcdddbdabbbbadbbbcaddbdccbcbcabcbbcbdcddadadaaddacadcbbabdaabbdbbbdcbbabddcaccdbcaddddaacacddbcacabdbabdaddddcadadaadaabbaadbddcdccdcacdcbbcdbdcaaaabdabbacbcacaccbcdcaabcacdddabaddabaadccbcbcdbccbdcabdabddcbdaccbdaacbacaccaacaddcddcbdadcaaabadaabdccbadadacaadcdaacdbbbaaaaabcddbbdddbbccacddbcbcbbadcaacddbccbddbbabcaaadabbddcaadbbadabcacdbbddccaccdabbcdbabdaacaadaabadbcbaabcdbddcaacbadbaccbcbcdbdbaadccccdbdabcabbbdacaabccddacbcaaadcbbccacdbcababdbdbbadbaabacbadcabbcbaacccbdababcdbacbcbcabbcaaabaabaccccadbcdcaaabbbccdbaaacbbbaacbcdabddbdacabbbcbabdbdaacbdcabbddacabadbaacbcbbccaabcacdadccbdcabcdcdddabbabcbadcdcbaacdacbbbabcbdadcdaadabccbccadcddabadbdbdbddddccdddbbbccadcddbbcdbddcbbdbaaaaabdacacdadaaaadabbbdabbadbbabdcddacadadddaaacbcbadbdabbbdbcdacbbababbcbbbbddbccbbdddcdcadabbdacdbdbadbdacdcbcaacdccacccaadacadabbaccbadbddbcabbacacadcdcdcbbbaabbdcadbabcbaabdcdaccddbbabcdcabbcddbbaaadacdcaddbdcccabcaadbacbdbaacacbaacdbcdbddbbdadbadcaaddadadacdbdcaacdabdabccdbcdcbaddcccbcddbaddabbacbdcccaaabddddaaaabcddbcbbcbcdbaacabbacbabbacbcddaabacbaccabbcccabbcdaccbcdddabbbdbaacbdaabadbccdabccabdcdcaaabdcacdccddbbcbbcdbbcabccbdabaccdbdcdcdaaacaccbbabbacaaabbccbcbdcddcbdddbadbabbbddccabacbcaccdccdadaaadcdabcdacbddcbbaadacbcabcdabbbcddaacdaacccdbaddbabdabdabcdabadabbdbdbaacccbdaabbddbccbdabcdcadbaadbbbbbbbdccdcdabdaadddccdbadaabaaadbdbcaadddbabbcaabbabccdbdcdcbbcadcdcddcdbdcbaadcbcbababbbdbdbbcbbcbacbbbdcdbabbaaaddcdabadacacbbaaddbbbcddacabbbabdddbcdadcaadcbdcdcdaacbadadabccabaddabbaccccacddcbacddcddccbacdabccdbbbbcccccaacccadbcccaabbcbbbdacadcbccbccbdcaddabcbbdcbbaacadbbccaacddaaaddcacdbbadadadacdbbcbcacaaabbacdaaaddcacbbdbbdbabdddddadababdabcbddacbcbbacdbbcbaacccdadaaddaccacadcaddbbcabddcabdbcbbaccabcbbcbbddccacccbbcdbcdbcbadddaadbcdcddbbaabcddbacbbdbbcdbbdcadadadcbbdcacbcccabcabcbccabbabbdcbdbcccadaccbaaadddabcbcabbcacccbacdddddadccabacacababbdadbaddbddadcdabdbccadbcdddbddbdcbabdccdcabaacacbbdbbdaddccccbdcddaddabdbcadbbdadabddadcbdbddcdacbcaddcddccabbbcccaddaadddcaacbdcddbacaaaddadbcbbacbccddcbabcccaabccadbbcabcddaacaaacaadabaaabaddbdaabcaacadbaaadddcadccbcaaddcacdaaadabdbcaadaccaadccdaacbacdadbbdddaaabdbcbcbaababcaadaddaababbdccacadbbcdcbbcaddbcbaddbbaaabdbaadbacadcbdbadbcdbabbabaaabdcbdcbdcabbbadabbbddaaddbccbadbbbbdddaabacddbadcccbacdbdbccaaacbbaabadacbbacdaadbcadadbdabdcacbdabddabdacbadcadcaadbddcdcccaadcdcccbdacddadabaddadcaadacaababccdacddccbdadacbbabaababaccacacacdaacacdaacdadbcaddacdacabdadcdcadddcbbdcdcdadbbbbccbcccbacabaacddbbdcbcbbbdbcdaccdbacbcdbbdacacccabddacacddabcddaadbddbdbcabbdcacbaddacadbddbabdadcacbdbcdbcdddcbcadddaccdabbbddbaadbdddbcbdbdabdbcdadaacbddbaacddbbbdbcbbdcaadccacbccdddbdaaadcccdcaaaddacdcbdbcacdbbdaacddadaacacbbaacdcadccaddccdbdacccaaabcccadcdabacabcbaaaabcbbaacdaddcddbcddadaabaaddcbdcaccbdaddbabcbdccbbbdaacbabaadabcbbcadbaccbddbbcaabcaacbbdbcccbdabcadbccbcacbbcbccbaacacbcaccbccbcbbbbacbaccbaccdddbbdaacddbbbcbdabaccbcadcbdaddbdbddaddbaabaaaaaccbcccdbdbcbcdbcbabddbdbdbabbddcdddacaacacacdbdababcddadbabccdcacbcabcbccbdcdbbbaaacbbbadccaccccddddcbabadabbaddbababacadcaaddddabbabccabacbbadaccacbcbacdbabdcaccdbcdbddcccbbbbadccaaacdaaccaabdbccccccbcdbaadcaaadcccbdbabcbbbbdaabacbacbddaaadadbcacdcdcacadadddbbadbddabbcbbbadabaadbdbcabdbddccaadcbcabaccabdcdbccbdadbddabcdaadccdbbdadbadaaabbbabaaabaddbacacadcbdcadbddacbacbdbaadcccbccbabbcbadabdcaccdadccadacabbbaacddbdabdaadcbacacdaabddaaddaaaabbbdddbdcdbbaaddabddcbbaaacbadcdcbbacdadabaccbccabaccbaacccdaaaccccbbaadcdaaadabaaccaaaaaadbdccaacdcdaaadbcdbaaaddccddbbccaacccabaccadbdbbcbddbbddccbdddaacadcdcdbbaacbdbaabbbbcbbcadbcadcabbcdbabccddcdaaabccbadbaccaaabbdadacbbbbdccddcccbddcdadcccbbbbacdcccccbcaddbadbdddddabcddbddbddacdbcdccdadcbacaddbdbdbccbccacabcdcbbadbababdabaccabbbadadaaaadcacccabddbadababdaadabaccabbdaaddcabbbadbcdabcdbccbbaaababdccabcdddcccccaadaaabacadacdabcadcddaaaadcbdacbacbbcbcdcbabbdccaaddaccbcdbdacddcabbcddabccbbabacdadacbaacbdcacdcbabacbccbcadacbddddcabadadbaaddbdcbbdccaadcbdadcccacdcdccdaacbdddcacdcabdcdabdcabaadabddcbccadcaacadbcdcddcbbdccbbddcbdbbaddbabdbbdbbcbcdcbaacccdabdbadcaddadcbccdaacabaababddadbdbbdcaaccadddaadadabdcdbdcdccbdcaadaccabdddacacadbddbcaadabddbddbabcaddbcddcdbddadccbcadcdcaddaccdcdacbaddbcbcaaabbaddcbbdacdaaaddcbbacbacdbcadaabcbccbbbbccabbbacddcdbadbbbbbccdabbcbadaddccccbbdabcaaacddbaabbdaacdbbddbacaacddbacbdaaabcabbcbcdbddabdaaccadbcbdcbdbcdadaaabcbdbdccbabbcbaaabbcdbdaaabadacdcdbcdaaadabbdbbaadaccaccdcdccdadcaddbdddbbaddcadcbacbddcddacdcccbdccdddaccaddaaaddadcdbadbbcadbdbdabacbaddaccdcbbaddbdaddccbcdbabcddccddcbddcbccabdababddbcdaabdbbaadcacccabbcbbacbdbbacacddabcdbaaabacbccabdcdadccaaddabdbaddaacccdddcccaabcabbbaabaabaacabccaddbdaacdaaaaadaddcbadbdabbdabbcaaaddcbbdbdbbaacdddbdbadadadaabcbccbbadaddbddbacdadaadccbcbdbbccacaacacbdcdcdbbdcabdadacbbdbdcbdbcacdbdccbadddbbcbaabcddccdccbccaadacbccbbabadbbddcdbcadadbdacacacadcbcaccdbbbbabadbccccbcbccbaaaabdbdddbaccbcbacdccbacbbbdcbbaadacacabddbbadcdadabddccbbbadaabbbbcabadddacabdbcccbbaccdccbdbdacbcddbacdadbcdcbdbdbacdcddbcbdaabcbaccbacaccdcabbcabadbbacaadacbcaabdaabadccbbdacbddadabadcadaacbccdbbaccdcbcbcddabacdbbdcacaaaaccabdacbdabcabddcacdcbcbcaccbdddbdaabddbbbaaccddccababacddbbcbddacddaabdadcbcacbcdcccadcbdabaacbdddaacdcbdaaddcbaacbaacadbbaccbcbdcbcdbaadcaaddbbdabdcacdccdbabbccabdcccbaababdccdbcababbadbdcbbcdcbcbaacdadcaacdabbdccbabcdacdbdbdcbadbccbbbdcbbbcaacbabbacaadadabdcbdbdcbbbcdbcbccaaccccacbcbcaacaaabdadcdabcdbcadcabccddcacaccabbcbbbdbdcdadaabaddadbcdbdaabbabaadacbdaccdcaadbddaaaabccccccccaabcacadddaaaaddbacdcbdbddcaaddcdaadaadbadbcababdcbdbdcbaaadbbaaabdaddbccdddddbdbdddddacaddcabbdabdababacddddbacdcacdbccacaaddbaabbccccdadbdacbddbaabddbbaaccbabdaaacaacbcbbcbbbdbadabdcadbdcbddcbddcccbcccbabdcbcbbdacbcaabaabbdbcaabadcddbdcbabdbcacdbbdadbadccdaccbdabcbaabbdccccbbbdbadcbcbcabdacbbdccacacabaadbcdabdadccdbdadddbdbdcdcbdbccbdcbcbdcdcccbbcdbbaccbdaabadcabdcbcbcdcdaadcbccdbcaccdccddcbcdbddddacacbaccdbccbbabbaaacdabaadccbbbddddbbdbbcadbdcbacadcdbddbcdbaccacadddccdbdbdcabdbacaabbcdbabbcbbaabdbaddccbdcbdcdddadabcbbadbbaddadcaaabbdccadcadbaccabccaabacabdbacbacdabccacbadacadbdcdadaacabbbdbdcdabccbdbaabaaadcbddaccaaaaabcadbaaadccbdcbbaaacbdbdadadccadbccdcbbdacdacdaaabacbccaaabccadddaacbcdabccdbbaaacdabcbdcdcbbdccccbacdaaaabccaadbccabccdadccdacadbdabcbddadbddccbbdabdbcabcdacdbbabbabaddabcbdaccddbaddcdcddccadaccacdcaabddacaaaabbaacbccaccbacacbbddadabccdcaabbbdadbbddcdcacbbccaababbdbaadaddbabaddbababcaccbcbdacdbcdacaddbcddabddadbbcccdcbcdbaddcddcbabcbbddaaabddaacababbdadaabcbbaaccdacabcacbdacbdbbcdbdaccdbbdabcacbacdaaadacbaaabcdddcbbddcdabaddabcddcdbcbbcddbcbbccbbcdadcccbbacbbcddccabddbabdacbcacadabbacbdabbadccbbbaccdacdadabbacaddbaccacabcdbcababaacdcabdcaadbabaddadbadabcdcbbdbbbcbcdcdbdacadcdcacdbcdddbdbcdacbcbaddbcdadbcdabaacccaadbbbbcadbadbbbdbbbdcdacbbcdbdbcdcbacabcdccdcacddbcddcdcbccdacbbbbdcbabbcbadcbcacadbdbaaccabaaabcddbcdcdbbbddbbbbbcbadadbacbbdabcdaaddcdacbbcbdcbbabddbcdaacacbdcabaacdbaddbbabacbaacadbaabacabcabcddbbcaadaccaabdbdaaabcbdbaadcbcdbccccdcadbcccacdacbcacabbdcabccaccababddbcadaccadddbdacaddabbcccbbccdabbdaabcbaadbbddaabbdbbdcbdaabadacdaadcadaddcbcdabacbacdacdbabbccabcabbaadadabcddbbbbbcdcaaacbabbddbdaadddadabaaaabcacccdbbabccccbacdabdcccbadcdddaadcaacdaabccaadacdbdbaccbadaaabbdbaddababbcbbacdbaddaddadddabccaccbcdabccbaacaaacaabddbdaadbbcaacdbcccbaddaadaccdbcacbcbccacdbbddccbabcddaaaccdcaccabcdaddbbbdcabdddcccbbabbcddcbdabcdbacabadbdbabbddcbabaabacdcaaacbcaabcabbbacddbdbcdcababdcdbbddddbccdcddcbbcabacdbdbbcbacacaacdcdcccbdbabaacadcccacddbaaaddbbaaabddcbbbbccbdcddaacaccbabcbdcaaddbcdbddaaddaabaaddcbdbaacabbbacababdcbaddcaabcaacbbccaccbdbabbaacbddaacdabcbdbccbccacbacddcacadddccdddbdccbbdbdadcaadcacddbbbcaaacddcbcdaccacccbadbcaccacbcbbabdbbbcbcdbadbdacdccdcadbadaccadbcbbccbdbcddacababbcabdabbabbcbcabbaccbababdaddaccbbcacdcdbddcddccaadbcabdcdbdcdcddccdadcadadcbbacaccacabacadccadccbadcbcbadbacaadddcaddaaddbdaacdcaaccccacaacdbbbdbaabdadcadcabbbadbccbccccdabcdacdcbaaddcdcbaacbcacbbcdddcdcbccabcaccccadbacbacabdaabaadddcbcbcdcccaabbccadaacaaaccbdccdaadbcbdbbcccddabdbacbbacdacdbdbccbadddbdbadbbaadabbcdcbcaccbddaaabaddbcdbbccaadacaddaaaaadcbccbabcccacbcdcbaabbccddbbdcbacdbdbaccbcdccdddaccccadcbddbccabdcbcacadabdbdddacdcdccabaabdcbbbddcdabaaccaacaabccbaddacdbacadbddabacddadabccbbbccbaddaabbccacadaaacdddacdcacaacdacbddaabbdbbbdacaabbbdaccddacbbcaacbdccbcbcabcbddadadcbccbadcdcdabcccaadbddbddaddcbbdcaadbbbdacccbbbacdbbadcdbcabddcbdcdacdbcacdbaddacdbdcacadcbcaabcbadaabdacaddbbbbbbbabbcabdadcdcaddaabbdacabacdbbaacadadbdcabbaabcbaddbddbbbccbbdddbdbaabccaadcaddabcbaabbdbaacabdabccdbbbbccbdcdbdbcdabcbabbccacabacaacddbabadddccdbabcbbdbaacabbdbdbdccadcbaadbabcaacdddadaaddcaabcdaaaadcaddcadababccaddbadbccadddbabaabdbcacdbadbbbabbacdbacbcdaaccddabaccbacbdcaabaacaadadcabbdbabcaccacddbadbbadadcaacbadabcbdcbcabbaacbcbaadccbccbcabdcadcccbdddcaaadccabddadcbaacbddbdcdddbbdbbbbdbacddbabccdbdadabbdabdddcdbacdabddcddcabccdabddbaabacaacaaccddaaddbdbaaacaaaacdcbcddcddabcddddcabccbdbddabcbdbdacadbabccddcbbdbadddbcddcddaabcccbcccabbaabaaacbbacdddcccccdaacbbdbaccccbaaaccbddbdcbcdcbcddcbbdcaaabcaabcaddacddaacbbbacababacaaabdaccbbbcabcbbacacccadbdcbbcacdcbaabbabdaadbdcaaadbacacabacaaaaadaddaabbbbaababdcbbdaacbaacadbaabbbcccadcbbdbadcdabbbaadaaadbbacdbcdabdcdbdadabbbddcdaddcdcaabaccbcabbdacddcccdbbdabbccbddcbccdcabccdbabdbbdaaaadcbbddcdacbababbcadcaddddbadbcddcaddababbadbbdcccbcdccadcdbcbacbacdccbbbaaabdcabcddbabbbdddcabbcdcdbabbcddcbdabbbcccbacbdacbdddbddcabcadcdabcdacdddcabadcadbddcddbaaadbbcabcdbcdabaaddbddbdddcbdcbbacbcdbdbadddbbdbcbcdcdabccabaabbdacdccdaacadbcaccbdcdbadcbbcddcbcdcabbcbaddccdaddcbadaaaaaabdbcbdbdcccbabdbdacbbbaaadbdaabcaccbbdaabddbbaadcbaabacbbacbdbcddcbacacdbacbbacbacdadadbbcdcdbddcbcabddbabddabbbaaadbaccdcbbadcbddbcbaacdabcaaaabbbaaacaacaccbdbadcbddcaadaddbdcbddaaabcacccbcbababcababcdcbacacdaabdbdccddbbddbbaadcbbdbbbddbabbcdbdadcacabadaaaaaddbdadcdabbdabcbdacccdddddadbcccbbbdacdaaccbaabaccbbdddbcbdcdaacbacddacaacbdcbacabcddbbacdaabbdddacbdcababcabdaaaddbacabcdbaadaddaddccccabcbbadabbbacddbcbadacdcadddbcadaaadcabacabdccddddbbcabdbbbabdbdbacbbdabbcdddadcadcaccacbdccdcbdaddbbdadacbadbcddadcbcaabcbccaddddbabcadabcdabcdaaacdbdcbbcbccaaababddcbdbbcaaadbdabdaddaabcdaddcacddbaabbbbbabddcaacddbaddcabcdbababaaabaacbaacdaaadbbdbbcdcabccdbbccadcbadaabacbccdaddbbcbdacdaccdccbcdbdaccbbcccbddbddbcbdacdadcccddacabbaddbdbdaaddbbcdaabcdddbbabdcdcdbddcddbbadbbababaddbacacbacadcbabcaccccdbcabdcddccddbdcabdcdaaabccabbdaacabaabaabbacadcbdcbabdbbccdcabaaddcaacddccdbaccadabcdabcddaacdcbdbdccbbbdbdbddbddccbacccadccdcabcacccbdbaddbdacdcadcdadbabcbaccdbcabbababadbcbdcdabcdaadddbbccabcacbaccbcaadcdbddcadcbaaaaacddcbbaddbaddcdbbcadacaaccacacaacadadcabddcabcbbbcdabdbccdadaaaabbdbccdbbdabcbcbacacdaaaadbbdbbbadaaddccaacdcdbaccacbaabbcabdcccbabbabbacdcbddaddddabacdaacbbbadadcacddcbcaaadcadcddcdadacbdcacddacbcbdbcacbcaccaabcdabbaadbdccaaadbbcddcdacbdddbbacaacbcdddbcbdacaabcddadbddacdcdcdbbadcdcacacadabbdddbdcabacacbbccadbdbcdcabbabbcaaacbbdddbdddadcbddbccacdacddaaaddddacdcaacbabaccccdaabacadcbccaabacccadbbccbaccbcbbcccacaababbabdcaabbabbaadbdadbdccabcdabaacbdacdadbdbbcbcddcaabdcbcbcbdcaacdbaaadadcaabacacbdaccccacbcdcdddcbdbcbdabdacaaadddacacbdbaadacaabadacadaacabdcddadbbcabacdacaabddbcacbcccaadccbcadabcbbbdbacbadacaacccbbdacdaabbccdcccdcdcccdddbbbaabdcccaccbcbacddbbccdaddbbbacccbdbcaaaaaabbaaaabbdacbcaccbadbacbddbabbcaddbcdaabdbbbdcabdbbdcabbbdbadcbdadaccccaabaccbbdadabbbdbdcabcbaadadabcbacbcbacabcadcdaaaaddcbddaaacaddbabadbddabdddacccaddaaaaccdbaabbdbcbacacadacccccdddcabbdabdcbbccdacacdbcdccaaabcaaadddadcdabaaacdccbaaadbbcaaadbcbcbadbccbddcaabdddcbcaabbbaccacacbabbaddcccaabccbaadbbcbaabcbadaccdacdbbdcdbabbddccdbddbccdcaddabadabddaaaddbcbadcadddbbcbdbbcbdacddadabcdbddcabbbbbacaacdbccbbcbddaacdabdcdaccaccacbbcbbbadbaacddcdbcccdbabacddbdbccdadcbcddbabdbbbddddbdccadccacddddbabaddaaacdbcdcdbcaddbabccaabdbcdaadacabadbdcbcacdadbacaabcddcadaaacaacaabdbbadddadcadabdacdadaccdbacddaddbabcabccdbdbbbcdbbdbdabcaabdbbcaaabadaaabaddbbbdaabcdbadacaaadbcdddbdbcbddbdcbddbaaaaaddbadaddbccbcddaaadcddbccadbcdabacddcdadddcbabbbcbdcdacacbcccaaadadcacddaddacddaaadcabdaabcdabbacdccbdcddcbdddccbbcacbaddcaabbccdcabdacacaabdadcdcabacbcbcbabbdccaabcacbdcdbccabdccadcdbaabdcaaacaccabcabccbcdabcbbbcaaabdbaccabbbbddaacbddccdadbabdcbadbcbdabcbabbdcbdabdaabcdddbbdadacadbabcaaacbddcacadcbabbbbcbdbcdddaabdbcbaabdcabdadbacdbbbbbbacbbccccaababdbcaadadacdcdcbaacdbbbadbacabcbadbccababcdbbbacbadcbaaadbcbddcacbdbddbcadbdabbdabccbacddbaadcbabdabbaccbcbcbadbbabaaccbcddbbdacbacccdccdddabbddbaddbaaacbadcabbabadacdabcddacdacccdddacdddbdbbcadbaddccabadcbcdcababccccaddccddcdbddbdbbdaaaabadbdddabadcbcdbbbbdaadbaccbcbcbbabbabcacabbbbabbadddccabacbbadadadaccdabcbbabbccdcbcbacdabacbabcbbaaacbccadbbcccbaccbdaaaaacbccabbcbacbcbdcdbbcadadbcdbaadbcbbdabacccaccdacbabcbabdaccaddcbabaabcadabbddadccababaadadbbbccabaccbabcdabadaabadadbddbacddbddbabdabdbdacadbdacdccbcaaaacacabacdccadacdabadaabddacdcccbcccaacdaaadbbbcdddabbbcccaccabdbabacdbdbccccaadabccdacacbabccdccbbacccabbbccabbddaabadbdabcbdbcaddcbabaccbbbcdccabbcbbddabcbcdababbbabcdbcaccacdcacabdccaddacdccabdcababbcdbbddbbdbbdbdcccbadddaacbadbbcbabadcccdbcbdabaabcdcdbdddbbcccddddccbbbbcacaadbbddaabdadaadcbdbccacccabbacadddbbdbdbabcabbcdbadbcbdcaacaadddbdaadcdcaabcccddcbbdbbdbaaadaaabaabaadcdbccbcaccaaccddbbdddccbbabaadabcbcabaddabccbcddcdbbcabcbacccccbadaddbddcdaacbcaadababaacdadcaacccbcbadbadcccdaabbaaacadbcdaccddbcbdabbadabdddaacabcdccdbacbbabcdcbccdbcdcbadcdccccbabacbadcbaacbadddbbdbdacaabcdcbacbabcccbacbcbcbdcaadaaababcaddbcdaaccbbbcbaabccddbbaaabcacadcbcbaaccaabdabaabdadbbcbbcbdbacbbbacbcdbbdcaadddcbbdaababcacacadbcbdacadaadcadccbbdbbcddbdcbcaaacccacdabcabcdacdbbaccdccddbbcdadaaddbcddccbbdbadbadcdaabddddcaaaddcbcdabdcacbbdbbbdadadadadddaacccdaddbaadccadbbaddbdbbddadcbdbbacbadabcdcbdcacabddccbcdbabdcdccccccddaddddbbacbccdcdccdabaadcbbbbdadaadabdccbbacaacbbddbacbddcdccbdadacadcacadaaaaacbcddbbcbdbbbccbcdaddbbbbcdbbcadadadbddbcddcddbbdadcccbdcbaccaababbbdcadbddcdadcccdcbcbabcbcddcbdcbabddaadbbcbdcdbaabddabcbaabaadadaabcccbccaaccdcbbaacbcbbacacabdacdccaacddabbadadaadaaaddcddbcdbdbbcbcbcaddadcaabbdddaacaadbcbdaabbddcdabacbdacaaddbbcdaccadbbdcdccaabcacdabbacbddbdcbbbbdcdaadbddcccdacbcdccadabbaabbabbcdcbdbababdacabaddadaacaaaacbdbbcabcdcdcddcbdcdaabbadbcbdddaddbababbcacdaddaddcaacddbcacdbbbbddbcabbadcdcaddbcdadbabdcdabdbcaddbbaaccdbbbcadcabdcacbcaaadcdccacdbddabbcccccbdacabcbcbcdcddaadaadcbdbabbbdcdbdbababcbdaadccabbcccaddcdbbbadddaaaddbbddbbbdbddadccccaaaccdbccddaccdacddacddaacbbdaddabbabcbbbdbbdcacdaabbdcaaaabbcabcdbadbaaacbcabacbbdddbcbcaaabaddbddadcacddcbdadaabbcaabdaabcbbabbcccddabaccdacdcaacccdabcdbbdcabbdabccbcbbabcacbbaadbbbdaddcbbcabaccadbacaabadcdcdaabbccdcbabbdccccabdabdbaccbbdbadaadbaadccacabccbdababbcbbbddababdcbddadcadbaadbddbdbaddddcddbbaccaaabbbbcccaddaadacbbdaabbcbbcdddbbbdcbbacbaddadbbbdbaacaacadbcccabcaaddcadaacdcddadbaadcccbdddcaaabcababcbbddcccddbdbcadabababbcccbbdbbbacdacdbbcbcabdcdcaaabdcdcaaddbcccaacacbbadacdcadbbddbcbdccddcaaadcaccccddbacccdcadcdcddbdcbaaadddaabcdbabadbadadcacbaacabdabaccadbdabbaaabcbdddddcbaddbdaaabcbcdaacacaabdddddbacdbdbadcabbaddbaaacbacadcdacdbdaadabaadcccddccbbbabccabbbadaccbaaadbabcbcddabcabcaabcbbcbbcdcdddadadaccbcbdbbccabbaccbcdaacabccddbaacdddacbacdcddbaddbbcbbaacccbaabcccadbcbcbadbcaddccdadbccbaabbdbabacbbdadacbacddbadcaadacbbbcbcccdaabcacbbccbcabcacddccdcdbbacddbcbccbaddaaadaaabcdacbbdacadadddcdcdccabaaabaabcddbddcadbbbaadcbcbbbbbdbdacdbbbdcdbcbaacbadacabbdcabbccbcabbdcaacabddababbcdacdbbadacdcaabadaaaadbdcdacdccaddccbdabbdbcdcdabccdaaaddddabbbcddcdabadcbbbbbacddbbdbabadbacbcbadcbbabdbbbcaacdbdabdcbcdacdaaabdcacaacdadbaaacbcdbcdacccccdabaccadcddbdcdbbbdccaacaaabbdaabdbccdbbcaadabcddbadbdabacaddbcadabcadcacadddbdbaccbddaccdcbbdadadaaadbddbacbccdcbdadbccbacdaccbccdaabbbcacbdccaddabbddbdbbcddacbddbbcbdcbbdbbbddadbdabdaabcbacdddbbccbcdaacbbbacdaddadddaaacabbcdbabcbddccabdadacbbdcdcccbcdccbdbcdcdcdadddcbcbaccdcadbccdcccdadbdaddcabdcacaabbcbcdbcbcbbcbdccbddbbbccdcbdacdacdbbcacbaddbbbabddbadcbccddacdbbccdacaddccacbbdcaaaabcababbdabbaccdddcbcabbabadcbdbbabadcaacadaccdddcbcacbccbcbcdaadadacdadacacdccccbcdbadadbadcacbdccdadaaccacbaabbaaacdbdddbadcdcbbcbdcbdbaccabddbcabbbddacbddddbacccbcdcacacbacdccccbbbadcbbaabddacabbadcbbbbcbaacdaaccdccdbabcabbbbdbcbaaaccaccdbbccabadccabbccdcccacaaadaabdcbdabdadddccdaaaccbccacbdddaddbdbdcadcbbabdbcdbdcdadaabcaccdaaaadcdadddccccdaabcabddbbacbdaabbaacadcdcbbbabbbbadcdabadaddbaddaabacaabcdaabbdabbcddcacbaabcacddbababdbdaacdacbadacaabbcbbdbbdccbcbaccbaadaaacbbbcacbabdadbaacbbcddbdbbdaacdbaccdbbdcdcaabbbbabdbdacabbcddcadcaaccbababbcbacdccddccbbccdddccdaacbccdaadddcdbaabadcddbbcbcbadaaadccbcddbbbbadcbaacadababbbacbccbcccbccbadbdccbdccacaddbcaabadcacbbcdbdbabdcddababdddcaccadcadbdcbbaadcdbbbcacabacbbcdabbddadcabccddbbaabcdabdadbbdcacdbadbdaccddbaddadcaddaabaacdcdcddbadbcbcdacbadddcbacdacdddcdaadaddbbabdabaaddbddcddadbbccbacbdcddccabcdbbdccbbdaadbcadcdcbbaadaccdbabaabccaadcabccbaaabaacacbbbdabaaadaabdccbdabdbdababcbadbbbbcadbdcbdbacacdbaabcabcbdbbdcbbdaaadcdbaacbcbcdbacbcacbcddddccacacdabcadcacdacaddcbccabacccccbdcbdddbcaccaacdacaabcbdbaadacaddaaaccbcbcbcbbaadbcaacbbcbbadbbaadddbbabaddddcdaddaaaadacdbdcacccdbcccdbaaacbbbabcdcdbcbbdaacadbcbdcdcaddddabadbbbbbaabcdccdddaaddaadadcdabdacdaaccbbbabbccadacdabcbcacdbcadadbdacbabdcccbcddacbacabccbaabbdbdaacddbbaaacccaadaccbaabaaabaddcadcaddbcaabcbadbacdccbaaacdbcddadbbccdbdbbaabccbcdddabbbdacbcbcadccdaaddbadcdbbcbccabcddabcbcbdacdadccccaabbcbbcddabccacccaabdcdabccbaacbbccbabdbdbacdadcbbcdabdaacddbcbbccddcadcabddcabdbcddcbacbaabccdcbcdccacdacabdddadbcabbaacdbaacacdcdaabdbdbacbcbbadbdabdbccbbaccaabcdaadaabaacccccdcbcacadbbbdaacbacbabbbcabccbaabccccdccbabaaacbaabbccdbcaaddddcddbcbacbdcccbbcddcacbbbaababbbbdcbdacbbbabaaaacadaccbdabadadaacddbbccadcbbddacbcddddacabbdcbdccdbbabdccbccbcaacabdadbdaaddcabdbaadbaddabaaacacccddcbaabdabcabcaacababbdcbcaabadbcddcdcbbcaabcbacacddccbcbdacdaccddadbcbcbbdccddacabadcaaaaabcbddacbadacbbbcdbacccdcdbbcbbdcbabccddaddccacadbcbbbacdbdcdabbadcadddbaaaddcdabbaccabacbcdcadabadcadcbbcaaaabdaddbaadabdbcbcadbbbabaadadaadadbbacabadacbcbdbcabbaaaabadaaadadcbdddacadadabdadccbcbccddbabbbabcbadbadbdbdcccddcacbcdacadabdcaabdbcccbdddaacbcdbaaaabccabbdbddadccbbabcdcbcabbcadadadccdacadaadacddcabcbacdbbccdcdccabaddacabacbbcddcaaadddcaddacdccacabadbbacddbbcdbbabacccddabbaaacdccdbccdababccbbcdcddadbadbcdcbcbdaabdcccbdccbdadcaaabcaccadcdcbddbadbdccacbccacbdaabcaddccadbbaabdcdbabbcadcdcbccdcbbddbadbddbadcacabccccdbcaddcbddaccccddadbbdbcddbbdcabcbabcdccbadbaddcaacdcbcacabaacdbbcaccadaaddaadbbcbbcdbbadaddcccbdcacadabbcdcaddacadadabbcdddcadddcccbdbccbbaabcaabccdcbccabbdcddbdcbdacbcbdcccabaacacadddcdcdcabdcccacabdaddabbaabbcbccaacccbabbcdbbaabdcbacbdcacbdbacdabcaabdcdacdaaabdabadacddbcbbdbacaacbbdbcdddaccdddabcbadcddbdcaaadccccccbaccbdcbaacdccccaadbbdabccdabbcbbddcacbdccbadbabaccacacdcdcbabbbacadadaacacbbbdbdbbcaadcddddcdaabbadbaddaddabaccccbbbdcbadadababcadaaacbdbdcbbdbdcccbcddccdddacbddcabbaadabaacadabbccbbcccbcbdbcdaccaabccbdadccddbccabbdcabbaddcbdacdcabdcbbdccdcdddcbdcbaaccabbadaabadcadabbadbdbbaccababccabcdbabdaaabcbcccacaadadcddacacdcbdbacbdcbcdbbcdbabbadcbbbadacdcbabbacaaccdbaacbaaddccbdabbaaaccddddabcbdcabaddbaaccbaaaacdaabcdcdcaaaaddabddbbcbabdbcdadbcadbacdabaaccbbbdcbabcbacbacbdabadbcbdbbbadabccbbdacdcccaccccaddabaababadcdcdbabdbdcbbadcabbdcbddddbcaadbcbabbddccaacbaccabcdbdaddacbddcdbcbccabadacdbdccaccadbbadbccdaccbaccaabadbbccbddbcddbaddacddcbdcdbddddabcbbabbddadbddcaaadcaabacddcbdbbdcacbcdbbbdddcadccbdbdbcbcddbbbcbadcacbbabdbbadaadabadadbdbccadabbbbaddddddcbbaacaaccbdcbcbdbdcababbdcbadbbdaccabcbbcbdababadccaddbbacacadaababbbbadacaaadaadbbacdaaaadbbcdccbccdcaccdadbcbbcaacadbdcccdcccdcdddacbbabcbacacdabdcbdcdbbcaaccadcbbddbaabcbaaabdcdadbbaadcaaddbdbbbbdccbbcadbacbabccdccabddcbaabbdadaacdcabcbadbbaaaaaaaabdbcaaabacaddabadbabcddcaccdcbdbcdddcdbdcacdddcdaaabccacacbbddbdddadabbcdbddcbbbacadbcbccbbdcadaabddaaacdccbbdbacdcdbaadaabaacbcdbdbabccadcbcbccbbbadbcdcbccbabdbdccdccddaacaadbaddcdcdabdbabdcdbbbbccbccbdcacabdaddbcdabcaccabccaaccbddaacaacadadcdabcdbdcdcabadcaacbabbbcabcaddcdcababbccbbdcdcdcddccbcbbdacadcaabacadabcacddcbdbcdcccaacadcacacaaacabaabcbcabbbbacaacbdacbcdacccacdbcbddabbababcaaabdbaccbbbdadcbcaaaacbabadcbcbddbbdcaccbadacbcbccbbbdaacaadbccdbddbddaabcccbaccbdbddcadadadccabaccacadcbbcbaddddbbbcbaadcbabbdbdbdaabddabcaddbdbddadacbdbdadcbcddacbbaadaccbadadacadcccbbdbadbcdbadcbbacdacccdabbdadbadbbddbdbdbcaddadccbdddbcdcddadbdbabcdddaccdcacdaacdcbdccacbcbacdadcdababcdbaabadcccabcddcbbbdbcddcddbbbbabcbabdacbbdcbacccdbdccaaababcadadbbbddcdcbccacbbcbccaddadccadcaddcacaaaddcbbbdcadcbdcbcbadbccbbabacaddcaddccacabcbccddcacaccbacbdacadbcdadabbdacdcdcacabacddaabdaacbbccbdaacdaadaacddcbddacdbbcababddbddddbcabbddcabdddcdccdbbcbccdadcbaabbabdcccacddcbdcdaccaacddcadadcccbacdadccbbbdcbdcbaacbacbadabcbbdbadccaddddbbdbadadcdaabddbaaabcdadbdcddbacccccabcbdadbcdcdbabbacadbdcaaabbdddcacadacbdabacbabdbcdaccadbddacaccdddacaddaaccadbdabddcbdbcdbaddddcbcabdbbbdaadacacababdcbabdbadbacccdcbbdcaababccadcabcbbcdaddddcbccccabddadbbcabdccddccabdbbdaadbdbbaccabcbadcbcacadbccbdddcabccacbdbdbdcdcbaacbabbaccccabbbccdbbcddcddcdcbacdaababdcdadddddcdcccabbdcbcaadadccbdcbcaccabaabadaacdddddabdaddababacacdbaabccbcbdadcbbadacaabccbdddbabccadaaacbbcadadacdadabdcbaababcadbaccbaddcacbbbbcbddadbddcdbddcbcaaacabcbdbbcbdabcdbdabccbadbbcbbddcbcbcaadddbddacdcdbcaddcdccacbbbbadbdbadcddacbccdbbadcddcddcaccaaabbbbbabcbaaaabccdccabdbcdcaddaaddccdcbacadadcbbddcadbaddcdbadbdcdbdcccdcbbcaabbcadacacadbbcddcddcabbaababbcaadacaaddbddbabccbababbdbbbcccbaabbaccdcccaaaaaabddaddcdcccdacbdbacbcdcdcabccaacbdbccddbbcacdabdadbcadacbabdddcdcdcdbdbabdbcbcdbbacbcdccddaaadbdcbdccbbcbacdcaababdabadcccbcbbaabcddadcacadcdbcdbbacbbcdcaaaabcddaabaacbadcbbbcdddabdaaacaaccacdababcbbbdbbddccdbdcaabcddaababaabcdcbdaadadadadbbbbddcddabcaabdaadbabbcdadbbbabdadabcccaccdcaabdcccccabaadcdbddbbaabbacddbbccbbaddcdabacabbbdccdbadcaabcbdddbcbaddcbabddddbacabdabbdddcdbbcbcdcdccccbcadacccababdbccddcccdcddacdbbbaabcaaabcaababbabdbdbcdcbbdabbdadbbdbadbbbbaadbabbabdcddccccbdbbcbaddddbcccabadabccabaacbdbbbbbbabaddaadcddcadcdadcadccdcababacdaabaccbcabdcaabdacaabdaaaaaddcaaadbdaabbdbbbdbbadbaccadcbbbadadbbdcaccdaaabbbbaacbcddbdbabbbdbcdcbbbdbacddbdbbdabaacbbbabbcbddddddbbdadddbcdbacdacdbcdbbcdabcdbababcaadddacacbcbbbacacbcbddacbdabaabdbbddababaadddabaccabdaabcaabbdcbcdabcccdacdbbddaccabdccadbadbcacdcdcabcacdadcdcdacbddbaabbbbcdbaaacabbdabbbbdbdcdaaaadcdadbbdbaacbdaddcacccadbcdabddbbbbdcabcdadabbabbdcabcccdbbdacccbabbccdbcbdbaaadbbcddbbabddaadabbbadbdddbbcdcbdcbdbdcdccddcabbdaaabcabcbbadaccdcaddacdbddacdccccdabbddaaabbcdbdbcababcabbbbbbdbdaabddabcdbbcbdbbabbabdadcdcccadbdcbccbdcbcdbdcabdaacaacdaaabbadacbccaaacbbcdbcaacbbdddddacdcbdddcdcccdbbcdddbcbccdbcdabdcaacdbbaabcbddadcaaabdccdbacbbcbdddaabbbdabdcaabaaadadacbbdcddadddcaacacbdcaabcacdcbbbcdaadcadbbdbabbdbaaabcabcccbbddabbccddcccdcccadacddbbbcaddccddcacddddbdbaacacbbdadcadaacdadbbdbbacdcbdacadbcbdbbdbddbbcdbdbadcdcbaccbdaaacbdbdcaaccdbaddadabbaccbdacacdccccbdddbbdbdccbbcaddbbbddccdddabccdcbdabccdaddcdbbbccdbcdcacbcaaaabccacbcddcbddacaabaccbccdcbdaacccdbccdcaadadbdccabbbdabbbbcdaacdbddacadddccbdacccbcdbdcacbdadacdbabdaaadddaaaaccabdcdbdddcacbcddbdaacbcacccdcbabbbacdabdcdadcbbbacddbdbcababcbcddcdbbacdcdbbdbaaccadcbccbcbcaaccbacbabbcccdddaddbccaaccdababddccaddcacacddbaabdbdcbaddbabddcaaddadadcaaddaccbcbdddcadddacdabbdbbbdbbbadbbaccadadccaaaabcccbcbbbacabccaaacacdccabbaaadbacadcbbdaaddbdcbdbaabbaccdbcabaabbaaddcacdbbccbbcdcbddccccaadbcbbcddabdbccabaadccddcdabdcdaccaccbbbbbbbdcdbdbccabbacdadddbacbdccccacbbdbdbabbcbbddbbdaaacbdabcaccdadabbdacccaaacaaddaccccbaddcbdacbdcacabcaccdcdcbcaacbcabbcdadcdbcccdaadbabdbdacdbabbaacbcabcddbcdadaabbaccbcbaccccadbdbaccdccbdbdddbdaadacccccadccbcaaccbddbaaabcccbcacdaaaaccccbdcbdaadacdbbdcdccbcdcbccbabdbbbcabbbaaacabacbdbdabddccddacbdaadaadadacabbcdccaccdddacdbaadccdadddbbcaddbbbacbcddaccaadbbbaabaadddcacccdadaacccaaabccdcdcdbcdcdcacdcaacdcdbbbdcaabadbadadabdbbbabaababacdddadaabaadacbcbcabdabdcdaaaacbdbcaadabcbcdaacddabbcbbcbcbbddacaaacaaabaacdbcdcbbdabbccccbccbadcacbbcbdacadcdbabcacacdbcdbdcdcbddabaaaccaccdcaddddbaabdabbaabaccbbcbcbdbdbabababbbcccddbcadabbabcbbcaadbadbadaaaabdbbddcabbdbbbaaadcbcccaabccaacaaccdaadcaccacddbdaaaabcddadcaccbacdacbdbdbacabadbaaaccccbaddaaaddbaabdcdaadadccbbbdacdcdcaaadcabbdaddaddbacdcdcacdcacdbcbccbcacbdacbcacdaaadcbbbaddcabbcaacbcabcbabddcacbacadacbaaadabbdccdbbaacbdcddbdbadccbcbbdcaaabdbddacdcabaabbdadbbabdaaaacbcbdabacdbbaccdbbaddbddabadadaacadbbbabbcbbabcdcabccbcdcbabbaccdacabcdcbbacbbdadccdcbbbcbaabcabcaccbcdabdacccdcccdddaaccacdabcaddcbabaabbccbadbacbbbaccbacbddcdaaccaddcbdacdccddccdabbbabdddcddabbdaadbbcccdbaacacaadabadaabdbcddccddccdacbbddaadcacdbddcabcccdcdcdbacbacccdddccddccddbaddcdccabcdbacbadaaddbaabadbaacadaacbabcbcaabbccabaddccaaddababadcabccbccdccaddbbbabacdbddacbbdacacddadbcacdaadbbbcacadcddbbabbbbacabacdcbddacbcddacaadbcdcccdbcdccabacaabaadaddbbbdaacbaadabdaccabcabccaabdbadddbacdacbadadacaccddabbaccbadacbabdacadabbdadcabacdacdaacccdadacbdaddcdbabaacaddbcdcbbaaddbcbbbaabbacddabbdaddaadddbcddabdacdbdddaadaabbdccadabcaaababdabbdcdaacbcbddbbcbabcabcbdbdbaddaaaacbdddcaaadbbdbbabdccaacbdaccabddddbbccbcbcbaaacbddaabaddbdcaccbacbcccaadbbcbdbaadababadbdcadababbbbcbabbbccbbcdcddddacabdbcabdbacbdcddcdbbbbdaadbdcdcaabdadcdbbcdcbacbdbcadbaadacdacbdababdbbccaadddabbddcbbbdacbaadbaaaddcbdaddaabbabaacadaadbbccacccbadbcacabcbcbabaadabaccbdbacaaddcaaadbabccabcaddacdbaacadadbdadccbdbccccdadcdbcdadabcabbbdddbababbbbddabcabccdcbbcbddadccccbadaaabcbbdbcdadadbaacaacaddbbdddaccccdbdcabacaaccababddcdbbdcdbcbddbbdacaccaacbaabcbbbadaadbadadbcbccbabadbbaadcddbcddaaabadadbdbbbbdaaabbdacbaacadaacccbacbccccdcddabbbdbcbdcbdddbcdddaaddbcbddaaccaabddcbbbcbdacabacacadccacdccdddacbadccdccacbbdcdbaaadcababdaccdbabdaddbddbdbadababacaaabdbbaabddbbadbdcacdcdaadaaaccccadbdcdaccdccbcdcbaacbcbdcaddabbddaaddacadadcbcdccdbbacabcaacbaaaadabbccbbaadcdbcbdbacccdbcdddbdacabdababacdadbddabddadbabcdaaacabcdcacacbcdacbaaccabacdbcacbdaaacdacaddaaccaaabcdaddabbcccdcacdacaadcbaaaddccbbcadcabbaddbbdcbbcacbcbaddcbcddddddadcababdccabaaaccdcbacaabccaaacbbcaadbcaddaaadddabbbcccbbccbdabbbcdcdbaacacbacbaaabcbcbddaabababdacacdabaacbccbddaacddbdcabcdaddbcdbbbddbbdacbabadddbbcbbcbcbacbbbcadabbabcabbbadadbbbdbbbacabadddacbcadcbaadbdcbddbadbbbcdaaaacbcabcaacccbccbacaacddbdbadcbcdcbaacdbbdbcababcdbdacbabbddaabcbdbccbaabbbdcdbccabcaacdabbaccdabdbbbcacbbbaadcbcdbcbdddaaddcdbaccdaacbbdbaadcbbdaacddadccccbbdbdacadbcacbcadbadaabbdbbcdbdadcbbadaadbcccbcbddcdadacabdbdadaadccbbababacbbdbbcacbdcbcddccdbabddbdadbaababdbdcacbdccacccabbddddabddbacbdbdccdabddddabdaaccbddbbacddbbdbdaaacbbbdcaabccbadbbcbccbabbacbbddbadabdbcdbdccababdabcaaaddababdbcdcadaabccdbbbcdcaccbacacccbbababcacdacbaccbddcaaccccdbcdcbacadcdbcbdcdccaaaddaacaadcdccdadaabcdcdadacbccdcddcdccdcdacaabdabbcddabbcbbccdccbcdbdacacbdaaabaacbacaaaaacbdacabdbdaddcabaacdabacdccacdabccddacbacdcabaacaddadcdcacadabacbaabaacdadbddcabcadabcdddaaadccccccbcdaaadccddddadabadccbccbabcccbdbbdbcdabaadbabcbaabdbccadbccdbcbaadaaadcbaddcbcbdbbacddadbccbccdaacdbdaccacadaddcbabccacdadbadddbacbbbaddbabaddadddbcbadddbacbcbbccddbddcbaccadbbbacddadcccbdadbaddcdcbdbdddcabbbcdccdbabbdddbcdcadaacbcabdbcacbbddbcabbacbbdacdccdabcbdaaaaddaccaaadbacdcbbaacddbdbbabaccbacbcddacddcccdcabdcddcbdaadbdabcbdbbabcaccabababbcadbaacbdcacabddcaabbcdacdadcadbbcdcddbcaddadbbabcdcbccbbcbabbababdabaacdddbadaabcadcbdbccdabdacbacabbaadcbbcdabcabdddbadcdcdcccbbcabbcbbcddbbbadccbdbbcdaadaaadccbbccccbdddbadbacdccacbdbcabbdcddbdcbcbbddcbacadaddbccdacdcddbaabbcdcadccddddbdddbaccdbdddddadbdcdaadaadccaddadcbbaacdcddbddcaddadbddabcddcdcbdacddbaccbcccaaadbcbdccbdbddcabcccddacdcbcdaaaadbddbabcccbcbadbbdbbccdcadabddccabcdddaaaccacadcddbbdbcaacacddcdbabccddbaadbbcaadcbaacbcbddabcadcdccaacbadddbcdbcbccddbcdcdabcccddacdbcabcddbcaacdbaabacbcbcdcdbcbcbaaabdddddbccaadbccabcaadaabcbcadbbbdcadbbaacbadbbbdbbdbbadbccddcabbcdadabdbcbdcbbcccccbabadacbdbcbcdcbbbadcdcccacbbabddaaacdaabcbcbaacbcaccbdabcddcaaddcaacbbdadcbbbdbcdddacdbabadbabcbdccacacdabbbadbacbadbbaccaaaadbacdcadcbddacabdbcbcbdabddacadbaddbaadbdcddbabaaccbdbabdbbcadaabaaabaacdccbcdacaddaddbaaddcdcbbcaccccabdcccdddbbcacbcbabdcccdcbcadccccbddcddcbcbcadaddddbddbcdcaadabccbaadacbadbbddadcadcdbbddbacabcccdaabbbcabdbabadadabadbbaddadabcdccdaadadbcabbabaadaaddbabdccaccbbaddcdddbdbccccaaddcddaddbdbbddcdcbbabaaaadbcdbdbdacaabdcbdbddadbadbcdbabdcdccdadddcaccbbdbdaaabbcddbabcaacadbcababcabcdbacacabcbddaaadcbcbacbdbddddccddcbdcbdbccacdcccdabaaddcbbdbadbddccdadcacacaacaccddbccdaadbcaaabcddaabdcdacbabaabcbbcadddabccadcabbcacadbabbbddbbbbcbcabcbaccdbccbacddbcaacdaaadcddbbadddacabdaacacadbcadaccdccbbbbcdacaacadbcdacccddbdbbbdcbbdcbbcbbaaddbdbbacaacbddabdbddbbcddacaccdddaadcabcabadccdbdcdabadcdcaacbadbccacbddbaadacbcadccacabcacdccbaaccbaddcbcbdadbccdbdababdbabbdacbbacabaadcaabacbbddadadbbcdcbadacddcdaabaaccbacdabacbabdbcbdadcbabdddabbcbcacdbacdbccddbbbbbbdaacbabbaddddaaaaadcbbdcbcdcaaddcabcabcccbcccaabacdccbbbbbbbacccbcdaadbccdcaacbadccaabbaddabddcddcacdbabbdacaacabcddcbaabbaaacdbaabdcadcccaacbccadaaddbbbcbbcacdbccdbadabdabdcaaacabbaabcddcbbcbbddbddbacbdcbccbbcadadddccbdbccdadbccbddaabccbdbcbbadbadcbbdccacbcbdbabcdaaaaaababcdbcbcadbdcdaaccdadbcbcbcccccabccdbcacaaddabdbcbccabaacdaaccbacdbbacaddbbbaccdccdcddbcaabbcdcbbaccbadbdbcdabaacadddbcaabdadbccbbcadddcdacaaabaccbacdcbcdcdcabdcdacdaccdccbaabbadcaddbcdaaccddccdacdabbcdaccdccbaaaabddcccadcbbcacaabadadbcbbbdccddddddabbcbdaccddcacbdbcdbaacccbdddaccbabcddaacbddcbbdadadcdaabdacccdaacbcbbbbbccdbaabdcaccaccbcaacbdbcdcbacccdbccacbacdaacabbcdacdabccdaadbccbddcbcaaccbabcadbcbddbaddcadcaabdaccbaabcaccdacdbcccabbdcbbcdbcadaccacbcbaccdcdddbbdcbccabadccacbdbabcbdbaddaaadbbaadccdcaaaddabbbabbddadccaaadbcdbadbccacdbdcddbcccacaacbacbdaddbddccddabacacdccbbdbbcaaccdddbdaddddaddcadaccdccacdaadcddbaaaccdcbcbbacdcacadaabcbdadbcabddccbddcbcababbcbaacbcaaccbcdbbacaaddbccacbbddcccdbbbdcaadaadcacbccbaccadaadcaccbcabaacadcaadabcccbabdcccdbcdbcddddbbdccbcdccdcbdcdaddbddcddaaaccbdbadbbaccadbabdabbcdacbacabdbcdccbbdbddbddcdaaaabccabbcdbbdddbaaadcbbbbcaacdaabbdcbababdcccdaddaacdcbadcbbcbdddbcccbddddacaadbbbcadbdbdbdbdcacacaaacdadacabdbcabaaabbcdccadccbaddbbbdccccbcdcaddddccdadbdddcabccdddacbbcddbddbdcdddcadbdbcbacccbbcbbcabcdaaacdadbbdbacddcbadbddbbccdbbcaabbccbadcbddabaaadadcadddbcacbbcbdddbaddcaacbccaddaadbdabaccbcaabcdaccacdcdbcaaccbbaabbacbaccbbbabcbbcbcdacbabacdadccabbaccdaddaaccacbdacdadbbbcbbaddadaaccbbcbbcdddabcdabddddccdbcacdbacbbcdbcddcbddcaaddddccbbadccaddacaaadcdcbabbbccdddcdabdcbbdacbacadcdadacbbabdbccaababbaccdadbbbaadaaaaaaaaaccdaddadaabddcdadabcdbddcdcadcdbbcababdcccccdbdbbacadcbdabadbbacadbbdaaacbbbacbcdaddaccccaaabdacabdaabdadaccbbccccadbcacddabbddbabbdaabcccdbbbacadcaccbdcaadadcbccadcdbccbdaddbcbdbadbbadbacdaddbcddabbcddddabcdbbbcdbbcdcccbbbacaababccbbdcabcbababaacadaaacbbdbbcdcacbacbaabdaaabaacdabbbdbabbcbbadbddbbdbcaadadcbbaccdcdcbbaabdcdbabbdacdadbbcccbcdadddabbbcdbbacddbddabaccbdadccdcacaaaaabcbabbcddcaddaacbdbbabbddaabddaaacddcaccadcabcbaaddaadaadacdddcababbdcdbcdabbcdaabbdddadabbaaddbbacbbbbabbadadaccadbcbadcadbbbcbbabcacbacbcaaadbcbabccdbbacabbcdcdcbcabdcdcddbccbbcbabbbbdacbaadbacbcbbacacaadaccdacacdcbcaccadbacbdaccddcaabbddbcdacbabbddcaacddbacccdbaddbdddcccabbdbcdbddbbabcccddacadacacccadcadcbabbccbdbacacabccacacbccdcbccaacddcabaccbaabadaabadcdabcbbcbbacbaddadabcacaadababbdcaadddcbcaaabbacdbdbbbcaccabdcacadccbabcbaccaccacdacdbddaacaaccbabdaacbddaaabcbbddccbcacdaababcacddacccaddcccacccbcbaacadacbabccdaabcbcaabbbbabbdcccbcdbdadabccccddbbcabdccdbabccbdcdaaccbddabacdbdddccaadddadbccbacacbdbddcabbbccadabcdaacadbcbbbdbdccccabbcdbadbbabdbcaadadbdaabdadcbbcdbdcbccdbcbbbadbbbcccccbdccbcbdbabaddcabdccdbabdcddbadcaaabcddcdbbbcaddccdcbbcaccbaabccdddabbbdbbabddadbdcdbdaabbcdbacccaaacbdabcaadabccbabdbadcaabbdadcbbccababaaabcbdacdbadcccadcacbcbdcdcaaaddcadbcddcabacdacdbdcabbcbbacaacbddccbbdbbadcdababddadccbbdbdddadcbbadaddadaacccaaddaacbcbccadaddacbadbaacbaaaabdaaabbddddaaabcddaacccbcbaadcdaadbddcccbcddbccdbddcdbcccabcccaccbabcbddcbbadccdddbbddabdbdbdcdcaadbabcdcbbcccdddbbdaabdccbdccdddcacbdaddaddddccdbdaaabacccbabaaabbabcbcdcaabbcaddbabaaaabcadcccacdcadbabcabbaacbbadbdbbdcbcbddadccacaccabadadccdccdbdaddddbcadacdaabacdbbdcbcbdaaccbdabadbbdacbbddddbbccaacdccbccabaddaabcbdadbcacaddcbdabacdccadbcbddddbbcddcabcadbbccbcabdbccdcbbdcccdadaddcaccccbacdcbbcbaacadcbacddbdaabcabaccccbddbacbbdbabdbcbbdabdcabdbcadbcaddcdcbaadaacaacdacabcdcbdcbabaabdbcbaaccbdbddbcaacbcbdaabaccabdbdabacddacdabcdbddcdcbabcaaddbbababdcbaddcaadadcaccaccbcaccbcddcdcdaabbadaabaacdcbbbadbbcddaccacdbbcbcddcaddbadbdcbbcaddaaaacaddacbddccaabcbcccccaacadbdbbbcbccdcbacddabbaabdcbddbcdbbbccbbddbdcdabdccabccbdccacaadadddbdcdccbbaddcdcccabdcdcddbadababaddcccdcbbdddcbacccadacdabcbdcbabbccdaabbdbabdbdbbddacbcaadbacbcdabdcababdabddbdcdaadabdcbccddaababccabadaabdabcaadadcaadadbccbddaaadadccaccdcababdbdcdcddbcdbadcacabadcdcdbdcbbacbacbbcabaaadabbccbadadacbaddaacddbdcababddccaccddbdaccdaacddbadbdcbdccddbaacacabbcacbdcabcdbabdaadbccdcadabbbcaccacbcbdbacbdbcbabcbdbcbcdbcdaccbabdaacbdabcbbcbccacabdacdadcdcadccaaabdaaddcbabcbabadadaaaaabdbaccdabdcdbacdcdaacdabdbbbbbbdcdbacabddacdcaacccabddcdacacbadaadccdadbcadbdbadcdbbbbbbdadabccdacbbbccaccdbddbbaccaccaccbcaaacbdadcaddacccccbbcdddabcbcdcdcbccabbdbadbcccccdacdbcdcccccadbababcaabdcdbadddcdbcdaababddbcddacdbabcbcaacbdcabcccbccdbbbabadddbbcddcdacdadadbdcacbbdcdabcbbbddbcdcbcabbacccbabdacbaacbbacdaacdaaabcdbccadabcadccdbadcabbadcabbcaaadbadcdcbbabbadcadaabaadadaaddddadcccabbadbddcddcabcbbdcdabccbbbcabddcaadaccdbdbdacaddcdbdaaaadcaabccbbccdacbdbbdbcddadcdddbbababcaadcaaaacaacdbaabdcdcccacbcbcaabcadbadbcbacdccadacaaddbdccabbdcbadbcdabbbabcdccaabcccdddadbabbabdcbabdbddaaaadcadcbaadadabcabccdbbdbaadaadbddcddcabddababdccbcdaabddbcdccabacbaacddabbacbcbcaaaaaddadabbdacdaadadaadaddbcbcbdbcdddadcdadcbcdcdcaddadcaadcbcacccdcbbdcaadddddabaaabaaabccaddabcddacbbcddbcaacccbabddcaddaadddddbdacadaaabaccdcaabacdabcaaaccccddcbdacdbcdbbbcdbbcdadcadccdadaadbabddcccbccbbdccbddbabbdcdabddddadadbaddabbbdbddacbacdadadabbbccbcbadbbcdbbdacbacbcaabcddacaabacbddbcdabbbdcbadabaadcbddaddcacdbbcddbaaabddcabbacdbdcdbbdcdccadbadddddcaacbdbcbbaacbdcdcdaccdaaccacabcaaaaacbaddadbbaabdacdbddcacdcbaaabacbcacdbdbdcabbacaacbbbaddccccdaccdcbcacdcadadbcbadaaacdbdacccacbcddcddabbcccdbdcccdbbbbaacdcadaaaacccaaaabddbbddabccbacadcddabcbddddbcccdbbdcbcaddabddbacacabbbbbbdbacccababbdadddaccadddaadababaadabbcbaabbbdacaacbdccaaddbbaddbabdbcbababcdcbbbacbbbccdcdcccdaacbadaddbdcdaabadbcacabbbcccbcaadbdacddcabadadacaccdddcdcbbddaacadadbababbddbbcdbddabdbcbcbcbbbdbccacbbdcabaddcbcdaddadaadabbdbbddadccccaddcbdddcacadacdbcbdcdabaaaadaacbdcabcabadcddbddbbaaaadccbccccddaabbadcbcbdacdcbdbbbcbcadbacadbaadbddcddadbabbbacabbaadcdcababcdabdcabddcdddcdadcaacaabcdbbadcadddcabbddbdcdaccdbdbddcabdbdbccdabcbacbadcccbaddaacdaaabbdbcbcaaaabaddcabbdadacbdbabbbaccddabccdabcaadbcbbddcdbdccdaaaaacddcbbdaddbbcdadddbabadbabdabccbcdacbababbbdbadddbbbcbddcaabbddbbbaaccdddddddabadcbbddaccbbdabacdbbbccbacbdbdcccdcbdccbdabadbcbccddaabaacabdadcbcdaabbbbdadabdccacbddccacdcabbdcbdbcaacabdddbbbbabccddcbbabaabdcbbbbacaabdcdbacddacadabdbccdcccadcacdbddacdcadbbaadbcdcaabdcaaacdbbdcddbbcddabcaacdbccdabccccdaababbddadccbabbbacacbdbdaabddacbbcaadaccbddacdcacadbbdcdddabccdcacacbbbbbdbbbccabaddcbcdcaccbbacbdbdccbcdaadbbabcdaadadccdcdcbaabcacdadbcadddaacbcacbadbdbaccacbcdabcbadaddaaabccadbdabbdaaddbabcbabadcadddaccaabbbbbacbbaabdbbbcaaadddacdacdcbcbbbdbccbaccacbdaabdaddccacaabccbbdbcabababbabdabdbbbbaddadbcdccbdacbdbccadbbddddaaddadccbaaddccababdacbcbdddbcaaacbccdaabcadddacbacbaababadddcbaddbbaddaaccbddcdcbddcdbbacaadbccbbddadabcdbacccbdcbdcaacacdcbabdddadacbbccbcaabcdbdbccdabcbddccacdbbbddbbbbcaabdadbcdaccaabaadbdcbcbacdbdcacbbabbdabbdddabbddcbdbcdcccaccaddaaadbcbcacbacadccccbcbbdaddbdbbbcdcdabbdcdaacaaabadcaccacbaabadaddccdacdbddbbbadaabdacdaaabbcbaadabdcbbbbcccdcccacbdcbdbbddcdcccacddcacdcddcabcdadcdccdbccddacdcaddbaabcbcdadbcaacdcdbbdbcabdaadccacbdbbadaddcdcacddbabacdbbddbaadabddbdabaacccbbdbcdadcbddabccbaacacadbdacaabcbcdbbbdddacbbbbaacccbccabcdadbdddbbadbdabdcadacabdccbaaaaacccdddbaadaabadcabddadbdbddbdcaaaadbaabdcaaababdadbcdbbcdadbcadacbdbddddbbccccccbbbcccddbcabacabcdccaabdbdbbdbdbddbdaacacccaacccbcdaaaccbdcacdbacabaacccaacabaabccacccbccacddabacaabacdbccaddcdddaabcacdcbbddabadbcdaaabdaacccdadaaccdbcadbccadababdacdcbaadbcbacaaababcccdcabdbaaabcabaddacacabbdbdbdaaacbbcbaccddddccdbacaaacdabcabbadaaccaaabadcbddcccadbddacadddbaacbdcbdacccbbacdbcddadadcdcbbacabbcdcbaaddcacbadadbccadddcddcbaaddcabcaccbdadbcabbbbdcccaabcdcbcaddadacdacbcaacabacbdabcabbaadbddbcbdcbacbaddadbbadadbbbbddbabcdcdbabcbccbddcdbbaaadadaacaabdacdadddbcddccdddbbbdcaaccabdcaddcaabdcdccadbdbbdbdcbbcaabcdacbdbccabaddcababdacadadaddcccbbddcabbbbacadcbabdcaddbbdcadbaddabdacbccadddcddddddbcbaccdadcadadddbcddbdcacdcbbdbcaaacbadadcbcbcddaaabddccadacbabcbdabacccaddcccabcdcbaabacbbadbaadaacadbddaddaaabbcdcbbcbbbbaccdcdbcbcababacdbbabdbccabcdbdacaccdaadadacabbddccadccdbababbcbcbcbcdcbccbbdcbcbccabcccabbcddbaababcabbbcdcabcacdddcabcdcddbdcadbbadacbddcdbbdaaddbdcbcdadadcdacdadbccbbdddaaaabacdbdbadbbdadaabbbcadcdadacdababbcbdcaacddbbbcdcabbbababacbbdcadcabbdaadaadbcdbadbbcdabddddccbcbdccdddddddcbbbbdaadcabadbccacbdcabddaaacacaaaaacababdacbbddaccdcaaacbbddcdabcaccacdbdcdadcdbabbacbbaabbddadbddadcacbcaaddbbcaaabddbdaaabdacbdbabdcbdabbcbdbabdbcbabbdaadccacaddccabdadcaababdacdcddbabdcbdddbcdcddbbcadcbaadabaddbdbacbbaacabbccaddadddcabdaabcadbbcdbbdcacdbdcbcbdbdaaddaabcaaabaadbbbdbdbbacbcacbdaabcddbdaacacccbbaacaaddaadadcddcbccdbccdcacccdbabcacdcccaddabaaadcabdadbcdbdbbabbcdaabbbcbbbcdabaaadbacaaddddbbbbcdabbaaacbdbaccbbcaabbcabdabbabadadaddaaabcbcdbdadcaddcbdbdaaccbdcbadcbdcbaabadaddbacabdaabababbaaaaaaabbddbbaacacabddccdabbccdcddbaadddcdddcbcadddacbadadcbacccdacabbcdddbaacacadbabbdbacbdadcacababcbacacccbdbabaaacbadddaaaaababccddabaabbbabbdacbdcdcbdaadbabcbcdcacdabdaaaabddddcbcddcaaccaaccddddabbabdbabdccacdddbbcdadbabcbcbbbdbddccbcbdbbadbdaacddaabdcdadddadbbbbbabdcbaddabddabbbbbcccccbddddcccbdddcbcaddbdacaacccacbaabbcdacadddcddbcbbcbaacacdaabaabcacabcbbcadbdbbccbdbdcacbcadbabbbbabbdbcccbdaacbbacdccbdabdaabbabdddddddccabccdbadbcbbaaabdaddbdcbccadcacbdbccdcdacaddbdbacacbbdabdcdcaaddabaccbadddaacadbdcacbcacbabcbaccbcaacbcddaaabdcacacbccdaccbadabdcbdddccbdcccbcdbaabcccaabbabcabdcaabcbacdbdaaddabaabcdddbcdabdcbdccbadbbbcadcbdddbdacabbdaccadacbbadbbaaaddbadcabbababcabccbadbabbcadaddddbbbcadaadccadbbdcbabbbadbdbdbcdcdcdaacaddcabbcdadcacaacdcdacdbbcabcbdaaccbdbababcdbdacdabcbcdbaaabdadcdadcddbdccbaabdbdcacabcbcbbcdbddbabbaaacbddbbccacdabbddddbbdbcdbaacddddcabaaaabadcabbccadbadbacddbcbbddbcbcabdbbacddcabcbaabbcdcacadcaccacbadbaccaaaaaaadbbbbbaacabdbdadddccbcddaacaccbbcdbbdaccdacaccaddddaaacbccccaddcbcdaaaacdcccbabdbcaaccaabbcbbdabdaaaaaadddcbabccdbbaddcdaddcabaacbdbdadcbcccdccbbccdaadbdababbbcdddcbbababaababcabcaddcabacbddcacabacccdbbbbadbcaacdacdcdaccaadcadcddaacabcdcbccaccacacadacccbbbaabdcbdcdabcdddbcdccbacbacdcbbbaaadddcdadaaadabaabbdbdcccdadcabbcbaddcaaadbcacbadbcdadbaccddddccabcaacbdabdacdcbdccacddbdcdbdabdbabcddcdcdddcdadcaaaadcbbbcddbbbccbdaddabdadbbcbbdccdacbaadaccaacacbbcbbdadcccabbdcbdbdddcaddcacbbbaacdbadbbcbbacdbcbdcbabbaadbcccddadbdcabcaccaadcadcddabcdaacbaaaaacabababcaddababbccbccbcdbddbbbaabaacdbcbbbbacbcddcbdddbbdbcdddabadaacbacadabacabadcbcbdadacbdbbbcaaacadbbdaabbacdbaabbabcacaaddaadadbdbbabcddccbaabadbdcacdbabccbcaccbaabbabacdadcbcbbcddbbbccdacbaddbdacbdbbabccddbabbccaabacccbacbddadbbabadbdbbbcbdddcabadcbbabbdcdcbcdccccabcdacddabbcadbacadabacacabcbaccaacdababacdbadcbcddbacbbcaaabbdadcdddadababcdbcddadcabdbacdaacccdcadacdddbcadacaddbdcccbddaddddbbbabdabbdcdcbcacdaccabbddbaccccaadabbbbcabdcbcdbdbdaacccbbabadccabbcaaddbbacccddccbabadccdacccabdbadbdddbabccacacabddbdddacbadbbccccddacbdbdcccaacbdabadbbcadcbbcdbbdaddcccddabbcdcaadcdabcabbaabdcadbcddcbdbadbdcdcbccadbdaaabacadbdbbadaccdacccadcacbaabddaaaacbddbbdddacbdbcacdddacdbacbdbccdbaddaacddcdbabdcaccaabbbdcbcbdabccadcdcdbadddbcccaaadbaacacabbddccadbdcacbcdacbdabbccdadcbbbdbccaccbacdaccadbcdddbacdddadbaacaddcccccbbdacbdaabcccaaaabaabccbdcbcddbaaadabdcccbdaabbbbcacdabbcbdacdbccacacaadbcabcdbdbacaccabbdcccbdbdaadccbadbcdddacdbccbabbdaddbbbabbadbcbccdadbccbbbaadccbabacddcbcbcbddadbadbacdacbabacdbddaaabcabdaccdbbddcbbdacbbdabcdaaaaccbacbacadbdbbcbdaabbccbaabacdccbaaabdadabcaccaaadbabadcacbbdccbcbbcccbcaabccccaadacdcdadcdccddbbbcdbaadcbadacddccacdbcddaaaccddbccdbdcbbbdacbbacbccaaabdddcadbacaacadaaddcdcbacdabbadbddadddacccacbccccabcccdbadaacddddbccacadadbcbaccbccbbcccacabdcadcdbdbbcabdccdadbcdadbdbbcdabbaaacaddaacccadbaadcbcaccbddbaaacbcdbadbaccabcccdabdbabcaddddcbcabdbbcdddddbabadabdcdbabcdacaccbcddabcdbcddaaadaaadbacdbbaacdcdccdcaadaacbcaaddaddcbbcabccabdbbbcacdbbaddcbcbaaddbcdbddccbacdabacacadddccbbaddbdcdabddadbcdacabbdccbadacadbbdbaaacadaddabaaacadbdcdcabbbaaacccdcabacaaaccaabddcabaadbabdcdadbaaaaadcdabdbaadccbadcacbbcbcacaadcaaadccdbdccaaddaacbcdcbddbbaabdddcccdabddbbddaadbadbddcbcdccbdacdbadacabdabddacaadcdabccbcdcacaadbbdcbdcadcccadbadbbcacdddcbcddccaadcaaaacdbdbddddddddcbcdccdbccbbaadbbacdcdbaaadccbdaadaadcbbacbbbabddcadabbcbdbbbcddbabbadcddbbbbbbbbacbcbacaacbcdbdddddbabdabccdcbbabbbcbdcabcddbddcabaaadacdcdaaabbaddadbddababbaacdadbdaabbbadbababbbbabaddadbbcbbbadaacccdbcddaddadbbabcaccbbbdbcbcbcaabdcbcdabcacbdaaabdcddbcddadbbbbaadbcacdcbccbdaaddaadbacccabddaaaccabcacbddcabbbcdccabadcbacdadabdaddbacadbccddabdbbaacbbdbcccdaadcadcddcdcbccdbcbdddbcdbaadcbbbbcdcdbdbdacdadcdddcabcbccaadadbacdabdcdcbaccdbcbcdabcddddcdcbbacaabbcbbaadabacacccacccbbcbddbabcadbcacdcdacdbbcbbddccdbadbababbacdbdccdaddabacaacdcddccdbbbbddacbddcacdadabbaadadacdcacddcaadbcacddabcadcdbbbccbbabddaadbccabdcadcdcbdccbadcaaaadbabbaadcbacbbaccdaacdbcabdbadbbdddbdcaaabcbcaaccddcacddadcdccdadacbabcaaadacabdcaddccbbbccadddadbacaccdbabbababbaadbcadbbccbcdcdccabdabadddbdcdacbbbbbbbadbbddbdbbbcabcadbdbcbdbcbdcbdddccbacbabcaaccdbaddbcacdabdcaabcdabcabbadcbdbdaccdcaaddcaacadcbacaadbacdcabdbacababadbbabbcdcdabdcddbaaddabaaabacbdbaddcbaaacdbbdccaabcdccaaccabdacdddcbbabadaccddcacdcbcdbccdbccadaaadccaabcdbcaccaaaabacadbcdcbaccaaddccaabccbcbbcdbcaadccdabbdbcaccababdacdbddbbbbadbbbcacddbccdcbdacaacbcbddaacdabccbdbdacccacdccdcbcccccddadbadcbdddcdabbadbbacbadabaabdbacbdbcabddbddbdaabbbcdbdabdaadabbcaccadcbccdbcacaacdabaadbbccccbbcbcabaabcbbdbaacdddddaccaacaccaadcbbaabbbbdcdcbcaddbbcdadbdbacbbcccbabcbabacccdcbdbbacdcacabaccccddccaddbcaabadbbbdbbbdabbcbadacbadacdbbadadbbaaacbdcdaabcbdbcbdbdbbadcdddcdbdbddacbacbaaabdcbccccaadabcaadbdcdbdccbccbddbcdddaabdbaadddabbbadcdcbcdcbabaacbbaaaaacbdbbacadbdddadaccadaadbdcaaddbacaabdabccdaddddbbdbcbdcbcdcbcadadadadbdacbabdcadbbabdcbccbbcbbabdcbabbcabacdcddbcdccadbdcaccacaddbcccbacabcddacbbaaccccbbadcdcbcadcdbbacaccbdaacabbcababddbadbaddbacadcdbbdaccbdadaccbdcbdadcacdbdbbababaddcdbbdbcadacabbbbacacbdaccabdcdaccdbdacdcbadadadbdacabcbdbbdadabbabbdbadbababacbccbbccbadddadddbabbdbbccabdbdcabcabcbdbaacdcbabcbaadacbacabaccbdcabcdabadcbacaaaadbddcbbcadbcaddbbdacddbddcbdaaddcacbcaacbdababadcddcbaadabddbabaacacbabdddbbcaacccacdcadcdddadddcaaddabcdacddbbaaccacbbaaacdbdcbaccbbbdbdbcbddaadccbcabddccdabcdacaadbbddccdaccbdbddcacabadbbbcaabcdaaabaaaaaaccdaabcdbdabdacadccabccccaccbdccdbbaccdacdbbadbcbbbaabccbdbccacdbdbcbabbbcaabcbcacababddbdcddaabccaccccdbabaddbddccaaaabbbbcccacccbcadbdadaababbbdbabaabdadadbccdbcbbdcbcddaacadabccaabcbcdcdcccabdcddcdaadbbcbacbabaacbdcacbaddadabccadacacdcdbcacaaacbddbacdacaabcaccaddbbcbaddaaaddacababcdbbcddabcdbcaadbbdadabbcddbdbbcdddbbcbcddcdbdbdadacbdaacdbbbcabababccdbcccbdcbdaccdbccdbdadcaadbddbdcbdacdadacabaccaabddbbcacdbdddddccacbddbccbbcaacbacabacccbbbaacdbacababcbcbddbccdcdbbdccbbabaaaadabdccacbcbccacdcdbdccbbcbdacdbbadcbdacbadbcabdcadcacababbddcbbaaabcbcadaacbbcabbdcabbcaddbababdbdbabdcaadcddbcccadbadadcccacddbccabcaadbaacbcddbdbaaaacaacdabadbdbbcaaabdbbbcaacbaddcaaabaccaacdbdcbcdcddacadcbcacabbbabddcccacaadcaddbbacbcbdcbdccbbdccddadcabbaaabbabddacadaadddccbcbbadbdcbaaadcbcdddddaadaadbabcbdacbbcabbcaacbdabddcaddddbadbaabbbddcddaaabccbcabadbddbcabbdcddbbabddbccdaabcbcacbbbadcdcacddaababbcabcadbbabccbacddbdbdddcdbbcacdadccabdbcdacabcbadabcdcbcbcaaccddcaacccadbccbaaddadaacdbdcddbacdcaaacdbbdbdacbbbdbdaadbdcacacabcbdcbbbdadbddaccdacbcaccbcbcabccdbcbdcadbabcddbbdbcbbabbadaabaaacbbcdcbaabcabdccdaaabaacabcaaaabdddaacdbaadbdbcaddbccbbdcbdaddbcbcdbadabbbccbcaddddbccdcaccdcdaccddbdacaabcdbcdbdccaacacadabbcbcabcacbdabacddbcaacddbaababdbacdcbaccdccdaacddadddbbdbcacabadcaaacdacbabbadabacababccdadbccaccbccddaddaabcbcdccdccbabdaaaaadbcdcdcacacbadaabdbdadcaabcbcccddbbacbaaddccdcaacdabdaabbaddaabdacdddbadadbcaaaaadbaaabdcaddacabacbacdbaaaacbcaabccacaabdccccbbbcadbbddbaacdaaccbdbccdabbbbdaabadcdaadbcbaabcccbaadaadbadbaacccacadbadcacacbcdaadddbbaabcbdddcaaddcddbabdcbbcdcaaadbbdcbcdaddbaabccaabcdcdbbccbcdabbabdccaddbcccdabbcbbcbbcbcadddbcbdacdcaaaabaacbccdccbcadbaaabbccccbcabbabadacdcbdcbdaadcdbddacbbbdbadadbaccbbccdaddaadaacbaaabbdabcbcbabbcdbabdcaaaacbcaadadcdbabdcddbcacbbdadcddaddbcaccbadbcbbbbdddcabcddadbbddbcababdcbaaababacbddaacdccbaccccdaccaadcaadbabbddacdccacddabadbddcdbccdabadadbdaddacdccbcdbdcdbacdaccabbadbdadbdaabcaabbdabacabbaddaabdacddbabaacddcdcbdaddbcdcdbbacbaabdbbbaaddbccdaababdbbaababaccdcdddbaabdbbdddadbdbcabbabadcaadaccaccddabbbbbabdbdaddadbbbcacdbccbcacadcccbdcabddbcbabbcccdbbdcbbaaadcbbbbdbcbdcdbdacddaccaabbddcabaadbdaccbacbaabcbabbcdaaacdbbbbadadcccbadbcaddbaabbbcdcbaccbbcaabdcaacbaacacdbabcbaadaacaacaaccdbbbacacbbdbdcacbddcbdcdbcacdbdaadcdbacbacabcdbdccdaaaddddccdbbaccddbbaccddadacdcababbddcbabdcbcadbacdbaadbbaddcddadcbbbbdddcdbadcaabdbccabcaccdbdaaabaabcddaaabccdcaddabdacdbdbccabaabbbbcbdbdcdbadaadbdcdcdbbabbddadaacadcbcbcdbccdcdcdbdbdcdddbabcdbabaddbacbdcababacccbbbdadadacbbddadbddddddbdadccadcadadccaaccdaddcccdbdaaabbddadabdbacaaabddaaaccabaacdbccddbccddbbbadadaabcabcdbdddbacacdbbbdbcccdbadbbbbacbddabaacdaabcdabadabacdaaddbdccbcbbdcdbbbbddadccdaccaaccbbcbcbaacdabadabcdccbdbcdadbbbdbdbacbbbacdbacdbccbcacbdcdabbbdbdcabaabaccbabcacddbbaacacccbbcddabdcaaacaccdbdcdcacbaddcacdccbbbbacdadddcadbbabaddaababccbcdaabadddbdadbbcdcadadccccdccbacbdbadadbbadcddbadcbcddaddadcddccabaddccabadadaacacbcbbabcabcbbdacbacdaadbadbddbbababcaccadacadbccdcacadccbbddabdccaababbbaccdaadbdacacaddccdbabddccdcaabcaacacbdcccacdddaddbbacabdcddbbccdbbddcbbbabccdacdaccddadbddaabcacaddcccbaddccbccbacbbdaacadddcccbaacbcbadbaccdbaacaadcacadbcbbcacbbaaacbdbaabdcabdddbbbbdabadbccadaadbcbdbdabdcbaacadbddccdabddabccbaddaaccbddddbbcadabaccddddbabbbccaccddcacabbbddaabbdadcabccbdbdacadabbadddbcaccaacaccccbbddbbdadddddcbabbaabccbcaabcbaaabddcbaacabbcdcccbabcacaaaaccccbabdbaabababddabbcddbbcdaadcacccbcacdcaabddaabbcddbddbcdaaddbaacbcbdcccacadcacbbabaccaccbcbdcadbadcccabdcaccdbabddcdbbadcadddaaacdcadcccaaccdbbdcbddbbdccaccbabcaddcbdabadbcdcadbcdbabdbdcddabbabcccadaabcdbcbbbaaddbdbcccadcacbddbaaddccdbdabcaaddccdbccbadbadbdacaccaaaabaabcbdaadccbacbbacaddadccdbbcbbabccbddddcdcacadccbcbacbbadccbdbbbcdcdaabbdacabdbabbabbdaabddbbcbcdddcccacdbadcdbcbdaabcbbdbdabbdcddbaccbdadcdaaddaabbacbabcaddacbccaababcbcbdcadccabddbdaacdabcbbcbcbdacdbacbcdcadabdadbddbbbcdccdabdcdadbbbbcdcccbddadcbacbdabadbdddcacbbdcdcdbdcbbdccabcddcaabbcaacdbaacddddbbacbcaabaaccaabcbdccaaddbaacdbccacbbadbacacaadbdccdddcbbbdaddaccaccdcdddaddbdddbccdaaacccabcccacdbbadbcbccadbdbdbcbabadbcacadcdadcdbbadabdaacdbdbaddacacadacabacbcbccdbccbbccdadacbdbabcdadddcccbacbdbddcbbdddbbadabcacabcccacacddabbcdadaccdaacccaccabadadbdbccbcaddcabbdbcbabccadbabdccadadccabbdaccbdbcbcbbbcbabcdbadcccacacdbcacabbcabcaabaabcadccaaccbdaddaabdaabdbcbdcdbaadabbcbcddbcaddbdcacdbcbdbbbcdccbacadcbabbbaacacacdcdcaddabbadccaadbccbddaaaadcdaaabaabddccbbddbabacbcacabccacbadcaadadaadacbbbccbcddaccdccccbacccbabdccadabcccaaccdadbdbbabcbdbcabbdbabaccdbcdbbbcdbcbadacadbbdbdaccbadcadccccbccbddbbcadddadcadbdcccbaaacbbdbabcadbbcabdcbcdbabcdcbadcddadccaaaddacbcccdbcabdabbcacdabbcddcbcabadcdddacdbcdbbdbbadacddabaaccadbddddcbccbaaacbadccacdcaabdcadcdddaabbabdbdcddbbadccddaddccadaccbbbdbadaddccaddccacacddbbdbadcdcbbaacbbccaaabddcaaadaadbabacddcdabacaacacabcccacadacdcbacdaddcbcbcacadacaccaccdcdcbbccaccbccdcbdbbdabdaacddcabdacddaaaaabdcdabaabdacbcbdacccbbdacabdaabbbdbcaabcacaaacabdbdabdcabdbcdcadadbacaccbbaccbaccdddccbdcdbddabcaabcadbdabadcabccabdccbbadcbcaddcadbcdbadadccadbcadcddbcbabdcddcdabccddcdccccadcdbbddcdadddcadcdadbaddacdabdcbdcbccdddcabbadcabacccdaabcbaddbcadbdaacbdadaabcbaddbcdcdaadaacbbdbbdcbbdacccccaaadcdaacdbdccadabcbcbdccccaaadaaabbcaccbbbcbbacbcbaddbabcbdcbbbcaccaadbbbbdcaaddddabdbcddddcdbcbcdcbadcbadaaccddbbccbcbaccbbbccbacaacccdcbbbcbbabdaccbbcdbbcababdabaadddbbadacbbaabbabbbabadadcdadcadcdabcbacdbadcacbadbcccbbdbcabcccdacaccdddadcbbbccbddadbcacabcddbbcddbcdcabcbdcbdbddbdcbccabcbdacbcbcbacaccdaddacccbadbdcdabaaabdaaaddabcdaccaddbdddccbbaadcadbcbabdcbdbddcdadacdbcbbbbbbcbdaaacaccdabdcbbabbbcbbaaabaddcbbddccdadabaabdcabacbabdbcdbabbcddabdbbdbdcddbaaadccaacbabbabcdbcabdbdbadcacbbaadcdcdcbadabcccacabdcbbcacdacaabdadbbbdacadcaccabcacddcbddcabdcdddcbbcacbccdbdaccbcccbdbbbbdcaddbdcddabcaacaddcbadbddcbbcaacaccbdcbdcadadddaccbaadccadddcbdbadcbcbaddcbdcdaccdcbcbbbbccaaccdcbabbbbdbacabbbadacccdbcabbddbcbcbcccaacabdabddbcdccbbcbcddaacbccadbdabdaacaabcaadacbbbdadcdbadaccbbdcddaadbbbbcdbbdccbbcddbbcbdddaddbcddbbcbccbdbdcdadddaadbbdbabadaadacbabcaaccbdabcaadcacdaabbbbacaaccabbaaaacccabacccddcdbaaddbbddbbdadbaaccbdabcdaacbabaaadcabddccaadacdbcbcdddcdbdbbdbaadcdaccbbccadddbddcabdcbaaccaabbdacacbddbbbcaaaababdcddbdcdbdcbccdcdcdcdcbadaaccaaddbbbdabdadcabdacddbacdadbadbcbadbdbcabddbbcdbbacbcbddaabdddcbcdbaccbdcbbcaaaadaccdbbcabcdbabbdddbbbcdaacdabbbbaccdbcbabdcdaacaabcacccbbbcdbcbccdcacbcdadbbadbdccdacbbccccadacddcbbdcbcadccadbbbacdaacbacaccaddabbadbadcbdaabbaddaabaabdaaacadcacacaacdbcdabbccbdcbabaabcbaaccabcbcacdbaadcacbacaacabbaacdadaacbdacadddbabccbccdccacbdbadbaccccabdcadcdcdcdaabacbaacdaabcabdaaadbacdacbddbdbacdbcbdabacacaccababbccbabbadbbacaabccdbccdbcbaabbcbcbabdcacdabcccdbcdcbdcacaadaddbadadacbbababbcdbdbbbababcaaddcdadbdcacaadcabbcdcbdaabdbcacbcbdbbbabaccadacbcbcdabdbabddbcbbabccabdcbbcdaaaccdddcbbdadcabddbcaaacbcddccaabcdabcdddbababbcabcaccdabbdaaabbdacacbbccbbdaccddddddabcbcdacadbdadbcbbbbadbbcabbdddabcccccaccbaaaddabcbadddcbdaabbcdadabbababdabbbaadbbbbdacbbccbadbbadbcabdaadbadaddaccdbbaacdacccababdbcddaddbccdccbcddcbddcadcadacbdccbcdcadadbbcadddbdbcdaaabcacbcaaababbbbdcbcbcbbcddbdbbdcacaacddcbbdbcbddabdaddcbaababadacaccbbabadacdcbdcdccbbdbdcdcabcacbcdccddbdddcababadcccacbbdadccdabccadcabdddbdcccccbdadadbbbbdbaddcdaabcabbbbcbdbbabacdcababbacbdbbdccaadcdaacdacadbddddbacdacbaadbacadadcbacdddcaabdaccccbcadcbdadcbcaadbaabddabbcbbbbaabadadbdaaaacdbcddcbabcaaadacbbbdacaadbbadbbaccdbccbddaaaabcccacaddcdbbdacadbadbccbadaddcadacdadadbcdacdbbddabbccbcccbaadabcbbdbbcdcdacbbbcbbdcaaabaddddaccbcbbdbbbdbbdbdadadbccaddbdaaabadabadcaacbbbbadbcdbbabcbddaacabbabccacaaccdcdaabddaabdbddbadcaddcabddcbdcaadbacbdacdbadbacadcaabbbddbdaacbaddcadcccddddbdadbddcacdabcdccddabdbbacbdaccbdacbbdbabdbddbbdcadbcabbcddadbdcadbddcccbacdacbddabcdabdbbbcccdcbbcbbdcadcbbcadcacdbccbdadcdccbbabcabadaabcbacdbadbabbcbcbbbbdbcadaacbdcddaaacaccbbddaccdccabdaccddabbdcddbabbaaaadcacdbabbdbacaddadcabcdaabbcdbaccbcbdabcccbbaacbacccbbccadabcdbbddcdcdbdccdcdddacdcdcadaaccbbcbbbccaaaacccaadaacaddabbcdabcbbbdcacbbcdddcbdacaabbaabbbaacadabddbcddcbcdaabcacbbdacbaaddbccadcaddcaacdadabaadddacbddaabbbccccdcdcddcdacaaadcbcaabcbaadddacacdddabaccaabcbaadbcccdaadbacdddbacbccabccbdbadacbbcbadbccaacabaacbddbacdcaaadbcbabcbabcdcdbccbbbcabdccadbdcdcaaccaababdbbbddddcccacdcbbbdbbccddabddcdaacccccbbbcccdcbcadacddddadabdacbbbcbbacdadbcacdcccaadaadbbaccaabbaacdcdbabdcbcbbacbdcddccdcddacbddcbacdccbdadcddacbdbdadbabccaabbbcadddaaddbdbadddcdbbbddadacadabcdaacbadbcdcabbbadaabccccbbbbadcbcbbaacdabcabdccadabadbbbacbbdabcadabcabdcaabccdadbabccacbcacdacaccbdcbccdbbadcbacbcbcbcabcdccbbacadddbabccaaaacbccdbbccaaaddabbddcbcbadbbcbbccdbddbddcdaadbddcabcadddccdaccbcccdcbabbdccbadcbabaddacbddabcaacabccabcdcaabacabadcacbdadccacadbbaccbcaccdcdbccaddaaacaacbbbbbbbddbbabbcbcbbcbacccbcaccdccaddaabdcbbbcbadaadbdcbbcbacccaadbbdcdcadaabbaaccddacbacdadacbadabdbdcdccdbccdcdddddbbccdaccaccacbaaadaadccacccdbdbadddcacbbacdcabdccadbaabddacacbbaaacbabaaabaadbaaccbdbbcabccaddcabcacaacabdbaadabdbaddbadadcacbbbbaabdaddaaaabcacbaccacbaccbdcdddacdaddbbaaccacdccbdadccdacbcbbcdbadbcadadccadbabcbacabbbcdaadacbdadbabdaacbcaacbcaaadbcdccacaabbdddbacabacdabdddabdabcdccabadbbaadbbcbaccdbbaccaaddbbbdbccbcbddacbdadcaaabacabdcbabdbdbcbcddcbcaddcdbabaabacbbdcdadaccacdcbdcadabaccacccdbdcbbbcadcdaddddcbbbbbbcbcccdcdbaabadacacbddcbadaadbbbcddadbdbbdccdacbbabcbabdbdcaabccbcbaacbbaacacdccbccadcdbaacaaccdcbbdabbadbabacaaacdabbadcaccdbccbadbccadcacddbdbacdadddbdaadbbbacadabcabccbbaaaabcbcdcacdabcabccaaabaaadacdbdcacaabadadcbcbccbcaabadddcdbbadcbcbcbdbadbcdcaabcacabbaabadabbdcdcbbbdaadadbdcacdbdaaadcabcdbdbbbddcdaadccadacacacacadddabbbdcaddadbcdccbbddbcdbdbddbaacabddcadcabaacaaadacddaacdaddbbbaddbaddbabccabddabdaddcdacadcaccaabdacbbdabdbdbdccaabcbcccabdabbbaadccbabcdcaadbdbcccaacacdbbdbabaaaabdbcdaaacdbbdcaaccccccdaccacdddcaadaacbcccabcadbbbbdddcbcdcdacbdddddbbbbaaadbaaadcadacdbbbcdcddaadabbbcdadaaaddddbdacabdcccbacbcbccdacbdbbbcdbccccbadccbdbbdcdcdcdadbbabbcadbdcbaabacbbdcabbcdbccdccdaadbbbadcdaccaccabdbacadcdacdbdabbcdaaddaabcbcdcaababacbdacaddcbdcbcccdacdababaaaddbddaacdddcaabccadcaaccdadaddcddddbcbadaadddccaabacdbbccdadddccdbbdbcddbdabdadaccccddaadadccdcdcabacddacabbcbbdaabbdccbcbbdcaaccbaacbacddcddabadcbbbaddcabcdbcbdabdddbcabbaabbbccdadcbabbaddbccdbddcbaacbdcbdabcadccdcddbddccaaacadcdbbdbcbbcabddbcdcbcbadccbccdddacaadbbcbacabccadadbccccacdabdacdabadbdccacbbbcabcadabccaabcadaacacabddaacdaabbbbababbcaabbdcaaadaddaadbcbcadcccadbadccdbadbacbbdbbaaacabbdbabdcddcbbcadbaaabddbdccbadbcdbcacdccbadcadbccbbccaaacdccbdabddbdaaadbaaccbbaaccadbccdbacadaacbacbcdacdccbddabbcbacbaacbbabcaccaaadcccbdbacdaddcabbccadadaccadddcdaabdcacddbdabadcbccbbddcdabbcddbdacccacdbbbdcccddabcbdacaadbaccbbacdadcabaccaaabcdddbdaabdaacacdadccdbccbadacbcdcbaadbcabaacccbccdcaaacacddbbbdacaabdcbcbbabadbabbadccbcbaaaabcadcdaccddaacadbbaddcdadbddbaadddccadabbbbccaabdcbddcbcabcbbaaccaaabcaaccadadddbdacbccbccbacaddadddbadcabdaccadacddcdcadbddbcaaddbacaadaddddaacbddbbabaadccdddbdaacbcadcccadcbdddbcdcaadddccbdaadbdcaccdcadadadbcabbbbaddccaacdbddbbaadadcacbcdccdcbbbbcabcdbbbcdcabdbcadcbcccacaaccccdaabbbccadadcaccdccbccdabbadacbdcbdbdcbdabdcbadbcaddcabadccdadbdddddabcdbddcaabcdcabbacdaaabcdaddabbccbcababaccacbbacccaddcabcacadccbadabbacbbbdbddbbccabaabdccdcdcddccacaadccbdcabadbdadbabacadadbddddcdcdccbbbcabcdddbbccaabdbabacdcccdcdaccadcacbdbacaabcaabaacbaccdacdddbdaabbdcdbcacdbbdbddbcaacbacaaaacccdccaabcdabdccbbbbdddcddabadbcbbcdaccdbbbcaccadbccdcadddccbcbbdbddcabccaaadbabaadaacaddddcbbaccdbddcddcdaaacbdbabadabccdaddabbbbaadcdcbaabdacbbcdddbbcbbccccbcdbddadbabbdcaaaddcdbbabccabcdbbcabcccbaaaaadbcbcabdbccbaccdbddcddbcdcdbbbdbaaddaacacbcbaacaabcbcccbbacabbabbdbcaadadccacccaaccccbdacbcaabcadcdababdbaaddddaadadcbdabdcbbbdbdbddbadcbaaabdcbdcbcbdadbadbcdabadbabbcddccdbbabcddadcacdbaccabcdbcccadbdcbaacdabbccdabccacbddcdbababdccaaccbbccbbccaaabbccdcdaaaadcbdadabdabdcadbdacaddadaacccacccdcbcaababcdbcccdabdccdddcbccdabcaacaacbddcbcaaadbadaaccdacdcbddcababdaabacbaababbcaaadadadbbaccacdbdcdcadacaadabcdadcaccbcdcbaaccdaadcdabbbbbddbacacddcbdcdcaacddabcadababadacbdabadbbcdbdbccbdbccacddccbdbcdabcbbaccacddadbacccdbcdcbcaaabbdccdacdaddbbcaababcdcbbacabbabdbdccacabcdbcddcddbdacbbadbaddcbabbacdcccdabccababdabdacbccdcbdbacdcbaadcbdabbaaabacbcacabbbbabadacbdacdcadadcaabcacbcacabbcdcbddddcaccdccdbcdbbbaacddcadacdcbbbbcadadaabbcabdddcbadcdcdbcbcabacacdcadbdbdbacdaddacabadbdadabccdadbcaadbadbbdaddcbabbbadaaabacdbbcbccdbabaaaacaabbadbbcdddcdabaacbcacdbcdccddacccadbbbabacabbcdbdccacbcabcdaaaabacacdddcbcdcabddcdacdaadabacdbcdbdccaacddbbbdbabbadacdadbccbbaacbabcbdccbaacdaaacabdccbddbdcbbbdddacbaddbbbacbbcbaabcbaabccdcbabacccbbccadcbcddcbabcacbbcdbdaccbadddccbccaaacccbcdaaddbabcdcdacbbbdcaaccbddacaccbcacbcbbaabcbdcbccacbcdbbabcbcbbacbdddabadaacdbdaddacbbaabbcdcdcbbccbbbdcaaaadacadccadacdabbccdbaacdadaaabccbbbcadbcabadccacdaccccbdaccadbcbdcdcddcabbdaaadadbbdbcdcdbbcaaaccbccbbaccacbcccbdccdbadabaaadddcdbbdcccbcbbadbbcadabbcaabaaddaddaaabdbdbcdacccadcccccaabbaddbbcaddbcbaacddbcdbcbcaadabaaadacddbddccacdacbcabbcbdadaacabcddccaddbcdcbbcbbcdbddbbdbaadcbabccdcccccdcdddbdcdaccdaacbbaaacdbacdacdcadcacaaacdacbccacabdcaacbaddaddbcddbbaaabccdbcbccdcddccbdbdcdcbccbcccdacbbabcdbcaadabaadadcbdccdacbabbbbcbabaaccddddbcacbbadbbbbcdbdadaccadbbcdcbcddccbaddaacbddbdbdbacbcdaacccdcabacbbbcccdaccbaddbabbcbaaccdbbccdbdacabccbdbdcccaadbbcddaddcccadccdadacccdcbbbcbdddcccbacbddaccbbbdcdbcabccddabdbdcddccacdcbcccbbccabcbabaaaabddbadcdcdccaacabbddabaabdbcdcadbaaacadbadbabdcbdbbadbdccdbabccbaacdacbbbdcddcaadabbdbccbadbddbcbbbabcbcaadadaccadbdbcdcbccabadbabbbbbbdadbcdddddcabdbbadacdadadbdadcbdabdbaabbaacbadccbaddbbabdddaabcdbdbbadbababddcaccadbcddcbcdabcbbadbbddcccaabcbdccaaacabbccbadcaaaaadddcadcddaabdcdabbbcdcdaabcdbabccdcccccacdcdbcbdacdaabbdbaddcabddbccdacaabbbbccadbcabcadbdaccdbacddaccaddcdccadbbdadaccbcaacacddbbbaccdbccacbbcdbcdbbbdaabaabddcbcdddacabdccacbadbaacadaaddbbaacabaaddacdcdbbddddcdbcadcacbabcacbacddcacbbbbbdcabadccdadbdacdcdacbdaaddabdbcbdddddbbccdadcccdacbaccbbdabacdcdaaccaddcdadaccabbcccbccccaabcaabccaddabdaadacddbcbcaaddbbbaabddbbabaadcbabcaccaaaabccdadcaccbbaddbbbabdddababaabdcabdbbbcbbbbdacbdcdbddcaadbadcacddbccabacdbbbacbcbacddcdbabdacdaaaddabadaabacdbbdaaadbbdacaddcbdbcadbacdbbabbdcdadbbddaddbdadaddbdbaccbdadcdcaabdcbccbdbbaddaaddcddbaababaaccabcabbabbddabacacacbbaaababcbbacacccdbbdadcbbaccaadadcccdccccbcbcddacdcdaadadbbbdbbdcdbaadcdacddbddacabcadccccbabbcddcdbdabbdbdacbacbaddaaabcbddbaddaaadccaaaaccaaadabbcbbbddaddcdbbbddccbbcaacadadbddccdaacbcaadabbaadcdbabbdccdabcdcbabccaaacbcdcbdaadbbadbcbdbaaaabbaaabbabbaaaabdbcacdadddbcddbddddbaaccccccdbddbabbdcbbaabaaddaaadbdaadccdcacdcabbdabddcabcdbcbbccbdbcaaccaadbdcaaadcdbacdddddadacbcdabbccdbadbdcbbccbdacbaabdaadbaadaadccabcbabccdbcdacadadbbcbccacdcddbbabbcdcbdddbbdddbadbccccbcacbdcddaaddbadbaabddddbaaddccbabaadcacdadcbbaacbccbcdabcaddaccdbcabddccdbccbabbcdcdacdcaaaabcddaaaddcbbcadddaaacbdabcbcddcbbcadccccdbdababcdaacdacadccaabcdcddccdacaccaabbaccdadbdcaabbdcbbcccddadccbbaddbaadbdadacccadadcaaacccbbccbcccdbaabaaaddcabaadbbcdaacadcacaadacdacbbdbdccdabdabadaddbadbaccbcaadabbcdaddddaacbbbcbdaddbdacabdddaaccacaadaddcaccabcccbabcadbabadbabdbcdddabcbcbdcaabbbbaccacddacdaadaabbabdccdbcdccbaacbcabcccabdccabadcbdabcaabaaabbacbbbadaddddadabbdcadabbdabcaacdccdbcbcaccbdadddbabdcbbbcccbacabbccdaddcbaacabdbbdccdbbdbbadacdabbbccdabababcdcddcddaccacacbaaabcbccdaccddcccdccdbaaabaccddbbacdadcacdcdbbadddabbdcabbbbdabcbbbdabbcdcaacabddcdacdcbbbcbbadadabcbadbddcaddacaadcbcbccaadcbbccbaadadcbbaadbddbcbddadddabbdbbcbbaadabcccccadadaccbbccadacbbbaaaabaaccbddcbdabcadbacccaaadcbbdddaaadbdacdcdacdbdabdbbbaadadcdacbbadddcdcdaaccddbccbacadacddabcacabaaadcbbbdacbacccbaaadbcdacbadbdddadddcdcbacbabbbadaaddbccdadcacbbaddcdaaccaddbbddbbcddccbbcddccddcbaddcbdabcddddcaaddbdababcbcacdabbdabbaddacdcabcadbbdbbddbbcdcbdbcaccdaddccabdccdbdbbdbbdcdaaabdcddadadaadaaddaabcabddacacdbabbddadabcdadcbdbaaddcacbcbcbbdbbabdbdbddbbcbbdacbdbcbacbbdbccbadacacddcaadacbcccdcaabdbdbcaadbbccdbbaaddabadccccadccbbddcdbcbbccabbadbdaccbdacddcdbbcabacbcbdcacbccdccbbbbbcdacbcadcdcccaacacaabcabcbdcabdcbcabadcdbccdacdddaadbabbbbaccadbbacadcacbaadaccaddddacdcabcddadbcdacdcadadcccbadbcbcddcdcccdaccccabadcdbbcdbccdcbacccaabaccaabbbbccabacccacbdaaccccbadabcccdacacddabadaadddaabdbadbdddcbabccbaadddbdabdaddabcbbcbbacabbbdacbaabccbbdcabacaccabbacacccdaddadbcdbdddbbdbbdbbabddcabdaccbcaddddbbacaccddbbcdcdcdabccdbcdbcdbccdbbdcbbadbdcbadaabcbddccadcacbdccadcaddabdbcbbadaacaadbcbaabacbbcccccbdcadccdacaccbbbbbdcaadaddaccbcabaacabbdbdccbcbdaabaccadcdccbcdbcabcbcdcccddcddccbabbbdbaaadcbdbacdddadadbbdadaacabdddacdccbcbadbabadddcdbaabaadadbbbbccdcbacdaabcaaadabbcccccaaabdddacdbdacdbdacddddaadabcbbcdcbcccabaccdbaacccbdacbaaabacddbdbcaadcbbdabcbddbcbbadaddbdaabbbdabaacccdabddbddbbacbbadddccdadababdbdbcadabaddddbdaaadbdbdbadbabbbdabbcbcbccacbacddccddadbcbdacbbbbccbbbbcbbabddcbdcbabddddbbbbdcabadddabddbdcdcdccaccccbdddddcaadabbcdbbbadabdcacbdaaabbabcdabbddabbcdaddcdddadbddaddcadacccadccdacaadddcdcababcbaddbdccabdadcbdababbabbbabdaacbacbabcaabcbdaabbabcdcabbdaabbdabdaadbdbbdbadddcaabadbbdbacddddcdacbdcababbccdbbcdccdbddcbadbabcdbabaccaaabcbdabbbacaadbcacabdcabcccbbcdcaddddcbaaadddbdccbbbcbadabdbdbaaddadbacdabdabadbddcbbddadcabbcadbcdabaabddbbbbcabdbccdcddcdddabdcbbdabadcdccadcaccbbcadbbcbcbaaabbddcbcbdddacabbbcbcdabbadaccacaaabcdaccdcddaabbaadbcbaabddbbcddcbcabbbcbcbaacbbdbccbbdbddacdcdacdbabbbdaaabbdbcbcbaacdabdbdbcbaccbdcadaabbaccbadddadbaddaabcbadcbbbcbddaaabcabaddaccccabddadcabdccbccdaddacaabaabbacacabbabcdadcdbdcbbdcaaaadddadbcbaddbabccccaacaccaadabbdaacbdbddcaaccdcccadddacddcaadaadaabcacbcaccddadccbdbbbccbabacdbbbcabcbcdaccdccaddbaddbcacaadbcaccbababdccbdbddaccdbaaddbabbadacdbbbcadcdabaddbdbbbacabbbbdcacbdbdbadccbcaccadccbbabcbcdbbdaacdbbbabaaacbbbbacbcddcddccccbcddbadbcddadddacbcccbaadcddaacccccbcabadcddcababacbbcdcdbdcdbdccbdababdadacddcbdcabcbccccabddbadaacabdaadbcbbbaacdbdcdbbdaadcdbdabcdcadcccdcbbddbadddcacdcdcacadbcddbbdbdadbaddabbaacdbaaaccabcbaacacdaccbbdbcdacbdcacbabddbcbcbabaababaadbaababcadcdcbabdbdaacbdcadcbabbcacaccabbccbbabadabdaadccbaacccbacabacbabaccdddadcbdadccdcbadcdabacdddcdabcbdccbbccdbccccaddccccdbadcadacbcdcdbbbddaabdadbaaadddcdcddadaacaadacdbabbaaddcddddddcbbadaacacaaccddbddccdbbddbdadcdabcaadbabddbdbaddabaabcdaacccdaabadddabbdaaddddcaaadbddcabddddbbdbdddacabdacdddcabbcbadcaacadadbaaabddacdbcddbddaacadabaabacbbdadadcaabbbbcbcadabddcbbaacbcaabbccbcccacadbbdddcccbccbcadacabcddddcadcabacbadacaabcacbdcababadcccbadbaccacccdbccdbddcadcbddcccaacbcddccadcabcaacdccdddabccbbacdbbbacabcdbcccbaddbabccbdaadddaacabddbcdcacbbdddaaddcdbccacadbabaaaccaabdbddabcccadaadabdacabdbdbbbaabcdabadaddbdddbdbcaccbbbaaccbcaacbbabddcacdbbbdcabdabcbcddcdcbcbccacccdadcccaccacdcadaacacccbcbccacdacdcaadccaaccacaaabbaadddddcbbdbadbadacdabaacdcacacdaddaabaddbaadcdabadcdbbabdadaddbbaaabbdbdbaacdadabdbabcddddaaddcacbaabdbabbaacacdbabbccabacbdcadabdddccdbaddadbcdabadddbcdbdddabbbdacbabbaaddaaacdcbdcddabbdacabdcaadbabdbaaccacacbcaaccaabdcbdccbbbcaadbdaddbbadbbbaadabdccdbacdbddcabddadbaadabcccbdacddcacccadaaacbaccabdddadcdddbcacdbccaccdaddbaacbcaacdccadbbbbcabbccbcacddcabccdcabcbbdcdccbbcdcbcbdabdccadaaacccadbcbdccaabcabbbddbaadabddacabacddacbadbcacbcaccacdcddcbcddacdacdadcbcbdbbdbdbbbbdacaacadbcaaccbdaccbadacabdcbdacdadadddabcaacdcadccabaacbdbacccbbcbdbcccdbbabadadbbcaacadbbaaadddbbabcddacadadbaadacacbdadcdbaadbbbdcbabcdabcdccacbcadabdcddbadcdccddcdabaaabbccababcccacaaabdcbddbdadbadbcddbbabccccbbaccdaddaaabbbaaccccbdbacdbaabcdccdacbacdcdaabdbbbbccbdbccbccadabcaaccdaddcabcdcbdbbcbbadaadccabdcddacdbcbadbacacdbadcdacdcabacddcbacaaaaaabbbbdbbcaccaadcbccbaccbdcaababdaaabddabdcbdbaccbacbcdbcadabaddcaacdadbbbadaabbcccdcbdbcbddcddddaddddcabdddbacbbdaadabcabbcbcccdbddbccabdacadcaaacbaabbbadcdcbccbddcaccbdabddabadcdaccacacdccbbabccadacbabdabbbdbaaddcaabdacdadadbdcaaacccbcddbccaadccbaddcbbaaaadbccdcddbcbbcccdbdaacacccaccdabdddcdcdbaaaabaacdacaaacbdccdbbcbcdababbdbccabbbbdcaacaaadcdbdcdcacbaaacabbaacddcbcdabcbdccdccccadbdaadbccbadacddbbcddbcbcacbadcabcbababbddcacddaadbacacdacdbddcddabaadcbbcaddbaaaacccdadcadcdcbcadadbdbddaabdbcccddadacdbaacbbdabcacbdaaaddddbcdacbbaccdcbbdbcacbcaaddaccccccadbabdcadcaacccabcabcdcdcbaacbcaaccbdcdacacbabdcaaabddbdcdcdacccbdacaaaacdcacaccccacbaacdddadaacdcddcbaabcbdabbdcacbabdbababdacdbddbbdabaabababcaaabadcacacdcddbbacbbbddbcacdabcaacababdaadcacaccdcacbcdadcdaadadadbbaabdbacbbbbcdbaddccaabddaccdbacdabcddcaddaccdcdcdbdabdaaccddadbcdbacabcdadccccbbbdddbcbddcdddcccbdaadcacdbbccadbbcadbdbaabcdadcbdaacccabdbddcdaddbcdbdacbccdbcbcaccbdddbbdbccdbbaccbcbbacbbacadbcdacccacdbcdbdabcbbcaddccdcabdcdbacbcdcadbbabaaadcbdddcadabbdbbbbbabaacdcdcbddcdccdcaabbbcdbbcacadabacccaccbcadcadccdccdddbccdaccabddaadcbdcbcccbccccabcaacccadcaabacbbaadbbacbbdcdaabcaaaccbbcbdadaccbadbbbadadbddacadcbcaabacddbbbaaacadbaadcdbdacabbbcdbdcabbbcddaabcdabbabaaddadadadcacdcbadbbbcdbcccabbcdccdabadabbcdabdadbbdadcbaacbdbdcbdbbaacdabcaadddbbcbdccaaadbabacabadaadbabbcdbadaabaadcbdbbcabdddbacddbdcbbadabacbaabccddbbcabcdbbbacabacbbaadaaacdccadbcadbcacbbacbbaabddcdbaabbcdcddaaadbdbbddbaaaaddbaddaaccdccaddacadcdddcbbdaddcddbbbbbadddaaddbbbdbbdccaaadbdbccbbacbdcadcabbdcdcabdadbbbddccdaacadccadcbddacdaccbabccdabbbbbbbcddaacddadaaadacaabccabccdbadbcabadddcabbbdbbddcbbbcdcdacbdabdacaadabbabdadbccdcbdbcdcabbccbcdaddacbaacaadddbbaacdbcddbdccaadaaaacabcaccbcbbcdddaddcdadcabcdddccacddcacbaccaddcbbbadbdcadababacbcdbbabccbbabacdaaaacaabadccaabddbddcaaabdacbccbbcbdcdacaacbababdacccbbababdaacbbdbcbbbcdadcdcbcdabbbccbcaababcddbbccbcaaddcccabcdcddaccdbcbbdddabcadbcddcccbbbadcdaddcdacddadbbbacaadadcbabddbcadaabbbcbabddcccbacbacbbdcbddcdaccccdccadbacacdacccddcadcbbadbcbadababacbcbbdacbcaadbacbbddbcabcccdddacadbcdabdddababaccbabcaccaabbbdaabacdbaccbddabcdadacadcddcaccdacdadcccdabbcbdbbdcdbadbcbaabdbccaabddcdacdcaadabddaabbdbcaadbddcaccddbcccdddacbbbcdbdbabaacaddbadabdbaaccaaacadaacbbdabcdbcbdbdbaddaadcaacaaddabbbbcacdaacaabddbcbccaaaaccaacdcacacabcadabcdaaaabbddbbddccbadcdddbdbbcdbcdddbdccddcdaabadadbdacbcabdbdadcccaaddaacddbccbabcdaacadbbabaccdcaadcbcbaccbbccdbbdbcabcdaddcdcacbdcbaccbabccbdcdbdcaccdbbddbaaccdbadcbabcaccdcdccdbdbddababcadcacadaccdadacdddbcccacddbbbdddacbacbcdcbaabccbaccdbdbbdbcdabaaaabbdcccaaacbdbcabaadabdabbadbbbadabbcdccbabbbdcddacdccbdbcadbbbaaababbdbbdddcbacbaaddccaaabddabacaddbccaacbdacaccccacacccacddaadacacccdacabcbcdbcdbbdcbddccabbdaaddaddabbccdccbdcaadcaaccdcacdabdaccbbdccddcbdadbdabaaadadcdabcbbbccbbcbbbdbbcdbbdababbcaacccdbcabbcbcbbccacacbcabcabbbaccacdbbdbbbcbbbaaccbccdadbdbabbdadaabcdcbdbaccabbdbbdccbcbbddcabcddccbcaacabdbabcacccddaabcbabbbcbaaabddbdcbadcccbabbbadabbdacdddddcdcbbbdbdbccbabacabbaaabcaccbadbdadbdddabdddabbcdddcccacaaabbdddcdbdbdcbbaddccbbaaabcccdcbbadbbadacdbdbbadbdabdadbbacddadbdacbdadabdcbdbcdcacaacddabccbcbbcdbdacaddadabddbcacbddacadababdbdcaaabbbabcbdbaadcdadabbcbdcccdbcadcacddddbdcdacccbacccccdbbaddabcababbcadcbccbbbcccacdaaabcbcccadabcdabbaaddcaacdcbaaadbccbcbcacabbabaacadcacddcabccbbaddbbcabcacacdbcbabaabbdadaaaadbbbbaccbbcbcacdddaddacbcdbcaadcdacbddccaadbcacdcdabcbaabbbbaaadcdcaadcdabaaddcdadbdcabbddabaaacdbadbdcaccdacbbbaadddbacccdbaadddbadaddcaaaddccdaaabdababdbddacabdbcaaacbcabcdbbacabcccadabcabcbabdcdcccbbabbccbacdbbcacabdddaddacccdabcdbbdcddddbbacaaabdccacadbdbbbaabbadbdadbdcabdaacdbaaacdcbbadcbbdbcdcaddddcacdcbcbbabccdccabcaacbadadaddbadabdadaddababddbadbcbabaabbbabbacadaaccdadabaddcbaaabcabdcaabbcadbcabbbdcbbdbdddadaababaddbcddacbbacbddbcabbccccdaddbbaccbccccdbbbabbcbcdcadddaddccacbabaaababbbdbbcbadbacabbcbbbadbadbdccdccbdadabdabadddbabaaacdbcacddccabaaddbdabaabbacadadacccbacbdacdddabdcbababdbcaddacbaadcdccbacacdabcdcabbaaaabbdbcddabcacbabcacddbbbbcccbaaaddacacdaaddbdbabdcabbcccaddbbaaabbdaddbbaaabaabcbdddbbbaacdaadaaadddbcbdccccdcaacdccdaacdbcacdbbaabddbaacbcadacdbdbbbcddbaacbdaccacabaadadaadcccddbacaddbbdcabbaccddcabbbdabddcaddbbcbadbacdaaaadbdbcbccdbcddcbcdabaaaacbcbdacbdbcbcabaccadabaacdaaddadbbddddbbbddbbccdabbdbbacddcaabacbbccbcdcaacbcaaddaadabcaacdddbabcccacdabacdbdddcdbacbcaddbbaaddababdbaabbdcbdaddccdadddddbbcbcdaacddddccbdabbabcacdcbdddcaaabcdddcbaadcbbadbacdbcbbadbadadddabbaccadbabaaadbaabcbbdbccdaaacdcdacbdbaadccbaaaccdbcdcadbbbaddcdadbcaddcbbdcdabbbdbaddacbdbacdbadbdcdcdbddabdddacdbabbabdddddcdabddddcbcbacdbacaaadbbcdddbdccacacdcdabcbaacaaabccdcaddbdbccbcccdadccbccadabaacbbddbbdabdadadacbacadaddccadcbbdbcaadabbdccadaaddaadadcacccddbbcdcbcdbdbbbbcaaabdcbadcabdbcdadacccababdccddcbccaabbcbdaabddcdabccbcdaabababdadbaacaababdabbddbaacaababcbaccaaaccbdbabacbcacddaacddbdbcbbdacadbbbdbadbaacdddccbadbababcddbbcbaddbbcabddcbaaccbdccdbbadcddcbcdbdbbbdcdbaabcdbbccdaddccabdccdccdcacbdcdcdbadadcdadccbdddcddbbbcaabcaccbaadbcdaaccdbbacdadbdbcdccdbaacabbabacbccddbacbabccdabbcaccbddbccddbabcbadbcbbcadaaacbcdcccdadcadbbdbbcaadcdabbbccabaaaacbccdbdccbabccaadcabbcdbcabdabcddbcabdbcacabcdaaaddddbaacddacccddacbbbdddcddabccdabbdcabbadcabadcadbbccacbadaacabcdcbcabccddbbcccdddadabbcbadbdcdbddbdbdccbcaaddcadacabddaddbccaaaddcdabccccbacaadcdcdcadbcbcbdddcacbbaccabdbddcbabacabccdddcabccdaacbbabaabaadbbabccdcbbaaacdaddccccdacdacdcccbadbcbdcdaccbbdacaabcaaaddbbbabcacadbccdabbdcdccdadccbbbacdcdaddbbcddcccbbacaccdacbdddccdcabbdbbcbaadaacbcdcacaaddbbbcbcbbbbadbbbcaddacdbaccbcdddbdbbaddacdbbbabdadbbacadbcdaaadbdbabacdddabdccacbdabdccacdabbcaacbbcaaddcbaabacdacacaacbdcdcaaccdbacaacbabcccbdaadcaccbccbdddbbbacacdcdbcabcacdcddcbdbcabcbbbaaddacbcccadaacdaddaadcbaacddccdcdbcaddadcacbbabddaaabacdccaabbcddcbddccacacbcdaaddbdaabdcabbcdbabcddccbdbdbabbabcccbdaabbcddcdddcababcbbdddcaacaabaabaadbcbaaabcbdaccbcabbcbbadddcaddccbbccddaadbdbcdddabbdaddacadccaccdcdddaabaccbdccadbcdcadbddccadabcbccacdbcbbdaccccadccccabdbdbdccdcccdacddcaadadcbcccaadbcaacabddabdbaabccdbaacdabccbbaccabccdbbacbabcdaacddddcacccadbbccdabbdccddbdbddadccadccdabacccadbdbaaacadbbabcdcbddaddadcdbadbcccdbabbcdbacbbdddabaaacaccadbcaacadcbbadcdadcdbbbadbccdcbbbdbbddddccdabaabddcaadaadbacabdddccdaddbcdbaddaccbabdddbacbcbaacdbdbccdcddcaababbbabaaabacdabcdabacaccbdbaccbcaabbdddcabbabcabcabcdbcacaaccdccccbccbadbbdbabdbccdacaddbadaadcbabdadbdadbaadaabbaccddcbdaaddcaaacadbaabaccadabbaadbcdbdbabcbadadcababddcccadcbcddbbabdacbbbcaccdcddcadbbadcbadcdcacdabbbbadcbdabbbacbdbbdabaaabacacaccdccccdabcddcbdcddcccaadddbdcbdbcdcabaacaadcdcacbbdaccadaaabccdcadabddbcbddaadcabacadbadcddbccbcabbaabaddddcdbdbdddcccdadadbcbaaaabacababcdcaaabcbbbbbdaacadcbcaabaaabccdddaaabbdcbcaddbabcbdccbdadbcbbcabadcbbaabacdaadcbaddddacbdbbbdccdbadcadbcabcbaddbcabcddabbdbcdddabcdcabbaaccabddbbddcdadbcddacbabcadcccacccadddbbcdbbdacbdcadbbdaaabbcbaaccdcdcdcddddbaaaadbcbbbadabbbdbdddcabccadcbabadbbbdbdabababaacdaabbbdcbbbcdbbdaabbdacdcaacddadbccaabcbcccabaccbacbdabacaadacbcbadbabccabdacabbaaccdcaaabdaacaaabbddcaaaaacacaaabadbccbcdcbdcabacdadaccbbacbaddbbcabdbccbbabadcbbacabcdcdccdcddbbcccabbcccbdddbbadcadcdcdabddadcacdbaccaabddbcdcddcbddbdddabbbaacdadadccdbabbcdcdaabadacdacabbbabcabcacdcbdccddbadbabddbaccdbdabadccdbccdcddacadaccccdadbdacbaddcdcdbcbdcbaadbcdcacbbcdcbbdabbdcbaddbbaacddcccbcdbcccddbdbbabccabaccdbccdcdddabbbabacdabcbcbcbddcdddccdabddbddddacbcbaadbcadcabdbcccaddbbbcabbcaddbacaadadabbbbbdcddddadccddbcadcddcccdcaabadadacdabddacbddcbdbcabdcbdabbdacddbcaccdabbddbbdadadcbaabdcddacbabbdddadbdcbbcacbcccaccbcacddccddaadbcddbadcbcccdbdbcbdbcbabcacbccacbbabddadadabddacbbdcacbbbbaaaaaacababbbabbdcdddcbbacbdacbaadcddbdbadcbccbaabacdadbbbbdccbadbcbbabadaaacacbabcacdcdcdbcbdcdcbaabaccdbbdaaddacbdbaddaddbddacbabacadddbacbcbadbdcbdbcabcbdbcccaddcaadcaaccacabdadacbcdacadbbbabaadbacdbdaacbbbaaabdabcabbcddbadcbcbddbbbbbccacccaabbdccaddbcccdaccaabbdabbdcbbbbacdbdccdacddbcdccdccdadacccbddbcacbbabdcaabbbbdbddaacacdabdbaddbbaddaabbbddbdaacdbcacbcdbbcdbcabbbcaccadcdabcccddbbabddccccdbdddbbdacbadaadbcdcabddacadccbdaadaacacccabbaccccddddacccaccdcddbacbcaddcacbdaaaadbddbddbadbbabbbdadcccabacbaaadaaadbbdaaddcbcaccacbbbdcaadaaaddaabbcabdbbadbcbddbdabddbcddcbaacbaaddaccaabbccdadabcacbcdcbdbccbbbddccabaaadbacbbbbdccbdbcbdabdddcadacbcaabaccbdcbbcccdddbcbbadadabaadaddbaacdbcccbbadbabacbcaccdbacdabcabcccddabcacabdbacaddddbbbcdcdddbbddddcaacbdcbabaaadbcccdbaccabdbbdccdbcccbdccdbcbcabddbddcddcbcbadbdacdbcbbaabbacdcccbbdddbbbcacacabcddadbcacdcabacbdccbbbbcdacdabdadbabcdaadcaacadcbbdbcaadbbbcdcacdaddbcacaccbaaaccadbdcbabaabcbdcbabbdddccbdbaabbbcbbdbddbbbbbbbbcdbcdcbdaccaddbbbdbdccccbbacbcbcaaaadbadbcbbdadbcbadaacdccbcdaccdccabcbdcddddaaacbadadbdbbbdcddbbcdacabccddbaabbaabcaaddddcdccbddccdcabddbbbacbadcccddbcdcdddabbdbacbbbbdbaacdcdcddadbaddbccadcacbbdacbbbbbbddadaaacccdabdddccadcbacbcbdacacacddcaaadccdcccdccaddbbdccacdcadccabcbcabbccccddccdcddaaabbdcabbbdabccbabacdddabadddaccddaabbbdaaaabcbaabcbcabcbdadbdcdcccdcdaacbbadcbcacadbdbcdaabbccaaacacbdbccddbdcdddcbacbadbbcdbaabacacbbdaddbbaaababadbcbaccbacccdabbbdadabadbcdaaaacbadcbddccdbccdbadbacaaddccbccbdccdbcacaccadbddcbcdcbcdacaaadcacbbcdadbabdbabdddabdcdbacbddcaddacbdabacbadadadcbdaddacadadcbcdbcdcbcddaadbaaccdbddcdaababddbcacbabddcaddcbbdabcbbbbaabdcddcaaccbdaacaababdadddaacacdabadccabbbbcddcadbdaadadacbabbbbadddadabcdcacaacbbdccbdcdbaabcdccacdbdcaccccbbcbaabbbbababababbcaaacbbbcccaabdcdcbdbdacdbaacdcdccacdadabbcddacdbabcaacdacbabdbdcdacddbaacadcdccdbcbddabcbbdababdbddcdaddbcbddcccbccbabbacacaacbcdacddbbaaabbcdcbccdbcdcdccbbabcdaccacabcdcccbbbcdaaddbdcabddadddccccadacbbaaabdbdbdbbdbcacdcbabcbddcdbcddbddbcbbabdcdacacbbddbddbddbbddbccaadabcbbaaadaaddaabadaaaccbdababcdaccaaacaaddbdcaacdcaacaacdbbddbdadacadcdbcaaaccddbcbbbabaaccccabcdaabccadbacbdadbcbabaabbddbdbdbabddcaacdbcabababddbcdadcbaaaccbbcdaccbcdbbccabadabccaabdbcbdccdaaddbcbcaccdbbdddacbddccbaacbaabcbbbbadbcdacddccccdbbdaaaaadabdacdcdadacdcbbabcadcaabacabcadcacdaaccbbcabddcccbbcccdcabccddcabadbacabaddacbbbdcbbabadcbbcbccabbbacbacaabccccdbcbbbddadddbcbccccacadbdacbdabdbadbaaddccbadcbacacbbacadbbdadbdbcadbacdcdddbcdaaccbcbabbccadbbbaccbaabbdcadcadcdcdddcbcbaadcbaccaacbcbaaaabcdbbbcdadaaccccdacccbbbccbcbadccdcabaaaddbaddcaaabdbdbddddcdaadccabbddbcbccddacdaddbacabcaadcbabcbaaabcdcdaddcbdddbcaaacabbdbabbabcccbabccdaacaacbcbcddacabaccbaaacbdddbcaabbaaabcdccbbcbadcadccbaabccbbcccaadcadcadbaaadbcaabbabdcdbabdddbdbdcdbcbcacdbcacdacbaaababdccbabbadadbdbadbdcacaddccdaabbbdaabcdaaccccabcdbbbaadaddbcbbcadcacabbacdbadcddbcdbabddcccbdcabccbbdcaaadaaaaaacdcabdaddccdadddabcabdcdadbccbdcdccadaddaccdbdddcabcdabdcabbdcbadbdcbabbdbcadbacdcaabadbdacbdadabadcaaaadcbbbcccabbcaddaaddbddddaaaddcdacbbbdaaadbddcdddbdbdaabbcacccdbcdddcbddcbabcabdababcbaacadcaaccdabcbdacddccbcadacdbdcddbddadccabacbdbcadbaaadadbbcbdbbadddcbdbaccbdbdcadcddcdbadbdabcbcaacdbcabccbabdacccaddccaabbddbdccdaccabcddcbdbadcdcabbdaaadddbacaddcdcbacbcbbbbbcddbaadccbaabadabbabdbacaccbbaaadbdaddabcdbbcadcacdcacdcbababbbcbdcbbbcacccddbccddcaabccbbbbddccaabacddacbabbadbbdbdacbcdccadcbbcbabaccdcaadddbaaaaadacbadadcccbbdabcbcdabbbaddabcdbbbdacddaaccadcbaddaddaaccaaabddcdcbaabcccbbabdaabdaaccaabddaadccbadcbadbdddacbdcaddddbccadacbdbbaacbcbadabcbbddababadcbddccbdaddaaabadacbabdcdbadcadacccacddcaccbadbcabcdbdbcbcddaaabcddbbdaccaddcdbbcddddbbbcbccadaaadbbcaaabddcdbcbbdccdaaaacbacbbadbabcdbbbbddddcdadcdacaabaadacadbbcddbabdcbabbbbbccacdddabcadccacccdaccacdbcccbddbcaaddccbaadbbbdddbacccabaccbbdaaccdbccdbbbabacdacaabcabaaaccbabbcdcaabcccccdbccdaadabcbbdddcdabdaaabcaaaaadcddabdaacadbcbddacdbcacadbcaabbcadbdddbbccbdacdaabaadbbbbacbdbdbbbdaaccbcababbbdcadbcbaaaacdaacbdbacaacadcdccdadbbcabcbcdbcadbdacddbdcddcaaacbcadcdbbabcdbbdbabccbaabbbabbdbdcacacbccaaacddadccdcdaaaddcdbbcccbdabcbdabadcdaacbbcadbcadccabccbccbdabdbbacbdbbdaacacbbbcbbbababcbdbdabbabcdddcdcaccbcddadacdaaddbbbdccbbbaaaabdcbbcbcaadccbaddddcdaddbcdacbaabdababbdccccccbcbcadaccccbdcdbadabdbddcbcccabcbdbccdcbcaddaaadaadbabcabaaacacbdccbaacbdaccabcdbcddbbdbbacbaacbcbdabbabbacbcbcdcdcbadadaaadbddccbcababdddcbacaacccdadbaadbabcadabcaddabbcdabdcbbdbdcdaabbaaccaacccdddcdbccbacadacacaaddaadccadbbadbbaaccbbddbdbaccacbadaccabccaaccdabcddbadbbaccacccbbdbbdbbccbcbbcccbadbcbaadcbcacacbcbbbabcddddaaccbcddabbcabcbccbddaacdddbaddabddddccaaccbdcbbcdbacdbdacdbaccdacaaadbbccaabcbbcbabbbcabdbcdbabddcdccacbddbbdbcdabaacbdadabdaabddbadddccbbbbaddabacabcdababadccddbdbbddcadccdddcbdddaaadddcadaaddbcbababaaccbbddaacdcdcbcdbbcabacacbbdbdacbbbadadddbddaabcbdddcbdbcbbccddcabadcdcccaddbbbacdcdadddbcaddcacadabaabadcbdaccddcbcbbacadbdadaddbdbbbacbadbabacbaccbaddbdaddddcccbcdbdcbbbcdadcbbbcbadaaacbcbbacacbdccbcdadccdbadabdbacbdbdcbcddcbbaaacbdbbbbaabcbdcadccadabddaacdaaabbaacbbabaadcccbdcbcddaddbbaaaaaacabcadbccbadcccccbdddcabcccaabacbabbaabaabddbddbaccbdddcbccbcbadaccddcbacadbbbabbadcbabaabdabbdacadbababcccbbbbbaddbdccbcdbcbdcdabcdcaaabdabbbaadbdccdbdbdcccddacbddcccbccacdbccabdcaaacbbbddcdacabaaabccdddbcddcdaddcbddccddadbdacddcacdbacbabbccaadddcdadcdaaadadacccbadbdbcaaacadcccdabbccabccacdbccbcdbbdbadbbdadbcabcbbccadabbbacdadadaaacacddbdbdcbbcabbcdaddcbabdbcadaccaddabbababdabdbbcbdddccdbcdbbddbdbcbccacbdcdabccaadacdbacdabdccdccdddbbadabbbadbbaacddacdaabcbbacbcdbcbacccdabadccdbbddbdcdcaabaadccddbacbcaccdcbdabacccbcbaabddcdcddcbddbccdcbdabbccccdcccbcaadcccbbdcddcabbcacbbcabcbddddaaaddadbdadbcbcdbadddababddbdbbcadbbdaadcbbdacbdddcaccdbabbcbbcbdbadbbbcccaccbabbbddcaddccaacbddbacbbbcddbabbdddaaadaadbcbacdddccddbbcdbdbdcadabaccdbbbcadbabdccbbbaccbabbdcaccaabbbddacabddcaabbddddbadabddcbbbcbdbdacdcadcbadaacdcbcdbddbdbbbadbbbdaabacaadbcbbaddcddaadaaddddcdcbcbaadcdbbbdacdaccbddccdcccabaaacadddbcbccbccdcdabcbccbbddbcdcccabcaacdbbabddcbcabacdcdadbcbbcdadccdadcdaabbddbcbcddaadcbabccccbdbdbdddccbdadacccdccbdbdadaaacbaddbbbbbacbcacadbcbccaabdaaccddcabbbddbbbacadababbdbcabbbbcdcddddccbddccacdcdccdcccccaccbccdbdababadadacccbaacaccbabbbaaccbcaccccbbbccdbcbacaaddddbdddcacbaabaccbacbdcdbabaacccdadcbbaabbdadcbacacccacdaadccddbaddbbaccaaccdddddbddcdaccdddcacabcdacbbadbaabddcccbdccddbbbdcdcacddddabddcdddbbbddccbbaadcacaddbbccdacbaacadacdacbdbbbdbdbdcbaacdaaaddcdabbbaaccbbdabacccacabbdaacacddcdcdbdcacdcdabaaddbdababdbdadaccaaddbcdbdcbaddadadcbdccabbaabcabcdadbabdbdddaabbddacadbddbadadddbdbcadacdbaaccbbabaddcbdcbdabbdadbcbccbbacdbacabddadaacdbcbdaadbcbbabdbadddaadbcadbadccbbbdbaddbbaddcbddbbcdbadacccddbcadadbcbabcdaccdbddbdaadcabacaabddbcababdcbacdcddcddabadbdccabccacadaaadcbddbddbcdadbabddaacaccbdddbbcdbaacddccdbbbadbcabccacbadcbbbcdabbbadabbadccacaabbbacadbcddcccccbbbdbadcbdaabddcabccbaaacbacdcaabbcdccbcbaddbbddcadabbcdaacaabdcccaaddaacbaaaadbdacbadaccdbbdddcdcaddbcaddcacccdbabbbcbcdaacacacdcccccdcdabacbacbbddbcbbcbdddacaabbccbdbdabaacbacabdbacbacbbaccdbbacbbacbcbcadbaadaccacdbbbcbbddcddbcaacaaddcdbbddaaccbcabdcdbbbdbcddaabbcddaaacdaddaababccccddbcdcdababdcdbaaddbabbbccddccbcaccccabcccbddcadcbdbdcdddcbdabacacbdabdbaaddaaacddbdcbcaaadcbccaadaadccbcdacabcbcaabcccbcacabdbacbcabcbcdaadbccadadccbbbccdcdbadaacaacdacaccdbadcabbcdaaccabadacdcaaabababbaabaabddcdbacddbcaddbdcbadcacbbabcbbbccbcdcacbabaaadaddaaccdbadbcadbdabdcadcccacaabbcaadacdabdbaaabbdcbbbbdbcbacdabccdcabaabdaacbbbabdbcddcdcacdadccaddbabccdbaabadcbcbbaccdaddccdccccbddbccdacdcdabcadccabaadccabadbabaaabcddbbcccdccddbbadcbcabbabadaaabdaacbbdcbccbaabddddbdcaadbcdbcacacbaabadddbbdccdbddacddbdbbbdabcccbbcbcbdbbbcdccbbbbbabdbadadcabbaadcbdbdcbbcbcaaadbaccdcbcacbdcddaccadaccbdacbccbdcbabadbadbcdbbdadccbaacccdacccabddddacacbdddaaccccccabdbaaaacdcccdbcabdadddccbbdbaaddadcbdbccbacdbabcdbdbddcadcdaadbdcabddcdbdcddabcdaabcadacdcdbaacbadbbacdabcdacdabacabdbccbdbbadccbaaccadbdcccaabbcddacdcaaacddacdbacaccdddbaaccaadcccbcdbbddabcbcbddbdcdcbbcbcdcbbcbabbcabddaababcbbbbbbdacbcbdcaddbbacdacacacccbbbdacaccccddccabddddccdaddddbdadbbcbbdacadbbbcdbdbbabbbbdbbdcdbaddccaabbdbdabbddadaddacbcadcaddbdcaacddbddbabaccbdadcdadcadbabbbadabadddcadbdbcbbdcccdaadbbadcacdbaccacbcbdddbbbdcbdbdcaaacbdccbbbaccacadcddbacdbaadddddbacabbdcdbaccdadcdacadbbbdccbaacddbacdabcbbddbdcacbdddccdbabcbbacdaddbddaadcbaaacaaaccdcdbbdbdcacacadbcdcacccdaddbcbbacdababcdbccdbdabbddbcdcdabccbdbcaaabbbcccdabbacccaddaabcdbdbacccaadcbddaaacabbcbcbdbcabadcdbcadcdddadbbdbacbbdbcabccadddbdaccddcadcbdaacabbbdadcbcddbcdaadaaaacaddabcacadbacdcdbdbccdbcacbcddcbacbbdabbbcaabcacdabacbdababcbaadaaacbcaaddbcdbbadabdabcbdbdcdbdcadabbccbabacdddcabcabdcaddbddcadbbbaccccdabdcaaacdababcaabaacccbaaaadabcbcccdacccbcaaccacbddadbacbdaabbbacccbdcbbcadcdabbcaacaacccaddaacdbcabbadbadcdacabaabaccccdacdacbbabccdcdacacbdcbdcdcdccacadcdbccbcdadbccdbddbbbbaacbbddcaccbdbccdacaccacbbdccdcccbcbcbbdcdbdbdcddccaccadcdbdabcbaaccdabababcbabbcdbcacccabdacdadcadbdcbaacddbcbacddbdbbababcbbdaccdaacccacbbbacacaadbbcabacaccbabdbccdbbccddccaccbcaccbaababbcdbcabdccadbbbcbbdaccdbbdcdadddadabcbccbabdbadddddaddcccabddadbadbadbdbddbdbdabdccdcdccddbabbbbbcbacbcbbdbaababdaaddbcbacdabbadccdcdaabdbdcdcaacdddcaaccdbbadcdcacbababdccdccdabaddcbbdacabdbdbdbaddccdabaadcaaabddcbbcdadcdccccaaabcaddadaccdcaaadabbddaaadaddcaadcbdabacccddbdbccacdadaccaadaabcdccadbcacbbabaaaaadbbdbaabacbdcadbbbbadbaccacabadddbcaabdcbbddccbddbdbabaacabcdbbbcdacdcdacabdcbccbacbaccbdcdacbbcabcabacdcaccbabddddaacbaacbddabbdbbbadbaabababbadcbdacccbbcccbdabadbacddcdabacdaccaddaaacbdbbaaabcaacdcccacbdcdadacaddadabccacbdbcbbdcacacddccacaaadaccbbcbccbdcabbdaacdbcbdccbbacbcaccdcadcdaaacbddcbacaadacddadcacadcabacbccacdacacbdbccdbdccddaccdcabaaaacacccdabdbcbadddcbbabccabaddaaaaaaabcbdacdddccabacbdcddbbbbcdbccadbccbddabcadcabbdbbddddbbbcbdbdabccadddadbcdbbbdcdccdabcabbbbcdddcacddbaacdccdbccbddbaccbbbddcdccccdadcddccaaddacdaccaccbcccbcdcaacaacdcaadbcaabbcdabaacdaadadddbabdbacdcddabdbbcaaccacbbadccabddbbbdbbcadcaccdacbbddddadcbcbadbabcbbcdbccabbdcdbabaaadccaabcabcbdcdaadcdbcbdcbcadaaacbdaacbadabcdbbdbbcdaaabdbbcbdcbcbbaaabccbabadcacbbaabadcccbacddcbbacdbdcadbacddbbbdacdbdccaddbddcdccdcccadabbccddcdabdbaabbacdaccdcabcadacabcdbbabbbcdabcadcbbddbdbbdcacbabbddaadbdbdddccbadbbbcacddddaaabddddbdcdccabdddbbdbbdbabcdddabcccbdbddcccccadbccdcbbdccdbabcdcabdcaabbaaddcacacabadccbabccdcbdcabadcbdacdadbbdaacacddbbbadcbccabababbcbddcdbababdbbaadccbaacacbcdadcabbbcbddbccccbadadaddacddcaacbbadcdddbacbcbddcacdbdcacdacdbbdacbccaadcddcabaadbacacdbdadabadacabccbcabcdcaccbddbbdabadbbbccaccccdadccdaccdccacbaacccdaacbaaccadabcbaaadcadbbadccaaaabccccbadcbcaaadadcbbcdddabaadccdcbbaabcdbcddbbdcdddcbdccbaddacabbabacccdcaacdbacddbdddaaadbbcaccaacaaadbabacdddbdabcddacbcbdacbadadbaaabcaacdadcbdaacbabaabcaddbdbbcadcaccacaadcbdaaaaabcacaaaadddaabccccadbdccbdddbcadababbcdabbdbdadbbaadcdcadbabbbbabadaacccdccddaccdbdbddababcadbbccbcdccacbdcadbbaccddccacbabdaddcbbabcadaccaddcdaccadddcddbaaccdaabaddccabcdabddbdadbbbcdadaaadcddcbccacbaabccdbaadcddccdbbcacabcdacddaaddaccbaadacaccdaacaadaddaacdcddbabdbcbaccadbbddbbccdccdbbdadcbccbddacbbcacaccaacbcccaabcdbbdbbadadbbbabdcddbbddbbbbbaccadccabbdbdbbccbccddbbdbbacdddbcbadaabacadacdacbcbadcbacdaaabbdacccbacbbadccabbadbcadbccaccdbbaccbddcbcabdcaccaddadbbbdaccbbbbdaccadadaccccbaddbabbaaccdacadadaccbdcbcaaddcabddddcbcccdcddbcabaadbdbaacccbaddaadbdbddaaacbcbccdcdabdcbcdacdabcabbddaacadabdbcbadaccadbcccdadbccbaaddbdbabdaddcdabacaaaadacbbacbcdbccacccabacdbbdcaddadcdcaabbdbbcabcbdbdccacdacddcaacddcbddcbadccbccdaadaadbcbbccabdbccbcbbbcdaacadcdcdcdbcddcdbaddbbcbdbbdaabdabcdcacdacccaaacabdddbabbcabacdaaccdbabcbdaadbbbabddcbcabbabadccbcbaddbabdbbdccdbddbccddaaccddaabcdbcaabbbabacdbccdcaaddbabdaacbcbacdbaaadbbbcbbbdcdccdcdcdbbadbbdadbcdbadcbcbdbdbbdbabaadcccaadabbbabcbdbcadbdaaacbdcbcbcaabbcddcabcddcadddabcbaacdcadabcaabcdcaadaabcabbdbaabdcdaadaadcccaddddddcacdaadcdabdbbccddbddacadadbdbdbdccabacbbcbdcbaadaccacddacccbbdacaacacbdcddabdbaaacabdacbcbcbcbdaabbcbbaadbaaccaaadcaabcbaaaadddaadadbdbdadadbacbcdbcbccacbcbadaabbdbddadabdadcbacababbbddbdaacdbaacacccabddbacdcabdacbadbdaaadabdcbcadaaccbbcdbbbddccccacadbddabbcbbdbcddcabcaaabddcbddcdabcbbcabbaddabdddaaddcdcbccdccabdaaaccbdabddcbddacbbbabdacdacdadbbacccbcacbddcdbdcccdcacaadbbaadaddaacadbaadabddabbaabccaccdabcacccaddaacadbbadaadacbadcbbcdadcccbacbcdbbbccabaabdadccadaadbbbdbaaccdcccdbbcaadcbddcaacbbadcbaabbaaaaacdbccbccdcabbbbccdbdcabdddbbabbadbacacdbacbcdcdbaccdccabddcdaccdcadcdbbacaadddbddbaaacacacdccacbbbaacbadabdaacbddbcdadcdaaccbdabbcdcdcddaabacdcaddcdbdbdbbddcddabccadbabadbcbacacbcddbddbbdccccaddcaddbdacccadbbbdcbabbccdabdabdbcdbadaaaadddacbcccbaddbbdbacccdbdcbaddccbdadabdcaddbddaaabcdcadaccdadbbaccbddbdbbddabddbaaaadddcbddbdddabaddbdccbaaddddacccaacbacaabbccadddbddcbbcaaacadcbbabcbabbbbbacabbaaccdcdccacbbbbbaabcacdabbcbaaacddbacdcdddaabdcacadccaabcbcdcbccadadacbccbddddbddcdbaddcddcacccdddcbcdabcacdaaccbcaaadaadcabcaaabaccbccabbbbaabdaccdbbddccbacbacabcbddacdcbaabbadbdbccbbabadbddbbbbabdbbadcbabcddaccbcbdcaababadbddbdcccacdbdcbbaabdbcdddcbcddbaadbaabddcdcbacbacbaacacbddddccdbdcdbdaddacacadccacabacaaaacacddabadaadbcbabbcddcbcdbdbadabccabdcbcbdaaabcadbddcddaccdbcdbbbcbdabcdddcbcdaaabbbabdbcbdcaabcadacdabccdcccbbbcaacccbabbbbaddaddacbaddbbcdaabdcbdcbacdcaadaaddcaabacadababcbacdbddbadbdbbbddadacdcdcddaabbcdacbacddccaacaababcababcacddcabcabbcbdaccbdbcbabcaddcbbbbdbadddcabdcbdcabbacccbbaacbbddabdbbcbcadbdbdddcbcdcdbdcaaaadaaadbcaabbdccdaaabcbaacbaaadbdabdbbcdcbcabcaacbccdaccaddbaccabbcbdaddbdbaacdadacdaacddccbcddbaaabccdcbaaacbddbdadbcddaccbcaabdbacaddbbbbaaaccbaccdabcabcccaccddadacbcacaccacccadaaacdadabddbadbabacccdabbcddadacbacdaabdaddbaaadddbabadbbdbbddcccbbccacaacaaadcdcbacdbcdadadcddadcbabdbdcaaadbabdbdbcacbddbacbbdbabbcadccddddcacdacdcbcaabcddcbabbabbbbbabdabaacacdaabddbccbadbaadabddbbdaabdadbdcbcdcabccabcbdbdddacbcbacbbccacddccccdcdaddcccbcaccdcdcbbcabdccddbdacdbccaacbccbcbbbcabadaaddbdaaaaacbddbcadbcbaacadcccddaacadbbbcbacbcdbdaadadbbcaadbcdadbcbbcddcabaacadcdccabcadcaaabaacdccdcadbbbdbddbccbcbcaaabdbdcadccabcbbbcbaddbbadccbdacdddaadcdcaabaabbcdbadcbbacbccbbaabdddacbcbbbdaabbcabdccdacddbcaacdddcbabacadaccdcbbbddadacababdaacbcdddddabbabacaabdcbabcaadacbadcacdbdbcbcacbbbacddcbdbdbdcddccbddcabdaaaacdbddbbacddbddccdaddbaabcdcdddbbdbadbdbaabacaabdcadcbccadcaacbcbabcdcdbbdddddcbdbcabddcddbddbbbbbcaababacddbdbdacadbdadddaccbddbdcdddaccccdbccbcdcccccaccdabcaacdbbccccabccdacdadccddbccddddcacdcbddccbbddadbccabbccabccadabdadbaabacaabcdadaaacbdaadbcbdbcbabcdadabcabbbaadddadadcbdbbaabdcbdacbaadabaabcabdbdcacbbdcabbcbcbadbcbddacbcadbdbaacbbaadbbcbcadcdacbaaaccabacdbdbcabdcabdccccadabbcbcaabaadccababddddbadcaaabccbacbaabdbcacdbbbabbbaacccbbaabcaabcaccddccadadadbbacbbadabbcccadbabbbacbcabcbbaacbbdccdbacaaabcadabadcdacaacadcdbadabbabadbabdaddcadbacabadbcacddcaccaccbccbdadccdccdabbddcbacadabcaddaabbbaaaddabcabbdbbcddbddcbcbcaddcdbdabdaaaccddabcccbaacdaaccacaabcdaadacabacbdacbcccdabdaabdccccaaddacccabbdcdaaabcdcbbcbabbccacddacaaadbdcdddcdacabadacaabcabababdddcabacbaaacaabdacbdabaacbadcbdadccaccacdccaaddaaabcabcbcdcbadcaddabacadcdaabddcaccabcbdadcdbbdcacabdccbdddcacabddaaaabcdcddabcaccdcbddadbabbcaccabbcadaadcabbdbaadccdbbbabdbdcbcdcaddbacdbabcddacbcaaddadcbdabaaaadbbdcdaddadbbacacabacdabcbbbbccbcdabbdacbdccdcadaabcccabcbbddddddcaabcbbdabbddbbddccddbdabbdcdccabbdcaacaaddaacabbdcddcbdccbbaccddcbdbdcbcdcaaadbbcacbacddaddddadabccdcaacdaddccbdccacabbdcddcbdccaddbdacdbdcbbadabdbbbabdccabcbbbbbdcbcaaddabdadcaadcbbcdaaccdabccdadaabdacaccdccadbdadcdbddcbaabcdaddbbdccbacdcadbdbcbcbbcdcbdbaccbabbcacbacdabbbbbbdcbcccddabaaaaaaccacbcabcccbbddaabbddabcadbbcaacbaabdbbcaaddabadccbdcabbbbbadbbddbdbbadcddcbdddbdaacbcaabcbacaacdbdaddcddbadadbcacbcbcdaadcdabddaddccbabcdddcabbadabdacdadbbdbadabababcdbaabaddbdbdacbcbcaaccccaddcdaaadaacadbadddbcacbdaadabdcdadbdbabbabccbabbcaaacdcdcbadccaaccccabababbacdcbacaabacddcccabadbbaddaacddcadaccdcdbdbbdbdbbcbadbcdddcacdcbdcdddddcdbbdadadcbbccabadbcbaabcadaddacacaaadabdcaaddbcadbbbbbadadcaabdbbcdcdaabaaaddbcbccbdbcabdbddaccdcabcdaadbbbdcadbaabadcdabcbabaddaddaaaacdccaaaddcbacbcbcbbbdacbbdbdbcbabaabaacdacabbaccacddbdcddacbddaabdbbcabbbaadcdddabcadacdbacadabadddccaabbbdaccbcdcacdbdbdacdbabbacaddabcabdcacdaaaddbddcbaddbbccbbcbbdaabbcdcccccdacbbabbddddabddddddcbdacacbaccaabbcbabddcdcbdcaadadabdcbccbacaabdadcabbdddbadcdcbdccddbbbccadcbaddadcbacdbcccbbbcacdcbdabadaadbdbcdccdccbcbdccbcbaacadacccdcccacacbadddabddcaabdbcbbbabcbbcccbddaadacbdaacdcccbdcdbabccdbbbbddbbbbcbbdabacbaccddabdabddbcadbdacdbacdbdcbdbbdcdadcbadbcbadbbcaaaacbadcccccdcdabccdbdaacddadccbdccdddaccadcddcacbdadbcabcaddcbdabaaaaaddcabcbabadacdacabbcdbbccdbdbbbdabbbcadddbadbbdadcdbaacaddbbacabcababcbdbdbacadbadbdcabddcdbccabaaccdcdcbadbbbaaacddaddacbdbdccdcddccbddcbdcdddacbddadacbcacaaaaccbaaddbaccabdcbbbdcdbccaaccdcddacdbddaaaacdadadcbabacbbbabcbdacabcddbbcaabcbcbbcddbdbadbbdbcdcaaacccddbbabaabdbdbbddcccbcaddbdbaacbaccbbcdbadbbbcdbbdddddaadaacbbbccdacabcbdadababccabdaaccddbbbbcbbdddcdcadddbcbdbbaaacdcbdabadbddcacdadbdabdbabddbbbadbaddbaaacbcdbcbadbcbadcadabdbaabaaccbddcbcabcbdabdcbaaabcaacdabaadbdacccdabdcbbdbbbbaabcbdbababbdcbcabdbbaacdcdbadbbdadddbdbddcdabcaaaaabbdcccdcabbbadcdccdbbbbccdbaadacadbdbbdbabccdabddbbabaacdbcaaabaabdbabdcdbaaacbadccbcdaddcdbadcaccbdccccdcbcbccbcaabadcaaadbcbbbcdbaaabcbabaaabdcbabcbcadcabdbdddaaabccaddbcddbcbbacdbcdcadcbadbccbbdcbbcabbadccdaadccbbdbbdbbcbbddabcbbcbcbbbdbccacbdaddbbddcddacadcccacbcaadcabbbaadddbaadbbadbdaabadbccadcaabccccbbacbaddbccaabbdaccbcaadacabaabdaaccdabacdcaababbbdbcbbccbaabbacdcaabcbabcdbdaadbcddcbdcbbcabadaccaadddabaaaabaddaaaacdacaddbaddcbccccccdddccabbbccdbccbadbabdbbadabaacaddbaabccabdcdddadacabbaabaacaadcbadadcbdaccabdbbbbcacabcacbcaacbdbadabcdaabdabccbbbcbcbbadddddcbbddcdbaadaabacaabdcabaabcddcdcadcbcdaccaddcdbbdcbcbddaadcbaadbbbccbdcccbcabdabadaabbbdbdaccabbdacbacadbbccbdbacaaddbabbadbabacdaabdcbccbbabbadcdabbcabccbbdadcbadddddbcabcccdddacddccadadccbabbbbdaabbcdbcaabdabdadcacdcdacdabbdabdcabcacbcdbccbbbbbcbdabbbacbccdcddadccbdccccdbbabbdddaaadbdadbbcaddacccaccbabacdbbcaddaabadcdddcbbbcabacdddbcdddbcdccbdbcbcddcabcaabdacbdccdbbdbaaaccbdcddbcdcdbaacbcabdbdbbddbaabcaccaabbbbdcbdbabcaacddbbdcdbbcbccdccccdaccbbacdaddcdbadacbcbdaaccddbcdbcaadabbacadbccbcbccbabccbdddcbacadccdaccbdcaadbaacaaaabbbdbbcbccbcddcbbbadcadddaacbcdcbdadccaddddadcbacbdcacddcccbbcbddadbaccadbaaaadcccdcabbcbdbbcccdabbdcadaacbacdbacbadddaddacacdbbbbbbdcbbbaacaccbdaacdccddaaacdbbcbdddabbcbabdaaaabbdaaaddaadacdcdacbbdbddadabdaadabbaabcaabadbbacbdabaabcdadcddcdbbcdccccbcacddbaabacaddacacdbbabdabacaaccbdcbcbdcdccdbadbdcbbbaccdaddcacabbcbcaadacbbcbbaddadbadbbcaccadcaaaddbabcaddcddcbcaaaccbabbbcccddcbbacaacbbcddccbaadccbdadabdbdaaccbdbbdaababaadaaddcbccdddddaccbaddcabbcdacdabddbadacccdacdccbcbaaacbddabdddcdcbcbadbcbaadcdbcabbdbcaddbbcabbbbdcacccbabacbaaaccccdaacbbbaacdcdbccbccccaccddbcddcdcadbcdadacdcaccaddbbabcbccbadcdbdbacbbcbbbdacabcacabcbbddaabbdbbccbccccdbaadaacdcddbbcccaccacdabcacadbddcbbacabaabdbcdbabccbbabccbcbcacdccccbcabcaaaabacaaacdbccbbccddabdcacddbddaabcbcabcaaccbdbbccdabdbccbaacbcccacabbadddbdccacccacadcacacbbdbaaaaacbcbccabbdbabcaabbcbaccdadaadaacadbcdcbbcabadcbbbabcdbaaaaaabcabadbaabaadcabcbaaddabbddbccbcccaccbdbbdaabddacaaabdcabadccabdbbacdbcdcddcccbabddbcadddddcdbadcabbaabbaaaacbcccacdbbcccabcdddcdadbdaabddbdaacaabbdcdcddcbdabdcbaaccaddddbcbbcaaddacbcdcddcdddbaabdbdccdabaaaddabdadcdbacaabcacddadabadcdaacccbdaabccdadbddbbdbbbbbabbacbcbabcabcdcccadbcababbbdcdabdabddcccbcacbadabababcaabdcdacaaadacccabccddbabcbdadaacdbadccdadbdddbaacdccbdccdababccabdbdcbdaababdaadccdcbbdcdcccabcabbdcaadcdbdadbbdaccabaabdcbcbbcdacaccaddcacbbdbcccaaadcadcdcdabddaababacaacaaadcbcbbcaabdbdcbabacdddbcaacdcdadbccbcdacaacabdccabcdaddabadcaccbcbcbcabbabbdcdaddcccadababccabdaacbccdcabcaadaabcaacabaadacabbacdabaadabbabadbadbdbdacdcccaccbbabbbabdccacabaddcbddcdabcdacbcabdbbbbdacaadbdbcdcdbddcddabadcbbbccaccbddbabbadbcabddbcccccdbdaddccbdcdccccdbbbabdbdacdddbaabaccbcbbdaabbcbcbadcdcabbaccbcdacadbacdcdabbadcbbdcdddcacbadddcbcdddcdcabbdaccabccbaadcbddaccadcbacdaaccbcbadcacddbdccccdcdcdabdaddadcbbdacddcdbabadccdaccbadcbcaacaabdbcabacacacdcacaadddadccdbadcbcbdcdabbdcccababbbccbacabaddbbbdcbddaabdbcdcaccbcbabaccbabcabbabdbcacadcbcbbadcddccdbbcbdbdcccdbbbcddddaacddacdcdbadbbdabadbdcdbadaddaabbdbcddbadcaacdddaadcadbcdccccacaaadaddcdbcdadadbdcbbdbcdbcbcbcabdaabdddacacaacbbbbdcbaccbbbcaddadadccdbacabdbdaaccaacadcbacaadbbcadadcbbbabacbadccbdaadbaddbdcdbcdaccaadcccbdbababbbbcadbbdcbcbddcdcddbdbcbcbbbddbcdbbadbddbcdaadabdcbabbbbbbabccacdcacdadddaaaaabddbcddccddabacddbdcbbdcbaadcdddbaabdaadccddbcbcabdbababdcbbbbabacdbccbdddbbbaaacaaccaadcdcbdcaccbaabdbbcccdcccbdddcadcbacbdbcacaddbbdcaacdacbbabaadcddcaccbcbcdbacabbddaabadaccdcbcbadcaabadbaccdabbbcbaaddbacbdcadcbcdcbbccdcdacbaaabddcadbacdcdadadcaccbbccadbbbaaabbdcccaaddbbaacdaadcadadbddcdaadadadcbcdaaaacddcccdcbdbbbddbabdadcaadbbbdbcbcbbbdccdbcdcdabaaddbacbcabbdbddbaddccdacbdcdddacbcbaadacababdddbdcdccbdcaddbcddddbddccddabccabbdbdbcccdbadacccabbdaabaaccdddabdbabcbdcbcbddadaacaddaabbddcdddbadacaaacadcdbaddddddaddccccbaaacaddbbbadababdcaccacbacbbccdbbbbabaddabbabbbcabdddddcbbdddddadddaabbbdbcbcddacbcbbbaacaacbaccbcaccadcbdacaddbbbbddadcccbcdbcdbdabdccaccdabacddbcdadaaadbacdcaccbbbaddbdabcdacdddcacccdccbcaadbbdabaababadaddcaccaaaaadacababbdabbcbacabbaccbbabcbdbaacdccdaccbabdbaccaccccdccaaccddacabacacddcdaaadbdabadbadcaaabdcacacaadcbaddbaddddddbbcddddbcbdadbdbadbaadcbacdadcaaaabbabbabaabdccdaaabbdaccabdcddaaaadbbcaacaaddaadbdddbccacdabcbaaadcdddabbbaabdacabbccdcddabdbacddabbbcdadcdddcdabcaddbccbbdacdccaabbbabacbacadccccbadaaabcaaddccbbaaadaadbabbccbccadcbdbcaaacacaabdcbdacabbcdaadbbbcacaaabdcabbbdcdcbbbddbddaccdcbcdbcabbbdbdcacbbcadcdbcbbaacbabaacddccbaccbacabacbbaabdbbbabdccdbccdbcbddacbbbbdacbacdcaacadcbcadbcbadccdaaaddaabbcadccacaaacabcdcddabcabdbdcddbbadaacacbacaabdbbacdbbdccabcaabbcdaddaaaddacdcbabbbdbbdcbacdddcbbdbcbbdacddcabcaddbbbbcadbcadaababbbbcbbbabaccadcbacbababdacbbadbaacadbabcccddcadcabdbcdddcadacadcdacccdbcbbdaabcaaadbdddcbbacbccdabcddbbbcadbabadcaddcabbadccdaaadccdddabdbabbbddbbcbcbadbabddaabbddabbccaaabcacdabccacccdddaadbaccddbbdddcddddaacacdcbccacbabbccdbbddbaddbadabcadacacbbbccbdccaccdbcbdbdcbacaacbcbbaaaddcdcabcadabbcadbaabababdbaaaccddcdbbcbdaaacbccdcacccdccdacdadcaaabccbaccaaacabddacadbaacdcdbcadcdcdbcdbdabdcaacaadcbddbbaadcdbdcbadccbbbadccaabbdbaaaddaadbabbadddbdcddbbbaddadddacdbbbadbdcacdabdcdddcaacddccadcaccaadddbcaacabddbdacbbccdbccddaddadbababdabcdbcabcddabcbddddbabdcadbbcdacdacdaddbbccbbdcdaaabcdacbbccdcbacbaadaacacaaccccddcdacddcdccaddacbabdcbabbbaaddaabccaabddcdcaaadaacbbbccbbdcdcddbcccccabdcdcacdadbadbabdddccadbddbcabbabdddccdacacddbbdaddbddadbaacadacbaaacbdaccbdbcabdabbbabacbcbcbaccbcdcddcaccbbacbcadcaacadacdcbbccdcacbabdbbccdcdccbcbbadbdbbabbacdbacbccdcbcaddddddaccadbbaaacddccdccacbdbbacdacdbbbcccbadaacbddcbbbcaabcdbbddddaabaadacbaabbbccaabdcbcabadcdbdbabcbcdcdbccdbbbcdadcbbbddbcdbaddccccacaddadacabaddcbddbdccdccaaadddadcadccbccbcdaacdadbcaddddccbbcbbcdadcdccabdacabcadcbccdcbacacdabbbaccadacaddaccaabdcdbdbaacbaabddabcbbbabbbcabbbcaabadbbdbbbcbcacdbaabcdbbbcccaadddccddacccabdadddccaaacccaadbcdaacadaadcbbdacbdbcbbcabdccbadbbccbabbddddaadaadcacabccdccacbdddcacaadbdddcbbdbdbbdaadcddcdabbddbdaddaccbbabdcbbdadbacddacddcdbbabadbbbaddbbaabadaddadbaadcddaaaabdbdadbcaacbbcbccbcbbaadcbdcdbacccccbaaacbaacabcacbccbbdbdcbbdddddddcdcbbdcbccbddcdacdddbdadabbabdccadadadcbdbacdcaadbdaacbcccddabdccbcbdbcbabcdcbbccdcacbcacdabbbcabbddddbcbbaaccbcccaddaccccacbdacbcdbbaccdbccacadacbbbbbadcabccddabdcbdbccaccdaaddcdcaadcaabdabdbbaaadbcccbdcbaabcabaacdbdccbdabaccbdacbcbbadadcbcaabbdcbabbbbcacadddbcccdcaaacdadbdccbcaddbdcdcbdddbaadbcbadaacacddddbbccdacbacbdbaabacbaaabcacbccbbbadbabaacdbbaccbcbabdacacccabacaddddbbbddbddccbbababdcadbdcdbdcdbcbcbbbbdaccdcbcadbccaaddbcbbcbabddaddbbbadacdacdbacadbbbbdbbadcadacdbcabbdaddaadaaddacbacababcacabbacdccbadaadddaaddcddacaccabdaadbaacadbcdbdcaacbdcbbdcbdadbadaccaaaaaacdcbadabbccbcbcbbcaadbcbccddcbbbbcdbdcbadcbadadbccdacccadcdbcdabcdbaaacaacdacbdaabdcddaadbaadacbdaadcbdddcacadbabadbcbcacbdddcadbabaacabdaabbbdacbcdcabbadcdacdbdcdbacacbbccaadcaacbdbdadbccaacdcbbcddbbbcaabaabdccbbcdbbbadcdcddccdbcdddabddbadaddcacccdbdbbcbcaaabbdbdbaabacbddddbdcccdaadccdcabcacaccddbbadccdcaddcbaadacbcdcaddcdbcccaadcdbcdaccacacdcbbbdcacadcddbcdbcbabbdcccdacdaaacadbdacbccdcdabbbdbabcbadbcbcddaccbdddddbbccacdbddabdacacccccdaadddcdbabadadcabdacbdcaccbcbccadccbbcdacbcabbcbdcdaccddcacddccbabbaadcdbbbdabbabccbbcacbabbdbadadbddcdbccabbabababbdcadcbcdbadddcabcccbddacacbcdacbdbbaaacccdbaaaaccaacbbcacadadbacabccabdaddcddcbaddbabcbabadbdddcadccadbdccbbbdcdcbadacdcdcbbccddbbccdaabddaadaadcbaabcaaabadbacaaabdcccbaccbacbadcacadddcaacabcbcabdddaacaddbacaddbdbcdaabccddbaaccabaadadbbaabdbddbbdcaccddcacdaacbbbdcadccbacacdcdaadbccbbadacddccbccbabbccbbbbccbdbadbdbddbcaabdcbabcbccadadacdaacadabddadddadabdadbbdbbbddabdcdbccdabdbbacdcdaccacbddbcdacabbcdbcccacbcdbcabddbbbcacabaacddabbccaccbdaacccddbbcbcbadbdbbdcaccbccddbadddbdbcbacbcddcbcbacbcdbbadcbddcadcdbbcbdddabcbdcbabbaaddddacccbaabcbdabbdcaadabdacbdcdbacbaaccdabdabbdccbbccaadacdcabcabbadddcccdbbdcaddacaaaadbdabcadacbdabcbbadcdddbcbbbcaaabdbccacddacbbddbadacdadabbdcbdabdddacddcaccaccdbdcdbdbacaaabdbababdbabbddcaadabdbcccadcabcdccadbdbabdbacdbadddbdbccacbbacccadcccdadabbccbaacdaaabbdaacdcdcbdacaacdbcacdcaaccdcadbbddcdcaddbddaaddabcccddcbddbaabddcaccaadddaacdcdcdacaabaadcdbdddabcaddbbbbbcaabbbbcdccacdbdcaddacaadbaadcdbdaddaddadaaddbaabddbacdbdbabcdbbccccdbddadbcbbbccabbbacdcabcddabdbbaacbdcacdbddbbdcccdcbcdbbabbccdabbbcdabcbdabdabcbaacdaadbbdcaacbbbaabdaabbadccdacdadcacdbacabbbdbddcdbaacccccbdbdbaadaabcbcbbbcaddacadcbadcadcbcdcddaacdcddcdaacabcdcbcbcadcbbdcbabccacdaaadcccdcbdabbacbacdcdbdcbadcacabcacbaadbcadcbaddcadbdaddbddbbacbcbbcbcccdaaaccacdbbacaccaabbadadbaddcccddbbabbabaacaaaddcaccccacabcdbddcbdbbddabddcccdbdccccadabadacadaabcabcabcbdacaaccbddcabddccdabbbcbbdcbdbbabbaaaaacacccdcdbbbacdbccdcbdbaacbdccdcbaaabdcbaaacacadbacddcdddcdccacdbccacabbbabaadcccdcabbdaacdcbcadccacbaccacddddadbcccdaddcccdbcadccaacabacaaacbdaccdaccdabddaccbdbcaadbadccccccbbbadccabbcaddadcccaddcccabaabdcdbbbbdbdaaadccdaddcdcaccabadaccadccdbcbbbdddddbbdddbddabdaacbdcccaaaacdabadcbbdcbbadaccbdddddccaadaabddacacdadcbaabcdaadbddbbdbadbcbaddcbbadbadddbabacdacdcdccadbcabdccadabbbbbabcdaaababbdacbcaddcbadcccbbbdddadbabbcbccccdadaddbbbddccddabdbccbddbdcbabbccdcdabacddbddccbbaccdabdddcadaccccdbbdcdbcccbbaabcadbdbcdcdbabdbbacddacbcaaabcadbacdddccbcbcbadbbcdacbabddbcdcbaabcbdccaccdabaabdaabdccbadbcabadcaccbdaacbddacdbbcbdcbdbdaccdccaadbacddadabbbdcbddacbacbabbdadabbdddbcadabccbcaabacdadabcdadbcabbbcdcccdcccdbcadabcdbabbcdbbabbbacbabdadbdaddbcccdaccdadbcbbcadaccbcacccdaccbabdaaabbbadcdbbdaccadbcadcbcadcaaacdcccacddabdbbbdabadabccbacaaddcbdacddacadaaaaaadcadaddbabdcaddbacddbcadbcabbbbbddaaadcccbdcbccddcbabbcbaccdacaaaaabdbabccadadcacabcaddddabddaacacdcbacdcbacacddaaaacacbbdbaacddbdbacabbacabcacbaacbdcdcccdbbddbbcacddaadcddadabbbbaabcabdcdbbaabcbcbabddbcdaccbccadcbacdaddcbccdbccdbccccadbaddcdabacdcbcdcbdbccbaddbbbacdbbabcdddacbcbadcbcbaacbdacabccacaabcdccbccddbaadacaddadcadcbbcdacadcdbdacaccbadbacacddacdabadccbcacaddadaccccdcacdadaaabcdbbcdcdbcbadbcdbdbcbdabbabadaacccddbddcabcbcccbbdbcacbaaacabcaccabddcdacaddddbbbabbcdcabddacabaaddadbdbdadccbcdbabaaadbbbcdddcdbcbbaddabdbccbcbbcdcbadbddcabaaddaccccadbbdcbaddbddacdbcddabccbaaabcdabcacdccaaadabcadcdcbbabbcadbdacbabbcccbccbbdcabbcdaccaccbccbaaccaaacacdcbabcdbdacbbbbdbcbccbcbcbdaaccbbaadcdbbaccbbddbaccddaacbdbabadbdbdcaaccbbbcbcbccdbcdbbcdbadcdddababbcddcddccacddcaddcaddacbcbcbacabbbbadbddccbcaadddadcacdcdbabaaccdbcbcbdcdabdcabcdacbdccacdcbabbdacddaacaacbddadadbaaaddacbcbccbacbbbbcabdbbacabadccadbdcddaaadddcaaddcdddaaaababdcbbcdddbdbdbadcdacddacdbbdbacbcdccaabdaaaacaadacbbccccadaabbddbccaddddbccabbbacbdcabcdbdadbddabcacdbddbadabddbdcbadaabadabbcababbddcabcccbbdcddcddcadcbadaadcbdacddcabcacdaaccccbdcabcabbbacabbdabcbcddcadacccdaccbbacaacadddbdacdadddaacdcbbbadcdbbcabbaacdaccdcabbccabaaaadbcaabcbcccdccbcabdbdaaaabbadcdbabdadaaacaadbdbcddcdccddbcdabaccdbbcdccdbcddddcccccaccdcccbdbdbadbdddbacdccaaddddbacaaadacdcdaabbdaccaabdccddcdbccaddcbbbacababacdaaacbcdbdbbadddcdcdcddbbadddaabcdacdadddabdbdbbbbcdbbdddbccbbabbcbadcabbcbacbadacbbacbbaacabdcbadbbaacdddcdcababcadbdcaacddbababcbaadbacbdbaaadbbbaacbaaccaaacbabaababbbdbbbcbadababaacbaacdbddcadbcbcdcabaadbdaaaabbbbbcabdcdcabbdcbbabbcbddabdbadbacbabaacbbadbabdcdacbabbbdacdadbbacdbcdcccddbddabadcaccddbaccbdccabdbabbcacaacbcacdbdbccbcdbcbcbbabbcbcacadbcbcdbacaddabbddaabaaddadbacaaacddcdbaacdbaacddcdaddaaccdabddbaabcacbddacdcabadbadddccbcacddbbbcabdbdbbbcacdaadcdabcaaacbbbddacaccbcbbacacbcdbbadadacacbbddbadbcccadddccaacbdabbacccadddabbbcccacdaacaccaaddcaacdcdcdcadddbdddbcabdbbcbaabcabcdbaababdcacccbaabacdabadbcbabccabddccdcacccabaddbbcacbaccdcbddccdbcbbcbacccbdcaacdbbbbcdbcadbddbcdbabacccddcbddcdcbaaccacabdcbacbaabcdcaccbbbcbbbdacbabdadbbcabaabdcdbcabcabddabcdccdddbbbbaddacdbcadccccaaabcacacabcacabcdddccccacddddbadccaaadccddddabcbdbcdbbbdcdbadacacbcacacbdddcdacacddadbcdccbcbabbcbbbddbdaaacbadcddcccddbacabaabbadbaccbaccaccdcdabbcacadbcaddaccadccbdbabcbabdbbabdaaaaccaabbcdcdcdbbbabaccdbcdcbdaccbaaadbbacdababccdabdbbdaadbaaaadbbdabcabaadcacaccadcdbdadabcabbdbccdddbbbccccaadcdbbacaaadcbdcccdadbacbbbabdabccabaacbaadbcddadcccbacbbaadbbdcacaacabadcdadadcaacaacbdbdaaaacbdcaadacabbbaacadcccbacdabbcdbadadcbdabababbbbcabdbccaaccababbabaaccaaaacbcccbadcdcbbcbacaccadbdbccadccaadddcacdacbdbcacdccbdbdbdbcbaaccbdccddcacdabccccabdbadadabdabbcbbabdbaaadcccbbacbadadcacbcccbbdcbbbdbdaccdacbddbccaaddaadccacaaaaaddacacbdacbbdabbcdbbbabaacccbccccbddbabaaccdbddddcadaaabccacbbacdcdccbdaabdddddcdbcadcbdbbaccbcdcddaaaabdbbcbcbbbdccacccaccbbadccbcaaabbbbbcbcaddbaabdcabdaacddcabbccddacddbadbcddadddbcadbccbdddbbcbdcaaddadbaacdbabcdcaddbbbbdcbcabbcabdcdcacacddabcdddccccbdcbdabcacadaadabababcabaabdbdccacbaadacbcaadbdababcbbdbabdabbddcacbabdccbcdcddabbccbabbaabcbdaaababcbccacdbdbdadbadcdbdddbcaadaccadbdcacbabcbbdadaccdbbcaddabcbcacbbdcbbcaadbbdaacbbabbcacaaacacbdaaccabaadabaabdaacbabcaabcddbdabcaaddabbbbdccbdaccddaddacbbbdadcdcdcaabccaabadcaadbacdbbbaccaabbcdabbbbddcacddabddaabdaccdacbbadcdaabadabaaacdbaddaccbbcdbbadddbdccbbaadababdadbabacdadddcacabbcbaabaadbaaacadbdbaadddacbaabcacacabbbdacdabadbcbbaabaacaaadcabcbcaacbadcabaddabcabbdbadcbcbcaddbcdcbacadaaccbabacccaabdcccabdacabcacbaaccbdcadcbdbdbcdbddadaadccdacdadbbbcccbdcdcdaddbbbbbdacbcdddcabcaacaaaaaacccacbaaacadbbcaababdbbacbaaccbdabcacbdaddbccccdaaacaabcaaccacacbcacbbdbdbccccbbcdbadccbaadcaccccbbdcbcdadcacdadcdbdcdbcdcbbccadcccdbcbbdcddbddcccccabcbbdacdbbcdcabacbdbbccbabcabcdabcbbbdbabadadbababcbaadababddcdbbdacbbbdadaabbbcbcacddabbdcadaabaabdaddccbcdcadcacdccdddadaaacabaacacccbdbcdcbddcbaaccdbbbbbdccdadacccbcbabdabadabddaabaacaccadddbaadacbcbadccbbdddddbccadaaaadbbbaacbbccacacadcbadacabbccabaacbaddbcbbbcdcadaabaddacadbacddbbcaabbcadbbdbbbbbdbbdbcaaabcddbcadbbbccdcabbbbcbdcdaddbbaabbacbdcacdbddbbbdaabdddcddaacacbaabddcabaccadccdcdbdbbbbbdbabaababdcaadbaddbabcacbcbbbddbbdbdcaacdaacdacacddcbcbacbadbbbbadbdbbdbacccdcdcdcddaaaabcbddacbbadcbacbbdacadddadaacdadacdaaccbcccbcabcadcacddabaaacdbadccbaabdcdcacdabadaaacdccdcbdddcdcabbdbabadddbacccdaabbccccbbdcacaabbacbcbdbacdccaaddabacccddbabaaabccdbbbbcdccadcabddbccddbccbaaaaacdabdcdccccbdabdbcbdaadbbbcccccabcbbcccaccbadcbbbbddbbbdbdbcadbbcdacbcdbcacadbbccddacbcdbbcbabdcaccbcbabddcdadcdacdcbaddccdcbbbcbadddadddbbdcbbcbabcbbaccbaacaaaacccdbccdabbbadbddbdaabbbbabcdcaacdccbadcadddcabaaddddacdaaabdcbdcddcbaccbcdbbaabadcaccbcccbbbaaaaabcccacabaabdbabaaddbcbaccaaaaaaacdaccacbcbdccdddcccbbcbbabdcccabdddbcbdcdaddddddddcccbbdbddabaacbadbdabdbbaccddcbddbcdbcbacbbccbabcaabdcccadbccdcddadaabbdaaabaaccbdbdcbddbcabbcbcccbbaaaababbdacbbccbbbbcbddacbbccdbbaabbbabcdddcccabacdcdccbbadcbdbbabbababcaadaddbaddbcbcdaabcdbbbacadcdcbbcbbaddccabbdbaaddabcabadccadddaabccbadabddccadbdbbccdddaccdcdbccdddbcacacabaaacbbdbbbdbcaddccddbddabbddbccbbacacaddcdaabadbaacdddbccababcdcabdcdbdbddabdabdcccccccadbdcddaabdaccdccacacbdbdbabbccccbbaaabccdccbbacdabcbdbdbaadacbacdacddaadccbacddcddbdabccbcacacbbbbbaaccdbcbdbacbddbbdbcccbadaacbbacacadcaadbcbddccdcdaddbdccdcdacacbcdabacdbbbabccdcaaddcbaaccddbbbacbbcccbabbaabbcddcdaacdddacbaddcccbbadcdddaccdacddbddbaddcdaccccdcaadcbcdcabdbabdaacbbacbcdddaacdcdcacaaccbbbcdaabdbdccbdcdbcaababacbcccdabbadbbbacbdbadaccaaaabcaddddddadaabcccbbdcbabaadcabcdbaacdbbccdccaaccddadbdaddcccbbbbdddcdbbacdcabbdcaccdddcdcdcabdaaabbcaaaddcddcabbaabcaabddaacbcabcacbbabdbdabaccdcccbcdaacaaddadabbccabcdcbcabbcdaadbbccbcadbadabbaadbdcacddddbdbbbdcdddacdabaacdccdcbdaddcccabaddbcabdabdbcbccbdccacabccaaadabcdcababcdcbabcccdcaacdacabacdaaacacdbbdabdcbacadacabadcbabdbdadddcabcabcddbbddcbdccabdaadddddccdacbbbadbbcdcdcabddddbcddadaddbddbdbdbcaadaacdabdbddbcbcaabcdaaaddaabbdcdbcbbcbcadacaccdaabadaddadbaabcdadabcdbbadbaaaacabdcbaddaaccddcddbcccdcaacccbadabdaaacbbacabbcaccbaaddcabdbddadcbdcbcacbabcadcccccbbaaaccbaaccbadadaacccaacbabdabcbbdaadcbbdcacdbccaabaabbaadaaabddaccbadbcdbcacddcbcaadccadcdbddccdacabbaccddaaadddbdbdbcbbddaaaddbbccdabbabddbaaabbddcabacbddbbcbbbbdacddbbcdbaccccdaabadacdbcdacddadbcbdbadabccdaccdadbabbbcaabddaccddbcadbdacbddccdddbaabddcdaabdaaabdbcdccaadbdbddacddcbdbacbdaadccdbbddccddbccdcccdbbbcbdccbdadcacaadcacccacacbadcaddbdabcdabbcdbddcabdbaabaacbbdcbcbaacbaadbbdcdcdbcbabaabcdabbaadbccbdbddcbdcdacadbcdaccadbdcdcdbbaabaabdcdabaabbbccaddbbacddcaabbcacacccbddbabadbdddabacdadcdcadbcccaccbdadcbacccadbcbdcbccbcbadaaccbccccccdbbccbddcacdaacccbbdbddbbacbdcccadbbabddcdbbcbdcbbcddccdbbcabaabdbaddcbbbacdbaacdbcadccddcbdcdbcdbdcaadccbbddadcabbdacaaddccbddddbddaacadbdcabbcdbbabdabdaacadabaadbdbcdbaabbacdaaddcaabbcadbdbabcacddccbdabbaddaadabbabcbccadadaacccabbbbbddbcaccadccadaadccbabaaadcdaabbdcbcddbadbaaadbcaaaacbcdacbbacddacaaadcccbbbbaccbcadcacbcdadcacabacbdcaaccacbccddabcdcdabdadbaaacbbbaabccdbaadcdcccdacbcbdbcddabdccbaacbbbdacbbbacdbcdbbdccccbbbcddddcdcbbdddaddbbabcbaaaabdddaaabaccaddbbadadbaccdbabaaacaacbdaddaccdbcdcbaadabaaccdccbbddbcddccbbabcaddabcacbabaccadcdaaaaddcaacdabdcaaabacacacbbbcdbdbdbcbdcadadbcdcbcadbbaadcbabccccbdaabddbccdbdadaccbcdbdabbdadddaabcaddcdcbacadbcadbbdcdbbcbcaabcadbacccccabdddcaccaccabcdccdbbacaddbddabcacaccbbdaddabddacacacaaaaadbcacdadadaddbbaadbaddbcadcadcbcdbbcaaaaabccdddcbcaabcdbaaccbaacdcbbbcadbddcbacacbdbdbaaccdcbacadacacbdbbbaaadcbddacdacdbabcacdddbbcacacddaccbabbadcbdcddaacbbcdddacdaadcbcabcbdadbcacbbacddaabcdcccacabcabdbacaabddadbbbdbdcccddccdccccbacdabaababcbccdccacdcdcabdddbadaddaabdbcddbcbcdbacdbcadabaacdbdcdbdcccacaababdcadacadbcadcadcbacaddbcaabdadcccdacdbdbdddddbacddbacdcdacaaadddbacacadcccbbbacbacabcaccdbadadbdbbbbcdcadddbcbcaabbcccbbaabdacbacccadcdbbbcabdccbddbcbbbdbbdbcbbdbddcaddcbdbbdadbccbcabbdaadbdcaccbdcaccaddbcdbaababddccbbabcbcaabdaddddbbaabbadaacddabcddacbcbabcdabcbdcbbdbadaabcbcdbaccddabdacbccbbcabddcaddbacdbddabbacdcaddbcaccbacbcadcbbcddbdaccaabdabaaacccbaabcadbbbdbdbbccbbaddadbcccabdccabcdddacbacbabdbbccdbacdabdccbcacaababdbdabcdcdbdcdbacdaacbcddcadabdabdcabdcccabbadbdacaacddcccaaacacddaaabcbbccccdadbdbccccacdbcacccddaaadbcadcddacbcdccdcdcaaabbadadaabadbacacabbcadcdaabbdccddcdaacbbabddbbcdcbddadbcabbcdaccdbccddbdabcbbbaacaacbabcaabdbccbcbcdbaadacaaaabdccaaaabadccadcbabcabdccddbbccccbbbaacdacabbccdcbdbdacddbbbabadabaccbccccdaddadacadadbaacbaacddacabaacadaaabacccabdbccacbdcadacdcdcdcadaadabccdcdaaabcccdcdcdbdbbdbbbaacdaacbabddddbaabbdbbdacacdbdaacbadbdbdbacaabbddacbdcadaccdaccabccabdcabdcdcaacacdcabdaddbbbcabdcccdadbcdbcdaaaddbcdbcbacbdccdbacdaddbadbdbbdcdcbbccadaccbcaacadaabdcdadccabddcbcabcdaaddcabdcbbbbabbccdacaaabbbcbabbccdbbdddbadadbcbadcaaacabbacddbdbbbbdbdcdcbcabcbcdbbcabccdbbbbbdddacddbcacdaaacbbcdadadacbcbcdcdacccadbaabcadbbacbbbacbdcdcbacbcbbcdacdbdbacbbaccabbdacbbccdabcbbbaacdddaaadbaaaabacbbdacdaadddaabcadbacdadbaabdadccaadcdcdbcbbbbcaadcdcaaabbbbacddbabbcaadbaadddcbdbacbabaccbabcbaddbdcabacdcdaddbdacbcddddbaacacabaaccccaabdbdbbdccdcbbbadcbacdbcbababcdbbacdaacddcbcbdabccaaaadbacccadbbdccbbcccaaddcabbdbbcaaccbdcabcbabcaccbbbcadaddbddbbcaadbabddcbcdcdcddbcdbdbdbacaadbacdacdcaadcabdcccaabcbccaaacdaccdddcaadbbdbcbddaabbcabcbcdbcbdbdaccccacabdbacddcdadadaadbcdabacccdaadadbdccdbdacbaccadabacdcbbcbdcccbcdcacddbabbcbbbbddabcccaaaccccbdccccbbbddacbddccadbabbdadabdcdccaababdbdbaaddccdbdcdbdabaaaabaaaabdbcabadbcbcbbcacadcbcbbdcaabadccbdaaaddbdacddbbabdbdadbbddccddcccbcbaaccbbdbdabdcddbcacadabadbdacdaccdbcacacacbaadcdddcdbbccdcabcbabbdadcabddcdcabdbabdabccdcdcbaaabcaaabcdabdcbbdddbddacaccdababbcdaaddccdbdcaacbdcbbbccdddccadbbcaccccbadcaabcdbdcadadabdccbadbcdaddacaaadbadcbcaaaadcabaddaaababaadbdbabaadbcbccacbaaadabcaaccddadbabcdccdaabaacbdbadbcdacdadcddabddcadaabdcdacacaaacbbddcaabdacbdacdbbcaabbadbdbabdbcbddbcabadadaddabcbccbbcdccccdabbaabbdcbdadcbbdcacbaddcabaacbdbccaabaadacbccdcbcabddabaabcaddbadacbcddabbdbbacdccaaacbdcbcbdaabaaacdcdbacdacdbcdcadabcdcadbbbbcdcacdaaaabcaadccdddbabdcadadbccabdbbdaabbdadabbdbcccbbbcaabaddbbddbbdddcdccaadccabdccbccdbacaadadddacdcccccbdbbcbcbacbddacababcaacacccaaddbbaabbdcacbcbdaacabccdabbbcabadcaabaadcdbcacbbdaabddccaacadccadadbbaacabdbadbccbddaabbadccacdcbaaacaacaadbdadcddcdbadcbadbdcdccbddcbbdbbaccadcabadccacaabdacccaaccaacadaaacabddcddaccbccdadcdcddabadbcaabaabdadbaaababdcdaddadacbcdbccaabaadbbddabaaddbdbbaaaaaaaadbabbbddadbbaacacbcccdacdcaaddabccdadaabbabddadaccabdabdbbdccddbababbcbbdddaccdaccdabdacbbbbcabbbadcdbddccbacdbabbdcdbadcadadbabaaddacbdaabbcdddcccbdccbdaaddaacccabdbbcaaabddaddcdbdabdadddacbbdacacddcbabadcadcddcbcabbbccaaaddbaadaccbcbcdbdcaaccdcaacabdadaddbbbaaadbaaabdcccadcddbccdccadababccccdabcdaaabcbdcaabacbcabdccbadcbbcbbcdbacccaaccbcabbbaacabacadcccdbdbccbbbabdbccadbbbabcacaccabbdddcddcdbccbbdbcacccbcdbccbdbbabdaabdcbdccadcbbacaddaadadacabdcbaacaabdcacbabbbccbcabdabbdbccacbcbcdabbbbcacdbadbaadccbbcdbadbbbccbaaaaabbcbbabcabcdcccaacaacdcadcbdadcddbacbcaccccaaccdacdaaabcaddcacabdcdbbaadabdbcbddbddddaccccbbbdcdbbbcacddadaaddbaadbbbbcbddacbcaadcaacacbadcacacaccbacadccdcaddcdcaccdabcdbbacbdcbcbbbbabccbabcbbdcabcdccbdcaaaabddbaadaccdbbbcacdadcbaaadcaadbdccacddcdcadcbbddacaddbbaaabacbaabacdbbdaabddabccacacaddbbbccbcadddcbcdabccbccaaccbbbdcbcbcdadbbdbbddbbddcacbabdacadacaccaaddaccdbbabacdadacbbddacddaddcadabaadccdcdbdaabbcdbbdcdaddbbaadabcaacdbcbcbcaddaddcdbacbcbcdccabccbbbaabacdbbbabdbdbcdddcaccdaadcbcbddbccbcdcbccddaacbbacbaababbaabaccbbabcbdbdcadcdbdcccabaddadcabcdbcddccbdbcbabccbadccbdadabdabcabcbdccdddabcaacbcacdccccabcbabcadbdbcccadcbadabcaabaabacdaddaaaaabdabcdacbccbbcdbbbccadcbbbabccaddbbcdcccddacbdddcccabbcadddbcdbabcdbaadddaadbcccccadbdbaaaadabdcbcccdbabcbcccacbcdccdabacbcadcdcdcaaacadbcabbdabcadbdcdcdcddcababdabdbccacadbcdbaababdbcccdcacbaabddcdcacdccdbdcdbcaaadbcaaaddbadaadcdbdaaaabcdbcdccdccbdbcdbbdbdbaadcdabdaaccdadabcbaddddaacbacdcdccaadaacadbbadcbabbdbdaccdbbccbbbccdddadabcbccacaadcbbbacdcbbacdabdcdcdbdadcbadddbccadadbbabaaacbccbadcddabdbaabadcaaaacccbbcbbcdcdaaccabdddcaaabaaadbbdcdacbabbdcbaddaccdbbccbccacaaadbddcdccccdadbabcdcadbcdababcaadcbabacbcacdaddadbcbddcdddcbacadcddcaaabacdabaabdcbadbbabbccaacccdcdbbaddcadbadddcabcacabbaadbcaddbbbddaccdbbcdbbaadaacbddcabbcabdddbcdbabcdaacccacacacdacdabcddcbadddbcbaccccadbcaccabcccbdcabccccadabbbddabdbcababacddbbbccbbcadcadcbabadabccddbdabbdaacbadcaccdaabbdcbdabdcbcbdcdcadadabccacbbacabccccddddcddbdddddbdbccadbabadacabcccbdbccbcbbcdacbbcaccabddbabaacacbcdbadaddbdbdacbcbbacacdacdaacdadaadbacdbccabadbabccabacbacbddbaabbcabadccddddbacabdbaacdabcadbabcbccddabadadcbccdbcbcacbaccadbbabddababbdadbcaddbaabcdaaacbbdaaaaddbcbbccdbacbbdadcabddcacbcdaaadddbabcaababcdcdcabacccbdacccbdcaabadaccdcdbdccbbccdbbaadadccdcabccabacdbddbbadcdbadccaabacabbcdaaccdacbcbccddabbadccccbcdbcadaaccbabaaadcaccbbbbaadbcdddccdbccaabcbacbbdabdbdcababdbacbdaaccddbcdcadbabcddccbbdcddbbcbadccdcdbcdbdbdcbdbdaccbbcacabcddbdcbbadaadabdcabcabaccaadccabccdaabcddacbdbbbdcbddbcdacacdcaacbbcdcaacabdbabdadcaacabbabcbcccbadbdddcbbcddbdbdbdaabaadacdbcdadcacccababcadacbdaacdcacbbbbddcbcdaababcbdadbbdbbbdcdcadbdaddcbbdbbbbabacdaadbbdacadcbaacacacaccbabaccabdbddaaadbbcacabcddcdcbaabbabcaaacccddbccabaaccdddbdabbaacccdabcdcabdacbaacbcddbadababadcddbbccabdcbcbbdcbbbcdbadadddcbadbcccbbadccbabdadcccddadcccaaccbccacbabddbcaaadcbcabbcabdacbadabcbddadcddaacadccccddccdcdbdaacdddbcaabcbcbbacbcaacdbababbdcbdcdcbdbbccbdadcbbcabcbaacadbddabddcbbdadcccaaacdaccbcdbbbcdaaddadbcaacbcacccabdaadabdbddacddcbcaccbdcdcddbdccaaabacbaddcdbdcdbcbccacaacabcdcdbddcdcacbccaddadadacacddcbaccaaadbaaabcacbdaddabbdcbdddcaadccaabcabaaabbcadadacbabcacbdddddcddcbdcccddadcaaccbcbabddcdcbdaabaccdacababddcbcadbdbbadabbdddbbbcacbadcabbcabcdbbaadddbbdadabddacabcdcbcddbbbabdaaccacaacddacaddbddbbcaabcdbbdbbddbbddddacbcbcacdbacccdcddccdaabbbdbcbbabccdccaddcbabcabbbcbccbbbbcdddaabcaddbacacaabaabaadbacbcabdccaaabdbcabbddcbbaccabdcbbbbdbcadbbddbbadaaaabdcbabbbcbcddaacdbcacddbdaacdbadbbabcdcbaaadcaabcacbaaaaadcbcacacbddaaaadaaabdcacccaccabdaadbddaaddaabdacdabacdddaccbcbdacdcdbacccdbccadabdacbbcddaddaaabdaccbdcbddddcddcdabdadabacdcdabcbdccdddaadaccacadcbcdddccdbbdadabaadccddcdddbaccaaadddbcacbbddcbbdbccbaabcbbabdacbbbdccbadacabcbdbcdddcddcdaadaccacaabaccdccdcacbbcccccbddaccdddddabdcbdcacacaacbbddabadbdcaadbbabcddddcdcbabdbcaddacccabccaabacbcdbabcbabdabdcbbdaabccaccdaaccbadaadddadbdbbbaadaacabbddbbaddccdcbccbdcbabbacabadbbaadbddcccccdcdaabdbcbcdadaaabdcbbcbcddddadbdccdcdbcbbadaaaaabaacccaabbccaddaacacdacacabaabbbadaabacbcaccabdabaddbccdbbcdaccabdccbcbadaaccdabcabcaaccbbacccaaadcacccdcbaaadddbcdcdbcbcbcbccbbdccababbcaccaadaacacbdcbdccccbdbabbcaaaaacddadaacaabddccacbdcdacdcacccbacdcabaacdddbadabbccddacdaaabbababaabcccabcdbabcbabbbbcacbacddcdbabacbcccabaddadddbcdcbbadadcacdddccbaadccddabbbcdbddddbabccadbabdcbcdbddadaddbaddcacbbababadcdddbdadabaaacbdccccacadaaddabbccddcdcadcbcbccbabaaccbdbcabdacbbbcaabccbcbbccbaaadbcdcabcdcdabbdbaabcddccbbabbbccbcbbdacccbacbadcabddddaadddbdccabcddbaccdcbbcccbabccacabaabcdddccbabcadabacacaacbabababdbaaccdcaabbbacdadbaadbcbabcacbbaaabadbaaccbaaaabdbbadbdccaadabbcccaddcdcdddcaacadaacccdaddaccacbbaccabdbbacdbccdccdabbdddbcbabccddbaacbbdcdaadbabadabccaabdbbcadbcaaaababbbcbdaabadbacdbbbccdcbdcbdabaaadcdaacbbbabdcaababaacadaddabcabacbbddcdbacadaaabbbcabdcaaacccacdddcdababcaabddcabbdadcdccbbdddabacbcdcdababcbcbabdadabccbcccbcacdadccadabbbcacabcbaddadbacbcddddddcdbacbabddcbbdbcddacaadccbddacacccdadabbbcabcabbcdabdcaaccdabdbbadacadadbbaabdcaaadabbbadbbdcadbcddbabcdcddbabddaacdadadcdbbabddcddcaaabcbcddababdadaccdbccbcdbdababcbdabcccadcbdcacaaaacacaddabadccadddcadccaacaabadcbadbbdacabbbcabdabbddadcabbbacbbcadaccdadcdbbdadbabbdcbcaabbcdaccddddbacadddddcbbcccabacbaadadcccbbddabaaaadbbaaababdaadccbdabadaccacabbdcadaacccbdbbdacacdaccabdbdbbabdbccbcbacccabdaaadcddbdadbadaacdcbcdadaaddbcadaabdccaacbccbdabbbdcbbaaccbbadccdbadadbccdbaacdbdbdbccbacadaaadddabbcbbbcdaadbdccaaaddbbbdaacaaddbadbabcdabbcbbcadccdcaadbddbbccdbddbcdbabbcdbbccccbdbacdbccdacabcaccacabbadbacbbddacadadbccabdddcbcdadcdacdcdbacacddbcdcdcdcddacdacdacdcdccbdaccabdbbadcacdbbbaccadcadbacdbddacddaabbccbcacabdbbbbcaabdcbbbacacddccabcdbabdcdccdcaaccdadcbaadacdabdddbdbbbdddcbbddbddabbaccdabcbcabddacaacaaaddaddaccbacdacdabbdcbaaaacdcbabddaccaaaddbccaadcabbcccbadccacbccacddccdddddadddbcdadbddcadcdcabbbcddcaccbaddccdaaabcbaadbcdbcabaacbdbbdbdcccabaabdddabcdcbdbddcadbbaccacddcbcaabdabbbcacdbbacbdabaabadbbdaaacdcccdbabaabcdbcacbbaacccbaacddabddbabbaaaccbdbcddbdccddbdccdccdabccbaddcdbdaabccdcadbaccbcbdcddcdccadbacbbaaaddcbadbcbddaccdcbabddbacbbcdcacddaadadacdadaddcaacdbbbcdaccaddcddcbdacbccacbaccdcbdaaaccdbdcaacbbddccbbcbdacaaabbdcdbdbbbccddcaadbababababddaaccccbcaaddaccbdcdadaccbaaacabbbaadbbddabddcdacdbdccbdddadbddaddbbbacdcacdaabacdcbbacddddcaddaaaccbccbbcbddbacbaabbadcdccadbccaccbbbdccbbdccddcacbbcdaaacaaccaacbcbbacacddbcbcccbacaccdacbbccacdcdddadacbbbccddccbadcacacdbddaababbbccdbcdcbdcbbdabaaddbdcbdccdcaddcbabbadcdcaacbcadcdcabbabadabdcddabdccadbcabcabacdbcddaabacbdcbbaddddbccdaccbddddadbcbaddbccdbcdccbbadadcdbcccaaadcaacaacdacbccacdbbdaacdcdaccdccccaabbcdadddddcaddbdadccacaabdddbaccdcabcacddacdadacbddadbdcbaddcaddadaddbbbadbccbccabacddbbcbaacabddaacdbabbdcdadbdabadabdadacabcbdbbcdbabcbcccdcccbccbabbccddbcbdcbcbdcdcadbbcdadcaaccabdbcbbddcaabbadbdcabbcbdacdadcabdbdbccbbadcddbdabcddcddbcdbdaaccbbbccdbcaadcccccbcabcdccbabbddcbaadcccabbabccdacaddcabbddccbaaaccdbaaaddacabbcdbcabbdccdcdcbbbacadddcaadcccdaddbbbdccaadaccbbbacbcbbadabcbbabaccbbcdcddacdcdccdbbbccaaabdadaccbddbddbdcaacdccddbddcdabdacddabbaaabacccbdbcaccdcdaadbaadabcacbdbbabbbbbabdddbbcbadaacdcabdcdddbabaddabbabbdbaadacbdbbdccdcabccaabddbbaabdcaaacbbaabadcdcbcbabbabdcbbcacabdbdacccdaabacdccacccadcabadcabcabccaccdddbddcdbccbaaacdbcbcddbaadaabdaacdbcdcbdcdcabacddabadbccaadcaccbcadcabddcdddaccbcacdbdaacaaaacccbadabbcddcddcbcddaabdcdabaddddaccaccbbaabcabcbdadccdcddccccaadbacbdcccacdabcddbaacbccbaaaaabaacccbdcabdaabbdadabcddccdddcabadccdccacacacdccdbcbddbacacbcbdabbcdcacdacdbcbadcddabcbdbbbcaadcccbdbdcbbcdbadddcdccdbccbcdccdcbbaabdbbddbdbdcdbabdccacbaaaddadaacbbcabaaacabdcadabababadbbcccccccaabadadccdaacacaaacbbdbbaccdcbabbabbddcaadccddabacbccadbdacababdccbabcadadabbaaabbcaacbbdcbccbacdabdabcaaadddbcacaccccdbaddbcacccddbbadcaadbdacbdcbacdcbbdbccdcbdaccaaacadadaacdabbadddddcbcacdbaddaabcbdabccacbadccbbbddbdbbbdaaddbbadabddcbcadbaaadadababdadddcbdabbdaddbaccbcddbbcadbbbccbbcbdcbdbacbbcacccaadcbacdadddcdadddbccbacacddabbdcadbdbdbbabcbdddadaddadaddccaddacdabbdcaccbbbbaddbddddbacbaccbcbaadbcccbabdcbccadccadcbdacbbdccbcaabddaaacbddbaddcabadcbddbadabdabcaccddabbadaaacadbbabbcacbaadcbabddabbabadbbaadadbdcbcddcccdbccdbccdadcdccdbbbcdacccabbaabbbadbaaabdddaabdbabbbcbddcaacabdacdbbbdddcdcdbacbabbbcaadacdbddddbbdcccbdbaddbdbbbbbacdbdbacddadddbadccabcbcbdbcdabcabbcddabccabcdbbabacddacbcbaccddcddccdabdddadddacccaabbbdbaabdddadbccdaacbdcdbaaabacccbdaacbddcaaabbaaaadbaabbdaddbdbdddaacaaaabcbaccbcdbbbcdcddbadbabcddadcaccbcdacabcaadaabcdddabcccdcabaaaabadadadbdabacabaccddbdabdaaabbbcadcabdaacdaaccdadadbadaabbacaabddbabdcacbadddbacdbacbdccabdbadabddbdbbcaadddaaccdcdcbbcbbabadbdcdadbbcddbddaabacacbbbddadbdcddacdbacdcccddcaaccabcddccadccbddccbadddadcbddbaacbbdaccdcbbbcbcbcacccbaddccbbcbbadbabdbadbbdaccddabdabdabcdbdaaccbdbdcbbdbaadcacacccbcbbacdcbbadaddccbbcacbabaccdadadddccaabdacabadcdbaccdccbbabacdcddbddcaadacbdaacdbdabdcdddadacdcabcbcdbaccccbcbbadddbcdacbadbaabdaaddbacadbbbdddabbadabbaddaccacdbbaacbbbdaadbbddaadaddcbcbdaadbbdacadccaabcbdcbacbdaddbaaccadbcdddddcbcddbdaaddacbbbcaaaddccaaadaccbabcdbddbbbaabaaaddadadccbadacdbcabdbddcddbdccacdbdadacacdaabdcacbaaacccbbcdadabdbbcbbaadcbdbbdcaababcacddaacdccddbccabcaaccdaabcbbacdaabacccccbbdbcbcabdbcaabbccabcadacbdbdaddcdbaccbbdbccaabcacabccabdddcadbccbacaddbbcbcabbbadbdbdbcbcbbbbccdbbdbbcbacddbdbccbadcbdabcadbabbcacadadcadbadbdddcbdddcacbcaaacabdaccbabcdabccdcbdbcdaabbdadcdddbdbbaddcdadcdadacddbcdbccaabcccdabacdaccddbcbdcdcacbbaadbccbbdacabcbdbaabdaaaaacbcbacdbbcddabaaaaabdbbadccbdcddabcdaadcbcadccadabbdaddbbdbcacddcacbddacdcadbdabccbababbbabddaabbdccdcadccbbcaaaaacacadddaccabcacbdaddcddcbbbbcbbbaacbdadbbaaccbdcbaadaabddadbcbdbadacbbbadabcacbadcbcbcccbbbdcacaaaadcccdbbccabadbbbabddccccdccbcaabddaaccabddaddbbcaabbcbcacbbccccadacbbcbbacaccddbdadbbaccddbcadccbdcccdcbdbbddcacddbbbcdaddbaddaacbdaadadcbdaababbdbddcaaccdcbdbbbcbbdbbdbccdabcabcdccacdcadbdbdcbadadabcdcbdbaccbddccbccadccdcbabaaaccddddcdbdbbcadcaddcbdaddcccaaabdbdcddddcadcbcbccbcbdaacacbddbbabacabbcddaddaddadbcbcaacacdcdccddbaddbccccddcadbddccdcbdcdacabcabbbcdcadcaaaabccbccbcdcbcacbdccdcdcacccadaadbdbcbdccbdacbcadacaccddbdabacdaadaaaddbcbbcbacadcddccbbdaaacdadabdcdcbacabdddbbacccbbdacabbabccbdccdacabaacccdbaaddbaaddaccabbaacdccdcbbbacbabbdcbcdccaddddcdccbbcbcccdcbabdadcddabaabdaacabbacbababcdccdbdacccdadcabcabdcbabdacbcaccccaacccacbbadbaabacccccbddcbdddddbbdbadccacbbdcddacccbcaadbbcaadddabadbabdbdaddbdcabdbadcadbccdcdcdbbdcbdcabacadadbccaadbbbcadcdbccbcddccababdabdcdddbcbaaaadddccbdadaaabdcdcadaaddaacaddbcccccabcbbacbaccdabacbdadbbdcddaaaacabdaaabcdabbaaaadadbcbdabadcdccdddaadbcaddabdbaacddbdbbcaacaaabdbbdcdadbbaddacdaddcbdddccbcdabdabacdccbbcdcbbdabcabaccccdcabbaddaadbbaaadbbbccacdacdbacddcbbcccbbdcaccaabadbaccdcacbdbadaacddabbdcdcbadbcbadaaaccdaabdabcaccdabddbaabcbddcbdddccabdcdadacccbaacabccdbdbbabaacdabbdccaaaccdaccbbcdbbdabbadacccaadcbcadcbbdaaabcacadddbdbcbcbbbbcccbbcbbdbbdbdcadcbadcadadbcdcbdbbcdcdbbdddcbdbbcbbacacaabcdacbcadddbbcabbbddbdbaddcbcbcdbdcaadccbacabacdbbbbacddccabcccbadbbccbaaddababadacdaccdabdddcacdddacdddaacddcbddaabccbddabbdaaccddcbdacdbbaabddbcddcdcacaadcbbacaadddddccbdacadaaddbaadadcbbabbabaaccaadbddabccabdadadbbddcaaabbdaaccdccdabdadccbcbabbccbbaddabcacbadbcabccccabcdaaddadaabcabbcadcddbdcdadccdacabadabcaccddbabbabdacabdaadbdcaacbddaddcdbdddaaaadbbbacadddcbcdbcabccaabcbcacacbcdaccbaaccdbdcbadadcdababdddcbcaadcdadbbabdcadcbcaaabbccbdbcdcccbbdccabccdcdbbabacbddcabddcbddacdbbcbbbbcddcdacbdcaddcbbbaaadddbdaacdddcddbdabdcdacdbaabdbdaadccdbdaadcbbdbbbcdbdcabacbdcbdaaaccacdbddbbabdccccbadaacdcccacbcabcbbccbbabcbcbaabbdabddcaadcdcdbacabcbbcdacdbbccbbbbcdbbcdbccdbdccaddcccabbabacaaccbacdaccddaaaccdcbdbddabdddddbcaaadaaabcdabacaddbddbbdabbbabbdbddbbdcaddcbabcbcaacacddcaddbdbaadacbadbabbbcbccbaccabbccbcdabccdcaddbbdabdabbcabdcdccdbcdcacadbcbcbbadaaccdbacacbababbcbaddaccacbccddbcdbcaadcbbcdcbccbbacacbdcacaddabdbabcbbccccccbadcaaabacddbdaaaddcaccadbdbcaabbdacadabddcadbcacdcabcdcacdabdcacbddcdcdbbccdcbcbbcaadddcadcdbbdbabccddacdabdbbddcbdbddcbccdccbdaccdacaaaaaabdcdbdddcbadaaacacbdbddbdbdcdddbdcbbcabbdbabdcaacaacccacdbdababdcccababddbddbadbccbdbbccadacaadacccddbdadbbdaabcccccacdddbdaadccddbddacdddaaccdaababacadadbcbdadcbbcaabaddacadacaadddcacbaddbcdbbdabcbcadadbadadcabcadddbddaabcabbcdaadadadadccaababcbbadbbabccdcacabababacabcdcbcdabadacdbcabddbaadcbcaacbbddccaaacccddadadddbdcccbdadccdbdacbcabdadabddabdadcccdcbcbdbbdbcbaabbddcaccccddccbbcacccacdbbdaddcccadccbdcddbabddcbddacacccaddabcbaddbabbaacdacaddaaaacddbacbbcbdacdbaabcddbbbabccadabbbbbbbcbbdcdadbbcadcabbaaaaacbabdaabcabaadcaadbabbdaadaadcaadaddddbabdbaadcaccacdbccdcacbbdbbdcdcbdacdadacbabbbcdddaaccbaaacdadbabcacacccbbacabbcbdabcdacbbdcabdcccbdcdbdbadadcdbdcbccbdbdbadacccadddbdacddadcabddadccbcddbdccbdcbcbdbaaccabcbbcadccaaabdbabcdbdbadbabccaaddaacaabadbbdcbccadcdbcaacdcbcbbdbdabbcbabdcbabacbcddcabdccbbbdaddbdcaaabdaacddbbccbdbcbadbcbdacbbacabcdadabdacddcdcbcbadaaabdabacabcddbcdbbddccdcaacdbadadaabadcadcdaddbbacbbcbacdbadddabaabcbcccabccbcbadbcdabbbaccdabccaaadabacacccdaaabcbbcdbacababccbddddcbcbccabbbbbacdcddcdbbaccdbaccccddcababcbcbcadaccabddbbbdbdadbbddadcdcaacdadacbaadadcaabbcbacabcbdadbcbddadaaccaddddbbbadbbadbbabdabccddddbbdabcbcbabccddcdccdccccccbcaacbcbcccccacadaaaabcdbadbaaabababdcbdbbccddccaadccaadaaddcbbdadabbabbcacbbdbdbdcdbdcbaabccbcdbbdccdccdccdbcacaaadcdbaaaccacbdcabdaccbdabcbccdddabbccaabbddaabbcdddbddadabdbbddabbcddadcdbbbcbbdbdcdbbbcdaaadadcbdbadcdbddcacbdcabcbccaaddbbcabacbdaabcadabaacbcacabddaabbbccdcabdbbcabbccdcabbccdccdcbcdbaabddaadbadacabdabacbddbcccdcddbbdbccaaaddaacbbccabbabadacabaaacdbccddcbacdbbaccbcdbcbbccbbdbbbcdbcaadddcccbadbdbbabccacbaaddcddbbdcdcadbabbadadcacdabaccbadacacbabbbbacbadddddacadaaaaacccbddadbbdabbbbddbabcdbacbabccabdbcbbdddaddcdababdbbccdcdcdcbbadabcddcaaadcdbbabacaabaaaadccdbbaabbcabcbdbdcadadccbcdabcddcaadcabddcddccdbacdccdbadabdbcdbcddbabaacdbbbcbabdbababcccdbcccbabbccdddaccbdcddddddbcabdaddbccaaddcaacabdadcdcabacabaaadbccaaddcaadccccdaaddadbabbdacbabcaccbbdbbaaadbcaaabdbccdbbdaabaabbadcbbcadabcaadcdcacaccaacbabcdcdccbbcbbcaccdbabbbdbaaabdcadacadbcbdbaadaadaacaabcdbcaadbbbadcabcdabdcdaaacdcbbddccaccbbaccdbcdcbabdbabcdaccbbbbcaddacdddcdccaaaaaaaacbcacccdbbbabbdbccaacbdbcacbcdaaaccbaadccdbaaaabbbdcdacccbddbbbdddadabbcddccdabbdcaacbaccdabbabaababcbdacaaacaadccdcddddcadcdacbbadddddddcbcadcdbccdacaabcbbaddcbdcaddcdcaaaacdbdddbaacdbdddabbacbabaddbcbaaadbaccbaaacbbaaaadcadcdcacccdacadacdaccaccbdbdddbbdabdcabbdcbbccbccbccbdbacdbbaacccadbbdddbbbccabbbadaccdbbaadacabadccaaaadddaaadccdbbacdcbcbbcbaabbdcdcabdbabacbbbbccbcdabaababdbbdbaabaccdabacbdaabcdbbbcadbdbabbdacadbacbccdaaaaccdccdbbbabdacccbbbbdadbdaaadccbbddbbbbcddddcdbdddccbdcbcbcadaacdcadacdadaaaccdcdbdbbadcbcdcabdbdacbdcbdcbdcadbadddcdabcadccabbaaddddbabbcabdacddcdbbdaccaabbdaddcdcaaaddacdbdadcdaddaabbcaccabdcbbccbccbccbddcddaddaacbbcbddaacbadddbdbacccbdccbbabcaacccbbadcbddadcccacdbbbcaaabacacaadcdbbdbbbdabccbccabbcbdaacdacacddcbcbdbcdcdbacdaaddaacadbacaabbcacaaabdcadcdcdbacdccbcbcddcdbcdbcadbaadbcacbbcddddaababbaabcabdaaabdbcacdacdddacabbaccabcbcaabbccbaddccacbdbacbcccbddbcdaccdbcddccdbcadaaccaabbacbcdcbacbbbadcacddaacbdcbcdcacdcdcaccabbcacdbabaaadbadaaddccaddabbacdccaccbcbbcbdddddcbacbabbccdcaddbbdbdbddbadbbcdccdacdcabcdcbadacccbcbcccddbcbabcdabbbadbbbbdbadaddadbbcababdbabcccadadbcdbbbccdaddbddbcbadbaacababddbacbaadaddbcdddadccacbacacacbadbddddbdcabddbdcdddababcadaacaccaccddddccdadcabbddbbaabcdacabdbdcaddbdaaabacabbcdcbadbbdbadcbcbcdacbcdcbccaaaaccababcadacacbddaddababccddbabdabcacdaaacbcabadbcacdabbcbabdbcaabadadabcbbddbcbbdaacbbddbcdaabcdbdbdacbcdddacddccdbbcbcddcdbbdcccbcdcdbbccbadbcccbbaabdcdcdbbbbadcdbaddcbcdbabacaabdcabbbcddcabbbaaddbadbdcaaabcbbacbcbbcddccccdbbadbddaadddaccdcbcdcccaadadabbacdcdbababdcabbccbacbacadcdadcdcacccaacccbcbcbdabccdaacdddcbcbcabdcbadcbdddaadbdcacaaaaaddacddbbadaaaddcccdccdbbccddcddacaaabadababcccacdbbdcbaabaddcdaccccaccbbdaabddddaadccaaacabbacabaddbdccdccaabddccaddbbabcdadabbadcddacbddcbadaddaadbddbdbcbcadbcdcccacdddaadaadbcaaccbbacaccababdcdccddabdbddcabdcbbaacbcbadbdadcbbbabcadabdbdbdbddacaabdddaaacbbbacbabbacdbdcadccbbbaaacadcaddcddbbbaadcbbbaaccbcdaacaacadddadadbcabbddcddbabadcdcddcaddcdabdcacaabdddcdbbbdcddbcccbbcdadddbabddcccdccabbcacccaddbabadadcdbbadcaabbbdadadcbcbbdbdbababbccbaabbbbdacdacacbdccdcbacaadcbaccadcabbbbcbddadaacbadbdabccadccbabcdbacddacbadbbcdabcccbcdddbbcdbbccbcdacabdbdbbacadbbdddaaacbaabdddcbbbcbadadbbcbbdaadacbcaadddddbddacbaaaabaabbddabdccabdbcbcbdacddadccddbcccbdbabcbdaddadcbaabcbbdcabbadcabddcccccccdaaccaddcbadbdacbababccbcdccaababaadccbddbbaaccddcdacabdcbcbaccbabddabbcbcdabbbcabaaadddaccdaaabbbcdcbcbcddcbbdbbbacddbcdcaabcdccddcbabdaacbdadabdcaabcabadbcbcadcddccbcdddbaccaccddacddaccababbbabaabdaadbbbdbaabbaadddaddcddddbbcabadbbddcbbdccbbdddabdcabcdcdcbabbacbddbbbaaabacbcdddccccbdadbccccadbddaaddababadccddacacaabaabacbdccbacdccbdcadcccbcddcabcbdbbddbdbdaaacdcddacadccdaadddccdbccbddccdbacabbcabadbbbacdadabddbbbcabdbbddbdccaccadbbdacbabacbcdcdccbaddbbdacdabdccbddcacdbddcbdabbacabcaabcccabdbcdaaabccdaddcccbcacbcacdbaabccacccbbcbddbcdbdddcddacdbacbbdadcccdabcdcaadacaabcaabbcddcdabadcdbcabdbdbcabcbcdbbdaaabbddbcdbadddabdbbcdaddbdabcdddccadaaadddbbbabcaddcbcccabdcbbdabdcbddabdddaabcccadaccdabdddbcddaabcddacbbccdbcaccddabddcaddbccadadddcacbbcbbbcdadcababccabbcdcbdccbadacacacdcacddcbcacdadcbaddbbaddcdbbcdbacbdccdaabdacabcccdabbbbddaabddddcadddbbcbbbccbcacacbacdbbddddcccadabdbbcbadbaaabaaadacacddcbcdbdcddbbbdcddcbadcccbaadcadcbaacacaaacbdcbcccbcacaacadadbaddcbdabddaaddccbbbdccbbdbbbcacbbdbdaaacccacdcaccaaadadcdddadbcdbabbcdabbaabdddbbbaacdbccccccccdbcddadcdcbdabbaabacabcccacacdbacbaababdaddcdcbccbbddcbdababdabddbdacadabacddbbcbcadcbaddccbbcadbacddbadadadccdbbdcddcadacdddacddcbdcbbbaadabbdbcbabbbcdcdadcdbcbbdccbddbadbdddbbadacccbbdbadcddddcdcbbbbccdcbdbcabbbaadccacdccbdbabadcacdbabaabcacbbdccacdaaaccacdcbcbaabaccbacaccbacadbaaadaacabdbbcacdbaaccaaccccaddcbdbdcbdaacdacbbbcadbcccdcacbddcaadbbdbdbdaccabbcdbadcdadacdcbadbacdcbdbccaadcbdccdaddcdcdcddbdcdabddacccabacabadbabdadccdbdcdddbabbdadcbcbbcbaadbcacbdbbabbbdcccbbbdcccdcdcbbbcdaabababdcdabcdccddbcacdaabcbdcbddaadbacccdddbbadacbbdacccdcbaaabcddddddadcbcdcbbaaccbdbbabbacbddabccbbccdaaaaddbccbdbcabcccbaacdbbababbaabadbccaddaddddddbdbbaabdbaccbccdbcadabbcdaadadaacacbaabddbacbcccabdbcadacdddcaaccddbadbcacbbacdddcaaaddaaabaaabcaccddbadbcdbbbcbabacadadcbccccadabcadbaacabcacdacbccadccbbbcdccacadadacdcacbacbcadcadbaadccaadbaadacdacccdbbdcdddddaabbacbbdadbcbddcdbccacabccabadadcdbabbbbdbacbdacbdbddbcaabdcabacdcdcdcddcabdadabcadbdddbbbaaabbcadaadbbddbcdacddbdbacaddcdaddaaadbcdcdccbbcbcaaccccabaadccbcbabdcdccdbdbddbddcbcbdadaadddacabbdcdadcbbcdbbbbdbccabbdcbcbababcdacadccabbcbbcccbababacaabbbaacddadadbaabdccbbdcbacbdccdddabbabbcaadbdadabcbaddccadbadcabaddabadbbbbaadcdcadcdbadacadbcbaabaaadbdacdcddbddcaccabbcbbdabcccdcaacddabdbbaccbbabccddccbbcaabdbacacdacdccadabacaaacbbbdaccdbacdbbcdadbabbaddcdbdabcabacbcbbbabbbcdbbbbcbaaaabdcbbcdbaccbbbabdbaaacabbaabdbaaddbdcdcdabbabdccccdbaccbbccdbcaaadbdcadbbabcdddbcbccdabbcbccddcaadbcaddbbdabdadaaadabadabadbbdbbabddbaccadccadabbdcbbbbadabcaacbbcabcbddccddccbacdaaacaabcabcddbaadacddaabdadddadbaacacacdcaccbabcbcbdacaababccccdaccacadbdbcdbbbabbcbabdddaadaacdbbccacbdddacdaacbccccdcddccaddabcdcbdbccbdcdccbabdcdbccbacbddbdacacdddcaccbccbaddaaacddbaacdabdaaabbdacdacadcbabbddaaabcbdbbcbadcadccaccccdbacadbacbcaaabbcaacbdacdacdadaaacccabdaddddabdaacbbdaccadacbacbbbbdbcbdadcacabbbcadbabdbdadbdababadbabdbbddddcbadccacdabcacadccdcccbaadaacbcbbdadcdaabbdacbaccdbdddbccbcbddcbdaacadddbdbbcbbdbbaabcdddaacacdddcdcbaadaadadbaaadcbddaaaaaddadbaccabccadcacabbbddacccbcacbdacaacbccdadbdabcacdadccacbbcbbdccdbabbdaaadcddbaccbbdccacbcaabcbacddadadcabacaaddbbdbcbbcbdcccdcdaabdbabbabcdcdbccdadcbdbbcbcacaaabaadaddcccdbbbaccddaddccdbdaacbddbaaadabacacbccdbbcdcbcbcbcabaaadbbcdadbccadbbcacbcddbdbccbdadcddbcbddbdbdacacbcbbdadabaaaadabdcddacccccbaddbdddcbabbadbcdcaadbacbddacddcdbdcdadaddbddcbcdcbaccdcadabcbcddadabdacbaddcbcabaaacabbaccddcdbcddabcdcabddbcaababcdcdbabadccbdbddaaaaccdddccdaadaaadcbdbbbacdacbddcbbdcacbcdddcdbbcabccbccaacbdbcdcddcbadabcaddadbcddabdaadaaaacbbcbcbbcddcbdbbdbbcabbcbcadaacaaadcbbbbddcddbdacabdcdbcdbcdcbbdabbabddcdddaabcadbacadbbbaacdcbaaddbabdddaacabcbaadddcabccdbaadadabaddadcdbcaacacdbacddaacadcacddadacabdcccbdabdcdbddcbadbcaabcaabacbabdacbdddcaccadcadccccabacadcddaacbbdbadbabaddadbbadbbcccabbadbccbaccddaddacddcaaccccaacdcbaaaaaadabdaadadadbbccdaadacccabccacdbdcccbbddaadadaaabbbdaabaabcbdbbaacbdcddacccbcbcbabdcbdaccccaacdccacdbdabbbcccaacadbddbacadaacccabacbbadbbcccbacbdccbdbabcbcbcabaaaccbbdbabacacbcbcadccbabbcaabdbaaaacccabdbbdaddcbacddbdcadbdccbadabdaccbabdaaaacddcabacdabddbcddaadbddbbcbacbddbcbddbcababaacacdddbdcdabacccdbbbbcaabddababaadadcaabbabdbccccdcdbdaacdbddcabddbcbbbabcbabcbadbdbddcbccbdcbccaaccabcddcadabdccacaadbbdaddbcccddcdddabaccbadbacaddcaabdcacbddbbbbdaaacbadaaabddcabbbdaccababbabbcdbdbddacdbbcdbcccdbaddbdbdcbcbcdddcbcbbbacddcaacaadcddacbacdccdaabcdacdbababdbbdbcdcdcabddbddacacacddcdcaaaabdadbacaccccdabaaccaaaaaabdadcdadabdbbadcdddbbcadbabaadbcacbbccbcdaaacddcdaabbbbdcaabbcaccdddacddcaabcaaaadcdcdadacdbcaddaaaabdbbaabdacdcbbbddacaacbabbbadbabdbaabbbcbbdcabdbbadcbcbacdbdabdddacdcddadcbadbddcaddcdcbadbdbcdacaacbaadbaddbadbadcadabddadacbccbcdabddacbcabbcccaaadcbdccccdbdcbacdcbaabacadbbabcdadddcdbcabcccbddddcdbbbccbbbaccacabbbabcabacacddbdadbbdaccbbdcadabdbaaacdbadbcbddcdbbccaccabcaddaadbdcadddccaabcaabdbabbaaccaccaddaddabbcacbdcdacbbccbcdaacbacbadccdcbbadbbababcadabbbddabddbdabcdbccdcbadcabbddacccbacabcbcbadadcbcccbcadccccdcbbcccbbadddbabbcbdacbcdbdcbabadabcacaccdddbdcdcadbaaaadddadbddbadbdaaddbbbaddddcbacbaccacccabcbdacbbdbccddbcadbbcdbcbbdbaadacdccabdccbbbdcdbddbdbadbdcbadccdbcddaaaacbabdadacaccdbbcbabcbddddddcaaddccddcacbcaaaaabcbddadddacababbdaadcbacbdbcacaaadccaacdddadbccbbbabcacbcbdaaaabbbddacaaaccddaaccbabcdcdccddcdcddcaabddbabddcbabcbdbdabbdadacacbdacbcdcdaabbaadbbccacbcaaabbbbaacbacdacadcaaabaaaddaaddbacbbacbaccacaddadcabdcaaddaaaccbcdaddccaadbaddabcbdadaadcdaaabdddcccbbadaababbbdbdbbbacccbbccadccbbbcccdcdcccacddababcabcaacccbdddbbdddcdacdabbcdcaccabadbbadcdddcbcdabcdcdacbabdcdccbdaaaaaddbcdcbcbbccbbcadacdcadabcbbbcabadbbcaccbaccddbacbaadadaaadddddacdadaadccddbadbcccaaadbabdcaddccacdddadbdaacdadbaaacaaccaacacaccdcdadddbbdccdadaddccbadcbbacabbbbdadcdcdaddcdacadbdbdadabddacdaddabadcbcdbccaadabdddcaacdbbdbcadcadabbadbbccbddadccaacacbbacbaabacccbcabddcbbaaccacccbabdccadccaddcbddbabbbcacadcbbbdbdbabaaccbaadaadacccacbabbcaadcbbdacccdcccaabbcddcbcbcaccadcbcbdcbddbcdabacccdacbcccccbcdaacaadbabaabcdcadcbcbabdaabadadbdbcbbabcadadadabbcbddaadddacadbbbbbbdccdbdcdbbccabbdbdbaaabddccbcacaabcbbdbaaacabadacacbbdddcbdabddcbdbcdaccbaccdaaaaacbbccbcbccbdabdabcbaaaadcbdbaddbdcdbcbcabccdcaddaaaabbbbabdccabaabdadccdcaccdcadcbdcadadbbdbbccccddcddaddcaaccdaacccbccdadbddbcbabdbccbcbbbbacbbbadabdbdddbbacbadadaacaaabcbaccbccdcdbccaaaabbdabaaddbbdcddaccccdbdcbbdbbddbccabccbbdbcccddccbbbacdddaccbabcaacaabcccabbdbcacdcaddaddacbbaccdbadbcacddbabdcaaacdbdacdabbdadddbacadacababbddbbdbddbbccbdbabccaaaadadcbacabbbddbddddbabacbbbdabddadaadddcddadccddbbdcdbdcdddabaccdcbdbbccbaacacdbaabccbbaabdbcbadddabcdccadacbbddcacccdcaabcaacddaaadcaabcbddbbcdbbcbcaacdbbadbabaaadaacacdacdccdbdbccdbdbcbdcbccabaacdcacdaadbbcabccadddacdbdbbadcabadadbaccabcddbaacbdbcbcbbaabdadacbcdcbcaadccdccbdddcccabcdccddacadcbdccadbaaccdbbcaddcadcbaabbaadaccabcabadccdcbaabbcdccaacdadabcabbaacabddcbcccdabbcaaddbdbcbcbddacbdacbadcdbcadddabbadbbdbcaabbddddbdbcbcaccacbbaaccbcaaabdaabddccaccccadbccbdcbdbccacdddddbcccacbcbcdbdbbcdbabcbcadcddccbbbcacddbbdadbcadbdadbdacbdbadcaacddcddccbcdadbdbdcccbbbbadbadadcbdcdcccbdadbdbbdccadcdbddabaaccbadcbdcdaabbabdcdbcdaacddbbcbbdacaacdbadadbdaaccabbcdbabdcbbcbcaacdcbdaccbcbdbbadcdbacbaabddadccccdbdcccbdcacdadddabcdbadcccbbaacdddbdcdadacdbdcdcdbbbbcbddbcdaddaddbbbdcababcbdabacaacccbabccaadddcacbbcdacacababbbddcbdcdbadbdbbacdadbdbccbbadccababadbbdabadbcddbcddaddcdbdddbadcaddddddbabbdbcddaababbacaaaacaadadaabdabacbbdbacbcacdddbbadbdcabdadcdcabadddcdbbbaaadcdaababcdcacdacacbdabadcbdddcdadabaadcababbacdbbcddacbbcccdccdbadadbbcddbccbcabcbaaabccbbbbbacdbbbcaccbcdddbbacbcadcddbbabbaacabaabbddccdcabcbbdbdaaaaddbbdacaccddbacdcadcccbabcadcbaddcdacbbcbccbbbcbbabbccddbbadddcbcbddaacccbcddbdddcbadcbbdcaaabccababacaacbaabdccccbdcdbdaabdaabccdcbaddddaddccabacdcdcadacdaaaabccccdcdcbdddcbbbcaadacacbbabcaccacadaacbbadddaadbcdcbbbcacadadcddadaddbcaddcbabacdcddbaddcaadcabcdcbbdaabacabaadccccbacaabdccdbcbccabaadbabcabdabcaddbaccbddcaadcdabadadccccdadccccbacaddacccbddcccadadcccabaccbaacbcabbcbadcbdbdbbabaddaabcddcbcaaacdacbbcccbabaaadbdacbbdcbbdbcbcdbddaddadcaaaaccadacbcbaacaabcadddaddaaaddaaddbdabbadabcacddbdcdaaaccaaadccaacadacacdccaabcbaccbaccccddaacbdabdbdcadadbbbcdcadabdbcbdbdcabcccaaaabdbdcdadbabbbddcdaaccabbbbdaacbbdbddacbccadaabbdbdbaacaddacbdcdacbabbccccadcccccbddccacbbabddabcdaaadcdbcdaaadccdaaaccdabbdbbbdbbddcbdcbbaacacddadbadaaacdcaacdbaaacabbddcbbcbdcbddbacdcddbddaaabcdaabcccbcdaddccbbbcabcaaabcbcbddcddbdbddccdbaacbdcbbcddaaadbcbdbbdccbadbbcabcdababdbadcdbbadaabccdbcbbacacbcbbbcbbbadbabbadcdbaaababddddcddbddcdbbccadabadbccdacbdbbacddcbcbabcccdcbcdbdacdaccbcadadaabdcbcbdbdadbaddcbbcdcadacdabcaddcdddbaadbdbdddaabadadaacabaccbcdaadacacadcdabdcccbdcbaaadacbabcaacbadadcadaabcaacccbdccdbabacacaadaabadbbadddbcddbaadbbaabacabccbdccdbaaadabdcccacbcbbcbddbabaabccbbacbdbbddbdadcddddbbabdbcadabbadccdadbccccbbacddddacaccdcbacdabdabccabbacdddcaddbdbcadacbbbacdcbbcdddbbbcdaadbbdbbbccbabadcbcdbdabdcbbdcadaadbbacbcdcddacbcbacdcadbccbadbddbbcbaacbdcbbcbacbacdadbaabacbdcdccbdbbdcdbabcbdccabbddcbdbcdcbdccaaccdaccddaddabcbbcbcadcdbdaaaabddcbbddaadabdaacaacdddbddadbaccbbdabbabcaaacbcdddacbdbdadccadbbbdadddcabdadbccbbaabdcdcdbdbbcdcaddaccdbbbcabacbbadccdbdabbbccbabbcdcccbacbcdddadaabaaacbabaaddbccbcadbdbadcbacabdcbbcdcbcaabdbccacbdaabcdcdcacdcbbaccbcdabdcbbbaabcdbddbbdadabcabccabdcadaacdcadadcbccbcacddbadcadcdddbbadaabcaacbcbdccaadaddababbcacacabbcddaaddccbbbbbabbcaadbbbdccabbcadbdcdcdbadccbbdadcbaddcacabbbacbccaaccbdcaadbbccddcacaacbababadcbdcbbdbbbadbcbcccadacabcaaddaaacaabbbbdaabcadbdcabcbcacbddcbbadcbcdbdbcbddccadaccbabbabbadaabbdaacbdbacbabaaadabcabdaadbaadbddaabddbdcbdabddaabdbbbccadadabddbadacadabdbcdbbcbacaddaabddcddabcbbaddcaacdaabacccbbbbbcabaabbbababcabaacbaddbbaaaaaddbddccccddbbabaabccddcbbddcccabcdbbabbbbbcaacbdadadccdaadddbabbddccdadbcddbaadaddccadacbcbcddacdbbddabbabdacaacdaaccdadbbadcadcbccbdbbabbbccbcabacbcadbcbccdcbacacccadddcccacdbcaddbcdcbbbabdabcdccddddabbbadcabadbcdccddbcbadacbbcdddcbdbbbcbbbcbccaaddcdababcbdbacabdabdcacbadcaddcddddcbaaacbaccdbbbaadcbadccaddddccbcdcaacabdbdacdcccdcbadbbbddccabcdabdcdcdbbddcadbccababdaccccdcbbbccadcbaaacaddddbadccddccabdbabaadbbcdcdabdccaaaddccdccbaddabbdbaabcbbccbaadcbbdacddcacbcddcbcbbcabacdabaddcadcbcaaccbbbbdbbabbddcddbacadcbabbadddacaabaabadbdacabadccbabcaddcabbabaaadcabdcbbbbabadccdabacbcaaabcdccadbddbdcbdbabbbaababcabdcccdbabdccabacdadccccbcbcddbdccbcddbbbbdccbabcadadbcbdbcbdbadadabbbdadbcdcabcabbcddcabbcccadbdcbbdcbdacdbddacbaabaacadbaccaabdcbbbbbbcddddcddadaaddacbaccdbbcbadbaacdbdbdadacbbacdcabdaccbccdbcbdadaabaaabbdbcaccbcddaddabdbbcbcbbdbbddccbbcdcabbcbbdbdabbdbdcbadcabdacccaaccacabddcddbdddccadcaaddcddcdcbcccdcbccabacdbcaddbccbcdabacbaccdddcbbdddaddccacbcdbdcaabddaabdcaabcbdbdacbacacaacccbbccbcdccdacbdbaaccaccbacdcccbbbbbadabbbccdbcbcdddcddcbdacddcacccbbabacbbaddcdccdaaaaaadbdcacbbdbbacddbdaddaadbdbdccbaadddddcdabdbbcdcaddaccaacadaccbccaacdccccbaaccdabdacccaaababdaabaadcbcdbadbcbcadaadcccdbabaaacbddcbdbbbccbbdcccdacdbdaabcacbddcadcbadccbcabacacdacabadbbdaacbabcadcadbcacbdbdcbdbdbaccaaabdbaaccdccbacbacaccbbadabdcabacdaccbcddacacbccacbdbbdaccccdddabcddacdbbadcababcbbbbbbcdaabacaaccbbdaadcdbdbccdacccabdaccaaacbababcccdcaccabbaadbcbdbcdccbacaaaaadccabdbbbbabdcbbbbcdadcaadcbdbbbcdbdcbdbccaccddbadcbbbdcddabcabddaacdcdcacadadccaddacaddbdbddabcddadbbacacaacacdadbbacdbddbdaacacbbddaaddcbdddaacbddabaacacbccabcaabbcacdbcccbadcbbacbcddbbadacbabdbbbdacaccaabdadacddbabbbccdcbcaacdabacbdaccdcbcddbaacdcbcbccbbcdadddcddccccbdbbccdcbccccaddadddccdcabbacdcdbdacdabcbbacbcbddaacbccdbacabdcbbccbaacaadccbbdcdcbaaddadbdadcadccbcaddacbccbbcbbbdbccadcdcbdaaaadcabadcbaadddabddbaaaadbcdcccaaccabcdbdbddddccccabbdddadcdbbdcccdaddcadbcbbbbbdcdaabcddacddcdbbbdcbbaddbdcacdbdccdacacdabcbdbaddbdacadddadacbdbcbadbaaddbdaaccdcdaadbbabadcabadabbcccbbccbbbccadaaaccccbcbcbbdaacabcdacbbadbadbdbccdadddcbbdabbbbddadbcacbcccaacdbaabbcdcddababbdddbbdcddaadbdaaaabdbbadcccbddcdbabbadccaabcbaadbbbaadbbdacdcaadababacccccbccdacdbdacabcddcbcadddababdaddcadabacbbcbccdccdbabadaadababddbcabddbacccddccacbaabbdcbabbcbbddbbdbdbcccaddaacbbcbcacdadcabdcdddabadbaaaadaabbacdbbdaababdcbbabbbdcccabbbbaabaccbcbcbababacacbcdbdabcdadbdacbccdbddbacbddbdadcaadccdbdcacaabcbbbddccdabdbdbcdbdddddcbdbcbacdcdbadabccdaddcadccddbadadcacdcabaacddabacaccabcdddbdbcdbadadacbdcdbbcddabdaaaccaccadbadaabbdaaaadbcadddaadadcbdbcdbbacbdcbddbbacababbccbadcabadacdbacbdcbacbbabcdadabadcadcacdcaddabadbdadccdddcbcbbccbbdccacbbdbbadcccdaadcaadcabadcbdcacbccdcdbbbbcdccbcbadaacdddbccdaddbdadccadbdbdaabcacccaabcbcdbbcddbbbdddbababaabdcbadcccaccaabdbaabcbbccbcbdcacadabadcdcbbdcdcdccdbababbbadabdadbdcddcbaacbdcaddaadbaddcdccdddcaacabbdbbabbbaacbdccdaaadcbabbbcdcddabddbabaccacadabaddcbcbbbbaabcaccbcddadbadddcdbaaccbabbbdbdaaaccbbccdcdcadcddaddcabccaddbdadbacdadaacbdcdbbadbdbbddbdcbcbcbcabacaccaadaaadccdadbacdddaadccaacdabbabadccdbadacbdbabadbcdccdadcbcaccbabbdadaadcacaaacadcbaacaddcabacbcdcaacdcaadcabbcababacddbcbcdddbddbcabbcbdabcaadbcdaacacdbbbcbcabdddbaddcaaabcdadcabdbdbdbcbbdcacdadbcbbdddcabcccacdadaddabcdcccbbdaacbbbbdcdbaaddbdcbbdaaabbaabdbbaaaddadccdddccbabdaaaadccaccbcdacbcdcbcbdadcbdbbdccacbddcbbdbcccccaaabbcdcaacabaabcdcbaaabdddddcbcbaabcadaddcbbbabcbcbdddcdadbbcdbdcbbcacccaacbcbadaabbcbcaabccacccccbbdabccdcbdbdadddbadbccabadbacaadabdcbcabdcddcabddcbabbabaccbdaccdcddcccccabbdddcdabbdbbacccdacdcacbacbbbcbcddcdddbcccbdaacbbacdacaddcabcdbbcbbccbcacdadbbdabdbdbdccddbcdbabcbacdbbbddadbbadbaddadbbdcbabccdacbabbadcaadaabacddcabdcdcaacabbdbccdaadbabacdabbdabadccadcabbcbadcdbdcbbdddbbdcbcacccbaabbdadcabbdddcbcbccbaccbdbaadadaccaacbdbcabcddcddaadddbacabbdcbbcabbadadccacadbacbccaacabddbaaddaccbadcdaaaaaccdcbbaccbdccbababbbdababdbdcccbaaddacdbcbcbcddcbcbacbddbdabccaccbcbcdacbbcaaadaabbbcdbcabbdcabddbdbcaaccadcdacaacaacbabbddcddaaaaadbdcbbbacdadbcabdaabbcccdcddcbabcdccadddabdbccdabaddbbddbbdabcbcaacadddadaaaccdaadacaccddadcbacccaaaadaaacadcadcbacbcdabcdaadccbcbcdbabacbcdacbcacddbbacbcbccbbcabdbccadbbddbbadcadcdabdcdddbccadbddbcbddadcaaddcddcddcacdbcabbcdcabcabbdcdbabadddbcddbcabcccbbbccaccdbcddaddbbbbccbcbbddcbabaaaabaaadcbcaaddcbbacbcddaaacbaaadaccbacaabcadabdacaadabaadbcbadcaddcbcddccadaaacaddacbbbcbaaddabbbcdadbcdcdbddcdbbdddbdaaadbacbbdaacbccbadddcdddbcbdcbabdabbbbadbcadddcbbbbdccaccdcbcbaccccddadaadcacdacaaaadaadaddcaabbbabaaaccccdcacaccaacacacbabcbadabadadadaabdcdbdddacdbadbacbdcccdcdcbaacddbdbaaabddcbcdbbacabddabdccccaccccdbadbbcbdbddbcbabdcddcdbcdcbbaaacddcdbbbbacabbdbbccacabcbbcadaaadadcacadccddaaabaddcacbadbaaacdddbddbacdbadbdcbabdadaacadababdacccdcaaabcdbadcabcbcabdbbdbabaabcdbdcdbdcccbbdccaabbcaacadbddbabdbbbdbacbcabdbccbdbdaadccbbcccaccabaabbddccccbaadbdccaabcacaacabcddaddbdcbdaddbaadcabbdababdcbaacabbbccaadababbabbadadbccaadbcdcbabcadaacaddaaadbacdbcdccadccbcccaababaacdbaddcbabaccbdbdccabadadccdccbaaabdbbcacdddcabdbaabdbcaaacdbaadbaddacdcbaddcbbbaccddbcaaccdadaaddbabdabbdabcabbbaadaadaaaaccbdbcccbadbdcaaaddadadbcdbddbdcaabdbdabddcdaabbbdabdbcccdbbcdaddacdcaacddcacadddbacadcbdaddaaadaadaadccadcdabadccabaabbabcbbbacbdadaabdccddcddbcaddabdcbabbcabaccaccacdcbdabaaccbdcbbccacaabbdcacabdcdcddddcadbcbbadaaacdaacaddcbbbcdcabadccccbbccdacacdcbdddadaaaaaddcbaaacbaaabbdcdbcabcacbccdaaddaabaacadbcaaabcddbadcddbbcbacbcbaccacbbdbccbccdddbaccadbdccdaadcbbbbadabdaccbaddcacbddccdaddadbbdbcddbdcdcacaacdcdcbaadbcddaaccaacdaddbbbbaabadccdcdbbbacccdabcbdbbbbdbccbbdabbcddcbabdddddbddbdadbdadbdabbcaacdaaabbacaaaccabcdaaaadcaddbbcadbabdaabcdccdbbcddbbbabdddcacaaccbbdddcddcbbdcaddadcbcbccbcabaacdcaaabcadbbbdddabdabbaaaadbcdcabddbcdbaabdbcaccadabbcddbcadbcacdaccdbdcbbaddddaabdbdbcbddabcdcccbbbbaabadddccdddbcddcadbabdbcdbdcacaabacbddddacdbdcacccbcdabcaaadddbacbaadcddcbcccadabadddbcacaabaccccbbcdbcbdcdcaddaacbdaaacdbababcbadcbbabdabcdbabaddbbbbadddccbbacbcaabdbaddadddcbbccabcccaacdddaacbabbbaccacadcaabacaaabaccdbdbadbaacdadaaaabdbbcaabcacaabdcbaccdaddacbcabdcdaabdacaddbddabadcdbcaadaacbbcabcbdbadbcbccdbbccddcdabddabdcdadbbaabcbbacbbaaadcddcdabadcdbadcdddbacacccdabadcaddbaabcdabcaddcddddbbabbccacbcdaadabbadaadadbaaadaabdcbcbcabcadaaadcccdbaacabdbbbabaabbcaacaccdadbddaabdddbcaddabcadcbacdacaabbabbddacbcdbcbabccccabdcbdbcddcaaadcddbbdcababdaaaababbacddbdabbdbdcddadaabdcacdcbddccdcccbaadbddbdcdacbcabbaaddbddddddcaccadaccababbbdcbccdcadcdbcabbcacbdcdabdbcbcbaababaabaddcbdbdacdbbbdbdaadabaababccaadacbddbddbbdbdcaadaacbbbbbbbcddcabacadcccdddcddacdcacaacaddbbdcaaddcbccdbadbcbcacbacacdacdbddbdcddbcddbbdddcdccbcabcadbcaaddacbaaadacdccbdbacccdadbccbacddadbacdacabcdbdbbabacacabacabcddbdacbcaacbadaacdcccacdbabcddcccccbabbcddacdadbcadcbcdbcacbccabdacdacaccccbccacaabdccaaabcbccadbaccbcabdbacccbdcabdbbcbcbdbcdbdbcacadacdddcdbbcbbadabbccddccabcdabcbcccbddcabccbabcddccaaaaccbbdbdbccdaabbdaddccdaacdccdcbddbccddddcadcaaadccdbdbccacaddacdababadacbdbccddddaacaddcbbccdccabcacddbadacccccbaddcdaadcccccacbcddbdddabcdadbbccbbdccbdabdcadadbbcabaadacddddaddabdccdacdbbbdbbcccdacdbbbbdcbacdddcacbadbdddcbaaabadabcbadbbdbaacbdacbdbbcabcccaddaccaabbddbcbbcdbbababbaabddcadcadcdccdabccabcbabcabbbddbdccbbcccbbcbabaadcacaddbbcbccbdbccbcacabdaccaaccdcbdadbbabaabbdabdbbcdcdbdbdcacdddacbbbaabacbaddcbcdaddacdaadbacabbdbbccdcdcaccaadcdcbbdcdadabdcbbaabdadcadbccbbcbcccabbcadddcbadadccbcabdcabaabacbddcadbdddbcadadcdcacbccbbacaabcbcadaabdccbacabccdaaabdccbacbccbabccbdddcdcbcddacabccddbbacbdbdbcbacdaccaccababcccbddbcddddaccaccccbababbbcbaabbdaaabdbbdccbacabdbdcdcadccdccddaddcaccababbccbdbabddddbcdbadbccabaacdacaaccaabadcdbcbcadaacdaddbdcbabbdcbabddacbbadbbccbcbaaaaccbabddccdbdadbacaaaabbcbaaabcbddcbccbddcacbadaaddbdcbbdcdbdcdbaaabacdbaddbccadcdaddccbabcadaabcbcaabcbbabcccccdadacaadacbdbabacbcdddacdcbadadaaadbadddcabdacabacdcddbbbbcbdbdbacdbddadacbbcdcdaacdaaabbdcabaacadbddadcacdadaadadbdaccabaabccbcaabcbacbbbdabbbcbbbbadddcdaccbbbbaaacdacdaccbadadbdcbabbaacdacccbccbdbdbdbabcbaabcbdcaacacdddcdaccbacacbcbacddbdcdddbdbcbcdbacabbbabccacccbcaabaabdcbbdbbdaadcacadbbccadadbddccbdcdbbbdbbdbcdbdddddbaddbadcbcbbdcccbccdbcdccabadbddaabbdadbabababdaacbcbccbacbcccbaabaaccabcdaaddacadcccdadabddccaccdcdcbbccddbbbbcbcdcccbdbdccacbabacdddaaaccdcdaacbcdddacaccaaddbcaabdbdbbddaacccbdbcdccbaaabbcaaddddabdcbadbcccdabdadacbdbbcddcdacbdacccdaccbcbbbadddcbacadbaddaccbadcadccbbbcaaaacacaccdaaabbdbdcbaaabbccaabccbcdacbbbaadbaadbadbadcddcdcbbbabacaabdaabcdcbbbdcaddccbbccacdddddbdcbbacaadaaaabdbcaacbdccccdadcdbbdcdcadcdbcbaaaaaadbdabccccabdbbccbddabaabadddcdcdaadbbdcbdbaadabcabdabccadbccaacaddddddaadddacdcdabdbbadabdabdddbcdcacbbaabbddcbcbdadabdaacbcaddddcbcddacbadcbadacbbbacacabdcbabcbbaccdaadccbdddcddbacdcabbddcddcabaabccacbadbcddaabcdaddcadcdcaaacddacbadadbabdbdcabdabbccbaddbbaabccccacadacdcdcdacadcabaacddcacbcdacdaaaaccdcaddbadadaacdcbccadaddbbdcaadbaacabcabccddcbccddddbcddcabadcbbcdcbbdcbbcbabbbcaacaddcadcdcbdcbdaababccaccdaccbcdddddcdaddcbcccbdbabdbaddbadaadbbbaabbaabdabcbccaddbdbbdbbcbccdacddbbcabcdacbbddacbdbdaabdbbacdbdaccdcdddaddbdcacadaacaccbacbacbbbbbbdccdadcaabcbdbaddccdadbbadcccadcbbdddcacadbbacbcdadccacbabacdbcdadaccdadcacbcdcdcaddbcbdbdbcdbbcabcacbbddbcbcadaaaaabdabadccacaacddbcacabaabbcddddadbaadaabdacaaadccccbbdaaacddcdccbbbcdaabcbdcaaabdbccaaccbddadaadcaddbabcbddcaaadcabbbcdbdadcaddcbacabcbaccadcdadaababdcddcabddadbbacdbbacbdbacbdaccbbdbbaccbccabdcacabacdacccaacdbdadbdcacadacdbcdabbdaadbaaacabacacdcabbaacbdcdadcdbbcddadcbadaacccbdddacbcdddadaddbdcacabdbccbbaaccaabbdbcdadcabbabcdaabcdddcdddabcaccaccaccbdcbdcddbadcdddbcadbddccdaaccbcacbadbadbaabaabaccacdcdbabbcdacbddbddabacccaabcdcacacddddcbbbcddbccdbbdcdbbacaaacdacbbccbbbaadbadcbdabbdbacbaaacaccdccadbcbdcadcabbacdbdabdbcdbbabbddaacdaddadadbbabbbaccccacbbdcbccdacabbddccdabdabdbdcdbdaddcbddcdccdadcaacaaadacddadcddddbbdddabccabdcdddabaacccdcbaccccdcabbcdadcadcbcbadbadddddbbdadddadcdbadcbdcbbadaabbadcdbaacccaaabcbddcadabacdbdaacaabccbcaacdcaadaddbaccbdbcadacbadbdbacbaddcacddccadadcbaabdbddaccbbbbcbdbbdbdbdabaabacdbdbcaabcdaaacadacddacbaaacabaadbaacbacddbbbbdcaadbdcbcbabdddacadddddbcaadcabbdbaaabadabaccaddcccaccdbccbacbacbacddaabcbaddbcbddaaacdcaccbbadbdaccbcdcdaccabdabaabcacbaaddabdbabcccdbadccdaaaccababbbaddadadcbcdacaacdccbdacaadbcdcdccbbabbaababbadbbdbcbdcaabcddabddddbaddadaabcdcaacacacabbcbbcbbcdbccbdadadbbbabcaccbccbabdbdcaccdcdcacdbdcdddbcbbdcadcdbbbccabcabdccbddccadccddccaaacbddaabadccacbdbbadaabdaacddbccdcacaaddbaddabdbdddbabadddadadaacddcabacaadcaaadbcdcaadbdaadddbdaddbdbaddcacdadcddcbbaacbaaaadcddcababbdcabdabbaacabccbdccbcccaacdabcdbbbcabdbdbdbbaaccbdcdaaaaccabaacddcacccbbaaaacdddcacbbdcbbbcadbabaabdbacaaadcdcbdacdbcbbbdcddbababdbcaccbcbddccdbababcadbdbacbbbbddcbbbcdaabbdbcacaacbcadabadbdcbaaddcccbdadbcbaaccdaddbadabbbbbddcdcaacaddbddadccaacabaacabadbbcddbdbbcaacaadabadcbcabdcdaddbbbcbaadcbdbacbbcccabdcacaabbbadbaaacadcacccdabbbabcbdbdcbbcababcbbadccddabcbbdcbcddacaaaadddbbccbccbaccabbdbccdbabbbaaacaacadadabbaabaadddbdcccddbabadbaaabdbbaddbddbaccadcdbdcdbbdcdddaaabddaabdadbcaabdcbddbacbcaccdabdbbdcdcdaaadaaaaaddbbbbacdcbaaddddcddbbddabcddbcdcdbdcaacdbbbbaccaccbbcadadbddaccaaaabbdadacdcbddcbacbccaacdadddaacdcbddccddbcabadbddbcdadadacbdaadccdcbbbcdabcdcdbbabacabbaddadbabcccdaadabbadbaccabdadbaacbddacdaddcbdbaccabdbccdccccddcdcbcbaddadcccdcadbdcabccabcaacdbababbbdcbbaacdbdbdbcdccaabdddbbaabaaadbabcacadabbcdbbbcbacbdacabdaabbcaaabdbabddcbbcddaadaaadcabdaddadcdaaabbaccddbadbcaaddccbbacdcbbbbcdccccacdadacabdbbbbcdbbdabbbdbabddcddadcbabdaaabdccdaacdaccbccdbccadaacdbcbacabacccccbccaadcbcacbccabcdcdadcaabcacdbaaaccddcccdbcabdcaadacbabdbddadbbbbcddccbcdcabcccdaabadcccddabadbaddcabcccacdcdbdbabdddbbcabccbabccdbcccbbdabddcbbdddccbddbaccbabacddcbadaddcaacabbababadcdadbacbdbbccbbabcbbabdbaddcccddcacdbcdaddccbbbbcccaabbcdbadcaccdadbaaaadabbcddbcdcdcdbcaadbaacdcaddcdcccdbcabbaaccccbbcacdcbdcccbbccccaabccbbcdcadbdcdadbdacdabbcaccbaabaddadcbdbcaddbcdaacbcbbccdaadbbbbbcbbdabdabacaabcdcbccbdacccdaddcaadabdbabbccbccdbdcaccbdacbcacdcccbacccbbdccaccbcadcdbacabcbdcccdbaccbaddbacddaabcacabbbbdddacabccdcbbdbbcdcabcbbbcccccbcadbccaabadadccdbdbdddccabbbdbadddbaaabbdbbababbdaabaaaadbdacdbaddbcdabbdbbdccccaddabcabacbbaacbbbbabcacdadccabdcdaddccacabdcccdcccacbacbaadcaddbdbbcbaaccdadbaadddbaddccccaaacddaacaacbccdacbadbaacabdbbdacabaaaacdbcccddcdccddccaccaabacccaadcacbccbbaacdddaccbcbbdbacbbdcbcbccbbaaadccadcdaaabcacaacabdccbcadbcbcddbacccbaabcbbcdccbabbdacccdaabdacbbaddaadcaaddcbcbabbdcdbabaacbccabdbccbcbbbddbadbbcddbbbdbacbbdcdbdccabdcdaadcaaabcdbbadbbaabcadaacbacbaddcddbaadaddabddbaacbcacdadbdddcacdbadabcddbabdbbabadcccacdacdaaacddaaadadbccdccbcccbbdadccdddabbbcbcbdbddaabaaddcbacbbdccddcbcbdacacbdacacaccabddcdbbddaadbdbdaacabcaaabdbbddaabbaccccdbabbabbbcadbbdbcdcabbaadddbbcbccbcdcbacbadbcdddabdcacccccadcadacdacabccccacccacaadbdadccabbbcacdcadcddbdabcdcaabddbbadabaccdbbccddbaaacbcdadbdadddbcaadcdccdddbdabbbabdccdccbbdadcbbbdddbddcdccbbcddddccbbaddbbacbbacdbacccbddbdbaccbcdbcbabdbccccbacdbdbdddaadddbdbccbaacaabdaddacbdcbdbaddcdabcbddcbdbdcbbadbcacbcbccabcdbdbbdaaaaababbadcdadbccabbbabdbdabbabddacccdcdabacdbcddbaccabbdadbcbccdddaabcadbdaddabcdcbbaabcbbbcaddcaaaacaccaabcaddcdbdcbddadcbbadddadbcaaabdababacdbaacdcdbccdbcddddcaddaccccddacbcadbbbaadddaabcbabbabaadaccaaaadacdbdaaccbdcadbcaabccdacccddddbbdcbbdadabaabbbcadbadabdcaddbbdbacbbcacacabdabaabaadbccdcbbdddcdbadbddaaaccbadadbdbdbcdcdbbcadcabaddcaaacdacaadabbdddaabacdadcdcaabcdcbbaabaabdbbbaaabbcaacddaadddaabdddabcbaaadaccbccdccdadbdbcccdaaacdbdadbbdcabddcbacdcdbbccbcbaaabadcccddacdbbcbcabaadcddabcbddaddaacddccbaddbbadbdabdaccccaabbadbbbcbddbadbccbabbadaabbaabbabacadbaadbcdddbbdcabdacabcabcccdabbacaaddacbabdbcacbadacdacaaabcabdddbacbaadddbbbcaaadbbbabaacdcacbbaacddbbaabbbdbbdadaddcdabccbbbdbdaadccadcacbcbcababadbdaddaacbbcbbbbdadaaccdccbcbcaadcccbaccbacddcccdcacdabadadadabdbabacccccdccbbbadddcaadaaaddadaadcbccbccddcccbcddcdacddcaabadddbcbbcbadbaadcdbbbccdcbdaaacdbcbbbabbabdcaddddbddaaadaaadcbbcaccbaacdabdbcadbbddabcdccdabbbdbbaabcdbbadbcadabcbdabcdbcdcddbaadcaddccdacbcccddcccbbaadabbbbaaaddddddbdddcbababbdcbaadcccdcaccaadddcdbbccdacdcdcbcbbbcdddcbbbacdaaacadbbdccaacbacdcbbdadaccdcacbabbbccbcdbcaaabbdcbccdbdaaaccabdcbbbabbddbabcbbcdccabaaaabacaccdbdaaddbbcacdaddaddbaaacbdddabadcdcabcacdbcacdbcdaccdcdacabaabbdaaadbadbcacdcdadcadbacddadabbabdadbbabcdbccadcaacbaabbabaadbcbdbcabdadabbbdccabababaadcdbbabdbaddbccccacdbbdccdbacccbbbbbaabbcacdacabdacbbaabbabcbbbacdbcacbaaccbabaadddbadadbababbcbacbbaaccccddaaadcdcddacccbadabbccaabbccacdcbdcaaacbbcacdbbcbabaadbbbdadddbababdbbcdabddcdabaddbabddaacabbcdbdbddaddcdcccdbcabbcdcacdbccbccaaadbccbbbacbdbcaccacbdcdbaadcbbadacbaadadddaabcadccbaabbcccaccbadabdadabdbbcddbbcccddbdabaccbcadabdbdcbccccbcbdacbcbdcadacdaaacdbbbcaddcdddbbcacaaadcbadcbbbddadbbdddaccaadbcadabddcddabaaacaacdabaacdbbcbdddccacacbcdcddccdaccadcdbdcbabdddccacdbcdaaccdddbcaababbcdcdbdddaddbbbaddcbcacdbcccdbabaaddcdcbccaababbadddccabbacacadadababdaccbdacaaacdaddaacadccabbbadaabacacbddabbdacbdddabddccccdadcacdcdbdccacaaacdcbbcdddabdbdccabccbcccbaaddacbccaacdcabdcdcbdcabcbbdcadcbcdabcbaabdcbabcdaddadabcbcddcacdbbcaaadcdddbcdbccbcddbdcdabaabbdbdadccaaacdbcdbcbbbabccadccdbacccabaccbabbdabdbcdbdcbcabdabcdbabdcdaaacadbcbcccddbdacddbcaccaacabdccbaadabdcdcccaaddcdaaaaadaaadcbabdabccdbcbbadbbbbdadbcddccbcddbadbaadbdbbbcaaaaacdabcadadccabaadcdcadccbbbaabacbbcabdccdacaabcaccbddbccaaddaddbdadcccccabbdcadcadaddcccadabdbdcadaabbdccccdccacbdbcdbacadabaaabbcdacbccbcbadaaacbbaacdbacadbddcaadadcbdcaadbbdbdcbbcacaddcaddacbdbdcbbccacacdbaadaccadbbddcabaddacccaacdddbababacdbdbcaacacbcdabcdcbdcadcdcdbacabbbccbbabbaaabaabbacddcbcababcddcadcddbdabcdacccbcbaacacddbbbcbabdaaccadccbabbbaabcadccadcacdcdddcbcadbcbdbbccdadbbaadcabdabbabadccdabdbddcadacdcbdbdadcbbdbcbcdcaadaadbbcaaacbaabdcbabbcccdabdadaaacaacaacababaabacbccdcbbdbbddacbadcadadbcabbcacacbbdddbbdcbddccacbddaabdacbdbaabddcdcabcabadcbadadabcdbbadabddbaccdddcccccdadadaadacaddacbbbcdcbcabccddcbaadbaccaccdaadcbadbbaaddcdabcccabaacaddbdbdcbddccdbcccdaccbabddaaaccdbbabaaababbbacbcbabcaacdbcdbcaaaaddccbabbcaabbdadbdcaadccadcbdcbdbbabacdcbbcbadbadaaaabbccbcbaacbccddaaddbbdcdcadabdacdbadddcdcddadbbaaaadcddcddadbbdbdacacbddcbddbbddcacbddaabbcdacbacdbadcabacabaabbdbabcabadabdccacccbdaaabcbadbbddabcdacdddbcbcbbabbbbcdaccabcaddddcbdabbcaacacbaaccabbdbddbcacdbbcdaddacccdacdcdcdbbadcbbcbabcaaccbbbbabbbcbcbdcbcbcabbcbdbaabdadbccddbabbaacadddcbbdbbbadccbbadbbcbbabdbcbdccdcccaadccdddcbbccacadadcbccabacabdcdcbdccdadaddcddddddbadbcddaadcbacccaadbbdaaacadcddddbadadaaccdcbdbbcbaaaadbbbcbaddbdbaadabadaaacbbcaabcccdbaacdaaadaaaabbbddddaccdbdbdbacdabcbdcbccadcccbcccbdcbabbaddcbcdcaddbbbbccddabbcabaaddcccacccbbadbacdcdcbbbbccccbadadcbdaddccabcdaadbdbcccbadacaadcccccadbddabaacabccabbcabacdcdadabbcacbabbbaacaddcaddbacacbcbbcbdcaddccbcbbdcccaadbcdbbbaabcdadccccddadaaaacaadaddcddaacbbadadabbadacaadadddbdabcbbdbdcadaadcdcdabcddaddcdabbbddbdddcadadacabbbbdccbdbabadcbbbabbadbddbcdadbcaddbadcbcbaaaabccddbbadaacbdacccdbacdacbdacaadcdaddbadbbddbddcaccccbdbaadcbdbacddabddcababdbccdcdacdccaacbdadcbbcddcadcbbabcbdcdbdbcdaadaacdbdaadacabdbaabcadcdcddcaccaddccddadabacbacbdaaabbacbadddbbaabdbbdbabccacdcacaadbdabaddccdacdbcabccbbcccbcbadbccbaddabcddbabcbaaacdadcabaacddbccddbabaadbbdabaabcaaddddacaddbcdaaacccdbababcacaadbbaabbccbdcacddbadbbabccdaaccabccaddccbddabddbdbabcaccacbcababaadbbbdadcddadabaddbbccbdcccbccbdbbcabcbaccbbbbbaaaddbdccaddcdaddbddbbdbaabdcadbaadcadbdaadbdcbacabcbcddbbddccbcbbadddabdddcccbddcbaaabcaddadcaadbabcacddddabdbcacadbdcaabbcbbccbdbaddcdbadbbcadbbddaabbcdbccacbcaabdccdcdaccaabcccdddbbcdaddcdaacbccaabaccbbcccbbbdbadcbaaacbbbcbbdcaacadbabababcdcbbadccdcabbcadcdacbbbbcadbadbcbccbbacdcbcccabbddbcbaadadbbacbcdcbdadbdccabbcddbbcdbaaabadbbacacdaddccabbccccabdcabddaadddddbbaccdbcbdbdacdbdbbaabbdbbbcdabcccdcbdcaadcbbacdcabadabcccbdbbcdacdcbdccbbacababadaadcaddcbdcdabcadbacdabacbbbadbcdaaaacdbbcacdabcadacdbdbabcbcbdcbbbbcadabbbcaadcbbbccacbccbacbdcdacdadbadbbabbbddcbbbbbcddcdadcdcbbabbccdbbcddaacaaddddbabdacaddabddbabaacbdcdcbcbaddaacadadadbddcbbbcaccddaadcddddabcabbcbbcbcdbdabcdbcadccbbdbbdabbdbdbdaabaadabacbdcdbdabcaabbcabbdcaabddbcbcadabbcdbdabbddaddabcadacabbadbddbcbcdccacbcaaccacddbcbdbbcdccacdbcccdbbbabdcbddbaddbdbbdbdacdddadccbbdbdcbdabcadaddbacbcbcdcbdddacaabcaabaadacbcbdcdbddcbabdcdbbbaddcccadbaccabbdadbbccacbaacbdbcccccbaadbcdbababcadcddcdbbdabccabbdbdbabacbccacababcbdbdaaaabaacccdaacdaaccbbcdacadccbcccbccdcddbadddddddcacdcadddbbaaabcbbdddbdcdbabacabcaaaabddcbdcddcbcdaadbbcbddcbacdadddaabacadbbcdcadccbddbddbcacaabdddbbdcbdacbacddaddbacbadcbcccbaadccbaddcacddcbdccbbbcbbbddacddbccdadaddbaadcaabcdbbaabdbddbbcacbbdaaccddcbddcdabcdcdbaacadcbcbabcdbbaccdababcdcdcbcccdddbddbadcbccabacdbdabddacdbdcdbaadacbddccaabdbbbabaaddcbdcaccdddddacbcbbaccacdccbabaccdcdadbdacbdddaabddddbacbcddbcbcadbdabddcbddbdcaabcbaacbaabbddddaddacdcbaabdbbadcddbcabbbbdcdacbdcdcaabbbcbcbcaadabaddbbbcbddaacdbaabcbcdbaddbccdbcbcdcbbddaccadbbddaacabaabccacaacddcdcbbadcdacbbcacbaadbdaddbbcaacacaddbaccbaaacbdcdaaddcbdccdccadbbdddacdbbcccdadccddbccbcbddadcdaacbadccaddacacabbdbbdabdccbbddabccadbabbcdbaddaadadbbdbccbcdaaabdaacbabcbaabdcddbacacddaccabdcabbddadaaddbcbbaabbbabccdaababdaccbacdaabbcbdccbbcacacddbdbddbadbbaacbbcabcccbaaddadcabdbcaccdcbdaabccadbdcdccbddaabbaaaacccdacbddabaccdadbcccdcdbdbdaabaacdccaccbccbaccacddccaaaabacccaabccaddacabaccabbbbccacddaccbdddbdbabdcdddbacccabddcabcabbddadcbbdcbbbbcadaabbbddddbcaacaddbaaabacbbaddabcdddcadcabddabaddcbdbadabcaccdbccdbaacdaababbadaaccdaacaacacdcaccaadabcbcdbbdbcdbdbdcdaccbbaaacbcddaabaabdbdccbdddcabcaccddaabdadacaddcadbcdabbcbbbbcdcaabcacdbaabbcdcdabbcddcbcabababcbdaacbcdabbdbcbcacabccdcadbbababbcacdcdabbaccacbcdbbbaabadabcabbccddaadcdcaccccdaabcdbdbcccccacbabdadbdcacbbdbabbcbcadbcbdbdabadacabbdbbcccacdaabbbdbdaccbdacacddaccbdabbbadccacdcacacbdaaadaddccbcabcaddcbddaccdcbaaaccddcabdcdaaabbdbbdcbcddcdccdbaddadabaaacaddddcbabbcabacbbdccdbdddaabdcdbadabcacadaddcbbbaacdcdbbdacaabcadddbdcdbdbcbbadcbdabbcbbbcbbacdbbdcdbbadcadabddbcbcddbadcacadaadbcabadbdabcdbbbbccdaacabdabadcbabcabbaaaacdaaadaabaaabcdaabcaaabbcdbcdaabddcacacacdabdcbbcdbabcccaccaabbcbcabddddbdacdabcbbccbdbddacddcdcdbddcbaddbcdddbabdbcacdaaacccaaccdaddbcbbaabadbabddcacaaacdcbcbcadaaabdbcadadcadbbbdaadcbcdabdacabbbbbcbddaccacacaddadbcaacdbcccacbdadccadacacdcbcccbbcaadadaaabadbccdaabbdddcabbbcaddabccbbcdaadcbabbcbdcbcbdbcccddaddbdbbbbaccbcdbcdcaacbddcaccbcdbcbdcabdbddcbabdccbddbabbbbbaacdcdababbddddcadaacbcacbabaddaccbbcacdadadbcaccaadaaaccabdcdadbdbbaddadaadbdbbadabadcdbcbbaababadccdccacaacbaddcddddbbdccdccbcadadacacaaacbcdccaccbcddcddcbcbdbdcadbaabbaacaaaadcacabcbcdcbaddcddadbdcbabaadaabcdcdbdcabdccbdbbdcabaccadbcbcabcccddcddcabdbdabadaaabbdcccbdaddcbbacdcddcdddbddbbaacdaacbbdddcaccacaaaccbccaadaabbcaabdbaaaccacdcaabbcdacbabccbcadbbadbbdbbbbcdaabccaabaddbdaaacabccdcccacbdcaddbdbabbbdcccbccdcbacbcaabdadcaacbdaaaacbcdaadcacbcddcbbcaadcabbcbdcbbaadbdbcddadbddbbbbcbabaacaccabcbadccbbcabdcaacbaaadaacdadacaaabdddbbaadbacadcdcbbbaddbcbdccadcdcabbbcaaaabbbabaccacaacbdbbdbacdcabacbacbadaabccbbbbbcabbcabadaddcaabdbacabdaabddbbbacdaaccbbadbacabcdbdaababbbbcdbabdddaadbacdacdbbbaccbdbabaddddbdddadbcbbacaadddddbaccddababcdcadcbdacbcaabcdbdbacdccbbbcdbddcacdddcbaaabcdbaddadddadcbdabdacbadbbbbcbcdadcdacdaabdabdbacaacaccacbaabacaccabdddbcdcacbccabbdadcccabbaaddadbacdbdcddbcabdbbababbdacbabbdaabbcbabdadbcbcabbbaaccbaadaccdadccbbbbcbcabbacaacdcbaaadcacccabaacbcdbdbacdcaaadacaddcbbbdddacbacbcaaaccabaccddadcbabaddacbbcbcdbbbddbadccdcccacdaabcaadacbcabccdaaabadcabacccdacbdaddbcdddcacaccdcddcdbddacbacdbddaabacdbababaabaccadbcdbacdaaacbcaaccbcbadacbcaaddbbacdacacacdccddbbdddbaddbdbdccadbcaaacdcbdacaadcdbaddbacbbccbbabdcdbbdbabdadadaacccadcbdbcbdababbddbbcbcbcbabaacbccbdabcbbcbcdaacadbddaadbaabdabddaaabdbdaabbcacdddacbbbcdaadccbcbdadcacdcbadbaccbabcbccdbdcccdabcccbaccdcddbbbdaaddbbcbbccbadcbccdddbbdadbbaaaabddcdcaadbcbcbcbbabdddcdadaacccacbcdacabcdbdbcacaaaccccacabacabccacbbadbdcbccdbaaccbbacbcdbbbdaddadbdbcaabcbbaadabbacdbcdbacadbbadbcacdaabbadbdddbbdbcbccbdaadcdcadaabaabcbdaadbbcadcddbcbdadacabdcddbcacbbddbcdcabcdcdbccdccddcdcaaacaadddddabacaabbbacddcdabddababcddbcdcabdccadccadccdbadaddddcdaddadbaccbadbcaccccddabdcbaaddacabadcacbbcbdcdcaacaddccacbaccbdcbabdbbcdddacdddddcababacbdbaabadbccddbadbbdbbbdbabddabccacabdcaccadddcaadbcbcdbaabcadadaaccbddbacbdaabadadbadbccbcbdcabdadcacdabdaabccbcdbbbacdaacbdcdcccbaddabddaadcddaaabccdbcddcddbcddcadcbacbbdbbdbbcabacddbaacabdbbadaaacadccccbbcaccddccadbaabccdcbdbadbcdbcaadaaddcdbbaaacdabaabdcadbcbccdcaacdacbccbccdacadcdddacdaccbcbbccacacdcabdccdcbbdbdaccbdbcaccddaacabadcddabaacacacbacdccaaabbdcbacddddabdaddbadaadaaccabbaccdabbdadddbdbcbaccdbdbdccddccbdaddcbbabacbbaaaadbcabddacabcaabcccbccbadacbddbcadcdacaccdcdcbbbbbddacabccbbccbacbdcdbbadcaadadbdabdbbbcccdcdbbdddddbbbacdacccdadddacaccdbbcbadacdccbaacabccacdadcaadbabcdbcbcacabbbbcdddacaccdcdaadcbdcdabdabdbddccdcacccadccddccabdaccabcbbabdbabddcadacbcdbcdbaadacaaacdcbaadbcbbacacbaddccdaadbaccdbccacaddcbaddadbacabdabbdcabbdddcdbdbbdcabbdbdddcbabbcbddddbbbaddaaadacbcdccbccacbabddadbaabdddbddacbabbbadbacbaaaacdaadadcadbbcccdadcacbbcccabcdbacccabdcbacccbacadadddbbaacbbcbcdacbadbaacacbdbbaabadcdbccadcbdcdadccacdaddbddbdccbdbbaaddaccdcdcdcccabaaddcddbabdbbbcaabaddccbaaaabbcaaabddaacbbbadbbdabccaccdbaccbbbabdcddbbccdbcdcacaacbcdabcbccbbcaccbaaccccdcbadabbccccabbbcabadabcbddccaadbdcbbcbdcabaddaadccaccdbcadcdcdaccbdaddcdacbcbdabdabacbabcdaaaacccdcbcbacddbbdcbbbaabbbcbabdbdbbcdccdbccddcaabdbcdbdbabbbcbcacaddabdbbaabdcddacbaacaabacaaccdabacaabbaddaadacbbcbbbccdcbacbccaddddcbbbbaacdcacabacababbadbaabbcacbccabccdcaddcbddbaadbdcbcdbdcdacddddccddbccdaccbddbcdadbbacddddcdadbcabdcacadddbabddbbccddcdaabadcacdabcbadaadbbbadabdcdabdcdccbdbddcdbacdadbcdbcbbdbcbdcbcbcadcbbaccdbadacccaccdabcbbdcaadcdbaaabadadabaabccdacacddabccbdbabbbaadcaabbbbcbddbdabcabaaadbdaccccdcdbdcddbdacadacdcdabdcbddabbabcdaaaadbadbcbaadcacbacbdccdadccbaacabdadbbadaaabdacaabcddcbaccacbbadabdccadcbdcabccbbacdbbdadbcabbcdcdddddcbaabdbddcabdbcbccbbdcbbdcdcbcdadddccaabdbcccadccabbbcbdadacaddcbbabcbcaaccbcdcbdbddddbaabbcacddbdbaabbbaaaabcbddbbcbadabaaaccadcbaccaababcbdaabbadcaadadcadabccbacacbbbaacbacdadddabcbbbdacadddaabacdadbbabdadadacbcaacdcccbbacbcdbadcddaaccddccaadabdababaaabaccadacccacdbcdcadcdaddcddcbbddccbccaacddbaddbbcdacbdadbdbdcbdbdabbddcabdccbccdccdacacacccddcabaccacadbcccddbaacdddacbcbbddcabaacbcdbcbaddddbdbbacaddababbdaaccbbcaabdbddadabbaadadacbcccabcccdbcddaacbbcabddaccdabadabddacdcbadaddcbabbbabadcbdacacdbdcbcbdbcacacacdbbdbaaabddddcabbdcbacbbdddacaccaccaabcbdbacdbddacdadbcaadbdbabccadcacaaaadbdccdcbcdbcdbadacdcacdaccddbcbacdbbaabbbbcdabcdcdaaaabcdabdcdcdbadcbdaacdabcbccaaaaaacabdbcbdaccacacdbacccacbbddcbacbbbbaaadaacddacdacbbbadabadbbbcdaadbbcddbccbcbabdaabaaccbdbbcbcdabdbdbaccdaabdadbccadcbaacccdabbbbbbcaabbdabcddaababcdcacadbdabaddbddadbaccdcaadbbdbdccdbddccabcaccdbcbdadabddcdbbdddacbbdbdadabccbdadaccddcbcabccbacadcbaacccddcbcaccacdcbcacbdbdabadcdddbcbcaabbdbcbccbabbdccadddbdcacbaacdcadadbadbabbddadcdccaaabbbbdcccabdbdaccacbbcdcdacadbcdbcbcbadccdbdbcddaadacbababddacccadcdaabadccaadddabadabcbaddcaabccdbdbdabbbdbddaccaabcaddaadadcacbacacddaacdadddabcbdaaadbcccdbdbadbadddbabcadcbabaddcdcccaccbcbbcbcdabccdacbcccccddddcccddccddbcaabadaacbbbcdcbcbdbbdcbadccbdccdcccbadabacabacdabacdbdbcbabbdadbdadcabccbbcdaadaccadaadbdbdcdabbdaaabaaddaabaacbadcbcaabccacadcdbcbdbcaccbdbdbbbddcdaaacacbabccaddbccacdabbbdbccaddbadccacadcbdadccccdccbadacdbddadcbcbbbcdbbbcdbbcbbadbaaacaabbabddbbabbacbabbcbabdddccbaacdaaadbbbcddccdddbaabadbcccacbccacbcadbaacadbdbdacddcbcbaadbaacbdbabddaababcdddbbbcdbaaccabcadbdacabcaaccddbababacabacdbbaabcadcaacdbbcbccbddababbdccbbcbcbbdadaddaaaadaaaadbbcabbbccabdbddaaacaacdacbcaccdbbdacccaadabdcccbaaacbcbcdbbcdbaacaaaaabacbabbbbadaaabbbbcdadaadbbbdbacababcaaaaccddaabcccbdcdaacbccdbdacbababcdadcdcbaabdcaacdbabdacabdbdaddcbcbbcbdbbcdcabbddbaabbbbcbddbbaabaaabadbbdcddcdbacdabcadcdabaccabdbcdababaccccadcdbdbdcaddbbabbaacdbaadbdbabdcdddbcbcbdccaaddcaadcaadaccadadaadcabcddbcccddddcdcdbbcbbbbaabccbdadacddbbbccdcbbadcbdccaccdcaabbbdbbbcdbcdadccbaccbcdadbdbdcddacbbbdcaacaabccbcacbacbbcbccabbabdcbdbcbbbbcdcddbbbacddbacbbacaddbbadcbaaaabbddcbbcbbadbabcbbabbabccaaadcacccadcdbccdbbbcadbddbbdbadadcddaadccadadabaccacabadddcbbadbdbdcabdcdccadbbaaadacabcddcadcddcaabdacbcdacdababdbcaaacbcbabdabbabdadcbcddaaaabadcaccadbddcbabbdbbbabddccadbddbbabdaaddccdcbbdacabaabddcbcaababdcbbcaddadabbaabcabccdabdcbadcadbdaabbabdbdddababaccdaddadcabdbdcdaaaaccbadcadabaaadccadddbaaadcbdcbbdaddacabcacabaabdbcdaddcadcbbdbbcddabddcacbbcbbdbdabddaaacabcdacddcbdcbacccbdbbaaaadabadbaacdbcbadabdbbdccadcbbadcdcbcadbccbbbdbccbcccbddaabdaaaadccdabbcccccdbabbcabbadaadaabbaccbacadabbdadaaddddcabdccbdacdacbbbabcbccdbdabbdccabbbadbbaabadcbddbaddcccbbbdcdccccadddcddcdccbdbacddadcaacddabbcadaddacbaaabacacccddcbccdbdccacdccaddcaadddcacacdcddabcddabcbcbcdccdadbbcaacadacaddcdadbaabacdabddabcdcdccbcdaaadccdbabdcdbcccacaccdaccbbbcabcbaaacadadddacabcbdbcdcbcbdcabbdadbcdaabbdcdddcbcddaacdbbbcabccccaaccdcaccdbbdbdabccbcbcbcddaccdabdddbdaacdbcdcaddbacbadacdaccdadabcaabcadbadbccadaabdcbdccdaccbabadacaabddbbddcddcbaadddbcbbcdddcbaacabbccaaddacacdaacbadccbacbbababcbaacacdacabcabdcadaaacbadbcdbdbcdaddbbbcddabaccaacaacdcacaaacacadbaaacdcbbabaccdbbddacadbacbadaadccabccabaababdbdabcbdacaccdaaabcabcbcbcbbabcccabdaadbaacbdaacdccbcdaadddbdacddccdcabbcdabcabcaabbdbabcbdacbdaaccdcacacbaaccdcbcdbcaccaaccbccadccabdbcdcaabadcacbbababaacbdcabddccdcdadcbddddadccaabbabbcdccabbbdbcdaaaccabbcabbcbabdbccbcbcbcbadacbbbcadabbaabcadcdcdacdbdaaaddddddccaaabbcdadbcbdcaacaabcbdddcbaccadddbdbbbabdcabaadbaddaaccbbddbbacbbdabdcdbcabcdcccccabadacbacacbbabcbbcbaaacccbbdddbdddccaccdbddcdabdbcbcdbddbdcabddabbcdabdbbdccccadbdaccbaaddbdadaaaacdcbcddbdbaacaadacbabdaacaabddddacbbcdcdddaabcacbbbacbbcdbdabaadbdcdbbabacbacdadbdcbbdaaaadaadbbccbbdcccbbcdbcbbdaabbaaccbdbcbababbccaadabbbccdabddbcccabdccabbbdcaabcdbdccbddccbcbbdcaddbddddbababbcccababdcbccbcbaccabbbabbbaccbddddccdddabbdbdadbbdbcdbcdacdaddccbabbadbbbbaadadddabcacaddccacacddadcdcbaacbddbdaabbbbacabdddddacdbdbbabcbdbbbcaabadbdacdaabaababaddbaabddbcddcbdacadcaccbddccdcaacdabadcaadcadadbbbdaabbdddabdcadabbbbbbcbdcbcbcccadbcbcbdbadacbadcbcbbcdadddddbdbcdddbacbccbabdbdcdabbbbdcbabbcdabbdcddcbabccaacbadbbbbacbbcadbcccbddbcccdbbbcbcdddcbccbcaddbaadbcabdbddababddddbcdbccdcabdaaacbbdacbbbdcababcaaaaccabcdcaaabcbccdacdabddcbaddbaabbacadbaabddcacbbbcdcacbcbbdcdbbaabaabbbbbbaacaaaccdcdacdddaaaacdabaaddcdaadcdadacccacbdbacaacbdcbbaacddddcdcdcbdbccdccbaabbbbccdbbbabcdbdabcacdadaccddccccbbccaabacdbcbcdabdbccdbaddddbcabbddbcbdaccacaaacaaabdacabdcabdaadccaabdaadacccbababbdacbaacdcccddbcbbbbdbcbccdcdadbbbddcdcabdcaacbddbbdcabdcdbcabbbcdcdcbadadbdccbcddbbddbbaaacacbbdbdabaccdcdaabcacdabdbbdaccccabdbccbcdbacdcabbbacdadbccddcaababbbbbaaddbdababddcccddcdcbadaabdcbdccdcadbdaabbaccdbdbbddabbccbacbdacddcbdcacaaadbccdcdbabbdbbbddccaccccdaaaaddcdddbcccbccbacacbbdacdcbbdcbbaabbbbcdbdccdcabbcdbdbbdadadcbadacababbcadadaddadcaacbbdbdbbadcdcdadabadddbdbbdadabdaadcbcccddbbabbcadcabbdbacdacccbdbdaaaddbcbccbcaabcdaaddacadabcdaacdadbbadccccccaadcbddacbcccbcaccdcadbcddbaabadbacbdbabaaaaabacbcbdadacdabdadbcdaadcaacdddcaacdcaacaadabcdddcaddccbbdccadcbabdddaaaddbddbddcdadaccccadccddcdbaccabbccddaadaaabbcacdbdabddadbacbddbdaababccccabcdbdcccdacbdabbdcdbddacaadddacdcdccbadcadcabcbddbbcbdbdccadcaddaadadcacbaddbdcbbabadcbdbdacdacababababacbddcddcbaabadbcadbaddbddbddacdadadbddaccdbccbbcdcaacbcadcaadbccbdacadacddadccddaccbddbcdddaacabbddcbaddabbabaaddddaacabdcacbaaddcaccdaacdaaabacabacdcabbdbaddbacbbdacdbabaadcbbaabdbbdbddadccbbacdcdcbaaaaacaddcddcddbbbdcdccbdacbaacbdbacddccbdbcabcddbdddbdcddaacdcbccbdbdabcdcbbcdbbcbbbaabcacacbcddacaaaadbcdaadcacdbaccbadbccabdbdbccccdbcbbbbbdbbccabaabdacbdcddcadaadbaddaabdabcaacccbbacbcdbaaaaaddddabdcaccdadbcacadbcdabacabcdcaaacccbdadccbbdbcccbdbaadddcbcccdddaddcbaaadcabcbccdaccadddabbcaadadcccbddaaaaabaabaccaadabdbdccacdaabddbdbaaccccdacddcddacdcadbbacddaadcdddcacacacbcdccbcbaddadababadcbdbcbaabcbdccadbbcbbaadcabdcbcddacbadcaaaabcccdadabdbcaddbccbdbbdcadbaabbddadcbcbcadacabadbdbacaaaaaacddddbdabdbbadaacbdbbbdabcdaaccdaaccaadbcccbbcdbacbcabdabcaadcccadbdabdcdadbcbcbdaaabddabaadaabdaabddbabbbadccccadaaddccddbcadcacaaaccababdbbaaccccccdaddbaacbadbcaddacacdaadadccbcdddaacbcbdbccdcdbadaddabaaabddbcdaddbdaddbdaabdadcdbccacabdacbcdaaccbcbddbbbdcacbcbcacdbbbbadbabbcccccacaadaaadbcccdcabcddacdccbcbdcbbcbbbdcbcdccbcaaddbdbdbbcaaacaacbcaabdcacdaababbdadaaccacaddcbcbcbbadcacbcacbcccabbcabbddadcbaddcbddbbaaabaacdccbabcdbdaccaabbcdbcdbcccbbaabdcacbbbcbdcaabbbdadcbadadadbbbbcbacddbacdbaaababdcacbacbaabbdcbacaaddabdaddcdcadbabbcabaabbccccdbccddadaabccdacbbacbbdddaadddabbdbabcaabbddcbdaccbdadcabbdacccbbbddbdcdadccdddaaadcabbddcbdddacbcdabaadbdbdbdbbdaaccabbdccdadaadbabdcdcabbadbcbdadbbccddddaabcdbccbcdabacadbbbadaacdcdddddcccdcaacbbbbacdbbdbcbcccbbabbdadabcdbbdacaadbadcdcdddddcdadadddabddcdccbdcdbabadbcccccaabcccdcdabaabbddddbbbadabcdbccdaacadbbcbbcaaacaaccbbbaabacccdadaadacbaadbbdabddabaddadcbabcddcadcbadaabcabbaabaacbccdaccbcadcbaaccabbbadaabdddaaaaacaaccbccabcdabadccadbaacbcaabbabcccdbaaadaaddbacadbbbabbaaaacddbddaacddcabdcdbcbdccdbccdcbbcddccbdddddcbbdbccacdbdbbadcbdcbacdbcdcbdcadbddaccbdadbdccdaddbacccadacbbbbcababaaacacbccdcacbcbcddcaabbcabbdbbdbcddcaadccbaccaddabcbaacbdabcdbcabcaaddbabbcdaaddbbcadcdaccabcbdaacdccccccbaadcdcbdbdbacbbbaacbcabbcabacbacbdacbbcccacdaccbadadbaacdcacbbdbacbcdcaadcacbbddbdbaaddbdbcdacccbbbccdcdacbccacabacbacbdcdbcacaaabcadcdcbdcbacbbbcddbbbabdaddbcabddcabdccdbaccdaaaaddccbccddacdbdddaaabaccdadaacacadadbabaaddddcccdbbcdbabdcddcababdddbdaacacdabccadcdadcaddbdbbcadaaccdaacdabbadcccacdaabccddadbcbdaacaddcabcbdbaaddcabbbdcdabdadadcbcaabadaaaabddaadbdddbbbabdabadbddabbcdbdbddacbacdbddbbacddddacbdaadbdcacabdccaacacdcbdadbcbaadbdaadddcbccbdcbdcadaaddcbddaccbdbdbcdadcbbdbaddadcadbcbacbabcdacbbddbadbaacabcbcadabdbbbcacadcdacdbbccbabccdcacdcadbaddbbcdbdcabbdadcbaccccbdadcbbdcdacabaaaddadbddaddcbbbaacabddadbbadcdbdadcaaadcabdaabdddcacbcbbadcaadbdcababcbadbddddaadacccdaaadcdbdabddddaddbccdccbcbdacaabababbadbacdacdadddcacdaabaaabdacdbbcbcdbbabcbccacdacccccaaaadccbcdbcbcbbbdbdccbdabcdcccdacdcaaccdddcddbbaddbccadddccbbdaccabbdabbbcbccbcccacadcabdbdbacadcdcccccdcbabadccbdcdcaacdaaadaaaadbacccacbccaaadddabccbccddbdcaabbabadcbabdaaabbcdcabadadcdcbdbbdbbbacdbacdbcaacacbacddbcbcdacabaccdcdddaacbcbabbaabbbaaacabbbadaaadbcddbadbadadabcaabddaccaddcdabdcabdbbabddadcabbbcabdaadbccdcdaabdbdacbabccbcccccbaddccbcccabbaccabdbbabbbdbbcabaacdbcccbcdabbbddddbacbbbbbacdbbaadbccdcbcdcdcbbccaccdbddbadabcabbabcdcbbcacccccbaabbbbbbacbcbbcccbcdbdcabacddaaaccdbdcddbbacbcbcbcdddcaddbddccaccacdaabdbddabbcbbdacdbdddbdacbabcadadccddbadbbadbbaaddbddaaacbdbcccaacdbbacbccaddbccbbabbcdcbdcbacbdddbcacddcddbdbcaccacabbdaaabcdcccbbadaacbcddcadbcdcdabaabbcdbdddcbdcbdbacbdadaacbaadaadabbadcddcaacbbacdbaabcdcadabadcddaddacbdcbcddaaddccbdbdaaccdddbaababcddaaaacdbbaaacadbdaadcbcdbdbabbdbbaaddccbbbdbbcdaacbdccbcddabcaadadbaacccacaccbbbdbddadaaadbaccdbbcbcbddaddcbddcdbdacbdbbadbdadcaadcbacbabbdaabdbbaddadbcdaaabdbdaacdcbcaadccccaddcaabbcdcbadcacaaababcabbdcdddadabdbcdcbdabdbcddcbdcabdbcdabcadccdcccacaddbbbcacdbdcdaabbbaacdbababbcbbcaaddaaadaabacbaabcdacdacdcdcabdddcbcccbacddcdadbaddcbbccaadacbddbbdddaabccbbccbabaadcbdacaaadabbccbbddbadbbdabbddacaccddbaadaccabdbbaddcbddacacbadcbbcddcacdddcbaaddcbcabdcbbcacacdbddacbccddcbadababcadabaddddddabbdbdaddbccaaacaacbabccdadbbcbaaabbcacbbdbbbbbcadcacadcadaccddaddacdadbbadbcadabbcddddabcabbdcbdcdadaddcabddabcbddcbcdadbcbcbcdabdddcacbbbdaaaadbdadababdcdcdcababccbacddcabdcdadccdbcabdaabdcaaaabbaaacddacdaacbdaacddcabddaaaadccacaaadcabcabdaaabbbbcccbcbcccbdaccccdbdcdcdddcadddabbccadcddcacabddddbccadbddcbabcddccabacaaaabdbcccdacbbcccddbbacabdbcbdddbcbcacbbbdbcabccdbcccacdacbaaadccdcacdbdbcdccaddaacbdcabbddcadcaccbaacbddaaaaccddbbcccddbdbbddcbbcbadbcaabacdacabcadbbaababbdcadcdadabcabaccbccbcacadbbacbdccaaaccabaaaadacdcdcbdbcdcbacbdabbcaabaccabccdcdbdabcdddcdaadcaddbdbacaacbdbadaababccabccabbdaddbbcccabcabdcaddddbaacaddcdbaabbccdbbdadcaabadbccaacbcdbcbcabbacbaacadddbbdccacdbbbdcdbadbdddaacdcaabbcdadacdcadbdaaaddcbcbbbcbdabccabaccadccbbddababbcbaddcacddcbdcbcadccbbbdaabbbbdccaddcdcbaaabcbcdcaddbcaadbcccbabbcaccbacdcdaabcdaddcdbcbbaccaacbbbcddaaacdccbdbddaadcbaacbcacdabadaababcdadabaddacbdddcdcccbdaadcdaabdacacadcbddabcdcbadcabcbbccdbaaabccdbbdacdbbdcdaabbccbbdadccdccbcbabcddacddbbbcdbcbabaaacbbbcdabdadadacddbdccbaabaaadbdccdaaacadbdcbbababdcadcddddcdcbddccdacdbbcdbbdcbdcaadadddddccdbadacccbcacadbcdbdcbaadcdcadddbbbbbbbbddabdcadbdbddababaabcddccbacabaccdabbbcccbdbbbaabbaddaaaccbacabacbcbbaddccbddbbabbacaddabddccbcbdbbbcdcddbcdcbdbdddbbcdbcbbacacdbbdbdbaacddacbaaadababdccbddaccdbdabaddbdccbdccadddbddaaabaccddbcccbbabbdaacbdcbbbbcccddcacccccabbbabdaacbdcacbbabacddbcdcdadbddaacaacbdabdabcacbcaccbdcdbcadbbcdcdabbdbabadaaaaddcbccadacacdaabbdcdddbadadabcdcabadccaccabbabacccdbdcbdccabcddaaccccbbdadddabbaaadbbcbacdadaaaabcadbbaabbcacccdbccdbbdcdaccdaabaabbcadaddbdbbaddaaccdbadbadacadbdbcccabbaacacadbbaadabdbaadbdddacbdbaadabbbbaddcdadbbddabdbbbbbbcbddaabbdacbdcbdabddacdcdcaadadaddbdbcaabbacdcbbcdacbaabadabcdabcdcbbccbcdaabdacacbbdbdcdcdbcdccbaabbcccacdbabaabbddcddbbcdacadacbaddcdcdcdadcdaacdddbdcdcdbdcbaababbacdddabadbabbabcdbabadacdccaaddcdcbcbcadadbcabbcadddbadddbbbccaddaddaccdbbbcdcbdccbdcddaacaaaabdacababbdaabbbcdccaadaddcdcacdabbcdcdcdabbaadbdbbadaadbabaaadbcacadaddaabbadadbcbdcbbbdbaabadaabbcdcbcadacccddbcddaccabacaadacccbacdcdcccbddbcbdbdabccdacabdcbddccdcbdbcacaadaccdbaaddaddaddaadcdadbbbdbcdccccbbaacabdaadaabbcbcccdbaabaaaddadbcddcdddcaadcdabccaccacccaccadcbdababcdababdbaadbdbdababcbddcacabbbaccadbccbcaabadbaccbccbcbddacaddcdbccbcbcbcccbacadadddcbcdbbddbbdccdaacaddcdbbccacdbadcdadcdaaabadabdcabddadbccddbaabdddcbcbabbcabdbbabcbdcaaddccdacbddadaadcabababacabddcbcdcaddbadcdbbbcccbadacdbdbacabcabaabcabcccadadadbbbbabdbdacdbbbbcbbacccbbacadadabcdcdaccbbccbccbbabdccbacddbbddbdccddadcbbddababbdacadacdacbbccdbcdacabbacacaabcabbbcbadbcacbdbdaddcbdbdaacdaccccaddaccadbbdbcbbdbcbdadbbacbdccabcaccddccccbcbadcdbbcbcbdcddbadbdbbdbdcbdbacabcbdcadbddbcabaccddacaaadbacdbdbdabdbdcbcccbcaaabbdccacdcabbdcccdccacdbdababccccbcabbddbaadcaabbccaddbbbababbcbdcbddbabdaddabaccdaaacabacbcbabdcaabcadcaacdbddcaddbcbddccbdbdcdbadbdcdbbadacdcbdbbacbbbbdabadbbadddbccdabaddccaccadccacabadcacabacacdbdadaddacbdacadcddbbbaacbcacbdbcbaacaddbbcabddbcbadadbcbcdaaaadcdaabcddbbbacaccddbdbdaadbcaabaababbdaccbbbddbdcabbbcbbaaccbcdbbaababbdaababddcabccbddcdccbcacdbacbddcbcacbdcbbbcdadabadcabaaacaaadacadacddbdddaaadabdadabbddccbccaacdaacaabdabaaddadacdadacaddbabbddcbbccddbdacbaddcbdcadabdbdaaaabdddccdcabdacdabdcaccddcccdacdcbaccdbadaddcccddbdbdabccddddacdaacccbbdadbbcbdbdbbaddccdbbadabdbcaccdddbdabcbabccababbcbdddaabcdbbcbcacacabbccbbabdcbacbcabbbcbdbcabdbcdbaaabbabbaddcdbacdccbcbccadbabddddcabbabdadccabababbbccbdcdbdcdababdcbdddcccdcbdcdccacaaaabcbcacabcbdcbdbcbbbdcbbddccbcaacddccbcbdccbdcaadcbdadaccdabcdccacdcbadadbdbbbadbdbdbcccaacccccadabdacdbcccacbacdccccdcbbabcbdccddcaaddcadcccccadcadbcdabdababbbcdbbdcbaaadbcdcababaabbbdcccacbabcdcacaacababbadbaaddacacaccbaadaabbadcbccaabaaddbaaddddadaaacadabccbdaacbbbacbddadcaabadacadacccadbadcacdcdbbacbaaaddbcbcbbabcdcbdacabcbcdbdbccdcdaddcacbdbcaccdbccbbcdcacbaddcbcdadaaacccadadbbdbbacaabcdcbcbdbdaddbbdcdcddacacbcdbcadbccdaabbcbdddccbcadabcccbbadbabdbbabcaacdadbcdcccabddccbcddccbddbbdadabdccdcbbbabccccabbddbdacbaccbdacabadcacaddcccaaccbcadacacdcaccdcdaadddadbaccccccbaaccbadcacdbdbdabacadbbbcdbcdbcabbbbbadbaabcbcbdbdbddbdcdddbbbbddaaddbdddcaadaacdaaadaaddabccdabbaddcdcdddbadcdadbaddddcddddaaaddabacaacacbbadccbcdabcbbdabcabbdbdbddbabcdccbaccdbbddaadbcdabadbdbacdbccdbcdcbddbabcacababbcbcbbbccdbccbadddcbabbcbbadcabbdcbbdcdcddddaacbdbcdbddabbbbbacddadccbcdacdacbaaaabcbcaccabbbbbcddbbdaaaccbacabaddacdcdabdcbbbabddbabbbabaccabbdddbaddccdbcddacabadaddbdacaadbdbdcbbccaccbcaccbcdccacbabbcbcaabcaaadbcbaadcabaaccaaadbcdbcccbabadabbadaabacacdaabdbcadadddacaabddacbbddbbcddbbdcdabcadcaadbccdccdabbdcadaadadcdcbbaddbabbccadcaabbadbbacaacdacbbadacadcccbabacbcdaadcdddcdadbbbcabbdbbbcaaccdddaabdccbacbdcabdbadaaccbdcaadaabcccccacbdcabbbbbccbbabddcddbddcbbddbdddacccbdacbbadbddcdccdcacbbcbbbdccadaccacdaaadcacdbaddbcbcdabcbcadbabdaddacabbbbddbbabddacddbabbacbadbcdbadccbaddcbdcabadcdbddcdbabdbcbbcacbddabaccdddacdadacbcdaccdccbddcbcdbcbbdcdcddabbcdbcbacadcaddbcccddcbabccadbcddcdddbbbabddbcabdcbbabddcaabbcdaacabacbacbcbbaccbdcbabdbdbdbcaaaaabdccbdbcdcbbdddbccbdbbcdbcbcdcddadcdbacddbbbbacddbdddcdddcaccbdadbaababdcdddbbdacbaccccabbbcdcdadaddbcbddaddbdbddbcaacaadcacdcddadadbdcdccadcbbcbacdabbbdadcdaadccdacbabbdcbbcbddccacaadabdbcdaacccadaccadacbcdcbbbabbbabacbacbaaabcbbcdabdbaddacadcbbcdacabcbcadbcbabdaccaabdaddbcccbabbbcbbdbccabcdbaadcbbdbccdbbdcacbbccadcacadcacdcaaaacaddcddcbbcbacadcddccdddabadaabbbdbaabaabbabaaddabbccdcadcbccbdccccdbcbbacaddabdcbacaccbaaccbbcdcabaaddcacdacaaabababdccabdcdaddbaabdaadcbddaadbdacbdabaadaccacbcbdcadbcdbdaccdbacdcbbdadbdaaacccdcccdbbcabdcbaccdcbcdacdcdcdadacacdcbcbcacbddbaadcdccddadbdcccadbdbcbdccbcddbcadcacbbcbcacdbcbdaabacabcbdacaccbadcacddacdacbdccbacdacbaddbdbadaaabddadaadabdbddccbdadaccaaabbbabbdcddabcdabdacddabdbbabbaabcdccbdcbdccabccbaadaadddbabcbddcbdadccbbddadcdcdbaaaadbdccacaaaabbdcbbdddbcabbcdbdddaaaccbcbaccbbbbbaddccbabaadcbaaccbadccabbbaabbccbbddbaccabacaacdbbbabdacbadbaaddcddbbdccabdcaabaaacbdadacadcddcbabdbcabcdccaabcbacdcdabdcaddacaacdbaabdcbbaccabdaadbdabdbcbcbdbadabaccbacbbccaccacadddbbcacbacaaccdbbbbdbccaccdbabbbdbccabbbdaaabadcadddbbbbdbdaacbbbacdbacddbcbcdcccdadcabcbdacbdacababdbcacdacdbcccbccacaabdcdbbbbcbccacddaddcaabaadabcadbdadbddcdbbdccbbdacaccccbcadccdcdadabcdabdccdcacbcbbbdaacaabccacbbcbbbbdcbaccdbccdcdcbabcacdadbcdacbbcaacbaaacccdbcabcdabdadacaddacabcbbadaaadadaacadbacdcdddccbbcdcadababbbaccccddddcaacdcdbacbbbabbdcbbaddcccdcbcbdddbccccabbddabcbbddcbcccdbdddccdaddbabcdabbabdbbbcbaccbdabdbbcbacbdbbadcdbbdcadbbabacacdadddddcbaabcdbcaaadbcccdaadadbdaaadaaaddccccbbbaaabadccabdbbaabbadcabddbccbabadcdbcbbddbbcbbabcbdcddadccbabdcdacdbaaacdacbccddadcdccbcadbadcbbcbdacabdabdcbccdbdbcbdcbddcdddbcbbaaaaccbdbbbbaabcadaddbdbdacddabbdaccbcddbacbdacdcadaddadadcdabacbaddabbbdcaddcccadcabbcbdcdbdbdcacababdabdbbdabdadabdadcdcdbaaacccbcaacdcdcbddddabaaccaccddcbccdccccddcbbbbdbbdadbcdcdbabdcccabcdccdadcabacbacdbadaadbbcbacbdabdbbdadcabdacbbbddadbacdcbcbcdaaaaddcbddddbbaaccaccddaaadddadddabdaccdccacccadbccdbacddadbacdcbabbdbdbcbbdcbbbcacaaadcbbbbbdcbbcabbbbcaabcdadbcbdcdbcbbdbadcbbadbbdcdaacbaaaabaabcadbaccbaaddaaccdbcadcadcadbcadabdbacadaccdbddbbcddcdaddccccababcbbbaaccbcdaaabcaaabbcdacdbadcbbdaacdbbaaacdaaddbaaddbcdbddbccdadbadcdadacbbadacdacacdcabdddbdcbbdbcdacddacddababacbcbadaababcbdadcbabaaccadccabaabdcccabaddcbacddaacbcdcccabddbaacbdadbbabccccadbbbbbacbbbdaabadbaaacaacdcdcaabcaaaadabcaacaccabaaccadcbbacbdccaadcdccbbdcabbabdbbaabacbdbdddbadaacbcdbaadbbbadbcacbddaadaabdcbdccaacabadddcdbddbbcdaaabdabababdbbdbbcbacabddcacabdadccdacccaabdccbcdcddbdadddddbcdaaaabdbbbadaccdccdbadbbbaaacddbbbcbdbdbbbaccddcbbcbdbcbcdaaadacdccdbabdacccaaccacacdbdbbcbbdcdbbabacbaccabacdcbdbacbabdbbccdbcabbbcabdddcacaabbdcbaaabcaaacadbbaaddbaaddaaaaabacbbcabbdadbabcadaabbbccababbcadbcbbbbbcddbabdbdccbcbcbcbcdaabdbadabaabbcbcabbddbadbcaaacbabcadacdacdbadabdaccbddbbbcdabaadddacdcaacbdacbbcdcacaccbdbacdddcdbabddbcaddabacaadcabaddbcbbcdcacdcbabbcbbbadbdabdaabcacacabbbaddcadbbbaccdccbacaabacdaddbddbbcacddadaddadcbabcaabcbcabbcbacbbcbadaabdadbcbbbbdacccadbcbcdbbabaccdcbdcbddaadabcacadbcdbabacbbaaabbbbdacdcdcccbdadbdbacdbdacbdcdccadcddbdddbaccdcbdbbdbccaabccabddbdcdddbdbbaabaadadadbddbcddbdaddabdbacdcbabbabcabbddaccadddadaabbdbaabadbbdbccbabcaddcdaddaadbbbacccdcadcadacabbdbaaddcacadadbdadaacdbdaaadddabacbaaadccacaacacdabcddcbcdadbaaaaadabdacbbbdbcbacccddaaaaabbdbacbabbcdbcdcaabbbaacdbdbddbdbbcdacddccdabbcdcbbcdadcbaddbcbcaadbbcadacbaabbcdaddbcdcbaacbdbdbcaaaabcdcbbdabccbaacbcbbcaadcaaadddbacdccbcbbdaabaaaaacdcbdaadadadadadbdbcccbcabbbdbbacdddaaaabcdbbdcacabddacdbaabddbcadbcdbaddcddcdcbcbbcbabddcaccacdbdaaabcdcaadcbdddbbdcaccddaadabcbbaddabbbdccbccabbbacccddbbccbbadcabbbbdbabadddcbadbcacacdbbcccaadbdacddcddcbbbbbcdacbdcaccabaddbbdaaaaacabdacbabbacccccbadcbaadcdbaddddbdcddddacbaaddcbaddbccabccccaaaadcdbdbdaaadacdbaddbcaacdcdddbcbcdddaddabdccdccabcaaacaddbcbbccdcdabdaadddadddbbbcabbcbcbabdacccabdadbdccbdadddadacdccbdddbdcdcbbdcaabddbdcbddcadbbdcadbdadbbaccaaadbdbdacacaaddacabcadcdbacdaacdbddddbbabaddcccbcdbddcbddccdadcdccacbbbbdaaaabdbcbadbbdacacbacbababcaaccbbbccdddccbacdbbbaacbacabcccabdccddcaacadacdbadbbcaababacbdbcabddccdbbbdcbbccaadcbbbccbacddccdcacddabcadadabaddbdccbcdbbcdbcabbcdadbbdddddbadabbdcbcdbdabbacbdabadacaaccbccbdbccbddccacbdbabcdbbbddbbadbbbddbabcbddcacbdddcbcbcdacacbcbcbcababcbbcbbdabbdddbacdabddddcbaaaacdcdabccbdaacbbcccacaddaacabdcccdaabddbccaccacbadbabcbdbdcccbdacbbcdbbddccacbcdccacdbbcdcaabbdbddddcbcbcbbbdbbabddcbbabccbbbbbaaadcdcbccaabcdddadcaacaccddcdcabccccbdbdcabddabacbaaddbdbabaadbdcaadabbbabdbdadcabaadbbbbcaaacdbbcbacbcabcaaddcccdacaadbddabbbcbaabdaccbbbcadbaccbcbcbcadabadadaacadcbacbcacadcdcbbdaadddaccacdccdaccaabcaaabacbdcbcdcdacdaaacbadddadddaabdcbdaabdbdbcdcdcbcabbcdcabcaccbaaadddadbccccbaccaddababdaadbddabbcccbcbbdabbcadbadacbdcaadcaadbdabdcbacadbdccbdaccabdccadaddcddadadacddddaccbaddcabdbbaccaaccdddbaccddccacdadacbbaddbdadbdbcdbbdabdbccdbbabbcbdaabbaccbbadcdabacbccabbbbccacdbbbaddabbacddabaadaababbcbcbcddadbccaddbbaabbdadbdbabccabcdddaadccccacaaaadacacbacccbcaccdcbdcacdacaddbacababdcaadccbdcddbdabccdadabbadcaacabddbdbaddacdacdaaadbbbdcadcabcaadbdbccdabaadbabdddddaaadaabcabdcbabdcbdcccabcccdddbcccbbbddbcadbbadaaddcbbabddcdcdadaddbdaabadbbcddcbcdaadadbbbcaaabbcacacadaadbcbcbddacaacddabbbbcacccbacabddccccdddbdbbaaadacababbadabcdadddaadcdadccdbdaccccbcaabacdcdbbadabdacddcdcbbddddbddbacdbcdcdcbcccbabdabdbcbcccbaaddbadacccbbaadcbcdccbdbccbacdcccbbdccacabdaaaddbdacabbcdcadcdacbadbbbadaddcccacdbaadddbbdbacadbdbacdccdbabdcadddddbddcadbbccadaabababdbdccbadcadcbccacbdadbcdcbcacdcdabacbcabbdaaadadbdcdcaadbdacaadbddcccabbddddcdbcccddbbdcbccbdabbacabdcbacabbdccdbbacacdcddadcacbccaadcdababbacddcbccadaacdddbccdaabaccabcbaccaacdcdbdbcaacbbacccdbdabcbbbddcdabadbabaccaccbcabddbbbcacddbcdcadccbadaccbcdbccdbcdaabcbddabdaddacbdbabdccbcdcbacbbabbbbbdabacadcdbccabbbadbaaaabbdabbccadadddacdbddddabcabbadddccbadccadababcbcbabdcadaddbddbcdddbccbdaadabcaabaaaaaaacddaadaabdbcdaababdaddcddabbcccdcadbabaabccbdadadcaaaccdbdaccdadbdbcbbdcdcdcbbdddccabbacbddaaabcaadbddddcbddaaaaacbaaddaacdcbbddacddbadbbadbbbccccdcacadacabbcacccdbadaacbbbadbbbdcacdbcadbbaacddadbbdbbbcdaccabbaddadaddbcddcacbaddcbdcddbbcdcabadabbdcdcaacdbcbcddbcbcdccdabcddadcdbccabcbbdcbccacdaacbbdaabbbddbaaadbcabaccbaadacdadcadcdbcbcacdaddabcddbdbcddbdbbbabcadbcbddabcdacdabdcbbddaadcbadcddaadbbcacccabcbdaddadbcaddbcdaadcddccbbdcdcdabccddabadcdadcbbabcaccbaaacadbbcccaacbcbdcdaadbddcdbabdababadbbdcadbdcbdabcadbdbabcbdacacbbdbdbbabcbddaacbdcbcdababdbbabddcaccbdabcbadaccbdaddbbabaacdaabcabccdbaacbabdabbdbabdacddcbbdbccdbaadccddcdccdcccdbdaaabcddacadbcaaacaabddbcaccbbabcadcdaabbacbabbadcaacbbcbccacadcbddcadccdbcadbcdddacdcaddddcddcdcbdbcdadabcdcdddcbadbadcddcccaacaaddbcabcbaccadcddbcacdaaacbacaddbccdadbcdcddcacccbaaababacdccaddcccdccbdabbdababbcababaadabbdcaadacbaabdcacdcdcadbbdcdadbbcbacdbbccdbdcdadacbadbaabdbbbacccabbacdcabdacddacbabbdcbcbcbdddcacdabbbbcccbccbcbbacadbdbdbcbbbaccaddbaddbdbacbddbcbbadbbaabcabcdcbccaddbbdbbabdacaadcbbaadccdcbabbdbcddaddcdabbdacdadbbcdadcdaadcdccdacdcdbcddcbddbacdacdcdaddaaaaabddadccbdcaddababbabbaacbdbbbacacaababcbabbabddacadcaddacabaccdadadcabbddcaddaabdabcabaabdacabadbdacabcdadbcaabbbbbdcbbacaddcababaaabcbbdaaccddbdbbdbcabadbcbaacdbdadadbbdadabdabbdadacdadaccddcdbababdbabadcdbdcbaccbdbdaacadacabbbcbdadbcacbbccdcdabddabddcbbdadaacbbbcdcaaccbdbabdacbdabbdcdbbbaabbadbdadcbabccabbbbcdcccaddbdcddcddbaddbbdcdbacbabcbcababaccacacbcbcbcdaaabcaccddadcabbaacdcbddadcbbcccdaddcdaabdaddcdacaadaacbccabbdbdacddcdbbcbddcacbbacdbbcdbdaaacddacbdabbdcdcddaabbacbaddddbdbabddcdcddacbcdacaabbadcddcdcaabcdccdadcccbcbcababdaaadaddbbabadabbabbabbdaadddbcbbacabddcdcabccacbdbcdbbbdcaddadcbadbadcccbcbcbaacccdbabdadccbbbacddabbaabcdaaabdbbbbbdabcbcdadbccaacdbabcdcdddabcadcbdbadabadabbdbabdbadcdacabdcdadcdbdccccbbbcdbcbcaaddbdaadddcadabddaccccbabdbdbcbabbccccdacbdcdcbdacbbcaddccbbaadbddcccbcdbcaacacacccbbdaadaaabacdbdbcbadacbbcadabadabaabdbaccaadabbbdaacddcdcacaacabdaaabadbdcddddddbcbadcddddbcdddabdcddbdcbbcbbddcbadcaaccbccadaabdccbdabbacbcddacabddacaddbbaaaaabdccddddadabcadcdaddcacaabbabcadbbbdcbadbbdabacddcbddcbaabdbbbaadaddbbacbcbccdbdcbdcdddddcbdacdccbcbcdcabbbdaccddcddcddabddcccbddadbcbdbcbaaddcaaacdbbadbdbcdaaddadaabddadbacabaacbdcdabbacadcbaaabdaadcbbcdbdaddabbdcaabdccadddababdabcabaddccdbbacddcbaabaaadbadddcddbdddbbbdcddddcddadcabbbcabaddddcddcbcbacdbccbcacdbabadddcbdbaacabdacbdccabdaacbdcadbdbcdbdddccddcbbcbdbdbbdcbcbbbbaacddcbcdcdbbbaddcdbaaccddbaabcacddbabaacbadabcccdbadccdaaacbdddbdccbdbabdcbccdbcaabaddcdcbadbadddaacabcaaadcaadadaacddcccacadbcdadacdbbaadbdbcacaabaabbadcdcbdadbbdbadccccccccbcbcadacccacccdbcbcbabadaccbdccacabbdccadacdccbbdcaabbbccdaddcabaacbababadbdccdbaacbbdbaabddbcabcbbcbddddbdddacacddbbbdabbcbcacabdaabacdddbacccccadbaacaddaacdcbadabadaccabaadbaaaddacacadddbacccacdcdbaddcdabacacddccbababcddccdadadaaabbdccbccacccdccbbaaccdcbddaadabadbacdddcacccdcdbccbccdcddbbdcbbdbbcbdccadcbbabbddbaacbdbdbdbddccdbbbbabaaddadabacccabdddadaabbaadcbcbcdadaccbbdbddabaaaaaacacbbbbacbaccacdbdbdcacbdcccdccbcdcdaababadbcabdbdcdcdabbacbdcababbadaabcccbcbabddcacdbcabccbbdcbcbdaacbcabbccdbcccbcaaabadaddbcdddbdddbadcbccbcddddacdbdacabdcdacabbdbabbddaacdcadbcbaadaabcdbaabaccaccaacdbbabaadcaacbddbabbbdddabdcaddadbcdcdaaacaacdbaabdbbcaabddadbbadadbbaccbaadaacddadcbaabcdacbbdacdccbcdbacdddcbccdbabcbdbbdabbdcbbddbbacbdcacbdadddadbcddbaaabaccbaacbddaccaacddaccbbdcadabdcdccabbcbcabdccadaddddcdcbbdcbdddbaabbcaccdabbcbcccccadbbbbddaacabbbbbdbaccbaaddcacccddcbbbaabdcdccabccccbbacacbdacdddbadabdbbaccacbdabccaddcaccdaabdadbcbbacbbbacdacaaddbaacddddccbdcdcccabaaaccaabdccddadbcdadccbbadbcbdbabcbbdadbcbacaadabcabaadbabbaacddaaddcdcacdadadbbbabdcaddbadddddcbcbddbbbbbcadccbdabccabddbbbaaddbbcadddcbbababbddbabcabdbbabbacdcaadbaddacadcbdbadacacaabcdcacccbaadcbaddbdacadadabdccabdadbcbdbcdccabadcbabbdaaadbbbaabbdcaacbcbacdcdaadbdcdbaaaccacdcbabaccdcacabbaabcacacaaabcdcbaaccaccbdadcdbacdbbbccdbdbaabaadbbdcddbcdcbaabccaccabddbcaaabcdaadbaaccbcaabddadaddcdbcbbadbdcdcccdbccaadacadcabbcadbddbaabadaadbcbadcdddcabccdcbbcabcadaaaaacaddbddbcaaddcacaddbadddbddbcaaabaacbaacacccdacdbcaacbacaccdadcaabcccbccbbbbdbbbccbcaabddbdadcadbbcbdcddbcacdbaaccababdabbcadbabccbddddccadacabbaccbcdaacacdbddcddddadddcbddaabccacadcdaacdbcbbbccbbcbbdadcbdbbbdcdccdcbddbbdccabccacccdbadadbaadddaaaadadaadbbbadacbdddcabbdcccbbbbbbcdcbaccabcddaadbcbacbcacbadbacddaccdaacdadacdbcaababbbcabacbdcdcccbdbcdaccdcbddcbabdaacccaadacccdacacaddcadabacaadcadcaccdccabbaaccabcddbccddcbbdbcabbbdbdaadccdaaaacabacbcaaaaacdcaaacccbdacbbcbbcbdcdbddaccbaddabcaaccccbdbcbccbabacbdcaadcdccdaaadbbbacbadddbabadcdcaadbbdcccacddbdbcbccacaabaabdbbdbabddaacdcabaddccbddadadbaaaabbbcdccbdaddabdbbcaacdacadaaadaadcbbabccbbdacdcdabaccacdaaaddcadddababdbacbbbbcddcbdcababaadaababbbaadaddbaadacbdcbbcaacabacabacdbddbbbadaadbdbbdaadcdbbadcdaccdcadbdddccabddddacddbccbcbabddaabdbddcbcbddaadbcbdadcdadbbcdbdbdacdaadaccdbccdcabddabadbdbdccdddbcabacacdbadcdcccccbabdaabcaadcccaabcbdabccbcccbcadcdadcadbbddcdabdbcdcdddcbadbcadccaaccccdababacaddbcacbdadddacccbdddacdaabadccdaddaccbcabcdabdcbbdcacbdadcdccbaadaaacaddddbcaddbccaadcccddaadbabccbaacddbdcbcbbcccadacacbbaabcaacdcdbabddcaacbcaaadbabdcdcddbadccccbdcabbadbccdbabacbbcccbcdcbcdbadcdadddccdccddbdcbabdaddddcbcadbbcadccaabadcabbcabcbbaaabccdddaaacdddaaddababbabdddddaccdaacbcdcaccddbadddbbbdabccbdcdcbdcddacaabdababdcdccacdcbbdcdcdcdbaadbadabcabdcbbabdadabaddccbcccdcdddbccbbccdddaccdaccddbcccabcadcccacccdccdbcacbbabaabbbbaaacdacdbdcdcddbcadabaddbbadcdccbbbcbaadbddcbcbdaadabcccbdccbdadcdaadadccdbadbacbaabaacbdaadbdddbaccbbbdaaddcdbabbaabaacdcdbddcbacdacaadcddcdadcdbaccaaababcdacbcbbaadbaaddbbbbbbdcccabdbdcdcbccbcdbdbcacbcddabaccbacacbcbababcacaccacbbcdaccacccdaddbbacdbaccaadaddbccccadbcccccbbcbaaccbcbacbcdbcbacbabacccadcaabdbcdacddbcbbddbacdbbadbccbabacbcbdbcddadbbcbababddbdcabdaccadbbcabbbddbdabccdcbdabbadaacaababcaabcddbbaadcdbdccccdbdbdbdabaacdbadbccacbbcdacbacbccddadaccdddccddaaabcdadbbdbdacbccaabbdddacaaddccadbbbccbabadbdacabbacdbcddcbcbcbacdbcdabbcbdcddbbbbcdabbcadaaacaacbcdbaccabddbaaadaabcbdcdaaadacbdcbdaabcbbcdbbdadbabcaaabaabcdbaabbddacabdadbcbcbaadabbbdacdadcdbdbbbaaadbcaacabadaacbabbbdbbadcadbabcaacbdbdbdcddbadaddcbbcbabcbcbdbcacbdcaabcbccbadcdaaddbaaadabccabcbbabaaddddcbabbbbbbbcbabcadadaabbdbcadbddcbcccddacabcabdcaabdcbacdacadaabbbaabdcaabcaabaabccaaacbadbcbcadcdaacdccbddbdbccdbabaccdccaadcbbdbadbbbcdbdbbbbddbaabccabdbcdcdbccabbbbcabacdccdcabaabdbabaaddbdbbabddbccacbbacdccbaccabdaacacdcbaddddaadadaabdabaabadddbcacadcddddbbdabccbaccadbcacbddcbccbbdaddbcaadacaddcacccdaddcbccbdbcbdadbaccdaacddbdbcacccbabcdbcdccdaacbcddbabbdadddabbcdabcaaccabdacacccaadcdababcdddcadbccdcadccbbabddccdcddacaabcddcccbbdbcbdbadbaabbaccbcaddcbacbbcbbadbddbccaaabbbcccccccbbacdbccacbdaadabaaddbdcabdddcbdddccaccdcadbccaacdabcbcbbcbadbddadbdbaadbbacccbbcaccddcaadcbbbbaadbcddcaddbbbdcdddadbacbcacbabacababbcaaabacccbddbdcabbdbaccaacbdbaacadabbbbaadcbdabccdbdabdadbccddcaddbadcabcbddccbccdbccccdccaaddacdacdbbaabbacaddabaacabadcabbacddacbabaacbccbbdcadbaadbcbacacbdcdcacdbcdbccbbaaaabbbaccabdbabdacabccbddcdabddacbbcccdacbbbddbcaccdcacdcccddcacddddacbcdadbbcacbbaadccacacabbbacaacbaaccdadabcccdcccbdcbcaabdaabcabcdbabcbdaaaccbdddabdcadbacadddbbadcbabbdabbddbddddcbcabbdbddaccdcdbdcaaacbbbcccadaddbccbaaadcdccbdaadaaaddbdbddbcdcadcabdbbadddabdbddbcbbbadccdddadccbbddbdccbbbbdadbddcdadbbccddcacbcbbdbaaaddbcbdacaaddbbdbbccdaaadccabadadabbabbbdbcadaabadcaccabbcbdcaacdddaccabcbdabadcbbddaaaddabacaccbbcacabcadadcdddbadbaaadaabccddababcdddaabcdccdcbbadcbbaaccdccdbacacdcdaabcbaacbdabadbcacadbacdbbdcacccaccdabcddcadaaddbccddcdccdadccccdbddcdddacdbbdccdaadabbabddddabbcbabdaabcbdcbbcaabccadacbdcddcadddaabbaaccddcaddbaaccdaddbabbddaccabdcdcbddbccadccbdcbbdbcccbcbdadcccdccdcabdbadcadbdcacabaccaaddbbcddccbdbbccabbdcaacadbaadddcabaddabcdcbbacbdabbbdbbddbbcbbacaaccccabcbadcabcdacccbccbaccbabbcacaddaabcdbabdbddacbddbcbabbdcdcbdacdbcabdbcdabbabaddabbcddccdcadbcccdccdbbbcaaaabcdddacccbcbbadabcbdcdccdbdadacaacccacdcadacbccdbddcabcdccbabbdbbabadccacbacbaaccaaabcdcbdabcaaccaccabbadacdbdcadadbddabcbabbdbcbdcadcbcaacbbbdcadabcbabcdbbabacbbdaacdcbcaaacbaabacbbdabbddcbadbacadadddbaccbbccdbbacabdbaacabbddbcddbdbcaccbcccadaabbadcccaccbdbaaaabdddbdbcbbabacdcbbccbbaaacacdbbdbaccbbdccbbbbabcbcccbbcddabacbbdccabbddbdaccabdacaadbbbadbaddcacbadbbdcbbaacdaabbaacbbcbdaabcaacaccdccabbdcadddaccdccbbcadcabacbdbcbbaddcbbbabbaccbbcacccbbabccdabbabacaabadadabadcccdcdbcdbddccbcdbbcbccacbaaacabdbbcdddccddbdcbbdcaabaaabaabababbdacdddabbaaaabbabdabbbcbcadddddacddcbcababbaacabdcbaabbcabbaadcaacdbdbbacbdabbbabbabccdadcaacdbcddcbbddcdbddcabadcaabcbcabacdcbaaddcaaadbbccdaaddbbaadccabcbdacddbddcbbbdbccccdadaaabdcbaacccddbbccbcbabbbbcbabcbadbaaadddcdbdacbddaadabbdacabacaddbacaaacacbabcddbcdbcbcdbcabbcaabcdbaabcacccacbabcadddbcbaacaacdacdcddabcdcdacdddbbbdacbdcacbbdbaacacdacbbcbdaaaabdabcbacbdddbcbdbcabacaddaabccdacbaaaaddaaadaacbabadcadacddbacddabdababdbbddccccdbbccdadbcabbdbaadbaacddbdaddbdbbcccdadddcbaddabadcbdabcbbbbdcabadccadbacacdcbdccadbacbbcabaacddccabdcabdaaadcdddaccbacdadcbbcbdcdbbdbbddddadcdcccccabddcccbabcdddcbcccaacadaddbdbcbacbcdccaabbdbabdaabbcccbbcaccddaabbbabdcadbacabdabbccbbaaadcccdbdbacbbbadaadcadcdbaddcbccabddbcaddcbdadcbddadccdacbbadbabaadbbbbbcbddbcbbbdadcbdccdbcaacdaccdbacdaabcddcddaabbdadcbdcdcdcabcbbaabddabcddcbcbcaabbaccdaacdaaacbbdcccabccbaabdabcaccdcdcbdcbbcbdbccbadcbdadbcbbcacccadadcbacacabadbaabccbdcacccdccabdaacdadacdaadbbabdacdadbadabddcbdadcdccababccacbcbcdbabbcccdbbcaacdbddcacbadcbbbadbcdcadbabaadcdabccbdabaddacdaacdcbadcbcacaacbccbbdaadbcacaddddcdbaddddcbdaccabccadbcbcdbcbcbcbdaadcaaacbaccddacabdbbbabddcbabdcabcbdbbaaabaadbbaabdadadccdbaccdcccbbbaacabbbcbaddbdaccbadbbdabcadbccdbaadaababadbdcbbbdcdaabadaabcccbdbcdbbddccaccacbbadcbadbabddddcbbcadbddbdaaddbdaccdbbbcdcabbaadddbbabadbbbbbdbbbbadabdacbdbacccccaadbcdcadcbcdddcacaabdaccdccbdaadcadbaddaadcacccdadbdbdacbdcdbbaddacccbbbdccadcaaaabbcbccdcbbadbabcdbbaddaacabbbccbdccdbaadcacacaacbdccddcbbaabcaddcdbddbdccbccbbcccbddaacccdaacdabccbaddcbabdbbacdcbaadbcbbdabdcaadbdcdbbaaacbcdacddbcddcddacddddddadadbbaddaaacaababbbabbcbbcdcacabdbbcaaacabdcbcaaadcdbbdaaccacaacacaadbccacbccdacabaddbcadadccdcaadddbcbabdbaacdcabbabacbcdaadcadcdddccacccdabcbacaadcaacbcdbdadcddadddbaaddcbadaaabbdbdcacabccccbbddbdadccaabdaccccccbccddbadbdbacbddbbddadadadbcddcdddbdadadbaccadddcadbbbddaddcbabcddbdbadacdbcadcccaabbbabdbacdbabcaadbbbdcbbaabbacdbbcdcdbadcccaabcccbdbcdaadcadcdbcddcaaaccbaacadddcbaccbbbdabdabadabaaddaacaaccaadbccbacdbdbdcadbcdbdaaaaacccbcdccbdacbdabcaadabaddcccbacbacaccacabadbdbddbddccdbadbbdadadabaddcdaabbcadcabcadbaabaadcabbdabdbbbbaaaddddcccbddcacdbacdbacbdbbdabadabcadbaadccdaabddccaacacbcbdacdbcacbdaacbbacbbbbddcaacaaccddcbdddbcaabdccdacdccdaaadaadbdadaabaccdaaddcaaacccaadcadadbacdbababcbbcdccacddabddaadddaddcdccadcacdcacdaaabcdadcdcbdbdbbbbdacadbbdccdaaaacaacbaaadccddcdaddbbcbbcdadddabaacbdadadcddcbbbbccccdbdcbdddbabcbbbdbaadadccbdaddcabcbdddbaadacdaabdcabbccddbadaccaddacdadcdabdaadbdabbccccdbcccdadcadaacdddccbddcbbdbcdddbdbdcdcbbcacdcacacddbccdcbbadbcccaccdadbabcdcdbcbdbabdbabccadccacbacdbcbacbabbcbdaaadbacaadbdddacabddccbdcaaccaaddbcbdaabcbcdcdbabababdaaacabcddcbddccdcbdcabadcacbcddcacddaabdbadcccdcccacabcdaadbcadadbdbadbcaccadaccbbcbacaccbdbdadcddadadacbcbbaaaacbabbadacdabbddabaabdbadbbdcdbaddbdaaddcaddbabdcdcabdaacbcccccbcabcdaddaadccdacbbdacaabadbdbcbccccbccbaaabbbbbbabdbdcdacaaddbcbcddcdcabcdadadabbcdcccaabdadbdadabacdddbcabdcdbdcdbbbabccddaacadbbdaabbaaddbadaadcadbdcabcccdbcdaacdbcdaddbadadabdacdbbddbccdcdddbcaccdabbacadcccaaaadcaadbbaacaccdacccbbbddacdadcddbdacabdadbcaaaabbdbcacddabbbddccdacdadccaaabdaabdcdadddbdccacbbdbcdcaaadacacbbddaaabdacccacdddabdddaccdddcabddbcaababbddcdbabcbddbaabcdbbbabbbbccdcdcbdccdcbdabbbaabacdcabcdcaddbdabcabbabccbbadabadbccbccacbbaadbbcccbdcccbdacacccbdcdbbdccacdbddbdaccbdbaccadbbbbbbaadbbbacbbadbbccdddbbccddcbbdacaaddabddddcbadaacdbaadbbaacbcaabaadddbddcdcddddcdbdacabdaacbbabdbbdcdbdddccdbdbcddccccbbdbbbbbacacdaaacaabbbdcababbdbadccdcaaaabbaaadbacabaabddaaaddacaabdabddcaaddaadbdddbbdbddccdaaddadddcccbccbbcbadabcdabaccabaabdddbaddbadddddbddbcdbadbdcbbcadccbdbdaddababaabaabdadabbcabbbccaaccdacaadbbcbcdcddbdaadbbdddddbbcaddbddbcadcbaaabaabbcbcbbcddadabddabddccdbcdcdddbcdcdcbcadbcbdbabbcddaddcabbdbccddbacdbabddccdccdabcbbbdcadbacbabaabaccdaadcabddcbcbddaddaccaabaacadaaacdbbbaabcdbaaaabaaaccacadbadabccdadaadacbbbbaacbcccacdbdbcdabcccaababaddcadacdcabdadadccaabbcdaabbddcccdbbbcccbcccadbccdcaacccdaabbcaccdccbddbccddcadacbbbadacbcadaadccbcadbaddabbccadadabcbadbbcccbcddccaccdcdcdccabdbcaabcadbadbcacbddddbdccdbddadbbddbcccbdbbacbcbcadbaabdcabdadcddadbdcdbbdcccccacbbdacdbaddcbadaaddacddcbadccabcbcdaabbacccbdbadcdbcadaccddddbbcaababacccadbbbbacbcdacdcacccaaadbcbcbdaddacbcdbcaaccaaacbccdcbabdbcbbcddccdacadccadcadcacaabddadaacccddbcbccabdabadbbdcbcacaccddaabadccadbdbbcbaacbbaaadbdabdadadbaabdaddccbccdcbbdbaacadabbbdaaababbdaccaacdbcdcacaaccdacccdbdbadbdcaadbcccccacddababaccdcbcaddddbaadadddbdcacdcbdcbbccacabdaaabbbcddccdcddaacacabccbcbabaaccaabacbbddabdabdbbaabccbcdddcaaacaacdbbaccbbacdcdadccbcbaabbbaabbdbcadaadadbcdbcdcdcdcaaacbcbcdbcdcbbabcbdbaddaadbdcaaadbcdcdaccbdaddcdcbdbcccaadadddcdbbbdbdbadcddbdaabccaabbccbccbbcccdcbcadbbccbdbcdbabdcdcccaddccdbcbaacdaccbabbabddcabccababcbbccdaacabacdbdacbbdcdbbbdcbbbabdbdabadbdabccabcccabdcbcaabaacbbbcbccbadcdbdaccaadcacdacaccaaadbcbbbcdaadbddaccabbdcacbcabadadbaaacbcaaaadcdacdbdaaacaaabbcadabcbbdcdacdaacacaaddaaaddaaccaccbadcadababcaccbbdbccccbdbdaabdccadbcdabcbdcbbdbbaccbaddddbbdccdcdbccbbcdabcbdbadabdaabbbdbaadabbbdabadaddaacacadbcbaddbbdacaccababbbcccdabbddcdcabcaabbcccbbddaabbdaacbdabbbbbaabbacadcdaddadaacaccaadaabdadcdddddbdacaabaabbdabaccddcabaabcbacbbccbcabcdbbbccadcbbbdaddccccaabadcbbaaabbbcbbbdbdaaaaabdabccbaabddcabaccbacbccdabdabcbbbbbddcdbddccbadaabddabbdbbbbccbcbbacaacdaaccacbdaaaddcddadcbbccddcbdbdbacabbdaaacadbabcbbddbbbdddacbbddbbcbdbbdcccbccddcbaaabacbacbddcbbbccbaadbcbadcaacdbbdacaabdbcdbdabdbadcbcacadcaaccabdcddddabbbccdaccbcdabadcaaaacdcddcbabccddddcbcacbdbabcbdcbcddbaabaccabdbdbdbadcdbbacadddcabaadcadbadbcddcccabcabbdcdbdcaabdabcdbadaddaaccdcadcdddcbdcabbdcbacacdcbdcbbadcdcacbabcacacdcabaabcbbaadaacbddacadbcadcdbaccdcbbcadcdaacddbddbccdccddbaccbabcddbddcabddddccbacbdcadbbccddcddaaaddbcccacbcacbcaacdcaaaabbbacacdbcbabbbaddddacdcddcddbccddaacacdbcdbbaaddabdcbdcccbabddcadccddacddbaddbcbaacdcdbccabcbcddbaacbcdabacbccddaccacdaabcccdacdcbcdadaadcadbbdbacaddbdccbccaacddcacdcadacaaaddaabaccdddcbbccbbaaadddbbccddbbaaacbabdddbbcdbdcddcabcacbbbaadadbdaddcdaaaaaccdaabadbbbdbdcbbaddadabcdccdbaadbbdbcbdbdbdadcababadccdbacddcbbcddbaaadddcdcadaaaabbbcbacddccbcdbcbbbabdcadadcbacdaabcccdacdbacbbacdadbabbaaaccdbdbaadcdcddbaddabdccbccddcbdcadcacdbacbbcadbaabaaddbdcbdbddbcadadddabbbbadbbbcadcadabbbbbacbbdaddbcdbdbccdbdbdcbdcdbadddcacabadbdcdadabcbdddccaacadcbcabcbbabcacdadadbbadaacabbbacaccbbabcbacdaaabadcbacadcddcbbadddddcbcadbbdbabcdcddabaaabccccaaaddabdcbbdcbdbccbabaaabdaabbdacccaadbddabacadaabbcdbbcbddccadcdbcaccbdbbcddbacbcbcdadaadaccbbcdcdacbbcbacdccbcbacbabcbbcaabbaddbacdadabacaabbccdaacacbadacababdbbadacaacabcaadaccdcbbbdabdcaaaadcabbadadbabccdbabbbbdbbccddddadacbcbcdcdbbcddabdbccaaacbadcadcdccdbcbaddadbdbcbbdacdcdccabaabaddacbdbacaaccddaddadbdabdddcddbddbaabbbcdacbccbcbbaacbdacccdbdbbbaaddcbddbbbdbcaabcbcccbcbdccabbdacadccdbbcbdcdcacdabcbbadbbdabcacccdbbcbaabddbbcdbcaddbddabbdcdadaddccabacbbaccdaddbdacbddbbdaabcaacadadbaaaabbddbddbcdaaadcabcbcaaacabdaddbabacabacbbabbaccbbdaabbbbcadaccbaacccabdcacdabccdbbdbaaadacaddabbacdcabadaacddacdaccaccdbdbadccaacaaababbdaccdaabcadaaddcbdbcbbcbccaddadcdcdaccbacaaababddaccdcaddcbbbbbcbadadbdaabdaabbdaaaabbbbaadbcdbbbbacdbcbcbdcbaabccbaaaaaabdadbacaadacdacaabcdbcaaadddabbddbacddbccddacdacbbbdbccdaaaddcabaccbbcbbbcbbbdcacdbcadbdcaddcdbcbdbdadbddcbbbabadcaabcdbcbacccbcababbdbdbcbcbabbcdababddcbdacddbcdbbabdcbacaabaaabcdbdcacaabaabccbacdbcbcbdacbcbdbdbbbaacdbaaacadacdcdbbdddacabababcbbacbcccbdddacbdaaccadaaddaadadbbdbbddcbdabddadbdaccadcdcdccbabaabacccbacbabccadabbddbdababaabbcaabddbdbcbbdddbabdcddaacbbcaccacdaabddbbbbccdacddddccacabcdbddddbcdccabdcbcbdbdcabbcbcdaabdbbbdcccacbcbbdaaaaacadabbdcdacabcbacccaddcccaacdaadbdcaaacbdcacdcadababbdcacaaabcbbbdbdbdaaacaacbacbadbaacdcabdddbaabbdbadaaaddacaaccdbaccbadabdbdccdaacaabbbdadcdabcdacacbaabbaabcbdcdacdbaddadbbbbaddddbdddaaacbacddbadddddcbacaccbbbccbdcbaccdbbbbcdcdcdadaadcbaaccdbabcaadccacacaccdabdcaaadbacddcabccdbbcdcdcbdcaaddcdcaaccdbabacdacccabdabdbddbabbadbbbadcbaababcdabdbdbbcbcbcccccdbbacbcdbacbdbddbbbabdaaaddcdccccccccbacbbcaadbadabadbadadadcbcddcbaacdccbcdabdcbaabaabcdcddacdaadbaaaababbbbcddcdccbaadabadbdbddaabcdbcddcbccdbccaccacdbdbdaacabaabcccbbdadddcbcdddbbcddcabbcadcddacbcbcabdcdacbacaddbdbabddbbdbbaddbadacbabdcaddaabcbacccabbccbabbdaccbbadcaddadcbcbcbcbaaadccaddbadbacaadcaadcacbdddcddacdcbcadccbadaccccccdadabaabbbbdddbadcdbbcddbcacaccacaaabbdbbdabacabdadacaaabadabadbadcdccddcddacccaadbcdbddcaaacdddcccbadaaddaddddbacaacbbbdcddaaabbaabaacdcbdbdcbbddcddcaaccbdccdadbcbabdcdaababacbcaaababbbcaccbbbbaacdbbcbaccaddcaabddcabbbdbaaccbdbcacabcbbcaabdbbadccccaabbdaabaaddcaaadddabcccbacdbbacbabaacabdddcadbccbcbdcddddabcccbccdbddacccdddbadccaadaddbcccdbbddbaadcbacdaadaabdabdacbcabbddbbdadcdbcddbccdadccacdadadcdaadbcbdccdbdcdabbcdaacbbdbcbbaccbdddbdddcbdbbccdbacdbaccababbcccaaaccdcacaabbcbcdbbbacadbcabccbacbcdadbcadccdbcbbdbcbbbbbbbdbddcabbcddccaccbbcddbcccccdaaacbcbadcaacadaacdaaabdcddddaccccbddcdbcdddbcadcbbcadddbacadbdcbddcbaacaaababcaadcbbadaccbdcccccbdcdcbaaadcbaddddcbccabddcdcaabadcaabbcadcbdddccddbdbbccaabdaddabcccaabbabdaaddcdacabdcadaaabdbcaddabccdaccdcdbbddcbdbaadcbbbabdcaabacbbabdcabaabddcaadaadcdcbdcabcaaabbadacbdbbdcabddcbbdabdbcbabcbcbdadacdbcdbaccbddccabbbcbdaaddbdaaabdbcdcbddadcbaadddccdbbbacbabcaaacaaabcaaccbadaddcdaadbacaacdbaabcccbccacaabcbdccadcddadabddcdcabaabacbbcbbdbdacbaccdcacddaaaabcdddcabdcdacdccabbccdcaccbcabdcacdbdaadabdadaddbccacaaabdbbdcbdbdbbbaacacddbccccccccccddbabdaabccccbadaaacdcdbcbbddadbcddbaccccddccdcdccccbadabaacbbccbcdcdcabddcdcadbcabaabdcdaaddcdcadbabadcaababbdbacacadbabdbdabdcdbcbbdacdabdcbccddaabaaacbcdbcdbbadacbbdbaaabacbbdbadbbabdbacbcdacbdcccbbddbbcdbcabaadcbccbabcdcadccabdbcabacacadbdbdddaaddcaaaaabaabbcbbadccbdbdddcbababaabdddcbdaaabdddbabbdaacdddaabddbddbaddbaccaacdbaabbbdcbddddcbdbadaccabbdabbaadddbdccacbbddaadddbcadccbbbdddcbccdacccbcbbbbaaacacdcdbcbaaacbbdaadddccababacaabcbcbdbbddaadbdabdabcbaccacbaadacadcdcbcdcdbaccdcbbddcdbabaddbdccdcbcbaccdabdacdcacdadbdbdcccbddababdddaddbddcdcdddbddcbdddbcdcaabacabcaddcabaccbddcacdbabcaccadacacabbadbdbcbbadadbabccdbabaddacdcbaacadcacbdddcddbcdddaccdddbbbaabbcbdbbbcdbdbbdbddbbdcbccbbaadadbbcaccadcbcbaadcbaaadaccdbacacbaadbcddbcaaaaccbababbacddbbdbcacbdcbdcacacccbadcbbcaccdbdacbdaaaddbdbbabababbbdbabccabacddcccbaacbcbacbaaddcabcdbaadbabdcdcddccabcddbdaabbcdbdcabcdccddddcdbabbdcbccbcbbbcacdacadccbbbcbcbdbacabdbbabddccaadcadaabcadcacabaacdaabaadacacbddabdabcdaaabaccccddddbcdddcddaccbbdbacccdbdbcdbcccabdbacccbcabdabcaacdaaacdbadbdacddcbdbdabcadbcccabdccaccabbabbdbdbbdaacbcdacccdadbbaccddcabbbbcbcbbbccacbabbdddcbbdbcddacbcbcaddacdcacdddcbbdcbddccadbadbbccacdddddccccaddadbbdacbcddbcccbbcbcbcdabbdccbbbbaaddabcabdddcbbcddbbbaaadcaacadbdddabcdadcaadbcadbbddabaccdbacdbaaabaaaaabddabcabcccbcdaacaaccadbcddcbcacdddbbcdbcdcbbddcbbdcaaabcccccaccdcaacaccdbdaaacaacaadcacbbbdabccbaabddbdbddcddbcaadcbcadcdacdbccbbcbcddbcbbaccdbcdbcbccdccbddaaaaaadcdcddbaddadccaccabcbcdaaabccaadadddbaaacbababbcdcdcbddbcbbcddcadbcaaaaccbaaaaabbdcacaabaadabacdbcddaadabbdbadcdccddcadbabcbacddcadacbbaadbcdbadccdbababbdcbbaadadbdacbcbabadadbdcdadcaabdbaaaddcadcbdcabadcdbcbcdcbabaabbbabacdcabdcaddcddbbadcbcdccdbbadccadbbaccbcdaacadbccbccabaddbdcdbadadcbacdaaddcaaacdabbaaadbacbbadcdabdbacaabdbcabaadbcbcadacabbbabdcccabaabaabcccbdccdaabbcccdbccadadcabccdcbaccbadabddcbabbaccabdaccdbadddbcabbabdabdaacbcdbabdbdaadbdadbcbaaddbddbdcabcaacabdbbdccbcdbdaaccabdcaddcadbddcaadadcbabcadddcdcabcbcbaaccadacdbcaddabcdccddbdadbcbadbdcbbcbcbddacbbccaaaacadcdbbbcbcdacdaaacdaaddbddbccadcbacaabccaacdaadbbbcbbcbddadaabdadacbbdadaddaaccadcdacaccadcacbcabdbdcddaacdaacbccaaabcbaacdbdcccccbbcdccddabcacddadbdbadabaadbaacccacbdbccdcaacdbcaadbcbbbdadadaadbddcbadcbdacabaccdbcabccadaadbdcbcdddbcdbaacadaccbbbccacdcdccbcababcdcacdbbaadacdbadcdccbdbcdabcbcdcbddbbabbabccbbcdccbbcccaabbbbaacdabdcbbcbccabdadbcbdccdddadcdbadacabcdddabbdaabdddadddadadcbcaabaabadccababcbdbdddbacaaabcbdddddbcacbdabadacaacababdcbbabbcddbdcbbcdccdcdcaabcabcbaacadbbacadacbbacbcacacdbcaabccabbbcbdcbdbddcbbdbbbcacdacdadcadbcabdaacbcbbacacbbaaabbdacbbdcdcccabaabdadbbbdababdcddadbbabbdadbcabcbcdaadadcccdddbbaccaabcaaccdabbcddcdcaacddccbaabacabacdaccaabacbbdcdbbbcccccbabcdabbccbbdbdbcbdbbabcdbbbabbddbcbbadddbddccbabdcacbccadaacdcbdadcdddabbaacaaccaaaddddccdbbcdacdaaabbbcccdaacdcaccaaaadcaacadacacddcbaacabaccbcaddccdccdabaccaabaaadcdadbcabccbdcddddcbaadbcdddaabbcccacbcdcdcaaccabcdbddbaddbdcccdbdaadbacadcddccbbadbababbbbcbddcddbabcaabadaccabacbdbacaabcadcacacbadcacadcddcbabcaaaadaacdbddcadddddbdaddddacaccbdccdbaababacadaccadcabadbdbcdadadbabdaddbdabbcacddbcccbdadadbbcbbbdaccbccbbcbacddadbcababaccbdaaccdcbcacbabdaddadadabcdadabdaaadbcdcddddcdbdcddcaddddcddccbdaacbacbbadcdbcaddcdccbccbbaddaaabbcccdddccabcbacbcbdbcbbbbbbacaaaabacbdbbbccdcbdbbbcbacacbdaaddbbdbabaadcbdddbddabaddcddddccdbbcababcdbaacbbbccccaacdcdddaabcacaccdacdadabccddcdbaabdbcbacadcbadcbbbdadbdaaabaddcabbddcdbcbcdadbcdddcddaaacbababdacaaabccdcaddbacbbcdddcbadbbaadabbdaadacbccaaddcccbadddcdddbbccdaaacbabdacaababdaccbdabbdcbbaacbabadcbdcccbccacdaabdabbcadaadddbbdaddcdadccdcaacccaadbdbaadcbdccddccdccbbcbdacbddddddaaccbdaadcdcabddbbdadabaacddbbcddbdbcdcccdacaaccbcbcaaabababbcbcdbdbdcdbdacdabcbbdcaacaacdaccdbabcaddbabaddccdcbaabacaadcddbacddcbddbbcbcacbbaaddaabcdabbccdcddcaccdddbaadbdcbdcacccbbcaccdbaddcdbabcdbbcacdbddcdbadadddcdadbcdacbdadbcadaadaadddcccddcbaadccadacaccdbaccccbbdbcddbccbbcdbccabcbbcdaaadadbabbbcdddbddaabccdcaddaccacbbadbacdbbdbbbadbabbaddccdbcdbcacccaccadadadcddcccdbcccbbdddbaadcdadbacbbbcbabdbbccaaccccabbaddcabddaaaabcadddbabaaaabdbadacbbbcbdcbbadbcacbadccdacdadbdabaddbaacbbcdaabcaccbaaccccbabbdcbdabacddcbdacaaaddaccbccabccddccacdcbadbcdbaadccccbadccdccdbcbaacacbadacaadccddbaacaaadaaccbadcdcaacbcddbdbadaacbababaccccdbacbdcbadbbdcbbabcdcacdabdabbacbbacddcaacddcbddbbbaacadaaabacdaaddadccadbdbcbbbdcdaddacddddccbdbcadbdbccaaabbcadbcbacbdadbddbcdabdabaddcababdbcabcccbacdbbdcdbcadbadbbbadcaaadbcdccdbcbcaccbbcbdbbcaabacdcccadcaadddaaddbccbacbadcabbadacbbbcdadddaadccbcacddbabcbbddbddabcacdbcdabbbbbdabcdbbcbbcbcdcaacdcadddabcdbbaabbddabdabccaabcbcbacbcbbbdabbbbccacdcddccdbcadadbdcdaadacbdbaddbdadabaaacdddcabacbabcaaddcaddcdbccbbdbaaaddabbbadddcbbdbacacdddbbabacddcbabdccbdadbcbdadcdcbcccaddbcccadcbcdacbdbdbbbabcbaabdbcadaadaacbacbdcabddadcddabdacbddddccdcaabccccaadcbaccdadbcdcbabaacccccdcdbaabbbdabcabdbacccbbcdcbcddbbdaacbabaddababccbbbbacbcbaabdacbbcababbbcccaabbddcdbcadbcdadcacacbbabadcbccdbdbccdccbacccabdaaaddbaccddcccbbcbdbadacdaababbdcdacabcdaacbdbbcabdbadccbccbcccacbbadbaabbbbabcabacaabddacadbbdcadcddbdcdadcdadadddaaacbaaccdcccacdcccddcdabacbcdcdddcbcdbadbcdaddccddcbbdcaccdadbaaaaaaaacdbacabaabcaddbbdabbadacabcaccdbcabadbbbdbaadcabbdcdabcdbdbbabdcabbbdcdccbadddacddbaacacbddabbbacdaddccbbaadadbcdbaadabaacbbaaccbdaaddccdabcbddcdadaddbbbabddaaadabababdcdcdddcbacdcabccadbcbdbcdbaaabdaddabcaddbbbbbdbacbaaccbbabccabbdcacacdadbaabcdacbcbccdcbdcccaacdbbdbabadbaaacbacbdcacaaadcdccbbcbbcdccdcabdddcabdadbacdacdaaadcbcdddbdadbcbabadbaacdcaddbcaabbbabbcbdbcaccbaddbaadacbbaccacacdbbbbabdbacbabcbcdccaddadccbbcbacccaadbacbcccbbcabbcadacdacadccbcbbdacbccddabdcabaccabaddcbbcbcaacbdcdaaacddddbbbacacbbdabbabdbdbaababacaadababaacbacadbdadbdadbbaaacdbaccddadadbaadaacaaaccbaaccdcaacbacddbbccabcaccaaaacacadddbbddbdbaadcabbbdddbdaaadddbdbadcbbacccaabccbdcbbaccadaabadaacbbacadaaaccbdaabccacbddcdadabdcdbacdbabcaaccbdabbdbbdaabcacccccdcbbaddbbbbbabacbdadadcbddcdacaddaaddbcdbbbadcccadccbbbaaadcdcbcdbaabdacadacccddabcbbddaabbddcabacccdaacabbdcaddbccdbadcabdaccbabbabacbcbaacaccdccbadaddabbcdcccdbcdabbbbbbdabdcbdccbaaaabcaccccbdbbbdadaaadbcacbadacddccadaacbdaaabcbddcaabcaccdaddaabdccddcccbabcdcbdaacdaacdbbaaaacacacdcbcaccabdcbaddaadaacabddddaadbbdbdabbadbdddddcbaccbabaabbdaddcadabcddcccabccbddaabbcdcdabadbddaaaadddabdadccaacabaccddcdbabbdbdbdaddaaacdcdcbddbbbbcbaccccaccddddccdcdcaaadbbbcbbcdcbacbaaacdddabbdcccbbdbaccaaaaadbaccadddcbabbcddbcdabadcddbbdbcdcbdbbbbcdccccbaabacdbbddbdbbbcaabbcabdbdcdcacbbabdabcccdcdcbbbcdacdbddadacbdadcdadddadbbbadbcabbbddbaabaabbabccaddddcacadcaaabacccaabcdaabbcccbbcbcaadcbaaabccdcbddbcdcdcabbadabcadbbdaadadbbbacdadcbbdbbcdcaddddadcdacbadcbbccbaddaadcaccacdadbdbbcbcbdbacaacabdabbcdccaacabbbcdccadadbcadcadabbdcdbcddacadabddddbbbbbdcaccccbbbabddccdabbbbaadddddbbbcbbcbcdbbacbacbccdddcadabcadabbdaabdcadbdbacbbadadaadbbbabcbbcddbacadddddcbadadacbadbdbabdadaabacabbbdacdccddbddaddddbbbcdddbcabaacaabacdcbacaadbacddadabdcbaababacdaabacdcccccbacaadbacaacadbccacbcadbbcdaacdaddcbdcaaaaabdabdcbbacddcdabaacdbcbdbccbacbabccabcddcdcddbcadcbdbdacddbbbcdaadacadbacdacbaccadaccacabbaaacddbcdcaabcadaccdbaccbadcbccaddbcaacbbddbadcbddbbaadbdbbadbbcaaddabcbaaabaadcddadcaadbbbbcbdaaaddcdaaaabcbcaadccdaddcdabaddbbdabddbcbccbdadbbabbbcdddacdcadbaddbadcdabdcdacdbaccadbbdcabdbddabcddbdcbacbbbadaadbcdcbaaabddcaccccadcbdacbcaadcccadbabdcbaabcbbcabaadadcbbccbaacccabdbbbddcabddabacbbadcbbbdccababcbcacbbdbbdcababaacdbabdccbabdacdddcbdbacaacbbdacdbbcbcbbcadbdcccbdaaabbadaaaccbcdaabaccdbcdcbcbdbacbcccdacaaaccdaadbbdcbdcbbaacabbcbaaaabccabddbcaadaaabddbbabdccacddbbcdccdbdccabdbabbddbddcccaaacbcadcdcaaddcadcadbaabcccbddbbaaaddbdacbabcccbacddbacdcbbbaabcabcbdbdadbbdddcbabddddbcabdcdbabccbccbbdbabcabddccdcaddbdacbaadccabdbbacadadbdbdbdaacbbdbbdcccacadbdabbbabcbcadcabcbbabdaacdbbacbbdcdbcdbdabaacbdaaccbabcadddadcdbaccadabdccbddddcabcdabbcbddabddaadacadaaaabcadcccbdbbcbacbdddbaccbabbdabbacccdbdabbacaabbdadbcacbcadcbabcccaddddbcddddbbbacaccbacccccdadabdbadacaadacccacbcccddccbcbacdaccacdadcbdbccdcddaaabbdcabbaacdaccccabdccaaabcaabcbddacabddbaacccabdcbcccbccbcdccbdaabbcdbdadbadcaacabdadbadaadbdadddcacdcadaabcccbadcbcdccadcdbacbddddbaadadadaadacaacdadcacacddccbbaccacdcbcdcdcbdccbbdbdbdaacbadbdbbbcbbdbccaaccdcaabcddbddbabcabcaabccbacdbbddcddccaaaabcbadbbdbcbcccbdccabcdbdbadbdbaabbcbacccbcdcccdccbdaaccccaccdcdcddbdaccdccddbcaadbdbcadbcbdbaccabdabcdcdcbbadbabcaadbbbcabccbddaaadbbcbcccdbbcdcadbadccdcbbaccbccabcbcddbcccacbaabcbcadadcaadaaadddbdaabccdbdacadacdbabbdccddadbdbddddcdabcadaddddcbddcabdaccdaadcdbddaaacacbcbcdbcadadcbaacbcabcadbdabbabccabbadacbaacbbccbaadbabdbcadcaadccdbccdbcabaabcdbcaccccbbddccaaaabdbbbccbaaaddddbcdcbcbbbcabddcbacadbbddbccdcadabbbcdbcbdbbdadbbabbdcdbcdaadaadccabccbdddddccadbbdbaaabdaadcbaccacdabaabbbdaaddaccddcdadcdabdccdcdcaabbcbddddbddccabcacdaaadcbdcbbbbadcdbabdbabdadcdabadadcbaddbdbbdacbbcaabcdbadaacdcaacdddabdaccbbdadabbcbdcdaccadbcccbcadaacccadacbaddcbaccccdcbacdcdcdddcbcccbbcadbcccabdbddaadabccacddcddddadacaddbbbdabdcbcbcdbdbdaaccbddcdbadcbdcaaddddbadbcaaababdddcbbcdbbccaccbdddbddbdcbacbbcbbccccccadccaddababcddcbcdacbaabbcabdbbcaddadcdacbdbacbcccdddabccaabcadddcabdcbbdddcbdcacdcbcababbacacdbbbcccdabbbddcbbcbdabaacddaccdaaaacdbaddcdcacbccddbcccdbbadcbbaaddcdbdddcbaadacadcbaadcaccabcdcccdcbdadabdaccdbadbdcbaccacddcaadddacaadaabaabbbbbbbddbbcdaaccadabcbdbdbadcbabcbcdccdbcadadccaaaacaadacbbcdcddcacdbdcaaacdaccaababcddabdddbadcdcbbdadbbadadabdaddaacadbcbadbdbcabbbaddadadcbdcaabdcddbdbccdaaacbcadbabdacbadabbcbccdcbdaaacbacdcdcabdbcbbdadacbaabbdcabbabbbcccddadcdabcaaddcdaccacabccdbddcdabcbacbbaabdaccbdacdaaacbaadddbadaadcaaadcacdcabdbbbdacbbbdbdbddcdcaadaaaddcddaaaddabbcaccbbbccaaaaadcacaddcadccbdcaabcaddbbbdddaccbcdcdacbccbbddadcbbccdaddadbccacadbddbacabaaaccaccddacaaccacacbbacbcdacdaddbbbdbbcdbdbcabbbbdcdbacbdcdaddabbaaddabdbbdddbbcbcddbdacaddccbdcbdaadadcddadacbacbadcddcdcdcacdaccbcacdddacdbbaccbbbcdbdcacdcbbbddbbdabacccdabccacdbddabbaddaccbbaadbacccccddbacbcccdcacdbadccbcbadadcbcdaddcacbcabcdaabcdccdbddbcbcabcbbdabbacacdbbdbacaabbddcccdabdaacadababddabaddadbaabbaacacddadddaacbdabbcdaabbaaabdbcccccaacadcdabdbdbbacabcbabbddaaabddaccabcbcbdbcdaadcdaadabcdcbcadbccaccbdaadcacdbdccdddbbbacaccadaaacaaabadadabccadcabcbcdbcacacdccbacdadcdacdbccbcbcbacbdaacbbdcadbaccddaadbacadaabaacabbdcddbcddabaccddcbdcaabcdbccdcbadbcdaddcdbccaaaccdcbacbdddadbcccccaddadcababcabbddcddccbbcabcadabcbcaacbdbbcaaacacbbbcdacccdadaaadcaadaacdbcccbddadddcbadaaaddcddbacadadbbdaaaddaccabbbacbaccddbbcddabcadacbbdabcdaddcdccddcaddbdcbbbabaadaaccbdbcadbbadaadbcacbbcaaacdcbbabbabaabbbabbcdcccddccabbdadbcbdcdccababccaddbbddaddddbbddcbdbbdcbdbabcacadcbacbbdbbbaaccdccbadbbddacccbdbaacdcadddddbdddbdcaccabdbaaaddbdcdbcdcbbadddbbaadbccdcbacaccccadaddcaddcdaadccbabcccbcdcbcdacdbbccaddcbadacaacdcaaadaabdaaadbdcdacdacbdabcdcbdccabbbcbaccadbdbaddaaabcabacdbbbdcaadcdcbcbbbabbdcdbabdaacccdabcbccbaddabacadbdacaabdcdacdabacbbbabadbcaccaddbccaaacbcdadbbccbdadaaaddbccabadabcdacddcabaddbcabbdadaadcacbacacbacdcbbdcaddacbbcacddcbabcbaaabacbbcaadaacbabdbcbcadccdcdacbcacbacccaadcbbaadaabdbadcbcdadaabcaadbdabcbccdcbbbdbddaabccdccaaaabdcccbdbdddbcbccabadcabccdcbabcbdbccbaabcaacbacdcdabcdcadccbcdadcabbcabcddaddabaccdaaabcddbcdacddccbcdcabbdcbdadbdaddacccabcccabbbbbdccbadbcadbcbdadabdcabcaadabdccbbddccaadabcacdacdccbcdccbbdabadcaababbdbaccbdcadcbcabbcccccdcbabdadbaabdcabbcbbbaddccdaabdbadadadaaabcdcdcdbdaddcacaadbabddacbbaacabdbbdcbbabcaadbdbdcdcbdddaddccdccbddaadcacdacaabbdbdcddbccababbaaaadbcddaacaacbbbcbadcdaaadbdaadccadcbbbccbdbabccbbbcdddbbadabddcbccdcdcbddccacbaabacdacaacdcabdabccdbdcabcbbcdcccdddbcabacadbccbbdbdaccdbbacdddcaabccbdbacaddccdcccbbccbdbbdbabbccbddbddabbdcccbaaccaaccbbacdcbbbbccdaadbbcacdbdabacbabbdaadbddcadbdaabdbccbacbaccabacccdbdccacdbbaacdcdcbabbacdcdaadcdbacabadacdabdbdcbacbccadcacadcabdcbdddddccbddaadbccdcdcbaacadcadaddbddccdddacadadbccdccccccadcaddcdaabdabbddbcaddccacbdcdbacabcbabdbcdbbbacdaaaacbaccadacbdadbbcdcdabcabdcdbdbacbadcbcdbbaabbdbdacacbbbdaadddccaabbdadabdabbbcbabbccaaacdabdaadddcddddcabdccccdacdccbdccdddbbcaccdcadbdbbbdabbbcdadbcbcbcdccdbcaadcacdddcddabcadcaddddabbaccacacdabcadacddcabadacbcddbabbdbadbddccbdbdbbabaacacbbdbaddbcaadccccdbccbdccbcdbdababadabbcdddacccabcabbacaaaddaaaadddbadbbdacbababbcbadacdccadbbbcccbbbdabacbcbbccadcdabdabbdccbbbccbdbaddddbacbccbbbbcbbcaaaaaddcbadbdbdaadaaddcddaddbadcbdcacbacacbddbadacddbbbabdacdbcabcaadddcccccaccdadcaaaadcabcacccaccdbccaccccacabdccbccdcadbaabcbbcbddcacbccbdddcdbaadbcccbddbadddbcddabdcdbacabbaacccdadadbcabadbdcacdddadbbbdccccaaccdccbccacadccadbcdaccabdadcdabbccdbabcccdbbcdcaaddcccbcddbbdcccdcbabcdaccddcaaacacccbcabaabcaddabcacabdcacdadbcaaadcabdababaaaadabcaaacccccccccbdbbccabcdaadbdaadcacacbacaaacbaacccddcddbbdaccaddabbcdbdcadaadadabdcbbddbbbcaaaccabdcaaccbbadaddbadadccdbdccbdabcbcbcbbaacccdadddcadacddbacdbaabcdbdbacaabcadadcabbbabadbcbcbdaddccaacaddddcaccdddabaacccbbbdbdabaabbddadbddcddabbaaddddbddbcbbdbcdcdcabbcacccbcabcdadddbdcbadbbadbaccdbdaaddddbbcaacbccbcababdcacbadadbbbcadacdcbddbccbaddadaddaabddadcbcaaccdaacadaabdaaacdaacbdcccdccccbadaacbaadbaccbbdbcdddbddcabaddccbddcbabaaadadaabaacdbbadadbcdaacabbdcbacdaccdbbbccacbaaaadbcdccbbbbcbbadddbdbcbabdbacbbacbadbcbcabbdccaabdbcccdbadbcbbaadadacdddccdddacbcdbababdcccacbcdabaadabadcacbbcdacaccbbbaaadacbccbbaaabddabbdddbabacdcaccbcbacddbcbcbbbccbbcadddcdcadbcadbacdaabcbdbbbadadacdbbdcbbcadaabbdcbdabbbdaabdbbdabbcbaadcdbcbccddadacadbcdaaabaabcabddcadaabadcbcdbadadccccbcbcdcbdcdbbdcdcdcababdaadcdadcacabccadddcaadbbabbbdddcbabddaccbcabcccaabaaaaddbaacdddbadbbadacbccdacdbcbaddcaabbbdddaaaacadddcbacaccaccabcccbddaacdacacbcdcacbcccbccadbcaddcdabdbccccbbaddddaacabcbcddbacdaadabbadcccdbdabcdbaababcbcdadadabbbaaadacccdabbcddbccdacddacccaaccaddbbcccacbbacabddbbdabcbbbbdccaccabaabbcddbbbcaccdbdcaaddcdadaacbdddadbadbddacdddcbadcaccddcaccdbccabaacbbbccbacdbdccadaacccbdaaacdadacaccababaacabbbbcadadcadacbdbbbaaaaacbbaaabdacdbbccadcbbacbaaacaaaaaabaacabdaaabcdccbaadddbcbaddabaadcbaaaddcdbbabcbccdcbbddcabacbdcccadddcbadbbdbccaccadabbcbaccabadcabcbbbcdcdabdbadbdaaddaccddbbdcbbbacdcdabccdbdcbbdcbaddbcbbbbabbaaadddddddaadbcbccddddabcaddccbbbddbdddabdaabbbdaabcdcdacadbabdcdcbdccdaabcacddaacbccddcaabcbaabccbaddcaaddbdcaccccddbbddbdbcdbadcbdbdadadaacbcbbbabdddccbcabddddacbadbacbcdbcaacdabddcbacbdadabdbcdddcddacdbdcbaadaaaddddacbbaaabdccdbaadadcbaccadcbaaacdcaabdbbccdadddbcaabcccaabcdbacbbdbadabdbcabadaccacaadbdbdacdccabddabacddbdbcbacadbdbdcacbbbcadadcbbccbdbdcaacabddcacbacccdcbcabdddaddaacbccbddcdacdbdaccabccadbdbcacabddaaadbadabcacacdbdacaacbabcbbcdaadccacbdddbacdcdccdccaccaccbdabdbcbcabaaccdbdadbbacddaccbbbbdccccdcdbcddcbcbddabaabdddccdcdcbbcdddbdbbbcbcacadccdbcdaabcddcccbadacdabbabdcabccbbdcddddcabbadcbbaccbdbdaacaaccbdbacdaddbdacddbdbacdadcabacdbbbbdcbdcbdbbaccbdadcdabbcdbbcddccdbdaadbddcabaddbdccaaaccdbdabacaddcaaadccbababcadccadabacadbacdbdacbbddbbaaabbabadcacddcbdbbdacadbdbdbbacbcddbaaabbadacbcacbddababaadddabdbcbcccadcddcbdbbdcccadbacddcbbcadbdaccbcaccccccdaddcabaabacaabcbcbddccabddccdcccbdadbddabccdcddbcaccdcbbacacccdbdacbaadcabdadaddbaccabdccbbdadaaabdcccaabbbbadbaddacaccaaccabcdcbdcaaacadbccaaddacdbcbcadabbdaadcbbbbdbaaddcabddddcdbdcdbdbadbbddaaccbcbbdaadbddbbddbcbbabddacddcbacccacbdbadbbdddaaddddccbaddcabdacaacacccbabdcddcdcbadadcbbcbaabadbaacaaadabbbadbbbddaddaadddcdadbacbadabaacdcababbbccbdcdbaadbcccbccdadaabbddcccbcbcbbbccaccdaadcabcaabaaddccbcbcbcaccdcccaacdaacacbdbacddabcbcbccbdccccbaadbacbdaddcbbddccddcabbacbaadaacccbbaabdddbddbddbdabbbaddcbddddaacdbbabcdacccbcacadccabacdacbbdbdacaaaddaacacdddcdaacabdbbdbbacaacaccbbdaabbcaaabdabcbbdccbdacddacbcdabaacbdddcdbbbcacacddddcdccbcaaadacbaaddcbccbdaadbbbbcbabdcdbabdddcdbaabcabddaaaddadaabcbabdbdadbddcbddcacdbdaabdddccabacdbbacacabbabaadbdadaabdbbacaabddcddaaddccbacccbadabacabbacbaccbbabbdbabbbcaabdaaaabbabddccdcabbadaacdcdbabcbbaaddbdabbacbbacdcdbdddbbccbcacdcaccbadaaaaacbaccabdbbdbcbbdddacaaaabdbbdabaaccbcdddbadacbabaddbcadbdbdacddcaacccabccdcadbbabdacbdbaadbddcbaaabccacdbdbcdadadbacaaacbbaaadadaccdbdbdccdbbaaaddbbcdaabbabdaadbdabcccdbbdbbdabdddbadcbbdcdbbcbabdacadcdbdddcbbdacdccadbbdbbbadbabdddbbdbbcbcbadbacadddbadacdbaaacacddbbbcabacadbdcbdbaacaacdaaccdbacabcaadacacdccdccccdcccdaddcbcccbcccdcccdcbabcaadbaacddbdddabcadbacacdabbabcabbbdadadbbdaddbddbcbdbadabcbdbddabcbbaadcadcdbcbddbacbcacccdaddbadcdcddaadaabdaabcbcabbcddbcbaaacccdddbdbaabaddcbccaddcacacbabbadabacacdcdaaddcbcdabadaccaabcacaacacdbddadcacbaababccbcaabadaddadbbbabccabbbbbddaadbdacdccadcbbbbbdccbdaddabacadddabcacdcacabbacaccccbabbccbacbccbaccabaaababdababddacbabcabdbbabcaacbaccabbbbddbbccdcddadcbcaddccbccdbcccadcccbccdbbccdbdccbacbbaaddabcbaadaabbadaabdaacbddcdcddbccadcaabadadabdacdcdabcdadaabadccddbdbacacbcbdcdbbbdcccdabdabdacbcbddbcbddbbdaccadbabadbaaacaadbaddbcdcdbbcdbcadabdbabbbcbccddcabccbbaadddccdaaccaacbaaccabaabdaabdbadcbdacaaabcbabacdbadaadbbcdcdbaadacacbdbbcbbcbabbdbbddadbdcacbdbadccdbddaabccdbacccaabddbcdbaaaaacddbcdaddbbbbbcbbcdaccdbdaadcdcddcccddcabcdccdaddcabbbbbbcabddcdbcbccccaadbbabbbdbabadaccdabbaccccbaddbddbbbbddabaaddccbcaabdaccabcdacdcaabdcddcddcddcbccdcabcabdbbccbabbcaadbbabbacdbbcbbcabcbdadccbbbaaaadddcddcadcdabdbcdddcadcddabacbabaccddcdadabadcccdcacccbcadbaddcadaddcddccbcbabddaacacaacbdbdabadddaabdbcaadcbcadbcbacdbdcccacaabacbddbbdcbdaacbdcadabbdbabbcdbdbcbddddcabddbdacaaddbbccbbadadabbbadddababdcaadbcdcabddadcadbadbabddcdbdcdddbcaaaccbaadabbaacbaabbacbdddbcbccdccbaaaabcaadcbcbdbdbccccbcacdccddabacacabbdaaacdaacbccabdcbbdccadacbcabcdcbadccccbabbbadcaddddbbbdcdaccbccadbcccadbadcbdbdcadccdccacabdddbddadbcbacbdbbadddcadacdcacddbbcbcdddbaccbccbbcbbadadadcdddadbcabcabdaacabddbbbdbacaccddaaabacadaaabbdcbdbcadbcdcbcbdcbccdbcbaccbbdbadacabddacabdcddabcdcdcdabcdababaccddddbbcdaaabdcaadbdbacadbbcddaaacccdcddabcabddbddaccdcadcddaaadcbdbacbcdccacaaacaaaadbcdcbbadaabccbccaacabcccdbdbbbbbdbdadcabdcdbdbbccbacdbabcbacdcbbcdbcdacbdddbbbdcccadadcadbbaddabdccdbbdadccbcdbbbabbcccaadbbbcccddcdbacccdbcbcacccbddaacccaacdabbadccbcdacaaddcdabcdbdcaddaccaacdbccbaabbadacbccaacccaabbcdacdbadaadcbdbddcbcbabbdddbdcbdddcccbccdabdcddaaccbdcdadccbaabdbaacdbcccbacdbbddccbbccbaacabbdbaacccddbbbcbcadddcddbbbacdbbadbadbdabcbabdbabdcabccdbaddbbdddadbbdbaddaaddcdadabbaabccadcbdacadaaaadacbcadbababddbcaddacdbbccdabccacddcbddbcbacaddcbcddddbcacdbbbddbaccbacaddabbacadddaabcdaaddbdabdcbdccbadbcdaadbdbaacbbbaacaadcaacccabdadcbdbbddadcbdddcccbdcbbdcbddbdaddacccdbaddcbacdcdccaccdcddddaaddaccbdccadadadcabddbbbababadbbdcdadcdabcdbdbbbdaccbcbbabdcdccaaadbcdadbaabccddbcacaccddcdaadabcbcaadacaddaabdacbaaacdbabaaadacbcabdcdbabdbbbaaccaccbdbdaabbdcbbdabbdcabaabbbccbdacbccccbbcbbadccdcccabbbbadbdadbbacdadcadacbcdcadacbbdadddabdbcbabadbbbdabddbcaccbbddcdcabbcddbcbabbbccdddcbccbbaaddbaaccbbadddaaccbcacabbcbcdbbcccacadcdbdbbacaaacbcadadcbddcadcaadabbbbcadaddbdcaddbabbbdabacdadbdbbddccbddbcadaadacdcdaaddadccbaacbdbbdcdacdabdaabdddaddbccdadccdadadaabbcdadadddaddcdcdabdaabacabcacabccadadcbbdbbcdddcbbbdbdcbcddcdadccdbbcbdcccdbdcccbcbccbdbcaccabaacdccbbcacdaddbcbbababcadacdbaabdccbabaddbbbcdbdbdabdcbadbabcdcdcbdbdcdcaacbbdaacbaaabacccdcdbbdbcbabbbcdbcacacbacabdbbddbadbbcdadddacdaddcbadbddcbcadbacadcbccdbabcdcdbbacccabadadbbcabddbcacaaadbbbbdbcdabcbbbadcacbcbcddbaabbdcbaaccdccdcacddacbadbcbabbdbabcddabcbabacdaccbadbcbacaacbabdbbadcacadcbbdbacdbacddbcbcccacadaaabacaaacaddaadbddcaabbaccbbdbdacabdacbdbbbdbbccdcababaacbbcddbbdcdbdcbcddcaaddcbdcacaccabcdbacddadbddcacacadbabadaddbabadabdbbbddddbaabdddddbcadaacbbabcdbadbdbbddbdcaabaadbccbdadcababadaaadabbdacbbdcadbbbaadcdcabbabccbbdacacbbaacbacdadcccacbcdbcaaacbddaddbdacdbbaaaadcaddbbddbccdaddcbdbcbcdbacbbaadcabdaadbbacacabbcabcbcacdcdadddbcadacaacabdcdbdbdbdbdaabdcdabadcaabdbcccbbcccbbcabccdbaadcdcaadaadcdaacdcadbcabccccbbdcdacbbadabcdcbcbddbbcbccdbcdaacddddbdbdaadbccdbbadbccdacdbcaaacabbdabbcbcbdaacdabbcccdcdcdcdbdadddbadcbcbbdaabcacdccdbacbbcccbacbdcccaaabcdddbcaacdbbaccabdacaccaaaacadaaddaccccacbaaadcdbbccacccabcaacdcbbbdbcbcdcdcbccccadcacadcddccbdcdbbbbbbbcddddabbccdacdbddadccbdccaaabbdcdbcacabbddcaccdbadbcbabddbccccadbadccabbacdcabaabbcbbdbbbdbaccdbabdcbbbdacadbabccbbcccacdaddcdacdbcdadbabaadaabddbdcdbbbddcdbbabccdaaacababdaccdaacbdcdccdcddcacdaabcacbcdcdbbcbbbdbddbbdadaaddcaaabbaaababdbaadbaddddbcbabaabbdbdcaacbddbdbbacbcaadcacadbccdbbdacdcbabbbaccabaadabddbcdabcacabbadcbbdbabaccccbcaabaaabccdbbddacbaadbababccadccaaaddbaaadccbcbcacabacbbacdaacbcccababbbccadcdddaddbadaacbccdbaccaaccdaabbaaccbaddcddcbdbbbbcabddcabbadaadcdadbcdbbcaababbddbbdabcccabcbcbcdcbacdbbadcdbbdbcaadbcaaadadbabacdccdbddddcdccdddddcbbcdadbbbcaaadbbbcdacbadcadbbcdccdbccdaccddddcabbdbcbcbaddbabcbdabacbcabdaacdbdbdabaddbddbacdcdbdddbdcdcdbaccacababccdaddbdcacadbcdbbbbabcdaaadaaabcdcbacbcccbcccbcabbaccaaabbdccbdcaddcdabdcdaaacdddbbabaabbdbccbbbbabcddacccababbcdbabcccbcbdbcbbbbcaacbbcdbccccabadcccbadcacbababdadddbabbdcdbbbadaadbbdddccbdcbbcdbdacdbabddcccbcdcdaadcacacacbdbacdbcabddadddcbdbdaabacbbcdccbdcadccdbcbcbbdddcbbcaabaababdadbbacacdadcababcbcbcbddcdcbbbcaaadddbcbaccdadaabaaaabacddadcbcddabbcbabaacddadbcdccaadbaadbcabdcdcddccdbcacdbccccbacccabccbcabdcaabacbddaaabbccdaaadbdabbbbcabacabddabacbddbacbddbacabaccbaabddacdbadcdacabddbcabcbcbbbcddbaccdaaacdcacbdcaadcccacdcbdbcaddacbdacacdabcdacaccaacdbbcadddbacaadbdaadadacccadcbaabbaaccbadabcddbbbbdbbaddcacdababcdbbbcbbdcbcbcbcbdddcddaddabccbbccbacabdabcdcbbccdccbcdbdabdbabdbcdaddcccccdadbcbdcbaaccbaaaabcbdbccdabdbbadbbddcddcbdbdaccabcbbbbadbccabbbbdcbbbbbbbbaddddbcdbccdaccddbadabddabdabcdbcaddbcdccaabacccccabbacbdcacbdcabcabbadbddaccccddbacddcbbdbabaadbbaacaadcbdbabccabccdbcacadaaacadccacadbbdbadddcccbcdcdbddadbccdcddbbacbdcaadadcbdcaddadbbaaaabdaadbbbbcaccbbadadabdcbddccbdcdabbcaaabababadacacdbccdccadcadacadcddcbacddcdbbcbbbcbcbdcaadabadcdccadcacbbcadcccabacbacbaabbbccbaabbccacadbbbbcbacdacbbbaaabacdadcbdbbcccccdbbcbdccbbbcdaaaccdbdaaddcdbdcbddcabddcbcbadbddcdcaaaaabcbbdddddcbabcbbcdabdaccdbdddbdbacaccbdbaccccabaacadbacbccdcbdabacdacbabcaaddbbdaabcdddcbacdacdbaaadddbcbcdcddaddcdccbaddbdaccabbadbdacccbdcbddcbbddccbcbdadabadcdbbdccbcacdcbaddcdbcdbcbdbbabcdbcbbadadbabbbaccbaadddacdcdbacbdbdaaacacbcdddcdbbbddacbacbadcdcccadbccddaacbcdabbbdcacbccdcbaaaabacdbbbccaacbcdcddabdaacadcbadabddacccddabaaccbcadaddbbcbabacbaddcbcdadadaddcadccadcbabbbdcdbadcadbacbaadaabdaaabbaaacbbcbcadccdcbccabbbdcbddacaadaaccaabdbaccababaddbaaaadccbbcbdadbdddbdadcdbddbcbbcbabcdbdbdbbdbdacbabbbbacaadacbacbdadacdaadbddcabaabccbdadcbaabaaaaccdaccadabbdabdabdcbbcbaddcaadbcccaaccdcdddbdabdaabaaddccdddcbbadbdaacbcdbddbadaabaaacdcccdcbaabdcaabccddddbcdabbddbaddabdacbddaaabbdadaaaadabcbbdddcdacbcacacabdabbaabacabbaaaaaadbcacaacdabaacbdcabadacdbbcabdbcaddabbbcddbaccdbcacccdabbadbbbadbcadbdabadbdbadaddbccadaabcdbcbacdcdddacdbddbcdbaabacdaaabdbcccdcdbdaccdcbbbbababddbaacdcaabcabdcadaaaacdccbdacadacbaaddccdabcbccaacdcccccdadcabccabacbbdddaccccccbcbbadaadacbbbcccdcadcbdbaccccacdbccadacbcbcbddacdaaddcbccdabacbadbaaddaacdcabcbcadbaadcacccbcbcadbacadbbbdbbbcddacbbbddabaaabbcadcaabcbbdcdbbdadcabacddbabddadcbbcbaacbdbbaaabddbbbdbdbdadddbdbccccabbcacbabdcdbbccabacddabcdbbbcdbbcddbcabcacbbadcdabdcbbcbdacaacbacabbacbdcdaadaddcdacaccbbcddddbcbadcbdbadbcababbbadbddbcdabacbdcddbcabaaabdacbabcdbbcacdaccbcdddbacabbcddccdcbcbacbaaccabcdccbdbbaadbbcbadbccbadadbadaabdbcbdadddbdcdbaaadbbccdddbbcaadcdbacdabcbdaddcccbccbbaddaadbbddcddbdadbcbaabcbabcabbbdaabbaadadcdadaacbaaaddcddbbcacabccadbdacdaaaddcadcdbcccbadcaabddbdccaaabbccaabbdbccbcabdcacadbadabbcdcddabacbabadbcdbdbbdbcaadcdbddcddaddbabbacaaadcdcdaacbcccdbbdddcaccaccdbdbddbdbdcadcaababacdbbdabcaacbdaaadacccccadbbcdbacddbbaabcdcacadbbbdbdcabddabdcaaddbcbdbcabaaabbdcadabbaadcdddaacbaacbccacdbabbaddbdcbaaacdcdccacabbabcbdbdaddadababdbccadadaadbabcccdbbbcadcbcbabadcbcacbbccbbadaaabccdddccdcddaaacaabdbacddaadcbdababdcabbadbbaaacacadbacadbcddabaabcabdccbabadbcaadaaccdaccbbccaacbccabadbbdaaaaccdbdcabcdddcbdcbdacccbbcdcbdbdbdddcadaacaadadcbdaddbdccbdbdacbaaaccbccbdbbdcadaddabbdaabbaaabdadabbbbdbadcbdbabbdaabcbaaddaccbcbaacbaaadcddbdacabcdbcddbccdcacbddadacdaabccbaabcddcccccabbadadaacdbdbacaabccabacacdaddaabadbcdcadccdbbaadddaadcdbdccdbabccbcbddaaacbbacbbcbbbadbddbdbbdcaddccdcacadaddcdadddaacddcbdcccbababddbbaccdaddddbbadabcbdabadcdddcabcabbdabdbbaabcaddcbbbcbcdccbaddcbdbdbcadbabccaccaabbadabddcdcbaccadcbbbddbbccbdbcdcbbdaacabaabbbbdbdbcddbbddbaaccdbbacbbadcdddcaadbdcdbcbadccdcbbdabdaddaadabbbcbcccacbaabaabbaaabadaadcdddccbbaaaadacacbbdadbcdbddbdddbdabcccbacddccaaacccadcaddcdbaabdcacbcaccaacdddbcbddaddaaabbbdacacdababbdbccbdcccdccbcbcabaaabcacccbaccccaccdddacccacaddaaaccbbcbddaacdcdcaacadcdcabacaadbcadcbadcbdbdaadcddbacdaddbcdddbbabcbcdadbadcdcbdcaddbbdbabcabdddacdadaaacbbdadbadcddaabdcbcbbdaccdcbaddcdbacbbadaaacaabbcaccabbbbacbbcdcbdadbbddabdcdcbdabababacbbbdaddadadbbddbbbadcccacbaadbdacadccccaaabacdddcdccaccbbbaadaddcdbaddcddbbabcdabccbaacbcccbaccbbaaabbaadaaaabdaacaabbabbaadbcdbcabcaaddbcadcdbddadcadcacccdabbdbbdaddcadcbcbdcdacdcaadaaaaaccccbaabacddbddddadccacdcabcbbbdddcdbabcdcabdcacbbabdbbdccabaabdabbcbcbdbbdabdaadbababbddddbbcaadcdacaadabbdbadabaaacbdddbadbddacddaadbaccdccdcaadbdbaababbbcdbdbbacdcccdadbcacbdbacabacbacacbdbbdbcaddcccdbcccbdaabaccccccbaadabdcbabcacacacbbabbadbabaccadadacdcacdccacacdaccddbacabdbddbdccabdcdcbadddbcaadaaacbadacacaabacdcbdbdacabccacbaddaddbcbabbcadaaabaccddbbdbdcbabcaacbaddccbdbdbdacbbbadcccadbaabcbdddbbddccabbcbdcdddddcbacdbcadcaaccabacdccccacaddbcdbbddacccdacacacdddcadacdddcadabdcddcacabadacaaacaddddcacaaabcccbcccbaccbccddddddddcbcbdacdbadddbbdabcbdbcbadaddbaabababbbbbddcdabacccacdddacabbadcbddaaccbdcaaaacadbabbdbbaacbbcacbdbcbdcbbcbdbbbaabadbbcaabdddcbcbcbadcbdacaddacaabcabbbadccacaadcdddabcabcbadcdabadbabcddcdddabbccaadabbbdddacbaadddcacdaabcccbddbbbcddcccbdacddbabdcdacbbccaaccbbcdbcdddaaabdcdddcaddbbdaaabbbcdcadcbdaccddcdcbbddcadaccbdcbbcaaddbbaaadadaaacdaccaabcbbdcbdcddbbddadddbbbbcbdaabbbdccbcbdadbdbddacadcdcdaddadadcacaddbacbcccabadbacdbbcadabaaddabacbaadccadbbbdcddddcadaddbbbdabadcaaaccdaadddbdaabbbcccbcdaacbbdcccabdcbbaabbdbbcacbbbcadadbdcacdaaabacdcaadadccdbdcbaaadcccccccaacabbcdadaaaadbabdcdbbdaccddbdabcbccaaacbaddccadcbabdaccbacdacdabbdacddaaadbaadaaaddacabadaaacadccadcbcabbcdacdaaabbbcacddbaddbababcccaddbaacdaacbcbcdbaaddbadadddacadacbdcdcadbdadadcbbddacdaacdababbdcaaddcdcbdadcdcbdccdadacddbcddccacccddccdcdadcabaadccbccacabbaacaadbcdcbbcdacabadcbbbaaccaabccddccbdcdcdcbdccbaddcbddcdaccaaccdcbddaabdcacadadccbdadadaaaddcdaaacddcbabcdacdabacbbcabbcdbddcabadbbbacccaccaddbadcdccadaddcaaadabdccbcbaccabbdcdcbabbaabdbbdccdabadbcccdcbbdcbbaaacbaadbdcbdcdddacbcaaddbaabcadbccdcbdddcbdbcbadbabbdddbbcddacddababcdbacabcdcaccbabacbbdbcaaadbabcbacdaaabcddddbacdbdcddddcddccdaaccdababacccddbbdcccdaaddbbaaccdcbbcababdabacccadddadaaddacdcaccbcdcbacaccbaaadcbabadbddcabaacabcdcadcddddcaddccaabaabcbbbccccdabcccbcbdbbcabbacdacbabcddadccdabbddbdbdacdadbcbdccbccbddbaabcbbdbabccbbaadcadbdbcdaaccccabbdddbddcbbacaacacdcaadccbcabcadbdccadcccadadddbbadddbbacaabbdbbbdabbdacaccdaddbcddcbccbbbddcddbaacabaacbdadaaddbaaadaccabcbddcddaaddccbbdbcbacaddabcadcaaccdacbddcbdcbdbdaaddcadccbddcdbcacdcccdbcbccdbdcbbddddacadbcbbdcabcccadbabcbbbababbacdabddaaababddcacabdbbaabbcacaddbbcbbacacdbbbcacbababbcabdcdacccdbbaaccbbaddcaccaadbbadaaccdbccabcccddaaabddacaddccdabddadbbbadacbbadabbbaaccdcacdcbaddcdbdbdbbadcdcacadccdbcdabcababdbaacccbdaaacdccdacbcdacacabbacccdddbaccddbccaacbcddabaaadddcaacbbbdccddaacdccbddaccbbacbbcdbbaacaadbcdddaaaadacdbacddcbaaacaabbcaddcbbacbbcabbccaddcadcababcbbccdaaccabccabbdaadaaadbbddbadddbcaaadbccadcbbdacbdbcacdcdcaaabbaabaccabbdcdbacbbddcabbddbaddccdbdbbbcbaccdccaddcaddbababbdddbccaaacbdcbdabcbbdbbadddbccdcdbdcbdccadacccdadcccddccdbadccdddddcbddcabdbbbacccdbddccdacabbccdacabdcbccccdddaccaccdcaaccdaaaaddbaaabadccdbaaacccbbbbbabddabcddbcabcdcaacbccbdcdabbdccdaddbaaaadbccbdabdbdabdbbaaaabababbdcdbabbbdcbbcadcaadbddacbaacdbaddbaaabcbdbbbdbbdcadddcacbbbccdabdbcbcdaadbdccbcdadabbbcadbbaaabdaadcccbaacbdccaacadbbcdaadddbdddbbaabcdbddbabbadadaabcdccbaaabbdcabccccddcaccddccdaadacbabbdccdbcacdbcddddacdacabcbccccccacccdcdcbcbadcbcabcbababcdcdbcbcddbcaabcbcdacbdbcdaddcdcbababbcbdcdabadaddcdcdbcdbbdacbddaaacbaadbcbcdcaabcdacdcadacdcdadbbcabbdbcdcdbbbcaddddccbabcaaaabdcbbadbadccdbdbaabbccbabcabbbddabaaacbcddacccaabacbddddbdaccdbaaacccbddadddbabbadcddbdbbdbadbabacbaaadbcaababaddabbbacadbcadccadcacbdbaddbabcccabadababdaacaaccaaaaddcddbcacbcdaabdcabbdbaacbdbdacadbdcbccaaccabbadbcdacacaaacdbbbacbbaabcbdcbaadabdadcddbabbacddaaadbdbaadadccabdbadbababcdcabddddcadbdabbabddbdcdbddddbcdcbdbcdccdaacccdbacadabdbbbcabaadcadbdbbaaaadcbbdbdacaaaabdadabccaabaaadacabcacbbbbbacaabdbcbaaabcdbdbbddadaacbaabbadddacababccddbccbdaccadaacccacbdcdbcabbbcabddbbbdbcbcdbddbadcadccadddbccbbcadccbcdcdbccadabdadcaababbacbdbabbbabcadcbcccbcdbaddaaadcabcdddcdcdcccbabbbcdababdbabacdddcbbaddcabbdcdcbaaacacdbbcbccbabdccdbdbcdbbacbcdcbbcacbbacccbcbcbaaaaadadbadcccababbdbdbdcaabcaacadddcbcdaabadbcbaacbbaaaddcdcdcaccddcbbdbaddabbcdabdcdbddaccdcacbabacdddddcccdbcbbdcdadacabbabcddbadbacbcdadbabdbcddcddbdaacbaaabdacabdbdbdbdbadabdcabddaaccdbcbabdbaabbcddbcdacbaccbacdbddadbacaaabdadaacabdacbcbcdacacdccacdbacaacdadabbccabdabdbabadaaddbacddcacddcbbbcbdbcaaacacbbaaddcbabdabdabcddbdadcbbdbabbcddadbdaddbbccddadaabcddbbbabbcccbaddddaadcddcabcccdcddccaaacbdbadbdabdacbdaccbcddcbdadbdadbdabdbbdbbbadcdcdbbbacdbaacadbabdcdddccdacbccddbdaabacabdbbbdcadccadcdcacccadcaadbdacbcddaaddbcdbbbacbacdbcbbabcdbdcbaabbddbacdbcdadcddddbbbdacadbdbcbbaaaaccdccbadbbdddbdbbddabdacaacaacccaabcacbcbcaccbbadcbbdbddccbbccadbaccacbdadbbddadbdaccaacdacdaddccbadbddcdbdbacbbdbbddbcabbcbdaaadddbcbdcabdabdaabbcbbacadcddcdcccbadbbccaacbbacdaadddbacdbcbabbccacddbbcbbbadcbcbaabbacddcdcaacdbcdcdbadadcddaaacaabbabdacdbdbcacdddcddccbcddbcccdbcccacaaaddccbddadaadcbccddddbdaaadcdcdcadbbadccddababadbbadbbcabacdbbddcabcdaadacaabdbbaaaaaaaacdaccdbccbccaaaadddadbaaabdcaabdcbcccbbbbdbbadcbadddbcdaaababbbcbadbdacbabdbddddacabbbdbccbcbbdddcabdcdaaacddbbbbabdabaacdacbbabbaaabaddcadcadcacbbaaaccbabccabbadacccbccdaabaacabaccaccbdbdccbdcbcdaacbcacdcbbbacabbadcbbbbababacbcbbcbddccabbbcdccddadabdccdcdabbaabbcccadcbcbcddbacdbdadbacabaabbadaaccaadbdcaaccbccbdacbdccdccadcbaccccccbbdbacbdbcdacacdaabdbccccdcdabdbaabccccbdabddbccdaaacbbbbbacabacabacbacaaccbcdddadcccacbbacadbccacbabcddcacbcadcbddabdddddacdbcadababccbcaaaaaaacddcadcbbadcdcaddccdaabddcadadccadbbdbbbbadacbcdddbbcbbcabdcaccdcdabdcbdbacaaadbddcadaaacbcddbbdccacdcddabccbccadcbbbcababbbbaddbddabaacddcabacbccdcabcaabbcbbacccbccbabddbaacbcccbbdbdabcccbbbdcaddbadababccbcccbbbcdadcbbbccabadddbacccbcbbaaccbbabbaabcbdacbacaddcbdbdbadbacabbadbdaadabbbdddcddacdcddddabaabdacbaadacdbbbcbdcdcbabccbaadbaabccbbccdbcaaacdbdaccbcaabdabaccbbbaaaccccacaabbddbdacadbadddaccdccabacbdadbcbddbabdbbbabcaadbdcdbcddabbcadcdaacdddcccaaabbacbabbabadbacdcbdddcdaacaaaaabcacadacaabcacbaccccabbbbccabcadddcbadddaaddddbbdbcdcaacdcddabcdadcbdbbcbabdabadadbbbaaaaccdddddaaaccacaabbbcadcbdadcdccdbdccddaabddaadccdcabaacbcbbbccddcbabbcbdcbcbdbdcabdacaadabdbdbdacbbbbddddcaccddcbaabbbdddbcdbabbacbaadabaddabaaccacddababcacdbccdbaaaadaabcadcabcbcbaccadccbbcaabdacbbbdbbcdccdddcaddccdcbaadbbbdbdccdaabacbdabacbabddabbdacabbabadbccacacdbbaadbccbcbbaabbadccaddbddbdbbcccdbabcaabcdaaababccccbdbcdbdddccaccaabdbcddcabddbccadddbcdacbcdaadcaaadacccaddcddcacadacbdbccbcbcadbccbcdadcbcbbadcddaabbadbbabcbbdbacdacdbcddabdcdcbaacdacbbbcaccaccddddbcbccdbddadcbcbddbaccdcdcaadcabcaaacccdaabddaabcbbbdaccbccccbbadbbdccaaaabdadddbbdcddaaacbcbcccbabcdbccbadbdbbaccbcbcdabaddbabcbabdbddcaadacabaadaaccdddcdcbdccccdbddbaccdacbbcdcadddcdaccbcacbbbcdaacdbdccccbaddacbbdacdcdabdbddadbacdcccbbccaacdacbbadcabacdbddbdcccadaacbcdadbaaaddddbdacccbcdacbcadbaadacabdadcccaacddcddccabcbbbcacdabbaadcccabcabbdababcddcbdaabbadcbabbbcdbbababdbcbccbaddbccbadbaaaaabbcbacaacabcaacbabaacadcadbdbbadbcaadbcccdbcbdddcbadbcadccdbdaacbacabccaacacbbccabcbdaadcacaccbbdbaacdbcbcddcdccdaddcdbaadcbcaddabbddbbaaadcabdaadbabddbdddcbcaacbccdcacbacdadcaabccaaaababdcddbbbbdcbabaaacdcacdbaaaaaddadaaaddaabbbcdccbadcdabbdabacbabbbaacbaaababdbccabbccbdabbdbdccbdcbdbbdbdcbdcbbddccabdacadbbcbaddbbdcabacadabcabdbaacbbabdccbadcabbdaaadbcbbcacabbcacccdcbbaaccdbaabbdcbbbadbbbaacbbaabdbbadaacbbbcbadabacabcdcbbcbbaadbdaaaadadabaadccadaaabacaacabbbccaddddcccaaabbbdcbcbaaadcdddbbcaccbbacdabaabacbbacacdacdcabacbaadcdbaddbddabdbadcddcaccabccadbccddbbcdbdcbcbaddccdabbbabbbcacbbddacdcacdcbaaabcdcaabbdbacbaabbbbbcacbccccdbdbccdacddcccbadbdcddaccbbaaabacabadcbdddabcdabaacdcbcabbadccaddccbbccddaccdcdaabbdcaaddabbcdbbcdadbcdcdbbabcdacdcaadaccacccbdaccdbbbbaadaabcdcccbcadbcdbdadbcadbbbcddbadbbbddabbddabdbbbdaadbbdcdcbabdaacbbddcaaadcddabbbcbcaabbbddacdbacbbccbaccdcbcbbbbbcaadccaddccaabaacdcadabdddbcabbcaacaccbaddbbccbdcbdbbdcdbbbdcdbdcabbababdcbadbcbcccccbbcacbabcdddbbbdcadadaabbccccbccccdabbdbbaadccdccbcdcbdbcccacdbdbbbbabcdaccabddabdbacdacdbaadabcdcbadaddcbadcbcdbdcdacbadccdddbabbbacddbddaaaadcdaddbdddcdbddcbcbcbaccaadadadacabdbacbdcaddcaccaaadddacbbcdbbadbabbcbaddbbcbaacdcaadaccdcadbcbbbababdaddccdabadcaabcbdbaccbdcabaabadbbbddacacababccbbacacbdbabbaddcabaccbcabcbadbdbdbcbacccaaaadbbbddaacbdaaaddcadaaccbcbdbadcddbacabcbcbdbadbcddbdbcdbaadddcdcbbddcadacadcaabbadaacacbbddcbabbadddccaabadbdbbbabbdbaabbcddbbaccbabadcabbabddcdcdbdbdbdcbabccaabcbbbbabcabddddcdaacbdbdacbadbdbccdbcbddbabdbdacdbaddaaccadcdaccddaaabcacbdbcacabbcdbacddbccaadacdbbbddddabaadcbbcabbbdbdabdcbddabbacdcdccbaabcdbbcdddccbccbdbaacdcabdadbcbadbcdddabaaaadbbbbaaacbadbadbbcbdacabaddabbbadcdbccdcdccdddaadbbdcacdadcccbaaaaadacacadaddddcbbbdabbbbacadbdddcbdcdabdbbbbccbbddccacbbbddaacddabdaababdadbacbcaaadbccddcdaaddacbbbcdabddacabbbabbcbaacdccdcaaacddcbddcbbdcdccdccbacadbaacdbddaaadbadadcdcaacbcdaabbbabdccddccbbacadcbbabcdbabcbaabbabaaccccdaabdccabbdddddadadbadacdabbaadaaadaaddabdbadbbcadcdadbacaaaccdccccbdddbbadbdcadaaccbdcaccbabadcccaadbaacabbdbcbdabddddbadadccdbcacdbcdddabdbbbdcadddadabcbdabaaccdcaacdacadadcbaddbcbdbcbddcbcdbacdcbddbdcacddcacccdacbbbdababdcabaccbbcacadccdcddcbcbadccdbcaaadcaabbdcdbcdcadbaccaadcdbbdddbbbdddbbadcbdadcbdbdbabddaaadcbbbdadcabddddbcaddaababdaadacacbcdcadbdcabaadcbabcaccabccccbbddbaadaaabbdcbadbaddcbabcddaccaaaddbcdcdadbcacbcdcdadcbccddbabddbbbccdddccabbbbbaabcbbaabccccddcbddabadcbcbdbdacadbabcadacadddcbcbcbabcccaaabbcccccbddaddccbabdaaacddbccabcdcdacdaaabbabababcdbccdacaadcbccdaccddacbcbdccabaaadacbcadbdccabdcaabaddcdbdacbbbabdacbaaddcdbbbcdcbcdaaadcdcabadccccdbcaabbbddbcdacacdbdacacbdacbadccababadbdcabbaadbcadbccdcbacaddddcdccdabbadaaccabdbbbcdaadabaaadddcdaccdadcddcbdaddcacccdbdabddbacdadcbdcbccdcadbacacabdabaccbdbcaddbcbbabaacabacacdbbabbcccabcbbddbdabddcbddbccdacbcbcaddcbaadaabdbdadddcbdbaccdaabaccbadccdcbcbadaabcacabdcddaabcbcbadcabbcccabbdbcdbdcbabdadbcddacaabadbccbbbabcbacaccacddbbdbdddaaddbccbddadaacdbbcaaadadcaababcccbcdbadcbdcbcbcdcbccddccbbccccbcdddccabccbddbadaddbbddddddccbcbbcdabddcddddbdadbabcbcddbcadcdcbcddbcaadcaabbcabdcabadabddbdacacbdbbdcabccccdadcdcdddbadbbadaacacdbcbbacddcdbbcaddcbacdcbbbdcaccddaccacadaaacaadccdbdabacbbbbcccbcccbdcdbaabdaaaabaddcbbbcdbbaddcabcbbbdcaabdbcacbbdcbcdccbcbdadbabbabbabaddbdbcdbaccdbddaaaaadbadaacaddcacabdbbdadacccbdaadbbbaabbdbabdadbbaacacbabbaaddbacacdbccbdbddaabddabacccbabaaadbadacddbbabadcacaabbccabcddbdbcccbbdbbbcdccccacdbdbddccbacbdcccddbaaccaaccdadcacbcbdbbabccbcbadbcdaccabcacabcdccbbabaabbbdbdadababadbdcccacdcaccdbbaadbbbabacbacbbabcbadadbaabdbcbdadbabaacbabaadcdcccdbbadcabcabccdbdddadabcdcadbbcaadcccabaadabbddcdadcbddaabbdabdacbbcdddcdcccccdcabbcdcdbabdddacdcbcadbcdbcacdacdcadabdbccabacadbabcbbbbadddabdaadccaaddddaacbdadcabdbbabdacdbadbabdbbdaddbcddaabbdccbcdcaddccabcadcadbdbcdbbbabbabaabcdbacaadccbbbcdacadbdbcdcdbdbbdddbbddcbbaccdaabdcdcdacabbccdabacdadbacdcbbcbdbadcbcbdaccdbddddcddbcbacbbdcbcabbbccbabaddabaadddcbbbdacaacaacbbdbdcbccbacccacbbbdbcbcbdbdccbdccbccccbbbccdaaacbdacdddddaaabcacccdcdcdbdddacdacbcacacddcccbbabdaadacbacdcaadbbbbbdcdcdadccccddcabbbdcaaabccacdadbbacadcbdddbbbccaddddaadcabbdbdabdcddbcdbcbcabbabcccacacbdabaacaadabbdcdccacdcdacdcdadabbbbcaacdadbabadcdaabddbcbcbdbdcdacbccdaaacabaaccbcacbddbdabcbbbaaabababbabaadabcdbcccabccdbbbcaadcdbbacacabaadacaadccaabacbdddcadacbbccbadbbccadcacabadddcddccadaabbabbbadcabdadcbaacaacbbcdbcbbccdbacadddacdccdababadaabbdcaadaabbaabcdcdbbddcacbddcdbbdadbaadacddacaadcccadddaaadcbbaddbaabcaddddddabccdccdabdcccabbdcddddcaaaaaccdbaddbacbddcccdaabdbbbcccccadbdcdddbacddbccdaddbacddcdbbdadccbbcddbbccbbacdadbdababdacaaddcbdacddadacccbabcddcccadacbdccdacabadcdcabcbaddbbacdbdbcdbbbddabdccdbdadbdbcdacaacadaadcdbadddbccbdcadbaadadaaabdbcbadddbdcbaabccbccbaccabcaccacadbdbbddccaabcbabdacaddcdbddddcacccdcbcbacdcdabcdadadcdcdbadddcbadbabaddccbbdbcbaabcdabddcadcdaaadddabcacdcdabcbdccdbbcccaddcdaccbddabcdadadbddbbbcaddddbcacddaddabbbaccacccbadbbaadadabdadcdacbbcabaadabacdaacdbbcaddbccaddbddbbcdbaddcdcacdbcccbaddadadbdddcadacddabacbcdcdbcacabbababdacdabadddcccdcdcadaaaccdbabbaaabbccddcaccdbabaacdcdbdcdccabcbdcddabbdcadbcbccbcbdbddaddabbabaaaccaabaadbbddaacbaabdacaacacbbcdcdcdbacbccdaadabdddbacbaccbdcacdadacdcadcbabadbbbcbcadcddbdcdbdaabadddcdabcbdccadbcbbdaccccbbbcaadbdabdbdbbcbdcdbbdbbdcaddabcdbccdaabdadcbaacababbbaacbabbcddbcacaabacddbcccbbbdcdabadacddbbdbcbaacacddbcdcdadadcccaaddbcccbcdccbdadbccdadbbbcbdbbbbbbcabaabdcccacbdacdacdccccabcccbbcdcaccdadbbbbbadaccaabccabaabdbcaddabbbcbacdbdadbcddbbcbacbaaacaaabcadbbbdcbcbbcbbdabbcdbdbdaaaddadaadbbacbbcdabdddddddbcbdddabdccadbaabaddaaaacccbcaacbdbadbccbbcababaadcabacdaaddcbacddcdbdbcadaccabcdbacccbcbabcbdbdbdabaacbadcaabaabdaccacdbbdabddcbcbdbdbcddcabdabcdbccdabccbacbabdcddabdbbaabbcbadaadbdcbcabadcbcdddcaabcdbddbadccbdbbbbabbcbbcaabbabbcaccdacdcdbaacadbdbcdbabbdbaacaddbbbddaabacdbdddccadbbaccacaabcbabdacaaabdcacddcdadacbcbdbaddadcbdcaadabdccddddadcabbbcdaaadcaaaadddddbdccccbabdabacabbbcbbcbbcbcaaddcbaadbdcbcbcddcacacdbccacccbdabbbaacbcdbbadaaacdccbdbccdadbdbdbccddbdbbbbacdcdbbcaddadbbdacbddadbbbdcdbbdacbdccdbcdaabaccbcadcbcbacdabddbbcdcddcadadabcbbabcccbbbdbcbbdaacbbdbcdacbbbddcacbbcbddbdbdaaaadcaaccddacbbcdbaccacdddccdcbcbaadcddcdddaacccbbbbbacdcdbdcdbddcaccddcaadaabcdaadacbbabbbcccdbaadcabaacbdcbadcbcbbcbcaddddcbddcbbaddacabbbabadbabbbbbbcadcbbababdabbbbbdacbcddbbdacaabdcabbaabaabbcddcabadcbcbacbcbbdcbbbadababbbcdaacbbbcdccdbdaadaabbabccabbdaaaaccdbbcacdbaccbaabdcbcbdcdcbdccbbbcadadccaabddccdaacacadccadaaccadcadbabccacdaddddcbbdbdabbaaaaabbdadcabbadadaabccacaaddadcbacddaccabadbaabaacdadddaccacdcacaabcccbdcdaccabdaaaddcacbbcccbacdcccdbbcbaacbcbadcabcdbccacdcdcdbbbcdadadcddacaccddbdcadcaccdaaadbdaddcaaacbcbdcdddacbcdadababbbbababddbcdaccacbdbdcbcbbadccdbacdccdabdcdccbadcabacdddbaaadaabcbcaabbcabaadddadbbccdacbdcbccdbcbbdadaabcadabdbadcbdbbddadcadccbacdacccdcdacacdbcccdcccdababccbabbdccaacaaccdaccdbbdbbbcaaabbadcbdcdcbabbdccbccbbdbdddbdadbbcbcaccbbbadbcabdbcacaddbccdbcacbbcadabddbaabdbabdbbbcdaccbacacbccdcddbbcdbacdcdaaabbabdbdbcbcacaaadcbdcccddbddadddbcacdddadbacdaaddbcdadbadadadbdaddbbcbadadcabcabcdabdbbccdadcbacacbdbdabdcdcdcccacbcddbadbcbcdbaacdaaaabbcdcbbcaacbbbbcbabacbbbacbdddacbbabdbdbbacddccbaaacdbdbcbcbddcdcadbdbaacdbbadddcbbbdddabdadccbdacdcccabcacdddbcdbcdddcdcaabcadabdcccadadcbdabcabbccdcadbbddddadababbdcdbcabddbccdccadaadaacdbdbccadcaddbdacabacbbadacacabdbdbacabbacdbcbaabaddbaacdadbddccbaaadabcbbdabcdddcbddbbcbabbcbbdaadabcaaddabaadcbcbacabccdbdcbdabbadcaabbcbcbddccbbaaaaccdbdaaadadbbdbcddaabadacccbbcdccdbdcbddcbdddbddddabcddbaadcadacaabacdacbacaacbbbacaccaaabdcbcddcdabcadacdcacbdbbcdabcbccabdddabcbadbdcbbdadcbcdbbbdcbcbdcadbbbcbccbcabdbabcdadcadaaaabdbadccdabcacaaabadbabacaabaddcadabacaabdbdabdaccaaaabdaaaacbbacdbbaaaadcbdccacaabadaccdbddbaadccbaabbaaacabcdcbbdaabdadbdcadaabbaddadcdbaaacbcdbcddcddadcbbaddacddccadaddccdcadacabaacaaadcbbcbdbbcdbbadbbdbbcdaaadbaadcaacccaccaababccabcdbaaadbdccabddaacdcccdacccbcbacaccbaabddbdbcbaaaabdbacddbccbcaddaaacaacabaaccbcdacadaaacdababaabadcbdddbdbacccdcacccbddbaddaadddacdcdabdcbbaaccadbcdccddbdddabdcbbbcdacacdbbbdabdbbbcacbdabccacdcdcaabbbabbaabadcbdaddddbaacddadcdadbbdbcbaadccddcccddabbddbdccddaabaccbbaaddaaacaabcbbbaacabcddacdaaadcdbbcbbaacdbbcbacddbcbbabdcaccddbccddadcdbdcdcddadcaaccbaaacbdccdaadccbdcbaabcbcdaddaaddbcbacbbccbbbbbdcacbbcdccbcbcdbaabaccbcbddcbbcdcbaadcdcbdcacbbbdaddddcadbaddbddaadbaccbdacbbbcdaddcaabaabcdbdbcbabaddddcdbcdabdcdbdbccdcdcdcaccdddccbddaacddabadabbcdadbcccbacbcacccadccaacabdaccaacadacaabdaacdabcddbcbacaddddbadabcbdbdbabaaadadacbbbdbcdbbbacaccaaabababcdcbcbdbbacdacbcabaadcacbbbbabbacbbcdbbadccaadadcaadbaabcbaccabadcdbbbddbcdadaaacddbdcbccdbdabdacacddccadcacdddcabbbbacadcaacdbcbccadabcdacacdddbccaacbcccdcadddbcbcaadddcbcaadbccdabbaacbabdcaaacdaaadcbbadcbabdadaadaccbdcacccdbbbdacacbccabccacdacdbbddcdaacdbdaababcacaabbdabccccdadbbadccadcabcccbabaababcacdaadbacbddacabaacbaabcacdcdaaadddbddbdabbcabbdbddbdaaabddbbabddcbbacadcabbdadccaddacacbddccdccabacbbdadcadaacbbccbdbccacbaddbadaaaaabcdcbacdccabbaabacbcddcacaabccdaacdbaabccacbcbaadabbdbcbddbbaddacbbdcdcaddadbbabdcbababbcdabacadadbddbdbaddcdabccddadaadbbbbdcbcbaadbcacbadcbaadbbdabcdbddbdabbdddbccabbdccdbdbabbcabaadbcddcaaaccdccccadaccacdcbbbacbcbbcbccaaaaabcdddcaabdabaccbbdcdbcdddcbdcbbbbbddabdcbadcdabaabdbbccdabaacbdbccdaccbdcaaddbadbcbadbbaaacbdccbbcccbcddccdccaabbbbadcbdcdddabbaccacdbacacdcbacbbadbccacdadbccdcddcabdcdbdccbcabddddaddbbdacbdbacbbdcbaaddcddadabcbbcccbddcbaaacdbcbadcdbcdbabcdbcbabbddabdddbdcbcbacdcbadbabadcaacaabbbbccadbadaacdaaabbbaacdaabccbcddcadcdcbbcddcccbdbbdabdbdacccdcacdacadcdccaaacccacbcabbccdbacbbbcdbbadddaddcbdcbdccababadcdbaccbdbbdcbddddcacddbaadcbaaaacccdaddaabccbdadbaadbacabcbacddcbadacbdcabacbdcbdbabbaabbabbbbcccabadcadaaadcacdddbbdbaddbbdacacdbdbbcbdcddacbaddccbdbbcddcdabccddcabbadaccbdbcdbcccbadcadcbbcddcbbcaddbdaddbcbcdadcbbacccaddcddbddabbbaabcadaadcacbaabdccccabaaabadbcabaabadacabcaaccacdcdddcbadabbdbbaadcabcbadcdcbbccdadcabcacdabddddabcabcabaaddbaccbddbbdabcbddabbbdaacaddbccdbbacbdbacbddaccabccabdadcddcabdcbbabdccabcbdcabccdadbacccbcaccadcacabbcbadaccbbdaabacdacdddabcbabbaabacdbaddbadcadbacacdcacaaaaabdcdbbcacababadcdadbdddcaadcccabcacdbbdabdadadacdbdcdacadcaaaccddbdcbbcdcdababcdccdcdcaacaaccbdaaadacdccabdadccbbbbabddbcdddbbccccadddcbaccccbdcbdccabcaccabdbdccacbbabcdababdcddbbbddbadcdabaabccbcadaabcccacdcbcbbdcbabadadbbdbdcdacbadddbbacbcdcacadcabdccabbccbcabbcbaacbdddacbcddacaccddaabcdcabdcbabdbccbbaabcbccacaccadcddccbadabababccbdacbdacccddcdccddbccbcddcadbaddccbdccdcbcaaccabcabbccadabbbbdbbbdcbddaccaadbccbbacabadabcdaabbccbddababbdbdaaccccdbbbcaddabcbadcbdbacabddbdaadabcdacabcaabaddabbcdcdddbbdddccccdacbdbacbddacddabacbbadacddcccabbdcaadacddaaababbabdabdccaacdbcdbbbcbbacabcaacccadbaccbccddbcbbcdcdaaaaabbbddcdbacaadbaabaaaadbccbdcbbacbbabbcddacaadcbcbddbdadabcadcbadacbddaaddbdaadaccccbbadbabcbadcaadbaaacdbdcbddbbdadbdcdaacbaaaadbbcbdcdabcdbbcabdaaadccbbacdbdadcdabccadccdacbddacadabbbddacacbcbdccadadaccadcadbbaabdbddcaddacdccdcdbdddcddbdbdccdbcbdaadcdbcdccdcdbccdabdaacaccbabaddccdabccbdaaadbdbcaacdbabadcbbaabdccbdacdaabcdacadbdadddadcddcbbccadcabcadcdcddcbdbcabcbddbbbdbcaacdbbdaddbadcccacbabcdbbccbcadabccadbaadcaddadadccbdcbabcbacdcadcddbaddacbbaabaacdbbacdbbabbdaadabcaacccbcbcbdccdaccbddbbbbcddaaabbcadbcadabbccaaacdcbdcaacaddabcccbdababbadadacdddcaaadcddbcbadabaacddcadcdcccddcdddcdacbcaccabbabcadbaabcccabbacdcbdaccabbbbdabadbcdbcddacacddddabaccdcabdabcabcdddadcbdbdddbabdccdddaccadadabbdcabddcadaaabaaddabcbccbdbdcabbadadcabadcbccbdaaabaabcdabcaddcccdaaadbbadcacdcacccdadbaddadbbaadadddacddaabcbbdcabccdabdcbbbabaaddbdacdbaaabababaacccbdacbbccdbbcdccacabcccbadaaacaccccccdddabadadbcbcddbabddbdddcacacadaacbbaccbaccbcbbdcaacadccabcdadadcdbbdcdbdadcbadbcbbdbdcdbcccaacddcadcccaaadcdcdaddcdbbdcbcdaaaccbbdadacaccadadbacbdaccaadacbbdbcdbccdbdbcbdbabacbcacacaabccadbcbbbdacaaabbbacbaaabaabcdaddbccbbcbbcbabbbdcaaaadaabbccadcdaabbcdbaaccbbcbdcaaabcdbccbdbacbdcaabdaacdcddcbcddddaccbbababbbaadcabacbaaccddbbabcbcbabbacadbaccccdadddcbadbdabacadcbcabdabcccdcabcadbcabbcdadcadcbcadcacbabacdcdddbdbdbacbbdabbdcdaacccbdcacacdaabbddccacccbcbdaddbccddddbcdddaaadcbbdcbbbcbcacbbccdbcccdadacbaabcabbddcdcacbcbcdadbdcaababcababcacbdcccaacabbbcdcadcbbdccdbbdcaabaaacbcbccddcacadabacbbcdaabacbcaddbabbbcdccddbabbaabbdcbcabcbdcabdddbbdcacbbdaccbacbdbbacbcaccbbbcabbbbdbabccbdcbcbcaccdadbdbcbdcdabddcdbdacddbbbbcdcaaddccbdaadcbcbaaccabbbbcbcdcccabdacdbbbbadccbcaaaacbdabcabccadbbbabaabccacdbbcbaddaaaabdcbadadddbbbaaccbbcdcadcdadcddbdcdbdcbdddccdbadccdcbdcbacdcbdbabdbdabcddbcddcadddaccbacdbbdaacccabcdbcaabacbbdabccccadaddccadadcdbbdacbbbdabbddaaccbcdacdaadddaacacccbdbcdddbaaddcccaabbddacbaadccddabacaacddbdadccdccbacbdabcbdbcacbbdbddaaacbcacaccbbdddcaacadbddcacaabcbabbddbccaadabbaccdbcbdacaddbaaccaabacdcbdbddadcdcdbbcdcdbbadbbdaabcbbbdaacbdaddaddddccbcbcdcaabcacdabaadabcdddddbdbdaccbcabbddabcbdaddacccbcacadbdbaccddaccddaaacaaaabcacacdcaacdcdacbdbddbbabddbbaccbdbadcbadbbaddadbbbccdcdaacadacbccdcacddcbbdaacdbbaacbdcacacbbadaacaabadcddcabbababdabdddadaaabccbaabdababdabcccabcdbbaacbbbcabdbabdbbdadbbacdbcdabbaadbcdadcdcccdbcbaabbcdacbdaabdcbaccadbdbadcbccbcdaabcbabddbcdaaacdadccbabbcabacbccddcabcdcaddbbadacdaddbbcbbdbccaddbbaddbabbcababddacacaaddbddacaddbcbbaadacbccdcddcdbbaaabbcacdbcacddccbccbbacccaabcadcadbcdacabdcaddacbdcbdbcdcaddbbbacdabcbddaacbbdddbcbadcaadccbacacadbaadaadaccabccbcbbdcabddcaacaabacaddadabacaccbbaadcdbccdbbbdaccbcbcdaaabdbddcadabdadcddddccbccdddcadddbddddccbdabbbadccdbbbaaaadbbacababdadccacdbbdbbcacabbbddabcaabadbccaddcbdcadaccccbddaadabcadbacadaaadacdccbbcdcbbbcbbdbdccdbbdacccdddcabcddbcaababcbdbbacadccccdaabbcadcacbabaacaaaabcbcbcdcddcdaabdcbabcbdcaddcdabbacccbacabdababbbaaaccdbaddadcbaacadbaaacbaddadbcdcbcaabddadadbaabcaccdacbbacabadacdbbaadbbabcbcdaaabadaddabcdbddccbbccadbbcabbbcbabdccccbadcacadadbacadbdaabcbcabadbdadcaabadbaccccbcbddbbccaacbbcbbacbdbdacacbdacdcccdacbcbbbbdbcbbdabcdcccdadacdcabdbadbacbcbdbdccdcacdcabbbacddaaaccabddacacbdbbccdaddcdbbbdccdcddcdbbcbcbcdccdcbccbbcadbcaaccdabcbdbbcbcabadbbcadacdcdddaadcccaccbababadbacbabbdcbdbddadcdbcabbcdcaaabbabbabdaaadabcdbdbdcddbabddaaabbbcbadadcdbbbdccbddddbadacdcabdbabadcbdcddaccbbbcbdbdbbbccabadcdccbbcbaabbdacabbddbcbddaadcacadaadbcdbbbabcdaaaaccdbbabdddacdcacaaabdabdaaacbaccdbdcadcdbbcdbcdaaadacadabbdadddadaccacbbaccbdccacdacbbaccdcccdacbbbbcbdcdacddabdaddbbdadbaabbbcaccdbbdaaadcbbcccaacdbaddbdbabdacbcdbbcbcacdaabddbcdbdabdbcbdbaacbbabdcadcbcabadcccccbcccadabaaacbccddcacbddbdabadcbaacacbbaabadbabbadbcaccbadaadcaabcadbdccccaaccabcdcaaacbdbcacaadabdadcabababadacacaaddbbbdacacaccbccddacaabaacddcbbdadccbdbbdadcccadbdbbaabaadcbcbcaaadabdacdbdacbcbabdcdbbaadcaabbcdbbaaaaacadcadccacdaacabccddcaccddaabcdcbcdacabdcccddcddabaababadabacddbccdadcabcdbdabbdbdcdbabddbdcbdcaddacdcddbcbdaaaacaabcabdccbcdccddcabcdbcaaadddaccbdaabaddababdcaddddcdccadddddaccdacaabbdbdbdccdcddacdddcbbbbdddacabcdcddcbaaabacdacccabdaccaacccaddbacadaaacabcbacccabcacadabcacaaadcbcaabaddbcaaddacbbbdcdbcdadcbbdcabcbbcdddcdadcacacdddadcdbacdbcbbabcbccdcbadacbcabdcaabbdadbdcacaabcdbaddacadbcabdcdabcababccaaccbbcdadaadddaaccdccdddccdbbdacdbcbcbadccbdbdbdabdbbcddcbbabadbbdccaabaddabbdbdbbbcbccdcddabcaaaddacaabddbbcddbdcbddadbcacdaddbbbdcdadbaddaaccddbacccbbabbacbbdcdccdbaadadddbcadaddddabddcbcbccbcbdadccbacdcdadbcbbccadddcbcdacdbbccbdbacbabdbdabbacabdabadabadadccaaacadbbbabdcaabbadaaddcdddbbbaaccbcccbdddcabbdcccdcddbcdacabdcdaabadbdbdbdaacbbbdbdbcbcdaaccbaddadadbdacadbcdbdacabbbaddcbacdbcbbccacabacaddcacdadbcccdbbbcdaacdcbabaaaadacdccacddaccbdcccbaaaadbdbbbacacdabbbcbbdcacccdbbadcdcdcdadabddccacadcdccbbacdadacbaadabacdccbbdcdddcacbcaaccbdbaaddcddadcddbbbaddcabbabaaddccbdcbdddccdbbdbbddbbabacbcccabbbbabacbcbbccddcdabcaadcdbcdadbbccadccacbbcdddbbbcbcbbcdacbbbacabcbcdbbcbdbccacabaadacababdddaddcbbdabcbddabcbacbcccabcbcdbdadbbcdacbaababbcbcdcadbabdcbbbabadabdaddcdadacaaacacdccacacbbbbbbaaacaacadccbbbcdbabaababbcbdacabcbcbddcdaadaababdaabacaccacbcdadbdbabcadacdabdddbbaaccbcccddbaacdabdcadaabbbcbbaaacabbcdcdadccdacbabacaaccdbdbdcbddcbbcabdbbbdcaccabdcaadabdcacabbadaacccadaadccdbcbacbdcbccdbcdcbaabddaacbcbdcadddbacbbbdbbddcabcaaaaadbacbacdddaabcdbcadcaabcbbcabaacdabdacbaabbdccdcacccbbcdadcdcdbcccabcbbaacdccbbbdcccbcbdbaabacbbbdbadabddccbcababadcccbcdbbaaabadaacbcbadddacaaccabbbabaacbaabdcdadddcbdcbbbaaccdbaadbadcdbdbbbbdaaccdabadaddabcabadcbcbabdbbbadbbccbbcbdbbbdacdbcacbcaabaaadbcaccdcbbcabcaaddbdabdddbcddcadacccdbdccbccabdddabacdbbcbabcbbbccadcdccadcbadcccccbbdabcdaaabdbaacdcdbdbacccbdcdcdabbbbbaaaddcdadcbbcbcdadacaccadcabcadbcbaaddaccbdbddcbddabdcbccabdaaacdababbdbcccbbccbcdbbacccbcddbcccbcbaddbddcbbaddcdbcabbddacaccbabbabddbdabdabdbdacabadcdddbaccbdbccddcdcbddddcabbddaccbcbdabdabdadcaddaddcdccbaadaadbdbcbcacdcbccabcdadadadaddbbdbcccbdcdabcadbbbbccadcdabacbabaddcaabcdadacaaddcacadbcddadbaacdcbdbacbbaadbaacbacdbabacdcdcabaacacadbdaababbcccabacaadbadbbccbbacbbcbacbaccadccdbcacadcaadacbabbddcaababbcdabcadabbacbaacaddcbbcaaddcdbcadbcdabbbcdbaddcabaacacddadcdabbdccbcddaccbbaaccbadaadbbaaacacddadabbcdcdcadabcddaddadbcdcdadbadbbcabbaddabbaabcadbabcbbbcdcbacaadbaabddcdbddbccabadcabadababacbbddbcbcbcccaadcbbbdccdbdacbbbaadbdbdbdbdaacbcaacadabaacabddcadbbccdadbcbbcccdadbadbbaddbdabdabddbbccddcdbbbbbcdbdaabccdcadacbbbdcadddbdaaadcaaabdbcadbabbcbbbccabacdbcbdabcaadddddcdacbbbcadbbdddccdddcadaddacbaaabaaabbadbddddcbbdbbbcdbcbcacdadcaababaaababadcbdcccadccccdbadbddacaacccbcdccbbddacaaddcccbbdccdbdbaaaaddbbdcbcbdbdccdccbadacdcdbcbacbcdbdacdcbdbdbccddacbbdbaadccdbbaddaccadcccadddbcbadbcddbadabdaabcdaaccacdbbdcccbddbccbdacaddacadbcacdbcccbadaaddbbbadccddcbcdcbcdccbaaaaaaddbdddadccacbbdbcddabdacccccdcbcdcdcaabbbcccdbabdcabaaddbddaabccbbbabdcbddccccbdadbbabbbdcdccdccbaacaacbcccbcddbbbddaaabcccddbcadccbacbadbabdcbaacadacadaadddbbbddbdcaaabdcaacccabcddabbaddcdacbdcadabdbdadddaabacabadcddcadabddbaadbdcdddcbcdccdabadcabadcbcbbacbcacbcbdacbbbbccddcacdabbdcbdbcdbbcdabbaaaabdddbbddccbacdaddbbdaadcaaddbcbcdaacaddcdabdbbdcddcccdccbaccbdbdbbccadababbdbdcbdcdcaabcbcdbdabdbcdbccadddcdbcbdcddaacccdbaadbcdcbdddbcdccbacdccabacdddacadcddcabdcdabcbbaaccdcbdcbccdbdcddaaadcabdddacdbcdbcccaadcddcabbcccaaaacbadbbccadbcdcccdbbccbcdacbccddccccbaadbbddccddbacdabaadaabbadbbbccbddadccbcccdbcabdacdabbabacdacdadabcccadaddbcdcdbaadacbacacccadbbbadadbcbdbaaaaacbbbdabbbcdccbcadcdbcbacaccddcdbccaccdcaabacabbabcabcabcaaddcbaaccccbaddaadccaccbaadaadbbbcbcbabdcbccbbcdcccdaccdddcbbbdddbbccbadcddbcbbcccdbcabacdcdbcdbddcaccdcbdadcddaccbdbbddbacacdcbbbcdaaadbcbdcbdaaabcbcccabbbdaabaaccbadaddbcbcbcacccabbcacaccdddbddabbbdacccbabcbcbdcaccddaddabdacbddbbcdcabccbcbbdbbcccbabbbaddccbdcbbcccdcadabdaaadccbcacbabcabbccccaaaacdbacdadaaaaddbdccddabbaaabddaabaabccbadbaadaacacbcccaaddaaacdcdbacabadadbcacccaabbaaabccdccccddbaabdbccccdccbccbadddacadbbabcbcadaddcbdbdadddbdcdaabdcaabacccacccdbcadbbaadcbbccaddcbcabaaaaabcbbbbbaacaabdbbddcacdcbcbcbcdabbbdddcbadacabdcccadcabccacdccbdbdadbcbdcdbbababcdacbaddddcdbcacabababdaababbdcbabbacaadaacbcabbbbdbddaddcbbbadcabccdbccddaddaadbaaacabbcdcdacabccbbdbcdbccaaaddccdbbcbabdbcdacccbdddcaabbdcbbaabbcabdcbccccadbbabadacbcbcadadbabcdcdbcbbbabdcddaacdcaaddcdcbaaadababddbcdcadbadadccbdbaaaaaddcdccaabdabdadacddbcdcdcaadaccbdccacbddbbbdcabdccbabcbacbbbacccdcbabbbdddbbbddddbadaddacacbaadbcbcaabddcbbdcddccbbabbadbcadccbcddaddbaccbdddbbcbdadbbdcdababccbdccdbdbbccddaabaacabbabadbdacbcbaccbcadcbcbcbabbcacaddcdddcdbbddbddcbacdabdacdbbcddcbdddabbccbabdcaabcdacbacdadcdabaadbdbdabdacaabdcdbaacdbacacdcdadacaacaadbdcacabddccdcbababcddabacacaaacdccbdccaacccadabccadbcaddbbddcadacddcbdbdbdacbccaacdcacbadbcdcdaaadcaadbdbcccbccddacacdbccdddcbdabddabcaddaccbcbdcbacacddcbdbdaaababcdabccbadddcaaaddbbaacadabcacbddbdbaadaacadcacbbccabcabcdcbdbadbcddcabbcddbcdbccbccdbbadcabcdbdaabbabcaccddbbbcbbdcdabbaddcaddcddddaaabccbabcaddcabcdaaadddddabadcaccdddadcaacddbbcbabbabdcabbabacabdabdccccaaccaacdacbdcdddabcbbbacabdacddadbabcbcddccdbcdaabcbcaabdcddabcdbcbbdabcababbabaacbcbaacadbcddccdbbcadadddaaabcbdddaccadcaaaadbcbaabcadbbcdbabbdcabcdccaccabaaabbbcaaacbcdbadaabcbccbacccabbacdbbabccbcdddcddabaadabbbcaddcbaabbacdcdaadcbcddbccbcadcccaacdbabaaacdcddbcddddacbbbddbaaadaaabdbbabdcbabccddcabadaccdabcbdccbdbbccbcbcaccbddccbdaadaabbcabadbdaccdacbabbdbbccadbcdaabcddbdcadcbcdbacbbabdaadcaacbdbccbdababbdacbbdcbcbdabcbdcacabdcabaaaabdaadcaababbbbaaacdacbdacacacbcccdbbcabbdaacddadacccbbdbdbabbddbacdccaaddbddadbbddcdbaccdadacadcbbccbddabbbdccaadbddadaddacdbddbabdaaabcaccaddbcbadccbcbabbbabcabcdbbadbacdcdcbcaaacbbbabcdccbdbdccbdbadaabddcaddabdacdccaddcccacbaddbccaadcabdbdbdbaaddaacbcbcbdadaddcaacadbcaddbbccbdbbcabdbdadaaaddccdcccccbbcabdccaacbaadcdcbbcccacdaacaacbcbcdcbdddbbbccbdacdcacdcdadbbbcbddbaadabccaadbadcdaaccaddcaccddabbcaadacabcbbabcbacabbcdbdbacccbacddacccdddcacacabaaadcabaddacdaddbcbbddcddaccddbbcaddbdcbacacbbdcaddaaadbccddddaaddacccbcbdcbabbaaddcdbacaaacbabbccacdbccdaabbaaddccbdacaddddcbdcadabcdbaacdbcddcabdcdadbadacddaddbacbdabccdcbbccbababdbcbadabcbbbccdacdccdaddcbacacadabbccdcdbaabadbaddddadccbaddcddcbdaddcdbcdacdacdccbadbdadcbddabcbbbbcbabdabccddabbbabccdccbcbdacdddabcabccbccdbcdcaaacddaaacdcbcbddaddcdadcacbcadcbdccccdbacccdcdddbdababcdbddbbdcbabdaccdddaaacdcbdadcbbdbbccccbdcddddabcaabbccdbdbbbbcabacdcddaccccdcadabcdabcddaccbdccbdbbdbcbbcbaabbddbaabcbdbbddbbddbabaabcbbdabaddbcadabdabcbcbbdccdaacdacbaacacbbdbadaadabccadbcdaabcacacbdbbaacabaddbbddcbacbdcacaacbcaadbacbbaaacbdddabcdbcadccbddbddbddcaadbcaccadabcccaccadacdadacdacddadccaccbaaddddcbdcccbaadbdabbddadcbbdaaacbddaccababddadcddbbccdadbcbaadccdaabadcabcbcabadcacdddcdddcadadcbddbdcbddccaaabbcdccacacbacaddabcabcbbbbaacccbadadbddbbdcbacabddcbcaadcbbbcdacbdbdbadcacdbadcadaaabadbbbbbcbbabbadcbbaccabcddbcdcbddcbadbbcbbbbcbabdbcacacabaabdbccadbbdcbbaadddccadccbbcbdcdcdadabadbadabbbabaabcddabbdcbcddadcdbdaabbdcadacacdcbacbcdbbbadcbdcccbccdbbbccbbddcadcbbdaccacdaadccabacdacbacdddddacaaaababbdcdcdbabdaccbbbddaaccdbaacdbabacbbcbbaccbcdaabddacbdcacadaacacdbadaadcddaccaaddddbdbcbcbabccddbbdbadbbccbcdbccdbdcabacabaabbbcbacdcbdcdcdbbbaaabdbbdbabdbbbaacdbaadbdbcbcbacdabcdaccbcaabbaadacbcddbcadadcbdaabdaaadadbbdbbdcaccbddbaccccdcabaaddbdbbdddcdccdadaaaccccadabdabbcdbbdccacddacdccccbcdcbdacbccdbcccabbbbbcccccadaddcabbbcbacdcbcdadcdcbdddcbadaddbcdbcacaaadaccddabaaaddaddbdcddaaaacabddabdcddbadbdaccbabadcccaccadccdcdaaabbacddcbbbbabdabaccdbdcabddadabaccdadabcadcaaccabccbcccaacdbacbbddadbacacccccbddadccadddbdadcbbdcbddbdccacdcdacbabdbbdaaccabbddcbbaaacddcbddbaccddadcbcdbbbbdcccaaabcaccddbdcdadccdbddaababcadaadbadacbaaccacdbdaacddbbcbadcdaacbbacdbbacbbbbdbdddaabbddbbcababcaaadbbcadbacccbdbaabacccbdcddcaacbbbcabadbdcacdadcdabacdbacbddacaadcdacaccabccddbaaddbcadadbaccddadbadccbacbbdddccadcddddbadbaadadcadaacdbacdadbaaabdcbbcdcdbdcdabbcadccacbadccaccbcccbadddccabcbaccadbcdddadacdaacdbaabbdcdadbadbadccdcbabbdcccdacbbbcdbaccddcaabcddbacadadbdcaacaadbccabbdabbadadcccccabbaadcbdbdabdcbadbdbbdcbadababbbccdcdccbddbbabaaacaaabccdbccbdbcadcadccbacdbdacdddbdcbbcccadccabacdbacaadbbdbdccdddbdcaddcbacdcdbacaddaadadadbaccdadcdcddbccbdbaabcbdbaaccbccbcbabdcaccbbcacddbddcadaadcbadaadbbcabcccaabcacccbabdbcdaacabaaddcbddddcacaaababaddacabcaadbbdbdcdbcababdbbbabadacacdcbaabdabdadbddbdcccdaadadcababdbccbdcdbdbbbaacbdadacabbacabdbccbcdbabbccaacaaaccaaacdcbabbcbbcbcaabdbbdbdcdcdacccacdcddcaadbbabbbcdccaabcbbdbbdccdbdddbbbadbcdcbddaddabacabdbccabbbdccacbcdcadaadbaccbcaadbbdaadbdcbcaaccdcaaabbdccddbcccccbaababddabdbdbdacadbcbdadcccdaabdbcabbccdacbbcbbbabddaabbdbdccbbbcacdaddbdcbdaccbdccbbcbaaaabccbddbbabaabcddddaccaccccacbbbaadcdddbcdccbcdbadccbdccdddbaaacaddacdacaaacdbbdaaddaaddbacacdcddbababbcdbddbbdcadbddccabacdbdcaddcddadbbacbabbbddacddccdbabdbdabddabadcccbcabaaaabbdadcabcdbccdbbccccbadbbabbcbabdaddacdaccaadadadcdabbccdadbdaddaacbbcdcdcabbdddcdcdbbccaaacbcdadadabcaaddddadacbbccdadabcdaccadababdcbcdcbcacaacbdaaccabacdcaccaaabaabbddabcacbcddbbcdabbccbbdbdbcddbbccbdbdbdacadcccabddbacdabaadbcdcdccacbbdacbdadcdaabbcadbacbddabbbdacaacdbabbaaddcabcbcadadbcabccadcbadabcadcbdddabdadcddacddacdccacaaddbcbacddbaacbabbbddcaccaaaabcbdbcabadbcabcbaacaccbabdabbccabbdcdcccdcccdcdbcdbbacbccbcbddbbdcdcbbbbcabbddbbdccddcbcacdacbdacdadcbdadccadaadbacbddadbbabdcdbdadbdbdababcdaadbcbadcdaccdbdaddacbdcbcdacbadddbabcbdbdbbcddbddbbdaddbacabbcaaccadcadbcdacbadbaadacdbdbabbbadaccaaaabbbbbaaadcacbcccacdaadbbccdbaacdaaacbcdbababdcdbcdcaabbcddbadaccaacbadabbdbaaccbacbcadadbbbdcaacbaadacddccddbdbccbdddacddbababaaacadbaddacccaccdbdddbdcadadbadccacdcccbabdabbdbacdbaadcccccdadacddbdaddbdaccaaccbdaadadabdcccbddbcabbcdbbcbabbcacbaacdbdbbdaacccccddccdcbccbaabacbcdbbcadabacadacdbcdcccacabdbcbdddababdbdbbdaabbccbacdcbdcdcbbabdadbdbccbacdccadcadadadacbcbcdcbcabbcdcdaadcadcadbaadcdbdaacbabbbddbdcbcbcabaaadbacbcccbcabcabbaadbdcbccabdcaccdbddacdcdbaccaccccdcbdbdaddbccadaaadadddacdbbacdddddacadcbcabdaaddbdccccddacaaaccbbbbacdddcbcadbcbbcccadbdbcddcadadaababdbddddabbcdabaacaaadcdaaaddbaddadbdabaaddcdbddaabaabbaccadcbacbdbccbcccdbacbcdaadaaabdadbacbababddcdaaabbbddbbbdddccddbaacbbbbdcccabdabbabcbccddcccabcabdcdcadabbaaabbcbcdabadcadaacadcabdbcadabcbbdbbddabbdbcbabbcbaaabbdacdabdcbddccbbcaddcdcbbacabddaccbbaadaacacdaddddbcccbdadcccdcbdbacbabbbbbbcaabcdbaadbdcabcbdaccbbbbdcadccbdaaccdacdbacbbdbabbacddcaccacbbddbddcadcccdacdadbccdaccaadcbcdacadaddabacbcabacdaacadaacddaabbbabbcbdccddbccdcaddccbdcbbbccdbadabdbcbcdbcbacabacabddbcaadddccdcccddacbdbbcacadcbcaabababadbcabdbbcdadcdbaccbadcdadddcadbcaadbdcdbdadadcababbdbabbcabdcdbadddbccabccbaadbbabadacdcaadaabbdbbdcaabcacdbcdadcadbcaaadaadcabdbdabdbcaadcadaccdabcccddcbabcbabaadadbdabcdcdbabdbdbbabadddbdbccacacadbcccabcccacaabbabdccbbbcbdaccbdccdaccccdcbdacddcbaddcaddbabddbaaacccaaccdcbdcabbccabbadddcddacdcdaaaddbdadadbcaddcadcacbcdccdaccababccadacdbccdbbaaddddcbabacaccdcbbdbaabadccdaacbaaabbbabcbbadbcdcacaabcbccaabcadabbdcdaabccbbbbabbccddccadcbcbdcaccacbddcdcaacdbcbcdddddbdbdabdbadcadcbbabccbcdbbaacbddaacdbcdbcbdabbabaadbaadabadabadacaccbcacaddadcbbdbaacadcddbbdbcabddabcabdbdbcdcbbbdccdadbabccccaaddcccbbcbbbddbdbaacddcbdbacbbadbcacbaaacddbbbbbaabacaadacddabaccacbabaddacbdcabcdbadcdbcccabddbdbbbbdbddabaaccaababcdacaacbcccbbdaaddbcabcbabdbbbdacaddbbabdcaacdcdacdabaaadcabbddabdaddbbcacdddcccadbcdacbbccdccadcbbbaddbaacdbddcaadabacdadddbdaadcdccaacbbddbdacdbbbaaccdbaaccdaadadbaddaacaacddbaacbbadbbcdddcdaacacdbdcaadddacdcddbbcdbbacbdbcddadabcdcabccbcacddbcbddabdaddddcaddaccbbcbcbbcbdbcdddaacdddcccadabbdcdbaccaaabccdbddcbccacbbbdddacdabadcabaccddaccbaddcdabbacdcaacbddbbcbbdcabdcbccbdbcbcbcadcdbddbbacddaaaaaddbabdbccaddbcdcabaadbaabaabdcabcddaddcaddaabaaddbccacdaccbadaacbddbabddadbcdcaaaddaaabbddbaadbcdaadaadcbadbaadaaabaabbcdbbadcdcdaddcadbbdadcbcacaaacaabacacccacadcbcdcabbdaababdaabcabccccddbbccbbdadabddcbbbcaddcdbccadadbbbabcccadadcdcddacbdcccbdbdbdbdbbcaadcdccdddbaadcaccbaadbcddcbbbbdcbdbbbbdaccabbcaadacbaabdaabcddbdcdadcdccaadbbcccaaaccbcabacbcacbdcbadddcbbbcdbcdacabaddcadabcbaabadbcccdaababdddcdccaaddbabdcdcabcbadbcabdaabbbabbbbaccabdccbbbcdcdcacbabacadddadadacdaacabacbbcbccabaabddbbabdbacabcdaabcddddcadddcaaadabadcbccaaabdcabdbaacabbcccddbcabdbdadaadaaddadcbccddcbacabaabacddbbccdbcbaccaacaabccbcaddbbaabaacdadcabbbcccbcbabbbadbababdcdcadccacbbbddcaacadcbdcadbadbbaadadcccbbcccdcbbbbaccdcabcaadabaababcdbcbbbdbabaccbbcadaaacaabdbadcabaabbbaadccdcbccabccbdccbadcbbdcbabcacadbcadaccabbddcdaccdbbbbdbbcaaabadaadbbdabdcaabaabbacbcdabdbbbaaadabcdaabbdccddcdcdcaadbddcbaccbbbddbaabbaabcdbcdaccdccdabaaddbdadcacdbccdbadbdbcdabdcadbdbadcbdabcadcadbaaaddcdbbbbbdcdddccccdbbcccbdbaabcbddadbaacccabaaacbbbccbbaccaabbacaacdacbbcdbcabadbcddaabbbacdabcdcabcccbbaaddcbadcacbbcdcacbbbddbbabdadddddcddbbdaaabcbadbacbdacccddbcaacccbddacdaaddabaabaddabcbcaacadaabbcbccadbdbcdddbdcaaaccdcccddbbcacbccbbbcbabbaaabccabbcdcccabdccbddcdbacadccdaabcdcdabddbbbdccbbdcbddccbcbcdadccbdacabaabdcaacaddaddcbdbcbcabdddccadaacbdcdcaabddddddcdaabccbbbdbccaabddabbbcaddddcadaaacbdcaddcadccddcbaaabcbaacadbabbbabaddbadaaadacabcaacbbcbdabacbbadacacbccbcbbbababacabbcdacbddaacadabbcdabcddadbaddaadbabdacacbbbccaccdcadbddbbbbcaddbdddbcdbbdccbddbccccccbabdbbcdcabccddaaddccbabcdddbdccabbabcddcdbbaadbdbbbbdbababbbabcdacdbcbbcbdbadbabdbcdbcddabbbadcdaabcabdabdadbabbadcddbabcbabaabdadcbbbacdbbbaaddadbcaddcbdcadabaddbccaadddcadacdabcabbcbdcbcbbbcdbadbdcdbcadaddaaaacbcdcbbcbcaacadbcaadbcdddbaadbdcaaaabbdcbddddacccadaccbbdabcbadcaaabcbdddaacccaccacbbdabadbabaabddaabcdadabddabdbadcabcccaaccadbcbacaccdaccddbdbdaacabdcccbdadbddcbadcbddcaddbddcdbcacbdcabddcabbdaaaaabacadaacacaddcbcbaddaccbaadcaacdbddcbbaabddbabdabadadcdbcdcbadadbabbbcabcdcbdcbabccbcacbbabbbcbddddbbdcadbcadbcbbbdddacdabcdadbcbddabddaaaddccdbaaadddbccdaaccbdbacadbccbaacddbbaddadadbcbacbabcadccdcdacdddabbdcccddcdcbdbadcacddbdcacbdcdcabddbaacbcabbacbacabaaddddabcaaccaadcbdaccaddbddbdbdbddacdddbcccbdddbcdaaccbdababdabbcbdaddcacccbbaacbacbdaabdbaacbadcabcadaabccdcacabddabccbaaabcacdaddccccdbbbcccbccabbadacaabbbdbddcdbccbbbaabbbcaccbcdbdcdacbbcbbbdbdddbccadbaccacdccadcccbdbddcbaccccacbbddbacbacabccdccbcacbdbcbdccdcdcbdbbbcddaadbbbcaaadcabbacdaddadaaaaacaddadaccdcababdabbcbccbdabdccddaabbbbcbdcaadcdadbcbcbacccccdcaabbdcdadacdbcdcaaabbbabcaccadbbcabbbbddaabbabacabcddccbdbabcdbcdddbcdbdbbbaabababcabdaacdddacdcccdbcddbcadbbddbddaccbbbcbdbaabcacdacaabccdabcacdbccdddaccdbddbdabcacddababddcbdaaaaacddcbddbadcdaaaaaaabbdadbddccddbdadadddcbdaadabccdabdababdbccdcaabbaacbcdbcaccadacabbccbcbdbdbacabbdbabadbbcadbdcaccbbbdbacddcbbdadcbbaddbdbbabbdcdaaddbacaabaaccdadcddbaaddadaaaaabaaccbaabbddcdcbdbddcababccdcbaccdcbdcacccacbdcdadaabcddbbabcdcdbcbacdddbcacdbcbcbdadbacbdcabdcbccaccaddddadabddcacdcbcdddcbbabaacbcaddabacbddcaadacabdabdbdadddcccdaddabdaabcdbcdddababacadccabbabadbaaacaabbababbdacaabdbbdcdcabaaadbaabaccbaaabdcbaabdaddcbadccdcdbaadaacbdcabbbadcadbdcdbcdddabbaccdddcdaadcbcdcdccacbbadccbcccacdcaadaddddddadbdaabccbdddabcccbcccbdaaccdaadbaccddbcabccbaacabddadddbcbcdcacabcbdabbbbaabbdcadbcaadcbcdaadcddbddcdbddaacaddcaacbaaabdbadddbababddcdbdcdcbbaadaccabbbcdbdabdcddddaabbccccaaddaccbcccaadbcabbbdddcbcdbcbccadcdbbacddbcddadbaadaabbdbdcccbdddbbbbdbbcacddacdaadccbadbdadbbbaabbcdadcdcdbacdbaadbadadddaaaddcacacbaabddabcaabbaabbcddbdacabaaadbaddccbadadbdacbcdcbdabbdccbdabccabcdbcccbbaccaabccdccaaddddbacadcaabcdcacbccabcccacdbcaadaacdcdadbadbdaaacbdccdbdccdbdadccacbddbdcadacaadaacccacdbadbdbbaddabddcabbcbacdcacddcabacdbabdcbcdbbddacbbbcccbadcbcdbcbdddabbcdbadaadbaaadaabaaaabbaddcadbcdcddacdcbdcabaabcabadcddcbbcacaccaadbcdbcabdaadbdbdababdcdcdcaddccdbbbcbcbcbadbbaacadbddacccbcbdbacccdaabadacbdbbcdabdcccbcaaaccbdabbaadadddbcccbcbdcdcadcabddadaadaabcaccbacbccdddaadbdddbddbcbaaacacbcccacadcbbaacbacbbbcbcbbdabcdccbcdccccabadbaccdbadcbdcbaddbaabdccdadadddbbdcddbacdbbddbbbcaaddaccddbabdbbabaddaaacbaaaadcaaabbbddddacddbaadbaacacaadcabdcadcdbdddabbbddbdadadcdbcdaccaaadcdabbdadbdbcaaacadaaacadbbdccaabdcbaabaccdacbacbabcdaacccabbbbabccbbcdbdbacacdadcbcdabdaacbdbbdcadabbacbbabcbddcbccbaadcdddaabbdbccddcbcaaaaaccbcdccaabbcbbddbaacabccaccdcbdacdbbbdadcbacadadaadcacbacdacdbbddbabccdbddbbacbdacacddcbcccbababcbcacdcdcacdbbbcbccbbcaaadbcdaabdcacaabdabaccbadcbdbcadccddccaddbcadcaddcbdacbbccbccdbccbaacaadcbddccabbbaccabbcccddbcddddabdadbddaabdcabaddabbaaddbadcbaccadcacabdcdccacbcaadcdbdddbbbbadabcbdcbccdcdaaadabcdcadaccddccbbcabccbdbdacacdddaaddadddbdbbabdaabbcaaaacbddabddddccdbcabcdcbaabcbbdcbccabcccdcaabdbcdbbbaabbdaaccaccdbacadbcccbbaccbbabcaaadddadcadbdabbdaabbdbbddadbabaddddabbddbadccbaaccdcdbadabddcadcbbbadcdabdddcaadabdbadbbcabcbccbbaacbbcccaacaccabacdbbcdcdccbdbccdadbacacbbdcdcbcddccaabcccbcbdbaabddaabddcbaaddacdcbaacbdcaaadcaaddcacbdddbacacaccccaaaadbdbadbcbabadcbdbbddadadbcbcbbccbbbaadabcbbadcdddbdacdcdcacacbbddaadcbcddcdcbaccacdbccbcbadacdaaadaacbcdbcdcadcdcaabbbcddcdcacddddcdaabbcccbabcdadbbcddadaaaccbabbbcacaaadbacbddddccdabdadadcabbdcbadbdadabbdddcbcdbaddbbbdadbccbaabbcbdbccbdadbbbddbaacbcbdaddabaaaadbccbdddabddaabdcbabddbcacbcaddabaacbdcacdccbcadaacaabdbbbbaaacaaaadcadbbbdcbdcabdcbcaddbaccbcbccbacaadbccbaddaccdabbaddadbdaadcdddacaddbbdccadbbcdcccbbcaccbabbcbaaddabcdadccbdbdcacccdccbacdbaaccbdbadbaaccbdbddadcaabddadbcdccdddaccadbbddccbacbbccabccdcdabcdabdcdbcdddbdacdaccbabdbbadcdacbdacdabcaabbbddcacaccaaacdbadbaacbbacacadcbddadbbaaabdddaccccbcaaabbdbcbdbccadaccacbbdaaadcdbabbbdcdccdaccbcaabbbddcdbabdaddaccbcaaadacdcddddbcddaccacadcbbbcbcdbbcacdcabcbaddabdaccdddbdabcdababdabbacddbbadccbdcabccdcdbaaccccbcddabaccadbaaaacbcbbacbbcbaacbcbccacddcdacbbcacddbaadbdcccbbbacabdcdcaccacabcbddaccbcbcbdcaccbdccaabbaccabdbbacacbbaddacdacdadababbaacacbddcbcabbbaccbbacadddcadbaccadaadbbbdbabbacdaaddaadbbcaaaacadaadadaccdbdcacabaabbcbcacadcbcadcabdccaabcadbcbaccccdbcccbacbcbcadaaccdaabbdcdcaacbbacbbdcabbaaabcadacacddbbabbbacdcddbdddacaacdacbabcbaaddadcabdabdddadbdcbdcddcbbabdadbaacbadbdcadbddadbdabdbbbcaaababbacdbbabadcdbbdacdccdbadadcccaccdabaccdddacaccbcbdcbaaccaccabadabdccccdaddabbadcbcdccbabacbadcaababbdabaccdcbbadbcacddbaadddddaccabcadabbccdaabccaccdbbcddcaccdcccaabcccddddbcbcaccddccdbdddacaabaadddddccbabcdbbccdbabbabcadacadccccccaacddacbbabacdaaddcaccaabbccbadadbcdddadadcbadccaccbddcaccbdcaacacbcddbddaddadccddbbadbcabdcbaacbacdbddbccbadbcbbadbcadbcdbcbcbbadcbccaaccaacbcaabbacacbccabcaacdaccabcdabcdbdddaacaccdcaadbbbccddbdbacbbcaddbabbbdbabdbbbbcadbccbdabdcccbbbdddadadbadcadcbaabbaabaabbbbbcdcbaccdaaaccacaadcbabddbbcddbbbdcaddaaabaddccbddabcddcabbcbadaacdabadaacdddbbbabcadbcbaaacddacbcbbdddcbbabdcbbdddaadaadddccacaaacabaccaaccdabbbccdccdbbccdaccbbcbabdbabaaadadddddababdcbcddbddddbcdddacdcadddaaabaaaadbcddbdacccdcbccdacdbdcbbaabadababdddccbdacaccadadddcdcbaccbaacccabddacaaddcabcaddbdabdcadbddbbdacdbdacbccabaccdabccddaacbcbaadaacbabcabdcbdcadadbbcdadbaccbaccdbbacaaccabbdbdccdbbaacdddcccdbddcaddcaacbaadbcabbadbcdbacdadcdbdddadbdbccbbadddbcdbacaadddcdcacdccbcabbaacdcbddcbaadcbccacadbcdadadbbdaaccbdabadbacdbabdddcaccbdddbcadbaccdacdaaddccdccbadcbdbddbacbddbcccdcdcbaaaddadaaddabcdaadbccdaadddccbdccbadbdadacccacaabbaabbabbcdbddadabdaadccdbacdaabacbaddddddacddbacbbcddddcdabdbadbacdcdcadbcccdcbbcdaacacdcbcddaababddbcadaacdcacdcabbcbdcdaacadbccabacbdbdccabccbacccdbbcbddcdadddaaccbcbcaabdbaabcaaddbbdacddcbaababdcdbbdbddaddcdcaacdbdbbcddcabccaabaadbbcbcdccccccbadadbcadcabdbdacbccdcacbbbddbbbaaccaaabdcdccaadcdbcdcaadaaacddadaaaaddcbbabacaaabbacbcbddabccaddbbbaacdcccccadabdbdcbcadacacccaaacbabcdabcacbabcbcdbdadcabacbdcabcabacdbbcbaacbbbdbccdcacddbbbdbbacddcccbcbcbbccadccccdcbcdaaddaadbbbacabcaddaabbacdccbbbbcbddbdcddcdcdacbcaacbcacbddbacdaacadacabaccabdbaaddbaccabdadbdbcbcbdcbbacacdcdadadbcaacbbacbbdcacbaacabdaadcadcbcdaccbcacdddcdacdcbdaddbaadadddbacddcdcccbbabccdbbcdcddcdcabdacbcdcaddbaacdacdaacccccccabadbdaddddabccbadadbcadaadabcbcddbaccadabacccabadbdbabcbddbbadadcacdcbaacbadcccbddbccbdcdacbcabccbdbddcccadbaaadabcdcbbdcdcacaccacbbacabacacbccacdcdcaccbcbabccbaabcbabddadbbacccdacababdaadcdabcbbdbbbaccdbaadacddbcbcaaaadacdbdccabbddbaadbbccdabbbbbadaddcacccacdcaccbdacbbabadaabacdccccbcbdddabdbdaaacbaaadbaddcccbbdbaacbabddccbbdbcdbdabaadddadbabccadddaacddbcddaccaddbdcbbacbdabbbbbdaacadbbcbacdbdcbcdcdababcaddaabcadbbdbbcdbdbaadcdacddccccacccbaaaaaabbcccacaddaadabdcacaadddddacbaacaccbcdaacbdbbcdbbcdcdaadcabaababcbcccbbbdcdabdaadcbbcdcaadabdbcacbaabbbacdccdbbaccacadbbddcddbcccdaaaaaddadbcdcbabdbcabbbbdcbdabdddbbccdbacccddcaadbbaaacdcddabbccdccdadadcdabadacaddccbacaddbadbbbabccbdaacbabbddcbabccabaadcabaaadadadbcccabbbbbdcdcabcdccbacacccbabcabbbbdcdcdbccdddadabdcccadcddbadcdaccadbbbbdacacbabdbaaabaddcdbacdbccaacabbdacaadcadcbaabbdacacddaadbcbcdddddabdcdbadcadbcaaaaccbddcbaabcbbabaacdccbbbbbdaaddcabdcadcdbaabcbcccdcacbccbdaddbbddcbdaaacccdaccddadbdacbabdaccdbbcdadcbcacdcbbbddbdccbcaddbbaadaadbaddbabaddacbdcddabccdcadbcdacdaaddacdadababdaacabdcbbdddccdcbdddaabccbcacdbdbbdccdcadadabacccaadacadacadaaacadadacbabbbccaabbdbcbaacbadcbdacdacbdcdcdbcdbdddabaddadbaaacbbaabcaaddaddadaccbddbbaacaabdcbbccdbcddcabdcbccbabbbaddbadabdbadaddcadbbbdbcaadbcdbdcddcbccccdbbdaccaadbcbacaabacaccabdcdbdcbdabccdaccddbbbbbbadcccabbcdaaddcaaababdabaddadcbccaadcdabbddadadcacadbdbddccbbdbbcbbababdcbdbaadbcbcccbacdbaddcbababaadbadccbacbcdbddaaabdddacdbcbbcadccdddbcabbbdadcbaddccddcbcbbbadcbbaccacdbbdcadbdbdbbbdbcdcaadcadbbacbbcdaaabaccadabbaccccdcdcaadaabcbcbdbbddcbdcddabcdbbbccabbdbbcdbddbadbccdacbcacaadabdadcacbdabbbbacadddaccacadabbbcaccbdbbccabdacdbdaabadaaccbaabcddbcaaacacbaabbbbdbccbbaccbddddcabbdabacbdddcdaabdbabbadddbabddcbccdbcddbdccbdcaaabbbbdadccdbbbacaabdacabcddddaabbdccdaabdaacabbbbdaaacbcdbdbccabcbabcbdcdadaacbdbdcbbcadabadddaacdbacdddbcccdadadabcbdaacbaabddaabaabdbcadcdddccacbbbccabbaabcdcadbaadcabdcccabbcdbdcacbbcdcddbbbdbadbadacbdcdcdccabbcbaadbdcdbcddbdcbdcbddbbdcaabcabaaabdadadaddbbbabaaabddcbdbacbaaccabcdabacaabbdbbabcabcacbbcccaacdcbdacdcdbcdcaccdcdbaabbcacaddabddaddaadcbdbddaccbaacdcacdacbcaddacdbabbcdddacddcbdbdcbccadcacacabadadbddcaccddbbbbcbccdcdcaaaadcdacdcaabcdabdcadacdbccacddbadcdcaccdaaabdbbcbdcbbabcacbdcbcabddcbdcbcbcdbabbcbbcccadbbbabdaacccaaaabdcbadaccadcdacbbbdddaccccabccdaabbacdcbdadbbcbdcabcadccdaacababcacbdcbbaaabaccdaddaddbdbcdabadbdbadbacadaacaddacdddddaacadbccbabdabbbdadcacdccdccdddadddbcdcbbbcabcbbaabaadcddddacacadbcbaacdbbbbccabdaccbabbcdbddccadbcdaaadbcaaddbbaabdadadcccbdabdadacbdabaabdaaaddcbcadbacdcddbaddbccadbaccccbdccabbcccccaadbbacdadadcabbabaacbccddccaabdabccbdccccbaacbadadcdaccdccddabcddadcbbcdcdadbacabcdcddcbbdcbccccdbcacacacccdcbbcdcdbaababcddcadabcbbcccdbcbababcbacadacabbdacccdaabcaaddcdcbbcbaacdcbdadcddddabbdadbddbadbacacabbbdadbdbadddaddaaddcacbcccdbbaaabdcaacdacccaabdcddcabdccdccccbcbdcbaabdcddbabddbcddbbcadcacdbaaaabdcdddbbbbacbdbcdbcabcaccddabdaccdddabcdccadaddababcbadcbaaadccbabacdadcabddbbdccccddabcadcdcadcacadbadcbddabddbbababcbaccdbbbdbdaacbdcbcddcbdbbdacbdbacaabcdaabdcdccbdbcdbbdabadcbaabcdbbccacacaddcaadaaddbadbadbdbbcbbdaccaacbdddddbdbcaaacdadddaaccdcbddccbbadaadddbccccdabcaaaaadddadcaabacdbaddbabdacbdcccaabcbdcbcacbbabdcddabaaddadbacbadbcbcbdcaabaccccddaccabbaadbcbddcdccdadccbdcabcdcbcdcbaddacdaacaccbbbcdbacdbbcbbbadbabbdbdddcabcaddaddaadbcdacbaabcbaccdadaabdbacbacdccacadacbcdabdbdaadccaaacadbdccbdadabdabaaddcbbdcccaacadaabdddcbbdbcbdccddabdcaacaaabbacdbddabddbbdddbddbaddbddbddbcaadaabcbacdbbdcabdbccccbdcddabacbdccacabcacdcbdbbdddbacabdbbccdaabaabaadbdcbbcbdbcbbcbbabdabddbdbdcabdbcbdcacddccbcdabbacbbcadddddcabbbcadacaaccdbbcdcaaccabaaddabcbbbddbbabbdbdcaacaacaddacabddacdcacbabcdbccbbbdcabcbbbdbcbdbdcccdaacbdadddaccbaaabcbababbacdbbacdabbcbddcbdcdddcacacddbcbcddacdbabbaadddbdddbbbbaaabaacabcadcaccbddbdcbadacaacdbadcacadcbdbdbcacbbaddbbbccdcbbdbcdcbaacdcadbdcdaaaadcddbbbdbaaddbddddddacbdbabcdcddabddcaccabacccbbbabddcbdabdcddbdadddbcaabaddcadddbbbabbadabdbcaddddccbbbccdaddcbdbdabbddcbdddbcdddcbcddadcdcaaddbdaaaabadcdcadccabdaabaccaaddacddcabdccbcdbbdbcbbcbdbcdcdabcabcdbdadacddbbcdaaadacccdbdbbdabdcdaaacdadadccbbdcdcadddacbaabdbbbbbabcdcacabdbdcddacdbcdabbdbadbbdbbbbbaddadbdbbcababaddbbcbdbabcbadbbaabddccdcdbcadbdbddacaababaaacbcbabaadacadabbdbddcadacadabdccadbcdddcdacbddbabacccbbddcbcacbaadaacaabacdcaddbccbbaaabdccbcadbccccbbbacacaccdbcbadbbccabbcdabadcbdbcabdaaadccbdbcdadbcdaaacbdbbaddabbcbcccdacabbdcccaddaccdbbbabcdbccbcabaccbadccdaccbdcabbabcbbcccbcbccabcdccbcccdccdbcabbdbadbadabcaabaaadcbbccdbdcbbbaddcbacdcabdcdcbdbddbbcdcccdacbbbdcbadcdccddbacacacdcbbbdaaadcddaddbababbdacdadbcdcccbbdbadacdabccdcbacddbccbdcccdcdacbbcdbbdabcbaccdaaaaddabbadcbabdcddbbaccabbbdbcdaacdabdaadddababdcbbacddadcdaccacbdbddcaadacdcddccacddddcabbccdcadddbbcbdccccacbadbcbddbbbcdbcbbabbbdbbbddddddacaddaacdacbbcbbdbcbddbbadccddcbacaccdcaabdccabdbcccadcdbcbbcaabbbbcbbddaabcaadcbcddbdbbaaddadbbacadabacbabdadbbbcaaabbbbdcccddabbbbcacdacaaadacaaabdbbbbbdaddddadcabcbcbadadcbbbbabbcdaabbcbdddbabaddcaaaacbbacddbabbdcccdbcabadbabcdcadaabcbadccbdabcabbcdaaabcabbbbbbaaabadaacccdcdcbbcddadaaacabbaaccbbcddaccadcddadbdaacdaacdabadaabddbacadbabdacdcddacddcddaacdabcbccbcbcaddbcadbadbbcdcbadacbbbccdaccbadbcccddbacdccdaabcbdcdcacbdbabaccdbcadbacaaabdadaabdcbbbccdcdddaaaacccdbbddccbccdcadbccbdcbccdbacbdbdcbcdcddacaababadbbacadaddcbbadcbdbacbcaacdaaabdbcaaabbdbbacaccaaabcdaabdcabdbdbdcddcdbaccbcdabdcbdbbacccdbbddbccacccaaaacbcacabcdcdbaacaaddcccddadbccdcaccddcaccdcacdcadbddbabdbbcbccbccdbbbccbadbabcdcbaabccbbbbaddddcbbbddbdabadcddccaadbbaaabbaaddaacdaaabcbacaddcaababcccbaaddcdcddddaaacaccaacdccabcdabcbacbabaaccaabbddbbadaadbaabddcacdbccaacbbdcdabcaddbbcdacaddcccdbccabcacdadbccdbdbdcdbccbaadbdcddcabdbcbacbddacdaadcbadbccdbbaacbaaaabbccdacdcbadccbdaaacddaacbbcdcdbacbddbabaabbbbbaababcdbdcdbabdccdcbdbcadabcabcadcddacaabadddcacbcdadadccaccdbcdabbaadbbadbdbbdddbccdcbbbaadccdabdbccdbdadbdbbddbcabcacbbdabcdabadbdadbbdadbbcdabddcddbcddcdcdabbaadcabbdaaaacacaccdcbbcaadadbdddcdddadcddcdcbadaccdabdbcddbbcabcaaacdadacdadaabbdbddcdcdcdbbbccadaabadabbcbbaaccaaccabcacccbcccaaccacacbbbbaacabccdaaadcddcdbbdbabbabdccbaaabcdadbbccbaacddabcbdbdaaabdcbacddcaccbccbdacaccdaadcddcdbbbbcacddaaacdcdcabcdaabacccbbcabdaacaaadbaccbcbcacabdcbabddcbcbccaacdbdbddcacbabcddccbbdddbcdabaadbbcabaccacaadbccdccddacddcddcccbdccdcacdcddaccbddccabdadbdcbabbbaaccadcaccacddbbdaccbadbdcdccbdbddcaabaccabccbccadabbbddacbaccaadcbdbccbbddcacdcaddacbadadaaaccdcbabbcabacbacdbbcddcdadccdabaddbabbccbdaacbadbbabdaaacbdddbbcaababccadccabacdccaadabdbabaabbbabcadcbddddbcabcabacbcaabddcbabbabcaccdaaaadcdbaddcabbcdbdcaddcbdbdbbcbdddbbabaadabdbdadaabcaadbdbadbddcddcbdadccddbcaabccadccadbdaaacdddbcbbbcacbbccdcadccdaddaaabcbacacaddabbabacabbcbcccbbacabacabbbccacdcbdcabbacccdcdccdcbbdacbbcbbabbabddaadcdadccddabcbcdccadcadadaacbdcbacbddababdbbbbcbcbdbcdacacadbdacccdacddadccacbbaaaccbadcabacbaaaaaabdcdaaddcdacbcdcdaddcdbbdddcbdccaacaaacaaaccdcbcadcacdbddddaacabbacdcbccbbbdcacaaacdccbcdcabccdcdaadcabcbadcdcaaadcaabaacccabcdccddddaadbabcaccbaaacbcbbbbccbcadccdcbaadbdbcadcdcdcdcdcbbabcbbabacacaadddadabdbcbbcbbbdccadcadadcbcbacdbbbcdaaaacdbdddabdcdaabdabbdcccdbabbcbabcbbcdbdcdabccdaabcbcbdabaacbcbddaddbadacbbbcaaaacccbddbbdbdccbcccacbabcababccdbcccbcbdcbabadaacbddbadbaaaddaacdccbbdabbdbdcbdbdbaadabaccbaabccadcacaaddbabbdadadbbcaadcdbdcdcdacbaaaaabadaddbcdbbdaabdcbbddddddddbcbaadaaacaaacdbdbcbabbdcaaaacdcbadaadcdccbddddbcdcdaddbdbababdabbdcbcdddcddccaaddacbacdddabbccdbbccbcbcbddbadbacbdcacdaaacbdbbaccccbadaacddadbdccaacbccbccaacdacbbddbcbcddccddbbabdbcdcbddbbbdaacdbaabbcbcbcbbacbbadaccdbaadbbbabbddadcbbdccbbdbaadddbcadaabdabbcdbacbbcbcadcbdcbddddcdbacccdcddaabdccacbbdbaddbbaaacabbddbccbaadbcdccbcdadbbbdcdbaacdadbddcdcdbcbaaabbdaabaaabdccaadbcacddddbdcbbabdbdbdcabaddabdacbccaaacccabcdbbccddccbabacabbcbbccadaccbbaaabdcbcbdccabdacacabcaacacdcbcbcabdbcaaaaccaaababbdacbabccdadcddadbcbbabcbbdcbcdadacbabaabbccacdcbcdbacadabdcdbcaaacbaddabcacaccdabbacdcdaacababdbddadbdcddabdaaccbddbaccbbcbcbabbaabcdcbadadacbabadbbcbbadabdbaacddabaabadcdbccdacadbdcaacacdcdcacdaddbdcabcbbcaaadadcdddabccbbabbddcdcbdcccadbacdcbdbbcbcaaabbdcabcbcacbbbaccdcdadcadcddacccdcbdbbacbcdddbbbdbdbbbadcdbccbadbabbababbdacaddacaadcbdbbabadaddcaadcaabacacbbddcbcbcbdbcaddaadacdaaabbbbaadacbccdcbbadabadccdcbddcaaadccbbcadbbdacdcbcbbbccbbddbdcdcddbabbbcabbbddabdddadadddcacdcdabbaddbdcaccbdadadaacdaddaadcccdaacbcabbbcbdabbcacbaadcaacbbbbdcccabbacbdbabccaabddaacbaabbbddbbcaabcabbcbddaccdcadcadcabccaabddacbcaadabcddbbddbaccabbdcbbcaacdcdcbddcadadcddddadcbdbddddadbcadccbcaadcdcadbacbbbbcdcaadbaababcccbcddcbbddccddbaabcbdcccdddbbbcbbadabdccdbdcbcddbcaccabbaccbddcbdbdbcaccccbddaabbccaddccbcddddbbdbcdbdaadcabcbdccbadabcdbabacbcddacbcbbcdccbddcdacdaabdacaaabbcdbcccdacaacddbccadabddcdbdddccaaccdbaabbaabcddabbadadccccddddacbdaaacddbcbadbabbcdabcabcbdadabaccccbbdacdbbddbbbccbabdddcacaacbdcddbabaccabacbdadbdbccdbaaaddccbcadacabbddbbddcadabcaacdbbdcbbadddccbaabcdccaacdcccbabbddddcbbdbdadbadbcddbccdabbacddabdcccaddbdccaddbccadacdcccbdacaddacbdbdcdaabacdcbaddacabbccaacdcbdaddccdbabbdbddcdcdcbbbaabdddbbdcbccbabcccadddaacdcdaddbabcacbcadcacaaadabadcaabacdccabddcdcbaaadcacadadacacacbddacadbcdadaccbcdababbbabaadcdccddcdaccccbbdcdbcbcaaddadbdbdbdcbdacdcbbcbdbabcacabaaaabbccbdbadabacdcbacbccbaaacaabdccbabdcacdbbbaacdcadadddadbdddadbbcaaacdbabdbacddcdddcdbbadddadabbdabdacbdacbbacadacdaabbddabcccadcdcadcdccaabdadacbaabacbdabbdbdcaadbdbddacdabbbadddbcccbccdccaddaacaadabbddabaaccadcadddbadbdbcbaaacbbcdccbdacdccaabbccdcaaccaacaddcddccdddaabbdbacabbddbabbdbaccdabaaaaadbcdbdaacabdcdbdaabbcddddbcddacdccaddbbabacababdaacbbcdbcaadddcddabdcbabbdcdabdbdcaaaadccadbbdadabaddadabbdbcbcadccbdabddbacdcdacdaddccbabacdccbdbcdadbdcdbcaddcaadddcbcccdddbbbbddacbdcddaadccaadaddbcbaaaadbcbbbacaccadcaababdccdccdcdbcdcdbccccbaccbaddabacbbbccadccabdaabaccacabbabcdbcbabdcabdbbdbaacbccdbaddcbbbcbbccddbdbadcadacabdaaccbdcabbaabdadaadabaaddcbacaccaddabcacbdcbaadcbabbabaddbddaaddbadadadbdcadacddddacbabdaaabbddcccbbadbdaabddccabaaacdcbaccdbcbbadddbbababddbbdadbabcadaaddcdbbdbdadacdaabcdadabaccccdacdbdcdbababcddbcabadacbabbacbcabccbbadabcadadbaabadbccccbcacadcadcdcacccbabbdcbadacbddbdccbbacbbddbcaaccadaddcaaddcdccccaadbacacaddcdbdcbbdbadcabdadaadbaadabcdddbdabdbbcadaadbbbdddaaabcdbdcdcdabbabdbdbdcacdccbccadabccddcdbcdaacbaccacaccabdbbdbaaacaabacbdbccdabaaacaaacddccdababdbbababdccbdddbbbcccbabcdbadccbccddcadccdbcdbdcacddccaabbdcbcaadbabcccdaaabccadadbaabccdcccabddddaccddacacccbacadadbccadcdbcacacabccbbbdcccdccdccdacdcbcdddadaaacbbacaaabbaaaabadbacabbdbbdbdacabbdbbadccbdcbabababccddcadbcaddcacadbaddaadcacbcbbaddccccdcbabdccdcdbaaccabdbdadcbabadcdbbbccbaddaabadacbbcbabacdbadcacbbadcddcdabadbccbabccdcdbaabbdaddaadbcbcdadbcdbaabddaaaaddbdaaaccddbdcbadaaabdcbccaaacababbadabddbdadabcbabaccbdaccaacccbcbcaccaadaadcbcddadbcdccbbacadbabbccaadacbbacaacddacaadcaccbdadbbdcddbccdbaccaaccdaccddbcbaabddacdbcdadbbdbdadbbdacbdcbcdcdaabdcdcadcaabaabccbddcadddcdbacdccacadddbddadaacdbdcaadddcaaabacaacacdabbcddaababdddddbacdcabbcdabdcdcaaacbccaadbdbbcddaacabcbcacdcaacbaadcbccabbddbbaacdbcadbdbaaccacdaaddbdabcdbdbbadbcabddaaaaaddbddaddddadaadcdcbddbdbcbaddcbcdcbdaacbcbaccccdcbccdbbdcaddbbccacbbaacdcbabaabadabcdbbabbccdbdbbcdadaddbbbbddbdbacaccaabdddcabbbcbcbbaddabaccdabccbabacbdccbbaadbcdbaaccddadaabdbabadcdadcdbbabdaadddbbbcccabcdabcaaddbabddbbadaacacdcaddadbaabbdcabbdbabccccabbcdcccacbdbbdcbadbdccccccbcaabbdcbadabababcccdddbacaabcacddacdbbaacbadddababccaacaaccccacdacbbabddbddbadbbadadcccbdacdbaaacccbbdadccadcacadabcbacbdbaaddaabbcbdaabcaaadbbaabccadbaaaaaaaadbddadcacddcdccbbcacddddddcbdddaabbcdbcdadcdaadbaaccdaddaaadcccbbbaacdbbaabdbabdcbacbccdccdcbcacdcddadccdcddabbbacaaabcdccdacdddaacbabbabbaaaabaadcbaacdaabcbbadaccbbaddcacccaadadaaabcdcbbcccddacaaaaadbcadccbbbdadbaacccacabdaadbddcccddcdaabcbcbcdbcaccccdadddccbacccbbdcbcddcbdbcdcbcdadabaadbcbdccbaaddabadddbbccadbbabccbaacbdadcabbdcdbacaccaddadabcccbaaaccdbbbacccaabbbcacabdcadbbcdbdadbddbdbdbaacdcbaabbaacddaccaccaddcbdabdccdbadcdbbabcadcdbbccdacababddbcaadadadcdadacbdcbcdabdbbaccccabacdbcabcdbadcdcababaaabcdbbccbbccbdbdabdbcaaacabcadadbacdcbaacbabbaddcddddbdacaadaddccadaacacabaaaadcbcacabbdcadacdbbcabababbddcacaabcbbaaaadddcacdabbaabdaaddbcbaccabaadbdaacdacccadabaddbbdbcdbdcadcadbccbcadbaccaabdddbbbdccddacccdccccacababdccadacbbdaccddbdaaabbdaadcbcdadccdabcdcadabcbbdacadbdccaddbabcacbdadbcdddddbbccbacddbadababaabcaddbbbddbbadaabbcdcbacdaadddbaaddabaaadabacadbcdaaadbddcbdaaacabcddabaaccabbcdbdcdabdddddbcdccadbacbaacdcadddbccdacdbdbcacdbdbdddabbdbaddcaaadcacacbbbabbbaccbbddaccaacdbcabdbdacbcbabbacdcbdcbabdbdcdbaaaabbabdcbcabcacbdaacbabbbbcbaabcbdbdbbcacdabdcdccadabcbaabadccaccbbcadddbbccabacacbabccaabcbbadbacdbdababbbbcaabbbcdcdbbdabcdbbcdcddacdcccdadccdabcbbdddbdaacaaabbddacbdbbcacaccdbadddbdbadccacabbabcddbbadabbaaadaabccccabdcdbacbcdaacdbacbbbacccccabcccbcdcdadcdabdacabdddbdcaabaaadbdcbcabddbcddddbccbcbbabcabaddbbcaacddcccbabcdabbaccadabdcbaddbaacacbdcccacdadbbabaaabacbdbadabdbdcdddbaacddbbacddcccbccbbcabcdabaacdddaacbddbaabdcadcdaddaacbdcbaacbbdbdaacaabadcbdaaadababaacbdaabbacdbacdccbaaccdabdcadbdbbabddbabbaddbbcbaddcbaaacccaddcbcbacdcbcddcdcadddcbbcdcbdaadcdbdbcabadccddbbcdcaaccbbbccabaccbbbddbccccddbcbcccbcdbaacccaadddbcbdacabaddaccacdaaadbdaaacbbabbcddccacdcabcbbcabdbbbbcaacaccbcdaadbcbbccbcccdcaddbaccdcdbaabbacbbaccbbdaabbbdcabaccdbbabcadbddaddbbaadaadacaabbbcabddadbaabdacdabdcdbdbbcbababbacbaabadcbdbbbcaccaccaaddcadacdabbccbaddbbcdcdccabddabcdbdbbbbcdddaacabcccabdddbbacbaccacbdcbddbaacacdddbdcbbdcaacbacccddcbbdbdbcbcdcdbdcaabbdbdbdbccdbbddbadcaabdbdaddddbccbdadbbcbacdaccddcbbadcbcaadddcaccbaddabbbcaccccdbabbacbdccbcdcabcbaadcdcbaabdbbbbbdccbcdbaabdcbbaccbccddbaadbdbbcccbdaacaacbcdcdbcccaaddbacbccdaacddccdcbacaabaaacbbdaabcbcccaadbcccaaacdcbddbabcaaaabddcaabadbcabddcdccdabdcdcaaabcdbdbbdabbdbcbdcddcdbbadcddabbcabcdbaacdcbabcadadaaabccaadadccddbcccaacbbcdccddccdaccaadcdadcaddcdbcacbcadddbdacbddcbaacabddbbcdcdaaabdadddccdddcbbbdbccbabdaabbccbdbacbdbaadcaadcaaacdddbbbdabdbabcabdcbdcbbcbacdaacdabbacabddaccdbcacadccbccbadaadadbcbbabdaddadadcacdbabdddbddcdbcccacdabddaadcbcbabbcababcbcacbcaddcabbbdccdddddbcbaacbccdbbdbcabbbbbdcbbacaaacddcdcbabbcabaadcdacacdaccadcadbbadcaccbcbdcccaacaddbabdcbabcbacbcdbdabccbaadbdcbadbabdbdabdcabbabcadcaabbbcbbaddaccdacabadbaaabaaacacbcbabbdbdbcbdcdcdccddaaaccdcbcdabdbcbbdadbcdcdddbcddccacdcbbddaabbccdbddcaccdbbcbabadcbcbcddabccdcadabcbddcdaabdacdadbbadaabcbbddcbdcabddbddddbccaacdadbcabbabdccaccacdabbdaccaababdacaabdbaccbdadbdbdbdaacdccccdbccaaabdaabaccabdabcbccbbcdadacaadaccaaccdbcbadbddbcaabdddcadcadbbababdbddcccacddbcccbccdaadacadcabdacccddddbdadccdcbddacccbcbdaabacddbdcdcccbbabbcbaccdccaddbddabcdbadddbcabcaabbaccbacbddabdabbddcacaaaabdadbbccadcbdabdaacadbacaaccbbadbbbbccbcdabadbaccbdbaccadadcdbacbccbdccabddbbadacbcbaabbddcbcacdcbacbcbcdbdccaddcbddcbabcdcaaadadaddbaacbbdabcccdbaccdbbcabcddbabcadaacaddbcacbcabdabccbbcbdcdbcbbbcadddcaccdbdbccbbcacbdcbabaadbbccacdcbcaaaddddabadccccbcbcdabcbdcaddbbbdaabcacdccabcccdadabdcdaacaadcaadbdbdcccbabbcacaccccdaccbdddcbbcbabcbcaddabbdccbaccdccabccbacabdadaccaacadcbcddbcddccacbbcaccabdddaddabcacbabcbcbaaaccaabadaaadbbcdccaacccadbbcddcdcbbbdabcaddbaddbddbbcacdccabdaabdbbbadddccdaddcdcbcdccbbacbbadcdddccbbabdbcccbdbcdababdcacbaaccccaaaddbcdcacadaacbbdabbbbbcbcbccbbacdadbdcaddcbbbccdaaadcabcdaccaaddcaaacbdcbbbbbccadddcabddaaddcddbbcdaadbcdcaabdacaccadbbadcbadbaabbddaaccbbaaabcacbbbdcaccdccadcabcbbaadbcbbdcacddbdcadbcccdbbdacaddcbccaaaadcddbdbdacacababdcddbbcccdacbacbddabdcdcbbbddcbccbdcbacdcbbddadbbabdacbcbbdcbccabdbcbbbaaadadcacbbaabbadaccdaddcbadcdbcccdbcaddaaccaabbaabbbcdcdaccacbbbaadccdacdbdacbbcaadaaabababcccbbaadccaacdcbbbabcadbdadcbcacadaaddadbbbcbcaadacccabadbcadcbbdcccbaabbdcbcccdbabaadcabcbbdccbcbdaabaccdcbbbccbaccbcaccbccdaacabcbdacbdbdacdcddaddcaddaaadcdcbaacbcddbccaababdacdbbdcdcaddaadbbcaaaaaabcacaacbcdacdaabcdbcdcdaaacbbbdddccdcadacdbbbdcaabaccbbcdabbaddbbcdcabbabcccacabbcbcdacacddbaddcbbcbbabcdcadabbdaabbcddbabdacccaddddaccaddcbdccdcaccababbdcddbadcaadacbbabcbdacabaaaddddbbdcaccdddacbcdcbddadaacabbacdddacdbadcdcddbdcccabcbbbbccbdacbbbacaddccdbbccddcbdbcdbbbacdcabbbabdbabdbcbcdcdbbdbaabccbbdadbbcaacbcadbdbadaabcadacccabbbacdcbdbcddbaabadaadccacadcaacdbbcbbbabaccbabaacbadbadaadaaabcaddcadcabccbcabdacbbbbcabbabbcbbaaababcdcbdaaadabbabaababacdddaaaacdcaddabcacbacacdbacadadbccdcabbbabacabdbdacccdacbbbcaaaacdbcbbddbbbbcccaccbdaaacbabadbdbbddcdcadcdaaabaccaaccddbacabbcaadbbdccbbdcdbcddccbacdaccacbdbbcbbbcdbccddcadabcbbdbaadddddddbaabddaabdadaadabcbbccbddadbaccabacbdcacbcdddbbdbabadbdabdcdbddcccabdaabacbcdabddcadabcdbababbbbbdbdcaacacabbccbbcccdaadccbdacdbbcdcbabadbacabcaddddcccddadcdbbabcadcabaaacdaddddbacdacddbbbaddbdcaaacbdbcbdbcabbcaaadaadcaacccbdbabbcacabdddccadbdaaadacdadabddbdbacaaadcadcdbdaadddbdcdaadabcdabacbbaddbbbbaaaaccabaacdcbdabbabdcadcaaaccaadbcdabbbcbcccdbaddacacbabdcbbbdcabbbbbdcababbdcacadcbaacbcdaadbaacabccdddadddccabdcacacdcabdbbbddadccdabcdaadcccaaccabbbcabdaaadaaacdacbdcdaadbaccaaddacbbbcdbbadbdbdacdaadcbcbcddcabbadbcaddabcbccbcdbbabbdcdcbadbcaaddcbabdbbcbdbacbdaabbcadcabacdaabbcdabdcddddaadddbacabacdcaabcddaabbddbbbcddbdcdadbbacdbbcbacccaabdbbbddbcabddabbccdaddbdddbdcabaccbcdacaadbadccbcbcacbcccabbaddadbacbacabaccbddccaababdbadbcbddaacacabbbcdabcbdbbaaacaaacbbcbabbaddbadbbdcbbaddcdadadabdabddbdaaccbbdcddaaadcdbcdcacccdadcabcadbccabcbacbdcbcdcdbdbcbcaddaaabbabcacccccabacbcbbbbddddaaaadadbabbbbaacbbababaadabbbbbbaadabcdcdcdbdbcbdaaadcbaaacbccbbdccbbadaddbadddcddaaaadbccccadcbcdcddcbaabbdaabdbbdbcbaabddacabdacadaaaddbacddbbcdbdaabdcccabcbcbaccbcadbddcacdcadadbcabaaccbacbcddcbbadcbddaddbddcdcdadbaaaaddaacabcadbcbaaccadadbcabaddbabdabaacaaabaaadadaadacabadbaadbacdccbbcccaddbcacbddbdcacabdcaaabaabbaadbdbaacdcdabbdadccaaadcccaddddadadbabddbaabaccdddadbadbacbbcddbdbdbabcbddddcbcaacdadacdddaabbbcccbbcaaaacdaccccddaaacbdcbcbddbbabacbdcdbadabadabbbcaddaddcbaacbcddaddbdccabbacadbdadbcaccaaaacbdbabacbcacabdcddaabcddcabdbbbddcccddcbdadcddbdcdbbbcccadabcbabadcbbabcbcaaacadcddcbabaabdbbaddbacdccddbbaddddabddaccbbbbddadbdcbcacbdcddaacdbbdcdcdaaacadbbcdbbbcdbddccccaaabbcdbbcccdbdcdcababbdbcaddcbaadbdddaabdbbdaddcdacacdcbdbdcccdbccbccdddbabdbacabcdcccccdccccaacccacdbbdaddbabcdbdabacdcccddbcbadacadcaccbcbdccdbadbbdbdccbacbcacbacdbdbacbbccabddbbaccbbcdaadbcddcddbbcbcbbbdabadbddbcabbcbabdcabacbbddbbcadabaddbcdccdbaacadabbcdddbcadaddbcbbbaccdddbbccbdaccdabddbdcbdbbbcddcdcacbbbacccccccbacaacddaaaacdbbdddabcccabbbcabaddbbcaaadbdccabdbabacacddcbbaacdcadcdaacdbabdcadcdbcdbdcacccaadcbcaacbcaccbbcadadabdbabbdcabbdadabbcddbcaddccbabccbddbaddabdbacbacaacdcccdbbbaacaadbcdabcacbccacccccddcacbcdaddbbdcccdcdbdadbccccccdcdcbbaabdaaabccaadbdcbadccdbdbddcddcddcacccdabdacbabbddccbcabccddadbbddbbbcabacaccbcaddbaacccbbcaacacdccaaacadacadddbcbaadbaccdcaccaddcdcdabaddddcadcccabdbdaccbadbcbbabadbccddaacacbbcbabcdbdccbbdacbaacccddcddbdddbcddabbdbbdaabcacbdcabdbbcccdabaadbbcaabacabcdbdcdcbacabbadcdbdbdaaaacbabaacaaddbadbbaddbcdcbcbbccbdccbcdccaabcdcbaccdacaaccdbccbbbddbadacbbadadbbcdccbbbabcbcacaabadbcdaabcdccccabcdbaaadaaacdabbdaaabbdcddbbddcbbbdddddbbcdccdabaaaaadabbdcbcdbdbdbccbbdbccacacdbcbccacbcaababbccbcddaadcdcbdaaabbcbdcdcdcdbbddddcbdadcadcbbdabaaddacdaaaddaccadbdaaccbcaadabacccadadbcddcbccdaacbbccbdacbccacccccbcaaaaadabdcbccabaadcbddcdbbabdcbbddddabcdbbdadaacbbcacbbdbdddcabbbbacadccddbbaccddddbcbdbacddaddaacbdacbabcaaaadbcdbcadbbbaccabcbdcdbadbcaadbddacdbcdadddcbbacaccacdcbdcdbbabdccbdbdabaccdbadcacdccdbacccdabbabbcacdbcabaaabcbbaddbcbbbbaadbabccbccbcddbdccadcaaadddaabbcccccdaccaccddbdbddabbbdcbddcdbbbcdbbbcacccbcddbacdbaddcccdcabacccacadbcbbcbcbcbadbcdcadabdbddbabbddddcaaadabadccaccbdaddabdcabdabadcabbcbddbdabcddaaacaaabbbacadadddcabacccbbccccbdbcdbdddadbabccbbaacaaddbacaadbaddccabbbaddbabccccaabcbdbcbbcccbacacbacbcabacbdacbdddbbaaaccbdaaaadbcacbdadcdbaddcaadbbdbadadbdcabddbbddbacdabacabbadddbbcbcbccdabbddbadccbbaadababacbaddddacdcabbaaccdbcddcbbcbcaddaccbccbbdaddabddcdcbcbdcccaabacbdabbcaadaaaccacacccadbabadacadbdbdabbdaddbdddcddcddccadcbddabdbdadbdaccbcdbbbcddaabbcbbcbabaabaccaadbcacdabacdacadddcbadddbdcbcbdbdccbbdbacdaaadbddcaddbaabccaccdcbdbddcbabdbabdadcbbdcacacacaadacadcbcbbcdbdbdbcdcdaadccaaabbcbdacabcbaabdcdcccaacacaadbbbcabdcdacbabacbcabacbcaacaaadcabdabbabcadddadacadacacdbaabddbacadbaacddcdccabcdbcddadaabddbaddabcbddddcaabcbdcdbadcabbbbcbcacabddadbccbbbabacabcabcbbabccacddabaddabaacaabcddadbdddcadddabddcddcaccabbdacdbdcadadcbacdcbcdcdaaddbaadddcdbccdcdbcdccbdddbacbccbcbbdaadddcaabddcbdbcdcaaaddcccccabacdbddcacdcbcacccaacdcdaccaabacbcaddaabcbdbadcbddabcdabccacbdcbdabccdbacdcabdbbbccbcaaabadadacaccaddbcdaacaacabbdbccccaacccbaaaccaadaccdacddbddcbadaacdaaabcdabadcbbbccccbdbacabaacddcbacddaccacaadadababbdcdabdbabcbbbdcdbabdbabaaddcdbdbacdccdadcdbbcacddbbddbcdcdbbdbcbcbdcacbdacbadcaabbdaabbddbccadabcdcbbaadaabbcddcbdaddcdadabadcbadddabdbccdaadcaaadcacbcbcabdbdcabadcbcdbbdadccdacbdacacdcadbcbbbaddccdcbabcbbcdbabdddbcdcdaacadcadaaddacbcccdaadccbdcbbadcdbccadcddbbaccabbbbbdcadbabdadbdcdcbdcdbabcbdbaccbaaabddbabbadcaacdaaddccbbdacaadadcddccbacbbbabcabcaadcabcbaccbddbacaadbbbbcddbaddccdcacbcddccacaaabacdcbadddccccadcacdcdaadcbcccdccbdadbdccbaabdbbdcdcaabdabcbddadbbcbbdacbaddaadbdabcdbddcaccbccaabcbabcaaaaadccddbbbcbdacddccdbdbabbdbccdbdadabcbdcbcaddbbbdbdbdacbbcaaaddabcbccabbcbadabdbbbcdddbadacbcacddaadbdabdbbdbacdbaaabcccddabdccaabcacdaccbdbabcbbccbcdcbcbcacacbdddaccbdbabbaadcddadbdcaacbabbadbadcdcaaacbbcabcabadaddddaabcbcdcdbdcaabbdccddbccbcccadcdbdabcbbddbaabcadcdddbddadcdbbadabbbdbcbcabcbcaadbcadcbaadbabcbdddcbccbabdbbdabccadaadaadaabdcaabddddccccbcbaaacdcddbcdcbdadbdaabbbcbacbacdcbaaccdacddcacbddaaddbdbbdbacdcbbaaddddacdbadcbbacbabccdbdadaababdaabcdacbbaccbbadadacdbbcbacbdcdacdaabdccccccdacbbcaadbdacddbabbaddbabddcacbcaddaabacbddddabacacbdbcccdabdbcbdacaabbbdacddacdbcdbcaccdaadaaaadcabddaddadacadabddddbdccdaabbadcdbcbdabdbcacbadccabacacbadbdcccabcaaaddabddbbcddabccadcbdabbcbcdbbbaabddcbcddaccbadabccdadcdbbdbacbcadbbcbababacaabbbcbdadddcacbdbadbaccbabbcbcdbbbdabcdbbaabaddadaaddadacccccbaabadbaddacbbdadcbcabadbbbaaaccaaabccaabdbdacaaacddadadcbccabdadbcdbbcadabbadcaabbadbaabbbccbbdbcacabacdadcdddbdbbadacabcabcaacbbbcbabbbabbcdcbaaadddccdcacdaaabadddacddabcdbabbcbdbaccbcbabcadcacadacdbacdbbccdddcacdccbdaacbabacadbbdbdcabacbcccbbaababdcccccdabcabdbbccadbadcbaddbacdcbbddaacabbabbdccbbbaacabcdbcbbacbabdbaababdbbbdacadddbdccacdcadabbadacdbbddbcbaadbbadcdddadabcdabcaacaabbbbaacbcaacdddcbabadcadbddbbdbacbcdcdabbdacbbaadbbaccddbcdbadaacdaacbdbcbddaaaadbabccbcbcbbacbaabccadccddccaacdbaabbdbbcabdccabdacddaacacccddbaaacabddcbadddadadbaacbddcbbdadcadaddcaabddbdbdcbacbbccbdadbbacacdcbaabddabbabbdbadcaddbddcdbaadcdbbbdabdcacacdccbacdcbadbbbcbdcdaddbcabdbbccbdcacddddabadcbcccadcddbccbadbdcdabbadcaadddcdcaccdcbbbdcadaaddcbbacabadaabbabcaacbcdddcaacbacdbccdcadaaccbacbaaadcdcadcaabcbcbdacaddbdabcdacddbdabccadbdccdcbbbbdcdbbcacdbdbbaacabccdaddabdccbbcadcdaaabcbdddddbbbbcbacbbcbddcacbbbdbadaddbccaaacabbbcdcdbccaccabdcddbdbaacbddaaadadbbddddaccdbadadbdbaccddcaaccabdccdcbcbdcdacabbdcadabcaddcaddadcbcaccccbbdddbcbbaccccbaccaabccccbcccbbbcbaaddcdcacbddddaaadbadbaadbbcabacbcabcbabdcaccbacbddccaaabcdcaaabdcdcdcabbdcbaaacdabccdddbcadacadbccabdbcbcddacdccdddcccdbdcccbdbbbcabcdbabacdadccaccbbbadadcaaaaaddbadadcccadabcddcacabdadbcbddabadcbbddbacbbbbadabadcdccbadddadbcabdacbbcabddcbabbadccaaacbdacddcadacbccdcbacdcdbbdbbdadcdcacbcbcbbddcdcbcdaaaabbdaabdcccccaddabcdcddcacdccdbcdaccbbbdacdadbdbccddbdbcdcbdbccadbaccdaadaccccbbacbcaadadbdcdacbaaadcaaddbbdcbabaabcaacdaaaabdcccadaaddddccdbadacadacccadabcbbdcaabcacaccaddddbaaaacdabbcdaaabbaadbdcadabbcdbadaadbbdadadadccabaccbbcbbbacadcdddbaaababbdbdabdacddbacaccdaadbadbacbabbbdaaddbccadabdcbdcdbbababdddadcccaaaacbcaccadcdddadcbdcddcacddbacaccdcaacadcbaadabaabbbabbccadcdcbcadcacdacaaabcbbbcdccacdadccbbddaccdddbabcacdcabbddbcbadacdbbcaadaddbaacbdccbadbccbaabccabdcadbddaabdbdaaddabbdacccacaaabacaaddbacdccbdbbbcaaddabccccdaabbcaababaabbbbbcacdbbbbbbddadabdbbbddbcabbacddbbcbcbdbcadcabcbacaabbbbabcbaaabcdbbdbadbbbdbdabcaccdbcbbcccbcddcdcbacccbddadccaabaaaaadbbabcccacbdddbcabbaccabdcccadccdbaaccdddbdbadaddddbcccabdddccddaabadcbddadacaaaacdcabdbaabbcaaaccdccbdbabddacacbdaabadabcbaadadcaadcbdccdabcdcdbabddbcdadcabdbcacddcdcdcabbbcdabbbbaddbacadbbbdadbcdcbcbdadcccdabadbcdababdabbcbacbacadbabbaddaddbbaadccbabcdabcdaacbcdcdbacabdccabbacbbadbcbddccbbabddabcbcbbbbdcaccaabbabdbddbcbccabddbaaccdcbdddbbccccdacbaddbdcdadadbabbcadacbdaccaccdbbbbabbbcdbcddabcccdacabcdcdabbccccdddcadbabadcdacbdbabccdddbabcccbddbdabcdccbcaacadbaacbacababbbdcadbbaabdbacbbabdaddbaabacacdacaddcbdbcdcddcddbbbdbcdddabddbdbacbbdabbddaaccccbbaacbdbaadbcbbccbddaaabacdadbddaabcbbadcbaddadcadaabaccbccdcdbbbabbcaadbdbdcbbbbcdcbcdcbbdcbacadcbdbbadccbcaccbdbabbacaddddcdbccdccdddabccccdbdbbababdbcdabbbbbbcbacacabbbbdaccdccdcdbcadaaccbbadbbadabbdcddcabdcccbabadbbbacbccabadbbddbabcaacddbaccdccbdbbcddadbaabbddaabdacaaabcaaddccbbdddaaccccadcabdcbadaddcdbbcbddbbabdadaaacacbaacabadaacdbddddbdcdddaadddadaccababaadcadacaadadcabdaabcacdccbcacccaadbdccadbdcccbbbdaaabcbbadcbbaabacacaaddcabcdaaabababaacbdbcaadcaadbcdabbdcacaaadbbdddcadcccbaabbbdddccaabbccdbabddabaccdccacbcdaabaabdcaabcadcabbbdcbbdbdaccbcaacccdcaaaabdbdccddbcaddcacdbcdddbccddbbcbabbbcaccadaabcccdbcabccbcdbdccbbbccaabbbcbbcdabddbdddcabbccccccadcacacbdbabdcabddabbcdadcbcbbbaadaadbbadccdbdbdbbbddadbabcbcbbacdacdabacadbcaddadbacacccdddcdbabcaddabbabbcadacdabbbbacccadccaabddbdbbbcaaadbbbaddabbdcbabbcacbbcadcccbabdbbbccaaaaaabcaabcabdcabddcadcdababcbcddcddaababcacccacbbdbaaacdabcbabbdbcacdbaaccdcabddabaabbccaddadaccabaccdcaccbcacadabdabcbdddccccbcadbdbdcdcbcbccacdabcddbcbabdbcabbccadddbcdacacbbcbacacbbdcadbacabcdbcaadccabbdabbcbddcabadcbacccaadbcdbbadcddccddccbdaacbbbcaddbddbaadccdddcacaccaaacaccaadaadbcccaccddcdbbbcdaadbacbdbdadbcadbdadbdddbbbbdbcdaacabbbbbbccdcdcdccaccabdbadaababccbcdabaabcabdabcbdcacaacdbcbdcdddcbdcbcaaabddcddabddbcdabdbadcbcbdcbcadbccdacabcacdddbdabacbaabcdccbbcbcaabacdcbadacadbddadcbcaddbdbdbaaddaababaddccddbabbccdddabcdbccdcdbdbcaccdbdbaacbacdbbdddabbccbacabddcaadabaadddbdddbdabbaacbcdcdbdbccdbaacabdaddcccaaccdaddbcddbbdcddaacdcdcddddcbcccbbbccbdabddacdbdddcdccdcdbcccccbadbddbccdcabacbcdcbcadcddbbdddadadcccacadaacbbdbbabcbacbbdbccbacdabbbcaabddcadcaccdadddabaaccdbbddcdcaddcbdabbdaadacccadbaaabdbbdbbcdddaacdcccaccbccdbadcccbddbcbccbdaddabcdccbdabcabcaaaaababcccdaadcadaaababcdbddacddccdadacadbacbdaccddabcabdaccccaacccabdccabadaccbbbcbadbacdaabcacdddaacccbbcaddbcdbaabacccdadadcabcdccccbabcdbbcacdadadadccdddadbbabdccdbdabcbcddbdcbcabdacddcddabbbadaacbdadbdbdcadadbbaaadcabcbabdaababdbddababbbadaaddbdcdbcaacdddadcddbdabcaadbbcaabbdccadbccacabcbccbbcdcabbcccddbacadddccbbcdabaccadcbaadbaabccabaadbabdcacabbabacaaabaaaacbabacdcababdcbdcbabaccdbcbabbcdccaccacddabcccdadaddcdaaddbbccdacddbabadcaccbdbbccbbddacdcbdddcdacadcdbacbabddbdaabcbbdaabcdbdadcacbcbcabcaaddbacbbcaacbdccdbccaddbbdcbddbaaaccddbddbdccdbcadcbacdaaaabccdabddccdcdacabcbdbbccccdcbcbdadaadcacdbdbddacdacdccccbbbdcaaccaadcaaaaadcaccbbcbabababaccccdddaaacabaadabacabbcbaadbcaabacadaacabbbdbaacabcbbcbbbbdbbdcdccdaaaabbdccadbcadaddacaacddbbddbaabbcabababacdacadcacabadabcbdddbdcabbcbdaadadbaacbddcdadbcdbcbabaadaccbadcdccaaabdbbaaddcabdbadcaadcbddbdbdabaacadbacbbcaabacbdaddaacbdababacdddcbadacdccdcbbbcbaabaddaddadcbbbbbbaaccddbdcaddbaddabddbdddcdababacbdbddccdabbaaaadcccabcdcdcbabdcbbaadbdcdddcccccccccadddadbdaacabccccdddabcbcccbaaaaadadcdbdadabaacaadbcaacccadbacccadcdcacdadcbacabadacdcdcbddcbdddaddccbacdbdbbacdccaaadcdbddcbccadacbccaaadabccaaadadaddbccccaccabcadbabddbbbccccbaadcadcccddadadbcdcabddbaaaacdbdcbcabaacbbabdadbbccbcbbdbcbccccacccdbbcccdcbcdcbddaaacdddcccaccaabccddcabcadacdbdcdbdbadacddddcdaddbbaadcddcddacaccdbdcbadbbdbcadbdacdbccaadbdcbbbcdabbddcacccbaddacadbcabcaccaabdddccababbcaccddaaadbbbcbbadaabbbdbbdbcadbbbbcdbcaaddccbbbbbacdaadbabaabbdadbbdacaaaaddacababcbcbbbacbacaaccaaaaadbcbbadcdddcdbbccbdabaccbaddcbcdbdcbbccabdbdbcddbcacbaccaddaaccbaabccdcdcdcbbcadadcdddbdbcababdddddadabbbdcdaddadcdadbcddbdaaccbcbaacabcdcabaaabadbadbabdbaddbbabbcbaabddbaddaaabaacdcaddddccdbcdbdccbdaacbdbadcdbdcaabddbacdcdbbddabdbdbaacdcadbcadcdcdcaccccacdcdbbabbcccabbcaddbbcaaacaacdbdcacabaaaaadadccdbdbaadcdbacbbacaabcaadddaacabcabaddccadbacbdbccccadbabaaabcdacccadcbdbcccbcccbcacdbbaacbccbbcaacaabaacadcddadacbcbdcbbdbabbbcabbbbddbccbdbaddbdcabadcddbddaccbdddcacddaacabbccddaccbaabaaccaaaaddabdccabacbddbaaaaabddcaaaabdbadccbdbbcccabccbaabbdbadabacdaabbbdbddddcdcdadccaadabbdbacabdddcdbbdddadbdcbcaddadccbadbdcdbddbcddbccbbddbdcbcbcdabcdbaacaaaddbaddaaaaddadbccaaaadcdbaacdadbaacabdbcaaccdadbcaabbccabadbcddcdadabcaddaccddcacdadadbddbdadbcaabcabaccacdadbcbdcbbcbdaababaabdbacddadbaddaccbcaaccdcababbddbacdcbbbcccbabcabacbabdabcaaabcccdbabcccbdbcbaadccaacdababbabddabbbcdccabcaccbcbcabbcdcabcdccbccddbbcdcaaaacdbdbabcbadddcacadbccbbdabbdadbadbccbcbbadcdacaadcdbcaaadacddcdcbbcbccbbcddcbbcadbaccccaddcdacdcdccdcaababcbaccadacabbcdcadaaadacaaabbcccccdccbdcbdcdcaadbbcbbdbbbcdddccdcabcbbabdabcabadcccacdcbabccadddcbdcabddcdccdbbbdabcdbcbbbbbcacbdaabdbdddaddcaabbcdcdbdaddabdbbdaaaaaddbdadaccbcbcadbbcbacddcabbabbbbdbabbabbddabcdaadbdcbdaaddacdbadcbdaaaabcdadcaacdccabbabccacdcdddcaaccacaacaacabcadaaaadcabddbcdcacadcccacabbdbdbaabbabdcdacbacabcadbacdaaaaacddddbddbdabbdcacbddadcdcdacbdcbbdbdabdbbdcacdcadbbdddcacbababbdbacbaccbbcaaaadbccbcbcaabddbbbbcaacaaaccabbcccaccddabccdcdccacdaabdbbaadcbcbdbcacacbabdccbdaccbaaadaacdcbccbaddcddccaabbabaaaabddddddabbddaddbddaadacbdcbbadadddcadbbbcacbbbcaacdabcaccbdbbcaccdcababccdacdccaaddbccddcaadaaddabbbdadacbacdbacdabaabaddacdbccdaccbbacdacdbacdddbaadabadcccaadabbcdcaabcadbdbccacccaacbbcdbcccdaacbbbacabaadcabacdabdccaadddbcadcdcccaaacaadabcdddcdccddbccdcdabbccadcdddbdbabcbbadcccbdcadcbddbcbabccdccdccbbbaabcddacbbddcdcdbaaabadaabcacbacddbcdbdddadbbbcdbcbcccabaacdbdcccddddaacdacbabbcbccbccdccadcdabadbcacbbabadbacaddccdbbbbbcdcddbdabdcadaaadcdbabaddbdbacdabbadababdcddcabaabbbbddbdcabbabbddccaabcbdbdccabdbdbdbacacdcbdaccadadadbcdbadaaadbbcdcdcdbbabdbcdadccdbcacddabdabbcbdbbbdaaaabadccbbddbadcdbdacdbabddacabaccbcdaddbdddccbdbcddaadcacdcdadabcacbacbdabdbbbbdadacddabcbcbabadbbadcdaababdcbdaaaaccbcccadcabdbacdcdadaaadabddddbbaaabcbaaadcccdbaccbdaddccbdbccabbbabdddcbdaadacccaadababbbaabbbadaadbcbcaccaabbbabacaddadddaccccbacdbadcdadadcdcbaabdaaaaddaabcddabcaadcbbcdadcddadccaaacaabcddacaaadadbbadcacacdbdcddcbdddadcaaacdbbbcddcbaabddacbddddabbbcbaaabcddadcbbdccdacdcdbadcccacacaccdddbbcdddacabaabbdbcbbbbdbabcddacbdaadccacadacaaaccbbabaaadbdacdddaccdcdcaadcaadcccacdcadbbaabdddccbbabbadacbdbcadbcabdbdbcddcccadcddbcbcabbdbddabacdacadbbaddcbacbbbdcbdcbaaadcddcdbdccbbcadacacacabdbaddbcacdacaaabbabbcbcbadddbbcdbdadbcacaaaaaddcdbadbcaddaddacdabdccddaaacacacbaddacabaaddaacbcabbadbdbaaddcdbcaaaadddcdcadaaaddaccabdcacbabaabdcdbdacaabacbacdaddcbabcbacbabdcddcbdaacdddaddbbbaaababcdbdaccbbcadcbbbaddbaadddbcbdaacabaddcddcacdcccdcbadcddcdccbcdadcdcbdbddcbcabacbadccbdabacdaadbdcbdccbaccdadddabbdadacbabcbcabcadcababbcadabbcbbabddcddcadcddcadccacbcbabbabbbaacbacbdcbcddadaadadbddccbaabbcddcadcbbdbbdcdbbaaadccdbabdcacbadcabdadcacdaddaabdadbcdcbbadaadcbbcbadbcbbcdccbbccbdbcbddccbaccaadcacbcbadcbbcbcaabdddbcdbcabacaccbcdadcadbadacdcbaadcddbcccccddaddcacbbadcadcdaddccbcdcdadbcdadcbdabbbcbdcddabcdccbdbcdcbcacbaabcdaabacddbcdabbaabccaccdbdbcbccbadbcdcbcbcaaabbdcdcacddabdaaabdbadcddadddccaaccdcadbbcbcbaaccbddadcaaccdddcddacbabbacddddbdbaabcadbcbbcbdcacabbccbdbdcccdacabcbdcbcddccaacccdaaabbdcaaccabbcccccdaaddabaddcbdbccaadcabcbdcaccdccbbdbbcbbdccadcbdcdcbccdaddacbaaacddcccdadaccadbbccaaadadabadddddddbcaaaddaacabbdbddcbbabacddaadbcdccdbcbcdaabcccdaccadccdcccbcbbcdaccbbaaadcaaaacaabdbacabcdddadccddcaadaaddcbdabbccdcbdbcdbddcbcdabdccbbbdccbbcbcbbdacbbccbdcacddbbbdbccadbdcbadbddacdbbadcdddbaaaaacdadbddbbddadddcdaccddbdacddadbccdcdaadcddcbccbdcbbdcbbadccbbdcaacaabadadbbbaadbbcdcdcdaddbabdbadbdababdcdddbadadcbaacbccbaaadcdbcbbbcddbdabbadbbcbcadcccddbdddcdccdaaabcbdbadaccbcdacbcbbcabddacacbaadabacacddcccbdbababdcccdaaddabdccdbbcbbdaabdddadddcabcbbbccdccbbbabbabbbabacacddbccdbcbccdcacaaaabacdddcaabdabbadcdccbbaababbbbcbdbaddcdcabccdcccdcbaadadbbbacbbabcddbccccaaaadaadcaabddddcadbacbbbdcacbadccccadbdcdbaaddccabadbbcbccdbbccdcccaddddabdcbdadbacccbdbaddcdacdadabdbcdcaccaabbcdbadbcdcbdccbcdbbdddccdbbddabbbbbaaddbcadadbdabdbddcbbacaccddbaccdbccaadcdacbcbacaccdcbcbddccbdddadbbbdbbddbccbacbcbdabbdbdabdabacddadbdadaacbbbbabccbbbcabdccaaadbcaabcbacdcdbdadacaccbbcbabbdcdbdbaadbaabbabdcccddabcbbbcabbcabbcbaadcbbbcadcddddbabdcdbaabddbabcadddcdddcbaabdbddaccdcbaadcdaadbaacbcaadcbcdddcacccdbabbdcdbaddbcbdaccbdbabddbbdadcdadcbaddcdabcaddcaaccdddbbdacccdbbbaaadbdcbabcabadaccabbaadadabcccabcabaddddbcbbaccabdcacbbdabcdcbbbadcacbcbadbbbdacccbdacacdaaabcabcbdbabcdacaddaabcbacadcbcddbacbcdaaabbaaacadaadbdcabcbdbbdbbacabcbdcdbccaababbccaacadacdbbabbbcddbdbbddddbabbaabccbcabaaacdbacdbdcbbababcadccaccaddacabadbcaabcddcaaaaabcadcadbdabddadaacdacdbcbdaadacdaabccaabdbdddbdbdbdaacaababaacbaadcaabdbbabcdcaabaadadbbacadaabdcddbdccacabbccdcdcdccbbabdccadacbcdadaadacbcaccdaabdaadddaadbdbcbbbaaddbdaabbccbdcbbaaadcabcaccccbabacbbbbaacbaabcddcbcdabacabaabcabcccbcdbacbdccaaadadabddbabdcbbcdadbcbcbcdccbddbabdbcbbccdbbccacbbdbdaadbdccddbcbcdccaaacdccddbbacdbcadbabdaabbdbcddcacdadddaabddcbabbcbdcdabcdbcbdbadcadbccbcaccdcdbacdbcbbccbacbcbdbaabdbbcadaacbcddaddddbbabbdcdcacbbcdabaaabdbdbccababbbddbdbcbdccdacaaabaacbbcbdccdaadcabbdbbbdaadbcbbdcacdcacbaabbdcddaccbabcbbabcaddbdbcabdddacbbcddbddddbabaddcddabbdbdcacacdbdababbbaaadcdbacaddddacddbabbabbbaaaacabaaaabcacaadcadbbbcbdbcabcbcccbcddcbbdcabcabdddcbbbcbbbcbdccbaabdcdbacddadcbbdcabbcbcbabbcaabdbdbbcdccbbbbdbcdbabcbddbadcabcbcadcaacaccaabccadcbcbadbdacdccbcbbdccbabbcbcccbbcbdcadbcaccbcbcdabccabbdbaddacabbdabbbccbcbcddacdadbbdaaccabcabcaaccbaddbddbcabcadcadadabdcdcdbaccacabcccccdbbdcbcdccbddddcbcdbbaadabbdadcbaccbdaaddbbabaddbabaadbdadbbbbabccdadddadbddddcbbacbaadbdbdddaadcaabdbacacddcbadbbabbcaadcabbccddbddaccbdabdaacaadaccdabbcccbadbdbaddbbdadddcbbabcbcabbadcbcaccdbbabaaabdbdcaadccdadbcdacdccbbadcacbaacdccabbcaabddbccdcbcccddbcbcdbabcdabdbcbdaacdabcddcbbdacbcdaabbabbaaaabcdccddcacdadadcddaddbabcacdacbbbabdadbcababcdcbccabbcadcbaabdbcdbddcdbadadbacaccaaddabdacddaaaacddaccacdcabcbcabcbccacdcddcaabbaddcdcdcbdbacbacddcabaacadadabcddddaababbbbcccbcacbdcaaadcbcdacbddbacdcbaacbadbccaddbbbbbcdcdacbaaddabadbbcdbbabccbddbbababdbdadddacabacccdcdabbdcaacaaccbdcccdaccabdddcaabbbbdcbdabaccccaaacaabaddcdbcdcacaccbacbbbdaaacaadbaadccbadcdddaacbcabbdccdbcacbddaddbadacbccaccabdacdbacbbbcbcdbcdcdbdadaccdcddabbccaacbadcdcddadcbdcdcadbdcdccbbdbcdadbadabbbacdbcabdbcddcbaacdbdacdbcbbcaccbbadbdddabdbacbdcccddbcdcdaddddbcdaccdcdbbbcbddacdadbcdcbcbdaaddbdaabdaaabdadbabcdbbdbbdccaaabbcadadadadbbdcdaadcbbcaadcdabaaabcabccaabbbdabdddadbadabcaadcbabadbaabbabaadcdadbacbbbbbcbccaddbaddcdacaabaabccdccbcdcdccbccdccaabccdbdbadbbdccacdbbcbabccaadaddccabcddacddabdacdcbaddcdaddabbbaccaaaadadcbcabdddadaacbcadadcdaddddccbdddcbaddbdcddaaddbbaaaaadcaacdbcdbadbcbbdbbccaaacacdadbbcccdccdaccbccdbcbcdbcabaddbcacddcdbbaccdddccbddadbcdaaadacdacccabacbbadcbcdcadbcadbdcdbcadcbddcabaabbbbbcbdddcccbbaaabdaddbdddcbddadbacaaddcbddacaaabadccbaadbacdbdaacbccdbccddcdbcdbbdcdddabcbddbbdcadccbddaaccdbcaabcaddbdcabcdccdacbbaabadccbdcccbbcbdddddcadccdadabbdaabacbcbaaaacdabacaaaaabcbabaabcdbcaaacbbbbcbbaaabcccacbcadbcdcbcccbbcbcbcbcabdaacdcdbccccddcbbcbacaccacabbbccbdcdddabddcadaccaaaddbbcadcdaadaadbdaccacaaddbcbddcddbbcbcbaddbcbadcdbacbdabacbbacdbccadabdaccacccdcbaadbbdcadbdcaabbdcbbdbccccdaddabcbabbbbcbbcddbdaabacadcacadddcdadbbdddcadbacbddcbcbddcbbaaccbbacaacddbaaaddbabcabcbcdbcaacbdcacdcbaabccbbbdadddadbbbaadddccbadbddcdabdbadaccbcdbdadccabaacdcaaccbadcdbdcddaabbdaccccdcbbbbcabbbdacaddbaabbaadbcbccdbadabccbbdcbdbbbadbacbcdacabdaaacccbbacacbbbcdacbccbbcaccabcbccacbdcdacdbbbcbcbaababdadaacaccacadabbbbaddcbaacbbdddbbcaaddbdadcadbdbbacddabcaaaddaadaddaaccbbcabcdbdaddbddadbbddbcdccbcddbbddadabdbaddbacdddbbcaadcacabcddbaadabbdbbbbddbbaaccdcccadaadcaaacaadbbcabdcbbacdbbadabbaabcdbbcbccbcccdbacddbbbabcdabdacaabbadccabcbcccbbacbccaacbdcbcdbdbdacacaaadbbdcdaddacaddcccacdddccadbdcdacbddbdbaddbdbdbbcdaacdbcbacdabbaccdabcdbabdddabcdddaabdccaddcbcabdcacdbdcbcbcdcdbbbaabbbbcbcdcbabcbbabcbdabbaacbbbdabcaaaccccbcaaabbdcddbbbaaababcbddbdadcabbabaaababcabaaadbdccdaddcabbbaadcbdadcdbaabbaccdddbabccbabaadaaabcbcdbcbbbbcddddccdbadbcdcccabcbacbacacbbabcbdacbbbbcababcbdabbadacdcbdaddbbbccccbcddccacaaadbdcbdbcbdcabacbcbbccbbaccdaaabadddbdabbcdaccbbbcadccabdbcbcacdbbbabdabdaacaaaccaacadcabdadbdabdcaaaaccdadddacaadcbdccdddacbcdbbcabdcdbddaaabbddcbddcabddabcccdcbddccdababcdacabdacacaddbbbdddacdbabcbbbbbbabaaabbbbddacccbaadcbcaabdaaacdcdabdabaccbddabcbbaaacdacbdabddcabaadcbaacddccbabcdacbadcccbccbbbbadbdacdcccdaaabbbbdabcaddadbbdddcccdbddbabccdcbccddbbbacdddcdcddbabddccabbdabdaccabdacddbbbdddbdbcdcdddbdcabcacaabcabbdbcaaaaadabbcbbcabdabbabbadabbacabddbddbbdcbbcbdbbcaadddabcbadddaacccdccdacabacbddbaccddaaabaccbcaddbadcacbbdcbcbbdabddcaddbdcbabcacdabcaabcaadcbadaaddabadccddbcddababccdbbcdadaadcbcaccbbabdcdadabcdadacadccccabacacacbcabcadcbbdabcadcccdddaacadbdcdaaacbbabbcadbbcbdbdaccacbddbacadacaddacbcbcbcaacdabbcccbddacddabbbaccabdbcbcaaaacdbbaddaaacddabbbcbbabadbbdbdacabdabcddaddabcadbdadcaaddcbcabbdddddbccaabdbdccabdbdbcabbcbccbadcdcaddbcbdcaadaaabcdbdbadcabaabbdbadcdaabdaabbdccabbbbaaaaaacbbdccbbaaddbbcabaadaaccccbcaabdcbdbacdbcabaabcbcadbcaaadcdbbdbacdacccaaaaacbaccdddaaabcbcbaddcdcacbdcddcdacddbbabaddcbadddcaccdbdbcbaccdbcccabcabbabddacadadcdbbcaddcadaccbccdbacdacbdacddcabdadbaacdcbadcaadcadbdcaadbcdadcbdbabbbaadacdbdbacbdbbbbdadabdcabcdbbcacddcbdaaccaadadbcaadabbadcdaddcdabcadcdcbadddbcccbdaccdaacdabbcacbdaacabcbaddbaccdaabbdbcccbaadabcddaababcbadaaccadcbabacddbaaacabdcacbcacbbdaccacddcddbbbaaddcbbcabdaabdcdcdacbbddcacdaabbabdbdaddaacaabbbddcaadcccbdddadadabddcbbbdaacbcddccddbdacdbddadadbbcdcbbcbbbbbbaadabbdbbbcabbccacbbccbccaabcbcbdcbcbbadadcaabbabcbadabbabbaabdccbacacccdccadccbcdcbdbdbcbdbacaccabbbddcdbbbcdaccabdaaaadaaaabbbbcddcdcdbbbdaccdcdacadcdccccbabccbbcbcbddccbcccbcaccbcadbbccddadcbacccacccadcabaaadaaadbcbddcbbcdaabcdabaabdaccaaadddbdabbacbdccbaabdbabdadabdddbacacdddbdaaaaabdcccdcabbabbcbdbadccbbcdcabbdcacbadbcbdcddddbccadcbadbcdbdabbdacbcdcdbdadcccbcacacddbbdbbcdacacbbdbbcabcdabcbdbbdacdbaaddaabaaccabaaaacbdbcdbbcbdccbddbdcaacaccdaaaccaddcbcbbdcabbcabcccdddccabcaddcadbaaacdddacdcddbdcdacadcbbbcaacaddcdcdddbdcadcabadcacaadabcbbdbcadcbdadbaabdadbaaaadacdaabdacccacadcdbdccccadcbdbadadbadbaaddcbdaadbccdaaaccdcdbcbaacbaabacbdacdbbaacbdcddaaccccdcbcacdbdbacccdbbdbbbaadbddabddddbbbaabdcbaaabcdadcacadbbadabdbbaacbbbbbdbbbddcadacccaabaacccbabcaccbaabaaccbcbbbcdcdbbdbbddadbbddaabcdabdcdbccdcabdccbadccbabaaabbccbaddbaabaacccdbadaddbdcbdbccbaccaddacddbbcdcabcdcaabaabbcadbcdcaacdbbdbbadbabdcadccaaddbcbbbdacdbdbcbbddcbcadddcacadbabadccaddaabcbabdadadbcbcbbabbdaddccabdbcbcbbdcabdcbddcaddccdbacbcabccdddccdbccacaababadabcdadbddcbdbaaaabccbadaadadabcbdbabcdbdacccdccdabbdbdbaccbbdaaaacbdadbbabcdcacbbbbbbaadbacacdcacdbaacdcbbdcacaacbbacdacddddaabadcbdbcddabdbbbcbddbcbababbdabddcaddccbccdaabdababcbbbabcbabdcddbabcaccaacdababccacbadbdcaacbcdbcababbbcdddcbbabaabbbbbdcbddacbabadbcdddcbbacccbdddccabcabbacbcddbcdddcadcadcaabacacadcaadcdccccbaddadacbdcbdabddccbcadbbadadadcadccacbcaccabbabaccabbbbdddcddcacabdcbcddcdaadcdddbcddcbabcadadcaabacdddabdbcdababccbcacdcdacbadcdcbaaaaccdaacccacacdadadabbcabbdbbacddbdaabcdddbbbbdbdbacaccddacbabdadbcacddcabdaadcccacaaadaddddaabaaaabdadbabaadcdbdcaccbdccccaaabdbdddaabcbaddbbbdacdaacdadbdabcccddadaaaccbddcdcdadacdbacbdaaadacdcaabcbddbdacbcaacabdcdccdddcaabaaabaadbbbcdccaabcaddadadcaddbacccccbbcbdddbbababaaccbcccaaccdcbbcdcccdaadcbcbacddbbbaacdbadbdbbbacbcacdcbdbadccccddcadbadccdadcddccacbbdbabdbbbcdadaacaaddbbcabcbdabbabdcbacddaaadddcdaacddcbacaaacbabdbdaacaccdbbacdbbcdbdcbcdbdbabababdadcadbaccaadbcacbaabcdcbadcbbccddbdaabdabdbadabbdaccbabdabbbdcbabdddddabbcdbacaddaadcdcdcadcadcacbbabbbbbdadbacccddccdbcaaadcddcbabadacadaabbcbddbadaaddaaaccadcccbddcbbdbbddcdabbbdcdcabbcdcccabdcbddddbcdbbdaddbbddcdbdcaccdccbcdcadccbdbcccdcbdcdadaabddadcbabacccdddbdbccadccadaccbabadacaaaccddcbddabccdaaccbcbadaccbdbbccabacdbdacabcadbbdccbcbddcbcaaddaabbcbccbccbabdcddcaabdacbdcbcadcccdccccaadaddcacdbcddbccbabacadddbaabcdbddcbddccbbbcadbdcdbcaacbdbadcbbabadbbdbccdcccddbcaaccacdbabacadbbdccbabcdabbaacbdccbbabdbaabcaddaccacdbbbbacbadddccddbaddbadbcdbbcbbddccabbaaaadbadbddbbbbcaddbabaccbcddbdbcaabbbcabadccdcabbdaddbacccaaaabbadbccdbdaadcbadcacabaddddbbbbbbccbabcbddcacacacabccbcaabcdbadcacbbcccdcaadbabdaddbabddcbbdabaaccbbcadabdbabcdbdabcacbccdabdcbdbaaccdbadcdcacbcbbcbdadaaccdaddaaddaabaadabdbcdcabdabdbaddcbdcdddaaddbadcaadddbdddbadcddacaabadbcaabdcdaaadddbaabaacaccdbaaacdabcccaaddabdacdbadbabbcbdcadcadcabbdcdcdbdadabbadcadadcbdbbbbaddadcabccbaccbbbadcccaacbdcbdddbdabbabbbabcdabdbabbaacddabddadaacaccacdbccbabdabdcbdaccdacdacdacdcacddaccadcabbdcbdbcbdcbaccacbcddcbdcacacbdcdabbaadcdacadcbabbbddcbdabbabbdcbdbbadcaaaadbaabcdaaabdbdcacccddadcdcdcccdddadbbbccccbcadcdbbacdcbbccbabbcccddabbcdadbbcccbdcabcddcbddccacacaabcacbcabadddadcbbaacbdbccccabaacaabcbabcbaabcdaaaccbcbbdddaddabacbdaddcddcbaaddbdadbaacabcddaccddabcdabbdcddcbbccccbacdaaacadbbcadcaccdccbbdabbdbabacbadcbdcbdcdaaaacbcabddbaaacaabcabcaacacddccabbacadcdbddacdbbaccdbdabbdbbbbbddbbbaccbccbcabaaaddcddcdbdbdaccdabcdddccccbadddccaddaddbbabacccdbddccccbbcdbaaccddcbccbcccbabcadbaabddcccbadbcadacddaaadcccccaabcaabdcdabcdadbcbdabddcdbacdaaccbcaaacbaddcccddabddbbdcbcadddacabacbcaababacaacdcabbaacbaddadbbdbdcadbcbbdccccbabcaadcccbbddccbbaaabccccacabccaccdabbabaccbbbaabbbdbbacacbcaccdbcbbadbbdcccddacdcbcbcacbbccdccccaddbccbdcdcadccadbacdabdddddadcaacccadbdcddbcaadbbaccbaaaaadbbddaaaaacbdcbbcadaadbdaadbcddaccbbacaacbcdbccddbdadcaadcccabaacadddccdcbcbbcadabcaabccdaadacdadcdbccdbcbcadabacdcabcdadababadbaabbbacabdabcbdbbddbacdabccabdbdcabdadabcbccddcdbbbbcdcdbbabdacadcdacabbbaaccdadbdbcdacdabcbcdaaabbadcabbacdcbadbdbddbbaddbbbcbdabdaaccbadaddaaaacdbcbadccdbabdabaccbaababaacaabbadddcabcbbaccdadaacddbadcaddbdbdbbccaabcadacdbddaadbcbaccbcbccbaaaabbccadcbdddcaccbbbdacacdacdaaacbbacbdddddaddccbdcabbdbbbacbcbcbdbbbbddadabbcabdcdabcbbacaaccdababdcbdabacdcabccadcccdbbbbcaadcdddbcdddddbcbdcccdcdabbdddacbccaccdadacacacdcbacaaacbccccaabdbdcdacbbcccccdacabccddcddbdbbbacdaadbddbcbdbacabaddddcdaaabcaddadcbcbcaacaaaabbdaddaabbaccdadabaddaaaadaadbbdabcdbcdbdacdbbbdccdccabdcbbacdcaaadcabbacdcdaaacbbacddddbdacdacacadadbadcbdcabbababaaacaabadaddddccccacbcdabacccdcdcdbbbcbaabadcddacbaadddabadccbcbadacdabadadccbcabdbbbdbdccaabcadddbbdabddbbcacbdacbddacadbdaabadbbadbbadaccadadccbbccbbadabdcbcabcabdddaabdcdaadddacdbcbcdcccbabadadcdbbbdcdbacbdbcacdacbcdcbdaababadadabcdbadaabdcaddcbdbabbbabcdcbdbabdbaccbcabdadcbbaacbadbcbddbdaabcaddcaccccbddbadbbbccccdcbadbaccadbdcadbcddbaddbbbacddcbdbbacbcdddbcbdbccbdbcaacbbbccacaaddcadcbcbabdbdaabbdbcbdddbbcbbdcccbaccabddcaabbbbcabbadddcccbbccdbbacbababaabbabaabdbdccaadcccadcdaaddbdaadadbacdbbcccdbadabbcccdcadcccdaacaadbacbcccaaddadbccbcdcdbcbbddbaddabccbabbccddbaccdbdcdacbababcaddadadaaaddbbdcaaadcddadaacaadddbadbbabcacaddbacdbcaaaccdcbddbabcdadbacddddcdddccdbbcbcdbcbbdcabaabdabbbacbaddddadabdacadcaaaccaddbddcddcbaccbcdcbdadbabbaabcadcbcadaaccacdcabbbccabcdccdbcbaadcbbbcaddadadadcabcabadbabcdcdbabbabaaccaddcbcbdbacbcbbdcccabdbbbbdbbcadbbbdbcddabdbadbaddaaacbbcacccbabaccabacabdcdcddabbdbdddadddcadadccbdbadbddcddabbbabbddbdaacacadbbbbadacddbddbcabbdddccdadabdbbacabbaababdbadccccaaaacdcabcbddbcdcdbcaacdadadaadabccccbddbcdacbbbcddccacdcddabcdcabdcdccbcdacadadcaddcccdabbddadcbcbbddadbccdcababcadcbcbaabcacdacbacddaacabacbbdabcdcdabaddbcddcddcaaabcccadabbdbccacadbadbabcdadbacbbcadbddadaaacababbccdbcacbbaccdaabdabaacaadcbaabbdadcdbbcccccdbccadcdddcbbdbaaadadbcabccdbaccbaabbcbbbbacacadcaccdcabadbcadbacbbcabacccacddabbcdadddbaaaabaaaccbdccdaabacbbbbdaacdbbddddbcacddaabcbdacadbababddbaabbcabddddbbbbcaaaacbacbbadddcacbdcdbcacaacdbbbadbbdbdbdddddcdaaaaabacbbabadcadcccadccbddacdddcadcccdacdbcdabccaabacdcbabcadccccacbdabbcaabcbcbadbcadbaccbbacdaaadcacdaaccdcccccccddbababdcbccaacbcacddcccccaaaacacbdbbbdaadddcaabaaacadcccdcdcaadcbbbaabdabdcccacbcdbdbcaacabbdcdaacccddacddbbbbcaddcacacdadcabacbbacdadabbbcdbbcacdbcadaccccdbcddbdacaacdadcaaadccbdcddbbdbaacdccdbcdbdadcbbbdabbbcdbbccacbcadccbcacbaccdbdbaadcccdddbacddcdabcbdddccbbaadddacdabcbdacaacdcdaddbaadadacacccbbbdcdadddbacbcdbdbacaabcaaabcdabdccccaacdabcdbacdcbcadacbccadccdcaccbcbcbadabadbbacbdbaacbbcbbcadacccbabaaaababacaaadaddbbabaadcaabcadaaaddbddbcdaabddaabcccdbdcdabdbababcccabbcbabacacbbbdbacbdbdacdbcdcccbddccadccdacbbabdccaabcbacacdcccabbabadbabbdbcddacbbddbbcbacdaddbbcadaccbbadcbbcaaabdabaaccdcbbdbacdbbbbaadbcadabacbabcdaaabbaacaccdadacdccacbcabaacdbbbadbddadbcacaaddbddabacaddbddcdabbcabcaabddaacddbaacbdbadbdabdacbacccaccabcbaaadcdbaadbccaddbbddacbbbdacbcbdcbbcbbcbbcbaacdacbadccccdacbdadccabdcccdbbcaabcdbaddcbcdaaaaccaddadaabcbcaddcaadabacccbbddabbcadbbcdbccdccbcddcbdcbdbbdacccdacbdbaddacbdaccabbabacbadcbbccdbcdcdadcddcacbbbabdcbdccbacdadcacbdbaacbbcbcccadbacdbabdaacbadcbbcdbcaaaaacdaabadaacaacdacddbdabcabdadbcbbcabdcaadcdaabaaadbaddabacacdbadcdbbccccaddddaaccbcdccddadbadcaccadddccdbcaabcbbaddbabcbddbdacbbcddabaacbbaacbdbdadccdcbbdacbabbadaaadddcbbcbbadbcaaaadbbcddaadbbdaccbbbadacacdbcdbdadccacdbcdaacaadccbddbbdbbaadadcacdbbcdaaabbbabcaccddcbdcdaadbdabdcdaadadbdbadcaaaacaaaabcaccdacbadddccdacbcccaddbbccdaabdccbdacdaaabdbadcdabaacdaadacdcaccbdadcabcacbbcdaadcbdbdacbcdacccbababbaabccbbdacaaabdccaacccccbcdcbddadccadacbabcddcbcaadaabdddbbdabdacdcadcbcbdddddcabddaacbaadbdbdbbdccbaabcaacbadbbbdbdacbbbdbbbccccbadbdcabdcdcabadbdbacbabbaccddcbaaccaaddaccabbbcadabadcaabdcccabbdccdddbdabddbacdcdccadbddccbcaadbdcaddcabadabbbabcacaabdcadadcababdbdcaccbaaddccaaadccdbbbaabccddbddbbbbbbbbbadabdbcbdddaacddbbcaaabaadbcdbddadbbdbcbbdacdaaabadbbdabbdbbcbdbddcbcabaaccaabcdbbbbbbbccaddadcbdadaaaacbdddcddcbddbaadcbdaddcbcabcccddddadcbcbbccdbaaccdabdcbccdddcdcdcbaadbbabccbdcadadabdacaacdabcbbbacdadacdddcaacbdcdcbbbbddcdbccaddcddbadadcbdacacaabdcddcdccaacbbdcdbaaacadcbbbcaacddccbdcbacccdcaaccdbbabbcddddccdcacacbbaadacbdacbcaadcbdcccbdcdbdddbcadadadccbdacddddcadbcbccadadccddaddddaaacdaabcacddcdbcbaabcbcdcbadcdcadaaddbbabcacbbcacbaadcacddbacdbdadbcaddcdbdabdbbaddccadacbddccadadcdcccabbcacbcbbcbccaaaabddcbbabcacaddccddddbaabadbcdbabcdddcdadbbacccccbdddbdbdadcaaababdcdcaddcacabcdbbabdbaaadaacabaababccdbdcbadcdcccbaabcbdaadbcbbcdadbaccbabdadcbbbacddacddcacbcdddaaaaaddcdcbcbaaacaaddbabcbdaaddbbabaacdbdcdaddcacabbcbbccdccdbadaccabcddaabcacbddcdbdaacadbabcbddcadcacaccbcaaacbacdbbcdcccaacdccbbccacbabbbbcdcbabbadcdccabbbdcaacbbbccdaaadabababbbbadbdddbddaacaacacadbaabdcacdbcabbdacabbdaaabaccdabdbbdadbadabcbdcbcbdaaaacabcabadccdcadabcdabababdcadaaccccbdaddadbdddddddbadadbdbcbcbadadddcbbaccdabdcdcdbabbcdcdccbbcccacacabacacacbbabcbbbbbbaabddddcbbdadbcacddcadaddcdcbdbcccddcaabdacacadcddbbddcbcadaacdbddddcbbdbccaaabdbbabbdbbdabcbacdcaacacdcdbcbdaabddbdcbaccababcbdbadddcdbdabbcbcacabdccbcdddccccdacdccbaddbaccccbacdadddabcddbabdadbaccbccbabaacbbbacadccdbcbadbbbcbdabccdbdddaddccaacbbdadbdadbdadaabacacababaabdbbaacbbdcacbcdabbabadbbbbddbabadddccbdbcddabbbaadbbcbbbdabdabcccabadccdadbaaabcdababbbccddcacddcdabbddcabacacabcdcbbaacdaadbbcccddacadbdbbdcbdbcadbdabcbccbadbbbbadddadbddbdccbcdabccabdadaaddadacaaddbdcbaddcacdcdadadbccbaddaabcdadddcaddbaadcbbbadddaaddbcadadbcbddaaaccbcddbccbaaadcadddcbabbbadadabcddababadabbaabbddaddbacccacabdaddcdbadacbadcbbddabcbcabcdddcccabcaabacddcbcdadbccdcbdddbbabcdcdbbbdcabbbdbbbbbcbaddcadcdcbcdabacaadbaadddbbcadddcbaddaaadbcbcdcccbbcbdaadbdcabdaadbcddcdaccaadbdbcbabdccbddbbdcdbcdbdbacdbaaadcddaddacbbbcccabadcbbabaadbbcdbdbacdcadabaddacbdddaadaccddcdadcacdaaaccadacdabccabcccbddaccbccdbadbbdcaadaccbddcbddbccdbdccaccbbdddaccdcabbcdbcbbcbcdadcabaabccbcadcccbcddacaddbcdcabaabbdabdbdbcadabacddccbcdabdccdcabcdaadbacbacdcdccaabacccdcdcaadaacaaabdbaaccdaaacddbccabacdbadcdaaacbabbbbbcacdadacabcdbacadcdcbacbbdcabbbbdccdcdcbdcababacacacddbadbdaaddabcbbccccaddccbdaadccbbcbbaaddbabddacacabcdcacdcacadaaccbadaacbbdadddcbcabbaacaabbaccdcbacdacbdccbaccadbdacadcbcaabbacdbacbddccadbbbbbabdbccdcabcabdbddabdacbcacaccaacaacaadbacbcaadabdccbadcddbcbabadcadbdbbcacbccccaccbdcdadbabddbdccdcbbcdbccbacaddbbaabadabcbccaaddcbaddaccdacdacdbadacabababbabaabbccdbbcaabaaddacccacbdaccabdbbadaaaacadcadacdcbcaabacbddcbadbdacacbaabaaddccbacdddcccdccbaadbdabdcbacdacbccdddbdbcdabaddabbadcadcddbcaabaaabcbacbdbcadacbadbddbcbabbbdddcdbbdacaababaddadbddcddbabdaabdbccacacccaaacaddabcbabbcdaaddacddbdbddaababdbdddadcbcadbccddbddabdddcccccaadbacbadbacdadcdaabcdbbadcdcdaaadcdcbbddbcdaaaabbdcdbbadbbabdbddbbcbcbbaccbbddaddcdcaadddcbbaaacbbcbddcdcbccdcacccbbadadcdddddbabbccbddacccaaaabbadaaddcadcbbbcdcadbadcadacdddbcacbcdbbccdcbbddabcdbcbcbcdaacbdcadcadaaacabaadbaddaabadbcdbdcddababdddadabdbdabacdcdacbabcbaabcbbbdbdbdaddabdbbaabdababbdbccacbbdbddbbaabbcabcccdabcadaadddccdaacdcbaadddbcdcbdacadbdcccdbbbbccbbddbacbbdaababcadbdcdddcabaacabbcbabbccacdacabaabcbaacaadddbabbcbaadbcbaababbdccccbbbcbcabdddbbaaaaadcaadcddcbdabdabcacccbabbcbccdcabcadbcdcdcdacdcdccddaddbabdaadacbcabadbdacdcdcdbcaabbbcdaaadbdcbdaddbbadabbcadadcdcddcbdcccdbcabbdcdadcbccbadaadcbabdcdddcdabbdabdcdcbbbdaddabbcaabadbbdddaddcdaddaccbbadaabccdcbdccdadbcbdbcccabaaddcbccaacccbcacaaaacbadbaaaaadbabadcacabbbddbdcbcddacadbaacddcdcbbccbcdcbbbbbcbcbcdcabadccdccccaabdcbdcaddbcdcabdbbbbabdbaabdddbbabdabaaabddddaabdbbdabcabccdddcbbbdaabcabcabacacadccdcabacacbdacccaacabdbdcdcdcccbbbbabbdcbbabdcbbaccbadabdccccdadadaccccccbdccabcbccbbdbbbbdacbdddcddcccdacccaccacabaadcccbcdbbcddcbdcaacbcbbddbbbadcbbdbdadcbbbccbdbacadacacbbcbaacbcabacacdabadbdddbbbdbacdbbddddbcdbaddabbbcdddbbbcddaaabadbcccbabcbacbaaccbcddadccacbcdccbdbacddabbcbabaaadabdbbcccadcbcbccacababbcdcbaacaabddcccdadbbbaccabcdabbdbbacdcdacbccaddaadadacbabbacaaabacdadbbbbabbadddbddcabaccddbbcdcaabcabaadaddccbababaaacadaaabcaabadcccababbddddbdcccbaadcdbccabbdaabadcaabaaacabdbacacbbbbbccbbdcbbbdbdacadadbdbccacdccddaaaadbcdbbacaaacabacbcbcdbbddcbdbcaccacccabcadbdacdbacacbbdadccacacbbabadcbcbabdbcddaddcbadbbbccaadbaaaadccacabdccadcbbabccdbacbaaacbcdbabaaddddadcbdbabaadccabcbdccaadacccbdcddaaaccaadddaccaacdbacbbababbaccdcbbdbbcdddbabbbcdabacbbdcccdccabdbababccbdcadabcaddacbdbdadbadcadcaddcdcabbccdcddcdbcdbbbbcbacbbdcdadadbadcdcacddacbcbcabdbcbaabbcbcabdcbaacacdddabcdbdddccacbbdaddaaddbddabbddddbabcaacdbbdbabbaabacccddcbbcabdacbcabdabbdbdddccbbbdbcdddcadbcaacdbccbbddadadcabbcbaaabacdccbaabbacdabdacbbaabadcbdbdabccccccdbbaabcbaaccabcbbbaaacddcdcacadddcdbaabcdabbdddcbbcccdabaaabdbcddccddccaaacccabccaacddaccadbdbcabadcbbaaaddbbaacadaababbadadbadaaccadbbdbbacbacbdbbdbcaabbadaadadadcadccdbaadadaaccdbdcabbcdcadacbabcdbccdbdcdabdabddacdccdbbdccccdcabcddacadabaccdbdaacadcddadbacbcdcdaccdbbcddaccdbdbacbccbddbbaccbbbbcdaccbbabccbbdbdbbdaccbdabcdaccddcddcdadbbbaddadbbdbcccddbaaadaaddacabadadabbcdacddcbadaabddbaccaadcdabaddcacbcddadcbadcbdcddadbabbcaaabcbaadbbaabbbdddcbbabcbaabacadacbbacaddaadacdbdaacadaadbcccbbbcbccbaccaaacbcddcbbdabdbbdbbccdcccbaadcdbdacdaccbdddccbcabcbbbadcbdbdcbaabadacaaacabbcacaabacbbbadaaadccbdacdaadddaddbdcdbabddadccbdcbcdaaaaaddacbcdbaacddbcdabbdcabdabdabacddbcacccbdbbaaccccbbcddccabdbabcaddcdbbadbccacbcadabcbcbabaadbcadddaacccccbddddbacdacdcdcddacaddcaccccadcdbabbdbdacddbbdadbdbdcdadddabbcccacdbcbcabcdbcaaaddbdddbdcdbdaddcbcadbcbabdadacbdcaaaadbcaaccddbaabcdbbaacdcdcadcbcaaaadbdacccbcaaacdadabadcbbaaaabcccccbaaaaacaacdbdddaadbadacadaddcbdcdbabadadaddbabdaaddddbcddbdacdbcabdccdadabbdddbbdbbcbaacbcbccaddadcacddaabadddaddcdcacacccdabddcddcababdbbbadbdbabcadbacadbabdbbacadbacdcaadbbddcadbcdbddacacadbaccdbbbbdbbcacadcabccbbcbcbcaaddccdbbbacccbdaaacdddddaccdbcdbbaddcacddbccbbbcababdaabbabccabcdaaabcaddbdcdccccdaaabdddcdadbcbaddbbaddbcbdcbdaabcddcbdbadddcdbdbbabcddabdcddbbddcdcdbcccadbccabcdbbdcadacabacaabdbdbdbccbdbbbbbccacddcacccddccbaccacddabcabaddcbdacdacaaabbbccccbdacaacbbaccaadaccbcbaaaaadaacabcaddddacdccadbcadadbcdbbabbddaadbbcabdddbaaddbacbccbcdbdddaabbccdaaccdbdccbdbcaacddbbcdbbdddccdacccabddaaddcdbccababdaccbaaddaadcadccabadbdbbacaccdabacabadcacbbddacdbddadaabadcacbddadcddacbcacdcbaacbcddbbaddababbdbccacaaacacbbdddbbcdbbdabbdadbdcaddaddbcbdbacbaaddcccbcaababdbccbdcadccbacbbbbaadbbcbdadcdaabdddadaaadcdacbbdacdadacacccbdbdbaacaacbabacccaaddccdccaabadaddddcdbbdbcccddbcabdcdbcdccdbdabcbccbdaaaaadddcabaabaccacaadccdbcbbacabccbaadcbaabdbdccddccdbadbaabbdddddccbbabbdbccadadacbcacaabbdbbcbaccaddadbcdaddbdbcabcbaabbacdaaaaabccdaacddadadabbdcadbcadbbabaabdbbbcaddacacdadddbcabadcacacacdcddccbddcbdbabdbddbbdadbbbadddddbcaccaacadcacaacbbacbbdaacbcbcabbbcdcacccacdddacdacccbdaacdbdabdbacadbdccaadbccdaabdcdcdcbbdacdcabbcdacdadbabaaabbabddaaccacbbdcbddabcbdccdbbbbbbdbcabaadbadcaabcadddcdbccacdcddacdddbcaaddbaddcccdbccdacccacbbcddcdcbcbccbcabbbdabadcabbabcdbdaddbcdbabaccddabdadddacbbcbcccbbdaaaaabaacdabddacadcccbcbdcaaaacbaccbcaddabccccddabdaacbaaadddcaccaaaaccdbdacaabcbcbddcccdbcdaabadacbcabaacdbdccbcddabbaaacbcbacadddcdbbbcadcdbdbdbbbbdcdbcbcccadccdbaabccdbbbcaccacabbbdbdcbbccdcadaaabdbccdbcaddbdcdadcabaccddbbdcdabccdadbbddbcdcbddcdaadbbcddddcaadbabccddababdaadabcccbabbcaabaccccccbabacccccddcdacbbaaabbbcdcabccdbcbbcbadaabbadaabbcddaddaaccddddaaabbbaadbbbccbadaccbbcdccbadadacdbcdabdbbaadbacabaacdbbabdcbbcabccbbcadbcdadabadcbdbbcbcbaaadbacacacccccccdadbacdbaaacbadddbccccaacdbcbcdbddccdabaadccbaadcacbbddabcbdaddccbcdbcdaccacbddcdbbbaddbabcbcbabdddacaacaadcbddaacdcdaabccbbbabccdacddccdcbabbccbcbccdbacccccadbdaaccdadbbbddcadacccbcbccaacbadcdcabcabacbbcabcbcdcadcaabccbabbbcabbcacabbdddbdddcbcbddabdacdccddabdbdcdbcacaddccdcccaadbdabbbdbadadababdaccddcbbbaddcadcdbacdaacaabbaabbccccbbabbcacbbcdcaaacbdcbbbabcabacdabddadccdaaddacaacbadadbbbbbadabdacbacdabdbcdddaccaccdabddbdbadaddccccbbdadabbacaddddcdaddaacccadaadcccaacbabcbacbddabcbbdbabbadcabccacadddacabdcbddbdabbddcdbddadbacbcacbbbdbaabaccaddabccdaaaabaabdcacbdacdaacdccdbbcdbbbcbdcaccbbbabaaabdbacbbabcbaabadaccdabddacbaadbcbccbccaaaaadcaabcdbccdadcabbcbcbbacdbacdbcbbdbcbdbdaadccbbbdbcdaacacdaccabbdadddccbccdddbdcbddcdcbaccdbcabaaabcdcbdccaddcabdcbabdbadcccadccbdabbaddcbddcdbddccbcbadcabbadbdadcdbbbadbcbacdbcdbbcbddaaabaadcdcbdaaddddaaaacaccccddbaacbccabdcccbabdccbbdccaaccdbacbaddcbaabbacbabbbabcccbdccbbccbadadcaadddcddbccbbbbbbbdcdabdabdbadbcdcadaadcaccbcddaabddabcddaacbabdcdcacabcdcddcdbcbdabaabdadabccaddbbddccdbbbcdaaddacbbadbdadacbcaacbadadddcbadcaddbdcaaacdabddcdcbbabcaaaaddaccbdbcbaadadcbccdabbdcdccacbdcbcdddcacbbbdcdacadacccdadbbabbdcddacdcdaaadcbbcaadadacddbacadaddbbababcbbaaabcccddababaaabdbdbcaddbbbdadcbdcaadcbbadbacdcdcabbacaacbacbcddbaacbadabdcadddbabadcdcbbbdcbcabbddcbaccaacbdccddccadddbccbcbcbcaacbacddbbbddcacdcbcbdbdbbcadcaaaaddbdabcddadbcaadacccadcdacbcaadccbcbcbcacbacccccbbdbcacbcdbcbadcdadccbcadcaccbdadccbacccdaacdcccbdbccabacbccbbabddcacdddbccbccbdcdcadaddcdcbccbdcadaddcaabaaacbcaccdcdacbabcbdcadddabcbddcdcdbddaaccccadacadbdbaddbddccdddbdccbbabdddaaccccaadcbcbcabdcbaaacdabccdbaabcbccbdbdddcaabbbaaacdbcbadaacacccbbabcdbcbcbaccdcdaaaccaddcdbdcddacddbcbcadadabaaddababbabbcadacbaddcadbabaddaadbdcbccdbbccdcacacccdacabddabdaabacdcbcbcaccccadcdddaaabaacaabdacaababdacbbdcdabcdddbccadcaacbddcdbbddcbbbabdadaaccbbabbaddcaddcdcbbbcabccacadabbdcdbaacdddddaddcabdadadcaacaaccacbdaacdaaaadddabbbbdbaccdaabbacadaaacbcccabacaaacbccdbadadabdbdadccacbbbbadcadaaddabaabcccaddacddaddbccccbcdcdcabcbdacbcdabbddcbaadbdcccbadaaadadbabccbcccabbcaddcdccacacabcaaddaaaabbacaabbaccbabdbddcdcbdaabdbadbdbdcbcbcadbbcabbdddacbdacbabadddddacccbcabaccabacacbadabadcbaababaaabccdbbdbdbcadbcdbadddbddacbaacbdbccdbadcddabddaaddaaabaaaaabadbbdabbdbadacdcaccbcdddbbaddbbbccdcdbaaccbcdbadadaccbabcdbdacccabadcadbdadadbdacbcbacaabdabaacbbaabdccbdaddccddddcbbcdbbadbdacaabcdcaacaabdcbbdabcccbcddbbdbaadcbacadcdacbbdccacbabbdbbacaabdacdbdcdbaddababcabdbddbdbcdacccdbbbdbbbbcacbdcbccbdcdbaabdbcddcadaadcaacbddcbaacaacacabdcacddbbddbaddbaabcdbaccbacdbcbddaaddbcddadbcaddaadadadcdbbccdbcddcacdcdccdcdbcacccabccbacbbddbddbbbabbbcdbcacaabbbabcbdbbddccabdbbdcbbdbabbcbdcbccdcccbdbbcaccaaaabaaabcdcabbadabddbbbdabcacbccddcbaaabddcccdccdacbdcdbccacdaccaddbddcbdcadddcbabcbaddddcdbacabbdccddadccacbabddbaddbddaaccadaacadacdbdcdddcbbddbdddaaccdbccdcdcbadcbdcaadcabbdddbbcddbcadcaaddacbacbdaaabddbcdcdccaadacdbddbccaddbaadadaaaaadcaaacacadabacbcdccdabdcddddbdcccbbaaabaacddcbdccadacbdddddaabcabaadcccdbacacaabcdaadadabaabdaaabaacbdbaabcdcddabccaabbcabbdccdcadbbadacbdddacadcccbaadacaaaadcddabcddadcbbbcdcadbaccbcdcdadadabaddbcacbdaddadddcccbabcbbbdbbcdbbbabbaacbbcdadadabbabbbababccdadbbbbcdbaababcbabaaadcddddabbcbacadadddabcaababcaccabccdbacbaacddccddaaacabcbbcdbcdbdadddddacdcdccbbbdaabacbbbdbaccdcdabddbbdcdbbdcabccadcccdccdaddbaadbaacbdaacbadcaaccddbcbdcacccdbcbabbabadaaabbcbbcbacdbcdabdabcaabdbdcdacaacbbbaabdbbdacbabccaacdcadbacbabcccaabccdcdcaccbabbccdbcddcbabdaaadacdbdddddcabddadbcabaacbcccbdadbadbcbdcbdccaaddcdbbcddddcbbdcdadcbdddcccdaadbdbbcbbbdbdcdaaaacbacaadbadcbdddaabaddbabdbcacadadccccddaddbbcbccaadcdbdcddbccdbcbbcdacbadaaaddbadbdddbadccaacacabbabdaaabdccabdbcdbdcbadcbbacccbbddddbcabdcdcdadadcadabacbacbcacbdbcbdcabacaddacbcbacaaabddcacaadbdddacbcdbccbbdadacabdabcbaaadccaadadbbadababaccbddcdabcdccdadaadadbbddabaadbdbbabcaaacdbcbccdcbdcdbdcccdccaaccaabdbabbbccbcaacadddadcbdabaabaacddadabdbbbbcdbccbadcabbbaaacadbddbddbdbdcabcdbddbbdbdbcdcbabaccadadcdcaaadcdddddccbadbddccbacacbbdcabbbbccabccabaaabdddaadcdcaacaaacaabdacaaadacddcbbaddabbbacdbdbbddaabacdaccbcadcaadbdcaccdcbadbbdccccdacbcbddacaabcddccdcddccdddbdcaddaabbbbcbdabbbaabdaaccdadcaaaaddddbcbccbcbcabbabadcbaccabadbdbacbacacddcadcbaacdbaacddbdaabaaddadcabbbdccbaaacbadabadabcbbccddaddcaddbdacdadacadacabcbbbdadccabadcbaaabacadddccababcccddbadbbddbbbdacabdbadbbbdcbcabdccccdcbccaaccaccdaaaaacbabadbbbdbacaabbcdcadccddacbdcddbdccadaabdcccbbcadccdbbdbbaacaccdbaaaabacdbddacccdbbabadaccaccbababadbbacacaacbbaddcdbdbaccaddcacacbcccccadbbdadbaccbdadddcdababbbacbdacaacdcdbdccaaccdcbacbbacaabcbcacaaddaccddbcbcbabdbdacbcdbdcddadaaabccdddcdcdcddacdccdddcbbacabadcaabcabcccabdabcdbdababcbdccccaaddadcdadcaaddaabbcccbddbbdaadbcacdbcbbcacdbdcdbdccdddcbadcaacadcdabbddabdacbdacccabbdcacdaacdccdaccacacbbcbabcaabbdbaaadbccdadbdcbdbabcaccacbdaddacbbdadcdbbcbbdaaaaddbccbdabdbacbddccdcbdbbcdaddcddbbdabacaacadadcbbbcdbbcabbbcadacabdcbdbbaaaddbadcaddaadacaaabbddcdddacaaccdcabaaddbdddbcabcbcdcaaccabdaccbbdcbdbadbacdcabccaacdbaabbccdcdaddbdbaccaacacdbddddddcdccbcbddcdacaccbbcbadbccdbddacbdcacdcbccbdaddcacaddcbbbbbddcdabdabdcdbcacdbbcbacbaaddcdcdddcaaacdcbbbcbcbbdabaaacbdabacbdbddbbaadabcddadcccbbdbbbacadabacadddcbbddaadddddbbdaacbcbcdcaadbabbbbaadccaddabcbddccccabcdadacbcdaddacccdacddbbcbcbcdccabcaadcbbdbaacbdddcddcadadcabadacabcbbbdcacdcacddaaabdcadaaddbcbdabacbcbabcddddddbccdadadddaaaaadbcdabbdbcddbbacaaacacabdbcdccddddbabacadabbcadaccddaddbccdbcbdbcdccacdbbbcbbdcdcacdabacbacddcddaaacbdcbbcabbadabddcdbdccaacdadbabadaccabcbcbcacabdbbdbbbbdbdcbbcbaccdacdccbbbbbdcdcbbabbdccacbbbdbdbacbcdcaacabaabacbdacdbcdabbdbdbdbcbbccacaadabbbbcacdabbccaaccbcbbcbccaddacccbaddaadaddabbdaadcacbcaaadbcbbdcadbacbaadbbaabaccbcddcbabdbdaaddaaccadbadbadcabddabbccddadccdccdbadbccdccdbdcbdaadacdbaadddadddbcbadccdbbcacccdcabddcdcaadabbbddbbbbaddaabbbdbbcbbaacdaadbcbdadcbbadaabacddcabdabcccadabdbbdddbadbcccdcbbbaabcbaabddcacddbbdcdccaaccddcdcbcdcbcdaadcbcbbbcdaacccbdccbbcbbddcccabbcbbacdacccccacdcacaccbbbccaadaabbabbbaaadddbbacadadbacbadddcbdadabbcbaccdcacacbddbabacbaddcadaccbadadcdaccabaacdaddcababdabdcdabbadbabdbbdbdabcbabcbcdbabbabcbbacacacdbdacaaddabcacbbcaacacadcbddcbabcbcccbacbacdbdabdacdccdddbabbbadcbaaaacbaaccccadabbcbdddcabaacccdcdabacaadbcbadcaadbdacbaabababdddcdbaaadaacbcbcbccacbacbccbaaadadadacaacdbbdaadddbaddbcadddbacbcacbaadabbdcdaadbccddbacaabbccdbdaacdddadadddcddbcbdcbbaacacaabbabbdccdddaaccacaddbacbbcdccbbabcadcbcdccbbadcbdbcbcbdbcdbcaabdbccccabcccdbdbddcacaabdcdbcdbdcddabdcdcdcadbaccbacdcbaddcdacbbdbcddcaadccdabdcdbacbaddaabcabdbbaccddbccbbacabdbaccacdbadaddaaddcdccbacbdaadcaddcdaadaabcaacbccdabdcbbbdcdcbababdabbcadabdabdbbcaaadaccbdbcddabaacbabcbdaccadacadbddacdbabccbbacbadaaddcdaccaccadcdcbcbdabcdbdddaadcdcadbbbbbcbabacaccabddddbacddabbababccbbabdcdbabcdabbcbbabaccbaacabccdcaacabbbaddcadadddcaaccaaadacdddadcbccdaccdccdbcccdcdddbddcdbcbdbddbabaabaacbabbdbcacadbbdaabbaacabdacdadcdacdbaadacabadcbdcaabdbcdbdcbbbbccbdaccbacccdabdccbddacddbdadcccaacbdcbacdcbcbbbabcddadabbbacdabcbbcbabbbbcaccbdcacaaadabaddaadbcbabcbcbdddcbabcbaaacabdccdddccccccbbdabcbbadacabaabdbddbcccdacccdccaabadaabacabddcbaadcabacadcbcbdbdaaaabcbcdadbbdaadccbabdcdadbadcbaadcbdbcadcccdbbabcbbadacdbdddaccccadbaaaaabbcdbbbcbdacbadaacdbbbcdbccacabacdccbcbacddcacbcbadaddadacdbcacabaaabbdccbdacccdbadbbddbddddbcbbdcbcbaaaabdddbdcdbdcacdddddcdbccadcbbabaaabcdccbdaabcbabaacdbdaccacaaaaacdaaacccbcadbdbdbcdcccbcbbdbadcabdadbdbdadbdbdcdbdbdcdbbbbdcabcccdcabbaadcdcdbabddddcccdacdacdacddcdaacbbbdabbbbbcdbcaadccbdbbbaccacdadbdcabbcbbbbccbccacdbbcbbdaaabbbaaaabbcdbbabcddbccabadbaaabdabbbcdccacbcbabcaabcbbaddbddbaabcccababdbabcaacdbccacddcabcdddbddbacaabcababacaddddcbcacddbabadababacbaabccdcacbacacaaacbccdcdbcddddddadacdacadbbbdcdacaacdaaabcddbbacddbdabdbcaadadbaadbbcbbababdcbddcddaddbcdbbbaccdadbadcddcdaddbacddabaccdccdcbddbddcbdcbdaccbdbbdabcbcbabbbdbdbcbcbddbbbadcaccacbcababcccadbcbcdacdaaababadbbaaadccacbaddcdddbbcadacdaabbacacdbbbaadcbbcaaacaabcddcdcdababcbdacdccacbcccbbacdadbbdacdabacdbaacbccdadcadabcbbccdcdddabbabccccccaadbbcdcaaacbbddbbaabaacccacadcbcadbbcabcaadbcdddacbdbabbcacbbcacbccacccdcdabbdcbbbdcbcbbcaddccdadcbbcbabdbbcbcbaabdcccacbdadbbaabcbdbcbaadcadbdccaaadbbbcadbbcacbcabaadbbacdbcaadbabdaccbbabddbabddcdbdbabddacdbacbadabdabaddbbbbaaabbabcababbaabddcddbcccadcabacbcddabacababcaabbcabbddcdcbbddddaabbababddacdacacbacccbccadcbacaddbdbbbbbaccaacdaaccdcbabcdaccaacbcdacacbaaddbadabbdabbabdbbcbadbbcbabcbbdbbbdcdbbddcdaddddcbaadcaddcabcaddbdcabdaabcbaddacbcbbbddaacbbcbddcaccdcdddcbdbcddbccddabcacddddcabacdadadaadbaddcacacccaacaaabdbcbaddbccabcaadacacbbaaaadddadadbdabbdbacccdaadbdbdbaadccdddbbdacabcadbdddbdbddaadcddddaccdbddabdbbdccabababdccdadbbcddadcdccadcadadadccabaacddcbbccaccbcdbcccaabbddaccaaacdbbcaabbddcacabddaaacacdadadcbbcadccdbccbaabdddbbbcbcaacaadcbdbbabcdaacbddaccdccdabdbbadccaabdccbacdacdabdcdcabacadbcbbccaabcdadcddabcdbbdadcddcdaaadadcbaabbaddddbddbdcdbcbabccbcaccbcbbccbdccdabdcaabbdcbcbdccdbcdbcdcacababcbdbbacaacdbacbbdbbbcdacaaaaacddbadaadcdacabdbdcbbdcbaacabadcbcdcdacbcddbcccaccbccaaddddddcccadddbdaddcdadbdbacdbcbccccdaadbabdacadccbcbabaabcdbabdccdcbcbcaabaaaccccaacacaccdddbbbdbaaabcaacbbdabcbdbccbdacdcacbaacccdbdcabbdbbbccbaacbdbdbcacabbddddabcbccbddabcdddccaacbaaabcdacbabcbbdbcaccbcccdabcdcaccaacbbacccacabddabcbdabaacbabdbbcdddbbcdbccbacbddcdcbadddbbbacbcbccddabdccaaabacbbdbacaccbbcbaadddbbbbbcdbacdccdadcacabbabaaaccbbbdcddddbbacbccdddcbdabdcbbdcdbababdbcacdbdccbcdddaaddabcadaddbcbacabdcdbadbccaadbdbcddbbaccadabcaadcbacabadaadcabcbabdbdbdcbacbbbbbcbabaaddbabdbacbdcaacacdadabcacadddadcaddadcaacbbdddbbbbacacdddabccaaabcddacdccabcdabbdaccbdccbbcdbdcdaddbcbbdbdcabcaacddabdbdbbcddabcaddabcbccdcdcddbdbabcdbdbdccdbccdcaacdcadcdacbbabacbababcdcbbccbbcdddbabdbccbcaddcbbbcadbcaccddabcaaadabcdacdbdabacddcbaadcdacbdbccaaaabbbccbaddbababcbddccaabacbdccbbbdbacdcacbadddbdcccadaddbbbaabbbcadbbccacdbababaaacabcbddbacacaddbaaaddabbcacdbbacdbadddddaacaaacbdcccccaccabbdbccaaadaadcbbcdbbbdaccdddcbccbddbcbcaaaabccbadcaccdabaaabcdcbaabbabcccaccdbdabccddbabadadcbcdadbbbcabbdccacdccddbcaadabcbbbcbcddccabadccccaabdbcadabbacbaababdbcddacbdccaabbcdacaccdcbdcdadadbdddddddcadcbcbdaaaccbdccadbcdacaddcaacdccbddbdaacadcacddbaabdadddacbdabdbabacbaacbcaacaccdaddbdadcabdaabcbcabddabdaadabdadabaacdbbbbbdcdccccabaadbdabbbdaccaabaacdaddabbdcacbaabdbadaaacabadcacabdbacbadaacbadbaaabdabacbdbcaddcadcaccdcdadabddbdaddbdcdbbadccddccaaabcaadbccabaadcdacdabcbbcbbabbdcacacacbdcbccaaabbdddbbacbbaaabccacbdaddccbbbdaadcccbcccccadadabcacaabdbddbbddacbcadabaacabddaacdcadddbbcaabdbcabacbdcaddcddddaaaccbbcbacdabccddadabaaadbddbdbcdcdabccdcadcadaddbdbabbdacbccaaccdbabbabdcdaaccbbccbdbdcabbbcdbcdccdcbccaababaaacabacdbbaabcbbcbdbaabddcdbbcbddcbbaabccaabbcaadcdccbdbbbaaadbaaadcadbcddaabcddbbbcdccdaaccadabddbaaaadbaccabaabaccbabbabbcabcccbcaabddcadbbcdddbddacdbdbdacabcdcdaddccaadccbddabbbaadddbcdcacaadadaaccaadbdbbccbdadcbaadcddddbbdbcacbabdadabbdaaccaabaadbddbcdcdabaacaabbbacccddbacacccaacbbcdbbabbbadacbdcdbbacdaaaadadcdbccadcdbccdddbacbdcadcdccdccdabcbaadcabbcabdcdcbddabdaaabbccbadbbdabcdadbacbcadcabccdbacbdcdbadabacbacdbdadaaaabdccababbcbbcbabcbcdaccdcabcacabbdbbdcabacdadacddaabdccbcbbbcbdbcdcacccaadddbabddaabbbcbdacbdabbcaccbbbccdccbbcbbbbcacadbaaacbccdbddddbbdbcdbacaadabbabaacccabbcabbcdbacbdccaaaccabbdaabacbdcadbdcaadcadbadcbdbccccdbaadaaccbbdccdaacacdcbcaddccbacddbcbdabbcbaadcdccbbaccadabcadbacaddbbbdabacaaddbdacabcbadaaabccbdbccaaababadcdacbdaaabbdbbbdadcacbbbbbbdadacabcbdccaccbacdababcdacddbaaccddcababbaaabddaabbcbbbbdcdccabbddadbdbbbbcababddacddbacabacdacdbbcadbabccdcdbddcadbbbabcaaabcddcacabadaadcdbacdddbdccaabdbaccaacbcababadbdccbacbabccdadbcaadacdbbababccdcccdaaddaaddcaddacbadccabccaacbcdaccbdabccaacbcaccdbadcbbbbbccddcdcbddbbdbcbaaaaaccbadbddddbbadabddadddadadbaacaaddadbbbdaaccbccbddcabbaaaccdacdbabbccabdcacddacaccccabbdcacdaccdaadccdcdaaadadbdbaabadadbcbbadddacaacdaadbcbdcdaddadccddaadbacdccaccbccccaddbcabccabaacabacacdddcddaaadbabbbaabbbaadbabcaaadaddbbaaabbaaabcadcbdcccabbadbdaaabaadcaabccacabcacdcbadbdcbcabbbcdcbccbbaccacabdadbdcdacbcbdabaadcadcaccbadababcbcabccdbdbbcbcddddadbdbccccbadddabddbcbaaaabdbaddbcbaccadddccdbdbbcbcacabbcbdccdacbccddcbbaccddbcccadcbaaadcbdacbdbbcabcdcbdcdcbcddaccbdbcbddddbbdbdddcdadcdbacaccbcaccbbaccadabdcdabbcaccbcacaaabcaaadbdbcbbccdcbbdbabccbaaacccacdcdadbcbdbcbaaadbaddbbcccbcccacddcabdcaaccaadababbdbdcdaaabaabccbbaddabdaabbbacbdabbadcbbbdbabadacbabdcbcdcabbdabcccddcacbcdcdcacbcddbbcbbdddddbbaabcdaaabcbaaabbbddabaadacbabdbccbbccbacabdacdbccdabcbcbddbdacacdcbacbbaaabacbcdadbabdcbdaccdbcadcbbcadcacbcddacaccdababcaacacdbbccdcadcdcbdbbcbcbdbacbbdbaaddbcbbdccacdaadacdccbddccdadcdbbacbbdaaababaabbbddbbcaddabcdcbbdbbbccbbbcbadbbaadbddcaababbdcbadccdccbacdbcbbcbdbcdaaabcdbdccaaacaabadbcbbdddabdcbdaccaabdabdcbbadddbcadddccccaacdbcbcddaacddbadacbdcddabacdaaddbbbbbcbbcbbdcbbbcdaddbbaacabbbbaabbaddcadaaabddabbbaabadccbabcdacccbcdccdabdbcddcbdbadacbacbcdababbccacabcacbdbcdabababbdcddddcdcdbddaacbbbbbcacdbbbdabbdababdcadccccccacdacbbccdcdbbcbabddccaddccdcbbcbaadcadacacaadcdddcadabadbcaccaddabadddcdbadcdcbacbabdcccbacbbbdaddacabaccbcdcaaacadaacccacbadaccdbaddcadaccddccaabdaadcabadacccdccdcdcabbbbdaabcacbaabcbbadabbaccdabdbbbcccdaababdcdbbbacbbdcdcbcdcdbaaddddddbaaabacbbbcdbcddabbccdacbbdcbabcdabcbcddabdbdcbaaaadcaadacccbbdcbdcbdbdabbcacacabcbddcdabcbbbcdacaddacddcabbbaadbbacdaabbcabacdcbcbdcbabaaadacaabcadacbadbbdcbcdcbabaccddbbcaabbcaccaccdcbacaadaacdbdabcdcdcaabdddaacdbdcdbdccaacdbbdbbcbbcbcaaacddbdabcdbdcbbabcdaadbbdadddacdbdbddaaddbcbdcacabddbbbacdbddcaabcbdbdaacdabcddcdbdbaccdabaacdabaadadbdacbadbdacadbbdabdbbadbabadbcaabcddddcccaaabacdcabbcbaacdddadadcdacacadacdbbdbdacbacdcdabaccbcdadbbabaadcdaacaadacabaccacdcdadbbaaaabbdbaaabacdcbacdbcbbdcacadaaadacbcabdadbcdbaaccaacdcddccbabbcaaabcddcaabbcdccdcabaccaacdcbdccdbbbcdccacdcccadcccbaaabadcdccddacabadbbcadaddbbbbdaaacdacaddadaccbadbbcaabaabdbcbbddcbbcccacbcadbbdaddacabdbbdcacbcabbbbababbbadcbccbadbdbcaacbaabccadaadcaadbbdbdcacbaadcababbbcbbccbdbadbadcaddbdadddbcadacccbcdbaddcadacbdabbaaaacbbccbbaaabddacbadcbdaaacddbcaddabcbdaacccddabcbaccbbcccdcdabbccbdcaadcdabcbcdddaddacaabcdabdacbacbadcabadcaddaccaabccbdcbbacabdccbcddcddbaabbabcbdbcaccdbbdbcdcbabcdaccaacdddadaccacbabdadbabacbddadcdbaacbabacdacdcabbccabbacbacddcdcbaaaaacdcaaaccbcdddcadcabaccbbaabaabdcababccadcbccbbddbcdbacaaadabdbadbcccadabdccdaaaabcbadaccdbadabccadcddcacadbacbdccccdddbaaabcadbbcbadabacbcdbddbbbdddcdcbbabacaacbadaddbdbdcdcabacdbdcdbbabddcababaadadaaddcbdacbbcbcddddbbacabdbddcaaacaccdbacbcbcccbabddddbabaccbdddcbcdbbcdbacdbbddbddccdbcbadcdccdcbdccaaadbdacbccddbcbcbddbcbdccbdadababadbdcaddabbdadcbdcadadadabddccdabbaaacbbadbdcaddbcccaaccbccdcdbbacdcaacacbcacabdababaaddccccccdddcbdbabdcacacaddddbcbbdccdcaacbcbbacbaddadcaaadcdbddccadbbaccbcdbdbddbabdbcabcdbaaacddddcdddacbacdadaaddaacadbadcccaaabdcacdcacbcdaadadbbccdaadaabbabdbcdcabdaabbddcbcaddaadbadcabacaadaadadcadacbaaacbacbbbdadcaccbabbbbddbbdaaadacbadaddcbddabdbdabcccccccccadcaddaddcadbdbdcdbdcdcdddadabbddccadddaadcaccbbdbbacdacbbcdabdaadcdbbddaadbacdcaadddbddabbbaacaaadaacabcccaddacbadbbdbdadbcbbdaddcbaadadcccabbdacbdabaccdcbcabbabcdbacdbcdcdbbdabcbcddbbcaabccbbbccbbddbabbbadbcacaacccbbdaaabaccbcbaadbdcbaadccdccddacabbcbabbcbccdddcdadbcadaadacbdaccbbdabacabdabcaadababbaadddcaabcdbcddcccbbbdbbddcaccbdadaaddccaabccbddbdddbddbddabcdacaaccbadabcaaabbaadcacccdaddcbcdbbbddacdddbbbbdddbbcdcdcaadacabdabdaccbbcdccdbcbcacdddaabbdcaaddbccdbdaaadccabddcabbbdabadcbbaccbbbbdacaabacbbdbbcaccadbcdcbaadbcdcccbadbdddddacbbdcddbccdcddabaaabadaabdcabdbbcaabacbabbdbbababddcdaddbdbaabccccbcbcbaaabccbbbcccdabcbbdddccadaccbccdcbbcbabbdbcbdddddbdbcadacbcbadbdabaaaddbdddcccdbdbbabbbcbacbdbdbbaddcbabaabbabbaccdbbcddbabbcdaaabddadbdbccacaccacaaadbccccdbbcbccddbaccdbaddbaddddabdaacddabbbbbddbabccbddbbbdaacdcababdadbacdcdabcccdbaddaccbcaaabcbdacddbabbabbbcdcddacddbdadcadbbcaacdbbbccaccdabdabcadabadcbcbbddacaccbcddbbcbbcbdcaddcbbcadcdbbaabdcabadcbdbcadaddbaabddbbdadcddacbbabdcddaddacdddbadbddcbabdcdbbbacdcccddddabadcbdabdbcbdbbabacbdbbcdadbdaabaaaabcadbddbbcdabcddaacabbcdbadcccabacabdcdddcdbbcadbdadabbacbdaccddabddcadbcabbccabdaadbcdccbacccdbbabbcdcdaccaddacacdaaaaacabddbaccbabdaacbbcacaaabbbabdabaadbbbbbdddbdacaabacbbdcabddbdccbbcaacacbcddbbdbaacccdcadbdccdcaddbdcdaddbbcdddbdbccbaddcdccaccacaaadaddbcdacacdaadabcaadcabbacabbddabbaadbbdbcddbbbaaaadaacbcaaaccdaccaadcbcbaabcacaadadaabdabdddabcacbaadcbaddbabccbcabbadccadaacccccbbcccaaadcbbbabbabbbbdcaadccaccabdacdabacbaacdcbbcdaadcccdaacbdbadddcdccddaadcadacaaacbdcbaccdaabadcabaacddbdacbdbadbbaacaccdbdbbacaacdcbcbcbdcaacddcbccdaabddddbaccaccabbcbaabccabbcdddddbadbcbdcbdcaaadcdcdaddccbbdabdacddacadddcddaabbcadbcbcbdcaddadacbbbcbbcaaccdbbddccbcccdccccadcdcbbadaabccacabcddadabccdacbcdaaabdbacdbcccbbdbdabaacbcddadbccbdccdabdaadaadddddcbdcdbcabaacbbbbbcaacdbabbadabcbcbabaddcabacccdbddabbddccbdccadabacbcbacaccaccacdddcdaadababdaadbabcaadbbcdddadaadcacabcccddbcddcacbbbcbadbdcaaddddccaadadbddabcbccbcdcaccaccccbbbdbcbabcbddcccbcdddccadabdcddcbcabbabdbccbbddaacabaacdbbababbcccaabaaaabbddcbaaddcbbddcdabcbdddcbcdacdcbcdbaacabbbcdabdbcaddcdacbbacabadbcabbacccddbabdbdddbbdbbaaddadbcdcdbadbccbbdddcadbbbbdbbaccbdacaaaacdcbdbacdbcdbabcbcddbbbbbbdbbaabdaaddcddaccbcaabcabacbacacccbbcacaddbbabddbbabbbababbdbbcbaabdbddbcccdcadcccacbdcababddccbbababcddbcdaacbdddadcaadabbcdaacadcdaddcdcaddcacbdcadbccddaaacdbabadaddbabadcbdadbacabcabcadaaacdadbbdbddcdcaccaadbcddbbdaaaddddcdabcabadcbbaabcadacabcbbbabbcabbadcdcddddbcabcdabadbddbbdabdcdddcdbdacdcbcaaddddbccccaaadcaacdaaadbdddbdbdadaaccabddbbcaacbabbbadaccbabddcbadadbddaabbbdccccadccbdbdcabbbcbdcbabddbcdddaacbabcdddbbcbcbabdbbbcbcbdbaadbdacadabdddabdbabcdaaabbbcbabcbbbabdaaaddcbdbcadaaaacccbbabdabcacbacdbdcbaccdbcdddcaadddcbbbdbbbdacbdbabccadbccabccadbddbbbbacacabcacbdbdbcdacbbcabcdbcbccdabaadddbcccccaaccaccadcbabcdcbcdcdbbcacacbadddccdcaaadaaabcbbabdcadcaadbdbaabdabddcaadddccdbbdcbccacaabbdbdbadacbbcdadacdcdbcacbdcccdcccccddbbbddbdcdbdccacbacccdbbabdbcbadcccaddbbacacdabdaccdddbcabbdcaccdbdacbaaddadaddacbacccdbbbddabbaddbaaabbadcbdcbdbcdcaadbacacccddbadbcaddbbacbdadbdbbbdaacdcacadbbcaccdddbdbadbaaabddcbcdcbdbcacdbadbdadabbbdbbcdccbbadacabadadcacacabdccbcdbcabdaadcadaccdacababcccabdacaacbdabdcccbbcdacbdcbabcacdacacadaacaadbcdaacdacdabaccadccdddbaacbcbdbbaaabdbadbbcdcbaadcdaabbbadbbccdcddabbcccddadbaaacdcbcadbacaadbccddaadddabcbabbdaddbacbbccbcbcdadbcbcadacbaaabcbdabdbbabacdadacccabcdcabacbbdddaacdadcddabccbbbcbdcdcadddbacbadcbbdacbbbaabdbadccbdcacacaabaadcdcbbacbcdbdcddaacbdbdddadacabcdaabdcbdbcbcdcacbbaaaabbadddbbaaacdcdbbbabdcdcdccaabdbcdccdbdcddcabbbddadacdcadddaddccdddddbacdddcbcbdcbaacaccadacdbadacaaccccbbdaadbaccdcdcbbaacdddcdabbcbdbcaacbcddabdacadccabcccccbacdbdcaadbacbaddbcbbdddccacbbcdcdbadadaadabbbaaadcdacbbaaddbaccaddbbcbdabdbadcbbabadbadbcacbcbdacbdadadacaabcdddcaaaccdbdbccdcbbbddaabbbbccbbcbbcdbcccadbdcacdaababccacaccbacabbddcbcbaacddbacbbdbdabbbdadcadbacdccddbbabcbcdbdaaabdbbadcdcdcbaadabbacabdaadddbdddbdccacdaacbbadacbadbabdcadbbaacaacabbbcdacbcdbbdacaccbdccaccdcddbaaddbabaddbdcdccbbcbadcccabbdcbdbabaaaacaadacbaadbdbaadbddbabbabacbadbbdbddaabdabbcdcaccccbadbddbcbbcccbddbdcccacbdbcadadddabbbbbdaacdabccbabddbabbdbbdabcaabacaddadbbabadbccdaabcadbcaaaabbbadaddcccbdcbbaaacbcbbadcbcbbaacdacdbabbcabbccadbbcbcddaadbbaacbaacbaabccdccbcbabbddacbbbcaadacacdcababdaaccbcacdcaaabadbadbddabbbadbbbdddbdbcbacdbaacbaadcadaddbccacbabdaababbacdacbdccabddcacacccbababbcbabaaaaababcbcdaccbccabdcbcdbbbdcccdbdabbbbddcccddddbacabbcbcbdbcadacacdadcaddccabccadbcbbbaddbcaddabcacbdbcbbaacbcbaababcdacabdbacccbcaabaddcccacccdcbcccabddadbbcdbdccccccadaaacacadccdcacddbcbddabdadddbbacbbbbbcbacdabddadacbadcabbbdcaabbcbbdcdaadccddcccacbbccdabcabdccbbabadbcdbbcdcdcabbbddaaaadccaaabdcdbdddccaaabaccaabbbdbbaddbcaabcbbccadbbcbbdacdcabdcabdbddaabdacddcacadbaaabcddbbacabbbdcbcbcbddcdddbbcacabcbcdbbbcddaddacacdbdcdadacbcbdcabaaabdacbacbbdadaccccdcccdbabdcdbddaacdadcbaaadbbdaadcccdccbabbbbcbbaadadddcadbddbbbaddcbcbcbdbcdcdcdbcddaadcaabacccdbcaaabcdaadabddacbcacdccdbdacabdabadccccbabdcbbbbdbacabdaabddaccabcbccbdbbcdcabcdaacabcddbabbcbdcbbddcbccacbbccbcbbabbbdaccabcabbdabdaabadccadbbbcaaacadaabcdacaadbcdcdbabcbcabdbdccdccddcaccabcbcbcacdbbbdbdccbcdbdcabccdcdcdbccdbdcbdcaddacddcccbbbaabcddcdcbbbddacdacbcabacadbcbddcabacadbacaddbaacddacaacdccddadbcbaabcaacdccbbacbdcacdbdccdcdcaaacdaadbdcbaabcabddbddbcbcbdadcdbdababbcbadcaacaaacadbdbcacacacdbcbcbacccbbaacddcbabbbcccdbaabdcdbccacbccddbbcacabbbaacccaccabddbdbdadacabddddccbdccacccacdcbacbabccddcadbbddbbaababadcbccbccadcbcababcaccacdabcbbbbdcdccbdaddddacacdaabddbcdabcadbcdcdddbaccbcbdccbbbbdcdcbcdabacdbbbbabbaadcabbbbabaaacdcabcbddbcccbbabacadcbbccddbacdadccadddddcacbbabddacddcaacdccdabdccccbaabdcadabbbbaaddbabaaccadaccddcaaadcbdccccabbbccbccdacadccabdcbbbadccddaacddaadcbbadaccabadcdcdacbdbcdcaddababdddcbbbbcaadcdcbdbdbbcabcaabcbddbdbdcabacabcdcaaadcdddbadcadadaccddcadbdbabbccdabdbcbbcbbacdcbdddccccdbbabacbcbcababcddcdcbacaddaabadabccbacdccaacdacbddabdbdadaabdcbccbaadddadaccdcccdaaccdcaabaccdadacaddcaabadabcdcdacbbbcadaddbbdacddcccdbcaaddcddbdbbbcbacbabaaaccdcdcadcacbbabbbbcdbcbbabdddbdcbacbabadcabccbcabbacbaaabacadccbaccbdabcdcaccacadbadaaadacccddcddadabbbbbcacdbacdcccdbacadcddadcabcadcdcdcdbabadbcaacddbccddaabaacaccbdabadaccdbcdbdbabcaaabdacbcbbcbacbdcaaccaabccdcadadcaadcacddbccababacadbbbddcacccacbadbacdbbbdadcdbbbcdbaaacacaabdcadaccbcbaabcdcbddacccbbaddaabbcdbbdacdbccbcddadabccdcbddbbadddacddbbbaababccbaabbbcdbbbbdaadcccdabddccbaacbbcbbacbbcabacddbabcdadadbcdddbababdadadbcbccaacdadbabbabadaaacabcbbcdcabbbbcddccaabadcddbaaacbccadcbababbabcbccbbdbcaacdcbbdcbacdcdbbddbacbbddacbdbdbababaacbcadcbbdcbcdbbcccbadccbababdbbbacbbbacbbbadabcacbdbabaadaacdcbbbadadcbaacaacdddbcadbbdacaabacdcbddbadcddbbbbadaadaabddcdadadddbabbccaabcdabddbbccabcabacaacddabbddaadcaccccdddcaacaaacbdadcababdcbaabccbdbccabddcddabbbbaabbcbacdabaaddabdaaabddbacdadccbadbdcbdcabcbbabdaccbcadbbcbbcbcdcbcdbabbabdbcddcbbcbacacdccbdccdbcccacbdbdacabdbdbbdddcbccdcdadbacdcddcddacddcbacbdcdcccbaabacbccbbadabbaabaabcccabaccdaccdddcbbcbcbadabbbcbbcbdcbbadaddddccaccdcdaaaaaaddacaabadddaadcabccabbbaadbcacabddbbcaaddabaccbbdaabcbbabbadddadbabddcbcabcbadbbcdbcacbcddbdcaaadddadbcdaddbbcbdbabbacacaaaccdcddcdcbcdccadbaadddabcbbdddcbadabdcbabcbbccbdcacaccccccbaaadbccccdbcddbbaddaddddadbcbcbdaadacbdabcccbadabdddbbbdbddbbaabbdccdadbdadbadcacaabdcbbacdbdbccaabdbcbcccababdbbaadbbdabcbbadadcccdabbadbdbcbbcdbdaddcddddacbacdbbcdbbdbdadbccadbababdabdcabcabbaacccacaaadbdcacbddaaccbbddaabccbabddacacdbaccdcabcaacddcacadabbbdbabdabadabdcbdabdbccabdcdbddbbdbcbddbcccabcdcdbaaaabbdbddacdccababdacbcdcbcaacbbbdddbccdaccbadcdadcabddbdbcdcdddbcabdccdacbcddaacdaabaccbcbacdabcbacacdbabaccbdcbcadaacbbacaaddcaabbbdcabcbcbccdcbdccadcdabdbdcdbbdcaddcbabdbbbacdcccbbddaddcbdbdaacaaabddbabdaabcdaacbcdcbbbbddccaddbddaababbbbbcbccacdbcdcbdbaacdbcdcdcaaaddbdbcbdccdaadddbccdcaadbbabcdcaadbdbbbddddcaccabcbbaabbabcddbdbabbccbbdabdccbabbaabdcdcaccdccaacadbdcccbcadcdcbcbddbcdaccccccdccbbcacbcbbdcbddccbcabdbcaaabddaaabbcdbaacacccaadcddccbabaddcabbbdddadcdcdccadbcccdcadbabdadbaabbcdcbdddcacdbcbccaabcbbbbccaabaddbdadbabdaaaacdbdbdacddbbdbddadbcddbdadcdabbbbccdabdadabbbabacaadcccddcbaabdbccdcbcdccabcaaacbdbdbcddcdcbabcbccbaddcbbdcabcaadccaadbcbcddacabbddbbbbddccabadcdcbcdcbdacabdbbadadacbccbacaabadcacacadadcddccddddaccdabddbcdcbaadbaaddaddababdaddbadbbbabadcbdadcbbddddbccccddcdcacabbabdbbadbaaabbaaabdbcabaabdadadcadcabadcababcacacaadabadcacdcbdbaccababccdcdacadaacdabcddbcbcbbdbcbddccadaccbdbcabdbaabbbcddacdbbcbcaddbddaabadacaddccbbcdddbacbbccabcccbbddddcbcbccbccdcacbbcdbcbbdadcbcaabadcaacaddbabcbcbaaddbddcccdabdbbdcaccdbabcbbbdabdaacbbbbabbcbabaacadbdbccddcbbbbdcaccdadabaddbacacadcddadbacbddcccdccaadabadcbdabaddcddaaccdcdacdbbbcabaacaacdddccbacacadddbadacdaaadcddadaacdbbbabcbbaccdbdccddccbaddaaccabddcabcddcbdabadcbdbcbadbdbaccbcbcadaacacbabcbbbcadcbcacdbadcabdddabbdcdabdabccdbdbcbdbdbcdacdacdcddbcccdcbbcddacacbddbbbadbcdaddadcbdbdacbcbcbbcbbcababcabaabacbccabdddadccbbabbdcabcacddadabcdbddcacacadadbbbbadadaccdccdcccdcaccdcbcdcabcacadbbaacbcbabcdaddbadaacaaabbccaddbbcbabbccdcbaaabdadcdcaaadbbdbcdcbaacccaccaddbbdccacbbabadbbbbddbcccadbadadacdbcaccdcdaaccacddbdaccdbdaaaddcbcacdddadbabadcddcbadadabbcbcdbcaabccabdbadbcacacbbdcddddadbddadbccaaccbbaacbabcdcaddcaabacddacdbadbabcaccddabacdaadcaabcdbddcadbbcccddaabaabccddccaddabadbbaacaabbdacccaaddcccbddcdacdddccabbcbdbcdccacdacbabbbbacacbccbacccaccbcabccadadddbdbaccacdaabccaaadadacbcdcadcaddbccaaabaadddbdadcccaabccbcccaacdbcbbdaabccaacdcdcbccccbcbaaccdddbdabdbadadbcabbcaadcdcadcacadabdcabdabccaccadcdcaaabbddcadcddcdbccbcbbddbccbbacababddbdbbaabbbbcbbdbddcbcccbcddcdbdaabdbcaddadadccabcdcdddccabcccbdccbcccdcdaddbbdacabcaaacbcbccccbacdbadcddddaababadcababcdcbdabcaaaddbdccdcdcbaddabcaaadaaaaacaaacddabcaccdbccccacccdacdacccdbcccdcabdbbdcccdcacbbdacdacdcaccdccdcacdddbcaccacdccdbbadbbbccaadccccbbadacdccddccbaacabacbddbdaccadcbdcdabcabadcadddabbcaabacbbbabcaabddccadcdcacbabdbbcdcdbaaabcacabdcbdacdadcbbaddbddaacadcbdaccbcbdcadaadddbcbabacacadccbcbbdcccadbabddddbcababcddbccdbaccdbaadcacccdbddabbbdbbdbcccacaaacdbbbbadaccaaabaadcdbbdbbcbadbaddaacadccccdbddddadcaadbcdaddacbabbacdcdcacaacbbccbdcdbaadbcbcaddbaaccaaaacddcbbadbcaccacabaacbbdccbcbdcbcccaadbcddcbcabbccdacbcdbcccbabadcdbabddccbbccdccbadbdcadabccacbaaadcbdbdcdcddcacddabaabcdcddcacdbaaadccadacabbdcbbacdacccbddcbcabadbbdabdaaccdcdcbcacdcdbaddbddcbbccaccdaddacccadbbaabaabddcbdcdcbbbccbcaaddacdcdaabcaddcddccbbdadcacdcbdcdbabbcacadbdbccccdbacdcdbccbbddbdbcbdcbddbdcbccdadbddcdcaccdcdcaacbbdccddadacbdcdbcbbacadcddacabdaddaaccadcbcbcacbbaaaabccbcabdabadcdcddacabdbcdadacabcccaccccccddcbdaaacdddbbbbdcacabbcbbcadbcdbbbacbbdacdcacbbdbacbbbadddabaabccccadaccdaacadbdcbddcccbccaddcdaadbdaaaadacccdcacccccabddbcaddcbacbabdacdaddadcbabbbddbcbcbcabccbacdaaaabbaaadcadacbacaddccdacdbdcababcbcbcacdadabcbdacbbcbabbabdadbaddcccdcadacbcbbbdddbacdddacabdbbcadaddccbbaddbdbbadcbcdcabadcacbddaccbaccbabbdcdbaacabbdadcbabbbdddcddbddbadbabcacaacdcabbcbbcabbcddbdcbdbabcadcdbcccacbcadddbcaabcacccdcababbcacaacaacaacdabaddcdbbdabdccdccdcadcdaacddaccdbabcddbaaddaaaadccabbbdaddaaacbddaccabbbcbaccaaccddcacbaabbbddcccbaadadadccdcbcdaadbdbdabbbccadadcdcacacadadaabcbdbacbbdccaddbaabbacaccdbcdbabcdbdadddbacabcbdddbabddacdadbdccdbadcbaadbcccbabbcbcbaaacbbddabdacaabbbddbcdcadacdcbcccbbaabdacdbdbccdccdaaccadbbcbcbacbdbdbddbbabbaacdddcbdbcbbcbcdcdaccdbadbbbbdbdcdddbaadcbbdccddcbbdaaadcadacbbddabcdcacabbdabaaaabbabbdbacdaadcdcbacadabbdabcbcaacdaacbacbdadbccddbaccbcddbcbdaaddcdccbddaadcaabdcaabdcaacadaacbbdbbdbbccbacdacadabadcbcbbacbcdcdbaadbcbcabcbdddaaabcbcddccaccdaabadadaccdcddddddcaddacbdcabccadcaaabadabbcdaccdadbdbbdacacbdaaaabdbdddcdaacdccbcbcdcaabcacccbddddbcdbccadddbbcbabccabdccbcddadacbcaaabbaabababccbbbdbacaaaabdaacbccaddccddbacdcadbbbbadabcbdccbbadbcaabcabdcddccbdccacadcdcadbaadabcabdcaacdcbdacacdcdbaabddcdccdbacbcabbcddbbacbbdacabdbdbadabbbdaaacbdbcabcacbbccabbdddcaaaacaacdcabdadbccacdbddabdbbbcddacabbacddccaacddbbbdbcbadccbccbcbbccaccddbddabccbdadbbdbdddabdabcccdababbbddcaacbcbacaabaaacaadcdacaddccbbdddbadbcaaaacdbddacdccdabadbdcbcaaacaddbabaddbddcbccbbdbbbbbbbbdcaaddbdabddbdaadabdbaaabcbdbbcdaddbacbcadbdddbcacdacacaaddcbcabccbddaddbbadbbdadbbbbdaddbdddbacccaabcabdccdbaacccdbcaddaddabacdcadccdaaaaccddcbcddcdbccbcbcdabaabdbccbbcdbbadbdcdcccaccdcadacdccddbadbbaaaaabbabbaaabcccacbcdbbdbddcabcccdcbdaaadabbdacbbbbccbdcbdcbccdcbcbaabaaacacaccbcbdcdaabdbbbaacbabdbddbddcdbbbcbbacaccdcbbdbaabdaadbcbcbdbcccadcdaaabbabbdbcabbcdaadbbdddbccaadbbacabbcacbabadbacbbabdaddacacadccdaacdcbddcbdcddbbcdccdbadadbcacacacaaaaacadbddcaaacdacdadbabbacaababaacaadddbdbbbbdbcaaabacccbabdaccbbcaaccbdadcaaaaabadbccdaabccccbcdcaadbaaddacbcabddbcdbdbdaddccbdcacddcabbddbbcdcddccacbabbbccbadadaababbcaccbaddcdcbadabbabadcbcbcccccdcaabaacbbcddcbbdcdcdbbcbacbaddcdcabcdccaccaccbadaacaabdcaddbadadaadaadbbcdcacdbcbadbddaacaadaacddaccccdaadbbccabcbadaccdbbadadcaadbdccdadbabcadccbadddabbacddbadaddcacaddaabaacccbadcadbdadbcbdaddccbcaaacbbabddccabbcccaaccdccccbbaabdcaddbabcccbcaddcccddcaabaacdcdcacaadaaaccdababcbaaabddacdaadbbdddcaddcadcccccbdbcaaadaacadbacbdacbddbcdbdddbdbbabbddbbdaddbabcdaacdaddcadaccdcdadcbabdcaabadacddcdacdcaaddacbcdcdadbbbdcdccdbdcdcccbabaaaccbcbdbacbacbdabbddcdaaccdbbdbbabdddaacacddcccbabbbdbaaccdcaddccbcacccdcaacdddcdadbbcdccdcbbdacbabaccaddaababdadbadbbaaaadacaaddbbbccdbaccddbacadbcadddadaaabaaddccbcccaddddcacdcaccdaacbccacccdcdbbabacdbbbadacdacdabcbaabcabaaccaccbdddadbbdbccdddabbbddccdddcbadbbbcdbadabcdcbaadcadbccdadccaddacbddbbacabcdbacaccaabccaadbcacadaabddbcdaacaaddbddadbcbbdbccdabcbadaadcabccbcaabcbbcdccabbbbccbdbcbacbcbbdddadbcadaadadcabcdbacaddadbaabbdcbdbbdcdddcbbbdaddcaacbabadabbcdcdbcabaacaddcbbaadabddddabbabaabcdaaaabaaaccddcdbaccddbdccdcacabcabaadddcdadcbabdbbcadabadaacbadadbaccadcdbadaabaaaabcaacaadabbbbaadbdbbadadaaaabdbbdbbbdbadacdbddbbaacbbcabacaaddcdaaddbbcbccbbadddcbcaabbbacbbaadbadaabddaccadbbdcbdbadbcaaadbdcaaacaacbabdbcccacbcbbaccdabddacacdacabcbdacabbcbadcabbbaababdaccbaaaaadcdaddadcabaddbdbbcacadcabccbcabaabbcbbbdbddababbcdccaaacabccbcbadabcdaccbaaabbccdbbdbdddcaadbcacbcdabdbdadcbadbbaaacadbcbaadccbdaadabaddacacaacdcdaabddbaabaaabbbdbdbadaabbbacaaaabacbccbdbdcbaaacccacbacbadcddccaccccccdabbacddbdddcdcdcbbbaccbdbbdbabdacdacbbddccbdddbbdcaccadccddbcabcddbcacdaadbbcabdccdababddabcbbbbccccdddcbabddcadcbababcdacdabcaadadbcbddcdbacacdcdbabdbabcdaddbbdbaabadbdccacaabaaaacdcabadaddaddddcacbbbcbbadbdcbdccddacbbdaaccacadadcbbbaabbabbbdcdddabcaaaddbaccaccbcdcadaaacbcadbabaadadcdacbddbddaaccbdccbbdbacdcdbaaadaabddbddccbcbddcbbadbcdcdcabdacbbbdcaadcacbcaddaaccbcdbbdabacbacddaabaaccbbdddbadacbabdabbbbdddaccccabaabdabaacdbdbdaccdbcbdbdabbcadcabdbcddbcabaccaabbaccabacabdbcddbcbbcbcdcacabcbcbacdbdbbabbaaadbadbbdbbbcccadddbcdbdcbccdbabbdcbbbadacadcbdacabbaadcbcdbbcabbddbbdbbcacbaacaadaccadcadbbabbddbbaadacccbcdbaadadbaaccddbcaddbcaddcacadadcdcddabcacdddadacaddadaccbdcccccdcadbdddcdcadbacabdbcabbcbbcdcddbdcbdabcdccdadbbbcadbcddcacadddabbddcadccddcabaadbdadbbdaadbccabdadcaabcaddbadadbbbabacabcdbcabaacccdbccabcdbccabcdbacddaababdcaacacbcbdcadcabcacddaddcabaccaddcddbdaadbbacadbbbddcdcaaabadcccabddccaacdccdcaabcacdbdcbbdbaddcbdbbddbcbdddbabdcaababdbbabcbdaddcabaddcabddccccdadaccbddabbbcccdbdbaddabadacbaccdadabccbdaacdbadbddcbbbbdbcdcbcacaaacccaadbcccbadddcbbbabdcdcacdbddcccaddabddbacacbdddadcadaaaaccdbbadabbcacaacccbddbdcccacbdabcdcbbbaaabdaddcbdbccbadbddcccadcaccbcdaccaddadccbcdcddddaccbcacccbdddbbbaaaccaaaaacddaacaaacacbcdbacccaaabbbaacccdacaccbcacbcbaabcaaaddcbdbdcdbdaaabaccbcbcaabadcbbbcacbabaaadbcbcccaaadbabddabccbadacbbdbbccbdbcdcbacdbaabdaadcadaaabaddaacddbccbbcaccbadbdabbbdcaccdddbdadbbddabdcbddaabdaacaacdcdcadacbcabbaaccdbaaacdabcdbacaabbbdadcdacccadcdabaacbbacdcdcbcddaddcadacbcaccacaabcdccbcbdacbcbbdcbaadacdcdddacabdabaccdccacabbbdacaaaccccacabbbadabbaaadddaccbcbddbdadacaaddabadacabbbcdaaacaaccbacacadcccadaaacbccdabbcbdadcbdbbbbdbbbdbbcacdaabbabccbadccbdcbdcbbdbdcacabdbddcadbacabbacdddcbacbaddaadabdabcaaddbddcadbcdacccdbabccadcbbbbaccbcdaccbaddddadadbdcabdbaabacdbacbdacbaaaabaddbdbdcdadaaaaccaccacbdadcbaacacccadaacddbdcaaabcdadddaadadcbbbcbbcdbadbbccbbbadbcaaabaacadcbbdccaddaddbcddcacbaaabbaacadaabdaaadbbdbddcdbdbdbbcbcbaaacbdabbcaddbbaccdabdcbdaaacacabbdabcacdcabcaaccbabdbcbacacbdcbbddccccadcaddacabbbcbbadbbdbbcdcdddabcbccdbabdbbbdcbcabdbdcccbcddbbacdaabcabdccaabcddcdbadbcbbbdbcddccaacdccdccabdaccbacabbbddddadbdcdbcaadbdbadbaaadccabcbabcbbddaaabdcdcbaaacdbcdacbdbdaacbcacdccdbbbbbbcbcaadcadcdacdadacbbadbaaccadcbdcdcdabdcddbddcbdbccccbaadbcaadccacaabbadcbcaaaadccdcdbacbabcdbaabdcbcddbaddbbaabbaadbabcabccdcdbbbabbaabbcccadaadbbacabddddcbbaaacbccdbabccbcabbbaaadbaadbbbccccdcbcbbacacbdaaccbdaccdacbabbbbbabbacbbaaacdbbcdaadbadacddabcbdcdcaadbaadaacbdadadbdccbabaaddabbccacabcbdcbabaddaabdccaaaacbccbcccbddbabadacacaacbdadcdadbbacccddccbdaacbcaaababadddabacdbddadcbbbabcabdaadacaddacbbbbbdbdbbdbdcbcacddaabacbbbddadbbadbacaabdaaacabbdcaaddabccadacdcadcccbcabbdaddaacbbddadcbbcaaacadcccabbbcbacbbcccabcdacbcbdbadbdacbcdcdacacadcccaddabadbdbcbbccbbbdddcabcdbdabdddcdddbabaaacbbdcbbaaccadcaadabcccbcdbcdaabbabccbadbbbbddaadabbbdaaaddcabbbadccddbbbbdcccbccadcabbbbaddcdbcdcbdbaacddcdaadcbbbdaddbddbdaaccdbbadbaccbbbacdaadacaaddbcdaccbddbdadcadbdccddcacacadcacbaacddabdcbbbcbcdaddaabdcbadcdaacacdbcbdcbadbdaaddbaaadadcaaaacddbcdbdaadcabcbbbddddcabdacaaabcbdacdadbdddcabcdaddacdabdcdbaddbcadaacdddcdacacdbabdddbbccacdccddacacddcaacbaabccadcaaccdbddaaaccaddcddbcacaabdbaaabbaacdbdbacdcdabadbbabdabcdcdbabccdaaabcdcabbabcdabbddbdaddcddadaabbcabcbabdcdabccdcadbcccaccddbabacdbcddabdaabcbacdbbbbaadaaaddcccbcdbdbadbcccabcacbccbacbdbdaabbddcdcdbadbcbacccccbdccaabaadbdbacadadadcabdddcbbbcbbbcadabacdcbbdbcbadbcdcdbaccadbbabbbdaabbbaccbacbddddbccdccbabddccacaadcccbdbbabbcbdbaddddaaccbdbdbacddaacbbbccbcadaacdbacacabcdccacccbddcdbdddaaaddbcabacaadadcdaacdabbaaaacaaadbbcaadcdadbdcbddcbadacacdbbbaaadbacdbbdbdbabbbdccbaddccadddcddbbcbbcabbabdabdbaccddbdcaaabdcccbbabacdccddddddbcaccdcbdddaaaccacbdbdabccadccdbcbabdbadccbaadaaadccddbcbddacdaccadbbacbddbddbddddcbddbcaabadbccacdbaccdabccbaccbdbdbadbacbcccaaabccbccabaaacdaabaccbbbabdcaccbddcbcabbbdabcacadaabaccbcddbbddcbcdcdabcdddcdcdaccabdcccbdbbbabadbccaaadaadcbaaacbaccbdcaabbacadcbcdcddbbaaaddbdcaadabcacdbbbcbdaadcdaccddaaadcabddbadddbdbbbccabcbcbdccbdaddaccdcbbabbbbacdddacddcdadcbaaadddccaaddbdcddddbaaabadacaccbccdaaacbcdcdddcacbbbdcbbdaaabbdcccdddbbcadbcdbdbcbaddbcbddbcccbcadbdaababbadcaccbcadddbbbadbdbadadcabadddbdaddcdcbaacbbbaaccabacbaddbdaaabbcadcbdddbcddcdadbabbabacbcadbacbacddcbbcacaabdbdcdbabddacdacaaaddabaaacdbabccbdbbadbcacdcdbbaddcbbbcaaaacbbcdbcdabaaacccbdcbacbcbacabbbcdcaadaacadadcbaaaadcdbbcdbdcaaacbacaadbdddcdcaacdcbbaccaaddbacbbbacdaaabbcdadcadaadadadcdccbccddbbdcbcbdddadddcdacdcadbbaabddddadacbbcaaaabbdabaaadaaacbcdbdddcbdccbbdbabbcdbdcacabdbdbabbabaadccabbddbbcbdbdbbbcadbdaddacbadbadaabcdbbabbcdccbdcbabaabddaaddaddccbaadbdbdcdcaadadbddabdbbabdbaabaddabbccdaadbabaabcdabaaaadbdccbdaddaacabcabcbcababddbaddaaaaabaabacbcddcbddbdbadabcbbadadadbdaddcbacbddbcaaccababdccbabaacaacbcaabcdcdaddacbdbccddcdcbababbadcadbbddacaabdcbadbaababaaadccaaacbbddcdbbadbcaaddbcccbdacbadaabcdddbabddbbcdbbbcddabcbcbacbaaddbcaddbaacbadddcbcbdcbbbdbbabcdccbccddcdacdbdbdcdbdbdacdcdcdaabdcbaaaacbbcdadbcccbcbbcbddccbcbddcccddacdddbadbddcabcdaaadddbdbabbdaccaacdcaadbbbddaddcbbddbddaaadcbdacdbcaadacdcdacaddcbbcbbddcaacaccbbbcddbdadcdcabadacdadbcdcabbaddabaaabaaaaababdddaaaadcaaaadbbcaabdbcabdaaddaaaddacdccbbabadcdcbacbaaadcdddbdbbaccddaaabcadcbddbbdbabcbaadbabaacccbadddbddabdbacddabcdadddaadbccbcbbdcbbaccdbacabaabbdbdddcddbaddabdcccbdbabcbbacaddbccaccbacccdaaabcbacaabcbacbbdbcdbbbcddcbbbbadddcbbcddccdcacdcbaaccbaccccbbbbacaabdcbcbcbcadcbbcabccbabccbadacabdcdbadbdabaddccdbdcabdcabdabadbabcdcdacdaddacadaabbbbacacbbdcaaaacbdbcaccccadacdadcabcbddbdccbdaddcbbdbcaabbcadcbabbdbabdccdadbddbdadadbadbcbbdbddabadadbadbabdaccdccbddbabbabcdaddaabdbbaacacddcdadbccaaadcddcdaccabbcccbbdbadaacdbbacbcbaaadbbddbacacaadccdbadbdbccacabadbabcadaddadcdcdbcadbbcbbdbcababacdbbbcdadcaaaaabbdbddbbddccbdaccbbadabbadbabbaabaaccbbcdaccdbadbabadaaddbdaabbacbdcbbbddddacddacdadbcdcaccbbccbcabdcdbccccaadbcaadaabadcccbdccbbbbbdbdbacbcdbdcccbdcababbbbbaacaccaacbbabadddcbabcddabdbbdddcdddddbabdcdccdbabcbcdbbdaddbadcabbccacabacccaaadcdddcadacbcabdbaabcdbcaddacddbcccbbabcccacdbccacbcdadbbaabdcccdddaddbcccccdcbcccbadcadacddaaabdbbdaababacbabcbcbccaaddbccbccaacbcabcccdccaadaddcadabddadadabacbcbcbddaccdcdccbcacacabdbcdbaccdbdbdcaddacddcbbdddaaddbadcaddcbccbccdbdacbcddbaddaccdbbdabcccdddbaaabddaaacddcbcbcdcdcdcddbcccbaacaccccccaadbcbbcbdabbcabcaaacccbcbccaaddbcacccbcdccbbcbdbbaddcbddbbccabdbdabcddabaaaddbdabdaaadbadccdcacdddabdbabacacbadaaaddcdcdddacddccbbaaacacbaadabbabbdbddccbcdabbadccbbccccdaaabbdcdcdbabdccbadccaaaccbbcbdabbccabcbaabbcbdaacdddcdcbbbababdbaadccdbdbaddddbddaccabddadcadbccccbadaddaccccbbcbdaddccbbddddbbccacdbacbdcbbdabcabcadabaaadbabbaabddacdcbbcbaccccdcdcadbcdaadbaccacbdaababaaaaaadbbcdcbbcabdbbdbccdbcaacdbacddbbbdadddddbccdbbdbdddbccabaabdbacdccbdbccbabbbcadbaadacdddcbdaaccccabcdcabcbdcbbbbcbababbcdabaaabcabbaaaaadddcbacdbabcbbcaaaadbcbccabcabaaabbbadccdbabaaabbacdccaccaaaacdaabdcbcadbdadbcaadaabcaacbaabbdbacdddacacacdbbddaddadbcaabaccdcbccdbabbabddbabcdbcdcdcdccaabdbdbdcbbbdbdcabbddbdabdbbaaaaabbdbbcdabdbadcdaaadcabdbacdddbcababcbaabdcddcdaaaabbccdcccdddbbacaccdcbbdcdabdcabaabaabbaddccabbcabddaaaaddcabddccdddaababbdbabcbbddcccdaaaadabbbabdcadbcaabacbdbbbdbcdadddbbacacdcccaaabdadddabccdaccaaddcacdaddacadcadaaadbbaddcccbacbbaacccdccccadbaaadcbdcadbdaaccabaaabcbacbccbbbdbddcccbdcaacacbccddddbabcdcbabcdcacbaaaaadddbdbccccadcaaaccabadaddddddcddbacdbccddcaccbdabbddabaacccbbcabccddaabcdaabaaabdaadaaddbbbbabddcaaacbbccbcdacdbaaccacbabbcbabbdaabcdcdbaadcddcdcbccbcdccccadbacacdbcadacdcdaadcdddbbbddbdbddbcbcbcdccccbdbbbbacabcdbcbdaccdcdbaddbccddbcbabbadbbdadcbbccbcdcdcaddcabbbddcaadcbdabbdadadaaaabacddbccadbdbdbcaaacababccaccbcbaabadbbacbdbaabbbbdaddbdbcdaccbdbccaddbbacccddcacdcdacdaaaccdaabaacacbdabcccccabdbbaaaaddcdcddbbdaabccdbccdbaaabdbbcaacdcdbbcbccbdccbadabcacccbbbdddcbcdbaaadbabdbacdbdbdaaddcddccbdbcbaaaccccbabbdcadaaabdcdaacacdccaaddcaacccdcadbcbcdabaccdbcdddacdddddaabccbddacdcaddabbbddcdcdcbddcbbadaacbbcabacdadaddaccacabaabcbddadccbbdcbcabaddadbcadbdddbcacdabdaaadadabacddcdadadcdcdcadddbadaaabaaacccdbacdbccacdaadaaaadcabbbbcbacdcabaadcadcbcacbadabacddbbadcccabbdddbccbcdddaabadbbbbcabbbbabdadabdbbcbccdbabbcbdcbbaadbbbbaadabbbacacbaadcadcdaabbaddaccadddabcbcbbbcbddcdbddababbbabdaadbbadcddcbbbbbbabaacdbcacccbccddcababbaabdddadcdabdccabcabbddcdbabccbcdbdbcbbcbdbacabbddddccdabcdacacabbcadddaacacaccccacaacadababddacadddddaadbdbcaaccbbbdbabcddaaadbaaabbaaddbcabaabaaaddcaabbccdabdaaaddbdcacbcbbaaddaaaabbbcdadabbdbcbcaabdcbdbabcdbbcbbbccaaaacbadcbdbcaddddcbccabccaadabacccdddabdabcbaabdbdcdddabdbbadadccddbcaccdacccdaaabbadcdcbcadcdbcdaabcabcbdddbccccdcdddbbddacacbdbbabdbccadabaadbadbcdaabacbdcbdadddcbccddaaabacdaabacaaaddacadcaabdbcbcbaabcdcdcadbdaabbaaddcbdddaaaacadacbddabcbcccddcdacaaacbacddcbbbabdaddccbdadcbcdbadddbbddcbcacacbbdaaaadcbaacdababbacabbcdbcdabcbcacbcdcaaabdddcbbcccccdbaacbbbccccadcbdcdcbbdadabbdabacdcbcddccdaccbccbccbbabbbdaaaaccccdadaddcadacacdcbacdadcdcbabcdbaaacdabadcadbcddcbdcacbcbddadcabbcdadddbdacdacaccdbbbccddbdadaaadbacbbbaddabcdcbcbaadddcaacacdbadaddaadddbcdbbbddacdacccdcdaddadcabbdacbdabcdccbdacdbdaabdcbabaccabcdccaabddccacabadbbbabcbadbbccbccbacccaccdabaabbcdcaadadcdabcbbdbaadddbbcddabdadabacbcdbdacadcabacbabaaaaccaccdacdcbaaddcadcbcccdabccdabbdcbdbaabdcabbcabbcabddddabbcdbbbcddbabbaaddddaabbcbbbadadbaccbbcaadbacdcdbbcbaabccbbacaccdcbbacabaadbbcabbcbacbddcaadabadcbbbbbcaddbadbdaccadbadaaacdbcaabcaabdcbdbcccbcaddbcbcacdcdadcacaacdbbcabacabbbdadabcccbabcacbddbbbaaadbdcdadbcbdcaabddbcaaacbdccadbcbadccaacabbdadabacddbbbacdcaddcaccadbcdcdabcdcdadaabadaacadbdadbbdabcbbadabbbbddccbbdcadcbdbdbccbbcddcddaddbcbacacbccddddacaacaabdbcbcbabdbbbccaaaccdaabbccbdbbcdbdaddbbdbdaadbbcccadddaabbcbbcdbaabdadacadccbcbaabdcdbbdcdadadacadbccbabbadaccbddcabdbbcbbadcdbbdaacbbbdabddcbddaabdaacccccadbdaddadaccbabbcadcbdccadaacabaccbbbcbadaacacadaacbccabcddbccdcdcdbcddbdbcdbaddbaadbbcdcbbbadbbbabcdcbaacbaccbbbddccaacadaaaddcdbbbdacddbbddaddabcdbddbcbcaabdcbaabadbddbdcbccbdcddabaadbddcddcccaaaadaacbacaddddbaaadabcbbaaabbcbcabbbcddddcdbccbdbadaacaccaadcbdcdcbdcabdddaacdaddadcdcccadadccdcbaaabddbbcbabdadcabccbabcbaaacdcaadcdbbbacadcacdaaaacadddbabcacabbadcccadbdbdababaabdbdcaadbddccbcacbadaaccbdddcdabcabbaddccaadbdcdacbcadaccabaababbccadcbacaadcdcbcacddbcccababdcddccdbaaddacbbcbacabababbaabcdaaababcadcbcbbaddabbbcacddaaaddcbaabdaacddabdccaaacbacdadaabdadcadddcaabbcdbdbbcaaababbadcaadcaddcdcbcaccbbcabcbcacdddacadcdddcdadabccccbdadbabacabddcbbdddddaaadacaadacdcbcdbaacbdbddddababdbcdddabdbdccddcadbacbaddcaaacdabbdcbabbcddcbcbdadbaadaccdcbdaadcdcdcbcaabbabdddbcbbcbdddbcddcacbcdaaabcbaccabccadaadddccbbdccdcadcddacabcdcbdcbcddaadadadbcdddccdddacdcdddabbacadbbbcbbcbcbdbcbaccaccdbbdadbdaacadaacdadcaabcdcbccbbadcccaacbacbddabbddabbcabdbcdbadccbccadcbddddbcabbbdccbcaddcacbdcbacbaacddcdbbdbacddadcdcdddadcbaacbadbcbbabdabcccacbbbdaadbbddbabbcdcccdbaaaccadcaacccbbbcacccbbdaacbcbbcbdacadaabadbdbdbaddbbbdbdabbbcaddcabaadaacdbbdbcacdaacdacdcabcbcdadadaaaacbabdbbaaaacaccdbadaccbbbbdcdcbbbbacbdbdcdbbacabaccaccbbaddbaccacdbacbbbdbaabacddcccbaabdabbdcaacaddbcaaacacdacdbaacaaadcadbbbaabdbaaabdccaaabcbdddabcdcccdcbcaaaabdacdcdcbaaddaddacadcbbdabbbaddbbdcdaadabdbacdadcdaaadcdabcaacacabdbadcbbcdccccbdccbcaadcdbbcdccddaacaadabdaabcabdabdaadbcadabdabbbcdbdbaacadcbaddcdadacdccbaddddcbbdadcaaabdaacccdbcddbdaabaaacacdaabdbbdcbbaadcadabcbadcdadcddaacdbbdcadbcdddaadccdabadcdccbccdcccbdcdbdcabaccbdcdcaacbbdcabbdacacadadddabaccddcddccadababcadcdabbabdcacbcdcbcdcabcbbdbdadcbdbcaddaabbbdbaccdbbadababdacadcbbbaccbdabccbccbcbcdacacacdbccdcaacacdddcbcdbdbcadcacdcbabdccbacdccbcdcbddadccabacccddbccacddcccbbbdbabbdabddabbcbdaadacbabdaabacbbdbbcacdcddcbacadbcacaadcdabdcccbcacadacadaddddabbdabcbaabbccadacbddccbabbbacaddabcdcaababbdbbbaabadacaabddbbccacdcbdccdaabbbbcdddddbdcbcddabccaadbcdddbababaacbdddcaadcdacbcbdaaccbadbaadbbadacadddbabdcabacbcbdacdcdaadacccdddcdbadbaadcaccccabacbcbcaabcddbadaddabdbabaccbccdbbdabbdbbcadaadbcbdaacbdcbacbbabbbbbbacaadddacacbaddaaddddcbdacacbcbbdbaacbaacdcdbadcdbdadcddabcbdcaabdcccacddbddbccbacaacdcacbacdbaccbccbacabcdbabbcaccdcbccacdaacbaacaaabcdaacababadcdacbdadabdbbddabdbdcaabacadacaabaddaacdaacbbababbcdddccddccdbbbcbdcabdaddcbcadbacbadbabadccaccccdbacdcbccbcadcbcacdcbcdcbbcbbadcdadbacaadcaccbbdddcdcdbbaaacbbaabbbbdaddcbcdbabcbadaccabbcbbadadaccacabbacdabdcbadcadcbbbcacbcbcddbbcacdbbbbbbddcacbdbbdacdcabdcbbabdbaabdaadaaabaaccbacccaccbbbadadbcdadaddcddababcabdcadbdcbdbddaabaccacddbcbababaaabcbbcacbcdbdaacdcababbacbcdbbdcacdaddbaaacdadbbbdacddaacdadbadbccdbdadbbbacdddcadccddcdadacdcaaabacbbcccbcacaddcdcbcdbbadcabcadccccddcbcdadbbdaccddccaabbddbcaaacabaabddaabbddddccbdacacdaddbdadbacccbcdbcbcabacaadcacacaacbdcaabaccacbcdcdbcdcddddbabbddbcabcccadbcacacaaaadbdcbcbcadcdcaddcdddbcccddaadbccdbbacaabdbcbababdcddadbdbbbdcaaacdbadbaadbcdacdaabdcaabbcacbcacadaabddddaddacabddbbcddbacddadbcbbbcbabcddbbaacbccabdaddadcccdbcadaccdadcaddccadbccabaaaddbbdbdcbbabddabbcbbabadaccbcabbdbcdaccdcabadadccaddbbbbbbadddbdadabddcbaadadbbddcadbcacddcbbccccbacabbddabadbcbbddbbabccdbbbadccacaabcabcddababbcccbdbadabdddbdbcbbcbbbaabdbbacbacccabccbbccddcabccadcabddbdbdbcccaadadacabbacdabbaaaadbcacccbcabcdccbcdcacadcdbbdcddcaaccacaddacdcddaadaccccdcdcadacccbadddccadadbbbdbacabcaccbcbcacaadccdbdcbbdcddcbacbabcaadbbbaabdccacadabbdccbbbdcdadcbbabadccabacdcbbcdacddddbbbcbacdcdbdabccbdabbcdcadccdbabbcaaaabbacadbbadaadcdcacabdbdaabdbccdcdbbbaabaaadddddcabcdcaddacbccaaababbaddcdccbcbcaccdcbacdaadaabcccddcbcaabadbbadbadddcdadcbbadccabdbcdccbaddacdbddcbbaacaddbbacabaaccddacdcbbdabacdbdccadaadbdacadaccbddaccbcdacdadcddcbcdccdcbcdbadbbcbbdabbacacbacabccbcdbcabcbddbbcbacacdcddbddbcadccccdbacddbbbdacbdcaacaabddcbcacdbdbbacbbcbcccabcbacdcccdbdddaccddbcdaddcacbabbddbcadcbddddbbdabdcacaddaadcdcadbccbcabdcaacabbacbcdbbdbaaddabbabbacdcccccaccabccdbccbbabddadcaddbdacbaacbdbcdadbabadbbdacbacccdbddcddcddcdabcddddbdbcccdcabdcddbabdcadacbcbcaaaacbdcdacbbcdcdbdbcaccddaadcbbcdcbaddcdabdccddccabaaabaabbbababbccdccabacbdccddcbbbbbddadadadbbaaaaabbccdcdbbcaaaaabadcdcbdacabdcbdadbcdbacabbbbcdbbdcccaacdcacccacaacabcbadddcbcbccdcbccdaabcccdcbbbccabdadacbdbaccdddabdcddcbccbadbbdbbaabbdbabbcadccdcbbcadbccccccbacbadbcaaddacdabbbdabdbacabddcbcbbdbdbadbdacdcdbdabaddbcbcdbcabbabbacdcbdbbabdddcddabdaacbadcadbccddadddcddddadbbbbcbdccacaccbacbadccdcddccbcbacabbbdbaacbbbbdababbbbcacdcdddddaadddcddcbcdbadacbcdbdccdcdbcdcadaaaaacabcccdadbabdbcadddcbdddbbbadcaaacdadbaadcbabcbcbabdbccccddbcbbacbacccbbddaddaaddcbcdaaddabdbbbabaabdabcdbccbbacdcbacacbcbdcdaddadcaddcdadbddacbccdccbdabdababbaacadccaddabbbacbacccaaddccccccbcdbcdbaacbacbdcbcdbaaacbbadccdaadbdcbbaadbddcbaadbdcdddabbaacacacadcaacddbbdaababccddddddddcbcadabcaadbdabcababbddbcbacdadbcddadbbdbcbacaddbdbdddcaaaaaacbdbadababadabbbbbabdabddadbaaabbdccdbdabbcdcccbabaaabdbbaabbcccadaccbdabcbcaccadcabdbbdddcaacbabbbacccbbcbcdacdabccdacdaaabccdbdbaaacdaadabacdaabbdcddbbbbcbabcaaadbbcabaacaaaaccdbdbdccdcdcdbadcccdbcccdbbbbcdbcbcbbabdacdccbbddbaaccbbcbddcaddadadaacccbbddbbbaddbdcdabcddccddcddbcdadcddaccddbbabbcdbbbadaaadcaccbabdbbadbbddcdbcbbaccadcccacccadbadaacbdabcccbdcbcbaacdcbbcaddaabadadbddaabbbacbaccccdacdabbadabdabacccccaaabaadaddcaabcddadcbdbdbcaaddbbabcdaccddbcaccaaaadbdcddacbccbcacbaacdbcaadbbcdacdabccbdcaccaabcbaadacbacdacddaabddaddbadacccadbbbaddbbcaaddbcaabdccacdaabcdcacddabadbacdccccaacdcabadcabcabdbaaccbbaacbacccbaaabaddcbdadaadccaaacaabbaddbbadcadbddddcaacabaabddcadccacdbcacbcdcabadcdbddccbbdddddaadaccabbccdacddddbddcaaadcdcbbddcbdcdaadbacdaabaccadaabbbabcbcabadacdbaddbdbbbaaacbabdadadbbabbdabbabcbdaddccbacdbbbaddacdbdbcaadccbdbbbaddbabaddacdaabbbbdbacbdddcbcccbdbcdbdddcbdcbdadcacdccbcacbbccbaddcadacbdbcbaabcacaddbbbdbdddbbbacdaaabcaaccdcddaabaaabcdbacccdaaaaddcababbbacdbbacbabbcdbbdcadddcaacddaaaccbbddacddabccaaadbcbcbcabbcddbcddaccaacbdbbacbdcdabaabbcbbaccbacabaaabbccbbbbcdcacadabdadabcdacacdbdabbcdbdbcdabdbcbdacdbbdbaabaccbccccacbdcaabbbacadcdaadddcacabdcbadddaadbbbcdccadbcddccaddbbccaabccbdacccdbaabcdababbdcdbbacbabdcdabbaabadacbbabcabbbcddcabdcdddbbddbbdddcdcdabbcabcbcaacbcadabacbbccddacccbddcbcaadbcdaccccbdaaaaabcaaacabbaaacddbdbdcbdacbaabadaabcccaabaacadacaacddababacddcaddacdcdccabcdcabdacdbaaadcaabccbddbbdbcccbadcdcdddbdcacaccacbddcddddccbbdccdbcaacbcabcabdabdaddbbadbbcbdaaaabaaccbadccbddccbddcdccbcccaaccdbbcabcabaddddbdbdddcaabddcababaddcdcdacadbcbbbacadcbccaadcaadacaadcbbccadbdbdcbcdbcdacdbbdbaddaaddbbcdadcbccbabbababcadcbadbcaadbccaccbbabadbcbadabbcbaacaadaaabbccbcabadddcdcadaccdcccabbaddcbbcaabcdcdcabcdcacddcbcdbbcbcaddaaabddddbbabdcccdbbdbcaacdcbdcbbdacacbbacdabcbaddbcdadaddccaaddbcbcaabbadcbadbbbcdbbcacabddbdcacaadbcadcbbdabdcddcababaadbadccbacbdccdbbabcdccddcadaaddbcbcdbaaddcbaacdbabdcccaddaacdbcaacccdddacbcbacbcbaaccdcbdabcacabddacaaacdbadbadcacbdbbdaacdcadcbbdcdbdbdadcabdcdabccbccdbdaaacbdcdbbbacbdccbcaacdcbcbbbacbaacbbadabbacababddcbdbdacbbbddbcddbdbdbabcdbdbbacacbadaadadacabacaadaddbbccadcdabdbcdadbadbddadcdbadabbbdaaacabdcdddcaadcdbacbcdadcbbddaaccaabdcaccadcdbabbadbdbadbaacddacaaddcbdcccdbdbddcbacaccbcbdcacdaacadcddcbdcdcdbbdbabccacbcadbbbddcdbbabaabbabbdccdcaacbaaccabccacbcdddcbaacadcabcacdaaabcabdbaabdaccbbaabdddadacadcaabdacbdbdacadacdadcdbcbbdbdccdbcdcabadcaacccbddacaacbacdbbddbdbdccccbcccbccbddaccdccdcdbacaacdaddcbdadddcadadaadcdcccddaaaacdcbbbcbbacbcbaccdcbdbccdcacccaabcaadcccbacbaaaccbcabccabcaccbacbdbdbccccbddbcbddbaabdaccbcdaacbddbaadbaadacdcccbbddbadbcbdbabddbaacdadbddadcadaababbdacccabcadcdbdddcdcbbbcdddabdabbcbccabdddbdddaacddcbbaccadbcabbbcacacbdbaccadcbbadacadbcacadcbcbbddcdcbdbcbbbcdabdccbaccacdbdacbabdccdaacadacdccbccccadbacbdacbbaddaddbbacbababccbdbbacbccddaadbbababdbdadcacbcbbdcadbbcbcdccdbcadcadcdaacccbdbcccbdadbdcdaaaabaadaacabdcddddadaaccabcaadcbbbbcbccdbabbabdbbadccaadbdaabadccabdaccbdbaaddadbcaaabddabbdcbbadabdbcccdbadacdbbbcadccdaaaaddadccaabdbabdacadaadcadccdacdaaccaddddbdcbcdacacbddbadbabbccddaacbbabdccbcbccdcaaacccababcadadacccbcbcdabcacaddbddaacdbdabaabdcaabcdcdbdcdcdbdcbdbdccbccbaababacacabababbbadbaddbcbcabbcddaaddcbaccdbdddabcdbbcbbaacdbdbddcdcadadabbacdbcadbadddbacadaaddbbdbcaaddbcaacbddadbdacdaabdcdccbcadbacabbbbbccaabacdacdaccddbcccbabdcccbacabcdccdccdabadbccadcabcbabccccaabcdaacdcbbdbadccadbaaabcddbdcbdbaacadbdabbadbdacdcaabaaaaabaacdcdcbabddccddcbccdcbbddbabdcdbbdbbbddbdccbbdcdaacadcaacacbdbbbcdaddccbddacdbbddcdabaacdbdaaadddbaaacbcabacbdabbcadcacaddcbacdbdaabbabbbcdbbbabaabaaabdbbcbdcbacdcccdabdbbdabdaabccaadccbcbcadabacbcacaaaaacadaacbccbbccbaddcacdbdbacdccccbcabdabbbacdacdbabadbddbbbbccbbbacbaaddadbddcccbcadddcbcbddddcadcadddbccdabbcbbadacbcdcbddddcadbddccbcadbccbcdcbbbabaaccbccdbcdbdccabbadcbbcaababbbabbcdcacabdacacdabaabaabdddaccdadabcacbcdabbcdddbacccbbcbacadddaaacdbbbcabdaadbbdcbcbdaccaacabdbbcdabdbcdcbddccdacbadccdbaccbdabddccbddacdcdccdccddabacddcdcbacaaaadbbbcbdaddcbdbccdacaaabdbaccaaacadbdcbbdcadadbbdbcaabbadadadcabbbcdaccadacdaaabcddddadadbddacbabccbaaacabaddbaaacddbcdbbcaccabaccdbccbaaacdacaccadccbbabcbabdcdbcdadaacbdadccdaaccccbdaaccdaaabdccabadbadcaccdcbbdbabdacaacddcabcbcdbaaddcccbcbbbbcacdcacadcbcaadddddbbbacdcabdbbaabcccacbccdaabbdaacccaaaddcbbcadbabcccdabbdcdddcccbdcddcabbcdccbdcbbdbcbacabdcabacaccbaacddcdbcaabcdcaadcbcccabdbdcdaddddcdadaaddbbaabdbbaccbbccddbccbdccabbadcdbabbaddacbabbccdaabbddcccbcadccccdddccbcdbcccbdcdbdacccbbdbdacdcdbcdbbaacbaabbabcdbccccbdbbcdbccabbbcbddbdbaacddbbbbdddbdcbdcbbccacacdabbccbdcbddcbdcccdacdcbccdbddcaabbbbdabadbdcbbbdbacddbacdcacacabcaaddddcccdbcaddddcabbcbbaccbcdcbbaabbbddcbaabbcddaccacdaabaabdbaadaadabaacaacbacdabaccccadccdcaccdadcacabbcaacdcabacdbadacbbaddcdabddbbddbdaccacbdddaadabcdcbcddbadababcdcadcdbdabbcbcdaacdbbbdbbbdddadccaacabcaccbdcbcdcbcbabbbacbaacaababdabdbdbdcdbddacdddacdccdbddccacacabbbcacadabcbcddbbdacbdcdaadccbbbcdabdcddddbdaccddddbcaacaddbdabcbbdabddcddadcbbacddbcbbbccadcddddabcdbbaccadddcabddabcbabaccbcdddcaadcddacaddbcbbaddbdabbaababbcdcddcabcddacbdddaaadbbaabaccdcdadabbcdcccbbacccbdcbbacacdabadddcaadbdaaddccddcadcbabbbbdcbdbaacdaadcadabccbcbabddccbcaadabcadbacdadcaddccabbcdccaabbcbddabdcccbcccccbcbadbbadabcdbcbbdcdbdacbbddbcaaddccdbbaddbdabdccbdcabbabcbacaadccaadadddccaddcaabdcbdcbbdcbcbdcdbdbaddddbddcddcaacdabaaacdcdadaadcbddadbccdaddbbcdcacdccccbdbbcdabcdacdabbcdbdbbdaadbddbdbcbcababbbaddcbaaaababdbccdaabaccdccbcbcdddcbbadbaacdaabbabdcdacdabbbdbbddaadbbcccbbbaadabbcaadcccdcdbdacdaabaddcadacacdccdbbaccbccddccacabadaccaaabadbcdbacbadabaddbbccbcdaacacccaccabbddddcacaacdcdaacacddbcabcdcabbdbcbaaaaacbdcacdbabcaabcbacbddacdacdbaddbcacabcbdcbcbacdbcdabcdcbddbddcbaaadcdbdadcbdcbbcacdaccdbacaacabadcadcccabdcabcaaccdbadadcaaaacbcaadbacacddcbcabdabacdadbacadbaacdbdabcadddccbbccbacaacbadababbbcbcbadadbaacadbcabcdddcccabccdbaabcbccdaccaddcacbbdacccabaacaaabaababddccacbbcbbccadcdcbcabcdabacdbcbadbcdccdaacdddbcbaadddbbddadadcccadddbddbdcbccabdadbcaababacdccdddddadcdaacbcbaacbdcdbabdbaddbdbdccdcddacbdabbbdbbccddaacacacbccbdadadbbaaacdbcddbacbaacccbbbacbaabcaaadcdbcdddccbadacabacbadacacddcbbcbadccbbdacccaaabbaccddcbddddaadbbdabdacdadcccaaaadaccaadddcaacdbcaccbcdbabacdbdaabdcdcccbadacdabddcddcbdacacddcbaadbdacddbabdddabccacdbbaabacacadabbbadbaadbccdadcbbcaddbddacdcbbccbddbadcbabbbcacabbadcbbbdddabcacabccbbbbcdbcbccdcadabbccbbdddbccddddccbcddaacbbcbdbadaaccbccccccdcdbdbacddccaaaaccabadbaacdcdbcbcbbcccaaacddabccbbddddabaaddacacdbbbdadbbbcbccaababbccbbabdaaccacadcdadddbababbcdcdcdaabcaaaadbadbbcaaaddddbbccdccddbdcdbbaccadbababbadcaaadacbadbbdabbaacdbcacbacadcccdabaddabbcbabcadbbdaddcaccaccabcaadabbabcddbdcbbbdadabdccdbbacdcbaabddacadbbcaadbccbdcdabaacbdbdbdbabddcbdbdbabbbdabccacadaabcadcbacabbaaabaddcbbacacbdbbadcbccacacdacdcbbadcccdcbabbddccdbcbbcdacdadabcaaddbddddacddccbdcbbdcaddbadacdadcbdadbdbbcbcbddabadbbabdbcccbcbbbbacacaabaacccabadbdbdcdbbcbbddaadaabdcaaaadccbadadcdcdaccabbdaabcaddbcbabaabbcabcacaddacccbacdccdcaabdacddcbbdddccdddcdaaabaccbadbbdaabddbdbbaaadabbcccdbbdcdaaddcccbaddccabcbabdabbaababdadadcdcbdaacdcacdbdacdbbbadaabcadcabdbdcbbbdbcadaadacabcbcbabdcbdbdabdcbbaacabaadbbabcbaccccbcabbcddabbcbcabbddacbbaddbddaacaddbdcaddddcddbadcdcadbbdadcabbbdbdbdababbabbdbcacdbacaacbcaacdadbcbdcabddbdadabbdbcaadbaabbcddbccaaadacdbadbdaccadbaaadaccbdcacdbdcaadacbcddddabddcbdbdddcbcbbadbbbbaddbcacaabdaddcaacbccddcbaddaddcbdcbaadbdbdbcabdcdcadbabaacbadadbdddcccbbddcdadbcacbbbaabadcacddcbdcbaaaddddaabadbbcbddbcaddbbccddbddcadcabbcbbbcabadbdacacbbbddbabadaccddddcdddbcaddaabbcbcbbccdadcbabaaaaddaccbbdccbbaabdbbcbdbdaddcdbbcabdbcbcbdacdabcccaaccacadacdcbaaddabdbdbbbdabbacbccdadddababbdcdaadddbadbaccbdcbddacbcbcbdaaacdbadbcabaaddddaacadbbbaabdcddcbadccadccdacbadabacdacbcbdbbcabbcddbbcaadbabbdaabdacbcdccccdadddbbccabddabadcddccaddbdabbbadcdbcbbcddbcdcdccdcbbcabbcdabbdbbcacabccddaacbaadbcdbacabcddcddbdbbddcbbccadbacdcddcdacdabcbbbcadbddcbdabddddccdadcccbbcdcadcbccadccaadbbdcdcdcabccaccacaabadcdbcaadbdaccdaddbacbccbcbaccdbdbbddbbcacdcccddcdcbdaaddadadcbcbdcadcabbbcaaacbcdbddadddbdcaabadbbbabccdbadaaccddbaaaabccaaddadcdadaababdbbabccbcbcbbcabdddbdcccacdabaaabdccbcacdcdbbdabbdcccddcbdacdbaadbadcdadaadddcaabcaabccdbddbdbdcdabbaaaadbadcbdddcacbcabbaaccddcbbcaaabcabcbdcbacddcdcacdbacddaacacccdcacbddcbbddbbbdcbcccdbacdabadbbbbcacadddabbdcdcdabbccbbabcabddaabbabbdcbcdaccacbddaadbddbbacbacabdcdcdbbdbacabaadbadadbaadabbcbabccccdaabddcdccccabdbbdddbdaacddccdacbbbbcdbdddddbddacadcacccdbcdaabaacdaabcaddddbabcdcdacdadcbadaacdaccdcddaccaaddaccbbbabacbdbcdddacacdaaabcbabaacbcdbbdbbcbdccadbdbddcddbbaacaadbdcadccdaddcaaccdcbcbaddbadadaacadccdcddcdaccdbdbbdbcacddbddacaccdaddadcbacaadcbbcbadbddddbcaaddaacacdbdcbbcbaadbacadcaaabcddacbbddcadacacdaaaccccdcddbaccbbaadbdaccdccdccbbcbcdbdcacaacbacbddcdcccaddacbaccabdabadbdbdbaacbcbadbaacbcbbddbdcaccdbdbdbcdbdadcadddbdaabdcbdddadabcdcdbdbbacbbadbcbadcbaacabbdccddbbadcbdababbbacaacbddbdaaababacabdcdcdcacbccaaadaadadbdcaacdbaccababcbdbccaddbabadadbabdaacdabcccbcabbbcddacbdaadcdacaddbcdcdcccbadddddbddccababdbcdbcdbbaccbdbbdccaaccaddabacbdcbcbaddcacddadcdcabbccacdbcadbaababbcbabbccdbdddacbcdbdcbacbddbcdaabbdcabaadbababbdcabbcbbdcbbbabdadaacbbcabaadacbcbbccadcbcabdcabbacbacaaaadcdaccdabdddddaabddcccdaadaadcbbbbbdabcaacddcbddddcdddcbadddccbddaabccdadcacaadacadacacbabdbabbbbacccaaccbdacbcbdabacbdcbddaddadaccbccaabbaacbcaaacddcbdbdadbaaccdadcabcadddbdbbadccbdbbdcaadabbbcdcdacccdbaacaacaabdaadddcaadaaddacaadacabddcddcadadadcbdcdddbddacdbcdadcccdccbcaaaacabdcbabadddcbaadbbaddcbbacbdbadccacadaacdddbbacddddcddcdcdbccacbbdcabdcbdaabadabadbdcadbddaaccdccbbcadacbadcadbbcadaddadccbccbdaadaacddacbccbcbdbdbaddbcadbcaaaabcdaabacbccbdabbbacdacbbcabccdbadbdccdddddcbddddadabdaacacbddccadaaaaabbadbcdaacabaacddbcbabcdbdddbbabdbdbbaaacbaaccbcdbdacbcacddddacbcacdccbdbdaddacbddbdcdaaabbcbdaacacaabaccababcddcccbbcdbbdbbbdababdcbcddbddadabdacadaabcbabbcacbbadcddcdadbcaabdbddddddcaaccdcabbbadacacaccbadbcacdaacbcbcaaacbdaadaacdcddaddbabadddaacdcdcdccabbbcadbabdbdacacacabcdcbcacbbdcdccccadabccbdbbdcaabacadaadddddabbcacbcdddcbbadcccaaddacbcdccdcacdacdbaaccdaadcbcacdaddabdbdbcdaddbdcadacadbbaadbcabbdbcacbddcbaabddbccdcbabdddddbddccabdadcdbcdabdbccacabaabcaacacdaccbbbbabbcaddbbcaadbcdcbbdcbcacdcabcdbbbdddbabcbcccbddddcadacbcabbbdbcbcdcdaccbdbddaccbcaddbcbbcdddabcdccddacbbbddcddbcabbbccaddcddbacbaabcbdbcbbbbbbbacccdddbaccbddadaccdbbdbdadbdcabdccdddcadcbcabbaccdbccbbdbcaaadaddcbaaaabddcabcabdddacdabdddddbbbbacaaaabcdacbccbadddbaaddbaddcbdcddcaadcbcaadbccbcccbddcbdaccadbcdbdcdcbaddcbadbddbcaccacbcbcaccbdacadcadcbdcdbcbaaddaabcddabdaaaabbbacadabbcccdaddaadcbbdadddbbcbaaabacbaddbaabccabbcccbcbbbdbaadaaaccaaabcbbcbbacdbddbaabbabdccaadbddacaabdcacbddadddaadaccbcbcaabdccbbadcaabcabbdadcaabbdbcdbababbbdacbddaaddcadbbcaccabdabdbdccaacaadbcabdabadacbbcadcbbdbaabcdccddcbbbdaabcaadacddcadcdbbbcaabcbbdadbdacdcddbbdcacacabcaddbbadcaccbbcccbacccccadacabacbbdcaccdcabababcddccbadbdddacdcbbdbcbccabaaccaaddbcbddacadbddcbadbdcadbbdbbdbaabbbccacbbddaddabdccabadbadaaccdcadbccbddbdddbbddabccadbcababaabbbdadaaddddadddabaacbbddadbacbdbdcabadbaadacccacccdcbdadadbabbbadbdbcdcaabccccbddcbcbcdbcccaabaaccdbdbbabbabaaaadaddcdcadcbacdaacaddbbadcddaaaddabaddbbaccabaaacbdcdddbadcddacbbdddddbdacaddcabbdbbabcabdcacbadbddadccdbbdadcccbbbbcdcbcaaabadddddbddaadcbacbabdccbdabbcaabcccadcddbadcacbddbddcbdbddacbaccaabcdccbddcadcbbbbddbddccadaacacacccaabcacacbabacdaaaadbcadacccabddaadacabaccdcdaaabacbacdcccdabdaccacbdccbcbdacccbcbbcabadbabcbbaccacccdaddccbbbdbbdaccacaabcddbbcbcababcbcbababdbbdbccaccdcacdabaabcbbdcbcbcbaddcdaccbddacccbcdaadcbbbaccbcdcabcbdabbcbbbccdcddbcddabdcabccbddaaabcbbccdbdadbbdbcbdbddadbbbcdaccabdcddadbadbdbabbbbadcbdbcdbaaaccccddbdacbbaadacbacacacbddbbabacaadaddcbcbabcaababbdbbbdcabadbadbcbaabaabcbbdaccbcddddbadacabbddddbbbbbbcbccabaabacdabaaabbcddcdbdbbbcbdbbacacdcbabdcdcddbcbddcdbabcbccccccdcdaaadbbdbcaaaaacbabbadabbaccccddaacaadaccbbadbddbaaddccbdaccbbdabcbacbaabcdadadbadadbdcadbdbcacdadacbbdbabdacbaddaadccddcdcddcccdaacbbcdcbbacdcabdbbaaabccadacdbbaabddbbadbcccbbbacacacdcbddcdbcdcdbcdbaaababddcddcbcdbaabccddbddbccbaccdbdbacdcbbacbcddadadcdccddaaacadcacbdcaddccdbcbbbdcbdabacadbcabcabbcdddabcbbbadcdcbccdbadaabacdbdacdaadddcbdcdccabbbdbabcadaacaabdabaccbacadbbadbcdbdccabcadaacdaadadbcdcbdcbdcdccacbdbbdabcaaacdadcadcabcddcbadbcbcbaacbcabccccddbaaccdacbddddbbccddbbcdddbccaadaaabcbaacbcdadbabbbbaacaadbbadaccbcddacaaabdccccbaddabdaddbacbaaabbbacbcccbbcacdaaadaaccdbcbcacbcaadcacdccbdbbddbdcddcdbaaabbbadbaaddbbdbaadcabdcdcdaabddbbdcdaadcaabcadbdbcbadcdcdccdcbaccaacccaddbccbbacacdacbdcbbbbaaaacdabaacababdaaaaaddbadbbcabbcddcbacddacbcbadabcbacdaccdcbaacbadddbcddccadbdcbcdcbcbacdcdccbdbbbadbaddddddabddbdcdaacbbdabdbbdbdcabcabcacbddaabbcacdbdbaaaacccaadcbdbccdbbbddcacdbcdccdbabacddbabdddaccbcabcbaddcdacdbbaabadcacdcbaddaaddaccdcbdddcbbabdddabdddaddadbbcadaccaadcdcadbdabdaaccaadadbbcbddaabaccbacabdccdbdbabacbaaaadbacccacadcbbcbdbccbcdabcbbacdacdccbabdabdaaaabdccccdcaabcdcbdcbaaaabcdbbaadaddabddadcadcbcaabdbcddcdabcdabcddcbbccbbdacdcacdcdcaadcccbdbaccbbdaddbcbcacadbcadbddadcddcdcaaaccbdadaaacadbdcddaacdbbddcabdcabcdbabddbccbdaaddccbabdaaabcbccbabdadabbacadbbadcdbbbcddccbbddbcdccdbbabadcccaacaaddadcadaacccaaaaaddacbbbcabcccbaabdaacddacadabbdacdabaaccdaadbbbbcbabdabdbcaddbaabcabddbbbbdcaccadcddcdcdcdabcbbbabdadcdbdbccabbccbaacbbcdabdadcddcdabcbadacbdcccccdbabcbcaddbdbddbbdcbcdbaabcbccabbdbaacaaacdbbbacbbcdcadacaabbdcaadaacacdabbadcbbaabaababcbaababcbabadaadaabbcbccaadddbcadbcbcdccbcdbcaddbdddcdcdcbccdcdcbbacdcbdbddabcbcaddbcaacaadbcbbcccccdcbaabddcbabdbbbadcdcdbbcbacddccdbabbabdabbcaddcccbabdadbaccaccccdbdaadcabbcccabacddaccabbcdacdcbbcaddadbdbabaaddaabdbadacaccdddcdbaacbdadbbbabadcbabcdaaacbdababaadbaddcbcbbdbdadcddcabccbcaddbcbbccccdbccdaddaccbbcdbaaccacaaaccbbdcbbbbbacdcbdbbadcdadcdbdbaacbdbbcddcddcaddbddbadacbbdbdbacbacaacdacbdcccbadcccaaacadcbadcddacdabcdaccbbdcddbcaacddbbdcbcabcbdbabdbbbcbddabdabadbbdbbbacddddcdadbaabdacdbbdbbbacaccadddadabbbcdbdadbbbbbabbacddcdaccbccddaacbcaacaacdadccbabbabccbacadcaadccdbccacbadccbacdbccdbdcbdaaddcbcbdcabdbbddaadbdacbcabdaddbbacbdddacddbccbcbdbcacacabdccdabbaaaabcabadbbdbbbaddaddcbaadaadaabbadbabdddbbbaddabcccdadacbbcbbabbcbababbbbbabdcbabacacabdbadbdbadbaabdbcaaacbbcdcaaddbdbbdcbadaabccbaaccadbddccaccdacbdbbabcbbdcadaddaabcddaddcabbcacdbadbaacdcbcdabcdbdcdcbdabccdbddaaabdbdbabbdcbdcddccdbdaaacadabcabccbbcdcdcbcdaaddacbaacdaaacbaddcbabdccbaddaacdcabdcabcdcabadadccaadacdbcbdbcabddbbbcbcdadaddbbaabcbdbcdbabdaabacbccddbaaaccddbbdabbdbdaaacdacbaccdbbbddddbaabbddbccdbadddccaddcbacddaaddcacadcaacbcdddabccbaadbbbaabcacbcabccacccbbccdcadbcadccdbcdbaacdcbcdbdcdadbdccabadbdbacdbdabddccabaddacabaabcaddcacaaadabbbaccdccbbacbcaadcabaabdaaaacacacccbdcbadddcbbbcdbadcbbaddccbbabddaccaaccbbbbacdcdaaadadbbbcbddcdcadaaaddccabdbccbddcbcacdcdcdcddacdbbdcbcdcabdababddcddcdddcdcabccddccbbccbbbbcbbcdbcbacbcbcbcdabdbdbdbcddcdacbdadaddccbdbcdaabaabdcabddcabaadabccdadbcbaacdcdcccbddaccddbcdddbbdcbbacbcaddabaadabbdbcdaaabadcbbcdabaddddbdbccadadababcbcbbcdababddcbdbaaabaaacaddddbaaacdcabdbdbbdbddccabbbacdbabccbcccddbdcbcdcdabcddbcbcbcadacdaddcbabcbdcadcbbcabbccdbcddccddcddccadaccdabdbbbdabbbacbbbdbaadbbadcabbababbbbadbccdbadcdbabccddbaaaaddacbdbccabbaddadabbabcdabcaadbbdcbabcccaaaabaaacbbbcbbbbcbcccddccbbaadcadbdbbdccbcbdcacadadcacbcbcdcdabcdbabdbdbccbbbdcbaccbbdddaccddccbcaabbdcbbbbdcbbdbcddacbadbbadbbcabdacbbdddacbddabcbcaacddbddbabbbbabbdcdcbbaaacbabcbddcadabadcadbdabcdbaccacaccccbbddddbcaddcddbacdabaaadaabdabbbadaaddcacbabacbcaacddddbbdbbdcbbaaabdbcabdbcdcbbdadabbbdccccdcccbaaadbbabdcadccaabbccdcdaabbbaacaddaddbdbbcaadbcbaabbdcbcbacaccbcbcadcababdbadaacdbbbaadbbdccdbdaacbacaadacacbacbddcbacabdbbbbaaddddcaaaaaadcdbcbacbccaddccbcbddbaaadbababdbcaabbabbbdcbabcdccacdabcbdbbcaacddabdcaacadbbabaadbaaddcabddbbdaadadcdcbbcdacdddbdcbcbadcccdcccddbddcdbaacdcabaacbdcacbabddcaddbddbbabccccdccddcddaabcddaccabadbcddddadbbccacbaacddcabcdcababaacdddddaabcccddcaabadbdccadcabbabbdbbcddccdadcabbaaabdcbbbbbacbbbdcbababdbdabcbcdadbddabcdaddbaaccaabdcdcccabbbcacddbcbbcbcdcbcaadacabcabbccaacbdbcdcbaaacdcacbdaacdddbcbccdbaabddaddcadaddbaabbcddccabdbcdbbaabcacbdbdacddacaabaababcbaadadacdabbbcdddadacdbcccbaaabdacabccbbdcaadcbcdbcacbdbabbddbacaaadaabcdabacdbabddcdcddcdabadddddbbadcccbdcdbbbacbddabdddacddccbddadcbdcadcdbacdcbcbcbaabcaabccdcccabdacaadbdbbddcaaabdccdcadddcadcddcdbabcdcacbaabbcadddbcdbaccababbaaccccbbdcaadacacdacdadddbcdbcbacbcdaabbadccabdbddcbbabbdbaddbcabdddadcdacbabcdddddcbbbcdabaccdddcadbcadbcdacaccddddcbccaadcacccadbbcdabdbdaddadacacbbbcbcaacccbbdccaddaabdbdcdadadacacdcbdaddbdcbbdaddbacdaadaccaccbcabcabcacacacaaabacdccbcdccbcdccaddbcadcadbadcdabdbcbbccccbadcacddddbddccaadccbbabcaddadbaaacddabaacdcaadbdddacadbcdbddacddaacdbcacbdacbaaaaacabbcaccbdaaabdbcdaddbbdbddcdcddaacdddcacdaacddabdbadadddccadcbdcdbaacadcbcbaadddcbccbabdddacabdbbacdcbdaccdcccbcdcdddadadaabaacabbdaacacdbcdcaacdbaabcddddcdadbdaccabbcababdcaddccdcdbcacbcbcabcadbcaacbddbcbbbbcdbddcbcdbbbdaccaacadbddaaccdcbacdcdbbabacaacddcbdccbdcccccacbcdadabcabdcbbcbccdcddbdaaabdcbccdabbabccaadabbabdcbddcdcbabdcaabcadadabbbcabacddcddbcacdabcabbcabdadbbddcadbacbcabdcacaacacdddbddbacbbdbdabaaaadbacabbababbccbdbabdaabbccabbacccabaacdaaddcddddaccacdbcadcbaccadbddacaadcbdbcdacacabcccaddcabadbbcbabccdbdcdccbcdbdabdaccdaaccdcacbbabcbabccbdbdacbbbccaaaaddbbbdaddcddbbacddbacdccdaaacabbcbcccdabaddaabaabcadacabbadbadacdbdaabcdccadaccabbcdcaaccaccbbaaadabbbbbbaacbdcaacdcbccabadcabaccadbcbcbdbdadccbcddacdcddcbcdcabdddbaddccacbabbddbbbaacdcbccdabdacbcacdcdabbdbdabdbaaabdbadccdccbbdccbcddccacabbbbaccbdaaaabbdbddbdaadbdcdcdabcaccbacaaddbbababbcdacbbdaacbcddbcddabbaddddbccaddddbcbbbbdacdbcdbbabcbcdcbbadddbdcabbbbdbccdcccacdadbcdbccdddabcaccbcbdbcdccddbbcbacdbaabbbdaaacbbccdacddadbbbbccabadddadbabcabbbdbcbababacbaaaaccddadadaaadbdcccddabcdbdcbabbddabcbccbddbadabcacaddadbbacdbcdcdbaddbadcbbbcaadccabbaabbdddbccbcbbacdabbaddaaabaccccdadcdbccccddbdabdcbbcabcbbddcabdbdbadcbbbccaccaddcbaccdcdaabbabaabaddcbbcbcabaabdbaacadbccabbdabcdcdcbbccccaacdddaccacbcdcbdbadbacacccddbccdbcdccccdbdbabdbbdddaacdabdcccbccbbadcbadbdcbbcbddcaaccccbccaccdaddadacbdcdabaddcdccabbccaccdacadacadcaacbcaddbccdaccdccbdabdcbdadadddbbdddcaacaaacbdacaaaddbbdadbabaaabcddbadacbbcdaadcbabacaaadacdacbccddbbccbbccbabbacaabacbacccbbbcaadcbcdaacaadbdaaabccbbbacdaadbcbbabaadbcdbcabdaaaabcdbcabcbdcacdccadbdabcabdbbcababcdcdacacabacbcdbdcbadadadbccddbcbababdcbdcaadcadcccbbbbbabcabbbdcadaabcdcadbabbdadcacadcbdbbaababcbadaccdccdaaadbbadbdacbddbddbbcbdbddbcccaccabcbbadccbcacdccbaccdcbbbccadbddddbdcdcbddcdadcdbddabcbacaadccccadcbbbadcbadbdbabdbcbacdaadddddccaacaccbadbabdccbddccddcbcadbcdbbacbcddaabaadaadabddabadcddacbdadbabbcdbcbcaaddbbbbcbbdabdbaadaccdbbdacbbddacbccbbbcadcbcbdaaddababbcdaabcaaaaacdaddddddabccbbbaadcadcbabdbbadacbdadbddaadcddccadaccadcdccacdadcbdccbaadcbbdbbbadcacdbddaccbcbaddbabbaaadbdaaadaaaddadaacbdabbddcaabadbdccacccdcbddccdcbccbaababbdbdccbbcbbbddddcabcddbddddabccbcdcdaaabdadbbaaddbdaaaacaacadcdacbccbbaccacbbadbdbbccacccadddadabcabdcdddcdbbbccbbcabdacabbcaabacadacbbbabcccbdaacaabccdbadadcbacadddccdacaadbcaddabaadcdccdbadbacdbbcaabbaddaccaaaccdaccdaabadcbbacbdaaabbcabcdccddcadacdddcacdccddaadbdcbcdbadccaddbdaaacbbacadbabbbbbcdaddcddddbaccbdcabbbdccdbabcdadbabdacbaacaabcccaaddaacbbbdcaacbbbbbbcccccaabacbcbdcbdcdbbaccaabaccabbbcbaadbaaacdaaaaabccabcacacacdabadcccadaaaddbbdbdcaddbccaaaadddbcaabdbabcabcccbbcacabcacbacccbdbbaccdddaacdadaaaacdadbdcbcbccadabccdbcbdcdcbccaadcacadcabdccddaaaacbadcccaddddbadaaabaccbadabbbdaccccbdbcdadddabcbcddabdcbacdccdabbacadbdbccadaabdbaaabbdbcacdcdbbacdcbbcbaaaaaadabcacbaacdcddbcdaccdddbccabdbccdcdcdcaddbacacbcabcddccdaddabcbbdaaccccdabdbaccdcbcabacbaabcbacacadaabcabdbbaccbbdcdccbdcdcdadccdbabbcbbcaccacacdadadcabbcacccdbcbcdddccdbddcbdaccddbabadddbaaaccbcbbcdccadacdcdbabbaaacdaadccdccddbaacddaadcdcdbdacaacdbbcdbcddcdcdadbdabdbbcabdaaaddcdcadddbbdbcaadcdabccdcdddccdbbdbcdccdcacaaaaadddabbbabbbdbadbadcbbadbabdcddcabdccabacddcdbbcccdcdcccaadaddbcbddcbdddbdadbbdbdbbbdcdbcabaddcbbdacbdcbdaaabaabbacaccadaadcbbdcbcdacdbcaaacaccdcdccdbddaacdbaadadddbabbadcadbadbcdbaddaacaadcdccdbbaccaccdbbbdaabdcaacaabdaccacbbaaddaadcccabcdcadcbbadbbaaaccbcdcabacaaaaddbbbdbdddddbadbbcaacbbdabbaadcaabbbdbacaadabdbbcccbdcbaacaccdbcabcccdcaacdaaabcdcbaabdbabcddbdbaabbaaaabcacdabcddddcbabdcdabbcbabcdbdbacadacacccdcacabcaacbdbbaccabdbcbcaaaaadbababbadbbbacddcbccddddacccccdbadbddcbbdaaadaccdadacbcacacbdddcaaaaccddbbdcbddcbcdbbbcdaddabdbbdbdbcbaddbddddcbddbacbaabddadbbcbdcbcdbdcbadbabcdbcdaadcbacdadbaaadaadbdddbadbaadcacddadbbdcbdcaddadcacbabbcacdbccbbaadbbabdbcdcbcaabdbadbdcddbdbcbcddcabddccdbbaaddbcbddccacbaddddcbcdabdbccccbabddacdcbccbdddaccacadcddabacbbddcddbcabcabddcbcccacdddcaacabaabacbbaacdcadbdaacbcdcbcdcdaabacabacabababccaaccbbaadbaccaccbabacbdbdccdacadcdababccaacdabcdcaadadccbabdacdabccdacdaaadbbdcaddddaabdcccabdbddcaabcbdcbdcabadaddbadbabdbcacbaaaadbdccacddacacbbdcbccbbbccbabbbcaaaddbbcddbacbabbcacaabadbcdbabbddcdbcaadadaccbabbddccbccccccddabddcdcdbacbaccaadaaabcabaccbabbdbdcaccadddacabbbdcdbaaaabacaaddcbbdbdccbdcbbddccbdbabbccbdabdaacadccdbcbdaacbdabccacbabbbadabcbadcbbacadcdbadcaccbcddbbaccdaaadadaddcabccbdcacdddddcdcaccbdadcaccabaaacccbbcbdacabbcadbdbdcabbbaacabcccbdcdccadcacddacadbbcdbdcbaacccabdbabadcaadccbdccabbbaccbcddcaddbaabccbaddadbcdccccbbccacbbccbcabbcacdcccaccadcdabdbbbacbcadbdbcccabadcdbadadddddcbdbacacdbddbbbdadccabdccbacdccdccbdbbcabcabdcccbbbaacbcdaabcbdbbaadcadbcaddabbadcbbcabcdadcbccbddbaadbaccbccddbbcdcaccdddcbddccdddaadbccacacdaddccacccdabcabaccbbcdcbcbcaadcdbabbbcaadbbcaddcdcbbbddaaadaaacbabadadccacbbdacbaacbdacbbbbadcaacccdbadaabcddaccacbcbccadacddcdcbcccbdbbaadbbbaababdccabadbacbdbbddaaacddcbcdbbdaabbddcacbccdcaacacbbcbbdbbbdbbadddbdaacdbaaaaacabaabbbdcdacabdcccbabcaadccdbdaaacdddabdbdbbadcabccadbbcaddcabbcdbcdacdcaabdbaddadcbbdcbcdccadcbccbcbdcadbdacaaadaddccbcaabaacbbabaaadcdcbcdcbcbcbcbdcbccaccbcccdbdcdbccacbbcdbdcbcbabdbbacbabacadbabbcabccdcbbdcbbcbcdcbbbacbbbcaaadacbaccdcdbcddbbdcdbccdbbdcdabdbbdccddbdbcdabacccdbccdcaabbaadddadcbacdadabdddcbabaabdcccccbcddaacdddacdddcaadbdbcbbdaadbdabbadcdaabaaadbabdadcccbddbbbbadbbadcadbbacdbbbccacddabdabcacadaaaccbdcdcddccbbdcbacdaaadbaaccdaabacddcdaacbaddbaaaaacddcbcdbcdbddddaaccdcbadbdcabcdbcbbdacacbbadcabababddaadbcaddddbbacbabdcccbaccbcdaaccdbcadbbabbdbdccaaaacdcaddacacaabdcabdacdbababaccaacdaabcbcaadbbdabaaaadbcbabccdaddbbdcdbbccadbbbdddbcaddbabcdcbccccbcbbcacadcbcabcdacacbbacdbdadbbaddbaadcdcdacbbcbaccdbddbdcbcbaaddcccddbdbbddabdccbabbdabdbbdcddaabaabdcdacbdccbdcabaddddbbabadcbbadaaccdacddacdcddbbcdcdbbccbbdccdbccdccbadddcacacddccaccacbdbaaddcddcdbcadaaddcbdcddcaddacbbbadbbbadbacccadabbdabacacbcabdbbcbadaaadbbaabdadacdccdccdabbdadacbccddcbdadacdbcdbabdacbacaadcadabbcbdadabbaaaabccdcdccaacaabcccdbcdadadcacaabacddbdcbddacbcbcbbcbccadbddadbbdbdddccccaadddcbbbcdbdcacdaadbacdabccadbcdbacbdcccbbcdadacadacdaaccdacbaaabddacbcdbdcaddaabcccabcaacbcdbbddaabbbcdaabbabbdddcdbabcbbcbabdadababaddbbbcbcadcbdaaccbddbabbabdbbadabdbbbccbdcaccadcbbabdacdbbadbdbdccbddbddadbadacbbccbddbaacddddcacddbdcaccaabbccccbbbbcaccabcdbbcabcbdbccbadacbcdabccddcddbbccbbdacdcaacababbaadcbbabdbcadcbbbcbbbbcbadbacaaaacbbcccbbdabadcbdaadaadccddabcdcbccbcadbdcaacdabcaabaccbadddbbccbadbdaccddbbabcbcbcddbbcabdccadacdbadbcaacbccdcabdcdbddacbbadcddcbbcbcdbbdcddcaabcdbcacdccddbaababadaaaabbdbcbddcadadcaadbadbcbccbbccacbbccccdbdbdbcadbcacddbddcabccaddccccacdaaaddcacacddbacbdbaaadadbaabaabacccdcdcdadcbdabbbbadaacdcbcacdadcdbbacdadcdbcdbbacadcacaaacbdcbcbdcddbabbabbabacacdcbbdddcacdbccbaaccccadaacdccddcbdcdbcadcbdbabccbccddaddddcadaaabbdabdcbbabadabdadbdddaabbcdddbcacdcadbadaaccabcbcbbdbdcbbadbdbbbcabbacbddacbdccbbbdbcaabbdacbdccccdcadbcbbbbbadaadccdddccdbdcbbacbaaccacdacbcdcccacbbadbdcbddbcdbcacbcbcaddbbbadcabcacacabdcaaadcddcbaaabcbbcabbbadcabadaacbbbdbbbadadcddaccccadaabacbcaccaccaabcddaacbbddbcadacaacddaacdcadcbdbcdcbcdbadddcaccbbbcbbcdbabbbcbdbbbdbdcbbcacaddccadcdcdbcbcbbdbaaaaabbdddcaddaacdbcbbcbcbaadccbdbdcadbaaaabcaadabcdbbbbaadacdadbcbadddbddcbddddccddcadacdbcacdcbabcbabbaccdbbcdbbadbbaaabbdbbcdaadcbcbaacdbaadadbaacdaadbdadacbdbdaaddcadbdabdcddddcbcdaaaccabdabcbbdacbaaadadbadccbcbadabacbdacccacbdbaaadadacbdaccbdacbdbdabdbcbbdcbbadbaaabadbcdbcbcadddbcbdddddbbcacabcbcacdccadbcbbbcabdbdabcbdacdccaabbbadacbaadaaddbacdbdddbdbabdbbaddddbacaccdbdccdadcddddddbaadbbcbcbccaadccdcbadcccabbcbccadacabcacdbdccbcdabbadbcbcacdadbddcbbacccbcacccabdcbbcbbababbaaddcdccbddbacddacbbcccbabccccabacbccbcbdcabcdbbbddcdcaabadddacdcddaccadcbbdaaddaddbdccabaaacbdcaacccbccbccbcdabcbcdbababccbabbddbbcbacdbbddbdbbdccbbccbbaccddbbcaddcbcdadadaacdbcaabbdddbccbcdcddadcbdabdbbbdabdbdcbacdcddbcdbbcdcabbbdccacabcdccacacaaadaadddcccadcaaccdadcdabcaabddacbacdccacdacddacabdbbbddadcccaaacacacdacbddcacdaaadadacbbaabaacbbdccbbbbcbbccdcaaddaaabababcbdddaadcbbadbdacacdbacbaabcacaacadccccccbdadbccbdacddadccbbdcdccbdbcaddcdabbcacccbcddcbaaacddcbcaddcbdbabadddcddccdccbbabdddacabaabbaaadabadadabbcabbbdaddaaddccdaccbbcdbacdaacaaddadbcbbcdbdcbcacbdddbbbdbcdcbcdcdcacbcbcdcacababacccdacaacbcbaccccbdaadbbaadcbaabaadaacbadbadcdacaabcbbbdbbcdabbdbadcccaaaabababcddbacabbaabaadabddbabcbacacbbcbcabadbaaacdccddcbbbcababbabaddcdabaadcbabcacbbdbcdbbdbdaccccddbdddccaabbdbcbdcadaacaadbccdccaacacbbbdcbaadddbdbadccbdccbcadadadaabcdcbabcbdadccdbabcdccaccbddbbaddcdbbdccacbacbcbcbaacccbbcbabacbdaccdcdcbdcbbcacbacbdbbdaacbddacbbcbadbdcbdbbbdbbbddcdadababaabcbdcddccdcabdbcddcabbabaddcbadbadaaadcdbdbbcaddaabdacddcacbbaacadcdadacaddcaacdbddbcadcaacabdadcdabccbcccbcddadccbbaccdadccabbdbabddbadcdbbacdaabdbadbcacabbccccbacabcdbccbcdbdcabddbccbaadcddaccbdabccaacabacadabccbadabbcabbbaddcccdcdcdcddddbadcddbbabdddddbbdcbbcbcdbbcbabccccacdaadacdcddacbddddcbcaaadcdcbcbcadadadaadbbdaaadbcdcabacbcaabbbcdcaaadacadbccbdaaabcaabbdadabbabdccbdbabcabacbaabdccaadbcadcddddcdaadbdadbdcddcaaccbbadcadbcbbcdaacdbdadbdaacbcdbcccbbbbcbcdbaadaddddaccccbadccdccbcaadbaaddaddccddbdcdbdddbbadddbbccbddbdcbbddcdcbdcdacbcddbbcdabcbaddddccdaddcbbabdcddaacccabbdcabcbddddbbccdcbbccddbcbcdbcdaccdccbaaacddadbbbcdddcdaacbcabacddabcdcacacbccdabaccacccabcbcadcabbaaddcbdbdbabadbdddaabcbbcadaababcbcaaccaabaaddbbbcaadaaadcacdddcabdadaddaaacdbbacccbdbcbaaacdccaaaccccdbbabcdbdabdacadbdddbbddabaacdbbdabcbbbdacbdaccababcbbcacdbdbadcbdcbacadaaccbccabddaaadbdacacbbbadaadbdddaddbdcabbabcddaccddbbcbcdbabcbcbabbabdccbadadacaacbdaaacdadbbdccdbbcadababbdbbdbbbcaadabbbaadababccbcabddbacadbbdabbdbbbaadbdccbabddcddcadbddcacbdbaaccccbabbdcbbcdbcabccdbbabccaabbaacdddacaccbcdcbccaacaaadabcdadccdbabcdabddbccbcbbddabaccdbbadadabbccddccaccadcccbacbcdaaccdabbbccdcabcddbccbdbabbcbbcccddddaaccdaabaddcaacacaccabcdccdbccbccbcbacdbcdcacdadddcadcaaaaadcdccbcbadcabdbaddacbadddaadadddbcbaacacdcbdababadbaaaabbccbcbccaaccbccdcdcacdbcbdaddcadcbcdbbaadbcddaacbcdcbddbdccccadacdabdbddcbbbdcadcbcbbcdabbdbacbaaadcbcabadbcacaadcabcdbaccdddaabbcbccbbbcdbcdcbaaabaabaaababaaaddbabdaaaabaabbdaaaaaabadbcdbbcdddacdcdcccdacdcdbbacabbccbaccccdaadbdddbbbdbdbdcbacaacaabbaaddaacabdcbddaaddddbcbbabaddccbcbcacbdddccddbadcdddadbdbbdcabcaaadcacdbbbcbccccbddbcdbdcadddcbbbbbbdccbcbdaaaaadaaacbcbacbbccbcaddbaaaabdbcabcbaabccabcdccdccddcacbbadbdcabacabbcbcacacaddaacaadccabddddbccddabcddddccadadcacbacadacdcacbacbbacccaabacdcadabcdcbcacbddddacbddadbbccaddacbccdbccdcadcaacdddcbbddadddcdbbbdbccbdbcbcdacadbbcdadbbdddbacdbddbcacaabdbbbddbcacdbbbdddabbccbdcbcdddacbdadbbbcbcccbdadbbbdcadcccaaadccadaacdbbdcbdaddcbdabcbbbdbdbccbcabddbcdcbcccabbcaaccaacadabacbbdcdccbbcacbcabdbaabaddaccadabbaabcccacdcddaacbbbbbabdcabbdbdbdadcdcbcccdaccaabacbbabcddabcccacddacdcacdddcabbdaccaadbbdaadacdabdbcdddadacbdaadaaabdcdbcacdcbcdbbbdaadcccbdcabcaaaaababbcaaacdbcccdaabdbcabaadcddbaacccdbdbaacccdadcdaadcdccccdaaddacbdabcbadacbaddcacadacdbcbabaccdccacddcdccdbcdbaccbaacbbbdbbcbaaabaadccdcbcadbaaaacdbbbadabcaabaddcbbacaadcbcdccadacdabdbcddcbcbbcdbccccbdaabcaccbdbababadacabccbadadddabaabcaabbcccbbcbaaddadbbbaaabdcbaaaccdcddabababccaccbabddbcaaaaabbcacdcbbabaabcbadadacbcbcaabcbaddbabcddddcdcdabcdbcaadbabbbbbccdccbcbbdcddddbbabbcdadbddabdccdbbdccadddbddbccdbabddbbcdacacccbadbababbbacdcaccadccacabbaadddaadbcbbacdddaacccbcbaadddcbadbcdddbbadbdbcbdaabccccbcbdcbcbadbcacdbdaabbcdaccadcbbbddbcbbacccbdbcbcbabbbdadddaadaadaabbdabbbabcacbabddbbacddcdaadbcaacbdbbaddbddcdbcdabbacaaccaddcbdaaadbdbadcdcacbbcccdbdbdcddaddcdaabadbbadbddadcbdaacbbddddcacaabadbcdabdbbdcacbccbaaadbbaccadbcbddbdabccaabcbbdbcacbdcdcdaabdbacbaaabdbbdccdaacbacaaabadbbdccdabaadccacddbcaacbdcabacaccdcdcddabbbcdcababdbabdbdddcddbbdabbbcaaaddaabbbddbcadacdaadabcbaccdbbcdbbcabbbabaccbcbaaaddbdcccdcddcacbbccbcdcabdbbabccccdddccdcadbdcaadadaadcdccabbcdcbbadadadcacacabcadabdcbbacaacadcabddabdbbbddccbbacbbcbadadccccaacaddaabbccdcacbdbbcdadcbbcbadbbacddbbcdabacbddddabcadacddcabbbccdbacbabcccadcbacbdccacdddcdcdbbadcacabaaadcadadacbcdbcbacaccddacdaadaaaabcccdabaacdcdcbcadcccccbabbbcbdbcacacbdbaabacabbaadadcccddabccbaabdbabdadadcbcacbcaaacabadadaaacadabddbccbbdacccbbdcaaacddcababcdbccaaacbbaaabcadcdcbcaccddbadcdcadaaaabcddbcbabacdaabbadddbdcaccdbbaaabcbadcabdabbaabcadabdababdcbddcdababbabcdbdddbdabadcbdbaaadbdbaccbcddbcddabbcaccadbdaaabccddbcbabdbcddbbbcbdaabcaaacdccbcbbbcabbbbbccabbcadcddbccbaacbcbdacdccddcaddddccaacbcaddcaadbbcdbaadcacacdaccbdbacddabadacabdaccacadcdddbaaaabadbacccbcbcaddaccadbcbdabcabdacacbaacbaddabbcbdbaadcdbbacbbdabdcacaabbddbdcbbaccbddbccbbcabdbdababdaccdacddcaabcbccddacbbcaaacacbccdaacabaaabddbcadbdbaaaddddabdaaaccbdaaaadbdcbadbdbdabddcacabdbcbbdcbdaabbaccddcabdcbcabccdbaadbaccbdaddccabcabccdccbbaadcbbdcaccbabddccaabbcdaacdbbddbacbbbabcbddacdcdccccacbdabbdabbbdcdbddcbdacccbddcdbdabbbcbcdaacaddabdaaadbdbbadacddbccdccbdccbcbaccbbabcdcdddbcadbddddaddccdcdcacaacdbccbcdbcbdaadaaddaacaaacaaabaaccacbcaabbdbcbddaaaabbdadbccaccbcdbdaaacdbdaaccdccaaaadaacdaddbbaacbdcdccbacdcadadcbbccaacdaabddbadabbdacbbbbccbdbbaabbdbdaddcdabcdcabaaabddcdacaccaaabcdbcaadbadcacbcdddcabdabcdadcccaacaaabcabcabccdddaaddcbbaaccbaccbdbdbaabccdbdbdabbcdcdcdcabadaabbadacabcaaacccbbcdbbcbbacdabaabbacdcbbabacdcadacabaaaabbbbdbdbadbdadcabbccbdcacbdcbdaccbcbbcdabcdabcbbdcacbdddbcbdcadabcaaadacbddcbcbabbdbccabcbbadadacaaabbabbadcdabbdbcbabcdabaadcabaddadadacdbcacaddddccbdbcadcaacabdabcbbdcdbbcbbdcdcdadacdadcddccbacadadcbdacbcdcdcacacabdbbcdccbcddbbaaacbbaccbbbcbcaaadbacbcaaacacabccbadcbcdacccaabbdbddaccadabbbbbbcdaaccddcdcadddabbbcdacddddadbadaaaabccdbbcbddcddcbbcaadcadccdcacdccdcbcdddcadcbcbdcadddbadaccddddbaddadaccabacaacdaaaddbdcadccbcabccacdbbdaaaacdacbddbabbbbbddcdaabbcadbbcbcabaccddabddbddcacadacdddcabbdcddbcaacdcbdcbcdbdcbdccaabbcdcdaddcdcbacbcccdaacbcacbbabdcddddadbbbcbccdcabdddcdbddbabcabdaccabdbabbcbabbbdacccacaacbbcbcbbbaaacbadbdcbdcdcbccabbabbaaaadddbdbcbbdbdadcbaacacdbaadaccadabbaaadcdcdbddbbbaaadbdaabddcaabcbbcbddcccaadbdddddabbacdddcbdcdcdcaaaabccbdbacbcabcbcdcdbccddbbcbcdabadcbaadbdbdbabbabccddaccaaddbaadbabcabaccbccabbadcdccdbbdbdacacdccdabdabcdacccaddbbbacbdbbdccacaacdaacadbaaaaaddbbbaadbbdbcddadbdbacadcaddadbddacccadacdcbcaaaacaddcbaaddddddbbaacadbddbbbdabbbddadaaaabaaddbcbcaadbbdbaaaabbdabbacccacdbbdbcbdabbbbbacbdcacabbdcbadcbaabbbcaddadadbbbcbcbdbacdcabdccdbcadcbbdbabcadaccacaaaabccdcdbcbdcadabdacaccabbbccdccdbacbdcaccacbcbccccbdabbcdddddaacbccbcddcaabcdddbcabbdaadadcdddcacdbaddaaccdcdcdccdaddaddccbaddbdabdbdcdddbcdcbdbcdadbcbaadacaaadbbbaadbdcdbccddadadaabcdcddacdacddcdbcbcaccdcddbbcbaadbadacccdbacbbccbdbdbacdcdbadccddbdacbbaadbbdccdcddaaddadabbbddcadababddbcbadcdbdaddbdccaddbcabdcdbbccbcdccacbdaaadcdacddcbcacaadcdcccbaabbcadddbdacdbbdabdbccbcbbcdcdddbdaacdddccacadbabadbaccaadddaaddccbabaacdbbdcccbbaadcbacdcdcddadacaddcbcdadacaaddbdabdcdbcabddacdbddbbdbcbdabdcacbacdbcababbddabcdaabcdacbdbacacdbabadbacdbadabccadacbcdacadcbbababbdddaddccddacccaabbacddbcbbabdababaaabcbcdabcacccadabdbdbbdadddbaaddbdadccbadaaaacccddccdcadbdaaadbbddadadcccabdabbcccbabaacbadcdbcccaaddaddaadabcdacbbdaaddabbbcabaddccdcdbbadbdccaadbccbbdddcadcbacdaaadcaddcadcbabadbdbacddadcdbbbcbddaabcbdcccbbabbabaaaaaacccdccccbbcdadbdddadcdcabcacbcdaadabaccbabbddbcadcbabbddaacddbcccabcdcaaaabaccbacbbcdddcabacccacdbdbbcbdcdccdbddcbbbccbbccaadacdbacaddbbbbdccbadaabbacbbacadbaadccdbbcbbdadadadcbddbbdbabdccabbbcbcdaacbabcabbcbdcbabdcadddcabdbbcdbdbcacdabcababcdaaabbdabcabbdcdbcccabdadbbabababbcbbdbdddadcbdcbbcddadddbdcdddbdddbacaaadddbaaddcbbdadaabcdbcaccdaddddcddbdabdcadacdbdcadcdccdcddccbdbcabbbaabbcbaccbcbbcdbdddbcbbabdacbacdabdcddacbdacdbbbcaacdbaacadcacacbdbcbbaddaacbaacbadacccbacdadccadddbcaacccacaaddacbadcbbdabbaaababbdcbaaaadabbcdabcabcbbbdaccdccdcbabdcdbdabdabbacbcbddbcbbcdbbcabccabdcbcccbbcbcbbacaddcbdacccdadcccccddccacdadccdadbdacabcbcaccbdddbcacdddaccbacddbadabbccbdbaaddbbdccccbdaccadccdabbcabcbacabcacaaabacababaccacccacddbdbccaccbccdbcabaabbabbbbdcacabcdcabaabbdcccabcbbbbbddbbdaccdcacbaddcbaccbcbcbddbcbadadcddaadbccbbdcaacbcbcccbddcacaabbabdcaacdbdddcaaadbddbbdabaddddbdbacbacaabadbdaabdbbdccdcbdbbaddabddcbabbbcddabdbaaaadadcdccccdcddbaabbabccccbdbaaccccbcaabaabadaadcbdcbdadddccdddbaaccbcacdccaaaaabbccdbabadcacacccacaaacdabccbaaaddcbaddacbacdacbabbdaaaabcabbbacccadbddaddddddcadabaaaadaaddadddbbdbabbacbdbabdcdcbbdcbbdddcacacdbbbddcabaabccbbabdcabaccaadcbcddccdccccaaddababcaaabbdaaababdacadccaaaabbbdcbdadcdddcbbdacbbabbbbbbbcdccdccacbddaccbbdabdadcdbbddddbcabaacddbabdbbcccadbdcbbacaacccdcdabacabdddcaccddacbadbdbbcccccabcabcbaaccccbdcdadbdccbacaabbcaabcbcdbcacabcacddaccdabcdabcacdacbdbdaacadbbaacacbaccdbdbbcabbadbcccccdcbbcabdbdaaccacccadadbbbccdcbadcbccababaabbcbccdcbdbcababadbcdbacccaacddacdbaaabbcccdcbdadadccadcbaacdbddcbdcaadacacbccbcbcbddbbbddabbcddacbbbaaccbcadccbbcbbcacdbdcdbadacadcbdbabacbdcabbabcaaadddaabaabbcdcdcaadccacaaaacddaacbbdacacdcdabdaaccadaaabaddcccdcacacbbbcbaaabbdbaacbbbdadddcadbccbbbbddccbdabbdcdcaccdddabcdbacdbdaaccbdbbabcbcabbacbbcddadcbacbbdcbacbcdabcacddcbadadcadbbacaaddaacacbdaaddcdbdaaadccbbcddddaaaccaaabdcacccbaddbccaacbbbadadacbcbccdcadadabccdcdcaccdbdaddabadbacbabdaacadcadcdcaadbcbaadbbadbbabcabdbbaaaccacdaacaddcdccbaaaadbdbadccbcdadbddccbcdcddcacbbacdcddbbbbaddaaaddccdbdabcddadcdbaadcdccabacdbdabacadbdcdddcbabcddcaabcccdaaddbccdddccacbacadddbcbbcbadadabbbdaabddaabcadadabadbddddcbbaaddcadcbdcdcddaaccddcbabcacaccbdcdbabbbcbdadacbadaddbabbaccaabbdcacccbcaccaccbaacacacaadbdadabcbacbdabadacabbadabdddcaacdcbcadcbcccbbcdbcadcaadbadabbdbacdbbabbcccaadbccddbcaabaddbdcdddadcadbbadbbaacddabbdbcadbccbbadacdddcdbbacdcdbbddbddcdaccddbddcbaaaccbabcbcdbabdddadbcdabbbbdbbacaacadcbcccdabaabdbadacbbacacabbbcaccbcccaaccaadacdcaccdcddabcbdccdcbacbdddbbadadcbcccadcbbcaaadcacccbbabbbdbcccbbacddccdaccabacabcdcdcbaaaddbbdbcdadadbadabdcacddbcaabdbdaadacbaccddcddbbabbddbdbbcdccdbdcdcccddcdadaddacbaadaccbcdbccacbacdccbbadbccadbbbabaaaabbbccdbdaddabdcaacaabcbbabdcddcdcdcbdcbbaacdabcabdcdddcdccccacabadcccabaccaaacbdbbbaadbddbacdccaaaadcdabaadbacabddbbddcbacabcdabcaccbdaccbaddbbcdaadccdddadadacaadabcacabaaaadcccbbaacbddbbcacabdadccadccdbabdbacbbbabadccccdccccdacdcdabddbdaddcacdbcacabacccbababadacbdadbbdabbcbbacdcacddbdbabbcbddbadddcddbbdcbbccbcabcdddccbbbbdbdbdabaaaabcbdbcdadaacdbcdccbdbbbdcabccbdbccddddcaddbabdcbccddddbbcccbbaccbcdcdbccbadbbdabaabbbbbabcaadaaaacbbcdcdcaddcccabcdaacbabcccbbabaccccddbacadbcdaddacadcbdbdcacadacbccacbbaabddcaabbbbbbdddadcdbbdccdadcadccdbcbcbdbbcaccccbcbdcbbdbddacdacdcbcaddcaacddddcacdddacbdcddbdcbcbacadbcacdabddaadddcdcaabcbabbdcaadadabbcbbddcddabbadaacabcaacbbdaaabbdabbbbcccbaabbbbcbdbacacabbdaabadbabbcbcaccbaacacdbbcddbabaaabdbbdccaddabcddcabccaccdcabacacbcaaaddbbbbaddabdabdacadbcadbaadccdacbdcbdcbcaabcddbbdbabbbdddbacaddadaabddccdbaacacccdccdcbadcdabbcdacccaddaccbccddadabacaccaccbddcbcaacddddaaaabdddbdaddaabdccdbcababcdbbcbbdccdcddbacbabbbdabdabaaaabadbbdaabcbcadadcbbbdcaadacdaaacdcbdccdaaadbcbcbdcdabcbbacdabcbaaaadbbddacdcabdcbddcdcbcbbbccdbaaabaccdcadcbdaaabbcdbdccbcabdcbaaacddcccaddbcdccddbbabdacbdbddcbadbdcaccdabadadccdccaabadcdacacacdaddcaadbbadcabcaaddbacbbdabcbcbbdddbdadacbbdadaadbaadcbadcacbadbcbcddbccacbbbddbadbbdddbbbbcdccdadadaadcdccddaabaddbcbacdccbcadadcdcddccdaaacacaccbcadbbddddcddadddddaadcbddaaadcaaacdaacabccdccdbcdacdbbcababdbdacbcdbadcabadababacdadadcddbdacbdddcbcacacdabcccddbadbcbababcaddacdddddbbbbaaccdaccdabcddbbdaadaccdbabbdabdbcddbdbdbcaacdcabcbddcadadccabbadbbcbdcddcdaddbddbbbccdbcccbcacbdbdbcbdaaadccabdbcbcaabccacbbabdcacdbdcaaaaddbccccbdcacacabbaaacbcacbbccddcbccbccccdbbcdddaaabddadddcccccbddbbbbccabcaabadddaccaadadcbddddabbcadcbacbbbbbdcccbcbdddadaaabdcdabbadadacdcccdcbabdaaddccabccabcacadcbdbadbdbaddbbccaacaaadcaacacdcbabcdabbdadcddaccbcaccdbcdbadcbbcaaaaaabcadacbdcdabdddbccdccbcbaabddddddbdccadbbaadbddbbddddabdccbdcdaaacdaccbcaacaabdcbbdacaabbcbbdcdaabadccdabaccdddccdcbccabacbbadabccccbddabcbcaabbbababbabbbdbaddcbccdbdbdddddcdccdcbacddbbaaadadadbccbcdcdcadcbbcbdbdbcdaaacbaaaacbdcaaabaabdbcdcadcbbdacabbacbadabbadccbcbdbacaadadcdbbbacadbccbdcbcdcaddadaccdddcbaabddbaccbcccdbaacdcbaacacabaaabbbadccbabcaadadbcabaddbdbdccacbbabdadbaadaabbbadaddaddcdaaaadbdcbcdcadabbaabbccbadcaccbbbddccccdbcbdcddcdccbcaccbadacbdbadabdbdacbbacaaabadcacbaddcaadcbdcccdcdabbcabaaadbbccbdaadbcbaddbadaacbcadaabddcadbdbbabcdbccaaccaadddbaccccdabbcabdacaabdbddbacccddaddddabcabbabacaaadddccdaadadbbcbddddccdbccbaabddcdddacbbdaddcbddadbadbbbccdabddaccdbbbccddcbcaaaabcddaabcdcaddbaccababadbcabccddddadbbdbdcbcddcddcacdabdadcbababdcddbacadddbaadcaccbbdcabdaabbbccaddbbadabcabdccababdcdccbdacccbbbabdccdaddcbcbdcbaadabaabbdddbbaacdbabdcaadbbaddbbcbbdadccbcadabcadbdbbdbcbcdccbcdbbadaadbbccbbbbccbcbdddcacaaaddadbaacccdadbdbcaaadacdbadcaccadadcdaadabcaaaccccbccabbdaadbcadacacbcbdaddbddacaddddacdbccbdcbbdabadabacbcdbbcbdbabcbcdbaacdacabddcbcdaabcdadbddbdabaabbbaadcdbdcadaabbddcbdaaabaacadcbcdbaccbcddadaccaaccbbccabbcdcdbaaddaddcacbaaaddaccdbacccbdabaadbaabaddabddbdcadadadbcbbadcabddbacadcabbbacdcbbdadddbdaabcbcbbddaccbcddcacdbcbdcaaabcbcaddaddcaacbaacbdcaddbbbbaccbabddccadbbbdaddadbddbdbbdbbcdcadbbdbbdcabdddbbbaadbccbcdcccddbcabccdbcdccbddbabddaccaadbaddacaaabdbddbcdbddbddbbddddaddcbababdddbbadbababcdadcbdddcccbacdaacbcaccdcacaaccababbbdaabccbdbabdcdbacbdbaccddadddcbcbadaaabddabaaacddbcbcdabdaddaabbacbbdabaddcddcbbbabccdbbbccdbdcbbbaaaddadaaaaabaccadcccbdbbbbdadcccbcdcdcbdaadcabcadccaccbbaabbdbaaabdbacabcaadbbdabadbaadbabdadabbcabdbabbdcccdccadaabbdbaacbdbaabbdbcdcadabdcacdbbdabcaddaccdddddadacbaacdcbacddcccbaddcbaadcacddabbdccabbbdcacccbddacabcdbbdaadbcdcbdbbdbadbbddcacbccaacbdbadcdccaadadddddcaadccadacdabcabcdadaccbcbccadabbabcdbdcadbcaabdbabbcccbdcaaacaadabdbabcaaacdabddccddbbcadddbdadbacaabbaaaabcaddddbcaadabbacaaccbbdaabaccbbabdadbdbadbccbdccabdcabbaadccdaadddddbdbcbcbaabacbcababaaacdaddbbbdbbdbacbbaacdbcbbbbcabdcccabcddcbcbcdaacabdbaccacddadcadababdbddbabcbccbbdacccdbbaccccaddcaabdbcbcbccbbabcdcbdacbbbbadccbbcadbaabaabcacccaabaadcdbbbbadbbadabcddbacbbcdcadacccacdbbbdbbabdaaddcdbdabdaccacdbdcbccbacccbcaaddbccbadbaaadcbbbaaabdadaacdcddbddccbaccadadccbbdabacacddaddbbcdaadcbbbacdcdbbdadcccadcdddddaccddbbbddcdcdbdcdccddaaddbdbabbccdccddcbbdcbbccbbacabcdccabcdccbcbbdaabbcdbddddbaadddddbbdcbbbcbabbdcabbaccabcddbddcdcbbcacbadbcbdcabadbacdbaaaccdabcbabccabaabbadcaaacdaaadabbcacccbacbcdadccbbabcdbdbbcccdcddccdabcdccbddccbbcccbdabcbadabaaadbcacccaabdcbcdccdbcbbccbacbaabbbbddbaacdbbdcdacdbdacddcbcaacbcbddbdccadbcbccacdaadacacddbaacabbcababbddabdcabdbacaadaacdcdacdcdaabcccbdbbbbbbcbccaacbaaddaacbdbacddaabdbaadacbaabcdabcdcdcbbdcdaccdcababbaacbaadaddaaadaadabdbadcaaacabdcbddddbbcadddaabbdbdabacbccaabdababadcbbabaabdbdbcbdbdcaddabbacdaddabcadbccbcadbadbacbcabcbbcdccbddcaddacbccbdacdbdaadbaddcbabdabdaddacccbcacbabccaaabcdadbbadcadcdaababbcbaddcbdbadccabcbbbbdcddbbbbcacdbbacacbccadadccdbcaaaabcbbdbaabdcddccdddaccaddbddcdcbacadacbccddccdcdaccbadadcdbcbacacaabdabadcbddbaccbdadbadbbcdbadbacdbbccabbdccbdbabbbadadaccdcdbdaadbbcaaaadddcbdcbacadcddaacbdadabcacdbdcdbbddbcbddddacacdbadcbbacddaacdcccbccdabcbadcababacbabdccbcdbcbaddbaddccbaacacabcbbacacdaddadbabbbaddbbccbbadbdcdbbcbacacaddbdbacdcbcbacdcaaaacbdabbadbbabcddacdbdaccbabdbcacdcccbbcaadadacdbacdbbdadccaaaccdabcbcbabadcddaadaddbbdaaddccdadbdccbcdbbdacadadadcbccccabbadbcbbadbabbbccddbacaddaadacddcacccddaaaddadaacbdcbcaaccabcaadadabbcacdababcdccccabbddbdabadabcadbbaaabbcbaddcdacdcdaadbdcbcdbaddbcdbdbadcdcbccaabbcccbcdddaacdaacabddddbdbdbacadaddbdcbacbabbbbbbaccddccbcabcbacddcdacdbaaaccadbbcbcaccbbdacccdbbbdccbbbbacbbdbbacadcdadcddcdbaaabbababadddbcdbaabaadaddbcddabbdacabdddbdccdbbbddcbabbadcdccbadabaacabbdaadbacbdcdaadabbdacabcccddadcddacdadcdbdbadabcdcdbaccbcabcbddccbbbacdccddccdaaadcaccdaacdcbdbcaacbaddcbabdcaabbbdccdbaadcdcdcbcbdcdababccbadcbccbccaccdaadcaadcaadabbdcaacbabdcbacacbdcbabdabbaadcdadcbdadbadcadcdcabcddbadbbbcdabcdacdcdaddbbcaadbccdcaadcadbdaccdcdbbccaadaaadaadbdaaddacccbddaabcbdabcddbaaaadcccaaabcdbbdabccabdddbbacdbcbbaadbddbdbabbbdbabbdccdbddbbaabbcbdacdcbcacacbdbdadbbabcccaabacacdcdddabbbdbcdadabbccbacccbbbbbccbbcccacccbbccbaccbaadbdaadacbdcaaadacdcccdcbcbcacbdbabacbdabdcabcbbacaabbbbbccddcdbbbabbcaccddddacaddaccbccddaaddcbcdcddcaacacdbabdacddcabbbdabbcbccabbddabbbbdaddacbdbaccababbbdbababcdccaaacbdbccbbddbdccadabbdbdbcdcbdcabdbcadcbabbacdbcccccbccbdcddcbbaabdbddcdcabaabcaaacadabcbcaaabcbbdccbaccdcabdbacdcadccdcbadcabbaccaaaadbdddacbdbdcbcbaadcbbcaccaaadccbdaddccbbcdcdbbddbbcabbabddbbbbbdcdddddccababbbdadddaaabadabbddbdccdbdaddabbcbdcbbaddddcbbcbdcababbccabdbbdcdbabbadbcbdccdddbabdbcdacacdbbbbbbdabbcacdcbdbabbdcdcdcdddbcdcbdcaacadababcacbcbcaabcddcbabcccaccaadbadabdcdabbdbbdddbdcbcbccbbaccaccbabbcbcacdccaacaacbbdabdcdcabbdccdddbacadcdcddbddaabcdacbabcdcccbadbaccaabaccaacbbcdbbddadcdbaadbaccbdcacccdbbcacdbacbcbcbbbdcddadcdabdbdbdcadccbdddcbbdaadbcbcdbbdcaaadbaacabacadcbabdcbcdacbbcdbdbbdaabbcaaaabbdcacaaaddaccaabddacbdccbddadbccccbdcbaaccccaadcbadadbdcdbccabadccabacadabcadddbbccccccbbccadbdcdccdaddacbaddbcbcccbcbcdbbdccbcabbcaabdacaadbdcbaacbcdbbdcdbbaddcaddabccdbbddbcdcadaadababdbadcabbdcbdddddcbaabbacccacadbddaabbacaaabcaadbbbcbddbbbbdacccabccdbbbcbacdcbbcbdbaadadbdbadbaccabcccdcaaaaacbcdcdbaccabdaadcacadccdacccacbbbddbdadaacddaddabaabddcbbaddaadaaacbbdadabccdcabcbbbcbddcdacbcdaacdbaaaddddbadbdddcabcdacdddcccdabadabadabdbcbaaaacdbbdddabcbdaaddabcdcadccbbbbbddbdcacbdbcaababcbbcdbbacaabaacccacdbdcccbdddabdaaccadccdabacddaddadbbbdbbcdccaacccbdddddcbdaaabddcdbacbddaadaaabcddcbacdcaabcddcabddccdcaaadadbadcabacaacdbbbccdacabbbdcdcabdbccdccdbbcbdbbcaaaadadcccbccdacbccabadaddaadaccbcacadcbdacbaaaaadcacbacdacbbaadabcddcdddcddacacbbccadaddabdbccdbbcacbddadddbcbccadcbcddabdcbcdbbdcccadadcacccbbadcdcdddaddbdcabdcdcbdbdcdbdaadadaababcdbaabdbcbcadbaaaacdabdbddcacdbbdbdcaccbbdddbbbabcddccdbabaaccbacdbdbadbdbdbdaacaabbacdbbdbbacbabbadabdcddcabcaccbdcbcbbabccadddcadddadbbadaccacbcbdbbcbacdbdcadaacadddbaacaaaacdbbbddaaadaadbcbdcaccdbcdacabdacbabdabbadbccbddccdccdbbdbbaabacabcbdcddbaabdacaccbbacbdddbadbcbabbdabbcbcacaadbccacbaaacacdaaabacbcdccadabdacdadacbbdccdaddcadcddbacbaaaaaaaabcdadccbccbbadccddbcbaddddccabbdbaaddcadacadaabdcacdacaaaadabccbbcddabbcbbbbcdcccabbacabaccbaddbcacaaabaaaccabbabaabbddaacaadcacbcacbbccddcaddcbbdadabacacbbbddabbbcbdabcacaddaacbbaabdcccdcddacbdccdbcdacabcdcbacadabcdbbabddcdbadaaabcacbbdbbbddadbcdcbacbcbdaccbbbbcaccbbcdddbbddacaccddcbccbcbdcccbbcddbadabbbbdbaadbdcbdbccdcbbacbabacdcadbddbbbadabccdddbabcdbcadcdbcdccaacdaccbbddaabcbcadcdbaaaaccccadbacbcaadacbdadcdadbbddcabadaaabacaddacdbcabaaaacdaaadaacacadbcadccabaaabcbdacddaadbddcdcbcdccdaaabddadcddbabbbcaabadcdcbdcddbdacddcbdcbcadaccaccdbcbaaaaadbdbcccdacdcbaacaacddaadacdaaababdbcdddbabbaadacdacbabcbaadabacccccacaccacdabdccbaaaaadcabbdabbccadacbdbcadddababaaacadaddbbaaabbdaaabadadbcadbaaababbbadababbacadacadddbadddacbbbcbdadadacbcbaaaacbbadacadaddcdbbdacadddadccdbacacadaadbdbdabbdcdcdaacbdbbacbcadaccbdccacbdcdadaabacdbbbcdaccbbcbcbbaadcdcdaadaccaadcccdcaddaccccbdbccdbbbbbddcbabcabcddacabcbdcabcaabacbbdacdbddacadbbbbbbaddbdaaddbabdbbdaaddbdabdccacabaddadacdbdaadbadbdcabccbdadbdabccdaddcdababcdcdbbdddbbbcadbbacbbbbcacaaabdcaaaaaaddaaabbabdbcdacabdbdbbaddbbdbbaccaaddabbcbccdbacaddadccaccadbcaadcbaaadbcbaadbbbcbcbdbcabcbacbababdacbbaabaddcdbdddaadbadcdccadbadbccccbaaddaddabccccbdcdadcaaaacbcbcbddaaaddabcbcaabcbbaabcccaddcbcdacbcdababababdabcdacabcccbbddaccacdcbaddcbdcacbaaaccbcbaaadaaabcacabcccbacaddcbdaaadccccbddddbcdbcccdacbacdaccdaddaadabacacaaadcabacaaabaadcdbadbdccdcddbacbacbcaaaaadbcccbdbbdacadadbdaaaababdccacccccacacbabadbccdadbadbcbaaadacdcccbdababaddaabdcbccdacabbbaaddbcdabaaadabdaacbcccbadbbbdaddbabbcacacbabacdcddcaacababbbdcbbcaaddaaddbabdbabaddcddaadcdaaabacbbcaadabacbabdacaccacbdbcdccddbdaccdaabdcaababcaccbadbbabaadcbaababdbbddaaaddcddcaabcadbdbccbbbddcbadccadbccadddccdacabbddddbdcbbbdabdacbbbbacaabdcdaddbddccdbccaaadbdadadbbdaaddbcbbdabaacacacaaddcaaddcdddbdddabbcabaadccdcddcdababbbccbcbbaadbdcdbbcaccbbcbdaabdabdabccbbdccdaabbbadcddcdaadadbddadddcccacdadcccabdabcdcbacbbcadbadcdcdbaacdbaaacbcbcdbbcadabcdbbbcbbdadacdadabbaddbdbcdbabbadbcbcdddcbcddddcbcdcddbadbbcbdcccbbbadcabadbbacdadabadacdcbbdaccaacaaaccbaaacbccaddaddcbcdbcbdbabddbbbcabacbaacccabbcadacdabccbacbacdbdadcbcabbdbbbdbcbacacdddcabbacbbdccbdbcaaaddddcdbbabababaabcbccccbdcbadbaaabaccacccdccbcccdabdabcadcdcacdcacaabbbbaaaaabacabdbbbcababbdcbddabcdcccabdaccdadbbbcddcbadbcadbbadbbcdcdcbdcacadcabaacddcdacdcbacccacaaaaaddcbdcddcddcbdaabccccbacadbcdbbbdbcbccadcacbbdbbbcbddbdaacaaccddddcdccacaacadcbbadcaccacccbcacadcddbadcababacccbaddabcbbdbbdccccbdcbdddbcbcbcadccdacbbadaaaccbdaaaadcbbdbdabdabaabdcababbcdacaddccdbbbabbbccababacdbcbcabbcdcadbbdbbdbdcacbabdaccbadaabbaadcbdbadcacaaacadbbbbddbdbccdaabbdbadcadabdcaccadcbbdadbcccccbcbadcabdbbbaabdbadabadabdbbdcdcdabdaddcabbbacdacccaddbddcbabacbdadcbdcaacccdcbcabaaaabbbddabaacacdaadcdadababadbacadbdbcbdccabdaadabbcaccbcccacabcaccaccccbaabbbcacabaddabdbcbccaccbacddbddbcdbbabbccbbdadddbbabbdcacacdacbacccddddacccdbbddcbccdacaadbbdcacdcbcdddaacabaadbacbacccdabbcccbdabccbdddbcbdcbdbbaccaacadcbdbacddccaacaadbcabbbbbbcdccdbbbcbbbbbaddbdbbdaddbacdadcbaddcdbadaabcbbbacbbcadcbabbcdddcdddbbdbababbbddcccbbddcdccbbccbaadabcbcbababcbaadaaabcddbdabacccbddccbcadcbcaccabbbccdccacdccdbbcbcdabdcbadbcabacdbaacddaddcaaaaadabcaabcbcbadbcdadcaacadbdabadbddbbbbadbccabddaacccbbacddacccdcddbcddabbdcdacbcbbccccbdcdacadadcbbadcadccaddaabaadcdabcdaacabcaabbcdaabdcddccbbbbcbdadbcaaddcabdacaabbabcabdddddcdbcbdbbaccadaddccaadcddbbdbddbcaadacbcacbccbcacdccbbcddacbcabdcdbbbcbbbabbcbddcbdcaadabbdabbaddbdadccbacbaddaadbddbcbccaabcaacbbaadacbaccaddddcdbbaddcacdabcbbbcaccdcabcdbbccabadbacdabadccdbdbcbbcbacdaaaaddbaadaacbacdaaddadadbaaccbdabcbbaadcacadbbdccbdcaacaabadcbdcaaabbcbdabcbddbdabaddcdbdaccaddcabcadccabbbcdbbacdcbccacdddbcbbabadcdddcbbadabaaadbbacabdddabbaaccbcaaadadcbbbccadadccbabdbabbbadbaacaadaabcdacdbbaaadcaabbcadbdcdbbcbcadcbddacadddcabdbcdacbcbbbdddcbabdbdcbadcddbbbbccbdbbddcaadcbcdbadcbacabacaaddbdcabdcabdaabbdddbdbcccabdcacdababdaaccccbbbbaaaaacaabdbbbbbdbbdcadbcbcbacccbbacdbadcaadcdbabbdddcaddbdccaadccdbcbbdaddbbbaaccbbbacdabccaddbdaacdcccbdacccbbbdcaaaaccbccdbddbacabcaddddaacbbcaaacaacdcdbdcccdcbdccdcbacacbdacddcbabbbcacacacbcdadcadbcabcbbbdcbbddacabacbbdacadbdbdaaabbbcdcbaaddbadbbadbdbacadadadbbcadcdccdaabccabadbbacbdbaddcccbabdbcdadbddacdbccdaddaabccddcccacdbbdbbbdababbddadaacaaabbcbcdcdcdbaabbabbddcaaacbabddaadcdbacaddbaabddbacbbcccabdaccddbccccbaabbccaadaacbbcccccbabbddbcddbacaadcadaacacbdaccaadbdcbcdcdddcdcbabccdcdaabdaabdbaaddbacccbcbdbacbdacbbbabbcbdbbcbaaababbbaddddcadbbcdcdccdaddbaabbcbccabddcacbcadbdaccaadacbdbcccdbcaaadabddbcabccbcdbdaabdaaacddaddbadcaaabddbacdbdbddcbbacbbbdcbddadacbabbdcdbccdcbbadccbbccacdababcbbbbcaababbabdbcdabbddabcaaccdbcbacaddbdbbcdbbcdcaaabdcaccabccbadacdbdaadcdbcdbccadbdcdcdadacbbcaaaddcdaadadcbbadbdccadaccaaabacbccddccadbbcccaaabcacddcabaddcadbbadcbdadccaadcacbbcdcbacdcdcdbdcbadacbacdbacaacdcbbbcaabdccacacbbbcdaacdaadadcdaadaabdcddacdcbdccdacdbabacbcbcccaaadbccbcadddcacdaababddcacbbaacaadccbcadbabbbddcccddaacddaabdadccbcdaadaddacdcacbbcbccbccdcadddbabccadacababacccbcdcbcbbddaaccaddddbddbabdaabbddcddbacccaccccbbbddbaacbddcaabbbadacdcbabbacdbaccadbbdccadbdbaccccdcabaaaabacdbdcbcbcbbdacbbcbdcabacdadbddabbbdadcbdbbacacdbcbbaddcaaddbcdaacbdadbbdcccaabdbacbdbbadaacdbcdbddbcbadbddbbdaaabaadcdacbbadddacababbacbcbbcbbddbacbbddcdbdbcbabcabaddabbcdbadccdbccadbdacaadbbbbdccdaabbcabaaccbbbbbdbbbacadabbbcccabdaaccaaccaaaacdabbddcacbcabdccadbdcaacdabddcbbabcdcdbaddaccacccccabaccbaaabcbdaccababcdbdcbcccaacabadaddddcbbccabdbaaddcdaaacadcdcdaabaaddbddbdabdbbbabbabaccadcaddcdddbacbbaadbcdadcbbdcbbaddcaccccbcbddbaccddaaacacaccaabaaabcccaaddbdddcbccbacbcadbdaaaacdaabcbccbcccccadbcdacbbdbcdabccbccccbadacacdcadddadbcccbcbacaadbbcbcbbbbaaaaacbcbbccdbcddcbaabdcbacccaccaddbdadcbbccdbaddcccccbcaabacbabacdaacbaccbdaaacbcbbbaacaacdabdcccbbcbdabbabdccbdcaddbdddcbbddbdbbdccadbbbcadcdbcbacaccaabacddaddcdabdcbdddaacabbcbdcabbcaccdcddbdcadbbdbcdcbacabacadcbaabbabddcaddccaadbadcbcdbbaacaaadcadbbbadbdddbbcacdadbcdbcadbabcacdcabaaacaacbbacddcacbdccdadbcadabaababbdccbcbddadbdbcbbcacbcabccadbabcdcadaddcdbcaccdbdbcdbbadbdaacdaaacccabaccccbabddccbddaccdadbcbadabcddaddcbaadadabbddcdddbadadcaddcbadaddccacdaacabdccbbacaabdbcdbbacdbcaadcbadccabacdbdacccbbbacddbcacacccabacdcddcccadddbbcacdaabddbdadcdadcadacddaaaddcadacadbdddcdaadbadbaccbabbbdddccbabbcbdcbabaaccabdbddadbccacdcacdbadbaacccaadccdaaabdccaccccdbadbbbbddabdadaabdcbbbdbddbbbbdbbabaaccbadcccdaaccdddcbbaaccaaaacadbcdabdcabdcbbaccbccdacdadabbadadbcababcacabddbddadadcabddabcabddcbbdcdcadccbcbdbabccccbababddbdbabbaadcdaabdcbdcbcabbaddbcacccbcdabbdcbdbdadaabbdcadbcbbdbbdabdddccdccdddadbdbbbabddddcccdabaabbaccaccaabadcdbadcddbaaccbcbbbbabbbbbacaadabcabbbddbabdbcbbdbbdbabdabcabbcacccbdbadbdbbddcabdbdcbdccccbddbcbdbabcdcdacccbbdcaaddabcaadacaaabbbdbbdcbbbabbacbddccdddcddbccbcbdbbddcdbdcbcddababbcdbdabcabacdbccbbbbbcccdcdadbcbcdbdbcadbbbcdaacdbdbddaddcaadbacbdbdbcddabdcaacdabdaacacaddddabadabbcabadccacbcbaaabacabbabbaadcababcdcacadabcbdcdacdbacbdbdccddaabbacacadabbbddbdbbdbcaaddabacabbcbdccddabacabcddacbbacdcdcdcccabcbacacdaddbdbcbdabdbacadcacdbabadacbcbaccaacabdccdccbabbadddccccdabccadaccbadddbdddcacbbdbdddddcccadaadadcbdbaaddcddcbdcadcbcacadbdcbaccbccbaabdcdaddcdabdbcbdbacddddbbcddcaadcaabccaaccdcdcddaaacaabadbdcdcabddbbadcabaaaadcdbababaadcdcdbadcdbccabdcbdbaddbaaadbdadcdacacbabcdbcdbbdcbaaccccaaadbaabbabcdbbcbcdaaacdddbcaaabadcdcdaddcbccbabadbbbabbacddabaadbccaabdadbbcabbccdcbcbbbcadacacdacbdaadcdbcddddcbadcdbbbddacbaadaccdcaadbdbbbbdaddadcbbaccacccccabcccaddccbadbddcaacdaacbbddbadaaddcdbddadcbdcdbabcdabccbcaacdbdbdbdcdaadcababbabbcddcbccbdbcdabaccddcbaacdacbbcdcbaadbccbdacbadbbdddbbdccccabdbbaaababdbaccaddabbbcbddcacabcbaabdcddbaddbaddaccdadcbaaddcbbcbdabaadcabdbccacdcaacddcbdcaacccbbcdbadcdadcdbdbbbcbbdcbadccadbdaadbcbbcdcdbcadcbdcacdcdbaaaadaaadcbdbdddbabdccadcabbbacdddcbcdbccdbbbbacdcdcbdcdadacdcbaadbdbbcccacacdacacdbcbbaddccbddacbdbdbaadcdcbdadbdbbaccabadbdadcabcccdcdcaacbcadccbbccacaabdcaddbacbddcdabdbbbdddcabcbaaccbcbcabccabcbcadbaccdcaccabcabdbddadbdccbcbcdadbacabaccadacacbbbbccbaabdcbcdbaddadbbdddbacbbadbddadaacaccbadcadcadbbabdbdbadbbbadbdbaaacdcddcbadbdcadbdacdcdddbccdaddcbccabcaadaabcdabaabdaaaacddaaabbdacbdbdbdccacdcabcaaaddbcbccdbdcbcadadadcdacdcadbcdbbdddabcacabcbadbbadbabadacadababcccdbadbdabcdacbccbccdbadcbaaabddbabdcbcccdcbadcaabbcdabdacdbdccdcaabbddcbdabccdaabaadcdbdabbadbbacadaaccaddabccdbadcdadabddcdaaaddabdacbbdcdabbcabdbaabababadbdaacacbbacabcbcbbcbcccdaabdcccdcbaaddccdbdcccbabacdbdabcaacbcaaacbbacaaaabadadabdddacaabbddddaddcdccabadbacbaadbdadbbcccccbcbdbaaadbcbadbabddaabbbbddcbbdabdadbaaadbbbcbdcbbacccdaadabdccdcdbadadacbdcddbccaabdaccccccbdbddcbdbbabdcdbcabaddddacadadcbcdbcbacaddcdacabdccbbcbbccbdcbccacdababadccbdddbddacdbdcbcbdbbcaaabbbaaacdbcccdaaabaababdcdbdbdcaaaaccddccdbdacacbccadaaacdaaacdbdccdddbbacbdabcabdadbccdabdbdbbcdbbcdaaadadcbdbdaaacbcbcacbadbabbbdccbbbccccbabbcadbadabdbaacdabbcacdabccbbcccbbabcbacbaacaddbbcbbdacbaacbadabadbdacdbadbcddbbbcbaddccdbbcbdcacbbaacbdabaadabdbcdddbdbbddcdbbccaacdcaddddaaadbbbadbbacabdbdcdaccaaacaddbbdbdabdbbaabaabbbbcccdcddcabcbcdcacddadabdaccbabacabaaabdaadcdddcdbcacbacdbaccaabdaabbcccbccbaddaadcdccccccdabddcaddddbdabcdddabbaaddbbccdcdbcaaaabbcbbdabbabdbbadcadacdaaadadaddbcadabddbadbbcdcddacbbdadaacbcdadbdacadcddaddcccaabddabbcccbcdcbdccddcabbdadcaddabacbbbddcbdccbdccadabaaaadcbcdbbbbccaaabdcdabbbdcdccbabdbbcbabbacbcccaadabbbdcdddaccadccdcaabbddcccbccaacbaacbcbcddbaccaabcdbabdbbcbdddcbbbdcaacbdcadadadbbccbdcdaaacaaacadbcccabdadcdcccdbacbbbadcddbabcccacabcadbacacabcadacbbdbdbacdcdccddcdaabdbcbdcdcdaacbaaddacbbabbccaaabbdabaabcccdabacbbcbcdbcdbcadaaddcdccadcdbaccdadacdbcadbbccbaabaccbdcaaabbbabaaddcbbcabaddcaaccadbddaaadcbcacbbbadbdbacbdcacbaaabcaabdccdcadadcacddccbabdbcbbbcbcaabbccadbaacbadbcdddbbcaaaaacbdadccccadccbbcaabdaacccdbdabaadbaabcdcdacdccdbbbcdcabccadcccbbbddcabdcbbcaccbbdbacbdacdddcacaabadbbbdacbbddcdabbbcdbaacdacbcdbbdbdcbcdacbdcabbbbaaabdccabcbbdacaabbcdaadacbbbcbdbcacabaaacddcddacbaabdccdcaccbbbdbdbccbddabacacccdacddadbabccbdbbdaaccacdccccbccadccbadaacaddbddbdbbdbbdacbbaabbabadbddcddbadacbabadcdddbddadcddaaabdbbabbddbcadddcdcaccbaaddbbcbcabdbbadbcabcaaddbbbaadcaaccaddadccddcbdaccccccddbcdaabcdccdcdabdbdabaadcddbcabaadadbaababdadaddcdaadcdabdaabcdbcbabddcccccabaabdbcadabcacaadbdabadddbcaccdddbbdaabcbbcbbcadabaaacbbcdcaccccddaddbdcbddcdcdcacbbccccdbddababdaddbdbcaabaccaaacacaadacbbacabdbbbcdadabdddcdabadbcadcdcbcbdcabdaaadccbbacdcbdbadbbbcdbabddcbccbbacbbbbcaababadabccaddddabcccabcdbdaabbdcabdabcbdcccdabdaccdabddbabaacadcbcccaccbadabadbbdbbccddbaabbaddccdbccbbcdcdbbbccadcbddbaababcbcddbdccddacacacdcddbaacbcddcbaadbdcdcdaaaadcbbbdabdabccbbdabdaadcbabdcaddcbbadcaaaabbbaaacdcbcaabbdaacabdcdbbbdbcccadcddbdbadadcdaaadcaacadacaaabaccccccabcacabbdbbaaadbcacadcbdcaccdaadaacccbabbcbacacccacacaccdbbddbdcdbbabadccbbcaabdcbcdbabddcdadaabcbbdbabdaabbdcacddcabbcdacdccccdbacacacbdddcbaddabbcdaabbacbccddaaaccbdcbcdcddaacbdaaadddcaadbdbccadbccbbdcbacaaaddbddcccacabddbaacddcbbdccdadabdbbddbcdbdccddcccccbdcbdcaaaacaaccccabbbababdcacbdbabadacbbdcadadaaacccaaadacabbaccbbbddbdddcaaabababdddabdbacbbaddcbdcdbbbddbdbabcbcccaabaadaddbdddbbdbacccddbdbccccbdbdbccddbcbaccccbbabdcbacddabccbdacabccdddcabbacaccdaacddacacbddaabacacacbdcbadcbcaaabdadaadaadabdccbbbabcbdabcdcddaaadbccccadabbcabbcdabbaddabddacdbcabbdcdacbdadddbbbdccbbdaadddadcacdaadacdccacdaabccbcccccabbbccaaacbbcdbcccabbbbcbdcdcbbdccbbdaccadddadddcdbacbdbbaaaddacaababcadadacaccbdabcbccdadbcdadcdabdaacaaddcacbcabccccccdcddcaacbadadcddababacdccaacdadcbbaddaccabaccbbbbdaddcbccbcaccddddccadccaabdbbacbccbdcdacadadbbdabcbaddabadaaabadacdcdbddbcccaaddbddcdddbbdcccaabaabbcccaddbdadccaaabaccacbdddacbadcaadabaddaabddaddabbddddcbdbabaabccdcbcddbcdcbcbbbadaddacdcdaaacdcdcccaaddbcacbadbdaddcacbaccbdddabdbcaddbbcdccaaacbdbdddbabcaddcddbdacccaccdbccaadccadcbbdbabbadadccabbddcbdbddacddbdbcaaccdbccaabcddbaadccabccacbbdddcbcbcaddbbacbcaddccccaabdcacbbbdbddadacccbcddcdcacaacbcbcaaaabbbdccbdaacdbbbbddaacadbababcdcbcabaacbdcccbddaaabdadabacccbaccbdbdacbacbaddccacbddbbbcbdbddaaaabaaacbabbaabbdbaaadbccabdbdccaadbcbcdcdbcabdccdcaddaaacdcbdabaaadabddcdcccacdacaaccccbabcaadacbdddaacdbdbbbacdbaacbcababcdadbbbbaacdababaabdbabcbcababaadabcacaadcbbadcbdbbddcacdbbbcdadddabbbadcddcccccbdacadbaabdbcbacccacbcccbcdbddbcdbcdacddabdcacddaacacdcbdadccccaabcdcadaaabaddbccadbcccdabdcabaadabcaabcdddbadbccbaccdcccbadadadadacddabdcbbadbdcabadcadacbddbacccccdabdbdadbbcdbbcadbcbabddddcbdacdaabacdbbccdbcdadbaadbcbbdabadabcabbadbddacdadabdbabbbcccddcbdadbdaddcacdabdccabaababbacbbbddcdcacbdddcdcaddcabaabbbdbbcdbadadbbcbdbdaabdbbdddccdacacbbabbcabadccbbdbbabdaabbbbbaaaaacabcdcadabcbaadcadaadbdcdaccaddaccdbabbddcadabdabbbdaabcdbacbcdcaadbadddbcbcbdabdbadcdacbabcacbabdbddcacacbcbccbdccadabcbbaadadcdabdbccbdbdbadabbabbbccaaacaabaacbacabcbbdbcbdaddbbadbaadaacbaabaccbddcacdcadbbbdaadbabacdbaaaaccbdbbdadbbbddcacbacdaccddaaacdcbbdcabbabaaabaacdbdababbacbbbdbbbbdaddcddbcaacbbbabcbcbcdbbdcbaccbdacacaaddbadaddcdaabaddccdcbbbabbcaddacbadcbadaddcdbabcdddabdbdbbdcdddbccbbaddddbbbdddddabcdccccbcdddcdbbaddccdccabcadabbdcccbbcadddddccaaadcaddacbcccbbbddbbcbcddcababcacabdbbadcdacbcdadbdaadcaabbabcdacacdabaddddcabbdabbdadbdaccadbacccabdbdcabbaabaaddcabcdcccacbcbbbdbddcdbdacdadcaaabbbacddbbbdbbbbdddbadcbdbddacdcaabcdcddaacbcdadabacbdccdcbcbbacdddaabcccdbacacbaaaacaabcadcddcddacabbabbbbabcdddbdcbbbbbddaddccaddcbcbacaaaaddcdcbdbadaaacaadccbccbcadbccaadabadcacccccaaccabddcdaaadcdbdcdbcabbbbaddccdcbdbbdcbabcbdcababadcacbdbbadbacddadcccaaddabbdaddbabaabcaaaaaacacbcdaadcccaccdbdaccdabdccadcacbdbdcacabbdddacadbcbbcbdcaabccccabcdcdbbbdaccddcaababccaaabbaadbbcddddaaaacbbabbbbadccdadabddbabccacaabbbbdddcacbaddcbdddbdcddbcaccabdddabbbcaccdabccadabccdbbaacabcddbbcdcaaaadbbbcccbdcdcccabcabaabcbcbcacaaadcbdadcdacdbbdbccdacabcbccacaccccbcbdcacccccdbcbcbcdcdacaaacdcaddccbdcdddcbbcdcadaddaddbaabddaadddabaaacdaaabbdadacbccaccadaaadadacbbbcccababcacabbbccbaabdacacddabaccdcccdcaadadcbddcdbccccddaaddbabcddabdbbdbacabcabadccbccbcdddcbcdbbcdacbddbdaaacccddcbbcaddbabdaaadbaababadbbccabcacdddbadcddccddbbbdbbadabbbdbabddbabddcacdccccabbbaccadcababcaadcccbcbbbccbaddbadbacabbbcbaacddbdcadcaacdcdddaaabdaabcabcdcadcacadbbbdbacabbdbddbabacdbaaccabdabcbbdbccacadddabbbcadcbdbddbcbbabaccbcdbabbbaddcdabdddcadccbddacdcdbbbcacddcbdacdbacdbbbccabccadbdaacacddcbabccbcaccadddaabbacabcaccddbacbbacccccbabdbaadbcaccabbdcccddcbccdcbddbbbadacdbaacccddbaaabddbacbadccbbdbdaaacadacbdbccbbcaccbbdddbaaaabddbdacabdbaabdbacddbaddbaccacbbdcbbabcdbcacdacdcadcaaadabadabdaaacdddbcaabbabaaaaaadcbacbacccadbbdcbccbabdabdadacdbcbccbccdcadcaccdcbcbacaaababababbdcdbdabacdbdbadcbaccbbcccaccbbadddbbbcbaddbbbccddbacabaaaaadadbcaccdbdbbdaabbbdbbbcaabbaacbbcaacbaacdbbadaacddcddaadcabcbaaaaddababaadacdbddaacdccaaddddbddabccdadcacccbaabbcaaacdcbacccbddcdbdaddaadccabdddbbbdcbcbcdbabaaabbdaadaacaadccdccacadcddbdbcaadbadbdcdbbbddaccaddddbcdccacccbabcbdcbdbaccaabcbabddcdcadbbccabbdaabadbdccccabbccddabcadbbbbdcdabbcbcabbbcbbdacacdbacdadcacccdabbcdbaabcdbaadbabbcabbdcbacddacadbdbddbbaabbadabdbccddddddbacddbdbadbbbacaacabcddcaddccbaddccdbaaacbccdcdcccbcbcddcdabcccccddcacbcdaccdacccdabacdcdadaaddacacabbdaddcdddacbbdacbacacaadbdbdbcdbcdbddbaaaadbbddbcccaadbababaaacaaabacdddcbcccacdcaccadbddbbacadbadacdcdbbcbcabddbbccbacbcbcbaabadddaddaadcddbdabbcdbcddbacaabdbbaacacdbaaadbdadcacdabcacadcdcdccadadaccdabaacddbcbadcaadbbdbcccbbdcabbbaddbcdabcdbbadbadabbabadcdcabcdbacdbacaabbacadcbdadcadadccbdcddccabccdababbbbabadbcdccdaaabcbdcabddbbcbcabbcabdacbbaaadaabcacacaaabcabbadbbccbbabccaacaabbcbbbbddddcdccbaacbddaccdcbabdabdcdaacabcbcdccbbcbcbccccabababadacacaccdbacbddadccbcbbbbaabdcacbabaadcdaabccabcabcbcbbcabcbabbbdcccbbcacbabddabdbaadacaadaccbddbadbddbcccbccaacdbaccadacdaacdccadbbcbbcbcbbbabaadbdcaacadbdbbbdabdcbbbddacaaccaaacadbabababdbccdabdcabdacbdccbdcdabddcaabcccbaccadddbcdbddbbbadcbabbbdcbdbacadbcaaccaabbaadbbbacacdccadbaaaaddcdabcacacaddaddacbcdaabbdbbaacccbdcabacccaabbddaaabdbdbbddbaddaacbcbacbccdadbaadddbbaaabacaccadbadbdabacddcdacdbabbadabbbcdacacdaddccbbaaabdbdbbbdaaaabacbcadcdadddbbccbbdaabccacdaddabdbccbbbbaabcaacaabdabbbbaabcdccccadabcbddbdcbaadbdabbbcbbdccbcddccacdadabadbacaaccdbadddabbbdadacabbcbccdccccabbdcabccddddbdaaddbbbbabbbbcdccdaccccbbaababaadbdbcbbcdacabaddabccbcddadabbbcbadcabddcababacdcdcdcddadbadbbdadcadbbbacaddadcbaaabbabdccbcadcbacbacadbbcbcbdcdbbabcddaabbdacbadabdcbbcdabaadabdddbddccacaabadcbbaddbacccbbcadbdbdadccabacdccdaccabcdababcdbacaabcabadcbbcbbdbddcccdbbdabcccdadbdbaccabdcccdaacababbbbaccbddcbccdcdbdccadcdaadbadabdccccaadcbadcbdcadaadaaabbabcacabadbbaddbadabdaabddaddabbbcdcbdccaadabcdacbbddccbcabcacdaccaabbadabccdcbaddabcdbbdaaccbacabdadbcdacabdbbaabccaadddbbadabdccbcbbddadccbdabbddadacadbaaabaaaadcbcccddadccdadcccaaabddbbdbcbbdbbbdcacccbbbbdbdcdabdadadbcabcdcdadbccbdbcbcbaadddddacabdaadbccacacbccdddcbbddacaadccbbbcdbdacbbcdbcbdabcdbabcbacacdddbcaacacdccbaabcaabbdadcaadccddbadaadcdbbbdbbacdabddcdbbaccdcbccbdadcbcadccdabbabbcbbaabbbcccaabddcbdbbabaaaddadcbcdddbbbbcccacadaaaabbabbbcadbadbbdcaaddbccbbadabccabbdbbabdcdadbbcbdbaadddadacbbbbdbadadddadbacadcaaababdabacaabcabcdaabccacabacbdcdbbddbbdacadbdccbaaccccbaabdabbcaaaadacbbabbadddbbdccdccaaabdcbcbbcabdbddabcbdbaadccdbbbdddcddaaadbbbbdcccaadcbaaaabccbdabaccadcddabacddbabcbcdcbcdbcdcddadbacdcbbdacddddbaacbcbcbcbdbaaddbccddacbddbbccabcacadccabbaadddabaadbbbbdcbadaddddbbcadbbababdcbbdcccbcbddcadbbdccbcacccaaacaccdbccbddbcbccdadacaccadaddccdcddccbcbdcabadbbbcdcdbdcacdcaddddbcadbabcccaacbcacaabcbcbaacdcbabcccdbcabdbddadcbababcbaccbabadbbabbcdddadaaadbcdcbdbbacbaddbabdbabdbdbbcdbcbadacbabdcbdcdabcadcabadabaccabdbbdddbdaadcdcacbacdbbddbcdcadddacddbbbcabdbbaadbcacbcadacaaddadbddaabbccbcbdcbdabcccbdaabacdbbdddbaadcabcbadaccacaababcdddbabacdbabbdbcbbaccccbbabcbddacccdddbaccbbcaddadbacdccaabaabbdbdaadacaddccadadacabdcbbcdddbbdcacadccdbccbbcddacddcbdddadbbcdbaaccddcdacccadadccbbbdcacbcccaddaaabdcdabcacddcaddddbacddcbdcdacbabbbaaddcddcdcbdacbbcadaaacdddaccacdbabaadcaaadadaadcadaccdaacbcbcdacdaabbccaacbabbddbabbaabdbccbbaaaabcbadddbbdadcdcbbbbbaddbdcabddbadbadabdccbabbdcbbdaabbdbbcabaccadcbccbdddcdbdddccbacdbbacdadabdbcdcbcaaccaddaabcdbadcddbdcdccbdabadaccbbacdbbccaddddbdcdaacaacadccccadbbccaaaccabcaaccdcbbdbbbbababcddacadcbadccaabbbdcaacaadaabddadccadcadbbdaadccbaaabbaaddddcacbbaacaacdbcdcdcaacbbbabbacdabcbdcdabdaaaddcddbdcccdccabbbabdbcccddbbbbcabdaccacadaabdcabaadbbdaadccacccbdaaaddcaadcbbadacabbaacacaadbaddabcbccabcadcabccaacddbdbadddaabbccaaacdbaabcaaabbbbbaddbaabdabbbdbbdadbdabbaccdddcaabdbdadbcbcbabcddbaaaaabbcaabdcabcbbcdcaacdacbbabbbbcdcbadabdbabbcccccdbddcdbdcabddbaabcacbccdccaadaddaadbbadcbdbbaabacbaaaadacaacdbcddbbdaddbbccadbcaccdacbbadbbaddbaabddadaaddabdbabaaccbcaabacccdadbcbaddacacdbbbcacadabbcacababcdcaaccdcacdcbacacdbcccdcaaccbacbaccabacdadcdddccadbdcdbbdababbabbcddabaaaadddaaddaddbdaddabbcdbbbaadbabddcadcdcddcbaaadbcddbcbbddccbbaacdaacbbddabbccddcdbcabdbcdaaabcabaddbabacccbcbbbcaccdddcbbabbacdcdcdddcadccacbdcdbadacbdacbacaddaacdbccaacbdabbcbabccaccaaddbcdbaaacddbbdccdcddbcaddbcccdbbadaddbbddbbaadbbcbcaabbdacdabacdccbdadccaddbadaaadaadddaaccdbaccbddcbaaabbcbbdccdabaabdbcbdddadddddbadaaccbbdadbcababcdbcdddcaddddacbccdcbaddcbdabdcacdbdabdccadbacbaccbdaabdaccabcddaaddadbcbbccdababbcccaabccabbcaddcbadabdadbcacdaabcbdcbdcbaadcdbddbccbccbddcbadbccaaacbccbdbaddcbddaccaccaacbbbddcaddbddbacaacbcaabacccbbdbbababbbcddccbacabbcdbacdcccdacbdabaadadcbbbabbcddbadaaccaccdddcabcccadaaacabbbcaaacdbcaadacbbaccbbdadacdcadbddbabdbddccbaddadddaccdaaacccdbbdbbccddadcddcaaddbbdaadbccddadccbaddaadadaddbaddabaccbaaaddabcabbcdaddbcbccddaddabccaacdaaaaabcdabaaabbbbcdccbbacbdacdbcbaddbaccdddbaadbcdccccdabacbbcaaadbdcccbccbbbdbcaacbdbbcccbbbcabcaadcdbadaccbcbadbbddbcaaaabbcbcdbabbaabcacccdccdacdcacbcadacbaccdbdcdabcacbbcabbbcdcbbccbabbacaaddddcddacbaccbcadbbcdabcbcdcbbcbdadbacbbddadbaadadddbcddbbbbcadcabcdacdaaabaddcddcdcdaabcdccbcaacbaddabbcbadccdadadababacbcadcdcbbdbadaccbdadacaadccabbcdbdabacdbabaaaccdcdbbbccacacbbbddabdbacdcdadadbbcddcccabbcdabdabadadcccbaabacbccbabacacbdbabdaadacaaacdbcddbdcdaadbbdbaaabbdbadbdccdcbbacdabacabadbbadcbcaccddbaddbcdbdcaacaabcbdbdcddaaaabbdadddabccadbacdcdadbacbabcccbbabadccbcbababddabdabddbaabddddcaddadcbabbbcbcacabcaaddcdadacbbadddddacbdbcdabdbbbcabcbcddacdadcaccbbbbddacdddbdddcadaadcbcbdcbcacccdbcbcadbacddbaabdbacbddbbcdbbdabdcccbddddbdccdacbbdacbababacdcadacdbbbdcbacbcacdcbcbaacbabaacdbddaccbabcdccddacadccdadadbcacdaddcdabcdcbbcccdbbcbdabcdadbddabaaaabdbccdaadcacdccdabbdccbddcacbbcccdddcbbcacbdacacdcaabdacdbcddcbadbadddacddbdbddabdbaacaddbacbddaccdcacbdcbcbadccaabcdcbadababcaaacbccbccddbcddababbdcddbcbdabdbbbacaddbcdbcdddbdaccdbcabcbadbcdabbabbcdcdadcbbcadbadbcaccccbabbbdcdbdbbdabadbbbddcadacbbddcbbdcdabcadbbaddddabcabdabaabcaacbbccdabdababcadbacbabccbbacdbacdbbddbacccccacdbaacaabdddbbaaddabaddbbdaddadbbdabbaabccddcbdbaccabaacbccbdbddddabcbbadadcddbcbddadcddcadbbbccaaaaacbbcdddcaddddccbccbdcdacaccadcdccaccdcbabddbaadbaccacdbaaadaacdacbdabdcccaacbaacbdabcbccaaabdccbabdabcdbaddbaadcccaccadbbbbccbcbbbacbbdadcadbadccddbdddadddabaaaddabdadaabaccdcccacbbccdcbaabcabbcbacdddcdbcdadcabdcabdbcdacaadbcccaadbcccabcdbcbabbdcaadadcbdcaacaababbacabbabbccaadaddaddadabbaddcdbcbaddcddcbcbdaabbbddbcabdabcdadabcdacbacdddacaabbdaaaacddbaacbcabbcbbbcaaddaadcdabaddccdaccbdabdbcbbbcdbabcbdbcacacbbcdcbcccbbcbadcbdaccdcbbdababbbbdcdbdcbdcbabdcaddaddcbbddcdacbddcdbbccbdbdddcccbdccbcccdbcbdbdcacadcacdbaaddadbbcbabdbacddbadcacbbcbabadcbbdabbdbbbabababaaddadabcbbdbadcddacccacbacbcbdcdbbcdcdbbbadbbddddbdcdcbbddaabdbcbbcbbdcdaadababdccacadbabbdaabdaacadbddcdbabcddccbddcccdaacdaccbdbabbbdbbaabdacadacbbdbcabdbbaadddddcbdcdccabcbcccdccdcbdcbdddcbddbbbbbbabccbcdcdbdababcccddacaabddaddcbbbdabacaadccacdbdbdabbcbcbdccacdccdaccbdcdbdcbabccbdabcbabbdcacdcaacddaccddbddccdaddbadababacbdbcadacabacdacaacaccbddaacacbcbbbcbcacbbaaccccbadcabdcdadadbddaacbdbcacccbaadbdadababaabdbcdcabaacdabbaacaccbaddabdbbdcaaacbccbdcbbbaadbcbaacbbddcaccaddcbbdadaabcbbabacbbcdbcabcccacdcbbddddcdcdddbbadbcbdadddccaccdababcddbcabaadcacccadbadbcbaabadcdababbdccbdbbaccaaccbbaadaaccaacdcacdcacbacaabcbcbcdaacdaaaacadbabdabdadddadbdbdbdbddabaaabcdbaaaaababdbbaadbdccacbdabccdabadaabcccbcacadbbbbaaddbdabacccbdddacbaabcdcbccacabcaccbadcdccaddbadbcdccaadddccddcacbdcbbdddcacadacdadaddcbbcdaddcabaabbbbcaddbaaadababaaabdccdacdbabdbbbdbdacacbbababbdbdaccdddbabbacaccadacbdcdddbbdaccbdcdadaadcbdbadabcbacddaaadddaccbdcacacdcdcdddbbcddcabaaabcddadaaacbdaddbdabacbcbabcdccbdaaccbdbadcbbdcddcdcbaabadbddddbbddccbdcbdadcdbbbacabbbdbabacddbbadbbbdddcddccacbaddbcbcdbcaaadbbcdbcbbadccadacdcdcdaacbccacbaabbbaccbdbabbdacdadacdadbcccdabdaaabcccaabcbddbbaababcbbaabcdcbacabdbcbcdadddcdabcbabdbcbdbacdbabbdadaadacdccadaadcdcddbdbcacabaaaaaddcadbcabdbcbcaaaabacdcbbbbcbdbbadddabdadbcadaddabaccbcbcbadacbbdadcccdaadbccbdadcddbabadcbacbddaabbddcbcabcbcccabddadbbbdabbbdacbdabbadcbdbdbdddcbcddbbdaccdcababababbddbccacddbbacccbbcbbdbdcccbbabbbaddaaaacccbccaabbdbbdbabbaababadabbccacddadcbacbddababbaaadadacadbbacddbcaddbdbbacbdbccabdbbcbbababccbaabaaddbbcabcbacadadcaaaabdacdccddbcdbcdbcdccabaaaddbcbadcbaadbdccbaadccdddbdcdaabaadacccabdadabdabaacadbdaccdbbddbaaaddcdddbaacdddbacaacabaccbabdaabdabdbaacccaacdccbaacadaddabcccdbbabbbbababacacdbadbbccbbdcbdddadbdbaddbdccbccacbbbbadbdbbbabccbdcabbabbddcadcdccaddcaabcabcbbddabaacdabdbaddacdcadcabccdacabacaabcacbdbaacadbbaabdbabcacbbccddbbdcbbacacadcbabdabacddcaaaacaddaadaccbadaddbcdbbbdccbdcadabbbabcbcacbddbaaaaccbcbaabbdcaaabddabccddbabaddcaccdbbdadbadccaadabdadacbbcdaaaddbcabddcacccddbadaadaccdbbcdcdbcabbccbdcdccdccababbdadddaccaccccccdcbbccdddbbdbdababaabbddcdbbbdbdadcadcacadbbaaacbbdbbcccbdbdcabddcbbabdbcdddbdaccacacccddacabdcbabbcadcbacaccaadcbbdcbcaadcdccbaccbaddbddacccdaccbcccaddcbbbdbbcddcbbbdbacbdbaabdcaccadaccadadcbbbdacbacdbaabdcbcbddcddbaadcaacddbaddbaadccdddbaccbcdcadabbdcbdcdacdaacdababdcdabdacdaadaabdaddabdbbabbadbdabcddccbcbaccdbcacabcbcaacacbaddbbadcdbacbbcccabbabcccaabaddbabddcbacbadadcbbbddacadbcdaabbcdcbbcddbcccaacbbccabdbdacbccbadabddaadbabbbbadbcbcdbbdacabddddcbdacdccdcaacddacbcacdcacbdacbabcbacbaadaddaddaccddbdcacccbdbaacaadacdadaddbaddaaabcbddbcadaaddbcbdbacbdbbcdbadabaaccbaaddbbadbaaabbbcbcdcdcbabacdabddbbdcdddccbcbccccabbcbbbbbddcbbbbdabddbaddbaacdbdcacaaacdddbbcadaccadaddbddbcbabdacdbdacbbdaadabaaaacabbaaadcbcbaaccacbcddccdbaabbbacbbdacdabcbbaabccccdaabcddcbbabcdcddabcdbbbbacdbacdbcdaabdbccbcaadaddbdcaddcbbdabcbbdacddaaccddbbdccaabdcdddaadccbccdacacaaddddbbccbddaacccbccdbcbabdaddbddcbcdaddbddbdcadcbacbbadbbdcadacabccacadbdbdacabbbbbbacabaccddccbabccaacbdcbbbdcdbdbdbdabddbcbdaadcddcbdbcaadadabbabdddbaddddddccbddaabcdcddaacabbbaabdbccccadaacbbaaddabcadabbcddcacccdcabcbaacadcdbdbccacabdcdadbbdbbacacbdbcddbabaddccbdcdcbabdbbbbbcabbddbacdbadcabcbadacacdabccdacddadadcabdabdabdcbdccdddbbdccccdbccccaababbbbbcacbaccbacdbdabbdbdbbdbabcbcadbbacbbdadcaabdbbbabcbccdbbcbdbdcdbddacddaccccddaccccbcdbbbddccbcbcdaaacdbdbcddbdddbddbabaaacdcaabccadbcadcbdcddccacadcaadcbbbdadbabbcaabdcbbadbabcdbbcdcbcabbaccdccbbabbccacacbdbcddcdbbdcdacabddbddbbbbcbbccbbdbdaacbcaddcdbaaaacadcbddbcdcbcaccbabccccccbacdbdbdcdcdcbcddabbbbbcbbccdcbcbbcbddaaabbbdbdcaacbbaaaccdbabaaabaccacadcccdacadaccdaabdbbcdccdbbcbbadcacabcccaabdabacababadaadcdddbccaddbacaacdcbacdcbcdbabcabbdcdadacbdadaccddccccaaadbacadcdbbaacadcbcccaddccccdddbbaccbacabcabbbdaccdbaacaadaacabbbdccadbabacaddbcddcbcacdadcabcababbabcbbbdbbdcddddaccbaacdabbbaaacccddbddadcdbddcaccaddcadbaacbbcacdbadcddbcdddbbadabdabdccdcdccdddccdaccdacddcbbcadcabddaddcbddabdaabcbacbdbdadbccbabdbabbcbcbcabcdddccbcabdbbadbdbdcadcabdabcddabcddbdbaaddbaabcdacacbdbacccaddcddcaabaabcccaaccbaaadbccbbddbdbabcddddddbdabcbabcbddabaaaabcaabdabcdbcdbacbdccbdbbdcddcccbcabdbcbdaacbadbbbbcdcdadbadcdccabbaddddadbcdcdadccaaaabaadacddcbbdbccbdcbddcababbddabdbbccaabdabcbcdabaaccdabdccddbbcbdddddbdcabbdcdadbdabacdddbddbabdadbdabacdbcacaacbdbaccddddadacddcabbcdbdcbccbabcbdccbadccacacbcdadbadcdaaadaacdbaadbcbcddbcdcaaabcabdccbdbacbdaacdcacbcadcabbcabcdabdbdabdaabcbddcbcacaadbddbbcdabcbdcbdbcadacccdababbcdbabdbbddbbbdaabbdbbbdddabaacaaccbdcacacacdbcbcbdcdbcccdaaaaccdcbbbaabdbddcbddbbcbcacacbcdbbdbdcbdabcdbdabddacccaabccaacabdabcdddadbabacaacbabdbdcbbbadaccdccddadbccdbbbcadababbdcbcbabdadabaccbcacabbaddaabdbdacaacadaabcbccbaacdcdcadcbcddbdcbacdaadccdacadddaabbcabdcbacadaccbddccbaddacabbdbacddacddcaabaddbcddddabacddbbcbaaaacadbccddcadcbcadbdcbbcadcbdcdaadbabdaadbddbbbdbcdaaddcddddcbcbdbdbddcdcacdbdbadaaddabaadacabbcadbdabaccbdadaadabcdbcacbadcdcdadcacadbbbdbdccccabdcaabcaddbadababdbbabddbcbbabadacabcadcbbdacabdbdcaadbddccacdccabcabcbbaacaaaaddabdcaaccbbbcbddadbcdbbdcdbcdacbdcdddaabdadbadcbadaacdbbccccccddcdbbccdcaccbcdccdaccccaaadcdabbcbbaddacaaaaddacadddbbbdbdaabbdadbdbddaabadbddcbbdcbbbaaaadaadcdcadacbaccaababccddacaabbbadbbbaddacbddddadbdccbbcddababdccbcccdcadaacacabbccacbdbbbadcbaaccbdccccadbaaabbadbcacbaaddbbadccbdcbacdadacabcbcbdacaaccabbbbcbcaaddadcccacdccadcaabaaacacddbabbbccccaaccbdcaabaabcbaabdaabdbaccdcdbddbbcdccaaadabcbadbcabccacacdcbddaaddaccaabadaccddacbbaaabaddddccccdbccdcdcbaacbcbdddcabddcdccccddbacdcdacccbaacbbccddcdcadabcccdadacdbdddbccbccdaabbaadcbbdaccdcbbcaadacacbcbbadcbbababbaadacadababaabcdcdddaadabdaabcabadccaccdbcbbcaacdcdbcaacdabcccdaacbaddcbdddacbacaacabcacabaadbbcdddbaaaddcddcdcbbbcbbbbdcdbacabaadbddbdbbcbadbcabddacddabdbdacaaabbccadaccababdbdabdaabadcccadccccbacaccaadacccbbdaacacdaadabdbaadcdbacbddccbadcbcdccbbaabacbaadbdcdaacbcccbddaadbcdcdbbbcaccdcacbdbbdcccdcaaaabacabcbbdaaaadcaaadbcdcdbaabaccdaabcadbccdbdcdadcacbcbdcacdccdcbbcccadbdbbcdcbbadabcbdaccabbabcdaaacdaacaaddccbbdbcdcaaadaabdaabadbbabbbbcbdcaacbacaacdccccabaddbcbdaadacdccbacbadaacabdcadccabdababbdacdbdaabcacdbabbcadbdaadbbcbcaadaadbcadadaacddcaccaacacdbdacdacdbdcacccdbbcbdcddbdcaacacddaababcccbaabcbccbaccbbacdcabbaaacdaadccaccaadbdddadbaacadcababbaaadcdbcdcdcbdcbbddbabbcbddddaaacadbabadabbcbdadcaabccdddadcdacdbcbacddccddabccbbabccadabbddddaabddcccddcaccbbdccaccbcabddcdddcaacdbdccbbbcdcccdccbbbcbadbdaabcccdcdbbaabaabadabccacbdaaaabdacabdaacdbcdbcacdacabacbaadaaddaaabcdbbacccdadcbcbaacdababdabababcbdcdaaaabcdaaaaaabdaccdcbdcddbbbdcbbadadadaaacadbaaabacbccabccdaccdcbadaabbcabdbaddbdbdbabadbcdccdcdaadbabaadbcbadbcccdcbbdaabcacddbcdbdcabddcbdcabdcdbdaabbabaccacdbbbaddddabdcbccdccbdcadbcbadcabdccdabbdddbdbcabaddbcbcbbddddddabcbccabdcdacaacbcbddbdcdadcbcabccdacdcacadcdbdbbcbaadaacbcbbcaaddcdbaabdcdcbcadddabdbabaccdaccbacdbacdacaabbaacbbddcadcabbdbcadcadddaadbaaadbdcabcdbbbabdcdccbdadabbddcddbdcdcadbbabbcdbaadaabdbdabacaaccacddcdabdcbaaabdbaaccbcbbbddccdbdcccdabaadcdcdbdabcdcbcbcaccabbbdcbacadaaccdcdcddbcdabbddddbacbcbdbddbbabcdbcadabdbabbddbcddabadabcddcabbcbbbadbbbcaacacaabccaddbadbacbdabcdddcccbccdddaabccdbcaabacdaaabbcbabadcbdbddabdddbbcadaddbaaaaddddbbcadccabdcdcccabdccabbaadcbaaabcbddddbadcbcadbcbbbcdbbadbdcccbcddcccbbcabbbbacbccaabcbddbdaccadcdcbbaccccdacaddbcccbabbabbbcaabbcbcbddbbdacdcaddaadddadabddddbbdccaccddcbcabdabcbabbcbaaadcccadaacdcdbcbacbacadadaadbaababbccccabbabcdbdabdbcdabccbbaabcdacccaabdbcbdadadbbbcacabddaacbabbdcaddbdcabacacdcaacbacababbaaadadbababaddccdbdacaddcdbbcabdccbabdbbcbddccabacdacbcdacaccbcbbbadbbacadcbcaabadddddcddbcdcadaacaacbacacbcddbadcbcbadaadbbaacbbcddadbdbcbccdddbddaabdbaccbcdbcaccccbcdccbadaaacdcbbcaaacbddbbacdbcddabbdabcdcacaddccdbcbcbabcdadccaababddcbabcdabbccccdabbaabdcdcabdacbaaddbbcbcdcdbdbbbdcbdadcbdadbbacabdbaacdcbccadabcacadcadabdababdbacbcbddddcccbcccbbbabadbcdcdddbbaadcbaaccdbbacdcbbcdddbacdcbcbcabdccccbcdbaaaccadbcbabdabbbabdddbdcdbcbadcdccbdaccbabaacdcbbddadddcaaacdbbcbcadadcdaccddcdbbdcdbbdbdddaaaabbbddbbcdbdaabadccaaacbaaabddddbddbcbbddaddbbbacbbadcccddaadccadaadddacbbadbaaadcdccbcdcbacbaabbadacbbadbdcbacbbddaadddadacaddaacdbdcdbadcdbaaacccbadcdaadcdcdcdcaacbccbdbcbddcbdcdaabcbdcdddbcbdcdabcbcadbdcdaaabcdcdbacdbccdaccabcabababcaadbdbbadbbbbadbbdbdaaacabccbcbbbcabdccbbadadcbbdcbbaaccddddcbbcbabadbabaabcdbbddbdaaccdbdcbdbbcabadbbdcdddabdabcabcbcccaaaabcccbddcdabbdaabaccbbdbbaaccdddbdccddbccbabcacbbccdbadbcbcabbdbdabcabcabbdbbbdccabaadabcaadabddbaddacdbcacbacadaadabbacabccbbbacccaccbabacccbdcbcdccdccdcacaddaadababaccbaadbcdaabbbadaacbabdbbddaadbcdaaaadbcdcbabadbbdbccbbbbcbccbdaddcdddcbcdbdbbbbcddabcaaacabacaadddccdbbbdddcdcaacdcbadbaaacaabbcadbaaddcbabaccacdddbbdadbadcccbbabaaaabadccabadadaadcdcdcbadbaccbcdcaddacabdacaaccabcadbbddbdbdcbccdbababbacdaddcdddddbbcbaacaacbccbbacacacbcadbccadcabdccbddabaddacaccdbbddbcdbacdbdccbaddbadcaaacccccbaabcaaacbddcadacddacbdccbadbbdaccabddabcdbbbbccbaddddcddccccaddadcccabcbdccbbbddbcddcdcdaacbdbdbcdaababadddbadcbabdddbdddadcddabcdadaadbddabbccabbdbbaacdaacabdbdacdbadbbbbbacbabddcdccbbdcdcdacbcbdcccddcddcbaddaccdcabdcdcbaabccbdaaacabacdaacbdcaabaacdbaacaadccaaaaaccaabbdccdadadadcbadacaabdacdbabbdcdddcccbcbbaacacdcbbacadccdcbddddcbbabadadaacbaaaaaaddccccbcabbdbcbdcabdacbdccaabcdabbcadaaabbdbbdcaddbbcacbbabdbcdbbabaadaadaaccbabdddbbcdbbbabadbdadadddccaaacacccbcddbabcdadcccacdbcaddaddbaccccaabcadadbbcdccbbcbbcdcccdbcdbbddcccdababaabbdaadcbbdcbccccdccbcddabbbcbbdbadabdcbbaadbddcaabacbdbbccacdcdbdccbaccacdbbaaadcbbdbbabdbcaadccaaaccaddddbbdbabdbbadcbdcabadaababdbbcdcdaabcbdcaadabbaabaccabbdbcadddacbdabbcbcdcccabcacbcddbccadcabacdadccaaacadaabddbbbcacaadcacbaddccbddccabdcadcdacabadcabcaadbcadbaadabaababacdcaaddaadbbcadaacbcbdcaaadbabcddaaabaaabdcbdbbacdcabbabcbcaacddacacadbdbbddaacdaadbcccbcccdbcabaddbaabcccaacddcdbbbccdbbcbaadddbdaabacacdbcddacbababacacdbacdacddbaacccddbcaabbacddcbabcadaaacdcccddbcbdbbccbccdadbbcdabdccdbcddbdcdbbaabbcdbcddcbddaaaacddbbcacdbababbaabbcacdaadadcabcdccbbbddcbabbbdbdabbbcdcabcabbabcdcabdcbdccdacbacbbddacbbcbbabdcabadbacdaabadbbddcdacdcbdbbbacadcdaaabdbdaddaadbcdbacaccbabbccbcbacdccdbdacacaadaaabcadabbaccddddddcbcddddadbcdbddabcccacccdbacacadcabcccacdadcbaabcadadcbaacdabbbddadadcbcaadacbaaddcaccabdaccaaaadbbbbbcacdabbcddbcabddccbcabbabbaccbadbcadbbabdaaadbdbacacbdadbbdbbccabdcacbaadcaaadabbddacaadbaabdcbbaaacaabbdcabbdccdddaaccdadababcbbacabbddcdcbbcdacbadbbabdbaaaddacccdaadbdbbbddcdcababbdaddaadcaaabacacbcacbcdcdaabaaddbdaddbbcaacbcbaabbabbbadbcaadcbcddbdccdadcdbadcddbdcdacaabaccbdddcdcbccbbbdadaaabacbbabdcbabdabaddabbcdaaaddadabaaccccaacccdbaadacdbccdcdcbcdbdaabccacacdbddccdaccacbbdadacdcababcbccaccbbcabcabbdbaacdbdaadabbddadcaddbdabdcbdacaacabcddadaaacaddacccbabcacaadabbadaccccadccabcdabadbcdddbdcadcccbbbabcbabdaaaddbccdaaacbbadcbbdccdbaabcaccacddabcbbcbdbbbccbcbdcabcddabcaacabaccddccdccbcdbbbcdbcadcbcbacbaababcacbbaddaaadadacaadcabacbddcabdcbbdadbabcdbaddadacbbcbaaabcaadcabbcbddacaabbcaddbcdccbddccdadcdbbabbbaabbbadaaacdbbcbdaaaccaadbbabcdccbddbabdaabbcabdbaaccdaababddcabbdaaccbbdbcbaaadbdccadabcaaddadaaccdaddcabaddbcdbcadaacaaccddbadbdbcbbbacbccbdcddbacaccdcdbcbadbbdadbdccdcbbdddbcadcdacccbcbdbbcccdbbdcbdbbbcabbbabcbabaaabccbbaadbadbdacddcccacddaddcccacbcdacabbcdadbbadcadaadaaaadcbaadbabaddddbbbdddcdbacaadcccbcbaacbbbbdadcdbdcbbbcbdaaadccdbaacacadaccbcaabcacdcccdccaababdcabbcacccbddaacaabddabdcbdcbcdbacaaaddbaddccabddaccbbaaabdabbaaaaddcbdcacccadccdaaabdaacdadccbaacbcdcabbbbcddabdabddadbccaaccbbacbdccbccbcadbbdbbdccccdbbdbaaddccadbdbdbdcbdcbbccbbdabbbcddcdaabccbabacaacbbabdbbabdbaadcbadaddbadccaddbdacccbdbaddaaacaddadadbdcbdbdcadccccbdbcabababdadccdacdacbdacbdaabddcbddbbcdcbcccbacbabbbbaacbaababddbbccabadaccbddaaacabdbbcbbadcdabbdbababcbabbccdbdadacbcbccdabcdbaabdccaadccabddabcbccbbddaaaddaaabbcacbababbbccaddddcbacdbbabdaaabacbbbcacbaaaadcccacbbabbabbdbcbddbacddcdacdcdccadddbbcdcdbadbbaabccaacdbbbdbbccbdcacdacdcdadaabcbcbacdcbcbdabbbdbdcddacbabddbddaddcbdcdddcaadcbbbaabbbcbbabbccdbabcabdadbabdaaccacaacbacdbaadcacdcdbdbcdbaacddccacadbacbbbdacddccdabddccccdaaabbbdaaabccccbbbbadacabcadbacdddcabaacddccabbacbaadbdddbddbccbbabdbdaacddbdaaaadbcbaabcacacabacabaabcddcdbdcdaabbcdcdcdabacaddcbadbcbacaccbbcacbbdddbbccbdcaccccdbcdbabcdbaaabddccacabbdcaadcdbacaaabaccdcccdaccdddaccacbbabcccbccdbddccbdbcbabaaaacaacadadabdcdabcbdaccbdccacbabddcdacddacacbbdcbbbbcbaccdaaccaabacddbdccaabddccdadaccbdadbbcdcdcbaddbbdbbdcadbbcabcbddbbdcbdacccadcaaadcacdddcbccdddaacbbcccdcaacdabaabccabcccdccdadacaaaaadcdbcdccbaabadcdbabddbddbcdcdccadccabadbbbcabdabcbcaacdbdadacddaabcbcbdbdddddaaaccdbaacaabacababddaccdcacbcbbadbbbbdaaccaccaddcddaacbdddcddccdbcaddbddcacccdacadabadcccdcacdabcbbaaababbcdbddcccdaacdcbcdacadabcbdcccadddcdcdadccacddabadaaccbddaadabcabcbdadbdcbbcbbbacaabdbdcbbabbdcaddaaaabcaccbbdadabacbbcbccdcbaccacadccccbcacdccadacaadaabcaddddbdadaadadbcdcacbababbbbbaabbdbacddbcdcddbdaccdcdbdacbcdbbbdbdaccccaadbcccbbacbabcdbddaaadcbdbddbdaddcbbcddcdbcabdbabaccacddaaacacaccdbadcbacacacbbadbbccccacabdbdaaadbadcdbadbcdaccddbbcaadbdbcdcccbabcdbbdccaadbcacbdaadccabdcaddacaabbccbdbadddcccadcddbaadbcdabccbdddabbcacbcdcadcdcbdabaabacbbddadccdacdaaaddbcaabbcaaaabcddaaaddacababdbbbdbaaabdbabadcbaccdbcaadcbdacadaaddabacccbbdadcbccdccdccdccabbcabbbaddbcbbdccacddababcadaadacdcdabbbadabdcdcdaadcdabcacddbdaabcbbbbadbdbcdaddaabdacdbaddbbbdcbbcbbcaacbadbbdcbdbbbcdbadcccabddcbcabbdadbbcbbcccbbcdcaaabacdccbbcabbaadbddcccbaaabbadccbddcadcbdaadbadcadaadcbdbdaccabcdcbabbdaabacaadaddadadcaccccccccdcdaddbdbcbaadcbddbcabacdadccbcccccbadcadacdabbdadbccbddbdcddcacbabbbdbaabdcbbbaddbcccbcddddddbccabcdbbaadbbdacbcabcdccaddcdbacdaadabbcadbacbcccaacbacadcbbbdcdbbacddbbcbcccadbccdcacdcbcbdabdcccccddbbabadbdacaaacadaaccbcddaabdcdccabdbaccdadaacbbabcbbcdacccaabcdbaddaadcccbabbcbccccbcdcacacdcdbaabcacdcccddabdccdaadcdbdccbadadcbbbbbcadddadbcddbdaccdbddabaaddbacabcbcbdacadbddabddddcdabccbccaaadccbaacccbbbcacbccaccaccbaabdcadcbddccccabccbcabccccbdccabccbcaaabbacbbbdcdbaccadaddbaddccdaddccbbbcababaddcaacbadaacccaaadaacbabbdcaaadddccacdaadacbbcaccbbbaccbbdadccdbbbcdbddacccacdacbcccaccaaccdbbaabdabbbdcdccbcbcccbccddcaccdcdacaaaccbacaaaadabbcbdabcadacabbaaabbbbcaaadaccbaaabadbbdcdbcaabadbbacdbdbadbddabcbabcbbddbbbdcabdccbaababbacddacbbcaacbcbccbbcbcdcdcdadccbaccbdbabcabdbddcaccacdbbdbcdddacdcaddbbaadcdabbadcadbdacbccdadabbdddcbdbdabbcdcdcacbbcbcbcbbcddbabccdbbacadbcccdcbadbdadadaadccdcccccbbbccbdbaddbbdddaaacbbacdacaacbbdbabdacabdaabcdbabdcbdbadaabacdacacdabcdaaccddbdcbbcddbdabaadcadcadcccccbadadcddcbdbbbbbcaadcbcbbddcbdbacdaabaacccaacbdcddadbbaaababaccdcdabdaccbacdbbaccdcdddbbbddcbbaddadbdacadccadbaddacbacbababbbadcdacabcbcadaaabccccddaabaabbcccadacadcadbdcdccbbcbdbaddabdcbcccccadbacccaccabadbbbddbabddcbbcccababacababaabacdbcddabddbbbdcacbabddbadadabaacbdaabdbcbbbcdbcbacaaacdbdbcccacabcccddbdacbadccdaabaddcaddcacbddcccacdcbdbaabbabadaabdcdbacadaadccdbcdddabbacdbadcdaacacaabdccbaccddcddcddcdbbcbaadbdcdaddbacdcabbdccaabccadbaabcacbaccdcddadaabbaccbaaabaabbdaddadccdaccdcdaaacccdbacbdaddaaacbdaaaaabdcdadaabbbacabbccdcaccbaccabaddabaaccabbacaacaabacbaacacacabbbbdbddbbddddabadbabaccdcbdcacacbaacdcdabcbbddbabbacdcbabadabdadbddbbdbbaabacbdadbacdabddbbcddcbcccabadaabdbcdaccacddcacacbabddccabbaacbccaddadddcdabdcdbcabdbbcdcddccacdacbcddbabbbcadadcaaadbacddbacdcadcccddbbddcdbdcadbbbaabccbdcddbbdcdbbabaabdcacaaccacbbccacbccdaddccaabacaaddabbababacddcaccaddabacdaddbbccdabacddbcbdcccdaadcabdcacbcbbcdccadadabdaabbadabbbcdccaddacdbddbdddcacdbabdbbccadbbbdaabadabdbaacadbadcdcdcbcddbdddadcbddaabbbcbabbacdcccbaabdbadccbccdbaaddcbbcaaabccbdcdabdcacdcadbaabcdbcdddccbcbccaaaadbdbdccddbdbbbacdbbddbbbadbacbbdcbccabdcbdacddaccacbcdcabcbbcbbbcdabbbdccbcccadbcdcbbcdbddcaabdddadccabacddcddccbacabacdbccbacacadcbccdaacbdcdacbcddaddddcdbddcbacbdbbdadddbaacccdcdaacaaaadadcdddadbccaacdcbacaddaddcdbdddbbaaddccbbaddadbdbacdaccacacababdccaaaccdccdabadbbccbcbcaccbddbdbcdbcdbdaabbbccabbbbacacadcaddadbbaddcbdabbbcdcdcdaccdaddbddabbbacbcbaabbaabcdcacbdcdbddadddcbdbcbdbbdaaaabdabacadbddcbacddaccacdbbbbdddaddbacddbddbacccddcabbcccdbccdbadbbcbbcacdcdabaacaaccbdabcbccddcabcddadabdbadddddabccabcdbccaacdcacdbacbcabdccadddcbbadadbaaaadddddccadcbccadbdbabbabadbcdbcdcadaccccdadccacdbcabcdbbaddcaacaaddbcacadbcbaaabbdabacbacdabadcbaabadcdabadccbdcddbdbcdadacbadcadbdcdcdcbdccacdcacacbadcbdacccddcdaabdbabcbcadddddbaabbaabbbbcdadabadccbdaaacbdbbcacbdacbcbbccdcbdbababdcdacdbcabbccbcdadbabbdaccadbacabcdcccddcbcbabbaaaddbcabbcadcdddcabaabbabbccccddccabcdccadaacacbddbdcbcaabdaaabddabdaabddbdcbdcbdabdbcbdbccbaadccaddbccddabcabdcaabcbcbcddaabaacddcacddcdcbdbcadadaaaaadcdcdbadbddcbdbaccbccbadcdbdabcadadadddaddcaddcadbabcacdbbbcaccaddbcbdddbdabcdabcbdbcaacdcbaabadbacaacabbbcacbdbbbbadabcddbadaacccdccadabccbbbdcabadbbacdbaabacaddbdcbabdadbdadacccacaabcadaabcaadadbcdadcddcacbbaaacdbcaabcbaaabaaddcbbaadccbabcaccbdacbdbadacccbccabcdbaadbdacdbccbbddbccaabbdbadcaaddddadccdccbadcaacdcccddabddaabcbaddcbbbdcaabbbddaaacabdadacbcbdddbcbbbabbcbaccaadadabdcaccdccddacdcddcddcdbcacbadcdccccbdbaabcdabcdbdbcddddbabcbbacacaaadcddabccabddabdddaadcabbdbdcaccbbcdbcdcaaaaccabbadbbaddbcdcdbdbadbaccdadcabcbcbabaabdabbcaadaadbbdacbddbaddccdadaadaababaccaddbdcddabcbdcbbcddcbddacbccbabbcbcdbacabcbaaadbccbdcacaadabbbddcabbbbabbabbacdcbddbbcacbaaadbbacdddbdadbadbaaaabaabaaacdcdcdadacdcdcbbcdababacdcbbbabcdaaabddcbdbaabdcaccdcdaadabacbccccdaaacccdccbbdcbdadcddbadcdbddbbbacbbadabcbaadaadabdbdcddcaacbbbccbcbadaaabcbcbddaddcbacbabcbcbdbbbdbaccbdcbabcaacccacdbbdbadcdcdabddcaaaabdcbbbddbdbbaadbdbdddcbddccadaabdbcdaaccabddabbaaaddbabdbdcacbadacbdbadabaaacabdcadbabbdcbccabddcadcadaccaaaccbbcbdcbddacabacdddbdddcdddcbadbdcbdacbaccdbccbdbaccccadcdcbdcddacbadcaabadbbdddabbccbbdcaccdccccabbbbbdaadbadbcaadabbdddbdacbbdcdacaacddcbcbcbccaabcbbddcadbccdbcdbaddbbaaaadaaacdccbbdcccadccdbadcbdaaddacacbdabbadaabadacdcaccbdcdcdadadacdadbabcbaaaacdcaaccdaddaaccadddddadcbabaabdcdcadcaaaaccdcbdbccabbdbcacdbacdcbadccdaadcdacbdaccacbdacbacdcabcaaabbdaccdcacaabbdcddaaccbadccadddaccbdabcaabccddbcaddcbddcbcccbdccadacadcddacabcababddbadabbcabacdccabacbdadbcaaccbcbcdbdbabbabacadacbdcbbcbbcddcdcdabddbadbadadddcbacbcdbadbbdacadcadccbdaacbbbccdcaadccbddabacdabcdabdadaddadacdabbcaadbcacbcdbdaaadacbcaccbdcaadacdcbacccdbaaaabdcaaacdddabbddabacddaddcccaccdccdadacadadacbdbcacbcaddaccabcbdbdacbdadbacdbcbddccddcbacdcbaccabbdbdccddcabaacdabaddacacbdabcdacacaccccccbdcabdddabcabbccdadabdbbddcacadaaacdbabbaccacdacbbcdbacacdbcadcbdddcccbdbacbabddabaaadddbddbaddaacbaabcaabacbadcdacbdccabcaabbacccbaccdabdccddabaabbdcadacbadbadbbbdbababaaadacccddcaccaacadcdaadbddadabbaacbcbbdcbaadacccbcabbcaadcdacadcabbacdabdabcabddcbaacbbcbabadbcdadcbadbaddabcdddbbdadacadddcbacaabdccadccaccabbdcadccdbaacdbbaccadaaabaddcaadbdabcbccdbbaabdcddccaabacadacdbacacdddcbdbaaabaabadccababaaadacdcadadbaacccdcddaadcbccdddacbadaacbacdccddaacbaadabdadbddbabcaadbdddacddcccbbbbbaaabaababdcccabdcaaddcbbacccaabdbbdcbabddbbcbbddcccbadcbbdbacabbabacbcbacaddbccbadabacaaddcaccbabcbbbabaaabaabdddbabbcabbcbddabcbbdbbbbddabccacbadaccbbddcbbccbbdddacbacccacbddbdddabaaccbaadadcdcdcbcaddbcadddcddcddcdddaacacbbcbcbdbabddcdaaddabaacccadaacccddadbacdababacbaaaaaaaacccddddabaccbbdcabcddadacdadadccabbcaabdbdaabadbdacacacdddcdacbdcbadabdbbcaabcdbcadcddcdabaccdaaccaccdcabdacbdbabdacddcdcdbaabccdccdccdcaccddabaddadaccbcdbbcdbbbdbdbabcabcccdbdccbdcacccaadddacddcadaaccabbdbcdbadbdacbdcbbbdabadddaccadbbcabddcbcbbbabcbcadaaddbbcddcacdcbdbcbacaabcdddddacdababbdccbacddabdcbdbaaaacbaaabdbdadbadbcdaadbaacbdbddbdcdcaddaddbbdaccbbcddcbbddbbbcabbcacbbbddbbabcacaccddcadcdbdadbbdbddaddcaaacbaaccadcdacdcbcbaccaabbcacdabdabdacbaacbcdadccdcabdcaabcaabacbaaccacdbdbdcdbbdcdacdbbccbcbccbdbbcbacbbbcdccbddcadbcdadddbddaacbcddcddcccbcddaccacbbcbbbcbccacadcacadacbcadacbddcaaabbdbddbbdbcbadccacbbcdadabccdcadcadcddabbbbbbdabcbbbcccdcdcbbbbcdaadbcbccbdddcdbdbdccbdccbadaacbbdabbaaddcddcbdabcbdcbadccacdbcadbacadccccbcbdabcbbdadcdcdcabdbccccccddcccadcddcbbdbbbabdabbcddbdbbbacdbaccbdddaacbadabdddcbacdcadbcaaaacacaabddbdcdaababcacbbaadbbcacbccdbaabbcddaaccaaaccaaacaddaaacdcbbcdddabdabbbadcdccbbcacbaadbdaaacabadddbdcbbbbadadabbcdaacdccdddacbccdbabaabddbdadcbaacddaaadcddbddbabccdddadccaadcbdaaadaccdcddaccdcdcdcccdabdbdbddabcdaadbacbcbbbdbcabcadddaddabdbccdcdccbdcccaadcdabcbaacbbccbcbcabdcddabaccdcdaaaabbadaccbaabcbdacccaddcbccdddbccdbdbbcbbcaabbdccbccbaababcddabacadabaacadbcccadcccccddbbaabccbdcbcbcccaacaabbddddddbdbadccdacaddababacabbdcccbabacddcdbaaadabccadccbcbcbbcaadbbcbbccbcdbcbdcabaadccacccaadabcdadbacddcbdcabbbbbacdbdccdbbbdbdadcbbdabbaabbabddbaddbdbddcddcacbbdbcbcddadabcdabbabcdacabaaddbadcdadabcdadcbacaacbcbbabbdcbbcddddcbcbbcacdbaaccaadbbacbbbbaacddcadbbbacbcadcaaccbbbacdcddadcbdbbdbadbbdddbdacbbaccacdabadacadbbdadababadcdaadbbaabbcdbabcbcbaabbadacdbdcbabdcbcacbdacdccbcdcabbaaccaadaacdcbcbbccbadaabbbabacccabaccdabbacabaacbadbbacabbdbaabbaccabbbacbcacbaccbdccaaccbaacabccacdadcadddcddaccbacdbaabbaabbdcdcadadadaaabadbcbcbcbbbaaaacddbbbaccbcadaabcaabbccbcdcbaaacccbbdacccacacbcbcbdbbadaabaccdcaabbcaccadccbcbacdbbbbdacdaccccbacacbbcbadaaaccbdbccbdbcbcdcaccabadcbbdcdbabcccbccacbdacddbcaddbdbcccacdaacddadddacbbcdadbcbadbaccbdabacaadacdcdacbcdccdddbbabdaaacccccdbaadadbbddadaddbcdadbcabdbbcbabbaadbcbadcddaaddcddcaabbaaacdbacacaabdcddaacbcbbbccacacbacadaabdbbaddcddcdcbcadacdabadaaacccbabdacbbaddbbbacddbdddbaaccbdcdcdcbacccbddcbbdddabbdaccbcdababcacabbbbaabddcddadbccbcaccaaacdbdddaccbaabbaaccdaadcdcabbababccadbbabcccacbdadbabdcdacbbdcbabdabdbabccddabdbbcbcdcddaaddbbabcabbadbdbadbabccdcbacbacaabbabacdbddabdabdddbbccdabadbbcabcbbbcacbabaddcccbbdcdcddabcdcadcaadbdddaccbabdbbaacddbdbdbdbadbaccabdacbdddcdadaabbcacbdbabadbbbaabbbbadadbdddadaabdbcdddcaadbdcaaaddaccddcdaaccdaaaaadbabaabdcbdacbddaddbbddbdbcbbcbabacababcabdbcdccbcdbbcadaccbdcccccbbdcdcadbaababacbbadddcabbcdbaaacbbdccbdcbbadaabbbccaddabbaabcbabbacacbbaacccccdbbaaadacccdcaccabbdbaacdbcbcadcdbdabdddadcabcaddbcbabcddcabcabcccadcdabcadbdcababdcdbbddddadcccbabacccacccbaacaddbbbddcdadcacdcdbddaaddcbcdacabdbbbabbbaabddbccbdbcaabddcbbaddcdbdacddabdabbbbdcbddcbdbbdcdadcacccabbaccabbabaabcaaccddcbcdabcbdaaabdaadddbbbabbcbabbcdabdbddbacaadddcdcaacdaabbccbdcddcadcdaabbbbbcaacccbddcacccacbbaddadadbdccadcdaccddbacddbbaccddccbacadccbadaacdbcdbbcbdcabcbbabbbababcdbdaadbdcbabdcdcbddaacaaccbbcdccbbcccdbaddccccdbbaabaaabbbacaccddbadbadddbbacdcbdbabbacacbaddcabbcaddcbbabdcccaabdcbcbddbdaaddddbadadbddbcbbcccabbddcbdbaccaddbabdcbcdbaccabbddcbaccdbaaddcdbcabcbaaadccbbdcabbccbcdddbadacdbdadcbadccdcbcbcdcbadabbcacbdcbabaadabacddbcacdcacacbcdbdbbdbcaaacccaacdbbcacddccbdbbbaaaadcacbcabadadbbbbccbdabbcbddaacadcacacccdbcdbdacbbdbccbcbcaacddccbacbcbbbacdacbbbcadabadaadccdcbbdabddbddabbdbabdddaaddaabadbbadcbdbacaabbaadbbcbdccdbddbccdccbaabbaccacbcdaaddaaabbdadcbadaadcacbabbbadbaaddcadbccdacccccbcaadbcadbbaaaacddadcabddbdcbbcdabdcccbcbbcccdbdcdcaadcdcdcaaacdddaddcdddacabadaadadaddacdaababaddabbcacacdcbacaadccdaaabccddcabaadcabcddaacdbaabbbaacdacddcacabdbccaacacbababddcccddacbbaacacbccbaaddccccbdbdbcbccdcdccaadacacbccbbcadabdccaddabcdbdddcbaaabbdbccdcacabbbabbcadbddbbbadddccbbddddbcacddaddbdbbcdaacddabacacbaacbdddbdbabbdbaddababddcdcbaabdcdbcaabbcadddcaaadaaaddbdddaabccacccccdabbabcccccabddacbcccbcdaaddabdbddadddddcdaadcbbbbacdcdaaaccbdbadacaabbddbbaaacdabcaacbcbdcbbdaadbbabcadbccaaccaacbbdcdbacdcccbbacbacbdcdbbaacbbbabadcbacabbcdabcbaabcddadcbcacdcdccadcdcaaabacdcbccbbaadabdaddbdadcdcbbbbdabbbccdcaaaabacbbacdddaddbbddbabbbbcacaabdccaadaabbdaccdabdbccdabacbddbdcacddbdabcbbcccdccdbdbacdbbdaaabbabddaccdaacbaacbccdcdcbdabdbdcdddbaaaabcadcaddabbdbbdabccaaacdcdcabdcadbcbdcdbabbadcbaacabacdadccdcaaababcdbdccbbcbacacbdadbcbbadacbddadcaaaaddaabdaccbbbbcacbabccbbdbabdbdadcbcdadcaacbacdadcdbbbddacadadcacbcbadbbadaaabcbaaddcdacabcdaccdbadcbdbddcdbaacabdbcdbccddcbbbacdacdbcdaaadbbbaaaabbcbcacabcaadddcabdcdacdddcdbdacdaddadbcdbaadbcbbbbacdacabdccbdbdcbdbadccbadcbddcccababcacddcbbccddcccaadcbcbbacdcbdabaaccdbbcdddbbacdccadccdcdaadcadccdbdddaabdadcbddbcddbbacbaacbcbbcacdbdbcccdadabddbdbccdadcccbbacccddcdaaabcdcdddabbbcdcababbadcdccddaddaaadaccccacbadcbbdcdbdaaadbbaddabbadbcdbdcbdbcbbbaabdcdddccddaddcbddbbbdacdbddbacbbacdbbbadadccabcdbdcdabcbbabcaabcbacbaaddaadacbbdbdbcccbcadaaacbdccbadadbbdbcbdbdbabadddccccbaaaaddbdabcaddddcdacbbcdcadcaaccbdadabdaabcbbdbdcdcbabdacabbadcadcdacdaadadcdaabdadaabcbdbbdcdaadccccccabdacbabacbbdaacabcdbbddbbbaadacadbcacabaccbdcbdcbbabbddabcaacdcadcbcddbabccdcbdccaaddaacbadddbbbdddabacdbadcaddcbaccccdcbaabdddaddaaccdcabadcdabbcdbcaabbcbaaadbddbbbaddcbcccdadcdccaaadaabdddadabdabaaabccddabcbbacbcabcadabacabcaacddaadcdacaacabddbcdcbaaadddcabcabbddadbbdbbbcaddcadcbadaccadaacbdabdabacccaccabadabcdcccabbcccabbcacadbdbadcdacbadbbabbbbdbcdbcdcacacbcacdcbddccadcbdabcbdbabacdbdacddbacdbcaddaccbaddbdaaadddccbbbabdbcddabbacaaccccaddabbcbacdcdaaabcbadcddcdddbbdacbcccacdbadacacdaabbddbbabcdbcccccdcacbbbbaccddcdacbabcdbbcaabcbbdbdaddcaadbaccabdaabccdbdddbcbddbdcdbbcdabaaacbaacccccccaaabcadccdabdbbbddcadbaadbaadbcaccdbdcdbabcadcaccacdacaccbcbbcdbbccbcaaccdbbdbcbbabbabcbbdbaacdacabcdbdcabdabbbbbdbbbdbcdacdcdaccdabcddbccbdaacaacccddbbcdcbbcaababbdcacadbcacbbdacdcbbcbcbbcbddaddbbcacddcddbdadccbdccbbdbaddbdbdabddbcabcdccdbbbdadccdccdaacccbdbccccdcdbbbaccaabbbbabddadbbdcbdcaaabcbcbdcaaaabbabbacccacaaabbbadbbbadaaadbddcadbabbddaacabcddcbcccaaccaadcbaddbcabdadaabbbabddbbccacccddabcdbaddacdcdacbcabaabdcddcbcaabdbccdacaacacaadabcabcdcbcbcdabbdccccacdccccacdddbabbbbddabaaadbbcbacbcbdacacaaccdcdbcaacdbcdbdddbbabbbdbdcbcbdcadbabdcabadadcdbabbbbdbcdacdaabbaadcbbcdbcdddbaddcabbbabcacdbbdcdbdaadddbbbacddbdaddbcacaadaadcacaabcbadbcdccbbcacccddbadddaaabaccbdabbccaababbabbccbcdbadcdccdbabddcdcdabacdbbcdbbcacdcbcccbacacadbcbbbcaabaabbaaadabdddaaccddcaddbcbadadabcdbaccadccdbcbcddbabbcbaabacacdbaaddcddbdbadaccacddcdbadbadbbdcbababbcabcabcbcacacbdcddcccacddaddbadabdaabbdcddbddacdbbdbccdadccaabbcdddbacdbbbbdbadcbaabdcadbccbddcaaccbcaababdccddaacdbacdbaacdbdbddddbbabcdcccaabcacaacadcbbdbbcbdbdbddbdcbabcbddacabacbbaaddccbabaccbdaaaacacccdccdccadacddcddabaccaabcdddbcbcbbdccbabcbdadaddcabacddaabdaaaabdcacbcbbaababbcaacbaddcdbacddddbdababdbbbcabacdddcbcccdcdcabdbbcaadddcbddbacbabcccdcbbdbabbdccccaddcdbdcdbbabbbdbdbddaacbdaaacacaaadcbbccbcbbccaabbdababaaaaccddddbbcabbbcabcbcdcbdddbcabbbcabbadcdccbbdcdaadabaabbbccbcdacdcddddaaaabdcbaddababdbaaabcbbadcabbdbaaaaaaaadcabcbdbbddabcabbbbbcbbcbcbdccbddbddbcbdacaacbdcaacdccdaaadcbccababcdcabdcaadaddaabacdbcbbdcbaaddcacccdcdaccadbdcbbcdabccadbcbcaacabcbccddacdbcaaddaaaccdcbbcccccdbdbaaaaadbddddacdcabbdcdadabddaddadddbbcacddcaaacbaacbcdbacccdabdcbabbadabccdbcabbacbcacddddcdadaacccddabbdbacadabacadaabcbdbcabbdbdbbcaaabcabcdccbddbbadcbcaadccadccdadddbcabbcbacbdddcdcdcaabdadcbaaaaacccbbccdaacbcccacbdbabbbbdcbddbadcddcaadcbcccddccbdabcabdadcbbcadbbadccabccaddbdcabbbadacacddddacdbaaaaccbcadcacadadbabdcbbbbbcdbacdaccbaadbbcabadaabbcddccaddccdddcddddabbdddcabdccabccdbdbcdcddcdbddccabdaccdadacbbdacddcacdcbaabdccbddadbbddbaabadccdcccbaccbbcbdbaabbabadbdcadcdcbccdbccbcadabdbddacdaccdccdbbdbdbabccacabbbbaddbddcbbcbbcdcbadcbdadbaadbaaddddabadcaabcddbbacadbbabbdacbaaadcdccaddddbccddddccbcccaccdbccbaccbdcadbbddccaacbcaaaaaadabbabccadbdcdbdccdabbddabdddbbbccdadbddacabcaaabcdbcbbdccaccdbaadbaabcddaabbbbbcdddccaddcabbdbaccbcbdbcbdcddbbbbcccbddcdbccbbbababbbbbbbdbcdacbcbcbdaaadabbdcdcdcccdbdccdcacccacdaabacaccddbbacbadaacbcbdccaddcadaacbdbcabbdcadadbadbdacdbdcaddacacccbdaabbdadccadcabdcdcacadacacadaddbccababcbcabbbccccddcbcacadbdacacdaccccddbbddbdacccaccbbcdddbdccaabcccdaabbdcddbdccdbcdabdcbccadabdbacabdbcdcdddaccacdddbcaadcdbbdcabbbccbbcbabacbabadacbbcccbbbdacbabdcdbcacaadbaacbcacaccddbcbdcbbbccdccbcbdbbdadaddaccabbcabdbcbccabacdacdadacacddcbbddcaadcaacdbaabddcdbdccabddbcaaddcbcbadbabdbcacddbdbadccabcabaddcdabbcbdcbcdcaadbcadbdcddadacbddbdcbcbaadaabcbdbbabcacbddbabdaddaacdadccdcaaccddabbacdcbabdccadbbddbaddbdcacbadbabdbbacbbdccbbcaaaaabbcbbadadbccbcdbacdcaaaddcdaccabbddcbddbacaaadccdabaabbbacaabcaabbbadcdbbbddbbddcdaadddcbaadccaccdcddcdbaccabbaccdabadaccaadadccabadaaaadccaccccbdaaabbbadddadbcbacabadacbdddabbdaabdbbbccbaccbcbadbcacbdbaaadadadbabdcdcabbcbaabbadbdcbdcbcadccccbbdbcbacdacacccdacdcdbbbdadbadcdbcbbdacdcddbddcbbadccabcaadbabdcadbbbadaabbacadaadddbccccdadbccadbacadbcabbaaddbadbaacadcbaccbddbacaaacbaaabdaddaccaaabddbbcdddabbcaccacabccbddccaaaaddbccdbbcdccbadcadbdbdbdddacdabcbcacbddddcaadddcacacbcbdcdaccaacbcccabcbcaacababdadbdbcbadaabbaadbbacddacbadbbcdcaacdadadbdcbdcdccbdbabaaadbddbcabaabaadcbabcadbaabbcbcacaccdcacbdbcdbddcdbbaabbaaccadcacadcabccbadabcdbdcdbdbbbbcbbddadbbcdbcaacdbcbdbaadddbacdabbdddbadbaaccbcdccaacbdacbcbcdcacacadbdddbaabbdddddabadaaadccbacabbbdabdbcccbccbaacbbcabbaaacbbaccdbbdccdcddaabbadbdcdbbdbabcdbdcacbacaaaacdcadcbabaabcaacdacccadccbcddddddadaadabdcdcbccbaabcbddcabcabadcdcabcbbccbacdbadcbadabcbcaadaaacbacbabaadacbcdcbccdabcacdcadbbbaaacacdcdaabdabaaccbbdabdabbcdaaadccbccaccdbdcccadaadaadcdabbcacbddabdbccbaacddccbccdabdbbabbaabbbcbdadacdbbaadbacddaabadcccbacbbcadababdddddaaaacaccddadbcdcdbbacccacbbbdaadabaccdbcdaadcddbaccddcbbddccbbdccaccaadabacabbbadddbccddcdddadcddddadbadaacdabadddcbaccdbbdddcbdcadbdadbddaaacbcdbdcdcbbcdacccdadddaaaddadcccddaadbaabbaadbddacbaaddbaabcadaddcdcabdbaabdadbcbbabdbaabcbbabababbabbddccaadadaadddcbbabbdaddcaadbbacdaccbccdaabcbcdccbabaaacdbcbcbbbdbcdaacabdcdddbdacbbaaadcbaacddbbbdcbddcdccbabcdcdcddacadcccdadccddacadddaabdaaacabdcacccaadcdadddacadabbbbabbdacbbaabbdcbcabccbbaabdacadaddccaadadcbcdbdcdccaacdccdbcdcbdbdbdadaabbabdbbadccbcdbcacaabcdaadccacdddcdbbabdabaddbdbcabcadabadbcbaaaccaabaadbbdcbbbadcbdbdbdddabcbbabdddbcadcdbadcdcabdbdababdcbbdccddcbcbcdddddcbcddbdbadaabaacbccbcaddcdbabadccacadabbadbaddbccdddbabacaccccdbbcbbbdabcccbcbcaaadcaabdacbacabcdadcaadcdcdddddbabdbacdcabbdbbacbcddcaaddacabcdaabdadabbacdaaabbdaccdccdbadccacadaadacdaaaccccdbdcdcdbcabaaadbaccdcadaaaadddbcdacaadcdcaaaabdadaacaadcaabddcddcbbcdabcbdabddadbcdcabccbcaaaabdcabaaaddbbbcbccdccbadbabbbbbbbbbaabdccdabacbddbdadcdaacbcdabcabccccdaabddacadadbdcaaadbacbddbaadcdbbbabdcdabddbcbabdabbabcdcabdddcabdcbabcbabbaaaaacbabbdbcbddbabdddcbabbbdccccaddadabacaddbcbabcdcaaccadbcabbadadcbbacbdbaabcbabccacbbadccaaaaaacbbbcbcccdbccbbccddccdcbbbadcdbbaaccbcaccdddcdbacdcbdcccacbcbdcaabdddbdaacbcadddcaddbbdaabddbdbdcabadcdadcabbddbbbddcdabaddabdadbacdccbdcabccabdbaabcdbadacdbbaccbcbcdbdaadcadbbcdbcadccdacaadccdaddacadaabcabcddaabbaaaaabaacaccdbddbdabdcbbadaaddcddadbbdbdddbdcbadbdddcdacdadabbdbcddacbcbcdbddddabddbcdcaabbcccbcdccabcbbbadddccccdcadcacadcaaacabbdadbcbbacacdbcacdbdadbdbcdddbaccdadddcdccbaaadacddadadacacbdddbdddbbdacdaabbdadaadccaaccbcbbaabcbcdadadbdbcbcccaadacdccabdbaccbcdcdcaacdcdcdbcbaaaabbabaccdbbbdddbbdcbdadadcbdcaabadaaccadbcbbbbcabcdbddbddaadadaaccaaaabcacadaadddaabdcacacdaddacacbcdcddcbddbbbcdaacbabadcbbbcbcbccccbcbdcdcdabbddadbdbacbdcabaccabbcadbdaabbbbdbabbcdadadbdaccbdbcbbcadcbbdbccbbbacdaaaabcbcbbddbcdbbdaddcccccdbdabcbcaddddabdccacbbbcadabdaaacddcadddaaabcdaabdbdcdbbbabacacbbabbadbacbbbaccabbaadaddacdbbbbdbdbabaabcabdcadbacbbddcaddcbabcbdabdcaadbaaabccdababdaadccddadbbbbcccbcbcacdbbacdbdddbbbabdccbaadcdbccdbdcdbabbcacccdbcbdbacdcbdccccababdaaaabdcadbbabcdbaacdbcbaadbabdabcccaddbcdcbaaaabbbbcdbcaabbaaacdacabacdcdccbbccaaacbadbaccccaadcdcabaaabdcaadadcbcbddbdadccbaddbaabbbdcdcbdcacadadcadacbddadddccccdbdbddccdbcbbdbbbbadaddaadcaacdccbcbdcbabadadabbbaddccacadccbcddccdbdcdaabacaaaadbbdccdacbdacaccccdabbabdbaaacdcdccdbbccbccbcbcdabaaadbbcbbbdcaaccaaacbbbdbdbbbddbcddabdbccddbbbcbadcabacdbcacbdbdddbaccdcdadabadddaadcccbdcbadcdbbaadacaddaaabdddacccacbddccbcbbaacbacaccabcbbdadaccbacbcdcdaadccdcbddadddbaccdabdcadbaadcdbcccaabddaadcaccaaabdaabadddaabacdbaaddbdcadbdcacbcdaddbcbabcacacdcccaddcccbaabbcbbbbdccbcacdbcdacacbcbbdaadccddbdcaaadabdaadbbcbcbcabcadcdabacddadcbcbdcadddccbbddacbbbbccddacabcaaabdbdbacaaabdacccbdaaaaabbbdddcaaadacacddadbadbbaaabbcdaddcbcdbddbbbbbccddcdcccddcbddbaaabdcbcadbbbdcdadadaddadcdadbbbdbccbbddabbdcbdbcccbccbabdcddbccbdbcdacbddadbdaaabdbbacdddcdabadcbcbdccbbdccbdcbbdacacbaacadbacdcdbbbdbcdcabbbabbdcdcbcbaacabdbdddabbcdbdacbacdabcaddabadaaaaabdaaddccabbabddbaddadabadbbdaadacdadcbdcdcadbdbbccdcbadbbddcccdbdbdbcbaccdcdcadbdddddcccbdacaabaaddbdababcdcbcdbdbddadddbabbcaabccacbaaccacbcdbcabcdabcbdbdcdababadcbbdbadcbbdddcabacdcbcdaadcbdcbbbcbaabcbdcadbadadbabdbbddbdddbcadccabddbbbaacdcdbcbbdabbaaabbcabcaddabbbbacbacaacbdccadaabdcbcdcbccdadbbcdbcbcbdbdbacdbdcbcaccdcdcbdaacaabbbdccabadbdcddcbdabddabccccddcdcddbbdddaddbbdbdbdcddbdcacddcbdbcaadbdbbdbaabbbcdacbcbddbaacdcdbbcbddbccabcaadbbdbbdcdddaccbcadccacadcbaadbcdbcbdbddcbadcaaacacababadacdddccbdbdabddbbacddddadbcaabccacddcbddbabdabacacabcdadddbdcbdadbbcbdbcbddcdcbacbdacccbddadddabdbadabcbabcdcaabbadbaccdddccdbcacacdbdbbacbbcbdcaddbccbabccadcbadbadabaabadcaaaaadcbbabcccdbadbcaabacadcabababadcabacabcadabcdccacdabbddaaddcaccddcabacccccbadadabbddcabddcaabadadbdbcbccdcabbcdddbcaadcabbaddddbdcbabaabdcbbbaabddcacddcdccbbbbacacdacbbdcaaadcadbbdcaddbbcbbddcdbbdbabacadbdabdabbbbccccaddbcbbbdddcbbdbdcbbacdcbbaaadbdbcbbcbbcbcdacdbbadcadaaacbbdcccabddcbccbadacbbddadcacadcabbcbcdcddadacbdbcbcbbdcdcabaadcddacdadababccbbcaddabbcacabddaacadddbdaabacabcdddcadaaddcabbbddbbbbccaddcbccbcabdbabaadaaccdbdcdaaadbcdbbcbaccdbcaabdcdcbcddbbcbcbaacbdcdccddabadaabaaaaccaadcacdbbadcaabadcaabdcbbcaaadcbbccdbbddbccadacabadaadbdabccaabcdcacadabdddcadbbabacdbcdbcbccdcaabcdaacaacdcacadcccbdaacbcaabccbaaddcaabaacbdbaacbabdcccdabddccccdbabcbbacdcaadbbadbacdbbbbcbddbccadacacaacdcaaccbbaabbaabbbdaddbccdabcacccccbaaadcbbbbaaddcddacccbdaaadcddcabcaddbcbcadbcbdcbbdcabaaacaabbdacdaccddcddccbcbdccbbbccdbcbbccbbcaaadadcdcaabcbadbadbcdacccdcbcdcdbbbbddbcdcaacabdadadbaccbdcbcbbbccadaacacdcabbbabdababdbcdcddaadabbdcccddaabbcbbbdacdbddbdbdbcabbcaddbacdaddcdbcdccbabbcabcacdbbcaabaacbbdabdcbacbdadbccaababadaccabbbcbcccbbbdbaaddddccdbccbbacdadddaaaccdbababddcbdabdcdbbdabdcdbbcacdbbdbcbccdbabdacadcbbccdccccdcdbdcabbaacdacbbcbdacdbbddbbacdbbaccbdbabcdcaddaccadacadcbabcdbadbccbdbcdaadadbcdbbdbddcdccddcddcadbacabcccdacaadcaabdcbbdcdbcbdbbddaabcadaddccdbdbcadbadcbddabadbcabdccbabdcbcccccbcddbdcadcabdcacacaddaabaaccdcabccaadbbabadcdaaddcccacaccdcadcddbdccaddaaadcaadcddbcaddddaccaacaadcdbbcdccabbbcaadccabbcaddccddddddbdadcccdcdbddbaadbcacacaddbddbcacbbaabbdbababbbdacabdaddadcaaabdabcdacbcdddacdbbcabbbdaacacbadaacccbbaacaccddddccccdcacddccddabacccaabbabdabccadacaddcbaadbbbaacccabaddddccddbbaacaaacaabdabdacbbccddbcddbbccccaaadaacaadadccacbcdcddabaccaaddbcaaacabaccddabdbaaaccddbaddcaddaacabcbbbabccadbcbbdacccddddcbadcbcddacadddbacdcbadacaddcacbccdacbccddbcbbdaadbcccaddcdbdcabccabadbcdbcadddadadbcdcacbbdcaabbacddcaababdcbdbbaabccaccccdaddbcaabcbcbdcadcaaabaaabacaaaadbbdabaadbbaaaaaddccddddabccadcdadadbcdaaaacaacbdddabaacddaadddacaadcabddcacbcaccbdadbbdadccdacbcdacbcbbabdbbcccdbbbabdddabdccbdbbbaadbcdcbabccbacdbcdccaddcabaddddbcbbcbbbbaddaccbbcacbdcdccaadadadaccccbdaddbcadaaddadacadcaadaccdaabccbbbdcbaabcbadcbcdbbcadbbccdcaadadabddaabacddccdacbbdaccacadadcccdbbabcbcdcdcdbbdaddaacbcaaadbccdcbbabbacccaaabaadabbbacadacbabcdcbccabccabaadadbcababdddadacbcdbdcdabbbbbdcbbcdcbadabdbbbddcaaadbddccddcacaacdddcaaaddbadaccddbaddbdbadbbddacdbadbaadcbaaddcaaabcbbcbabdccacbbaadadcbcbdaacbbdcdadbbbadacbbdbadddacbdbadbdbccbcdadddcbbccaacbcddcbbbdccbdbbdaddadbdcbdaaacdbcaaaacdabdcacabbacabacccbcbaccddabbccabddcaddacaacadaaaabbaaaabcadcaadbdacbbdaabbaccccdaaabadcadbaaaaddddddbdaccbbadabdaabdabcbaccbcddadaabdadddadbcdbdbbcabaddabbddcbadaadbdadbccbbbdcbccdcacaacbdcbdacbcabccbbcadbcaabcaabbcaaddddcccccddcbdaaaaadddcdaacadccabcdaddbabccdabcbababccdabbcbbbcdbdadadbcbddbabbddcbbcaadacdbbccadcddcdabacaabbdbadcddbacadacdacbacabbabdaaabbcacbcddcacbdadbcbdbdddbbcbcdaaaddababbcbaaabcbabcaadddacdacbcdabadbddccbbaaacaaaaadccbccacdbacabaddcddbdcbbcbbadbabcdbabdddcaccdccbcbbaccadaccddbacbccbaacbdccbabdccbcdcbcacacbacaabcaadcadcabcbbbaccdcbaccbdabbcabbbacccacdccdcaadbaaddbdcddbabacbdbcbbbaccadbbdddadadaddcdcccaacccaddacadaadadcdcbcdccacaacabadcadcddaaadaccbadacbcabbcabaacdaabbddccaacccdddaaadbadaddcdacacbdacbbcddabccacdbcabbabdcbaabcddaabdacadacbbddddbbbbccdabdadacaadccadcabbdcdddcaccdbcdacbddbcabbdadccabdcbabdbacbdcbabddddcacdbbdbccacacdcaddbdddababadbdcadbaadbdbdacbddbbdabbcdbcbbbaadcbbdccdaacbcddddadadabaccaacadaaddbadcbaaabdaacdcccddddbdacaacbaaabbdaaabbdaaadbadaaabcbadbadbcbcaddcabcdcdaccaacdccabdabacccdaaccdccbcbacbddbdabdcddddbdcbbbdcaadcacdcaccbaccdcadaaaabdabcababdaccacacdcdbccdbbbcbabaadacbcddbcbbccbabddbddccccdcdbcdddccddcdccbbbacdcdaacdcdacaaacbbccdcabbcadbaaadbdaaccbbdcdccdadabcdcdadaaacdadccbcacccdcbbacddbdcdbcdbbccaccdcbddadddccbabaaadcbdaccbcabacbdabacdbacadcdaddbdbbcaaadaaccbcacacddddcddbbaaadbccbdcacdbabacbdccbabaddadcdcadddcabcdacbbacadcdbbadcdabbcdbcabaabbacdcbdbabadacacbdcacadabbbbdddbccbddbdcdcdcdcdcbcaacababaadabaacbdabccbdacdabbccbdcdcabcdbcccddddabadcdddadbdadabbcccccdbcccaccacdcdcadcbddccacabaddcdddabdbbcccaacaccbbcaababaddcbbccbbbbccbbcbcacdcbcddbacadaccaccdcdadbcccbdddcbbcbaabadadcccabbddcbbbadadbbdcbbcbdcaddbabcacacbcbccccbacdcdcabddbaadbcacbdaaccacbdbcbadaaddbccdcabbbdadcadacdbbdabbdbdbacbdbccaaadbcccdddbadbdcabcbdbbacdbbcdddcdcababdbdbccadbcbbcaaaaddbccacabccbdcbcacabcadddbbaacbaababdaabdaddbacbaaaddacaddcbbbccddaacacddccaaadddacdbadddbcdadbdabbbbaccaaccabbdcdbbbbadbcbabacbdacdcdcccdcddadccaaddbccdacabdcbdabacdabcbbbcbcdbdadddcadabdbbdcacabcdbaddddaacaaaabbccdcabcacbbbdaacbcbadcddcddcadcddaccdabddbcdcdbacdcacccdaaaadcccddccabaadccdabddbcdbdcddddbbabddcdcadbbacadcabdabcddbadbdabaddaaacbadbabacddcbbaaccaddcbaacadacdccacddbbbbaadbdadbdddbdabccacbdacdaccadcccdbdbabcdbaacbbcccadcbdcbadcdcabaabbdabdacbcabcdddbabbcaccbcbcaaacbbcdbdddcbddbbadcdabacbcbccdbbcddbcbadaaabbadcbbbbbdbdcdcbabcccbbcbcddbcdadadadbbdbcbadccbaaccbcdbadbcaccbaaccdbaadacccbbaabdbabbddcbbccacdbddbccbdcacdbbabdadadabcbabcacaadbaadcaabbbcbbabcbcbcddabcddaabcbcacbddbadbabadacbbddaccdcccaababccdacbacccbbdbdbdaaacbdcccbbcccdadcbcbbbbaaadabccacababdcdcdabdabacdaaacbbdccabdacdcccdccbdabdadbdbacbdcaaccdbbcbdcddddaddcbdbcdbdabcabacdbcbbbadcaabdcccddcdcdcdddabcabcbcbcbbbaccbacabccdccbaadcbcbabcaacbdccbccbcabadabbcaccaaabadbdaabbccacdcdbccbddbaccdbdbcaaddaacbdbdadddacbacbbaaacaaaaaadacbacbbccddbaaccbacdaacdcbccbcbadbcbccddbacddaadddabcababcabbdbcabbbbacbbbadaacadbaaaccadccdbbbdabbabcacdcbdaddbacbaacbcadddcddbbddabdccaccacbadddcabcaddbddddcbacdabaababbbcccbdbabadcacbbdbabbacbaacdacdcbaabbddbdacdaddadddccdccaccadbbbdaddbdcabdcccaadccacbdacaaaaaadbbbbcccabcbcccbbcbadcadcbdadbaaabcdbdaadcccbabbbcbccdcbacbcddbbaddacddbcabbcdbbdddcbaccaaaacadadbbbdbbabbaabbdcddadabbabcdcdbabbcdacddbcabcabcdbcabbbdddddccabddcadcbacdabacaaaaabbacbcbadacddbadbdbcbdabdbddcdbbbcaadbddbbbccccbadcddbbdcaccdaadaaadbbdccdcabacadaccabadbbdcdabccadcacbbccddddabcdcaddaaddcddabdbcccbbddcdabbabdaabdcbadbddadabcdcbcbcabbbaacdcdcccccaddacacbdbdcccddddadadabbbccabadacbbcadcbacdacaababbdaddcdaaddbbdbcbbccadbdbbdabdcdcdbcaadadcbddadcdbdddddbbcbdbbbccccbdddacdcdcdccbbcdccbcbabcbcbcacbbdbadadadadbabdbacdbcddccdabdcbcbadcdcbcdaadadcbacabdcaacdcabdabbcadabbcbcdddcabcbdbdadcbcddbbbacbdcacdbdcdcbbdbacbabdbbcacacbdcccbdccbdcaabcccbbbccddbadcbcddabbacaacaabcacbcbdbaaaddbbcdbcddcbaabacabbbaacdaccbdaabdbcdddbcdddbcbacaabacccdcacbbacaabbdccdaaacbcdccddaddcdbcaccbdcadcccbdcddcdccdacdccdaaabacadccbcdbbadbbadbbaccddbcdbaabaccdadcbdcdaaabdacdbacbaacaadaaaddabbccbcadbdbcadbccbadcaaaacdaadbbaadcdbacdcccadbaddddcadbdbdbbddccdadbabcacdaaaaccdacdbdbbbaddbadbcbddbabbccbbabaccdbabbbdbadadbbadddabaaddbbcaaddbcddbdddacbcdcbdadccaacdccadcccdcdccdaacabcbbcbdcbabccabcdbabaccadbbaabdccdacbacdacacddbbbadbbbabcdbdcdaaccccbdccacabdcbdbdcbbcbaabdaddbcaaadcdaadbccccbbbbbdbdbcaabadccacbdbbbcacaacdcaaacaabaaaaabaccaaaddbbaaacbabdcbdaaabddcabbcdcbdddacbdabacdcdacadbcbbaddabcbaabbcccbaabdccaacdadabadcddbbdcacdcdadadccbadddaadaddaaacacaaddbbbcdccbcabacaabdcdbcbdadcbbdacccdbacacaabdadccccbbcbbbbddcbddcabbdcbbdcbaccabcabaadbadadabddacbbcbbadaddacdacbdddacdcadbdcacccdbdcdddbbdabcbdccbabbcccaadcdddaaadabcaaaaadcbcbccdcaadbcbbbdddcbababacdabadacacaaccabadbcdadbababcddbdcbababbdbabccdcbbcaddbcccaaadadbcaadaaddcadcabccbaddcddcbadabaadbadacdccabaadcadbbdbadcbddacbcabdcbbdaaaabccaaccabadabbdcbadbcacbdccdcaacdcbcbabbcbacbbccccdddadbdbbbdaabbbdbdacdcbaddbcaadcaccbdcbadcdbdcaddbbbcdddacdccaccbbacabdcbaddcbbaaabbddbacdcddbadbbdbcdbcbdacdbccbddcbbdddcbdadaacdcacddcbacaacccbcbdcdccabdcdccbbccdcaccacbccddbddbccddaababbbacdbadbcdaaacabdcbbcbcbbabbccaabadabdcddabaaddcadbdbdbabbadbbdbabcdbbbabbcabdcbcbaabadbdcbdcadaaddbadaaadbcaacaabbcacadaadcbdbadcddaccadacbbccaaaadcdcbcbbcbbbaccaaacccddbbdbaadbcabadbcdcdbabdbaabddccdcdddcbcabdbdbacabbcacacdcdccabdadbacddcbdbbcdcbccabdcacbcbbdbbabdbadbcdadacdbdcdabbcdcaadaaabbdcacadbbcbababbddababdadaabdadddaccccabcadaacdacbddcaababcccacccdbacccddbbadcdadbdbacabbccdaadbbbbdcbabdbdaabbdccaaaadbbdbbddcaabccdcbcbcbdadbaccadcccbcadbaacdadcbabbcdacadcdacccabccacbdaacaddaaabccdccabbcaccbbccdddcabcaddcbacbccacbbcdaccdaaccccdcbadccccbcdacabdcaccbdbddbcaddabababbcdbcdcacddadabdacdbbddcadddaaacdbbbaccccbadadcaaccbbdbcacbcddaabdbadbacdbaaaddbcacaaccbbabbaccabdaadcbbaaadcaaddbdaccbaabbacddbbaaaadcccaacddacbaaaaadaacbdcdcdbdaaabccdddcccccdbababaaabdabcbacacababdaccbbaaddacaaddcddadcbadadbdaddbcbddccbbadacbadcbadadcabadcddddaaacccbdcdbbdbcbcbbadbaccaccdadcdcccdaaccaaacbcddbdbddbacbaaccacdbdbbcabcdcbdbcaacaabacadccaccaaaacaabdcdbdcadddbcbcdaadcadbcdddcadcabcaddcabbdabbaddbabbbcddbddbabaaccbaaacaacdabccdcdccdadcacababaaabcddccadcaaaadbddcaacdbdabdbdaabccdadbcdadaaccaaaaadaaccccbcbaddbbdaacdaabbabbdddddcbbdddbccbbdadaddadbcacacdbabbbbbabdabaddbabdccbcaadcccaaaaddcbaccdccddbccacdabbdbcbdcccdaaaabadcdaaccacdbcacbddcacccadbdcdbabadbddccacddcbacbdbbcaaacdcdccaadddabdddcacbdbcbbabbdabccdbddaabbacdcababbcdbcadcaacabddbcbbaadbbccabcdcdadcbcddccbcbbabadcadddcabdbadccdccddadbddbdbbbcccbbbabdbacdbcabacbbdaccaacbadcabbddcaaddcbbcdcbaccbcbdadbaddcbbcdccbbddbcdcacdcdacdaaabababcddbccdddaddbddbdabcbaddbbcabcdcababacaabbcacddcaddabaccaabbaacaacbcbdaccddcbccbcbccccddcccdcbdabaabcddbaddacacdcdcdcccdddabacdbccacaaaacdcacaaabdbdbcbacddbaddbbbabcbcaacacbbadddbcdbbaacdcdbadadcccdcccddbaccdbbccbdbaaabadcdacadaabbbaabdabdbaddbabadcdbdaacccacdabadadbacccbabbcadcdcdccabdcccbadacbaabdaccccdcacdbbbaccbbcacbabbadcbadcaacbabddacdbdbbdbacbabcabaadcddddcadbaacbcdaddcbccdccabaaddaccdacdcddbdcabdacbccbcbddabadbddbbbdacbacbdaabdabbdbcccadbcdbadccccdbcbbdcbabaabbcbcdcdbcaabbacadddbbddaacadbdbdbdcbabcabcddcaaadacddcaaabbddccdaaaddcdadacadbacadaabadbcabcacaacbacabbccbcdabccbacacbbabbbbcdaaadcddbaadbcdaddbddaabbacbadcbbddacadcdddccdcdbdcdcdcaddddcdcdcddaaaacdbdaddcddbccdcbbbbbadbcadabbdccbdacadaadbacbdbbbadabcaacbadabdcacabbbcbccaaabbbdbabdbdbbcbccdcbdcbbbdabccdabbdcbdadacabcbbabacaccdcbacacbbaccddaddacdbaacbdccbdcbcadbabcbabacbbcacbbdacbddadcccdcdaaddadbacaadbdabcbdcadabddacadcbbdcdabcabbcdbccdadbdacacbbbacbcaccbaacdcdcadbbabbbadbcadcdccdccbaacdccbbcaaaaccabaacbbbcadbddcdbadddabbadccacdcdbccbbabacccadbdaaadcaaaabacbadaaccacbccabbcdabadcabaaacaaaaaacabcbdbaddccacaabddaababcbbbdcabcaababcccbddbcdbddcbbddbbcccdabdaccaabcddccabbadacabdbcadaadcaacaadadbbcdaccbbdbaddacdddbbcadbaccaacabacaabcdbccadcdbdcbadccabbcabcdbdcbaaaaabddbbddaaddbbdaadadacbdcbacdacbbcbcabacacddbadadcdcdabdcdbdccbbbabaaccddcbacdabcbbccbabcaddacdaccadbadacddcccaabaaacddacbbbaabcabaabbaadbadcdbcdbcbadccdccdadddcaadcacbcccddaadbddccadcabdbddcacdbcadbacdabdacdadccddbbcaacbaddbbddcabddddddaadadccbccabaabbbddbdbcaabccabacdaccaabcadbcabccddaccacaacadbacdcdcdbcbdcccacabbcadadaadbaaaabccbabbcdabccbccaddaaaaaabcdbadcbcacccbadacaaddbbabbbaadbdadcdcbbcadcbbcdacbdbbabcaddadbdcccbdcbaacabbdacdcccdabadaadcdbbcaadcabcddbcdcabdbbdcccadabbcabdcbadbdbccdcbccbccdccbbcabbbcacdddabbcbdaabdcadadaddbccddcdcabdacdbccaadaadacdbbacddacbdcdbddadacddddcccbccbbbbdcbcbbccbaaadadbbadaacdbdbaadbbddcdcdddcdcddcbbabbdbbdbbccbbcaaaadddcacbaacddcaaadaacabcadddaaabadbcccdcbaadabaccdddbdadcadbaccadccddcaaccdaddccdaaacacaabddcabddaadbdacbdcbadddcabcaacdcabbcbaadaddcdcbcbccbbaadcbbbdccdadadbabdcadbbababddcabdbbaccabcdabdcaadabadababbcdbbadcadacdcbcdcadcbbbacbbccccdacbbadbaccaccbdddbbdcdacbdcdbacbcdacdbdbbbbccbaaaabbcddacaababaddcdbbdbaabcbcdbdcbacadcdcbcbbaaacdacddbbcabaddbbdddbcbddcbaddccabcdbbdcdccdcaacabcbccabdacaadacbaabbdbbadcbcabadacaddcbddbbcdaacaabdaccbcacddbacacdabbabbaaccaaabcaaaabcdcabbbbbdabccbaacaabbbdadabdddacabbcdcdccccabcadcddcbcbcbccaccbcadcdcddabddcddccbdcdbabbddabcabbcbcacaaabaddaddccdbddadcacdcccbcccbdadbddddddbbbbddbacacacaadadcdcbcddaaccccbbadacccaaaaddbbcddcbdaaadaabcabbbaabcdcdbcbcadddabaabdaaadadabddabdcccacdaaaacacbddcacdcaccdadbaadccdccabdcddabddbabcbccadcdcbcdcbbcddacabccabdabbdbaddababacadbcbacabbcdbcbcaccdcdbabaaabadbddcddcabbbcdbdcbcbbccddccbadbddbcdbcadcabacbdbbbcabadabcdccdbdbaabbdadbabdacdadbbbacbdadbbaddaccbdabddcbbabcaccacbababcbadadcabcadcbcdabcddabbdccbcdbccaddcadabddadacacdaabbcddadcbacddcccdbbadbacbaaccdbacbcbcdaaabbbddccabaddababbcaccddbadcaaccdcbbdadcdcbddabcddadbbdcbabadcaabdaacaacdaaabbadbadcddbaddbddaddcbadbbcddbccbacbbacbccbbdbabddabaddbdddaddbbacdabcbabbadccbdbddabccddcbcccdcdabcbbbcaaabbddddaaabbbccadcdcabbdacdaaadcdbbaaccacbbbbccbababcabbaacabdddccadddbddaccdadcccacbbadcbaccbbcbacdccddacbdadcacbcbbbacaabccdcadcdadcdddcdbcbadcbdbcdabcacbbcaaaadabbbccadcdbddabddaadaddcbadddcbaabcaadbdddabcdccdcabadccccbcbddaaabccabdcabbdaabdccabaabcdaadcbddbddbdbccbcdcdabdbaadbabdcdbcaabdbbcddcacdbccdcadbdbcbddcdadcababcccaacdbadcbcbbbbbdaadadaddcddbbccdbabaccdbddcacbcdacdcbdbabacaabadbcdddbaababababaaabaabdabcbbbccbdadcaadcaaccdcacdcacabccdaaddbddcddbaabcbdbabcdaccbabacccadacccdccabbacbddccbdacdbcadabdbcbcaaabaabadbcccabcbabdadbacabcbcbbdacacdcaadcbddacaddbcbadcdcadacaaaadbcbaabddaabaccbacdaddabdbabbaadbcdbccdddbcadcadbdddbddabdcddaabbbaabadbcbbabcbddccadbabbcdbbcaabadbadaacddcdcadbaccdaccaacdbabbddccabccddadcdbdabddabbadabaacdccbbaaadbbbbccbdaaddcddacbbddadccdabbadbbaaaadabdcbaddcbcddabadaadacaacbbcaaacadabcbabccaaddcaabcabdabdcccadabddbbcaaabcababdcdbbbcaabaacbccaadcbdddccdbaacbdcadaaacabcdbcdacbaabcddaacabaccaccbbbbcabbaddaadabbcdcddabcdabbcaccabdbdaddcdddadccaaadacbadccaabbdcbaacabbbbbdadbaddabacadabccbccddddbdbadcdabddbcadaaddcabadddcbddcadadcaabcbcadccbdcabaaddcadcadbabbddacddddaddababdbdbadbbdcdbbbdabcdaacddcdbdcbcadcbacdddbdacbdababdcacccabbdccdcadaabbdcbbcdaacbdcdadbcbccbabcbcbdccbcacddcaccabadccdbcacdaccadbabcdbadbcdaabbbbbabbbaacaddbacbcddabcbbaaddbcbcadbcbabcdccaacaaacbcdacdbcccdbcacbadddcaacdccbdccbddabacbaddcababbccbbddbcbdabcabaaccbbcdcabadcbccbaadbddbbbcadbcaabbacacdadacccbdcadcbdbaaacbaddadcbcbdcaabbcdaaabbbdcbaddbaaddaaabccadbdbbadcbbdcaddcadacccbdcbbacccbdbdcaadccabdccaacccbaacccbaaaabcdcbccdbcbbdbbcdabcdbcdcbdddbabbaadcdacbadddcccbdaacbbccadaadabdabaccbcddbbdcdbaddcbcbaddaaabbcaaddabbcbdaccbbdcbaccdbdbdbdadcbbdddabccdddaabbdbaccadcdbacadcbdbbabdcbdcdcadcbabbcdbbbdbacddddaadbccbbbbcdabcddaddaaaddbdbbcdcabdcddbabdddcdbcacbdcddbabacbabcaddabbaacaacdacdddccdadbdcdbcbadbdbadbbcaaaaaabcccacdacadccbdbddbbdcdaacdaccccccddcbbaacccbcbaaadcaacbadbdaabddadaccdbdadcdddcacaddbbbcbabcacbcccaabbcaacaabbabadbaacdbdbdcbbbadbddddcdcddacbcadaabadcabbdcbaadacbccabbdcadcdabaadadacbdaddaadccbddcdbbddacccddabccaccdddbbbdcbabacdcddcaddbdbadccdcbcacabdbaccdaadcdbcaabdbbdaddcbbadcdbaabacaddabcaddbcdbdccbbbaccabdccdddcccbabdbbabbccabccdcaccbddddbabcbdbcdadbaaaabcbacbddaaddccdacddcabccaccbabcccacdbbcdcdbabadbdcacacccccccbcbcccdbabadddaadbcdadbadcccbbbbdbcdbbdddcccdacadcdddbbabaaddbccdaaccdddccbcdaabbacbdbcbbcddccacacbcaaadbcbcdaaabcdbbcadabbaadbcdcaacbdddddaababacaadadadcbcbaaddadabbcddcbcdcdbbddadcacabcccbcdbddcbbbabbbdadabbccbbadaaddadbcadcddbcaabdbaccadabaaaadaadadabbbbacbbbaacadadbaddbbdcacabbbbbddddadbdadcbbbbdcbbdbabccbbcadcacddbbcbadbbddcdadacabdaacbbaabadbbaaccbddccaaaadbbdccabcabcbcabadabdbbcdaabbccdabdbbbbbdaadcadaadbdddccddaaddabdbadcaadbbbbacccbccacdccddbcccbadcabbdadcddabbbdabcdbbcabcdadadcddddabdbcddbcbdabadaaabaabccbbaddccaacbbdabbdcbadbabdbdbaaddaacaaaccbbdcbbaadcbbaddbdbbaabcabdadcccacdaacccccdccbaadaccbdbbbaaabcbdbdbcbacdaaaaccbaacbcdbcdcbbbddcbacaacaddcddbcdacbdccdabaababccacaddbbdacddaadcaaacdabcddddacbaccbdabbbcabaddcdbdaddbddadaccaacddbadadadcdddaaaabbccdabbcdadbacddcacdbddcdbbbbdcdcbaaadacdbcabbdbbaddcacbdbacaabbaddabdbddcccdcbbcddddbdcbcddcdbbbbabbddbadbbadcbabadcdacbbdbabaadbaccbcaaaddbddbdbcabaabddddccdbbcadcbdbdbcbdccbacbabdcabaaadadbdcbbbdaacccbcdccadaccbcadacbdddcaccccbadcacccdbbbccabdbbdbcccbbcaccbbcbccbaacdcccbaccbdabdbcccdcdcdcbabdcbccdadbdddcaadabdcabaabaddacbbbbacccdcbcdcbabddbcbcbabcdcddbcddadbdacdbbddacbadcaaadadbbcbbacaadbddcbabcdddccbcabdbbcdcacbcdcddccddbbcddbabacacbcbcdaabddccabdddbcaacdacbbcdabbbcaccbcdccadbaddcabcacdcbcaaaddccaddbbddcaaadddddacdddbdcacccdbdbadbdcbdadbbbdbbbcdadbaddcbdddaaaabdabdcdddcbbcadbaadcdadddacddbacdbbcbadacdaddbcbbbcdcbbabdabcdaccdcbbdbdacbcbbacbddabcbaccacaabcbddabbcbdadbdbdadddddbdaadcddddaddcaccccddadabccbcabaabbcccdabdbccdacbdabadabbbdccbcdaabbbcbcbabbcccabbcdacdbcbdbddbcddacbcaddbddacacbaadcbcadacbddacbdacbbdbaaacbddabbadbdbacbddddddddbababbdccbdcadbdcaacaabbaadbbabbcdbbbbacccbadbbccdddbbadacbabcbcbdccddcbcbbcaddabdbbdbcbdbcbbaddccddbaacccacacaacdcbabdadcbccbbacacdbcccbbcbdabaaaccbacbcbcbaadbbdcdbadaaccdddbcdddcddccdbdacadbadabccbcabcabcacdbcdddadcbddabddccbadbccaddbaadbbbbcbaadbdbddddacabaccdbcdaaccabbdbbcaaadbcbaaabcccaadcdddcdcddbccbcbdbdbcbaadbbbaccaddacccaadcaadccadabdddcdaaaacddcadbdadbcabccdcacadbbcadddabcddcdddccbcdaacabdddabbaddcddacacbccdcddbabbacbbbcccbdbabaaccdddcabdbdaddaabcdccbaaccbbbbdbaddbadacccadbbbcababcaaaaaddbadccbacbadcacbaabbcdcbdcdccbdbccbcbaccababbccccbaccaaaabcacadccbcbccccabdaacaaccaccbbbddcdcdaaccbbacccabbabdadcbabcabaaadccababccacdbabbdabbcbbaadcbccaababbaababbbcadcdcccaadbbdbcddcaadddcccddbdadacdadadbbbadaacdabbdcdcbaacabbadbbcbdddccdccaaadbaccdaacdcadbcdaabdadacaadbaadcdbdadcaacadacdbaacbbbcadbdcdadabcdadbaacddccddbbbbcdadbaddddcbdddcbbcdcccbadbaababcdcdbaaccacbbdcbbbdacabcdcbdacacbcdabacddcadadbccccccbabbdccdcaadbaccaacaddcbdcbbcbcbaacddbcdcdbcadaadaabdddccabcabaadcbdbddadcababdaabdbdadadbcdbdcaacdadcdcabddababdcdbbcdcabbbccddaabdcdcccdaaaabdcdcdbbadaccaabbcdcabadbabaccbbcdddacdabdbbbbadaadcaabcadcccababdaabdcbacddadbcaabdacaabccababbbcbcccadcbacbbccdaababcdcdcadbcbadbbacacbccbabccacabddcdaddcbacdaacbbcccddaadcdbccadddabbdadcacabcadbddadcadcbdccdbdddcdacccdadabcbdbbdcddabcddabcbcadbabdcbdabbabcdbabbcbdcdacccaaacacacbdddabdadbbdaaaccbccdabcacadacdaacdcbcdabaacbcbbccbccddbbcddbdaaaabbdbdaaababddcdacdaacccdcacbcdcddacdaaddbcaaadabddacddaadcbddddbaabbaccdadadacaaccbcaccadccaccdcbbcdacbbcccbaabaacdcaacbabddcabdcbacdcdabbbdadadaadccbdbacaadabacdbbaacbcdcdaaddbbcabadbccadddccccdbdadbbbccdddcccbaccacdbdcabdaacabdcbbabaddccddaacddddacdaabbdabaaaadaddcddcbdcccdcbcbdbadabbacbadaccdcbadbbcbbddcbdacdbdddddcccdcbadbabddabcacdbaccbdccccbcacbdbdcbdcdbddaccabbdadcbcbcbcdcbdcccccadababcbcbbccbbddbbcabcaadcccbaabbdacbcdbccaadbabcacabbcdaaabbcaaccacdaddbaacdcbacdbccaddcacacdaabbadccaddbdcacbaabbbbdacbcaadccbcbaccbddbaaacdbbacbcddcdaaadddcadbdbbbabbabcadbdbdadabcbdacacbcabaccccabbdaaadbcbdbdcdaacacbcdddadadcbbdbddcabdcbacadcdaababcccaddbcaccdadbadbbcddadccddadacbcbcdcbbdadadcdcdcbacdadbbccdbdccdbbddcadbaacbabaacabbaadabccbaaaadccbddcababbcadbbadccdbbababcdadcbabcadcbbcbbdcaaccccccdaadacdbbbabdbbcabcabcbabacdbbdabddaacccbdbbcaaacdaabbbcacabaccbdbbcadcadbbcbcacbbdcbccbaaadadacbbbaccbdddacdcbcbdbddabbcdacbcbacccbdcbbdacbbadabcbcbddadccaabbbabbcddaadadadacaaabdcddbddabaddadabadabdbdbdddddaabadbcdadbdacadcccccbdddcdbaabaaacccdaaaacadcacbadbcddcbcaadcbaacabbdcabbcdcadacaabcccbbcccbcbbcadbdbcbcbdbbbcdaccdddcddaabdddadbbabdcccbcbcbacdabcaaccdbcbbbccadacabddadacadbcddcaabbdabbddaddaaccbdaacbcdbcbbbdbcccdaacccbbbdcbbbdcaadabdaaabbbdaacacacdbcbabddddbdaacaccbaabccdccbcbcbbddccdaaadacbbcbcdccaababcaaccbccaccbbabadbdccbaacdbbdccadbcadbacadbdccbddaccdabbaacacbcabbbbabbdaaaccddaacadcddbdacdacabaaccdbdadbbacdadbccabdabacdbdbbdabdbabccacbdcdccaddcccdabbcabbdcdaaaabccccbdcbacbbdababaacbabdcccaaadababaabadbaaccacbadacaaddbbcdaacdaddaccacdaddaccdabaacddbbdccacccccacadacbaddcadacccdbbbdbbcdabbbcbacbacbbbacabbccccacbbaaaacccacddcdddbcabbddaaccddcccabddbbdcaccbdcbdadabcdcbdbaaacddacabdcdcaddcacdbdddbdadadbdaaacaccdccaabbbbcdabcdcaddcbddabbbcccadbbcbcbbbdacabbbbaccdbbdbbdbaaaabdcccdccbbbabcadabccbdabaacbdcdbccdccdcdaaabcdcdbcadabdaadcdcdbdccdcaabdacbababccdbcdacdcdbcbbcddbabdaaaabcbbcacbdaabcdabdddbaababaacabccddcbdbcdbabacdbdccbcbacdbbcaaadcdacbaddbbaadacbabdabdbacccbdabbdcadcbbababbbcabcdbaacabaabdddbcddbccbcbadacacaaabaccdcaacbcddbdbacdaddabcbbbabbcdcbcabccabaaadabdccadbbdbbaaccbcacddbaaadaccbbcabddbcbadbdaccbdccdddbbdbdabadcccbabdabdbccbdbbdccacabdcaaddabdddcdbbcbacdbccadaddbbacdcbcdcbabcdcadacadbbcbbcabdbbddcddacbcccbadaacbbddcdaacdadadbabbdbaddbcdaddcdbaccccadcddadbcdbcccbdccbddaaabbcccbbccdcbcddbacabdcacbcabdaaaabdaaabdabacadcdbbacdbcddabdbbcdbbdbbabacabbdbdacaacadacaacdcdcacbcaabbaaaacbccddbbbcdcbcaabccdbddbccadbbddbddacbccbdbdbaadaacbdbbdacddcabbdbddacdcbbddcaadacabbddcdaacddcdadaaaaaacbacdaabcabbdadbcacaadbcdcbbcdcdcbdcdaccbcccbdaaacdbddaabcaabddcbdacadbddbbbbabacabdbdbabcdbdddabaaacbadccaacccbbcddaaccbbddaaacbbbdccaaccaaadadccbcaccaaacabccaaadbccdcacdabbdabcdcaddbcaabbabaaddbbdabdcacdacbaacddbacaadccbadccaabbadaddbdabddbdcbabbbabccabdddbcccacbdddbcbbdabdcdddcccaacbbcaaccdadbcbadddbbacaccdcbadcacbbcdaadcdddacbbdcbaddcaadccacbcdacbccbbadcabccadcbbdcaadbadcbaccaacbdcaabbcaaddbbcdbddcbabbbcccbaaaabdbddaccdcabdbcadcccbdaabacaadacdcabbbaabaaadcbdcbcdaabbbaabcaabacddccdbcbacdaadaddadaaddabaccabbaaccddcaddddddadacbadccbdabdadadcabaabaaccbccacaccbddbccbaccabddcccacababddbaaaccacabccdaddccddadacdcadaadbdbccbaacbddccddbcddacbbbaadbbaaabdbbcbbdccbdbbcababbadaadddaddbcdacccbcbacbcddbccccabcacaccaacacddcbbdadddcbadabcbbabddbbabcdcabaadacbccdababddcbbccababbdbbcccaababcbdbaabcdabbabbddacacdacdbabdcdcddacbdaadacabcaddcbbacbcbbcaacadacbdabbaaabcdcdbbbbcaadcddcdcccdadaaddaccccdcdcaabbadcdbbccabcccbddabdadbdccdcaacdbddddbdbdcbdcaddbadbcbcbdcadbcadcabbacdccaccacdadadabbaabcddddacdcbcaacdcbaccdaddcbcabccbcddcccabbacbccbcddcbabbdacacbcdccbcbdbcbcdccbddbdccaabdcdadbbdbcbadbbbbcbacbccdcacacaadcabadaddcccabacdbbbaccbaabcbaccabccddcdbddcaacbaddbddbbcdadcacdcdadddcdbacddbcbcaccabaccddbbadcacdabcbdacacaabcabddbabbdccaaaddaccbcbcccbcbbbcdaacaabcadabbabaacabdddcddacddaaddadcdccaddddccbdacbaaaddcbdbbbaacbdabaadcdcacdabadbbacdbabdacacacbacdbabadaaaccdabadcccbbdaccaabcabdcbbacbdcbbdddccbcbccaadadcaadbcdbbaabaddbadbaabbdadacbbbcaacbdbdaccadddbbbdbbabcaddacbacbabacadabaacadddaaaaaabddbddcaacadacddcabcadaaadcdabccbaaabacccbaccbddaaaabadcdabdbbabbccbadaabdadccaccbcbabacdbddcacdacabbcccbdcbbcaadbbddcccaccbccbaadcdadbccadaaabaadbbbaddcadabddbcdbcdbadccdbadadbbaadbbdaadaaaddbcacdbdcdddaadcbacdbacabddcaddbdabacdacdbbcdacabddababdaaabacdccaaaddcddcaaaccbabbbadabcdbdabdaccadcaacbddbacbcbbbdccdcacdcaacbbaadccccbbadbcdcddaaaaacdbcdbbddcaaaaadaddaccaacdbabdabbdddbbadcbaaccbccddcddcbaadcaadbdbcacddcbbabadabcabcaadbbbaddbdcabdcabbcbbbdbadabddddcbddaaacdaacbabadabccdcdbddbddbaccadacddadccaccbacaccbbcbdcdddbdccdcabadaaaaccabddbcacdbacccdcdaacdbaccbdbdddbcbbaacaccdcdabacdacabdbdcdcbcbbacacabbcdcbacdbbcadddcdccbdcddacdbdbcadaccdacdbaaccbccbbacaaddaddaadcadabccbdbccbbdccadbdbadbdbdacadadccdbdbbbdcdbabacaaabdcabdaabcaccbaaccddbaaabacabdcbccadacddadcbbaadabcdbabbdacdacdbaacbacdccadabdbbbaccdcadddbdbbaacaacadbcdcbcdabdabcabaadcddcbdaadbbaaddcbbdaddccadddbcacdbbabdabddcbaacbadddddccbcabbbbcbadddbacbcaadabcabacbadcaddadbbdacbaaccbadbddbbadbccabacaadbadcabcddbdbdadbddaddaddcdbcbdbbbdbacaddcbcbbdcdbdbbdcbdcccccdbdaaaccdaaacdcdddcccdbbcdaabacacbdbbddddabdacababaaaacbaacccbdbdcbaacacdbbcdacbcaddbdddcbcacdbccaabaccaacdbabcbbbadadddacacdaddddcadcbbbdcabacdbddddbbbccdcbbddadabacbcdbabddaaaddbcabddccadabcbdbccbcaddbbaaccaddddadcdbbdadbbdbdacbabccabaacbabcabddbbaacdadbcadccdcbcdaacadbbabcbcdacacadddbddbdbccaacbddaaabbbbccccbaacadbdcbcbcabbccbdccbbddbdccabbcbdbbbcbcdddbadccdcdbdccadcbcbbacccdddacbdbcadaaddabbaaddbbcdcbcabdacbabdbbccabdaabcaaddcbbddcbbbdcdcaccdbdbaaadcabadbcadbadadaaacaccaadbadaaacdccddaabddadbddabcdbabddbcddaccaadbccdbdabddcbddaabcabbacccddcccaddaadbcacbcabdbddccbbabdbbcacdcbdaadbccbbccdbbcddcbaccbbadcccadbdbbbddcadddcbcbdcbaaabcaaccabcbbadadcaaccbaadabdccccadccbbcdadbabddadaabbaddadbcacabdbbdbdcccabbdbbaaaaaadbaadbdadbbdbacbbbacbaadddcccbabbcbcbccbdbadddaccdadcbbdabcddbcddcbcbcbddccaddabddccaddcadcccdadadccbcdadbccbcdbbdabccdabcacaacbbbcdcadbaacaababcaabbdccddabaacddcaadcbbdcdaaaddccdcccabccbccaddacadbadcbdbbaabbcabaccbbadcaaadcbdbdccdddaabdbbababcbcabbcdbbdccdabaabbdaddddcbcbcdcabbadadadabdabacdbdadbbaddccaabdadcdccababddddccdcddcddbdcbbcdcbdaaaccbdcabbabaaaacacbbdddcacbabdbabaabdccbacaccacdaccdcbbcbaccbcadbbacdddbabadbdabadcccccbbbabcccccdabacadcbaaddcccbacbabddcaacbbcbdadbadbbdcdbccbdcaabbdbbcabdaaadccddabccaadcdbdddbdcabccccbbdcccadccbbdcaabdbddbdabdcacbadcdadbaabbbdcdaacbbccccaabcccbaacdabbbcbbddadcdacbdbcccacdbacdaadbadcccadabbbdbbbccbadbcdccbaddacbbbaddcbdcbcddadcdcbabbbaabcddbbbccdbbacddcccbddcddddbabdabcbacbdbcaaddbabadbdcdccccdaaddcacadbdbdbaabddabdccddcdadcdbbdbbdcacdbaabdadacaddacaaaaccbdccddbdbddabbcaddddcacadacadccdabacabadaaabdabaacbcbacdbbcadbdcaacbbabdacdcbaabbcdddbdbdcabaddcbaddaadcdbdcdadccaddccabbdadcccaaacadccccbdccdabddaaadbaccbdbaaaaadcabcbddaccddcadbdaddbadcbddcdabcdbaaaddbdcbcdcbbadddadcbdbddcdbdababacbdcbbacabaddbcdadacbaacbcdacacabdacacbddbcdaadbaadaabdaadcbbdacbdccdbabbdcdcbcbcddccdbcbdbbcadbddccdbdbbbbbdddbabadcdabcdbaadadbcabbdabcdddccbacdddabdcbcbcabaddcadaacadabbcababdacbbadabdacccbdadacabbcbdbbbcbdcbdabbadcbdcacacabbbaabcbdbcdaaccabccabbdaabaddabbdddccaaabdbcbcbadabccbabaababcadcadccadbcdaccbdabacccddaaadacbadaaacdadaaadbbdbdcbcbcacadddddaacbcdccaabadbcdcacdacdccabbcdbbabacbcabdddddbacacdcdbcaabdcddbbddccbddbcabacadccbcdccddabbdbdcacdbdbdcccabaaabcadbbaabacadcddddcccabbddacbdcccdbbcccbdaaaadacccabdbbcaacdcdbcbadacaabacbddaadbaaaadccbacacdcaadddcdbbaccbabdadadddbdaacdaadbbdbcbdaacbbbbddabbdddbcadcacdbbbdacdaaaacdcdcbaddbbadcbdccbbadbcdccccdbbcacdbccbdabcbbcaadbcaacbcdadcbabbbddbbbacdaabdcaadcacacadbbcdbcaabaadbadddcacdacbcabdbcababbbdacaacbbcbadadcdabbcadadcabbbcabcacbcbdaabbbddaadcaadacbdcddadbbacabcbaddbbaccbdaddadadddbaacbbadbcaccddcbacdcdbbcdaacdabdbdaaddcaadbbacbaadcdcddacbbddbdbdbbdcddcacccbbabdadbbccabdcadaabcaabacbaccbbcdddcaddababdbdcbdaacabcbcdcbcddadbdadcbccaadbbaddddacdbbbbcccbadabdbccaacacacbaadcbcdcabaacbbbadaccabdcbcabdbcddbdcdcacaabdcaadccccbabcdbabddccaabacddcbccdcbdabacadcbcdddcccdaadbccdddddcaddcbbabbbacaaddaddddcbdccccbcddbdcacadaacccacbcadbddbbccbcccddbadccdbbccdcadcdbdddbcdbdadabdbadbaccddbadbbcddadacabccaabcaadbcccddaaadacdacdabacbadbbbddbcddbbbacbabacbbcccccabddabdadacadbcbcbcdccccbbdbdadbbbcdcdabdacbbadadbabdbdcdbcbdccabdaadacddbdacdbcdadaadacdddabbcbcaabadddaaddacacdbdabbdcdabaddbacbdaabacacccdabdccdabccabddaddadddbadcddcbbdbbbabdaaacdbbabbcdbaccbdaaacadbcacdbcaabccbacacabcdabbcdbaacbbbaaddacdccbcdaadbbbaacabbcdcbacbdcabdcacccadacccabcdddabaddcbbdbccdbacadacabcccccaaaabdaadccdaabcdbbcbcadabbbcddaacdcdcbabdbdcabddaddabddcbcdcadbadbbacbcacacbbbdbdbbdddddcdacacacaabbaacbdccbaacbabbcbdcbdcbadadddbbadbbbcbaddcbdddaacadcbcadacccdaddbccdddbabddacabcacbdddcadbdbbbccacdccdbcccbdcdbcabddadddcdadadbdddaabcbdabaaddcbbdaadbdcbcdbdcaabbabcdcccddcbdcddbccbcddccaacbcbcdbcbcaaaacbbabddacbcaabbaacaccaabbaacdaaabadcabccbcadbccbacbbbdadcdbdcdaabddaabcacbdacdcaccdcbcaaddddadcdbbdaadbadccabbdbddabdcbdacadbbdacbbadadaddbbddccbbccacdaabbabacbccdacccccabcbcaadbbabddcbdbbcbbaabdcdaabacbbcabdabdbdadbaaacdacdccddaaccdaccabddadabbcaddcabacaabddbcdbdcdadccdacadcdaababbacbcbccbdbdacacabbcdddbdcdbdadbddbcdabdddcabbbbcabcccacdcacbbbbbbbcbdabbcbdadaaccccdaaabdcbdaadaddcadcdaaacdcbbccdabcddbaacaadbbbdacdabdbbbabbcddbabbddddbdddbbcbbbdaacabcabbcbdacbcbcbadaaccbddabddbacaacdcccaadabadabccabaabbdaaadbadddcdcbaadaadcacacdbcaacbdabdabcadccddabddaaacbbaacbcdcadcbadcdcddbdabaddcbcccbaabbcaaacdbcabbdaddbacbccdbcabbaaccbbdcdbabbdcdbcdbccbadccadcdddbdabaabbcadcdbdacdbcbdabcddbbccbbbacaadcadddbdaaccdcacdaccbaccabddabdbaadbdbdaaacabccbddabaaaaaabdaddcbcdcddddaaacbdccccbbaccaaaddaaabcadbbbdaaddadadbdaccacbdbacbaccbaabcbabddbcacacbdabbcccdbbccabadbabcaadbcabbdccccbcddccddbdcdbbbdcdccddddcaadadcdabbdbccdaacccaacbcdcbdbcbcaabbdbddcbdadcdcadbabcaabdbbccbaccaaabaacdbcbddcbddddbcbdcbacdbadcdadddcbdcadcbcbcbabdcdacddaacabbbbbccbcaaadcabaaaddabbaaddbdddbbddbdcdadacababbcdbbbabababdddbccdccabbdabdcacaababaaacbbdabcddcbadacbdaddabbcdddadbabbdadabaddbbcdcdcdabaddcdcacadabbadadcddddcaccadacdbaabcbccbdadcbaccbaddccbdabaadbdcaacddcabbbbababdcbdbabbabacccbbadcbbdcdcbadbcbddcacabccabacadaabcbabbcdaabcbbcbacacaacaadbbbdbcbddbbcadadacccdabcdacdccaabcbccbcdbccaccbbbdddcdccacdadacdcdddabdbbaaaccccacbcacdcdcdcabdbcdccacaaaccbaacddbdacdcbbcdaacadcdccbaacccacbdcbdcccbcbdcbdbcbccacbbdddaddbaadcdcacbaccbdbadacddcdbdbccdcaabcbddabbabdbbbbbabadacdcacdcbaabcacdbbbbddaddbbcbbabbabdbcbbcbccbadcdacbbddbcdcbdbdaabcdbbddccdacbdcbbccdaaabbbababdaacdcbdbcdadadccdcbabcbdbcdaabdbdbabdccacbddbccaaccbaadcbddabbabdaacbdcaaaddbaddaccbccbababbcbcdbaaaabbabcbaacbbaabdccbacdcbaacbcaabacbadabbbacdcbdcccbdcdddacaadcdcddddadcdabdaadcaabbdcaccabdbdabbccbcadcdacbbccadbdcbdbdadaacaaaddcababbbbcdbaddddbcdcbbddccdbbadcdbdbcbadcbaababddcadcaccaccdaaabbddcccdddababaaccadacabdbacabbdccdcadaccaacabbdcaabdcdaccddbabbcddddbdbacaaddcbabdbcdbcdacbcacabbdacabcbddcccaadaaccdcdcaadaacabcbcbbadbccbccbcbaabcddcdcbcbccbcddaabaacdadcdbbdcaadccbaccdcdbbcccbddaccaaaacbddcbdacbdbdadbbccabbaacdccdcadccabbabcaacdaaddbbbbadbabbdcacddbaabbababdbccccacbdaabaacbadabbdaacdcdcbdcacdcbbaabddbdcbbabbcdddaaccbaddcdbabcbacccdaddcddcaabcabdcaadaaabdbbcdcbbacadcbbdbcbacbcdaccbdcdccdabcaccbdbcaccdccadbcdccaacddbdcbbcbacacbcaadbbcaccbbddcbbaadcccbccabbccbdccdacdbacbdbbabbaabdcdbbdcacbaabacbdbcddabcacabddadbbdbdabdbccadcabcadbbadccacddadacabcdccccdcdcdcacddaddcbbdabdbbcadbcdabbbacccdcbbcdbaadbcdbdbdbcaaccddcccaaaadacabccddcbddccbcadaacbcddcbcbdddabbbcabbcadabbbbcdcacbcbbaaacabbdcaaccababcbbcadcacaabddbcbacdacbcbabdbadcdabbaacbdccbcccaacaaadccabbcdbcbcbacabcabdcacddbccdccddcdcbadadacdbadcdccaccdbbccbdacbbcbdbcbbcaacdcaacdbcdcadaaadbacacbdbddbaadbcbbbdcccacabbdbbddbccaddbcbaabadbcadacccdbbdcbbcadbdadabdbabcdccbdbaabbdcbcdccbbabacbdaaddcadbddabdcabcacacacadddbccaddcbacabdcbcadbcdddbddbadbdddcccbbaccbcbcbdddccbcdacbadccdbadabadbaadddcccdbddbaacabacbaaadbbdcaccdbabdaacbabbbccdcdcaddddbaaccccbcddcaccbcaaccddcbcaaacbabaadcbdbbbacccdcacacaaabcdcdaccadacacadccccbadabbacbdddababadcccabdcbacddacabbcadcbccbbcdbbbbdbaaabacbbdbcdcdadabccbcbbcbaabddcdcabdbccaaaacbdbabdbbdddaccccadbbcadbbaabaacadccacdbbdbadadbbbcdbacbcdbbcbbbdbbcdcacddcddbbbdbdbbdacabcdaddbdcacbbcdddacbdaabdadcbacccbcddddbdabbbaaaababdbdaccdaaadbcdbdbddddbdcadcabdcbdbbbcbcdcddbbacbdccbbaccdddadacccacabcbdbcbbccddddabdadaadabcbcccbcdcddccdcddadcbabaabdbcdbcdcccbaaaaddbbccbadabcdbbdcdcbbcbcaabadbdccdccbcbbddddacaddbbaadbbbdcddcbadacccccdabaaaacbdadacabcddcadbcddccdbdbdcabcaabbcabbbcbacbabccabdbdbabbbaacadcdcbdadbbacdaadcadacbbbdadabaccacaaacbdbcdabdaadaabacabcacbaacaaabdccbccabcdddcddcdddacbacbcbcabbabaababcadcacababaadcbbcbcbcdbcbacbcbbaddbdbaaacccbbbacbbbaccddabdcbbbaacbccadcbbadbbcbabcccbbabccadbdccbccbadccdababadbdddccdabccabbccadcdbddcbbdaddbbddaacbabdbcbacdadadbcadcdbbddaccbbdbcaccacdbcccaaadbcabababdababaacbabaccddabdbcbbadbcaababbcbadadabdaddbccbdcdaaabacacccdadaccdbbadabbcdabccaddbdbbaaddbbbbccbbaaddadadcdabacadbadbccccabaaacaaaabcdbdcbdddbbaaabccddcbcbdbbcddbcccbadaadbacccddbaaabdcdbacdcaabdbdaaaabddabdcbbbadbcbaaabdbbccadbdaaddcccadccdddabacbcbbbdbdadddcccbdbaaabdadbddadbacabbabcaaddbdddbcabbbdcccadacdabddabccdababdbcddbdcacccddabdabbabbcccabdcacdbccbadadaacabcccbadacccabdaabadabdbaccaaccbacdccbcdbcaaadcdabdabacaccbccbaddababacdbcccbcdbdcdcccabacabbdaaddaaccbbaaddaadbcbdccacdaaabcacdacdcbdcdcabdbcabccbbbdccdbbdcadacadcbbcdaccabcacdaacccdacdcaadbbdacabbcddaacdacdabbdcdcddbbbdcaadbbbdaadcadcaabccbabdcccccbaddbaacdacbddcbbdddbacaaadadbdaccbacbccbaaccbdbbcdcbbcdccaabacdbdaaaaadcadcdbbabadbcacddcdcbccddaacabdbccabcbdbcddcaabbcdbbadabcbbbacbccacbddaddbaddcdcccacbdcbcacdcdcabbbaadaaddccddaabddbcccbadcaccaddbcdadddcccabddacddccbaccdcacbaaacbacaabcaacdcdccdbacbbccbbccabadccbcbaccccadaadcbccacbabbacbcacccdbbcdbccbdaddcdcbcdbadacdbddbabdacacccbbaadadddabbbadcdbcccbaccacdddcbaaabbacadcccabdabdbababdcdddaaaddbbccdbabadbdddbadabcddbacccaccdacaabadadacabbabdbaccdbbbbcbbcbbdbcdaadcdbdabaaabcdcbbddcccaddcdaddddddddccbcabadaabbcaadaaaacaacadaaaaacbbbbdbcdbbaadddacacaacbcdcacaadbbdacacccacdddcbdaacabcbabaddbaadcaccdadcdccddaaacdaaacdbabacabccbbdabbdbabadcbaabbcbaddbcabccbabbdabdddccbdcddaddbdcaabdcdcaadddbbdacaccbbbaacdddadcbcdddbddbaddbcccdaaddcccbbdcabdbabbadaadbcadccccddacacdbdadbdbabacaadacacbbcaaaddcabcdddccacbbccadabacdcdcdcbcbcdbacadbdcccbbbdabcbcccaacbcdcbcbbdccabbdaadcaccaabcdddaaddabcacbddbdcddaadddcaacdadcadabccccdaadbbcdacdbabcbccaabddcddcaccbadcadbbbabbaddcbabcadddcbabbbdbccbcbaadcbbdddcadddabcbddcccacdbadbbdbcabbccdcccdcdabdddbbdccadbcaaaaadddbdddbaccababdacbbacadcbccdbddaacbddcbcbcabdaabbcdabdcbabddacaabdbaddadbabaabdacbcddabdaadcaccdbcdbddcdacdbcbbabbbbbbcddcacbbcabcacaacabaacbacdbabdbacacbdbabdabcaaaabadcbbdabacbaddbacabaddccdbcaaadcbcacbcdcdccabdabcbabacddcdbdabdcabcaaacabbdbcccdcadbdccdcdcdcdadbcadaaaadbdbacdbdcdabddbaadaacadaabacaccdcddbbdbdacdbdaddbdddabaacadadccbddcaacbabbbaccabcdcaddacbdcdbbabbdcbaadbadadadcabcbaccadbbbbcbcbaadcbbcdbdcbbbbabbabdabdccddcaaabbdbbbcdddaacbaabaacddcaababadabdddacbbccbaadaaccbcbcbbccdbbdbcaaacaabadbacabadccbdaabbddcdcccddbccabaaadcdddabadaccaaaccbabbaaadbbdcbaddbbadbcbcbcbdbcbbdbbbbbdcaadcbdbbdcaadcddbcdbbcaaaaacadcabbcdbdbcadadbbabbdcdbbaaaadcbdcacabbdadaacbcbadaaacbacbabccaabbababacabadcdcdaadbacdabcbddaaaccbbcccaacacaaccacddbbbbdcdaabddbdddaabadcccdababcccbaaccbabbdbdadcddbdaccaaaacaacbcabbbccdbcdababcddbcabbbdbdddacddacbcabcadcbdcddacdabddcabcdacababbcbdabdbaccdcdbddddccbaccdbbcaabcbdbaacdcddabdcbcbccbbdccbabaccbaacbdccdacacacdcacabcabcdabcddbcacdadcadcccddabbcaaaabdaaaddcacbbbabacddcaadbbbacabdadbdcddccaabaadcbaddcbabaadbdddddbccadacacbadbabddbdcddcbadcdcbcbdaaacdaccdbcdddddabddcdaadbbbacbaabbcaabdbcabaabbabdaadbcbbdcadddddccacdaadabdbbdbabaabcbcdcdacbdcaaaaaabbbbcdbcdbbbbcacbcddcdbcbdddcddbddcbacbaaacbdcdddcabcdddacabacbdcbcacdbbbdcadcaaadabccababcbabccdcccaaddcaaccdadbcdccbbacdbabbdbcaabcdacbbdbcbbcbadcaabbadacdcdbbaaadcadcdadcdcaddbbddbbcddbacbaddddbacbdccbdcabaabbbbbadabcacbdbcdaddcbcdcdcabaacbccccdacdabacdacadcaddcdbadcadcdaacbdbddadcbaddcdbdacbccbcabbaabaabacabacdcbddbacabdcbaccbdaabcdddabbdcacbcabacacaaabccbdabbddbbbdddcaabcccddbcaacbcdbbdaddcaddcbcddccadbcdbadaacadbbcbbccaabccabccacccbcacaddbcddddadaccacdbdadaabbaaabbacbdcdccadbccbbddacbcadbddbabbabacbacbbbbacdcddcdcabdccbbdcaccccaadaaabdccdbdadaaabcacdbaccabcbacccbaccadcacaccdacbdadcbacbbddbabdadcbbddadcaacbcbbcdbabcddbdacabacbccaaccbdddccabccdacaadbbcbbbdadacacdaabaaaccbaacbadadccbdcdcccdcaacddcdccaabbacccbbdcbbabaabacbcbdddaccabbcccaaddbdabddbabbbbbcddcbccdaccccdcdccacbdcabdaacadbdbcbbddddcdabcdddcddccbacccbbaaaddaacccbabdabadbabadbdcadcddbdcdccbdacbaaaccbbbbadaaabbcdcbdcbdbddbdcabdcddcbccaacbbdabcbdaacbddbbddbbacdaacaabbabcadbbccaaaddacbabbdcdaaadcdbaacbabbddacaccdccbdddbbaddccbcbbabccacadadcdbdbcdaccaccddddccdcbccdabcdacabbbabcbadbbdbcdabcdacbaddbabccabdabdcbbaabdaacaabacdadbbccbdbdbbabbdbddccabbcbadabbcaddaddbbadbddadadbcbcabbdcbacaddcbddcaccbbdbcabbabcababaccbdacacbddaddbacdcaadacbccbbbabacddabbbddbabdbadbdababcddccaaacabbcaaabcddcadccadacbbdbcdacadddcdccbcbdbbdadabaaacdddacaccaaabaaadddcbddbaaccaacbcccccbdbdcaadacdccbacacbbbddaaaaadacddcabcddbacacdcbbabbbcbaddbdabdccbcdcacabbacdbdcabbccbbdadcaaadbcabaccadcadbacccdabbacdbbcccaaacadbabcaaddcacaabccdcbadccadbccbcccabbaadbcaaadcbcababdabacbbcdcaaabcabddabdcdccddbcdbaaacacadaadcabcadabbbaadbadcdcbbdcdadbbadcabdacbddbaacdccdaaddbdcbbbdadadacacddbadabadbdccbcdddbbbdacdbbdcbddadcdcdddadacacdacbdddcbdcbababacdccbdcddbaacaacacadbcaddadabdbdccdabcccadcdaddcbdcbbaababccaaacacbbbcadbbcacbbcdbaccaaadccdcaaadcadbdccaadccdaaddbddcacbacbabdbadddcbbccdadcabcaacdccbbbbabaacaddabbbdcdaaccddaadabbdbdadcddcdcadcdabdabbcddbbdacdaabbdddbadddabcdabdacbadbcbbcbbddadbacbbabcdcbbabccdcaacadccdcaacbdcdabacbbabcacadaaabaadccbacdacabdabddabddcaadbcbccdccacbbdbcdabadcaadaccdddbcacddabdccabababdcdccadbcddddbdcbacabdddadbcdcabdacbabdbcdaabddadcdadcadbcadacdcaaaadcccaaabbdbaaccabbabbbddabccabdcdbdacbcbdbacdbdabbccddadcdadbbdbddbcdbcadcabcadbbabadbbabaccacbaddadacadabaaaaabaacaccdbcacdbdacbaccdaadadaacababcccacdacbdbbaaddaadbacccabcbcaadbcbacbcccaabddbbadbbbaddacbbddccabbcaacddbdaabadddbbdaacdccdaaddbbcdabccdcbacadbbcacddcbccbdbcacaacacababdddcbccdbacdddcbadcadadcdadcdcaacdabcbbcdccbcaddcabdacacaadcbcbbdacabccdbcdccdabcacbacaaaaddddbabccababadcabdacacdbdcbbbaacdacddaabbbbadacbbdaabcdabdbbddaaddadadcdaabddbbbcddcaadbbabbccaabaacdacbcacddadcdcbdcbbdbcdcdaacaacddcddbbcabbbcccccadaddccbaaddadaddacbcbadbddadbbdbadccabccadabcbbcaddccbbbbdbcbddcbbcbdcbdcaaaabcbcbacaaacaaccabbacdaaddcccbdcbccbaaaadbdbbdcadcacacbddcabbdddbccabcddcdaabdcacdccacbaadadacdcdbcdddcdbbdbdbcdaccdbbdbbbdbabbbccaabcbdbabbaaaaabacdcbbbcabbbbdcadabcdadbcaadbddabaabcdbdacaadbbccbabcdcaabbaaadaaaabdadbcbcbddbbbdcabcdbbcabaacabacddbddadbbaddbdddcdcacabadaacdaddddbdaaabbaccaabbcabaaaddcdddcbdaddcbaababdabccbbadddbadcdbccadccdacddcbddcaacdddcacdbadbdccdcdddabcbbcacdabbdbccabacbbccbacbbaaddddddddbddcdaacaabbaaccaddbbddbbdbdabbcdddabbbddcbbdbdbbabaaaaaaccbcdbadcbacdbadcbdadacdbbdadbcaabdcbbcaaccbdbcbbddbcddcbccbbddcadabcbbbadbcdddddcbdccbbabcbbbbdadaddcdcbbbcaaacddcdcbbaacbccbacaaacdddcdcabbbddadcaaaacdddadbdccaddcbcabbaadbaaacbcaacadccbacdcadcddcbccbbaccbbbdbcdabaadddcaadddbcaabbdcbcbcabbbddbddbcdaadabbbdcdcdcdbbccaccdacadadbbabcdaadcdadcaccabadcdcbacccdadbbdcadaacdacdacbaaadababbbcabdbadbaccddcccabddcddadadbcdadacdcbaddcaacbcddcdabacddbbcdbbdacababadbdccbbbacddabbbdccaaabacacbdddcdcbaaabbaddbacdadbdcadbbbadabcdaaadccdbdbcddcabbacdbcacaabcbdbbbdddaadbddabcacaabacadddcacabcbcbadcbcadacbdbbbdaaadbdbdbaddbbbdadccbcdbaddccdbdbbbdaacadaadbbabdcabadacdacccbabacdaccdcddcdbadddcacaadabcdacbdcaaaaddddccdbabbabbadcdaddcdaadbddbaabdddabcadbadabddaaaddbbadbacdddddabcdcbcdcdadcdacabadabbcacdaacdabcdaacbaddbaadabbcbddaaacdacddbdbaacaacdcddcdcdbabaabdbdbaccbbacbbbacaacccabbcbadbcdbbabdbbcddacdbabbaadcdadcccdbccccbbadbdacaccadabbddabacbdcbbbabdacaacdddbbbbbacbabaabdabdadabcccacbddcddcbdbbccdabccaaccccacadadcbcdccabdabacddbcdcbbbbdaccdcadacadadacbaabcbacbadacbdcbbabadcabddbbccccaccbcbadbcddacdaabbbcaadbddabddbbadcccdbaababbccccdddcbbacbdbdcadddcddabdbacdbcbddbdddccaaadaaacdabbacdbaaddabdbddaddcbbaabbacdcbbbaddbcbdadcaaddacdbccdbdcbdcdddaaacccbccbcdccdabcdccbcbaacbbbadcccbbdddcadddcdbbadadcbcbbdadaddaccbbbbadbbcbaccabdbccbbbdadccddddbcbdbdcccbbcadddacdcaccacdacdddabcbbcbcacadbbbaddddaccbccadaabdabbdbcddcdcaaadbccddcddbddbaccddcbabacbbaacaccadbababcdaabbdcdbaacdddbcadcaaaadcaadbdadbcdcbbcccdbaacdbabaddbbcabdacaddcdaacdddcbaaccdbadaadcdbbccacbabdbddabcdcaacdabbbdbdaaadccadacacbddddbdbbbbccacccdabacdddbabbbdddabbdaccddbabacccacdabbadaabccacabcdbcddadcbbaabacdbbdabaabcbdbbcbbbbabcdbdaccbabacdbbbcabdcabbddcbbdbabbbbcbbdcdabdbcdddbaababddacdbdccdcbddcbdabccdcccaabcbbbddacadbaabbdaccbdddcdcdbadbaacadddacadbddbaaaccbccddaddcccbdaaabbbdbccdcccbadddbcdadcacccdcbabbdbabdbbaabbaabddcdabccaccbdaccbcdacbcdaadddacdacbaadddcdcbbbabdccbacbccaddaadbaccdbdaaadccbabbbbddbccddccdabbdbdaccabbacbabcbcbbadcdaddbcbbadacacbcccbaccbbabcbdcaaaccdabdbabbcdbdaaddbbdbbcdcbcabbdacabcacdbdacbcbaccacbacdaabbcacbaabcccbcdddacbcbdbcdadabccbbdcadcccbdbddadcaaacdadacacbccbccbacadcddaabdbaccabaaccccdbabdaabcaacdbdaacdbccbcccdbdbbdacccbcbbbcdcadadabacdcdddaccccddcadbdbbdbbddaadadacbcbbaacaccdcabdabbccaabbdcadcddccaacacdbbdcacbcbacacdacbdbbadcaadbdbcabbbdbcbbcbdcdaabaabbddcbcdccadaadaddadbbabcdbcadbcbdaaacbdbdacabddddadadbbcbacbacadacaccdccabdabbdacaacbdbaddbcadbbbdbcbbabcacbbbdcdbdbdcbddbdbaccdcbbcadddcbbbacadabababbdabcbdbdddbccbbdaccbdadcaaadbcabcdbaabdadcaaaaacaacddaadcdbdaabcdcbdbacdcddcbdcaadccbacdddccbdabbcadddbcadbccdcadaddaaddddbcccccbdadabcabccaaccdcbdbaabbbacbbabdadbdcddabdaccccbdaadcdbbdaaaabdbacabddadacabbcaadbaddccbcacdcdbacbabacddcbbabbadbaacdacbdaabcbaddacbacdcabbbdccddbcdcbbaabddadcbcccadaabaadddcbabcdbbccbccadccdccdbbbcdcabbadbcddaacacbcbbdadddccaaccbccccdaddcdadcaabdadbbdbcabaddadaabdcbddaddbddcacdcbcadaaacdbddaadbaadcacccbacabccbadaadcdbcdaabbbbdbcdcdddddbbdaddaacbcddbbdabdadadbbbccbbcaaddbaadcaadbadbbbadaadbaadbbcdbccdcadcaccccdbaacddaadcaabdbbdcdbabdadccbbbcdbbbcadcaabbbababbdadbddbcdbbbcdcbadddbbcdbbacaacbbdcbbbbdcadddbddcbbbacdbccddaaacbcadacadbbddddbdadbcbbdbcaaaabddcdaddadacdaaddaaddbdadadddcdddbcdddbbbaccbadaacacdbabdadbdababbdbcccbbdacabbacabcbbdcbdabbaabadcccabbcbdcbadbcbdcbdccdccbccddddccccdaccccacabcaddcbcabddaabcbbadbbadcbbaccbbabdccbdbbcddadbcbdddaccccabcbacdbbdcbdddadaccdacbacdbcdccdaddccadbdccdabbaacbddaaabbbdddadcabddcbaaccdccbcdcabadccaacbdbbababbdcdadbddddcadacbccbbbdbcadccacacdbbbcdbbdabcaaaadabcbcbdbcabdadddccdbcccabdbcdbccaacccdcaadcdddcbcaabdcddbcadbbcccdbcabbbdbdacacbcbaaadadaaddddadcbbcdcaababddbcbddbadbdadacdbaacbaccaacccddbaadaaccdadadcddbcadccddbadaddddcbdaccdabbadabddbaaacccdddcadbccbadcbbcccbddccbadacdcacbbabbcbdbaccacdcacdbdabcdcdbcbaadacccccdddaddcbcbbadacbdbdadadbbdaaaabccbaabaacaccbaaddccabdbcabcdcaaddddbdcadcbadbabaadaaacabaddbaccdbaabdbabbdadbcbbdcaadacdadacadcbaabbdabdcacdbdcbdadbcaadddaabbcadccbabddbabdbabaacbbddcdcdcdbaabaabbccdcabddbcbbbacbdaaaacbdddccddbacabcdcbcabbcdcbcacbcdcaaacbdbdbdcacbbdadaadbbcacdddcbdccbbaaabddacbdcccddbcdaccdccdadbdcdbdcdabddababcbdcadadcbdbbbcadacdddccdacdadacccacccdcacbbbadababbbaabaaabacdcddcdbcbaabdabaadbdddbddbacdabbdaaaabddddaccbababdbddadcdbbccaadbaaacbccabaabdcbdacacbaacaaacddadcbbccaaabcdddbaddcadaddcdadcbbdacbcbbdcadacabddabdabdddcacbabbacadaaaaacabcdbbdccacbdcdacbbcaccabdbdbbaadccabdccabbcbccdabadcadbbcbdbcbddbaacbcabdbaacdcdacabdccaadcdaaccdbcbcadcacddcdabcacdacdbcddbdcadbcadcdbdcacbcabacdbdabcbddaadacadaacaacacbaadcddddcabdadbbbbcaabbbcbddcbcbadaaacacabbddccbcddacdaaadbbaacadaddaabadbaaddaddcccdbddcbaccacbadaddacbabdccadcccadaaadbdaadcacccccccabddcdcdddbacdabddcbaaabbbbbdcdcbbbcbaabbabadcbbccadcbdbdddcadcaddbabdacaccbdaacbcaccddddcbddaabbbbadbdaacabaddcbbcbdadbcdabbbaccdabdbaacadddcaddadccabcdbbacaadabcdabacccaddcdcdbccbcaabdcddbbbcbdcdcdbdcdadbcddccbadaccbaabcbdcdbddadbcaccdacabccadadbaabbcdcaabdcbbdcccabaadbddcccbcacbaaddadcbddacbcdbdcbccbaabcdabcaaaadbcbcdcabddcbaadcbabcbdaacaabadcaadabdcbbadcabadadccbaadaaddcbdabdbdcadadcaabcdaabbdadadddaabdaababdddcaccbdcbbdbcadcddacbabbaccadddadacddaadacddababbdbaccaacdbcdcdabddcddcccdbccdcbbcdcdcadbbdddbadcdadbaabbcaaddcadcdcabddaadcaabacaddccbdcdadadacabddcddaacccdcbdacaddddbcddbcaddbaacdbdcadaaccadbaaaabccdbcbacdbccbbcabcaccdabdabbbbcbbdbcdcbcbddabddaaabbadabccdbdcbdbdaccbddadbcdbacdadddabbbddaabacdbccdbdbbbcacadbdbdadaadcbbddbbadacbbbbddbaccdacbcdbbcbccabdcadcbcdccadcadaaddcbcccdddccabbcccbaaaccbdbdbcaccdcdcdcbdaabbbcdbcadabdbdcabbaccacbbaabcdcbbbddcbcbbbdacbdbabbbcdcadabcddbddbcacacadabcbbacbcbdddaaadbbbccccacdbbdbcadccaddbccdacabcddbdbabccadcbbadbcdbcbddccbcabddaddadacdbaadccbadaccddddbdcddcbdaccbbddaaaddabaddacbaadbbbcbadcbadababbbcacdcbddbcadbbacbcbddcbbcacdbdddccccbdabcddbaaadbbbacdbcbcaaddaaabbdcbccaaccaccdddacddbacacdaacabbbcabacadadcdbdacdacdccadcbbbaaacdacccdcbadbacaddbdcdcdbdcddabcaccbcdbbdccaabbdabadabadbadbacccbbadcbadbbcdaaaddbbacdbcddbbadacacdbbacccbacbaaddcbdcbbcdcbaaddacacdcaabdcabbbccccbcdbcdaacbcadbbccdcdadbbdbcadcbcdbbccbbadccbbadcababaababddddaaabccdcdcaadbdcdabcacacbacabaadbccbddadabddbbcccdcbdddaabbbccccacaccbbdaddcabacbccdcbabbaaaabbbbbbadbcdadbdbdbcdddbbaccdadbccabacbaacabdccbcbbddcaddccddbdabbcbacdcbbcdbaddacddcdcdbcbcdadbcbbdbdddcbcccdcbdbabdbcbdbbbdcbccaadbacddbcdaaddbaddababdcbbacdabbccdbdcddbcdcabbcdbdbaabcbdbcdcdbaaaabdaadabcccdaaccccabbcdaaaacbddbbccbadcdcbdbcdadbadabbcabacacbaaadccbaccdddabaacddabdbbcdabbdbdbdbddcbbaddacabdcbaabacdbdaabdcdccddbdaaacadbcddcddabdcadaadccbbbbcdddcddbacacbdbcddbcdaacbbbddababacbbbaabbddbaacabccbcbbcbbbdbaabbacdbabddaccacaadabdcbbbaababacdcaaccbdbdadaddbacabaddbccdcccbadbbbcabcaadcdbacdadcbcbaccbbacbacccabbcaababdbdbdaddabaddcaabdbcaacddabbaddcdddddaaccaabbbaccccadbbbdddadbbbadabbadcbbdbccdadacddcadddaacaaacdababcdbcdabbbdddabbaabdcaaabdddddaacbbabbcbdaabdcbddadcbbcdcadbcacbdcdaabdbccbbbddadccaaddddccadcdaabdaaadcbdcbbbdabaaaddaccbaccaaddccadcdcacbcdbbabccbcacbabdbbdadbcdcbdbbbbcaddddcccbdadbddcaacabdbdcbaaaccaddabaaaaabbbccacbbdcdbcbababbccaacbcdcbbccaadbccbcaadbccaadcbaddddaccccdaadcdddabadbbdbdbaacbaadcbaaaccaadcbbcbaabccdadcacadddcdcbdbcabaddbddadbaccdabdcccbadcdbaddddaabcbdaadbddaaccdbccacaddacaadabadbbbddabaddaababdcdbdbddddcbbddbbdcbdaacddcbdbbdacdcddcbcccaabbabaadbddbbcdcbbdcbbabbddcdbcddaddbacacadcabcaadbbbbabdcbcbbcbdbaadaabadbbbdcabbbbcbbaacdcbcaddbbbddccacbcbdddbcbccbbcbaccacdadbcacbabddcbcacdaabddaacacaabbdaadacbcbcadbbbabdaaadacaaaabcbbabcdbabaacbbcbdaddcabbbdbdcbccccaddcbcbdcdccaaccaddbccdbabcacdcacdcabbccccadacaaaacbbddbdadcababaaabaacbacdadadbaacacbacdcddacbaacbacbaccbadbcbaadccaacadbcccddcadbaccdcdabacacbbbdbdbccdbcabaccacbbdabbabaaacbaddbcaacddbcbccbcbdcdcbadddcadddbccccdbcbadccabababcabcddaabbdadcaddbdcddddbcbcbdaaacbdcdbacbacccbbcbdbbbadadcdadcdbdcbccbcbdadcdcaaabbdabdadacddbcbdaadabbdbcbdabdbccabaadcddcdcabbddbaadaabababadcbbbbddccdcbdbcdccccbacbabbbacbacacaadccaabadccbcbbacbaaaacccdbcbadaddbcacdbcbacdbddcdacadcbbcbccbadccdadcbaddbadcacbccbccababaccdbbdacbbccdccdaabdbccdbacccdcabdddbbccdccabababcbcbbadbdbcdadcacdcacabaababdbbabcccaccacccaacaaaaccdcbcdadddccdabcdacddccdbabdcbabbbccdbdcbadcaabacabcdbdaccdbacccdbddcddbcbcdacdcdcdaddabbbadaacdadbdcdadacaccbccdddadbdcccddccaddbcccbadadbcbccaaddbdbadaaadbdcbccaabcbadbbaccbbdcdbaccdabdaccaabadbcbbababaaccdbbcbdbdbdaaabaacadababaaabccbbcdcbcddaabdbababddbdbabbddbdabdcdbcdabdcdcaabcbcbdbaaacacdcacabdbccabbcccbdbdddcddcdcbabcadbdbdbddbcccbabbbbabcdccbacbaaddabdcbadbbcbdacacbbddccadaddaddcbcbdaaadbbcdcdccaccddbbddbbdcdbcbbadcbababbadddbcabcbdaaadcbbaaddabccbdacdcdacabbacdadaccacadbcccdbcccdaccdbbacaadbdcbccaadddddbbabbabbcbcbccdabdbaacacdbbadcbdbaaacabbbcbcdddaddddcaadabcdcdccbbcddbdbcbaaabcbcabacbdacbbcbcdbaadbccdbddbcaabbdacdcbdaacabaddacabaaaccbdaaabbdbbbacbbdbccddaadabcadcbcbddbaadabcacdaadbbaaaddbaabaaacdaabdabbdacdcddabacbdaccacddbaddabdcdbbbccdccdababddbddbaccabdccbbddbcbbdaacbaddbdddbabddcabdcddbacbdaddbddcddacdcbcdbdcdbdadddbaddbbadcdaaddcbcccdbcbbcadbdbccaaddcbcbacddbaacadbdbacbaaabbaaccdcdcabdccaacbadbcdddabbbcbbbccbabdbbdadcddabdacabddccccbccaccbaabadabaddbaddacbaddbabaaabddacabdacddcdcbcddcdbbdddbdbaabdccaabbacabcbbabccbcbbdcbcccdbdcaadaacdaabcddbccadaaaadcaaacdddbddcdddbdccbcacdbbddcddccacaacdacdadddbdddbacbbcdbccabcdaaabbcccdaaabcadaacabacdcddcbccccbbddccbcaaadccbdcbdbbbcccbdacbcadddaccaaccabbcaabddcbcbccbbcbdccdccbcdaabcabadaccbbaddcabbaddaaadccaddbddbcaaacbcbcaccbbbbaccbbddcccbaabaadccbdbadbaabcdacdaadddbadddcacccbdbcacdccbaccbcbbccdbabcacadaabadddaccdabbdbdabdddaabacabcbaabbbcdabbcadabdaccdbdddbccdbabcdbcddbdcccadbcbdbcaabbbabcccaccbacaaadcdaccbbcbabdbbacabbbaccacadadbadadaaabdddaaacbdddbccbadddcabcbdadbabdbbdbdaabcacbbbadaaadcbabbaaaddaadcaddccbbbccaaacacdabcdbddabdbaabcbbaddbaadbddadbaaccabadacbdbdacdddccbacbbbcccbdaacbbcabcacdcdadbbcbbbbddbbcdaccadadbbabdbabdbbaacbbdbbcdbdaccaaabdadbdbbdddcabbadbbbaadbdacaabcbcbccacddadbcadcdabadbbaddadcbdabaaccbaddcccdbcaaddbdcbbdccdadcbbcbcdabaadaacaadaccdaccbabdbdacbbdbcabababbdbdcddbaddbbdcccbdddcdbabdbdddbdddcddccadbadcadadbacaccbddabcacdcbbdcbcabdabcccbddbaadaaaaccacaadcbaadcadddccabbdbadddbbbaaddadccacdaccaccdbdccdadadabcabbaaadddccaaaadddaddadaacbcbdccbadacbcaababacbbbabbacacccbcacbabbaadbaacdaccdaccbbbaabcdacaddcadadcdddacddbcababbbddaadcabdcaddcabbbadacbccacbddcadcabcabacaccdbaaddbbbbdbccdbdccddbbaaaaddcccbdcaadcdbdcadcbbbcaacabddccaacdadabdbbcbbcbaaadbabbbadbacdaaabdbdadbdbcacdbccadacabdbdcaccaabbcbbdbbabdbccadbbdbaccaaadaaadaccddddadcbbbdcaabbaaabdbdadbbadddccbdabacbaddddacacbddadcbacdbbaabcaaaadbaadddbabccbbadddbbbbdcbddaddaadcbcaabbccaaadabbcddbccbbaacccccdcbacbadcadadbacbaddcdadacbacaaadacaaadbcbadaadbabbabaacbbbbddcabcdabcccdcccdccdccadccadccaabddaacaadabababcbdacdcccabbcaccdbdaddacabdccccacddabcdcaccbabdbdbaddbaaadddbbcdabdabaaadccadbabbccaacbbcddbbbacacdbaabdcdddcaccaacbbcbadcbadbabbaccabcbdbdaabadccccdbaaddbabbdcbabcbdaddbbdcbcdbadcdadbcdbbbbdbddbdaccddcdadabbbadcdaabbccdcbadbaacdaadbdcccccbacbaaacddbdaccabddbaacdabcccddabdcadbbbcacbbaacaaababcadcbababaddbbccdaadadbacacaaddbcadbbacbbbacadcadababaabbaabbcbdbcadcbdaccbacbaddabbcdcddadbaadbdcaadcbacdcaacccbccbddadadbccbbdbdccccbcadddcaaadabaaddacaabcbaadacbbbacbbdadcabdcbadbbbbccadbacdaccddcdbdbcbaccbacdadcaabbccdcbaaadbcbcdaadbcbddaadadddacbbdbdcbbddccaaddccbadccaacbadccabaccbabcaaccabccbbbcbadcabcddbacaccabacbbddabcddbbbdaccacdadbdbdbabbbbddcdccadcababcdbabccbcbaacdbacbdadcbcccadbbbcaccabccbdaddacddadbdcbdadbbdabbaaddbcddabbdabcdbaabacadacdabbbbbbdacabacdcbddbbcaabdccaabdabdcaaacaadbdbdcdbbcabccbadacccdadbdadabddccccddabbacabaabbbdcdddbdbccbcdcbbcabcbbbbacbcddbbccaccaaddddadcbbaadcacdcdabbdacdccbcdabccbdbbdbccbbacccdcabcccbcbadaaaabbdbdbccbbaccbcbbaccdddbabccdadcbdcabccdcbacabdbbacbababbabcacdcdadccccabdacbdcbacacbddcaddbbcaaaaddcacddbcbabdddbbbbdbdabaacddbccacaccaabcbbcdadcbcbdbdddbbdcdbdbdadddcacdbaccdcacbdaccacdddaadbdbaabdadbcdbabcabcdbaabdbadabacbbbbdcdbaaaacbcbcabbbbbadbcaabddccdacbdacabcbbabdbbdbadcaabcddbdcdbaddaaaaacacdaacacbabbcabbaddbccdcaabdcdddcaaacdbaddcabadbadadbcaccaaaadabcbaacaacbaabadccdacacadaddbbabaaabaaacaacdccdbbaacbaacabdbddabcdddacbadcbccccacddadcbdbdaccbaacdadaccdacbdbacaaacdcdcdbaddbbadddcccbdbbbaacbbabdbdadcadddaccbdbacdddacdcbbcabbbcabcabcbdcacbbabcbbadddcddaabaaddbcadadbaaadbadbcdadbaccbdbaadbaddbcabddbdcacaaaadccacacbadcccdbcccbabddaacaacacdddacbcdacdcacbacdcdaccbbcdbacbbabdcdaccabaddccaaacdadaaadccbbbbaadccabcccbcdbcbdbbaccddbbdaaabdbbabdacaacbcdadcbddbcbbccbcccccbaccdbbbbbadcbbacbdabcacbbbaacbabddccabddaaaaccdbccbacbdbaacccdaadbcabdccbdbccacdabadadcbbdcadacacbcbbddbbcdcdbccddcabbadbbcccdcabddacabccacbcbdbbadddcddacaabadbbccccdabababcddabaabcdababddcdacdcbcddaababcdcacacdbbabdbabcadbddbaccdcbaccbadddccbdbcbdddbbcccdabcbaabdccbacbcdbacabbaddaaacbaccccabdcaadbcdadaacddbdacdbaccccaddcaacbbbaddadcddaddcbdbacccbcabbdadaaccbabcbdbdccbdcaccccbabadbadbcdbcbaccbccbbacccbcbabbccccddabadadbbadbcabadcadbbaacbcacdcbcdbbcbabbbdddbabbbdacccabbcabbbabcbddbaacbbabcabcdadbcbdaabacadbbcaccdcdbccccadbbbcadcdaaccabbcbccbdacbdcbcccbdabdbbbbddccbabadbdcdadbabdacaabdcdabaabccbdbaacdadacbdcbcdcadcdacccdabdddcaddaddadcacccdcbbacdccdddbcdacbdbbddcbbcadbcadacdccacddaccbcdcacccdabbaababcdbcccabcaadcdbcddcdbcdddabccddcddadaaadccddcddabdaaddbdddadbdcbbcaabcadacabddbcdcbcadcabbcbddccbdbcadadbccbbbcbdaddaaaacdadabbbdcbdcdbaadabacbbdbddcdbcbcccbbddadcaadbdadcddcbbcdaccdbbcaddddcbaacaadadaccdbdccbacabdbabadabbcbcdacdaacacdaabbacdbbabbcdbdabbcbacccdcdabdcbacddadcacdaaacbdbcaccdadcdbabadaabababdbbabbcbdddaccbcdcaaaabdcdbdcbacddcbabddababdabacacacbbcddbdbbbcbaacaddccdcaacddbddabdbccccbabbbcccdbccdaddabdcbaaacbddcdcdddadcacbccabdbbddaadbdbccbbaaabbccacbdbdbaaacabadaaadabcbcaacabcbdaadbccccdcddaacbdcabbcabbabbbabccdddcdcddaabaccbcbacbaacabcadcbcdbdddddcccdbbbdbcbaacaacdcdacbbdcadcaabcdaadbbdbdbdbcdbbbdabbccdabdaaadbcaabcaddaaadbcadaaaccccdbccdcdcbaacbbbcdaccbddadcbdcdcdbbccbcdbbcbbcdadbdcbadcbdaadaabbdbdacacbcdbacccbdcbcbaaccabaccdaabdaaaadcccacdcabacdcbbbacbacadadcabaddbcadddacbbdababbadabddaabcaaaddcdbdddddaabbbacbcbbdbbdcdcccadcbcbdcabaacbccdbcaaaadaddbdbddcdcddbadbabbdbcadabbacccaacccbcabaabbdbddbcdddbadacaaacbcacdbacdcabbdccbaccacbabdcdbdbbddacbcbcdaddabccabddbdaddcaddabbdbdbdacccaaabbbcdabbbccaaaccdbccdbdbadbddcccdddacbcbdcaabaacacddcbcaacdaabdabaabcbcbdadbdabccdacadbaabcbbdcabbbddbdcddcdbacacbcbcbdddbccabcdacacadcabccdaaacbbccdcdabdabccccbcaabbaacabccadbdaaaabaaadbbbccabcaddcaacdccaaccacddcdbbcbaadccbabadbbcaacbcaddcacdcaadbdbabcbacbdccbcdbdcdbdadadcbaacbaddabbbbbacccdbbccbacbcdcccabdddaacaccdbddabcbbadccddbcbcaadabdabdcbcbacbaddaacbacbbacccdcbadabbdcdbccbaccbcbbccbcccdadcabdcccbdacaddcddcaaaadacdbcacbcdcabbcbcaabababccdccbaddbdacdccddbcaaadcbabaaaccabbdcaabccbbcabcaaaacaddaadaadaacbbaabbddbadbaadaaddcddbdbcccccdacadbcbbcbccacbdcbbbaabdbadaaaddbbcbabbbddccdbaacbccadcbbcccbbdacbabaacbcccbddccdbdbadbbbbbcdcacdccdbbcaaccddbbababccdbccaacacbcabdbcbcdcbcddaaddabdbcdacddadbddbdccaaddaacadccbaadbaaabbccaaabccbbabcacddababbcadadabddadaacbbddcaaddaacccadcdcbdbdbaabdaacdddccdbbaccbdccaabdbdadaaaadcbdcbdddababababcdaccbcccdcccaaacaaaccacccaaadadcdbcdcdbadcacbdbcbcdacbbcdcbdacaaaaacbdadacbddddbaccbdbaaadbcadbccaccbbdaabababccaadbbbcdcdacbaabdcacbabdbbccbcccddacbcbbbaddcdadcdacacbaababccbadbabdbbdcacadbcbbacabcbcacccadaabddacdcacddadcbabccdcbddaddcbadbcdbcbabcddacccbddbbdddacabcadadabdabccccddddadccbcadaddddbaaabaabddbdbccdbadbdacadaabcdbccbcabbdbdccaacbcaaadbdbaacbcacbbdcdcdccaadaddabddacccccabcaaaadcdddcbdadcdabdbcbcdbddaaabadcdbaccdabdbabadabcddbaddbbcddaaaddcaabdaacbabddacbbadcabacadaacddbdcdcbddbdbacbbadabdbbaaababdbbcddbdcdadbbabbdbbcdbaadbaadaacabbdbbdaabdbdaadcddabcdcbddcbccbcccccdaaaabdcbbccdcacdbbdcbdcacdcbdccabbcabcdacadabcbcabccabcbaadcbcccaccdacacbdcbbacbbbdabbbcdbccbbddabdddbcadadaaaaabccacbbcdaadbdbdbdbdcaaadbbacaccccbcbbcadbcbaacaabbcadbcadbdbdabccbdabaadcaacabccdbcdbdaabadcadaabdcdddabadaccaccddadaaddccadacdcdbadbdbdaaabadbbababcabdabddddaabbababbaccbddabbbbbadcccbcbbbacaccdadbdbadddadccdbbcacdcacdbbbbdbcacdddabcacdcdaccbcaaacbacdcadccdacdadababaabbdadbccddbbdacdcabbdaaaccabcaababdcccbbbbdbabddcbddbcdcbadbdbbcddbcaddaaaacdcabdbccacdcaadbbbabcdcaaaaaabcccccaadacdacaddcacabaaddbaaaabbdaaabcbcadddabcbccacadbabdbcbabdaaaddbcaccbcacabdacadbaabdbdaacdcdabccbadbccdacaadbdaddcbccbaddaadddacaadcddbbabbcdcbaadccddabacbcccdbddcbdccccacbcddcdbdbbddbcdddcaaccbacadbccdabcacddcaddacbadadcaacabdbdddcdcdaabdbaacdbacbbcccbaaacadabaadabacabbbacbddbcbcabcacbabdcbcccbbbcacabdbcbaddcbccdcbdddaaadcbdbadbcbbddbcbabcadbaccdacbcdccbddabbbddccaadacaadcabbddcabcdabadcacbcbdcabacbcbccdaaadcbdbbbdadacdaababddcdcbcadcdbbccddddbdbcdbabbaaabdadcadbdbdcbbcdbaccccabaadcdadccbccaacaabdacbbbcadabaddbabcbccbdddccbbcbdbbcadaddabbabcbdabdcabdaaacbaccdccccbbdaaadaacccbcbcaccbcacacdcaaaaacacbbaddbbcabaabddbccacbabdacdaddbcbdddddabbcdaaacaadacbccbabdddcdcdddbadbababadcadacbbdcbaabcdbadabbaaaacaabcdbbbbbbbdcdbadcccabcaadcaabbdbdaddcdbbbbdbdcbcdaaacbaddcbbacdddbddabbcbadbbcaaabcbaccbdcacadbbdaadbdccadbcccbddaaabddacacdabbdcbdacabadcdaabdbbdccccddbbdcdadccaabacccadbcabaadabcadccbaddbdbabbbaabbbcabcaddabbbdbccdcbadbbbcdcdaaadacbcaddbbbddcdaadadbcabacadbbabadbaabcdaccaddcdbdaccddcbddbbbdaaaddadabbbaccbcbadabcdaccdadabdabcaabbbacdccaabdbddacdcdaacbcaccacabdaccacdadcdbbaadcdddadcdbaabadbccabbaccdddadcbbddcadacbdaddcdbbdbcbacdbdbabbbabcabbdcbdacadcdddaaccacbcdcadbbaadccabdabbabbadddacaabdacbcaacbdcaddcabcbadacdddddbdaaabdaabbbaaddcdcadacdbbddacabacccdcdbbdccacdaccaaadbadaaacdcacdadddddbbacacbdaaaacabdaccbcccadbdbaacacbcdcdbaacbdccaacadaccdbbcadbcaabccabddcaddcacddabbbcdcbbccdbdbabacccdbdcdbbabbddbbdccabdbcaadddbcdddbdacdcccddadbdaddccdabdcbabcaadadcbcadbbabcbbbdadddadcaccaaccbaddcbdaabcdacadbbbddbddddacbdbcacacbccabbcdbcabbcccacdabdddcdcacdacdbcaccbaacdbcdbbabadddbdaadbcbabaacabdccdccaaabbcdbabbbdbabcbaacadcbccadcbcdbaadbaabbacacaacdcaddaacaccdabcbacccaccaacabcbcddbcdaabacdbabaabddcccadccbacdccbabaacbccabdcdaacbabcdbacaaaadcdcbbdcccacbbdbddcbaadcabbaaccabdcdbdaabdbcbcdcccbcabdacacaabaddacaaccabdbaddadcbdbabbdcdbadacaadbbcdbdbdabcaacacdbcbcddadcadcaddbaacdacbcbdbdadbbbdcabdaaadbddddbdbabacdbcbbacdddcaaadbdbabddccdadcbcbacbcbadcbddcccbaacdccdccadcddcdbbdabbbaababcacdaaacbbdcdadcccbbbcccbcccaadcadbbabacbddadaddacdbbbbbdaacbadddcbcbcbbbbdaacbbbdacdadcacadcabbacccaaacaacdbbdccccdcbdacbdcaaaadcdabbbbadccabbcdacbdacabcddbccbbbbccdbdcaaacbccabdacdcdccdaabdaadcdbbddacccbbdbdadabadcaabcadadaadbaddbdadadaabcbdacddddabaabbbacbbbadbadddcbdacbdcdcddcdbacaadcadacbcdbadcabccdcdcccbdaccabcacdacccddbabadddcbbddbbbaddbbaaccbbccabddaaaadaadcddcaacadbcabbccddcbbcdaabdaaadaaadaacbccaaaaabcbdaabbdacbacadbddabdbacddbcdbcbdacbbbbcddcdcacdacbdaaccdaadcdcbcbbbbccbbddaaddaddadbbcbadcadbbbabaabacbdababcbcabdaadcddaaaabcbaabbcaacddacacaaabccbbdacdbabcdbbbcdaadccdddcdadacaabddaaadbcdbcccdaabdcbabbdcdcdbbacbccccbbccbaacbccbacddcdbaddbcdbcdbbbaadcbaaccdaadccdbbbbdbbabbddadccbcaaaaccadbccddbcddbbdbddabbdcdaddbadbacabcababbacdabaacaccccdadcadcaaccaaccbaccbdbcddacacbabddcabdbdaabcaabccadbcdcababbdadaccdbbbbadaccbddacaaddbaadcdcbbcddcdcdcaccaadbddbdaaddadbcabddbbaabcaabaddbabababdbbddbccdbabbdccdbcadaccadbcabadcbcbbbcdddbcacadaabcbcabdadbdabdabadbcdacadbbcabbdabcdacbcbacbbcacadbdbcbcdbbdccababdbdbabcdabbaadddbcacdcbbdadcaabcbdddabbdadabcddadccddbacccbdbbcbdcadaadbbdaacabcaacbdcdacbdabccccbbcbacbcbdccaddcddaaacaaddbdacbcbdbaaadbbabcbdddcbabbbaccbbdddbccabaabcbbbabcbbbcccbbadccdcdabbcddbcaddddbadcdabdaccadacabbaacdaaaddbbdbcbccacbacdabccdbcacadcaddccdcdddbcaaabaaaddbdddbbdddcadacadaddcbbabdbdaddcdabdadddccabdcbcbbdaabdcdcadabbbbdbcbabacaaaaadbccabbcdaacaacdcdbccddcdadaaaaccdbcadacbcdaabaaadbdbdaacbbdcdacdcbbcbabbdbcbcdcacdbcabbccddcbbccaabcbbacbabacdacadabdbadabddddbbdbbbcbdcbcadcdbbcccaddbdcbadaccbcabcacacccbcdbdbcaadbdcabcbbaaccdbbbcdbcbabdcccdbddadbbacaadbccabbccdcaccdadaacbcadccbaaccaabcdbbbacaccdcdbabaaaddbbacbaabbddabdabaaacdccaadacccdbcadbbddddbdadacbadabcaacbadcbdddccbbcaaddcabbdbdbcdabdddacaadcdbddabaaabdbabadbcbdabddbbdaadcabbdadabdadddbddccdbcacaadbaabcadbadacbcabbdddbbbabcbbcbaaabccdbccdaadcabadbaacdaddabcdacbcbbcbadabcaadbcdcbbdcabdcbabaadddacbacadccdbcbcdcdaabacacbaacaacdbaaacbddbddbcbaddadcbdcbbbbbddbbbdaccccccadcbbbddddddcdccddbdbaddbaccbcbdccbbddddaaaaccabadcddadbbbbbdbcbdbadadbbcbbdcaaacabccbaacacbccaaddabbdcaadaabbdbabbcccccdccadcabdccbaabcaadbdacacccaddbadbaacacbcacbbcbdbbdabacaacabccccbbdcdbabaccaccdbdcdabccdddbaddadaaddadcddbbacdccdcbccabbbbaacccccbccbbcbcbadbdbcccadbabcbaabdcbbdbbadacddcdcbbddabacdaccabddaddcccbdaaacabaabcdcddadaacddcaddddcdbbdabbcbacadcccdbddccbaacbaacccabadbabddbadbbdbaacdddcdbcbdbbccdbbdbaadcbbdbcdaccdddcdabaadaddabbcbabbadccbdaddcbbbbacddbcdcdbbdaadabddbcddccaddcabdbbbabcbbdcdadcbaacddbbaabadaaddcacacabaadbdcbccccdaacaadaaaaaaccbcbbdaccaddabdadccdcccbdbabdbbaaccdddbcabbcddcdcbcabbadbadbbaccbdbdcacbbddbbbbadbcccdbbbccbcbcaaabbabbdccabdcbacabcdaccaabbcbcbacaacdaddbaadddcdbdacbadcddddbbabacaaccddacdddccaaaaaabccaccabbccdcbbdccbddbddacdcbdbbabcbcdddaccaacbdbcddcdaaabaabccaadadadbabaaabbabbdcdacdbabaddbabccbdbcacadcdacadbcbabbadcbdacdadccddbbbdccadcadcbbabadcddbabbbbabddadbbabccdaaabdccabbbbadacabadcadabaddadcaaaddbdcaaadabadbbabbacdcccbbbddadbbcabdcccbbdddcacdbcbcaacddacdbdbcbaccaadaaaccadcabccbcddddcbabacbccddbbcbacccbacdbacdddcaccadddcaaddacdbacadababcdddbdabaacabcbdccbabdacbdbbcabbabddccabbcdbddcadadbdcabcddcbbdddcabcaadccdbdacbabcdbdbcddccaadabcddababbbacbbaacddacdbccbbcdacabdbbdcdbdccbbdbccccdabdbabbbdbbbcbdacddbcdaaddbdcaacccaaabdcaaabcddcbdbcbabacadddcaacbaaabcccdcccccbaabcaabcddcaabdaccbdbdadcbacabdccacacadacbcbbadbbcbcbddcbdacccbadbcdcabbcbddcccadbbbccdaccbadcaccddaaaaddbaddaadaadacbbdddddbdcacbabacccaaacaadcdaacaabbabddccababcaabdcbddbabbccabcadbcbbcdcaabcdccdaacddbaccabbacdbcdcbacbcacbdddcbaddaddcbbbccdacddccaabacccaacbbcaddcaacdabaaabddbccaaabbcaddbdddbbdbaacbbaabbacadbdadbabdbdcbabadbccccdbcaabdccbadccbabbaaaaacddbbaccbbdadbbdcbcdabdcadcbacdbccbddaaaacdbbcabcbbddcddcdcbbbbbaddbdbabbbdbacdcababbbabcdcbabcddbaddbbabbcddbdbdadbaaccbacbbcaaaaabcdbaddbccbabcacacdaadadccbcacaacbcbccccbbcbbbddcaccaacdaabddbadbadbdaacaadaabbccbcbadcddcbadabaaddcddcccbaaaccccdacacbdcbdddacacccaadabadabdbaccacddacdbcabdcbbdbbbccbbaacbcbdddbacaadbbcbbaaacadccadaccbabcdadcacdcbdbdccdacbbcabdccdcbcbcdadbabaaddccbcabbccdbdcdabccbcadaacbbaabcbbdcdbcbcccccdbcbabdbbddabbaccdabaddbbadbaacbdbcbcbdbdaababddbcddabddbbcbcdabbbcbaadcadbbcdbbcabbbcddcacdcbbdbdadcdcaddcccddccbcbccbdbdabcbccbddaddbccdbbdccaaccabcbabddadcbdbbbdbadaacdbacbaacadacccbbdbabaaaaabdddbcbdaacbdbcabacdccbbcbbcdbbbadccdabcccbbacbabaadadcbdaaccbdbbcaaabadabbccbcdcdaadccabbcbcbddbdcccccdddbddadbbdbbdcdadababbbddacabccbdaaddbcdcdbccdacdacbddabbdbaddaaacaccbaaadabbdaabdacaacccccacbcadacaaaaddcabacacddbbaacdcdcadbbaadabdccdcdbacbacacdbbddbbbdcdaaddacabdbbdccbcdddacabddbaacbdaadaadcccdbbadcdcbdcdcabdbdbcaddaacbbdaadcbdaadcccbbadaccaadabdababbbdcbacbbbabddbbaccddacaabcddabacbbdbbcacbdaddadcaddababadbbdccabcbcdbdacdbaadddccdcdbbcdacadddbdcacabcdaadddcdcbcbaddccabaddbccbcdadddbdabbcaacdadacadadbddbabcccacaacaadbcacbaacddcbdaadbbbdcacccaaaadaddacaacdacbcabcdcdcddaacadadcdccddbcaadccaadddacacabaaabbcaacaaadbcadabadcdbdabbcccccdabcaacababbbccbcccbcadabbcdadaabadcbacaacbacabacaacccbbcddaccdaaabdddabdbaddabbcdcdbcaddcaabccdcbcbbdaccbacdcdacabaacbdcbcaacaaabcbadcbaaccaccbcbadadcddbddbaacacdaccdcddbaaababcaccbcaaaaabbaabbcbabaabbdbbadadacdaaaaabbadddabcbdbdbdcccdacacbcadabadababdacbbcddabdddccbbdcdcdddbaccbbdacbbdbdcaccbcbddcbadaaadbcdbcabbcadccbdbbacbbdccabdbccdcbcaccbdccdcdbbdbabcacdccabdbccacbdaacbcacdbdcbbcaacbabbaaadaadaddddadcddbccdbadacbbbbacaadadacbdccaaddacbcbacbbbadadbbabccccdcdbccbaccacabcaadbbddcccdcccbccbbdaaacbbcdcdbdccddaccbbddcadabdddbbacadcdcbbbacdbcaaadaabadaadddbbaabaddcdcbccccaaabadbccacaddbadcbcccaaaacacbaadbcdcaddbdbdcbaabbbcaadbdbccbddcadacdcbbcbccabbcaccaacaabadcaabccadcacaacaadddbdbdcbaddadaaabaccdcdbdaacccbdbcacbccccdccccdcdadcddadaadbadcbbbcccdbaccbcbdbbcbbdabcbbadddacaaaabcbbcbbbdbbdcbbddbaaddaaacbbaccbcadcccaaadacbdcacabccdddccbbdddcdcbaccdccaaadccbccbcaddbcdcdccbbbddbbdabadbdccaadabdabbcbdbcabdddcdcbacdbdbcbdadcbabbbdababcdcdcabcadcaaabddbbbabcabcacdcbdbddcadbdadabdacadbaacdcaacbcccbddcbcbccaabbbaacaaddddbbbbbaddcbcbcaccdbacbcbbcccadbcccacacbdbdcbcbaacdbacadddbdaacbadadcacdcbddbbcacbbccbaadabacdadcdbadcdbcbbdcbbdcaabadaabaaccdabbcadbdcababccbdbdbbcbdbdbddddbdbcadacacbdadbbabbcacbacbaabbdabbcbddbbcabaabddaadacbdbcabdabbdbabbbbbcaccaaabbbcbdbbdcbabbcacbddaaddcbbdcdccaacbddadcacccaddacdbadccdabdcabacccccabdddcaabcddcdbaddcdaccdbdbbdbaacbadbdbbbddadddcacccabdaacbbacaaaadcadcaadacdaaabdcdbdbcdcbcadbbcbadbaaabdaacacabddabdabccbbbdadccbbaababcbaabcabcadddacabcadbdbdbbdbcdbdbdabdcbbccbdaabbcbdacaccdcdbdcaddadbddacdbbcdcdcbcadaccbdbdabcacbcacdcadccaddcbcddccacbcdccaabadabddbbdaacdcbdaaabbaabdacadbdcadbaacdbbacaabadccdbdcbdcbacccccabccabcdcbcdcdbbdbbacccbcadababbaacddadcdbacdddbdabbbccadabbacddbcbbccdaaaddaacacbccdcddddbdbbcccdcbcadcddcdbdddacabadcdbaddbaaabcaacdbadbbcbbbdcccabadbdadacddbcdbbdbdbacabadaaaccdadbcbbababdbadbacdbbbdaaacdaacaaccddaccccdcadcadbddddbcccadcaccaadadddbdadcabcbbadbcbcbbbdacbbdcacbabbabadddccadcdcdacacbbbcbccdbcbdaaabbdabdbacbbcbbcacdbacbcccacbcbbaadbdbcddcdaadcddddccbdcabbccbcbabacbdbbcadbaabaccbbcbcaadbcdabbaccddaacbcccddcccadcdcddcbbddacbbabbbcccddbdccbbdbaadbdbaaaaccadacbbbbcacadcdcddbbccbdbbcabddbdbbaacddabcbacaaaaadcbbccdbdbbaaabdbdacbadaaadbdcddbddbcdabdadadbbdcacaadcdbdbbccaadccbcbbbbdcbcbaccdddcdccccaacddbddddabccbbdadcbdbddaacccbbcbabbdaddababadbcbcdbcaabbbcbdcbdbabbcdbdbbbcdcccbaabcbdcccaadabaacbacaabaaccccbcccacbcbcadccddabbdbccbbbdabcadbbcaccbbbbaccccdbdadaabcdbddbbaaccddbcdbddababcacbcadbadadcacaacaabdcababdaabbddcacdbadbdbcbabbbbccaddcbbcaadbbdabbbbdccbacbddabcdadcaacdabdaaaacadaaabbbadadbaddadbddbccbddaccababccbbdadccbacdbdaabcdbbbabddcccbcbbadcccababccdacadadabbccbdcadccbabbbacdbddbddacbdaadbbddbdbbadaaadabbbabacaadbcdcdccbaaccdbbbbbdbbaacbcdbdddadcaabbbbbdbcdcccddacdabaabbdcdababcadaacabbabdbbaddddbdccdcadccadaaacdcdadccaaabdcdbddcbccbabbcddcdbdccccaccddbbaadcadacbadcddcccacddbdbcadaabcddbbbbdcdadadabbdccdadbbacaccdcacaaccbbaabddcaaabdbaabaccdbbddadcabadcbdabdcadbacdcbcbbdaaabcdcaaabbdaababcddcabcbcababdcbcdddcbcdbdacabccdacddbdbcdddacccacbcccbbcbbcaaabbbdbbadaaacadccadddbccccdcbddaabbacbcdbcdbadbadcadcbabadacbdbdbcbdaaaadddbcbddaabdacbddaccbaabacbcdaccbbabacabbbacbbcaccdccadcaacbaacbcbcdabaddbaddcaacdbdcbcabbddcacdabbbcaaabdcddadbcdbcbaddbdbddccdccdbbdbadbaaaddddadcabbdadaacbbbacbbcbcdbabbaddcccaccdbadacabcabcdabdbacdcaacbabdaacbdadacacddbdcbadbbadcabbbdadabccdbabbabbbabacddcbaabbdbbdabcaddddcaaaacdcbaadbcbbccbbbbcddadbdbdbabbbadacabcbcdbddadaddcbaabaccacddbcaccadcabdcbacacbadacabdabcaadddbabbbdbbaababaabcbcbcabacbdcbccbcdbcbdacccddbbdadabbbcadcccaaccdbdaabbcbcdcdbdbdaacdacabbcdabaddabcdbacccbbdaabbccbcadaabddababacbaadaddbcddcadacabababbcdbbbbdbdadcccdddacbccacacdaabbaddcbbacadddbdaccadcadddbbccddbcddcacdddadbbcccbaddcacbacaccdaabbbdcdcaadbccadcdcdddabbdbdddbaadcddcdbccdabcbbdcccdbadcccbaaddbdcaddddbccdbbacadcaacdddcaaabbcbacabcbbdabcbabcabaabdbcacdbddbcacdccddcabccbdcbacdaadcccadaccadcdacdacbcbbdbcddacdcdccabcbbdbabcbcdbbabcdabdabdaabdababcadaabdcdcdacadbccadacababcdbdcccaaacacbcbdcbcabbababbbabbadddbbbacdabccdadaadcbdaaaddadadaaccacbbaaccbaabbadbdadacdbbbacaabddbbadadaadacdbcdcaccbbcbcbcbbadddcdbcdccbbddaaaacbabaabcccddbdacaadccdadcadaadccbccdcdccdbaccbcbddaddbcbdddaacbabccbacdaddadbabccbddadcccbcbaaccdabbbbabdbcbbccbcbaadacbdabadbbdccabcdaddbdccdbbbcaccdcacddbdaabdcdbccbdbbbccbaabadbdaabbccadbccaaaadbcdccdcbaccdaccccdcdabdaacdccdccbcbbdccbdaadbbbaaadddbdddbaaaacbdcdcdcadbacbdabcaabbbacdadbabbbdaccdcbaabcccdcbbacbbbdbabcacccbdcabdbbdabcbcdbabcabbdbbdccaaccbddcbaadacddcbccccaccbddaaccbbbbcbcaaddbaacdaadddabbdabdcabdddabaddbabbaadcddbacbdaccbbddaabcccabbbaddcbabadcbdbabcaaadcaaadbadaddcdcacddbbdaaaddccbbaabbadcdcaacbbadcdadcadabadabdaddababbcdacacdccccbaacdbbcdbaaadccbcbcccabacabbbddbbacdcbcbbdcacdbaaabbccabaaaacabadacabcdbcbdbabbbccbcbcacdddbcdbabcbdbabcdccdbcbadccccdbdbdcbabdbcaddadcdbcbaaaaaccbaddadbbdabdccbbdbcccabbcaaadaacdcabccabbdcabbbaabbadbbddabaacdacadcbaacbbbdddccbbcccaccaacbcabadcdadddcabbadcbcdcdcdbccbbaacdddcbbaddaaacaccbadaacdbcdbabacdbaacccccacddabbbbabbbbdcccadddcddcdcccdccabbccdbcccadbcbcbbddacdadbdaacabbbddaddbadacddbacabbbccbdbcdadaccccdcccdbcdaabbdcacdbbbadddbbbcadaabcdbbbdddbdbadccbbabcdcdaadcdbbdadcadcbdbbdbbcddaabdbaadacadaacccbcbbdbaaccbaabcbbddabadcddbcabccbbaacababcdcaaabbacabcabaaddbbdcdabadccccaadacccccbbdddadddbcaddccdadcccdbdbadbbacabdabbaacccaaadbbcccacaaccaaabcdabbccbdcaadcbabbbbbdcdcaddcbbadaddacbabcbbdddbccccaadbdcaaadaaaccdacbdddbcabbbadbcbacdbbcbdaaacdacddacaaadcdadbabaddcbdcbdcdbcabdcdcbbbdcacbcbbbcdcacdacbddabacadcbcbddcbdbbbcacacbcdcabccadacccdbbcabbcbcdacbabadcbccbbdaddcddcbdbbbaccbdadcdbadcdcdbcaabbbdbacacbadcdbbddbbcaddbbbdaabcadccbbacdbbbbcdddabcbcdcadaddcccbacdcbccabbbdcabdabccdbdbdbbccbdccccbddcabdaadbcbaaadccbcdcadccaccbccdccbdbcdadccababcbcbabcaabcacbcbcbcaacbdcbdcdbddddcccdbbbcbdcbdddabdacddbbaccabdcbddadbcadbbbddccdccadbddadabcdcbaabadccaabadbcacdbdcddacaabbacbdcbcddacdadbcadcddcbbdbdbcbcacbabddbacbbdcbddbdabbbcddabcadbcbdbcdccdcccbdccdbbadbcbbcdbadcdbcbdbacabbdcabacaadaadaaadabdbddbcbbdbaaabccaacaacaddcddabccacacbadcdccbccbbcbcdccdcacbaaabaccccabcbddbcccbbcabbcdbaabccbbdbcdaccacdbcabcbbabaabcdddadbaabccdbddccbcbdabbcaaccbbcbcaaddcbccdbdcadbdddcbdcccbdccbdddbcdcbbccaabdcdbdddcccdabcccaaabcdacadadbdcaccacbaaadacabacbccbbccdccdbadbbcadcadaddddbcbbccaaddbcbaaacaccddcbdabbdacaccbcbbdabccbbcbbbdcdadcbacdcaaddbadccadbababadadabbcddbccabbdcbbdbbcdcddbdacccdddbbaaacabacdaacabbcabbbcddcababdaddbdabbddaadbddcabbbadaddbcabbcbbcbdadabbbddaabaccbcdddbaacccddbbbdcdaddddaacbbcbdabaaaccdbdbdaabcddaabddacccabadcdbacadccbcaadcbaaaaacbcbdbadcacbacdcacdccabaabccbdaccabcadcdccbaadcccddbaccccacbadacbcbcdbbccbcccadccbbbdbcacacbcbdaaacbbccaccdcbcdabdbbdaccdbccbabdbaacdccbbccbcbdacdcbccabaddcaadcccdadcdaabaabbaaaabbbcbbcccacaabbcbdccbbddbdbdaaccaccbcccadcbadcacdcaaacbacadcdccdbcbdadadacaacbadcbcabccbabccbcbabdbaddbbabcbacdcdbdbaadbabacdbcdcbdbdccacadabaaccddbbacbccbbadbaabdcdddcdbcccdcbbabcdbadddbccdacbdbdbbdccdcdcccaaabbaacdbacdadadbdbbdaaccdbdadcdccdcdbabdbbbccbadaddddbbdadddbcbcadaccbbbcbacddacbdbddbaaaadacbaaabdcbadbdcadbcbdccbdbadbcdadbaddabdcdcbcdccabacbdadbcddccddaaaaccaaadbdddaaaabbdbdbcddaaacbdddbddabcbacdccaddcabbddccaacbddddcbadabcbcdbcadbdadbcdbacbdcadddaadbcabcdbcbabcdcdcbdcaaacaddacaccbcacccaacccdabbacccdcaddadbccddbcbaaaaadbbbcbadaaacbdaccacaddddcaadabcbcabcccbbbcaccadababaabddddddcbddabdbbacdbcacbbcaabdaacaaaabbbccdaacaccbaaaaabbdcaddbbadcdbbcbadcdabcccbabbdbdcbbadbbaadcdcbabdccccbabddaacbcdbbabbddabbadbaddabdbcadccdadcadabbccdccdcbdaabbcddbdabcdabcadcbcccdcaddcddadcadbaaaaddcbdaacabddbcbddabdbabcaadcacabcdacddbaddadabaacdcbdcadbbdccadbdbccdbccbaadccbacbaabcdcaddcacabbbdbacdcddbaabcbcdaadcdbccbddabbbdbcaabcabcabdbccacdccbbbaabdaadbcbcdbdccacbdadacdaddbdccccbaaadbccbbbbcaaacbbdbadbabdbccaadacbdbbbbddcccadbbcabaadbabcdbbbbadcabccbcbbbcddcdcbdabadbcadacaadaaccccacbdddcadcdcbbbaddcadabddbcbcbbadccbabaccbbbadbcbcdbccbdbbcaadcbbbabbbbdccdcdddaababdcbbadddcabdcddcadbcadabdddbbdabbabdaacbccaadccdaacadbbbcaaadcbbdabcaababdcabdbccacbaadabaaadaaabbcbdcbadababcbbadccbcaccaabcdbdccbddbdacbbaaadddabbcbcbbcbaabcdbbadbccbaccbbdcaddaacabdbbbbcdbcddcdcbccabcaddadddbbbbdcdddbdadaabcddababaaaccbcdbdabcdadabdbadadcbbddcbcdddbbdadabbabbcdbacaabcddcdacdbcdbaccdacdcbadbbbdbabcabcaccbbacdbacccdbadcdaddacbaaacbcbbbaabbabdcccdbbddddacddaaabcdabbbddcccdbbbacdddbcdccbbcdabccbadbdaccdbdbabdddacabcbbdadbaacccddbaadbbdbbccdcbadbaaabbadbcddbcddbbdaacddcbacbccdacbabbdaaaaabacbdaacddcaccbddabbdadabbabdabacaadcadbcdcaccabdccdcdbccbbbbcacccdbccacdcbbcccbaaacbcdcaaadbaddcbadabababcbaadacdaadbbaddbdaadbcdadaaabccacdbbbdccaaacacccbdcbaadadabdbadbbcdadcabbdddcdbcbbdadbdaabbaaaaabdcabbbddacdbddcdbadadaababdbdabbdacccaaddcbcabccdbbcdbadccaccababbddadbddbbbccbcdabdaadcbcbabcacdcaacbdcbccdbdcaaacddcaabcbbdcbbcccccdccaabddcaadaccbbccddbabcadccabbcccbdcabadbbadadddbabbadadbcbbcdbcbadcadcacdddddcbdbcccaccabcddcdbbdccdaacaacdddddaadcbbaccadccbddcacaacbbdccbdbaadaacbadaabaabccccbdbdbcdccbdcabccdaacadccbbcbadbbcbacadbbdcdcdcacbacdbccddacacaadcdbaadabbdddbdaddbabaabdbbababacbbcccbbadcdcaaccdbccbcdaaacaccccaddbcbdbaabdacbbbbaacbcdacabdcccccabccdbcccdcabadccccbcadaccaccadbcbcadcdccbcbcdbbadcbcddddbababbccbcbaabbcbcdbcaddbabdbbdcbcacdcaabcdccddcaddababcbbcccdadcccacabdacbbccdacbcdabccdcdacaccbcdacadadbbbcbddbdbaddadadcaabdadbddccabdbbdcbacadbaabdaacaccccbcbadaadccaaccdddcacbbdcdbbdaddbbacbdbdbcccaacdabbdccaabbcddabdaccccccaabddbbcbdcccccbadbbaadcccbdbcbbbbaabdbbddacbcdddadcbabdbbbadcabbdcaccacbddbddaddbdccaadabcdbcdbddadcdbcabaabdbdbaacdaccbbdcaccbdbaddbbabdcccadabbacdaaaccadbdbbcabbcbbcccaaaacdbadcadddadabdcdbccbbadcaaacccbbadbbbbdbacddddcbddbbccadccaadabbaabcddddddbabacbadaabbadcdcaacdbacacabdaccbadcbcdadaaadbbaddbdbcbacccddbcbbddbaccdaddbbcbcccccdaaadbacacbabacadcbaaccbdcbddbacbcaabcddbbddbadbbbadcbcdcdcbaddddacbbddccccbacabdccbbdbadbdacaabaadddbaddccaddcabbbcdccaaabdbaadbcddcdccddabcdcadaaadababdacbabbcccddadbcaaddddddaccdccabbddacdcabdcccdaadbcdabccbcaaddcdddabadbddbccccbcbcccdbbcbcdbcdabcdcbadbdaaccdccbcbaaadddadcdacbbcbbbbdcbabbcaaadadcabbcdbaabdaccaaabdccbbccdbbabbddccbacbaacaddbdacbdddabbaabcacbdcadcbcccbddccbdabcbcadcbccddadacdcaaadcdbbdbcdbddaacabacadacbddcbaccbbdbbdccacdbcbabdcacccccbdcbadbbbdbdcdbbdccaabaaaccbaaaaaaccbcadccdbdabdacbadaabcaadddadbcbdbbaabbccbdcbbdcbdbadccdacbddadcacbccbbcdbddcacaddcbacdcdcadabbdcaaacdcacaacbdaabdaccaddcaacaacdbddaccaacbcaabbcdcadbcbababbccddabaaabbacbbacbcbbaddccdccacddbdababdcdabbbbdabbacddccdaaaacabdcddcdddaaacbddaabbbbaddadcdbabdaadcabaacdaddaaadbbbcccdcdabcbbcaabbcdccbaddbbdadbcbbcdddcbddcddadbaadadaddddacbacbdabacaacddbaddbbabbcbdadddccaacbcaabbbacccdcdcaabcddbcdcbadaccddcadcaaaabdcbcccadcaddbbcdcabcaacaddbbaccbcbcacbcaabaacdcaacacdacdccbddabbdabbbcdacdaddaaabdcbdacabbadbdadaddcacdbaabdaacaddbadcddccabadacdaaddcadaabcdddaccdaaaccbcbabdddcbbdbaacabbcdbcdbddabcdbabbccaaaaacbbbdbabbdbdbcdaadacdbacdbacdaaacddbbddabcbddabcadcacbdbcababaabddbcbacbbbbaddadcadcadcbdaadccbddaacadddcbacbbbdbcacdcdabdcccaccacccbbcbababdbdaabddbabdbacdcbbabbccaadbdabbdabcadcbdaadcbbbacdcbdabbbadddbdddbdccacbcaaabcddbaacadbaaacccbaadcdacaaabbaacacaabdbccdccbadcdcdababcbacdaabcdababdddbcdaacabbdaabccabadaddbdbbcddbadadddcaccccccdadccaabbdaddadbcacdbbccccccbddbdddcdaacbdaaaaddcdddcccaaacbaadddaccbabdccddcccbcacccaadcbaabbbcaacdbccbcdadbdcacdccaabacadaccdcbacbccabacdbcacbddaacdbadcaadcaacadbcdbadadddbaadbadacbcdbbddccacdcbbccccbcabaacdcadccdaacbabcbaddcdbcbdddcbbaabacccaccbacacacabbacacccbbbdadcdccaababdcdbddacdabbacddaadddbdcbccabbaadaaaccadbbdabcaddbaabaddddbcbabaacdccbdccdbbbbbdccccacabcabdbbacabddddbadbaaddbccbdabbababddadbdbadbabdaabcaaadbbdbcdddaadcbcccbabcaaabbabdbadbbcaacaacadabadcdabaabacdccbccadccdbbaddaadcccbbdaabccacbbdabbacacacbddddddcadbbbaacddabacbbacdbdabadacdcdccdcbcbadddbaccbcdadbdbcadcaaccccadaaacdbbdccadadccababdcbdbdaadcbadadbbccbccbccbbabaabdcddabaaababcdacddadcdabdcdcbaadbadddcbdacbacaacbcdcdbccaaaddacddcddabcddbdbdcadabdcbbcdaabcadccaabdddccdabdbccdddddabdbabdbbdccbaacddaadabbddccddbddabbcbddbaaadcddcbacdadabccbabbbabaacccdbabcbaaaccdbbdbbbacdaaacacacbcabdabcacddaddacbdcdbcdaadacdcabccadbcbabcabcabbdcabaccadadcdadbddbabbaddccbcaabbdbbcbddadadcccaaacbaddbbdacbadcbdadabbdbabcaccbcccbabdbcacaddddcacbbadabbabccababaaccbcacaccadbdcbabacbabcbbbdaadcbbcdbbbdcdddccadaadaaaccbdacccadddaadcbbbababbccdbcddccabcddbcaabcabcdcbaaaccccbddbbcccacababdcbcabccbabbcabbbbcabddbbcccbdacadbdbbccbbcdbdbcbdabdadbaddbacbcacdadacabdcaccbbdddbbcaaaacdbdcdcaaaddadbddddaaaabacddcccdacdadbddcbdaaccbdbcbbaabcdabbdcbbdabcbaacaacbcdacdcccddcccbdabcaccdcbbabdabcabbcbcaaaaababdbdaabdcdcdccdcbbcbbbadbcccdbcaacbaadcaaaaddbabacaccbabaadcbacbacadbdcccacddccbadaddcbacacabbdbbadcdababcaddbadadcdcacaccccccbbdbcadddccaaaadcccbadbbdcabbabdddbadcbadcccddbcbacdcdccbcadbdbdcdaaadacdadababddacbcbaccdadcadbddacbcdcaadbccccccdababdbdcbadcbbacdaacbdaabaacddabdcacdabbddaccdcdcddacacbddbccabbbddcbbabdaaadcdbabadbccabbbadbbcadcaabbaaccbbbbbddaabdddacbcaacbcbdcdcbdcbbaccbcacbdcaddbbdaabcadbdcbdabbcccbbbdbccacaccddaadcdbccbdbcdbcbbbbdadaabdbacbcbdcbcbabbdddbcbcbadddbaccbacdbccbdadbacdbcbccaaacbacccddaadbdcaacdddccbababdcdccbadcbacbaddbaddcbbdcacdddaabadccabbcbdcdccaabbbacdaaaaddbadddacadbbbdbaaddacbcaddbdacbcdbadbddcbccdbdbbacbaabdccaaabcdbabddcdbdaabcdaadbcccbbabbcaaccddbcbbdcacccdddcdabccddcacbccbdaacdddbddcbaccdccaadddaabbccbacccdcbcdbbbaadbacbbdacadccdbcbcbddbabaacdacbabbdcbdbcbdadbdabaabacabadaddbbaaccbcbdccbadcbbdaddcbddaaadddbbbcdbacbbddbcadbdcddcbaaadcdadcacdabaaccbbaadcdaddccdadbbcddbbaacdddacdadddbcbbbbdcbbcdccdacbdccbbaaacccddcdbddcbbcacdcddcdbadcbbdbbdddbccaddbbcddccbbadcaccaabddabbbbcababacabbbdcbbddbccdacbdcadbadcaaacdcabcbdcbaaddcaadbcaabdcaabbdbcbdbadbcaadacbacbdcbbadaacdbcadccbbccbbdddabbcdadadddaddbbddbccdbbadbddbdaacdadadbaacdccdddcbbbcccccadabaabccdbddabbcdbdccdcdbbbccaaddddaacbaaddddcbbcaadabaddacdbddbdbcdaaaddbbbbdaaccbacbaadccaabadbccdbdcabbbbdccdadbdbdaabaacddaaaaaaaacadcaccbcdccbcabcccccbbccabaaaabaddccdaaadbcccbbbbcdbdcaacabbadcdaabbcdacaadadcccbadccddcdabbcdacddbaaccdacbaaadbddddddacabdaacbabbdbcabbdbccdbbcabadcbbababacbbcbdadddcacdbcdccadcaddcdacdddbccdacabacaaddadaadaadaccabcaabbacbccdbbddbbabcaacbacdaacbcdddccadaccddaaddcccdcddbbbdbcdcabbaadcbaabbbcacbaccbacbcddabbbddbadbdcbaaaadbabdadaadbbcaabdcbdcaddccaadcaabdaabaddcbccbdbaddbcbcadccacddbbdacdbdbabacaadbcadbcaacddbdbcbdadcbbbacbbadcbaaaaaabaacacbcabbaaaadbdcaaadcddaddbacabdcadbbccbdcdabbcadbdaccdbdcccdabddaaadabaadbcdcbdbbabaaadadbccddacdddddccaadbdbbacbadbccdbcbbdddadadaababacbdaaddaccccaadacdcdcdcaccdcddbbccacccbcbbdbdbcdcdcdadcccbbbbbcdadaaaaabbbcddcccbdaaddcccadbacabcacccddcbdaddddccabacacacaaadbddcddacaaacdddadbadbaaabcbddacddbcaabbbbcaaccccdbdaacccadcddaacbcbaddacdabdcbadbddccddaaadaabcadaaaaabaccdbdaddbcbacadbdccadcbbabcddabdacaaddcccbcbacdccbadbaabbbcddaddbdaccdaaabdcdacadddbaabdbcdaadddddccdababcbaacadcdbcbaacacbbadddcaccdbbdbdcbcdbadbbcabdcbcdccdadbdaaacbcddcbabdbbcdcabdcdbbabcbaadabcdddcaaaacbacbbdacdbcadbaababcdabacaddaaacdaaacdaadaccbadacdadadcccdbaadcdbacbccbbcbdcbaacdcdadcaaaacdaabcaadddbcaacccbdcdcddcadcbacbcdcdcdbaacbcbacdbccbcdccbdaacbbbaacbcacddbcccdddabaabacdbbbbcdabbaaacbabcdcacdcbcaacdbdacbccaacddadbdcbddaadbcbaabcddacbdacabbdbcdaccdccabcbaccacccbbabcbdccaadabcccbcdccccadababcdbadabaabbbcbadacbbdaabcddcdbbacdbcaddbdbadbcaabbcddbabbcdaccadbccabdbbcbcaadbccbbdcaacddaaacaadadaaccbbadadacccacbdbdacbdabcdadbddbcddbdbbadacdcbcadccbdccacabdcbbacccbdaddcddccdbaadadadddcacddcddddcbcacbabbabaacbdcbcbbddabcccddaddcadcdcbbccacdacddcdcbacdabcbadacaaccccbcabbddbdcabaacbabcbbcbcaaadccdcdddcdaadabcddacacdbbdcacbdaddabdacaccdccaaaccacabacbdcdbacccdcddadddcdacdcdacdbbcdbcddbbbbaddcdccbadcdcbcdbdcbcadabdddbabdcaccdcccdcdbccbbdbdaacbcdadbabccdcddbbdabbcccdccaadbbaadcbcbaddddaaaacbbbcdcddaacddaacddbdddbdccddbdcdadbaacdbbbacddbabbdaabdbbcbbdadaddabddccabaaaabbdbacabbaacbccbcbccccbcbbbdbccbadacaaaccbbdccbaacdcccdbbaddbaddbabdcbddaadbaddddcdbacacdbaadbcccabacdbaacbaaabacbbddcdaccdbbbdbcdcbcccbaddbcaccbdcbbdabcbbcbbcdccaacbbcabccdddaadbdcccbabbbaccabbaabacadcdbadccbcdabbdbcdcdbccbcbddacabbbbdddadbcaacddbdccdadbccdccbbcacdcddccaccaababaddabcdacabdcccbbdcddaabaddbaaacbacabcbdabdcabdddaacdcbdcdabbabdcdbbbdadabdbaabbbddddcbbbbccacdabbbcabbbbacdbadabccbcbccccbacbaacdaabdacbbbaacddcbdbcacccbbaabdcacdadabaddaccbbccdcbdaaadbbabbcdabbadbadddbcacbaddbdadbbcbbdcaacaddcadddababacddcacadddaddadbbbccbccccbbccacdbcbbdadacabcbcbadadccbaacbbddbaccbcabcddccbbbbbddbadcacbddaccdbddcdbcbabddcbbccabbcabbbbadabdcaaabccbaddbdcbbabadcbabbabbdccdcdddcdddcbccbcabbbbbadbccddaaacaacacdcbcbacdccdddbcccbcdacdbacccdacbbccabbaaaacdbdccccbaddbdaaddbacadbaaabdaadcdbdcbcbbacdacbcbadcccabdbadbddbbaddadcaaaccdcaacdbbacbcccabdacbdddbcbbaabcbddbccbddcbcdbaadabcadbccdabbddadaccbdabbdadbdccadaabbcbabcbcdbadcbaacaabcbbcbaddaddcbbadddbcbbdadddcacaaacabbdadcccbbdabcaaabccbbcaddcdbcbdbcadbdacbddabaccdaccdddbdaacddcbadabcdddaddaadaccbbabdccaadcbdacacccdcadabdacaaddacbaccddccaabbacbdacdbbbabbdadbcbddbbddcbabdacbcbaacaadacaadbbccbdaadccaacbccacabaacbcabbbacadbadbdbabccdcddacddaaabacadabaddaaacbccbbadadbdadddaaabccdbddbbdcddadaadabcdcbaacbdbcccaaabbbbacabdaddcdacdbacaccdaadadbcacaddaadcdabbdbcabcdacbdcaacddcdabccdcbaacaadaacabcbdabcbcaaccccbaacbbacaaaabcccdbdaacbccabcaacacdcaabdacbbadacddbcddcdadacacdbdaadabcadbbadadddbacdbbabadcdccdbdadabcbbdcbacbcbbadbaabaccbddcabaabcadbbdbbcdacdbbbaaadbdaddaccadcbcababdbabcabbcbbacbdabcbcdcdbccccdaddaaaddaddbabcaacdaabcbccbddbbccdbdcbbddbcbdbcacdbaacabacacbdabcabbcaddbbcaddcadcbccacbcdbaaddcabaddcccaddddaccdbdbcbccdddacadcdcdbbcaddaabbaadbbaaadbacbcbbcddacacdadabcddaddcacbdcaadbaddddcdadaddabbcbcbbbdbdadcdbacddacdacdcaaacddbdccddcaacabbaacbcddadabaadabcddccdaaadbdcbcbddddbcddaddcabcaadbcaabadbddcbcbacadbbdbcbaaabddccdddddabbddacbcdbcaacacbabbcaabccaddabbcbbcddabcbabcacbcdcbdacadaabdbbadcbadddadbcccddadbcbccacdaaddbaaabcadaabdddbdbdbdaddbbccbcbbbdacbcdccccddbcdadbabbcadabdacacbbabbadcbbcabbbcadaababdacabdcdccccdaabbdbbbcadacdcbdbacacdadcbbdbbcbaddabaadcdcbddacabcbdbcbbbcbacdbdddccbabdcdcabcacacddbaccbddccbccbdababccabccaaacbadcbbcdbacdabcbcbcbcbddcaacccddbccbabaaabddabdddaacbcbdbbcacadddddbdbddbdbcadabdcccabddcddbadcdbcdabbaadccacdadbbaabdabddcbcbdaddadabccacbbcdbddcadadadbbbcacadbddbcabacddaacabbadacdbbaccddbdddccdadbcdaddbddbdaccdbccaabbddbacdcbadaaadaaadadcddababccdaccddaaabbcaabcbdbacabdaccabaabcdadaabbbdcdbaaaabaaadabbbbacaaaccdaaacdbbabdabcacbcdbababcdccaabcdaadbadcbbaadabcaacbdddbcabaaadcadcdccbdcddbcbddaddbcbdddccdddabdbabcdabdabcaacbddadbdcccbabcdcacddbcccbcdaabdabaddabbcdadaaccaabbbaacabcaabbacdbbabadcdcddaccdabadbdbdcdaaacabaadcabdbbbcdbcadcdbdcadababdbbabacbababaaaddabccdcbdabbdcaadabacccaabbcacbcbdcbacabbbabddaadcbdacccbcaacdbaacaadbdbbaacccadaaadcccbbbbdcbdabcccaddaadccabacaabcbbdbddcbbacdbbbcadbdccabdcabadbdbbcbcadbcbccbadbdbabdddabcdbabcaacdcbdcbcbcdadbaabcbcbadddbdacbacadddcbdacadcbadcdcbcccccddcbbbcdccadaaaadbddccbdbbbddbaabcbbacadcdacabcccdbbdacddcbbbcbcdbdbdcacbbddbacdabadaabbbcdbcaaabaabdcabccaadbadaacdbbbdcddccbbbbdcdcdbcabacbacddbbcbabcddabbacbadcacbccdadacaddbdbcdbbadcaacacddddcabcdadabdccaabddacacbabaabbbacdbccbabadacbdbddcbddbcddcccdabbbdbccbdadcaabbdbcbcdcddbadbaaccbaabccbdddcaadbcddbadbaacbbccababdcbbcbbccabdcdcadaaaaaabdcdcbdbbcbbaddacbcacbdbddbbcadbddcdbbacccdaaaabbbccacbabcaddddccdbabcbbaadcabcdccadccbcdaddcbdcabdbddaccaabaacdabbabcadcbdcdddbcdcaaccbdaaaddccbbcadcdbadddbacadabdcbcbacadbcccbbccdbacbaacbbbbcdbbddbdcdcabbabbdabaddcdadaaddbdbaacbadadbbcccacbcabbcdbbbdadcbccacdcaacdaaaaabbbbbacdbcadbbaaabdaadaaddccdabccbabbdacaddcaaccdbdcdccbdbadaaaadabaddbcbdcbadbdcddbdcabadadbcbaacbdacbcbadcacabaabadaaabbdcdaadcbbccbadcdddaaccddbbacbcddaadabdabbabcbbbcacddddbbbdcdababddcbbddbcdbaabbccadcdcadddbadcdbccbabbdcbdabbabaababbdbbbabbdbbbabaadbdadbdcadadbdaddbdbabcdcabbdbbddcddcbbcbdddddddddacdabacaddccdcabdbccdabddcacacaccdbacccbacaabddbbaccaadbaadcdaccdccdaadccacdbcddddcabcdabadccaaaaacbccbaacaababccaabdadacbaadadaddaadadbbbdbabadbcddbbcdccbbbbbbdccaacababadbadaadcbdcbacabcbaabdcdabdadccccdadddadcccacadbddcaacdbdbbbbdacdabacaadbabadbcbccdbcbbcabcdbcbadcababbaccacccbbcbcbbbccdcbbbaaacdbbbdbacbbccdbcddddbdcccddcdcdccddadbbbacbcdcacccddbaacdbcbccbabadcbabdacacbabbdadbaddcbdaacabbbcabacaabcaabcabdbccdbcaddccbdcccacaccbbbabaadcdcddaadaabbbcaccabaccddcdcdabadddddbdbcbcbcaacadbbdccbabacccaaababcdbcbbcdaddadcddbcccdddcaabbbbddaabbaadadcaaabdbcdadcdbdcdadcacabbcdbcdbdcabacadacbbababcaacbdacdddaddcbdbbabddadabbddddbadbddaacdacdadbabccacbdabcaaddaccabaddbaacdccacdaaadccbcabbccccdabbcbdcdabadbcbbdcadaabcdddadccdccadbdccdbdbddbddaddcbabbbddcdbcadbdcbccbdcddcdabcddcabdabacabbabbbbcaacdbadacacabcbddccbdddbccbabbacaaacdaccabadccbabccdacdcccabcacbdabbabcacdabdcabaabacccdbcbbdbbaddaaadddcbdccbcbbcddddaddcccddcdacdabcbdbabbbacccbcacdbbdcbdddaaabbcddcbbaadbbdddadabbbbbaadadacbbdacacdacdabcbcadaacbdccbcbaabcdacaadbaabdcbdaddbdaadadddbdbdcabdbadadddadddbcdcbabcdbcbbabaadaabadaadbbaabacacaacbbcadcdbddaabdacdcacbabacacbbcdbcccccbbaaabacbabdacbdbabdaacacababdcdaaabbcbadaadbcacabadbcaabdbcdccaacdbccbdbaaddcbbacdadddbbcbabaadcbdbbcdbdbbbadcbdaacbbbdaacbdaacbabbaaadbaaabbcbbbdacdaabdbbbcdcbbbbdbcbacaddddccbacccadbcdaddcacaadcdbbbcdbcdccbbdbbdacbcbcbcdbbdabcbacddbbdcbacaccdadddabbaaaabbbdcccdacbdddddcabcdcddddcdccddcbbddbbaacccbdccdcadacacacdaabbacccaacdabccdbdcdbdabdabbbccddadaccbabcddbcbbbacbddcbaccdaabcacdddadbdabacccdcbdadbcacddbbbccccbcaccdaccbcabdcbcaacabbcaabdbacbbcdadaddbddbacbbcccabbcbabbabaaabbdbadadcdadaddbabbdabcbccdcaccadcdbdadacbdbaaadddaabbdacbacbacdabbbdccbdbabddddadabdbcdbaccdbddcabaccaaaccbbcabaacddcdccdbcbcabcbcdbdaabaacaddadcababadbabcaabaddddaadaadcabaddbbcdccdbabbaaddacbcabbbacddcccccdcbdccabbdddabccdaaabaacdccadaabcabdccbccddccabcbdbabbacabccdaadddccdababbdbbdaabdcbabcbaadadbdccddccbdcdbadbdbdddaaacddbcabbbdbdbaabbacadcdddabaadcbaadddcaaabcbaacbabccadcaababacaadaaccddcdabdbdbbbdbcbcdabcccccbabcbbcbacbcacdabcaccbbacdbbbbadcbdabbbbdbaabbcddbbbadbbdacbddbcbcadddccacddbbdacbcbacabdcbabdcbaabbacdadaacabacdbdacdbdabdcccbdddbcdbbddcdbbbbcaabaddbdacccbcbddabcadbabbcadabacbcaaabaaacbadacaccdccaddcdbdcabbdacccacccaaabadbcdbdbbcacdccbdccaddaccbccadcbcdabdabadddbbddaaabdaddbabaaabbbddaddbaadcccdccadbbadbcadbddaaadcbbdadbbbbdabcccbbcadddccbabbabaaacdbbdddbcacaacacddbbdcbbcbcbadabcdaaacaabcbbcccbadbcdcdbcaabbddbaaddabadadadccdaaccbdbdbbcccdbbcacbcbacdcbdaacabdbadacdbaabaacababdcdbbcaacdaabcdcdcaccddaaddbcdbdddbaaddbdbdccddddacadddccabbabdcdddcabadacccdadbbabbddaadccabbddacdcbccaddbdaaccccadcdcaaccdaabbccdccdabbccccbbbbaababbacaaaabccddccdbdcacdbdccbbacaddbcbcbcdcdacdabbbddbcccddcdccddadbcbababbbcadaaacdbdaaabbbbbadcdaadaaababdaabbbabadcbdcaacacddccbcabcababcdadcbbaddcdcdaaabbdbbbdbbdaadbdbccaccdbdcdcabcdcdcccddbaaaabdbccbacdadaabbdadacdaabdcdcaadcdcddbcbdbcdbabcdaccddadabbcbbbbdaadabbdcbdccbdabbdbcabccbacddcbbaabcaabdbbdcbbacdbcdcbadccccbccbabaacbbbdcbcdcbaaaadcbcdcacaacdbbcdbabbcabdcabbbcdadcbdcbbabcaaaddddacbdbbdbcdbcbdcaccaddddbbdbdabdddbddabbaaddadaccabccbadbdcaaadabbbcbbdccbdbabcaacccaddaacdcdcdabcabcdacbcacacbdcabdbbaaabdaadddddbcabcbadcabcddbbcaadbdaddcbbcabbbbdbbdabddccabadcdabdcbbbddacaabbaabdbddbdcdcaddccdacbccdbbcbbdacdddddccdbbccddacbcdcdaacacbbabcdadaaaddabcacbadccbbcdcdabbacddabdbdbaddcadbbbbcdccaccccadcadcbaddcdbaabddcdccccdccbdacacbaaacacccccbccacbcabcaabddcccccaaacccadadbbcacdcbdddadabddcabdbbbcaccabdbdbdbaccaddcddcbdbcbdcdaddadaacccbdddbdbabbabccccdccbcdcdacdbacbccababcabdacbdcadddadddadcadddcdcbccdcbdbbbcacdaacbbaabcdbcbdbbcbabdababcaadccdbbdbcbdadddbbaacabbdadbbadadbbddaadbabaaaddddadbdcdcddcadadcbdadbbcaabdbdcbcabcdbbdabddabcabdcdbbacadcbdacccdbadaccdcccdcbbcababbaaacaaacbcbbcadacadddaddbdaddaaadacbcdaddbbbadcdabdaaabbcdcbdbcbccbcccabbccdbcdcdacccddbabdacaccabaabbdcaaaaccabdbcbcdccdaddcccacabbddccccadaabbcabacabdccbccdcbcddbabdcaacadcaabbcbdadaabcdaabbadcdbaacbbcbddaaddbdbcbcbbcbabbaabdbaacdcdbadcadbcdcdcadbccbdabdaaabdcbddaddccdaccbdadacabddcacababdcdbddcacadadcaadbcadbddddccddababdbadcdacadddcbacbcaacbacaacbcaaabdaccabbcadccdbdccddacdacdbbbbddccbcddcaacaaadadbbdaacacadacbcdccadcdaaccadcddbcabdbccddcbcabcbbbcddaddabbbdacbbccbbcdaddaacbbddccbcbccbabddacababacbdabbcbdbcccdbbcbbbcbdcccaacbddacdbdcdbbbdcabbcbaacddacabdabcdcdbdccdaacdadbabaabacccbaaccadbabcdddbcbabbcaadcbbbabcdcddadbcbcdbbbbcadadbaaadbdbdcabbbabaadddbddaccbcbaccdbacdbaadacdccabdabdacbabbbadcbbccddcdadacbcbbbabaddaadbdbcbadcabdaccadddbdabaddcacbcbdbbcbcdcbcdadbbcadbcabbadcdccacccccbdbbccaacdaacaaabddbdaabbbccabcbdacacbdabbadbdaccccabacdbbddbbaddaaacdabddcbcaaddabbbdabcbbdddbbcadacdbdaddbcbbcadcdbdbcddddbcbcdbbccaccdbdabbbabdcdccbddbdcacdbbadbabddcaacdccaaadadacbdbccbaacaccabaadadbabcdbbddcddccbbbccbbaadbaabacccbbdcacaccbbbddbaddcaacbaadccddbbdcbcaaadababcbaadccccbabbcbadbccdcddadccacaccddcabcdacdbadcaddcbddabadddbddcaadcddcaccccacaaabdddcadccddcbabbbdacacacddacbbcaaccdbabdaabbbdccadcadccdbadcdbccdbacccaabbccccacbbbcbcbacdbabbdbaddbaabbabddbbdddacadabbdcccdcccccbabbacadabacbbadacbacdcaaabcdbdccbcbdccacabacdadcaddcdccdccbccddcacbaddadbddbcbbcabaabacdaacbdaddbdbbccbaaccaddadadddcabadbabaacacbbacdcccdbbdcbdcbcbdcbadaaadbccacacbddaaaadbbcbdacddaddcadadadbbcbadbdccbbccbcaaadabddcbaaabddbbaabbabdaaaccadbacaddcdcdbcadbcaabcbdbdbdbadaddcddcdbbaaccacbadbacdaccbaabbcdbdadccbaadccbabbdcdcdbadcbbdddabbaabacacdccaabcbabdacbdddbaaccdbdaacdcdbabcbccaaadabcabcdaacbadaccbadadcadabacdcaccbddcdaadbcddbdbcacdadbbabddddaaacaadbcaccdbcbddacbaadabcbaaadbdbccdbbbabbadcbbbaddbaddcdccddbabdccacdbbabdabcacbadbcacabaadbbdddacadadcaddbdbaddbdaabdbdabcabacbbbcabcccbdcdcaacbcaaccdaadbaccdbbddcacaddcbacabbdcbcadcbcaacadaacbcdaabacadcaaddcdcbadaaacbdcbdabbdbdaadaddadabaabdbbbcabdcbdaaadabdbccacaaadbcbcdccabdabbdbaadcbdddaddcdadababaaddaaadaabdccbbababbaacdbaddaaaddddbaacbcaabaadbbbacbbcaacadaacbbcbccdbdcccdadbddcadddbaaccbdcacbddadadbadcdaabddcbbcdbdadcabaadaaabadccdaacdaaccbaccaddbcbcbdbbbdabbaabdbcdddacabdcdbcbcbbababcaabdccabadddbabddbccccbcdcddbaaadaabaacddccaadcbcbdbadbbcbaabaccbddbbdcbbadbdbabbbddcdddadbbbbababcacbacddadbbcaadadbbbdbddaacbddbcaaddccbdddbddcdbbdcbddbcbcabdacaccaddabccdaccdacadbbbaabcccbcdcbacbacbcddbcbaadadddcbdbdadccbacadacaadbbbcbcaabacdbcbbaabdcbabdabbbdcbaacadcbcadcbdbbbcdddccccaabcdbddadabcbbdbaabdccadadbccbdcadcbdabcbcabcbdaaccdabbacbddccbdabdaadbdaddabcccbbdbabccccbcacbbbaaaacdbdccddadddabbcbbacdccbcabadcacccdddadcdbbbccaaccacdccdccbdcacdaabbdabaadaadacbdadacdbacabbbdcbaacbdcbcadacacaabcddcdbaaaaabaccdbacacdbaddaabbadbabacaaabbcacdcdaacbbcacadcaaccddcbbabaacbcacdddddcddbaacddaacbddcbcccdbbadadadcdacbdcdababdaabccbbdcdddbadbabacadcddaddcdccbabdcaaabadbcdcddbddaabadacadcddbddaddacbabdbcbaaddabcccabccdaaadbbdbcaaabaccdadaabbdacbddcdccacadaabddbdddcddddbdababdcaddbcbbbaaccbbddccabbdbbdbaaaddbcdaaacbccccdccabdcbdcdacccbdcdcacabbccadbbbcccbaddcadbcbcddbabbacdcddadcacadadacdddbaacbcccabaaabcbcbbdaaddcaadbcaaacccbbabdbdddabcaacdbcdbcaaacdcadbdbdcabbdaaddbbabcdacaacdbccaaacadaddbddcaccbcdaababbccdbdcddbcccbbbccababacddadcbddddbdcbcddcdbbcacbbcadcadbdabcdcddaaddccddcaabbccaabcdbbbdddccbccbaccbadaaacdcbabbbbacdcccabdacabdbcbcadaababddcbcbcdcbcdddbcbccccdbddadbacbbbabccadabbdbdbbcacdabbdaabdddddabccbaddbbbdcaddabacaddadddaaadaaacbbacadcadacdbbbbcaaabcccddddbcbcdadbbcbadcdabcbccadabaabddcabacdaaaccbaabacacdccbcadcacbbbcadcbcabadbaddbaabbdacbbddcbbddbcccacdbacbbaacdcdcbbabdddabccdbcdcbbbbbbcddbaaccdcbabdababcaccbbaadccbacaabbcddbdcbbabbcbccbccdacbcdcdabcbbcdccaacbdbbabacdacabbadaaddccabcabdcacbdbbbaddacacacbdcbaaabcbcddddcadbaacbdddaabccbdbacbaddbbcbbaaacaaabbacddaaadbacabbcdbbdbbdacaacdabdbbbccbbddbddbaabababacddccccbaaabbdbdbcadababcdccacacaacbbdcacccdcacbbacdbccccadcdacdbdbcbbdabaabcccbdbdbdcbdbbdbdbdabccbdabcabacadabadbdcccacababdbccababadcdabadbbddbbacabddcabbdadbbcddbabbbcadaaadcdcdcaadddbabcaabcabcbbbdddbacddadaccbccdcccaadcbcdbcacccaccbbddbdabbbcaabdbcbddbdbccbdaaacacabdadadbcdcdbaddcbcaaacbbbababcabaadcbadacccdabadadcbcbdccaaabacbbcdcacddcacccddabbcdabadccaaccdddbaacdaadbdabaddcadaaaaadccbaaaaabcadacdacdcdadbdcdaabdbdcccbbcdcaaacacbbbdbbcaabbbccbcbaaaccdcccdbbcdabbbaadbadadaaabdccacccbdcccdcbdcddccccbdaaacbcdaaacdbcabccbbcbabcaddddaacdcabdbcabbadcbbccaccadbcdbcabbcadacccaaacddadbadccacaacdabdcbcaacbbbacbcdabbbdcaccdcdabcddddabcaddbdccbabdcbcadbbcccabacabdabbadbbdcccaccacddcdcdbbbacdddcdabaaabcbacdcccabbccbadaaddccbbdddabccdaadadcccbaddccbbaabbddaadcdbdccddbbbcabdacabdcdbbddccabccdcaaaadbccddcacdbaabbdabbbcadaccbddaaccadbcdacaabacaacbbcdcdabccbacdbbdcabbccaadacdcabddcababacdadcccddcccdbbcabdccccaabdbacadccbadaacbacaaadabbbdadbbbbbbdcacccddbadbdcaddbddacaccdcadbccbacacddbddacaacbadcaadcaadcbaacdddacdbcaccdbdaababbcbcbbdbddcaaadccdcacaddcadbdcdcbcaacabbcaccaccddcaddbbbbacdbcadadbbcbcadbbbbaadbaadbbdbabbbdcbbdcacddabbdcbaadbbcacdbcacdcddababbaacbccccddbcabbccadbbbababbbdccaaaaacddbccbbccacdcacbacddcaddaadababacddadbacbadcbbbbabccbdabcccbbbaacdcbcacdbdabdbbabbcbbccadaadccaaccccdbabdcdcdaaddabcdabadcadcabcbbbcaaaccadbddcbddcabdcbbaabdbacbbdddcbbcbccbdcbbcaacbdababdccbddcccacdbdaddcbbabacbabbcccdaacbbadbbcdccaadcdbaabacbcdcbcdcacddcccabdaccccbabdddbbcdaddcababbbdbbadcacbdbdbddcaccbdbbabcbdbbbbacabbcdbbdcaacddcdcbbcccbabadbcdacdbccccbabbcacbdbacbbcddabadbdbbabcdbdbdbbcdacbdbbdacddcacadcababccaddbddbddaaaddcadabaccbaddcdcdacdcbcddbcbcadddcbdbcdccabdcdbaddcdcdbabaacbdbcdcdddbcdbaaabacbadbdcddbaddbcabbaccdadcbdbdabccdadddbabaccddccbcabbcdadbaacdbbdadbaadcaaaadbbdbacadacadbabdddbdcbbcadadcdddbbdcbdbdbacbabadddacdbbbcadbdacbdbbdabcaabbadccbdacdcbdcbaadadbdcdaaaddbccbbabdbaaaccddbdcdcaaaccbbdddaabdcdcdbdbdbcabaaacaddbbbbbcbaabdaaabcacdbcabcbbacdadcddddcbcadcccbdcbbcddcbabaadddcdaaacbbaacaacacbbdccdacabdcaddbcabdbdabaacddbcacaaadbbdcbbcdaddcddcdcacddcadcacbacbbcbaaadadbbbdcabdbacacdaccbbddbaaabaabdacacbcdcdddabccadcdbdbdbdababacbcadddddddcaaabadbaddaaddacbaccbddccddbabdbcdcdcaaaaacddcabcbdcddbacccbaddbdddbbacddacadcbbbddbcacdadbbbccaaabacbbbcabcadaabbbbdcaacaabacdabddbacdadadacacadbaddaadcddcbdcddbbbbacaccabbaaacdcbddcdacacddcdbddcccbdbccdabcaaacadadcdcacabbdcdbaababdbcbdabcbdbdcdabbacaacbacdbadadacacabaacdbdccdcddabbacbbbcabccbddcaabaaabcabccadacaacbcabccacccbbaccddabaddbcadbbcbdbbaadddadbacdabdbbcdcdbdaccacbbddcabdadaaaabbddbcdcabddccacdacccbcbaddabdbcdacbbdbcdabaacbbbdaddabdcadcbacdadaaabddbaddcabcbabddbdacbddbbbddadbccbcbadccbabddbdadcbadbbadadabddadcdbcbbcabcaadcabddbaccbadcbabcacabcccbccdcbbacdadbdcbdbcbaabccacbbbbbddcacaabaaabbbdaadbbdaadcdcbabddadbdababccbadabababcacdbbbdcacccdadccddadadbdccabcccabbacadccaaabbcbdbacddbdcdcbdaaaccdbaadaadbcbdbacdddacddddbcbbbbddbaddcabcdcbaaabdcbccaabdbbbbabbacdbdaacadcadaacacdadcbcacdadaaaaabaaaccbacbbaabdaabbcbbacacccacdbdbddddadabdacccbdbbbadcdcdacabbcdddacbcbabadbbccdcadccaadcadaabbbbbcdadcbbddbacbccbbdadbbadaccccaababcdcacbaaaabaabbbaacabbbadbcbdcbbadddbdbdbbbbdbcdadacadabadcaddcaadadcdcdcbcbcdaddccdacdacabadddabdbcbbcbbbacacdbadbcbbdaacbabdbcacbddbcccbbdcbbdbdcdddcbbdaabacdcadaabcaaacdaacdaabdccddabbbddbdbccacadbacaddddcaaddcacacadabacbcbddabccbaaaacccabdacbbaadadccddbabcdaaddbacdadbbccabcbdddbbcbaabdaccabdbcdadcaabcbbabcdbdaaacbbaacbacbcbcdbabddddcaaaaadbcacabdccccaadbdabccaabccaacbcaabbccdcbdaaacaccbbbdbddcabaaccbddaccbadddbcbacbdcdbdcaddbdabdbbadadcbacadbdddbdbacacdbacdbcdbbdaabdaadccbadbbbddddddabcbdcdccbaabcbdbcadbdaacdbaddddaabdbccdcbbbdcddddaabadbcbaacbbbcdcdbdcbdcccdcdddcaadabbaaabdbbcbacaaaaaaccbadbbabbdabdccbbbccadbccdddadcdccaccddaddbacaabaaaddccccdacccadbbbcbbcdccbddadbddcacadbbcbbabbbaabccbbabdbaddcaabddccbcbbcbcacdbbabbbcabbcdcbbbaadbdddccaabdbbbbbcbcbadabbdbdcdaadbddddaaabaadaadcdcadcdcdcdbadadaccadaadddbbbdcbbcbabaaccbddabcdcccdccbbacdbdabddadabccbacadcacabadcdadbcadabccdbcacbbdaddaaddaabcdabdcabdacadcbadadddbbccbabacbdabbcabccbbaadadbdbcdddaabdacacabbabadaaddbadcbbbbbdabbdacdaabaaacbcdbcbbdbbbadbaccccdbcdaabbbaddccbbacdcadcbacbaacdbbbbacdddbbbcacaddddabcaaadcababbcddbdadcabdaaacabaabbcacaabbcddacaddaadbadacbbbcdcabadccdddbadaddcbddbdbaacdddbdbddacbccdbabdadcbaadcdbaaadbaaccbcaccbbbcccadbacbdbadbcbadccddcccbacdabbadaadddadbcbccbcabdbabbabdacadcdacdddbcdcbabcaddcdcdccaccccccbcdddaabcbacdaababcbadaccacbcabcbabdddbdbadcbccdacdaaddbbbcadadbbaabbbddacabacbdccdbbcccaaadcbdbcbabcdbcbabdcbadcdacccaacabbbbbadcaccbbdbdacdcdddaacadacdbcdbdbccdcbbbbdcaabdcdaaadacdbbadabacdbcabbdaaaacbdbaabacdcddaccadbabddbccccdccacdbccacababdbddaddcadbcadaadcaaaacadbbaacdccddaccaddbabbcbcababddcdaddbabdcabdbbddcbbacdabadbcdbadddaadcbcacddbabaacacbcaadcaccdabdacccdbabcccabbdbccdbbbbadacbdacbbddbdcadaccdaabadcbaccadacbcdbcdcdbdabbdcbcccdbdaaacdbcdcacdcdccbbaaccdcacadabcbbdcbcbdcacbddbdbcabcdaabbdabcacbdaddabaadccdadddddddacadcadaddbcabdbabbaaaaabbaddcddcddcccbaddbbddcbbddabbcdbddaadadacaccadcdddadbdabbbadbbcbcaacbcbcdccddabdccbbbacacbdbccaaddbabbdabcccddbbabddccdaccdccbbccdcacabacdacbaddaacddddacabaabbdddbcddadadabdcabbdaddcbabdacbadbcddddddabdbbbbaadddbdcdbdcbbacccaadaadcccbddbbbdbcaabddadadaddddadddbacdbbaabbbdbbdddcadadcabcbbabdbbdabacbdcbadaaadaacccaddacadbdbbccbdbcbadcbcaacdcbacadcdcddabbddaabaabaaaccabbbdabdccacbbdabbaccabdbcdddacdbdbbaacbabadaccbcbabdcdddbbdcdacccbddcccccdababbcbdbacaddaccaabdcdccadbccabcbdcdbabcaadbbadaacdabacddadcaacadcdadcabbdccadcdaabcbdcabddcbcbccbbabdddcbaddbdccdbbbbdcabbdabbdaccdcaaacccbdbccaabdacdbdbddbabaacadccbbccdcabcaacbbcbacdcccbaadaaadbcbbcbaacdbcddbacbacbdcddbddacddbccdddacabdbbabcdcdaabddcacdcbadcaabccadbadabdcdadbbaadaadabcccacacadcbdaacabddacbdadcdbbaaabcbabbdacaaddaaccbadaaddbadccccdaaccbbddbcbdaabddddaadcbcbccacccdccdcabadcbabacdbbcbacbddcabcbadcbacbadcdcaadcbbacbcbbbcbababdbaccbcccccdddabacaddddbccdbbaaabcbdcdbadddcaadccdcdbcacbacabddbabdcaadadbccaddabadacdbbadcdbbbbdccdcdadddcbccadccaadaacbdbabccadbbbdbdbdabdbabbcaabacbcdaabcaaccbadcbbcddcabbbcdadbaaacbddabdcacabdadcddddbccddaabccbcacccaaaabaacdabbcbaccbdabbacbbbcdbbcbcdbbdbccadabccccbbdbcaaaabaaaaabbcaaccaaadcabcbabbbabcacdacaabbcbacabbcdadaacccbdddcbddcabcabbcdcabaccacadaaaacdabcdbdbcadbcacccadcbccbcdbbcdcbbccbdcbcdabdadcbcdadcaadbccaabadadbbcdcbcccddccaacdcdbdbacaadbbdbabdbdbcbbdadabaabcbbacdababdabaccbbdbdadadabbdcccdbbbbcaccdcbcbddccaaadcaabcbcdbdbcbcbdaddacbddbbbccadaaaccdbbcddbccacccdbadaaacaccddabbbddabbccbcabbcdcddcbcbdaabcaacddbaddddcbbbddadadcbdbabaccbbccbbacddcbbaddcbdabdbcdbdbcaaddbacaabbcdaacbccddccbaaddbaabcaadbbdadbbcadbbbcddccbacadbaddbbdadadcadcddddbcacccddccddbcbacbdbdacddadcdbdbccacabbccdaccaacbbbaccaaaabcdaaaddcdccdbcbddaacdbccdcaabbcccadadccdccadbcaddaccbbccdbdcabdcccbbcddddcdbbbcaddbbcabbbbcaccaabcdddccbcdccbbcabccbbbcdbdcccacbcdadadddabdcadbdaccabccdddbdbbdabadcadaccdbcdaaacdbccbadcadddbcbdcadcdbdcacbdbadcadcdcabcbdccdaadbcddddddcbbcbdddbcadcdbdddadccdcdbdddcbcdaccbccaccaaacbadcbdaddbbabbacadaaaabccccbbccbdcddcdddacaccdcddaadbddabcabccbaddcbdcbbccbadbdcdcbcdcddcdbbdbccbddccbbabcddbbaddaacabbdbbbcbdddbdcadaccddbdcbccbcbbcbdabbbcbbbbabababcabdaadcbcccacccabcbbbaaddcdcabddcdadcdbdaddacccbabaacbcdcabdbaaaddbcccabddaddbdadabaacdaaabbdaabaacdcdaccdaccacadbadbbcacbccbcaaaadcabdaabbcadaabbadaabaabaacacabacdbccadacbccaadaabcadbbdcadcbdbaabaabdcaababadddccdbbddddacdcdddbbadacabbcaaccbcdddbccabcbdddcbcddcbaaacdbbadbcbbcbacacadcbcdbaacbcdcdccdbdbabcaaabaaddacabaabbbbdadadcadcdcaccdadbaabbbabbbacccbabbdcbdcdaccbaaddbbacacabbaddbabcbbbdccbaaacdaddccbbbdabaadbbaadcdacccbdaccbcddcbddddbddacbdcdacaabaaadadbdabacbddbdbbbcaccbacabddbccdddccbbbbbabdccdddaccbbbadbabbbdaacaabddbaddddabddbbaabdcbcabcdabdaadabacbbcababbabcbacabbcdaddcadbccddcbabcacacbbcbbcaababbdaabacbbaaaccccadddbdaacdabbcbddcccbabcaaabaadcabbcadcabdbddbcdabbabcacdcababdaabadbaabccccbbdadcbacaccdabcaddaadbadabdccabbbcabcddacdcaadddccddccaacdddddcacabbcdabacddbcaccababbbdbabcbbaaddbccccbaccadaaadcdaaababdbcbcddbbdaabbdcdaabbcacababccaabccabbcddabadccdbdddccadbcbdbacbccacbcbbbcddabcdbbccddadcdddbdacdddbdcacacbbdcaaaababcdbacddddacddcbddccaacacacaabccadadbcdabdcdbdcbddbdbbdadcbdacadaccbbadcadddcdbcdccbbbbbdabddbcabdadddabaacbbdacbcbdbdddccddccbaaccbcaadcddddccbdddbbcaabbbccddadcabaaccbcbcacacdbdacbaddcdcaddddccdcbabacbaabdcbcbbcaacbdadcdbcdbcbcbdccdcdcaccdcbcacabdcaaaacbbaadcdacaaaadbabcbaaabcdbdddcbccbcdbdccaddddbadcbcdcccbaaccddaacacdcbdbcaddaadabcdacbccbdcaddaaaaaddddcddcacdabccddabadacadbaabdcbabaacbdbabcbabbbaaccdababadadcaabddacadcbcbccdbddbddacdacaddcccbcaddabaacccdcdcacaaccaccabaaccbbccaacbbcacbbdccccddcadacbbdddaacdddbbccdddbcddddbccdbcdbdcccabddbbcabcbcdcdacccbadcbbaccaccbabdcacdcbadbccbcbccccbaadcccdccbbcabcbcdcbccbdcccbcbbdbcabbdaacbcacbabbacbbdbdbbaacdbdbbaadaaacccdaadccaaabbcabbcdcddbdccaaadbdabdadadabaaabbdbadaaaabbcaabbcccaabccaddaddbaaadcadbdbdaddcddbdaddaabddbdbcabdcbaabdbddcbaccdacadababdcaabbadcbcaaabcaadaddbcaadbcdcdabaccccacdacdadddaabdbccdbbdbbabdacccdabadbdcddbddbcadbaadccccdacbabcbcbbadaccccbcbccbddbddaacbacbbacbaccadabaddbccaabbdddaccbdcbdaabdcddaacabddabaabdbdbcdaaabcbcbadbbabddcdcbcdbabdbaabdddbcbabbaddabbaaccabdbaabcaddddddccbdaaacacabcbbacabaadadaacdcbacbcccaddaabcdaddacadbcdbbaccdaadddabdbaaaadbcabbddbabddbccbcaccdcdbdcdbcbaccbadccddddbdcbdabcddccacaccddadbabdcddacaadbbabdacdddbddaadaccaaadcdacdadbcdcbdbacdccddaddbdcdcabacdcddddbbbadacaabdaccbacaaaadadccabcdbdcaddcdacacbadaacccddabcdcadbabaaccdcbbbdbccdbccadbbcaadbcddaacbcbbdddcaadcccdccbbaccacbacbdcabdcabcaabadaddbacdadccadacaaacddcccbbbcbcbcddbdbacddcbcbaaaaddcbaaaacacbcccdddadbcbcbccacbcacadbdcdcabddacadbaabcbabaabbabaaaddbcadccbbbdcbcbbadccbbbaacacbdddacbacaacbddaadddcdabbcccdbabacdadcbbabcccdacddcbbdadaabbacdbccadbcbbbccddcabdcbccbbddcbaccddaccbadbccaccabcccccdcaadbdccdcdadcdbcacddbdbcaadaaabdcddbbcadbbdbbccaaadbdbdbdcccaccbbdcadcbaaddbacdccdacabbaccdbcadbbadbcddcaabbcbcbacadaacbaaabacdccadccbddddcacdbbdcbdaaaacdabaadadbbddcdcadacdbbddddaddbbaddcadcdcddbccbdbddadddcadabdadbacbacaddbbcbacbacdacadbcbbdbbcbbdcabdbcdcdaabacaaaadcbaadcddaaadbbadadbaddcadcaacbccbcbdbdcadcbcbbbbaabcbcbdaccdcbbbdbbcadcabaddbddbababcdddccdbbbccaabcdbcdcdcbccaaabbdbbcbcbddbcdddccbbbbccbccbbdbadbadbadcbbbcbccbddabcabcdaccacadababddcccacdacddbbcaaccbabaccbbadaccababdcdacddaacadcbdcccaacbdcdadbbbadbcbdaccbddbbdcbaddccbddadddbbabaaacdbcbdbadaaddcdbcacccdabacbaacabbcbccadcbddbaabacbaddcbacbdcdcacabcaaccdacdbabddbbdcbbccbbacadbdccccabdbbccbdbadccdcbbbcdaacdabcbadaadaabccccdccaddbadaddcabbabbdcccccdabdddaaddccbcdbbdabdbdbcbbddadcbbbccdbabcabdbdbacaaddcbacdcdcadacadaddddcbdaddbddabcdaaccaccbacdbbccdccbadcaaaccbaadaccacacbddccadbbbdbdbbcacbdabdccdbddcbabaaaaddadbacaccdccdccbaadadbaaacadabbddabdcbcbcaadccdadacbcabbacdcbcaaaababddcadcbadcabdbabbdadbbcbcdbaacaabcdcabcccdcddcdacbdbacdaddbccbddbbbbcbdbdcccdadcdcdaacdbabbcbdbdaccadbddaacaaabdbadbdbdaaacabdadbdabcbdbcbbcddbcbcbacccbaadcbdacdcbdaaadadbcddcaddccbaddcdaccbbbdbdbcabbadbcdbabbddcadddccdccbdbbcaccacbccccbacbacdcbaaaadbabddadccdabaaadbcddaacdcdcbcbaaaacbabadcbbcaadbbcaaccdbbbdaddbdacbbbddacdabbaabaaccddccbdabdacacbccacdccbdbaddabccbacbbbbbddabbacbdbbbcaccaaddcabaaddcbbdaccdcacdacbcacdbbbbbdcbbdbaabdbbbbdcaaaabaccaddabcdabbdacabccdabddbbaadcaacabcbcaaddccbdbbccbdddcaccbabdccdccaddbccbcdbdddbcddbcbbadbbcabaadacccbacbbbabddddabbcacdcccbaadbcbcbdcadbcbdccbadadcaaaacadbbadddbccaacbccbdbababdadbbcaaacccdbcabcbacbccddcdababddccdbadaddcbcbadabdaddbdbdbdbadcabdddaabaddaadbdacacccddcdaaccccaaacbddbaabddbcdbbdbccbcdbdbcccabcbbbbaadbccdbcbbbabbcdcdaaacabccdcadaabcbbddcdadccbcbcbbacbadadbbbcdcaddbcbcddbaddaaabccbdbdcbdbbabddabbacccabdacaccbccaacdbcdcdcbadcbaaacdbdacdbacadcbbdcdadbbacaaadcaaadabbaababcdcaaabccdbcabacadbbddcdadbccbacdbabcddcaabdddbcbccdcdbbdcdcddcaaabdccccccccdadcdcbddcdddcdbabdabcdcdbbaccbddcbbbcdbabaabdbdbbdadccbcdbaaacbdccacbdcccaacdcdadbdccaccbbdadddddcaadbddbbbbadcadcbcbbbbdbdcbabbdbacbccaaddadbcabdbcccadcddacacccbbddabcbacaadbddbbccabadaadbcabacdddbdadbaacbbbacbccdccabacbccccddcbbcaccdbccabdadbccbaabccbcbdcbacabcbaccbaabacdadddcadcbcbacbcbdcdcacbdacacdadaaaddacbbbdcbbccddbdbcbcdcddabdabcdcadadbadccabdcdbdaaabccadaccaadadabadaadabdabdcaaddbbcdaccccbdbddabccbabacdbdddbdaaddcaccdabcdacadcbdaabdabcccdcaacbcbcdcbaabaadabbcadcadddacdddbbaaabaaccdcdcbacdacdcdcbaaacacbaccdccabcbcbcbdddbddcadcbccaabcadcaadcadddabdcbbcabaadbbcacbddaccbadcdaadcbbbccdcbadaadbccbdcdbacaddbabcbcbcbacadccdcdadacacabaabdddcaadacaaabbdaadaaadadbabdacdaabcaaaddcbddcaadddabcdaaccbbbdbdcdabcbcdaddddabdaccbcaccbacacacdcaadaaccbaaaabcabdbbdaacbcdbcdbababdccbddcababadcaacabdddacdcdadbbdbcbcacbbbccdaaacdddccdadadabdcbabcddcbcadaacdbaaadaaddacaaacdabdcdaaddadccadcbbbbccbbbbcbddcbdcbccbaadbacbcadbaccbbdacabacdabbadcdcbcaccaadcdaaddadddbccabbbabdcbabbbacadddcdbcbacabcbacaacdcaabdbadacbbdacabacabccabbaccbcacaaccddbaccbddaccbdcdadbacadabbacdccabaaabaabaadcdcdccadccacdabdbbcaacbdaaabccadcdabcacbcaacbcdbadbbcacdadaabbacbdbbcabccddbccbcbdcadaaadbaaadabdbabdadcacadccbdcddcdbabdddacadcbddddbcaddacdabdbabddddaabbbabccbcddaddcccdabbadccdbabccababacbddcdbdcddcdcababccaadbaccbcbbddccbdcdaccbbddccdbbcbaaaaccdcccccdcdddbcbbabcabcaaddabdcbbadccbadbcadaaabcaadbbdddabacbabacaaaddaadadabbbcdcdcdbbaabcabaaadbdacacbdbbabbabcdcaadcaabcbcaacbcbbabbbaacabddaaccbacddccadbbbadddcddbcaaddabadbcdbdcbbadddbbdcccddbaaaddaadaadcdbdddbddcacddbccbdaccdcaaaabaaaddaabddaccccaabcdcbbbadcadbdaaddabbcdcddccabaddbaccdadbabcadbdaadacbadadadddbbbdccdbaacacdacaadabaabaaabdaaacdcaaddccadccccabddabbbcacbadabcbcdbdbdccabdadcdaacaadaabbadaaccbaadbcadcdacbbadcbbdbdabdaacabdbaabcbdcaccdcdaaadbadcdadacdadbbccabdcbadddabcdcabbaacaaaadccacbcdcbaccccacbdddddabadcaddcadababcbdcddabccbbcadcacbbdbbbcccdacbadaaabcabaaaadadadaaaccadccbbacacddcdadbabccaabcaaadaccbbbbdaacbbabbcabbabccddacabcabdbacccabbababbdbccbbcadaddbbacaccdcbdbbacbbbaabdbbacbddbdddbbabcbacbcacccbbacaabdbaadddbaaccaabcbbcddbcccaccbabbcabacccdbdbbbcdddbbdbaaccbddbbdaacbbdcbaaabaddcdbbdbbaadcacccdaabbadcadbaaccadaaaacbaadadbadbdcbabccdaaabcadbbdacdcbbaaaaaccdddabbcabccacacddbbbcdcbdbdccbdaadaaaccadbbbbbdddbcdbcdcbbcbccbdbbccabbcbadbacddaddcacaddddabadcabdbbabbcadbcbdcbadddadadbcadaaabccaccdcacbddadabddbddbdbcaacabcdbcbdcccaabaadcdccdcdcbcacdbcdccdbdbaaccdcdcccbbdbaabcdccccdccbbaddbbabbacbdcbcabdccdaacccaadddcadbabcabdaabbbdddddacbbdbaaccbcbaccaadcbcccccbaadcccdbdadaccaacdaacacbaadbaddadcdbcbcddacacadbcadadabaacdaddaadbccddbbadcbbddcabdbbcacbccdbddccdcaabaaadcbaadccddaaddaacccddcbbcddbaaacbdddaaadbdaccbaddadaacacababccdbdccdaababcdaccdaaaacadaccbadbdbbabaaacbbcaacbdbdcacabddbdababadcaddabbbbdddbbccdbcabccaacbabdcccacaabbacbcdddddbacacacccccddbaacabcddddabcabaadcadabbcbccabaccbdcdbdbbaddadbbcabbdcacababcabbaacaadacdaadccaccaccdbccdacddbcdddcbdbbbcdcdddccbaadabdcbdbbacbabbddbaaaadbadcaccbddacdcaabaaaaaaaacdcbddabadadcdacdccbcddbaccabacaccbdbabcccacbdacbddcaaddbcbabbbbccdcccdcddbcbbcccbcbbcdbabbcbbdbdcacdcdbacbcccbbbcbccadabbcbadbdbacdadabdcccdcadddaddddcbdaacadbdbbaaababbbbabdaabbcbabacbdbddbbdabddccccbbdcccdcabccddcbccacbcaddabdaccdcaacdcadcaaddacccaaacabaaccaaadaccdcaaaacbacdabdcccbdbbbccbadacadaccdacbcadcaccacababdcaaaabadcbaaddadaabcdbccbababdacaccdadcbcdddccddccdbcbabbcdcbcdddbbbabcbcdcacbdcbdcacccacbdacbbdcacbadabbaccabccbbdcbbcbaabbbadcbbdadcbdbbabbddccadabacbdbdbadccdbccdbbbbbabbdccbcabcaaddcdbbdddbaacbccaabdccadadcccbcccbddadccaccdabdbbbcbbcadbbccddabaaccccbacdcbdbdabbdaacbcdcdbadcacbdbadacdaacdadabaccadaadbbdacccbdccddbcbccacaddcdcdbbbbabddaabcbbacaddaaadaaacdadbdaaabdbababcdadcbcdddcacaddbaaddbbdbcbdabcdddddbdcbbbbdadaabadadaaadbdddbaadccbdaabbaadcdddbcbdbadadcbdbcdccbbbcbddadadaabdabbdccbbcdbcbbaaabacaadadcbcddbabbcdccccdddabcccadbbacadbcababbdcdadabadbccabcccdcacbbaabccbdcdbdbddcbbdbcdaccdbbacbacabbdaaabacbacbaaddcccccbaabaacdbbaabdabdcdcacdcdacabcdbacdbbcbbbcababadccbabcccccbcbccbcdcbbaacadcacbcbbbdbddcbbcbddcccccacabdbcbdcabcccdccbccbacbbababacbaacccddabaccbdbdaddcabbbadbbcdcacabbbaaaccabbbccadbdacccaabbccdcacacdbcadacabcdcbbdbbdaaddaaacaaabcdbcdabcaccdadbbacdddacdcacdacbcbbacbadbcaabddbcbbcbcaacbabdacccbaadbdbdacbbbabdaddaabadbddcccdaaddbabbbddbdaccacbbbbddddddcdacadbcadaddaddbadcbcaadcbcaacbaccbabdbdaadcdcbddbbdbacaadcdaacdaddaaaabbcdbdcaccbbcddacdbadbddcdccadccbadaadbaabcdbabbabbbdccabbdaccccbcbaaddbadddccaccddaabbaccdbcddcbbaccabcdbaddaccacddcbbbdaabcbdacbcdabdcaabcdadbbbcabacbcbcdadcbdaadcccbbacacbdabadccaaccbbbddbaccdadbbdaacaaaccdaacbcdccdcdcdbaaddacbcaadbadcddbadbaddddbbbacbacdbacdcdaadbdadccddaabbbbcdbbddcdbbcdaccdbddbbdbdcaacadaaabdacdddddcdbcabdbdaadcabcdcccccbaaaccabbddabccdcbabbbdbadbbaacacdbcabbcaabcbcdcdadccbadbdbbdcbcdcdccdababdddddcccbcaaaabbddaacbbbcaabbbdcbbdbddddcdcbadcbccbcccabacdbacaabcdcacadbadcbcdcaccacdaaabbccdaaadacbdbbbacacbccdbbbaddabbaadcbcdadcdabcacbdbadbadabddbdabaadacdcdbcaacdcbbdccaaacdcadbaacdbbaddabbadbdbcbabdccaabdccddbcadcaabacbbbccaadaccdabccbadcdccbbcbbccacdacacbabaacaaabdbddccdcbdddacdcacddcdbdacaadacbbdddcadabdabbdabaccccdbbdadcbbacbacdaacdcccadadcadacaaadddaddaccdbcaabdcbaddcddddcdbcdadbbddabcbbdbabdbcdcdcbcccbddbdacbbbbddccdcbcabaadbabacdcbabaabaacdcccbbabbabdabadcbcacddacbcdbdcdcacbbdddaadcbdcadbdcacbcbcabaacdbbadddaccbabdcdcadccbabcdcbddabbbaaadbdbbaabdacdcaacadacbddbabbabbcbdddbdacaddbcbbccdbadddcdbadbadbccbbbcacabbcdcadadbacacabbddacaaddbbdcbbddbadcdcdabdbaccdbdbdcbddcabababdcacbbccddddcdcdacdabcabcddcadcbaabbbbdddaabbaaccaddbcdcbbdcbcdddbabdbabccabaccddbbddbadbdbdbcbabaddadcdbacddbabdabbdabaabcbcabbdbcaddbcbbcbcbbbaadbbbcaacaacbaaaaababbabbcdbdcbcddcabdbcbaacbbacdacacaabcaadbdbadaadcbabddbcdcdaacbacbbbaabddbddbbdcdccbdccaabcccababaccacccabdaabbdddcacddacaddaadbdcdddcadadbdabaaacbbbcabcbbbbccadddaaaadbdadcbadacccaccdbddbadcaaccabccbcdacbdcadbacbddbbdbcdaabdabcbdccccaaaabbcdaaddcddbdcbdcdadbdcccdadaaabbddbabdcabbbcdbcbdacbcdacadcdbbbdabdcdacaabcdcbaacccddbbcdbbaccbdddcbacccdcdbaddcbabdaddabdaacaccdcddccbbdacbbbaaaddabcdcabacdcccabdbdbdcbaabbbddabacbdbaccaadccdcbbccbacddbcdbaacabcbbdbacbdbcccdccbaacbcabbccdaaadbdbdacccdacbddcacbcbcdcccbddcddaababacbbabddacdabddacbdadabadcbadccddbbddcccdacbabdcacdcdacddabaaccbcdddaabcbbbcccddbcabccccdddbcaadaddcaadaccaddcdbdadabcbbcbaaccadcabcbadadcacdcaaaabdadcdaccddccadaacccbdbbccadbcbbadadcacccddbccbbddabdbabbbbbbcdadbcacaaacddcbcacbdcbccabccaaaccbabaccacaddadabdccdaacccbaaccbadbcababbaaacadacbbbcbbbcbccaaaabadabaabbacbcaacccbcdaaacaacdddbcaabaadcbdcddacdbadcbdbcacbbcbcccbcaacbdaadbdaabbdbccdcccbcbddbccbabcadaacaacbadcccdcccbbbaaddbcbccdbcddaacbaddbadbaaddbaacdcdddbadbcaadddbbdbddaddbbdabbacbabccbbbacaccbdcccdcdcabbccdbdcdcaddbbdcdaddbdcbdabbcaabbbbadbacacaacdcabdbdabdbcbdcccbccacdbcbaaacdbcdbddcbaaccadcbbbcbbbbbddabbdabdcacaacbdcbcddaacbbacabdbcbabcbadbbadcbbcabaccccabbcbdcdccbcabdabcbdcbbbdccaaddaddccaabcdaccabccadabbbcaaaacdccaaddcbbdbccbbcbbadcaaabadadcbcdbcbdbddddabcdadcbacdbbaddbabdddbddabcdaaccccabbdbbcdacbbabdddbbbdddbdbbcbdbababbcbdcdabbdacaaccddaabdaadbbddacbbababdabbdcacbbccddaaaadcbcbbcbbdcbabcbcadcaaaccabcbbbbdbbbcbdccddcbbaaabccbbbddcbaddbbacddacbccbdcaabadbbaddbbdddcdbabccddbbdccddaaadbaaddbbdababbdcdcdcddcaabaccdbddcaaabdbbbcbcabcbdcabccdacddcdbccdadbdabbaaddadaccbbcbcbcddccdccdcccbaacabcbcbdddddaabcbdddabbaddcddcbadaadabbdcabcbdbdacccbabbdbbddbcbbcddabcddadaadcdbabcabaddccaaadcdbcaaabccbdbbccaabababaadaacbdaccbbddbadadcddddddbdadcacbdabdacdbddcbbbcdacbbbadcdcacdadbaaddccadacdbadaccbccadcdabbdcbacbbdbcbccacbccabdadcbbcbaccaabbccadaccacdaabbcacccdacbcaabaaaabacbbbbdacabccbbddaaaaacdbdbbcdaaaaadcdcbbcdcdddabdaadadccbbdbbdbbbdcbcdababbbcabbabdbacdbccadabddacabacccccadbcacbdacadadbddabdacadcaabadacbcbbbadcdabbdcbaabdacadbbabddddcacbcdcababbbdadabcbababcbccacbdabaaadbcddadcbaabcdadccddaabbdbadbccaccbcadaadaaadbbbcdbbdabaabdbccbcabadbdabbdccaadcbdadcdbaadabcabcabadddaadadcabbddcdcacbdbbbccabbcdacbbccbcbcbadacdaacbaadcccdddddbbcdccbccddbdaabcbbbdabcdadccaacabdccbccbdbdbacdbcdcacbdcbbdbbcbcaddacdcdaddbbddbcaadacaacdcddaddaaaddccccbbacdcdbcbabdccdccaabacadbcdcdbcddbaccddacaabbdcaaaaabcbbdccacbdbdacbbddddaddbcaccbbdadddbdadacaaaabcbdcabddcbdbcbababadbbbbaaaacabbddcabddbaabcbbdacbcbdbacdacddcdbaaaabccddadbbbbcadabdbabdbbcdbabbabccdaacbdaabddbbccdbccdaaabcbbcaccaccadcdcbabbabbcadbdbcbaacbdbcaaccccacdddabdbaabbadbdabaaabbbdcdbbdbcdadcadcadcbbbdcaadcdaccbbaabbdcdcacbbbacbabbadcabaccbcbdcaacdaadbabdacacbdbbadbcabbcaabbadadabaaacccadcccadcdcaabacbcbbccccdcdacadcdadbabcbbcbccacbdcbaacabccbcbcccccbddaababaacbadcaaaccadcbabcdbaaccdabcbbcbdbddaaaaadcdbcabadcbbdcbadbdadddcddadddbbcadccbbabdddddcbadcbcdacbbcccccbccacbbcdccaddbacdacccccccbdabdadcccdaccaacbbccdbaadccddbcbddbdaaddaaabcdcaabadbababbabacbabbaddcadcdcabdccddcbaabcbcbabcbccaabbbaaddcaadabdaadaacbdcccccacadadaaabbadaaadbcbaccbcdadaabacbcbacbbbbdddddcbbdaacbaabdaadbcbbcdacabcbccabdacacdbaadabaabdcacadacbddcbbdbbddbbbadddcaacbacdcbadcacaddbddcadcccacbcdcaaadbcdbacbdadacaaaddcbdabbccaacbaaabbbabbbbacbadcdcbbdbccabcacabdbcbacbcccabbabdaaadcabdbaabadadaacbbbbacdaabadbaccabbadcaacdadcddcdabccacbcaddccbdacdbcbdcdbabcadaadbbddcccccdccdcdaccdabcbbccadabccdbdcbdbaaaabcabbabcadcdccdbadbacbaabccaddbadbacaababcccabccccdddbbacaaaabccadaabdcdacbbcdcdcbacccacadbddbaabbcbacacbddbbbbadbddbdbcbabadaabaccdcddaaacabcbbbbccdacdbcbbbabdcbcaaddabdbacbaccbddcdbbcdacbdbcddabadabadadaddcacddcacddbbccdcbcabcdcdddddabddcccbbabbbccdadcabaadcaaacabadacbadddcbcabbacacbcbbadacccccdbbdaaacaaacacbdddddacdaacaaddccacddbbcdccacbadccabbdddddbdabacacaaacbdcadacccdabcdcdaccbbadcbacddcccacdaaaabcbbbdddcabbbbcccbcbccaadccaaddbabbbadadacdcdcadabbdcccbdbcccbcbaccbdcdbaccdaddcadbcaaaadbbdddabcadbabcddbdbacbcacccdacabccbdcdbddcddadbcaddaabbdcacbddcabdabdcbcbddddddddaddcccdcddbdaccadddaddcbabdadababaaaacbddbbdcbcdadcbbdcaaccdcaacbabcddcbdabcccbbabcabccdcbacadaccadccdbccbcdaadbbabcccddacabaaadaaaaaddbbabccadaccaadaacbdcbbbcdbbaabdadbbbdabdadcdaacbbaccbacaaddabdcbaddbbccaabddacdcacdbbdcdabcdabaacaabdbcdbcccbabbadacaaacbcddabbbcaadacbbcdadabaddbabcabbdacbbbbbbacaccbdbbabaadadbdaabcdcbccbaacacbdbacddaaacbdaabdadcbdaddbacdddcbbddacdcaacdaaaabaccadabdacbdbddcabbdcdccadccdccaadbaddbaabbcbdacddadcbbccdcacbbbccabcaddcddadcbcaacaadcbbabdbdbbcabaadccabcbccddcacdaddcdcaddcddcddddccaacadabbdcbcabcadacadbcbaadccbdabdcaabcdaabcacacdbadaddcbbbaddcacadbbadababbabaabadacbbadaaddadbcdcaaddcbdbdccacddbbbaaabaddccbbabadbcbcabccadcbcdcbbcdbcbababdcbccacbaddadabdaababcadcdcadababccadcdabaddcdbabcbcacacdaadaacaaacbaacccbdcabcddbdbacdbaddcdbdbdbacbbddacbcabdbcccaaadacdcadabcdaaacbaddbbbcacbcadbcdabacddaaddddccdcacaccddcaddcacacbdbadaccadbcabaacadbadbdaadaccbaabadabbcacadccbcbbadddabbdaccbaccabcddddddbbccabcbadcadaccdcabbbcbcbacdcaccdadddbcabdabdbcddddbcabcbddacaababdadcccdbdcdcacdadcaaabaabdbccbbdbaaddbbbcaaaccddbccabbddacdaccaaabcbdcdddacbaaacbacaabdaacddacaaaddbbbbcaacbacdcaabbacccaccdcddcaacbadbbdacbaddbdabaddbabcddcdbcdcababdadbdaabccdcdcddcccbcbddcbbccabbdcdadbacacbcbabbaaadaadbadbdabbbadaddaaccccdaadccdadaabbbaaddcddcaababcbbcaccbdabdbbcddbdccdbcabdaabadbdabdaabcbcaaddcdbddbbdacddbcababaadaaabacdbcbdaaaabacddcabbbdcccadbaabbdabacbcdadacbddabdacdaaddccbbdaccadadbbbbbbaccbadabdddcbaaddccacadabdcdcbdcbaaadbdbddcbabdbbcadabababdcbddbaaaddcadbcaaadcbddcccbccbbdbbcabddaadcddaadcdccbdabbacaddbadaadabababddddbcdcdabbdddadbcadbabddacdaaaadcdbcbdacbccaaadaddcababdbadaabbbbadcdcaacddabcccdddbddddacbbbbcabdccabdbdccddaaccabadbdbabbbcbaadacccdbaabcccbdddabdcbbaccdccbdcaaadaddccdababdbdbdbbbddacabbbcadabdbcbbacccbdbbdddddcbabcdbbaabbbdbcaabbddadbdbdaaacdaaacddddccdccccccadcdcbcbccabdaaadcadddbaacbbbabcbccbdcdcbcaccbcacdcbdcddacbbbddbbcdcbadabddcbddacdcacdbcabdcbcbbbddddbacccdcbbcacaaccbabacaacdddcdbcddacdddbbcaabdbabadbddbcdaddcacbcdbdccccddadcdcdacbddaaacadcdcadcacadababdabdcbbcadbcaabbaddbacdbbbdbaaabdbcddabdaaadadbcdbdddbbbcaabddaaaaabbaadcddbbdaaababdcaaacadcbbdabaabaacbbbcdaacbbccadaabdaaabbdaababdccddbdddbdbdbdaccadaaacdbacdddbdccbaaddcdddcddccdcdbcdadccbaaabaddcabbddacbbaddadaabcdbadaccccbacccbcaabaabbdacaadaabbaabbdbdaababcdbdddbcdcabbdcbddadabcadbbcadcbcaddabbabbbdcbdcccbcadcaadbbadbbcdaabdddaacadbabaaabcccadcbcddaacbbdbccbccdccbabdddcabbaadabddcadacaabcdadcbcbcdbdbdbbddcdaaacaadabdbacabddcabcaaacdbdacdccdadbdacabdcdadbdcacaacdcbdcaaabdaaaddbbdddbdbddbbabbadbcabaabbdaaabcbadacbcccaababbdcaadcbabbcbbcabdbaddbcdcacbbcabdbbccdbbdaacabdbacbadccdbcbacdbdacbcbbacddadddabbddbdabadababcccdabbdbaababcbbcadbacccdcabbdbbcbbbcbddaacacaabaaddadddcbcbdcaadaabaadcaabdbaaddcccaabbccadcbcbbddaaabababaabcadcccdddbcbcdaaddbcbacddcaacbdacddacdddcabdadacbdaaacaaabdccacbcaaaaaacdbcaadcdbbbccbcdbcbcdddbacaadaaccbcbacdcacacbabaccaccdababcacbcdcabbadcdabaddadccbdbadcbcbccbcacdbddaaabbdaabdcbbaddcddbcbdbaccdcccddcacdbadaabaddadbccccaabdcdacabcaadacdbcadbcbddddcddbbdadbabdaabcdcaacbbbadbaadabaaccadcbdbddcbdcbdadabdbadcddbdbddcdbcdacbcbaaccdadacbdcbabcdcacbacbaaabdcacacaddaddacababdcaacacddabcdaadbbcbbdcabbacaddadcbdccdbadcbcacbbdddcbdcddabacbacdacbdbabdbbdbbabccacccadcacbbdccabdddbacddbccaccacaccadbccccbcbdaaaacdbcaadcdcbdccadddabaabbacdbadcdddbadaaaccbacdbdabbabcdddcdadcddadbccbbcbbdbacadabbdbcbbcbcadadccccdabcabdbddddbbacaadadccdabbdaccacdcdabcbabdcaabacaddbdcbdcabdacbccdcbabbadabccaddcbaddcaadddbdbdcadadaabccaabdbadbdacbacdbdbccddbbcdbdbabcaddbccabcacbdcddaadccccbccbcdccbcccdabbcbbcadadbacbababbaccbaaccabaddaabdabcddcbccacabdabcbcbddabcdcaddccaacdccdbabacdadaddacacbccdcdcbabddcaaddbcddcddbacbdaddccaabcccdbcabdbabcccadaaccdcbadbacbdacabbabbcdbcbabaddacdcadadaaccaccbdccdccbdbadccbadaaabdbbaabcbdabcdaacdacdbcbccadbddbdbbbbdadacababbbbbbdbacdcaccadbcdadabddbbbcbcabacabdadcbbcabacddbdaddabcdbcdbdaaacabcddabdbbddbcbcadaddbdaadcaadbaacacbbddbacaccacacccbccdbabddbcccccbddbabaddbddbdadccadbbddcabcacabacddacdabbcabccbbabbbabccbdbcabcdabcbdbabbabdcdccababcadcababddccdabdbdaaabdcadaddcabacbdbabdabddddabdcbccbbccbdcabdbdbbaaabaacccddddabccaaacbacbabbcaddbccbdbdddbbdbddaaccbaccaacaabaadbaaadbaacccdbdbcdaddaccaddabaccdbadabbcabcacbabcabdabadabcdcbddcaadabbaabdabaacaddbacbacbddddbcabcbaabacbdacbdcccbcbbcbaddbacaaacbcbbdcbdadbdaabccbdbaaaaaddaadbdddadabdccacabbbbbbcacdbdbacccaadcbdadbaccbbcdbbcdbcbaacccbadccddcaabdbaccbaaaabbacdcdcbddbcdcacbbdcbaabbadbcbbaabbaabccbabdabdcddacbdcaaacbcaabaabccdccbdcbddcddddddbabbcdddadacacaddbdddbdadbddbbabaaacdadcabaadccaaaabbbdbadbcdacccdddbbacddbdcddbbbbccaddcdabdccddacabdbdcbbcadccccdbbbabbddabcbdcdacddbbadabbaacbabbaacaadcdabccbdcababccaccacbaaacaababdcaccaaabdccccbdbdbadcbcddababbabcbbbcdcdbbbaadcbabdabaabcacdccccdabcddbbbcbdddcdbadbddccabddddadaababbbdbacbbbabbabccbabbaacdbcadddbcdbdddacbabcdbaaacacddaacadcbabadbabbcbabbcdcdaaccbabccbbdcdabcddcdacccaddadcadcacacdccdbccababbddbcdaadabdccccdcbcbdbbbadaaabbdbcabccabcbdccdbaacdabaaabdaabcddccbdccacbccddabccdcbccaaacbbcabbbbaacbcdcbaccbcacadcacbaacaacbabccddcddaaddcbbbaddabdcbdbbcbacbcbcccdccacbcbbbbddadabaacdcbabccddbccccbaadddbdbcabbbbbabcddcccdaacbabddabcadddacddabcbdbbbcaadbabbaccbcccccbabdbbcdbcdadbabbdadcccdacacabdcadcaacccccdcccccdcadcbbacbcadaccabcbdbacbdccabbbbabccbdabdabbcdcbddabcddcdccaabcabcdccbcbdcacbbdadbcaaadccdbcdadbcbcdbbbbcbdabdbdacdcdcbdcddbcabbabcdcacccdbcbadccbcdbcbdddbaadcbaabbadddbdbcbdabcdbbdbbbbcbdcbcdadcccadacccbdadbcdccbbaacbdabbdcdcdaddbaabaccabacccccbcdbcddbcbbaabacbcdbddcddddadcabccbbccbdabcadcdcbdcddbdcdcbaaadaddcaadccdddcbdddccadaddadcacdbbddcbdabdbadcdcddcbbdbaaabdbcdcaaabdccadaddacdabdccabcadabbdcdacbcaabadcdaacbcbddbbdddaaddadbaabbdabddbbbcccabcaacbcdbabacdcacccdbcdabbccdcbbbdbaaadcbccddbbccdaccaaccbcabaaacaacbacdccacdbcbdcbdddabaaccdbccadccbdaabaabdacabdcbadadbabcbbbbbdabdbcdaaadcacabcaadcccbdcadcdbaadccaddabddbbacdacbcbcdcbdbbcabbdbbbcacdddcdcacdcbbccacbabaddbddaadbcaabbbcbdcccaaabaaabcdbccbcbcbddaacdadcddbaaaddcdaccdccdabbdccadbccaccaacdcdbcdadcdabaabacccaacbcbcdabbddabbcdddabadadadccccaabbacbbababcbddbacbbdccdbdbdcbccacdcccbbcbbdadcadacbacacbccacdcacdbcddabcbacdacadcdabbcccbbacbbadabbabdbaccaadadccbcaacbbdadbaccbccabacddcaabacbdcbadcdddbaaabbddbdacbabaababdccdddcdcbbddcaaaaacabdaadbcdcbcbccabbcdaaaccdcdaaccbacacaadcaccddaadbaddbdbaabbddadbddbabacccaccddababdadbbdacadaaacbabbbabdbdbcacdbcbbbbbdccbaaabbddbbcbbbbabdbadcaacbbadbaccaddacacaaddbacccdbccacbbdbadddbccaddcccddaabbccbababdbdabcaacdadaccdbcabdacbddbaaadcbddbbaadaacadaaabbcbcbdbbdcdbdbccabcbcabdbdbccdadbbbdddbadcaadbcddaacabbdbdacadcdbabcbaaacaacddaaaacbbcdccdbabdacbdcdddcbdbbababdbdaaabbddadcbddbcaddabddbabdcdaaacaadaadbdcbdaccadcddcaaccdbcadbddddbacccbcccdababdacbdbbacdabcddbaccdbcacdaacaadbcddcbaccdaaccaccdccdadaddcadbdaccacabacbdbccdcccccabccabcccddcbcbbacbbabbcccbdcdbddddacbdbddbbcbbbbcbccbbcddadbbdcadbddaabccbccccbadddcabbddbcabbdcadbdadcddabcddcdaadabdbabdbaccdcdbcddddddbcbadbdcadadaabdccdabcbdcdacbbbcdbaccbbdbdbdbaaacababdabadccccdacbbdcdbccddabcbacbacdbadbadcccabcbbadbcadbddcdbbbbcbacdcabbbcbbdbcbbbacacacabdadbccdcaacaadbabdacdbbcabccadccccadcdddccacdddaadccacbcaabbdbabdbcdbdaddddddddaaddabddabdcbacbcacdbadbddddbcdadbdaacddbacdccccbddccacddddbcadddcbdcdccbccdcaadadbdccddabdbbaaaaaaadbababccacbddaccaccabccacabbbbcddbadcbccaccdcbbcbdbddcadaccddcabdccbdadadabdcaababcacbbddcccaabcbdcbbcaabbaacbdddbacadccccdaccbaacdbbdbbabbcbbadbcbaacdcbdcdcccacbbdbcacdadcbdaabaddbaaabcbaabdabbddabbacdbabbccbddaddaccddcccbabacccdcabccacdcaaaaccdbbddccadcddccdababadcdbddbdbadacbdbddacccbcacdcdbdcabbadaabdbadddcdbcbbbcabcabcabcabbaacdbcddbbbaadcabcadbddcbdbbaddbaabbcaccbdccadbbdbddbcbdccbcadcadbdcddbadbaccbbbbbddcbbccdddbbbadbdaabcbcbddbcabadcdbbdddbdbdbdbadaadcbccdbcdacbcdaaddabdccacccbcabadcbccbcbbbbccdacdcbcccbbcdaccaccaddbbdbdcbadbdadbbaadcdaacbabccaadbacdabdddadbacbbdcdbbddccbadcbbdbadbaabcbdadcdcabbaabcaadbcacaccbdbbabcdcdddadbacdacbbcacbbaccaaadcbbddaccdcdcbcadccabbcabbccadddcccdabccaaadbcabbbddcbaacadabacabadaccdbaaddacaccaacbdbcbdbcadbcadcdcbcbcbbbacbcabbcabccadbccabdcbddacabaacdadbdbcdddbdddcabaaadcddaaccacdcdaacbddcaabcbadbcbdddbcbcabddbadbdcbdbcdcadddbbaadaccdabdcacbbabacadaddcabdddcdadaaaccadbacbbbcbbabdbadbcdacbdbcbddbcbdbcccdbcadacbadabbdbbcbdcaddbbdcaacabaacbcdabcbbbcadbdcacbbcabcabadaaccaacdbaababdddbbccabddcdbdcdcacaaccdddacbdbdbbdbbcbbaadcbdddadbacabcbccadbdabcbdddbbdababbadbbbccacccabdbaabaadaabbdbccaabbccbdcbabdbcbddbcdbcdbaaacdadadbaccdbdbacadbbdacdddcbdddcbcdcbbadbcdbcdccdadcbdadddbbaadcbbddaabcddaabacbddadddbbcdbbdabbcbacadcaaacbdbbaaddaadbadabbbddbcddddbccabcddcdcaacbadcadcbbabcacbbadbaaacdabddbcbacdaaccdbbbcadaabadccddaddddcaadcbbbaabbabdaaabbddbbdadcdcdccddcbcddbbcdacbddcdcdcbcacadddccbdcbccdaacbcdddddbcddcabbbaaabbbdadcdbacbabaddadaadacdcadcbdaaaacabcadddcbddbdcaadccdcabcddddabaabaacaddddddbcdadbddacbbabbbbbacdacdcbdccbdbaddbabaadbcccacbbddaddbcacdacbdaacdacbabdabcacbabdadaacdbcbbdadbcbaaabcccccaadcaccdcbbcbcdbbdbccdccddaadcccaacaabbddcacdbccbcdadcaccddadaacadbaaabcdbdbadbbddacbdddcddaddacdbadbdbbadadcdaadabadaabcbcbabdaddcccacaadcbbdcccdcbbddccaddabdbbccabdadcddbadccdcddccbbaaccbdbddabdabcaacdbdcccacacbbbbdccadacaaccaadcdcacaabbdcaabcdadbbcbddddbdbabcdbcadabbbdcdbcddccbdbcadaccaddcabbdadacbdcaacaaccaddcdccddbcdcadbdcdaddbcacbccbadbaccadccabcbbacaccadcaacacbbabdccdcbdbadadadcaacaaddcccbbbbdccbbcddcadadaaaaccbddaccadaadddbccddabdacbcabcaababdabcabacbcaacccadccabaccddaabccdcbcbadbbadaaacbbcdbadadcaadddcccdcddbacdaccdcdbcdaddbaddbadacadacabadcbbddaaacccccdacbccbbbcdbdadbccddbbcaddabbdbcbcaaccbdddbacdabdcaaabbbacadcbcbcdaddaccdbccbdbcbdaccbbaddaccbcabadadcbbbcbdbabbcddaccdbbabbbcdcbacdbcaaabccaabaacccbcbcdddbabcacbaccaadaddaaaaaddcaabdcbdaabdbcccccbbccacabadbcabbcbccbbbabccdaccbabcccbdbdaccaddcbbadaabcccdbcadbbcbddccaacaadabdcbbccdaacacdaabcbbbabcabcadcbbccdbcacdbcbddbcbaacccbccccdbaccacdacbbcaaddccbaacbabcbacccadbabdcabcdbcadcdbdcbcadacccddaccdbbcbbddadcabdcccdbcddbbabdbcbcddacbcbcbdabaabddccbadbccadbbdbcdbabdacbdadccdaaacccbaacdadbaacababddbadddbacaddabcaabccddcdcadaabbcbddcdddaddcadcbbdbdacdcbbcaccccdabdaacacccbdbbbcdcacbcdbdbbcacbbbbdabaccaccacdaadaabdcaadacabdcacacbbadcbcbbcaabacbacbbabcddddbcbbbbcbccdbbdddcdccdbcdddabcbbadbdbcbacdbacbacbdbdcacdabbdcbcaadbbbbdccbbaacccbadbdbdaaccbcdbaaaccdbaacddccabdadbbdbdaabadaaccdbbabcbaabcdabdbacdbcdcccdddddccbbdbbbddaabaabbaccccbdadbbadadbdacabcacaaaddcdbaacaabdabbacaacaddacaaaaadaaddccdbabdbcabcaaaaabbbccdccdddaabadbcccccadcacdbacbbcaaabcadaaabbbdaaaacccadaabbcdacdaacbaabbcdabaddabbccbcdbadacbccbbcacddccacbbccbbbbdabaadcdcbdacdaccdbacbbdcaaadbbcddbdccaccbaaccdddaddacaddadbabacbcdabcadccbdbcbacaaddcbbccadddaddddadaacacacdcccbddcabbcacdbcdabdadbaadccacbddabbbdbcdaabbacabbcdbbbdadccaaccbccbcbbbdacaaccbbbacacabcdcbcaabbadbbaccabdacccacadadcbbcacbbcaaaadccdbdbabbddcdaaddadaccbcbcddcaccabadadaabaacabbdddacdabdacbbadcacccaccdcbccdbcbcddbccaadcacabadaacdcbaacbacaddddcbadbdacdbbcbdaccccdabdabcbacadddacbcbabcdadbbdcdbbbbcbcddbcdaadbbcaaddaccdbdaaabcabdccbdbcdacbccbcdadcdbbcbcacdcadadbccacacacabcbcbbaccbacadbdabdcbaaccbddcabcdbabaccdbccdaabacdabcdddcbbabccdcdbadbddbbbaadadddbdbbadaacadcbabbccbacbcbdbbbdacdaccacaccbabdabacbcdcadbbabaabacbbbdacbdaddaaabcddccdaddbdacddcbcbdbdbccbcdacaabaadcddbaccadbcccccdcdcddddbabbaddccbabcabddbcabaccddbabbcddbacdaadbdbadcdbcbacaadcacdbaabaaccacacccbddacaabacddbcbaddcbaddabadbbbabaaabadacccbdaddaadacbdbccdcbbcbaaabbdccbacdcbdabaaacacbccdddcacbbcbcbdcacdbcbbacbbdacbdcabcccdaddcabbdbcdccbabcaddbaaabaaccaacbdcbbaadddcddbbdcaabbbdabdcdaddccbbacdddcbcadabdcacbdddabdbcdbddcaddaadaadcacbddaadbcacbacaaadcbababcaaadccddcbdcdddddbacddcbcbcbcddaadbbdcddacabcdcabbadadcbdbbaccdbbaaabbcddcabbccaacabaaaddadbcabddbadddcabaaaadccccbbbbadcbbbadbcbcbaaddacdcaaaccdbccddaaaddbcabbbbcbdabbacdabcaadabbabdcadddadadcddadcabcbdcacbbaabcbadbbbcbdbaacddaccabcbcdcdbcbbdbcddacaaabccbaabbabdccddccdadaddbcaacbdacadbddcadccbbbcabbdabbadacddcbdddaccaadcbaaccddbcbbbdddcbccbdcdadcacbddddcbbaabaaaacccadddaadacddcdcdbdacbaccdbbacbdabdddacdbcdccabdbacbdbbaccddcdbbadddaaadbdccacdbbcabbcabacddbcbcbccacddbcdbccbbabdbcacccadaabcbccadbbdcddcdadbaddccacbbaadbdbaacdadddbbcccbcddbdaacdcddaadbbaacadbabdbccbdbadcdbababcdbaaacbbcbbbcaaacaccbcbaccaaddcabaccbadaddccdaddacadaaadacbacdcbbaadcbdccdcbbbabaacbcdbbcccbcdaababdcdcdbdbbadadabbdcaacabbaaaaabbacbaaccccbbcabaadadcddbdbdbdbcdcaaaaaaacdbccaabdaabbabaddcccaabddcbcdcacbcdbacdbbcabcddbacabcccabdabacbdcadcdadbabacddacacccaccbcddabccbabdaaacbdddbdabdbaabaddaccbacabcbdaaccbcacdabdbbacdccbbcbabdbdacaaaccddcddbbbbadcbbdcacabdcdbccababbadccbbbadadbaacdccdadbdbdddacdbdcddacdabaabadacbaccdaddabcaccbaccdadacbdcadbaacbbbacbccdbcccbbddbbddacbabcabdddcadcbbcccccadacccdaacbccbdbddbddbbbdacddadcdbbccadcadaacbbcacccbbabadabdbcdcddcdcdbdcaaabcdacbdbadddcdbacddaadcadddccabdbabacaddccaacbbaabdadaaaadbaacdbdcbcdddcdcbcbdabadbadccccbdccbbaadabcdbdaddabbaaaaaaabdbabcbbbacbaaabbaababcabdcaccaddcbbcbcdacdaccddbccacbdcaacdacdabbadcbddbabcadbaacccbbdbbbbdaaddbaabcccdbdcdccdcdacdaaaaabaaddaddddabccbcdcbcaddbbaababdacdcbccacbabbabaaccbbacdadabbbaacaaabcdcdccdbccbdacbcdaadbadcaddabbcadcacbccacbabbcaadbccdadcabdaaabddccaaddbdaaababbdbbbcaaddccbacbbbaadddbdabdaccaabcdacaacdabbcbcdddadcddbbbbdbcadabcbdbcbbcbdcdcbadddcaacbbdcccaccdbddaabaabacdadbddccbdadccdddbccbacdbabaabaddccbcbddccbdcbbaadccdccbaadabdcccccbddcadcbadcbcacbbbdaaabaacaabcbabbacaacbdcaddbcaacdbdbbbaccddadcbacbddadcbcabadbdbcabaacbbbdbddabdcbcdaddcddbaabddbcaacccabbcddaaaacbcdaddabbadccadcddcaddabddabbacbbaadbadadcdccaaaacbdaaccaccbaabdcbcbabcaacbaabacdaabbaccccdbcadaccadacdacabcdcddbddbcccdcdbadbcacbaaddcbcacaccadbccbbbbcdaacdddbbaaadbcccabcbbadacacacdcbbcabacaaaacbacbcdacccaabacacdbdcaabccaacaddacdccacdaddbbbacaddccbddcdddababdddccabcabdbcdbdbbdddbcbcbbbbbdbdbdacaddbbbdacdbacddcbbaacdcabacdcbcacabbadccdcabdadbdbcacddbdacdcadabacdbcdbdabccccbaacbcadacbbcdbadacbdbbcaacccabbdccccadcdbbdacaabbbccbdcdbaaccabacaaccaabcdbcccbcbdcbbaacbdbabcabdbcaaacaaaccbadaddacbbcdbadbbccbcdbaaddbdcbabbbabcabccaaabdddcadbcabacdaddcbdbaccbcddabdbdabaddadabacdbaabdbaaaccbadcaddbdacadbbadcbcdabcdabbbbbccdcadcddcccbbcbbbbabbddcbcaddcbdbdddacacbcccdbdddabcdcaadcbdadcdcabbcacbdbcbabbcbbcdddadaadbbabaabddaabbbdaccdccabaccababbaadacdacbbccdabddaacaaaccadadbabaddaddcdabacddbbddbbadbcdcbabcbcbdcdbbbbadbbbbdacabccdcacbccdddabdcadbcccbbdccaabbbbacddadbaabdaccddaccadcacadcdbbbadaababaddaddcbdbbacbabdcbdacbbacadccbbaaacccdbbddbacdcdcabddbdcccdabbcccbadabdacbbadadbddaabbdbadcadcdbdaabdbbcdcbbcbcdcdbddccbdbdbcdaaacddcbcacbcbaacdddcadadcdcdccdcbdadbdcbcbaadccababccaaaabababcdbabbcbacdabcdadddcbbbdacdbcdcbbbabbaddadbdcbdaaaddaaccdbbbdcbbdbbdcabbbdccddcddccbdccddbbbddacbdcabadcbacaabddaaacddacbbaacdcdcadbbdcddacccacaaacaccbbabcbddaabadcacbcdbddaddabacbddbbadccbdaadbaddabdcbdcbacaadaacdbbaaccabdbcccbaccdcabbddddbdddaacddcbdcbdacdcbabbcbcadaaabdacacabdbccadabadaacccacacddbaadabccdaabdaacddbdbaaacbaddcdddccabaabddcbddbcbacddbbbbabbccacacbddbaacccbcacdbddcdbcdddcdacaaaaddaacbbbcddbdabaabbabcccacaadcbacaccbdbdabcabbdaacaddcdacddcaadaaabcaacdcdadddccaccccddcddddbdddbabdabbabcccaacbdcbdaabcdaaaabdbdccccaacadaccdcdcbdcddddbddcdaacbcaaacddbdcabbdcbbcbdaadbbddbabcddcacabaacdcbbdcbbacabbdbbbaacabbbbbbadaabddbbbcadcaaadaaacbccdccdddccacdddabaddcdcbdaabddbccddbdbdccdbddacddbaaaacbcaacacddccbdbdaaddcacadbcbdbaccaadaadabcdddbaabcdddbcbbccdabbbcbbadcdcddaaddababbdcdddcccacbccacbbabaacbbbaddbcddbdbabcddcccdbaaabbbbdccadcbbacccbbadbcadcabaccbaadadacaabababdcbbcdddbddcdccccbaccabbcdaddbbcddbcdadddbbdbbddbddaadaadcdadcbdbadccdacccdbbabbdcbaddbaaabacdcaaccdbbcadcdabdabdccabaabdcdcbcdcccdbadccccdcbdddbcbdcaaabcdbcdacddcdaddbdcbcdbbadccccccbddbaaddccacbcadaddabdabcbcccbabbcadddacbdaadaccbcadaccbabdbdcbddcddccccdcbadcdaddbabbdddaddadcabddddbabadaacbbaacadadaadccccdacdcdacbacbbacbddbdcdbacadcbaacdcdaacbbdcabdbdacbbcdacaccbbdbacdddadbbbbddabcdbcadccdcbacccabbcacdbdacccaaadbbaddbcdadbdbdbaabdddbaabbabaccdacabababbbcdaccdcbcbaababbabbdcdbaccbbaacdbdbbcbabcbcbddaabbcdabdaadddbbbbbcbaccabdbdcadbcaaaccbdbdabdaccacadababcccadcabdcbdabacaacbbbbdaabbdbcdaaddbdbcadacbacccadddbbbbbacbababbdcadbbddaaccdabdbcbcdadbbabacdccadbbbdcbccbdacbbbdcccaabcdbbddbcaaccdaccbbaddccbbbcccabbdcbdbbadabcdbacdbdadccbcababdbacdbdcbbdadbbdbddadcdcccbddabdbbcbbbdbccdccbbdcddadadbdbcbdaabaaadabbcdabcaaccdbcdbddcdaccdcbccbccdcdadcacacddacdbabbdbaddbcccccdaaabddccbcccdaddbcababbddcdcaaababbcaabaaacddbcaacccadbcacbdbdbdabaaadacbbcaacaddbbbcbdcaccdccccdcdabddacbcdcbbcaccaaadaaadabcaabbaabbaaabdacdbdbdbbdcbbddcbcdbdacbacbdaabacbcbbdabcadaaddabababbadadaaabbdbcdacbaccbbcabaaabdbddaadcabaadbdbdbacaacacdbdcaaadbdbcaccadcabcbabaabdaadbdbbddcaabcbaabdbcaaabaaadcbbadddcdaadaacbccdcdabdddcbdbbdcbbaabdccadacaaddddadccdaabcccdaccdcdcadcaabaabaaadbacabdcbadbcabcaacdbbbaabdcdcadadccdbbdaccaccdababbbddbabccacdddbacadcdadddadcddbadbaacacddbdabadbcbbcccbcacaaaadacaabaccdadcdcadabbdadcacacbabcaabbaddacbdddcbcddcdcdadbaadabcacccccaccdabdbcacbdacaccaabddbdbbbcdabccadcabcbccbbcbcdcabaacacddbcbcdadbbaccbacaccdabcabdaddccbbabbadbbbadaabcbdbcbcbcaccabbcdddabcccddddbacbbdccccddcacddbbcdbacbbcbaccbcbaaaadaaabbadabaaaddabacbccddaabdcdbabbdaaaadacbacbadbadbcababbbcadcccddbddcdaabcadabaccdcaaacbbccbabbdabbbcbaabacabcadaddbdaaaccbddaadccccabdbbdabdbcaadddccbaabdaabbbdcbaaddabdacbcddbcbddddcabdbaccdbaabacaddaddadddbcdccadcddcbbdaddccccbdbbacbdbbbbbdabbbacdcabbcdabbaddaccbaaaddbdbddabdbaddabdbbcbccacbaaccaaadcccdaabcaadaabbccdabacaaddaacabadcdccbdaddbcbbbbbbabddbadaadababdbabdbdbabddabddabbbacabadcbbabcabcccadccccbaabcdadadacaccbbbbdcabbbaaaaddbadaaaccdbbdadbaabdaabcbbcbbbccdabcacccacbadbabaaadbacaacbdcabbccabbcbccccaacbacaadcaddacbbcaaaaaadcbbdadadbdccadacbacabadaabbcdbaadcadbcdddcbdcccabbdbadcacdbbcdbadbdadacbbaabbccdcaacbddbcbabdcccccbcdaaacbdbbcaadccddbcbddbbabcddccdcbbdbcdbcdccdcbdcabdadbbcacbbbadccbdacccadbccaaccbddaddcbbcaacdaccddbbcdbdbacdccdcdbccccdaccbabaadbddbcdcbbddddbdacabcddcdbaaadcacbcbdbbbcabcdaddacacdccdaccbddaaadadbadadbaabbaabbbbbdccdcbdccadccbbdaacddacddaddbbdcbbddbccbcbcbbbddcdaabcacbbdbdcccdddbbdcdbddddbacdaabdccdadabbcdaddcbabbaabcdcdadacdcdbdaaddbaadcdaadadbaaadadcdaddcadddcdcaacdadbbaaddcaaaaaccccacccbdadcccbacabbdcdcbddcaaadcadaabcacdddccdbcdccbadadccbdacbabbadabadbdbdbdcdbadbcacbdabbdccbbbaccaaccbaabcbddbbabdcaaabbddabbdabcdcdabacbbadccacccbbaacbbddbbccbddddcadbbbabcabdbbdcadbccdcaadcdcacccabbabcdbcddcaadcaccdcabcdbcacdaccaaddabcbcccbaacacacacddbbdbdcbbadddddaabbbddabbdbacdccccdddaabdacdacbcbbabbaddbbccbacdbaccadabbcacdbacdadddcbaddabcaddcacdabaababaccbcbadbdcabbadbcaccabaddcbadadccabacbdaddccadcddbdadcccacccdacbcddccbbaababccbbdcbcaadcbadcccbccbcbabbbaccaadaabcdbcbcbddbabddbacabadbacdacccbdbdadbacadcadddccdcbcdcccbcdddbababdbbddbbaacbcdcdbbaacddbcdaabbacdccdcdddbbabddbbcdadbdbacacbdacdbcbdadbbcbdbdacdaabbbaccbacddabcbdccacaaabcaacbccdbbbdabdddbdcdcdbaacaaabcadbacbbdaacbbcccbcccababbcccbccbbdbaccbdddbbccaccbcbcdbcbabdcbccdaacbbbacacacdbadabadcddbdbdbacbabcbcccdcddcadaacbcaaaacbbadcbadacadadbdbabdadbbbcbaaacdbdddccbacabacccbacbaaaabbadcdccccadbabdbcccabdabadddaccbabcbbaaabcaabbbdcbaaccacdaccaddbaddbcbcadaadcdddbbadcdbdbcbcccaaabcccdcccdaadacddcacdbcddbadbbdacabdabcbaacdcbddbcbbdcadcbacaaaacddabadaccacaddbccbbdccabbdcbcdabcdddbcccccadacccccabcdddabbddbcacdacdccdddbaaaacdbcabadacadcbbcbcbdcbadbcdbcbcbacabcbbcbdabbaaacccdbabcdbcbbbcabcabcbdacaccbddccbcacccadccbddddadaabcbcacdccabcddaacbddcaadddcbcdbadbcccbcdcdadbcadadbbcaadadcdbbbabddaccbdddbbdadbddcaddddabbadcccabbdbbaddcacabcbddadaabcaccbdbabddbacccaaacbcbccaabacdbddcbabacdacdabbdabaddccacbcdcdddbddccdbdabccbbdcacbddcbabaaadcabcacbdbaacbbaabcadadadbbaabdaacdabddbbdcadadcdcbbcdcaaddcabdddacacaabcbdddcadddaadcddbacdcdcdddcdcccadadaccacabdcdbbdbddbbddccabcabdcccbbddcbddbababbbbbcbdcbcbccbcbcbbabcadcdbaaacbccdbabccbadacbadcdcbabcddbdbdaddadaddcacbddacdabadaabccbabbabdacabdccabcccacccccdddacdbabdccdddabbdcbddcdcdcdcbcddbbacabdaacbadcddccbdadcdcdadcbbcddcadbccbacbdbccbcdddacdaaaddadabdbccaaddbabbadcabccaaddccadddcdbaaabbaccbdbcbdcadcabdcdacbbbcdabdadddadacaacdaaadbccbabaaaaabdccdbacbbdcacdbcabbaddcccacddacadacaabaaaabbccdbaaabcbcbddccbabcbdddcbcbadbbbbbcbbbcbbbaabadccaacbdabadadadbdbcbcdbbacdbbcbbcbccadbbaddcdbbbbcccdcbbabbbcbbdcdacdddbbbdaddaabadcbdadbcdabcbccbbccadabccdaabaddbbcadbbabdabdbbaaadcadccacbacbdaccdbcddcbcbbbadcdcbbdaccbdcbdabaacaacccbbccddabbbaadcbdbdcaaabdaacdbbcbdcbabdcabccbdcaddacabddacaaddbbabadcadccacbaaabadbcacbbbcddbbadaccbaacbccdcdbcababddcabcbcbcbddddddbbdcbabaabccdadbcddaddaccaddbdcabbbacadbddadbbbdddaccdcadbbbaabcdbdaccaabadcbcdbdabaccbbbdddddcdacdcdcaaaaccaccbcbcabbbbaabdaacaccbcababcdcdddabbbabaabbdcaccdaabbabdbdcbcbbddcbccccdaabddbabaababdacdddbcddbaaabddddddaccccdcbbbbaacbbadabdaccbaaddacaccbccacaaccdadbdbccacabccbbdddccaadbbbdaddbbbcbbdcccdadacdccbdaaaaddadcdbdcabcddaaddadadadbcbadcdacbcaddcdcaacddbabbbcddbbabcbdcbbbdbcdaddabddddddacbbacbdbdaadaaddcaacbbddaccdbccacbdbacadddbcddddccccdbccacdbcacbcbcaabdbcdabdbdcdcdaccbabaddabdccbadcdbdcabcadacbdcdcccaadacaabacacdcbdcddbdaabbbdcdddadccdcbbcccdddbbdcbccabcbdcdcddcdbbadaadabbacdcdabbcabaaabdbdcadbcdbdabbaaccdcbbcadddbadcbcddccbcbabbbaabbabbdaadaddadadbdaddbadbadddbdbcccdcbbdaacdbdcbaabcacccabacccbaaacbaabacdcbaccaccbbdaaacabcabcbccdadbddddbcbcbababbccaacbcbdbdaadbdbcdbcddaaacddcdacadadacddcdcdcbdbadbdcbcccbdbdddccbccdaaacdcdbdcaddddbbdbcdccbdcdbcbbdcaadcdacbaccdbacccdacdcacabdcddbdddcdbacbbadccbddaabcddacbabdbabaccaddabbadaadcbbdacbccabdabaaacbbbdbdadacbcccdaadbbbdcadaabdbbbdbacddbbbdddaacadddacbbaadabccabdcdbcdaabdbdaaadbcbddbcacdadabcaacdadbdccccaddacdcabbdadababaadaacbadabbdccbdddbbacbabcbccbdacdaddacdcdddadbddadaddddbdacdabdacbaacbdcbaccccbcccbadcdbabbacbcbcbcacccbdcbacbaaaabdadaadadbcaaddacaadacbcaaccacbdcaaadbbbdaddbaddaaddcdbbdbbbcadccdbdccdbdbabdcbcbbabadddbaabbccaaccadaaaadabcadcbbbcddcbccdcabdccdcadbdbbcabaaabcaccbabbcdbcbcaacabcdbbbbcccaabdbccbbadcabcdcacaddccadbbbbccbbabbdacaccbbcdcbdbcdaadadaabaadacdccaaaabcdaadacacdabdcddbdadaaadbcdacbbcacbbabbacbabaddadabcddcddddabadbddccbbacccbaaaccbcbbdbdbbabaaccabccddbccbbabadcdaacbcdddbabbdabbaaacbaccacadbaabcdaacdcbacccaabcbbbdacabccddaaabdaccdccbbdabcabbcbccdbdcdacbddbcccdaddabbdadaabdddbaadcbadabdbcbacddbdbbbcbcccbbcaabaccabcbbaccadadbdddbdabdaaabbcdcbadbccaaddbccbdccdadbdaccccababacadaadccabccddbcbcbbaddcbdbbdcaddbaabddacbcdadbcdacaaddbbbadbccacdabdcdbabacabdadbcdddaddcdbcbaccadddcddcaabcaadcadccbacddacdbacaabacdaaaddbcabbacccdaacbaaaacdcadccbdddbcdacdbccdcdcbdabaddcdabadbcacbbabbcdcdcbdabcacdcdcdcbabacababcbdbccbdccbcdadcbbbdacddadcddbaaccbbbccabaadbababdcbccbcacdcddcaacabbcdbcdddcddcbbdbcdbcadbcdddcdbddcdbdcddbddaaabacaadcbadccdbbaaaaddccaccdbdbcdcdccadadabaacdcaddcaabcbadcccaadccaadbbbdbbbdcadaaabcdcbbbbccbaacbdcbaccabcbabdbbabdddddccacabbabccabaabbadbcdcccabbbbccdbdddadacaaabbbdbdccadbdcccacdccbbbbcadbcadacabdbccdaddbcdaadabccaababbbdacabbbdddbcbbaacabcbcbaaccabadadcaabaacbbcabdbdadbdcdbcadacccdcdaccdbaaccaabdcadbacabcaddcacdbdabbbddccaaacbdbaabddcdbacdaccdacbcacbbcbcabddaddabddbddccbbacddbdcbadbddbdddcccddacbacdaaacbcabcabcadacdcaccbbcabccaaadcbccbadadababbaaccbacdccbbcabccacaaacbadbcdadbacddbcaaadbcdcbaaddddaaacdcbdacbbbadddaacbdddddbaaabcdcbcacdcddcccdccaccbbaaacabaadadbbcbbadcabddaaddcbbbccddbcabacddcdbbbcdcadaaaacabadadbdbcacbbdaadbbaaacccdccdcdbcbbbababccbddbacdcdacdddbcaacabdbbabddbacbaacbccccdacbacdaccdaacdacadbdbcdbdbacdbaddbbbaccdcddbacbbdabbcdcbcbcaadbaaaabccaacbcaaaccabcacadcaaacaabaabddcaaaaadcdaaaadbabdccbdababbaadddacbdbbbdaadcbcddacbadcdcaaaadbdbbdadacdbbbbccaaddcaddccbabaadccbacbadbbcbdcdabaacbaccdccaaddacaaabbbddcddcccacaacaacbdbddcbcacdbacbcdcbacaaadbbdbccddcadbacbddcbddbaddddacbbdbddddcbdaacabcdadbbaccbbcabcddbdcdcbdcacacdbaadbabaabcbbadadabcddbdbadacabbdbccccbbacbcdbbadbccccdcccdbbccbdcccbcdddaccddcabddcaaadcdcdbcdaaacccdbaabddbdbcbdbadbdcbabbbdcdcbacddcbbddcddcddacbcdabdacbbcbdbdddcbbabbdacaacadbacdbbdbbcdabaabccacbcdbbaaacdbdccaabcaaadabdaddcdaabadabbbbbabbbcaccacadadbbcabaabacdddcdabaabaccbbdabddaadcbbcdbbbdaaabdbcaddbcdbdbddcabddbaabdcdbaadaabdabaaadbacacbdbbaadadadadbdabdabdabbbcbbbbbdbcbbaccdaddcdccbaabcadbadbcbcdacbdcadbaabbbabcabaadcdaabcddcccacbcaadcbdacaddcbcdcaddcddbaacadaaddcdabbcccdcbaacdbabdbbaacadbccdcdbcbdccaacbddcccbdccbbbcdbbbcddcdcdddcccdcacbbbbacbdacbadcaccddaacdbadcadccaabdadadaacbccdccccccdcbdcdbcadacdabdbbaaaaaddcccdbcbdbabcdccdabbccabcbcadccdbadcdbbbadadbdccbcdabcacdcdbaccdddaabcacaddcdccaadbbdaaacdbaaaddddbaaddbbdbdbdbaadcbdcadddcbddcbaababbdccbdcbccaddddacaadcbaababcccbaaddcacbdcabbacdaaddabbaabadabdabacdcbaadacbbddcadbbcacdcddbdbbabdadaaddccccbccadaccdbcbadcaaabbbcbcbcaaccbbdbbcbcaddadacdbbadddaddccdccdaaaccaccadccaaadbadbcddaddccbbabcbbbbcaccdabdccdbabcbbccaddadcacbcccbacbbabbadadcbbaabcdacaabdbbcdcdabacdbdaacddadaabbbcccadbbbbadbaddbbdddbdaaacadabcabbbddbbddbdbbadbdacdcdcbbadadcdacddcbcbbcabbbcaddbdabcdddabbbcacbddcbbbbabcacacbddbacaaaaaabaddddddadcbbabbbbbbdccdddbbabaddadadacdccdabcdcabdccacacaaadaaaaaaccadabddbdcddbaddacdcccbbcbbdcdddacdbcabbaaccabdadcdccdbdbcdadaacbdcbcddbcaddddaddbabaacaddcddbaaacbdabdbbbdaccdacccadccdaadbdbccaaddbadcacaddcbaadacbcccacbabddbaaadcbacddbbcccaacccccaccaaddcabbabccbcbcaddcddccbabcbcdadccdadbbcbaabdaccbbcbaaaadbdbcabccbccccacdcdccbabcbccabbdaacccaddbacbcbcbcdacdcbddaabadadaacbbcccccdabbdbcabccdcababaaadcacbbcdbababbdcaabadabcaadcccadccdaacbdbddcdaabdbcdaaaddcdddbdabbdbcccddcbdcabdcbaababbbdbdbbbddacbbacadcaaaaccccabcbccacaddbbdcdacacdbdaabcbcabbdaccbaccaddcccbbbdccbbdaadddadaddabddccadbdcacacdbdbaccaacccddabcdcbdaadcbbbdcdaabcdcbbbcaaddccdcbdbdcaaaabdcbadabddabbdacaaacdbabdbaaaabadbdddddcaccaacbbaccdbbcacdbcdbbccbabcbdbaddbdabbdccbccbaddbdaddcbddbbaccdccddcadabadabcabcaaddadcbdbaacdcdbbbcbabcccbbaadbadacacdbbdcddbbadccbddbdaacdcdccbaccdcacbaabccbabdbcdadababdacbaaaaacccbbdcbbbadbcbcdadadcdcdbcdccaacbbcdccbadacdacbcdabacbbacdcccbddbbcdabacabbbadcabcdcdbcacdbdcaddadbddbbdcddbcbdaccccdcdacbdabdccababcdbcdddaacaddadabbaddacacdcddddcbdddaabadcabcbcdddccaddcdbacdbcdacabdaaddbccbbcddddcaaadcababadacadabddabcbcbdcadbaadadcbcbddadbacaadabcdcdbcacbcbbbaacddcaaaaccccadaadcbdddbbdbacabcdcbaacbcbadcbdbbadbbcaabdbabdbcabdaadbacadbdadddaacdcccacabdbbccbbcabacacdddabcbcdaaccdaaadaabbccbdcbacbdbbbcbdcdadcbdbdddccccbdccdbcbdcbbdccbacacbabdbcaaccdbdaacadccddbdbbbadcdabdbdadcbccaddccdababcbcddabbdcdbccdbbadbacbdaabbccbcbbcdbcbcdcbdbbaaababadacccdadaddaabcbbbbbbaccdabccbbbdaddcacdcddaaadadcadbdccdcacbcdddcbaaacbdaddcbbaacbcbaaddcbbcbadbcabbacbdbdcbcaabcadddaddabbaabdabacbcaabdadccadaabccbdbcdccbcaaabcbdaaabdccbcacddcabbbbacbbcbdccabbabadbaacbabbaadacacbbdcddcbddcaadaccbbbccdcaacadadaabbccbaabcdbcabcabccdadaacdaddbbcbcbbdbcddbbdcacbaaddbbdabcdacdbadadbcdcbbcabddacdddabababaabdacdcadccacdcaaaabadcadadbbadddbddaadabbcdabcdccbabcaacacddccadaaaaaaaabbcbbaccccbccadaaacacbcbacadaccddddcbbccdbddddacacdcdaadbccddbcdcaacddbabdabbcdcbdadadacbdbdcadcaaabbdbddbacddbccaadabbadadaaddadcdaccccdccdbbacadabdbbacdcbbccdadcdcacbbddadbcdadccbaababaacbabddadcbcbbdbdddbbbabddcbbbcabaaddabbcadddbbdcbccbbcbdbdbddaaaabdbccaacaabdadcaccadcabbcbabdbaaaacacabcaadccabcaadbcccbacbbbcbccadccbddabbbbbbbbcaccaaadbabcaadaabddbdcdbbbacdbddaaaaabaadadddaccddcbbaddbbbbabcbbddabdddcbadccabaabacacbcbcbddddcbbdbdbadaacbbdabaacdddabdadcbbadcdbadbbdccdaadbbacccdcaddbdbddcddcdddccaaabdddddaaccdccbcdadddabadabbdabaadbcabcadcddbcdaadbabcabdcccdcaaccacacaadabddcadbabbcdddaacdbbaccbdbbabaccbacababdaccbaaaaddbadababacdbbaddccbddddddcacdcbabacabbcbaddddaaabacbacbcbccabddbacaaacabaacbdbdabcaaabcdacccaccbccdadbbbdabdcbabcddddbacacbacabbcdadcbcacabdabdadcbacddadccadaaadabcdbacbcbadaaababbbdadcbbadbdbcccadabbccbaabacdbcaaadcabcadcbacdbddbddacbddbbcacbccbdbccabbbbabcaabadbdadbddcbaaadbdabcdddadcbbcdbbccbbbacdcbcdbadcbdbaacbddaccdabdccdadcdadcbbacadccddaadbcabdcdbdaabcdccabcccaabadcccbdabddbccddaadadbcacadbdccbacacdaddbccaccdcabaadbccdbbdabbccaadacbcbddacddbcccaddccdbdcaadbabcaccdaadbdaaddbcbccdcaaadcdbbbcdbbaacadcbabdddabbbdacdbccdbcdaadabcdbcdababdaadabbbdabddcabbcbcdabcbabcdabdddbdadbbdcdbabdbddadcbbccbdabbbadaabcabdcbbcdcabcbbdbcaabacdaabccddcadcadccdacacccddbdddcdadacbccbaadbcbcaaddabacdacaaabdaabaabcdacaccbcbdbcbdacddadbbcabadcbdaccddbbbadbabcddcbbbcbcbdbbadbcbbdaaadbbdddcbaadddbccaccabbbdddaccdcbacdbcabcdcaacbdbccbcabcbbadaaccbcdbadcdaacabcdcacbcacddcabbaaddbbdbbccadcbcdbabcbacbbdcdccdddaadbcdabcbdcbbdadaabbdaccdbcccbbbccbdccbdaabdcdadacbcacdcdbcaadcccbccdcaccbacbcabccbbadccadaddccdaadaabcbabacabacbbbcacdcdccdccbbbdacaadccdacbbbcadabadbaaabbccdbccacccacabcddcacbcabcadaccbbdaabccbdcdbcbcbcdcadadabbcacacaaaabbacdabaccaddccabbaadbaabdabdddddbbbacdabbaacadbcbdcdcbbbdbababaddadcccbdaccabbcaadbdabacddbccabbcccbbacacdddabaaacbdcadcadddbcdacdcdaabccccbcbaccabcacdcccabbaccaccbcbaabbcdcaacaacabcaacabcdcccadabcdddcbbaadabcacddacabbcacbbdadcadadcacdcabaaddaacacbbcaabdbaccacbdacdcaadbcaabbdadbccdcbdbadacdadccbacaddacaccbcdadbbccdbccbbaccbdadcbaacaccccccbadbadaacaaddaaccbaadbdacbcddabcadaaabccbaabcbacccbabacbdbbbaddcbbcdbbacaacacbcdbcdbaaddacccbbdbcbbdcbbaadacbaddcdbbbcabacaadcbdcddddacacaddcdbbbccbbbdaddabdcdabaacaddaccbcbbbabdbaddbcaadadcdaacbabcbdddbddcbdddbdbadccbdaabbddbdcbaccacabcccaacadcadaacacbddabadacbbdcdcdacbadacbaaccbdcbacbcabdadbbbcbcdcadddcdbadaccccdaabcbccadddccbabcddcdcadcaacbacbbdacacadadccabadaccabaaadccabdabaacadddbbcacaaaaadbabcadadbdabccccdacdabbdbdaadadababbbabcddabccddcbcdddbbcdbaaadddbaddbddcacdbdaddcbacbcddbdabcddcbadbcadbdbcddbadbabdbabdcacdcddabbcacadaacccccacbbbacbdbdbdccccbbddcacbdbdabacccbaaddbddbdaccddaaadbaaaaadacdaabbdadbbdccdccadbdacbdccabddcdbbcabadbcbbdbbbbcaddcababccccddcdccaacbaaacbadddadcadbcdccacabbaccdcdbadcadbccadaaddbaccbdbdccbbbabbdbbabdcbacdccccbaccdbdabaaadddcdbcadccaadbacaadabbccacacabbacdaadcbdaaacbdaaacbbcbbcaddbddbcdbcadbacbabddbccdaadcbbcdcadcdcbaaabdacdcbccccbbddadabdacadbdabaddabdcacacdaadcacbbdabbcaaddbccddcaadddaacccbbdcbdcacbcadaddadacbccdaabbbdaabcadacbaadcdaacbbadadaaddaccabdcdbcbbbdcadccdaacdbaaaddbdaadbdbbabdcbbddbabbdddbaacabdbdadddcdbbadcabcabdcdbacbcacddaadcdabbdaddcbaadadbbbabacddaccadbccdbdabddabbcbaadccccccbdddbbbcdcdbdaddcdacccdcbbabccbcaabbcdcccbdbaabadcddbddccadbaadcabbbddaddacababbdddadcbccacabaacddddcbccadbbcdacaaccdddaccccdabddcadccbdccdacabbdabcdbabaaadbbacdaadcccbadcddbcbacaacddbaadcddcdaadbccbbccacbcbccdadabdcbcdaabccaacbddcbaccacddbdbcdcdcaaaccbbbddbddadbbddabddadadbcbbcbaacababdaabbdaabcaddacaaacabddddaacacabdbddcaddcdadcdbabbcbabadddbbdbcdbdababdddacabbbdcbdadaaabcddbabcacbcabcdabadadccbccdcdbadbadbcccbabdacaadadacaadaaccbbdaabdcdbddbdaccacdcadbdadcbbbcdcdcddcacaddaabaadbaadbcdadbbadbbccadcbbacadbcabdaaadddddcbbdccdccdcdaacbabcacdaacccbacbbbacdbbcdbddcdcacdcdcdbaaadcdddcdcdcaddaddaacbdcccabdabdcdacadbabbaaadcbacbadcadcaddddadaddbbaaabcbacbcddcabbdadbccccdaacabaaabdbabbbbdabdcccadbbcbbadaacabaacbcaabaaaadcdaddbacbdbcdaadccdbbdcdddbbbccadbbbcbdacccbbbadcdadbccdccdaadaabadccbbaaacbbdcaddaddaabbcccbcddbdbbbaddacdcddcbdbabadbbbcbdcddbdbdadcacddcdaaacdbacbbdddddaadcdbaadbbbaddcbcdbcccbadabababdcdcbbcacaabacdccdbbacdbcccacdcdbccaacbbcacaabdbbdcbadcacabaaddacaddacabdbdbdadbadddadadbbdaacbacaddbbccadbbdcbbcacadbdacccaccabaacaaabdaababaacbaadddbcbddacdacbbabbadbaacaddccacbcbbbcadddcabbdbacacbddccbddbccbacbbddaccddadaaddadadbaabbaacdbdbcbbcbacddddadddacdabdaaacdbbcaddbccccbdbbadbcbbdddccddcacbbdacdabbbdbdcdbabadaacbadaabdccacacdacaadbaaccbabbbdacacddbcccbdadcdcbaacabbdcddcdddcadcadddcadcdabccdbcaccccaabaacdabbbcacccbcbcccbaabdbbdbdcbdababcabddbccbbdabcbdcadcacaddbddadbadcaadcaabacaacaadacaadddcbdbcdadccbabacaddbaacddcdcdaddcbddcbbdccabcadcbccdccaabcddcadbbdcadccaaccaabaabbccbdbcdcadadbdabddccaccabcdaccababbdbbbaccacabdadabaababbdbacaccbacbacbcbcccbabdaaccaabddbcdbbbdbcbacdacadccbcaddcddacdaccdbddbbddabbcaadadcabbbdabddcaacccaabbccccbbdadbcbdbaabdcaacbbbdcacdbbaabccbddbbbbdcbcdcaaaabacdabaccacdadcaccadacdaddbcaadadbdadbbaabcbbbcdbdacdcbabcbbadbabaccdabcbbbddbccadccababddcdaccadbdccbccdbcaddbdacbdccacbbbabacbdcdadcddbcdaabdabccaadbbabbdbaddacbaccbaaadddabcbbdaabcbaabaaaddcbbddacdbabadcaacddcccadbbaaddcbdcbaaadbdabddbdcabaaacabbbaddaadcaddbbcadabcdcadbaadccadcddddccccacbbaacdcdaaabcdbcadaadabcddaaddcbbbccbbcbbbbdcbadcdcddcdcaacababddddcccbabbdabadabddddadcddacacdaddbaadaadbaabcccccdacdbbbbbbbaaaadbdaabbacadadbbdacdabdadbbacadabacabbbbacbdbcadbdcddabcbbccbdbdacabbdcaaadcdaddcdaadbbddabdbccbcadcbcbbbbadcddbacaddabdacacabdcdacdcbbcaddcaaccbbdbacabcdcaadaadbccdaabcadbbcaaaadabbccadbabacaadbbdaaaddcabdaaddbadbcdcdcdbacaadaadcdacbdcbbcddbdbcbaacdaaddccdadaadacdcdddabbaacbcdcaddddaabdcccdbccbcaaadabdbadcdacaabcdacaabcaacdcbadacddbaacdbaaaddbbcaabbaaacbadbddcdbababcdaddabbcbacaacdcaddbbcdddbddbadabaaabcdccbdbdaddcccdaaddcacdcdccacbaccacdbdddbcbcccdbbcabcadbabcbcbaacbcdbbdbddcadcccdbbdcaddccbbbdacbbcadaabbbabcaabccdadcabdcbdbaacccccaacaacddabcbcddcdaddbabababacdbabbbacbcbbdbccadcdbaaccbccddabcbdcbcdbccbbbccdbdaabdadcdacdcdaaabcbbaadbddbddcbbbdcccacacaddadbacdcabdbcbacbddabddccdbbcaaccaaabdcdbabdbccdadcdbdddddbadbbccacbadccddcdcabadcdbcaabcbbddbcacbdbddcacdddbaabcbbcdbbdaabddbccbbdbcabaacbddbcabdbccbadbbcabaacbdacabbccdcaccbbcaadaadadbcbaaccacddbdacaaaadbddbabcdddcbddabaadadadadbbccccadadadccdddbbccbdadbdabaacaacdcdaddadbdcbacdbbccbdbbbbbadcdddbccbabcccbccaabbdbbcdbaccadadacacdaacbadcbbbbddddcacabdbadcdcbbaadbbbcbcacbbaaccbacabbdaaaaacbabacdbdbbdcdcbbacaacaabcdaaadcbcbacbbaadaddcdabdbadcbcbbbabaccccaacddccaadbbbacddcddbbbabbcaaddcccccbbaddcdbcdddabbcbcbbbaabbcaacabccbbbabcdaaabdadbccacacbacbdbbbdacbdadccdcababccbbbabcdadbdccadcbbbdbdcadbddacabbcbbbdbdcbadcdccabcbbbdacadbcabbcddccbddabdabbbbaaabbbadaaadbadccccbcbcbdbcaddcdbcddbcccadadcdaacccdbbadbcabddcacdaabcdacddbbabdcdddcababbcadbcadbdcbcdcadbbdbdaacbdccacdadaaacddccababbdbbbdaadacddccbbadbdbbbddcbcdacdbaddccaabcdbcadaabcddbadccbacbddbbdbdbbdaadcadddcddbddcddbbddbacbadbabbcadadacbdacddbadaddccbaadbabdaaacccdabcddcbdbdcabdacdcdaabccadcbccbdddbaaaadbbaabcaadcacadcacabbadddabddaadbccacabbacabbbbcbdbaaabddadcdaacdbdaddcaaaabaddaccccccacccdcbcaaaaddbcbdacabaacbcbabddbcddcbcdcbdbbaababcbbbdddbbbbdbdacdaccabacbddbadcbbabbcdaddcacbaacccdcdbdabadbdbcbbcadbdbddabcbabdcccdccdbccaabbccbaabadaabaadaccacdacadbbabdcadccabcacabcdbadddbcbcdaabbbbccacabddbaacadcaccbbbcbddbddcbdbabadadcaacdcdbcdabaabaaacbadcadbbadcabaddacdbdddacbcccdabbdcaabbdbdadbabbdcaaaacdbaadcadcadccddccadaadadcacdbacbababcadbaddbbddcaababdabaadddcddacadcdbccbcbbabadbbbccbadcbcacddbbddadcacdabdbdaaccbbaaaabddaabacdcbcdbcddccccaaaaaaaabdaccdadabdabdaddacbabdabdbacbbaabbcadbcaccdddadbdbcacbccbdcddabaabacbdbdcbabaddaaaaaababbbdbbcaccacbcddbddabbdadcacccbbdbdabccbbbddacbcbacdabdbccdcdddcbdbbaaaacdcbcbcbacdbbacddadbbbdcacddaddccabcccdacacdccacbcaacbcaccaccbdbbdcdbabbbdbcdddabadacccacdcbaabacbcabaabdaaabdccddcabcddcdaaaacdccddabdddbdcbcdadbadbdabadcddbbdaaccccacbadbabbbdadacadaadacbbabaacdacadbddbdbbacdaacaabcabcbbaccdcbabcacbadaccccaccdcaacabcbbbbdccccacbaadbdbbbdccacbcbbcaabbbcdddcbcbacbacccdcbbbbbbdcbdbaabaccadcbbcaddaacbcbabbdbcdbcccddaabaddddacaddacbabbbcacccaddcbcadaaacbaabdaacbdacbbcabdcddcaaaadabdadbbcdcaadccbdacdbcabcaacbcbbddcbbcbadadbdadcdabbcabcdbcacccbddcbbbcbdaaacbbaadbbdcbccdbaaacdcddbadacbbabaacdcabaacacadabcdbdcadcaadbbadbdbbacdaccdbadbbbdaabbcbcbcbabcacdcadbccdabaaddbadbcbbbccddbcaacdbdccacadbdbabadbabadbcdaaadccacccdbcdabadcdcaccabacdadcbbdabbbcaabaaddabdddaadaacaddbbbcbdcbadbabaddbcdaaddcadcbcddacdbadbacdcdbbcacbdadbaabcdaaccadbacdcbbacaabcdabbbdbddddccbddabbcaaacaccbbabcdbcbdadaacddddcabcaadbadabaadaaabdaacaaadbcdbdacaacccdadacdbddccbdcabcbbdbdabccbbacabbbdcabdacddcdbbabdaccacacacbddadcdbbbbcbcabdadaacabcbdadcdbbcabdaabacaaaaadcbcdbabddcdccdbabdcbdcaddbaaabdcdbdbadadcabaccaaadbbbcbaadbabadccaadcbcbabdadccadbdadabcdaddcbdaacbbcbacaabcaacddbdaaabaccaacaddcdcbbdbadbbbcddaacadcccaacabbdbdbdcdaaaccabbaabbcbdcbdaaabcadcacdccdadacbaaaccabcabcdbbdaccaacbdbcdbaccbcaaccbababcaddabacdaadcddbaaacdcabdcaadbccdbaabddccdbdadbbdcbadbacbababddbbbcdcacaaddadbbbdacdbabdccabcaaaadadadddbcadbaabdacdddaabdacaabbdbbbadbcbdcbdcbcddccbcabcdacbdababdbdccaabbcacabdddccbdacababbcdbadbadcddcaacadcdbacccaacadabcaacadabcddcbcdadcbbdabaddadbaaddcbcccbacbbdcacdcadccaacabbacaccbbbcbbccdccbcdcacbbdadccaccaccacdadaadbbdaacadbacdbddcbadddaadbddadabdbbdadcadbcbdcccddbcbbbdcbdcdaabdacdbcccaaddccacddbcddaabcaabbcbbdcdbbbadddaccdcaabbcbdaccccacdadcbcddabddbbcdcbccdabcbdbcbdcaccacdbcdaccdcdddbccbcaacdaabcaaabdccbbaaabbccdaacbadcdbcbddaacccababbcaabcdddcccadaacddbddcbaabcaabddaabbbcadacdbcdabbabcbdcadadcacadbccbdcdbcdbddbbacbbaddcdaacddbbcbababaddbacaaabdddaccbbcbadcaccabaaacdbaacdcbddbbdcabcdbdbabbddaababdbdabaaadacbcdcaaaadcbadbaaacbdbddcbadcdcbccccdabbccbbcbcdbdadcdcabbdaabbaaacdbdabcbbbccbbcbbdabbcdaccdcccdddbcaddbbcaaacbbabadaddbbddcdbbdadddbbacdabdacaddbaacdbaaacbaababbcccabbccccccababdaabbcbcaacddaaabbcbdcbaaaddcadabdcdcbaaadabaaddadbcdbcacdcdcbbbbcbcacbbccaaaaacbaaddabbcbacddcadccbcbadbdabcccbabaaacccabcabbabdacccdbdbdaadbacbdccddaccccccadccbcdccadaddcbcbdbacabbbdcbddbabcddccccbccbbadbabdcdbdabbabddbaacdadabcbaccddbdaddcadabbadaddbcbbaabdbdcbdadadcdbcbdcacabcbcdbbbbbaccabddacdbcdacccadacaadaadadabdabdcabddbcccdbacbdbacacccababcdcddabcddddacdbdbabccadddccbdabbadabdbaabddbdcabadbabadbdacdcdddabccacacadbcccdabcccdabbdddbbdbbbbaabbadbbdccddddaaaaddababddcddaaaaadbcaacbddacbbcdaaadadcadbdabdadabdcccbddbabcbdadbaccdabbbcbacacbbbcbdbabcabdaaacabcbbabcdcaadbddbdbbdbadbcdddcabddddbcbdcddcdadcbdbddcaccdddccdcaaadbacaacdddbbcbbbbcaadddacabbdcbcabadbaccacccbcbbadabdddcdbccddcbacabccabcbadcddacaddadadacccbcdbcdcaddaaccddacdbcaacbddadadddadcbacdcabdadcccabdccacdcbadbbddbcdbaddabdccbbcccddacddadadcacdcaacdaabacdcddccdbdddabbbcbaacccbcddcdabadaabcdcbbccaabaccccadcbacccddabdcbbddbabbabbcbbccbdcdbbccdbdcbcbdbdacbbcadaabdcccabbbacbccaaacbabaaacdbbcbcddccbbbdcdacddcdacdddcbcccdaddcdbbbcaaccbcbbdbdbbbbdbbbdbbaacabbaaadacddccdcaacdcdcbcbbcabddaaabdcbaaadbbdcdbaccadbdcbbdbabbacbdadccacbcadddccbadabbcbadabdaccbcddbacdabdcdcbdaddcaccbbbbdaabdcdddcdcdddbcbacabcbcdcbabbacbcbbddaabddbcdabbabdbcdbcbdbabccadcbcccaadcdbdbbcadbdadbdacabbdbbdcdbdcadaccababddddbcacccbaabcaddcabbcadbdacdcbbccbcbdacbcaccdbacadcbbbdbbdcadbcabcdbaacabdbdcdaaaaabcdbbbadbcbaddcacbdbdbdadbcadababbbabddababacbadabcdadbbcbbddaabcbbcdadaccdcddabacabcbddabbbbbbadcdcdbabbcbccadaadaaaddcdddbabbaaaabddaddbcbcbdacdaaabdcddbddbbaaddababccaaddacdcabbddddadababdcdbdaddbbcccbaddbcccdcababcacdabdddcdbdadbbcaabdcccbdbcccbdbdcdbaadbadcbcdbaaddcbbbccdaccccadacccadcadddaabcaabccdddabcbcdbaccdcbbdbcbccacabbabbbadacdabcbadddbaaacbbadbcbbcbddccbdacaadadbcdaccbbabddaacdbdddacdcbdbcbdcdcaccdaacadabaacaaddacbdcaaaacddbbaadaadbcaacbdaadbbcddccaaddddcbcccbcaaddbadcbddddbcabbbddcccbddbabbdcdbabcbcdbbcbdbadddbacccccacbccdbdbdbabcdddacdacddbdccabacdccccbbcccabcbababbbbbbdcaabcdccbbacbcbdaaaccacaaacbcddbcacbbbabddbddbdbbbabcbbbadddbaaaccccaabbadbabcdadbdbbacbcbcbacacacccacdbdaaaacccadbcbbcbcbdddcbcdbdbadcadcadadbdcbbbddbabcdbabbadccccaacccdbdacddabbbaadddbbdbcaabadcadadcaaaddadbcadcadccaacbabdbcbabcbdcabcaacdacaccaabbbbadadabccadabaacbcbbcbcbaacdddcbadaaacccbbbaccddaacbbbcbbdaaabcbdbbabadcdddcdcbccddadbaccbdbddbbdccbddacddcabcaacaccbcadcbbcddacbaccdadbbdaaaacddadccaacadcabbbcbcdddbbaadccdbcadacdcdddbbccbbabaaccbbbabbdbdbcccdadcdbacabdbbcbbaccabcccaaabadcaacacabbbdaccccadbdbabbbdabcdbddbcacccbadbdccacbddcbdcdbcdabbcacbdcdddcabadcacacccbdaccdbbbddbbaacbbccbbbdcbdbbbadadcdaabbdabaccbabdabdcdcabbcbabbadaaaacdcbcacdadcaddbcbbcdadabcbabcbabbacbaaacaabaadadaddaabccbdacdccbbbadcbbdbddacccaabcdcdccbdddabbccccabbaacbcdaaddacbbcbdddbdccbbaacdddcbdccabaababcadcdbcbcbbbacabcbacacacaadcdcccdabddbbaabcbcaadcababdbbcacaacdbcdccbdaadbbcaaacbbbacbadaabaaabaabcbaaaaccabcbbadbddcabdcccccdccdccaabadbdaadcaaacaaaccbbcdacabbbcdabcbbadaacdcbdaacadbacadcbabbaaabaabbbdadccbcaddcdcbacbbacbbddcdbbacdcaccacdabdcbaddcacadbcbcdcbdbcacdbbbcaaddddaadcbcdbdcaaccbcdbbaaddbdcacdbaaabccddabbdabdabcbbbbabbacdaccccddbcccddbdcdbdcbddbdbdbdbaabacadbdccadcbbaddbcdddcacbbacaadcdddddcbcbbbabdcbcddadbbadccccbbcdbcbcbcbbbaaacacdbacadcbbbbdcaaccddcdaacabbbdcaabaaabbcddaabcccdaabcdcdccccbcbbdbabcdcacbadacccbdcacdbddbbdaaccdcdaccdcbbdbcddabadcdadcbcddbcddbadbcbbacddbcabaaadaccbabdcbbbcabdaadcbaaabdcbbbabbdaccbbaaababacdabdbcbdccddbcbddcbdacddbcccbbccddddccdcbacddaacadbbadcaccbbdbdabcbaacdbbccdcddbaccaabbaccbbbcbcbbdabaaddcbdacbdcddababadadcddcccadabbdcacdcbbcddcbadbddcbcbdcaacbddbccdccbdabbbdbbcbcbccdabbcaddcdcccdcccaddcabdbabbddcabbbabbdadbcadcdccbcbcdaddadacddaaaaccbdbaaaaccdbacbacbdccdddaddabdccdbaddbaabdcdddbbcbbbbabdadddadcbbbadbabacdacbdbbacddadcbbdbadbacdabaadddbdbbaccadabaadcabddbadbaaadabacccdbdbcbaaaddbcbbbbabcbbadaaaaaddaddbdaabbcccbdaabccbcabdadddcacbaabaadbbbccddacabaccbbbacabcbbacacbbcdcbacadbcbdadbcbabaddccccdbbbbaaabcbabbdbddddbcccbbccbddcadaabdaabccbcdbcaccbabbabadabbbdcbadabadcdcbcbccbbbcddaaacdacbacacaabbdcaabbccaadcadadcbbdbaabdcdacdadccdbacbdacaaddcabbaddabcabcdbabcdacaabdbdaabcddcdccaaddabcbcdacaacbdcadadadbcbddaacccdcdaaacbadabbdcabbcadcabcccbaaababbadcacbbcdcadbccdbdacbbccadbddabaddabdbddcdccabbadbdadddbbbcdbccadcdcdbbacbdcabaccadddabcdbccddacaacccaccddacdacbddcaccabbcacabaccabbbadbdcbcaabbcaaacbaddbbaabccbabaaaccddbcdabbbbcbbbdbcddcdaccbbadadacdbaaaaabcabcabcbaacbdcddbdacaddbcacdacbbdbbbccabdcabdcbccabccbbdadbcbcdddcdccaccaaaadbcdacaccbacbcbdcdddbbaddbccbbabcacbdbaadccddacaaacdaababddddbccaccdbbcdaababbbabdadadddbabbbbdbaddddbddbbbbcdcdadbdcabbacbddbdaacabcdcaccaccddbcdbdcabbddccdbaadbdcdbbbcbabbcdadabbabaaadbdaababcdbcbacbdabdacacbdcddddbbbabcdbdbbccadaabaddabacbbbccbdddcddbdbddbbbdbabadddacccacddbbaadbcaadddacdccbddccddcaaaabcacbdcabccccaddbbddacddcddccdaadbbddbbabdddadaddacbdbaccaddcbcbcacbcdadbcabddadbbdacdacbcbaacdbbacdacccbcabbbabbbddaaabbaccbdadcbaadbadbaaccbadbcddcdababaaccbbdaacadbdaadbbcdcbaacdcdbacacbbbadcabcdcacdabccaaadbdcacbcbcaadaacacdaaabacdadbbddaacaadacbaadccadbcacacbaabddccccacbacccdadacacddcadcdacccabbcadbdacadddddacabcdaaccddaaadaacaabbbcdbcdadcdbadddbbcdcccbabaaddbdbbccdcdddbbcccbcaaadcbbccbbaabadccbbdaabbcdbbbdcbcbccbcacaadddbaacadcdbbcddcbdbcadbbcbbaaacddcacbdacbcabcdcccbcdbbdddcabcadccddbacdaabacadbcdbcdcdddbaaabbcbdddbabbccdcdbacabacadbacccbacabdcacbdcdbcbadbcabcaadaabaccbbbbcaccccdbbcbcabcbddbacbadcbabacbdaacabcbacccacddbddbbcdcaddddaddabbdbbadaacbadbacbdbaacbcadbcdaccbdbdabcacdddbccdacacddbacbbdbdbbacbaadbabcdaabbaaaccdadaddbacabaaabdabdcdabcaadbdcdacaababcdbddcdcbbdabdbaccddbadaabcdacabbddddbbadccbdaabcbbbdaccbaccdabcddbbbaadaabbaaabdbaddccaabbdbaadcabcbadcdbdbaaccbcbbdcbbdbadadacdaaabdcaddaccbcbdaccaddccbdaaaddccbbbcccbcdddccbbbbabcabdbcdddccdcbbddababdbcbacbccadbccccdaacaacdccdbccbadaddaababddcdabccadcdadccbabbaababcaddaaddadcdabbadbcbabbdbbadaadcddcdbbcdcbdcccbdbadcbbcbaddadaabbaabdbdcbaccdadddddabbcdabdcbadbaaadcbadcdbacbbbcdacadaaacdbdacddaabdccccadbbaaddbcdadcccdaccbdcdacacadcadabaaddbcacdbabdcaddddddaaadbbcbcbdbbabcabdadacdabcaaacbddccbacadaddbaaddacccddcadbaddddacbbdbddaccbcbccaaaadcabbcddcccbccaacbdcbacddabdcccabdadddbacacbddaccaacabbbccdcbaccaabccbdadcbaadbcacdcdcbbacdacdcadccbdddbdaccaabbbbdbccbacddcdaacddcabcbadabcdbbcabbbddccbdbcbdcbbdbddabbabbbdcbbaccaacaabddcacadccbcacdabbbadddcbbdcadcacdaddbdabdacbbbddbadbbbacaccdacdabccdadcdcadbccaccbbddcbbddaaccdcbcdaccbbddbaacabacdcaadcccaadacbbdaadaaddcdadababacaccabcbddbddbacdbddcbdabcbcbbdbdbbabccbadcdddacdabacdabdcccdacccbcccbbdddcdadcddacdacdbcdcadacaaaabbdabdcdabcdadccccccabbbbbcbdbbdadcddaccaccbdcdabdcbcddbccbccdadaabbacccbbbaacdcdabccdaddbdbadabcadddcbcbbcdbaccddcadabbbdbabcdbbdadbcdacadabaccadbcbddcdabbddbdddccbbdacaacacbabadaacabbcbdaaabdbadaaaacddacabbabcacadddabdcdcbbabbabbcbcadcdcbadccbacaacdddbabaddabbdbddcdabdddadbcbbaacadccdbcddddadaccadcbcbdbbaabacddcddcdcdbcdbdbbddcabcadabadbabcdbabdaadaddaaacaccadbcdbdcdcabcbbbccbbbcccbadbaabacdbdbbcdbbcaddbadbdacdcaaacbdaaaccbbacdaabdcdaadbadccccadabbcddcbbbbdabbadadcabcbbabdabbacbbcabbdbababdabacbcadadddbbbaabbdcdaabdbcbdbacbcdbbddccabaabbaaacababcaabbaccaccdacaaacbdbcbbbcdbccadadadccbcbbbbbaaabbaaaadbdcdadabaacbadddacaabcdacdaddabbbcaddddaacabadacbdbdbbcbbabbadcadabddbcadadcdbacadbabddaabacadaccbdacadabdddbccabaadbdcaddadbdacbabdddcbaabbbadbacabacbbdccaaccabcccbbdbdbdaadbdacccaabdbadadbcababadbaaacabcbcdacccabdccddcbaaccbdabbdabbddcaabbabccbdaadadcbacaababdbacddcccbdbbddccbdddbbaabbbcabcbdacacaacbabaaddcacabaddbccccddaadadabcbcbcdbbbbbadddabdcabcbacdbdaccdacbbaacccabbdbbacaaccccacaabcbddacdcaacddcbcbcbbcabccdbbaaabcccacdcabadddbbbddacdabbdaddcbdbbbbcdcdbadadaacbbddbabadcdaddaadcacdbccbbccbcbbaccbcbcaccaadabbbdcaaaabbdddadcababbbacaaadbaccbadcddddcadadabdaaabcabbbcbdcbdbcdbaaabdbcdbdbbadccdabcadaaccbcdcbbabccbacbdcddbcacacaaabdbdcdddabbadaddbabcdbaddacddadbdccbbdcbadabdccdbacabadcbabbdcbddacdaacbaddcaaaadcabdbcbacadcbdccdacabddbddbbccadbcddbccbacddbbcdbbcbcbcddacdbcdcbbdbacbcbabccbdaadbccacbbcdbdbbcdbaadbbdbadbdcaacddaaddbabdcacdccdacdababbadacadaddabcdacacccccaacbbaddabdacacadacccdacbcbbccaaccadddbddcbcdddbdcddacbdaabdacbcaaacadbabccaacccaddcdadbddadaaaccdbdcbcddbabdcdddabcbbbdaadcdbdcdccbcdacbccbacabadbbadcdabccddbcdcbadcabbdbaddcdcbdababcadbcbcaacccaccbdbbddbbcdbddbbcaccbcacdbbccdbbdddbaaabcbaccbdbbcbcaaabacddccbcbcccdbbbacacbdddbdcaacbccbacbcbabcddbabdcacabadbcbaccdbdbabadcccbbadaaddadbcccdacbbddcbbabcdbaabbdbababdaabcbbbcbdaababcadbbbacaddbcccddbbbdcabdcabacadddccdccddabdbddddadabdaddbdbdddaabbabbaabababbbbbcddcabcacbacdaaabcabbbcaaabacbdabdadadcaccacdacddbadbcabbdcdccdddbaddddcbdbdadccdcdbbbcdddddcdcaacbdbaaadabcbcddacbadcdddbcbddcacdabcdddcabdabdddcacadcaddcadbdcbddccbdabdaccaabbdbdddaccbaaccbacdbbbbabdbcddaabbcabbccdcbddadabadbaabddcddbddbaaadbacbbdbacdbadddbadbcdcadcccbcaaddaccccdcbbacccacdabaabdddddbcacaaaadaddbbbcabacaadccdcdacccdcacadbdbccdbcacaddbddcdcdcccbaddcaabdbdcadccdbbaacdbbcaddbccaabaabbdaaaaccbcdacdadddcdcbccccabccbbacdbbbbbcbdbccacbdbdcbbacabacbcadabbcbdaabbddcdbacddbacdccbdbaacccddccaddacabaacadabccdbddababdccbdbadcdacadabcdadbdbcbacbdbaccacdaaabbaadaabcaacaaabbbababaddcbadbdcdcbbaabdadbbcbddddccccbaddccbadbdbccbbcadabcdbaabcccdcaadaabacbdbaadaddbbdbbaabccddcbdaacddbaabbaaadddadacacaddbcbaadbdcbbdadbccddcdccaaabadbabddabaddbcbbcaddcadbbaadcbcaaddccaadabccaadbcbcbcaddadbbdcdcdbccadadbbdbbbccbabcacdbcdbbbbbdaadcacdbbdbcddbbcbaaadbcbbcdbbcccccbbaddccbcaadacdbdbdbcbdadcddadcaacdaabdcaabbabbbddadaabcccdbdadaacababbabcadccbabdbdbdbddcacbcadacacddaaccddaaccabccdbadddcacaddcddaacbaaaddddbaccdaadaadbacbacabdbadccdcdccbbdbaddbdcdbaacbbbbbbbacbbadcbccacdcdccbbdbccdbacabbdaaacadcbcccaddcdcccbabadadcccddaaccaabbdcaccaaabdbbbdadaacdcadaababccacbbabdbbcdddaaacdabbdbcbcbdbcdaaccdbbabccdaccadcccbadadadabdaddbacdccadabcbbcdaddcbcadcdcaababcdcbdcdadbccccaadcaaccabcbcdddbbaaccdbadbcdabaccabdcdbccddbadabdacaabbbcbbdcdbcadcddaadbacbccbbbababdbcdadccadbcbdddadccacdbcdaabddbadaacbacbadbbccaaccdcacddbaacddcbdcacdbdcdcddbcaacdcaabadbcadcbdbdaaddcddabbbacbacabbabadcaabadbdbabbcadabcacdbccdbadcababddbcdbacbadadadacdaaadcddaabbaaabacbbcadbadcabcdbbcdabccbbdcabcadcccdcadbdbcbccdadcabbdbcadaddcdcaabdcabbcdcbadbadcdaabcbcaaacbddcbbbbababdbcbabcbdcbbadcdbabcaddccbadbabadcdaabccaabdccdadcddcaacaddddccccbdbbabacdbbcbcdcbbbaddcaaabbdbddccaadccddcdabcddbccacddacbbbcadacbaddbbbaadacacaacdcaababdaccaacbabcadaadccdaaacbdbaadbbadcadbbbcbabbccabacdcadacdcdaaaaccdadcdcabbbdbacdcdbaddcabcdcaaddbdabbdacccccbbcdddcdcdccbbdaabdbbcacbcdbabacddbbcdaaaddacaaddcbcbabdcdcaccbabbcdabaaadaddbccdaadddcccccbbcccbbabadaccbadccbcadcddacbbcdbcdcccccdaaddbdcbbacaddadaadbcccadcbbdcbabccbaacaccadbaccacabaabdccddccbadbddddacbddcddacdbddcadbacdbcdccbaadbaaacacdabccdadbaaaabdbabcdaabcdcadbabbadddcbcccbabdcabdadddbbcbabababccaadbacbcddabccababcaacdcdbbbaabcdabbcbbdcdcadcbbaaaadbbadbabdcccbabbbdbddaddbbdbbcbcddacbdacabcddbdcbccbbdbbbacbcccddbbdbadabccacdbcaccdabcdbabdbadccdcdbcdcbdacbabacddbacaaadcdabcabadcbcbcdcabbbdbdbaacdabaabbcdcbddadbdbdcabdccccbabddddcbddaababbbaccbbcbbccbbbaddadaadcabddbcddbadbcbbdccbdcdbaaabcdccdbbbacaddbdcaadbcabdbbcacdbbbaacadbbccadaddcaabcadbcbaadcadcaabdcbdcdcbaaaabbbdcababccbccccbbbccaaabddcabdbdbccaddcbaaacccdddbcabccbbddcccdadabdcabbbdaddcabdaadcdabbdccbcdbcaadaacbabaabdaacdaccbaaccbddbcdcdcadccbbbcbdddaaacdbcbbadddbccdabbccbacdcbbcabadbcdbacbaaadacdcddcaadbdaddbdaddbbdbcadadcaccccdabdcbabacbccbaabaabcbabbcdbdbbdadcdbaaacccccabbdccbaadcdbacccbaabacaaacdbababadabcadaaaacadcdacdddbcddaccbadbacbabdbccddadaaccadacabbccccaadcdcacbdcadbbbcaddbdcadbcbcdaacdcbdaaaabdadbcbbdcdcbaccaccccbdccbdabbaaddbbacacddddadacaddaaaacabcbacabccabbcddcbdaabdadbbacdddacdcddbdddbbcdadcdcdbcdccbaacdbcadccacbdbccdaaccdcaddbcbbccdaaddabddaaabaaccaccbbbddcaadbccbcabbbbccaabccccabbbbbdbdcabdcdbcdadbdcbcabbcbbbadcbdaabaddbadadaaaadccdaadcdddaabdbbabacbadacbaccdabacdcdccbaaaaabcddaccacdabacdaacbdcdbccdaacbbcdbdbbbadcbbddbdacdcbbdddacddaadccbbbbaaacabadbaaaddbbadadcdaacccbadbadbdabccdaacbddcadababcabbdacbcadcbacbdadcdabcbccaaadbcaabddcdcdbcccadcaacdabdbcccaddacbcaaaaccdcbaddcbdcadabdcdbaabcadccccdacaabbbbbcbadbcaaacdacacabcddacdadbcddbbbbcdcbbacdaabcaddadccacdcccbdbbbccbbcdbbcdaabdadcccbacadaddbdbccabdaccdcbcddcdaabbabaadaaddaddacacbddabadcdbacaabbbadcccbcacabbbcdbccbbdaddabcacbbddcbdddbabdccdaabcdaddacaaddbdccbaadbdbbbaddabbabdabadabccabcbccbdbcbbbcbcabadacacaacababacbaadbbdcdadcdcdbabddbacdccadacbaacddccababbaaadacdaaccbdcccbdbacbbcbbabbadabdccdcdaadbaabbddbacadbdbdbabdbdacbcbdcdbadbacabcdcaccaaccdacccbacbdaacddcdaacacaacbcbabdbcaabbbbbcaacdbbbdbdcdbacddcaaaacdddaabdadbaaadccdabdbdbbacddcddbcddbdacacaaabdbdddabbdcbcabbcaaaccabbaabcabcccdcbdbdbbbbbbadcbbcabccccbbdabccabccddddbcdcdccbdccdcadabccacaccddbbbbacdbbdcbacbdbcbdcbcdabadcbbbcabcccbccbdbabcccbbacddcaacaccaabacbbbbdcabbddbbddcbaabaadbdcabcabadaddaadbaabbbbbbadaaaddcccddaddabdbccdbbabcbabbbcaddbbdcadabbbbcbddcdaccbdaadaccadaccccacabdacdddccbbacabbdbbbcbcddbbdcdcabcbcaacbbcacaddcbcbccdbbdaacbbbbdabbabcadbbacbcbacaabbcaabddacabcaddcdcabadbdbdbababdbbaadbdcbbbddccccdacdadbdbdddacaacddbabcdaadbdcddbbbbbdcacccddcbbabbbdaaaacabdaadcdaadcdadcdddaaadabaadbbbbdccbcdaddddababccbcdccbbbcccddaabbdbaddacabbbccadadcbacadbacbdbdccdcadadcbdcadaadcbbcdaacbbbcacbcbcbcdacbcddccacdddccdbaccdcdaddabcadbaacbcbcccacaccacaadaaaccbdcbbbabadbdcacbdbcbdbccadcdbcdaadadbddcacdbaddababbcdaddcabacccabbbddbdbdcddbbdbdcaccdcbbdadcababdadbadddddacdcdccacbccddbcbcddbcdddacdcbcdcdcbbbbccbcdadadadddbcdcbadaabcbabdcbddbdbaacabdbacaddaabbabbddaabccccbbccbabdacbdcbaacbbbcddbcacaaadccccddcdabdcdbadcdbddcdddbbbabbdabcbdbbcbcddadcdbbabbddaaacabdadccbcaaadacadbaadbbbbadcbdaaadbbdbdacddbadabbdbdcccacddcdcbcaadadcdbdcdccddbdacbbccacabcbbddacbcabbbccdadccadadbdbbbbdcdacccdacabaacdabbcaddcddaadcacbbccdadacbacbcbbaacbadbabcbbbdcabadabcdbaabadabaadadbbcdaacdcadadbdcdcdadbbbabbdcccaabddbabbccbbabbbbccaabaabbacaaaadccbbbbdabcacdaadbbdcccdcbaaddbccdacccbbbbdbbacbdcdcbbddacaadadadcadcabaddbdbdbaabbabcddbcdcbcdbaabbbcdacabdbddbabbabbbcaccabdbbdcdabadcdaacbadcdccadbbabcdacacaacbbaaaadadacdaccbddbbdcdcddbcbcbaacbacbacbcbbabaaadacbdcbaabbcabcaddbddcbbdbaccbabadcbcddbccbaabbdbbbdcbcdbdbddcabcdcdbacdcadcaababcbcabcccdccababacddcaaabcdcaabdcbcbaaddadaabadddbbbdbcdbbcdbbcddabbbcabbaddcbcabddbacdadacdcdbabcadbcacddbcddbacadaaacdcaabdabcdddbabacbacdccaababcbcdbcaddbbdbaabaddccdccbbcaaaccddaccdbdbadbcdcacbbbcbdbbccdaaaabacacadadcabcccbddbacabbbccaaabddbccbabcdabaddcbcdbdadccacbccaccdddbddbbdcabbddcadcdcdcddccadcbdabacbccadbdabcdccabbabccccccabccbbbaacccccaadbaacbacdcdbaacdbacddcdaaddddcaccabacbdcacbbacabdcdbadcbccbbbbccaabbdbcbacbbdbaacbddadadcbabbdcadbddcbcdcbccdcaabcdabbbbcacadaccaacccdbbaddbdcdddbdabcbcbcdabaadbcaaccabdcbdbcddccdcddaaaaaaabbdbdcaddaaacaacaabddcaadddabdbcddddcccabbdbbddccabdabdcddaaccbbbcdbbaacaccbdcdccbccaacbadaaabddddbaddadcbbaadcbacbcbdddcadbacddbdacbbccbadaccadadcaaadadbdcadacbbcbdddacdadbdddbdddaaaacbcddcbadaccdcbdbcaaadacbdcacdbbabaadccacbdcabcccbaabacbababdcbabbbbcdaaacdaaabdadacbbbadbbddcddccbacaabdccdbbcadddabbcabdccbabccabaabdcccdbccdbbbbaaaccdaddacbccdccbbdadbdccddacacabdcacadabbbacdbbddadbaabdcdccabbcbdaccbcccbdacdcbcdacbdbbbcabcaaabbbaaabbbbcbccdcdcbabcbadbabdccdabbdabadcadbdabdbcdabbadbdddcadbadadbbcabaacabcacdcacbcccabaccdcaaacdbbddaaddbdcdccbacdcdcdbbdccdababbccdddbcdabbaabadbdbdbbaacdadcdadddbacaccbdccbbdbbaaacbcadaababbbabacdaddacbadbcabacbcabbcbcbbcabcadbaaddcbabaaabddccacadddaccbaddbbadccbdccbcdbbcbaadabdbbbcbcdcddbaacccdacddbddaaddccddcaabdadcdbabbaddcdabbdbbcdaadacdaacdbddaadcdadadccbddcabbaacccbdccbcbbddcdbaddadbcbdbabcdcaddadbdacaddbcbaababbacbacdadbcdccbbdaacbddadaddcccbacddadaaccbcccdabaacbdbbddaabacbbcccaacacbaabccbccadbcdaacacacacaaadccbcbaddcbdcabcbbdacbcccddbbacbdadcaadbcadabadbdbadacdacdadcdcbbdcdcbbacaccbaaccdcbbdabcdddddabccddccaabddbbbdabccadabcabddbbcaabadacaaddaaddcbdbacbcccbabaaccaaabaccdbddaacbdbaddccbbdabbcdcddbcabbdbccabdacbaadcdbdabbdcddcdcaaaddcdcdacadacaadccdcbacdbbccbacdddacbcbcaccddadbabccddbcaabdabcdbcccdcacccbbbbaaadddcabbadabcaccdcadadbdacdbaacddccbcbdcabbbbdbcccabbddadcaadbdbbbdaddcbdbdaaddaddbbadbdabcaaacbbaadadadcdcddacccbcddcbbcbacbcaabbccbcaaccacbdcaddabbaabaaaaaccddcbcddbcbcdddacdacddabbabdbaacdbdbbbaddcdacdbbdacaccdbabcbcddddabbccbacccbcbbdcbccdaccbabbcabbcdbdadbdbcaaddbcacdaabababbcbbacadbbdcabbbdaacbdabbabaadccdcdcbdaddcbcddbbaaacdcaaddaaccccccacdadcdbbabddaadbaaacadbcacaadbabcaacacccabbbbbccdaddcaccabddaaaddcacbbbacdccadbacacccbcbdccccadccabdacdbbcbbaababdcccbaacdccdcbcdacdbcaabdababdbcdddcbbaacabddbaabbbbaaacaabaaabacdcdabaabccadcdddaadacdabccccbbdddbcaaaadcadcacacdbdcdaaddddccdbacdcbacdcdabdacdbcddcccdadacdadaadaddbdbcbcdadbabdcbacdacaadcbbaacbdbbdcdcbdcacbdbabdccdacabdbbcddcdbadabaadcabdaccbdcbbddcbcbdbbbaddacdcdacddcacccabbabacbcccdaadcccdbdabbaabdcdbacdcbabcaaaaabdbcbdaccaaddabaadcbabddadacabbaacccabdddbcacbdaadbbdacccadbacbddbcaaaaccabcdddccaaacaabcbcccacddddccdbabbdbbbbbbddacbdbdcddcbcbddbcddbbaaadbcabbdabddcbcbccadaacdcdcbdcbcbbddbacbbbbbaddbbabccdacdbcbcddbacdbdccabadbadbabddddbbcbbadabdadbabdcdcbdcdacaadacabdadbbbdbadccacabdcddcbbddcdcbbbaacbbcaacbdabbddacacbbcbdcadbddcacbdaccbbdddabccdcacaaacaddcaaaddadacddccdbacddcdcadabddbbcccabbadbaacbdaadaccbbabcdbabbabbdbadbababbdbaaddccaaacdcdbdcacabdbabcbcbcdccabcaadcadaadcbcdccccbcdcabadbadcabcabadaabddbacdcccbbaabbdcaaabccddccbdccdaabdaccccdadbddbdcaacdcdabbbaabddaaddcdddddabdcaadabdbcdbcadacccaaabaccbbdaaaacacdbccbadbcbbcbcccacacccdbcbdbccccbdaadbdddaaaaaaabcacadccbdcddaaabddacdbdbcbdbcdadddbccdaaaaabadaadbccddccdbdcccaadaccabcadddaacacccdcdabbcababbabacbddbcbaaccaccbabcdcccbbbccbcdcacbcbaacbdbcaaaabdbaccdddabcddbbbdbcabacccdcbaddaaadcccdccdadbddcadabccccdaabbbbcaaabbaaacabbdcbbbdbbdcaaacaabdaaacbdaabaaddacbdbdacddadabdcdcbcdbacdaddbbbdbdcadcadaabaaaadcddbccddcabddccdcdddddcdcdcbdadddbabbbcddcadaacbcdcddbdbcbabcadbbbddacabccdacaddbdadbdbdcbaaaaacbccaabacdaabadbaacacddcbcadabddcdaadacccdbdacbacdccdbadbcbdaaaddabadcccbbaaaaaabdaaadacdaacccbabccadccddaadadcbbaddcabbcadabdbdacbabaccacbbacbdadbaccdaccbddcbaccbaccabdbdccdcabbbbccaaadacacacadcaacdcabbbadaacbccaccbdabaccddbaabacdaaadcbcadbbaaccdbbcadabcaaabdbbdcccdcabcbcaadaabcdadabddcbdabdbdcaddcdbdbaabddcaabcacccdcbcbdccaddaddbaaccdcbbddccacacdbaccbcbcacababddcacdbccdaadddaccbdadcbcdcbccccbccbbdcacbdabbbcdaabbcdbbbbcadadaccdbacadbacbccadbdbdabdacbadaaacdaadccdbdbcdabbaccccdcaabbbbaadcdadbdcbbdaccbabdaaaccacbbdbcbbaacabcdabcccadbcaddbabdabbdbaadaacdcdbbbbccdacaccdbccacbdadddbbbbdbacbbbccaaacdccabbacdcbdccadacaabaddbbaaababcacddcccbaababbbdcaabbdaabcccadbacbadcbdddbaaacbacdbddaddbdcbbdaabcdcdaddcbcbddddabbcacbadaabcdccbdacddccccaaccadcbbbbcadddbcadbccdcabddaccddbdadacccabcbabaabcddbbdccabcdcbabacbdcadcdaaddaacdbabaadbdcabacaadbbcacacbacdbbaaddbcbdbbccacacccaaddcdacbbddacdadcdddcdbdbbdacdbdcadccbaddaccaaddbbbccbbadaddacdddcccdbcbcbcdcdbbbcadbddacadbddbbabbbcdbddcabaaacdcbccaacabddbbbcccdcdaddbccbdadccbbbbdbadccbcdddadabbdbcccbacbdcbddbdbdcdbbdaadacbcbccaaabccacabaabcccadcbddaaadcabbcadcabcddbcccccbbbadabaddcadbdabbbbdabacccacbbcacbdbddccaaadadbdaaaaadbcbaccccbdadbbbacddcadddabccbaacddaacdabbaaacbcccabcaddaadcdcdadcabdaaccacacdddcadbaccabbddacabcbcbbddadabccbdbcdaaddabcbcbbabadbdaaaccdddddddabaddabddabacaddccdbccacbddadbccbaaacabbacabbdcbccaacdddcdccdddcbdcacabbccbdbcdbbbcbcabbcabddaabbabbbacbbadbcabacbdbdbbcaaaacbadccbdaabbdaaaabbbddbddcbbdaadabbbdcacdcaaaccdbbdcdbcdbcdcbaccbcddcdbaaabdcddacdbdacccacdccbdacbbddacacdacabbdacdadbaaacabdababcdbbdddcdcddbaabdcaacdccbdbadccbdbabcbcdcbbbdbccbdacdacadcacdbddacbdddcbcaccbabacbdcacddbdacabbdabacdbabaddaadcacadbdbbdddbbcaacdbaadbcbdacbadabaabbadaccdadbabbadddcdcaadccaadaddacacdbbcddbaabddbdabdcbbcccdaaadbddcbcbcdddcdacbbbbbbbacbbdabdaaaaddccccddaccccadccbabbcbccccccbcdcdbccbdcbccdaadddaabdccdbacdddabdbdaacadcbacbaacacabdadaadadbbddbdbabddddaadacacdaacdcadbaadddbbabdcabbbadcacbcbdaacbcdccaddabdbdccadbadaacabcaadacccbbddddbaccdadccaacadbbbccdaddaccbccdbddbccddcbcabdbacdbbdabbccccbcbdaddbabbabadddcccddccbcdabacadacabaabcccadcbbcddccadbbaddcbcadaaadbcacbadcbddddbcabbcbbdccbdbcbbabdbdbcbcccabccccbcdbaacaacdabadddbcccbddbdcbbdadcbabbbcbdbccdabdaacdcbdabbbddbbdcccabaddddbccbcbcdbabbcdbcdddcaaababadcadabadcacdccdcdcccbacacdacadbcbacacccacccccbaaddacddbdbdabcaabadaddbddddaccdbabaccbdcccdccbccdbcabdabbaabbbcdddaddccbcddbccbbcaabadaaadcaccdddbbdbdbdaccbacdcbdbbadccaabbcbcbbcdcdcacadcdadddddcadbddaaccddacdccbcdabcabcdacdbdabaccbccdbbaddbbddbcadaddcaddadccabcdcddcbbabccabbadcbbdadacbddacdabbdbabbcaacabbcdccccabbdddccaccabbcbbaddbcbbacbdddadbddcadbaaadcaddcabadcaadbbcbccbddccbdabbcaadcbadcddbcdbdbcadbdccddaaabacdbdcbbccbabbabdcdbacacbacacbcbbdacaaacaadccdccccdcdbccbbbdaacddaadbcbaadadbbadaddaabccacccacaaccaaadbccbbcabaabacdbdbaccdbdcbadabbbbaacddbdcdcacdccdbbcdacdcdcadadbccbdcdcbbcbdaacdcccadaaabbdbabccdddaadcccbacacbdcbdbbbcdaaaacccaddbcbccadcbbbcacbaaaaabbbbbcbadcbbbddccdacabdcbbabadcdcdbbbcabdcccddcadacdbcaaaacdacaacbadddcccaccddcadbbdcacbcdbaaabbccacaadcbcdacbdacbddaabdbbdcadbcbbbaddacdcbcbcaabdcaacadbbbdcddccaabaccbdbccaddbcbaaabcccdadccddcaadccccccaaacdcccbddbbdbaaddaddbabaaabdccdcccddbdaadbadddbbbbbccdcbbdbbccdcadaacddccbcabcddadbbcbacdbaccdcbcacdcbaacadbcccaabcddbbcadcadacbcdccddaccacbdcdcdaababcdbbadbaccbdbcbabccdadaaddaccabdccbaaaaadaacaadbcbbbcabdccdbaaddccdcddbbaadbdabddddbbdbadcdbabacaaadbacbdbaaadccacdbbdabcabbbcccbcddbdbbacbcaadaabddacdacabadabadbaaacacabcbdababacbacccdcaaccdbdcbacdaadaaddcdbddaccadccbcadbdaadaddaaabbbbcadabddbbdbacbbabbacaaddbcabbcdabdaadabbdcbccdbcabbabacdadcabacbdbabaadccadacbacadbdccbbdadcdcabcadcadcaadaaddddbabcbabadacdbdbaddbcccdacdcdcadccacccdddacdcbaddbbcddaabbcddbdddaadabdcbacdbdbdcdcdaabdccadaadddcdbbaaacdaddcbacdbdccdcadbddcdabbdcabbbadabaabddbdbdabccbcbabacbddabbadcdcbdcadcdbbdaaccdbdcbcdacdcaddbaabcccaccbcabddbdacccdabccbdcaabdabbcacddbbbacbbbdaabcdbbadbbaddadacdbbcbabbaddbbbbcaadcbcbdcbdaddcdddacccdddacbccdcbcaccaabacdbaabaabccdbcbdccbcbbaabadcccdbcddabbddadbaaacdddacddabbcccbdccabaaaabdacdaabdabbacbdaaaabdbbccdccaacadbddbbbdadaccccdbcacbbacdcdbcbcaddbabbcbdbbacdcdaaaaccbccbaabdacbabcabadbadadddbddcddaaaadcacaadbdbbdcddadcbacabdbdacdacdcdcddddcbaddcaacacaaabbddbdcccdbbbdcbbdcdcdccbcabcccbdcdcbdbbabaaababcccaacdcdbddbccbbbaabbadbcdccadbdbbbbcdaadbddcbadcaccccccdbdabbaccddabbbcbccbbbddccdabccbbbdbbddcbdbabbaacbbddddcaabbbcaaacbaddadbccbcdabddadacabcacdcdccdbbbcacbbbbcdbaabdbccdabdccdcccaadddacbbcbcabadababcbdcdbdbccbaddbcdbccacbbabdcbdbabcccbaadcabaabaadccbccccbdcdbcbadaddacddcdaccdbdbcccbbccbcdcadabdabacddddbacbbdcdbdadadbbddacdddadbdaddaabaddbcaaaccbadabbdbcdadbbacbbaacaadccaadbdaaacadadbccbdcdbadadacbdbddbabaccccddadbacaacabcaadaccbbdcbacacaabdbddccadadddddaacbdbdcacbdbbbcabddbdabaabbbddbdbdddbacabcbabddbcbddbdabbabdcccdadaabcabbccadcaadbabcbbdacadbaacadcacbcdadcacacccaccabbdcbabaccadccbdbdcbbddbdcdabdadaddbdabadcbbdabaacadccbdbdbcaabadadcbaccbcabbbabadcaccdaddabcdaabdbacbabcbdccadbdbdabdcdbacdbabbdcdadbbaaaadabbbcacdcacdbabaddcbabbcbdbaabbddaccbcaacbadbabbbcdbdacccdadaccbcbdccaadbdcdccddaabcaadbccbddccacdccbccaccddcccbbccdcccabbbbbcaaddabbccbbcbbbbcbbbdcdcdcdcbcdbacadaaddbccbccdcbcbbaadbdccdcdcbbdbdcdaacdbbcacccbcdbbbcacacddadbcbccacdbbbacbaaddbdbcccdbcdcbacbbccdcadacbbcdcdcabcabbabaacddbbabadbadcbaabcabbcadbdbdbabbdddaccbaaabbcddcbdcddacdccddacdadccdaadcbaaacdbbaabaababcdddadacbbaacacddaabadcaaccacdabcdbadbbdcbbcabbacdcaaddacddcaccddbbcddddbbdaadbaddbadaddbbacbddaaadbcccacabbaabadaddbbcaadccbabbbaccbddbabbbcddcccacbccdaddadcaacbdaddcdcbcbdcddbbcacadddbccabccdbdcacbaccdddcccdbacbddaadbbacbccbabbdacccabbdbbcbcdabacabbbcdacdbdbccdbddaccbbdadbdbddaccbcabcacccbbadaaabdaddbbadccbaccdccdddacacadddddcdcbdbdacacbabcbacbbbcacccbbcdbadbdabdadcddbdaccacdcdcbdbbbdbccdadbbcdcdaabacccdabdbabacaabdbcdaabcaccbcddcbccdaacdacdcbbcbbcacaaadccbaaacadddababcdccaacbaadbabbabdcdaddadbaadabcbacaadbddbbabcbdaacccadcabdcacbbdddcddabcaaabbccdbbccdcbcacdcccadcbbcadcddbdcabbabbbcddbcbbaccacdbabcbcdbdbaddcbacadddabdccacdbddcdbdbbabddbcccbcbdabadaaccaacdddcddcdcbabdadcdbdccdbdddbbbbcacdcbbddbdcabccbcbcdbdabccdacacbbdaaabaccaadcadbdbdbdabddabdcbdbbcabbdcdccdaaaadcdabbcddabbccbadbacaadaaaabcddcabdabacbacbbcddadbbdcacddddcbdaddcbbabaccdaadbddbaccbddccbacbbcccdbabbdacbcdabccaccbaaccaaccbcdbaaacbcbadaaadcddabcbbcdbdacabcbacabaadbbdabaaaaacabccacadcbacadacdadbdbcdaacbbdacbbbdadacbbbcdbcbbacccabccbddabcddadadbcbbdacdbbdbaabdcdcccddbcacccdcbaadddcddbcaadabbccaddbbadcdccbccdccdabbcbbcbddabccbdcdbcccbaccadaacbcbbbbabbdcabcbbaaddabadcddccddaccaabacdbaaacadddcadcdcaccbbadabcbcddbdabbabdacddcbabaababdcbabcacacabcadcddcabddabddcadbcadacdacddbcdabcccbddbdacdacddbbcdacdbccaacbcdaadaacbbacadaaacdabccdbcdccdbaaacdbdbccabcbadabddbadbbaadcacaaccdbcdbbccabcabddabdbbadbcabbacabaaddddcccddadbacdaacacbbdaaddcaaccdcdbbbbbaaaddbcbcbcacabbccbbdbbadabbacbccdbdaddabacdcbbbcbdabbcaddbcaabcaccbdbbaddcbdddcabdccbccbdadacbacdcaccdacdaaddcabdaddaacdcbbaddcacdbbdbbbbdbcbcacaddcbddddbbacbddacabcccaaaadbccabacabcaddcbddcdcdaccbddbaacdbaadbaddcccdbcaabbaddbdbcccaadadbcccacabccccccaabcabaccacdcddbabdbddbbbdbaaabdadabbdbdcdaacdcbadbbaacbddddabdbabdaadacbcadcddccccdaaadddacbdadcaabbcbddbbdadddadbcbbccacccacbdaabbdaccdbcdbdabbcddcbdddcdbbdddbbddacaaacdadddacbabbdccdccdbdaccabbccccbdcccccccbadcbdabcddadadbccdbbacbbdcaaaabcdaccddacdbcaabbbcbddbdabbdcbdacbaaddaccdbcdbcbdacdadcabdbddaaddacddcbbdbcbcbaaacbbbbdcbddabacaadcdbdbdcacdddbacbdbbdacbdccddbbaabbaabaadacddbcbcbbadcbbdddacddcadbcccbdabcdbdcdbadcabcbdabbcabaccdadadaabdcadcadcddcccbadcbccaccbcdbaadcabdbdbcddcdbaacbbbbbadbbbadbbbbacaaccdabaaaccaccbdcbdabcadcdddbdbcdddacdcbabaaaaacdcbcccbdcdbadbbdabbddcccbaddaabbdbccddadcdbbcccdaaabdcbadcadaddcabdbbdbaadddcccadbdcacdddccddcacacdcdcdadaadabdcbbaadaccbbcdbcadbacccadcdcaadadcacccabcddadcadccdddbdbdadcaddcdacdabcdcadcabbaadcadbaaccbadaabbcddbabbbcbcdccccdccadabadbbdacbbacbccabcbddacbcbaddadddccaabddbbcabdaabdccabccccddccaacabcbadbbbadbabdcdcbcbacbabcccdcdbdabddacddcacabbcbcdddcabdcddccbdbcdddcabacacadaddcaacccbbbabddddcaccdcbbbbbabbcbbdabbbcddabbabbbcdbcdbcdbbdbaabbaaaaadbbadddadadbacdbabdccbcbabadacbaccadbbcccbdbbaaadabdabbcabcdddcbabcdcdabcddbbacabddbccccdcddcabcbdadadadcdacadcaddccaadbadbcabaabdcacdabcddbcdabbdbbabbbbcddbddaabdddabbcabadcdccbdcddbcaacbbbbdcdadaadcdaacaddadbccaaaabdbccbccbdcacccbadcabbcadcaacddccadaaabbbcdcbacadbbddcdcccabdcbadccdbcbdadaadccbccaaacaabdbdbbacadadabbcdbddccabccccccdcbaccbacbdaaaddbabbcccdabdadcabdcbbbacbbcbabaacdddabbadcadbaaccacddcbbbabadbdacdcbbdcdccadcdadcdacdadaabcaacdbdabdcbcabaaabaaacadcbbabbabdadcbaabaddccdbababcaabddbbbcdacbdaaadddacbdddbbcaccaddacbdcdacbacbababacdacdabdcdbcdccaabbadadcdbcbccddaacccdbcdcbdacbccaacddcdccbacdabbdcbadddacddaaccbdbbcdaadccccbdbdbddbaabcbccbaaaaabbdbabbdacdadbbabaddbcaaacadbacacabbcdbacccbddddbaaccdadcbddbcbbcbdbbabdacdbcaddadddcaadbcabcdddcadccbdadcdccaacdbdadcccdacbdcbcaaabbdabddccdbbacdbbdccbdabadcbddadccacbbaadadadacdadabbccabacdaccadcabbdcbccaabcdaabcddadccaaccccabbcdcddadcbababacbaabddbdccbbaacbdddccdabcdaaadaabbaabdacdaddabdcbbccdcbaaddacddbdcbbcabcbddddbbcdcdcbdcdaabadbaadaaddddbddcdaccdaaadbddcdccadbdababdacaabdbcabbdccaadbadcabdbbbccbbbdcaacdcddcbdcdddcbdcdadbdbbabdabbdbbcbdcaabdabaabacaaaadabdaabaabcdbbdabdcdbbabaaacbbabaaacbbddabadbdadadcbdadadacadcbacaacdbabbbdaadbadbdabcdcccbbacaabbddacbcbdcbddccaddcaaaaabdcdcccaccddcacdaaabcaacaccaabaabcaabddabccdbcadcabadaaddabddbdcbadabddbadbcacccdabcabdbdadcdabadcadbaabcaddcbdaabbadcbdabdaaacbdbdbbcbcbbcbddaddbcabbbdaaccdbccbaaaadcdcbcbdbddbbbbcccccaabaadcadabbadccbbdcbdcbacabacaccbdaddddbcbdddbccaddddacaadbbdbdacacaacacbcaadcccccccddccbadabaccabcdbbccdcaadadbbcdccccccacddcbbcdcaddbdadddddacbcbbdadaccdcaacbdcadccaabadcabccaddaabdacadbabbbbcacbdbccccadccaaacbdadbddaaadcacbddcddcbdbdcaabcbdacddddcddadbcdabdccabdbdacdabbabbbdaacbbddbcddabbcdcbbaabbccdaccdabbbacdbcadaaccbddaadccbbdbcbccaacbacacbcdcddcadacabdabcbaaadabcdbdadcaaddcbcddddbacddacabadaaadbaacacadcddcaabccbdccddbaddcadbaadcccacccbdccbdacddbbccdaccabbdccbcdbdabcdbbcadccddadaacdbacaddcadbbabcaaadccbbcdbdcbdabdbaaddbabdcbbddacbdaaabdaadcccdccddbbbacabaddcbaadcadcaabcbdacaddbbddaaddaabbdbdacdadabaadbbdcadbcccccaccabdcdadbdbbabcabcaadababaddddaadccabdddbcbccbbaabbddccdacdacaaabbabbacacabcbcbbbdbcbcddbadbcaaabacbabaaaaacdddaadcdcdaddadbbacbdcdccaacdcadcbdbbadccabbdcadcacccbccddbabcadbddcaaabacaddacbabddddacdbcddadbababcbcbbcbbcaabdcdbcbddddcbddcbcaaacbdbadcbccbbdcdadddacdbadabdccabaaddaaacdbdaddcbdacbcacaabaabbabdccbabaccdbcdbcccddbcbddcaadcabdacbdabbaadaabbdbbdababdbaccdbbbcddbbcbcdddabdcacddaaccadbabdccccccdbbbbacbbcbdcccdaabbbaadcaacaccaadbcbacabacddcccaddcbabbdbbbbbadacaadacbcbdbcbacbbdadbadddbdacdcbddabbddccaadababdbadabdddadbabaddbbcabaaddcaacccabcdcbbaccbdaabcacbdbbddcbaddaaadabaacdbdcccdcbbacbbdbcdcabcdbadcdabbcababcbdadbabbdbcddddbdcbcddbbdbcadbdabadadaadaacbaadaadacbbcbacbcadbdbabbddacdbcccbacaacadabbabaadbaaadbaccaddaccabbcbbdbabbcbbabbcbcbaccaadabdcaaccddabdacdbcdabbbbccdabbbbccabcccdbaaddcccacadaadaadacdcbcbbbcbcacbdbbddcccaabddbcbcabbbacbdcdcdbdacbbccbbabdbcadacbdaabdaabddccacabaddcccadcdbabdaddadaccadaabadcbcacabbddcbbbaadcabcccbcaccadddccaabbcbaaababcaacddbdaaabdcacdacccddabcaacacaaabacaadbadbdbccdabaadccddbbbbacdbdccddbbdbaddaccaacbbbbcbacdacaaccdabdbdaadaabcbabdbbbabdbcbacdcddadbdccaadcbcddbcabacabbccdcddbddabdabbdbddbbabccddacaddbdabbdacccccbbdbddabdbbddddaabbacddccbadadaaabcdddbcabcdcacdcbcdaaaccccacacdcccddaabbbbcbcdbabdaccaddbccddaabbcdccabbabbdcbbabadacdcdbcddbcbcbdadadadadcadcddbcbadadddddcacdcbadddcddcaabdbccdbabbcabbcadbacdadcbadbcacaddcddcddccbcaddcaababadbacabbabccabcccbcbbacdacccacbcaacabcdbdaacbdaadadaaabcabdcdbcbaddbcbddddacabcbbbaadcaadadbabddacbdbcdacdbcbdcaabaacdabdaabbadbbaacabbdcbbbdcadbaacbddbbbabddcdcbddacabcbbdaaccbbdaaacacbcaabdcdbccabbcddcdaaaccadaadaaadcbbbbadadcbccdcdbdcdbddbcbdaabbdcaacabcabbacadcaabbdcbbdcbdadbbdabaadadaacabadcacbaabbdaccabcbdadccaaadbdcdaacdbbabbcbbcbdaaacadccbbbbdcdcacbbbdcccaadccdaadaccdccdcddaadcccccbbcaaaacdcdaddadacdaadaacdadbadacbcdbbdabbdbdcdccddabadaadccdcbdbdbddcdacabdccdadcaadaabbaacbbaccdacaaaaaaddacabddbdadbddcbddbbddccdcdcbbbcbcbbcbbdaabdacabdcbdabcbbbcdcbadcdbcbcdcbbcdcacbaacdaadbddbaaabdddcddddbbbacccaadadddbccbadccdabdddcbbadbbaddaddaadbbddcbbdcabaddddabbadaaccdcacdaabcbcdbabdacacadbdacbaccacaabcadaacacadcaadcabdcccbbcbacdbdbbcccbcacddccbdbddabcbdabddccccbcadbbdbcaabbbaccbabacabacbbbaddbadacdabccdaadacdcaccadddcaacbccdadbcbcdddddbbbbdbbcacccdcadadbddcdcddacbcacdaccabaacbdaddccddbaccdaaaaadbcdabcbcbdcbaadcaaacababccbabdcddccadcaadbddaaaacdabacccaaaddabdacbadadaacadccacdbcbbddabcdbcdbbaaddcdadccbbbdbdbcabcbbbaddaadadcccddcdabacabccaaacacadabbaacbbbcbbddaaddccadadbaabdbcdcbccadbbddcbdbcccdcbbdaacccabdbbdcaddcbdaabcacbdcdcdbbccdccdaaabbcaddcbdadbbbaacdddaacccbdbdbadbcaaacabacababbadcaaaccbbdabbaabdbacadadabbbdbbbdbbbbdbbdabcccdcbacbadccdaccdcdbdcdbdcdabbdccabddbbaadddcccddcbaadadcdbdadbadabcdbdcabdccaaacbbbadbacdcbbadadbbddadaccbbbccaaddaddaadbadadbcadadcdbcbbabbadbdbcadacaacabbbcbaccdadddbcadbacbcddddcbaccbabacaaddccdcabcbaabadcccabdcddaabcabdcbdccddcdcbcdbbddcbdbbdadacdbaaddababcdcdcddbdaabccaabdcdbadacbbbabdadcadaacaccbbcddcadbccaccaacabbdbcdcddcdcddacbabcbbbbcbcbccddbabbdacdccabbadddccaccabacabbbbbcdaddccdddabaaabdabdbbbbbaaadcdcbbddaaccbacbdaacaabdbccbbdaccddbdbbaccdcbbabdaaddcccdccbabcabcaaaacbbdabcdacacadddabadcaddabccbccabdcbcadccddaabbbdabcaabdcabbcbdacdbcccbcbdddcdbccbdabdadacbdccaadaaaababdbdaddbdcddadbdaabddacbcaddbacacdadbcacadadbbaddbbdccdccdaaadadcadccdaabdccccbaddcabbcdddaadabacbdcadcdbacddacbaacbcdbbbccbcaddbbdaaabbccacacabddcdacdadadcaacbcdbabcbdaababdcdbbacadcbdcacbcdadcdbcddcbccbbcacaabbcacdadaddcabdcadcbcaddcbddaddaababddbaacdcaadabacdabaaddabdcbbabaadabcaddbadbacbddcabccbcadbaaddbacaacbbcaabbdcdbddaacbdacdddcdbaacaadaaaadccacaabadbdcbbdabcabbacadadcabdaadcacdcccadaaddcacadcdbabbaaacbcdabdcbcaaccabcccbababcdbdbdbcbabaabbadcaacddddbcacccbdcdbcadbbddccdccacddcbccabaacdcdabdbdbdabadcbdaabcccdbddaddabacababdcbbaaddddddbcaabbbcdbadcddbadddcdbdbcdbdadcacbbcbbcadacdccadaabbaccababdcbacbdabccdccbbcdcccccdaababbcdaccddcbdabaadacbcbadbdabdbbadcbdbcaacccaacbdbbddadbadbbcaaddaaacdbdbacccadbbddaacbacbcbccbddccdadcddaabcdbadbcbbaaddbacbcacddbaaaadbddaadbdccabdbddaaaabdbcbaacadddbbcbbaddbcdcbbdacdbacdccbbbcbabaccdbcacccacbbdadcacdccdddbdacbbdadcdaddcdbabbcaddaacaaaadddabdbcadccddbcbacddabbbccaddcbacaadabdbabbdabdabcdadbbcabccdbadcadbcdcbbbacbddcacbcbbcacdbdcabddcbbabcaddbccabcbadcbcdccbbdcabadcaddbcbdbdacbbdcdbacbadadbdcabcdbacabadaacbadacbdbbadcbbaaaddbcabaddadcccddbcdbdcabdcabbbacccbdcddcaabbcbbaccaadbcabbbbaccbcccaacacdcacddccbacbdbdaaddcbcdacbbdccbdbcdabacbdbdacbbcdaacdcccabaabbbcccbdbbadbbdbcbddcbbcddcccccddcdbdcaabbbaabacadbbcabcabcbdbbcabddaaaccadbcabcdbcbcdbddabadaaadbaabdabbdcbacdddbbbdbbddbccdbdcacccddddbcadddabadccdbcbacdcbbddcdcbcbcabbacaddbcdbcaddacadcaadcddbdddacbddbdbdcacbadbacbdcbabdacccabcacbadabbadbdcdabdababbcbbaaaccbbdadaacbbacdcbbdbbacbacbbaabcadcabcaaaaabcbdbbdacaadddcbacccbccabacdbcbdabdddbcabbacdacdaddbddaddcadcbaabdacacddcdcdbdbdaccabacdddbcdcbcadabdacdbdabbdcadabbbbcdddbcbcdbcbdadcddabbcaabacaabbbcccddccbcababdcadbdaabdaaabadacdadaadaddacbdbacabcdcdbacaaadacccddcadacbbbbbdcacbddbaabdccabaacddbcbcdcdcdccbcdcabddaacabbbababbadbacbcdadcbaabdcacacbdbcbcdbdddbdbdacacadccddcdccabbadadabbdabddadaadabbcbadacccccadaddbdadabbacbcdccbbcbdddacabaaadbdbbbdcacacadbbccbdbdadaaccbabcadbdcdbbcabbcbcbdaddaadbdcddddacdbddabdbadaaabaadcbccdbbcbcdadbaadcdaccacbaadbadbbbcacdadadbbdbbccacabcbdbdccbcaaadaaabdadabccaadaccbdaaddbcaadbcbdcababccdbcabbadbdbaccabaacabbcccbcaacadbbdacddacdabbbcdacdbbccdadcdadabccbddbbddbcdbbbabbccacbbcccaadcdabdaccadbacdaabacdabdbcddbbcbbddbbacbbbaaadaacdabaaacbccdabdcbbbcdadaddddaddbcdabbccdcabaaddccabbaabbdcbadbbbbbcadabaacdbbabcbddbbdddcaadbbccbdadadbdbccaabbbacabdbacbbcdacdbadddaacbdbcddbccbacdbbaadcaadcdbdadacddccabbbddadcdbacacccabdaabccadccbcbbccaddccbaccbbdcbacadbcdacaccacacbbcccccbdaaccbdccabacbdadddcabaacbacccbbdbaaadbcbacdcbdcaacbacbbadbaddcbaaddacccbbcbbaabbacaaaaaadbbaddadcbacbaacbddbaaaddcbbdbbcabacadcddaddaddbbbddcabbcbbdbaccccacbccccdbcccdccacbdccbabccdadcabbbbcbaabadcbdccadcdccdcdabdabbbbdccadbdaacdccaadbcbbbaaccabbacddbccadbaaacddbdbabaddbdacbdbaacdbadabdbdbdccdcdaaadcbcbbcaadddcbddccadcbddccddcbddbcbbbcbabacaacbbdacababcaddbbccbbabadbaccbaddbbcbaadaddcdadbddabaacbcddabbaacaccbadbcbcdbbdbabacccbacaaddbababcadcadcdaddcdcacaacccbcbddcbcccdcdcadbcdbdddbcbdabcddbbcbcdbabcbcabaacccadabdbdbcbdcbdbabbdaaccbddcdbbcdcdbdcdcbbbccacbcccddccdabcacacaccaacdbbbcadbacddddaabaacaddccbacbdaadbdbbcbbadcbcbbbccdcdabccbbbacbacdaacdbaabdabbbacbcababbadddaaaadcbddaccddaaccdacdccabbaaabccbcdcbbbcbdccacdccadcaacacaddddbaaabaccababcadbacdabdcdabdbcbaccaadddbacbdbdddddadbbcbacdadcdaabaacdacadccddbccddbbdcbcdacaadcbacddacabccbadbdcbddddacbaaddaaaddbdbbaaddbbcaaccabdbbdbbdaaccaacbacbcccabdbcdcbcdcbcdacbabacdcacaabbbcbabcbbcccdcabcbccbabccaaacacabccaadbadadabcbccabacaddcdbccccadcddbcaaaabbdcccaabbdcdcbbcbbdadddccdbaaababbddbddcbdbbadabbbdcacbdddcbdbddbdacbdbadabcabcdddabcdbdacadcbbbcababacbbcddbacbdccaddddacccaabccabccdbbbdbbbbdabbbaadbabcbdcdcbbbadbcadbdbcaabdbdbddddbccbdbacbdccddccacddccadabadbabccdbdddbdcaadadcdaccdbaddbcbacaabcbcbdcdbdddccccdcbdbddcdbbbdbadaacdacbcbddadbbcbbadccdbbbbaacbdaddcbccadddbacabbbcbacdacdccbcdbbddbcddcbabcaaaaabcabdbdbbaccadbcdabdcaaacddccbbbccdbacadcabbcbbcabdbcacccddabadaccbcadbbadadadacabbcbbcbdbcadaddddcadcbabacdaaaacddcccbcbbabcaaaaacbddaadbadadbacbbabbbcbbcccaccabdadcbbcbccdbddbabcbdcbcbdcbabaccaaabaabcbdbbdadbbccdcbabacccaaaabbbcdbbcadabababdbbccdccdccddabbbdabcaccbbcbbbdbdccbadddaccababcdddacaabdbcdbddbaabbbdbcabbcdbaabccbadccdbaaddcaabcbddccdccdccbaccddcddadbcbacccacbcbadabaddbdcccbcddabdcdbdacaabbddbcabdbadadcdcddbbadddbbbcccbadddadadabddadcbaacaabccacdcdadabcacabbdaadbbbaadcacddaaddabbcbcddadddcadbababcaccddacaababbdddaacabcdaccaabaddcdabbbbddcdababbcbdcccadcaabccdacbdbcccdaababacdcbbdacddbcbcbdbabbbcdadcacaadabdcbdccdbddddddccbcabbcacddddddcdcbacbcdbbbddacbdabacdcaaccdccbdcabaabaacabbbddcdbdabcdabddbacaabddcabacabccacbadaccbbbcadbbccbbdbdbbcdcdbddbdabdbbbacddbdcdbbabbbaaaabbdcacabccdabbddcdcbadbaccacccadbaabcbdbdddbbaccaabcbadacadccbcaabddbcbabbadcadcbaacdcdcaaddddddaaccdaadcbddababbdcdbbabccbdacddcbddbdcaccabaccaadbbccacbdcccdbaccbdcaaaddcacaddacbbdbbbbaabaadcaccaaabcdabaadaaccacdaadcaaddcdcbdbbbdbaadbcacbccbbadcaaddadbdbcababbaacacbacbbaccccadbddbbbdbadabdccaaabcbcbcdbdccacdbdcbaabbbcaadbbbcaadddbdadcccdccacdadababdcbbddbdcadcbbbbddccbbcbdbbbbcdcdabbddbbaaacaaabbcabcdcdbaccbbcdcdaabbcadcbcbaaccabddbacdadcccbcddbcccabdbabcaaabbcccabdaadaccaaacaddbaabdacdaadaccdbccaadacbacabaaccccdbaadbddbcccddcccaddbaadcaaccddcbaadbccdbbbccbdcbabbbabdcbbbacababdaabacdbbdcddcadaaabbcdcacccaccbcdbbcabaccddbccbcccdcdbaddadbbddadaccadccdabdabdabcdacbaddcbddbadcbaddacdacddcdaddcdabddbbbbbbdcdddaabadcbabcdcbaadcdbadbbbcaaadabdddbcababbcadbccacaabcabccccbbbcacaaabcddacbbadbbbabbdcbabbadaacccacdcbadabcdaaabbbcadaaaabdaccdcadcbdbaabbcdacadcdccccdbbbabbcdacbdabcacadccdccbdaabcaacbcccbcadccbbbcbabdaaaaabdbdacbacdadccaddacabbdcacbdabcbcbbbbaabaadaccbccdbabccdccccbdaabbadaabccbcaabdbdbccbaccbbbbcdaaaacccbabdadcddcbdaaacbdddadbacaddcadbadaccaabdcabcabbcbaadbdbdadcadbaabaadcadccbadbbcacdcdddcddaaaadcdccdbddcbcdaccddcaccabcdcddbadcaadadadcbccaaccacdbcaadcbbbbdcacabdacadaacbbddadabbaacbbdcddaacbdccdabdcadacdbcaabbbdaacaaadcacddabdacbacdcccacdabcdaadabaacaadadcdbbaadadaacabdacacdcdcabdcddaddbcadcbbcbcbddbdddacadcacbbdcddaabdaaaaddddbcbacddcddcdbcdbdcbacccabcbcbcabcdabcbdaddaccaadbaaadcacacbdacddddbbbbbbcbcbdabbabcdbdbccdccacdbbdabbccdcbddcbacbdaaadaaadbabcabddadcbccdcbcdcadccbabbbcdbacabddabaacbaaadcdacbadbddcdacddddcabbbddaaadcaabacbcccdbbaccbdbabcaabdaadcbcbaccacacaccbadbaacbcbaabcdbdacccbadbccaabbbdbbcadddcbbdbaaccacadaabaddaabaaccabdcdcbaaadbaacdaaadacbcbbdcbccdcdccddaccabcbdaadcdccbbbdabadcabaaaacdddbdabaaadcbaaaccbdbcdbbaacbbcaaccdcbdadaaaccdacadbaccddabdddbadbabaacacbccbdcadccadbdbbaabadbdbbcabbabbcccbcbbdcbbbbabaaddbaacbbdadcacbdbcabdcabdbacddcccaacdcdbcccbccdadcbddbddddcddaccddcadaddacadaaccdaaddaadbbbaccbddababdcabbbadcbcaacbaccbdcddddcaddbacccbdaaadacbdbdcbdacabadadaabbadabccdcbcaabcddcbaabccccccacdcdadbdbdababbdcdaacdbbaaaadcccdcdccddcbdaaccddaabddddccbcdadbccabdcbcbdcadacdbbccdcdaadccaccbdadacbcbdcdcbaacacdcbbbbbacabcaccdbdaabdbaacbacadddaccbbccdcdcccccbbdacdaddcbcbacacdbaadcabbbcaaccdbbdbaaccddaddbbddddbccacdcdbbcdcdccccdadbbcdccaaadabcdbddcdbdaccaacdbdbadbddbadcbabbabdbdabbdcbbbaacbdbbcdabbccaccddddabaccdcadabdddaabcdccbaabbdbbaccddbacacdddccddbdbddbacadcbadbddabddcdccadbddcdbddcadbdcbbbcdacbcacdddbbbaabbdcccaabbdcabbcbbaccdcccdcdbbdbcaaddacadcbdcadcabdacacdbacbbdcbcdbadccbaddbbcaccaacdbcbcabadcbaaabcdcddcdbcbddabdcddddcacddadbdddaaabadabaccdbcadaccadcbaddbdbdcabbacadbbcabbaabbddbcbbcbcddbaddbcabbadddbabadababcbcbddbbcaddddaacabbacbbbbabbabdacdcabbddccbcbddcdcdbddcdadcacacddcadacbcdcdccaddadbaaabadacdabadcdaacaddcadddcbbcbbbadabdcabbccbbcaabbcbdcdbadbdbdcdddbbbaaddacaddbcaabcdaccaacacaacaaaabdcaaddcbcadbdbbdbbcadbbddadbcdcdddbbabacadaaddbcababcacbdabdcbabdbabdabbcdadcdccaddaacbddadbbdabaacaccacdbacdaaddcbbbdbacbdadabaccdbcbcacbdcacccdbddcbbcdddddbaccbdbabdadaacaabcbdddbbdcbdbaacabbbdbaccbbababadbacdcbccadaaacbabaabdaadabcddaccccadadbdaabcadaaadcbbbbbbbaccdbadcccddbaadbacddbcdbcccacdddabcbabdbbccbbdcdbadbdddacdabdddddcbabcbddccddddcbddadbcddaabcbbbdadadaacdbcddcbcadbcbddcccbcbddbbcbaadbdabcbabcbbbacdcadcddacdaddbaccaddaadaaaadccddacacdbbabaaaadbdaddcaabcbacdcbcaacdaaddcbaababaaaccdbadaadbdddabaabddcabadcdbadddadbcdadcdcdaddcbabaaaddbaddcacaaadbaccdcbddaadcadbbdabbddabbdbcbbbacbabaabbadbdabdabcddbbcbdadcbbbdbaaaccacbccaaddcdcadbdabadaacbdddcacbccbddbcdcbbbacbcdbbdcacdacdcacdadaaabdbcadcbcadcbaddabbaadbbbccadbadcbcbddccbaadabbadcccddadadabdadaaacccdcaaacaadbcbaabadaaddbccacbbaadabddadbdcbaacadcdbdcabadbaacddaaacdaacdcaacbbbacdcdddbdbdabbbadcabbcbdbdcdcaccaadcccdcbbdddacdbcdbccbdbdabbbbbcdccbdbaaacbddbdcbddcdacadbccabdbaccdcaadbbababbbccacabcbaadbdbbbdaabacdbaddbabdbacbacabccdbdbcacbacddabdddcaaababbabdbcdaaabdcacdccdadcbabadbdbbaaabcbadbbaadadcabbccaabcaaccddddadcdccbadbdcdbaaacbdcbcbdacaacbaacdabcabaccbccabbaaddbdadbabacaccdccbaadcbabddcabddadbcbabdabaccdbbdbcbaabdcddcbacadcdcdcbccddbdaddcbcbdbbbabdcaccbdbdbddcabddcaacadddaaccdabbdcddacbacdadccccdbbcadabccdaadadbbdcacaababddbccddbbcadcaccdbcdddaaddcbcbdccccddbadcdccddbabcaacdbbaadcccbbcbddcbaccbdabccdbacabbbadcbbbdcbdaaacaaabccbdcccbbaccdbcadbaacbcbccadccdcccbabdcabdaddbcaacddaabbcbbcacddcdaabddabdbccabdadbcadccabcdcaacacdbcbcacbbcababcbabddbaaddccccaacddcdabddbddabcdabdbbdcdaaabcdbddcccccccdddaabbdadaacbdacdaadadaddbbbccbaacdccacdbadbadabcaddbccbdcabbadbabdbadbcbadcddbddbccdbdbbddbadcaccbcbdbdbaabbacdcbcbdaacbcdadbbdadadabaaacaccdadcdaacbaaccdabcbcdcadaaadabcacdcaacbabdabcdbcdbbcbacdaaccdabbaaccbabbcddadcaddbaccddadbdbddccbbcdbcaaacdacbcddddbddacdbcbbbaccadcbabaccccdaadbaccddcbdcdbddcacabdadbcdbdcdadcdaddcdbcdaabadaddbcddaccadbdbcaccbadcbaaacacddadabcbcbcbccdcdaabccbbbcadcbadcabdddbabcccaccbcadbcbababbbdabdbcdacbdbbabaaadaaabcdcbacbbcadbbdadcabcacdcdcbbcadbdbdadaaccdbaccbbccdcdaabbbddacacadaabbaaadbdabdcccbadaabbcaccdcdccbddddbcdbccaadadadcaacdcbaabcbdbbdcabbacbaadbbcbdbbbddabdddbacbcbabccccbcccccdbcddacdcbbdaaccbabbdbddbccddcdcdcabcababcbddcbabbcaaacbbaaacdabdacdcdccbbccaabbccccdcacaacbdcaacacaaddbcddabdaddbcdaabbcdbddbbcbbccdbadcadcbcdbacccaccbacddcddddbbadacabbdadccaaccbaadadabaaaacabcbdaabddacdcbcbbcdddbadbcaabacadbdcdaacadcbbacdcacbbbbabbbbbbcbbcddbcabaccdbabdabcdcbbbccbddcdaabbcacbbddbbacddacdaccaccddcaccacabadccbbadaadcadcaddcaacdaddbcbcdbbabdaacbadbdaccadbacadbbaccbddcaddacddbbaaadcccbcdabddbcdadabbadbcbacbbabcdaaddcbbcdaadccaadbaddcbcdbbbaabdbddaacabbacbdcbdadbcacacadcdabbdabadacdddcdadabccdbdbbaddbadabddbdbcbababacaacbdbdabaddaadaadbdabbacccdadadcccabdbaddcaaacaacdcaccbcdacacadcccbdcbdbdcaabbcabadabadbbdaadaabaccbacbacbcdacbcaacbcaaddcbcbcddbcacdcbabddcddddadabbaaabdcbbcbccbacdbcdcabccdddaadbbbcdddddbdbdccdadcdacaadbbbcbacddcdaddbbcbcdadadddccdbdbbcbdbbcabbbbcabaaacabcaabbccbbaadcaacddbbaaddcabcdcbcaabadabcdbbbccbbbdadddabaacdabdcaabdccbdbbbdbbcbdccbbcbddadaaaccddcbdcbcadcadddbdadddcadbabcdabbdbdccbcbbaadccbbaadcadaaacccacacccbabcbacdbdaccddcccbaddaccabdbbdabdddcadbaddbdbbcadbabababbbdaaadaaaabddaabcaadcabbbbadcaaacbccbcccccccdcaabbdcdcbdbcabddcadcadcddcddddbabcbddbdbcdabaabbaadcddcbcbcacdcdbdddcadbaaddcdbbaaaacadbdbddacadcadabacbccbcdcbacbdbaaaabcbacacbbbcbdadadddaaaacdadbcbcacaadcdbcbadbbababbcbcaaabccdabbacddcdddcbbbaddcbbabaacddbcaddcabdbbbcddcdabddbacaabaaabddaaacdbdddcdbcadaadcdcbccbbbadbadbdaaadbdbdbbbdcdcabdbaaacbabdcdacabdbcbcdbacaaacaadacadabdccccdcbadbabdccdcdbdacbdcbacdbbdbaacadbcbbbdaccdbcddaabdcaabacbbbbabacdcdbccdaccaadadacdcadbacadbdcbcadaadcdcbaabbbabdabddbddcbbbabdaccbcbcbdcdddbdbdccbdccbacbcddadabaadaaaabbdbdbabccbcaccbdcccadabcdacbddaaacbccdbabdcacabddabddcadacacbcacccccbbaccbadaabdbacdbddcacbcbbabaaccdbbacddaaacbddbcbadcacbcbbbddbcdddcacccccdcccacbdcaddadabbcdcbcbabcaaaaddabdaaddacaddabcbaaabadcccbddddcccccdadcabddabdbcdccdbccccdaccdbdcbcbdbcbcbdbdbbcbcccdbbbbaccaadabddddaccdcaaaadbaddacadbccdbddcbacaadccbcccbdcdbcadcbddccdcbbacbaabbcdabbbdacacdaadddabdbbadcacaababacddadcccbadbcaccdaddbcbdccbddcacbcbbcddbbcccacbbacbbdacdadccbdbaddabcaacbadacdadaaddbbdbcbdccbddabaacbcdcbaddabcbdcdaacccdcdcbdcacbadcdbdacaacadbccdbdcaccdccadbccddbbbbbddcdabbabadbbcbaabcdcdbbdcccabbdbbbdbaaacdabcdbccbcddaadabbcdadacdbbbbbccbcdddabcabbbcbaaadbccaddcadbacbcddddabddacdcabcdbadaaccdaaabbbdacbadaabcadacbcaaacddcdddadcdacbbdbcbaadbbcdaddabbbcabcddabdbcbaababbbabdbdcddcdadcddbbbaadccbdcccbdcaaadadbcadaaabbdcbaaccdccdbdccaadccdacaadcbbdccdaaccdbdccdddadcdbcbadabccddadddaccbcbbcddbabacbacccbdcbdadccdabdcdbbbcaabcabcbdbbdacbacadadbdbbbcbcbbdbccdcbdcbdbbcbcbdabdaabbcdcabdcadbddbaacbaaacacadababcbddabbdccdcacbabcdccabdabbcdbdbadacbccacdbaacddbcadcbbccdbcbbcdabccbcbddcbdcbaccdcbdacbadbbadcabbbccbdaabcdadbcaccaacabccacbacdbbaaacadbdddddaadcbddbcccccdbbcccdaabbccdbbdbbddaacbaccddacaccdcddccdcccacdacccdacdbcbddbaadbdcbaaaacdcabbdccadccbabcdcbdbaabdadbdaabcdcdbbdabadcbacacbdbabddbcacdbabbcdcbdabbababdcccdddcaaccdabdbdbdcccdacddcadbbbbccbbdbadcdadcbdddbbabbbbcdadbabacbcadbbadddcbbdcabccbbacddbababbbddcddacbacddadacbbdaadbdaacccdbadddaddbabaadcdcacaadcdbbbcdcddccdcdadacdcbdbbcddaabbccdabacacdadacdbdabdababbccaacadaccbbbcabbcaacdcaabdaddaddbbdcdabcdbccadaaccbcdddcadadacbdbaabdaaaccdcacabbcbdccdbbdccbbdacbaabacacdbbbacbcaddccbacadbddadaadcbbdaccbbbbadbdabcadbcccdcacdabacbacacbdabddbadabbbdcadaacbbbdcdbaadadadcaccdcbddddcbcdaaddddadbcbdabdcbaacdcdadcadabdbabcabcdbbdcaabdddcadbdaabbadaccdcbdbbbbcdaadccacabbacccbadaccbbbcddaaadbdaadbbdbbacbcaccbbdddcccabbbabdaadacbdabaadbccccabcacacaddccbdaaaddcdcdccbbaabadbadabcaacacadcbaccaadaaaabdcbdadadabcacacaddaddbacdacbaccccbdaddbcbdbadddddabbdacadcabaddbabdbbbccdbdddbbcdaadcacabcbdacbaabcbdabdcdbdaabcabdaddcccdacbbbbabccdddcdcaaabdbdabdacbdddbaaabccacaaabcbababdddaaaadbcbbddababaabccbbddbbabdbdcdbccdcabccbccdcdbddccabcbdbadccaaadacadaaabacdbaacabcbdcbbcbabbaaaccabdddbdadcddbdabcdcadaaaabcdaabdbcbcacbdabdcacccabacabababbdccbcdbcacaccaccbcccccccaacdccbbaabcbcdccabdbcddacbacccdbbcccadaaaadaaadacccdddadbdbbddbbdcccdbdddaaabacbcabbbbdaacddadddddbcccccacdbddcacadcaddcdabcdcaccdcbdadadddcbacdaddbdbbccdbbdbbcabddbaabaadbabbbbcdbcadaabaadbdcabacadcaabdcbbbbbaaccdcacacbdccddbbdcdcdddaaddaddbabdccaddbcacddcabcbdaaccbaadddcdbccaadaccabacbddcabcaaacaaabcdddcacbadbaacabbabcaabdbbbdccbdcdabdadacbcdccdddcacacbdddbccbbddddaacdddadcdacbdbbccbababbddcacddbdabdbccabdbadbabadddcacdbaddbbaacdbdabbcdbbcaaadbcdbcbabbdadcbddbbcbdcacabcccbadccdaaddccdbdcdbdcdcbbcdcadadbddbbdddaccdbcabddcbdbbcaaaaddbdbadbbccbcadbcabcbbacdcdaccbaadabbbccbadcbbbadbabdcabbccacbbddcacacbaadbdcadbacccbcdddabdbcdcddabaabbbcddbdbabaaccbccbccdadbabbaaadaccbcdcbbcaddacabcccdddccdaadccdbacbaaacaccdbaadccbbcaabbaadbcbbbbddaddacdaabdcddacaaccddddcddddccbdbcadcdcaacaaaccacbdabbacdbdcacdadddcbaadcdacbcccdbdaadcabdcdbadccbaddacabdaaccddbbacccaaddddbcbcdaabbcacdaccddabddacbcbccdadbccbacaabcadacddcadbcddcadcbcbddcaadcbdabdaadadbbdcccaacdddacbaddbdbdccccdabdbbccabddabdcbabccbaccbcbadcdbbabcbcbcdbadbabadbbbabddabccabcadcdcbbdbcbccababbadcdbaadcacdacddbcddabbacbdcbabbbdbcccdcddddcaaccbddbdbbcdacadaacbaacaacdccbdcdccbbdacbabcbccaaddaadbdbadabdcbbbddadddcddadcdcbcbccabdadbbcddbddddccdcacccccbccabcaabddcddbcaaaccdabccbbadcbbbbdcadaccaaacbdbcddbadadbbbaabcabdccddbaccbdbbcadccdadaabbbcbccabacaadcdbcbdacaaabccaccbdabdadcaacdacbdcbddaaaaccabcdbdcdddbbcbdbbcacbcbcdaadcdaccadacbaddabccbbabbacbcbccbacbacadbbcbbacdbbdadbbbcdacddaaadaadcdbcccbaadabadabdcaddcdcdaadacbbdbdacabacdbbadddcabbbbadcddbbabbbcbadcdcaddabdccaabaddccddcbdaabdddacdcdacadaccdbdaccdcaadbbacddcdabcdcbccaababdacaabaacbaabaadbdcdadbabcaacacabdcddacdccddcaabdcccdbaadbaadbdacdcbcccccabacccdabbabccdbcacaaddaddcdadddadacdcacdbbdcdcadcccbdbaaacccacbdcddcdaadbdaacbaadaccbcadcbcbbabddbbdcbaaacbbcbcddbadbbcdaabccaccdbcadacdbdcaacddcaddbcbabbdcdbbdbcaccaccaadbbbbcbaddcbcabcabccdcccaaddcccabbdcdcdddabbbcbadbccadcbbabacdadabaacdcdabcbaddcbacbbdccccbbaaccbabbdccbdaddcabbdbcabacccadacbadaacbcddacdcbaacdcdacccabbbdcabdadaacddcdaabbccacacddbabaddaacbabcdbccaaabaccddabbabaabadaaaaddbcbbdabdbdbbabdcaacccdccdbbddbccaabcaddaaaddddabcdddccccddcdbccbdadabaddadccbaaaddbabdbacbdbccbaddbbaacbddcbadbdbcbdbdccacddbbabddabbcbadcdcdbbcadbccdbadcaabcccadbddcddcbaabddcddbabdbcaaaadcbdbcadbbcdbdcdcddcdcddbbacbddbcdbdbabcbdaacbcbabbaddbaaadcacbdabddabcacdacbababccddddcbbbbdcacabdaadbdbcaadadbddcabdaadcaabccbcaabbdbbcabadadcdcdaccdacdbbaacabcdbdcccdbdcbadcbaddadbbddbccadadabbcbcdbcbbabbabcddcabadbddcdaaaadabcaaabcbabcacbabcddacaadcadaddaacdccbdcddcdcbccddabbadbbcdacdaabdacdadadddaadbbdaabaaaadadcbbabbcdcaaadbaacacdadabbcdcbdcbccbbaadcbccbbbbaccbbabdadbbcbdaaabcbbaadacbcbddbdadcdbddadcddbbdccdbcabadcccddcadabddaaaaabdddbdbbccdcbbbddbdacbddcadbacaabdbacaddaddddadaaaaccbbaadacacabdbdaccddddcbccacddbcaacbabbbcbcacabcbbccabacabbcbbcaddbcddcdbcaaddaddcbbababcdbbaacdbacccdaccdabcbbbbbcbcaabbdcdddbbbccababddccbdcaabddabcaddccbdcbbcbbdaadddddaadadaddaabbdcacccccaabacbabcccdaabdbcdbaababbadbbabaabdbbcddbbabccbcddbaaadbaddccabbbaaadababdbaabaaaacddddcabbbcaabbbcdadcaccdcdccaabbbcbbdbcdddbadddacbbcccaaaabbaabcdaaadabcbaabdbddccccbcadacdabbcddbcaddacaccdbbababdbbdababadccbcaaaadabbdbadaacdcdbaddbdcbdddacdcacbccaaaaddbccbddbbbcccaacdcabbccacccadddbcdcbccccdddbddaaabddabdaadaabdcdbcbbdaaacaaccdcbcbbbadbdccaabbbcabbdaccbbacdbcbcccdabbacacddadbddaadbbcccdbacacbcbdaddcbcbcdbdcabbdbcbdcabacdadaaaadacbacddacdcbcccccddbdcbbbbcacaabaadbdaacacbabdbbcaccccaadcbadabaadacddbcbbcdccbddaddbcccbdbdbbbcdacaccbdaacbaacbdddaadbdbacdcdaabdbaccabdbaadbbbbabbdbdcacdacbccbbaaadbababcacccdadacbcdadccddacddabdaadabbabaccbcbddcdabacbaadccaddaaadbdbdaabbaaabcbcdcbcddbaabcbcbbbcccbdadcacddaaabbbaadbbbbdddbdcbcdabdcdcbdbdaadaddcbaccdddbcabbdcacacabddaabbdacbcdbcbccdbacacbccabdabadbcbacbdabbcadaabbbdbdabcdddbcddadbccbcdbdddcbcabadccadbcbdadbbbbbacccdadbcdbdccbcacaaddadbaabcdadabddadcbaccbadbcdcddddcbadbadabdbdbdabbddbdbbdcbdcbcbccbbdcbccdacdbdccdcacccddcdccbdcadbcacabcbabbbcabcaacaadcdabcabcabdbbbcaaadcadcadadbabbbddbcbbabbccbabcaaddddddaacdbaabdbcbdbabbacdcdaabcbdaadabcabbaabaaaaadaadaabbbbbbdcaacdabdcddddabaaadbbcdddbcbabbcaadbbadccddbbcbbaddbaccabcdbabbdadccadbabbabdabdaaabcddcbbdaabaacbabbddbdabdbdbcdbbabdcbdadabcbddccdcabadbdcbbbaaddaddbbbbbdbaadddadabdcacaddadccbdbdaabdbbabcbdabbcadbbbcbacdbcdbbbbdbbaaccdaabdadaadbbddaddccbcdcadcccdbacddadcbbabdaadcabdaadbbcbddadccadabadddbdbaddcbbdcbcdadcbbbaccaccddbddadcaaddaacbbdaccadabcbbadabcadcddcbacdacbcacaadddbbbcadcdddbcadacdaabbaadbacbcdbabbdbcaaddbdcccdddaaddbadaacacccbcdabdabdbdbdacacaaaaccbddbaaddadbdaccbdcbcadcbacbdbbbdacaaacaacadacaddcabdbaadaccddacddcaabdbababbbaadbcbaaabcddaddccdbcabcddbdcdbdaccaddcbdaaccbadacddbccbabccaaabdcbbddcbdababdabbcbdcbbabdbdbdaabbaacbdcbddbabdaacabbdbdbdacacdddabcbbdabbddadbcccaddaccadbbcaacccacadcbcbcbddddbbdbcbdacbcbbdacbadbbcbbdcdadabddcababacddbbbbbdcbabcacbcabcadcbbdcacdcbadbbbabacccccaacdacaadaacdcadcbdbbcbcbbadcabacbdbaaaabaabcddbadaddbaadaccccaddcbbacacbbbdaaabbcdcccdbdccacadddcbbdcbaabbbcacaababbaacddaaaadbbcdddcacbbdaabaabdcdacbaadcbaadacacaddababadabccbcbbddadbdadcdaaabddccbadaabcbdaccdbccdadacbdddbcccacbdadcbbbcbccbcbcaccabbdbdcbddadcaccdcaddbcbbdbdbbdbcdabbbcacaabdcbbabaaaaccdddabcbbcaaacadbacbadccadcadabbcadcdbcddbcaccadadcccdadbaadacbdbcdddcadabccaadccbcccadaaacacdaacbadadbbcddbcdbdaddcdadbdcaadcdbaccddadbcadccbccaabdbbccddadaccbdbbabbccccaabccbcdcdaabacbacabadcadabadbcbcaccdcddcbbbdcbdddacbabbdbabbadbababbaddcbdadccacbddaaacdbdbdbcacccaccaacddabbbdaabacbdaaccbdbacacddbaacddcbbbdcbdccaccbbaccdcbcbdaddaccddabaddbdbdababacbaabbbabbacddadbdbdbbaadccaabccacaacbaadcccbdaccbddacbadcabbacdcaddaaddacbbcaacaacaccbcbdbbaaadcbabcdadcbaaccddccaacbcaddaacdadccabacbdbcacacadbbcbddcadbbbbddbabcabbdbabbabdbccaddadcdcbcbbaacadbbadccabcddbccccadbcacacdbacbbccaaaaacbbcdcaddcdcbcbbddadbabbcadbdbbacaaacdacdddcaccccaaacbdbabbdcbbcddcbbddcdcdbcbbdcccdaadacacddbddbddacbbcdddcdbaaabccbdcdaacdabbbaaabbaacdddbabbbdbdaadcdccaacadbaddbbacddababcdacdbadbaabacadcccddadddcbdbccdcbcdcbccbbaccacbddbdbacacacaadbdbdaddccadcdabddcacdabddbbddadaaabbccbcdcbbbaaadbcabbbaaabababcdccdcbdccbccbbccddcddadaabdabacabbadabcabacbccabdacacbdbccabcdddbbacadddbbdbcbdcbcacccaacdbcadbddaabacdbbabbbaadadcdccadbcbbadacbababaaaadbdcdbaabccbbdcabbbbadbbdbabadbdabdaacabaccbdaaacbbacdcbdaaabaacaadcccbacbbaaccdaddbbbdaaccbcadabadcccbddaccdabdbddcdddcbdacabbccaadbdbbacdacaaaabadbcbbcdaaddcbcdbbbbbbccbbcbabadbadcdbacaccdddccbadccbcccbadddcabbbccbbccabdccdaabcbaccccddcdcacdcabaacccacaabbbbbcddadbcacbcdaaabbbacddbdcdabdadbcdcaabbdacacdadcbcbddbbccdcabcabbcdaabcbcaddacdbbbabccadddbcabacbabcbdabcaaabdccabbcbdcbbdbcaaccccaabdbddbadaccbaadbdadbdabbdbddbbbccdcaacdabbdaabccccddcabccdccbbabcdddaacaacdcccabdbbbdccdddccbbbabacbcdcdbbdcbcdbaacdccdbcaaadaadcbbbddcaaaccabaaaabdcaaccddcdcccacbabaacabcabcadabdbabdbcabdbcadbbdbadacdddccdabbdbcadaaadbdbdbdcbacdcbcabcbcabcadbddacaabbdacbdacdaaaadccdababbcbdcadcddcaadabddbacdadcadbbcddacbdacdcbdbcaadaacbbabbabbcccbbabdaddddadbcdccdccacadaaaaacbcaabbbdaacbbaaacadbbacbddaddbbdadbbddadbaaadccccbadaaadbbbbbbcbdcabaaacdaddddaaabacaddbcdacbbaaddaccdcdaadbcbcbadcbacadcbbadbbccacbdccbdaabcbccccaacbacdbccdaaddbcacccdccbadcadabcddaddcbbdddccdccabacaacbadcdaadaccbcbccdcababccbbbadabdabcbadabbcaabadaadddddaacbdcbccaacdaacbabccabdbaccacdaabcaddadbbdbccacaaccabbcdaadddcaddbcccdaadbcdaadabcbacdcaacacbacbbbddaddddcbabbbcbcbabdbbbcadcdccaddaaaddcaadbbaaacaaabacbcaadddabbbcaacacdbdadcbdaddcbaaaadaddbcaaadabaabdbbbacaaccdbacdddddcbacdadbdaddaabbdcdcabcdbcaabdbdbadabbcabbadcdcbcbddbcadacadabaadbacdcbbadccccbcbcadcbcddadddcbadacddddaaddddccbdddccaacdadcacbcdddabaccadbabbddaabddcdbbcaacabcccbbadbdadbdcdccadabbacaddbacddbcaadbaabaaaabbbdaacabcbcbcbdbdbbaabdcbbccaddbacbdabcddababcbdddbdcdcbaadcbdbdbaacbacbbdadbddcbbdadccccaadcdaadbccdcbaacadabcacdacabcdabaacbbdbdaabcbcbccaadbacbacacbabcacdccdcddcddadbdaddcaddbbbadaaccbaabaabbabcbadbdddddaaadaaddbdbbccddddbbbaddabaccabaccdabadabbcaacbaccdcdaadddabaccaaaaaddacdcaaccacdadbdbcaacdaaabadbccccdbcddcdbbaccacacddbcbaddabbbcbcdbccccdcadcdbdccddababbcccadaabcdbcbcadddbcdcdbbaaabcbadaaababccaabadcaadcbbcadcdbbbcbccddadbbbdadabbddaddbccbbababdbabbdacacbabbccdbddaacbaaacaaaacdbcbabdbbbcdbabcbaabcaacdddadbdabdbcbdbbbbbabcacddaababdbbaaccccbbbaccdcaccacbddabddaddcbdcbbcddcbcabacaacdbdaccaaddbccdbbddcbddcbabcddbcbcadcccbcbbbcdbdaacadabbbaabaadcddcdbdabccdcadbabbdbdbaaaccacbdbbcddadcacbddaabdcddcbdadbccbdcdbabbccacaaaddcbabcdaaddacbbbaabbccdbdddabccbcaabdcccaacaddcbadabadcabbcaccbdcdacbccaadaabccdddcdabdbcacbcabcbbacbdacabadbcdccadbdbaadcbcbbdcacbbbcabdcbbbddbbbcadaabdcbbbdadbaddadabbdcbabaddbcbccbabcdadbccbbdbbbbdacaaabbbdbccbdcacbdaaaadadaaadbbcabadadbadaaacbccdcdabbbcacbcdaaaccabddcbbcbccbbaacbcbbbbcbbbabcababcbdcbcacdcdbdacaddacbbcabcdadacacccabaadadcaddbdbaccbcdbbaaddbbaccbbaaadcbaaacbcbdabaddddcbcdcdbcdabdcaacccbaccddcccaacbacacaacbaaacbbdcbbbbbccdaaaaadaacdccacacbadbcadddabaaddddabdbbcabbacbbddacaaadccadcacbddaaacbbaadddbdadbaccdadcbdbdccddbdacddcbbacddccccbaaaadcddbcdbdacbbcbdbabcccbccaaddbacbddcddddbbdaaacccacbabcbaaabadaabadcbbbaacdccbdbdbdddbbcacdacabccbadabbabccbaaddddcbcddcbabadcadabbdacccccccbadcababbbddbdcbddcabadccbbcbcdabcacbbbdbacbbadbbbbbaabbdbaacbcabdcdaaccadcacabdcbdadccbadbadabbadabdacbbbdbadccdadbcdbcbdddcbbbccdadcdccbabcbcbdcbbcbbcbaacccdcbaddacdaadddbadbddadbdacbbddabbbdbadaabccdbdddadaaacbbccaacdccdbddcbddbacaaacacbdcbcbbbaadbddabdcbcdbdaaddddbaabdcadabdbdadabdbcddbcccacbdcaccbdcbdcdbbcdcdbdddbacdabcbbcbcdcaaabcbdddbccbdcbdadbbdbcbcacddddadadadbaacbcdcdcdbccaacbbcdaabcccacdbbbbddbdbdbacdbdddadaaddbbcaacdadcddcbdbadcccaddbadabdbdaaaccdadcadbcbbcdbcbabcdaccabdbadcdabcbdbbcbbbaaadbadcadbcdbadcbbabbccbccbdbaaabcddbcdbabacaabbaabccbcdaadbcacbbbcbbbbccadbadbbabddcacbaaaabaadabaccddcbcdddcbddaddbcaaadcacacdabcbaddacbddaadbdddcaccbcbcadbabddabdbdcbaccbbaadcbccadbadcaacbdccdabbdaaadbadbcdabdababbcbccadbddbabcbdcaddacbdbdcbccccdccbaaddbdbdaacbdcacddcabddddabcccdcdcccdbcdacabaddbaaaabadccabaccacabdabcabcdbcacacbaccadbccbadacaacccdcdabdcbdabbbbcaadabbccbdadacccdbcaaabaaddacabcccacbcadbbbdacacacaadabaacbcdcdddacbbdaadbadbdbdabaabccbcbdcababdccddaccccdaccaccacccaccaaaacbbacddadbddcbacbdbdbcdabccbbcbbdcadacadbacbdcbccdcacabbbdbdbbcbaabcccbcadbddcccdbacdbbdcdcbccadaddbadaabcccddaddbdbbacbdaabccbadaabdadabddcdadcbaddbadddddddabdabbdddcbaaddbbccbdcabcdacababdbaaccbdddbdadccdcdbcdbabcabcaaaddaacbadaacddcdbdadcabbddbcbbbccbcdadcabacbddcdbbaddbdcddbccbddabbcccabcdabcdacadadcabcccabadcabbadbdabcbbacdcccdabbbbdcdbabcadacccbbdccddadcbdabadcaccbbcdaccccabcccbcddcbdbaaadabcadacdcddacacbdaddbbdbdbabbddddbaacddcadbdaddbcdaacabcaccabdcbbcaddabdcbacbddadbbcbcdbacbddcaddaabbcacdbaacaaabccbbbbaadccaabcbcabbdbbbdadbabdcaaddbbdccdcccdbccbccddbccababdcdbbabbadadbcdacbcbcbdacababdccbaabcdacbcbcdbaadaabccaabcddadccbcdcacacaaabcbcadccdadcbdbcddabacbddbabbbadddbbbdacadbddabbbcccdcdcadaabccdbadbbabdabcaaabdcdccccdcbdcbcababcaadaaccdcbbcbcbaaaaaacadacacbbbcbcdbcdcdbbbaabcbcbaccacdccacbaadabdccbcbcbcdadbbdbddccdbcddbcdbbbaddadacbaacbababcccacaabcdcaadacddadcbbbcccdbccbbdadbdadaabccbbccbcbccadcccdbccbabbcbbbcbaacdcbdacacbbcdcdbacacdcaacccdbcadcbbabcaacaadcdaaadcdcbbbcacccdadcdbcdaaccaabaacadbcdacdbbcbcbbaccdbbbccaaaaaadabadcbdcabdbaaadcbdbccabadbcddabcadacdcdacdacadbabbbccdabccaabbaadaacbacdbdcbdbdddcdddcacabbdcaabbdbadbdaabbbacbacddaabcbdbcddccadbcdddbaacabbddcadbabdabbcccbaabaacddcdadcaaaacaaabdbdcacbcdcddcaacccabddaadabbaabbdacbdbccbbbbcbdadadadcabaabaaaacccdaadbddcdbddabdadbdaaaadcddccabdccdabddbccbdbacbadbabdadcdaaabbcbbbbabababcbdcdabadcdbbccbacdccabacbcbcacaadccbbbddcdcadbbdbcabbabbddadcdcbdabddaddccadacbabddcbababdaddbbbdbbcbaddcbddddcddadaaaaaaadacccbcbacdbaadbbdbcdcadbaadcbbbaabcaadddaabbccbadbdaddadddaddcbcaaadbcbbddabbdadccdccadcaaadbdacdbdbddcabccdbcbdcabddddbabbabbcbdcdcddabdcbdacacccbdadabbacacdabdcaacaacdcdbddbdccdbaabdbbcacadcadbbacaacdddadbdaacccadcbbababdcbdbdcbbccbccbacaccaadbaccdddddbcacbbbdacddcaabdbdbddabcabaccabbbacaacbcdbcabccdbdaabccdacdababaaaccacbaccdcbddacdddabdccdcbcbbbbaacdacadcddaccbccdaddcadccdbaacbcadcdaaacbdccddbabbabdcadcdcadbdbabcdcdcaacaaccdddacacadbdbdcdcccdadcaddabadbacdacadaadcbcdddbacdddabdddcbdccababaccddddddbdaacdccdcdcaddbdcacacaaaddcacabadccabbaacabdcabddddaabcdcddaabdabdbbddccdbccdabbbccdadaaaaaacabcdbcbacbccaccccddaacbddaddaaaaacaddaddadaaaabdbbdcdcdadddddaaccdbacccacdcadbbdacdcbcbadbcaacbacbdcacdcbaacccadbdbdcbcddddccaadcbbcacbadbbdcbabddcdcabbaababaabaacbbcdcacaadbbadbdcababbaabadbadccbdaabbcbbaccacbdcacccbabbaaacdcadbbaaaccadaadabcbcdbdbcadcadbbddacdbcacbaacaddbdbccadbbbaaabdbcbacadbddbdbdccbadcdcbdcbdadbddacbcadddccdcdadbdadccaddacccbbdaabccddddadabcddcdadcdabdaabadbddbbacacbcdcbcabacbabadccdbaacdbcadabbbccacaccabccbaadcbbdccbdbabcbcdbabbaaabcadcdbacbdcdddbaabcbabaacbbccacdddddcdcbbaacdbbcbabbccbdadaadbcdaabbbddadbcdbddabcbaddaacacddcacdcbbccabacbaaaabdbccdccadbadccbacaddacbabdbaacabccccdbbaadacbccddcacccdcdaddccdabbddaacbaaccdacdcbdbabadabdccadcdbbaccbdaaccbadccacadcdaabdadbdbadacabbaaabcdacbdccbbabdacadccaddbddddaccaabaacdaddcbbcdbdadadabddcbaaddacadcbccdcbcdbdcabdbacccdabdaaddaadcbbdacbbbbbccdbaccddbbddcbdbcbaaaaacbccbabdbcdacdabccdcbacabaddabaadcbdaadbaacabdbaddabcbbaadbbcdacadaccdcbcadccacccbadacabcbbdacbbaaddcabdacccbbdbddaabdcbaadadcacdbbcaababcaabbbaabbbccaadddddcddbadccbbbadddbadbdaaddddddaddbcacdcbbbadbdddbccdacccbcbbaadddddbbaacadddbbbbbccacdadaccccbddbdabbdabdbcacdccbbadacbadabbcdababbbcaabcddacdaaccadabadbccaacaadcaccdbadbdbbccdbaccbacadadbbdbaddbaaacdadcbcdaacdbddcdddcccccdbaaababbcdbdcadcaccbaabacccaacdbbccdaaddbaddaddbdbbcdbbdbadbdbcacdbcabacccccdbdccadccbcbccbccddacbdabbdaddbbabdccdccbacdcdadbadbdabccbbcbbcabbdccaabcbdacdbadbcadacabdadbccacdaaddbaabadabdcdbabdddcbddcbbbdddaaaaacdccccabdabaccdaddcabcabddbddbbdaaaabaccbacadcdcadadccdacabbbbcbaddadaadacacdadbdddddbdadccacddadddaccbbdabdbbaabcdacacddbcacdcbaaabdcbadaaabaaadcaadacaddcaccaabadacaacbcccdbccbddabbbaacccccabdaaadbddabddaddcdbccaccccdaccdacbddddcbcdbbdcabaddccdddbaacaadbcbddaaacbabbdbddabbddaabcdadbccdbcdcccddbcdcdadbdcbbabadccaddacaddbacbacacbdacbdddcdcbddabcbbbcdbcbdddccccbabbbbbbcbcbbbcbdadcdcddbdddaabcacdccdacbbbbadcdadcaddbbcbacdacaacbbaabdbdcddbadadbabababddbbcdaddbdcdbdccdabdbddddddadcbcdbdbaaddbbaadbdcabdcddbdcdbabdaacaaabdbddcdcbdccdaddbacbccbcdadccbbcadddbdcbbbdabcbdbbacabcaaddaccabccaaababaaaaddcdbdcdaadbdcadcbccacddadddbadccdbcdbdcdabbadcdcdabbcdcdaacadbbbccaccbabcdbcddbbbadccbddadaabcabaaaaccbbbaacaddadbcbcdbadccdcdcddddddadddaddcabcbacccddbdddccbcdcddbaacbdaacbaccdaabbcbcacabcabbadbabbdbacbdbbacacbbdcccbaccaddaccbdccbaccccbbcddbdbdccaccccccccabcadbcadcbddabbbacdadbcaddadcadbcbadabcbbabacaaadcaabbcccdacccaccbbdcccaaadaabdbdcdcdccdadcbacaadbdbdcddddcbadccbddddddaadacabccbcccbbaabcbdabacabcdabacbadddbaacdbcaadbbdbbcaddacadbbabaaadcadccdbcdbdcadcbbabbdcaadababbdaabdbdbdacadbaddaddacbadcdcbaacbbbcddcccdcccbbaadbbaabdddabbacbacdaaddbadbdacccbbcdccadaddcdcddbcdcadbaaacdabcdbdbdcadcbadcbdbadbbaadbdaabbbabcdabacbbdcbbacbbdaddadbbcddbddbcadbaaaabacdaaaacabdcbbacaaddcadacacaadbbacccaadcaddaabbddabdcdaacbdcadabbaccbbddbcbaddbaaabbcdcbcacbdcdccbbbddaadbcaacbacaadbcddaabcbccacdbabbabcaabacbbccacdcdacbbddcabbbbddbbdbaadbbcaacaabbbbaccacdbbacabdcbbcabbdbabbadcadabaacddaddbdcbcdcadbaddabbbdbdabbbdcddddddbddbbabbdcdaadcbbbdbcbccbdcdddaaccbdcaacdcdcddacdbabbdabdaaaadbaacbbbababadabbacdcaabccadbcdcabaabcaddbaaadabbcdbbaacdaabdbdcabbccadcaddabdcaccacdbacbadddcdadcccaabddcddabdbddcccbbadbddddacaccddcddadacabaadcbabbcdcacccaadcbdacdcbcabaaabbcabbdcbdbacddacbddabadbbbcacccccabbabddadcabcdabcabccdbaabdbbdcdccaacdcdcbadaaadddcabdcababddbaaaddabadcbacdacccaacacccbdbbcdbcacaabbbacdbacbbabbcdbdccbdccadacccbcadaddbccbaacaacadadbcacbacdccadbacadabdccadbbdababbddbcbbcdcbddbccacababbbbadbabddbdbcccddacbcaaacabcbcccdabacbcbccdabcccbbcbbbcccdabddaacadbbccdccbdbaaacacdabdaddaaacccdbccdaccaadccdcbbbcbdabcddccddcabbbacabcccdcbbabdababcdacbbbcaaaacbcdbabcccacdbdcddcacacbddcccacaadaadaabdaccadbcadadbcdacdcbdbccacdbabdacacaabccdaabcbabdadabcdddcbcdaacabbdccdaaadaddbaaabdabcddbbcbcdcdcbbddcaddbbcddbcbbabdadaabbddddacbbadaabbcadcdabaaccdaccadbcbdcbbccbdabdcabccbccbcddacdbcbdaadbddbbcdacacabdbbdacabcbcaccbadbbbdaadccbacdccacbccddaddbbaadacddbaccddcaadabcdadbcddccddbcddbddbaaddcaaccdcbdcacdcccbdadaddddbbccdbbaabbdbbbbdbbcadbcabbaccbaaaaacacddaadddbccaaabcaaddcadccddadaabbcdbbdcadcccdbcdacabaaadbbbaaadccbbdbbddcabcdacdddcbaabbdbdbccbcdddadcbbaabdcbaccbcccaacdcccccbdddcababcddbdbadcbcabcacddacaddabaadbddbddbbdaaaabcdcddccbbdadbbbccdcadbbdbbcbdbccddaaaabdbdcabcdaabcbdcbbdbcbabcbddbaabcadbccbdcddbdadcabbbdcbabbbabcddddcaaacdaccabdbbabcababacaadbcddbadddccdbbbacdacbbaaabaccadbcdbdaccdcbcdcccdcabcdacbaaacddddaaacdaddadabbabbacbcabdcbcaacacadacbdadbbdcdcccdddbaddbccaddababddbaacdddacdcabdacaaccbbdadccaabdabaccaccbdaddbccdbdbabdbadbabaacdbdabbbcdddaaabddcdcacadcdaccbacdaaacdddabaccccaadabcbadbacbdccbbdadddaacddadcbccabddaacbcbdbbdbabddcbdabddadbccccbdabaaadbbabaadbcddbcdbddcbcccaddadcdcddbbbdaccbaccabbbcbdbbccdbbaabbcdbcbaacacadbdababdaadcaacbcaacabdabdbabdcbdccbdbacaccbacadbcdbdacadabbaabbbaddcacabddbabccccbbabacabdccadacadcabbcaaadacccdddccdaabbaddaaabbcdddacacbcbcccbbbbdbbddbbcdcdccddbbbdcccacacdaabdbaabbbddbbbcbcdabbdddbaadabadcaaabddcbcccdbaccdccacacbacaaaaddbabdbbbbdbbaddbbaadaacdcdaabacaabdcbbaddbdcccbdcacbacdaddaabdcbadbabaaccaacbaadaaabaacdabbdabdabaabadbcbcaaccdbbabcdbbabbbaabbdbabddabcdccddccdcaaacdcdcdacbbcbdcabcbabcbddadadbdccccbccdaabddcccabdbddbdadbbabbdcabbcbbdaadabcabcadcbbdbaadddbabacadbbcbaccdaaacccdadddcaabbdcbadcbdcdaacbddadddacbbcdccdaccacadadcdddadadacccbabccbdcadcbdcbdbbdabdbcbcacbacadabdccaaaddbcaaaaddaddabddbcbcccdabacbaabdbbbdccddacdbaacddbbddaaccabccbdcdddbdbcdbbcbdddbcacddcdbcdbacbcddbcadbcacbcdabcadadcdcabdcbbbbbddcacacdddcbaadabadaadcbdbcadaadbbaabdbabddcddaaacbddbcdccabcbabcccdcabdcbdbcacbdbbbbcaaaacaadbcacadbacdbcdddcdccbaadaadbbdaaccdadaacddaddbbdcccdaacbcdccdbcdbdaadacccbdabacababdcbdbabbaacaabcdccaaddcdacabbccdabcaddaabbacbdabcbbdbbdccabcaaabbbacbcacabcaaddcadddbccbadcaabaaadbaabbdbdddddadcadccccacddadadabbdbdbcadbaaadcdcdcaddcaadcdccdaccccdacaacaccbbccdcbbabcbbccabbcaacccdcdababbacdbacabcddbbacacaddadcddabccddcbdaabcbaabacbbcbdbaccaddabddbddbcdbccacddccbdbcacaabbbbbcddadbbbabdccaaadabcbdaacbddbcbccdbcadadccddbbdaccbabacbbccdddcbacbccbbabddadddbcbabdadbbaddcbdaacadadcdccdadcbadcaacccbdcbadbaabcdcbcabadaaabbdcccccabcdaabadadbcbcdbaacadbacbbccbbcbccdacaabdcbdbbdddcbcdbcacdcbbbdacccaccdbdcbdabbadccdbcccccabadaabbacacbaacdaaacbcccbacadddacaabcbadbcccdbdccdacccdaacaacbdbaabadcdcdbbcddbccabcacdbdbbbccbbdccadbbbcdaabcddbcbbdbdaacbcddddcbdabbabadddaddbbddacdcbdbdacbcdcaccbbbadaacbcbddccdadbacddacdbcccbbdcbdccbcdabcdbcbcdbacbcaaababacddddaddddaadccddcabdcaadccbddaabaddddbdcbccdbadcabacacdbbcaaacdcadbbcdaadadabcdaaccabcdccbabccdcddadaabdadccdcabdcbdbcdbbabdcacdcbbcaddddbccdbbbbdbcaccaadcddddaaadadbaccddaaaadcbaabdbbbbaacbbcbaccdadaccdbaacdcbadbdabccdddcadaadaadbddccacaacdddacabdbcaddbdadccddbbcccbcccacdbdbbdbbccbbcccdabbbcdbbaabbcbacbbccdbbbbcbdcbdcbdabbaadbdaabdbddbacbbccaadbdccdacdacaaaddcdabcbbbdbbbacabdacdcbcbcdbdaaaaddbacadadbbaabadaabcbcadbaaccccabbabbbaccddcbcbdcbacaacdbaabcdcdadbdcbbcdbcbbddabbbcbbdcddcbcacdbbbcdabadddcbdbccddbcdadcbbdbacbbddcccdbcbaabcbccaabcdaaccbdbaacabdbcdbcbbaabbacaddcdbdbdcdbdadddadccbbcbcaacddcaccdcbadcbbcbbdccccccddbbabbaccbaccbcacbcadaacaaabdadbccbacbaddcaabbdabdabcadccaddbbcadcbbdcabbaaaabbaadaaacdbacdcacbddbdaadcbabaadadbbcbaccabcabacadbdacaabccbbdcbdccdbbdccbdababcdcbbcddbbcbddabdbdccddbaccabcabcbdaddabacabbcbbcadbacaddacdbbacbadcacbbacbabcccccbcbbccaaaadbbadcadcccbbaacbbdadbbbddcbcbbacabdabdbaacbcababdbbaadccbbacabcdaacccdaddcbaacbcaddcabdcdabddbdacdcacdcaccaabddcadbabbcadcabbbcddaaabadbacdbbccaadbcdcbccccdbbcccabcdbddaccdddddabdcaaddbdddabbdbaaabdcdcddadbabcaddddaccaaacabccbadadddcadabdbddcbdabbcbaabacdaacabcbbdacbabbdabdaddcbcccaacaacdccabddccacdabcbdaaccbbbcbbaaccbbadccacabbcdbcbadcbdbcacdcdbcdccddbabcddbcdcbbcbdccdcacddbbacddacdccbdbcacbddadababaacaccadabddabbbabadabdcdcabcaabcccbbbbadbbbbaccbbdbadacccbadcbadaddddaaddbbcdbaaaaaadbacdcdccaacdacdacbcadacaadacabcaadcbccacbcbbbbdccacadcabadccdcdbcdbbbccacacdcaaddcbdcaaddaaacddcaabccdcdcdddabcbbdadaddaccdbdcdbddaadabcbbbacbadcdaabbbaddbbbcbacddcbbbbacbdacbdabbbdaccbacacabcbdcdbdcbbdccdacccbddbacabcccdaacabdddabadaccbabbcaddcbdbabcdbacadbbdacdddbddcbdcdccccbabbbacdcbdcacddcbadbacbacadbdbcbabbacbcabbacaccacbbdbabaccdbcaacaccccbdccccbccbdddcccccdcbcaadcddacbbcdaccbdcaacdbadbcacbaddaaccbbbaabacbddcdabdcacdaabbbcadbcccdbdaaabdaadddddcabccadcaabdadcaccbbbccdadddacabdbdbabdacdcbbbaadbbacbdcdcbabbbadbbdaadabdbaabbdacdcbdccdbdcbdadbccabadbbbccadaadcaadadadbadbaaadabbddadaadaadbaabacbbbcadcdcbcabdbbccabbddddbbbcddcacddcdadcccccccdaacaaccbbcbdcdbbddbdbbdcacbcddbdcddbadaacdbaccabbccbacbcdccdacabddbacdbdbcdabcadcccddaccddbdcaaabcabdbcaccdccdabdddcabbababbdadabbaaaabbdbcccccabbdcbdadbacadadaccababdbbbcbbcdbbddcdddbaacbbcaadbcaacdcdaaaadadaccabcccbdabccdbbacdadcbbdccababbaddabbccacbadadddcddbaaaadaddadacbacaabcabbadbababdcdcbadcadbcdccdadbccaddcccbdabbccccdabbbabdccaccddaacbdbadaddcccddaacabbdddcbccdabbddcdbabccddccddcabcdccacdbbaacbbddddbbabddabbadaacdbdacabddbdcbbacbdaaaacdbbacdaacddaaadabdadccaaccbabbcacabacccaacdbacdbccaddabaacaaabadaacbaaacabadadacdccbcbcbaccdddacdcbaaacbadcbcacbddddadbbbbaacaacadaadcababdadccdcbbbabccddccdddcdbcbddcaccbdbdbbabcdaddcbdcadadcccbdaaaaabdbabdcbcbcbdbaacbbadbcdbddbbaadbcbbcbcdbdcdcddbaddadbaccabcaaccbdcdccdbaddcaaaadcaaaccadcbaaacdabacdcaacbcaabaaaaddadaacaaacbccaabddccadacbdbbbbcabddaaaabadddbcbdcdcabdbcbaadcdccbdbccbddaccbbbbdbcdacbbaadbadcdcccbaacddbcacdcbaccadbcccdcabbbbadbdaccbbabccaddbcacdddbbababdbaccbdbdaddbcdacbbdddadbbbbdabaacbcddcbcbbcdabcabcdacccbcdcadcabbcccbdabacdadcdbacadccbbaadadaabbaaaadccdababbdccabababbbdbbbdabacdcacacacdacaddbbcdddaadbbadbddcbdaacaabbdbcabddadaaacbabdbdcddcaadabacdbbbaadabccddbcddcdbaacdacdccaccbcdbdaccbcbababccccccbdcdbbaddddaccaacbbabdccdddbbaabacabbbbdbcdbaaacadabbbacdaaaddabbacabbcdcdaabcabaabcaccadaacbdadaadbbccdacaddbcaadacbacccbdabcaacdbddcabbcccbcabaaabdcadbcacaacdbadddacabadaabcaabdbbaccccdaadccbbdacddaacbcacadcdadbbabbdabdacdbccbbadadbdbbcdccacdadaaadddbddabbcacbddcdadbdbdadbaaaacacdccaaaddabdcaabdbcccbbacacaadccdccdbcdbdccabddbccddddacbabababbcddbcbddcddadddadcbdbdacbddcaabdbcbdadcabaababbddcddacdbacdcbcbabbddaadaacacdccadbabdbbcdcccdaadcbcddabcdbababcaacdbbbbcdcaabcbbdaaacdccbabcbccdabdaadbcddabbdacddcbaabdbabbabaaaacabccbcbaaaabdadcdbbcbcdcdadaacdbdcbabcdaccddadddcaabccabcbdaabcbbbabacbbbdbadbcbcabdbbcdccbdbcbccacdabdbbaaadabcadddacaadbcadabdababccdacbbbbbcddbbddaabbaccabbcdcacabaabbabcbbbcabbbcadddcadbadcbabdccbabaadadabddcbaaccabdacacabbadbcccddcdbbddddddaddcbcbcdbbacaadccbddcbcccbcadadacabaaadcddbbbcdaddbadaaaadcdcdacacbaddbcabcacaacadbbdbcabaacaabacacdadddbacadccbccabbcbcdadcabcdbccccaddddaccddcdaaccbddabdbcbcaaaadbcbbbcbbdbdbbdcbccdabcccdacabcddabcbcbdabacadadbbabbddaaadcbaaccdccdbcaccadadabcdbbabacbabbdbabddaccdadabdabbcdadccacabacdabbcbcabaabacacbdddbddbabaababccddabdddabbdcabaadccbcaacccdadbddcabaabadccadbddbadcaccdcadabcdabdaaacccabadaaaddabbbacddbcacbdacdcdcbacdabbcadabcccdcbbdccbdcaadcadbcaaabdaacbaaccdabadddcaddccacbbcdaccbbcadabbbabbbacacbcbacbbaddbacabdcddbaabbbbaabbaabccabcccbdaabbddbcaccabbbcaccddaaaaccbbaccaacaddabcbadcdacdbaaccadcbdbddbcaddccaaddddaaaadbabbabbccbdcdbbadbacdabdcbdaddbbbcaabddbaabacbbdccbcdbbdbabbcdccccaababdbddaacddbbdbdcbaabcddbbcdbddcaaabdcabdbabbcbcdbadbdcaaddbbcdcdbbdccbabccaadbddcabdbcbddcaccbadbdaaaabacdacbbdaddccdcdcbbdbcdabacbbdcaccccbbbabacbcaddbdcdcacbbcacbaaccacbddbbbcdaddbdcbbcdcddadbcdbaaaadaabcdbaaadbcddcdbdcacbaabadaccddbacdcbcadabddddababccbcdbadabcacbccbabcaacaabcdddaccdddddaaddbcbbdcdcdcccadcbcddbaadccbbccabbdbdaadadacddcaddbddbbaadaaddcaacdacbaddbdcaacadddbdbadbccdcccabcabcbabbbdabbbacccddddcccaaddbaacaaccaacaccaaaacbcaddacbcdacadbcbddbaddaccbdcbbcbddccddaacbdacbadbdbdbdbaddababadcbbdbcacdcbcbdcdacdacccbabcabbbbaabdaadbddbcbdbbccdcccbbaabbdabbcaadcddbacbcaabaccbdccbbaacdbaccadabddabadbbabdaabacbdbaabaddabacacbbacbaaabcaaabddcdcdbdccdababbbbcdcccbcdcddabdbdadbdcbcddacbbdbdddccbadbaaaabaacabaadddbbddbbababdddacdcacbadbaddcbadddbbbabdbcbabcccacaabacbaccacdbdadddbbabdccacbacabbadcaacabccbaadbbbbdabdcbdaccbaaaacaacabbcaacdcadbdaacdbbcddbbaaaaaddadadddbdabbaabacdccbdbddacbbcacabcaaaacbaddbccbcdadbbdaddcabdabcdaabccbccbbbdccbcdbacbdcddccccbdaaadcbbdcdcbdabadbbddbcbaabcdbadcdadcaababcbadcbbdaccbdcccaacdbaaccbddccbbbcbacbbadbbccbdacbdbbbbbccaaabcaabbddddccbdaddbccbbccaadcadbabcdbbadacdccddcbcdbbaacbcbddaccbaddccabccdaabacdacdddacccaababcbadddabdababcddbadcdbcacdcddcabcbcddbbbccacbbcadcccdbabcaabcdbdcddbbaadcdddacbabacaaaddaacabdaddaabadacacbbcdddbdbcaaaadaaaddaddadccdbaaaddabdabaaddbbdbcdbbbbcbcacbcbabddcdacabaddaabcdccbbdabcabdcccdbccbbbbaaaababcbbcbbcbabadbdaadccdbadcdbababcbacddddcbbdcbaacdbcadcabdccdbbababaacdcbbabbddbadbcdaababdcdccbabbaaadaadcdaddaddccbdbbabbbbabbadcbdbbaacddaaddacaacacaaaabdbaacbdddcbbbcdacadccaacbdcdaacadbcdacbbcddcbbddaddabbbdadadbccbcccbacbcbbcbcddaaddddcbdbcbbcddbacdabdddaabcdaabbccdccbbccdadbcdcccacbacbbdbccadddcdadbcdbcbadccbdcabdcbaabdaccdadaadbbabdddccaccccadccaabcdbccdcacabddaaabdbdccbacbccdcdbaddbdabacbcaadaccbaabadadacabdbcbcdbdbddcddbbacdccbdadcbdbacbaabbccdaddbdbcddbcaaccbbccaccddcabdbdddacddcddbdabaabbdbadcbadccdcabdacadbdbbbadacadbdbbbcbadaccaccdcbccaaaabaacbabdbbdaadbbcbcdadcdbdabbaacbbbacbcbacdabaabddadacdaaddbbcbbaadbccccaadacdcbbdcaadcbcdacadbddacbcbbacccdcadccdaddbccabddaaacddadbbacdbcaabadcadddabbadbdbaccddddcaabccdddbbdabbbccbbbdaaaabababbdbdbcbdadaaaaccaacaabcccdabdacbcbadbadddddcbdbdcbadddbbcaccbbcbdbbdcbddaaddcacccdabccdcdbacdaacabaacdcbacccddabbdbcbbabbbdabcccaccacbddcabbaddcbccbcabddccacbadcadbbdbccdabacacacbdcabbbaaccbdcdcbbaacdcddaabbbabdbcccbbbabdcabcbdbbddbabbcaaccbcabdbbcadaccbdbaddcadaabcdbacdabadbcdadacaccdbcbcacddcaccdacadabbbcadcbdcbacdccabbbaccccbcbcbcccbbdaacaacdbcdbdccacabaabaadabcbccbcbdadccacbcaccdadbbcacbcbacadbabbddccbbaabaadbddbbacaadbbaadaccbbabbbbdacabaaddbcabacccccbcbadbbbcdbdccbaccbdcbdbcdbbcabdadcbbdbdcaacaadbdbcdcdabcbcdcccbbcbaabacdabbccdbadabbabddcddbddbcaabbccdacccdbbccabdaccbacabaaaacadaaacccaaddbcbadaddbadbdcdcbbaacbccbadccdacaabcbbbbbacadaaadcbbaadbbdbcbaabadabdbcacdccbddcbdddcbacaaaaadbbbbdacbdaddbdbcccadaabdddacbabaaacacbdaacbbcdaacabcbbadabdbbacdcdcacddbdbcdbbccbbaddacbcacadabccadcbdcaaaddaacbcacbabbabccdaacccccdadcbadbadbcbbdacabccaadcdbdbcccdcbabaccacddcaaacbccacbabaabcdadaddcdbbbbaddccbcbacaaddbdccdaddabbdcddacdbbdddccbbadcccadbbcacddbcdbcbcdbbbbadabadbaababacbcbdbbabdabbdcbcaabacdbcbdbddcdadacdaacddaabcadaacdbaacccdcabaddacadbbdacbacccadcdcacbbcadcdaaacabdcadabcdbdcdadcdbcaababccbadacdbccadbccaddccabdaaccddbabccbcdaadbaacadcdadcacaabacabbacaaddabcdcbbdacccaacacdacdccbbdccdbdcbdbcdcccddbaaaddacbbcbaabbaaabadabcbbddddacbacbbccdbadaaabdbcabcdcadbbbbbbbaaccbddabbcaddaadcdbdabdbcaaabcdccdcaacddadaabaddaacbcbddcbaabdbdacbdddaacdbabbbcdccacbaadabadadacdcbadabacbbccdccccccbacacdbadacacdccaaaccaccacaababcddcbdcbdcabaddbbcadcbbbdaabaccabdadaacbccdbcdcdbaaccaabdddbdaaccdacddaccbcacaabaacdbaccaddbcccbbbdcabbbacccdccbcbbdacdddcaabbdacbbccddadbbbccbddcaaadaacbdaaddbbccccacbbdbaddccabdcbbcbacbcbdcdadcdbcddcbdaadddabaaaaadcabbcddcadbbabaaaaabccdcbdaccddbadacbbccdadabaccddaccabcbabcacdcbacdbaabbcccaddccababaaadabbdddcdaadadcbaacdcbccadbbbbaaaaaccdccadcdabdacddbcdabcaacacaaddddcbdcbcddbbcccbadbbdbaccddcaacdbdcabcdcdcbcdcbdacdcdbcbddbdaddadcddaabcababbcacbddcdacddcdbbabbdcccacdbdcccccaabdccdabcadacdacdcababbdadaaccccaabbdaccdccbabaadbaaabdcbcdbcccdcccdacabbddaabcbdcdabdbacbbacddbdcadaacaddbbdbddcbdcdccbcbcbaacabacadbdadbdabdababaddbcbadadbdcaacbbacdabbadcabbbadbbdddcdabbdacbccbcdbbdcdcaabdbddcadaacdcabcdaddacdbacaddddddddaaacdcbdcbbdacdcbdbdaddabdabaabcacbcbabaddabcaddcaaaddbbadabacaacdadaadbabbdbdbddddcbcabdcbdabbdccbbcccbbacbcaabacbaababaccdbbbaacbaaaadccdbdcbdccbdcdacabbaddbbbcdaddadbaabdcabbdccbcdaaacdbcbcdabcacdabbcccbdbdbddddcbdcabdaccaddcbddbcccbdababdbbadcacbccbacdbbaacdacbbdacadcdaddbaadcbbdbdbdaaacddacccccadcacbcbdbddabcaabdabaacabababddaabdabbbacbdaddbaddbaadddbcadcaaccdcacabbdbbaddddbcdabacbbbdbacddbadbbcddcaabbdbabbbbcdbcccaaaacdaaadabdccdbccbdacaacabbdddbcbabcaccdcdddbdbcddabdccccbdbbdbbdaccdadabdaadcbcbabacabacacccbacdccbabddabbcddcbbccbaddcaaacdbabaacbcadddbbccccdabdcbacbccbcaccacadbdbcdddcddbaaadabdadaabbddcabaaccadbaaadadbbdccddbbabbadadadcdbdddcbcbbcaaddaaddbcdaadbdbcaabadcaacdaabdacbbcacdbcacacabddddadcbccaddbacaacabbcbabccabbabdadbdabbbbbdbcadbaaaaccbbabdbbabdcccdbdbabaaaaacdbabbbadbcadbdadbaccadcdbbdbdddcabcaacdcdbbdcbddabbbacdbbcdacdacbbbaddcadbcdcdccbdbbdaccaccdadbbbddddabaccbdaddcbcbcdacabdabadcaadbbabdadacacaabcdddbaaaacdbdbcaabcbbbacdaddccacbcaacdcaaabaaabdbadbadbbcaccbaababddbbacacacdacbddccbbdcbccdcadacbcdadbacabbbbadbcaabbcabadaccbcbdaaddcdadcbbcaacccaccadccbbacdcbcdcdcbcdbccdacbaccaaaaaadccacccddcadcadadddbcdcadabbcbdcabcbaababaddcccccbcbbbbdaabaddabdadcabddcaaddbbadcdcbbdcaccacadadbddbcbdddcacaabdabadbcabadbbadadacbcdacbcabababcabcabbadcbdadddcadacccbcabadbbcabdcbbcbdddbdabbbaaddbacadbacbcbabcdbdcdabdbcbacccbcbbddaacdbcdadaccacdddbcacacbcaccaaabcddcabccabccadadddccacbdadacbadadcbbdcdcacbaaaabadddaddddbcbababcdcbadcabaacaccacdacbcbaabaacacdcaaabbbcabaadcbbbdccddccddaaccabdccbdadbdddaadbdbbbcbcaaabdddabbcacdbcbaaaabbdbaadbbcacbaacaaadddaaccbcadaccbbcacdacccbbcacdcbbaccabcdacdcbdcabccdacabbdcccbadbabddbbdaadbddcbabddccbddcdabddbbacaaadbddcabaadcddbdadbdddadcdbcabadddbaddbddcacacddcabadcadadaacaabdcdbdadbdaddaaadbbcbbaccaddacdbccadcbdcbababcacaccacbabcabbbccbcaaacdabacbcbbacadbbcabdacabdaadcaccdcadabbdbcddccaabcbbccbaabdcdaccbdcaaccdaacabbccccaabbcdccccdbcdbaaacaadabbaacbdacbbaacabcdbcdaaccdadaabadddbdabaaccadacaabacaadaccabbabdcbbcbadacbbaaaadaabbbbabddbcabaccbdbcacdcccadacacbbcabdaadcabddaaabcccbdabccbbcbcbccdcadddaaaaddcdbbdaadaabbddcbcabaddbcddbcbdbdcccadbaaacbcbcbdccbcdacabcccadddccdcddbbbdcadcaacbbdbdacadbaabdaacbaaddbccdcaaacabdabcddaadcdbdbacccbbbacdddaaaabcacdcabbcbdabcddcddaababaabbadbacacbdccdadbccabdacdbacadadabdccdaccccacdddaccdaabdccdabbccbccdaacacddddbdbbcdadccbaadddccccbcdbbcdbcadcdababbbaaaadbadccacaccbbadccaadadcdcaacabdbaddccbdabacbdddacddbddaddddccbcccaddccdcababbddbcadcddbcbccbbdadacbdacaddbdbbdacccbbaabdbcbcabdaacacbcdbadcccbcdbdacdbcdaacaaaacbcaababcdaacabddacddbbcbcadcccddbbcbcbaaabcddadaccdababdccccdbdcbabaddcadbccbcddaddcaccddadcbdddacdddcadcbcbaabbcbbababbdddcbacccacbdbcadbbdaaddbaddbdcdaaabdccdacdcddbcdcbacbabbcadbccddacccdbdbaddbdccaddddbbcbbddbdadbcdcccabcbaabbcbcabbacacdcdadabacbcbdcbbbcbdcaaadcadaaccbaccbdabccdccdccdcbccddbbbbdbbcdaccbddccdcbacdabdadbddabbabccadaaacdbbdbdacabbaabcaaccddbdbaaaacbdbcabdadbaccaaadabcddbacdbbadbbdabccddddacdddcdcdccacaddabcddaacdabdbbdcbddbdcadbbdcaddadcadccacadccccadadabbaaaabbacccddaaccbcaacbbbcabaabdadbccadaaddbaaaccdbcabddbbaaaddcbaadabdacbbdaaaababadaccbabdcaddccbdcddbaccdcdddddcddcbccaadcdaaadbaaabdbcbacdaadababbdabadabaabbdaabdccbbcdddcabcbbdbdacdcaadcaaadbcbbbcdbcaccbcbabdbcadddcdbdcddadcdcaabadaccabcabbcbcbbdccbddbabbcaddabdbcdacacdabcabadabcbdaabcabcbabddbcabbacdbcdbbadadcabdcbbdabaccbcdabcababaaabbacddcaabcdcbbbacccacadcbdbbadcbdabddbdccadbddbbcdacbbaaddddcccdaadbdbbdccdcddcaaaaccddbdcbbdccbcdaabcdddbcbddabbacddbaccdbbadbbdbabcdacababdddabcbaabbcdabcccabaddcacbdabbcbbabddacdaacbcdadacaccbbbbadcdadacbbbaaddacbcddaadadbdacaaaaadcbcaacadabacdabacabdabacaadcbbbaddbdddadcdbabcabdacdaabdcadcdaaaaaacabbacddbdaadaddaaaaaabbaccabcbdcbbbacccbbacadbcddbcabcdcabdcbddbcccabacbaacdddcbcabaadccdcacbddcacadaddbbcbacdcbaadcaabbddbbbddbbcabdbdacbaddabbbdbacbbaccbcbccdbdbaaaadacdbabdcababbddadadaaaddbabdcdcdcaccabaacbcccdccbabacbbbaccddddbdaabbddaddcccabcccdacbdbbcaccbabbcbbbabccbcaacdaaaacaaabcddcbacbcbdaabdadcdacdbcbdbabcacaadcbdccacacbdddaacdcccdbcbccdadcdadaaccaddbadddadbccdbadbacdabcdcbbcadddcbdbcbbcbaacccbbcaaccdbcacbddcdaabcdcdddcddddccabddddcdbabccacdaccdaabcaadbaaaccccbdaacacdadbbbbaadaccdbabbadaaabbddbcdddbdcadcadabadaadbabdccbaababdbcbbabacbdcbbdcacbbbdaccdadadbdcccdcdccdcddaadacccbdabdabddabbdccbcdcdbbacbdcbbbddacadaadaddcaddbaaabbbbaccdaacaaacdccabbcabbbddbcabbdbaaabddcaccaccbdadbaaabbabbccdbbddbbccadaccbbbadaaccaadcbabccaacbbacccddabacdbadacaddcbcbaddbcbcbadddaaaacbabdccccccadbadddbcdbdddddbdadabbccbbdaddaddbddcacbcbdacdabdddcbbcbcbadccdbcaacdcacbadcbddadbbcccbdcdadcbbbbdbddaabbbabadbbdacdcbccadbcbcabaacccddcbcaddaacbbadcacdddabbadbaddddbbacccdcdcbbdbdabdbbadcaaababbcbcbacdcdcacbaaacabcacbdaabbbdaccabbbdbbcdaababbcccaaaacbdddcdaccdcbdcdbacbaaddbcccbbaababbbabaababcdabacababddabacadabcddcccbdcaddcdbccdcbaabbbbcaddaaddadadacccbcddabbccadbdcdcbbdcaadabcdaadbdcaccaacdbcdbcddbacdbdbaaabdcabbbbbababacdbccdaadadadddbaadaadaaacddadccbdadbbcddcaaddaabccddaadbbcaddcdadabbddadddbdcddbbdbacdbdcaacadcaabdcddbdcdbcacadbdacaddbaccdbaaacbcddcbddcccddcaddbdccaadcbacccadbdcdabbadbcbbdadbacbaadcbdcdaaccaabdbbdbaaccbccbadbcbaaacccccaddbbbaabdbcbaabddbcaaabcbbbcbaaabaccdbddcababdbaabcaaabcaadabacddddcaacadbbbdadcabdcacabdbaccbcaccdadddbabcaacddcaabcdacbaacbabbccccbdbbcaababccbbbddaabaddacbabdbdddcabcbabbddddabdaadccaddcadcdcdacccabbddabacbdbadcccdcadbaaccccbddbdbbbbbdcbbaaadbcadcbabdddddcdbbbdadadcdbadacdaaadcaabdcacaadbaccdbabbabbcaaacbdabcdbcadadaccaadcbbcbcaddbcabdbccdcddccddbaccadbaacabbddacccbbdaccdabaaccabbccaabaabacacbbaddcbcdcaacaddcaacccacbcbcccaadabaabcacdcddcadaabbdcddaaaacacbaaaaacbccbbabcaabbddbbccbbadcdacaadbcccccabdcaacabababddacbcdcaaddbccccddabdabcdccacbdbccbacaaabbbbcbcccdbbccbddcddcbbbabbdccacbdcbdbcccbbcadbacbbacbaaabddaabdabaddabcbddcbbabbdddaacbdabddadbdbabcdaadddcaddbadaacbcbcbccaabcdbacdcbcbaabacdaabbbcabccdacacbdbdcacacbdccbddabbacdadabcbcdbdddbddbccadbdacddccddbdcdddaaddaabdccdabddadabcccbdcbadcabacadbaddcbcbdaacaacbddcabdbcbcbbaddbbcdcabdccccadabbbabaababbbdadabcdbabcdacdacadddcaadbadbccbdaabcbbdbdcbcbadabbcaccdaaccccacaddaccabcbcabdbdcdabbbdadaccabbbadbdbddccccaccbaccbcaadccbabcbdbabdcaadcadaaaccbddbbbbadbcbaaabcacaacdabdcccdbbccacbbaddcadddbaddaabcdcbdaaddadcdabcaddbdbadcdaacabcbbdcacbacccdcadadcabbabddccddacccacbaabcdababccbcabdaaadbdccdcaabacaaccccbdccbadcabcdbccabcdbcaaddacbdcbadbccdbcdbdcbddcdadbcdccbbacaabdcbcdddadbdcacbdbcbbcbbbabbacbdcbbcbdacdacdbadddabcdabddccadcacadbbbadaabccdccaacadcdaacacbcdbcababbacadbbbadaacddadbadcddcaddbabcbdadbcddababcdabacacbaccabcbadabdaaadcdadbcacbbbdccddaccddbdbcccaacdcdaabdcadbccacadaccdbbcabcdabddadbdbddddbcacbaccbddbbaadaddbaccdcbdaadcabbbbdaabbdcaddbabaaabacddadbdadcccccdcccacaaadcbcbdabdbabcabdbcbcdadcdddbdbbcaacdacabddcbcdacabadaccccbbdadbaccaaaaaaacaabdbcccbcaaccabaddcaccabaaddaadadbcabcbadbdcbabccdcabdbcbdbbaddddbcdbbabadcdabacacbdacaadcdddcdcdccdcdbcdaabadbbccbdbabddcdbbcbdbcbcacbcbbacacddaadabbcbdacaadccadbccbbbbdabbadccdbbdccbadbcdcbacadcacadcdabcabbcdcaacbbcccccbdcbdabadbcabaacbaddcacbddccbdacdaccbbbbbddbbdbbbdbccddcaddbcdcddddcdbbcbddbdbcbbcddcaabcadcdcaddaaabbdbddacdbacbabcbbddcdadbcbacdadbddabbcddaacaddbadcadcbbbbcdbbacabbddcddbcabadcacabcbdabbbadaacaaddddbbccacaccbdcabdbbcacdadbacdcacddccbcbcaccbaadabaddbaacaaacbcdaddbcaddbcbdbccabaadbbadbbdbcaadddccdbaaccadabcdbbdbccabbbdaccddcbcdcacadacdadbbbbdbabcccbaccbbcdbabacaabaadabdaadacaaddbdcaacdcbaaaaacdbbbdacccaaacdaaddccaacdddabddbaabacadcccdcccdbcbcadcaacadcdbbadaaaccaaaabcabbacccdbccddddcdcdbcdcdcabbaccddabbcaccaddddbcddccaddacddbbcbbadabcaabcbcaadcaccbbdcacbaccddaddbcacbdaddbcbaabdacdcbbbbccdcddcaadaabcddabdaacdaaabcbccaaddbccdadaabcdccacdccdadbbdabcdcabaabaddccccbbdcaddcacbbddbabbaccdbdbabcdcdbbaacadcbccddccaccaccabaabdbdcacdcbbaddcbbddacaccdadbcdadccdbcbadcdbdccbbccabbcdbdcaadccdaddbddbcbbcdbdddcacaacdbccbdcbbdcdbcbdcbbbbddbdddaadabaabadadaacaabcddadddcddcbcbdddaabadddbccabbbbcaddacbbaaabacbadcddccbccdacdcccdaaccbbccccbadbbcacbccbcabcadaacacbcbbbbbabbbcbdddbaabdbacabbcbacdccddbbcbabddadddcbbdaacacadacbcbbdcdcdaacadababbacbddddaadcbbbdbacbcadddbdaaaadbcacbdaadabcaabbbccabaccbadbddcdbddbabcbccdacdadaacbcdacbaacdadcddcbacadbabdababacbacdacdababcdadcbbdcbddbacdccaccbdcbccadcdcadbbcdbddbacbbdcacbbabcdaaaccbcdcddbdbdbccbdcbaacdcacbddadbdaccdbcaacdbbdcbdaccbaaabccbcbbdbbbaaaadcbabacddbbbbbadbabbadaccddcdccaadbaaadbddbbacadcdbdbcadccbdcbaabacbbcababbccbcaabdbcbbdbabcbcacbdcdbcddbdbadacddbabbbddabdccdacaddcbddbcddccdcaddcbcabcaaabcdbacbcadbccddbacbdcbacaadcdbdcbaadbbdbabcbbaadaddaddacdcdddcabababdbddbdcaacddbbcdccadcdcdacabcbdbaddaadabbdaaabdacabdbbbadadccbaacccadbcccbdbcdcadccdcdaccdccdddcaabddcccbcddaacbdccdcbccbbabcaaccdcdcbcdadbabcbacbaddcbccdbdacccbccbcbcbaaabccbbadcabdbdccbacbcbdadacadbbaaaccdbcdcabbdababbdbacaaaaccacbababacacdbdbbaaacbbccbbaaabccaadbabbadbababaabacccaddbdbbbdbabbdcbccabbcdbdaacdaaddadaccdcbdaabdaadbcbaadaacbdbadddcadbdbdacddabbbccccbcaccbcccaadbddcbabcaadbcabcacdbcddbccabbbaadabdbcbdabaacabbadcadcaadbbdcdcdcabbdddaabaacbcbbdadbdbdcbbadcbcaccdddcbcbbdcdbbaacabcdaddddbcccbacbabdabdabaadacbccbcbacccadabbccdbbdaaacdcaaccdabcaabcbcbdcbdacbddacdabdcabbbadbcabdcbadbdcccdcdccdbdcaabaacbdbdacdccadbbaabdddccbddabbdddcaaabdccacbbcdcbcacddbcdccbbdaacddaccbbbbddaabbcbbaccbadcdcdaabdcaddddbdcbbcbcccbbcdaadbdbcdacabdcddcbacadbdaddbacccadbcbdddbadbdbbbbdcaadddcdcbabaabaaaaccaccaddddbbbcdddaacbbbccbacddcdbcabaacabbbddadadbdbacccdcabdadcdababbaaddcbbdaaabdcaccdadbddbcacbbccccabaaabaacaadbabdbddddbbadbaaaccadcaccaadacbcdadabccaaadccabaaccdabccacdbcbccdccbddaccdbcccccdbdcbccadddbdacabbaaabdbabcdbdbcaaacccbacabbccbabaddbaacbbddcbdcbabcaabdcbacbbacdcbbbcadbdcacabcbabdaacbbdbcdcabaacdacdcbbdcdcadcacdbcbcaabbcacacdbccdbdcbcbccbacdcdccadaaaabbacaabbdbbcdcbbddaacbdcbdaacbababbbbddaacacadcbccaddbbbcabddccdadbbccdbbacabcddbdbdaddadcdcabbbcdbbaacadcaadcacccabdddadcdbcaabddbdbccdcbcaccdcbcbbdacccbcddddbaacbdacbacabbcdccacdadddbcccacbadbabdbdccbaacbddabbacdcbdacadcaacbabccbaacbcbdcbcdbdddaddcdacdabcdaaaaccbaaaabbbdbcdadccbccddcaaabccccddddacbadaaabdcbdaaaaaabcbbcbbaacaabaccdaaacdbbbdccbcbbdcdadaabaacbccccbdcdabdddabbadbbcbbdbaabcbcddbbdbcdddbdabbcadcbcbcbbdccaaddbdbcddabaacacbabccbaacadaabcbdabbbddccbcbbbccabbcbaaddbdaaabccddbcbddcdbdaddbcccbcdabbcddbcdddacdcababcbdbbbbddcdabaabcacbbbabcbdbccddbbadbddcadcaabdadcbccacbbdaddadbaaccadcabbcdbbbaaaddabcddcabdcabcaaaacbccbdbddcabcdbbcbcbcdabbbdddaccbdbabddabbddbddbabaccdacbbabcabbdcddaccddcdabdccadaccccdabcaddadacacabcabcacccdbabbbbaadcaadabcadaaddbacddcbacdacaadbaddcdcadcaabddbcacdabccacbddcdabcdcbdccdddbcabcdddadcbacddbaacbabacbbbbcdcdcbdbacaacbdcddacabccdbaddacacaccbaabaaaddbcbbbbbdcddadcdddbcbcabacbdcdcbccadccaadbccdbcbbacabbbbaaacdddaaccbabbdddcbabdbaaadadbdadcaabacbccddcddbdadddaaccadcdaccbdcbacbbddbcccbacbcaaccbabccdbcdaddcbcdaccaacacadccbdacddcccdbccdbcbddcaaacadbcaaabaadcdbbdddcabcbdbdcbcdccbcdcadbbbbbaaccdaacbdcdcadbabdddcddbacacaddaddbaaccdabdccdabbcbadbbadbabacdcdcabbbcbbdcababbaaabddcddbabdcbadcddcacaabacccdbadccabaacccbbbbccdabdacddaaaacadbabacbbbcaaacabbbbbcbadadbcdbaadbcdcbaaabaacdbabddccccdccbabbdbbadadabdbcccdaaaaabccaaddbadddbbbbdcccccbdddddaaaaacbbbcaadabadddcbdbdddacabdcadbcaccbbdaacaaadccaadddcbddaddadcabcbcbabbcbbcdbcadcdacbccaaddbcbcaaaccdbbadbdbddabbccabbabdbacacaddbdcdccdbdabcabbdabbbbdacabdcadbaabbaaabcdabdcbabdbdbaddbccabbcbdadcacdaaacbdbaabbcdddbaccbacbabccdbbcddbacdadddbaddabcdcdbcbaddcaccabcababaacdadbdabbbdddbbbacdaddcdbbacdabdbdccbcabdadaccacddabdcccdcdbdbbdbcdcaacabdacbccaadbabdbbccbdbcbdaabbddcabcdbbcadcdddbcdccabdcdbcccaaddbbdcabcababccacbdbbaccdabcabbcbabddccbbaaddaddbccbbbbbabbdbddabdbbbaccadbabddadaabacdcaaaababaddccdabadddcbaccadccdccacdbcaadadbcabddbdabbcaddcdaddacdbdabcbbdadacbabddbcddbbcbbddadaaddccbddabbcccccadccadbdccacbabdbadaadcacdcbccacaccccddbaddbdcbcbbbdcdcbbbccbaabccacbdccaabbbddddcddcdddbcaadadaabcbaddbbbbdbdbbddcaadcdacbcdbbaddbdadddbccbadabcdbacdadaccccbdabdbbdcabaadadacacbdcbbbbabdaccaaddacbccdcabcdcddbaaadaabaabbaaaabdabbddbcaddaadcbddadabddcabcdbddcdaccbcacaacddcccabadbbdaadcabddcbcbabdbbaaaaadabdbcccdbadbcdadbaccdaadbdabcbcccccaadcbbaabbbaabcaddadacdadcaccbdababcbdbdccbcbaddcccbdccdbcbcccddcbbbdaddccaaccadcbdcddbbacdcbadbdcbddadddcaaabadbdcbdcaccbddddbdcdbcbdbcdddddddcdbdcdbbdbdadccabbbbdddbbbcccddcbcaddbabadadabaccdccccbdbcddcaacccabcbaccacddbacdccdcbabccdbbadcccabaacbacdbdabbdbaaaabcbcdddccacbcbbbacacccdcbcbdabddbcaddcddbbaadcddccdbbdcbadbccadcbcdcccbbddbbcadbccaacbcacbbacbdbaaacadcbacbbcdacacbadcaabbbadbadccabcbdbdcdababbcbadcdadacabdcccaaaddbddadadaabaadbdcdabccbcabaccababaabdabbdadcabbaddacddababccbbbaccabcbccddabbbadcacadbdabaddabcbdccdaacdadacadbadccbdcbadcadcaddccbcabacdcdaadadbbbacdccbcdbacaddadbcaacbcdabdbbbcaabccabcaddcbdabdabadabbdcdbbbcccacdbbadcddccadbcdbbabcbdacbbcaabddddddbbdababaadaacdcadacaacabbdbbddabccddbbcbaadcdacdddcaacdcddddbcbbdccddcdaaabcabcaacdccaadbbdadcaaaaddcccccdbbdbbbddbccccbdaccaacaacbbcbdadbddbcbadbdaccdadaadacddbcccdcbaaabbdbabdadadddbdbccabaadcddcabddaddadbcabaabaaabccbbbbbddcccdadaccbccddcbadddbdccbccaadadddcbccadbacdbabbdbadbccddcbdbaacddcabbbcdcccadbaacdbbbbbddddacddaadabaacdadcddbabdbcadcaddcabdddddaddabbcdddccadccaaccbcbbdbcbcdbdccbdccdbaabddddbbacbcbcaaacdbadbdcacacbcbbdcbaabcacabccbcdaadabccdbadadccddcdbacadcdddccacbdabdcbabccaadadaacacbbddaabdabacbcdddabbcddcbcbaadcbddadcaacbaddbaabcbcdabdbcabbccbddbcacaacdbdcaabbdbbdbdadbacdbdcacbcbadbaabbcdbdcddbdadadcacbaaacabcbbbcacbaababdacbcdbadbaacddcadcccaddcbbabbabbccadbcdabbabbacbbadcbabccdbbbbcbcaadacdbbabbdbadbadcdccdbccadabcdcdddaccdcddbccacbbbabacabcdccabdbabcbadbbccdbabaadaaaaadbcdaadabbddacccbacbbbaaddbabcdcbbcacbcbaddaacbdbdcdaacdbacadabbdabcdcdccdbcdbbadabcdddcbbabdccadaadbabdcdaacaaccababaddcacbbbcaacabccbcccdbbaaddcccbbdcaaccddbcbbaccbdabbacaabddabcabcbbdbaaaaccabaadbcdaddcbdaccacdacbbbaaaacabdabbdbbbaabbdacbdbdaacdcdbdabcbaabaaddddabbabdbdaaaadddcaacbdbdbbcaadacbcacccbdcdddadadbdaccacdcbbaaababccddcacdbbcdacdabbdcccddaadcdaadbdcacddbdbdcdcadabadcadbbdbdbbdcdacdcbaacbbbcbabcbcbdabdabadbddcdadadacbdacbccbaddaaacacccadbaaabaaaabcaadddbddabacbdaaadbbcdabdddcbbbcaadcccdacbdacbbdaacbbbaabacbcbbdaaadddccdcdaddadacadbcdaddbdcbdbbadacbbdcabbabdbdbdabdcacaabcadddbdacbcdcaacabddbddacadaabddbcbcdacadcbbbadcaadbdacdadccbbaadbdccdcabbcacbacbbabcbdadcdcaabccbcddddaacccadcccabacdaadbcaddcacaabbabcdcdbcacdaaadabbcddbddbbdaabaaccbcccbdcccdadaaadddcdbdaadbccdabddbdbaabdaddbbbccdaddadaadccaabacbdcccccaccdacccbbdaabadbbdbbabbbcbabbddaccbadbbadbabdccbbddcabdadadcdcdbdcdbabbbcaddbdacaccbacdcbdcbacdddaaadadddabdaabadbdaaddcadabadcdbddbbbcbaaabadcaaaacacabcdaaaacddbacbbbaaadcbbcabdadbadbbbbccdcaadcacbdadccbccabdacacaccdddabaaadbbdcbaddcdacbccaddcbdbadbcdabbadccabbdcdcaddbddddcbdcaacbabcaabdcdabccbadbdcbcbdacbabcacaacabdaacdabbbbcbacdccbddcdbabdcbdddbbacdddcaabbdbccaabaaadccabbbaacdccbdddcbdadcabcdccbcadbbbbcabdcbdcabbbbabbdbccdcbdcbbdcdbcddbaccdadcbbdcaadbccdaddcbdacababbddacdaadbbacdbdadcaacaadbcaadcbbcbdabcbdaccacabbbabaadaaaababadadbcbcabaacbabbccaaaccdcabcdcccdddbaacbcbddaaccadbccbbacddaababaccbdccadcdbbcddaabbaababbcdcacacabacddcaccbbdccdbccbdacddcbcacabdadccdbbdcddaddaacadcdbbcadbcaccabbaccbcccccbacadbaddbadddcaadcdbaccababdbaabcdcbcdacdcbbbbadadbcccacbbbabacdabddcacbcddbdabccacdccbbccbadaaaccabddacacabdcdaccbccacccacdaaadbcbabababcadcccacabbacbbcdabdddbccaacbbabbcdbddaabacadbbcabcbdbaccdbbdaacdddccbbababcbcbaacdbbcbbbbbcabaaaacbdbbcabdacbdbdbbdbbbbbabdabdbacdcbbcccaabccdbbadaabacacacaadccbdbabcdbacaadbbadacbcbbaddcdbbddadabdbcddbcdaccdddccdcbdaadcbcccdccabacdcdcaacccccaacbbaccddcadbbdbcddbdadddcbdacabcacbadbddcacbccbbacdcabcaabbcabdbacbdadddbccbcaddaaaaddcbbcdbadcddbdcaddbaaabbdcacabaabcdadacddabadadbbccbddaaadcdcdbdadbcaabbcdbcbabbbadaccabdabbbaadddbddbbcacaddbccbcbdcbacbcacbdabbcbddddbdbcaccaacdbbcabcacaddcddcaacbbabadccbcadcbbbaccabaabbbadcaaadadbdadadbcbaabdcbdcadadaccccbbbaadcdbbccaddaabacaaddaaacbddabbdbadcabbaadadbaadabdaabdcacaaabcccbcddcddabbaccdabcdbbcacdabdbdcbcabcbcbcdacdaabdabcccdcbaaabbbaccdcccadadcbdaddaaadccbdbddaaacdcbadabadabbaacddbbdcabddcdabcbadddbcdddcdadccdbccbacabacadcdacaacdbbaaacaccccdabbbbbcacdbbcabdaacbcaabbddacddacdacbccaadbbcaadacbabcdddcdcbcdcaddbbacbbaaccdacababccdbbddcdaccacdbddabddbccaaaadcdcbbdaadcbbcccabcbcadcbbdacddacbbbdabdbdddcdacaccbcdadbbdbbaaabbccbabbcddcbcdddcabadbdadbdcdcbaacbbadbccdbdcbbdddbdabaadcbaaadacabaccaadabccccdcbdbbcdcaccaacabbddcabaacdcdcaacdbcdcdabbadbaaaabdbcdcbdaabaadcbbccadbbbddddbbcdcadacbbcdbcabcadaadbccadbbcccccacdbaadccaaabbdabaddcbcbcbdcdbabcabccbbabcaaaaccabadcadcadabdaccdcddacccaccbabcbccdadcbdaabcadbdbaacccdbbacbcaabbdaadacddaddbbacbbaccacbcbddadaddcbbcdcacdaaabdccabcbadbbbbdbcbaddbccacacdbccbbccdccaccacdaabacaaabcadacaaaabddadadbbaabdacdadbacbdbcabacdaacaadccbadacbaaabcbbadcabdbcccadacadccbaabdcabaadcccddbbbbadbbdacabbcdbbddbcccabaddcddcaccdabbccbcddacadcbabcadadcccbbcdbaacadbbddaaddaabaaaacaacbabacaaacbbdcddabccdcaadabcccbddabbcbdbcbbabddcbdaddaaaabbacadcdadadccddbccbadbdcdbbdbdbbdbdaccbdabbbabcbdbcaabbccdddccbcbccbdcddaabaadcbbddbdcabdcddbdcaadaacddaaadbbaabdadbabdaabdadadccbddbdaabdbadcbcbaccdbdabbcdddbcddccddcddbbbbbdddbacdadabdbaabaadbbaaaccccccabdbbcaaacbdaaaabbccdacdbdbadbcadaaddccacdcdabcdbbbacadbdcdabccacdacdcbadbadaddddcadacbcaadbaacaaacccacdddcdbadbacdaabdbdcaadcabbaabdbddabadacabccbadacccabcaccdbbddbadbabbcadbaacaabcddcdcdcdbcccbabadaddcadcbbdaacbdadcaccdcbdcacdcbcbbabaddaaddddaadacdcddbbacaadbcdddadabbbdacbaabbabccddadbbbcadbbadaaadcbbbdaacdbddaddaddbcaabaaabacacadbbacbaabcdbacbabaacdadbaacdabadbbabbadccbdcdaccdcdbaccbbddcdadbdbdbcbaaadbddccacdacacadbdcadcaadacaabcbcdddaaadbaaadadcbabdaababbaaccadcadccaacccdbbdabcbdbababdcddaaabdcadcdacdbcacbaacccdbcbadcdadaccdcbacbccacdccbdbdcdaaccacadaaabaabdddbabcadcbbcaccddbabbbbdcddbdbaccbccdbbcbdddadcbbdbbbbadaaadccdbcaccbcbbcabdaccccaccccdaaddcdcddbdbcdddabcccbddbabacbaadcabadcadcacddcabaaabcbdccdacaacddbabbbbdadbbadbccabbaadababaaaaccabccbdbaadaddacddaaadbdadcadbcacbccdcacdbdacddbbbbdcdddbddbccbbcabcaacddddabcadcadaddcabbdacbcaaadcdbcdacaacaacbdcdddbdcdbdcaddbcbabcbaabcbcdddccdccbdacbbcbbbdcddaadbdcccbdbdaaccddacadddcacaacbbccdbdccdddaabdbcaaabbbdcbabdaabbcbaadabcbcbdbbcdabcacabadddcddbbadaddaccdaccabbcbacaaaaadbbccdabcbcbaaaabddbcadacadabddbdcbbddccdcdcadbbdbbaddddbaddccddacbcbbcabbaadadabcdbccdddacdccbbaadbdcadabacddcbcdddcbbbacaccddcdacccdabdaadcadcdddbadbaadcacadbdadbbaaaacacabbcdbdadabcbacabaddddbdbadbcbbdaddccccdabbdcbcacdcbbbcabdcaabddbcdcabbaccaccaddacacbcdcbcabdacdadbabbabbccdaabcdcbbcbbcbbabccbdcacbbbdbacdaabccdaddaaadbcdccaddcbdccadbdcbbcbccbddbddccccddaadbbaadbcdccddccccadabaadcaddddacdcbccccdbbbccaddccdacdbbcdcdcdccabdbbdbbaaccdbadaabadbdacbbbabaadbabccbacdcdacadacbcdddadabcdbcbacbdaddbdadcaadccacdaaacacbcdbaddcbdadacbadddcadabaaddabcccbbabcdddacbcdaaddbbcaaaaccbbcababbcaacbbcbcbdbbccdadaccbadaaddaaabdbcbcbbdbaccadaadbbcaaddaadaacacddadacddccbabbdddbcaddcabcdacbbddaaddccadadcdbacbdcdcbcabddabadacbdacdaadbbbadcadbdbcdbddabbacacddbbaabcdccdddcccbadcbaabdaccddadcbcbcdbaddaddcbaacdbbacdcbcdccdaaddcaababbdacbdbbcbccddbddbacccbdbdaacabbbcccbccbcacbbaabcbacdbdbacacbabbbccbdcbbaadaddccccaacbddaaccbcbacccccbddadbacabacbabbdbadbaaaaccdadcbcbdbdcbcdababcccadaccaabdaaababdbcddcccabddadbcbdbdcbadaaacdbdbdcbbbbbddcbabcaadcbacdadccbbdbdbbdcaadbdadaaacbaaccdaccbdcbcabbdccdcacdcddbbcaadcacbcbabdbbaaacbddcbcbdbaababdadddbacdcbbcbacacaabddabccccbacdcdbdaadbbbbdbadbaacdcacdbccdbbdababdbdcdaaacbbcacddcccdbadadcbacacabdcdcaaadabbdbabcdbcacabacbbdcdbcadcbdacaacadcbdbbabbadaccaadbdadabdddbbadaadadabdaddadaadcacccdcbbbbbbdcbddddbbdcadcacbddbcadcaaabbbcdbccbdbabbaaddbdbbabadbcaadaaaabbbcdbdaaaddcaddcacaacbdaabcdddcbbddbdadcbabbdcdcabcccdbbcaacabbadbbdddbaccdadbdabaabcadadcccacabbcaaabaaadcacddbaacdaaacacccbdaddcadacdccbacadbabcaddaddbdbcbccddabcaaacbaddcdddbbbcbbbdbcdacbdbdacbbcbdcaadcbcabccbcdcdaaabcabdaccbccaaacbabaabaccdddcdaddbbdacbabcbdbcbbcccbccaccdaacbbabbcbccacdbdcacbcaaaaacbbacacacdddbcdcaadbdcddadacbacaadbbbaddbbcddabcabdbcdbddddcddcccabaccabdadbcbbbacadbdbdbabdaddacadaccddbbaccbbdabaadacdcdaacdbcacccabccaaaadccccccbaccddaaaadddbdddcdccadacabccccbbbcbccccccaadadbbdabcbbadcbaccaacccaadbcccbcbbadacaddddddcaccabbddcabdbdbdcddcbaaaaacccbcadcbcbcadadcccdadccddadacbacbdadcbdcbbccdcdccbbcacdacbacbaabbbadaabbaccbdabbcdcaccadbddbadddbbcdbcbbcbdccdbccbbcbbcadabddabcbaaabaadcdacdadbcaacdcdddccddaacaabdbbcdacddbaacdcbddbacaadbbaadaabbbabcadbabaaaaaadcadcbaaaccadadbbbbcadabbdacadcaabccdbadabcdbcbddbbdbccccadadaadcaccdacabccaabbcadcbcacdcbbbcdccbddbccabcbbbcabbccabdacbababcdacabdabaadcabcadccbdcdabdacabbaaccadbcddaabbcddbbddcddaddbdaaddcdbcadaadcdbdccdabccaaacacbdbdbbbdddbdcccbaaddbcadcbcdacdbbdabaacabacdadbddbbdcacbcdaabdaaccccbddbddbdcadcdcbbccdadddbdbaaccdcabccbacccccaaddbcbccbbcccbbdddbdccbbaacddcaacacbcacdbaaadbabddaddcaddcccadbcdbbdbbbcccdbaacadaadbcdcacdabcccbcbaddddaccbcdaabddccbabbbddadcabbabcdcdcababdcbddaacbadacddadcbbdcbddabdbddacadcacdabadbabcccbbbcaaaadabdddbbbcbccbbcccdbaddcdcbcbddddabaacaababddabbcdcddabadcdbcadcbabbadadaaacadcdbabbdbdbcaddbddcbdadcbdbaaddcdcdbccdacbdcaadddaacdcabaaadbbdaccbaabcdcadcacccacacddacbbdcdbaddaaddadddabbdcdcccadbbcbacbbabcdadcbdbcdbcadcbcdabbabbddcdbddbdbadbbccdbccdddbbbbadaabdabcaaabdbaacadadbdbadcbcabcabacccbdadabbdabbdbaaccdcbdbabccbabdddbbdcbcaacadadbdbccccabacacacbddaddccdbbbcacddaabdadadbdbadacbddddabaacbcbbdddbaaaacbabcbdcdcbbdcabdbcbaabdbadaddccadbbbdbdcadbacbbbaadcaaabbcdbdbddcbabbabbacccdbaaccccadcdbdacbbadcddbcaccabdaccdcdcacbcbdccdadbaccabacdcbbdddadabaccbadbdcdcaacbbcaabdddaacbccbaccbaddacaabcabdbdbabdadccaabbddccbccddaabdaabadabdcdadabdcabcabcdbddbbcddbcbdccbdddcbabbcadbcddbaaaccacdbbaadabdccaaddddaaacbbdccddabbbdbdcabcaddabbdabbbabaddbadcadaaabacadadcbddcccbaacdcacacbdacddccbaadcdccabdadaadbbdbccbcdabdccdaacbaddaaaacbacdacddcccadacbdabbccbbdacbdaddcdbcbbaaadbdababadcddaababbdadabddaddbdcadbaabaccbdadbdcabbbbdddadaacbaadcddadacaaaccdbdbcccdcdaddbacabbbaabadbadddaccbaaccddbbdaacacbaaddccacbdaabbbbdcccbdccaaddbabbdbcdbdbdccddbccdadcabaadbbddcbcadaaaaddbbaaaadbaccbaaddabbdddcaacccdabddaadacdaacadaacadadacbddacbbaabacbdacbbaaccdbbcabbbacbadbddbbccbbdbbccddbadabcddcacbdacbaddcbddbcabcdadacacddaacbcbdadbacddcccbdaddcaaaacddacdccaddbdaaddabdcabadbdaaacaacccdbdcbdbcccddabaacccbddddabbadcddddddcbbaddcdbbabaddbdaaaabdaaabcbdbadabaddbbbdadcdbacdbabcbbccabccaaabcbdcdacabbbbdaccdacbacacbddcdbaaabbacbccdccbbdaaccddbacbddcccbaddbddbccccbdccbbbaccddccdcacbaacdbbccabadbaaaccbbbbbccacadaacadacdbcaadddaccdcbcbacaaadabadcabbcbccadbbcccbcbdcaddbdcccccbdbdcddabcccddbcbdcadbdccdbbcaaabadcdaacbcbccdddcbddbcbdadcacdbdbdcbcbbaddddaddaccbaccbdacaacabbcdccabbabccdaacbcabbdaddcbddcbcbcdcdbbcbcbcbccbcbbddaccaaadbaccbcaccbbdabdddabbdcdddadabcdcbabcbacbabdbcdacbcadcddcbcdcadbcddccbddacbacddbabcaccbbcddccddcccadbcccabccaddacbcacccccddabadcbdcbaabddcddbddcbccccbdaccacdaacaccaaabbbbbabbadbbdbdddbbcabbddcbacbbaacacacaddbdccddaaacdddbbcccccdcdbddccadbdabbcdabdcbbdccadbccadcaddbaccdcbcaaddcbcbbcdbbaacbdcbcddadabbadaabbdcdadacdabdabbbcbbabccdcbbdaadbdabddcbababcacaccdddddaacacdddcbcbadadcabdbbcbbdadaabcdbaacbbbdcabdbdaaddacaccdacabadaaaadcbabbbcbabcdadbbccbdacacdcdbddcdaacacbaabccadcccbbaaacadcaacabdbbdbbabddcbbdbdaabaadaabaacdbaadabbdbaddaaaadabddcdcabdbbadcbbddaddcdccacabccdabdabdcddadbccddbaaccacabddacbbbcbbcbdbcdcaaacabacbbdddabdacdddbaddababdddbdbbcbbaaddbccabcbdbbcbbdadadaacadcacaacabcccddcbaaadbcbccbdabbbccddaaabadccacaacbddaadaccbbaccacbdacabbccbcdacdccdacdcdbadbdcddbacbcddcdaacbbcbaaccdbbbdbadbccddbadbbcbbdabdbbacdadbcdaaccbabbaadaaadcaaccdbadcdccdaccbcabcdddbbadddbdacbcabbadacadddbcaacaabcbbbadbbabcaadacbbddcacdcaccdcaccabdcbdababaddacddbbbabcdccbcccccabbdcbdabcaadabaadabbbddccccaddaccacbbbcbdcacbdbadabddabaacdccabcaccabaaabdcaaaacdcbdabaccacaddcbaaaadddcdbccaadbdcdaadcabdbccdbabddabaddccaacccddabadbcccbacdaccdbabbabaadbbbdcccbcabdbcabddcbabaacbdcbabaaabdaddcbdabacbbbcddaddbdcdcdcbddcbdbcabadccbcdbcbadcaccbdaaccdbcdadbbcddbbcbcbacaaadabaabaabdcaddbbcabaadbcdabcbbbdacbbddacdbacdaddbbbbabcacbdbbdbbdcbcacdbdbccabdadcddbaababbdcbdbbdbdcdbcacbbbbdcaadccddcbddadbbcbcacaadbcbbdcdaadadabccbbdabbbddbcbdabdbcababdacbabbdcaadabdcacbdccadcdbdaacdcbaaccbcadaacbdddcdaccacaaababbdbcaccbbcaadbccdacbccabdacdbbcabdcaabcbbbbaacadccdcbadbaaddacbbacccbdcaacaddbabaadaaabdbadabccadaaaababbdabbabaadabbdbbbdaacbbdcddcbdddbabdbaabdbaacadbccdababdddbbbdcbaadccaaddcbdccacdcbbabbdbbbbbcadabccacbbdbddcccbcbcdcbcbbdaccabaabddcabbbbcacdacddbdbcaccbadabddbbdcabcabbaaccaaddddacdcbcaddbadbdbbcaaadbdcbadaddddaadababcdabccccabdaccbdbdaabcdcbddcccbdbcccaabbabddddacabddbcdbbddbcdbdcadcabccbdcdadadaadbdadcddcaaacccbdabbbabbcacdcabaaacccdabdccbcddddcbabddcccdaabcacdcaadabaaacadaabcdaccbddcbbcccdcabbbadadddabdcaaabdbaaaadcadcadcdaccbbadcbcbaddcddbcdccaacabddcbabcaacbabbdadddbcacadddbbddbcdbaaabbddcdbbccbddbbbbcdbbbdabddaaadddacbbabaccbddcbdbdccbabaccbadcbbbadadbadddaaddbacbddbadbccbcdaabddadbabaadcdbbaccbbbbacdcaccadbbdbbcbdacdaddcdaabbabdddbccdbbdadabaccaabaddbcccbbcccdaabcddbadaacaadbbcbddbbadabbcbabadbbdbbbcccacdaabccdcdadabbdaddbddcbcabadaccabbbadcabdbbadbcccbcaaabbdaccdadcaaadcddaacdccacaadbdaacaadddacddbadbbabaabdaacddcdcbacdaadabbbdccacbdbcaaaddcccbabbaaddccdabaacadccaabbaabacdadbbaadbccddbdcabccdaccdaccddbaababacddacdbcbbdbaababcabbbadaccdacbbcabcaabccaacabcdddaccbdbbccdacdabdccbdcddbdbacabcdbcbcdacbccddbdbcdbbcadabadabcacdcabbdaadcdabdddbadcdbbdabccbaaababbdabcadbdaaaaaabdccaadacaabdbddccbcddbacaddacdaccbccddccccdcaddaaaacdbdccbbcbaacdcccdcadbbbabddcdddacccbbadacbdbbbaabdabccdaaacbdaacccccdcdacabbcdbbddcdbcdbccdddbbbdbbcbabccdbaaccddabbccaabdabaacabcdadacdcbddbbbdabcccdcccbacacaacdaacbacbbcaaddaddbdbccbbcdbdcdcccdbdacdaaaacdadbabaccbbbabccddcbbccdbcacddabcdacbbccdcdbcdddbacbccdccdabbddccabbaadadbadcadcddcacbcdccbaacddbcddacaddbbadabcdcbbcadcbcaacbbcddadcaabbdccacbbbcdaacbdaacaaccdcbdbabacadabccabccacdcbaaabcadbdbacdbdaccabaadcbbadccbcdacddabddcdaaacdcdabdbccbabadddddcdcbbdcabbbbbddacadcacdaaaddcdbbddbdbabdacccdabbadcbbcdaddcdcccdcabdcadbbabadbbbaacadadcdbccadcdcaaddcaacbaccabcbdadacdcbddbbabaccbbbddbccabbbddbcdcbcaabdcbabbdddccdaabddbcacbaabcaccccbcaadbbbadaacaddbadbbdbcbadaaccacdcabcbbccaccbbddabaadbaaabdbddbabbbdcdcccdacbdcbadccbabbbdacbccbdbcdabdbbdbdcbbcdcbacadbdabdaaccadddbbccbdadcbbdbcadcadcbdaccdbaaacaadacbabbaccdbcdbdbbbcdcaddccbddbbacdacccccaaababdbdaacaaadccbcacbdadaacddccbacbbbddaadccbdcccccaacdcdcbaacbcbccbbabcadaabbdabdabadabccbadcdcccbdababdcdbdbacaacdbdcabbcadbccdbbabbadacaadabaccaaabbaaaccadbdaccdccbdcaabdabbcdbcbdddcbdcadbdccdcccbabbbbaacaddcdbcaaabdbbcdabbcbababbacbbccabcdacbacadbaddbbacaacbbcdbcdbcabcabadaadabaaabcbcdbbaaacccabbbdddbacaaccacadccaadcbcaabbbdabacdbbdccbbdacbabbdbbcccbbbcbbddbacaccacacbabdabaaddcabddcdbcccbbcdbccddccacbbcbbddcdaacdcacbcddaadcdadcddadcdcdbaaacbcbaabbcddbacbdccccbbddcdccdccacacadcbacdadbadaadbaabbbacbabababcdbabaaabbccaabadbacdcacddbadbcaddacaacbadcdabbaaaddacdcbbdcccdadcabcbacacccbcaabcbbcadcdabacbacdcccbdcadbcbbbdbcdbcabdabccbababdddddbdaaccbcbbdadddacbbdcbbbadcddbadcababddcdcbbbbcaadadcabcaaddaddddabcbddddcadbaaaadcdadbcaddcbbacbbccbacbbcdabbcdacaaaadabdaaabaadbcaadbbddacbbcddcddabadbcdaacabbbadbadacdcbabbddccbdadabdddabbadbbccabbccabababdcbabdcdbabcacdbccdaaacbbbcdbdbcbbbbaacadcadcbdadabaabdacbbbadbaaaacdaacbacaaadadbcacbcabddddcbcabdbcaaaacbbbddbbbabadbbddcaaaacadaaccbcdaacbcaccbcaddccbdabacddabbdabacbbbaadacaabdaabbbcdaddadbadccbcbbcddabddaccacbaacdacdddaaddabcddddccdbbaddcdcbcadddcbaaddcadadadcddbbaadbcdbbbbabbcbdacbabdbcdbddbcaccbbabccddbdbddddddbcddadcaddccbdbdbcbdaaccadcbcaaaacddcaccbdbcdcbaaabaacbabbcdbdddccdbbdbcddbadbbdcbcdcbcbacdbbadabbdccbbdcacdcccbdddcbbcaddbdbccabddbbacbdcdbddbcdddcdacbadccccccbbcbbbdbbcdaaaadacbbccdccbaaabbbbcbaadcbaaaabdaacdcbdabadaaccdcbabbbbbabadccdbbbbbdabbccbcbdcccadbcdbbccbcdcacbcddbdadccabbaaabcddbabddabcbccacdcddcdbccccbcabcdcabcbabbdcabcbbcdbcaddbacdcacbcabdbabaaacdbdbccbdaddbcbaabdcaabcaacbadacbcbaacadbcaabdadabddcabbbddcdbdcacadaacacbaacddcacbbbdcbbbdbbaaddbdbdabcadcaacdbbbccccccdcaddcabbdbdabbdaddadbccbaadabcabcaadaabaabaaacdbabbdcbcabcccdacacaaaddbbdacbacbaabcbaabadadbaddcaadccbcabcdadbbabcbbcbcaccadbbcddddaccabdbdbdbcaabbcadddaabbaaabcdcdadbccaaaccdaabbadcdbadabacaddaddabdcaadbaaaabdadcaabbdabdbccccacaaaddaacbbcdaacdbbcdddbaaaadcbabddbbaadbdcacaccbcaccaccbbbcdcabbcdbdbdabcaaccddababbccbabbadcccbbcdbcccadadbbbccacdcbaddcbddacacadadaaacdbbacaabbcdaaabadbcccbcdbddadabcbcaacbcdabdaccdcaaaccbbdabdcdbbccabdbacabbabaddcdbbdccccacdbdaadabdcabbcbccccccbcbcdbcaddacacdaacbdbdcaacbadbbdccacaabbbabbdcdbaacccdccdbdadcbddbdccccacaacdaccdabadadddaccbcbabadddccabbbcdbabbacbbbabdabcdcdaaabaaddbbcbcbbabbcacacdcbbcccccdbccabcacaacbcbdbbbacbdabbbabbccdabcdaaaaacccadbadccadddaccbccccdcbbcacacbcbddbcdbbdccaadcdbddadbcaddcbcdbdacbdaadbccabbcbbdcbcabcbbbddbddcdbddbdcdbacdbdcddcadcdbcadcddaccdcdcdabccdbbbcbcccdadccdcbdbaabcdbdccadcbabdbcabaadddcdbdaccddbdcbbbcbdcbbdcccddadcbabbabddadbbbcddcdbdacddbbaabbddcbdaaccbadaaaabdcabccbbbbccdbacaddccdbcbddcdacdcbdcddbdaadadcdcdccdcbdbbbddbbbbaadadbacccddcdcbbdcacbcddddacdbdabbdbaddcddbbddcddccbcdcbbbbbcbbdbdbcddaaabaacdbddaabbcbaabdadcdaaababacbccbacabadbaabcadcbbdbdccbadbdbabbacddbdbabdcaadadbbccbbddabdbaddbdddacbddadacdccdabbabcacbbddbbddbbdddcccdaddacbaaabbbadccadddbbadbbbbabdabdbdbbcdcbcbbbcbdcacdadcabbddbdcacddbcbaaaddcdbabdcabcbccdbabcbdaabdacaabdbdcabbadccabdacabaadbacccabbcbdbbccdbdccaacdbbdcdbabbbbbbdddabcabbddcaccbcdccacabbddadbaacbbcabcacbdadcddcaadabcdabdbdbddddcacdcdaaddbbcaccbbbddcddcbaaabdbbaaadbbcddcbbdacccbaacabccbccddcbbddcabdbdccbbdbcabdcabdbbbdadcbcbbbcadacddcacaacababadbbdbabadbddbccbcaddadbcabdcddacbbcbdcbdacbabcddcbacdcaabbdbbccdbaabddcbdbccbcddcdcacaabbabddbbbdccdcdadaddabdaabccaddccdbcdbaadddadbdcbdcdcbadbbcdbcddbbabcccbcacacbbaaaabdaabcacccdbaadbaccdaccbdabcdbbdbbccbbddccdcacaddcdcacbbacbcaabdbcdabddbbdddcadacddadbaabaadaabdbcddccbdadcabadbabcdaabdbcababbcadddcbddcaccbbdcbcdbbddcddddbaabdcdbbbbbbccbbdbcccdacccdccbaddcdddbaacaabaabccacabdadcacbaadacbddbccddbacaadccbcbccabdcadbbdadbdcacbccdcbcaacbadbdcaccdcadadabadbbadcccbdacaaaadbaabddddbdccccbabcbbdadaddccaaaabccdadcdaccacacacbdaadadcadddadddbdbdadabccacccccccacdaacdbdbbacdddabdccbaccdddacbddcaddcbacbdabbdcccacbcabbddcaababcaacdaccaaddddbdcdbbbcacddadbdcddadaaabdabdcbadbcdabbacbaabbcadcdacbadadacadcbcdbabcdbadaddcabbdccdabadaddcaccbdccaacdddacadacdccdadcccaaddbddadbadbcdbbccdbacbbdddabdcabbaabbddbdbaddddabdcdcbccbcbccdbcdbbbabbbdccdcadadbaccaddcbbbcddcdacabacacaddbdaabbbcbdddaaabbdddaacbacdbddabbdcdbdcdddbdddbdabccddadcbbdbbbcddbbbccccaaabbaccbcacddcdcbaaadccddddcdcbbdbdcdcadddcddbddacbbadbadadbaaaaabbdadadcccdcbddaccbbbbdccdabbbacdabcbbcaaccdbccbaadbadddabaacdcbdcbdaddcbcabdbabcaadddbddbdddcaaadbdbbcaaaabbbabcdcabbcaccbabbddbccdcddbcdaabcbddbcdcbcddadcdbbacaabcbcbdadddadbcabbcbddcbdddddcbabdbacaadbdacddddbcddbbdcdcccdabcadcdccbbacdbbdbccaddbccaabbaaccaacbccbdababaacadaacccdcbddabbddababccdacddbcaabbdbccccddabdbbddbdbddaaacadaaccbddbbbdbdddbccdaadbabbdbdacbbadcbccdcaaddcbbbbccdbdcadaccccbcddcbabcdadabdabcbdadcbcdbbdcacabdcbbdddabccdbcacbcbadbcdbddbdbbbcadabcaacbdbdddcddccbbddaabbadaacbabbdbcbcbdcadcbabcbdbcddcbbbdaddaccccaadbbcaccddccacdcbbadcbcdbccdddcdddacbbddabcbbddabdcbdcdbaabddbbdccdbabcbacadaccdcacbdccadcdcddabdbadbdcbdbadcacdadbdddbbacabbcaadaaaadaaaabbdbcacccbcddbdaadbdcaacbdbabbacbaddabacddadcadababddbbbdcacacababcbbbaaadcdddddcdabdcadabcacccccdabddbcbbaabbacaccbaadbdcacababaaacbddaabcacdbabcaaaaacbddacdbcaaddcacbdcdccdbccbcdabcccddcaddbdccddbcddcbdaaaaccbbcabacbadcbaabbabacdbbadbdacdbabdaaadbcccabdbcdabcbbdbadddbddbddcdcccdcabdcaabccdcacddcddcbbddadabcbcdbaabbacddbacbbcaccacccaadddadcdbcddcccbcbdabdcdaccacbbacbdaadcbacdddcaadcadbcaadaccaaacdabbcbddbcccdadbccadbabbbadaaacdddbcbbbdbcdacdaabcadcacaaaaabbcabbaaaadbccbdbdbcaadbdadabacbccbadcdccadcddccdadcaadabaadbbaaadcbbdbdaabadcbbbdbcdddbbcacabbcbbcbddadccbccadbbcbbdcacaccdaacbadbdbccdbbaabaaaacddcbbbbbbccccccbdcaaaaacdbdcaccdabbaccbcdbcacddcabddcdadddbdabccabccdcadcbdcdbbadbbbccdcdadcdabdccdabdcacababaadbbcbdcaaadbbaadaacdaaacccaadbddbadcbaddbbacdacdacdadbdcdbacddabdbacbaaadbacdcdcdbccdcdcbaaacaadbcbcbacddabbcdabbadcdbadcaacabdbaacdcacbbccddaddcbadbcdaaacbbbdbdddcadbacdcaaababacbcddcbbdbbdcdddcadbbbadbcbcabbbbcaddcdcdcbcdcbcaacdcbdabbcaaabdacaabbbccddbcccddaacadacadadcddbbaadacabcddadcdddadbadccbadabaadbdbcdaaadcdddbbdaacdddbabdcbdacccdaaaadcddcdbdbccaaadccdccbabaccdcaabddcbbbddababaddabcacdbbaabbcbbbabcaadccabbcadcabacddcbbbdbcdcdccdcbbcdcdcddacacbaccccddadcbcdbbbdcbcbbabacdadcbcbccdcddbbcdadbaadbaaadbbddbcdcaabaaddccccadddaaababbcacdbacabcccbcadacbcbcccadcabccdbbdccadadbdcdacadaaccaadccbdcddacdcabdccbdcbdcdcdcdababdbcdadbbddabddcccaaaadacacccdbbcdcdabacdaaacaaacbbbabaabcdcaaccdadcdadccabddbbaabccbacdcbbccccbaabcaadccdabccdcdbccbcdbdbaaabbcdddabcbacbdbadbbacacccacadababbdbdcacbdbdbaadcdcdcacdcacbabaabdbcdacabbbbdbdcbdcddbcbadddcdddbdbddbabcccbdcdddadbcbddbbdbccdadbbdccdadbccbbcdbbadaaacadcccddabadbbabdaccbbabaadcdddcbbcaaabaaaabcbbcaabbcdbbcaddbadbacaaccbaacdcabccacadaadaddaadbbdccbdbcdcdddcdbcacaabddbbbacbdbaabbcbddcaddddaabddaabcccbcddbddadcdababaaacbbcbbaaccadbbcabbbdadbbbabadccdcbacbaddaaadccaaaccdbdaaadbcddccdadbdddbacabadcbdccbbdbabdbdbbabcadcbcadcbcdcdbdadbcaaccacaccdabdaabddcbbcdbdababbbddaaabbbdcaacdabbaadcabbccbbadaddacdddadccbaaababdbccdaadacdabdbcbbadddbbababbaacdbccbddbacacaadabdddabacabaacbcccbabbdaccdcbbbbdadababdaddbddcbcbbcbccadcbbacdbbbdcbbddbdacdadcccacdbbbadcbcabaadcdcbcddbddddcbacbcbbabcbdadbacadadcbdbbabdaaacaadabbdaacbaaacbbabacbddabbddddddcdbdcacbbdbbbacabdbabdcbdccdbaabdcdbbacccbbaaacdddaabbadbcccaaddacddadbdcccaccccbcdabbaaddcadaabdadbdccdcacccbbadccabdabcbbabdcbbcbadadddbddacabdbbdcbcdbaddccadcdaddadddabbdbacdbcbcdccccdccbcaaadcbbcadddaddcaacadabaddcbbdaccddccdcdbdabdbacdbaaacadbbadbbdadcacbbbcddbcdcadacbacccbcdcacadccddddabbbbabacdbcbabadbbbbcaaaabbbbbdcaaccdcdbbaaacbbcdbcdcbbccacccaadddabdccaadddcabcbdadcdaacaadbbabdaaccdaddcacddddadadabcdcbdadcacdaddddccddcbdacadcbccddbaddbdadbccccbcbcbcdaabdbabbdbabcacddbdcbaabbbdbabccadbaacdabddabacabaccacdadbbbdbabbcdddabbbbddccdbcabcccbaadbdcaabdaddcddcbcadaabddaaaccbaaaabbdbbdacbccbdcbcadbacadbabccbcdbcbdbbbdbdbcbbdaadccabdddcbdadccabcbbcdbbabdccabcaaaaabcaaddadcdbcdcdbddbbbccbcbabdbccabadadcacabaccdddadadaabbcabadccacddacbadbbdddbabdccacdddbbcdabbcaaaaaccbdcaabdbdcdccaabdacacdbcdddbadcacaabadcabdbbccccdaddabccdddbcbcbccbcdabaaddddcabbbcaabdacbcddcbaddbaaabdaabdcdccacbcaadccddbcbbcdbacacaaaaacaddbdaabadcdcacdbddaddaacbdaacaccbbadbcadbddacbadbbcdcabbcbaccbadabdbcacadaccbccdccdccaaadbdbadccabcbaabacdacaaddcbcdbdaaacabaddcccbadddacbddacdadbdbcbbbbadbbcdabbddcdcdccaabcddddbbbcacbcdbbabdcadaacbbaaadbdbbaccdabdbbcbcccababaddcaadcaacddccbdccabbddadddbabaddddadcaadbadcbcbaacbaadabddaacccaadddbbacddbdbbcbdadbbbbadbacdcbbabccddcabcabbcdbbdabccbbddbabcacbabcadcaaadaaddddbdcbdababcacdadbddbdbbdcaddddababccaabcaaacbbcababaddbdbdabbddbdcadbaaddddadcdaadcbadaacaccaacbaabaccabdaadabddcadbdaabccabddbddbcdcccbcdabdbcbdbbadbacdbadbadcdccacbcbaababccddabdacbbaacccbabbdcbcbccbcaccccaacdaacbdadabdbbdccbcdadcccacbcddccadcccaabbbcdcabdbcbbbbbabbabbdcdbcaadadbabcabcdbddbccaccdddbcbbcdacccdccdaacacbbcacadcbdbdcaadbdbcbcaddbaabbbabadaaccbdaacbbcadbbabbdccdabbadcbbbbaaaadbbcdabaccbbbabcbdabaabdbaacbbbdcbcdbdbdcbaccdcbaddacadbcbdcccdbdcaadadcaddccdaaddabadabadbcbabaabdcdabaacabcdbbdaacdbccbccbbabddcdbbbabdbdcadaccbdcadadbcabdcbbddabbbaddcddcaabcbabbbdcadadbabbdddcbaacccdbddbcccabdaacdabcaccddddbdaadcdddadcdbbdaabddabddbaccddbdcdabdabddbdcaadabdcbdcdbaaaddaddcbdaaccbbbbaabdcdadcaaabaabacabadddcbaadbbdcbaacddcaaadbbdabbadbbdcacbabaddcbdddaccaccdcccdbddabccacccdddaacaacaabbacbccddbdcccbcacddcdadcabdabdcabcabaddabdcaddbadbdabaabbdacbcbdcdddcdaccaadbbddbcccacadabccdadcdabdbbadbbabbccdaacabdbdbcdcdaaadcdbcbdabbbcbbdcccbcccadccdabcdcddbbacddaadbdccbbabbddabbbbbaccdabcacbcdacabbbdaacdadbdabcabcaadadccbbbbdbddbbabdacbadbadddaadcaddcdabccbcccadaadbabaaacadbcadccbadcbccbdddbcbcadabcaaaccdabadacadcbdabdabdacbacbcccabadadaaaabdaccaddbdacaccdddadcdaaccabcacbccbbcdaccadbccdbbbbbbacbcadcbbadbcdaababcbbaacaaccdcdbbdbdcbaccccacabbdddccdaddbacaadbdcacdacabbcbaaabaababcaabdcdccccdcddcdccbdabcdbcadaddbbbcaadccdbcccccaaabddcbbcadcbbcdbcaadabbbbdaddaadaabdadabdbdadbadabbdadadacdbbcdbcaaccbbcaabdddcccbdabababddddbccbbabdaaddddbdcbcbddaacbbbaddbdabdbdbbbadcbbaaaddcabcdbbcbadddcdcadddadbcababbaabccbbbaccdbcbddadabddacdbaaddcabacabbbaacabbdcbacacbaabcbdddbacdacbcbccbbcbaadadbbaddaaadaaadccaadbaaaccabcbdaabbbbdadacdbcbdcbadbbbcbdababbabbacbbccbdcaabacaaaddcacaabcaaccbbbbcbbcaaabbdcadacccddcbdabbbbcdaddddacdcaabddcdcbabbdaddddbbbcccbaccdddbbbcaadbbbddccacaacbabaccdadabddacbbaccbaaccbabaabdbdcddaccbbcccbbaacbcbabcdcaccaddbdabadcacdbbdadcacbbcccadbcaccbaabaabbbddaabcbbaaacdaddccbddcbbabbbddadcbcdadbbbdbaadabcacdabcdacdabdaddaabaabcdcabcdcdbccadcbabbdaacbaddadaadaacabdbdcacdacdcdbbacbccdcdbbbdcbdaacccbccbbdcaddbbcacddcbcadabdcdbaacdbccabdcadbdddddccdcdbddbadadbaaaabcdcbbabacbcdcdbcbabccbdacbbdcaadaaddcccbdbaaacacaaadddddadddcbbdbcdddacaaacdbdacabccbaadcdacccabbdccbbbcbaaaccdcbabacdcbcccacabacbcbcadbabaadbadbdbcaadbbcacdaaabadababdabddbacadaababbacbaccbcbaacdacccacabababcadaabdbccdcbaadacbdaddcccbbaadccbcbdddbadbdbcccaabdbbcaadccbccbaccbabbdccbbddaabbcbccdcdacdbdabdccccaaacbbabbdcbaaacdbdaaadcbacdadbaccbbdbaddbdaaabadadcddbababbcbbcdacdcbbcadcdccbdbcaaadcdddbccdbcbacdbadbdcdddcbcbdabccadddacdddbbdbcbacdcaaadaaddcdbddbbcdcacccbaacadbbcdcdaccaaaacdddddddcdaabbdbdddacabbabddaddbdaaaaabacadbcdccbabbcabdcaddddddbbcaadcbaccbacddaadbbaccbadddacabaabbdcaabbcbdccddbbaccabaccccdcddccccccaabaacbaddbaadbcbdccbcbdbbbddcaaaacbdcbbcbbddbdabcacbbcdcccbacbcbdbcbcbddaabdaacccdaaddcdbddddbcaddabdaacbadbcbaddccacabcaddccbbdaaabacadaddbcbcabbbaadbcdbdaddbbcacdadbdcdbdadabbbbddcdaabadcbdcadbdcdadddccaadccbaddddcdaaadaaacaabacaccbdaddcabcbcbaaabadbbcabaabacbabadabbdbaabdccbccdcdbdaccbadcdbdacbdbdcbcddacbcbbdbdcabacdbbcabacdcadaabccbbdadcccbdbdbbbdbdbaababbadbaddbbabadccbdcccdcacdabddaaaabacccbbdacdbccdaabadbdcadacadbcbddcddaaddbbaabacbbccbccbcaddaabadbaacbbdcdaacdacbdcdacbacccdbacdaccabacbadacbabbcbbcbdbaacccbbdbdccbacdbbbbddbaabddbdccacdcdacbbaabbcabdbdddbccddbcbaccaddbdbbdaadaaaaadddbacdbddbaaccdaaacdcdabacaacbacdaddbddbadcccdddccdadcadbbdaadaacadcddaaccabccccbddbcbaccaaaabbabcadcdbcbcbdcadcbddacccddaaaddcdadbbccddcbabcaccadcaadadbbbbaccdacadacacbcbdbdbabadaabbcaddcbcdacdacbbbadccacdbaddaabdcbdbaadbdcbdbbbaacdcaabdbbbcbcccbadccddaacaaaadaccacdccbcdbdabbabdccdbddabcdaadbdadbcdcdadabbaacbccabcbadccadcaddbdcbbcbcacbddcdbddbcdbcbdcddaabadbaccacbbacbaadddabdbabaaddabbccccdddadcdbbbbbbcaacbacbbabbcdbdbadbbbddddbbcdadbbbccbcadcaabadcddbdddbbabbacbacbadccbcccacbbaccbbaabaadaabbdcccbbbbacbadcabcbadcdcadcadbcacdcddaaddbddbadbbcdddcaaccadcbacbdbbbacdbabdcbdbdcbcdddbbbdabacddaabcccaddbbaabdaadaccbbbbdbabaccccdcbbaadbcddccdadbdcacaaabccbbabbdaccaaaabbabdcadcdcddbbbdbaadbabcdbcdccabdaaaabdbbacbdacddbacbbccadbbbcbdbbbbacdacadddbbddcccdcbabaaadcbcdbbabccdcbbbcacbdccbccdcacbbaccbabdadcaaccadbcddcacddcddadddccadbddcadbdcdadbccabdcccdbcccabdbacacaabdadbdacabcaaadadcabbccadcaaadbbcaccdcadbadacbaddbadadcdadbddaddddaccbacdcdbbabbaacbadcaaadbadadcbabbddbccbbacbdaaacdbcdaaccccddcbddabdcdcacbdcbdbcaabbbcdddbabaadbbbacadacaaaaaaacabaccdccabddbcddbddcbcbcbcdddabaaddbdcdcadcbadaccdbabdcbdddccbdcddcbdbdcbdccdaadacabdbcabadacdbcdbbdccbdbaccbbabacdbaccdbdacaadbdcccaaadacadbbdcdaacaadbdcbacbbdbdabdbbabbbddaaabcbdaababbcddbbddcbacbdababcbaccdbbadcabcbcbacdbbdccadaaabbddbbcdadbbabdaabaadbaaaaccbcbcccbddabbcdabcdbdccddaccbcddaababccdacbdbccadddabbaccbbbccdbaabbdabddbbaddacbdbcbbbbcdacdbcabcbbcabaacacacacadaaabcbddbbbbbccddbcadaabdccdcdbcabdaddababacbbbcadccabcdbcdabccbbddcadbdcaabdccbcadacccbcbdccbbacdbdabdbbaacbbaadccddbbaabacbadbdbbbaacddadddccabcaddaacbddbaacdacacbcdadbbacdcacabbaacddabccbdccbbacaaacdabadaacacaacbacacdcddbbadadbbdccbccaadbdbcabccddbcbadadccdcdaccddcaadccabbcaacbadaddaddbdbaddadacdbdaddbaddddbbdabdbbbadabbbbdcbbcabddaddcdbdadbacaaccbaabcbbdccabdadbacaaacacdbddbbcabcaccacddaaabbaaabcbbcaaaaaaabaccacbbdbadbabcadcbddbbcccdcbbadcbbccbcdddcbccdbdaccacaaadaadbccabbbbdbcdbcddcadacacbcbccddcbcbcacccddacbcacacbddabbddbcbddcbbbccccbcabbadbcaccdaacddccaaaaacddacaaababbbcbaaddbcdaacbbccdccdccaadccbcddacdaabaccdacdcdbcbabddacccdaababbddccaaabcbabbaaadddbdbdddabbacdcbdbdcadcbbadbaadcccaddbcccdacaddbbccaccddbbccccacbabbdcbbbbbdbabdadcbdcdddabadcbcaddbaadacbcbdcdbbddcaaacbcbdbcddbbbaacadbacdabacbbaacdadadbabcbdacbdbdbdaddcbccdbbbbcacbddadcbacddabccbbdaaaccdcacabddcdaabcbcaacccbabbbdabdbcabbbcbdadccacddccdbaccdbacbbdcbdccaaccdcbcbabdccabdccaaccccddccdcccccaaabbacdbdacacacdabddbabdbacabdabbdcbcbdbdbcbbbcabacacdbdccbacbabbbdbbbbbcadadbbddadcdcbadcbcacbbdbdbaccdcabbabbcccaaccdbaaabbbadddcdccccadbbcbcdbcaaddbdbcccccdccadccbcbbcdbbaadbcddabacadabaaabdbdaacccdbcdcdcdbdbbbcbdbbddcaacdbcccadabcccaaaacbdddbadcabcadbaabcdaaccbbcdacabadbbbabccdcbbdcaccbcdbaaccddcddaadcccbcccbaccaabdbabdaddcddaadbaadbbacdbcbbbacaaddabcaddbbacbcbccacbabcccabbacacdbbcaaddadbbdabdabdccbabadaaadddbcbbabcbdcbcddaadcadaadcbdbbaccbcadccabcdbccbbdddbcbadadbaadbadcdaaacabbdcddccdacadbcbbbdadbcaccbcbdccbcddbcaadabbdbbacddabcdcbdacdaabbabdccbdacaaccdddddabcbcbbdaccbcbddadddaddbbbcddcaaccbdcacdbddbdcacdddcdccddcaaacbccccddaccaaaddaaaaabdacacaabadcacaaaadcbdcbcacccabdccabcddcbdadbadbadbbcabcaccdbcadabddbadcaacbdddcbcbcbacbacadddcadcbcbccadacdbaadbacacabaaaaaadbabdcdddacbdaacabdccccabcabcabdccdaacbbdadcbdaacacabaddcbdcdcdbadbabaaabaaaddbadcccababcaabdcaacaaabddaddcbdccbacdadddcdbacbbadbbbbcbdbdcadcccaaaabbcbdcdcadcaacbdacacbabcdbcabdcbbccbddbadadbdcdcbdbbacabcacbdadbaabadabbdbcddcadbdccdaacdaacadccbcdbaacaadccacaaabdbadbaadadddaadbdbcdbbcdccbccbaaaddccabbdccdbabdbbbddcddaccbccabddcbccbddddbadcbacdbbddbccbbbbdaabdbcbcaccacdcbcbdcadbdbdbbcbadabcccbaacaadbabbdddcadcbcdcbcdbadcbacbadaaacaaabcaadaaabdbccacbccdcabcaccbabdddcbdabbcaccdbdcabdabacacaaaabcbacbccbcdadcacbbcdbacddcdbbcdbbddbdadbaccbcdbadacadbbcbcaaadcbadacaacabbaaadbcaacdbcabadbbadacbaddacdbaadabbddacaaccddbdccbbaccddddacaabadbbcaccbabaabbaabcaabdaddacbbabbabddccdaadbbabbbdcbdddcacacbdcccbbcabdaddcacdddcdacbadabbddddabdaccadcbacabaabbdbbcabbcaabacdcabdcdaaccbbdabadbcabbcbdabbabbcbabacbabdabbbddbacccddcdbbaaccdddbcaaddbbdadbbddaddacacbcbcbbdbdaddddaddbcbcdddcbbbdcdddbbbdbdadaadaccccddcadbcddaacadcdacadcadcbbcbcbddbacbacabaccbdccadccabdbabaddcbcddcdadadcdaabcbacabdcbbdcdccdabbbbbdccacabacbddccdadabddcaacaabcbbbaadabcccccadcbadacadbaaacadbdddccdcdccccdbbbcccaaddbadcbbbbcadbadcbddcccdaaaacbbdcbbdacddcbcdbbcacdcaadccccbaabbddcdaddddbdbaaadcadcdbaabaaabdbbbcabaccbdabdbaacdaaabcbbacadbcaddbcacadccbacbcccddbcbcacccacbbddddacdbcbadaaadbcbabadbabaadcddddadcacbaabbacdadccbbdabadabcadbbaacaaabbddaaaccdcccaaadccbbabaabbbccbacabddaaadbbdbcccdbadbabaaababccdbbaabbaccbabcaacccbdcdccddbdcbbbdccacaaaadcadbabccddaadadacdcdcdcbcaacdcbaabaabadadcdababacabccdcbbdbadadabbbdcadbcbbccabadcdbbaaaacadbccbaaaacdbcacadabacaddadbaadbdbbcbbdadcbdcdbabbabadbccccdccdddabccbccdaddbbdacaacaacbcdbdaadadcdcbccaaabcdbdacbddcddbdccadacabacadcaadbabdcadaccaadbddbbbdaccadaccbcbbdadcabadccbdccabbadadacbbcacbacbcccbbdcaadddcdbdcaadcbaccbaabddddaadbacdbcdacbbdaddaacbdcbadadcadabbababcbaaabacadcccdadbaaaddcddcaacbcbccdadaccdccaabbddcabbabdbbadcbdddaccdddbcbbcdbdacdbcbdccdbcddbbcddaaacaabcbddacadddbcadbcbcbadcdbcacaabbddccddacddcaccbcdcdddccdbdbaaaaaccbaccbadaddabcabadcdbcacacdaacbddbaddcddacabadaccbbbdddbadccdcbcaadacbcaabbccccadabdbcaabbabacbbaaabdaccacdcbdccadbbabddcccaadcbcbbbccacdaaadbbdacdaacabadbcaabdcbbaaaabbaaccabacdbdccdbbaacacdabcdcadcccdacacbabdacbdccdbbabbbdcccccbdaaaabdacdcdaaddacdcacbcbcbbcdbdcacdcaccaccbbcbaaaccabbbacccaacaacaccadccaacbcdbdadccbdbbbacdadacdccadbdccccbabbdcbcdabadabbacbbbbdcadbbabcacbaadacbcdaccccdcaddacccdcdaaabadadbcccdcbdcbbbcababaabcacccbbbbcbbcabcdabbdabcadcbcbbccbccbdccdacaaddbaddcccdcbababccbabadddbdaabcdcbcbdbcdbcccadaabcbacdbdaabcbddccbcdadaaaabcdbbbabbbbcddbbdccddbddbbadcddbcaabbacdcbccadbcabdddcbaaabababdccbccabbdbcbdbbaaadbacabcaaccccccabacadbdccccabbacbbbbddcaabddabcbbcadbcbadddccaddccbcaadbdcbcddccdcbccbdddbbccdaaddaabacbadddbacbdcabbadcdddbcabadcbbcdbbbbbcdddddcabaadbadadcbbcddbcdbacbdbbcbddacaabdddadaaadccdacbcabbbcbacaaaaccbacdddaacbddbcdcbcaddaabdccbddaabcaacdadcbabccabddcdbcabbbaccbccbbdbbbadccacbcadcaacbdcaaacabccaacbccdccccccbdbcbdbbbcbbcccbadddadbdabbacacaccbcdcaacadacbcaadadbaccaaaadccaacdcbcdbdabaccaaacddddaacabacabdcccbdbbdaabacccbdbbabdcbbbbcddabdaabdaaccaabdccccbabdaaddcbbcababdbddddabbaadccbadcdcbbaabddadadabadadbabaadbbadbacabbaadcbcbcbabadabababaabcbadbcbbdbbdbcdadbacdddbcdadcddcbbddddcdbbccabcadcabdbdababbaaaaadccbadbcacdddbcacaaccaabcdcbdbdababacadabdaddbdddcbabdcacdbadbdbbadacdcddccaabcababbbdbccacaadcaaaccdacbbaabaadaabcdadccadcabbccaccddababdcacdaddbaacbbaaadbcaaadadbbaddacccbcaabcddaadaacbdaaabbbcacdcdbdabaabdadcadbadbacadccdbadccacbdbdcddcbcddcbbbbadaccccdaddbaddcdccbdcbabadaddddaacadacaadcdcaddbbadbdbccccbbadaccdddbcabbdddadddadadaacddacbdcbacbcacddddacacacaadadadcbabacaabdbdbccaababcbcbdacdcdbadddbcadbbcbccbddbacaadcccdccabcaabbabacdacadadbaaacadcddcaaccbbbadcabacbcdcdcbdbbdbdbddcdccacccbdcbdbddcbbbbdcdddaddbddadbbaacccdddadcadaaaaabcddbaacbabdcdabbccadcbaabacbcdadbcbddabbbbaadabdcdbaccadbbcabcbdaaccaaaccdadbcddcaabadbcbadbdaaaccdbabbdbaacbbabbccbaaacdacbabcbcccacacbcdabcdccbadddddaadcbbdaabdcdccddbbbcabcabdcddbcaccbdbddbcdbcadbbbadabddcbcbcbaabdadaacbdbcdacdccadddaadaccdcbbddcaaccbacadccddbbacdcabbdadaddadcbaccddaaddcabcdbabccaddcacbbacccbbbdbcaaaddbadaccbcdadbaabdcbbbddcbadacbdbabccaadcacadacbccacaacbdcbcabacbbcaacabacccabbaabddacddbcbcacdaaaabbaddccdccdcaccbbdaabcbacaadbcabbaaddbbabbbabadbadddadaddbdccdddbbdaddddadaddacccbcdbdcdddaaacbacbbbbadddbddbddabbdaadaddacdaaaaabaaddbacdcdcbcbccddacdcccdbabbaddccbcdbdaccbbdaacaaaadacaadbaabdadcaacbbaccacbddccdacdbddbbcbcdabcacdbdcdcaddddabcabbcbdaaacddbadbddcaaaacbcbcbbacacbcdabbdccaadccdcdacaabbbcdacbbdcbbbacaaadcdbdbbaddbbcacbcaabddcadaddccdcbcbadbdbbdacaccdaaadabcbcadbaabdccbabdaddbaaddccddddbcccbddadbdcbbbcbabbdcadbadaacbcddbaaaabdabddbdcddabcbbaadababcddaaacbdbdcdbacacbccccbbcdccadacaacbabadccadaacdcddaaccbcddaaaccacaacdadbbddcbcdbaccacdbcdbcabcbdadbabcacbbcbaddabcdddbbccdccaccbddadcbadadabbdaccacacabddbbaabbcabadaadcccbaacdcdcdcbcadbdbbddbbbbbcdaaacacbdbbddddbbdbdcdcccaaababadcbbbddadbacabcabdcacaddcdddacadcacbddadbadccdaacbbcccbbaddcacbbddccccdbbbadcaabcccbabaddacaacccbdcbcaaacdcccdbdccaacdabdcbacbdcdbcbcbcbdcdbccbddabacdcdcaadcaaaadaadbcabaaadbcbcbbdbacbbbadccadcbcbabbdabdddbdcbccbcccadabbbdcaacbbaccbadbcdadbcaddaddacabbdaabddcdcacbcadaaccddaddabbacdbbcadcabadcaccdaccabccaaaccdadbdaadccccabdcdcddabacdcbabdcbaabcaddcabcbbdbbbdadadcadbbdcdadbbdddbaaaabdcaabcaaddccacdabdbcbcbbbbaabcdcdcbaabbbadbcbadcdaadcadddadbadadddcbbbbacddcdadccddcbdbcdbdaddcaabbacdabcbaabaaabacdbababbadcdadbabbaccacababaabcacabacdadbdaaddccdbaadbacdcaadddcbbbdcadcdbbdbdaadabdddabaaccaacdbaddcbddcbcdcabddaaaccbdbbcaccbacdadbbabcbadbcaabadaccacccbaabdabbaacbbcbdabaadadbbdccbbaacacbcccadaddbbdadcbadcdaabbdbdcdcdaabccadbcaabccbdabddbdaadabcbadbcbdaccccdcdddbaaacaddabddadbccdbcacacdacacdbddbcbaacabbdcbaadbbbbcbdcdbabbcabbddcbdbbaccdcdcaddcbabcbdabddbcabcbbdbaacbabbcbdbbbabcdcbdcbdbabbaaaabbaababbcbaaaccddaccbdaaaabbdbbbbabaddcdbccdaacbcccdbdadadbbabdcacabdcddbbccdbadaadaccdbcccbcbbcababbcababcbdcabccbbcadadabdcabdbbadcdabaadbbbcbcdddacaaabadabdbdcdaabaddccbabddadcabacccabbccbacacaaadbccbcbabcaaadaddadaacbcbccbbdacdbbbabaddabacadbccbccbbcadbdccbacdbacdbaddbacdcadbbbdccbcbbccddddcdbbbbbdcacabadddcbdccdacbbbaccddaadddbddbbdcbcadcdadbbcadaaabbacadddaadaccdbbcbdcabdcabbcadbbbccdaacdbcbbcaccbbbbacbbaadccbadcbabcaabacbacadccaddcdbbdabbaaabbdbacdaadacbabdcddbccbbdcbdbabbdcdccbccddabacbdbdbdccccaddbdcbadaacdddcaabadcacadbdcbdddcaccbaabbcbaadcadaaacdbcabaabbdadabcaaabacbbadaccbbdbbcbccaaaadbadadddcadddddddbaccbadbbcbcadbdddababdbadcabbabdcdddbbdaaabaccbbcabaacdaddccadcdabadcabcacabccacadbbdacbdcddaacacdaabcbdcbadadddcdabcaabcaadbabdddcbdbabcdbbdbdabadaddadaccbbbbadbabaccbbdbcbbdccccdadbccabdabdbbbddabbdcccaadadbdbcbbaddaccbdababdcacddabbccaabbdbbacdadbabaabbdcdaabccccbabbccbaddbacdaaaccadbacbbbadcddddaaccdbbadcabdccbbbdabdcdaddcbbadacabcaaaccddaccabcbcaadaaaadcbdbaadaaacccdacadaacacdacdbccdaadabccabcdccaddcddcbacdcdaaaabdaaccbccbcbdcadacacadaacbcbdaccbcdacdcdbdbdccbcadbcaacbbcaaadbacbdcaacbaddaaacbacacbdaccbddcbabdccddddcddbcbadbbbdbacdaadaadaacdccacddbadaabbbbaddbaaddadbdbdabbaadbcccacbabdcaabcccadccaddaaadcdddcccdcbcadbbadcbdcaadbbcacbbaabcacbcbcbbdddacaaccbbdccdadacbcaaacdcbbccdcbdaaaaddacbcbdbbbcadcdaaccbbaccccbdcdadcaccbdcccaccaccdacbacaddcccaddccaaaaacbadccacacbcaacccdbdcaccbaadcdbddabcdcddacdbcccaddacccadbcaacaaaaaabcbdbdbcacddccdaadbadccbdccbccddccdacdddadacabcabdcadbbbdbbbdcdadbbcabcadbddabcaccaabaadcdcdbbbaadccabbbdbcabadbdcbdcddbdccadadbabbbbcbbabccadcdaddabababbcbadbccbbccabbddaacdbaadbaaabdccdbbbacabccbbcdbadaaadadcbdaaabdabccacbabccadaadcadacbbabccddccbddadcdbbacaaacaddadacddbccacabccbdabaaaabacbdbaacabcbdccccdcdcbdbcdbcbdcdbbcdaccbcacbdaabdddbbcdcdbaccdddadddbddbbcbcacbdacccdabcbbbcbcdcbbbcdcbabbcdbbaaddcaddaddbcdccaaacadddacbbdccadadcadcccdaabcdbbccdcdbacbbacccccbbaabaadbaccbcaababcddabbddabcbbbddbaacbccdbddddbdcdcdbaccbbabddcaddcadacabbbabccaddbacdacdaabddbccacdddddbcadddacddbdcbbaddaddaccbdacbdccacbbbabbccbbbddabbbbccbcbdaabdcdccbaacccadbdbcacabacccbacddbcabbbddcbdcaddbacaaaadabaddcadbaaabbadcbbacbbcbadadddcdbdccadddacacbacaddddaaccbbacbbaacddcdbaddababdcdcdbbccaabbcabbbddcacbbbdcbddcadcaddbaabacbbbaabcadccabaacbdbadaddadadbabaacabbcaaaaacaadcbaadbbadcaacdcdccacabadaadabbacbdabbacabaaaaaadcccbdacbbbbdabccadcadabccbbcdbdcdadbdbbdabdacabdaddbadddacccaacbbdbdaadccabbabacabdcbdcdcbabbdbdbbbbbaadcbbacbccbaaaddbaccccbcdabddacdcdbddbbbbcbbaddccaabcbcccdcbdbacbdbdcdacadabbaccdbbdbbbabadccccaaadbacdadbcbabdaabbadcbbdbbbbaccaccbcaddcaadbbdacdccbcddbaaadabcbcaddacdcadabcdabdacacbdabcaacdddabcbbabdbcdabbbdccbdbdadbbbddcccdcbdbbacccdaacdcbbaaaddaacccbdbadccbcdcdccbbdcabddbdcbbccdcdcdcddaabcabacaccabbaabababccdbaddacdaadaabaddadcbcdddcacccddacbcabbaadcdaddcdcbabadddbcdccdabbbcdacaaaaccbbdadddacdddbadddbcbdcccddbacbdcddddbababdabdbbabddaddddbcbcacaddcbdacadccbabbbadbdbdaadccabbabddadaabadcbdabdacccbbcacacdddadcdcbdaabadbdacdbbbbdddaddcccbacddcbbadcbdddcabadacbdcbddcbcadddabdccdcabaabbcbbdaaabdbbcabdaaaccbabdabdcbaadcccbcbcdacbccccccbccdadacacbacdabdcadbddcbccdcbadadaddddbdacaaabaddcabdcadbbcacbbdaccdddcdbaacbcccbdadabccbdbbaaaaadcbabcdcbcbbdcacacdabdaaababbcbddbbcccbabddbacacbbadbadbbaaaadcbbbddcaddabcdbcdccaaabcbbaabaaddcbbacdcdaaddbaabdbbcbabacadbabbbcbabddaddcabccacbbaacaabcbcbbacabdcbacbcddbdcbcddbadcddbdcdadaccdbbcabbcbbbdaddaddbccdbdadabbcadabacbcccdcdcdddbbaddadcaccadcbbbddcdcbbdacaabcdbcaabddcbdcbdbbcbcbccdcdaabccdcdcbadbbdbddacaaacbddcbcddbccdbcdcabcbbcababacdccccdbbadbaabdbdacbcadccdddbaccbbccdccdbbdcbdadcdbbaddbbaaddddccbacdbbcdaccbdaddabbdaaddadbbcaacdacdabaaddbbdcaddccddbdcbdaacddaccccabbdcababadabbcacbdbdbcbddacbbacbbdbdddadbabbccdbaccbccaddcabbaddaaacbadddccacacabcbbdadbaacdacaacddbcdabdacadccaccaddbdcdbbdbadcbbcdbcacadbdabcacaccadabacdbbbccabbbacdabbccdcdabbcdcaacbcabbacaaadbccacabcdbdabdaadadddabbccacabcbcbcabcbcadabcadabbbdacbabdbadccdccddacdbcbabcdbbcdaadbdadbbbaddcdbabaacbacaaaabcddabccbdbdadcadabdbacdddbabbcabcaccdccbdabaadddbaacaacbacdbbaacdbcbddacabddccbaacadcdccacadbcdcdaaaadddacadbbdadbaadbbdbbcadadacbddabcbdbcbccbbdabdcdbcaadabdcbdbbdabccabbbccbbcbbcdaddbcdcccbdaaddcbdccdbbcbdcdccbacaccdabdcddcaccaaddaaccdabccbcdcbbdbbdbaaaaadadcddcdccaabaadbbcbadacdcadacdcbdbbdacdadbacccdcacbdccdcdddbcacaddcaaadacbbbbcbdadcaabbcbdabcabaabbdbbadbcaccaabbccaacbaabadadccbacabaadaacbdcbbdabbdbdddaddcdccbcadbdcbddadcacdacbbbdbcdcbbdbaaacdcaaaaaddcadbbaaaccccbddccdaacdcdcbdcccbcabbbcaaddaabddccaadadabaacacaadcbaadabdcbacadaaddadbacadcddbaaddcbbcbcbddbcbbbcbbaabcacdadcadcbadabcacdcdddaabdddcbcabaadbbaadaaaababddddddbbbbacdcacbbbbacabbdbcdbdbddbacdcbacccbabbdccabbbbcddadbbbcabcdcdaccdbccbccbbcddccddaacdabadbababcbdaacbdaabcbbbddcacadbaacacddadacdddbbdbdaccddcdcbcadcdcbdaddaccdadcadaaabbbabaaaccbdbdacdcdcbddddbadadcaccddcdcdcacdbadabaabcabcbcccddcdaabaabadbacdaddcddbbdaadcdbdddbdbcddaadaadddabbcbcacbdaabdcbdbaccdbdcbcaccdabaabbdcabddbadcadbdbdbcdddbbdacbabadcdbcdbbbcdddcdabaddbdbadabacabbaacdaacbdbaddbdccbdacbacbcdcdcacccabdbcaadabccaabbcdadbbcaddaacbdacbcaabddbbbcabbadcdcddbbdcddbcabadddcabcacbabaaadccddcabadaabcbcabdbcddccabbbcbbbcbdcdbadacddacbccabcacbddbdcdadcbbadacabbabbbbaadadbbbdccccdcbdbbbbaadcadacadaadbcbdbacdddcaadaaaadacababcaddbcbcbdbcccaacddcddabdbdbacacdddddcbdccbdcdbbbabddbdbdcddbacbbddaabdabbdbccaccdbbcbddabdbaccaacbcbbddcbbbaddaabaaddbcaadcbdbbbbbcdaaddbcaadabaadbbacabbdcaaaaabdcdbadaddbdbbabcabadaddcabbdbcdcccbcdadcbdacacdbcbdadabddacbcadcddbacbcbdaaabbbbbdccaabaaabdbbccbcabcdcadcbadcabcabaaabaaaddccbbabbdbacccdcdcdcacabdbcabcbbadccdbabccdcbccbccbcadabdddcccddcbdcadcbacabdacaccbbccbbbdabacadccaacabddbcacbaddaddadddaaaabbbabbbabcdcddbdaddadacbcdbdddcccdaaddcbcbaabcbbccbccbcdaccaaaabccccadbcdaabaacadbdcacbbbbbcbcbbbcbdacadbabbadddadabdcdccdbadcdcabcaacbbaddadcadbcdcdccaaaccdcadbaddddabcaadcaacbacbbadcdcbcdddaacdcddbcabbcdbcadabddabbacbcabcccaacacccbbcbdbabbcdbcacbdbdddddaabddbdadadbccadcabcbadcddbbabdddcbdddbbccdabadccaaadaaddcdbacccbcabcdcdbdcacbacabcdbbdcaddcdccbcccbcccdcabcdbdababbdccbcbadcbcdbbccababaccdbcddcbccdcdaddddbcabbdddabccbdbccacaadccdadaadddcababcdaaabbcbdbbacbcdcdcdabbdbbbabdacdadccddbddabcabcddcaccbdadbdddcbaaacbcbdbcbadaacbddaacdbbdcbdcbbacdcdaababacaddcabbcdadcbaccdcdcddaaacdaacacadbdabbdaacdbbbbdcbddabcdccdccbadbbbabccbaacbdbaadaaacaabaccbadbbacbbdcbadddcacbbddaaccbdbbbaadbcbbcadbdaddadcacdcbabbabaccadbbbdbdccdaacdcddabbbcddcacbdcddacbadbbbacbabacdadcbcccbbbbcacccbdadcaaacdbdbbaaadbccaddaccbcdbdbabcbaadddbbcdaccaddcadcdcdadccabddbbbccbcbbcdccdbacabbacaadccadddaaabbaaadccccdadcdadacabdbbbccdaaabacaccadccbdabddbaabaccaaaacddcaadaccccaaadccdbdddbbbabbbbcbbabadcadaccccbacccdabdadacadccabaaddcbaacaddaccadcccbbdabcabaaaadabcbccadbcbdbccacbacdbdbabbdbabbcbdbbbadaacadbaabdaaddadbabdbccdcdcdbadbddbdabdabddbddccdbbdddcbbdbbcbdcabdccdaccdbbaccbccbcbacdbcbaadcbbaddbbabacccdcdaaaadcacdbbaddbdccccbdddacdbbbcabacdbbcadbcbbaabbdbdaddacccbbadaaadcdaccdddabbabcdbbdbdabdababbddaacbaabaccaddcadacbccdbbadcabcabcacdcdbcbddbbcccdabcdbccbdbaadcddbdddbcabcccdcbcbdaababbbbdacdabababdbcacbadaccbaddcaccabbadcdbbaaacbabbccaaacddcdcadbbcbddaacbabadccdbdabddbbacccbdacddcbcacacbabcbaaadcdcbaacddbaaaacdbabbddaabcddbacdcbcacddaadbbadbaddbacbbbcdacccbbacbcacbbbbcddbcddbadbcbbaadccbbdcbdccbbccddcbccdbcaadcadcaccdddabcadccdadbaadbdacbcacaddcdbbdaccbbbbaaddbcdbadbdbaadcaddbdbbccccbbddcdbddddddbcbcddbbdbcabcdbcabccccbadbddcdadabadcbdbcaabcbcbbbaaacbabaccabbdbcbcadabcaaacdbbbbabcddacdbbbbdbbbaaacadabbdccacbbbadabddddaabdabdacccadcabbadaddacdbbadcacdbacabdadaaacabbbadacdcdddcbadacbdccdbbdababcabcaacdadccddcbdcacdcbccbdcabdcdadbaccadadcadddddccbabcdabaddddccbabbacbbaccddcddaddbaadaaaccdbdddccbcbcacccbbaaddbdbacadaabbccdcbbdcbccddbabbcdadaddbdacbcccdacadccbaacdcbbcadcccdccbbbcccbdcbdbcddcbbdcbaabdbdbaaddadcacdcdbbcacacacdadaabdcbccaabcdabbbacaacbbaccabcadcdbbdbbaccaaacabdcbbacadbbcccccdcbbaadbaabdbaacaaadaababdddcadcbadadacddcbcbcacadaababbcbbadcdddbaccccdcdcadabcdddbcddddacadccacacddbadbcdadcdddabadcbadcbcdabbabcaadddbaddbdaaabcbaccbbdbbbadccddcccbaaabbccdcbcccbaccbdbaccbcdbcddcabdacabbaaabdbcccbdabcbaadacccadacabdabbcdccbdcbadccdcbbaabcaaddaadcabbabccbaacbdbdbdbdcdcdcbbcbcdaaacdddbbaacddbadddbbadadaddbbadccabdcdbbcdcbdcabcaabbddccbcbdcaddbdcddaacdccdacdccbdabdacbbdadabccabcababbddbcaccdcabcccabdcbcbaaabaccdadbadbcbbadbddcdddbaaaaacbbabbbdabcaabdddcbbdaadabbbdddcbdcbaaabdcdbcdbabacaaacdaacdbbadcbbdcacdbbcaababdcbaaaccaaadcabcbcccbadbdbdaabbcdddadbbaadabdddcddcdcadabbcadaccbccdaaaccaccccdddbcbdcbdacbaadbdabcaabcdbdacacacbaccacdbddccacbbccbccdaabaccbdbacbdddacabcdcccacccbabaddbdadcbddcbabcdadddacaadaadababddcaccadaccabddddccdbbbcdaadcaddccbdacdbcbaddcaccaddaabadcdbcadbcacbcdaddccababdcadaccbbdcabccdcadbbbbcccbaddabbacbdddccbbcccdbdbddddbadaabcaccbaabdaaacacbacddadcacccabdbacbbcabaaadbbbaabcdabbddbbdbbdccadcabaaacccdbdbcbcadccbabcaddaaadbbcbbcddbdacddcbbdbadaacccacbbbadadbcbbadcdacdccdccabaaaddcbbdbadadbcddbcddcbbbbccacbadddcbbcbaacabaabcbbacabccdcbbaabbbacdccbdaacaabacaacccdccccababbddbbdaacbcccaabddbbacbbdcdabcdcabdacbbccbdaabbbbcccdbbaaadbaacbaaaacacabcaabacbaccccbccdcccabdbdbabbaacaacbcbcaadaacbbcdcacaabdbbbdacbbbdbdcadcbacbcadcacbdbbaabbabaaabcbcaadbddabcacbcbbadaaacdabcaabcbabcdabdddbadacbcccadbbcdbabdbadbbcccbbbabdcaddbdddbbbcddadcdcadacccbcdbabaddadbbdccabaddccdababacacdabcbdacacaabcddbdcdabbabccaadcddcccbdbadcccaaaccaaabacabbdadadbcabaabdcbdbcbacaabbbccadcbacaacdcaaccadcdcccddabdccdccabccdadbbccdbcddbddcabacbabddcbdabcdcdbbbdabdabcdddddcddcdccacaadadacabbbbdacdcacbbcbbabcabadabdcdaccadbbdcbcaaabaddbdabaacdccccdacbabcdbddadadabbcccddbdccdcdacbaaaaadbddaadbdccdccaaabcbbcdcdabaabbbaadccbbbdbbaddbcaacbcacbadbccdcbadddaacabacaccacacbadbbbcaadbbbdbdbbabaabbcbacccacbdbdabbbcdaccababadbbdadddbbcabacbcacadbcabbaaccdbcbacadcabddbbbbcbaabcadadcdaabccdccacadddbddcdbcabacdcbbdaddbcbccbcadccdbcddcaadbdcbaadaaaccbaddadabaccacddddbabbcdcbcaadddccdbcaddbdcabbdcabbabccbaabbbbdbdabbcdcbbbbabdaabcdaacbbbdaadbbadcdccbbaacacdacdcbcccbdccdcdcbcbcbbaaddabccbadbccbbdabbcdcadbabbadddcccddddbbdddccbadccdbcaaadadddbacccbbddbbdbabbdbcccbadcddbdaacbbcbaadcbcbbcbdcbcaaacdbcccdcddabcbddbdcaacaadaadcadbccbbccdabbaadcaabbbdcdbbabdbcdbcdbcdabaacaabacbbdbaabdababaddcbbbcadddcddcdbdaabcbbccaccadbdcdacdabcadabbdcabccdcddaabdcbdbbdbdbbacddcaabaaacbdacacdacaccdcaadababcdabbdbbbdaacbcccbdacdbccbbacbcacaaabdacacbabacabddbacbdbdaacacadddbadadadcaccdbcabcbadbaabbcdabcabacbdabcbbbbaacddccbdbabbbbcccbbcbbdbdbddcbacddccacabcadcacabdcbdcbbcaaacddcdcbaacccbdbaccbcbaddbadcdddcdabbdcddddbcbbbabaacdaacbadbaabddaccbadbaaaaddacbbabacbdbbcbaaccbaccdbdaacaddcdabcdbbbbbdbdacabbbabbdbbbdccdcdcdcaaadbcbacaaccdbcadcabcddccabcbabdabacbaddacbccbdaccabdddbdaabcbcbddabbcbbcabcdcdbddddbacacacadcccbaadacccadbdbdbcccddccbabababcddabbddbcdbbdcbadacdabddbabacdbbabbbdbcacaccaabcabaaaccdbbdcadacbadbcdbbcbbddbdbbcadcabdddadbbaabadbcabbabdbdabdbcddbbdccccdcadbabdbbcdcbbcabcaddddbbaccaaccabbcdbcabcabdbdccbaaabdbabcaccabddddadcccbcdddcccaddbcdbcbabccbdbbcbdaaacaccaddaadbbcaabaddadccbaaabaaacbbdcdcdcbdaabccbbbbaacacbdcacacdacdddcbcbabadbcaaccdacdbaaddcaadcbabdbccbcbaacbaccddaaaaadbcabdbabdcbbbbcbdbacdabcbbdbccbacabcccdbcacbbddaadacaacccdbddcdbaaddaacadaacdabbcddcccbbadbaabbdbabcaacdbcccdbdddcdddabcbdddacacadccbbdcbdcdcdaccabcdaacbbabdccbbadbddaaddbdcccacbdbddcccbdabdddcdbbbbbddacbbaaacccccbaccdccabcddbbbaccbddaadddbcaabbdbacbaaabbcdabcbcabdddacbdabbcdcccaddcccbaaaddcddcacddaabcbcbaccacbaadbabddbdddccbccbbdbabdcdaabcbbbdbabaddadcddcdcabacaaddaabdabadcddaddacaadabbbacdaabbdaccabdddcdabdccdcccbbdbbcdbbcaabbdccdacacabcaccaabcaabdddbdcccdddbadabadaabbcaabccbdcadcacdcbabbdadbaddbdcdcbccadbbbcbcbdcdcbbccbaacdaacabcacbcdadcaadcddbcddbcbbabcaadccbddcddaaadbcaadcbbcabaccdadcdbcdaaaabadddcabcbaabdbbaccbcbabcacddcadbacdabbbaddacacddddbdccdacabccbdcabdcdabdacbadacccbbcabbadcbdadbcaacdccccbbdbaadcdbbddcaddcacdbbbdbbdaaddcdacbadccacabacddaaacadacdadbacddccdadcdcbadaacbaccccbaabbdacddcbbcbadacaacacdbdcddbcbbabcaacaaaccadccdbcdbacaaababcbcaadddacbdabddcdbbdbdccdddcdddababbabadccabbccaacabccacabadccaaabcaaacaccdcdbbaacbdcabbcccbabbdacdbbccaacdbaddacbbcaaddacabdacadabbbbabbddccacbdddbbbcadddcadcbcdbccabbbcbacddcdddabbabcbcbbcbddabbcddbcdcdabbcddabbaadbacbcacdaaadbbdadcddadbddcaccaacdabdddabccddbcdbbbbddbaddccaaabaadaabbacaabaacdbcabaddbdcbcaabcacbadbcdabadccacbbdacdaaabccdadcaacdcdcddaaacabcddbbddbdadabcabcbdcabbcbddabaacbbbbcddcdcbbadcbbcccbaaddcbadbbaadddbcccadacdbcabbddbbcbabcccbcadaacbdaddcdaaadaddccacbbacbbccdcaccaaddbaccbbcadabbadacccbcaaacbacababdbdbacbccabbaaccbcdbdcbbbcabcbcbbbdaacccccbbadcbadababccaddbbbdacadbccdaadaaadabbcddcabbcbdddaabbbabddcbbbaaccbcdcdbbcdcbbaacacbbaacbaadbcaccdabababccbbbbacccdcacbddbddadbbcdacbdcbabbaadbccaccacbcccddddccdabadadcbccbccaabdabcaabbdadaddbacdcddadbcacadbccbbaadcbdbabbdbddacacabbabdddacbccddabaadbdacacdcbcbddbabcbdaccaddaabddddbaaaadbdbabaaaabaccdbabcdabcbbdccdccdbdbbcdcbacaddcabcacaddbbddddadadccccabdccddddcdcbaadbcdbddbdbdcdaaabbcdaabbdadcddadcadcbdbaabbdcbdcddacdddcabdaabcacdbdbbadcdddcbdaadcbdbbaaadadaaadcccadcbacabbbdcabddccaaaaadabbacbaabcbcdbbabddbccdacacbdabadcdbcbddaabdaacaaddccbbbaabadbabacbdbbccacdcadbbbadabadaddbdbddddaaddabbccccabccaaddabddcbddcbaadadcbaddbccacbbcbbccdaaadabacbabdadcaacbccdcbabacabdccddaadacdabddcddcccdcddcadbaaacbbddcabbaddddbadacddadacaaccccdaabacdcaaacbddacbdcdabdcbdaddbcabaaaadadbdbccabbadddadbddccbdccdbdbcdcbabccccabcddabdbbdaccacaaddcdbccdacdccabcdbcbcbdcbcccbaccacddcaababdbaccdcdbdaadcdcdbcdcbacdadaccaabccdacbacbaabbcdadcaacdcadabdadadcdabdadabacacdaadabbccbaddbdaababcbcbbaabdddbdbbaabacaaddaabbdccbaacbbbdadbaaabdcccdcdaaadbadcaabdabdbdbabcdadacbdbddababccbbcdccddbdcdcacdcddcdadcacbcdbddddccbddddcdacbdadaccbabcadadbcdaadcdcbaadacbddaabddadaaddbaabbcaacabcbabccdcbbbaacdcbdbabdcccaabbdcddacadadacbbdbbabaabdcaddacdadccbdbadbcbabbcadcdabdcbdbcdccbdbbadcdcdcadadbabaabcbcdaadacbabcdabdccdcbbaaaccdbabdadcbabaddadbbddaabcaadcbccdbadcdcdcbcaccdaccbdabdaccdbdadbbcdabcccbbcdcbdcabdcbcdabcacadbaccaddbdbbadcadaabaadabacbbcaddadbdbbabcacdababbcccaccbaacdccbccdaabdbbdaabadbcadcbcbdcddcadadbdbbddacabccdadbaddabccddbcdbadcddacdcacacacbcadaabaaadcbbbbdcaddabcabdbcdabcbbcddbcadcddccacdacdddaadbbacaababcdbcdadbddcdcabdccbbcdbdababaaaddbaddccdabbbaadadbcdbbbacaadcdbcabdbbbaaabbaadbbadbdbdbcdbdddcdaaaccccbccdbaacadddbaddbdabadadacddcddaccaccbbddddabccaaabdbcdbdbacdadbbababdabdcbacbacdacbcabdbbacaaadccccbababcdadadaccddbcaadbbdbddbdacabbcccdaabdaccadbbddaadadcacabbcccaccabbcaacdbabbacbbbcadcaacdadbaaddacbcacdccaccbdcdbddbddbcabaddbdddacbdadbaaacbdbcaacabcccaaadcabcbcdabbdcabcadcdbddcddcdbddcaacadccbdabaddccacabacdabbaaddccbbbdbbbadccaddccbdbcccbcddcddbdbccdcdadcdddbdcdbdacaaabdbdcadbccaccabacdabbdcbadbdbacbdbccdcdababbdcababbbbaadacaabbcbbdddbadbdacccbaacaadacacccbcccbcbdaaddaddbdbcacadaaabdccdaadadcbbbaacdabdbdbaaaaaadddcacbcbbddcddbdacbddabacbacaccacbacaadbbdadcdacdacbbcddacaabaacbcdcdccacdaaddcbcdabddabdcbcdbacbadacdabdbbddaacbccadbccaddcdacaabdadbdbbabcdcbccdcbcbdbcccbaaabcdbdabccabcdadabdcaccdcbcacbaaddcbccdbdacacddccaddbbaabcbbaddbbbdabdcabbcbdbdaaabdbcbbaabaaaaaccbaddcbbadddadbcdacdbcacdbdbdbcdcabdbbbcaaacdbccbbacdbddcacbcddcadddcadddacaccacbbbacbdbcdcdacbdbadddbaddacabbdccbdacaacabbccdaadcbdbdbabcaccabdcbbcdbcdbcdabbbdcdccbacdbabbbaabcabcbadbadaacababcdccccaadbbdcddaaddadacdabbccaacbdaaacaccdabcdbacbacbaabcbbdbdddaababdadcbbbcbadcdabaddabacbccacbbbabaddaacdadcadbacdbcaadcbcddacaabbcbcbabdddbbbadbcaabcbbbbddaccdaadbdaaaacbbbacabdbcaadabacdbdaacaddcacbaaabcdacdbcacbcaaadabababaadcbbbbbbbcdbacddddcbaacbbbbbbabbbdddcacdaccccbbdbcadcdcdacbbabacacbcbbbdacacbcdccdcaacdbacdaadcdabcbaadacddabadbcdaadccccdddadaabbbaddaaaabbbddcacaddadbabadaddbcccdcadddabbbbddcbbcaaaadbdccdccacdcaaaadcdcadabadadbcccdbcdcddcbdddcacbbcdddddcdddbbcdbcdaacccbcadccccaaaacaadccbbdbdccabcbdaabdabdddbddbdabbdadcbdbdaacbbabdbabbdcdabbcbbbadbacdbcbccbcaadcddcbbdcbbcddcbddbdccadbcdcacaadabacadccddcbbbcdbccccdddaadddabadcdbaccacaadcbacddcdbbadcdadbcbccaccbdaadcdddbabbdcccdadbaacdcbbcbaabbacdbdcbdcaabadbbadadcdadcadbddbccaacbaddadcdaadbdaadbcaabdbadcaaccabacadadbcdbaabacadcacabcacacaccabddcadbadcbbddddbbacbbaacccaaaaadaccadcaadaadacdddaacaaadbdbabdabdcbabbabadcbbacddbcabbbadadcadcbcacdbcadaabbdcbcaacbddddbdcbcbdcaadbabbdcbbdacaddcbadbcccddbdddabbcccddddababbabaccdcddcdbccbcbaddbbddbdbdabdcdacacdadccadddbbbaacdcbbbbbddadadddccbaadacdbacadabccacbababadbcbabbddabcccddcbbadbbccccaabcaddbacabbabacaddcaddddbadbabbcaabacdbadcddbdababbdccacdabbadcabdaadbaaadccbacaaacabacbbddbdaccccbaacbccadbdcbdcbcdcbdadbaabaccdcdcdddbbcbadbbdcbccadbcaabbabcaaccbddabccdadacdcaccbadcccdbbcbabacbbabbcbdbccacdcbbdbcabbabacccddcbbdabdccaccbbcdcabbbadcbaaacdbacddbccdbdccdbabaadaadcdbdcacabcbddcddabbbddaabccaccbcdcddbcbbaaabaddbacabbdcddbacdbbadccbadbdababbcdbabcdcccdbbddddcaadcaccdbcbcbadddaaacddcdcdbbdccadcacdabdccbdddabbabcdbdddccbbcacadacdcbbddbbbccbccacbcddbcdbbababadacdccacdacbbdbcdcbbacdcbbcccddaacbdbaabbdcbdbdcdabbbdcacbacdaaadcddadcddadbabdabdcaababdbacaabacddadbccccdadbdcaaddbdcadbacdbdcdadbabbdccacdbbcbdacddbcadccabcdacbccabbbaaadabbddbddabcdddaddbaddbaadbcbcdbbcbabcdcbbdcdccdcdbaddaccdbccdddabbbbdcbcadadacbdbdbdbbbcbccdbbaaaddbaabbdddcdabbcabbcdabbadbdadbabbcbaadcabcdaaaaacdcbdbbbadcaaadddaacdddbdbcbdbdcdcbcbaadcdcabdbdbbacdbcbbcbdbddaadadaaaabccdbadcaaacdaabdabbdabaccaccddbbbadbadbcabdcdbddccdcdcccdbcbdbcbaabdaddcadcacbdabbcbbcdabcdcdcdaabbcdadbcdadacbdcaabbccbaabccbdaddcbbabcacabbbacaadcdcacbacdbabccacacaccdcabbccccbbcacdacbdbbacddacbdabdbbddbadcddddbcdadccdbcccbaccbcbbdbdbccabdabbaababcccdcbcabbabbcacddcdacaaddacddadbbacddcbbacaabccdcdcadccdbbaabdcdaddccbdadbbdacccbbdcdcdbddabbcdadcbdbacacddcacabbdbcaacbbaadcdcdaacdbadcddbacddcacdccdaadddbaccbabacababadcdbbdbacbcabdcbcbcccacddbbadcdadcacadacccbbbcdcdcddacdabddddcdbdadcbacbccabbccbcabddbbcacdcbcbdadccdcabdddcdabacdbcbbdddbdacddcbbcacdaaabbabcdabacacaaccaaabadbadccddccddddddadbddadbccbbcabdbaacadbacdbdcaaaaaabbccadadddaadaabcddaccdccdcdbabacdbbccabbcababcacbbbadaacbbacbdaccbdaabadaddcaacdcaacaababcbdbdcbadcadaaddacdcaaacdcdaaddccbacdadcdddbbbaadbaadbbbdbcccdaddcbbbccdaaaabcbddbcbbbaccccdaaabddacaccdaccdcddcddddbbbcadbbadaccdbcccdcabbdadbbbbadbdbddbadcabcaacddbabbcbdcdccaaddcbaacdbdabbddadadbbdcbdaccabbdaccdbbbcbaccdcbbbddcabdbbccdcbcbbcdcaaadaccbcabcaadaadaacdbaadddcdbcdaadabadddbadbbacbdcaacdcaccaaddbdaaacbacbdbacddddbbbccbbaadccccbadbccbaadbbbcbacdbcbbccdcadacaabdbbacddbcccabbbcccbccaabadabccbbbbabaacaabbcddccbacdbdacbabbddbcbbdacdddabcbaadcddcddcadccddcacddacbbcdbcdaadbadbcabbccbbadbbaacaaabcacdcbadbbdddacdabdaadadccdaccbcabaabcacdadbabbabbaadddcaabcccbbaaaaababadbcaaabcdadbddaaabbbdddbbbcbdccadcdcdcdbbdaaaaccbcaacdbbcbbadccbabbadadbdddddbddabbaabaadacaabaabdcdcbaacbcddadcbbdaddcdbcacbcacbddbbcaaabbdadcbcdccaaaabbaaccababdbbcddcbdcdbcbaaddaabddabcaaaababdcccdcabacaadbdacddbcccadbbdbbdcbaddcadaaadbacdadabbcaacdadcdbbdcadcbcaaaabcbbaddacacdaadcbaabbaaaacaaaabcadaabcdcdbcbbddabacacbabcbadaaabaacbdcadccbabdaddcbdbdaddbdbadccddaddadbbddbdabcbbcbaabbbcbaddabbbdbdbbcccbbacdabdaaadcbadaabcaddcdadcbdbdbcbaadbcccadbbbcdcddcaababdcbbdabddcaaddcadacadbddcddbabaaaadbcbbbcadbbaddcabdcdbaccbddaaadbadbaacccabddbdddaaacdaaddcddbbbcccdabddcababaabbbbcadababababadcaaaddaccdbadaaaabdcabdacbcaddaabaadabddacccbddadaddabbcbbccaabbdcaddaddadcbddcbadcdbddcccdbbbcaccbabacdddcccbbdbdbccbdddacccbbbddbacaadabcbaabcbcbdbaabbaabaaadaccdaddddcdcdaadaaabdccbaadcaaacaaadcddbabbcdcdadcdaadbdaabadaacbacdbbabcbdcaccbccbdbdabdddacacadbadbbcbaaaadcbdabcdadadadbddddbcadcbaaacbcbcdbbaccbcdadbabccdcbddaddcbadacababbbccbcaabbdabcbbcdbdbcaddcdcdaaaddcbdbbaccbabbdcbaaabbcccbdcdbbadbabdbbaddcacbcbbcadccadbabcdcacbdbbacdaabbcabcbaccbcccadbdbcbdbbdbcbddbacbcacbdcbcbcbdacbbaacdcbcddbabbaccdabaaccabaddbddabaccabaadddacdabbabcabcbdbdcccddcddbabdbbabbcaaddbacccaacadbabbdbbdbcaaccccbbdbdcabdbadadcadbcbabdaadabbbcccabdaacbaaccddccbbdadccadcbaccdcbcddbbadcdbbacddddbccbcacdbaacbbdabddbddbaabcbcbaddaccccdababdbbdcbacabccdbabbbabcabddaabbcadabbcdcaadcabdbaddabdcbddaabdddcdbabbdbccdacccaabbcacbadcabbcaccbbcdaccdcbbdbaaabcbaaaacadcbddbdaadaabdcbbadcdbdcacabbdbaaadbcacdbdbadbaadcdaadcbcdbbbddbbaaadcbccbcdadaaacdcabadcbdcdccbdbcdacccccaaabcacaacdddcbdcaddcbbdbcbcdaacaabbbabacbdacddbbdaabbacadadcbbbdbbcbcbadbcbcccdbdddcbcadbadcdabcbcadabbaadadbdacbcbdbbcbddcdcccccaaaabdcdabbbbdbadbadbcaacddcacdbacbdbddabccdddcacdaaccdcbaacabdbacbbabcabcbcadbadbabaadbccccbbbcdbdccddbbdcbadccbabacdabbacbbacdadcbbdcbbbbbcbdcbacacadbbaaddabbdbacbaabdababbbadccddaddabccdddddccbdccabadbddcbbbdcdcdaaaddacccdbbabbcdabcdbcdbabbdadaacbabbaaacabbcddcdbbabbbaaadacdabddbbccccbacacacacaddaccaccdabbbcbbcbbbaccdcddacbbaaabaccddddacccdbcdabaaddbcaadccbbcdbbaaabccbdddbbddcbbabcddaaddbabdacbbadacacdbbcbcddbcbdbacbccdacdcababaadcbdddbdddccabbcbacaaaacbcdccdddaabdbddcdbdddbdaaccdddcdacdbcbbcadcdabccabbcbaddcaccabdbaccddadaaacacadbbaddbaaddaaacbcbbcddcbacadcbbabbdabadaddacadabcbddccabdcaaccbdabcdcabccbccabdbaddccbcdaaadbccbbdbddacbcddacaddacadcdbababdabddabadccaaddcbadcdbbccbddbbdbabbdaccacaaabbacaaaddabcabbbdbabdaaccaaabbcaadacdddaacbddbdcbccdbcacacadcbddcbccbcaacaddbdadadabadcdccabbdadcccdbcccbadaabccaccccadbbbcdccabababcbcccbacccdcabbccccabbdaaaaacacbcdcdcabbabacbdcdaabaddaccdbbacabadddcdaadcdbdcbcdcdcdcbdbbbdcccbabbcaaadcbdadcccbaadbbccccccaccdbdaabcbccbdcaadacacdbdbdcbcbaaabbacbacddcbdbdbaddabdcccbccbbacbbacacabcbadadaccbcdadcddbbbbaabdadcbdabbbbbaddddcacbcddbbaacbacbdcdcdbaddcdbccdbaacbbbdccadcbcddcdbbdacdcdaadccbaadbdaadcddcbdbcbdddbccccdadcacdcddabbdbcabbbdbadbcdacaaccbdbcbdabcdbacdcbdcddcbababdbaadbdcbaccadbaabdccaddbcbccbcbbdddddcaadcdcbdbcbbcaddadcdccbbcbacacacddbccbbbadbdadcbdacdcaadabdaadbbbdddbdcaaaaadcbbbcbdbdaddbabcbabacbadbcbbcaaddcbbccdcdaadcadcddccdbbdbcacbcadccbcbbbacbcabadababacdcbaaabbdddccdbdadabcdcdcddcddbabbcbccacbbcaaabaadaddbddaadbbcabcbcbccddcdddacdcdcdcbdaaacddbcabbbddcbcadccddacdcbcaaadcccdaabaaababaabaddadbbbcbdaccdccdbbcdaddaacbddcccdaccbcccddacaaaaaaabbdacbaccdbbbdddbbdddbddddcbacaadbccabbbbdbadbbabcbcbdaacbbdbabbadddadcababadbcccdcbdcdacaababbdbddddabdabdbcdbabccdbdbadacbaadcdabaaadccdaadadcadcbcdbbdbbbcacbaadcdcccaaccabbcbdbacccabadbccbacbdadaaabadbaadbcbcabdaacbddababbadacdccddddddbacabadabbabbbaabbccdbcacacbbdbadbcdcccdcdbdddbabcdcbbcadbabddbbdbaaaaaadacddbdbbabdccdcdcbcdddcbaccddacbcadabbacdddaddbbcaabacddabddcaadcaccdcbaacabbaaacdabccbdaccdaacadbaadaaaabccdcbbddcbccaccabccbcbabdaabacabcadbcbaabbdbacbbbadbbddddaaaadadabcdcaaabbddcbbdbdcdcdbbaccbbdddcdcccddaaccaccccdadddbabcbddddcbbdadcbbcbaabddbbabcbcdddcaabcdbdbddbacdbddaabaabccabcbbaabdcbdcbcbdccdddcbbcdbcdbabaabbbcaddabcaabadbabbdbdccccdabbbdccadadaabcacadcbaaacdddcbbbbbdddabbcdaabaddbdaabbdcbdacadbccbdcaccccaacabbcbbdbcdabdbdcaddccbadabdbddbdbddadddbacbaabdcabbccdcddcdacaadddbcbbacacdcaaaaddabbcbcbcccdcdddaddccacbdccdbbdbdbdccaaaddcbddddbabbdbabaccacabbdbcdddcdabcddcdcbddbcbcabcbcdaddbcdbdcdabdcabdbaacbbaabbbaaddcbbcaabbcdaddbdddacbdbbcacbacdcacadbacdddbdabbcabdddcdaaaacbccbdcbaabccaccaacaaabdccaaadcdbacadbadcbaccdcabcddbaacddbbddbdcdcbcbcbdcdbdbddcddccadddbdabcabcbdccbccaaadbbacacccddacdcaccdacbbdbdbbcddbcbacbbcabdcddbcbaddcccabadacaabaabaadacdabccaabacacbcdcdacbdbbcadbcaabcaddabddbdcdbdaacdbdacddddbdbcccdbadadacdbdbdabdcdbbaacabcdabddcaaaadaaddacabdcdaadcbddcbdbbcdcacdaacdbbcccccababddbccbadababbaccbbaacbdbbdbcacabdaddddcabbdaaccbcdbbbbccdbabacdaaccbacacaabdccdaddadcdabaddcbbbdcdaadcaabacddbdadabcdcbccbaaadcaccabadaacdcdadabbaadbccadddaacadbdbdccdddcdaccbdbdcddaabdbcdbcdabdbcbbcbdabccaacccbcdbccbdcdcdcddddccacbbcbbbddacdadadaabadaacadbbdcbbbcdadbcdbaacddadbdaddbcaddbcdabcabcddadaacaddcbbddccddbdcbcdbdddddcdcbabbcdadacbabdcdbadbbcbcbaaadcbdbbbcabccbdabaccdaadcabcccdcacaacbdcdbaadbcacbbccdbcbbcacbdddacbbcdbcaadaaddcadddcaaddbcbadabbcacadcbddadacabdcdacaccbbbdadabdbdbdcdcbddaaccabccbcbcbdadbaadabcdbabbdccdaaabddbbdccaacababcdabaabaabcaabbaacaacddacadadcdccddacbcdbccbddcaddbbcbbabdcbddaacaacaadbbbcaccadbcbaaaaacabadbbbdbadccbadbdccaddadabcbdcbabddcbddddbbccbbdcccdaccbdcbbbccabcbcbbdbdbaabacadcaacdbcdbcadcbbbdcbabddadbadcdcddaaabcdadcaabccaacbcccaacdadbccdbbcacbccbdbabccbaabbbadacbadbbbaaabccaaacaaabcbdadaaaabbacbbacdcccbaabdcaababbbbaaadabbddcbccabbbbaccbbcccacbcdbdcaddbdbdccabdcddcdbdabbdaacaccdcadbbbbcccddccddacacddbbacadbddabbdccbdcdacdbbbadddbaabbcadbbbaddbbcddbadacbbbdcddabcdcbcbbabddadccadccaabacbcadcddcaabaacdbcbbbdcdaaaabddacabbaddacdcadaccdabcdccaadadbddaacddabddbcdaaacbccdcbbcdbcddcacaaaadababbcccbbbbccabaadbabacaadabdbcdbdaaacddbbbdadaadbcbacbbaadaacbcbabddcbcbdbcabadadccacccababdbaccbbbaaabcdddcbddbcaacbddaabaaacbcbbbadcdcddacdcdbdbcbadbcdadaabcbbcddaaabdccddabbbbacdccbccccbdacabaadbbacadbccabcabcdadddbbbadabbdaabadabbacddccdbccababcdbcccccddababacaabcbadbaacacdbdaadaabbcdacdacbaccccdbcaaccdddcbaaacddadcbbccadbcabcaabbabbbccacabcaabbdccdcdcdbabaadbdcadbbbacabdcadbcdbbccbccdbdcddcbbdcddbcaddbbbdabccbcbcddbcdcdcadbadadddabacaadadbadbbcdbddcbbbadcbbcbdbcbddcdcaccdbcccdaacacbbdbcccaacdcaadbcddabccccaabdadabadabcbccdaadbaacddddaddcddabcbaddaccdbabcabdcabacaababacbddaccabbbacdcbdccacbddbbcbabaaadacdddadbacacbbcabccadbbbbacacddccbdcbcaabdbbdbcbcdbbbdddbacdbcbbdabaacadcbadbdccabbabbccdaacaabcacaabccddddbaabdbaddcdaabbadbcdbccdbbcbacdacabbcddbcbbcbcccaaaabccbdaddccadbcdcdaddcbbbbabbacbcacadadabbbbcdbcdcbbbbababddacacbccacaadadcbaaadccbdcdcbbacbbdcabddcbccddadcdcbddcbddaadddcbacdabdddaccbadbdabbabcbdbadcccbabcccaddabdaacacbcdabdbbbbabdbadabbddcaabbabcaaccdbcddcbdabcbbadbdbbaddcdabcdcdacdbabbacaacadabccbabdbbbcacbbcddacbcabcdddddadcadbbddaadbabbdddadcaacbdccacacdacdddaaddaacbdcddadacddaaccadacdabcbbcccabbddbcabcccbacaabbacbcdcdacdaadacabccbaadcdcbddbbbaadbbccbdcadbdbaabaacbcaccddcdaacddcbaaddabdcadcabaabbbaaadcdcbadbacdababccadbbcbcacddcdbaddddaacabdbcbbaaadcbaddaacbdacdddaccdbbcbdbbaaccaccabdbcabddbaaddcccdadcdbbcdbdadaccaabbcacdddcdabdcbdcadddaacabbcbbbdbdcdbaabadcbdbcbdcdbdcacadcccbbddaaccdcabaaaddcddcbdbbcaabadbcdcccddcbcacadcaaddaabacdadbdbbdcadcbddabaabbbcacdaaaddcdcadcdbdacbaaadbdadcccddbcaddcbccddadaadaabbaabbddbadbcbcdacddcaacbbadbdcdcadaacdacddabccadccaabccdbaaaadbabdabaddcaadcdaacacddcdcadccbcbaacbcacabaaddabdbcbabbcddcadcbcacccbadcaddbadbdaddbdccaddabdbadbadbbcccdcdbaddbbdbabcbbcbcdabbdbbaadadbabadcbcdcbdbcdababaaddacbcaaacdbbbabcbbcbcbccbabbdaadcaaaaaddaacbbcbabcbdaccbbbcbabcbbccbbccbacdbabccdbdabdbccbcaccbbaccacbbacbdcbdcbdccdcbcdaccadddadddcabbabccccbaabdaddbcccaabcbdaaccabbabadcdbcdadaddcdbadcdbacadbabaacadbbbddbcbcbccdcaadcabbbdbbdbcccabcbdbcccaaaababaddbacbcbdcadaabacabcabdaccbcbcabcdaadccbdadbbbacabcbcbacbdcacbacbcbaacaaadbdcaaaabbdadcdcccacccbbaccdabdaccbcdcacbdbdcadbadabbccbbdbcadbccddbbdcbbbcbdcdbddbdacdcaddcadcbccdddbddbbbcabbcaabbdabbaddccdcbaddacdacaaddbcbdcaacbbcabccbcbbcdcbcbbdbabaacaaddcdadcaccbccaacababbbdbcccabdbccaabdaaaacbbcdacdcccdbdbbaacdbcabddbcabbbcccaadccddacacbddcbbdbcbcdbcbadaccacbcaacbddcbdbcdcddbabcaaaacdaccdcacdaddbccdabacdacbdbbdababbbdbbbacacccddccbbdaadcadddcdbbcadaabadaadccbbbdbcbcbbcdcdbadcbcbcacbcabcadbdaabccdcbaaccdbdccdbbddcbcccbcbadbbcccbbabdacaadacaccddabcbaaabacddaaddbdcacaabadcdcdddabcdaacbdccbcacadadabbaccabdbbbccddacccacdcacadaccbcabcdbbbbaacdcbccccaacbdacaddbbaaaadcbaabddaaabbcbddddbdadcbcbbdabadabbbdbdbbccdadbcadaccbdbabbdabdbbbbdcaabccadbaabbcdabcdcaaacdcdbdacccdbabbbacbaadadabdbdbdbcdaadcbbaaaacbcdddcbbacdccdcccaccdcadcbabaadaaddabddaddbbbbabddbdaacaddbbbccbbcdcdcccccccbbdddaaadbabbbcbdbabbdbdabacdccdcaaaabbabcbacacdadccbddadcddddbcaacdaadccaaadaadddbaabddcbdadadaaacbbcbccabbabcbadddaccbabbbaddadddcbbdbaacbacbddabadccdbbbdbbbbdbadabcdbbdbabddacbbddcababaabbbcbbcabddaaabdcccddcdbbccccaddbcdddbccacdccaadaacbaacabccddbaadbdabddadcdcaacaacdadbabaaaadcbaddcbcbbbaddbbccadcdcbaaabbccbcddcbcddbcbaaaacdaacdcdbdccadcacadbacbcdbcdaadbadbbbadaacbcbdcaaacccbadbdbaacddbacccadcbcccdcbcccdcbbadcbabddbbdadbdcddadbcdabdbadcabdacdabbbbbbabbaddaacabaadcdbccdbcbdcbbcdaaddbdcadabddacacbbcbcdcbddacbcbbdababdccaabcdaadbadbacabddcbaccdabdcdcbdbbdbabdaabdadccaacdacbdcbcbdbabdcbcdcdcacbbaaacbcddcacbdcbddbaccadddddbabddbddbddcbdcbdbcabddbaacaccbbaddbdabbdbdccccadbcbacccbccdcaaccbccbdcbccbbbabcbbdbdbcdcdcbddabbddcdbbbbbddddddabbbccaacdadddcdababdbcdbabbdaaacaaacbabdaddaaccddabbabccaabdacdbcaddccaccacaadbcbccddddbacaabcddbccdbcadacddaadbbbcaaabbdadbcbdbbabdbccccaddbccdbcddcaadbbdcdcbcbbcdbccdcdbcdaddadbddaccbabcabccabccbaddacabdabdaabacbacdccdddcacbacdaacbbacdbbabddabcddaabdcacccbbbaabddcbbccccbbddbcccabddbdccaaabddbbacdbbbacaacdaddadcbcbdaabaadacbbdbdacbababcddbbcbcdcdaacdaacddbcdabdadbacddbbdadaaadcadbbddbdacacaddcdbcccadabdcdadcacbacbbbcabbcdaabbabccdddccbdbacaadbbaabbaaccabddcbaddabcbdaddabcbcddbdddccaacdacbabbacdadabdbadbcdbdbcaadbadcaacaacccbbdcdbccabadcabcbdaccdcbcdbcdabcbbbadbdabcbbacdcbbccdddbbdbadbdccdcdcdbcccdabbbacaddbbbaabccaddadbabdbbaabbdbcccaabcbdcaddcddabababaaabacbcbdbcbdbdadbaccaacaadcdcdbdadadbcaccdabaaccadcbcaaacbcddcccbdcbbbcddcbdacdbdaabaabbaccbaaccaddacddcbccdaabadbdbccddbcaadbcccacdabbdbbddcbacaddcbbbbaaadbcadbacbdbddcccddbbdcbccdaddbaddcdaddbddacddaaabadadacccdcaacadbcddddbbddadcaabddccabcabccbbbaaaadacaaadcaadabaaccaccdcdcbdbcbcbdaadbdcdcbbcbcdaccbdcbbbcbdacdbaabdaabbabbbdadbdbadbaaacdacddabcdcdbbacadbdadccbabcacddddbabcacbcdcbccababbabbbddabbbdddacbacdabbbbcdbaadcccdcbbdcbbdaddbdccaccdadcccdbdbcaaccababcbdcdbddddaabcbababadaababbaadbcccbdddabbbbbcabddadbcddabbdbdccaddaadbdcdcdccdbacabaacdddacacbdabbabdbaddbdddaadadbddbcddccbdadbbacabddddcaabbdddcdbdbcdadbcbdddcdbdcdcaccadababaadacccddccddbbccddcdabcaadababcbdbbbabdddddbddcdacadbabdbbaacbdddacddddcdaabcabccbbbdccdddadacaacbcdaccdaabccacccbddcbadacabacbcddccbadacbcadddcccdcdacccdcaaadbadcdbbbabcbdbbdccabbacccdabdabcccccddaabababbcdcbbbbddbcabaadcbabadcdcbbabbbdbddcbabcbbadaddaadcbccdddadbccdbbbbddcaaabdbbabadccacaddbbcddbacdbcabddccbbabbadbdaccbacababacccdabbabcbcddcbdccddbdcbdacbdcbddcdbcbcadabcdadbdddcaaacdaccdddbcaaabdabcbbcbcabadccacacbdcbdbcdccabadaaacaaaddccaabadddbbdddcccbbccbaacaacbbdcaabccccccaaaacdbdcdcdaabbaacbbacdbabaaabddddadddbcdddaadaadbbbababdbcaacbdbabbdbcbaddbbbbdbdcbbbddabdcdbccbcacbddcbbcccabddcbcbabccbccbbcdcdbcbacbbabdbaadbdbcbddbdcbcaaacbcadcbabdacbdcacddcacbbccccbcdbddccbdbccbaccccdbbdabdcbaaadcccacaccbddcdbddadcdbcdddcabbaadabadddbdcabaabcdbabbbbabbcdcdbdabbaaacbdddbbccadaadbbcbacaadadcbbaabacdbddcddbbacadbabdccbbacabcabaaddbdbacadbaaadbcbbdbbccabddbcddbcdbbbccbaaadbbbbcccdbbadddaadaabbaddbddddccaddbddbdcbbdacdcbddddcdbabcddddcbbbdadbbbbabcacbdabdcaabbddadaabababbdbcddbbbdbacbdcbcbbbddbdaaddabbacbbacbcbdbbbdacbdbdccabccdaabadbbccdcbcbbdbcababaabaaaddcbbcabdcbbadbaccccddbbdbdcadbccaaaddacbacbbdaddbdcccbacbcdcaaaaaddaabaacbcaccbcbacbcaabcdbdbcaacacdcdcabbdcdacbaccbaadcbabdcabbaacddcaaaaabbdcbdddadcbcbdacddbdcabbaacdbdcdaccabdcbaabacbcddbcdacbbddadbbaaccbdadccbddbbbbbacadaabacaabaaacacbbdabbabcabbbbaaddabbbdcddaadbbbaacbcbccdbacabdaacabccdccaadcaccbdbcddbadcdcbdbacccabdabaabaacdadaacbacbdcdaacbbadcadbbcddddadbcdbabacbddbcccddbbdcccabcaddcbcdbcbcabadabdddbdababacbdbdcbbabbcaaaaabccddbcdadbbcadbddbbbbbbaaabbdcabbdcdbbcaccbcdddbcdacbcbaaadccbaadbcdbcacbbbbbbaddcbcaabadaccbaacacccbaaacbbdbbbcabcbccadaaadbccbdbadbbaabdbcadaddbbddacdaadcdacccaabccabccbaaacdcccabcdaadaadbbadadaaabdbbbacaaaababdcdbdbdddcccbdabcddcdadbacddacddadddaacaacdaaabbdcadbdcddcddcaccbcbbbcbddaddcabbdddabdabdbcbaddcddbddbddbacbcaacdcabcacdbcadbbcbbddbbcbdccaccdbbbcddbabacadbccbabdbbacdcacbcdddcbabbbabcbcdadbccddabaadccaccaaaccacbacbaccbccabbdbcacaccabcccacadadabbdccbbdbbccabbdbbbcabcbaadccadcacbbbcbaacdabbdadddabdbdbcaacaddbbcdcabacddccaaadbbdddbcabcaddccdbaaaaacacdddacdbddaccdaaaaaccccabcdbdbacaabdabdbcacbbaabcbcccbbbbbaacddddcaaacbabbbdabaaaddabbcbcacddcacaabddcaabbdcdcaaabdaccdabcdcbacacadabaabaabdbbcdabcdddcbdcbabadbdcbadccdabccbaddddbaaabbcbcddbacdcabcdcdabdcbbcaacbdccabcdbbcdbacabbaadcbbbbccbddaadccbdcddcdccabaacbdddbcabcdaccdaabcdbbbdbcdcccbbbaaddaacbbbbbbcdaaadbdadcdccbccdcbcbccdcbaaabacbbaadbccddbcaadcaaacbabdcdabcbdbaaaacdcddcddabdadaacddaaaabaadbdbccdbadbdddbbccccabcccddaaddaaaccabcddbdddabaacdaadbacaabababccddaabdbcbcbdccdadddcaacbcdcbadbdaabccdcbcbcacaddbcddbcbadccbabdccbbaaadccddabcdabbccabcdadacbdbdcaaacbaddaadadddddccbbbdababdcccacdadcdaddbabbabdaccdbacdaaabdcacdcababbbbdbdddbadcacdbbdbcacbcdbbaadbbaabdbaabdbbcddabaabddbbbbcdaaadccdbbcdbdabcbcadcadbabbbaccbdbddbbcdaccabdbddbaccbcbbdccdcbdadbbbdcbdadbbabdabaadadbcbabaabcbbadbccddcccdbabcdccaaaccbbcacaaadaccaaccbccacaddbddccacabccdbdaabacabccacdcabbcbaddccbdaacddaaaabacdcbccbcbdcbbbadbdadcddaccabbcbdddbcbdccdbbacddbdcdabddbaacbaacdaacdbbaacabdddddadcddababdbabdbbaacdcbcdbaadccccdbcaaaccdcbdddbacdbaccddcacddddddcbacdddcbbbccddabcabacbdcaaabcaddadcaddcaabcbcacbbcbdbcacabadaccdadcbbdbdaaccacadcaddcacdaadababddacbcdaadadacdaccbadbaabdbbcbacbacbdcdbacaadacbacaaccaacbbcbbdaaddaacdcbaddcbabbadcadbcdabbadddbcbbdbaaaccbdadbbbaacbccdcbabbcbbbdaddddacadddbaaaacdddbabccbcccdbcbacdaacbdcccbbabdaaaadcabcabcdbcabcbbdbddbbcaaacdaabdddacaccbbbcaabaaddbacddbbdcdbbdddcdbaaadbcdbaacaaacddabaabbadbaacadababcabbcccacbbaabadcbadcccccaadbcaabdcaaadcbadababccbbdaccdaacaccbdacabcdadacbcaabadbadbbdccbdbacadbbdaabbcacbadcabdccabddcdcdabaadbaddadcbcdaabbbcaaccaabbddcabaaddabcadcdddcdcbcbdbadcdaddbdbabcdcccdcdaccdcbcaaacbadbacbaccccbacdaaaaadbcdadcdbaccaabcdbaaccaacababaadbbbbaacbddcdbaaadacbcadaacabdccdcdbaaaabbbbdababcddaccabcbddabaadddaadbcabbcdccbaddcabbdaccdcccbcacaadbdcddaddaabcbddddbcdbababdbaddcbdbadbcbdaccbcdbcabadbccddadbdabbbcaacadddadcdbcdcbcdacccbbcdaaaaaadbdcaaabcacbcbaddbdcdaddadccabcddaaaabbaababddbdacabbcabdccbaccdccbbbaaadcdaaacbaadddcdadccabdbadadbbbcbcdabdddcbdcbaccbccdcabaacbbbbadcacadaaabcccdcacaabacbbcaddcdbdcddabcdbdaabdaaadabdabcaacbbddbbabcddadaddbdbdddadccdaadbdddbdaadddcadadbaabbbdaccaadcbaddababcdccdbbbabaadabcaaaaccaacdddccbcacadacabdaccbdaaabdcbdbddccbcadccaabddbbbddacddabadcaccacdcbacdaaabcdbadcbddcbbcaabcddcacbaaababbabcdaaaabdacdddcabddaddccaabcaabbabbbcbdabddbdacabcacdadcbccbdbccabdcbbccbbbaaddabdcddabccdcbaabcaacacbbababccbacaadcaddabbacbbddabccabcdaacaadcbdccaabbaaabdadcacddccdbaabaccccccaaaddcdacddcaacaaacccaacdaccadbcdbcdcdaaabcabbdddcbdaccaddbaaabccbbbcbdbddcdabdaccbdbaabcdbdddcaccdabcacabacabbdadccdcbabdbcbcbaadddabcaccdcbbdabbcaaccdddccaacdcdcbcdaacccabddadbddacacdddbbbadaddbddbbcbbbcdcdadcdccbbddcdadbdaaacbaaccccaaaabdddddbbadcdaaabbcdbaddbdabddcccaabddabbccabdabddadbddacadadadaaabbcbdbcbbabacbbbddddccbdaacacdbcadcbdaadcddbbdddcdaaaabdccbbccbdadababbbbcccdbacdbcbbbcaabdbdaaccadbbadcddaadaacbacddddccbadbbcadbaddabcbcdcabacbbabddccdddbbadcbabacaddbbbcddbcdccdcbabbddabbdbccabcdaccdaacacadaacdbdaacbacccbdadcdaaabbadbabcdccadaacbbcddaabdbcccddadbcdabaaabaddadaaccbccbbbadbaddddbabaccddddbbbcdbdbabdbabdbacaaccacdabbabaadabaccdaaabcabbcaaacbadbbbdcbaddabbabadadcadaaaadbbbbccacbbabcaddbddcaddbcdbddbaaadabbccabacbcacdbbccabaadbadbdbabbaabdbadabbbcbccdddddcabaaababdabbbbaccacbcccbacaacbacdbdbabdddacdcbdadddddcacadbcbadbaacddbdbdbaaabbaabdabcbcacdddbaaaacaaabdddadcacabbacbbdbbcbcadbccaacabdbaddcabadcababbbcbdaadccdbdacbddcacdbacbbcbcbabdcbcadbcbbcdaddacdaaddbdbbaddacbaaccddbdabcdbabbbbbaaaddaacccbdabbdcadcdcddcadccacdbdabcbccbbbdcabbdaaaadaddccdccbbccaddddabccbcacdadbacaacdbacadbdacbcdadcdcbcbdbbdccddadacadabcdaddbcabdaddbdcccabdddadcbdcaadddcdbdccbabbbbbddbdbbbdcbbcabbccdcbcbaacabadccdbacaadaddbcababdadabcbdbadcaddacbdcdacaacbaccbabccabbaaaacbbacadabbbdabbdcdcbbdabdbddbaabdcdbadcbdbabcbcaccbdddcccccdbccbdbbddcdddbcbbdddcadcaadcacaabcaddcdaabcbcbcddbacddbcaadbcddddcdcbbcaccddbddcbdaacdddaccccdabbbdacccbbadbabdcdbabccccdaaabcbbddbcadbdbbddbdaddbadbaccbccdbbbaabccbabcabcbccbdccbcbbbccaadbdcdbddabadaaababbdcaccdbabbabbacddabbbbbddadbbdddaadbbaddbcadcabbabaaccbabdcaaadabddbccdbcadbaaaadcaabcaaccaaacbbddacbbdbaacadaccdddcaabdbcababbbacadacddadcaadacbdbdbbadbdcabaabcccbcbbbbcdcacacddaacdacbbabacabcbaddcdbadccdcaadacbdbccacbddbcbcddbbdaddbcdadbdcccdddcdbdacbccdbaddabddddbabcacaddabaadadabdabdbdacaaaaaababaabcdcacbabdcdbacbaaccadbdddaabdbbcdddccbbaabdcdadaadcaacaacdaccddcdaaccdcdabbbbcbbbbdacadaaabdcdddbcdcbbabdbaddaddcaddbbdbbcabcbccaddbccbacdbdbdabbcdcadddcaddcbcbdbdaaacbcbcdaaaddccacccdbcdcbccaaccaddabbbbbdbadabbacdccccdddbbabcadaacbadddbabbabacadabdcdddcbccabdddbbdadcaddcccddacbbbdbaddaadcdddacdbddaabaabbbdaacbadbdadbdbdddcdbbdcadabddcbbaaadcdbddaadcbacadddcdbdbdddccbdcaadcbadabbabcccbdbddadabddcadbacacbcbddcaadddddaacabbccbdbddaaadaacbbcddaabadabadcaabbbbacdcdccbcbdaaccabcbcadccddacbdaabdbcbdbbadabdbabacdcdadabadbacbbddacbddccabdbcccccabacbbabcdcacacccbddaaabaccacddaccdbaccddbbdcacaddbcdccdaddcbbbabddddccaacbdbdadcbccdccacaaaccabdacdcaaddddbddcdababbacdcbddcbcbbbcdcdcbacacaacdacadaadcccbaabcadabdbbaabdbbbdadabacbcaababdcddbcbbabccdbbcbcaabbdbcdcbaddaabbababbdccdbdcabcabacadccbaababbacacbddbccdabcbcabbcbaddaabcdcbdcdcacaacdcbdbddbdcaadbbcaddcabbaaaaddccbdcdadaacdbcbcbcbaabdbbddcbbacabbaaddbdddbccdddaaccdbbaaadadcbcaabbcccdccdcbaadcaaddcabbdbababdddbaabbcddcdbcadbcabcdbcbdcbdaadbcdcdaddaaaaadcdcbbabadcbbbbccbcadaabbbdcdcdcccaddaaacbdaadaccaccdcdcbcababacdbdacccabcaadcdbdabcbadbdddaddbaaacaadbdcacbbccdddcddcacbbababddbccabaaadcdabcccbadabcabcdadadacddddabcccdcaabdaacacddabdccccdabcacadcbaaadbcbaddcbddaddaddbdbdabdbccaacabaabcbabbbbbcabaccaaacbccaddbbabdacbabaddadabbaabbbdabbdbbcbdcbbbcdddacadcbbccddddddcbabdbacacbbbabababcdababbcaadbdbbdcdabdbcaabdddddbbccdabddadbacbdbbccdcdbabcddcdcdbbdacbddddbaddaadbbbabbdbdccdcdbacbdabcaadbbaadbdabddaaaccdccaadabccbdbacaccbbacdcdccbdaccddbbddbdcabccbacdbbbddbddabcabacdcbacdbdabdbcbacbbabadacbcadddcbbddacbaabaabbcabcadbbcdadaaadcbbbbabcbcddcaaadbacbbdcbbcdacbaaccbbdcdbbcaacbbccbccabdacadbabaddcbbaadddadcabdabcacacadddbbdadbddcabbdcaaabdadbaccbcbbadaccbacbdacbdaccbcbabbcadacdcacdbaabdcaabbcacbcaaaccbccbbdadbbaaabbcdcbcdcdccbcbcbdadbacacddbadbbcccddbcabbaccddcbddbdbcdcbacbdacbbbccddadbbcbabadbacacbdaacaddbdaaccaadcbddabbababbbcdbcdcaacddcacbaacbbbbbadaadbdcbdcdddddaacccbbbcbcbbaaacbcdcccccbaacacdbddbbadbbcacdadacddaaddccacdbbbcccdaadbcddcabadbcabcdbccbccbabadbcabdccbdbcdcdddabcabdccdcbbbadbaadcadcccdbcaaaabcdbacbadadcaabbaadacddacbabcdabbcabbcdbaccbdaaddcbddcdcbdacdbcdbbcabbbcddccddabbcbbdabbacbbbaaccaaddbacabdbddbaacaddbcacabbbaacdcaccbddbadcdddbacabdcadcbadcdcbdbbbbaabbcdaccabaccaddcacabbdacdbdbaccbbacabdbcaabbadbbbcaddbdcddaaddcbdcbdcabacabbdabcacbddbccdddbdccbadbadbbcbcadacbaccdadabdaacdcdbdcdabcadbbbcbabbddbcbabdcbddbadbdaccacaddabbcdcdabacbdcdcacbcdaddccdaabccdcbbddcbdcadcacacbacadaccbbccabcacdaacacdaacccbccadabddabbcaadbdbddcadadcbcbadcadaaccccbcbdcbbcdbcdcbbadccdbacadbacbabaabdcacdddaccdabdabbcabbbbcaadcabbbbdddcccdabaacadccabddadddccbcadbcabbadcbaddccddacdbbdbcabdbaadadbaccddadbdddbdcabcdadcbacccacbadaaaccccdbdbdaaacdbdaadbddbabddaabcbbcccbccabbbacadacbdbabdcadcccadcdcadabdbdcbabaababddbcadaadcdcabdbdccbdcdccbcbcbddbdccaccbcdacbcaaaadbadccccdcdbbcabaccbbaabcbdaaacbbbabdcbadababaddbcaaaacccbdddaddcdddbacbcacdbbcdacbcddcddcbadbbddaabdcbaabadacdaccaacbcdababaddaaacbabbcacacdcbbadbbdabacbdccbaccbdacaacdcddccadbcbcdcbcaabdcacaacdcbbadcdabcbaddacaccbcbcdbabadbadbabbadcdaacbadadbacaadcdbbbabdcdddacbaacbddcccbbcbacdabccaabdadcdcaadbdbcbcdaababbbdaddbbdddddabcdadabddbcbdabdadabbdbcabacadbdbbbcdacbcadbddcdbaaadbddccbdacccdadcaaadbccddddbddaddbdccaccbcacbdaaaccbbaabcdbbcccacdccabbddcdabcacbadcddcddcbdadbdcbacdcccbacaddbcacccadbbddcbabbdcccddadbcbbcdaaadccddddadabdbacdadaadbbadacdaabbdddbddcbddbbbdcccbddddbcddacdccadacaabaabbbcbdabcbacacdbcccdaaaadbdbdbcbddaddaabadcadbcadbbcaabcccbcdabdbddddbdcacddbdaabdbdccabbbbaadcadacaadbcdbbcccccdbabdcabddcdacacddbadbadbcdccdbccdacdbadabbcdbdbaabcbcadcbcdaabbabdcadaaccbacbdbcaaaaabadcdacdbbbabbcbccadadacccdcdaadddaadaaabcadbaccabdbbdbbacbdbdbabaabadcabcbbbdbdcacbadbddacdbbddcbbdaacccdaddcdbcbdcbacaacbadcaccccccdbaadabaacabcbbadcddcadbbbccadbdbabcdddabddbabacbbaacaadbbbacdbcabaacabcbadadaaadaadddddadcaaabcdddcaccacbbcbddaaccbbddbaaaddadbdbdabbdccbcdabbbabaadabcccddaadabbbdbabbaaacbbadaddbabbbbbabddbccccacbaacccacaadcddadcbdabacaabdabdcaaacbdddddbcabbdcddbcdacbdadcdbbcacdcbdbdbcabdbdddccacccbabaaabbbbaddbcccdbdcacbdbcacaaabbbdcdddbdcaadabcccbddcadcbdbbaddabccbadadabcdcadcbaabccccaaacdabbcbcdabdbbdbbdddadbadbdadcaadabbddccdbccaabacdbdbcadbbdaccaabcabdbaaddddaccbdbbbdaacbdcabdbdcabccccababadaabdddacbcbcbbcdcaddaadcabcbcdcacdadadcdddcaccadbccddaaadcaaababdcddacbaadcccabdbdcdbabcccdcaadbcaacabacccabcbaaaadabcbcbcdabbcacdcbbdcdbabbcabbbacccdcaddaaacdcacabccdaacbbcaabccaaaccaadcabbcdbadbaacdbaaddbbabdbbabcddacbdacbacdaddaccbdbbdadcdcbaddbdbbdbcacddcbaadcdbddbdbadaaaacabbbddbbdcacacbdcdaaacdbccadcaccbcdbacabdacadcbaadadcddabbdcbbbddadabbabababacaaacbcddaabaabbbacbcdcabccdcdbbdbbcdccccadacdbaabbacdbdacbdaddabdbdccdbbdabdbccddaabddbbcdccbbbbadadabbddaabccadddacdddaddaaaaadaacdcddccccbcadddbaaababaaababcdaaacbbaddccdcddcdcdbaadbbdabacdadbccddddcabbdabcabacadcabddbcbbddbacaccdbcbbabdbbadcdbcbcddbcadcbdaacbbabcaabcddccacdcdccbbbccbabaabdbbaaaddaaccbcbcaddabbaadbbdbadabcbccbccbddcbbbacdccdddbadacbaaacabcdddcabaabbcdcbdcdccbcbcbaccdcacbbcdaacadbbddcacadccdccccacdacbdccdbcdbaadacaaccdcadccabbbdddccbbdccadbccababbbabbadcadacdcaadbdcddbaaacbcacdcabcdccabacbddabcdaddaabadaabccddcbcdcdbbacadcaccbdbdbabaccaadbadbbbbdcbdbccbdcccbaddadcdbbcadbdaadcddcbdbccdcccdbccdbccadadcbabcabbddababdaaccbbcccdacbbbabcdcdbaabcddbbbccbabcddcbdbccadbacaadbdbdaccbdbdabddadaccaabbbadcdcabaababddbbacbbcbbbdccaccbbbdccdacdcdcdcacdccbdbdaccabbaccacacdaabdcccccabbacbacaddbbcaabcccdaabbbcbddccaccadacaabaadcdacbaadbdadcbccacbdaabcddcacbbbbbadbbcdcdbcadbcabacbadcccabadddcdbaaaabdadbaccaccdddbcdddbccacdccbbddababdacddcdbcdaacacccbbdbddcacbbbccdcdbcdcbcdccdcacbbadaadddbbdaccbbaacdaddaacbdccbaacbddacabbbadbbdbdbcdbdcaaddcddaadacabaadcababbdaabacdabadcdadccbbbdaabbbbdaaadddcadabddbcddaccbadaaddcdaabcdbcbbcbdcdcabacadbbbdadadaacbbbbdcadcacdcadbcadbabcaacdbacdabbdbdcccadbdcccddccaccdccbdbcddacabddbcbcbcdccdcbbcadcddaddbccaacaadbddadaadbddadcdaadabddbaaaabccadbdadaacdbadcbddcbcbbbdcbaadddcddddbadadcbdaabacbcacbcccadabcdcabadbaadbadbcabdbbdabcbcbbbadcbbbbadbbcbabcdbbdbccdbbaabbacdadacdcdaabdabcadcbcbbbcbcbadcbbddaccaabbbccaadaaccadcbcbcdcacdccbccdbcaacabbcccabdbabbaaadadbbdaabaacdaacdaaaacbabccaabaccbbaaccaccbdddadababadadaacdacccdbdbdcbcdacccabccabcbbdbcddabdbaccaacddbacadadcbaddbdcaadabcdbdabdddcddbacadaaccbacadbabcdcddbdadbdcccabadbdbcccbabdcbbdabcacadadadacdccdcdddccdadcbaaccbdbbdbddccccaabaadbbaabccdabdbdcdbbcbbbabbcaddbbcbdbddddcdcabbcdbdcdcadddcddcdbdccbbbbbbddadabdcbddabababcbbbbdaddcdbadabdcbadacddbddaababccdaccaacdddcabcbbbadbdbbddccaabadadcddabcdadbabaacdbccbaaadabdcacbdacdabcabbbcddcddadcddcbabadabccdcddcbbcdbbadbcabcbaabdaddabddcbcacddbccbadabddacddbdccaadcbbaacadbadaadbabbabcadddacdccadddbaccccbbbdaadcbccabdacdccacdbcdcbaacdabcabdbcddbbbaacdadbadcdbdabdbddadcdccdcacdddcacdcbbaddbaacaabcbcdbdabcaabacbadbaacbbdbcbdabddcdbadbaaaddbbaadbbccbdddbcbcbcdcadddcccabdaccdcccbbacbbbcbdcccdbdddaadccdabadacbbcccddacacbcccadbaaaabdbcbaadaccccababbdadbcccabaaabcbccdaacdaaadabdacdadcddabadcbcbacbbdcbabbcbdcabbabbbbbaccccacdcaaabacbcacdbcdbdaaacacbaddccacaaacdbbcddabaabcabdcadabaaacdddabbdbacbcddbacccacadbccddcbdcdbcbbadbdccbdcdcccbdabddacdddbcdaadbcccaababdcadcbcbbbabbcaacaabddcdccadbabbbdbcccaacbddabddbbdbddaabdacdabbbaddabbabcbaabddbabdacbccbbcabccadaadbcabadddadcdcbabdaaacaaaddacaddacaaadcbadadcdabaaabacabdcbcdacdbcdbddccaabdaadcdcbdbbdabdacaaadcadbddcbccbadcbbdbcdbdbcddabdcdbdaddccadaadadabcacaacccdccccccccdabaccbacbccbcdaadcbcabdbdcdbdaabaacdcdcabdcbbdacdadbacaddcabdaccadbaaaadbdbdddbddbbcbabbabcacdcadaacbaaacbabbdbccdaddadcbacababacddabdbdaccdacacbacccbaccbdcbddbdcccccdcdbcbcddbdabbccbcddbbbdacdccdcbbdbbddcccbdbaaaadbcbacbccbbadbbcaaccdccadbdccadccbbbaaadbdccccabacdcdbdaacdddbcdbcdcbbdbadbcdbaacbbcbdacbacbbbabcbccbaabdbabddcdbdddcdbbddaaacdccdbdbaaddccdbdbbccadbcbaaadacdbccbcbabcaacbababbdaaadacbcbbacbdbbacacbacddbbccbabbccddbdbacbdbcdbbbadbddbdbacccdbbccdbacbaaadcdcbccdbadabadcaccccddcbcdbabcbcbadcbbbbdbaddaaccbbadcddcbbdcdadaacbdddcdadadbccdabcacaacdcbdadcddbbcbdcacddbdacbccccababaaccabcaddbdcadccbbbbacdddddbbdbdbccacdabbcbcdbaaacccabbddacaaaadbdabcbcaababbbdadacaaddacbdbccbacbacbdabbabbaccddabdddbdcdbadbaccccdbdcddbdcabaacdbcccacaabdcacbcacdbcbaadddbcabcdcabaadccbaabdbadcdabddbcacbaacbbdaddcdaadbccbbabcaacdbbcaadccddbbabdbaccabdcddcbacaacbbbcdcdadaccccddccbabbcbdacbccaaacadbdbabbddcdcbadbddbacbbbbcaddbcbcacdbbcbabaabcabbaadbddbbacdddddcbcadaacaccdaacdddcbadbcabdabbaaadacdcabaacdadaccdcbbacaacbaaddbdaabcccbbcbbddbacccadccacadcdcbcddadcdbbabcacbaabdbcaabcadbaaabcccaacdcbaaabacaaaddbccbccdadcbbcaccacdbccccbaaabcbcbabaacddaaaadbbcabdcaabbddaabdddaddcccabdacddaadaccbdddabacbbaccdacaacaabbdbdabcaddabcbdbbacdbcddbdccdbccdacaccacacdbdbcdacbbdccaacdbbcaadddbddaaabccaadcdadbacbaaadcbcdaaadddbdbabdddadcdacdaddcccadddcbbdacbaabccbbacdabcbdaabaacaabaaabbcacdcdbbdabcddbcacabddadddacbaccdabadabcacbacbdbabbcdabbadbdbadabcbbcadbbcddadbcabcddcbadcccbcacddbcbdcdddddbcbbdabccbadabdbccdacaabcbdaaccacdddddbdcddaddbcabcaddcdabcaccdddbddaddaddaccbbbddadadcbbdadbdccbbdcbbccabbddbbaacaadcbbdcccbcbaabacddcddcccdcbbcadddddcbaacbabddbacacadacdadcccdbadcdaaadabaabbdcbcddcdacbdbbbddcaddaaacdbbaaaabbdcaacbbddadbadcdcccacdccccabdbdaabacabbabcbdcbcbbbdbddacdadcaaadabdadaaaabcaddcdacbcbddccacacbcdcabbddadbdcdacdacbcaaddcbdcadabadbcbadabaabcadadbaadaddddcbadcaadbcaaabdbcbccdbccccdacbaacabaadbdbdbbbcadcccadaddbcdcbcaaacbbccaadbcbdccadcddbcbccbadaaabbaccdacddbdbdcacbcbdadddcddcaacadbccbcccbbadabcbdaabbdcaadaccbadcdcbdbcaddaabacbcdcddbaddbabccbcbdbdccdbbbdcdacbdacdcbcbbdbdbdabbccdacddaaaabcaadaadacbcbbabccbbbdbcabaaacabcccbbbbdabacadbabdbdcdccdbbdabcaacbddcbacddbdcadbaabaabbacdddabcbbabadcadccdadcbdadddddddcaabbacbddbbddddaaacaadabddcbccdcaaadcdbdbabddbcbbddccdccddbdaddbbdcdbacdadaadcbbdbabcccaccbacbbdbaababddccbcabdcdbccaaadccbadbcbabcccabbaacbcacabbdaddcacaaaabdabcbdcbaabdbddadacdaaabababcabcaabadbcacbabcbbdaddbdbabcbcacaaadddbdcddcaadacaaadadacddaadbabcacdaadcbccacddadabadbbbdbdbbcaaabdbdccacccdabdbacddbcdcdaabdcbabcbadaddcaddacacdbddbabdddcadddddaaccacbcadbabbacccdabacdbcadacbdaaccaadcddcbccbdaccdcdcdcabadcddddabacadbbabcddcbdcbcbcccbcdbbcbdbbccaddbdcddaacdbbcdbbddacccccccadddbbddaccbbdbacbbdabcdcaaddccbbabbbaaacbaaadcdbbdccbccbdaaccdaacabdbbdddabdcaadbdbdaaadcccdbcbccbaaadaaabdddcbcaacaacbcaadabcccbbddaadcccbadcbdcadcbbacbddcbcbadbadaaddcbbbcdaacbacbabcddbcdcddabadaadadaaadbdbaacddbddcbbdbdaaabbdadbdababccdbabbcbdbdddabbbcdcbdbacbadcbdbaadaabcdcabaadbcaddbaddcdcbdbacddbacddbcbddadbbcabadbbbccdbbbccbcbacadabaaccdacdccdbabdcbacbbccbcdbdcabacaadcbcddcccddcbbaaaaacacaacbccbbabcaacbdaadbbacbbccdaaccddcbccdaaabbcbbbdbabbacdabaadbdaaddbbaddbccdcccccdabaabcccaadbbdaaadbddcdbdadbaddbabbbbabdbcabddbdcbbdddcabacbcbcadacbbacccdcadddcacbcbbcbddabddcdbcaddbdcbdccddddcdbdcacccbaacccaacaddadbcdcabdbbadbcdcbaaccccdcadcbcacbacdddccabbddbbbbaabacbacbdccacddcddbbbaaaacacacbadcddcdadddbadadddacaccccadcaacdbddbcbadcacdbbababadabcdabbcbbccbbbccadadabbbbccbcdbadaadcddddcabbadccdcaabadacbdcabcbddaccccbabbbdaabaaadcdbddddbdccdaacdcdbddabbbcbdbabbaacdcbdbccaccbdcabbbcccdaacaadcdacaabacccccaabdddbdbccbdabcbabcbdddadbbbdddccccdcdadbcdccaddaadcacadcdbbcddddabbbbabcddcacbadacbcddcdbcccabdbbdbbbcbadaaccadcbacaadcabaabbadabcbcdccacbbddbbbdcabbadbabcbadddcabccdabbdcbccbaaddddabaacadbcbacaccaaccacabccdabdaacadbbcdbcaaaacbdcddddacdbbcdbcbdcaacadaaddabaacbaaaadacccabcdcdadaaadccdcadbacaacadabccdbadddddbcbbbbcdabadacbcaacacddcdddabbddcacaaabccccbbdbdddbcbcaaacbabadbbcadaaacdccadabdbabdbcbcacbbbbacacbbdaadaddbcacdbdbbcabacdccdbbbcaccdbaadbdbaabbadbccdacccddaabccbdbabdbbcdcccdaacbbdacbddcbdaaadaccdccbcbaaddcbbbadacdabadcdcadaabdaadccbbbdbabbbdaddcbacddbcaaddcdbaddadcbccbdccdabadcaccdbcabadcaadbbdcbcdacaacccccbccacdaddbcbccbdacacdadcadddcbabacbcadcbdcdacccdcddabacdccbbdbbccbabcbbbdcddddacbbdadbdbcccbbadbaaccaccbadcaddbdaabbcbadccddccacbdbaaabaaccddcbbabcbdbcbddabaaaccdcbccbabbadaaadbaacbbdacccbdcbcabaccacdacdbadcbcddbabdbbadcacddcdadabdbdabdbbacbbcdababdddacdbaacccacdbdddccababdbdbbccbcdadddbbdbbbaabbcacbaabcbcbcacdbaaaccbbdbdccabccdbcadddcbcdbbaddbbbcacbdacbaaabbbdbcdcccbbcccacbccbbaabcabcddbdbcaaababcdbbabdcaacccdcaccdbcccbdccdacdcadddddbbdddddbadcaadaadaaadcadcdddcacabadaaadddcababdacbacbbddcadbacdbacdbabcbdacbbcadcdbbcbdadacbbdbbbcadacacccadbcddcbdddcbcddbcacabccabdcddbdddabacccacddadcacaabcbcbddbabbdacbaabcdcdbabdcbbcdadaaadadddbbacdddabddcddbbdababccdbcbcddcaccdaabbadbbabbbabdacdccbdddddadbddaaadabdcdacccdcbadccacbdddbcbbddaaddababdbccdbacccacbdbaddabacddadcdbcacbbbccbddcbdcbbbdcbcaaccbdaaadbcccababbacadcbcaddbddbdaabaddbbcadddacacadccabdbdbadbdacbbaddabddabcbbdaaaabbbcaaccacddabbcbdaddcbabdbaccbcbcbbdabdbadbbcdbcccddcbbbdaacadbacbbdcadabcdadaabcaaabbcaaaccacddbcadacbdcaaccccbbbcdabdcdcbbabadbabacadaacbaabaccbbdbbcdbabcacacbaabcdcbaaadcbdbddbbbaacadbddcabaadcdabaabadacdcbcbabacabbcddcaabaaabbcdbccbbbcadaaabaadacddddaacacacacaddadaaddbadbbcbcdabbacbdacbcbadadacbbdadacbbddbaacbddccddcbbbbddbbcabcacabbdabdcbbdabbbcdbbddcdaddbcdbbbcacddcdddabcbdaabcbdcbbbadbdcdabbacbadabccbbbaaabbabbdabbabaabbdbbdabdcaddcdccccabdcaaddaaddacaaacbbbdaaaaacacddacdcabbbacdbcaacaddcacddbacdbccdbaacaaabcdbdabaaacbcbdaaadaacbdbaacbdddabcaacbdccaaadcbdadcbbcbdbcaddbcaddddaabbbbcaaacddcbadbcdbcaabcccbaaadaadadadcbbbaccabadcbdacdabbdadcbcbdacbcdcdbccddbaccbacbbcadacadadbcabbabbcdbbbbcaccbccdacbdddcaccdbbbbbadcbbddcbbbdbaaddcacbabccdaddaddbcadcadcbbbcbaadbbccadadadbbbbaabdbcdabcabcbabaddcadbbdaaacbdcbacbbbdccccddacbacddbdcbbcaaccbabddbdccddcbdbdbcaddadccddbdccacccccaabccbbcccbbcbbcdabccdcbdbbccaccdabaadbababdccbcddbdcbcccacabcdbbdcabadbcaaaabcbbcddccacdaadcaddbaaccadbbacccabccbadcabdccadaaddabdabdccabcbbcbbcddddacadbdcbacabacaacaadadccabcdcaacbddbbdaabbcababdabbaccccabcbdadbacccabdbaaccbdabccacdabbcddccbacadbbdbabdbbaacdacccddbaaddabbaaaaadbadadddcbbdddccbdcaccacbdadbdbcabacbccbacddbbdccdcdbacbbdcdbbacccbbcabaacabbdcbbadbdbbddbccdacbdaadcbccccaddabaddaacdadbbacdcbcacbccaadadadcadaddcabdccaaaababaacadddbabccccacadbacbaaaacbcbaabacbdacbdacbaacdcdbadcdabacbcaaabccbaaddbacaacacbbbbdcddacdcbdacabadcbdccabdcbdcdaabccdcdccdbccbcacabbbdbbdcdbabbccdaabcddbddcbbaabdbaadbdabadaaadddbcaddabcdbdadabbcbbbdabdaacaadbdbadcccbcddabcdcdccabdaabbccdbcdcdbdddcbdccdaabdccadacabdddcbaacaccccacaabdcacdaddcacbdacdddadcacadbbcdbbdcbadcbdaddddcbbdabacbdaccabdccdbdcababadbddddbdaabcdadaaaabcbacaccdabcdbbccbbdaaabdabacdbabadddbbacadcbdcccbdbccbabaddbbdadbdbdcbdbdaaaaddcdddbacddbaccdbbbadbbbcbbbccdcaababcadbbdbdabbbddadbbdcddaddcdcacdbdbcbabacaadcdacacabdbaaaddabbccccaaaacddbabdbdbacabadcccbabcaabddddaacadbcdbbacdcdacdcaaaabbbcbcdcbbdcbddcaacbbdddcdacabadbdcadababaabcbcdcdabdaccabadcabbcabbccbbabbdbbdcabbcadcdcdbacccdbabadadacbaaadbdaadabddcadbddacdaaccddcaababcadaadbcdccabcbbbacadcbadbdbddcabdcbbbdadaadcbcbacbdbbbbdbbbabaccbcdccbdbbbdbcbbdccdaddbcadcadacacacabbbaacacaddaaacdcbbcacaccccbaabbdacdcccccacabdcbbabdbdbdcbaadcccddaabaabcbaacbdcbbdadbaccadcbdbabbdbabddbbbdadcbcaccddabdbbaadabaadcbadaddabbcbdbdcdadbcddcadccbaccbbcbaaabdaadcabaaadccdadaddabdbcaacbadbddbdbbadbdccddddbdcabbcbddddccbbacddbcdacaccabcadbbbadabadadadcabacbaadcdbcddacccadbbbcdbcdadacaadbabdbbdcaaacacbcdababaddabdcccbccccdcacaaaadccbdddadcddcdcdcbadaabdcadaddaddddcbdbcaddcbdccbbbaacbdacadcdcdbabbacbdccabbccdcbcbbcacbaaccaccadadcaccbabacdaaccdbdbdcdabcbccadbbbccdddbaabbddacbcccbbbccacadabdddddaabcacbddaababacbccddccadabddacabadddbbbabcbacdbaccaaacbccdcadadabbdcddbcacacabaacdbccabcddbcacdadacadacdbccccbddccaadcbcdbddadaadcdccaacdbbacdabdcccacababccbcaaacbcbdacadcdacabbbaddcaabcddbcddabbcdbcaabcdaccbdcbccabdcbcbccdcdacbccdbdbaacbaccdbbadcadaaaadccdbcdaaacadcdbcdbaccbbdddbcbbcbdacbcabcaacacbdadadccabbddcbddbaabababdcacaccabcdabacdabddaccbddcabdbabbcadaacddbbbadaacbabdabcaccadccdcbabddcbcdcdbccdbbddcbcadbabccdbacaccbbccadcdccddabcbbcdcccabaddddbcccabbdaabbbcdcaaabacbbdabcbacdcaccdbabcddadbbacaabcdacdacadacabcccddbdccbdaddddadcdbabdcbcbadaadacbbdadabbddadcdcababbbcbdddbccadcddbacbccdccadcdbdaabdccccbabdacadddcddcbdcadbccacbbadcbdbcbdacaadccabbcdccdcddbdddaaabcaabdbbdcdbacacadcbdacdddcdddbdbacbcbadbccacbdacdbabdccabcadabadbadcbdadaabbcbbcacbbbbcbbbddcadadcbcbbbaccbabcabbcccbdcacaacddcdbabdbbdbbddcdbaddaadaddcbdacacddadaabdaddccaacadaacddbdacbadbcdcbcddaadbaaddddcbadbaacdbabddbdcadadbbadbabcadcadbdcacddcbddcdadaddbdddacdbaacabaacbdbdcdddbbacddacdcbdccddbddcdbadaabdabbcbcaccadaccababaabdbbacddadddcbcaaaacdbcdccbdbbcabbddccabadbcbccddcdacccbbcaabaddbcacbadccaaadbcbdaddcbccabcabcbabdcbbcbddabdbbcdcdbaccccacaaacabbdacbdcbabaaddbbbbaabcabdaabcabdcbbdcdaacbdadadbcdacaaaacadabdcdacbaccdbcaacbbbcbabbbbabadbbbbbcbcbacbabcbcbbddcdadcddbbaadbcacbcccadbbbadabccaadbcaccbcccccbbaabbbcaaadcbabcdadacddacdbdbddcbaadaaaacbccacbbddcdabdacddddbabbcbcccbbbaddcccddddacdddadaadbdcbddacdbababbbbdbcadbadddddcdcdddbcacddaddcddcbcabdccbdcacdbdbddcaccbacbbcbcabdaabbdbcbacbaadcaaccdcaddcdaadababcdbddcbcccaaaaccdcbaadcbdbbcdaaaaaacadabbaadcacdbdbdbdadddadcbaadabdcdbbbcbccaaabcadbdadcaabadbcbdccbcccbdaacccccdcacadddaabbcbcbdcaaaddabdaadaddabdcacdbcaccabaaaabbbddcabadaddbbbccbbdacbcdcdcbbbcbcddbcdadccdabacbcdbbcdcdabccacccbdbadbabbadadcbabdcccaaaaabacaabbbcadbbccaccdbddbabccddddcbbccccdadbacbbabcaaaddcdabbccdbdbadaccadbcbabcabaddbcaaddaddbbcadacabddcbadcccadbcacbdacdabdbaacdbccbabadbbcbdddcabdcccabacacdabdcabddabcabacdccaccdacbbdabdbaababbaaacdbbabacbbdacacaaaabdddccbcbcdcabbcbdccdacccadaccabaccacdcdcaddbbdacddcddddccccabcaadcadcddaabadbbcbcabacacabaaccdcdcbdcbdcdabcdabbacddbddbcaaaadddccabbcdccabddcadbbccbaaddadcbbddbdddadcacdddccddddbdadaccaaabdabdaacddcaddbcabcdbbdaadcaaaccacaaccacbaabdcabbcaabaaddaaaadccdadbbaccbdddccbacadbaddbcbcccdacccadbbdadbabdaddbdddbbdacdbcadacddadacbbdabaadbcabadcbccacbacbaacccdabcaabbcbcdddcaacadbdadcbabadbdacaadabcacaccccdcbdaddbcbdbacabbdabadbcdcabdabacabbabcbddcdcdaadabcdaadabcddccbbadabbdccabdabacccdbadbcbaccabbcdbaadbbadaaadbdabccccbadcabcdaddcdcdcbbbbcacbdababbcadadbbbcdbddaabccaacccabdbddbccadcbdcdcbcadaacbdadcbbaddaabdbbaabcdcaacbdddcbdaacbbbabbccdbbcdbaccdcdacddadddcabcdbaaddcbaabacdddbdbbdcbbacdbaabdddcbaccabcadbbbadccacdbaaaaccbbdcdbbcdaaddbbbccdbcbcbdbddcbddacaaddbccbdcbdbbdcdacdcbcbaddabbcdcaabbababbccadaaddbbccbcccdbbbbaddabcdbadabdcaaadbdadabbadbacbdadbcbdbabcccadddcbbdabdaacdacadbcaadadbbbddaaddacbadbbcaacdacbaadcabadcdacbdddbabdcaccddaabddcaabcbaabbabdbcbcbacadbaddabcacbaabbdddddcdbbbaaadbdabadcbacccdcdaacdbbadacbdbdacddddddbbccabadabccbdbbcdddcbdaddddacbacbacbdadddbbdccdadddbdabbcbbdccddbcccabcadabbdadcbccbddcbbbdcacdcbaaaadddcadddddbabcdbdaaddcabbcbccbbdbacbabbbbcbaaacacdabdcbdbaccdbbdadddaaddacadcbbaacbdcbdaaddcbbcbcddbabcbdbddcbdabaabccdbdabacbcadcdbcccbbadadaddcccbadaadbcaabddaabcbdcddbbbdbcbcacabacaacdaccaddcbcaabcaadabdcbbbbbddbaacccbccccbdbdcdcdcacacbccdcaccdaabcabacddabcbbaddcaacddabcccadaaaccdbabccdbbcddcdbbcacbddacabcddbdcdcdcbadcadcaaacccacddbabbbcacabadaabdddadcddbbddabdbdbbbbbbddbbbdabddcaddddbdbcadcccdbdacbbcbbddabcbcbdadbabdccacbbbacadcdcdbbccbcddddcddbcaccadbacaabcbbcadcddcbbacbadacadddcadabcccadbaccbdcbacddbbaabadabaccbcaabacdbdccbbbdacdabdccbbaaccddacdccbadbddddbbbacabccadaaaacdaccabcbcdabddcaacaddbdbdbccadcaabbbbbacacbbdcacddbcbcccdcadcacaacabbadcdbdbacaccadcaaabacccccbddacbbccbddcbddcdadcbcdcdabdabddadbbddbabdcbdacccdababcdadacccabadccbbaadadbbdaddabcddacdadacabdaccdcdcdbbcaadadcbacdbcbdccccccdacbbaddabcdaabccdbccbadbbabdbbdbbaddccbbbcacbaabcaacdccccadcbbdcbdcbbbdbbacbdabcbbbbaabbabccbaacacbddabadbcbdadabcdacdbcccccdacdbabbabbcadaabaddccdbdbccadbacdcdcdaacaccbdcbdbbcaaadbbdaddacacabcaccddbdbbdaabbbbbabaadcbcdbdaaaadbaaabdbbacabaabccddcddaadbdbdddabbcbabaadbaccbccababcbdacdabcdbdcbbacdcdddaaaacabbabadcbcbccaaddadadbbaacdadaaaccbdbddacddbcbaabadbadbdbcdbcbdcaabdabdaddbabaacdaaacadbdaabbcddcdcbbbcdacdcacbacdcaaaadcaddbbcbabdcaccadcaabbdadcdabcddcddababbadbbbdcbcbdabcdbcacacaaabccacabcdacaacddadbbbdbdcabaacbacacddabaccbbdbcbddbadcddcaacccccadbbdcbdbabaddbdbacadaabdbbbbdbcddbcadbddcbbbdcbcaaccbcadaddabbbacaadbccbcdcacccabaccbdbcbcabbadcbdbdcdcccdcdcabcbdcddcbcbbdaabdadccbdcbabcccddbadcaabbbbaaabdbdbbdcbdbccabadcaddacadcccdcacacaaaadaccadcadaadcccbbaddcbaaacabbbdbdbaacbbbadddadddbcbcbddbaddadccdaaabccadccaadbbdddbcccbbbccbbbcccadddababbabdbadcadaabcdccddaadaaccddcdcaacdbdbdddabdccabccbaadbbbaddabdabcadaccbcabaaacdbacbaaaabddabcbcddacbadcdaabacbabcbaadbadbcbdbdbaaacddcabddabadbdccdcdbcbccadbdadccdbbcacbbaaabcddbbbbdbcbbaabaddccaababcdcadbacbbbaccccbccdcacdbdbcaddadcdabaabcbbadaabaadbdaabcbdacbbabbccdbabbdbcbbbadbbdbbcdacaccddadaaaadaccdabdddcbabdddcdccacbbacddbddbbcadacbdcdbbdcbcadbbbaaadaaaadaacabcabbbcdbdcadbdacdcbaddbdcdccbaabdacbddddcccacacacbabbbbabcbccbabcadaaccbdaddbddbcdbbacccababaddddccbaaccabccbaadcaadbbbcadcbdabcdcbbcbcbaaadbcbcdcccdadddbdcabcacbbdadbdadbcacabadcabcacdcdbdcdbbcbaacaccbbccaadbbbccbdbdcddcdbadbddcacadbabdabccbdbdaddddbccaadadadaccbbbdbacdcadaddccabaaddcdcdcbabbcbadbaaabcdaddcbabcddcadbaaddadbacdddabcacdadbcbbbbbcbbdcbbbbabdadbccabdbbabadadbddbaaaadccccddbacbaaaabdbdadbabdbabcbbbdcadbadbcbbaacbadcabdddcadddbccccccddccabbbadbabaacdcbcdccacbdddcabcaadabbbadccdbcbcdbbdbcbacdbdadadbbcbcacbaaabbbcadcbbdabddacdcbbcbdaacdddccadccbbbabbbacbabbdddbacbcadadbadccccbbaddddbdcbbbcdbbbcabcddccbcdadcaddcbbbaccdddbcccdbadbaacdacabddbdbacdadcdbbbbbdaaaccabbbbdbbbcdcccbadcdcadddcaddcadccadcaabbdbaccabdbdbcdcadbcbbbdacbaaabaacdcadbccbaabdcababdddacbbdcacbcbcacbadaababdcccbbbbabdbcacabbaaabaacdaddbaacbaaaaaadadddbccddbdcbcaabdbcadbaccdccabacabcdcbccdaacddddccabbacbdabbcabcaabbcdbadbbbbaccbdbdcacddabcbcbacdbdadbcdccabbcadcbbbdabbbadbadabaccabbbddabacbdbbdbcbbaabcacbaddaabbcaacacbcdaabbcddbcacddbacdbcbababddcbdaddbdcadcaccdbbcdbdbbbdccadbcbabadcaaacdbbbbdbcdacaddcdccbacbcbdbddbbccbadbaabbddcbaaccabbcdabadacbdaaadccddaaababbdadadabdabccdabaadcadccdcaabacbcbaadcacbcdcbaacbcaaaadddadbdabcdbdaaccccadbacbcdddcadbbdbbcadddabdbcbabcdadddadccadacdaacccbdbdabcadacaabdbabbcccadadccdbadaddacbdaaccbddccdddcbacdcbabddbccbdbcaabdbbcaaddcadbdbdbabdcabccadcaadabdcbcbacaccbcbdacdcacbbabddbaacbdbbcadaacbdcaabacbacabbcddbacbccdccdacccbabcadacaaccdbddccdbbbbbdddbacdadbccbbdcacbbacabbaccccacdcdbaacabbbccadccbbbaccaaccddcddbdbddddcbaccbdbbddcacbacadbaacbbbdaaadbcacdddcbaadddddbcdacbbbdcbbdbccbdabbdaacdadbbdbadacbbbdbdacbadadbadbbccddbacbaadcdbbddcddbbbacbdcaaccdcbaacaccccddcddbbcaacadbbcdbdddbccddcbcacbcabdcabbaaddcbdbcccdaccacbbcbcddaabbabaadbcdcddbdadcaacaddddcddaacadcdbcaccaddbcccddccbcaacccccbdadcbcddcbdcbaaccababacaadbabbcdddadcbacdcbaaaddcbbacbdaabdaacbacbadccbcaabacbbbbcddcabdcaacaadcdddaabddaabbdcbcaacdbcadbdcddadcaadaabcbdbadccbdabcbcbacbdddddbdcccddabbddaaacccbcdcddbcabcbadaaaddddaaccbacdabbdababbcdaccddbbadcdcbcbbccccddbbccbbddcaaccbccabdbbaabcacbddbabccadccdadcabcacbaaadcccbaccbbccacabadccdbdbadcccbcaccaddcddbcdbbbbbbdaaaacaaacaabddbcdacacadbbbbcbcdbcabbdadacdadcadcabdcadbabccdbcaadcdcbdcbddacdddadcbadcbbbdbdccbaacacbcacabbbdabbcadcdadadbaaaaaaccabcbaabaacdaababbbacbaacbaaadadacadcaddbacddaacdababcdabcadbdddccbdbcabadbdbcbcbccabbdcdddcbddacbaaadcddbcacdcdacadbcbabdaadbacddaaddbddbacbddabccacbaaaadbbcdcdcbdbcbcbbcbbdbacabcbbbacbcbdacbdcbaacbbbcaadbbbbaaabbabcdadacddbbadddadddbaabddbbcaaacdccaaabacbdddbccacbbadbcbbbbadcabadbbdadaaacbdcdaabbdcacccacadbacbbdddbdddaaddcdccdacaacbbcccbcdddbbcaabcdbdaccabccdcccdccdcdacaccbbdabcacdaacbacccbbadaccaadbbabddadbabcddbadbbcbccadddbbcbacaccbacbbdbdcbbbbbcaaacbcadcaacacbcacdacbbdacaaccbcdccdbaddcabcbaabbadcbadcacdaccbbccdadadcdbcbaddacddbddbdbdccbcbddaadcacbdcbdaaadccdbbdadcdbbdbaaaaccabacbdddaabcccdbababaaabdbbadcbdabcabacccaabdaacbbdcaadacaabbdccccaaddacacbaccbcccccbcbdabcbddadabdbdbcddabcacdbabddabddaadcadadbbaaaddbcdbabaabbdbabddcccdcdbcbdbddbdbcbaaacbddcbdbbabbcadacadbbabcaacbbbbbdaacabacdccbabdadbddbbdcbbbbacdaccdacdaccddcdcdadcaabdbdbbcdcbadacadadabcbaaaabcdcacddbbaacaaccccabcadcaabccddacadadbdaddcbadddcbdcbbaddaabdcbbcdaaadcbcaabddbcaddbabbccdbaccdbbbbbddaddacbbabadcdbbcadbcddbddaacbcaadacaccbabddbcbbaabaccabdbcbdbdbdddadacdccdacbcbbddacacaccbbaaaadaadcbbdbcbddbbbbabcddbbdbcccabdacadccbbbaabcbccbbbaaaacabbdddbdadccdadadadaadacbddaababaacadddadcdbacdabddbcccdbacdbabbcbbacbacadacabddbcbbbbcaaddbaadddddabdcacacdbcbaabcabccaaabcbcdbbabcbaabdaaaddcabcabdacbacdbbbcadbbcdacbbbaabababadacabdadcaabbadadcbcaadbcdbdcadabcabbbabaddccabddabcacacbccdccbcaacccdbacadbbcaaabbadcbbcbacbcdbddacccbabaccbbddacccabcabacbadbbbccadbaaccbdcdbdbcbdadbbdbaadbbadaaddaabbabacbbdabbbbcbcbcbbbbcbbddbdcacdcaacccccadbcdcccbcaaababbacadcdcacdddaddcbaddacadacabbbbdaabacababbadaabcbabddadccaacaaadbbaccdddaacddbbaddacdbababcaabcddbbdbcccddcabbabccbaaadddbbcdbbcbaacccabadbbaadcdcabcbbbaccbbdcbdbdbdcbbdddcbbbdbacdddbdbdcddcadddbacaacdccccdccdabcbdcbddaccdcbbbaccdbbacccbacbcdcccacbcbaabbcdcadbdbaadacdcdbbbbdacbacacaacbccabadcabbaccccabbcbbacccadacbabdacadabdbddcaabbbcbbdadbbbdccadabcaadbbbdbccdabcadabcdcaadccbbbddbbacddadccbaaaababacaabcbcbabcccdaadcbaaccaabccbddcaadcbbaaddbddbacccababcbbbccdcaadcbdabbacddbdbadbbaccdababccbaaccbabcbbcaaaadcacadcdcbcabbccaddddbbadcaabbddbbacddbdbacacddbaadddbacccbcacccdbadbcbdbdcbdbccddbbdddcdbacdaccbddbccaaacbcdbddccaccddbcbadcdbbdbbacacabdcababacaabcadbdbbbdcaaaabdcbdadbccbadbabcabbcabbabbccdabacccbbcacdcdaadcbcadbdbcddadcacbaccadacacadddddbbdcbcccdbaaaacaadcdbcabbdaaaadabbbbdbcbccdabcdcbabbbbcdabacdcdccdcababcddbccbcddbcdddabdcdccaadadadbddbdbabcbaaadbcbcabbaacadbadababbccaaddcadcaddbcdacadbabcbacbdcacbbdddacacabbdbddacdcdcdaaaaabaacdcccbdbdabbcabdbaacdadbacccadcbdbcaaacddbcdbccadaadacbbdaacaacddcadaabddbddababaabdcccbadadbacdbdaacbcacddccddacbbdaaabcaaccbcddccaaadbdcdbaadbaadbdbccccbbcadddabddadcaadbbaaccaaacbaddbabbadcadbddddaacbbcadacdbaadaabcaacacdbdbabbbabadbadcbddaccdcbbdbabddcccbbbabdacacddddaabbaccddaccbdbdabdcddcbcccaadbdddaacbbddbccddacbadcdbabbddabaacdadbcdbadcdaddaccacbcbbababadbcacdbcbcccacaadcacdbdcbacaacddcdbbddaacbbacbcbaaccdbccabbbaaacbbcbbccacaadbbcdacacadcaacdabacaddccbcabbcbdccaddbcbdddabddcbbadaabdacadbcacdbbddbdccbbcbcdadabbccdcbabdbaabcdadabbcccccbcbbbcdbbbaaccccdbbdcccaccbcacaddcbbddacbadaacbccbbdcaaddbdaacabcaccaccaabdcbaccacdbddbcddccacabdaadabdbbbccdddadcaabcababdbacabdbacdcddbbcadcdbabddcbacdabcdbdcddcddabccadabbabbbbbdbdbbbdddabdbdcabcadacbcbdcdcdadddaacdaccabcdcbcccadacabcbaccbccaaabddbadbbcbaadabcabccddaabbbdacadcbddbcccbdbbbbbaacdabccaacbddbabbabbaabdaddddbabbdcadabddcdbbacbcbaccbbacabbadcbccdaaddbbcbcdbdbcadacbdbbdcdccaabdcdaabbdcdcaacccdccaaaaabdcbccacbacbadcadabaaccaccacaadacbdcbacadcdcccdbaccbbaacccdcadadbaaadddacddbbbdaccdbcddcacccbbdbaaccbacacbcabbcaacdccaaaabdbbbddbdaaacabdddbcadcadbcdcccbbbbbdcddcadcacdabbacbccaaddbccaadbbdbaaccddcacccacadaaaccbaaddcbacdacdcbabddcabbcadbdaccccddacacbdbbccaadacbacaababdadacbdddbdcabbcbcaccdacbdcabcbadabacaadcbcacccadbccbccccdcacbacaddbdbbbdbcdcabdababbbabaadcdabdbbaaadccbbddcbcccddadcbccabcdbaddcdbcdbccbabddabddaabdbaacbbbadccabaaaaaadbbbadcbbacdabadcbadabcddcdadccaacbbadbacaddabdbcccbbadbdabddbddabdbcbaaaaaabdaadadabcdbbccbbbdbaddabdaabadbabddbacadcddbcdbbbdbaadcbcababbdddcabaddbdadddbdaaabdcbddbbadaadadcbaccdbacacadddabcddcadacbddbcaddcbdabcdcadcdbaaaacbdcddaadcadbbbaccbddaabbaacdbaaadaacdcccbcdaccaabcbbabcabbbbddbccacccbdabdadbdbcbdcadcacdbbabacbccccadabdabcbdaadbabdaacbbcdbddddacdcbdbddbddcbbbbdcdbdcdddadacbaccbccdcbccdcabcbccbcccdaadaaabbadbcbdbcbaabdbadcbcaadaccbbcbacbacbaadadcaabbdacbdaaaacabbadccddaabbddbcabacaacbaaccabbababbcccbcabcbdabccdacdadacaaddbbcbbcacbcdccadcaabadababacdcaacddabdcbdccbaccacdccdacccdadddbacaccccdababddcdbacccabcadcbdacadcadbdbcadcacaadbccbdddcaccbbbadcddcbacccddabcaadaaaacadaabdacbdcdacadbdabdaccbdbaaabdcdccdcdabbcbbdbdacabdcaddccccbacdddbabdbdcabdcdbbcaadacdbbdccbcdacaccbcabdddaaabdcbabcbdaabadbbcbbdcbdbdabaaadccabcabcdbdacdccaccaadabcbbaaaadcdbbbdcccadabccaccaaaccacbabaabaadcbdbddaacbcaccdbccccddcbaaadabbaddddcadababddbcbddabbdbaaccaacaadcadcbbbbddaaadddbcbcbdbcadccadccccbdbdcddccbcbdccdcddbadbbdddbbbcabddbbcccacccbcabaadbdbbdccddaaddcbcaddddabaccbcabacabbadbccccaaccacacbaadcdaccdcabacddacaccbdbabcbadadbbacdadabccbcbcddadbcdbbcacaadbbccbdacccbabacdacdbacaacdaaaddaabadaaddcababdcbacbacccdadbdccacbcaddcddbbcddddbcbacbddddbbbaadadbcabcdbbdddabbbababcbbbbbcbdadaadbcddbdbaddadabcaacdcacbdcbccdabcbabbdbddbcbdaccdcadbacacbcadbdaccadddcdccdbadacdbddadbabbcdcaadadacadcbbbdcbbbadbcaddabbadbabdbacbbdbbdcbdcbabcdccbabdddcabaccaaadcddccdbdadcdacdadacddbaabdbabbcbccbbabccadbbaddcbdbdbdaaacbcabbaddaadddcbbadcdbcddddcddbadbaadddccdbaccbbaaabadbdddbcdaaadaaadcdbbbddddddbabaababdabdbcabcbccdccbccdaabacbaacbbadcaacacbaaadabcbcccadaaaacbaddcdcacddccacadadbacbadddcaabbabbdccabdadacdadccbacbbbdaabdcbbcbbddbacacbdbddddbcbbcdccbcaacddbbaccbcdcdcdbddabcccabbaadbbbababddcdbbaaabbabbabbbcdccaaacaabdacdcdadacdcaabcdbdabdaddaaccbcdbaadbadcaaccbbbaddacdbdbccdaacdcdbbbdcaadcccdcaccdabcdcdbbbbdbcdabaacdacccbdacddacbcdccdadbcabcdbcbdbdbacddbbaddbbbaaacbccccbcdccbbbabdbddcbaaddabcdacacbcbbcbadccaabbccdcaacbabbdbcaccccacbdaaacdbcbdcdcaacbbadbadaddddccddbcdbdbdbabdcacdbbcabcdccbbdaadcaacabacababccbaabddddcccacaaacdbaaabccadbadacacacbabbccdddbcddcdcdbbdacbabacdaaaababacadcdddabadbacbcaabcaaccbadbacadbdcababbbcacbbbdbbaadddcdddaacbcddcbadbdadadcacbacbacdcbbbcbdcdaddddadbddaadcbaacabdcababcdcdcaabdbddaacdbdcbbddacdacdcaaacccacacababcdbbbcbdbddadcdcbdaaaadcdbdacaccbdcdacaabbdcdbcbadadaadacacbbcbaaddbbbaaaaacdabbbccccccbdcaaabddabbbccbcdacdcbccaaabdccbaacaabadaaddccabcbcdaddbbbddccbdcbccdacccdcaaaddbddcaacdbaacdddbabbddcbcaaccdbdcdcacdababaccacabbdcaddbbbabadbbddabaaaabdaaccbacdcadbdaacdbdabcdcccdbbabdabbccabcbdaaabddccddccdabcccbcccdbcadcbcaabcdadddaddbbaaddcdcacbbacadacbcadadcbbcbbbdcabcbaccbbcabddbbbcdadabdbdbcaaccdccbdbdacdddbbbdaccabcbdcdaccbcdccdabcdabcacdcaccbdaaccbccacbdabacacdcbabbdaccadacddacbacbcdcdddaacbabadbdddbdacaaaabdccbadcaadbcbbabcbcacdabdccccdcaccbcadbcbbcbaadbdddbbbbbadacaabcbaccdabddbacbbbbbccbccacadbdabacbcbdacadccbdbbdccbddbabcdaddbadbcaabdddbbbcccccbcaaadacbcadbcaaaddbdcbacbbbbcaccacabbdccaccdbbbbddacbcbabbcadbaadadcaadadbdcccaabcbcddbdacabcbddacadcddabbacabacddcbdcadbbbbcbadcbbcbdcbcbcbcddbacccbbcdcbdddcbbabdacacacddbdbcabadccbbadcacbbdcccbdbadcbbddccadcbbddbddbbacccacbcbacaabacadbbbcdcddcbdacaccaaddcacdddcdcacccbbccbbdacbaccdcdbdbbddbbbdcddaabbdadbaaaadcdaadcabbaaddbbaadaabcaabbcddbaabdddddaabcbbcacbbaccbbcdcbadcdcadcccdbdaaadaddcdbaacabaacbccbdaacddabcdadbddcdbacbaacbaadacdabcbbbcadcddddddbdaddacbbdcdbdcaddacaddbaabcbbccdaacacacbcbdcbdadddcccabdcdcbdbaaddddcbdcbcaaaabdbdadacdbdaddabbdabdaddbdaabddacdddbccaccddbbbddcacccadabaddacdbbbbdcddddaaccabbadccacddbbcabacdccccbbcabddaacbccddababbdcbaaadccbcbcdddadaabbadbdacabcbabdbadccacabcddabdababcbbabaabbababdddaaddcbbdabbacbdcdbdaddbcbcbbcddcbaadaabcbcbcbcdbcdbbbdaacaccacaabadbcbcbccbddabaaaadbddcbbbccccbacccdaadbdbcddcdbdccabcbbddbbcbbadcddcddcbcaccbaadccabcbdcacbcdbbdaacbbbbdbbcbddaaadbccadabdcadadcbabcbdbdacddcabdbcaaccaccadccbbabcbdcbdaddacdabccccccbdabbdbccbbddbbabbacaacabcddcdddcdbdbdcdcbcdddbbcccbaaadbdadbddbbdabddbddccbdacdbbcaabcdbabcbacbabdadadacdcabdaaacbdbbbcbddbaaabcccacabbcbddbbaacbbacbbcabbcdabdccbabbccccccdbcbcadddcacbabacbaabcbccacccdabdbacbaadbbaaabaaccdcbabbbdcbdadddabcdddadabddccbcabdcbcabadacacddacbcbdbdabacbacbadbadcbccaaadcdcddbcbdadaabbbaacccccbacddbdabadbadaacddcbaacdbcdabbabadbddcbbaacdddacdcbcbdcbdacbabcdacabcdcabddaabdabaddaccbadcdcbcbbacadaaabdcbcabbabccdcaabbbcdcbacdbaccbdababacddbdccabacadadbaaadcddddccbdcdbcdddccdcadddcbabbbbadacaddddcabaaabcaddcdadcaabcaabcdcdbbdaabbcddbbbdcabbdacccbabadabdaddbbaddbbbcadadccdaaaaacdbbccdccbadbaadddbccbbadccbbadbbacdcdcabdcdbaaaccbcdbddbcaddbadcacdcccaadaddbbcccacadddcccccdaccdadaddcbabaadcbbacaddaacbaacccbdbbcaabcccbbabcbdbcaabbdcbccbdbdddadbcbbcbbbbadbacdbacadcaabadbbacbacbcacdadcccbdaabaabdcddaabbcbcbbbcbbcbaddcdbabccaaadddbadcdddabbcbcbaadadabcdbddaadcaadababdbcacbaadacdddcbcdacbbdcdbaaacbccdbadcaadaadbdddcabacaadbcddadaabbcbadaabacaccbbbcdcaaddcaccaabdacccccbdbccdbcdbadbddaadcbadababbbadcdabdaddaaabdaabcdcdcdcaddbddbcddcdddbdbcdbdbcaaadadcbbabcbcccdcadaddbcbdbddbccbcbdacdadbbcddadbcdabbabccbdcadcabcaabdadcabaadbcaadbadaacccbabccbcdbcbcdaccbaaddabdbcdbcccadbaababcddacabdddbbccbbccbabbdbaadbdbbcadddcdcbacdbdcbdbccbbddbcaacdbdccadbbabaabccabcdabccbcddcddbdcacaadcddbaadbbcaabbbbccbaddcbcbbdbacdabaccdcbbcacacccbaadadddacdabcbccacdaccadbaabcbadcdccdabcadcdcbbdccccccdbddccbdbaddccadbcdddbcabbbdcbcccaabaadddaaccdadbcbbbcbbcabbaddddaaacdaaabdaddcacdbbcdbdbcbbdcdcacabbbdbbccbbdcaccbbddccdbbcccccdcbddccdbdccbccbdbbaacdadbbddaddabccdacbbabaccaacbddbacaababcacdbcadabdadbbdaaabbbcaabdcbdadadcabdbdaadddbdbcabacadcddcbdadacbbbacccbdaaaadddacacaacadbdcdccdddaaccdabccaaadbbdadbdabbccbbadbadccabcaaaaadadcbdaacdcdbabcdddadabbdbddbbccaaddcdacdaabccbbdcccabbccbbdddcddddcaccdaabddddbcaaacbaaddbcbcdadbadcdcaaccdaccccbcdcddbdcddbabacadccdaccccccbdabbbddbbbabbbbcccbbbbdcdccdbabcbabcaccbdbaabbcabaadccbadbdbbcdbcccbcabbdbcbbcacccacaddcdabcbbbdbadcabaccdbcdadcdbcacbdcabbcadbdabdcddaacddcdaabdbadabbdcdbdbacacdbdcddcaadaaaaaacddddacacccdabddbdccbddbbcdaacacccabddbcadbabdcddcadbcaadbccacbccbadddcccdccadabcaccbdddbcbbdbddbacdbbbbadcadccccaccbdcbdcaacdbccbaddbadacbbbbcbdbbbcdbccddddbdbccadbcccaabcaabbcbcacdbbbbadabcadbabdccddcdaabddddaabccbbbcbacddcccacdbcaddccdacaaabdccdbcbcbdbccdbadaddbabaacabaacbbbaabddbbbbcbcdbbddbcddbadcbbbadbcccadaabbccccddadbcbcdcabbbbccddbadcddbdcacdaaaaabbcbcbddabbaddbacdbbaacdadbcbddcaadbdcbacccbcbbacbacdcdcadaabbadcbbdadbdbacbcdbcdaadbbbcbccdbbcbbacbacddcbbdcdcdbcbccccdbacddaaaccccaccaaccadcacdccaabaadcbbcdaacbdcdaacbabcddcdccbabbacbccaacdaddbaadaabdaaccdddaadccbcbccaaadadcbcbadcadacbbcbabdbaabbcbcbdbbbcadcaabddcbdcdcaaaaccbbbaddacdacdbcbaaccbdbaabbccddccdcadbaaacddaaadbbaaddacccccaaadbbdadcabbbccacbbaaaaccacbcbacbddccdccbcbddaabdaaaacddcacbbbcccbabcdddabadcdcdbccccbaddaabdacaddadbadbcadabacaabcbbadabaadbbdcadcabdbdccbbabbcdbbdcddcddccbdcaaddaaccbbbddccdbdaabacabcdbdacddabadabacdccaccabdbaabbbdcbbdbcbadadcddbccabdccbbdaddaadcdcbdadccdccabacbacdabaabbbabadbdbcddbbcacaabcbbbcbcabcdcbddbcdcccbdbbcbbbddababbcdadaddbdadabcdbacdcabdbbababcaaadcdcabbcadaacbcdadbdcbddacbbdbcacbbaddcdcbbcaccbabdcbbaadbcbabcddcdcbbbadccccdbcddababbcbacccadacbabadddaacacbdcddacccdcdaacdcccbaddacabdbdadddddbccaaabcdaabbabddcdcdcaabdadbdddaddacbacdbabdcdabdccadaccbdacbacadbccdbabdaadacbbaababdccacadbccaacaadcacbcabbacddcccacaadadcbddcabaadbadcccddbbaadbaccabcacabcccbdcbcacbccabaaacdbcccbcbccddcbabcdbdccadbdbcdbdddbadcddcaddcaccaaaccddacabcddcdcdbdcaabdbdbdbcdbaaccbbccaccbdbcdccdabccccabbbdbdbbbcadcdcddddabddaccaccbbddadbbaccadaadacadadbccbddababcacdacdbcacbbdabbcbabdcabcddbddbbcddbacbcdaaaccadacccbbddbbbadcdaacdbcacdcadccdddacaacabacadcdbbbabdadcdbcaabdbdcdbcddddabbacdccabbddccbcddaddbccbcadbcdcabbdbcbdaadbbabdadcbdccbcadbbdcdbcabaaaacbcdddbbdaaaadaacccadbcadbaacabdabdccdcdddaabcbdbdccaaabababdaacddcddbcccdcccddcadacbdaaddcadacbdbddbccbcdcbacadacabcaaddcdcbcbdbbaabaacbccacbbbbbddaadbbadbbdacbbbcadbbbddadcccadbdcaddaaadaccbdddbabcddcbbccbcbdcbccabdbbdbdabbdbbddcbaddcabddbacccddccacaaabababcddddababbaacdbaabbaaaaabddbadcdadadbccbabcdddacadbdbddaabcadadcddbbcbdcacbbcadabcbdbcadcbdbadddcdcdbbaababbbdabbdaccccadbccccdabbdaabbabbdbcabbcdbacbcdbdcbdccadbacbcabbdcdbbcadadcbdddaddcbdcdaddbcdbdbdcbdaabaacdadadccdbdcbabdcabbabdbcdddcdbcccdacdbabcdcdcaddddbadbbadccccbdcabdddadaabcbdcbaddcddacdacbcbcbbcacddaadddbaabccbabccbaaddaddcacdadcadabdbbbdcbdbdbbbbbdacdbdababaadcbbcbcadaabcbbddababaabadddaabbbbcdaccbdaaabdccdabbabddbcaccaadcadbadcdddaddaaaaadbddbaacbaadbadcddcaaddcacdcbaccbcdaacbddbadcbacdcddcacababdbacccbcaccacdccdbaddcacccabdbccbdcacbdcccccaccbcbbddabdacabbcbcbddcacdcbdbabadcabbddaddcdabcddbccdddadadaacbaccbabbcbddbbbccabadadcabbacacdabdbdcddbdadacadcbbbaddddcbdbccddccdaaccdadabaccbdbdbaaacdbdadbcbaacdddcbbcabbcdbbcdadadbcdbddbbcddacbccbddaadcbdcaabdaccdbacbcbacbbdbccacacbdccdbdadcacdacadcbbacbcabcdbaadabdacbaacccdcdaaddddddbaaccbdbbcaccddbbdbaadccbacdbacadcbbdcacbadbbbcccaabccbcccbcdbcccacbdccdbdcaddacdacbbaadcdaadaaaccdbcdcdadabbbbaabacbbcbabbdcdbcdbadbdddbcadcaadcbbdbcbdcddbbbbbbdcccbcdbdcdbbadbcacacabaddacbdbabccabacacaabdbcaacdbddababddcdbacbaccdddbdbddbbdadbcbdbbddcdbcabdddbadcdadbbddabbacadcdabaaadbcbbbabacbdacadccaabdddcbacdcccbbaabbadbccbaacdccaddbbddccbcdbadabbcaabcbdddacbcdccdcaabcaabbdccbaababcccdabbaadbabacadbcacdccbcdccbaaddbdcabcddbcbcccbcbdadaccbdaabcdabaaccacaadabaccddbdcbdcacdcddaadbacbcadccacccdbabbbccaddbcbcaacdcccdcacbcadbcabdbbbdcccbaadccbadbadcdccacdaaccaabbbbbdaaaaaaadacdaddcdbdcddbdaddaabcacabcbbbadbabbbbbbaacadbcadcbaabbacccabdbdcbadaaaaadabbdabdcdccadcdcccbdaccbdacbcdbddcbdccccbcadccabbcabddbababacbaacaaadcdcaccdcdcaaabcabdacacdbbaacdcaacbbadbadccccaaabddbaaccccbdacdacacbcbcbaacaadbcbbdcadaddadabcbbcbacadaddaacaaacccaddbacdcccbbbcccddcdcaccadcbbbdacabadaadcddaacaaadbabdbccdcacbbddbcaddcadaccbaaacbaacdcbababbabcacdcccbadcbdddbbcaacbdaadbbdddbbacabcaacbccdbdbcccdcacbacbbaadcdbddbaabadcbbbddcdaacdccbacaccaadcdbaaddcabaadaaadabaadccbcbbabaadbbaadaccddacdbdadaaadadddcbdbabcddaaababcacabcacdcccbddabdcdbcaadbabcacaaddcdacaadadbbdaadcbdbabbcabcdcdbddbaacdcdbacdcabcbdcaaccabdbdcddabdcaddbcadbaaabbbcabaddacbbcdbbaddacacbcbcdddabbcababbdbaabcccabacbcbcbcccccbcacbcdaabadadadbddabdbcdddadaabdbdbaaadddcdcbaabdaacdaddbacdaabaaaacccddacbdccadbcbbbbacdadacbadbdaacdaaccbcbdddababcdaacabacdabadcdcddcbdbaabaabbbdcabdbbabddaadadaaacdaadacdddabadbddadbcbbbbabacbbbdbcadcabcabcacabacbdbacacaaaabaddaaababbbcacaaababcdccabadcaacbcdbaabaaaabcdbcaacbaacbaabbdacbaaaddbdcbccddbdbbaabbdbadabbccaabdddcdabccaddbbcdadcdaddddbbbdcaacdcabcabbcbdaababbabdcbbacbbdabcdbbcaccaabacaadcdbabcaaccdcbcabbbcaacabcccbddaacccadbccabaccbadcabadbdbbcacaabacdabdcccadbccdbcddadabbdddddccbcdccaccaccdaabddacccdbaacacbaddadcadbabccccbcddcadaaaaaaacbacadabcdbacdbcadabacbaadccdacacdacdbcbdcbbddccbdbbcbdbadbabdacacbaadccdaccabcacdbcddcabdadbbbcdbbcacbdaaacdcdbcababcababbbbcaccccbbabddbddcaaddcabaabbdaaddaddbbcacbdabbbcccccaccbbdacdddbccadbcccbcbacddaddbdddbccabadcbbacdccdbbdbadccbcddcacdaccaabcbcbdacaaccbabcacdcdaddcbaccdddbddccabcbcdbaaabbdbbccddabbbcbccdadcccdadacbcdddacabbbcdccaabbdbcdadbdcdbcbaaacbcbaddabaabcbddadbbdbdacdaacabccbbaaabbdaccaababdabadcdacbcbcddbbadacbacbdddcbbbdadabcddcaddccdacdbccddbdacbcdbcbbbdaabdacdccdddcdaddccabaaabdddcbbadbabcaabdcdacdcbcacadabbddcaaaabbbadbbdbdbacbbadacddaadadbdcacbacacdcbbaaadaacdcabbcdadbddadbbbcaaddbbbadabccabdcbcbbabccdbbcdccacbdcdcbdacbaacadcaabbdbdcbbbccabccabadabbddddbaacadbbdabacbbabccbaaacbbaaddddbccdddcdcbccdbbdadcccbdabcccdcbcdcbbbcacaaadaddbbabccddbcbdaccacaacbacdbddbaddcdbcccbdaccadcadaabcccadabacddabaddacaacbabacdbaacddccbcdcacadaabdbacaadbacbdbbbdabcabcdbcbccbbcbacbdcdaaccaaabcbcdaaaabdaaadcbbcabdadbcbcbcbadbdbdcbadbdccdcbcdcdbcbdbcdbaabbbbbcdaddbbabdcdcaccaccabcaddbaadbbbbcadaadbcbdcbddbbbdcdcadcacaabdcaadaaaadbbbbbcdcbdacadbaaccacdaaadcacdbcbaaaacbccabaadbcbbdbcdbbaabdacdcdccbadadadddababcaacbccdabbcddbcadcabbccabbbccabbaaadccdcbdbbadbdddbadaabacbbcddaaccdabddadddccaacdadadcbbcddbacbcdccacbabacdadcaccadbadbbaaabacbabacdcacccabbabcadcdbccaacaadccdddccddaccbdbabbababbcadccbdcaaaaccacdddaaabbaaccbadcdbbcccabaabdabdacdccbdabccccccddbccdadcadbadaccdacdcbcadddbddbcacdabcbbbddddacadddaddccdcdbdbabddddbacddcdcdbcddbdbcbdabdaaddccdddcddcabcbcdaaadddbdcabbbdcbddacdbbbaaaaddcabccbcddcadbbbbbbbddddbcddadcdadddacadbbbbdaabdabdcabacbacbbdcacbcaccadadcaddacbdbbaaaadccbacbabccacccaccdbbcbbdcbcdbbbbddacdbcacbcadabcacbdaaadbababdadccddaaadcacaacadccbbbbdbdbacddddcbdcacadacadbadbdaccaabddddbccbdaddbddbbddaaaaacabddbbdbcacbbabbabcaaadccbddccccbadbacbbdddacdccdaacddbacadcdccdcbdacdadabcccbdacaacddcbdaabbddbccacddcbcbbabbdabbacadbbbacadcaabdacdabcbaaadabaacadaccbdbcabcbabbdbbcccadbcaaacdcbbbddabaacdcdaaaaacababbadbdaddcbbccbdbdaddccdbbaabcbdbbdbcaccdbadbddcadcbcdaabdbaaccdcccdcdadcbdaabbbdcdcdccabdbaddcccdcccddbdbccdbddabbcbaccddcbdbcdcccdddcdaaadacdddacbccadbbcbaddbabcbadcdcaadaacaaacbddcaccacddcacbdcabbdbdbbadbbbadaadacdaabdaaadbdbbddadbcdcbddacdcdacddcbaacbbcbddabdccddddcbbcdbaddaacddbcbddbaccbcddadacdabdcaadbcaaadddbabdacadabbdbadbacddcbadbdabdbaacbdaccdadbcbadddaabaabbbbdbacbacdcbbacdcddccacadbcddcacacdcdacddabdcaccbabadacbbccadcaddabccdcbaabcbdddbccbabccdddaadacacbdcdcbdadcccbaacbacdaccbcdcccbbddbbdbccababcbababddccdacaabcbdbdaaccaaabcdadaabddaccbacbabaabcbaabbcacabcabdcabbbdadabddbabaabdaddbdcdacababdabdadbdacabcacdddabbbccdbababacadbdbabbacdcddacbccbcbbdcbabacbacdbbdadaaadcaabacaaccdbbaadcbdcccbcdbacdadcbaadcadbbacabbbddbcaadacaabacdadcccddaacacbdcdddddaaaaabacbcababdabdbaaacacacbddccadbaabbdbacadcaddabcbcbdabbbdddabddccaddcdbdcdccbbabacabdccbbbabadcbacabbbbcbdbabbadcdababcadabaaabcbabdddbbabcaccdadaabacdbbabacbadbdbaccdddcaccbbdcabdaabccadbbbcaaaccadccdcbbcbddcddcdbaaccdbbccbacacbcadcddddabdbacbdcdcacbaacdaccdcccaadbcbdbcccaabbdcbadddcbcacdbdadddbcdaacaadbadddaabbdcbcdbaacbbbacbacdccbbdadbdacadaadcbcdabaaadaabbddcbabcdadcacadcbddbcbbcccddacabbbacabacddcdadacdadbcdcbcbbdcadaababbcbbabadbbabbbbccbadbaccdcbbddccacdacdcdbdcdcbabcadbacdcccbccaaabddaadbaaacbccbdabcadbcacbaacbaaddcbaabccbdbabbadabcbdbcdbcdaadbbbdddcaddcbbbaccbcbadcbcbcdabdcdabcaaabdbdacaaabcdaabdacacaddcdcbdadcdddcacaccdcdadcbabbdddbadaaacbdbadbdccbaadaaadaccddabacbbcbcbbadccddcdccbaadcdddaaddbdcdaabbdbbcacaacccacbaabddaabccdbdadddddccdcdaccacbbacadabddadaaacdcccccdacdabaccaaacbbdacdbbbaccbdcacaaddcccccccddabbaadddadadaaacddaabcbacdacbbcbaacaabbddccddcbccaaccadcdcbdaabaabadcadddadbcabcdaadabaaccbbaabdbdaaadbbccaaadcbdbabcdbbbbcadaadcaccccaabdacabbaaaccacddbccadcbccbbaacddbbbdbadbabbdaacdaaccbaacbcaabcacbbdbbdddcbadbadcdcdabcbbddacbbabdbbbddaaddadbaddbbccadabcdddcadaaaaabcbaacbbccadddbaaaadacbacbdcabdbabbccbbbddbdcaaaadaacbbdbddabddcbbcbbbddbbbdbccacadaaccdabbabadabbdaddcddaacbdbaabbbaadabcaabaacdacabcdcbbccbddbdbdcdccaadcdbbaddacdbadddbccdcddddbbbccddccbbbccdaccccabddaaaababbaabcbdbcbcbacbbcabbcbcdbcccbacbcbdccbaabcccbcdaaccaaaaaabdbacddbbdaadcbaaacbdadcccdbbdacdbcaadcababbacadbbbdcdcdbbbaddacadbbdaabbdabbcdcddaaabcacdcccbabaaadccccbcbcaccdcddbadbcdbcbadaacccdddbcddcabbabcbcbaadbddabccadccdbcbbddddbccccdacdcaadabacaddacacbbabdcbbcdbcdccbbaacbdcbdbbbbcbcddabcccbdcdacabaacacddbbabcccdddcaaabccacbdcadbabdccacbaacaadddccaadbdaaccbaacbaccddacacdcbaacaadbbabdbcbbacdcbadabdbadcbaabddaababaaddbbccaaadbbabbbaaaacddddaccabbcddcbcddcdccbdbabaddbcccddacaaadbabccaaabbccdccddbaacdbbbbbbaacccdaddddbbbdbaddaababbdcdadacabdbbbacaacabcaacaadcddbaabbbbbdbabcdbcdadaaacacbddaadabcdcddaaddabcabcdcabadcaddddcddcacdcbcdcdccbabbaabbaaddcccbabcabdbcadcdbccbcccbdcabcaddcadcbcccccabbbbbbadbdacbacbacabaabbcdbabccddcdbaacdcaddabcddaacbabdbbabccacddddbbdacaaddbdcbbdcddddbbbadcadddbdaabdadcababcbccdbbbbcbbdcccacbabbadbddccccacdcadcccaddaccdadcbadccacacadbacbdccdbbbdcacdbcbdacdbdbccbcdccbbcbbacbadabacadccccccbbaabddbcdabacaccbddabcbdabccbbcabbddadaabcdbaaadaacdbbaacaddcdabddbcdbdcdccabdccadcbdadccbdbbcaccbcdddacdcdcdddbbbabcdcdbcaadcdccacbacbcdaaaabaddabdabbcabdddcdcdcadbcaacddcdbdcacccbbacdbabbabcabdbbaabbbccdadcdbddcdbdcabdccdddacbbdbcabaaddacbcaacadddabbbadcddbdadccbccccaacdddcdcaccdccdbbbdbacbadbcadbbabdcaabdcadcccdababaadbddadbdbdabacdabdcbadbdcccbdbabcddbdbcaacaadbadddcadacddcbadbccabcadbbacabcbbacbdcdcdddbdbcadddcadacadbbcaaaabbddcdddcabcccddcdadccadbdcdcdbdcacbcadabdcacbaabddbddbddcabddccbdbcadbbdbcaaddbdcdaaadadaacdcacaabcabbddbdacbbddbbbbbcaadcdaaccadabdbccbcbdacaacbadcaacaabcbcccdbdababcccbccdabcdbccacbadabaaddddcdaddbbbbaddadbbcaaddcaccbacdbbadacaabaabaadadbdbdcdcdcccdcaaaadccbcdcbcadbdddbcbddacadccdadcccddcabdbdcdccdaaabcacdbbcbdadbaadacdcbbbacdbdbcccaacbbdcacacbaaaccdccccacabbdbddabdbabdaabcadbccdcaaacddbcbbacbdcbaadcdddddcbaaadcbdaaacababbbdddccccdccacbaadadadcdddaccdababacaccbcacdcdbcdabbbbcdcccbdcbbdcbcdccadaccdbabadbccdcdabcdbbbbdcbadabccbabcbbaaacaacadabbbbbcdcbbcabdbbacdbddaacbddcbdcaacdacddddcdcacabaabcdbcbbacabcdbbbcbbbcbcbaccddabaadabaadcddcacbbdbaadcbbdaccacbcdbdbcdccbdabddcbaccbbbcbcaaaaadcaabcadbaccbddbbcbadaccbacddccdabbcbacbdddddbddcacadbabdbcdcaadbbcdcabacdbbabcdbdaadbbbdacbcaaaaccdcacdddcbbbdbadbcddcdddbbbbcaacabcdacddbabbcbcadbdcbbccdddabbccccaddcacbabddcbadacadbccddbcabaccccdddacbddcccdaacbdabbdbcccbdcdaabbdcbababdacbbababacbdadcbbadcdddbaddddaaddacbbcdbdddabacbddaabbcbacddacbdbacdbbbaaabdbcaababcabdcddacaddcddbccccbbbddbdadcbabcbaddacaaaaddcbcdaadaddccddaabdadadcaabadbdccbdcabddcdbabbcacddbbccadacaadbbccbadcacaaddcdbdaccbaccccadcaccbacabcbbacadcbddcdadaaabcbdbbabbccabadddccdcbbdadbcddaadbdabcadcbdbdbdddcabaaddcddbcdcbcccabacddbbbcaaccbdcccdbcadcbdaccbbaccabaadcacadddbbacdbdccddadbcccbcddabbddbabadcaabdacbbcdbcadcaaddcdadcdaaabdabbbcdcaadaabdbdcacababbdddcbcbacbcdcbdbdaddadcacdadcdadcbbadbbacdbcadaabdbbccccaddbacdcdcbcbdcbcdbbdadbdadccacdbdbcaabddbcbdadcbcbdbcbbdbcbdbcacbccdbccadabadcccbadabbbbaaaaccbadacbcbadbdaccbdbcadbcbdbaaaacbacbbbdbbbabbdcadbbacccaacaaaddcaabddabdcbcabbdaabddacbccdaddcacaaaaddadbaacaddaccaadbabcdddacbdbacbddbcacccbaabdabaabbcbaccaabddddacdbbbdabbddbaaaccbaabadababadacbbbbcccbabbdaabdddcdcaadcbacbddbccaacacdcddddcbaaaccadbbabaddacbadacbdadcbaabcaaddcdaddcbacabdadadbbdbdaaabdbacacdbdbacbcacadacbcdadcccadcacbbcdbadcbddbbdcadabbaaabaacaaccbacbddabcabdddcdabdaddcdabccaacbbcbbccdabadcabccabcbcdbabdddbbcacddaaaccaabaacacdbbadcbbcbbcbdbdabbbbaabdaacaaddbcdcadbcaaddbbdccdbcdabdcbaadabbcbbcdddabcbbcccdddacdcdbccabcbdabdcccddbbddbccbbdbabcdaadabdbadadcbacaddbdaabaabcabcbccabddaabdbcaddddababbacdbddbcdbdcaadcabcbacbbddddbcdbccadbbccadbcadaaccbcbcacacbdbdbacbdcadddcdbccbbabcbdbbabbadcaabbaaacdcbbdcbdbcdaadaadcccabbcacdaadbbccabdbdddbbaaddcbcbcabddbbdbddacdbcaacbbbdaadcdbdcaadddbccdbddcccbdcaddbdaaadcbdaddaabbcadcdbbbbbdbaabdabbccbdcbbbadcdabdbccabccacccabdaadacbadcabcddbbababcbacccabbcadcddbbcdccabacabbabdcaacddbaabddcdcbcbaaccbcabddcbdccacbcbabddcbddcccbaadbcbddaabbbaacabccbababbaccdbcbdbacdcbbbcdadcdabccbdcbbbadbdcdcadaaacddcddbccbabbcdbdbcadabcaabdbaabcacaaccacadddccaccdddcccbbbdbbadaaddddabbacaadbbacaacbaaddbacdbccbbbbddbdccadaabacabacacbbaacbdcbccdadaacacadbcacdcbaccdbdddbdaaccacbccccbdbbaacdaadaddcbbcabcaddabcabbadccacaaabddbbaabbaaaabdccadcbcabacacaaaaabbdadcccbbaacbbddccbcdadbabddddacadbcabbcbcdcaabbdbabbabdbaaaaaacdcdcabacbbddabcbccddddcdccaaabaaddbbccdbaddbbccdbdadbaaabbbddacdadbbdbaaacabaabaccccccddddcdbbadcdcbadcccdbbbcdcddabdaaadaadcdddbccbbadadbabbddbbadcabbcdcabadaddaacdccaaadcdbccdbdcdddcdddccaabbbaadbcdbbabcaabdcbaadbdadcbcacbacdcdaabdcaaccdcddabbdddddbadcacbbaabacaabbabbacbcdbbdadcadccbcaaacacdabacdbcbabdcbbabddddccabacabdcbcadddcabbcdbbcbaabbdcbdbabcdbacadabdaccaabdacbdaddacbcaabbbdacbdbcdcbbadaacdabbdcddcbbbddbdcdbdbcbdababcaabaadaddddbdbbdddccacbcdabbcaccddcbbdabbaadcccbaabdbaaaddddcbbbbdbdaabbdaccccddadadadccbbbbcbaaddbabcbabdbdcaaddcdbacdcbdabbaabacbabdbddcdcacddbccabbccdaacdddbdaaccacbcdcacdbdcbdcdaacddbbddaabcbaadaccdccdddbcbbbbaaaacabccccaabdddadbadbacdddcbddccbacabacaddddcbadbaababaadaaddaadcdbbbbabbacabcadacdbbddcaccccdabaadcdcacbddcdaaabcddcdccbbccbcacbbbcccdacbdbdadbbcbbaddcdacadadaadbccacddddbaacbdabaabaaddcbbcdaaddbaccccbdbccaaacdcbadbacbbcccabcccabcaccbbcadaadbdbadccddbcaacbcbbbddbdaabbbaaccbcdccbdddbcacdbdddacaccbcddadaadccabdbabccbaaaddcaddddacbddddbbbbbaabdacdabbddddaadcadbadcccaccdcadcbbdbddacbacbdaddbdacdddbbdbadbcaddaaaaacccdcaaaaadbbacadadcbdcacddaabcbcbccaabadcccbdaabacaacbbdabdadadbdbabccdabdbbaaacbbbcabcbbbabddaccbaaacccbcaccbbaadacbadddcbddbdadcdbcdbdbabaccdbdacbddbddcccadaaaacbcbbbcaacccdccdbbbddddcaccdddbabcbaddaadadbbbbbacadcdadcdcddbddabbaaaaabcbcdbcbbcaacdcccdadabbbcdbccdabadadccaababccdcacbdbdbddbadcabcbdcaddbbbccababcaabacbacdcbcbabcbbcbacadadbdbabcbccbcbdadbaddcbaaddddbdadacaccadbdaadcabbccabcadabdcaacdaacbcbabbcaaaaccaadadadcbccbdddbbabdcccdcdcbddbcbbdccbaacdadbabcdadcababbacaabcbcdadbbdbdcdabccbaaacacbabbdcbbdadaacdddaaccdcdbadcbacbccaddcbcdbcccdabcdbcbaacdbdbbccdbdcdddcdddbbddbadccdaaaadddbacacccbaadcacccbdcdbcdaaaccadcadbdcabbadcacdcbdadbddddbaccadaadcadcccabbdbbbaabadacdcacbabbdcdcccdcbcaabaccabdddbbadbdccbdacbaadabcaadcadaccccdadbabcbaacadcddccdcadbbccccbdbcddbbdbdbbcaacadabcaaadabcbcbdcaaccdcadccacdacadbbabbbddbbabadcaabccbbaaccddbadbbdadcbabdbdcddcacbbcacadcaacdcbdbaadcacacadbdcbabccdccddcddbdcadccddddccadcbddabdccadabdadccacbdcaaaaabbdaaadcaadabdabdcdadcbbbddacbbbacadbaadbacabdbdcdaacbbadaaaacaddccacaaddacbdcdaddadabaaccbaabbddcdcdcddddaacdbbbadabcdbcdcbbcaadacccdadcaadcccaaacabacccadbacdbdbbaaaddbbbcabcacbccddadbcddbcdbcddddddaadaddabdddbcbbcaacbddadaacaadcdcddcbbdccacddabacaaccdaadbcbababbaacbdbbcbacacbbcadbdaddddcdcacadadcbdbccddbdcbccacddbabcdcbccccccccaabddbbaadbccdbddcbcaaccbabcdddbbcadcbdacababcaccadcbdbccdbabacaaadccdadcddbdcdbdbdbacdcaaaddcccdcdbaacccaadadabbabccbbabdbccddccadbacccdbacccdbbbccacbdbdadddbdbbdabbdbaccdccbbddcdabadadbcbbdcabcdabcdcccdbaccbdaccbaacaadccbcdccabccbcdddcdbaccabdccbabacadbbccadacbdcabcdbbbdabacabacdbddadbcddbcbcbbdbbcddcaccbbbbcdcbcbcbaddddcacbcbabbbdacaadaccdcccdaadacbcaaadcbdabbcbddaabccbccdacbccbdaccdbadaddadccbbdcbbbccbaabcabddbdccaadbacacdaabccaabadabbbbaadddcbcabcdcacabbbacbaaaadacccadddadaaaadbbddcabccbdabdacbbdddbaddacbabcdabbcccdadbdcaabbacbaabbdabbccdadbbaabacccaadbacacbcacccacdaaadbcbbcadbdddcdadddcbabdbabbccbccabdbabbbcdbabbabbbbdbdadbcaabcbdabbcbaaacdcbbbacdaacabadcdbbddcbacddbbddadaaddbdcddccdacbdbaccabdcabcacabacbcdacdacbccbbabbcadbbccabdcacbbbcabddbadbcddccadaddbbcabbdcbdaddabcbabcabbdbacaaacddbdbbbbbaacbdcdccdbdcddbbaaaccacdbbcccacddabbcacaadbdadcbbdacbacbddcaccabacbdbaddcdbabdbadcbbacddabcabbcacbdcdcbdbcbbcddadcabaadccbabcdaaaddccbbcbcdbabacbdabbdcdcbcbbccbcdbdbbcccbdadadbcddbcabcaaddbadcccbcaddbdbbaadaccdacccddccdbbbbdacbbabdabbcbcadbcabbcbdccbbbaabacacbdddadbbdcbcbaccaadcccbdbcbcaaaaaababcdbcbcbacddddbabdcacbcaaadabbcbabdbdbbabcbcbcadababbaaabbcbdacabaabbabcdbadcbcaadbcccbbddcbabdabcdbccabcbaccbddaacbbbdbbdddacbcbdbaddcdbbaababaccddaacdbaabbaacbbbaadacaddddadaddcbbaddaccbbadacccabcbcadabbcabacacabacdccdcbababccabdacaddcdcaccbdaadcacbbddcdaddacdccddddbbacbabadccdabbaddddccacaabbdcbabddcddabadaabcbaaddcbddbacacbccdcaacbcdabdbddcdcadbcdbcbdbbabdcbaccdbcbacabcdadccaacbaacdbdabbcacaddcddcaaaacbbadcabcbdcbabbaaadcddacbaaabddabdabacbcdbcabbccddcacbbbdbbbbabaddadacddccacbacdbddbadacbbddbacbaabaacdcbbcacacbcdcbcddbabcacdbadaadbdcccacababcdcdaddadbdaaccbcacdddbacbbddcbabaaabadabacbdcbabdadcdcdabacbabbdbacbaadbcdcaadbccbadbbadabaaddbcaddcbbccabdcaadccadcccdcbcdabccbbbdcbdccabdcbdcdddccbcadcabbcdadadcadbaaaaabdcadbadabcdccdccadbdbacddbcccacacbbcaccbbbadbaccaadbdababdbccbacbbdabddbaccbacdddddbccdddbdccdcbbababbccacadbcdabdbdadcbacacdadbacbacdaddbaaaabccbcaccaccabdbacadbbdddcdddacbadbddbbcadcbbdbcadcccdaabbdbabbbdcbddbdaaadcddbadcbdabcbaabbaadcbdcbdabbcadbcddbcbbbdccadacbdacacbaddbcadbabdadbbacdaadcaaaaabbdbbcdacadddabacaacccdcdaaacdabaccddcacbcdddbcacbadcbcdbdbbabbddcadacccdbcacbbaaadacaabdcdbdbcbabbdaadbcacbcddadcaaaaaddcabbadcabcdcadabdbbadaaabdbcbadadcdcdbadcbcbdadacbbdcacbbdcabbcdcacdbbaddddabdabbaccddbddcbacdddcadbccccbbadbccaadadbbcbbcbccaccabacdbcdaadbbbbcacaabddcccdcbbaabbccbbcbadcbcdacadadbdcddadabbdabdadcdbddbabdadaadccccbccbbdcbbbcaddadabdbadabbdcdcdbdbbcdcddaadcbcbdccbdbdddcbdaabdccddbcbcdabacaacdbaddcddccdccbadccddaacadbacaabaccaabcccbcdccdaddcacdddccaaddacdcdbddbabddabbaabdbadcaddbababcdbcbaabcacbabcaccaaaddadddbadcdcaadbbaacbbadabbbcdcdbadbababcdddadadabcccccacdbbabaaccbbadbbbdbdcdbcadcaccccdccddabbaadbbbacacabcdddbdbbaccadcaaacbacbaccdbbaaaabaddcdbbbadacaadbcdbccaabbbbaddbdbccadcabbdabddaaccbbaacdbbacbcdabbdddacbadbbbcddacadbaddddabccccbbababacaaaccdaaddaabcbbaabaadcadacbbdcbdbbcadbbaacdcdbdabdacccabbbcbbabbbbbdcbbdacabbcbdcdaadbcaacaccdacdcadaaacaacbccbcddcaabdabdcdcaabbdbdadbabcdbadbbdcacbbabcdadbcccbadabddcaccabcbdbdddcbdbbadcccdcdcdbdbcbbdddbabcdacdabcbbbcddacdaaaaddcacccadcaddddadadabbcbbdccabbddcacaadcdbdcbdadaccdbdccaddccccbcddacdadddadbbcaadbdabcacbabbadbacdccbcbdcdcdcbbbccaddcacdccbbcddcaddcdbccdccaadbcdaaabcbadcdbcadcdddaabdbdcddcddbbbaacbdaddabdbacccbcadcdbddcbdddcbdbcddabbcadddaabadaabbaacadaabadcacccbbdcbadddcabcdcbdacbcadaaabdbabaadddcadbdcccdadacccccbdcdbbdbaddbbbdbdaabadbbbabcbccabdaabbdcabdcddcddcaaacbbadcbbddbcbcccbbbadbcbdddcabbddbdbabadcacddaddcdbcbcadabbaacaacdabbbccdacbdacbbddcddbbabccbbddabddbccbacabccbbbbcddaaadcbabacaadddadbaccdabaaabddbacabbcbbbbadbcadddabcadcbcdabadadbbcabadbcacadbbcaaddacacdcaabccadabbacbbabcdbacdccabcbbaddabcadccdbdbadbcbabaadbcdaadcbddacaccbdcdbdddbddcddadabdbbaddbbbbacababcdbacaddccbbbcccccbabaabddacbdacbadcacaacdcdcbbbbcbbdcdbadacbcbadcbdaabbdcababbacabbbaadadabbdbaadcadbbbddaadbbddaccadbcadcbcbadaddbbcccdbaacabdbdccbaacbacbdcadbaadcdacdabcabbdbdaccbcdaccaaddccbbddbabddbbdbdabcadacbbbdddbccbbdabadcbcdbbacdcbcdcbbcbacdddabcbdcaddacbcbccbbbaccbaabdbdccacabbabadcdbdcdccdbabbcdccbdaadcadbcbcaabbbddccdcbcbaadddaddbdacccbbbbdbbacacdbbdddabacaabbaaaccdcbcdbacddbabbbbbadcbcaadaddbadbacbdaaaaadcbadddadcaabbbabddabcccadbdbcaaccbbcbccccdaabacbaabcbaaaccbbcacdbbbcbbbbcaaddccababccaddbcbaaccaadbcbadadadaabaabaddadaabbbcdabdcabadaddabdacdcddcbcdbcbdbdbaaccaddbcdabcabacaccccccdcbbcdcccbdcaaadcaaaacbacacdddccdaadbddbbdccbbabcabbbcabbcaccbbdcbdaaddccbcbdabbabdabdabbcbdbbbdbcbbbaadbdcbcdbcddbcddcbdcdbddacddabddadbcacdcbbcdadaaccabbddcbcbbacddadddabaacbdccbadcadbbcadcaaadbbccabaabadacdbadacbcccbbddbcbbdcdadaadadbaacccadabbcdacdacdddcbcbbabbacddaccaaabdabdadbabbbdabdbbbabdacbdddcadacabacaabbadbdbadbbbcbccccbcadadadaccacbdcbbddaaddaddadaacbbddddbaababddcbcdcccbcaabdadacccdccbddcdbcccdccbcdcbaacaddcbcadcadbbdccbdadcadbcdbabaacbabcdbccaabbbccaadcabcdcadbcdbabbcdaaaaabadabcdccacbbaababbcdcbdcbccbcdcddcabbaabaaabddbdbabbcdbabbddbacadbdaadccbcbccddcdbbcadbaacabcbbbbabdcccabcbbbcbcbacbdabbbadbdacacaddbbadccbddabaaabdadcddbabdbabcabdbbcccbccccbcddaabdbcaadacbdadaddadabdcbcbbaacaccabcaaacadbcacbcaaccdcdaccbddadcadcbbaaaddbdaacbbaabaadcbbaaabcbabdbcbaaaacccbbacbdccdcdbdddabbddcdddabdbabbdccadddabaabcdadbcadbdbbcdcbabbbdbbcbdcadbbdbcbbdbbdcdbccdddcbaaccbbbacacbccbabddaddbbcdbdaacccdaaacaddcbcadacaaabbdbcbbbbddcadaccbacbcdbbddadcabbcdcabdbababbbbcdabdcdbcdaadaddadbdadbabbddbaccdbaaadcdcdcabcbcddbacdddcbaabbbdabcdccbdaabdbcacadbcbdcaccbbacabcbaacaaabcacadcaadadacdabcccaababaccaaadccbdadcbcdabbabbcbdabbaacaccbcbbdbadadadbbabdccbbbcccbdbaccbbdacdcbcadbdbbcdddbdbccbaddbbcdbbababdcaadabccaacabacdccacbbaccdbbcaadbddabbdaccbaaccdabbcbdcacacaacabbabadccdacdddcbdcabbbaabcbcbcddcdcbbbdbddbdbcddaddaddbdacacdaccaaaacdbadabaaabdbbdbccbabccbdcdcacdddbcddbaabaddddbcaccabdbddccdcabbbadadcdbcddaaddcadccacbaadbdadbdacbacbbcccbddaccababdaabbabdcbdbccdbcbabdcaddbaddcaddaddcbabbcacbbdddaacdacbadbcadddaaccbddddcdcbadcdcbcadadbacddbcadcbdbbdbbcdbdcabcccdccabbddbabaacbbdaabaaccccacdbdcbabdcaccddccacccbddbacadbbabcbdcbdbddacdcdbcabdbdcdaadbbcbabccbdbacbcdcbddcadddbccaacabbbbaadcbdbdbaadabbabaabcddcccacababcccacbbabdacbcbdcddbcbbdcbdbdddcdbacaddcdcaabbcdcaabbccccdccbddbbddcdbbababbabcdabbdcbacadddbcadccaccbcdcadbbcdaccdbcaaddccdbdbcccadbbaacaacbacdbaadbccbadadabadccdddccdbcdcccbdbbdbddcdacabcdbadbcadabcccdcdbdacaadabbbbdddbbbacadbcbcabbbababbbaadbbbaccabdccabaadaddacbabcbacaabbccbbdcbcadbdabbcacdbbcabbddbbdccbccbdbbdadaacbcadaadcdccddaadbdbdabaadcbbabbbbbdbdbcbbbbaaccbccadcdaaaacaddbdcbaddacadcaabbacbababbaadcccbaddcabbdbbaaabbbcaaccddcbdadacbccdbbadcdacaadccacdcdbbdadabdcadbbcdcaaccacbcddbcddcadccbaadcdbdcdccdaaaccdabcccbdbccbbcbdbbddcddacabdbdddabccacaabbcbbddacbdbbdaccabddaccdbdbcadbacaadccdabbcddbdbabcdddcbbcccbaccbdccccbadccddcdbdaaaaacadaadcadcbccabbbacbacadbdaaacabacbcbcccbbddabbaabacaaacabaadbcadacacbdcabcccbdcaddcbababacbdbbccbbcadbcacabccbadbdacaacbcdcccabcacacbaadcdcbcbccdbcdaadccccaaabaabaaaaadbbcadbbdcbbaaacaddcacbcbccbbdbcddaadbcbdcbbbdbdaccddcdbdacacbdbbabdaadbaaddcadbcbcabcddbcdbabcbaabbcbcaaaabdddacbdbcaccabacbbadcadbbcbcaccdddaaccdbccdabaaccdccacbcaadaabcbaacabcddcbccacccdddbabacdddbcdbcdddccddbdadddcbabbcadcccbdbcccbbbbcbacdaabccccdadcdadadcbbadbacbaacbdabdacdcbccaabbcccbcbabbacbddabbbcbcdcccaabdcaabbdccdbdbdbadacdccaaabadccaccccaadbdbccdaacaaddabaaabaddaddabccacdbbdccaacabccdbbdcbbdccccdadbcaadbbccbdabddaaddcbbacbcadbbaabdaaaaaacadddbcccbdaadbaadcadcbadcdddbccabccdbccdabdbcccbbbbcdbabcdbbdcddcccaabbabbddacbdcdcabccbaacaabadacaacadaabbccbdcbbaccbadcdcccbcbddabcdaacdccbadbdccdcccabadabaaddbcbbdcacdacddbdcbaabccdabcabdbabbddbacbddccdbddadccdddacdbccaaadbadadddddbccdcbcdadaacdbcbcaaccbcaccdcacdbaacaabaccabaaacdbaadabbddcadccdabacabadaabddddbbaacdbdbddaccdbbcdbdacbabcdcbbccabcbacacccbddabcccaaaacccdbaccadcadbddacdabdacbaabaacddddbabacabcddbbbbadbadbbddbabadbbabacdbbdacdcdbbacaaddcadabacccacdbaaadddbbcbbadbbcadddbbbabdccaccacbcaadcdcdbacaaaadbdcdadcdcabdcbcacbacaddcbbaddbaddacabcdccbaabbaddcddbdbbbadcaaddcddaaaccbccaccaccddcbbaaaabadcabdcccbcbababcadcbabbbbdcbcdabdcabdcddaaccadbdaccbdbbaabcdccbabccdbaaabdbadaadbdaddbccbbdacdaabcbccbbadddcaccbdcdcbcbcadbccbcdaacccabbbdddabbddddbcddaddbababacdcddbbbdaabbbbacdbbabaabbadbdbcdbaacacccdcadbbcdabcbdabcbbbaddbbadadbcdcddccdbacadbcacdcdbbbacddcdbadacbbcbadcdcdcabaaabaadccabaacbcdcbcbbdcaadacdcdddcddacbcacbbdaaaacaaaaacbbdadbaaaccacdababbbdcbadadbbcacaccddcacdbcdaccbdddacdaabdcbdcddaaccabcbddbadcadbccbcccccaddaccadcdbdddccadabadcbadccdcccdddccbdbdbddcaabbcddaacbcbdbcdcdcbdcdbaabcbbaabdaddbbdbbbdcbabcaccdbdcccbdacacdccbccccacbadbcdcdddbdccdbccdcddaaabcbcacbbdccbdbbbdbbdcdcccaabaddbabbbcaacbaaadabbcccdcdbbdcbbbbdbaacaadcbdacbdbaabdbdcdcdabcbacddaaadddabbdbbadcddbbdbccbbaacdccabadcbdcdddcadabccdacacdabadaddabddbbcabcadbbcdabbdbcbabdddaabcbdbbabdbcacadcdabbcbdbcbaadcacdcdbccbbddcccccdcddddbcacaaaabcbaabcaaadabdaadcdcaaacbdabcacbdbccdacccbbdbacddadbdcdaccddaababcaccacaadccbdacaaaabcadbcbddadaaaddbcababadaccdddbaaacabccaddccacbbcddaabdddacadcbbbbcdbdcccdddbcccdaabdcacdbcdcdccbabcdadbabcbaacbddadbdbdabcdbccbdcdaccdddcaaadccdbddddcdbaccaacdbaddabddcbddcdbcaccabdadcddbbabcdbadddcccddcbbdbbcacbadddcaadacddbbccacbbcadbdbcaadabbbcdccbdcccabcaabdabcdbcbbbabdabccbbcbaaaacacabadabcbadabdcbabaccccbacbbcadcaaaabbbbcdddddbcaccdaaaccdbddccdccbaddcbcdaaccbbcccdaaaaaabdbacdbabcaaadaabcbabbaabcccdbbaaccdcacdcbcadcddaadddcbcaddbdbadcbaddcadccccbbadbaabdacbadddcadcdabbabadddcbddadadabdaccdcddcaaaaadbaccabbbcaadbbdcdbbdadbdbbccbabccddbaadcbabbcabcccadccddbdaddbabbbcbbdccdcbbadbdaaaadabcdccabdcaddcbdbbadcdccbabddddccbdcbcabbddbcdabaaacacabcbbbccaadbccbadcbabadbcddcadddbcbccbccbadacbbcacbdbdbcddcaaabacababdbacdddcadbbcabddacdcdacbddbaabccbddbbbabcadbaccdbbccbbdbacbabbadddbbbabaddbdbabcbdbaabdabcdcccacacdccddddcacccadaaaddcccacccdddcdbcdbaacdddbdcbcbbdcadbbdddbccadbbdddcbdccdacbdcbdbbcdbdbcaccaccacbbaddacacbdaadacccadadccbddadddcbdcbddcadcbccbdbdadbcdcaaabccaaddaabbacaacccbdcbbdbcbcbadbbaadadbbdaccabadbacdaabbdbdbaadbcacbcaccacbabcccddadccdbacaacbddcdbdacadcabadababacaabdbdbbabacabddadbaacbaccacbcdcccbadabacddddbaabacbdabacbadcdddbcbbcacaddcbbacaadadccbddcdcacabdadadaacbaaddbabbacdbdddbdacdacdcbbdcabcdbdbccccdcbaacbcbcadbbcdbadacabadbdbdcdbdcdccdcdaaddcbbcdbddaaccbacabbcbcdddcaddcaccbdbccacbabcadccbccbddaacbabcbbdaaacbbbdabbabdacdcaaccdbdaccbdddddccaabaacdcabbbbaddcbadbddcaabccdbbaacbbdaccbabddcdddbdaccbcbbcbcaadccaadcadadbdddddbbdcdccbcbcdabbbabbcacbcbdaabbdaaccddacbdaabdacbbdaaadbabaabaccaabbabdcbcdabcbacaddcdbdababccbaccbcaabdbbbbdddaaabcdaaabcacabbaccdaacbabaabbaccddcbccacbdbbadabacbdbdabdddbdbacabbbacccbcadbcababaaabbbdbcbcabbaabadbdbaaaadcdbcabddbbaacbbacdcacdddabbdadbbddaadcbdabdcdbdabadaaccbaccbaacccbababcbdabcbdacbddcbdcdcdacabdcdcadacbbacbacbdaabcbbdacacccaaacacadbdcdcdbabdaccbdccdcaaabdaadddcccddadbcdbcbcbdadaddbcdaddacddcbbacadcdaaadcddabaddabdaabddccbcdddbcdcdaabdcacaabdbdbcccddbcdcaddbddabbbaaacddacaacbccaccabaaacdbbdccbbbaadbbdaddccbdacdcddbdaddbaabacdbbccdccabdcaacaadccadcbcdccccadcaaabaababcbbdcaabbddbbddcabdbaccbcdbcdadccddddbaaadbdacdbdbcdddddcbdbdddabaadadbadbdabdcddcbbbbddccbdddaaaacbabbaacbcadcdaadbbcbbacdabcbdbcbaddbcadcdbaaaccbabbbabdbdbadccdaaaabacabdabbcadddaadbabcdcdbaddbddddbacbbaaaacaadbccaaaabcdddacaaaabdcabdcbbbcbbcbdabcdacbcadaadbdabdadacbdccdcadddbdacdbabcabdddacababcddadcacddaacabdcbdcacccaacdcbbaaadcdbccbdddadaddadadbaadcddaaabbcbbccbbddcdcbacccdcddcacbcadbcdccdacdbcddbdbdbabbdcbabbcaaadbcaaadddcddbdabaccdadcdddaccabcdbdcdbcdacdbaccabcdbdacabcdbaaaadcbccabcddadccbacaccbabbacdbdbdcaabcadcdbaaabdccbbbcddcddabbdddaaddaabaccacaabdacbbbadbdaadccdaababcdaccbaccadcbbbbdbcaaaadacdcdbadcdcccbbbaadbddbcbaacaaaccdcdccaacadbdbccbaadacbacbcbcbbbbacdbaaaccdcdabbcaabbaabdabbcababacbddababcadbbadcaaaacdccccbbdddadcddcdbcdabaacadabcacabadbdaadadbcabbcabdaadccbabbacdbdaacdcaadcaabbcdaabccaacdacbbcadddbbbbdbdadbcbdaabbbbaadbcdadddaabcccbcbcdccbaaabddddbdbdbcabcccbbcdbaacddbdbcdacbdcdacacccaddbaccbdabbbcdddabdcccadabbabcdbbccdbbaaccdbbcadcdbbbbbccabcbccdbbdcbbbccadccddbabddcadccccbdccaccaadccbabcadbccbbbaddcaabcdcddbabbdbbdcdbaccaaadbcdcbacabaccabbbbccacadbdddddcadaddcaadadadadcacbdadbbdcaddbbccdcaaccababdaadbcbadaacbcacdadbddbacddacacbbdbccbbbaadbccdcbdcabaadccdadccdadbbbdaadbbdadcbcdaccccccccbbbbdadadaaaddcaccbdaddcdcbacbcbabaadaaddabddbddcdadcddbadaddaacbaddcacddbaadadabaabadabadacadabaacacdddaccccddcbcabbacadadabcdcdccbccdbcdaacbcbabaaaccdbbdddddadabacbadcbabcbbbcdabccbcdbbabcdbcbadcbbcbdacaaccccccccababbcaaabccbacdccddbcbbadacbaaccbcddbccababbbccbcdbcdcccadbcbcaddacccaaddcbabbcddaacabaccbaddbaadbbcadcdbdadadabbaccaccbaababccdcabaababbbcbbbaaacbdbcddcacdccbbddcbdacdbbabcaabcbcbdabcdbdaaadabbccacdabcaadcddbcdbbbccddcadbcababbcbbadcccadcaabdacacaddbdadcaabaacdacaabddadcbdddaaadccddaddbbcdbddccabaaddbdadaddbdbbdaaccaaabddcbdbcddbabacacbbbbdcddccdccbbddccabbcdabcddbbbcbcadbaadababcbcababcddaccdcbcbdabaccabcacaddadaacbbccdabdbabdabdbacbadcadccbcbdcabcddadbdbaadbddacbadadbcccaccbaccbbaabbbacbbcaccdacabbbddadcbbabcdaddbaabacdcbcacadcadcbabcaaacbababcdbccbccbaabbccccbcdccabddbabcaccabdbbdcbddccaddacbdbcbbacdbaacddcdcccbbabaacadaaaaddbcbbcdbdbcabcbcbbaabaabcddbaacbbaaddbdacddcbbbccadbbabdcbadadbabaaabbcdcdbadcbaddbadababbcccdadccadacdcbdcbbacbadcbdcdcabbcbadcbcbbbdacdcbadbdaddcdddabccabddacaacccadccddcdaddcdbdaadbccbdaccccdbabcdcbaabdcddccaccdbabbdbbdbacbdcbdbbdadcacdcdbcbcdbacccbaaabbdbdacdcdbcaddaadadbbacdaaaacbccddcbcdcacabaacccbcbdcbcdaddbbbbcdacbdadbcdabadcadbcddcacddccacacbcadcaadcbcbbddacbccabbcddcdcabdaacaddcdacdcaddbabdddddddbacabbaaaddcbcdbdcdbdbcbcdbcdacbccbdcabbbaddaadddaccababdaabcddbbacbccddddcaccdbdadbcaccddaccdcbbdaccbdbaacaadaccdcbbbcdbacccbccaacbbcbddcbabdadbccbbadbccdadaddddbaacbcccdaaadbdaaccbbdaadadbdbccabcbadbdcdaadbacadcbcdbcbaaccbbaadddcdcbdaacdaacbcdbcbdcacbccbcddcaadcabddcdacbbaaabaacbcabaadbbadaaabcdaaccaadddcdbbddcacdadbbdcddbbacbbaadaddcadbcbacaaacbadcbcbacccddccabccacaabdcabcdbbbddcdbcadcbbdcdbbbdcdababbccaabdaaddaaaacbdcaccabcaadbcacbcacbaddbdacbdbbcadcaabadadabccccdbddacdaabcaabdbabcbadacbaabddbcdbccbaabddcbdbcddaadacaaddbabddbcabdcdcabbbdaaccdacaccbdaddcbaddcdddadddbbcdcdddbdbcccccdacdbcdbaccacaadddbddbaacbadbcacccaacaacdcabbbccccbadacdabddcdbababbcbaccacbbcbdadadbacbababbcacccdabdaddbcccabccacddbbabbcaddbbbaacccdcbbcbaddcbbdbdddbddbcdabdccaadbabdcbbcdbaccacadacabadbaaadaaccbbcabbbdaadaabaaccbacdbbabdbabacdadacbdabccdcabadbdcbbbacdacbacbbccaaccdbdddccaabaacddcadcaabdbddccddaacbbcbbbbcbbbbdcadccdabdadcdbacccdaaaddaaaacddddcadccdcacdbcbbbcabdacdcbbccadaacddcdccddbacbbcdbbcacbbdbbbaccbaabbdcbbddadccbcddcaaabcdcacdacbdccabaddbabcaaabacccbcabcacbbcdadbdbaccbdcdaacbaccbdbbbdbddddccdbadaacbcdddbabcbdbdcdddcabadddacdbccbcaabbadddaacdcdbcdabccbdaabbdddddabddccdbaacbadcadcbccbcaacaacacddacacbccccbcadacddacadddabcbabbbcbadccdccabbdccabdbadccdbccbdcbbbdacbbdcacbadddcabdbaaabbccccbbbcdddadccccdacdbabdddcacdddddaacababcdbaadccacdcbcdaddcdbddbaadadccbdcdbcbddabdcabcbdacadcabaadabdcacadbdbcbccaacbcbcbcacbcccadcdbccacbcacbbcbddccccddaaacbbbadbcdbcbdcacaabdcaaddcdaaacabcabbbadbdadcbbcdaaccbdadccddcababbacaaddbdcbddbdaabcacaccabbcbaacbbbaddbdcbcbbdcaacccaaccabddabbddaacdbbbbdddddbabadcaadcbaadacccdbccdbcaccbdacdbbabbcdddbcccccdcdadadcaabcccbaacdcccabbcddcdccddcaadaaaabcdabcbcdddcbbbbccdcddbdbbcabdcdbaaaadadbdddbdbbbabbaadccddabccdbaccdaabbbacbdddaaccdcccbcdaabbdcdccdaabbbaaabcdddbbabdbbabbaababdaaaaddcaabddaaddbddababcdbaacddbdcadcccccbcdcdaacabbdacbbbabcabbbacabdccacabbbdbdaabadccbaccdcbcdabccdaacbdadaccbabadccbdacabcbdbcadabccddcbbdabddbdddadbacdcdababdbdccdcdbcbdbbbbbcdbbbcdbbddbcbbdbcdccbcbdcbcaaddabcbcdadcbdcbbabadccdabcbdbbbabdcadccdaadcdaacbcbccbdcacdcdcccbdcabdcdadaaaddaccacbcabcddcddbcdabdcdbadcddaabbccabbddcaaaadbaacdcbbcdbcbbcbcbcdadcbddbdcdcbdaddbccbdacadcaddcdbaadbddbadbaddcdcdbabbddcbdcddaaaabcbdacdbdbcbacbbdcdcaccdccdcadadbacbbaaacbabbcbbaadddccabdaccdcbcdbdbdcbcddcdabbbbcbbdbcbdbaadbabcadddbbdcdacccacabbdbcdaaacbabcabdabacdbadddbbbacccddcbbcabcbbcbddccbbdcdaadddbdcbdacaabccbaccddcacbbdaadbaacadaabdaabbabdabacdcdaaabbdbcdcabdddbddacbdbaabaccdbadbbabbacdccccddcadcbdaccbaccababbdbabdacbaaaadababdadcdadabdcbaddddccaacacddaabbcadbccddbcdaaabaddbcddadbcddbcdadbbddabbacbdddccddadacadbacbcbdbbbddccabccbabddbbdbcbcbdaabcddbdbcddccbabdacbcbcaaaadbbddbacaabadbdbbbcccacaadccdcccaccabdaacbbbbcadbadabdadbbbdcbdaadddaadaacadadadcadbddbaaaabbbbccacbbaabbdcdbcdcbdbabdacabdccdbcdcdcadbbdbcbcdacdaddbabcbcdcbdccacbbcbdabbccacccccadabdbabdccccccdbbdcddbabaaaadbdaacbcaaddddbbdcdadbabddbddcccddacbcdadddadaaaaccddaddacbccacdacabcdaabdcccbcdabdcdbbbaddbdbadbbdcadbadccadcabdbbabadbdbbcdaaadbcccdccccabbadadcacdbaddacaccbabdadddaaacbccdcbdbadddcbabcbccdaabaddcddbbbabbdbabcbbbbddddbaaacabcacdaacbdabbdbdbdaadbaddcadaaaabcacdaccddbdabbbdbdcdcbabadbbbdbaccbcdbccdbddababcbbabacdccaaabcccbbcabbcbdddcdaadbbdccaabbdcdcdbdadaabcdbabbabcdbddccadddabcdcdadbbcbacbadbcbaaccbbbdadbdcdabcabcadadaddbbbbddbaaddddcabaababcbaabccadbddddcacbcdbdacaddcccccabccddbabcabdbaaddbcccabbbdaabdbaacadadbcabdccbaadccdaddddbadbdbabdabddadababccdabdcabaccaaaadcabcbcacbbaadbcaccdbabbbaddbdabccccababcbbdacaacddcdcdbccbaddcdaccbabacaabcbdadcbabcdacadddabbaaddaadccadadaadcbcabdcabbbbccbbbcdbcbbccbabcbddcadbbabaccbdacacacbbcaccddabbcdbcabcccaabcaacdbbdccdddaabdaaacbaccdaacbacaabaadcddbcababbabadddcbddaddabdcbbcddbcbadabaaabaacccbcaaaadbcddbadadcbdbababcadacbbcddbcdbdaadbdacdccbbababbccbacbaccccbababbacbbacaacbbdbccdbcadaccddcdbabaddacacdccbbddbcacabbaddbcddddcccaacbcdbcccbcabbadadbdbbbcdaadcddddabddadccabacdcbbcadabcbbbccdadadacbacccdddaacdbadaddbbadcdabcababcdaabacbdddcbccdabbdaccbabcacbdabcccdbaabdddcdcccdababbcdbdccbcbadbdabadbcbacdcdaabcdabacbabbcdbccddcbabaacccaadaabbbbdabdadddbaddbadcdbbcacdbdcdbbabadbdcdbddabdaddacdcaddccdadddddbbdcddcbccdbaacaacdbcdabcaabbcacbdcbcddaccdcddcaaddbbaccccbbbbcdddabdcbdddbdacddabacdcbcaaacbdddcabbdacccddbdabcbbcbcacdbaadbdbbdadcddcbacbcbbbdaacccacccccdbcdcbbcccbddacccbababbbdcbdcbbddacccddcbadcabcbdbdbabbcdbcdbbdbbcdcccdbabbddcbbababaacccbcccadacbbaabdabaacccacdcabbbabcbcddcabdbaccdbbabcadacbcddcbddacdbbddcbaccdbcbccdccabbbcdcddbaddabdabbadbdaccdadddbaccaadcbbdccbddcbbacadbaadaabacbcacabacdcdadbddcbdbdbaaacabddadbcccdbcaacbbabbdadabcdaddadbaddccdacccaddbbdadabcadbcdddababbbbcdbbbbdcddaacdabddaadacbcccccbcaabbdbbdbbadbcdbaacbaaddbdccbbcaadbcbddccadbaabddbccbdacbcbbacadccccbdaddadccbbadcbcbdccddcbccaaaacbbcdbdcabdadbcdcbdcacbabdccdbacddadcbccccadadbddbcbddddbbdcabccbdddddbbbdddcdcddcdabbacaccbbbabcddaccdbdadabbaddaddbcbddaaaaaadaaacccdaabcddabaabdbbccabbcbabadbaaaccacacabbdcbcaddcdacbdcbbdcdcacdabdbddcbabbacdccdaacddcaddaaababaddbadbdabbbdccababdcdccdccacbdbccaccacabdcabbaddccabdaccaaddaaaabccaacadbcbbbacbbddbbdbdcacdbdabcdccabaaccacddaccbcdaddaadbadacaadaaaadcdccbcacddbabdbaccdbcbbbdcacdaaaccbcbbacababaaddcaccacbcdadddbabdabacbbababdbabaacbbddacddcdbdadcccccbbaabbcbbbccdbacbdaadadbacbcdcbccbbbabcddadabdcdadaddcddcaccbdaaacbccbbaaaaccbdadddccababbaaabacadabdddccadccbbaddbdccadddbbcaaaabdcdababcddbddabcabcbbabacaacdbbabadaaaaaaacbaddcdcbbccdacbcaacaccddbacbbadbbbbacabbbaddbdabadcadacadadadcbbaccbbdadcddcbbcaababcaddcbbbccabcddddcabdababdccababdbdacbcbbbdabcddccccdcaddacddbaabcdcdccabcdcbcdcbbadddddbddaabbcdbddbcbccbcbaccddcaacccaaadcaadabaaadacaabcbbbadbadbadabcbdddbdabccdcaacaadaccccbcdccbbadccdbcbdcbccddcaadaccbbaaaaabcaacbbbcdccdcdbbccabbcdcddbddddcbbdccdacbaadddddcdcbbbddbcadaccdaddccbaddddddbdbcddcddadbcccddaaadacbccadddabbcadbbcbabdacaccabcdcacadaccdaccbcdaadbbabccccdcdaadbaaaabbdcdcbbccccacacacddbabbcbcabdcbbaaccbcaabbacddbadadcdbaddcdddadaaaadbcabbdcadbbbabbdaccddadbbcddaacdbbdccaabbcadcdccadbcdaadabcbcbabadccbccccccddaacabbbdabccbabcdbbdbbbcbdaacdbacaabdaabccaacdcaabbcabccbaaccdcdbbadcaacdbbbadcbdadddccdaddbdaccdbbbadcbacaacbcbadadabcabcabdcaadadbacacadbcbbbdbcdddbbbbddadcdabaabddcbbaaaddaacdbacaabcbbcdbbcbbcdbcdccdacbacdacbdbadcbdbcbacdddcbaaaccbddccabddcaadddabaacdaaaddacdbcaaaacccaccccacddddaabdcbddadadabaddbbaabaccbbaabaddcbdabaabdbdcccadbadbbcdabbbbcadcdccbabddbccbadaaaacdacddcabbdbdccadaabddaccdccdddcbcdbacaddbcbddacbdadbacbacbacbbacaacbbcbbdbbbdcaaaabdccbcaacbabbacbbaddbbdaacbbbdcccbdbdbdadccadacabbacaabddcbdcbaabcadcccabdcacdbacbadabbcbbdadcdbaabdabcdccdcdacbcdcdababcacdcadcdccaccaabadcaaccbacdddcadddaccddcadaabbbcdaacccadcdccdbdcbdaccddcdbcadaaccaaccdddcdbcbdcacadbddadabbabccccbadcdccddcabdacabbadcaddcbbdddcbcacaacbaccaaaddcddbbabadcbabcccdbcdbbabcbccbbccbdaccddbbadbbcabbdcacbcccadbadcdbdbcdbdbdaadcbbbadbaccbccbadbcdbaddaaadbadccdabbabddacbbccacaabcdbdddbdbaaaaaacdbbcdacddcbaaccddabbcddbcabacdcacacaabdbdbdcddcbcbcddbcdbabacabdabbbbaadbbacbbdddcdcadcbbdddddcdabdbadddbdccdcaaabdccbbdccdbbdcddccccaadbbcccbbddacadadccaaadcaabdacbbacdcdbbdbcdbbcbdcbcdccbacccadabbbdaccbbccabccbcdaccaaaddbaacaababdcaabdccbccdabcbccdabacdadacccbbbcbabcacdbdcbcacddccaccadcbccacabdadcccdababdbacccbaddaacdcccdccacadaabcacddcdddadacaadcaccbbaababbcdddcbddabbdadcdabbbbdcbccbcdbaabcbaddbcaaaabbccbabccdcdaacccaabbdcaadacbacdccbadababababcbddcbbdcccaccbaaaddadbbbbacabcbbacddbaacadacadadadcddcaacaaaccccdbdbbbcaacccaabaaaddaddbbacdccdabbbbdbadbdcacdcdcbbadbabaabaababadcdddcdbbacaccdbcbaddcdbbdbcadcbaadadcabbccbdaaccddddaacdbabbcdcadbbcccdbddbdbaccddbabcdbbbbccdbcadabbbcacdbdbcbddabcadbabaaadcaacaddbcaaaadaacbcbacdbdbbdaadcdbcbcccbcadbcaccabcdacadbadbcaaddcdcacddbddabcabaddbccabdcbdabadbbdbaacddabadcacbcabdbdcbbbacbacbacaaadddcaaabacbdbdbababcaccdcbccadabdadcdddcbadbdbaabcbaaadcaadbadabaabcbbdabdddacbadddbddccabbddccaaaaabadbbaccabaaacbaabcbacaabdadcbabcbbcbcacabadcbdccacddbacbabdcaacadcabbbbbdaaddcbbbbbccadacaccadbdabdacddcabdcddbbcddadccacddadbaadabbcccccbaddcadadadaaaccabdccddaddccddaacdbbacdbbbaaacdccaaabdadbbddbbbdcbdddccabccadabaddccdccbcbabcdbdcadcacbaaadbcbdcacabbadbcccaaccadbcadbdaddccaabdadccbdcddbbbbbbaadabdbaaadaaddddcdbadcddccbbaaacabaaadbadbdaabdacdbdbaacccabddcaaadaabbddbcddddcabbdcddbcabacbbadddcddcadaadaddcdadadbabcdbcdccbbdabbcbdbddaabcbcbdbcddbcbbbacaabbbccbccdbacaddbbbdbbcbbcddcbadcddddbcbdbbcbdbcabcbabcccaaabbbbdbcddbbddbaabbabddaadbcdccadbbdadcdadbbdbaaaccacabdbdabbbbcdbaabdaaccdbabbbbaadbcccbbdbaaacdddcaddbdbbbddabdbabdaaddbacbabcbcbdbdaacbccaabbcdcbdabcaaccaaaabadcbdabdacdbdddadbbbaabaddadbbaabaaccdaddcdcdbacacaaabcaccabbdaadbcdddbdccdaadbaadcbabadaddbaacbbcbdbdbdabddcddccdbaacaacbbaadbadccadabcbdcdcccccdcacaaacbddcabcdacaddbabdabbcdbddccababbbcacbaadbdcbcbadddcadcaabbcbbabaadcccdbbbddcaaccddbdaccdcdbacbcbdaaabbddbdbdaacddcdddddbacccccbcbadbdabdabbacadcbcbaabbadadacddbbccbacdcdbdcbabdacccbadabbaddcabdacdabccadacbcddbdcacdbbbdabbccdbcbbbdddcddabdbabcbddabbbaacaadddacccbbdcbadaabcaddcadcddabaadabbcaccaccbbcbdbacbccdbaccacdccaccadbccadbbdabaacacaddddcaaababcbaccaababaacabdbcaaabacbcdadcacdccbcadbabbdbaabcaabcabbacdbbddacdabdddcabbdaabdcbacbcadbaadbdcdcaabbbbddaabacccdccdcdddcddbcbaacccaabdcdccaddcbddbcbaadaadbcdbaddabbcddddddccaccdcdccababdbaccacadcdddbcdbdbadaabdcdaaadbadbadabdbbacacaabdabbcdbdacbdddbddcdbddddabccdcddcdcdbccccbbdccadcbbaaacbadaabdaddcadbcadcaacbbcbccdaaacdcdbcbdadcdbaacabccdbccaccddbcbbaddadcccbdabacdabbbadaccdbddbbabbacacdaabdbaddbcbcaddaabbbcdbcddddaddbacddbddccbbadbdabdcddaaddaadbdbdbbdbbcddddccdbdbcaabdccbbaaccbbadabcdaacdaaaccbccccddadbbbaabdddcaadadbccabbbababadcbdcdcccbaadabaccdadcbcbddaacccddadbcdbcadcacbddbccbabacbbbcacabaabccbddadcadddbdbddcddcbbabbbabdbbcdabdccbdbbbcabcaadcabdbcccddbabbabaaacdacbdbdcdcdbcccdcaacaccadabdbaadcaacdbacadcdabddadcacdacdddcbaaacdbabbcaccadaccdacdbccabddcdcbcbabbdbbadcddccaaadbacacbaccbdadacbdbddbdccbbbcaaabcccbacdccaddcdbbabcbddabbadcbaadbacadaaccabcbdcbbcbcabbacadaabbccbbbacadbbbdbdadcdbacdbcdbbabdccdcabddbdbccbddaadadaaacaacbbbcccddccdcacabacbccdcaddbacdabcccbbbbbaaaacddcdccddcabdabaabbcaccdbadddabccbabcacdddccdaabcddadaddbaaabbbddccadcdcbddcdbbdcbccdccaacdbaaacdbddabcddbddbddccbdcbdadaacbcddbabcdacdccbddbdcacbabdabcdacadbbacdbadabbdaaadbcaabbddcadabdcddaddcdddbcbcdbaaacbbaddcddbcaadbbddadbaacdddbccbdabdaabccacbcbaadccbdaddadaccddccaaccabdaadccdcbaadcacdcbaaccabbbdadcdbdcbbcbbcaadbacccbbcadabdcdbdcbabbbbbbaabdddadccdcddcddcadadbcadcbbdcccbacadcbbdbcdbdaabdbaaaddaccdcdbcabdcaaabaaacacbccbdbdcdddbcbbaddddacbccbcbadcbcaccdccaaabbcbcbbcdcbbdcacbaaaacddddbbcaaccbcacbacdabbbaaacdaabdbbbdacadcdbbabcadbbdcccacdbdddaadcdbacbabddbccbcabbcdddccbdadabaabcaaaaddabacdbbabbcdbbcababbdcbccddabbdbbdcccdcaacababbdabaadbbdddaccbbbbadbbdabbcbdccddccbababaacbbdcccddbacbcbbaaccadccbccdcabcbcadbabdcdcdabaaddccbacdccdbaaabcdadadcdaadbcabbbabdbdadcdbcbcddbdddbdbbdddbbaacdcdadacbbcacdbdddddcdbdacbaaaaddbadaaacdcdacccaddbddcddacdddabdcdaaacabbbaccbaacdccabcddcddcdbbbcdcccaddacdabcccaaaadddcaaabcbdcaadcbcbcaababbaacdcbddbcadbdaccbdbdbbbcbdaddbadbdabadababbbcacdccacabbdaadbbcccccbbdabacacdddabdaaddcbbdacadacbabbdbabbbddacbdaadaddabbbbcacaadbdbbddaaadcdbdbccaaadacbbacadddbcccaaababbbbdaabbdaaddcbbdbcdcbcaabbccccdcaadbaacdadbddaddadcbdadcadcddaddabccbbbbbaaaddbcaaacabccddbddbabcbcccbacdbabcdbaacaadcddcbacaabdddaababaabcacccbccbdcdaaaadaccdadbbdabaadadaadbcddcdaabdddcdbaaabcbcdcaacbdcddaccccbcacddbaaacdbccbdaabadbdabbabadcdbccaabddaddbadabdccbcdadacbacddbdcabddacdabcbbcdcacdcbdacbdbcadcbbadddaaadbddacdaccccbdcaadaacbabcddcbaabdbbaabdcbdbbddccaabacbddcbaadcabbacddcdccbbadbbacabccdaddbdcdadaabacbdbcbacbacbadabaadbbcbabdccabddbcbcddaacacddcbbddcdbdcccbacaaccabccdbabdcbcbcdbdbabcddddadaabbdcaacbbdcdddbcbddbbcadacdadcbbbccacbbbadcbbdbcddbdddaddaddbcccddbabdadddcddddadccccaddcaacdbacacbcacaccabbbaadadccaaabbccbcddbdbaddcaacccdccbadccbbaacbdaaacdadcdbddacdacbbbddaadccccacadadbabbcabcabbbabddcbdcbcaccbbbadccbbbdcacccbaadbaacbdcaaabdbbbaacbddccbdddcbddccddaaddccaacdcacaddbacdcddcbdbcadcadbcdbdcbdddaabcaacbadacdabacaadccbaaccabdaaabcdacbcccbddbadaaadadbcbdddddabaaadcbaabbaacdbdccabcbbdacabddabadcabdadcbdcbbadcdbdbabcadcaacbaaaddaabcbadccaccbabadcdabcbbccdbaaacddbbbacadbcbbbbacdbcbcbadccbdbbdcbdacadccbbddddbdababcdbdbbdccaaaccabdbbdabdacaacbdaabbaddbbaddaabbccbbaabdabdcccbcdbcdbadaaadcdaaabadddcacacaacaacccbabccdadccdbbccaccdcdbccddddcbbbddbaddbadbaccadadcbbdbddccdddbdbbcdcabadbbbcdacddacbacadaacbcabcdaddadcdcabaabcbcdaabbcbcbbcadcbabdbadbbbcaaacdbccddbbabbbaadadbbdcaaabaccddaababccacadcabbdcaabacadddacadbdcbdccddbadcdbbaaacaabbcabcbdccddddcbacbdcbdadabacaabbbbbcabbdbccbbacddcabbbddddddcaaadcdadcacacabdcadcbaacccbbbbbacbdcdcacadaabaabbcacccdabccbbbcccbadbadbaddbcaadaadbabcbcdbbccabadabdabcdddcbadadaddabdbaaabdbbcdabadabdbcccdbabddcbbbadcbbdaacddaaaadcccdcdbddaccbbababacdddaadcbcadbabcaacdacdcabccdbbaaabbccdaadbacbadaddcdaadcdccbbcdbbdadccdcdbccacaccaddcdaabdcabdbaddddcaaacbbbbdcddabdbdaddadbcacbdadcaabccdbcbdbaacdcdcdadbddccdbcaaacaddbdbccdbbaccddbbdabddbabbcabcdddabacdbbbbbbdcbdddbacaddbbabccadccdacbcbccbcaddcdbbbacbabcbabbabddbcaccdadcbdaabdcadccadadaabcbdcddbbccdcadbbadddaaaccdbcdcccadbcdcdabbbcddbcddadbcadbcaaddcbdcdaddcccaddbacdaddcddbadcdddcddbbdcdcadabdddbbddccdcdcbbcbcdadbabcdccbabcadbdabdadbcddbcaccdacbdbbddbbddccbaccacbbddbbbbdbbbbcbbdbadccbacaacbcabdbdbcdabdcddcbaabbddbacadddddbaddbabbbbdaadaababaaccabcaaddcdcbbdddbdbbccaabddadabccbcacdcddcabcabcdbccbadacdddacacccdcaadbcbcbbadbbabbcccddbaaddbbdcaacddaddacdccbbddcadabdcbbcbcdcddacabccadbbbdcadcdbbbadcaaacddabbbcaaadaccdcccbdbacaddcdcdbbcdbddccaabddbbdadaaacabdadcccddbbadbdabcbaddacdbbaaaaaadbaccadabababdadcacaacadcbddbddccbddcdbdabbbdacadddaabddddcdbaddcccbacdcbacbddbacaddabadcdcaccdcdbbdddbddcbbbcddddbcacdadcadacdbaadbaabbacdaddacaadccddccabdccdaddbbaddadbbaccdcdcbdbaadcdaddbcdaacadaaaabdaadcbbdcabbccdadcbcddaacabaacddadaddadabccccdccacbbcacbcbadaccdcaabaccbabbccabcbcacaabcbbbddacdabababadababdcbdacacbacaddcccdcdbaccdbbdccabcababcabdbadabdccdacddacdcbcaddadcbcbddbadbcccbdcdbdccbdacbbbcaccbabdcdaaabcccbcabaacadbaaaabbccbccbbaadcaaadbabcdccadbcbdadaabddbccdcdabbbabacbabaaddccaacbbcbcdaccacdbabccdccadcabdabbcdbabcababcbaadddbdbabbccbbbccadcbbcbdbcbabcbddcadddbdbdbbbdbcbbacdaccddddacbacbacbcdccddcdacaadcdccbaddaacaadadbbbddddaddacbbcabcdabcdacadbcacdcdddcaacdadccabcaacccdcbbddabdbadaddbcdacdcadbbadcbdbdbdcbaabdabdadbcddbcaaccaadadddbdbbdddaabbbaccbdbadbddabcbcbacdcbdcacbbbaccacddcbababdcccaabcbcbaabdbcdaddccccabbaddbaabccddddcbcdaaabaacbcbddbbdcddbdcaaabbbcbaddcdbbccbacbaddddabddddcbccacdbddaaacaaccdbdbdcadcdaddabbdacbaddacdcbcddadcabbbbdadcacaddacbcccbcaaccccaaccadcaccbbcbcdbbacdcddcddbbbcbdaacddccdacdcbbaadcdabbddbcbdcadaacbcaabbcdabdadcbbdbddcbbbbbadddddccdcaddcabdbaabcdddcadacadaacddccbdadcdccddcacbdccabcbaaddbacddcbdccccbdbdbaddcbdcabbcabcbaccbadccbadcacdcbbaadbcdbcbaabbbbbddbdbadaabcddddaabadcacddbdccacbddcbadbacdbacaccbabaabdbccbcadddaadcabaadcbddddbbacdcdcccbddbdcaccbdaadabdbdbdbdcccddcbbcaccbdbaabccdcbddbdcbccadddbdddaccadccababcdddbcdbdbdccccacacabbcdaadcaaadbdbbbcadccdccabbbcdcbbcccddcaddaaacdaccbdcadddaccddccccbcbaadacccbabcddababcaddcdadbbacabdaccddbcbddcbccacaccbcacadcbbdccdcbdaabcadabcdbdbdbbddcabdbbccccddcccaaabbaccadcdbbdaadbbaacbaddbdadcaccdbcabbababdcacbcbaacaddbbbbdadababaaddbacabcadbcaaaadbbaaaddacaacbcbcdcaacbbabbbaddaabcadacababbdacaccddddbdacbaccbcdcdbcbccaabaddadcabcaaadcbbccbbaabcacccdaddbbddccacbaccbbcbcdddbcaaaaabbddacadcbbcddacbadaddccdacaddbdbccccbaacbbbdbcacdcbddddadddbabbaabbbccdadadccaccbabdaabdacacccbccdaccbccdcaaaadacaccaccaaacaddcabaaddcddbccbdcdcacadcaccbbbbcdabdbdbdcdcddadcbcaaadddaacaaabdabbbdccdcbaadaddbaaaacabdaaccbcaabcdbcabccacdcccdddcbbbadaadcbacacaacabdbdbbccadccabaccdbabbccddcaadaacbdabcbbdcbbbbdcdbccdbccabbbbcabddaaabbadacaddbabbcddbbccdccabcaccabbcabbbacddbcdaabccbbdaaaccacbddacbcbdcccacabcbdaddaadcddbcbdaadbacacbbccaadbddbacadaaaabacbdbcbcaabdbbbddbaacaddbcadbabddacccbbcbcdadcabbbbabdbbbabcacaaadcbacdbcdcaccccadcddccaadddbbcbbbcbbcdbbddddabbbccbdabbcadaadcadbccdbabcacadcdbbabbbddcbaabbddcddbbccdabdbbbcbbdcccacddccddbbbccaaddabdddbaadcaaadcbaacddcdbccdbdadbcddcaccdbacdaccdabbdcbaacdadaabaaacccddcacdcacabdddbbaaaaccabdcbcabcabbcaabdccdcdabdcabbccdacaaaaadcadbdbabddbacabcdabbcdbadaabcddddccbcbdbabcccbccdccbaaabccddacacbbabdaddcbadcdaabbdccaababdabddadacbcaabcbbdbacdbbdacaadabbcdaabbddbbbbbacbaadbacbdacabacccadbbaaacabcddaacbbdaabcadddaadacdbcdaaacbcdaabdcbcacbcdacaaacaccabdabdbbbbabcbddbddbdabcbcdccbaacbbcaaaccbcdaccddbcadddbdccaccccbdcacadbccaacdadbbcdbdcdbcbdaccaaccabdccadccdbabbdcadcbcddbccadabcaaaacbdababbcbbaabbddbdaadbcdaaddbacdccbbcbdacabcccdcbbbdacdccddcdcbdcbcabdcaabbadabbdacbdadbbbbcccddbddbcabbaadccadbaaccbcddaacaaadbbadcbbcdbbdbacadbdbbabaaddaccbaacbdcbcabbbcddbbcddacdccdcddbcaaddcdbbbcbbdcdcccacbdacadbccdccacdbcdaabdbccdcbadabcaacabdcbadaccddadbddddbccbaaaaabcaacdcbdcacabdbbdcdbbcdadaabcbbadddcbccdbdbcbdadaadbcbacdcddbccdbbabcbabddaaababcacdddbbbbcbddbbdaaadbdbbabbbcbadacaacabbbaaaadaaacdbcadcdacdcdadabaabaddbbbacbcbdadcddbabddddcdacabdbbdbcccbddbddcdbdbbbcdccbcabccbbacbabdbbbbccddbbcadbcdcdcccbdaccbdbcbbbdcbdaabbcbabbcbabdcabadddbcdcbdbdcdddbbbbdaddbbcaabdbbaaadcbcabdbdbdbcbabcddaaddaadacdcddaccabbbccbabddaccbabdbbddaadacbacacbdccbbdbdbcbadcbdaccdddbddaddbbabbabacbbdacaaaacdddccaaacbcdbcddbaddbcacbccccdabcaaccbaccdcddaddbbbbabbaccdcdbcbabdbbcdcbacbbbdcadbabadaabaaabaccabaddacdbdacbbbabdbcdabdaaddbbcbdcaacaddcacbddbbbcbdcbddbcadcbabaabdadbdbcbbcaadbbdbdaabcaabcabdadabcbbbbadacbddbdbbdbdbcdadbcbccbddadacbacbdcbdabddadbadcdcbabcbacacbcabacaabcabbdddadacdccdcabccddbcbbaadcccdcacbcddacbaccbcaaaabbdcdccbcbbbbbdacdbabbbaccdbadbcabbbadabcacbaccbabdbbcddacadaacaaaabcabcbcddcdbcbabbbddbbadbdacccdaacbbdddbbbbcddcdbbcddaabbbcccacdbacaaddcabbaaddadcdccadbdddaabaddaacbccbdbdcbaaabcacbcbccdacbbbacadbcddadbadbcbcabadacacdcbbcaacddabcbbccabbaadabadddbdbabcbdddbbbccbbbbddaaaadbababcbcaacacdcacdcabaaaaadbdcddacdcddbdcabccaaacabcdcadaaaabaccadbbcdaaadddccabdacbbdbbcdcbbabbdacdddccaabdcccbbadcdbacdccbbbcdcdcabccbbbcbdbbdccdcbbbdabddabcdaddbccbdabdbbdddadaadcdaacdcbbdadaaadabcaabddabaddcbbdcddaaddccbcccdbddbaddacaadaadbddbdabbabbaaacdaccddbbaabccbbccdbaccabaddcdadacadbabbcdcbdcbdbdabadaacdbaccacccabbdcdbabadcdacbacdbcaabdcddcdbaadacccbdbdabbadccaabcadbbdbbaaabdaababdadadccaadcadccbadabaacbccaccdabbdbdbbbccbaababadcadcdddcaacbddcbcbbacbcdacdaacaacbacbcdacbdbaacdacbbacaaccbccbbbddbbbcababaccbdabdabdcbdacbbddbcaabaabcaddcaaccccbcabcbdaadcaddbdbaacabbcdbabcacacababadccdcdcbbcacdacdcddadbacbcdabaabccbbaaadcbddbdccdcacdacbaabaccaadbdaacddcdcaccbadbcacaaadddbbabdbbadccacaddcacacdbbaaccabdcbacdbcdabcbaccbcbcdaacccbbadbcdaacbccbbbddbccadabbbacbbcdcbaabbabcdbcabcdadccabbadcbcccadadaadbaddbdccddadacbdbddbdddcdbccadccbabbcbbbadbbabadbdbdabbcdddcbbaccdcdbddccbbcddaacccbdcccbbacdccaddcbdacccaaabcbbddabbabdcbcddbcbcbcdbcaaadbaddcaddabcbdcbacddaaaadbcdddbadddabcabddcdbbdababbbacccddcbadbcacbdbbaabdccdcddcdadcadaccbcbaabbccccbdacbcaaddccaacddbcaababcaddacbabcbbddaaaddcbaaaaadcbbdcadddadcdacdabbdcdccdcacccaaccaddaacddbdcadcdcaaaaabbdddbaccaabcdcacaacbddacbaadabcddaacccdacccbbbbcabdbaaadbdcddbcdabcabdcddcadccccbabddcbcbbcaaccddccdbbcbaabacbdcaabcdcdacccaaccdbddbdddbacccabbccbccbbaabacaddcaccaccddbdaccbaadcdbdbccbcaaacbcbcbcbabcdcbbccbccdadccdbdabccddadcddbbddadabdacaaacdddabcdadaaccbcdacccccccdabadbdbacdbcdcdbbbbdaabacdacabcacadadbbccaaabbdbcbdcaaadbcbcbcbccaadbbbabdccdabdcaccacdcbccbcbacbbbccdbbdcabbdbcadbbdccbdbbdcaaadacacaccbbbcdbaaaabbabdcdcabcdbcddcacbadbbbbddbadbabddbbdacbdcdccdcacabdbbcdddacddabcdbcccbacdccbabcaaacdbbcdcbdbbccdbdbbcdccddcbbadbdcabddbbddbccdacbbacdddabcabdbdddbaabaaddabcbacddbbbcadcacbaabbbbbccbbddcbdbddddbacbdaabbaaadcbadbbaacccbcbcaccccdaabacdacccabbbdcaddacaacddadcddadaaacbacccbbaccdcddbadabddbbaaabbdcccbaaadbbbadacdbddaacccacccdacbbbddcbacaabcabdddcbccbaabadabbbaccbbaaabbbbdddbdbbbbabcdcaabadcdbdcdadaacbaddcdbbacdabcddddddccacacbdacbcadcacadadadbdadbdcbdccdddccabacaadbcbbaababacabdcaacbcaacdabdddbdaacabdadaabccdccddbaccabbbddbddaaccaddacddabbbddccdabdbcddabbbddccabbbcacacccbabdacdadbdcaccdcdacadaaddcacdcbbbabcdddcdccdbcbadbdabdbacbcabdaaadadcccddcdcdabcaaddadcbbaaaddacbdddbadaccacdacacadcbcbddbcdbdddaabdbdadbccbddbbdadacdbcdcbdadcabbccdbccadcbaabadbabaccdaacacdcbabddcccabdbcdcbaabddddabccdccbbccccacadbdbdbddadcabaababaaadbdcbbcbdcacddabcddbcabadadbdbcdcdacdccdddccccbbddbaabbbcaccadabacbbcacaddbaabdddbacbcdddccacabdddbbbccbcbbadbbbdcadadaccacaabdbddadbcaadaaadcacaaaacbaaabaadcabccccddadbbddcabbddddadaacdacabcabdbccdabdbbbaabacbbddbdcdcbbadccbdaccdbddcadabcdabbbcaadadcbdccddacabbbdadaabcabdcacccdacacdcbbccaabcbabbbddadcaadcbdddaccadabdcddbdccabbdcbdbdaddccdadaadbaccdabccadbbbbadbcabbcdbacabcaaabddabccabcbbcacaddaddbbbadaddbacbcbdaddbdbcbcbadbcdaddabdadccdcabbdcccadbadacaddabdaddbbccdbcabcdcccccbcbccccbbcaacbddbddbdacacccaddcaddcaccbacaddcccbbdbbadcdbbbbadbcbdcdcacbccddbcadcbbddbbcdddaadacabbccbabddcbbcccbccaacabccbbccddaddadddabbbdabdcacdadaaacbbcaabadbcbaacbabaacbaacbdcbbadbbcccbdabdadbdbdabbabdbccbdbaababdcabadabbabdbdbcccbbccccccadacabcccdbcbbbacacdbcdbdaaccbddadbdaaccbbbbcbacacdccdddbabbcddcdbbbacbcdaaacbabcbbddbddcbbddbbcdaddbdbabdacabdbaadddbdddcddcaccdabacaacbcddbdcdcaaaabaacdcbabdabbcddbcbdcbaababbaddcdccdadbcdbcaabcbabcabbcaaadbcbcbcccabaacddaabccbdddccabcbbccbcbbcbdbdddaabadcdaaacaccdbacabcbcacddacbdbbcadadbdaddddbcbcbabccccabddbbadcbdabdccadababcccbdcdbdcccdbccaaadbabcdabcaabdabaaabcdbdbbddbadbacaadbaadccddbdaabadbcacdcbbddcaccdcdbdccbdbcdaddcbcbddabddbcdbaccdcbaaadcbdcbbdbabdbdcddbdaaaabddabccdacbdadabdacddacdccacaabbbadbcdcadbcbbbddbdcbcabadacdbbaacddbadbddadcacbdbddacaacdbdbbbacacacdbaabbdbdcdcbababaaabbbdadaadbcddacbdabddadaacddbaccbcdabccbaccbbdacabbddddcabbdbbbcbcbdbcdbdcacacdbbddcbbbbccaddacdbacccaaadbddcbbaacddbabaccbcbccbdadaacdaaccddbddddcadcbadabbdacbcadbcbacbacddddbcaacdddaacabaaababcbadadcbcbdccbadccaccaaacadccdcbaaacbdbacccaccdbdddccdbcdddcdcbdaaacccabccdcdcdbccadaddccbbbddacbacaabadababddbadcacbadcbabadddcaabbbddacbcabaddacdcaddaaabbdadbdacaadbcdbacccbcbcccadbccaadbbbddaccbbdcdcbaadbbcaddadadbbdaddacaaaddcbbcdbdbbbabaaabdadcabcbadddcaccdcbbbdbabbbaabbcaccdddbaaaddcabdadbcdbbadddbadddbacdbbaddabdaccadddcbdbccdbddbdcaddcabccddababbcdbddacaccaadcddcaababcbcbbadabcaaaacdcbbbddcdcdbdbabcadaacadcabdbcdbbbacaaddcddbcdcbdabdabbdbddbbacccddabdbbadabadcdbbcbabbadacacabbdccddccabadbccabbcaaaccbabcddabcbaabbbaabbdacdaddcbdaccbbcdbcdacbdddddacadcbaadbbcdaacccbcdacaaacabccdabdcacbdaabbddabbcccdbcbddcdcaabcbbbddadccbdccbbbacdbcaaddcbdabdcabadbcdbabacdabaaacbaccaaacacbaadbddcdaaadaccbbdabdbacbacdacdaadbbdaaabaaccdbaacdbcabaaabdcdaccbabcabbaacadaacacabdaddcadbdbacbcbbbcbbdbbdccbdadbdabbadababacbaaaacbaddcaacacabdbadcaaabcdcaddadbcaacdbadbdddacabccddbcbdbaadaccdcabbbdccadbaaadadaccdccadadadbbaadcabacbdcaccaacdbacbaabaadacdaacdbaadaddbcbdabddabbaadbcadcbabbdbcaabaaddccdcacbdadccdccdcbdacbabbdaaacbcadddbdbacadacbbbbcabacdbadaaabddbcaccdbbcacbbaadabdbaacdcaabbccaabcabdccacdccadbccbacaababbcdbbdcbaacaacacdabdcbcccacbcbbdcdaddabdacdadbbdbdcccbbabddbdcccbccaacaadaacdcbdbaacdaadbcbddbbbcadadadaddcddbcccadbdbccbddddabdcbdbacdbccdccbbcbddcddacacccaddaccdcbacbadcddbaabbccccacdcdaccdcadaacccabbabdabbcdcadbbbaabcddbdadadbadbbdbcabdbbaaabddbdcaaddcbbadbdbabccdbdddacdbababdcbcccbcabdbccdacbadcddabadaadddaddbdcbddaaddbdcdbbadddadadbbdcbdbccacddabacddbbccacdcdbdaaccbcbbabcaaddddcbdbddddbacbdbbcbdddbccdcdcddbcaccaadbbabcdddddadcdbccabdddcdabadbdacdbdadabbddddadbccbbbcdbccbcabddaabcbbcbcdadcddccbdddbbbcbcdbbdbddbabaaaccdbdccadaabadbcbdababccaccdcccdbcbddabbdadabbddcdcacddbcbaacbcbccacbbccbcbcdabdcabbdabdcbacbaaaccbbbcaccbaabcacbcbdaddcbcccddbdadacbdcbdaabddbadbbcaacabdabcadacdcbcdcabccabcaaabacbccbbcabccaddcabdaccdabadcdbcadadccccccbbdadddabccdaadccccbcadddbcbcaadccaabbdbccbadddddaaaaccacaabcdbbcdacccbcbbadcaaaaaadbccdcbadbbdacdabbcbcbacddbaacaddbdacdbbddadadbbdbcdadcaddbababbdccdbcbadabbadacbadcbcbcabccdccdcbbccbbacccadadcbbcdbaaaababccaababcccbdbadadcccccdcdbdcaaabbabcbaccbaabdcbcdbcbabbadabcacdcccbdbaadacccdcababcdddccbadaddcbdccadbadcaaaabaadbbabdbccdbadccbddcbddabbcabdaadbbddcababccdcabbdcdcbcbbaccdaddbbbbbcccdccdcddcbccddbbcdbbcbacaccabcbccadccacdbaddaddcbdabcbcdaabccadbbadddacbcadcbdaddbacababdbcbabbbadcbacabcdbbdadabdbccabdaaacbbcddbaddbdbddbddadccbcbaccadbcdacdaadbadcdacccdabddadcadbbddababbadddbbbcacadadbdacbcacdbdcbcadacabccdcaadbadcacccadbabadddadaaabdcddddaadbaddaaccbdcaadaadcabacccdacdcdccbcbcddadabadbdddababddbabbbbcbccbcbaaddcdbbcbaaddaacbcdcdbddddcdabddbcbbdcbdadadabdcabaaabbaddcccacaabccdabcacccbacccdbcaddcddcdabaddcaddbbaaadbcdcbccababddbdcbddadcadabadbaacaadbcabbbadcbccaadcacbbccbbbddddbdbaccddacdaabcbdbccaacbdddcadbabaadaabdbabadbbbdaaadcbbabaaaacacccbabcdcabdadccccabbbcccabbaaadccaccbdcbbbacaaaadababcbbbaabacdadddabddacbdadabadbdadcbccababadbbcdcbacbbccbdcadaacbbdbccabbbacdbaacbdddbbbbdabdcaabbbddcdbddadcacacbbbdddadbdbddcadddcddcdcbbaaddbabddadaccbadcbabcadaabcdadadadaacaabacabcbcbbdabaccdddcbadccacbdadabbdaabaaccdccddabddbdbbadaccdabccbcccbaabadbdbbcdcddbacaaabccbdccddbabbabbdaccadabdbccaddcaadcacaadcdccaabcddddcabdaaaaccccbaddaaccccaabbbbdadabcabbcddbcacdbaaddbddbccdccadbbccdbdcaaabdcacccdcabbccdbbdaacbcdadadbddacdcdbcdcaddabbcddabadcdcbbdbcacdcacabdbdababdcbaabdbbbcddbddbdaaaacdaabbbccdbdadacbabbbabbdcccdacdccabcaaadbbaddcaabcdcbcdcacdbbcbddcdabdddaddccbbaabbdaaadbcdadcadabdbbbddbabbbcddadcabaccdbccbbcaaaadcbadcdadacdacbcbcbcdaabcadcbacabddbdcddbbdbbcbccdcacbdaabdcdcaadbaabadcbcddcccccaddcdccbadcbbacdabdcbcaacbabddbaddadbdddbdcddddacbcadbcadbcbbcaddcddadcdaccabbdcbccbbcbadcdddaadbbbcaddbbddcbaddbddbacacbbdbcdcccdbddbabaaacbabbacdcbcdaaaadbdaddcddaaddcbdbcdcdbcacaddcbbcbcbabbddacadabdbbbbdacdababcbbacabccdddabccbcbccadbdcbddddadcddbaaadbdaadbcbdadaccdbacadaaabbadaabbdccadccdbccadccaaabcaacabddbdbabbddabbdbdbdaadcdcabcbabaadabbadddbbbadcaabbdcabdcacbbbcbdddcaacdbdddcadccabbccdbcddadbcdcaadcabcddcdcabbccdbabddbbaccababccbbadbbbabbbaaacbcbbcabbdacdcabddcdacabacacdbcaaddcabaacddcccdcbabdbababddbcabadadabbdccaacbbcbacccbaabbbbdadaadbbbadabcaadcbaabcbdccacacacdbcccdadcbaddcbacacddbacdbadbddaaabaaaaadbdadbcdcdddbdabbdbcbcaccccdbcbbbbdcbddcddbdabbabcabddcbccdccaadbbaadaacabbadadcdbddacdcacadbbbcbbadadccabbbdbbdbdbcbaccaddbbcccbdadddbaccbbabbdadbcccbccdccadbaadcdbdabcbdadcdadcbcbaabcacacaaaaaabcdbadbaacdcccbdddbdabbbddddacdbdcadbcddddbcaadbbcbcddbdcbcabbbddcdddddbdbdbcdadbdaaaddaacbdddbdaabdbabcbbadbabbaaabbbadddbdadcbbccddccbabcdbcaddccddcbbabcadccbadabddcbcbacdacaaadbacacccbbacadcddcadcdbadaccdbadbaaababddababdabbcdadbcbbaaacabdbbabaabdccaccbaccdccbdaccabcdacacbbbadbccbabccccbbaddadbabadacaabcbcdaddcbacbdddbbcbbaccddcdadbbbdbadddcabbadbbbacbdbcdaabaddaadaaadcdcdadbadbbbdadbdcdbbbaabcbaabcbdbcbbbabbbddbadccbdaaaacdcdccbaabaaacbadddacbbbadaacabddaabdbadcbbacadbdcbabcadabcacddcacbdcbadadbadaddbdaadcabdabbcbbbabcadbabdaacadaaaaacdccacdbdabccabdcbacdccacdadddccbccccdcdabcbbdbcbbcccbdbadccdbdcdaadacddacdbdcdaacdabbcbdcabcadcabacabcdaabbcbbdcbaadbcaddabbcccaddababadcbcbcacdacbcdcadcbcbaccabdcdaacdcbbdccbdabbacbdaacddcbbccdcccddbacbdbddbabcdbdacacdcdbacabcbcbaccdddcaacccacdcddacccdbdbcdcdccdadaabddcdcadcaddddaccadbcddcacbddbddadaabdaacacadcdccdabaaabacacdccaccdbbbcabadcbacccaacaccaabbabbcbbabddbddbdadacbdccdbbacbabbbccdbbcbdcaccbbbadaacdadabaddddbbadcadbacadadcbcaacdadcdcaaacdbbccabaacdbadcbdbbacaddddadabacacaaddccdabacddbbbcdcbcabbbcaaaaddccdbdbdcdacdcccccdbbcddbcdbbadccabbbdbbaaabbcdaccbadaacccddbbacbbadaacdcbccbccbdccacbacdabdacdadccaaacdadbabbccacbdacdcbbcacccbcdbcbddbcbbdabddabaadbacbcbadadabcdccdbcdbbadaabcbbbacbdaccabddbaaacaddbccacaadcbabaadbabbbcddcbccaddbccabbbbdacacbcbaddaccddddacadbbdbaacccabdbacadbaadddcbdcddbccdabaadabcdbddbaacdddbaddbdadbdcacaabbaadbdbcccaabacdcddccaaadddacadacdcddddabcbdbacbbbadaacccbdadbcacadacbadbcddaaadcadcbacbdddbadacdccddaccdcdbbbcbbacddddcdcdddbbbaabcaaddaddbacacadbcddaadcddacdadacddbaadddbaaddbcabcaccaabbdaabdccdabaaccdacbbadacbcacdbcbcbadacbdabdcbcababcaadadacbbbbbcbcabaabcdcadbacaacbdababbcdbacbbbcddccdbcbbdddbbcbcadacbbaaccaaddddcbdcbadadbadcabbaddbcdcddcddcbcbccddacadabbacbcacbadcbdccdcaacdcaacbdbbcaccdbdbacadcdddddabcdbcbcadcabccddcacaddcaddacdaabdadcbddaaccdabcabaaabcdccbbbdcddcbdadcbaaddcdadddcbadabcdccaacdcddacaacbddabacdbbaabaacdbcbbdcbcddbadbcdcddacadbdcccdcabdbababcdcbcbbcaacbacbaacdcadaabacbdacccbcdadbddcdbdacbccdcacacabdcbdaccbccbadcadcbaacddddcdcddcbcbadbcababbdbbdaacbbdaadcaaaddbaabdadabbcddbbccabcbcacbcdaabcbbacddcdadbdcccaccdcdadaaddcabaadacdcbcdaadabaadddcbadcddcbdcacadbdacdbbababacdbacbbabaddcbbcadccaabaaaaaacbbbdcaddaadcadbadbdabbabaaccacbabababccdcacdbaaacbaaabacacadbaccbccbcabadaabadcadcabbcdcaddaaacaccadbdbcbdacbcccbdababddccccccdcdccbcddbcacddcdaccdcdbaccbddaddbadbbbcbacddbbdaacdaadddccdbdabcdcdabbcbaabbdddbdcdbaaacccdaccccdaacdbdbdaacdcbdcadcddabbcdadcacdcacdddccccbdadbdbddbccbdabaccbdcbcdacbcaaacaabaaacbdcddaacaadbbbddaccacbddccabdddaddacddbddccbdabdcdcbbccdcbaddbdaadcccaaaabcabdaddadbcabdaccbdcababbdcdabacbdadcccbcababbaabdadaabcaabacabdcdabdbbdddddbcdcbaaabdbadbccbcdadddbbdccdcababbbbcbccdadaaacaaaccdbabdcbdcbaacdccbcdbadcbddcaaccacaaacadcadbbdcbccaccccadcccbbdadcdcbbcbaccbbadaacabcdacdbdcacdbbaccbadbbbabccdbabacadaaadbcccbcdacadbddbbddcaadbdcadccbaaaccacabbadbabaaadabccabcaacdbbbbccbbaacbaadddacdababbacdcdbaadbacacbbbbbcbddcccddabcccbddabbdcdbbddcbcddcbadbccbddaddaccdccdcdaacbbbaabdaaabadcaadccbbbbbdddaaccdbcaaccbacdaaadbcadcbdbbbcbbddbbcacadcadcaacdcbbbaaaaddbbccacddbacdbccabbacdbcbdbbcdbdadbaddbcbcaadbbddbcabbcadbabacbddcbacccaadcdbbbdbcaccbdabdaddbcaababaaadcaacbcaaabdbbbcccbcbcaddcbbababdbccbddaaabdcddbabddaacccddcaadbaaacdacaacdddbcbdddbadbdbaaaddcaacaabaaddddaddbdcdbacadbbaadadababdbaaabccdacccdaacbbbddcbccaaccdbcbddbadbabaabbccaabbdbadaabcdbaacdaccbaacdcbddcdcacaaaaccccbcccaacbbaababbacaacccdabbdaaadabbddcbbbbabdabadbccbcdaaabaadbcdaaacddcbacddabbbdbdabccbdacacdbdcdbaddadaaddbbcdaccbcbbdcccbcccaabcbaaadddbdacdadcabcbcacdbdcbcacdcbbbaadaaaabcaadbcbbacbadaddbcadacbaddbddddabdcadbcbcbdccbdcbcadadbdabcddccdddadbdaacbcccccadbdcbdacbbacccccccacbccaadbcccabadacdcadaabdadabdbabbbaadddddbaddadacdcabcddddcdacdccdbdcbcacaccbabadccabaaaabadbaaaabccacdcbbbbbccdacbadbcbdcadcddaddbabbdbdadaaddcdaabadcdabdbcbacdbacabbcdbbabcbcaddaddcbadadbbddadcaddcbcbbacddbcdcaaaccbccccabaccabddabddbccbbaaccdacbaaadacdbcbadcbaddadabcadcacbddddcbaacadcdbadbcddadcacdabbacdbadadacacbabcbdbcbccbbbbacdccbaadaaadcacababbcadbccbbbadbdadbdbdbdbcacdacdaccacdbccbaaccdabadaacbacabdcacddbdbbaaabbdccdbdcacbbabdaadcaaddbdccbadadccadcddddccabccdabddddbbaaabdaabaddcaccdabcdaaacdacbccdadabbcaaccccbadcaacabdbdbbdbaaaccddbcbacbdbabacabcadbcdcdbcdadaccadaacdbdbaccbdadcccbccbdcacdddbcbbcdbaddadbbddcaabddbbbddbccaccddbdabbbdcccbcbadcabbadaacdbcabdbbaacadabbbcbaabdddcabbabdbcdbbbaabbacbbdbacdcbcbaccccccccbbdbbabdadbcbdaacacbacbbcaacbcaaaabdbbbcbdbbdacddcbacbaacacbcbacddcbadbadacdadbddaaddcacdbadbbbcddcbabbaaaaabbabcadcbbaaaaacaacadaabacbbdbabcdadcbcccbaccdccacaadabacdddbddcadabdaccbbbcdabdaaccddabacbbabbbacbaabbdcddbddcdccadacbcdbcdbcacbdacbabaadccabddabcdadbdbcdcabaabcdcabccdcacbcabccbbccbaddaadbabcaabbcacaabdcbcacbcdcadbccaabaddccdccbabbbdcaccccabccbcbaaddacdabdbaddcaddbbbacdbbdacaaabcaaadadabbbdcdadabddccaccaabdbdaddddccabddacdbbcadbdacbcabadaccaaacdabcaccdbbacbbdadcccddaadabdadbdddcdacdcacbdbcddbbbacdbddcaabbacaccaccabcbdccaadadacaadcbdcbdccaddcadaaacdacadbaddbacdddcdcdabccabdbbcbdcdbdcadccdccdcbdcbbcbcaacacbaccadadcdadbabcbcacdccaaaacacadccdabaacbadbbaadacabbabccabbbacadbbcdaaabdcccdcadcbbccccdacdcabdbdbdadbdbbdbdbddbcabbdadcddcdcacdbbbbcbcdcadbcbbddbccacacaccdbdbdacdcacdcdddcbcdcadacdbccbdaccccdabadbabaacdababccdccccbcccddbbddbaaddbaadabcacadbcadbbadbcbadbbcaacacadabacddbdbcccbcaabdcddcccbdbdcccadaababbcbbdadadabbdccacabdbbadbdbccbadadbdbbcbcbcbaccdbbbadbdcdaaadddcbabbcbbbbadacdaaacbaabbdbcdaaadcdacadbddcabccbccacdbbcdbdcdbcacabbabccdacccccbbadbcbbdaaadbdcccccddbccabacaaadacacddaddcadbadabacbabbcccaaaacccaabcacbbdcbbbddaccdbbccaaabcbccababcdcacccadcdcbbaacddbddbbabacbdadcdadababadcdaccccdcccadcbbbdadbaccbcbcadcabccdccabaccbdcaccbbbbcdcddadccdcdbbbaabbaabacdbcbdaabcbcabdccbbabbbcbcaccdcbcbadbbbaabdacbccacbacadbcaacaaabbbdcbcddcaddabcccbccbbcbaadacadbcdacaccddbddabdbcbbcaadcbaacccacaacdcabcbddcbaacbcabadccbddaabacdabacdcaddbbcbcbdbcdbcbbdcaacbacdcbbdbbcccabbcbaacbdadaacacdabcdbddaacdaabdcbcddaccdcacdbaababadaddaadbbcaddbcbbadbcbbbdaabbcaaabdacabaddcabcccabaadcadddcbaabcdddaaacbcbdbabadcaaabdbacbdddbbccdcacbbaabbcdadccacaabaaaaabaacdacbaabbcddcaaaadcbdbdbdccccaaadcdbbccdbaaabdcaacabdbdccbbcbcdbdcbccbcbbcbcccacacdbacbdbcdddbbcabbdbcdcbdaaabcbaccdadacbabacbcaaaaadbccbaadbdcabdbcdcaddaccccbdcddcbcdcdcabcddcaacaacaccabcabcdacdbadaadddabbaacbdcacddbdbaaacadbdbccabacbacbcccbaabcaaabbacabbbaddddbabaacbcdaaabbcdbcccbcbcdbbbcadbadacabadddacdbadcccabadcbabdaacbbbbdaddccbcbdcbaacaddcdabdbdadbddbadcbabcbbdbccdccacdbcdadcadaddddadbadaccbcbcddaadccbcadadbaadcacdcdadacdbaddddadbdbbdbdaabdbdbbdcddacdaaaccaabdacbddbbbcaaddbcaacbdadddadcddbaccbcabdcbabddcbdbaaddcbccdccbacbcbbcbcbddcbdbaaddaabcabbcbacdcbacadaccccababbbcdacbaddcbbbaccaacdbaaaacbddabdadbccdbbdddccbdbdddaabbdbbbcacbcddaddcdcacdaabcacbcbbcccddabacbdbbadadcdcdbbabbbaaaddccbcdadaddacdbdbbcadccdbbdacbccdabdcbccabbcaaadbbccababdbadbccdbdbaaadbaccdaacabcccdacabbbdcbcbdacbbaaabbabcccaacabaaccbacdbbbababacdaddbcadcddacadcdcacaababacaddaadbcbabaabcbcbccaccadaacaaabcabdcaabbbdbdbdddbbddcdbcadbacbdccdaddcaaccbbbadddcccbaccababdbcccaddcdcdadbbcbacdbcbccaadbbcdcdccacadccaabbababbccdacaadaccbadbacbdddadcaccbddaabaaccbcaaccdacbdddabcbaadcbbabadbbadabcbacaaaaadacccdddacccdacccaccccaaabcdbbbbbacdcddbcbbddcdacabaaabbabdccdbcabcdccdabcdbadbaabaddaaadabdabbbacbdbdccdcdadadababdbcabddcaaaadccccddcadadcbcdbaaccacaaaccaacbdcbbbbadccacbcddbcbbdcbccdbadbcdabbbadaacaaacbbcbbcbccaabbdbdcabbbcdacabddcdcdaddcaddbdcabdccbdcdcbdbbabaacbddcbdddcbadadbcbabdcddaabdbaccaaacccabacacaccccbccdccbcbbdadccabbbabaadbbcbbdaddaadadcabdcaadbccaacadadbabdddcbbccbbaccadbcdaddccaaacdadbdbbabdababcbccbbccbddaabbbccbbdcaaddbcdcdcdcbddcabcdacddcbddbdbdbacbdcddbacacddddbbacbbdbdcccbbcbdaacaadabddbdbcabcbdcbdccdddbabaabbabacadcbaddcadbaddcabcccabdbdbaaaacadaddbcdbcbbdaabcdaaccdbcadacccbbdadbaabaabaccabddacbdaddbcdaadbdadcbabddbdbcddaacadbbdadadcdddaddacacdbddbccadcbcdcacadcaaabbccadacddbcccddbcacabcbbcccdbbaadcaacbcaadbcadcdcbdacbabcddbcadcabbcbbbcaacbccaacbbbdbcdcaacdabbcbbdaabbaaacdccaccbbcdddbdadcdacdabbbbadcbaaaacdabadcdbbdcdaaccbdabcbabccaaddbcccbcdaaaccdbaddadbddbbadddbaccddacabdbdcccabcadbaaabbbcdbddbdcacabbcdabcbbcbdbbcbbbacdbdadcbbbadababbbbcaadadcbadcdbcabdbbcbadcaaabbbbcdddacabbdaddbadcabbbcaaadddacbddbccaabcbbbdbadbbddaddccddcdaccccdbacbcbdaadcacabccdaabdaddabbcbbaacbbcbcccbcaabdccabbcaabdbcccbaabdbaccacccdbcdddaccdbaabcabcddcdacdccdccbcbcddabcdccabaddbacdaacddcbacccaaacbbddbbddaaabadaabaabbdadbadaaaaadadcbbdccbbcbcbddabcaddacddcbdadabbccadabccadbcbcdadadbadcdbddadbcaaabcbccaabdddccbcacddbcaaadbcbbdadbdcbbbaddcbdadadcdbabdcacdabacabadbdbdadcacbbdddcbaccbddddcdaaadcbcbbcccbdaadaaadadccacbddcdbdcacabcddccacacacbbdbbdddbcccbbacbabaccddcdbcdadbccbaacbadccccdccdaabdbdbdbbbbadcbcaadbbddbbcbbaddbcdabaacbbdbbabbdcaccaddcaabaadcaaadadbabbacbddacdddcddcccaaacdcccdccabddbdaccddadaaabbababcbabddbabdccccaacdccddcadcabcdbadbcdbbcbbcacdaabccacdddcacddadbbacadbadbdbbcdcbbabbddddaccadcddddacaaabadcbbcdbaabdbccddbccdcbcaaccbbdbddacaaddcbddabcdbabdbdaaacbccbcadbbcabccccdddcdddbadccbcbcdbbcaadbaadddbddcbbbbbcdbdaacdcccbabddbcacacdbaccabdbabcaadcacccdcdcbddbbcbdcddaacabbdabbbdccadcbaccccaacdcddcdbdbcdcbaabcdaccddbcabbdacdbdbbddcbccabbabbbbbcbdacacdddacbbccdbbcdacddabdbadcdddadcdccccabbdaaaacbacdbbadaacddaddbbbcbcaccbacaaddccbdbabaababcdcdacddcdbbccaccbdbacdbbcdddcbccabadbadaadcbdabbbccbdbbcbccbbdbcaaacbdaccdaccaaababadaabdbdccadcbcdccbdadddacabacadbcdbcbcaddcadaacaadcdccdbdcdcbaccabccbdbcdcbbaddbacbbbcaabddbdccccccbdcacdbbbabbdcaacccdaaaacacbbcbddacaabbaabacbddacddcaaaaacadaddbbbbcacabbccddbcccdddaabaccbababbddbbdbbccdddcdacabccdcddacccdbbcbadcddaadcdabacbdbdbdaddbcaccdaddbbaccdbacbaddacdbaccddbacbbdcaddbcddabaaaddbdacdbaacbabcccabaaadccbccaaabdbdacdcbddacacdcccdbdcbdccbdbbaaccddbccdcdcbabaacdabaabbcaaaccbadbbdbdbcbcbaccdbbacdcbbcbcccbacaddcbaadbababddaacbbbabcddacacdaaabdaabdddcbdbcbbacbcacccdabbbcabadaaccbbbcdacdbbdacadcabbcdbadbbcccccdaacbbaacbaaaaadbcacddcdadadcccdbbbbbbaaadcdaddbbdccdddddccacaacacbacbcadbadddadaacaddcdbdbbcdcdbbdddcaacabbbcbcdcdcccdababcccaabaabbcddddddbddbddaaddcabdcdbacbdccabcbcdadbcaccadcdbbabcbdbddacdabddaabcadabacbdcdacacddcbcccacbcbaddaabbdddadabdabaacdbacccbccbddacabbaaaacbcdacaacdcccaaacdbbcabbbddbbbcdbdbbcbccdaddadcbaacabccdbabbcacbccadbddbadcddbaddbdcbdbabaadbcbbbcabbbcdadcadbcadadbaaacbccdbaaacbdcabdbdcbcbdacacdaaacccbbacabacabcbddaabdbadababadaadacddadccacaabdcbadddbdcccacbddcababbdcdbcddcadbbadacadddaadbcacdcccccdccbdbbcbcdccbaaabdbcdcacdcadbcdccdcddaadabdadadadcbdccbcabdadcaddadaadbdcaccadaaaaacacbddabacadcbadbcaaabaddadbddabdabcabcbdbbadbbbbcdcdbcbccbccaccddcdcdcabdccccccabaddcbbccbabbbdcabdacdacaadadadddbcbbadbbddaccdbadbbddbdbdbdcddbccbccabacadcccbdcbdccddaadaaacdbabcabccccdcdacaadaaccabcdaacadbddcbcdddddbbbabcbdabdcbaacdaddcbbcacbbcddcdbdcbabacdcbbcddcacbcddbbbbcabbdcddcbcdcddddcaadbbabcdbadcacccdbaaddbcddbdcbbddccbbcabbaacbbabcccbdbbbdbacadbddaabbbaaadadbcabcdccddbccacaabcdcbbbabbababcaadccbcabdcdbbaaabacdcadddcbcabbbdcaaddbcbdabccbbdcdaccdbbbcacbabbbcccaadabbdddbccbadacdbbbbacaccadadabbdcdbcccdacddccacaccacdabcddbaaabdccacbbdababbaacbddaadacabbbbdbbbaabaadcdbaaadacabbcadbabaddacbbbadbadadbdbaabccbdcabcabccadcdaadcbdcbdcdaddccccbbcaccccbaadccabadbccadcadaddacadcaddcdcaadbbabcdddbaababdabcdddbbacbbbdcdaacbcbccdbdbabcbdabbbbddabddcbdaababcacaabbacbaadcdacadccbbbabbcdbbdabddcdcbadabaaacdcabaadcbdbbdabbdddcaacacbdbabacccdaccbdbdcbdacacacdaacaaabbacacadddddbcaddaabadcbdccbdbabcadddbcdacbaacccbdbdadacbcbdbbddbbddadcdcbaacbaabacbadacaadabbdabacddaaabddcbadacddbbdbbdcbaadddababccbdaacabdbcdaacaccacaabdbccdbbdaddbddbdcbdacabcdcddadbcccaaccbdddacabdddbcbbdcdcadbbaccddddaaadbabdbcabccdaacabdcdabbbbdaabcababbdccbadbdbcccbcabdbccdcdababccbbcbacaabacacbcdddbccbddadacacadcccacdccccadabddddccadaddaabbabcacadbddddcdbcdcbdaabcbdacaaaacccdaddbbacdaaadccaaccadccaabdacdbdaaddbbcbdbddccbaaacabdcdcddadacdcccbbbbcdacacabdbcadadbadbcbababbdddddccdabacccbaadaccbdbdbaababacbccbbddcccadccdbbabaddadcdbabbddbbacabdccaadaadaaabdbdaadbbacdabadbaccdadcaaabbcadabcbdcbcadabaccdcdaccabdcbacacdacbdadadcdbcbaabbccbccbccbdaabcbbacacdcbbccacbbdaaabddbccaadbadbddbcdaddcadacbdcadbbaacacbdbaaddbaadddcdcbbadbabbddbbbabbdcaadcdbccaaacdadbadccddddcaacbbaabcdcddbdcdcbbcdcacadaccccccaadacccccbdcabdbcbabcdcdbabaabaaaadbdadaacbddadaaccabcabbabdccdaccbdccacabbbcaadcdddbacbaabdbdbccbbabacbbadbbbcbcbaadcdccacbdcbabccbbcadddbdbdcaccbdbbbbbaadacbddadaaccdcaacdabcbbbdcbcbccbbaddddbbdaddbccddbdddbccdccabababdcbdabbdcabcbdaddcdadbdcadbcdacabcbbcadcabbacbcdcccdabaabcbccdadcdcdcaacdbacabaaccaabdacadcbbcabcacbabccddbbdbcdabacbcbdaadcaacccdbbcdaaaaacbdbddacdccbabdcacccdacddabbdddbbacbddbcddccddabdcbdbbdbbadaadbddbbbadaddbbdbbabbdddccbacabccdbcddabacbaccaabababcddbdadbbbadbddcbbbbccccacdbadabbbababbdcccdbaccadbbbbccbdbaadadadaaccbdddacbaacacbbbccacbaaadcadacbdacddcacadacbacbaaddcdaaadbdabbcaddbacccaddddccbbdcacadacddbabbdddcabbbcacdbcbbaabaccabdddabaddaacbadbaddcbbaaaaccccbbabcddacdcdddbbdbaaccdabbcccaddcbcbbcacdacdaccdacbcaabdddccbcddbbbdbaddacbbdcadbacddaabcabdcbdcabaacacdcaadabbadcabbbbaccdaaaadddbbbcaadccbaaadbcdddbcaabcdddddcbcbabcaabacbcdccddaabbcdaaacccacbdccdcbbabdccbbbcbdbdcdaacaadbadbadcdcaaccdddacadababbdcbbadadddcbcddaacacdccabaacaaccdccacacdaaaaaadcdddbacbdadaabccdacaddccbdabcbbdccbbbbbdcbbddbddbbacdcbaabdaabaddaaaacdbcccdcbababbbdbaadccbbdcbcbdabccccbcacadaddcaaaaacdacddddacaabaccdcaddbacacabdaaadaccacccdccddcdcacdcbadbcadbdabddbbaaaccadbccddbaaaaadccbdbbaccdbbdaaaadddddcacaaaacdccabbdcdcddbcbbaabcbbbbadcbdccaddddacdcccbcccccbbcacbccaaaddbbaabbcccdadcdddbdddccdcabdcacabadbcbadbaacaddbdaabbdddcadadbbccccdbdaabbacabaaadacbdddcccdadbacbdbbddaaddbdbdabcccbccdbaaacabacbcdbcbcdbabdccdbabddccdbcdbdabddabbcabcccabbbcddaadabcbaacadaabcabbccbcbcabbcaadccdadcbccaabddaabcbbadacacbdbddadbbdabcbdabdbcaccdcdbacdaddddbddcdbadbaacabadbbbaddabacbacdbcabddabdddacdbabcaacbbaaadcaabbccbdccdcbacadaadadbdbbcdbdbaaaaccbbbababddadddbbcbcacddaaadcabbcddbbadadaccdadbbabbccaaddcdaaddbdcdcdababbbdbdabdcacabbdbdadccacdcaabcabbacadcdbbbbdccaddacbbdcabaccdcdddbbbaddadccccccadcdbdabcbabcbabbdddcbacbadadcbabdcabaadabaabadbcdbbbdccdaadabdbbcababababdadddbdaccbaabdbbdabddcddbdbbbdbccaddcbabdcccbaaacdaaddadccdcbdbcabdabcdbadabdaddacacaddcdaddacadbadbbdcdbadabaaabccccbbbcbcdbcdbccdddbcdcacdbaadcbcabbbadbbcdbbbddabacbcbcaabacadbadaadaccbddabddbbaaaadbbcdbbccdadbccbdacaccbabbbdbabbdbccbddacbdacdbaadcbdbbcacdbcbdbcdcadcdadcacabbdababadaaadacbddcdbacacbaadccbdacadaacbcbbbcbcdbaacbabcacdcdcacaadbcbabbddacadccbdcbbbdddacddcbadbcadacbbabadaacadabaccdddaabcacbacbdbaaaaabbabaacdaccdadadbbabbababcdcdadccbccdacbbabbadbaaadaccacaaadaaaacdddbdaaacdbaccbcbdabdaabaadacaadcdbbbbbcabdbcaabddaadacadbaacadabbccadabdcdbdccbddbccbbabdcaaacbcbaadaccdbabcabdaabdaddaadbbdcdacddcbbbbccbdaaaddbaadccbbcaabdbadbdabbadcbbbbcadadcccbadccdacacaabdadaccbabaadaabcbadcdcbdccdabdadcbcadddacdcdcbabcddcbcbdccbdadbdbbdcacaccdcdbacbddbcbdbddadcccabdabaacdaccbcbabdaacbadaccccadbbabdcccaadccbbaabacdacaacdccccddcbbdadabbbaccabaabdcbcccaaadccbbbbbccaacbaaddaddaaacaaddaaadbdcdbabaabcbbadbbbcbdaaddbccbcbadcdcabdccabbdddcbcdbcdbddacabbcaccdbdcdaacbcababbddddcbcddbcddbcddadadbdbdaabdcdaadbacdbaddbacddcddadabbccadddadabbbbbdbcbabbcbbbabacbbcaacccbdabbcacdcbbacdcaadbdbacbdcbddabddadcadbacdbcbbdbdadacacabcdaddadbddcbaccbbccbdbbabcdadabdaaabccaccdbdcbcbddcccadddccdcacaabccacdddbcacaabddcbddabdbbdcadddbdadacdacdcbbbbbbdcaacbdcccacbdbbcbdbaccbadcbbcacdcbcccbdbaacaacbcccccdacdabbbbdbabcbcddbabadcddaadccbadbdcbcacdbdcbabbdcbcdbbbdcabdbbdbcaabdbbbbcdcddacbdcddbdcddddabccabcadabddbdcccccacaadaccadcabbcaaabbdbaacccadbbaccadbacccaccbbbccacdccacdcdbccddcccaadabbcdcbabdbbadacbadabbcdadaacbbbcbcbbccacaadabbacbabdacabbcdadddacbaacbaacacccbcbddbdcbbdcbdbcccdbdbabbdbcdbbaababbcdacccdacadcccadcdcdbdddcbddadacbdcbbcdcbcaaaadaadcddcdbdacbadcadaccadcbdbbbdabcbacbcbbadbaaadcbccaaacaaddddbddccbdddcbcbadbaccdbcdccadbdaabdabbabbaadaddadacababcaacbcdcbbcdbcbbcacccbcbbaabbaddcbbcabacadddbbaaadcbcbdcbcccddacbabbdbcbaaacdcadbbdccacbdbaacbbbbdaaccccccaaabdbacbdbddbabcdabdbbbdbccbacdcdcbbcabacbbcdccadbdddbbdadacdaaaaadacbbddadbcbdddbbbbdadaabdbdcccdbabbdcadbddbcbddcaaccacdbaadadcaddddcbaacabdbdbdbcdccaaabccbdbbaddccaddccaacaccababbccbabcccdccadbccbabbdacddddbbcbabbadabdcabcdbabbdcbabdcaadaacaaaddcabbbdacdacadcbdcabadbbccabdabadbdbdbaaaccccbbaaaddbbabaddbbccdddacacbaadabadbacadcccdcaaadcbaddaccdcdadcdcdcadacabdbcacdccadcadddbccabdaccccabbcaddadacddbbaacbdabdababdbdcaaabdabdcbaacadadbabacaadaaddcdbacccdbcbabbbbdbbbabcdcdbbdcdccbadacdbabbddddbbcccccbcadcaaaadbcbdadabcbdcadaaddcddcdababaddaababbcdbddaccbaabdcbbddbcaacaacbaddcbccaccbcbcccdadababbbbacddaabdbbccadbbcaadadccbdbbcacbcbddcabcadbacaaddcdcaabacadcbdacaadccbaabdbcdccaacccbcbdbdcbdbbabbdcdcbaacaaacacccabccbbbabbdabbbdaccdccbcbcbccbdbdbbccacbbaaacabdcbbaccddadbbddabdabcbcccbbdcabbbbbbcabdbbdbdccbcccabcdcbbcbaacbbaaacdaccbbcbcdbccdcbcccaacddacaddbbbacccdbadadddbccabbcccbbdacaabaacadddadcaadbbbccccbaaddacdadcacbcbaacdadddddabbddbcbdacccccabbabccbabbaabccdcddbdabcaaadadbdcacbbacdccbacbbdcbddcddbcdcdcbbacabdcababaadbdddbcddbadadaabcdcacacaaaacdadcdbacdccccdcbdbbdcdddbdbcbcbcbddddbaddbdacbcbcbcdadbaabcbdabacadddbcbdbbadbcdbacdccaaadcaddacbcbcbcdacdcabacaddacbabcbabdcdccbdbabbdcdcbdcddaaabacbabcbdccabadadaabbadddcdcaabdbaaddcaaadccdabdbdbdbabbabddaaadbdbdcbbdcddbddddbdaabbdcddbccbdaaadbaabaacdbcabdabbacbcddbbbacabaddbbdadacbbbabbbbccacccadacdccaccbabadbccdbbdacaadcccccddcccdbbccdacaacbacaccabbbcadcdddddcaaadccdbbaaacbbabacbbbdcaadcbbaadbcdbabdabcbcacbdacabbaddadcbdcadbccdabaddabbcdcbdcddbabcbdcbdcccbbbacbddbcbddcbdcaaccdbcbabccbdbbcaaaaddcdacbabdbaabcbdabaaccbabcabdaddcbbdcdcdcadabdcbdcabbddacdddbaacdcabbdacaabdbcaaaacdabbdabababddbbdabbaaccacbabcbdadacabcadaabadcbbcdbabbcdadacadadbcbcbddcdcbbaabcdcdcabbaacbcdaccaddbdbbddbcbddcddbbcaabcdadbbdccdcaddddcadacbccabbbdbbadaabacbcbbdcdbcddcccbbccbbbaddbbddbabbdabdbabaabdddbdabbcabaadcabccbdacadccbbadabcdbbbcddccabcaddbaccbccbbcaabaaccacdcbadccdcbbccdcbcdadcbbadddbbabacbaaabbddcbabdcbbacadadbbdacacbdabcdadcacbaccbdbcaadccdcdddcabccbadaabddddacabbaaccbcadccadaddabdbacbdcddbcdadbdbddadbbddbdcccdadacbaabcacbdcdcdacadcdbdacccdbacacabaabbadbdacadccdabaccddcddbadcbcbbacadccdbcdbbcabdcdcdccdacacaaacbcddaadbbacbcdcdddacaacdbdcacbdbcdadccdcadddadabcadcdcbcaccbccabccbcbcbdabbabcbccdcbcabccbbdbdacacbadcabdbdcccdbcbcbbcdccbcaaabcdabcbdbcdbbbcabbcdbacbbddbbdddbaccaabbacbcaddbabaaaaddccadcbbacbbaaaaabacdcdadbcaaabbccccbbddccaddbdaadbddabbcddddcbdddcbacdcdbbababaaaddaaaaaabddccddcabdabadbaddbaabacacabbaaccabdbaadbdbbaccdbddacadbcbcbaaacbbaabacdddbacacdacdabacdcccdbbdbdccadcdadababaddadcdccbddabcaaaccdbacbadcaaabbacdcddababccabbacadbadcacabaccbdbadccdbbadddcadccccaabaddddcdbaabcbaabbcacadacdbadbcadacbccbddbaddbccaddccbddcabdaadaccbadabddbbcbdadbdcbdbbbccdcdadaddbcbdbddbbbaddcacbbbbdbcadadaddadddcbccaacdabcccaadadaadddbbabbdcbdacaacdcdaabdaaadbcbacbadaacbcbcbcdcabdccacbbccbcacdbaabcccccddbacdaaddddcbabccacaadcddaacaddbdbbadbbdadddaadbbcbbaadadbccabbadcaddcdddadcaacaacadabaacbdbacbcabaaacacdadbaaaaabacabdaccbcbdbaadbbaaabdabdbbdbabdaaabbcddcbbcacaccbdcbccccccaddadcbbaacdaccacbcbcababdddcacabcbbbdcbdbdadabdbbbdbcbdacabbaadcdaccabbdbbbabaabcaaacbcaabdbabdddcccbabcadcdcaaddcbdadcbcdcdacadbdcdcdacbbcacbacaaccdabdadbaddaacbabcadaacaabdbabaddcbddcbdbbbbacacabcaadabdaacbcaaddccadbbdaacbdddbddbbabbcadadccdbdddccddcabbccdaccdbdbddaabbbbbdaaccbddaadadbbdadbcaddcabbccdbbcdbdabbddbccddadcdcdbbcdccbbbddabcdacddaabacaadcddacdbbdcbaaddccadbbdddbcbdbdcadbaddacacbabdacbadaacbbcabcaddddcadccacbcccaacdadabcccdcaacccaadcddbadadccdbccacbddaaccbcabdabdbbcbbacbaaaaaacccccdbcaaccaccaddaacaababdccbabbdadacaacbbbcbabaacddbbcccbbbbbdcacbdacacbcabdcddadaacbbbdbbdabcddbdaacddbdcbbcccdabbdcccaaadcabaaadcccdaacbaadbabbcbacabadddbddddaadcbbbadcabacaddccdacbabaadaaadbcccaccddcddaadcdcadbbadbabcbcabbccadcbcdbcadaddbccbbdddcccabadbdadcadccbbdcbccdbacbabbdddbaccddadbadbaabcabcaabbbbddcabcbcdcbbbaddadddcacbbbcdddaccacbabddadbababdbddbccaaaaacacaabdbdadacabbacaaacaccdbcbaadbdbcdbdaccacbbbbbdaabdcaadadaabcbaacacbbaddadcbabddadddccbacadccbbbaacbcdcdcdbdabcaaaacbcdbabadbaaddbdcabdcbbdcccdbbbbcccdcccddcacddbdccdbcabbaccbbcbdcbbcdcaacdacacdbcabaddcccdccbdaccaccacdabdbaadddbbdcacbaabbaddbdadacdabcacaabdcdbaddbdccdcddcacbdcccacaaaaadbaaacacbddddccdbbdcbbadcdccaaddbabdbacbdbdacaacccaddaacdcdbacbbabcdbcbdccdbcdbaddcabcbdbacbcdbccbaccccdccddcdbdacaccdbdadbacbcbdccacbaadccbbbbbdccdccdbcacaccbaacbbbaaabdbcccdbabcdbdadbabbcbabdaccbbbbacadaacacdcbcdadcbbdbbabcabdbddaadacdcbdacacdacbaacdcdddcbbaaaccabcdbcacaabbbccbdaadcdbdccdcbcacdcdbddbccddaadaccbddcadbbbdbacdabaabaabdadcadaaccbccccbdadaddddcbcbddbcdbbbcdbccaadbdcaadaacadbdcaccdbbbcacaaadadbdcddbbadcacabcccacabcdddaaaacdbadcdadadacbbddcadaabbbcdadbcdddabaadcaadcbbdadbdddcdcabcbacaddccbabcacbbbdcbdabcdabcaddbdcacabcdccbabbbccdaddadcddaddaaabbaaacabcbcaaaccbdadbaccbdcbabacbaacaacbabdabcacddddddddaaaacabcdaaddbbacabcadbabdbaacadacbcaaadbdaadcbaaddabddbbcacbcbdacbdabacabcbcaacbabcadcdbadccaccdbacbccaddadbddaddbaacccbddbdcddbddaadccaaaadcdabdcbbadddacadadccdaacdbcdcabbcbccadccadbbccbbbcabcaddcbbcaccdcccadcbadaabadabdcdcbcacdbdddcbdcadbbcaddadbadbddddbdccbacacdcdddacaadbabcbaababaaadccccbabbaccbdcadadcbccaddadcdbdbbbbcddbabdcdaadddbcbcdbccadaddacbdbaabcddddacadbddbccbbcbacdbabcccbdadcaadabbacabbdcbbdccbbbccbcbcadabbbddcddbbcbaccaabcbbabddcadcdacdcdbbccdbbddcbdbcaddbdabbcdccccccdbbacbbbaddcbdabdbaadadaaaccadbaacccbbcddcaadddadbdbbbdadbbadccabdacdbbcdcbbadbcaacccbbbbcaacdbdcbbbdadbccaccabccadacbdcacdddcbddbdcbbdacbdcdccdbcbbdddaccdcbbbdadaabdcaccaadbdaaccabcaaaabaacbdcddcaddbcdbdbdabbdbadbbdbbcddcacadaabbabdbccabbddbdaccdcdcaabccbbacbddbdcdccabddddacabccbddbcaddcccdcabdddcbadabbcbabddcbbcbacaccbcacbadcadabbabbbababcdccdccbabbcdcdaadcbbcadaccabbbacccbdcddbaacdcadadccdadaacbcaccaacdcbccbddcbcadadcdacacdddbdbccbdbaccbabcacaabccadbcaaaabadabbdbbdccdcccadaabacbcaacdcbacdbacdcbcddcdabdaccbbccaacdcdaadcacadbbcbaaddbbadbaadbaccaccbbddcbbdaaaaabdccacbdcaacdadcbcdabcaacdcbccbbdcdadaaaabbdddcadccbcddcdcbabbdcaaaccbbdbdbdccbbbcdaaabddabccacbbdbcbadadcbcdddddccdbaddbcbaaadddcabcccdddbbacbccddacaadcddcddbadbbbcbadcaabacabcbacbdbabaacdabcbaccbbcdbbccddadaabcbbcccbdbddacdcacacaabadbbddddcdbbabbdbdcbddddbbaabdadbbacbdccbcbdacaadccddcbbcccdddcbdbdadacdaddbdadbdabbbadcacdabdabacbccddaaccacddcbcadbacdbdadddacbbdcdacccacaabaccabbdbacaaddbabdcddaaacdcacbcddadbcbbbccadadcbbacdaddcdadacbcdbabcdbddcddccbdacacccadcacbccccbccbdbaccadabdbbdcaacadbadccadaddccdacbdcbabaccdbbbdcbcdbaddccaccbcdbacadbbbcabbbdbbccbdbcaddadcbbbccbdbbcabaccbaaadbbbddbcaccbcdaadbbabcbddbbaccccaadbbaddaadaaddddcaddbbcdcabaaccacdadcdcdcaadaaadddcbbdcdabaabcababbcacbcbddaccdbccbaccaddcdacbbadbbdcbadacbaaddadabbaaaababdbcbbadcdbbbcaddddbabcbdddccbbadcdaccadbcdabdabaaacddbbbbdbdcbcdbdacbbcbccccadababbabcaaaddacbabdcdabdcbccbbbbdbaddbbcccdabbcbddcdadaacabbccbbbdacababaaaaddacdcdbcaacbcbbbbccbbbbbdbcacbdcdcdccdddaacdaddaadaaabbccbabaabacaccdacdacdabcdaacdcdbacbaaddbdddaaaadbacaddbbdddadddbabcaabbabdccacdadaddcbdaaacdcaccbcddbcbdbbabdadcdccdaadcdbddbcddacbaacacaaddbcdcbbdbdacdccaacdcaaccbaddbcdabadaaaabddcaabdabacacddaabdccccabaadacdccaabdbbdacbcadadddddbbcdddbacddacacbbdccdacccccaababdbcdcddbcdbbbaddcabdbababdababcdcadddcbcbaddcdacbdaabaaadcdbdbbbcabcaadbcabaacdbaccdacadadcadcdbcbccdcdcadcbddacbdcadcaadadcdacbbcadbaccdaaadaddadbccaabddcbcacabdbcadaaacbdcdaababdaacbadbbddcdcabbddccbdbcadddabbcabcdaaabacbacabcadcacbcadabbadcbadaacbdadaadaddbbccdbaacacbdcacaabccabdcdadbabcaddbdababaaaacdbcdcbbcdbbdddbdcabccacdccbddccabbadbbdacccaaabaacadabacbcccbcdddcdcdddbddaaaacddddcaccdbdacbdbaadcbbddddabdbadbbddcdadbcaccbabacabbbdabbccbabbadbcaaddbdacdaadcbccdccdccdccacdbbccaddddadddadababcaaddabaaddbcdccdbcddccbbbccbabddbbabcabbdcabbcdadccbbbdcbcbbcaabbabadcdbbaaddbabdccccbcbbbbacdbaaaccabdbdcbccbdabdbcddababbcdbdbcdaacacabbbbbbdcacaacccbbcaabbcddabdbdadaadddbbbacdbdcabccdbbdbbcaacdabbcbaadcbbacbccdaaaaddcaabacbdcdbacbddadcbdbbccaabadddbcdbcadcabbddcabdcdcabdaacccdccabbdcbdacbdbddadadcbdccdbbccabddcdaaadbaacbdadbcaccacaddbcbbbababbabbbbdcddccdcaadadbbdcbcdcdcdbcbbacbbcdbababdbdcaccccbccbcdaadbaddcacbaddaccbaddbdcaaaadcdbdcbabbcacdcdcdcacdbbddbddccccaacdddcaacdbccbdcccdcbdcadccbbdccdbadbbdbadaddadadcddcdccddddbdadcbabdadbaabdcddaabaabdbcabbabdcaabccabccadacdaabdabbadaadcaddaddabddabdcccaabddbdacbbbcdaabdaddadabccbaccbcbaddadaddaaaacadcccadcdabaadddaabadccbdddbabdacdccacdcaaabaccdccaddcaacacbcbdccbadbcdabdbccadacaabdcacabdaaddcdbdbaabcdaacddacaadbadbbcadccdddcbcadadadabccdccadadccccbcaaabcdbabdbababccbadabdaabadcccadcbcddcababdbbddcbccccbbddaaadbdcbbadbbdaacacdcaccbccacddcabccbcacdacdcadcbdabadbbddabdaabcbddacabbddcbadbacdccacbbdabbbadcbcccdbadacdadcdccddaaaacbabcdcbabbcdbbdbbabbcbcaabbacbddbcbdcdcbcbcddccbbbcbbbadacadbccdcbdbbddbdddddbcadccbcbdcaacaaddbbabcbcdcdcbdcabdbcdccbabbaccccbbadacbdcddaddabaddcaaadbbddabcaaadaacbcadcbbddcbabcbbbacdbbcdbbccbabddbcdcddcbdbaadbadccbbcbdddbacbbbaadacbddbccacddbcbbbbabaddddacbcdacbabdbaacdcbcccabbdacaaadbbbcbabbbacbaddcbdbbcbadcdabbbcbcdddcdbaccdbdcbcabacdabbabddbcdabdadddccaadddbbddacdddbcccadabcccbabdbcccaadaccbcabacdabcdcbccacacbcbcbaacbacddbabacdbccccacbbdabdccccddbadcbbddcdbaabddcdbdbccdcabbaddcbdbdbdababaabdabcbbbcdbcadccdbdcbacdababadbbddbaabcddbdcbacabaabcdaaabaacbaacccabbbccdabbadccbbbbdbadadadabbaacacdddabaaaabcbcbabbabadcacadbbdcabddcccdcccccaaababacbbddadccdaddabcdabdcbdbbaccdbbaabaacdadbaaaaacaddcbbacdcdaacbccacadcdcdbaacdcccbcccbdccbcdcbbccdaccdcbabbaabcacdcddaccdaaacbdbdbadaadcdaccdabcbdcbbadddbdbbcbcdcaabadcbaadcabbadccdbcdddabdaddcdcbcaccbdddbcdbcabbcdcdccbaabdaaacadddbdabbaddbdcabbcacbacdcacdacabacbddbddaccdbacccaacdacbabddaccacbcbcbbbcabdadbaaadddbdbddcaacbdcbaabacbcbbaddbdbbaaaacacbbccdacbbcccacbcdbcadadbdbcaabbdababbbaaacabacddcdadaacbdaddbcbcbbcabbcbddcaaccadbcddaaacaabcadadcbaccadbcbbabcbbcbcbcbccadacbbcbcdbddddbaccacaabcbccbbbabdbcddddacbaddbcdbbcdbbbdadabaadaabbccccabcbbaacadacdbbadcddbbccccddbcbbabadbbcbdabccabdccddcaaadcbabdadbcdaaabadadccdaabddaabdadddaabbbbdaadaaabbabdbddcaddbccacadccbcdcdcdcbcbbdbdacbbcdcbaaabcbcabbabccdddabbdaabcabdccbccbbcdccadcdbaccbdadcbdcadccdbacaacbabcbddacbadaabcaccdbcaabcbcdbaacadadddcdcbccccccdccaadcdcdbcaacadbabdadcbcdacbabddddadcbccbdabddbbcaaccaadcadddbcbabdaaaaacaabcdccadddbcaaaabcbdadddccccdabcbdadbdbdaadbbdcbbbcddcacacaccadacbcbbbcdbbccbcbacdcadbcadcabbdccddddbbcccdbabcabbdbbacdcccbdbaaccccdacbccaaaddcbdccaaccdbdcdccbcdcccdcdcadabbccbcccacdcbdacaabbddbaacccbdbdacbbdbcbdcdacbcbcadddbddcdcbaabdcaacdabcbbbddcacacbdcaacbddcdbbbdbaacadcadabdcbdccdaccddbcdcdbadcddcdcddacdbbabacdbadbadaadccabcbcbcbdabbdacdbbacccccbababbaddbcddacbdabcdcbdabcdacaccadacddbabcadccaacbbddccdcdabdadadcbbdbddbaacdbbbbdcbbcbddbccccbacabcbddbdabaddccbcdbbdbacddcdccbcbcbbcbcdaccdcbadbabdbdaaddcadccbcbcdcbddbdcdaadbdaabcadadbcdcaddabccccdaadcddadbdaadcbcbdcbabcacadadccbbbbddcdcabccdaabcbabdaadbdcdaddadbacccbaaabdbbdcaabccdabdacbadabacabcdcadabbdbbdacdcadcddabdabadccaaabbbbdaacbdadbdaccdabccbbdadcccaabcddcddbbaaacdbbadcacadbcdbdacdcbbdbcaacddcaabaadcaddabaacdabbbdbcccacdcccbcaddacbbdbaadcaccbacdcabccbdbabacdadcacbcdabbdbdddacdadabbccbbaccaadbaaacabdabbbaaccaddadbbbacabacaaabdbcaacdcdcbddbdbbccbbaacaccbbacaabacdadddccbcccaabcbdbbcadadcaaaacccdacccdcdddccbbbdcaaaddcabbcbadbaaabbacacdcdcaacddacaaadbcccbddbbaababdadbaabcccadabbbbbadbadccddacaaaccbcdccaabdcbcacddadcdbccbbcdcbdbdbabacbdcbbabaabbcbcbdcdbcabbcacbddbccccccddcaaadcabbbbacbdcbbaacadbcacaacaadacdbddacadacdcccaddcbbccaaaddcdcdccaddacaadccccdadcacadccbcddcbbbacccacabdbcbadccabbccccaadababaddddabdbbdcdbacabbbcbbbcbcccccdbcaaccbacccdbcaabdcdccbcdbdbbddababbccbbcbbdccbadddbcabddccacaadbabdabdabdaddcaddadbcccbcccbbdbadaadacbccabaadbaadcacabadcbbabaaadcdccdaddccbcaddcbbbaddadaacacbcbccbabcabddcdcccddcaddacdadabccdbdbddbbaaacbbccccccaaabaddabdcacadbddbbcbabccdaddbcadcdabcbabadbcbdadcccbdbbddbaabcabbbabdcccbaddaabacacbabcbdcddbadcbabdbcddccacbdbbabdbbcbbdbbabcdaddacdcadbadbdbdddacacabcbbbdacdbbbdcaaaabcccdcdadbdcbbacabdbbdbcabdaaacbdbbdbbaacaabbdbbdacdbcabcbbbdbbbcadaadddcbddcbbdcaddbcacbcacdbcbdddbaaabdbdabccddcdacaabcabcaabdccacbaacdcdddabddabdcaddcdabcdbdadcbccdabbcdbbccdcbdcbccdcaaaabddcbddcbdbcbbaaacaaaddbcacdbcbdcbccbbacddcbbccbdaabccdbacdcbbacdacadcbadcadadbbdabddbdadbadccdcbdabacbbdddcdddcaddccbadaadbbcdbccbabccdbbaabbbdbdadbacbccbcbdabddcddbddaaacddabbcacadcbbdcbcacdacaacbcdaccccaaaddbbbaaabadadacdbbdcdcaddddbacccabcbdcdacddcbcbdbcacaabdccdbbcbdbdccbabcdbdacccacbbbaccaacbbbddbccddabdbccdbcbddadddddcaadcddadaccadcaddacbababaadaabbddcccbbdbdacddcacdcadbdbbaabbaaadbbbdacccdcacacddcbdadcadcaadcdcdabcaacadaabbcacccababddadbccdacdacdbabbbdbbcccaabaddcadcbdcaadccaaabbccdacacdcadcbccaacbabbababaababbdaacddaaaccddcbacdabdcbacbbaaddaddbaaabbbbdbdcdbddcdcdccdccbccaabcabacbdbbcbabddbbacdabbcbbabcadddbccababdaabbddccbcdcbbbccccbabbdbcbdcdacddaddcaabddbdbdbbdacccbcadccdbdbdaabdcabdddcbdddcbcdaabacaabdaddddaabbabacbdbbbcdbbaadcbdaccdcbaaccabacddbadcdcaabdddaacadcdcdbacbddadbcaacbadbcdcbabcbaadbbcadccdcbacbbbabbcacacacdcddcbbddbdbbcbabdccacabaabcdaabababcadaaaabcaaabcbacddadddccdcddbbbbacaabccddadabbdbbddbdabaaaababccbdaacdbcadbaacacaccbcddabaababbaddcdabbdaabccdbdbabddcacabdaacddabadcddaadcbbbccccdaabacbcabcbcbdacbbbbcdddbdadcabdbbccccccbcddabcbdcabdbbdcddcaddcdbbdbbadbdbdbadcdcbbcbccbaaddddadcdcddbcbabcbacdddddcccadbcadcccbdbcdacddccbbddddadbdccaddbdbbbcbdccdbdcddadacdddbbbdaccaacddacacbdbdaacbdaccaccdacbbdadbbbabbbcbadccccddcbdbadcbccaddbcacddabdddbccadcccbcaabcddbccdcbbcdcbbcdbddbddcdaacbcdbacbcaacdaabcccbadccbdcbabbdcddcaaabddddaadacbdbdcdcbadababbadacbcbdcccabadcccbbcdbddaacacbacaadcdaaabacbaccdddcdcdaaabcbabaddabdacdbddadacbcbcccbaadddadcaadacaabdbdbbdadbbcdaacbabbbadbdccbdadcdcdbccaacaaabadccbcaaacbccbcaabddcaacdaabaccddddadddadabdadacacdacbdbcbadcabcccbdddcbbcdcbccbbacddaabadadacdcabbdbaadbdaddabacdddcbaccdcbabaddcbdabcaccbacccadadaababaababbdbbdcdaabcdbdadccccabbccbdabddcaacbcdddbadadadacdcbccddaabbaccdbcbdacdbadaddbbccbdbbcaacbaccdbbabbbddbabccddcabcaacccccabaddcbaddabcdacaabdcbcdddcccaabdabccdababcabbcbaadbabcccbdaccacbccaacbaadbcdbbcbcbabccbcbcbbdddcddbccdcbdacdbddbbacccbbaadacdabaabbbdccaccdcaddcdadadbdbbadbddccaabdabadcacabdaaacbacabaacacacadccadabbcbaacbcabaddcbacacacbbdaddcdcdaaaaaaaccbddacbddcdcdbbdadaacddbabadbdbcdcdacdcdcbbccbcccbcacadcdcabaddbdadbdadaaccbcdacbacbbbdbdcbdaadddaadbbbabbcbaadadabbadbbccdabcbccacdccbaddbabcdddacbadbdadbbcadcabcbbaabcbadabcbbcdbcbbcbdcbacbabbcacacbdaabbbcdcdaaacabbadabbdbbbdccccdcdacdadbcdbbbaabdbdbabaadcbcdaccbbcbbcdbbcbdabcaddbdabbdddacabcacaaababdccddaaacccbcbcccdbbacdbdabcdcccbbcbbdaaabbaaabadacbaddbddccbaaaccabcadbabddcddadddacdacddbcbbdbcacbdccbcddcbcbccbdbdbcbcabbbdddddbacdbbaabadbbbbaddacbbbaabcacadbcadabdbaddddadccbcaaaabcacbbdbbcaacdaccbddbccbbbccaabbdacdaaccbaabbcdbbddabacaddadababaabdbcbbdddddbdcdbbcbdadaaabccababbcdacccbbcadcaacdccdbccbdabacdbbcddbcddabddacbccbbadacbbaddacbcbccbaaacdbcbbabbcdadaaddddaadaabdcdbaadddbcdbadabbadaabccacccadbcbacbcdbdccbbabccdccccadcbdaddcbbdbccaccaaaadcadaadcdcdccdbccdacdcaacbcacaadabdcbacdcbbdaabbadccaabbdabaddbdcbabcadaacababccaccdbbabacdcdccddbacccbdbccaaadbbdbacbbabcccacccbddbcccacbacbdabacdcbcaaddccdddaccbaaacdcdcdbdcbdcdacadababadccdaddabbadbdbcdadccaaaacaccaacccccbbacbdcaadccbdbcdadcbcbbdddabcacaaccadcbbbdbbcdbaabbdcbdbbacbbdbbadccdbacbcdcacbbacbbcddcaadcdaddbcddadcadaacdbacdbdaddcddabadaaddaadbbcaddddbcaddbccbccdcadbaccaabbbcccbacdbccdaadbadbadacabcbcdccaddcabbbdddaabccccbaddcbddbdbabbcadbbabbaabbadccdabdabdadbbccabbdbddaabddcbabbbcadacddaccdbbdcdbcacbcbdadbaddabcaadccadaacaccaaddbdbcbcdccddddccdcaccbaadadbbcccaddadbccdbcbbbdbcaabccacccccdcadbaabadaaddaabdacbaacdaabdbccdaccabcbbbcdbadcccdbbdcddcaaccccadccbaabbccaaabbacdccbdcaccdbaaabdbcccadcaabaddaabddbacddcccddbaddcabddbcaddbddccaddbccbaababaabdcddcabbacbcdbccddcbadbabbdbbdbdcbaadadbaccaabcbbdabdccaaadaaddbdcccbddabcbdabbccdaadcadaabaaaaacdabdcaccadbccdcdcadccbcaaabdddcdadadcbbbdaadbaabddcdaabcdaacabccaaacdccbcbbbaabbaccabdcccdbaddcdbaddaddcdbbaadaabddbcdccacbcbacdaacbddacdcccbbdddccababadbbdcabcbaacadaaddcdcbadccdcbddaabddadadacdbbdcbdbadbaababccaababdabcbcbbdccbaaccddadcbdaacccdbcdcaaaacccddcaabddbbdadaadbbdbbcbbcbdbddaaadabbbdabbbdacdbdadbbddbbcddaddbcdbcdcddbcacccaadacdbbcaddabdaddcaaddbacbacdbaaddccaccbdadcadbccdbccaacdbbcddabacccbacbbbadcacdcddcdccbacddaabbbaadabbbaaccbcbabaadbadddbcaaabbbbcabbbdcdcdcddcdcadccaddddababdbbcbdaaccaabbbbbbdadacbaabbdadcadcdbddcbadccabaadaaabdbabddccdcdccbbbcacdddddddcabddadacbdcccccbcbaacbcacdadbadadbbdaaabbdbddbbcbccaaabbaabddabacccacdbbabccdadbadabcdccbddbddbbdbaabccacbdcbbdbdbbacbbcbdaabbdaadbabddabaaadbcddcbcadaabbbcdcacddcdcbcccdabababaaddcdacaaadbaaadccbacdababaaaabaaabcdbccdccbbdaadbbddcbcbbbbcabaabdbbbcbcbccdadccbccdaacdddbdbabcaabcadcdbaddadcacdcacacbacaccddaacbdddbaacadccbadddbcbcbaddbadbbddccdbcdcaaacddbdaccaacbaabcbbdcabaacbcdaabbaddbbdccbcdcbbadbdccccabacbbabbbdbdcbabcabaabbdabdcaddaabdcdbbbccbbdacbbbabdcadccdbbabadaddbcacbdacbddcccccdbaacdbbcabdaadcbbddddcbdabbcbaabbdbbacdccdbbbdaaddbdaacbbcdcacccabbcbbdddbcabaaaadbcdabacadbaaacdaadadabdacbbddcdcabbbdbabcbcdbdbcaacababbccbdacdbcbcbadbbacccdbbbdccdaadbabacabbdccbabbabbdcbddddaccdbbcdcdcdddcacbcdcccdbbcdbcdcdbccdddcadcdacddcaaadbcabaaaaabcadbccadbccacbbcaaadcdcaddbabdcbddaddbdccdbdcbbaacbaddccbcdbabbccabdbbbdadcdcdbcababaaadccaaddcdcdadacbabcbdacdccabbcaabcaadaadbdccdddbbadcccbdddaddcbcddddbddbbbdbaacadddcacdbabacdbcdcdddbcabcbbdbabdcabadaadaaccadccadabadccdabaacbbaadcdaacadcdbdbbabcadbbaacadcdccbaddcaaacccabacbbacaabbaadaabaabcbbdbccbdddbcbcdaddbabaadbbaadccccbbbaddbdbbadbddadbcbcbbcaddabddabcadcacaabdcbddacbbaddccaccaabbbddbbdcbabbdcaadcbbbadaaadabadbdbdacdabcdbcdabbbdaadcccdabbbccbaccbcccabdbadbaadbbbbdcabdbbbdadcbbcaabddcbabacacbbddacaadcbdbaabdaddcbddcbaddbcdaabacdaadccbcbbacabbaadbabbabdaddadbcbacbdbdcaadadbcdbbbdddbcdcdccccbbbdcaadcbbcbdbaccabcbbbaacacabaaacccbadbabbadaabaaaaaadbdcababbcbbcadbcbbbcbbaddccaddbccbcaaaddcabbddaddbadabadadbaabbaaabadcbbacdccdaccdabadddaddabdcbabcacbaccdcbdcdddbacdcccbccdcdbcabdadadcaacdababdddadaccbacbcbddbbabadccadbbbaabbcdcabcadcbbcdbabccacbbabcdcabbbabdcdcdcdddcbdbbbdacdbdadbaddadcdaaadaadbbabdbcbcbbcdaadbdaacabcddddcbdbaadcbbcdcbcdbdabcbcbcacbddbbadbaabcbcbdbacdbaacddcaaccddbdadcbacdbbcaadcbacbaabddacdaacaabcbabbbabbcccdcdadbbcbabcdcaaadbcabbabddccdbbbcddcbcbdabbcaaddcccaabbcbccbabddbabacaadcbbdddddddcccbcbbccacbacddbcaacadaabcbddadbcadcaabcdadddacdbbdccdbdccdbcaadadabdabdbbbaabcdcbaaabdbdcaccddabcaadadcacdddaaaadbacadddccccbbadcaadacddbbbacbacacdcaacaccbdcbacbbccdabddbcabcbcadadbcaaaddbcccbbdbbdbcdcaccabbbccabcaaadaabbccabcacabaadcbbdbdaaadabddbadcbbadabdabcdcaadbbdddadbccbbccbddbabddbbdacdcbccdcccdabadaadcdddddbadbccddbaaddbbdcaadddbdcadcdacabbbabbbcbadaabdccbbddbbbcddcdbddccbdbbdddaaccbdaccdcabdadbadcabbacbccadbdbaacbdbdaacaaddaacbdbaacbdcbabdaaddaccccdabaccabaaabaabbccddbcbcdbdbdbbdcabcacaacbbbbddcbcaccccadacdddcacbdaaccbbccabcabdaabaadabccacadcbaadccbabdbbabdbaacaccaacacbcccbcddbadaaaccaaaddbaadbcbbddcdcabbcadbcbcadaabadcaabbdbaccbcbdadaabdcbcdabadddddabcbcbbbccddaadcbdcddabbbaaadbdbdababdbcbcdaddaadccaaccdcbbaddabdbcdcdaabcbacbaaabbbdbccbdacccabadbddcacbabddadcdccdbcbbcccbadbdaaddcbbacbdcdcacddcbbbdccaccbaacbdddbaadaaccbabacdccaabadadbbcbaddcbbdacaddbabcaddbcdcaadcabddcbccadddcdaaaddcccaddadbdbababcababcaadbbcaabdbbddabdcbbcaaaabccbcccdddccbcdccdacbdcacdbbbddbccbbbdabccbbdcbabaccbcdbddbbdaaabcdaddbacddaadadbbacbdbbcbcbcdbcdbbacbaddddcabbbcabcdaabbbcdabbcaabddcdbcddccaaacdaaabbbabdcaaddcccdbbccdddbddabdcacbcbcbcbdcdbbadbbabbbdaaadcadbcbaccdcadadbcbdddddaccbbbbcacaabcabaadcbdaadcbcbbcdddcabbaaccadddbbadabcdadaaaaadbbcbbdbbadccbbacddadcadcccccadcdbdcccaacbbbbdabdaaadbdcadbdbaadcbadaaddbdbccacadaddaaaabaadcccbadadadcaccddadccdcbbadddbcbcbddbbabddddadaadbccbcbdabddbbcdacdaaddbadbbbdcbdadbdabccabaddccbcbbdadacccacddadcbdbadaccdcadaabdbbccbababdacbcdddddaccdbadcbabadbadddccabbadbdadbbbbcbcaaacabcacabcbccccbbcccadbddabcadbabbabcbbbabcbcdaabdadadcbcaababaaabbbbccadcdaabdddcaacaccaaaabbdcaaaacbbacdcdcdbdbdadbaabaacaccbdcdbcdabccdcdbcdacbdcaadbdbbcabbccaadbdcdbadcdbdbaacbdaaccaaddaabcddaadddabcbdbacadbccbaadacbdabbadacccacadcbddccaddabadddbacbabbdbbbcbbbbddcacdcddabddddababcccadbaaadccbbdcbdabadbcadcdccacbdbbdbaacdcaddacddcbbdddabacdcadddbbcdacdadabdabadadcaabccacdcadccdbdcdaaabcbacacbbcbbddddcababcbcbddbdcbadcbdaddbcbcdcdaabcbbabcbcbdaccbcbbcbcbbabcccabbaaacbdccccadababbbadadabdbbcbcbbbddbabcccbcddbadaddacddcbabadcacbacaaabdaacdbacbcaddcbdddbdcdccbbcadccbbbabacadadadabdbcdddbbcccbbcbaddcccabdaaadadbbcacbaacbabbacbcabdcaabcacacaadacaabdbbddbaaaccabbbaddcbabbdcacaadbbcabdbdbddbcddbdbdcaccdbdbddadaddcaabbdaadbdccccabbcdddaccbabcdbdcdbddabdcbacbaaacaadbcbdbdcdddaaadddcabdcbabbbdabaaabcabdcbaddaadcaaabcdacbadabbbbbcadcadabbbbcbdccbdddbcbcbacdddcaaabcaabbadbadbddbdbaadcccaadbbcccadacdcacdaccdbcdbcabddbabacccbdcbdaadbccddcddabbdbabbdcabbbddcaacabcaddadcbcbdacdaaddcdcccbcacadbadcdbdabdbaacbdddbbdabccbaaaadbbdbadadcbdbdccbabbcabbdbdbcdddaaabacdbababbaccaacbcdabcbaccaacbcbadcabdbcddadbcacabbcbcacdaaddaaaaddcabcacdcaaaacbbdadbbbbbcbbbdccaccaaabcabdbbabbbdcddbcaddbabcacadbabbbadbdbcdddaacadbdccccdacdcabbdddbccabcccacabbcacbcbabcbdcdbacccaaccccddbdbdabbcbadccabadcdcddabcabababcbdbacddbaddcbacacbcaabccbdccddddaadacabdacdbabbabbddcadaabcccbacadbbcdcbcdbcddacabcdacbacdabadcacacabddcbabcadcbbbdddbcacacbbbbbdaabcadabbabdddaddcdbacbaadbdabbbbaadaacabdccdbddbacaccddcacadcbbddcbabbcaacdacdcdddaddccbadadcbdabbccadadcccbdcabccccadddcacbacabcdbaadacdabccdcbadadbcaadaaaccbcaccdadadadcaaaaababbdcaabcaacccbbbddcdcbabdcbbddcadabddbbcdbdbddbaccbaddbaadacdbbabaccbadbacbbbaddadaaadbabbbddcdacdaabddccaddcdbcaccbaccdadcddbcabbccacdccdadabddaaccdcdacbabaaabdddbdababdabdbbabcbbbaacbbbdbdacddbdbbbdacadacaaadbcddbbabdbaabcdbcdadcdbdcabcdbbdabddcdbbcadbccbdcbacbcbaaabcdaccbbddcaacadaadcbbcaadbdcacdadddbaaadbbaddbcaacbdccababbadcdadabbbbcacddcbdccdbcbdacbbabacdccaadcbcbaccbbacaddcbaaacdcadabbbbcdacadbbdacbbaadacbbaaacbdabbddaadbadaaadcdacaabacdbabcbddbbcbdbdcddabbccbbdcbdbccbbbcdadcdcdcbdabcbaadbdbdcccaaccbadcdcdcacacbbadcdbbcbcccbbcacaccadccaaacacbdaabadbcdbabccdcbbdadcbaadcbbcbacbbbaabacdacadcdacdbcddcabcabddbccbbcacccbbaadaddabbccacdaaaaacdbdacacdbbcdbcbdccbdddaaabbdcddacbdaadbcaabacddadaabcbbdcbcbccaabcaadcbcddbccbadbdacdcabadbbbacaaabbcbdcdbbabadcbccbbddaadcbcbddbcacbddaccddaabbcaaaadcabbaabaddacadcdddabcdbddcaabbcdbbcddbdaddbbcddcbcabcbadddaccabadccabbcdbbadaabcaabcacbdcbddcbdbdabcccdbbabcacabdddcaccdccabdcbaccbaabcaccccaadadabccdbbabaaaadbccbbdcbacbdbdabbddccdaadbabaaadbdbbbbbaabddccacaaddddaaadaabbbbaccbbbdadcadbdbbbacbaaabbacddcabbcdcbbbabdddacaaaabcdcadcdaddbdabbadbcadcbbdadadcacccacaaacbaacbdacabcabcdcbaddcacdadbbcdacaaadbdcddcabbadcbabcdddbdaccccdccbbbcacaaccccadabcbdbcdacbccccdccacdbdaddaadddcdbdabdddadacdbbadaccdcadbaddabcbacbbbcacddddadbcbcdadddbdacbbadbcdcbcbcddbdbaabcbbcbdabbcbaaadaaddcccacacdcabbcbbdabaababcdbdbaaadbadaabcbdabcdcdbaaadddaccbabdacabdccdccccaacabbaddccbbcbabbbabbbbaadbbdddccdcdaababdcbcaddcaddbbabcccdaaadbcabdcacaaacadacdbdabbbadddbcbbdaccdbcbacaacdbccaaacbaadcdacbcbaddbcacacbcdcccdaddacccdccdbccaadadddbcccaccadabbdbabacdaddbdbcddaadacadaadcdabaadcabcddabdcadbbaadbabbbacbdbcdbdbaaaacadcdabaabcbccbcdbadadbacdbacdcbbababbddbbabcbaaaddcacdaacdadbbcbcbdbbcdbcbcbcdcbdbaddaadbddbdbacababdababdacdcbabbdabbdbbabacccccbcabdaaaccdadbccccdbbddddaabbbcdabdaddddcbbcacabadbccdcccadbbbdcbacbbcbabcdbdcabadabcacdabaacccbaccacddcaccdaadbacddacdbcbddadcacccadccbcabbbbdbadcdccdcdbddadaacaccbacaddcbddabacdbdacbabccadaadadcabdacddacbccdbdaddabdccbdddbdaadaddcbaddcacbcbabcbbadabcbddaaabdacadbdcbaaaccccabacbdbcdbcabddcaaadaacdaabcabcccaaaaaaadddacddabdbaddcaddbaaddadbbccbcaabdcdbaccbbcaccbaacdcddcbbadacbdaccabbdaabddcdbdcdaacbababacdbaccbbbdaaadcdbcdddbccbdacaddacbbacdbbaacdcbabaccdadadaadbdcccacbacaaadbcdabacabcaaabccdcbacddabdccdcbacddbcbdabddbdddadddaccadddaaadbaccaaddccdcaccdbddaaaadaaabdccbccdbdcbabcbddabdbdcadbdbccbaddcddccccdbddccccbbabddbcadaccdcaabdcabdcccbbacaabbcbdbcadbcdbdccabdaabdcabaddacbcbacbadccbbcddcdaacdcbcddaaabcacdaaccdcccdcdbadbbbbcabdacabbbdbcabdcdcddcabcbabbcacbbddcdadbbbcbadbddcadaaaaabadcaacbbbdcbadabacbdadadddbdadbbcdccdcddbbcaabadbccacbdbdbcdbbcaadbdcacdccabbccacccbdacdbadaaaaddbbacdcbdbbcacaabbbdadbcabadbbbcbcbdacaccdbcbccccddcdbacddccaddaabddcababaddabbddadaddccaadddcabbcddaddddcaaddadcabdbaacdaaacdbadacddbbcacdccdbabcabbdcddbabbacddadaabcadbacacdbdabaacdcbbdccbbdbdadcdbccbbdacbbadacddabddabbabdbccdbaadddaacccdddcabaabaddcabbadadadcadabbbbacbdacaabcddbddbbdbcddcdbcaccbabcadadcadaddabbddbccbccbdcbddccddbabddadcdbbbcdcbccccaabbdbacaaacaddbbbbccccbccdbaddaabcbbadcdaddadddbddaaadbcbadbcbbaccaabdbbddcdbabddacabadabcbcddcdbbaadabccaccdbacdcdcccdacabdabdaacdbcabdcdcaccdaacbabbbcaabddacbdbbddbbbbbddbbccdcbccbcdccbdaadbbdcdbbdaabbcbcdacbbcddcbabdcdcddabacaaadaaaadaacadbddbcadcbadbcdcbbacdadbbaadbbacaadbddbabcdcbccbddbccabcadddcacbccbabababcacddacaccacddbdbbdbccccdcddaaaaacaadadbdababbdcaadcbcdbcadbdcdbbbacaaddaacddaaaaddbaabadddcabdabdbacdbbdaddaadbbccdabcdabbcbcabbcddadccdacdabadcddabdcdbdadbaacbdbccabbaacdcacccbcaacbdacabadcbdbaaaaadacdabacbbcdcacbcbbbcbdbcbcdbcddcdbbccbdbdcdcdcabdbbcbcaaaaabddcaaadcbdbabcddbbbaabdcabbaadabdaccbdaccccadaddcdccddaabdddcddbdacbcbbdbdcdddccaabddbdbabbbbaaaddcaabbaaccbadacdaacacacabdddcbdaacddabddddaacbbcacabdaaccbacbcbcacdacbcadbacbbaadddddcadcddbcdacbcdaccddadaaabbbacddbbdbaacbbaacacdcbcddcdbcddbdbdabddaddbdaaaccdbdacbacddaddadabcdcdddaddbcadabaaddcccccccacbabddcbdaadaaaadccabccdcddacdaccadbbbdadcddadacadaacbdbcbdddccdbadcddaddbbdabbcacbdddacdbacbcdcabcadccbdbcdcdbdbabbddcadbbcbddaacabbadbbdbbbdcadcbbcbbaddbbcdaddcaadbccacdbdcaccabccbdacccadcaddbbbdadcbcacbdadbacdbdbdabdbcccadcaaabaabdbabddabbadcbdcbbacdbbaacdbcdbbcccaaaadbccabbbbdbddadcddcbabcbadcdabdbccdabbbdbadbabaadacddcccbcbdddcddaabcbbacdaccbbccdccababcddcdbcbbadbaccbbacabccdadcdaaaadacaacaaccaccabaaccdddacdadabccbcbacacaadcdaadaacdcbaacaacccadbbccabdacaaadbbcadbcaaabbccadacbacacadcadccaaccccbabbdadaababccbddcdcbddadccddabcabaacbbbbcccdcccadacdbdcddcbabaddccdbcbcbbbadddacdadbdbddaacdccccdcdcacdccaabccaadbaaadadcadcbccacaabbcdbcdcdaddadbcbccbddcacdddaddbcdaadcbcdcbdddbbddbaabdcadaaccacbcdaabdcbbacaacdadcddddddbaaabcadccdadbcdddaddbccbaccabcbdbababbaccacdbbdbbcbaacadbacdbabbbbccaabaabbbacbbbaabbdccbcdcbabdabcbdcadbaaaacdaacbbacabbcabdcbabbcadcbbbaabddabcbbdbdacabacbcabccbbdadbbbabcdddababccbcdacbdaccccbbcdacbdccbacbbbaaddacddcbaabcbcaababdcddadacbdccaabacdccacbbbcacccbdbcdddcddadcccdcbadadccadbdadcacaaddcacdccdbcaddbddababbdcbabadcaccdcbbcacddbcbcaadcddacddbcdbadcdaabaaaacaccacacdbacdddaddacbbaddddaabdaadacacbdccbdbabbcabaddcbdbbbbabccdcccbbbacbacddbdbcccccbaaacdacbbdbccabdaabbacaddabcddbbacababcccbddadbcababbcccdcdbcdadbcdbacbcdaabdbaabadbccdcdcaadaddbddcadbcaaadbadacacccaddccadbbcdbdbdbdacdbdaabcbacbdadacbcbaabdbabaacbddcddcdbbbbbadacbcabdcdbdabcababcbadbccaabacdbbabcccaddcbbddacabbccbbbcdcdaaaccdcdccadbddcbddddadcccccbabdccadcbbddaacacddaccccbcadddbcadaaccaaabcbadccbccadccacbbdadbbcbcaabaaaacdbbbbbbddddcacbdacaaacddcacbdcabcbcccaabcbcdabdbcddbdbcbcccdbdcbacddbdacccadddbdababdaabbdaabaadadadbdcadbbaabcaaabbacacadaabccbacadbcabaccbaddcabcdbcaaddabdcdcadacbbcdabdbccdbcaccbddcdaadccbcdbdabcdaabbbbadcddbacbcbdbdaaaaacaabbcabcdbaaacdaabaaacaabbadbdccbaccacccaacaabaabaccabacbaccdbcaaadbadadacbbabccdbacacdccddacbaaaaaddbcdbaadbbacbaaaaddcaabdccacbadbdbccadacbdbdddcbadaabccdcaadacddcacdbabacbbdbabbaddcdcbbabcbdcaabbcdcddadddbabcbabbbaddbdcbbdcdbadbcbcddbabcbacddadbdaabdcabdbbaddbdcbacacccdacbcbabadccadacaacbbadbbbabcbbcbbdadcbbaaacddaaabcaccaabaabbdadbdcadbdabbdddadbbbbbccbdcadbddbddddbcabddadbdbcdddbcbcbaaaaaadcabdacddaccccbccbacabbaadaadccccaaadbacacaacbbaabdddaaccbdccdbccabacbcaadaddadbabaccdccabbcccaadcbdbbcbcaabcbbcbbdcaababdbbdddddbabccadcdbccbacdabbbdaabcdaabbacdcccadababacaddcdcbaccccccaabbcbacbcdbdddacdcccbddbbcdaabdcdddcbbcbcbbddccaccaaacddccdaabcbccdacddbacadccdcddbcddbaaddbbbbbabacddadddddddddabdabbcbbcabbadaddddadbadaadbcabbbdccbacbddbbdcaadacbdabddddadadbdaabdcbdabcdbdbaddccdcccaaaabbdacdbdcbdcbdccbcadddaadddbbabbcadcadabbaddaaabbacbcbbddcadaadddadcbacdcdcbccacddcdaaabbbadbdabdbbddddabcbbdddadbabdcbadabcabaaccaacdcbcabcbcabcbbacbdaaddbbdccddbadaaddacabcadacbdaddcdbdadadabcbcabaddacaabaccdddbaabacbcbadcdccabaadaacbcbcdacdbddaacacdbcddacdccdbcaaaddbcbacdcdcabbcabcdccbbdbaccbddacddbddadddbdcdddaabbcddacccbcdcbcdcacbdabdabaadaccbcadbdbacbcdcbbbcdcdcdbcbdbbaacacbcabaacdcaddaabbdcbdbbaacabcbcaabadacdcbccbdcadbbdadbaacdbacccbdcccaadbdadadadaccdbbbcbbacbcacacdcdccbacbcccdcccaadacbbdabcddcddbdddbbcbdcaadbabbcbaaddacabcccbbabaccbbaddcbaacaddcabdaacdccbbcaddcdcacddbbaccbaabaabdccacbcbdddacadcaaccbdbcaaaaddcaaadaaacccccddcacddadddbcdadabacacbcddcaabbadddaaaacdcaabdccddabbacdaddcddbbcbbcbbbbcbabaaaccdbbbacaabdbdbdbbaabadbacdbabcdcbddabcbcbbbaccddabbadcdaaadbcadacdbaccbbacdabbaddbacbbacbdccacddddaabadbcdbcdacaccbaddcbddcaaadddadaaadadbdcaaaccacbcddacabbccbddcbaaabccabdaabbcdbaabbcbabadadcdabbaacacdababdcacadcddaaabccdccbbdddcdaabbdbacccdbbcccdaaacddaadbbbddcccccadddccccadbbbbdaacdadabbdbcdbdadabbbdddccdbacdccddbccaccaccaadbcdbaddabbbbcbdccdbdbadabcbbcadccadbacdabbbabcbcbbccbdbbddaabdccdadacbbcbbaabddbaaccaacdbcdbaacbdddcbdabcacdddbacdbcdbcbddabacdaddbcccbcadbbdcbbabdbdcdbdbccbbcdcadaadbdcadabdaddcccccacdabccabdbccadcadcdabcbaabdacbdabccdbbbcbbcdbaacdbcabcddbaccddadaadbcbdcdacbbccbacdcaadcccdbacdbddadbdbbdbdaacdbaadbababdadaddbaaddaabdcddbcabdbacdcddadddccdadacdbbdcdacabcdccdabddccbccbabbdbcabbdcdcdaaadacaddddaddadbddaccbcbabbbcdbaddddbaccbcbbaaaabbcbdcbacbaaabaddcdddcbdcddcabcbdadbbacbacaaabdaacbbacaadcaaacdbcdcaadcbdcddddcbbdcbddacdbddbabaddbbabdbddbbcbbdadbbcddbcdbddaaaddcdabdbbcacaccbddbbdaddcbcdaacddbacbbbddbcdcdddbddcddbbcdabcbbaaccacbacdbadcbbaaabdbadcbaccdaddbacaaadcadadbadbcccacacbbdcdbdbbdbabaabcabbaccabbdacabaadbdccddadadadaaccaabbaddbbbccadccaadccaaaaababddbbbbbbcdacaddabacbabcadcabcbbaabccbddbdcaadcbcbabdbbaacdbddbcbbacabbcccacabbbacddcbddaccdcadaadababddcaaaccaddacbaaadddacaaaaaadbdaccbaaaacacaacbabbbaacbbdabdddababbcbadacccaabcabdccddcdabdaddadabacbabcbdccccbbaadacccadadabddbbcbbadcbcdbbbbbccaddcdaacdaabaabaadddbdabbcacdbaaacbcaaacccdbcbdaacadbcccbabaaadddabacaacdacadbacddcabbbabcbabbdacbbabaadbbddbccacddbdcbaabbbdcdcbabcdbbddccdbdcadcccbbacaaaadcdabadbdbadabbbbccbacbdcadabbccccdbbbdccbdaadbabbabdbccabaabdccbacabcacdacacdbbbacdcbbcdccbccabcaaaadbabbdcbbcadbdcbcabbdcbadddaaabcdddccbbacbcaaabbdcadbdbacdcadbcbcbbaddaccbaabddaadccdacadaccacaaccacbabddbcbbbadbdccaabccbbdbcdcddcdbbacddbabbbdccadcbcdccdbbdccaccdabdcbbcbaabbdaddccbabcdcdcdbddcccbcbcadcdcbdccdacbdaccbbdaacccdacddcadadbadbaadbbdacbcdadbacdbacbadadcdddbccbbccdaadbcdbcbdccbacbdddcbccabaabcbaabcaccaddacadcddccbddaacdbdabaccbcacadbccccacacdaccddcacadcabbabccaacdbccccddaabbccbabbbbddacbbdabadaaaadaabdcddbdaadcbccaacdcdacadcbacadddbdbbbbaacccabccaadddabbabdcaadcaaddbbcabbababbbacdcdabdcbbcaadcbdaddaadcbdabbdbdcbaabbbbbcacdbcbaabbcbccdbaccaddccaddbdbcaabdbbdabcdabcadaaddcdadaabbbccdadbdababccadbddcdadccbbabbaacabcdbcdbbbbdbbbaaaacdabacacadcdadcdcbdcbdbbdbdacbbaabaabcdcbdcbabbbddbbdbaddbadabacdaadbdaacadbbaddacbabbacccabaacaadbdabcabddacbbbcdcccddbcabbdcaccccdbcbaacbddadcbabdbddcddacbcacbdccdbcccbcabcdcbcbddadddbbbcacdbccbcaccbbadbddcbbcddadaadbadddbaaaddbccdbbddbddbcdabcbacacabdbcacdccbdadabaaacaaaacdaccccacddacaddbbdacabdbbaadacabbcbacbdbdbadaadbcdacbdaabdaabacdabdbbacdddacbadacadacdbdbaccbacdcabdbcddadbdaaaaacdbcccbbbaacacbbadccbbbccdbcdccddacdcdcbbdddadbaabbcbbccadddcabcdbcdbdabddacdadcccacadbabcbdcbbbbdadddbbbdcdccdaccccbbbdcdadcbacdcdddaddaaddbbaccbcabbbdaacddcbbdbcbdaccbaaaabaacdcabbabaaddbbdacbddbbbcabbbdadacabdbddcbcddcccaadddadaaabcdcdabbbaccaddbaabbbbaabbadabdbccdadacbddbcaddcaabddbbcabaccadbaacbcadaddbacbdaadbbadcbcccbbcbbcaabcaaadcdcddcbacaddbbdbccccbacadbbccdcbddbbcaaaccbcdadacaaabbadccddccadbbabdababcccddbaaacbacdcdcabcaabbabcdddbdbbcbababcacbaabcbbbaddcdbbaacbbbcccbaaaabaabdcddadbddddddaaadcccccaadbbcacacdcbdbcaaadcaaddbbbacbabdbbcaccccddbdbddbbacccacacaabacbdcbdcbcababcbabcaaaddbbcdaaaccabdccadacacdacbbdabacabddadccbbabcbbccddcdcadbdbbbdbdacdabdbddcdadbacadbdcabddcccbaacdadbcaabacddadcabcddccaadcacaacdddcdddaaaccdababacddbbabbaabbbdcabdcadaaadcdadcaccbdbabdacccccaabcbcbadbcbbcbbcdddcacbdcbacdddadacdcdadadcbdbdadabbaaacdacaadaaacddcaabaaddcdcdaaaadcccdddcabbbdbbaadabaaadbdcbcddbcbdabcacbbcbdcbdcdbcaddbacbbbbbabcccbbacbcdbcbacaaabccbacdaaaddadadddcdbbdcdcadcdbbbdcccdacabdaddcdbddcaaaaabbaddbdaaddaabbdcdbdcccbcccaddddacbabadabacdcdcbdabbddabdbdaaccbaddcbacaddbddaddccacdbbadbcbaccaacbbdcacbbcbbadabbbccbabcacccdabaacdbccdaadcabdddbbddaadcccadbbcdbadaccbdaaddadcbcbdccdbbdbbaaaabdcaadadcdbadabbcabacccddddcbdbbcbcabbbcdabacbdbdabbbabdcadcabccaababdacabbbbdbcccabdcddaccacadddaabdacacbbbacbbaddddcadcdaaccbacdbabdacacdbaaabcdacbaacadcbaacdaabcbdbccabccbacaaaddbddbbdccacaabbdcbbbdcccadacacdacdbdbadcdbaabcacbccbccbbddadbcaadbbbbbccddbdcddccbbbbcdccdacbccdbadbabcbadddbdaacbadbccadccabaacaabcacdaabaddadcbcbccdacddcccdcacdddbbbcbdcdadabbdddbabbbaabbcbaacdcacabddbdbbabddcbdcdbdbdaabbccdccdcbcbdaabcadbcaccdabacdcbbadbddabbcdbdccbccbaaacdddcbdaabcbcbabdccabbcbabcdbbcabcaadadaddddcddbaadcbcacbbbbabaccdadabdbaaabbbadaadadabccdbcabbbbcccbddcbbbccababddacabaabaacacbdbacaaadcdcdaabdbdccaadcdddbdbcaddccddbdbcccbbcbacbdcaabbdadcdacdbaabbbbbaabdbbbbadcbcdcaadbadcabdcbadccaababcacacdadaccaadaadcbcacaacaccdadddacbbbbbbdcddbbbbddbbbbddbbacbcadbbbdcddaadadbbadcbbaacbcdbcbadababbbbccdcbdacccadaaaddcbaabcdbdbdbcdabddccdbbbcacacbadbbdadcacdddaadacdbdddaddcadccdbbcdccdcccbdbcabbcdddaabdcbbadbadacadbbbdcccccdbddbdabbdcbabdcabababdddddabcdabcbdddddbcaaacacdbcbbbbdddbabbacbdbdddaadaabbccacbdcabdabadbdadbdbbdabdbbdaddbbdcccacdcaadbdbdddcbabdaabcddbaadcacbaaddcbdbdcbcabbbbdcbcdbccacbbcadcbdbdabcbbdcbbccdacdbbacabcddbbcdddbacdadccbdccabdccbddcdcbacdacccbccadbcdacadcacdaabcdaaabdddabaccacacadabcdbdaccdcbdcddccccdbbcbcddabbbdbbcdcaacccaddcdaddcaccbbaabcbddcbbbaaabaaccbddcbddabcbabaddcddaacabdbaabaccdbddabddcbcbabccbddccdbdbdabcacabbbbdbddbacbdaadbbccbbdadabcddbaaadacaaddaadcdaabccdcbbdcadabbbacaccccbddadabbcadbcaacbcbdcaacdbccdddccdaadabcdcacabacabacdcbbbadcabccacbbacabcdcabacadddddbddadbbdaddbbddadabdbbcbbddddabdbdaddaaaadccacaaddbdcccabadbbcccabccabbddbdccabddcbbabcadcdcdbbddbddbbbbaacaacabbddbbaccdbcdacaabdbaccccbcdaccdabacccccabcaaaccdccdbbacbacbcbaddccdcdcdaaabacdabdadbacdabccbcabaabdbccaadcabdbbddcbbbcdccacabbbbbdcddcdacabadcaadbdcbbbaacbaabaacaaadccdbabdadccbcdaadaabdcaabdbabdbcbbcacabaccabcdcaadadcacbdaabdbaddddadcaacaddddcaaccbadabbdddcbdabcacbacbbaababacdcbddcdcccabcabccdcdbccbcadcbbcaacbbcadcddcdccbbcbcbbcdbbccbcbdaadaaabcbccabbaddabdcddabbaccdddadadcabdbcdbacdbcaadadbdccaccdbdbabcdadddcabacabcaaabcdcddaabaabadaacdbaccbccccddddbbbcaddbbaaaadbbddcbababdaddcddddacaddacbdddadcaabdacadccacdbbcdadbddbabadabaacdcbabcbaccdcbcdcabcadcbdbbdcbcdbcdcdabbcbacaaaccdacacddcbccdbcbacdabcabaadbacdbdcbadccbbbdadabbbbbadccabcbcdbcbaacbacabcdcdcbcdcbddabbccaadbcddaabbcbcaaacbcdbadaddbdabadbdcbdaacdadbcadaaccbacaddabdcdcbcdaaaaabdccccdaaacbbdbbcacadbaadababdcabdabbadcbaacbbbaaacabcaadcadaacaddbcbadaaaadccaccadcbdbbcdbddbcccbadadccdbddcbcdaccaadabdcbdbdbdabcaddccdcdabbdbbbbccddcccabbaddaabdbbddccaabccbcaadcbdadbdabdabccdcbdbdbcbdaaaaddaaacbbaccbaadddadcdbccadadddacbcabbcccbcddcbddabcdbaadcaddbbabcacdcdaacbbcdbadbbcddacbdcbddaabbbabcbabaadaccaaccbbbadcdabbcacbddaddcadbaacbdcddcddcbbbbcbbbaccabdbbcdaaacdaadbaaccbccacbadadcadcbdcabcacbbdcdbbcbddcabcdabcdbbccdbbccadbabcadbdabccadaddbcbbdbbbaadcaacacadbcabcabdaccdbcdcccabadccddccaacdadbdacdaddcbdadddaabccaddddcbcadddbdbbdcbcdacabdcdaaccbbbbbcccccadacbacdaddbbdabadaaabbddcdbbadbbdbdaaadcdadadcabcabddabaaaccddcaabcbbbcaccaabdbadcddaccbcacddaabddddbbadaaadbcdadcabbabadadacbdcccbcdaaabbadabdddcabadadcdbbcadaacbbccacbdaaddcacbdaccdacaaaaaadacccbbaacbbabdcaddcddbbcdcccadabdcbbcdbcbdccdbcacbdaadbddccaddbcdacacdcababdadddbcbdadbbdaacabacbdadcddbcadccadbccbbbdddccddacbbababdbacccadbcddcccbacbaacddadbdcdabbddbaacdddacacdcdcdcabcbdabdcbaccdddcacbbaaabacddbbdbddabcdcbccccbadbcacdbdccdcdbcbbbdbdccbbaaccdcabacbbaaaabdccbbddcbbaabbcbdbddbcddbcccbaccaacaabbbcdadadbbbcddcacacbccdcacadbcbddcbadabdcacacbcbabccacccddcbcaacdadbabdbcacdcabaccabbbcbdbcbbdbcdcaccddcbaddaacacabdcabbbbcbcaacbcbadabadbcdcbcdbdbaabacbaddabbccdddcdcdadcbbdbbdccbcbcbdcbdbbbcbdabadcabaadbabadbdcccaadbcccaabadcdcaababcbbbddbabcbbdddcdabddcadcaaaccaabcaabbbbdadbcdccddcdacdabdaabaccbbdadbcdabdcaaaadbbaacdbdaacacaaaacdccccabaabdcabdbcacbadbbcacacdacdcbadcdadadddcabcdbcbcbdcabcdddcabcaabdcabbdcccdaaacdbbbdccbcbccdabadabcbcbdccaadbdbaacaddddaadcabbccdbdcbcbadaccbbacaddcaaacbabcbacdbdccadcdbbcccbacbabacbacaadadabaadcbccbdabdbcdcbabcddbcbcbccdacadddddbabcabccdbbabaaabcacabdcadcbccbdabbcdacbacadbcbdbdaadbadddbccdaccbdabcdcdcdaddcccbdacbbcdbdbbadacccbdaddcbcacccbbcddccacbaadbaaadadadabdabdadbcaacbaacdabaadcddcbcaddccbbcdadbaccabaabdcabacdadaaccaadabbadbdcaccacdbcbaaacdaacabaaaaaadabdacababddcdadacdacdbddccdbdbbaadcccbcaadaacbdbbbbcdddbbbcccaaabbddaaadbbbbdbcbdabbccaddaccbdabbdacbaabbacdbcaaabcddcccddccbaaddcbbbbdcdcbbbdcababccdaabaaaaacccabadbcdbadbdbcaaaddacbacddcbbdaaaabcdcaabbdccaaaacbccdcdaaaacacbdbcaccbdbaadaabddcdbbdddaccccaabbcddbbadbcddacdcccdcbaddaababadbacdaddcbdcbcdaddbbddbcbabddabbdaadabadabddcaddccbddcdadcccbabdcdabdaccababddbcbbbbdababdcbbaaaacabbcadbdacccbdbbccccaadbddcdadaabbaddcbdbbdadcdadcdcbaccaccdacbcbbababbdbaacbacbbbdadaaabddcbdbbbacaaabbbaaddccbbdbdbcdbcddbddcdcdbcbddcabbcbccccabcacbdddacdddabcbcdabbbdcbcddddcbacaabaadddacbdcccabcaddbdadabbadbadcdbdccadcaccbdccdcdacdcdaddccccdbddaddbbbaacddcccbccdbabbbbcacbcaccbbadabddcddcbddaabcdbcdcabdcabbdaacdbabccbadcdccdacdadaabcbdbccbddabdabdcddbdbddabddbbcdcdacdcdbcddcccacdcdccbadacaacdcdcbdcbdbdaacddaaabcccbaadddddddddcdbcbccbadacacdaababaadadddccbddcaddcccabddadcabbcddbbcdbabbddbadcabaacccdbbaaadcacaaaddddbcaaacaaabccacdbcccccaaaccdddcacbbdddacaaacbcdbdcabbcdddcbdacccaccccdacccaacdabdbcbbbbdcddcbcdaabadcccadadddabdaaddbccdcadcdabdcdacabbdaaabaccaddbadcaaabbcbccabbcacccaddcccdbcbdaccbbababbccaacacdabbcccacaaaacdadbcbbbdbcaabadababbbccbadcdcaccbcbccbcbbaaabddbcbcbbadcddabdabcddbbacccbbbccdbcdbabcabacbdaddbdbadadbaccbdbcbdaacddaddaddcbacbdbbdbbbcbdcbcdacabaabdddcdadcdcdccdbddbcddcddadbbadbcbcbccdbccbbcbadabcdbccbabdadcbcdcbabddbccdcdaacdbbbadcadaccbadddcddadaaccadcbdbbaabcbabddaccbbdaccddbcbaabcbbacdabbbbcdcccddabcddddbabbcdddadccbabbadcadaabdcabaccbbcdccaabadaacadbadcdddbabbbaacbbdcccdbcdbdaccbbdcdbaadcdabbcccddddbcdbdddcccdcbabdcacddbbddccabdbcccacbbdbbabdbbbbacacbccdadacdccabcdbbdbacaddcbbbabbccdbddaaadbdabdbcddadcbdcdbdcbcdaacbcacdabccddaddaccbdcccbddadaabcbdabcdbcbdcbdccdabdcaddcabdaabddcddbcdcbabcbadabbababbacabddbddcacbdcacbcccabbcdcddccbdcbcdbcccabcbcbadabcdadcabbdaacadcbacabccddcaaddbaaccccabacdadcbcdccaccbabcbbabdbacdaddcbaaaacdccaabcabcbaccbddcddbbaadcbdcbdbcbbccccdacaccacccbadaabddaaaabddababdcdabcddacabacbcdaccdaadbccbbbbcabcbbdbaacddbbbdccadcddbdddacbcdbbdcbacadbdbcbcabcdbbaddbddabdbdbaabcbabdbbddaabccaabbaacddbbbcadddccdcbdddcaddadcbcdadbbbbbdabcacdacdaacbcbbabdcadbccbbdadbdacabaccacbcbbdadbdcacaaadbdccaaadbbadbdbaaacacbcdbcaacdbdcdaccabbbddcbaabdbabacbcacbccadbaaaaadcacdddbbdbccbacdbbaaaadbcbbcabbabcdbbaabcdacbbdbcdacbdbcaccbcbddaaacbbdbcbaabdbddaaddacacdbdabbadabcddcbbbcdddadaddacdaacbbdbadddbdabccacdaccccaaddcdbbbaacdcabbdbdadadccaadcbadddbbaabbaadcddcbacbcaaccaaaaacdcabadadcdcdabcdacbabbaacddbddacaacdbdababbcbcccaccbcccdddcdcaccdcccbaadaacadbcacccbdbdbcbaccdcdcabbcdccddadbdaaababacaccbbdcdcaabbbaaaddbbdaabacccbdccbbbcdadabbbbcbadabdbbcdddadbbdaccaddddddbabbcdbddddbbababaddacbbdddacbcbadaadbaaabbcaadbadcddbaaaaccbbcccbdbddccdbbbaabcdbabcdbddbbadccdbcdaabbbabdcddaaaabbdcbdbbaacddcbdaccdaddbaddabdcaadaccadccacabdcccadddaccdbcadabadcbdaaaadadcadbdcdcacdbcacdadcdabdccdcaabbcbddcbbaaddcdadacadaabdbcbcbbcdadbaccbadcdaaabdaddaaadabacacdababadbabccadbdddbaddbccabcaacdddcadcbcacabbdaddcbdcabdabdbbbbbbccabcaadbabcdbaadadadbcdbbaaaabbdcdddbacbbcbabaadcbdbddaccdcadadacddaadbdbcbacccbadaddcbcaabdbcacdbdcccddcacccaadaddbcaccbddbadbbbbdbaddacdaaddcbbddcdaabbaacbaabccdadddcabcddcbcaaaddbdcccbabcdcdbacbaddcdbdbadbdccdbacbbaabcccdbadccccbdddaacadccbcbdcabcdbcadabadbdccdcbadbbcaaacbddbcbdcabdbcdccdbdabbadcbabcbdcaccaabcaabbdcddcbdbdaacdabdbdcaddbcacdacbcababcdbbdcadcdcbaadbcdbbcabadacddbabdcbdccdcbcacccdbcbcbabccdcdabdccdccbbaabbbaaacbcaababdabdbabbadaabadaacdabdcaadabcbbabdbcbdcccbddaaacaabbcbddbccbbdaabcbcaccddcaddacbddbabcbdbcabdcddddbdccbadbcabbddbdbabccabcabbdbcbabddcddbbacccdacddbcdddbcacdaacabdabccadccabcbdcbaddbccaababdaacdadbbcbbadaadbbddddaacdadaaadbccbdbbbdcdbcbdbccbbdaabccadcabdbadcaabcbbcbbbbdbcdabdbabdcdcdcdbaddacccbdcbcbacbabcaccdbaddccacbddcadacccacdddbcabbddccbdacdcadabdbbcdbdcdadbadaadddcccdbccabbacdcbaadbbbbcadcaacdccbacdbccacaabaddaacdbbabddabbcdcdcbcaddbcacddcdcdbbbdadbdabccabccaadddcbdddcabbcdddbcccdacadcaadabbccccaacadcbbbadabadbaadbaacddcbabcbcccabaaabdaaaaddbbdbcaadbbdbabaacbaddddbddddcaaddddaccccaccadadaadaaadccbabddcbcadccbababcbbaccbdddacdadabbccbcddddcdaacdcbaddccccdbbcbccbcbddbdaaddcaacbadcdcddadccbdcacadccabdddcdbcaadbcbcabcbccbabbbabddabbccdbbcadccdcdddbdbbcabcccddacccabccdaabacabadabbaaaccadbcbcacadccdddddcadbabacabbcadbaddabadcaccdddbbccbdccbccdbacbdcddcadabdadcccddcbcbcdbabccaadddddaddadadbcbadcddabdbddabbdcbdcddabbddbbabacabadbcbbaabddbbbbcacbdbdbbaadddcbbdcddaadababcbddbbaccabcadbddbadcdcbdddcabddbbbadbdccdccabcccaddaadddbaadcccabbbcbababdaadbcabbbddbcadbacaaabacabdadcabbcabbddddadabcdaddcbbcaddbdbaddabbbbcbdcaddbaaacbdcddbccdaacacaabbdcdcbaadbbbcdaaddccbdcdabcddbcdbddbbcaddddabcbbcddbabbcdcbaadbcdbdaccbacabbbbabbabdaaaaaacccabcadabbbbaddbdbddaddabacdababdbaabdadabbadcccaddabacadcbddcdbadaaabaacabaabbbabcddbcabbaaabcdaccdcdcacddbcbbcddadadcaabbabdcdbccdcbacbcacdaddcbabdcbbcbaddacaabbdcdbabccdccabbbbccbddabdbaaabddaddcdacbdabbdbbcabdcaaaaadccdadbcabcabbacccaddccadbcbbcdbcaaabbbcbdccbbcbdcbdacacddabcccbdaadaabbdcbbaddddbdbccbdccaabccacacccdccddaacdacabdaaaccbbcdbbcabcbaddcdddacccabbbbabadadcbccdadbabccdcacdaaadcaabacddadbdcdcdadccaddabddbdabbcdcccbdcabccadcabddbcabcaacbaadbbbadddccbbdabaabccbcddbccbdbbadcbadcdbaccbbcaaaacbdbcaacbdadbcbadbcbdbaacadccacdbbaccbaababadacddbccdadbbaacabcdadadadcdacbccaabbbdabadcacbdbacaaacabaccdbdbaccdaabdaccccccaccababdaadbbdbdacdadbaacbdbcabbcabcbdacdcdacbcacdabdcababddacbcabbdabccdacadabcabaddbcaaacccaabbccacabbcaabbbacbacabddbcbabcacdbacbabdbddcddccabdccdccbaddcadcbcbbcbdbacdaacdcacdbacdbaddbcbbdadaacdacdadbdcdcdabbdbaadcdddddbdacbbdbaddcdbbaabbbcbbdcaacababacaaaccdddddcdcdddcbaacdadbcdbbdccadbcbaaabccbdbdbcaacadadabdaccccabcbbcbdcbcbacdbdadabbcbcabccdbbdbdbaacadbccbacbbbbccddcadccddaaddbcdbcdaacbddbccdddaaddbcbddadddaaabbdaaabaaacdbabbccadcbccdaabcacabddacabaddacdbcaacbdabcccbdcbdacbabddccbccdbaabcacddcbddcabbcddccbddbbcccddaaccadbbdddacbbdcbdbcccbcadddaccaadacbacdcdbcbaaccdadaadcdadbdcbadcbccdbcbbbcabdaaacbbdcabcadccbdcccdbcbbabcaadbcbcbcdcccbcccbdcbadadadcdabcbaacbccbbcaccaddaabcabcaaddaabbcadbddddabbdbbacaddaaaabaddbcbddaaaccbbbdbabbdadbacabadabbcabdacbdadbcbabccbcabaaacccbabbbddaddcbcdaabdbbbccabaccaabbcdbcdadcbdcacbdbdcccacdcbabbdadddbdacadcccdabcccadbbacdadacbdbbdbbadbdbdddaaaddbcdcabacdaadabcaaddacbaacdcbaccbaddacdaaadcbacaaddaccaacdccaaadaacdddbbdbcdadaadacddacdacbadcbbccbcadbbbbdcabbbcbdcdbbdabaacbacccdbadabacbcdcaaabdabdacdaaadbcadcacdbbaacdccaadddcdbabbcddcadddbdcbdbdbdabdabddacddbbaabcdbbcacbcacabaddaaabbaadccbdccdacccbdccddccccabdacdbbdcbdbadaccbccdacbdaadbdabdbdbbccdadbddaddbdccacbacdacdbccddbccbcdacabaccbaccaabbdbaadcccdcbccaabbdadcddbabaadbbadbbbacabacaccbadddbcaabcbcaccabcaaaccdcabcbcabacbcdbababdabbbcdcdbaadcabbdcabcadcddcbcddabcabcbbbddcadbcbbbcdcaccdabbccdcdcabcddaaababcbcadbadaabddbddacdccdcbcadbacddcbdcddaadddddbcacbacabadabacdaacbacaccbccddcadcadbdcadcbcbadcdaabbbcddacbdcdbdaddacacababadaddaacdaaadcaaabcdadcbcccddddabdbddacdbbdadbcabdaabacccadadbccddaacbddaadbdcaabcacddddcddaaccaaacbcaccbbcdacddccdbadbdbccadbaaccccbdcaababcbabbbcbbacddddbccbbacdcdddabbcdcdaabbabddccadbbbadaacdbccabccdbdcacacabdccabbdccadcaacddcbcccbabbbdbbabadaabddbdbdbbababacdbcbbaadabdbadacaaacbdbdcbdbaaabacbcddbaaccacadadcbcabcbcbbdabdccdadddaaacbbabbbdbbdccccadbbcbdddccdccbcccaadabdddaaddbabbbbbcdccabdcbbaacabdabbaccdcaababaccdcbadbdbcaaddadbabaabddddcbdbaddbacaadaaababadbadbddbdbdadcdaccdbbcbbdbccdcdbadaabaadcbdbacdaaacbacdcbcbdabacaaacddacbcabbabbabbaadaadcdaddabccdbbacbdccddadcadbdcbbccbcaadacabacccdbcabadbbacdaccacdbdadbdaacbccbaddccbdbdbabdaaabadcaadbaddabbdcaaccbcabccabcbcdaabccdaddcbbcbaddccabcdbbcadaddacdadcccbcdbcaddcbdabbcbccbddbbcbbadbaddcaadbacacaaadacddddcacddbcaabdbbbcadbddbcbdaddaadaabddcbcdccaaaabcadacddacadaccadbababadaadacaaacbbdcdbccccbaaadcaaacdabdddbdcbbacabacbabaddcdababbadcbcbadcdbdabccddddcbdaadcaaaccaadccbbcbacaaabddcdcbacbcdccddcdccddbbccbcbcbdbbccadcdcbbddabdbccdbcbbcbcbbcdcbccdbcbccdcbcdccdcdcabdcdccaddbbcabaacbddbbbcbccaaacbbbadacbaaacdcddbbcadcbbbdbddaabbdaddddbbabacbacdbcbccccabaccbddbdbcdbcaacbcccbcddccadbbcbdacbcbdadcbcdbdbbcaaddddbcbaaccaaaccaaadaaadcbabccaadadbbdcaaacbaccbbcddddbdcdadacdadcadbcaaccbdcdaaddcdacccdaadbaababdaabccadbbbacadbdddcdbbaddcaaccdbaaddbcbbaabdbdacbbbcaaaaaddddacdaadadacacdcbaaadbcdadacbbdcdaadbbcdcdcacbdbcdaaccbddcddcaaadabbdbadacabbbccaabddaddabbbbdabbbbdbccbcbdcdaadbbbdaaabdcbcccbdabbdaccbacbccabbdcbccdaadcacdbdcaddabcdbbdddbdddbaddcbdbcacaddccbcbdcdbbbabadbbbdbadcacabbaabdbbdaadbaccbbbbcabdacbdaabbabddbbdcccdabaabdcbbbdbbbcbcccccdbbbcbdddbacddbbabdcdddbcbdaaccbbaddabccbbacdbcdabadbdbbcddbbacbacdbbbcdcbacbdaacaccbdaacdbcdbadadbbdcdcddbbbcaaabaddcbdabdaddcbccadaccddbbddcabddacabbbacdcadcbbddbbccabdcaadbcdccbabddbddbdcadddabdcdbbbbdadaccccdacbbdbaccbadcccacbaddacccaacbabdcaacbaadbcbdbdcabadacaadcddacadaddadabcbbbdabacbcabdaaabcdbccdaccbbbaddddaabdddbaababbbbcdccbdcaccbabcdabbcdacadcacadbcbcddbdcaacccacbddabbadbcacbbbbccacdddcacacbcccbbabbbaddadccbdbacbcdcbdaacdcaabbbcbbdcacbbabbdbdcdabcbadbbabbbbbacbddacbabbdddbbbacdaacbadcaccbadcaabdccacbabdabbdbbdbdbcbbbcacabcbaadbacbcaddcccbaaabaabbbadbadcaccaddcacbcbddacbcdbccbaaaadacbaddadacbcdaadcdbbcbcbacddbbdcaaabbcdbaabaddaddbcddccdcccbdccaddbcdbaccbcadcbacacaddadbcacabcbbccbadaacabddbcbbdbbacacadcdaaccaddcacbabcaccbcbcdbbccbaddbbadccbbababaacbbbabadaccabbbadcbbdabcbcbcacdcacbbccacaaadccacaaaabddaadbcabaddcaddcdbdccddabbbccccadbcdcdccdcbcccbbaacddddcbcadbdacadcbadccadbcbbbacaccdabcbcaacaaadccbaacbbbddbdcddbddccddcbababadacdbcddbdaccdadabbcccaadbcacacadabdcdbcabbcaadbdabbdadccacdbdccadcbcaaaaddddbdabadabbbdabacdadadabddabddacacbbcbbbcacacbadaabdabdacadcddbcddcdbcababbadbdbddadbbbaddcdbadbabbcbdaaddccddccbdcdacadbaaaadcbddcbbbbddcbccbbdddbccabacdbbdcbccaaadcacadccdccbaacdcaddaddcacdddcdbbcccbbadcdabbdbccddcbdbbabacbabaddabdcdaabbdbdcccabdbbabdcddccbcbabddccdcaccbccbaabbaacdddbcdbcbbccdcdaacdacabcbbadccbdacdbccaadabbabbdbadbacbbaaadbbcaadcababdabbbdcbbaadaacdccacbacaccbccbaddcbdbdbcdbaabddbaaadadacbdabbccadacbbbabcaddaadbaddbbaddcdbbbaababcdbdcbbaabcdccbcbdcdddaabdbcdacdbddccabccaaadcdccbacccadcabdddaaaaddccbaaccbccdbdadadacbbcbdcddbcbbdbbcbdacbbcdbccdbddcaccaaddccadcbcacbadbddbbdddbaabcccdcadadddddcacbdbddddaababbcdabdabccbdadbacabccadbbcccabdbcadaddcdadddbbdcadbbadaabadaabcdbcadddccdabccaccbbbacaabdcccbadabbdcdbbbcdcbababcbdcbbaabcaadbdcdcdccdcbdaccdcdcdbadddccdcbaabdcccaacaddcdabcbacabddadcbdcaacadadbbcdbdaccacbdbcddbacabaddaadddadcdabadcbabccadabcbadcabdcdcddbcdcdbadbdddcaacacccbbbcbdddcabccaacdabbbddcddabbcbbcdcccbcabcdcaaabccacbddbbccbdacdbacbccbabaddbdddddadabaabdadcadadbbacccddaaaabadbdcdadddacbbccdbdbbdaadbcdbddcabdcadaccbcabccbdacdbacaccbddbabaacadabdbacbbbdbcbcaccddacacdbbddddabbccbcbcdccaaccabcccdacabbbadcbdaacdbacbcadcaccdaddcaabcdbccdabacbcaabcddacbcabbbbdacadbdddbccbbdaabbbaddaadbccadaadbbbbacabdadbbddddacbbcacaddddadcdbbbcbbcbdadcaddbdcbddddcabcddbcdbccdcddddaaadccccbccccddcadaacbccbacdddabbdcbcadabacbbcabaacadbcabdbdcdcddbcbbacabbdabcbadcaacadbdcaadccabbddcccacaaccabadbbdbdbcacdbcbdbbacdccaabccbabccabacdcbcbbaaacdabcadcadbbcdabddbccccabbaaaaaababadcbdabcabadacbddbcaadcadbccaaacdcababbadacdacacdacacacaccdbddbcbdbccdcbaacbccbbcbcdcdbdadbcabddcbabbccaddcccaabadcbaaddcacbccccdcdbaadcdaacdaddbaacacacbdbbcbdcddbaadbdccbbbcccbadbdbaacdbabccddcaabbbadabdaadccdcbbcbcaddaddbadbdbdabddcbccaaacdbbadcbcbccbcbbbbddbacddaaaaacdaccacdaddddcaacabcdbbbcaacdddcaaccbdddabdbbccaddbcdadacbdaadbcabcaaaacabddabaaaabacaaddcabcdcdbddbdadaaacacdcadbaacdcaaacdcbdddbcdcdbaacaabdacbbaaddcbbbbcacbcbaaadaadbbdcddcadcaacbcdcbaccacaadaccdbabaddccacaccddacccacdbacabbddccddddabadadddbcccccdcccdadaabbbccbadcadcabdcacdadadbbdcdbdaccbaabdacdcdbbcbcdabcbccacbadcbacabcaaccacdaabadcadabababdcbaabddcadbabdbccbcbdcabacaaaacddcdbdcaaabcaadbbddacaabdababdcddadbadcdadabcadacaaccacdbddabcdccacdaaaaddcccabcdbbbdcacaadaaddbbcaccbbbcbbdddabbcaccbcaacddaccacbcccbbdcbabacbdccdadbcabdaaacdaddbccabadbbbaabacdcbdaaabcdbdadccadcbcaddbddacaaabbdadbacadccbbdccabcdacacaacadacbbbcdcaababcdcddaccdddbaabaacacdabcaadbbabccdadacacadddacbdcabcacdddbabdcbabcaabdacbdcabdbacccccaddcaddbcbbdcabdcbcadacbacdacabdaacbacdabcdcdadcddadaabcddbaaddadcacdabbaccaaaddbaadbccbbadccaddacacadacdbabcbdbadcbbadcddbcddbadbbacaacdcdcaddbabaccbcdbdaabcabcacddcdddbddbcbcbadbcdabcbbaddddbbcddbdcdbdcaacddbcbdccddbcbcbbdcbabdacdbbcccacbabdaaddbbaaccacacbadbbaabccddccabbcaadcbabcddbbadcbcadadbacdbaadddcbcbaddcadbdaabccabcddbcbcabbbcbadadabcdbbbbacdbbddadccbabacbbdbbaadbbacaaabbcddbbcbbdbaaacabbdbcbbdbbdaacaadbccabcddbbdaddbabaddbcaccaacacaaadaabcaacbdcabcaabadbbcccaaaaaadadddddbdccdcadcdcaddbaadcdcdcdddacbcaddadccacaddabbbabadaacbdbcbbdaaddaacbddccbccacddbbbbaddbdbccbddddaddabadabccadccddaadcddcbbddabdcacaaaaccbbdbbddbbdbdcdcdcdcadddaaadaabadbcbcabacdaccdbbdbdbbdcddcccabdccaddadccdbdcbcadcbcdadcdadcdcccaaadacbadbcbdacbabddbcddadcddbddbbcdaacddbacbdcdbaaaccccaadadcbccaadbcbdadaabdddabbadcadaaccddaacdacdcbdadabbdbacadcacddaccdcadbbcccbcaabbbbbabbbbcbcacbcccbdaacbaaacdcbaccadcdaabbccbcacbaddadbddbdaaacdaaabadccdadcccdbcddaabaaccaacbadcaabbcdbaabbdccbbdcadddcacbbaaaacdacbbdccadbcaacbcadcaabdcddcdabccaccdbbaddddcbbccabddabdcdccaacaddbddacdddbbcccaacbbaccbccbcaabcdcbcdddbbcbdbbaacaacbdacbcdbbcdbcccbbbdcdcdaaabddcdbbcaaabdccbdccdcbbdcdbccaabcbacabdadddcaaabbdadbdbbcabadbbdacabaaaacbbcbcbacadbaddbbbaadadbdcbadbacccbdbbcabddaadbabcabdccdcacbdccbccadcbcdbabcdcdcaccaababccbdbcbacbbabbbbadbcbdcddbddbcbbbdcbccadabaabddcbbaaccddaadbccdbcabbddabbaadaabcddcdbdadddacccdaaadbabdddbaccaacdddaabbcddacbdbabbbbadbdadabdabcaaaaabbbcbcaaadcbdcbdaaadabbcbdaddcdbcdaacbcdabacaccdacddcbdcddccacbbcaccdbadbbcdaaaaccabaccbbbcbaddcddbddcdcabcdbcbdddcbcbcbccbdbaaddaddcdcbbddbaacabccdaddaabcdbccadcdbadccacddcccbbcdabdbdcdbacddbdddbabcbbbcddcdcaacbbbbbdadbdccaadaccabbbdaaacbcddbbacaccbbbcaccdbdddcddddbabbabcbccbbbddaadacbbbdcdcccdddaddaabbcbadabdadadacbdbddcaadbcadabbacbadcdadadbbaccbdcbcbaccbbbbcaaacdcbabbaaabcccadbabdadadbcbdbbadcdddbbccbacbabaddcbccababbdadbdabcdcccdabaddccadacacaaddaddbccaaabaabadacbaacdddacdcacabbdcbacabbbcabdddbccacadbdcbaacaabbdadccdcabcaacacddccddbcaccccadabbbccbcccccbacaabbbbaaddaadabbacdbadbcbccbcccdaacaccdcdcbcaacbbabbadadcacbcbcbccbcabdaacdccbcadbdbccbbccdacccacabbdcccdddbcbdbbadaddcabaddcaddccdbcbbcbcbdbcaccbacbcbbdcacaabdadbcccdabdbdcddbcdcaccdccaddcdbaddacdaabbccaaabdddaadbcbadadacbddddcabbadacaabaacaaabdbccaddbbbbccdccccadbaccbccbadaabddabcadbadacaccacacbbdaadaaabdcabcaabaacbadcabccbaddcbbdaaddddacbaccaabbaddacdbdbbcdbacbdddabcdabadbadacaddabccacdaaadabcaaadaaccddaaabcaddccadccdcddcacabbddcdadbcacdacdadcdcddbdcadcddbbcddcdbcdabacdcadbdadacbadabcbccddcbcccbbdbbbbaacacbabcdaacbbcbadbbbbbdcbbcadbdacddabdbbdbdccdabaaabcaaddcdcaacadaadbbcbdcdacacaddacdbbcacbcbbaadbbbdccbacdccdbaccadaabdbcdddddaddcdabbaabdbbabbcccbdabbdacbbddabcccbddcabdacdcabcbacaababbaddbccabbddccbacabddadcaaadccbbdaabbdabbdbbacbdadcdbcabcacbbccdcbdaabbdbcadccadbccddbbadcadcbabbbbadcbaadacdcbcccbadaacccbbdaabbccdcdddaaabbbbbbdadaaadabcbadcccaabbcddbacbcdbdaadbcdddbabaaacdadbbcbabdbbadbbaccacbcbbcdbdcadaadcdcbbcbaabadcadabadbccbaddadabbdadddcdaccbcbabccabbcbcadbdaadbadaaddbcddbdbbbbabbaadcccdcabcabddcdbdcccbaabbcbcdbabbdaaabccbbdbbdcdabccddddbbdbdbabbcbadadcdbbcdcadbdbbcbbcdaabadbcdabbabaddabdbcdbacdaacacccbcbddccdcbbdbcacccbabcbdadcbadacaaadadbbadcdadcdddaccbdcbaadcabccaaccaccbdbacdaaadacbaaaccdbaacacddaadaaacbddadccdaadbcaababdcbbdaddaccaaadddddccdcacaacaddccdadccbcacdacbbdabbdcaabbbcacbacdadddbbadbcdaadaacacaadcbabadddddccdbcdbbaccbbdadacccbbadbbbacbadcacbdbccdddcdbddacbdbccbbddacdbbcabbacdddcdbcdbdbbacbadcadabbbbbadacddcddaadadadddabbccaddbdcccaccccadaaadacdddbddbdcdbadbadcbdbcbdbbbacbdadabaabdcbdbbdcbdcbddcbccdcbcccbbdddcccaccadcddabdabdccbaddbbbdbabbaddbddddaacdbccacdaadaccdbabcbababccadbccbdacbdbacbcbcdcbdddadcabcbbacacdabdadbbcbdcbaabdbcdbdacbbdaaaaaaabcdcbacababaadcacacdddddcaccadcaaacabdaddcdabccdbaddbcdccbbabaabbbdddbadcbdcbbbaadabdbcdbbacaaacacdbdccaacbaddbabcddcabdccbbbbdaaddacbadabcaacbddddcbbdaabbadbcbcbbccdccabadcdaadbaadaddbabcdbabaddbadbdcaccdcdccaacddabcddabaadbcbcaadddbdbcaabccccacdacdabbaaabbbcdccacbcbdddbbbdabdabbaaaabadbbbdbbbbbdddabacdbbadbacdaacaaacddcbddaddcabaaabaabccdcaabbabcdbaddabcccbddabbacbbccacabcbcddaddaddcdccabdaacadbaacddcbadbccaacddccbddaabadaaadbcacdcadbcacbacdbdaaccdacbbbdbbbbbccdcdbbcaddbdcbaddaababaccbacdccadccdacacadbabddacccadbbdbccadbcaabdaaabcabbbaddccbadaaacccccbdccbdacddbacadbcddadabadbaaaacdacabbdcccbabacbcddbaacadbddacdaabbcccabbcbdcdaccbbbaacbdbddabbaabccbcadbbccbadcdaaccadbcdbaacdbdcdacbabdaccdccbabcdbbcadaacacdadadbabcdaadbccdbcacdbcabadabcaacadbacccaacdcccddabbbcabadaccccaabddbabbcacadaccbaabbadbabcbcdabbdccdcddddadadadabdbccdbcbddbabaaacbdabbaaabcdbbadadccbabcdbddbabaaadaadddcaacabcbbbdcccaadbbacacaabaabdbadcabbdbbadbbbdaaabccccbacadbacbbbadbbddadcdaabddbddabcdcdaddbcdabbaaadaabbcdabbdaacacdbdcdbddbaacdbaddabacccdcbccccbbdcbacdcabacabcabaabbadaabcbccadaacbbdbdbbacccbcadcbbddbcbbcddaaadcbcccdcabacacddacaaabcabdaabdbabdcadbcbcbcddcabadacabdddabdaacadddccdcaacbcbbcdccccbbdbabdcdbdacabbbadaababcaccbabccccdacbbcaabacadabaddabdacbbacddbbcabcccccbdcdaddadadbbacbbddcbbbcabdddddbbacdcbabdccccaabcaccbacaaabbaabacaddcabbcddcadccadaccddaacaadddbcaddcdaadbbcbabbbddabadbabbddbccddddcabccabcccaccbbacdbbaaccacbdacbacabadabcdacadabcadbaccdaaabcacaaabddabbcbcdbbcadaabaacdabdcabbacdddabcacbddbdcdbbbaddbdabdaaabdbdbccbbcaadadccbdaacabcbccdbccadbaadcaaacaddccdbddbaddcbaabccbabbaddbcddabdadadbddabcbcddabbddcbccaccabcccddbabbbabcadcadddaadabaccdcdcccacbbdabcadcbbbdadcadcbddacbbcdbadaccbbdbabbcccbdcadaccbadbcdbabcdbadbadcdcadbbcccaabcacbbadcaddbdcdbdbdbaddadadbcbbbbbbbcdadddacabccccbcdaccadbacbcaabaabcaaabadabdddbadbadcbdacbdbacaabbbbdacdddcdcdbcdcacadababddbdadbddaabcacdcbccadbacddbcadbccacdaccbadccbbabcadabdbacacbbbcadcbaccabbcaaaababcdbbdccbcababbdbcddacbcdbadacbdccdccabbbbaacbacdbaccddaabccbdcabbadddddcdcbdbbddaadaccaabbaddcbcaccadcccacaacabcdccacddadbddcccdcdbcaaadaabaaaacbbcbdabdcabbacadcbbaacbcadbdcddaadcaabbdacbabbcdcaacdacbaabcaccdddadbcaccaddadcccabdadcccbbdcdbbdcbcbbbbdddbaabccacddddbdadaaacdcdcaccdcddddbcabdaddddddbcaddbbcaccbdacbadbcbbccabddcacbcbbaaddabaabdbcbbdabdbabacadabdccaadddaabdbacbcbdddcccbbababdcdddccccaddcbabbabddccaacbdbaaccdbdbdbbdcbddaaccbcbcddacccdaabadbdaaddabacbcbcddccdcadbacacdbdccbdcbdabcdcdddbdbaddabbaacbbacbaccbdbdacadbdbbabbcddccdbabcbdadbcbbcccaacdccbadcbbddadcabddbdbdcbcadcdadcbacadbcbaacabcbcacbdadbcbaaddcdaacddcadcadadcbacccbdccadbbdcaacabbdacdcdcbddacadbdacbccadbaccdcccbcadcbcaaddbdaabddddbbacdbcaaabacbcabbcaabdacbbcabbcbbdbcdcaccdaaadadccadadbadbcccdbbababaaabbacbddbddbcaabbbbabbabacdaaabbdcaabdcdabaadabdaabcabdaddacaadacaadddccbcbacaadbbcacbdbbbbbccccadcdddacaacccddbbdadabdcddbcbcdaacbbdcdacdcdadbdabddacdabaddcaabdacbacccdabccdbdddcdbbadbdcdcccabccabbbdabbbdcdbcccbbabdcdbabbcbdbbabaadacabbbadbaaabbddccaccadddbbddccadcaacabddcacccbcbdbacccbbadbbddccbadcbddaccdabdbbbdabaacbbadaadbcdbabaacaabbdabcdddbdcdbccbcbbdcddccbbddbbbcbcbabbadcacddbbbabaddbbaaababbbccbcbccdaabdacaadbabbaddcbbcabdadbdabdbbabccbbcabccadbdaaaabbdbdccacabcbabdcbbbbbdccdabbaaacbaacabdbdbddddddbdaaadbcaadbdcbadcbddbaadcdccabdabdaacaaaabddabcddbbcddbabaddcabdbcadaaabcdaaddddbccbccdadcccbadadcdbbaccdabbbdaccacabbbcaaccacdbbccdcccbcbdbacbbaccadabcdccbbacacaabdccaadcdbcadbdbaadbcbaccacaadcbccbacbdbcacddbdcbdbbcbdbbdacdcacdadaabaccbcdbcbaacabdaacbbdaddadbccacdbadbdadcaddbddbacabbabbddaccddabbacdbacacdbdbddaacbcaddcbbacccbcccbbaaabbcaacaabacbaaabddbcabaaabcdccbadcaababdccabcaacccbaadbcccccbbcdaacbdccacbacbdbcabadcdaacddccddddacddcdddddcddadbbcbcaddbbbbadcbbdadacacdaddcbbcccbcdcdbbbbdaaccbcaadadcbbadcadbdbadaaaabbdbcdaabadaaaccacccdbabaddcbcdbdacacacdcabacddaabdbaadaaddbdbcdadcccadadcbcddddcdaabdacbadabcdbdbbddacbbbbddccabbaddcbcadcabdacbcabaddbdaaacadabaccdcdadbdcbbbaadbcccccbcdaccbcbbdadddcdddddabdbdbaddaccbcdacbbacbcadacacbcdbadbdcddbcacbccabbacdcaabcccbddacdbaddaccddbdaddbdbdbadccbadbbdbbbbaddbabbcacdcdbaccbcbaacbbbdaaddadaaacaddcdbdaccabaabccbbaddcdddadadbdadadcaacccddabdbabbbbabcdaacdaaddcbdaaddddadcbadbbcbcbddaccdbaaadcdabdababddaaabccbdadadadbadcddacbbbdcdaaadccaacbbccdaacadccbbdcddaaaacbaaadddcabadbdacbcbdbddcccbabbdbcbbbcaddbddccadbbbbcddbcbaddbaacdbaacdcaaddcdcaacadcadcadaddabdddbbcaadbdadbbbadacaacbcbdbcaacbdbbdcadabcdcacbddadcaddddcbddcbadbcdbddcbcbdbbdaaadccacdcacbddcbabbddabdcbdbbaabbbabbcdacccabcbbccddbbbddddbdaadcddabadccdcaabaadddaaabadcbaccdaabbbbddcabdaacdacacccdadacadcbddabddaadadbcbbacdbacdabbaaabcabdcdbdddccdcddbabcaacaabdbcbbbbaddabbcccacdcbbbbbcabadaccccbadadaccaaddbcdbdddcabcaadbbcccdbcaddacdaaccacdcbabdcdbbbaccabdaacadabdcaabbdacabccadbdcababadbcbaaadabbacadaddcacabacaacbcadabccdcbdacacabcdccddaaadcdabcbdcbcbdbdcdddcdacabdbcdaccaaaddaacbddbbdadabcaccbbdabdbddbadabbbbbdcdbdcdabaddbddaadcdbadacccaabccaabdbddddbaaccbdcdadaacccbdcccaabaddcdabcabacbbacbcddbccbcbbbddbdddbcdbcdcaccccbacbbacadcbbabadaabaccabbbcadcbcdddcabcbacadacccdddadcacccadcadacbddccbcbabdcbcdccccccddadcacdaaaaaaaaddaaddccdacddddbcbbdbcdddbbcacbcabdcdbadadbcaaadadcdacbaccbbdddccaddaaacbadadcbdcbbadacbcdddcacaacddbdabacccadcbcbaacbdcddcdadcdcbcdacdacbadaaaccadaadddcadbddacccbcdcccbcaddbadadccccdddbabbbddbbddbdcdbdaabccdaccccabdacababdaaadddbbdbcbddbccaabdcbadcdcdabbcdcbcdbbabbbcabcccadddbacdccbadadaccbacbadccbbccaadabddbabdadbbdbadccaddccbaacdbaabccdcabbbcdcbabbdbacabaaacadbdcdddddacaccacdcbbabcadcbaadcdcadcccaaababdddccdbcaaabbaadddadaaaddcdcccccacccabccbbcddbdadabdddaabacdbbdcdabbdabdbbcaadcabbccabaaaaabaabaaccdbabcbccbbdccbbddcabacbdbddcaacbbdbacbabcccbabbacbbaacbbadacdbcbaaaabdbdbbdaadcbabdababcadabbaaccccddccccacdabcaaccddbbdbbcadccacdbdaadddaddcdbdaadbbcccbcaabcaabdacbabbacdcbcbacbccbadcdddcccdccadcadccbdddbcdaaabcadcdbdbabdcddbbbcaddbccbcdbbcbddaacaccaabacdcaddbadacbdadcabcbdacbcddacdbdabdcadccdadcbdcbdacabbdacccbacaccbbaddccbddabcbbaccbccdddacdcdbcdbdccbcbccbbbcdbdbcdcccbcacadadbbdbabbdcaaabcccabbdbbbddccacdcdbabbdcaccdccddccbcbcdbacbaccbbbbbdcadcdacdadcbcdaacbcdbdbdbbadbacaacbbcccbdcbccccadbabacacdcdaaccabcbdbdcabbcdcabdcdbdcccacdbcdbbcdcadddddabaaacbbabddbdcdbaabbaccaaaaccccdbbababbdcccddcaadbabdbacbdcbadabadcddbdcdbbcacbadccbbdbdbbcdabbbababdcacababadabbcdbccacccbdadbbdbcdabcaabcaabdcddcdaacddacbdccbaaabdadcddadaababdcdaaccadacaacbaacbabbdacddbadbcddcbcadacacccdcbccdddbaccacdccadbdabcbbddacdddcbcdcaacbcabdbdcdbdacadcaaddbaaacacbbbaaaccccbacdadaababbddcdbadddaadbdccbddaaddccdccbaacdabccadbaacdddcbaadacaaadabcccbbddcbcbcdadabbabaabccbdaabbdcdadabcdaabbaabbdadaabcabaaacaadadcacadccdbdacbabdbcacbaccabcccdaadccddaaccdbdcdcabbbcdaabdabacabacbcdcccaadcccbaddacdbbcadbacddababbbdddddccdbdbbbabdaadcabcbaabacdccbacddacdccbbbccbcacdaddcadddbadbdabbbbbccdcddbccbccaaaacdacbaacbccdbbbdcdcdddddbdcabadcaabdadcccdaaccccbdcaadccccbacdaaacaabdcaacbbcddccaadabddbddcabbbaddcbadbbbabaddbbdcdcdbbdaacddcbaadacbcdaccaabbabddaacabadbcbcdcddddbcaaabddbcdbbcbacaadccdbcbbbaabaccdbbacdcdbdcdbdddcbcdccbbddcdccddcbdbddbacaababddaddbbccdbdbcddcabdcbcdbacaaaccadadbbccdbcccbaabccdaddbbabcabbcdaadabbbcdbddaccabcabcbcbbaccdbadbbaddbbabdcacaddabaddcdcacccbadadadcacbbcacccdddaddacbbacbdbcccccdcdbcddabdacabaaaacbabbaaaababccddbddabcaddcdccbcacbdabbcbbadccabbdadcddbaabaacdadddabdadbccbadadbbddadbcdabaddcbcaddddadbadcbaaccaadcddccdcacdaaddaaadaabddbddcccddadbbdadcbbabcbbcdabcddddcdccdacbcccdccbddddaaddadbbddabcbccbabcbdcdbccadcbaccadbdcabbaaacaddabbbcdccaccdccadaaddbadccabababbbbdbaabccccdbcddcbcccacdcaacdadadcabcaabbaacaccccdbdddadcdbcbddacbcaabcdbddccbaaabdcdcdaadddadccdbbaacbbbdcccaccbaacbbccccabdcabadbaaaaabaaabbabbdadddadbbbccccabddaabdbdbbabbddccbcbcddbdaabdcdcadaacdddbdabbccabaccbddabddcdcbbacddcddcbdaccaadbdbcbcaacbacbdabccbbcdcabacbddbcdbbaacabddbcadbaadbbacdbdcccddbaacdddabdccbcbbbbabdbabadaaadabdcccccdacadcdbbabbaababdccaccaaddacddcdcbadadccacddacbacddddbcabadcbbcbaaaccdbcbcaabbcaccacbddabbdbcaccacbdddcabbbddadabaaddbdddadbccacbccacbaabbdddbabdacaaabddbbcababaabdbcaaaccdadbbccbbccdcaadabcdbbdbdddbccdbbddaddbbbaadcaadbcdadcdccdacbabdcbcabcbaaaaacccaccaabcccdaabcadccccbdaccadacaabcccaadacadcdaccadcbdaabaaccabccaacdcbdbabcdcdcbdcadabdaccaccbbdbbbdbacbabcccdbdadbccadbdbccbdaccbabbdddbddababdccbdaabaaadabdaccdddabcbccbbcacaabbcbabccdadcdcbdbcaccdbcaabbddabaaabaaabbbcdadcbdddadabacddbdadbbcabcddbaabacbcbbdbdcdcadaddbabbbdbcbdacabdcdabccccacdbdbddbcaccbadbdcbdbcbcdcabccbbcadccaadaddbdcdcbbddadabdaacdaabcddddacadabbcacdbbbdddbbadbbdcacddbcbabbabbacbaacbcaccdabbccdbbbbbdcdbbdcdccdaccbaabadabbdacaadccdaabaddcdbcdaaccbcabbbdcabcaacaccbabdaaadadcbcacdbdbacdabbdabbbacabdddbacbccabacaccabacabbbdcaaddaacbcdddbddbcbacbdadcdcdaacbcabaddbbbdbbcaadadccdbdadcbbbcbbdbaaadaadabbbcdbcccdbdbbcaaccccdcdacccbbcbddacadbcbbaabbadbbcdbdcbcadccdbdbbabbabacbaacccccbadadbacaadccaacdcccccaabaccaaaaaabacddaddbabcacaadaaacdcdccaabbcabcabadacbabbdacacaaacaacacbdadcbdbdbcbbabbddccacbbaabbccabcbabbbdbbabcdabbddbcabbbbccabdadaccaabbdcacccdaadddcacddacbbbbaccbdaaaccdccbabcaaabadacdbcbbcacddabbdcddadccdbacacdbdbaaccbbabcacdcaacbbbcbddaaadabadcdbbdbdacccaccbccbdcbaaacbdacacdcdbadcbbcddcaadbaccadaddaaadaadccdaaadcddccbbbadcadbcadbddbdaadadcdcddadacdadabdacdaabcaabbccbccacbbbaacdcaacaddbaccabbdcdcdaccbdcabdbccdccbbbbcbaccdaadabdadbbaadadcabbcbabcdcadccbdbaabdddbdbabbdbdbcaddbcdcabadddbaaccdadbdcdbdcbcdbaadcccdcbbcadcddacdaabbbdabbdbaaacbbdddcadcbddbcdbddacdbcdbcabcadbcdaacddcdaccddabcadcddbbcccbcbadbcacaaabbdadacabdcbcbbacbbcbacadbddbbabbcacdbcabadbcccbadbcaacdbcdbbdbaddbbdaacaadcddaccadccaccaaadbdbccbbddbbbdaddbcdbdcdaaddaddbcaacaabbdcaaaabccaadabccbdbbabbabcdaadccadcbdbbcdbbbdcabbadbcdbadaaaadcdddddcacabcaddcadacdcbcbcccbbcaaadcdcddcddbddabcaaacbabadbadabcdbcbddabddcaaddcbccbcaacdabaabbdacadbcddcdddbddacaaadcbbdabdcdcccabdbadcdacaabdbdaabcbcdbdbaaddddabacddcaccaabcacbcacddaabbbccdbcdccaadadddaddbbaadbbddcdadaddaadaabcabbbbabddbababbbdcabdbcbdacdccdcacaabddabbcccdcacbbbaaaaddabbabacbbbbbacbbaaccdddbcbaccddbaccabccddaabacbadacdacacaddccdddcacbdabdabcbcacabbcccdabadbdaccacdacaabaadcaacbbdadbadcdabaddbbacdaaabbdbddcdaadbbdcccccdbadbcaaadcbccdbdbcdddacabbabbbaaaadbadcbcabbbcaadcbbbbdaccadcdcbbaabdbabcdadaabcbadcacacccbaaaaddacacabccbcddadbbcdcbdccdcddccaacbcacadabdccdccbbddbddcbadbdbbbdbdcbacdbdbcadcbbbabddbdbccbcddaadcdcbccdbaccdcccdabdcaccdccaabcdaddacaacdccdddadbaababbccacaccbaccbcdaccabbcabdddddddcadbaddccdacbdbcddbaabdddcdcdcadbcccdaadbbaabacbdcccadacccadcacadbdbbabccbcdbcddcaaaccdadaabacbdddbadcadcadaaadacadddccbccbacdbccddbdbdbbabdadcbadbbadcacbbdbbbabdadddcbabbddbbdaabcbaacaabbbadacacdadadbcaccdbbcbdbdbdbcbacabddacacdcadbacdddadcdcacbccccdddcdcdababddbaacdaccdbbbdbcadaccdadaccddbaacbacdaadbdcdddabcccdacddbbacadcadabbcdaacaaabbdabbcadabbbbdcdddacabacbcbcbccbbabbcddccaaabcadcdabdbbcaaaadccbaaaabdacccacdcacacbbadaaddacbabcbacabdddcacadbadacaacbadacbddbdddbcddacbcddcdabbaaaccacadbccacccddbdbdcbcbdacddacacabadaabacdcdadaabccdaddacbddcbacdbcadbdcbaacbbbbadcbaddcdaaadbaddbbcdbdaabacbdccabadaabcdbabbcadcbdbddddabddbdcaadbcacdbbadbaaacabaabbdbdbcbbdbaacbbccbabbcbdddcccabbcdacbbcdacabbccdbaacdccddbdacdbcbbbbbabbcaaaaabbaadadcbdddadcaccdccabddcaadbbddbdcababadbbbbccadbbcbaddadbaaabbabbccbdddcabddbccabaaccdbdabcabacccdaababbdaadabcbabaccadadabdcacbbdbcbbddbabaaaacabddddbdccabccbcdddcdaddbdcdbcdbcccbcadccddbbbacdcdabdbdacdccadcdcddbadaadbccccbadbacdcabddabccbcabbcaadddcadadcbadbdcccbdababccaacccbacbbdccbbadcabaaacddbbdbdbbbacabdaacbcabcdbcadaccacaadbabddcbccdddacdacdcddadccdcbdcddcbcbcbbacbcbccbacdbccbbbcaacbbcadaacddaababbcdbcbbdcddcbcdacbaaabdccaabadacbcbdbaadbaccabbaaabccadccccadacbdcddcabddcbbccadcdbdbabddbbabbddabbdcdabacddddabccbddbadbcccaacdadbddabbacbcabbaacacbdcbbabbcdaabcccaabddcbdbbcdcbdbaacbbcacbabaccbbdcbddabdccbbaccddbcddacbcbabbbdbaacbbddddddcdabdbddbbdbdcbbbbcaaabdcdddddbccbbbdabcbcdcddacdcccbdcbbbcbbbadcdbdcadcbbaacabdbdcabaacdbacbbdcccbdcdbdcabddbcadaacaacbddbdadaddbbddbaaadbabbbdacbbbbaaaacaaabcabadbabbbacacacdcaadbddaddacdbdbabddcddbcbbcdcaacdcdabbcbccbacdbcacbccaadddbbaacbcacbdddacbccabdaadddccaaaaadbcddcadaacbcaddbcbddccbdadacacbcdacdddacdcdbaaaaadbdcbdbaabcdccadbbddbddaddbddcdbddadbbcdbcbcdcdbaccdaaddcacabbacdcaabbaacdcacdddcdbcdcbdaccaabbdadabbdabaddaadaddabbaacbabccbdcbaccdbcbabdbcbabcdadabbabaaacabcbadabbcbaddacbddcbcaddbdccabbdddbadadaaadcdaacbcbadcaadaccddaaccbcaabddbddbdacbacacdcccbabdbcbdbacddccbdcacdcaacdcaaaddaddaacaacabaaaddbdbaddddbddadadbaadadacddddbabddacdbbccababbcbcbaaacacaabdacbaacbcbccbdcaabdcaabacbdcaabbbababbbcdacbbdccdbcdbdabadacbccdabcbbdadccdadccdbdbdaababbcacacdbbdbaccbdaabacbcdabdbbbcdcccddcdcccbcdadaacccbbbcbddaabdbcbacacccadcbaadcbcaabaacdaaccdbddaadabbadccabcdbbaadaacaaaabbdddcabccbbbbcddcdcbbaccabaacbddddbdcbbdbbaddcdabcdbadbadaccadcacbbaadddadccadadbbddbabcdbbabbcbbadbddadadadddbaadaabdddbbaacbcbadcbadcbabcbcccbbddabdacaccdcddddaacdccaaddaccdbbbbbabcbaccabcdbaacbcaabaaccbbccbdcaadcacbcdcdadbdbcaaadcadcacddcdabdcaabbcbabdabaabdbdddcddddcacabddbcaaadaadcbcdbbadbbdaabcbdbcbbcbbcaacbdbcdadcbcadbbdcbcabcacbacdcadcadaaddcaabccadbbdbadacaccbdbccbcdabaddcacbbacbacbbaaaacccaadcdbdcddddcacbbbddbccadbddddbcbdcbdacdcbbdbadbadabddcabdbddbbaababdccbabbbdbdddbabbdcdbbcbaddcddaaacaccbdabaabbdbcbbbbbccdabbccbdbccbcbcccdccabbdcbdcabcadccbdbcdcddddcaddadccccccadcaacaccbcbcdbaccccbbcdadccbbdbddddbcbddaddbbdcdaabbacbccddbdcaaadccabccdbdcbdabadbacbabcdaccaaadcaacabccadaddabcbbbaadcdddabcbabcacabdbdccccaaadcacbdcacbbdadabdbcaabbdabadbabaaadacacdddcdcdbabdbaaacdccbbcddcbcdbdacaabbabddbdbcadcabcbbbacdddcbbadcddbabcccdaaddabcdcbbdcbbbcbccbcacbddddacacddcccacaddccccccbadacdcbcbccbdadddbbbbcabbcccabcccdcacacdbbcbcdcddacbddbdadcacbabddbddbbcbadbabbcbadbcdadccbbcbcacdaccabaabcbabdcdbaabcbadbdaaaccddbdaadbddbacaacbcbdabbbacaacabddacabbddacbacdaccccacbacddacdbcddcbcadababbcccccdcbacdcdbabaaacaabccdabaddccbddbadaddbadadcadbcacdbccaaddddbbdaabbdaccbbbcbdddcbabcacaadcbdddcbaacadccbbcbaccacddccbcccaacddabdbbddcbcbbaddcaaacbbdaaadddabaacacaabdddadcbcdbacbcccdbbdaaaadbcdacabdccbcbdcabbadaabcbcabaacbccadcccaddabdbaccacbaccbbcdaadbcdbacdbaccabdcabdcbdbbbaaabdbbabbbdbbabdacdcabaadaacccbcaacccdaaabbcaadadbadcdbdcdbcadacdcadbdacdbccdabbcaccabbacdabbdbddbbcababbbbbdcccccdbbcdccdabcacaddacaaacddadccabadbdabccaaddacdbbacaddabdacbcbcaacbdaacdaccbbccccabcdccbcccdbbdabccadabcbaddcdababadabdabdddddbadccbbcdacbbdadbcbaabdbbddbdabbbdcccaaadcadcdddcbabaadddbacbdcbabdddabacaacdcbcbbbbcdbacadadcaabbaadaabdcccdcacdbaddccbbadaddbacdcccbdccacdbbacbabdcbaacddaacacacdbcacbbdbbccdaaccccaccdacadaddadbacdddaaadacccddbccdddaddaadbacaaaacccdcaaddcdccabccdbcdbbcadccabcbdccadcdabbccbbbaccaadcbdcdbaddcaccbcaabbcabcaacbcbcbdcadadabdbcbadacbdbcdcacaacdacacbbcbabcdbaadcacddcddaccddccaaacacdbcdbbcaddcddadbabadbdddcacabdcbdaccbdabccbabaacbccddbadadaabbbcddbcaddaddbdbbcdbccbdaabaaddaddaccdddcaabbbbbcbaacabaccccadacddaacdbaacdddadbbaaaabccbbabacccddddcccbaaaabccbbbbacaaadadbcdcbacaaacadaacacddcadcbadabbdcbdacaccdcaacaacccdbbcbabdaadcbbaacadbacccbbaccbacaaccdbdddaacdbbbdbbbbddaaabcdcdaddbaadbbadbddcccbdddaadabdabbcacaccdcdbdbdcbadacdddbbbbaccbdcddaddbadcbbaadaadaacbaaaddcdaaabaccacdccadadabbbacdaabbcddadabccbbbbcbacdbbdccccdbbabcbddaabaadadcbacdadbdaadbcdbdbaadabbccaaadbbacbbddbcddcbcdadcdacabcbdcbbdbcaadccdbdabdcdabbccacdacbdcbaabdbbbbbbacabadcacbbbdbcadabbcbadcdabcdabbabbbdaccccaddddbadabbcbaaaacaddbcbbcbccbcabbcdacdbddbdacbabdabdddabdbbdbaacbcddcddbcaccbdccbdaddcdaaddcdbddcdcbdabbcabccccbcadcccacccdbdcbadcaaccdbcbccaccdabcabaccabbadcadbadadabbddbdbdaacabbbaaadacbcdbddbcbcddadddbbaadddbabbbddadabbadbbdbaabbcbcdbcaacdbcbbbcddddccbbbddaddadbdccabbdaccacbbcaccbdabaadbbddbacdbabdcbcbbdbdbadbbdbaadccbcccccabcbccbbdccbcbabdbacbcbccbcbdabdddcaaddbccaabbdabcdacbdcdbddbadddddcacaddcacadaccbdbcdbddcababcbcdaccacdbbbadaddddbbcadaacbcacbdcacdbaaaaabbbbdabbbbbadcadbbcbababbbcdacabacdbbdcdcaaadbadaccdcabcccbdbadabdbcddcbacacaccbacadadccdaadabcbbdbadaaaccdcbddddcccdcdabcbacabadcbccabaacdbadadacabbbabaccadbcbcbaddcadbabdadbaaadcdbaabdacadaacdcdbbcdcbcaadddadcddbabdbdcacabaabbdbcddcbcadadccbdacbacbcaacbadacbdbacdddaaccdbbcbbdcddbaddcbbaaabdaacdcabbbdccddababdcbdbcbbacabddcbdadbacaabdbdcdacbabbdcbbdcbddddcccaadacbbcadbacdbdcbcdcddadcadadcacbbbccbadcaaddabddadaddccccdbcdacaadbbccdcabbbadbdbacdbcaaacdccbadcdaadacdcdbdcbcaddaadbaacdcbabbacbbccacabcdbbbbbabaabccccbcdcbbccaabcdbcaadcbbddbacdaccdbbcccccbbccbbcdcbbaabdbacbdabaabddabacdbaccdbdcacadbdcaadcbddacddacadcdcaadaccbcaccbdcbbddcddaadcbaccadaaddddadcbbcaacabbdaccbdbadbcdaaccbaddbdadbabbddcacdccbddbdbdadbaadccbccbacddbbaabacddacdcaadbdcabadcbccdbccdbcadcadcaabcaaddcddadcddcbdcbcaadddcaddcddbcababddcbcadddaacadaabbaaaddcdadbbabacddcdadddccbdcbdcbbdacdbaabddabdcacbcbcaccabdabccdbcbaacddcacaadcbaabcdaaddddcdcddcadccadadbdbdcabdabddabcbbbbcadbbdbadaddbbcdbcbcaaddbbaabbbcaabcccadaaddbabbddcdacababcbdacbddcaacbbbccdcdbadabdbccababbcdadaddcdbddcbcaacddcdabcdabccddcaddcdabddbbcbabbcccbbcdcaaabacdccaccbccacbdbbabbbaadcbdcccbcccdcbdadacaddcdbbbcbdaccadbbccdbcbdddadabcbaabcbabbbbcdabaaacdcbacaaadaaacaabbacdcbcbadddcbbdcdacbbbcdddbbdcdadcbabadbabcabbbbaadcadcbdaaacbbaddaadbdcabddbaaaddbdbaddadcaccdbacbaacccacbcdcabbabcbccdcbcccbcadcbddddaddaddcacbbabdcadabaacabbbabadaccadddbbaddbaccaadbccdaddcbbbddbabbabcacbcadaaacdcbccaaacdcbbbccaaadbadaddcbdccbccdadccbcddccacaacdbacccaaaabbcaaddcabdbabbacdbbdadcbbdbbabddaddcadbdcabadaccbbbacadddbaddbacdbbdababdacadbbcbcccddaabadaabaaabadacaaaadcacdabadaccaccdccbbdcaabcabaacbabaacbdaadbdcbbdcbdbbccaaadadcdadacbababdbddadaadacbdaccdbdcdabcbcdbbccabcacaaababbccbbdaddcccaddaddbdabcddadbbbcadbbdcbbdbadcbdbbbdcccaddcabdabcbacbcdcaadacbdaacdbcaaacddcdbaadcadbaabcbbcbcaddbcbddbcbbdccbccdbdcaccacaabbbdcdabbbdadccbcabccbbbbbbdbdadccabbadcccaacbdbcbadddadacdbbabadbdbbcdbcaddacbabadcdcddcdacdbcaccadadbcabcdcbbbbbcaccccdcbbcbcccdacdbcbdcdcbcabcbbbadcdcdcadbbdadbabddcccaccdcadbcdbbaacdbadcacacbadacdacbcabacbcdcbddccdaddbabadbdbabbadcacdbadbcaaaabdaadabbbcbabbdadcddacbbaacadacaaccaaabacabcdbbddaabdbbdcaddcddbccbcbadbdbdcdbdbaccdcbdadacbcacaadcccdcbcbcbdcabaaacbdcaadadbbbbccbdacaaabbcaccbbbcacddbdadccbadddbcabcaadabbccbdbbddababddcdbddacbadabacdddddacddaadaddbabaaacdacddcdadaddccbacadcdcdadbbbdcadbdbddbccdacccadaadcccaabdcadbcbcbcbdbdadcdadaaccaaaadcbddadaccccbaadddaddadbacbbbcadcadbbadcbbcabacdcacdbadabbaaadcaadaaadabdbaabcdbbbbbbcaddbaacbaabddcdcbcabcdaabcaabaadddadcdccbbacdcdbaacdabadcdbcaaaadcdabcbdcbddcdccdaacbbcccdbbdbdcadcaadcbaadccdddcacbcdbaadbbabddabadbcaacaddccadadcbdacacbcbbcaaaddacdcbadccbdcaadacbaabbbaadcaadbbcdbacaacaccdcacdacaddaddbaacdcbdabacbbbccdbacdcbdacdbdbbcdaadbcbabaabaabccbbcdadbabacddaacdccddcadbdcbcdcdddcabdddb